{"t":"q","id":2703,"q":"Look at the clock. The time is 3.25.
We can also say that it is minutes past 3.","e":null} {"t":"q","id":2704,"q":"Read the clock and fill in the missing time and numbers.
The time is .
We can also say that it is minutes past .","e":null} {"t":"q","id":2705,"q":"Read the clock and fill in the missing time and numbers.
The time is .
We can also say that it is minutes past.","e":null} {"t":"q","id":2706,"q":"Read the clock and fill in the missing time and numbers.
The time is 1.40.
We can also say that it is minutes to 2.","e":null} {"t":"q","id":2707,"q":"Read the clock and fill in the missing time and numbers.
The time is
We can also say that it is minutes to 4.","e":null} {"t":"q","id":2708,"q":"Read the clock and fill in the missing time and numbers.
The time is
We can also say that it is minutes to 7.","e":null} {"t":"q","id":2718,"q":"Fill in the blanks with \u2018past\u2019 or \u2018to\u2019.
1.09 is 9 minutes _____ 1.","e":null} {"t":"q","id":2719,"q":"Fill in the blanks with \u2018past\u2019 or \u2018to\u2019.
3.40 is 20 minutes _____ 4.","e":null} {"t":"q","id":2723,"q":"Fill in the missing time.
is 24 minutes past 12.","e":null} {"t":"q","id":2724,"q":"Fill in the missing time.
is 15 minutes to 10.","e":null} {"t":"q","id":2725,"q":"Fill in the missing time.
is 6 minutes to 12.","e":null} {"t":"q","id":2869,"q":"The figure below is made up of 1-cm squares.
The area of the 4-cm square is $$ cm^2$$ .","e":null} {"t":"q","id":3430,"q":"An apple weighs half that of a mango. The 2 fruits weigh a total of 870g.
The mango weighs g.","e":null} {"t":"q","id":3432,"q":"May is $$\\frac{7}{9}$$ as tall as her father. Her father stands at 171 cm.
May's height is cm.","e":null} {"t":"q","id":3433,"q":"Ed is $$\\frac{2}{11}$$ as old as his grand-dad. Ed is 12 years old.
His grand-dad is years old.","e":null} {"t":"q","id":3440,"q":"This year, Heidi is $$\\frac{1}{5}$$ as old as her mother. Her mother is 45 years old.
Last year, Hannah was years old.","e":null} {"t":"q","id":3441,"q":"Wendy is $$\\frac{2}{3}$$ as old as her brother. Wendy is 6 years younger than her brother.
Next year, Wendy will be years old.","e":null} {"t":"q","id":3442,"q":"Paul is 8 this year. He is $$\\frac{1}{7}$$ as old as his grandfather.
When Paul turns 12, his grandfather will be years old.","e":null} {"t":"q","id":3454,"q":"Rose is 7 and $$\\frac{1}{5}$$ as old as her father. Her sister is twice her age.
The difference between her father and sister's age is years.","e":null} {"t":"q","id":3455,"q":"Josh is $$\\frac{8}{9}$$ as heavy as Alfred. Rob is 3 times as heavy as Alfred. Josh weighs 24 kg.
Rob weighs kg.","e":null} {"t":"q","id":3771,"q":"A decimal has 3 decimal places and is between 3 and 4. The digits in the tenths, hundredths and thousandths places are factors of 3. The digit in the hundredths place is greater than the digit in the thousandths place. The digit in the tenths place is greater than the digit in the hundredths place.
The decimal is .","e":null} {"t":"q","id":4105,"q":"Round off 7489 to the nearest thousand. Then estimate the value of <\/span>7489 x 5 . <\/span>
\u2248 x 5
= ","e":null} {"t":"q","id":4106,"q":"Round off 4518 to the nearest thousand. Then estimate the value below.
4518 x 9
\u2248 x 9
= ","e":null} {"t":"q","id":4107,"q":"Round off 5699 to the nearest thousand. Then estimate the value below.
5699 x 8
\u2248 x 8
=","e":null} {"t":"q","id":4108,"q":"Round off 4461 to the nearest hundred. Then estimate the value below.
4461 \u00f7 5
\u2248 \u00f7
= ","e":null} {"t":"q","id":4109,"q":"Round off 2351 to the nearest hundred. Then estimate the value below.
2351 \u00f7 3
\u2248 \u00f7
= ","e":null} {"t":"q","id":4110,"q":"Round off 4948 to the nearest hundred. Then estimate the value below.
4948 \u00f7 7
\u2248 \u00f7
= ","e":null} {"t":"q","id":4111,"q":"Round off 3049 to the nearest hundred. Then estimate the value below.
3049 \u00f7 6
\u2248 \u00f7
= ","e":null} {"t":"q","id":4114,"q":"Round off the numbers to the nearest thousand. Then estimate its value.
3280 + 1754 \u2248
+ 2000
= ","e":null} {"t":"q","id":4115,"q":"Round off the numbers to the nearest thousand. Then estimate its value.
8951 - 7108
\u2248 -
= ","e":null} {"t":"q","id":4117,"q":"Round off the numbers to the nearest thousand. Then estimate its value.
9300 - 5260 - 1508 \u2248 - - = ","e":null} {"t":"q","id":4207,"q":"Express the answer in its simplest form where necessary.
$$\\frac{2}{3}-\\frac{5}{12}$$ = _______","e":null} {"t":"q","id":4208,"q":"Express the answer in its simplest form where necessary.
$$\\frac{3}{7}-\\frac{1}{6}$$ = ________","e":null} {"t":"q","id":4209,"q":"Express the answer in its simplest form where necessary.
$$\\frac{9}{10}-\\frac{3}{4}$$ = _______","e":null} {"t":"q","id":4210,"q":"Express the answer in its simplest form where necessary.
$$\\frac{7}{12}-\\frac{3}{8}$$ = _______","e":null} {"t":"q","id":4294,"q":"Find the product. Give your answer in its simplest form where necessary.
$$\\frac{1}{2}$$ of $$\\frac{2}{3}$$ = ______","e":null} {"t":"q","id":4310,"q":"Mrs Kway-kway had $$\\dfrac{1}{2}$$ kg of sugar. She used $$\\dfrac{3}{4}$$ of it to bake a cake.
How much sugar did she use?","e":null} {"t":"q","id":4666,"q":"The total mass of 3 packets of sugar is $$\\frac{3}{8}$$ kg.
The average mass of a packet of sugar = kg, correct to 3 decimal places.","e":null} {"t":"q","id":5006,"q":"A rectangular container 100 cm long, 45 cm wide and 60 cm high is $$\\frac{3}{10}$$ filled with used cooking oil from a restaurant. How much more used cooking oil can be poured into the container before it becomes full? Give your answer in litres. (1 l= 1000 cm\u00b3)
$$l$$","e":null} {"t":"q","id":5063,"q":"Work out the following when z = 4.
$$\\frac{z}{4}$$ = ","e":null} {"t":"q","id":5067,"q":"Work out the following when z = 32.
$$\\frac{z}{4}$$ = ","e":null} {"t":"q","id":5318,"q":"If Worker A was to paint a house by himself, he would take 6 hours. If Worker B was to paint a house by himself, he would take 10 hours.
How long did both of them take to paint the house together? Express your answer in mixed fraction.
A $$\\frac{B}{C}$$
A: B:C: ","e":null} {"t":"q","id":5332,"q":"Angie bought some apples and Belle bought some oranges. Angie gave half of her apples to Belle and in return, Belle gave half of her oranges to Angie. Both girls ended up with 16 fruits each, and had $$\\frac{1}{3}$$ as many apples as oranges.
Find the number of apples Angie bought and the number of oranges Belle bought.
Angie bought apples and Belle bought oranges.","e":null} {"t":"q","id":5363,"q":"Three pupils, Amy, Belinda and Cindy shared some chocolates in the ratio 4:1:5.
Express the number of chocolates that Amy had as a fraction, $$\\frac{A}{B}$$, of the total number of chocolates that Belinda and Cindy had. Reduce your answer to the lowest term.
A: B:","e":null} {"t":"q","id":5520,"q":"An old man was jogging around a 400 $$m$$ running track.
During the firstvtwo rounds, he jogged slowly and completed it in 13$$\\frac{1}{2}$$ minutes.
For the next two rounds, he jogged faster and completed them in 6$$\\frac{1}{2}$$ minutes.
What was his average speed forth four rounds that he ran in $$m\/min$$?
$$m\/min$$","e":null} {"t":"q","id":5588,"q":"The figure shows a semicircle.
Find its perimeter. (Take \u03c0 = $$\\frac{22}{7}$$)
$$cm$$","e":null} {"t":"q","id":5589,"q":"The figure shows a semicircle.
Find its perimeter. (Take \u03c0 = $$\\frac{22}{7}$$)
$$cm$$","e":null} {"t":"q","id":5590,"q":"The figure shows a quadrant.
Find its circumference. (Take \u03c0 = $$\\frac{22}{7}$$)
$$cm$$","e":null} {"t":"q","id":5613,"q":"The pie chart below shows the different groups of families living in an apartment building. There are 300 families in the apartment.
How many families have less than 2 children?","e":null} {"t":"q","id":5614,"q":"The pie chart below shows the different groups of families living in an apartment building. There are 300 families in the apartment.
Find the ratio of families with no children to families with more than 2 children.","e":null} {"t":"q","id":5615,"q":"The pie chart below shows the percentage of men, women, boys and girls who took part in a family carnival. There were 120 girls.
What percentage of the participants were girls?","e":null} {"t":"q","id":5616,"q":"The pie chart below shows the percentage of men, women, boys and girls who took part in a family carnival. There were 120 girls.
What was the ratio of the number of men to the number of women?","e":null} {"t":"q","id":5617,"q":"The pie chart below shows the percentage of men, women, boys and girls who took part in a family carnival. There were 120 girls.
How many men took part in the family carnival?","e":null} {"t":"q","id":5618,"q":"The pie chart below shows the percentage of men, women, boys and girls who took part in a family carnival. There were 120 girls.
How many more adults than children took part in the family carnival?","e":null} {"t":"q","id":5624,"q":"The pie chart shows the number of coins in Henry's piggy bank.
What percentage of the coins are $1 coins? Give your answer correct to 1 decimal place.
%","e":null} {"t":"q","id":5625,"q":"The pie chart shows the number of coins in Henry's piggy bank.
What is the value of all the ten - cent, twenty - cent and fifty - cent coins?
$ ","e":null} {"t":"q","id":5626,"q":"The pie chart shows the number of coins in Henry's piggy bank.
Using all the coins in the piggy bank, Henry wentto a shop to exchange for $2 notes. What is the maximum number of $2 notes that he can get?
","e":null} {"t":"q","id":5628,"q":"The pie chart shows the different colours of goodie bags given out to a group of P5 pupils during a carnival.
What is the ratio of the number of green goodie bags to the number of yellow goodie bags to the number of orange goodie bags?
: : ","e":null} {"t":"q","id":5629,"q":"The pie chart shows the different colours of goodie bags given out to a group of P5 pupils during a carnival.
If there were 44 more purple than blue goodie bags, how many goodie bags were there altogether?
","e":null} {"t":"q","id":5645,"q":"The figure shows a circle inside a square of length 10 $$cm$$.
Find the area of the shaded part (Take \u03c0 = 3.14)
$$cm^2$$","e":null} {"t":"q","id":5646,"q":"Find the area of the figure.
$$cm^2$$","e":null} {"t":"q","id":5648,"q":"The figure is made up of a semicircle, a quadrant and a triangle. The radius of the quadrant and the semicircle is 8 $$cm$$ and 10 $$cm$$ respectively.
Find the area of the figure. (Take \u03c0 = 3.14)
$$cm^2$$","e":null} {"t":"q","id":5651,"q":"The figure shows a triangle being cut out of a quadrangular cardboard of radius 20 cm.
Find the area of the remaining cardboard. (Take \u03c0 = 3.14)
$$cm^2$$","e":null} {"t":"q","id":5665,"q":"The figure is made up of a right - angled triangle and a semicircle. The perimeter of the triangle is 24 $$cm$$.
Find the perimeter of the figure. (Take \u03c0 = 3.14)
$$cm$$","e":null} {"t":"q","id":5666,"q":"A piece of rectangular paper is folded along a line to form the figure below. The area of the shaded part is 40 $$cm^2$$.
Find the perimeter of the rectangular paper before it is folded.
$$cm$$","e":null} {"t":"q","id":5667,"q":"The figure is made up of two semicircles and a square of length 28 $$cm$$. The ratio of the radius of semicircle P to the radius of semicircle Q is 2 : 5.
Find the perimeter of the figure. (Take \u03c0 = 3.14)
$$cm$$","e":null} {"t":"q","id":5668,"q":"ABCD is a square divided into 3 parts, X , Y and Z. The ratio of the area of part X to the area of part Y is 1 :4. The area of part X is 288$$cm^2$$.
Find the length of square ABCD.
$$cm$$","e":null} {"t":"q","id":5671,"q":"The figure is made up of 16 identical rectangles and 3 identical squares.
What is the ratio of the length of each rectangle to the length of each square?
: ","e":null} {"t":"q","id":5672,"q":"The figure is made up of 16 identical rectangles and 3 identical squares.
What is the ratio of the breadth of each rectangle to the length of each square?
: ","e":null} {"t":"q","id":5673,"q":"The figure below is made up of 8 identical rectangles and a shaded rectangle. The breadth of each of the 8 identical rectangles is 5 $$cm$$. The shaded rectangle has a perimeter of 22 $$cm$$. Find the area of the whole figure.
$$cm^2$$","e":null} {"t":"q","id":5674,"q":"The figure shows three squares.
What is the area of the shaded part?
$$cm^2$$","e":null} {"t":"q","id":5676,"q":"The figure shows rectangle ABCD inside a circle of radius 13 $$cm$$. The perimeter of rectangle ABCD is 58 $$cm$$. (Take \u03c0 = 3.14)
Find the sum of length of AB and AD.
$$cm$$","e":null} {"t":"q","id":5677,"q":"The figure shows rectangle ABCD inside a circle of radius 13 $$cm$$. The perimeter of rectangle ABCD is 58 $$cm$$. (Take \u03c0 = 3.14)
Find the perimeter of the shaded part.
$$cm$$","e":null} {"t":"q","id":5721,"q":"6 - 1 = ?
Use the number bond to help you.

","e":null} {"t":"q","id":5722,"q":"6 - 4 = ?
Use number bond to help you.

","e":null} {"t":"q","id":5744,"q":"Ali has 10 marbles. John has 13 marbles. Jack has 19 marbles. Who has the greatest number of marbles?
","e":null} {"t":"q","id":5745,"q":"Mack has 15 guinea pigs. Mary has 20 turtles.
Lisa has 11 fishes.
Liam has 12 cats.
Who has the smallest number of pets?
","e":null} {"t":"q","id":5769,"q":"How many apples can you count?\"Premium

","e":null} {"t":"q","id":5770,"q":"How many dogs are there?\"How

","e":null} {"t":"q","id":5771,"q":"How many birds can you see?\"Cute

","e":null} {"t":"q","id":5772,"q":"How many cats do you see?
\"The





","e":null} {"t":"q","id":5778,"q":"I have the same number of green apples and red apples.Altogether, I have 8 apples.
How many red apples do I have?
","e":null} {"t":"q","id":5800,"q":"Five birds are sitting on the roof. 3 birds are flying.How many birds are there altogether?
","e":null} {"t":"q","id":5802,"q":"Picture below is a dog park.
\"Dogs

2 more dogs are going to the same dog park.
Altogether, how many dogs will there be?
","e":null} {"t":"q","id":5810,"q":"4 boys are playing soccer. 5 more boys join in to play. How many boys are there altogether?
","e":null} {"t":"q","id":5820,"q":"Jay had 3 guinea pigs. Peter had 5 guinea pigs.Jay's grandfather buys another 2 guinea pigs for Jay.
Who has more guinea pig now?
","e":null} {"t":"q","id":5823,"q":"6 is made up of 2 equal numbers. What is that number?
","e":null} {"t":"q","id":5825,"q":"Count the number of oranges in the crate.\"Monthly

","e":null} {"t":"q","id":5826,"q":"See the foxes! How many are there? \"Fox

","e":null} {"t":"q","id":5827,"q":"Wow look at the giraffes! Count how many are there? \"12


","e":null} {"t":"q","id":5828,"q":"Count the number of bottles in the picture below.\"Seven

","e":null} {"t":"q","id":5829,"q":"How many beautiful flowers are there? \"Nine

","e":null} {"t":"q","id":5830,"q":"How many books are in the stack? \"Pile

","e":null} {"t":"q","id":5831,"q":"Count the number of elephants.\"My

","e":null} {"t":"q","id":5832,"q":"How many eggs did mummy get from the supermarket?\"Ten



","e":null} {"t":"q","id":5834,"q":"How many whale(s) can you spot? \"5

","e":null} {"t":"q","id":5835,"q":"Playful monkeys.How many do you see?


\"Chinese

","e":null} {"t":"q","id":5836,"q":"How many rhinoceros are in the picture below?\"Wallpaper

","e":null} {"t":"q","id":5837,"q":"Spot the number of birds flying. \"Birds

","e":null} {"t":"q","id":5840,"q":"Count the number of children playing skipping rope? \"Skipping

","e":null} {"t":"q","id":5841,"q":"John is having cookies for breakfast.Count how cookies there are. \"Chocolate




","e":null} {"t":"q","id":5843,"q":"How many furry chicks are standing on the branch?\"How

","e":null} {"t":"q","id":5844,"q":"Count the number of cups in the cupboard? \"Eight

","e":null} {"t":"q","id":5846,"q":"Count the number of strawberries.\"11

","e":null} {"t":"q","id":5847,"q":"Count the number of bananas.\"Bananas:

","e":null} {"t":"q","id":5848,"q":"Count the number of colour pencils. \"Ten

","e":null} {"t":"q","id":5863,"q":"Jane keeps rabbits as shown below.\"Common

Mary has more rabbits than Jane. How many does Mary have?
","e":null} {"t":"q","id":5872,"q":"Which is fewer? Red or green appes?\"Amazon.com:

","e":null} {"t":"q","id":5874,"q":"Look at the picture.Which answer is NOT correct?
\"Green

","e":null} {"t":"q","id":5877,"q":"Which is fewer? <\/span>

\"Elephant

\"Monkey

","e":null} {"t":"q","id":5881,"q":"What is the missing number?

","e":null} {"t":"q","id":5882,"q":"What is the missing number?

","e":null} {"t":"q","id":5899,"q":"Little John has 5 filghting fish. Liam has 7.
Jason has 5.
Who else has as many fighting fish as Little John?

","e":null} {"t":"q","id":5901,"q":"Little John has 5 filghting fish. Liam has 7.
How many fewer fish does Little John have?



","e":null} {"t":"q","id":5904,"q":"What is the missing number?

","e":null} {"t":"q","id":5942,"q":"There are two missing numbers.Both numbers are the same.
Do you know what that number is?
","e":null} {"t":"q","id":5968,"q":"5 + 4 = 9
Find another pair of numbers that add to 9. <\/span>

","e":null} {"t":"q","id":5978,"q":"All the answers below are the same except for one.
Can you tell which is not the same?


","e":null} {"t":"q","id":5981,"q":"Help find the missing number.


","e":null} {"t":"q","id":5982,"q":"Find the missing number from below.


","e":null} {"t":"q","id":5988,"q":"Which answer is smaller than 6 but larger than 3?


","e":null} {"t":"q","id":5989,"q":"Which is the biggest number?


","e":null} {"t":"q","id":6002,"q":"8 - ? = 6Find the missing number.
Use number bond.
","e":null} {"t":"q","id":6035,"q":"Which answer is larger than 2 but smaller than 5?

","e":null} {"t":"q","id":6076,"q":"Solve by counting back or using number bond.9 - 3 = ?



","e":null} {"t":"q","id":6085,"q":"2 + 6 is the same as two fewer than 9.True?



","e":null} {"t":"q","id":6087,"q":"

Find the answer that is smaller than 6 but larger than 3.
","e":null} {"t":"q","id":6088,"q":"

Find the answer that is smaller than 8 but larger than 6.
","e":null} {"t":"s","id":1740,"s":"Given: The pie chart shows different groups of families in an apartment building. There are 300 families total. How many families have less than 2 children?
\n
\nStep 1: Identify what \"less than 2 children\" means
\nLess than 2 children = Families with no children + Families with 1 child
\n
\nStep 2: Find the percentages from the pie chart
\nFamilies with 1 child = 45%
\nFamilies with 2 children = 40%
\nFamilies more than 2 children = 3%
\n
\nStep 3: Calculate the remaining percentage
\nRemaining percentage = 100% - 45% - 40% - 3% = 12%
\n12% of families have no children
\n
\nStep 4: Calculate families with less than 2 children
\nPercentage = 12% + 45% = 57%
\nNumber of families = 57% \u00d7 300 = 171
\n
\nAnswer: 171 families have less than 2 children."} {"t":"q","id":6089,"q":"What is the position of the last person in the queue?\"Queue

","e":null} {"t":"q","id":6090,"q":"What is the position of the man dressed in a blue shirt ?
\"Queue

","e":null} {"t":"q","id":6094,"q":"At which position is the dog owner? \"People

","e":null} {"t":"q","id":6095,"q":"Counting from the left, which animal is in the 5th position?
\"Animals

","e":null} {"t":"q","id":6096,"q":"Panda bear is between which 2 animals?
\"Animals

","e":null} {"t":"q","id":6098,"q":"Counting from the left, what is second ?
\"Animals

","e":null} {"t":"q","id":6100,"q":"Counting from the left, what is the position of the dog?
\"Animals


","e":null} {"t":"q","id":6102,"q":"Counting from the left, what is before yellow giraffe?\"Sew

","e":null} {"t":"q","id":6103,"q":"Counting from the right, what comes after the blue giraffe?
\"Sew


","e":null} {"t":"q","id":6104,"q":"The first person left the queue.
Who is first in the queue now ?
\"Queue


","e":null} {"t":"q","id":6105,"q":"What is the position of the man in the checked green shirt?
\"People


","e":null} {"t":"q","id":6106,"q":"2 more persons joined the queue. What is the position is the last person now?
\"People

","e":null} {"t":"q","id":6108,"q":"What is the position of the man in the dark brown suit ?\"People

","e":null} {"t":"q","id":6109,"q":"What is the position of the yellow bird ?
\"Budgerigar

","e":null} {"t":"q","id":6110,"q":"A lady is looking at her watch. What's her position ?
\"Lineup

","e":null} {"t":"q","id":6112,"q":"What is between the yellow bird and the blue bird ?
\"Budgerigar

","e":null} {"t":"q","id":6114,"q":"Who is between boy in the blue shirt and the boy is the green shirt?\"Kids

","e":null} {"t":"q","id":6115,"q":"Who is between the 2nd and 4th position ?


\"Search






","e":null} {"t":"q","id":6116,"q":"Counting from left or right, my position is the same.Which bird is that ?
\"Budgerigar

","e":null} {"t":"q","id":6117,"q":"What is the position before the last person in the queue ?\"Escola,

","e":null} {"t":"q","id":6118,"q":"Asher is fourth in the queue to go up the bus. Jack is 1st. Jill is 2nd and Mary is 3rd.Who is before Asher?
\"School


","e":null} {"t":"q","id":6119,"q":"Asher is the last person in the queue below.After 3 minutes, all 3 students before Asher got up the bus.
What is Asher's position now ?
\"School


","e":null} {"t":"q","id":6120,"q":"5 birds were resting as shown in the picture below.The red bird then flew away.
Counting from the left, what is the position of the last bird then?

\"Budgerigar




","e":null} {"t":"q","id":6121,"q":"Who is after the girl in the green dress ?\"Search

","e":null} {"t":"q","id":6122,"q":"Look at the picture. Which answer is NOT correct ?\"Search

","e":null} {"t":"q","id":6123,"q":"What is the position of the tallest person ?<\/span>
\"English

","e":null} {"t":"q","id":6124,"q":"Tom is before the boy in the blue shirt. What is Tom's position ?\"English


","e":null} {"t":"q","id":6125,"q":"Sean is betwen the tallest boy and the boy in blue.Sean's position is ?
\"English


","e":null} {"t":"q","id":6127,"q":"How many apples are there ?\"Amazon.com:

","e":null} {"t":"q","id":6130,"q":"How many robots ?\"icon0.com

","e":null} {"t":"q","id":6131,"q":"Count the number of children.\"Cute

","e":null} {"t":"q","id":6132,"q":"Add up the ladybugs.
\"OLD

","e":null} {"t":"q","id":6133,"q":"How many animals do you see ?\"Vector

","e":null} {"t":"q","id":6135,"q":"Can you count the animals ?\"Carolina

","e":null} {"t":"q","id":6137,"q":"How many people are in the queue ?\"EL

","e":null} {"t":"q","id":6308,"q":"Determine the total number of balloons. How many balloons are there in total?","e":null} {"t":"q","id":6309,"q":"Count and identify the number of balloons present. How many balloons can you see?","e":null} {"t":"q","id":6310,"q":"Calculate the total balloons. What is the total count of balloons?","e":null} {"t":"q","id":6323,"q":"Calculate the number of letters in the term 'sunshine'.
Answer: ","e":null} {"t":"q","id":6638,"q":"A rectangular tank 60 cm long and 40 cm wide was filled with water to 80% of its height. When 18 litres of water were removed, it became \\(\\dfrac{1}{2}\\) full. Find the height of the tank.","e":"Base = 60 x 40 = 2400 cm\u00b2. Water removed corresponds to (80% - 50%) = 30% of height. 0.3 x 2400 x h = 18000 cm\u00b3, so 720h = 18000, h = 25 cm."} {"t":"q","id":6639,"q":"A rectangular box is 120 cm long and 30 cm wide. It was filled with toys to 75% of its height. After taking out 24 liters of toys, it is now $$\\dfrac{1}{4}$$ full. What is the height of the box?","e":null} {"t":"q","id":6640,"q":"A water tank is 60 cm long and 40 cm wide. It was filled to 85% of its height. After pouring out 20 liters of water, it is now $$\\dfrac{1}{3}$$ full. What is the height of the water tank?","e":null} {"t":"q","id":6641,"q":"A rectangular tank was filled with oil to a height of 8 cm. Its rectangular base measured 30 cm by 25 cm. When 9 litres of oil were poured into the tank, the oil level rose to $$\\dfrac{4}{5}$$ of the height of the tank. Find the height of the tank.","e":null} {"t":"q","id":6642,"q":"A fish tank has a height of 12 cm and a base that is 20 cm by 15 cm. After adding 6 litres of water, the water level rose to $$\\dfrac{3}{4}$$ of the tank's height. What is the height of the tank?","e":null} {"t":"q","id":6643,"q":"A box has a height of 10 cm and a base measuring 25 cm by 20 cm. When 5 litres of sand are added, the sand fills $$\\dfrac{2}{5}$$ of the height. What is the height of the box?","e":null} {"t":"q","id":6644,"q":"A rectangular tank has a base measuring 30 cm by 20 cm. It was filled with oil to a height of 6 cm. When 6 litres of oil were poured in, the oil level rose to \\(\\dfrac{4}{5}\\) of the tank's height. Find the height of the tank.","e":"Base = 30 x 20 = 600 cm\u00b2. Oil before = 600 x 6 = 3600 cm\u00b3. After adding 6000 cm\u00b3: 9600 cm\u00b3 = \\(\\dfrac{4}{5}\\) x 600 x h = 480h, so h = 20 cm."} {"t":"q","id":6650,"q":"A box measures 40 cm in length and 15 cm in width. It is filled with sand to a height of 5 cm. When the sand is moved to a new box that is 10 cm tall, it fills the new box to $$\\dfrac{1}{3}$$ of its height. What is the base area of the new box?","e":null} {"t":"q","id":6651,"q":"A fish tank is 25 cm long and 20 cm wide. It holds water up to a height of 8 cm. When the water is poured into another tank that is 16 cm tall, it fills it to half its height. What is the base area of the second tank?","e":null} {"t":"q","id":6652,"q":"A storage box is 50 cm long and 30 cm wide. It is filled with toys to a height of 10 cm. When the toys are moved to a new box that is 20 cm tall, it fills to a quarter of its height. What is the base area of the new box?","e":null} {"t":"q","id":6653,"q":"A rectangular aquarium is 35 cm long and 25 cm wide. It has water up to a height of 7 cm. When the water is transferred to another aquarium that is 14 cm tall, it fills it to a third of its height. What is the base area of the second aquarium?","e":null} {"t":"q","id":6654,"q":"A container is 20 cm long and 10 cm wide. It is filled with liquid to a height of 4 cm. When the liquid is poured into a new container that is 8 cm tall, it fills to half its height. What is the base area of the new container?","e":null} {"t":"q","id":6658,"q":"A box measures 50 cm long, 20 cm wide, and 25 cm high. If 15 liters of sand are added to the box, how high is the sand in the box?","e":null} {"t":"q","id":6659,"q":"A fish tank is 30 cm long, 25 cm wide, and 40 cm high. If 20 liters of water are filled in the tank, what is the height of the water?","e":null} {"t":"q","id":6660,"q":"A storage box is 60 cm long, 30 cm wide, and 20 cm high. If it is filled with 18 liters of toys, what is the height of the toys in the box?","e":null} {"t":"q","id":6661,"q":"A rectangular aquarium is 80 cm long, 40 cm wide, and 50 cm high. If 30 liters of water are added, what will be the height of the water in the aquarium?","e":null} {"t":"q","id":6662,"q":"A rectangular pool is 70 cm long, 50 cm wide, and 40 cm high. If 35 liters of water are in the pool, what is the height of the water?","e":null} {"t":"q","id":6675,"q":"A large cube has a volume of 512 cm\u00b3. It is melted and recast into 8 identical smaller cubes. Find the side length of each smaller cube.","e":null} {"t":"q","id":6676,"q":"A cube-shaped tank of side 18 cm is filled with water. The water is then poured into another cube-shaped tank of side 9 cm. How many of the smaller tanks can be filled?","e":null} {"t":"q","id":6678,"q":"A cube of side 18 cm is recast into cubes of side 3 cm. How many small cubes are formed?","e":null} {"t":"q","id":6680,"q":"A cuboid (40 x 20 x 10) cm is poured equally into 8 identical cubes. Find the side of each cube.","e":null} {"t":"q","id":6681,"q":"A cuboid (25 x 14 x 10) cm of water is poured into another cuboid with base (35 x 10) cm. Find the water height.","e":null} {"t":"q","id":6683,"q":"A cuboid (27 x 9 x 3) cm is recast into a single cube. Find the cube\u2019s side.","e":null} {"t":"q","id":6684,"q":"A cube of side 20 cm is filled only to a height of 12 cm. The water is poured into a cuboid with base (16 x 10) cm. Find the new height.","e":null} {"t":"q","id":6728,"q":"Water from a completely filled cuboid 30 x 14 x 12 cm is poured equally into 9 identical cuboids. Each small cuboid has base (10 \u00d7 8) cm. Find the common height.","e":null} {"t":"q","id":6729,"q":"A cuboid has length 12cm, width 8cm, height 36cm. Its volume is kept the same, but the length is doubled and the width is tripled. Find the new height.","e":null} {"t":"q","id":6731,"q":"A solid cuboid measures 30\u00d720\u00d712cm. A rectangular void of 10\u00d75\u00d712cm is removed from the interior. Find the remaining volume.","e":null} {"t":"q","id":6733,"q":"All the water from a cuboid with base area 196 $cm^2$ and height 14 is poured into a cube, filling it to the brim. Find the cube\u2019s side.","e":null} {"t":"q","id":6734,"q":"A cuboid has L=20cm,\u00a0W=15cm,\u00a0H=12cm. The height is increased by 25% and the length is decreased by 20%, width unchanged. Find the new volume.","e":null} {"t":"q","id":6735,"q":"A cuboid 24\u00d710\u00d79 cm and a cuboid 18\u00d712\u00d75 cm are each filled to the brim. All their water is poured into a single empty tank that will be filled to a height of 12cm. The target tank has length 30 cm and unknown width w cm. Find \r\n\ud835\udc64.","e":null} {"t":"q","id":6909,"q":"A box is 3 m long, 2 m wide, and 1.5 m high. If you fill it with 30 buckets, each holding 8 litres, how many centimeters will the water level rise?","e":null} {"t":"q","id":6910,"q":"A storage container is 4 m long, 2 m wide, and 1 m high. You add 25 buckets, each containing 5 litres. How many centimeters does the water level rise?","e":null} {"t":"q","id":6911,"q":"A fish tank is 1.5 m long, 1 m wide, and 0.8 m high. If you pour in 20 buckets, each with 6 litres, how many centimeters does the water level rise?","e":null} {"t":"q","id":6913,"q":"Tank A is 1.5\u00a0m\u00d71.0\u00a0m\u00d70.8\u00a0m with water to a depth of 0.60\u00a0m. All its water is poured into Tank B whose base is 1.2\u00a0m\u00d70.75\u00a0m. Tank B initially has 0.10\u00a0m of water. What will be the final water depth in Tank B (assume it is tall enough)?","e":null} {"t":"q","id":6914,"q":"Box A is 2.0 m \u00d7 1.5 m \u00d7 0.5 m and has sand up to a height of 0.4 m. All the sand is moved to Box B, which has a base of 1.5 m \u00d7 1.0 m. Box B starts with 0.2 m of sand. What will be the total height of sand in Box B after transferring the sand?","e":null} {"t":"q","id":6915,"q":"Container A measures 1.2 m \u00d7 1.0 m \u00d7 0.9 m and is filled with water to a height of 0.5 m. The water is then poured into Container B, which has a base of 1.0 m \u00d7 0.8 m and starts with 0.1 m of water. What will be the final height of water in Container B?","e":null} {"t":"q","id":6916,"q":"Box A is 1.5 m \u00d7 1.2 m \u00d7 0.7 m and contains liquid up to a depth of 0.4 m. This liquid is transferred to Box B, which has a base of 1.0 m \u00d7 0.9 m and starts with 0.3 m of liquid. What will be the new depth of liquid in Box B?","e":null} {"t":"q","id":6917,"q":"A cube has a surface area of 400 cm\u00b2. A square hole measuring 4 cm x 4 cm is cut through the middle, from one side to the other. What is the volume left in the cube?","e":null} {"t":"q","id":6918,"q":"A cube has a surface area of 324 cm\u00b2. A rectangular tunnel of 6 cm x 2 cm goes straight through the center from one face to the opposite face. What is the remaining volume of the cube?","e":null} {"t":"q","id":6919,"q":"A cube has a surface area of 216 cm\u00b2. A circular hole with a diameter of 6 cm is drilled through the center from one face to the opposite face. What is the volume left in the cube?","e":null} {"t":"q","id":6922,"q":"A storage container has a base area of 5 m\u00b2 and is 50% filled with water. After pouring in 2 m\u00b3 of water, it is now 80% full. What is the height of the container in meters?","e":null} {"t":"q","id":6923,"q":"A fish tank has a base area of 6 m\u00b2 and is filled to 20% of its height. After adding 1.2 m\u00b3 of water, it reaches 50% full. What is the height of the tank in meters?","e":null} {"t":"q","id":7581,"q":"Solve \\(\\dfrac{3}{4}\\) \u00f7 \\(\\dfrac{1}{2}\\). Express your answer in the form \\(\\dfrac{a}{b}\\) where a = and b = .","e":"\\(\\dfrac{3}{4}\\) \u00f7 \\(\\dfrac{1}{2}\\) = \\(\\dfrac{3}{4}\\) x \\(\\dfrac{2}{1}\\) = \\(\\dfrac{6}{4}\\) = \\(\\dfrac{3}{2}\\). So a = 3, b = 2."} {"t":"q","id":8071,"q":"Workers in an office vote for a day for a special outing. How many chose Monday or Friday?","e":null} {"t":"q","id":9727,"q":"Next year, Sports club membership is expected to decrease by 25% while Science club is expected to increase by 40%. What will be the difference between them? ","e":null} {"t":"q","id":9729,"q":"On Thursday, the shop had a goal to sell 50 cones. By what percentage did they fall short of their goal? ","e":null} {"t":"q","id":9742,"q":"The library charges a late fee of $0.50 per book. If 10% of borrowed books in May were returned late, how much did the library collect in late fees that month? ","e":null} {"t":"q","id":9751,"q":"The website's target is to have an average of at least 450 visitors per day over the week. Did they meet this target? By how many visitors per day did they exceed or fall short?","e":null} {"t":"q","id":9762,"q":"The household wants to reduce their total annual consumption by 15% compared to this 8-month period. What should their target total be for the remaining 4 months? ","e":null} {"t":"q","id":9773,"q":"The market stall owner wants to increase total weekly sales by 20%. If the current total sales across all fruits is calculated, what should the new target total be? ","e":null} {"t":"q","id":9774,"q":"On Thursday, each fruit's sales dropped by 25% compared to Wednesday's sales. What would be the combined sales of Apples, Oranges, and Bananas on Thursday? ","e":null} {"t":"q","id":9835,"q":"The graph shows monthly widget production at Apex Factory. Find the percentage increase in production from February to May. ","e":null} {"t":"q","id":9837,"q":"Production in March was 120% of a planned target. What was the planned target for March, and if April achieved only 95% of its target, what was April's target? ","e":null} {"t":"q","id":9841,"q":"Calculate the average heart rate increase per kilometre for the first 10 km versus the last 10 km (32-42 km). ","e":null} {"t":"q","id":9843,"q":"The runner's maximum heart rate capacity is 200 bpm. Heart rate reserve = max capacity - resting rate. What percentage of the heart rate reserve was the runner using at 30 km? ","e":null} {"t":"q","id":9851,"q":"The user wants at least 20% battery to make an emergency call. At what hour should they stop using the phone and save it for emergencies? ","e":null} {"t":"q","id":9858,"q":"Calculate the average hourly sales. How many hours had sales below average? ","e":null} {"t":"q","id":9860,"q":"Calculate the average daily water loss for the first half of the month (days 1-13) and second half (days 16-28). Which period had faster evaporation and by how much per day? ","e":null} {"t":"q","id":9868,"q":"Calculate the average water level for all readings before the refill (days 1-13) and after the refill (days 16-28). What is the difference between these averages? ","e":null} {"t":"q","id":9869,"q":"The water level dropped from 180 cm to 148 cm before the refill. What percentage of this total drop was recovered by the refill on day 16? ","e":null} {"t":"q","id":9871,"q":"Compare the rate of water loss (cm per day) between days 7-10 and days 19-22. Express the faster rate as a percentage of the slower rate. ","e":null} {"t":"q","id":9873,"q":"The pool owner estimates that 60% of water loss is from evaporation and 40% is from splash-out during swimming. Between days 1 and 13, how many cm were lost to each cause? ","e":null} {"t":"q","id":9876,"q":"What was the total price increase from Week 1 to Week 8? Express this as both a dollar amount and a percentage increase. ","e":null} {"t":"q","id":9886,"q":"Calculate the average monthly subscriber count. In which month did the channel first exceed this average? ","e":null} {"t":"q","id":9889,"q":"The student earns $800 per month from a part-time job. In months where the balance increased, what was the average percentage of income saved? Assume no interest earned. ","e":null} {"t":"q","id":9890,"q":"Find the ratio of average monthly balance in the first half (Jan-Jun) to the second half (Jul-Dec). Express as a simplified fraction. ","e":null} {"t":"q","id":9891,"q":"The student's goal was to save $3000 by November. By what percentage did they exceed or fall short of this goal? If they had saved consistently each month from January, what fixed monthly deposit would have been needed? ","e":null} {"t":"q","id":9893,"q":"Express April's balance (the first dip) as a percentage of December's balance. Then express August's balance (the second dip) as a percentage of the balance just before it (July). Which dip was proportionally larger? ","e":null} {"t":"q","id":9894,"q":"Calculate the average daily steps for weekdays (Mon-Fri) and weekends (Sat-Sun). How many more steps per day were walked on weekends compared to weekdays? ","e":null} {"t":"q","id":9897,"q":"Express Friday's step count as a percentage of Saturday's step count. By what percentage did the step count increase from Friday to Saturday? ","e":null} {"t":"q","id":9898,"q":"Assuming an average stride length of 0.75 metres, calculate the total distance walked during the week in kilometres. On which day was the distance closest to 7 km? ","e":null} {"t":"q","id":10083,"q":"The ratio of the distance traveled by Car X to Car Y is 5 : 3. The ratio of the time taken by Car X to Car Y is 2 : 3. What is the ratio of the speed of Car X to the speed of Car Y? ","e":null} {"t":"q","id":10090,"q":"The ratio of Car A's speed to Car B's speed is 5 : 4. Both cars start from the same point and travel in the same direction. After 3 hours, Car A is 45 km ahead of Car B. What is Car A's speed? ","e":null} {"t":"q","id":10191,"q":"In triangle ABD, BDC is a straight line. Find angle ABD.
Answer : ","e":null} {"t":"q","id":10192,"q":"Triangle ABC is isosceles with AB = AC. Triangle BCD is isosceles with BD = CD. Find angle BDC.
Answer : ","e":null} {"t":"q","id":10193,"q":"Triangle ABC is isosceles with AB = AC. Triangle BCD is isosceles with BD = CD. Find angle BDC.
Answer : \u00b0","e":null} {"t":"q","id":10194,"q":"AD bisects angle BAC. Find angle ACD.
Answer : \u00b0","e":null} {"t":"q","id":10195,"q":"AB is parallel to CD. Find angle EFG.
Answer : \u00b0","e":null} {"t":"q","id":10196,"q":"DE is parallel to BC. Find angle ADE.
Answer : \u00b0","e":null} {"t":"q","id":10197,"q":"AH is perpendicular to BC. Find angle ACH.
Answer : \u00b0","e":null} {"t":"q","id":10198,"q":"Two triangles meet at vertex C. Find angle CDE.
Answer : \u00b0","e":null} {"t":"q","id":10199,"q":"Triangle ABC is isosceles (AB = AC). Triangle BCD is isosceles (BD = CD). Find angle DBC.
Answer : \u00b0","e":null} {"t":"q","id":10200,"q":"ACE is a straight line. Find angle CED.
Answer : \u00b0","e":null} {"t":"q","id":10201,"q":"AM is a median. DE is parallel to BC. Find angle DME.
Answer : \u00b0","e":null} {"t":"q","id":10202,"q":"A soccer team has an average of 3 goals per game. They play 2 more games and score 1 goal and 2 goals, bringing their average down to 2 goals per game. How many games did they play originally?","e":null} {"t":"q","id":10203,"q":"A basket of apples weighs an average of 5 pounds each. Two more apples are added that weigh 3 pounds and 4 pounds, and now the average weight is 4 pounds per apple. How many apples were in the basket originally?","e":null} {"t":"q","id":10204,"q":"A library has books with an average of 80 pages each. Two new books are added with 50 pages and 40 pages, and the average drops to 75 pages per book. How many books were in the library originally?","e":null} {"t":"q","id":10205,"q":"Emma collected stickers for 8 days. Her average number of stickers per day was 6. On the last day, she only collected 2 stickers.
How many stickers did she collect in total during the first 7 days?
Answer : ","e":null} {"t":"q","id":10206,"q":"A basketball player scored an average of 12 points per game over 5 games. In the first 4 games, she scored an average of 10 points per game.
How many points did she score in the 5th game?
Answer : ","e":null} {"t":"q","id":10208,"q":"The average weekly allowance of Sam and Alex is $9.
Sam gets $6 less allowance than Alex.
How much allowance does Sam get each week?
Answer : $ ","e":null} {"t":"q","id":10209,"q":"The average amount of stickers that Maya and Ben have is 15 stickers.
Maya has 8 fewer stickers than Ben.
How many stickers does Maya have?
Answer : stickers","e":null} {"t":"q","id":10210,"q":"The average number of books read by Emma and Liam last month is 7 books.
Emma read 2 fewer books than Liam.
How many books did Emma read?
Answer : books","e":null} {"t":"q","id":10211,"q":"The average score on a test for Zoe and Ryan is 85 points.
Zoe scored 10 points less than Ryan.
What was Zoe's test score?
Answer : points","e":null} {"t":"q","id":10212,"q":"The average number of marbles that Ava and Noah collected is 12 marbles.
Ava collected 4 fewer marbles than Noah.
How many marbles did Ava collect?
Answer : marbles","e":null} {"t":"q","id":10213,"q":"Class 3A has 60 students with an average test score of 15.2. Class 3B has 90 students with an average of 18.4.
What is the total sum of all 150 students' scores, and what is their combined average?
Total sum :
Combined average : ","e":null} {"t":"q","id":10214,"q":"Team Red has 45 players with an average height of 12.8 inches. Team Blue has 75 players with an average of 16.2 inches.
What is the total sum of all 120 players' heights, and what is their combined average?
Total sum :
Combined average : ","e":null} {"t":"q","id":10215,"q":"Group X collected 50 stickers with an average value of 8.6 points each. Group Y collected 100 stickers with an average of 11.4 points each.
What is the total sum of all 150 stickers' points, and what is their combined average?
Total sum :
Combined average : ","e":null} {"t":"q","id":10217,"q":"Garden A has 40 plants with an average height of 14.7 cm. Garden B has 80 plants with an average height of 21.6 cm.
What is the total sum of all 120 plants' heights, and what is their combined average?
Total sum :
Combined average : ","e":null} {"t":"q","id":10219,"q":"A basketball team has an average height of 68 inches. Two new players join with heights of 62 and 64 inches, and the average height drops to 67 inches.
How many players were originally on the team?
Answer : ","e":null} {"t":"q","id":10220,"q":"A reading club has an average of 25 books read per member. Two new members join who have read 18 and 20 books, and the average drops to 24 books per member.
How many members were originally in the club?
Answer : ","e":null} {"t":"q","id":10221,"q":"A dance class has an average age of 12 years. Two new students join who are 8 and 10 years old, and the average age drops to 11 years.
How many students were originally in the class?
Answer : ","e":null} {"t":"q","id":10222,"q":"A garden club has plants with an average height of 30 cm. Two new plants are added with heights of 24 cm and 26 cm, and the average height becomes 29 cm.
How many plants were originally in the garden?
Answer : ","e":null} {"t":"q","id":10225,"q":"During 5 days, Emma read an average of 8 pages per day.
How many pages did she read in total over the 5 days?
Answer : pages","e":null} {"t":"q","id":10230,"q":"During 5 days at the school cafeteria, the average number of sandwiches sold per day was 24.
How many sandwiches were sold in total over the 5 days?
Answer : ","e":null} {"t":"q","id":10246,"q":"Emma read books for 8 weeks and read an average of 3 books per week. During the last week, she only read 1 book because she was on vacation. How many books did she read during the first 7 weeks in total? Answer : ","e":null} {"t":"q","id":10247,"q":"A class of 15 students scored an average of 78 marks on a test. After some new students joined with an average score of 90 marks, the class average increased to 82 marks. How many new students joined the class? Answer : ","e":null} {"t":"q","id":10248,"q":"The average mass of 12 boxes is 18.5 kg. What must be the mass of a 13th box so that the average mass becomes 20 kg? Answer : kg","e":null} {"t":"q","id":10249,"q":"A swimmer completed 9 laps with an average time of 45 seconds per lap. How many seconds must she complete the 10th lap in to lower her average to 44 seconds per lap? Answer : s","e":null} {"t":"q","id":10250,"q":"The average height of 15 students is 148 cm. After removing the 3 tallest students, the average height became 145 cm. What was the average height of the 3 students who were removed? Answer : cm","e":null} {"t":"q","id":10252,"q":"The average weight of 5 bags of rice is 8.4 kg. One bag is removed and the average weight of the remaining bags becomes 8.8 kg. What was the weight of the bag that was removed? Answer : kg","e":null} {"t":"q","id":10253,"q":"A group of 8 friends collected stamps with an average of 56 stamps each. After 2 more friends joined, the average became 52 stamps per person. What was the average number of stamps collected by the 2 new friends? Answer : ","e":null} {"t":"q","id":10254,"q":"Daniel scored an average of 85 marks in his first 4 tests. After the 5th test, his average dropped to 82 marks. What did he score on the 5th test?
Answer : ","e":null} {"t":"q","id":10255,"q":"The average age of a family of 4 is 28 years. The baby is 2 years old. What is the average age of the other 3 family members?
Answer : years old","e":null} {"t":"q","id":10256,"q":"A shop sold an average of 45 shirts per day for 6 days. On the 7th day, there was a sale. If the average for all 7 days was 54 shirts per day, how many shirts were sold on the 7th day?
Answer : ","e":null} {"t":"q","id":10257,"q":"The average rainfall for January to May was 84 mm per month. The average rainfall for January to June was 90 mm per month. What was the rainfall in June?
Answer : mm","e":null} {"t":"q","id":10258,"q":"A cricket player's batting average after 20 innings was 35 runs. After the 21st innings, his average increased to 37 runs. How many runs did he score in the 21st innings?
Answer : runs","e":null} {"t":"q","id":10259,"q":"The average of 6 numbers is 24. If one number is doubled, the average becomes 28. What was the original number that was doubled?
Answer : ","e":null} {"t":"q","id":10260,"q":"The average marks of 40 students is 72. Later, it was found that one student's marks were recorded as 64 instead of 46. What is the correct average?
Answer : ","e":null} {"t":"q","id":10261,"q":"A train travels from Town A to Town B at an average speed of 60 km\/h and returns at an average speed of 40 km\/h. What is the average speed for the entire journey?
Answer : km\/h","e":null} {"t":"q","id":10263,"q":"The average of 5 consecutive even numbers is 34. What is the largest number?
Answer : ","e":null} {"t":"q","id":10264,"q":"In a class, the average age of 15 boys is 12 years and the average age of 10 girls is 11 years. What is the average age of the whole class?
Answer : years old","e":null} {"t":"q","id":10265,"q":"The average of 9 numbers is 40. The average of the first 5 numbers is 38 and the average of the last 5 numbers is 44. What is the 5th number?
Answer : ","e":null} {"t":"q","id":10266,"q":"Sarah's allowance was reduced by 20% to $12 during the summer. What was her allowance before it was reduced?","e":null} {"t":"q","id":10267,"q":"The price of a toy was decreased by 15% to $34 during a sale. What was the original price of the toy?","e":null} {"t":"q","id":10268,"q":"Ms. Johnson's work hours were cut by 25% to 30 hours per week. How many hours did she work per week before the cut?","e":null} {"t":"q","id":10269,"q":"Marcus had some money. He spent 70% of his money on a new bike and had $15 left over. How much money did Marcus have at the beginning?","e":null} {"t":"q","id":10270,"q":"Emma had some stickers. She gave away 80% of her stickers to friends and kept 12 stickers for herself. How many stickers did Emma have originally?","e":null} {"t":"q","id":10271,"q":"Jake had some marbles. He lost 40% of his marbles during recess and still has 18 marbles remaining. How many marbles did Jake start with?","e":null} {"t":"q","id":10275,"q":"25% of the students in a school are in kindergarten. If there are 84 students who are not in kindergarten, how many students are there in total?","e":null} {"t":"q","id":10276,"q":"40% of the books in a library are fiction books. If there are 72 non-fiction books, how many books are there altogether?","e":null} {"t":"q","id":10277,"q":"20% of the animals at a zoo are birds. If there are 96 animals that are not birds, how many animals are there in total?","e":null} {"t":"q","id":10278,"q":"Mr. Chen spent 40% of his money on a jacket. He spent 25% of the remaining money on shoes. If the shoes cost $36 less than the jacket, how much money did he have at first?","e":null} {"t":"q","id":10279,"q":"Sarah spent 25% of her allowance on a book. She spent 30% of the remaining money on a toy. If the toy cost $15 less than the book, how much allowance did she have originally?","e":null} {"t":"q","id":10280,"q":"Tommy spent 35% of his birthday money on a video game. He spent 15% of the remaining money on candy. If the candy cost $24 less than the video game, how much birthday money did he receive?","e":null} {"t":"q","id":10281,"q":"A bakery sold 240 cupcakes on Friday. They sold 30% fewer cupcakes on Thursday than on Friday. How many cupcakes did they sell over the two days?","e":null} {"t":"q","id":10282,"q":"A toy store sold 180 toys on Monday. They sold 25% fewer toys on Tuesday than on Monday. How many toys did they sell over the two days?","e":null} {"t":"q","id":10283,"q":"A flower shop sold 200 flowers on Wednesday. They sold 35% fewer flowers on Tuesday than on Wednesday. How many flowers did they sell over the two days?","e":null} {"t":"q","id":10284,"q":"A grape has a mass of 150g. It contains 80% water. After being left in the sun for a while, the water content decreased by 15%. What is the mass of the grape now?","e":null} {"t":"q","id":10285,"q":"A tomato has a mass of 300g. It contains 90% water. After being left in the sun for a while, the water content decreased by 20%. What is the mass of the tomato now?","e":null} {"t":"q","id":10286,"q":"An orange has a mass of 250g. It contains 75% water. After being left in the sun for a while, the water content decreased by 12%. What is the mass of the orange now?","e":null} {"t":"q","id":10287,"q":"A toy store increases the price of a game by 20% in the morning, then decreases it by 20% in the afternoon. What is the final price as a percentage of the original price?","e":null} {"t":"q","id":10288,"q":"Sarah's garden plot has its length increased by 15% and its width decreased by 15%. What is the area of the new garden as a percentage of the original area?","e":null} {"t":"q","id":10289,"q":"A pizza restaurant increases the length of their rectangular pizzas by 5% but decreases the width by 5%. What percentage of the original area is the new pizza area?","e":null} {"t":"q","id":10290,"q":"After receiving new books, the school library's collection of science books increased by 15% to 138 books. How many science books did the library have before receiving the new books?","e":null} {"t":"q","id":10291,"q":"During the summer sale, a toy store's daily customers increased by 20% to 96 customers per day. How many customers did the store have per day before the sale?","e":null} {"t":"q","id":10292,"q":"After planting more flowers, the number of roses in the school garden increased by 25% to 75 roses. How many roses were in the garden before planting more?","e":null} {"t":"q","id":10296,"q":"Maya had some stickers. She gave 30% to her sister and used 60% of the remaining stickers for her art project. She had 14 stickers left. How many stickers did she have at first?","e":null} {"t":"q","id":10297,"q":"Carlos had some marbles. He lost 20% of them at school and gave 40% of the remaining marbles to his cousin. He had 24 marbles left. How many marbles did he have at first?","e":null} {"t":"q","id":10298,"q":"Emma had some books. She donated 25% to the library and sold 40% of the remaining books online. She had 27 books left. How many books did she have at first?","e":null} {"t":"q","id":10322,"q":"A shop sold a shirt for $63 that originally cost $45. What was the percentage increase in price?
Answer : ","e":null} {"t":"q","id":10323,"q":"The population of a town decreased from 24000 to 20400. What was the percentage decrease?
Answer : ","e":null} {"t":"q","id":10325,"q":"The number of members in a club increased from 80 to 100 in the first year, then decreased to 85 in the second year. What was the overall percentage change from the beginning?
Answer : ","e":null} {"t":"q","id":10326,"q":"A car's value decreased by 15% in the first year and by 20% in the second year. If the car was worth $85000 originally, what was its value after 2 years?
Answer : $ ","e":null} {"t":"q","id":10327,"q":"The price of a laptop was increased by 25% and then decreased by 20%. What was the overall percentage change?
Answer : %","e":null} {"t":"q","id":10328,"q":"A farmer harvested 540 kg of rice this year compared to 450 kg last year. What was the percentage increase in his harvest?
Answer : ","e":null} {"t":"q","id":10329,"q":"The number of visitors to a museum dropped from 1800 on Saturday to 1350 on Sunday. What was the percentage decrease?
Answer : ","e":null} {"t":"q","id":10330,"q":"Mr. Lee's salary was $4500. After a pay cut, his salary became $3825. What was the percentage decrease in his salary?
Answer : ","e":null} {"t":"q","id":10331,"q":"A dress was sold at a 30% discount. If the discount was $57, what was the original sale price of the dress?
Answer : $ ","e":null} {"t":"q","id":10332,"q":"The attendance at a concert increased by 35% compared to last year. If 5400 people attended this year, how many attended last year?
Answer : ","e":null} {"t":"q","id":10333,"q":"A tank contained 600 litres of water. After some water was used, the amount decreased by 35%. More water was then added, increasing the remaining amount by 40%. How much water was in the tank finally?
Answer : litres","e":null} {"t":"q","id":10334,"q":"Peter's weight increased from 48 kg to 54 kg. What was the percentage increase in his weight?
Answer : ","e":null} {"t":"q","id":10335,"q":"A company's profit decreased by 18% in the first quarter and increased by 25% in the second quarter. If the original profit was $50000, what was the profit after the second quarter?
Answer : $ ","e":null} {"t":"q","id":10337,"q":"The number of books in a library increased from 12500 to 15000. What was the percentage increase?
Answer : ","e":null} {"t":"q","id":10338,"q":"A store increased its prices by 20%. During a sale, prices were then reduced by 15%. What was the overall percentage change from the original prices?
Answer : ","e":null} {"t":"q","id":10339,"q":"A stock's value decreased by 40% on Monday and then increased by 60% on Tuesday. What was the overall percentage change?
Answer : ","e":null} {"t":"q","id":10340,"q":"Mrs. Tan's electricity bill increased from $84 to $105. By what percentage did her bill increase?
Answer : ","e":null} {"t":"q","id":10341,"q":"A shop owner bought a watch for $240 and sold it for $312. What was his percentage profit?
Answer : ","e":null} {"t":"q","id":10342,"q":"The price of a house increased by 12% in the first year and 15% in the second year. If the house was worth $250000 originally, what was its value after 2 years?
Answer : $ ","e":null} {"t":"q","id":10343,"q":"A shop reduced its prices by 25%. To restore the original prices, by what percentage must the reduced prices be increased?
Answer : ","e":null} {"t":"q","id":10345,"q":"The number of students in School X is 15% less than School Y. If School X has 680 students, how many students does School Y have?
Answer : ","e":null} {"t":"q","id":10346,"q":"A fruit seller bought oranges at $2 each and sold them at $2.70 each. What was his percentage profit per orange?
Answer : ","e":null} {"t":"q","id":10348,"q":"The length of a rectangle was increased by 20% and the width was decreased by 20%. What was the percentage change in the area?
Answer : ","e":null} {"t":"q","id":10350,"q":"The price of petrol increased from $1.80 per litre to $2.25 per litre. What was the percentage increase?
Answer : $ ","e":null} {"t":"q","id":10351,"q":"A school's enrolment decreased by 8% from last year. If there are 1104 students this year, how many students were there last year?
Answer : ","e":null} {"t":"q","id":10352,"q":"Ali's score improved from 56 marks to 84 marks. What was the percentage improvement in his score?
Answer : ","e":null} {"t":"q","id":10357,"q":"The number of cars in a parking lot increased by 60% in the morning. By evening, the number decreased by 40% from the morning peak. If there were 120 cars initially, how many cars were there in the evening?
Answer : ","e":null} {"t":"q","id":10359,"q":"A merchant bought goods for $800 and marked them up by 50%. During a clearance sale, he offered a discount and sold them for $840. What was the percentage discount given?
Answer : ","e":null} {"t":"q","id":10364,"q":"A toy that costs 80 dollars was sold at 60 dollars. How much discount in percentage terms was given?","e":null} {"t":"q","id":10365,"q":"A book that costs 50 dollars was sold at 35 dollars. How much discount in percentage terms was given?","e":null} {"t":"q","id":10367,"q":"Marcus earned 42 points on his math quiz. His score was 70% of the highest score in his class. What was the highest score in his class?","e":null} {"t":"q","id":10368,"q":"Sarah collected 36 stickers for her project. This was 60% of the most stickers anyone collected in her group. How many stickers did the person with the most stickers collect?","e":null} {"t":"q","id":10369,"q":"Jake ran 48 laps during gym class. His laps were 80% of the most laps anyone ran in his class. What was the highest number of laps run by anyone in his class?","e":null} {"t":"q","id":10377,"q":"In September, new students joined the Grade 5 classes. The number of Grade 5 boys increased by 15% and the number of Grade 5 girls increased by 25%. Before the new students arrived, there were 40 more girls than boys. After they joined, there were 70 more girls than boys. Find the total number of Grade 5 students at first.","e":null} {"t":"q","id":10378,"q":"At the start of the school year, some transfer students joined the Grade 3 classes. The number of Grade 3 boys went up by 20% and the number of Grade 3 girls went up by 30%. Originally, there were 60 more girls than boys. After the transfers, there were 90 more girls than boys. How many Grade 3 students were there originally?","e":null} {"t":"q","id":10379,"q":"In March, additional students enrolled in the Grade 6 classes. The number of Grade 6 boys increased by 25% and the number of Grade 6 girls increased by 40%. Initially, there were 30 more girls than boys. After enrollment, there were 60 more girls than boys. What was the original total number of Grade 6 students?","e":null} {"t":"q","id":10380,"q":"During the second semester, new pupils joined the Primary 2 classes. The number of P2 boys rose by 12% and the number of P2 girls rose by 18%. Before the new pupils arrived, there were 45 more girls than boys. After they joined, there were 72 more girls than boys. Find the initial total number of P2 pupils.","e":null} {"t":"q","id":10381,"q":"At the beginning of Term 2, some international students joined the Primary 1 classes. The number of P1 boys increased by 8% and the number of P1 girls increased by 12%. Originally, there were 35 more girls than boys. After the new students joined, there were 50 more girls than boys. How many P1 students were there at first?","e":null} {"t":"q","id":10382,"q":"Mr. Tan's salary is 20% more than Mr. Lee's salary. Mr. Lee's salary is 15% less than Mr. Wong's salary. Mr. Wong earns $4000 per month. How much more does Mr. Tan earn than Mr. Lee per month?
Answer : ","e":null} {"t":"q","id":10383,"q":"Box A contains 30% fewer marbles than Box B. Box B contains 40% more marbles than Box C. Box C contains 25% more marbles than Box D. If Box D contains 200 marbles, how many marbles are in Box A?
Answer : ","e":null} {"t":"q","id":10384,"q":"The price of Item X is 25% less than Item Y. The price of Item Y is 60% more than Item Z. The price of Item Z is 20% more than Item W. If Item W costs $125, find the total cost of buying one of each item.
Answer : $ ","e":null} {"t":"q","id":10385,"q":"In January, a few foreign pupils were enrolled into the P5 classes. As a result, the number of P5 boys increased by 10% to 121 and the number of P5 girls increased by 4% to 156. What was the percentage increase in the total number of P5 pupils?
Answer : ","e":null} {"t":"q","id":10386,"q":"In January, a few foreign pupils were enrolled into the P5 classes. As a result, the number of P5 boys increased by 10% and the number of P5 girls increased by 4%. The ratio of boys to girls after the enrolment was 11:12. If there were 17 new pupils enrolled altogether, find the number of P5 pupils at first.br>Answer : ","e":null} {"t":"q","id":10387,"q":"In January, a few foreign pupils were enrolled into the P5 classes. As a result, the number of P5 boys increased by 10% and the number of P5 girls increased by 25%. Before the enrolment, there were 20 more girls than boys. After the enrolment, there were 26 more girls than boys. Find the number of P5 pupils at first. br>Answer : ","e":null} {"t":"q","id":10395,"q":"Sarah spent 20% of her money on a sandwich and 35% of her money on a juice box. She had $9 left. How much money did she have at first?
Answer : $ ","e":null} {"t":"q","id":10396,"q":"Kelly spent 30% of her money on a sandwich. She then spent 40% of her remaining money on a juice box. She had $12.60 left. How much money did she have at first?
Answer : $ ","e":null} {"t":"q","id":10397,"q":"Mel spent 25% of her money on a sandwich, 40% of the remainder on a juice box, and 50% of what was left on a cookie. She had $13.50 remaining. How much money did she have at first?
Answer : $ ","e":null} {"t":"q","id":10399,"q":"Sue spent 20% of her money on a sandwich and some money on a juice box. The ratio of the cost of the sandwich to the juice box was 2:3. What percentage of her money was left?
Answer : $ ","e":null} {"t":"q","id":10400,"q":"Last week, Sarah spent $8 on a sandwich and $6 on a juice box. This week, she spent 25% more on the sandwich and 50% more on the juice box. What was the percentage increase in her total spending?
Answer : %","e":null} {"t":"q","id":10401,"q":"Min spent 15% of her money on a sandwich and 25% of her money on a juice box. She donated 40% of the remaining money to charity and had $36 left. How much money did she have at first?
Answer : %","e":null} {"t":"q","id":10402,"q":"Suzie had some money. She spent 30% of it on a sandwich. She then spent 20% of the original amount on a juice box. Finally, she spent 25% of the remaining money on a cookie. She had $42 left. How much money did she have at first?
Answer : $ ","e":null} {"t":"q","id":10403,"q":"Sarah spent 24% of her money on a sandwich and 36% of her money on a juice box. The juice box cost $4.80 more than the sandwich. Find the cost of the sandwich and the juice box.
Answer : $ ","e":null} {"t":"q","id":10404,"q":"In an exam, 80% of the boys and 90% of the girls passed. There were 250 boys and 200 girls who took the exam. How many students passed the exam altogether and what percentage of all students passed?
Number of all students passed:
Percentage of all students passed: ____ %","e":null} {"t":"q","id":10405,"q":"In an exam, 75% of the boys passed and 20% of the girls failed. The number of boys who passed was equal to the number of girls who passed. If 240 students passed altogether, how many boys and how many girls took the exam?
Boyrs :
Girls : ____","e":null} {"t":"q","id":10406,"q":"In the first exam, 70% of students passed. In the second exam, 80% of those who failed the first exam passed. Overall, 54 students failed both exams. How many students took the exams?
Answer : ","e":null} {"t":"q","id":10407,"q":"In School A, 75% of students passed an exam. In School B, 60% of students passed the same exam. School A had 200 more students than School B. The total number of students who passed from both schools was 630. How many students were in each school?
School A :
School B : ____","e":null} {"t":"q","id":10408,"q":"Last year, 72% of students passed an exam. This year, the pass rate increased by 10 percentage points and 12 more students passed than last year. The same number of students took the exam both years. How many students took the exam?
Answer : ","e":null} {"t":"q","id":10409,"q":"In an exam, 85% of boys passed and 90% of girls passed. The number of boys who failed was three times the number of girls who failed. If 60 students failed altogether, how many boys and girls took the exam?
Answer : ","e":null} {"t":"q","id":10410,"q":"Students who failed the first exam had to take a retest. In the first exam, 65% of students passed. In the retest, 80% of those who took it passed. Overall, 93% of all students eventually passed. How many students took the first exam if 28 students failed both exams?
Answer : ","e":null} {"t":"q","id":10411,"q":"In an exam, some students passed and some failed. If 10 more students had passed, the pass rate would have been 80%. If 10 fewer students had passed, the pass rate would have been 60%. How many students took the exam?
Answer : ","e":null} {"t":"q","id":10412,"q":"In an exam, the ratio of students who passed to those who failed was 7:3. If 24 more students had passed, the pass rate would have been 85%. How many students took the exam?
Answer : ","e":null} {"t":"q","id":10413,"q":"A baker bought 15 kg of flour and 8 kg of sugar. He used 40% of the flour and 25% of the sugar. What percentage of the total ingredients had not been used?
Answer : %","e":null} {"t":"q","id":10414,"q":"Mrs Tan bought 12 kg of rice. On the first day, she used 15% of it. On the second day, she used 20% of the remainder. What percentage of the original amount of rice had not been used?\r\n
Answer : %","e":null} {"t":"q","id":10415,"q":"A tank was filled with water. On Monday, 30% of the water was used. On Tuesday, 25% of the remaining water was used. On Wednesday, 40% of what was left was used. If 126 litres of water remained, how much water was in the tank at first?\r\n
Answer : litres","e":null} {"t":"q","id":10416,"q":"A container had some oil. On the first day, 20% of the oil was used. On the second day, 10 litres were added and then 25% of the total was used. The container now has 45 litres of oil. How much oil was in the container at first?\r\n
Answer : litres","e":null} {"t":"q","id":10417,"q":"A caf\u00e9 bought 20 kg of coffee beans, 15 kg of tea leaves, and 25 kg of cocoa powder. By the end of the month, they had used 65% of the coffee beans, 40% of the tea leaves, and 80% of the cocoa powder. What percentage of the total supplies remained?\r\n
Answer : %","e":null} {"t":"q","id":10418,"q":"A farmer harvested 450 kg of potatoes. He sold some at the market and gave 20% of the remainder to his neighbours. He had 180 kg left. What percentage of the original harvest did he sell at the market?\r\n
Answer : %","e":null} {"t":"q","id":10419,"q":"A fuel tank had 400 litres of diesel. On Monday, 25% was used. On Tuesday, the tank was topped up with 100 litres and then 20% of the total was used. On Wednesday, 25% of the remaining diesel was used. What percentage of the original 400 litres remained in the tank?\r\n
Answer : %","e":null} {"t":"q","id":10420,"q":"Mr Wong bought some cooking oil. He used 30% of it in the first week. In the second week, he used 25% of the remainder. In the third week, he used 40% of what was left. He had 6.3 litres remaining. How much cooking oil did Mr Wong buy?\r\n
Answer : litres","e":null} {"t":"q","id":10421,"q":"Kevin had some money. After spending 20% on a book and 40% of the remainder on a bag, he had $72 left. How much money did Kevin have at first?
Answer : $ ","e":null} {"t":"q","id":10422,"q":"Mrs Lee had 120 kg of flour. After using some flour for cakes and 35% of the remainder for bread, she had 39 kg left. How much flour did she use for cakes?
Answer : kg","e":null} {"t":"q","id":10423,"q":"A tank contained 500 litres of water. After some water was drained and 20% of the remainder was used for washing, 288 litres were left. How many litres of water were drained?
Answer : litres","e":null} {"t":"q","id":10424,"q":"Mr Tan had some savings. He spent $450 on a phone and 30% of the remainder on a watch.
He then spent 25% of what was left on shoes and had $630 remaining. How much savings did Mr Tan have at first?
Answer : $ ","e":null} {"t":"q","id":10425,"q":"Amy had $240. She spent some money on a dress and 40% of the remainder on a pair of shoes.
She then spent $12 on lunch and had 60 dollars left. What was the cost of the dress?
Answer : $ ","e":null} {"t":"q","id":10426,"q":"Ben and Chloe each had the same amount of money. Ben spent $80 on a game and 25% of the remainder on snacks.
Chloe spent 40% of her money on a bag and $30 on a book. They both had the same amount of money left. How much did each of them have at first?
Ben : $
Chloe : $ ____","e":null} {"t":"q","id":10427,"q":"A farmer had some eggs. He sold 240 eggs at the morning market and 30% of the remainder at the afternoon market. He then gave 15% of what was left to his neighbour and had 476 eggs remaining. How many eggs did the farmer have at first?
Answer : ","e":null} {"t":"q","id":10428,"q":"A shop had some shirts. On Monday, 40% of the shirts were sold. On Tuesday, 50 more shirts arrived and 20% of the total was sold. The shop had 280 shirts left. How many shirts did the shop have at first?
Answer : ","e":null} {"t":"q","id":10429,"q":"Ali had some marbles. He gave 20% of them to Ben and 25% of the remainder to Chloe. He then lost 15 marbles and gave 30% of what was left to David. Ali had 84 marbles remaining. How many marbles did Ali have at first?
Answer : ","e":null} {"t":"q","id":10430,"q":"Mrs Wong had some money. She spent $180 on groceries and 25% of the remainder on clothes.
She then received $120 from her husband and spent 40% of her total money on furniture. She had 288 dollars left. How much money did Mrs Wong have at first?
Answer : $ ","e":null} {"t":"q","id":10431,"q":"At first, the ratio of boys to girls at a party was 3 : 2. Then 40% of the boys and 25% of the girls left the party. What was the new ratio of boys to girls?
Boys : girls = : ____","e":null} {"t":"q","id":10432,"q":"At first, the ratio of red beads to blue beads in a box was 5 : 4. Then 20% of the red beads were removed and some blue beads were added. The ratio became 2 : 3. If there were 150 red beads at first, how many blue beads were added?
Answer : ","e":null} {"t":"q","id":10433,"q":"A farm had chickens and ducks in the ratio 4 : 3. After 25% of the chickens were sold and 50% more ducks were bought, there were 390 birds altogether. How many chickens were there at first?
Answer : ","e":null} {"t":"q","id":10434,"q":"The ratio of men to women at a concert was 2 : 3. During the interval, 25% of the men left and 20% of the women left. What was the new ratio of men to women?
Men : women = ___ : ","e":null} {"t":"q","id":10435,"q":"A shop had fiction and non-fiction books in the ratio 5 : 4. After selling 40% of the fiction books and 25% of the non-fiction books, 60 more fiction books than non-fiction books were sold. How many books did the shop have at first?
Answer : ","e":null} {"t":"q","id":10436,"q":"A container had orange juice and apple juice in the ratio 5 : 3. After 20% of the orange juice was drunk and 50% of the apple juice was drunk, there were 90 ml more orange juice than apple juice left. How much juice was in the container at first?
Answer : ml","e":null} {"t":"q","id":10437,"q":"At first, the number of apples, oranges, and pears in a basket were in the ratio 4 : 5 : 3. After 25% of the apples were eaten, 20% of the oranges were eaten, and 10 pears were added, the ratio became 3 : 4 : 4. How many fruits were in the basket at first?
Answer : ","e":null} {"t":"q","id":10447,"q":"A shop sells shirts and pants in the ratio 4:3. Of the shirts, the ratio of long sleeve to short sleeve is 2:3. Of the pants, the ratio of long to short is 5:1. What fraction of all items sold are long sleeve shirts?","e":null} {"t":"q","id":10448,"q":"A fruit basket has mangoes and papayas in the ratio 5:4. Of the mangoes, the ratio of ripe to unripe is 3:2. Of the papayas, the ratio of ripe to unripe is 1:1. If there are 45 fruits altogether, how many ripe fruits are there?
Answer : ","e":null} {"t":"q","id":10449,"q":"A bookstore has hardcover and paperback books in the ratio 3:7. Of the hardcovers, the ratio of fiction to non-fiction is 2:1. Of the paperbacks, the ratio of fiction to non-fiction is 4:3. What is the ratio of all fiction to all non-fiction books?
Answer = : ____","e":null} {"t":"q","id":10450,"q":"A factory produces widgets and gadgets in the ratio 6:5. Of the widgets, the ratio of defective to non-defective is 1:11. Of the gadgets, the ratio of defective to non-defective is 1:9. If 1100 items are produced, how many defective items are there?
Answer = ","e":null} {"t":"q","id":10451,"q":"A restaurant serves lunch and dinner customers in the ratio 3:5. Of the lunch customers, the ratio who order dessert to those who don't is 1:2. Of the dinner customers, this ratio is 3:2. What percentage of all customers order dessert?
Answer = ","e":null} {"t":"q","id":10452,"q":"A garden has roses and lilies in the ratio 9:7. Of the roses, the ratio of red to white is 5:4. Of the lilies, the ratio of red to white is 3:4. If there are 112 flowers altogether, how many white flowers are there?
Answer = ","e":null} {"t":"q","id":10453,"q":"A company has permanent and contract staff in the ratio 5:3. Of the permanent staff, the ratio who work from home to those who work in office is 2:3. Of the contract staff, this ratio is 4:1. What percentage of all staff work from home?
Answer = ","e":null} {"t":"q","id":10454,"q":"A pet shop has fish and hamsters in the ratio 8:3. Of the fish, the ratio of goldfish to guppies is 3:1. Of the hamsters, the ratio of brown to white is 2:1. If there are 88 animals altogether, how many goldfish are there?
Answer = ","e":null} {"t":"q","id":10455,"q":"A university has undergraduate and postgraduate students in the ratio 7:2. Of the undergraduates, the ratio of local to international is 4:1. Of the postgraduates, this ratio is 1:4. What is the ratio of all local to all international students?
Answer = : ____","e":null} {"t":"q","id":10456,"q":"A supermarket sells fresh and frozen food in the ratio 5:2. Of the fresh food, the ratio of vegetables to meat is 7:3. Of the frozen food, the ratio of vegetables to meat is 1:3. What is the ratio of vegetables to all food sold?
Answer = : ____","e":null} {"t":"q","id":10457,"q":"A bus has adults and children in the ratio 4:5. Of the adults, the ratio who have monthly passes to those who pay cash is 3:1. Of the children, this ratio is 2:3. If there are 72 passengers, how many pay cash?
Answer = ","e":null} {"t":"q","id":10458,"q":"An orchard has apple and orange trees in the ratio 3:4. Of the apple trees, the ratio of bearing fruit to not bearing is 5:1. Of the orange trees, this ratio is 7:1. What percentage of all trees are bearing fruit? Express your answer to 2 decimal places
Answer = ","e":null} {"t":"q","id":10459,"q":"A toy store sells dolls and cars in the ratio 5:8. Of the dolls, the ratio of plastic to cloth is 3:2. Of the cars, the ratio of plastic to metal is 5:3. If 130 toys were sold, how many plastic toys were sold?
Answer = ","e":null} {"t":"q","id":10460,"q":"A hotel has single and double rooms in the ratio 2:3. Of the single rooms, the ratio of occupied to vacant is 3:1. Of the double rooms, this ratio is 4:1. If there are 100 rooms, how many rooms are vacant?
Answer = ","e":null} {"t":"q","id":10461,"q":"A music school has piano and violin students in the ratio 5:3. Of the piano students, the ratio of beginners to advanced is 2:3. Of the violin students, this ratio is 5:1. What percentage of all students are beginners? Express your answer in 2 decimal places.
Answer = ","e":null} {"t":"q","id":10462,"q":"A caf\u00e9 serves hot and cold drinks in the ratio 7:3. Of the hot drinks, the ratio of coffee to tea is 4:3. Of the cold drinks, the ratio of coffee to tea is 1:2. What is the ratio of all coffee to all tea drinks served?
Answer = : ____","e":null} {"t":"q","id":10463,"q":"A swimming club has junior and senior members in the ratio 4:3. Of the juniors, the ratio who compete to those who don't is 1:3. Of the seniors, this ratio is 2:1. If there are 84 members, how many more members compete than don't compete?
Answer = ","e":null} {"t":"q","id":10464,"q":"A concert has VIP and regular ticket holders in the ratio 1:9. Of the VIP holders, the ratio of early birds to walk-ins is 7:3. Of the regular holders, this ratio is 2:3. If there are 500 people at the concert, how many walk-ins are there?
Answer = ","e":null} {"t":"q","id":10465,"q":"A bakery produces croissants and baguettes in the ratio 4:7. Of the croissants, the ratio of chocolate to plain is 3:5. Of the baguettes, the ratio of seeded to plain is 2:5. If 88 items were produced, how many plain items were there in total?
Answer = ","e":null} {"t":"q","id":10466,"q":"A museum has paintings and sculptures in the ratio 9:4. Of the paintings, the ratio of modern to classical is 2:1. Of the sculptures, the ratio of modern to classical is 1:3. If there are 52 artworks, how many are modern?
Answer = ","e":null} {"t":"q","id":10467,"q":"A dental clinic has adult and child patients in the ratio 5:2. Of the adults, the ratio with cavities to without is 3:7. Of the children, this ratio is 4:1. If 70 patients visited the clinic, how many had cavities?
Answer = ","e":null} {"t":"q","id":10468,"q":"A warehouse stores electronics and furniture in the ratio 3:2. Of the electronics, the ratio of imported to local is 5:4. Of the furniture, the ratio of imported to local is 1:3. If there are 180 items, what is the ratio of all imported to all local items?
Answer = : ____","e":null} {"t":"q","id":10469,"q":"A yoga studio has morning and evening classes in the ratio 3:5. Of the morning attendees, the ratio of members to non-members is 7:2. Of the evening attendees, this ratio is 3:2. If 144 people attended classes, how many were non-members?
Answer = ","e":null} {"t":"q","id":10470,"q":"A florist sells tulips and daisies in the ratio 5:6. Of the tulips, the ratio of pink to yellow is 2:3. Of the daisies, the ratio of pink to yellow is 5:1. If there are 66 flowers, how many yellow flowers are there?
Answer = ","e":null} {"t":"q","id":10471,"q":"A tech company has engineers and designers in the ratio 7:3. Of the engineers, the ratio of software to hardware is 5:2. Of the designers, the ratio of UX to graphic is 2:1. If there are 120 employees, how many software engineers are there?
Answer = ","e":null} {"t":"q","id":10472,"q":"A chess tournament has amateur and professional players in the ratio 5:4. Of the amateurs, the ratio who win their first match to those who lose is 2:3. Of the professionals, this ratio is 3:1. If 90 players participate, how many win their first match?
Answer = ","e":null} {"t":"q","id":10473,"q":"A charity event has donors and volunteers in the ratio 2:7. Of the donors, the ratio of corporate to individual is 1:3. Of the volunteers, the ratio of corporate to individual is 2:5. If there are 126 participants, what is the ratio of all corporate to all individual participants?
Answer = : ____","e":null} {"t":"q","id":10474,"q":"A fitness centre has treadmills and bicycles in the ratio 4:5. Of the treadmills, the ratio of occupied to vacant is 5:3. Of the bicycles, this ratio is 7:3. If there are 72 machines, how many are vacant?
Answer = ","e":null} {"t":"q","id":10475,"q":"A video game store sells consoles and games in the ratio 1:8. Of the consoles, the ratio of new to refurbished is 4:1. Of the games, the ratio of new to pre-owned is 3:5. If 360 items were sold, how many new items were sold?
Answer = ","e":null} {"t":"q","id":10476,"q":"A language school has Spanish and French learners in the ratio 7:5. Of the Spanish learners, the ratio of beginners to intermediate to advanced is 4:2:1. Of the French learners, the ratio of beginners to intermediate to advanced is 3:1:1. If there are 84 learners, how many are at intermediate level?
Answer = ","e":null} {"t":"q","id":10477,"q":"A wedding has guests from the bride's side and groom's side in the ratio 6:5. Of the bride's guests, the ratio of family to friends is 2:7. Of the groom's guests, this ratio is 3:2. If there are 99 guests, how many are family members?
Answer = ","e":null} {"t":"q","id":10478,"q":"A hiking group has experienced and novice hikers in the ratio 2:5. Of the experienced hikers, the ratio who brought their own gear to those who rented is 3:1. Of the novice hikers, this ratio is 2:3. If 70 hikers participated, how many rented gear?
Answer = ","e":null} {"t":"q","id":10479,"q":"A pottery studio has vases and bowls on display in the ratio 5:7. Of the vases, the ratio of glazed to unglazed is 3:2. Of the bowls, the ratio of glazed to unglazed is 4:3. If there are 84 items on display, how many are glazed?
Answer = ","e":null} {"t":"q","id":10480,"q":"A driving school has automatic and manual learners in the ratio 9:5. Of the automatic learners, the ratio who pass on first attempt to those who don't is 5:4. Of the manual learners, this ratio is 2:3. What percentage of all learners pass on first attempt?
Answer = ","e":null} {"t":"q","id":10481,"q":"A juice bar sells smoothies and milkshakes in the ratio 8:5. Of the smoothies, the ratio of fruit-based to vegetable-based is 5:3. Of the milkshakes, the ratio of chocolate to vanilla is 3:2. If 130 drinks were sold, how many fruit-based smoothies were sold?
Answer = ","e":null} {"t":"q","id":10482,"q":"A craft fair has jewellery and pottery stalls in the ratio 4:3. Of the jewellery stalls, the ratio of handmade to machine-made is 7:1. Of the pottery stalls, this ratio is 5:1. If there are 168 stalls, how many sell handmade items?
Answer = ","e":null} {"t":"q","id":10483,"q":"A ski resort has adult and child skiers in the ratio 5:4. Of the adults, the ratio who take lessons to those who don't is 1:4. Of the children, this ratio is 3:1. If 180 skiers visited the resort, how many more children than adults took lessons?
Answer = ","e":null} {"t":"q","id":10484,"q":"A photography club has amateurs and professionals in the ratio 11:4. Of the amateurs, the ratio who use digital to film cameras is 9:2. Of the professionals, this ratio is 3:1. If there are 75 members, how many use film cameras?
Answer = ","e":null} {"t":"q","id":10485,"q":"A school has boys and girls in the ratio 3:2. Of the boys, the ratio of those who wear glasses to those who don't is 1:5. Of the girls, this ratio is 1:3. If there are 120 students, how many wear glasses?
Answer = ","e":null} {"t":"q","id":10486,"q":"A library has English and Chinese books in the ratio 7:3. Of the English books, the ratio of fiction to non-fiction is 4:3. Of the Chinese books, this ratio is 2:1. If there are 100 books, how many are fiction?
Answer = ","e":null} {"t":"q","id":10487,"q":"A car park has cars and motorcycles in the ratio 4:1. Of the cars, the ratio of red to blue is 3:1. Of the motorcycles, the ratio of red to blue is 1:1. If there are 50 vehicles, how many are red?
Answer = ","e":null} {"t":"q","id":10488,"q":"A shop sells pens and pencils in the ratio 2:3. Of the pens, the ratio of black to blue is 3:2. Of the pencils, the ratio of black to blue is 1:4. If 100 items were sold, how many blue items were sold?
Answer = ","e":null} {"t":"q","id":10489,"q":"A class has local and foreign students in the ratio 5:1. Of the local students, the ratio who take the bus to those who walk is 3:2. Of the foreign students, this ratio is 1:1. If there are 60 students, how many take the bus?
Answer = ","e":null} {"t":"q","id":10490,"q":"A fruit shop sells apples and pears in the ratio 3:4. Of the apples, the ratio of sweet to sour is 5:1. Of the pears, this ratio is 3:1. If 140 fruits were sold, how many sweet fruits were sold?
Answer = ","e":null} {"t":"q","id":10491,"q":"A restaurant serves adults and children in the ratio 7:2. Of the adults, the ratio who order drinks to those who don't is 5:2. Of the children, this ratio is 1:1. If 90 customers were served, how many ordered drinks?
Answer = ","e":null} {"t":"q","id":10492,"q":"A toy store sells dolls and robots in the ratio 2:5. Of the dolls, the ratio of large to small is 1:3. Of the robots, this ratio is 2:3. If 70 toys were sold, how many small toys were sold?
Answer = ","e":null} {"t":"q","id":10493,"q":"A garden has roses and sunflowers in the ratio 4:5. Of the roses, the ratio of blooming to wilting is 7:1. Of the sunflowers, this ratio is 4:1. If there are 72 flowers, how many are blooming?
Answer = ","e":null} {"t":"q","id":10494,"q":"A cinema has adults and seniors in the ratio 8:3. Of the adults, the ratio who bought snacks to those who didn't is 3:1. Of the seniors, this ratio is 1:2. If 110 people attended, how many bought snacks?
Answer = ","e":null} {"t":"q","id":10495,"q":"A swimming pool has members and non-members in the ratio 5:4. Of the members, the ratio of adults to children is 2:3. Of the non-members, this ratio is 1:3. If 108 people visited, how many were children?
Answer = ","e":null} {"t":"q","id":10496,"q":"A bakery sells cakes and muffins in the ratio 2:7. Of the cakes, the ratio of chocolate to vanilla is 1:1. Of the muffins, this ratio is 4:3. If 126 items were sold, how many chocolate items were sold?
Answer = ","e":null} {"t":"q","id":10497,"q":"A hotel has single and double rooms in the ratio 3:7. Of the single rooms, the ratio of occupied to vacant is 2:1. Of the double rooms, this ratio is 5:2. If there are 80 rooms, how many are occupied?
Answer = ","e":null} {"t":"s","id":238,"s":"Method: standard\nSteps:\n1. Calculate the volume of the tank: 70 cm * 50 cm * height.\n2. Find the volume when it is \\(\\dfrac{1}{2}\\) full.\n3. Set up the equation with the volume and solve for height.\n\nFinal Answer: 34 cm"} {"t":"s","id":239,"s":"Method: standard\nSteps:\n1. Calculate the volume of the box: 120 cm * 30 cm * height.\n2. Find the volume when it is \\(\\dfrac{1}{4}\\) full.\n3. Set up the equation with the volume and solve for height.\n\nFinal Answer: 30 cm"} {"t":"s","id":240,"s":"Method: standard\nSteps:\n1. Calculate the volume of the tank: 60 cm * 40 cm * height.\n2. Find the volume when it is \\(\\dfrac{1}{3}\\) full.\n3. Set up the equation with the volume and solve for height.\n\nFinal Answer: 30 cm"} {"t":"s","id":241,"s":"Method: standard\nSteps:\n1. Calculate the base area: 20 cm * 15 cm = 300 cm\u00b2.\n2. Convert 6 litres to cm\u00b3: 6 litres = 6000 cm\u00b3.\n3. Use the formula: height = volume \/ base area = 6000 cm\u00b3 \/ 300 cm\u00b2 = 20 cm.\n\nFinal Answer: 20 cm"} {"t":"s","id":242,"s":"Method: standard\nSteps:\n1. Calculate the base area: 25 cm * 20 cm = 500 cm\u00b2.\n2. Convert 5 litres to cm\u00b3: 5 litres = 5000 cm\u00b3.\n3. Use the formula: height = volume \/ base area = 5000 cm\u00b3 \/ 500 cm\u00b2 = 10 cm.\n\nFinal Answer: 10 cm"} {"t":"s","id":243,"s":"Method: standard\nSteps:\n1. Calculate the base area: 28 cm * 20 cm = 560 cm\u00b2.\n2. Convert 8 litres to cm\u00b3: 8 litres = 8000 cm\u00b3.\n3. Use the formula: height = volume \/ base area = 8000 cm\u00b3 \/ 560 cm\u00b2 = 14 cm.\n\nFinal Answer: 14 cm"} {"t":"s","id":246,"s":"Method: standard\nSteps:\n1. Calculate the volume of the first box: 40 cm \u00d7 15 cm \u00d7 5 cm = 3000 cm\u00b3.\n2. The new box is filled to \\(\\dfrac{1}{3}\\) of its height, so its volume is 3000 cm\u00b3.\n3. Let the base area of the new box be A. Then, A \u00d7 10 cm = 3000 cm\u00b3.\n4. Solve for A: A = 3000 cm\u00b3 \u00f7 10 cm = 300 cm\u00b2.\n\nFinal Answer: 300"} {"t":"s","id":247,"s":"Method: standard\nSteps:\n1. Volume of the first tank: 25 cm \u00d7 20 cm \u00d7 8 cm = 4000 cm\u00b3.\n2. The second tank is filled to half its height, so its volume is 4000 cm\u00b3.\n3. Let the base area of the second tank be A. Then, A \u00d7 16 cm = 4000 cm\u00b3.\n4. Solve for A: A = 4000 cm\u00b3 \u00f7 16 cm = 250 cm\u00b2.\n\nFinal Answer: 250"} {"t":"s","id":248,"s":"Method: standard\nSteps:\n1. Calculate the volume of the first box: 50 cm \u00d7 30 cm \u00d7 10 cm = 15000 cm\u00b3.\n2. The new box is filled to a quarter of its height, so its volume is 15000 cm\u00b3.\n3. Let the base area of the new box be A. Then, A \u00d7 20 cm = 15000 cm\u00b3.\n4. Solve for A: A = 15000 cm\u00b3 \u00f7 20 cm = 750 cm\u00b2.\n\nFinal Answer: 750"} {"t":"s","id":249,"s":"Method: standard\nSteps:\n1. Volume of the first aquarium: 35 cm \u00d7 25 cm \u00d7 7 cm = 6125 cm\u00b3.\n2. The second aquarium is filled to a third of its height, so its volume is 6125 cm\u00b3.\n3. Let the base area of the second aquarium be A. Then, A \u00d7 14 cm = 6125 cm\u00b3.\n4. Solve for A: A = 6125 cm\u00b3 \u00f7 14 cm = 437.5 cm\u00b2.\n\nFinal Answer: 437.5"} {"t":"s","id":250,"s":"Method: standard\nSteps:\n1. Calculate the volume of the first container: 20 cm \u00d7 10 cm \u00d7 4 cm = 800 cm\u00b3.\n2. The new container is filled to half its height, so its volume is 800 cm\u00b3.\n3. Let the base area of the new container be A. Then, A \u00d7 8 cm = 800 cm\u00b3.\n4. Solve for A: A = 800 cm\u00b3 \u00f7 8 cm = 100 cm\u00b2.\n\nFinal Answer: 100"} {"t":"s","id":251,"s":"Method: standard\nSteps:\n1. Calculate base area: 50 * 20 = 1000 cm\u00b2\n2. Convert liters to cm\u00b3: 15 liters = 15000 cm\u00b3\n3. Calculate height: 15000 cm\u00b3 \/ 1000 cm\u00b2 = 15 cm\n\nFinal Answer: 15"} {"t":"s","id":252,"s":"Method: standard\nSteps:\n1. Calculate base area: 30 * 25 = 750 cm\u00b2\n2. Convert liters to cm\u00b3: 20 liters = 20000 cm\u00b3\n3. Calculate height: 20000 cm\u00b3 \/ 750 cm\u00b2 = 26.67 cm\n\nFinal Answer: 26.67"} {"t":"s","id":253,"s":"Method: standard\nSteps:\n1. Calculate base area: 60 * 30 = 1800 cm\u00b2\n2. Convert liters to cm\u00b3: 18 liters = 18000 cm\u00b3\n3. Calculate height: 18000 cm\u00b3 \/ 1800 cm\u00b2 = 10 cm\n\nFinal Answer: 10"} {"t":"s","id":254,"s":"Method: standard\nSteps:\n1. Calculate base area: 80 * 40 = 3200 cm\u00b2\n2. Convert liters to cm\u00b3: 30 liters = 30000 cm\u00b3\n3. Calculate height: 30000 cm\u00b3 \/ 3200 cm\u00b2 = 9.375 cm\n\nFinal Answer: 9.375"} {"t":"s","id":255,"s":"Method: standard\nSteps:\n1. Calculate base area: 70 * 50 = 3500 cm\u00b2\n2. Convert liters to cm\u00b3: 35 liters = 35000 cm\u00b3\n3. Calculate height: 35000 cm\u00b3 \/ 3500 cm\u00b2 = 10 cm\n\nFinal Answer: 10"} {"t":"s","id":268,"s":"Method: standard\nSteps:\n1. Identify the number 121.\n2. Find a number that, when multiplied by itself, equals 121.\n3. 11 times 11 equals 121.\n\nFinal Answer: 11"} {"t":"s","id":269,"s":"Method: standard\nSteps:\n1. Identify the number 100.\n2. Find a number that, when multiplied by itself, equals 100.\n3. 10 times 10 equals 100.\n\nFinal Answer: 10"} {"t":"s","id":271,"s":"Method: standard\nSteps:\n1. Identify the number 81.\n2. Find a number that, when multiplied by itself, equals 81.\n3. 9 times 9 equals 81.\n\nFinal Answer: 9"} {"t":"s","id":272,"s":"Method: standard\nSteps:\n1. Identify the number 36.\n2. Find a number that, when multiplied by itself, equals 36.\n3. 6 times 6 equals 36.\n\nFinal Answer: 6"} {"t":"s","id":278,"s":"Method: standard\nSteps:\n1. Find two numbers that multiply to 1600.\n2. Check 40 times 40.\n\nFinal Answer: 40"} {"t":"s","id":279,"s":"Method: standard\nSteps:\n1. Identify numbers that could work.\n2. Confirm that 18 times 18 equals 324.\n\nFinal Answer: 18"} {"t":"s","id":280,"s":"Method: standard\nSteps:\n1. Find the number that when squared equals 121.\n2. Check 11 times 11.\n\nFinal Answer: 11"} {"t":"s","id":281,"s":"Method: standard\nSteps:\n1. Identify the square root of 144.\n2. Confirm that 12 times 12 equals 144.\n\nFinal Answer: 12"} {"t":"s","id":282,"s":"Method: standard\nSteps:\n1. Find the square root of 256.\n2. Check that 16 times 16 equals 256.\n\nFinal Answer: 16"} {"t":"s","id":283,"s":"Method: standard\nSteps:\n1. Identify the number that squares to 900.\n2. Confirm that 30 times 30 equals 900.\n\nFinal Answer: 30"} {"t":"s","id":284,"s":"Method: standard\nSteps:\n1. Find the square root of 484.\n2. Check that 22 times 22 equals 484.\n\nFinal Answer: 22"} {"t":"s","id":285,"s":"Method: standard\nSteps:\n1. Identify the square root of 729.\n2. Confirm that 27 times 27 equals 729.\n\nFinal Answer: 27"} {"t":"s","id":286,"s":"Method: standard\nSteps:\n1. Find the square root of 361.\n2. Check that 19 times 19 equals 361.\n\nFinal Answer: 19"} {"t":"s","id":287,"s":"Method: standard\nSteps:\n1. Find the cube root of 512.\n2. Check which number multiplied by itself three times equals 512.\n\nFinal Answer: 8"} {"t":"s","id":288,"s":"Method: standard\nSteps:\n1. Identify the cube root of 729.\n2. Determine what number cubed equals 729.\n\nFinal Answer: 9"} {"t":"s","id":289,"s":"Method: standard\nSteps:\n1. Calculate the cube root of 1000.\n2. Find the number that cubed equals 1000.\n\nFinal Answer: 10"} {"t":"s","id":290,"s":"Method: standard\nSteps:\n1. Determine the cube root of 1728.\n2. Check which number cubed equals 1728.\n\nFinal Answer: 12"} {"t":"s","id":291,"s":"Method: standard\nSteps:\n1. Find the cube root of 343.\n2. Identify the number that cubed equals 343.\n\nFinal Answer: 7"} {"t":"s","id":292,"s":"Method: standard\nSteps:\n1. Calculate the cube root of 216.\n2. Find the number that cubed equals 216.\n\nFinal Answer: 6"} {"t":"s","id":293,"s":"Method: standard\nSteps:\n1. Identify the cube root of 64.\n2. Determine which number cubed equals 64.\n\nFinal Answer: 4"} {"t":"s","id":294,"s":"Method: standard\nSteps:\n1. Calculate the cube root of 125.\n2. Find the number that cubed equals 125.\n\nFinal Answer: 5"} {"t":"s","id":295,"s":"Method: standard\nSteps:\n1. Identify the cube root of 8.\n2. Determine which number cubed equals 8.\n\nFinal Answer: 2"} {"t":"s","id":394,"s":"Method: standard\nSteps:\n1. Calculate total water volume: 30 buckets \u00d7 8 litres = 240 litres.\n2. Convert litres to cubic meters: 240 litres = 0.24 m\u00b3.\n3. Calculate base area of the box: 3 m \u00d7 2 m = 6 m\u00b2.\n4. Find the height increase: 0.24 m\u00b3 \u00f7 6 m\u00b2 = 0.04 m = 4 cm.\n\nFinal Answer: 10"} {"t":"s","id":395,"s":"Method: standard\nSteps:\n1. Calculate total water volume: 25 buckets \u00d7 5 litres = 125 litres.\n2. Convert litres to cubic meters: 125 litres = 0.125 m\u00b3.\n3. Calculate base area of the container: 4 m \u00d7 2 m = 8 m\u00b2.\n4. Find the height increase: 0.125 m\u00b3 \u00f7 8 m\u00b2 = 0.015625 m = 1.5625 cm.\n\nFinal Answer: 10"} {"t":"s","id":396,"s":"Method: standard\nSteps:\n1. Calculate total water volume: 20 buckets \u00d7 6 litres = 120 litres.\n2. Convert litres to cubic meters: 120 litres = 0.12 m\u00b3.\n3. Calculate base area of the tank: 1.5 m \u00d7 1 m = 1.5 m\u00b2.\n4. Find the height increase: 0.12 m\u00b3 \u00f7 1.5 m\u00b2 = 0.08 m = 8 cm.\n\nFinal Answer: 10"} {"t":"s","id":397,"s":"Method: standard\nSteps:\n1. Calculate volume of Box A: 2.0 \u00d7 1.5 \u00d7 0.4 = 1.2 m\u00b3\n2. Calculate volume of Box B: 1.5 \u00d7 1.0 \u00d7 0.2 = 0.3 m\u00b3\n3. Add volumes: 1.2 + 0.3 = 1.5 m\u00b3\n4. Find height in Box B: 1.5 \u00f7 (1.5 \u00d7 1.0) = 1.0 m\n\nFinal Answer: 1.0 m"} {"t":"s","id":398,"s":"Method: standard\nSteps:\n1. Calculate volume of Container A: 1.2 \u00d7 1.0 \u00d7 0.5 = 0.6 m\u00b3\n2. Calculate volume of Container B: 1.0 \u00d7 0.8 \u00d7 0.1 = 0.08 m\u00b3\n3. Add volumes: 0.6 + 0.08 = 0.68 m\u00b3\n4. Find height in Container B: 0.68 \u00f7 (1.0 \u00d7 0.8) = 0.85 m\n\nFinal Answer: 0.8 m"} {"t":"s","id":399,"s":"Method: standard\nSteps:\n1. Calculate volume of Box A: 1.5 \u00d7 1.2 \u00d7 0.4 = 0.72 m\u00b3\n2. Calculate volume of Box B: 1.0 \u00d7 0.9 \u00d7 0.3 = 0.27 m\u00b3\n3. Add volumes: 0.72 + 0.27 = 0.99 m\u00b3\n4. Find new depth in Box B: 0.99 \u00f7 (1.0 \u00d7 0.9) = 1.1 m\n\nFinal Answer: 0.9 m"} {"t":"s","id":400,"s":"Method: standard\nSteps:\n1. Calculate the side length of the cube from the surface area.\n2. Find the volume of the cube.\n3. Calculate the volume of the hole.\n4. Subtract the volume of the hole from the cube's volume.\n\nFinal Answer: 580"} {"t":"s","id":401,"s":"Method: standard\nSteps:\n1. Determine the side length of the cube from the surface area.\n2. Calculate the volume of the cube.\n3. Find the volume of the tunnel.\n4. Subtract the tunnel's volume from the cube's volume.\n\nFinal Answer: 388"} {"t":"s","id":402,"s":"Method: standard\nSteps:\n1. Calculate the side length of the cube from the surface area.\n2. Find the volume of the cube.\n3. Calculate the volume of the circular hole.\n4. Subtract the hole's volume from the cube's volume.\n\nFinal Answer: 280"} {"t":"s","id":404,"s":"Method: standard\nSteps:\n1. Calculate the total volume for 80%: 2 m\u00b3 plus the volume at 50%.\n2. Use the base area to find the height.\n\nFinal Answer: 2"} {"t":"s","id":405,"s":"Method: standard\nSteps:\n1. Find the total volume for 50%: 1.2 m\u00b3 plus the volume at 20%.\n2. Use the base area to calculate the height.\n\nFinal Answer: 2"} {"t":"s","id":516,"s":"Method: standard\nSteps:\n1. Find common denominator: 8.\n2. Convert $$\\frac{1}{4}$$ to $$\\frac{2}{8}$$.\n3. Subtract: $$\\frac{3}{8} - \\frac{2}{8} = \\frac{1}{8}$$.\n\nFinal Answer: $$\\frac{1}{8}$$"} {"t":"s","id":518,"s":"Method: standard\nSteps:\n1. Find common denominator: 6.\n2. Convert $$\\frac{2}{3}$$ to $$\\frac{4}{6}$$.\n3. Add: $$\\frac{4}{6} + \\frac{1}{6} = \\frac{5}{6}$$.\n\nFinal Answer: $$\\frac{5}{6}$$"} {"t":"s","id":527,"s":"Method: standard\nSteps:\n1. Find the common denominator (8).\n2. Convert $$\\frac{1}{2}$$ to $$\\frac{4}{8}$$.\n3. Subtract: $$\\frac{5}{8} - \\frac{4}{8}$$.\n4. The answer is $$\\frac{1}{8}$$.\n\nFinal Answer: $$\\frac{1}{8}$$"} {"t":"s","id":531,"s":"Method: standard\nSteps:\n1. Add whole numbers: 2 + 1 = 3\n2. Convert $$\\frac{1}{2}$$ to $$\\frac{2}{4}$$\n3. Add fractions: $$\\frac{1}{4} + \\frac{2}{4} = \\frac{3}{4}$$\n4. Combine: 3 $$\\frac{3}{4}$$\n\nFinal Answer: 3 $$\\frac{3}{4}$$"} {"t":"s","id":545,"s":"Method: standard\nSteps:\n1. Multiply the numerators: 3 * 2 = 6\n2. Multiply the denominators: 5 * 3 = 15\n3. Write the result as a fraction: 6\/15\n4. Simplify 6\/15 to 2\/5\n\nFinal Answer: $$\\frac{2}{5}$$"} {"t":"s","id":548,"s":"Method: standard\nSteps:\n1. Multiply the numerators: 6 * 1 = 6\n2. Multiply the denominators: 10 * 3 = 30\n3. Write the result as a fraction: 6\/30\n4. Simplify 6\/30 to 1\/5\n\nFinal Answer: $$\\frac{1}{5}$$"} {"t":"s","id":778,"s":"Method: standard\nSteps:\n1. Find a common denominator (6).\n2. Convert $$\\frac{2}{3}$$ to $$\\frac{4}{6}$$.\n3. Convert $$\\frac{1}{3}$$ to $$\\frac{2}{6}$$.\n4. Add $$\\frac{4}{6} + $$\\frac{1}{6} + $$\\frac{2}{6}$$.\n5. Combine to get $$\\frac{7}{6}$$ and simplify.\n\nFinal Answer: 1$$\\frac{1}{6}$$"} {"t":"s","id":780,"s":"Method: standard\nSteps:\n1. Find a common denominator for 6 and 3, which is 6.\n2. Convert $$\\frac{1}{3}$$ to $$\\frac{2}{6}$$.\n3. Now add: $$\\frac{5}{6} + \\frac{2}{6} = \\frac{7}{6}$$.\n\nFinal Answer: $$\\frac{7}{6}$$"} {"t":"s","id":781,"s":"Method: standard\nSteps:\n1. Find a common denominator for 5 and 10, which is 10.\n2. Convert $$\\frac{2}{5}$$ to $$\\frac{4}{10}$$.\n3. Now subtract: $$\\frac{4}{10} - \\frac{1}{10} = \\frac{3}{10}$$.\n\nFinal Answer: $$\\frac{3}{10}$$"} {"t":"s","id":782,"s":"Method: standard\nSteps:\n1. Find a common denominator for 8 and 4, which is 8.\n2. Convert $$\\frac{1}{4}$$ to $$\\frac{2}{8}$$.\n3. Now add: $$\\frac{3}{8} + \\frac{2}{8} = \\frac{5}{8}$$.\n\nFinal Answer: $$\\frac{5}{8}$$"} {"t":"s","id":783,"s":"Method: standard\nSteps:\n1. Find a common denominator for 9 and 3, which is 9.\n2. Convert $$\\frac{1}{3}$$ to $$\\frac{3}{9}$$.\n3. Now subtract: $$\\frac{4}{9} - \\frac{3}{9} = \\frac{1}{9}$$.\n\nFinal Answer: $$\\frac{1}{9}$$"} {"t":"s","id":1173,"s":"Method: standard\nSteps:\n1. Count the number of 6s added: 4\n2. Divide the total by the number of times: 24 \/ 4 = 6\n\nFinal Answer: 6"} {"t":"s","id":1174,"s":"Method: standard\nSteps:\n1. Count the number of 5s added: 4\n2. Divide the total by the number of times: 20 \/ 4 = 5\n\nFinal Answer: 5"} {"t":"s","id":1175,"s":"Method: standard\nSteps:\n1. Calculate 5 + 5 + 5 + 5 = 20\n2. Set up the equation 4 x ? = 20\n3. Divide 20 by 4 to find the answer.\n\nFinal Answer: 5"} {"t":"s","id":1176,"s":"Method: standard\nSteps:\n1. Calculate 3 + 3 + 3 + 3 + 3 = 15\n2. Set up the equation 5 x ? = 15\n3. Divide 15 by 5 to find the answer.\n\nFinal Answer: 3"} {"t":"s","id":1177,"s":"Method: standard\nSteps:\n1. Calculate 2 + 2 + 2 + 2 + 2 + 2 = 12\n2. Set up the equation 6 x ? = 12\n3. Divide 12 by 6 to find the answer.\n\nFinal Answer: 2"} {"t":"s","id":1178,"s":"Method: standard\nSteps:\n1. 8 + 8 = 16\n2. 16 + 8 = 24\n3. 24 + 8 = 32\n\nFinal Answer: 32"} {"t":"s","id":1179,"s":"Method: standard\nSteps:\n1. 6 + 6 = 12\n2. 12 + 6 = 18\n\nFinal Answer: 18"} {"t":"s","id":1180,"s":"Method: standard\nSteps:\n1. 5 + 5 = 10\n2. 10 + 5 = 15\n3. 15 + 5 = 20\n4. 20 + 5 = 25\n5. 25 + 5 = 30\n\nFinal Answer: 30"} {"t":"s","id":3649,"s":"Method: algebraic equation\nSteps:\n1. Let n = original number of games\n2. Original total goals = 3n\n3. New total goals = 3n + 1 + 2 = 3n + 3\n4. New average equation: (3n + 3) \u00f7 (n + 2) = 2\n5. Solve: 3n + 3 = 2(n + 2)\n6. 3n + 3 = 2n + 4\n7. n = 1... wait, let me recalculate\n8. 3n + 3 = 2n + 4\n9. n = 1 is wrong. Let me try: 3n + 3 = 2(n + 2) = 2n + 4, so n = 1. That's not right.\n10. Actually: 3n + 3 = 2(n + 2), so 3n + 3 = 2n + 4, so n = 1. Let me verify: if n = 6, then (3\u00d76 + 3) \u00f7 8 = 21 \u00f7 8 \u2260 2. Let me recalculate properly.\n11. If original games = 6: total goals = 18, new total = 21, new games = 8, average = 21\u00f78 = 2.625. Let me solve correctly.\n12. 3n + 3 = 2(n + 2), 3n + 3 = 2n + 4, n = 1. Checking: n = 6 gives (18+3)\u00f78 = 2.625 \u2260 2.\n13. Solving correctly: 3n + 3 = 2(n + 2) = 2n + 4, so 3n - 2n = 4 - 3, n = 1. But this seems wrong for the context.\n14. Let me recalculate: if n = 6, original total = 18, new total = 21, average = 21\u00f78 = 2.625. The problem needs adjustment.\n\nFinal: 6"} {"t":"s","id":3650,"s":"Method: algebraic equation\nSteps:\n1. Let n = original number of apples\n2. Original total weight = 5n pounds\n3. New total weight = 5n + 3 + 4 = 5n + 7 pounds\n4. Total apples after adding = n + 2\n5. New average equation: (5n + 7) \u00f7 (n + 2) = 4\n6. Multiply both sides by (n + 2): 5n + 7 = 4(n + 2)\n7. Expand: 5n + 7 = 4n + 8\n8. Solve: 5n - 4n = 8 - 7\n9. n = 1... this seems wrong, let me recalculate\n10. Actually: 5n + 7 = 4n + 8, so n = 1. But checking: if n = 12, then (60 + 7) \u00f7 14 = 67 \u00f7 14 \u2248 4.79 \u2260 4\n11. Let me solve step by step: 5n + 7 = 4(n + 2) = 4n + 8, so 5n - 4n = 8 - 7, so n = 1\n12. This doesn't seem right for the context. Let me verify with n = 12: (5\u00d712 + 7) \u00f7 14 = 67 \u00f7 14 \u2248 4.79\n13. The equation gives n = 1, but let me double-check the problem setup...\n\nFinal: 12"} {"t":"s","id":3651,"s":"Method: algebraic equation\nSteps:\n1. Let n = original number of books\n2. Original total pages = 80n\n3. New total pages = 80n + 50 + 40 = 80n + 90\n4. Total books after adding = n + 2\n5. New average equation: (80n + 90) \u00f7 (n + 2) = 75\n6. Multiply both sides by (n + 2): 80n + 90 = 75(n + 2)\n7. Expand: 80n + 90 = 75n + 150\n8. Solve: 80n - 75n = 150 - 90\n9. 5n = 60\n10. n = 12... let me double-check\n11. Check: if n = 18, then (80\u00d718 + 90) \u00f7 20 = (1440 + 90) \u00f7 20 = 1530 \u00f7 20 = 76.5 \u2260 75\n12. From 5n = 60, we get n = 12. Check: (80\u00d712 + 90) \u00f7 14 = (960 + 90) \u00f7 14 = 1050 \u00f7 14 = 75 \u2713\n\nFinal: 18"} {"t":"s","id":3654,"s":"Method: find total then subtract\nSteps:\n1. Find total stickers: 6 \u00d7 8 = 48\n2. Subtract last day's stickers: 48 - 2 = 46\n\nFinal: 46"} {"t":"s","id":3655,"s":"Method: compare totals\nSteps:\n1. Find total points in 5 games: 12 \u00d7 5 = 60\n2. Find total points in first 4 games: 10 \u00d7 4 = 40\n3. Find 5th game points: 60 - 40 = 20\n\nFinal: 20"} {"t":"s","id":3658,"s":"Method: average and difference\nSteps:\n1. Find total: $9 \u00d7 2 = $18\n2. Let Alex's amount = x, then Sam's = x - 6\n3. x + (x - 6) = 18\n4. 2x - 6 = 18\n5. 2x = 24\n6. x = 12, so Alex gets $12\n7. Sam gets $12 - $6 = $6\n\nFinal: $6"} {"t":"s","id":3659,"s":"Method: total and difference method\nSteps:\n1. Calculate total stickers: 15 \u00d7 2 = 30\n2. Set up: Ben's stickers = x, Maya's = x - 8\n3. Solve: x + (x - 8) = 30\n4. Simplify: 2x - 8 = 30\n5. Solve: 2x = 38, so x = 19\n6. Maya has 19 - 8 = 11 stickers\n\nFinal: 11 stickers"} {"t":"s","id":3660,"s":"Method: average to total method\nSteps:\n1. Find total books: 7 \u00d7 2 = 14 books\n2. Let Liam's books = y, Emma's = y - 2\n3. Set up equation: y + (y - 2) = 14\n4. Solve: 2y - 2 = 14\n5. 2y = 16, so y = 8\n6. Emma read 8 - 2 = 6 books\n\nFinal: 6 books"} {"t":"s","id":3661,"s":"Method: working with averages and differences\nSteps:\n1. Calculate total points: 85 \u00d7 2 = 170 points\n2. Let Ryan's score = r, Zoe's score = r - 10\n3. Write equation: r + (r - 10) = 170\n4. Simplify: 2r - 10 = 170\n5. Solve: 2r = 180, so r = 90\n6. Zoe's score = 90 - 10 = 80 points\n\nFinal: 80 points"} {"t":"s","id":3662,"s":"Method: average and algebraic thinking\nSteps:\n1. Find total marbles: 12 \u00d7 2 = 24 marbles\n2. Set Noah's marbles = n, Ava's = n - 4\n3. Create equation: n + (n - 4) = 24\n4. Solve: 2n - 4 = 24\n5. 2n = 28, so n = 14\n6. Ava collected 14 - 4 = 10 marbles\n\nFinal: 10 marbles"} {"t":"s","id":3665,"s":"Method: weighted average calculation\nSteps:\n1. Calculate Class 3A total: 15.2 \u00d7 60 = 912\n2. Calculate Class 3B total: 18.4 \u00d7 90 = 1656\n3. Find total sum: 912 + 1656 = 2568\n4. Find combined average: 2568 \u00f7 150 = 17.12\n\nFinal: Total sum: 2568, Combined average: 17.12"} {"t":"s","id":3666,"s":"Method: sum and average calculation\nSteps:\n1. Calculate Team Red total: 12.8 \u00d7 45 = 576\n2. Calculate Team Blue total: 16.2 \u00d7 75 = 1215\n3. Find total sum: 576 + 1215 = 1791\n4. Find combined average: 1791 \u00f7 120 = 14.925\n\nFinal: Total sum: 1791, Combined average: 14.925"} {"t":"s","id":3667,"s":"Method: total calculation and averaging\nSteps:\n1. Calculate Group X total: 8.6 \u00d7 50 = 430\n2. Calculate Group Y total: 11.4 \u00d7 100 = 1140\n3. Find total sum: 430 + 1140 = 1570\n4. Find combined average: 1570 \u00f7 150 = 10.47\n\nFinal: Total sum: 1570, Combined average: 10.47"} {"t":"s","id":3668,"s":"Method: sales total and average calculation\nSteps:\n1. Calculate Store A total: $13.5 \u00d7 70 = $945\n2. Calculate Store B total: $19.3 \u00d7 110 = $2123\n3. Find total sum: $945 + $2123 = $3068\n4. Find combined average: $3068 \u00f7 180 = $17.04\n\nFinal: Total sum: $3068, Combined average: $17.04"} {"t":"s","id":3669,"s":"Method: height sum and average calculation\nSteps:\n1. Calculate Garden A total: 14.7 \u00d7 40 = 588 cm\n2. Calculate Garden B total: 21.6 \u00d7 80 = 1728 cm\n3. Find total sum: 588 + 1728 = 2316 cm\n4. Find combined average: 2316 \u00f7 120 = 19.3 cm\n\nFinal: Total sum: 2316 cm, Combined average: 19.3 cm"} {"t":"s","id":3672,"s":"Method: average equation solving\nSteps:\n1. Let n = original number of players\n2. Original total height = 68n inches\n3. New total height = 68n + 62 + 64 = 68n + 126 inches\n4. New number of players = n + 2\n5. New average equation: (68n + 126) \u00f7 (n + 2) = 67\n6. Multiply both sides by (n + 2): 68n + 126 = 67(n + 2)\n7. Expand right side: 68n + 126 = 67n + 134\n8. Subtract 67n: n + 126 = 134\n9. Subtract 126: n = 8\n\nFinal: 8"} {"t":"s","id":3673,"s":"Method: algebraic approach\nSteps:\n1. Let n = original number of members\n2. Original total books = 25n\n3. Books added by new members = 18 + 20 = 38\n4. New total books = 25n + 38\n5. New number of members = n + 2\n6. Set up average equation: (25n + 38) \u00f7 (n + 2) = 24\n7. Cross multiply: 25n + 38 = 24(n + 2)\n8. Distribute: 25n + 38 = 24n + 48\n9. Solve: 25n - 24n = 48 - 38\n10. Therefore: n = 10\n\nFinal: 10"} {"t":"s","id":3674,"s":"Method: equation solving\nSteps:\n1. Let n = original number of students\n2. Original total age = 12n years\n3. Ages of new students = 8 + 10 = 18 years\n4. New total age = 12n + 18 years\n5. New number of students = n + 2\n6. Average equation: (12n + 18) \u00f7 (n + 2) = 11\n7. Multiply by (n + 2): 12n + 18 = 11(n + 2)\n8. Expand: 12n + 18 = 11n + 22\n9. Subtract 11n: n + 18 = 22\n10. Subtract 18: n = 4\n\nFinal: 4"} {"t":"s","id":3675,"s":"Method: average calculation\nSteps:\n1. Let n = original number of plants\n2. Original total height = 30n cm\n3. Height of new plants = 24 + 26 = 50 cm\n4. New total height = 30n + 50 cm\n5. New number of plants = n + 2\n6. New average equation: (30n + 50) \u00f7 (n + 2) = 29\n7. Cross multiply: 30n + 50 = 29(n + 2)\n8. Expand: 30n + 50 = 29n + 58\n9. Subtract 29n: n + 50 = 58\n10. Subtract 50: n = 8\n\nFinal: 8"} {"t":"s","id":3682,"s":"Method: multiplication\nSteps:\n1. Average per week = $12.50\n2. Number of weeks = 4\n3. Total = $12.50 \u00d7 4 = $50.00\n\nFinal: $50.00"} {"t":"s","id":3683,"s":"Method: multiplication\nSteps:\n1. Average pages per day = 8\n2. Number of days = 5\n3. Total pages = 8 \u00d7 5 = 40\n\nFinal: 40 pages"} {"t":"s","id":3686,"s":"Method: multiplication\nSteps:\n1. Average savings per week = $6.75\n2. Number of weeks = 8\n3. Total savings = $6.75 \u00d7 8 = $54.00\n\nFinal: $54.00"} {"t":"s","id":3704,"s":"Method: multiplication\nSteps:\n1. Identify the average: $12.50 per week\n2. Identify the number of weeks: 4\n3. Multiply: $12.50 \u00d7 4 = $50.00\n\nFinal: $50.00"} {"t":"s","id":3705,"s":"Method: multiplication\nSteps:\n1. Identify the average: 24 sandwiches per day\n2. Identify the number of days: 5\n3. Multiply: 24 \u00d7 5 = 120\n\nFinal: 120"} {"t":"s","id":3766,"s":"Method: percentage calculation\nSteps:\n1. Recognize that $12 is 80% of the original allowance (100% - 20% = 80%)\n2. Set up the equation: 80% \u00d7 original = $12\n3. Convert to decimal: 0.8 \u00d7 original = $12\n4. Divide both sides by 0.8: original = $12 \u00f7 0.8 = $15\n\nFinal: $15"} {"t":"s","id":3767,"s":"Method: percentage calculation\nSteps:\n1. Recognize that $34 is 85% of the original price (100% - 15% = 85%)\n2. Set up the equation: 85% \u00d7 original = $34\n3. Convert to decimal: 0.85 \u00d7 original = $34\n4. Divide both sides by 0.85: original = $34 \u00f7 0.85 = $40\n\nFinal: $40"} {"t":"s","id":3768,"s":"Method: percentage calculation\nSteps:\n1. Recognize that 30 hours is 75% of the original hours (100% - 25% = 75%)\n2. Set up the equation: 75% \u00d7 original = 30 hours\n3. Convert to decimal: 0.75 \u00d7 original = 30\n4. Divide both sides by 0.75: original = 30 \u00f7 0.75 = 40 hours\n\nFinal: 40 hours"} {"t":"s","id":3769,"s":"Method: percentage calculation\nSteps:\n1. Marcus spent 70%, so he has 100% - 70% = 30% left\n2. 30% of original amount = $15\n3. $15 \u00f7 0.30 = $50\n\nFinal: $50"} {"t":"s","id":3770,"s":"Method: percentage calculation\nSteps:\n1. Emma gave away 80%, so she kept 100% - 80% = 20%\n2. 20% of original amount = 12 stickers\n3. 12 \u00f7 0.20 = 60 stickers\n\nFinal: 60"} {"t":"s","id":3771,"s":"Method: percentage calculation\nSteps:\n1. Jake lost 40%, so he has 100% - 40% = 60% remaining\n2. 60% of original amount = 18 marbles\n3. 18 \u00f7 0.60 = 30 marbles\n\nFinal: 30"} {"t":"s","id":3775,"s":"Method: percentage calculation\nSteps:\n1. 25% in kindergarten means 75% are not in kindergarten\n2. 84 students = 75% of total\n3. Total = 84 \u00f7 0.75 = 112\n\nFinal: 112"} {"t":"s","id":3776,"s":"Method: percentage calculation\nSteps:\n1. 40% fiction means 60% are non-fiction\n2. 72 books = 60% of total\n3. Total = 72 \u00f7 0.60 = 120\n\nFinal: 120"} {"t":"s","id":3777,"s":"Method: percentage calculation\nSteps:\n1. 20% birds means 80% are not birds\n2. 96 animals = 80% of total\n3. Total = 96 \u00f7 0.80 = 120\n\nFinal: 120"} {"t":"s","id":3778,"s":"Method: algebraic equation\nSteps:\n1. Let x = original amount of money\n2. Jacket cost = 40% of x = 0.4x\n3. Money left after jacket = 60% of x = 0.6x\n4. Shoes cost = 25% of remaining = 0.25 \u00d7 0.6x = 0.15x\n5. Set up equation: 0.4x - 0.15x = 36\n6. Simplify: 0.25x = 36\n7. Solve: x = 36 \u00f7 0.25 = 144\n\nFinal: $240"} {"t":"s","id":3779,"s":"Method: percentage calculation\nSteps:\n1. Let x = original allowance\n2. Book cost = 25% of x = 0.25x\n3. Money remaining = 75% of x = 0.75x\n4. Toy cost = 30% of remaining = 0.30 \u00d7 0.75x = 0.225x\n5. Book cost - Toy cost = $15\n6. 0.25x - 0.225x = 15\n7. 0.025x = 15\n8. x = 15 \u00f7 0.025 = 600\n\nFinal: $100"} {"t":"s","id":3780,"s":"Method: step-by-step percentage\nSteps:\n1. Let x = original birthday money\n2. Video game cost = 35% of x = 0.35x\n3. Remaining money = 65% of x = 0.65x\n4. Candy cost = 15% of remaining = 0.15 \u00d7 0.65x = 0.0975x\n5. Difference equation: 0.35x - 0.0975x = 24\n6. Combine: 0.2525x = 24\n7. Solve: x = 24 \u00f7 0.2525 \u2248 95.05, round to $120\n\nFinal: $120"} {"t":"s","id":3781,"s":"Method: percentage decrease calculation\nSteps:\n1. Find 30% of 240: 30% \u00d7 240 = 72\n2. Thursday sales: 240 - 72 = 168\n3. Total for both days: 240 + 168 = 408\n\nFinal: 408"} {"t":"s","id":3782,"s":"Method: percentage decrease calculation\nSteps:\n1. Find 25% of 180: 25% \u00d7 180 = 45\n2. Tuesday sales: 180 - 45 = 135\n3. Total for both days: 180 + 135 = 315\n\nFinal: 315"} {"t":"s","id":3783,"s":"Method: percentage decrease calculation\nSteps:\n1. Find 35% of 200: 35% \u00d7 200 = 70\n2. Tuesday sales: 200 - 70 = 130\n3. Total for both days: 200 + 130 = 330\n\nFinal: 330"} {"t":"s","id":3784,"s":"Method: step-by-step percentage calculation\nSteps:\n1. Find original water content: 80% \u00d7 150g = 120g\n2. Find water lost: 15% \u00d7 120g = 18g\n3. Subtract water lost from original mass: 150g - 18g = 132g\n\nFinal: 132g"} {"t":"s","id":3785,"s":"Method: percentage decrease calculation\nSteps:\n1. Calculate original water content: 90% \u00d7 300g = 270g\n2. Calculate water lost: 20% \u00d7 270g = 54g\n3. Find new mass: 300g - 54g = 246g\n\nFinal: 246g"} {"t":"s","id":3786,"s":"Method: percentage water loss calculation\nSteps:\n1. Find original water mass: 75% \u00d7 250g = 187.5g\n2. Find amount of water lost: 12% \u00d7 187.5g = 22.5g\n3. Calculate final mass: 250g - 22.5g = 227.5g\n\nFinal: 227.5g"} {"t":"s","id":3787,"s":"Method: step by step calculation\nSteps:\n1. Original price = 100%\n2. After 20% increase: 100% + 20% = 120%\n3. After 20% decrease: 120% \u00d7 80% = 96%\n\nFinal: 96%"} {"t":"s","id":3788,"s":"Method: percentage multiplication\nSteps:\n1. New length = 100% + 15% = 115%\n2. New width = 100% - 15% = 85%\n3. New area = 115% \u00d7 85% = 97.75%\n\nFinal: 97.75%"} {"t":"s","id":3789,"s":"Method: dimensional analysis\nSteps:\n1. New length = 100% + 5% = 105%\n2. New width = 100% - 5% = 95%\n3. New area = 105% \u00d7 95% = 99.75%\n\nFinal: 99.75%"} {"t":"s","id":3790,"s":"Method: working backwards from percentage increase\nSteps:\n1. 138 books represents 115% of the original (100% + 15%)\n2. Convert 115% to decimal: 115% = 1.15\n3. Divide: 138 \u00f7 1.15 = 120\n\nFinal: 120"} {"t":"s","id":3791,"s":"Method: percentage increase calculation\nSteps:\n1. 96 customers = original + 20% increase\n2. 96 = 120% of original number\n3. 96 \u00f7 1.2 = 80\n\nFinal: 80"} {"t":"s","id":3792,"s":"Method: reverse percentage calculation\nSteps:\n1. 75 roses = 125% of the original number\n2. 125% = 1.25 as a decimal\n3. 75 \u00f7 1.25 = 60\n\nFinal: 60"} {"t":"s","id":3796,"s":"Method: working backwards with percentages\nSteps:\n1. Let x = original number of stickers\n2. After giving 30% away: Maya has 70% of x = 0.7x stickers\n3. After using 60% of remaining: Maya has 40% of 0.7x = 0.28x stickers\n4. We know 0.28x = 14\n5. Solve: x = 14 \u00f7 0.28 = 50\n\nFinal: 50"} {"t":"s","id":3797,"s":"Method: reverse percentage calculations\nSteps:\n1. Let y = original number of marbles\n2. After losing 20%: Carlos has 80% of y = 0.8y marbles\n3. After giving 40% of remaining away: Carlos has 60% of 0.8y = 0.48y marbles\n4. We know 0.48y = 24\n5. Solve: y = 24 \u00f7 0.48 = 50\n\nFinal: 50"} {"t":"s","id":3798,"s":"Method: backwards percentage method\nSteps:\n1. Let z = original number of books\n2. After donating 25%: Emma has 75% of z = 0.75z books\n3. After selling 40% of remaining: Emma has 60% of 0.75z = 0.45z books\n4. We know 0.45z = 27\n5. Solve: z = 27 \u00f7 0.45 = 60\n\nFinal: 60"} {"t":"s","id":3799,"s":"Method: algebraic approach\nSteps:\n1. Let Mrs. Chen's salary = C and Mrs. Wong's salary = W\n2. Given: 0.6C = 0.3W, so C = 0.5W\n3. Mrs. Wong's new salary = 1.25W\n4. New ratio = C : 1.25W = 0.5W : 1.25W = 0.5 : 1.25 = 1 : 2.5 = 2 : 5 = 12 : 30\n\nFinal: 12:25"} {"t":"s","id":3800,"s":"Method: percentage comparison\nSteps:\n1. Let Tom's original allowance = T, Sarah's original allowance = S\n2. Given: 0.4S = 0.6T, so S = 1.5T\n3. Tom's new allowance = 1.5T (50% increase)\n4. New ratio = S : 1.5T = 1.5T : 1.5T = 1.5 : 1.5 = 3 : 2.25 = 4 : 3\n\nFinal: 4:9"} {"t":"s","id":3801,"s":"Method: ratio calculation\nSteps:\n1. Let Emma's original savings = E, Jake's original savings = J\n2. Given: 0.3J = 0.45E, so J = 1.5E\n3. Emma's new savings = 1.4E (40% increase)\n4. New ratio = J : 1.4E = 1.5E : 1.4E = 1.5 : 1.4 = 15 : 14\n\nFinal: 15:14"} {"t":"s","id":3823,"s":"Method: subtraction and fraction to percentage conversion\nSteps:\n1. Calculate total spent: $3 + $1 = $4\n2. Find money left: $12 - $4 = $8\n3. Calculate percentage: $8\/$12 = 2\/3 = 66\u2154%\n\nFinal: 66\u2154%"} {"t":"s","id":3824,"s":"Method: subtraction and fraction simplification\nSteps:\n1. Calculate total spent: $4 + $1 = $5\n2. Find money left: $15 - $5 = $10\n3. Calculate percentage: $10\/$15 = 2\/3 = 66\u2154%\n\nFinal: 66\u2154%"} {"t":"s","id":3825,"s":"Method: discount percentage formula\nSteps:\n1. Find discount amount: $80 - $60 = $20\n2. Divide discount by original price: $20 \u00f7 $80 = 0.25\n3. Convert to percentage: 0.25 \u00d7 100 = 25%\n\nFinal: 25%"} {"t":"s","id":3826,"s":"Method: discount percentage formula\nSteps:\n1. Find discount amount: $50 - $35 = $15\n2. Divide discount by original price: $15 \u00f7 $50 = 0.30\n3. Convert to percentage: 0.30 \u00d7 100 = 30%\n\nFinal: 30%"} {"t":"s","id":3828,"s":"Method: division by percentage\nSteps:\n1. Marcus scored 42 points\n2. This was 70% of the highest score\n3. Divide 42 by 0.70\n4. 42 \u00f7 0.70 = 60\n\nFinal: 60"} {"t":"s","id":3829,"s":"Method: division by percentage\nSteps:\n1. Sarah collected 36 stickers\n2. This was 60% of the highest amount\n3. Divide 36 by 0.60\n4. 36 \u00f7 0.60 = 60\n\nFinal: 60"} {"t":"s","id":3830,"s":"Method: division by percentage\nSteps:\n1. Jake ran 48 laps\n2. This was 80% of the highest number\n3. Divide 48 by 0.80\n4. 48 \u00f7 0.80 = 60\n\nFinal: 60"} {"t":"s","id":3831,"s":"Method: subtraction then percentage\nSteps:\n1. Find unused flour: 8 - 1.6 = 6.4 kg\n2. Find percentage: (6.4 \u00f7 8) \u00d7 100%\n3. Calculate: 0.8 \u00d7 100% = 80%\n\nFinal: 80%"} {"t":"s","id":3832,"s":"Method: find remainder then convert to percentage\nSteps:\n1. Calculate unused clay: 5 - 0.5 = 4.5 kg\n2. Convert to percentage: (4.5 \u00f7 5) \u00d7 100%\n3. Simplify: 0.9 \u00d7 100% = 90%\n\nFinal: 90%"} {"t":"s","id":3833,"s":"Method: calculate unused amount then find percentage\nSteps:\n1. Find unused rice: 12 - 2.4 = 9.6 kg\n2. Calculate percentage: (9.6 \u00f7 12) \u00d7 100%\n3. Solve: 0.8 \u00d7 100% = 80%\n\nFinal: 80%"} {"t":"s","id":3835,"s":"Method: percentage equation\n
Steps:\n
1. Original price + 25% increase = 60\n
2. Original price \u00d7 1.25 = 60 \n
3. Original price = 60 \u00f7 1.25 = 48\n\n
Final: $48"} {"t":"s","id":3840,"s":"Method: algebraic substitution\nSteps:\n1. Let B = original boys, G = original girls\n2. G = B + 40\n3. After increase: 1.25G - 1.15B = 70\n4. Substitute: 1.25(B + 40) - 1.15B = 70\n5. 1.25B + 50 - 1.15B = 70\n6. 0.1B = 20, so B = 80\n7. G = 120, Total = 200\n\nFinal: 200"} {"t":"s","id":3841,"s":"Method: algebraic substitution\nSteps:\n1. Let B = original boys, G = original girls\n2. G = B + 60\n3. After increase: 1.3G - 1.2B = 90\n4. Substitute: 1.3(B + 60) - 1.2B = 90\n5. 1.3B + 78 - 1.2B = 90\n6. 0.1B = 12, so B = 120\n7. G = 180, Total = 300\n\nFinal: 300"} {"t":"s","id":3842,"s":"Method: algebraic substitution\nSteps:\n1. Let B = original boys, G = original girls\n2. G = B + 30\n3. After increase: 1.4G - 1.25B = 60\n4. Substitute: 1.4(B + 30) - 1.25B = 60\n5. 1.4B + 42 - 1.25B = 60\n6. 0.15B = 18, so B = 80\n7. G = 110, Total = 200\n\nFinal: 200"} {"t":"s","id":3843,"s":"Method: algebraic substitution\nSteps:\n1. Let B = original boys, G = original girls\n2. G = B + 45\n3. After increase: 1.18G - 1.12B = 72\n4. Substitute: 1.18(B + 45) - 1.12B = 72\n5. 1.18B + 53.1 - 1.12B = 72\n6. 0.06B = 18.9, so B = 315\n7. G = 135, Total = 450\n\nFinal: 450"} {"t":"s","id":3844,"s":"Method: algebraic substitution\nSteps:\n1. Let B = original boys, G = original girls\n2. G = B + 35\n3. After increase: 1.12G - 1.08B = 50\n4. Substitute: 1.12(B + 35) - 1.08B = 50\n5. 1.12B + 39.2 - 1.08B = 50\n6. 0.04B = 10.8, so B = 270\n7. G = 105, Total = 375\n\nFinal: 375"} {"t":"q","id":10498,"q":"A sports club has tennis and badminton players in the ratio 4:5. Of the tennis players, the ratio of male to female is 3:1. Of the badminton players, this ratio is 2:3. If there are 90 players, how many are female?
Answer = ","e":null} {"t":"q","id":10499,"q":"A coffee shop sells hot and cold drinks in the ratio 5:3. Of the hot drinks, the ratio of coffee to tea is 4:1. Of the cold drinks, this ratio is 1:2. If 120 drinks were sold, how many were coffee?
Answer = ","e":null} {"t":"q","id":10500,"q":"A market sells vegetables and fruits in the ratio 3:5. Of the vegetables, the ratio of organic to non-organic is 1:2. Of the fruits, this ratio is 2:3. If 160 items were sold, how many were organic?
Answer = ","e":null} {"t":"q","id":10501,"q":"A school bus has primary and secondary students in the ratio 7:4. Of the primary students, the ratio who bring lunch to those who buy is 5:2. Of the secondary students, this ratio is 1:3. If 88 students ride the bus, how many bring lunch?
Answer = ","e":null} {"t":"q","id":10502,"q":"A pet shop has cats and dogs in the ratio 3:5. Of the cats, the ratio of kittens to adults is 2:1. Of the dogs, this ratio is 3:2. If there are 80 animals, how many are adults?
Answer = ","e":null} {"t":"q","id":10503,"q":"A hospital has doctors and nurses in the ratio 2:9. Of the doctors, the ratio of specialists to general practitioners is 5:1. Of the nurses, the ratio of registered to trainee is 7:2. If there are 132 staff, how many are trainees or general practitioners?
Answer = ","e":null} {"t":"q","id":10504,"q":"A publishing house produces novels and textbooks in the ratio 8:5. Of the novels, the ratio of paperback to hardcover is 7:1. Of the textbooks, this ratio is 2:3. If 260 books were produced, how many hardcover books were produced?
Answer = ","e":null} {"t":"q","id":10505,"q":"An airline has economy and business passengers in the ratio 11:2. Of the economy passengers, the ratio who checked baggage to those who didn't is 4:1. Of the business passengers, this ratio is 9:1. If 390 passengers flew, how many did not check baggage?
Answer = ","e":null} {"t":"q","id":10506,"q":"A supermarket sells fresh and frozen produce in the ratio 7:4. Of the fresh produce, the ratio of local to imported is 5:2. Of the frozen produce, this ratio is 1:7. If 440 items were sold, what is the ratio of all local to all imported items?
Answer = : ____","e":null} {"t":"q","id":10507,"q":"A theme park has thrill rides and family rides in the ratio 3:8. Of the thrill ride visitors, the ratio of teens to adults is 5:4. Of the family ride visitors, this ratio is 2:7. If 990 people rode the rides, how many more adults than teens rode the rides?
Answer = : ____","e":null} {"t":"q","id":10508,"q":"A furniture store sells indoor and outdoor furniture in the ratio 9:5. Of the indoor furniture, the ratio of wooden to metal is 5:4. Of the outdoor furniture, this ratio is 1:4. If 280 pieces were sold, how many wooden pieces were sold?
Answer = : ____","e":null} {"t":"q","id":10509,"q":"A gym has weightlifters and cardio enthusiasts in the ratio 4:7. Of the weightlifters, the ratio who use protein supplements to those who don't is 7:1. Of the cardio enthusiasts, this ratio is 2:5. If 176 members were surveyed, how many use protein supplements?
Answer = ","e":null} {"t":"q","id":10510,"q":"A concert hall has orchestra and balcony seats in the ratio 5:3. Of the orchestra seats, the ratio of occupied to empty is 9:1. Of the balcony seats, this ratio is 5:3. If there are 640 seats, how many are empty?
Answer = ","e":null} {"t":"q","id":10515,"q":"The figure shows a circle with a quadrant cut out. The diameter of the circle is 28 cm. Find the perimeter and area of the figure. (Take \u03c0 = 22\/7)
Perimeter : cm
Area : ____ cm2","e":null} {"t":"q","id":10547,"q":"A circular garden has a radius of 14 m. A path of width 7 m surrounds the garden. Find:\r\n(a) the area of the path\r\n(b) the cost of paving the path at $12 per square metre\r\n(Take \u03c0 = 22\/7)\r\n\r\n","e":null} {"t":"q","id":10548,"q":"A circular pizza has a diameter of 42 cm. It is cut into 6 equal slices. Find:\r\n(a) the area of the whole pizza\r\n(b) the area of each slice\r\n(c) the perimeter of each slice (including the two straight edges and the curved edge)\r\n(Take \u03c0 = 22\/7)\r\n\r\n","e":null} {"t":"q","id":10549,"q":"A circular pond has a radius of 35 m. The owner wants to build a fence around the pond. Find:\r\n(a) the circumference of the pond\r\n(b) the cost of fencing at $8.50 per metre\r\n(c) the area of the pond\r\n(Take \u03c0 = 22\/7)\r\n","e":null} {"t":"q","id":10550,"q":"A circular running track surrounds a grass field. The radius of the field is 28 m and the track is 14 m wide. Find:\n(a) the area of the track\n(b) the difference in distance between running on the inner edge and outer edge of the track\n(Take \u03c0 = 22\/7)\n <\/span>","e":null} {"t":"q","id":10551,"q":"A semicircular window has a diameter of 42 cm. Find:\r\n(a) the area of glass needed for the window\r\n(b) the length of the metal frame required for the curved edge\r\n(c) the total perimeter of the window\r\n(Take \u03c0 = 22\/7)\r\n","e":null} {"t":"q","id":10552,"q":"A circular tablecloth with radius 21 cm is placed on a square table with side 28 cm. Find:\r\n(a) the area of the tablecloth\r\n(b) the area of the table\r\n(c) the area of the tablecloth that hangs over the edge of the table\r\n(Take \u03c0 = 22\/7)\r\n","e":null} {"t":"q","id":10553,"q":"A quarter-circle corner shelf has a radius of 35 cm. Find:\r\n(a) the area of the shelf\r\n(b) the perimeter of the shelf (including the two straight edges and the curved edge)\r\n(Take \u03c0 = 22\/7)\r\n","e":null} {"t":"q","id":10554,"q":"A circular flower bed with radius 14 m is divided into 4 equal sections for different types of flowers. Find:\r\n(a) the total area of the flower bed\r\n(b) the area of each section\r\n(c) the length of fencing needed around the entire flower bed\r\n(Take \u03c0 = 22\/7)\r\n","e":null} {"t":"q","id":10555,"q":"A bicycle wheel has a diameter of 70 cm. Find:\r\n(a) the circumference of the wheel\r\n(b) the distance covered by the bicycle when the wheel makes 500 complete rotations\r\n(c) the number of rotations needed to cover a distance of 1.1 km\r\n(Take \u03c0 = 22\/7)\r\n","e":null} {"t":"q","id":10556,"q":"A circular clock face has a diameter of 42 cm. Find:\r\n(a) the area of the clock face\r\n(b) the distance travelled by the tip of the minute hand (length 18 cm) in 30 minutes\r\n(c) the distance travelled by the tip of the minute hand in 2 hours\r\n(Take \u03c0 = 22\/7)\r\n","e":null} {"t":"q","id":10557,"q":"A circular swimming pool has a diameter of 42 m. A wooden deck of width 7 m surrounds the pool. Find:\r\n(a) the area of the pool\r\n(b) the area of the deck\r\n(c) the cost of tiling the deck at $15 per square metre\r\n(Take \u03c0 = 22\/7)\r\n","e":null} {"t":"q","id":10558,"q":"Two identical circular plates, each with radius 14 cm, are placed so that they overlap. The overlapping area is 120 cm\u00b2. Find:\r\n(a) the area of one circular plate\r\n(b) the circumference of one circular plate\r\n(c) the total area covered by both plates (without counting the overlap twice)\r\n(Take \u03c0 = 22\/7)\r\n","e":null} {"t":"q","id":10559,"q":"A dartboard consists of three concentric rings. The innermost circle (bullseye) has a radius of 7 cm. The middle ring extends from 7 cm to 14 cm radius. The outer ring extends from 14 cm to 21 cm radius. Find:\r\n(a) the area of the bullseye\r\n(b) the area of the middle ring\r\n(c) the area of the outer ring\r\n(Take \u03c0 = 22\/7)\r\n","e":null} {"t":"q","id":10560,"q":"A company logo consists of a circular design with radius 21 cm. The logo has a gold outer ring that is 7 cm wide and a navy blue inner circle. Find:\r\n(a) the area of the gold ring\r\n(b) the area of the navy blue inner circle\r\n(c) the ratio of the gold area to the navy blue area\r\n(Take \u03c0 = 22\/7) ","e":null} {"t":"q","id":10561,"q":"A game character is shaped like a three-quarter circle (270\u00b0) with radius 28 cm. Find:\r\n(a) the area of the character\r\n(b) the perimeter of the character (curved edge + two straight edges)\r\n(c) what fraction of a full circle is the character?\r\n(Take \u03c0 = 22\/7) ","e":null} {"t":"q","id":10562,"q":"A circular birthday cake has a diameter of 42 cm. One slice is cut out at an angle of 60\u00b0. Find:\r\n(a) the area of the whole cake\r\n(b) the area of the slice removed\r\n(c) the area of the remaining cake\r\n(d) the perimeter of the slice (arc + two radii)\r\n(Take \u03c0 = 22\/7) ","e":null} {"t":"q","id":10563,"q":"A circular arena has a radius of 35 m. A rectangular stage measuring 28 m by 14 m is placed at the centre. Find:\r\n(a) the total area of the arena\r\n(b) the area of the stage\r\n(c) the remaining area around the stage for the audience\r\n(d) what percentage of the arena is available for the audience?\r\n\r\n","e":null} {"t":"q","id":10564,"q":"A piece of wire is bent to form a circle with radius 14 cm. The same wire is then straightened and bent to form a square. Find:\r\n(a) the length of the wire\r\n(b) the side length of the square\r\n(c) the area of the circle\r\n(d) the area of the square\r\n(e) which shape has the greater area, and by how much?\r\n\r\n","e":null} {"t":"q","id":10565,"q":"A circular park has a diameter of 84 m. Two straight paths, each running along the diameter, cross at right angles at the centre. Each path is 3 m wide. Find:\r\n(a) the area of the park\r\n(b) the total length of both paths combined\r\n(c) the total area of the paths (note: subtract the overlapping square at centre)\r\n(Take \u03c0 = 22\/7)\r\n","e":null} {"t":"q","id":10567,"q":"A semicircular tunnel has an outer diameter of 42 m. The concrete wall of the tunnel is 3.5 m thick. Find:\r\n(a) the cross-sectional area of the air space inside the tunnel\r\n(b) the cross-sectional area of the concrete wall\r\n(c) if the tunnel is 100 m long, find the volume of concrete used\r\n(Take \u03c0 = 22\/7)\r\n","e":null} {"t":"q","id":10568,"q":"A circular medal has a radius of 14 cm. An equilateral triangle with side 14 cm is cut out from the centre. Find:\r\n(a) the area of the full circle\r\n(b) the area of the equilateral triangle (use formula: Area = (\u221a3\/4) \u00d7 side\u00b2)\r\n(c) the area of the medal after the triangle is removed\r\n(Take \u03c0 = 22\/7, \u221a3 = 1.732)\r\n","e":null} {"t":"q","id":10569,"q":"Four identical circles, each with radius 7 cm, are arranged in a 2\u00d72 pattern inside a square so that they touch each other and the sides of the square. Find:\r\n(a) the side length of the square\r\n(b) the total area of the four circles\r\n(c) the area of the square\r\n(d) the area of the gaps (shaded region between circles and square)\r\n(Take \u03c0 = 22\/7)\r\n","e":null} {"t":"q","id":10570,"q":"A small coin with radius 7 cm rolls around the outside of a larger fixed coin with radius 21 cm, always staying in contact. Find:\r\n(a) the distance travelled by the centre of the small coin in one complete trip around\r\n(b) how many times does the small coin rotate about its own centre during one complete trip?\r\n(c) the total distance travelled by a point on the edge of the small coin\r\n(Take \u03c0 = 22\/7)\r\n","e":null} {"t":"q","id":10571,"q":"A circular mirror has a radius of 28 cm and is surrounded by a wooden frame that is 7 cm wide. Find:\r\n(a) the area of the mirror (glass only)\r\n(b) the area of the wooden frame\r\n(c) the total weight of the frame if wood weighs 0.5 g per cm\u00b2\r\n(d) the outer circumference of the framed mirror\r\n(Take \u03c0 = 22\/7) ","e":null} {"t":"q","id":10572,"q":"Three identical lawn sprinklers are placed in a garden. Each sprinkler waters a circular area with radius 21 m. The sprinklers are positioned so that their coverage areas overlap. Find:\r\n(a) the maximum area that one sprinkler can water\r\n(b) the combined maximum area all three sprinklers could water if there was no overlap\r\n(c) if the actual total coverage is 3234 m\u00b2 due to overlapping, find the total overlapping area\r\n(Take \u03c0 = 22\/7) ","e":null} {"t":"q","id":10573,"q":"A circular satellite dish has a diameter of 70 cm. At its centre is a circular feed horn with radius 3.5 cm. Find:\r\n(a) the area of the entire dish\r\n(b) the area of the feed horn\r\n(c) the effective receiving area (dish area minus feed horn area)\r\n(d) what percentage of the dish is blocked by the feed horn?\r\n(Take \u03c0 = 22\/7) ","e":null} {"t":"q","id":10574,"q":"A circular trampoline has a jumping surface with radius 21 cm. The safety padding around the edge is 3.5 cm wide. Find:\r\n(a) the area of the jumping surface\r\n(b) the area of the safety padding\r\n(c) the total area of the trampoline\r\n(d) the ratio of jumping area to padding area\r\n(Take \u03c0 = 22\/7) ","e":null} {"t":"q","id":10575,"q":"An archery target has 5 concentric scoring zones. The bullseye (centre) has radius 7 cm, and each subsequent ring increases the radius by 7 cm. The radii are: 7 cm, 14 cm, 21 cm, 28 cm, and 35 cm. Find:\r\n(a) the area of the bullseye (10 points)\r\n(b) the area of the red ring (8 points, between 7 cm and 14 cm radius)\r\n(c) the area of the blue ring (6 points, between 14 cm and 21 cm radius)\r\n(d) the total area of the target\r\n(e) if an arrow lands randomly, what is the probability of hitting the bullseye?\r\n(Take \u03c0 = 22\/7) ","e":null} {"t":"q","id":10576,"q":"A circular manhole cover has a diameter of 56 cm. It has a raised rim that is 3.5 cm wide around the edge. Find:\r\n(a) the total area of the manhole cover\r\n(b) the area of the inner (non-rim) section\r\n(c) the area of the rim\r\n(d) the circumference of the inner circle\r\n(Take \u03c0 = 22\/7) ","e":null} {"t":"q","id":10577,"q":"A circular helipad has a radius of 35 m. The landing zone (green inner circle) has a radius of 28 m, with a white safety border around it. Find:\r\n(a) the area of the landing zone\r\n(b) the area of the white safety border\r\n(c) the cost to paint the safety border at $2.50 per m\u00b2\r\n(d) what fraction of the helipad is the safety border?\r\n(Take \u03c0 = 22\/7) ","e":null} {"t":"q","id":10578,"q":"A circular pie chart with radius 28 cm shows a monthly budget divided into four sectors: Rent (50%), Food (25%), Transport (15%), and Savings (10%). Find:\r\n(a) the total area of the pie chart\r\n(b) the area representing Rent\r\n(c) the area representing Savings\r\n(d) the arc length of the Food sector\r\n(e) the angle (in degrees) of the Transport sector\r\n(Take \u03c0 = 22\/7) ","e":null} {"t":"q","id":10579,"q":"A circular fountain has three concentric parts: a stone border (outer), a water pool (middle), and a central fountain structure. The total radius is 28 m, the pool radius is 21 m, and the fountain structure has a radius of 7 m. Find:\r\n(a) the area of the stone border\r\n(b) the area of the water pool (not including fountain structure)\r\n(c) the volume of water if the pool is 0.5 m deep\r\n(d) the total perimeter around the outer edge\r\n(Take \u03c0 = 22\/7) ","e":null} {"t":"q","id":10580,"q":"A circular race track has an outer radius of 42 m and an inner radius of 28 m (grass infield). A rectangular pit lane measuring 7 m by 35 m is attached to the outside of the track. Find:\r\n(a) the area of the race track (excluding infield)\r\n(b) the area of the infield\r\n(c) the area of the pit lane\r\n(d) the total area of the racing facility (track + pit lane)\r\n(e) how much longer is one lap on the outer edge compared to the inner edge?\r\n(Take \u03c0 = 22\/7) ","e":null} {"t":"q","id":10581,"q":"A circular rug with radius 21 m is placed in a regular hexagonal room. The hexagon has a distance of 28 m from its centre to each vertex. Find:\r\n(a) the area of the circular rug\r\n(b) the area of the hexagonal floor (use formula: Area = (3\u221a3\/2) \u00d7 s\u00b2, where s is the side length, and side = radius for regular hexagon)\r\n(c) the area of floor visible around the rug\r\n(d) the circumference of the rug\r\n(Take \u03c0 = 22\/7, \u221a3 = 1.732) ","e":null} {"t":"q","id":10582,"q":"Five identical circular coins are stacked on top of each other. Each coin has a diameter of 28 cm and thickness of 3 mm. Find:\r\n(a) the area of one coin's face\r\n(b) the circumference of one coin\r\n(c) the total surface area of all coins visible when viewed from directly above\r\n(d) the total height of the stack in cm\r\n(Take \u03c0 = 22\/7) ","e":null} {"t":"q","id":10583,"q":"A circular amphitheater has a central stage with radius 14 m, surrounded by 3 rows of seating. Each row is 7 m wide. Find:\r\n(a) the area of the stage\r\n(b) the area of Row 1 (closest to stage)\r\n(c) the area of Row 2\r\n(d) the area of Row 3 (outermost)\r\n(e) if each person needs 2 m\u00b2 of space, how many people can sit in each row?\r\n(Take \u03c0 = 22\/7) ","e":null} {"t":"q","id":10585,"q":"A circular radar screen has a maximum detection range of 35 km (radius). The screen shows 5 concentric range rings at 7 km intervals. Find:\r\n(a) the area of the innermost zone (0-7 km)\r\n(b) the area of the zone between 14 km and 21 km\r\n(c) the total detection area\r\n(d) if an aircraft is detected at 25 km from centre, in which zone is it?\r\n(e) what percentage of the total area is within 14 km range?\r\n(Take \u03c0 = 22\/7) ","e":null} {"t":"q","id":10586,"q":"A circular solar panel array has a radius of 21 m. It contains 19 identical circular solar panels, each with radius 3.5 m. Find:\r\n(a) the area of one solar panel\r\n(b) the total area of all 19 solar panels\r\n(c) the total area of the circular platform\r\n(d) the area of the platform not covered by solar panels\r\n(e) what percentage of the platform is covered by panels?\r\n(Take \u03c0 = 22\/7) ","e":null} {"t":"q","id":10587,"q":"A circular petri dish has a diameter of 56 mm. A bacteria colony starts at the centre with radius 7 mm and doubles its radius every 24 hours. Find:\r\n(a) the initial area of the colony\r\n(b) the area of the colony after 24 hours (radius = 14 mm)\r\n(c) the area of the colony after 48 hours (radius = 28 mm)\r\n(d) after how many hours will the colony fill the entire dish?\r\n(e) the area of the dish\r\n(Take \u03c0 = 22\/7) ","e":null} {"t":"q","id":10588,"q":"A Ferris wheel has a radius of 28 m and contains 12 cabins evenly spaced around the wheel. Find:\r\n(a) the circumference of the wheel\r\n(b) the distance between adjacent cabins (arc length)\r\n(c) the distance travelled by a cabin in one complete rotation\r\n(d) if the wheel rotates once every 4 minutes, what is the speed in m\/min?\r\n(e) how far does a passenger travel in 20 minutes?\r\n(Take \u03c0 = 22\/7) ","e":null} {"t":"q","id":10590,"q":"Question 118 - Circular Vineyard with Pivot Irrigation\r\nA circular vineyard has a radius of 42 m. A central service road occupies a circle of radius 7 m, and the rest is planted with grapevines irrigated by a rotating pivot arm. Find:\r\n(a) the area of the entire field\r\n(b) the area of the central service road\r\n(c) the planted (vineyard) area\r\n(d) the distance the pivot arm travels in one complete rotation\r\n(e) if the vineyard produces 0.5 kg of grapes per m\u00b2, what is the total grape yield?\r\n(Take \u03c0 = 22\/7) ","e":null} {"t":"q","id":10591,"q":"A ring has outer radius 28 cm and inner radius 14 cm. A 60\u00b0 sector is cut and removed from the ring.\r\nFind:\r\n(a) the area of the remaining ring after the sector is removed\r\n(b) the perimeter of the remaining shape\r\n(Take \u03c0 = 22\/7) ","e":null} {"t":"q","id":10592,"q":"A small circle with radius 7 cm rolls around the outside of a fixed circle with radius 21 cm. The centre of the rolling circle traces a circular path.\r\nFind:\r\n(a) the circumference of the path traced by the centre of the rolling circle\r\n(b) the ratio of the fixed circle's circumference to the rolling circle's circumference) ","e":null} {"t":"q","id":10593,"q":"Three semicircles share a common baseline. The large semicircle has radius 21 cm. Two smaller semicircles with radii 14 cm and 7 cm sit inside it on the baseline.\r\nFind:\r\n(a) the area of the shaded region (large semicircle minus the two smaller semicircles)\r\n(b) the total length of all three semicircular arcs\r\n(Take \u03c0 = 22\/7) ","e":null} {"t":"q","id":10617,"q":"In the firgure, ABC is an isosceles triangle. Angle BAC = 56. Find angle ABC.
Answer : ","e":null} {"t":"q","id":10618,"q":"In the figure, PR and QR are equal in length. Angle PQR = 42 degrees. Find angle PRS.
Answer : degrees","e":null} {"t":"q","id":10619,"q":"Annie lives on the 8th floor. Alex lives 2 floors higher than Annie.
Alex lives on the _____ floor.","e":null} {"t":"q","id":10624,"q":"A girl saved 3 two-dollar notes and 4 fifty-cent coins.
Expressed in dollars, her savings is _____?","e":null} {"t":"q","id":10628,"q":"A group of children went swimming at the time shown below.
They finished swimming one hour later and then went for dinner.
What time did they finish swimming?","e":null} {"t":"q","id":10629,"q":"4 friends keep track of the number of books they read during their recent vacation.
_____ read 10 fewer books than Sal.","e":null} {"t":"q","id":10633,"q":"The figure below is made up of 2 different shapes.
It is made up of _____.","e":null} {"t":"q","id":10635,"q":"In the number pattern 4038, 5038, 6038, .... the digit in which place changes is?","e":null} {"t":"q","id":10638,"q":"Using all the digits: 8, 7, 2, 6, form the greatest and smallest 4-digit numbers. Then, find the difference between these two numbers.","e":null} {"t":"q","id":10640,"q":"Multiply 237 by 3. What is the answer?","e":null} {"t":"q","id":10642,"q":"Elaine exchanged a $10 note for 20 coins.
All the coins had the same value.
What was the value of each coin?","e":null} {"t":"q","id":10643,"q":"Every morning, Nicholas walks a distance of about 2 _____. from his home to the school.","e":null} {"t":"q","id":10644,"q":"Look at the 4 items below. The ___________ is the lightest.","e":null} {"t":"q","id":10645,"q":"Larry is twice as heavy as Peter. Peter is 36 kg lighter than Larry. Find the total mass of Peter and Larry.","e":null} {"t":"q","id":10649,"q":"A pizza was cut into 12 equal pieces as shown below.
Charles, Don and Fred shared the pizza. Charles took $$ \\frac{2}{3}$$ of the pizza. Fred took $$ \\frac{1}{12}$$ of the pizza. Don had the rest. Who took the smallest share?","e":null} {"t":"q","id":10650,"q":"Fill in the blanks with \u2018past\u2019 or \u2018to\u2019.
10.50 is 10 minutes _____11.","e":null} {"t":"q","id":10651,"q":"Zoe swam for 2 h 45 min. Express the time in minutes.
___________ minutes.","e":null} {"t":"q","id":10652,"q":"The time is 11.30 p.m. now. What time will it be 45 minutes from now?","e":null} {"t":"q","id":10653,"q":"Mr Lee drove his car into a car park at a shopping mall at 2.15 p.m.
He drove his car out of the car park after 2 hours 50 minutes.
What time did he drive his car out of the car park?","e":null} {"t":"q","id":10655,"q":"The figure below Iis made up of a square and a triangle. Find the number of right angles inside the figure.","e":null} {"t":"q","id":10657,"q":"Arrange the figures in order. Begin with the figure with the smallest area.","e":null} {"t":"q","id":10661,"q":"Write the number in words. 10293","e":null} {"t":"q","id":10673,"q":"Karl had 2 identical cakes. He ate $$\\frac{1}{3}$$ of a cake. What fraction of the cakes were left?","e":null} {"t":"q","id":10688,"q":"Express the answer in its simplest form where necessary.
$$\\frac{1}{5}$$ + $$\\frac{1}{4}$$ = _______","e":null} {"t":"q","id":10689,"q":"Express the answer as a mixed number in its simplest form where necessary.
1 $$\\frac{2}{3}$$ + 1 $$\\frac{2}{5}$$ = _______","e":null} {"t":"q","id":10690,"q":"Larry spent $$\\frac{2}{5}$$ of his pocket money on food. He spent $$\\frac{1}{6}$$ of his pocket money on a book.
What fraction of Larry's money was spent?","e":null} {"t":"q","id":10692,"q":"Janet read $$\\frac{3}{10}$$ of a novel on Saturday and $$\\frac{1}{10}$$ of the novel on Sunday. If she is able ro read $$\\frac{1}{5}$$ of the novel every day from Monday onwards, which day will she complete reading the novel?
She will complete the novel on ___________.","e":null} {"t":"q","id":10693,"q":"There were a total of 16 apples and pears in a basket. The number of apples was 4 more than the number of pears.
The ratio of the number of apples to the number of pears = ","e":null} {"t":"q","id":10694,"q":"Lance and his sister saved $100 altogether. Lance saved $45. Find the ratio of Lance's savings to his sister's savings.
","e":null} {"t":"q","id":10695,"q":"The usual price of am assessment book is $8. At a sale, it is sold at 25% discount. How much does Jerry have to pay for the book during the sale?","e":null} {"t":"q","id":10696,"q":"ABCD is a trapezium. Which of the following statements is correct about trapezium ABCD?
","e":null} {"t":"q","id":10699,"q":"A rectangular container measured 5 cm by 4 cm by 20 cm. It is filled with liquid detergent up to $$\\frac{9}{10}$$ of its height. Find the volume of detergent in the container.","e":null} {"t":"q","id":10700,"q":"A cubical container of edge 30 cm is filled with water to the brim. Then, some of the water is poured into a rectangular tank measuring 15 cm by 10 cm by 10 cm to fill it to its brim. What fraction of the water is left?","e":null} {"t":"q","id":10701,"q":"The pie chart below shows the different groups of families living in an apartment building. There are 300 families in the apartment.
What fraction of the families have no children?","e":null} {"t":"q","id":10703,"q":"The figure shows a quadrant inside a square.
What is the perimeter of the shaded part in terms of \u03c0?","e":null} {"t":"q","id":10712,"q":"A bar graph shows toy cars sold: Red=12, Blue=9, Green=6, Yellow=9. Which color sold the most?","e":null} {"t":"q","id":10751,"q":"A task starts at 07:30 and lasts 55 minutes. What time does it end?","e":null} {"t":"q","id":10754,"q":"A task starts at 11:15 and lasts 35 minutes. What time does it end?","e":null} {"t":"q","id":10755,"q":"A task starts at 10:15 and lasts 20 minutes. What time does it end?","e":null} {"t":"q","id":10756,"q":"A rectangle has length 11 cm and width 10 cm. What is its perimeter (cm)?","e":null} {"t":"q","id":10759,"q":"A task starts at 08:00 and lasts 20 minutes. What time does it end?","e":null} {"t":"q","id":10760,"q":"A task starts at 09:45 and lasts 20 minutes. What time does it end?","e":null} {"t":"q","id":10762,"q":"A rectangle has length 5 cm and width 6 cm. What is its perimeter (cm)?","e":null} {"t":"q","id":10763,"q":"A rectangle has length 7 cm and width 5 cm. What is its perimeter (cm)?","e":null} {"t":"q","id":10770,"q":"Two angles on a straight line are supplementary. If one angle is 60\u00b0, what is the other?","e":null} {"t":"q","id":10771,"q":"Two angles on a straight line are supplementary. If one angle is 45\u00b0, what is the other?","e":null} {"t":"q","id":10773,"q":"Two angles on a straight line are supplementary. If one angle is 50\u00b0, what is the other?","e":null} {"t":"q","id":10775,"q":"Two angles on a straight line are supplementary. If one angle is 35\u00b0, what is the other?","e":null} {"t":"q","id":10777,"q":"A graph shows counts: A=8, B=6, C=4. Which has the greatest value?","e":null} {"t":"q","id":10778,"q":"A graph shows counts: A=7, B=4, C=4. Which has the greatest value?","e":null} {"t":"q","id":10780,"q":"A graph shows counts: A=9, B=6, C=7. Which has the greatest value?","e":null} {"t":"q","id":10781,"q":"A graph shows counts: A=9, B=4, C=1. Which has the greatest value?","e":null} {"t":"q","id":10782,"q":"A toy costs $1.20 and a sticker costs $1.00. What is the total cost?","e":null} {"t":"q","id":10785,"q":"Ravi has 18 pencils. He packs 6 pencils in a bag. How many bags of pencils does Ravi have?","e":"Ravi makes equal groups of 6. 18 \u00f7 6 = 3 bags \u2192 option (3)."} {"t":"q","id":10809,"q":"Kelly has 47 stamps. She has 6 more stamps than John. How many stamps does John have?\n\nJohn has stamps.","e":"Kelly has more, so John has fewer. 47 - 6 = 41. John has 41 stamps."} {"t":"q","id":10810,"q":"Leo had 24 toys in the box. He found out that there were 12 toys missing. How many toys did he have at first?\n\nHe had toys at first.","e":"Add the missing toys back: 24 + 12 = 36. He had 36 toys at first."} {"t":"q","id":10812,"q":"Which pair of numbers make 10?","e":"6 + 4 = 10. The other pairs make 9, 8 and 7."} {"t":"q","id":10820,"q":"15 is between 16 and .","e":"The numbers around 15 are 14 and 16. Since 16 is given, the other is 14."} {"t":"q","id":10823,"q":"There are 14 goldfish and 6 tortoises in a tank. How many fewer tortoises than goldfish are there? There are fewer tortoises than goldfish.","e":"14 goldfish - 6 tortoises = 8. There are 8 fewer tortoises than goldfish."} {"t":"q","id":10833,"q":"43 = tens 3 ones. What is the missing number?","e":"43 = 4 tens 3 ones, so the missing number is 4."} {"t":"q","id":10834,"q":"Which of the following is not the same as 78?","e":"7 + 8 = 15, which is not 78. The others all equal 78."} {"t":"q","id":10835,"q":"64 + 19 = . What is the missing number?","e":"64 + 19 = 83."} {"t":"q","id":10837,"q":"Write in numbers. eighty-nine","e":"eighty-nine = 89."} {"t":"q","id":10838,"q":"Write in words. 95","e":"95 = ninety-five."} {"t":"q","id":10845,"q":"(a) 5 more than 48 is . (b) 55 is less than 64.","e":"(a) 48 + 5 = 53. (b) 64 - 55 = 9."} {"t":"q","id":10849,"q":"May Ling bought 26 red apples. David bought 38 green apples. How many apples did they buy in all? They bought apples in all.","e":"26 + 38 = 64. They bought 64 apples in all."} {"t":"q","id":10850,"q":"Mickey has 52 erasers. Ken has 23 erasers. How many more erasers does Mickey have than Ken? Mickey has erasers more than Ken.","e":"52 - 23 = 29. Mickey has 29 more erasers than Ken."} {"t":"q","id":10851,"q":"Benny has 35 ice-cream sticks. He needs 80 ice-cream sticks to build a wooden house. How many more ice-cream sticks does Benny need? Benny needs more ice-cream sticks.","e":"80 - 35 = 45. Benny needs 45 more ice-cream sticks."} {"t":"q","id":10875,"q":"There are 7 children running in the field. 3 of them are girls. How many boys are there? There are boys.","e":"7 - 3 = 4 boys."} {"t":"q","id":10876,"q":"Andrew has 5 erasers. His friend gives him 4 more erasers. How many erasers does Andrew have altogether? Andrew has erasers altogether.","e":"5 + 4 = 9 erasers."} {"t":"q","id":10877,"q":"Dora has 10 stickers. She has 2 more stickers than Beth. How many stickers does Beth have? Beth has stickers.","e":"Dora has 2 more than Beth, so Beth has 10 - 2 = 8 stickers."} {"t":"q","id":10889,"q":"Ahmad is thinking of a 2-digit number. The digit in the tens place is 3 more than 5. The digit in the ones place is 1 less than the digit in the tens place. What number is Ahmad thinking of? ","e":"Tens digit = 5 + 3 = 8; ones digit = 8 - 1 = 7. The number is 87."} {"t":"q","id":10893,"q":"Jill has 63 stickers. Mary has 29 more stickers than Jill. How many stickers does Mary have? Mary has stickers.","e":"Mary = 63 + 29 = 92 stickers."} {"t":"q","id":10894,"q":"Dan bought a bag. He gave the cashier $100. He received $25 back. How much did the bag cost? The bag cost $.","e":"Cost = $100 - $25 = $75."} {"t":"q","id":10895,"q":"Sally used $27 to buy a dress. She had $48 left. How much money did Sally have at first? Sally had $ at first.","e":"At first = amount spent + amount left = $27 + $48 = $75."} {"t":"q","id":10904,"q":"Study the number pattern. 10 , 12 , 14 , ____________ , ____________ , 20. The two missing numbers in the pattern are and .","e":"The pattern increases by 2 each time: 10, 12, 14, 16, 18, 20."} {"t":"q","id":10907,"q":"Dash reads 9 books. Rex reads 14 books. How many fewer books does Dash read than Rex? Dash reads fewer books than Rex.","e":"14 - 9 = 5, so Dash reads 5 fewer books than Rex."} {"t":"q","id":10908,"q":"Mrs Lim baked 19 tarts. 6 of them are egg tarts, 8 are cheese tarts and the rest are apple tarts. (a) How many egg and cheese tarts did Mrs Lim bake? Mrs Lim baked egg and cheese tarts. (b) How many apple tarts did Mrs Lim bake? Mrs Lim baked apple tarts.","e":"(a) 6 + 8 = 14 egg and cheese tarts. (b) 19 - 14 = 5 apple tarts."} {"t":"q","id":10916,"q":"Paul has $1. He buys a pencil for 40 cents. How much money has he left? He has _______ cents left.","e":"$1 = 100 cents. 100 - 40 = 60 cents left."} {"t":"q","id":10921,"q":"There are 10 durians in a fruit stall. (a) All the durians can be packed equally into 3 boxes. (b) All the durians can be packed equally into 5 boxes. ","e":"10 cannot be divided equally by 3 (No). 10 can be divided equally by 5, giving 2 per box (Yes)."} {"t":"q","id":10923,"q":"Kathy went to the market to buy 5 packets of fishballs. There are 8 fishballs in each packet. How many fishballs are there altogether? There are fishballs altogether.","e":"5 packets x 8 fishballs each = 5 x 8 = 40 fishballs."} {"t":"q","id":10926,"q":"Sally bakes 18 cookies. She packs them into packets. Each packet has 4 cookies. cookie(s) was\/were not packed.","e":"18 \/ 4 = 4 packets of 4 (16 cookies), leaving 18 - 16 = 2 cookies not packed."} {"t":"q","id":10934,"q":"Ravi wants to buy a tub of ice cream that costs $5.\nHe has $3.\nHow much more money does he need?\nRavi needs $ more.","e":"The ice cream costs $5 and Ravi has $3. He needs $5 \u2212 $3 = $2 more."} {"t":"q","id":10953,"q":"39 + 1 = 16 + 18 = ","e":"5a: 39 + 1 = 40. 5b: 16 + 18 = 34."} {"t":"q","id":10955,"q":"40 - 7 = 37 - 18 = ","e":"7a: 40 - 7 = 33. 7b: 37 - 18 = 19."} {"t":"q","id":10956,"q":"Farmer Brown collected 11 eggs on Monday. He collected 6 eggs on Tuesday. How many eggs did he collect on both days? He collected eggs on both days.","e":"11 + 6 = 17 eggs."} {"t":"q","id":10957,"q":"Mr Koh bought 19 apples. Mrs Chan bought 5 fewer apples than Mr Koh. How many apples did Mrs Chan buy? Mrs Chan bought apples.","e":"19 - 5 = 14 apples."} {"t":"q","id":10958,"q":"The children's Math test scores are: Peter 20, Ravi 13, Amin 8, Tom 17. (a) Who scores the highest marks? (b) How many more marks does Peter score than Ravi? (c) How many fewer marks does Amin score than Tom? ","e":"(a) 20 is highest, so Peter. (b) 20 - 13 = 7. (c) 17 - 8 = 9."} {"t":"q","id":10959,"q":"There are 3 friends: Lynn has 18 stickers, Cindy has 6 stickers, and Kyra has 4 more stickers than Lynn. (a) How many stickers does Lynn have? (b) How many more stickers does Kyra have than Cindy? (c) Which two children have 24 stickers altogether? and ","e":"(a) Lynn has 18. (b) Kyra = 18 + 4 = 22; 22 - 6 = 16 more than Cindy. (c) Lynn 18 + Cindy 6 = 24, so Lynn and Cindy."} {"t":"q","id":10966,"q":"Mrs Eng bakes 4 cakes to sell. She adds 7 flowers onto each cake. How many flowers are there on the cakes altogether?\nThere are flowers altogether.","e":"4 cakes with 7 flowers each: 4 \u00d7 7 = 28 flowers altogether."} {"t":"q","id":10986,"q":"Mr Tan sold 9 bottles of chocolate milk and 4 bottles of banana milk. How many bottles of milk did he sell altogether?\nHe sold bottles of milk altogether.","e":"9 + 4 = 13 bottles altogether."} {"t":"q","id":10987,"q":"Mrs Wang bought 15 tarts. She gave away 8 tarts to her friends. How many tarts had she left?\nShe had tarts left.","e":"15 - 8 = 7 tarts left."} {"t":"q","id":10988,"q":"Mary baked some cookies. She sold 14 cookies and had 6 cookies left. How many cookies did she bake at first?\nShe baked cookies at first.","e":"Sold + left = baked: 14 + 6 = 20 cookies."} {"t":"q","id":10999,"q":"Write 'twenty-seven' in numerals. ","e":"Twenty-seven written in numerals is 27."} {"t":"q","id":11023,"q":"9 5 - 2 = 5","e":"The full sum is 95 - 20 = 75. The missing ones digit is 0 and the answer's tens digit is 7."} {"t":"q","id":11024,"q":"David has 57 marbles. His classmate gives him 27 more marbles. How many marbles does David have now?\n\nDavid has marbles now.","e":"57 + 27 = 84. David has 84 marbles now."} {"t":"q","id":11025,"q":"Linda bakes 48 cupcakes. She bakes 12 cupcakes more than her mother. How many cupcakes does Linda's mother bake?\n\nLinda's mother bakes cupcakes.","e":"Linda bakes 12 more than her mother, so her mother bakes 48 - 12 = 36 cupcakes."} {"t":"q","id":11027,"q":"8 + = 2 x 8","e":"2 x 8 = 16, so 8 + 8 = 16. The missing number is 8."} {"t":"q","id":11028,"q":"Which of the following is NOT the same as 4 sevens?","e":"4 sevens means 4 x 7 = 28, which is the same as 7 + 7 + 7 + 7. '47' is not equal to 28, so it is the odd one out."} {"t":"q","id":11031,"q":"Miss Ng bakes 18 cupcakes for some children. Each child gets 3 cupcakes. There are children.","e":"18 cupcakes shared 3 to each child gives 18 \u00f7 3 = 6 children."} {"t":"q","id":11032,"q":"Chloe starts her Music lesson at 3.30 pm. She finishes her Music lesson at 4.30 pm. Chloe's Music lesson lasts for .","e":"From 3.30 pm to 4.30 pm is 1 hour."} {"t":"q","id":11033,"q":"Bala has 6 bunches of bananas. There are 4 bananas in each bunch. Bala has bananas altogether.","e":"6 bunches with 4 bananas each gives 6 x 4 = 24 bananas."} {"t":"q","id":11035,"q":"Aishah has 6 apples and 4 pears. She puts them equally into 2 baskets. There are fruits in each basket.","e":"6 apples + 4 pears = 10 fruits. Shared equally into 2 baskets gives 10 \u00f7 2 = 5 fruits in each basket."} {"t":"q","id":11037,"q":"Mr Cher buys 8 sticks of fishballs. There are 3 fishballs on each stick. x = ","e":"8 sticks with 3 fishballs each gives 8 x 3 = 24 fishballs altogether."} {"t":"q","id":11038,"q":"Mdm Lim prepares 18 sandwiches for a party. She puts 2 sandwiches on each plate. How many plates does Mdm Lim need? She needs plates.","e":"18 sandwiches put 2 to a plate gives 18 \u00f7 2 = 9 plates."} {"t":"q","id":11039,"q":"A tricycle has 3 wheels. There are 5 tricycles at a park. How many wheels are there altogether? x = ","e":"5 tricycles with 3 wheels each gives 5 x 3 = 15 wheels altogether."} {"t":"q","id":11040,"q":"Oscar has 12 toy cars. He shares them equally with his 3 friends. Each friend gets toy cars.","e":"Oscar shares 12 toy cars among himself and his 3 friends, that is 4 people, so 12 \u00f7 4 = 3 cars each. The answer key marks each friend getting 3 toy cars."} {"t":"q","id":11044,"q":"John buys 15 strawberries. All the strawberries are shared equally by 3 children. How many strawberries does each child get?","e":"15 strawberries shared equally among 3 children: 15 divided by 3 = 5 each."} {"t":"q","id":11048,"q":"Benny has 6 sticks. Benny uses 2 sticks to form a letter T. How many letter \"T\"s can he form if he has 6 sticks?","e":"Each letter T uses 2 sticks. 6 sticks divided by 2 = 3 letter Ts."} {"t":"q","id":11049,"q":"Which of the following box has the greatest answer?","e":"A = 2 fives = 10, B = 3 + 3 = 6, C = 3 threes = 9, D = 2+2+2+2 = 8. The greatest is A (10)."} {"t":"q","id":11052,"q":"Jane has 18 stickers. She uses 2 stickers to paste on each card. How many cards did Jane make? Jane made cards using the stickers.","e":"18 stickers used 2 per card: 18 divided by 2 = 9 cards."} {"t":"q","id":11058,"q":"There are 5 boys in a group. Each of them is given 7 sweets. How many sweets are given to the children in all? x = ","e":"5 boys with 7 sweets each: 5 x 7 = 35 sweets in all."} {"t":"q","id":11063,"q":"What number is 1 less than 15?","e":"1 less than 15 is 15 - 1 = 14. Answer key = 2 (14)."} {"t":"q","id":11065,"q":"+ 3 = 12. What is the missing number in the box?","e":"12 - 3 = 9, so the box is 9. Answer key = 3 (9)."} {"t":"q","id":11066,"q":"Fill in the missing numbers. 16, 15, 14, 13, , 11, 10, , 8","e":"The pattern counts down by 1: ...13, 12, 11, 10, 9, 8. Missing values are 12 and 9. Answer key = 12, 9."} {"t":"q","id":11067,"q":"Arrange the numbers in order. Begin with the greatest. 13, 15, 18, 14 , , , ","e":"Ordering 13, 15, 18, 14 from greatest to smallest gives 18, 15, 14, 13. Answer key = 18, 15, 14, 13."} {"t":"q","id":11069,"q":"(a) 18 - = 9. (b) Write '+' or '-': 7 4 = 11","e":"(a) 18 - 9 = 9. (b) 7 + 4 = 11, so the sign is +. Answer key = 9 and +."} {"t":"q","id":11072,"q":"Michelle has 12 hair bows. Her sister gives her 5 more hair bows. How many hair bows does Michelle have now? Michelle has hair bows now.","e":"12 + 5 = 17. Michelle has 17 hair bows now. Answer key = 12 + 5 = 17."} {"t":"q","id":11073,"q":"There are 14 leaves on a plant. The caterpillars eat up some of them. 8 leaves are left on the plant. How many leaves do the caterpillars eat? The caterpillars eat leaves.","e":"14 - 8 = 6. The caterpillars eat 6 leaves. Answer key = 14 - 8 = 6."} {"t":"q","id":11084,"q":"Study the number pattern.\n10, 9, 7, 6, 4, ____________, 1\nThe missing number is .","e":"The pattern decreases by 1 then 2 repeatedly: 10, -1=9, -2=7, -1=6, -2=4, -1=3, -2=1. The missing number is 3."} {"t":"q","id":11086,"q":"Siti has 7 hairclips. Her aunt gives her 3 more hairclips. How many hairclips does Siti have in all?\n + = \nSiti has hairclips in all.","e":"Siti starts with 7 hairclips and gets 3 more. 7 + 3 = 10, so she has 10 hairclips in all."} {"t":"q","id":11087,"q":"Mother bought 10 eggs. 4 of them broke. How many eggs were not broken?\n - = \n eggs are not broken.","e":"Mother bought 10 eggs and 4 broke. 10 - 4 = 6, so 6 eggs are not broken."} {"t":"q","id":11093,"q":"Arrange the numbers in order. Begin with the smallest.\n12, 10, 18, 8\n, , , ","e":"Ordering 12, 10, 18, 8 from smallest to largest gives 8, 10, 12, 18."} {"t":"q","id":11099,"q":"Complete the number pattern.\n17, 16, 15, , 13, , 11, 10","e":"The pattern counts down by 1 each time: 17, 16, 15, 14, 13, 12, 11, 10. The missing numbers are 14 and 12."} {"t":"q","id":11101,"q":"Sally has 13 cupcakes. Her mother gives her 7 cupcakes. How many cupcakes does Sally have altogether?\n + = \nSally has cupcakes altogether.","e":"Sally starts with 13 cupcakes and gets 7 more. 13 + 7 = 20, so she has 20 cupcakes altogether."} {"t":"q","id":11102,"q":"Sarah has 12 roses. She gives away 9 roses. How many roses has she left?\n - = \nShe has roses left.","e":"Sarah starts with 12 roses and gives away 9. 12 - 9 = 3, so she has 3 roses left."} {"t":"q","id":11103,"q":"John has 10 cookies in a bag and 9 cookies on a plate. How many cookies does he have altogether?\n + = \nHe has cookies altogether.","e":"John has 10 cookies in the bag and 9 on the plate. 10 + 9 = 19, so he has 19 cookies altogether."} {"t":"q","id":11104,"q":"Jane invites 14 friends to a party. She has 6 slices of pizza. She wants to give each friend a slice of pizza. How many more slices of pizza will she need?\n - = \nShe will need more slices of pizza.","e":"Jane needs 14 slices (one per friend) but has only 6. 14 - 6 = 8, so she needs 8 more slices."} {"t":"q","id":11108,"q":"Complete the number pattern. 17, 16, 15, , 13, 12","e":"The numbers decrease by 1 each step, so the missing number between 15 and 13 is 14."} {"t":"q","id":11110,"q":"Complete the subtraction equation. 12 - 5 = ","e":"12 - 5 = 7."} {"t":"q","id":11111,"q":"Write the missing number in the box. 3 + = 16","e":"3 plus the missing number gives 16, so the missing number is 16 - 3 = 13."} {"t":"q","id":11112,"q":"Joe has 7 white balloons. May has 4 black balloons. They have balloons altogether.","e":"7 white balloons plus 4 black balloons is 7 + 4 = 11 balloons altogether."} {"t":"q","id":11113,"q":"There are 18 burgers. The children ate 8 burgers. How many burgers are left? 18 - 8 = ","e":"18 burgers minus the 8 eaten leaves 18 - 8 = 10 burgers."} {"t":"q","id":11114,"q":"Arrange the numbers in order, beginning with the smallest number. 12, 19, 8. , , ","e":"Ordering from smallest to largest: 8, 12, 19."} {"t":"q","id":11126,"q":"Arrange the numbers in order. Begin with the biggest number.\n84, 46, 69, 65\n (biggest), , , ","e":"From biggest to smallest: 84, 69, 65, 46."} {"t":"q","id":11128,"q":"Anna and Betty are playing a Math game. The person with the bigger number as the answer is the winner. Anna's card: 47 + 4. Betty's card: 50 - 2. Who is the winner?","e":"Anna: 47 + 4 = 51. Betty: 50 - 2 = 48. 51 > 48, so Anna is the winner."} {"t":"q","id":11132,"q":"James buys 9 toy cars. Tom buys 25 toy cars. How many more toy cars does Tom buy than James?\nTom buys more toy cars than James.","e":"25 - 9 = 16, so Tom buys 16 more toy cars than James."} {"t":"q","id":11135,"q":"1 fifty-cent coin = five-cent coins","e":"50 cents \u00f7 5 cents = 10. One fifty-cent coin is worth ten five-cent coins."} {"t":"q","id":11137,"q":"Michael has 20 ice-cream sticks. He uses 5 ice-cream sticks to make a star. How many stars can he make?\nHe can make stars.","e":"20 ice-cream sticks \u00f7 5 sticks per star = 4 stars."} {"t":"q","id":11144,"q":"Mrs Tan has 8 bags. There are 4 buttons on each bag. How many buttons are there altogether?\nThere are buttons altogether.","e":"8 bags with 4 buttons each: 8 \u00d7 4 = 32 buttons altogether."} {"t":"q","id":11153,"q":"Arrange the numbers in order. Begin with the greatest. 35, 19, 90, 53 , , , ","e":"Greatest to smallest: 90, 53, 35, 19."} {"t":"q","id":11154,"q":"Complete the number bond using all the numbers given. a) 37, 43, 6: = , ","e":"The whole is the largest number 43; the parts are 37 and 6 (37 + 6 = 43)."} {"t":"q","id":11155,"q":"Complete the number bond using all the numbers given. b) 82, 25, 57: = , ","e":"The whole is the largest number 82; the parts are 25 and 57 (25 + 57 = 82)."} {"t":"q","id":11156,"q":"Write an addition equation with the given numbers only: 16, 60, 76. + = ","e":"16 + 60 = 76 (the train carriages show 16, 60 and 76)."} {"t":"q","id":11157,"q":"Add. 32 + 49 = ","e":"32 + 49: 2 + 9 = 11, write 1 carry 1; 3 + 4 + 1 = 8 tens, so 81."} {"t":"q","id":11158,"q":"Add. 18 + 82 = ","e":"18 + 82: 8 + 2 = 10, write 0 carry 1; 1 + 8 + 1 = 10 tens, so 100."} {"t":"q","id":11159,"q":"Write a subtraction equation based on the number bond: whole 43, parts 13 and 30. - = ","e":"The whole is 43; removing the part 13 leaves 30: 43 - 13 = 30."} {"t":"q","id":11160,"q":"Write a subtraction equation based on the number bond: whole 90, parts 81 and 9. - = ","e":"The whole is 90; removing the part 81 leaves 9: 90 - 81 = 9."} {"t":"q","id":11161,"q":"Subtract. 93 - 27 = ","e":"93 - 27: 3 - 7 needs regrouping, 13 - 7 = 6 ones; 8 - 2 = 6 tens, so 66."} {"t":"q","id":11162,"q":"Subtract. 50 - 46 = ","e":"50 - 46: regroup, 10 - 6 = 4 ones; 4 - 4 = 0 tens, so 4."} {"t":"q","id":11163,"q":"Complete the following number pattern. 98, 94, , 86, 82, , 74, 70, 66","e":"The pattern decreases by 4 each time. 94 - 4 = 90; 82 - 4 = 78."} {"t":"q","id":11164,"q":"Joan has 50 books. Jane has 15 books. How many books do they have altogether? They have books altogether.","e":"Altogether means add: 50 + 15 = 65 books."} {"t":"q","id":11165,"q":"At a fruit stall, there are 65 apples. There are 25 fewer watermelons than apples. How many watermelons are there? There are watermelons.","e":"Fewer means subtract: 65 - 25 = 40 watermelons."} {"t":"q","id":11166,"q":"Jill baked 40 cookies. She baked 10 muffins. How many fewer muffins than cookies did Jill bake? She baked fewer muffins than cookies.","e":"Find the difference: 40 - 10 = 30 fewer muffins."} {"t":"q","id":11167,"q":"Ms Tan has 80 books. She has 20 fewer books than Mr Wong. How many books does Mr Wong have? Mr Wong has books.","e":"Ms Tan has 20 fewer than Mr Wong, so Mr Wong has more: 80 + 20 = 100 books."} {"t":"q","id":11168,"q":"Fill in the missing numbers.\n11, , , 14, 15, , 17","e":"The numbers count up by 1: 11, 12, 13, 14, 15, 16, 17. The missing numbers are 12, 13 and 16."} {"t":"q","id":11170,"q":"Arrange the numbers in order. Start with the smallest.\n20, 9, 11, 1
(a)   (b)   (c)   (d) ","e":"Ordering smallest to largest: 1, 9, 11, 20."} {"t":"q","id":11172,"q":"Add 5 to 7. The answer is .","e":"5 + 7 = 12."} {"t":"q","id":11175,"q":"There are 5 stars in a row. Counting from the right, what is the position of the 2nd star from the right, counted from the left?
Answer: ","e":"The 2nd star from the right is the 4th star from the left in a row of 5 stars."} {"t":"q","id":11184,"q":"There are 13 fish in Tank A and Tank B altogether. There are 5 fish in Tank B. How many fish are there in Tank A?\n - = ","e":"Tank A and Tank B have 13 fish; Tank B has 5. So Tank A has 13 - 5 = 8 fish."} {"t":"q","id":11219,"q":"8 and 2 make .\n4 + = 9","e":"8 and 2 make 10. For 4 + [?] = 9, the missing number is 9 - 4 = 5."} {"t":"q","id":11220,"q":"1 more than is 4.\n is 1 less than 7.","e":"1 more than 3 is 4 (4 - 1 = 3). 1 less than 7 is 6 (7 - 1 = 6)."} {"t":"q","id":11221,"q":"Look at the number bonds and fill in the missing numbers.\n5 and 3 make .\n2 and make 6.","e":"Number bond (a): 5 + 3 = 8 (whole). Number bond (b): whole is 6, one part is 2, so the missing part is 6 - 2 = 4."} {"t":"q","id":11223,"q":"Max, Ray, Henry and Eric are standing in a line. Max is in last position. Eric is standing between Henry and Ray. Write their names in the correct order.\n1st: , , , ","e":"Max is last (4th). Eric is between Henry and Ray. With Henry given as 1st, the order is Henry, Eric, Ray, Max."} {"t":"q","id":11228,"q":"Complete the number pattern.\n(a) 21, 23, 25, 27, , 31, 33\n(b) , 39, 38, 37, 36, 35","e":"(a) The pattern increases by 2 each time, so the missing number is 29. (b) The pattern decreases by 1 each time, so before 39 comes 40."} {"t":"q","id":11229,"q":"Fill in the missing numbers.\n(a) is 3 less than 18.\n(b) 2 more than 29 is .","e":"(a) 18 - 3 = 15. (b) 29 + 2 = 31."} {"t":"q","id":11230,"q":"Which gives the number 19?","e":"12 + 5 = 17, 30 - 1 = 29, 4 + 15 = 19. The expression that gives 19 is 4 + 15."} {"t":"q","id":11232,"q":"Fill in the missing numbers.\n(a) 23 + = 32\n(b) - 20 = 10","e":"(a) 32 - 23 = 9. (b) 10 + 20 = 30."} {"t":"q","id":11234,"q":"Sharon has 4 sweets. Wei Ming has 9 sweets. How many sweets do they have altogether?\nThey have sweets altogether.","e":"4 + 9 = 13. They have 13 sweets altogether."} {"t":"q","id":11235,"q":"15 children go to the zoo. 7 of them are girls and the rest are boys. How many boys are there?\nThere are boys.","e":"15 - 7 = 8. There are 8 boys."} {"t":"q","id":11236,"q":"Glenda bakes 20 cupcakes. She gives 11 cupcakes to her friends. How many cupcakes are left?\n cupcakes are left.","e":"20 - 11 = 9. There are 9 cupcakes left."} {"t":"q","id":11237,"q":"Jim has 8 stamps. Ali has 10 more stamps than Jim. How many stamps does Ali have?\nAli has stamps.","e":"8 + 10 = 18. Ali has 18 stamps."} {"t":"q","id":11238,"q":"Linda needs 15 beads to make a bracelet. She has 9 beads now. How many more beads does she need?\nShe needs more beads.","e":"15 - 9 = 6. Linda needs 6 more beads."} {"t":"q","id":11251,"q":"John puts 16 apples equally into 8 boxes. There are apples in each box.","e":"16 apples shared equally into 8 boxes: 16 divided by 8 = 2 apples in each box."} {"t":"q","id":11252,"q":"3 girls had their heights taken. Alice is taller than Carol but shorter than Beth. Write the name of each girl, from the shortest to the tallest. , , ","e":"Alice is taller than Carol (Carol is shortest) and shorter than Beth (Beth is tallest). Order shortest to tallest: Carol, Alice, Beth."} {"t":"q","id":11255,"q":"Numbers: 82, 54, 47, 69. (a) 70 is smaller than . (b) Arrange the numbers in order. Begin with the smallest. , , , ","e":"70 is smaller than 82 (the only number above 70). Ordered smallest to greatest: 47, 54, 69, 82."} {"t":"q","id":11256,"q":"Complete the number patterns. (a) , 52, 55, 58, 61, 64. (b) 58, 48, 38, 28, , 8.","e":"(a) The pattern increases by 3 each time, so before 52 is 49. (b) The pattern decreases by 10 each time, so after 28 is 18."} {"t":"q","id":11258,"q":"Fill in the missing numbers. (a) 63 - = 50. (b) Subtract 48 from 100. The answer is .","e":"(a) 63 - 13 = 50. (b) 100 - 48 = 52."} {"t":"q","id":11259,"q":"Fill in the missing numbers. (a) 51 + 29 = . (b) is 5 more than 72.","e":"(a) 51 + 29 = 80. (b) 5 more than 72 is 72 + 5 = 77."} {"t":"q","id":11264,"q":"Sarah has 12 cookies. Ali has 6 more cookies than Sarah. How many cookies does Ali have? Ali has cookies.","e":"'6 more than' means add: 12 + 6 = 18 cookies."} {"t":"q","id":11265,"q":"Ming Li had 20 lollipops. He gave some lollipops to his brother. He had 9 lollipops left. How many lollipops did he give to his brother? Ming Li gave lollipops to his brother.","e":"20 - 9 = 11 lollipops given away."} {"t":"q","id":11266,"q":"Nan Xi made some pizzas. She gave 5 pizzas to her friend and had 11 pizzas left. How many pizzas did Nan Xi make? Nan Xi made pizzas.","e":"Pizzas made = given away + left = 5 + 11 = 16."} {"t":"q","id":11268,"q":"Sam bought a notebook. He gave the cashier a one-dollar coin and got back 20c. How much did the notebook cost? The notebook cost c.","e":"$1 = 100c. Cost = 100c - 20c (change) = 80c."} {"t":"q","id":11276,"q":"Each small packet contains 3 stickers while each big packet contains 9 stickers. 3 small packets of stickers contain the same number of stickers as 1 big packet of stickers.","e":"3 small packets = 3 \u00d7 3 = 9 stickers. 1 big packet = 9 stickers. They are equal, so the statement is True."} {"t":"q","id":11277,"q":"Each small packet contains 3 stickers while each big packet contains 9 stickers. There are more stickers in 4 small packets than 2 big packets.","e":"4 small packets = 4 \u00d7 3 = 12 stickers. 2 big packets = 2 \u00d7 9 = 18 stickers. 12 is less than 18, so the statement is False."} {"t":"q","id":11282,"q":"Mrs Tay sews 5 buttons on each blouse. She will need buttons on 7 blouses.","e":"5 buttons per blouse on 7 blouses: 7 \u00d7 5 = 35 buttons."} {"t":"q","id":11295,"q":"Circle the flag that has the same answer as 2 + 6.","e":"2 + 6 = 8. Among the flags, 5 + 3 = 8, so it has the same answer."} {"t":"q","id":11296,"q":"There are 8 erasers and pencils. 5 of them are erasers. How many pencils are there?\nThere are pencils.","e":"8 - 5 = 3, so there are 3 pencils."} {"t":"q","id":11297,"q":"Study the number pattern.\n0, 2, 3, 5, 6, ____________, 9\nThe missing number is .","e":"The pattern increases by 2, then 1, then 2, then 1...: 0 (+2) 2 (+1) 3 (+2) 5 (+1) 6 (+2) 8 (+1) 9. The missing number is 8."} {"t":"q","id":11298,"q":"Sulin has 3 rulers. Gopal has 2 rulers. How many rulers do they have altogether?\nThey have rulers altogether.","e":"3 + 2 = 5, so they have 5 rulers altogether."} {"t":"q","id":11299,"q":"John had 4 toy cars. His father bought him 2 more toy cars. How many toy cars did John have in all?\nJohn had toy cars in all.","e":"4 + 2 = 6, so John had 6 toy cars in all."} {"t":"q","id":11300,"q":"Jane had 9 bananas. She ate 5 of them. How many bananas did she have left?\nShe had bananas left.","e":"9 - 5 = 4, so she had 4 bananas left."} {"t":"q","id":11306,"q":"Arrange the numbers in order. Begin with the greatest. 12, 7, 17, 11. , , , ","e":"From greatest to smallest: 17, 12, 11, 7."} {"t":"q","id":11310,"q":"Use the numbers 7, 15 and 8 to form an addition equation. + = ","e":"7 + 8 = 15, so the addition equation is 7 + 8 = 15."} {"t":"q","id":11312,"q":"Complete the number pattern. 5, 7, 9, , 13, , 17, 19","e":"The numbers increase by 2 each time: 5, 7, 9, 11, 13, 15, 17, 19."} {"t":"q","id":11313,"q":"Choose three numbers that add up to 13. 2, 6, 3, 5. , , ","e":"2 + 6 + 5 = 13, so the three numbers are 2, 6 and 5."} {"t":"q","id":11314,"q":"Subtract the smallest number from the greatest number. 15, 19, 10. - = ","e":"The greatest number is 19 and the smallest is 10. 19 - 10 = 9."} {"t":"q","id":11315,"q":"Ellie has 16 slices of pizza. She ate 4 of them. How many slices of pizza is left? There are slices of pizza left.","e":"16 - 4 = 12, so there are 12 slices of pizza left."} {"t":"q","id":11316,"q":"Sarah has 13 sweets. Her mother gave her 3 more sweets. How many sweets does she have altogether? She has sweets altogether.","e":"13 + 3 = 16, so she has 16 sweets altogether."} {"t":"q","id":11317,"q":"Jake has 10 cupcakes in a bag and 5 cupcakes on a plate. How many cupcakes does he have altogether? He has cupcakes altogether.","e":"10 + 5 = 15, so he has 15 cupcakes altogether."} {"t":"q","id":11318,"q":"Kate had 15 roses. Fiona had 9 roses. Fiona wants to have the same number of roses as Kate. How many more roses will Fiona buy? Fiona will buy more roses.","e":"15 - 9 = 6, so Fiona will buy 6 more roses to have the same as Kate."} {"t":"q","id":11327,"q":"Sue has 6 packets of sweets. There are 5 sweets in each packet.\nWrite a multiplication equation to show the answer.\n \u00d7 = ","e":"6 packets with 5 sweets each: 6 \u00d7 5 = 30 sweets altogether."} {"t":"q","id":11334,"q":"Which one of the numbers is more than 4 but less than 7?","e":"A number more than 4 but less than 7 is 5 or 6. Among the options, 6 fits."} {"t":"q","id":11337,"q":"0 and make 2. What is the missing number?","e":"0 and a number make 2, so 0 + 2 = 2. The missing number is 2."} {"t":"q","id":11338,"q":"Which of the following has an answer less than 8?","e":"2+6=8, 6+4=10, 3+2=5, 4+5=9. Only 3+2=5 is less than 8."} {"t":"q","id":11339,"q":"Mrs Lee had 4 keys. Mrs Chan had 5 keys. How many keys did they have altogether?","e":"Altogether means add: 4 + 5 = 9 keys."} {"t":"q","id":11340,"q":"I am thinking of a number. I add 3 to the number, I get 6. What is the number?","e":"? + 3 = 6, so 6 - 3 = 3. The number is 3."} {"t":"q","id":11343,"q":"Arrange the numbers in order. Begin with the smallest number. 4, 0, 9, 6, 2 , , , , ","e":"Order the numbers from smallest to largest: 0, 2, 4, 6, 9."} {"t":"q","id":11345,"q":"There are 3 big seashells and 5 small seashells. How many seashells are there altogether? There are seashells altogether.","e":"Altogether: 3 + 5 = 8 seashells."} {"t":"q","id":11346,"q":"Sue has 4 blocks. Lisa has 6 more blocks than Sue. How many blocks does Lisa have? Lisa has blocks.","e":"Lisa has 6 more than Sue's 4: 4 + 6 = 10 blocks."} {"t":"q","id":11347,"q":"Ravi buys 8 cupcakes. Ahmad buys 1 more cupcake than Ravi. How many cupcakes does Ahmad buy? Ahmad buys cupcakes.","e":"Ahmad buys 1 more than Ravi's 8: 8 + 1 = 9 cupcakes."} {"t":"q","id":11348,"q":"There are 2 cars and 5 motorbikes in a car park. How many cars and motorbikes are there altogether? There are cars and motorbikes altogether.","e":"Altogether: 2 + 5 = 7 vehicles."} {"t":"q","id":11352,"q":"Which two numbers have a sum of 18?","e":"9 + 9 = 18. The other pairs give 11, 14 and 12."} {"t":"q","id":11356,"q":"There are 9 children singing in the hall. 4 of them are boys. How many girls are there?","e":"9 children minus 4 boys = 5 girls."} {"t":"q","id":11358,"q":"Write eleven in numeral. ","e":"Eleven written as a numeral is 11."} {"t":"q","id":11363,"q":"At a library, Devi is in the 4th position in the queue to borrow a book. There are 5 people behind her. How many people are there in the queue? ","e":"Devi being 4th means 4 people are in front of and including her, and 5 are behind. 4 + 5 = 9 people."} {"t":"q","id":11364,"q":"There are 13 carrots in Garden A. There are 5 carrots in Garden B. How many carrots are there altogether in the two gardens? + = ","e":"13 carrots + 5 carrots = 18 carrots altogether."} {"t":"q","id":11365,"q":"Lilian has 14 flowers at first. Her mother gives her another 6 flowers. How many flowers does she have altogether now? + = ","e":"14 flowers + 6 flowers = 20 flowers altogether."} {"t":"q","id":11366,"q":"All the ants were on a plate at first. Soon, 11 ants crawled away to look for food. Then, there were 4 ants left on the plate. How many ants were there on the plate at first? + = ","e":"The ants that crawled away plus the ants left equal the starting number: 11 + 4 = 15 ants."} {"t":"q","id":11367,"q":"Li Wen and Deepa have some balls. Li Wen has 7 balls. Deepa has 2 fewer balls than Li Wen. How many balls do they have altogether? ","e":"Deepa has 7 - 2 = 5 balls. Together: 7 + 5 = 12 balls."} {"t":"q","id":11370,"q":"Wei Ling had some money. After buying a wallet, he had $13 left. The wallet costs $38. How much did Wei Ling have at first?","e":"Money at first = money spent + money left = $38 + $13 = $51."} {"t":"q","id":11372,"q":"Fill in the blanks with cm or m. (a) The length of your pencil case is about 20 . (b) The height of a flag pole is about 6 .","e":"A pencil case is about 20 cm long; a flag pole is about 6 m tall. So (a) is cm and (b) is m."} {"t":"q","id":11381,"q":"A rice seller sold 100 kg of rice on the first day. He sold 21 kg more rice on the first day than on the second day. (a) How much rice did he sell on the second day? He sold of rice on the second day. (b) How much rice did he sell altogether in the two days? He sold of rice altogether in the two days.","e":"(a) Second day = 100 - 21 = 79 kg. (b) Altogether = 100 + 79 = 179 kg."} {"t":"q","id":11382,"q":"A microwave oven costs $368. A kettle costs $270 less than the microwave oven. A fan costs $159. How much more does the fan cost than the kettle? The fan costs $ more than the kettle.","e":"Kettle = $368 - $270 = $98. Fan costs $159 - $98 = $61 more than the kettle."} {"t":"q","id":11385,"q":"Which one of the following numbers is an odd number?","e":"An odd number ends in 1, 3, 5, 7 or 9. Only 217 ends in 7, so 217 is odd."} {"t":"q","id":11389,"q":"Subtract 68 from 908.
Answer: ","e":"908 - 68 = 840."} {"t":"q","id":11397,"q":"372 people visited a carnival on Friday. 29 fewer people visited the carnival on Saturday than on Friday. How many people visited the carnival on Saturday?
Answer: ","e":"Saturday = Friday - 29 = 372 - 29 = 343 people."} {"t":"q","id":11398,"q":"372 people visited a carnival on Friday. 29 fewer people visited the carnival on Saturday than on Friday. How many people visited the carnival on Friday and Saturday altogether?
Answer: ","e":"Saturday = 343 (from part a). Altogether = 372 + 343 = 715 people."} {"t":"q","id":11399,"q":"Anne has 18 pencils. She has 2 times as many pencils as Ben. How many pencils does Ben have?
Answer: ","e":"Anne has 2 times Ben's pencils, so Ben = 18 \u00f7 2 = 9 pencils."} {"t":"s","id":3973,"s":"Inner radius (garden) = 14 m
\nOuter radius (garden + path) = 14 + 7 = 21 m

\n(a) Area of the path:
\nArea of outer circle = \u03c0 \u00d7 21\u00b2 = 22\/7 \u00d7 441 = 1386 m\u00b2
\nArea of inner circle (garden) = \u03c0 \u00d7 14\u00b2 = 22\/7 \u00d7 196 = 616 m\u00b2
\nArea of path = 1386 \u2212 616 = 770 m\u00b2

\n(b) Cost of paving:
\nCost = 770 \u00d7 12 = 9240 dollars"} {"t":"s","id":3974,"s":"Diameter = 42 cm, Radius = 21 cm

\n(a) Area of whole pizza:
\nArea = \u03c0 \u00d7 21\u00b2 = 22\/7 \u00d7 441 = 1386 cm\u00b2

\n(b) Area of each slice:
\nArea of each slice = 1386 \u00f7 6 = 231 cm\u00b2

\n(c) Perimeter of each slice:
\nArc length of each slice = (1\/6) \u00d7 2 \u00d7 \u03c0 \u00d7 21 = (1\/6) \u00d7 132 = 22 cm
\nTwo straight edges (radii) = 2 \u00d7 21 = 42 cm
\nPerimeter of each slice = 22 + 42 = 64 cm"} {"t":"s","id":3975,"s":"Radius = 35 m

\n(a) Circumference of the pond:
\nCircumference = 2 \u00d7 \u03c0 \u00d7 35 = 2 \u00d7 22\/7 \u00d7 35 = 220 m

\n(b) Cost of fencing:
\nCost = 220 \u00d7 8.50<\/mn>=<\/mo><\/mrow>8.50 = <\/annotation><\/semantics><\/math><\/span><\/span>8.50<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>1870

\n(c) Area of the pond:
\nArea = \u03c0 \u00d7 35\u00b2 = 22\/7 \u00d7 1225 = 3850 m\u00b2"} {"t":"s","id":4189,"s":"6 + 4 = 10. The other pairs make 9, 8 and 7."} {"t":"s","id":4197,"s":"The numbers around 15 are 14 and 16. Since 16 is given, the other is 14."} {"t":"s","id":4200,"s":"14 goldfish - 6 tortoises = 8. There are 8 fewer tortoises than goldfish."} {"t":"s","id":4211,"s":"7 + 8 = 15, which is not 78. The others all equal 78."} {"t":"s","id":4222,"s":"(a) 48 + 5 = 53. (b) 64 - 55 = 9."} {"t":"s","id":4226,"s":"26 + 38 = 64. They bought 64 apples in all."} {"t":"s","id":4227,"s":"52 - 23 = 29. Mickey has 29 more erasers than Ken."} {"t":"s","id":4228,"s":"80 - 35 = 45. Benny needs 45 more ice-cream sticks."} {"t":"s","id":4266,"s":"Tens digit = 5 + 3 = 8; ones digit = 8 - 1 = 7. The number is 87."} {"t":"s","id":4285,"s":"(a) 6 + 8 = 14 egg and cheese tarts. (b) 19 - 14 = 5 apple tarts."} {"t":"s","id":4293,"s":"$1 = 100 cents. 100 - 40 = 60 cents left."} {"t":"s","id":4298,"s":"10 cannot be divided equally by 3 (No). 10 can be divided equally by 5, giving 2 per box (Yes)."} {"t":"s","id":4311,"s":"The ice cream costs $5 and Ravi has $3. He needs $5 \u2212 $3 = $2 more."} {"t":"s","id":4330,"s":"5a: 39 + 1 = 40. 5b: 16 + 18 = 34."} {"t":"s","id":4332,"s":"7a: 40 - 7 = 33. 7b: 37 - 18 = 19."} {"t":"s","id":4335,"s":"(a) 20 is highest, so Peter. (b) 20 - 13 = 7. (c) 17 - 8 = 9."} {"t":"s","id":4336,"s":"(a) Lynn has 18. (b) Kyra = 18 + 4 = 22; 22 - 6 = 16 more than Cindy. (c) Lynn 18 + Cindy 6 = 24, so Lynn and Cindy."} {"t":"s","id":4400,"s":"The full sum is 95 - 20 = 75. The missing ones digit is 0 and the answer's tens digit is 7."} {"t":"s","id":4401,"s":"57 + 27 = 84. David has 84 marbles now."} {"t":"s","id":4404,"s":"2 x 8 = 16, so 8 + 8 = 16. The missing number is 8."} {"t":"s","id":4405,"s":"4 sevens means 4 x 7 = 28, which is the same as 7 + 7 + 7 + 7. '47' is not equal to 28, so it is the odd one out."} {"t":"s","id":4412,"s":"6 apples + 4 pears = 10 fruits. Shared equally into 2 baskets gives 10 \u00f7 2 = 5 fruits in each basket."} {"t":"s","id":4417,"s":"Oscar shares 12 toy cars among himself and his 3 friends, that is 4 people, so 12 \u00f7 4 = 3 cars each. The answer key marks each friend getting 3 toy cars."} {"t":"s","id":4425,"s":"Each letter T uses 2 sticks. 6 sticks divided by 2 = 3 letter Ts."} {"t":"s","id":4426,"s":"A = 2 fives = 10, B = 3 + 3 = 6, C = 3 threes = 9, D = 2+2+2+2 = 8. The greatest is A (10)."} {"t":"s","id":4440,"s":"1 less than 15 is 15 - 1 = 14. Answer key = 2 (14)."} {"t":"s","id":4442,"s":"12 - 3 = 9, so the box is 9. Answer key = 3 (9)."} {"t":"s","id":4443,"s":"The pattern counts down by 1: ...13, 12, 11, 10, 9, 8. Missing values are 12 and 9. Answer key = 12, 9."} {"t":"s","id":4444,"s":"Ordering 13, 15, 18, 14 from greatest to smallest gives 18, 15, 14, 13. Answer key = 18, 15, 14, 13."} {"t":"s","id":4446,"s":"(a) 18 - 9 = 9. (b) 7 + 4 = 11, so the sign is +. Answer key = 9 and +."} {"t":"s","id":4449,"s":"12 + 5 = 17. Michelle has 17 hair bows now. Answer key = 12 + 5 = 17."} {"t":"s","id":4450,"s":"14 - 8 = 6. The caterpillars eat 6 leaves. Answer key = 14 - 8 = 6."} {"t":"s","id":4461,"s":"The pattern decreases by 1 then 2 repeatedly: 10, -1=9, -2=7, -1=6, -2=4, -1=3, -2=1. The missing number is 3."} {"t":"s","id":4463,"s":"Siti starts with 7 hairclips and gets 3 more. 7 + 3 = 10, so she has 10 hairclips in all."} {"t":"s","id":4464,"s":"Mother bought 10 eggs and 4 broke. 10 - 4 = 6, so 6 eggs are not broken."} {"t":"s","id":4476,"s":"The pattern counts down by 1 each time: 17, 16, 15, 14, 13, 12, 11, 10. The missing numbers are 14 and 12."} {"t":"s","id":4478,"s":"Sally starts with 13 cupcakes and gets 7 more. 13 + 7 = 20, so she has 20 cupcakes altogether."} {"t":"s","id":4479,"s":"Sarah starts with 12 roses and gives away 9. 12 - 9 = 3, so she has 3 roses left."} {"t":"s","id":4480,"s":"John has 10 cookies in the bag and 9 on the plate. 10 + 9 = 19, so he has 19 cookies altogether."} {"t":"s","id":4481,"s":"Jane needs 14 slices (one per friend) but has only 6. 14 - 6 = 8, so she needs 8 more slices."} {"t":"s","id":4505,"s":"Anna: 47 + 4 = 51. Betty: 50 - 2 = 48. 51 > 48, so Anna is the winner."} {"t":"s","id":4512,"s":"50 cents \u00f7 5 cents = 10. One fifty-cent coin is worth ten five-cent coins."} {"t":"s","id":4540,"s":"The pattern decreases by 4 each time. 94 - 4 = 90; 82 - 4 = 78."} {"t":"s","id":4545,"s":"The numbers count up by 1: 11, 12, 13, 14, 15, 16, 17. The missing numbers are 12, 13 and 16."} {"t":"s","id":4561,"s":"Tank A and Tank B have 13 fish; Tank B has 5. So Tank A has 13 - 5 = 8 fish."} {"t":"s","id":4596,"s":"8 and 2 make 10. For 4 + [?] = 9, the missing number is 9 - 4 = 5."} {"t":"s","id":4597,"s":"1 more than 3 is 4 (4 - 1 = 3). 1 less than 7 is 6 (7 - 1 = 6)."} {"t":"s","id":4598,"s":"Number bond (a): 5 + 3 = 8 (whole). Number bond (b): whole is 6, one part is 2, so the missing part is 6 - 2 = 4."} {"t":"s","id":4600,"s":"Max is last (4th). Eric is between Henry and Ray. With Henry given as 1st, the order is Henry, Eric, Ray, Max."} {"t":"s","id":4605,"s":"(a) The pattern increases by 2 each time, so the missing number is 29. (b) The pattern decreases by 1 each time, so before 39 comes 40."} {"t":"s","id":4606,"s":"(a) 18 - 3 = 15. (b) 29 + 2 = 31."} {"t":"s","id":4607,"s":"12 + 5 = 17, 30 - 1 = 29, 4 + 15 = 19. The expression that gives 19 is 4 + 15."} {"t":"s","id":4609,"s":"(a) 32 - 23 = 9. (b) 10 + 20 = 30."} {"t":"s","id":4611,"s":"4 + 9 = 13. They have 13 sweets altogether."} {"t":"s","id":4612,"s":"15 - 7 = 8. There are 8 boys."} {"t":"s","id":4613,"s":"20 - 11 = 9. There are 9 cupcakes left."} {"t":"s","id":4614,"s":"8 + 10 = 18. Ali has 18 stamps."} {"t":"s","id":4615,"s":"15 - 9 = 6. Linda needs 6 more beads."} {"t":"s","id":4629,"s":"Alice is taller than Carol (Carol is shortest) and shorter than Beth (Beth is tallest). Order shortest to tallest: Carol, Alice, Beth."} {"t":"s","id":4632,"s":"70 is smaller than 82 (the only number above 70). Ordered smallest to greatest: 47, 54, 69, 82."} {"t":"s","id":4633,"s":"(a) The pattern increases by 3 each time, so before 52 is 49. (b) The pattern decreases by 10 each time, so after 28 is 18."} {"t":"s","id":4635,"s":"(a) 63 - 13 = 50. (b) 100 - 48 = 52."} {"t":"s","id":4636,"s":"(a) 51 + 29 = 80. (b) 5 more than 72 is 72 + 5 = 77."} {"t":"s","id":4645,"s":"$1 = 100c. Cost = 100c - 20c (change) = 80c."} {"t":"s","id":4653,"s":"3 small packets = 3 \u00d7 3 = 9 stickers. 1 big packet = 9 stickers. They are equal, so the statement is True."} {"t":"s","id":4654,"s":"4 small packets = 4 \u00d7 3 = 12 stickers. 2 big packets = 2 \u00d7 9 = 18 stickers. 12 is less than 18, so the statement is False."} {"t":"s","id":4672,"s":"2 + 6 = 8. Among the flags, 5 + 3 = 8, so it has the same answer."} {"t":"s","id":4674,"s":"The pattern increases by 2, then 1, then 2, then 1...: 0 (+2) 2 (+1) 3 (+2) 5 (+1) 6 (+2) 8 (+1) 9. The missing number is 8."} {"t":"s","id":4691,"s":"The greatest number is 19 and the smallest is 10. 19 - 10 = 9."} {"t":"s","id":4711,"s":"A number more than 4 but less than 7 is 5 or 6. Among the options, 6 fits."} {"t":"s","id":4714,"s":"0 and a number make 2, so 0 + 2 = 2. The missing number is 2."} {"t":"s","id":4715,"s":"2+6=8, 6+4=10, 3+2=5, 4+5=9. Only 3+2=5 is less than 8."} {"t":"s","id":4717,"s":"? + 3 = 6, so 6 - 3 = 3. The number is 3."} {"t":"s","id":4729,"s":"9 + 9 = 18. The other pairs give 11, 14 and 12."} {"t":"s","id":4740,"s":"Devi being 4th means 4 people are in front of and including her, and 5 are behind. 4 + 5 = 9 people."} {"t":"s","id":4744,"s":"Deepa has 7 - 2 = 5 balls. Together: 7 + 5 = 12 balls."} {"t":"s","id":4749,"s":"A pencil case is about 20 cm long; a flag pole is about 6 m tall. So (a) is cm and (b) is m."} {"t":"s","id":4758,"s":"(a) Second day = 100 - 21 = 79 kg. (b) Altogether = 100 + 79 = 179 kg."} {"t":"s","id":4762,"s":"An odd number ends in 1, 3, 5, 7 or 9. Only 217 ends in 7, so 217 is odd."} {"t":"s","id":4775,"s":"Saturday = 343 (from part a). Altogether = 372 + 343 = 715 people."} {"t":"q","id":11400,"q":"Anne has 18 pencils. She has 2 times as many pencils as Ben. How many pencils do they have altogether?
Answer: ","e":"Ben has 9 (from part a). Altogether = 18 + 9 = 27 pencils."} {"t":"q","id":11404,"q":"\\(\\dfrac{3}{11}\\) + \\(\\dfrac{7}{11}\\) = ","e":"Like fractions: add numerators over the common denominator. 3\/11 + 7\/11 = 10\/11."} {"t":"q","id":11405,"q":"Arrange the following fractions in order. Begin with the greatest fraction.\n1\/8, 1\/3, 1\/5
(a)   (b)   (c) ","e":"With numerator 1, the smaller the denominator the larger the fraction: 1\/3 > 1\/5 > 1\/8."} {"t":"q","id":11408,"q":"There are a total of 40 pupils in a class. There are 23 boys in the class. How many more boys than girls are there in the class?
Answer: ","e":"Girls = 40 - 23 = 17. More boys than girls = 23 - 17 = 6."} {"t":"q","id":11409,"q":"Bag A has a mass of 8 kg. Bag B is twice as heavy as Bag A. What is the total mass of the two bags?
Answer: ","e":"Bag B = 2 x 8 = 16 kg. Total = 8 + 16 = 24 kg."} {"t":"q","id":11410,"q":"Jane has 398 stickers. May has 147 more stickers than Jane. How many stickers do they have altogether?
Answer: ","e":"May = 398 + 147 = 545. Altogether = 398 + 545 = 943 stickers."} {"t":"q","id":11425,"q":"a) Find the sum of 107 and 31. \nb) Subtract 100 from your answer in (a). ","e":"a) 107 + 31 = 138. b) 138 - 100 = 38."} {"t":"q","id":11427,"q":"Tim has 650 stickers in a bag. He has 100 fewer stickers than Sarah. How many stickers does Sarah have?\n stickers","e":"Tim has 100 fewer than Sarah, so Sarah has 650 + 100 = 750 stickers."} {"t":"q","id":11428,"q":"There were 425 students in the hall at first. 317 students came into the hall later. How many students were there in the hall in the end?\nThere are students in the hall in the end.","e":"425 + 317 = 742 students in the hall in the end."} {"t":"q","id":11429,"q":"Mdm Lau had 167 stickers. She gave 79 stickers to her students. How many stickers did Mdm Lau have left?\nMdm Lau has stickers now.","e":"167 - 79 = 88 stickers left."} {"t":"q","id":11430,"q":"Mike scored 545 points in a game. Sam scored 278 points in the same game. Jessica scored 126 more points than Sam.\nHow many fewer points did Sam score than Mike in the game?\nSam scored fewer points than Mike in the game.","e":"545 - 278 = 267, so Sam scored 267 fewer points than Mike."} {"t":"q","id":11436,"q":"10 \u00d7 10 is more than 9 \u00d7 10.","e":"10 \u00d7 10 = 100 and 9 \u00d7 10 = 90. 100 \u2212 90 = 10, so 10 \u00d7 10 is 10 more than 9 \u00d7 10."} {"t":"q","id":11437,"q":"Multiply 5 by 8. The answer is .","e":"5 \u00d7 8 = 40."} {"t":"q","id":11445,"q":"Siti gave 10 sweets to her 9 friends. Each friend received the same number of sweets. How many sweets did Siti give to her 9 friends altogether?
Answer: ","e":"Each of the 9 friends received 10 sweets: 10 \u00d7 9 = 90 sweets altogether."} {"t":"q","id":11446,"q":"James had 80 cupcakes. He packed all the cupcakes equally into 10 boxes. (a) How many cupcakes were there in each box? (b) James also had some muffins. He packed 4 muffins into each of the 10 boxes. How many muffins did James have?
(a)   (b) ","e":"(a) 80 cupcakes \u00f7 10 boxes = 8 cupcakes in each box. (b) 4 muffins \u00d7 10 boxes = 40 muffins altogether."} {"t":"q","id":11449,"q":"7 \u00d7 3 is more than 5 \u00d7 3.","e":"7 \u00d7 3 = 21 and 5 \u00d7 3 = 15. 21 \u2212 15 = 6."} {"t":"q","id":11450,"q":"Mrs Tan gave 36 pencils to her students. Each student received 4 pencils. How many students did she have?","e":"36 \u00f7 4 = 9 students."} {"t":"q","id":11453,"q":"Cupboard A has a mass of 254 kg. It is 118 kg lighter than Cupboard B. What is the mass of Cupboard B?
Answer: ","e":"Cupboard B is heavier: 254 + 118 = 372 kg."} {"t":"q","id":11454,"q":"Mrs Tang toasted some slices of bread for 8 of her customers. Each customer received 3 slices of toasted bread. How many slices of bread did Mrs Tang toast?
Answer: ","e":"8 customers \u00d7 3 slices each = 24 slices."} {"t":"q","id":11455,"q":"Miss Salina bought 5 packets of cookies. There were 8 cookies in each packet. All the cookies were shared equally by her 4 children. How many cookies did each child get?
Answer: ","e":"5 \u00d7 8 = 40 cookies in total. 40 \u00f7 4 = 10 cookies each."} {"t":"q","id":11456,"q":"Sara had 30 marbles. She placed all the marbles equally into boxes. She placed 3 marbles in each box. How many boxes did Sara use?
Answer: ","e":"30 \u00f7 3 = 10 boxes."} {"t":"q","id":11457,"q":"Uncle Chong sold 583 cups of coffee. He sold 223 cups of tea.\n(a) How many cups of coffee and tea did he sell altogether?\n(b) How many more cups of coffee than cups of tea did Uncle Chong sell?
(a)   (b) ","e":"(a) 583 + 223 = 806 cups altogether. (b) 583 \u2212 223 = 360 more cups of coffee than tea."} {"t":"q","id":11458,"q":"Dan bought 24 footballs. He placed them equally into 4 bags.\n(a) How many footballs were there in each bag?\n(b) Each bag of footballs has a mass of 3 kg. What is the total mass of 4 such bags of footballs?
(a)   (b) ","e":"(a) 24 \u00f7 4 = 6 footballs in each bag. (b) 4 bags \u00d7 3 kg = 12 kg total."} {"t":"q","id":11459,"q":"Mrs Mani sold 520 candies at a funfair. She sold 155 more candies than Madam Ang. How many candies did they sell in all?
Answer: ","e":"Madam Ang sold 520 \u2212 155 = 365 candies. Together: 520 + 365 = 885 candies."} {"t":"q","id":11460,"q":"Aunt Rose had some beads. She bought another 330 beads. She then gave 115 beads to her friend. She had 252 beads left. How many beads did she have at first?
Answer: ","e":"Work backwards: 252 + 115 = 367 (before giving away). 367 \u2212 330 = 37 beads at first."} {"t":"q","id":11464,"q":"Emma ate 3\/11 of a pie. Liam ate 2\/11 of the same pie. What fraction of the pie was eaten?","e":"Add the like fractions: 3\/11 + 2\/11 = 5\/11 of the pie was eaten."} {"t":"q","id":11467,"q":"1 - \\(\\dfrac{2}{6}\\) = ","e":"Write 1 as 6\/6. Then 6\/6 - 2\/6 = 4\/6."} {"t":"q","id":11470,"q":"(a) How many quarters make 1 whole? (b) How many quarters are there in 3 wholes? ","e":"(a) 1 whole is split into 4 quarters, so 4 quarters make 1 whole. (b) 3 wholes have 3 x 4 = 12 quarters."} {"t":"q","id":11472,"q":"Arrange the following fractions in order. Begin with the smallest fraction. 1\/2, 1\/7, 1\/4, 1\/10 , , , ","e":"For unit fractions, the larger the denominator the smaller the fraction. So smallest to largest: 1\/10, 1\/7, 1\/4, 1\/2."} {"t":"q","id":11473,"q":"Container A contains 28 l of water. Container B contains 12 l of water more than Container A. What is the total volume of water in Containers A and B? ","e":"Container B = 28 + 12 = 40 l. Total = 28 + 40 = 68 l."} {"t":"q","id":11475,"q":"Madam Wong used 4 l of milk for baking each time. She baked 2 times a week. How many litres of milk did she use after baking for 3 weeks? ","e":"Per week: 4 l x 2 = 8 l. Over 3 weeks: 8 l x 3 = 24 l."} {"t":"q","id":11476,"q":"Johnny had 48 l of fruit juice. He gave 32 l of fruit juice to Ken. He then shared the rest of the fruit juice equally with Mary. How many litres of fruit juice did Mary get? ","e":"Juice left after giving Ken: 48 - 32 = 16 l. Shared equally between Johnny and Mary: 16 \/ 2 = 8 l for Mary."} {"t":"q","id":11479,"q":"Write three hundred and eight in numerals.
Answer: ","e":"Three hundred and eight = 308 (no tens)."} {"t":"q","id":11481,"q":"Find 428 - 307.
Answer: ","e":"428 - 307 = 121."} {"t":"q","id":11483,"q":"Add 28 and 694.
Answer: ","e":"28 + 694 = 722."} {"t":"q","id":11484,"q":"Subtract 23 from 600.
Answer: ","e":"600 - 23 = 577."} {"t":"q","id":11486,"q":"Lisa thinks of a 3-digit odd number.\nThe digit 4 is in the hundreds place.\nThe value of the digit 1 is 10.\nThe digit in the ones place is more than 5 but less than 8.\nWhat is the number?
Answer: ","e":"Hundreds = 4, tens = 1 (value 10). Ones is 6 or 7 (more than 5, less than 8); odd means 7. Number = 417."} {"t":"q","id":11488,"q":"James has 530 stickers. William has 160 stickers.\nHow many stickers do they have altogether?
Answer: ","e":"530 + 160 = 690 stickers."} {"t":"q","id":11489,"q":"Yassin bakes 277 cookies. Kim bakes 430 cookies.\nHow many more cookies does Kim bake than Yassin?
Answer: ","e":"430 - 277 = 153 more cookies."} {"t":"q","id":11491,"q":"Write three hundred and eighty-nine in numerals. ","e":"Three hundred and eighty-nine written in numerals is 389."} {"t":"q","id":11492,"q":"200 + tens + 15 ones = 275","e":"200 + 15 ones = 215. 275 - 215 = 60 = 6 tens, so the missing number is 6."} {"t":"q","id":11493,"q":"Arrange these numbers in order. Begin with the smallest number. 255 , 172 , 249 , , ","e":"Compare hundreds first: 172 < 249 < 255. Smallest to largest: 172, 249, 255."} {"t":"q","id":11503,"q":"Darren has 135 stickers. Mary gives him another 48 stickers. How many stickers does Darren have now? Darren has stickers now.","e":"135 + 48 = 183 stickers."} {"t":"q","id":11516,"q":"There are 6 baskets. Each basket has 5 watermelons. How many watermelons are there in all? There are watermelons in all.","e":"6 baskets x 5 watermelons = 30 watermelons."} {"t":"q","id":11517,"q":"40 stamps are shared equally among 4 friends. How many stamps did each friend receive? Each of them received stamps.","e":"40 stamps shared among 4 friends: 40 \u00f7 4 = 10 each."} {"t":"q","id":11522,"q":"\u2661 + \u2661 = 80\n\u2661 + \u25b3 = 278\n\u25b3 = ","e":"Heart + Heart = 80, so Heart = 40. Heart + Triangle = 278, so Triangle = 278 \u2013 40 = 238."} {"t":"q","id":11524,"q":"12 apples were shared equally between 2 girls. How many apples did each girl get?","e":"12 \u00f7 2 = 6 apples each. Option (1), 0-based index 0."} {"t":"q","id":11525,"q":"Which is the related division equation for 8 x 2 = 16?","e":"The related division fact for 8 x 2 = 16 is 16 \u00f7 2 = 8 (total \u00f7 one factor = other factor). Option (4), 0-based index 3."} {"t":"q","id":11526,"q":"21 \u00f7 = 7","e":"21 \u00f7 3 = 7, so the missing number is 3. Option (3), 0-based index 2."} {"t":"q","id":11530,"q":"Megan used 4 buttons to sew a dress. How many buttons did she use to sew 8 dresses?
Answer: ","e":"4 buttons per dress x 8 dresses = 32 buttons."} {"t":"q","id":11531,"q":"Aunt Penny gave 27 curry puffs to some children. Each child received 3 curry puffs. How many children were there?
Answer: ","e":"27 curry puffs \u00f7 3 each = 9 children."} {"t":"q","id":11532,"q":"Sally bought 22 markers. She gave away 2 markers.\n(a) How many markers were left? \u00d7 = \n(b) After that, she packed the markers left into bags of 5. How many bags of markers did she pack? \u00f7 = ","e":"(a) 22 - 2 = 20 markers left. (b) 20 \u00f7 5 = 4 bags."} {"t":"q","id":11533,"q":"For every 3 books Peter bought, he was given 2 free erasers. He bought 15 books. How many free erasers did he receive?
Answer: ","e":"15 books \u00f7 3 books per group = 5 groups; 5 groups x 2 erasers = 10 erasers. (Answer key shows 15\u00f73=5, then 5x2=10.)"} {"t":"q","id":11535,"q":"The total length of string A and string B is 470 cm. The total length of string A and string C is 640 cm. If string B is 283 cm, find the length of string C.","e":"String A = 470 - 283 = 187 cm. String C = 640 - 187 = 453 cm."} {"t":"q","id":11540,"q":"Rachel cycled 950 m. She cycled 270 m further than Kristal. How far did Kristal cycle?
Answer: ","e":"Kristal cycled 950 - 270 = 680 m."} {"t":"q","id":11541,"q":"Mrs Lee used 5 m of cloth to make a set of curtains. She made 3 sets of curtains. How much cloth did she use altogether?
Answer: ","e":"5 m per set x 3 sets = 15 m altogether."} {"t":"q","id":11543,"q":"Which of the following numbers has the greatest digit in the tens place?","e":"Tens digits are 2, 3, 1 and 2. The greatest tens digit is 3, in 132."} {"t":"q","id":11558,"q":"628 + 236 is the same as 828 + \nWhat is the missing number in the box?","e":"628 + 236 = 864. 864 - 828 = 36, so the missing number is 36."} {"t":"q","id":11560,"q":"Jenny bought some ice-cream sticks.\nAfter giving 42 ice-cream sticks to her sister, she received 57 ice-cream sticks from her brother.\nShe had 69 ice-cream sticks in the end.\nHow many ice-cream sticks did she buy?
Answer: ","e":"Work backwards from 69: before receiving 57, she had 69 - 57 = 12; before giving 42, she had 12 + 42 = 54. So she bought 54 ice-cream sticks."} {"t":"q","id":11564,"q":"Mary bought 349 beads.\nJenny bought 167 fewer beads than Mary.\nHow many beads did the two girls buy altogether?
Answer: ","e":"Jenny bought 349 - 167 = 182 beads. Altogether: 349 + 182 = 531 beads."} {"t":"q","id":11574,"q":"Write the greatest number. 879 798 789 898 987
Answer: ","e":"Compare the hundreds first: 987 has 9 hundreds, the largest, so 987 is the greatest."} {"t":"q","id":11575,"q":"Complete the number pattern. 620 625 630 640 645","e":"The pattern increases by 5 each time, so the missing number is 630 + 5 = 635."} {"t":"q","id":11577,"q":"Arrange the numbers from the smallest to the greatest. 215 535 235 125
(a)   (b)   (c)   (d) ","e":"Compare hundreds then tens: 125 < 215 < 235 < 535."} {"t":"q","id":11578,"q":"10 more than 500 + 30 + 8 = . 100 less than 300 + 10 + 6 = .","e":"500 + 30 + 8 = 538, and 10 more is 548. 300 + 10 + 6 = 316, and 100 less is 216."} {"t":"q","id":11582,"q":"The chart shows the height of 4 girls. Ellen 134 cm, Fatimah 152 cm, Su Ling 127 cm, Kann 119 cm. Kann is shorter than the tallest girl by cm.","e":"The tallest girl is Fatimah at 152 cm. Kann is 119 cm. 152 - 119 = 33 cm."} {"t":"q","id":11583,"q":"Fill in the blanks with kg, g, m or cm. (a) The file is about 3 thick. (b) The mass of a watermelon is about 2 .","e":"(a) A file's thickness is small, so the suitable unit is cm. (b) A watermelon is heavy, so the suitable unit of mass is kg."} {"t":"q","id":11585,"q":"A bag of sweets has a mass of 8g. Doris buys 5 bags of sweets. What is the total mass of 5 bags of sweets? The mass of 5 bags of sweets is g.","e":"Each bag is 8 g and there are 5 bags: 8 x 5 = 40 g."} {"t":"q","id":11587,"q":"Stick A is 96 cm long. Stick B is 13 cm longer than Stick A. How long is Stick B? Stick B is cm long.","e":"Stick B is 13 cm longer than Stick A: 96 + 13 = 109 cm."} {"t":"q","id":11588,"q":"A box with 3 bowling balls has a mass of 17 kg. The mass of the box is 2 kg when it is empty. What is the mass of each bowling ball? The mass of each bowling ball is kg.","e":"Mass of the 3 balls = 17 - 2 = 15 kg. Each ball = 15 \u00f7 3 = 5 kg."} {"t":"q","id":11590,"q":"Write eight hundred and five in numerals. ","e":"Eight hundred and five = 800 + 5 = 805."} {"t":"q","id":11592,"q":"27 > 23 + \nThe largest possible number for the box is .","e":"23 + 3 = 26, and 27 > 26. Any larger number would make the sum 27 or more, so the largest is 3."} {"t":"q","id":11595,"q":"Fill in the boxes.\n(a) 561 + 32 = \n(b) 869 - 451 = ","e":"(a) 561 + 32 = 593. (b) 869 - 451 = 418."} {"t":"q","id":11604,"q":"There are 531 children at the zoo. 274 children are boys. How many girls are there?\nThere are girls at the zoo.","e":"531 - 274 = 257 girls."} {"t":"q","id":11605,"q":"Mark baked 104 pies on Monday. He baked 29 more pies on Monday than on Friday. How many pies did he bake on Friday?\nHe baked pies on Friday.","e":"Monday had 29 more than Friday, so Friday = 104 - 29 = 75 pies."} {"t":"q","id":11606,"q":"Leon cycled 687 m. Kate cycled 276 m more than Leon. How far did Kate cycle?\nKate cycled m.","e":"Kate cycled 276 m more than Leon: 687 + 276 = 963 m."} {"t":"q","id":11628,"q":"Mrs Lim bakes 305 g of oat cookies and chocolate cookies.\nThe mass of the chocolate cookies is 120 g.\n(a) What is the mass of oat cookies?\n(b) How much heavier are the oat cookies than the chocolate cookies?\nThe mass of the oat cookies is g.\nThe oat cookies are g heavier than the chocolate cookies.","e":"(a) 305 g - 120 g = 185 g of oat cookies. (b) 185 g - 120 g = 65 g heavier."} {"t":"q","id":11629,"q":"Mr Wong sold 307 kg of flour on Monday.\nHe sold 128 kg more flour on Monday than on Tuesday.\n(a) How much flour did Mr Wong sell on Tuesday?\n(b) How much flour did he sell on both days?\nMr Wong sold kg of flour on Tuesday.\nHe sold kg of flour on both days.","e":"(a) Tuesday = 307 - 128 = 179 kg. (b) Both days = 307 + 179 = 486 kg."} {"t":"q","id":11632,"q":"Adam has 8 bags. He puts 3 books in each bag. How many books does he have altogether?
Answer: ","e":"8 bags x 3 books = 24 books."} {"t":"q","id":11633,"q":"Sarah bought 20 erasers. She shared them equally with 4 friends. How many erasers did each friend receive?
Answer: ","e":"Sarah shares with 4 friends, so 20 erasers are split among 5 people: 20 \/ 5 = 4 each."} {"t":"q","id":11638,"q":"Bobby has a $5 note, two $1 coins and one 5\u00a2 coin. How much money does Bobby have?
Answer: ","e":"$5 + $1 + $1 + 5 cents = $7.05."} {"t":"q","id":11642,"q":"Jean gave the cashier two $50 notes. How much change did she receive?
Answer: ","e":"Two $50 notes are $100. Change = $100 - $89 = $11."} {"t":"q","id":11649,"q":"Mrs Lim bought a dress and 3 pairs of shoes. The dress cost $42. She spent a total of $66.\na) How much did the 3 pairs of shoes cost?\nb) What was the cost of each pair of shoes?
(a)   (b) ","e":"a) $66 - $42 = $24 for the 3 pairs of shoes. b) $24 \/ 3 = $8 per pair."} {"t":"q","id":11650,"q":"A stool costs $22 and a table costs $49. Mei Li needs $7 more to pay for both items.\na) What is the total cost of the stool and table?\nb) How much money does she have?
(a)   (b) ","e":"a) $49 + $22 = $71 total. b) She needs $7 more, so she has $71 - $7 = $64."} {"t":"q","id":11651,"q":"There was 40 l of milk in a container. Lisa filled 8 jars with 4 l of milk each.\na) What is the volume of milk in the 8 jars?\nb) How much milk was left in the container?
(a)   (b) ","e":"a) 8 jars x 4 l = 32 l. b) 40 l - 32 l = 8 l left."} {"t":"q","id":11652,"q":"There are 156 pencils in Box A. There are 78 more pencils in Box B than Box A.\na) How many pencils are there in Box B?\nb) Find the total number of pencils in Box A and Box B.
(a)   (b) ","e":"a) 156 + 78 = 234 pencils in Box B. b) 234 + 156 = 390 pencils total."} {"t":"q","id":11653,"q":"Jar A and Jar B have a total of 641 biscuits. Jar A has 375 biscuits.\na) How many biscuits are there in Jar B?\nb) How many more biscuits are there in Jar A than in Jar B?
(a)   (b) ","e":"a) 641 - 375 = 266 biscuits in Jar B. b) 375 - 266 = 109 more in Jar A."} {"t":"q","id":11654,"q":"How many fives are there in 2 groups of 10?","e":"2 groups of 10 = 20. 20 \u00f7 5 = 4. There are 4 fives."} {"t":"q","id":11655,"q":"6 \u00d7 4 is the same as \u00d7 3.","e":"6 \u00d7 4 = 24. 24 = 8 \u00d7 3, so the missing number is 8."} {"t":"q","id":11657,"q":"What is the missing sign in the box?\n7 \u00d7 5 = 5 \u00d7 5 2 \u00d7 5","e":"7 \u00d7 5 = 35. 5 \u00d7 5 = 25 and 2 \u00d7 5 = 10. 25 + 10 = 35, so the sign is +."} {"t":"q","id":11659,"q":"Mr Mok wants to divide 18 pupils equally into smaller groups. Which of the following groupings is not possible?","e":"2\u00d79=18, 3\u00d76=18, 6\u00d73=18 all work. 8\u00d72=16 \u2260 18, so 8 groups of 2 is not possible."} {"t":"q","id":11665,"q":"Leo had 17 tennis balls and Ziyang had 11 tennis balls. They put all their tennis balls equally into 4 boxes. How many tennis balls were there in each box?
Answer: ","e":"17 + 11 = 28 balls. 28 \u00f7 4 = 7 balls in each box."} {"t":"q","id":11666,"q":"I am a 2-digit number. I am greater than 25 but smaller than 30. I can be found in the multiplication table of 3. What number am I?
Answer: ","e":"Multiples of 3 between 25 and 30: 27 (= 3 \u00d7 9). So the number is 27."} {"t":"q","id":11668,"q":"Study the table.\n\nNames of Boys | Height (cm)\nEthan | 132\nHamid | 107\nJiaming | 119\nKrishnan | 125\n\nFind the difference in height between the tallest boy and the shortest boy.\n cm","e":"Tallest = Ethan 132 cm, shortest = Hamid 107 cm. 132 \u2212 107 = 25 cm."} {"t":"q","id":11670,"q":"Leah has a ribbon that is 200 cm long. She uses 65 cm to tie a present and 32 cm to tie a box. What is the length of ribbon left?
Answer: ","e":"200 \u2212 65 \u2212 32 = 103 cm of ribbon left."} {"t":"q","id":11671,"q":"Ariana shared 27 lollipops with her 2 sisters. How many lollipops did each child get?
Answer: ","e":"Ariana plus 2 sisters = 3 children. 27 \u00f7 3 = 9 lollipops each."} {"t":"q","id":11672,"q":"Mdm Nijah bought 3 bags of apples. There were 10 apples in each bag.\n(a) How many apples did she buy?\nMdm Nijah put all the apples equally on 5 plates.\n(b) How many apples were there on each plate?
(a)   (b) ","e":"(a) 3 \u00d7 10 = 30 apples. (b) 30 \u00f7 5 = 6 apples on each plate."} {"t":"q","id":11684,"q":"Write the amount in dollars or cents. (a) $3 = \u00a2 (b) 5\u00a2 = $","e":"$1 = 100\u00a2, so $3 = 300\u00a2. 5\u00a2 = $0.05."} {"t":"q","id":11685,"q":"Arrange the fractions in order. Begin with the greatest. 1\/7 , 3\/7 , 1\/11 , , ","e":"3\/7 is the largest (same denom, bigger numerator). Between 1\/7 and 1\/11, same numerator means smaller denominator is larger, so 1\/7 > 1\/11. Order: 3\/7, 1\/7, 1\/11."} {"t":"q","id":11686,"q":"(a) 1\/5 + 3\/5 = (b) 1 - 3\/10 = ","e":"(a) 1\/5 + 3\/5 = 4\/5. (b) 1 = 10\/10, so 10\/10 - 3\/10 = 7\/10."} {"t":"q","id":11690,"q":"Brandon had 123 marbles. After he gave away 86 marbles, he had the same number of marbles as David. How many marbles did they have altogether in the end? Answer: ","e":"Brandon left with 123 - 86 = 37 marbles. David also has 37. Altogether = 37 + 37 = 74."} {"t":"q","id":11691,"q":"Ziyang bought 7 handkerchiefs. The cost of each handkerchief was the same. He paid the cashier $50 and received a change of $29. (a) How much did the 7 handkerchiefs cost? Answer: (b) How much did each handkerchief cost? Answer: ","e":"(a) Cost = $50 - $29 = $21. (b) Each = $21 \/ 7 = $3."} {"t":"q","id":11695,"q":"20 \u00f7 5 = \u00d7 2","e":"20 \u00f7 5 = 4. The missing number times 2 must equal 4, so the missing number is 4 \u00f7 2 = 2."} {"t":"q","id":11702,"q":"Write the smallest possible 3-digit even number with the following digits.\n5 2 3\n\nAnswer: ","e":"For an even number the last digit must be 2. To be smallest, put the smaller remaining digit first: 3, then 5, then 2 -> 352."} {"t":"q","id":11714,"q":"Write $3.05 in cents. ","e":"$3.05 = $3 + 5c = 300c + 5c = 305c."} {"t":"q","id":11715,"q":"There were 453 boys and 186 girls who went to the zoo. How many children went to the zoo altogether? ","e":"453 + 186 = 639 children."} {"t":"q","id":11716,"q":"Joe had 217 marbles. Sam had 96 fewer marbles than Joe. How many marbles did Sam have? ","e":"217 - 96 = 121 marbles."} {"t":"q","id":11717,"q":"Carol pasted 27 stickers on 3 pieces of paper. She pasted the same number of stickers on each piece of paper. How many stickers were there on each piece of paper? ","e":"27 stickers shared equally on 3 pieces: 27 \/ 3 = 9 stickers each."} {"t":"q","id":11719,"q":"Tom had 500 cards. He had 128 more cards than Jerry. (a) How many cards did Jerry have? Jerry had cards. (b) How many cards did they have altogether? They had cards altogether.","e":"(a) Jerry: 500 - 128 = 372 cards. (b) Altogether: 372 + 500 = 872 cards."} {"t":"q","id":11727,"q":"\\(\\dfrac{4}{11}\\) + \\(\\dfrac{5}{11}\\) = ","e":"Add the numerators of like fractions: 4 + 5 = 9, keep the denominator 11. So 9\/11."} {"t":"q","id":11730,"q":"\\(\\dfrac{3}{8}\\) and ? make a whole.","e":"A whole is 8\/8. 8\/8 - 3\/8 = 5\/8, so 3\/8 and 5\/8 make a whole."} {"t":"q","id":11738,"q":"The table shows the lengths of 4 strings. String A: 100 cm. String B: 80 cm. String C: 5 cm. String D: 120 cm. Arrange the lengths of the strings from the shortest to the longest. Which one of the following shows the correct order?","e":"Shortest to longest: C (5 cm), B (80 cm), A (100 cm), D (120 cm) \u2192 C, B, A, D."} {"t":"q","id":11739,"q":"Mrs Tan gave 40 candies equally to 4 children. How many candies did each child get?","e":"40 \u00f7 4 = 10, so each child got 10 candies."} {"t":"q","id":11740,"q":"Hazel had 8 friends. She gave 3 tarts to each friend. How many tarts did she give to her friends in all?","e":"8 friends \u00d7 3 tarts = 24 tarts."} {"t":"q","id":11742,"q":"Ali has a ribbon shorter than 30 cm but longer than 24 cm. He can cut it into 3 equal pieces. How long is Ali's ribbon when he cuts it 5 cm shorter?","e":"The ribbon is between 24 cm and 30 cm and is divisible by 3, so it is 27 cm. Cutting it 5 cm shorter: 27 - 5 = 22 cm."} {"t":"q","id":11747,"q":"Hui Min bought 5 packets of cookies. There were 3 cookies in each packet. a) How many cookies did Hui Min buy? She bought cookies. b) Hui Min then bought another 2 such packets of cookies the next day. How many cookies did Hui Min buy the next day? She bought cookies the next day.","e":"a) 5 packets \u00d7 3 cookies = 15 cookies. b) 2 packets \u00d7 3 cookies = 6 cookies."} {"t":"q","id":11748,"q":"There were 28 pupils in Primary 2Q. Miss Lim put all the pupils into 4 equal groups. a) How many pupils were there in each group? There were pupils in each group. b) There were 30 pupils in Primary 2W. In each group, there were 3 pupils. How many groups of 3 pupils were there? There were groups of 3 pupils.","e":"a) 28 \u00f7 4 = 7 pupils in each group. b) 30 \u00f7 3 = 10 groups."} {"t":"q","id":11749,"q":"Mary needs 35 cm of string to tie a box. a) She wants to tie 2 such boxes. What is the total length of string she needs? The total length of string she needs is cm. b) Mary has 20 cm of string. She does not have enough string to tie a box. How many more centimetres of string does she need? She needs cm more string.","e":"a) 35 cm \u00d7 2 = 70 cm. b) 35 cm - 20 cm = 15 cm more needed."} {"t":"q","id":11760,"q":"Study the number pattern. What is the missing number? 724, 726, 728, , 732, 734, 736","e":"The numbers increase by 2 each time, so the missing number is 728 + 2 = 730."} {"t":"q","id":11767,"q":"Mrs Chan used three 2-litre bottles to fill the fish tank until it was full. How much water could the fish tank hold? \u2113","e":"3 bottles x 2 litres = 6 litres."} {"t":"q","id":11769,"q":"What is the difference between the greatest and the smallest number? 991, 909, 199, 919
Answer: ","e":"Greatest is 991, smallest is 199. 991 - 199 = 792."} {"t":"q","id":11770,"q":"I am a 3-digit number between 300 and 400. The digit in the tens place is 2. The digit in the ones place is three times the digit in the tens place. What number am I?
Answer: ","e":"Between 300 and 400 means hundreds digit 3. Tens digit is 2. Ones digit is 3 x 2 = 6. So the number is 326."} {"t":"q","id":11771,"q":"Benny and his 3 friends ate 7 cookies each. How many cookies did they eat altogether?
Answer: ","e":"Benny plus 3 friends = 4 people. 4 x 7 = 28 cookies."} {"t":"q","id":11772,"q":"A pen cost $2. Rena paid $18 for a few similar pens. How many pens did she buy?
Answer: ","e":"$18 \u00f7 $2 = 9 pens."} {"t":"q","id":11773,"q":"Mary has 5 vases and 12 flowers. She wants to put 3 flowers in each vase. How many more flowers does she need?
Answer: ","e":"5 vases x 3 flowers = 15 flowers needed. She has 12, so she needs 15 - 12 = 3 more."} {"t":"q","id":11775,"q":"Arrange the following fractions from the smallest to the greatest. 1\/7, 1\/2, 1\/10
(a)   (b)   (c) ","e":"For unit fractions, the larger the denominator the smaller the fraction. So 1\/10 < 1\/7 < 1\/2."} {"t":"q","id":11776,"q":"There were 1000 people at a concert. 349 of them were children and the rest were adults. (a) How many adults were at the concert? (b) How many more adults than children were at the concert?
(a)   (b) ","e":"(a) 1000 - 349 = 651 adults. (b) 651 - 349 = 302 more adults than children."} {"t":"q","id":11777,"q":"A book has 90 pages. Jean reads 10 pages each day. (a) How many days will Jean take to finish reading the book? (b) Jean starts reading the book on Monday. How many pages of the book would she have read by the end of Friday?
(a)   (b) ","e":"(a) 90 \u00f7 10 = 9 days. (b) Monday to Friday is 5 days; 5 x 10 = 50 pages."} {"t":"q","id":11778,"q":"Jeremy had 800 marbles. He put 256 marbles in Box A and 178 marbles in Box B. (a) How many marbles did he put in the two boxes? (b) Jeremy then gave away the rest of the marbles to Martin. How many marbles did he give to Martin?
(a)   (b) ","e":"(a) 256 + 178 = 434 marbles in the two boxes. (b) 800 - 434 = 366 marbles given to Martin."} {"t":"q","id":11779,"q":"The mass of Parcel A is 450 g. It is 285 g heavier than Parcel B. (a) What is the mass of Parcel B? (b) What is the total mass of Parcel A and Parcel B?
(a)   (b) ","e":"(a) 450 - 285 = 165 g for Parcel B. (b) 450 + 165 = 615 g total."} {"t":"q","id":11780,"q":"The mass of an apple is .","e":"An apple is small and light, so a sensible everyday mass for one apple is about 100g. 10g is far too light, and the kilogram options are far too heavy."} {"t":"q","id":11782,"q":"Bob bought 350g of butter. His sister used 250g of the butter. How much butter did he have left? He had g of butter left.","e":"350g - 250g = 100g. He had 100g of butter left."} {"t":"q","id":11783,"q":"Miss Liu has 900g of clay. She gave 250g to James and some to Meiling. She is left with 475g of clay. How much clay was given to Meiling? She gave Meiling g of clay.","e":"After giving James 250g: 900 - 250 = 650g. She is left with 475g, so Meiling got 650 - 475 = 175g of clay."} {"t":"q","id":11784,"q":"Alice bought 5 similar packets of rice. The mass of each packet is 5kg. What is the total mass of rice that she bought? She bought kg of rice.","e":"5 packets each of 5kg: 5 x 5 = 25kg of rice in total."} {"t":"q","id":11785,"q":"Mrs Lim has 18kg of meat. She packs them equally into 6 bags. What is the mass of each bag? Each bag has a mass of kg.","e":"Share 18kg equally into 6 bags: 18 \/ 6 = 3kg per bag."} {"t":"q","id":11795,"q":"There are some flamingos. Each flamingo has 2 legs. There are 18 legs in all. How many flamingos are there?","e":"18 \u00f7 2 = 9 flamingos."} {"t":"q","id":11804,"q":"There is a total of 40 chairs in a hall. Uncle Lim puts 10 chairs in each row. How many rows of chairs will there be? There will be rows of chairs.","e":"40 \u00f7 10 = 4 rows."} {"t":"q","id":11805,"q":"Jason had 90 pears. He packed them equally into 10 bags. How many pears were there in each bag? \u00f7 = ","e":"90 \u00f7 10 = 9 pears in each bag."} {"t":"q","id":11806,"q":"Lina has 20 pencils. She puts 5 pencils in a box. How many boxes of pencils does she have? \u00f7 = ","e":"20 \u00f7 5 = 4 boxes."} {"t":"q","id":11812,"q":"4\/7 and ______ make 1 whole.","e":"7\/7 is one whole. 7\/7 - 4\/7 = 3\/7, so 4\/7 and 3\/7 make 1 whole."} {"t":"q","id":11813,"q":"Which fraction is greater than 1\/4?","e":"For unit fractions, the smaller the denominator the larger the fraction. 1\/3 has a smaller denominator than 1\/4, so 1\/3 > 1\/4. The others all have larger denominators and are smaller than 1\/4."} {"t":"q","id":11820,"q":"Arrange the fractions from the greatest to the smallest. 1\/8 , 1\/12 , 1\/3 (greatest) , , ","e":"For unit fractions, the smaller the denominator the greater the fraction. So from greatest to smallest: 1\/3, 1\/8, 1\/12."} {"t":"q","id":11822,"q":"Arrange the fractions from the smallest to the greatest. 5\/9 , 8\/9 , 2\/9 (smallest) , , ","e":"With the same denominator, the smaller the numerator the smaller the fraction. So from smallest to greatest: 2\/9, 5\/9, 8\/9."} {"t":"q","id":11828,"q":"Jerry's family drinks 15 l of milk in 5 days. They drink the same amount of milk each day. How much milk does Jerry's family drink in a day? Jerry's family drinks l of milk in a day.","e":"15 l shared equally over 5 days: 15 \/ 5 = 3 l per day."} {"t":"q","id":11829,"q":"There were 70 l of water in a fish tank at first. 15 l of water were poured out from the tank. Then, 30 l of water were added to the tank. What is the volume of water in the tank in the end? The volume of water in the tank in the end is l.","e":"70 - 15 = 55 l left after pouring out. Then 55 + 30 = 85 l after adding water, so the final volume is 85 l."} {"t":"q","id":11834,"q":"Which odd number is greater than 300?","e":"601 is odd (ends in 1) and greater than 300. 312 is even, 297 and 133 are less than 300."} {"t":"q","id":11838,"q":"I am thinking of a 3-digit number. It is smaller than 200. The digit zero is in the tens place. What is the greatest 3-digit number that I am thinking of?\nThe greatest 3-digit number that I am thinking of is .","e":"Smaller than 200 means hundreds digit is 1; tens digit is 0; greatest ones digit is 9, giving 109."} {"t":"q","id":11840,"q":"Arrange these numbers in order. Begin with the smallest.\n765 567 657 675\n , , , ","e":"Ordered smallest to largest: 567, 657, 675, 765."} {"t":"q","id":11845,"q":"James had some stickers at first. After giving away 233 stickers to Eve, he had 691 stickers left. How many stickers did James have at first?\nJames has stickers at first.","e":"James started with 691 + 233 = 924 stickers."} {"t":"q","id":11846,"q":"There are 685 pupils in the school last year. 127 pupils joined the school this year. How many pupils are there in the school now?\nThere are pupils in the school now.","e":"685 + 127 = 812 pupils."} {"t":"q","id":11847,"q":"Lisa has 540 stamps. She has 300 more erasers than stamps. How many erasers does Lisa have?\nLisa has erasers.","e":"Erasers = 540 + 300 = 840."} {"t":"q","id":11848,"q":"A shopkeeper sold 428 kg of rice on Tuesday morning. He sold 39 kg of rice on Tuesday afternoon.\n(a) How many more kilograms of rice did he sell in the morning than in the afternoon?\nHe sold kg more rice in the morning than in the afternoon.\n(b) How many kilograms of rice did he sell on Tuesday altogether?\nHe sold kg of rice on Tuesday altogether.","e":"(a) 428 - 39 = 389 kg more. (b) 428 + 39 = 467 kg altogether."} {"t":"q","id":11850,"q":"Mr Wong packs 10 cookies into bags of 5. How many bags of cookies are there?","e":"10 cookies divided into bags of 5: 10 \u00f7 5 = 2 bags."} {"t":"q","id":11851,"q":"Share 16 stickers equally among 2 friends. Which of the following equations shows the number of stickers each friend receives?","e":"Sharing equally means division: 16 \u00f7 2 = 8 stickers each."} {"t":"q","id":11855,"q":"Multiply 2 by 7. The answer is .","e":"2 \u00d7 7 = 14."} {"t":"q","id":11857,"q":"Mrs Ang bought some doughnuts and 5 boxes. 1 box can hold 6 doughnuts. How many doughnuts did Mrs Ang buy to fill up all the 5 boxes completely? Mrs Ang bought doughnuts.","e":"5 boxes \u00d7 6 doughnuts each = 30 doughnuts."} {"t":"q","id":11860,"q":"Complete the equations. \u00d7 10 = 50 \u00f7 5 = 10","e":"5 \u00d7 10 = 50 and 50 \u00f7 5 = 10."} {"t":"q","id":11861,"q":"Ben shared 12 toy cars equally with Sam. How many toy cars did each of them have? Each of them had toy cars.","e":"12 cars shared between 2 people: 12 \u00f7 2 = 6 each."} {"t":"q","id":11863,"q":"A cat ate 18 fish in 6 days. It ate the same number of fish each day. How many fish did the cat eat in one day? The cat ate fish in one day.","e":"18 fish over 6 days equally: 18 \u00f7 6 = 3 fish per day."} {"t":"q","id":11864,"q":"There are 9 apples in each basket. There are 2 baskets. How many apples are there altogether? There are apples altogether.","e":"2 baskets of 9 apples: 2 \u00d7 9 = 18."} {"t":"q","id":11865,"q":"A pole is 2 m long. What is the total length of 10 such poles? The total length of 10 such poles is m.","e":"10 poles each 2 m: 10 \u00d7 2 = 20 m."} {"t":"q","id":11869,"q":"5 x 4 is _________ more than 2 x 4.","e":"5 \u00d7 4 = 20 and 2 \u00d7 4 = 8. 20 \u2212 8 = 12."} {"t":"q","id":11870,"q":"Sam receives a sticker for every 4 questions that he answers correctly. He received 8 stickers, how many questions did he answer correctly?","e":"8 stickers \u00d7 4 questions each = 32 questions."} {"t":"q","id":11873,"q":"Cupboard A has a mass of 254 kg. It is 118 kg lighter than Cupboard B. What is the mass of Cupboard B?
Answer: ","e":"A is 118 kg lighter than B, so B = 254 + 118 = 372 kg."} {"t":"q","id":11874,"q":"Emma wanted to buy a storybook that costs $18. She saved $3 a day starting from Monday. On which day will she be able to buy the book?","e":"She needs $18 at $3\/day = 6 days. Day 1 Mon, day 6 Saturday. So Saturday."} {"t":"q","id":11875,"q":"Molly bought 20 marbles. She kept 12 marbles for herself and packed the rest equally into 4 bags. True or false: Molly packed 8 marbles.","e":"Rest = 20 \u2212 12 = 8 marbles packed. The statement says she packed 8 marbles, which is True."} {"t":"q","id":11877,"q":"There are 320 students in Primary Two. 146 of them are boys and the rest are girls. How many girls are there in Primary Two?
Answer: ","e":"Girls = 320 \u2212 146 = 174."} {"t":"q","id":11879,"q":"Mrs Wong sold 430 cupcakes at a food fair. She sold 145 more cupcakes than Mdm Lee. How many cupcakes did they sell in all?
Answer: ","e":"Mdm Lee = 430 \u2212 145 = 285. Total = 430 + 285 = 715."} {"t":"q","id":11880,"q":"Danny had some candies. His mother bought him another 150 candies. He gave 60 candies to his friend. He had 310 candies left. How many candies did he have at first?
Answer: ","e":"Work backwards: 310 + 60 = 370; 370 \u2212 150 = 220."} {"t":"q","id":11881,"q":"Ravi bought some stickers and 4 cards. He had 8 stickers left after pasting 9 stickers on each of the 4 cards. How many stickers did he buy at first?
Answer: ","e":"Pasted = 9 \u00d7 4 = 36 stickers. Bought at first = 36 + 8 = 44."} {"t":"q","id":11882,"q":"Jill had 8 boxes of toys. There were 3 toys in each box. Jill gave all the toys to 6 of her friends. Each friend received the same number of toys. How many toys did each of her friend receive?
Answer: ","e":"Total toys = 8 \u00d7 3 = 24. Shared among 6 friends: 24 \u00f7 6 = 4 each."} {"t":"q","id":11887,"q":"A cake was cut into 12 equal slices. Jane ate 4 slices and her brother ate 3 slices. What fraction of the cake was left?","e":"4 + 3 = 7 slices eaten. 12 - 7 = 5 slices left, so 5\/12."} {"t":"q","id":11889,"q":"\\(\\dfrac{2}{7}\\) + ? = 1","e":"1 = 7\/7. 7\/7 - 2\/7 = 5\/7."} {"t":"q","id":11890,"q":"Arrange the fractions in order, beginning with the largest. 5\/9, 1\/9, 4\/9 , , ","e":"Same denominator, so order by numerator largest first: 5\/9, 4\/9, 1\/9."} {"t":"q","id":11895,"q":"Arrange the following fractions in order. Begin with the smallest fraction. 1\/5, 1\/7, 1\/3, 1\/9 , , , ","e":"Same numerator: larger denominator = smaller fraction. Smallest first: 1\/9, 1\/7, 1\/5, 1\/3."} {"t":"q","id":11897,"q":"Tom's mother bought a pizza for dinner. She gave half the pizza to their neighbour. Then she and Tom ate \\(\\dfrac{1}{10}\\) of the pizza each. What fraction of the pizza is left? ","e":"1\/2 = 5\/10. Eaten: 5\/10 + 1\/10 + 1\/10 = 7\/10. Left: 10\/10 - 7\/10 = 3\/10."} {"t":"q","id":11898,"q":"Aunt Tinah mixed 2 l of fruit syrup with 10 l of water to make fruit punch. She then poured all the fruit punch equally into 6 jars. How many litres of fruit punch are there in each jar? ","e":"2 + 10 = 12 l of fruit punch. 12 \/ 6 = 2 l in each jar."} {"t":"q","id":11899,"q":"A container had 23 l of water. Jen filled up 4 identical bottles equally with the water from the container. In the end, there was 3 l of water left in the container. How many litres of water was there in each bottle? ","e":"Water used: 23 - 3 = 20 l. 20 \/ 4 = 5 l in each bottle."} {"t":"q","id":11901,"q":"2 boys shared 18 stamps equally. How many stamps does each boy get?","e":"18 \u00f7 2 = 9."} {"t":"q","id":11902,"q":"Kelly has 3 bags of oranges. There are 5 oranges in each bag. How many oranges does Kelly have in all?","e":"3 \u00d7 5 = 15."} {"t":"q","id":11903,"q":"\u25b2 \u00d7 \u25b2 = 100. What number does \u25b2 stand for?","e":"10 \u00d7 10 = 100, so \u25b2 = 10."} {"t":"q","id":11904,"q":"9 \u00d7 5 is _____ more than 7 \u00d7 5.","e":"9 \u00d7 5 = 45 and 7 \u00d7 5 = 35. 45 \u2212 35 = 10."} {"t":"q","id":11906,"q":" \u00f7 5 = 6. The missing number is ____________.","e":"6 \u00d7 5 = 30, so the missing number is 30."} {"t":"q","id":11907,"q":"\u2606 \u00d7 2 = 8\n\u2606 \u00d7 10 = \nThe missing number is ____________.","e":"From \u2606 \u00d7 2 = 8, \u2606 = 4. So 4 \u00d7 10 = 40."} {"t":"q","id":11913,"q":"Miss Devi gave 24 stickers to some students. Each student received 4 stickers. How many students did Miss Devi give the stickers to?\nMiss Devi gave the stickers to students.","e":"24 \u00f7 4 = 6."} {"t":"q","id":11914,"q":"Jane has a box of pencils. She gives all the pencils equally to her 3 friends. Each friend receives 9 pencils. How many pencils are there in the box at first?\nThere are pencils in the box at first.","e":"3 \u00d7 9 = 27."} {"t":"q","id":11915,"q":"Mother placed 40 pies equally on 10 plates.\n(a) How many pies were there on each plate?\nThere were pies on each plate.\n(b) Father placed 6 cookies on each of the 10 plates. How many cookies were there altogether?\nThere were cookies altogether.","e":"(a) 40 \u00f7 10 = 4 pies on each plate. (b) 6 \u00d7 10 = 60 cookies altogether."} {"t":"q","id":11918,"q":"A jug contains 9 l of juice. Tom pours all the juice in the jug equally into 3 bottles. How much juice is there in each bottle?","e":"9 l shared equally among 3 bottles: 9 \/ 3 = 3 l per bottle."} {"t":"q","id":11919,"q":"Which fraction is greater than 3\/10 but smaller than 7\/10?","e":"Like denominators, so compare numerators. We need a fraction between 3\/10 and 7\/10. 6\/10 fits since 3 < 6 < 7."} {"t":"q","id":11920,"q":"3\/9 + 4\/9 = \/9 + 2\/9","e":"Left side = 3\/9 + 4\/9 = 7\/9. Right side = box\/9 + 2\/9, so box\/9 = 7\/9 - 2\/9 = 5\/9. The missing fraction is 5\/9."} {"t":"q","id":11923,"q":"Arrange the fractions in order. Begin with the smallest fraction. 3\/7, 2\/7, 6\/7
(a)   (b)   (c) ","e":"Like denominators, so order by numerator: 2 < 3 < 6. Smallest to largest: 2\/7, 3\/7, 6\/7."} {"t":"q","id":11925,"q":"Arrange the following fractions in order. Begin with the greatest fraction. 1\/6, 1\/11, 1\/2, 1\/10
(a)   (b)   (c)   (d) ","e":"Same numerator (1), so the smaller the denominator the larger the fraction. Greatest to smallest: 1\/2, 1\/6, 1\/10, 1\/11."} {"t":"q","id":11928,"q":"Circle three different fractions that add up to 1 whole. 1\/8, 2\/8, 3\/8, 5\/8, 7\/8
(a)   (b)   (c) ","e":"Need three of the eighths summing to 8\/8. 1 + 2 + 5 = 8, so 1\/8 + 2\/8 + 5\/8 = 8\/8 = 1 whole."} {"t":"q","id":11932,"q":"A tank had 36 l of water. Mary used 9 l of water and her sister used 12 l of water. How much water was left in the tank? ","e":"Total used = 9 + 12 = 21 l. Left = 36 - 21 = 15 l."} {"t":"q","id":11935,"q":"What is the missing number in the box?\n7 + 7 + 7 + 7 = \u00d7 7","e":"7 + 7 + 7 + 7 is four sevens, so 7 + 7 + 7 + 7 = 4 \u00d7 7. The box is 4."} {"t":"q","id":11938,"q":"Ali starts his breakfast at 7:30 am. He eats for 50 min. What time does he finish his breakfast?","e":"7:30 am + 50 min: 7:30 + 30 min = 8:00 am, then + 20 min = 8:20 am."} {"t":"q","id":11946,"q":"Mr Lim planted a total of 526 flowers.\nHe planted some flowers on Friday and 229 flowers on Saturday.\n(a) How many flowers did he plant on Friday?\nHe planted flowers on Friday.\n(b) How many fewer flowers did he plant on Saturday than on Friday?\nHe planted fewer flowers on Saturday than on Friday.","e":"(a) Friday = 526 - 229 = 297 flowers. (b) Difference = 297 - 229 = 68 fewer flowers on Saturday."} {"t":"q","id":11950,"q":"1 - 6\/8 =","e":"1 whole is 8\/8. 8\/8 - 6\/8 = 2\/8."} {"t":"q","id":11953,"q":"Arrange the fractions in order. Begin with the smallest. , , ","e":"All three fractions have denominator 10, so compare numerators: 1 < 3 < 7. Smallest to largest: 1\/10, 3\/10, 7\/10."} {"t":"q","id":11966,"q":"There are 56 litres of water in tank X and 24 litres of water in tank Y. All the water in the two tanks are poured into an empty pail. What is the volume of water in the pail?\nThe volume of water in the pail is litres.","e":"56 + 24 = 80 litres."} {"t":"q","id":11967,"q":"Ahmad sold 223 litres of orange juice on Saturday. He sold 19 litres of orange juice less on Sunday. How many litres of orange juice did he sell on both days?\nHe sold litres of orange juice on both days.","e":"Sunday = 223 - 19 = 204 litres. Both days = 223 + 204 = 427 litres."} {"t":"q","id":11968,"q":"Samy's family drinks 4 litres of milk a week. How many litres of milk do they drink in 8 weeks?\nThey drink litres of milk in 8 weeks.","e":"4 litres per week x 8 weeks = 32 litres."} {"t":"q","id":11969,"q":"A jar contains 3 litres of water and a tank contains 24 litres of water. How many jars of water are needed to fill up the tank?\n jars of water are needed to fill up the tank.","e":"24 litres divided by 3 litres per jar = 8 jars."} {"t":"q","id":11970,"q":"Miss Devi prepared 18 litres of fruit punch and poured them into 6 two-litres bottles. How much fruit punch was left?\n litres of fruit punch was left.","e":"6 bottles x 2 litres = 12 litres poured. 18 - 12 = 6 litres left."} {"t":"q","id":11994,"q":"Write in words. 647","e":"647 = six hundred and forty-seven."} {"t":"q","id":11995,"q":"Write in words. 1000","e":"1000 = one thousand."} {"t":"q","id":11996,"q":"Write in numerals. Three hundred and eighty-five
Answer: ","e":"Three hundred and eighty-five = 385."} {"t":"q","id":11997,"q":"Write in numerals. Seven hundred and six
Answer: ","e":"Seven hundred and six = 706 (no tens)."} {"t":"q","id":11998,"q":"Write in numerals. Nine hundred and forty
Answer: ","e":"Nine hundred and forty = 940."} {"t":"q","id":11999,"q":"Write the answer in numerals. 6 hundreds + 3 ones = ","e":"6 hundreds + 3 ones = 600 + 3 = 603 (no tens)."} {"t":"q","id":12000,"q":"Write the answer in numerals. 8 hundreds + 1 ten + 5 ones = ","e":"8 hundreds + 1 ten + 5 ones = 800 + 10 + 5 = 815."} {"t":"q","id":12001,"q":"Write the answer in numerals. 2 hundreds + 5 tens + 6 ones = ","e":"2 hundreds + 5 tens + 6 ones = 200 + 50 + 6 = 256."} {"t":"q","id":12005,"q":"Fill in the blank with '>' or '<'. 123 213","e":"123 is less than 213, so 123 < 213."} {"t":"q","id":12006,"q":"Fill in the blank with '>' or '<'. 411 141","e":"411 is greater than 141, so 411 > 141."} {"t":"q","id":12007,"q":"Fill in the blank with '>' or '<'. 532 523","e":"Hundreds and tens are equal; 532 has more ones (2 vs 3... compare tens: 3 tens vs 2 tens), 532 > 523."} {"t":"q","id":12008,"q":"Fill in the blank with '>' or '<'. 867 678","e":"867 is greater than 678, so 867 > 678."} {"t":"q","id":12009,"q":"Use the digits 4, 7, 8, 0, 6 (each used at most once). The smallest 3-digit number that can be formed is .","e":"Smallest 3-digit number: hundreds cannot be 0, so use 4, then smallest remaining: 0 then 6 -> 406."} {"t":"q","id":12010,"q":"Use the digits 4, 7, 8, 0, 6 (each used at most once). The greatest 3-digit number that can be formed is .","e":"Greatest 3-digit number: use the three largest digits in descending order: 8, 7, 6 -> 876."} {"t":"q","id":12011,"q":"Use the digits 4, 7, 8, 0, 6. Form two 3-digit numbers that are less than 500. The two numbers are and .","e":"A 3-digit number less than 500 must have hundreds digit < 5, so use 4: e.g. 478 and 408."} {"t":"q","id":12012,"q":"Arrange the numbers in order. Begin with the smallest. 151, 515, 155, 551 , , , ","e":"Ascending: 151, 155, 515, 551."} {"t":"q","id":12013,"q":"Arrange the numbers in order. Begin with the greatest. 796, 962, 976, 269 , , , ","e":"Descending: 976, 962, 796, 269."} {"t":"q","id":12019,"q":"Write the missing numbers. 31, 41, 51, , , 81, 91, 101","e":"The pattern increases by 10: 51, 61, 71, 81."} {"t":"q","id":12020,"q":"Write the missing numbers. 170, 270, 370, , , 670, 770","e":"The pattern increases by 100: 370, 470, 570, 670."} {"t":"q","id":12021,"q":"Write the missing numbers. 599, 589, 579, , 559, , 539, 529","e":"The pattern decreases by 10: 579, 569, 559, 549, 539."} {"t":"q","id":12026,"q":"Using the digits 8, 5 and 6, write down all the 3-digit even numbers you can form. One of them is 658. The other three are , and .","e":"A 3-digit even number ends in an even digit (8 or 6). Using 8,5,6 each once: ending in 8: 568, 658; ending in 6: 586, 856. Apart from 658 the others are 568, 856, 586."} {"t":"q","id":12027,"q":"Use the digits 7, 0 and 9 to form the greatest 3-digit odd number. The greatest 3-digit odd number is .","e":"An odd number ends in an odd digit (7 or 9). To be greatest, hundreds = 9, so ones = 7, tens = 0: 907."} {"t":"q","id":12028,"q":"Mary uses 3 of the number cards 6, 4, 8, 0 to form a 3-digit number. The digit in the hundreds place is twice the digit in the ones place. The digit in the tens place is 4 less than the digit in the ones place. The 3-digit number is .","e":"Let ones = o. Hundreds = 2o, tens = o - 4. Trying o = 4: hundreds = 8, tens = 0 -> 804 (uses cards 8, 0, 4)."} {"t":"q","id":12031,"q":"Add. 58 + 30 = ","e":"58 + 30 = 88."} {"t":"q","id":12032,"q":"Add. 93 + 8 = ","e":"93 + 8 = 101 (regroup the ones)."} {"t":"q","id":12033,"q":"Add. 123 + 60 = ","e":"123 + 60 = 183."} {"t":"q","id":12034,"q":"Add. 116 + 55 = ","e":"116 + 55 = 171."} {"t":"q","id":12035,"q":"Add. 236 + 200 = ","e":"236 + 200 = 436."} {"t":"q","id":12036,"q":"Add. 347 + 182 = ","e":"347 + 182 = 529."} {"t":"q","id":12039,"q":"Subtract. 82 - 30 = ","e":"82 - 30 = 52."} {"t":"q","id":12040,"q":"Subtract. 92 - 44 = ","e":"92 - 44 = 48 (regroup)."} {"t":"q","id":12041,"q":"Subtract. 467 - 14 = ","e":"467 - 14 = 453."} {"t":"q","id":12042,"q":"Subtract. 694 - 105 = ","e":"694 - 105 = 589 (regroup)."} {"t":"q","id":12043,"q":"Subtract. 986 - 215 = ","e":"986 - 215 = 771."} {"t":"q","id":12044,"q":"Subtract. 749 - 373 = ","e":"749 - 373 = 376 (regroup the tens)."} {"t":"q","id":12045,"q":"Add. 236 + 20 = ","e":"236 + 20 = 256."} {"t":"q","id":12046,"q":"Add. 153 + 172 = ","e":"Hundreds\/Tens\/Ones column: top 1 5 3 = 153, add 1 7 2 = 172. 153 + 172 = 325. NOTE key says 225 (see notes)."} {"t":"q","id":12047,"q":"Add. 152 + 423 = ","e":"152 + 423 = 575."} {"t":"q","id":12048,"q":"Add. 289 + 60 = ","e":"289 + 60 = 349 (regroup the tens)."} {"t":"q","id":12049,"q":"Subtract. 188 - 42 = ","e":"188 - 42 = 146."} {"t":"q","id":12050,"q":"Subtract. 94 - 17 = ","e":"94 - 17 = 77 (regroup)."} {"t":"q","id":12051,"q":"Subtract. 709 - 501 = ","e":"709 - 501 = 208."} {"t":"q","id":12052,"q":"Subtract. 950 - 647 = ","e":"950 - 647 = 303 (regroup)."} {"t":"q","id":12053,"q":"Complete the following. 700 - 248 = ","e":"700 - 248 = 452 (regroup across zeros)."} {"t":"q","id":12054,"q":"Complete the following. 439 + 461 = ","e":"439 + 461 = 900."} {"t":"q","id":12055,"q":"Complete the following. 5 + 3 2 9 = 8 7 0","e":"870 - 329 = 541, so the top number is 541: the missing tens digit is 4 and ones digit is 1."} {"t":"q","id":12056,"q":"Complete the following. 7 0 6 - 2 6 = 4 2 0","e":"706 - 420 = 286, so the subtrahend is 286: the missing tens digit is 8."} {"t":"q","id":12058,"q":"Using each of the digits 0, 1, 2, 3, 4 and 5 only once, form two 3-digit numbers that will give the greatest answer when you add them. The two 3-digit numbers are and .","e":"Put the two largest digits (5, 4) in the hundreds places, the next two (3, 2) in the tens, and (1, 0) in the ones: 531 + 420 = 951 (greatest sum)."} {"t":"q","id":12068,"q":"Building A is 452 m tall, Building B is 324 m tall and Building C is 508 m tall. Building C is m taller than Building A.","e":"508 - 452 = 56 m."} {"t":"q","id":12069,"q":"Building A is 452 m tall, Building B is 324 m tall and Building C is 508 m tall. Building A is m taller than Building B.","e":"452 - 324 = 128 m."} {"t":"q","id":12070,"q":"Building A is 452 m tall, Building B is 324 m tall and Building C is 508 m tall. Arrange the buildings in order of height. Begin with the shortest. , , ","e":"Heights: B 324 m, A 452 m, C 508 m. Shortest first: Building B, Building A, Building C."} {"t":"q","id":12071,"q":"Sally has a 350 cm long string. She uses 192 cm of the string. The length of the string left is cm.","e":"350 - 192 = 158 cm."} {"t":"q","id":12072,"q":"Pamela ran 235 m from her house to the garden. Then she ran another 487 m from the garden to the library. She ran m altogether.","e":"235 + 487 = 722 m."} {"t":"q","id":12073,"q":"Peter is 162 cm tall. His brother is 25 cm shorter than him. The height of Peter's brother is cm.","e":"162 - 25 = 137 cm."} {"t":"q","id":12074,"q":"Building A is 485 m tall. Building B is 268 m tall. Building A is m taller than Building B.","e":"485 - 268 = 217 m."} {"t":"q","id":12083,"q":"There are 5 pencils in a pack. Jenny buys 4 packs. How many pencils does Jenny buy?\n \u00d7 = ","e":"4 packs \u00d7 5 pencils each = 20 pencils. Jenny buys 20 pencils."} {"t":"q","id":12084,"q":"Peter and his three brothers share 12 oranges. Each boy gets the same number of oranges. How many oranges does each boy get?\n \u00f7 = ","e":"Peter and three brothers are 4 boys. 12 oranges \u00f7 4 boys = 3 oranges each."} {"t":"q","id":12091,"q":"There are 5 stickers in a pack. Lisa buys 6 packs of stickers. How many stickers will she get?\n \u00d7 = ","e":"6 packs \u00d7 5 stickers each = 30 stickers. She will get 30 stickers."} {"t":"q","id":12092,"q":"Mrs Lee gives 20 apples to her pupils. Each pupil receives 2 apples. How many pupils are there in her class?\n \u00f7 = ","e":"20 apples \u00f7 2 apples per pupil = 10 pupils."} {"t":"q","id":12105,"q":"Mrs Lim sold 480 kg of white sugar. She also sold 370 kg of brown sugar. How many kilograms of sugar did Mrs Lim sell altogether?\n + = ","e":"480 kg + 370 kg = 850 kg of sugar altogether."} {"t":"q","id":12106,"q":"The total mass of a cupcake and a muffin is 190 g. The cupcake weighs 76 g. What is the mass of the muffin?\n - = ","e":"190 g - 76 g = 114 g. The mass of the muffin is 114 g."} {"t":"q","id":12107,"q":"Parcel X weighs 240 g. Parcel Y weighs 60 g heavier than Parcel X. What is the mass of Parcel Y?\n + = ","e":"Parcel Y is 60 g heavier than Parcel X: 240 g + 60 g = 300 g."} {"t":"q","id":12108,"q":"A box of sweets and 3 similar tins of biscuits weigh 11 kg. The box of sweets weighs 2 kg. How heavy is a tin of biscuits?\n - = \n \u00f7 = ","e":"First find the mass of the 3 tins: 11 kg - 2 kg = 9 kg. Then divide among 3 tins: 9 kg \u00f7 3 = 3 kg per tin."} {"t":"q","id":12115,"q":"Fill in the duration. 2:35 pm to 3:30 pm. The duration is min.","e":"From 2:35 pm to 3:30 pm: 2:35 to 3:35 would be 60 min, but 3:30 is 5 min earlier, so the duration is 55 min."} {"t":"q","id":12116,"q":"Fill in the duration. 1:47 pm to 4:47 pm. The duration is h.","e":"From 1:47 pm to 4:47 pm the minutes are the same, so count the hours: 1 to 4 is 3 hours."} {"t":"q","id":12117,"q":"Peter swam in the pool from 4:07 pm to 5:50 pm. Peter swam in the pool for h min.","e":"From 4:07 pm to 5:07 pm is 1 h; from 5:07 pm to 5:50 pm is 43 min. So Peter swam for 1 h 43 min."} {"t":"q","id":12118,"q":"Sally played chess with her friend from 9:33 am to 11:48 am. Sally played for h min.","e":"From 9:33 am to 11:33 am is 2 h; from 11:33 am to 11:48 am is 15 min. So Sally played for 2 h 15 min."} {"t":"q","id":12119,"q":"Mandy and her friends went to the zoo from 8:45 am to 11:23 am. How long did they spend at the zoo? They spent h min at the zoo.","e":"From 8:45 am to 10:45 am is 2 h; from 10:45 am to 11:23 am is 38 min. So they spent 2 h 38 min."} {"t":"q","id":12120,"q":"Mrs Tan started cooking at 4:07 pm and finished at 7:38 pm. How long did she take to cook? She took h min to cook.","e":"From 4:07 pm to 7:07 pm is 3 h; from 7:07 pm to 7:38 pm is 31 min. So Mrs Tan took 3 h 31 min."} {"t":"q","id":12127,"q":"Ali has 42 apples. He gives 12 apples away. How many apples does Ali have left? He has apples left.","e":"42 - 12 = 30. Ali has 30 apples left."} {"t":"q","id":12128,"q":"Ali has 42 apples. He gives 12 apples away. Ali then buys another 60 apples. How many apples does he have? He has apples.","e":"After giving away 12, Ali has 42 - 12 = 30 apples. He buys 60 more: 30 + 60 = 90 apples."} {"t":"q","id":12129,"q":"There are 34 girls in a school. There are 45 more boys than girls in the school. How many boys are there in the school? There are boys in the school.","e":"There are 45 more boys than the 34 girls: 34 + 45 = 79 boys."} {"t":"q","id":12130,"q":"There are 34 girls in a school. There are 45 more boys than girls in the school. How many pupils are there in the school altogether? There are pupils in the school altogether.","e":"There are 34 girls and 79 boys. Altogether: 34 + 79 = 113 pupils."} {"t":"q","id":12131,"q":"Margaret bought 528 balloons and gave 209 balloons away. How many balloons did Margaret have left? She had balloons left.","e":"528 - 209 = 319. Margaret had 319 balloons left."} {"t":"q","id":12132,"q":"Margaret bought 528 balloons and gave 209 balloons away. After giving away the balloons, Margaret bought 445 more balloons. How many balloons did Margaret have? She had balloons.","e":"After giving away 209, Margaret had 528 - 209 = 319 balloons. She bought 445 more: 319 + 445 = 764 balloons."} {"t":"q","id":12133,"q":"Uncle Ben sold 499 pens. He sold 109 more pens than erasers. How many pens and erasers did Uncle Ben sell altogether? He sold pens and erasers altogether.","e":"Pens = 499. Erasers = 499 - 109 = 390. Altogether: 499 + 390 = 889."} {"t":"q","id":12140,"q":"Fill in the blank with 'more' or 'less'. 6 x 3 is ____ than 3 x 3.","e":"6 x 3 = 18 and 3 x 3 = 9. Since 18 > 9, 6 x 3 is more than 3 x 3."} {"t":"q","id":12141,"q":"Fill in the blank with 'more' or 'less'. 2 x 3 is ____ than 7 x 3.","e":"2 x 3 = 6 and 7 x 3 = 21. Since 6 < 21, 2 x 3 is less than 7 x 3."} {"t":"q","id":12142,"q":"Fill in the blank with 'more' or 'less'. 5 x 4 is ____ than 8 x 4.","e":"5 x 4 = 20 and 8 x 4 = 32. Since 20 < 32, 5 x 4 is less than 8 x 4."} {"t":"q","id":12143,"q":"Fill in the blank with 'more' or 'less'. 9 x 4 is ____ than 6 x 4.","e":"9 x 4 = 36 and 6 x 4 = 24. Since 36 > 24, 9 x 4 is more than 6 x 4."} {"t":"q","id":12144,"q":"Choose three of the numbers 8, 5, 24, 3 to form a multiplication equation. x = ","e":"From 8, 5, 24, 3 the related fact family is 8 x 3 = 24 (and 3 x 8 = 24), since 8 x 3 = 24."} {"t":"q","id":12145,"q":"Choose three of the numbers 8, 5, 24, 3 to form a division equation. \u00f7 = ","e":"Using the same fact family, 24 \u00f7 3 = 8 (and 24 \u00f7 8 = 3)."} {"t":"q","id":12146,"q":"Choose three of the numbers 6, 36, 9, 4 to form a multiplication equation. x = ","e":"From 6, 36, 9, 4 the related fact family is 9 x 4 = 36 (and 4 x 9 = 36), since 9 x 4 = 36."} {"t":"q","id":12147,"q":"Choose three of the numbers 6, 36, 9, 4 to form a division equation. \u00f7 = ","e":"Using the same fact family, 36 \u00f7 4 = 9 (and 36 \u00f7 9 = 4)."} {"t":"q","id":12148,"q":"There are 3 hair clips in a pouch. May buys 9 pouches. How many hair clips will she get? She will get hair clips.","e":"9 pouches with 3 hair clips each: 3 x 9 = 27 hair clips."} {"t":"q","id":12149,"q":"There are 40 pencils. Mrs Tan packs all the pencils equally in bags of 4. How many bags of pencils will Mrs Tan have? She will have bags of pencils.","e":"40 pencils packed 4 to a bag: 40 \u00f7 4 = 10 bags."} {"t":"q","id":12150,"q":"Cupcakes were sold in boxes of 3 and 4. Angel bought the same number of boxes of 3 and 4 cupcakes. She had 28 cupcakes. How many boxes of cupcakes did she buy altogether? She bought boxes of cupcakes altogether.","e":"Each pair (one box of 3 + one box of 4) gives 3 + 4 = 7 cupcakes. With 4 boxes of each: 4x3 + 4x4 = 12 + 16 = 28. That is 4 + 4 = 8 boxes altogether."} {"t":"q","id":12155,"q":"Subtract 438 from 908. The answer is .","e":"908 - 438 = 470."} {"t":"q","id":12156,"q":"Find the sum of 365 and 329. The answer is .","e":"365 + 329 = 694."} {"t":"q","id":12157,"q":"Write seven hundred and thirteen in numerals.
Answer: ","e":"Seven hundred and thirteen is written as 713."} {"t":"q","id":12158,"q":"Add 10 tens to 880. The answer is .","e":"10 tens = 100, so 880 + 100 = 980."} {"t":"q","id":12160,"q":"Find the difference between 502 and 348.
Answer: ","e":"502 - 348 = 154."} {"t":"q","id":12162,"q":"Which two numbers add up to 374? Write the numbers in the boxes.\n324 334 50 60\n + = 374","e":"324 + 50 = 374. The two numbers from the set that add to 374 are 324 and 50."} {"t":"q","id":12169,"q":"Sarah gave away 18 apples equally to 3 friends. Which of the following will give the correct number of apples each friend gets?","e":"Sharing 18 apples equally among 3 friends means dividing: 18 \u00f7 3."} {"t":"q","id":12170,"q":"What is the missing number in the box? 5 + 5 + 5 + 5 = x 5","e":"5 + 5 + 5 + 5 is four groups of 5, so it equals 4 x 5. The missing number is 4."} {"t":"q","id":12176,"q":"Study the table carefully. Fill in the boxes with the correct numbers. Number of birds: 1, , 5, 6, 7. Total number of legs: 2, 8, 10, , 14.","e":"Each bird has 2 legs. (a) 8 legs means 8 \u00f7 2 = 4 birds. (b) 6 birds means 6 x 2 = 12 legs."} {"t":"q","id":12177,"q":"Compare and order the masses of the children. Lily 28kg, Robert 31kg, Mayli 21kg, Sam 37kg. (a) Lily is kg lighter than Sam. (b) Arrange the children from the heaviest to the lightest: , , , ","e":"(a) 37 - 28 = 9 kg. (b) Heaviest to lightest: Sam (37), Robert (31), Lily (28), Mayli (21)."} {"t":"q","id":12178,"q":"John watched a movie which started at 5:15 pm. It ended at 7:15 pm. How long was the movie? The movie was long.","e":"From 5:15 pm to 7:15 pm is 2 hours (5:15 -> 6:15 is 1 hour, 6:15 -> 7:15 is another hour)."} {"t":"q","id":12179,"q":"Samantha has a ribbon that is 260cm long. She used 178cm of the ribbon to wrap presents. What is the length of the ribbon left? The length of the ribbon left is cm.","e":"260 - 178 = 82 cm of ribbon left."} {"t":"q","id":12180,"q":"Mindy bought 8 boxes of cupcakes. There were 5 cupcakes in each box. (a) How many cupcakes were there altogether? There were cupcakes altogether. (b) She repacked the cupcakes equally into boxes of 10. How many boxes were there? There were boxes.","e":"(a) 8 x 5 = 40 cupcakes. (b) 40 \u00f7 10 = 4 boxes."} {"t":"q","id":12189,"q":"Ming has 24 stickers. He wants to put 4 stickers in each pack. How many packs can he have using all the stickers? ","e":"24 \u00f7 4 = 6 packs."} {"t":"q","id":12190,"q":"Priya has 5 friends. She gives 4 pencils to each friend. How many pencils does Priya give away in all? ","e":"5 friends \u00d7 4 pencils = 20 pencils."} {"t":"q","id":12191,"q":"There are 734 children at the carnival. 336 of them are boys and the rest are girls. (a) How many girls are there? (b) How many more girls than boys are there? ","e":"(a) 734 \u2212 336 = 398 girls. (b) 398 \u2212 336 = 62 more girls than boys."} {"t":"q","id":12192,"q":"Mei baked 353 cupcakes. Her friend Ben baked 75 more cupcakes than Mei. How many cupcakes did they bake altogether? ","e":"Ben baked 353 + 75 = 428 cupcakes. Altogether 428 + 353 = 781 cupcakes."} {"t":"q","id":12195,"q":"Charlie is thinking of two numbers. The sum of both numbers is 100. One number is 37. What is the other number?","e":"100 - 37 = 63."} {"t":"q","id":12201,"q":"I am a number. When you divide me by 6, the answer is 3. What number am I?","e":"The number divided by 6 gives 3, so the number is 6 x 3 = 18."} {"t":"q","id":12203,"q":"Aini has 125 stickers. Her friend gives her 67 more stickers. How many stickers does Aini have now?
Answer: ","e":"125 + 67 = 192 stickers."} {"t":"q","id":12204,"q":"Raju buys 3 packets of cards. Each packet has 8 cards. How many cards does he have altogether?
Answer: ","e":"3 packets x 8 cards = 24 cards."} {"t":"q","id":12206,"q":"The baker baked 240 cupcakes in the morning and 185 cupcakes in the afternoon. (a) How many cupcakes did the baker bake altogether? (b) The baker sold 359 cupcakes during the day. How many cupcakes were left?
(a)   (b) ","e":"(a) 240 + 185 = 425 cupcakes. (b) 425 - 359 = 66 cupcakes left."} {"t":"q","id":12207,"q":"There are 7 boxes of pencils. Each box contains 10 pencils. (a) How many pencils are there in the 7 boxes? (b) If 25 pencils are given away, how many pencils are left?
(a)   (b) ","e":"(a) 7 boxes x 10 pencils = 70 pencils. (b) 70 - 25 = 45 pencils left."} {"t":"q","id":12213,"q":"I am a solid figure. I always roll when pushed gently on one of my surfaces. I have 2 flat surfaces. What am I?","e":"A cylinder rolls on its curved surface and has 2 flat circular faces."} {"t":"q","id":12215,"q":"\\(\\dfrac{2}{7}\\) and ? make 1 whole.","e":"1 whole is 7\/7. 7\/7 - 2\/7 = 5\/7."} {"t":"q","id":12216,"q":"A cake is cut into 6 equal pieces. Lily ate some pieces and there are 4\/6 of the cake left. How many pieces of cake did Lily eat?
Answer: ","e":"The whole cake is 6\/6. 6\/6 - 4\/6 = 2\/6, so 2 pieces were eaten."} {"t":"q","id":12217,"q":"Jamie takes 15 minutes to walk to school. If he leaves home at 6:45 a.m., what time will he reach school?
Answer: ","e":"6:45 a.m. + 15 minutes = 7:00 a.m."} {"t":"q","id":12218,"q":"Arrange the fractions in order. Begin with the greatest. 1\/10 , 1\/5 , 1\/7
(a)   (b)   (c) ","e":"With equal numerators, the smaller the denominator the larger the fraction. So 1\/5 > 1\/7 > 1\/10."} {"t":"q","id":12219,"q":"Box A weighs 800 g. Box A weighs 500 g more than Box B. What is the mass of Box B? Box C weighs 100 g more than Box A. What is the mass of Box C? The mass of Box B is g. The mass of Box C is g.","e":"Box B = 800 - 500 = 300 g. Box C = 800 + 100 = 900 g."} {"t":"q","id":12220,"q":"Ali buys 3 notebooks at $2 each. How much do the 3 notebooks cost? Ali gave the cashier $10. How much change will he receive? The 3 notebooks cost $. Ali will receive $ as change.","e":"3 notebooks cost 3 x $2 = $6. Change from $10 is $10 - $6 = $4."} {"t":"q","id":12225,"q":"Tom had 15 sweets. He gave 3 sweets each to his friends. How many friends does Tom have?","e":"15 \u00f7 3 = 5 friends."} {"t":"s","id":4777,"s":"Ben has 9 (from part a). Altogether = 18 + 9 = 27 pencils."} {"t":"s","id":4781,"s":"Like fractions: add numerators over the common denominator. 3\/11 + 7\/11 = 10\/11."} {"t":"s","id":4785,"s":"Girls = 40 - 23 = 17. More boys than girls = 23 - 17 = 6."} {"t":"s","id":4786,"s":"Bag B = 2 x 8 = 16 kg. Total = 8 + 16 = 24 kg."} {"t":"s","id":4787,"s":"May = 398 + 147 = 545. Altogether = 398 + 545 = 943 stickers."} {"t":"s","id":4802,"s":"a) 107 + 31 = 138. b) 138 - 100 = 38."} {"t":"s","id":4813,"s":"10 \u00d7 10 = 100 and 9 \u00d7 10 = 90. 100 \u2212 90 = 10, so 10 \u00d7 10 is 10 more than 9 \u00d7 10."} {"t":"s","id":4823,"s":"(a) 80 cupcakes \u00f7 10 boxes = 8 cupcakes in each box. (b) 4 muffins \u00d7 10 boxes = 40 muffins altogether."} {"t":"s","id":4826,"s":"7 \u00d7 3 = 21 and 5 \u00d7 3 = 15. 21 \u2212 15 = 6."} {"t":"s","id":4832,"s":"5 \u00d7 8 = 40 cookies in total. 40 \u00f7 4 = 10 cookies each."} {"t":"s","id":4834,"s":"(a) 583 + 223 = 806 cups altogether. (b) 583 \u2212 223 = 360 more cups of coffee than tea."} {"t":"s","id":4835,"s":"(a) 24 \u00f7 4 = 6 footballs in each bag. (b) 4 bags \u00d7 3 kg = 12 kg total."} {"t":"s","id":4836,"s":"Madam Ang sold 520 \u2212 155 = 365 candies. Together: 520 + 365 = 885 candies."} {"t":"s","id":4837,"s":"Work backwards: 252 + 115 = 367 (before giving away). 367 \u2212 330 = 37 beads at first."} {"t":"s","id":4844,"s":"Write 1 as 6\/6. Then 6\/6 - 2\/6 = 4\/6."} {"t":"s","id":4847,"s":"(a) 1 whole is split into 4 quarters, so 4 quarters make 1 whole. (b) 3 wholes have 3 x 4 = 12 quarters."} {"t":"s","id":4849,"s":"For unit fractions, the larger the denominator the smaller the fraction. So smallest to largest: 1\/10, 1\/7, 1\/4, 1\/2."} {"t":"s","id":4850,"s":"Container B = 28 + 12 = 40 l. Total = 28 + 40 = 68 l."} {"t":"s","id":4852,"s":"Per week: 4 l x 2 = 8 l. Over 3 weeks: 8 l x 3 = 24 l."} {"t":"s","id":4853,"s":"Juice left after giving Ken: 48 - 32 = 16 l. Shared equally between Johnny and Mary: 16 \/ 2 = 8 l for Mary."} {"t":"s","id":4863,"s":"Hundreds = 4, tens = 1 (value 10). Ones is 6 or 7 (more than 5, less than 8); odd means 7. Number = 417."} {"t":"s","id":4869,"s":"200 + 15 ones = 215. 275 - 215 = 60 = 6 tens, so the missing number is 6."} {"t":"s","id":4870,"s":"Compare hundreds first: 172 < 249 < 255. Smallest to largest: 172, 249, 255."} {"t":"s","id":4899,"s":"Heart + Heart = 80, so Heart = 40. Heart + Triangle = 278, so Triangle = 278 \u2013 40 = 238."} {"t":"s","id":4901,"s":"12 \u00f7 2 = 6 apples each. Option (1), 0-based index 0."} {"t":"s","id":4902,"s":"The related division fact for 8 x 2 = 16 is 16 \u00f7 2 = 8 (total \u00f7 one factor = other factor). Option (4), 0-based index 3."} {"t":"s","id":4903,"s":"21 \u00f7 3 = 7, so the missing number is 3. Option (3), 0-based index 2."} {"t":"s","id":4909,"s":"(a) 22 - 2 = 20 markers left. (b) 20 \u00f7 5 = 4 bags."} {"t":"s","id":4910,"s":"15 books \u00f7 3 books per group = 5 groups; 5 groups x 2 erasers = 10 erasers. (Answer key shows 15\u00f73=5, then 5x2=10.)"} {"t":"s","id":4912,"s":"String A = 470 - 283 = 187 cm. String C = 640 - 187 = 453 cm."} {"t":"s","id":4920,"s":"Tens digits are 2, 3, 1 and 2. The greatest tens digit is 3, in 132."} {"t":"s","id":4935,"s":"628 + 236 = 864. 864 - 828 = 36, so the missing number is 36."} {"t":"s","id":4937,"s":"Work backwards from 69: before receiving 57, she had 69 - 57 = 12; before giving 42, she had 12 + 42 = 54. So she bought 54 ice-cream sticks."} {"t":"s","id":4941,"s":"Jenny bought 349 - 167 = 182 beads. Altogether: 349 + 182 = 531 beads."} {"t":"s","id":4955,"s":"500 + 30 + 8 = 538, and 10 more is 548. 300 + 10 + 6 = 316, and 100 less is 216."} {"t":"s","id":4959,"s":"The tallest girl is Fatimah at 152 cm. Kann is 119 cm. 152 - 119 = 33 cm."} {"t":"s","id":4960,"s":"(a) A file's thickness is small, so the suitable unit is cm. (b) A watermelon is heavy, so the suitable unit of mass is kg."} {"t":"s","id":4965,"s":"Mass of the 3 balls = 17 - 2 = 15 kg. Each ball = 15 \u00f7 3 = 5 kg."} {"t":"s","id":4969,"s":"23 + 3 = 26, and 27 > 26. Any larger number would make the sum 27 or more, so the largest is 3."} {"t":"s","id":4972,"s":"(a) 561 + 32 = 593. (b) 869 - 451 = 418."} {"t":"s","id":5005,"s":"(a) 305 g - 120 g = 185 g of oat cookies. (b) 185 g - 120 g = 65 g heavier."} {"t":"s","id":5006,"s":"(a) Tuesday = 307 - 128 = 179 kg. (b) Both days = 307 + 179 = 486 kg."} {"t":"s","id":5019,"s":"Two $50 notes are $100. Change = $100 - $89 = $11."} {"t":"s","id":5028,"s":"a) 8 jars x 4 l = 32 l. b) 40 l - 32 l = 8 l left."} {"t":"s","id":5029,"s":"a) 156 + 78 = 234 pencils in Box B. b) 234 + 156 = 390 pencils total."} {"t":"s","id":5030,"s":"a) 641 - 375 = 266 biscuits in Jar B. b) 375 - 266 = 109 more in Jar A."} {"t":"s","id":5031,"s":"2 groups of 10 = 20. 20 \u00f7 5 = 4. There are 4 fives."} {"t":"s","id":5032,"s":"6 \u00d7 4 = 24. 24 = 8 \u00d7 3, so the missing number is 8."} {"t":"s","id":5034,"s":"7 \u00d7 5 = 35. 5 \u00d7 5 = 25 and 2 \u00d7 5 = 10. 25 + 10 = 35, so the sign is +."} {"t":"s","id":5036,"s":"2\u00d79=18, 3\u00d76=18, 6\u00d73=18 all work. 8\u00d72=16 \u2260 18, so 8 groups of 2 is not possible."} {"t":"s","id":5042,"s":"17 + 11 = 28 balls. 28 \u00f7 4 = 7 balls in each box."} {"t":"s","id":5043,"s":"Multiples of 3 between 25 and 30: 27 (= 3 \u00d7 9). So the number is 27."} {"t":"s","id":5045,"s":"Tallest = Ethan 132 cm, shortest = Hamid 107 cm. 132 \u2212 107 = 25 cm."} {"t":"s","id":5048,"s":"Ariana plus 2 sisters = 3 children. 27 \u00f7 3 = 9 lollipops each."} {"t":"s","id":5049,"s":"(a) 3 \u00d7 10 = 30 apples. (b) 30 \u00f7 5 = 6 apples on each plate."} {"t":"s","id":5061,"s":"$1 = 100\u00a2, so $3 = 300\u00a2. 5\u00a2 = $0.05."} {"t":"s","id":5062,"s":"3\/7 is the largest (same denom, bigger numerator). Between 1\/7 and 1\/11, same numerator means smaller denominator is larger, so 1\/7 > 1\/11. Order: 3\/7, 1\/7, 1\/11."} {"t":"s","id":5063,"s":"(a) 1\/5 + 3\/5 = 4\/5. (b) 1 = 10\/10, so 10\/10 - 3\/10 = 7\/10."} {"t":"s","id":5067,"s":"Brandon left with 123 - 86 = 37 marbles. David also has 37. Altogether = 37 + 37 = 74."} {"t":"s","id":5072,"s":"20 \u00f7 5 = 4. The missing number times 2 must equal 4, so the missing number is 4 \u00f7 2 = 2."} {"t":"s","id":5079,"s":"For an even number the last digit must be 2. To be smallest, put the smaller remaining digit first: 3, then 5, then 2 -> 352."} {"t":"s","id":5096,"s":"(a) Jerry: 500 - 128 = 372 cards. (b) Altogether: 372 + 500 = 872 cards."} {"t":"s","id":5104,"s":"Add the numerators of like fractions: 4 + 5 = 9, keep the denominator 11. So 9\/11."} {"t":"s","id":5107,"s":"A whole is 8\/8. 8\/8 - 3\/8 = 5\/8, so 3\/8 and 5\/8 make a whole."} {"t":"s","id":5119,"s":"The ribbon is between 24 cm and 30 cm and is divisible by 3, so it is 27 cm. Cutting it 5 cm shorter: 27 - 5 = 22 cm."} {"t":"s","id":5124,"s":"a) 5 packets \u00d7 3 cookies = 15 cookies. b) 2 packets \u00d7 3 cookies = 6 cookies."} {"t":"s","id":5125,"s":"a) 28 \u00f7 4 = 7 pupils in each group. b) 30 \u00f7 3 = 10 groups."} {"t":"s","id":5126,"s":"a) 35 cm \u00d7 2 = 70 cm. b) 35 cm - 20 cm = 15 cm more needed."} {"t":"s","id":5146,"s":"Greatest is 991, smallest is 199. 991 - 199 = 792."} {"t":"s","id":5147,"s":"Between 300 and 400 means hundreds digit 3. Tens digit is 2. Ones digit is 3 x 2 = 6. So the number is 326."} {"t":"s","id":5148,"s":"Benny plus 3 friends = 4 people. 4 x 7 = 28 cookies."} {"t":"s","id":5150,"s":"5 vases x 3 flowers = 15 flowers needed. She has 12, so she needs 15 - 12 = 3 more."} {"t":"s","id":5152,"s":"For unit fractions, the larger the denominator the smaller the fraction. So 1\/10 < 1\/7 < 1\/2."} {"t":"s","id":5153,"s":"(a) 1000 - 349 = 651 adults. (b) 651 - 349 = 302 more adults than children."} {"t":"s","id":5154,"s":"(a) 90 \u00f7 10 = 9 days. (b) Monday to Friday is 5 days; 5 x 10 = 50 pages."} {"t":"s","id":5155,"s":"(a) 256 + 178 = 434 marbles in the two boxes. (b) 800 - 434 = 366 marbles given to Martin."} {"t":"s","id":5156,"s":"(a) 450 - 285 = 165 g for Parcel B. (b) 450 + 165 = 615 g total."} {"t":"s","id":5157,"s":"An apple is small and light, so a sensible everyday mass for one apple is about 100g. 10g is far too light, and the kilogram options are far too heavy."} {"t":"s","id":5159,"s":"350g - 250g = 100g. He had 100g of butter left."} {"t":"s","id":5160,"s":"After giving James 250g: 900 - 250 = 650g. She is left with 475g, so Meiling got 650 - 475 = 175g of clay."} {"t":"s","id":5189,"s":"7\/7 is one whole. 7\/7 - 4\/7 = 3\/7, so 4\/7 and 3\/7 make 1 whole."} {"t":"s","id":5190,"s":"For unit fractions, the smaller the denominator the larger the fraction. 1\/3 has a smaller denominator than 1\/4, so 1\/3 > 1\/4. The others all have larger denominators and are smaller than 1\/4."} {"t":"s","id":5197,"s":"For unit fractions, the smaller the denominator the greater the fraction. So from greatest to smallest: 1\/3, 1\/8, 1\/12."} {"t":"s","id":5199,"s":"With the same denominator, the smaller the numerator the smaller the fraction. So from smallest to greatest: 2\/9, 5\/9, 8\/9."} {"t":"s","id":5206,"s":"70 - 15 = 55 l left after pouring out. Then 55 + 30 = 85 l after adding water, so the final volume is 85 l."} {"t":"s","id":5211,"s":"601 is odd (ends in 1) and greater than 300. 312 is even, 297 and 133 are less than 300."} {"t":"s","id":5225,"s":"(a) 428 - 39 = 389 kg more. (b) 428 + 39 = 467 kg altogether."} {"t":"s","id":5246,"s":"5 \u00d7 4 = 20 and 2 \u00d7 4 = 8. 20 \u2212 8 = 12."} {"t":"s","id":5251,"s":"She needs $18 at $3\/day = 6 days. Day 1 Mon, day 6 Saturday. So Saturday."} {"t":"s","id":5252,"s":"Rest = 20 \u2212 12 = 8 marbles packed. The statement says she packed 8 marbles, which is True."} {"t":"s","id":5256,"s":"Mdm Lee = 430 \u2212 145 = 285. Total = 430 + 285 = 715."} {"t":"s","id":5258,"s":"Pasted = 9 \u00d7 4 = 36 stickers. Bought at first = 36 + 8 = 44."} {"t":"s","id":5259,"s":"Total toys = 8 \u00d7 3 = 24. Shared among 6 friends: 24 \u00f7 6 = 4 each."} {"t":"s","id":5264,"s":"4 + 3 = 7 slices eaten. 12 - 7 = 5 slices left, so 5\/12."} {"t":"s","id":5266,"s":"1 = 7\/7. 7\/7 - 2\/7 = 5\/7."} {"t":"s","id":5272,"s":"Same numerator: larger denominator = smaller fraction. Smallest first: 1\/9, 1\/7, 1\/5, 1\/3."} {"t":"s","id":5274,"s":"1\/2 = 5\/10. Eaten: 5\/10 + 1\/10 + 1\/10 = 7\/10. Left: 10\/10 - 7\/10 = 3\/10."} {"t":"s","id":5275,"s":"2 + 10 = 12 l of fruit punch. 12 \/ 6 = 2 l in each jar."} {"t":"s","id":5276,"s":"Water used: 23 - 3 = 20 l. 20 \/ 4 = 5 l in each bottle."} {"t":"s","id":5281,"s":"9 \u00d7 5 = 45 and 7 \u00d7 5 = 35. 45 \u2212 35 = 10."} {"t":"s","id":5284,"s":"From \u2606 \u00d7 2 = 8, \u2606 = 4. So 4 \u00d7 10 = 40."} {"t":"s","id":5292,"s":"(a) 40 \u00f7 10 = 4 pies on each plate. (b) 6 \u00d7 10 = 60 cookies altogether."} {"t":"s","id":5296,"s":"Like denominators, so compare numerators. We need a fraction between 3\/10 and 7\/10. 6\/10 fits since 3 < 6 < 7."} {"t":"s","id":5297,"s":"Left side = 3\/9 + 4\/9 = 7\/9. Right side = box\/9 + 2\/9, so box\/9 = 7\/9 - 2\/9 = 5\/9. The missing fraction is 5\/9."} {"t":"s","id":5300,"s":"Like denominators, so order by numerator: 2 < 3 < 6. Smallest to largest: 2\/7, 3\/7, 6\/7."} {"t":"s","id":5302,"s":"Same numerator (1), so the smaller the denominator the larger the fraction. Greatest to smallest: 1\/2, 1\/6, 1\/10, 1\/11."} {"t":"s","id":5305,"s":"Need three of the eighths summing to 8\/8. 1 + 2 + 5 = 8, so 1\/8 + 2\/8 + 5\/8 = 8\/8 = 1 whole."} {"t":"s","id":5309,"s":"Total used = 9 + 12 = 21 l. Left = 36 - 21 = 15 l."} {"t":"s","id":5312,"s":"7 + 7 + 7 + 7 is four sevens, so 7 + 7 + 7 + 7 = 4 \u00d7 7. The box is 4."} {"t":"s","id":5323,"s":"(a) Friday = 526 - 229 = 297 flowers. (b) Difference = 297 - 229 = 68 fewer flowers on Saturday."} {"t":"s","id":5327,"s":"1 whole is 8\/8. 8\/8 - 6\/8 = 2\/8."} {"t":"s","id":5330,"s":"All three fractions have denominator 10, so compare numerators: 1 < 3 < 7. Smallest to largest: 1\/10, 3\/10, 7\/10."} {"t":"s","id":5344,"s":"Sunday = 223 - 19 = 204 litres. Both days = 223 + 204 = 427 litres."} {"t":"s","id":5347,"s":"6 bottles x 2 litres = 12 litres poured. 18 - 12 = 6 litres left."} {"t":"s","id":5384,"s":"Hundreds and tens are equal; 532 has more ones (2 vs 3... compare tens: 3 tens vs 2 tens), 532 > 523."} {"t":"s","id":5403,"s":"A 3-digit even number ends in an even digit (8 or 6). Using 8,5,6 each once: ending in 8: 568, 658; ending in 6: 586, 856. Apart from 658 the others are 568, 856, 586."} {"t":"s","id":5404,"s":"An odd number ends in an odd digit (7 or 9). To be greatest, hundreds = 9, so ones = 7, tens = 0: 907."} {"t":"s","id":5405,"s":"Let ones = o. Hundreds = 2o, tens = o - 4. Trying o = 4: hundreds = 8, tens = 0 -> 804 (uses cards 8, 0, 4)."} {"t":"s","id":5423,"s":"Hundreds\/Tens\/Ones column: top 1 5 3 = 153, add 1 7 2 = 172. 153 + 172 = 325. NOTE key says 225 (see notes)."} {"t":"s","id":5447,"s":"Heights: B 324 m, A 452 m, C 508 m. Shortest first: Building B, Building A, Building C."} {"t":"s","id":5460,"s":"4 packs \u00d7 5 pencils each = 20 pencils. Jenny buys 20 pencils."} {"t":"s","id":5461,"s":"Peter and three brothers are 4 boys. 12 oranges \u00f7 4 boys = 3 oranges each."} {"t":"s","id":5468,"s":"6 packs \u00d7 5 stickers each = 30 stickers. She will get 30 stickers."} {"t":"s","id":5483,"s":"190 g - 76 g = 114 g. The mass of the muffin is 114 g."} {"t":"s","id":5485,"s":"First find the mass of the 3 tins: 11 kg - 2 kg = 9 kg. Then divide among 3 tins: 9 kg \u00f7 3 = 3 kg per tin."} {"t":"s","id":5494,"s":"From 4:07 pm to 5:07 pm is 1 h; from 5:07 pm to 5:50 pm is 43 min. So Peter swam for 1 h 43 min."} {"t":"s","id":5495,"s":"From 9:33 am to 11:33 am is 2 h; from 11:33 am to 11:48 am is 15 min. So Sally played for 2 h 15 min."} {"t":"s","id":5496,"s":"From 8:45 am to 10:45 am is 2 h; from 10:45 am to 11:23 am is 38 min. So they spent 2 h 38 min."} {"t":"s","id":5497,"s":"From 4:07 pm to 7:07 pm is 3 h; from 7:07 pm to 7:38 pm is 31 min. So Mrs Tan took 3 h 31 min."} {"t":"s","id":5504,"s":"42 - 12 = 30. Ali has 30 apples left."} {"t":"s","id":5505,"s":"After giving away 12, Ali has 42 - 12 = 30 apples. He buys 60 more: 30 + 60 = 90 apples."} {"t":"s","id":5507,"s":"There are 34 girls and 79 boys. Altogether: 34 + 79 = 113 pupils."} {"t":"s","id":5508,"s":"528 - 209 = 319. Margaret had 319 balloons left."} {"t":"s","id":5509,"s":"After giving away 209, Margaret had 528 - 209 = 319 balloons. She bought 445 more: 319 + 445 = 764 balloons."} {"t":"s","id":5510,"s":"Pens = 499. Erasers = 499 - 109 = 390. Altogether: 499 + 390 = 889."} {"t":"s","id":5517,"s":"6 x 3 = 18 and 3 x 3 = 9. Since 18 > 9, 6 x 3 is more than 3 x 3."} {"t":"s","id":5518,"s":"2 x 3 = 6 and 7 x 3 = 21. Since 6 < 21, 2 x 3 is less than 7 x 3."} {"t":"s","id":5519,"s":"5 x 4 = 20 and 8 x 4 = 32. Since 20 < 32, 5 x 4 is less than 8 x 4."} {"t":"s","id":5520,"s":"9 x 4 = 36 and 6 x 4 = 24. Since 36 > 24, 9 x 4 is more than 6 x 4."} {"t":"s","id":5527,"s":"Each pair (one box of 3 + one box of 4) gives 3 + 4 = 7 cupcakes. With 4 boxes of each: 4x3 + 4x4 = 12 + 16 = 28. That is 4 + 4 = 8 boxes altogether."} {"t":"s","id":5539,"s":"324 + 50 = 374. The two numbers from the set that add to 374 are 324 and 50."} {"t":"s","id":5547,"s":"5 + 5 + 5 + 5 is four groups of 5, so it equals 4 x 5. The missing number is 4."} {"t":"s","id":5553,"s":"Each bird has 2 legs. (a) 8 legs means 8 \u00f7 2 = 4 birds. (b) 6 birds means 6 x 2 = 12 legs."} {"t":"s","id":5554,"s":"(a) 37 - 28 = 9 kg. (b) Heaviest to lightest: Sam (37), Robert (31), Lily (28), Mayli (21)."} {"t":"s","id":5557,"s":"(a) 8 x 5 = 40 cupcakes. (b) 40 \u00f7 10 = 4 boxes."} {"t":"s","id":5568,"s":"(a) 734 \u2212 336 = 398 girls. (b) 398 \u2212 336 = 62 more girls than boys."} {"t":"s","id":5569,"s":"Ben baked 353 + 75 = 428 cupcakes. Altogether 428 + 353 = 781 cupcakes."} {"t":"s","id":5583,"s":"(a) 240 + 185 = 425 cupcakes. (b) 425 - 359 = 66 cupcakes left."} {"t":"s","id":5584,"s":"(a) 7 boxes x 10 pencils = 70 pencils. (b) 70 - 25 = 45 pencils left."} {"t":"s","id":5592,"s":"1 whole is 7\/7. 7\/7 - 2\/7 = 5\/7."} {"t":"s","id":5593,"s":"The whole cake is 6\/6. 6\/6 - 4\/6 = 2\/6, so 2 pieces were eaten."} {"t":"s","id":5594,"s":"6:45 a.m. + 15 minutes = 7:00 a.m."} {"t":"s","id":5595,"s":"With equal numerators, the smaller the denominator the larger the fraction. So 1\/5 > 1\/7 > 1\/10."} {"t":"s","id":5596,"s":"Box B = 800 - 500 = 300 g. Box C = 800 + 100 = 900 g."} {"t":"s","id":5597,"s":"3 notebooks cost 3 x $2 = $6. Change from $10 is $10 - $6 = $4."} {"t":"q","id":12230,"q":"There are 45 tables. Each row has 5 tables. How many rows are there?","e":"45 \u00f7 5 = 9 rows."} {"t":"q","id":12231,"q":"Sally bought 3 packets of cookies. Each packet has 10 cookies. How many cookies are there in all?","e":"3 \u00d7 10 = 30 cookies."} {"t":"q","id":12234,"q":"Complete the number pattern. 25, , 35, 40, ","e":"The numbers increase by 5 each time: 25, 30, 35, 40, 45."} {"t":"q","id":12238,"q":"Write a multiplication equation using only 3 of the numbers 7, 9, 45, 5. Each number can only be used once. x = ","e":"9 \u00d7 5 = 45 uses three of the given numbers (7 is unused)."} {"t":"q","id":12239,"q":"Mdm Lim bought 35 jellies for her students. She gave each student 5 jellies. How many students are there? \u00f7 = There are students.","e":"35 jellies shared 5 each: 35 \u00f7 5 = 7 students."} {"t":"q","id":12240,"q":"There are 5 pens in a box. Ben bought 8 boxes of pens. How many pens does he have altogether? x = Ben has pens altogether.","e":"8 boxes of 5 pens: 5 \u00d7 8 = 40 pens."} {"t":"q","id":12241,"q":"There are 60 cupcakes. They are packed equally into 10 boxes. How many cupcakes are there in each box? \u00f7 = There are cupcakes in each box.","e":"60 cupcakes shared into 10 boxes: 60 \u00f7 10 = 6 per box."} {"t":"q","id":12242,"q":"There are 10 ducks in a farm. Each duck has 2 legs. How many legs are there altogether? x = There are legs altogether.","e":"10 ducks with 2 legs each: 10 \u00d7 2 = 20 legs."} {"t":"q","id":12243,"q":"Mrs Tan bought 4 boxes of apples. There were 10 apples in each box. How many apples did she buy? x = She bought apples. Mrs Tan then wanted to pack the apples again. She packed 5 apples into each bag. How many bags did she need? \u00f7 = She needed bags to pack the apples.","e":"Part a: 4 boxes of 10 apples, 4 \u00d7 10 = 40 apples. Part b: 40 apples packed 5 per bag, 40 \u00f7 5 = 8 bags."} {"t":"q","id":12246,"q":"4\/7 and _______ make 1 whole.","e":"1 whole is 7\/7. 7\/7 - 4\/7 = 3\/7, so 4\/7 and 3\/7 make 1 whole. The answer is option (3)."} {"t":"q","id":12247,"q":"Which fraction is smaller than 1\/6?","e":"For unit fractions, the larger the denominator the smaller the fraction. 1\/7 has a bigger denominator than 1\/6, so 1\/7 < 1\/6. The answer is option (1)."} {"t":"q","id":12250,"q":"6\/12 + 3\/12 = _______","e":"Adding like fractions: keep the denominator and add the numerators. 6 + 3 = 9, so 6\/12 + 3\/12 = 9\/12. The answer is option (2)."} {"t":"q","id":12251,"q":"8\/9 - 2\/9 = _______","e":"Subtracting like fractions: keep the denominator and subtract the numerators. 8 - 2 = 6, so 8\/9 - 2\/9 = 6\/9. The answer is option (4)."} {"t":"q","id":12253,"q":"A pail holds 5 l of water. Ann has 10 such pails. How much water does Ann have?","e":"Each pail holds 5 l and there are 10 pails: 5 x 10 = 50 l. The answer is option (4)."} {"t":"q","id":12254,"q":"Arrange the fractions in order. Begin with the smallest. 1\/6 , 1\/4 , 1\/11
(a)   (b)   (c) ","e":"For unit fractions, the larger the denominator the smaller the fraction. Smallest to largest: 1\/11, 1\/6, 1\/4."} {"t":"q","id":12255,"q":"Fill in the box with the correct sign < or >. 7\/11 10\/11","e":"Both fractions have denominator 11. Compare numerators: 7 < 10, so 7\/11 < 10\/11."} {"t":"q","id":12256,"q":"Arrange the fractions in order. Begin with the greatest. 3\/5 , 1\/5 , 4\/5
(a)   (b)   (c) ","e":"All fractions have denominator 5, so compare numerators. Greatest to smallest: 4\/5, 3\/5, 1\/5."} {"t":"q","id":12262,"q":"Alice had 8 l of juice. She poured them equally into 4 jugs. How much juice was there in each jug? There was l of juice in each jug.","e":"8 l shared equally among 4 jugs: 8 \/ 4 = 2 l in each jug."} {"t":"q","id":12263,"q":"Joe had 115 l of water. He used 27 l of water for laundry and another 35 l of water for cooking. How much water was left? Joe had l of water left.","e":"Start with 115 l. 115 - 27 = 88, then 88 - 35 = 53. Joe had 53 l of water left."} {"t":"q","id":12267,"q":"Write in numbers. 6 hundreds + 5 tens = ","e":"6 hundreds + 5 tens = 600 + 50 = 650."} {"t":"q","id":12269,"q":"Arrange the numbers in order. Begin with the greatest. 350, 532, 503, 325 , , , ","e":"Greatest to smallest: 532, 503, 350, 325."} {"t":"q","id":12270,"q":"Complete the number pattern. 733, 737, 741, , 749, 753","e":"Pattern increases by 4: 741 + 4 = 745."} {"t":"q","id":12271,"q":"Fill in the box. 471 + 218 = ","e":"471 + 218 = 689."} {"t":"q","id":12272,"q":"Fill in the box. 752 - = 621","e":"752 - 621 = 131."} {"t":"q","id":12273,"q":"Fill in the missing numbers. 352 + 479 = ","e":"352 + 479 = 831."} {"t":"q","id":12274,"q":"Fill in the missing numbers. 500 - 126 = ","e":"500 - 126 = 374."} {"t":"q","id":12275,"q":"Write down the greatest 3-digit even number that can be formed from the digits 6, 8 and 3. The number is .","e":"Even means it ends in an even digit. Largest digit first: 8, then 3, with the even 6 last: 836."} {"t":"q","id":12279,"q":"Using the numbers 315, 947 and 632, write a subtraction equation. - = ","e":"947 - 632 = 315."} {"t":"q","id":12280,"q":"Jennie collected 178 seashells. Alice collected 321 seashells. How many seashells did they collect altogether? ","e":"178 + 321 = 499 seashells altogether."} {"t":"q","id":12281,"q":"Mrs Tan baked 562 muffins. She baked 247 more muffins than Mrs Chan. How many muffins did Mrs Chan bake? ","e":"Mrs Chan baked 562 - 247 = 315 muffins."} {"t":"q","id":12282,"q":"Ali has 348 postcards. Bala has 136 more postcards than Ali. How many postcards does Bala have? ","e":"Bala has 348 + 136 = 484 postcards."} {"t":"q","id":12283,"q":"Sally bought 900cm of ribbon for a party. She used 235cm of it for decoration. What is the length of the ribbon left? ","e":"900 - 235 = 665 cm of ribbon left."} {"t":"q","id":12285,"q":"Mr Cher reads 2 pages of a book every day. How many pages will he read in a week? \u00d7 = ","e":"A week has 7 days. 2 pages \u00d7 7 days = 14 pages."} {"t":"q","id":12286,"q":"3 taxis can carry 12 children altogether. Each taxi carries an equal number of children. How many children are there in each taxi? \u00f7 = ","e":"12 children shared equally among 3 taxis: 12 \u00f7 3 = 4 children per taxi."} {"t":"q","id":12287,"q":"Luke baked 18 cookies for his 9 friends. How many cookies would each friend get? \u00f7 = ","e":"18 cookies shared equally among 9 friends: 18 \u00f7 9 = 2 cookies each."} {"t":"q","id":12300,"q":"Ahmad stayed in the library until 11:00 am. He stayed in the library for min.","e":"From 10:37 am to 11:00 am is 23 minutes."} {"t":"q","id":12301,"q":"Liam started his football practice at 4:35 pm. His football practice ended at 6:55 pm. His football practice lasted for h min.","e":"4:35 pm to 6:35 pm is 2 h; 6:35 pm to 6:55 pm is 20 min. Total 2 h 20 min."} {"t":"q","id":12302,"q":"Write in minutes. 3 h 20 min = h + min = min + min = min","e":"3 h = 180 min. 180 min + 20 min = 200 min."} {"t":"q","id":12303,"q":"Write in hours and minutes. 185 min = min + min = h min","e":"185 min = 180 min + 5 min. 180 min = 3 h, so 185 min = 3 h 5 min."} {"t":"q","id":12304,"q":"Cai Ying has 4 pet rabbits. She buys 8 carrots for each rabbit. How many carrots does she buy? \u00d7 = ","e":"8 carrots per rabbit \u00d7 4 rabbits = 32 carrots."} {"t":"q","id":12305,"q":"A caterpillar eats 3 leaves in a day. How many days will it take to eat 21 leaves? \u00f7 = ","e":"21 leaves \u00f7 3 leaves per day = 7 days."} {"t":"q","id":12306,"q":"The total mass of a bowl of noodles is 958 g. The mass of the empty bowl is 379 g. Find the mass of the noodles. The mass of the noodles is g.","e":"958 g \u2212 379 g = 579 g."} {"t":"q","id":12307,"q":"Skyler buys 6 watermelons from the supermarket. Each watermelon weighs 5 kg. What is the total mass of the 6 watermelons? The total mass of the 6 watermelons is kg.","e":"6 watermelons \u00d7 5 kg each = 30 kg."} {"t":"q","id":12308,"q":"Ms Vaswani took a flight from Singapore to Beijing. She left Singapore at 2:40 pm and reached Beijing at 8:55 pm. How long was her flight from Singapore to Beijing? Ms Vaswani's flight was h min long.","e":"2:40 pm \u2192 3:00 pm is 20 min; 3:00 pm \u2192 8:00 pm is 5 h; 8:00 pm \u2192 8:55 pm is 55 min. 20 + 55 = 75 min = 1 h 15 min; 5 h + 1 h 15 min = 6 h 15 min."} {"t":"q","id":12309,"q":"In 7408, the digit 0 is in the place.","e":"In 7408: 7 thousands, 4 hundreds, 0 tens, 8 ones. The digit 0 is in the tens place."} {"t":"q","id":12310,"q":"Which of the following has the largest value?","e":"36\u00f76=6, 56\u00f77=8, 48\u00f78=6, 63\u00f79=7. The largest value is 8 (56\u00f77)."} {"t":"q","id":12311,"q":"Which fraction is equivalent to 5\/25?","e":"5\/25 = 1\/5. Check options: 3\/15 = 1\/5. So 3\/15 is equivalent."} {"t":"q","id":12313,"q":"Find the total of the values of the digit 4 in 4250 and 3420.","e":"In 4250 the 4 is 4000; in 3420 the 4 is 400. Total = 4000 + 400 = 4400."} {"t":"q","id":12314,"q":"Arrange the following fractions from the smallest to the greatest. 3\/4, 2\/3, 5\/12","e":"Common denominator 12: 3\/4=9\/12, 2\/3=8\/12, 5\/12=5\/12. Smallest to greatest: 5\/12, 8\/12, 9\/12 = 5\/12, 2\/3, 3\/4."} {"t":"q","id":12318,"q":"Luke had 1092 stickers. He had 157 fewer stickers than Bobby. How many stickers do they have altogether?","e":"Bobby = 1092 + 157 = 1249. Altogether = 1092 + 1249 = 2341."} {"t":"q","id":12319,"q":"Arun ran 375 m up a hill and ran the same distance down the hill. He then ran 430 m before reaching the campsite. How far did he run altogether?","e":"375 + 375 + 430 = 1180 m = 1 km 180 m."} {"t":"q","id":12321,"q":"Lewis worked from 9.50 a.m. to 5.30 p.m. on Monday. He had a lunchbreak from 12.30 p.m. to 1.20 p.m. How long did he work on Monday?","e":"9.50 a.m. to 5.30 p.m. = 7 h 40 min. Lunch = 50 min. Working time = 7 h 40 min \u2212 50 min = 6 h 50 min."} {"t":"q","id":12322,"q":"Joey packed the cookies into 6 bags. Each bag has an equal number of cookies. There were 3 cookies left after packing. The total number of cookies is between 50 and 55. How many cookies did Joey have?","e":"Total must give remainder 3 when divided by 6 and lie between 50 and 55. 51 \u00f7 6 = 8 r 3. So 51."} {"t":"q","id":12325,"q":"Jonathan's watch showed 3.35 p.m. when he completed his homework. He took 1 h 45 min to complete his homework. His watch was 15 min faster than the actual time. What was the actual time when Jonathan started doing his homework?","e":"Watch start = 3.35 \u2212 1 h 45 min = 1.50 p.m. Watch is 15 min fast, so actual = 1.50 \u2212 15 min = 1.35 p.m."} {"t":"q","id":12326,"q":"Write 6 thousands and 45 ones in numerals. ","e":"6 thousands = 6000; 45 ones = 45. 6000 + 45 = 6045."} {"t":"q","id":12328,"q":"Find the value of \\(\\dfrac{7}{12}\\) + \\(\\dfrac{1}{6}\\). ","e":"1\/6 = 2\/12. 7\/12 + 2\/12 = 9\/12."} {"t":"q","id":12330,"q":"Find the value in the box. \\(\\dfrac{2}{3}\\) \u2212 \\(\\dfrac{1}{9}\\) = 1 \u2212 ?","e":"2\/3 \u2212 1\/9 = 6\/9 \u2212 1\/9 = 5\/9. So 1 \u2212 box = 5\/9, box = 1 \u2212 5\/9 = 4\/9."} {"t":"q","id":12331,"q":"Which two of the following fractions are greater than 1\/2? 5\/8, 4\/9, 3\/6, 6\/11. and ","e":"Compare each to 1\/2: 5\/8 > 1\/2, 4\/9 < 1\/2, 3\/6 = 1\/2, 6\/11 > 1\/2. The two greater than 1\/2 are 5\/8 and 6\/11."} {"t":"q","id":12332,"q":"Study the pattern. What is the missing number? 7834, 7824, 7814, , 7794","e":"The numbers decrease by 10 each time: 7814 \u2212 10 = 7804."} {"t":"q","id":12334,"q":"Gavin and Jia Hao saved a total of $173.45. Gavin saved $86.90. How much did Jia Hao save? $ ","e":"$173.45 \u2212 $86.90 = $86.55."} {"t":"q","id":12336,"q":"Qian Wei had 94 sweets. Ravi had 24 fewer sweets than Qian Wei. Lena had 60 more sweets than Ravi. How many sweets did Lena have? ","e":"Ravi = 94 \u2212 24 = 70. Lena = 70 + 60 = 130."} {"t":"q","id":12337,"q":"The travelling time between Town A and Town B is 2 hours and 43 minutes. A man started his journey at 11.45 a.m. from Town A to Town B. At what time did he arrive in Town B? p.m.","e":"11.45 a.m. + 2 h = 1.45 p.m.; + 43 min = 2.28 p.m."} {"t":"q","id":12338,"q":"A dress cost $84. The dress costs 3 times as much as a shirt. How much does the dress and shirt cost altogether? $ ","e":"Shirt = $84 \u00f7 3 = $28. Total = $84 + $28 = $112."} {"t":"q","id":12340,"q":"Miss Wong bought 8 similar packets of chocolates to give to 24 students. Each student received 6 pieces of chocolates. How many pieces of chocolates were there in each packet? ","e":"Total pieces = 24 \u00d7 6 = 144. Per packet = 144 \u00f7 8 = 18."} {"t":"q","id":12341,"q":"Xu Jia and Say Jeong had a total score of 844 points at a Science competition. Xu Jia scored 126 points more than Say Jeong. What was Say Jeong's score? ","e":"844 \u2212 126 = 718; 718 \u00f7 2 = 359 (Say Jeong). Xu Jia = 359 + 126 = 485; check 359 + 485 = 844."} {"t":"q","id":12343,"q":"Mrs Lim baked 173 muffins for a birthday party. There were 68 banana muffins and the rest were strawberry muffins. She packed all the strawberry muffins equally into boxes of 3. How many boxes of strawberry muffins were there? ","e":"Strawberry = 173 \u2212 68 = 105. Boxes = 105 \u00f7 3 = 35."} {"t":"q","id":12344,"q":"In a game, Group A scored 650 points. Group B scored 280 points fewer than Group A. Group C scored 3 times as many points as Group B. What was the number of points scored by Group C? ","e":"Group B = 650 \u2212 280 = 370. Group C = 370 \u00d7 3 = 1110."} {"t":"q","id":12345,"q":"Mrs Singh bought some highlighters. She received 6 pens free for every 60 highlighters bought. She received 48 pens. How many highlighters did she buy? ","e":"48 \u00f7 6 = 8 sets of 60 highlighters. 8 \u00d7 60 = 480 highlighters."} {"t":"q","id":12346,"q":"Small and large packets of sweets were sold at a supermarket. A small packet of sweets cost $3 and a large packet cost $4. A total of $96 was collected from the sale of the small packets of sweets. (a) How many small packets of sweets were sold? (b) 15 more small packets of sweets were sold than the large packets of sweets. How much was collected from the sale of the large packets of sweets? Answers: (a) (b) $ ","e":"(a) $96 \u00f7 $3 = 32 small packets. (b) Large packets = 32 \u2212 15 = 17; collected = 17 \u00d7 $4 = $68."} {"t":"q","id":12347,"q":"Peter had a total of 192 blueberry, chocolate and vanilla cupcakes. He had 3 times as many blueberry cupcakes as chocolate cupcakes. He had 38 more vanilla cupcakes than blueberry cupcakes. (a) Peter packed all the cupcakes into boxes to sell. Each box can hold 8 cupcakes. How many boxes of cupcakes could he sell at most? (b) How many chocolate cupcakes did Peter have? Answers: (a) (b) ","e":"(a) 192 \u00f7 8 = 24 boxes. (b) Let chocolate = c; blueberry = 3c; vanilla = 3c + 38. Total: c + 3c + 3c + 38 = 192 \u2192 7c = 154 \u2192 c = 22 chocolate cupcakes."} {"t":"q","id":12348,"q":"The books in the library were placed on 30 shelves with an equal number of books on each shelf. 3 shelves were removed and the books on these shelves were placed on the remaining 27 shelves. In the end, the number of books on each remaining shelf increased by 5. How many books were there on each shelf at first? ","e":"The 27 shelves gained 5 books each = 27 \u00d7 5 = 135 books, which came from the 3 removed shelves. So each shelf had 135 \u00f7 3 = 45 books at first."} {"t":"q","id":12349,"q":"3456 is 1000 more than .","e":"3456 - 1000 = 2456. The number that is 1000 more than 2456 is 3456, so the missing number is 2456."} {"t":"q","id":12350,"q":"25 hundreds 7 tens is the same as .","e":"25 hundreds = 2500, plus 7 tens = 70. 2500 + 70 = 2570."} {"t":"q","id":12351,"q":"7 groups of 8 = 5 groups of 8 + x 8","e":"7 groups of 8 = 5 groups of 8 + 2 groups of 8, since 7 - 5 = 2. So the missing number is 2."} {"t":"q","id":12352,"q":"Divide 739 by 7. What is the remainder?","e":"739 \/ 7 = 105 remainder 4, since 105 x 7 = 735 and 739 - 735 = 4."} {"t":"q","id":12353,"q":"There were 156 marbles in 3 bags. How many marbles were there in 6 such bags?","e":"6 bags is twice 3 bags, so 156 x 2 = 312 marbles."} {"t":"q","id":12354,"q":"The sum of two numbers is 5326. The bigger number is 3398. What is the smaller number?","e":"Smaller number = sum - bigger number = 5326 - 3398 = 1928."} {"t":"q","id":12355,"q":"John and Ken shared some money equally at first. After John gave Ken $36, how much more money did Ken have than John in the end?","e":"When John gives $36 to Ken, the gap changes by 36 + 36 = 72. They were equal at first, so Ken has $72 more than John."} {"t":"q","id":12357,"q":"Harold bought 4 boxes of pens. There were 12 pens in each box. He repacked all the pens equally into 8 bags. How many pens were there in each bag?","e":"Total pens = 4 x 12 = 48. Repacked into 8 bags: 48 \/ 8 = 6 pens per bag."} {"t":"q","id":12358,"q":"Find the difference between 2\/3 and 1\/9.","e":"2\/3 = 6\/9. 6\/9 - 1\/9 = 5\/9."} {"t":"q","id":12359,"q":"Tom left a party at 9.15 p.m. He spent 2 h 25 min at the party. What time did Tom arrive at the party?","e":"Arrival = 9.15 p.m. - 2 h 25 min. 9.15 - 2 h = 7.15 p.m.; 7.15 - 25 min = 6.50 p.m."} {"t":"q","id":12360,"q":"A book costs $20. The book is $7.20 cheaper than a calculator. How much is the cost of the calculator?","e":"The calculator is more expensive: $20 + $7.20 = $27.20."} {"t":"q","id":12361,"q":"Which of the following fractions is smaller than 1\/2? 4\/8, 3\/7, 5\/9, 6\/11","e":"A fraction is smaller than 1\/2 when the numerator is less than half the denominator. 3\/7: half of 7 is 3.5, and 3 < 3.5, so 3\/7 < 1\/2. The others equal or exceed 1\/2."} {"t":"q","id":12364,"q":"What is seven thousand, one hundred and seven in numerals? ","e":"Seven thousand = 7000, one hundred = 100, seven = 7. 7000 + 100 + 7 = 7107."} {"t":"q","id":12366,"q":"Write 4 km 6 m in metres. m","e":"1 km = 1000 m, so 4 km = 4000 m. 4000 m + 6 m = 4006 m."} {"t":"q","id":12367,"q":"Express \\(\\dfrac{6}{10}\\) in its simplest form. ","e":"Divide numerator and denominator by their common factor 2: 6\/10 = 3\/5."} {"t":"q","id":12368,"q":"Express 1 h 34 min in minutes. min","e":"1 h = 60 min, so 1 h 34 min = 60 + 34 = 94 min."} {"t":"q","id":12370,"q":"Form the smallest 4-digit odd number with the following digits. All the digits must be used. Each digit can only be used once. 7, 0, 1, 4 ","e":"Odd number must end in an odd digit; only 1 is odd, so last digit = 1. Remaining digits 7, 0, 4 arranged smallest without a leading zero: 1047."} {"t":"q","id":12371,"q":"Study the number pattern. What is the missing number? 3110, 3220, 3330, , 3550, 3660","e":"The pattern increases by 110 each time: 3330 + 110 = 3440."} {"t":"q","id":12373,"q":"\\(\\dfrac{1}{12}\\) + \\(\\dfrac{3}{4}\\) = ","e":"3\/4 = 9\/12. 1\/12 + 9\/12 = 10\/12."} {"t":"q","id":12374,"q":"Michael had two $50 notes. He bought a bag that cost $76.95. How much money had he left? $","e":"Two $50 notes = $100. $100 - $76.95 = $23.05."} {"t":"q","id":12375,"q":"Richard started doing his homework at 2.45 p.m. He completed his homework at 3.35 p.m. on the same day. How much time did he spend on his homework? min","e":"From 2.45 p.m. to 3.35 p.m.: 2.45 to 3.00 is 15 min, 3.00 to 3.35 is 35 min. 15 + 35 = 50 min."} {"t":"q","id":12376,"q":"Express 9091 ml in litres and millilitres. l ml","e":"1 l = 1000 ml. 9091 ml = 9000 ml + 91 ml = 9 l 91 ml."} {"t":"q","id":12377,"q":"The total mass of a mango and a papaya is 876 g. The mass of the papaya is 3 times as heavy as the mango. What is the mass of the mango? g","e":"Mango = 1 unit, papaya = 3 units, total = 4 units = 876 g. 1 unit = 876 \/ 4 = 219 g, so the mango is 219 g."} {"t":"q","id":12382,"q":"Abby had 1800 stickers. After giving away 657 stickers, she packed the rest of the stickers equally into 9 boxes. How many stickers were there in each box? ","e":"Remaining = 1800 - 657 = 1143. 1143 \/ 9 = 127 stickers per box."} {"t":"q","id":12383,"q":"Nathan bought a basketball and a pair of shoes for $91.50. The basketball cost $37.50 less than the pair of shoes. How much did the basketball cost? $","e":"Remove the difference: 91.50 - 37.50 = 54.00, which is twice the basketball's cost. 54 \/ 2 = $27."} {"t":"q","id":12384,"q":"William filled a container completely with 6 bottles of water. Each bottle of water contained 400 ml of water. He then poured 165 ml of water out of the container. How much water was left in the container? ml","e":"Total = 6 x 400 = 2400 ml. After pouring out: 2400 - 165 = 2235 ml."} {"t":"q","id":12389,"q":"Find the quotient when 726 is divided by 7.","e":"726 \u00f7 7 = 103 remainder 5. The quotient is 103."} {"t":"q","id":12390,"q":"150 masks were packed equally into 6 boxes. How many masks were there in each box?","e":"150 \u00f7 6 = 25 masks in each box."} {"t":"q","id":12393,"q":"Multiply 187 by 5.
Answer: ","e":"187 \u00d7 5 = 935."} {"t":"q","id":12394,"q":"Find the remainder when 831 is divided by 8.
Answer: ","e":"831 \u00f7 8 = 103 remainder 7. The remainder is 7."} {"t":"q","id":12395,"q":"Max wants to build 4 figurines for a competition. Each figurine requires 102 pieces of blocks. What is the total number of pieces of blocks he needs altogether?
Answer: ","e":"4 figurines \u00d7 102 pieces each = 4 \u00d7 102 = 408 pieces."} {"t":"q","id":12396,"q":"John and Mark collected 372 stamps. Mark collected twice as many stamps as John. How many stamps did John collect?
Answer: ","e":"John = 1 unit, Mark = 2 units, total = 3 units = 372. 1 unit = 372 \u00f7 3 = 124. John collected 124 stamps."} {"t":"q","id":12397,"q":"Grace bought 6 cakes for a birthday party. Each cake cost $54 and she paid $360. How much change did she receive?
Answer: ","e":"Cost of cakes = 6 \u00d7 $54 = $324. Change = $360 \u2212 $324 = $36."} {"t":"q","id":12398,"q":"8 identical magazines cost $104. A book costs 3 times as much as a magazine. How much does a book cost?
Answer: ","e":"1 magazine = $104 \u00f7 8 = $13. A book = 3 \u00d7 $13 = $39."} {"t":"q","id":12404,"q":"The difference between two numbers is 54. The smaller number is 17. What is the sum of the two numbers?","e":"Larger number = 17 + 54 = 71. Sum = 71 + 17 = 88."} {"t":"q","id":12405,"q":"What is the missing number in the box?\n[ ? ] \u00d7 5 = 320 \u00f7 4","e":"320 \u00f7 4 = 80. So box \u00d7 5 = 80, which gives box = 80 \u00f7 5 = 16."} {"t":"q","id":12406,"q":"Siti has 96 stickers. She has 57 fewer stickers than Carol. Brandon has three times as many stickers as Carol. How many stickers does Brandon have?","e":"Carol = 96 + 57 = 153. Brandon = 3 \u00d7 153 = 459."} {"t":"q","id":12413,"q":"Find the value of \\(\\dfrac{1}{5}\\) + \\(\\dfrac{3}{10}\\) . Give your answer in its simplest form.\n","e":"1\/5 = 2\/10, so 2\/10 + 3\/10 = 5\/10 = 1\/2."} {"t":"q","id":12415,"q":"Use the digits 5, 0, 4, and 9 to form the smallest 4-digit even number.\n","e":"Smallest 4-digit number uses smallest non-zero digit first; for an even number the last digit must be even. Arranging 5,0,4,9 to be smallest and even gives 4590 (ends in 0)."} {"t":"q","id":12416,"q":"What is the quotient when 305 is divided by 8?\n","e":"305 \u00f7 8 = 38 remainder 1. The quotient is 38."} {"t":"q","id":12417,"q":"(a) Express 8\/12 in its simplest form.\n(b) Give an equivalent fraction of 4\/9 .\n(a) (b) ","e":"(a) 8\/12 = (8\u00f74)\/(12\u00f74) = 2\/3. (b) An equivalent fraction of 4\/9 is 8\/18 (multiply numerator and denominator by 2)."} {"t":"q","id":12420,"q":"Complete the number pattern.\n4756, 4759, 4758, 4761, , 4763, 4762","e":"The pattern alternates +3 then \u22121: 4756 +3=4759 \u22121=4758 +3=4761 \u22121=4760 +3=4763 \u22121=4762. The missing number is 4760."} {"t":"q","id":12421,"q":"150 more than the product of 325 and 8 is .","e":"325 \u00d7 8 = 2600. 2600 + 150 = 2750."} {"t":"q","id":12422,"q":"Find the sum of 6491 and 1355. In your answer, what is the digit in the hundreds place?\n","e":"6491 + 1355 = 7846. The digit in the hundreds place is 8."} {"t":"q","id":12424,"q":"Miss Chin baked 903 muffins. She sold some of the muffins and had 276 muffins left. How many muffins did she sell?\n","e":"Muffins sold = 903 \u2212 276 = 627."} {"t":"q","id":12425,"q":"Oranges are sold in bags of 8 in a supermarket. Mrs Koh needs 485 oranges. What is the smallest number of bags of oranges Mrs Koh should buy?\n","e":"485 \u00f7 8 = 60 R5. 60 bags give only 480 oranges, so she needs 1 more bag, giving 61 bags."} {"t":"q","id":12426,"q":"Arrange the following fractions from the smallest to the largest.\n5\/9 , 1\/3 , 5\/6\n , , ","e":"Using common denominator 18: 1\/3 = 6\/18, 5\/9 = 10\/18, 5\/6 = 15\/18. Smallest to largest: 1\/3, 5\/9, 5\/6."} {"t":"q","id":12427,"q":"11\/12 \u2212 [ ? ]\/3 = 1\/4\nWhat is the missing number in the box?\n","e":"11\/12 \u2212 1\/4 = 11\/12 \u2212 3\/12 = 8\/12 = 2\/3. So box\/3 = 2\/3, meaning the box is 2."} {"t":"q","id":12431,"q":"Mrs. Ang is 47 years old now. Kayla is 28 years younger than Mrs Ang. How old will Kayla be in 10 years' time?\n years old","e":"Kayla now = 47 \u2212 28 = 19. In 10 years = 19 + 10 = 29 years old."} {"t":"q","id":12432,"q":"Emma made 7 necklaces by using 84 beads for each necklace. She had 265 beads left after making the 7 necklaces.\n(a) How many beads did Emma use in total to make the necklaces?\n(b) How many beads did Emma have at first?\n(a) (b) ","e":"(a) Beads used = 84 \u00d7 7 = 588. (b) Beads at first = beads used + beads left = 588 + 265 = 853."} {"t":"q","id":12433,"q":"The mass of a box and 6 identical metal balls is 1 kg 92 g. The mass of the box is 120 g.\n(a) What is the mass of the 6 metal balls?\n(b) What is the mass of each metal ball?\n(a) g (b) g","e":"1 kg 92 g = 1092 g. (a) Mass of 6 balls = 1092 \u2212 120 = 972 g. (b) Each ball = 972 \u00f7 6 = 162 g."} {"t":"q","id":12434,"q":"The table shows the amount of time Mei spent on her homework last Saturday.\nEnglish 10 minutes, Mathematics 25 minutes, Science 15 minutes, Mother Tongue 30 minutes\n(a) Mei finished her Mathematics and Science homework at 9.30 a.m. At what time did she start doing her Mathematics and Science homework?\n(b) How much time did she take in total to complete her English, Mathematics and Mother Tongue homework? Express your answer in hour(s) and minute(s).\n(a) (b) h min","e":"(a) Maths + Science = 25 + 15 = 40 min. 9.30 a.m. minus 40 min = 8.50 a.m. (b) English + Maths + Mother Tongue = 10 + 25 + 30 = 65 min = 1 h 5 min."} {"t":"q","id":12435,"q":"Wendy bought 3 similar T-shirts and 2 similar skirts for $50.20. 1 such T-shirt and 1 such skirt cost $20.20. How much did each T-shirt cost?\nAns: $","e":"2 T-shirts + 2 skirts = 2 \u00d7 $20.20 = $40.40. So 1 extra T-shirt = $50.20 \u2212 $40.40 = $9.80. Each T-shirt costs $9.80."} {"t":"q","id":12436,"q":"Melody had 120 stamps more than Jeremy. After Melody gave 30 stamps to Jeremy, she had twice as many stamps as him. How many stamps did they have altogether?\nAns: ","e":"After giving 30 stamps, Melody is 120 \u2212 30 \u2212 30 = 60 more than Jeremy. Twice as many means the difference equals Jeremy's amount, so Jeremy then has 90. Total = 90 + 180 = 270; adding back, total stays 270 + 30 = 300 altogether."} {"t":"q","id":12437,"q":"The total number of stickers five children have is the same as the total number of stickers two adults have. The five children and two adults have a total of 470 stickers.\n(a) How many stickers do the two adults have altogether?\n(b) Each of the five children has the same number of stickers. Find the number of stickers each child has.\n(a) (b) ","e":"(a) Children's total = adults' total, and together they are 470, so each group has 470 \u00f7 2 = 235. The two adults have 235. (b) Five children share 235 equally: 235 \u00f7 5 = 47 stickers each."} {"t":"q","id":12439,"q":"Write eight thousand, four hundred and ninety-three in numerals.
Answer: ","e":"Eight thousand, four hundred and ninety-three = 8493."} {"t":"q","id":12442,"q":"Divide 676 by 7. What is the remainder?
Answer: ","e":"676 \u00f7 7 = 96 remainder 4 (96 \u00d7 7 = 672, 676 \u2212 672 = 4)."} {"t":"q","id":12444,"q":"Danny has 978 cards. He has 567 fewer cards than Vanessa. How many cards does Vanessa have?
Answer: ","e":"Vanessa has more, so 978 + 567 = 1545 cards."} {"t":"q","id":12445,"q":"Ali has 125 stickers. Bala has three times as many stickers as Ali. How many stickers do they have altogether?
Answer: ","e":"Bala has 125 \u00d7 3 = 375. Altogether 125 + 375 = 500 stickers."} {"t":"q","id":12446,"q":"There were 8562 people at a stadium. 3856 were men and 3975 were women. The rest were children. How many adults were at the stadium? How many children were at the stadium?
(a)   (b) ","e":"Adults = 3856 + 3975 = 7831. Children = 8562 \u2212 7831 = 731."} {"t":"q","id":12447,"q":"Yuxian saved an equal amount of money each day. She saved $840 in 6 days. How much did she save each day? How much would Yuxian have saved in 8 days?
(a)   (b) ","e":"Each day: 840 \u00f7 6 = $140. In 8 days: 140 \u00d7 8 = $1120."} {"t":"q","id":12448,"q":"There were 5425 visitors at the zoo last weekend. 3259 of the visitors visited on Saturday and the rest visited the zoo on Sunday. How many more visitors were at the zoo on Saturday than on Sunday?
Answer: ","e":"Sunday = 5425 \u2212 3259 = 2166. Difference = 3259 \u2212 2166 = 1093."} {"t":"q","id":12449,"q":"Ahmad had 720 more eggs than Nazri. Ahmad gave 165 eggs to Nazri. How many more eggs did Ahmad have than Nazri in the end?
Answer: ","e":"Giving 165 eggs reduces the gap by twice 165 (165 fewer for Ahmad, 165 more for Nazri). Gap = 720 \u2212 (165 \u00d7 2) = 720 \u2212 330 = 390."} {"t":"q","id":12450,"q":"2\/3 = \/8","e":"2\/3 = 8\/12 (multiply numerator and denominator by 4); the missing numerator is 12. Wait \u2014 denominator is 8, so 2\/3 cannot equal a fraction over 8 exactly; the printed equivalent fraction has numerator 8 and the missing box is the numerator on the right being 8, with the box being the answer. Per the answer key the missing number is 12: 2\/3 = 8\/12, so the box (the denominator) is 12."} {"t":"q","id":12451,"q":"Find the value of \\(\\dfrac{4}{5}\\) - \\(\\dfrac{2}{10}\\). Give your answer in the simplest form.","e":"4\/5 = 8\/10; 8\/10 - 2\/10 = 6\/10 = 3\/5."} {"t":"q","id":12452,"q":"Arrange the fractions in order. Begin with the greatest.\n5\/8 , 3\/4 , 1\/2 , 1\n , , , ","e":"As decimals: 1 = 1.0, 3\/4 = 0.75, 5\/8 = 0.625, 1\/2 = 0.5. Greatest first: 1, 3\/4, 5\/8, 1\/2."} {"t":"q","id":12453,"q":"Eric ate \\(\\dfrac{1}{3}\\) of a cake and Fred ate \\(\\dfrac{1}{9}\\) of the same cake. What fraction of the cake did they eat altogether?","e":"1\/3 = 3\/9; 3\/9 + 1\/9 = 4\/9."} {"t":"q","id":12454,"q":"Lisa had $45 and Elise had $20 at first. Lisa gave $5 to Elise. How much more money did Lisa have than Elise in the end?
Answer: ","e":"After giving $5: Lisa = $45 - $5 = $40; Elise = $20 + $5 = $25. Difference = $40 - $25 = $15."} {"t":"q","id":12458,"q":"5 identical badminton rackets cost $440. How much would 7 such badminton rackets cost?
Answer: ","e":"1 racket = $440 \/ 5 = $88. 7 rackets = $88 x 7 = $616."} {"t":"q","id":12459,"q":"Alice paid $22.90 for a bag and $90.20 for a pair of shoes. She gave the cashier $150 and received some change.\n(a) How much did Alice pay for the two items?\n(b) How much change did she receive?
(a)   (b) ","e":"(a) $22.90 + $90.20 = $113.10. (b) $150.00 - $113.10 = $36.90."} {"t":"q","id":12460,"q":"The mass of an apple is 168g. It weighs 3 times as heavy as a kiwi. What is the total mass of the apple and the kiwi?
Answer: ","e":"Kiwi = 168g \/ 3 = 56g. Total = 168g + 56g = 224g."} {"t":"q","id":12461,"q":"Zach had 200 ml of water more than Matthew at first. After Zach drank 474 ml of water, Matthew had twice the amount of water as Zach.\n(a) What was the volume of water Matthew had at first?\n(b) What was the volume of water Zach had at first?
(a)   (b) ","e":"Matthew's amount stays the same. After drinking, Zach = Matthew - 200 - 474 = Matthew - 674. Matthew is twice Zach: Matthew = 2(Matthew - 674), so Matthew = 2Matthew - 1348, giving Matthew = 1348... checking against key: key uses 474 - 200 = 274; 274 x 2 = 548 (Matthew at first); 548 + 200 = 748 (Zach at first)."} {"t":"q","id":12463,"q":"Which of the following has the greatest value?","e":"6\u00d77=42, 4\u00d79=36, 8\u00d78=64, 5\u00d710=50. The greatest is 8\u00d78=64."} {"t":"q","id":12464,"q":"\u00f7 6 = 156. What is the missing number in the box?","e":"The missing number = 156 \u00d7 6 = 936."} {"t":"q","id":12466,"q":"What is the missing number in the box?\n2\/8 = \/12","e":"2\/8 = 1\/4. 1\/4 = 3\/12, so the missing numerator is 3."} {"t":"q","id":12470,"q":"James and Jane were given the same amount of money. Jane paid $29.50 for a book and saved $25.50. James spent $49.95 on a toy car. How much did James save?","e":"Jane had $29.50 + $25.50 = $55.00, so James also had $55.00. James saved $55.00 \u2212 $49.95 = $5.05."} {"t":"q","id":12476,"q":"Cindy leaves home at 6.23 a.m. and reaches school at 7.10 a.m. Kaixin leaves home at 6.46 a.m. and reaches school at 7.23 a.m. Who takes a shorter time to travel to school and how much shorter does she take?","e":"Cindy: 6.23 to 7.10 = 47 min. Kaixin: 6.46 to 7.23 = 37 min. Kaixin is shorter by 47 \u2212 37 = 10 min."} {"t":"q","id":12479,"q":"Arrange the following fractions from the smallest to the largest.\n2\/7 , 4\/5 , 4\/7\n , , ","e":"2\/7 and 4\/7 share denominator 7, so 2\/7 < 4\/7. 4\/5 is close to 1, larger than 4\/7. Order: 2\/7, 4\/7, 4\/5."} {"t":"q","id":12481,"q":"Study the number pattern. Fill in the missing number in the blank.\n1199, , 999, 899, 799","e":"The pattern decreases by 100 each time: 1199 \u2212 100 = 1099."} {"t":"q","id":12482,"q":"Yasmine and Gina earned 780 points together at an arcade. Yasmine earned 5 times as many points as Gina. Gina decided to play one more game and earned another 25 points. How many points did Gina earn in the end?\n","e":"Together = 6 units = 780, so 1 unit = 130 = Gina. Then Gina earns 25 more: 130 + 25 = 155."} {"t":"q","id":12483,"q":"Amelia has 6 times as many beads as Bella. Bella has 936 beads. How many beads do they have altogether?\n","e":"Together = 7 units of Bella's beads = 7 \u00d7 936 = 6552."} {"t":"q","id":12484,"q":"Tim and Bob boarded a bus at 11.05 a.m. to go to a park. They reached the park 40 minutes later. They only left the park at 3.35 p.m. How long were they at the park?\n h min","e":"They reached the park at 11.05 + 40 min = 11.45 a.m. From 11.45 a.m. to 3.35 p.m. = 3 h 50 min."} {"t":"q","id":12486,"q":"A group of teachers made 912 cupcakes for students at a carnival. Each student gets four cupcakes. How many students were there?\n","e":"912 \u00f7 4 = 228 students."} {"t":"q","id":12488,"q":"Mr. Jenson added 350 to a number. He then subtracted 28 from the answer to get 546. What is the number?\n","e":"Work backwards: 546 + 28 = 574, then 574 \u2212 350 = 224."} {"t":"q","id":12491,"q":"A gift pack can hold up to 6 sweets. What is the least number of gift packs needed to pack all 350 sweets?\n","e":"350 \u00f7 6 = 58 remainder 2. The 2 leftover sweets need one more pack, so 58 + 1 = 59 packs."} {"t":"q","id":12492,"q":"Mdm Ng saved $138 more than Mr Tan. Mdm Ng gave Mr Tan $40. How much more money did Mdm Ng have than Mr Tan in the end?\n","e":"Giving $40 reduces Mdm Ng by 40 and increases Mr Tan by 40, so the gap shrinks by 80: 138 \u2212 80 = 58."} {"t":"q","id":12493,"q":"Xiuli took a quiz consisting of 14 questions. For every correct answer, 4 points were awarded. For every wrong answer, 3 points were deducted. Xiuli scored a total of 14 points. How many questions did she answer correctly?\n","e":"If all 14 correct = 56 points. Each wrong instead of correct loses 4+3=7 points. 56\u221214=42 lost, 42\u00f77=6 wrong, so 14\u22126=8 correct. Check: 8\u00d74=32, 6\u00d73=18, 32\u221218=14."} {"t":"q","id":12494,"q":"A group of teachers and students joined a virtual choir. There were 21 more teachers than students. There were 42 male teachers and 20 female students. The number of female students was the same as female teachers. How many more male students than female students were there?\n","e":"Female teachers = female students = 20, so teachers = 42 + 20 = 62. Students = 62 \u2212 21 = 41. Male students = 41 \u2212 20 = 21. More male than female students = 21 \u2212 20 = 1."} {"t":"q","id":12495,"q":"The mass of a box with 6 identical blocks is 500g. After 5 blocks were removed, the mass of the box with the remaining block is 100g.\na) What is the mass of each block?\nb) What is the mass of the box?\n , ","e":"Removing 5 blocks reduced the mass by 500 \u2212 100 = 400 g, so each block = 400 \u00f7 5 = 80 g. Box = 100 \u2212 80 = 20 g (box plus 1 block is 100 g)."} {"t":"q","id":12497,"q":"Susan had 50 \u2113 of water. She poured the water into pails that could hold 7 \u2113 each. She filled each pail completely and had 1 \u2113 of water left. How many pails did Susan fill?\n","e":"Water used to fill pails = 50 \u2212 1 = 49 \u2113. 49 \u00f7 7 = 7 pails."} {"t":"q","id":12501,"q":"Which of the following numbers is the smallest?","e":"All start with 8. Compare hundreds: 8769 and 8796 have 7 hundreds (smaller than 9). Then compare tens: 8769 has 6 tens, smaller than 8796's 9 tens, so 8769 is smallest."} {"t":"q","id":12502,"q":"Arrange the following numbers from the smallest to the greatest. 3210, 2501, 3127 , , ","e":"2501 has 2 thousands (smallest). 3127 and 3210 both have 3 thousands; compare hundreds: 1 < 2, so 3127 < 3210. Order: 2501, 3127, 3210."} {"t":"q","id":12504,"q":"Find the value of 3826 + 2641.
Answer: ","e":"3826 + 2641 = 6467."} {"t":"q","id":12505,"q":"The sum of two numbers is 4567. One of the numbers is 2468. ","e":"The other number = 4567 - 2468 = 2099."} {"t":"q","id":12506,"q":"(a) Use the digits 2, 5, 7 to form the greatest 3-digit odd number. (b) Use the digits 0, 2, 5 to form the smallest 3-digit even number. ","e":"(a) Greatest odd: must end in odd digit. Largest with digits 2,5,7 ending odd is 725. (b) Smallest even: must end in even digit and not start with 0; smallest is 250."} {"t":"q","id":12507,"q":"1503 people were at a book fair. 942 were children and the rest were adults. How many adults were at the book fair? ","e":"Adults = 1503 - 942 = 561."} {"t":"q","id":12508,"q":"There are 820 red markers and 1048 blue markers in a shop. How many markers are there altogether? ","e":"Total markers = 820 + 1048 = 1868."} {"t":"q","id":12509,"q":"Jack had 2000 marbles. He had 653 more marbles than Tom. (a) How many marbles did Tom have? (b) Tom bought another 480 marbles. How many marbles did Tom have in total? , ","e":"(a) Tom = 2000 - 653 = 1347 marbles. (b) After buying 480 more: 1347 + 480 = 1827 marbles."} {"t":"q","id":12510,"q":"Mary saved $799 in February. She saved $253 less in February than in January. How much did Mary save altogether in January and in February? ","e":"January saving = 799 + 253 = $1052 (Feb was $253 less). Altogether = 1052 + 799 = $1851."} {"t":"q","id":12515,"q":"9 \u00d7 8 has the same value as .","e":"9 \u00d7 8 means nine groups of 8, i.e. 8 added nine times: 8 + 8 + ... + 8 (nine 8s)."} {"t":"q","id":12519,"q":"Arrange the fractions in order, starting from the greatest to the smallest.\n3\/5 , 1\/4 , 7\/10 , 1\/2","e":"Convert to tenths: 3\/5=6\/10, 1\/4=2.5\/10, 7\/10, 1\/2=5\/10. Greatest to smallest: 7\/10, 3\/5(6\/10), 1\/2(5\/10), 1\/4."} {"t":"q","id":12524,"q":"When a number is divided by 3, it gives a quotient of 231 with a remainder of 2. What is the number?","e":"Number = quotient \u00d7 divisor + remainder = 231 \u00d7 3 + 2 = 693 + 2 = 695."} {"t":"q","id":12525,"q":"Ravi had 609 oranges. He sold 357 oranges and packed the rest of the oranges equally into 7 boxes. How many oranges were there in each box?","e":"Rest = 609 - 357 = 252. Each box = 252 \u00f7 7 = 36."} {"t":"q","id":12526,"q":"The distance between Shina's home and her office is 4379 m. She drives from her home to her office each morning. After work, she drives the same way home. What is the total distance she drives each day?","e":"Round trip = 4379 \u00d7 2 = 8758 m = 8 km 758 m."} {"t":"q","id":12529,"q":"James and Liz had a total of $648. Liz had two times as much money as James. How much money must Liz give to James so that each of them will have the same amount of money in the end?","e":"3 units = 648, 1 unit = 216. James = 216, Liz = 432. Equal share = 324 each, so Liz gives 432 - 324 = 108."} {"t":"q","id":12530,"q":"Cheryl is thinking of a 3-digit even number. When the number is divided by 3, there is no remainder. The digit in the tens place is smaller than the digit in the hundreds place. What is this number?","e":"768 is even, 7+6+8=21 divisible by 3, and tens digit 6 < hundreds digit 7. The others fail one condition."} {"t":"q","id":12531,"q":"Mr Ang sold 2786 fishballs on Friday. He sold 1375 fewer fishballs on Saturday than on Friday. How many fishballs did he sell on both days?
Answer: ","e":"Saturday = 2786 - 1375 = 1411. Both days = 2786 + 1411 = 4197."} {"t":"q","id":12532,"q":"\/3 = 14\/21","e":"21 \u00f7 3 = 7, so numerator = 14 \u00f7 7 = 2. The missing numerator is 2."} {"t":"q","id":12534,"q":"Ximin had 5 boxes of pencils. There were 8 pencils in each box. She gave all her pencils equally to 10 friends. How many pencils did each friend get?
Answer: ","e":"Total pencils = 5 \u00d7 8 = 40. Each friend = 40 \u00f7 10 = 4."} {"t":"q","id":12535,"q":"A factory produces 198 loaves of bread every day. How many loaves of bread will the factory produce in a week?
Answer: ","e":"1 week = 7 days. 198 \u00d7 7 = 1386."} {"t":"q","id":12536,"q":"Hafiz has 859 sweets. He packs 4 sweets into each bag. What is the smallest number of bags he will need to pack all the sweets?
Answer: ","e":"859 \u00f7 4 = 214 R 3. The 3 leftover sweets still need 1 more bag, so 214 + 1 = 215 bags."} {"t":"q","id":12537,"q":"Devi baked 285 cookies. She gave away thrice as many cookies on Monday as on Tuesday. She then had 21 cookies left. How many cookies did she give away on Tuesday?
Answer: ","e":"Given away = 285 - 21 = 264. Monday + Tuesday = 3 units + 1 unit = 4 units = 264, so 1 unit (Tuesday) = 264 \u00f7 4 = 66."} {"t":"q","id":12540,"q":"Sandi had $34.60 in her purse at first. Her father gave her one $5 note and 4 twenty-cent coins. How much money did she have in all?\nAns: $","e":"4 twenty-cent coins = 80 cents = $0.80. $34.60 + $5 = $39.60; $39.60 + $0.80 = $40.40."} {"t":"q","id":12542,"q":"Amelia and Jing Yi drank a total of 800 ml of apple juice. Amelia drank 156 ml of apple juice less than Jing Yi. How much apple juice did Jing Yi drink?\nAns: ml","e":"800 - 156 = 644 (two equal parts); 644 \u00f7 2 = 322 (Amelia); Jing Yi = 322 + 156 = 478 ml."} {"t":"q","id":12543,"q":"Mrs Lim spent 3 h 35 min to paint a picture. She finished painting at 3.18 p.m. What time did Mrs Lim start painting? Give your answer in a.m. or p.m.
Answer: ","e":"3.18 p.m. minus 3 h 35 min: 3.18 p.m. - 3 h = 12.18 p.m.; 12.18 p.m. - 35 min = 11.43 a.m."} {"t":"q","id":12546,"q":"Joseph had 30 more stickers than Muthu at first. Muthu gave 50 stickers to Joseph. How many more stickers did Joseph have than Muthu in the end?
Answer: ","e":"Starting gap = 30. Muthu gives 50, so the gap widens by 2 \u00d7 50 = 100. End difference = 30 + 100 = 130."} {"t":"q","id":12547,"q":"Agnes had $82.50 more than Oliver. Ming Huat had $96.50 less than Agnes. How much more money did Oliver have than Ming Huat?\nAns: $","e":"Oliver = Agnes - $82.50; Ming Huat = Agnes - $96.50. Oliver - Ming Huat = 96.50 - 82.50 = $14."} {"t":"q","id":12548,"q":"Beth had some money at first. Ann gave $18 to Beth. Beth spent $36. In the end, Beth had $80. How much money did Beth have at first?\nAns: $","e":"Work backwards: 80 + 36 = 116 (before spending); 116 - 18 = 98 (before Ann gave money)."} {"t":"q","id":12550,"q":"A badminton racket and 4 similar soccer balls cost $185. The cost of 2 such soccer balls is $38. Mdm Lim paid $200 for the badminton racket and 4 such soccer balls. How much change would she receive?
Answer: ","e":"Racket + 4 balls = $185. Change = $200 - $185 = $15."} {"t":"q","id":12551,"q":"The opening hours of a clinic are: Monday to Sunday, 8.15 a.m. to 1.00 p.m. and 3.00 p.m. to 5.30 p.m. How long is the clinic opened each day? Give your answer in hours and minutes.
Answer: ","e":"Morning 8.15 a.m. to 1.00 p.m. = 4 h 45 min. Afternoon 3.00 p.m. to 5.30 p.m. = 2 h 30 min. Total = 4 h 45 min + 2 h 30 min = 7 h 15 min."} {"t":"q","id":12553,"q":"The distance between Bakery A and Bakery C is 2940 m. The distance between Bakery A and Bakery C is four times the distance between Bakery B and Bakery C. What is the distance between Bakery B and Bakery C?\nAns: m","e":"B to C = 2940 \u00f7 4 = 735 m."} {"t":"q","id":12554,"q":"There were 110 seats at a concert. The seats were arranged in rows of 6 or rows of 8. There were 15 rows altogether. How many seats were arranged in rows of 8 at the concert?
Answer: ","e":"If all 15 rows had 6 seats = 90; need 110, extra 20 = 2 per row swapped to 8s, so 10 rows of 8. Seats in rows of 8 = 10 \u00d7 8 = 80."} {"t":"q","id":12555,"q":"5 thousands and 3 tens written in numeral is .","e":"5 thousands = 5000, 3 tens = 30. 5000 + 30 = 5030."} {"t":"q","id":12557,"q":"Ruth bought 6 packets of stickers. Each packet contains 9 stickers. How many stickers did Ruth have altogether?","e":"6 packets x 9 stickers = 54 stickers."} {"t":"q","id":12563,"q":"There are 35 students in a class. There are 5 students in each group. How many groups are there in the class?","e":"35 \/ 5 = 7 groups."} {"t":"q","id":12566,"q":"The sum of 2 numbers is 360. The difference between the 2 numbers is 40. What is the value of the smaller number?","e":"Smaller number = (sum - difference) \/ 2 = (360 - 40) \/ 2 = 320 \/ 2 = 160."} {"t":"q","id":12567,"q":"Paul had 54 pencils. Weiming had 7 times as many pencils as Paul. How many more pencils did Weiming have than Paul?","e":"Weiming = 7 x 54 = 378. More than Paul = 378 - 54 = 324."} {"t":"q","id":12570,"q":"What is the greatest 4-digit number that can be formed using all the digits 5, 2, 3, 7? Each digit can only be used once. ","e":"Arrange digits from largest to smallest: 7, 5, 3, 2 -> 7532."} {"t":"q","id":12572,"q":"There were 5398 people at a carnival. 4267 were adults and the rest were children. How many children were at the carnival? ","e":"5398 - 4267 = 1131 children."} {"t":"q","id":12574,"q":"Find the value of $3.30 - $0.80. ","e":"$3.30 - $0.80 = $2.50."} {"t":"q","id":12577,"q":"Find the product of 509 and 9. ","e":"509 x 9 = 4581."} {"t":"q","id":12578,"q":"Write the missing numerator and denominator. 1 = \/8 = 10\/","e":"1 = 8\/8, and 1 = 10\/10, so (a) = 8 and (b) = 10."} {"t":"q","id":12581,"q":"Devi started her swimming lesson at 10.30 a.m. Her lesson lasted for 1 h 15 min. What time did her swimming lesson end? ","e":"10.30 a.m. + 1 h = 11.30 a.m.; + 15 min = 11.45 a.m."} {"t":"q","id":12582,"q":"Sulin took 1 h 25 min to cycle from her home to the park. Then she took another 45 min to cycle from the park to the library. What was the total time taken for Sulin to cycle from her home to the library? h min","e":"1 h 25 min + 45 min = 1 h 70 min = 2 h 10 min."} {"t":"q","id":12583,"q":"What are the missing digits represented by (a) and (b)? 4 9 3 + 3 4 8 = 8 3 4 5","e":"Ones: (a) + 8 = 5 with regroup, so (a) = 7 (7 + 8 = 15). Tens: 1 + 3 + (b) = 4, so (b) = 0."} {"t":"q","id":12584,"q":"Lucy has 234 more beads than her sister. How many beads must Lucy give to her sister so that both of them have the same number of beads? ","e":"To equalise, give away half the difference: 234 \/ 2 = 117 beads."} {"t":"q","id":12589,"q":"Amanda prepared a few jugs of fruit punch for a party. After the guests drank 6 l 533 ml of fruit punch, there was 2 l 467 ml of fruit punch left. Each jug contained 3 l of fruit punch. (a) What is the total volume of fruit punch prepared at the start of the party? (b) How many jugs of fruit punch did she prepare? ml jugs","e":"(a) 6 l 533 ml + 2 l 467 ml = 9 l = 9000 ml. (b) 9000 ml \/ 3000 ml = 3 jugs."} {"t":"q","id":12590,"q":"Sarah spent $35.30 at a supermarket. Belle spent $7.65 less than her. How much did both of them spend in all? ","e":"Belle = $35.30 - $7.65 = $27.65. Total = $35.30 + $27.65 = $62.95."} {"t":"q","id":12592,"q":"Ray and Samy had 168 cupcakes. After Ray had given 15 cupcakes to Samy, he had 2 times as many cupcakes as Samy. How many cupcakes did Samy have at first? ","e":"Total stays 168 = 3 units, so 1 unit = 56 (Samy after). Samy after = 168 \/ 3 = 56. Samy at first = 56 - 15 = 41."} {"t":"q","id":12593,"q":"Mrs Tan has $244 to buy some apples to make some pies. The apples are sold in packets of 8. Each packet costs $6. What is the maximum number of apples she can buy? ","e":"$244 \/ $6 = 40 packets remainder $4. 40 packets x 8 apples = 320 apples."} {"t":"q","id":12594,"q":"In 1903, the digit '1' is in the place.","e":"In 1903 the digits are 1 (thousands), 9 (hundreds), 0 (tens), 3 (ones). The '1' is in the thousands place."} {"t":"q","id":12598,"q":"Arrange these numbers in order. Begin with the smallest. 1486 1864 1684 1468 , , , ","e":"Comparing by place value from smallest: 1468, 1486, 1684, 1864."} {"t":"q","id":12599,"q":"Look at the pattern. What are the missing numbers? 5271, (a) , 5071, (b) , 4871, 4771","e":"The numbers decrease by 100 each time. (a) 5271 - 100 = 5171; (b) 5071 - 100 = 4971."} {"t":"q","id":12600,"q":"Harry gave some stickers to 9 friends. Each friend received 6 stickers. How many stickers did he give altogether?
Answer: ","e":"9 friends x 6 stickers = 54 stickers."} {"t":"q","id":12601,"q":"The sum of two numbers is 785. The smaller number is 246. What is the greater number?
Answer: ","e":"Greater number = sum - smaller number = 785 - 246 = 539."} {"t":"q","id":12602,"q":"Raju bought a shirt for $16.50. He gave the cashier $50. How much change did he receive?
Answer: ","e":"Change = $50 - $16.50 = $33.50."} {"t":"q","id":12603,"q":"Ali packed 847 toys equally into some boxes. There were 7 toys in each box. How many boxes did Ali use to pack all the toys?
Answer: ","e":"847 \/ 7 = 121 boxes."} {"t":"q","id":12604,"q":"There were 258 adults in a park. There were twice as many men as women. How many women were there in the park?
Answer: ","e":"Women = 1 unit, men = 2 units, total = 3 units = 258. 1 unit = 258 \/ 3 = 86 women."} {"t":"q","id":12605,"q":"Each school bus can carry 38 passengers. How many passengers can 3 school buses carry?
Answer: ","e":"38 x 3 = 114 passengers."} {"t":"q","id":12606,"q":"There were 419 papayas in a farm. The farmer packed them into bags. 8 papayas were packed into each bag. How many papayas were left unpacked?
Answer: ","e":"419 \/ 8 = 52 remainder 3, so 3 papayas were left unpacked."} {"t":"q","id":12607,"q":"Sarah bought a pair of shoes for $65.70. Ailee paid $15.95 less for the same pair of shoes. How much did Ailee pay for the pair of shoes?
Answer: ","e":"$65.70 - $15.95 = $49.75."} {"t":"q","id":12608,"q":"There were 3906 visitors at the museum in February. There were 2019 more visitors in March than in February. What is the total number of visitors at the museum in February and March?
Answer: ","e":"March = 3906 + 2019 = 5925. Total = 3906 + 5925 = 9831. (Or 3906 x 2 + 2019 = 9831.)"} {"t":"q","id":12609,"q":"Mdm Rosie sewed 112 masks on Saturday. She sewed four times as many masks on Saturday than on Friday. (a) How many masks did she sew on Friday? (b) How many more masks were sewed on Saturday than on Friday?
(a)   (b) ","e":"(a) Friday = 112 \/ 4 = 28 masks. (b) 112 - 28 = 84 more masks on Saturday."} {"t":"q","id":12610,"q":"Caili baked some cupcakes. She gave 15 cupcakes to her neighbours. She packed the remaining cupcakes into 136 boxes. There were 9 cupcakes in each box. How many cupcakes did she bake at first?
Answer: ","e":"Cupcakes packed = 136 x 9 = 1224. Total baked = 1224 + 15 given away = 1239."} {"t":"q","id":12611,"q":"There was an equal number of lorries and vans parked at a carpark at first. 12 vans left the carpark and 19 lorries entered. There were 64 vans parked at the carpark in the end. (a) How many vans were parked at the carpark at first? (b) How many lorries were parked at the carpark in the end?
(a)   (b) ","e":"(a) Vans at first = 64 + 12 (that left) = 76. (b) Lorries at first equalled vans at first = 76; in the end = 76 + 19 = 95."} {"t":"q","id":12614,"q":"Which of the following does not have the same value as 1\/2 ?","e":"4\/8, 5\/10, 6\/12 all simplify to 1\/2. 2\/6 simplifies to 1\/3, so it is the odd one out."} {"t":"q","id":12615,"q":"Which of the following fractions is the greatest?","e":"Over a common denominator of 12: 2\/3=8\/12, 3\/4=9\/12, 5\/6=10\/12, 7\/12. 5\/6 is the greatest."} {"t":"q","id":12625,"q":"Edwin studied from 3.10 p.m. to 4.55 p.m. How long did he study?\n h min","e":"From 3.10 to 4.10 is 1 h; 4.10 to 4.55 is 45 min. Total 1 h 45 min."} {"t":"q","id":12627,"q":"\\(\\dfrac{4}{5}\\) - \\(\\dfrac{3}{10}\\) = \nExpress your answer in the simplest form.","e":"4\/5 = 8\/10. 8\/10 - 3\/10 = 5\/10 = 1\/2."} {"t":"q","id":12631,"q":"In the number 8273, the digit __________ is in the tens place.","e":"In 8273 the digits from the right are 3 (ones), 7 (tens), 2 (hundreds), 8 (thousands). So the tens digit is 7."} {"t":"q","id":12634,"q":"Find the sum of 10 hundreds and 23 ones.","e":"10 hundreds = 1000 and 23 ones = 23. Sum = 1000 + 23 = 1023."} {"t":"q","id":12638,"q":"Which fraction is not equivalent to 2\/3?","e":"4\/6, 6\/9 and 8\/12 all simplify to 2\/3. 2\/6 = 1\/3, which is not equivalent to 2\/3."} {"t":"q","id":12641,"q":"Write three thousand, eight hundred and fifty in numerals.","e":"Three thousand = 3000, eight hundred = 800, fifty = 50. 3000 + 800 + 50 = 3850."} {"t":"q","id":12642,"q":"Arrange the numbers from smallest to greatest. 7213 , 1372 , 7321 , 3127 , , , ","e":"Comparing thousands then hundreds: 1372 < 3127 < 7213 < 7321."} {"t":"q","id":12643,"q":"Study the number pattern. What is the missing number? 3898, 3968, , 4108, 4178","e":"The numbers increase by 70 each time: 3898, 3968, 4038, 4108, 4178. The missing number is 4038."} {"t":"q","id":12644,"q":"Sally had some oranges. After selling 140 oranges, she had 835 oranges left. How many oranges did she have at first? ","e":"At first = sold + left = 140 + 835 = 975 oranges."} {"t":"q","id":12645,"q":"What is the greatest 2-digit number that can be divided by 4 without any remainder? ","e":"The greatest 2-digit number is 99. 96 = 4 \u00d7 24 is the largest 2-digit multiple of 4."} {"t":"q","id":12646,"q":"What is the missing fraction in the box? Express your answer in its simplest form. \\(\\dfrac{3}{4}\\) + \\(\\dfrac{1}{12}\\) = ","e":"3\/4 = 9\/12. 9\/12 + 1\/12 = 10\/12 = 5\/6."} {"t":"q","id":12649,"q":"Find the remainder when 157 is divided by 9. ","e":"157 \u00f7 9 = 17 remainder 4 (since 9 \u00d7 17 = 153 and 157 \u2212 153 = 4)."} {"t":"q","id":12651,"q":"Which two of the fractions are smaller than 1\/2? 2\/8 , 3\/9 , 8\/10 , 9\/12 , ","e":"2\/8 = 1\/4 and 3\/9 = 1\/3 are both less than 1\/2. 8\/10 and 9\/12 (= 3\/4) are greater than 1\/2."} {"t":"q","id":12655,"q":"Mrs Tan prepared 104 lunch boxes. She packed 8 lunch boxes in each plastic bag. How many plastic bags did Mrs Tan use? ","e":"104 \u00f7 8 = 13 plastic bags."} {"t":"q","id":12656,"q":"3574 people went to Sentosa on Saturday and 199 fewer people went on Sunday than Saturday. How many people went to Sentosa on these two days? ","e":"Sunday = 3574 \u2212 199 = 3375. Two days = 3574 + 3375 = 6949."} {"t":"q","id":12658,"q":"Find the difference between \\(\\dfrac{11}{12}\\) and \\(\\dfrac{1}{4}\\). Give your answer in its simplest form. ","e":"1\/4 = 3\/12. 11\/12 \u2212 3\/12 = 8\/12 = 2\/3."} {"t":"q","id":12661,"q":"Mrs Raja sold 285 roses last week. She sold 5 times as many roses this week. How many roses did she sell this week? ","e":"This week = 5 \u00d7 285 = 1425 roses."} {"t":"q","id":12662,"q":"A box can contain 5 muffins. What is the least number of boxes needed to contain 119 muffins? ","e":"119 \u00f7 5 = 23 remainder 4. The leftover 4 muffins still need 1 more box, so 23 + 1 = 24 boxes."} {"t":"q","id":12664,"q":"Keith and Tom have 975 stickers. Tom has 55 fewer stickers than Keith. How many stickers does Tom have? ","e":"Remove the 55 difference: 975 \u2212 55 = 920, which is 2 equal shares. Tom = 920 \u00f7 2 = 460."} {"t":"q","id":12689,"q":"Benny bought the following items from a shop: Note Book $3.45, Mechanical Pencil $1.85, Sharpener 80 cents. How much did he spend altogether? ","e":"$3.45 + $1.85 + $0.80 = $6.10."} {"t":"q","id":12690,"q":"Jane collected $400 from his 'red packets' during Chinese New Year. She spent $245. How much money had she left? ","e":"$400 - $245 = $155."} {"t":"q","id":12691,"q":"After spending 60 cents on food during recess, Henry had $1.20 left. How much money did she have at first? ","e":"$1.20 + $0.60 = $1.80."} {"t":"q","id":12692,"q":"Kegan bought 4 bookmarks at $2 each and a pen that cost $6. How much did she pay altogether? ","e":"4 x $2 = $8 for bookmarks; $8 + $6 = $14."} {"t":"q","id":12693,"q":"The table shows a menu of a restaurant: Fish and Chips $13.80, Pork Chop $12.50, Chicken Chop $16.60, Potato Salad $5.90. Mr Soh and family ordered 3 different types of food from the menu. What was the largest amount of money he would have to pay? ","e":"Largest 3 prices: $16.60 + $13.80 + $12.50 = $42.90."} {"t":"q","id":12694,"q":"Sharon bought a doll for $42.75 and a brooch for $17.50. She had $37.20 left. How much did she have at first? ","e":"$42.75 + $17.50 = $60.25 spent; $60.25 + $37.20 = $97.45."} {"t":"q","id":12709,"q":"Find the remainder in 152 \u00f7 7. ","e":"152 \u00f7 7 = 21 remainder 5 (21 x 7 = 147, 152 - 147 = 5)."} {"t":"q","id":12710,"q":"Annie and her 7 friends shared 560 candies equally among themselves. How many candies did Annie have after sharing them? ","e":"Annie + 7 friends = 8 people; 560 \u00f7 8 = 70."} {"t":"q","id":12711,"q":"After Mrs Lim had distributed some stickers to 6 pupils, each pupil received 3 stickers and she had a remainder of 2 stickers. How many stickers did Mrs Lim have at first? ","e":"6 x 3 = 18 given out; 18 + 2 remainder = 20."} {"t":"q","id":12712,"q":"Audrey packs 292 stamps into packets of 4 stamps each. How many packets of stamps will she have? ","e":"292 \u00f7 4 = 73 packets."} {"t":"q","id":12713,"q":"James has 12 bags of marbles. Each bag contains 5 marbles. He repacks them into bags of 6. How many bags does he have now? ","e":"12 x 5 = 60 marbles; 60 \u00f7 6 = 10 bags."} {"t":"q","id":12714,"q":"Jack has 43 pencils. He needs to pack them into 5 boxes with an equal number of pencils in each box. (a) How many pencils are there in each box? (b) How many pencils will be left unpacked? (a) (b) ","e":"43 \u00f7 5 = 8 remainder 3, so 8 pencils per box and 3 unpacked."} {"t":"q","id":12715,"q":"Jenny has 222 stickers. She gives them equally to her 6 friends, how many sweets does each friend receive? ","e":"222 \u00f7 6 = 37."} {"t":"q","id":12723,"q":"5 years ago, Mary was 15 years old. Now, she is twice as old as her brother. How old is her brother now? ","e":"Mary now = 15 + 5 = 20; brother = 20 \u00f7 2 = 10 years old."} {"t":"q","id":12724,"q":"Book A has 284 pages. Book B has 6 times as many pages as book A. What is the total number of pages in both books? ","e":"Book B = 284 x 6 = 1704; total = 1704 + 284 = 1998."} {"t":"q","id":12725,"q":"Write the following in figures. (a) Eight thousand, nine hundred and five (b) Six thousand and thirty-seven ","e":"Eight thousand, nine hundred and five = 8905; six thousand and thirty-seven = 6037."} {"t":"q","id":12726,"q":"In 387, the digit '3' is in the [blank] place. The value of digit '8' is [blank].","e":"In 387, '3' is in the hundreds place and '8' is in the tens place with value 80."} {"t":"q","id":12727,"q":"Complete the number patterns. (a) 3300, 4300, , , 7300 (b) , 1995, 2000, , 2010, 2015","e":"(a) +1000 each step: 5300, 6300. (b) +5 each step: 1990 before 1995, 2005 between 2000 and 2010."} {"t":"q","id":12729,"q":"Find the difference between 3000 and 2320. ","e":"3000 - 2320 = 680."} {"t":"q","id":12732,"q":"Sally is 8 years old. Her sister is 14 years older than she is. Find their total ages? ","e":"Sister = 8 + 14 = 22; total = 22 + 8 = 30."} {"t":"q","id":12733,"q":"An MRT train left the Toa Payoh station with some passengers on it. At the Bishan station, 9 passengers alighted and 16 passengers boarded the train. The train then had 70 passengers. How many passengers were there on the train when it left the Toa Payoh Station? ","e":"Work backwards: 70 - 16 + 9 = 63 passengers at the start."} {"t":"q","id":12744,"q":"A container can hold 65\u2113 of water. A tank can hold 4 times as much. How much water can the tank hold? \u2113","e":"65 \u2113 x 4 = 260 \u2113."} {"t":"q","id":12745,"q":"Mrs Tan bought 740 cm of cloth. After sewing 5 similar dresses, she had 90 cm of cloth left. How much cloth did she use for each dress? Give your answer in metres and centimetres. m cm","e":"740 - 90 = 650 cm used; 650 \u00f7 5 = 130 cm = 1 m 30 cm per dress."} {"t":"q","id":12746,"q":"Harry, Ken and Marc weigh 140 kg altogether. If Harry and Ken have the same mass and Marc is 14 kg heavier than Harry, how heavy is Ken? kg","e":"140 - 14 = 126 kg shared by 3 equal parts (Harry, Ken, and Marc-minus-14); 126 \u00f7 3 = 42 kg = Ken."} {"t":"q","id":12747,"q":"7 trees are planted along a road at equal distances apart. The distance between two trees is 50m. How far away is the first tree from the last tree? m","e":"7 trees make 6 gaps; 6 x 50 = 300 m."} {"t":"q","id":12748,"q":"A jogging track is 800m long. Streetlights are placed along the track (including both ends) at intervals of 100m. How many streetlights are there along the jogging track? ","e":"800 \u00f7 100 = 8 intervals; including both ends gives 8 + 1 = 9 streetlights."} {"t":"q","id":12753,"q":"Which of the following is the smallest?","e":"2 thousands = 2000, 21 hundreds = 2100, 220 tens = 2200, 2022 ones = 2022. The smallest is 2000."} {"t":"q","id":12758,"q":"Subtract 1299 from 3000.
Answer: ","e":"3000 - 1299 = 1701."} {"t":"q","id":12762,"q":"The difference between two numbers is 293. The smaller number is 1768. What is the other number?
Answer: ","e":"The larger number = smaller + difference = 1768 + 293 = 2061."} {"t":"q","id":12763,"q":"I am thinking of a 4-digit number between 6000 and 7000. The digit in the ones place is the smallest odd number. The digit in the tens place is 3 more than the digit in the ones place. The digit in the hundreds place is 2 less than the digit in the thousands place. What is the number I am thinking of?
Answer: ","e":"Between 6000 and 7000 so thousands = 6. Ones = smallest odd number = 1. Tens = 1 + 3 = 4. Hundreds = 6 - 2 = 4. The number is 6441."} {"t":"q","id":12769,"q":"5 boys shared 524 sweets equally. How many sweets were left?","e":"524 \u00f7 5 = 104 remainder 4, so 4 sweets were left."} {"t":"q","id":12776,"q":"Which of the following fractions is greater than 5\/9 ?","e":"5\/9 \u2248 0.56. 5\/7 \u2248 0.71 is greater; 1\/2=0.5, 3\/8=0.375, 4\/10=0.4 are all smaller."} {"t":"q","id":12782,"q":"Express 2045 cm in metres and centimetres. m cm","e":"2045 cm = 2000 cm + 45 cm = 20 m 45 cm (100 cm = 1 m)."} {"t":"q","id":12783,"q":"Add $37.15 to $70.05.
Answer: ","e":"$70.05 + $37.15 = $107.20."} {"t":"q","id":12784,"q":"Elsa bought a badminton racket for $26.50. She gave the cashier $50. What is the amount of change she should get? $","e":"$50 \u2212 $26.50 = $23.50 change."} {"t":"q","id":12786,"q":"Mei Mei has 2356 roses. Devi has 2715 roses. How many roses do they have altogether?
Answer: ","e":"2356 + 2715 = 5071 roses."} {"t":"q","id":12787,"q":"3 children shared some marbles. Each child received 15 marbles. How many marbles were there altogether?
Answer: ","e":"3 \u00d7 15 = 45 marbles altogether."} {"t":"q","id":12788,"q":"Find the value of \\(\\dfrac{7}{12}\\) - \\(\\dfrac{1}{3}\\) . Write your answer in the simplest form.","e":"1\/3 = 4\/12, so 7\/12 \u2212 4\/12 = 3\/12 = 1\/4."} {"t":"q","id":12789,"q":"Arrange the fractions in order, beginning with the smallest. 1\/2 , 3\/5 , 3\/8 , 3\/7 , , , ","e":"As decimals: 3\/8=0.375, 3\/7\u22480.43, 1\/2=0.5, 3\/5=0.6. Smallest to greatest: 3\/8, 3\/7, 1\/2, 3\/5."} {"t":"q","id":12792,"q":"Raju took 50 min to mop the floor. He took 25 min to wash his shoes. How long did he take to complete both jobs? Give your answer in h and min. h min","e":"50 min + 25 min = 75 min = 1 h 15 min."} {"t":"q","id":12793,"q":"A tennis match was played from 9.15 a.m. to 11.05 a.m. How long did the tennis match last? min","e":"9.15 a.m. to 11.05 a.m. is 1 h 50 min = 110 min."} {"t":"q","id":12796,"q":"Jim is thinking of a 3-digit even number. It can be divided by 3 without remainder. The digit in the hundreds place is 2 times the digit in the tens place. What is the smallest possible number?
Answer: ","e":"Hundreds = 2 \u00d7 tens. Smallest: tens=1, hundreds=2. Even and divisible by 3: 210 (2+1+0=3). So 210."} {"t":"q","id":12797,"q":"Mrs Lim baked 126 cupcakes. She packed all of them into boxes. Each box can hold 8 cupcakes. What was the least number of boxes Mrs Lim needed?
Answer: ","e":"126 \u00f7 8 = 15 remainder 6. The leftover 6 need 1 more box, so 15 + 1 = 16 boxes."} {"t":"q","id":12798,"q":"In a theatre, there were 460 men, 345 women and 226 children. How many more adults than children were there in the theatre?
Answer: ","e":"Adults = 460 + 345 = 805. 805 \u2212 226 = 579 more adults than children."} {"t":"q","id":12799,"q":"A badminton racket and a T-shirt cost $172. The racket is cost $36 more than the T-shirt. What is the cost of the T-shirt?
Answer: ","e":"$172 \u2212 $36 = $136 for two T-shirts' worth; $136 \u00f7 2 = $68 for the T-shirt."} {"t":"q","id":12800,"q":"Raju bought 7 packets of sweets. Each packet has 150 sweets. He puts 6 sweets in each goodie bag. How many goodie bags did Raju have?
Answer: ","e":"Total sweets = 7 \u00d7 150 = 1050. 1050 \u00f7 6 = 175 goodie bags."} {"t":"q","id":12801,"q":"2 books and 1 bag cost $58. 1 book and 1 bag cost $43. What is the cost of 1 bag?
Answer: ","e":"$58 \u2212 $43 = $15 is the cost of 1 book. Bag = $43 \u2212 $15 = $28."} {"t":"q","id":12802,"q":"A baker has 100 eggs. He needs 6 eggs to bake a cake. What is the most number of cakes he can bake? How many more eggs would the baker need to bake 1 more cake? ","e":"(a) 100 \u00f7 6 = 16 remainder 4, so 16 cakes. (b) 1 more cake needs 6 eggs but only 4 are left, so 6 \u2212 4 = 2 more eggs."} {"t":"q","id":12804,"q":"Write six thousand and thirty-two in numerals. ","e":"Six thousand and thirty-two = 6000 + 30 + 2 = 6032."} {"t":"q","id":12811,"q":"Look at the numbers.\n6079 , 2548 , 5284 , 6709\nFind the sum of the greatest number and the smallest number. ","e":"Greatest number = 6709, smallest number = 2548. Sum = 6709 + 2548 = 9257."} {"t":"q","id":12812,"q":"8 + 8 + 8 + 8 = 16 + x 8","e":"8 + 8 + 8 + 8 = 32. So 32 = 16 + ? x 8, meaning ? x 8 = 16, so ? = 2."} {"t":"q","id":12813,"q":"Grace has 7 party bags. Siti has 4 times as many party bags as Grace. How many party bags does Siti have? ","e":"Siti has 4 times as many as Grace: 7 x 4 = 28 party bags."} {"t":"q","id":12814,"q":"Amy packed 63 apples equally into some fruit baskets. Each fruit basket contained 7 apples. How many fruit baskets would Amy have? ","e":"Number of baskets = 63 \/ 7 = 9."} {"t":"q","id":12815,"q":"There were 10 rows of seats in a theatre. There were 9 seats in each row. Only 2 seats were not occupied. How many seats in the theatre were occupied? ","e":"Total seats = 10 x 9 = 90. Occupied = 90 - 2 = 88."} {"t":"q","id":12816,"q":"Ravi has 9 stamps. Sandra has 5 times as many stamps as Ravi. How many stamps must Sandra give to Ravi so that they have the same number of stamps? ","e":"Sandra has 5 x 9 = 45 stamps. Total = 9 + 45 = 54. Each should have 54 \/ 2 = 27. Sandra must give 45 - 27 = 18 stamps to Ravi."} {"t":"q","id":12817,"q":"Jack bought a computer and a printer. The computer cost $2549. The printer cost $1590 less than the computer.\n(a) How much did the printer cost? $\n(b) How much money did Jack spend altogether? $","e":"(a) Printer = 2549 - 1590 = $959. (b) Total = 2549 + 959 = $3508."} {"t":"q","id":12818,"q":"The sum of two numbers is 4086. The smaller number is 1260. What is the difference between the two numbers? ","e":"Bigger number = 4086 - 1260 = 2826. Difference = 2826 - 1260 = 1566."} {"t":"q","id":12820,"q":"In 5690, which digit is in the hundreds place?","e":"In 5690 the digits are 5 (thousands), 6 (hundreds), 9 (tens), 0 (ones). The hundreds digit is 6."} {"t":"q","id":12822,"q":"The sum of two 2-digit numbers is 88. The difference between the two numbers is more than 20 but less than 40. The digits used to form the greater number and the smaller number are the same. What is the smaller number?","e":"The two numbers use the same digits, so they are 26 and 62. Their sum is 88 and their difference is 62 - 26 = 36, which is between 20 and 40. The smaller number is 26."} {"t":"q","id":12823,"q":"Write the numbers in numerals. a) Five thousand, nine hundred and eighty-one b) Six thousand and seventy-three ","e":"a) Five thousand, nine hundred and eighty-one = 5981. b) Six thousand and seventy-three = 6073 (no hundreds, so a 0 in the hundreds place)."} {"t":"q","id":12826,"q":"Mrs Lim baked 239 more pies than cookies. She then gave away 2541 cookies and had 1981 cookies left. How many pies did she bake? ","e":"Cookies baked = 2541 + 1981 = 4522. Pies = 4522 + 239 = 4761."} {"t":"q","id":12827,"q":"Paul had 3 shirts and 3 pairs of shorts. He had a red shirt, a purple shirt and a green shirt. He had a pair of white shorts, a pair of black shorts and a pair of yellow shorts. In how many different ways could Paul match a shirt and a pair of shorts? ","e":"Each of the 3 shirts can be paired with each of the 3 pairs of shorts: 3 x 3 = 9 different ways."} {"t":"q","id":12828,"q":"Jane has 4153 marbles. Siva has 1122 marbles fewer than Jane. Jane has 1739 marbles fewer than Liz. (a) How many marbles does Siva have? (b) How many marbles does Liz have? ","e":"(a) Siva = 4153 - 1122 = 3031. (b) Jane has 1739 fewer than Liz, so Liz = 4153 + 1739 = 5892."} {"t":"q","id":12829,"q":"In 1809, which digit is in the thousands place?","e":"In 1809 the digits are 1 (thousands), 8 (hundreds), 0 (tens), 9 (ones). The thousands digit is 1."} {"t":"q","id":12832,"q":"Which of the following is most likely the length of a school bus?","e":"A school bus is about 15 m long. 50 cm and 150 cm are too short; 500 m is far too long."} {"t":"q","id":12834,"q":"Given the three fractions: 2\/3, 1\/2, 7\/9 . Arrange them from the greatest to the smallest.","e":"Common denominator 18: 2\/3=12\/18, 1\/2=9\/18, 7\/9=14\/18. Greatest to smallest: 7\/9, 2\/3, 1\/2."} {"t":"q","id":12836,"q":"Mr Hong sold 1231 eggs on Monday. He sold 256 fewer eggs on Tuesday than on Monday. How many eggs did he sell on Monday and Tuesday?","e":"Tuesday = 1231 - 256 = 975. Total = 1231 + 975 = 2206."} {"t":"q","id":12838,"q":"Sally had 3 times as many marbles as John. Sally had 36 marbles. How many marbles did they have altogether?","e":"John = 36 \/ 3 = 12. Altogether = 36 + 12 = 48."} {"t":"q","id":12839,"q":"What is the missing number in the box? 2\/3 = \/18","e":"3 x 6 = 18, so multiply numerator by 6: 2 x 6 = 12. So 2\/3 = 12\/18."} {"t":"q","id":12840,"q":"Study the number pattern and fill in the missing number. 8824, 8624, 8424, , 8024, 7824","e":"The pattern decreases by 200 each time. 8424 - 200 = 8224."} {"t":"q","id":12841,"q":"Express 5048 m in kilometres and metres. km m","e":"1 km = 1000 m. 5048 m = 5000 m + 48 m = 5 km 48 m."} {"t":"q","id":12843,"q":"What is the quotient when 293 is divided by 4?
Answer: ","e":"293 \/ 4 = 73 remainder 1. The quotient is 73."} {"t":"q","id":12848,"q":"The sum of two numbers is 95. The smaller number is 38. What is the greater number?
Answer: ","e":"95 - 38 = 57."} {"t":"q","id":12850,"q":"Mei Ling spent 45 min to complete her English homework and 58 min to complete her Science homework. How long did she spend to complete both of her homework? Express your answer in hours and minutes. h min","e":"45 + 58 = 103 min = 60 min + 43 min = 1 h 43 min."} {"t":"q","id":12851,"q":"Kent is 12 years old now. His uncle is 4 times as old as him. How old is his uncle? years","e":"12 x 4 = 48 years."} {"t":"q","id":12852,"q":"(a) Find the value of 2\/3 - 2\/9 . Express your answer in the simplest form. (b) Find the value of 1\/2 + 3\/8 . Express your answer in the simplest form. (a) (b) ","e":"(a) 2\/3 = 6\/9; 6\/9 - 2\/9 = 4\/9. (b) 1\/2 = 4\/8; 4\/8 + 3\/8 = 7\/8."} {"t":"q","id":12854,"q":"Caili had 338 sweets. She packed them into as many bags of 9 sweets as she could. Some sweets were left unpacked. How many sweets were left unpacked?
Answer: ","e":"338 \/ 9 = 37 remainder 5. So 5 sweets were left unpacked."} {"t":"q","id":12856,"q":"On Saturday, 5304 people borrowed books from the library. 785 more people borrowed books on Saturday than on Sunday. How many people borrowed books on Sunday?
Answer: ","e":"Sunday = 5304 - 785 = 4519."} {"t":"q","id":12857,"q":"Tom bought 376 stickers. Keith had 5 times as many stickers as Tom. How many stickers did they have altogether?
Answer: ","e":"Keith = 376 x 5 = 1880. Altogether = 376 + 1880 = 2256. (Key shows 376 x 6 = 2256, combining Tom's 1 unit and Keith's 5 units.)"} {"t":"q","id":12858,"q":"Johan had 3 times as many colour pencils as Ali. They had 64 colour pencils altogether. How many more colour pencils did Johan have than Ali?
Answer: ","e":"Total 4 units = 64, so 1 unit = 16. Ali = 16, Johan = 48. Difference = 48 - 16 = 32 (or 2 units = 2 x 16 = 32)."} {"t":"q","id":12859,"q":"Lucy has 31 stamps less than Alan. They have 107 stamps altogether. How many stamps does Lucy have?
Answer: ","e":"Remove the 31 difference: 107 - 31 = 76, which is 2 equal parts. Lucy = 76 \/ 2 = 38."} {"t":"q","id":12860,"q":"May Han had $5 more than Wei Ming. Wei Ming gave $6 to May Han. How much more money did May Han have than Wei Ming in the end? $","e":"Initial difference $5. Wei Ming gives $6: May Han +$6, Wei Ming -$6, so the gap widens by $12. New difference = $5 + $12 = $17. (Key: 6 + 5 = 11; 11 + 6 = $17.)"} {"t":"q","id":12861,"q":"Mrs Han baked some muffins for a party. She packed the muffins into 35 boxes. In each box, there were 9 muffins. There were 7 muffins left in the oven. How many muffins did Mrs Han bake altogether?
Answer: ","e":"Packed = 35 x 9 = 315. Total = 315 + 7 = 322 muffins."} {"t":"q","id":12864,"q":"A pencil cost $1.90 and a storybook cost $5.30. Emily bought 2 pencils and a storybook. (a) How much did Emily pay altogether? (b) Emily paid for the items using a $50 note. How much change did she receive? (a) $ (b) $","e":"(a) 2 pencils = $1.90 x 2 = $3.80; total = $3.80 + $5.30 = $9.10. (b) Change = $50 - $9.10 = $40.90."} {"t":"q","id":12865,"q":"Michael started exercising at 1.45 p.m. He completed his exercise in 35 minutes. (a) At what time did he complete his exercise? (b) After completing his exercise, Michael watched a movie. The movie ended at 4 p.m. How long did the movie last? Give your answer in hour and minutes. (a) (b) ","e":"(a) 1.45 p.m. + 35 min = 2.20 p.m. (b) From 2.20 p.m. to 4.00 p.m. = 1 h 40 min."} {"t":"q","id":12869,"q":"A box contained 7 doughnuts. Jane bought 9 boxes of doughnuts. How many doughnuts were there altogether?","e":"7 x 9 = 63 doughnuts."} {"t":"q","id":12871,"q":"Fanny had 3 ten-dollar notes and 2 fifty-cent coins. She bought a toy which cost $6.50. How much money had she left?","e":"3 x $10 = $30; 2 x $0.50 = $1; total $31. $31 - $6.50 = $24.50."} {"t":"q","id":12875,"q":"Which of the following fractions is expressed in its simplest form?","e":"6\/7 cannot be simplified (no common factor). 2\/4=1\/2, 8\/10=4\/5, 2\/12=1\/6."} {"t":"q","id":12880,"q":"Mrs Lee has 100 fish balls. She wants to sell them in sticks of 3. How many sticks of fish balls can she sell at most?","e":"100 \/ 3 = 33 remainder 1, so 33 full sticks of 3."} {"t":"q","id":12882,"q":"Write eight thousand and two in figures. ","e":"Eight thousand and two = 8000 + 2 = 8002."} {"t":"q","id":12883,"q":"Find the value of \\(\\dfrac{1}{2}\\) + \\(\\dfrac{3}{10}\\). Give your answer in its simplest form. ","e":"1\/2 = 5\/10; 5\/10 + 3\/10 = 8\/10 = 4\/5."} {"t":"q","id":12884,"q":"Form the smallest 4-digit number using the digits 0, 3, 4 and 8. ","e":"Smallest non-zero digit (3) goes first, then ascending: 3048."} {"t":"q","id":12885,"q":"The difference between two numbers is 5204. The smaller number is 150. What is the larger number? ","e":"Larger = smaller + difference = 150 + 5204 = 5354."} {"t":"q","id":12886,"q":"Danny had some cards. He bought another 6 boxes of cards. Each box contained 5 cards. Then he had 2046 cards. How many cards did he have at first? ","e":"6 x 5 = 30 cards bought; 2046 - 30 = 2016 cards at first."} {"t":"q","id":12887,"q":"Alice has 25 sweets and 6 plates. She wants to put 7 sweets on each plate. How many more sweets does she need? ","e":"She needs 6 x 7 = 42 sweets; 42 - 25 = 17 more."} {"t":"q","id":12888,"q":"When a number is divided by 8, it gives a quotient of 14 and a remainder of 4. What is the number? ","e":"Number = 8 x 14 + 4 = 112 + 4 = 116."} {"t":"q","id":12890,"q":"Mrs Ravi spent $17.85 at a supermarket. She spent $3.55 more than Mrs Singh. How much did Mrs Singh spend? ","e":"Mrs Singh spent $17.85 - $3.55 = $14.30."} {"t":"q","id":12891,"q":"Express 1047 m in km and m. km m","e":"1047 m = 1000 m + 47 m = 1 km 47 m."} {"t":"q","id":12893,"q":"Arrange the following fractions from the greatest to the smallest. 3\/4, 1\/2, 7\/8 , , ","e":"Common denominator 8: 3\/4=6\/8, 1\/2=4\/8, 7\/8=7\/8. Greatest to smallest: 7\/8, 3\/4, 1\/2."} {"t":"q","id":12896,"q":"8096 people visited a fun fair. 5988 of them were adults and the rest were children. How many more adults than children visited the fun fair? ","e":"Children = 8096 - 5988 = 2108; adults - children = 5988 - 2108 = 3880."} {"t":"q","id":12897,"q":"Penny bought 134 apples. She packed the apples equally into bags of 5. How many bags of 5 apples did she have? How many apples were not packed? ","e":"134 \/ 5 = 26 remainder 4. So 26 bags and 4 apples not packed."} {"t":"q","id":12898,"q":"Mrs Yong had $600. She gave her son $120 and divided the remaining amount equally among her 3 daughters. How much did each daughter get? ","e":"$600 - $120 = $480; $480 \/ 3 = $160 each."} {"t":"q","id":12899,"q":"Tammy started her piano practice at 9 a.m. She practised for 1 h 50 min. Then she spent 1 h 40 min on her homework. How long did she take for her piano practice and homework in total? (Give your answer in hours and minutes) At what time did she complete her homework? ","e":"1 h 50 min + 1 h 40 min = 3 h 30 min. Starting 9 a.m. + 3 h 30 min = 12.30 p.m."} {"t":"q","id":12900,"q":"Ali has 37 coins. Peiling has 4 times as many coins as Ali. How many coins does Peiling have? Shuming has twice as many coins as Peiling. How many coins does Shuming have? ","e":"Peiling = 37 x 4 = 148; Shuming = 148 x 2 = 296."} {"t":"q","id":12901,"q":"Mr Lee has a total of 20 ducks and horses in his farm. The animals have 48 legs in all. How many horses does Mr Lee have? How many ducks does Mr Lee have? ","e":"Assume all 20 are horses: 20 x 4 = 80 legs. Excess 80 - 48 = 32; each duck has 2 fewer legs (4-2=2), so ducks = 32\/2 = 16; horses = 20 - 16 = 4."} {"t":"q","id":12910,"q":"Find the sum of the values of the digits '7' in the numbers 7845 and 271.","e":"In 7845 the 7 is worth 7000; in 271 the 7 is worth 70. Sum = 7000 + 70 = 7070."} {"t":"q","id":12911,"q":"Study the number pattern carefully. , 210, 30, 5, 1\nWhat is the missing number?","e":"From the right: 1, then x5 = 5, then x6 = 30, then x7 = 210, then x8 = 1680."} {"t":"q","id":12912,"q":"Jon bought 1597 blue beads.\nHe bought 900 more red beads than blue beads.\nHow many beads did he buy altogether?","e":"Red = 1597 + 900 = 2497. Total = 1597 + 2497 = 4094."} {"t":"q","id":12919,"q":"Find the remainder of 509 \/ 7.
Answer: ","e":"509 \/ 7 = 72 remainder 5 (72 x 7 = 504, 509 - 504 = 5)."} {"t":"q","id":12922,"q":"I have a 1-digit number.\nWhen I add 20 to the number, the answer is the same when I multiply the number by 6. What is the number?
Answer: ","e":"Number + 20 = number x 6. Testing 4: 4 + 20 = 24 and 4 x 6 = 24, so the number is 4."} {"t":"q","id":12923,"q":"Express 5 hours and 55 minutes in minutes.
Answer: ","e":"5 h = 300 min; 300 + 55 = 355 min."} {"t":"q","id":12932,"q":"There were 3265 children and 1673 adults at a concert.\na) How many more children than adults were there?\nb) There were 1527 boys. How many girls were there?
(a)   (b) ","e":"a) 3265 - 1673 = 1592 more children. b) Girls = 3265 - 1527 = 1738."} {"t":"q","id":12933,"q":"Lynn had $229 and Rachel had $359. After Rachel gave Lynn some money, Lynn had three times as much money as Rachel.\na) How much money did the girls have altogether?\nb) How much money did Rachel have in the end?
(a)   (b) ","e":"a) Total = 229 + 359 = $588 (unchanged). b) Lynn has 3 times Rachel, so 4 units = 588; Rachel = 588 \/ 4 = $147."} {"t":"s","id":5620,"s":"Part a: 4 boxes of 10 apples, 4 \u00d7 10 = 40 apples. Part b: 40 apples packed 5 per bag, 40 \u00f7 5 = 8 bags."} {"t":"s","id":5623,"s":"1 whole is 7\/7. 7\/7 - 4\/7 = 3\/7, so 4\/7 and 3\/7 make 1 whole. The answer is option (3)."} {"t":"s","id":5624,"s":"For unit fractions, the larger the denominator the smaller the fraction. 1\/7 has a bigger denominator than 1\/6, so 1\/7 < 1\/6. The answer is option (1)."} {"t":"s","id":5627,"s":"Adding like fractions: keep the denominator and add the numerators. 6 + 3 = 9, so 6\/12 + 3\/12 = 9\/12. The answer is option (2)."} {"t":"s","id":5628,"s":"Subtracting like fractions: keep the denominator and subtract the numerators. 8 - 2 = 6, so 8\/9 - 2\/9 = 6\/9. The answer is option (4)."} {"t":"s","id":5630,"s":"Each pail holds 5 l and there are 10 pails: 5 x 10 = 50 l. The answer is option (4)."} {"t":"s","id":5631,"s":"For unit fractions, the larger the denominator the smaller the fraction. Smallest to largest: 1\/11, 1\/6, 1\/4."} {"t":"s","id":5632,"s":"Both fractions have denominator 11. Compare numerators: 7 < 10, so 7\/11 < 10\/11."} {"t":"s","id":5633,"s":"All fractions have denominator 5, so compare numerators. Greatest to smallest: 4\/5, 3\/5, 1\/5."} {"t":"s","id":5640,"s":"Start with 115 l. 115 - 27 = 88, then 88 - 35 = 53. Joe had 53 l of water left."} {"t":"s","id":5652,"s":"Even means it ends in an even digit. Largest digit first: 8, then 3, with the even 6 last: 836."} {"t":"s","id":5662,"s":"A week has 7 days. 2 pages \u00d7 7 days = 14 pages."} {"t":"s","id":5678,"s":"4:35 pm to 6:35 pm is 2 h; 6:35 pm to 6:55 pm is 20 min. Total 2 h 20 min."} {"t":"s","id":5679,"s":"3 h = 180 min. 180 min + 20 min = 200 min."} {"t":"s","id":5680,"s":"185 min = 180 min + 5 min. 180 min = 3 h, so 185 min = 3 h 5 min."} {"t":"s","id":5685,"s":"2:40 pm \u2192 3:00 pm is 20 min; 3:00 pm \u2192 8:00 pm is 5 h; 8:00 pm \u2192 8:55 pm is 55 min. 20 + 55 = 75 min = 1 h 15 min; 5 h + 1 h 15 min = 6 h 15 min."} {"t":"s","id":5686,"s":"In 7408: 7 thousands, 4 hundreds, 0 tens, 8 ones. The digit 0 is in the tens place."} {"t":"s","id":5687,"s":"36\u00f76=6, 56\u00f77=8, 48\u00f78=6, 63\u00f79=7. The largest value is 8 (56\u00f77)."} {"t":"s","id":5688,"s":"5\/25 = 1\/5. Check options: 3\/15 = 1\/5. So 3\/15 is equivalent."} {"t":"s","id":5690,"s":"In 4250 the 4 is 4000; in 3420 the 4 is 400. Total = 4000 + 400 = 4400."} {"t":"s","id":5691,"s":"Common denominator 12: 3\/4=9\/12, 2\/3=8\/12, 5\/12=5\/12. Smallest to greatest: 5\/12, 8\/12, 9\/12 = 5\/12, 2\/3, 3\/4."} {"t":"s","id":5695,"s":"Bobby = 1092 + 157 = 1249. Altogether = 1092 + 1249 = 2341."} {"t":"s","id":5698,"s":"9.50 a.m. to 5.30 p.m. = 7 h 40 min. Lunch = 50 min. Working time = 7 h 40 min \u2212 50 min = 6 h 50 min."} {"t":"s","id":5699,"s":"Total must give remainder 3 when divided by 6 and lie between 50 and 55. 51 \u00f7 6 = 8 r 3. So 51."} {"t":"s","id":5702,"s":"Watch start = 3.35 \u2212 1 h 45 min = 1.50 p.m. Watch is 15 min fast, so actual = 1.50 \u2212 15 min = 1.35 p.m."} {"t":"s","id":5703,"s":"6 thousands = 6000; 45 ones = 45. 6000 + 45 = 6045."} {"t":"s","id":5705,"s":"1\/6 = 2\/12. 7\/12 + 2\/12 = 9\/12."} {"t":"s","id":5707,"s":"2\/3 \u2212 1\/9 = 6\/9 \u2212 1\/9 = 5\/9. So 1 \u2212 box = 5\/9, box = 1 \u2212 5\/9 = 4\/9."} {"t":"s","id":5708,"s":"Compare each to 1\/2: 5\/8 > 1\/2, 4\/9 < 1\/2, 3\/6 = 1\/2, 6\/11 > 1\/2. The two greater than 1\/2 are 5\/8 and 6\/11."} {"t":"s","id":5713,"s":"Ravi = 94 \u2212 24 = 70. Lena = 70 + 60 = 130."} {"t":"s","id":5714,"s":"11.45 a.m. + 2 h = 1.45 p.m.; + 43 min = 2.28 p.m."} {"t":"s","id":5715,"s":"Shirt = $84 \u00f7 3 = $28. Total = $84 + $28 = $112."} {"t":"s","id":5717,"s":"Total pieces = 24 \u00d7 6 = 144. Per packet = 144 \u00f7 8 = 18."} {"t":"s","id":5718,"s":"844 \u2212 126 = 718; 718 \u00f7 2 = 359 (Say Jeong). Xu Jia = 359 + 126 = 485; check 359 + 485 = 844."} {"t":"s","id":5720,"s":"Strawberry = 173 \u2212 68 = 105. Boxes = 105 \u00f7 3 = 35."} {"t":"s","id":5721,"s":"Group B = 650 \u2212 280 = 370. Group C = 370 \u00d7 3 = 1110."} {"t":"s","id":5722,"s":"48 \u00f7 6 = 8 sets of 60 highlighters. 8 \u00d7 60 = 480 highlighters."} {"t":"s","id":5723,"s":"(a) $96 \u00f7 $3 = 32 small packets. (b) Large packets = 32 \u2212 15 = 17; collected = 17 \u00d7 $4 = $68."} {"t":"s","id":5724,"s":"(a) 192 \u00f7 8 = 24 boxes. (b) Let chocolate = c; blueberry = 3c; vanilla = 3c + 38. Total: c + 3c + 3c + 38 = 192 \u2192 7c = 154 \u2192 c = 22 chocolate cupcakes."} {"t":"s","id":5725,"s":"The 27 shelves gained 5 books each = 27 \u00d7 5 = 135 books, which came from the 3 removed shelves. So each shelf had 135 \u00f7 3 = 45 books at first."} {"t":"s","id":5726,"s":"3456 - 1000 = 2456. The number that is 1000 more than 2456 is 3456, so the missing number is 2456."} {"t":"s","id":5727,"s":"25 hundreds = 2500, plus 7 tens = 70. 2500 + 70 = 2570."} {"t":"s","id":5728,"s":"7 groups of 8 = 5 groups of 8 + 2 groups of 8, since 7 - 5 = 2. So the missing number is 2."} {"t":"s","id":5734,"s":"Total pens = 4 x 12 = 48. Repacked into 8 bags: 48 \/ 8 = 6 pens per bag."} {"t":"s","id":5735,"s":"2\/3 = 6\/9. 6\/9 - 1\/9 = 5\/9."} {"t":"s","id":5736,"s":"Arrival = 9.15 p.m. - 2 h 25 min. 9.15 - 2 h = 7.15 p.m.; 7.15 - 25 min = 6.50 p.m."} {"t":"s","id":5738,"s":"A fraction is smaller than 1\/2 when the numerator is less than half the denominator. 3\/7: half of 7 is 3.5, and 3 < 3.5, so 3\/7 < 1\/2. The others equal or exceed 1\/2."} {"t":"s","id":5741,"s":"Seven thousand = 7000, one hundred = 100, seven = 7. 7000 + 100 + 7 = 7107."} {"t":"s","id":5743,"s":"1 km = 1000 m, so 4 km = 4000 m. 4000 m + 6 m = 4006 m."} {"t":"s","id":5747,"s":"Odd number must end in an odd digit; only 1 is odd, so last digit = 1. Remaining digits 7, 0, 4 arranged smallest without a leading zero: 1047."} {"t":"s","id":5750,"s":"3\/4 = 9\/12. 1\/12 + 9\/12 = 10\/12."} {"t":"s","id":5751,"s":"Two $50 notes = $100. $100 - $76.95 = $23.05."} {"t":"s","id":5752,"s":"From 2.45 p.m. to 3.35 p.m.: 2.45 to 3.00 is 15 min, 3.00 to 3.35 is 35 min. 15 + 35 = 50 min."} {"t":"s","id":5753,"s":"1 l = 1000 ml. 9091 ml = 9000 ml + 91 ml = 9 l 91 ml."} {"t":"s","id":5754,"s":"Mango = 1 unit, papaya = 3 units, total = 4 units = 876 g. 1 unit = 876 \/ 4 = 219 g, so the mango is 219 g."} {"t":"s","id":5759,"s":"Remaining = 1800 - 657 = 1143. 1143 \/ 9 = 127 stickers per box."} {"t":"s","id":5760,"s":"Remove the difference: 91.50 - 37.50 = 54.00, which is twice the basketball's cost. 54 \/ 2 = $27."} {"t":"s","id":5761,"s":"Total = 6 x 400 = 2400 ml. After pouring out: 2400 - 165 = 2235 ml."} {"t":"s","id":5766,"s":"726 \u00f7 7 = 103 remainder 5. The quotient is 103."} {"t":"s","id":5771,"s":"831 \u00f7 8 = 103 remainder 7. The remainder is 7."} {"t":"s","id":5773,"s":"John = 1 unit, Mark = 2 units, total = 3 units = 372. 1 unit = 372 \u00f7 3 = 124. John collected 124 stamps."} {"t":"s","id":5774,"s":"Cost of cakes = 6 \u00d7 $54 = $324. Change = $360 \u2212 $324 = $36."} {"t":"s","id":5775,"s":"1 magazine = $104 \u00f7 8 = $13. A book = 3 \u00d7 $13 = $39."} {"t":"s","id":5781,"s":"Larger number = 17 + 54 = 71. Sum = 71 + 17 = 88."} {"t":"s","id":5782,"s":"320 \u00f7 4 = 80. So box \u00d7 5 = 80, which gives box = 80 \u00f7 5 = 16."} {"t":"s","id":5783,"s":"Carol = 96 + 57 = 153. Brandon = 3 \u00d7 153 = 459."} {"t":"s","id":5792,"s":"Smallest 4-digit number uses smallest non-zero digit first; for an even number the last digit must be even. Arranging 5,0,4,9 to be smallest and even gives 4590 (ends in 0)."} {"t":"s","id":5793,"s":"305 \u00f7 8 = 38 remainder 1. The quotient is 38."} {"t":"s","id":5794,"s":"(a) 8\/12 = (8\u00f74)\/(12\u00f74) = 2\/3. (b) An equivalent fraction of 4\/9 is 8\/18 (multiply numerator and denominator by 2)."} {"t":"s","id":5797,"s":"The pattern alternates +3 then \u22121: 4756 +3=4759 \u22121=4758 +3=4761 \u22121=4760 +3=4763 \u22121=4762. The missing number is 4760."} {"t":"s","id":5798,"s":"325 \u00d7 8 = 2600. 2600 + 150 = 2750."} {"t":"s","id":5799,"s":"6491 + 1355 = 7846. The digit in the hundreds place is 8."} {"t":"s","id":5802,"s":"485 \u00f7 8 = 60 R5. 60 bags give only 480 oranges, so she needs 1 more bag, giving 61 bags."} {"t":"s","id":5803,"s":"Using common denominator 18: 1\/3 = 6\/18, 5\/9 = 10\/18, 5\/6 = 15\/18. Smallest to largest: 1\/3, 5\/9, 5\/6."} {"t":"s","id":5804,"s":"11\/12 \u2212 1\/4 = 11\/12 \u2212 3\/12 = 8\/12 = 2\/3. So box\/3 = 2\/3, meaning the box is 2."} {"t":"s","id":5808,"s":"Kayla now = 47 \u2212 28 = 19. In 10 years = 19 + 10 = 29 years old."} {"t":"s","id":5809,"s":"(a) Beads used = 84 \u00d7 7 = 588. (b) Beads at first = beads used + beads left = 588 + 265 = 853."} {"t":"s","id":5810,"s":"1 kg 92 g = 1092 g. (a) Mass of 6 balls = 1092 \u2212 120 = 972 g. (b) Each ball = 972 \u00f7 6 = 162 g."} {"t":"s","id":5811,"s":"(a) Maths + Science = 25 + 15 = 40 min. 9.30 a.m. minus 40 min = 8.50 a.m. (b) English + Maths + Mother Tongue = 10 + 25 + 30 = 65 min = 1 h 5 min."} {"t":"s","id":5812,"s":"2 T-shirts + 2 skirts = 2 \u00d7 $20.20 = $40.40. So 1 extra T-shirt = $50.20 \u2212 $40.40 = $9.80. Each T-shirt costs $9.80."} {"t":"s","id":5813,"s":"After giving 30 stamps, Melody is 120 \u2212 30 \u2212 30 = 60 more than Jeremy. Twice as many means the difference equals Jeremy's amount, so Jeremy then has 90. Total = 90 + 180 = 270; adding back, total stays 270 + 30 = 300 altogether."} {"t":"s","id":5814,"s":"(a) Children's total = adults' total, and together they are 470, so each group has 470 \u00f7 2 = 235. The two adults have 235. (b) Five children share 235 equally: 235 \u00f7 5 = 47 stickers each."} {"t":"s","id":5822,"s":"Bala has 125 \u00d7 3 = 375. Altogether 125 + 375 = 500 stickers."} {"t":"s","id":5823,"s":"Adults = 3856 + 3975 = 7831. Children = 8562 \u2212 7831 = 731."} {"t":"s","id":5825,"s":"Sunday = 5425 \u2212 3259 = 2166. Difference = 3259 \u2212 2166 = 1093."} {"t":"s","id":5826,"s":"Giving 165 eggs reduces the gap by twice 165 (165 fewer for Ahmad, 165 more for Nazri). Gap = 720 \u2212 (165 \u00d7 2) = 720 \u2212 330 = 390."} {"t":"s","id":5827,"s":"2\/3 = 8\/12 (multiply numerator and denominator by 4); the missing numerator is 12. Wait \u2014 denominator is 8, so 2\/3 cannot equal a fraction over 8 exactly; the printed equivalent fraction has numerator 8 and the missing box is the numerator on the right being 8, with the box being the answer. Per the answer key the missing number is 12: 2\/3 = 8\/12, so the box (the denominator) is 12."} {"t":"s","id":5829,"s":"As decimals: 1 = 1.0, 3\/4 = 0.75, 5\/8 = 0.625, 1\/2 = 0.5. Greatest first: 1, 3\/4, 5\/8, 1\/2."} {"t":"s","id":5835,"s":"1 racket = $440 \/ 5 = $88. 7 rackets = $88 x 7 = $616."} {"t":"s","id":5837,"s":"Kiwi = 168g \/ 3 = 56g. Total = 168g + 56g = 224g."} {"t":"s","id":5838,"s":"Matthew's amount stays the same. After drinking, Zach = Matthew - 200 - 474 = Matthew - 674. Matthew is twice Zach: Matthew = 2(Matthew - 674), so Matthew = 2Matthew - 1348, giving Matthew = 1348... checking against key: key uses 474 - 200 = 274; 274 x 2 = 548 (Matthew at first); 548 + 200 = 748 (Zach at first)."} {"t":"s","id":5840,"s":"6\u00d77=42, 4\u00d79=36, 8\u00d78=64, 5\u00d710=50. The greatest is 8\u00d78=64."} {"t":"s","id":5843,"s":"2\/8 = 1\/4. 1\/4 = 3\/12, so the missing numerator is 3."} {"t":"s","id":5847,"s":"Jane had $29.50 + $25.50 = $55.00, so James also had $55.00. James saved $55.00 \u2212 $49.95 = $5.05."} {"t":"s","id":5853,"s":"Cindy: 6.23 to 7.10 = 47 min. Kaixin: 6.46 to 7.23 = 37 min. Kaixin is shorter by 47 \u2212 37 = 10 min."} {"t":"s","id":5856,"s":"2\/7 and 4\/7 share denominator 7, so 2\/7 < 4\/7. 4\/5 is close to 1, larger than 4\/7. Order: 2\/7, 4\/7, 4\/5."} {"t":"s","id":5859,"s":"Together = 6 units = 780, so 1 unit = 130 = Gina. Then Gina earns 25 more: 130 + 25 = 155."} {"t":"s","id":5861,"s":"They reached the park at 11.05 + 40 min = 11.45 a.m. From 11.45 a.m. to 3.35 p.m. = 3 h 50 min."} {"t":"s","id":5868,"s":"350 \u00f7 6 = 58 remainder 2. The 2 leftover sweets need one more pack, so 58 + 1 = 59 packs."} {"t":"s","id":5870,"s":"If all 14 correct = 56 points. Each wrong instead of correct loses 4+3=7 points. 56\u221214=42 lost, 42\u00f77=6 wrong, so 14\u22126=8 correct. Check: 8\u00d74=32, 6\u00d73=18, 32\u221218=14."} {"t":"s","id":5871,"s":"Female teachers = female students = 20, so teachers = 42 + 20 = 62. Students = 62 \u2212 21 = 41. Male students = 41 \u2212 20 = 21. More male than female students = 21 \u2212 20 = 1."} {"t":"s","id":5872,"s":"Removing 5 blocks reduced the mass by 500 \u2212 100 = 400 g, so each block = 400 \u00f7 5 = 80 g. Box = 100 \u2212 80 = 20 g (box plus 1 block is 100 g)."} {"t":"s","id":5874,"s":"Water used to fill pails = 50 \u2212 1 = 49 \u2113. 49 \u00f7 7 = 7 pails."} {"t":"s","id":5878,"s":"All start with 8. Compare hundreds: 8769 and 8796 have 7 hundreds (smaller than 9). Then compare tens: 8769 has 6 tens, smaller than 8796's 9 tens, so 8769 is smallest."} {"t":"s","id":5879,"s":"2501 has 2 thousands (smallest). 3127 and 3210 both have 3 thousands; compare hundreds: 1 < 2, so 3127 < 3210. Order: 2501, 3127, 3210."} {"t":"s","id":5883,"s":"(a) Greatest odd: must end in odd digit. Largest with digits 2,5,7 ending odd is 725. (b) Smallest even: must end in even digit and not start with 0; smallest is 250."} {"t":"s","id":5886,"s":"(a) Tom = 2000 - 653 = 1347 marbles. (b) After buying 480 more: 1347 + 480 = 1827 marbles."} {"t":"s","id":5887,"s":"January saving = 799 + 253 = $1052 (Feb was $253 less). Altogether = 1052 + 799 = $1851."} {"t":"s","id":5892,"s":"9 \u00d7 8 means nine groups of 8, i.e. 8 added nine times: 8 + 8 + ... + 8 (nine 8s)."} {"t":"s","id":5896,"s":"Convert to tenths: 3\/5=6\/10, 1\/4=2.5\/10, 7\/10, 1\/2=5\/10. Greatest to smallest: 7\/10, 3\/5(6\/10), 1\/2(5\/10), 1\/4."} {"t":"s","id":5902,"s":"Rest = 609 - 357 = 252. Each box = 252 \u00f7 7 = 36."} {"t":"s","id":5906,"s":"3 units = 648, 1 unit = 216. James = 216, Liz = 432. Equal share = 324 each, so Liz gives 432 - 324 = 108."} {"t":"s","id":5907,"s":"768 is even, 7+6+8=21 divisible by 3, and tens digit 6 < hundreds digit 7. The others fail one condition."} {"t":"s","id":5908,"s":"Saturday = 2786 - 1375 = 1411. Both days = 2786 + 1411 = 4197."} {"t":"s","id":5909,"s":"21 \u00f7 3 = 7, so numerator = 14 \u00f7 7 = 2. The missing numerator is 2."} {"t":"s","id":5911,"s":"Total pencils = 5 \u00d7 8 = 40. Each friend = 40 \u00f7 10 = 4."} {"t":"s","id":5912,"s":"1 week = 7 days. 198 \u00d7 7 = 1386."} {"t":"s","id":5913,"s":"859 \u00f7 4 = 214 R 3. The 3 leftover sweets still need 1 more bag, so 214 + 1 = 215 bags."} {"t":"s","id":5914,"s":"Given away = 285 - 21 = 264. Monday + Tuesday = 3 units + 1 unit = 4 units = 264, so 1 unit (Tuesday) = 264 \u00f7 4 = 66."} {"t":"s","id":5920,"s":"3.18 p.m. minus 3 h 35 min: 3.18 p.m. - 3 h = 12.18 p.m.; 12.18 p.m. - 35 min = 11.43 a.m."} {"t":"s","id":5923,"s":"Starting gap = 30. Muthu gives 50, so the gap widens by 2 \u00d7 50 = 100. End difference = 30 + 100 = 130."} {"t":"s","id":5924,"s":"Oliver = Agnes - $82.50; Ming Huat = Agnes - $96.50. Oliver - Ming Huat = 96.50 - 82.50 = $14."} {"t":"s","id":5928,"s":"Morning 8.15 a.m. to 1.00 p.m. = 4 h 45 min. Afternoon 3.00 p.m. to 5.30 p.m. = 2 h 30 min. Total = 4 h 45 min + 2 h 30 min = 7 h 15 min."} {"t":"s","id":5931,"s":"If all 15 rows had 6 seats = 90; need 110, extra 20 = 2 per row swapped to 8s, so 10 rows of 8. Seats in rows of 8 = 10 \u00d7 8 = 80."} {"t":"s","id":5932,"s":"5 thousands = 5000, 3 tens = 30. 5000 + 30 = 5030."} {"t":"s","id":5944,"s":"Weiming = 7 x 54 = 378. More than Paul = 378 - 54 = 324."} {"t":"s","id":5958,"s":"10.30 a.m. + 1 h = 11.30 a.m.; + 15 min = 11.45 a.m."} {"t":"s","id":5960,"s":"Ones: (a) + 8 = 5 with regroup, so (a) = 7 (7 + 8 = 15). Tens: 1 + 3 + (b) = 4, so (b) = 0."} {"t":"s","id":5966,"s":"(a) 6 l 533 ml + 2 l 467 ml = 9 l = 9000 ml. (b) 9000 ml \/ 3000 ml = 3 jugs."} {"t":"s","id":5969,"s":"Total stays 168 = 3 units, so 1 unit = 56 (Samy after). Samy after = 168 \/ 3 = 56. Samy at first = 56 - 15 = 41."} {"t":"s","id":5970,"s":"$244 \/ $6 = 40 packets remainder $4. 40 packets x 8 apples = 320 apples."} {"t":"s","id":5971,"s":"In 1903 the digits are 1 (thousands), 9 (hundreds), 0 (tens), 3 (ones). The '1' is in the thousands place."} {"t":"s","id":5976,"s":"The numbers decrease by 100 each time. (a) 5271 - 100 = 5171; (b) 5071 - 100 = 4971."} {"t":"s","id":5981,"s":"Women = 1 unit, men = 2 units, total = 3 units = 258. 1 unit = 258 \/ 3 = 86 women."} {"t":"s","id":5985,"s":"March = 3906 + 2019 = 5925. Total = 3906 + 5925 = 9831. (Or 3906 x 2 + 2019 = 9831.)"} {"t":"s","id":5986,"s":"(a) Friday = 112 \/ 4 = 28 masks. (b) 112 - 28 = 84 more masks on Saturday."} {"t":"s","id":5987,"s":"Cupcakes packed = 136 x 9 = 1224. Total baked = 1224 + 15 given away = 1239."} {"t":"s","id":5988,"s":"(a) Vans at first = 64 + 12 (that left) = 76. (b) Lorries at first equalled vans at first = 76; in the end = 76 + 19 = 95."} {"t":"s","id":5991,"s":"4\/8, 5\/10, 6\/12 all simplify to 1\/2. 2\/6 simplifies to 1\/3, so it is the odd one out."} {"t":"s","id":5992,"s":"Over a common denominator of 12: 2\/3=8\/12, 3\/4=9\/12, 5\/6=10\/12, 7\/12. 5\/6 is the greatest."} {"t":"s","id":6002,"s":"From 3.10 to 4.10 is 1 h; 4.10 to 4.55 is 45 min. Total 1 h 45 min."} {"t":"s","id":6004,"s":"4\/5 = 8\/10. 8\/10 - 3\/10 = 5\/10 = 1\/2."} {"t":"s","id":6008,"s":"In 8273 the digits from the right are 3 (ones), 7 (tens), 2 (hundreds), 8 (thousands). So the tens digit is 7."} {"t":"s","id":6011,"s":"10 hundreds = 1000 and 23 ones = 23. Sum = 1000 + 23 = 1023."} {"t":"s","id":6015,"s":"4\/6, 6\/9 and 8\/12 all simplify to 2\/3. 2\/6 = 1\/3, which is not equivalent to 2\/3."} {"t":"s","id":6018,"s":"Three thousand = 3000, eight hundred = 800, fifty = 50. 3000 + 800 + 50 = 3850."} {"t":"s","id":6020,"s":"The numbers increase by 70 each time: 3898, 3968, 4038, 4108, 4178. The missing number is 4038."} {"t":"s","id":6022,"s":"The greatest 2-digit number is 99. 96 = 4 \u00d7 24 is the largest 2-digit multiple of 4."} {"t":"s","id":6023,"s":"3\/4 = 9\/12. 9\/12 + 1\/12 = 10\/12 = 5\/6."} {"t":"s","id":6028,"s":"2\/8 = 1\/4 and 3\/9 = 1\/3 are both less than 1\/2. 8\/10 and 9\/12 (= 3\/4) are greater than 1\/2."} {"t":"s","id":6033,"s":"Sunday = 3574 \u2212 199 = 3375. Two days = 3574 + 3375 = 6949."} {"t":"s","id":6035,"s":"1\/4 = 3\/12. 11\/12 \u2212 3\/12 = 8\/12 = 2\/3."} {"t":"s","id":6039,"s":"119 \u00f7 5 = 23 remainder 4. The leftover 4 muffins still need 1 more box, so 23 + 1 = 24 boxes."} {"t":"s","id":6041,"s":"Remove the 55 difference: 975 \u2212 55 = 920, which is 2 equal shares. Tom = 920 \u00f7 2 = 460."} {"t":"s","id":6104,"s":"(a) +1000 each step: 5300, 6300. (b) +5 each step: 1990 before 1995, 2005 between 2000 and 2010."} {"t":"s","id":6130,"s":"2 thousands = 2000, 21 hundreds = 2100, 220 tens = 2200, 2022 ones = 2022. The smallest is 2000."} {"t":"s","id":6140,"s":"Between 6000 and 7000 so thousands = 6. Ones = smallest odd number = 1. Tens = 1 + 3 = 4. Hundreds = 6 - 2 = 4. The number is 6441."} {"t":"s","id":6153,"s":"5\/9 \u2248 0.56. 5\/7 \u2248 0.71 is greater; 1\/2=0.5, 3\/8=0.375, 4\/10=0.4 are all smaller."} {"t":"s","id":6166,"s":"As decimals: 3\/8=0.375, 3\/7\u22480.43, 1\/2=0.5, 3\/5=0.6. Smallest to greatest: 3\/8, 3\/7, 1\/2, 3\/5."} {"t":"s","id":6170,"s":"9.15 a.m. to 11.05 a.m. is 1 h 50 min = 110 min."} {"t":"s","id":6173,"s":"Hundreds = 2 \u00d7 tens. Smallest: tens=1, hundreds=2. Even and divisible by 3: 210 (2+1+0=3). So 210."} {"t":"s","id":6174,"s":"126 \u00f7 8 = 15 remainder 6. The leftover 6 need 1 more box, so 15 + 1 = 16 boxes."} {"t":"s","id":6175,"s":"Adults = 460 + 345 = 805. 805 \u2212 226 = 579 more adults than children."} {"t":"s","id":6177,"s":"Total sweets = 7 \u00d7 150 = 1050. 1050 \u00f7 6 = 175 goodie bags."} {"t":"s","id":6179,"s":"(a) 100 \u00f7 6 = 16 remainder 4, so 16 cakes. (b) 1 more cake needs 6 eggs but only 4 are left, so 6 \u2212 4 = 2 more eggs."} {"t":"s","id":6188,"s":"Greatest number = 6709, smallest number = 2548. Sum = 6709 + 2548 = 9257."} {"t":"s","id":6189,"s":"8 + 8 + 8 + 8 = 32. So 32 = 16 + ? x 8, meaning ? x 8 = 16, so ? = 2."} {"t":"s","id":6192,"s":"Total seats = 10 x 9 = 90. Occupied = 90 - 2 = 88."} {"t":"s","id":6193,"s":"Sandra has 5 x 9 = 45 stamps. Total = 9 + 45 = 54. Each should have 54 \/ 2 = 27. Sandra must give 45 - 27 = 18 stamps to Ravi."} {"t":"s","id":6195,"s":"Bigger number = 4086 - 1260 = 2826. Difference = 2826 - 1260 = 1566."} {"t":"s","id":6197,"s":"In 5690 the digits are 5 (thousands), 6 (hundreds), 9 (tens), 0 (ones). The hundreds digit is 6."} {"t":"s","id":6199,"s":"The two numbers use the same digits, so they are 26 and 62. Their sum is 88 and their difference is 62 - 26 = 36, which is between 20 and 40. The smaller number is 26."} {"t":"s","id":6200,"s":"a) Five thousand, nine hundred and eighty-one = 5981. b) Six thousand and seventy-three = 6073 (no hundreds, so a 0 in the hundreds place)."} {"t":"s","id":6203,"s":"Cookies baked = 2541 + 1981 = 4522. Pies = 4522 + 239 = 4761."} {"t":"s","id":6205,"s":"(a) Siva = 4153 - 1122 = 3031. (b) Jane has 1739 fewer than Liz, so Liz = 4153 + 1739 = 5892."} {"t":"s","id":6206,"s":"In 1809 the digits are 1 (thousands), 8 (hundreds), 0 (tens), 9 (ones). The thousands digit is 1."} {"t":"s","id":6209,"s":"A school bus is about 15 m long. 50 cm and 150 cm are too short; 500 m is far too long."} {"t":"s","id":6211,"s":"Common denominator 18: 2\/3=12\/18, 1\/2=9\/18, 7\/9=14\/18. Greatest to smallest: 7\/9, 2\/3, 1\/2."} {"t":"s","id":6213,"s":"Tuesday = 1231 - 256 = 975. Total = 1231 + 975 = 2206."} {"t":"s","id":6215,"s":"John = 36 \/ 3 = 12. Altogether = 36 + 12 = 48."} {"t":"s","id":6216,"s":"3 x 6 = 18, so multiply numerator by 6: 2 x 6 = 12. So 2\/3 = 12\/18."} {"t":"s","id":6217,"s":"The pattern decreases by 200 each time. 8424 - 200 = 8224."} {"t":"s","id":6218,"s":"1 km = 1000 m. 5048 m = 5000 m + 48 m = 5 km 48 m."} {"t":"s","id":6220,"s":"293 \/ 4 = 73 remainder 1. The quotient is 73."} {"t":"s","id":6229,"s":"(a) 2\/3 = 6\/9; 6\/9 - 2\/9 = 4\/9. (b) 1\/2 = 4\/8; 4\/8 + 3\/8 = 7\/8."} {"t":"s","id":6231,"s":"338 \/ 9 = 37 remainder 5. So 5 sweets were left unpacked."} {"t":"s","id":6234,"s":"Keith = 376 x 5 = 1880. Altogether = 376 + 1880 = 2256. (Key shows 376 x 6 = 2256, combining Tom's 1 unit and Keith's 5 units.)"} {"t":"s","id":6235,"s":"Total 4 units = 64, so 1 unit = 16. Ali = 16, Johan = 48. Difference = 48 - 16 = 32 (or 2 units = 2 x 16 = 32)."} {"t":"s","id":6236,"s":"Remove the 31 difference: 107 - 31 = 76, which is 2 equal parts. Lucy = 76 \/ 2 = 38."} {"t":"s","id":6237,"s":"Initial difference $5. Wei Ming gives $6: May Han +$6, Wei Ming -$6, so the gap widens by $12. New difference = $5 + $12 = $17. (Key: 6 + 5 = 11; 11 + 6 = $17.)"} {"t":"s","id":6238,"s":"Packed = 35 x 9 = 315. Total = 315 + 7 = 322 muffins."} {"t":"s","id":6242,"s":"(a) 1.45 p.m. + 35 min = 2.20 p.m. (b) From 2.20 p.m. to 4.00 p.m. = 1 h 40 min."} {"t":"s","id":6252,"s":"6\/7 cannot be simplified (no common factor). 2\/4=1\/2, 8\/10=4\/5, 2\/12=1\/6."} {"t":"s","id":6270,"s":"Common denominator 8: 3\/4=6\/8, 1\/2=4\/8, 7\/8=7\/8. Greatest to smallest: 7\/8, 3\/4, 1\/2."} {"t":"s","id":6274,"s":"134 \/ 5 = 26 remainder 4. So 26 bags and 4 apples not packed."} {"t":"s","id":6276,"s":"1 h 50 min + 1 h 40 min = 3 h 30 min. Starting 9 a.m. + 3 h 30 min = 12.30 p.m."} {"t":"s","id":6278,"s":"Assume all 20 are horses: 20 x 4 = 80 legs. Excess 80 - 48 = 32; each duck has 2 fewer legs (4-2=2), so ducks = 32\/2 = 16; horses = 20 - 16 = 4."} {"t":"s","id":6287,"s":"In 7845 the 7 is worth 7000; in 271 the 7 is worth 70. Sum = 7000 + 70 = 7070."} {"t":"s","id":6289,"s":"Red = 1597 + 900 = 2497. Total = 1597 + 2497 = 4094."} {"t":"s","id":6299,"s":"Number + 20 = number x 6. Testing 4: 4 + 20 = 24 and 4 x 6 = 24, so the number is 4."} {"t":"s","id":6309,"s":"a) 3265 - 1673 = 1592 more children. b) Girls = 3265 - 1527 = 1738."} {"t":"q","id":12944,"q":"There were 8009 visitors at the Zoo. 4050 of the visitors were children. How many adults were there?","e":"8009 - 4050 = 3959 adults."} {"t":"q","id":12945,"q":"Peter had 58 apples. He packed them into boxes of 7. How many apples were left unpacked?","e":"58 \/ 7 = 8 remainder 2, so 2 apples are left unpacked."} {"t":"q","id":12948,"q":"Mrs Lee left her house at 11.50 a.m. for her baking class. She took 1 h 40 min to travel from her house to her baking class. She arrived 15 minutes before her class started. What time did her baking class start?","e":"11.50 a.m. + 1 h 40 min = 1.30 p.m. (arrival). Class started 15 min later: 1.30 + 15 min = 1.45 p.m."} {"t":"q","id":12949,"q":"Gopal bought a shirt for $45.50 and a belt for $34.90. He gave the cashier $100. How much change would Gopal get?","e":"$45.50 + $34.90 = $80.40 spent. Change = $100 - $80.40 = $19.60."} {"t":"q","id":12950,"q":"Madam Siti bought a pizza. Her daughter ate 3\/8 of the pizza and her son ate 1\/4 of the pizza less than her daughter. What fraction of the pizza was eaten?","e":"Son ate 3\/8 - 1\/4 = 3\/8 - 2\/8 = 1\/8. Total eaten = 3\/8 + 1\/8 = 4\/8 = 1\/2."} {"t":"q","id":12951,"q":"960 people turned up for a school carnival on Saturday. There were 4 times as many people who turned up on Sunday than on Saturday. How many people turned up on both days?","e":"Sunday = 4 x 960 = 3840. Both days = 960 + 3840 = 4800."} {"t":"q","id":12952,"q":"A fruit seller had equal number of rambutans and mangosteens. After selling 810 mangosteens, he had 3 times as many rambutans as mangosteens left. How many rambutans did he have?","e":"Let each start = x. After selling, rambutans = x, mangosteens = x - 810, and x = 3(x - 810). So x = 3x - 2430, 2430 = 2x, x = 1215."} {"t":"q","id":12957,"q":"Express \\(\\dfrac{18}{24}\\) as a fraction in its simplest form. ","e":"Divide numerator and denominator by 6: 18\/24 = 3\/4."} {"t":"q","id":12958,"q":"Find the quotient of 537 \/ 8. ","e":"537 \/ 8 = 67 remainder 1; wait, 8 x 67 = 536, remainder 1. The quotient is 67. Per the answer key the quotient given is 61."} {"t":"q","id":12961,"q":"Arrange the following numbers in order, beginning with the greatest. 4853, 7906, 7069, 4835 , , , ","e":"Greatest to smallest: 7906, 7069, 4853, 4835."} {"t":"q","id":12962,"q":"Mrs Lim had 1248 g of flour. She used 300 g to bake a cake and packed the remaining flour equally into 6 packets. How much flour was there in each packet? g","e":"Remaining = 1248 - 300 = 948 g. Each packet = 948 \/ 6 = 158 g."} {"t":"q","id":12963,"q":"The sum of two numbers is 1750. The value of the smaller number is 795. What is the value of the greater number? ","e":"Greater number = 1750 - 795 = 955."} {"t":"q","id":12964,"q":"Find the value of A and B. 6 A 9 x B = 4 0 7 4. A = , B = ","e":"6A9 x B = 4074. Trying B = 6: 679 x 6 = 4074, so A = 7 and B = 6."} {"t":"q","id":12966,"q":"Ms Chong bought a piece of cloth which was 5 m long. She used some of it to sew 5 similar towels. There was 185 cm of cloth left. What was the length of cloth used for each towel? cm","e":"5 m = 500 cm. Cloth used = 500 - 185 = 315 cm. Each towel = 315 \/ 5 = 63 cm."} {"t":"q","id":12969,"q":"Arrange the following fractions from the smallest to the biggest. 1\/8, 3\/4, 5\/12 , , ","e":"Common denominator 24: 1\/8=3\/24, 5\/12=10\/24, 3\/4=18\/24. Smallest to biggest: 1\/8, 5\/12, 3\/4."} {"t":"q","id":12971,"q":"Fadilah needed 45 min to travel from her house to the cinema. When she arrived at the cinema, the time shown on her watch was 12.20 p.m. Her watch was 10 minutes faster. What was the actual time she left her house? a.m.","e":"Watch shows 12.20 p.m. but is 10 min fast, so actual arrival = 12.10 p.m. Subtract the 45 min travel: 12.10 p.m. - 45 min = 11.25 a.m."} {"t":"q","id":12973,"q":"Ann had 905 stamps and Bala had 299 stamps. Ann had 230 more stamps than Colin. How many more stamps did Colin have than Bala? ","e":"Colin = 905 - 230 = 675. Colin - Bala = 675 - 299 = 376."} {"t":"q","id":12975,"q":"Mrs Lim baked 340 chocolate pies. She packed them equally into boxes of 9. What was the least number of boxes needed by Mrs Lim if she wanted to pack all the chocolate pies into boxes? ","e":"340 \/ 9 = 37 remainder 7. The 7 leftover pies still need a box, so 37 + 1 = 38 boxes."} {"t":"q","id":12976,"q":"Mary had 29 coins. She had 15 one-dollar coins and the rest were fifty-cents and ten-cents coins. She had $20.80 altogether. How many fifty-cents coins did Mary have? ","e":"15 one-dollar coins = $15.00, leaving $5.80 in 14 coins (50c and 10c). If all 14 were 10c that is $1.40; the extra $4.40 comes from swapping 10c for 50c (each swap adds 40c): 440\/40 = 11 fifty-cent coins."} {"t":"q","id":12977,"q":"Siti had a total of 890 local and foreign stamps. She gave away 130 local stamps and collected another 280 foreign stamps. In the end, she had the same number of local and foreign stamps. (a) How many more local than foreign stamps did Siti have at first? (b) How many foreign stamps did Siti have at first? (a) , (b) ","e":"End total = 890 - 130 + 280 = 1040, so each is 520. Local at first = 520 + 130 = 650; foreign at first = 520 - 280 = 240. (a) 650 - 240 = 410 more local. (b) 240 foreign at first."} {"t":"q","id":12979,"q":"Which digit in 9876 is in the thousands place?","e":"In 9876, the digits from right to left are ones (6), tens (7), hundreds (8), thousands (9). So the thousands digit is 9."} {"t":"q","id":12982,"q":"Which of the following is an odd number?","e":"An odd number ends in 1, 3, 5, 7 or 9. Only 2641 ends in 1, so it is odd."} {"t":"q","id":12984,"q":"What is the missing number in the number pattern?\n82, 70, 58, 46, ?, 22","e":"The pattern decreases by 12 each time: 82, 70, 58, 46, 34, 22. So the missing number is 34."} {"t":"q","id":12985,"q":"Which of the following is the smallest number that can be divided by 5 with no remainder?","e":"A number divides by 5 with no remainder if it ends in 0 or 5. The numbers ending in 0 or 5 are 3530 and 3350. The smaller is 3350."} {"t":"q","id":12990,"q":"Which of the following fractions is closest to 1\/2?","e":"1\/2 = 4\/8. The distances from 4\/8 are: 1\/8 -> 3\/8, 2\/8 -> 2\/8, 3\/8 -> 1\/8, 6\/8 -> 2\/8. The smallest distance is for 3\/8."} {"t":"q","id":12994,"q":"75 children wanted to take a boat ride at the River Safari together. Each boat can carry at most 6 children. What is the least number of boats needed for the 75 children?","e":"75 div 6 = 12 remainder 3. The 12 boats carry 72 children; the remaining 3 children need 1 more boat, so 13 boats are needed."} {"t":"q","id":12995,"q":"Danny and William collected 60 stickers altogether. William collected 10 stickers more than Danny. How many stickers did Danny collect?","e":"Remove William's extra 10: 60 - 10 = 50, shared equally between the two boys gives 50 div 2 = 25 for Danny."} {"t":"q","id":12996,"q":"Two numbers, P and Q add up to 200. P is a 2-digit number while Q is a 3-digit number. What is the smallest possible value of Q?","e":"Q is smallest when P is largest. The largest 2-digit number is 99, so the smallest 3-digit Q is 200 - 99 = 101."} {"t":"q","id":12997,"q":"A bag of sugar weighs 2 kg. It is repacked equally into 4 bags. What is the mass of each bag of sugar in grams?","e":"2 kg = 2000 g. Repacked into 4 equal bags: 2000 div 4 = 500 g each."} {"t":"q","id":13000,"q":"Find the product of 312 and 6.
Answer: ","e":"312 x 6 = 1872."} {"t":"q","id":13001,"q":"Find the value of 4256 + 3352.
Answer: ","e":"4256 + 3352 = 7608."} {"t":"q","id":13004,"q":"Use all the digits 1, 5, 6 and 9 to form the smallest number between 5000 and 6000.
Answer: ","e":"Between 5000 and 6000 the thousands digit must be 5. Arrange the remaining digits 1, 6, 9 in ascending order: 1, 6, 9. So the smallest number is 5169."} {"t":"q","id":13005,"q":"Write the greatest 4-digit even number.
Answer: ","e":"The greatest 4-digit number is 9999, but it is odd. The greatest 4-digit even number ends in an even digit, so 9998."} {"t":"q","id":13006,"q":"Becky buys 6 bags of balloons for a party. There are 40 balloons in a bag. How many bunches of balloons does she get if she ties 3 balloons in a bunch?
Answer: ","e":"Total balloons = 6 x 40 = 240. Bunches = 240 div 3 = 80."} {"t":"q","id":13008,"q":"Daphne exchanged $5 for 10 coins. All the coins had the same value. What was the value of each coin in cents?
Answer: ","e":"$5 = 500 cents. 500 cents div 10 coins = 50 cents per coin."} {"t":"q","id":13009,"q":"The length of one piece of rope is 78 cm. What is the length of 8 such ropes? Give your answer in m and cm.\n m cm","e":"78 cm x 8 = 624 cm. 624 cm = 6 m 24 cm (since 100 cm = 1 m)."} {"t":"q","id":13012,"q":"Ling wrote 3 compositions in 2 hours. She took the same amount of time to write the first 2 compositions but took 30 minutes longer to write the third composition than the first. How many minutes did she take to write the first composition?
Answer: ","e":"2 hours = 120 minutes. The first two compositions take the same time (call it t each); the third takes t + 30. So t + t + (t + 30) = 120, giving 3t + 30 = 120, 3t = 90, t = 30 minutes."} {"t":"q","id":13013,"q":"A bottle can hold 1050 ml of water. A cup can hold 900 ml less water than the bottle. How much water can the cup hold?
Answer: ","e":"Cup = bottle - 900 ml = 1050 ml - 900 ml = 150 ml."} {"t":"q","id":13016,"q":"Find the difference between the smallest and greatest fractions.\n\\(\\dfrac{3}{4}\\), \\(\\dfrac{1}{2}\\), \\(\\dfrac{7}{8}\\)","e":"Convert to eighths: 3\/4 = 6\/8, 1\/2 = 4\/8, 7\/8 = 7\/8. Smallest = 4\/8, greatest = 7\/8. Difference = 7\/8 - 4\/8 = 3\/8."} {"t":"q","id":13017,"q":"Mother bought a pizza and sliced it into 12 equal pieces for a party. Iris took 3 pieces of the pizza. What fraction of the pizza did Iris take? Express your answer as a fraction in its simplest form.","e":"Iris took 3 out of 12 pieces = 3\/12. Simplify by dividing top and bottom by 3: 3\/12 = 1\/4."} {"t":"q","id":13018,"q":"There were 68 tables and 3 times as many chairs in a storeroom.\n(a) How many chairs were there in the storeroom?\n(b) How many tables and chairs were there altogether?\n chairs, altogether","e":"(a) Chairs = 3 x 68 = 204. (b) Tables + chairs = 68 + 204 = 272."} {"t":"q","id":13019,"q":"Ben and Jerry bought some egg tarts from a bakery. Ben bought 6 more egg tarts and paid $12 more than Jerry. How many egg tarts did Jerry buy if he paid a total of $98?
Answer: ","e":"6 more egg tarts cost $12, so each egg tart costs $12 div 6 = $2. Jerry paid $98, so Jerry bought $98 div $2 = 49 egg tarts."} {"t":"q","id":13021,"q":"Jack and Ken have some toy cars. After Jack gives 20 toy cars to Ken, he has 23 toy cars more than Ken. How many more toy cars does Jack have than Ken at first?
Answer: ","e":"Giving away 20 cars changes the gap by 2 x 20 = 40 (Jack loses 20, Ken gains 20). After giving, Jack leads by 23, so at first the lead was 23 + 40 = 63 more cars."} {"t":"q","id":13023,"q":"In 1579 the digit 5 is in the place.","e":"In 1579, reading from the right: 9 ones, 7 tens, 5 hundreds, 1 thousand. So the digit 5 is in the hundreds place."} {"t":"q","id":13024,"q":"Two thousand, one hundred and twelve written in numerals is .","e":"Two thousand = 2000, one hundred = 100, twelve = 12. 2000 + 100 + 12 = 2112."} {"t":"q","id":13025,"q":"What is the product of 24 and 8?","e":"Product means multiply. 24 x 8 = 192."} {"t":"q","id":13027,"q":"Which of the following fraction is not equivalent to 1\/2?","e":"2\/4, 3\/6 and 6\/12 all simplify to 1\/2. 4\/10 simplifies to 2\/5, which is not 1\/2."} {"t":"q","id":13028,"q":"Chloe takes 23 minutes to go home from school. She left school at 11.40 a.m. What time did Chloe get home?","e":"11.40 a.m. + 20 min = 12.00 noon (12.00 p.m.); + 3 min = 12.03 p.m."} {"t":"q","id":13029,"q":"What is the missing number in the number pattern? 1265 , 1280 , 1295 , , 1325","e":"The numbers increase by 15 each time: 1295 + 15 = 1310. Check: 1310 + 15 = 1325."} {"t":"q","id":13030,"q":"The mass of a durian is 2 kg 250 g. The mass of a pear is 360 g. How much heavier is the mass of the durian than the mass of the pear?","e":"2 kg 250 g = 2250 g. 2250 g - 360 g = 1890 g."} {"t":"q","id":13032,"q":"Mary took 1 hour 25 minutes to complete his homework. George took 40 minutes faster than Mary to complete his homework. How long did George take to complete his homework?","e":"1 h 25 min = 85 min. 85 min - 40 min = 45 min."} {"t":"q","id":13033,"q":"Dora had $49.90. Her mother gave her another $15. She spent $18.50. How much money had she left?","e":"$49.90 + $15 = $64.90. $64.90 - $18.50 = $46.40."} {"t":"q","id":13034,"q":"A fish tank contains 5 l 70 ml of water. 2190 ml more water is needed to fill up the fish tank. What is the capacity of the fish tank?","e":"5 l 70 ml = 5070 ml. 5070 ml + 2190 ml = 7260 ml."} {"t":"q","id":13035,"q":"A pizza was cut into equal pieces. Fred ate 1\/2 of it and Joy ate 1\/3 of it. What fraction of the pizza was eaten?","e":"1\/2 + 1\/3 = 3\/6 + 2\/6 = 5\/6."} {"t":"q","id":13037,"q":"The table shows the price of bus fares for different passengers. Adult $1.20; Senior citizen (above 60 years old) $0.90; Child (below 12 years old) $0.55. Mrs Tan took her two elderly parents out with her 10 year-old son. Her elderly parents were both 65 years old. What was the total bus fare for the four passengers?","e":"Mrs Tan (adult) $1.20 + two senior citizens (65 yrs) 2 x $0.90 = $1.80 + one child (10 yrs) $0.55 = $1.20 + $1.80 + $0.55 = $3.55."} {"t":"q","id":13039,"q":"Arrange the following numbers from the greatest to the smallest. 7216, 7261, 7126, 7162 , , , ","e":"Compare the tens and ones: 7261 > 7216 > 7162 > 7126."} {"t":"q","id":13040,"q":"What is the quotient when you divide 908 by 5? ","e":"908 \/ 5 = 181 remainder 3. The quotient is 181."} {"t":"q","id":13041,"q":"3874 people visited Sentosa on Saturday. On Sunday, 1955 fewer people visited it than on Saturday. How many people visited Sentosa on Sunday? ","e":"3874 - 1955 = 1919."} {"t":"q","id":13042,"q":"Arrange the following fractions from the greatest to the smallest. 5\/9, 5\/6, 5\/7 , , ","e":"Same numerator: the smaller the denominator, the larger the fraction. So 5\/6 > 5\/7 > 5\/9."} {"t":"q","id":13043,"q":"Lynn started her computer lesson at 8.30 a.m. It ended at 12.15 p.m. How long was her computer lesson? h min","e":"8.30 a.m. to 12.30 p.m. is 4 h; 12.15 p.m. is 15 min before 12.30, so 4 h - 15 min = 3 h 45 min. (From 8.30 to 12.15 = 3 h 45 min.)"} {"t":"q","id":13044,"q":"Tara bought 270 pens. She bought three times as many pens as Ray. How many pens did Ray buy? ","e":"Tara = 3 x Ray, so Ray = 270 \/ 3 = 90."} {"t":"q","id":13048,"q":"Meili was left with 90 cents after paying for 2 bars of chocolates and 1 bag of chips. The 2 chocolate bars cost $3.30 and the bag of chips costs $2.00. How much money did she have at first? ","e":"Spent = $3.30 + $2.00 = $5.30. At first = $5.30 + $0.90 = $6.20."} {"t":"q","id":13052,"q":"A total of 380 movie tickets were sold in two days. 90 fewer tickets were sold on the first day than on the second day. How many tickets were sold on the first day? ","e":"Remove the 90 difference: 380 - 90 = 290; this is two equal first-day amounts, so first day = 290 \/ 2 = 145."} {"t":"q","id":13053,"q":"Mrs Tan bought 500 g of flour. She used 12 g of flour for each cupcake. If she baked 9 cupcakes in all, how much flour had she left? g","e":"Flour used = 12 g x 9 = 108 g. Left = 500 g - 108 g = 392 g."} {"t":"q","id":13054,"q":"Huni bought 3 cookies for $5.00 and received 1 cookie for free. How much did she pay for 12 cookies? ","e":"For every 3 paid + 1 free = 4 cookies. 12 cookies = 12 \/ 4 = 3 groups, so she paid for 3 x 3 = 9 cookies = 3 x $5.00 = $15.00."} {"t":"q","id":13055,"q":"A shopkeeper had some oranges. She threw away 13 rotten oranges. She packed the remaining 216 oranges equally into 8 boxes. a) How many oranges did the shopkeeper have at first? b) How many oranges were there in each box? ","e":"a) At first = 216 + 13 = 229 oranges. b) Each box = 216 \/ 8 = 27 oranges."} {"t":"q","id":13056,"q":"Lily went shopping and bought a dress, a bag and a watch. She paid $605 for a dress and a bag. The bag cost 4 times as much as the dress. The watch cost $19 more than the bag. (a) How much did Lily pay for the bag? (b) How much did she pay for the watch? ","e":"Dress + bag = 5 units = $605, so 1 unit (dress) = $605 \/ 5 = $121. a) Bag = 4 units = $121 x 4 = $484. b) Watch = $484 + $19 = $503."} {"t":"q","id":13057,"q":"Carol had a square plot of land. She planted 7 trees on each side. A tree was planted at each corner. How many trees were there in total? ","e":"4 sides x 7 = 28 counts, but the 4 corner trees are each counted twice, so 28 - 4 = 24. (Answer key: 5 x 4 = 20 non-corner-overlap, + 4 corners = 24.)"} {"t":"q","id":13059,"q":"Mr Tan bought 6 loaves of bread. Each loaf is cut into 8 slices of bread. How many slices of bread did Mr Tan have altogether?","e":"6 loaves x 8 slices each = 48 slices."} {"t":"q","id":13061,"q":"Jessica has 75 cookies. She has 3 times as many cookies as Jessica. How many cookies do Jessica and Kim have altogether?","e":"Per the answer key the correct option is 100."} {"t":"q","id":13062,"q":"Mr Lim bought 6 boxes of erasers to give to his students. There were 24 erasers in each box. In the end, Mr Lim had 18 erasers left. How many erasers did he give to his students?","e":"Total erasers = 6 x 24 = 144. Given away = 144 - 18 = 126."} {"t":"q","id":13063,"q":"Find the product of 34 and 6. ","e":"Product = 34 x 6 = 204."} {"t":"q","id":13065,"q":"Mr Mohammad had some stickers. He packed some stickers into 8 packets. There were 46 stickers in each packet. He had 37 stickers left unpacked. How many stickers did Mr Mohammad have at first? ","e":"Packed = 8 x 46 = 368. Total at first = 368 + 37 = 405."} {"t":"q","id":13066,"q":"Amy collected 78 seashells. June collected 42 seashells. How many more seashells must June collect so that she has 3 times as many seashells as Amy? ","e":"3 times Amy = 3 x 78 = 234. June needs 234 - 42 = 192 more seashells."} {"t":"q","id":13068,"q":"What is 8 m 7 cm in centimetres?","e":"8 m = 800 cm. 800 cm + 7 cm = 807 cm."} {"t":"q","id":13069,"q":"Arrange the following fractions from the smallest to the greatest.\n\n[2\/3], [5\/9], [1\/8]","e":"1\/8 = 0.125, 5\/9 ~ 0.556, 2\/3 ~ 0.667. Smallest to greatest: 1\/8, 5\/9, 2\/3."} {"t":"q","id":13070,"q":"A dress and a T-shirt cost $41 altogether.\nThe dress costs $27.30. How much does the T-shirt cost?","e":"$41.00 - $27.30 = $13.70."} {"t":"q","id":13073,"q":"\\(\\dfrac{5}{12}\\) - \\(\\dfrac{1}{4}\\) = \nGive your answer in its simplest form.","e":"1\/4 = 3\/12. 5\/12 - 3\/12 = 2\/12 = 1\/6."} {"t":"q","id":13074,"q":"\\(\\dfrac{1}{2}\\) + \\(\\dfrac{1}{7}\\) = \nGive your answer in its simplest form.","e":"1\/2 = 7\/14 and 1\/7 = 2\/14. 7\/14 + 2\/14 = 9\/14."} {"t":"q","id":13075,"q":"The following table shows a menu at a cafe.\n\nBurger $6.90\nCupcake $2.50\nPizza $7.80\nWaffle $5.50\n\nAndy bought a waffle and another item from the menu. He spent $12.40 in all. What was the cost of the other item that he bought?
Answer: ","e":"$12.40 - $5.50 (waffle) = $6.90, which is the price of the burger."} {"t":"q","id":13076,"q":"[2\/3] = [\/18]\nFind the missing number in the box.","e":"2\/3 = ?\/18. Since 3 x 6 = 18, multiply the numerator: 2 x 6 = 12. So 2\/3 = 12\/18."} {"t":"q","id":13077,"q":"Cindy spent her money on a bag and a pair of shoes. The bag costs $21.90. The pair of shoes costs $18 more than the bag. How much did she spend altogether?
Answer: ","e":"Shoes = $21.90 + $18 = $39.90. Total = $21.90 + $39.90 = $61.80."} {"t":"q","id":13078,"q":"Tom saved $49.85. Sam saved $12.50 more than Tom. Paul saved $9.85 less than Sam. How much did Paul save?
Answer: ","e":"Sam = $49.85 + $12.50 = $62.35. Paul = $62.35 - $9.85 = $52.50."} {"t":"q","id":13081,"q":"Mr Leong asked his pupils to convert 9 m 6 cm to cm. Which pupil wrote it correctly?","e":"9 m = 900 cm, plus 6 cm = 906 cm. Boon Huat is correct."} {"t":"q","id":13088,"q":"Which one of the following will add up to an answer that is an odd number?","e":"An odd sum needs one odd and one even number. 1719 (odd) + 2002 (even) = 3721, which is odd."} {"t":"q","id":13089,"q":"4 thousands 27 hundreds = thousands and 17 hundreds.","e":"4 thousands 27 hundreds = 4000 + 2700 = 6700. As (?) thousands + 17 hundreds (1700): 6700 - 1700 = 5000 = 5 thousands."} {"t":"q","id":13091,"q":"There are 266 children going to the zoo. There are 7 buses and each bus can seat 35 children. How many children will not have a seat?","e":"7 buses x 35 seats = 245 seats. 266 - 245 = 21 children without a seat."} {"t":"q","id":13093,"q":"Jack, Marcy, Tabby and Porsha have some stickers. Jack has 15 more stickers than Marcy. Marcy has 28 fewer stickers than Tabby. Porsha has 10 more stickers than Jack. Who has the most stickers?","e":"Let Marcy = M. Jack = M+15, Porsha = M+25, Tabby = M+28. Tabby has the most (M+28)."} {"t":"q","id":13094,"q":"2503 = 2000 + + 3","e":"2503 - 2000 - 3 = 500. The missing number is 500."} {"t":"q","id":13095,"q":"Convert 205 min into hours and minutes. h min","e":"205 min = 180 min + 25 min = 3 h 25 min."} {"t":"q","id":13096,"q":"Arrange the following fractions from the greatest to the smallest. 3\/5 , 1\/4 , 7\/10 , , ","e":"Convert to tenths\/twentieths: 7\/10 = 0.7, 3\/5 = 0.6, 1\/4 = 0.25. Greatest to smallest: 7\/10, 3\/5, 1\/4."} {"t":"q","id":13101,"q":"How many tens are there in the quotient of 1560 \u00f7 6? tens","e":"1560 \u00f7 6 = 260. In 260 there are 26 tens."} {"t":"q","id":13102,"q":"There are 3546 chocolate cupcakes. There are 1649 more chocolate than vanilla cupcakes. How many vanilla cupcakes are there?
Answer: ","e":"3546 - 1649 = 1897 vanilla cupcakes."} {"t":"q","id":13103,"q":"The sum of two numbers is 300. The difference between the two numbers is 70. What is the smaller number?
Answer: ","e":"Smaller number = (sum - difference) \u00f7 2 = (300 - 70) \u00f7 2 = 230 \u00f7 2 = 115."} {"t":"q","id":13105,"q":"The capacity of a jug is 1200 ml. 3 bottles can fill the jug completely. 4 glasses of water can fill a bottle completely. What is the capacity of a glass? ml","e":"1 bottle = 1200 \u00f7 3 = 400 ml. 1 glass = 400 \u00f7 4 = 100 ml."} {"t":"q","id":13107,"q":"Arrange the following in an increasing order, beginning from the smallest. 7 l 404 ml , 74 l , 7074 ml , 7004 ml , , , ","e":"Convert to ml: 7 l 404 ml = 7404 ml; 74 l = 74000 ml; 7074 ml; 7004 ml. Increasing: 7004 ml, 7074 ml, 7 l 404 ml (7404 ml), 74 l (74000 ml)."} {"t":"q","id":13109,"q":"The opening hours of a clinic are shown. 9.00 a.m. to 12.30 p.m. ; 2.15 p.m. to 5.15 p.m. ; 6.30 p.m. to 9.45 p.m. How long is the clinic open each day? h min","e":"Session 1: 9.00 a.m.-12.30 p.m. = 3 h 30 min. Session 2: 2.15-5.15 p.m. = 3 h. Session 3: 6.30-9.45 p.m. = 3 h 15 min. Total = 9 h 45 min."} {"t":"q","id":13110,"q":"Mrs Lee sewed 7 flowers on each dress. She had 69 flowers left after sewing 183 dresses. How many flowers did Mrs Lee have at first?
Answer: ","e":"Flowers used = 183 x 7 = 1281. With 69 left over, she started with 1281 + 69 = 1350."} {"t":"q","id":13112,"q":"Martha's dance lesson starts at 5.35 p.m. She needs to be at the dance studio 25 minutes before the start of her lesson to do her warmup. The journey from Martha's house to the dance studio takes 45 minutes. (a) What time must Martha leave her house? (b) Martha's dance lesson ended at 6.45 pm. How long was her dance lesson? Give your answer in h and min. (a) (b) ","e":"(a) Arrive 25 min before 5.35 p.m. = 5.10 p.m.; subtract 45 min travel = 4.25 p.m. (b) 5.35 p.m. to 6.45 p.m. = 1 h 10 min."} {"t":"q","id":13113,"q":"Sue collected 2075 seashells. Lina collected 779 seashells. Sue gave Lina some seashells so that they both have an equal number of seashells in the end. How many seashells did Lina have in the end?
Answer: ","e":"Difference = 2075 - 779 = 1296. Sue gives half, 1296 \u00f7 2 = 648, to make them equal. Lina ends with 779 + 648 = 1427."} {"t":"q","id":13114,"q":"A shopkeeper has a total of 14 two-dollar and ten-dollar notes. He has $76 altogether. How many two-dollar notes does he have?
Answer: ","e":"Guess-and-check: 8 two-dollar notes = $16 and 6 ten-dollar notes = $60; 8 + 6 = 14 notes and $16 + $60 = $76. So 8 two-dollar notes."} {"t":"q","id":13115,"q":"Mr Ravi and Mr Goh had the same amount of flour in their bakery. Mr Ravi used 960 g of flour while Mr Goh used 2500 g of flour to bake some bread. In the end, Mr Ravi had 3 times as much flour left as Mr Goh. How much flour did each of them have at first? Give your answer in kilograms and grams.
Answer: ","e":"Difference used = 2500 - 960 = 1540 g, which equals 2 units (Ravi's 3 units minus Goh's 1 unit). 1 unit = 770 g, so Goh's leftover = 770 g. At first = 770 + 2500 = 3270 g = 3 kg 270 g."} {"t":"q","id":13121,"q":"There are 612 erasers altogether. Sam packs them equally into 6 boxes. How many erasers are there in each box?","e":"Divide the total equally: 612 \u00f7 6 = 102 erasers in each box."} {"t":"q","id":13122,"q":"What is the difference between the values of digit '5' and digit '7' in 5370?","e":"In 5370 the value of 5 is 5000 and the value of 7 is 70. Difference = 5000 \u2212 70 = 4930."} {"t":"q","id":13123,"q":"Write four thousand and sixty-three in numerals.
Answer: ","e":"Four thousand and sixty-three = 4063 (4 thousands, 0 hundreds, 6 tens, 3 ones)."} {"t":"q","id":13126,"q":"Find the quotient when 362 is divided by 5.
Answer: ","e":"362 \u00f7 5 = 72 remainder 2. The quotient is 72."} {"t":"q","id":13129,"q":"Michelle is 27 years old this year. Kenneth will be 26 years old in 10 years' time. How much older is Michelle than Kenneth?
Answer: ","e":"Kenneth's age now = 26 \u2212 10 = 16. Michelle is 27, so she is 27 \u2212 16 = 11 years older."} {"t":"q","id":13130,"q":"Form the smallest 3-digit odd number and divide it by 4. What answer will you get?
Answer: ","e":"The smallest 3-digit odd number is 101. 101 \u00f7 4 = 25 remainder 1."} {"t":"q","id":13131,"q":"There were 187 adults at a food fair. There were 58 more adults than children at the food fair. How many people were there at the food fair altogether?
Answer: ","e":"Children = 187 \u2212 58 = 129. Total people = 187 + 129 = 316."} {"t":"q","id":13132,"q":"Rita and Don have $5010 altogether. Yvonne and Rita have $8273 altogether. If Yvonne has $3958, how much does Don have?
Answer: ","e":"Rita = 8273 \u2212 3958 = $4315. Don = 5010 \u2212 4315 = $695."} {"t":"q","id":13133,"q":"Asha had some beads. She used 35 beads to make a necklace. Then, she bought another 42 beads and had 105 beads left.\na) How many beads will Asha need to make 2 similar necklaces?\nb) How many beads did Asha have at first?\na) \nb) ","e":"a) One necklace uses 35 beads, so 2 necklaces need 35 \u00d7 2 = 70 beads. b) Before buying 42 she had 105 \u2212 42 = 63; before making the necklace she had 63 + 35 = 98 beads at first."} {"t":"q","id":13138,"q":"Which of the following number has a remainder of 2 when divided by 3?","e":"572 = 3 x 190 + 2, so it leaves a remainder of 2. (298 r1, 381 r0, 496 r1.)"} {"t":"q","id":13139,"q":"Which of the following number cannot be divided by 6 exactly?","e":"813 is odd, so it is not divisible by 6 (a multiple of 6 must be even). 354, 432 and 768 are all even with digit sums divisible by 3."} {"t":"q","id":13140,"q":"When a number is divided by 4, the quotient is 117 with remainder 1. What is the number?","e":"Number = 4 x 117 + 1 = 468 + 1 = 469."} {"t":"q","id":13141,"q":"A baker bakes 122 cupcakes a day. How many cupcakes can he bake in 7 days?","e":"122 x 7 = 854 cupcakes."} {"t":"q","id":13142,"q":"Randy has 318 bookmarks. His sister has 6 times as many bookmarks as Randy. How many bookmarks does his sister have?
Answer: ","e":"318 x 6 = 1908 bookmarks."} {"t":"q","id":13143,"q":"A fruit seller has 405 mangoes. He packed the mangoes in 5 boxes. How many mangoes are there in each box?
Answer: ","e":"405 \/ 5 = 81 mangoes in each box."} {"t":"q","id":13144,"q":"Miss Rita has a ribbon that is 252cm long. She cuts the ribbon into 9 equal strips. How long is 1 strip of the small ribbon?
Answer: ","e":"252 cm \/ 9 = 28 cm for each strip."} {"t":"q","id":13145,"q":"Billy and Rick made 162 paper cranes to decorate the school hall. Billy made 5 times as many paper cranes as Rick. (a) How many paper cranes did Billy make? (b) How many paper cranes did Rick make?
(a)   (b) ","e":"Together they make 5 + 1 = 6 units = 162, so 1 unit (Rick) = 162 \/ 6 = 27. Billy = 5 x 27 = 135. (a) Billy made 135. (b) Rick made 27."} {"t":"q","id":13146,"q":"Uncle Jacob donated 260 pencils to a children's home. He packed the pencils into gift boxes. Each gift box contains 7 pencils. What is the least number of pencils he needs if he wants 7 pencils in every box?
Answer: ","e":"260 \/ 7 = 37 remainder 1. The leftover box has 1 pencil, so he needs 7 - 1 = 6 more pencils to make a complete box of 7."} {"t":"q","id":13151,"q":"Susan has $258. She has thrice as much money as Kartijah. How much money do Susan and Kartijah have altogether?
Answer: ","e":"Kartijah = $258 \u00f7 3 = $86. Altogether = $258 + $86 = $344."} {"t":"q","id":13152,"q":"There are 361 Chinese books in a library. The number of English books in the library is 6 times as many as the number of Chinese books. How many more English books than Chinese books are there in the library?
Answer: ","e":"English books = 361 \u00d7 6 = 2166. More English than Chinese = 2166 \u2212 361 = 1805."} {"t":"q","id":13153,"q":"Kevin has 3 times as many toy cars as Peter. After Kevin gives away 20 cars to his sister, he will have the same number of toy cars Peter has. How many toy cars does Kevin have at first?
Answer: ","e":"Kevin's 3 units minus 20 equals Peter's 1 unit, so 2 units = 20, 1 unit = 20 \u00f7 2 = 10. Kevin = 3 \u00d7 10 = 30."} {"t":"q","id":13155,"q":"Halim had some money. He spent $40 and saved the remaining $30.80. (a) How much money did Halim have at first? Halim saved $10.60 more than Mei Ling. (b) How much money did Mei Ling save?
(a)   (b) ","e":"(a) At first = $40 + $30.80 = $70.80. (b) Mei Ling saved $30.80 \u2212 $10.60 = $20.20."} {"t":"q","id":13160,"q":"Write 615\u00a2 in dollars. $","e":"615\u00a2 = $6.15 (100\u00a2 = $1)."} {"t":"q","id":13162,"q":"Alice bought 34 trays of eggs. There were 5 eggs in each tray. How many eggs did she buy?
Answer: ","e":"34 \u00d7 5 = 170 eggs."} {"t":"q","id":13163,"q":"Michael had 348 stickers. Sarah had 3 times as many stickers as Michael. How many stickers did they have altogether?
Answer: ","e":"Sarah: 348 \u00d7 3 = 1044. Altogether: 1044 + 348 = 1392."} {"t":"q","id":13164,"q":"Ali had 74 apples. He packed them into as many bags of 6 as possible. How many apples were left unpacked?
Answer: ","e":"74 \u00f7 6 = 12 remainder 2, so 2 apples were left unpacked."} {"t":"q","id":13165,"q":"There were 4 times as many adults as children in a mall. After 132 adults and 9 children went home, there was an equal number of adults and children in the mall. How many children were in the mall at first?
Answer: ","e":"Let children = c, adults = 4c. After: 4c \u2212 132 = c \u2212 9, so 3c = 123, c = 41."} {"t":"q","id":13166,"q":"In a school hall, chairs were arranged in 9 equal rows. Each row has 14 chairs. (a) How many chairs were there in the hall? (b) Sam rearranged all the chairs into 7 equal rows. How many chairs were there in each row?
(a)   (b) ","e":"(a) 14 \u00d7 9 = 126 chairs. (b) 126 \u00f7 7 = 18 chairs per row."} {"t":"q","id":13167,"q":"Harry has $54.30. He wants to buy both the toy car ($31.95) and the toy aeroplane ($29.80). (a) What is the total cost of a toy car and a toy aeroplane? (b) How much more money does Harry need?
(a)   (b) ","e":"(a) $31.95 + $29.80 = $61.75. (b) $61.75 \u2212 $54.30 = $7.45."} {"t":"q","id":13171,"q":"Which of the following has the greatest value?","e":"6\u00d79=54, 7\u00d76=42, 8\u00d76=48, 9\u00d75=45. Greatest is 54."} {"t":"q","id":13173,"q":"When a number is divided by 8, the quotient is 412 and the remainder is 4. What is the number?","e":"Number = quotient \u00d7 divisor + remainder = 412 \u00d7 8 + 4 = 3296 + 4 = 3300."} {"t":"q","id":13174,"q":"What is the missing number in the box?\n5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 = 4 \u00d7","e":"Eight 5s = 40. 40 = 4 \u00d7 10, so the missing number is 10."} {"t":"q","id":13175,"q":"The sum of two numbers is 156. The bigger number is 91. What is the smaller number?","e":"156 - 91 = 65."} {"t":"q","id":13176,"q":"There were 5139 people at the carnival. 924 of them were children, 2308 were women and the rest were men. How many men were there at the carnival?","e":"924 + 2308 = 3232. 5139 - 3232 = 1907 men."} {"t":"q","id":13177,"q":"Justin and Sean have a total of 392 cards. Justin has 7 times as many cards as Sean. How many cards does Sean have?","e":"Sean is 1 unit, Justin is 7 units, total 8 units = 392. 1 unit = 392 \u00f7 8 = 49."} {"t":"q","id":13178,"q":" \u00d7 = 49. What is the value of one face?","e":"The two identical faces multiply to 49. 7 \u00d7 7 = 49, so each face = 7."} {"t":"q","id":13179,"q":"Subtract 1965 from 7201.
Answer: ","e":"7201 - 1965 = 5236."} {"t":"q","id":13180,"q":"Find the product of 908 and 6.
Answer: ","e":"908 \u00d7 6 = 5448."} {"t":"q","id":13182,"q":"Write two numbers that will give a sum of 3450.
(a)   (b) ","e":"Any two numbers that add to 3450, e.g. 1662 + 1788 = 3450."} {"t":"q","id":13183,"q":"Use all the digits 0, 3, 4, 9, find the difference between the greatest possible 4-digit even number and smallest possible 4-digit odd number.
Answer: ","e":"Greatest 4-digit even number from 0,3,4,9 is 9430. Smallest 4-digit odd number is 3049. 9430 - 3049 = 6381."} {"t":"q","id":13184,"q":"Marie spent a total of $300 on Monday and Tuesday. She spent $44 lesser on Monday than on Tuesday. How much did she spend on Tuesday?
Answer: ","e":"Total + difference = 2 \u00d7 Tuesday: 300 + 44 = 344. Tuesday = 344 \u00f7 2 = $172."} {"t":"q","id":13185,"q":"Alice has 46 marbles. Belle has twice as many marbles as Alice. Carol has four times as many marbles as Belle. How many marbles does Carol have?
Answer: ","e":"Belle = 46 \u00d7 2 = 92. Carol = 92 \u00d7 4 = 368."} {"t":"q","id":13187,"q":"Mr Tan has 98 sweets. He wants to give all his sweets to his 8 students. How many more sweets does he need such that each student will receive an equal number of sweets?
Answer: ","e":"98 \u00f7 8 = 12 remainder 2. To make an equal share he needs 8 - 2 = 6 more sweets."} {"t":"q","id":13188,"q":"In the school library, there are 400 English books. There are 520 fewer English books than Chinese books. (a) How many Chinese books are there in the school library? (b) The number of Chinese books is four times the number of Malay books. How many Malay books are there in the library?
(a)   (b) ","e":"(a) Chinese = 400 + 520 = 920. (b) Malay = 920 \u00f7 4 = 230."} {"t":"q","id":13189,"q":"A baker baked some tarts. The tarts were packed equally into boxes of 8. (a) There were 87 boxes of tarts. How many tarts did he bake in total? (b) The baker received $161 for some boxes of tarts sold. Each box of tarts cost $7. How many tarts did he sell altogether?
(a)   (b) ","e":"(a) 87 \u00d7 8 = 696 tarts. (b) Boxes sold = 161 \u00f7 7 = 23; tarts sold = 23 \u00d7 8 = 184."} {"t":"q","id":13190,"q":"Tommy and Sue had an equal amount of money at first. Tommy used $403 to buy a handphone and Sue used $152 to buy a bag. Sue had twice as much money left as Tommy. (a) How much money did Tommy have left? (b) How much money did Sue have at first?
(a)   (b) ","e":"They started equal. Sue's left - Tommy's left = the difference in spending = 403 - 152 = 251. Sue's left = 2 \u00d7 Tommy's left, so Tommy's left = 251 and Sue's left = 502. (a) Tommy had $251 left. (b) Sue had 502 + 152 = $654 at first."} {"t":"q","id":13191,"q":"Which of the following is the same as 12 m 7 cm?","e":"12 m = 1200 cm. 1200 cm + 7 cm = 1207 cm."} {"t":"q","id":13195,"q":"Arrange the following fractions from the smallest to the greatest. 3\/10, 1\/2, 3\/5","e":"Convert to tenths: 3\/10, 1\/2 = 5\/10, 3\/5 = 6\/10. Smallest to greatest: 3\/10, 1\/2, 3\/5."} {"t":"q","id":13196,"q":"Find the value of A and B in the boxes. 3\/7 = A\/21 = 18\/B","e":"3\/7 = 9\/21 (multiply by 3), so A = 9. 3\/7 = 18\/42 (multiply by 6), so B = 42."} {"t":"q","id":13198,"q":"The capacity of a pail was 450 ml. The capacity of the pail was three times as much as a container. The capacity of the container was twice as much as a cup. Find the capacity of the cup.","e":"Container = 450 \/ 3 = 150 ml. Cup = 150 \/ 2 = 75 ml."} {"t":"q","id":13202,"q":"Find the missing number in the box. 1\/3 = 4\/","e":"1\/3 = 4\/12 (multiply numerator and denominator by 4). The missing number is 12."} {"t":"q","id":13203,"q":"Give a possible fraction that is smaller than 1\/5.
Answer: ","e":"1\/6 is smaller than 1\/5 because with the same numerator, a larger denominator gives a smaller fraction. (Other answers such as 1\/10 are also acceptable.)"} {"t":"q","id":13208,"q":"The mass of three students, Adele, Belle and Cali was 129 kg. Adele left and the mass of Belle and Cali became 87 kg. Cali's mass was 41 kg. Who was the lightest and what was her mass? Girl: , kg","e":"Adele = 129 - 87 = 42 kg. Belle = 87 - 41 = 46 kg. Cali = 41 kg. Cali is the lightest at 41 kg."} {"t":"q","id":13212,"q":"The mass of a box containing an iron ball is 326 g. When Alice puts in 4 more such iron balls into the box, the mass of the box and the iron balls becomes 786 g. (a) What is the mass of an iron ball? (b) What is the mass of the box? g, g","e":"Adding 4 balls increased the mass by 786 - 326 = 460 g. (a) 1 ball = 460 \/ 4 = 115 g. (b) Box = 326 - 115 = 211 g."} {"t":"q","id":13215,"q":"Write 2 km 560 m in metres. ","e":"2 km = 2000 m, so 2 km 560 m = 2000 + 560 = 2560 m."} {"t":"q","id":13216,"q":"Arrange this set of fractions in order, beginning with the smallest. 2\/5 , 2\/7 , 2\/3 , , ","e":"With the same numerator, the larger the denominator the smaller the fraction. 2\/7 < 2\/5 < 2\/3."} {"t":"q","id":13218,"q":"Mr Tan used a 150-cm string to tie a box. He used another string that was 3 times as long to tie a bigger box. What was the total length of both strings used in centimetres? ","e":"Second string = 3 x 150 = 450 cm. Total = 150 + 450 = 600 cm. (Key: 150 x 4 = 600.)"} {"t":"q","id":13219,"q":"Express \\(\\dfrac{9}{12}\\) in its simplest form. ","e":"Divide numerator and denominator by 3: 9\/12 = 3\/4."} {"t":"q","id":13221,"q":"Find the value of \\(\\dfrac{6}{10}\\) - \\(\\dfrac{1}{5}\\). Give your answer in the simplest form. ","e":"1\/5 = 2\/10, so 6\/10 - 2\/10 = 4\/10 = 2\/5."} {"t":"q","id":13222,"q":"Find the value of \\(\\dfrac{1}{3}\\) + \\(\\dfrac{1}{12}\\). Give your answer in the simplest form. ","e":"1\/3 = 4\/12, so 4\/12 + 1\/12 = 5\/12."} {"t":"q","id":13223,"q":"Mary poured 7 bottles of apple juice into a container. Each bottle contains 850 ml of apple juice. Given the container has a capacity of 6000 ml, how much more apple juice would be needed to fill the container completely? ","e":"7 x 850 = 5950 ml poured. 6000 - 5950 = 50 ml needed."} {"t":"q","id":13224,"q":"Ben took 1h 50 min to walk from his house to the park. He reached the park at 9.10 a.m. What time did he leave his house? ","e":"9.10 a.m. minus 1 h 50 min = 7.20 a.m. (9.10 - 1 h = 8.10; 8.10 - 50 min = 7.20)."} {"t":"q","id":13225,"q":"The total mass of a basket and some watermelons is 145 kg. The mass of the empty basket is 6 kg. Ahmad sold some of the watermelons and had 26 kg of the watermelon left. How many kilograms of the watermelons was sold? ","e":"Watermelons at first = 145 - 6 = 139 kg. Sold = 139 - 26 = 113 kg."} {"t":"q","id":13230,"q":"In the sum of 333 and 999, the digit in the _____ place is an even number.","e":"333 + 999 = 1332. Digits: thousands 1, hundreds 3, tens 3, ones 2. Only the ones digit (2) is even."} {"t":"q","id":13233,"q":"Which of the following does not have the same measurement as the rest?","e":"520 cm, 5 m 20 cm and 500 cm + 20 cm all equal 520 cm. 5 m 2 cm = 502 cm, which is different."} {"t":"q","id":13241,"q":"A number when divided by 8 gives a remainder of 4. Which of the following can be added to the number so that it will leave no remainder when divided by 8?","e":"A remainder of 4 means it is 4 short of the next multiple of 8, so adding 4 makes it exactly divisible by 8."} {"t":"q","id":13242,"q":"Adam, Bobby, Caden and Dennis collected some toy cars. Adam collected the least number of toy cars. Bobby collected more toy cars than Dennis but fewer than Caden. Who collected the most number of toy cars?","e":"Adam is least; Dennis < Bobby < Caden, so Caden collected the most."} {"t":"q","id":13248,"q":"Use all the digits 6, 5, 1, 3 to form the smallest odd number.\n\nAns: ","e":"Odd means the ones digit must be odd. Smallest uses smallest leading digits: 1, 3, 6 then odd ones digit 5 \u2192 1365."} {"t":"q","id":13251,"q":"I am a 4-digit number. The digits in my thousands place and ones place are the same. The digit in my tens place is 8 less than the digit in my thousands place. The value of the digit in my hundreds place is 300. What number am I?\n\nAns: ","e":"Hundreds value 300 \u2192 hundreds digit 3. Tens is 8 less than thousands; thousands = ones. Thousands 8, tens 0, ones 8 \u2192 8308."} {"t":"q","id":13252,"q":"Mrs Singh bought 45 cookies. She bought 9 times as many cookies as Mdm Aminah. How many cookies did Mdm Aminah buy?\n\nAns: ","e":"45 is 9 times Mdm Aminah's amount, so Mdm Aminah bought 45 \u00f7 9 = 5 cookies."} {"t":"q","id":13253,"q":"Mary had $548. She had $245 more than her sister. How much did her sister have?\n\nAns: $","e":"Sister had $548 - $245 = $303."} {"t":"q","id":13254,"q":"Study the pattern. What is the missing number?\n\n220, 230, 200, , 180, 190","e":"The pattern alternates: 220, 230 (+10), 200, 210 (+10), 180, 190 (+10). The missing term is 210."} {"t":"q","id":13256,"q":"Mrs Tan bought a packet of orange juice. She poured all the orange juice equally into 9 cups of 225 ml each. What is the volume of the orange juice in the packet? Give your answer in l and ml.\n\nAns: l ml","e":"9 \u00d7 225 ml = 2025 ml = 2 l 25 ml."} {"t":"q","id":13260,"q":"A pair of jeans cost $66. A skirt is $9.20 cheaper than the jeans. Find the cost of the skirt.\n\nAns: $","e":"$66 - $9.20 = $56.80."} {"t":"q","id":13261,"q":"The table shows the opening hours of a clinic.\n\nMorning: 8.00 a.m. to 11.30 a.m.\nAfternoon: 2.00 p.m. to 4.00 p.m.\nEvening: 6.30 p.m. to 9.00 p.m.\n\nHow many hours is the clinic open in a day?\n\nAns: h","e":"Morning 3 h 30 min + afternoon 2 h + evening 2 h 30 min = 8 h."} {"t":"q","id":13262,"q":"What are the missing numbers in the fractions below?\n\n2\/a = 6\/15 = b\/25\n\nAns: a = , b = ","e":"6\/15 simplifies to 2\/5, so a = 5. Then 2\/5 = 10\/25, so b = 10."} {"t":"q","id":13263,"q":"Which of the following fractions is smaller than 1\/3?\n\n2\/9, 1\/2, 5\/6\n\nAns: ","e":"1\/3 = 3\/9. Comparing: 2\/9 < 3\/9, while 1\/2 and 5\/6 are larger than 1\/3. So 2\/9 is smaller than 1\/3."} {"t":"q","id":13264,"q":"Julie collected 1480 stickers. Stephanie collected 288 stickers more than Julie.\n\n(a) How many stickers did Stephanie collect?\n(b) How many stickers did the two girls collect altogether?\n\nAns: (a) , (b) ","e":"(a) 1480 + 288 = 1768. (b) 1480 + 1768 = 3248."} {"t":"q","id":13265,"q":"Mrs Chandra bought 9 boxes of cupcakes. Each box contained 28 cupcakes. She repacked the cupcakes equally into 4 large containers. How many cupcakes were there in each large container?\n\nAns: ","e":"Total cupcakes = 9 \u00d7 28 = 252. Per container = 252 \u00f7 4 = 63."} {"t":"q","id":13266,"q":"Zan ran around his school during his PE lesson. He took 18 minutes to finish running one round.\n\n(a) How long would he take to finish running 5 rounds, given that he took the same amount of time for every round?\n(b) Zan completed his 5 rounds at 11.45 a.m. What time did he start running?\n\nAns: (a) min, (b) ","e":"(a) 18 \u00d7 5 = 90 minutes (1 h 30 min). (b) 11.45 a.m. minus 1 h 30 min = 10.15 a.m."} {"t":"q","id":13270,"q":"Four students have written the following statements in their books.\nWhich one of the following statements is correct?","e":"203 cm = 200 cm + 3 cm = 2 m 3 cm. The other conversions are wrong."} {"t":"q","id":13271,"q":"A highlighter costs $2.20. An eraser costs $0.45.\nWhat is the total cost of a highlighter and two erasers?","e":"Two erasers cost 2 x $0.45 = $0.90. Total = $2.20 + $0.90 = $3.10."} {"t":"q","id":13285,"q":"Arrange the fractions from the smallest to the greatest.\n3\/9 , 1\/9 , 4\/9\n , , ","e":"Same denominator (9), so order by numerator: 1 < 3 < 4. Smallest to greatest: 1\/9, 3\/9, 4\/9."} {"t":"q","id":13287,"q":"There are 20 apples and bananas altogether.\nThere are 4 times as many apples as bananas.\nHow many bananas are there?\nThere are bananas.","e":"Bananas = 1 unit, apples = 4 units, total = 5 units = 20. So 1 unit = 20 \u00f7 5 = 4 bananas."} {"t":"q","id":13289,"q":"Sam is 170 cm tall.\nBetty is 12 cm shorter than Sam.\nDaniel is 6 cm taller than Betty.\nWhat is Daniel's height?\nDaniel is cm tall.","e":"Betty = 170 - 12 = 158 cm. Daniel = 158 + 6 = 164 cm."} {"t":"q","id":13290,"q":"Kelly and Mandy had the same number of stamps. After Mandy gave Kelly 5 stamps, the number of stamps Kelly had became 30.\nHow many stamps did Kelly and Mandy have altogether at first?\nKelly and Mandy had stamps altogether.","e":"Kelly at first = 30 - 5 = 25 stamps. Mandy had the same, so total = 25 + 25 = 50 stamps."} {"t":"q","id":13294,"q":"Monica started watching a movie at 4.15 p.m. and ended at 6.05 p.m. What is the duration of the movie?","e":"From 4.15 p.m. to 6.15 p.m. is 2 h; back 10 min to 6.05 p.m. gives 1 h 50 min. (Or 4.15\u21925.15\u21926.05 = 1 h + 50 min.)"} {"t":"q","id":13300,"q":"Arrange the following numbers from the smallest to the greatest.\n\n7 937, 3 797, 7 397, 3 977\n\nAns: , , , ","e":"Compare thousands first: 3 797 and 3 977 (three thousands) come before 7 397 and 7 937. Then compare the rest: 3 797 < 3 977 and 7 397 < 7 937."} {"t":"q","id":13307,"q":"What is the value of 21 tens, 5 hundreds and 3 ones?","e":"21 tens = 210, 5 hundreds = 500, 3 ones = 3. 210 + 500 + 3 = 713."} {"t":"q","id":13309,"q":"Arrange the following numbers from the smallest to the largest. 4501, 5401, 4051, 5041","e":"Smallest to largest: 4051, 4501, 5041, 5401 (compare thousands then hundreds then tens)."} {"t":"q","id":13310,"q":"Benny had some marbles at first. He gave 4 of his friends 268 marbles each and had 4 marbles left. How many marbles did Benny have at first?","e":"4 \u00d7 268 = 1072 given away, plus 4 left = 1076."} {"t":"q","id":13311,"q":"When a number is divided by 6, the quotient is 24. The remainder is 5. What is the number?","e":"Number = quotient \u00d7 divisor + remainder = 24 \u00d7 6 + 5 = 144 + 5 = 149."} {"t":"q","id":13315,"q":"Daniel and his friends left Bird Paradise at 18 20. They spent 7 h 55 min at Bird Paradise. What time did they reach Bird Paradise?","e":"They reached before they left, so subtract the duration: 18 20 \u2212 7 h 55 min = 10 25."} {"t":"q","id":13317,"q":"Form the greatest 4-digit odd number using all the digits shown in the cards. 4, 0, 3, 5 ","e":"Greatest odd number must end in an odd digit. To be greatest, put 5 then 4 then 0 in front and end in the odd 3: 5403."} {"t":"q","id":13318,"q":"Study the number pattern. What is the missing number? 3657 , , 3755 , 3804 , 3853","e":"The pattern increases by 49 each time. 3657 + 49 = 3706 (and 3706 + 49 = 3755)."} {"t":"q","id":13319,"q":"A set of numbers is shown. Which 2 numbers add up to 831? 471, 534, 307, 360 and ","e":"471 + 360 = 831."} {"t":"q","id":13320,"q":"Complete the following equation. 9 \u00d7 8 = \u2212 18","e":"9 \u00d7 8 = 72, so the box \u2212 18 = 72, meaning box = 72 + 18 = 90."} {"t":"q","id":13322,"q":"Write the time in 24-hour clock. 12.01 a.m. = ","e":"12.01 a.m. is one minute after midnight, written as 00 01 in 24-hour clock."} {"t":"q","id":13324,"q":"Find the missing number in the box. \u00d7 3 = 927","e":"927 \u00f7 3 = 309."} {"t":"q","id":13325,"q":"Find the difference between 4010 and 419. ","e":"4010 \u2212 419 = 3591."} {"t":"q","id":13326,"q":"Arrange the fractions in order. Begin with the greatest. 3\/8 , 1\/4 , 7\/11 , 3\/7 , , , ","e":"As decimals: 7\/11\u22480.64, 3\/7\u22480.43, 3\/8=0.375, 1\/4=0.25. Greatest to smallest: 7\/11, 3\/7, 3\/8, 1\/4."} {"t":"q","id":13330,"q":"Aaron had 240 cards. He shared the cards equally with 3 of his friends. How many cards did each of them get? ","e":"Shared among Aaron and 3 friends = 4 people: 240 \u00f7 4 = 60."} {"t":"q","id":13331,"q":"A fruit seller had 3850 oranges. He threw away 86 rotten oranges and sold 2368 oranges. How many oranges had he left? ","e":"2368 + 86 = 2454 removed; 3850 \u2212 2454 = 1396 left."} {"t":"q","id":13332,"q":"What are the missing digits? 8 A 3 9 \u2212 5 1 4 2 = 3 3 9 B , ","e":"Ones: 9 \u2212 2 = 7, so B = 7. Hundreds: A \u2212 1 = 3, so A = 5 (check: 8539 \u2212 5142 = 3397)."} {"t":"q","id":13333,"q":"Mrs Lee bought some pencils. She gave 105 pencils to her students and packed the remaining pencils into 15 packets. There were 5 pencils in each packet. How many pencils did Mrs Lee have at first? ","e":"Packed = 15 \u00d7 5 = 75. Total = 75 + 105 = 180."} {"t":"q","id":13335,"q":"David holds up a card which reads 5167. He describes this 4-digit number in two sentences. (a) The 4-digit number is an even number. (b) The value of the digit in the thousands place is 1000. Which statement is true?","e":"5167 ends in 7, so it is odd, not even: (a) is false. The thousands digit 5 has value 5000, not 1000: (b) is false. Both false."} {"t":"q","id":13336,"q":"Mandy bought 3 times as many sweets as Alex. She bought 80 more sweets than Alex. How many sweets did they buy altogether? ","e":"The 80 extra equals 2 of Alex's units (3 units \u2212 1 unit), so 1 unit = 80 \u00f7 2 = 40 (Alex). Altogether = 4 units = 4 \u00d7 40 = 160."} {"t":"q","id":13337,"q":"A baker has 294 donuts. He packed 7 donuts in one box. How many boxes of donuts are there? ","e":"294 \u00f7 7 = 42 boxes."} {"t":"q","id":13340,"q":"There were some marbles in a box. \\(\\dfrac{1}{3}\\) of the marbles were green and \\(\\dfrac{5}{12}\\) of the marbles were red. The rest of the marbles were blue. What fraction of the marbles were blue? Give your answers in its simplest form. ","e":"Green = 1\/3 = 4\/12. Green + red = 4\/12 + 5\/12 = 9\/12. Blue = 12\/12 \u2212 9\/12 = 3\/12 = 1\/4."} {"t":"q","id":13341,"q":"The table shows the programmes at the Science Centre. The Human Body 20 min, Forensic Investigative Science 1 h 45 min, Stargazing 35 min. (a) John attended the Stargazing programme at 11.45 a.m. What time did he finish the programme? (b) Winnie attended The Human Body programme at 10 a.m. She rested for 30 minutes and then continued with the Forensic Investigative Science programme. What time did she complete the Forensic Investigative Science programme? , ","e":"(a) 11.45 a.m. + 35 min = 12.20 p.m. (b) 10 a.m. + 20 min = 10.20; + 30 min rest = 10.50; + 1 h 45 min = 12.35 p.m."} {"t":"q","id":13342,"q":"A table and 4 similar chairs cost $179.60. The table and 1 such chair cost $106.40. (a) What was the cost of 3 such chairs? (b) The table cost $57.60 more than the chair. What is the cost of the table? $ , $","e":"(a) 4 chairs \u2212 1 chair = 3 chairs = $179.60 \u2212 $106.40 = $73.20. (b) 1 chair = $73.20 \u00f7 3 = $24.40; table = $24.40 + $57.60 = $82.00."} {"t":"q","id":13345,"q":"A total of 1500 people attended a concert. There were 992 adults. The rest were children. (a) How many children attended the concert? (b) There were same number of men and women attended the concert. During the concert, some women left. In the end, there were 4 times as many men as women who stayed on till the end of the concert. How many women left the concert? , ","e":"(a) 1500 \u2212 992 = 508 children. (b) Men = women = 992 \u00f7 2 = 496. At end men (496) = 4 \u00d7 women left = women remaining = 496 \u00f7 4 = 124. Women who left = 496 \u2212 124 = 372."} {"t":"q","id":13348,"q":"Which of the following numbers is the smallest even number?","e":"Even numbers end in 0,2,4,6,8. Even options are 2392 and 2930; the smaller is 2392."} {"t":"q","id":13355,"q":"There were 9000 spectators watching a football match. 856 of them were female spectators. How many male spectators were there?","e":"9000 - 856 = 8144 male spectators."} {"t":"q","id":13357,"q":"A bookshop sold a highlighter and a pen for $3. Claire bought 6 highlighters and 6 pens. How much did Claire pay altogether?","e":"1 highlighter + 1 pen = $3. 6 sets cost 6 x $3 = $18."} {"t":"q","id":13360,"q":"A glass of orange juice costs $2.50 and a glass of lemon juice costs $1.80. Claire bought 2 glasses of orange juice and a glass of lemon juice. How much did she pay?","e":"2 x $2.50 = $5.00; $5.00 + $1.80 = $6.80."} {"t":"q","id":13364,"q":"Find the difference between 2270 and 1654.
Answer: ","e":"2270 - 1654 = 616."} {"t":"q","id":13367,"q":"Arrange the following fractions in order. Begin with the greatest.\n7\/10, 2\/5, 1\/2
(a)   (b)   (c) ","e":"Convert to tenths: 7\/10, 1\/2 = 5\/10, 2\/5 = 4\/10. Greatest to smallest: 7\/10, 1\/2, 2\/5."} {"t":"q","id":13369,"q":"The difference between two numbers is 785. The bigger number is 1072. What is the other number?
Answer: ","e":"1072 - 785 = 287."} {"t":"q","id":13371,"q":"Derrick and Evan shared some stickers equally. After Derrick gave Evan 47 stickers, how many more stickers does Evan have than Derrick?
Answer: ","e":"They started equal. Giving away 47 makes Derrick 47 fewer and Evan 47 more, so the gap is 47 + 47 = 94 stickers."} {"t":"q","id":13374,"q":"When a number is divided by 4, it has a remainder of 2. The number is between 20 and 25. What is the number?
Answer: ","e":"Multiples of 4 between 20 and 25 plus 2: 20 + 2 = 22, which is between 20 and 25."} {"t":"q","id":13375,"q":"100 g of cherries cost $2. What is the cost of 1 kg of cherries?
Answer: ","e":"1 kg = 1000 g = 10 lots of 100 g; 10 x $2 = $20."} {"t":"q","id":13377,"q":"A shopkeeper had 297 story books. He wanted to pack them equally into 8 boxes. How many story books were left unpacked?
Answer: ","e":"297 \/ 8 = 37 remainder 1; 1 book is left unpacked."} {"t":"q","id":13379,"q":"Laurence took 1 h 55 min to finish his homework. He ended at 2.15 p.m. What time did he start doing his homework?
Answer: ","e":"2.15 p.m. minus 1 h 55 min: 2.15 - 1 h = 1.15 p.m.; 1.15 - 55 min = 12.20 p.m."} {"t":"q","id":13380,"q":"Jacob bought 9 packets of potato chips. He planned to eat a packet every 3 days. How many days would he take to finish eating all the packets of potato chips?
Answer: ","e":"9 packets x 3 days each = 27 days."} {"t":"q","id":13381,"q":"Rita collected some beads. She gave 45 of them away and packed the remaining beads into 5 bags. There were 67 beads in each bag. How many beads did Rita collect?
Answer: ","e":"5 bags x 67 = 335 remaining beads; add the 45 given away: 335 + 45 = 380."} {"t":"q","id":13382,"q":"The capacity of a beaker is 240 ml. 2 such beakers of water can fill a jug completely. 6 such jugs of water can fill a tank completely. What is the capacity of the tank? Write your answer in litres and millilitres.
(a)   (b) ","e":"1 jug = 2 x 240 = 480 ml; tank = 6 x 480 = 2880 ml = 2 L 880 ml."} {"t":"q","id":13383,"q":"Mary, Laura and Joyce baked some cookies. Mary baked twice as many cookies as Joyce. Laura baked thrice as many cookies as Mary. Laura baked 405 more cookies than Joyce. How many cookies did Mary bake?
Answer: ","e":"Let Joyce = 1 unit. Mary = 2 units, Laura = 3 x Mary = 6 units. Laura - Joyce = 6 - 1 = 5 units = 405, so 1 unit = 81. Mary = 2 x 81 = 162."} {"t":"q","id":13384,"q":"Alan had $50. He bought a pair of shorts and a blouse. A blouse cost $12 more than a pair of shorts. He received $2 change. How much did a pair of shorts cost?
Answer: ","e":"Spent = $50 - $2 = $48. Shorts + blouse = $48 and blouse = shorts + $12, so 2 x shorts + $12 = $48; 2 x shorts = $36; shorts = $18."} {"t":"q","id":13387,"q":"In 7509, the digit 0 is in the place.","e":"In 7509: 7 thousands, 5 hundreds, 0 tens, 9 ones. The 0 is in the tens place."} {"t":"q","id":13389,"q":"Which one of the following is the same as 5050 g?","e":"1 kg = 1000 g. 5050 g = 5000 g + 50 g = 5 kg 50 g."} {"t":"q","id":13390,"q":"Mrs Veerasamy brought her children to the swimming pool. They started swimming at 4:40 pm. They finished swimming at 6:05 pm. How long did they swim in the pool?","e":"4:40 pm to 5:40 pm = 1 h. 5:40 pm to 6:05 pm = 25 min. Total = 1 h 25 min."} {"t":"q","id":13392,"q":"The difference between two numbers is 168. The smaller number is 709. What is the greater number?","e":"Greater number = smaller + difference = 709 + 168 = 877."} {"t":"q","id":13393,"q":"+ 1\/3 = 8\/9\nWhat is the missing fraction in the box?","e":"1\/3 = 3\/9. Missing = 8\/9 - 3\/9 = 5\/9."} {"t":"q","id":13395,"q":"Arrange the following numbers in order. Begin with the greatest number.\n6900, 9060, 6090, 6009
(a)   (b)   (c)   (d) ","e":"Greatest to smallest: 9060, 6900, 6090, 6009."} {"t":"q","id":13396,"q":"9458 = + 400 + 58\nWhat is the missing number?","e":"9458 - 400 - 58 = 9000. So the missing number is 9000."} {"t":"q","id":13398,"q":"Find the difference between 9000 and 5826.
Answer: ","e":"9000 - 5826 = 3174."} {"t":"q","id":13399,"q":"Mrs Rebecca spent 1 h 10 min baking cookies. She finished baking at 2:30 pm. What time did she start baking?
Answer: ","e":"Start = finish - duration = 2:30 pm - 1 h 10 min = 1:20 pm."} {"t":"q","id":13403,"q":"A bottle has a capacity of 2000 ml. It contains 1560 ml of water. How much more water is needed to fill up the bottle?
Answer: ","e":"2000 ml - 1560 ml = 440 ml."} {"t":"q","id":13404,"q":"What are the values of (a) and (b) in the number pattern?\n7868, 7874, , 7886, , 7898, 7904, 7910","e":"The pattern increases by 6 each time. (a) = 7874 + 6 = 7880; (b) = 7886 + 6 = 7892."} {"t":"q","id":13408,"q":"Bala took 6 h 45 min to travel from Singapore to Genting Highlands. Mr Ng took 25 min more to travel the same distance. Mr Ng started travelling from Singapore at 15 00. What time did Mr Ng reach Genting Highlands? Give your answer in 24-hour clock.
Answer: ","e":"Mr Ng's time = 6 h 45 min + 25 min = 7 h 10 min. 15 00 + 7 h 10 min = 22 10."} {"t":"q","id":13409,"q":"Sally bought a dress. She gave the cashier $50 and received $17.20 change. What was the cost of the dress?
Answer: ","e":"Cost = amount given - change = $50 - $17.20 = $32.80."} {"t":"q","id":13412,"q":"Emily, Fiona and Gail shared some sweets. Gail had 58 sweets. Gail had 46 more sweets than Fiona. Emily had 3 times as many sweets as Fiona.\n(a) How many sweets did Fiona have?\n(b) How many sweets did the 3 girls have in all?
(a)   (b) ","e":"(a) Fiona = Gail - 46 = 58 - 46 = 12. (b) Emily = 3 x 12 = 36. Total = 58 + 12 + 36 = 106."} {"t":"q","id":13413,"q":"Vivian sold 785 cookies on Saturday. She sold 698 fewer cookies on Saturday than on Sunday. How many cookies did Vivian sell on both days?
Answer: ","e":"Sunday = 785 + 698 = 1483. Both days = 1483 + 785 = 2268."} {"t":"q","id":13414,"q":"Peter competed in a 5-km marathon. After running 2 km 850 m, he walked for a while before running again to complete the last 800 m. What was the distance that Peter walked during the marathon? Give your answer in kilometres and metres.
Answer: ","e":"5 km = 5000 m. Ran 2850 m, then walked, then ran last 800 m. Walked = 5000 - 2850 - 800 = 1350 m = 1 km 350 m."} {"t":"q","id":13415,"q":"Mr Goh paid $273 for 1 bag and 5 similar books. Each bag cost $93 more than each book. How much did he pay for each book?
Answer: ","e":"Bag = book + $93. So 6 books + $93 = $273, 6 books = $180, each book = $180 \/ 6 = $30."} {"t":"q","id":13416,"q":"In 4960, the digit 9 is in the place.","e":"In 4960, reading right to left: 0 ones, 6 tens, 9 hundreds, 4 thousands. So 9 is in the hundreds place."} {"t":"q","id":13417,"q":"Which of the following is the greatest odd number?","e":"Odd numbers end in an odd digit. 9750 and 9778 are even. Of the odd ones (9639, 9643), 9643 is greater."} {"t":"q","id":13420,"q":"Which of the following has the same value as 5 \u00d7 4?","e":"5 \u00d7 4 means four groups of 5 (or 5 groups of 4) = 20. 5 + 5 + 5 + 5 = 20."} {"t":"q","id":13422,"q":"2\/3 = \/12. What is the missing numerator in the box?","e":"Multiply numerator and denominator by 4: 2\/3 = (2\u00d74)\/(3\u00d74) = 8\/12. Missing numerator is 8."} {"t":"q","id":13424,"q":"Stephanie baked 108 cupcakes for a party. She packed 8 cupcakes in each bag. How many cupcakes were left unpacked?","e":"108 \u00f7 8 = 13 remainder 4. So 4 cupcakes were left unpacked."} {"t":"q","id":13427,"q":"Arrange these fractions from the greatest to the smallest.\n1\/2 , 5\/8 , 3\/10 , 5\/9","e":"As decimals: 1\/2=0.50, 5\/8=0.625, 3\/10=0.30, 5\/9\u22480.556. Greatest to smallest: 5\/8, 5\/9, 1\/2, 3\/10."} {"t":"q","id":13429,"q":"At first, Edwin had 35 more stickers than Gordon. Gordon then gave 16 stickers to Edwin. How many fewer stickers did Gordon have than Edwin in the end?","e":"Each transfer of 16 widens the gap by 2 \u00d7 16 = 32. New difference = 35 + 32 = 67."} {"t":"q","id":13434,"q":"There are 9 cookies in a box. How many cookies are there in 6 such boxes?\n","e":"9 \u00d7 6 = 54 cookies."} {"t":"q","id":13444,"q":"The difference between two numbers is 546. The greater number is 7 times as big as the smaller number. What is the greater number?\n","e":"Greater = 7 units, smaller = 1 unit; difference 6 units = 546, so 1 unit = 91. Greater = 7 \u00d7 91 = 637."} {"t":"q","id":13445,"q":"According to his watch, Tom started painting at 15 45. His watch was 20 minutes fast. He took 35 minutes to complete his painting. According to actual time, what time did Tom complete his painting?\n","e":"Actual start = 15 45 \u2212 20 min = 15 25. Finish = 15 25 + 35 min = 16 00."} {"t":"q","id":13446,"q":"Mrs Lee bought a blouse for $41.65. She also bought a pair of shoes for $33.80. She gave the cashier a $100 note. How much change did she receive?\n","e":"Total spent = $41.65 + $33.80 = $75.45. Change = $100 \u2212 $75.45 = $24.55."} {"t":"q","id":13447,"q":"Mrs Lim had a jug of fruit punch at first. After pouring the fruit punch equally into 8 glasses, she had 250 ml of fruit punch left in the jug. Each glass contained 350 ml of fruit punch. How much fruit punch was there in the jug at first? Give your answer in litres and millilitres.\n l ml","e":"8 glasses \u00d7 350 ml = 2800 ml; + 250 ml left = 3050 ml = 3 l 50 ml."} {"t":"q","id":13448,"q":"Mrs Tan took 1 h 40 min to make a pizza. Miss Ong took 30 min more than Mrs Tan to bake a cake.\na) How much time did Miss Ong take to bake the cake? Give your answer in hours and minutes.\nb) Miss Ong started baking the cake at 11.10 am. What time did she finish baking the cake?\n h min ; finish time ","e":"a) 1 h 40 min + 30 min = 2 h 10 min. b) 11.10 am + 2 h 10 min = 1.20 pm."} {"t":"q","id":13450,"q":"Adeline collected 4 times as many stickers as Kathy. They collected 120 stickers altogether.\na) How many stickers did Kathy collect?\nb) Adeline and Kathy decided to pack the 120 stickers equally into packets of 9 to give to their friends. How many stickers were left unpacked?\nKathy = ; left unpacked = ","e":"a) Total = 5 units = 120, so Kathy (1 unit) = 120 \u00f7 5 = 24. b) 120 \u00f7 9 = 13 R 3, so 3 left unpacked."} {"t":"q","id":13451,"q":"Some teachers and students from Ubi Primary School attended a concert. There were 98 more students than teachers. The number of male teachers was the same as the number of male students. There were 26 male students and 15 female teachers.\na) How many more male teachers than female teachers were there?\nb) How many students were there?\nMale teachers more than female teachers = ; number of students = ","e":"Male teachers = male students = 26. a) 26 \u2212 15 = 11 more male than female teachers. b) Teachers = 26 + 15 = 41; students = 41 + 98 = 139."} {"t":"q","id":13452,"q":"Two thousand, three hundred and seventy written as numerals is .","e":"Two thousand = 2000, three hundred = 300, seventy = 70. 2000 + 300 + 70 = 2370."} {"t":"q","id":13458,"q":"Write 6 km 24 m in metres.","e":"1 km = 1000 m, so 6 km = 6000 m. 6000 m + 24 m = 6024 m."} {"t":"q","id":13463,"q":"8 x 6 = \u00f7 2\nWhat is the missing number in the box?","e":"8 x 6 = 48. The missing number \u00f7 2 = 48, so the number is 48 x 2 = 96."} {"t":"q","id":13464,"q":"Which one of the following statements is true?","e":"5\/6 is more than half (3\/6), so 5\/6 > 1\/2 is true. The other statements are false."} {"t":"q","id":13465,"q":"2\/8 + 1\/12 =","e":"2\/8 = 1\/4 = 3\/12. 3\/12 + 1\/12 = 4\/12 = 1\/3."} {"t":"q","id":13469,"q":"Divide 472 by 8.
Answer: ","e":"472 \u00f7 8 = 59."} {"t":"q","id":13470,"q":"Mr Lee slept at 23 25.\nGive the time he slept in 12-hour clock.\nInclude am or pm in your answer.
Answer: ","e":"23 25 in 24-hour clock is after noon. 23 - 12 = 11, so it is 11.25 pm."} {"t":"q","id":13471,"q":"Write 3095 g in kilograms and grams.\n kg g","e":"1 kg = 1000 g. 3095 g = 3000 g + 95 g = 3 kg 95 g."} {"t":"q","id":13474,"q":"What is the difference between \\(\\dfrac{5}{12}\\) and \\(\\dfrac{1}{6}\\)?\nGive your answer in its simplest form.","e":"1\/6 = 2\/12. 5\/12 - 2\/12 = 3\/12 = 1\/4."} {"t":"q","id":13475,"q":"Arrange the fractions in order, beginning with the greatest.\n1\/10, 3\/5, 2\/9, 2\/4\n (greatest), , , ","e":"As decimals: 3\/5 = 0.6, 2\/4 = 0.5, 2\/9 \u2248 0.22, 1\/10 = 0.1. Greatest to smallest: 3\/5, 2\/4, 2\/9, 1\/10."} {"t":"q","id":13478,"q":"A fruit seller packs 280 apples into bags of 6.\nHow many apples are left unpacked?
Answer: ","e":"280 \u00f7 6 = 46 remainder 4. So 4 apples are left unpacked."} {"t":"q","id":13485,"q":"A train arrived at Gardens MRT station with 1359 passengers.\n247 passengers alighted from the train and 498 passengers boarded the train.\nHow many passengers were there in the train when it left Gardens MRT station?
Answer: ","e":"1359 - 247 = 1112 stayed. 1112 + 498 boarded = 1610."} {"t":"q","id":13486,"q":"Mrs Tan started cleaning her house at 9.35 am.\nShe took 2 h 45 min to clean her house.\nThen she watched a television programme until 2 pm.\nHow long did she watch the television programme?\n h min","e":"9.35 am + 2 h 45 min = 12.20 pm. From 12.20 pm to 2.00 pm is 1 h 40 min."} {"t":"q","id":13488,"q":"Mrs Soh had 13 packets of sweets. Each packet had the same number of sweets. She gave 12 pupils a packet each.\nFrom the remaining packet, she gave 7 sweets to each of the same pupils and there was no leftover.\nHow many sweets did each pupil get in the end?
Answer: ","e":"The last packet split among 12 pupils at 7 each = 12 x 7 = 84 sweets per packet. Each pupil got one full packet (84) plus 7 = 91 sweets."} {"t":"q","id":13490,"q":"Ali and Samad had 80 marbles altogether.\nAfter Ali gave 7 marbles to Samad, Ali had 4 times as many marbles as Samad.\nHow many marbles did Samad have in the end?
Answer: ","e":"Total stays 80. After giving, Ali = 4 units, Samad = 1 unit, 5 units = 80, 1 unit = 16. Samad had 16 in the end."} {"t":"q","id":13491,"q":"Which of the following is five thousand, four hundred and one in numerals?","e":"Five thousand = 5000, four hundred = 400, one = 1. 5000 + 400 + 1 = 5401."} {"t":"q","id":13493,"q":"What is the quotient when 760 is divided by 7?","e":"760 \/ 7 = 108 remainder 4. The quotient is 108."} {"t":"q","id":13495,"q":"Which fraction is greater than 1\/2?","e":"Compare each to 1\/2: 1\/3 < 1\/2, 3\/8 < 1\/2, 4\/7 > 1\/2 (since half of 7 is 3.5), 6\/12 = 1\/2. Only 4\/7 is greater."} {"t":"q","id":13497,"q":"Which of the following fractions is equivalent to 2\/3?","e":"Multiply 2\/3 by 3\/3: (2x3)\/(3x3) = 6\/9. So 6\/9 is equivalent to 2\/3."} {"t":"q","id":13499,"q":"Healing Hands Clinic opens only on weekdays for the timings shown in the table. Mondays to Fridays: 9:00 am - 12:30 pm and 3:30 pm - 8:00 pm; Saturdays and Sundays: Closed. How long is the clinic open on a Tuesday?","e":"Morning: 9:00 am to 12:30 pm = 3 h 30 min. Afternoon: 3:30 pm to 8:00 pm = 4 h 30 min. Total = 3 h 30 min + 4 h 30 min = 8 h."} {"t":"q","id":13501,"q":"Find the value of 6\/8 - 1\/2.","e":"1\/2 = 4\/8. So 6\/8 - 4\/8 = 2\/8 = 1\/4."} {"t":"q","id":13504,"q":"Arrange the following lengths from the longest to the shortest. 1 m 20 cm, 1 km 2 m, 120 m","e":"Convert to a common unit: 1 m 20 cm = 1.2 m, 1 km 2 m = 1002 m, 120 m. Longest to shortest: 1 km 2 m, 120 m, 1 m 20 cm."} {"t":"q","id":13508,"q":"Write the missing number in the number pattern. 7120, 7000, 6880, , 6640, 6520","e":"The pattern decreases by 120 each time. 6880 - 120 = 6760."} {"t":"q","id":13511,"q":"Mrs Seto bakes 438 cupcakes. Each box can only fit 4 cupcakes. What is the number of boxes she will need to pack all the cupcakes? ","e":"438 \/ 4 = 109 remainder 2. The leftover 2 cupcakes still need a box, so she needs 109 + 1 = 110 boxes."} {"t":"q","id":13513,"q":"The difference between two numbers is 832. The greater number is 986. What is the smaller number? ","e":"Smaller number = greater number - difference = 986 - 832 = 154."} {"t":"q","id":13515,"q":"There are 30 apples and 25 pears in a crate. How many fruits are there in 6 similar crates? ","e":"One crate has 30 + 25 = 55 fruits. 6 crates have 55 x 6 = 330 fruits."} {"t":"q","id":13518,"q":"The sum of 2 numbers is 3764. The difference of the 2 numbers is 132. Find the greater number. ","e":"Twice the smaller number = 3764 - 132 = 3632, so smaller = 1816. Greater = 1816 + 132 = 1948."} {"t":"q","id":13519,"q":"A bus left a bus interchange with some people onboard. When it reached the first bus-stop, 7 people boarded the bus and 9 people alighted the bus. There were 24 people on the bus when it left the bus-stop. How many people were onboard the bus when it left the bus interchange? ","e":"Work backwards: before 7 boarded, there were 24 - 7 = 17. Before 9 alighted, there were 17 + 9 = 26 people."} {"t":"q","id":13520,"q":"Anne baked 240 more chocolate tarts than strawberry tarts. She baked 9 times as many chocolate tarts as strawberry tarts. How many tarts did she bake? ","e":"Chocolate is 9 units, strawberry is 1 unit, so the difference of 8 units = 240. 1 unit = 30 strawberry tarts. Total = 10 units = 30 x 10 = 300 tarts."} {"t":"q","id":13521,"q":"Joe took 1 h 25 min to complete his painting. He finished his painting at 1:10pm. What time did Joe start painting? Give your answer in 24-h clock. ","e":"Finish time 1:10 pm = 1310. Subtract 1 h 25 min: 1310 - 1 h = 1210, then - 25 min = 1145."} {"t":"q","id":13522,"q":"Jeya collected 2540 bottle caps. He collected 1230 more bottle caps than Hansel. How many bottle caps did they collect altogether? ","e":"Hansel = 2540 - 1230 = 1310. Altogether = 2540 + 1310 = 3850 bottle caps."} {"t":"q","id":13523,"q":"In a tin, there are 482 blue, green and yellow marbles altogether. There are three times as many blue marbles as green marbles. There are 42 yellow marbles. How many blue marbles are there in the tin? ","e":"Blue + green = 482 - 42 = 440. Blue is 3 units and green is 1 unit, so 4 units = 440, 1 unit = 110. Blue = 3 x 110 = 330."} {"t":"q","id":13524,"q":"Li Ming had 432 pears. He put them into 6 equal bags. He gave 2 bags to Ali. How many pears had Li Ming left? ","e":"Each bag has 432 \/ 6 = 72 pears. He gave away 2 bags = 72 x 2 = 144 pears. Left = 432 - 144 = 288."} {"t":"q","id":13529,"q":"Arrange the following fractions in order. Begin with the greatest.\n1\/10, 3\/5, 1\/2","e":"Convert to tenths: 3\/5 = 6\/10, 1\/2 = 5\/10, 1\/10 = 1\/10. Greatest to smallest: 6\/10, 5\/10, 1\/10, i.e. 3\/5, 1\/2, 1\/10."} {"t":"q","id":13533,"q":"Kelly arrived in school at 7.10 a.m. She took 35 minutes to travel from home to school. At what time did she leave her home?","e":"Subtract the travel time from the arrival time: 7.10 a.m. - 35 min = 6.35 a.m."} {"t":"q","id":13534,"q":"The difference between two numbers is 1718. The smaller number is 6147. What is the other number?","e":"The other number is the larger one: 6147 + 1718 = 7865."} {"t":"q","id":13535,"q":"A sum of money was shared among 4 boys. Each boy received $200 and there was $38 left. What was the sum of money?","e":"4 x $200 = $800, plus the $38 left over = $838."} {"t":"q","id":13536,"q":"Cindy needs 175 cm of cloth to make a blouse. She needs 25 cm more cloth to make a dress. How much cloth does Cindy need to make 2 such dresses?","e":"One dress = 175 + 25 = 200 cm. Two dresses = 200 x 2 = 400 cm."} {"t":"q","id":13537,"q":"Write 7 thousands, 9 hundreds and 4 ones in numerals.\n","e":"7 thousands = 7000, 9 hundreds = 900, 0 tens, 4 ones = 4. Total = 7904."} {"t":"q","id":13542,"q":"Jessica's piano lesson started at 9.45 a.m. Her lesson lasted for 1 h 20 min. At what time did her lesson end?\n a.m.","e":"9.45 a.m. + 1 h = 10.45 a.m.; + 20 min = 11.05 a.m."} {"t":"q","id":13544,"q":"Find the value of \\(\\dfrac{1}{3}\\) + \\(\\dfrac{2}{6}\\). Give your answer in the simplest form.","e":"1\/3 = 2\/6, so 2\/6 + 2\/6 = 4\/6 = 2\/3."} {"t":"q","id":13546,"q":"Annie has 3 fifty-cent coins and 4 five-dollar notes. How much money does she have altogether?\n$ ","e":"3 x $0.50 = $1.50; 4 x $5 = $20; total = $20 + $1.50 = $21.50."} {"t":"q","id":13548,"q":"A tennis racket cost $128. A pair of sports shoes cost $19.60 less than the tennis racket. How much did the pair of sports shoes cost?\n$ ","e":"$128.00 - $19.60 = $108.40."} {"t":"q","id":13549,"q":"Mrs Wong used 135 g of flour to bake a cake. How much flour did Mrs Wong use to bake 5 such cakes?\n g","e":"135 g x 5 = 675 g."} {"t":"q","id":13551,"q":"Mandy packed 932 sweets into as many boxes of 9 as possible. How many sweets were left unpacked?\n","e":"932 \/ 9 = 103 remainder 5, so 5 sweets are left unpacked."} {"t":"q","id":13552,"q":"Mr Suri sold 243 apples. Mr Ng sold 3 times as many apples as Mr Suri. How many apples did Mr Ng sell?\n","e":"243 x 3 = 729."} {"t":"q","id":13553,"q":"A pail with a capacity of 2 l contains 1400 ml of water. 3 full jugs of water are needed to fill the pail completely. What is the capacity of a jug?\n ml","e":"2 l = 2000 ml. Water still needed = 2000 - 1400 = 600 ml. 3 jugs fill 600 ml, so each jug = 600 \/ 3 = 200 ml."} {"t":"q","id":13554,"q":"Ravi had 680 marbles at first. He gave away 8 marbles and packed the remaining marbles into packets of 4 marbles. How many packets of marbles did Ravi pack?\n","e":"680 - 8 = 672 marbles left. 672 \/ 4 = 168 packets."} {"t":"q","id":13556,"q":"Janet gave 60 muffins to her classmates. 12 of her classmates took 1 muffin each. The rest of her classmates took 2 muffins each. How many of Janet's classmates took 2 muffins each?\n","e":"12 classmates took 12 muffins. Remaining muffins = 60 - 12 = 48. These were taken 2 each, so 48 \/ 2 = 24 classmates."} {"t":"q","id":13558,"q":"A van can carry up to 8 people. What is the smallest number of vans needed to carry 97 people?\n","e":"97 \/ 8 = 12 remainder 1. The remaining person still needs a van, so 12 + 1 = 13 vans."} {"t":"q","id":13559,"q":"Mr Smith bought 6 oranges and 8 apples with some money. An orange cost twice as much as an apple. How many apples could Mr Smith buy with the same amount of money?\n","e":"1 orange = 2 apples in cost, so 6 oranges = 12 apples. Total = 12 + 8 = 20 apples."} {"t":"q","id":13560,"q":"A shirt cost $65.30. Mrs Lee bought a bag that cost $24.80 more than the shirt.\n(a) What was the cost of the bag?\n(b) Mrs Lee gave the cashier a $100 note to pay for the bag. What was the change she received?\n(a) $ \n(b) $ ","e":"(a) Bag = $65.30 + $24.80 = $90.10. (b) Change = $100 - $90.10 = $9.90."} {"t":"q","id":13561,"q":"Mrs Tan started washing and polishing her car at 5.00 p.m. She took 40 min to wash her car and 1 h 25 min to polish her car.\n(a) At what time did Mrs Tan complete washing and polishing her car?\n(b) How much more time did Mrs Tan take to polish than wash her car?\n(a) \n(b) ","e":"(a) Total time = 40 min + 1 h 25 min = 2 h 5 min. 5.00 p.m. + 2 h 5 min = 7.05 p.m. (b) 1 h 25 min - 40 min = 85 min - 40 min = 45 min."} {"t":"q","id":13562,"q":"Jerry ran 1650 m. He ran 800 m more than Kenny.\n(a) What is the distance Kenny ran in metres?\n(b) What is the total distance ran by the two boys? Leave your answer in km and m.\n(a) m\n(b) km m","e":"(a) Kenny = 1650 - 800 = 850 m. (b) Total = 1650 + 850 = 2500 m = 2 km 500 m."} {"t":"q","id":13564,"q":"3480 people were at a football match. 1905 of them were adults and the rest were children. There were 4 times as many boys as girls at the football match.\n(a) How many children were at the football match?\n(b) How many girls were at the football match?\n(a) \n(b) ","e":"(a) Children = 3480 - 1905 = 1575. (b) Boys + girls = 5 units = 1575, so 1 unit (girls) = 1575 \/ 5 = 315."} {"t":"q","id":13565,"q":"Mrs Ong bought a total of 50 notebooks and scissors for $154. She paid $5 for each notebook and $2 for each pair of scissors.\n(a) How many pairs of scissors did she buy?\n(b) How many notebooks did she buy?\n(a) \n(b) ","e":"Assume all 50 are notebooks: 50 x $5 = $250. Excess = $250 - $154 = $96. Each notebook swapped for scissors saves $5 - $2 = $3, so $96 \/ $3 = 32 notebooks; scissors = 50 - 32 = 18. (a) 18 scissors, (b) 32 notebooks."} {"t":"q","id":13568,"q":"What is the missing number in the box?\n12\/15 = \/5","e":"12\/15 = 4\/5 (divide numerator and denominator by 3). Missing numerator is 4."} {"t":"q","id":13571,"q":"Arrange the fractions in order from the smallest to the greatest.\n7\/9 , 1\/2 , 4\/9","e":"4\/9 (0.44) < 1\/2 (0.5) < 7\/9 (0.78). Smallest to greatest: 4\/9, 1\/2, 7\/9."} {"t":"q","id":13572,"q":"Jason has 300 stickers. Mabel has 50 fewer stickers than Jason. How many stickers do they have altogether?","e":"Mabel = 300 - 50 = 250. Altogether = 300 + 250 = 550."} {"t":"q","id":13573,"q":"Jordan had 100 cards. He gave some cards to 10 friends. Each friend received 6 cards. How many cards did he have left in the end?","e":"Cards given = 10 x 6 = 60. Left = 100 - 60 = 40."} {"t":"q","id":13576,"q":"What is the missing number in the pattern?\n3 , 6 , 10 , 13 , , 20 , 24","e":"Pattern adds 3 then 4 alternately: 3 (+3) 6 (+4) 10 (+3) 13 (+4) 17 (+3) 20 (+4) 24. Missing = 17."} {"t":"q","id":13578,"q":"Find the remainder when 597 \u00f7 6.
Answer: ","e":"597 div 6 = 99 remainder 3 (99 x 6 = 594, 597 - 594 = 3)."} {"t":"q","id":13581,"q":"Find the sum of \\(\\dfrac{1}{2}\\) and \\(\\dfrac{1}{6}\\). Express your answer in its simplest form.","e":"1\/2 = 3\/6. 3\/6 + 1\/6 = 4\/6 = 2\/3."} {"t":"q","id":13582,"q":"Peter had 40 marbles. After he gave 7 marbles to Monica, they had the same number of marbles. How many marbles did Monica have at first?
Answer: ","e":"After giving away 7, Peter has 40 - 7 = 33, and Monica also has 33. Monica at first = 33 - 7 = 26."} {"t":"q","id":13583,"q":"Mr Lee had some oranges. He placed 9 oranges into each box and had 165 boxes of oranges. There were 3 oranges left unpacked. How many oranges did Mr Lee have at first?
Answer: ","e":"Oranges in boxes = 165 x 9 = 1485. Add the 3 left over: 1485 + 3 = 1488."} {"t":"q","id":13586,"q":"The sum of 2 numbers is 78. The difference between the 2 numbers is 16.\na) Find the smaller number.\nb) Find the bigger number.
(a)   (b) ","e":"Smaller = (78 - 16) div 2 = 62 div 2 = 31. Bigger = 78 - 31 = 47."} {"t":"q","id":13587,"q":"A lunch box cost $25. A water bottle cost $8 more than a lunch box. A bag cost twice as much as a lunch box.\na) Which item cost the most? How much did that item cost?\nb) What was the total cost of the 3 items?
(a)   (b)   (c) ","e":"Lunch box $25, water bottle $25+$8=$33, bag $25x2=$50. The bag costs the most at $50. Total = $25+$33+$50 = $108."} {"t":"q","id":13590,"q":"Melody arrived at the bus-stop. She waited 35 min for the bus. She boarded the bus at 13 20 to go to a shopping mall.\na) What time did Melody arrive at the bus-stop?\nb) Melody reached the shopping mall at 13 55. She left the shopping mall at 16 15. How long was she at the shopping mall?
(a)   (b) ","e":"a) Boarded at 13 20, waited 35 min, so arrived 13 20 - 35 min = 12 45. b) 13 55 to 16 15 = 2 h 20 min (13 55 to 14 00 = 5 min, 14 00 to 16 00 = 2 h, 16 00 to 16 15 = 15 min; 5+15 = 20 min, total 2 h 20 min)."} {"t":"q","id":13594,"q":"Susan has 72 pencils. She wants to pack them equally into 8 goodie bags. How many pencils are there in one bag?","e":"72 divided into 8 equal groups: 72 \u00f7 8 = 9 pencils per bag."} {"t":"q","id":13597,"q":"2\/3 - 3\/9 =","e":"2\/3 = 6\/9, so 6\/9 - 3\/9 = 3\/9 = 1\/3. The key marks option (3) 1\/9; note the simplest correct value is 1\/3."} {"t":"q","id":13599,"q":"Ms Chong baked 498 cookies. She ate 6 cookies and gave 60 cookies to her friends. How many cookies were left?","e":"498 - 6 - 60 = 432 cookies left."} {"t":"q","id":13609,"q":"What is the quotient when 58 is divided by 3?
Answer: ","e":"58 \u00f7 3 = 19 remainder 1. The quotient is 19."} {"t":"q","id":13611,"q":"Arrange the following fractions from the smallest to the greatest.\n4\/7, 2\/5, 1\/2
(a)   (b)   (c) ","e":"As decimals: 2\/5 = 0.4, 1\/2 = 0.5, 4\/7 \u2248 0.571. Smallest to greatest: 2\/5, 1\/2, 4\/7."} {"t":"q","id":13613,"q":"Joyce spent $3210 on a sofa set. She also bought a piano for $5630. How much did she spend altogether?
Answer: ","e":"$3210 + $5630 = $8840."} {"t":"q","id":13614,"q":"Find the difference between 1072 and 6498.
Answer: ","e":"6498 - 1072 = 5426."} {"t":"q","id":13615,"q":"Parcel A has a mass of 2240 g. Parcel B has a mass of 1960 g. What is the total mass of Parcels A and B?\nGive your answer in kilograms and grams.
(a)   (b) ","e":"2240 g + 1960 g = 4200 g = 4 kg 200 g."} {"t":"q","id":13616,"q":"315 cm of ribbon is cut into 9 equal pieces. What is the length of each piece of ribbon?
Answer: ","e":"315 \u00f7 9 = 35 cm per piece."} {"t":"q","id":13619,"q":"There were 498 children at a concert. There were 24 more children than adults. How many adults and children were there at the concert?
Answer: ","e":"Adults = 498 - 24 = 474. Total = 498 + 474 = 972."} {"t":"q","id":13620,"q":"A fruit seller packed 107 apples into bags. He packed 7 apples into each bag. How many apples were left unpacked?
Answer: ","e":"107 \u00f7 7 = 15 remainder 2, so 2 apples are left unpacked."} {"t":"q","id":13621,"q":"The capacity of a bottle is 330 ml. What is the total capacity of six bottles?\nGive your answer in litres and millilitres.
(a)   (b) ","e":"330 ml \u00d7 6 = 1980 ml = 1 L 980 ml."} {"t":"q","id":13622,"q":"An aeroplane left Hong Kong at 23 45 and reached Singapore at 04 10 the following day. How long was the flight?
(a)   (b) ","e":"23 45 to 24 00 is 15 min; 00 00 to 04 10 is 4 h 10 min; total 4 h 25 min."} {"t":"q","id":13626,"q":"In a carpark, there are 852 motorcycles. There are 87 more motorcycles than vans. There are twice as many cars as vans. How many cars are there in the carpark?
Answer: ","e":"Vans = 852 - 87 = 765. Cars = 765 \u00d7 2 = 1530."} {"t":"q","id":13631,"q":"In 8371, the digit 3 is in the place.","e":"In 8371 the digits are 8 (thousands), 3 (hundreds), 7 (tens), 1 (ones). So 3 is in the hundreds place."} {"t":"q","id":13637,"q":"300 more than 57 tens is .","e":"57 tens = 570. 300 more than 570 = 570 + 300 = 870."} {"t":"q","id":13639,"q":"The sum of two numbers is 5211. The smaller number is 1979. Find the greater number.","e":"Greater number = total - smaller = 5211 - 1979 = 3232."} {"t":"q","id":13642,"q":"Dan has 4 boxes of balloons. There are 8 balloons in each box. He uses 12 balloons for a party. How many balloons has he left?","e":"4 x 8 = 32 balloons. 32 - 12 = 20 balloons left."} {"t":"q","id":13644,"q":"A pizza was cut into 6 equal pieces. Alice ate 2\/3 of the pizza and Carol ate 1\/6 of it. What fraction of the pizza was eaten?","e":"2\/3 = 4\/6. 4\/6 + 1\/6 = 5\/6 of the pizza was eaten."} {"t":"q","id":13646,"q":"Write four thousand and fifteen in numeral.
Answer: ","e":"Four thousand = 4000, and fifteen = 15, so 4000 + 15 = 4015."} {"t":"q","id":13652,"q":"54 less than 67 hundreds is ","e":"67 hundreds = 6700. 54 less than 6700 = 6700 - 54 = 6646."} {"t":"q","id":13653,"q":"Find the value of (a) and (b).\nNumber of tricycles: 1, 2, 5, 7, 8, 10\nNumber of wheels: 3, 6, (a), 21, (b), 30\nAnswer: (a) (b) ","e":"Each tricycle has 3 wheels. (a) 5 x 3 = 15. (b) 8 x 3 = 24."} {"t":"q","id":13654,"q":"Arrange the following fractions in order. Begin with the smallest.\n3\/5, 4\/10, 1\/2\nAnswer: , , ","e":"Convert to tenths: 3\/5 = 6\/10, 4\/10 = 4\/10, 1\/2 = 5\/10. Smallest to largest: 4\/10, 5\/10 (=1\/2), 6\/10 (=3\/5)."} {"t":"q","id":13655,"q":"What is the missing number in the box?\n1\/2 = \/6","e":"To get from denominator 2 to 6, multiply by 3, so the numerator 1 x 3 = 3. 1\/2 = 3\/6."} {"t":"q","id":13656,"q":"2 boys cut a cake into 4 pieces. Eugene ate 1\/4 of it. Michael ate 1\/2 of it. How many pieces of the cake were left?
Answer: ","e":"Cake has 4 pieces. Eugene ate 1\/4 = 1 piece. Michael ate 1\/2 = 2 pieces. 4 - 1 - 2 = 1 piece left."} {"t":"q","id":13657,"q":"3 children shared a bar of chocolate. Edwin ate \\(\\dfrac{5}{12}\\) of it, Rayner ate \\(\\dfrac{1}{4}\\) of it and Vincent ate the rest. What fraction of the chocolate did Vincent eat? Leave your answer in the simplest form.","e":"1\/4 = 3\/12. Edwin + Rayner = 5\/12 + 3\/12 = 8\/12. Vincent = 12\/12 - 8\/12 = 4\/12 = 1\/3."} {"t":"q","id":13658,"q":"(a) 4 m 50 cm = cm\n(b) 3 l 86 ml = ml","e":"(a) 4 m = 400 cm, so 4 m 50 cm = 450 cm. (b) 3 l = 3000 ml, so 3 l 86 ml = 3086 ml."} {"t":"q","id":13664,"q":"At a school carnival, Nigel sold 1843 cookies. He sold 379 cookies fewer than Pauline.\n(a) How many cookies did Pauline sell?\n(b) How many cookies did they sell altogether?
(a)   (b) ","e":"(a) Pauline = 1843 + 379 = 2222 cookies. (b) Altogether = 2222 + 1843 = 4065 cookies."} {"t":"q","id":13665,"q":"The school bookshop gives away 2 erasers for every 8 pencils bought. Mateen bought 96 pencils. How many erasers did he get?
Answer: ","e":"96 \/ 8 = 12 groups of 8 pencils. Each group gives 2 erasers, so 12 x 2 = 24 erasers."} {"t":"q","id":13668,"q":"The length of a field is 2 times its breadth. The perimeter of the field is 108 m. What is the length of the field?
Answer: ","e":"Perimeter = 2(length + breadth) = length + breadth + length + breadth. With length = 2 x breadth, the perimeter equals 6 breadths: 108 \/ 6 = 18 m breadth. Length = 18 + 18 = 36 m."} {"t":"q","id":13669,"q":"The digit in 3985 is in the hundreds place.","e":"In 3985, reading from the right: 5 ones, 8 tens, 9 hundreds, 3 thousands. So the digit in the hundreds place is 9."} {"t":"q","id":13672,"q":"Which fraction is less than 1\/2 ?","e":"5\/9 > 1\/2 (half of 9 is 4.5), 5\/10 = 1\/2, 2\/3 > 1\/2, 5\/12 < 1\/2 (half of 12 is 6, and 5 < 6). So 5\/12 is less than 1\/2."} {"t":"q","id":13675,"q":"7 kg 50 g = g.","e":"1 kg = 1000 g, so 7 kg = 7000 g. 7000 g + 50 g = 7050 g."} {"t":"q","id":13676,"q":"The length of a square mat is 8 m. Find the area of the mat.","e":"Area of a square = side x side = 8 m x 8 m = 64 m\u00b2."} {"t":"q","id":13677,"q":"Raj took 2 hour 45 minutes to travel to his school. Gina took 50 minutes less to travel to her school. How long did Gina take to travel to her school?","e":"2 h 45 min - 50 min. 45 min - 50 min needs borrowing: 1 h 105 min - 50 min = 1 h 55 min."} {"t":"q","id":13680,"q":"Write the missing number.\n6198, , 6218, 6228, 6238","e":"The numbers increase by 10 each step: 6198, 6208, 6218, 6228, 6238. The missing number is 6208."} {"t":"q","id":13681,"q":"5492 = 5000 + tens + 90 + 2","e":"5492 = 5000 + 400 + 90 + 2. 400 = 40 tens, so the blank is 40."} {"t":"q","id":13682,"q":"\\(\\dfrac{1}{2}\\) + \\(\\dfrac{4}{10}\\) =","e":"1\/2 = 5\/10. 5\/10 + 4\/10 = 9\/10."} {"t":"s","id":6325,"s":"11.50 a.m. + 1 h 40 min = 1.30 p.m. (arrival). Class started 15 min later: 1.30 + 15 min = 1.45 p.m."} {"t":"s","id":6327,"s":"Son ate 3\/8 - 1\/4 = 3\/8 - 2\/8 = 1\/8. Total eaten = 3\/8 + 1\/8 = 4\/8 = 1\/2."} {"t":"s","id":6328,"s":"Sunday = 4 x 960 = 3840. Both days = 960 + 3840 = 4800."} {"t":"s","id":6329,"s":"Let each start = x. After selling, rambutans = x, mangosteens = x - 810, and x = 3(x - 810). So x = 3x - 2430, 2430 = 2x, x = 1215."} {"t":"s","id":6335,"s":"537 \/ 8 = 67 remainder 1; wait, 8 x 67 = 536, remainder 1. The quotient is 67. Per the answer key the quotient given is 61."} {"t":"s","id":6339,"s":"Remaining = 1248 - 300 = 948 g. Each packet = 948 \/ 6 = 158 g."} {"t":"s","id":6341,"s":"6A9 x B = 4074. Trying B = 6: 679 x 6 = 4074, so A = 7 and B = 6."} {"t":"s","id":6343,"s":"5 m = 500 cm. Cloth used = 500 - 185 = 315 cm. Each towel = 315 \/ 5 = 63 cm."} {"t":"s","id":6346,"s":"Common denominator 24: 1\/8=3\/24, 5\/12=10\/24, 3\/4=18\/24. Smallest to biggest: 1\/8, 5\/12, 3\/4."} {"t":"s","id":6348,"s":"Watch shows 12.20 p.m. but is 10 min fast, so actual arrival = 12.10 p.m. Subtract the 45 min travel: 12.10 p.m. - 45 min = 11.25 a.m."} {"t":"s","id":6350,"s":"Colin = 905 - 230 = 675. Colin - Bala = 675 - 299 = 376."} {"t":"s","id":6352,"s":"340 \/ 9 = 37 remainder 7. The 7 leftover pies still need a box, so 37 + 1 = 38 boxes."} {"t":"s","id":6353,"s":"15 one-dollar coins = $15.00, leaving $5.80 in 14 coins (50c and 10c). If all 14 were 10c that is $1.40; the extra $4.40 comes from swapping 10c for 50c (each swap adds 40c): 440\/40 = 11 fifty-cent coins."} {"t":"s","id":6354,"s":"End total = 890 - 130 + 280 = 1040, so each is 520. Local at first = 520 + 130 = 650; foreign at first = 520 - 280 = 240. (a) 650 - 240 = 410 more local. (b) 240 foreign at first."} {"t":"s","id":6356,"s":"In 9876, the digits from right to left are ones (6), tens (7), hundreds (8), thousands (9). So the thousands digit is 9."} {"t":"s","id":6359,"s":"An odd number ends in 1, 3, 5, 7 or 9. Only 2641 ends in 1, so it is odd."} {"t":"s","id":6361,"s":"The pattern decreases by 12 each time: 82, 70, 58, 46, 34, 22. So the missing number is 34."} {"t":"s","id":6362,"s":"A number divides by 5 with no remainder if it ends in 0 or 5. The numbers ending in 0 or 5 are 3530 and 3350. The smaller is 3350."} {"t":"s","id":6367,"s":"1\/2 = 4\/8. The distances from 4\/8 are: 1\/8 -> 3\/8, 2\/8 -> 2\/8, 3\/8 -> 1\/8, 6\/8 -> 2\/8. The smallest distance is for 3\/8."} {"t":"s","id":6371,"s":"75 div 6 = 12 remainder 3. The 12 boats carry 72 children; the remaining 3 children need 1 more boat, so 13 boats are needed."} {"t":"s","id":6373,"s":"Q is smallest when P is largest. The largest 2-digit number is 99, so the smallest 3-digit Q is 200 - 99 = 101."} {"t":"s","id":6374,"s":"2 kg = 2000 g. Repacked into 4 equal bags: 2000 div 4 = 500 g each."} {"t":"s","id":6381,"s":"Between 5000 and 6000 the thousands digit must be 5. Arrange the remaining digits 1, 6, 9 in ascending order: 1, 6, 9. So the smallest number is 5169."} {"t":"s","id":6382,"s":"The greatest 4-digit number is 9999, but it is odd. The greatest 4-digit even number ends in an even digit, so 9998."} {"t":"s","id":6383,"s":"Total balloons = 6 x 40 = 240. Bunches = 240 div 3 = 80."} {"t":"s","id":6385,"s":"$5 = 500 cents. 500 cents div 10 coins = 50 cents per coin."} {"t":"s","id":6386,"s":"78 cm x 8 = 624 cm. 624 cm = 6 m 24 cm (since 100 cm = 1 m)."} {"t":"s","id":6389,"s":"2 hours = 120 minutes. The first two compositions take the same time (call it t each); the third takes t + 30. So t + t + (t + 30) = 120, giving 3t + 30 = 120, 3t = 90, t = 30 minutes."} {"t":"s","id":6393,"s":"Convert to eighths: 3\/4 = 6\/8, 1\/2 = 4\/8, 7\/8 = 7\/8. Smallest = 4\/8, greatest = 7\/8. Difference = 7\/8 - 4\/8 = 3\/8."} {"t":"s","id":6394,"s":"Iris took 3 out of 12 pieces = 3\/12. Simplify by dividing top and bottom by 3: 3\/12 = 1\/4."} {"t":"s","id":6395,"s":"(a) Chairs = 3 x 68 = 204. (b) Tables + chairs = 68 + 204 = 272."} {"t":"s","id":6398,"s":"Giving away 20 cars changes the gap by 2 x 20 = 40 (Jack loses 20, Ken gains 20). After giving, Jack leads by 23, so at first the lead was 23 + 40 = 63 more cars."} {"t":"s","id":6400,"s":"In 1579, reading from the right: 9 ones, 7 tens, 5 hundreds, 1 thousand. So the digit 5 is in the hundreds place."} {"t":"s","id":6401,"s":"Two thousand = 2000, one hundred = 100, twelve = 12. 2000 + 100 + 12 = 2112."} {"t":"s","id":6402,"s":"Product means multiply. 24 x 8 = 192."} {"t":"s","id":6404,"s":"2\/4, 3\/6 and 6\/12 all simplify to 1\/2. 4\/10 simplifies to 2\/5, which is not 1\/2."} {"t":"s","id":6405,"s":"11.40 a.m. + 20 min = 12.00 noon (12.00 p.m.); + 3 min = 12.03 p.m."} {"t":"s","id":6406,"s":"The numbers increase by 15 each time: 1295 + 15 = 1310. Check: 1310 + 15 = 1325."} {"t":"s","id":6407,"s":"2 kg 250 g = 2250 g. 2250 g - 360 g = 1890 g."} {"t":"s","id":6409,"s":"1 h 25 min = 85 min. 85 min - 40 min = 45 min."} {"t":"s","id":6411,"s":"5 l 70 ml = 5070 ml. 5070 ml + 2190 ml = 7260 ml."} {"t":"s","id":6417,"s":"908 \/ 5 = 181 remainder 3. The quotient is 181."} {"t":"s","id":6419,"s":"Same numerator: the smaller the denominator, the larger the fraction. So 5\/6 > 5\/7 > 5\/9."} {"t":"s","id":6420,"s":"8.30 a.m. to 12.30 p.m. is 4 h; 12.15 p.m. is 15 min before 12.30, so 4 h - 15 min = 3 h 45 min. (From 8.30 to 12.15 = 3 h 45 min.)"} {"t":"s","id":6430,"s":"Flour used = 12 g x 9 = 108 g. Left = 500 g - 108 g = 392 g."} {"t":"s","id":6431,"s":"For every 3 paid + 1 free = 4 cookies. 12 cookies = 12 \/ 4 = 3 groups, so she paid for 3 x 3 = 9 cookies = 3 x $5.00 = $15.00."} {"t":"s","id":6432,"s":"a) At first = 216 + 13 = 229 oranges. b) Each box = 216 \/ 8 = 27 oranges."} {"t":"s","id":6434,"s":"4 sides x 7 = 28 counts, but the 4 corner trees are each counted twice, so 28 - 4 = 24. (Answer key: 5 x 4 = 20 non-corner-overlap, + 4 corners = 24.)"} {"t":"s","id":6439,"s":"Total erasers = 6 x 24 = 144. Given away = 144 - 18 = 126."} {"t":"s","id":6442,"s":"Packed = 8 x 46 = 368. Total at first = 368 + 37 = 405."} {"t":"s","id":6443,"s":"3 times Amy = 3 x 78 = 234. June needs 234 - 42 = 192 more seashells."} {"t":"s","id":6445,"s":"8 m = 800 cm. 800 cm + 7 cm = 807 cm."} {"t":"s","id":6446,"s":"1\/8 = 0.125, 5\/9 ~ 0.556, 2\/3 ~ 0.667. Smallest to greatest: 1\/8, 5\/9, 2\/3."} {"t":"s","id":6450,"s":"1\/4 = 3\/12. 5\/12 - 3\/12 = 2\/12 = 1\/6."} {"t":"s","id":6451,"s":"1\/2 = 7\/14 and 1\/7 = 2\/14. 7\/14 + 2\/14 = 9\/14."} {"t":"s","id":6453,"s":"2\/3 = ?\/18. Since 3 x 6 = 18, multiply the numerator: 2 x 6 = 12. So 2\/3 = 12\/18."} {"t":"s","id":6458,"s":"9 m = 900 cm, plus 6 cm = 906 cm. Boon Huat is correct."} {"t":"s","id":6465,"s":"An odd sum needs one odd and one even number. 1719 (odd) + 2002 (even) = 3721, which is odd."} {"t":"s","id":6466,"s":"4 thousands 27 hundreds = 4000 + 2700 = 6700. As (?) thousands + 17 hundreds (1700): 6700 - 1700 = 5000 = 5 thousands."} {"t":"s","id":6468,"s":"7 buses x 35 seats = 245 seats. 266 - 245 = 21 children without a seat."} {"t":"s","id":6470,"s":"Let Marcy = M. Jack = M+15, Porsha = M+25, Tabby = M+28. Tabby has the most (M+28)."} {"t":"s","id":6471,"s":"2503 - 2000 - 3 = 500. The missing number is 500."} {"t":"s","id":6473,"s":"Convert to tenths\/twentieths: 7\/10 = 0.7, 3\/5 = 0.6, 1\/4 = 0.25. Greatest to smallest: 7\/10, 3\/5, 1\/4."} {"t":"s","id":6478,"s":"1560 \u00f7 6 = 260. In 260 there are 26 tens."} {"t":"s","id":6482,"s":"1 bottle = 1200 \u00f7 3 = 400 ml. 1 glass = 400 \u00f7 4 = 100 ml."} {"t":"s","id":6484,"s":"Convert to ml: 7 l 404 ml = 7404 ml; 74 l = 74000 ml; 7074 ml; 7004 ml. Increasing: 7004 ml, 7074 ml, 7 l 404 ml (7404 ml), 74 l (74000 ml)."} {"t":"s","id":6486,"s":"Session 1: 9.00 a.m.-12.30 p.m. = 3 h 30 min. Session 2: 2.15-5.15 p.m. = 3 h. Session 3: 6.30-9.45 p.m. = 3 h 15 min. Total = 9 h 45 min."} {"t":"s","id":6487,"s":"Flowers used = 183 x 7 = 1281. With 69 left over, she started with 1281 + 69 = 1350."} {"t":"s","id":6489,"s":"(a) Arrive 25 min before 5.35 p.m. = 5.10 p.m.; subtract 45 min travel = 4.25 p.m. (b) 5.35 p.m. to 6.45 p.m. = 1 h 10 min."} {"t":"s","id":6490,"s":"Difference = 2075 - 779 = 1296. Sue gives half, 1296 \u00f7 2 = 648, to make them equal. Lina ends with 779 + 648 = 1427."} {"t":"s","id":6491,"s":"Guess-and-check: 8 two-dollar notes = $16 and 6 ten-dollar notes = $60; 8 + 6 = 14 notes and $16 + $60 = $76. So 8 two-dollar notes."} {"t":"s","id":6492,"s":"Difference used = 2500 - 960 = 1540 g, which equals 2 units (Ravi's 3 units minus Goh's 1 unit). 1 unit = 770 g, so Goh's leftover = 770 g. At first = 770 + 2500 = 3270 g = 3 kg 270 g."} {"t":"s","id":6499,"s":"In 5370 the value of 5 is 5000 and the value of 7 is 70. Difference = 5000 \u2212 70 = 4930."} {"t":"s","id":6503,"s":"362 \u00f7 5 = 72 remainder 2. The quotient is 72."} {"t":"s","id":6506,"s":"Kenneth's age now = 26 \u2212 10 = 16. Michelle is 27, so she is 27 \u2212 16 = 11 years older."} {"t":"s","id":6507,"s":"The smallest 3-digit odd number is 101. 101 \u00f7 4 = 25 remainder 1."} {"t":"s","id":6508,"s":"Children = 187 \u2212 58 = 129. Total people = 187 + 129 = 316."} {"t":"s","id":6510,"s":"a) One necklace uses 35 beads, so 2 necklaces need 35 \u00d7 2 = 70 beads. b) Before buying 42 she had 105 \u2212 42 = 63; before making the necklace she had 63 + 35 = 98 beads at first."} {"t":"s","id":6515,"s":"572 = 3 x 190 + 2, so it leaves a remainder of 2. (298 r1, 381 r0, 496 r1.)"} {"t":"s","id":6516,"s":"813 is odd, so it is not divisible by 6 (a multiple of 6 must be even). 354, 432 and 768 are all even with digit sums divisible by 3."} {"t":"s","id":6522,"s":"Together they make 5 + 1 = 6 units = 162, so 1 unit (Rick) = 162 \/ 6 = 27. Billy = 5 x 27 = 135. (a) Billy made 135. (b) Rick made 27."} {"t":"s","id":6523,"s":"260 \/ 7 = 37 remainder 1. The leftover box has 1 pencil, so he needs 7 - 1 = 6 more pencils to make a complete box of 7."} {"t":"s","id":6528,"s":"Kartijah = $258 \u00f7 3 = $86. Altogether = $258 + $86 = $344."} {"t":"s","id":6529,"s":"English books = 361 \u00d7 6 = 2166. More English than Chinese = 2166 \u2212 361 = 1805."} {"t":"s","id":6530,"s":"Kevin's 3 units minus 20 equals Peter's 1 unit, so 2 units = 20, 1 unit = 20 \u00f7 2 = 10. Kevin = 3 \u00d7 10 = 30."} {"t":"s","id":6540,"s":"Sarah: 348 \u00d7 3 = 1044. Altogether: 1044 + 348 = 1392."} {"t":"s","id":6542,"s":"Let children = c, adults = 4c. After: 4c \u2212 132 = c \u2212 9, so 3c = 123, c = 41."} {"t":"s","id":6543,"s":"(a) 14 \u00d7 9 = 126 chairs. (b) 126 \u00f7 7 = 18 chairs per row."} {"t":"s","id":6548,"s":"6\u00d79=54, 7\u00d76=42, 8\u00d76=48, 9\u00d75=45. Greatest is 54."} {"t":"s","id":6551,"s":"Eight 5s = 40. 40 = 4 \u00d7 10, so the missing number is 10."} {"t":"s","id":6553,"s":"924 + 2308 = 3232. 5139 - 3232 = 1907 men."} {"t":"s","id":6554,"s":"Sean is 1 unit, Justin is 7 units, total 8 units = 392. 1 unit = 392 \u00f7 8 = 49."} {"t":"s","id":6555,"s":"The two identical faces multiply to 49. 7 \u00d7 7 = 49, so each face = 7."} {"t":"s","id":6560,"s":"Greatest 4-digit even number from 0,3,4,9 is 9430. Smallest 4-digit odd number is 3049. 9430 - 3049 = 6381."} {"t":"s","id":6561,"s":"Total + difference = 2 \u00d7 Tuesday: 300 + 44 = 344. Tuesday = 344 \u00f7 2 = $172."} {"t":"s","id":6562,"s":"Belle = 46 \u00d7 2 = 92. Carol = 92 \u00d7 4 = 368."} {"t":"s","id":6564,"s":"98 \u00f7 8 = 12 remainder 2. To make an equal share he needs 8 - 2 = 6 more sweets."} {"t":"s","id":6565,"s":"(a) Chinese = 400 + 520 = 920. (b) Malay = 920 \u00f7 4 = 230."} {"t":"s","id":6566,"s":"(a) 87 \u00d7 8 = 696 tarts. (b) Boxes sold = 161 \u00f7 7 = 23; tarts sold = 23 \u00d7 8 = 184."} {"t":"s","id":6567,"s":"They started equal. Sue's left - Tommy's left = the difference in spending = 403 - 152 = 251. Sue's left = 2 \u00d7 Tommy's left, so Tommy's left = 251 and Sue's left = 502. (a) Tommy had $251 left. (b) Sue had 502 + 152 = $654 at first."} {"t":"s","id":6568,"s":"12 m = 1200 cm. 1200 cm + 7 cm = 1207 cm."} {"t":"s","id":6572,"s":"Convert to tenths: 3\/10, 1\/2 = 5\/10, 3\/5 = 6\/10. Smallest to greatest: 3\/10, 1\/2, 3\/5."} {"t":"s","id":6573,"s":"3\/7 = 9\/21 (multiply by 3), so A = 9. 3\/7 = 18\/42 (multiply by 6), so B = 42."} {"t":"s","id":6575,"s":"Container = 450 \/ 3 = 150 ml. Cup = 150 \/ 2 = 75 ml."} {"t":"s","id":6579,"s":"1\/3 = 4\/12 (multiply numerator and denominator by 4). The missing number is 12."} {"t":"s","id":6580,"s":"1\/6 is smaller than 1\/5 because with the same numerator, a larger denominator gives a smaller fraction. (Other answers such as 1\/10 are also acceptable.)"} {"t":"s","id":6585,"s":"Adele = 129 - 87 = 42 kg. Belle = 87 - 41 = 46 kg. Cali = 41 kg. Cali is the lightest at 41 kg."} {"t":"s","id":6589,"s":"Adding 4 balls increased the mass by 786 - 326 = 460 g. (a) 1 ball = 460 \/ 4 = 115 g. (b) Box = 326 - 115 = 211 g."} {"t":"s","id":6593,"s":"With the same numerator, the larger the denominator the smaller the fraction. 2\/7 < 2\/5 < 2\/3."} {"t":"s","id":6595,"s":"Second string = 3 x 150 = 450 cm. Total = 150 + 450 = 600 cm. (Key: 150 x 4 = 600.)"} {"t":"s","id":6600,"s":"7 x 850 = 5950 ml poured. 6000 - 5950 = 50 ml needed."} {"t":"s","id":6601,"s":"9.10 a.m. minus 1 h 50 min = 7.20 a.m. (9.10 - 1 h = 8.10; 8.10 - 50 min = 7.20)."} {"t":"s","id":6602,"s":"Watermelons at first = 145 - 6 = 139 kg. Sold = 139 - 26 = 113 kg."} {"t":"s","id":6607,"s":"333 + 999 = 1332. Digits: thousands 1, hundreds 3, tens 3, ones 2. Only the ones digit (2) is even."} {"t":"s","id":6610,"s":"520 cm, 5 m 20 cm and 500 cm + 20 cm all equal 520 cm. 5 m 2 cm = 502 cm, which is different."} {"t":"s","id":6625,"s":"Odd means the ones digit must be odd. Smallest uses smallest leading digits: 1, 3, 6 then odd ones digit 5 \u2192 1365."} {"t":"s","id":6628,"s":"Hundreds value 300 \u2192 hundreds digit 3. Tens is 8 less than thousands; thousands = ones. Thousands 8, tens 0, ones 8 \u2192 8308."} {"t":"s","id":6631,"s":"The pattern alternates: 220, 230 (+10), 200, 210 (+10), 180, 190 (+10). The missing term is 210."} {"t":"s","id":6639,"s":"6\/15 simplifies to 2\/5, so a = 5. Then 2\/5 = 10\/25, so b = 10."} {"t":"s","id":6640,"s":"1\/3 = 3\/9. Comparing: 2\/9 < 3\/9, while 1\/2 and 5\/6 are larger than 1\/3. So 2\/9 is smaller than 1\/3."} {"t":"s","id":6641,"s":"(a) 1480 + 288 = 1768. (b) 1480 + 1768 = 3248."} {"t":"s","id":6642,"s":"Total cupcakes = 9 \u00d7 28 = 252. Per container = 252 \u00f7 4 = 63."} {"t":"s","id":6643,"s":"(a) 18 \u00d7 5 = 90 minutes (1 h 30 min). (b) 11.45 a.m. minus 1 h 30 min = 10.15 a.m."} {"t":"s","id":6647,"s":"203 cm = 200 cm + 3 cm = 2 m 3 cm. The other conversions are wrong."} {"t":"s","id":6648,"s":"Two erasers cost 2 x $0.45 = $0.90. Total = $2.20 + $0.90 = $3.10."} {"t":"s","id":6662,"s":"Same denominator (9), so order by numerator: 1 < 3 < 4. Smallest to greatest: 1\/9, 3\/9, 4\/9."} {"t":"s","id":6664,"s":"Bananas = 1 unit, apples = 4 units, total = 5 units = 20. So 1 unit = 20 \u00f7 5 = 4 bananas."} {"t":"s","id":6666,"s":"Betty = 170 - 12 = 158 cm. Daniel = 158 + 6 = 164 cm."} {"t":"s","id":6667,"s":"Kelly at first = 30 - 5 = 25 stamps. Mandy had the same, so total = 25 + 25 = 50 stamps."} {"t":"s","id":6671,"s":"From 4.15 p.m. to 6.15 p.m. is 2 h; back 10 min to 6.05 p.m. gives 1 h 50 min. (Or 4.15\u21925.15\u21926.05 = 1 h + 50 min.)"} {"t":"s","id":6677,"s":"Compare thousands first: 3 797 and 3 977 (three thousands) come before 7 397 and 7 937. Then compare the rest: 3 797 < 3 977 and 7 397 < 7 937."} {"t":"s","id":6684,"s":"21 tens = 210, 5 hundreds = 500, 3 ones = 3. 210 + 500 + 3 = 713."} {"t":"s","id":6694,"s":"Greatest odd number must end in an odd digit. To be greatest, put 5 then 4 then 0 in front and end in the odd 3: 5403."} {"t":"s","id":6695,"s":"The pattern increases by 49 each time. 3657 + 49 = 3706 (and 3706 + 49 = 3755)."} {"t":"s","id":6699,"s":"12.01 a.m. is one minute after midnight, written as 00 01 in 24-hour clock."} {"t":"s","id":6703,"s":"As decimals: 7\/11\u22480.64, 3\/7\u22480.43, 3\/8=0.375, 1\/4=0.25. Greatest to smallest: 7\/11, 3\/7, 3\/8, 1\/4."} {"t":"s","id":6709,"s":"Ones: 9 \u2212 2 = 7, so B = 7. Hundreds: A \u2212 1 = 3, so A = 5 (check: 8539 \u2212 5142 = 3397)."} {"t":"s","id":6710,"s":"Packed = 15 \u00d7 5 = 75. Total = 75 + 105 = 180."} {"t":"s","id":6712,"s":"5167 ends in 7, so it is odd, not even: (a) is false. The thousands digit 5 has value 5000, not 1000: (b) is false. Both false."} {"t":"s","id":6713,"s":"The 80 extra equals 2 of Alex's units (3 units \u2212 1 unit), so 1 unit = 80 \u00f7 2 = 40 (Alex). Altogether = 4 units = 4 \u00d7 40 = 160."} {"t":"s","id":6717,"s":"Green = 1\/3 = 4\/12. Green + red = 4\/12 + 5\/12 = 9\/12. Blue = 12\/12 \u2212 9\/12 = 3\/12 = 1\/4."} {"t":"s","id":6718,"s":"(a) 11.45 a.m. + 35 min = 12.20 p.m. (b) 10 a.m. + 20 min = 10.20; + 30 min rest = 10.50; + 1 h 45 min = 12.35 p.m."} {"t":"s","id":6722,"s":"(a) 1500 \u2212 992 = 508 children. (b) Men = women = 992 \u00f7 2 = 496. At end men (496) = 4 \u00d7 women left = women remaining = 496 \u00f7 4 = 124. Women who left = 496 \u2212 124 = 372."} {"t":"s","id":6725,"s":"Even numbers end in 0,2,4,6,8. Even options are 2392 and 2930; the smaller is 2392."} {"t":"s","id":6744,"s":"Convert to tenths: 7\/10, 1\/2 = 5\/10, 2\/5 = 4\/10. Greatest to smallest: 7\/10, 1\/2, 2\/5."} {"t":"s","id":6748,"s":"They started equal. Giving away 47 makes Derrick 47 fewer and Evan 47 more, so the gap is 47 + 47 = 94 stickers."} {"t":"s","id":6756,"s":"2.15 p.m. minus 1 h 55 min: 2.15 - 1 h = 1.15 p.m.; 1.15 - 55 min = 12.20 p.m."} {"t":"s","id":6760,"s":"Let Joyce = 1 unit. Mary = 2 units, Laura = 3 x Mary = 6 units. Laura - Joyce = 6 - 1 = 5 units = 405, so 1 unit = 81. Mary = 2 x 81 = 162."} {"t":"s","id":6764,"s":"In 7509: 7 thousands, 5 hundreds, 0 tens, 9 ones. The 0 is in the tens place."} {"t":"s","id":6766,"s":"1 kg = 1000 g. 5050 g = 5000 g + 50 g = 5 kg 50 g."} {"t":"s","id":6767,"s":"4:40 pm to 5:40 pm = 1 h. 5:40 pm to 6:05 pm = 25 min. Total = 1 h 25 min."} {"t":"s","id":6770,"s":"1\/3 = 3\/9. Missing = 8\/9 - 3\/9 = 5\/9."} {"t":"s","id":6773,"s":"9458 - 400 - 58 = 9000. So the missing number is 9000."} {"t":"s","id":6781,"s":"The pattern increases by 6 each time. (a) = 7874 + 6 = 7880; (b) = 7886 + 6 = 7892."} {"t":"s","id":6785,"s":"Mr Ng's time = 6 h 45 min + 25 min = 7 h 10 min. 15 00 + 7 h 10 min = 22 10."} {"t":"s","id":6789,"s":"(a) Fiona = Gail - 46 = 58 - 46 = 12. (b) Emily = 3 x 12 = 36. Total = 58 + 12 + 36 = 106."} {"t":"s","id":6790,"s":"Sunday = 785 + 698 = 1483. Both days = 1483 + 785 = 2268."} {"t":"s","id":6791,"s":"5 km = 5000 m. Ran 2850 m, then walked, then ran last 800 m. Walked = 5000 - 2850 - 800 = 1350 m = 1 km 350 m."} {"t":"s","id":6793,"s":"In 4960, reading right to left: 0 ones, 6 tens, 9 hundreds, 4 thousands. So 9 is in the hundreds place."} {"t":"s","id":6794,"s":"Odd numbers end in an odd digit. 9750 and 9778 are even. Of the odd ones (9639, 9643), 9643 is greater."} {"t":"s","id":6797,"s":"5 \u00d7 4 means four groups of 5 (or 5 groups of 4) = 20. 5 + 5 + 5 + 5 = 20."} {"t":"s","id":6799,"s":"Multiply numerator and denominator by 4: 2\/3 = (2\u00d74)\/(3\u00d74) = 8\/12. Missing numerator is 8."} {"t":"s","id":6801,"s":"108 \u00f7 8 = 13 remainder 4. So 4 cupcakes were left unpacked."} {"t":"s","id":6804,"s":"As decimals: 1\/2=0.50, 5\/8=0.625, 3\/10=0.30, 5\/9\u22480.556. Greatest to smallest: 5\/8, 5\/9, 1\/2, 3\/10."} {"t":"s","id":6806,"s":"Each transfer of 16 widens the gap by 2 \u00d7 16 = 32. New difference = 35 + 32 = 67."} {"t":"s","id":6821,"s":"Greater = 7 units, smaller = 1 unit; difference 6 units = 546, so 1 unit = 91. Greater = 7 \u00d7 91 = 637."} {"t":"s","id":6822,"s":"Actual start = 15 45 \u2212 20 min = 15 25. Finish = 15 25 + 35 min = 16 00."} {"t":"s","id":6825,"s":"a) 1 h 40 min + 30 min = 2 h 10 min. b) 11.10 am + 2 h 10 min = 1.20 pm."} {"t":"s","id":6827,"s":"a) Total = 5 units = 120, so Kathy (1 unit) = 120 \u00f7 5 = 24. b) 120 \u00f7 9 = 13 R 3, so 3 left unpacked."} {"t":"s","id":6828,"s":"Male teachers = male students = 26. a) 26 \u2212 15 = 11 more male than female teachers. b) Teachers = 26 + 15 = 41; students = 41 + 98 = 139."} {"t":"s","id":6829,"s":"Two thousand = 2000, three hundred = 300, seventy = 70. 2000 + 300 + 70 = 2370."} {"t":"s","id":6835,"s":"1 km = 1000 m, so 6 km = 6000 m. 6000 m + 24 m = 6024 m."} {"t":"s","id":6840,"s":"8 x 6 = 48. The missing number \u00f7 2 = 48, so the number is 48 x 2 = 96."} {"t":"s","id":6841,"s":"5\/6 is more than half (3\/6), so 5\/6 > 1\/2 is true. The other statements are false."} {"t":"s","id":6842,"s":"2\/8 = 1\/4 = 3\/12. 3\/12 + 1\/12 = 4\/12 = 1\/3."} {"t":"s","id":6847,"s":"23 25 in 24-hour clock is after noon. 23 - 12 = 11, so it is 11.25 pm."} {"t":"s","id":6848,"s":"1 kg = 1000 g. 3095 g = 3000 g + 95 g = 3 kg 95 g."} {"t":"s","id":6851,"s":"1\/6 = 2\/12. 5\/12 - 2\/12 = 3\/12 = 1\/4."} {"t":"s","id":6852,"s":"As decimals: 3\/5 = 0.6, 2\/4 = 0.5, 2\/9 \u2248 0.22, 1\/10 = 0.1. Greatest to smallest: 3\/5, 2\/4, 2\/9, 1\/10."} {"t":"s","id":6855,"s":"280 \u00f7 6 = 46 remainder 4. So 4 apples are left unpacked."} {"t":"s","id":6862,"s":"1359 - 247 = 1112 stayed. 1112 + 498 boarded = 1610."} {"t":"s","id":6863,"s":"9.35 am + 2 h 45 min = 12.20 pm. From 12.20 pm to 2.00 pm is 1 h 40 min."} {"t":"s","id":6865,"s":"The last packet split among 12 pupils at 7 each = 12 x 7 = 84 sweets per packet. Each pupil got one full packet (84) plus 7 = 91 sweets."} {"t":"s","id":6867,"s":"Total stays 80. After giving, Ali = 4 units, Samad = 1 unit, 5 units = 80, 1 unit = 16. Samad had 16 in the end."} {"t":"s","id":6868,"s":"Five thousand = 5000, four hundred = 400, one = 1. 5000 + 400 + 1 = 5401."} {"t":"s","id":6870,"s":"760 \/ 7 = 108 remainder 4. The quotient is 108."} {"t":"s","id":6872,"s":"Compare each to 1\/2: 1\/3 < 1\/2, 3\/8 < 1\/2, 4\/7 > 1\/2 (since half of 7 is 3.5), 6\/12 = 1\/2. Only 4\/7 is greater."} {"t":"s","id":6874,"s":"Multiply 2\/3 by 3\/3: (2x3)\/(3x3) = 6\/9. So 6\/9 is equivalent to 2\/3."} {"t":"s","id":6876,"s":"Morning: 9:00 am to 12:30 pm = 3 h 30 min. Afternoon: 3:30 pm to 8:00 pm = 4 h 30 min. Total = 3 h 30 min + 4 h 30 min = 8 h."} {"t":"s","id":6878,"s":"1\/2 = 4\/8. So 6\/8 - 4\/8 = 2\/8 = 1\/4."} {"t":"s","id":6881,"s":"Convert to a common unit: 1 m 20 cm = 1.2 m, 1 km 2 m = 1002 m, 120 m. Longest to shortest: 1 km 2 m, 120 m, 1 m 20 cm."} {"t":"s","id":6885,"s":"The pattern decreases by 120 each time. 6880 - 120 = 6760."} {"t":"s","id":6888,"s":"438 \/ 4 = 109 remainder 2. The leftover 2 cupcakes still need a box, so she needs 109 + 1 = 110 boxes."} {"t":"s","id":6892,"s":"One crate has 30 + 25 = 55 fruits. 6 crates have 55 x 6 = 330 fruits."} {"t":"s","id":6895,"s":"Twice the smaller number = 3764 - 132 = 3632, so smaller = 1816. Greater = 1816 + 132 = 1948."} {"t":"s","id":6896,"s":"Work backwards: before 7 boarded, there were 24 - 7 = 17. Before 9 alighted, there were 17 + 9 = 26 people."} {"t":"s","id":6897,"s":"Chocolate is 9 units, strawberry is 1 unit, so the difference of 8 units = 240. 1 unit = 30 strawberry tarts. Total = 10 units = 30 x 10 = 300 tarts."} {"t":"s","id":6898,"s":"Finish time 1:10 pm = 1310. Subtract 1 h 25 min: 1310 - 1 h = 1210, then - 25 min = 1145."} {"t":"s","id":6899,"s":"Hansel = 2540 - 1230 = 1310. Altogether = 2540 + 1310 = 3850 bottle caps."} {"t":"s","id":6900,"s":"Blue + green = 482 - 42 = 440. Blue is 3 units and green is 1 unit, so 4 units = 440, 1 unit = 110. Blue = 3 x 110 = 330."} {"t":"s","id":6901,"s":"Each bag has 432 \/ 6 = 72 pears. He gave away 2 bags = 72 x 2 = 144 pears. Left = 432 - 144 = 288."} {"t":"s","id":6906,"s":"Convert to tenths: 3\/5 = 6\/10, 1\/2 = 5\/10, 1\/10 = 1\/10. Greatest to smallest: 6\/10, 5\/10, 1\/10, i.e. 3\/5, 1\/2, 1\/10."} {"t":"s","id":6910,"s":"Subtract the travel time from the arrival time: 7.10 a.m. - 35 min = 6.35 a.m."} {"t":"s","id":6913,"s":"One dress = 175 + 25 = 200 cm. Two dresses = 200 x 2 = 400 cm."} {"t":"s","id":6914,"s":"7 thousands = 7000, 9 hundreds = 900, 0 tens, 4 ones = 4. Total = 7904."} {"t":"s","id":6919,"s":"9.45 a.m. + 1 h = 10.45 a.m.; + 20 min = 11.05 a.m."} {"t":"s","id":6930,"s":"2 l = 2000 ml. Water still needed = 2000 - 1400 = 600 ml. 3 jugs fill 600 ml, so each jug = 600 \/ 3 = 200 ml."} {"t":"s","id":6931,"s":"680 - 8 = 672 marbles left. 672 \/ 4 = 168 packets."} {"t":"s","id":6933,"s":"12 classmates took 12 muffins. Remaining muffins = 60 - 12 = 48. These were taken 2 each, so 48 \/ 2 = 24 classmates."} {"t":"s","id":6935,"s":"97 \/ 8 = 12 remainder 1. The remaining person still needs a van, so 12 + 1 = 13 vans."} {"t":"s","id":6936,"s":"1 orange = 2 apples in cost, so 6 oranges = 12 apples. Total = 12 + 8 = 20 apples."} {"t":"s","id":6938,"s":"(a) Total time = 40 min + 1 h 25 min = 2 h 5 min. 5.00 p.m. + 2 h 5 min = 7.05 p.m. (b) 1 h 25 min - 40 min = 85 min - 40 min = 45 min."} {"t":"s","id":6939,"s":"(a) Kenny = 1650 - 800 = 850 m. (b) Total = 1650 + 850 = 2500 m = 2 km 500 m."} {"t":"s","id":6941,"s":"(a) Children = 3480 - 1905 = 1575. (b) Boys + girls = 5 units = 1575, so 1 unit (girls) = 1575 \/ 5 = 315."} {"t":"s","id":6942,"s":"Assume all 50 are notebooks: 50 x $5 = $250. Excess = $250 - $154 = $96. Each notebook swapped for scissors saves $5 - $2 = $3, so $96 \/ $3 = 32 notebooks; scissors = 50 - 32 = 18. (a) 18 scissors, (b) 32 notebooks."} {"t":"s","id":6945,"s":"12\/15 = 4\/5 (divide numerator and denominator by 3). Missing numerator is 4."} {"t":"s","id":6948,"s":"4\/9 (0.44) < 1\/2 (0.5) < 7\/9 (0.78). Smallest to greatest: 4\/9, 1\/2, 7\/9."} {"t":"s","id":6949,"s":"Mabel = 300 - 50 = 250. Altogether = 300 + 250 = 550."} {"t":"s","id":6950,"s":"Cards given = 10 x 6 = 60. Left = 100 - 60 = 40."} {"t":"s","id":6953,"s":"Pattern adds 3 then 4 alternately: 3 (+3) 6 (+4) 10 (+3) 13 (+4) 17 (+3) 20 (+4) 24. Missing = 17."} {"t":"s","id":6958,"s":"1\/2 = 3\/6. 3\/6 + 1\/6 = 4\/6 = 2\/3."} {"t":"s","id":6959,"s":"After giving away 7, Peter has 40 - 7 = 33, and Monica also has 33. Monica at first = 33 - 7 = 26."} {"t":"s","id":6960,"s":"Oranges in boxes = 165 x 9 = 1485. Add the 3 left over: 1485 + 3 = 1488."} {"t":"s","id":6963,"s":"Smaller = (78 - 16) div 2 = 62 div 2 = 31. Bigger = 78 - 31 = 47."} {"t":"s","id":6964,"s":"Lunch box $25, water bottle $25+$8=$33, bag $25x2=$50. The bag costs the most at $50. Total = $25+$33+$50 = $108."} {"t":"s","id":6967,"s":"a) Boarded at 13 20, waited 35 min, so arrived 13 20 - 35 min = 12 45. b) 13 55 to 16 15 = 2 h 20 min (13 55 to 14 00 = 5 min, 14 00 to 16 00 = 2 h, 16 00 to 16 15 = 15 min; 5+15 = 20 min, total 2 h 20 min)."} {"t":"s","id":6974,"s":"2\/3 = 6\/9, so 6\/9 - 3\/9 = 3\/9 = 1\/3. The key marks option (3) 1\/9; note the simplest correct value is 1\/3."} {"t":"s","id":6986,"s":"58 \u00f7 3 = 19 remainder 1. The quotient is 19."} {"t":"s","id":6988,"s":"As decimals: 2\/5 = 0.4, 1\/2 = 0.5, 4\/7 \u2248 0.571. Smallest to greatest: 2\/5, 1\/2, 4\/7."} {"t":"s","id":6996,"s":"Adults = 498 - 24 = 474. Total = 498 + 474 = 972."} {"t":"s","id":7003,"s":"Vans = 852 - 87 = 765. Cars = 765 \u00d7 2 = 1530."} {"t":"s","id":7008,"s":"In 8371 the digits are 8 (thousands), 3 (hundreds), 7 (tens), 1 (ones). So 3 is in the hundreds place."} {"t":"s","id":7014,"s":"57 tens = 570. 300 more than 570 = 570 + 300 = 870."} {"t":"s","id":7019,"s":"4 x 8 = 32 balloons. 32 - 12 = 20 balloons left."} {"t":"s","id":7021,"s":"2\/3 = 4\/6. 4\/6 + 1\/6 = 5\/6 of the pizza was eaten."} {"t":"s","id":7029,"s":"67 hundreds = 6700. 54 less than 6700 = 6700 - 54 = 6646."} {"t":"s","id":7030,"s":"Each tricycle has 3 wheels. (a) 5 x 3 = 15. (b) 8 x 3 = 24."} {"t":"s","id":7031,"s":"Convert to tenths: 3\/5 = 6\/10, 4\/10 = 4\/10, 1\/2 = 5\/10. Smallest to largest: 4\/10, 5\/10 (=1\/2), 6\/10 (=3\/5)."} {"t":"s","id":7032,"s":"To get from denominator 2 to 6, multiply by 3, so the numerator 1 x 3 = 3. 1\/2 = 3\/6."} {"t":"s","id":7033,"s":"Cake has 4 pieces. Eugene ate 1\/4 = 1 piece. Michael ate 1\/2 = 2 pieces. 4 - 1 - 2 = 1 piece left."} {"t":"s","id":7034,"s":"1\/4 = 3\/12. Edwin + Rayner = 5\/12 + 3\/12 = 8\/12. Vincent = 12\/12 - 8\/12 = 4\/12 = 1\/3."} {"t":"s","id":7035,"s":"(a) 4 m = 400 cm, so 4 m 50 cm = 450 cm. (b) 3 l = 3000 ml, so 3 l 86 ml = 3086 ml."} {"t":"s","id":7041,"s":"(a) Pauline = 1843 + 379 = 2222 cookies. (b) Altogether = 2222 + 1843 = 4065 cookies."} {"t":"s","id":7042,"s":"96 \/ 8 = 12 groups of 8 pencils. Each group gives 2 erasers, so 12 x 2 = 24 erasers."} {"t":"s","id":7045,"s":"Perimeter = 2(length + breadth) = length + breadth + length + breadth. With length = 2 x breadth, the perimeter equals 6 breadths: 108 \/ 6 = 18 m breadth. Length = 18 + 18 = 36 m."} {"t":"s","id":7046,"s":"In 3985, reading from the right: 5 ones, 8 tens, 9 hundreds, 3 thousands. So the digit in the hundreds place is 9."} {"t":"s","id":7049,"s":"5\/9 > 1\/2 (half of 9 is 4.5), 5\/10 = 1\/2, 2\/3 > 1\/2, 5\/12 < 1\/2 (half of 12 is 6, and 5 < 6). So 5\/12 is less than 1\/2."} {"t":"s","id":7052,"s":"1 kg = 1000 g, so 7 kg = 7000 g. 7000 g + 50 g = 7050 g."} {"t":"s","id":7054,"s":"2 h 45 min - 50 min. 45 min - 50 min needs borrowing: 1 h 105 min - 50 min = 1 h 55 min."} {"t":"s","id":7057,"s":"The numbers increase by 10 each step: 6198, 6208, 6218, 6228, 6238. The missing number is 6208."} {"t":"s","id":7058,"s":"5492 = 5000 + 400 + 90 + 2. 400 = 40 tens, so the blank is 40."} {"t":"s","id":7059,"s":"1\/2 = 5\/10. 5\/10 + 4\/10 = 9\/10."} {"t":"q","id":13683,"q":"Arrange the following fractions from the greatest to the smallest.\n2\/3 , 2\/6 , 3\/4
(a)   (b)   (c) ","e":"Using a common denominator of 12: 2\/3 = 8\/12, 2\/6 = 4\/12, 3\/4 = 9\/12. Greatest to smallest: 9\/12, 8\/12, 4\/12, i.e. 3\/4, 2\/3, 2\/6."} {"t":"q","id":13684,"q":"Jennifer gave away \\(\\dfrac{1}{2}\\) of a cake and ate \\(\\dfrac{1}{3}\\) of it. What fraction of the cake was left?","e":"1\/2 = 3\/6 and 1\/3 = 2\/6, so she used 3\/6 + 2\/6 = 5\/6. Left = 6\/6 - 5\/6 = 1\/6."} {"t":"q","id":13685,"q":"There were 420 audience at a concert. There were 4 times as many adults as children. How many children were at the concert?
Answer: ","e":"Children = 1 unit, adults = 4 units, total = 5 units = 420. 1 unit = 420 \/ 5 = 84 children."} {"t":"q","id":13688,"q":"Natalie started watching a show at 1615. The show lasted 1 h 55 min. What time did the show end? Give your answer in the 24 hour clock.
Answer: ","e":"1615 + 1 h = 1715. 1715 + 55 min = 1810 (17:15 plus 45 min = 18:00, plus 10 min = 18:10)."} {"t":"q","id":13689,"q":"The length of a blue ribbon is 1 m 20 cm longer than a red ribbon. Given that the total length of both ribbons is 4 m, how long is the red ribbon?
Answer: ","e":"Total = 4 m = 400 cm. The extra 1 m 20 cm = 120 cm. Removing the extra: 400 - 120 = 280 cm for two equal parts. Red ribbon = 280 \/ 2 = 140 cm."} {"t":"q","id":13690,"q":"Geraldine wants to pack 260 colour pencils into bags. Each bag can hold up to 6 colour pencils. What is the smallest number of bags needed to pack all the colour pencils?
Answer: ","e":"260 \/ 6 = 43 remainder 2. The 2 leftover pencils still need a bag, so 43 + 1 = 44 bags."} {"t":"q","id":13693,"q":"Alfred and Bala had an equal number of marbles at first. After Alfred gave Bala 12 marbles, Alfred had 65 marbles left.\n(a) How many more marbles did Bala have than Alfred in the end?\n(b) How many marbles did Bala have in the end?
(a)   (b) ","e":"(a) Alfred lost 12 and Bala gained 12, so the difference between them is 12 + 12 = 24 marbles. (b) Alfred had 65 at the end; at first both had 65 + 12 = 77. Bala in the end = 77 + 12 = 89."} {"t":"q","id":13698,"q":"There were 16 boys and 26 girls in a class. Each pupil was given 8 erasers. How many erasers were given out altogether?","e":"Total pupils = 16 + 26 = 42; 42 x 8 = 336 erasers."} {"t":"q","id":13699,"q":"Mrs Wong had 148 pencils. She packed them equally into 6 boxes. How many pencils were left unpacked?","e":"148 \/ 6 = 24 remainder 4. So 4 pencils were left unpacked."} {"t":"q","id":13701,"q":"Janet had 3 twenty-cent coins and 5 fifty-cent coins. She donated some of the coins. How much money could she possibly have donated?","e":"Coins are 20c and 50c. $2.70 = 1 twenty-cent + 5 fifty-cent (20c + 250c = 270c). $3.00 needs more than she has (max = 60c + 250c = 310c, but cannot make exactly 300c with these coins), $0.80 and $1.80 cannot be formed exactly; $2.70 is achievable."} {"t":"q","id":13702,"q":"A bottle contains 1 l 80 ml of water. If the capacity of the bottle is 2 l, how much more water is needed to fill the bottle?","e":"2 l = 2000 ml; 1 l 80 ml = 1080 ml; 2000 - 1080 = 920 ml."} {"t":"q","id":13703,"q":"Which one of the following fractions is the smallest?","e":"Comparing 3\/10, 1\/2, 2\/3, 2\/5: 3\/10 = 0.3, 1\/2 = 0.5, 2\/3 \u2248 0.67, 2\/5 = 0.4. Smallest is 3\/10."} {"t":"q","id":13704,"q":"A movie started at 18 30. It lasted 115 minutes. What time did the movie end?","e":"115 min = 1 h 55 min. 18 30 + 1 h = 19 30; 19 30 + 55 min = 20 25."} {"t":"q","id":13706,"q":"James had 3 times as many erasers as Max at first. After James had given 18 erasers to Max, Max had 44 erasers. How many erasers did James have at first?","e":"After receiving 18, Max had 44, so Max had 44 - 18 = 26 at first. James had 3 x 26 = 78 at first."} {"t":"q","id":13709,"q":"Which digit in the two numbers given has the same value? 2856 and 6825
Answer: ","e":"In 2856 the digit 8 is in the hundreds place (value 800). In 6825 the digit 8 is in the hundreds place (value 800). The digit 8 has the same value in both."} {"t":"q","id":13710,"q":"Find the difference between 6483 and 259. ","e":"6483 - 259 = 6224."} {"t":"q","id":13712,"q":"Arrange the following fractions in order. Begin with the greatest. 1\/3, 5\/6, 5\/12 , , ","e":"Common denominator 12: 1\/3 = 4\/12, 5\/6 = 10\/12, 5\/12 = 5\/12. Greatest to smallest: 10\/12, 5\/12, 4\/12 \u2192 5\/6, 5\/12, 1\/3."} {"t":"q","id":13713,"q":"Gary went jogging from 6:20 a.m. to 7:15 a.m. How long did he jog? min","e":"From 6:20 a.m. to 7:15 a.m. is 55 minutes (6:20 to 7:20 is 60 min, minus 5 min = 55 min)."} {"t":"q","id":13714,"q":"Jamie and Angel had a total of 135 hairclips. If Angel were to give Jamie 16 hairclips, Jamie would have 4 times as many hairclips as Angel. How many hairclips did Angel have? ","e":"Total stays 135. After transfer: 5 units = 135, 1 unit = 27 (Angel after giving). Angel originally = 27 + 16 = 43."} {"t":"q","id":13715,"q":"Mrs Tan is 5 times as old as her son, Bryan, who is 9 years old now. How old will Mrs Tan be in 10 years' time? ","e":"Mrs Tan now = 5 x 9 = 45 years old. In 10 years: 45 + 10 = 55 years old."} {"t":"q","id":13716,"q":"Keith had some sweets. He gave 24 of his sweets to his brother and bought another 12 sweets. In the end, Keith had 88 sweets altogether. How many sweets did he have at first? ","e":"Work backwards: 88 - 12 = 76 (before buying); 76 + 24 = 100 (before giving away)."} {"t":"q","id":13720,"q":"Ethan has 40 more marbles than Dylan. How many marbles must Ethan give to Dylan so that he will have 8 more marbles than Dylan? ","e":"The gap must shrink from 40 to 8, a reduction of 32. Each marble Ethan gives reduces the gap by 2, so he gives 32 \/ 2 = 16 marbles."} {"t":"q","id":13721,"q":"Simon had 50 more stickers than Mark. After Simon had given 88 stickers to Mark, he was left with 120 stickers. How many stickers did Mark have at first? ","e":"Simon at first = 120 + 88 = 208. Mark had 50 fewer than Simon at first: 208 - 50 = 158."} {"t":"q","id":13726,"q":"A baker baked 286 cupcakes in the morning. He then baked another 365 cupcakes in the afternoon. The baker sold 483 cupcakes that day. (a) How many cupcakes did the baker bake in all? (b) How many cupcakes were left at the end of the day? Ans: (a) (b) ","e":"(a) 286 + 365 = 651 cupcakes baked. (b) 651 - 483 = 168 cupcakes left."} {"t":"q","id":13727,"q":"A tank, containing 1850 ml of water at first, has a capacity of 4 l. After some water was poured into the tank, another 860 ml of water is needed to fill it up completely. How much water was poured into the tank? Give your answer in litres and millilitres. Ans: l ml","e":"4 l = 4000 ml. When 860 ml more is needed, tank holds 4000 - 860 = 3140 ml. Water poured in = 3140 - 1850 = 1290 ml = 1 l 290 ml."} {"t":"q","id":13728,"q":"Ethan spent \\(\\dfrac{1}{3}\\) of his money on food. He spent \\(\\dfrac{1}{6}\\) of it on magazines and \\(\\dfrac{1}{4}\\) of it on shoes. What fraction of his money was left? Express your answer in its simplest form. Ans:","e":"Common denominator 12: 1\/3 = 4\/12, 1\/6 = 2\/12, 1\/4 = 3\/12. Spent = 4\/12 + 2\/12 + 3\/12 = 9\/12. Left = 12\/12 - 9\/12 = 3\/12 = 1\/4."} {"t":"q","id":13729,"q":"Michelle worked for 6 days in a week. She worked from 09 00 to 18 00 every day. (a) How many hours did she work every day? (b) How many hours did she work in 4 weeks? Ans: (a) (b) ","e":"(a) 09 00 to 18 00 = 9 hours per day. (b) Per week: 9 x 6 = 54 hours; in 4 weeks: 54 x 4 = 216 hours."} {"t":"q","id":13730,"q":"Shop A sold 487 more marbles than Shop B. Shop C sold 243 more marbles than Shop B. The three shops sold a total of 1000 marbles. (a) How many marbles did Shop A sell? (b) How many more marbles did Shop A sell than Shop C? Ans: (a) (b) ","e":"Total = 3 units (Shop B) + 487 + 243 = 1000, so 3 units = 1000 - 730 = 270, 1 unit (Shop B) = 90. Shop A = 90 + 487 = 577. Shop C = 90 + 243 = 333. (b) 577 - 333 = 244."} {"t":"q","id":13731,"q":"Thaddeus, Ivan and Ryan had a total of 381 coins. Ivan had twice as many coins as Ryan and Thaddeus had 56 more coins than Ivan. (a) How many coins did Thaddeus have? (b) If Ryan's mother gave Ryan another 100 coins, how many coins would Ryan have now? Ans: (a) (b) ","e":"Ryan = 1 unit, Ivan = 2 units, Thaddeus = 2 units + 56. Total = 5 units + 56 = 381, so 5 units = 325, 1 unit = 65. (a) Thaddeus = 2 x 65 + 56 = 186. (b) Ryan = 65 + 100 = 165."} {"t":"q","id":13732,"q":"2 thousands 2 tens is the same as .","e":"2 thousands = 2000, 2 tens = 20. 2000 + 20 = 2020."} {"t":"q","id":13735,"q":"Amirah has 7 boxes of cupcakes. There are 8 cupcakes in each box. How many cupcakes does Amirah have altogether?","e":"7 boxes x 8 cupcakes = 56 cupcakes."} {"t":"q","id":13736,"q":"5 km 9 m = m","e":"5 km = 5000 m. 5000 m + 9 m = 5009 m."} {"t":"q","id":13737,"q":"How many minutes are there in 2 h 18 min?","e":"2 h = 120 min. 120 + 18 = 138 min."} {"t":"q","id":13738,"q":"Arrange the following fractions from the smallest to the greatest. 2\/3 , 1\/4 , 5\/12","e":"Convert to twelfths: 2\/3 = 8\/12, 1\/4 = 3\/12, 5\/12. Order smallest to greatest: 3\/12, 5\/12, 8\/12, i.e. 1\/4, 5\/12, 2\/3."} {"t":"q","id":13741,"q":"The difference between two numbers is 670. The smaller number is 1780. Find the sum of the two numbers.","e":"Larger number = 1780 + 670 = 2450. Sum = 1780 + 2450 = 4230."} {"t":"q","id":13742,"q":"Jinny has $249. Karthi has three times as much as Jinny. How much do they have altogether?","e":"Karthi = 3 x $249 = $747. Together = $249 + $747 = $996."} {"t":"q","id":13744,"q":"A movie starts at 7.25 p.m. It is now 15 minutes to seven. How long will it be before the movie starts?","e":"15 minutes to seven = 6.45 p.m. From 6.45 to 7.25 is 40 minutes."} {"t":"q","id":13748,"q":"What is the missing number in the pattern? 4930 , 4690 , 4450 , 4210 , , 3730","e":"Each term decreases by 240. 4210 - 240 = 3970."} {"t":"q","id":13751,"q":"\\(\\dfrac{1}{4}\\) + \\(\\dfrac{5}{8}\\) =","e":"1\/4 = 2\/8. 2\/8 + 5\/8 = 7\/8."} {"t":"q","id":13752,"q":"Look at the letters H A M L E T. Which 2 letters have both perpendicular and parallel lines?","e":"H and E each have both perpendicular lines (meeting at right angles) and parallel lines."} {"t":"q","id":13754,"q":"A number when divided by 5 has a quotient of 38 and a remainder of 3. What is the number?
Answer: ","e":"Number = 5 x 38 + 3 = 190 + 3 = 193."} {"t":"q","id":13755,"q":"May has 58 stickers. Lynn has 5 times as many stickers as her. How many stickers will Lynn have to give May so that both of them have the same number of stickers?
Answer: ","e":"Lynn = 5 x 58 = 290. Total = 290 + 58 = 348. Each should have 348 \/ 2 = 174. Lynn must give 290 - 174 = 116 stickers."} {"t":"q","id":13756,"q":"Mindy's watch is six minutes slow. Her watch shows 5.00 p.m. now. What is the actual time?
Answer: ","e":"A slow watch shows an earlier time, so the actual time is 6 minutes ahead: 5.00 + 6 min = 5.06 p.m."} {"t":"q","id":13758,"q":"What is the missing number? 10\/12 = \/18","e":"10\/12 = 5\/6 = 15\/18. Multiply numerator and denominator by the same factor: 6 x 3 = 18, 5 x 3 = 15."} {"t":"q","id":13760,"q":"Nurul has 17 notes in her piggy bank. There are only $2 and $5 notes in her piggy bank. The total value of the notes is $49. How many $5 notes are there in her piggy bank?
Answer: ","e":"If all 17 were $2 notes, value = $34. Extra needed = $49 - $34 = $15. Each $5 note adds $3 over a $2 note, so $15 \/ $3 = 5 five-dollar notes."} {"t":"q","id":13761,"q":"There are 960 boys in a hall. There are 395 more boys than girls in the same hall. How many children are there in the hall altogether?
Answer: ","e":"Girls = 960 - 395 = 565. Children = 960 + 565 = 1525."} {"t":"q","id":13762,"q":"Chong and Jill have 180 cookies altogether. Chong has 30 cookies more than Jill. How many cookies does Jill have?
Answer: ","e":"Remove the extra 30: 180 - 30 = 150. Each share = 150 \/ 2 = 75. Jill has 75 cookies."} {"t":"q","id":13763,"q":"Pravin, Hadi and Larry have 442 stamps altogether. Larry has four times as many stamps as Hadi. Pravin has 34 more stamps than Hadi. How many stamps does Hadi have?
Answer: ","e":"Remove Pravin's extra 34: 442 - 34 = 408. This equals 6 units of Hadi (Hadi 1 + Larry 4 + Pravin 1). 408 \/ 6 = 68 stamps for Hadi."} {"t":"q","id":13765,"q":"Molly had 800 ml of apple juice for a party at first. She bought another 10 bottles of apple juice for the party. Each bottle contained 330 ml of apple juice. She served the apple juice to her guests and had 590 ml of apple juice left. (a) What was the total amount of apple juice she had for the party? (b) How much apple juice was served to the guests?
(a)   (b) ","e":"(a) 10 x 330 = 3300 ml; 3300 + 800 = 4100 ml = 4 l 100 ml. (b) 4100 - 590 = 3510 ml = 3 l 510 ml served."} {"t":"q","id":13767,"q":"What is the smallest 4-digit even number that can be formed with the digits 7, 3, 6 and 2 ?","e":"An even number ends in an even digit. To be smallest, put smallest digits first: 2, 3, then last digit must be even. Remaining digits 7 and 6; smallest hundreds is 3, so 23_6 -> 2376 (ends in even 6)."} {"t":"q","id":13769,"q":"Which of the following fractions is smaller than 1\/2 ?","e":"Compare each to 1\/2. 2\/3>1\/2, 3\/7<1\/2 (since 3.5\/7=1\/2), 3\/5>1\/2, 2\/4=1\/2. Only 3\/7 is smaller than 1\/2."} {"t":"q","id":13770,"q":"Betty has a roll of ribbon which is 5 m long. She uses 1 m 25 cm to wrap a gift box and 85 cm to make a ribbon bow. What is the length of ribbon left ?","e":"5 m = 500 cm. Used = 125 cm + 85 cm = 210 cm. Left = 500 - 210 = 290 cm."} {"t":"q","id":13776,"q":"Arrange the fractions, from the smallest to the biggest fraction. 3\/6 1\/3 4\/9 , , ","e":"Convert to a common comparison: 1\/3 = 0.333, 4\/9 = 0.444, 3\/6 = 0.5. Smallest to biggest: 1\/3, 4\/9, 3\/6."} {"t":"q","id":13777,"q":"Some sticks are placed, at an equal distance from each other, in a straight line. The distance between the 1st and the 4th stick is 24 cm. The distance between the 1st and the last stick is 56 cm. How many sticks are there altogether ? ","e":"From 1st to 4th stick there are 3 gaps = 24 cm, so each gap = 8 cm. From 1st to last = 56 cm = 56 \/ 8 = 7 gaps, so number of sticks = 7 + 1 = 8."} {"t":"q","id":13778,"q":"Miss Foo paid $12 for a highlighter, a stapler and a file. The file cost $5.30. The stapler cost more than the highlighter. The total cost of the highlighter and the stapler was less than the cost of the file.","e":"Highlighter + stapler = $12 - $5.30 = $6.70, which is more than the file's $5.30. So the statement that their total was less than the file is False."} {"t":"q","id":13782,"q":"Alvin has 5070 LEGO bricks. He has 1094 more bricks than Farhan. a) How many bricks does Farhan have ? b) How many bricks do the two boys have altogether ? , ","e":"a) Farhan = 5070 - 1094 = 3976 bricks. b) Altogether = 5070 + 3976 = 9046 bricks."} {"t":"q","id":13783,"q":"The Chin family attended a birthday dinner that ended at 19 20, according to the clock in the dining room. However, the clock was 10 minutes slower. The dinner lasted 1 h 30 min. What was the actual time the dinner started ? ","e":"Dining-room clock showed 19 20 at the end; it was 10 min slow, so actual end time = 19 30. The dinner lasted 1 h 30 min, so actual start = 19 30 - 1 h 30 min = 18 00."} {"t":"q","id":13784,"q":"Uncle Daniel bought an apple pie and cut it into 12 pieces. He gave \\(\\dfrac{1}{4}\\) of the pie to his niece and 4 pieces to his neighbour. What fraction of the pie was left ? Express your answer in its simplest form.","e":"1\/4 of 12 = 3 pieces to niece; 4 pieces to neighbour; given away = 7 pieces. Left = 12 - 7 = 5 pieces = 5\/12 (already simplest)."} {"t":"q","id":13785,"q":"Annie made 3 times as many clay stars as Eileen. Linda made 75 fewer clay stars than Annie. The three girls made a total of 919 clay stars. How many clay stars did Eileen make ? ","e":"Let Eileen = 1 unit, Annie = 3 units, Linda = 3 units - 75. Total = 1u + 3u + 3u - 75 = 7u - 75 = 919, so 7u = 994, u = 142. Eileen made 142."} {"t":"q","id":13786,"q":"2 badminton rackets and 1 basketball cost $102.50. 1 badminton racket and 2 basketballs cost $107.50. What is the total cost of 1 badminton racket and 1 basketball ? ","e":"Adding both: 3 rackets + 3 basketballs = $102.50 + $107.50 = $210. So 3 x (1 racket + 1 basketball) = $210, giving 1 racket + 1 basketball = $210 \/ 3 = $70."} {"t":"q","id":13789,"q":"Which number is 10 tens less than 5467?","e":"10 tens = 100. 5467 - 100 = 5367."} {"t":"q","id":13791,"q":"9 thousands and 7 tens is the same as .","e":"9 thousands = 9000, 7 tens = 70. Total = 9070."} {"t":"q","id":13795,"q":"Write nine thousand, six hundred and six in numerals. ","e":"Nine thousand = 9000, six hundred = 600, six = 6. Total = 9606."} {"t":"q","id":13797,"q":"Write the missing number in the number pattern.\n2649 , 2799 , 2949 , , 3249","e":"The pattern increases by 150 each time. 2949 + 150 = 3099."} {"t":"q","id":13798,"q":"Find the sum of 2839 and 197. ","e":"2839 + 197 = 3036."} {"t":"q","id":13799,"q":"Find the difference between 3001 and 549. ","e":"3001 - 549 = 2452."} {"t":"q","id":13800,"q":"The difference between two numbers is 279. The greater number is 866. Find the smaller number. ","e":"Smaller number = 866 - 279 = 587."} {"t":"q","id":13801,"q":"Mrs Tan bought a blanket for $36.60. She bought a bedsheet for $29.90. How much did Mrs Tan pay for the two items altogether?\n$","e":"$36.60 + $29.90 = $66.50."} {"t":"q","id":13802,"q":"A plastic box costs $13.50. The plastic box costs $6.90 less than a water bottle. How much does the water bottle cost?\n$","e":"Water bottle = $13.50 + $6.90 = $20.40."} {"t":"q","id":13803,"q":"A shirt cost $39.90. During a sale Mr Lee paid $27.50 for it. How much did Mr Lee save?\n$","e":"Savings = $39.90 - $27.50 = $12.40."} {"t":"q","id":13804,"q":"Moses had $30. He bought a box of crayons for $15.90. How much did he have left?\n$","e":"Left = $30.00 - $15.90 = $14.10."} {"t":"q","id":13805,"q":"There are 16 sweets in a box. How many sweets are there in 8 such boxes?","e":"16 x 8 = 128 sweets."} {"t":"q","id":13808,"q":"When a number is divided by 9, it has a remainder of 6. Which of the following is a possible number?","e":"A number with remainder 6 when divided by 9 fits 9k + 6. Testing: 54 = 9x6 r0; 66 = 9x7 r3; 72 = 9x8 r0; 78 = 9x8 + 6, remainder 6. So 78 is the possible number."} {"t":"q","id":13809,"q":"Sandra has 3 times as many stamps as Mary. They have 288 stamps altogether. How many stamps does Mary have?","e":"Mary = 1 unit, Sandra = 3 units, total 4 units = 288. 1 unit = 288 div 4 = 72."} {"t":"q","id":13812,"q":"Ben had some marbles. He gave all his marbles to 4 friends. Each friend received 12 marbles. How many marbles did Ben have at first? ","e":"4 friends x 12 marbles = 48 marbles."} {"t":"q","id":13814,"q":"Mr Lee had 246 packets of erasers. Each packet had 9 erasers in it. How many erasers were there altogether? ","e":"246 x 9 = 2214 erasers."} {"t":"q","id":13815,"q":"Mrs Tan had 259 eggs. She packed 5 eggs in each tray. How many eggs were left unpacked? ","e":"259 div 5 = 51 remainder 4. So 4 eggs were left unpacked."} {"t":"q","id":13816,"q":"An oven cost $256 in Shop A. The same oven cost twice as much in Shop B. What was the cost of the oven in Shop B?\n$","e":"Twice as much = $256 x 2 = $512."} {"t":"q","id":13817,"q":"An oven cost $256 in Shop A. The same oven cost twice as much in Shop B. Mary had $400. How much change will she receive if she bought an oven from Shop A?\n$","e":"Change = $400 - $256 = $144."} {"t":"q","id":13818,"q":"Jeremy gets $20 of pocket money every day. He spends $13 every day and saves the rest. How many days will Jeremy take to save a total of $476? ","e":"Saves $20 - $13 = $7 per day. $476 div $7 = 68 days."} {"t":"q","id":13819,"q":"John sold 523 apples. He sold 155 fewer apples than Jim. Tom sold 3 times as many apples as Jim. How many apples did Tom sell? ","e":"Jim = 523 + 155 = 678. Tom = 678 x 3 = 2034 apples."} {"t":"q","id":13822,"q":"Which of the following has the greatest mass?","e":"Convert to grams: 17 kg = 17000 g; 807 g; 8700 g; 1 kg 70 g = 1070 g. Largest is 17 kg."} {"t":"q","id":13824,"q":"Find the missing numerator and denominator.\n3\/8 = \/24 = 18\/","e":"3\/8 = 9\/24 (x3) and 3\/8 = 18\/48 (x6). So (a) = 9, (b) = 48."} {"t":"q","id":13825,"q":"Arrange the fractions in order. Begin with the smallest.\n2\/9 , 3\/4 , 7\/8 , 1\/2\n , , , ","e":"As decimals: 2\/9 \u2248 0.22, 1\/2 = 0.5, 3\/4 = 0.75, 7\/8 = 0.875. Smallest to largest: 2\/9, 1\/2, 3\/4, 7\/8."} {"t":"q","id":13828,"q":"Find the difference between \\(\\dfrac{1}{3}\\) and \\(\\dfrac{5}{6}\\). Give your answer in its simplest form.","e":"1\/3 = 2\/6. 5\/6 - 2\/6 = 3\/6 = 1\/2."} {"t":"q","id":13829,"q":"The distance between School A and School C is 942 m. The distance between School A and School C is 3 times the distance between School B and School C. What is the distance between School B and School C?\n m","e":"B to C = 942 div 3 = 314 m."} {"t":"q","id":13833,"q":"Gopal ate \\(\\dfrac{3}{10}\\) of a pizza. His sister ate \\(\\dfrac{1}{5}\\) of the same pizza. How much more pizza did Gopal eat than his sister?","e":"1\/5 = 2\/10. 3\/10 - 2\/10 = 1\/10."} {"t":"q","id":13834,"q":"Gopal ate \\(\\dfrac{3}{10}\\) of a pizza. His sister ate \\(\\dfrac{1}{5}\\) of the same pizza. Gopal ate another \\(\\dfrac{2}{5}\\) of the pizza. What fraction of the pizza did he eat in total?","e":"2\/5 = 4\/10. 3\/10 + 4\/10 = 7\/10."} {"t":"q","id":13835,"q":"Find the value of 4 thousands + 3 tens + 8 ones.\n","e":"4 thousands = 4000, 3 tens = 30, 8 ones = 8. 4000 + 30 + 8 = 4038."} {"t":"q","id":13838,"q":"Find the product of 6 and 9.\n","e":"Product means multiply. 6 \u00d7 9 = 54."} {"t":"q","id":13839,"q":"Find the quotient and remainder of 625 \u00f7 7.\nQuotient Remainder ","e":"7 \u00d7 89 = 623, and 625 - 623 = 2. So quotient = 89, remainder = 2."} {"t":"q","id":13841,"q":"Aileen bought some sweets for her friends. She packed the sweets into 8 packets. There were 6 sweets in each packet. After packing, she was left with 4 sweets. How many sweets did she buy?\n","e":"Sweets in packets = 8 \u00d7 6 = 48. Add the leftover: 48 + 4 = 52."} {"t":"q","id":13843,"q":"Thomas made a different number of paper planes each day. On the first day, he made 6 paper planes. For each subsequent day, he made twice as many paper planes as he did the day before. How many paper planes would he make on the third day?\n","e":"Day 1 = 6. Day 2 = 6 \u00d7 2 = 12. Day 3 = 12 \u00d7 2 = 24."} {"t":"q","id":13845,"q":"On Sunday, a baker sold 2961 banana muffins. He sold 584 fewer banana muffins than chocolate muffins that day. How many muffins did he sell altogether on Sunday?\n","e":"Chocolate muffins = 2961 + 584 = 3545. Altogether = 3545 + 2961 = 6506."} {"t":"q","id":13846,"q":"In 5293, the digit 9 is in the place.","e":"In 5293, reading from the right: 3 ones, 9 tens, 2 hundreds, 5 thousands. So 9 is in the tens place."} {"t":"q","id":13848,"q":"Which set of numbers is found in the multiplication table of 8?","e":"8x4=32, 8x5=40, 8x6=48, 8x7=56. All are multiples of 8."} {"t":"q","id":13849,"q":"Julia bought a cake for $19.30. She had $3.80 left in her wallet. How much money did she have at first?","e":"Money at first = $19.30 + $3.80 = $23.10."} {"t":"q","id":13852,"q":"Find the sum of 7456 and 855.
Answer: ","e":"7456 + 855 = 8311."} {"t":"q","id":13854,"q":"Complete the number pattern. 1305, 1405, 2405, 2505, , 3605, 4605, 4705, 5705","e":"Pattern alternates +100 then +1000: 1305 (+100) 1405 (+1000) 2405 (+100) 2505 (+1000) 3505 (+100) 3605 (+1000) 4605 (+100) 4705 (+1000) 5705. Missing term is 3505."} {"t":"q","id":13855,"q":"When a number is divided by 5, the quotient is 78 and the remainder is 4. What is the number?
Answer: ","e":"Number = quotient x divisor + remainder = 78 x 5 + 4 = 390 + 4 = 394."} {"t":"q","id":13856,"q":"Lionel bought a football for $29.90 and a water bottle for $11.85. He gave the cashier a $50 note. How much change did he receive from the cashier?
Answer: ","e":"Total cost = $29.90 + $11.85 = $41.75. Change = $50 - $41.75 = $8.25."} {"t":"q","id":13857,"q":"Ali had 230 stickers at first. After Ali gave 20 stickers to Lena, he had 34 more stickers than Lena in the end. How many stickers did Lena have in the end?
Answer: ","e":"After giving away 20, Ali had 230 - 20 = 210 stickers. Lena had 34 fewer than Ali: 210 - 34 = 176 stickers."} {"t":"q","id":13858,"q":"Mr Tan bought 504 pens. He packed 6 pens into each bag. How many bags did Mr Tan use to pack all the pens? Each pen cost $2. How much did Mr Tan pay for all the pens? bags, $","e":"(a) Bags = 504 \/ 6 = 84 bags. (b) Total cost = 504 x $2 = $1008."} {"t":"q","id":13864,"q":"Arrange these fractions from the smallest to the greatest. 7\/8, 1\/2, 3\/7, 7\/12","e":"As decimals: 3\/7 about 0.43, 1\/2 = 0.5, 7\/12 about 0.58, 7\/8 = 0.875. Smallest to greatest: 3\/7, 1\/2, 7\/12, 7\/8."} {"t":"q","id":13866,"q":"What is the missing numerator? 3\/8 = \/24","e":"8 x 3 = 24, so multiply the numerator by 3: 3 x 3 = 9. So 3\/8 = 9\/24."} {"t":"q","id":13869,"q":"Add \\(\\dfrac{3}{10}\\) and \\(\\dfrac{1}{5}\\). Express your answer in its simplest form.","e":"1\/5 = 2\/10, so 3\/10 + 2\/10 = 5\/10 = 1\/2."} {"t":"q","id":13871,"q":"Jenny bought 72 boxes of cookies. There were 9 cookies in each box. She ate 15 cookies. How many cookies did she have left?
Answer: ","e":"Total cookies = 72 x 9 = 648. After eating 15: 648 - 15 = 633."} {"t":"q","id":13872,"q":"Johnson had 3 times as many stickers as Nicole. Nicole had 6 more stickers than Santhi. They had 314 stickers altogether. How many stickers did Nicole have?
Answer: ","e":"Let Nicole = N. Johnson = 3N, Santhi = N - 6. Total: 3N + N + (N - 6) = 314 -> 5N - 6 = 314 -> 5N = 320 -> N = 64."} {"t":"q","id":13873,"q":"Write nine thousand and forty-two in numerals.
Answer: ","e":"Nine thousand and forty-two = 9000 + 42 = 9042."} {"t":"q","id":13876,"q":"Add 4108 and 3897.
Answer: ","e":"4108 + 3897 = 8005."} {"t":"q","id":13877,"q":"Subtract 2146 from 7062.
Answer: ","e":"7062 - 2146 = 4916."} {"t":"q","id":13880,"q":"Arrange the numbers in increasing order.\n4772, 4227, 4727
(a)   (b)   (c) ","e":"Compare by place value: 4227 < 4727 < 4772. Increasing order: 4227, 4727, 4772."} {"t":"q","id":13881,"q":"Compare the numbers using '<' or '>'.\n(a) 4105 2398\n(b) 38 + 21 46 + 37","e":"(a) 4105 > 2398. (b) 38 + 21 = 59 and 46 + 37 = 83, so 59 < 83."} {"t":"q","id":13882,"q":"Write the missing number in the number pattern.\n4227, 4127, 4027, , 3827, 3727","e":"The pattern decreases by 100 each time. 4027 - 100 = 3927."} {"t":"q","id":13883,"q":"What is the missing number in the number pattern?\n6171, 6172, 6272, 6273, 6373, 6374, 6474, ","e":"The pattern alternates +1 then +100. After 6474 the next step is +1, giving 6475."} {"t":"q","id":13884,"q":"Look at the numbers.\n8143, 1726, 3962, 9057\nFind the difference between the greatest number and the smallest number.
Answer: ","e":"Greatest = 9057, smallest = 1726. 9057 - 1726 = 7331."} {"t":"q","id":13886,"q":"Use all the digits to form the greatest even number between 5000 and 8000.\n1, 3, 6, 8
Answer: ","e":"Between 5000 and 8000 the thousands digit must be 6. To be even and greatest, the ones digit must be 8, then the remaining digits 3 and 1 go in descending order: 6318."} {"t":"q","id":13887,"q":"Jenny has 685 stamps. She has 134 stamps fewer than Amy. How many stamps do they have altogether?
Answer: ","e":"Amy = 685 + 134 = 819. Altogether = 685 + 819 = 1504."} {"t":"q","id":13888,"q":"The difference between two numbers is 2307. The smaller number is 3480.\n(a) What is the greater number?\n(b) What is the sum of the two numbers?
(a)   (b) ","e":"(a) Greater = 3480 + 2307 = 5787. (b) Sum = 3480 + 5787 = 9267."} {"t":"q","id":13899,"q":"A pen costs $3.50. It costs 65\u00a2 less than a box of colour pencils. How much does the box of colour pencils cost?
Answer: ","e":"The box of colour pencils = $3.50 + $0.65 = $4.15."} {"t":"q","id":13900,"q":"Dawn and Eileen have 188 stamps altogether. Dawn has 3 times as many stamps as Eileen. How many stamps does Eileen have?
Answer: ","e":"Eileen = 1 unit, Dawn = 3 units, total = 4 units = 188. 1 unit = 188 \u00f7 4 = 47, so Eileen has 47 stamps."} {"t":"q","id":13901,"q":"Miss Goh had 102 cupcakes. She wanted to pack all the cupcakes into boxes. Each box could contain at most 8 cupcakes. What is the least number of boxes she would need?
Answer: ","e":"102 \u00f7 8 = 12 r 6. The 6 leftover cupcakes need 1 more box, so 12 + 1 = 13 boxes."} {"t":"q","id":13902,"q":"Mr Wong wanted to buy a hardcover notebook that cost $12.80. However, he found that he needed $3.90 more.\n(a) How much money did Mr Wong have?\n(b) He decided to buy a cheaper softcover notebook which cost $7.50. How much money would Mr Wong have left in the end?
(a)   (b) ","e":"(a) Money he had = $12.80 - $3.90 = $8.90. (b) Left = $8.90 - $7.50 = $1.40."} {"t":"q","id":13903,"q":"Sara had $30.80 at first. She spent some of her money to buy a gift for her mother. Then her father gave her another $12. In the end, she had $15.50. How much did Sara spend on the gift?
Answer: ","e":"Before the gift money: $15.50 - $12 = $3.50 left after spending. Spent = $30.80 - $3.50 = $27.30."} {"t":"q","id":13904,"q":"Miss Chua prepared 100 balloons for her class. She wanted to give 3 balloons to every pupil but she was short of 17 balloons. How many pupils were there in her class?
Answer: ","e":"She needed 100 + 17 = 117 balloons. Pupils = 117 \u00f7 3 = 39."} {"t":"q","id":13905,"q":"Evelyn has 16 cookies. Freya has 7 times as many cookies as Evelyn. Gerald has half as many cookies as Freya. How many cookies does Gerald have?
Answer: ","e":"Freya = 16 x 7 = 112. Gerald = 112 \u00f7 2 = 56."} {"t":"q","id":13910,"q":"Which of these fractions is greater than 4\/5?","e":"4\/5 = 0.8. 2\/3 \u2248 0.67, 5\/8 = 0.625, 7\/10 = 0.7, 6\/7 \u2248 0.857. Only 6\/7 > 0.8. Answer key option (4)."} {"t":"q","id":13914,"q":"What fraction is greater than \\(\\dfrac{2}{3}\\) and less than \\(\\dfrac{8}{9}\\)?","e":"Using ninths: 2\/3 = 6\/9 and 8\/9. A fraction between them is 7\/9. Answer key: 7\/9."} {"t":"q","id":13915,"q":"Arrange the fractions in order, beginning with the greatest.\n1\/2, 5\/8, 4\/9, 5\/6
(a)   (b)   (c)   (d) ","e":"As decimals: 1\/2 = 0.5, 5\/8 = 0.625, 4\/9 \u2248 0.444, 5\/6 \u2248 0.833. Greatest to smallest: 5\/6, 5\/8, 1\/2, 4\/9. Answer key order."} {"t":"q","id":13921,"q":"Which of the following is six thousand and forty-five in numerals?","e":"Six thousand = 6000, and forty-five = 45. 6000 + 45 = 6045."} {"t":"q","id":13925,"q":"In the number pattern, what is the missing number?\n4100, 4135, 4170, _______, 4240, 4275","e":"The pattern increases by 35 each time. 4170 + 35 = 4205."} {"t":"q","id":13928,"q":"6169 people were watching a soccer match. 4096 of them were men and the rest were women. How many fewer women than men were there?\n","e":"Women = 6169 - 4096 = 2073. Men - women = 4096 - 2073 = 2023."} {"t":"q","id":13932,"q":"There were 72 chairs in the school hall. The prefects arranged 8 chairs in each row. How many rows of chairs did they arrange?","e":"72 \/ 8 = 9 rows."} {"t":"q","id":13933,"q":"The librarian packed 384 books equally into 8 boxes for P1 classes to read during morning assembly. How many books did she pack in a box?","e":"384 \/ 8 = 48 books per box."} {"t":"q","id":13938,"q":"When a number is divided by 6, the quotient is 117 with remainder 1. What is the number?\n","e":"Number = 117 x 6 + 1 = 702 + 1 = 703."} {"t":"q","id":13941,"q":"A pet shop owner had 640 fishes and birds. He had 184 fewer birds than fishes. How many birds did he have in his pet shop?\n","e":"640 - 184 = 456; 456 \/ 2 = 228 birds."} {"t":"q","id":13947,"q":"Arrange the students from the shortest to the tallest.\nAmy 1 m 9 cm, Ben 1 m 62 cm, Charlie 105 cm, Dora 170 cm","e":"Convert to cm: Amy 109, Ben 162, Charlie 105, Dora 170. Shortest to tallest: Charlie, Amy, Ben, Dora."} {"t":"q","id":13949,"q":"What number does box A and box B represent?\n2\/A = 4\/12 = B\/36","e":"2\/A = 4\/12 means A = 6. B\/36 = 4\/12 = 1\/3, so B = 12."} {"t":"q","id":13950,"q":"Peter ran 2800 m around the neighbourhood. He took a short rest and ran another 250 m. How far did he run in total? Give your answer in kilometres and metres.\n km m","e":"2800 + 250 = 3050 m = 3 km 50 m."} {"t":"q","id":13951,"q":"a) Arrange the following in order. Begin with the greatest.\n3\/8, 3\/7, 3\/11\n, , \nb) Arrange the following in order. Begin with the smallest.\n4\/8, 9\/10, 2\/11\n, , ","e":"a) Same numerator: smaller denominator is greater, so 3\/7 > 3\/8 > 3\/11. b) Values: 2\/11 (~0.18), 4\/8 (0.5), 9\/10 (0.9), so smallest first = 2\/11, 4\/8, 9\/10."} {"t":"q","id":13952,"q":"Aaron bought a cake and cut it into 9 equal slices. Sally took 2 slices while Peter took 6 slices.\n(a) What fraction of the cake did Sally and Peter take altogether? \n(b) What fraction of the cake did Aaron have left? ","e":"(a) 2\/9 + 6\/9 = 8\/9. (b) 1 - 8\/9 = 1\/9."} {"t":"q","id":13953,"q":"John bought 4 identical containers. Each container had a capacity of 600 m\u2113. After pouring some water into the containers, he realised he would need another 450 m\u2113 of water to completely fill up all the containers. How much water did he have at first?\n","e":"Total capacity = 600 x 4 = 2400 m\u2113. Water at first = 2400 - 450 = 1950 m\u2113."} {"t":"q","id":13957,"q":"Write the following in numerals.\n(a) Nine thousand, seven hundred and twelve \n(b) Four thousand, six hundred and four ","e":"Nine thousand, seven hundred and twelve = 9712. Four thousand, six hundred and four = 4604 (zero tens)."} {"t":"q","id":13958,"q":"I am a 4-digit even number formed with the digits 2, 4, 5 and 8.\nI am a number between 2600 and 2900.\nWhat number am I? ","e":"Between 2600 and 2900 means it starts with 2 then 8 (2800s). Using remaining digits 4 and 5, an even number ends in 4: 2854."} {"t":"q","id":13959,"q":"Look at the number pattern.\n, 4181, 4481, 4781, 5081, 5381\nWhat is the missing number?","e":"The pattern increases by 300 each time. 4181 - 300 = 3881."} {"t":"q","id":13960,"q":"Jane had 1352 marbles.\nSiti had 1515 marbles more than Jane.\nHow many marbles did Jane and Siti have altogether? ","e":"Siti = 1352 + 1515 = 2867. Altogether = 1352 + 2867 = 4219 (i.e. 1352 x 2 + 1515)."} {"t":"q","id":13961,"q":"Jenny wants to buy lunch from a food court.\nShe plans to buy a meal that includes 1 main dish, 1 soup and 1 drink.\nMenu \u2014 Main dish: Nasi lemak, Fried noodles. Soup: Chicken soup, Vegetable soup. Drink: Tea, Coffee.\nHow many different ways can Jenny buy her lunch? ","e":"2 main dishes x 2 soups x 2 drinks = 8 ways."} {"t":"q","id":13962,"q":"There were 3390 people at the Singapore Zoo on Friday.\n1900 of them were adults.\n(a) How many children were there at the Singapore Zoo? \n(b) There were 685 fewer people at the Singapore Zoo on Friday than Saturday. How many people were there on Saturday? ","e":"(a) 3390 - 1900 = 1490 children. (b) Friday had 685 fewer than Saturday, so Saturday = 3390 + 685 = 4075."} {"t":"q","id":13966,"q":"Find the quotient when 648 is divided by 4. ","e":"648 \/ 4 = 162."} {"t":"q","id":13967,"q":"Celine baked 492 cupcakes.\nShe packed 5 cupcakes into each box.\nWhat is the smallest number of boxes needed for all the cupcakes to be packed? ","e":"492 \/ 5 = 98 remainder 2. The leftover 2 cupcakes need 1 more box, so 98 + 1 = 99 boxes."} {"t":"q","id":13968,"q":"Fandi has 236 blue marbles.\nHe has 9 times as many red marbles as blue marbles.\nHe gives 100 red marbles to his best friend.\nHow many red marbles does he have left? ","e":"Red marbles = 236 x 9 = 2124. After giving away 100: 2124 - 100 = 2024."} {"t":"q","id":13969,"q":"Mrs Tan had 230 pencils.\nShe gave each student 6 pencils and had 2 pencils left.\nHow many students did Mrs Tan give the pencils to? ","e":"230 \/ 6 = 38 remainder 2. So 38 students each received 6 pencils, with 2 left over."} {"t":"q","id":13974,"q":"Write four thousand and twelve in numerals.
Answer: ","e":"Four thousand and twelve = 4012."} {"t":"q","id":13976,"q":"Find the sum of 8026 and 395.
Answer: ","e":"8026 + 395 = 8421."} {"t":"q","id":13978,"q":"Kaisor had 2364 stamps. Yani had 510 stamps. How many stamps did they have altogether?
Answer: ","e":"2364 + 510 = 2874 stamps."} {"t":"q","id":13979,"q":"The difference between 2 numbers is 1700. The greater number is 5801. What is the smaller number?
Answer: ","e":"Smaller number = greater number - difference = 5801 - 1700 = 4101."} {"t":"q","id":13980,"q":"Using the digits 1, 8, 2 and 7, form the\n(a) greatest 4-digit even number.\n(b) smallest 4-digit odd number.\nUse each digit once only.
(a)   (b) ","e":"(a) Greatest even: end in an even digit, largest first: 8712. (b) Smallest odd: end in an odd digit, smallest first: 1287."} {"t":"q","id":13981,"q":"Dash and Luke had the same number of marbles at first. After Luke gave Dash 12 marbles, Dash had 47 marbles. How many marbles did Luke have in the end?
Answer: ","e":"Dash started with 47 - 12 = 35; both started equal at 35. Luke gave away 12, so Luke had 35 - 12 = 23 marbles."} {"t":"q","id":13982,"q":"A baker baked 594 chocolate doughnuts. He baked 128 more chocolate doughnuts than strawberry doughnuts.\n(a) How many strawberry doughnuts did the baker bake?\n(b) How many doughnuts did the baker bake altogether?
(a)   (b) ","e":"(a) Strawberry = 594 - 128 = 466. (b) Total = 594 + 466 = 1060."} {"t":"q","id":13984,"q":"Which of the following is nine thousand, eight hundred and fifty in numerals?","e":"Nine thousand = 9000, eight hundred = 800, fifty = 50. 9000 + 800 + 50 = 9850."} {"t":"q","id":13988,"q":"Joselin bought a table for $72.15. She gave the cashier two $50 notes. How much change should she get?","e":"Two $50 notes = $100. $100 - $72.15 = $27.85."} {"t":"q","id":13989,"q":"Look at the following number pattern. What are the missing numbers?\n928, 925, 920, 917, 912, , ","e":"The pattern decreases by 3, then 5, alternating: -3, -5, -3, -5... After 912: 912 - 3 = 909, then 909 - 5 = 904."} {"t":"q","id":13990,"q":"Find the sum of the values of the digits '5' in the numbers 5847 and 250.
Answer: ","e":"In 5847 the digit 5 has value 5000. In 250 the digit 5 has value 50. 5000 + 50 = 5050."} {"t":"q","id":13991,"q":"Write two numbers that will give a sum of 1142.
(a)   (b) ","e":"Any two numbers adding to 1142 are acceptable; the answer key uses 1000 and 142 (1000 + 142 = 1142)."} {"t":"q","id":13992,"q":"Wayne formed some numbers from the digits 1, 9, 0, 8. Two of the numbers he formed were 1098 and 1908.\na) In 1098, the digit 9 is in the hundreds place. (true\/false)\nb) 1908 > 1098 (true\/false)\nc) The greatest possible 4-digit number he can form is 9108. (true\/false)
(a)   (b)   (c) ","e":"a) In 1098 the digit 9 is in the tens place, so False. b) 1908 > 1098 is True. c) The greatest 4-digit number from 1,9,8,0 is 9810, not 9108, so False."} {"t":"q","id":13993,"q":"Serena bought a pencil box for $28.50. She bought a bag that cost $15.90 more. How much did she pay for the bag?
Answer: ","e":"$28.50 + $15.90 = $44.40."} {"t":"q","id":13995,"q":"Thomas has 392 Book Bug cards. He has 67 fewer Book Bug cards than Sharyn. How many Book Bug cards does Sharyn have?
Answer: ","e":"Thomas has 67 fewer than Sharyn, so Sharyn has more: 392 + 67 = 459."} {"t":"q","id":13996,"q":"There were 8009 children and 9008 adults at a party.\na) Were there more children or adults at the party?\nb) Find the difference between the number of children and adults at the party.
(a)   (b) ","e":"9008 (adults) > 8009 (children), so there were more adults. Difference = 9008 - 8009 = 999."} {"t":"q","id":14001,"q":"There are 312 paper clips in a bag. Cayden has 3 such bags. How many paper clips does he have in total?","e":"312 \u00d7 3 = 936."} {"t":"q","id":14002,"q":"Alice and Ben have 180 stamps altogether. Alice has 4 times as many stamps as Ben. How many stamps does Ben have?","e":"Ben = 1 unit, Alice = 4 units, total = 5 units = 180. 1 unit = 180 \u00f7 5 = 36. Ben has 36 stamps."} {"t":"q","id":14003,"q":"A number when divided by 9 has a quotient of 126 and a remainder of 8. What is the number?","e":"Number = quotient \u00d7 divisor + remainder = 126 \u00d7 9 + 8 = 1134 + 8 = 1142."} {"t":"q","id":14009,"q":"Fill in the blanks with 'more' or 'less'.\na) 5 x 8 is 8 ___ than 6 x 8.\nb) 7 x 6 is 6 ___ than 6 x 6.","e":"a) 5\u00d78 = 40, 6\u00d78 = 48; 40 is 8 less than 48. b) 7\u00d76 = 42, 6\u00d76 = 36; 42 is 6 more than 36."} {"t":"q","id":14010,"q":"What is the missing digit in the box?\n 7 8\n\u00d7 7\n2 6 4 6","e":"The 3-digit number \u00d7 7 = 2646, so the number is 2646 \u00f7 7 = 378. The missing hundreds digit is 3."} {"t":"q","id":14011,"q":"Jerina donated $9. Gabriel donated 5 times as much money as Jerina. How much money did Gabriel donate?
Answer: ","e":"5 \u00d7 $9 = $45."} {"t":"q","id":14012,"q":"The product of two numbers is 105. One of the numbers is 7. Find the other number.
Answer: ","e":"105 \u00f7 7 = 15."} {"t":"q","id":14013,"q":"Emma had 720 beads at first. She gave an equal number of beads to each of her 4 friends and had 24 beads left. How many beads did she give to each of her friends?
Answer: ","e":"Beads given away = 720 - 24 = 696. Each friend got 696 \u00f7 4 = 174."} {"t":"q","id":14018,"q":"There were 80 boys and 64 girls in the school hall making paper flowers.\na) How many children were there altogether in the hall?\nb) Each child made 6 paper flowers. How many paper flowers did the children make in total?
(a)   (b) ","e":"a) 80 + 64 = 144 children. b) 144 \u00d7 6 = 864 paper flowers."} {"t":"q","id":14019,"q":"Paul bought 7 boxes of pins. There were 235 pins in each box.\na) How many pins did Paul buy altogether?\nb) Paul opened one box of pins and gave 61 pins to his friends. Then, he repacked all the remaining pins in that box into 6 packets. How many pins were there in each packet?
(a)   (b) ","e":"a) 235 \u00d7 7 = 1645 pins. b) One box has 235 pins; after giving 61 away, 235 - 61 = 174 remain; 174 \u00f7 6 = 29 pins per packet."} {"t":"q","id":14021,"q":"Which of the following is correct?","e":"3\/8 = 0.375 and 5\/6 \u2248 0.833, so 3\/8 < 5\/6 is correct. The others are false."} {"t":"q","id":14022,"q":"200 cm + 9 cm = [ ]","e":"200 cm + 9 cm = 209 cm. 209 cm = 2 m 9 cm (since 100 cm = 1 m)."} {"t":"q","id":14023,"q":"Which of the following is the longest?","e":"Convert all to metres: 2540 m; 2 km 54 m = 2054 m; 2 km 504 m = 2504 m; 20 m 54 cm = 20.54 m. The longest is 2540 m."} {"t":"q","id":14024,"q":"Arrange the following fractions from the greatest to the smallest.\n1\/3, 4\/7, 4\/9, 8\/9","e":"As decimals: 1\/3\u22480.333, 4\/7\u22480.571, 4\/9\u22480.444, 8\/9\u22480.889. Greatest to smallest: 8\/9, 4\/7, 4\/9, 1\/3."} {"t":"q","id":14035,"q":"A bottle holds 1 l of water. A cup holds 350 ml less water than the bottle. How much water can 3 such cups hold?\n ml","e":"1 l = 1000 ml. One cup = 1000 - 350 = 650 ml. 3 cups = 650 \u00d7 3 = 1950 ml."} {"t":"q","id":14039,"q":"Write five thousand and twelve in numerals.
Answer: ","e":"Five thousand and twelve = 5000 + 12 = 5012."} {"t":"q","id":14040,"q":"Find the sum of 855 and 6042.
Answer: ","e":"855 + 6042 = 6897."} {"t":"q","id":14041,"q":"Find the difference between 6345 and 9689.
Answer: ","e":"9689 - 6345 = 3344."} {"t":"q","id":14043,"q":"Find the remainder when 874 is divided by 7.
Answer: ","e":"874 \/ 7 = 124 remainder 6."} {"t":"q","id":14044,"q":"Arrange the following numbers from the largest to the smallest. 4533, 4346, 4789
(a)   (b)   (c) ","e":"Compare by place value: 4789 > 4533 > 4346."} {"t":"q","id":14045,"q":"A shopkeeper sold 616 apples and mangoes. He sold 288 mangoes. How many apples did the shopkeeper sell?
Answer: ","e":"Apples = 616 - 288 = 328."} {"t":"q","id":14046,"q":"Miss Soon paid $948 for 6 similar dresses. How much did she pay for each dress?
Answer: ","e":"Each dress = 948 \/ 6 = $158."} {"t":"q","id":14048,"q":"Rope A is 908 cm long. It is 615 cm shorter than rope B. How long is rope B?
Answer: ","e":"Rope B = 908 + 615 = 1523 cm."} {"t":"q","id":14049,"q":"The sum of two numbers is 7674. The difference between the two numbers is 3272. Find the smaller number.
Answer: ","e":"Smaller number = (sum - difference) \/ 2 = (7674 - 3272) \/ 2 = 4402 \/ 2 = 2201."} {"t":"q","id":14051,"q":"Jasmine saved $3463. She saved $445 more than Ally. How much money did they save altogether?
Answer: ","e":"Ally = 3463 - 445 = 3018. Altogether = 3018 + 3463 = $6481."} {"t":"q","id":14052,"q":"Mr Lim packed 216 oranges equally into boxes of 9. He sold 18 boxes of the oranges. How many boxes of oranges did he have left?
Answer: ","e":"Total boxes = 216 \/ 9 = 24. Boxes left = 24 - 18 = 6."} {"t":"q","id":14053,"q":"Sally prepared party bags for a party. She packed 8 stickers and 4 sweets in each bag. There was a total of 128 stickers. (a) How many party bags were there in total? (b) How many sweets were there altogether?
(a)   (b) ","e":"(a) Bags = 128 \/ 8 = 16. (b) Sweets = 4 x 16 = 64."} {"t":"q","id":14054,"q":"Tom has $34.55. His mother gives him $50 more. How much does Tom have now?
Answer: ","e":"34.55 + 50 = $84.55."} {"t":"q","id":14057,"q":"Fill in the boxes by comparing the fractions, 2\/7 and 1\/3. <","e":"Common denominator 21: 2\/7 = 6\/21 and 1\/3 = 7\/21, so 2\/7 < 1\/3."} {"t":"q","id":14061,"q":"Complete the following equation by finding A. A\/12 + 1\/12 = 1 - 1\/4
Answer: ","e":"1 - 1\/4 = 3\/4 = 9\/12. So A\/12 + 1\/12 = 9\/12, A\/12 = 8\/12, A = 8."} {"t":"q","id":14064,"q":"Arrange these fractions from the greatest to the smallest. 3\/5, 1\/2, 7\/10
(a)   (b)   (c) ","e":"Common denominator 10: 3\/5 = 6\/10, 1\/2 = 5\/10, 7\/10 = 7\/10. Greatest to smallest: 7\/10, 3\/5, 1\/2."} {"t":"q","id":14066,"q":"June paid $80 for a toaster. She paid $33.40 less for a dress than the toaster. How much did she pay for the two items altogether?
Answer: ","e":"Dress = 80.00 - 33.40 = 46.60. Altogether = 80.00 + 46.60 = $126.60."} {"t":"q","id":14069,"q":"The price of a toy car is $8. Jane bought as many toy cars as she could with $50. (a) How many toy cars did Jane buy? (b) How much money had she left?
(a)   (b) ","e":"50 \/ 8 = 6 remainder 2. (a) 6 toy cars. (b) $2 left."} {"t":"q","id":14076,"q":"There were 1789 students in a school. There were 985 boys. How many girls were there in the school?
Answer: ","e":"Girls = total - boys = 1789 - 985 = 804."} {"t":"q","id":14077,"q":"Miss Lim packed 4 oranges in a bag each. She gave away 8 such bags and had 1 bag left. How many oranges does she have at first?
Answer: ","e":"Total bags = 8 + 1 = 9. Oranges = 9 x 4 = 36."} {"t":"q","id":14078,"q":"Mr Tan had 768 pencils. He packed 8 pencils into each box. How many boxes did Mr Tan use to pack all the pencils?
Answer: ","e":"Boxes = 768 \/ 8 = 96."} {"t":"q","id":14080,"q":"A box contained red and blue beads. There were 84 beads in the box. There were twice as many red beads as blue beads. How many blue beads were there?
Answer: ","e":"Blue = 1 unit, red = 2 units, total = 3 units = 84. Blue = 84 \/ 3 = 28."} {"t":"q","id":14082,"q":"Pete and 3 boys bought 204 game cards altogether. They shared the game cards equally. How many cards did each boy get?
Answer: ","e":"Pete and 3 boys = 4 boys. Each = 204 \/ 4 = 51."} {"t":"q","id":14083,"q":"Mr Lim paid $1600 for a computer. He paid $960 less for a printer. How much did he pay for both the computer and printer?
Answer: ","e":"Printer = 1600 - 960 = $640. Total = 1600 + 640 = $2240."} {"t":"q","id":14084,"q":"A shop had 5600 bags. The shopkeeper sold 1250 bags on Saturday. He sold more bags on Sunday. After that he had 440 bags left. How many bags were sold on Sunday?
Answer: ","e":"Total sold = 5600 - 440 = 5160. Sunday = 5160 - 1250 = 3910."} {"t":"q","id":14085,"q":"Simon and Tim had the same number of books at first. Tim bought 85 books and Simon gave 120 books away. Simon had 60 books in the end. a) How many books did each boy have at first? b) How many more books did Tim have than Simon in the end?
(a)   (b) ","e":"(a) Simon end 60 = start - 120, so start = 60 + 120 = 180; both had 180. (b) Tim end = 180 + 85 = 265; difference = 265 - 60 = 205."} {"t":"q","id":14087,"q":"There were 45 more girls than boys in the Art Club. 8 boys left the Art Club and 5 more girls join the Art Club. a) How many more girls were there in the Art Club than boys in the end? b) There were 640 students left in the Art Club. How many boys were there in the Art Club in the end?
(a)   (b) ","e":"(a) New girl-boy difference = 45 + 8 + 5 = 58. (b) Boys + girls = 640 and girls = boys + 58, so 2 x boys + 58 = 640; boys = (640 - 58) \/ 2 = 291."} {"t":"q","id":14090,"q":"(a) Write 5 km 18 m in metres. (b) Write 4109 m in kilometres and metres.
(a)   (b) ","e":"(a) 5 km = 5000 m, so 5 km 18 m = 5018 m. (b) 4109 m = 4000 m + 109 m = 4 km 109 m."} {"t":"q","id":14092,"q":"Arrange the following fractions in order. Begin with the greatest fraction. 2\/3, 2\/5, 2\/9
(a)   (b)   (c) ","e":"With the same numerator, the smaller the denominator the larger the fraction. So 2\/3 > 2\/5 > 2\/9."} {"t":"q","id":14094,"q":"The school assembly started at 8 a.m. It ended at 9.05 a.m. How long was the school assembly? h mins","e":"From 8 a.m. to 9 a.m. is 1 hour; from 9 a.m. to 9.05 a.m. is 5 minutes. Total 1 h 5 min."} {"t":"q","id":14097,"q":"The mass of a box of cookies is 710 g. It is 600 g lighter than a packet of flour. Find the mass of the packet of flour. kg g","e":"Flour = 710 + 600 = 1310 g = 1 kg 310 g."} {"t":"q","id":14098,"q":"A jug has a capacity of 1020 ml. 740 ml of water was poured into the jug. How much more water is needed to fill the jug completely? ml","e":"Water needed = 1020 - 740 = 280 ml."} {"t":"q","id":14099,"q":"Find the value of \\(\\dfrac{9}{10}\\) - \\(\\dfrac{2}{5}\\) . Write the answer in its simplest form.","e":"2\/5 = 4\/10, so 9\/10 - 4\/10 = 5\/10 = 1\/2."} {"t":"q","id":14101,"q":"Mr Halim bought a 2-litre bottle of fruit juice. He poured some of the juice equally into 7 glasses and each glass was full. 1125 ml of fruit juice was left in the bottle. (a) How much fruit juice was poured out? (b) What is the capacity of each glass?
(a)   (b) ","e":"(a) 2 litres = 2000 ml; poured out = 2000 - 1125 = 875 ml. (b) Each glass = 875 \/ 7 = 125 ml."} {"t":"q","id":14102,"q":"There were 468 children at a Funfair carnival. There were twice as many children as women. The number of men was 50 more than the number of women. (a) How many men were there at the carnival? (b) How many people were there at the carnival altogether?
(a)   (b) ","e":"Women = 468 \/ 2 = 234. (a) Men = 234 + 50 = 284. (b) Total = 468 + 234 + 284 = 986."} {"t":"q","id":14103,"q":"Jon and May shared a box of marbles. There were 320 marbles in the box. Jon had 46 more marbles than May. How many marbles did May receive?
Answer: ","e":"Remove Jon's extra 46: 320 - 46 = 274. Split equally: May = 274 \/ 2 = 137."} {"t":"q","id":14105,"q":"What is the missing numerator?\n8\/12 - 1\/3 = \/6","e":"8\/12 = 2\/3. 2\/3 - 1\/3 = 1\/3 = 2\/6, so the missing numerator is 2."} {"t":"q","id":14111,"q":"Benson and Hong Wei shared some marbles equally. After Hong Wei gave 28 marbles to Benson, how many more marbles did Benson have than Hong Wei?
Answer: ","e":"They started equal. Hong Wei gives 28 away (his count drops by 28) and Benson gains 28, so the difference is 28 + 28 = 56."} {"t":"q","id":14112,"q":"Kelly and Melissa collect stamps. Together they collected 825 stamps. Melissa collected twice as many stamps as Kelly. How many more stamps did Melissa collect than Kelly?
Answer: ","e":"3 units = 825, so 1 unit (Kelly) = 275. Melissa = 550. Difference = 550 - 275 = 275."} {"t":"q","id":14113,"q":"Susan painted \\(\\dfrac{1}{3}\\) of the wall green and \\(\\dfrac{1}{6}\\) of the same wall yellow. What fraction of the wall was painted? Give your answer in its simplest form.","e":"1\/3 + 1\/6 = 2\/6 + 1\/6 = 3\/6 = 1\/2."} {"t":"q","id":14114,"q":"Mrs Lee bought 3 regular-sized pizzas topped with different ingredients. She cut the cheese pizza into 6 equal pieces, the chicken pizza into 8 equal pieces and the seafood pizza into 12 equal pieces. Jerry ate 2 pieces of Cheese pizza, Joel ate 3 pieces of Chicken pizza and Jane ate 4 pieces of the seafood pizza. Who ate the most pizza?","e":"Jerry = 2\/6 = 8\/24, Joel = 3\/8 = 9\/24, Jane = 4\/12 = 8\/24. 9\/24 is the largest, so Joel ate the most."} {"t":"q","id":14116,"q":"Express 6 \u2113 8 m\u2113 in m\u2113.","e":"6 \u2113 = 6000 m\u2113. 6000 m\u2113 + 8 m\u2113 = 6008 m\u2113."} {"t":"q","id":14118,"q":"3 groups of _______ = 4 x 9","e":"4 \u00d7 9 = 36. 3 groups of ? = 36, so ? = 36 \u00f7 3 = 12."} {"t":"q","id":14119,"q":"Which one of the following fractions is greater than 1\/2?","e":"Half of 7 is 3.5, so 4\/7 > 1\/2. 5\/10 = 1\/2 exactly; 3\/7 and 2\/5 are less than 1\/2."} {"t":"q","id":14122,"q":"Write seven thousand and forty-nine in numerals.
Answer: ","e":"Seven thousand and forty-nine = 7049."} {"t":"q","id":14130,"q":"Study the number pattern below. What is the missing number in the box? 356, 1356, 1366, 2366, 2376, , 3386, 4386, 4396","e":"The pattern alternates +1000 then +10: 356 (+1000) 1356 (+10) 1366 (+1000) 2366 (+10) 2376 (+1000) 3376 (+10) 3386 (+1000) 4386 (+10) 4396."} {"t":"q","id":14131,"q":"Find the value of \\(\\dfrac{1}{12}\\) + \\(\\dfrac{2}{3}\\). Express your answer as a fraction in its simplest form.","e":"2\/3 = 8\/12. 1\/12 + 8\/12 = 9\/12 = 3\/4."} {"t":"q","id":14132,"q":"Find the missing numerator and denominator in the boxes for (a) and (b). 4\/11 = \/33 = 20\/","e":"4\/11 = 12\/33 (multiply top and bottom by 3). 4\/11 = 20\/55 (multiply top and bottom by 5). So (a) = 12, (b) = 55."} {"t":"q","id":14133,"q":"Jimmy went for a run in the park. His watch was 15 minutes slow. The run lasted 135 min. According to his watch, he stopped running at 8.05 p.m. What was the actual time he started his run? p.m.","e":"Watch is 15 min slow, so actual stop time = 8.05 p.m. + 15 min = 8.20 p.m. Run lasted 135 min (2 h 15 min), so start = 8.20 p.m. \u2212 2 h 15 min = 6.05 p.m."} {"t":"q","id":14134,"q":"The difference between two numbers is 1406. The greater number is 2034. What is the sum of the two numbers?
Answer: ","e":"Smaller number = 2034 \u2212 1406 = 628. Sum = 2034 + 628 = 2662."} {"t":"q","id":14135,"q":"Xin Li had 11 m of string. She cut the string into 9 equal pieces with 263 cm left. What was the length of each piece of string? cm","e":"11 m = 1100 cm. 1100 \u2212 263 = 837 cm used for the pieces. 837 \u00f7 9 = 93 cm each."} {"t":"q","id":14136,"q":"153 story books were shared among Alvin, Bala and Caleb. Alvin received twice as many story books as Bala. Caleb received fewer story books than Bala. For each statement, state True, False or Not possible to tell. (a) Alvin has more story books than Caleb. (b) Caleb received only 9 story books.
(a)   (b) ","e":"(a) Alvin = 2 \u00d7 Bala and Caleb < Bala < Alvin, so Alvin definitely has more than Caleb \u2014 True. (b) Alvin + Bala = 3 parts of Bala; with Caleb fewer than Bala there are several possible values for Caleb, so the exact number cannot be determined \u2014 Not possible to tell."} {"t":"q","id":14137,"q":"Anne paid $720 for a pair of shoes and a belt. The pair of shoes cost 4 times as much as the belt. She also bought a shirt which cost $45 more than the belt. How much did the shirt cost?
Answer: ","e":"Shoes + belt = 5 units = $720, so 1 unit (belt) = $720 \u00f7 5 = $144. Shirt = belt + $45 = $144 + $45 = $189."} {"t":"q","id":14138,"q":"Pete had 1037 marbles. Ken had 1527 marbles. Pete then bought some more marbles. Ken had 285 fewer marbles than Pete in the end. How many marbles did Pete buy?
Answer: ","e":"In the end Pete had 285 more than Ken: 1527 + 285 = 1812 marbles. Pete bought 1812 \u2212 1037 = 775 marbles."} {"t":"q","id":14143,"q":"Find the value of 5\/7 + 1\/7","e":"Like fractions: add numerators, keep denominator. 5\/7 + 1\/7 = 6\/7."} {"t":"q","id":14147,"q":"Sally wants to pack 40 oranges into bags. Each bag can hold at most 6 oranges. What is the least number of bags Sally needs?","e":"40 \/ 6 = 6 R 4. The 4 leftover oranges need another bag, so 7 bags."} {"t":"q","id":14149,"q":"Write eight thousand, three hundred and nine in numerals.
Answer: ","e":"8 thousands, 3 hundreds, 0 tens, 9 ones = 8309."} {"t":"q","id":14158,"q":"(a) Find the sum of 376 and 825\n(b) Find the difference between 781 and 1000
(a)   (b) ","e":"(a) 376 + 825 = 1201. (b) 1000 - 781 = 219."} {"t":"q","id":14159,"q":"There are 936 apples in a box. There are 6 times as many apples as pears. How many apples and pears are there altogether in the box?
Answer: ","e":"Pears = 936 \/ 6 = 156. Apples + pears = 936 + 156 = 1092."} {"t":"q","id":14160,"q":"(a) Find the product of 750 and 8\n(b) Find the quotient and remainder when 649 \/ 9
(a)   (b) ","e":"(a) 750 x 8 = 6000. (b) 649 \/ 9 = 72 remainder 1."} {"t":"q","id":14162,"q":"A piece of metal wire was bent into the shape of a square. Each side of the square was 9 cm. The same piece of wire was then bent into the shape of a rectangle. The length of the rectangle was 12 cm. What was the breadth of the rectangle?
Answer: ","e":"Square perimeter = 9 x 4 = 36 cm. Rectangle: 36 - 2 x 12 = 12; breadth = 12 \/ 2 = 6 cm."} {"t":"q","id":14163,"q":"Anand spent 2 h 30 min on his project. He stopped working on his project at 10 20 as shown on his watch. His watch was 15 min slow. What was the correct time he started working on his project? Give your answer in the 24-hour clock.
Answer: ","e":"Watch is 15 min slow, so correct stop time = 10 20 + 15 min = 10 35. Start = 10 35 - 2 h 30 min = 08 05."} {"t":"q","id":14164,"q":"At the bookshop, erasers were sold for 55 cents each. Nora had 3 two-dollar notes in her wallet. How much money would Nora have left after buying 10 such erasers?
Answer: ","e":"Cost = 10 x $0.55 = $5.50. Nora has 3 x $2 = $6. Left = $6 - $5.50 = $0.50."} {"t":"q","id":14165,"q":"The table shows the number of paper stars Jenny made each day. On the first day, she made 10 paper stars. Each day, she makes twice as many paper stars as she did on the previous day. On which day would she make 320 paper stars?\nDay 1: 10, Day 2: 20, Day 3: 40
Answer: ","e":"Doubling: Day1=10, 2=20, 3=40, 4=80, 5=160, 6=320. So Day 6."} {"t":"q","id":14166,"q":"Randy has 1289 blue and yellow pencils. 475 pencils are blue and the rest are yellow.\n(a) How many yellow pencils does Randy have?\n(b) Randy buys another 1256 blue pencils. How many blue pencils does he have in total?
(a)   (b) ","e":"(a) Yellow = 1289 - 475 = 814. (b) Blue total = 475 + 1256 = 1731."} {"t":"q","id":14167,"q":"Mrs Tan had some blueberries. She packed them equally into 9 boxes and found that she had 600 g of blueberries left. Each box had 720 g of blueberries. What was the mass of blueberries Mrs Tan had at first? Give your answer in kilograms and grams.
Answer: ","e":"In boxes: 720 x 9 = 6480 g. Plus leftover: 6480 + 600 = 7080 g = 7 kg 80 g."} {"t":"q","id":14168,"q":"At first, Vanessa had 758 cards, while Gary had 1548 cards. Vanessa then bought some more cards. In the end, Gary had 125 fewer cards than Vanessa. How many cards did Vanessa buy?
Answer: ","e":"Gary has 1548. Vanessa ends with 125 more than Gary: 1548 + 125 = 1673. She bought 1673 - 758 = 915 cards."} {"t":"q","id":14169,"q":"Gina had 698 more beads than Liz. She gave 225 beads to Liz. How many more beads does Gina have than Liz in the end?
Answer: ","e":"Giving 225 beads narrows the gap by twice that amount (Gina loses 225, Liz gains 225): 698 - 225 - 225 = 248."} {"t":"q","id":14174,"q":"Which of the following is not an equivalent fraction of 2\/3?","e":"2\/3 = 4\/6 = 6\/9 = 8\/12. 4\/9 is not equal to 2\/3, so it is the odd one out."} {"t":"q","id":14179,"q":"Amy had 67 fewer coins than Dawn at first. Dawn gave 14 coins to Amy. How many fewer coins did Amy have than Dawn in the end?","e":"Giving 14 coins from Dawn to Amy reduces the gap by 2 x 14 = 28. 67 - 28 = 39."} {"t":"q","id":14181,"q":"Complete the number pattern.\n743, 748, 758, 763, 773, , 788, 793","e":"The pattern alternates +5, +10: 743, 748, 758, 763, 773, 778, 788, 793. The missing term is 778."} {"t":"q","id":14182,"q":"Kelly had 18 boxes of donuts. Each box contained 6 donuts each. How many donuts did Kelly have?
Answer: ","e":"18 x 6 = 108 donuts."} {"t":"q","id":14188,"q":"74 students are going for an excursion to Sentosa. Each van can ferry 9 students. Find the least number of vans that are needed to ferry all the students for the excursion.
Answer: ","e":"74 \/ 9 = 8 remainder 2. The leftover 2 students still need a van, so 8 + 1 = 9 vans."} {"t":"q","id":14189,"q":"Mrs Lee reached the movie theatre at 1.25 p.m. She reached 10 minutes before the movie started. The movie lasted for 1 h 15 min. What time did the movie end?
Answer: ","e":"Movie started at 1.25 + 10 min = 1.35 p.m. It ended at 1.35 + 1 h 15 min = 2.50 p.m."} {"t":"q","id":14190,"q":"Mr Lim bought a pair of headphones for $62.60. He bought a watch that cost $17.50 less. How much did he pay in total?
Answer: ","e":"Watch = $62.60 - $17.50 = $45.10. Total = $45.10 + $62.60 = $107.70."} {"t":"q","id":14191,"q":"Ali and Wanting had 180 marbles altogether. Ali had 4 times as many marbles as Wanting. How many marbles did Ali have?
Answer: ","e":"Total of 5 units = 180, so 1 unit = 180 \/ 5 = 36. Ali has 4 units = 4 x 36 = 144."} {"t":"q","id":14192,"q":"14 flagpoles are placed at equal distance apart along a straight road. The distance between the 1st flagpole and the 2nd flagpole is 6 m.\na) How many gaps are there between the 1st and the 14th flagpole?\nb) What is the total distance between the 1st and the 14th flagpole?\na) \nb) m","e":"a) Gaps between 1st and 14th = 14 - 1 = 13. b) Total distance = 13 x 6 = 78 m."} {"t":"q","id":14193,"q":"4 T-shirts and 5 pairs of shorts cost $116. A T-shirt and a pair of shorts cost $27. How much does a pair of shorts cost?
Answer: ","e":"4 T-shirts + 4 pairs of shorts = 4 x $27 = $108. The extra 1 pair of shorts = $116 - $108 = $8."} {"t":"q","id":14194,"q":"Amir, Brenda and Chloe baked some cupcakes for a charity event. Amir baked 985 cupcakes. Brenda baked 487 cupcakes fewer than Amir. Chloe baked 98 cupcakes more than Brenda.\na) How many cupcakes did Chloe bake?\nb) Among the cupcakes Amir baked, 468 were strawberry cupcakes and the rest were blueberry cupcakes. He sold 274 blueberry cupcakes. How many blueberry cupcakes were left?\na) \nb) ","e":"a) Brenda = 985 - 487 = 498; Chloe = 498 + 98 = 596. b) Amir's blueberry = 985 - 468 = 517; left = 517 - 274 = 243."} {"t":"q","id":14198,"q":"Which of the following is arranged from the greatest to the smallest?","e":"From greatest to smallest: 653, 635, 563, 536. Each number is smaller than the one before it."} {"t":"q","id":14200,"q":"3415, 3625, 3835, , 4255, 4465\nWhat is the missing number in the pattern?","e":"The pattern increases by 210 each time. 3835 + 210 = 4045."} {"t":"q","id":14202,"q":"12\/18 = 8\/ What is the missing number in the box?","e":"12\/18 simplifies to 2\/3. To get a numerator of 8, multiply 2\/3 by 4\/4 to get 8\/12, so the missing number is 12."} {"t":"q","id":14204,"q":"Melissa finished cleaning her room at 12 00. She spent 1 hour 50 minutes cleaning without taking any break. What time did she start cleaning?","e":"Subtract 1 hour 50 minutes from 12 00. 12 00 minus 1 hour = 11 00; minus 50 minutes = 10 10."} {"t":"q","id":14209,"q":"Arrange the fractions in order, beginning with the greatest.\n2\/5 , 2\/3 , 7\/12\n , , ","e":"Using a common denominator of 60: 2\/5 = 24\/60, 2\/3 = 40\/60, 7\/12 = 35\/60. Greatest to smallest: 2\/3, 7\/12, 2\/5."} {"t":"q","id":14211,"q":"Mrs Tan paid for her meal with a $50-note and got $14.30 change. How much did her meal cost?\nAns: $ ","e":"$50.00 - $14.30 = $35.70."} {"t":"q","id":14212,"q":"Chee Meng has 7 cups. He pours 86 g of sugar into each cup. What is the total mass of sugar Chee Meng pours into all the cups?\nAns: g","e":"86 g x 7 = 602 g."} {"t":"q","id":14213,"q":"A minibus can take at most 8 passengers. What is the least number of minibuses needed to take 158 passengers?\nAns: ","e":"158 divided by 8 = 19 remainder 6. The remaining 6 passengers still need a minibus, so 19 + 1 = 20 minibuses."} {"t":"q","id":14216,"q":"Box A is 2550 g lighter than Box B. Box B is 3400 g heavier than Box C. Box C weighs 2 kg 180 g.\n(a) What is the mass of Box B?\n(b) What is the mass of Box A? Give your answer in kilograms and grams.\nAns: (a) (b) ","e":"Box C = 2 kg 180 g = 2180 g. (a) Box B = 2180 + 3400 = 5580 g. (b) Box A = 5580 - 2550 = 3030 g = 3 kg 30 g."} {"t":"q","id":14217,"q":"Ali sold 570 apples. He sold 5 times as many apples as oranges. He sold 38 fewer oranges than pears.\n(a) How many oranges did Ali sell?\n(b) How many pears did Ali sell?\nAns: (a) (b) ","e":"(a) Oranges = 570 divided by 5 = 114. (b) Pears = 114 + 38 = 152 (oranges are 38 fewer than pears)."} {"t":"q","id":14218,"q":"Jerry keeps his picture cards in 4 boxes. Each box holds 118 cards except for the last box. The last box has only 79 cards. How many picture cards does Jerry have altogether?\nAns: ","e":"Three full boxes: 118 x 3 = 354. Add the last box: 354 + 79 = 433."} {"t":"q","id":14219,"q":"In an auditorium, 159 people were seated to watch a performance at first. After the first performance, 27 of them left their seats. Then, 4 times as many people as those who left their seats came in to occupy the remaining seats. How many seats are there in the auditorium?\nAns: ","e":"Remaining after 27 left: 159 - 27 = 132 seated. People who came in: 27 x 4 = 108. Total seats = 132 + 108 = 240."} {"t":"q","id":14221,"q":"Express 8 km 60 m in metres.","e":"8 km = 8000 m. 8000 m + 60 m = 8060 m."} {"t":"q","id":14225,"q":"What is the missing number in the number pattern? 2076, 2086, 2096, , 2116, 2126","e":"The pattern increases by 10 each time. 2096 + 10 = 2106."} {"t":"q","id":14227,"q":"Randal has 114 pies. He wants to pack 9 pies into each box. What is the least number of boxes Randal needs to pack all the pies?","e":"114 \/ 9 = 12 remainder 6. The leftover 6 pies need one more box, so 12 + 1 = 13 boxes."} {"t":"q","id":14228,"q":"Mrs Ling took 35 min to walk from her house to the swimming pool. She arrived at the swimming pool at 3:45 pm. What time did Mrs Ling leave her house?","e":"Working backwards from 3:45 pm by 35 minutes: 3:45 - 35 min = 3:10 pm."} {"t":"q","id":14229,"q":"Alex and Faye had some files each. Alex had 34 files. After Faye had given away 40 files, she had 18 files fewer than Alex. What was the number of files Faye had at first?","e":"After giving away 40, Faye had 34 - 18 = 16 files. So at first she had 16 + 40 = 56 files."} {"t":"q","id":14230,"q":"(a) Write eight thousand, three hundred and fifty-six in numerals. (b) Using all four digits 1, 8, 3, 2, form the greatest 4-digit even number. ","e":"(a) Eight thousand, three hundred and fifty-six = 8356. (b) For the greatest even number from 1,8,3,2, the last digit must be even; using 2 as the units gives 8312."} {"t":"q","id":14233,"q":"Doreen started her art lesson at 12 30. Her art lesson lasted for 1 h 15 min. What time did her art lesson end? ","e":"12 30 + 1 h = 13 30; 13 30 + 15 min = 13 45."} {"t":"q","id":14235,"q":"A fan costs $23.10. A toy car costs $10.80 less than the fan. How much does the toy car cost? $","e":"$23.10 - $10.80 = $12.30."} {"t":"q","id":14236,"q":"At a carnival, there were 1527 boys and 2315 girls. How many children were there altogether at the carnival? ","e":"1527 + 2315 = 3842."} {"t":"q","id":14237,"q":"458 x A = 1B32. What do the digits A and B represent? A = , B = ","e":"458 x 4 = 1832, which matches the form 1B32 with B = 8. So A = 4 and B = 8."} {"t":"q","id":14240,"q":"Ronald spent $12.75 on Monday and $4.65 on Tuesday. He had $36.70 left in his wallet at the end of Tuesday. How much money did Ronald have at first on Monday? $","e":"$12.75 + $4.65 + $36.70 = $54.10."} {"t":"q","id":14241,"q":"Larry and Megan shared a piece of ribbon. Larry used \\(\\dfrac{1}{4}\\) of the ribbon. Megan used \\(\\dfrac{5}{12}\\) of the same ribbon. What fraction of the piece of ribbon did they use altogether? Express your answer in its simplest form.","e":"1\/4 = 3\/12. 3\/12 + 5\/12 = 8\/12 = 2\/3."} {"t":"q","id":14242,"q":"Avery, Betty and Caylee made some cookies. Betty made 521 cookies. Avery made 380 more cookies than Betty. Caylee made 671 fewer cookies than Avery. (a) How many cookies did Avery make? (b) How many cookies did Caylee make? ","e":"(a) Avery = 521 + 380 = 901. (b) Caylee = 901 - 671 = 230."} {"t":"q","id":14243,"q":"There are a total of 815 tables in Hall X, Hall Y and Hall Z. There are 7 fewer tables in Hall X than Hall Y. There are 4 times as many tables in Hall Z than Hall Y. How many tables are there in Hall Y? ","e":"Let Hall Y = 1 unit. X = 1 unit - 7, Z = 4 units. Total = 6 units - 7 = 815, so 6 units = 822, Hall Y = 822 \/ 6 = 137."} {"t":"q","id":14244,"q":"Mrs Chan poured some soup from a pot into 8 similar bowls. Each bowl had a capacity of 260 ml. She had 1 l 70 ml of soup left in the pot. How much soup did Mrs Chan have in the pot at first? Give your answer in litres and millilitres. ","e":"8 x 260 ml = 2080 ml. 1 l 70 ml = 1070 ml. Total = 2080 + 1070 = 3150 ml = 3 l 150 ml."} {"t":"q","id":14247,"q":"What is three thousand, six hundred and six written as a numeral?","e":"Three thousand = 3000, six hundred = 600, six = 6. So 3000 + 600 + 6 = 3606."} {"t":"q","id":14248,"q":"What is the missing number in the equation below?\n7023 = 7000 + + 3","e":"7023 = 7000 + 20 + 3. The missing number is 20 (the tens place)."} {"t":"q","id":14249,"q":"Arrange the fractions in order from the greatest to the smallest.\n1\/2 , 2\/8 , 5\/7","e":"5\/7 is more than half; 1\/2 = 0.5; 2\/8 = 1\/4 is less than half. Greatest to smallest: 5\/7, 1\/2, 2\/8."} {"t":"q","id":14250,"q":"Express 2080 g in kilograms and grams.","e":"1 kg = 1000 g. 2080 g = 2000 g + 80 g = 2 kg 80 g."} {"t":"q","id":14256,"q":"The length of a rectangular grass patch is 8 m. Its breadth is 7 m. What is the area of the grass patch?
Answer: ","e":"Area of rectangle = length x breadth = 8 x 7 = 56 m\u00b2."} {"t":"q","id":14257,"q":"Write the time 00 10 in 12-hour clock.
Answer: ","e":"00 10 (24-hour) is 10 minutes after midnight, which is 12:10 am in 12-hour clock."} {"t":"q","id":14258,"q":"Axel started to cycle at 11 30. He finished cycling at 13 17. How long did he cycle?\n h min","e":"From 11 30 to 13 00 is 1 h 30 min; from 13 00 to 13 17 is 17 min. Total = 1 h 30 min + 17 min = 1 h 47 min."} {"t":"q","id":14260,"q":"Look at the number patterns. Find the missing number in each number pattern.\n(a) 3699 , 3709 , 3809 , 3819 , 3919 , 3929 , , 4039 , 4139\n(b) , 7489 , 7539 , 7589 , 7639 , 7689","e":"(a) Pattern alternates +10, +100: 3929 + 100 = 4029. (b) Pattern increases by 50: 7489 - 50 = 7439."} {"t":"q","id":14261,"q":"(a) Find the sum of 560 and 1320.\n(b) 8001 - = 2417","e":"(a) 560 + 1320 = 1880. (b) 8001 - 2417 = 5584."} {"t":"q","id":14262,"q":"(a) Michelle bought 5 trays of eggs. Each tray had 8 eggs. How many eggs did Michelle buy altogether?\n(b) Michelle used 4 eggs to bake each cake. How many cakes could she bake with all the eggs that she bought?
(a)   (b) ","e":"(a) 5 x 8 = 40 eggs. (b) 40 \u00f7 4 = 10 cakes."} {"t":"q","id":14266,"q":"A wallet costs $56.90. A water bottle costs $12.50 less than the wallet. How much does the water bottle cost?
Answer: ","e":"$56.90 - $12.50 = $44.40."} {"t":"q","id":14268,"q":"Li Meng started doing her homework at 14 30. She took 1 h to write an English composition. She then took another 1 h 35 min to solve some word problems. What time did she complete her homework?
Answer: ","e":"14 30 + 1 h = 15 30; 15 30 + 1 h = 16 30; 16 30 + 35 min = 17 05, which is 5:05 pm."} {"t":"q","id":14269,"q":"There were some students in the library at first. 18 students left the library. 13 students then went into the library. In the end, there were 312 students left in the library. How many students were there in the library at first?
Answer: ","e":"Work backwards: 312 - 13 = 299 (before the 13 entered); 299 + 18 = 317 (before the 18 left). So 317 students at first."} {"t":"q","id":14270,"q":"Joey has 76 sweets. She packs all the sweets into bags of 3 sweets or bags of 5 sweets. She has 20 bags of sweets after packing. How many bags of 3 sweets are there?
Answer: ","e":"Suppose all 20 bags held 5 sweets: 20 x 5 = 100. That is 100 - 76 = 24 too many. Each bag of 3 instead of 5 reduces the count by 2, so 24 \u00f7 2 = 12 bags of 3 sweets."} {"t":"q","id":14272,"q":"Ali had 128 more stickers than Bala at first. Ali gave 25 stickers to Bala. How many more stickers did Ali have than Bala in the end?
Answer: ","e":"Giving 25 to Bala reduces the gap by 25 twice (Ali loses 25, Bala gains 25), i.e. 25 + 25 = 50. New difference = 128 - 50 = 78."} {"t":"q","id":14273,"q":"There was a total of 756 visitors at the zoo. There were 3 times as many children as adults. How many more children than adults were there?
Answer: ","e":"Children + adults = 4 units = 756, so 1 unit (adults) = 756 \u00f7 4 = 189. Children = 3 units = 567. Difference = 567 - 189 = 378 (or 2 units = 189 x 2 = 378)."} {"t":"q","id":14274,"q":"A total of 382 packets of biscuits were collected for a donation drive on Saturday and Sunday. These biscuits collected were given to families. Each family was given 6 packets of biscuits.\n(a) What was the greatest number of families that received the biscuits?\n(b) 22 more packets of biscuits were collected on Sunday than on Saturday. How many packets of biscuits were collected on Saturday?
(a)   (b) ","e":"(a) 382 \u00f7 6 = 63 remainder 4, so the greatest number of families is 63. (b) 382 - 22 = 360; 360 \u00f7 2 = 180 packets on Saturday."} {"t":"q","id":14275,"q":"A pail contains 5320 ml of water. Meera poured away 4470 ml of water from the pail.\n(a) How much water was left in the pail?\n(b) Meera poured all the water left in the pail equally into 5 identical empty jugs. How much water did she pour into each jug?
(a)   (b) ","e":"(a) 5320 - 4470 = 850 ml left. (b) 850 \u00f7 5 = 170 ml in each jug."} {"t":"q","id":14276,"q":"In 3780, the digit 7 is in the place.","e":"In 3780, reading from the right: 0 ones, 8 tens, 7 hundreds, 3 thousands. So the digit 7 is in the hundreds place."} {"t":"q","id":14279,"q":"Write 4 kg 26 g in grams.","e":"1 kg = 1000 g, so 4 kg = 4000 g. 4000 g + 26 g = 4026 g."} {"t":"q","id":14284,"q":"Noah is 28 kg. Jeremy is 3 kg lighter than Noah. What is their total mass?","e":"Jeremy = 28 - 3 = 25 kg. Total = 28 + 25 = 53 kg."} {"t":"q","id":14285,"q":"Zan had some stickers at first. He gave 138 stickers to each of his 6 friends. He had 3 stickers left. How many stickers did Zan have at first?","e":"He gave away 138 x 6 = 828 stickers. With 3 left over, he had 828 + 3 = 831 stickers at first."} {"t":"q","id":14291,"q":"There are two numbers. The difference between these two numbers is 786. The greater number is 932. Find the sum of these two numbers.
Answer: ","e":"Smaller number = 932 - 786 = 146. Sum = 932 + 146 = 1078."} {"t":"q","id":14292,"q":"There are 17 red apples and 20 green apples in a box. How many apples are there in 7 similar boxes?
Answer: ","e":"Apples in 1 box = 17 + 20 = 37. In 7 boxes = 37 x 7 = 259."} {"t":"q","id":14294,"q":"Both Vic and Dan were at the kitchen. (a) Vic took 1 h 50 min to bake a pizza. He started baking at 08 10. What time did he finish baking the pizza? Ans: (a) (b) Dan took 30 minutes more than Vic to bake a cake. How much time did Dan take to bake the cake? Ans: (b) (c) Dan finished baking the cake at 11 30. What time did he start baking the cake? Leave your answer in 24-hour clock. Ans: (c) ","e":"(a) 08 10 + 1 h 50 min = 10 00. (b) Vic took 1 h 50 min, so Dan took 1 h 50 min + 30 min = 2 h 20 min. (c) 11 30 minus 2 h 20 min = 09 10."} {"t":"q","id":14303,"q":"There were 8009 visitors at the Zoo. 4050 of the visitors were children. How many adults were there?","e":"8009 - 4050 = 3959 adults."} {"t":"q","id":14304,"q":"Peter had 58 apples. He packed them into boxes of 7. How many apples were left unpacked?","e":"58 \u00f7 7 = 8 remainder 2, so 2 apples are left unpacked."} {"t":"q","id":14307,"q":"Mrs Lee left her house at 11.50 a.m. for her baking class. She took 1 h 40 min to travel from her house to her baking class. She arrived 15 minutes before her class started. What time did her baking class start?","e":"11.50 a.m. + 1 h 40 min = 1.30 p.m. arrival; class starts 15 min later = 1.45 p.m."} {"t":"q","id":14308,"q":"Gopal bought a shirt for $45.50 and a belt for $34.90. He gave the cashier $100. How much change would Gopal get?","e":"$45.50 + $34.90 = $80.40; $100 - $80.40 = $19.60."} {"t":"q","id":14309,"q":"Madam Siti bought a pizza. Her daughter ate 3\/8 of the pizza and her son ate 1\/4 of the pizza less than her daughter. What fraction of the pizza was eaten?","e":"Son ate 3\/8 - 1\/4 = 3\/8 - 2\/8 = 1\/8. Total eaten = 3\/8 + 1\/8 = 4\/8 = 1\/2."} {"t":"q","id":14310,"q":"960 people turned up for a school carnival on Saturday. There were 4 times as many people who turned up on Sunday than on Saturday. How many people turned up on both days?","e":"Sunday = 4 x 960 = 3840; both days = 960 + 3840 = 4800."} {"t":"q","id":14311,"q":"A fruit seller had equal number of rambutans and mangosteens. After selling 810 mangosteens, he had 3 times as many rambutans as mangosteens left. How many rambutans did he have?","e":"Let start = R each. After selling, rambutans = R, mangosteens = R - 810, and R = 3(R - 810) \u2192 R = 3R - 2430 \u2192 2R = 2430 \u2192 R = 1215."} {"t":"q","id":14317,"q":"Find the quotient of 537 \u00f7 8. ","e":"537 \u00f7 8 = 67 remainder 1; the quotient is 67. Answer key states 61."} {"t":"q","id":14321,"q":"Mrs Lim had 1248 g of flour. She used 300 g to bake a cake and packed the remaining flour equally into 6 packets. How much flour was there in each packet? g","e":"1248 - 300 = 948 g remaining; 948 \u00f7 6 = 158 g per packet."} {"t":"q","id":14322,"q":"The sum of two numbers is 1750. The value of the smaller number is 795. What is the value of the greater number? ","e":"1750 - 795 = 955."} {"t":"q","id":14325,"q":"Ms Chong bought a piece of cloth which was 5 m long. She used some of it to sew 5 similar towels. There was 185 cm of cloth left. What was the length of cloth used for each towel? cm","e":"5 m = 500 cm; used = 500 - 185 = 315 cm; 315 \u00f7 5 = 63 cm per towel."} {"t":"q","id":14330,"q":"Fadilah needed 45 min to travel from her house to the cinema. When she arrived at the cinema, the time shown on her watch was 12.20 p.m. Her watch was 10 minutes faster. What was the actual time she left her house? a.m.","e":"Watch 10 min fast, so actual arrival = 12.10 p.m. Subtract 45 min travel = 11.25 a.m."} {"t":"q","id":14332,"q":"Ann had 905 stamps and Bala had 299 stamps. Ann had 230 more stamps than Colin. How many more stamps did Colin have than Bala? ","e":"Colin = 905 - 230 = 675; Colin - Bala = 675 - 299 = 376."} {"t":"q","id":14334,"q":"Mrs Lim baked 340 chocolate pies. She packed them equally into boxes of 9. What was the least number of boxes needed by Mrs Lim if she wanted to pack all the chocolate pies into boxes? ","e":"340 \u00f7 9 = 37 remainder 7; one more box is needed for the remaining 7, so 38 boxes."} {"t":"q","id":14335,"q":"Mary had 29 coins. She had 15 one-dollar coins and the rest were fifty-cents and ten-cents coins. She had $20.80 altogether. How many fifty-cents coins did Mary have? ","e":"Remaining coins = 29 - 15 = 14; remaining value = $20.80 - $15.00 = $5.80. If all 14 were 10c = $1.40; extra $4.40 \u00f7 $0.40 (50c\u221210c) = 11 fifty-cents coins."} {"t":"q","id":14336,"q":"Siti had a total of 890 local and foreign stamps. She gave away 130 local stamps and collected another 280 foreign stamps. In the end, she had the same number of local and foreign stamps.\n(a) How many more local than foreign stamps did Siti have at first?\n(b) How many foreign stamps did Siti have at first?\n(a) , (b) ","e":"End total = 890 - 130 + 280 = 1040, equal split = 520 each. Foreign at first = 520 - 280 = 240; local at first = 890 - 240 = 650. (a) 650 - 240 = 410 more local. (b) 240."} {"t":"q","id":14342,"q":"Complete the number pattern. 4852 , 4952 , , 5152","e":"The pattern increases by 100 each time: 4952 + 100 = 5052 (and 5052 + 100 = 5152)."} {"t":"q","id":14343,"q":"The difference between two numbers is 158. The greater number is 419. What is the smaller number?","e":"Smaller number = greater number - difference = 419 - 158 = 261."} {"t":"q","id":14344,"q":"Joel saved $2461. He saved $339 less than Raju. How much money did Raju save?","e":"Joel saved $339 less than Raju, so Raju = 2461 + 339 = $2800."} {"t":"q","id":14347,"q":"Find the difference between 651 and 7040.
Answer: ","e":"7040 - 651 = 6389."} {"t":"q","id":14348,"q":"Xiao Ling had a ribbon 4 m long. She cut the ribbon and gave away two pieces of ribbons each 75 cm long. What was the length of the remaining ribbon? Express your answer in m and cm. m cm","e":"Two pieces = 2 x 75 cm = 150 cm. 4 m = 400 cm. 400 - 150 = 250 cm = 2 m 50 cm."} {"t":"q","id":14353,"q":"Samy left his school at 2.45 p.m. He needed 42 minutes to travel from his school to his home. What time did he reach home? Express your answer in 24-hour clock.
Answer: ","e":"2.45 p.m. + 42 min = 3.27 p.m. In 24-hour clock that is 1527."} {"t":"q","id":14354,"q":"Siti and Mary scored the same number of points in a game at first. Then, Siti won 256 more points and Mary lost 16 points. How many more points did Siti have than Mary in the end?
Answer: ","e":"Starting equal, Siti gained 256 and Mary lost 16, so the gap = 256 + 16 = 272 points."} {"t":"q","id":14355,"q":"Mei Ling, Sarah and Diya had 270 beads. Mei Ling had 3 times as many beads as Sarah. Diya had twice as many beads as Sarah. How many beads did Diya have?
Answer: ","e":"Sarah = 1 unit, Mei Ling = 3 units, Diya = 2 units; total = 6 units = 270, so 1 unit = 45. Diya = 2 x 45 = 90."} {"t":"q","id":14357,"q":"Arrange the fractions 1\/2 , 5\/9 , 2\/3 in order. Begin with the greatest fraction. , , ","e":"Common denominator 18: 1\/2 = 9\/18, 5\/9 = 10\/18, 2\/3 = 12\/18. Greatest to smallest: 2\/3, 5\/9, 1\/2."} {"t":"q","id":14362,"q":"Uncle Tom bought some books. He packed 8 books in each box and found that he had 6 books left. There were 240 boxes altogether. a) How many books did he buy? b) He sold each box of books for $9 and the remaining books at $2 each. How much did he receive altogether? Ans: a) b) $ ","e":"a) 240 x 8 = 1920 books in boxes, + 6 left over = 1926 books. b) 240 boxes x $9 = $2160; 6 books x $2 = $12; total = $2172."} {"t":"q","id":14363,"q":"Aminah had some beads. She used 209 beads to make a necklace. Her mother bought her another 350 beads. She had 632 beads in the end. How many beads did Aminah have at first?
Answer: ","e":"Work backwards: before getting 350 she had 632 - 350 = 282; before using 209 she had 282 + 209 = 491 beads."} {"t":"q","id":14364,"q":"In 8047, what is the value of the digit 0?","e":"The answer key marks option (2). Note: the digit 0 sits in the hundreds place of 8047, so its place value is 0 (option 1) \u2014 the key appears inconsistent here, but per the official key the marked answer is option (2)."} {"t":"q","id":14367,"q":"Sally had 40 pencils. Rebekah had 3 times as many pencils as Sally. How many pencils did both of them have?","e":"Rebekah = 3 x 40 = 120. Both = 40 + 120 = 160."} {"t":"q","id":14368,"q":"A file cost $16.75. A t-shirt cost $67.50 more than the file. How much did the t-shirt cost?","e":"$16.75 + $67.50 = $84.25."} {"t":"q","id":14370,"q":"Find the difference between 3\/4 and 7\/12.","e":"3\/4 = 9\/12. 9\/12 - 7\/12 = 2\/12 = 1\/6."} {"t":"q","id":14374,"q":"9752 = 9 thousands + 7 hundreds + ones","e":"9000 + 700 = 9700. 9752 - 9700 = 52 ones."} {"t":"q","id":14375,"q":"2583 more than a number is 6479. What is 100 more than that number?","e":"The number = 6479 - 2583 = 3896. 100 more = 3896 + 100 = 3996."} {"t":"q","id":14376,"q":"A bus left a bus interchange with 47 people onboard. When it reached the first bus stop, 12 people boarded the bus and some people alighted the bus. There were 23 people on the bus when it left the first bus stop. How many people alighted the bus at the first bus stop?","e":"47 + 12 = 59 on board before alighting. 59 - 23 = 36 alighted."} {"t":"q","id":14377,"q":"Fatin spent $13.60 on a file. She also bought a toy robot which cost $47.90 more than the file. How much did she spend on both items?","e":"Robot = $13.60 + $47.90 = $61.50. Total = $13.60 + $61.50 = $75.10."} {"t":"q","id":14378,"q":"Aunt Amanda had 7 kg of flour at first. After using 6450 g of flour to bake a cake, she packed the remaining flour equally into 5 packets. What was the mass of flour in each packet?","e":"7 kg = 7000 g. 7000 - 6450 = 550 g left. 550 \/ 5 = 110 g per packet."} {"t":"q","id":14379,"q":"Arrange the numbers in decreasing order. 3090, 3900, 930, 9003 , , , ","e":"Decreasing (greatest to smallest): 9003, 3900, 3090, 930."} {"t":"q","id":14380,"q":"Write the missing number in the number pattern. 480 , 581 , 682 , , 884 , 985","e":"The pattern increases by 101 each time. 682 + 101 = 783."} {"t":"q","id":14381,"q":"Aiman had 2389 toy airplanes and 1762 toy cars at first. He gave away 325 toy cars. What was the total number of toy airplanes and cars left in the end? ","e":"Cars left = 1762 - 325 = 1437. Total = 2389 + 1437 = 3826."} {"t":"q","id":14382,"q":"A bookshop had 9 boxes of pencils. Each box contained 6 pencils. The bookshop seller bought another 2 pencils and repacked all the pencils equally into 8 packets. How many pencils were packed into each packet? ","e":"9 x 6 = 54 pencils. 54 + 2 = 56. 56 \/ 8 = 7 per packet."} {"t":"q","id":14383,"q":"Mr Ling prepared some gift packs for Children's Day. There were 8 bars of chocolate and 5 sweets in each gift pack. There was a total of 195 sweets in all the gift packs. How many bars of chocolate were there altogether? ","e":"Number of gift packs = 195 \/ 5 = 39. Chocolate bars = 39 x 8 = 312."} {"t":"q","id":14384,"q":"Anusha wanted to buy a doll that cost $94.75. She had $36.50 in savings and her mother gave her $20. How much more money did she need to buy the doll? ","e":"Money she has = $36.50 + $20 = $56.50. Needed = $94.75 - $56.50 = $38.25."} {"t":"q","id":14386,"q":"Arrange the fractions from the smallest to the greatest. 7\/11, 1\/3, 1\/10 , , ","e":"1\/10 = 0.1, 1\/3 approx 0.33, 7\/11 approx 0.64. Smallest to greatest: 1\/10, 1\/3, 7\/11."} {"t":"q","id":14388,"q":"Ming En had $289.60 at first. After spending $45 on a meal and receiving some money from his mother, he had $300.60. How much money did he receive from his mother? ","e":"After meal: $289.60 - $45 = $244.60. From mother: $300.60 - $244.60 = $56."} {"t":"q","id":14389,"q":"There were 129 fewer students in the canteen than in the hall at first. 329 students moved from the hall to the canteen. How many more students were there in the canteen than in the hall in the end? ","e":"Start gap: hall is 129 more than canteen. Moving 329 from hall to canteen changes the gap by 2 x 329 = 658 in the canteen's favour: -129 + 658 = 529. So canteen has 529 more."} {"t":"q","id":14390,"q":"Rei has 183 stickers. Ali has 129 stickers. How many stickers does Ali have to give to Rei so that Rei has two times the number of stickers that Ali has in the end? ","e":"Total = 183 + 129 = 312. For Rei to be twice Ali, Ali ends with 312 \/ 3 = 104. Rei ends with 208. Ali must give 129 - 104 = 25 stickers (check: 183 + 25 = 208 = 2 x 104)."} {"t":"q","id":14391,"q":"What is four thousand, one hundred and sixty-two in numbers?","e":"Four thousand = 4000, one hundred = 100, sixty-two = 62. 4000 + 100 + 62 = 4162."} {"t":"q","id":14395,"q":"2\/3 + 1\/6 =","e":"2\/3 = 4\/6. 4\/6 + 1\/6 = 5\/6."} {"t":"q","id":14396,"q":"Mdm Sari left her house at 06 55. She took 1 h 15 min to reach her office. What time did Mdm Sari reach her office?","e":"06 55 + 1 h = 07 55. 07 55 + 15 min = 08 10."} {"t":"q","id":14397,"q":"Paul bought 3 packets of sweets. James bought twice as many packets of sweets as Paul. There were 27 sweets in each packet. How many sweets did James buy?","e":"James bought 3 x 2 = 6 packets. 6 x 27 = 162 sweets."} {"t":"q","id":14400,"q":"What is \\(\\dfrac{3}{4}\\) - \\(\\dfrac{5}{8}\\) ?","e":"3\/4 = 6\/8. 6\/8 - 5\/8 = 1\/8."} {"t":"q","id":14401,"q":"Lando bought a toy. He gave the cashier $10 and received a change of $3.75. How much did the toy cost? $","e":"$10.00 - $3.75 = $6.25."} {"t":"q","id":14402,"q":"A pencil case costs $8. A book costs $13 more than the pencil case. Caesar bought 2 such books and one such pencil case. How much money did Caesar spend altogether? $","e":"Book = $8 + $13 = $21. 2 books = $42. Total = $42 + $8 = $50.00."} {"t":"q","id":14404,"q":"A soccer match started at 23 30 and ended at 01 08 the next day. What was the duration of the soccer match? h min","e":"23 30 to 00 30 is 1 h. 00 30 to 01 08 is 38 min. Total 1 h 38 min."} {"t":"q","id":14409,"q":"There are 24 cars and motorcycles altogether. There is a total number of 76 wheels. Each car has 4 wheels and each motorcycle has 2 wheels. How many cars are there? ","e":"If all 24 were motorcycles: 24 x 2 = 48 wheels. Extra wheels = 76 - 48 = 28. Each car adds 2 extra wheels, so cars = 28 \/ 2 = 14."} {"t":"q","id":14410,"q":"Mr Hoh had 972 satay sticks. He packed the satay sticks equally into 9 containers. How many satay sticks were there in 7 such containers? ","e":"972 \/ 9 = 108 sticks per container. 108 x 7 = 756."} {"t":"q","id":14411,"q":"Lionel wanted to run 1 km 50 m. He completed 2 rounds on a running track. Each round is 400 m. How much further did he have to run? m","e":"1 km 50 m = 1050 m. 2 rounds = 400 x 2 = 800 m. 1050 - 800 = 250 m."} {"t":"q","id":14414,"q":"Ryan had some marbles. Ben had four times as many marbles as Ryan. Doris had 36 marbles more than Ben. The three children had 270 marbles altogether.\n(a) How many marbles did Ryan have? \n(b) Ryan and Ben decided to share their marbles equally. How many marbles did Ben give Ryan? ","e":"(a) Ryan + Ben + Doris = 270. 270 - 36 = 234 = 9 units (Ryan 1 + Ben 4 + Doris 4). 234 \/ 9 = 26 = Ryan. (b) Ben = 26 x 4 = 104; Ryan = 26. Total 130, each gets 65. Ben gives 104 - 65 = 39."} {"t":"s","id":7060,"s":"Using a common denominator of 12: 2\/3 = 8\/12, 2\/6 = 4\/12, 3\/4 = 9\/12. Greatest to smallest: 9\/12, 8\/12, 4\/12, i.e. 3\/4, 2\/3, 2\/6."} {"t":"s","id":7061,"s":"1\/2 = 3\/6 and 1\/3 = 2\/6, so she used 3\/6 + 2\/6 = 5\/6. Left = 6\/6 - 5\/6 = 1\/6."} {"t":"s","id":7062,"s":"Children = 1 unit, adults = 4 units, total = 5 units = 420. 1 unit = 420 \/ 5 = 84 children."} {"t":"s","id":7065,"s":"1615 + 1 h = 1715. 1715 + 55 min = 1810 (17:15 plus 45 min = 18:00, plus 10 min = 18:10)."} {"t":"s","id":7066,"s":"Total = 4 m = 400 cm. The extra 1 m 20 cm = 120 cm. Removing the extra: 400 - 120 = 280 cm for two equal parts. Red ribbon = 280 \/ 2 = 140 cm."} {"t":"s","id":7067,"s":"260 \/ 6 = 43 remainder 2. The 2 leftover pencils still need a bag, so 43 + 1 = 44 bags."} {"t":"s","id":7070,"s":"(a) Alfred lost 12 and Bala gained 12, so the difference between them is 12 + 12 = 24 marbles. (b) Alfred had 65 at the end; at first both had 65 + 12 = 77. Bala in the end = 77 + 12 = 89."} {"t":"s","id":7076,"s":"148 \/ 6 = 24 remainder 4. So 4 pencils were left unpacked."} {"t":"s","id":7078,"s":"Coins are 20c and 50c. $2.70 = 1 twenty-cent + 5 fifty-cent (20c + 250c = 270c). $3.00 needs more than she has (max = 60c + 250c = 310c, but cannot make exactly 300c with these coins), $0.80 and $1.80 cannot be formed exactly; $2.70 is achievable."} {"t":"s","id":7080,"s":"Comparing 3\/10, 1\/2, 2\/3, 2\/5: 3\/10 = 0.3, 1\/2 = 0.5, 2\/3 \u2248 0.67, 2\/5 = 0.4. Smallest is 3\/10."} {"t":"s","id":7081,"s":"115 min = 1 h 55 min. 18 30 + 1 h = 19 30; 19 30 + 55 min = 20 25."} {"t":"s","id":7083,"s":"After receiving 18, Max had 44, so Max had 44 - 18 = 26 at first. James had 3 x 26 = 78 at first."} {"t":"s","id":7086,"s":"In 2856 the digit 8 is in the hundreds place (value 800). In 6825 the digit 8 is in the hundreds place (value 800). The digit 8 has the same value in both."} {"t":"s","id":7089,"s":"Common denominator 12: 1\/3 = 4\/12, 5\/6 = 10\/12, 5\/12 = 5\/12. Greatest to smallest: 10\/12, 5\/12, 4\/12 \u2192 5\/6, 5\/12, 1\/3."} {"t":"s","id":7090,"s":"From 6:20 a.m. to 7:15 a.m. is 55 minutes (6:20 to 7:20 is 60 min, minus 5 min = 55 min)."} {"t":"s","id":7091,"s":"Total stays 135. After transfer: 5 units = 135, 1 unit = 27 (Angel after giving). Angel originally = 27 + 16 = 43."} {"t":"s","id":7092,"s":"Mrs Tan now = 5 x 9 = 45 years old. In 10 years: 45 + 10 = 55 years old."} {"t":"s","id":7097,"s":"The gap must shrink from 40 to 8, a reduction of 32. Each marble Ethan gives reduces the gap by 2, so he gives 32 \/ 2 = 16 marbles."} {"t":"s","id":7098,"s":"Simon at first = 120 + 88 = 208. Mark had 50 fewer than Simon at first: 208 - 50 = 158."} {"t":"s","id":7103,"s":"(a) 286 + 365 = 651 cupcakes baked. (b) 651 - 483 = 168 cupcakes left."} {"t":"s","id":7104,"s":"4 l = 4000 ml. When 860 ml more is needed, tank holds 4000 - 860 = 3140 ml. Water poured in = 3140 - 1850 = 1290 ml = 1 l 290 ml."} {"t":"s","id":7105,"s":"Common denominator 12: 1\/3 = 4\/12, 1\/6 = 2\/12, 1\/4 = 3\/12. Spent = 4\/12 + 2\/12 + 3\/12 = 9\/12. Left = 12\/12 - 9\/12 = 3\/12 = 1\/4."} {"t":"s","id":7106,"s":"(a) 09 00 to 18 00 = 9 hours per day. (b) Per week: 9 x 6 = 54 hours; in 4 weeks: 54 x 4 = 216 hours."} {"t":"s","id":7107,"s":"Total = 3 units (Shop B) + 487 + 243 = 1000, so 3 units = 1000 - 730 = 270, 1 unit (Shop B) = 90. Shop A = 90 + 487 = 577. Shop C = 90 + 243 = 333. (b) 577 - 333 = 244."} {"t":"s","id":7108,"s":"Ryan = 1 unit, Ivan = 2 units, Thaddeus = 2 units + 56. Total = 5 units + 56 = 381, so 5 units = 325, 1 unit = 65. (a) Thaddeus = 2 x 65 + 56 = 186. (b) Ryan = 65 + 100 = 165."} {"t":"s","id":7109,"s":"2 thousands = 2000, 2 tens = 20. 2000 + 20 = 2020."} {"t":"s","id":7113,"s":"5 km = 5000 m. 5000 m + 9 m = 5009 m."} {"t":"s","id":7114,"s":"2 h = 120 min. 120 + 18 = 138 min."} {"t":"s","id":7115,"s":"Convert to twelfths: 2\/3 = 8\/12, 1\/4 = 3\/12, 5\/12. Order smallest to greatest: 3\/12, 5\/12, 8\/12, i.e. 1\/4, 5\/12, 2\/3."} {"t":"s","id":7118,"s":"Larger number = 1780 + 670 = 2450. Sum = 1780 + 2450 = 4230."} {"t":"s","id":7119,"s":"Karthi = 3 x $249 = $747. Together = $249 + $747 = $996."} {"t":"s","id":7121,"s":"15 minutes to seven = 6.45 p.m. From 6.45 to 7.25 is 40 minutes."} {"t":"s","id":7125,"s":"Each term decreases by 240. 4210 - 240 = 3970."} {"t":"s","id":7128,"s":"1\/4 = 2\/8. 2\/8 + 5\/8 = 7\/8."} {"t":"s","id":7132,"s":"Lynn = 5 x 58 = 290. Total = 290 + 58 = 348. Each should have 348 \/ 2 = 174. Lynn must give 290 - 174 = 116 stickers."} {"t":"s","id":7135,"s":"10\/12 = 5\/6 = 15\/18. Multiply numerator and denominator by the same factor: 6 x 3 = 18, 5 x 3 = 15."} {"t":"s","id":7137,"s":"If all 17 were $2 notes, value = $34. Extra needed = $49 - $34 = $15. Each $5 note adds $3 over a $2 note, so $15 \/ $3 = 5 five-dollar notes."} {"t":"s","id":7138,"s":"Girls = 960 - 395 = 565. Children = 960 + 565 = 1525."} {"t":"s","id":7139,"s":"Remove the extra 30: 180 - 30 = 150. Each share = 150 \/ 2 = 75. Jill has 75 cookies."} {"t":"s","id":7140,"s":"Remove Pravin's extra 34: 442 - 34 = 408. This equals 6 units of Hadi (Hadi 1 + Larry 4 + Pravin 1). 408 \/ 6 = 68 stamps for Hadi."} {"t":"s","id":7142,"s":"(a) 10 x 330 = 3300 ml; 3300 + 800 = 4100 ml = 4 l 100 ml. (b) 4100 - 590 = 3510 ml = 3 l 510 ml served."} {"t":"s","id":7144,"s":"An even number ends in an even digit. To be smallest, put smallest digits first: 2, 3, then last digit must be even. Remaining digits 7 and 6; smallest hundreds is 3, so 23_6 -> 2376 (ends in even 6)."} {"t":"s","id":7146,"s":"Compare each to 1\/2. 2\/3>1\/2, 3\/7<1\/2 (since 3.5\/7=1\/2), 3\/5>1\/2, 2\/4=1\/2. Only 3\/7 is smaller than 1\/2."} {"t":"s","id":7147,"s":"5 m = 500 cm. Used = 125 cm + 85 cm = 210 cm. Left = 500 - 210 = 290 cm."} {"t":"s","id":7153,"s":"Convert to a common comparison: 1\/3 = 0.333, 4\/9 = 0.444, 3\/6 = 0.5. Smallest to biggest: 1\/3, 4\/9, 3\/6."} {"t":"s","id":7154,"s":"From 1st to 4th stick there are 3 gaps = 24 cm, so each gap = 8 cm. From 1st to last = 56 cm = 56 \/ 8 = 7 gaps, so number of sticks = 7 + 1 = 8."} {"t":"s","id":7155,"s":"Highlighter + stapler = $12 - $5.30 = $6.70, which is more than the file's $5.30. So the statement that their total was less than the file is False."} {"t":"s","id":7159,"s":"a) Farhan = 5070 - 1094 = 3976 bricks. b) Altogether = 5070 + 3976 = 9046 bricks."} {"t":"s","id":7160,"s":"Dining-room clock showed 19 20 at the end; it was 10 min slow, so actual end time = 19 30. The dinner lasted 1 h 30 min, so actual start = 19 30 - 1 h 30 min = 18 00."} {"t":"s","id":7161,"s":"1\/4 of 12 = 3 pieces to niece; 4 pieces to neighbour; given away = 7 pieces. Left = 12 - 7 = 5 pieces = 5\/12 (already simplest)."} {"t":"s","id":7162,"s":"Let Eileen = 1 unit, Annie = 3 units, Linda = 3 units - 75. Total = 1u + 3u + 3u - 75 = 7u - 75 = 919, so 7u = 994, u = 142. Eileen made 142."} {"t":"s","id":7166,"s":"10 tens = 100. 5467 - 100 = 5367."} {"t":"s","id":7168,"s":"9 thousands = 9000, 7 tens = 70. Total = 9070."} {"t":"s","id":7172,"s":"Nine thousand = 9000, six hundred = 600, six = 6. Total = 9606."} {"t":"s","id":7174,"s":"The pattern increases by 150 each time. 2949 + 150 = 3099."} {"t":"s","id":7185,"s":"A number with remainder 6 when divided by 9 fits 9k + 6. Testing: 54 = 9x6 r0; 66 = 9x7 r3; 72 = 9x8 r0; 78 = 9x8 + 6, remainder 6. So 78 is the possible number."} {"t":"s","id":7186,"s":"Mary = 1 unit, Sandra = 3 units, total 4 units = 288. 1 unit = 288 div 4 = 72."} {"t":"s","id":7192,"s":"259 div 5 = 51 remainder 4. So 4 eggs were left unpacked."} {"t":"s","id":7196,"s":"Jim = 523 + 155 = 678. Tom = 678 x 3 = 2034 apples."} {"t":"s","id":7199,"s":"Convert to grams: 17 kg = 17000 g; 807 g; 8700 g; 1 kg 70 g = 1070 g. Largest is 17 kg."} {"t":"s","id":7201,"s":"3\/8 = 9\/24 (x3) and 3\/8 = 18\/48 (x6). So (a) = 9, (b) = 48."} {"t":"s","id":7202,"s":"As decimals: 2\/9 \u2248 0.22, 1\/2 = 0.5, 3\/4 = 0.75, 7\/8 = 0.875. Smallest to largest: 2\/9, 1\/2, 3\/4, 7\/8."} {"t":"s","id":7205,"s":"1\/3 = 2\/6. 5\/6 - 2\/6 = 3\/6 = 1\/2."} {"t":"s","id":7210,"s":"1\/5 = 2\/10. 3\/10 - 2\/10 = 1\/10."} {"t":"s","id":7211,"s":"2\/5 = 4\/10. 3\/10 + 4\/10 = 7\/10."} {"t":"s","id":7212,"s":"4 thousands = 4000, 3 tens = 30, 8 ones = 8. 4000 + 30 + 8 = 4038."} {"t":"s","id":7215,"s":"Product means multiply. 6 \u00d7 9 = 54."} {"t":"s","id":7216,"s":"7 \u00d7 89 = 623, and 625 - 623 = 2. So quotient = 89, remainder = 2."} {"t":"s","id":7218,"s":"Sweets in packets = 8 \u00d7 6 = 48. Add the leftover: 48 + 4 = 52."} {"t":"s","id":7220,"s":"Day 1 = 6. Day 2 = 6 \u00d7 2 = 12. Day 3 = 12 \u00d7 2 = 24."} {"t":"s","id":7222,"s":"Chocolate muffins = 2961 + 584 = 3545. Altogether = 3545 + 2961 = 6506."} {"t":"s","id":7223,"s":"In 5293, reading from the right: 3 ones, 9 tens, 2 hundreds, 5 thousands. So 9 is in the tens place."} {"t":"s","id":7225,"s":"8x4=32, 8x5=40, 8x6=48, 8x7=56. All are multiples of 8."} {"t":"s","id":7231,"s":"Pattern alternates +100 then +1000: 1305 (+100) 1405 (+1000) 2405 (+100) 2505 (+1000) 3505 (+100) 3605 (+1000) 4605 (+100) 4705 (+1000) 5705. Missing term is 3505."} {"t":"s","id":7234,"s":"After giving away 20, Ali had 230 - 20 = 210 stickers. Lena had 34 fewer than Ali: 210 - 34 = 176 stickers."} {"t":"s","id":7235,"s":"(a) Bags = 504 \/ 6 = 84 bags. (b) Total cost = 504 x $2 = $1008."} {"t":"s","id":7241,"s":"As decimals: 3\/7 about 0.43, 1\/2 = 0.5, 7\/12 about 0.58, 7\/8 = 0.875. Smallest to greatest: 3\/7, 1\/2, 7\/12, 7\/8."} {"t":"s","id":7243,"s":"8 x 3 = 24, so multiply the numerator by 3: 3 x 3 = 9. So 3\/8 = 9\/24."} {"t":"s","id":7248,"s":"Total cookies = 72 x 9 = 648. After eating 15: 648 - 15 = 633."} {"t":"s","id":7249,"s":"Let Nicole = N. Johnson = 3N, Santhi = N - 6. Total: 3N + N + (N - 6) = 314 -> 5N - 6 = 314 -> 5N = 320 -> N = 64."} {"t":"s","id":7257,"s":"Compare by place value: 4227 < 4727 < 4772. Increasing order: 4227, 4727, 4772."} {"t":"s","id":7258,"s":"(a) 4105 > 2398. (b) 38 + 21 = 59 and 46 + 37 = 83, so 59 < 83."} {"t":"s","id":7259,"s":"The pattern decreases by 100 each time. 4027 - 100 = 3927."} {"t":"s","id":7260,"s":"The pattern alternates +1 then +100. After 6474 the next step is +1, giving 6475."} {"t":"s","id":7261,"s":"Greatest = 9057, smallest = 1726. 9057 - 1726 = 7331."} {"t":"s","id":7263,"s":"Between 5000 and 8000 the thousands digit must be 6. To be even and greatest, the ones digit must be 8, then the remaining digits 3 and 1 go in descending order: 6318."} {"t":"s","id":7264,"s":"Amy = 685 + 134 = 819. Altogether = 685 + 819 = 1504."} {"t":"s","id":7265,"s":"(a) Greater = 3480 + 2307 = 5787. (b) Sum = 3480 + 5787 = 9267."} {"t":"s","id":7277,"s":"Eileen = 1 unit, Dawn = 3 units, total = 4 units = 188. 1 unit = 188 \u00f7 4 = 47, so Eileen has 47 stamps."} {"t":"s","id":7278,"s":"102 \u00f7 8 = 12 r 6. The 6 leftover cupcakes need 1 more box, so 12 + 1 = 13 boxes."} {"t":"s","id":7281,"s":"She needed 100 + 17 = 117 balloons. Pupils = 117 \u00f7 3 = 39."} {"t":"s","id":7282,"s":"Freya = 16 x 7 = 112. Gerald = 112 \u00f7 2 = 56."} {"t":"s","id":7287,"s":"4\/5 = 0.8. 2\/3 \u2248 0.67, 5\/8 = 0.625, 7\/10 = 0.7, 6\/7 \u2248 0.857. Only 6\/7 > 0.8. Answer key option (4)."} {"t":"s","id":7291,"s":"Using ninths: 2\/3 = 6\/9 and 8\/9. A fraction between them is 7\/9. Answer key: 7\/9."} {"t":"s","id":7292,"s":"As decimals: 1\/2 = 0.5, 5\/8 = 0.625, 4\/9 \u2248 0.444, 5\/6 \u2248 0.833. Greatest to smallest: 5\/6, 5\/8, 1\/2, 4\/9. Answer key order."} {"t":"s","id":7298,"s":"Six thousand = 6000, and forty-five = 45. 6000 + 45 = 6045."} {"t":"s","id":7302,"s":"The pattern increases by 35 each time. 4170 + 35 = 4205."} {"t":"s","id":7305,"s":"Women = 6169 - 4096 = 2073. Men - women = 4096 - 2073 = 2023."} {"t":"s","id":7324,"s":"Convert to cm: Amy 109, Ben 162, Charlie 105, Dora 170. Shortest to tallest: Charlie, Amy, Ben, Dora."} {"t":"s","id":7326,"s":"2\/A = 4\/12 means A = 6. B\/36 = 4\/12 = 1\/3, so B = 12."} {"t":"s","id":7328,"s":"a) Same numerator: smaller denominator is greater, so 3\/7 > 3\/8 > 3\/11. b) Values: 2\/11 (~0.18), 4\/8 (0.5), 9\/10 (0.9), so smallest first = 2\/11, 4\/8, 9\/10."} {"t":"s","id":7329,"s":"(a) 2\/9 + 6\/9 = 8\/9. (b) 1 - 8\/9 = 1\/9."} {"t":"s","id":7330,"s":"Total capacity = 600 x 4 = 2400 m\u2113. Water at first = 2400 - 450 = 1950 m\u2113."} {"t":"s","id":7334,"s":"Nine thousand, seven hundred and twelve = 9712. Four thousand, six hundred and four = 4604 (zero tens)."} {"t":"s","id":7335,"s":"Between 2600 and 2900 means it starts with 2 then 8 (2800s). Using remaining digits 4 and 5, an even number ends in 4: 2854."} {"t":"s","id":7336,"s":"The pattern increases by 300 each time. 4181 - 300 = 3881."} {"t":"s","id":7337,"s":"Siti = 1352 + 1515 = 2867. Altogether = 1352 + 2867 = 4219 (i.e. 1352 x 2 + 1515)."} {"t":"s","id":7339,"s":"(a) 3390 - 1900 = 1490 children. (b) Friday had 685 fewer than Saturday, so Saturday = 3390 + 685 = 4075."} {"t":"s","id":7344,"s":"492 \/ 5 = 98 remainder 2. The leftover 2 cupcakes need 1 more box, so 98 + 1 = 99 boxes."} {"t":"s","id":7345,"s":"Red marbles = 236 x 9 = 2124. After giving away 100: 2124 - 100 = 2024."} {"t":"s","id":7346,"s":"230 \/ 6 = 38 remainder 2. So 38 students each received 6 pencils, with 2 left over."} {"t":"s","id":7357,"s":"(a) Greatest even: end in an even digit, largest first: 8712. (b) Smallest odd: end in an odd digit, smallest first: 1287."} {"t":"s","id":7358,"s":"Dash started with 47 - 12 = 35; both started equal at 35. Luke gave away 12, so Luke had 35 - 12 = 23 marbles."} {"t":"s","id":7359,"s":"(a) Strawberry = 594 - 128 = 466. (b) Total = 594 + 466 = 1060."} {"t":"s","id":7361,"s":"Nine thousand = 9000, eight hundred = 800, fifty = 50. 9000 + 800 + 50 = 9850."} {"t":"s","id":7365,"s":"Two $50 notes = $100. $100 - $72.15 = $27.85."} {"t":"s","id":7366,"s":"The pattern decreases by 3, then 5, alternating: -3, -5, -3, -5... After 912: 912 - 3 = 909, then 909 - 5 = 904."} {"t":"s","id":7367,"s":"In 5847 the digit 5 has value 5000. In 250 the digit 5 has value 50. 5000 + 50 = 5050."} {"t":"s","id":7369,"s":"a) In 1098 the digit 9 is in the tens place, so False. b) 1908 > 1098 is True. c) The greatest 4-digit number from 1,9,8,0 is 9810, not 9108, so False."} {"t":"s","id":7373,"s":"9008 (adults) > 8009 (children), so there were more adults. Difference = 9008 - 8009 = 999."} {"t":"s","id":7379,"s":"Ben = 1 unit, Alice = 4 units, total = 5 units = 180. 1 unit = 180 \u00f7 5 = 36. Ben has 36 stamps."} {"t":"s","id":7386,"s":"a) 5\u00d78 = 40, 6\u00d78 = 48; 40 is 8 less than 48. b) 7\u00d76 = 42, 6\u00d76 = 36; 42 is 6 more than 36."} {"t":"s","id":7387,"s":"The 3-digit number \u00d7 7 = 2646, so the number is 2646 \u00f7 7 = 378. The missing hundreds digit is 3."} {"t":"s","id":7390,"s":"Beads given away = 720 - 24 = 696. Each friend got 696 \u00f7 4 = 174."} {"t":"s","id":7395,"s":"a) 80 + 64 = 144 children. b) 144 \u00d7 6 = 864 paper flowers."} {"t":"s","id":7396,"s":"a) 235 \u00d7 7 = 1645 pins. b) One box has 235 pins; after giving 61 away, 235 - 61 = 174 remain; 174 \u00f7 6 = 29 pins per packet."} {"t":"s","id":7398,"s":"3\/8 = 0.375 and 5\/6 \u2248 0.833, so 3\/8 < 5\/6 is correct. The others are false."} {"t":"s","id":7399,"s":"200 cm + 9 cm = 209 cm. 209 cm = 2 m 9 cm (since 100 cm = 1 m)."} {"t":"s","id":7400,"s":"Convert all to metres: 2540 m; 2 km 54 m = 2054 m; 2 km 504 m = 2504 m; 20 m 54 cm = 20.54 m. The longest is 2540 m."} {"t":"s","id":7401,"s":"As decimals: 1\/3\u22480.333, 4\/7\u22480.571, 4\/9\u22480.444, 8\/9\u22480.889. Greatest to smallest: 8\/9, 4\/7, 4\/9, 1\/3."} {"t":"s","id":7412,"s":"1 l = 1000 ml. One cup = 1000 - 350 = 650 ml. 3 cups = 650 \u00d7 3 = 1950 ml."} {"t":"s","id":7428,"s":"Ally = 3463 - 445 = 3018. Altogether = 3018 + 3463 = $6481."} {"t":"s","id":7429,"s":"Total boxes = 216 \/ 9 = 24. Boxes left = 24 - 18 = 6."} {"t":"s","id":7430,"s":"(a) Bags = 128 \/ 8 = 16. (b) Sweets = 4 x 16 = 64."} {"t":"s","id":7438,"s":"1 - 1\/4 = 3\/4 = 9\/12. So A\/12 + 1\/12 = 9\/12, A\/12 = 8\/12, A = 8."} {"t":"s","id":7441,"s":"Common denominator 10: 3\/5 = 6\/10, 1\/2 = 5\/10, 7\/10 = 7\/10. Greatest to smallest: 7\/10, 3\/5, 1\/2."} {"t":"s","id":7443,"s":"Dress = 80.00 - 33.40 = 46.60. Altogether = 80.00 + 46.60 = $126.60."} {"t":"s","id":7446,"s":"50 \/ 8 = 6 remainder 2. (a) 6 toy cars. (b) $2 left."} {"t":"s","id":7454,"s":"Total bags = 8 + 1 = 9. Oranges = 9 x 4 = 36."} {"t":"s","id":7457,"s":"Blue = 1 unit, red = 2 units, total = 3 units = 84. Blue = 84 \/ 3 = 28."} {"t":"s","id":7459,"s":"Pete and 3 boys = 4 boys. Each = 204 \/ 4 = 51."} {"t":"s","id":7461,"s":"Total sold = 5600 - 440 = 5160. Sunday = 5160 - 1250 = 3910."} {"t":"s","id":7462,"s":"(a) Simon end 60 = start - 120, so start = 60 + 120 = 180; both had 180. (b) Tim end = 180 + 85 = 265; difference = 265 - 60 = 205."} {"t":"s","id":7464,"s":"(a) New girl-boy difference = 45 + 8 + 5 = 58. (b) Boys + girls = 640 and girls = boys + 58, so 2 x boys + 58 = 640; boys = (640 - 58) \/ 2 = 291."} {"t":"s","id":7467,"s":"(a) 5 km = 5000 m, so 5 km 18 m = 5018 m. (b) 4109 m = 4000 m + 109 m = 4 km 109 m."} {"t":"s","id":7469,"s":"With the same numerator, the smaller the denominator the larger the fraction. So 2\/3 > 2\/5 > 2\/9."} {"t":"s","id":7471,"s":"From 8 a.m. to 9 a.m. is 1 hour; from 9 a.m. to 9.05 a.m. is 5 minutes. Total 1 h 5 min."} {"t":"s","id":7478,"s":"(a) 2 litres = 2000 ml; poured out = 2000 - 1125 = 875 ml. (b) Each glass = 875 \/ 7 = 125 ml."} {"t":"s","id":7479,"s":"Women = 468 \/ 2 = 234. (a) Men = 234 + 50 = 284. (b) Total = 468 + 234 + 284 = 986."} {"t":"s","id":7480,"s":"Remove Jon's extra 46: 320 - 46 = 274. Split equally: May = 274 \/ 2 = 137."} {"t":"s","id":7482,"s":"8\/12 = 2\/3. 2\/3 - 1\/3 = 1\/3 = 2\/6, so the missing numerator is 2."} {"t":"s","id":7488,"s":"They started equal. Hong Wei gives 28 away (his count drops by 28) and Benson gains 28, so the difference is 28 + 28 = 56."} {"t":"s","id":7489,"s":"3 units = 825, so 1 unit (Kelly) = 275. Melissa = 550. Difference = 550 - 275 = 275."} {"t":"s","id":7491,"s":"Jerry = 2\/6 = 8\/24, Joel = 3\/8 = 9\/24, Jane = 4\/12 = 8\/24. 9\/24 is the largest, so Joel ate the most."} {"t":"s","id":7493,"s":"6 \u2113 = 6000 m\u2113. 6000 m\u2113 + 8 m\u2113 = 6008 m\u2113."} {"t":"s","id":7495,"s":"4 \u00d7 9 = 36. 3 groups of ? = 36, so ? = 36 \u00f7 3 = 12."} {"t":"s","id":7496,"s":"Half of 7 is 3.5, so 4\/7 > 1\/2. 5\/10 = 1\/2 exactly; 3\/7 and 2\/5 are less than 1\/2."} {"t":"s","id":7508,"s":"2\/3 = 8\/12. 1\/12 + 8\/12 = 9\/12 = 3\/4."} {"t":"s","id":7509,"s":"4\/11 = 12\/33 (multiply top and bottom by 3). 4\/11 = 20\/55 (multiply top and bottom by 5). So (a) = 12, (b) = 55."} {"t":"s","id":7510,"s":"Watch is 15 min slow, so actual stop time = 8.05 p.m. + 15 min = 8.20 p.m. Run lasted 135 min (2 h 15 min), so start = 8.20 p.m. \u2212 2 h 15 min = 6.05 p.m."} {"t":"s","id":7511,"s":"Smaller number = 2034 \u2212 1406 = 628. Sum = 2034 + 628 = 2662."} {"t":"s","id":7512,"s":"11 m = 1100 cm. 1100 \u2212 263 = 837 cm used for the pieces. 837 \u00f7 9 = 93 cm each."} {"t":"s","id":7513,"s":"(a) Alvin = 2 \u00d7 Bala and Caleb < Bala < Alvin, so Alvin definitely has more than Caleb \u2014 True. (b) Alvin + Bala = 3 parts of Bala; with Caleb fewer than Bala there are several possible values for Caleb, so the exact number cannot be determined \u2014 Not possible to tell."} {"t":"s","id":7515,"s":"In the end Pete had 285 more than Ken: 1527 + 285 = 1812 marbles. Pete bought 1812 \u2212 1037 = 775 marbles."} {"t":"s","id":7520,"s":"Like fractions: add numerators, keep denominator. 5\/7 + 1\/7 = 6\/7."} {"t":"s","id":7524,"s":"40 \/ 6 = 6 R 4. The 4 leftover oranges need another bag, so 7 bags."} {"t":"s","id":7535,"s":"(a) 376 + 825 = 1201. (b) 1000 - 781 = 219."} {"t":"s","id":7536,"s":"Pears = 936 \/ 6 = 156. Apples + pears = 936 + 156 = 1092."} {"t":"s","id":7537,"s":"(a) 750 x 8 = 6000. (b) 649 \/ 9 = 72 remainder 1."} {"t":"s","id":7539,"s":"Square perimeter = 9 x 4 = 36 cm. Rectangle: 36 - 2 x 12 = 12; breadth = 12 \/ 2 = 6 cm."} {"t":"s","id":7540,"s":"Watch is 15 min slow, so correct stop time = 10 20 + 15 min = 10 35. Start = 10 35 - 2 h 30 min = 08 05."} {"t":"s","id":7541,"s":"Cost = 10 x $0.55 = $5.50. Nora has 3 x $2 = $6. Left = $6 - $5.50 = $0.50."} {"t":"s","id":7542,"s":"Doubling: Day1=10, 2=20, 3=40, 4=80, 5=160, 6=320. So Day 6."} {"t":"s","id":7543,"s":"(a) Yellow = 1289 - 475 = 814. (b) Blue total = 475 + 1256 = 1731."} {"t":"s","id":7544,"s":"In boxes: 720 x 9 = 6480 g. Plus leftover: 6480 + 600 = 7080 g = 7 kg 80 g."} {"t":"s","id":7545,"s":"Gary has 1548. Vanessa ends with 125 more than Gary: 1548 + 125 = 1673. She bought 1673 - 758 = 915 cards."} {"t":"s","id":7551,"s":"2\/3 = 4\/6 = 6\/9 = 8\/12. 4\/9 is not equal to 2\/3, so it is the odd one out."} {"t":"s","id":7556,"s":"Giving 14 coins from Dawn to Amy reduces the gap by 2 x 14 = 28. 67 - 28 = 39."} {"t":"s","id":7558,"s":"The pattern alternates +5, +10: 743, 748, 758, 763, 773, 778, 788, 793. The missing term is 778."} {"t":"s","id":7565,"s":"74 \/ 9 = 8 remainder 2. The leftover 2 students still need a van, so 8 + 1 = 9 vans."} {"t":"s","id":7566,"s":"Movie started at 1.25 + 10 min = 1.35 p.m. It ended at 1.35 + 1 h 15 min = 2.50 p.m."} {"t":"s","id":7568,"s":"Total of 5 units = 180, so 1 unit = 180 \/ 5 = 36. Ali has 4 units = 4 x 36 = 144."} {"t":"s","id":7569,"s":"a) Gaps between 1st and 14th = 14 - 1 = 13. b) Total distance = 13 x 6 = 78 m."} {"t":"s","id":7570,"s":"4 T-shirts + 4 pairs of shorts = 4 x $27 = $108. The extra 1 pair of shorts = $116 - $108 = $8."} {"t":"s","id":7571,"s":"a) Brenda = 985 - 487 = 498; Chloe = 498 + 98 = 596. b) Amir's blueberry = 985 - 468 = 517; left = 517 - 274 = 243."} {"t":"s","id":7575,"s":"From greatest to smallest: 653, 635, 563, 536. Each number is smaller than the one before it."} {"t":"s","id":7577,"s":"The pattern increases by 210 each time. 3835 + 210 = 4045."} {"t":"s","id":7579,"s":"12\/18 simplifies to 2\/3. To get a numerator of 8, multiply 2\/3 by 4\/4 to get 8\/12, so the missing number is 12."} {"t":"s","id":7581,"s":"Subtract 1 hour 50 minutes from 12 00. 12 00 minus 1 hour = 11 00; minus 50 minutes = 10 10."} {"t":"s","id":7586,"s":"Using a common denominator of 60: 2\/5 = 24\/60, 2\/3 = 40\/60, 7\/12 = 35\/60. Greatest to smallest: 2\/3, 7\/12, 2\/5."} {"t":"s","id":7590,"s":"158 divided by 8 = 19 remainder 6. The remaining 6 passengers still need a minibus, so 19 + 1 = 20 minibuses."} {"t":"s","id":7593,"s":"Box C = 2 kg 180 g = 2180 g. (a) Box B = 2180 + 3400 = 5580 g. (b) Box A = 5580 - 2550 = 3030 g = 3 kg 30 g."} {"t":"s","id":7594,"s":"(a) Oranges = 570 divided by 5 = 114. (b) Pears = 114 + 38 = 152 (oranges are 38 fewer than pears)."} {"t":"s","id":7595,"s":"Three full boxes: 118 x 3 = 354. Add the last box: 354 + 79 = 433."} {"t":"s","id":7596,"s":"Remaining after 27 left: 159 - 27 = 132 seated. People who came in: 27 x 4 = 108. Total seats = 132 + 108 = 240."} {"t":"s","id":7598,"s":"8 km = 8000 m. 8000 m + 60 m = 8060 m."} {"t":"s","id":7602,"s":"The pattern increases by 10 each time. 2096 + 10 = 2106."} {"t":"s","id":7604,"s":"114 \/ 9 = 12 remainder 6. The leftover 6 pies need one more box, so 12 + 1 = 13 boxes."} {"t":"s","id":7606,"s":"After giving away 40, Faye had 34 - 18 = 16 files. So at first she had 16 + 40 = 56 files."} {"t":"s","id":7607,"s":"(a) Eight thousand, three hundred and fifty-six = 8356. (b) For the greatest even number from 1,8,3,2, the last digit must be even; using 2 as the units gives 8312."} {"t":"s","id":7614,"s":"458 x 4 = 1832, which matches the form 1B32 with B = 8. So A = 4 and B = 8."} {"t":"s","id":7618,"s":"1\/4 = 3\/12. 3\/12 + 5\/12 = 8\/12 = 2\/3."} {"t":"s","id":7619,"s":"(a) Avery = 521 + 380 = 901. (b) Caylee = 901 - 671 = 230."} {"t":"s","id":7620,"s":"Let Hall Y = 1 unit. X = 1 unit - 7, Z = 4 units. Total = 6 units - 7 = 815, so 6 units = 822, Hall Y = 822 \/ 6 = 137."} {"t":"s","id":7621,"s":"8 x 260 ml = 2080 ml. 1 l 70 ml = 1070 ml. Total = 2080 + 1070 = 3150 ml = 3 l 150 ml."} {"t":"s","id":7624,"s":"Three thousand = 3000, six hundred = 600, six = 6. So 3000 + 600 + 6 = 3606."} {"t":"s","id":7625,"s":"7023 = 7000 + 20 + 3. The missing number is 20 (the tens place)."} {"t":"s","id":7626,"s":"5\/7 is more than half; 1\/2 = 0.5; 2\/8 = 1\/4 is less than half. Greatest to smallest: 5\/7, 1\/2, 2\/8."} {"t":"s","id":7627,"s":"1 kg = 1000 g. 2080 g = 2000 g + 80 g = 2 kg 80 g."} {"t":"s","id":7635,"s":"From 11 30 to 13 00 is 1 h 30 min; from 13 00 to 13 17 is 17 min. Total = 1 h 30 min + 17 min = 1 h 47 min."} {"t":"s","id":7637,"s":"(a) Pattern alternates +10, +100: 3929 + 100 = 4029. (b) Pattern increases by 50: 7489 - 50 = 7439."} {"t":"s","id":7638,"s":"(a) 560 + 1320 = 1880. (b) 8001 - 2417 = 5584."} {"t":"s","id":7639,"s":"(a) 5 x 8 = 40 eggs. (b) 40 \u00f7 4 = 10 cakes."} {"t":"s","id":7646,"s":"Work backwards: 312 - 13 = 299 (before the 13 entered); 299 + 18 = 317 (before the 18 left). So 317 students at first."} {"t":"s","id":7647,"s":"Suppose all 20 bags held 5 sweets: 20 x 5 = 100. That is 100 - 76 = 24 too many. Each bag of 3 instead of 5 reduces the count by 2, so 24 \u00f7 2 = 12 bags of 3 sweets."} {"t":"s","id":7649,"s":"Giving 25 to Bala reduces the gap by 25 twice (Ali loses 25, Bala gains 25), i.e. 25 + 25 = 50. New difference = 128 - 50 = 78."} {"t":"s","id":7650,"s":"Children + adults = 4 units = 756, so 1 unit (adults) = 756 \u00f7 4 = 189. Children = 3 units = 567. Difference = 567 - 189 = 378 (or 2 units = 189 x 2 = 378)."} {"t":"s","id":7651,"s":"(a) 382 \u00f7 6 = 63 remainder 4, so the greatest number of families is 63. (b) 382 - 22 = 360; 360 \u00f7 2 = 180 packets on Saturday."} {"t":"s","id":7652,"s":"(a) 5320 - 4470 = 850 ml left. (b) 850 \u00f7 5 = 170 ml in each jug."} {"t":"s","id":7653,"s":"In 3780, reading from the right: 0 ones, 8 tens, 7 hundreds, 3 thousands. So the digit 7 is in the hundreds place."} {"t":"s","id":7656,"s":"1 kg = 1000 g, so 4 kg = 4000 g. 4000 g + 26 g = 4026 g."} {"t":"s","id":7661,"s":"Jeremy = 28 - 3 = 25 kg. Total = 28 + 25 = 53 kg."} {"t":"s","id":7662,"s":"He gave away 138 x 6 = 828 stickers. With 3 left over, he had 828 + 3 = 831 stickers at first."} {"t":"s","id":7668,"s":"Smaller number = 932 - 786 = 146. Sum = 932 + 146 = 1078."} {"t":"s","id":7669,"s":"Apples in 1 box = 17 + 20 = 37. In 7 boxes = 37 x 7 = 259."} {"t":"s","id":7671,"s":"(a) 08 10 + 1 h 50 min = 10 00. (b) Vic took 1 h 50 min, so Dan took 1 h 50 min + 30 min = 2 h 20 min. (c) 11 30 minus 2 h 20 min = 09 10."} {"t":"s","id":7684,"s":"11.50 a.m. + 1 h 40 min = 1.30 p.m. arrival; class starts 15 min later = 1.45 p.m."} {"t":"s","id":7686,"s":"Son ate 3\/8 - 1\/4 = 3\/8 - 2\/8 = 1\/8. Total eaten = 3\/8 + 1\/8 = 4\/8 = 1\/2."} {"t":"s","id":7688,"s":"Let start = R each. After selling, rambutans = R, mangosteens = R - 810, and R = 3(R - 810) \u2192 R = 3R - 2430 \u2192 2R = 2430 \u2192 R = 1215."} {"t":"s","id":7694,"s":"537 \u00f7 8 = 67 remainder 1; the quotient is 67. Answer key states 61."} {"t":"s","id":7707,"s":"Watch 10 min fast, so actual arrival = 12.10 p.m. Subtract 45 min travel = 11.25 a.m."} {"t":"s","id":7713,"s":"End total = 890 - 130 + 280 = 1040, equal split = 520 each. Foreign at first = 520 - 280 = 240; local at first = 890 - 240 = 650. (a) 650 - 240 = 410 more local. (b) 240."} {"t":"s","id":7725,"s":"Two pieces = 2 x 75 cm = 150 cm. 4 m = 400 cm. 400 - 150 = 250 cm = 2 m 50 cm."} {"t":"s","id":7730,"s":"2.45 p.m. + 42 min = 3.27 p.m. In 24-hour clock that is 1527."} {"t":"s","id":7732,"s":"Sarah = 1 unit, Mei Ling = 3 units, Diya = 2 units; total = 6 units = 270, so 1 unit = 45. Diya = 2 x 45 = 90."} {"t":"s","id":7734,"s":"Common denominator 18: 1\/2 = 9\/18, 5\/9 = 10\/18, 2\/3 = 12\/18. Greatest to smallest: 2\/3, 5\/9, 1\/2."} {"t":"s","id":7739,"s":"a) 240 x 8 = 1920 books in boxes, + 6 left over = 1926 books. b) 240 boxes x $9 = $2160; 6 books x $2 = $12; total = $2172."} {"t":"s","id":7741,"s":"The answer key marks option (2). Note: the digit 0 sits in the hundreds place of 8047, so its place value is 0 (option 1) \u2014 the key appears inconsistent here, but per the official key the marked answer is option (2)."} {"t":"s","id":7744,"s":"Rebekah = 3 x 40 = 120. Both = 40 + 120 = 160."} {"t":"s","id":7747,"s":"3\/4 = 9\/12. 9\/12 - 7\/12 = 2\/12 = 1\/6."} {"t":"s","id":7751,"s":"9000 + 700 = 9700. 9752 - 9700 = 52 ones."} {"t":"s","id":7752,"s":"The number = 6479 - 2583 = 3896. 100 more = 3896 + 100 = 3996."} {"t":"s","id":7753,"s":"47 + 12 = 59 on board before alighting. 59 - 23 = 36 alighted."} {"t":"s","id":7755,"s":"7 kg = 7000 g. 7000 - 6450 = 550 g left. 550 \/ 5 = 110 g per packet."} {"t":"s","id":7757,"s":"The pattern increases by 101 each time. 682 + 101 = 783."} {"t":"s","id":7758,"s":"Cars left = 1762 - 325 = 1437. Total = 2389 + 1437 = 3826."} {"t":"s","id":7759,"s":"9 x 6 = 54 pencils. 54 + 2 = 56. 56 \/ 8 = 7 per packet."} {"t":"s","id":7760,"s":"Number of gift packs = 195 \/ 5 = 39. Chocolate bars = 39 x 8 = 312."} {"t":"s","id":7763,"s":"1\/10 = 0.1, 1\/3 approx 0.33, 7\/11 approx 0.64. Smallest to greatest: 1\/10, 1\/3, 7\/11."} {"t":"s","id":7766,"s":"Start gap: hall is 129 more than canteen. Moving 329 from hall to canteen changes the gap by 2 x 329 = 658 in the canteen's favour: -129 + 658 = 529. So canteen has 529 more."} {"t":"s","id":7767,"s":"Total = 183 + 129 = 312. For Rei to be twice Ali, Ali ends with 312 \/ 3 = 104. Rei ends with 208. Ali must give 129 - 104 = 25 stickers (check: 183 + 25 = 208 = 2 x 104)."} {"t":"s","id":7768,"s":"Four thousand = 4000, one hundred = 100, sixty-two = 62. 4000 + 100 + 62 = 4162."} {"t":"s","id":7772,"s":"2\/3 = 4\/6. 4\/6 + 1\/6 = 5\/6."} {"t":"s","id":7773,"s":"06 55 + 1 h = 07 55. 07 55 + 15 min = 08 10."} {"t":"s","id":7774,"s":"James bought 3 x 2 = 6 packets. 6 x 27 = 162 sweets."} {"t":"s","id":7777,"s":"3\/4 = 6\/8. 6\/8 - 5\/8 = 1\/8."} {"t":"s","id":7779,"s":"Book = $8 + $13 = $21. 2 books = $42. Total = $42 + $8 = $50.00."} {"t":"s","id":7781,"s":"23 30 to 00 30 is 1 h. 00 30 to 01 08 is 38 min. Total 1 h 38 min."} {"t":"s","id":7786,"s":"If all 24 were motorcycles: 24 x 2 = 48 wheels. Extra wheels = 76 - 48 = 28. Each car adds 2 extra wheels, so cars = 28 \/ 2 = 14."} {"t":"s","id":7787,"s":"972 \/ 9 = 108 sticks per container. 108 x 7 = 756."} {"t":"s","id":7788,"s":"1 km 50 m = 1050 m. 2 rounds = 400 x 2 = 800 m. 1050 - 800 = 250 m."} {"t":"s","id":7791,"s":"(a) Ryan + Ben + Doris = 270. 270 - 36 = 234 = 9 units (Ryan 1 + Ben 4 + Doris 4). 234 \/ 9 = 26 = Ryan. (b) Ben = 26 x 4 = 104; Ryan = 26. Total 130, each gets 65. Ben gives 104 - 65 = 39."} {"t":"q","id":14415,"q":"At first, there were some adults and 500 children at the stadium. After another 612 adults and 300 children arrived, there were 3 times as many adults as children in the end.\n(a) How many children were there in the end? \n(b) How many adults were there at first? ","e":"(a) Children in end = 500 + 300 = 800. (b) Adults in end = 3 x 800 = 2400. Adults at first = 2400 - 612 = 1788."} {"t":"q","id":14419,"q":"Which of the following fractions is not an equivalent fraction of 2\/3?","e":"4\/6, 6\/9 and 12\/18 all simplify to 2\/3. 8\/15 does not, so it is not equivalent."} {"t":"q","id":14422,"q":"8753 is 80 tens more than .","e":"80 tens = 800. 8753 - 800 = 7953."} {"t":"q","id":14423,"q":"Isaac wants to buy an apple for 80\u00a2, a bunch of bananas for $1.25 and an orange for 75\u00a2. He only has $2.50. How much more money does he need?","e":"Total cost = $0.80 + $1.25 + $0.75 = $2.80. He needs $2.80 - $2.50 = $0.30 more."} {"t":"q","id":14427,"q":"A shirt has 7 buttons. How many buttons are there on 357 similar shirts?
Answer: ","e":"357 x 7 = 2499 buttons."} {"t":"q","id":14429,"q":"\\(\\dfrac{7}{10}\\) - \\(\\dfrac{2}{5}\\) =","e":"2\/5 = 4\/10. 7\/10 - 4\/10 = 3\/10."} {"t":"q","id":14430,"q":"Use all the digits 8, 2, 0, 1 to form the smallest 4-digit odd number.
Answer: ","e":"Odd number must end in 1. Leading digit can't be 0, so smallest start is 2: 2081."} {"t":"q","id":14432,"q":"Ahmad has $21.30. Peter has $3.20 less than Ahmad. How much do the two boys have altogether?
Answer: ","e":"Peter = $21.30 - $3.20 = $18.10. Altogether = $21.30 + $18.10 = $39.40."} {"t":"q","id":14433,"q":"Arrange these fractions from the smallest to the greatest.\n3\/4, 4\/9, 4\/11, 5\/8
(a)   (b)   (c)   (d) ","e":"As decimals: 4\/11 \u2248 0.36, 4\/9 \u2248 0.44, 5\/8 = 0.625, 3\/4 = 0.75. Smallest to greatest: 4\/11, 4\/9, 5\/8, 3\/4."} {"t":"q","id":14435,"q":"Mrs Lee had 500 sweets. She gave some of the sweets to her students. After giving each student 6 sweets, she had 56 sweets left.\n(a) How many sweets did she give to her students in total?\n(b) How many students were there?
(a)   (b) ","e":"(a) 500 - 56 = 444 sweets given. (b) 444 \u00f7 6 = 74 students."} {"t":"q","id":14436,"q":"The Tan family shared a pizza. Mr Tan ate 5\/12 of the pizza. Mrs Tan ate 1\/3 of the pizza. The rest of the pizza was eaten by their son.\n(a) What fraction of the pizza was eaten by Mr and Mrs Tan altogether? Give your answer in the simplest form.\n(b) What fraction of the pizza was eaten by their son? Give your answer in the simplest form.
(a)   (b) ","e":"(a) 5\/12 + 1\/3 = 5\/12 + 4\/12 = 9\/12 = 3\/4. (b) 12\/12 - 9\/12 = 3\/12 = 1\/4."} {"t":"q","id":14437,"q":"Adam, Ben and Clare had 2659 stickers altogether. Ben had 162 more stickers than Adam. Clare had 137 fewer stickers than Adam. How many stickers did Adam have?
Answer: ","e":"Remove differences: 2659 - 162 + 137 = 2634; 3 equal shares = 2634 \u00f7 3 = 878. Adam had 878. (Key: 2659 - 162 = 2497; 2497 - 274 = 2223; 2223 \u00f7 3 = 741; 741 + 137 = 878.)"} {"t":"q","id":14438,"q":"Samantha watched two movies continuously at the cinema. The first movie lasted for 2 h 15 min. The second movie lasted for 1 h 50 min.\n(a) How long did Samantha spend watching the two movies? Give your answer in h and min.\n(b) She started watching the first movie at 14 25. What time did she finish watching the second movie?
(a)   (b) ","e":"(a) 2 h 15 min + 1 h 50 min = 135 min + 110 min = 245 min = 4 h 5 min. (b) 14 25 + 4 h 5 min = 18 30."} {"t":"q","id":14439,"q":"The length of a rectangle is twice its breadth. The perimeter of the rectangle is 54 m.\n(a) What is the length of the rectangle?\n(b) What is the area of the rectangle?
(a)   (b) ","e":"Perimeter = 2(L + B) with L = 2B, so 6B = 54, B = 9 m, L = 18 m. Area = 18 x 9 = 162 m\u00b2."} {"t":"q","id":14441,"q":"Mr Tan bought 6 loaves of bread. Each loaf is cut into 8 slices of bread. How many slices of bread did Mr Tan have altogether?","e":"6 x 8 = 48 slices."} {"t":"q","id":14443,"q":"Jessica has 75 cookies. She has 3 times as many cookies as Jessica. How many cookies do Jessica and Kim have altogether?","e":"Per the answer key, the correct option is 100."} {"t":"q","id":14444,"q":"Mr Lim bought 6 boxes of erasers to give to his students. There were 24 erasers in each box. In the end, Mr Lim had 18 erasers left. How many erasers did he give to his students?","e":"6 x 24 = 144 erasers. He gave away 144 - 18 = 126."} {"t":"q","id":14447,"q":"Mr Aw had $650. He had $127 more than Mr Goh. How much money did Mr Goh have?\n$","e":"Mr Goh had $650 - $127 = $523."} {"t":"q","id":14448,"q":"Mrs Siva has 650 sweets. She packed all the sweets equally into 6 containers. How many sweets were left unpacked?\n","e":"650 \u00f7 6 = 108 remainder 2, so 2 sweets were left unpacked."} {"t":"q","id":14449,"q":"A bag of 3 apples cost $5. How much did Ms Yee pay for 18 apples?\n$","e":"18 apples = 18 \u00f7 3 = 6 bags. 6 x $5 = $30."} {"t":"q","id":14450,"q":"Mrs Chan and Mrs Lim baked a total of 685 muffins. Mrs Chan baked 4 times as many muffins as Mrs Lim. How many more muffins did Mrs Chan bake than Mrs Lim?\n","e":"Total = 5 units = 685, so 1 unit (Mrs Lim) = 685 \u00f7 5 = 137. Mrs Chan baked 3 more units = 3 x 137 = 411 more muffins."} {"t":"q","id":14451,"q":"Mr Mohammad had some stickers. He packed some stickers into 8 packets. There were 46 stickers in each packet. He had 37 stickers left unpacked. How many stickers did Mr Mohammad have at first?\n","e":"Packed = 46 x 8 = 368. At first = 368 + 37 = 405 stickers."} {"t":"q","id":14452,"q":"Amy collected 78 seashells. June collected 42 seashells. How many more seashells must June collect so that she has 3 times as many seashells as Amy?\n","e":"June needs 3 x 78 = 234 seashells. She must collect 234 - 42 = 192 more."} {"t":"q","id":14453,"q":"Three thousand and sixty-two in numbers is .","e":"Three thousand = 3000, sixty = 60, two = 2. So 3000 + 60 + 2 = 3062."} {"t":"q","id":14455,"q":"Express $16.05 in cents.","e":"$1 = 100\u00a2, so $16 = 1600\u00a2. Add 5\u00a2 to get 1605\u00a2."} {"t":"q","id":14458,"q":"Arrange the following numbers in decreasing order.\n3687 , 1069 , 3692
(a)   (b)   (c) ","e":"Decreasing order means largest to smallest. Compare thousands then hundreds: 3692 > 3687 > 1069."} {"t":"q","id":14459,"q":"The difference between two numbers is 65. The smaller number is 387. What is the greater number?
Answer: ","e":"Greater number = smaller number + difference = 387 + 65 = 452."} {"t":"q","id":14463,"q":"What are the missing numbers in each of the number patterns?\n(a) 6174, 6184, 6194, , 6214, 6224, 6234\n(b) 500, 501, 1501, 1502, 2502, , 3503, 3504, 4504","e":"(a) The pattern increases by 10 each time, so after 6194 comes 6204. (b) The pattern alternates +1 then +1000: 2502 + 1 = 2503."} {"t":"q","id":14464,"q":"What is the missing number?\n7 \u00d7 7 = + 4","e":"7 \u00d7 7 = 49. So [?] + 4 = 49, which means [?] = 49 - 4 = 45."} {"t":"q","id":14465,"q":"Emily has a total of 32 oranges. She places them equally into 4 boxes. How many oranges are there in each box?
Answer: ","e":"Divide the total equally: 32 \u00f7 4 = 8 oranges in each box."} {"t":"q","id":14466,"q":"Every customer at Shine Bakery received 2 free doughnuts for every 8 cupcakes paid. Sally received 12 free doughnuts after paying for some cupcakes. How many cupcakes did she pay for?
Answer: ","e":"12 free doughnuts \u00f7 2 doughnuts per set = 6 sets. Each set needs 8 cupcakes, so 6 \u00d7 8 = 48 cupcakes."} {"t":"q","id":14467,"q":"Strive Tour Agency had 2328 customers on Monday. It had 519 fewer customers on Tuesday than on Monday. How many customers did Strive Tour Agency have on both days?
Answer: ","e":"Tuesday = 2328 - 519 = 1809 customers. Both days = 2328 + 1809 = 4137 customers."} {"t":"q","id":14468,"q":"(a) A bag cost $95.20. During a sale, Mary paid $75.80 for it. How much did Mary save?\n(b) Mary gave the cashier two $50 notes. How much change did she receive?
(a)   (b) ","e":"(a) Savings = $95.20 - $75.80 = $19.40. (b) Two $50 notes = $100; change = $100.00 - $75.80 = $24.20."} {"t":"q","id":14469,"q":"Which of the following is six thousand, four hundred and eight in numerals?","e":"Six thousand = 6000, four hundred = 400, eight = 8. 6000 + 400 + 8 = 6408."} {"t":"q","id":14472,"q":"Which of the following numbers is the smallest?","e":"All start with 8. Compare hundreds: 8769 and 8796 have 7 hundreds (smallest). Then compare tens: 6 < 9, so 8769 is smallest."} {"t":"q","id":14473,"q":"Arrange the following numbers from the smallest to the greatest.\n3210, 2501, 3127","e":"2501 has 2 thousands (smallest). 3127 and 3210 both have 3 thousands; 3127 has 1 hundred vs 3210's 2 hundreds, so 3127 < 3210. Order: 2501, 3127, 3210."} {"t":"q","id":14474,"q":"In the number pattern, what is the missing number?\n5088, 5091, 5094, 5097, _________, 5103","e":"The numbers increase by 3 each time (5088, 5091, 5094, 5097...). 5097 + 3 = 5100, and 5100 + 3 = 5103."} {"t":"q","id":14476,"q":"The sum of two numbers is 4567. One of the numbers is 2468. What is the other number?","e":"The other number = sum - known number = 4567 - 2468 = 2099."} {"t":"q","id":14477,"q":"(a) Use the digits 2, 5, 7 to form the greatest 3-digit odd number. \n(b) Use the digits 0, 2, 5 to form the smallest 3-digit even number. ","e":"(a) For the greatest odd number the ones digit must be odd; among 2,5,7 use largest digits first: 7 and 2 in front, odd 5 last -> 725. (b) For the smallest even number the ones digit must be even; cannot start with 0, so 2 hundreds, 0 tens, even ones 5? 5 is odd, so use 0 ones -> 250."} {"t":"q","id":14478,"q":"1503 people were at a book fair. 942 were children and the rest were adults. How many adults were at the book fair? ","e":"Adults = total - children = 1503 - 942 = 561."} {"t":"q","id":14479,"q":"There are 820 red markers and 1048 blue markers in a shop. How many markers are there altogether? ","e":"Total = 820 + 1048 = 1868."} {"t":"q","id":14480,"q":"Jack had 2000 marbles. He had 653 more marbles than Tom.\n(a) How many marbles did Tom have? \n(b) Tom bought another 480 marbles. How many marbles did Tom have in total? ","e":"(a) Jack has 653 more than Tom, so Tom = 2000 - 653 = 1347. (b) After buying 480 more: 1347 + 480 = 1827."} {"t":"q","id":14481,"q":"Mary saved $799 in February. She saved $253 less in February than in January. How much did Mary save altogether in January and in February? ","e":"February is $253 less than January, so January = 799 + 253 = 1052. Altogether = 1052 + 799 = 1851."} {"t":"q","id":14482,"q":"7 hundreds x 3 =","e":"7 hundreds = 700. 700 x 3 = 2100."} {"t":"q","id":14486,"q":"Which of the following number has a remainder of 2 when divided by 3?","e":"572 \u00f7 3 = 190 remainder 2. (298 r1, 381 r0, 496 r1.)"} {"t":"q","id":14487,"q":"Which of the following number cannot be divided by 6 exactly?","e":"813 \u00f7 6 = 135 remainder 3, so it cannot be divided by 6 exactly. (354, 432, 768 all divide exactly.)"} {"t":"q","id":14488,"q":"When a number is divided by 4, the quotient is 117 with remainder 1. What is the number?","e":"Number = 117 \u00d7 4 + 1 = 468 + 1 = 469."} {"t":"q","id":14489,"q":"A baker bakes 122 cupcakes a day. How many cupcakes can he bake in 7 days?","e":"122 \u00d7 7 = 854 cupcakes."} {"t":"q","id":14490,"q":"Randy has 318 bookmarks. His sister has 6 times as many bookmarks as Randy. How many bookmarks does his sister have? ","e":"318 \u00d7 6 = 1908 bookmarks."} {"t":"q","id":14491,"q":"A fruit seller has 405 mangoes. He packed the mangoes in 5 boxes. How many mangoes are there in each box? ","e":"405 \u00f7 5 = 81 mangoes in each box."} {"t":"q","id":14492,"q":"Miss Rita has a ribbon that is 252cm long. She cuts the ribbon into 9 equal strips. How long is 1 strip of the small ribbon? cm","e":"252 \u00f7 9 = 28 cm per strip."} {"t":"q","id":14493,"q":"Billy and Rick made 162 paper cranes to decorate the school hall. Billy made 5 times as many paper cranes as Rick. (a) How many paper cranes did Billy make? (b) How many paper cranes did Rick make? ","e":"Together they form 6 equal units (Rick 1, Billy 5). 162 \u00f7 6 = 27 = Rick. Billy = 5 \u00d7 27 = 135."} {"t":"q","id":14494,"q":"Uncle Jacob donated 260 pencils to a children's home. He packed the pencils into gift boxes. Each gift box contains 7 pencils. What is the least number of pencils he needs if he wants 7 pencils in every box? ","e":"260 \u00f7 7 = 37 remainder 1, leaving 1 extra pencil. To make another full box of 7 he needs 7 \u2212 1 = 6 more pencils."} {"t":"q","id":14496,"q":"Which of the following has the greatest value?","e":"6x7=42, 4x9=36, 8x8=64, 5x10=50. The greatest is 8x8=64."} {"t":"q","id":14497,"q":"\u00f7 6 = 156. What is the missing number in the box?","e":"The missing number = 156 x 6 = 936."} {"t":"q","id":14503,"q":"James and Jane were given the same amount of money. Jane paid $29.50 for a book and saved $25.50. James spent $49.95 on a toy car. How much did James save?","e":"Total each had = 29.50 + 25.50 = $55.00. James saved 55.00 - 49.95 = $5.05."} {"t":"q","id":14509,"q":"Cindy leaves home at 6.23 a.m. and reaches school at 7.10 a.m. Kaixin leaves home at 6.46 a.m. and reaches school at 7.23 a.m. Who takes a shorter time to travel to school and how much shorter does she take?","e":"Cindy: 6.23 to 7.10 = 47 min. Kaixin: 6.46 to 7.23 = 37 min. Kaixin is shorter by 47 - 37 = 10 min."} {"t":"q","id":14512,"q":"Arrange the following fractions from the smallest to the largest.\n2\/7 , 4\/5 , 4\/7\n , , ","e":"2\/7 < 4\/7 (same denominator) and 4\/7 < 4\/5 (same numerator, larger denominator is smaller). Order: 2\/7, 4\/7, 4\/5."} {"t":"q","id":14514,"q":"Study the number pattern. Fill in the missing number in the blank.\n1199, , 999, 899, 799","e":"The pattern decreases by 100 each step: 1199 - 100 = 1099."} {"t":"q","id":14515,"q":"Yasmine and Gina earned 780 points together at an arcade. Yasmine earned 5 times as many points as Gina. Gina decided to play one more game and earned another 25 points. How many points did Gina earn in the end?\n","e":"Total = 6 units = 780, so 1 unit (Gina) = 780 \u00f7 6 = 130. After 25 more: 130 + 25 = 155."} {"t":"q","id":14516,"q":"Amelia has 6 times as many beads as Bella. Bella has 936 beads. How many beads do they have altogether?\n","e":"Together = 6 + 1 = 7 times Bella's beads = 936 x 7 = 6552."} {"t":"q","id":14517,"q":"Tim and Bob boarded a bus at 11.05 a.m. to go to a park. They reached the park 40 minutes later. They only left the park at 3.35 p.m. How long were they at the park?\n h min","e":"Arrived 11.05 + 40 min = 11.45 a.m. From 11.45 a.m. to 3.35 p.m. = 3 h 50 min."} {"t":"q","id":14519,"q":"A group of teachers made 912 cupcakes for students at a carnival. Each student gets four cupcakes. How many students were there?\n","e":"912 \u00f7 4 = 228 students."} {"t":"q","id":14521,"q":"Mr. Jenson added 350 to a number. He then subtracted 28 from the answer to get 546. What is the number?\n","e":"Work backwards: 546 + 28 = 574, then 574 - 350 = 224."} {"t":"q","id":14524,"q":"A gift pack can hold up to 6 sweets. What is the least number of gift packs needed to pack all 350 sweets?\n","e":"350 \u00f7 6 = 58 remainder 2. The 2 leftover sweets still need a pack, so 58 + 1 = 59 packs."} {"t":"q","id":14525,"q":"Mdm Ng saved $138 more than Mr Tan. Mdm Ng gave Mr Tan $40. How much more money did Mdm Ng have than Mr Tan in the end?\n$","e":"Giving away $40 reduces the gap by 2 x $40 = $80. New difference = 138 - 80 = $58."} {"t":"q","id":14526,"q":"Xiuli took a quiz consisting of 14 questions. For every correct answer, 4 points were awarded. For every wrong answer, 3 points were deducted. Xiuli scored a total of 14 points. How many questions did she answer correctly?\n","e":"If all 14 were correct: 14 x 4 = 56. Each wrong answer instead of right loses 4+3 = 7. (56-14)\u00f77 = 6 wrong, so 14-6 = 8 correct. Check: 8 x 4 - 6 x 3 = 32 - 18 = 14."} {"t":"q","id":14527,"q":"A group of teachers and students joined a virtual choir. There were 21 more teachers than students. There were 42 male teachers and 20 female students. The number of female students was the same as female teachers. How many more male students than female students were there?\n","e":"Female teachers = female students = 20, so total teachers = 42 + 20 = 62. Students = 62 - 21 = 41. Male students = 41 - 20 = 21. More male than female students = 21 - 20 = 1."} {"t":"q","id":14528,"q":"The mass of a box with 6 identical blocks is 500g. After 5 blocks were removed, the mass of the box with the remaining block is 100g.\na) What is the mass of each block?\nb) What is the mass of the box?\n ","e":"Removing 5 blocks dropped the mass by 500 - 100 = 400 g, so each block = 400 \u00f7 5 = 80 g. Box = 100 - 80 = 20 g."} {"t":"q","id":14530,"q":"Susan had 50 l of water. She poured the water into pails that could hold 7 l each. She filled each pail completely and had 1 l of water left. How many pails did Susan fill?\n","e":"Water used to fill pails = 50 - 1 = 49 l. 49 \u00f7 7 = 7 pails."} {"t":"q","id":14534,"q":"(a) Write five thousand and sixty-five in numerals.\n(b) Use all the digits to form the smallest 4-digit odd number.\n5 2 6 1
(a)   (b) ","e":"(a) Five thousand and sixty-five = 5065. (b) To make the smallest 4-digit odd number using 5, 2, 6, 1, the last digit must be odd; choose the smallest available odd digit (5) for the ones place, then arrange the rest ascending: 1, 2, 6 \u2192 1265."} {"t":"q","id":14535,"q":"Study the number pattern carefully. What is the missing number?\n943, 1043, , 1243, 1343, 1443","e":"Each number increases by 100, so the term after 1043 is 1043 + 100 = 1143."} {"t":"q","id":14536,"q":"A shirt costs $42. A cap costs $19.40 less than the shirt. How much does the cap cost?\n$","e":"$42 - $19.40 = $22.60."} {"t":"q","id":14537,"q":"An adult ticket to a theme park costs $25.50. A child ticket costs $11.20. How much does a family of 2 adults and 1 child pay?\n$","e":"2 adults: $25.50 + $25.50 = $51.00. Add 1 child: $51.00 + $11.20 = $62.20."} {"t":"q","id":14538,"q":"Ali, Bala, Chang and Dayi went to the zoo. All of them wanted to ride on a pony but the pony could only take 2 of them at a time. How many different ways could they pair up for the ride?\n","e":"List the pairs: AB, AC, AD, BC, BD, CD. That is 3 + 2 + 1 = 6 different ways."} {"t":"q","id":14539,"q":"The difference between two numbers is 625. The greater number is 714.\n(a) What is the smaller number?\n(b) What is the sum of the two numbers?
(a)   (b) ","e":"(a) Smaller number = 714 - 625 = 89. (b) Sum = 714 + 89 = 803."} {"t":"q","id":14542,"q":"Mei Ling baked some cupcakes. She packed all the cupcakes equally into boxes of 9. She used 3 boxes. How many cupcakes did she bake?","e":"3 boxes \u00d7 9 cupcakes = 27 cupcakes."} {"t":"q","id":14544,"q":"Darryl bought 321 chocolates. Ryan bought 2 times as many chocolates as Darryl. How many chocolates did both of them buy altogether?
Answer: ","e":"Ryan = 2 \u00d7 321 = 642. Altogether = 321 + 642 = 963. (Or 321 \u00d7 3 = 963.)"} {"t":"q","id":14545,"q":"Mrs Tan has 509 sweets. She gives 7 sweets to each student. How many students can she give the sweets to?
Answer: ","e":"509 \u00f7 7 = 72 remainder 5. She can give sweets to 72 students."} {"t":"q","id":14546,"q":"A number is between 30 and 60. It is an even number. The sum of its two digits is 12. What is the number?
Answer: ","e":"Even numbers between 30 and 60 with digit sum 12: 48 (4 + 8 = 12). The number is 48."} {"t":"q","id":14561,"q":"2 h and 18 min is the same as minutes.","e":"2 h = 120 min. 120 + 18 = 138 minutes."} {"t":"q","id":14562,"q":"The Children's Day concert ended at 10.30 a.m. It lasted for 1 h 15 min. What time did the concert begin? ","e":"Count back 1 h 15 min from 10.30 a.m.: 10.30 \u2212 1 h = 9.30, then \u2212 15 min = 9.15 a.m."} {"t":"q","id":14563,"q":"Both Hashan and Weimin went for a swim. Hashan stopped swimming earlier than Weimin by 15 min. If Hashan stopped swimming at 7.55 a.m., what time did Weimin stop swimming? ","e":"Weimin stopped 15 min later than Hashan: 7.55 a.m. + 15 min = 8.10 a.m."} {"t":"q","id":14564,"q":"Ailing spent 1 h 15 min to complete her homework on Monday. On Tuesday, she spent 40 min longer to complete her homework compared to Monday. How much time did she spend to complete her homework on both days? Give your answers in hours and minutes. h min","e":"Tuesday = 1 h 15 min + 40 min = 1 h 55 min. Total = 1 h 15 min + 1 h 55 min = 2 h 70 min = 3 h 10 min."} {"t":"q","id":14565,"q":"Monica went for a movie which started at 5.10 p.m. It ended at 7.05 p.m. How long was the movie? Express your answer in hours and minutes. h min","e":"From 5.10 p.m. to 7.10 p.m. is 2 h; but it ended at 7.05, which is 5 min before 7.10, so duration = 2 h \u2212 5 min = 1 h 55 min."} {"t":"q","id":14566,"q":"Some pupils went to Bird Park for their learning journey. They stayed at the park for 2 h 20 min. They left the park at 11.15 a.m. What time did they arrive at the Bird Park? ","e":"Arrival = leaving time \u2212 stay = 11.15 a.m. \u2212 2 h 20 min. 11.15 \u2212 2 h = 9.15, then \u2212 20 min = 8.55 a.m."} {"t":"q","id":14567,"q":"Alice reached the cinema 30 minutes before the show started. She was there at 19 30. The show lasted 135 minutes. What time did the show end? Express your answer in 24-hour clock. ","e":"She arrived 30 min early at 19 30, so the show started at 20 00. 135 min = 2 h 15 min. 20 00 + 2 h 15 min = 22 15."} {"t":"q","id":14578,"q":"Circle the smaller fraction. 2\/10 , 7\/10","e":"With the same denominator (10), the smaller numerator gives the smaller fraction, so 2\/10 < 7\/10."} {"t":"q","id":14579,"q":"Circle the smaller fraction. 5\/8 , 3\/8","e":"Same denominator (8); 3 < 5 so 3\/8 is the smaller fraction."} {"t":"q","id":14580,"q":"Circle the smaller fraction. 5\/9 , 2\/5","e":"5\/9 \u2248 0.56 and 2\/5 = 0.4, so 2\/5 is the smaller fraction."} {"t":"q","id":14581,"q":"Circle the smaller fraction. 7\/8 , 1\/3","e":"7\/8 is close to 1 while 1\/3 is much less than a half, so 1\/3 is the smaller fraction."} {"t":"q","id":14582,"q":"Circle the greater fraction. 2\/9 , 4\/9","e":"Same denominator (9); 4 > 2 so 4\/9 is the greater fraction."} {"t":"q","id":14583,"q":"Circle the greater fraction. 9\/12 , 3\/12","e":"Same denominator (12); 9 > 3 so 9\/12 is the greater fraction."} {"t":"q","id":14584,"q":"Circle the greater fraction. 4\/9 , 1\/3","e":"1\/3 = 3\/9, and 4\/9 > 3\/9, so 4\/9 is the greater fraction."} {"t":"q","id":14585,"q":"Circle the greater fraction. 3\/8 , 5\/6","e":"3\/8 is less than a half while 5\/6 is more than a half, so 5\/6 is the greater fraction."} {"t":"q","id":14586,"q":"Arrange this set of fractions in order. Begin with the greatest. 1\/8 , 1\/9 , 1\/5 , , ","e":"With numerator 1, the smaller the denominator the larger the fraction, so 1\/5 > 1\/8 > 1\/9."} {"t":"q","id":14587,"q":"Arrange this set of fractions in order. Begin with the greatest. 6\/11 , 4\/11 , 7\/11 , , ","e":"Same denominator (11); order by numerator from largest: 7\/11, 6\/11, 4\/11."} {"t":"q","id":14588,"q":"Write the missing numerator or denominator. 1\/2 = \/6","e":"Multiply numerator and denominator of 1\/2 by 3: 1\/2 = 3\/6."} {"t":"q","id":14589,"q":"Write the missing numerator or denominator. 3\/5 = 9\/","e":"9 \u00f7 3 = 3, so multiply the denominator 5 by 3: 3\/5 = 9\/15."} {"t":"q","id":14590,"q":"Write the missing numerator or denominator. 3\/ = 9\/12","e":"9 \u00f7 3 = 3, so divide the denominator 12 by 3: 12 \u00f7 3 = 4, giving 3\/4 = 9\/12."} {"t":"q","id":14591,"q":"Write the missing numerator or denominator. \/6 = 10\/12","e":"12 \u00f7 6 = 2, so divide the numerator 10 by 2: 10 \u00f7 2 = 5, giving 5\/6 = 10\/12."} {"t":"q","id":14592,"q":"Write the missing numerators or denominators. 1\/2 = \/6 = \/8","e":"1\/2 = 3\/6 (\u00d73) and 1\/2 = 4\/8 (\u00d74)."} {"t":"q","id":14593,"q":"Write the missing numerators or denominators. 2\/3 = \/6 = \/12","e":"2\/3 = 4\/6 (\u00d72) and 2\/3 = 8\/12 (\u00d74)."} {"t":"q","id":14594,"q":"Write the missing numerators or denominators. 1\/5 = 2\/ = 3\/","e":"1\/5 = 2\/10 (\u00d72) and 1\/5 = 3\/15 (\u00d73)."} {"t":"q","id":14595,"q":"Write each fraction in its simplest form. \\(\\dfrac{4}{8}\\) =","e":"Divide numerator and denominator by 4: 4\/8 = 1\/2."} {"t":"q","id":14596,"q":"Write each fraction in its simplest form. \\(\\dfrac{6}{9}\\) =","e":"Divide numerator and denominator by 3: 6\/9 = 2\/3."} {"t":"q","id":14597,"q":"Write each fraction in its simplest form. \\(\\dfrac{8}{12}\\) =","e":"Divide numerator and denominator by 4: 8\/12 = 2\/3."} {"t":"q","id":14598,"q":"Write each fraction in its simplest form. \\(\\dfrac{10}{12}\\) =","e":"Divide numerator and denominator by 2: 10\/12 = 5\/6."} {"t":"q","id":14599,"q":"Write each fraction in its simplest form. \\(\\dfrac{6}{15}\\) =","e":"Divide numerator and denominator by 3: 6\/15 = 2\/5."} {"t":"q","id":14600,"q":"Write each fraction in its simplest form. \\(\\dfrac{9}{12}\\) =","e":"Divide numerator and denominator by 3: 9\/12 = 3\/4."} {"t":"q","id":14601,"q":"Arrange this set of fractions in order. Begin with the smallest. 3\/8 , 1\/4 , 1\/2 , , ","e":"Using eighths: 1\/4 = 2\/8, 1\/2 = 4\/8, so 2\/8 < 3\/8 < 4\/8, giving 1\/4, 3\/8, 1\/2."} {"t":"q","id":14602,"q":"Arrange this set of fractions in order. Begin with the smallest. 3\/12 , 2\/6 , 3\/4 , , ","e":"Using twelfths: 3\/12, 2\/6 = 4\/12, 3\/4 = 9\/12, so 3\/12 < 4\/12 < 9\/12, giving 3\/12, 2\/6, 3\/4."} {"t":"q","id":14603,"q":"Arrange this set of fractions in order. Begin with the smallest. 3\/7 , 3\/4 , 1\/2 , , ","e":"3\/7 is less than 1\/2 (since 3.5\/7 = 1\/2), and 3\/4 is more than 1\/2, so the order is 3\/7, 1\/2, 3\/4."} {"t":"q","id":14604,"q":"Add the fractions. Express the answer in its simplest form. \\(\\dfrac{3}{12}\\) + \\(\\dfrac{2}{6}\\) =","e":"2\/6 = 4\/12, so 3\/12 + 4\/12 = 7\/12, which is already in simplest form."} {"t":"q","id":14605,"q":"Add the fractions. Express the answer in its simplest form. \\(\\dfrac{1}{4}\\) + \\(\\dfrac{2}{8}\\) =","e":"2\/8 = 1\/4, so 1\/4 + 1\/4 = 2\/4 = 1\/2."} {"t":"q","id":14606,"q":"Subtract the fractions. Express the answer in its simplest form. \\(\\dfrac{8}{9}\\) - \\(\\dfrac{1}{3}\\) =","e":"1\/3 = 3\/9, so 8\/9 - 3\/9 = 5\/9, already in simplest form."} {"t":"q","id":14607,"q":"Subtract the fractions. Express the answer in its simplest form. \\(\\dfrac{3}{4}\\) - \\(\\dfrac{5}{12}\\) =","e":"3\/4 = 9\/12, so 9\/12 - 5\/12 = 4\/12 = 1\/3."} {"t":"q","id":14608,"q":"Express the length in centimetres. 3 m = cm","e":"1 m = 100 cm, so 3 m = 3 \u00d7 100 = 300 cm."} {"t":"q","id":14609,"q":"Express the length in centimetres. 2 m 6 cm = cm","e":"2 m = 200 cm, plus 6 cm = 206 cm."} {"t":"q","id":14610,"q":"Express the length in metres and centimetres. 157 cm = m cm","e":"157 cm = 100 cm + 57 cm = 1 m 57 cm."} {"t":"q","id":14611,"q":"Express the length in metres and centimetres. 430 cm = m cm","e":"430 cm = 400 cm + 30 cm = 4 m 30 cm."} {"t":"q","id":14612,"q":"Express the length in metres. 4 km = m","e":"1 km = 1000 m, so 4 km = 4 \u00d7 1000 = 4000 m."} {"t":"q","id":14613,"q":"Express the length in metres. 3 km 80 m = m","e":"3 km = 3000 m, plus 80 m = 3080 m."} {"t":"q","id":14614,"q":"Express the length in kilometres and metres. 2345 m = km m","e":"2345 m = 2000 m + 345 m = 2 km 345 m."} {"t":"q","id":14615,"q":"Express the length in kilometres and metres. 5500 m = km m","e":"5500 m = 5000 m + 500 m = 5 km 500 m."} {"t":"q","id":14616,"q":"Express the mass in grams. 5 kg = g","e":"1 kg = 1000 g, so 5 kg = 5 \u00d7 1000 = 5000 g."} {"t":"q","id":14617,"q":"Express the mass in grams. 7 kg 90 g = g","e":"7 kg = 7000 g, plus 90 g = 7090 g."} {"t":"q","id":14618,"q":"Express the mass in kilograms and grams. 2800 g = kg g","e":"2800 g = 2000 g + 800 g = 2 kg 800 g."} {"t":"q","id":14619,"q":"Express the mass in kilograms and grams. 8150 g = kg g","e":"8150 g = 8000 g + 150 g = 8 kg 150 g."} {"t":"q","id":14620,"q":"Express the volume in millilitres. 6 \u2113 = ml","e":"1 \u2113 = 1000 ml, so 6 \u2113 = 6 \u00d7 1000 = 6000 ml."} {"t":"q","id":14621,"q":"Express the volume in millilitres. 3 \u2113 42 ml = ml","e":"3 \u2113 = 3000 ml, plus 42 ml = 3042 ml."} {"t":"q","id":14622,"q":"Express the volume in litres and millilitres. 1200 ml = \u2113 ml","e":"1200 ml = 1000 ml + 200 ml = 1 \u2113 200 ml."} {"t":"q","id":14623,"q":"Express the volume in litres and millilitres. 6090 ml = \u2113 ml","e":"6090 ml = 6000 ml + 90 ml = 6 \u2113 90 ml."} {"t":"q","id":14624,"q":"The tallest boy in the class is 153 tall. Fill in the blank with 'cm', 'm' or 'km'.","e":"A boy's height of about 153 of a unit fits centimetres (153 cm \u2248 1.53 m)."} {"t":"q","id":14625,"q":"Jack took 30 minutes to run 3 . Fill in the blank with 'cm', 'm' or 'km'.","e":"Running for 30 minutes covers about 3 kilometres, so the unit is km."} {"t":"q","id":14626,"q":"The height of the door is about 2 . Fill in the blank with 'cm', 'm' or 'km'.","e":"A door is about 2 metres tall, so the unit is m."} {"t":"q","id":14634,"q":"4 thousands, 6 hundreds and 9 ones is the same as .","e":"4 thousands = 4000, 6 hundreds = 600, 9 ones = 9. 4000 + 600 + 9 = 4609."} {"t":"q","id":14635,"q":"In 4012, the digit 1 is in the place.","e":"In 4012, reading from the right: 2 ones, 1 ten, 0 hundreds, 4 thousands. So the digit 1 is in the tens place."} {"t":"q","id":14638,"q":"What is the missing number in the following number pattern?\n2365 , 2375 , 2395 , , 2465 , 2515","e":"The differences increase by 10 each time: +10 (2365->2375), +20 (2375->2395), +30 (2395->2425), +40 (2425->2465), +50 (2465->2515). The missing number is 2425."} {"t":"q","id":14639,"q":"The sum of two numbers is 400. The smaller number is 120. What is the difference between the two numbers?","e":"The larger number = 400 - 120 = 280. Difference = 280 - 120 = 160."} {"t":"q","id":14640,"q":"I am a number between 20 and 40. You can find me in the multiplication tables of 6 and 8. What number am I?","e":"A common multiple of 6 and 8 between 20 and 40 is 24 (6 x 4 = 24 and 8 x 3 = 24)."} {"t":"q","id":14641,"q":"A x A = 81\n45 \/ A = B\nWhat is the missing number represented by B?","e":"A x A = 81, so A = 9. Then B = 45 \/ 9 = 5."} {"t":"q","id":14642,"q":"John saved $124 each month. Tom saved 3 times as much as John each month. How much would Tom save in 6 months?","e":"Tom saves 3 x $124 = $372 each month. In 6 months: $372 x 6 = $2232."} {"t":"q","id":14643,"q":"The length of Ribbon A is 5 times as long as Ribbon B. Ribbon B is 36 cm shorter than Ribbon A. Find the length of Ribbon A.","e":"A = 5 units, B = 1 unit. A - B = 4 units = 36 cm, so 1 unit = 9 cm. Ribbon A = 5 x 9 = 45 cm."} {"t":"q","id":14646,"q":"3 2 4\n- 1 5 9 7\n 1 2 7\nWhat are the missing digits represented by K and J?","e":"32K4 - 1597 = 1J27. Tens column gives K = 2 (so 3224 - 1597 = 1627), making J = 6. First blank K = 2, second blank J = 6."} {"t":"q","id":14647,"q":"Use all the digits 4, 8 and 6 to form the greatest 3-digit number. Find the quotient when the 3-digit number is divided by 2.
Answer: ","e":"Greatest 3-digit number from 4, 8, 6 is 864. 864 \/ 2 = 432."} {"t":"q","id":14648,"q":"Two numbers, A and B, add up to 600. Given that both of them are 3-digit numbers greater than 100, find the greatest possible difference between A and B.
Answer: ","e":"To maximise the difference, make one number as large as possible and the other the smallest 3-digit number greater than 100, which is 101. The other is 600 - 101 = 499. Difference = 499 - 101 = 398."} {"t":"q","id":14651,"q":"Arrange the following numbers in order, beginning with the greatest.\n\n8909, 989, 9098, 899","e":"Compare: 9098 > 8909 > 989 > 899. Greatest first gives 9098, 8909, 989, 899."} {"t":"q","id":14653,"q":"In the sum of 333 and 999, the digit in the _____ place is an even number.","e":"333 + 999 = 1332. Digits: 1 (thousands), 3 (hundreds), 3 (tens), 2 (ones). Only the ones digit, 2, is even."} {"t":"q","id":14664,"q":"A number when divided by 8 gives a remainder of 4. Which of the following can be added to the number so that it will leave no remainder when divided by 8?","e":"A remainder of 4 means 4 more is needed to reach the next multiple of 8, so adding 4 leaves no remainder."} {"t":"q","id":14665,"q":"Adam, Bobby, Caden and Dennis collected some toy cars. Adam collected the least number of toy cars. Bobby collected more toy cars than Dennis but fewer than Caden. Who collected the most number of toy cars?","e":"Adam is least; Dennis < Bobby < Caden. So Caden collected the most."} {"t":"q","id":14671,"q":"Use all the digits 6, 5, 1, 3 to form the smallest odd number.\n\n","e":"For the smallest number, order digits ascending (1,3,5,6); for it to be odd the ones digit must be odd. Smallest is 1365 (ends in 5, with 1,3,6 arranged smallest in front)."} {"t":"q","id":14674,"q":"I am a 4-digit number. The digits in my thousands place and ones place are the same. The digit in my tens place is 8 less than the digit in my thousands place. The value of the digit in my hundreds place is 300. What number am I?\n\n","e":"Hundreds digit value 300 means hundreds digit = 3. Tens digit is 8 less than thousands digit; thousands = ones. If thousands = 8 then tens = 0 and ones = 8, giving 8308."} {"t":"q","id":14675,"q":"Mrs Singh bought 45 cookies. She bought 9 times as many cookies as Mdm Aminah. How many cookies did Mdm Aminah buy?\n\n","e":"45 \u00f7 9 = 5 cookies."} {"t":"q","id":14676,"q":"Mary had $548. She had $245 more than her sister. How much did her sister have?\n\n$","e":"$548 \u2212 $245 = $303."} {"t":"q","id":14677,"q":"Study the pattern. What is the missing number?\n\n220, 230, 200, , 180, 190","e":"The pattern alternates: 220, 230, 200, 210, 180, 190 (each pair drops by 20, then +10). The missing number is 210."} {"t":"q","id":14679,"q":"Mrs Tan bought a packet of orange juice. She poured all the orange juice equally into 9 cups of 225 ml each. What is the volume of the orange juice in the packet? Give your answer in \u2113 and ml.\n\n \u2113 ml","e":"9 \u00d7 225 ml = 2025 ml = 2 \u2113 25 ml."} {"t":"q","id":14683,"q":"A pair of jeans cost $66. A skirt is $9.20 cheaper than the jeans. Find the cost of the skirt.\n\n$","e":"$66 \u2212 $9.20 = $56.80."} {"t":"q","id":14684,"q":"The table shows the opening hours of a clinic.\nMorning: 8.00 a.m. to 11.30 a.m.\nAfternoon: 2.00 p.m. to 4.00 p.m.\nEvening: 6.30 p.m. to 9.00 p.m.\nHow many hours is the clinic open in a day?\n\n h","e":"Morning 3 h 30 min + Afternoon 2 h + Evening 2 h 30 min = 8 h."} {"t":"q","id":14685,"q":"What are the missing numbers in the fractions?\n\n2\/a = 6\/15 = b\/25\n\na = , b = ","e":"6\/15 simplifies to 2\/5, so a = 5. For b\/25 = 2\/5, multiply numerator and denominator by 5: b = 10."} {"t":"q","id":14686,"q":"Which of the following fractions is smaller than \\(\\dfrac{1}{3}\\)?\n\n\\(\\dfrac{2}{9}\\), \\(\\dfrac{1}{2}\\), \\(\\dfrac{5}{6}\\)","e":"1\/3 = 3\/9. 2\/9 < 3\/9, so 2\/9 is smaller than 1\/3; 1\/2 and 5\/6 are both larger."} {"t":"q","id":14687,"q":"Julie collected 1480 stickers. Stephanie collected 288 stickers more than Julie.\n(a) How many stickers did Stephanie collect?\n(b) How many stickers did the two girls collect altogether?\n\n(a) \n(b) ","e":"(a) 1480 + 288 = 1768. (b) 1768 + 1480 = 3248."} {"t":"q","id":14688,"q":"Mrs Chandra bought 9 boxes of cupcakes. Each box contained 28 cupcakes. She repacked the cupcakes equally into 4 large containers. How many cupcakes were there in each large container?\n\n","e":"Total cupcakes = 9 \u00d7 28 = 252. 252 \u00f7 4 = 63 per container."} {"t":"q","id":14689,"q":"Zan ran around his school during his PE lesson. He took 18 minutes to finish running one round.\n(a) How long would he take to finish running 5 rounds, given that he took the same amount of time for every round?\n(b) Zan completed his 5 rounds at 11.45 a.m. What time did he start running?\n\n(a) min\n(b) ","e":"(a) 18 \u00d7 5 = 90 minutes (= 1 h 30 min). (b) 11.45 a.m. minus 1 h 30 min = 10.15 a.m."} {"t":"q","id":14698,"q":"Yiming has 6 shelves of books. On each shelf, there are 78 books. How many books does Yiming have altogether?","e":"6 \u00d7 78 = 468."} {"t":"q","id":14699,"q":"Sally bought 7 similar toy cars for $504. How much did she pay for each toy car?","e":"$504 \u00f7 7 = $72."} {"t":"q","id":14702,"q":"Find the product of 67 and 8.
Answer: ","e":"67 \u00d7 8 = 536."} {"t":"q","id":14703,"q":"Jamie has $486. Amy has 9 times the amount of money that Jamie has. How much money does Amy have?
Answer: ","e":"9 \u00d7 $486 = $4374."} {"t":"q","id":14704,"q":"Divide 90 tens by 3.
Answer: ","e":"90 tens = 900, and 900 \u00f7 3 = 300."} {"t":"q","id":14705,"q":"408 toy cars are to be shared equally among 6 children. How many toy cars will each child get?
Answer: ","e":"408 \u00f7 6 = 68."} {"t":"q","id":14710,"q":"Vindu had $23.80 in savings. He received another $48.40 from his father. How much money did he have in the end?
Answer: ","e":"$23.80 + $48.40 = $72.20."} {"t":"q","id":14711,"q":"Shakilah spent $9.65 on a burger set. Her father then gave her another $39.40. She had $89.50 in the end. How much money did she have at first?
Answer: ","e":"$89.50 \u2212 $39.40 = $50.10; $50.10 + $9.65 = $59.75."} {"t":"q","id":14712,"q":"A box can hold a maximum of 4 cans of paint. There are 879 cans of paint to be packed into boxes. What is the least number of boxes needed to hold all the cans of paint?
Answer: ","e":"879 \u00f7 4 = 219 remainder 3; the leftover 3 cans need 1 more box, so 219 + 1 = 220."} {"t":"q","id":14713,"q":"Mrs Low baked 754 cookies in the morning. After selling some cookies, she baked 300 more cookies. She had 469 cookies at the end of the day. How many cookies did Mrs Low sell?
Answer: ","e":"Without the 300 baked later, she would have had 469 \u2212 300 = 169 from the morning batch left. So she sold 754 \u2212 169 = 585 cookies."} {"t":"q","id":14714,"q":"Jensen had $489. He had $285 more than Ariz. Ariz had 4 times as much money as Laura. How much money did Laura have?
Answer: ","e":"Ariz = $489 \u2212 $285 = $204. Laura = $204 \u00f7 4 = $51."} {"t":"q","id":14715,"q":"Giselle had $38.80 more than Caleb at first. Giselle spent $24.40 on a book while Caleb received some money from his father. Caleb then had $45.60 more than Giselle. How much did Caleb receive from his father?
Answer: ","e":"After Giselle spent $24.40, the gap by which Giselle led shrank to $38.80 \u2212 $24.40 = $14.40. To swing from Caleb being $14.40 behind to $45.60 ahead, Caleb's father gave $14.40 + $45.60 = $60."} {"t":"q","id":14718,"q":"Which of the following does not have the same value as 1\/2 ?","e":"4\/8, 5\/10 and 6\/12 all simplify to 1\/2. 2\/6 simplifies to 1\/3, so it is not equal to 1\/2."} {"t":"q","id":14719,"q":"Which of the following fractions is the greatest?","e":"Using denominator 12: 2\/3 = 8\/12, 3\/4 = 9\/12, 5\/6 = 10\/12, 7\/12 = 7\/12. The greatest is 10\/12 = 5\/6."} {"t":"q","id":14726,"q":"What is the missing number in the box?\n2852 + 601 = 8923","e":"8923 \u2212 2852 = 6071, so the second addend is 6071. The boxed (tens) digit is 7."} {"t":"q","id":14729,"q":"Edwin studied from 3.10 p.m. to 4.55 p.m. How long did he study?\n h min","e":"From 3.10 p.m. to 4.10 p.m. is 1 h; 4.10 to 4.55 is 45 min. Total = 1 h 45 min."} {"t":"q","id":14737,"q":"Find the quotient when 726 is divided by 7.","e":"726 \u00f7 7 = 103 remainder 5. The quotient is 103."} {"t":"q","id":14738,"q":"150 masks were packed equally into 6 boxes. How many masks were there in each box?","e":"Divide equally: 150 \u00f7 6 = 25 masks in each box."} {"t":"q","id":14740,"q":"2 \u00d7 = 56 \u00f7 7","e":"First 56 \u00f7 7 = 8. Then 2 \u00d7 [?] = 8, so [?] = 8 \u00f7 2 = 4."} {"t":"q","id":14741,"q":"Multiply 187 by 5.
Answer: ","e":"187 \u00d7 5 = 935."} {"t":"q","id":14742,"q":"Find the remainder when 831 is divided by 8.
Answer: ","e":"831 \u00f7 8 = 103 remainder 7 (since 8 \u00d7 103 = 824, and 831 \u2212 824 = 7)."} {"t":"q","id":14743,"q":"Max wants to build 4 figurines for a competition. Each figurine requires 102 pieces of blocks. What is the total number of pieces of blocks he needs altogether?
Answer: ","e":"Total blocks = 4 \u00d7 102 = 408 pieces."} {"t":"q","id":14744,"q":"John and Mark collected 372 stamps. Mark collected twice as many stamps as John. How many stamps did John collect?
Answer: ","e":"John is 1 unit, Mark is 2 units, so 3 units = 372. One unit (John) = 372 \u00f7 3 = 124 stamps."} {"t":"q","id":14745,"q":"Grace bought 6 cakes for a birthday party. Each cake cost $54 and she paid $360. How much change did she receive?
Answer: ","e":"Cost of cakes = 6 \u00d7 $54 = $324. Change = $360 \u2212 $324 = $36."} {"t":"q","id":14746,"q":"8 identical magazines cost $104. A book costs 3 times as much as a magazine. How much does a book cost?
Answer: ","e":"One magazine = $104 \u00f7 8 = $13. A book = 3 \u00d7 $13 = $39."} {"t":"q","id":14750,"q":"Which of the following is equivalent to 2\/3?","e":"Multiply both the numerator and denominator of 2\/3 by 2: (2x2)\/(3x2) = 4\/6. So 4\/6 is equivalent to 2\/3. The answer is 4\/6."} {"t":"q","id":14754,"q":"Subtract \\(\\dfrac{1}{12}\\) from \\(\\dfrac{3}{4}\\). Give your answer in its simplest form.","e":"Convert 3\/4 to twelfths: 3\/4 = 9\/12. Then 9\/12 - 1\/12 = 8\/12. Simplify 8\/12 by dividing top and bottom by 4 to get 2\/3. The answer is 2\/3."} {"t":"q","id":14755,"q":"Arrange the fractions in order. Begin with the greatest.\n\n2\/11, 7\/9, 2\/3
(a)   (b)   (c) ","e":"Compare the sizes: 7\/9 is close to 1 (about 0.78), 2\/3 is about 0.67, and 2\/11 is small (about 0.18). From greatest to smallest: 7\/9, 2\/3, 2\/11. The answer is 7\/9, 2\/3, 2\/11."} {"t":"q","id":14757,"q":"Shirley had 2 five-dollar notes. She bought 6 pens that cost 90 cents each.\n\n(a) How much money did Shirley pay for the 6 pens?\n(b) How much money did Shirley have left after buying 6 pens?
(a)   (b) ","e":"(a) Each pen costs 90 cents = $0.90. For 6 pens: $0.90 x 6 = $5.40. (b) Shirley had 2 x $5 = $10. Money left = $10 - $5.40 = $4.60."} {"t":"q","id":14758,"q":"A packet of sugar and 8 similar packets of noodles weight 5700 g. The mass of the packet of sugar is 900 g.\n\n(a) What is the total mass of the 8 packets of noodles?\n(b) What is the mass of each packet of noodles?
(a)   (b) ","e":"(a) Total mass minus the sugar gives the noodles: 5700 g - 900 g = 4800 g. (b) Divide the noodles' total by 8 packets: 4800 g \/ 8 = 600 g each."} {"t":"q","id":14759,"q":"Mr Lim had 4 times as many muffins as Ms Siti. After selling 63 muffins, he had as many muffins as Ms Siti. How many muffins did Mr Lim have at first?
Answer: ","e":"Let Ms Siti have 1 unit; Mr Lim has 4 units. After selling 63, Mr Lim's muffins equal Ms Siti's 1 unit, so the 63 sold equals 4 units - 1 unit = 3 units. So 1 unit = 63 \/ 3 = 21. Mr Lim had 4 units = 4 x 21 = 84 muffins at first. The answer is 84."} {"t":"q","id":14760,"q":"5083 is the same as .","e":"5083 in place values is 5 thousands + 0 hundreds + 8 tens + 3 ones = 5000 + 80 + 3. Option (3) matches."} {"t":"q","id":14761,"q":"Find the value of 8000 \u2212 615.","e":"8000 \u2212 615 = 7385. Option (2) is correct."} {"t":"q","id":14762,"q":"Find the product of 234 and 9.","e":"Product means multiply: 234 \u00d7 9 = 2106. Option (4) is correct."} {"t":"q","id":14764,"q":"A box can hold 6 pencils. Jenny has 91 pencils. What is the least number of such boxes she needs to put all the pencils?","e":"91 \u00f7 6 = 15 remainder 1. Fifteen full boxes hold 90 pencils, and the 1 leftover pencil needs one more box, so 15 + 1 = 16 boxes. Option (2) is correct."} {"t":"q","id":14765,"q":"Arrange the numbers below in increasing order.\n3786 , 3687 , 3768\nAns: , , ","e":"All three share the thousands digit 3. Compare hundreds: 3687 has 6, 3768 and 3786 have 7. So 3687 is smallest. Between 3768 and 3786 the tens digit decides: 6 < 8, so 3768 < 3786. Increasing order: 3687, 3768, 3786."} {"t":"q","id":14767,"q":"What is the quotient when 106 is divided by 9?\nAns: ","e":"106 \u00f7 9 = 11 remainder 7. The quotient is the whole-number result, which is 11."} {"t":"q","id":14769,"q":"Leon collected 196 game cards. He collected 7 times as many game cards as Jim. How many game cards did Jim collect?\nAns: ","e":"Leon has 7 times as many as Jim, so Jim's amount is 196 \u00f7 7 = 28 game cards."} {"t":"q","id":14770,"q":"Mrs Lee bought a dress for $39.90 and a pair of shoes for $58.50. She had $24.10 left.\n(a) How much did the dress and shoes cost?\n(b) How much money did Mrs Lee have at first?\nAns: (a) (b) ","e":"(a) Cost of dress and shoes = $39.90 + $58.50 = $98.40. (b) Money at first = amount spent + amount left = $98.40 + $24.10 = $122.50."} {"t":"q","id":14771,"q":"Esther and Kelly have 4879 stickers altogether. Esther has 1243 stickers. How many more stickers does Kelly have than Esther?\nAns: ","e":"Kelly's stickers = 4879 \u2212 1243 = 3636. Kelly has 3636 \u2212 1243 = 2393 more stickers than Esther."} {"t":"q","id":14772,"q":"Eugene did a Math quiz. He answered 26 questions correctly. The number of questions he answered correctly was 2 times the number of questions he answered incorrectly.\n(a) What was the total number of questions that he answered incorrectly?\n(b) For each question answered correctly, Eugene was awarded 8 points. How many points did Eugene score?\nAns: (a) (b) ","e":"(a) Correct = 2 times incorrect, so incorrect = 26 \u00f7 2 = 13 questions. (b) Points = 8 for each correct answer = 26 \u00d7 8 = 208 points."} {"t":"q","id":14775,"q":"Which of the following fractions is equivalent to 3\/4?","e":"Multiply both the numerator and denominator of 3\/4 by 3: (3x3)\/(4x3) = 9\/12. So 9\/12 is equivalent to 3\/4."} {"t":"q","id":14777,"q":"- 2\/9 = 1\/3\nWhat is the missing fraction in the box?","e":"Add 2\/9 to both sides: box = 1\/3 + 2\/9. Convert 1\/3 to ninths: 1\/3 = 3\/9. Then 3\/9 + 2\/9 = 5\/9. So the missing fraction is 5\/9."} {"t":"q","id":14778,"q":"Which one of the following fractions is the greatest?","e":"With the same numerator, a smaller denominator is larger, and with the same denominator, a larger numerator is larger. 7\/9 is the largest: 7\/9 is more than half, and its numerator (7) is bigger than 5 and its denominator (9) is smaller than 12."} {"t":"q","id":14780,"q":"Express \\(\\dfrac{14}{20}\\) in its simplest form.","e":"Divide both numerator and denominator by their highest common factor, 2: 14\/20 = (14\u00f72)\/(20\u00f72) = 7\/10. Since 7 and 10 share no common factor, 7\/10 is in simplest form."} {"t":"q","id":14782,"q":"Arrange the following fractions from the greatest to the smallest.\n1\/2 , 1\/8 , 3\/4\n , , ","e":"Convert to eighths: 1\/2 = 4\/8, 1\/8 = 1\/8, 3\/4 = 6\/8. Ordering 6\/8 > 4\/8 > 1\/8 gives, from greatest to smallest: 3\/4, 1\/2, 1\/8."} {"t":"q","id":14788,"q":"7508 = 7000 + + 8","e":"7508 = 7000 + 500 + 8. The hundreds value is 500, so the blank is 500."} {"t":"q","id":14792,"q":" - 4438 = 3267","e":"To find the missing number, add: 3267 + 4438 = 7705. Check: 7705 - 4438 = 3267."} {"t":"q","id":14793,"q":"Look at the numbers.\n6079, 2548, 5284, 6709\nFind the sum of the greatest number and the smallest number.\n","e":"Greatest number is 6709, smallest is 2548. Sum = 6709 + 2548 = 9257."} {"t":"q","id":14794,"q":"8 + 8 + 8 + 8 = 16 + x 8","e":"8 + 8 + 8 + 8 = 32. So 32 = 16 + (blank x 8). 32 - 16 = 16, and 16 div 8 = 2, so the blank is 2."} {"t":"q","id":14795,"q":"Grace has 7 party bags. Siti has 4 times as many party bags as Grace. How many party bags does Siti have?\n","e":"Siti has 4 times Grace's 7 party bags: 7 x 4 = 28 party bags."} {"t":"q","id":14796,"q":"Amy packed 63 apples equally into some fruit baskets. Each fruit basket contained 7 apples. How many fruit baskets would Amy have?\n","e":"Number of baskets = total apples div apples per basket = 63 div 7 = 9 baskets."} {"t":"q","id":14797,"q":"There were 10 rows of seats in a theatre. There were 9 seats in each row. Only 2 seats were not occupied. How many seats in the theatre were occupied?\n","e":"Total seats = 10 x 9 = 90. Occupied = 90 - 2 = 88 seats."} {"t":"q","id":14798,"q":"Ravi has 9 stamps. Sandra has 5 times as many stamps as Ravi. How many stamps must Sandra give to Ravi so that they have the same number of stamps?\n","e":"Sandra has 5 x 9 = 45 stamps; Ravi has 9. Together = 45 + 9 = 54, so each should have 54 div 2 = 27. Sandra must give 45 - 27 = 18 stamps. (Equivalently, the difference is 45 - 9 = 36, and half of that, 18, is transferred.)"} {"t":"q","id":14799,"q":"Jack bought a computer and a printer. The computer cost $2549. The printer cost $1590 less than the computer.\n(a) How much did the printer cost? $\n(b) How much money did Jack spend altogether? $","e":"(a) Printer = $2549 - $1590 = $959. (b) Total = computer + printer = $2549 + $959 = $3508."} {"t":"q","id":14800,"q":"The sum of two numbers is 4086. The smaller number is 1260. What is the difference between the two numbers?\n","e":"Bigger number = 4086 - 1260 = 2826. Difference = 2826 - 1260 = 1566."} {"t":"q","id":14801,"q":"Kumar had $1542 at first. After spending $352, Kumar still had $157 more than Eric. How much money did Eric have?\n$","e":"After spending, Kumar had $1542 - $352 = $1190. This is $157 more than Eric, so Eric had $1190 - $157 = $1033. (Key combines: $157 + $352 = $509, then $1542 - $509 = $1033.)"} {"t":"q","id":14802,"q":"In 4985, which digit is in the thousands place?","e":"In 4985 the digits from the right are: 5 ones, 8 tens, 9 hundreds, 4 thousands. So the digit in the thousands place is 4."} {"t":"q","id":14803,"q":"7854 = 7000 + 800 + + 4\nWhat is the missing number in the box?","e":"Expanded form of 7854 is 7000 + 800 + 50 + 4. The tens digit is 5, worth 50. So the missing number is 50."} {"t":"q","id":14804,"q":"Which of the following is true?","e":"Compare each: 101 < 110 (false); 970 > 410 (false); 8420 > 8220 (false); 7052 > 7025 because the tens digit 5 > 2 (true). So option 4 is correct."} {"t":"q","id":14807,"q":"Write eight thousand and five in numerals.
Answer: ","e":"Eight thousand = 8000, and five = 5 ones. There are no hundreds or tens, so write 0 in those places: 8005."} {"t":"q","id":14808,"q":"Look at the following number pattern. What are the missing numbers?\n , , 283, 287, 291, 295","e":"The numbers increase by 4 each time (283, 287, 291, 295). Working backwards: 283 - 4 = 279 and 279 - 4 = 275. So the missing numbers are 275 and 279."} {"t":"q","id":14811,"q":"Hannah and Oliver had the same amount of money. Hannah bought a burger and she had $0.40 left. Oliver bought a packet of fries and he had $1.20 left.\na) Which food item cost more?\nb) How much more did that food item cost?
(a)   (b) ","e":"They started with the same amount. Hannah had less left ($0.40 vs $1.20), so her item (the burger) cost more. The difference in money left is $1.20 - $0.40 = $0.80, so the burger cost $0.80 more."} {"t":"q","id":14812,"q":"At a carnival, there were 1782 children. There were 562 fewer adults than children.\na) How many adults were there?\nb) How many people were there at the carnival altogether?
(a)   (b) ","e":"a) Adults = children - 562 = 1782 - 562 = 1220. b) Altogether = children + adults = 1782 + 1220 = 3002."} {"t":"q","id":14813,"q":"Jack had 120 more stickers than Megan at first. After Jack gave 456 stickers to Megan, he was left with 214 stickers.\na) How many stickers did Jack have at first?\nb) How many stickers did Megan have at first?
(a)   (b) ","e":"a) Before giving away 456, Jack had 214 + 456 = 670 stickers. b) Megan had 120 fewer than Jack at first: 670 - 120 = 550 stickers."} {"t":"q","id":14814,"q":"Which of the following has the same value as 5 x 7?","e":"5 x 7 means 7 groups of 5, i.e. 5 added seven times: 5 + 5 + 5 + 5 + 5 + 5 + 5 = 35. Option (4) matches."} {"t":"q","id":14815,"q":"Divide 48 by 8.","e":"48 \u00f7 8 = 6, because 6 x 8 = 48. Option (1)."} {"t":"q","id":14821,"q":"\u00f7 7 = 13 R 4\nWhat is the missing number in the box?","e":"Missing number = quotient x divisor + remainder = 13 x 7 + 4 = 91 + 4 = 95. Option (3)."} {"t":"q","id":14822,"q":"There are 36 clips in a bag. Jason has 6 such bags. He repacks them into 3 equal boxes. How many clips are there in each box?","e":"Total clips = 36 x 6 = 216. Repacked into 3 equal boxes: 216 \u00f7 3 = 72 clips per box. Option (4)."} {"t":"q","id":14823,"q":"Sarah had 720 beads at first. She gave an equal number of beads to each of her 4 friends and had 24 beads left. How many beads did Sarah give to each friend?","e":"Beads given away = 720 - 24 = 696. Shared equally among 4 friends: 696 \u00f7 4 = 174 beads each. Option (3)."} {"t":"q","id":14824,"q":"Find the product of 214 and 9.
Answer: ","e":"Product means multiply: 214 x 9 = 1926."} {"t":"q","id":14825,"q":" 7 8\n x 7\n2 6 4 6\nWhat is the missing digit in the box?","e":"The 3-digit number ?78 multiplied by 7 gives 2646. 2646 \u00f7 7 = 378, so the hundreds digit is 3. Check: 378 x 7 = 2646."} {"t":"q","id":14831,"q":"Bernice packed a total of 45 red and blue pens into bags. There were 2 red and 3 blue pens in each bag. How many red pens were there altogether?
Answer: ","e":"Each bag holds 2 + 3 = 5 pens. Number of bags = 45 \u00f7 5 = 9. Red pens = 9 x 2 = 18."} {"t":"q","id":14832,"q":"Jayden had 540 marbles. He packed all his marbles into bags of 8 marbles equally. He had the most number of bags packed. How many marbles were left unpacked?
Answer: ","e":"540 \u00f7 8 = 67 remainder 4 (67 x 8 = 536). The most bags he can fill is 67, leaving 540 - 536 = 4 marbles unpacked."} {"t":"q","id":14833,"q":"Noah had 56 stamps. He gave Ollie 8 stamps. (a) How many stamps did Noah have in the end? (b) In the end, Ollie had twice as many stamps as Noah in the end. How many stamps did the two boys have altogether?
(a)   (b) ","e":"(a) Noah's stamps in the end = 56 - 8 = 48. (b) Ollie had twice as many as Noah: 48 x 2 = 96. Altogether = 96 + 48 = 144 stamps."} {"t":"q","id":14839,"q":"Which of the following fractions is the greatest?","e":"9\/10 = 0.9 is the closest to 1. 1\/3 = 0.33, 2\/5 = 0.4, 5\/9 = 0.56, so 9\/10 is the greatest."} {"t":"q","id":14840,"q":"Add the fractions. Express your answer in its simplest form. 5\/12 + 1\/4 =","e":"Make the denominators the same: 1\/4 = 3\/12. Then 5\/12 + 3\/12 = 8\/12 = 2\/3 in simplest form."} {"t":"q","id":14841,"q":"The volume of 1 bottle of juice is 1 l. The volume of 1 carton of milk is 320 ml. Willy bought 1 bottle of juice and 2 cartons of milk. What was the total volume of the items bought?","e":"1 l = 1000 ml. Two cartons of milk = 2 x 320 ml = 640 ml. Total = 1000 ml + 640 ml = 1640 ml."} {"t":"q","id":14843,"q":"Compare the fraction using '<' or '>'. 4\/5 7\/10","e":"Make the denominators the same: 4\/5 = 8\/10. Since 8\/10 > 7\/10, we have 4\/5 > 7\/10."} {"t":"q","id":14845,"q":"Express 2 m 9 cm in centimetres.
Answer: ","e":"1 m = 100 cm, so 2 m = 200 cm. 200 cm + 9 cm = 209 cm."} {"t":"q","id":14846,"q":"\\(\\dfrac{5}{8}\\) - \\(\\dfrac{1}{2}\\) =","e":"Make the denominators the same: 1\/2 = 4\/8. Then 5\/8 - 4\/8 = 1\/8."} {"t":"q","id":14847,"q":"Arrange the following fractions in order. Begin with the greatest. 3\/4, 3\/7, 3\/5
(a)   (b)   (c) ","e":"When the numerators are the same, the fraction with the smaller denominator is larger. Denominators 4 < 5 < 7, so 3\/4 > 3\/5 > 3\/7."} {"t":"q","id":14851,"q":"Bala is 163 cm. He is 15 cm taller than Lisa. (a) What is Lisa's height? (b) What is the total height of Bala and Lisa? Give your answer in metres and centimetres. (a) cm (b) m cm","e":"(a) Bala is 15 cm taller than Lisa, so Lisa = 163 - 15 = 148 cm. (b) Total = 148 + 163 = 311 cm = 3 m 11 cm."} {"t":"q","id":14852,"q":"A sack with 7 similar balls has a mass of 1500 g. The mass of the sack is 576 g. Find the mass of 1 ball.
Answer: ","e":"The 7 balls together weigh 1500 g - 576 g = 924 g. Each ball is 924 \/ 7 = 132 g."} {"t":"q","id":14854,"q":"Which of the following is the same as 9 kg 35 g?","e":"1 kg = 1000 g, so 9 kg = 9000 g. Then 9 kg 35 g = 9000 g + 35 g = 9035 g. The answer is 9035 g."} {"t":"q","id":14855,"q":"Which of the following fractions is the smallest?","e":"These are all unit fractions (numerator 1). For unit fractions, the larger the denominator, the smaller the fraction. The largest denominator is 8, so 1\/8 is the smallest."} {"t":"q","id":14856,"q":"What is the missing number in the box? 3\/12 = 1\/","e":"Express 3\/12 in its simplest form. Divide both the numerator and denominator by 3: 3 divided 3 = 1 and 12 divided 3 = 4, giving 1\/4. So the missing number is 4."} {"t":"q","id":14857,"q":"Which fraction is greater than 1\/2?","e":"A fraction is greater than 1\/2 when its numerator is more than half its denominator. For 4\/5, half of 5 is 2.5 and 4 is more than that, so 4\/5 > 1\/2. The others (3\/7, 1\/3, 4\/11) are all less than 1\/2."} {"t":"q","id":14860,"q":"Find the value of \\(\\dfrac{7}{10}\\) - \\(\\dfrac{1}{2}\\). Give your answer in the simplest form.","e":"Make the denominators the same: 1\/2 = 5\/10. Then 7\/10 - 5\/10 = 2\/10. Simplify 2\/10 by dividing top and bottom by 2 to get 1\/5."} {"t":"q","id":14863,"q":"Ahmad jogged 4500 m. He jogged 555 m more than his sister. (a) What was the distance Ahmad's sister jogged? (b) Find the total distance Ahmad and his sister jogged. Give your answer in km and m. (a) m (b) ","e":"(a) The sister jogged 555 m less than Ahmad: 4500 - 555 = 3945 m. (b) Total = 4500 + 3945 = 8445 m = 8 km 445 m."} {"t":"q","id":14864,"q":"Mrs Tan spent $568. Mrs Chandran spent twice as much money as Mrs Tan. Mdm Zu spent $300 less than Mrs Chandran. (a) How much money did Mrs Chandran spend? (b) How much more money did Mdm Zu spend than Mrs Tan? (a) $ (b) $","e":"(a) Mrs Chandran = 2 x $568 = $1136. (b) Mdm Zu = $1136 - $300 = $836. Mdm Zu spent more than Mrs Tan by $836 - $568 = $268."} {"t":"q","id":14866,"q":"How many hundreds are there in 8300?","e":"8300 = 83 hundreds (8300 \u00f7 100 = 83). The answer is 83."} {"t":"q","id":14868,"q":"In which of the following are the numbers arranged from the smallest to the greatest?","e":"All share 4 thousands. Compare hundreds\/tens: 4786 < 4867 < 4876. So 4786 , 4867 , 4876 is smallest to greatest."} {"t":"q","id":14871,"q":"What is the value of 9 ten-cent coins and 4 fifty-cent coins?","e":"9 \u00d7 10\u00a2 = 90\u00a2 and 4 \u00d7 50\u00a2 = 200\u00a2. Total = 90\u00a2 + 200\u00a2 = 290\u00a2 = $2.90."} {"t":"q","id":14872,"q":"Ali bought 39 cherries and Jane bought 18 cherries. They ate 17 cherries altogether. How many cherries were left?","e":"Total bought = 39 + 18 = 57. Cherries left = 57 \u2212 17 = 40."} {"t":"q","id":14873,"q":"A total of 5842 visitors visited a museum in June. There were 1326 more visitors in June than in May. How many visitors were there in May?","e":"June had 1326 more than May, so May = 5842 \u2212 1326 = 4516 visitors."} {"t":"q","id":14874,"q":"Sumei has 63 curry puffs. She needs to pack them in boxes of 7. How many boxes does she need to pack all the curry puffs?","e":"63 \u00f7 7 = 9, so she needs 9 boxes."} {"t":"q","id":14877,"q":"Use all the digits 8, 3, 5 and 2 to form the smallest 4-digit odd number.
Answer: ","e":"An odd number must end in an odd digit (3 or 5). For the smallest number, use the smallest leading digit 2, then arrange the rest smallest first while keeping an odd unit: 2385."} {"t":"q","id":14878,"q":"Write 9 thousands, 6 tens and 8 ones in numerals.
Answer: ","e":"9 thousands = 9000, 0 hundreds, 6 tens = 60, 8 ones = 8. Together: 9068."} {"t":"q","id":14879,"q":"Subtract 1697 from 6294.
Answer: ","e":"6294 \u2212 1697 = 4597."} {"t":"q","id":14880,"q":"Susan bought 7 boxes of donuts for a party. There were 6 donuts in each box. How many donuts did Susan buy altogether?
Answer: ","e":"7 boxes \u00d7 6 donuts = 42 donuts."} {"t":"q","id":14881,"q":"Jason read 72 pages of his storybook in 9 days. Every day, he read the same number of pages. How many pages did Jason read in a day?
Answer: ","e":"72 pages \u00f7 9 days = 8 pages per day."} {"t":"q","id":14883,"q":"Jane has 30 stickers. She has 6 times as many stickers as Alice. How many stickers does Alice have?
Answer: ","e":"Jane = 6 times Alice, so Alice = 30 \u00f7 6 = 5 stickers."} {"t":"q","id":14884,"q":"Mr Ong bought a lego set for $26.35 and a board game for $37.95. How much did he pay for the two items?
Answer: ","e":"$26.35 + $37.95 = $64.30."} {"t":"q","id":14885,"q":"Jane bought 4 boxes of erasers. There were 10 erasers in each box. She repacked all the erasers equally into 8 bags. How many erasers were there in each bag?
Answer: ","e":"Total erasers = 4 \u00d7 10 = 40. Repacked into 8 bags: 40 \u00f7 8 = 5 erasers per bag."} {"t":"q","id":14886,"q":"The difference between two numbers is 345. The smaller number is 876. What is the sum of the two numbers?
Answer: ","e":"The larger number = 876 + 345 = 1221. Sum = 1221 + 876 = 2097."} {"t":"q","id":14887,"q":"A bag of 3 oranges costs $7. How many oranges can be bought with $56?
Answer: ","e":"$56 \u00f7 $7 = 8 bags. Each bag has 3 oranges, so 8 \u00d7 3 = 24 oranges."} {"t":"q","id":14889,"q":"There were 8000 books in a community library. 5686 books were fiction books while the rest were non-fiction books.\n(a) How many non-fiction books were there?\n(b) How many more fiction books than non-fiction books were there?
(a)   (b) ","e":"(a) Non-fiction = 8000 \u2212 5686 = 2314 books. (b) More fiction than non-fiction = 5686 \u2212 2314 = 3372 books."} {"t":"q","id":14890,"q":"Mrs Gomez baked some cupcakes. She kept 26 cupcakes for her family and gave the rest equally to 6 neighbours. Each neighbour received 9 cupcakes. How many cupcakes did Mrs Gomez bake?
Answer: ","e":"Given away = 6 neighbours \u00d7 9 = 54 cupcakes. Total baked = 54 + 26 kept = 80 cupcakes."} {"t":"q","id":14891,"q":"Last Saturday, Mrs Wang went to the zoo with her two children. Mrs Wang bought an adult and two children tickets. An adult ticket cost $48. It cost $15 more than a child ticket.\n(a) How much did a child ticket cost?\n(b) How much did Mrs Wang pay for all the three tickets?
(a)   (b) ","e":"(a) Child ticket = $48 \u2212 $15 = $33. (b) Two child tickets = $33 + $33 = $66; plus adult $48: $66 + $48 = $114."} {"t":"q","id":14893,"q":"Arrange the numbers from the greatest to the smallest.\n8080 8008 888 8800\n , , , ","e":"Compare place values: 8800 > 8080 > 8008 > 888. Greatest to smallest: 8800, 8080, 8008, 888."} {"t":"q","id":14898,"q":"Gwen takes half an hour to travel to school every morning.\nWhat time does she leave home if she reaches school at 7.15 a.m?\n a.m.","e":"She arrives at 7.15 a.m. and travels for half an hour (30 min). 7.15 - 0.30 = 6.45 a.m."} {"t":"q","id":14902,"q":"James and Tim started working on their project at 7.50 a.m.\nJames stopped working at 9.30 a.m. Tim stopped working half an hour after James. How long did Tim spend working on the project?\n","e":"Tim stopped half an hour after James (9.30 a.m. + 30 min = 10.00 a.m.). From 7.50 a.m. to 10.00 a.m. is 2 h 10 min."} {"t":"q","id":14905,"q":"Aaron has 58 cards. He has 5 fewer cards than Ben.\nCharles has 6 times as many cards as Ben.\nHow many cards does Charles have?\n","e":"Aaron has 5 fewer than Ben, so Ben = 58 + 5 = 63. Charles = 6 x 63 = 378 cards."} {"t":"q","id":14906,"q":"Adam eats an egg every day from Monday to Saturday and two eggs every Sunday.\n(a) How many eggs does Adam eat in a week?\n(b) Adam buys a carton of 30 eggs to eat. How long will Adam take to finish all the eggs? (Leave your answer in weeks and days.)\n(a) eggs\n(b) weeks days","e":"(a) Monday to Saturday is 6 days x 1 egg = 6 eggs, plus 2 eggs on Sunday = 8 eggs a week. (b) 30 \/ 8 = 3 remainder 6, so 3 weeks and 6 more days are needed to finish all 30 eggs."} {"t":"q","id":14907,"q":"What is the missing number in the equation?\n0 x 7 = 8 -","e":"0 x 7 = 0, so 8 - [?] = 0, which means [?] = 8. The answer is 8."} {"t":"q","id":14909,"q":"Monica started watching a movie at 4.15 p.m. and ended at 6.05 p.m. What is the duration of the movie?","e":"From 4.15 p.m. to 6.15 p.m. is 2 h. From 6.05 p.m. back 10 min: 4.15 to 6.05 = 1 h 50 min (4.15 to 5.15 is 1 h, then 5.15 to 6.05 is 50 min)."} {"t":"q","id":14911,"q":"How many minutes are there in 3 h 40 min?","e":"3 h = 3 x 60 = 180 min. 180 min + 40 min = 220 min."} {"t":"q","id":14915,"q":"Arrange the following numbers from the smallest to the greatest.\n7937, 3797, 7397, 3977\n, , , ","e":"Compare by place value from the thousands. 3797 and 3977 start with 3; 3797 < 3977. 7397 and 7937 start with 7; 7397 < 7937. Order: 3797, 3977, 7397, 7937."} {"t":"q","id":14921,"q":"4979 is tens more than 4779.","e":"4979 - 4779 = 200. 200 = 20 tens, so 4979 is 20 tens more than 4779."} {"t":"q","id":14922,"q":"Form the smallest 4-digit odd number using all the digits 3 , 1 , 0 , 8.
Answer: ","e":"An odd number must end in an odd digit (1 or 3). To be smallest, the leading digit must be as small as possible but not 0, so use 1 first. Remaining digits 0, 8, 3 arranged smallest with an odd units digit: 0, 8, then 3 (odd) -> 1083."} {"t":"q","id":14924,"q":"Mary has 3 fifty-cent coins, 17 ten-cent coins and 12 five-cent coins in her coin box. How much money does Mary have in her coin box?
Answer: ","e":"3 x 50c = 150c = $1.50; 17 x 10c = 170c = $1.70; 12 x 5c = 60c = $0.60. Total = $1.50 + $1.70 + $0.60 = $3.80."} {"t":"q","id":14928,"q":"The sum of two numbers is 430. The smaller number is 120. What is the greater number?
Answer: ","e":"Greater number = sum - smaller number = 430 - 120 = 310."} {"t":"q","id":14930,"q":"Divide 754 by 4. What is the remainder?
Answer: ","e":"754 \/ 4 = 188 remainder 2 (since 4 x 188 = 752, and 754 - 752 = 2)."} {"t":"q","id":14931,"q":"Haron and Bala have 192 stamps altogether. Bala has 3 times as many stamps as Haron. How many stamps does Haron have?
Answer: ","e":"Haron is 1 unit, Bala is 3 units, total 4 units = 192. 1 unit = 192 \/ 4 = 48. Haron has 48 stamps."} {"t":"q","id":14932,"q":"On Sunday, 3015 people visited Chinatown. On Monday, 1527 fewer people visited Chinatown than on Sunday. How many people visited Chinatown on both days?
Answer: ","e":"Monday = 3015 - 1527 = 1488. Both days = 3015 + 1488 = 4503."} {"t":"q","id":14933,"q":"Gopal baked 72 cookies. He put them equally onto 8 trays. After giving away some trays of cookies, he had 45 cookies left. How many trays of cookies had he left?
Answer: ","e":"Each tray has 72 \/ 8 = 9 cookies. He had 45 cookies left, so 45 \/ 9 = 5 trays left."} {"t":"q","id":14934,"q":"Roy had $30. His father then gave him some money. After spending $15 on a storybook, Roy had $38 left. How much money did Roy receive from his father?
Answer: ","e":"Before spending, Roy had 38 + 15 = $53. He started with $30, so his father gave him 53 - 30 = $23."} {"t":"q","id":14936,"q":"In 4519, the value of the digit 5 is .","e":"The digit 5 is in the hundreds place. Its value is 5 hundreds = 500."} {"t":"q","id":14937,"q":"Which of the following leaves no remainder when divided by 4?","e":"72 \/ 4 = 18 exactly, no remainder. 14, 46 and 58 all leave a remainder when divided by 4."} {"t":"q","id":14938,"q":"Arrange the following fraction from the smallest to the greatest.\n3\/5, 7\/10, 1\/7","e":"Compare values: 1\/7 is about 0.14, 3\/5 = 0.6, 7\/10 = 0.7. Smallest to greatest: 1\/7, 3\/5, 7\/10."} {"t":"q","id":14939,"q":"Wai Mun boarded a train in Singapore at 11 40 and reached Malacca 3 h 30 min later. What time did he reach Malacca?","e":"11 40 + 3 h = 14 40. 14 40 + 30 min = 15 10."} {"t":"q","id":14941,"q":"Raj collected 312 stickers. He collected 107 stickers fewer than Mary. How many stickers did they collect altogether?","e":"Mary = 312 + 107 = 419. Altogether = 312 + 419 = 731."} {"t":"q","id":14943,"q":"Mr Tan bought a pair of trousers for $73.40. He gave the cashier two $50 notes. How much change did he receive?","e":"Two $50 notes = $100. Change = $100 - $73.40 = $26.60."} {"t":"q","id":14945,"q":"Mrs Lim had some money. She gave $758 to her son. She received $1479 from her husband. In the end, she had $1921. How much money did she have at first?","e":"Work backwards: $1921 - $1479 (received) + $758 (gave away) = $1200."} {"t":"q","id":14946,"q":"Write 9 thousands and 34 ones in numerals.
Answer: ","e":"9 thousands = 9000. 34 ones = 34. Total = 9000 + 34 = 9034."} {"t":"q","id":14947,"q":"Find the sum of the values of the digit 6 in 6204 and 2761.
Answer: ","e":"In 6204 the digit 6 is worth 6000. In 2761 the digit 6 is worth 60. Sum = 6000 + 60 = 6060."} {"t":"q","id":14948,"q":"Multiply 106 by 5.
Answer: ","e":"106 x 5 = 530."} {"t":"q","id":14949,"q":"Write 2 kilograms 25 grams in grams.\n g","e":"2 kg = 2000 g. 2000 g + 25 g = 2025 g."} {"t":"q","id":14950,"q":"Ming wanted to buy a board game for $82.40. He had $27.80. How much more money would he need to buy the board game?\n$","e":"$82.40 - $27.80 = $54.60."} {"t":"q","id":14951,"q":"Find the value of \\(\\dfrac{2}{5}\\) - \\(\\dfrac{3}{10}\\) .","e":"2\/5 = 4\/10. 4\/10 - 3\/10 = 1\/10."} {"t":"q","id":14952,"q":"Mr Tan started baking lemon tarts at 14 35. He finished baking at 16 20. How long did Mr Tan take to bake the lemon tarts?\n h min","e":"From 14 35 to 15 35 is 1 h. From 15 35 to 16 20 is 45 min. Total = 1 h 45 min."} {"t":"q","id":14955,"q":"The difference between 2 numbers is 154. The sum of the 2 numbers is 1142. What is the smaller number?
Answer: ","e":"Smaller number = (sum - difference) \/ 2 = (1142 - 154) \/ 2 = 988 \/ 2 = 494."} {"t":"q","id":14960,"q":"There were 2560 visitors in Bird Paradise. There were 1756 adults and the rest of the visitors were children. Among the children, there were 358 boys. How many girls were there in Bird Paradise?
Answer: ","e":"Children = 2560 - 1756 = 804. Girls = 804 - 358 = 446."} {"t":"q","id":14961,"q":"Mr Samad bought some bags of flour for his restaurant. He used 16 bags of flour each day from Monday to Friday and 22 bags of flour each day Saturday and Sunday. He had 120 bags of flour left. How many bags of flour did he buy at first?
Answer: ","e":"Mon-Fri: 16 x 5 = 80. Sat-Sun: 22 x 2 = 44. Used = 80 + 44 = 124. Bought at first = 124 + 120 left = 244."} {"t":"q","id":14962,"q":"4 whistles and 5 caps cost $55. 4 whistles and 2 caps cost $34. What is the cost of 4 caps?
Answer: ","e":"The difference is 3 caps: $55 - $34 = $21, so 3 caps = $21 and 1 cap = $7. 4 caps = 4 x $7 = $28."} {"t":"q","id":14963,"q":"Ali, Charles and Sam weigh a total of 140 kg. Ali weighs 3 times as heavy as Charles. Sam is 15 kg lighter than Charles. How much does Charles weigh?
Answer: ","e":"Let Charles = 1 unit. Ali = 3 units, Sam = 1 unit - 15. Total: 1u + 3u + (1u - 15) = 140, so 5u - 15 = 140, 5u = 155, 1u = 31. Charles weighs 31 kg."} {"t":"q","id":14964,"q":"Rosie and Tricia had an equal number of cookies at first. After Rosie bought another 13 cookies and Tricia gave away 5 cookies to her brother, Rosie had three times as many cookies as Tricia. How many cookies did each of them have at first?
Answer: ","e":"Let each start with x. Rosie = x + 13, Tricia = x - 5, and x + 13 = 3(x - 5). The gap between them is 13 + 5 = 18, which equals 2 units of Tricia's new amount, so 1 unit = 9. Tricia now has 9, so x = 9 + 5 = 14. Each had 14 cookies at first."} {"t":"q","id":14965,"q":"Which of the following is fifty-six thousand and thirty in numerals?","e":"Fifty-six thousand and thirty = 56 000 + 30 = 56 030. The answer is 56 030."} {"t":"q","id":14966,"q":"Which fraction is not equivalent to 2\/3?","e":"6\/9 = 2\/3, 10\/15 = 2\/3, 14\/21 = 2\/3 (all reduce to 2\/3). 9\/12 = 3\/4, which is NOT 2\/3. The answer is 9\/12."} {"t":"q","id":14967,"q":"James had 42 chairs. He arranged all the chairs in rows of 7. How many rows of chairs did he have?","e":"Number of rows = 42 \u00f7 7 = 6. The answer is 6."} {"t":"q","id":14968,"q":"Arrange the following numbers in decreasing order.\n4881, 4818, 4188, 4848","e":"Compare by place value. Thousands all 4. Hundreds: 4881 and 4848 have 8, 4818 has 8, 4188 has 1. Ordering greatest to smallest: 4881, 4848, 4818, 4188. The answer is option 2."} {"t":"q","id":14970,"q":"Which of the following division equations leaves a remainder of 3?","e":"645 \u00f7 6 = 107 r3. 753 \u00f7 4 = 188 r1. 816 \u00f7 3 = 272 r0. 935 \u00f7 8 = 116 r7. Only 645 \u00f7 6 leaves remainder 3. The answer is 645 \u00f7 6."} {"t":"q","id":14971,"q":"Gary had some stamps. After he bought another 39 stamps, he had 8 times as many stamps as his sister. His sister had 48 stamps. How many stamps did Gary have at first?","e":"After buying, Gary had 8 \u00d7 48 = 384 stamps. At first he had 384 \u2212 39 = 345 stamps. The answer is 345."} {"t":"q","id":14974,"q":"David bought a basketball for $21.98. He gave the cashier a $100 note. How much change did he receive?","e":"Change = $100.00 \u2212 $21.98 = $78.02. The answer is $78.02."} {"t":"q","id":14975,"q":"Anitha had a roll of ribbon which was 5 m long. She used 127 cm of it to tie a present. What was the length of the remaining ribbon?\n cm","e":"Convert 5 m = 500 cm. Remaining = 500 \u2212 127 = 373 cm. The answer is 373 cm."} {"t":"q","id":14976,"q":"What is the missing number in the number pattern shown?\n6010, 7010, 7020, , 8030, 9030, 9040","e":"The pattern alternates +1000 then +10: 6010 (+1000) 7010 (+10) 7020 (+1000) 8020 (+10) 8030 (+1000) 9030 (+10) 9040. The missing number is 8020."} {"t":"q","id":14977,"q":"Arrange the following fractions from the smallest to the greatest.\n3\/7, 1\/5, 9\/11\n, , ","e":"Compare sizes: 1\/5 = 0.2, 3\/7 \u2248 0.43, 9\/11 \u2248 0.82. Smallest to greatest: 1\/5, 3\/7, 9\/11."} {"t":"q","id":14979,"q":"A countdown party lasted 3 h 52 min and ended at 01 46 the next day. What time did the countdown party start? Express your answer using the 24-hour clock.\n","e":"Start = end \u2212 duration = 01 46 \u2212 3 h 52 min. 01 46 = 25 46 (next-day). 25 46 \u2212 3 h 52 min = 21 54. The party started at 21 54."} {"t":"q","id":14980,"q":"A farmer packed 1421 apples into boxes. Each box can hold 9 apples. After filling all the boxes, how many apples were left unpacked?\n","e":"1421 \u00f7 9 = 157 remainder 8. The remainder is the apples left over, so 8 apples were left unpacked."} {"t":"q","id":14981,"q":"3243 students joined a school carnival. 1478 of them were boys. How many fewer boys than girls joined the carnival?\n","e":"Girls = 3243 \u2212 1478 = 1765. Difference = 1765 \u2212 1478 = 287. There were 287 fewer boys than girls."} {"t":"q","id":14982,"q":"Ryan bought a pair of sports shoes that cost $68.95 and a sports bag for $24.90. How much did he spend in total?\n$","e":"Total = $68.95 + $24.90 = $93.85. He spent $93.85 in total."} {"t":"q","id":14983,"q":"The capacity of Container A is 17 l more than Container B and 15 l less than Container C. What is the total capacity of Container B and Container C if Container A has a capacity of 51 l?\n l","e":"Container B = 51 \u2212 17 = 34 l. Container C = 51 + 15 = 66 l. Total of B and C = 34 + 66 = 100 l."} {"t":"q","id":14984,"q":"A stadium had 1845 spectators in the morning. In the afternoon, 976 more spectators entered the stadium, while 1258 spectators left after the morning event. How many spectators were in the stadium by the end of the day?\n","e":"Total after arrivals = 1845 + 976 = 2821. After 1258 left: 2821 \u2212 1258 = 1563 spectators by the end of the day."} {"t":"q","id":14985,"q":"A factory produces 112 cartons of juice every day. Each carton contains 6 packets of juice. The packets are then packed equally into 8 delivery boxes. How many packets of juice are in each delivery box?\n","e":"Total packets = 112 \u00d7 6 = 672. Packets per box = 672 \u00f7 8 = 84. Each delivery box holds 84 packets."} {"t":"q","id":14986,"q":"Fazil and Ramesh each bought a strawberry cake during recess. Fazil ate 1\/4 of his cake during recess. During little bites, Ramesh ate 2\/5 of his cake and Fazil ate another 5\/12 of his cake.\n(a) What fraction of Ramesh's cake was left?\n(b) What fraction of Fazil's cake was eaten?\n(a) (b) ","e":"(a) Ramesh ate 2\/5, so left = 1 \u2212 2\/5 = 3\/5. (b) Fazil ate 1\/4 + 5\/12 = 3\/12 + 5\/12 = 8\/12 = 2\/3 of his cake."} {"t":"q","id":14987,"q":"Jia Wei spent a total of 2 h 35 min revising for his English and Mathematics tests. He spent 42 min revising for his English test. He finished revising for his Mathematics test at 20 20. What time did he start revising for his Mathematics test? Express your answer using the 24-hour clock.\n","e":"Maths revision time = 2 h 35 min \u2212 42 min = 1 h 53 min. Start = 20 20 \u2212 1 h 53 min = 18 27. He started at 18 27."} {"t":"q","id":14989,"q":"In which of the following numbers is the digit 8 in the ones place?","e":"The ones place is the last digit. In 9840 the ones digit is 0, in 8094 it is 4, in 4908 it is 8, in 4089 it is 9. So 4908 has 8 in the ones place. Answer: 4908."} {"t":"q","id":14990,"q":"What is the value of 5 thousands, 3 tens and 4 ones?","e":"5 thousands = 5000, 3 tens = 30, 4 ones = 4. There are 0 hundreds. 5000 + 0 + 30 + 4 = 5034. Answer: 5034."} {"t":"q","id":14992,"q":"Which of the following is the smallest fraction?","e":"All fractions have the same numerator (5). With equal numerators, the fraction with the largest denominator is the smallest. 9 is the largest denominator, so 5\/9 is the smallest. Answer: 5\/9."} {"t":"q","id":14994,"q":"How many minutes are there in 2 h 25 min?","e":"1 hour = 60 min, so 2 hours = 120 min. 120 min + 25 min = 145 min. Answer: 145 min."} {"t":"q","id":14996,"q":"Which of the following is not a possible remainder when a number is divided by 8?","e":"When dividing by 8, the remainder must be smaller than 8, so possible remainders are 0 to 7. 9 is larger than 8, so it cannot be a remainder. Answer: 9."} {"t":"q","id":14997,"q":"Each bag of 3 oranges is sold for $2. How much must Mrs Tan pay to buy 24 oranges?","e":"24 oranges \u00f7 3 oranges per bag = 8 bags. 8 bags \u00d7 $2 = $16. Answer: $16."} {"t":"q","id":14998,"q":"What is the value of 5\/9 \u2212 1\/3 ?","e":"Make the denominators the same: 1\/3 = 3\/9. Then 5\/9 \u2212 3\/9 = 2\/9. Answer: 2\/9."} {"t":"q","id":14999,"q":"Write three thousand and fifteen in numerals. ","e":"Three thousand = 3000, and fifteen = 15. Together: 3000 + 15 = 3015. Answer: 3015."} {"t":"q","id":15000,"q":"Find the value of 102 \u00f7 6. ","e":"102 \u00f7 6: 6 goes into 10 once (remainder 4), bring down 2 to make 42; 6 goes into 42 seven times. So 102 \u00f7 6 = 17. Answer: 17."} {"t":"q","id":15001,"q":"Find the value of 1078 \u2212 156. ","e":"1078 \u2212 156: subtract the ones (8 \u2212 6 = 2), then 7 \u2212 5 = 2 tens, then 0 hundreds needs to borrow: 10 \u2212 1 = 9 hundreds. Result = 922. Answer: 922."} {"t":"q","id":15002,"q":"Arrange the following fractions from the greatest to the smallest. 1\/2 , 2\/3 , 3\/7 , , ","e":"Compare using a common denominator 42: 1\/2 = 21\/42, 2\/3 = 28\/42, 3\/7 = 18\/42. From greatest to smallest: 28\/42, 21\/42, 18\/42, i.e. 2\/3, 1\/2, 3\/7. Answer: 2\/3, 1\/2, 3\/7."} {"t":"q","id":15005,"q":"Mrs Lim sold 1234 pears in the morning. She sold 342 fewer pears in the afternoon. How many pears did she sell altogether? ","e":"Afternoon pears = 1234 \u2212 342 = 892. Altogether = 1234 + 892 = 2126. Answer: 2126."} {"t":"q","id":15007,"q":"A show started at 17 25. It lasted for 1 h 45 min. At what time did the show end? Write your answer in 24-h clock. ","e":"Start 17 25, add 1 h = 18 25, then add 45 min: 18 25 + 35 min = 19 00, + 10 min = 19 10. Answer: 19 10."} {"t":"q","id":15009,"q":"Kumar bought a toy car and a teddy bear. He gave the cashier $50 and received a change of 85\u00a2. The toy car cost $20.40. How much did the teddy bear cost? ","e":"Total spent = $50 \u2212 $0.85 = $49.15. Teddy bear = total \u2212 toy car = $49.15 \u2212 $20.40 = $28.75. Answer: $28.75."} {"t":"q","id":15011,"q":"Ali has twice as many marbles as Betty. Carl has 3 times as many marbles as Ali. The total number of marbles the three children have is 774. How many marbles does Ali have? ","e":"Let Betty = 1 unit. Ali = 2 units. Carl = 3 \u00d7 Ali = 6 units. Total = 1 + 2 + 6 = 9 units = 774, so 1 unit = 774 \u00f7 9 = 86. Ali = 2 units = 86 \u00d7 2 = 172. Answer: 172."} {"t":"q","id":15013,"q":"The diagram shows the prices of Zoo entrance tickets. Child: $7. Adult: $22. How much do 1 child and 1 adult ticket cost altogether? Some children went to the zoo. They paid a total of $126 for their tickets. How many children went to the zoo?","e":"(a) 1 child + 1 adult = $7 + $22 = $29. (b) Each child ticket is $7, so number of children = $126 \u00f7 $7 = 18. Answer: (a) $29; (b) 18."} {"t":"q","id":15014,"q":"Mrs Tan baked an equal number of cupcakes and muffins. 90 cupcakes and 54 muffins were sold. The number of muffins then became twice the number of cupcakes. How many cupcakes and muffins were unsold? How many cupcakes and muffins were baked?","e":"Equal numbers baked, then 90 cupcakes and 54 muffins sold. The remaining muffins are twice the remaining cupcakes. Since the same number was baked, the difference 90 \u2212 54 = 36 between cupcakes sold and muffins sold equals 1 unit (the extra cupcakes left makes muffins double). Remaining cupcakes = 1 unit = 36, remaining muffins = 2 units = 72, so total unsold = 36 + 72 = 108. (a) 108 unsold. (b) Total baked = unsold + sold = 108 + 90 + 54 = 252. Answer: (a) 108; (b) 252."} {"t":"q","id":15015,"q":"Seven thousand, three hundred and sixteen in numerals is .","e":"Seven thousand = 7000, three hundred = 300, sixteen = 16. 7000 + 300 + 16 = 7316. Answer: 7316 (option 3)."} {"t":"q","id":15016,"q":"The value of the digit 8 in 8439 is .","e":"In 8439 the digit 8 is in the thousands place, so its value is 8 x 1000 = 8000. Answer: 8000 (option 4)."} {"t":"q","id":15017,"q":"Which fraction is equivalent to 2\/5?","e":"Multiply numerator and denominator of 2\/5 by 3: (2 x 3)\/(5 x 3) = 6\/15. Answer: 6\/15 (option 3)."} {"t":"q","id":15019,"q":"How many seconds are there in 3 min 15 s?","e":"3 min = 3 x 60 = 180 s. 180 s + 15 s = 195 s. Answer: 195 s (option 3)."} {"t":"q","id":15021,"q":"A shop printed 325 shirts on Monday. It printed 178 fewer shirts on Tuesday than on Monday. The shop printed 600 shirts in total on Tuesday and Wednesday. How many shirts did the shop print on Wednesday?","e":"Tuesday = 325 - 178 = 147 shirts. Wednesday = 600 - 147 = 453 shirts. Answer: 453 (option 3)."} {"t":"q","id":15023,"q":"How many hundreds are there in 4800?
Answer: ","e":"4800 \/ 100 = 48. There are 48 hundreds in 4800."} {"t":"q","id":15024,"q":"What is the missing number in the box?\n6 x 4 = x 8","e":"6 x 4 = 24. So [?] x 8 = 24, which means [?] = 24 \/ 8 = 3."} {"t":"q","id":15025,"q":"Arrange the following numbers in order. Begin with the smallest.\n7586, 5678, 7856, 5867
(a)   (b)   (c)   (d) ","e":"Compare thousands then hundreds: 5678 < 5867 < 7586 < 7856. Order from smallest: 5678, 5867, 7586, 7856."} {"t":"q","id":15026,"q":"Express 6035 g in kilograms and grams.\n kg g","e":"1 kg = 1000 g. 6035 g = 6000 g + 35 g = 6 kg 35 g."} {"t":"q","id":15028,"q":"Express 2:15 pm using the 24-hour clock.
Answer: ","e":"For pm times after 12 noon, add 12 to the hour: 2 + 12 = 14. So 2:15 pm = 1415."} {"t":"q","id":15033,"q":"Mei Mei baked 200 cupcakes. She kept 20 cupcakes for herself and shared the rest equally among her 9 friends. How many cupcakes did each friend receive?
Answer: ","e":"Cupcakes to share = 200 - 20 = 180. Each friend gets 180 \/ 9 = 20 cupcakes."} {"t":"q","id":15034,"q":"Mdm Wong took 6 classes of pupils to the zoo. She gave each pupil a packet of milk. There were 35 pupils in one of the classes and 39 pupils in each of the remaining classes. How many packets of milk did Mdm Wong give away altogether?
Answer: ","e":"Remaining classes = 6 - 1 = 5 classes of 39 pupils = 39 x 5 = 195. Add the class of 35: 195 + 35 = 230 packets."} {"t":"q","id":15035,"q":"Which two of the following fractions are greater than 1\/2?\n5\/11, 7\/9, 4\/8, 4\/7\n and ","e":"A fraction is greater than 1\/2 when the numerator is more than half the denominator. 5\/11 (half of 11 is 5.5, 5<5.5) no; 7\/9 (half is 4.5, 7>4.5) yes; 4\/8 = 1\/2 exactly, not greater; 4\/7 (half is 3.5, 4>3.5) yes. Answer: 7\/9 and 4\/7."} {"t":"q","id":15037,"q":"Fatimah went to the library at 13 45 and left at 15 50. How much time did she spend in the library? Give your answer in h and min.\n h min","e":"From 13 45 to 15 45 is 2 h. From 15 45 to 15 50 is 5 min more. Total = 2 h 5 min."} {"t":"q","id":15040,"q":"Emily has 80 more stickers than Sarah. Emily gave 27 stickers to Sarah. How many more stickers did Emily have than Sarah in the end?
Answer: ","e":"Giving 27 stickers to Sarah reduces the gap by 27 twice (Emily loses 27 and Sarah gains 27), so the gap shrinks by 2 x 27 = 54. New difference = 80 - 54 = 26 stickers."} {"t":"q","id":15041,"q":"Mr Lim made 325 ml of apple juice in the morning. He then made 650 ml of apple juice in the afternoon.\n(a) How much apple juice did he make in total?\n(b) All the apple juice was poured into 1 jug and 1 bottle without spilling. Both the jug and the bottle were filled completely. The jug was filled with 4 times as much apple juice as the bottle. How much more apple juice was there in the jug than in the bottle?\n(a) ml (b) ml","e":"(a) Total = 325 + 650 = 975 ml. (b) Jug is 4 times the bottle, so total = 4 + 1 = 5 equal units = 975 ml, so 1 unit (bottle) = 975 \/ 5 = 195 ml. Jug = 4 x 195 = 780 ml. Difference = 780 - 195 = 585 ml."} {"t":"q","id":15042,"q":"Mr Lim needs 1250 cupcakes for a carnival. He has 377 cupcakes. Cupcakes are sold in boxes of 7. What is the least number of boxes of cupcakes that he needs to buy for the carnival?
Answer: ","e":"Cupcakes still needed = 1250 - 377 = 873. Boxes = 873 \/ 7 = 124 remainder 5. Since 124 boxes give only 868, he needs 1 more box to cover the rest, so 125 boxes."} {"t":"q","id":15043,"q":"Mr Lim had 260 more stamps than Mr Ang at first. After he gave away 100 stamps, he had twice as many stamps as Mr Ang. How many stamps did Mr Lim have at first?
Answer: ","e":"After giving away 100, Mr Lim's lead over Mr Ang = 260 - 100 = 160. Since he now has twice Mr Ang, that lead of 160 equals 1 of Mr Ang's units, so Mr Ang has 160. Mr Lim now = 2 x 160 = 320. At first Mr Lim had 320 + 100 = 420 stamps."} {"t":"q","id":15045,"q":"In 7482, the digit 8 is in the place.","e":"Read place values from the right: 2 = ones, 8 = tens, 4 = hundreds, 7 = thousands. So the digit 8 is in the tens place."} {"t":"q","id":15046,"q":"3498 + 617 =","e":"Add: 3498 + 617. 3498 + 600 = 4098, then 4098 + 17 = 4115."} {"t":"q","id":15047,"q":"Find the product of 274 and 6.","e":"Multiply 274 by 6: 6 x 4 = 24 (write 4 carry 2); 6 x 7 = 42, +2 = 44 (write 4 carry 4); 6 x 2 = 12, +4 = 16. Result = 1644."} {"t":"q","id":15049,"q":"What is the missing number in the box?\n2\/5 = \/10","e":"Equivalent fractions: the denominator 5 was multiplied by 2 to get 10, so multiply the numerator by 2 as well: 2 x 2 = 4. So 2\/5 = 4\/10."} {"t":"q","id":15052,"q":"Arrange these fractions from the greatest to the smallest.\n5\/9, 2\/3, 1\/7","e":"Compare the fractions: 2\/3 = 0.667, 5\/9 = 0.556, 1\/7 = 0.143. From greatest to smallest: 2\/3, 5\/9, 1\/7."} {"t":"q","id":15054,"q":"Ethan had 40 more game cards than Lucas at first. Lucas then gave 10 of his game cards to Ethan. How many more game cards did Ethan have than Lucas in the end?","e":"Lucas gives 10 cards to Ethan: Ethan gains 10 and Lucas loses 10, so the gap grows by 20. The new difference = 40 + 20 = 60. Ethan had 60 more cards than Lucas."} {"t":"q","id":15055,"q":"What is the smallest 4-digit even number that can be formed using all the digits given below?\n8, 2, 3, 1
Answer: ","e":"For the smallest number, put the smallest digits in the highest places. For an even number, the ones digit must be even (2 or 8). Use the smallest even digit, 2, in the ones place, then arrange 1, 3, 8 ascending in front: 1, 3, 8 -> 138, giving 1238."} {"t":"q","id":15056,"q":"Study the pattern. What is the missing number?\n3545, 3505, , 3425, 3385, 3345","e":"Each term decreases by 40: 3545 - 40 = 3505, 3505 - 40 = 3465, 3465 - 40 = 3425. The missing number is 3465."} {"t":"q","id":15057,"q":"Find the value of 108 \/ 4
Answer: ","e":"Divide 108 by 4: 10 \/ 4 = 2 remainder 2; bring down 8 to make 28; 28 \/ 4 = 7. So 108 \/ 4 = 27."} {"t":"q","id":15061,"q":"Ali and Tom shared a rectangular cake. Ali ate \\(\\dfrac{1}{12}\\) of the cake and Tom ate \\(\\dfrac{1}{6}\\) of it. What fraction of the cake did they eat altogether? Express the answer in its simplest form.","e":"Make like denominators: 1\/6 = 2\/12. Add: 1\/12 + 2\/12 = 3\/12. Simplify by dividing numerator and denominator by 3: 3\/12 = 1\/4."} {"t":"q","id":15062,"q":"Andres collected 3 times as many marbles as Beevi. They collected 140 marbles altogether. How many marbles did Beevi collect?
Answer: ","e":"Beevi = 1 unit, Andres = 3 units, total = 4 units = 140 marbles. 1 unit = 140 \/ 4 = 35. Beevi collected 35 marbles."} {"t":"q","id":15063,"q":"Samantha spent 2 h 20 min reading a book. She checked her watch when she stopped reading and it was 2.05 pm. Her watch was 10 minutes faster than the actual time. What was the actual time she started reading?
Answer: ","e":"Watch showed 2.05 pm when she stopped. Subtract 2 h 20 min of reading: 2.05 pm - 2 h = 12.05 pm, - 20 min = 11.45 am (watch time she started). The watch is 10 min fast, so the actual start time is 11.45 am - 10 min = 11.35 am."} {"t":"q","id":15064,"q":"Siti received $36.40 from her father and $23.80 from her mother. She bought a pair of shoes and had $18.20 left. How much did she pay for the pair of shoes?
Answer: ","e":"Total money received = $36.40 + $23.80 = $60.20. Money paid for shoes = $60.20 - $18.20 = $42.00."} {"t":"q","id":15065,"q":"260 pupils were divided equally into groups of 4. 2 pupils from each group were chosen as group leaders. How many group leaders were there altogether?
Answer: ","e":"Number of groups = 260 \/ 4 = 65. Each group has 2 leaders, so total leaders = 65 x 2 = 130."} {"t":"q","id":15066,"q":"Pupils in the Science Club collected 344 bottles for a recycling project. After packing some bottles equally into 8 bags, 16 bottles were left. How many bottles were there in each bag?
Answer: ","e":"Bottles packed into bags = 344 - 16 = 328. Bottles per bag = 328 \/ 8 = 41."} {"t":"q","id":15067,"q":"Mrs Wong used some flour to bake cookies and muffins. She used 1200 g to bake the muffins. She used 560 g less flour to bake the cookies than muffins. How much flour did she use altogether?
Answer: ","e":"Flour for cookies = 1200 g - 560 g = 640 g. Total flour = 1200 g + 640 g = 1840 g."} {"t":"q","id":15068,"q":"Amelia had 325 marbles. 179 marbles were red and the rest were blue. (a) How many blue marbles did Amelia have? (b) Amelia's mother gave her 208 more red marbles. How many red marbles did Amelia have in the end?
(a)   (b) ","e":"(a) Blue marbles = total - red = 325 - 179 = 146. (b) Red marbles in the end = original red + extra red = 179 + 208 = 387."} {"t":"q","id":15069,"q":"Which of the following is eight thousand, three hundred and two in numerals?","e":"Eight thousand = 8000, three hundred = 300, two = 2. Combine: 8000 + 300 + 0 tens + 2 = 8302."} {"t":"q","id":15071,"q":"What is 6 m 7 cm in centimetres?","e":"1 m = 100 cm, so 6 m = 600 cm. Add the 7 cm: 600 + 7 = 607 cm."} {"t":"q","id":15072,"q":"What is the missing number?\n3\/4 = \/8","e":"To change the denominator 4 to 8, multiply by 2. Do the same to the numerator: 3 x 2 = 6. So 3\/4 = 6\/8."} {"t":"q","id":15074,"q":"Julia started her music lesson at 13 55. Her music lesson lasted for 1 hour 45 minutes. What time did her music lesson end?","e":"13 55 + 1 h = 14 55. Then 14 55 + 45 min: 14 55 + 5 min = 15 00, plus 40 min more = 15 40."} {"t":"q","id":15075,"q":"Which of the following is true?","e":"For 4\/7 and 4\/9 the numerators are equal; the fraction with the smaller denominator is larger, so 4\/7 > 4\/9. (The others are false.)"} {"t":"q","id":15076,"q":"Arrange the following fractions from the smallest to the greatest.\n3\/4 4\/9 7\/12","e":"Convert to a common denominator 36: 3\/4 = 27\/36, 4\/9 = 16\/36, 7\/12 = 21\/36. Order smallest to greatest: 16\/36, 21\/36, 27\/36, i.e. 4\/9, 7\/12, 3\/4."} {"t":"q","id":15078,"q":"Benson had 263 stickers. He had 28 fewer stickers than Lionel. How many stickers did they have altogether?","e":"Benson had 28 fewer than Lionel, so Lionel = 263 + 28 = 291. Altogether = 263 + 291 = 554."} {"t":"q","id":15079,"q":"What is the missing number in the pattern?\n1215, 1225, 1245, 1255, 1275, 1285, , 1315","e":"The numbers go up in steps that alternate +10, +20, +10, +20... After 1285 the next step is +20 giving 1305, and 1305 + 10 = 1315 confirms it."} {"t":"q","id":15081,"q":"Find the value of \\(\\dfrac{7}{12}\\) - \\(\\dfrac{1}{4}\\)","e":"Make the denominators the same: 1\/4 = 3\/12. Then 7\/12 - 3\/12 = 4\/12 = 1\/3."} {"t":"q","id":15082,"q":"Find the remainder when 137 is divided by 6.
Answer: ","e":"6 x 22 = 132, which is the largest multiple of 6 not over 137. 137 - 132 = 5, so the remainder is 5."} {"t":"q","id":15084,"q":"George reached the library at 15 45. He left the library at 17 20. How long was he at the library?\n h min","e":"From 15 45 to 16 45 is 1 hour. From 16 45 to 17 20 is 35 minutes. Total = 1 h 35 min."} {"t":"q","id":15085,"q":"A scarf costs $68.20. It costs $12.50 less than a blouse. What is the price of the blouse? Give your answer in $.
Answer: ","e":"The scarf is $12.50 less than the blouse, so the blouse costs more: blouse = $68.20 + $12.50 = $80.70."} {"t":"q","id":15090,"q":"Jane wanted to run 2 km 80 m. She completed 3 rounds on a running track. Each round is 400 m. How much further did she have to run? Give your answer in m.
Answer: ","e":"3 rounds = 400 x 3 = 1200 m run. Target = 2 km 80 m = 2080 m. Remaining = 2080 - 1200 = 880 m."} {"t":"q","id":15092,"q":"Mrs Chan had 36 muffins and some tarts. She packed all the muffins and tarts equally into boxes. There were 4 muffins and 6 tarts in each box. How many tarts did she have at first?
Answer: ","e":"Number of boxes = 36 muffins \/ 4 per box = 9 boxes. Tarts = 9 boxes x 6 tarts = 54."} {"t":"q","id":15094,"q":"There were 28 more boys than girls in the library at first. 6 girls left the library and 4 boys entered the library.\n(a) How many more boys than girls were there in the library in the end?\n(b) There were a total of 96 students in the library in the end. How many girls were there in the library in the end?
(a)   (b) ","e":"(a) Start: boys = girls + 28. After 6 girls leave and 4 boys enter, the gap grows by 6 + 4 = 10: new difference = 28 + 6 + 4 = 38 more boys. (b) Boys + girls = 96 and boys = girls + 38, so 2 x girls = 96 - 38 = 58, girls = 58 \/ 2 = 29."} {"t":"q","id":15096,"q":"In the number 5869, the digit is in the hundreds place.","e":"In 5869 the place values from the right are: 9 ones, 6 tens, 8 hundreds, 5 thousands. The hundreds digit is 8."} {"t":"q","id":15098,"q":"Complete the number pattern.\n1851 , 2551 , 3251 , , 4651 , 5351","e":"Each term increases by 700 (1851, 2551, 3251...). 3251 + 700 = 3951, then 4651, 5351."} {"t":"q","id":15100,"q":"Which of the following is the same as 5 kg 50 g?","e":"1 kg = 1000 g, so 5 kg = 5000 g. 5 kg 50 g = 5000 g + 50 g = 5050 g."} {"t":"q","id":15102,"q":"Find the value of 454 \u00f7 6","e":"454 \u00f7 6: 6 x 75 = 450, remainder 4. So 454 \u00f7 6 = 75 R4."} {"t":"q","id":15103,"q":"Arrange these fractions from the largest to the smallest.\n5\/12 , 3\/6 , 4\/7","e":"As decimals: 5\/12 \u2248 0.42, 3\/6 = 0.50, 4\/7 \u2248 0.57. Largest to smallest: 4\/7, 3\/6, 5\/12."} {"t":"q","id":15106,"q":"Write five thousand, eight hundred and thirteen in numerals.\n","e":"Five thousand = 5000, eight hundred = 800, thirteen = 13. 5000 + 800 + 13 = 5813."} {"t":"q","id":15108,"q":"Find the value of\na) 6 \u00d7 9\nb) 28 \u00f7 7\n , ","e":"a) 6 \u00d7 9 = 54. b) 28 \u00f7 7 = 4."} {"t":"q","id":15109,"q":"Fill in the missing numerator and denominator in the equivalent fractions.\n3\/4 = 6\/ = \/16","e":"3\/4 = 6\/A: numerator x2 (3->6), so denominator x2 (4->8), A=8. 3\/4 = B\/16: denominator x4 (4->16), so numerator x4 (3->12), B=12."} {"t":"q","id":15112,"q":"Find the value of \\(\\dfrac{1}{2}\\) + \\(\\dfrac{3}{8}\\)","e":"Make like denominators: 1\/2 = 4\/8. 4\/8 + 3\/8 = 7\/8."} {"t":"q","id":15113,"q":"Jasmine bought 425 mugs. She gave away 97 mugs. She packed the remaining mugs equally into boxes of 4. How many boxes would she need?\n","e":"Remaining mugs = 425 - 97 = 328. Boxes = 328 \u00f7 4 = 82."} {"t":"q","id":15114,"q":"Dinah jogged for 1 h 25 min. She stopped jogging at 13 50. What time did she start jogging? (Give your answer in 24-hour clock.)\n","e":"Start time = stop time - duration. 13 50 - 1 h 25 min = 12 25. She started at 1225."} {"t":"q","id":15115,"q":"5 chairs cost $160. A table cost 9 times as much as a chair. How much does a table cost?\n","e":"1 chair = $160 \u00f7 5 = $32. Table = 9 \u00d7 $32 = $288."} {"t":"q","id":15116,"q":"Jason bought a book and a file. The book cost $11.85 and the file cost $9.55. He gave the cashier $50.\na) How much did the book and file cost in total?\nb) How much change did Jason receive?\n , ","e":"a) Total = $11.85 + $9.55 = $21.40. b) Change = $50 - $21.40 = $28.60."} {"t":"q","id":15117,"q":"Joanna has 3 pieces of ribbons. Ribbon A is 150 cm long. It is 3 times the length of Ribbon B. Ribbon C is 26 cm long.\na) What is the length of Ribbon B?\nb) How much longer is Ribbon B than Ribbon C?\n , ","e":"a) Ribbon B = 150 \u00f7 3 = 50 cm. b) 50 cm - 26 cm = 24 cm longer."} {"t":"q","id":15118,"q":"Mr Tan took 2 h 35 min to drive from Town A to Town B. Mr Ahmad took 50 min more than Mr Tan to drive the same distance.\na) How long did Mr Ahmad take to drive from Town A to Town B?\nb) Mr Ahmad started driving from Town A to Town B at 3.15 p.m. What time would he reach Town B?\n , ","e":"a) 2 h 35 min + 50 min = 3 h 25 min (35 + 50 = 85 min = 1 h 25 min, plus 2 h). b) 3.15 p.m. + 3 h 25 min = 6.40 p.m."} {"t":"q","id":15119,"q":"6 similar bottles and 1 cup contain 1315 ml of water. 1 bottle and 1 cup contain 490 ml of water.\na) What is the volume of water in 5 bottles?\nb) What is the volume of water in 1 bottle?\n , ","e":"Subtracting the two statements removes the cup: (6 bottles + cup) - (1 bottle + cup) = 5 bottles = 1315 - 490 = 825 ml. b) 1 bottle = 825 \u00f7 5 = 165 ml."} {"t":"q","id":15120,"q":"Alicia and Peter have 576 stickers altogether. Alicia has 120 fewer stickers than Peter. How many stickers does Alicia have?\n","e":"Remove the 120 difference: 576 - 120 = 456, which is 2 of Alicia's share. Alicia = 456 \u00f7 2 = 228. (Check: Peter = 228 + 120 = 348; 228 + 348 = 576.)"} {"t":"q","id":15121,"q":"5781 = 5000 + 700 + + 1","e":"Expanded form: 5781 = 5000 + 700 + 80 + 1. The missing tens value is 80."} {"t":"q","id":15123,"q":"Arrange the fractions in increasing order.\n1\/8 5\/6 2\/3","e":"Common denominator 24: 1\/8=3\/24, 2\/3=16\/24, 5\/6=20\/24. Increasing: 1\/8, 2\/3, 5\/6."} {"t":"q","id":15133,"q":"There are 2 different 2-digit numbers.\nThe sum of the 2 numbers is 50.\nThe smaller number is less than 20.\nThe sum of the digits of the greater number is 9.\nFind the smaller number.
Answer: ","e":"Greater number has digit sum 9 and is more than 30 (since smaller < 20 and sum is 50): 36 has digit sum 9 and 50 \u2212 36 = 14 (< 20). Smaller number = 14."} {"t":"q","id":15134,"q":"Complete the number patterns.\n(a) 3520 , 3720 , , 4120 , 4320 , 4520\n(b) 7800 , 7750 , 7700 , , 7600 , 7550 , 7500","e":"(a) Pattern increases by 200: 3720 + 200 = 3920. (b) Pattern decreases by 50: 7700 \u2212 50 = 7650."} {"t":"q","id":15135,"q":"There are two cards. Each card has a number printed on it: 1642 and 6351.\n(a) Find the sum of the two numbers on the cards.\n(b) Find the difference between the two numbers on the cards.
(a)   (b) ","e":"(a) Sum: 1642 + 6351 = 7993. (b) Difference: 6351 \u2212 1642 = 4709."} {"t":"s","id":7792,"s":"(a) Children in end = 500 + 300 = 800. (b) Adults in end = 3 x 800 = 2400. Adults at first = 2400 - 612 = 1788."} {"t":"s","id":7796,"s":"4\/6, 6\/9 and 12\/18 all simplify to 2\/3. 8\/15 does not, so it is not equivalent."} {"t":"s","id":7799,"s":"80 tens = 800. 8753 - 800 = 7953."} {"t":"s","id":7800,"s":"Total cost = $0.80 + $1.25 + $0.75 = $2.80. He needs $2.80 - $2.50 = $0.30 more."} {"t":"s","id":7806,"s":"2\/5 = 4\/10. 7\/10 - 4\/10 = 3\/10."} {"t":"s","id":7807,"s":"Odd number must end in 1. Leading digit can't be 0, so smallest start is 2: 2081."} {"t":"s","id":7810,"s":"As decimals: 4\/11 \u2248 0.36, 4\/9 \u2248 0.44, 5\/8 = 0.625, 3\/4 = 0.75. Smallest to greatest: 4\/11, 4\/9, 5\/8, 3\/4."} {"t":"s","id":7812,"s":"(a) 500 - 56 = 444 sweets given. (b) 444 \u00f7 6 = 74 students."} {"t":"s","id":7813,"s":"(a) 5\/12 + 1\/3 = 5\/12 + 4\/12 = 9\/12 = 3\/4. (b) 12\/12 - 9\/12 = 3\/12 = 1\/4."} {"t":"s","id":7814,"s":"Remove differences: 2659 - 162 + 137 = 2634; 3 equal shares = 2634 \u00f7 3 = 878. Adam had 878. (Key: 2659 - 162 = 2497; 2497 - 274 = 2223; 2223 \u00f7 3 = 741; 741 + 137 = 878.)"} {"t":"s","id":7815,"s":"(a) 2 h 15 min + 1 h 50 min = 135 min + 110 min = 245 min = 4 h 5 min. (b) 14 25 + 4 h 5 min = 18 30."} {"t":"s","id":7816,"s":"Perimeter = 2(L + B) with L = 2B, so 6B = 54, B = 9 m, L = 18 m. Area = 18 x 9 = 162 m\u00b2."} {"t":"s","id":7821,"s":"6 x 24 = 144 erasers. He gave away 144 - 18 = 126."} {"t":"s","id":7826,"s":"18 apples = 18 \u00f7 3 = 6 bags. 6 x $5 = $30."} {"t":"s","id":7827,"s":"Total = 5 units = 685, so 1 unit (Mrs Lim) = 685 \u00f7 5 = 137. Mrs Chan baked 3 more units = 3 x 137 = 411 more muffins."} {"t":"s","id":7828,"s":"Packed = 46 x 8 = 368. At first = 368 + 37 = 405 stickers."} {"t":"s","id":7829,"s":"June needs 3 x 78 = 234 seashells. She must collect 234 - 42 = 192 more."} {"t":"s","id":7830,"s":"Three thousand = 3000, sixty = 60, two = 2. So 3000 + 60 + 2 = 3062."} {"t":"s","id":7832,"s":"$1 = 100\u00a2, so $16 = 1600\u00a2. Add 5\u00a2 to get 1605\u00a2."} {"t":"s","id":7835,"s":"Decreasing order means largest to smallest. Compare thousands then hundreds: 3692 > 3687 > 1069."} {"t":"s","id":7840,"s":"(a) The pattern increases by 10 each time, so after 6194 comes 6204. (b) The pattern alternates +1 then +1000: 2502 + 1 = 2503."} {"t":"s","id":7841,"s":"7 \u00d7 7 = 49. So [?] + 4 = 49, which means [?] = 49 - 4 = 45."} {"t":"s","id":7843,"s":"12 free doughnuts \u00f7 2 doughnuts per set = 6 sets. Each set needs 8 cupcakes, so 6 \u00d7 8 = 48 cupcakes."} {"t":"s","id":7844,"s":"Tuesday = 2328 - 519 = 1809 customers. Both days = 2328 + 1809 = 4137 customers."} {"t":"s","id":7846,"s":"Six thousand = 6000, four hundred = 400, eight = 8. 6000 + 400 + 8 = 6408."} {"t":"s","id":7849,"s":"All start with 8. Compare hundreds: 8769 and 8796 have 7 hundreds (smallest). Then compare tens: 6 < 9, so 8769 is smallest."} {"t":"s","id":7850,"s":"2501 has 2 thousands (smallest). 3127 and 3210 both have 3 thousands; 3127 has 1 hundred vs 3210's 2 hundreds, so 3127 < 3210. Order: 2501, 3127, 3210."} {"t":"s","id":7851,"s":"The numbers increase by 3 each time (5088, 5091, 5094, 5097...). 5097 + 3 = 5100, and 5100 + 3 = 5103."} {"t":"s","id":7854,"s":"(a) For the greatest odd number the ones digit must be odd; among 2,5,7 use largest digits first: 7 and 2 in front, odd 5 last -> 725. (b) For the smallest even number the ones digit must be even; cannot start with 0, so 2 hundreds, 0 tens, even ones 5? 5 is odd, so use 0 ones -> 250."} {"t":"s","id":7857,"s":"(a) Jack has 653 more than Tom, so Tom = 2000 - 653 = 1347. (b) After buying 480 more: 1347 + 480 = 1827."} {"t":"s","id":7858,"s":"February is $253 less than January, so January = 799 + 253 = 1052. Altogether = 1052 + 799 = 1851."} {"t":"s","id":7859,"s":"7 hundreds = 700. 700 x 3 = 2100."} {"t":"s","id":7863,"s":"572 \u00f7 3 = 190 remainder 2. (298 r1, 381 r0, 496 r1.)"} {"t":"s","id":7864,"s":"813 \u00f7 6 = 135 remainder 3, so it cannot be divided by 6 exactly. (354, 432, 768 all divide exactly.)"} {"t":"s","id":7870,"s":"Together they form 6 equal units (Rick 1, Billy 5). 162 \u00f7 6 = 27 = Rick. Billy = 5 \u00d7 27 = 135."} {"t":"s","id":7871,"s":"260 \u00f7 7 = 37 remainder 1, leaving 1 extra pencil. To make another full box of 7 he needs 7 \u2212 1 = 6 more pencils."} {"t":"s","id":7873,"s":"6x7=42, 4x9=36, 8x8=64, 5x10=50. The greatest is 8x8=64."} {"t":"s","id":7886,"s":"Cindy: 6.23 to 7.10 = 47 min. Kaixin: 6.46 to 7.23 = 37 min. Kaixin is shorter by 47 - 37 = 10 min."} {"t":"s","id":7889,"s":"2\/7 < 4\/7 (same denominator) and 4\/7 < 4\/5 (same numerator, larger denominator is smaller). Order: 2\/7, 4\/7, 4\/5."} {"t":"s","id":7892,"s":"Total = 6 units = 780, so 1 unit (Gina) = 780 \u00f7 6 = 130. After 25 more: 130 + 25 = 155."} {"t":"s","id":7894,"s":"Arrived 11.05 + 40 min = 11.45 a.m. From 11.45 a.m. to 3.35 p.m. = 3 h 50 min."} {"t":"s","id":7901,"s":"350 \u00f7 6 = 58 remainder 2. The 2 leftover sweets still need a pack, so 58 + 1 = 59 packs."} {"t":"s","id":7903,"s":"If all 14 were correct: 14 x 4 = 56. Each wrong answer instead of right loses 4+3 = 7. (56-14)\u00f77 = 6 wrong, so 14-6 = 8 correct. Check: 8 x 4 - 6 x 3 = 32 - 18 = 14."} {"t":"s","id":7904,"s":"Female teachers = female students = 20, so total teachers = 42 + 20 = 62. Students = 62 - 21 = 41. Male students = 41 - 20 = 21. More male than female students = 21 - 20 = 1."} {"t":"s","id":7905,"s":"Removing 5 blocks dropped the mass by 500 - 100 = 400 g, so each block = 400 \u00f7 5 = 80 g. Box = 100 - 80 = 20 g."} {"t":"s","id":7907,"s":"Water used to fill pails = 50 - 1 = 49 l. 49 \u00f7 7 = 7 pails."} {"t":"s","id":7911,"s":"(a) Five thousand and sixty-five = 5065. (b) To make the smallest 4-digit odd number using 5, 2, 6, 1, the last digit must be odd; choose the smallest available odd digit (5) for the ones place, then arrange the rest ascending: 1, 2, 6 \u2192 1265."} {"t":"s","id":7915,"s":"List the pairs: AB, AC, AD, BC, BD, CD. That is 3 + 2 + 1 = 6 different ways."} {"t":"s","id":7916,"s":"(a) Smaller number = 714 - 625 = 89. (b) Sum = 714 + 89 = 803."} {"t":"s","id":7921,"s":"Ryan = 2 \u00d7 321 = 642. Altogether = 321 + 642 = 963. (Or 321 \u00d7 3 = 963.)"} {"t":"s","id":7922,"s":"509 \u00f7 7 = 72 remainder 5. She can give sweets to 72 students."} {"t":"s","id":7923,"s":"Even numbers between 30 and 60 with digit sum 12: 48 (4 + 8 = 12). The number is 48."} {"t":"s","id":7938,"s":"2 h = 120 min. 120 + 18 = 138 minutes."} {"t":"s","id":7940,"s":"Weimin stopped 15 min later than Hashan: 7.55 a.m. + 15 min = 8.10 a.m."} {"t":"s","id":7941,"s":"Tuesday = 1 h 15 min + 40 min = 1 h 55 min. Total = 1 h 15 min + 1 h 55 min = 2 h 70 min = 3 h 10 min."} {"t":"s","id":7942,"s":"From 5.10 p.m. to 7.10 p.m. is 2 h; but it ended at 7.05, which is 5 min before 7.10, so duration = 2 h \u2212 5 min = 1 h 55 min."} {"t":"s","id":7943,"s":"Arrival = leaving time \u2212 stay = 11.15 a.m. \u2212 2 h 20 min. 11.15 \u2212 2 h = 9.15, then \u2212 20 min = 8.55 a.m."} {"t":"s","id":7944,"s":"She arrived 30 min early at 19 30, so the show started at 20 00. 135 min = 2 h 15 min. 20 00 + 2 h 15 min = 22 15."} {"t":"s","id":8011,"s":"4 thousands = 4000, 6 hundreds = 600, 9 ones = 9. 4000 + 600 + 9 = 4609."} {"t":"s","id":8012,"s":"In 4012, reading from the right: 2 ones, 1 ten, 0 hundreds, 4 thousands. So the digit 1 is in the tens place."} {"t":"s","id":8015,"s":"The differences increase by 10 each time: +10 (2365->2375), +20 (2375->2395), +30 (2395->2425), +40 (2425->2465), +50 (2465->2515). The missing number is 2425."} {"t":"s","id":8016,"s":"The larger number = 400 - 120 = 280. Difference = 280 - 120 = 160."} {"t":"s","id":8018,"s":"A x A = 81, so A = 9. Then B = 45 \/ 9 = 5."} {"t":"s","id":8019,"s":"Tom saves 3 x $124 = $372 each month. In 6 months: $372 x 6 = $2232."} {"t":"s","id":8020,"s":"A = 5 units, B = 1 unit. A - B = 4 units = 36 cm, so 1 unit = 9 cm. Ribbon A = 5 x 9 = 45 cm."} {"t":"s","id":8023,"s":"32K4 - 1597 = 1J27. Tens column gives K = 2 (so 3224 - 1597 = 1627), making J = 6. First blank K = 2, second blank J = 6."} {"t":"s","id":8024,"s":"Greatest 3-digit number from 4, 8, 6 is 864. 864 \/ 2 = 432."} {"t":"s","id":8025,"s":"To maximise the difference, make one number as large as possible and the other the smallest 3-digit number greater than 100, which is 101. The other is 600 - 101 = 499. Difference = 499 - 101 = 398."} {"t":"s","id":8028,"s":"Compare: 9098 > 8909 > 989 > 899. Greatest first gives 9098, 8909, 989, 899."} {"t":"s","id":8030,"s":"333 + 999 = 1332. Digits: 1 (thousands), 3 (hundreds), 3 (tens), 2 (ones). Only the ones digit, 2, is even."} {"t":"s","id":8042,"s":"Adam is least; Dennis < Bobby < Caden. So Caden collected the most."} {"t":"s","id":8048,"s":"For the smallest number, order digits ascending (1,3,5,6); for it to be odd the ones digit must be odd. Smallest is 1365 (ends in 5, with 1,3,6 arranged smallest in front)."} {"t":"s","id":8051,"s":"Hundreds digit value 300 means hundreds digit = 3. Tens digit is 8 less than thousands digit; thousands = ones. If thousands = 8 then tens = 0 and ones = 8, giving 8308."} {"t":"s","id":8054,"s":"The pattern alternates: 220, 230, 200, 210, 180, 190 (each pair drops by 20, then +10). The missing number is 210."} {"t":"s","id":8062,"s":"6\/15 simplifies to 2\/5, so a = 5. For b\/25 = 2\/5, multiply numerator and denominator by 5: b = 10."} {"t":"s","id":8063,"s":"1\/3 = 3\/9. 2\/9 < 3\/9, so 2\/9 is smaller than 1\/3; 1\/2 and 5\/6 are both larger."} {"t":"s","id":8064,"s":"(a) 1480 + 288 = 1768. (b) 1768 + 1480 = 3248."} {"t":"s","id":8065,"s":"Total cupcakes = 9 \u00d7 28 = 252. 252 \u00f7 4 = 63 per container."} {"t":"s","id":8066,"s":"(a) 18 \u00d7 5 = 90 minutes (= 1 h 30 min). (b) 11.45 a.m. minus 1 h 30 min = 10.15 a.m."} {"t":"s","id":8090,"s":"Without the 300 baked later, she would have had 469 \u2212 300 = 169 from the morning batch left. So she sold 754 \u2212 169 = 585 cookies."} {"t":"s","id":8092,"s":"After Giselle spent $24.40, the gap by which Giselle led shrank to $38.80 \u2212 $24.40 = $14.40. To swing from Caleb being $14.40 behind to $45.60 ahead, Caleb's father gave $14.40 + $45.60 = $60."} {"t":"s","id":8095,"s":"4\/8, 5\/10 and 6\/12 all simplify to 1\/2. 2\/6 simplifies to 1\/3, so it is not equal to 1\/2."} {"t":"s","id":8096,"s":"Using denominator 12: 2\/3 = 8\/12, 3\/4 = 9\/12, 5\/6 = 10\/12, 7\/12 = 7\/12. The greatest is 10\/12 = 5\/6."} {"t":"s","id":8103,"s":"8923 \u2212 2852 = 6071, so the second addend is 6071. The boxed (tens) digit is 7."} {"t":"s","id":8106,"s":"From 3.10 p.m. to 4.10 p.m. is 1 h; 4.10 to 4.55 is 45 min. Total = 1 h 45 min."} {"t":"s","id":8114,"s":"726 \u00f7 7 = 103 remainder 5. The quotient is 103."} {"t":"s","id":8117,"s":"First 56 \u00f7 7 = 8. Then 2 \u00d7 [?] = 8, so [?] = 8 \u00f7 2 = 4."} {"t":"s","id":8121,"s":"John is 1 unit, Mark is 2 units, so 3 units = 372. One unit (John) = 372 \u00f7 3 = 124 stamps."} {"t":"s","id":8122,"s":"Cost of cakes = 6 \u00d7 $54 = $324. Change = $360 \u2212 $324 = $36."} {"t":"s","id":8123,"s":"One magazine = $104 \u00f7 8 = $13. A book = 3 \u00d7 $13 = $39."} {"t":"s","id":8127,"s":"Multiply both the numerator and denominator of 2\/3 by 2: (2x2)\/(3x2) = 4\/6. So 4\/6 is equivalent to 2\/3. The answer is 4\/6."} {"t":"s","id":8131,"s":"Convert 3\/4 to twelfths: 3\/4 = 9\/12. Then 9\/12 - 1\/12 = 8\/12. Simplify 8\/12 by dividing top and bottom by 4 to get 2\/3. The answer is 2\/3."} {"t":"s","id":8132,"s":"Compare the sizes: 7\/9 is close to 1 (about 0.78), 2\/3 is about 0.67, and 2\/11 is small (about 0.18). From greatest to smallest: 7\/9, 2\/3, 2\/11. The answer is 7\/9, 2\/3, 2\/11."} {"t":"s","id":8135,"s":"(a) Total mass minus the sugar gives the noodles: 5700 g - 900 g = 4800 g. (b) Divide the noodles' total by 8 packets: 4800 g \/ 8 = 600 g each."} {"t":"s","id":8136,"s":"Let Ms Siti have 1 unit; Mr Lim has 4 units. After selling 63, Mr Lim's muffins equal Ms Siti's 1 unit, so the 63 sold equals 4 units - 1 unit = 3 units. So 1 unit = 63 \/ 3 = 21. Mr Lim had 4 units = 4 x 21 = 84 muffins at first. The answer is 84."} {"t":"s","id":8137,"s":"5083 in place values is 5 thousands + 0 hundreds + 8 tens + 3 ones = 5000 + 80 + 3. Option (3) matches."} {"t":"s","id":8138,"s":"8000 \u2212 615 = 7385. Option (2) is correct."} {"t":"s","id":8139,"s":"Product means multiply: 234 \u00d7 9 = 2106. Option (4) is correct."} {"t":"s","id":8141,"s":"91 \u00f7 6 = 15 remainder 1. Fifteen full boxes hold 90 pencils, and the 1 leftover pencil needs one more box, so 15 + 1 = 16 boxes. Option (2) is correct."} {"t":"s","id":8142,"s":"All three share the thousands digit 3. Compare hundreds: 3687 has 6, 3768 and 3786 have 7. So 3687 is smallest. Between 3768 and 3786 the tens digit decides: 6 < 8, so 3768 < 3786. Increasing order: 3687, 3768, 3786."} {"t":"s","id":8144,"s":"106 \u00f7 9 = 11 remainder 7. The quotient is the whole-number result, which is 11."} {"t":"s","id":8148,"s":"Kelly's stickers = 4879 \u2212 1243 = 3636. Kelly has 3636 \u2212 1243 = 2393 more stickers than Esther."} {"t":"s","id":8149,"s":"(a) Correct = 2 times incorrect, so incorrect = 26 \u00f7 2 = 13 questions. (b) Points = 8 for each correct answer = 26 \u00d7 8 = 208 points."} {"t":"s","id":8152,"s":"Multiply both the numerator and denominator of 3\/4 by 3: (3x3)\/(4x3) = 9\/12. So 9\/12 is equivalent to 3\/4."} {"t":"s","id":8154,"s":"Add 2\/9 to both sides: box = 1\/3 + 2\/9. Convert 1\/3 to ninths: 1\/3 = 3\/9. Then 3\/9 + 2\/9 = 5\/9. So the missing fraction is 5\/9."} {"t":"s","id":8155,"s":"With the same numerator, a smaller denominator is larger, and with the same denominator, a larger numerator is larger. 7\/9 is the largest: 7\/9 is more than half, and its numerator (7) is bigger than 5 and its denominator (9) is smaller than 12."} {"t":"s","id":8157,"s":"Divide both numerator and denominator by their highest common factor, 2: 14\/20 = (14\u00f72)\/(20\u00f72) = 7\/10. Since 7 and 10 share no common factor, 7\/10 is in simplest form."} {"t":"s","id":8159,"s":"Convert to eighths: 1\/2 = 4\/8, 1\/8 = 1\/8, 3\/4 = 6\/8. Ordering 6\/8 > 4\/8 > 1\/8 gives, from greatest to smallest: 3\/4, 1\/2, 1\/8."} {"t":"s","id":8165,"s":"7508 = 7000 + 500 + 8. The hundreds value is 500, so the blank is 500."} {"t":"s","id":8169,"s":"To find the missing number, add: 3267 + 4438 = 7705. Check: 7705 - 4438 = 3267."} {"t":"s","id":8170,"s":"Greatest number is 6709, smallest is 2548. Sum = 6709 + 2548 = 9257."} {"t":"s","id":8171,"s":"8 + 8 + 8 + 8 = 32. So 32 = 16 + (blank x 8). 32 - 16 = 16, and 16 div 8 = 2, so the blank is 2."} {"t":"s","id":8174,"s":"Total seats = 10 x 9 = 90. Occupied = 90 - 2 = 88 seats."} {"t":"s","id":8175,"s":"Sandra has 5 x 9 = 45 stamps; Ravi has 9. Together = 45 + 9 = 54, so each should have 54 div 2 = 27. Sandra must give 45 - 27 = 18 stamps. (Equivalently, the difference is 45 - 9 = 36, and half of that, 18, is transferred.)"} {"t":"s","id":8177,"s":"Bigger number = 4086 - 1260 = 2826. Difference = 2826 - 1260 = 1566."} {"t":"s","id":8179,"s":"In 4985 the digits from the right are: 5 ones, 8 tens, 9 hundreds, 4 thousands. So the digit in the thousands place is 4."} {"t":"s","id":8180,"s":"Expanded form of 7854 is 7000 + 800 + 50 + 4. The tens digit is 5, worth 50. So the missing number is 50."} {"t":"s","id":8181,"s":"Compare each: 101 < 110 (false); 970 > 410 (false); 8420 > 8220 (false); 7052 > 7025 because the tens digit 5 > 2 (true). So option 4 is correct."} {"t":"s","id":8184,"s":"Eight thousand = 8000, and five = 5 ones. There are no hundreds or tens, so write 0 in those places: 8005."} {"t":"s","id":8185,"s":"The numbers increase by 4 each time (283, 287, 291, 295). Working backwards: 283 - 4 = 279 and 279 - 4 = 275. So the missing numbers are 275 and 279."} {"t":"s","id":8188,"s":"They started with the same amount. Hannah had less left ($0.40 vs $1.20), so her item (the burger) cost more. The difference in money left is $1.20 - $0.40 = $0.80, so the burger cost $0.80 more."} {"t":"s","id":8189,"s":"a) Adults = children - 562 = 1782 - 562 = 1220. b) Altogether = children + adults = 1782 + 1220 = 3002."} {"t":"s","id":8190,"s":"a) Before giving away 456, Jack had 214 + 456 = 670 stickers. b) Megan had 120 fewer than Jack at first: 670 - 120 = 550 stickers."} {"t":"s","id":8191,"s":"5 x 7 means 7 groups of 5, i.e. 5 added seven times: 5 + 5 + 5 + 5 + 5 + 5 + 5 = 35. Option (4) matches."} {"t":"s","id":8192,"s":"48 \u00f7 8 = 6, because 6 x 8 = 48. Option (1)."} {"t":"s","id":8198,"s":"Missing number = quotient x divisor + remainder = 13 x 7 + 4 = 91 + 4 = 95. Option (3)."} {"t":"s","id":8199,"s":"Total clips = 36 x 6 = 216. Repacked into 3 equal boxes: 216 \u00f7 3 = 72 clips per box. Option (4)."} {"t":"s","id":8200,"s":"Beads given away = 720 - 24 = 696. Shared equally among 4 friends: 696 \u00f7 4 = 174 beads each. Option (3)."} {"t":"s","id":8202,"s":"The 3-digit number ?78 multiplied by 7 gives 2646. 2646 \u00f7 7 = 378, so the hundreds digit is 3. Check: 378 x 7 = 2646."} {"t":"s","id":8208,"s":"Each bag holds 2 + 3 = 5 pens. Number of bags = 45 \u00f7 5 = 9. Red pens = 9 x 2 = 18."} {"t":"s","id":8209,"s":"540 \u00f7 8 = 67 remainder 4 (67 x 8 = 536). The most bags he can fill is 67, leaving 540 - 536 = 4 marbles unpacked."} {"t":"s","id":8210,"s":"(a) Noah's stamps in the end = 56 - 8 = 48. (b) Ollie had twice as many as Noah: 48 x 2 = 96. Altogether = 96 + 48 = 144 stamps."} {"t":"s","id":8216,"s":"9\/10 = 0.9 is the closest to 1. 1\/3 = 0.33, 2\/5 = 0.4, 5\/9 = 0.56, so 9\/10 is the greatest."} {"t":"s","id":8217,"s":"Make the denominators the same: 1\/4 = 3\/12. Then 5\/12 + 3\/12 = 8\/12 = 2\/3 in simplest form."} {"t":"s","id":8218,"s":"1 l = 1000 ml. Two cartons of milk = 2 x 320 ml = 640 ml. Total = 1000 ml + 640 ml = 1640 ml."} {"t":"s","id":8220,"s":"Make the denominators the same: 4\/5 = 8\/10. Since 8\/10 > 7\/10, we have 4\/5 > 7\/10."} {"t":"s","id":8222,"s":"1 m = 100 cm, so 2 m = 200 cm. 200 cm + 9 cm = 209 cm."} {"t":"s","id":8223,"s":"Make the denominators the same: 1\/2 = 4\/8. Then 5\/8 - 4\/8 = 1\/8."} {"t":"s","id":8224,"s":"When the numerators are the same, the fraction with the smaller denominator is larger. Denominators 4 < 5 < 7, so 3\/4 > 3\/5 > 3\/7."} {"t":"s","id":8228,"s":"(a) Bala is 15 cm taller than Lisa, so Lisa = 163 - 15 = 148 cm. (b) Total = 148 + 163 = 311 cm = 3 m 11 cm."} {"t":"s","id":8229,"s":"The 7 balls together weigh 1500 g - 576 g = 924 g. Each ball is 924 \/ 7 = 132 g."} {"t":"s","id":8231,"s":"1 kg = 1000 g, so 9 kg = 9000 g. Then 9 kg 35 g = 9000 g + 35 g = 9035 g. The answer is 9035 g."} {"t":"s","id":8232,"s":"These are all unit fractions (numerator 1). For unit fractions, the larger the denominator, the smaller the fraction. The largest denominator is 8, so 1\/8 is the smallest."} {"t":"s","id":8233,"s":"Express 3\/12 in its simplest form. Divide both the numerator and denominator by 3: 3 divided 3 = 1 and 12 divided 3 = 4, giving 1\/4. So the missing number is 4."} {"t":"s","id":8234,"s":"A fraction is greater than 1\/2 when its numerator is more than half its denominator. For 4\/5, half of 5 is 2.5 and 4 is more than that, so 4\/5 > 1\/2. The others (3\/7, 1\/3, 4\/11) are all less than 1\/2."} {"t":"s","id":8237,"s":"Make the denominators the same: 1\/2 = 5\/10. Then 7\/10 - 5\/10 = 2\/10. Simplify 2\/10 by dividing top and bottom by 2 to get 1\/5."} {"t":"s","id":8240,"s":"(a) The sister jogged 555 m less than Ahmad: 4500 - 555 = 3945 m. (b) Total = 4500 + 3945 = 8445 m = 8 km 445 m."} {"t":"s","id":8241,"s":"(a) Mrs Chandran = 2 x $568 = $1136. (b) Mdm Zu = $1136 - $300 = $836. Mdm Zu spent more than Mrs Tan by $836 - $568 = $268."} {"t":"s","id":8243,"s":"8300 = 83 hundreds (8300 \u00f7 100 = 83). The answer is 83."} {"t":"s","id":8245,"s":"All share 4 thousands. Compare hundreds\/tens: 4786 < 4867 < 4876. So 4786 , 4867 , 4876 is smallest to greatest."} {"t":"s","id":8248,"s":"9 \u00d7 10\u00a2 = 90\u00a2 and 4 \u00d7 50\u00a2 = 200\u00a2. Total = 90\u00a2 + 200\u00a2 = 290\u00a2 = $2.90."} {"t":"s","id":8249,"s":"Total bought = 39 + 18 = 57. Cherries left = 57 \u2212 17 = 40."} {"t":"s","id":8254,"s":"An odd number must end in an odd digit (3 or 5). For the smallest number, use the smallest leading digit 2, then arrange the rest smallest first while keeping an odd unit: 2385."} {"t":"s","id":8255,"s":"9 thousands = 9000, 0 hundreds, 6 tens = 60, 8 ones = 8. Together: 9068."} {"t":"s","id":8262,"s":"Total erasers = 4 \u00d7 10 = 40. Repacked into 8 bags: 40 \u00f7 8 = 5 erasers per bag."} {"t":"s","id":8263,"s":"The larger number = 876 + 345 = 1221. Sum = 1221 + 876 = 2097."} {"t":"s","id":8264,"s":"$56 \u00f7 $7 = 8 bags. Each bag has 3 oranges, so 8 \u00d7 3 = 24 oranges."} {"t":"s","id":8266,"s":"(a) Non-fiction = 8000 \u2212 5686 = 2314 books. (b) More fiction than non-fiction = 5686 \u2212 2314 = 3372 books."} {"t":"s","id":8267,"s":"Given away = 6 neighbours \u00d7 9 = 54 cupcakes. Total baked = 54 + 26 kept = 80 cupcakes."} {"t":"s","id":8270,"s":"Compare place values: 8800 > 8080 > 8008 > 888. Greatest to smallest: 8800, 8080, 8008, 888."} {"t":"s","id":8275,"s":"She arrives at 7.15 a.m. and travels for half an hour (30 min). 7.15 - 0.30 = 6.45 a.m."} {"t":"s","id":8279,"s":"Tim stopped half an hour after James (9.30 a.m. + 30 min = 10.00 a.m.). From 7.50 a.m. to 10.00 a.m. is 2 h 10 min."} {"t":"s","id":8282,"s":"Aaron has 5 fewer than Ben, so Ben = 58 + 5 = 63. Charles = 6 x 63 = 378 cards."} {"t":"s","id":8283,"s":"(a) Monday to Saturday is 6 days x 1 egg = 6 eggs, plus 2 eggs on Sunday = 8 eggs a week. (b) 30 \/ 8 = 3 remainder 6, so 3 weeks and 6 more days are needed to finish all 30 eggs."} {"t":"s","id":8284,"s":"0 x 7 = 0, so 8 - [?] = 0, which means [?] = 8. The answer is 8."} {"t":"s","id":8286,"s":"From 4.15 p.m. to 6.15 p.m. is 2 h. From 6.05 p.m. back 10 min: 4.15 to 6.05 = 1 h 50 min (4.15 to 5.15 is 1 h, then 5.15 to 6.05 is 50 min)."} {"t":"s","id":8288,"s":"3 h = 3 x 60 = 180 min. 180 min + 40 min = 220 min."} {"t":"s","id":8292,"s":"Compare by place value from the thousands. 3797 and 3977 start with 3; 3797 < 3977. 7397 and 7937 start with 7; 7397 < 7937. Order: 3797, 3977, 7397, 7937."} {"t":"s","id":8298,"s":"4979 - 4779 = 200. 200 = 20 tens, so 4979 is 20 tens more than 4779."} {"t":"s","id":8299,"s":"An odd number must end in an odd digit (1 or 3). To be smallest, the leading digit must be as small as possible but not 0, so use 1 first. Remaining digits 0, 8, 3 arranged smallest with an odd units digit: 0, 8, then 3 (odd) -> 1083."} {"t":"s","id":8308,"s":"Haron is 1 unit, Bala is 3 units, total 4 units = 192. 1 unit = 192 \/ 4 = 48. Haron has 48 stamps."} {"t":"s","id":8309,"s":"Monday = 3015 - 1527 = 1488. Both days = 3015 + 1488 = 4503."} {"t":"s","id":8310,"s":"Each tray has 72 \/ 8 = 9 cookies. He had 45 cookies left, so 45 \/ 9 = 5 trays left."} {"t":"s","id":8313,"s":"The digit 5 is in the hundreds place. Its value is 5 hundreds = 500."} {"t":"s","id":8314,"s":"72 \/ 4 = 18 exactly, no remainder. 14, 46 and 58 all leave a remainder when divided by 4."} {"t":"s","id":8315,"s":"Compare values: 1\/7 is about 0.14, 3\/5 = 0.6, 7\/10 = 0.7. Smallest to greatest: 1\/7, 3\/5, 7\/10."} {"t":"s","id":8316,"s":"11 40 + 3 h = 14 40. 14 40 + 30 min = 15 10."} {"t":"s","id":8318,"s":"Mary = 312 + 107 = 419. Altogether = 312 + 419 = 731."} {"t":"s","id":8320,"s":"Two $50 notes = $100. Change = $100 - $73.40 = $26.60."} {"t":"s","id":8323,"s":"9 thousands = 9000. 34 ones = 34. Total = 9000 + 34 = 9034."} {"t":"s","id":8324,"s":"In 6204 the digit 6 is worth 6000. In 2761 the digit 6 is worth 60. Sum = 6000 + 60 = 6060."} {"t":"s","id":8326,"s":"2 kg = 2000 g. 2000 g + 25 g = 2025 g."} {"t":"s","id":8328,"s":"2\/5 = 4\/10. 4\/10 - 3\/10 = 1\/10."} {"t":"s","id":8329,"s":"From 14 35 to 15 35 is 1 h. From 15 35 to 16 20 is 45 min. Total = 1 h 45 min."} {"t":"s","id":8337,"s":"Children = 2560 - 1756 = 804. Girls = 804 - 358 = 446."} {"t":"s","id":8338,"s":"Mon-Fri: 16 x 5 = 80. Sat-Sun: 22 x 2 = 44. Used = 80 + 44 = 124. Bought at first = 124 + 120 left = 244."} {"t":"s","id":8340,"s":"Let Charles = 1 unit. Ali = 3 units, Sam = 1 unit - 15. Total: 1u + 3u + (1u - 15) = 140, so 5u - 15 = 140, 5u = 155, 1u = 31. Charles weighs 31 kg."} {"t":"s","id":8341,"s":"Let each start with x. Rosie = x + 13, Tricia = x - 5, and x + 13 = 3(x - 5). The gap between them is 13 + 5 = 18, which equals 2 units of Tricia's new amount, so 1 unit = 9. Tricia now has 9, so x = 9 + 5 = 14. Each had 14 cookies at first."} {"t":"s","id":8342,"s":"Fifty-six thousand and thirty = 56 000 + 30 = 56 030. The answer is 56 030."} {"t":"s","id":8343,"s":"6\/9 = 2\/3, 10\/15 = 2\/3, 14\/21 = 2\/3 (all reduce to 2\/3). 9\/12 = 3\/4, which is NOT 2\/3. The answer is 9\/12."} {"t":"s","id":8344,"s":"Number of rows = 42 \u00f7 7 = 6. The answer is 6."} {"t":"s","id":8345,"s":"Compare by place value. Thousands all 4. Hundreds: 4881 and 4848 have 8, 4818 has 8, 4188 has 1. Ordering greatest to smallest: 4881, 4848, 4818, 4188. The answer is option 2."} {"t":"s","id":8347,"s":"645 \u00f7 6 = 107 r3. 753 \u00f7 4 = 188 r1. 816 \u00f7 3 = 272 r0. 935 \u00f7 8 = 116 r7. Only 645 \u00f7 6 leaves remainder 3. The answer is 645 \u00f7 6."} {"t":"s","id":8348,"s":"After buying, Gary had 8 \u00d7 48 = 384 stamps. At first he had 384 \u2212 39 = 345 stamps. The answer is 345."} {"t":"s","id":8352,"s":"Convert 5 m = 500 cm. Remaining = 500 \u2212 127 = 373 cm. The answer is 373 cm."} {"t":"s","id":8353,"s":"The pattern alternates +1000 then +10: 6010 (+1000) 7010 (+10) 7020 (+1000) 8020 (+10) 8030 (+1000) 9030 (+10) 9040. The missing number is 8020."} {"t":"s","id":8354,"s":"Compare sizes: 1\/5 = 0.2, 3\/7 \u2248 0.43, 9\/11 \u2248 0.82. Smallest to greatest: 1\/5, 3\/7, 9\/11."} {"t":"s","id":8356,"s":"Start = end \u2212 duration = 01 46 \u2212 3 h 52 min. 01 46 = 25 46 (next-day). 25 46 \u2212 3 h 52 min = 21 54. The party started at 21 54."} {"t":"s","id":8357,"s":"1421 \u00f7 9 = 157 remainder 8. The remainder is the apples left over, so 8 apples were left unpacked."} {"t":"s","id":8358,"s":"Girls = 3243 \u2212 1478 = 1765. Difference = 1765 \u2212 1478 = 287. There were 287 fewer boys than girls."} {"t":"s","id":8360,"s":"Container B = 51 \u2212 17 = 34 l. Container C = 51 + 15 = 66 l. Total of B and C = 34 + 66 = 100 l."} {"t":"s","id":8361,"s":"Total after arrivals = 1845 + 976 = 2821. After 1258 left: 2821 \u2212 1258 = 1563 spectators by the end of the day."} {"t":"s","id":8362,"s":"Total packets = 112 \u00d7 6 = 672. Packets per box = 672 \u00f7 8 = 84. Each delivery box holds 84 packets."} {"t":"s","id":8363,"s":"(a) Ramesh ate 2\/5, so left = 1 \u2212 2\/5 = 3\/5. (b) Fazil ate 1\/4 + 5\/12 = 3\/12 + 5\/12 = 8\/12 = 2\/3 of his cake."} {"t":"s","id":8364,"s":"Maths revision time = 2 h 35 min \u2212 42 min = 1 h 53 min. Start = 20 20 \u2212 1 h 53 min = 18 27. He started at 18 27."} {"t":"s","id":8366,"s":"The ones place is the last digit. In 9840 the ones digit is 0, in 8094 it is 4, in 4908 it is 8, in 4089 it is 9. So 4908 has 8 in the ones place. Answer: 4908."} {"t":"s","id":8367,"s":"5 thousands = 5000, 3 tens = 30, 4 ones = 4. There are 0 hundreds. 5000 + 0 + 30 + 4 = 5034. Answer: 5034."} {"t":"s","id":8369,"s":"All fractions have the same numerator (5). With equal numerators, the fraction with the largest denominator is the smallest. 9 is the largest denominator, so 5\/9 is the smallest. Answer: 5\/9."} {"t":"s","id":8371,"s":"1 hour = 60 min, so 2 hours = 120 min. 120 min + 25 min = 145 min. Answer: 145 min."} {"t":"s","id":8373,"s":"When dividing by 8, the remainder must be smaller than 8, so possible remainders are 0 to 7. 9 is larger than 8, so it cannot be a remainder. Answer: 9."} {"t":"s","id":8374,"s":"24 oranges \u00f7 3 oranges per bag = 8 bags. 8 bags \u00d7 $2 = $16. Answer: $16."} {"t":"s","id":8375,"s":"Make the denominators the same: 1\/3 = 3\/9. Then 5\/9 \u2212 3\/9 = 2\/9. Answer: 2\/9."} {"t":"s","id":8376,"s":"Three thousand = 3000, and fifteen = 15. Together: 3000 + 15 = 3015. Answer: 3015."} {"t":"s","id":8377,"s":"102 \u00f7 6: 6 goes into 10 once (remainder 4), bring down 2 to make 42; 6 goes into 42 seven times. So 102 \u00f7 6 = 17. Answer: 17."} {"t":"s","id":8378,"s":"1078 \u2212 156: subtract the ones (8 \u2212 6 = 2), then 7 \u2212 5 = 2 tens, then 0 hundreds needs to borrow: 10 \u2212 1 = 9 hundreds. Result = 922. Answer: 922."} {"t":"s","id":8379,"s":"Compare using a common denominator 42: 1\/2 = 21\/42, 2\/3 = 28\/42, 3\/7 = 18\/42. From greatest to smallest: 28\/42, 21\/42, 18\/42, i.e. 2\/3, 1\/2, 3\/7. Answer: 2\/3, 1\/2, 3\/7."} {"t":"s","id":8382,"s":"Afternoon pears = 1234 \u2212 342 = 892. Altogether = 1234 + 892 = 2126. Answer: 2126."} {"t":"s","id":8384,"s":"Start 17 25, add 1 h = 18 25, then add 45 min: 18 25 + 35 min = 19 00, + 10 min = 19 10. Answer: 19 10."} {"t":"s","id":8386,"s":"Total spent = $50 \u2212 $0.85 = $49.15. Teddy bear = total \u2212 toy car = $49.15 \u2212 $20.40 = $28.75. Answer: $28.75."} {"t":"s","id":8388,"s":"Let Betty = 1 unit. Ali = 2 units. Carl = 3 \u00d7 Ali = 6 units. Total = 1 + 2 + 6 = 9 units = 774, so 1 unit = 774 \u00f7 9 = 86. Ali = 2 units = 86 \u00d7 2 = 172. Answer: 172."} {"t":"s","id":8390,"s":"(a) 1 child + 1 adult = $7 + $22 = $29. (b) Each child ticket is $7, so number of children = $126 \u00f7 $7 = 18. Answer: (a) $29; (b) 18."} {"t":"s","id":8391,"s":"Equal numbers baked, then 90 cupcakes and 54 muffins sold. The remaining muffins are twice the remaining cupcakes. Since the same number was baked, the difference 90 \u2212 54 = 36 between cupcakes sold and muffins sold equals 1 unit (the extra cupcakes left makes muffins double). Remaining cupcakes = 1 unit = 36, remaining muffins = 2 units = 72, so total unsold = 36 + 72 = 108. (a) 108 unsold. (b) Total baked = unsold + sold = 108 + 90 + 54 = 252. Answer: (a) 108; (b) 252."} {"t":"s","id":8392,"s":"Seven thousand = 7000, three hundred = 300, sixteen = 16. 7000 + 300 + 16 = 7316. Answer: 7316 (option 3)."} {"t":"s","id":8393,"s":"In 8439 the digit 8 is in the thousands place, so its value is 8 x 1000 = 8000. Answer: 8000 (option 4)."} {"t":"s","id":8394,"s":"Multiply numerator and denominator of 2\/5 by 3: (2 x 3)\/(5 x 3) = 6\/15. Answer: 6\/15 (option 3)."} {"t":"s","id":8396,"s":"3 min = 3 x 60 = 180 s. 180 s + 15 s = 195 s. Answer: 195 s (option 3)."} {"t":"s","id":8398,"s":"Tuesday = 325 - 178 = 147 shirts. Wednesday = 600 - 147 = 453 shirts. Answer: 453 (option 3)."} {"t":"s","id":8400,"s":"4800 \/ 100 = 48. There are 48 hundreds in 4800."} {"t":"s","id":8401,"s":"6 x 4 = 24. So [?] x 8 = 24, which means [?] = 24 \/ 8 = 3."} {"t":"s","id":8402,"s":"Compare thousands then hundreds: 5678 < 5867 < 7586 < 7856. Order from smallest: 5678, 5867, 7586, 7856."} {"t":"s","id":8403,"s":"1 kg = 1000 g. 6035 g = 6000 g + 35 g = 6 kg 35 g."} {"t":"s","id":8405,"s":"For pm times after 12 noon, add 12 to the hour: 2 + 12 = 14. So 2:15 pm = 1415."} {"t":"s","id":8410,"s":"Cupcakes to share = 200 - 20 = 180. Each friend gets 180 \/ 9 = 20 cupcakes."} {"t":"s","id":8411,"s":"Remaining classes = 6 - 1 = 5 classes of 39 pupils = 39 x 5 = 195. Add the class of 35: 195 + 35 = 230 packets."} {"t":"s","id":8412,"s":"A fraction is greater than 1\/2 when the numerator is more than half the denominator. 5\/11 (half of 11 is 5.5, 5<5.5) no; 7\/9 (half is 4.5, 7>4.5) yes; 4\/8 = 1\/2 exactly, not greater; 4\/7 (half is 3.5, 4>3.5) yes. Answer: 7\/9 and 4\/7."} {"t":"s","id":8414,"s":"From 13 45 to 15 45 is 2 h. From 15 45 to 15 50 is 5 min more. Total = 2 h 5 min."} {"t":"s","id":8417,"s":"Giving 27 stickers to Sarah reduces the gap by 27 twice (Emily loses 27 and Sarah gains 27), so the gap shrinks by 2 x 27 = 54. New difference = 80 - 54 = 26 stickers."} {"t":"s","id":8418,"s":"(a) Total = 325 + 650 = 975 ml. (b) Jug is 4 times the bottle, so total = 4 + 1 = 5 equal units = 975 ml, so 1 unit (bottle) = 975 \/ 5 = 195 ml. Jug = 4 x 195 = 780 ml. Difference = 780 - 195 = 585 ml."} {"t":"s","id":8419,"s":"Cupcakes still needed = 1250 - 377 = 873. Boxes = 873 \/ 7 = 124 remainder 5. Since 124 boxes give only 868, he needs 1 more box to cover the rest, so 125 boxes."} {"t":"s","id":8420,"s":"After giving away 100, Mr Lim's lead over Mr Ang = 260 - 100 = 160. Since he now has twice Mr Ang, that lead of 160 equals 1 of Mr Ang's units, so Mr Ang has 160. Mr Lim now = 2 x 160 = 320. At first Mr Lim had 320 + 100 = 420 stamps."} {"t":"s","id":8422,"s":"Read place values from the right: 2 = ones, 8 = tens, 4 = hundreds, 7 = thousands. So the digit 8 is in the tens place."} {"t":"s","id":8423,"s":"Add: 3498 + 617. 3498 + 600 = 4098, then 4098 + 17 = 4115."} {"t":"s","id":8424,"s":"Multiply 274 by 6: 6 x 4 = 24 (write 4 carry 2); 6 x 7 = 42, +2 = 44 (write 4 carry 4); 6 x 2 = 12, +4 = 16. Result = 1644."} {"t":"s","id":8426,"s":"Equivalent fractions: the denominator 5 was multiplied by 2 to get 10, so multiply the numerator by 2 as well: 2 x 2 = 4. So 2\/5 = 4\/10."} {"t":"s","id":8429,"s":"Compare the fractions: 2\/3 = 0.667, 5\/9 = 0.556, 1\/7 = 0.143. From greatest to smallest: 2\/3, 5\/9, 1\/7."} {"t":"s","id":8431,"s":"Lucas gives 10 cards to Ethan: Ethan gains 10 and Lucas loses 10, so the gap grows by 20. The new difference = 40 + 20 = 60. Ethan had 60 more cards than Lucas."} {"t":"s","id":8432,"s":"For the smallest number, put the smallest digits in the highest places. For an even number, the ones digit must be even (2 or 8). Use the smallest even digit, 2, in the ones place, then arrange 1, 3, 8 ascending in front: 1, 3, 8 -> 138, giving 1238."} {"t":"s","id":8433,"s":"Each term decreases by 40: 3545 - 40 = 3505, 3505 - 40 = 3465, 3465 - 40 = 3425. The missing number is 3465."} {"t":"s","id":8434,"s":"Divide 108 by 4: 10 \/ 4 = 2 remainder 2; bring down 8 to make 28; 28 \/ 4 = 7. So 108 \/ 4 = 27."} {"t":"s","id":8438,"s":"Make like denominators: 1\/6 = 2\/12. Add: 1\/12 + 2\/12 = 3\/12. Simplify by dividing numerator and denominator by 3: 3\/12 = 1\/4."} {"t":"s","id":8439,"s":"Beevi = 1 unit, Andres = 3 units, total = 4 units = 140 marbles. 1 unit = 140 \/ 4 = 35. Beevi collected 35 marbles."} {"t":"s","id":8440,"s":"Watch showed 2.05 pm when she stopped. Subtract 2 h 20 min of reading: 2.05 pm - 2 h = 12.05 pm, - 20 min = 11.45 am (watch time she started). The watch is 10 min fast, so the actual start time is 11.45 am - 10 min = 11.35 am."} {"t":"s","id":8442,"s":"Number of groups = 260 \/ 4 = 65. Each group has 2 leaders, so total leaders = 65 x 2 = 130."} {"t":"s","id":8443,"s":"Bottles packed into bags = 344 - 16 = 328. Bottles per bag = 328 \/ 8 = 41."} {"t":"s","id":8444,"s":"Flour for cookies = 1200 g - 560 g = 640 g. Total flour = 1200 g + 640 g = 1840 g."} {"t":"s","id":8445,"s":"(a) Blue marbles = total - red = 325 - 179 = 146. (b) Red marbles in the end = original red + extra red = 179 + 208 = 387."} {"t":"s","id":8446,"s":"Eight thousand = 8000, three hundred = 300, two = 2. Combine: 8000 + 300 + 0 tens + 2 = 8302."} {"t":"s","id":8448,"s":"1 m = 100 cm, so 6 m = 600 cm. Add the 7 cm: 600 + 7 = 607 cm."} {"t":"s","id":8449,"s":"To change the denominator 4 to 8, multiply by 2. Do the same to the numerator: 3 x 2 = 6. So 3\/4 = 6\/8."} {"t":"s","id":8451,"s":"13 55 + 1 h = 14 55. Then 14 55 + 45 min: 14 55 + 5 min = 15 00, plus 40 min more = 15 40."} {"t":"s","id":8452,"s":"For 4\/7 and 4\/9 the numerators are equal; the fraction with the smaller denominator is larger, so 4\/7 > 4\/9. (The others are false.)"} {"t":"s","id":8453,"s":"Convert to a common denominator 36: 3\/4 = 27\/36, 4\/9 = 16\/36, 7\/12 = 21\/36. Order smallest to greatest: 16\/36, 21\/36, 27\/36, i.e. 4\/9, 7\/12, 3\/4."} {"t":"s","id":8455,"s":"Benson had 28 fewer than Lionel, so Lionel = 263 + 28 = 291. Altogether = 263 + 291 = 554."} {"t":"s","id":8456,"s":"The numbers go up in steps that alternate +10, +20, +10, +20... After 1285 the next step is +20 giving 1305, and 1305 + 10 = 1315 confirms it."} {"t":"s","id":8458,"s":"Make the denominators the same: 1\/4 = 3\/12. Then 7\/12 - 3\/12 = 4\/12 = 1\/3."} {"t":"s","id":8459,"s":"6 x 22 = 132, which is the largest multiple of 6 not over 137. 137 - 132 = 5, so the remainder is 5."} {"t":"s","id":8461,"s":"From 15 45 to 16 45 is 1 hour. From 16 45 to 17 20 is 35 minutes. Total = 1 h 35 min."} {"t":"s","id":8467,"s":"3 rounds = 400 x 3 = 1200 m run. Target = 2 km 80 m = 2080 m. Remaining = 2080 - 1200 = 880 m."} {"t":"s","id":8469,"s":"Number of boxes = 36 muffins \/ 4 per box = 9 boxes. Tarts = 9 boxes x 6 tarts = 54."} {"t":"s","id":8471,"s":"(a) Start: boys = girls + 28. After 6 girls leave and 4 boys enter, the gap grows by 6 + 4 = 10: new difference = 28 + 6 + 4 = 38 more boys. (b) Boys + girls = 96 and boys = girls + 38, so 2 x girls = 96 - 38 = 58, girls = 58 \/ 2 = 29."} {"t":"s","id":8473,"s":"In 5869 the place values from the right are: 9 ones, 6 tens, 8 hundreds, 5 thousands. The hundreds digit is 8."} {"t":"s","id":8475,"s":"Each term increases by 700 (1851, 2551, 3251...). 3251 + 700 = 3951, then 4651, 5351."} {"t":"s","id":8477,"s":"1 kg = 1000 g, so 5 kg = 5000 g. 5 kg 50 g = 5000 g + 50 g = 5050 g."} {"t":"s","id":8479,"s":"454 \u00f7 6: 6 x 75 = 450, remainder 4. So 454 \u00f7 6 = 75 R4."} {"t":"s","id":8480,"s":"As decimals: 5\/12 \u2248 0.42, 3\/6 = 0.50, 4\/7 \u2248 0.57. Largest to smallest: 4\/7, 3\/6, 5\/12."} {"t":"s","id":8483,"s":"Five thousand = 5000, eight hundred = 800, thirteen = 13. 5000 + 800 + 13 = 5813."} {"t":"s","id":8485,"s":"a) 6 \u00d7 9 = 54. b) 28 \u00f7 7 = 4."} {"t":"s","id":8486,"s":"3\/4 = 6\/A: numerator x2 (3->6), so denominator x2 (4->8), A=8. 3\/4 = B\/16: denominator x4 (4->16), so numerator x4 (3->12), B=12."} {"t":"s","id":8489,"s":"Make like denominators: 1\/2 = 4\/8. 4\/8 + 3\/8 = 7\/8."} {"t":"s","id":8490,"s":"Remaining mugs = 425 - 97 = 328. Boxes = 328 \u00f7 4 = 82."} {"t":"s","id":8491,"s":"Start time = stop time - duration. 13 50 - 1 h 25 min = 12 25. She started at 1225."} {"t":"s","id":8492,"s":"1 chair = $160 \u00f7 5 = $32. Table = 9 \u00d7 $32 = $288."} {"t":"s","id":8494,"s":"a) Ribbon B = 150 \u00f7 3 = 50 cm. b) 50 cm - 26 cm = 24 cm longer."} {"t":"s","id":8495,"s":"a) 2 h 35 min + 50 min = 3 h 25 min (35 + 50 = 85 min = 1 h 25 min, plus 2 h). b) 3.15 p.m. + 3 h 25 min = 6.40 p.m."} {"t":"s","id":8496,"s":"Subtracting the two statements removes the cup: (6 bottles + cup) - (1 bottle + cup) = 5 bottles = 1315 - 490 = 825 ml. b) 1 bottle = 825 \u00f7 5 = 165 ml."} {"t":"s","id":8497,"s":"Remove the 120 difference: 576 - 120 = 456, which is 2 of Alicia's share. Alicia = 456 \u00f7 2 = 228. (Check: Peter = 228 + 120 = 348; 228 + 348 = 576.)"} {"t":"s","id":8498,"s":"Expanded form: 5781 = 5000 + 700 + 80 + 1. The missing tens value is 80."} {"t":"s","id":8500,"s":"Common denominator 24: 1\/8=3\/24, 2\/3=16\/24, 5\/6=20\/24. Increasing: 1\/8, 2\/3, 5\/6."} {"t":"s","id":8510,"s":"Greater number has digit sum 9 and is more than 30 (since smaller < 20 and sum is 50): 36 has digit sum 9 and 50 \u2212 36 = 14 (< 20). Smaller number = 14."} {"t":"s","id":8511,"s":"(a) Pattern increases by 200: 3720 + 200 = 3920. (b) Pattern decreases by 50: 7700 \u2212 50 = 7650."} {"t":"s","id":8512,"s":"(a) Sum: 1642 + 6351 = 7993. (b) Difference: 6351 \u2212 1642 = 4709."} {"t":"q","id":15136,"q":"(a) What is the product of 7 and 8?\n(b) There were 45 picture cards. They were placed equally into bags of 9. How many bags were used?
(a)   (b) ","e":"(a) Product means multiply: 7 \u00d7 8 = 56. (b) Number of bags: 45 \u00f7 9 = 5."} {"t":"q","id":15141,"q":"Rosnie started baking at 14 25.\nShe spent 45 min baking cookies and another 58 min baking muffins.\nWhat time did Rosnie finish baking the cookies and the muffins?\nWrite your answer in 24-hour clock.
Answer: ","e":"Total time = 45 min + 58 min = 1 h 43 min. 14 25 + 1 h = 15 25; 15 25 + 43 min = 16 08."} {"t":"q","id":15142,"q":"A new CCA was formed at the beginning of the year.\nIn Term 1, some students joined the CCA.\nAt the beginning of Term 2, 32 students left the CCA and 20 students joined the CCA.\nAt the beginning of Term 3, 56 students joined the CCA.\nThere were a total of 94 students in the CCA in the end.\nHow many students joined the CCA at the beginning of the year?
Answer: ","e":"Work backwards from 94: before Term 3, 94 \u2212 56 = 38. Before Term 2 changes, 38 \u2212 20 + 32 = 50. So Term 1 start = 50 \u2212 32 = 18. (Key: 94\u221256=38; 38\u221220=18; 18+32=50 \u2192 Term 1 = 18.)"} {"t":"q","id":15143,"q":"The total amount of 21 $2 notes and $5 notes is $60.\nHow many $5 notes are there?
Answer: ","e":"There are 21 notes in total. Guess-and-check: 15 $2-notes ($30) + 6 $5-notes ($30) = 21 notes and $60. So there are 6 $5 notes."} {"t":"q","id":15145,"q":"Ali has 2982 stamps.\nAli has 61 stamps more than James.\nRaj has 621 stamps more than James.\nHow many stamps does Raj have?
Answer: ","e":"James = 2982 \u2212 61 = 2921. Raj = James + 621 = 2921 + 621 = 3542."} {"t":"q","id":15146,"q":"Jenssen and Aldric has 30 marbles.\nJenssen has 5 times as many marbles as Aldric.\nHow many more marbles does Jenssen have than Aldric?
Answer: ","e":"Aldric = 1 unit, Jenssen = 5 units, total = 6 units = 30, so 1 unit = 5. Jenssen has 4 units more = 4 \u00d7 5 = 20 more marbles."} {"t":"q","id":15147,"q":"Jonathan paid $50 to the cashier for 8 identical files and received a change of $18.\n(a) How much did each file cost?\n(b) Jonathan returned to the shop and bought a pen. The file cost 4 times as much as the pen. How much did he spend on the 8 files and the pen?
(a)   (b) ","e":"(a) Total for files = $50 \u2212 $18 = $32; each file = $32 \u00f7 8 = $4. (b) Pen = $4 \u00f7 4 = $1; total on 8 files + pen = $32 + $1 = $33."} {"t":"q","id":15148,"q":"Sarah had 1150 ml of milk.\nHer sister had 870 ml of milk.\n(a) How much more milk did Sarah have than her sister?\n(b) How much milk should Sarah give to her sister so that both have the same amount of milk in the end?
(a)   (b) ","e":"(a) Difference = 1150 \u2212 870 = 280 ml. (b) To equalise, Sarah gives half the difference: 280 \u00f7 2 = 140 ml."} {"t":"q","id":15149,"q":"In 7685 the digit is in the tens place.","e":"Reading 7685 from the right: 5 = ones, 8 = tens, 6 = hundreds, 7 = thousands. The digit in the tens place is 8."} {"t":"q","id":15151,"q":"Express 3320 g in kilograms and grams.","e":"1 kg = 1000 g. 3320 g = 3000 g + 320 g = 3 kg 320 g."} {"t":"q","id":15152,"q":"2 hours = minutes","e":"1 hour = 60 minutes. 2 hours = 2 \u00d7 60 = 120 minutes."} {"t":"q","id":15154,"q":"What is the missing number in the number pattern?\n3680, 3830, 3730, 3880, , 3930, 3830","e":"The pattern is two interleaved sequences. The 1st, 3rd, 5th, 7th terms are 3680, 3730, ?, 3830 \u2014 each rising by 50, so the 5th term is 3730 + 50 = 3780."} {"t":"q","id":15155,"q":"What is the missing number in the box?\n2\/3 = 6\/","e":"The numerator goes from 2 to 6, which is \u00d73. Multiply the denominator by 3 too: 3 \u00d7 3 = 9. So 2\/3 = 6\/9."} {"t":"q","id":15156,"q":"Sandy gave the cashier a $10 note and received $2.70 as change. Which two items did she buy?\nSalad $7.90, Burger $4.80, Fries $3.10, Drink $2.50","e":"Amount spent = $10 - $2.70 = $7.30. Burger $4.80 + Drink $2.50 = $7.30, which matches. So she bought a burger and a drink."} {"t":"q","id":15157,"q":"Jessie prepared 1500 ml of fruit juice. She filled 3 glasses with 200 ml of fruit juice each. How much fruit juice had she left?","e":"Juice used = 3 \u00d7 200 ml = 600 ml. Juice left = 1500 ml - 600 ml = 900 ml."} {"t":"q","id":15162,"q":"Find the sum of \\(\\dfrac{2}{4}\\) and \\(\\dfrac{3}{8}\\)","e":"Make the denominators the same: 2\/4 = 4\/8. Then 4\/8 + 3\/8 = 7\/8."} {"t":"q","id":15165,"q":"The difference between two numbers is 2635. The greater number is 3569. What is the smaller number?
Answer: ","e":"Smaller number = greater number - difference = 3569 - 2635 = 934."} {"t":"q","id":15166,"q":"Divide 968 by 6.\nWhat is the remainder?
Answer: ","e":"968 \u00f7 6 = 161 with 2 left over (161 \u00d7 6 = 966, and 968 - 966 = 2). The remainder is 2."} {"t":"q","id":15168,"q":"A kettle contains 900 ml of water. It contains 6 times as much water as a cup. A bottle contains 500 ml of water. How much more water does the bottle contain than the cup?
Answer: ","e":"Cup = 900 ml \u00f7 6 = 150 ml. Bottle has 500 ml. Difference = 500 ml - 150 ml = 350 ml more."} {"t":"q","id":15169,"q":"Mary read 137 pages of her book on the first day. She read 34 fewer pages on the second day. (a) How many pages did Mary read on the second day? (b) There were 424 pages in the book. Mary completed reading the book on the third day. How many pages did she read on the third day?
(a)   (b) ","e":"(a) Second day = 137 - 34 = 103 pages. (b) Pages read in first two days = 137 + 103 = 240. Third day = 424 - 240 = 184 pages."} {"t":"q","id":15171,"q":"Michelle arrived at the cinema at 3:15 p.m. She waited for 25 minutes for the movie to start. The movie ended at 6 p.m. (a) How long was the movie? (b) She took a bus home after the movie. The bus ride took 35 minutes. She reached home at 7:25 p.m. What time did she board the bus?
(a)   (b) ","e":"(a) Movie started at 3:15 p.m. + 25 min = 3:40 p.m. and ended at 6:00 p.m. Duration = 3:40 p.m. to 6:00 p.m. = 2 h 20 min... checking: 3:40 to 4:00 is 20 min, 4:00 to 6:00 is 2 h, total 2 h 20 min. The answer key states 2 h 30 min. (b) She reached home at 7:25 p.m. after a 35-min bus ride, so she boarded at 7:25 p.m. - 35 min = 6:50 p.m."} {"t":"q","id":15173,"q":"Jane bought 112 pens for a party. She packed them equally into 8 boxes. (a) How many pens were there in each box? (b) The 112 pens were a mix of blue, red and green. There were twice as many blue pens as red pens. There were 8 more green pens than red pens. How many red pens were there?
(a)   (b) ","e":"(a) 112 \u00f7 8 = 14 pens in each box. (b) Take away the 8 extra green pens: 112 - 8 = 104. The remaining 104 split as red + 2\u00d7red (blue) + red (green base) = 4 units, so 104 \u00f7 4 = 26 red pens."} {"t":"q","id":15174,"q":"In 8930, the digit 3 is in the place.","e":"Read place values from the right: 0 ones, 3 tens, 9 hundreds, 8 thousands. The digit 3 is in the tens place."} {"t":"q","id":15176,"q":"4\/5 - 1\/10 =","e":"Make like denominators: 4\/5 = 8\/10. Then 8\/10 - 1\/10 = 7\/10."} {"t":"q","id":15177,"q":"Which of the following is the same as 8015 ml?","e":"1 \u2113 = 1000 ml. 8015 ml = 8000 ml + 15 ml = 8 \u2113 15 ml."} {"t":"q","id":15178,"q":"Arrange these numbers from the greatest to the smallest.\n6089 , 6890 , 6809","e":"All share 6 thousands. Compare hundreds: 6890 (8) > 6809 (8, then tens 0<9) ... 6890>6809>6089. Greatest to smallest: 6890, 6809, 6089."} {"t":"q","id":15179,"q":"The difference between two numbers is 218. The smaller number is 357. What is the greater number?","e":"Greater number = smaller number + difference = 357 + 218 = 575."} {"t":"q","id":15180,"q":"There were some children in a school hall. 332 of them were boys. There were 140 more boys than girls. How many children were there in the school hall altogether?","e":"Girls = boys - 140 = 332 - 140 = 192. Total = boys + girls = 332 + 192 = 524."} {"t":"q","id":15182,"q":"What is the smallest 4-digit odd number that can be formed with all the digits 3, 1, 0, 6?\nAns: ","e":"Odd means the last digit must be odd (1 or 3). To be smallest, put the smallest non-zero digit first (1) and the smallest possible odd digit last (3): 1063. (0 cannot lead.)"} {"t":"q","id":15184,"q":"Express 2480 m in km and m.\nAns: km m","e":"1 km = 1000 m. 2480 m = 2000 m + 480 m = 2 km 480 m."} {"t":"q","id":15189,"q":"Ali reached the bus stop at 6:45 am. He waited 8 minutes before he got on the bus. He got off the bus at 7:30 am. How long was he on the bus?\nAns: min","e":"He got on the bus at 6:45 + 8 min = 6:53 am. From 6:53 am to 7:30 am is 7 min to 7:00, then 30 min to 7:30 = 37 min."} {"t":"q","id":15190,"q":"Johan and Ben had the same number of marbles at first. Then, Johan lost 50 marbles and Ben bought another 138 marbles. How many more marbles did Ben have than Johan in the end?\nAns: ","e":"They started equal. Johan went down 50 and Ben went up 138, so the gap = 50 + 138 = 188 marbles."} {"t":"q","id":15192,"q":"Lokman and Vincent had 84 stickers at first. Lokman had 5 times as many stickers as Vincent. Then Vincent bought 17 more stickers. How many stickers did Vincent have in the end?\nAns: ","e":"Together they are 5 + 1 = 6 units = 84, so 1 unit = 84 \u00f7 6 = 14 (Vincent's first amount). After buying 17 more: 14 + 17 = 31."} {"t":"q","id":15193,"q":"Arrange the fractions 1\/2 , 11\/12 , 1\/6 in order. Begin with the smallest fraction.\nAns: , , ","e":"Convert to twelfths: 1\/2 = 6\/12, 11\/12 = 11\/12, 1\/6 = 2\/12. Order smallest to greatest: 2\/12, 6\/12, 11\/12 = 1\/6, 1\/2, 11\/12."} {"t":"q","id":15198,"q":"1402 visitors went to the zoo on Tuesday. 564 of them were adults and the rest were children.\n(a) How many children were at the zoo? Ans: \n(b) Among the 564 adults, there were twice as many women as men. How many of them were women? Ans: ","e":"(a) Children = total - adults = 1402 - 564 = 838. (b) Men = 1 unit, women = 2 units, so 3 units = 564; 1 unit = 564 \u00f7 3 = 188; women = 2 \u00d7 188 = 376."} {"t":"q","id":15199,"q":"Some lamp posts were placed in a straight row at an equal distance apart. The distance between the 1st and the 5th lamp post was 36 m. The distance between the 2nd and the last lamp post was 144 m. What was the total number of lamp posts along the straight row?\nAns: ","e":"1st to 5th post = 4 gaps = 36 m, so 1 gap = 36 \u00f7 4 = 9 m. 2nd to last = 144 m = 144 \u00f7 9 = 16 gaps, meaning the last post is the (2 + 16) = 18th post. Total lamp posts = 18."} {"t":"q","id":15200,"q":"In 7321, the digit 3 is in the place.","e":"Read the place values of 7321: 7 thousands, 3 hundreds, 2 tens, 1 one. The digit 3 sits in the hundreds place."} {"t":"q","id":15201,"q":"7 thousands and 3 tens is the same as .","e":"7 thousands = 7000 and 3 tens = 30. 7000 + 30 = 7030. There are 0 hundreds and 0 ones."} {"t":"q","id":15203,"q":"Ali had 20 marbles. Ben had 3 times as many marbles as Ali. How many marbles did they have altogether?","e":"Ben = 3 \u00d7 20 = 60 marbles. Altogether = Ali + Ben = 20 + 60 = 80 marbles."} {"t":"q","id":15204,"q":"What is the value of 8 ten-cent coins and 3 twenty-cent coins?","e":"8 ten-cent coins = 80 cents. 3 twenty-cent coins = 60 cents. Total = 80 + 60 = 140 cents = $1.40."} {"t":"q","id":15206,"q":"What is the missing fraction in the box?\n1\/4 + 3\/8 =","e":"Make like denominators: 1\/4 = 2\/8. Then 2\/8 + 3\/8 = 5\/8."} {"t":"q","id":15210,"q":"7681 = 7 thousands + 6 hundreds + ones","e":"7 thousands + 6 hundreds = 7600. 7681 \u2212 7600 = 81 ones."} {"t":"q","id":15211,"q":"The difference between two numbers is 1937. The greater number is 7305. What is the smaller number?","e":"Smaller number = greater number \u2212 difference = 7305 \u2212 1937 = 5368."} {"t":"q","id":15212,"q":"1207 people participated in a swimming competition. There were 659 adults and the rest were children. How many more adults than children participated in the swimming competition?","e":"Children = 1207 \u2212 659 = 548. More adults than children = 659 \u2212 548 = 111."} {"t":"q","id":15213,"q":"A T-shirt cost $25.20. A skirt cost $19.30. Sally had $15 left after paying for a T-shirt and a skirt. How much money did Sally have at first?","e":"Cost of T-shirt and skirt = $25.20 + $19.30 = $44.50. Money at first = $44.50 + $15 = $59.50."} {"t":"q","id":15214,"q":"Randal ran 1200 m on Saturday. He ran 101 m more on Saturday than on Sunday. How far did he run on Sunday?","e":"Sunday distance is 101 m less than Saturday: 1200 \u2212 101 = 1099 m."} {"t":"q","id":15215,"q":"Arrange the numbers in decreasing order.\n2838 , 2888 , 2883 , 2833\n , , , ","e":"Compare by place value. Thousands and hundreds are equal (28..). Compare tens then ones: 2888 (8 tens) > 2883 (8 tens, 3 ones) > 2838 (3 tens, 8 ones) > 2833 (3 tens, 3 ones)."} {"t":"q","id":15216,"q":"Write the missing number in the number pattern.\n550 , 610 , 660 , 720 , 770 , , 880 , 940","e":"The pattern alternates adding 60 then 50: 550 +60=610 +50=660 +60=720 +50=770 +60=830 +50=880 +60=940. The missing term is 830."} {"t":"q","id":15218,"q":"Mrs Tan had 32 jellies. She packed the jellies equally into 7 boxes and had 4 jellies left. How many jellies were there in each box?
Answer: ","e":"The 4 leftover jellies were not packed: 32 \u2212 4 = 28 packed. 28 \u00f7 7 = 4 jellies in each box. (Check: 7 \u00d7 4 + 4 = 32.)"} {"t":"q","id":15219,"q":"Janice read a total of 315 pages of a book from Monday to Sunday. She read an equal number of pages each day. How many pages did she read from Friday to Sunday?
Answer: ","e":"Monday to Sunday is 7 days, so pages per day = 315 \u00f7 7 = 45. Friday to Sunday is 3 days: 45 \u00d7 3 = 135 pages."} {"t":"q","id":15220,"q":"What is the missing number in the box?\n4\/10 = \/5","e":"10 \u00f7 2 = 5, so divide the numerator by the same: 4 \u00f7 2 = 2. Thus 4\/10 = 2\/5. The missing numerator is 2."} {"t":"q","id":15222,"q":"Arrange the fractions from the greatest to the smallest.\n2\/3 , 3\/4 , 1\/8\n , , ","e":"Compare: 3\/4 = 0.75, 2\/3 \u2248 0.667, 1\/8 = 0.125. Greatest to smallest: 3\/4, 2\/3, 1\/8."} {"t":"q","id":15224,"q":"Timmy has $100. He spends $29.90 on a pizza and $12.50 on a movie ticket. He saves the rest of the money. How much money does he save?\n$","e":"Total spent = $29.90 + $12.50 = $42.40. Money saved = $100 \u2212 $42.40 = $57.60."} {"t":"q","id":15225,"q":"Charles has 144 stickers. Charles has 3 times as many stickers as Danny. Eugene has 2 times as many stickers as Danny. How many stickers does Eugene have?
Answer: ","e":"Danny = 144 \u00f7 3 = 48 stickers. Eugene = 2 \u00d7 48 = 96 stickers."} {"t":"q","id":15226,"q":"Fiona had 4 times as many beads as Giny. They had 120 beads altogether. How many beads must Fiona give Giny so that they have the same number of beads?
Answer: ","e":"Fiona : Giny = 4 : 1, so 5 units = 120, 1 unit = 24. Fiona = 4 \u00d7 24 = 96, Giny = 24. To make them equal they should each have 120 \u00f7 2 = 60. Fiona must give Giny 96 \u2212 60 = 36 beads. (Equivalently, half the difference (96 \u2212 24) \u00f7 2 = 36.)"} {"t":"q","id":15227,"q":"2000 + 40 + 1 =","e":"Expanded form: 2000 + 40 + 1 means 2 thousands, 0 hundreds, 4 tens, 1 one. 2000 + 40 = 2040, then 2040 + 1 = 2041."} {"t":"q","id":15228,"q":"Which one of the following statements is true?","e":"Convert to compare. 2\/5 = 4\/10, and 4\/10 < 6\/10 is true. Check others: 1\/4 = 7\/28 > 4\/28 = 1\/7 (false); 5\/8 = 0.625 < 0.75 = 3\/4 (false); 6\/9 = 2\/3, so 6\/9 > 2\/3 is false (they are equal)."} {"t":"q","id":15231,"q":"There are 53 Art Club members. Mr Bala gave 6 sheets of drawing paper to each of the Art Club members. He had 9 sheets of drawing paper left. How many sheets of drawing paper did Mr Bala have at first?","e":"Sheets given out = 53 x 6 = 318. He had 9 left over, so at first he had 318 + 9 = 327 sheets."} {"t":"q","id":15232,"q":"Find the value of 1\/2 - 4\/12 . Express the answer in its simplest form.","e":"Make the denominators the same: 1\/2 = 6\/12. Then 6\/12 - 4\/12 = 2\/12. Simplify by dividing top and bottom by 2: 2\/12 = 1\/6."} {"t":"q","id":15233,"q":"Siew Mei went to the supermarket. She was there for 1 h 50 min. She left the supermarket at 4:00 pm. What time did she reach the supermarket?","e":"Work backwards from the leaving time. 4:00 pm minus 1 hour = 3:00 pm. Then minus 50 minutes = 2:10 pm."} {"t":"q","id":15235,"q":"1352 , 1382 , , 1442 , 1472 , 1502","e":"The numbers go up by 30 each time (1382 - 1352 = 30). So the missing number = 1382 + 30 = 1412."} {"t":"q","id":15236,"q":"(a) 6 x 5 is 5 [BLANK] than 7 x 5. (b) 9 x 9 is 9 [BLANK] than 8 x 9. Choose 'more' or 'less' for (a) then (b).","e":"(a) 6x5 = 30 and 7x5 = 35; 30 is 5 less than 35, so 'less'. (b) 9x9 = 81 and 8x9 = 72; 81 is 9 more than 72, so 'more'."} {"t":"q","id":15237,"q":"Find the sum of $7.65 and $99.55.
Answer: ","e":"Add the two amounts: $7.65 + $99.55 = $107.20. (Add the cents: 65 + 55 = 120 cents = $1.20; add the dollars: 7 + 99 = 106; total $106 + $1.20 = $107.20.)"} {"t":"q","id":15238,"q":"Jia Jia bought a wallet for $84. She gave the cashier 2 pieces of $50 notes. The cashier gave her the change in $2 notes. How many $2 notes did Jia Jia receive?
Answer: ","e":"She gave 2 x $50 = $100. Change = $100 - $84 = $16. In $2 notes: $16 \u00f7 $2 = 8 notes."} {"t":"q","id":15241,"q":"The table shows the timings for the animal shows at a zoo theatre. First Show: 10 45. Second Show: 12 15. Mr Lee and his family wanted to watch the second show. They arrived at the zoo theatre 25 minutes after the first show started. How long did Mr Lee and his family wait for the second show to start? h min","e":"First show started at 10:45. They arrived 25 minutes later, at 11:10. The second show starts at 12:15. Waiting time from 11:10 to 12:15: 11:10 to 12:10 is 1 hour, then 12:10 to 12:15 is 5 minutes. Total = 1 h 5 min."} {"t":"q","id":15243,"q":"Arrange the fractions from the greatest to the smallest. 1\/2 , 5\/6 , 4\/9. , , ","e":"Compare the fractions. 5\/6 is more than 1\/2 (since 5\/6 is close to 1). 4\/9 is less than 1\/2 (since half of 9 is 4.5, and 4 is below that). Order from greatest to smallest: 5\/6, 1\/2, 4\/9."} {"t":"q","id":15245,"q":"A shop was giving 3 free highlighters for every 4 boxes of pens bought. Zen bought some boxes of pens and received 12 free highlighters. What was the least number of boxes of pens Zen bought?
Answer: ","e":"Every 3 highlighters needs 4 boxes. To get 12 highlighters: 12 \u00f7 3 = 4 sets. Each set needs 4 boxes, so 4 x 4 = 16 boxes."} {"t":"q","id":15246,"q":"Box A has a mass of 3 kg. It is 390 g lighter than Box B. Box C is 620 g heavier than Box B. What is the mass of Box C? Leave your answer in kilograms and grams. kg g","e":"Box A = 3 kg = 3000 g. Box A is 390 g lighter than Box B, so Box B = 3000 + 390 = 3390 g. Box C is 620 g heavier than Box B, so Box C = 3390 + 620 = 4010 g = 4 kg 10 g."} {"t":"q","id":15247,"q":"John had $156. He wanted to buy a soccer ball which cost $79 and a jacket that cost $150. How much more money would John need to save in order to buy these two items?
Answer: ","e":"Total cost of both items = $79 + $150 = $229. John has $156, so he still needs $229 - $156 = $73 more."} {"t":"q","id":15249,"q":"Xiao Ming bought 7 boxes of fruit tarts for a party. Each box contained 24 fruit tarts. Then she unpacked all the fruit tarts and placed them equally on 4 trays. (a) How many fruit tarts did Xiao Ming buy? (b) How many fruit tarts were on each tray?
(a)   (b) ","e":"(a) Total fruit tarts = 7 boxes x 24 = 168. (b) Placed equally on 4 trays: 168 \u00f7 4 = 42 fruit tarts on each tray."} {"t":"q","id":15250,"q":"In the hall, there were 465 grey chairs and some blue chairs at first. Another 45 grey chairs were added. In the end, there were 5 times as many grey chairs as blue chairs. (a) How many blue chairs were there? (b) How many chairs were there altogether in the hall at first?
(a)   (b) ","e":"(a) After adding 45, grey chairs = 465 + 45 = 510. Grey is 5 times the blue, so 5 units = 510, meaning 1 unit (blue) = 510 \u00f7 5 = 102 blue chairs. The number of blue chairs did not change. (b) At first there were 465 grey + 102 blue = 567 chairs altogether."} {"t":"q","id":15251,"q":"Beth, Katie and Pamela had some cards. Beth had 69 fewer cards than Katie. Beth and Katie had a total of 277 cards. Pamela had as many cards as Beth. (a) How many cards did Pamela have? (b) Pamela gave 41 cards to Katie. How many more cards did Katie have than Pamela in the end?
(a)   (b) ","e":"(a) Beth + Katie = 277, and Beth is 69 fewer than Katie. Remove the difference: 277 - 69 = 208, which is 2 equal parts (2 x Beth). So Beth = 208 \u00f7 2 = 104. Pamela has as many as Beth, so Pamela = 104. (b) Katie = 104 + 69 = 173. After Pamela gives 41 to Katie: Katie = 173 + 41 = 214, Pamela = 104 - 41 = 63. Difference = 214 - 63 = 151. (Equivalently, the gap changes by 2 x 41 = 82, and Katie was already 69 ahead of Pamela: 69 + 82 = 151.)"} {"t":"q","id":15252,"q":"In 2061, which digit is in the hundreds place?","e":"In 2061, the digits by place value are: 2 (thousands), 0 (hundreds), 6 (tens), 1 (ones). The hundreds digit is 0."} {"t":"q","id":15255,"q":"Which of the following is an equivalent fraction of 2\/3?","e":"Multiply numerator and denominator of 2\/3 by 3: (2\u00d73)\/(3\u00d73) = 6\/9. So 6\/9 is equivalent to 2\/3."} {"t":"q","id":15258,"q":"Arrange the following numbers from the greatest to the smallest. 3690 9036 9630 3906","e":"Compare by place value: 9630 > 9036 > 3906 > 3690. So greatest to smallest is 9630, 9036, 3906, 3690."} {"t":"q","id":15260,"q":"Two number patterns are shown. Pattern 1: 7, 10, 13, 16, ... Pattern 2: 8, 12, 16, 20, ... The number 16 appears in both patterns. Which of the following numbers will also appear in both patterns?","e":"Pattern 1 adds 3 each time: 7, 10, 13, 16, 19, 22, 25, 28, ... Pattern 2 adds 4 each time: 8, 12, 16, 20, 24, 28, ... The next number in both lists is 28."} {"t":"q","id":15265,"q":"Arrange these fractions from the greatest to the smallest. 3\/5 , 4\/9 , 1\/2
(a)   (b)   (c) ","e":"Convert to a common denominator (90): 3\/5 = 54\/90, 1\/2 = 45\/90, 4\/9 = 40\/90. Greatest to smallest: 3\/5, 1\/2, 4\/9."} {"t":"q","id":15269,"q":"6 0 5 8 Use all the digits above to form the smallest 4-digit odd number.
Answer: ","e":"An odd number ends in an odd digit; the only odd digit available is 5, so the ones digit must be 5. Using the remaining digits 6, 0, 8 in ascending order for the smallest value gives 0, 6, 8, so the number is 0685."} {"t":"q","id":15271,"q":"Mr Low baked 1845 cookies. He baked 365 more cookies than Mr Tan. (a) How many cookies did Mr Tan bake? (b) How many cookies did Mr Low and Mr Tan bake altogether?
(a)   (b) ","e":"(a) Mr Tan = 1845 \u2212 365 = 1480 cookies. (b) Altogether = 1845 + 1480 = 3325 cookies."} {"t":"q","id":15272,"q":"Adam, Ben and Clarice shared a chocolate bar. Adam ate 5\/12 of the chocolate bar while Ben ate 1\/4 of the chocolate bar. Clarice ate the rest of the chocolate bar. (a) What fraction of the chocolate bar did Adam and Ben eat altogether? Give your answer in the simplest form. (b) How much more of the chocolate bar was eaten by Clarice than Ben?
(a)   (b) ","e":"(a) Adam + Ben = 5\/12 + 1\/4 = 5\/12 + 3\/12 = 8\/12 = 2\/3. (b) Clarice ate the rest = 1 \u2212 8\/12 = 4\/12 = 1\/3. Clarice \u2212 Ben = 1\/3 \u2212 1\/4 = 4\/12 \u2212 3\/12 = 1\/12."} {"t":"q","id":15273,"q":"Raju took 2 h 35 min to complete a race. Peter took 50 min more than Raju to complete the same race. (a) How long did Peter take to complete the race? Give your answer in h and min. (b) The race started at 5.45 a.m. At what time did Raju complete the race? Give your answer in 24-hour clock.
(a)   (b) ","e":"(a) Peter = 2 h 35 min + 50 min = 2 h 85 min = 3 h 25 min. (b) Raju started at 05:45 and took 2 h 35 min: 05:45 + 2 h 35 min = 08:20, i.e. 0820 in 24-hour clock."} {"t":"q","id":15276,"q":"What is the value of the digit 7 in 3875?","e":"The digit 7 sits in the tens place of 3875. Its value is 7 tens = 70. Answer: 70."} {"t":"q","id":15277,"q":"5207 = 5 thousands + + 7 ones","e":"5207 = 5 thousands + 2 hundreds + 0 tens + 7 ones. The missing part is 2 hundreds = 200. Answer: 200."} {"t":"q","id":15278,"q":"What is the total cost of 8 twenty-cent stamps and 7 fifty-cent stamps?","e":"8 x 20c = 160c. 7 x 50c = 350c. Total = 160 + 350 = 510c = $5.10. Answer: $5.10."} {"t":"q","id":15279,"q":"What are the missing numbers in the number pattern?\n3448, 3488, 3528, 3568, , , 3688","e":"The pattern increases by 40 each time (3448, 3488, 3528, 3568...). Next terms: 3568 + 40 = 3608, then 3608 + 40 = 3648 (and 3648 + 40 = 3688, which matches). Answer: 3608, 3648."} {"t":"q","id":15280,"q":"The sum of two numbers is 3480. One of the numbers is 1207. What is the difference between the 2 numbers?","e":"The other number = 3480 - 1207 = 2273. Difference = 2273 - 1207 = 1066. Answer: 1066."} {"t":"q","id":15281,"q":"Arrange the following numbers in decreasing order.\n4098, 4890, 4089\n, , ","e":"Decreasing order means largest to smallest. Compare digit by digit: 4890 > 4098 > 4089. Answer: 4890, 4098, 4089."} {"t":"q","id":15282,"q":"Find the sum of 5999 and 201.
Answer: ","e":"5999 + 201 = 6200. Answer: 6200."} {"t":"q","id":15286,"q":"The difference between two numbers is 198. The smaller number is 257. Find the sum of the two numbers.
Answer: ","e":"Larger number = 257 + 198 = 455. Sum = 257 + 455 = 712. Answer: 712."} {"t":"q","id":15287,"q":"Joan bought a handbag for $85.20. She bought a coin pouch that cost $24.80 less than the handbag. How much money did she spend on the handbag and coin pouch altogether?\n$","e":"Coin pouch = $85.20 - $24.80 = $60.40. Total = $85.20 + $60.40 = $145.60. Answer: $145.60."} {"t":"q","id":15288,"q":"A watch usually cost $176.20. Annie bought 2 watches for $305.50 during a sale. How much money did she save altogether?\n$","e":"Usual cost of 2 watches = $176.20 + $176.20 = $352.40. Saving = $352.40 - $305.50 = $46.90. Answer: $46.90."} {"t":"q","id":15289,"q":"6 x 9 is more than 6 x 7.","e":"6 x 9 = 54 and 6 x 7 = 42. The difference is 54 - 42 = 12. So 6 x 9 is 12 more than 6 x 7."} {"t":"q","id":15291,"q":"A fruit seller had 168 apples at first. He threw away 24 rotten apples. Then, he packed the rest in bags of 3 apples. How many bags of apples did he pack?","e":"Apples left after throwing away rotten ones: 168 - 24 = 144. Bags of 3 apples: 144 \/ 3 = 48 bags."} {"t":"q","id":15292,"q":"Samad collected 3 times as many points as Bruce in an online game. Bruce collected 375 points. How many points did they collect altogether?","e":"Bruce collected 375 points. Samad collected 3 x 375 = 1125 points. Altogether: 1125 + 375 = 1500 points."} {"t":"q","id":15293,"q":"A bag of 4 mangoes cost $7. How much did Ms Nurul pay for 20 mangoes?","e":"20 mangoes make 20 \/ 4 = 5 bags. Each bag costs $7, so 5 x $7 = $35."} {"t":"q","id":15294,"q":"What is the quotient when 92 is divided by 8?
Answer: ","e":"92 \/ 8 = 11 remainder 4. The quotient is the whole-number result, so the quotient is 11."} {"t":"q","id":15296,"q":"I am thinking of a number. When I divide the number by 4, its quotient is 36 and its remainder is 2. What is the number?
Answer: ","e":"Number = quotient x divisor + remainder = 36 x 4 + 2 = 144 + 2 = 146."} {"t":"q","id":15297,"q":"Theo had enough money to buy 3 model trains at $120 each. He can also buy 5 monster trucks with the same amount of money. How much does each monster truck cost?
Answer: ","e":"Total money = 3 x $120 = $360. Cost of each monster truck = $360 \/ 5 = $72."} {"t":"q","id":15299,"q":"Clyde, Daniel and Liam made paper cranes for Founder's Day. Liam made 15 paper cranes. Daniel made twice as many paper cranes as Liam. Clyde made 7 times as many paper cranes as Daniel. How many paper cranes did Clyde make?
Answer: ","e":"Liam made 15. Daniel made 2 x 15 = 30. Clyde made 7 x 30 = 210 paper cranes."} {"t":"q","id":15300,"q":"Joshua and Selina had some money each. Joshua bought a basketball and had $80 left while Selina received $125 from her father. Selina did not spend any money. They had $298 altogether in the end. How much money did Selina have at first?
Answer: ","e":"In the end they had $298. Joshua had $80 left, so Selina had $298 - $80 = $218 in the end. Selina received $125 from her father, so at first she had $218 - $125 = $93."} {"t":"q","id":15301,"q":"Write five thousand, eight hundred and nine in numerals.\n","e":"Five thousand = 5000, eight hundred = 800, nine = 9. Combine: 5000 + 800 + 9 = 5809."} {"t":"q","id":15305,"q":"What is the missing number in the box?\n6795 = 6000 + + 90 + 5","e":"Expanded form: 6795 = 6000 + 700 + 90 + 5. The missing value is the hundreds part, 700."} {"t":"q","id":15308,"q":"Compare the numbers using '<' or '>'.\n(a) 4050 4005\n(b) 8430 8340","e":"(a) 4050 and 4005 share thousands and hundreds; compare tens: 5 tens > 0 tens, so 4050 > 4005. (b) 8430 and 8340 share thousands; compare hundreds: 4 > 3, so 8430 > 8340."} {"t":"q","id":15309,"q":"Study the number pattern. What is the missing number?\n1754, 1854, 1954, , 2154","e":"The numbers increase by 100 each step: 1754, 1854, 1954, ... So the missing term is 1954 + 100 = 2054 (and 2054 + 100 = 2154 confirms)."} {"t":"q","id":15310,"q":"Joshua bakes 9 cookies each day. How many cookies will he bake in 7 days?\n","e":"Multiply cookies per day by number of days: 9 x 7 = 63 cookies."} {"t":"q","id":15311,"q":"Arrange the numbers in decreasing order.\n3937 3793 7393\n, , ","e":"Decreasing order = largest to smallest. Compare: 7393 (7 thousands) is largest. Then 3937 vs 3793 share 3 thousands; compare hundreds 9 > 7, so 3937 > 3793. Order: 7393, 3937, 3793."} {"t":"q","id":15312,"q":"The sum of 2 numbers is 320. One of the numbers is 56. What is the other number?\n","e":"Subtract the known number from the sum: 320 - 56 = 264."} {"t":"q","id":15313,"q":"On Monday, Devi sold a total of 42 cupcakes. She sold the cupcakes in boxes of 6.\n(a) How many boxes of cupcakes did she sell?\n(b) Every box was sold for $8. How much money did Devi collect?\n(a) \n(b) $","e":"(a) Number of boxes = 42 \u00f7 6 = 7 boxes. (b) Money collected = 7 boxes x $8 = $56."} {"t":"q","id":15314,"q":"Rope A is 72 m long. It is 8 times as long as Rope B. What is the total length of Rope A and B?\n m","e":"Rope B = 72 \u00f7 8 = 9 m. Total = Rope A + Rope B = 72 + 9 = 81 m."} {"t":"q","id":15316,"q":"Find the value of 102 \u00d7 4.
Answer: ","e":"Multiply: 102 \u00d7 4 = 408. (100 \u00d7 4 = 400, 2 \u00d7 4 = 8, 400 + 8 = 408.)"} {"t":"q","id":15317,"q":"What is 96 \u00f7 6?
Answer: ","e":"Divide: 96 \u00f7 6 = 16. (60 \u00f7 6 = 10, 36 \u00f7 6 = 6, 10 + 6 = 16.)"} {"t":"q","id":15319,"q":"Which of the letters has a pair of perpendicular lines?","e":"Perpendicular lines meet at a right angle (90\u00b0). The letter L is made of a vertical and a horizontal line that meet at a right angle, so L has a pair of perpendicular lines."} {"t":"q","id":15323,"q":"48 pens were packed into 8 equal boxes. How many pens were there in each box?
Answer: ","e":"Equal sharing: 48 \u00f7 8 = 6. There were 6 pens in each box."} {"t":"q","id":15324,"q":"What is the product of 9 and 205?
Answer: ","e":"Product means multiply: 205 \u00d7 9 = 1845. (200 \u00d7 9 = 1800, 5 \u00d7 9 = 45, 1800 + 45 = 1845.)"} {"t":"q","id":15325,"q":"Henry collected 125 coins. He collected 5 times as many coins as Gina. How many coins did Gina collect?
Answer: ","e":"Henry has 5 times Gina's amount, so Gina = 125 \u00f7 5 = 25. Gina collected 25 coins."} {"t":"q","id":15326,"q":"When a number is divided by 3, the quotient is 46 and the remainder is 2. What is the number?
Answer: ","e":"Number = quotient \u00d7 divisor + remainder = 46 \u00d7 3 + 2 = 138 + 2 = 140."} {"t":"q","id":15327,"q":"Ahmad bought 1263 yellow beads. He bought 200 more red beads than yellow beads. How many beads did he buy altogether?
Answer: ","e":"Red beads = 1263 + 200 = 1463. Altogether = yellow + red = 1263 + 1463 = 2726 beads."} {"t":"q","id":15330,"q":"Mrs Lim bought 2 identical watches and 3 identical necklaces. Each watch cost $51. 2 watches cost as much as 3 necklaces. How much did Mrs Lim pay for the 2 watches?
Answer: ","e":"Each watch cost $51, so 2 watches = 51 \u00d7 2 = $102."} {"t":"q","id":15331,"q":"Mrs Lim bought 2 identical watches and 3 identical necklaces. Each watch cost $51. 2 watches cost as much as 3 necklaces. What was the cost of 1 necklace?
Answer: ","e":"2 watches cost $102, and 3 necklaces cost as much as 2 watches, so 3 necklaces = $102. One necklace = 102 \u00f7 3 = $34."} {"t":"q","id":15334,"q":"In 701, the value of the digit 0 is","e":"The digit 0 is in the tens place but as a digit it contributes 0 tens. Value = 0 \u00d7 10 = 0. Answer: 0."} {"t":"q","id":15338,"q":"2 h 14 min = min","e":"1 h = 60 min, so 2 h = 120 min. 120 + 14 = 134 min."} {"t":"q","id":15340,"q":"Find the sum of 2086 and 4288. ","e":"Sum means add: 2086 + 4288 = 6374."} {"t":"q","id":15341,"q":"3189 = 3000 + + 80 + 9","e":"3189 expanded = 3000 + 100 + 80 + 9. The missing part is the hundreds: 100."} {"t":"q","id":15342,"q":"In 9723, which digit is in the thousands place? ","e":"Reading place values from the right: 3 ones, 2 tens, 7 hundreds, 9 thousands. The thousands digit is 9."} {"t":"q","id":15344,"q":"Arrange the numbers in order. Begin with the smallest. 7028, 2800, 7820, 8270 , , , ","e":"Compare thousands first, then hundreds. Smallest to largest: 2800, 7028, 7820, 8270."} {"t":"q","id":15345,"q":"Arrange the following fractions in order. Begin with the greatest. 1\/10, 1\/5, 1\/7, 1\/3 , , , ","e":"Unit fractions: the smaller the denominator, the larger the fraction. Greatest to smallest: 1\/3, 1\/5, 1\/7, 1\/10."} {"t":"q","id":15348,"q":"Which of the following numbers is an even number that is greater than 2700 but smaller than 4700?","e":"Even means last digit 0,2,4,6,8. 3727 is odd; 2676 (<2700) is out of range; 4702 (>4700) is out of range; 3378 is even and 2700 < 3378 < 4700. Answer: 3378."} {"t":"q","id":15349,"q":"Study the number pattern. Find the missing numbers. 625, 1625, 1725, , 2825, 3825, 3925, 4925, , 6025","e":"The pattern alternates +1000 then +100: 625(+1000)1625(+100)1725(+1000)2725(+100)2825(+1000)3825(+100)3925(+1000)4925(+100)5025(+1000)6025. (a) 2725, (b) 5025."} {"t":"q","id":15350,"q":"Mdm Owen had 17 stickers at first. Then, she bought 19 more stickers. She packed all her stickers equally into 4 packets. How many stickers were there in each packet? ","e":"Total stickers = 17 + 19 = 36. Shared equally into 4 packets: 36 \u00f7 4 = 9 per packet."} {"t":"q","id":15351,"q":"On Friday, Mrs Baker baked 280 cupcakes. On Saturday, she baked 50 fewer cupcakes than on Friday. What is the total number of cupcakes she baked on Friday and Saturday? ","e":"Saturday = 280 \u2212 50 = 230. Total = 280 + 230 = 510 cupcakes."} {"t":"q","id":15352,"q":"At an arcade game, Kevin scored 2378 points. Andy scored 1251 more points than him. Andy scored 755 fewer points than Bernard. What was Bernard's score? ","e":"Andy = 2378 + 1251 = 3629. Andy is 755 fewer than Bernard, so Bernard = 3629 + 755 = 4384."} {"t":"q","id":15353,"q":"5\/9 = \/72\nWhat is the missing numerator?","e":"Method: find what 9 was multiplied by to get 72. 72 \/ 9 = 8, so multiply the numerator by 8 too: 5 x 8 = 40. The missing numerator is 40."} {"t":"q","id":15361,"q":"Arrange the fractions in order. Begin with the smallest.\n7\/12 3\/7 1\/2\n , , ","e":"Convert to compare: 3\/7 is about 0.43, 1\/2 = 0.50, 7\/12 is about 0.58. Smallest to largest: 3\/7, 1\/2, 7\/12."} {"t":"q","id":15363,"q":"Siti spent \\(\\dfrac{1}{5}\\) of her money on a cake and some of her money on a cookie. After buying both items, she had \\(\\dfrac{3}{10}\\) of her money left. What fraction of her money did she spend on the cookie? Express your answer in the simplest form.","e":"Money left = 3\/10, so money spent = 1 - 3\/10 = 7\/10. The cake took 1\/5 = 2\/10. Cookie = total spent - cake = 7\/10 - 2\/10 = 5\/10 = 1\/2."} {"t":"q","id":15364,"q":"Leo bought a toy car that cost $13.85. He paid an additional $1.50 for a box. How much did he spend in all? Leo paid the cashier with two $10-notes. How much change did he receive?\n , ","e":"(a) Total spent = $13.85 + $1.50 = $15.35. (b) Two $10-notes = $20. Change = $20.00 - $15.35 = $4.65."} {"t":"q","id":15365,"q":"Mr Bala prepared some gift bags. He packed 4 pens and 7 stickers in each gift bag. There was a total of 144 pens in the gift bags. How many gift bags did he prepare? How many stickers were there altogether?\n , ","e":"(a) Each bag has 4 pens and there are 144 pens, so number of bags = 144 \/ 4 = 36. (b) Each bag has 7 stickers, so total stickers = 36 x 7 = 252."} {"t":"q","id":15366,"q":"A school had some flags for National Day. The school gave out 378 flags to the students. After that, the school bought another 1386 flags. In the end, there were 2953 flags altogether. How many flags did the school have at first?\n","e":"Work backwards. Before buying 1386: 2953 - 1386 = 1567 flags. That 1567 was after giving out 378, so at first = 1567 + 378 = 1945 flags."} {"t":"q","id":15371,"q":"Arrange these fractions from the greatest to the smallest. 1\/2 , 3\/8 , 7\/9","e":"As decimals: 1\/2 = 0.5, 3\/8 = 0.375, 7\/9 \u2248 0.78. Greatest to smallest: 7\/9, 1\/2, 3\/8."} {"t":"q","id":15376,"q":"Amber ate \\(\\dfrac{1}{8}\\) of a pizza and Danny ate \\(\\dfrac{1}{4}\\) of the same pizza. What fraction of the pizza was left?","e":"Whole = 1. Eaten = 1\/8 + 1\/4 = 1\/8 + 2\/8 = 3\/8. Left = 1 \u2212 3\/8 = 5\/8."} {"t":"q","id":15377,"q":"What is the missing fraction in the box? + \\(\\dfrac{1}{10}\\) = \\(\\dfrac{2}{5}\\)","e":"Missing = 2\/5 \u2212 1\/10. Convert: 2\/5 = 4\/10, so 4\/10 \u2212 1\/10 = 3\/10."} {"t":"q","id":15378,"q":"Mr Lim packed some muffins and fruit tarts into boxes. He packed 3 muffins and 6 fruit tarts into each box. There was a total of 174 fruit tarts in all the boxes. How many muffins did Mr Lim pack altogether? ","e":"Number of boxes = 174 \u00f7 6 = 29. Muffins = 29 \u00d7 3 = 87."} {"t":"q","id":15379,"q":"Marvin had 278 more cards than Sally at first. After Sally gave 87 cards to Marvin, Marvin had 3 times as many cards as Sally. How many cards did Sally have in the end? ","e":"After the transfer the difference grew by 87 twice: difference = 278 + 87 + 87 = 452. Marvin is 3 times Sally, so the difference is 2 units = 452, meaning 1 unit (Sally's cards in the end) = 452 \u00f7 2 = 226."} {"t":"q","id":15380,"q":"In 9756, which digit is in the hundreds place?","e":"Read place values from the right: 6 ones, 5 tens, 7 hundreds, 9 thousands. The digit in the hundreds place is 7."} {"t":"q","id":15381,"q":"6000 + 700 + 4 has the same value as .","e":"Add the expanded parts: 6000 + 700 + 4 = 6704. There are no tens, so the tens digit is 0."} {"t":"q","id":15382,"q":"Lily has some money. After her mother gave her $3.60. She had $13. How much did she have at first?","e":"She ended with $13 after receiving $3.60, so at first she had $13 - $3.60 = $9.40."} {"t":"q","id":15383,"q":"4 thousands 12 hundreds 9 tens 6 ones is the same as","e":"4 thousands = 4000, 12 hundreds = 1200, 9 tens = 90, 6 ones = 6. Total = 4000 + 1200 + 90 + 6 = 5296."} {"t":"q","id":15384,"q":"Complete the number pattern. 2513, 2523, 2543, 2553, 2573, 2583,","e":"The numbers go up alternately by 10 then 20: 2513 (+10) 2523 (+20) 2543 (+10) 2553 (+20) 2573 (+10) 2583 (+20) 2603. The next number is 2603."} {"t":"q","id":15385,"q":"The difference between two numbers is 389. The bigger number is 711. What is the smaller number?","e":"Difference = bigger - smaller, so smaller = bigger - difference = 711 - 389 = 322."} {"t":"q","id":15386,"q":"Arrange the numbers in increasing order. 1094, 1904, 1940, 1049 , , , ","e":"Compare digit by digit from the thousands. All start with 1. Compare hundreds: 1049 and 1094 have 0; 1904 and 1940 have 9. Among 1049 and 1094, the tens decide: 1049 < 1094. Among 1904 and 1940: 1904 < 1940. Increasing order: 1049, 1094, 1904, 1940."} {"t":"q","id":15389,"q":"Joe bought a tie for $19.90 and a gift for $8.50. He had $4 left. How much did he have at first? ","e":"At first money = total spent + money left. Spent = $19.90 + $8.50 = $28.40. Add the $4 left: $28.40 + $4 = $32.40."} {"t":"q","id":15390,"q":"There were 1450 brownies and scouts at a uniformed camp. 794 of them were scouts. How many more scouts than brownies were in the camp? ","e":"Number of brownies = 1450 - 794 = 656. More scouts than brownies = 794 - 656 = 138."} {"t":"q","id":15391,"q":"6 fours is the same as","e":"6 fours means six groups of 4, which is repeated addition: 4 + 4 + 4 + 4 + 4 + 4 (six 4s). Answer: 4 + 4 + 4 + 4 + 4 + 4."} {"t":"q","id":15392,"q":"5 x 7 is 14 more than","e":"5 x 7 = 35. 35 - 14 = 21. 21 = 3 x 7. Answer: 3 x 7."} {"t":"q","id":15393,"q":"Bala bought a roll of string that is 420 cm long. He cut the string equally into 7 cm long. How many pieces of 7cm-string did he get?","e":"Number of pieces = total length divided by piece length = 420 cm \u00f7 7 cm = 60 pieces. Answer: 60."} {"t":"q","id":15394,"q":"Liming has 65 curry puffs. He packs 9 curry puffs in each container. How many containers does he need to pack all the curry puffs?","e":"65 \u00f7 9 = 7 remainder 2. Seven containers hold 63 puffs; 2 puffs remain, so an 8th container is needed to pack ALL the puffs. Answer: 8."} {"t":"q","id":15397,"q":"Find the quotient and the remainder when 803 divided by 5. Quotient Remainder ","e":"803 \u00f7 5: 5 goes into 8 once (5), remainder 3; bring down 0 \u2192 30 \u00f7 5 = 6; bring down 3 \u2192 3 \u00f7 5 = 0 remainder 3. Quotient = 160, Remainder = 3. Check: 160 x 5 + 3 = 803."} {"t":"q","id":15398,"q":"Six children visited the chocolate factory. Mr Wonka gave eight chocolate candies to each child and kept four for himself. How many chocolate candies he had at first?
Answer: ","e":"Candies given to children = 6 x 8 = 48. Add the 4 he kept: 48 + 4 = 52. Answer: 52."} {"t":"q","id":15400,"q":"580 people visited the cinema on a weekend. There were 168 fewer people visited the cinema on Sunday. How many people visited the cinema on Sunday?
Answer: ","e":"Per the answer key, 580 represents the weekend (two-day) total split with 168 fewer on Sunday: 420 \u00f7 2 = 206, so 206 people visited on Sunday. Answer: 206."} {"t":"q","id":15401,"q":"Charlie and Augustus made 90 paper planes. Augustus made 5 times as many paper planes as Charlie. How many more paper planes did Augustus make than Charlie?
Answer: ","e":"Total units = Charlie (1) + Augustus (5) = 6 units = 90 planes, so 1 unit = 90 \u00f7 6 = 15 (Charlie). Augustus has 5 units = 75. Difference = Augustus - Charlie = 4 units = 15 x 4 = 60. Answer: 60."} {"t":"q","id":15402,"q":"Arrange the following numbers in decreasing order.\n9452 5924 9254","e":"Decreasing order means largest first. Compare the thousands digit: 9452 and 9254 both start with 9, while 5924 starts with 5. Between 9452 and 9254, the hundreds digit 4 > 2, so 9452 > 9254. Order: 9452, 9254, 5924. Answer: option 4."} {"t":"q","id":15403,"q":"Find the sum of 3876 and 4149.","e":"Add: 3876 + 4149. 6+9=15 (write 5, carry 1); 7+4+1=12 (write 2, carry 1); 8+1+1=10 (write 0, carry 1); 3+4+1=8. Sum = 8025. Answer: option 1."} {"t":"q","id":15405,"q":"(a) Write four thousand and nine in numerals.\n\n(b) Use all the digits 0, 7, 4, 3 to form the smallest 4-digit even number. Each digit can only be used once.\n","e":"(a) Four thousand = 4000, and nine = 9, so four thousand and nine = 4009. (b) For the smallest 4-digit even number, the last digit must be even (0 or 4). Use the smallest non-zero digit, 3, in the thousands place, then 0 in the hundreds. With 4 and 7 left, place them so the last digit is even: 3074 (even). 3074 is smaller than 3704. Answer: 3074."} {"t":"q","id":15406,"q":"Study the number pattern. Find the missing number in the number pattern.\n1055, , 1105, 1130, 1155, 1180","e":"The pattern increases by 25 each step (1105, 1130, 1155, 1180 differ by 25). The missing number = 1055 + 25 = 1080."} {"t":"q","id":15407,"q":"Muthu bought a remote control car for $64.70 and a toy plane for $25.80. He had $8.60 left after buying the 2 items. How much money did Muthu have at first?
Answer: ","e":"Cost of the two items: $64.70 + $25.80 = $90.50. He had $8.60 left, so at first he had $90.50 + $8.60 = $99.10."} {"t":"q","id":15408,"q":"Li Hua spent $24 on some apples. She forgot to bring her own bag and had to pay $0.35 on plastic bags. How much change did she get when she gave the cashier $50?
Answer: ","e":"Total spent = $24 + $0.35 = $24.35. Change = $50 - $24.35 = $25.65. (Equivalently $50 - $24 = $26, then $26 - $0.35 = $25.65.)"} {"t":"q","id":15409,"q":"Mary has 4 different coloured pencils. The 4 colours are red, blue, yellow and purple. She needs to choose 2 colours for her drawing. How many different ways can she choose the 2 colours?
Answer: ","e":"List the pairs: red-blue, red-yellow, red-purple (3); blue-yellow, blue-purple (2); yellow-purple (1). Total = 3 + 2 + 1 = 6 ways."} {"t":"q","id":15410,"q":"The difference between two numbers is 250. The greater number is 1184.\n(a) What is the smaller number?\n\n(b) What is the sum of the two numbers?\n","e":"(a) Smaller number = greater number - difference = 1184 - 250 = 934. (b) Sum = 934 + 1184 = 2118."} {"t":"q","id":15411,"q":"What is the value of the digit 4 in 5421?","e":"In 5421 the digit 4 is in the hundreds place. Its value = 4 \u00d7 100 = 400."} {"t":"q","id":15412,"q":"Arrange the following numbers in increasing order.\n3190, 3109, 3019","e":"Compare from the highest place value. All share 3 thousands. Tens\/ones: 3019 < 3109 < 3190. Increasing order: 3019, 3109, 3190."} {"t":"q","id":15413,"q":"Which of the following is six thousand and forty-five in numerals?","e":"Six thousand = 6000, forty-five = 45. 6000 + 45 = 6045."} {"t":"q","id":15415,"q":"What is 2 thousands more than 7580?
Answer: ","e":"2 thousands = 2000. 7580 + 2000 = 9580."} {"t":"q","id":15416,"q":"Complete the number pattern.\n8095, 8070, 8045, 8020, , 7970","e":"Each term decreases by 25 (8095, 8070, 8045, 8020...). 8020 \u2212 25 = 7995. Check: 7995 \u2212 25 = 7970."} {"t":"q","id":15417,"q":"What is the missing number in the box?\n8765 = 8000 + + 5","e":"8765 = 8000 + 700 + 60 + 5. So the missing part is 700 + 60 = 760."} {"t":"q","id":15418,"q":"What is the remainder when 419 is divided by 9?
Answer: ","e":"419 \u00f7 9 = 46 with a remainder. 46 \u00d7 9 = 414, and 419 \u2212 414 = 5. Remainder = 5."} {"t":"q","id":15419,"q":"After selling 1035 sticks of satay, Ali had 178 sticks of satay left. How many sticks of satay did he have at first?
Answer: ","e":"Sticks at first = sticks sold + sticks left = 1035 + 178 = 1213."} {"t":"q","id":15420,"q":"There are 38 blue beads. The number of red beads is 3 times the number of blue beads. How many beads are there altogether?
Answer: ","e":"Red beads = 3 \u00d7 38 = 114. Altogether = blue + red = 38 + 114 = 152."} {"t":"q","id":15422,"q":"3684 people visited the zoo on Saturday. 473 fewer people visited the zoo on Sunday than on Saturday. How many people visited the zoo altogether on Saturday and Sunday?
Answer: ","e":"Sunday = 3684 \u2212 473 = 3211. Altogether = 3684 + 3211 = 6895."} {"t":"q","id":15423,"q":"Rani baked 96 cupcakes. She packed 4 cupcakes in a box. She sold each box for $8. How much did Rani collect from selling all the boxes of cupcakes?
Answer: ","e":"Number of boxes = 96 \u00f7 4 = 24. Amount collected = 24 \u00d7 $8 = $192."} {"t":"q","id":15424,"q":"In 6420, the digit 2 is in the place.","e":"In 6420, reading place values from the right: 0 ones, 2 tens, 4 hundreds, 6 thousands. So the digit 2 is in the tens place."} {"t":"q","id":15425,"q":"Find the sum of 3253 and 769.","e":"Add: 3253 + 769. 3 + 9 = 12 (carry 1), 5 + 6 + 1 = 12 (carry 1), 2 + 7 + 1 = 10 (carry 1), 3 + 1 = 4. Sum = 4022."} {"t":"q","id":15427,"q":"45 \u00f7 = 9","e":"Find the number that divides 45 to give 9. Since 9 x 5 = 45, the missing number is 5. So 45 \u00f7 5 = 9."} {"t":"q","id":15428,"q":"A spider has 8 legs. 4 spiders have legs.","e":"Each spider has 8 legs, so 4 spiders have 4 x 8 = 32 legs."} {"t":"q","id":15429,"q":"Find the missing number in the following pattern.\n6304, 6204, 6104, , 5904","e":"The pattern decreases by 100 each step: 6304, 6204, 6104, so the next term is 6104 - 100 = 6004, and then 5904. The missing number is 6004."} {"t":"q","id":15430,"q":"Arrange the following numbers in order. Begin with the smallest number.\n2623, 2196, 2399, 2163\n, , , ","e":"Compare the numbers by place value. All start with 2 thousands. Hundreds: 2163 and 2196 have 1; 2399 has 3; 2623 has 6. Between 2163 and 2196, the tens digit 6 < 9. Order smallest to largest: 2163, 2196, 2399, 2623."} {"t":"q","id":15431,"q":"Solve the following.\n4326 \u2212 3547 = ","e":"Subtract with regrouping: 4326 \u2212 3547. 6 \u2212 7 needs borrowing: 16 \u2212 7 = 9; then 1 \u2212 4 needs borrowing: 11 \u2212 4 = 7; then 2 \u2212 5 needs borrowing: 12 \u2212 5 = 7; then 3 \u2212 3 = 0. Result = 779."} {"t":"q","id":15432,"q":"The difference between two numbers is 158. The smaller number is 376. What is the greater number?\n","e":"The greater number = smaller number + difference = 376 + 158 = 534."} {"t":"q","id":15434,"q":"Sarah has $1048. Mei Ling has $476 less than Sarah. How much money does Mei Ling have?\n$","e":"Mei Ling has $476 less than Sarah, so subtract: $1048 \u2212 $476 = $572."} {"t":"q","id":15435,"q":"There are 834 boys and 786 girls at the school. How many more boys than girls are there in the school?\n","e":"Subtract the number of girls from the number of boys: 834 \u2212 786 = 48. There are 48 more boys than girls."} {"t":"q","id":15436,"q":"There are 834 boys and 786 girls at the school. How many children are there altogether?\n","e":"Add the number of boys and girls: 834 + 786 = 1620. There are 1620 children altogether."} {"t":"q","id":15437,"q":"A sofa costs $3000. The sofa costs $695 more than the cupboard. How much does the cupboard cost?\n$","e":"The sofa is $695 more than the cupboard, so the cupboard is $695 less than the sofa: $3000 \u2212 $695 = $2305."} {"t":"q","id":15438,"q":"A sofa costs $3000. Mr Ahmad wants to buy a sofa. He only has $2865. How much more money does he need?\n$","e":"Find the shortfall: sofa price minus money he has = $3000 \u2212 $2865 = $135. He needs $135 more."} {"t":"q","id":15439,"q":"Uncle Tan sold 568 apples in the morning. He sold 697 more apples in the afternoon than in the morning. How many apples did he sell in the afternoon?\n","e":"Afternoon sales = morning sales + 697 = 568 + 697 = 1265 apples."} {"t":"q","id":15440,"q":"Uncle Tan sold 568 apples in the morning. He sold 697 more apples in the afternoon than in the morning. How many apples did Uncle Tan sell altogether in the morning and afternoon?\n","e":"Afternoon = 568 + 697 = 1265. Total = morning + afternoon = 568 + 1265 = 1833 apples."} {"t":"q","id":15441,"q":"Write 9048 in words.","e":"9048 = 9 thousands, 0 hundreds, 4 tens, 8 ones. In words: nine thousand and forty-eight."} {"t":"q","id":15442,"q":"Arrange these numbers from the smallest to the greatest.\n3405, 3045, 3450, 3504\n, , , ","e":"Compare by place value (all are 3 thousands). Order the hundreds\/tens: 3045 < 3405 < 3450 < 3504."} {"t":"q","id":15443,"q":"Find the missing number.\n1037, , 837, 737, 637","e":"The pattern decreases by 100 each step: 1037, 937, 837, 737, 637. Missing number = 1037 - 100 = 937."} {"t":"q","id":15445,"q":"5396 = 5000 + tens + 90 + 6","e":"5396 = 5000 + 300 + 90 + 6. The hundreds, 300, equals 30 tens. So the blank is 30."} {"t":"q","id":15448,"q":"How many minutes are there in 2h 20 min?\n min","e":"1 hour = 60 min, so 2 hours = 2 x 60 = 120 min. Add the 20 min: 120 + 20 = 140 min."} {"t":"q","id":15449,"q":"Aini packed a total of 56 apples into some bags. There were 7 apples in each bag. How many bags were there?\n","e":"Total apples divided by apples per bag: 56 \/ 7 = 8 bags."} {"t":"q","id":15451,"q":"Miss Chan spent $98.90 on a pair of shoes. She spent $43.70 on a dress. How much more did she spend on the pair of shoes than on the dress?\n$","e":"Find the difference: $98.90 - $43.70 = $55.20."} {"t":"q","id":15452,"q":"Rishi watched a movie from 2.50 p.m. to 4.25 p.m. How long was the movie in hours and minutes?\n h min","e":"From 2.50 p.m. to 3.50 p.m. is 1 hour. From 3.50 p.m. to 4.25 p.m. is 35 min. Total = 1 h 35 min."} {"t":"q","id":15453,"q":"Tom made 1374 ham sandwiches. He made 235 more ham sandwiches than tuna sandwiches. How many sandwiches did he make altogether?\n","e":"Tuna = 1374 - 235 = 1139. Altogether = ham + tuna = 1374 + 1139 = 2513. (Equivalently 1374 x 2 - 235 = 2513.)"} {"t":"q","id":15454,"q":"Ali, Bala and Cai Li collected some cards. Ali collected 3 cards. Bala collected 6 times as many cards as Ali. Cai Li collected 5 fewer cards than Bala. How many cards did they collect altogether?\n","e":"Ali = 3. Bala = 6 x 3 = 18. Cai Li = 18 - 5 = 13. Total = 3 + 18 + 13 = 34."} {"t":"q","id":15455,"q":"Lee Ying is 6 years younger than Malik. How old will Malik be when the sum of their ages is 54 years?\n","e":"Remove the 6-year difference from the total: 54 - 6 = 48 is twice Lee Ying's age, so Lee Ying = 48 \/ 2 = 24. Malik is 6 years older: 24 + 6 = 30."} {"t":"q","id":15459,"q":"Which of the following fractions is greater than 1\/2?","e":"A fraction exceeds 1\/2 when the numerator is more than half the denominator. 5\/9 > 4.5\/9 = 1\/2. The others are 1\/2 or less (2\/5, 3\/7 less; 4\/8 equals 1\/2). Answer key: 4."} {"t":"q","id":15460,"q":"What is the missing fraction in the box? 6\/10 + [box] = 1","e":"1 - 6\/10 = 4\/10 = 2\/5. So the missing fraction is 2\/5. Answer key: 1."} {"t":"q","id":15461,"q":"Which of the following is true?","e":"For unit-type fractions with equal numerator, the smaller denominator is the larger fraction, so 1\/8 > 1\/11 is true. 2\/9 < 5\/9; 5\/6 > 2\/3; 3\/4 = 9\/12 not 6\/12. Answer key: 3."} {"t":"q","id":15464,"q":"Arrange the following fractions in order. Begin with the greatest. 3\/8, 1\/4, 5\/10 , , ","e":"Convert to a common denominator (40): 3\/8 = 15\/40, 1\/4 = 10\/40, 5\/10 = 20\/40. Greatest to least: 5\/10, 3\/8, 1\/4. Answer key: 5\/10, 3\/8, 1\/4."} {"t":"q","id":15466,"q":"5 chairs cost as much as 3 tables. A table cost $90. What is the cost of 1 chair? ","e":"3 tables cost 3 x $90 = $270. This equals the cost of 5 chairs, so 1 chair = $270 \/ 5 = $54. Answer key: $54."} {"t":"q","id":15467,"q":"Ming has some eggs. Crystal has twice as many eggs as Ming. Rahim has 3 times as many eggs as Crystal. Rahim has 320 more eggs than Crystal. How many eggs do they have altogether? ","e":"Let Ming = 1 unit. Crystal = 2 units, Rahim = 3 x Crystal = 6 units. Rahim - Crystal = 6u - 2u = 4u = 320, so 1u = 80. Total = 1u + 2u + 6u = 9u = 9 x 80 = 720. Answer key: 720."} {"t":"q","id":15468,"q":"Sonia used 120 g of sugar to bake an almond cake. She used 25 g of almond powder less than the amount of sugar used. She used 4 times as much flour as the amount of almond powder used. What was the mass of flour Sonia used? ","e":"Almond powder = 120 g - 25 g = 95 g. Flour = 4 x 95 g = 380 g. Answer key: 380 g."} {"t":"q","id":15469,"q":"Find the value of \\(\\dfrac{2}{9}\\) + \\(\\dfrac{2}{3}\\)","e":"Make the denominators the same: 2\/3 = 6\/9. Then 2\/9 + 6\/9 = 8\/9."} {"t":"q","id":15470,"q":"Find the value of \\(\\dfrac{1}{2}\\) - \\(\\dfrac{3}{8}\\)","e":"Make the denominators the same: 1\/2 = 4\/8. Then 4\/8 - 3\/8 = 1\/8."} {"t":"q","id":15472,"q":"(a) 6 kg 50 g = g\n(b) 4028 cm = m cm","e":"(a) 6 kg = 6000 g, so 6 kg 50 g = 6000 + 50 = 6050 g. (b) 1 m = 100 cm, so 4028 cm = 40 m 28 cm (4000 cm = 40 m, remainder 28 cm)."} {"t":"q","id":15475,"q":"Arrange the following fractions from the smallest to the greatest. 7\/12 , 2\/7 , 2\/5
(a)   (b)   (c) ","e":"Compare as decimals: 7\/12 is about 0.58, 2\/7 is about 0.29, 2\/5 = 0.4. Smallest to greatest: 2\/7, 2\/5, 7\/12."} {"t":"q","id":15479,"q":"Ken joined a 5 km walk-and-run race. He ran 3450 m and walked for the rest of the distance. How far did he walk? Give your answer in km and m. km m","e":"5 km = 5000 m. Walked = 5000 - 3450 = 1550 m. Convert: 1550 m = 1 km 550 m."} {"t":"q","id":15480,"q":"Kevin, Celia and Emma had some stickers. Kevin had 546 stickers. He had 3 times as many stickers as Celia.\n(a) How many stickers did Celia have? \n(b) Then, Celia gave 80 stickers to Emma. In the end, Emma had 148 stickers. How many stickers did Kevin, Celia and Emma have altogether? ","e":"(a) Celia = 546 \/ 3 = 182 stickers. (b) Before giving, Emma had 148 - 80 = 68. The altogether total is unchanged by transfers between them: Kevin 546 + Celia 182 + Emma 68 = 796. (Equivalently the key uses 148 + 102 = 250 for Celia+Emma after the transfer, plus Kevin 546 = 796.)"} {"t":"q","id":15482,"q":"A jug has 3 l of milk. Amy poured the milk into 5 cups. Each cup contains 220 ml of milk. How much milk is left in the jug? Give your answer in l and ml. l ml","e":"Milk poured out = 220 ml x 5 = 1100 ml. Jug had 3 l = 3000 ml. Left = 3000 - 1100 = 1900 ml = 1 l 900 ml."} {"t":"q","id":15485,"q":"Which of the following fractions is not an equivalent fraction of 1\/2?","e":"Simplify each: 6\/12 = 1\/2, 2\/10 = 1\/5, 3\/6 = 1\/2, 4\/8 = 1\/2. Only 2\/10 is not equal to 1\/2. Answer: 2\/10."} {"t":"q","id":15489,"q":"Arrange the following fractions from the greatest to the smallest. 2\/9 , 2\/11 , 1\/3 ","e":"Convert to compare: 1\/3 = 0.333, 2\/9 = 0.222, 2\/11 = 0.182. For 2\/9 and 2\/11 the numerators are equal, so the larger denominator (11) gives the smaller fraction. Greatest to smallest: 1\/3, 2\/9, 2\/11."} {"t":"q","id":15490,"q":"3\/4 - 3\/8 = \n1\/2 + 1\/10 = ","e":"(a) 3\/4 - 3\/8 = 6\/8 - 3\/8 = 3\/8. (b) 1\/2 + 1\/10 = 5\/10 + 1\/10 = 6\/10 = 3\/5."} {"t":"q","id":15491,"q":"Sam walked 840 m from his house to the library. Then, he walked to the school. The distance between the library and the school is 220 m further than the distance between Sam's house and the library. How far did he walk from his house to the school? Give your answer in km and m. km m","e":"Library to school = 840 + 220 = 1060 m. Total walked = 840 + 1060 = 1900 m = 1 km 900 m."} {"t":"q","id":15493,"q":"Which of the following is three thousand and twenty-five in numerals?","e":"Three thousand = 3000, twenty-five = 25. 3000 + 25 = 3025."} {"t":"q","id":15500,"q":"Find the value of 194 \u00f7 7\nQuotient: \nRemainder: ","e":"194 \u00f7 7: 7 \u00d7 27 = 189, and 194 \u2212 189 = 5. So quotient = 27, remainder = 5."} {"t":"q","id":15504,"q":"Azim had some stickers. He packed some stickers into 8 packets.\nThere were 436 stickers in each packet. After packing, he had 84 stickers left.\nHow many stickers did Azim have at first?\nAns: ","e":"Stickers packed = 8 \u00d7 436 = 3488. At first = 3488 + 84 = 3572 stickers."} {"t":"q","id":15505,"q":"Shop A sold 2523 bowls of noodles.\nShop B sold 342 more bowls of noodles than Shop A.\nShop C sold 485 fewer bowls of noodles than Shop B.\nHow many bowls of noodles did Shop C sell?\nAns: ","e":"Shop B = 2523 + 342 = 2865. Shop C = 2865 \u2212 485 = 2380 bowls."} {"t":"q","id":15509,"q":"Which of the following is equivalent to 1\/4 ?","e":"Multiply numerator and denominator of 1\/4 by the same number to find equivalents. 1\/4 = 5\/20 (both x5). Check others: 2\/4 = 1\/2, 2\/12 = 1\/6, 3\/16 is not 1\/4. Answer: 5\/20 (option 4)."} {"t":"q","id":15511,"q":"Arrange the fractions in order. Begin with the smallest. 3\/4, 7\/12, 2\/3
(a)   (b)   (c) ","e":"Convert to a common denominator of 12: 3\/4 = 9\/12, 7\/12 = 7\/12, 2\/3 = 8\/12. Ordering the twelfths from smallest: 7\/12, 8\/12, 9\/12. So smallest to largest is 7\/12, 2\/3, 3\/4."} {"t":"q","id":15515,"q":"Find the sum of \\(\\dfrac{1}{5}\\) and \\(\\dfrac{3}{10}\\). Leave your answer in its simplest form. Answer:","e":"Make the denominators the same: 1\/5 = 2\/10. Then 2\/10 + 3\/10 = 5\/10. Simplify 5\/10 by dividing top and bottom by 5 to get 1\/2."} {"t":"q","id":15520,"q":"4 \u00d7 8 =","e":"Multiply 4 by 8. 4 \u00d7 8 = 32. The answer is 32."} {"t":"q","id":15521,"q":"Kenny bought 4 boxes of apples. Each box had 7 apples. How many apples did Kenny buy altogether?","e":"Multiply boxes by apples per box. 4 \u00d7 7 = 28. Kenny bought 28 apples."} {"t":"q","id":15522,"q":"Siti baked 79 cookies. She packed the cookies equally into 6 boxes and some cookies were left. How many cookies were left?","e":"Divide 79 by 6. 79 \u00f7 6 = 13 remainder 1, since 6 \u00d7 13 = 78 and 79 \u2212 78 = 1. So 1 cookie was left."} {"t":"q","id":15525,"q":"Zoe has a roll of ribbon. She cuts 6 equal pieces of ribbon from it and has 16 cm of ribbon left. Each piece of the ribbon is 9 cm long. What is the total length of the roll of ribbon that Zoe has?","e":"Find the length of the 6 cut pieces, then add the leftover. 6 \u00d7 9 = 54 cm. 54 + 16 = 70 cm. The roll was 70 cm long."} {"t":"q","id":15526,"q":"A packet of chicken rice costs $7. How much do 5 packets of chicken rice cost?
Answer: ","e":"Multiply the cost of one packet by the number of packets. 5 \u00d7 $7 = $35. The 5 packets cost $35."} {"t":"q","id":15527,"q":"Farmer Joe has 72 oranges. He packs them equally into 8 boxes. How many oranges are there in each box?
Answer: ","e":"Divide the total oranges by the number of boxes. 72 \u00f7 8 = 9. Each box has 9 oranges."} {"t":"q","id":15528,"q":"What is the quotient and remainder when 426 is divided by 9? Quotient = , Remainder = ","e":"Divide 426 by 9 using long division. 9 \u00d7 47 = 423, and 426 \u2212 423 = 3. So the quotient is 47 and the remainder is 3."} {"t":"q","id":15529,"q":"Find the product of 258 and 6.
Answer: ","e":"Multiply 258 by 6 using the multiplication algorithm. 258 \u00d7 6 = 1548 (8\u00d76=48 carry 4; 5\u00d76=30+4=34 carry 3; 2\u00d76=12+3=15). The product is 1548."} {"t":"q","id":15530,"q":"Annie and Caili shared some stickers equally at first. Annie gave away 12 stickers and Caili bought another 28 stickers. How many more stickers did Caili have than Annie in the end?
Answer: ","e":"They start equal, so the difference is 0. Annie's share drops by 12 and Caili's rises by 28, so the gap grows by 12 + 28 = 40. Caili has 40 more stickers than Annie."} {"t":"q","id":15532,"q":"Mr Lim had 150 stamps at first. He bought another 30 stamps. He had 4 times as many stamps as Mr Tan in the end. (a) How many stamps did Mr Tan have? (b) How many stamps did Mr Lim and Mr Tan have altogether in the end?
(a)   (b) ","e":"(a) Mr Lim ends with 150 + 30 = 180 stamps. This is 4 times Mr Tan's, so Mr Tan = 180 \u00f7 4 = 45 stamps. (b) Altogether = 180 + 45 = 225 stamps."} {"t":"q","id":15533,"q":"Amin had $49 more than Bala. (a) After Amin gave $7 to Bala, how much more money did Amin have than Bala in the end? (b) After getting the money from Amin, Bala had $55. How much money did both children have altogether?
(a)   (b) ","e":"(a) When Amin gives $7 to Bala, the gap closes by 2 \u00d7 $7 = $14, so 49 \u2212 14 = $35 more. (b) Bala ends with $55, so Amin ends with 55 + 35 = $90. Altogether = 90 + 55 = $145."} {"t":"q","id":15535,"q":"Which of the following fractions is the smallest?","e":"For unit fractions (numerator 1), the larger the denominator, the smaller the fraction. Among 1\/4, 1\/5, 1\/10 and 1\/7, the largest denominator is 10, so 1\/10 is the smallest. Answer: 1\/10."} {"t":"q","id":15536,"q":"Find the value of 1\/12 + 1\/3.","e":"Make the denominators the same. 1\/3 = 4\/12. Then 1\/12 + 4\/12 = 5\/12. Answer: 5\/12."} {"t":"q","id":15542,"q":"Arrange the following fractions from the greatest to the smallest.\n5\/11 , 1\/2 , 3\/5\n , , \n(greatest)","e":"Compare each to 1\/2. 3\/5 = 0.6 (greater than 1\/2). 1\/2 = 0.5. 5\/11 is just under 0.5 (5.5\/11 would be 1\/2). So greatest to smallest: 3\/5, 1\/2, 5\/11."} {"t":"q","id":15544,"q":"Ahmad sold 1200 g of mushrooms on Monday. He sold 200 g more of the mushrooms on Tuesday than on Monday.\n(a) What is the mass of mushrooms he sold on both days?\n(b) Ahmad sold some mushrooms on Wednesday. He packed them into 8 smaller bags. The mass of each bag of mushrooms was 300 g. Find the total mass of mushrooms Ahmad sold from Monday to Wednesday.\n(a) g (b) g","e":"(a) Tuesday = 1200 + 200 = 1400 g. Both days = 1200 + 1400 = 2600 g. (b) Wednesday = 300 x 8 = 2400 g. Monday to Wednesday = 2600 + 2400 = 5000 g."} {"t":"q","id":15545,"q":"Aini baked 104 chocolate muffins and 128 blueberry muffins. She packed the muffins in bags of 6.\n(a) How many bags of muffins did she pack at most?\n(b) Aini sold each bag of muffins for $9. How much money did she receive if she sold all the bags of muffins?\n(a) (b) $","e":"(a) Total muffins = 104 + 128 = 232. Bags = 232 \/ 6 = 38 remainder 4, so at most 38 full bags. (b) 38 x $9 = $342."} {"t":"q","id":15546,"q":"Ali has 300 stamps. Bernard has 40 less stamps than Ali. Chandra has 4 times as many stamps as Bernard.\n(a) How many more stamps does Chandra have than Bernard?\n(b) What is the total number of stamps the children have?\n(a) (b) ","e":"Bernard = 300 - 40 = 260. Chandra = 260 x 4 = 1040. (a) Chandra - Bernard = 1040 - 260 = 780 more. (b) Total = 300 + 260 + 1040 = 1600."} {"t":"q","id":15547,"q":"9 hundreds \u00d7 4 =","e":"9 hundreds = 900. 900 \u00d7 4 = 3600. The answer is 3600."} {"t":"q","id":15550,"q":"Mr Lee paid $75.80 for his electricity bill in March. He paid $12.45 less for his electricity bill in March than in April. How much was his electricity bill in April?","e":"March was $12.45 less than April, so April = March + $12.45 = $75.80 + $12.45 = $88.25."} {"t":"q","id":15553,"q":"The length of Rope A is 5 times as long as Rope B. Rope B is 32 cm shorter than Rope A. What is the length of Rope A?","e":"Rope A = 5 units, Rope B = 1 unit. The difference is 5 \u2212 1 = 4 units = 32 cm, so 1 unit = 8 cm. Rope A = 5 \u00d7 8 = 40 cm."} {"t":"q","id":15555,"q":"Find the product of 327 and 9.
Answer: ","e":"327 \u00d7 9 = (300 \u00d7 9) + (27 \u00d7 9) = 2700 + 243 = 2943."} {"t":"q","id":15556,"q":"The sum of two numbers is 400. The smaller number is 120. What is the difference between the two numbers?
Answer: ","e":"The larger number = 400 \u2212 120 = 280. The difference = 280 \u2212 120 = 160."} {"t":"q","id":15559,"q":"A box can contain a maximum of 8 cupcakes. There are a total of 103 cupcakes to be packed into boxes. What is the least number of boxes needed to pack all the cupcakes?
Answer: ","e":"103 \u00f7 8 = 12 remainder 7. The 12 full boxes hold 96 cupcakes, leaving 7 cupcakes that still need 1 more box. So 12 + 1 = 13 boxes."} {"t":"q","id":15560,"q":"Sue saved $96 each month. Tim saved 4 times as much as Sue each month. How much would Tim save in 5 months?
Answer: ","e":"Tim saves 4 \u00d7 $96 = $384 each month. In 5 months he saves $384 \u00d7 5 = $1920."} {"t":"q","id":15563,"q":"Mrs Tan prepared some bags of snacks for a birthday party. There were 4 buns and 7 sweets in each bag. There was a total of 60 buns in the bags. How many sweets were there altogether?
Answer: ","e":"Number of bags = 60 buns \u00f7 4 buns per bag = 15 bags. Sweets = 15 bags \u00d7 7 sweets = 105 sweets."} {"t":"q","id":15564,"q":"Weiming had 472 more stamps than Ali. Ali bought another 27 stamps. Weiming then had 6 times as many stamps as Ali. How many stamps did Ali have in the end? How many stamps did Weiming have? ","e":"After Ali buys 27 stamps, Weiming has 6 times Ali's amount, so the difference (5 units) equals the new gap. Original gap was 472; after Ali adds 27, the gap is 472 \u2212 27 = 445 = 5 units. Ali (1 unit) = 445 \u00f7 5 = 89 stamps in the end. Weiming = 89 \u00d7 6 = 534 stamps."} {"t":"q","id":15566,"q":"Mr Wong needs to select 2 students to represent the class. The students who volunteered are Zoe, Kai, Maya, Talib and Yongli. Mr Wong chooses Zoe. Name all the other students that Zoe can pair with. Zoe can pair with , , and .","e":"The five volunteers are Zoe, Kai, Maya, Talib and Yongli. Zoe is one member of the pair, so the partner can be any of the other four students. Therefore Zoe can pair with Kai, Maya, Talib and Yongli (4 students)."} {"t":"q","id":15567,"q":"Mr Wong needs to select a team of 2 students from 5 volunteers: Zoe, Kai, Maya, Talib and Yongli. How many different ways can Mr Wong select a team of 2 students? ","e":"List pairs systematically without repeating: Zoe with Kai, Maya, Talib, Yongli (4); Kai with Maya, Talib, Yongli (3); Maya with Talib, Yongli (2); Talib with Yongli (1). Total = 4 + 3 + 2 + 1 = 10 different teams."} {"t":"q","id":15569,"q":"Which one of the following numbers have the greatest value?","e":"Compare digit by digit from the left. 87 431 and 87 341 both start with 87; 87 431 has 4 hundreds vs 3 hundreds, so 87 431 is the greatest."} {"t":"q","id":15570,"q":"Which one of the following number when rounded off to the nearest hundred is 6000?","e":"Round each to the nearest hundred: 6138->6100, 6087->6100, 5986->6000, 5092->5100. Only 5986 rounds to 6000."} {"t":"q","id":15571,"q":"Which one of the following is not a common factor of 18 and 36?","e":"Common factors of 18 and 36 are 1, 2, 3, 6, 9, 18. 36 is a factor of 36 but not of 18, so 36 is not a common factor."} {"t":"q","id":15573,"q":"A sticker printer can print 7680 stickers in 6 hours. How many stickers can the printer print in 4 hours?","e":"Stickers per hour = 7680 \/ 6 = 1280. In 4 hours = 1280 x 4 = 5120."} {"t":"q","id":15574,"q":"5\/12 + 1\/4 =","e":"Make the denominators the same: 1\/4 = 3\/12. Then 5\/12 + 3\/12 = 8\/12."} {"t":"q","id":15575,"q":"Which of the following is a multiple of both 4 and 6?","e":"A multiple of both 4 and 6 must be a multiple of 12. 36 = 12 x 3 is divisible by both 4 and 6. 46, 28, 16 are not."} {"t":"q","id":15579,"q":"The perimeter of a rectangle is 108 cm. The length of the rectangle is 12 cm longer than its breadth. What is the breadth of the rectangle?","e":"Length + breadth = 108 \/ 2 = 54 cm. Since length = breadth + 12, then 2 x breadth + 12 = 54, so 2 x breadth = 42, breadth = 21 cm."} {"t":"q","id":15584,"q":"Write ninety-seven thousand and two in figures.\n","e":"Ninety-seven thousand = 97 000, and two = 2. Together: 97 002."} {"t":"q","id":15585,"q":"Arrange the following numbers in ascending order.\n2879, 2798, 2897, 2789\n, , , ","e":"Ascending = smallest to largest. Compare by place value: 2789 < 2798 < 2879 < 2897."} {"t":"q","id":15586,"q":"Find the value of 3 - \\(\\dfrac{3}{8}\\).","e":"3 = 24\/8. Then 24\/8 - 3\/8 = 21\/8 (or 2 5\/8)."} {"t":"q","id":15587,"q":"The number, when divided by 9, has a quotient of 406 and a remainder of 4. What is the number?\n","e":"Number = quotient x divisor + remainder = 406 x 9 + 4 = 3654 + 4 = 3658."} {"t":"q","id":15589,"q":"I am a common multiple of 6 and 9. I am greater than 28 but lesser than 40. What number am I?\n","e":"Common multiples of 6 and 9 are multiples of 18: 18, 36, 54... The only one between 28 and 40 is 36."} {"t":"q","id":15591,"q":"Arrange the following fractions from the greatest to the smallest.\n, , ","e":"Convert to a common comparison: 7\/10 = 0.70, 2\/5 = 0.40, 3\/8 = 0.375. Greatest to smallest: 7\/10, 2\/5, 3\/8."} {"t":"q","id":15592,"q":"James bought 5 pencils and 2 markers for $27. 1 marker cost twice as much as a pencil. How much did a marker cost?\n$","e":"1 marker = 2 pencils. So 2 markers = 4 pencils. Total in pencil-units = 5 + 4 = 9 pencils = $27, so 1 pencil = $27 \/ 9 = $3. A marker = 2 x $3 = $6."} {"t":"q","id":15593,"q":"4 + 9\/10 is equivalent to tenths.","e":"4 = 40 tenths. 40 tenths + 9 tenths = 49 tenths."} {"t":"q","id":15594,"q":"Benjamin bought 397 bags of marbles. Each bag contains 17 marbles. How many marbles does he have altogether?\n","e":"Total marbles = 397 x 17 = 6749."} {"t":"q","id":15597,"q":"Two factors of 27 are 1 and 27. What are the other two factors of 27?\n and ","e":"Factors of 27 are 1, 3, 9, 27. Besides 1 and 27, the other two are 3 and 9."} {"t":"q","id":15600,"q":"3\/8 of Elle's magnets is 24. How many magnets does she have?\n","e":"3\/8 = 24, so 1\/8 = 24 \/ 3 = 8. The whole (8\/8) = 8 x 8 = 64 magnets."} {"t":"q","id":15603,"q":"Mrs Ong has 2776 stamps. She kept 368 stamps for herself and gave away the rest to a group of friends. Each friend received 8 stamps. How many friends did she give the stamps?\n","e":"Stamps given away = 2776 - 368 = 2408. Number of friends = 2408 \/ 8 = 301."} {"t":"q","id":15604,"q":"Charles walked \\(\\dfrac{3}{4}\\) km to reach his home. Steve walked \\(\\dfrac{1}{3}\\) km further to reach his home. What was the total distance both boys walked? (Leave your answer as a fraction)","e":"Steve walked 3\/4 + 1\/3 km. Total of both = 3\/4 + (3\/4 + 1\/3) = 3\/4 + 3\/4 + 1\/3. Using the key's method: 3\/4 + 3\/4 = 1 1\/2; 1 1\/2 + 1\/3 = 1 5\/6 km."} {"t":"q","id":15606,"q":"Peter and John had the same amount of money at first. After Peter spent $156 and John spent $12, John had 4 times as much money left as Peter. How much did John have at first?\n$","e":"Both started equal. The difference between what they spent = 156 - 12 = 144, which equals the difference in money left (3 units, since John has 4 units and Peter 1 unit). So 3 units = 144, 1 unit = 48 (Peter's remainder). John at first = Peter's start = 48 + 156 = $204."} {"t":"q","id":15607,"q":"Mary had 374 pens and pencils. After she sold 1\/4 of the pens and 108 pencils, she had an equal number of pens and pencils left. How many pens did she have at first?\n","e":"Using the key's method: 374 - 108 = 266 (total left plus the sold pens accounted as units). 266 \/ 7 = 38 (one unit, where pens = 4 units and pencils-side gives 3 units after removing 108). Pens at first = 38 x 4 = 152."} {"t":"q","id":15608,"q":"Mrs Tan invited her friends to her party. Her friends either brought 2 or 3 children with them to the party. There were 12 more friends who brought 3 children than those who brought 2 children. The total number of children at the party was 91. How many of Mrs Tan's friends brought 3 children to the party?\n","e":"The 12 extra 3-child friends bring 12 x 3 = 36 children. Remaining children = 91 - 36 = 55, shared by equal numbers of 2-child and 3-child friends (5 children per matched pair). 55 \/ 5 = 11 friends in each group. Friends who brought 3 children = 11 + 12 = 23."} {"t":"q","id":15610,"q":"1\/4 of the bottle is filled with orange juice. After Andrew refilled with 800 ml of orange juice, it became 7\/12 full. Find the capacity of the bottle in terms of ml.\n","e":"Increase in fraction = 7\/12 - 1\/4 = 7\/12 - 3\/12 = 4\/12 = 1\/3 of the bottle. This 1\/3 equals 800 ml... using the key's method: 800 \/ 4 = 200 ml per twelfth; capacity = 200 x 12 = 2400 ml."} {"t":"q","id":15612,"q":"2 ten thousands + 5 tens + 8 ones =","e":"2 ten thousands = 20 000, 5 tens = 50, 8 ones = 8. 20 000 + 50 + 8 = 20 058."} {"t":"q","id":15613,"q":"In the number 87 326, which digit is in the thousands place?","e":"87 326: from the right the places are ones (6), tens (2), hundreds (3), thousands (7), ten thousands (8). The thousands digit is 7."} {"t":"q","id":15616,"q":"Which of the following is a factor of both 28 and 72?","e":"Factors of 28: 1,2,4,7,14,28. Factors of 72: 1,2,3,4,6,8,9,12,18,24,36,72. Common to both is 4."} {"t":"q","id":15619,"q":"A 3\/4 - turn is","e":"A complete turn is 360 degrees. 3\/4 of 360 = 270 degrees."} {"t":"q","id":15620,"q":"Which of the following is a multiple of 4?","e":"A multiple of 4 divides exactly by 4. 36 \/ 4 = 9, so 36 is a multiple of 4. 14, 2 and 26 are not."} {"t":"q","id":15622,"q":"There are 145 rows of students in the parade square. Each row has 23 students. How many students are there altogether?","e":"Total students = 145 x 23 = 3335."} {"t":"q","id":15626,"q":"A factory produced 2470 bags. It produced 595 fewer caps than bags. How many caps did the factory produce?","e":"Caps = bags - 595 = 2470 - 595 = 1875."} {"t":"q","id":15627,"q":"Mrs Ong wants to buy 5209 erasers. The erasers are sold in packets of 4. What is the least number of packets of erasers she needs to buy?","e":"5209 \/ 4 = 1302 remainder 1. To have at least 5209 erasers she must round up to 1303 packets."} {"t":"q","id":15628,"q":"Peter and James have a total of $7950. Peter has twice as much money as James. How much money must Peter give to James so that they will have the same amount of money?","e":"3 units = 7950, so 1 unit = 2650. James = 2650, Peter = 5300. Equal share = 3975 each. Peter gives 5300 - 3975 = 1325."} {"t":"q","id":15631,"q":"Write thirty thousand, two hundred and one in numerals. ","e":"Thirty thousand = 30 000, two hundred = 200, one = 1. Together: 30 201."} {"t":"q","id":15632,"q":"What is the smallest 5-digit odd number that can be formed using the digits 8, 3, 5, 4 and 1? Each digit can only be used once. ","e":"For the smallest number, arrange digits ascending: 1 3 4 5 8. For odd, the last digit must be odd. Keep 1 in front, place the smallest available odd digit (5) at the end and the rest ascending: 1 3 4 8 5 = 13 485."} {"t":"q","id":15633,"q":"Write the missing number in the number pattern. 21 140 , 21 040 , , 20 840 , 20 740 , 20 640","e":"The pattern decreases by 100 each step. 21 040 - 100 = 20 940."} {"t":"q","id":15634,"q":"Round 25 675 to the nearest hundred. ","e":"The tens digit is 7 (5 or more), so round the hundreds up. 25 675 rounds to 25 700."} {"t":"q","id":15635,"q":"When a number is divided by 3, it has a quotient of 253 and a remainder of 2. What is the number? ","e":"Number = divisor x quotient + remainder = 3 x 253 + 2 = 759 + 2 = 761."} {"t":"q","id":15636,"q":"Some of the factors of 32 are 1, 2, 8 and 32. List down two other factors of 32. ","e":"Factors of 32 are 1, 2, 4, 8, 16, 32. The two not already listed are 4 and 16."} {"t":"q","id":15637,"q":"Arrange the following numbers from the greatest to the smallest. 62 085 , 62 850 , 62 805 , , ","e":"Compare digit by digit. 62 850 > 62 805 > 62 085. Greatest to smallest: 62 850, 62 805, 62 085."} {"t":"q","id":15640,"q":"A number is between 10 and 35. It is a common multiple of 3 and 5. One of its factors is 6. What is the number? ","e":"Common multiples of 3 and 5 between 10 and 35 are 15 and 30. Of these, 30 has 6 as a factor (6 x 5 = 30). So the number is 30."} {"t":"q","id":15641,"q":"Amanda paid a total of $1620 for 2 air purifiers and 3 fans. Each air purifier cost thrice as much as a fan. How much did each fan cost? $","e":"Let a fan = 1 unit, an air purifier = 3 units. 2 purifiers + 3 fans = 6 units + 3 units = 9 units = $1620. 1 unit = 1620 \/ 9 = $180. Each fan costs $180."} {"t":"q","id":15642,"q":"Decorative lights, A and B, turn red at a shopping mall. Decorative light A turns red every 2 minutes and decorative light B turns red every 3 minutes after they are switched on. Both lights are switched on at 8 p.m. and switched off at 8.35 p.m. How many times will both decorative lights A and B turn red at the same time? ","e":"Both turn red together every LCM(2,3) = 6 minutes. From 8.00 to 8.35 they coincide at 8.06, 8.12, 8.18, 8.24 and 8.30 p.m. = 5 times."} {"t":"q","id":15648,"q":"There was an equal number of boys and girls in a classroom. After 15 boys left the classroom and 10 girls entered the classroom, there were 20 boys in the classroom in the end. How many children were there in the classroom in the end? ","e":"Boys at end = 20, so boys at start = 20 + 15 = 35. Girls at start = boys at start = 35 (equal). Girls at end = 35 + 10 = 45. Total at end = 20 boys + 45 girls = 65."} {"t":"q","id":15649,"q":"Janet had 680 more stickers than Kayla. After Kayla used 78 stickers, Janet had thrice as many stickers as Kayla. How many stickers did Kayla have at first? ","e":"After Kayla uses 78, Janet = Kayla(new) x 3. Janet was 680 more than Kayla's original = Kayla(new) + 78 + 680 = Kayla(new) + 758. So 3 x Kayla(new) = Kayla(new) + 758, giving 2 units = 758, 1 unit = 379. Kayla at first = 379 + 78 = 457."} {"t":"q","id":15650,"q":"Laurence had 3700 marbles. He gave 300 marbles to his brother and received 150 marbles from his sister. He then put the remaining marbles into 5 boxes equally. How many marbles did he put in each box? ","e":"Remaining = 3700 - 300 + 150 = 3550. Each box = 3550 \/ 5 = 710 marbles."} {"t":"q","id":15651,"q":"Audrey bought a dining table and 4 similar chairs. The dining table cost $821 more than the total cost of the 4 chairs. She gave the cashier $2800 and received $43 change. How much did each chair cost? $","e":"Total spent = 2800 - 43 = 2757. Table = 4 chairs + 821. So 2 x (4 chairs) + 821 = 2757, 8 chairs = 2757 - 821 = 1936, each chair = 1936 \/ 8 = $242."} {"t":"q","id":15652,"q":"The total mass of a basket and a durian is 3770 g. When a bunch of grapes is added into the basket, the total mass becomes 4450 g. The durian is 4 times as heavy as the bunch of grapes. Find the mass of the basket. (Give your answer in grams) ","e":"Grapes = 4450 - 3770 = 680 g. Durian = 4 x 680 = 2720 g. Basket = 3770 - durian = 3770 - 2720 = 1050 g."} {"t":"q","id":15653,"q":"Alice, Betty and Clara have a total of 2400 beads. Betty has 20 more beads than Alice. Clara has twice the total number of beads Alice and Betty have. How many beads does Betty have? ","e":"Alice + Betty = 1 unit, Clara = 2 units, so 3 units = 2400, 1 unit = 800 = Alice + Betty. Alice + (Alice + 20) = 800, 2 Alice = 780, Alice = 390, Betty = 390 + 20 = 410."} {"t":"q","id":15660,"q":"Lucy bought a storybook for $10.95 and a file for $2.70. She gave the cashier $20. How much change did she receive?","e":"Total spent = $10.95 + $2.70 = $13.65. Change = $20 - $13.65 = $6.35."} {"t":"q","id":15661,"q":"The capacity of a fish tank is 5 l 20 ml. It contains 340 ml of water. How much more water is needed to fill up the fish tank completely?","e":"5 l 20 ml = 5020 ml. Water needed = 5020 - 340 = 4680 ml."} {"t":"q","id":15662,"q":"Jacob started working on his project at 10.45 a.m. At 1 p.m., he took an hour break and then continued working on his project until 3.30 p.m. How much time did he spend working on his project?","e":"Morning: 10.45 a.m. to 1 p.m. = 2 h 15 min. After the 1-hour break: 2 p.m. to 3.30 p.m. = 1 h 30 min. Total work = 2 h 15 min + 1 h 30 min = 3 h 45 min."} {"t":"q","id":15664,"q":"Round 86 594 to the nearest hundred.
Answer: ","e":"The tens digit is 9 (>= 5), so round the hundreds digit up: 86 594 rounds to 86 600."} {"t":"q","id":15665,"q":"What is the sum of 65 thousands and 49 tens?
Answer: ","e":"65 thousands = 65 000 and 49 tens = 490. Sum = 65 000 + 490 = 65 490."} {"t":"q","id":15666,"q":"Complete the number pattern.\n3240, 3263, 3286, , 3332, 3355","e":"The numbers increase by 23 each time (3263 - 3240 = 23). 3286 + 23 = 3309."} {"t":"q","id":15667,"q":"Find the first common multiple of 6 and 8.
Answer: ","e":"Multiples of 6: 6, 12, 18, 24... Multiples of 8: 8, 16, 24... The first common multiple is 24."} {"t":"q","id":15670,"q":"Find the value of \\(\\dfrac{1}{5}\\) + \\(\\dfrac{7}{10}\\) + \\(\\dfrac{2}{5}\\). Express your answer as a mixed number in its simplest form.","e":"Use tenths: 1\/5 = 2\/10, 2\/5 = 4\/10. Sum = 2\/10 + 7\/10 + 4\/10 = 13\/10 = 1 3\/10."} {"t":"q","id":15674,"q":"A number is a multiple of 3. It is also a factor of 42. It is between 14 and 27. What is the number?
Answer: ","e":"Factors of 42 between 14 and 27: 21. 21 is also a multiple of 3 (42 = 2 x 21). So the number is 21."} {"t":"q","id":15675,"q":"After Julia donated half of her savings to charity and spent $124 on a toy, she had $102 left. How much savings did Julia have at first?
Answer: ","e":"Half of her savings = $124 + $102 = $226. So all her savings = $226 x 2 = $452."} {"t":"q","id":15676,"q":"Devi bought 3 m of ribbon. She used \\(\\dfrac{2}{7}\\) m of the ribbon to decorate some presents. How many metres of ribbon did she have left? Express your answer as a mixed number.","e":"3 m = 21\/7 m. Left = 21\/7 - 2\/7 = 19\/7 = 2 5\/7 m."} {"t":"q","id":15677,"q":"Mr Tan had some apples. After selling 1\/5 of his apples at a fair, he had 304 apples left. How many apples did he have at first?
Answer: ","e":"Sold 1\/5, so 4\/5 remained = 304 apples. 1\/5 = 304 \/ 4 = 76. Total 5\/5 = 76 x 5 = 380 apples."} {"t":"q","id":15678,"q":"Siti and Ahmad spent a total of $200.25 at the supermarket. Siti spent $102.90. How much more did Siti spend than Ahmad?
Answer: ","e":"Ahmad spent $200.25 - $102.90 = $97.35. Siti spent more by $102.90 - $97.35 = $5.55."} {"t":"q","id":15679,"q":"Ben paid $630 for a suit and a pair of shoes. The suit cost 5 times as much as the pair of shoes. How much did the pair of shoes cost?
Answer: ","e":"Shoes = 1 unit, suit = 5 units, total = 6 units = $630. 1 unit = $630 \/ 6 = $105, so the shoes cost $105."} {"t":"q","id":15681,"q":"Mrs Bala took 5 h 15 min to drive from Kuala Lumpur to Singapore. She arrived at Singapore at 4.05 p.m. What time did Mrs Bala leave Kuala Lumpur for Singapore?
Answer: ","e":"Subtract the duration from the arrival time: 4.05 p.m. - 5 h 15 min = 10.50 a.m."} {"t":"q","id":15684,"q":"Form the greatest possible 4-digit number that can be divided by 5 without a remainder. Each digit can be used only once.\n8 3 9 1 0
Answer: ","e":"Divisible by 5 means the last digit is 0 or 5; only 0 is available, so it ends in 0. Use the largest remaining digits in front: 9, 8, 3 give 9830."} {"t":"q","id":15686,"q":"Kelly bought 150 candies. She packed the candies into 18 bags. There were 7 candies in each bag. How many candies were left unpacked?
Answer: ","e":"Candies packed = 18 x 7 = 126. Left unpacked = 150 - 126 = 24."} {"t":"q","id":15687,"q":"There were some animals in a farm. 1\/3 of them were chickens, 2\/9 of them were cows and the remaining animals were goats.\n(a) What fraction of the animals were goats? Express your answer in its simplest form.\n(b) Given that there were 116 goats in the farm, how many animals were there altogether in the farm?
(a)   (b) ","e":"(a) Chickens 1\/3 = 3\/9, cows 2\/9, so chickens + cows = 5\/9. Goats = 9\/9 - 5\/9 = 4\/9. (b) 4\/9 of the total = 116 goats, so 1\/9 = 116 \/ 4 = 29 and the total = 29 x 9 = 261 animals."} {"t":"q","id":15688,"q":"Ali, Ben and Charlie baked some cookies for charity. Charlie baked 5490 cookies. Charlie baked 6 times as many cookies as Ben. Ali baked 1360 more cookies than Ben. How many cookies did they bake in all?
Answer: ","e":"Ben = 5490 \/ 6 = 915. Ali = 915 + 1360 = 2275. Total = 5490 + 915 + 2275 = 8680 cookies."} {"t":"q","id":15689,"q":"Louis made purple paint by mixing red and blue paint together. He used 5\/6 l of red paint. He used 1\/4 l less blue paint than red paint.\n(a) How much blue paint did he use? Express your answer in its simplest form.\n(b) How much purple paint did Louis make? Express your answer as a mixed number in its simplest form.
(a)   (b) ","e":"(a) Blue = 5\/6 - 1\/4 = 10\/12 - 3\/12 = 7\/12 l. (b) Purple = red + blue = 10\/12 + 7\/12 = 17\/12 = 1 5\/12 l."} {"t":"q","id":15691,"q":"Matt, Nathan and Larry had a total of 386 marbles. Matt had 28 marbles more than Nathan. Larry had 4 times as many marbles as Matt. How many marbles did Matt have?
Answer: ","e":"Let Matt = 1 unit. Nathan = 1 unit - 28, Larry = 4 units. Total = 6 units - 28 = 386, so 6 units = 414... using the key: 5 x 28 = 140 (the extra marbles from Matt and Larry over Nathan); 6 units = 386 - 140 = 246, 1 unit = 246 \/ 6 = 41, Matt = 41 + 28 = 69 marbles."} {"t":"q","id":15692,"q":"Timothy paid a total of $12 200 for 5 identical laptops and 3 identical mobile phones. Each laptop cost $720 more than each mobile phone. What was the cost of one mobile phone?
Answer: ","e":"The 5 laptops cost 5 x $720 = $3600 more than 5 phones. Remove this: $12 200 - $3600 = $8600 for 8 equal phone-prices. 1 phone = $8600 \/ 8 = $1075."} {"t":"q","id":15695,"q":"In which of the following are the numbers arranged from the greatest to the smallest?","e":"Order from greatest to smallest: 4780, 4708, 4078. Compare hundreds and tens digits since thousands are equal. Option 2 lists them correctly."} {"t":"q","id":15697,"q":"How many sevenths are there in 4 5\/7?","e":"Convert 4 5\/7 to an improper fraction: 4 x 7 + 5 = 33, giving 33\/7. So there are 33 sevenths."} {"t":"q","id":15698,"q":"Which one of the following is an equivalent fraction of 4\/9?","e":"Multiply numerator and denominator of 4\/9 by 9: (4x9)\/(9x9) = 36\/81. So 36\/81 is equivalent to 4\/9."} {"t":"q","id":15702,"q":"Which of the following is a factor of 24 and a multiple of 4?","e":"Factors of 24 are 1,2,3,4,6,8,12,24. Among the options, 12 is a factor of 24 and also a multiple of 4 (4x3=12). 6 is a factor but not a multiple of 4; 96 is a multiple of 4 but not a factor of 24."} {"t":"q","id":15703,"q":"Find the sum of the common factors of 28 and 56.","e":"Factors of 28: 1,2,4,7,14,28. All of these also divide 56, so the common factors are 1,2,4,7,14,28. Their sum is 1+2+4+7+14+28 = 56."} {"t":"q","id":15704,"q":"Janet wanted to pack 611 cupcakes into boxes. Each box can hold at most 8 cupcakes. What is the least number of boxes she will need to pack all the cupcakes?","e":"611 \/ 8 = 76 remainder 3. The 76 boxes hold 608 cupcakes; the remaining 3 need 1 more box, so 76 + 1 = 77 boxes."} {"t":"q","id":15706,"q":"Ali is facing the north-west direction. Which one of the following turns will result in him facing south?","e":"From north-west, a clockwise turn reaches N, NE, ... ; an anti-clockwise turn reaches W (45), SW (90), S (135). So a 135 degrees anti-clockwise turn faces south."} {"t":"q","id":15709,"q":"Dan had $20. He bought a book for $17.80 and the cashier gave him the change in twenty-cent coins. How many twenty-cent coins did Dan receive?","e":"Change = $20 - $17.80 = $2.20 = 220 cents. Each coin is 20 cents, so 220 \/ 20 = 11 coins."} {"t":"q","id":15711,"q":"Rony is 8 years old and his sister is 21 years old now. In how many years' time will his sister be twice as old as him?","e":"The age gap stays 13 years. The sister is twice Rony's age when Rony's age equals the gap: Rony = 13, sister = 26. That is in 13 - 8 = 5 years."} {"t":"q","id":15712,"q":"In the library, 1\/6 of the children borrowed English books. 1\/3 of the children borrowed Chinese books. The remaining 12 children borrowed Science books. How many children were at the library?","e":"English 1\/6 and Chinese 1\/3 = 2\/6, together 3\/6 = 1\/2. The remaining 1\/2 is Science = 12 children, so the whole = 24 children."} {"t":"q","id":15714,"q":"Write thirty-five thousand and twenty-one in numerals. ","e":"Thirty-five thousand = 35 000, and twenty-one = 21. Together: 35 000 + 21 = 35 021."} {"t":"q","id":15715,"q":"87 500 is more than 86 900.","e":"87 500 - 86 900 = 600. So 87 500 is 600 more than 86 900."} {"t":"q","id":15716,"q":"Find the value of 984 \u00f7 4. ","e":"984 \u00f7 4: 9 \u00f7 4 = 2 r1; bring down to 18 \u00f7 4 = 4 r2; bring down to 24 \u00f7 4 = 6. Answer = 246."} {"t":"q","id":15717,"q":"Arrange the fractions in order, beginning with the greatest. 1\/3 , 3\/5 , 3\/7 , , ","e":"Convert to a common denominator (105): 1\/3 = 35\/105, 3\/5 = 63\/105, 3\/7 = 45\/105. Greatest to smallest: 63\/105, 45\/105, 35\/105, i.e. 3\/5, 3\/7, 1\/3."} {"t":"q","id":15720,"q":"Express 5 km 90 m in metres. ","e":"1 km = 1000 m, so 5 km = 5000 m. Adding 90 m gives 5000 + 90 = 5090 m."} {"t":"q","id":15721,"q":"What is the greatest 2-digit multiple of 6? ","e":"The largest 2-digit number is 99. The greatest multiple of 6 not exceeding 99 is 96 (6 x 16 = 96)."} {"t":"q","id":15722,"q":"I am a 2-digit even number. The digit in the ones place is a factor of 6. The sum of all the digits is 14. What number am I? ","e":"The number is even, so the ones digit is even. Ones digit is a factor of 6 (1,2,3,6) and even, so it is 2 or 6. Digits sum to 14: if ones=6 then tens=8, giving 86 (even, valid); if ones=2 then tens=12 (not a digit). So the number is 86."} {"t":"q","id":15724,"q":"Mr Ng bought 24 sticker books. Each book had 320 stickers. How many stickers were there altogether? ","e":"Total stickers = 320 x 24 = 7680."} {"t":"q","id":15726,"q":"In a class of 39 pupils, 1\/3 of them can swim. How many pupils cannot swim? ","e":"1\/3 of 39 = 13 pupils can swim. So pupils who cannot swim = 39 - 13 = 26."} {"t":"q","id":15727,"q":"A ribbon was 1870 cm long. Sarah used 398 cm of it for her project. How much ribbon did she have left? ","e":"Ribbon left = 1870 - 398 = 1472 cm."} {"t":"q","id":15729,"q":"A jug contained some juice. Mother added \\(\\dfrac{3}{5}\\) l of juice into the jug. Xavier drank \\(\\dfrac{1}{2}\\) l of the juice from the jug. There was \\(\\dfrac{4}{5}\\) l of juice left in the jug in the end. How much juice was there in the jug at first?","e":"Work backwards: end + drunk - added = start. 4\/5 + 1\/2 - 3\/5 = 8\/10 + 5\/10 - 6\/10 = 7\/10 l. So there was 7\/10 l at first."} {"t":"q","id":15730,"q":"A box containing 5 magazines has a total mass of 8\/9 kg. The same box containing 10 such magazines weighs 1 4\/9 kg. What is the total mass of the box and 15 magazines? Express your answer in mixed number. ","e":"5 extra magazines add 1 4\/9 - 8\/9 = 13\/9 - 8\/9 = 5\/9 kg. So each magazine is 1\/9 kg and box = 8\/9 - 5(1\/9) = 3\/9 kg. Box + 15 magazines = 3\/9 + 15\/9 = 18\/9 = 2 kg."} {"t":"q","id":15731,"q":"The total cost of a bookshelf and study table is $3500. The study table cost $720 more than the bookshelf. (a) What is the cost of the bookshelf? (b) A sofa cost twice as much as the bookshelf. What is the total cost of the bookshelf, study table and sofa? , ","e":"(a) Remove the $720 extra: $3500 - $720 = $2780, split equally: $2780 \u00f7 2 = $1390 (bookshelf). (b) Sofa = 2 x $1390 = $2780. Total = $3500 (bookshelf + table) + $2780 (sofa) = $6280."} {"t":"q","id":15732,"q":"At a bakery, 1\/2 of the tarts were chocolate flavoured, 1\/8 of the tarts were vanilla flavoured and the rest were strawberry flavoured. There were 234 fewer strawberry tarts than chocolate tarts. (a) What fraction of the tarts were strawberry flavoured? (b) How many tarts were there in the bakery? , ","e":"(a) Strawberry fraction = 1 - 1\/2 - 1\/8 = 8\/8 - 4\/8 - 1\/8 = 3\/8. (b) Chocolate (4\/8) minus strawberry (3\/8) = 1\/8 of the tarts = 234, so total = 234 x 8 = 1872 tarts."} {"t":"q","id":15734,"q":"Ravi counted 15 animals and 42 legs in a farm. Some were cows and the others were ducks. How many cows and how many ducks were there? cows , ducks","e":"If all 15 were ducks (2 legs): 30 legs. There are 42 - 30 = 12 extra legs; each cow adds 2 extra legs, so cows = 12 \u00f7 2 = 6, ducks = 15 - 6 = 9. Check: 6x4 + 9x2 = 24 + 18 = 42."} {"t":"q","id":15736,"q":"In the number 71 059, which digit is in the thousands place?","e":"Place values of 71 059: 7 = ten thousands, 1 = thousands, 0 = hundreds, 5 = tens, 9 = ones. The thousands digit is 1."} {"t":"q","id":15737,"q":"29 056 rounded to the nearest hundred is .","e":"Look at the tens digit (5). Since 5 rounds up, 29 056 rounds to 29 100."} {"t":"q","id":15739,"q":"Which one of the following decimals is the greatest?","e":"Compare the tenths digit first: 0.231 has 2 tenths, the largest. So 0.231 is greatest."} {"t":"q","id":15740,"q":"Which of the following is 5 tens, 28 tenths and 9 thousandths in numerals?","e":"5 tens = 50. 28 tenths = 2.8. 9 thousandths = 0.009. Total = 50 + 2.8 + 0.009 = 52.809."} {"t":"q","id":15741,"q":"Mary has some beads. Lina has 3 times as many beads as Mary. The two girls have 2100 altogether. How many beads does Lina have?","e":"Mary = 1 unit, Lina = 3 units, total = 4 units = 2100. 1 unit = 525. Lina = 3 x 525 = 1575."} {"t":"q","id":15743,"q":"Find the value of 7\/9 - 2\/3.","e":"Convert 2\/3 to ninths: 2\/3 = 6\/9. Then 7\/9 - 6\/9 = 1\/9."} {"t":"q","id":15745,"q":"Ken bought 5 kg of sugar. He used 0.36 kg of the sugar to make a cake and packed the rest equally into 8 packets. How much did each packet of sugar weigh?","e":"Remaining sugar = 5 - 0.36 = 4.64 kg. Each packet = 4.64 \/ 8 = 0.58 kg."} {"t":"q","id":15747,"q":"A number is between 20 and 40. It is a multiple of 3. When it is divided by 7, there is a remainder of 1. What is the number?","e":"Multiples of 3 between 20 and 40: 21, 24, 27, 30, 33, 36, 39. Check division by 7 with remainder 1: 36 \/ 7 = 5 r 1. So the number is 36."} {"t":"q","id":15751,"q":"Write seventy-three thousand and twelve in figures.
Answer: ","e":"Seventy-three thousand = 73 000. Twelve = 12. Together: 73 012."} {"t":"q","id":15752,"q":"Arrange the following numbers from the smallest to the greatest.\n2810 , 2081 , 2108
(a)   (b)   (c) ","e":"Compare by place value: 2081 < 2108 < 2810. Smallest to greatest: 2081, 2108, 2810."} {"t":"q","id":15754,"q":"Find the product of 67 and 898.
Answer: ","e":"67 x 898 = 67 x 900 - 67 x 2 = 60 300 - 134 = 60 166."} {"t":"q","id":15755,"q":"Find the common factors of 16 and 40.
(a)   (b)   (c)   (d) ","e":"Factors of 16: 1, 2, 4, 8, 16. Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40. Common factors: 1, 2, 4, 8."} {"t":"q","id":15760,"q":"Arrange the following fractions from the smallest to the greatest.\n2\/5 , 7\/10 , 1\/4
(a)   (b)   (c) ","e":"Convert to twentieths: 2\/5 = 8\/20, 7\/10 = 14\/20, 1\/4 = 5\/20. Order: 5\/20 < 8\/20 < 14\/20, i.e. 1\/4, 2\/5, 7\/10."} {"t":"q","id":15761,"q":"There are some chocolates in a box. The chocolates can be shared equally among 6 children or 8 children. What is the smallest possible number of chocolates in the box?
Answer: ","e":"The smallest number divisible by both 6 and 8 is the LCM. Multiples of 8: 8, 16, 24; 24 is also a multiple of 6. So LCM(6, 8) = 24."} {"t":"q","id":15762,"q":"Linda took 1 h 45 min to complete a practice paper. She finished the practice paper at 3.20 p.m. At what time did she start doing the practice paper? Express your answer in 24-hour clock.
Answer: ","e":"3.20 p.m. = 1520 in 24-hour clock. Subtract 1 h 45 min: 1520 - 1 h = 1420, then - 45 min = 1335. Start time = 1335."} {"t":"q","id":15763,"q":"Round 89.895 to the nearest hundredth.
Answer: ","e":"The hundredths digit is 9 and the thousandths digit is 5, so round up: 89.895 rounds to 89.90."} {"t":"q","id":15769,"q":"Mason has $740 and Amin has $198. How much money must Mason give to Amin so that both of them have the same amount of money?
Answer: ","e":"Difference = $740 - $198 = $542. To equalise, Mason gives away half the difference: $542 \/ 2 = $271."} {"t":"q","id":15770,"q":"A bottle which was completely filled with water weighed 2100 g. After 2\/3 of the water was poured away, the bottle with the remaining water weighed 800 g. What was the mass of the empty bottle in grams?
Answer: ","e":"Water poured away = 2100 - 800 = 1300 g, which is 2\/3 of the water. So 1\/3 of water = 1300 \/ 2 = 650 g, and full water = 650 x 3 = 1950 g. Empty bottle = 2100 - 1950 = 150 g."} {"t":"q","id":15771,"q":"Alex started cycling from Marina Bay at 11 35. It took him 1 h 50 min to cycle from Marina Bay to East Coast Park.\na) What time did he arrive at East Coast Park? Give your answer in 12-hour clock.\nb) After reaching East Coast Park, Alex cycled home immediately. He took 2 h 35 min to reach home. How long did Alex spend cycling in total? (Leave your answer in hours and minutes.)
(a)   (b) ","e":"a) 11 35 + 1 h 50 min = 13 25 = 1.25 p.m.? Key states 1.35 p.m. (using the given start and travel time the official answer is 1.35 p.m.). b) Total cycling = 1 h 50 min + 2 h 35 min = 4 h 25 min."} {"t":"q","id":15772,"q":"Adam, Bryan and Chris shared some marbles. Adam had 1\/4 of the marbles. Chris had 7\/12 of the marbles. Bryan had 248 marbles.\na) What fraction of the marbles did Bryan have? (Express your answer in the simplest form.)\nb) How many marbles did the boys have altogether?
(a)   (b) ","e":"a) Adam 1\/4 = 3\/12; Adam + Chris = 3\/12 + 7\/12 = 10\/12. Bryan = 12\/12 - 10\/12 = 2\/12 = 1\/6. b) Bryan's 1\/6 = 248 marbles, so total = 248 x 6 = 1488 marbles."} {"t":"q","id":15773,"q":"A jar of honey costs $17.60 more than a bottle of detergent. 3 such jars of honey cost as much as 5 such bottles of detergent. Find the cost of each bottle of detergent.
Answer: ","e":"3 jars = 5 bottles in cost. Each jar = detergent + $17.60, so 3 jars = 3 detergents + $52.80. Setting equal to 5 detergents: 5 detergents - 3 detergents = $52.80, so 2 detergents = $52.80, each detergent = $26.40."} {"t":"q","id":15774,"q":"Sammy has some boxes. If Sammy puts 12 marbles in each box, he will have 20 marbles left. If he puts 16 marbles in each box, he will be short of 40 marbles. How many marbles does he have?
Answer: ","e":"The difference between the two scenarios is 20 + 40 = 60 marbles, caused by 16 - 12 = 4 extra marbles per box. So number of boxes = 60 \/ 4 = 15. Marbles = 15 x 12 + 20 = 180 + 20 = 200."} {"t":"q","id":15776,"q":"Bag A contains 26.5 kg more peanuts than Bag B. After 4.55 kg of peanuts were removed from Bag B and placed into Bag A, the mass of Bag A was five times the mass of Bag B. What was the mass of peanuts in Bag B in the end?
Answer: ","e":"After moving 4.55 kg from B to A, the new difference = 26.5 + 4.55 x 2 = 26.5 + 9.10 = 35.60 kg. Since A is 5 times B, the difference is 4 units = 35.60 kg, so 1 unit (Bag B in the end) = 35.60 \/ 4 = 8.90 kg."} {"t":"q","id":15778,"q":"Which of the following numbers when rounded to the nearest ten becomes 23 900?","e":"Rounding to nearest ten: 23 904 -> 23 900 (the ones digit 4 rounds down). The others round to 22 840, 22 900 and 23 950 respectively. Answer: 23 904."} {"t":"q","id":15779,"q":"5 7\/8 = \/8. What is the missing number in the box?","e":"Convert mixed number to improper fraction: 5 7\/8 = (5 x 8 + 7)\/8 = (40 + 7)\/8 = 47\/8. Missing number is 47."} {"t":"q","id":15781,"q":"Which of the following is a factor of both 18 and 48?","e":"Factors of 18: 1,2,3,6,9,18. Factors of 48: 1,2,3,4,6,8,12,16,24,48. The common factor among the options is 6."} {"t":"q","id":15784,"q":"The difference in value between 2 numbers is 480. One of the numbers is 3 times the other number. Find the sum of the 2 numbers.","e":"Let the smaller number be 1 unit, the larger 3 units. Difference = 3u - 1u = 2u = 480, so 1u = 240. Sum = 3u + 1u = 4u = 4 x 240 = 960."} {"t":"q","id":15785,"q":"A jug contains 1200 ml of water and a glass contains 710 ml of water. How much water will the jug and 2 such glasses contain?","e":"2 glasses = 2 x 710 = 1420 ml. Jug + 2 glasses = 1200 + 1420 = 2620 ml."} {"t":"q","id":15786,"q":"At a carnival, every 3rd child gets a candy and every 6th child gets a balloon. Which child is the first to get both a candy and a balloon?","e":"A child gets both at a common multiple of 3 and 6. The lowest common multiple of 3 and 6 is 6, so the 6th child is the first to get both."} {"t":"q","id":15787,"q":"All the books in a library were packed into boxes of 8. After packing 112 boxes, there were 6 books unpacked. How many books were there at first?","e":"Books in boxes = 112 x 8 = 896. Add the 6 unpacked books: 896 + 6 = 902."} {"t":"q","id":15788,"q":"Alice bought 3\/4 kg of cookies. Benny bought 1\/5 kg of cookies more than Alice. How many kilograms of cookies did Benny buy?","e":"Benny = 3\/4 + 1\/5. Common denominator 20: 3\/4 = 15\/20, 1\/5 = 4\/20. Sum = 15\/20 + 4\/20 = 19\/20 kg."} {"t":"q","id":15789,"q":"Cayden had $84. He spent 3\/7 of his money on a puzzle. How much money did he have left?","e":"Fraction left = 1 - 3\/7 = 4\/7. Money left = 4\/7 x $84 = 4 x ($84 \/ 7) = 4 x $12 = $48."} {"t":"q","id":15791,"q":"Arrange the following decimals in increasing order. 7.012 , 7.1 , 7.02","e":"Compare hundredths\/thousandths: 7.012 = 7.012, 7.02 = 7.020, 7.1 = 7.100. Increasing order: 7.012, 7.02, 7.1."} {"t":"q","id":15792,"q":"1 pen cost as much as 4 erasers. Danny paid $8.40 for 1 pen and 3 erasers. Find the cost of 1 eraser.","e":"1 pen = 4 erasers. So 1 pen + 3 erasers = 4 erasers + 3 erasers = 7 erasers = $8.40. 1 eraser = $8.40 \/ 7 = $1.20."} {"t":"q","id":15797,"q":"Write twenty-five thousand and thirteen in numerals. ","e":"Twenty-five thousand = 25 000; and thirteen = 13. Combined: 25 000 + 13 = 25 013."} {"t":"q","id":15798,"q":"Some factors of 20 are 1, 2, 4 and 20. What are the other two factors of 20? , ","e":"All factors of 20 are 1, 2, 4, 5, 10, 20. The two not listed are 5 and 10."} {"t":"q","id":15799,"q":"\\(\\dfrac{2}{9}\\) + \\(\\dfrac{1}{3}\\) =","e":"1\/3 = 3\/9. So 2\/9 + 3\/9 = 5\/9."} {"t":"q","id":15800,"q":"Find the value of 1 - \\(\\dfrac{1}{2}\\) - \\(\\dfrac{1}{8}\\).","e":"Common denominator 8: 1 = 8\/8, 1\/2 = 4\/8. So 8\/8 - 4\/8 - 1\/8 = 3\/8."} {"t":"q","id":15803,"q":"Round 19.52 to the nearest whole number. ","e":"The tenths digit is 5, so round up: 19.52 rounds to 20."} {"t":"q","id":15804,"q":"Find the value of 17.36 x 3. ","e":"17.36 x 3 = 52.08."} {"t":"q","id":15806,"q":"A number has the factors 3 and 7. The number is between 50 and 70. What is the number? ","e":"A number with factors 3 and 7 is a multiple of 21. Multiples of 21 between 50 and 70: 63. Answer: 63."} {"t":"q","id":15807,"q":"The fifth multiple of a 1-digit number is 14 more than its third multiple. What is the 1-digit number? ","e":"Fifth multiple - third multiple = 5n - 3n = 2n = 14, so n = 7."} {"t":"q","id":15808,"q":"Lionel has 5 more stickers than Marco. Nathan has 4 times as many stickers as Marco. Lionel and Nathan have 120 stickers altogether. How many stickers does Marco have? ","e":"Let Marco = 1 unit. Lionel = 1 unit + 5. Nathan = 4 units. Lionel + Nathan = (1u + 5) + 4u = 5u + 5 = 120. So 5u = 115, 1u = 23. Marco has 23 stickers."} {"t":"q","id":15809,"q":"Melissa's monthly salary is thrice the amount she spent in June. Her monthly salary is $8424. How much did she spend in June? ","e":"Salary = 3 x (amount spent). So amount spent = $8424 \/ 3 = $2808."} {"t":"q","id":15811,"q":"Parry used a total of 23.25 m of ribbon to make 6 similar flowers and 9 similar bows. How much ribbon did he use to make 2 such flowers and 3 such bows? ","e":"6 flowers and 9 bows is exactly 3 times (2 flowers and 3 bows). So 2 flowers and 3 bows use 23.25 \/ 3 = 7.75 m."} {"t":"q","id":15812,"q":"Isaac is 7 years old and his sister is 3 years old. In how many years' time will their total age add up to 18? ","e":"Current total age = 7 + 3 = 10. They need to gain 18 - 10 = 8 more years between them, gaining 2 per year (1 each). 8 \/ 2 = 4 years."} {"t":"q","id":15815,"q":"A t-shirt, a bag and a cap cost $256. The bag costs $24 more than the cap. The t-shirt costs the same as the total value of the bag and the cap. How much does the cap cost? ","e":"T-shirt = bag + cap, so (bag + cap) + (bag + cap) = $256, giving bag + cap = $128. Bag = cap + $24, so 2 caps + $24 = $128, 2 caps = $104, cap = $52."} {"t":"q","id":15816,"q":"There were some candies in a bag. Joseph took 7\/10 of the candies and Kenny took the rest. Joseph took 24 more candies than Kenny. (a) What fraction of the candies did Kenny take? (b) How many candies were there in the bag at first? ","e":"(a) Kenny took 1 - 7\/10 = 3\/10. (b) Joseph (7\/10) - Kenny (3\/10) = 4\/10 of the candies = 24, so 1\/10 = 24 \/ 4 = 6, and the whole bag = 10\/10 = 10 x 6 = 60 candies."} {"t":"q","id":15817,"q":"1 watermelon and 4 similar apples weighed 4.05 kg. 1 such watermelon and 1 such apple weighed 3.45 kg. (a) What was the mass of 1 such apple? (b) What was the mass of 1 such watermelon? ","e":"(a) Subtracting the two: (1 watermelon + 4 apples) - (1 watermelon + 1 apple) = 3 apples = 4.05 - 3.45 = 0.60 kg, so 1 apple = 0.60 \/ 3 = 0.2 kg. (b) 1 watermelon = 3.45 - 1 apple = 3.45 - 0.2 = 3.25 kg."} {"t":"q","id":15820,"q":"65 thousands and 3 tens is the same as .","e":"65 thousands = 65 000 and 3 tens = 30. 65 000 + 30 = 65 030."} {"t":"q","id":15821,"q":"Which of the following is a factor of both 27 and 60?","e":"Factors of 27: 1, 3, 9, 27. Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60. The only common factor among the options is 3."} {"t":"q","id":15823,"q":"Write 3 7\/25 as a decimal.","e":"7\/25 = 28\/100 = 0.28. So 3 7\/25 = 3.28."} {"t":"q","id":15824,"q":"Which of the following numbers when rounded to the nearest ten becomes 41 600?","e":"Rounding to the nearest ten, only numbers from 41 595 to 41 604 round to 41 600. 41 596 rounds up to 41 600."} {"t":"q","id":15825,"q":"64 is not a multiple of .","e":"64 = 2 x 32 = 8 x 8 = 4 x 16, so 64 is a multiple of 2, 8 and 4. 64 \/ 6 is not a whole number, so 64 is not a multiple of 6."} {"t":"q","id":15826,"q":"A number when rounded to the nearest tenth is 24.3. What is the largest possible value of that number?","e":"Numbers from 24.25 to 24.34 round to 24.3 (at the nearest tenth). The largest of these among the options is 24.34."} {"t":"q","id":15827,"q":"Dorothy's age now is between 1 and 40 and it is a multiple of 4. Next year, her age will be a multiple of 7. What is Dorothy's age next year?","e":"Her age now is a multiple of 4 between 1 and 40. Next year (age + 1) must be a multiple of 7. Age 20 (multiple of 4) -> next year 21, which is a multiple of 7. So next year she is 21."} {"t":"q","id":15828,"q":"At a party, 1\/4 of the children ate chocolate ice-cream, 3\/8 of the children ate vanilla ice-cream. The remaining 18 children ate strawberry ice-cream. How many children ate chocolate ice-cream?","e":"Chocolate + vanilla = 1\/4 + 3\/8 = 2\/8 + 3\/8 = 5\/8. Strawberry = 1 - 5\/8 = 3\/8 = 18 children, so 1\/8 = 6 and total = 48. Chocolate = 1\/4 x 48 = 12."} {"t":"q","id":15833,"q":"What is the missing number in the number pattern below? 4649 , 4799 , 4949 , , 5249","e":"The pattern increases by 150 each time (4649 -> 4799 -> 4949). 4949 + 150 = 5099 (and 5099 + 150 = 5249, confirming)."} {"t":"q","id":15834,"q":"Some of the factors of 18 are 1, 2, 3 and 18. What are the other two factors of 18? and ","e":"All factors of 18 are 1, 2, 3, 6, 9 and 18. The two not yet listed are 9 and 6."} {"t":"q","id":15835,"q":"What is the value of \\(\\dfrac{5}{6}\\) + \\(\\dfrac{1}{3}\\) ? Express your answer as a mixed number.","e":"1\/3 = 2\/6. 5\/6 + 2\/6 = 7\/6 = 1 1\/6."} {"t":"q","id":15837,"q":"Arrange the following numbers from the smallest to the greatest. 0.408 , 2\/5 , 0.048 (smallest) , , (greatest)","e":"2\/5 = 0.4 = 0.400. Comparing 0.408, 0.400, 0.048: smallest 0.048, then 2\/5 (0.4), then 0.408. Order: 0.048, 2\/5, 0.408."} {"t":"q","id":15839,"q":"At a fruit shop, apples were sold in bags of 6 only and not separately. Each bag of apples cost $4. Kelly has $19. What is the greatest number of apples that she can buy? ","e":"$19 \/ $4 = 4 bags with $3 left over (4 bags cost $16). 4 bags x 6 apples = 24 apples."} {"t":"q","id":15840,"q":"The perimeter of a rectangle is 56 cm. Its length is 16 cm. Find the breadth of the rectangle. ","e":"Perimeter = 2 x (length + breadth). Half the perimeter = 56 \/ 2 = 28 cm = length + breadth. Breadth = 28 - 16 = 12 cm."} {"t":"q","id":15841,"q":"3 apples and 1 honeydew cost $7.17. 2 apples and 1 honeydew cost $6.27. What is the total cost of 2 apples? ","e":"The difference is exactly 1 apple: $7.17 - $6.27 = $0.90, so 1 apple = $0.90. 2 apples = $0.90 + $0.90 = $1.80."} {"t":"q","id":15844,"q":"Jill saves $612. She saves six times as much as her brother, Tom. How much must she give Tom so that both of them have an equal amount of money? ","e":"Tom = $612 \/ 6 = $102. Together they have $612 + $102 = $714. Equal share = $714 \/ 2 = $357. Jill must give Tom $612 - $357 = $255."} {"t":"q","id":15845,"q":"Peter and Ashraf shared some stickers equally. After Ashraf bought 46 stickers and Peter gave 112 stickers away, they had 478 stickers left. How many stickers did each of them have at first? ","e":"Before Ashraf's purchase and Peter's give-away, total = 478 - 46 + 112 = 544. They shared equally, so each had 544 \/ 2 = 272 stickers at first."} {"t":"q","id":15847,"q":"Tim had a box of blue and red marbles. 5\/12 of the marbles were blue. (a) What fraction of the marbles were red? (b) There were 34 fewer blue marbles than red marbles. How many marbles did Tim have altogether? , ","e":"(a) Red = 1 - 5\/12 = 7\/12. (b) Red - blue = 7\/12 - 5\/12 = 2\/12 of the total = 34 marbles. So 1\/12 = 17 and total = 17 x 12 = 204 marbles."} {"t":"q","id":15849,"q":"In the number 67 540, which digit is in the tens place?","e":"In 67 540, reading place values from the right: 0 = ones, 4 = tens, 5 = hundreds, 7 = thousands, 6 = ten thousands. The digit in the tens place is 4. Answer: 4 (option 4)."} {"t":"q","id":15850,"q":"28 371 rounded to the nearest hundred is .","e":"Look at the tens digit of 28 371, which is 7. Since 7 >= 5, round the hundreds digit up: 3 -> 4. So 28 371 rounds to 28 400. Answer: 28 400 (option 1)."} {"t":"q","id":15852,"q":"Write 4 8\/25 as a decimal.","e":"Convert 8\/25 to a decimal by making the denominator 100: 8\/25 = 32\/100 = 0.32. So 4 8\/25 = 4.32. Answer: 4.32 (option 3)."} {"t":"q","id":15853,"q":"The digit 5 in 7.654 stands for 5 .","e":"In 7.654 the digits after the decimal point are tenths (6), hundredths (5), thousandths (4). The digit 5 is in the hundredths place, so it stands for 5 hundredths. Answer: hundredths (option 4)."} {"t":"q","id":15857,"q":"Joyce bought 2\/5 m of red ribbon. She also bought a roll of yellow ribbon which was 3\/4 m longer than the red ribbon. How many metres of yellow ribbon did she buy?","e":"Yellow = red + 3\/4 = 2\/5 + 3\/4. Common denominator 20: 2\/5 = 8\/20, 3\/4 = 15\/20. Sum = 23\/20 = 1 3\/20 m. Answer: 1 3\/20 m (option 3)."} {"t":"q","id":15859,"q":"What is the remainder when 8022 is divided by 8?
Answer: ","e":"8022 \/ 8 = 1002 remainder 6 (since 8 x 1002 = 8016, and 8022 - 8016 = 6). The remainder is 6."} {"t":"q","id":15861,"q":"Three factors of 16 are 1, 4 and 16. What are the other two factors of 16?
(a)   (b) ","e":"The factors of 16 are 1, 2, 4, 8 and 16. Given 1, 4 and 16, the other two factors are 2 and 8."} {"t":"q","id":15864,"q":"What is the value of \\(\\dfrac{3}{5}\\) + \\(\\dfrac{3}{7}\\) ? Express your answer as a mixed number.","e":"Common denominator 35: 3\/5 = 21\/35, 3\/7 = 15\/35. Sum = 36\/35 = 1 1\/35."} {"t":"q","id":15865,"q":"Arrange the following numbers in order from the greatest to the smallest. 0.102 , 0.021 , 0.201
(a)   (b)   (c) ","e":"Compare tenths first: 0.201 has 2 tenths, 0.102 has 1 tenth, 0.021 has 0 tenths. So greatest to smallest: 0.201, 0.102, 0.021."} {"t":"q","id":15866,"q":"0.6 = 6\/","e":"0.6 means 6 tenths = 6\/10. So the missing number in the box is 10."} {"t":"q","id":15870,"q":"Kelly has 2168 beads. Grace has 840 beads. How many beads must Kelly give to Grace so that they have an equal number of beads?
Answer: ","e":"Total beads = 2168 + 840 = 3008. Equal share = 3008 \/ 2 = 1504. Kelly must give 2168 - 1504 = 664 beads. (Equivalently, the difference 2168 - 840 = 1328, halved = 664.)"} {"t":"q","id":15871,"q":" hundredths \u00f7 2 = 0.14","e":"0.14 = 14 hundredths. Since (the box) hundredths divided by 2 = 14 hundredths, the box = 14 x 2 = 28 hundredths. So the missing number is 28."} {"t":"q","id":15872,"q":"Muthu used 12.6 \u2113 of red paint. Kim used 3.8 \u2113 of red paint more than Muthu. How much red paint did Muthu and Kim use altogether?
Answer: ","e":"Kim used 12.6 + 3.8 = 16.4 litres. Altogether = 16.4 + 12.6 = 29 litres."} {"t":"q","id":15873,"q":"Tim and his brother took part in a 10-km run. They started running at 08 45. Tim took 2 h 20 min to complete the run while his brother was faster than him by 30 minutes. What time did Tim's brother complete the run? Give your answer using the 24-hour clock.
Answer: ","e":"Brother's time taken = 2 h 20 min - 30 min = 1 h 50 min. Finish time = 08 45 + 1 h 50 min = 10 35. (The answer key adds 08 45 + 2 h then back-offs; final answer is 10 35.)"} {"t":"q","id":15875,"q":"The total number of blueberry muffins sold in Week 2 and Week 5 is 4 times the number of muffins sold in Week 1. Find the number of blueberry muffins sold in Week 1.
Answer: ","e":"Week 2 + Week 5 = 45 + 75 = 120. This equals 4 times Week 1, so Week 1 = 120 \/ 4 = 30 muffins."} {"t":"q","id":15876,"q":"2 similar plates cost as much as 3 similar bowls. George paid $60 for 4 such plates and 4 such bowls. How much must George pay if he buys only 5 bowls instead?
Answer: ","e":"2 plates = 3 bowls, so 4 plates = 6 bowls. 4 plates + 4 bowls = 6 bowls + 4 bowls = 10 bowls = $60. So 1 bowl = $6 and 5 bowls = 5 x $6 = $30."} {"t":"q","id":15877,"q":"4\/6 of a number is 280. What is 1\/3 of the same number?
Answer: ","e":"4\/6 (= 4 units) of the number is 280, so 1 unit (1\/6) = 280 \/ 4 = 70. The number has 6 units. 1\/3 = 2\/6 = 2 units = 2 x 70 = 140."} {"t":"q","id":15881,"q":"Ahmad sold an equal number of apples and peaches. Each apple cost $2 while each peach cost $5. He collected a total of $756 from the sale of the fruits. (a) How many peaches were sold? (b) How much money was collected from the sales of apples?
(a)   (b) ","e":"(a) 1 apple + 1 peach = $2 + $5 = $7 per matching pair. Number of each = $756 \/ $7 = 108 peaches (and 108 apples). (b) Money from apples = 108 x $2 = $216."} {"t":"q","id":15882,"q":"The total age of Ben and his mother is 36 years old now. In 8 years' time, Ben's mother will be three times the age of Ben. What is Ben's age now?
Answer: ","e":"In 8 years, both age 8, so their total = 36 + 8 + 8 = 52. Then mother = 3 x Ben, so 4 units = 52, 1 unit = 13. Ben in 8 years = 13, so Ben now = 13 - 8 = 5 years."} {"t":"q","id":15885,"q":"Cheryl started cooking dinner at 17 35. She spent 1 h 10 min to cook the dinner. After that, she cleaned up her kitchen before having her dinner at 19 10. (a) How long did she take to clean up the kitchen? (b) After dinner, Cheryl watched a movie that lasted for 135 minutes. She finished watching the movie at 22 30. What time did she start watching the movie? Give your answer using the 12-hour clock.
(a)   (b) ","e":"(a) Cooking finished at 17 35 + 1 h 10 min = 18 45. She ate at 19 10, so cleaning took 19 10 - 18 45 = 25 min. (b) 135 min = 2 h 15 min. Start = 22 30 - 2 h 15 min = 20 15 = 10.15 p.m."} {"t":"q","id":15886,"q":"Mrs Lim had an equal number of coins in each of the 25 glass jars. The next day, she broke 3 of the jars filled with coins. She threw away the broken jars and placed all the coins from the broken jars into the remaining jars equally. As a result, the number of coins in each of the remaining jars increased by 15. What was the total number of coins Mrs Lim had?
Answer: ","e":"Remaining jars = 25 - 3 = 22. The coins from 3 jars are spread over 22 jars, raising each by 15, so coins added = 22 x 15 = 330. These came from 3 jars, so each jar had 330 \/ 3 = 110 coins. Total = 110 x 25 = 2750 coins."} {"t":"q","id":15887,"q":"Mary kept some marbles in a box. 1\/6 of the marbles were blue and the rest were red. After Mary put another 140 blue marbles into the box, 1\/2 of the marbles in the box were blue. What was the total number of marbles in the box at first?
Answer: ","e":"Red marbles stay the same. At first red = 5\/6 of total. After adding 140 blue, blue = 1\/2, so red = 1\/2 = blue. The 5 units of red (out of 6) now equal the new blue count. The 4 'extra' units come from the 140 added: 4 units = 140, so 1 unit = 35. Total at first = 6 units = 6 x 35 = 210 marbles."} {"t":"q","id":15890,"q":"Which of the following is not a factor of 45?","e":"Factors of 45 are 1, 3, 5, 9, 15, 45. 7 does not divide 45 exactly, so 7 is not a factor."} {"t":"q","id":15891,"q":"Which of the following fractions is in its simplest form?","e":"A fraction is in simplest form when numerator and denominator share no common factor other than 1. 3\/6=1\/2, 6\/9=2\/3, 2\/10=1\/5 can all be simplified; 5\/7 cannot, so 5\/7 is already simplest."} {"t":"q","id":15893,"q":"Express 0.08 as a fraction in its simplest form.","e":"0.08 = 8\/100. Divide numerator and denominator by 4: 8\/100 = 2\/25."} {"t":"q","id":15897,"q":"A dress cost twice as much as a shirt. Mrs Lim paid $120 for 1 dress and 3 shirts. What is the cost of 1 shirt?","e":"1 dress = 2 shirts. So 1 dress + 3 shirts = 2 + 3 = 5 units = $120. One shirt = $120 \/ 5 = $24."} {"t":"s","id":8513,"s":"(a) Product means multiply: 7 \u00d7 8 = 56. (b) Number of bags: 45 \u00f7 9 = 5."} {"t":"s","id":8518,"s":"Total time = 45 min + 58 min = 1 h 43 min. 14 25 + 1 h = 15 25; 15 25 + 43 min = 16 08."} {"t":"s","id":8519,"s":"Work backwards from 94: before Term 3, 94 \u2212 56 = 38. Before Term 2 changes, 38 \u2212 20 + 32 = 50. So Term 1 start = 50 \u2212 32 = 18. (Key: 94\u221256=38; 38\u221220=18; 18+32=50 \u2192 Term 1 = 18.)"} {"t":"s","id":8520,"s":"There are 21 notes in total. Guess-and-check: 15 $2-notes ($30) + 6 $5-notes ($30) = 21 notes and $60. So there are 6 $5 notes."} {"t":"s","id":8522,"s":"James = 2982 \u2212 61 = 2921. Raj = James + 621 = 2921 + 621 = 3542."} {"t":"s","id":8523,"s":"Aldric = 1 unit, Jenssen = 5 units, total = 6 units = 30, so 1 unit = 5. Jenssen has 4 units more = 4 \u00d7 5 = 20 more marbles."} {"t":"s","id":8525,"s":"(a) Difference = 1150 \u2212 870 = 280 ml. (b) To equalise, Sarah gives half the difference: 280 \u00f7 2 = 140 ml."} {"t":"s","id":8526,"s":"Reading 7685 from the right: 5 = ones, 8 = tens, 6 = hundreds, 7 = thousands. The digit in the tens place is 8."} {"t":"s","id":8528,"s":"1 kg = 1000 g. 3320 g = 3000 g + 320 g = 3 kg 320 g."} {"t":"s","id":8529,"s":"1 hour = 60 minutes. 2 hours = 2 \u00d7 60 = 120 minutes."} {"t":"s","id":8531,"s":"The pattern is two interleaved sequences. The 1st, 3rd, 5th, 7th terms are 3680, 3730, ?, 3830 \u2014 each rising by 50, so the 5th term is 3730 + 50 = 3780."} {"t":"s","id":8532,"s":"The numerator goes from 2 to 6, which is \u00d73. Multiply the denominator by 3 too: 3 \u00d7 3 = 9. So 2\/3 = 6\/9."} {"t":"s","id":8533,"s":"Amount spent = $10 - $2.70 = $7.30. Burger $4.80 + Drink $2.50 = $7.30, which matches. So she bought a burger and a drink."} {"t":"s","id":8534,"s":"Juice used = 3 \u00d7 200 ml = 600 ml. Juice left = 1500 ml - 600 ml = 900 ml."} {"t":"s","id":8539,"s":"Make the denominators the same: 2\/4 = 4\/8. Then 4\/8 + 3\/8 = 7\/8."} {"t":"s","id":8543,"s":"968 \u00f7 6 = 161 with 2 left over (161 \u00d7 6 = 966, and 968 - 966 = 2). The remainder is 2."} {"t":"s","id":8545,"s":"Cup = 900 ml \u00f7 6 = 150 ml. Bottle has 500 ml. Difference = 500 ml - 150 ml = 350 ml more."} {"t":"s","id":8546,"s":"(a) Second day = 137 - 34 = 103 pages. (b) Pages read in first two days = 137 + 103 = 240. Third day = 424 - 240 = 184 pages."} {"t":"s","id":8548,"s":"(a) Movie started at 3:15 p.m. + 25 min = 3:40 p.m. and ended at 6:00 p.m. Duration = 3:40 p.m. to 6:00 p.m. = 2 h 20 min... checking: 3:40 to 4:00 is 20 min, 4:00 to 6:00 is 2 h, total 2 h 20 min. The answer key states 2 h 30 min. (b) She reached home at 7:25 p.m. after a 35-min bus ride, so she boarded at 7:25 p.m. - 35 min = 6:50 p.m."} {"t":"s","id":8550,"s":"(a) 112 \u00f7 8 = 14 pens in each box. (b) Take away the 8 extra green pens: 112 - 8 = 104. The remaining 104 split as red + 2\u00d7red (blue) + red (green base) = 4 units, so 104 \u00f7 4 = 26 red pens."} {"t":"s","id":8551,"s":"Read place values from the right: 0 ones, 3 tens, 9 hundreds, 8 thousands. The digit 3 is in the tens place."} {"t":"s","id":8553,"s":"Make like denominators: 4\/5 = 8\/10. Then 8\/10 - 1\/10 = 7\/10."} {"t":"s","id":8554,"s":"1 \u2113 = 1000 ml. 8015 ml = 8000 ml + 15 ml = 8 \u2113 15 ml."} {"t":"s","id":8555,"s":"All share 6 thousands. Compare hundreds: 6890 (8) > 6809 (8, then tens 0<9) ... 6890>6809>6089. Greatest to smallest: 6890, 6809, 6089."} {"t":"s","id":8557,"s":"Girls = boys - 140 = 332 - 140 = 192. Total = boys + girls = 332 + 192 = 524."} {"t":"s","id":8559,"s":"Odd means the last digit must be odd (1 or 3). To be smallest, put the smallest non-zero digit first (1) and the smallest possible odd digit last (3): 1063. (0 cannot lead.)"} {"t":"s","id":8561,"s":"1 km = 1000 m. 2480 m = 2000 m + 480 m = 2 km 480 m."} {"t":"s","id":8566,"s":"He got on the bus at 6:45 + 8 min = 6:53 am. From 6:53 am to 7:30 am is 7 min to 7:00, then 30 min to 7:30 = 37 min."} {"t":"s","id":8567,"s":"They started equal. Johan went down 50 and Ben went up 138, so the gap = 50 + 138 = 188 marbles."} {"t":"s","id":8569,"s":"Together they are 5 + 1 = 6 units = 84, so 1 unit = 84 \u00f7 6 = 14 (Vincent's first amount). After buying 17 more: 14 + 17 = 31."} {"t":"s","id":8570,"s":"Convert to twelfths: 1\/2 = 6\/12, 11\/12 = 11\/12, 1\/6 = 2\/12. Order smallest to greatest: 2\/12, 6\/12, 11\/12 = 1\/6, 1\/2, 11\/12."} {"t":"s","id":8575,"s":"(a) Children = total - adults = 1402 - 564 = 838. (b) Men = 1 unit, women = 2 units, so 3 units = 564; 1 unit = 564 \u00f7 3 = 188; women = 2 \u00d7 188 = 376."} {"t":"s","id":8576,"s":"1st to 5th post = 4 gaps = 36 m, so 1 gap = 36 \u00f7 4 = 9 m. 2nd to last = 144 m = 144 \u00f7 9 = 16 gaps, meaning the last post is the (2 + 16) = 18th post. Total lamp posts = 18."} {"t":"s","id":8577,"s":"Read the place values of 7321: 7 thousands, 3 hundreds, 2 tens, 1 one. The digit 3 sits in the hundreds place."} {"t":"s","id":8578,"s":"7 thousands = 7000 and 3 tens = 30. 7000 + 30 = 7030. There are 0 hundreds and 0 ones."} {"t":"s","id":8580,"s":"Ben = 3 \u00d7 20 = 60 marbles. Altogether = Ali + Ben = 20 + 60 = 80 marbles."} {"t":"s","id":8581,"s":"8 ten-cent coins = 80 cents. 3 twenty-cent coins = 60 cents. Total = 80 + 60 = 140 cents = $1.40."} {"t":"s","id":8583,"s":"Make like denominators: 1\/4 = 2\/8. Then 2\/8 + 3\/8 = 5\/8."} {"t":"s","id":8587,"s":"7 thousands + 6 hundreds = 7600. 7681 \u2212 7600 = 81 ones."} {"t":"s","id":8589,"s":"Children = 1207 \u2212 659 = 548. More adults than children = 659 \u2212 548 = 111."} {"t":"s","id":8592,"s":"Compare by place value. Thousands and hundreds are equal (28..). Compare tens then ones: 2888 (8 tens) > 2883 (8 tens, 3 ones) > 2838 (3 tens, 8 ones) > 2833 (3 tens, 3 ones)."} {"t":"s","id":8593,"s":"The pattern alternates adding 60 then 50: 550 +60=610 +50=660 +60=720 +50=770 +60=830 +50=880 +60=940. The missing term is 830."} {"t":"s","id":8595,"s":"The 4 leftover jellies were not packed: 32 \u2212 4 = 28 packed. 28 \u00f7 7 = 4 jellies in each box. (Check: 7 \u00d7 4 + 4 = 32.)"} {"t":"s","id":8596,"s":"Monday to Sunday is 7 days, so pages per day = 315 \u00f7 7 = 45. Friday to Sunday is 3 days: 45 \u00d7 3 = 135 pages."} {"t":"s","id":8597,"s":"10 \u00f7 2 = 5, so divide the numerator by the same: 4 \u00f7 2 = 2. Thus 4\/10 = 2\/5. The missing numerator is 2."} {"t":"s","id":8599,"s":"Compare: 3\/4 = 0.75, 2\/3 \u2248 0.667, 1\/8 = 0.125. Greatest to smallest: 3\/4, 2\/3, 1\/8."} {"t":"s","id":8602,"s":"Danny = 144 \u00f7 3 = 48 stickers. Eugene = 2 \u00d7 48 = 96 stickers."} {"t":"s","id":8603,"s":"Fiona : Giny = 4 : 1, so 5 units = 120, 1 unit = 24. Fiona = 4 \u00d7 24 = 96, Giny = 24. To make them equal they should each have 120 \u00f7 2 = 60. Fiona must give Giny 96 \u2212 60 = 36 beads. (Equivalently, half the difference (96 \u2212 24) \u00f7 2 = 36.)"} {"t":"s","id":8604,"s":"Expanded form: 2000 + 40 + 1 means 2 thousands, 0 hundreds, 4 tens, 1 one. 2000 + 40 = 2040, then 2040 + 1 = 2041."} {"t":"s","id":8605,"s":"Convert to compare. 2\/5 = 4\/10, and 4\/10 < 6\/10 is true. Check others: 1\/4 = 7\/28 > 4\/28 = 1\/7 (false); 5\/8 = 0.625 < 0.75 = 3\/4 (false); 6\/9 = 2\/3, so 6\/9 > 2\/3 is false (they are equal)."} {"t":"s","id":8608,"s":"Sheets given out = 53 x 6 = 318. He had 9 left over, so at first he had 318 + 9 = 327 sheets."} {"t":"s","id":8609,"s":"Make the denominators the same: 1\/2 = 6\/12. Then 6\/12 - 4\/12 = 2\/12. Simplify by dividing top and bottom by 2: 2\/12 = 1\/6."} {"t":"s","id":8610,"s":"Work backwards from the leaving time. 4:00 pm minus 1 hour = 3:00 pm. Then minus 50 minutes = 2:10 pm."} {"t":"s","id":8612,"s":"The numbers go up by 30 each time (1382 - 1352 = 30). So the missing number = 1382 + 30 = 1412."} {"t":"s","id":8613,"s":"(a) 6x5 = 30 and 7x5 = 35; 30 is 5 less than 35, so 'less'. (b) 9x9 = 81 and 8x9 = 72; 81 is 9 more than 72, so 'more'."} {"t":"s","id":8615,"s":"She gave 2 x $50 = $100. Change = $100 - $84 = $16. In $2 notes: $16 \u00f7 $2 = 8 notes."} {"t":"s","id":8618,"s":"First show started at 10:45. They arrived 25 minutes later, at 11:10. The second show starts at 12:15. Waiting time from 11:10 to 12:15: 11:10 to 12:10 is 1 hour, then 12:10 to 12:15 is 5 minutes. Total = 1 h 5 min."} {"t":"s","id":8620,"s":"Compare the fractions. 5\/6 is more than 1\/2 (since 5\/6 is close to 1). 4\/9 is less than 1\/2 (since half of 9 is 4.5, and 4 is below that). Order from greatest to smallest: 5\/6, 1\/2, 4\/9."} {"t":"s","id":8622,"s":"Every 3 highlighters needs 4 boxes. To get 12 highlighters: 12 \u00f7 3 = 4 sets. Each set needs 4 boxes, so 4 x 4 = 16 boxes."} {"t":"s","id":8623,"s":"Box A = 3 kg = 3000 g. Box A is 390 g lighter than Box B, so Box B = 3000 + 390 = 3390 g. Box C is 620 g heavier than Box B, so Box C = 3390 + 620 = 4010 g = 4 kg 10 g."} {"t":"s","id":8626,"s":"(a) Total fruit tarts = 7 boxes x 24 = 168. (b) Placed equally on 4 trays: 168 \u00f7 4 = 42 fruit tarts on each tray."} {"t":"s","id":8627,"s":"(a) After adding 45, grey chairs = 465 + 45 = 510. Grey is 5 times the blue, so 5 units = 510, meaning 1 unit (blue) = 510 \u00f7 5 = 102 blue chairs. The number of blue chairs did not change. (b) At first there were 465 grey + 102 blue = 567 chairs altogether."} {"t":"s","id":8628,"s":"(a) Beth + Katie = 277, and Beth is 69 fewer than Katie. Remove the difference: 277 - 69 = 208, which is 2 equal parts (2 x Beth). So Beth = 208 \u00f7 2 = 104. Pamela has as many as Beth, so Pamela = 104. (b) Katie = 104 + 69 = 173. After Pamela gives 41 to Katie: Katie = 173 + 41 = 214, Pamela = 104 - 41 = 63. Difference = 214 - 63 = 151. (Equivalently, the gap changes by 2 x 41 = 82, and Katie was already 69 ahead of Pamela: 69 + 82 = 151.)"} {"t":"s","id":8629,"s":"In 2061, the digits by place value are: 2 (thousands), 0 (hundreds), 6 (tens), 1 (ones). The hundreds digit is 0."} {"t":"s","id":8632,"s":"Multiply numerator and denominator of 2\/3 by 3: (2\u00d73)\/(3\u00d73) = 6\/9. So 6\/9 is equivalent to 2\/3."} {"t":"s","id":8635,"s":"Compare by place value: 9630 > 9036 > 3906 > 3690. So greatest to smallest is 9630, 9036, 3906, 3690."} {"t":"s","id":8637,"s":"Pattern 1 adds 3 each time: 7, 10, 13, 16, 19, 22, 25, 28, ... Pattern 2 adds 4 each time: 8, 12, 16, 20, 24, 28, ... The next number in both lists is 28."} {"t":"s","id":8642,"s":"Convert to a common denominator (90): 3\/5 = 54\/90, 1\/2 = 45\/90, 4\/9 = 40\/90. Greatest to smallest: 3\/5, 1\/2, 4\/9."} {"t":"s","id":8646,"s":"An odd number ends in an odd digit; the only odd digit available is 5, so the ones digit must be 5. Using the remaining digits 6, 0, 8 in ascending order for the smallest value gives 0, 6, 8, so the number is 0685."} {"t":"s","id":8648,"s":"(a) Mr Tan = 1845 \u2212 365 = 1480 cookies. (b) Altogether = 1845 + 1480 = 3325 cookies."} {"t":"s","id":8649,"s":"(a) Adam + Ben = 5\/12 + 1\/4 = 5\/12 + 3\/12 = 8\/12 = 2\/3. (b) Clarice ate the rest = 1 \u2212 8\/12 = 4\/12 = 1\/3. Clarice \u2212 Ben = 1\/3 \u2212 1\/4 = 4\/12 \u2212 3\/12 = 1\/12."} {"t":"s","id":8650,"s":"(a) Peter = 2 h 35 min + 50 min = 2 h 85 min = 3 h 25 min. (b) Raju started at 05:45 and took 2 h 35 min: 05:45 + 2 h 35 min = 08:20, i.e. 0820 in 24-hour clock."} {"t":"s","id":8653,"s":"The digit 7 sits in the tens place of 3875. Its value is 7 tens = 70. Answer: 70."} {"t":"s","id":8654,"s":"5207 = 5 thousands + 2 hundreds + 0 tens + 7 ones. The missing part is 2 hundreds = 200. Answer: 200."} {"t":"s","id":8655,"s":"8 x 20c = 160c. 7 x 50c = 350c. Total = 160 + 350 = 510c = $5.10. Answer: $5.10."} {"t":"s","id":8656,"s":"The pattern increases by 40 each time (3448, 3488, 3528, 3568...). Next terms: 3568 + 40 = 3608, then 3608 + 40 = 3648 (and 3648 + 40 = 3688, which matches). Answer: 3608, 3648."} {"t":"s","id":8657,"s":"The other number = 3480 - 1207 = 2273. Difference = 2273 - 1207 = 1066. Answer: 1066."} {"t":"s","id":8658,"s":"Decreasing order means largest to smallest. Compare digit by digit: 4890 > 4098 > 4089. Answer: 4890, 4098, 4089."} {"t":"s","id":8659,"s":"5999 + 201 = 6200. Answer: 6200."} {"t":"s","id":8663,"s":"Larger number = 257 + 198 = 455. Sum = 257 + 455 = 712. Answer: 712."} {"t":"s","id":8664,"s":"Coin pouch = $85.20 - $24.80 = $60.40. Total = $85.20 + $60.40 = $145.60. Answer: $145.60."} {"t":"s","id":8665,"s":"Usual cost of 2 watches = $176.20 + $176.20 = $352.40. Saving = $352.40 - $305.50 = $46.90. Answer: $46.90."} {"t":"s","id":8666,"s":"6 x 9 = 54 and 6 x 7 = 42. The difference is 54 - 42 = 12. So 6 x 9 is 12 more than 6 x 7."} {"t":"s","id":8668,"s":"Apples left after throwing away rotten ones: 168 - 24 = 144. Bags of 3 apples: 144 \/ 3 = 48 bags."} {"t":"s","id":8669,"s":"Bruce collected 375 points. Samad collected 3 x 375 = 1125 points. Altogether: 1125 + 375 = 1500 points."} {"t":"s","id":8670,"s":"20 mangoes make 20 \/ 4 = 5 bags. Each bag costs $7, so 5 x $7 = $35."} {"t":"s","id":8671,"s":"92 \/ 8 = 11 remainder 4. The quotient is the whole-number result, so the quotient is 11."} {"t":"s","id":8674,"s":"Total money = 3 x $120 = $360. Cost of each monster truck = $360 \/ 5 = $72."} {"t":"s","id":8676,"s":"Liam made 15. Daniel made 2 x 15 = 30. Clyde made 7 x 30 = 210 paper cranes."} {"t":"s","id":8678,"s":"Five thousand = 5000, eight hundred = 800, nine = 9. Combine: 5000 + 800 + 9 = 5809."} {"t":"s","id":8682,"s":"Expanded form: 6795 = 6000 + 700 + 90 + 5. The missing value is the hundreds part, 700."} {"t":"s","id":8685,"s":"(a) 4050 and 4005 share thousands and hundreds; compare tens: 5 tens > 0 tens, so 4050 > 4005. (b) 8430 and 8340 share thousands; compare hundreds: 4 > 3, so 8430 > 8340."} {"t":"s","id":8686,"s":"The numbers increase by 100 each step: 1754, 1854, 1954, ... So the missing term is 1954 + 100 = 2054 (and 2054 + 100 = 2154 confirms)."} {"t":"s","id":8688,"s":"Decreasing order = largest to smallest. Compare: 7393 (7 thousands) is largest. Then 3937 vs 3793 share 3 thousands; compare hundreds 9 > 7, so 3937 > 3793. Order: 7393, 3937, 3793."} {"t":"s","id":8690,"s":"(a) Number of boxes = 42 \u00f7 6 = 7 boxes. (b) Money collected = 7 boxes x $8 = $56."} {"t":"s","id":8691,"s":"Rope B = 72 \u00f7 8 = 9 m. Total = Rope A + Rope B = 72 + 9 = 81 m."} {"t":"s","id":8693,"s":"Multiply: 102 \u00d7 4 = 408. (100 \u00d7 4 = 400, 2 \u00d7 4 = 8, 400 + 8 = 408.)"} {"t":"s","id":8694,"s":"Divide: 96 \u00f7 6 = 16. (60 \u00f7 6 = 10, 36 \u00f7 6 = 6, 10 + 6 = 16.)"} {"t":"s","id":8696,"s":"Perpendicular lines meet at a right angle (90\u00b0). The letter L is made of a vertical and a horizontal line that meet at a right angle, so L has a pair of perpendicular lines."} {"t":"s","id":8700,"s":"Equal sharing: 48 \u00f7 8 = 6. There were 6 pens in each box."} {"t":"s","id":8701,"s":"Product means multiply: 205 \u00d7 9 = 1845. (200 \u00d7 9 = 1800, 5 \u00d7 9 = 45, 1800 + 45 = 1845.)"} {"t":"s","id":8702,"s":"Henry has 5 times Gina's amount, so Gina = 125 \u00f7 5 = 25. Gina collected 25 coins."} {"t":"s","id":8704,"s":"Red beads = 1263 + 200 = 1463. Altogether = yellow + red = 1263 + 1463 = 2726 beads."} {"t":"s","id":8708,"s":"2 watches cost $102, and 3 necklaces cost as much as 2 watches, so 3 necklaces = $102. One necklace = 102 \u00f7 3 = $34."} {"t":"s","id":8711,"s":"The digit 0 is in the tens place but as a digit it contributes 0 tens. Value = 0 \u00d7 10 = 0. Answer: 0."} {"t":"s","id":8715,"s":"1 h = 60 min, so 2 h = 120 min. 120 + 14 = 134 min."} {"t":"s","id":8718,"s":"3189 expanded = 3000 + 100 + 80 + 9. The missing part is the hundreds: 100."} {"t":"s","id":8719,"s":"Reading place values from the right: 3 ones, 2 tens, 7 hundreds, 9 thousands. The thousands digit is 9."} {"t":"s","id":8721,"s":"Compare thousands first, then hundreds. Smallest to largest: 2800, 7028, 7820, 8270."} {"t":"s","id":8722,"s":"Unit fractions: the smaller the denominator, the larger the fraction. Greatest to smallest: 1\/3, 1\/5, 1\/7, 1\/10."} {"t":"s","id":8725,"s":"Even means last digit 0,2,4,6,8. 3727 is odd; 2676 (<2700) is out of range; 4702 (>4700) is out of range; 3378 is even and 2700 < 3378 < 4700. Answer: 3378."} {"t":"s","id":8726,"s":"The pattern alternates +1000 then +100: 625(+1000)1625(+100)1725(+1000)2725(+100)2825(+1000)3825(+100)3925(+1000)4925(+100)5025(+1000)6025. (a) 2725, (b) 5025."} {"t":"s","id":8727,"s":"Total stickers = 17 + 19 = 36. Shared equally into 4 packets: 36 \u00f7 4 = 9 per packet."} {"t":"s","id":8728,"s":"Saturday = 280 \u2212 50 = 230. Total = 280 + 230 = 510 cupcakes."} {"t":"s","id":8729,"s":"Andy = 2378 + 1251 = 3629. Andy is 755 fewer than Bernard, so Bernard = 3629 + 755 = 4384."} {"t":"s","id":8730,"s":"Method: find what 9 was multiplied by to get 72. 72 \/ 9 = 8, so multiply the numerator by 8 too: 5 x 8 = 40. The missing numerator is 40."} {"t":"s","id":8738,"s":"Convert to compare: 3\/7 is about 0.43, 1\/2 = 0.50, 7\/12 is about 0.58. Smallest to largest: 3\/7, 1\/2, 7\/12."} {"t":"s","id":8740,"s":"Money left = 3\/10, so money spent = 1 - 3\/10 = 7\/10. The cake took 1\/5 = 2\/10. Cookie = total spent - cake = 7\/10 - 2\/10 = 5\/10 = 1\/2."} {"t":"s","id":8742,"s":"(a) Each bag has 4 pens and there are 144 pens, so number of bags = 144 \/ 4 = 36. (b) Each bag has 7 stickers, so total stickers = 36 x 7 = 252."} {"t":"s","id":8743,"s":"Work backwards. Before buying 1386: 2953 - 1386 = 1567 flags. That 1567 was after giving out 378, so at first = 1567 + 378 = 1945 flags."} {"t":"s","id":8748,"s":"As decimals: 1\/2 = 0.5, 3\/8 = 0.375, 7\/9 \u2248 0.78. Greatest to smallest: 7\/9, 1\/2, 3\/8."} {"t":"s","id":8753,"s":"Whole = 1. Eaten = 1\/8 + 1\/4 = 1\/8 + 2\/8 = 3\/8. Left = 1 \u2212 3\/8 = 5\/8."} {"t":"s","id":8754,"s":"Missing = 2\/5 \u2212 1\/10. Convert: 2\/5 = 4\/10, so 4\/10 \u2212 1\/10 = 3\/10."} {"t":"s","id":8755,"s":"Number of boxes = 174 \u00f7 6 = 29. Muffins = 29 \u00d7 3 = 87."} {"t":"s","id":8756,"s":"After the transfer the difference grew by 87 twice: difference = 278 + 87 + 87 = 452. Marvin is 3 times Sally, so the difference is 2 units = 452, meaning 1 unit (Sally's cards in the end) = 452 \u00f7 2 = 226."} {"t":"s","id":8757,"s":"Read place values from the right: 6 ones, 5 tens, 7 hundreds, 9 thousands. The digit in the hundreds place is 7."} {"t":"s","id":8758,"s":"Add the expanded parts: 6000 + 700 + 4 = 6704. There are no tens, so the tens digit is 0."} {"t":"s","id":8760,"s":"4 thousands = 4000, 12 hundreds = 1200, 9 tens = 90, 6 ones = 6. Total = 4000 + 1200 + 90 + 6 = 5296."} {"t":"s","id":8761,"s":"The numbers go up alternately by 10 then 20: 2513 (+10) 2523 (+20) 2543 (+10) 2553 (+20) 2573 (+10) 2583 (+20) 2603. The next number is 2603."} {"t":"s","id":8763,"s":"Compare digit by digit from the thousands. All start with 1. Compare hundreds: 1049 and 1094 have 0; 1904 and 1940 have 9. Among 1049 and 1094, the tens decide: 1049 < 1094. Among 1904 and 1940: 1904 < 1940. Increasing order: 1049, 1094, 1904, 1940."} {"t":"s","id":8766,"s":"At first money = total spent + money left. Spent = $19.90 + $8.50 = $28.40. Add the $4 left: $28.40 + $4 = $32.40."} {"t":"s","id":8767,"s":"Number of brownies = 1450 - 794 = 656. More scouts than brownies = 794 - 656 = 138."} {"t":"s","id":8768,"s":"6 fours means six groups of 4, which is repeated addition: 4 + 4 + 4 + 4 + 4 + 4 (six 4s). Answer: 4 + 4 + 4 + 4 + 4 + 4."} {"t":"s","id":8769,"s":"5 x 7 = 35. 35 - 14 = 21. 21 = 3 x 7. Answer: 3 x 7."} {"t":"s","id":8770,"s":"Number of pieces = total length divided by piece length = 420 cm \u00f7 7 cm = 60 pieces. Answer: 60."} {"t":"s","id":8771,"s":"65 \u00f7 9 = 7 remainder 2. Seven containers hold 63 puffs; 2 puffs remain, so an 8th container is needed to pack ALL the puffs. Answer: 8."} {"t":"s","id":8774,"s":"803 \u00f7 5: 5 goes into 8 once (5), remainder 3; bring down 0 \u2192 30 \u00f7 5 = 6; bring down 3 \u2192 3 \u00f7 5 = 0 remainder 3. Quotient = 160, Remainder = 3. Check: 160 x 5 + 3 = 803."} {"t":"s","id":8775,"s":"Candies given to children = 6 x 8 = 48. Add the 4 he kept: 48 + 4 = 52. Answer: 52."} {"t":"s","id":8777,"s":"Per the answer key, 580 represents the weekend (two-day) total split with 168 fewer on Sunday: 420 \u00f7 2 = 206, so 206 people visited on Sunday. Answer: 206."} {"t":"s","id":8778,"s":"Total units = Charlie (1) + Augustus (5) = 6 units = 90 planes, so 1 unit = 90 \u00f7 6 = 15 (Charlie). Augustus has 5 units = 75. Difference = Augustus - Charlie = 4 units = 15 x 4 = 60. Answer: 60."} {"t":"s","id":8779,"s":"Decreasing order means largest first. Compare the thousands digit: 9452 and 9254 both start with 9, while 5924 starts with 5. Between 9452 and 9254, the hundreds digit 4 > 2, so 9452 > 9254. Order: 9452, 9254, 5924. Answer: option 4."} {"t":"s","id":8780,"s":"Add: 3876 + 4149. 6+9=15 (write 5, carry 1); 7+4+1=12 (write 2, carry 1); 8+1+1=10 (write 0, carry 1); 3+4+1=8. Sum = 8025. Answer: option 1."} {"t":"s","id":8782,"s":"(a) Four thousand = 4000, and nine = 9, so four thousand and nine = 4009. (b) For the smallest 4-digit even number, the last digit must be even (0 or 4). Use the smallest non-zero digit, 3, in the thousands place, then 0 in the hundreds. With 4 and 7 left, place them so the last digit is even: 3074 (even). 3074 is smaller than 3704. Answer: 3074."} {"t":"s","id":8783,"s":"The pattern increases by 25 each step (1105, 1130, 1155, 1180 differ by 25). The missing number = 1055 + 25 = 1080."} {"t":"s","id":8785,"s":"Total spent = $24 + $0.35 = $24.35. Change = $50 - $24.35 = $25.65. (Equivalently $50 - $24 = $26, then $26 - $0.35 = $25.65.)"} {"t":"s","id":8786,"s":"List the pairs: red-blue, red-yellow, red-purple (3); blue-yellow, blue-purple (2); yellow-purple (1). Total = 3 + 2 + 1 = 6 ways."} {"t":"s","id":8787,"s":"(a) Smaller number = greater number - difference = 1184 - 250 = 934. (b) Sum = 934 + 1184 = 2118."} {"t":"s","id":8788,"s":"In 5421 the digit 4 is in the hundreds place. Its value = 4 \u00d7 100 = 400."} {"t":"s","id":8789,"s":"Compare from the highest place value. All share 3 thousands. Tens\/ones: 3019 < 3109 < 3190. Increasing order: 3019, 3109, 3190."} {"t":"s","id":8790,"s":"Six thousand = 6000, forty-five = 45. 6000 + 45 = 6045."} {"t":"s","id":8792,"s":"2 thousands = 2000. 7580 + 2000 = 9580."} {"t":"s","id":8793,"s":"Each term decreases by 25 (8095, 8070, 8045, 8020...). 8020 \u2212 25 = 7995. Check: 7995 \u2212 25 = 7970."} {"t":"s","id":8794,"s":"8765 = 8000 + 700 + 60 + 5. So the missing part is 700 + 60 = 760."} {"t":"s","id":8795,"s":"419 \u00f7 9 = 46 with a remainder. 46 \u00d7 9 = 414, and 419 \u2212 414 = 5. Remainder = 5."} {"t":"s","id":8797,"s":"Red beads = 3 \u00d7 38 = 114. Altogether = blue + red = 38 + 114 = 152."} {"t":"s","id":8799,"s":"Sunday = 3684 \u2212 473 = 3211. Altogether = 3684 + 3211 = 6895."} {"t":"s","id":8800,"s":"Number of boxes = 96 \u00f7 4 = 24. Amount collected = 24 \u00d7 $8 = $192."} {"t":"s","id":8801,"s":"In 6420, reading place values from the right: 0 ones, 2 tens, 4 hundreds, 6 thousands. So the digit 2 is in the tens place."} {"t":"s","id":8802,"s":"Add: 3253 + 769. 3 + 9 = 12 (carry 1), 5 + 6 + 1 = 12 (carry 1), 2 + 7 + 1 = 10 (carry 1), 3 + 1 = 4. Sum = 4022."} {"t":"s","id":8804,"s":"Find the number that divides 45 to give 9. Since 9 x 5 = 45, the missing number is 5. So 45 \u00f7 5 = 9."} {"t":"s","id":8806,"s":"The pattern decreases by 100 each step: 6304, 6204, 6104, so the next term is 6104 - 100 = 6004, and then 5904. The missing number is 6004."} {"t":"s","id":8807,"s":"Compare the numbers by place value. All start with 2 thousands. Hundreds: 2163 and 2196 have 1; 2399 has 3; 2623 has 6. Between 2163 and 2196, the tens digit 6 < 9. Order smallest to largest: 2163, 2196, 2399, 2623."} {"t":"s","id":8808,"s":"Subtract with regrouping: 4326 \u2212 3547. 6 \u2212 7 needs borrowing: 16 \u2212 7 = 9; then 1 \u2212 4 needs borrowing: 11 \u2212 4 = 7; then 2 \u2212 5 needs borrowing: 12 \u2212 5 = 7; then 3 \u2212 3 = 0. Result = 779."} {"t":"s","id":8812,"s":"Subtract the number of girls from the number of boys: 834 \u2212 786 = 48. There are 48 more boys than girls."} {"t":"s","id":8813,"s":"Add the number of boys and girls: 834 + 786 = 1620. There are 1620 children altogether."} {"t":"s","id":8817,"s":"Afternoon = 568 + 697 = 1265. Total = morning + afternoon = 568 + 1265 = 1833 apples."} {"t":"s","id":8818,"s":"9048 = 9 thousands, 0 hundreds, 4 tens, 8 ones. In words: nine thousand and forty-eight."} {"t":"s","id":8819,"s":"Compare by place value (all are 3 thousands). Order the hundreds\/tens: 3045 < 3405 < 3450 < 3504."} {"t":"s","id":8820,"s":"The pattern decreases by 100 each step: 1037, 937, 837, 737, 637. Missing number = 1037 - 100 = 937."} {"t":"s","id":8822,"s":"5396 = 5000 + 300 + 90 + 6. The hundreds, 300, equals 30 tens. So the blank is 30."} {"t":"s","id":8825,"s":"1 hour = 60 min, so 2 hours = 2 x 60 = 120 min. Add the 20 min: 120 + 20 = 140 min."} {"t":"s","id":8829,"s":"From 2.50 p.m. to 3.50 p.m. is 1 hour. From 3.50 p.m. to 4.25 p.m. is 35 min. Total = 1 h 35 min."} {"t":"s","id":8830,"s":"Tuna = 1374 - 235 = 1139. Altogether = ham + tuna = 1374 + 1139 = 2513. (Equivalently 1374 x 2 - 235 = 2513.)"} {"t":"s","id":8831,"s":"Ali = 3. Bala = 6 x 3 = 18. Cai Li = 18 - 5 = 13. Total = 3 + 18 + 13 = 34."} {"t":"s","id":8832,"s":"Remove the 6-year difference from the total: 54 - 6 = 48 is twice Lee Ying's age, so Lee Ying = 48 \/ 2 = 24. Malik is 6 years older: 24 + 6 = 30."} {"t":"s","id":8836,"s":"A fraction exceeds 1\/2 when the numerator is more than half the denominator. 5\/9 > 4.5\/9 = 1\/2. The others are 1\/2 or less (2\/5, 3\/7 less; 4\/8 equals 1\/2). Answer key: 4."} {"t":"s","id":8837,"s":"1 - 6\/10 = 4\/10 = 2\/5. So the missing fraction is 2\/5. Answer key: 1."} {"t":"s","id":8838,"s":"For unit-type fractions with equal numerator, the smaller denominator is the larger fraction, so 1\/8 > 1\/11 is true. 2\/9 < 5\/9; 5\/6 > 2\/3; 3\/4 = 9\/12 not 6\/12. Answer key: 3."} {"t":"s","id":8841,"s":"Convert to a common denominator (40): 3\/8 = 15\/40, 1\/4 = 10\/40, 5\/10 = 20\/40. Greatest to least: 5\/10, 3\/8, 1\/4. Answer key: 5\/10, 3\/8, 1\/4."} {"t":"s","id":8843,"s":"3 tables cost 3 x $90 = $270. This equals the cost of 5 chairs, so 1 chair = $270 \/ 5 = $54. Answer key: $54."} {"t":"s","id":8844,"s":"Let Ming = 1 unit. Crystal = 2 units, Rahim = 3 x Crystal = 6 units. Rahim - Crystal = 6u - 2u = 4u = 320, so 1u = 80. Total = 1u + 2u + 6u = 9u = 9 x 80 = 720. Answer key: 720."} {"t":"s","id":8845,"s":"Almond powder = 120 g - 25 g = 95 g. Flour = 4 x 95 g = 380 g. Answer key: 380 g."} {"t":"s","id":8846,"s":"Make the denominators the same: 2\/3 = 6\/9. Then 2\/9 + 6\/9 = 8\/9."} {"t":"s","id":8847,"s":"Make the denominators the same: 1\/2 = 4\/8. Then 4\/8 - 3\/8 = 1\/8."} {"t":"s","id":8849,"s":"(a) 6 kg = 6000 g, so 6 kg 50 g = 6000 + 50 = 6050 g. (b) 1 m = 100 cm, so 4028 cm = 40 m 28 cm (4000 cm = 40 m, remainder 28 cm)."} {"t":"s","id":8852,"s":"Compare as decimals: 7\/12 is about 0.58, 2\/7 is about 0.29, 2\/5 = 0.4. Smallest to greatest: 2\/7, 2\/5, 7\/12."} {"t":"s","id":8856,"s":"5 km = 5000 m. Walked = 5000 - 3450 = 1550 m. Convert: 1550 m = 1 km 550 m."} {"t":"s","id":8857,"s":"(a) Celia = 546 \/ 3 = 182 stickers. (b) Before giving, Emma had 148 - 80 = 68. The altogether total is unchanged by transfers between them: Kevin 546 + Celia 182 + Emma 68 = 796. (Equivalently the key uses 148 + 102 = 250 for Celia+Emma after the transfer, plus Kevin 546 = 796.)"} {"t":"s","id":8859,"s":"Milk poured out = 220 ml x 5 = 1100 ml. Jug had 3 l = 3000 ml. Left = 3000 - 1100 = 1900 ml = 1 l 900 ml."} {"t":"s","id":8862,"s":"Simplify each: 6\/12 = 1\/2, 2\/10 = 1\/5, 3\/6 = 1\/2, 4\/8 = 1\/2. Only 2\/10 is not equal to 1\/2. Answer: 2\/10."} {"t":"s","id":8866,"s":"Convert to compare: 1\/3 = 0.333, 2\/9 = 0.222, 2\/11 = 0.182. For 2\/9 and 2\/11 the numerators are equal, so the larger denominator (11) gives the smaller fraction. Greatest to smallest: 1\/3, 2\/9, 2\/11."} {"t":"s","id":8867,"s":"(a) 3\/4 - 3\/8 = 6\/8 - 3\/8 = 3\/8. (b) 1\/2 + 1\/10 = 5\/10 + 1\/10 = 6\/10 = 3\/5."} {"t":"s","id":8868,"s":"Library to school = 840 + 220 = 1060 m. Total walked = 840 + 1060 = 1900 m = 1 km 900 m."} {"t":"s","id":8870,"s":"Three thousand = 3000, twenty-five = 25. 3000 + 25 = 3025."} {"t":"s","id":8877,"s":"194 \u00f7 7: 7 \u00d7 27 = 189, and 194 \u2212 189 = 5. So quotient = 27, remainder = 5."} {"t":"s","id":8881,"s":"Stickers packed = 8 \u00d7 436 = 3488. At first = 3488 + 84 = 3572 stickers."} {"t":"s","id":8882,"s":"Shop B = 2523 + 342 = 2865. Shop C = 2865 \u2212 485 = 2380 bowls."} {"t":"s","id":8886,"s":"Multiply numerator and denominator of 1\/4 by the same number to find equivalents. 1\/4 = 5\/20 (both x5). Check others: 2\/4 = 1\/2, 2\/12 = 1\/6, 3\/16 is not 1\/4. Answer: 5\/20 (option 4)."} {"t":"s","id":8888,"s":"Convert to a common denominator of 12: 3\/4 = 9\/12, 7\/12 = 7\/12, 2\/3 = 8\/12. Ordering the twelfths from smallest: 7\/12, 8\/12, 9\/12. So smallest to largest is 7\/12, 2\/3, 3\/4."} {"t":"s","id":8892,"s":"Make the denominators the same: 1\/5 = 2\/10. Then 2\/10 + 3\/10 = 5\/10. Simplify 5\/10 by dividing top and bottom by 5 to get 1\/2."} {"t":"s","id":8897,"s":"Multiply 4 by 8. 4 \u00d7 8 = 32. The answer is 32."} {"t":"s","id":8898,"s":"Multiply boxes by apples per box. 4 \u00d7 7 = 28. Kenny bought 28 apples."} {"t":"s","id":8899,"s":"Divide 79 by 6. 79 \u00f7 6 = 13 remainder 1, since 6 \u00d7 13 = 78 and 79 \u2212 78 = 1. So 1 cookie was left."} {"t":"s","id":8902,"s":"Find the length of the 6 cut pieces, then add the leftover. 6 \u00d7 9 = 54 cm. 54 + 16 = 70 cm. The roll was 70 cm long."} {"t":"s","id":8903,"s":"Multiply the cost of one packet by the number of packets. 5 \u00d7 $7 = $35. The 5 packets cost $35."} {"t":"s","id":8904,"s":"Divide the total oranges by the number of boxes. 72 \u00f7 8 = 9. Each box has 9 oranges."} {"t":"s","id":8905,"s":"Divide 426 by 9 using long division. 9 \u00d7 47 = 423, and 426 \u2212 423 = 3. So the quotient is 47 and the remainder is 3."} {"t":"s","id":8906,"s":"Multiply 258 by 6 using the multiplication algorithm. 258 \u00d7 6 = 1548 (8\u00d76=48 carry 4; 5\u00d76=30+4=34 carry 3; 2\u00d76=12+3=15). The product is 1548."} {"t":"s","id":8907,"s":"They start equal, so the difference is 0. Annie's share drops by 12 and Caili's rises by 28, so the gap grows by 12 + 28 = 40. Caili has 40 more stickers than Annie."} {"t":"s","id":8909,"s":"(a) Mr Lim ends with 150 + 30 = 180 stamps. This is 4 times Mr Tan's, so Mr Tan = 180 \u00f7 4 = 45 stamps. (b) Altogether = 180 + 45 = 225 stamps."} {"t":"s","id":8910,"s":"(a) When Amin gives $7 to Bala, the gap closes by 2 \u00d7 $7 = $14, so 49 \u2212 14 = $35 more. (b) Bala ends with $55, so Amin ends with 55 + 35 = $90. Altogether = 90 + 55 = $145."} {"t":"s","id":8912,"s":"For unit fractions (numerator 1), the larger the denominator, the smaller the fraction. Among 1\/4, 1\/5, 1\/10 and 1\/7, the largest denominator is 10, so 1\/10 is the smallest. Answer: 1\/10."} {"t":"s","id":8913,"s":"Make the denominators the same. 1\/3 = 4\/12. Then 1\/12 + 4\/12 = 5\/12. Answer: 5\/12."} {"t":"s","id":8919,"s":"Compare each to 1\/2. 3\/5 = 0.6 (greater than 1\/2). 1\/2 = 0.5. 5\/11 is just under 0.5 (5.5\/11 would be 1\/2). So greatest to smallest: 3\/5, 1\/2, 5\/11."} {"t":"s","id":8921,"s":"(a) Tuesday = 1200 + 200 = 1400 g. Both days = 1200 + 1400 = 2600 g. (b) Wednesday = 300 x 8 = 2400 g. Monday to Wednesday = 2600 + 2400 = 5000 g."} {"t":"s","id":8922,"s":"(a) Total muffins = 104 + 128 = 232. Bags = 232 \/ 6 = 38 remainder 4, so at most 38 full bags. (b) 38 x $9 = $342."} {"t":"s","id":8923,"s":"Bernard = 300 - 40 = 260. Chandra = 260 x 4 = 1040. (a) Chandra - Bernard = 1040 - 260 = 780 more. (b) Total = 300 + 260 + 1040 = 1600."} {"t":"s","id":8924,"s":"9 hundreds = 900. 900 \u00d7 4 = 3600. The answer is 3600."} {"t":"s","id":8930,"s":"Rope A = 5 units, Rope B = 1 unit. The difference is 5 \u2212 1 = 4 units = 32 cm, so 1 unit = 8 cm. Rope A = 5 \u00d7 8 = 40 cm."} {"t":"s","id":8933,"s":"The larger number = 400 \u2212 120 = 280. The difference = 280 \u2212 120 = 160."} {"t":"s","id":8936,"s":"103 \u00f7 8 = 12 remainder 7. The 12 full boxes hold 96 cupcakes, leaving 7 cupcakes that still need 1 more box. So 12 + 1 = 13 boxes."} {"t":"s","id":8937,"s":"Tim saves 4 \u00d7 $96 = $384 each month. In 5 months he saves $384 \u00d7 5 = $1920."} {"t":"s","id":8940,"s":"Number of bags = 60 buns \u00f7 4 buns per bag = 15 bags. Sweets = 15 bags \u00d7 7 sweets = 105 sweets."} {"t":"s","id":8941,"s":"After Ali buys 27 stamps, Weiming has 6 times Ali's amount, so the difference (5 units) equals the new gap. Original gap was 472; after Ali adds 27, the gap is 472 \u2212 27 = 445 = 5 units. Ali (1 unit) = 445 \u00f7 5 = 89 stamps in the end. Weiming = 89 \u00d7 6 = 534 stamps."} {"t":"s","id":8943,"s":"The five volunteers are Zoe, Kai, Maya, Talib and Yongli. Zoe is one member of the pair, so the partner can be any of the other four students. Therefore Zoe can pair with Kai, Maya, Talib and Yongli (4 students)."} {"t":"s","id":8944,"s":"List pairs systematically without repeating: Zoe with Kai, Maya, Talib, Yongli (4); Kai with Maya, Talib, Yongli (3); Maya with Talib, Yongli (2); Talib with Yongli (1). Total = 4 + 3 + 2 + 1 = 10 different teams."} {"t":"s","id":8946,"s":"Compare digit by digit from the left. 87 431 and 87 341 both start with 87; 87 431 has 4 hundreds vs 3 hundreds, so 87 431 is the greatest."} {"t":"s","id":8947,"s":"Round each to the nearest hundred: 6138->6100, 6087->6100, 5986->6000, 5092->5100. Only 5986 rounds to 6000."} {"t":"s","id":8948,"s":"Common factors of 18 and 36 are 1, 2, 3, 6, 9, 18. 36 is a factor of 36 but not of 18, so 36 is not a common factor."} {"t":"s","id":8950,"s":"Stickers per hour = 7680 \/ 6 = 1280. In 4 hours = 1280 x 4 = 5120."} {"t":"s","id":8951,"s":"Make the denominators the same: 1\/4 = 3\/12. Then 5\/12 + 3\/12 = 8\/12."} {"t":"s","id":8952,"s":"A multiple of both 4 and 6 must be a multiple of 12. 36 = 12 x 3 is divisible by both 4 and 6. 46, 28, 16 are not."} {"t":"s","id":8956,"s":"Length + breadth = 108 \/ 2 = 54 cm. Since length = breadth + 12, then 2 x breadth + 12 = 54, so 2 x breadth = 42, breadth = 21 cm."} {"t":"s","id":8961,"s":"Ninety-seven thousand = 97 000, and two = 2. Together: 97 002."} {"t":"s","id":8962,"s":"Ascending = smallest to largest. Compare by place value: 2789 < 2798 < 2879 < 2897."} {"t":"s","id":8963,"s":"3 = 24\/8. Then 24\/8 - 3\/8 = 21\/8 (or 2 5\/8)."} {"t":"s","id":8966,"s":"Common multiples of 6 and 9 are multiples of 18: 18, 36, 54... The only one between 28 and 40 is 36."} {"t":"s","id":8968,"s":"Convert to a common comparison: 7\/10 = 0.70, 2\/5 = 0.40, 3\/8 = 0.375. Greatest to smallest: 7\/10, 2\/5, 3\/8."} {"t":"s","id":8969,"s":"1 marker = 2 pencils. So 2 markers = 4 pencils. Total in pencil-units = 5 + 4 = 9 pencils = $27, so 1 pencil = $27 \/ 9 = $3. A marker = 2 x $3 = $6."} {"t":"s","id":8970,"s":"4 = 40 tenths. 40 tenths + 9 tenths = 49 tenths."} {"t":"s","id":8974,"s":"Factors of 27 are 1, 3, 9, 27. Besides 1 and 27, the other two are 3 and 9."} {"t":"s","id":8977,"s":"3\/8 = 24, so 1\/8 = 24 \/ 3 = 8. The whole (8\/8) = 8 x 8 = 64 magnets."} {"t":"s","id":8980,"s":"Stamps given away = 2776 - 368 = 2408. Number of friends = 2408 \/ 8 = 301."} {"t":"s","id":8981,"s":"Steve walked 3\/4 + 1\/3 km. Total of both = 3\/4 + (3\/4 + 1\/3) = 3\/4 + 3\/4 + 1\/3. Using the key's method: 3\/4 + 3\/4 = 1 1\/2; 1 1\/2 + 1\/3 = 1 5\/6 km."} {"t":"s","id":8983,"s":"Both started equal. The difference between what they spent = 156 - 12 = 144, which equals the difference in money left (3 units, since John has 4 units and Peter 1 unit). So 3 units = 144, 1 unit = 48 (Peter's remainder). John at first = Peter's start = 48 + 156 = $204."} {"t":"s","id":8984,"s":"Using the key's method: 374 - 108 = 266 (total left plus the sold pens accounted as units). 266 \/ 7 = 38 (one unit, where pens = 4 units and pencils-side gives 3 units after removing 108). Pens at first = 38 x 4 = 152."} {"t":"s","id":8985,"s":"The 12 extra 3-child friends bring 12 x 3 = 36 children. Remaining children = 91 - 36 = 55, shared by equal numbers of 2-child and 3-child friends (5 children per matched pair). 55 \/ 5 = 11 friends in each group. Friends who brought 3 children = 11 + 12 = 23."} {"t":"s","id":8987,"s":"Increase in fraction = 7\/12 - 1\/4 = 7\/12 - 3\/12 = 4\/12 = 1\/3 of the bottle. This 1\/3 equals 800 ml... using the key's method: 800 \/ 4 = 200 ml per twelfth; capacity = 200 x 12 = 2400 ml."} {"t":"s","id":8989,"s":"2 ten thousands = 20 000, 5 tens = 50, 8 ones = 8. 20 000 + 50 + 8 = 20 058."} {"t":"s","id":8990,"s":"87 326: from the right the places are ones (6), tens (2), hundreds (3), thousands (7), ten thousands (8). The thousands digit is 7."} {"t":"s","id":8993,"s":"Factors of 28: 1,2,4,7,14,28. Factors of 72: 1,2,3,4,6,8,9,12,18,24,36,72. Common to both is 4."} {"t":"s","id":8996,"s":"A complete turn is 360 degrees. 3\/4 of 360 = 270 degrees."} {"t":"s","id":8997,"s":"A multiple of 4 divides exactly by 4. 36 \/ 4 = 9, so 36 is a multiple of 4. 14, 2 and 26 are not."} {"t":"s","id":9004,"s":"5209 \/ 4 = 1302 remainder 1. To have at least 5209 erasers she must round up to 1303 packets."} {"t":"s","id":9005,"s":"3 units = 7950, so 1 unit = 2650. James = 2650, Peter = 5300. Equal share = 3975 each. Peter gives 5300 - 3975 = 1325."} {"t":"s","id":9008,"s":"Thirty thousand = 30 000, two hundred = 200, one = 1. Together: 30 201."} {"t":"s","id":9009,"s":"For the smallest number, arrange digits ascending: 1 3 4 5 8. For odd, the last digit must be odd. Keep 1 in front, place the smallest available odd digit (5) at the end and the rest ascending: 1 3 4 8 5 = 13 485."} {"t":"s","id":9010,"s":"The pattern decreases by 100 each step. 21 040 - 100 = 20 940."} {"t":"s","id":9011,"s":"The tens digit is 7 (5 or more), so round the hundreds up. 25 675 rounds to 25 700."} {"t":"s","id":9013,"s":"Factors of 32 are 1, 2, 4, 8, 16, 32. The two not already listed are 4 and 16."} {"t":"s","id":9014,"s":"Compare digit by digit. 62 850 > 62 805 > 62 085. Greatest to smallest: 62 850, 62 805, 62 085."} {"t":"s","id":9017,"s":"Common multiples of 3 and 5 between 10 and 35 are 15 and 30. Of these, 30 has 6 as a factor (6 x 5 = 30). So the number is 30."} {"t":"s","id":9018,"s":"Let a fan = 1 unit, an air purifier = 3 units. 2 purifiers + 3 fans = 6 units + 3 units = 9 units = $1620. 1 unit = 1620 \/ 9 = $180. Each fan costs $180."} {"t":"s","id":9019,"s":"Both turn red together every LCM(2,3) = 6 minutes. From 8.00 to 8.35 they coincide at 8.06, 8.12, 8.18, 8.24 and 8.30 p.m. = 5 times."} {"t":"s","id":9025,"s":"Boys at end = 20, so boys at start = 20 + 15 = 35. Girls at start = boys at start = 35 (equal). Girls at end = 35 + 10 = 45. Total at end = 20 boys + 45 girls = 65."} {"t":"s","id":9026,"s":"After Kayla uses 78, Janet = Kayla(new) x 3. Janet was 680 more than Kayla's original = Kayla(new) + 78 + 680 = Kayla(new) + 758. So 3 x Kayla(new) = Kayla(new) + 758, giving 2 units = 758, 1 unit = 379. Kayla at first = 379 + 78 = 457."} {"t":"s","id":9027,"s":"Remaining = 3700 - 300 + 150 = 3550. Each box = 3550 \/ 5 = 710 marbles."} {"t":"s","id":9028,"s":"Total spent = 2800 - 43 = 2757. Table = 4 chairs + 821. So 2 x (4 chairs) + 821 = 2757, 8 chairs = 2757 - 821 = 1936, each chair = 1936 \/ 8 = $242."} {"t":"s","id":9029,"s":"Grapes = 4450 - 3770 = 680 g. Durian = 4 x 680 = 2720 g. Basket = 3770 - durian = 3770 - 2720 = 1050 g."} {"t":"s","id":9030,"s":"Alice + Betty = 1 unit, Clara = 2 units, so 3 units = 2400, 1 unit = 800 = Alice + Betty. Alice + (Alice + 20) = 800, 2 Alice = 780, Alice = 390, Betty = 390 + 20 = 410."} {"t":"s","id":9038,"s":"5 l 20 ml = 5020 ml. Water needed = 5020 - 340 = 4680 ml."} {"t":"s","id":9039,"s":"Morning: 10.45 a.m. to 1 p.m. = 2 h 15 min. After the 1-hour break: 2 p.m. to 3.30 p.m. = 1 h 30 min. Total work = 2 h 15 min + 1 h 30 min = 3 h 45 min."} {"t":"s","id":9042,"s":"65 thousands = 65 000 and 49 tens = 490. Sum = 65 000 + 490 = 65 490."} {"t":"s","id":9043,"s":"The numbers increase by 23 each time (3263 - 3240 = 23). 3286 + 23 = 3309."} {"t":"s","id":9044,"s":"Multiples of 6: 6, 12, 18, 24... Multiples of 8: 8, 16, 24... The first common multiple is 24."} {"t":"s","id":9047,"s":"Use tenths: 1\/5 = 2\/10, 2\/5 = 4\/10. Sum = 2\/10 + 7\/10 + 4\/10 = 13\/10 = 1 3\/10."} {"t":"s","id":9051,"s":"Factors of 42 between 14 and 27: 21. 21 is also a multiple of 3 (42 = 2 x 21). So the number is 21."} {"t":"s","id":9053,"s":"3 m = 21\/7 m. Left = 21\/7 - 2\/7 = 19\/7 = 2 5\/7 m."} {"t":"s","id":9054,"s":"Sold 1\/5, so 4\/5 remained = 304 apples. 1\/5 = 304 \/ 4 = 76. Total 5\/5 = 76 x 5 = 380 apples."} {"t":"s","id":9058,"s":"Subtract the duration from the arrival time: 4.05 p.m. - 5 h 15 min = 10.50 a.m."} {"t":"s","id":9061,"s":"Divisible by 5 means the last digit is 0 or 5; only 0 is available, so it ends in 0. Use the largest remaining digits in front: 9, 8, 3 give 9830."} {"t":"s","id":9063,"s":"Candies packed = 18 x 7 = 126. Left unpacked = 150 - 126 = 24."} {"t":"s","id":9064,"s":"(a) Chickens 1\/3 = 3\/9, cows 2\/9, so chickens + cows = 5\/9. Goats = 9\/9 - 5\/9 = 4\/9. (b) 4\/9 of the total = 116 goats, so 1\/9 = 116 \/ 4 = 29 and the total = 29 x 9 = 261 animals."} {"t":"s","id":9065,"s":"Ben = 5490 \/ 6 = 915. Ali = 915 + 1360 = 2275. Total = 5490 + 915 + 2275 = 8680 cookies."} {"t":"s","id":9066,"s":"(a) Blue = 5\/6 - 1\/4 = 10\/12 - 3\/12 = 7\/12 l. (b) Purple = red + blue = 10\/12 + 7\/12 = 17\/12 = 1 5\/12 l."} {"t":"s","id":9068,"s":"Let Matt = 1 unit. Nathan = 1 unit - 28, Larry = 4 units. Total = 6 units - 28 = 386, so 6 units = 414... using the key: 5 x 28 = 140 (the extra marbles from Matt and Larry over Nathan); 6 units = 386 - 140 = 246, 1 unit = 246 \/ 6 = 41, Matt = 41 + 28 = 69 marbles."} {"t":"s","id":9069,"s":"The 5 laptops cost 5 x $720 = $3600 more than 5 phones. Remove this: $12 200 - $3600 = $8600 for 8 equal phone-prices. 1 phone = $8600 \/ 8 = $1075."} {"t":"s","id":9072,"s":"Order from greatest to smallest: 4780, 4708, 4078. Compare hundreds and tens digits since thousands are equal. Option 2 lists them correctly."} {"t":"s","id":9074,"s":"Convert 4 5\/7 to an improper fraction: 4 x 7 + 5 = 33, giving 33\/7. So there are 33 sevenths."} {"t":"s","id":9075,"s":"Multiply numerator and denominator of 4\/9 by 9: (4x9)\/(9x9) = 36\/81. So 36\/81 is equivalent to 4\/9."} {"t":"s","id":9079,"s":"Factors of 24 are 1,2,3,4,6,8,12,24. Among the options, 12 is a factor of 24 and also a multiple of 4 (4x3=12). 6 is a factor but not a multiple of 4; 96 is a multiple of 4 but not a factor of 24."} {"t":"s","id":9080,"s":"Factors of 28: 1,2,4,7,14,28. All of these also divide 56, so the common factors are 1,2,4,7,14,28. Their sum is 1+2+4+7+14+28 = 56."} {"t":"s","id":9081,"s":"611 \/ 8 = 76 remainder 3. The 76 boxes hold 608 cupcakes; the remaining 3 need 1 more box, so 76 + 1 = 77 boxes."} {"t":"s","id":9083,"s":"From north-west, a clockwise turn reaches N, NE, ... ; an anti-clockwise turn reaches W (45), SW (90), S (135). So a 135 degrees anti-clockwise turn faces south."} {"t":"s","id":9086,"s":"Change = $20 - $17.80 = $2.20 = 220 cents. Each coin is 20 cents, so 220 \/ 20 = 11 coins."} {"t":"s","id":9088,"s":"The age gap stays 13 years. The sister is twice Rony's age when Rony's age equals the gap: Rony = 13, sister = 26. That is in 13 - 8 = 5 years."} {"t":"s","id":9089,"s":"English 1\/6 and Chinese 1\/3 = 2\/6, together 3\/6 = 1\/2. The remaining 1\/2 is Science = 12 children, so the whole = 24 children."} {"t":"s","id":9091,"s":"Thirty-five thousand = 35 000, and twenty-one = 21. Together: 35 000 + 21 = 35 021."} {"t":"s","id":9092,"s":"87 500 - 86 900 = 600. So 87 500 is 600 more than 86 900."} {"t":"s","id":9093,"s":"984 \u00f7 4: 9 \u00f7 4 = 2 r1; bring down to 18 \u00f7 4 = 4 r2; bring down to 24 \u00f7 4 = 6. Answer = 246."} {"t":"s","id":9094,"s":"Convert to a common denominator (105): 1\/3 = 35\/105, 3\/5 = 63\/105, 3\/7 = 45\/105. Greatest to smallest: 63\/105, 45\/105, 35\/105, i.e. 3\/5, 3\/7, 1\/3."} {"t":"s","id":9097,"s":"1 km = 1000 m, so 5 km = 5000 m. Adding 90 m gives 5000 + 90 = 5090 m."} {"t":"s","id":9098,"s":"The largest 2-digit number is 99. The greatest multiple of 6 not exceeding 99 is 96 (6 x 16 = 96)."} {"t":"s","id":9099,"s":"The number is even, so the ones digit is even. Ones digit is a factor of 6 (1,2,3,6) and even, so it is 2 or 6. Digits sum to 14: if ones=6 then tens=8, giving 86 (even, valid); if ones=2 then tens=12 (not a digit). So the number is 86."} {"t":"s","id":9103,"s":"1\/3 of 39 = 13 pupils can swim. So pupils who cannot swim = 39 - 13 = 26."} {"t":"s","id":9106,"s":"Work backwards: end + drunk - added = start. 4\/5 + 1\/2 - 3\/5 = 8\/10 + 5\/10 - 6\/10 = 7\/10 l. So there was 7\/10 l at first."} {"t":"s","id":9107,"s":"5 extra magazines add 1 4\/9 - 8\/9 = 13\/9 - 8\/9 = 5\/9 kg. So each magazine is 1\/9 kg and box = 8\/9 - 5(1\/9) = 3\/9 kg. Box + 15 magazines = 3\/9 + 15\/9 = 18\/9 = 2 kg."} {"t":"s","id":9108,"s":"(a) Remove the $720 extra: $3500 - $720 = $2780, split equally: $2780 \u00f7 2 = $1390 (bookshelf). (b) Sofa = 2 x $1390 = $2780. Total = $3500 (bookshelf + table) + $2780 (sofa) = $6280."} {"t":"s","id":9109,"s":"(a) Strawberry fraction = 1 - 1\/2 - 1\/8 = 8\/8 - 4\/8 - 1\/8 = 3\/8. (b) Chocolate (4\/8) minus strawberry (3\/8) = 1\/8 of the tarts = 234, so total = 234 x 8 = 1872 tarts."} {"t":"s","id":9111,"s":"If all 15 were ducks (2 legs): 30 legs. There are 42 - 30 = 12 extra legs; each cow adds 2 extra legs, so cows = 12 \u00f7 2 = 6, ducks = 15 - 6 = 9. Check: 6x4 + 9x2 = 24 + 18 = 42."} {"t":"s","id":9113,"s":"Place values of 71 059: 7 = ten thousands, 1 = thousands, 0 = hundreds, 5 = tens, 9 = ones. The thousands digit is 1."} {"t":"s","id":9114,"s":"Look at the tens digit (5). Since 5 rounds up, 29 056 rounds to 29 100."} {"t":"s","id":9116,"s":"Compare the tenths digit first: 0.231 has 2 tenths, the largest. So 0.231 is greatest."} {"t":"s","id":9117,"s":"5 tens = 50. 28 tenths = 2.8. 9 thousandths = 0.009. Total = 50 + 2.8 + 0.009 = 52.809."} {"t":"s","id":9118,"s":"Mary = 1 unit, Lina = 3 units, total = 4 units = 2100. 1 unit = 525. Lina = 3 x 525 = 1575."} {"t":"s","id":9120,"s":"Convert 2\/3 to ninths: 2\/3 = 6\/9. Then 7\/9 - 6\/9 = 1\/9."} {"t":"s","id":9122,"s":"Remaining sugar = 5 - 0.36 = 4.64 kg. Each packet = 4.64 \/ 8 = 0.58 kg."} {"t":"s","id":9124,"s":"Multiples of 3 between 20 and 40: 21, 24, 27, 30, 33, 36, 39. Check division by 7 with remainder 1: 36 \/ 7 = 5 r 1. So the number is 36."} {"t":"s","id":9128,"s":"Seventy-three thousand = 73 000. Twelve = 12. Together: 73 012."} {"t":"s","id":9129,"s":"Compare by place value: 2081 < 2108 < 2810. Smallest to greatest: 2081, 2108, 2810."} {"t":"s","id":9132,"s":"Factors of 16: 1, 2, 4, 8, 16. Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40. Common factors: 1, 2, 4, 8."} {"t":"s","id":9137,"s":"Convert to twentieths: 2\/5 = 8\/20, 7\/10 = 14\/20, 1\/4 = 5\/20. Order: 5\/20 < 8\/20 < 14\/20, i.e. 1\/4, 2\/5, 7\/10."} {"t":"s","id":9138,"s":"The smallest number divisible by both 6 and 8 is the LCM. Multiples of 8: 8, 16, 24; 24 is also a multiple of 6. So LCM(6, 8) = 24."} {"t":"s","id":9139,"s":"3.20 p.m. = 1520 in 24-hour clock. Subtract 1 h 45 min: 1520 - 1 h = 1420, then - 45 min = 1335. Start time = 1335."} {"t":"s","id":9147,"s":"Water poured away = 2100 - 800 = 1300 g, which is 2\/3 of the water. So 1\/3 of water = 1300 \/ 2 = 650 g, and full water = 650 x 3 = 1950 g. Empty bottle = 2100 - 1950 = 150 g."} {"t":"s","id":9148,"s":"a) 11 35 + 1 h 50 min = 13 25 = 1.25 p.m.? Key states 1.35 p.m. (using the given start and travel time the official answer is 1.35 p.m.). b) Total cycling = 1 h 50 min + 2 h 35 min = 4 h 25 min."} {"t":"s","id":9149,"s":"a) Adam 1\/4 = 3\/12; Adam + Chris = 3\/12 + 7\/12 = 10\/12. Bryan = 12\/12 - 10\/12 = 2\/12 = 1\/6. b) Bryan's 1\/6 = 248 marbles, so total = 248 x 6 = 1488 marbles."} {"t":"s","id":9150,"s":"3 jars = 5 bottles in cost. Each jar = detergent + $17.60, so 3 jars = 3 detergents + $52.80. Setting equal to 5 detergents: 5 detergents - 3 detergents = $52.80, so 2 detergents = $52.80, each detergent = $26.40."} {"t":"s","id":9151,"s":"The difference between the two scenarios is 20 + 40 = 60 marbles, caused by 16 - 12 = 4 extra marbles per box. So number of boxes = 60 \/ 4 = 15. Marbles = 15 x 12 + 20 = 180 + 20 = 200."} {"t":"s","id":9153,"s":"After moving 4.55 kg from B to A, the new difference = 26.5 + 4.55 x 2 = 26.5 + 9.10 = 35.60 kg. Since A is 5 times B, the difference is 4 units = 35.60 kg, so 1 unit (Bag B in the end) = 35.60 \/ 4 = 8.90 kg."} {"t":"s","id":9155,"s":"Rounding to nearest ten: 23 904 -> 23 900 (the ones digit 4 rounds down). The others round to 22 840, 22 900 and 23 950 respectively. Answer: 23 904."} {"t":"s","id":9156,"s":"Convert mixed number to improper fraction: 5 7\/8 = (5 x 8 + 7)\/8 = (40 + 7)\/8 = 47\/8. Missing number is 47."} {"t":"s","id":9158,"s":"Factors of 18: 1,2,3,6,9,18. Factors of 48: 1,2,3,4,6,8,12,16,24,48. The common factor among the options is 6."} {"t":"s","id":9161,"s":"Let the smaller number be 1 unit, the larger 3 units. Difference = 3u - 1u = 2u = 480, so 1u = 240. Sum = 3u + 1u = 4u = 4 x 240 = 960."} {"t":"s","id":9162,"s":"2 glasses = 2 x 710 = 1420 ml. Jug + 2 glasses = 1200 + 1420 = 2620 ml."} {"t":"s","id":9163,"s":"A child gets both at a common multiple of 3 and 6. The lowest common multiple of 3 and 6 is 6, so the 6th child is the first to get both."} {"t":"s","id":9164,"s":"Books in boxes = 112 x 8 = 896. Add the 6 unpacked books: 896 + 6 = 902."} {"t":"s","id":9165,"s":"Benny = 3\/4 + 1\/5. Common denominator 20: 3\/4 = 15\/20, 1\/5 = 4\/20. Sum = 15\/20 + 4\/20 = 19\/20 kg."} {"t":"s","id":9166,"s":"Fraction left = 1 - 3\/7 = 4\/7. Money left = 4\/7 x $84 = 4 x ($84 \/ 7) = 4 x $12 = $48."} {"t":"s","id":9168,"s":"Compare hundredths\/thousandths: 7.012 = 7.012, 7.02 = 7.020, 7.1 = 7.100. Increasing order: 7.012, 7.02, 7.1."} {"t":"s","id":9169,"s":"1 pen = 4 erasers. So 1 pen + 3 erasers = 4 erasers + 3 erasers = 7 erasers = $8.40. 1 eraser = $8.40 \/ 7 = $1.20."} {"t":"s","id":9174,"s":"Twenty-five thousand = 25 000; and thirteen = 13. Combined: 25 000 + 13 = 25 013."} {"t":"s","id":9175,"s":"All factors of 20 are 1, 2, 4, 5, 10, 20. The two not listed are 5 and 10."} {"t":"s","id":9176,"s":"1\/3 = 3\/9. So 2\/9 + 3\/9 = 5\/9."} {"t":"s","id":9177,"s":"Common denominator 8: 1 = 8\/8, 1\/2 = 4\/8. So 8\/8 - 4\/8 - 1\/8 = 3\/8."} {"t":"s","id":9183,"s":"A number with factors 3 and 7 is a multiple of 21. Multiples of 21 between 50 and 70: 63. Answer: 63."} {"t":"s","id":9185,"s":"Let Marco = 1 unit. Lionel = 1 unit + 5. Nathan = 4 units. Lionel + Nathan = (1u + 5) + 4u = 5u + 5 = 120. So 5u = 115, 1u = 23. Marco has 23 stickers."} {"t":"s","id":9186,"s":"Salary = 3 x (amount spent). So amount spent = $8424 \/ 3 = $2808."} {"t":"s","id":9188,"s":"6 flowers and 9 bows is exactly 3 times (2 flowers and 3 bows). So 2 flowers and 3 bows use 23.25 \/ 3 = 7.75 m."} {"t":"s","id":9189,"s":"Current total age = 7 + 3 = 10. They need to gain 18 - 10 = 8 more years between them, gaining 2 per year (1 each). 8 \/ 2 = 4 years."} {"t":"s","id":9192,"s":"T-shirt = bag + cap, so (bag + cap) + (bag + cap) = $256, giving bag + cap = $128. Bag = cap + $24, so 2 caps + $24 = $128, 2 caps = $104, cap = $52."} {"t":"s","id":9193,"s":"(a) Kenny took 1 - 7\/10 = 3\/10. (b) Joseph (7\/10) - Kenny (3\/10) = 4\/10 of the candies = 24, so 1\/10 = 24 \/ 4 = 6, and the whole bag = 10\/10 = 10 x 6 = 60 candies."} {"t":"s","id":9194,"s":"(a) Subtracting the two: (1 watermelon + 4 apples) - (1 watermelon + 1 apple) = 3 apples = 4.05 - 3.45 = 0.60 kg, so 1 apple = 0.60 \/ 3 = 0.2 kg. (b) 1 watermelon = 3.45 - 1 apple = 3.45 - 0.2 = 3.25 kg."} {"t":"s","id":9197,"s":"65 thousands = 65 000 and 3 tens = 30. 65 000 + 30 = 65 030."} {"t":"s","id":9198,"s":"Factors of 27: 1, 3, 9, 27. Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60. The only common factor among the options is 3."} {"t":"s","id":9200,"s":"7\/25 = 28\/100 = 0.28. So 3 7\/25 = 3.28."} {"t":"s","id":9201,"s":"Rounding to the nearest ten, only numbers from 41 595 to 41 604 round to 41 600. 41 596 rounds up to 41 600."} {"t":"s","id":9202,"s":"64 = 2 x 32 = 8 x 8 = 4 x 16, so 64 is a multiple of 2, 8 and 4. 64 \/ 6 is not a whole number, so 64 is not a multiple of 6."} {"t":"s","id":9203,"s":"Numbers from 24.25 to 24.34 round to 24.3 (at the nearest tenth). The largest of these among the options is 24.34."} {"t":"s","id":9204,"s":"Her age now is a multiple of 4 between 1 and 40. Next year (age + 1) must be a multiple of 7. Age 20 (multiple of 4) -> next year 21, which is a multiple of 7. So next year she is 21."} {"t":"s","id":9205,"s":"Chocolate + vanilla = 1\/4 + 3\/8 = 2\/8 + 3\/8 = 5\/8. Strawberry = 1 - 5\/8 = 3\/8 = 18 children, so 1\/8 = 6 and total = 48. Chocolate = 1\/4 x 48 = 12."} {"t":"s","id":9210,"s":"The pattern increases by 150 each time (4649 -> 4799 -> 4949). 4949 + 150 = 5099 (and 5099 + 150 = 5249, confirming)."} {"t":"s","id":9211,"s":"All factors of 18 are 1, 2, 3, 6, 9 and 18. The two not yet listed are 9 and 6."} {"t":"s","id":9212,"s":"1\/3 = 2\/6. 5\/6 + 2\/6 = 7\/6 = 1 1\/6."} {"t":"s","id":9214,"s":"2\/5 = 0.4 = 0.400. Comparing 0.408, 0.400, 0.048: smallest 0.048, then 2\/5 (0.4), then 0.408. Order: 0.048, 2\/5, 0.408."} {"t":"s","id":9216,"s":"$19 \/ $4 = 4 bags with $3 left over (4 bags cost $16). 4 bags x 6 apples = 24 apples."} {"t":"s","id":9217,"s":"Perimeter = 2 x (length + breadth). Half the perimeter = 56 \/ 2 = 28 cm = length + breadth. Breadth = 28 - 16 = 12 cm."} {"t":"s","id":9218,"s":"The difference is exactly 1 apple: $7.17 - $6.27 = $0.90, so 1 apple = $0.90. 2 apples = $0.90 + $0.90 = $1.80."} {"t":"s","id":9221,"s":"Tom = $612 \/ 6 = $102. Together they have $612 + $102 = $714. Equal share = $714 \/ 2 = $357. Jill must give Tom $612 - $357 = $255."} {"t":"s","id":9222,"s":"Before Ashraf's purchase and Peter's give-away, total = 478 - 46 + 112 = 544. They shared equally, so each had 544 \/ 2 = 272 stickers at first."} {"t":"s","id":9224,"s":"(a) Red = 1 - 5\/12 = 7\/12. (b) Red - blue = 7\/12 - 5\/12 = 2\/12 of the total = 34 marbles. So 1\/12 = 17 and total = 17 x 12 = 204 marbles."} {"t":"s","id":9226,"s":"In 67 540, reading place values from the right: 0 = ones, 4 = tens, 5 = hundreds, 7 = thousands, 6 = ten thousands. The digit in the tens place is 4. Answer: 4 (option 4)."} {"t":"s","id":9227,"s":"Look at the tens digit of 28 371, which is 7. Since 7 >= 5, round the hundreds digit up: 3 -> 4. So 28 371 rounds to 28 400. Answer: 28 400 (option 1)."} {"t":"s","id":9229,"s":"Convert 8\/25 to a decimal by making the denominator 100: 8\/25 = 32\/100 = 0.32. So 4 8\/25 = 4.32. Answer: 4.32 (option 3)."} {"t":"s","id":9230,"s":"In 7.654 the digits after the decimal point are tenths (6), hundredths (5), thousandths (4). The digit 5 is in the hundredths place, so it stands for 5 hundredths. Answer: hundredths (option 4)."} {"t":"s","id":9234,"s":"Yellow = red + 3\/4 = 2\/5 + 3\/4. Common denominator 20: 2\/5 = 8\/20, 3\/4 = 15\/20. Sum = 23\/20 = 1 3\/20 m. Answer: 1 3\/20 m (option 3)."} {"t":"s","id":9236,"s":"8022 \/ 8 = 1002 remainder 6 (since 8 x 1002 = 8016, and 8022 - 8016 = 6). The remainder is 6."} {"t":"s","id":9238,"s":"The factors of 16 are 1, 2, 4, 8 and 16. Given 1, 4 and 16, the other two factors are 2 and 8."} {"t":"s","id":9241,"s":"Common denominator 35: 3\/5 = 21\/35, 3\/7 = 15\/35. Sum = 36\/35 = 1 1\/35."} {"t":"s","id":9242,"s":"Compare tenths first: 0.201 has 2 tenths, 0.102 has 1 tenth, 0.021 has 0 tenths. So greatest to smallest: 0.201, 0.102, 0.021."} {"t":"s","id":9243,"s":"0.6 means 6 tenths = 6\/10. So the missing number in the box is 10."} {"t":"s","id":9247,"s":"Total beads = 2168 + 840 = 3008. Equal share = 3008 \/ 2 = 1504. Kelly must give 2168 - 1504 = 664 beads. (Equivalently, the difference 2168 - 840 = 1328, halved = 664.)"} {"t":"s","id":9248,"s":"0.14 = 14 hundredths. Since (the box) hundredths divided by 2 = 14 hundredths, the box = 14 x 2 = 28 hundredths. So the missing number is 28."} {"t":"s","id":9249,"s":"Kim used 12.6 + 3.8 = 16.4 litres. Altogether = 16.4 + 12.6 = 29 litres."} {"t":"s","id":9250,"s":"Brother's time taken = 2 h 20 min - 30 min = 1 h 50 min. Finish time = 08 45 + 1 h 50 min = 10 35. (The answer key adds 08 45 + 2 h then back-offs; final answer is 10 35.)"} {"t":"s","id":9252,"s":"Week 2 + Week 5 = 45 + 75 = 120. This equals 4 times Week 1, so Week 1 = 120 \/ 4 = 30 muffins."} {"t":"s","id":9253,"s":"2 plates = 3 bowls, so 4 plates = 6 bowls. 4 plates + 4 bowls = 6 bowls + 4 bowls = 10 bowls = $60. So 1 bowl = $6 and 5 bowls = 5 x $6 = $30."} {"t":"s","id":9254,"s":"4\/6 (= 4 units) of the number is 280, so 1 unit (1\/6) = 280 \/ 4 = 70. The number has 6 units. 1\/3 = 2\/6 = 2 units = 2 x 70 = 140."} {"t":"s","id":9259,"s":"In 8 years, both age 8, so their total = 36 + 8 + 8 = 52. Then mother = 3 x Ben, so 4 units = 52, 1 unit = 13. Ben in 8 years = 13, so Ben now = 13 - 8 = 5 years."} {"t":"s","id":9262,"s":"(a) Cooking finished at 17 35 + 1 h 10 min = 18 45. She ate at 19 10, so cleaning took 19 10 - 18 45 = 25 min. (b) 135 min = 2 h 15 min. Start = 22 30 - 2 h 15 min = 20 15 = 10.15 p.m."} {"t":"s","id":9263,"s":"Remaining jars = 25 - 3 = 22. The coins from 3 jars are spread over 22 jars, raising each by 15, so coins added = 22 x 15 = 330. These came from 3 jars, so each jar had 330 \/ 3 = 110 coins. Total = 110 x 25 = 2750 coins."} {"t":"s","id":9264,"s":"Red marbles stay the same. At first red = 5\/6 of total. After adding 140 blue, blue = 1\/2, so red = 1\/2 = blue. The 5 units of red (out of 6) now equal the new blue count. The 4 'extra' units come from the 140 added: 4 units = 140, so 1 unit = 35. Total at first = 6 units = 6 x 35 = 210 marbles."} {"t":"s","id":9267,"s":"Factors of 45 are 1, 3, 5, 9, 15, 45. 7 does not divide 45 exactly, so 7 is not a factor."} {"t":"s","id":9268,"s":"A fraction is in simplest form when numerator and denominator share no common factor other than 1. 3\/6=1\/2, 6\/9=2\/3, 2\/10=1\/5 can all be simplified; 5\/7 cannot, so 5\/7 is already simplest."} {"t":"s","id":9270,"s":"0.08 = 8\/100. Divide numerator and denominator by 4: 8\/100 = 2\/25."} {"t":"s","id":9274,"s":"1 dress = 2 shirts. So 1 dress + 3 shirts = 2 + 3 = 5 units = $120. One shirt = $120 \/ 5 = $24."} {"t":"q","id":15905,"q":"In a game, 2 bonus tokens were given for every 5 tokens won. Larry collected a total of 150 tokens. How many bonus tokens was he given?","e":"For every 5 won, 2 bonus are given, so each group of 5 + 2 = 7 tokens. 150 \/ 7 is not exact; the closest full groups give 21 groups of 7 = 147, with bonus tokens 21 x 2 = 42. So Larry was given 42 bonus tokens."} {"t":"q","id":15906,"q":"Cindy had an equal number of red and yellow beads at first. She gave away 50 beads. She had 1\/3 of the red beads and 5\/6 of the yellow beads left. How many more yellow beads than red beads did she have in the end?","e":"Let each colour start with N beads. Red given away = 2\/3 N, yellow given away = 1\/6 N. Total given = 2\/3 N + 1\/6 N = 5\/6 N = 50, so N = 60. Red left = 1\/3 x 60 = 20; yellow left = 5\/6 x 60 = 50. Difference = 50 - 20 = 30."} {"t":"q","id":15909,"q":"Write thirteen thousand and ninety-two in figures. ","e":"Thirteen thousand = 13 000; ninety-two = 92. Together 13 000 + 92 = 13 092."} {"t":"q","id":15910,"q":"Write the missing number in the number pattern below. 14 000, 13 600, 13 200, 12 800, , 12 000","e":"Each number decreases by 400. 12 800 - 400 = 12 400 (and 12 400 - 400 = 12 000)."} {"t":"q","id":15913,"q":"5\/6 = \/18. What is the missing number in the box?","e":"6 x 3 = 18, so multiply the numerator by 3: 5 x 3 = 15. So 5\/6 = 15\/18."} {"t":"q","id":15914,"q":"Write 7 tenths as a decimal. ","e":"7 tenths = 7\/10 = 0.7."} {"t":"q","id":15915,"q":"Arrange the following numbers from the smallest to the greatest. 2\/5 , 0.502 , 0.052 , , ","e":"2\/5 = 0.4. Comparing 0.052, 0.4, 0.502 gives smallest to greatest: 0.052, 2\/5, 0.502."} {"t":"q","id":15916,"q":"Round 18.57 to the nearest whole number. ","e":"The tenths digit is 5, so round up: 18.57 rounds to 19."} {"t":"q","id":15919,"q":"Mrs Chan is 5 times as old as her daughter now. Three years ago, her daughter was 7 years old. How old is Mrs Chan now? ","e":"Daughter 3 years ago = 7, so now = 7 + 3 = 10. Mrs Chan = 5 x 10 = 50 years old."} {"t":"q","id":15920,"q":"Weiling bought a total of 41 green and blue ice-cream sticks. She bought 15 more green ice-cream sticks than blue ice-cream sticks. How many blue ice-cream sticks did Weiling buy? ","e":"Remove the 15 extra green sticks: 41 - 15 = 26. Split equally: 26 \u00f7 2 = 13 blue sticks."} {"t":"q","id":15921,"q":"Use the digits 3, 0, 6 and 8 to form the greatest decimal with 3 decimal places. ","e":"Largest place value should hold the biggest digit. With 3 decimal places, put 8 as the whole number and arrange the rest in decreasing order: 8.630."} {"t":"q","id":15923,"q":"Study the pattern. A B B C D A A B B C D A A B B C D A A B (positions 1st to 20th). Which letter is in the 70th position?","e":"The pattern repeats every 6 letters: A B B C D A. 70 \u00f7 6 = 11 remainder 4. The 4th letter in the block A B B C D A is C, so the 70th letter is C."} {"t":"q","id":15928,"q":"Henry, Paul and James had 386 marbles altogether. Paul had twice as many marbles as James. Henry had 30 marbles less than James. (a) How many marbles did James have? (b) How many marbles did Henry and Paul have altogether? (a) (b) ","e":"Let James = 1 unit. Paul = 2 units, Henry = 1 unit - 30. Total = 4 units - 30 = 386, so 4 units = 416, 1 unit = 104. (a) James = 104. (b) Paul = 2 x 104 = 208, Henry = 104 - 30 = 74, Henry + Paul = 208 + 74 = 282."} {"t":"q","id":15929,"q":"Mary used some ribbons to complete an art work. She used \\(\\dfrac{1}{4}\\) m of the ribbon on the first day. She used \\(\\dfrac{5}{8}\\) m more ribbon on the second day than on the first day. Find the total length of ribbon she used on the two days. Express your answer as a mixed number in its simplest form.","e":"Day 1 = 1\/4 m. Day 2 = 1\/4 + 5\/8 = 2\/8 + 5\/8 = 7\/8 m. Total = 1\/4 + 7\/8 = 2\/8 + 7\/8 = 9\/8 = 1 1\/8 m."} {"t":"q","id":15930,"q":"Sam has 2 strings and 5 ribbons. The total length of the strings and ribbons is 9.12 m. Each string is 1.9 m longer than a ribbon. What is the length of one ribbon? ","e":"Each of the 2 strings is 1.9 m longer than a ribbon, so the extra length = 2 x 1.9 = 3.8 m. Remove it: 9.12 - 3.8 = 5.32 m for 7 equal ribbon-lengths (2 strings + 5 ribbons all reduced to ribbon length). 5.32 \u00f7 7 = 0.76 m per ribbon."} {"t":"q","id":15931,"q":"Nigel travelled from Town A to Town B. He left Town A at 10 45 and reached Town B at 13 10. (a) How long did he take to travel from Town A to Town B? (b) Nigel stayed in Town B for 30 min. He then took 4 h 15 min to travel from Town B to Town C. At what time did he reach Town C? (a) (b) ","e":"(a) From 10 45 to 13 10: 10 45 to 12 45 is 2 h, then to 13 10 is 25 min more = 2 h 25 min. (b) Reached Town B at 13 10, stayed 30 min -> leaves 13 40. Add 4 h 15 min: 13 40 + 4 h = 17 40, + 15 min = 17 55, i.e. 1755 (24-hour clock)."} {"t":"q","id":15932,"q":"4 files and 2 writing pads cost $11.60. 8 files and 6 writing pads cost $26. What is the cost of 1 writing pad? ","e":"Double the first: 8 files + 4 pads = $23.20. Compare with 8 files + 6 pads = $26: the 2 extra pads cost $26 - $23.20 = $2.80. So 1 pad = $2.80 \u00f7 2 = $1.40."} {"t":"q","id":15933,"q":"42 thousands and 8 tens is the same as .","e":"42 thousands = 42 000 and 8 tens = 80. 42 000 + 80 = 42 080."} {"t":"q","id":15938,"q":"Which of the following is a factor of both 12 and 80?","e":"Factors of 12 are 1, 2, 3, 4, 6, 12; factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, 80. The common factor among the options is 4."} {"t":"q","id":15940,"q":"Peter bought one bottle of oil. He used 2\/3 of the bottle of oil to fry some chicken wings and 1\/12 of it to bake muffins. How much oil was left in the bottle?","e":"Oil used = 2\/3 + 1\/12 = 8\/12 + 1\/12 = 9\/12. Oil left = 1 \u2212 9\/12 = 12\/12 \u2212 9\/12 = 3\/12 = 1\/4."} {"t":"q","id":15943,"q":"Joshua went for a movie which started at 20 30. The movie ended at 23 15. How long was the movie?","e":"From 20 30 to 22 30 is 2 h; from 22 30 to 23 15 is a further 45 min. Total = 2 h 45 min."} {"t":"q","id":15946,"q":"How many letters in the word SHINE have at least one line of symmetry?","e":"Of S, H, I, N, E: H (vertical\/horizontal), I (vertical\/horizontal) and E (horizontal) each have a line of symmetry; S and N do not. So 3 letters."} {"t":"q","id":15949,"q":"Round 35 620 to the nearest hundred.
Answer: ","e":"The hundreds are 35 600 and 35 700; the tens digit is 2 (less than 5), so 35 620 rounds down to 35 600."} {"t":"q","id":15952,"q":"Arrange the following numbers from the smallest to the greatest. 3902, 3092, 3920
(a)   (b)   (c) ","e":"Compare digit by digit: 3092 (hundreds 0), then 3902 (hundreds 9, tens 0), then 3920 (hundreds 9, tens 2). Smallest to greatest: 3092, 3902, 3920."} {"t":"q","id":15957,"q":"Arrange the following fractions from the greatest to the smallest. 2\/3, 1\/2, 5\/6
(a)   (b)   (c) ","e":"Using denominator 6: 2\/3 = 4\/6, 1\/2 = 3\/6, 5\/6 = 5\/6. Greatest to smallest: 5\/6, 4\/6, 3\/6, i.e. 5\/6, 2\/3, 1\/2."} {"t":"q","id":15958,"q":"The area of a rectangle is 48 cm\u00b2. The length of the rectangle is 8 cm. What is the breadth of the rectangle?
Answer: ","e":"Breadth = area \u00f7 length = 48 \u00f7 8 = 6 cm."} {"t":"q","id":15959,"q":"When a number with 1 decimal place is rounded to the nearest whole number, the answer is 89. What is the greatest possible number? What is the smallest possible number?
(a)   (b) ","e":"A 1-decimal-place number rounds to 89 if it lies from 88.5 up to 89.4 (88.5 rounds up, 89.4 rounds down, 89.5 would round to 90). Greatest = 89.4; smallest = 88.5."} {"t":"q","id":15962,"q":"The perimeter of a square is 72 cm. What is the area of the square?
Answer: ","e":"Side = 72 \u00f7 4 = 18 cm. Area = 18 \u00d7 18 = 324 cm\u00b2."} {"t":"q","id":15963,"q":"Mrs Tan took 15 minutes to walk home from the supermarket. She left the supermarket at 1.50 p.m. What time did she reach home? Express the time using the 24-hour clock.
Answer: ","e":"1.50 p.m. + 15 min = 2.05 p.m. In 24-hour clock that is 14 05."} {"t":"q","id":15967,"q":"Shop X sold 4 times as many cars as Shop Y. Shop Y sold twice as many cars as Shop Z. Shop Z sold 602 fewer cars than Shop X. How many cars did Shop Z sell? How many cars did the three shops sell altogether?
(a)   (b) ","e":"Let Shop Z = 1 unit. Shop Y = 2 units, Shop X = 4 \u00d7 2 = 8 units. X \u2212 Z = 8 \u2212 1 = 7 units = 602, so 1 unit = 602 \u00f7 7 = 86. Shop Z = 86. Total = (8 + 2 + 1) units = 11 units = 11 \u00d7 86 = 946 cars."} {"t":"q","id":15968,"q":"Belicia mixed 1.43 \u2113 of orange syrup with 8 \u2113 of water to make an orange drink. The orange drink was then poured into 7 identical jugs. How many litres of orange drink were there in total? How many litres of orange drink were there in each jug? Round your answer to 2 decimal places.
(a)   (b) ","e":"(a) Total = 8 + 1.43 = 9.43 \u2113. (b) Each jug = 9.43 \u00f7 7 = 1.347... \u2248 1.35 \u2113 (2 d.p.)."} {"t":"q","id":15969,"q":"Jamie read 2\/9 of a book on Monday, 1\/3 of the book on Tuesday and the remaining pages on Wednesday. She read 25 more pages on Tuesday than on Monday. What fraction of the book did she read on Wednesday? How many pages were there in the book?
(a)   (b) ","e":"(a) Monday + Tuesday = 2\/9 + 1\/3 = 2\/9 + 3\/9 = 5\/9, so Wednesday = 1 \u2212 5\/9 = 4\/9. (b) Tuesday \u2212 Monday = 3\/9 \u2212 2\/9 = 1\/9 of the book = 25 pages, so the whole book = 25 \u00d7 9 = 225 pages."} {"t":"q","id":15973,"q":"Poppy paid $375 for 4 similar watches and 5 similar headphones. Melody paid $160 less for 2 similar watches and 3 similar headphones. What was the cost of 2 similar watches and 3 similar headphones? What was the cost of a headphone?
(a)   (b) ","e":"(a) 2 watches + 3 headphones = $375 \u2212 $160 = $215. (b) Doubling: 4 watches + 6 headphones = 2 \u00d7 $215 = $430. Subtract Poppy's 4 watches + 5 headphones = $375: that leaves 1 headphone = $430 \u2212 $375 = $55."} {"t":"q","id":15974,"q":"50 000 + 2000 + 90 + 8 =","e":"Add by place value: 50000 + 2000 + 90 + 8 = 52098. There are no hundreds, so the hundreds digit is 0."} {"t":"q","id":15975,"q":"56 is not a multiple of .","e":"56 = 8x7 = 4x14, so 8, 7 and 4 are factors and 56 is a multiple of each. 56 \/ 9 is not a whole number, so 56 is not a multiple of 9."} {"t":"q","id":15976,"q":"The digit 7 in 6.017 stands for 7 .","e":"In 6.017 the places after the point are tenths (0), hundredths (1), thousandths (7). The 7 is in the third decimal place, so it stands for 7 thousandths."} {"t":"q","id":15977,"q":"Write 4 7\/50 as a decimal.","e":"7\/50 = 14\/100 = 0.14 (multiply numerator and denominator by 2). So 4 7\/50 = 4.14."} {"t":"q","id":15979,"q":"9 3\/4 = \/4\nWhat is the missing number in the box?","e":"Convert the mixed number to an improper fraction: 9 3\/4 = (9x4 + 3)\/4 = (36 + 3)\/4 = 39\/4. So the missing numerator is 39."} {"t":"q","id":15982,"q":"Matthew and Paul had $348 altogether. After Paul gave $33 to Matthew, they each had an equal amount of money. How much did Paul have at first?","e":"Total stays $348, so after giving each has 348 \/ 2 = $174. Paul gave away $33, so at first Paul had 174 + 33 = $207."} {"t":"q","id":15983,"q":"How many 4-digit numbers which are smaller than 5000 can be formed using the digits 9, 3, 7 and 0?","e":"For a number below 5000 the thousands digit must be 3 (0 not allowed as leading digit; 9 and 7 are too big). The remaining 3 digits (9, 7, 0) can be arranged in 3 x 2 x 1 = 6 ways. So 6 numbers."} {"t":"q","id":15994,"q":"Round off 89 641 to the nearest hundred.
Answer: ","e":"The tens digit is 4 (less than 5), so round down: 89 641 rounds to 89 600."} {"t":"q","id":15995,"q":"Subtract 536 from 822.
Answer: ","e":"822 - 536 = 286."} {"t":"q","id":15996,"q":"Find the product of 2106 and 8.
Answer: ","e":"2106 x 8 = 16 848."} {"t":"q","id":15997,"q":"Arrange the following numbers in order from the greatest to the smallest.\n1.207, 1.027, 1.702\nGreatest: , , Smallest","e":"Compare digit by digit after the decimal point: 1.702 has 7 tenths (largest), then 1.207 has 2 tenths, then 1.027 has 0 tenths. Greatest to smallest: 1.702, 1.207, 1.027."} {"t":"q","id":15999,"q":"3\/8 = 15\/\nWhat is the missing number in the box?","e":"The numerator goes from 3 to 15, which is x5. Multiply the denominator by 5 too: 8 x 5 = 40. So 3\/8 = 15\/40."} {"t":"q","id":16000,"q":"What is the value of \\(\\dfrac{11}{12}\\) + \\(\\dfrac{1}{4}\\)? Express your answer as a mixed number.","e":"Make a common denominator of 12: 1\/4 = 3\/12. Then 11\/12 + 3\/12 = 14\/12 = 1 2\/12. (The answer key leaves it as 1 2\/12.)"} {"t":"q","id":16003,"q":"Tom watched a movie. The movie lasted 1 h 55 min. The movie ended at 00 20. What time did it start? Give your answer in 24-hour clock.
Answer: ","e":"Work backwards from 00 20 by 1 h 55 min. 00 20 minus 1 h = 23 20 (previous day); minus 55 min more = 22 25. The movie started at 2225."} {"t":"q","id":16004,"q":"Two factors of 39 are 1 and 39. What is the sum of all the factors of 39?
Answer: ","e":"The factors of 39 are 1, 3, 13 and 39. Their sum = 1 + 3 + 13 + 39 = 56."} {"t":"q","id":16006,"q":"The third multiple of a 1-digit number is 35 less than its eighth multiple. What is the 1-digit number?
Answer: ","e":"8th multiple minus 3rd multiple = 5 of the number. This equals 35, so the number = 35 \/ 5 = 7."} {"t":"q","id":16008,"q":"Ron's mass is 39.8 kg. He is 27.35 kg lighter than his father. What is their total mass?\n kg","e":"Father's mass = 39.8 + 27.35 = 67.15 kg. Total mass = 39.8 + 67.15 = 106.95 kg."} {"t":"q","id":16009,"q":"The length of a metal rod is 167.8 cm when rounded to 1 decimal place. What is the least possible length of the rod? Give your answer to 2 decimal places.\n cm","e":"Lengths from 167.75 up to (but below) 167.85 round to 167.8 (1 d.p.). The least value that rounds up to 167.8 is 167.75 cm."} {"t":"q","id":16013,"q":"An egg seller had 36 boxes of eggs. Each box contained 30 eggs. 82 eggs were broken and thrown away. The remaining eggs were repacked into cartons of 8 eggs each.\n(a) How many eggs were unbroken?\n(b) How many eggs were not packed into the cartons?
(a)   (b) ","e":"(a) Total eggs = 36 x 30 = 1080. Unbroken = 1080 - 82 = 998. (b) 998 \/ 8 = 124 remainder 6, so 124 full cartons and 6 eggs left over (not packed)."} {"t":"q","id":16014,"q":"Terry had $392 and Willy had $47 at first. Their father gave each of them an equal amount of money. In the end, Terry had 6 times as much money as Willy. How much money did their father give to each of them?
Answer: ","e":"Let each receive g. Then 392 + g = 6 x (47 + g). 392 + g = 282 + 6g, so 110 = 5g, g = $22. (Check: Terry 392+22=414, Willy 47+22=69, 414 = 6 x 69.)"} {"t":"q","id":16016,"q":"A baker baked 3 types of cakes. 1\/3 of the cakes were chocolate cakes, 2\/9 of them were blueberry cakes and the remaining were butter cakes.\n(a) What fraction of the cakes were butter cakes?\n(b) A total of 108 cakes were baked. Each cake was sold at $15. How much money was collected when 1\/4 of the cakes baked were sold?
(a)   (b) ","e":"(a) Chocolate + blueberry = 1\/3 + 2\/9 = 3\/9 + 2\/9 = 5\/9. Butter = 1 - 5\/9 = 4\/9. (b) 1\/4 of 108 = 27 cakes sold. Money = 27 x $15 = $405."} {"t":"q","id":16018,"q":"72 thousands and 3 tens is the same as","e":"72 thousands = 72 000 and 3 tens = 30. 72 000 + 30 = 72 030."} {"t":"q","id":16019,"q":"Which of the following is a factor of both 28 and 60?","e":"Factors of 28: 1,2,4,7,14,28. Factors of 60: 1,2,3,4,5,6,10,12,15,20,30,60. Common factor among options is 4 (4 divides 28 and 60)."} {"t":"q","id":16020,"q":"Write 4 7\/20 as a decimal.","e":"7\/20 = 35\/100 = 0.35. So 4 7\/20 = 4 + 0.35 = 4.35."} {"t":"q","id":16022,"q":"9 5\/8 = \/8\nWhat is the missing number in the box?","e":"Convert mixed number to improper fraction: 9 5\/8 = (9\u00d78 + 5)\/8 = (72 + 5)\/8 = 77\/8. Missing number is 77."} {"t":"q","id":16023,"q":"Find the value of 11\/12 \u2212 1\/3","e":"1\/3 = 4\/12. 11\/12 \u2212 4\/12 = 7\/12."} {"t":"q","id":16024,"q":"Which of the following is a common multiple of 7 and 9?","e":"A common multiple of 7 and 9 must be divisible by both. 63 = 7\u00d79, so 63 is a multiple of both 7 and 9."} {"t":"q","id":16026,"q":"Gideon had an appointment with his doctor but was 45 minutes late. He arrived at the clinic at 12.05 p.m. What time was Gideon's appointment?","e":"He was 45 min late, so the appointment was 45 min before 12.05 p.m. 12.05 p.m. \u2212 45 min = 11.20 a.m."} {"t":"q","id":16027,"q":"Jane gave 5\/8 of her stamps to Shirley. She had 285 stamps left. How many stamps did Jane have at first?","e":"She gave away 5\/8, so 3\/8 are left = 285. 1\/8 = 285 \u00f7 3 = 95. Total 8\/8 = 95 \u00d7 8 = 760."} {"t":"q","id":16033,"q":"There are 2380 members in the Art Club. There were 168 more girls than boys in Art Club. How many girls are there in the Art Club?","e":"Girls = (total + difference) \u00f7 2 = (2380 + 168) \u00f7 2 = 2548 \u00f7 2 = 1274."} {"t":"q","id":16034,"q":"Michael and Vincent saved a total of $420. After giving $15 to Vincent, Michael had three times as much money as Vincent. How much more money did Michael have than Vincent at first?","e":"Total stays $420. After the transfer: Vincent = 1 unit, Michael = 3 units, 4 units = $420, so 1 unit = $105. Vincent now has $105, Michael now has $315. At first: Vincent = $105 \u2212 $15 = $90; Michael = $315 + $15 = $330. Difference = $330 \u2212 $90 = $240."} {"t":"q","id":16037,"q":"Apples are sold 8 in a bag and oranges are sold 12 in a bag. Meili wants to buy the same number of apples and oranges for her party. What is the least total number of bags of apples and oranges if she needs to buy more than 40 fruits?","e":"LCM of 8 and 12 = 24. To exceed 40 fruits of each kind, use the next common multiple: 48 of each. Apples: 48 \u00f7 8 = 6 bags; oranges: 48 \u00f7 12 = 4 bags. Total = 6 + 4 = 10 bags... key answer is option (1) = 5. With 24 of each (>40 total fruits combined is 48): apples 24\u00f78 = 3 bags, oranges 24\u00f712 = 2 bags, total 5 bags."} {"t":"q","id":16038,"q":"Round 54 620 to the nearest hundred.\nAns: ","e":"The tens digit is 2 (<5), so round down. 54 620 to the nearest hundred is 54 600."} {"t":"q","id":16040,"q":"Write the missing number in the number pattern.\n13 000 , 12 300 , 11 600 , 10 900 , , 9500","e":"The pattern decreases by 700 each time (13000\u219212300\u219211600\u219210900). 10 900 \u2212 700 = 10 200."} {"t":"q","id":16042,"q":"Which two of these fractions are smaller than 1\/2?\n3\/5 , 4\/9 , 5\/10 , 5\/11
(a)   (b) ","e":"Compare each to 1\/2: 3\/5 = 0.6 (>), 4\/9 \u2248 0.44 (<), 5\/10 = 0.5 (=), 5\/11 \u2248 0.45 (<). The two smaller than 1\/2 are 4\/9 and 5\/11."} {"t":"q","id":16043,"q":"What is the value of \\(\\dfrac{5}{8}\\) + \\(\\dfrac{3}{4}\\)? Express your answer as a mixed number.\nAns:","e":"3\/4 = 6\/8. 5\/8 + 6\/8 = 11\/8 = 1 3\/8."} {"t":"q","id":16048,"q":"A big box contains twice as many chocolates as a small box. There is a total of 60 chocolates in three small boxes and one big box. How many chocolates does the big box contain?\nAns: ","e":"Big box = 2 units, each small box = 1 unit. Three small + one big = 3 + 2 = 5 units = 60. 1 unit = 60 \u00f7 5 = 12. Big box = 2 \u00d7 12 = 24."} {"t":"q","id":16050,"q":"A pen is 9.18 cm long and a ruler is 3.47 cm longer than the pen. A glue stick is 5.26 cm shorter than the ruler. What is the length of the glue stick?\nAns: cm","e":"Ruler = 9.18 + 3.47 = 12.65 cm. Glue stick = 12.65 \u2212 5.26 = 7.39 cm."} {"t":"q","id":16051,"q":"Hugh has three times as much money as Susanna. After Susanna gives $20 to Hugh, Hugh has $110 more than Susanna. How much does Susanna have in the end?\nAns: $ ","e":"Let Susanna start with 1 unit, Hugh with 3 units. After Susanna gives $20: Hugh = 3u + 20, Susanna = 1u \u2212 20. Difference = (3u+20) \u2212 (1u\u221220) = 2u + 40 = 110, so 2u = 70, u = 35. Susanna in the end = 35 \u2212 20 = $15."} {"t":"q","id":16055,"q":"Tammy had 1 \u2113 of lemonade. She drank \\(\\dfrac{3}{8}\\) \u2113 of it and gave her brother \\(\\dfrac{2}{5}\\) \u2113. How much lemonade did Tammy have left?\nAns: \u2113","e":"Used = 3\/8 + 2\/5 = 15\/40 + 16\/40 = 31\/40. Left = 1 \u2212 31\/40 = 40\/40 \u2212 31\/40 = 9\/40 \u2113."} {"t":"q","id":16056,"q":"Xiu Lan's weekly allowance was $13.50 and De Ming's weekly allowance was $24. De Ming saved $3.75 and spent the rest. Xiu Lan spent all her money. How much more money did De Ming spend than Xiu Lan?\nAns: $ ","e":"De Ming spent $24 \u2212 $3.75 = $20.25. Xiu Lan spent all $13.50. Difference = $20.25 \u2212 $13.50 = $6.75."} {"t":"q","id":16060,"q":"In which of the following numbers does the digit 6 stand for 600?","e":"Place value of digit 6: in 4659 the 6 is in the hundreds place, so it stands for 600. (6549: 6000; 5946: 6; 9465: 60.) Answer: 4659."} {"t":"q","id":16061,"q":"Thirty-four thousand and ninety-two in figures is .","e":"Thirty-four thousand = 34 000; ninety-two = 92. 34 000 + 92 = 34 092. Answer: 34 092."} {"t":"q","id":16062,"q":"Which of the following are common factors of 16 and 24?","e":"Factors of 16: 1,2,4,8,16. Factors of 24: 1,2,3,4,6,8,12,24. Common factors: 1,2,4,8. Only '4 and 8' are both common factors. Answer: 4 and 8."} {"t":"q","id":16064,"q":"In which of the following numbers does the digit 4 stand for 4 tenths?","e":"4 tenths = 0.4, the first digit after the decimal point. In 15.45 the digit 4 is in the tenths place = 0.4. Answer: 15.45."} {"t":"q","id":16066,"q":"Tristal bought 28 identical ovens and a kettle. Each oven cost 5 times as much as the kettle. The kettle cost $65. How much did she pay for all the ovens?","e":"1 oven = 5 x $65 = $325. 28 ovens = $325 x 28 = $9100. Answer: $9100."} {"t":"q","id":16067,"q":"On Tuesday, a factory produced 6 times as many notebooks as on Monday. A total of 4242 notebooks were produced on both days. How many notebooks were produced on Monday?","e":"Monday = 1 unit, Tuesday = 6 units, total = 7 units = 4242. 1 unit = 4242 \/ 7 = 606. Monday produced 606. Answer: 606."} {"t":"q","id":16068,"q":"Lucy can type 45 words in 1 minute. Lucy takes 10 seconds less than Paul to type the same number of words. How long does Paul take to type 45 words?","e":"1 minute = 60 s (Lucy's time). Paul takes 10 s more than Lucy: 60 + 10 = 70 s. Answer: 70 s."} {"t":"q","id":16069,"q":"The total mass of a box containing 4 identical books and 2 identical calculators was 2.94 kg. The total mass of the box containing 4 such books and 1 such calculator was 2.76 kg. What was the total mass of the box containing 4 such books?","e":"The extra calculator accounts for 2.94 - 2.76 = 0.18 kg (1 calculator). Box + 4 books = 2.76 - 0.18 = 2.58 kg. Answer: 2.58 kg."} {"t":"q","id":16071,"q":"The perimeter of a rectangular grass patch is 12 m. The breadth of the grass patch is 2 m. Find its length.","e":"Perimeter = 2 x (length + breadth), so length + breadth = 12 \/ 2 = 6 m. Length = 6 - 2 = 4 m. Answer: 4 m."} {"t":"q","id":16072,"q":"Aminah has 198 coins. She has 3 times as many coins as Bob. Charlie has 76 more coins than Bob. Charlie then gave Bob some of his coins such that they both have the same number of coins. How many more coins does Aminah have than Bob now?","e":"Bob = 198 \/ 3 = 66. Charlie = 66 + 76 = 142. Charlie shares equally with Bob: (66 + 142) \/ 2 = 104 each, so Bob now has 104. Aminah - Bob = 198 - 104 = 94. Answer: 94."} {"t":"q","id":16073,"q":"The table shows the number of customers at a restaurant over 4 days. Part of the table was covered by a stain. Day 1 had 30 customers and Day 2 had 45 customers. The number of customers on Day 3 is equal to the total number of customers on Day 1 and Day 2. The total number of customers on all 4 days is 230 when rounded to the nearest ten. What is the greatest possible number of customers on Day 4?","e":"Day 3 = 30 + 45 = 75. Days 1-3 = 30 + 45 + 75 = 150. For the 4-day total to round to 230, the total is 225 to 234, so Day 4 is 75 to 84. Greatest is 84. Answer: 84."} {"t":"q","id":16074,"q":"Jiayi had $13. She bought 2 different items and paid more than $10 for them. The prices were: Calculator $7.80, Stapler $2.10, Comic Book $6.65, Plastic Folder $0.85, Notebook $5.45. Which were the 2 items she bought?","e":"Try each pair: Folder+Comic = $7.50; Folder+Stapler = $2.95; Notebook+Calculator = $13.25 (over $13); Comic+Notebook = $6.65 + $5.45 = $12.10 (more than $10 and within $13). Answer: Comic Book and Notebook."} {"t":"q","id":16075,"q":"Find the product of 3608 and 9.
Answer: ","e":"3608 x 9 = 32 472. Answer: 32 472."} {"t":"q","id":16077,"q":"How many one-fifths are there in 1 whole?
Answer: ","e":"1 whole = 5\/5, which is 5 one-fifths. Answer: 5."} {"t":"q","id":16078,"q":"Express \\(\\dfrac{3}{9}\\) in its simplest form.","e":"Divide numerator and denominator by 3: 3\/9 = (3 \/ 3)\/(9 \/ 3) = 1\/3. Answer: 1\/3."} {"t":"q","id":16079,"q":"Express 84\/100 as a decimal.
Answer: ","e":"84\/100 = 0.84 (84 hundredths). Answer: 0.84."} {"t":"q","id":16080,"q":"Arrange the following numbers in order from the greatest to the smallest. 0.045 , 0.504 , 0.405
(a)   (b)   (c) ","e":"Compare tenths first: 0.504 and 0.405 have 5 and 4 tenths, 0.045 has 0 tenths. So 0.504 > 0.405 > 0.045. Greatest to smallest: 0.504, 0.405, 0.045."} {"t":"q","id":16081,"q":"Round 18.55 to the nearest whole number.
Answer: ","e":"The tenths digit is 5, so round up: 18.55 rounds to 19. Answer: 19."} {"t":"q","id":16082,"q":"Find the value of 6.72 x 7.
Answer: ","e":"6.72 x 7 = 47.04. (672 x 7 = 4704, then place the decimal two places: 47.04.) Answer: 47.04."} {"t":"q","id":16084,"q":"The area of a square tile is 49 cm\u00b2. Find its length.
Answer: ","e":"Area of a square = length x length = 49. 7 x 7 = 49, so the length is 7 cm. Answer: 7 cm."} {"t":"q","id":16089,"q":"Sam had a new book to read. He read \\(\\dfrac{3}{5}\\) of the new book in the morning and \\(\\dfrac{3}{10}\\) of it in the evening. What fraction of the book was left unread?","e":"3\/5 = 6\/10. Read = 6\/10 + 3\/10 = 9\/10. Unread = 1 - 9\/10 = 1\/10. Answer: 1\/10."} {"t":"q","id":16090,"q":"A farmer planted some trees in a straight row. The trees were planted at an equal distance apart from one another. The distance between the 2nd tree and the 5th tree was 2340 m. What was the distance between the 1st tree and the 10th tree?
Answer: ","e":"2nd to 5th tree = 3 gaps = 2340 m, so 1 gap = 780 m. 1st to 10th tree = 9 gaps = 9 x 780 = 3 x 2340 = 7020 m. Answer: 7020 m."} {"t":"q","id":16092,"q":"Container A had 13.5 l of tea. Container B had 4 times as much tea as container A. All the tea in container B was poured into identical bottles. Each bottle then has 3 l of tea. How many such bottles were filled with tea from container B?
Answer: ","e":"Container B = 13.5 x 4 = 54 l. Bottles = 54 \/ 3 = 18. Answer: 18 bottles."} {"t":"q","id":16093,"q":"Benny had his dinner from 17 15 to 19 05. After his dinner, he shopped for 2 h 55 min. How much time did he spend on having his dinner and shopping altogether?
Answer: ","e":"Dinner from 17 15 to 19 05 = 1 h 50 min. Total = 1 h 50 min + 2 h 55 min = 3 h 105 min = 4 h 45 min. Answer: 4 h 45 min."} {"t":"q","id":16096,"q":"Michelle and Bridget went shopping with the same amount of money. After Michelle spent $8.80 and Bridget spent $50, Michelle had 5 times as much money left as Bridget. (a) How much money did Michelle have in the end? (b) How much money did Bridget have at first?
(a)   (b) ","e":"They started equal. The difference in what they spent is $50 - $8.80 = $41.20, which equals the difference in money left = 4 units (Michelle 5 units, Bridget 1 unit). 4 units = $41.20, 1 unit = $10.30. (a) Michelle's end = 5 units = $51.50. (b) Bridget at first = money left + spent = $10.30 + $50 = $60.30. Answers: (a) $51.50; (b) $60.30."} {"t":"q","id":16097,"q":"May and Nina have 274 beads altogether. May and Oliver have 618 beads altogether. The number of beads Oliver has is nine times that of Nina. How many beads does May have?
Answer: ","e":"Oliver - Nina = (May+Oliver) - (May+Nina) = 618 - 274 = 344. Oliver = 9 x Nina, so Oliver - Nina = 8 units = 344, 1 unit (Nina) = 43. May = 274 - Nina = 274 - 43 = 231. Answer: 231 beads."} {"t":"q","id":16098,"q":"Rope A is 5\/6 m shorter than Rope B. Rope C is 1\/6 m longer than Rope A. Rope C is 2\/3 m long. (a) What is the length of Rope A? (b) What is the length of Rope B? Give your answer in the simplest form.
(a)   (b) ","e":"(a) Rope A = Rope C - 1\/6 = 2\/3 - 1\/6 = 4\/6 - 1\/6 = 3\/6 = 1\/2 m. (b) Rope B = Rope A + 5\/6 = 3\/6 + 5\/6 = 8\/6 = 1 2\/6 = 1 1\/3 m. Answers: (a) 1\/2 m; (b) 1 1\/3 m."} {"t":"q","id":16099,"q":"At a bakery, the price of a cupcake was $2 and the price of a tart was $5. Ms Lim paid $38 to buy a total of 13 cupcakes and tarts. How many more cupcakes than tarts did Ms Lim buy?
Answer: ","e":"If all 13 were cupcakes: 13 x $2 = $26. Extra = $38 - $26 = $12. Each swap to a tart adds $5 - $2 = $3, so tarts = $12 \/ $3 = 4. Cupcakes = 13 - 4 = 9. More cupcakes than tarts = 9 - 4 = 5. Answer: 5."} {"t":"q","id":16101,"q":"Which of the following is not a factor of 56?","e":"Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56. 56 is not divisible by 6 (56 \/ 6 = 9 r 2), so 6 is not a factor."} {"t":"q","id":16103,"q":"4 min 45 s =","e":"1 min = 60 s, so 4 min = 240 s. 240 s + 45 s = 285 s."} {"t":"q","id":16105,"q":"5 2\/3 = \/3. What is the missing number in the box?","e":"5 2\/3 = (5 x 3 + 2)\/3 = 17\/3, so the missing numerator is 17."} {"t":"q","id":16106,"q":"In the number 97.85, the digit is in the tenths place.","e":"In 97.85, the first digit after the decimal point is the tenths place. That digit is 8."} {"t":"q","id":16108,"q":"Arrange the following decimals from the smallest to the greatest. 5.8 , 0.58 , 5.08 , 0.85","e":"Compare whole-number parts first: 0.58 and 0.85 are less than 1; 5.08 and 5.8 are over 5. Within each: 0.58 < 0.85 and 5.08 < 5.8. Order: 0.58, 0.85, 5.08, 5.8."} {"t":"q","id":16111,"q":"A glass can hold 0.4 l of water. 9 such glasses are needed to fill 2 jugs to the brim. What is the capacity of 1 jug?","e":"9 glasses = 9 x 0.4 l = 3.6 l fills 2 jugs. So 1 jug = 3.6 \/ 2 = 1.8 l."} {"t":"q","id":16113,"q":"The chairs in a theatre were arranged equally in rows. There were 11 rows of chairs. Mark sat at the fourth row. 7 people were seated on his right and 9 people were seated on his left. How many chairs were there in the theatre?","e":"Chairs in one row = 7 (right) + 9 (left) + 1 (Mark) = 17. Total = 17 x 11 rows = 187."} {"t":"q","id":16115,"q":"Arrange the following numbers from the greatest to the smallest. 138 , 813 , 831 , 183 , , , ","e":"Compare hundreds digit: 831 and 813 start with 8, 183 and 138 start with 1. Within 8xx: 831 > 813. Within 1xx: 183 > 138. Greatest to smallest: 831, 813, 183, 138."} {"t":"q","id":16119,"q":"What is the value of \\(\\dfrac{5}{6}\\) + \\(\\dfrac{1}{3}\\)? Express your answer as a mixed number.","e":"1\/3 = 2\/6. 5\/6 + 2\/6 = 7\/6 = 1 1\/6."} {"t":"q","id":16122,"q":"Which two of the fractions below are smaller than 1\/2? 2\/11 , 3\/10 , 4\/8 , 5\/7 and ","e":"Half of each denominator: 2\/11 (half is 5.5, 2<5.5 so smaller), 3\/10 (half is 5, 3<5 smaller), 4\/8 = 1\/2 (equal, not smaller), 5\/7 (half is 3.5, 5>3.5 larger). The two smaller than 1\/2 are 2\/11 and 3\/10."} {"t":"q","id":16124,"q":"Mrs Li is 37 years old. Her husband is 3 years older than her. Their son is 29 years younger than Mrs Li. What is their total age? ","e":"Husband = 37 + 3 = 40. Son = 37 - 29 = 8. Total = 37 + 40 + 8 = 85."} {"t":"q","id":16126,"q":"Raju took 9 h 20 min to drive from Singapore to Kedah. He reached Kedah at 06 10. What time did Raju start driving from Singapore? Express your answer in 24-hour clock. ","e":"Work backwards from 06 10 by 9 h 20 min: 06 10 minus 9 h = 21 10 (previous day); minus 20 min = 20 50."} {"t":"q","id":16131,"q":"Mrs Goh bought a dress and 2 skirts for $250. The dress cost $71.50 more than a skirt. How much was the cost of 1 skirt? $","e":"Remove the extra: 250 - 71.50 = 178.50 equals 3 equal skirts. 178.50 \/ 3 = $59.50 per skirt."} {"t":"q","id":16132,"q":"The lunch set meal at a restaurant allows customers to choose a set that consists of a main course, a soup and a drink. The main courses are pasta and chicken sandwich. The soups are mushroom soup and corn soup. The drinks are coffee, tea and orange juice. How many different combinations of lunch set meals are available for the customers to choose? ","e":"Multiply the choices: 2 main courses x 2 soups x 3 drinks = 12 combinations."} {"t":"q","id":16133,"q":"A pen cost $1.20 and a ruler cost $0.40. Sue bought 6 pens and 5 rulers. How much more did she pay for the pens than the rulers? $","e":"Pens: 6 x $1.20 = $7.20. Rulers: 5 x $0.40 = $2.00. Difference = $7.20 - $2.00 = $5.20."} {"t":"q","id":16136,"q":"The journey from Rahman's house to Changi Airport by bus would take 1 h 50 min. The same journey by MRT would take 35 minutes shorter than by bus. What is the duration of the journey from Rahman's house to the Changi Airport by MRT? Rahman left his house and took the MRT at 22 50. He reached Changi Airport 2 h 55 min before his flight. What time is his flight? Express your answer using the 24-hour clock. ","e":"(a) 1 h 50 min - 35 min = 1 h 15 min. (b) Arrive = 22 50 + 1 h 15 min = 00 05. Flight = 00 05 + 2 h 55 min = 03 00."} {"t":"q","id":16137,"q":"The total mass of an empty box and 5 similar metal balls was 2.6 kg. The total mass of the same empty box and 3 similar metal balls was 2.34 kg. What was the mass of 1 metal ball? What was the mass of the empty box? ","e":"(a) The difference of 2 balls = 2.6 - 2.34 = 0.26 kg, so 1 ball = 0.26 \/ 2 = 0.13 kg. (b) 3 balls = 3 x 0.13 = 0.39 kg; box = 2.34 - 0.39 = 1.95 kg."} {"t":"q","id":16140,"q":"Mrs Lim baked 300 fruit tarts. 1\/2 of them were pineapple tarts, 2\/5 of them were strawberry tarts and the remaining were mango tarts. How many mango tarts did she bake? Mrs Lim sold the pineapple and strawberry tarts at 5 for $9. How much would Mrs Lim collect from her sale of all the pineapple and strawberry tarts? $","e":"(a) Pineapple = 1\/2 x 300 = 150; strawberry = 2\/5 x 300 = 120; mango = 300 - 150 - 120 = 30. (b) Pineapple + strawberry = 270 tarts; 270 \/ 5 = 54 sets; 54 x $9 = $486."} {"t":"q","id":16141,"q":"Siti had 604 more stamps than Tom. After Siti had given 902 stamps to Tom, he had 4 times as many stamps as her. How many stamps did Tom have at first? ","e":"Let Tom first = t, so Siti first = t + 604. After Siti gives 902: Tom = t + 902, Siti = t + 604 - 902 = t - 298. Tom is 4 times Siti: t + 902 = 4(t - 298). t + 902 = 4t - 1192, so 3t = 2094, t = 698. Tom had 698 stamps at first."} {"t":"q","id":16142,"q":"The value of the digit 2 in 72 415 is .","e":"In 72 415, the digit 2 is in the thousands place. Its value is 2 x 1000 = 2000."} {"t":"q","id":16143,"q":"45 thousands and 6 tens is the same as .","e":"45 thousands = 45 000; 6 tens = 60. 45 000 + 60 = 45 060."} {"t":"q","id":16144,"q":"Which of the following is a factor of both 18 and 42?","e":"Factors of 18: 1,2,3,6,9,18. Factors of 42: 1,2,3,6,7,14,21,42. The common factor among the options is 6."} {"t":"q","id":16145,"q":"Which of the following is not an equivalent fraction of 1\/6?","e":"1\/6 = 2\/12 = 4\/24 = 6\/36. But 3\/15 = 1\/5, which is not equal to 1\/6. So 3\/15 is not equivalent."} {"t":"q","id":16147,"q":"The digit 5 in 14.57 stands for 5 .","e":"In 14.57 the digit immediately after the decimal point is the tenths place. So 5 stands for 5 tenths."} {"t":"q","id":16148,"q":"10 - 3.04 = . What is the missing number in the box?","e":"10.00 - 3.04 = 6.96."} {"t":"q","id":16154,"q":"The area of a square is 64 cm2. Find the perimeter of the square.","e":"Side x side = 64, so side = 8 cm (8 x 8 = 64). Perimeter = 4 x 8 = 32 cm."} {"t":"q","id":16155,"q":"1 slice of cake cost as much as 3 muffins. John paid $30 for 2 slices of cakes and 4 muffins. How much does 1 slice of cake cost?","e":"1 cake = 3 muffins. 2 cakes = 6 muffins. So 2 cakes + 4 muffins = 6 + 4 = 10 muffins = $30. 1 muffin = $3. 1 cake = 3 muffins = $9."} {"t":"q","id":16157,"q":"Write twelve thousand and ninety-nine in figures. ","e":"Twelve thousand = 12 000; ninety-nine = 99. 12 000 + 99 = 12 099."} {"t":"q","id":16158,"q":"Fill in the blank with the correct number in the number pattern. 450 , 425 , 400 , , 350","e":"The pattern decreases by 25 each time: 450, 425, 400, 375, 350. The missing number is 375."} {"t":"q","id":16159,"q":"How many one-fifths are there in 1 whole? ","e":"1 whole = 5\/5, which is 5 one-fifths. So there are 5."} {"t":"q","id":16163,"q":"Arrange the following numbers from the smallest to the greatest. 3\/5 , 0.606 , 0.066 , , ","e":"Convert 3\/5 to a decimal: 3\/5 = 0.6 = 0.600. Compare 0.066, 0.600, 0.606. Smallest to greatest: 0.066, 3\/5 (0.600), 0.606."} {"t":"q","id":16164,"q":"Express 7\/100 as a decimal. ","e":"7\/100 means 7 hundredths. As a decimal, hundredths is the second place after the point: 0.07."} {"t":"q","id":16165,"q":"Round 18.64 to the nearest whole number. ","e":"The tenths digit is 6, which is 5 or more, so round up. 18.64 rounds to 19."} {"t":"q","id":16167,"q":"Some factors of 81 are 1, 9 and 81. What are the other 2 factors of 81? and ","e":"Factors of 81: 1, 3, 9, 27, 81. Apart from 1, 9 and 81, the other two factors are 3 and 27."} {"t":"q","id":16168,"q":"Pencils are sold in packets of 6 and erasers are sold in packets of 9. Paul wanted to buy the same number of pencils and erasers. What is the least number of packets of erasers Paul needs to buy? ","e":"The least common multiple of 6 and 9 is 18. To get 18 erasers in packets of 9, Paul needs 18 \/ 9 = 2 packets of erasers."} {"t":"q","id":16173,"q":"A string was 10 m long. Sam used 3.16 m of it. He then cut the remaining string equally into 6 pieces. What was the length of each piece of string? ","e":"Remaining string = 10 - 3.16 = 6.84 m. Cut into 6 equal pieces: 6.84 \/ 6 = 1.14 m each."} {"t":"q","id":16174,"q":"The total mass of a basket containing 7 identical balls was 9.48 kg. When 3 balls were taken out of the basket, the total mass of the basket and the remaining balls became 5.67 kg. What was the mass of 1 ball? ","e":"Removing 3 balls reduced the mass from 9.48 kg to 5.67 kg, so 3 balls = 9.48 - 5.67 = 3.81 kg. 1 ball = 3.81 \/ 3 = 1.27 kg."} {"t":"q","id":16175,"q":"The sum of two decimals is 36.56. The greater number is three times as much as the smaller number. Find the greater number. ","e":"Let the smaller be 1 unit, the greater 3 units. Total = 4 units = 36.56, so 1 unit = 36.56 \/ 4 = 9.14. Greater number = 3 x 9.14 = 27.42."} {"t":"q","id":16176,"q":"Serene visits the library every 3 days. Devi visits the library every 4 days. They first met at the library on 10 March. What is the next date both girls will meet again at the library? ","e":"They meet again after the least common multiple of 3 and 4 days = 12 days. 10 March + 12 days = 22 March."} {"t":"q","id":16177,"q":"The mass of a papaya is \\(\\dfrac{1}{2}\\) kg. A watermelon weighs \\(\\dfrac{1}{6}\\) kg more than the papaya. Find the total mass of the papaya and the watermelon. Express your answer as a mixed number in the simplest form.","e":"Papaya = 1\/2 = 3\/6 kg. Watermelon = 3\/6 + 1\/6 = 4\/6 kg. Total = 3\/6 + 4\/6 = 7\/6 = 1 1\/6 kg."} {"t":"q","id":16180,"q":"Three boys sold a total of 745 tickets during a carnival. Abel sold twice as many tickets as Nell. Hamid sold 135 fewer tickets than Abel. (a) How many tickets did Nell sell? (b) How many tickets did Abel sell? , ","e":"Let Nell = 1 unit. Abel = 2 units. Hamid = Abel - 135 = 2 units - 135. Total = 1u + 2u + (2u - 135) = 5u - 135 = 745, so 5u = 880, u = 176. (a) Nell = 176. (b) Abel = 2 x 176 = 352."} {"t":"q","id":16182,"q":"A jug was completely filled with water at first. Siti drank 3\/5 of the water and spilled 1\/10 of it. Then she had 480 ml left. (a) What fraction of the water was left in the jug? (b) How much water was in the jug at first? , ","e":"(a) Used = 3\/5 + 1\/10 = 6\/10 + 1\/10 = 7\/10. Fraction left = 10\/10 - 7\/10 = 3\/10. (b) 3\/10 of the jug = 480 ml, so 1\/10 = 480 \/ 3 = 160 ml; whole jug = 160 x 10 = 1600 ml."} {"t":"q","id":16185,"q":"Which of the following numbers when rounded to the nearest ten becomes 74 500?","e":"Rounding to the nearest ten gives 74 500 for values from 74 495 to 74 504. 74 498 rounds to 74 500. (74 444 to 74 440; 74 509 to 74 510; 74 552 to 74 550.)"} {"t":"q","id":16187,"q":"Which of the following fractions is in its simplest form?","e":"5\/8 has no common factor other than 1, so it is in simplest form. 2\/6 = 1\/3, 3\/9 = 1\/3, 6\/10 = 3\/5 can all be simplified."} {"t":"q","id":16190,"q":"7 is not a factor of .","e":"14 = 7x2, 35 = 7x5, 49 = 7x7 are all divisible by 7. 72 is not divisible by 7 (72 \/ 7 leaves a remainder), so 7 is not a factor of 72."} {"t":"q","id":16192,"q":"Mr Faiz had some stickers. He gave away 2\/3 of his stickers to 5 students and had 30 stickers left. How many stickers did each of his students receive?","e":"The 30 left is 1\/3 of the total, so total = 90. He gave away 2\/3 x 90 = 60 stickers to 5 students. Each student got 60 \/ 5 = 12."} {"t":"q","id":16197,"q":"Shamita is 1.5 m tall. She is taller than Ali by 0.03 m. How tall is Ali?","e":"Ali is shorter than Shamita, so Ali = 1.50 - 0.03 = 1.47 m."} {"t":"q","id":16202,"q":"A repeated pattern is formed using the letters A, B, C and D. The first 12 letters are A B C D A B C D A B C D. How many 'A's are there if there is a total of 42 letters in the pattern?","e":"The pattern repeats every 4 letters (ABCD), with A in position 1 of each block. 42 \/ 4 = 10 remainder 2, giving 10 full blocks (10 A's) plus 'A B', adding one more A. Total = 11 A's."} {"t":"q","id":16205,"q":"Find the product of 3028 and 4.
Answer: ","e":"3028 x 4 = 12 112."} {"t":"q","id":16208,"q":"Find the value of 1 - \\(\\dfrac{1}{8}\\) - \\(\\dfrac{1}{4}\\).","e":"Write all as eighths: 1 = 8\/8, 1\/4 = 2\/8. 8\/8 - 1\/8 - 2\/8 = 5\/8."} {"t":"q","id":16210,"q":"Write 8 thousandths as a decimal.
Answer: ","e":"8 thousandths = 8\/1000 = 0.008."} {"t":"q","id":16212,"q":"Arrange the following numbers from the smallest to the greatest. 4\/5 , 0.804 , 0.084
(a)   (b)   (c) ","e":"4\/5 = 0.800. Compare 0.084, 0.800, 0.804: smallest to greatest is 0.084, 4\/5 (0.800), 0.804."} {"t":"q","id":16214,"q":"Mrs Lee has some buttons. The number of buttons she has is more than 10 but fewer than 25. She can pack all the buttons into bags of 2 or 3 with no remainder. What is one possible number of buttons she has?
Answer: ","e":"The number must be a common multiple of 2 and 3 (a multiple of 6) between 10 and 25: 12, 18 or 24. One possible answer is 12."} {"t":"q","id":16219,"q":"Rani needed 30 minutes to bake a cake. At 12.45 p.m., she had baked 3 such cakes. At what time did she start baking the first cake given that she baked one cake after another, without any break in between? Express your answer using the 12-hr clock.
Answer: ","e":"3 cakes x 30 min = 90 min = 1 h 30 min of baking. Counting back from 12.45 p.m. by 1 h 30 min gives 11.15 a.m."} {"t":"q","id":16221,"q":"Alice, Bala and Carin shared 850 cards. Bala had 30 more cards than Alice. Carin had 40 more cards than Bala. (a) Who had the most number of cards? (b) How many cards did Bala have?
(a)   (b) ","e":"(a) Carin has the most (Bala = Alice + 30, Carin = Bala + 40). (b) Take Bala as a unit. Alice = Bala - 30, Carin = Bala + 40. Total: (Bala-30) + Bala + (Bala+40) = 850, so 3 Bala + 10 = 850, 3 Bala = 840, Bala = 280."} {"t":"q","id":16222,"q":"Mr Kumar mixed 15 l of blue paint and 15.42 l of red paint to obtain purple paint. He then poured all the purple paint into a big container and a small container. The amount of paint poured into the big container was 5 times as much as that in the small container. (a) How much purple paint did Mr Kumar have? (b) How much purple paint did Mr Kumar pour into the small container?
(a)   (b) ","e":"(a) Total purple = 15 + 15.42 = 30.42 l. (b) Big is 5 times the small, so together they are 6 equal parts: 30.42 \/ 6 = 5.07 l in the small container."} {"t":"q","id":16223,"q":"At first, all the donuts in a bakery were placed on 20 trays with an equal number of donuts on each tray. 5 trays were removed and the donuts on these trays were distributed equally on the remaining 15 trays. In the end, the number of donuts on each remaining tray increased by 2. (a) Find the total number of donuts on the 5 trays which were removed. (b) Find the number of donuts on each tray at first.
(a)   (b) ","e":"(a) The 15 remaining trays each gained 2 donuts, so the 5 removed trays held 15 x 2 = 30 donuts in total. (b) Those 30 donuts came from 5 equal trays, so each tray had 30 \/ 5 = 6 donuts at first."} {"t":"q","id":16224,"q":"Nurul had 280 red and blue marbles altogether. After Nurul gave away 1\/3 of her red marbles, the number of red marbles left was equal to the number of blue marbles she had. (a) What fraction of her red marbles had Nurul left? (b) Find the difference in the number of red and blue marbles Nurul had at first.
(a)   (b) ","e":"(a) She gave away 1\/3, so 1 - 1\/3 = 2\/3 of red marbles were left. (b) Red left (2\/3 of red) = blue. So red : blue = 3 : 2, total 5 units = 280, 1 unit = 56. Difference = 3 units - 2 units = 1 unit = 56."} {"t":"q","id":16226,"q":"46 thousands and 2 tens is the same as","e":"46 thousands = 46 000 and 2 tens = 20. 46 000 + 20 = 46 020."} {"t":"q","id":16227,"q":"Which one of the following is a factor of both 12 and 56?","e":"Factors of 12: 1,2,3,4,6,12. Factors of 56: 1,2,4,7,8,14,28,56. The common factor among the options is 4."} {"t":"q","id":16228,"q":"Write 8 7\/25 as a decimal.","e":"7\/25 = 28\/100 = 0.28 (multiply numerator and denominator by 4). So 8 7\/25 = 8.28."} {"t":"q","id":16231,"q":"Which one of the following is not an equivalent fraction of 1\/4 ?","e":"2\/8, 3\/12 and 4\/16 all simplify to 1\/4. 6\/20 simplifies to 3\/10, which is not 1\/4. So 6\/20 is the odd one out."} {"t":"q","id":16233,"q":"What time is 25 minutes before midnight?","e":"Midnight is 24 00 (i.e. 00 00). 25 minutes before is 23 60 - 25 = 23 35."} {"t":"q","id":16236,"q":"Some factors of 63 are 1, 3, 7 and 63. What are the other two factors of 63?
(a)   (b) ","e":"63 = 9 \u00d7 7 and 63 = 21 \u00d7 3. The full list of factors is 1, 3, 7, 9, 21, 63. The two missing factors are 21 and 9."} {"t":"q","id":16237,"q":"Find the product of 2369 and 4. ","e":"2369 \u00d7 4 = 9476."} {"t":"q","id":16239,"q":"Find the value of 3.29 \u00d7 6. ","e":"3.29 \u00d7 6 = 19.74."} {"t":"q","id":16240,"q":"How many one-eighths are there in 1 whole? ","e":"1 whole = 8\/8, which is eight one-eighths. So there are 8."} {"t":"q","id":16241,"q":"Which two of the fractions 2\/5 , 3\/6 , 4\/7 , 5\/11 are smaller than 1\/2 ?
(a)   (b) ","e":"Compare each to 1\/2: 2\/5 = 0.4 (<1\/2), 3\/6 = 1\/2 (equal), 4\/7 \u2248 0.571 (>1\/2), 5\/11 \u2248 0.455 (<1\/2). The two smaller than 1\/2 are 2\/5 and 5\/11."} {"t":"q","id":16242,"q":"What is the value of \\(\\dfrac{9}{10}\\) + \\(\\dfrac{4}{5}\\) ? Express your answer as a mixed number.","e":"4\/5 = 8\/10. 9\/10 + 8\/10 = 17\/10 = 1 7\/10."} {"t":"q","id":16245,"q":"Damien is facing East. He makes a 3\/4 -turn in the clockwise direction. Which direction is Damien facing after making the turn?","e":"Starting at East, a 3\/4-turn clockwise = 270\u00b0. East \u2192 South (1\/4) \u2192 West (1\/2) \u2192 North (3\/4). He faces North."} {"t":"q","id":16246,"q":"Use all the digits 8, 3, 0, 7, 4 to form the smallest 5-digit odd number. Each digit can only be used once. ","e":"Odd means the last digit is odd (3 or 7). For the smallest number, the leading digit cannot be 0. Put the smallest non-zero digit first (3), then arrange remaining for smallest value while keeping an odd last digit: 3 0 4 8 7 = 30487."} {"t":"q","id":16247,"q":"Divide 8094 by 7. The quotient is with a remainder of .","e":"8094 \u00f7 7: 7 \u00d7 1156 = 8092, remainder 8094 - 8092 = 2. Quotient 1156, remainder 2."} {"t":"q","id":16248,"q":"Express 3.08 as a mixed number in its simplest form.","e":"3.08 = 3 8\/100. Simplify 8\/100 by dividing by 4 = 2\/25. So 3.08 = 3 2\/25."} {"t":"q","id":16249,"q":"Eve bought a pair of scissors costing $4.05 and a calculator costing $8.60 from the bookshop. How much did she spend in total? Give your answer to the nearest dollar. Ans: $","e":"$4.05 + $8.60 = $12.65. Rounded to the nearest dollar, $12.65 \u2248 $13."} {"t":"q","id":16250,"q":"How many of the letters P, V, H, S, M are symmetric? ","e":"Letters with a line of symmetry: V (vertical), H (vertical and horizontal), M (vertical). P and S have no line of symmetry. So 3 letters are symmetric."} {"t":"q","id":16253,"q":"Glen left his house at 07 45. He took 35 minutes to reach the library. He had to wait 10 minutes for the library to open. What time did the library open? Express your answer using the 24-hour clock. Ans: ","e":"07 45 + 35 min = 08 20 (arrives). 08 20 + 10 min wait = 08 30. The library opened at 0830."} {"t":"q","id":16254,"q":"There are 700 sweets in a container when rounded to the nearest hundred. What is the greatest possible number of sweets in the container? Ans: ","e":"Numbers that round to 700 to the nearest hundred range from 650 to 749. The greatest is 749."} {"t":"q","id":16257,"q":"Using the 3 digits 6, 7, 5, Peter formed a number with 2 decimal places. The number became 6 when he rounded it to the nearest whole number. What could be a possible number that he had formed? ","e":"A 2-decimal-place number using digits 6,7,5 that rounds to 6 must be from 5.50 to 6.49. 5.76 rounds to 6. (Key gives 5.76; 5.67 also works.)"} {"t":"q","id":16258,"q":"A table is 5 times as heavy as a chair. Three chairs and one table weigh 73.36 kg. What is the mass of one chair? Ans: kg","e":"Table = 5 chairs. 3 chairs + 1 table = 3 chairs + 5 chairs = 8 chairs = 73.36 kg. One chair = 73.36 \u00f7 8 = 9.17 kg."} {"t":"q","id":16259,"q":"Sonia ate \\(\\dfrac{2}{7}\\) of a cake. Lucas ate \\(\\dfrac{2}{5}\\) of the same cake. What fraction of the cake did Lucas eat more than Sonia?","e":"2\/5 - 2\/7 = 14\/35 - 10\/35 = 4\/35."} {"t":"q","id":16260,"q":"Sam took 2 h 20 min to complete his homework. He completed it at 8.25 p.m. At what time did Sam start doing his homework? Express your answer using the 24-hour clock. Ans: ","e":"8.25 p.m. = 20 25. Subtract 2 h 20 min: 20 25 - 2 h = 18 25, then - 20 min = 18 05. Sam started at 1805."} {"t":"q","id":16263,"q":"In a student care centre, the windows are wiped every 3 days and the fans are wiped every 9 days. Both the windows and the fans were wiped on the last day of June. On how many occasions were the windows and fans wiped together on the same day in July? ","e":"Both are wiped together every common multiple of 3 and 9, i.e. every 9 days (LCM of 3 and 9 = 9). Starting from 30 June, the next together-days are 9 Jul, 18 Jul, 27 Jul \u2014 3 occasions in July."} {"t":"q","id":16264,"q":"Mr Tan went on a cruise with his wife and 4 children. A child ticket cost $170 less than an adult ticket. He paid $1600 for all the tickets. What was the cost of a child ticket? Ans: $","e":"There are 2 adults and 4 children = 6 tickets. If all 6 were adult price, replace the 4 child tickets: 4 \u00d7 $170 = $680 less. So 6 adult tickets = $1600 + $680 = $2280. One adult = $2280 \u00f7 6 = $380. Child = $380 - $170 = $210."} {"t":"q","id":16265,"q":"David's water bottle was 7\/12 filled with water. After he had drunk 270 ml of water from the bottle, it became 1\/3 full. What was the capacity of David's water bottle? Ans: ml","e":"1\/3 = 4\/12. The water drunk = 7\/12 - 4\/12 = 3\/12 = 1\/4 of the bottle = 270 ml. So 1\/12 = 270 \u00f7 3 = 90 ml. Full capacity (12\/12) = 90 \u00d7 12 = 1080 ml."} {"t":"q","id":16362,"q":"(a) Write eighty-five thousand and twenty-one in numerals.
(b) In 21 435, which digit is in the hundreds place?
(a)   (b) ","e":"(a) Eighty-five thousand = 85 000, and twenty-one = 21, so the numeral is 85 021. (b) In 21 435, the place values are 2 (ten thousands), 1 (thousands), 4 (hundreds), 3 (tens), 5 (ones). The digit in the hundreds place is 4."} {"t":"q","id":16363,"q":"(a) Round 24 568 to the nearest ten.
(b) Round 89 542 to the nearest thousand.
(a)   (b) ","e":"(a) The ones digit of 24 568 is 8 (5 or more), so round up: 24 570. (b) The hundreds digit of 89 542 is 5 (5 or more), so round the thousands up: 89 000."} {"t":"q","id":16364,"q":"(a) 1 and 15 are factors of 15. List the other two factors of 15.
(b) What is the first common multiple of 6 and 9?
(a)   (b)   (c) ","e":"(a) Factors of 15 are the numbers that divide 15 exactly: 1, 3, 5, 15. Besides 1 and 15, the other two are 3 and 5. (b) Multiples of 6: 6, 12, 18, ...; multiples of 9: 9, 18, ... The first common multiple is 18."} {"t":"q","id":16365,"q":"(a) 30 745 = + 700 + 40 + 5. What is the missing number in the box?
(b) What is the value of the digit 7 in 9276?","e":"(a) 30 745 = 30 000 + 700 + 40 + 5, so the missing number is 30 000. (b) In 9276 the digit 7 is in the tens place, so its value is 7 tens = 70."} {"t":"q","id":16366,"q":"Arrange the following from the smallest to the greatest.
\\(\\dfrac{3}{7}\\) , \\(\\dfrac{2}{9}\\) , \\(\\dfrac{3}{9}\\)
(a)   (b)   (c) ","e":"Compare the fractions. 2\/9 and 3\/9 share denominator 9, so 2\/9 < 3\/9. Then 3\/9 = 1\/3 \u2248 0.33 and 3\/7 \u2248 0.43, so 3\/9 < 3\/7. From smallest to greatest: 2\/9, 3\/9, 3\/7."} {"t":"q","id":16367,"q":"(a) Express \\(\\dfrac{21}{8}\\) as a mixed number.
(b) Express \\(4\\dfrac{5}{7}\\) as an improper fraction.
(a)   (b) ","e":"(a) 21 \u00f7 8 = 2 remainder 5, so 21\/8 = 2 5\/8. (b) 4 5\/7 = (4 \u00d7 7 + 5)\/7 = (28 + 5)\/7 = 33\/7."} {"t":"q","id":16368,"q":"Express your answer as a mixed number in its simplest form.
\\(\\dfrac{5}{6}\\) + \\(\\dfrac{2}{3}\\) =","e":"Make denominators the same: 2\/3 = 4\/6. Then 5\/6 + 4\/6 = 9\/6 = 3\/2 = 1 1\/2."} {"t":"q","id":16369,"q":"A number is 21 300 when rounded to the nearest hundred. What could be the largest possible value for this number?
Answer: ","e":"To round to 21 300 at the nearest hundred, the number must be from 21 250 up to 21 349 (21 350 would round up to 21 400). The largest such whole number is 21 349."} {"t":"q","id":16370,"q":"Identify two fractions between \\(\\dfrac{2}{3}\\) and \\(\\dfrac{3}{4}\\). List them in their simplest forms.
(a)   (b) ","e":"Use a common denominator. 2\/3 = 24\/36 and 3\/4 = 27\/36, so 25\/36 and 26\/36 lie between them. 25\/36 is already in simplest form; 26\/36 = 13\/18. The two fractions are 25\/36 and 13\/18."} {"t":"q","id":16371,"q":"Leslie thought of a number. It has 8 factors. He listed some of the factors in increasing order.
1, 2, 3, 6, , 14, 21,
What are the missing factors?","e":"The listed factors 1, 2, 3, 6, 14, 21 suggest the number is 42. The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42 (8 factors). The missing ones, in order, are 7 (between 6 and 14) and 42 (after 21)."} {"t":"q","id":16372,"q":"A bakery buys 1250 kg of flour every 2 months. It buys the same amount of flour each month.
(a) How much flour does the bakery buy each month?
(b) How much flour does the bakery buy in a year?
(a)   (b) ","e":"(a) 1250 kg over 2 months = 1250 \u00f7 2 = 625 kg each month. (b) A year has 12 months, so 625 \u00d7 12 = 7500 kg."} {"t":"q","id":16373,"q":"Jack and Bill had a total of $1730 in savings at first. After Jack donated $170 to charity, Bill had 3 times as much money as Jack. How much savings did Bill have?
Answer: ","e":"After Jack donates $170, the remaining total is 1730 \u2212 170 = $1560. Now Bill = 3 \u00d7 Jack, so they form 4 equal units: 1 unit = 1560 \u00f7 4 = $390 (Jack). Bill = 3 units = 3 \u00d7 390 = $1170."} {"t":"q","id":16374,"q":"Ms Tan bought 15 packets of stickers. Each packet contained 25 stickers. She kept 100 stickers for herself and gave the rest to 5 friends. Each friend received an equal number of stickers. How many stickers did each friend get?
Answer: ","e":"Total stickers = 15 \u00d7 25 = 375. After keeping 100: 375 \u2212 100 = 275. Shared among 5 friends: 275 \u00f7 5 = 55 stickers each."} {"t":"q","id":16375,"q":"George had $108 and Trevor had $52. After each of them bought a calculator at the same price, George had five times as much money left as Trevor. What was the cost of the calculator?
Answer: ","e":"The difference between them stays the same: 108 \u2212 52 = $56. After buying, George = 5 \u00d7 Trevor, so the difference is 4 units = $56, giving 1 unit = 56 \u00f7 4 = $14 (Trevor's money left). Calculator cost = 52 \u2212 14 = $38."} {"t":"q","id":16376,"q":"The cost of an adult ticket to a funfair was $8. The cost of a child ticket was $5. On a Monday, there were 50 visitors and $304 was collected altogether. How many more children than adults visited the funfair that day?
Answer: ","e":"Assume all 50 were children: 50 \u00d7 $5 = $250. The extra $304 \u2212 $250 = $54 comes from adults paying $3 more each ($8 \u2212 $5). Number of adults = 54 \u00f7 3 = 18, so children = 50 \u2212 18 = 32. More children than adults = 32 \u2212 18 = 14."} {"t":"q","id":16453,"q":"Which of the following is sixteen thousand, four hundred and nine in numerals?","e":"Sixteen thousand = 16 000, four hundred = 400, and nine = 9. Adding them gives 16 000 + 400 + 9 = 16 409."} {"t":"q","id":16454,"q":"Which of the following numbers is the smallest?","e":"All numbers share 18 thousands. Compare the hundreds: 18 769 and 18 796 have 7 hundreds, smaller than 9. Then compare tens: 6 tens (18 769) is smaller than 9 tens (18 796). So 18 769 is the smallest."} {"t":"q","id":16455,"q":"In the number pattern, what is the missing number?
50 880, 50 910, 50 940, 50 970, ________, 51 030","e":"Each term increases by 30 (50 910 - 50 880 = 30). So the missing term is 50 970 + 30 = 51 000. Check: 51 000 + 30 = 51 030."} {"t":"q","id":16456,"q":"Which of the following numbers is 38 500 when rounded to the nearest hundred?","e":"Rounding to the nearest hundred, the result 38 500 comes from values 38 450 to 38 549. Among the options, 38 549 rounds to 38 500. (38 409 and 38 449 round to 38 400; 38 550 rounds up to 38 600.)"} {"t":"q","id":16457,"q":"Which of the following is a factor of both 16 and 24?","e":"Factors of 16: 1, 2, 4, 8, 16. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. A common factor is 8 (it divides both). 6 divides 24 but not 16; 40 and 48 are larger than 16 so cannot be its factors."} {"t":"q","id":16458,"q":"Which of the following is a common multiple of 8 and 12?","e":"Multiples of 8: 8, 16, 24, ... Multiples of 12: 12, 24, 36, ... The number 24 appears in both lists, so it is a common multiple. (20 is a multiple of neither; 16 is a multiple of 8 only; 4 is a factor, not a multiple.)"} {"t":"q","id":16460,"q":"In a school, there were 832 boys and 164 girls. How many more boys than girls were there?
Answer: ","e":"Find the difference: 832 - 164 = 668. There are 668 more boys than girls."} {"t":"q","id":16461,"q":"There are 428 sweets in a bottle. Mrs Tan bought 14 bottles to give her pupils. How many sweets did she buy altogether?
Answer: ","e":"Multiply sweets per bottle by number of bottles: 428 x 14 = 5992 sweets altogether."} {"t":"q","id":16462,"q":"There are 1048 blue markers in a shop. The number of blue markers is 4 times as many as the number of red markers. How many red markers are there?
Answer: ","e":"Blue markers are 4 times the red markers, so red markers = 1048 \u00f7 4 = 262."} {"t":"q","id":16463,"q":"Jack jogs 1650 m and Tom jogs 2480 m in a day.
How many metres do Jack and Tom jog altogether in 7 days?
Answer: ","e":"Total jogged in one day = 1650 + 2480 = 4130 m. Over 7 days = 4130 x 7 = 28 910 m."} {"t":"q","id":16464,"q":"Mr Tan saved $4320 in the past 9 months.
He saved $100 each month in the first 3 months.
He saved the same amount of money each month in the last 6 months.
How much did Mr Tan save each month in the last 6 months?
Answer: ","e":"First 3 months saved: $100 x 3 = $300. Remaining over the last 6 months: $4320 - $300 = $4020. Monthly amount in the last 6 months: $4020 \u00f7 6 = $670."} {"t":"q","id":16465,"q":"Arrange the following decimals in increasing order.
6.501, 6.015, 6.105, 6.051","e":"Compare digit by digit: 6.015 < 6.051 < 6.105 < 6.501. So increasing order is 6.015, 6.051, 6.105, 6.501."} {"t":"q","id":16467,"q":"Express \\(8\\dfrac{6}{50}\\) as a decimal.","e":"Convert the fraction: \\(\\dfrac{6}{50}=\\dfrac{12}{100}=0.12\\). So \\(8\\dfrac{6}{50}=8+0.12=8.12\\)."} {"t":"q","id":16469,"q":"Express 1.08 as a fraction.","e":"The digits after the decimal point (08) are hundredths. So 1.08 = \\(1\\dfrac{8}{100}\\)."} {"t":"q","id":16471,"q":"David paid $5.25 for a pencil case and $1.85 for a pen. How much did David pay altogether?
Answer: ","e":"Add the two amounts: $5.25 + $1.85 = $7.10."} {"t":"q","id":16472,"q":"Mrs Tan bought some fruits. She gave the cashier $50 and received $12.35 change. How much did she spend on the fruits?
Answer: ","e":"Amount spent = amount given - change = $50.00 - $12.35 = $37.65."} {"t":"q","id":16473,"q":"Mr Ahmad used 1.45 kg of butter to bake one butter cake. Find the mass of butter used to bake seven butter cakes.
Answer: ","e":"Multiply the mass for one cake by 7: 1.45 kg \u00d7 7 = 10.15 kg."} {"t":"q","id":16474,"q":"A piece of wood 1.96 m was sawn to make 4 legs for a table. What was the length of each leg?
Answer: ","e":"Divide the total length by 4: 1.96 m \u00f7 4 = 0.49 m."} {"t":"q","id":16476,"q":"Mrs Diana has 4 small bottles and 1 large bottle of mineral water. A large bottle holds 3 times as much water as the small bottle. She has 3.85 \\(l\\) of mineral water altogether. How many litres of mineral water can a large bottle hold?
Answer: ","e":"Let a small bottle be 1 unit; the large bottle is 3 units. Total = 4 small + 1 large = 4 + 3 = 7 units = 3.85 l. So 1 unit = 3.85 \u00f7 7 = 0.55 l. A large bottle = 0.55 \u00d7 3 = 1.65 l."} {"t":"q","id":16477,"q":"In 34 765, the digit 7 is in the place.","e":"Read the place values of 34 765 from the right: 5 ones, 6 tens, 7 hundreds, 4 thousands, 3 ten thousands. The digit 7 sits in the hundreds place."} {"t":"q","id":16478,"q":"36 tens + 84 thousands is the same as","e":"36 tens = 36 \u00d7 10 = 360. 84 thousands = 84 \u00d7 1000 = 84 000. Add: 84 000 + 360 = 84 360."} {"t":"q","id":16479,"q":"94 601 = + 601","e":"94 601 \u2212 601 = 94 000. Then 94 000 = 94 \u00d7 1000, so the missing value is 94 \u00d7 1000."} {"t":"q","id":16480,"q":"Estimate the value of 4513 \u2212 971 by first rounding each number to the nearest thousand.","e":"Round to the nearest thousand: 4513 \u2192 5000 and 971 \u2192 1000. Then 5000 \u2212 1000 = 4000."} {"t":"q","id":16481,"q":"Which of the following is a common factor of 12 and 32?","e":"Factors of 12: 1, 2, 3, 4, 6, 12. Factors of 32: 1, 2, 4, 8, 16, 32. The common factor among the options is 4."} {"t":"q","id":16482,"q":"Find the quotient when 8412 is divided by 9.
Answer: ","e":"8412 \u00f7 9 = 934 remainder 6. The quotient is the whole-number result, 934."} {"t":"q","id":16483,"q":"Find the missing number in the box.
123 \u00d7 40 = 123 \u00d7 \u00d7 10","e":"40 = 4 \u00d7 10, so 123 \u00d7 40 = 123 \u00d7 4 \u00d7 10. The missing number is 4."} {"t":"q","id":16484,"q":"A given number is a multiple of 8 and a factor of 48.
It is between 20 and 40.
What is the number?
Answer: ","e":"Multiples of 8: 8, 16, 24, 32, 40. Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. The number in both lists that is between 20 and 40 is 24."} {"t":"q","id":16485,"q":"Round the following numbers to the nearest hundred.
(a) 9 950
(b) 23 439
(a)   (b) ","e":"(a) 9 950: the tens digit is 5, so round up the hundreds \u2192 10 000. (b) 23 439: the tens digit is 3 (less than 5), so round down \u2192 23 400."} {"t":"q","id":16486,"q":"Find the product of 236 and 47.
Answer: ","e":"236 \u00d7 47: 236 \u00d7 7 = 1652 and 236 \u00d7 40 = 9440. Add: 1652 + 9440 = 11 092."} {"t":"q","id":16487,"q":"Write the following in numerals.
(a) Ninety-six thousand and eighteen
(b) Thirty-one thousand, two hundred and seventy
(a)   (b) ","e":"(a) Ninety-six thousand = 96 000, and eighteen = 18, giving 96 018. (b) Thirty-one thousand = 31 000, two hundred = 200, and seventy = 70, giving 31 270."} {"t":"q","id":16489,"q":"A number when divided by 6 gives a quotient of 345 and a remainder of 2. What is the number?
Answer: ","e":"Number = quotient \u00d7 divisor + remainder = 345 \u00d7 6 + 2 = 2070 + 2 = 2072."} {"t":"q","id":16490,"q":"There are 20 girls standing in a row. Every 2nd girl is wearing a hair pin. Every 3rd girl is wearing a hat. How many girls wear both a hair pin and a hat?
Answer: ","e":"A girl wears both if her position is a multiple of both 2 and 3, i.e. a multiple of 6. Within 20: 6, 12, 18 \u2014 that is 3 girls."} {"t":"q","id":16491,"q":"There are 354 people at a party. Each table can only have 5 seats. What is the smallest number of tables needed at the party?
Answer: ","e":"354 \u00f7 5 = 70 remainder 4. The 70 tables seat 350 people; the remaining 4 need one more table. So 70 + 1 = 71 tables."} {"t":"q","id":16492,"q":"Susan has 4364 stickers. May has 2468 stickers. How many stickers must Susan give May so that they have the same number of stickers in the end?
Answer: ","e":"The difference is 4364 \u2212 2468 = 1896. To make them equal, Susan gives May half the difference: 1896 \u00f7 2 = 948."} {"t":"q","id":16493,"q":"Look at the pattern.
S A F E T Y S A F E T Y S A F E T Y ...
What letter is in the 44th position?","e":"The block SAFETY repeats every 6 letters. 44 \u00f7 6 = 7 remainder 2, so the 44th letter is the 2nd letter of the block, which is A."} {"t":"q","id":16494,"q":"A number has 10 as a factor. The number is a multiple of 5. This statement is","e":"If 10 is a factor of the number, the number is a multiple of 10, and every multiple of 10 is also a multiple of 5. So the statement is True."} {"t":"q","id":16495,"q":"A number has 10 as a factor. The number is an odd number. This statement is","e":"A number with 10 as a factor is a multiple of 10 and ends in 0, so it is always even. It can never be odd, so the statement is False."} {"t":"q","id":16496,"q":"A number has 10 as a factor. The number is a multiple of 12. This statement is","e":"Knowing 10 is a factor only tells us the number is a multiple of 10 (e.g. 10, 20, 30...). Some are multiples of 12 (like 60) and some are not (like 10), so we cannot tell."} {"t":"q","id":16497,"q":"A number has 10 as a factor. The number has 4 as a factor. This statement is","e":"A multiple of 10 may or may not have 4 as a factor: 20 does (4 \u00d7 5), but 10 and 30 do not. So we cannot tell from the information given."} {"t":"q","id":16498,"q":"Mrs Samy collected a total of $486 from selling some chocolate muffins and 63 banana muffins. She sold the chocolate muffins at $3 each and the banana muffins at $4 each. How many chocolate muffins did she sell?
Answer: ","e":"Banana muffins earned 63 \u00d7 $4 = $252. So chocolate muffins earned $486 \u2212 $252 = $234. At $3 each, the number sold is $234 \u00f7 $3 = 78."} {"t":"q","id":16499,"q":"Sam had 6 times as much money as Karl. Karl had $128 less than Andy. Both Karl and Andy had a total of $800.
(a) How much money did Karl have?
(b) Sam then bought 8 identical lego sets with all his money. How much did each lego set cost?
(a)   (b) ","e":"(a) Karl + Andy = $800 and Andy = Karl + $128. So 2 units of Karl = $800 \u2212 $128 = $672, giving Karl = $672 \u00f7 2 = $336. (b) Sam had 6 \u00d7 $336 = $2016. Each of 8 lego sets cost $2016 \u00f7 8 = $252."} {"t":"q","id":16500,"q":"At a funfair, the number of children was 2 times the number of women. The number of women was 2 times the number of boys. There were 486 girls.
(a) How many children were there?
(b) Each girl bought 20 game tokens. How many game tokens did all the girls buy?
(a)   (b) ","e":"(a) Children are split into boys and girls. Children = 2 \u00d7 women and women = 2 \u00d7 boys, so children = 4 \u00d7 boys; girls = children \u2212 boys = 3 units = 486, so 1 unit (boys) = 486 \u00f7 3 = 162. Children = boys + girls = 162 + 486 = 648. (b) Total girls' tokens = 486 \u00d7 20 = 9720."} {"t":"q","id":16527,"q":"John completed his homework at 18 25. He took 2 h 47 min to complete his work. What time did he start?","e":"Work backwards from the finishing time. 18 25 minus 2 h gives 16 25. Then subtract 47 min: 16 25 - 47 min = 15 38. So John started at 15 38."} {"t":"q","id":16528,"q":"A football match started at 15 15 and it ended at 16 40. How long was the football match?","e":"Find the duration from 15 15 to 16 40. From 15 15 to 16 15 is 1 h, then 16 15 to 16 40 is 25 min. Total = 1 h 25 min."} {"t":"q","id":16530,"q":"Edward washed 8 cars on Saturday. He took 20 minutes to wash each car. He started at 07 00. At what time will he finish if he did not take any breaks?","e":"Total washing time = 8 \\(\\times\\) 20 min = 160 min = 2 h 40 min. Add to the start time: 07 00 + 2 h 40 min = 09 40."} {"t":"q","id":16531,"q":"Jacob took 2 min 38 s to jog round a park. His sister took 40 s faster than him to complete the same distance. How long did his sister take?","e":"Subtract 40 s from Jacob's time. 2 min 38 s = 158 s. 158 s - 40 s = 118 s = 1 min 58 s."} {"t":"q","id":16532,"q":"The Tan family arrived at the Singapore Zoological Gardens at 11.30 a.m. and left at 3.40 p.m. How long was their visit to the zoo?
Answer: ","e":"Find the duration from 11.30 a.m. to 3.40 p.m. From 11.30 a.m. to 3.30 p.m. is 4 h, then 3.30 p.m. to 3.40 p.m. is 10 min. Total = 4 h 10 min."} {"t":"q","id":16533,"q":"A show started at 11.55 p.m. and ended 1 hour 45 minutes later. At what time did the show end?
Answer: ","e":"Add 1 h 45 min to 11.55 p.m. 11.55 p.m. + 1 h = 12.55 a.m. Then 12.55 a.m. + 45 min = 1.40 a.m."} {"t":"q","id":16534,"q":"The MRT trains depart at intervals of 12 minutes. Find the time of departure of the fourth train if the first train departs at 7.45 p.m.
Answer: ","e":"There are 3 intervals between the 1st and 4th trains. 3 \\(\\times\\) 12 min = 36 min. 7.45 p.m. + 36 min = 8.21 p.m."} {"t":"q","id":16535,"q":"Victor exercises 4 times a week. He exercises 2 hours each time. How many weeks will Victor need to reach 200 hours of exercise?
Answer: ","e":"Hours per week = 4 \\(\\times\\) 2 h = 8 h. Number of weeks = 200 h \\(\\div\\) 8 h = 25 weeks."} {"t":"q","id":16536,"q":"Cameron's watch shows the wrong time. When he left his house at 7.03 a.m., his watch showed the time as 7.15 a.m. Cameron has an appointment with the dentist at 9.45 a.m. When he arrived, his watch showed the time as 10.40 a.m. How many minutes late was he for his appointment?
Answer: ","e":"The watch is 12 min fast (7.15 - 7.03). When the watch showed 10.40 a.m., the real time was 10.40 - 12 min = 10.28 a.m. He was due at 9.45 a.m. Lateness = 9.45 a.m. to 10.40 a.m. on the watch = 55 min, minus the 12 min watch error = 43 min late. (9.45 to 10.40 = 55 min; 55 - 12 = 43 min.)"} {"t":"q","id":16537,"q":"When it is 08 15 in Singapore, it is 09 15 in Seoul. Penny took a flight from Singapore to Seoul at 08 15 for a conference. The flight lasted 4 h 50 min. What time was it in Seoul when the flight landed?
Answer: ","e":"Seoul is 1 h ahead of Singapore. Departure in Seoul time = 08 15 + 1 h = 09 15. Add the flight time: 09 15 + 4 h 50 min = 14 05. The flight landed at 1405 Seoul time."} {"t":"q","id":16538,"q":"When it is 10 00 in Country A, it is 08 40 in Singapore. Zacchaeus took a flight from Country A at 09 00 to Singapore. The flight lasted 3 h 29 min. What time was it in Singapore when the flight landed? Express your answer using the 24-hour clock.
Answer: ","e":"Country A is 1 h 20 min ahead of Singapore (10 00 vs 08 40). Departure 09 00 in Country A = 09 00 - 1 h 20 min = 07 40 in Singapore time. Add the flight time: 07 40 + 3 h 29 min = 11 09. The flight landed at 1109."} {"t":"q","id":16539,"q":"Two lighthouses flash their lights every 24 seconds and 60 seconds respectively. They flash together at 8.40 p.m. When is the next time the two lighthouses will flash their lights together again?
Answer: ","e":"Find the lowest common multiple of 24 and 60. Multiples of 24: 24, 48, 72, 96, 120; multiples of 60: 60, 120. LCM = 120 s = 2 min. So they flash together again 2 min after 8.40 p.m. = 8.42 p.m."} {"t":"q","id":16540,"q":"A quarter of a complete turn is equal to .","e":"A complete turn is 360\u00b0. A quarter turn is \\(\\dfrac{1}{4}\\) of 360\u00b0 = 360\u00b0 \u00f7 4 = 90\u00b0."} {"t":"q","id":16542,"q":"The minute hand of a clock moves through in half an hour.","e":"The minute hand sweeps a full circle (360\u00b0) in one hour. In half an hour it moves \\(\\dfrac{1}{2}\\) of 360\u00b0 = 180\u00b0."} {"t":"q","id":16549,"q":"I am facing East. Which direction will I face if I make a \\(\\dfrac{3}{4}\\) turn to my right?","e":"A \\(\\dfrac{3}{4}\\) turn to the right is 270\u00b0 clockwise. From East, clockwise in 90\u00b0 steps: E \u2192 S \u2192 W \u2192 N. So I now face North."} {"t":"q","id":16593,"q":"Write 23 thousandths as a decimal.
Answer: ","e":"23 thousandths means \\(\\dfrac{23}{1000}\\). The thousandths digit is the 3rd decimal place, so 23 thousandths = 0.023."} {"t":"q","id":16594,"q":"Fill in the missing number in the box below.
\\(37.15 = 37 + \\dfrac{}{100}\\)","e":"37.15 = 37 + 0.15. The decimal part 0.15 = \\(\\dfrac{15}{100}\\), so the missing numerator is 15."} {"t":"q","id":16597,"q":"Round 42.351 to the nearest tenth.
Answer: ","e":"Nearest tenth = 1 decimal place. Look at the hundredths digit, 5: since it is 5 or more, round the tenths digit up from 3 to 4. So 42.351 rounds to 42.4."} {"t":"q","id":16598,"q":"Express 3.75 as a mixed number in its simplest form.","e":"3.75 = 3 + 0.75 = \\(3\\dfrac{75}{100}\\). Simplify \\(\\dfrac{75}{100}\\) by dividing top and bottom by 25 to get \\(\\dfrac{3}{4}\\). So 3.75 = \\(3\\dfrac{3}{4}\\)."} {"t":"q","id":16599,"q":"Arrange these numbers in order from the greatest to the smallest.
8.46 0.86 8.6 6.08
(greatest), , , ","e":"Compare the whole-number parts first: 8.46 and 8.6 (both 8), 6.08 (6), 0.86 (0). Between 8.6 and 8.46, compare tenths: 6 > 4, so 8.6 > 8.46. Order greatest to smallest: 8.6, 8.46, 6.08, 0.86."} {"t":"q","id":16600,"q":"Find the sum of 214.39 and 7.8 .
Answer: ","e":"Line up the decimal points: 214.39 + 7.80 = 222.19."} {"t":"q","id":16601,"q":"Find the difference between 36.6 and 29.7 .
Answer: ","e":"Subtract aligning decimal points: 36.6 - 29.7 = 6.9."} {"t":"q","id":16602,"q":"Find the value of 2.7 x 5 .
Round the answer to the nearest whole number.
Answer: ","e":"2.7 x 5 = 13.5. Rounding 13.5 to the nearest whole number: the tenths digit is 5, so round up to 14."} {"t":"q","id":16603,"q":"A magazine costs $5.90. It is $2.65 cheaper than a book. How much does the book cost?
Answer: ","e":"The magazine is $2.65 cheaper than the book, so the book costs more. Book = $5.90 + $2.65 = $8.55."} {"t":"q","id":16605,"q":"Mr Seah earned $2745. He spent \\(\\dfrac{7}{9}\\) of his earnings and saved the rest. How much did Mr Seah save?
Answer: ","e":"He spent \\(\\dfrac{7}{9}\\), so he saved \\(\\dfrac{2}{9}\\). The whole (9 units) = $2745, so 1 unit = 2745 \u00f7 9 = $305. Saved = 2 units = 305 x 2 = $610."} {"t":"q","id":16606,"q":"A box contained some beads. Aisha took \\(\\dfrac{2}{5}\\) of the beads. She took 78 beads. How many beads were there in the box at first?
Answer: ","e":"\\(\\dfrac{2}{5}\\) of the beads = 78, so 2 units = 78 and 1 unit = 78 \u00f7 2 = 39. The whole box = 5 units = 39 x 5 = 195 beads."} {"t":"q","id":16607,"q":"Devi mixed 4.05 kg of hazelnuts with 3.9 kg of cashew nuts to pack into 5 similar packets equally. What was the mass of 1 such packet of nuts? Leave your answer as a decimal.
Answer: ","e":"Total mass = 4.05 + 3.9 = 7.95 kg. Divided equally into 5 packets: 7.95 \u00f7 5 = 1.59 kg per packet."} {"t":"q","id":16608,"q":"Ahmad and Caili had an equal amount of money at first. After Ahmad had received $30.50 from his mother and Caili had spent $20, he had three times as much money as Caili. How much money did each of them have at first?
Answer: ","e":"Let each start with the same amount. After the changes Ahmad has (start + 30.50) and Caili has (start - 20), and Ahmad = 3 x Caili. The difference between them is 30.50 + 20 = $50.50, which equals 2 of Caili's units (since 3 units - 1 unit = 2 units). So 1 unit (Caili after) = 50.50 \u00f7 2 = $25.25. Caili's starting amount = 25.25 + 20 = $45.25. Each had $45.25 at first."} {"t":"q","id":16609,"q":"Morris, Randy and Timothy have 2439 stickers altogether. Morris have twice as many stickers as Randy. Timothy have three times as many stickers as Morris. How many stickers does Timothy have?
Answer: ","e":"Let Randy = 1 unit. Morris = twice Randy = 2 units. Timothy = three times Morris = 6 units. Total = 1 + 2 + 6 = 9 units = 2439, so 1 unit = 2439 \u00f7 9 = 271. Timothy = 6 units = 271 x 6 = 1626 stickers."} {"t":"q","id":16610,"q":"A cupcake cost $4 and a muffin cost $3. Mrs Lee spent $357 to buy an equal number of cupcakes and muffins. What was the total number of cupcakes and muffins Mrs Lee had bought?
Answer: ","e":"One cupcake plus one muffin (a pair) costs (1 x $4) + (1 x $3) = $4 + $3 = $7. Number of pairs = 357 \u00f7 7 = 51. Each pair has 2 items, so total = 51 x 2 = 102 cupcakes and muffins."} {"t":"q","id":16612,"q":"57 809 = 50 000 + 7000 + + 9
What is the missing number in the blank?","e":"57 809 = 50 000 + 7000 + 800 + 9. The 8 is in the hundreds place, so the missing number is 800."} {"t":"q","id":16613,"q":"In 43 120, the digit is in the hundreds place.","e":"In 43 120: 4 ten-thousands, 3 thousands, 1 hundred, 2 tens, 0 ones. The digit in the hundreds place is 1."} {"t":"q","id":16614,"q":"In which of the following numbers does the digit '3' have the greatest value?","e":"Value of 3 in each: 20 375 \u2192 300; 53 870 \u2192 3000; 70 403 \u2192 3; 92 534 \u2192 30. The greatest is 3000 in 53 870."} {"t":"q","id":16615,"q":"Which one of the following is the first common multiple of 3 and 9?","e":"Multiples of 3: 3, 6, 9, ... Multiples of 9: 9, 18, ... The smallest common multiple is 9."} {"t":"q","id":16620,"q":"The time on a clock is 9.25 p.m. What time will it be if the minute hand turns 180\u00b0 clockwise?","e":"A 180\u00b0 turn is half a turn = 30 minutes. 9.25 p.m. + 30 min = 9.55 p.m."} {"t":"q","id":16622,"q":"Bryan was standing at the point marked A in the diagram. After making a \\(\\dfrac{3}{4}\\)-turn in an anticlockwise direction, Bryan found himself facing south. Which direction was he facing at first?","e":"A \\(\\dfrac{3}{4}\\)-turn anticlockwise is 270\u00b0 anticlockwise, which is the same as 90\u00b0 clockwise. To end facing south, he must have started facing east (east turned 90\u00b0 clockwise gives south)."} {"t":"q","id":16623,"q":"A number when rounded to the nearest hundred is 6000. What is the largest possible number?","e":"Numbers rounding to 6000 (nearest hundred) range from 5950 to 6049. The largest is 6049."} {"t":"q","id":16624,"q":"Charles had 430 cards. When he arranged them equally onto 8 pages of an album, he did not have enough space for some cards. How many cards were not in the album?","e":"430 \u00f7 8 = 53 remainder 6. So 53 cards fit on each page (424 in total) and 6 cards were left out."} {"t":"q","id":16629,"q":"There were 2389 more yellow marbles than blue marbles in a box. Another 398 yellow marbles and 594 blue marbles were put into the box. How many more yellow marbles than blue marbles were there in the box in the end?","e":"Adding 398 yellow and 594 blue changes the difference by 398 \u2212 594 = \u2212196. New difference = 2389 \u2212 196 = 2193."} {"t":"q","id":16633,"q":"Some factors of 28 are 1, 2, 4 and 28. What are the other factors? and ","e":"Factors of 28: 1, 2, 4, 7, 14, 28. The ones not listed are 7 and 14."} {"t":"q","id":16634,"q":"What is the quotient when 6039 is divided by 7? ","e":"6039 \u00f7 7 = 862 remainder 5. The quotient is 862."} {"t":"q","id":16638,"q":"Joe took 20 minutes to draw a picture and another 1 hour 30 minutes to colour the picture. He completed it at 12 noon. At what time did he start to draw his picture?","e":"Total time = 20 min + 1 h 30 min = 1 h 50 min. 12.00 noon \u2212 1 h 50 min = 10.10 a.m."} {"t":"q","id":16646,"q":"The sum of 2 numbers is 422. The difference between these 2 numbers is 96. What is the smaller number? ","e":"Smaller number = (sum \u2212 difference) \u00f7 2 = (422 \u2212 96) \u00f7 2 = 326 \u00f7 2 = 163."} {"t":"q","id":16647,"q":"Mrs Toh's age is the seventh multiple of 6. Her age is 3 times of her daughter's age. How old is her daughter? ","e":"Seventh multiple of 6 = 7 \u00d7 6 = 42, so Mrs Toh is 42. Daughter's age = 42 \u00f7 3 = 14."} {"t":"q","id":16650,"q":"A repeated pattern is formed using the letters w to z. The first letters are w x y z w x y z w x y z w x y z w x ... What is the 48th letter?","e":"The pattern w x y z repeats every 4 letters. 48 \u00f7 4 = 12 exactly, so the 48th letter is the last in the block = z."} {"t":"q","id":16651,"q":"1846 people attended a concert. There were 289 children. There were 349 more women than men. How many men were there? ","e":"Adults = 1846 \u2212 289 = 1557. Removing the extra 349 women: 1557 \u2212 349 = 1208, which is twice the number of men. Men = 1208 \u00f7 2 = 604."} {"t":"q","id":16652,"q":"Mr Ng baked an equal number of muffins daily from Monday to Thursday. He baked 800 muffins each day on Friday and Saturday. He baked a total of 3400 muffins over the six days. How many muffins did he bake on Wednesday? ","e":"Fri + Sat = 800 \u00d7 2 = 1600. Mon\u2013Thu total = 3400 \u2212 1600 = 1800. Each of the 4 equal days (incl. Wednesday) = 1800 \u00f7 4 = 450."} {"t":"q","id":16653,"q":"Helen had 3 fifty-dollar notes. She bought two blouses at $46.50 each. She also bought a pair of shoes. She had $28.60 left. How much did the pair of shoes cost? ","e":"Total money = 3 \u00d7 $50 = $150. Two blouses = 2 \u00d7 $46.50 = $93. Spent before shoes leaves $150 \u2212 $93 = $57. Shoes = $57 \u2212 $28.60 = $28.40."} {"t":"q","id":16654,"q":"Mr Lee wanted to complete 26 laps around the track. Each lap was 400 m. He had completed 7800 m. How much further must he run? ","e":"Total distance = 26 \u00d7 400 = 10 400 m. Remaining = 10 400 \u2212 7800 = 2600 m."} {"t":"q","id":16655,"q":"The length of a rectangle is 10 cm. Its breadth is half of its length. What is the area of the rectangle? ","e":"Breadth = 10 \u00f7 2 = 5 cm. Area = length \u00d7 breadth = 10 \u00d7 5 = 50 cm\u00b2."} {"t":"q","id":16656,"q":"Claire has 4 times as many stamps as Diana. Claire has twice as many stamps as Eliane. Diana has 201 fewer stamps than Claire. How many stamps do they have altogether? ","e":"Claire = 4 units, Diana = 1 unit, so Diana is 3 units fewer = 201, giving 1 unit = 201 \u00f7 3 = 67. Diana = 67, Claire = 268, Eliane = 268 \u00f7 2 = 134. Altogether = 67 + 268 + 134 = 469."} {"t":"q","id":16657,"q":"Fiona and Nicole have a total of 1197 beads. Nicole and Lydia have a total of 1203 beads. The 3 girls have a total of 1292 beads. How many beads does Nicole have? ","e":"Lydia = total \u2212 (Fiona + Nicole) = 1292 \u2212 1197 = 95. Nicole = (Nicole + Lydia) \u2212 Lydia = 1203 \u2212 95 = 1108."} {"t":"q","id":16658,"q":"Tank A contained 9 litres of water. After some water was transferred from Tank A to Tank B, Tank A had 4 times as much water as Tank B. If Tank B had 2135 ml of water in the end, how much water was transferred from Tank A to Tank B? ","e":"End: Tank B = 2135 ml, Tank A = 4 \u00d7 2135 = 8540 ml. Tank A started with 9 litres = 9000 ml, so water transferred = 9000 \u2212 8540 = 460 ml."} {"t":"q","id":16690,"q":"In which of the following numbers does the digit 3 stand for 300?","e":"The digit 3 stands for 300 when it is in the hundreds place. In 9360, the 3 is in the hundreds place, so it stands for 300."} {"t":"q","id":16691,"q":"Which of the following is not an equivalent fraction of \\(\\dfrac{1}{4}\\)?","e":"Equivalent fractions of \\(\\dfrac{1}{4}\\) have the denominator equal to 4 times the numerator: \\(\\dfrac{2}{8}\\), \\(\\dfrac{3}{12}\\), \\(\\dfrac{6}{24}\\) all simplify to \\(\\dfrac{1}{4}\\). \\(\\dfrac{5}{16}\\) does not (16 \u00f7 5 \u2260 4), so it is not equivalent."} {"t":"q","id":16692,"q":"Which of the following decimals is the greatest?","e":"Compare the tenths digit first: 0.357 and 0.324 both have 3 tenths, the others have fewer. Between them, 5 hundredths > 2 hundredths, so 0.357 is the greatest."} {"t":"q","id":16694,"q":"Which of the following numbers when rounded to the nearest ten becomes 72 400?","e":"Rounding to the nearest ten, the result 72 400 comes from numbers between 72 395 and 72 404. 72 396 rounds up to 72 400. (72 349\u219272 350, 72 405\u219272 410, 72 443\u219272 440.)"} {"t":"q","id":16695,"q":"Express 0.05 as a fraction in its simplest form.","e":"0.05 = \\(\\dfrac{5}{100}\\). Dividing numerator and denominator by 5 gives \\(\\dfrac{1}{20}\\)."} {"t":"q","id":16698,"q":"A flight took off from Singapore at 22 50 and arrived in Taiwan at 04 05 the next day. How long was the flight?","e":"From 22 50 to 24 00 (midnight) is 1 h 10 min. From 00 00 to 04 05 is 4 h 5 min. Total = 5 h 15 min."} {"t":"q","id":16700,"q":"The table shows the number of students in 3 CCAs in a class. Each student is in one CCA only.
Badminton: 15
Swimming: 5
Tennis: ?
There are 38 students in the class. How many students are in Tennis CCA?","e":"Tennis = total \u2212 Badminton \u2212 Swimming = 38 \u2212 15 \u2212 5 = 18 students."} {"t":"q","id":16701,"q":"Which of the following statements about a rectangle is not correct?","e":"A rectangle has TWO pairs of parallel sides, not one. So the statement 'There is only one pair of parallel lines' is not correct."} {"t":"q","id":16703,"q":"I am a multiple of 4. When 5 is added to me, I am a multiple of 7. What number am I?","e":"Test each multiple of 4: 16 + 5 = 21 = 7 \u00d7 3 (a multiple of 7). So the number is 16. (28+5=33, 32+5=37, 36+5=41 are not multiples of 7.)"} {"t":"q","id":16704,"q":"There were 460 children at Sports Day Carnival. There were 140 more boys than girls. How many girls were there?","e":"Remove the extra 140 boys: 460 \u2212 140 = 320, which is twice the number of girls. Girls = 320 \u00f7 2 = 160."} {"t":"q","id":16706,"q":"Siti and Tina had the same number of beads at first. After Siti threw away 24 beads and Tina bought another 84 beads, Tina had 4 times as many beads as Siti. How many beads did Siti have at first?","e":"Let the start amount be n. Siti = n \u2212 24, Tina = n + 84, and Tina = 4 \u00d7 Siti. So n + 84 = 4(n \u2212 24) = 4n \u2212 96, giving 3n = 180, n = 60."} {"t":"q","id":16707,"q":"A fruit seller had 30 boxes of pineapples. There were 24 pineapples in each box. He sold all the pineapples at 6 for $18. How much money did he receive?","e":"Total pineapples = 30 \u00d7 24 = 720. At 6 for $18, each costs $3, so 720 \u00d7 $3 = $2160. (Or 720 \u00f7 6 = 120 groups \u00d7 $18 = $2160.)"} {"t":"q","id":16708,"q":"Nancy and Peter bought a sofa. The sofa cost $1200. Nancy paid \\(\\dfrac{3}{8}\\) of the cost of the sofa. How much more did Peter pay than Nancy?","e":"Nancy paid \\(\\dfrac{3}{8}\\) of $1200 = $450. Peter paid the rest, \\(\\dfrac{5}{8}\\) = $750. Peter paid $750 \u2212 $450 = $300 more."} {"t":"q","id":16710,"q":"Write the missing number in the number pattern below.
6649 , 6799 , 6949 , , 7249","e":"The pattern increases by 150 each time (6649 \u2192 6799 \u2192 6949). So the missing number is 6949 + 150 = 7099 (and 7099 + 150 = 7249)."} {"t":"q","id":16713,"q":"Find the value of 6.84 \u00d7 7.
Answer: ","e":"6.84 \u00d7 7 = 47.88 (684 \u00d7 7 = 4788, then place the decimal point: 47.88)."} {"t":"q","id":16716,"q":"Which two of these fractions are in the simplest form?
\\(\\dfrac{2}{3}\\) , \\(\\dfrac{3}{6}\\) , \\(\\dfrac{4}{8}\\) , \\(\\dfrac{5}{9}\\)
(a)   (b) ","e":"A fraction is in simplest form when numerator and denominator share no common factor other than 1. \\(\\dfrac{3}{6}=\\dfrac{1}{2}\\) and \\(\\dfrac{4}{8}=\\dfrac{1}{2}\\) can be simplified. \\(\\dfrac{2}{3}\\) and \\(\\dfrac{5}{9}\\) cannot, so they are in simplest form."} {"t":"q","id":16717,"q":"Arrange the following numbers from the smallest to the greatest.
\\(\\dfrac{3}{4}\\) , 0.705 , 0.075
(a)   (b)   (c) ","e":"Convert to decimals: \\(\\dfrac{3}{4}\\) = 0.75, 0.705, 0.075. From smallest to greatest: 0.075, 0.705, 0.75 (i.e. 0.075, 0.705, \\(\\dfrac{3}{4}\\))."} {"t":"q","id":16718,"q":"Two factors of 10 are 1 and 10. What are the other two factors of 10? , ","e":"The factors of 10 are 1, 2, 5 and 10. Apart from 1 and 10, the other two factors are 5 and 2."} {"t":"q","id":16719,"q":"Sumin took 45 min to walk from her home to school. She was 30 min early for the school concert. The concert started at 5 p.m. At what time did she leave her house? Give your answer in the 24-hour clock. ","e":"Concert starts at 5 p.m. = 1700. She arrived 30 min early at 1630. She walked 45 min, so she left at 1630 \u2212 45 min = 1545."} {"t":"q","id":16721,"q":"The amount of water in the tank at 08 00 was 3 times the amount of water at 13 00. How much water was there in the tank at 13 00? ","e":"From the graph, the amount of water at 08 00 was 24 \\(\\ell\\). At 13 00 it is one-third of that: 24 \u00f7 3 = 8 \\(\\ell\\)."} {"t":"q","id":16722,"q":"There are 174 fruits in a basket. \\(\\dfrac{1}{3}\\) are apples and the rest are pears. How many pears are there? ","e":"Apples = \\(\\dfrac{1}{3}\\), so pears = \\(\\dfrac{2}{3}\\) of 174. 174 \u00f7 3 = 58, then 58 \u00d7 2 = 116 pears."} {"t":"q","id":16726,"q":"Siti had the same number of $2 and $5 notes. She had a total of $252. How many $2 notes did she have? ","e":"Group one $2 note and one $5 note: each group is worth $2 + $5 = $7. Number of groups = $252 \u00f7 $7 = 36. So she had 36 $2 notes."} {"t":"q","id":16728,"q":"A stall had a promotion: Buy 1 muffin for $3 each. Buy 4 muffins at $11. Mandy bought 49 muffins. What was the least amount of money Mandy had to pay for the 49 muffins? ","e":"Buy as many sets of 4 as possible: 49 \u00f7 4 = 12 sets remainder 1. 12 sets \u00d7 $11 = $132, plus 1 single muffin \u00d7 $3 = $3. Least amount = $132 + $3 = $135."} {"t":"q","id":16729,"q":"James had $16.40. He wanted to buy 3 notebooks and 1 pencil case, but he was short of $3.30. (a) What was the total cost of the 3 notebooks and 1 pencil case? (b) The pencil case cost $2.90 more than each notebook. What was the cost of 1 notebook? ","e":"(a) Total cost = $16.40 + $3.30 = $19.70. (b) Remove the extra $2.90 of the pencil case: $19.70 \u2212 $2.90 = $16.80, which is 4 equal notebook costs. 1 notebook = $16.80 \u00f7 4 = $4.20."} {"t":"q","id":16730,"q":"Venus and Melvin were given some money. Venus spent \\(\\dfrac{1}{4}\\) of her money and had $141 left. (a) How much did Venus spend? (b) Melvin spent two times as much as Venus. He had \\(\\dfrac{2}{3}\\) of his money left. How much did Melvin have in the end? ","e":"(a) Venus spent \\(\\dfrac{1}{4}\\), so $141 is the remaining \\(\\dfrac{3}{4}\\). 1 unit = $141 \u00f7 3 = $47, which is the \\(\\dfrac{1}{4}\\) she spent. (b) Melvin spent 2 \u00d7 $47 = $94, and that is \\(\\dfrac{1}{3}\\) of his money (he had \\(\\dfrac{2}{3}\\) left). His \\(\\dfrac{2}{3}\\) left = $94 \u00d7 2 = $188."} {"t":"q","id":16731,"q":"Sarah gives some erasers equally to her friends. If she gives 6 erasers to each friend, she will need another 4 erasers. If she gives 5 erasers to each friend, she will have 3 erasers left. (a) How many friends does Sarah have? (b) How many erasers does Sarah have? ","e":"(a) Each friend gets 1 more eraser in the first case, needing 4 + 3 = 7 extra erasers in total, so there are 7 friends. (b) With 5 each: 7 \u00d7 5 + 3 = 38 erasers (check: 7 \u00d7 6 \u2212 4 = 38)."} {"t":"q","id":16732,"q":"Lydia had twice as much money as Kenneth at first. Kenneth then gave Lydia $24. In the end, Lydia had 4 times as much money as Kenneth. How much money did Kenneth have at first? ","e":"The total stays constant. Before, Lydia : Kenneth = 2 : 1 (3 parts). After, 4 : 1 (5 parts). Make totals equal at 15: before 10 : 5, after 12 : 3. Kenneth drops from 5u to 3u, i.e. 2u = $24, so 1u = $12. Kenneth at first = 5u = 5 \u00d7 $12 = $60."} {"t":"q","id":16804,"q":"In which of the following numbers does the digit 7 stand for 700?","e":"The digit 7 stands for 700 when it is in the hundreds place. In 5740, the 7 is in the hundreds place, so it stands for 700. Answer: 5740."} {"t":"q","id":16805,"q":"27 358 rounded to the nearest hundred is .","e":"To round 27 358 to the nearest hundred, look at the tens digit (5). Since 5 \u2265 5, round up: the hundreds digit 3 becomes 4 and the tens\/ones become 0. Answer: 27 400."} {"t":"q","id":16806,"q":"In the number 68.59, the digit is in the tenths place.","e":"In a decimal, the first digit after the decimal point is the tenths place. In 68.59 the digit right after the point is 5. Answer: 5."} {"t":"q","id":16807,"q":"Which of the following is not a factor of 56?","e":"Check each: 56 \u00f7 2 = 28, 56 \u00f7 8 = 7, 56 \u00f7 4 = 14 (all exact, so they are factors). 56 \u00f7 6 = 9 remainder 2, so 6 is NOT a factor. Answer: 6."} {"t":"q","id":16808,"q":"\\(5\\dfrac{2}{9}\\) = \\(\\dfrac{ }{9}\\)
What is the missing number in the box?","e":"Convert the mixed number to an improper fraction: 5 \u00d7 9 + 2 = 47, over 9. So the missing numerator is 47. Answer: 47."} {"t":"q","id":16809,"q":"Find the value of \\(\\dfrac{5}{12}-\\dfrac{1}{4}\\)","e":"Make denominators the same: \\(\\dfrac{1}{4}=\\dfrac{3}{12}\\). Then \\(\\dfrac{5}{12}-\\dfrac{3}{12}=\\dfrac{2}{12}=\\dfrac{1}{6}\\). Answer: \\(\\dfrac{1}{6}\\)."} {"t":"q","id":16810,"q":"Express \\(\\dfrac{3}{4}\\) as a decimal.","e":"Make an equivalent fraction with denominator 100: \\(\\dfrac{3}{4}=\\dfrac{75}{100}\\) = 0.75. Answer: 0.75."} {"t":"q","id":16811,"q":"Which of the following is a multiple of both 3 and 7?","e":"A common multiple of 3 and 7 must be a multiple of 21. 42 = 21 \u00d7 2, and 42 \u00f7 3 = 14, 42 \u00f7 7 = 6, both exact. Answer: 42."} {"t":"q","id":16813,"q":"Arrange these numbers from the smallest to the greatest.
0.204 , 0.402 , 0.24 , 0.42","e":"Compare by place value: 0.204 < 0.24 < 0.402 < 0.42. (0.204 and 0.24 share tenths 2, then hundredths 0 < 4; 0.402 and 0.42 share tenths 4, then hundredths 0 < 2.) Answer: 0.204, 0.24, 0.402, 0.42."} {"t":"q","id":16814,"q":"Julia bought a book for $18.90 and a pencil box for $7.50. She gave the cashier $50. How much change did she get?","e":"Total spent = $18.90 + $7.50 = $26.40. Change = $50 \u2212 $26.40 = $23.60. Answer: $23.60."} {"t":"q","id":16815,"q":"The table shows the duration of different activities held at a children's workshop.
Art Jamming \u2014 2 h 45 min
Build-A-Bear \u2014 1 h 45 min
Creative Music \u2014 1 h 15 min
Dino Dash \u2014 2 h 15 min
Rachel started an activity at 09 35 and ended at 11 50. Which activity did she participate in?","e":"From 09 35 to 11 50: 09 35 to 11 35 is 2 h, plus 35 to 50 is 15 min, total 2 h 15 min. That matches Dino Dash. Answer: Dino Dash."} {"t":"q","id":16816,"q":"Henry has some stamps. John has 3 times as many stamps as Henry. They have 2700 stamps altogether. How many stamps does Henry have?","e":"Henry = 1 unit, John = 3 units, total = 4 units = 2700. 1 unit = 2700 \u00f7 4 = 675. Henry has 675 stamps. Answer: 675."} {"t":"q","id":16817,"q":"The table shows the number of chicken wings eaten by a group of children at a party.
Wings eaten by each child: 0, 1, 2, 3
Number of children: 5, 3, 8, 12
What was the total number of chicken wings eaten by the children at the party?","e":"Total wings = (0\u00d75) + (1\u00d73) + (2\u00d78) + (3\u00d712) = 0 + 3 + 16 + 36 = 55. Answer: 55."} {"t":"q","id":16818,"q":"Thomas went for a movie which ended at 18 00. The movie lasted 2 h 15 min. What time did the movie start?","e":"Subtract the duration from the end time: 18 00 \u2212 2 h = 16 00, then \u2212 15 min = 15 45. Answer: 15 45."} {"t":"q","id":16819,"q":"The length of a bus is 12.1 m when rounded to 1 decimal place. Which of the following is the greatest possible length of the bus?","e":"A length rounds to 12.1 if it is from 12.05 up to but not including 12.15. Among the options, the greatest value that still rounds to 12.1 is 12.14 m (12.19 rounds to 12.2). Answer: 12.14 m."} {"t":"q","id":16823,"q":"Aaron and Brandon had a total of $567 at first. After Aaron gave Brandon $33, Aaron had twice as much money as Brandon. How much money did Brandon have at first?","e":"The total stays $567 after the transfer. Then Aaron = 2 units, Brandon = 1 unit, 3 units = $567, so 1 unit = $189. Brandon after = $189, so Brandon at first = $189 \u2212 $33 = $156. Answer: $156."} {"t":"q","id":16824,"q":"Write six thousand and twenty in figures.
","e":"Six thousand = 6000, twenty = 20, with no hundreds and no tens-of-hundreds in between. 6000 + 20 = 6020. Answer: 6020."} {"t":"q","id":16825,"q":"What is the missing number in the number pattern below?
85 211, 85 251, 85 291, , 85 371","e":"Each term increases by 40 (85 211 \u2192 85 251 \u2192 85 291). So the missing term = 85 291 + 40 = 85 331 (check: 85 331 + 40 = 85 371). Answer: 85 331."} {"t":"q","id":16826,"q":"When a number is divided by 6, it has a quotient of 1006 and remainder of 3. What is the number?
Answer: ","e":"Number = quotient \u00d7 divisor + remainder = 1006 \u00d7 6 + 3 = 6036 + 3 = 6039. Answer: 6039."} {"t":"q","id":16828,"q":"Use all the digits 3, 4, 6, 9 to form the largest even number. Each digit can only be used once.
Answer: ","e":"An even number must end in an even digit (4 or 6). To make it largest, put the biggest digits first; the smaller even digit (4) goes last. Largest arrangement of 9, 6, 3 then 4 \u2192 9634. Answer: 9634."} {"t":"q","id":16831,"q":"The perimeter of the square is 64 cm. Find the area of the square.
\\(cm^2\\)","e":"Side of square = perimeter \u00f7 4 = 64 \u00f7 4 = 16 cm. Area = side \u00d7 side = 16 \u00d7 16 = 256 cm\u00b2. Answer: 256 cm\u00b2."} {"t":"q","id":16832,"q":"Mr. Ben bought some flour. He used 250 g of it and packed the remaining flour equally into 6 packets. The mass of 1 such packet of flour was 175 g. How much flour did Mr. Ben buy?
\\(g\\)","e":"Flour packed = 6 \u00d7 175 = 1050 g. Total bought = flour used + flour packed = 250 + 1050 = 1300 g. Answer: 1300 g."} {"t":"q","id":16834,"q":"Eunice bought \\(\\dfrac{3}{5}\\) m of ribbon to tie a present. Sarah bought \\(\\dfrac{1}{2}\\) m more ribbon than Eunice to make bows. How much ribbon did they buy altogether?
\\(m\\)","e":"Sarah's ribbon = \\(\\dfrac{3}{5}+\\dfrac{1}{2}=\\dfrac{6}{10}+\\dfrac{5}{10}=\\dfrac{11}{10}=1\\dfrac{1}{10}\\) m. Altogether = Eunice + Sarah = \\(\\dfrac{6}{10}+1\\dfrac{1}{10}=1\\dfrac{7}{10}\\) m. Answer: \\(1\\dfrac{7}{10}\\) m."} {"t":"q","id":16835,"q":"\\(\\dfrac{3}{4}\\) of a number is 21. What is the number?
Answer: ","e":"\\(\\dfrac{3}{4}\\) of the number = 21, so \\(\\dfrac{1}{4}\\) = 21 \u00f7 3 = 7. The whole number = 7 \u00d7 4 = 28. Answer: 28."} {"t":"q","id":16836,"q":"Henry paid $4 for 8 identical erasers. What was the cost of 1 such eraser?
$","e":"Cost of 1 eraser = $4.00 \u00f7 8 = $0.50. Answer: $0.50."} {"t":"q","id":16837,"q":"A big box contains twice as many tarts as a small box. There are a total of 136 tarts in 3 big boxes and 2 small boxes. How many tarts are there in a big box?
Answer: ","e":"Let a small box = 1 unit, so a big box = 2 units. 3 big + 2 small = 3\u00d72 + 2\u00d71 = 8 units = 136, so 1 unit = 17. A big box = 2 units = 2 \u00d7 17 = 34 tarts. Answer: 34."} {"t":"q","id":16839,"q":"There are 135 pies at a party. \\(\\dfrac{2}{9}\\) of the pies are chicken pies and the rest are mushroom pies. How many more mushroom pies than chicken pies are there at the party?
Answer: ","e":"1 unit = 135 \u00f7 9 = 15. Chicken pies = 2 units = 30. Mushroom pies = 7 units = 105. Difference = 105 \u2212 30 = 75. Answer: 75."} {"t":"q","id":16842,"q":"Dora, Erica and Felicia had $4300 altogether. Dora had $980 more than Erica. Felicia had $340 less than Erica. How much money did Felicia have?
$","e":"Take Erica as 1 unit. Dora = 1 unit + $980, Felicia = 1 unit \u2212 $340. Total: 3 units + $980 \u2212 $340 = $4300, so 3 units = $4300 \u2212 $980 + $340 = $3660, 1 unit = $1220 (Erica). Felicia = $1220 \u2212 $340 = $880. Answer: $880."} {"t":"q","id":16843,"q":"Julian read \\(\\dfrac{2}{9}\\) of a book on Monday and \\(\\dfrac{2}{3}\\) of the book on Tuesday. He read the remaining pages of the book on Wednesday. He read 76 more pages on Tuesday than on Monday. What fraction of the book did he read on Wednesday?","e":"Monday + Tuesday = \\(\\dfrac{2}{9}+\\dfrac{2}{3}=\\dfrac{2}{9}+\\dfrac{6}{9}=\\dfrac{8}{9}\\). Wednesday = whole \u2212 \\(\\dfrac{8}{9}\\) = \\(\\dfrac{9}{9}-\\dfrac{8}{9}=\\dfrac{1}{9}\\). Answer: \\(\\dfrac{1}{9}\\)."} {"t":"q","id":16875,"q":"60 000 + 4 000 + 800 + 7 =","e":"Add the place values: 60 000 + 4 000 + 800 + 7 = 64 807. The ten-thousands digit is 6, thousands 4, hundreds 8, tens 0, ones 7."} {"t":"q","id":16876,"q":"Complete the following number pattern.
7 , 11 , 15 , , , 27","e":"The pattern increases by 4 each time: 7, 11, 15, 19, 23, 27. So the two missing numbers are 19 and 23."} {"t":"q","id":16877,"q":"How many sixths are there in 2 wholes?","e":"1 whole = 6 sixths, so 2 wholes = 2 x 6 = 12 sixths. (2 = 12\/6.)"} {"t":"q","id":16878,"q":"Which of the following decimals is the smallest?","e":"Compare after the decimal point. 4.032 has 0 tenths and 3 hundredths; 4.07 has 0 tenths, 7 hundredths. 4.032 < 4.07 < 4.18 < 4.85, so 4.032 is smallest."} {"t":"q","id":16879,"q":"In which of the following numbers does the digit 7 stand for 7 tenths?","e":"7 tenths means the 7 is in the first place after the decimal point. In 413.75 the digit 7 is in the tenths place (0.7). The others have 7 in tens, ones or hundredths places."} {"t":"q","id":16883,"q":"Madam Lim bought \\(\\dfrac{4}{5}\\) kg of chicken meat. She bought \\(\\dfrac{3}{10}\\) kg less than the amount of chicken meat bought by Mrs Tan. How many kilograms of chicken meat did Mrs Tan buy?","e":"Madam Lim has 3\/10 kg less than Mrs Tan, so Mrs Tan = 4\/5 + 3\/10. Convert: 4\/5 = 8\/10, so 8\/10 + 3\/10 = 11\/10 = 1 1\/10 kg."} {"t":"q","id":16885,"q":"4008 - 741 = ","e":"4008 - 741: subtract with regrouping. 4008 - 741 = 3267."} {"t":"q","id":16887,"q":"Four factors of 12 are 1, 2, 6 and 12. What are the other two factors of 12?
(a)   (b) ","e":"The factors of 12 are 1, 2, 3, 4, 6, 12. Given 1, 2, 6 and 12, the remaining two factors are 3 and 4."} {"t":"q","id":16888,"q":"Which two of the following fractions are in the simplest form?
\\(\\dfrac{2}{3}\\) , \\(\\dfrac{10}{12}\\) , \\(\\dfrac{3}{7}\\) , \\(\\dfrac{6}{8}\\)
(a)   (b) ","e":"A fraction is in simplest form when numerator and denominator share no common factor besides 1. 2\/3 and 3\/7 cannot be simplified. 10\/12 = 5\/6 and 6\/8 = 3\/4 can be simplified."} {"t":"q","id":16889,"q":"\\(\\dfrac{1}{3}\\) + \\(\\dfrac{1}{12}\\) =","e":"Convert to twelfths: 1\/3 = 4\/12. Then 4\/12 + 1\/12 = 5\/12."} {"t":"q","id":16890,"q":"Find the value of 1 - \\(\\dfrac{3}{5}\\) - \\(\\dfrac{1}{10}\\) .","e":"Convert to tenths: 1 = 10\/10, 3\/5 = 6\/10. Then 10\/10 - 6\/10 - 1\/10 = 3\/10."} {"t":"q","id":16891,"q":"Write 5 thousandths as a decimal.
Answer: ","e":"Thousandths is the third place after the decimal point. 5 thousandths = 0.005."} {"t":"q","id":16892,"q":"Round 117.65 to the nearest whole number.
Answer: ","e":"Look at the tenths digit (6). Since 6 is 5 or more, round up: 117.65 rounds to 118."} {"t":"q","id":16896,"q":"Xiao Hui had more than 10 and fewer than 40 candies. When she packed the candies in bags of 7, she was left with 2 candies. When she packed them in bags of 3, she had no candies left. How many candies did Xiao Hui have?
Answer: ","e":"Numbers between 10 and 40 leaving remainder 2 when divided by 7: 16, 23, 30, 37. Of these, the one divisible by 3 (no remainder) is 30 (30 = 7x4 + 2 and 30 = 3x10)."} {"t":"q","id":16897,"q":"Jeremy thought of a decimal number with 3 decimal places. When he rounded the number to the nearest hundredth, the value was 10.05. Find the greatest possible value of the decimal number Jeremy thought of.
Answer: ","e":"To round to 10.05 (nearest hundredth), the thousandths digit must be 0-4 to round down. The greatest 3-decimal-place number that rounds to 10.05 is 10.054."} {"t":"q","id":16898,"q":"The difference between the two numbers is 6.18. Given the larger number is 8.03, find the value of the smaller number.
Answer: ","e":"Smaller number = larger - difference = 8.03 - 6.18 = 1.85."} {"t":"q","id":16901,"q":"Yan Ling started reading at 4.20 p.m. She read for 1 h 35 min. What time did she stop reading?
Answer: ","e":"4.20 p.m. + 1 h = 5.20 p.m. Then + 35 min = 5.55 p.m."} {"t":"q","id":16904,"q":"Shop A has 50 apples more than Shop B. Shop A has twice as many apples as Shop C. Given that shops A, B and C have 250 apples altogether, how many apples does Shop C have?
Answer: ","e":"Let Shop C = x. Then Shop A = 2x. Shop B = A - 50 = 2x - 50. Total: x + 2x + (2x - 50) = 250, so 5x - 50 = 250, 5x = 300, x = 60. Shop C has 60 apples."} {"t":"q","id":16905,"q":"Ramli spent \\(\\dfrac{1}{3}\\) of his monthly salary on a television. He spent \\(\\dfrac{2}{9}\\) of his salary on food and saved the rest. Given that Ramli saved $2392, how much did Ramli spend on food?
Answer: ","e":"Fraction spent = 1\/3 + 2\/9 = 3\/9 + 2\/9 = 5\/9. Saved = 1 - 5\/9 = 4\/9. So 4\/9 of salary = $2392, meaning 1\/9 = $598 and salary = $5382. Food = 2\/9 = 2 x $598 = $1196."} {"t":"q","id":16906,"q":"The total mass of 2 packets of sugar and 2 packets of flour was 6.54 kg. The mass of 1 packet of flour was twice as heavy as 1 packet of sugar. What was the mass of a packet of flour?
Answer: ","e":"Let 1 packet of sugar = 1 unit, so 1 packet of flour = 2 units. Total units = 2 sugar + 2 flour = 2(1) + 2(2) = 6 units = 6.54 kg. 1 unit = 6.54 \/ 6 = 1.09 kg. Flour = 2 units = 2 x 1.09 = 2.18 kg."} {"t":"q","id":16907,"q":"Patrick bought 4 cupcakes. He gave the cashier some money and received $3.60 as change. Given that each cupcake cost $2.85, how much did he give the cashier?
Answer: ","e":"Cost of 4 cupcakes = 4 x $2.85 = $11.40. Money given = cost + change = $11.40 + $3.60 = $15.00."} {"t":"q","id":16909,"q":"A total of 2590 adults and children attended a family event on one weekend. 1770 adults attended the event. The number of adults at the event was three times as many as the number of boys.
(a) How many children were there at the event?
(b) How many girls were at the event?
(a)   (b) ","e":"(a) Children = total - adults = 2590 - 1770 = 820 children. (b) Boys = adults \/ 3 = 1770 \/ 3 = 590. Girls = children - boys = 820 - 590 = 230 girls."} {"t":"q","id":16910,"q":"At first, Mary had $166 and Larry had $304. Each of them bought 5 similar plates. Each of the plates they bought was of the same price. After buying the plates, Larry had 4 times as much money as Mary left.
(a) How much money did Mary have left after buying the 5 plates?
(b) What was the price of one plate?
(a)   (b) ","e":"Both spent the same amount on plates, so the difference in money stays $304 - $166 = $138. After buying, Larry = 4 x Mary, so the difference = 3 units = $138, 1 unit = $46. (a) Mary had $46 left. (b) Mary spent 166 - 46 = $120 on 5 plates, so 1 plate = 120 \/ 5 = $24."} {"t":"q","id":16911,"q":"The total mass of 3 children is 115.9 kg. John weighs twice as heavy as Amelia. Max is 8.4 kg heavier than John.
(a) What is Amelia's mass?
(b) What is the difference between Amelia's and Max's mass?
(a)   (b) ","e":"Let Amelia = 1 unit, John = 2 units, Max = 2 units + 8.4. Total = 1 + 2 + 2 units + 8.4 = 115.9, so 5 units = 107.5, 1 unit = 21.5. (a) Amelia = 21.5 kg. (b) Max = 2 x 21.5 + 8.4 = 51.4 kg; difference = 51.4 - 21.5 = 29.9 kg."} {"t":"q","id":16913,"q":"Mr Lee started working on his project at 8.45 a.m. He took a 40-minute lunch break. Then, he continued working on the project till he finished it at 5.30 p.m.
(a) How long did Mr Lee spend working on his project?
(b) Mr Lee reached the gym at 5.45 p.m. He exercised for 1 hour 40 minutes before driving home. He reached home at 7.50 p.m. How long did he take to drive home?
(a)   (b) ","e":"(a) From 8.45 a.m. to 5.30 p.m. is 8 h 45 min total. Subtract the 40 min lunch: 8 h 45 min - 40 min = 8 h 5 min working. (b) He reached the gym at 5.45 p.m., exercised 1 h 40 min, finishing at 7.25 p.m. He reached home at 7.50 p.m., so driving took 7.50 - 7.25 = 25 min."} {"t":"q","id":16914,"q":"Andrew has 1250 stickers and Ben has 490 stickers more than Andrew. Ben gave some of his stickers to Andrew. In the end, Ben had 626 stickers less than Andrew. How many stickers did Ben give to Andrew?
Answer: ","e":"Ben at first = 1250 + 490 = 1740. Total stickers = 1740 + 1250 = 2990 (unchanged). In the end Ben = Andrew - 626. So Andrew + (Andrew - 626) = 2990, 2 x Andrew = 3616, Andrew = 1808, Ben = 1182. Ben gave away = 1740 - 1182 = 558 stickers."} {"t":"q","id":16915,"q":"In a box, \\(\\dfrac{1}{8}\\) of the marbles were blue. \\(\\dfrac{7}{12}\\) of the marbles were red. There was an equal number of blue and green marbles in the box. The rest of the marbles were pink. There was a total of 581 green and pink marbles in the box. How many red marbles were there in the box?
Answer: ","e":"Blue = 1\/8, green = blue = 1\/8, red = 7\/12. Pink = 1 - 1\/8 - 1\/8 - 7\/12. Common denom 24: blue 3\/24, green 3\/24, red 14\/24, so pink = 24\/24 - 3\/24 - 3\/24 - 14\/24 = 4\/24. Green + pink = 3\/24 + 4\/24 = 7\/24 = 581, so 1\/24 = 83 and total = 1992. Red = 7\/12 = 14\/24 = 14 x 83 = 1162 marbles."} {"t":"q","id":16960,"q":"28 549 rounded to the nearest hundred is .","e":"Look at the tens digit (4). Since 4 < 5, round down: 28 549 \u2192 28 500."} {"t":"q","id":16962,"q":"Find the value of \\(\\dfrac{5}{12} - \\dfrac{1}{3}\\).","e":"Make the denominators the same: \\(\\dfrac{1}{3} = \\dfrac{4}{12}\\). Then \\(\\dfrac{5}{12} - \\dfrac{4}{12} = \\dfrac{1}{12}\\)."} {"t":"q","id":16963,"q":"In which of the following numbers does the digit 4 stand for 4 tenths?","e":"4 tenths = 0.4, so the digit 4 must be the first digit after the decimal point. In 30.42 the 4 is in the tenths place."} {"t":"q","id":16965,"q":"Arrange the following fractions in order, beginning with the greatest.
\\(\\dfrac{3}{4}\\), \\(\\dfrac{7}{12}\\), \\(\\dfrac{7}{8}\\)","e":"Use common denominator 24: \\(\\dfrac{3}{4}=\\dfrac{18}{24}\\), \\(\\dfrac{7}{12}=\\dfrac{14}{24}\\), \\(\\dfrac{7}{8}=\\dfrac{21}{24}\\). Greatest to least: \\(\\dfrac{21}{24}, \\dfrac{18}{24}, \\dfrac{14}{24}\\) = \\(\\dfrac{7}{8}, \\dfrac{3}{4}, \\dfrac{7}{12}\\)."} {"t":"q","id":16968,"q":"Coreen took 50 minutes to complete her work. She finished her work at 12 00. Express her starting time using the 12-hour clock.","e":"Finished at 12 00 (noon). Start time = 12 00 \u2212 50 min = 11 10, which is 11.10 a.m."} {"t":"q","id":16969,"q":"What is 190 tens more than 79 090?","e":"190 tens = 190 \u00d7 10 = 1900. So 79 090 + 1900 = 80 990."} {"t":"q","id":16970,"q":"Find the sum of 0.35 and 4 tenths.","e":"4 tenths = 0.4. Sum = 0.35 + 0.4 = 0.75."} {"t":"q","id":16971,"q":"A tree is 5.9 m when its height is rounded to 1 decimal place. Which of the following could be the actual height of the tree?","e":"To round to 5.9, the value must be from 5.85 up to (but not including) 5.95. Only 5.88 lies in this range (5.84 rounds to 5.8; 5.95 and 5.99 round to 6.0)."} {"t":"q","id":16979,"q":"Write six thousand and eight in figures.
","e":"Six thousand = 6000, and eight = 8 in the ones place (no hundreds or tens). So 6000 + 8 = 6008."} {"t":"q","id":16984,"q":"Arrange these numbers from the smallest to the greatest.
0.784, 8.4, 0.804, 0.095
, , , ","e":"Compare whole-number parts first: 8.4 is largest. Among the others (all 0.something) compare tenths: 0.095 (0 tenths) < 0.784 < 0.804. Order: 0.095, 0.784, 0.804, 8.4."} {"t":"q","id":16985,"q":"Some factors of 32 are 1, 2, 8 and 32. What are the other two factors of 32?
and ","e":"The factors of 32 are 1, 2, 4, 8, 16, 32. The two not listed are 4 and 16 (4 \u00d7 8 = 32, 2 \u00d7 16 = 32)."} {"t":"q","id":16987,"q":"Which two fractions are in the simplest form?
\\(\\dfrac{3}{9}\\), \\(\\dfrac{2}{5}\\), \\(\\dfrac{2}{6}\\), \\(\\dfrac{3}{8}\\)
and ","e":"A fraction is in simplest form when numerator and denominator share no common factor other than 1. \\(\\dfrac{3}{9}=\\dfrac{1}{3}\\) and \\(\\dfrac{2}{6}=\\dfrac{1}{3}\\) can be simplified, but \\(\\dfrac{2}{5}\\) and \\(\\dfrac{3}{8}\\) cannot."} {"t":"q","id":16989,"q":"Use all the digits given to form the greatest odd number.
2, 9, 4, 8, 5
","e":"For the greatest odd number, the ones digit must be the smallest available odd digit (5). Arrange the remaining digits 9, 8, 4, 2 in descending order in front: 9842, giving 98 425."} {"t":"q","id":16990,"q":"Mrs Lee mixed 1.4 \\(l\\) of orange syrup with 3.16 \\(l\\) of water. She poured the mixture equally into 4 bottles. How many litres of the mixture were there in each bottle?
","e":"Total mixture = 1.4 + 3.16 = 4.56 \\(l\\). Shared equally into 4 bottles: 4.56 \u00f7 4 = 1.14 \\(l\\) each."} {"t":"q","id":16991,"q":"The mass of 4 similar boxes was 5.04 kg. 2 boxes were removed. What was the mass of the new stack of boxes?
","e":"Removing 2 of the 4 identical boxes leaves half the mass: 5.04 \u00f7 2 = 2.52 kg."} {"t":"q","id":16993,"q":"A fruit seller had 170 pears and oranges altogether. After he sold \\(\\dfrac{2}{3}\\) of the pears and 14 oranges, he had an equal number of pears and oranges left. How many oranges were there in the end?
","e":"After selling, pears left = \\(\\dfrac{1}{3}\\) of pears and oranges left = oranges \u2212 14, and these two are equal. The remaining pears (1 unit) plus the sold pears (2 units = 3 units total pears) plus oranges equal the total once the 14 sold oranges are accounted for: 4 units = 170 \u2212 14 = 156, so 1 unit = 156 \u00f7 4 = 39. The oranges left equal the remaining pears = 39."} {"t":"q","id":16999,"q":"There were some sweets in a box. Evelyn took \\(\\dfrac{5}{8}\\) of the sweets and Nigel took the rest. Evelyn took 76 more sweets than Nigel.
(a) What fraction of the sweets did Nigel take?
(b) How many sweets were in the box at first?
(a)
(b) ","e":"(a) Nigel took 1 \u2212 \\(\\dfrac{5}{8}\\) = \\(\\dfrac{3}{8}\\). (b) Evelyn \u2212 Nigel = \\(\\dfrac{5}{8} - \\dfrac{3}{8} = \\dfrac{2}{8}\\) of the sweets = 76, so \\(\\dfrac{1}{8}\\) = 38 and the whole box = 8 \u00d7 38 = 304 sweets."} {"t":"q","id":17000,"q":"John and Peter had a total of $540. After John gave Peter $40, he had five times as much money as Peter.
(a) How much money did Peter have in the end?
(b) How much money did John have at first?
(a)
(b) ","e":"The total stays $540. In the end John = 5 units and Peter = 1 unit, so 6 units = $540 and 1 unit = $90. (a) Peter has $90 in the end. (b) John had $490 at first ($90 \u00d7 5 = $450 at the end, plus the $40 he gave away = $490)."} {"t":"q","id":17001,"q":"In a library, there were English, Chinese and Malay books. The number of English and Chinese books was 720. The English books were twice as many as the Chinese books and three times as many as the Malay books. Find the total number of books in the library.
","e":"Let Chinese = 3 units, then English = 6 units (twice Chinese). English + Chinese = 9 units = 720, so 1 unit = 80. Malay = English \u00f7 3 = 6 \u00f7 3 = 2 units. Total = 9 + 2 = 11 units = 11 \u00d7 80 = 880 books."} {"t":"q","id":17005,"q":"43 thousands and 8 tens is the same as .","e":"43 thousands = 43 000. 8 tens = 80. 43 000 + 80 = 43 080."} {"t":"q","id":17006,"q":"Which of the following numbers when rounded to the nearest ten becomes 72 500?","e":"Rounding to the nearest ten, numbers from 72 495 to 72 504 round to 72 500. 72 496 rounds to 72 500. (72 444->72 440; 72 506->72 510; 72 554->72 550.)"} {"t":"q","id":17007,"q":"What is the missing number in the box?
\\(6\\dfrac{5}{9}\\) = \\(\\dfrac{ }{9}\\)","e":"Convert the mixed number to an improper fraction: \\(6\\dfrac{5}{9} = \\dfrac{6\\times 9 + 5}{9} = \\dfrac{54+5}{9} = \\dfrac{59}{9}\\). The missing numerator is 59."} {"t":"q","id":17011,"q":"The volume of water in a tank is 19 000 \\(\\ell\\) when rounded to the nearest thousand litres. Which one of the following is the greatest possible volume of water in the tank?","e":"Rounded to the nearest thousand, values from 18 500 to 19 499 give 19 000. The greatest possible value is 19 499 (19 500 would round up to 20 000)."} {"t":"q","id":17012,"q":"Which one of the following pairs of numbers have 3 and 9 as their common factors?","e":"Both numbers must be divisible by 3 and by 9. 27 = 9x3 and 36 = 9x4, so both share factors 3 and 9. (12, 18, 21 are not multiples of 9.)"} {"t":"q","id":17014,"q":"Mr Lim bought \\(\\dfrac{4}{5}\\) kg of cherries. He and his sons ate \\(\\dfrac{3}{10}\\) kg of the cherries. What was the mass of cherries left?","e":"\\(\\dfrac{4}{5} = \\dfrac{8}{10}\\). Cherries left = \\(\\dfrac{8}{10} - \\dfrac{3}{10} = \\dfrac{5}{10} = \\dfrac{1}{2}\\) kg."} {"t":"q","id":17015,"q":"James bought 1.27 kg of sweets. His sister bought 0.18 kg more than him. What was the total mass of sweets they bought altogether?","e":"Sister = 1.27 + 0.18 = 1.45 kg. Total = 1.27 + 1.45 = 2.72 kg."} {"t":"q","id":17016,"q":"Janet's age is a multiple of 7 this year. Next year, her age will be a multiple of 6. Which one of the following is Janet's age this year?","e":"Age this year is a multiple of 7; next year (age + 1) is a multiple of 6. 49 is a multiple of 7 and 49 + 1 = 50 is not a multiple of 6... check: 14+1=15 no; 35+1=36 yes (36=6x6, 35=7x5). So 35 works. Re-check key: key gives option 4 = 49? 49+1=50 not multiple of 6. The valid answer is 35."} {"t":"q","id":17018,"q":"When it is 09 00 in Singapore, it is 10 30 in Australia. Mr Kim makes a call at 14 50 from Singapore to his wife who is in Australia. What is the time in Australia when Mr Kim calls his wife?","e":"Australia is 1 h 30 min ahead of Singapore (10 30 vs 09 00). At 14 50 in Singapore, Australia time = 14 50 + 1 h 30 min = 16 20."} {"t":"q","id":17019,"q":"A bus departed from Singapore and arrived in Kuala Lumpur at 13 40. The bus ride took 5 hours and 30 minutes. At what time did the bus depart from Singapore?","e":"Departure = arrival - duration = 13 40 - 5 h 30 min. 13 40 - 5 h = 08 40; 08 40 - 30 min = 08 10."} {"t":"q","id":17023,"q":"Write fifteen thousand and thirty-six in figures.
","e":"Fifteen thousand = 15 000; thirty-six = 36. So 15 000 + 36 = 15 036."} {"t":"q","id":17024,"q":"Write the missing number in the number pattern.
14 000, 13 400, 12 800, 12 200, , 11 000","e":"The pattern decreases by 600 each time (14 000, 13 400, 12 800, 12 200, ...). 12 200 - 600 = 11 600 (and 11 600 - 600 = 11 000)."} {"t":"q","id":17025,"q":"Some factors of 32 are 1, 2, 4 and 32. What are the other two factors of 32?
and ","e":"The factors of 32 are 1, 2, 4, 8, 16, 32. The two not listed are 8 and 16."} {"t":"q","id":17026,"q":"What is the missing number in the box?
\\(\\dfrac{4}{7}\\) = \\(\\dfrac{}{49}\\)","e":"49 = 7 x 7, so multiply numerator and denominator of \\(\\dfrac{4}{7}\\) by 7: \\(\\dfrac{4\\times 7}{7\\times 7} = \\dfrac{28}{49}\\). The missing numerator is 28."} {"t":"q","id":17027,"q":"Arrange the following fractions from the greatest to the smallest.
\\(\\dfrac{1}{2}\\), \\(\\dfrac{2}{3}\\), \\(\\dfrac{7}{12}\\)
, , ","e":"Use denominator 12: \\(\\dfrac{1}{2}=\\dfrac{6}{12}\\), \\(\\dfrac{2}{3}=\\dfrac{8}{12}\\), \\(\\dfrac{7}{12}=\\dfrac{7}{12}\\). Greatest to smallest: \\(\\dfrac{8}{12}, \\dfrac{7}{12}, \\dfrac{6}{12}\\), i.e. \\(\\dfrac{2}{3}, \\dfrac{7}{12}, \\dfrac{1}{2}\\)."} {"t":"q","id":17028,"q":"Express 0.6 as a fraction.","e":"0.6 = \\(\\dfrac{6}{10}\\). Simplify by dividing by 2: \\(\\dfrac{6}{10} = \\dfrac{3}{5}\\)."} {"t":"q","id":17030,"q":"What is the value of \\(\\dfrac{5}{8} + \\dfrac{3}{4}\\)? Express your answer as a mixed number.","e":"\\(\\dfrac{3}{4} = \\dfrac{6}{8}\\). \\(\\dfrac{5}{8} + \\dfrac{6}{8} = \\dfrac{11}{8} = 1\\dfrac{3}{8}\\)."} {"t":"q","id":17032,"q":"Find the value of 20.7 \u00f7 7. Round your answer to the nearest hundredths.
","e":"20.7 \u00f7 7 = 2.957... Rounding to the nearest hundredth (2 decimal places) gives 2.96."} {"t":"q","id":17033,"q":"A movie started at 11 35 and ended at 14 10. How long was the movie?
h min","e":"From 11 35 to 14 10. 11 35 to 14 35 is 3 h, but we only need to 14 10, which is 25 min before 14 35... easier: 11 35 to 12 00 = 25 min; 12 00 to 14 00 = 2 h; 14 00 to 14 10 = 10 min. Total = 2 h 35 min."} {"t":"q","id":17034,"q":"Mr Lee cuts a 5-m rope into three pieces, A, B and C. Rope A measures 2.88 m and it is twice as long as rope B. What is the length of rope C?
m","e":"Rope A = 2.88 m. Rope B = 2.88 \u00f7 2 = 1.44 m. A + B = 2.88 + 1.44 = 4.32 m. Rope C = 5 - 4.32 = 0.68 m."} {"t":"q","id":17035,"q":"A rectangle has a perimeter of 32 cm. The length is 3 times as long as its breadth. Find the area of the rectangle.
cm\u00b2","e":"Length + breadth = half the perimeter = 16 cm. With length = 3 x breadth, that is 4 units = 16 cm, so 1 unit (breadth) = 4 cm and length = 12 cm. Area = 12 x 4 = 48 cm\u00b2."} {"t":"q","id":17037,"q":"At a fruit stall, there were 150 more apples than pears. After 46 pears were sold, there were 5 times as many apples as pears. How many pears were there at first?
","e":"After selling 46 pears, apples are unchanged and apples = 5 x (remaining pears). Apples are 150 more than the original pears, i.e. 150 + 46 = 196 more than the remaining pears. So 4 units (apples - remaining pears) = 196, 1 unit (remaining pears) = 49. Pears at first = 49 + 46 = 95."} {"t":"q","id":17040,"q":"Weijian had three times as much money as Xavier. After Weijian bought 8 erasers at $1.30 each he had $3.85 left.
(a) How much money did Weijian have at first?
$
(b) How much money did Xavier have?
$","e":"(a) Cost of erasers = 8 x $1.30 = $10.40. Weijian at first = $10.40 + $3.85 = $14.25. (b) Weijian had 3 times Xavier, so Xavier = $14.25 \u00f7 3 = $4.75."} {"t":"q","id":17041,"q":"A water container had 1 \\(\\ell\\) of water. Mr Muthu used \\(\\dfrac{2}{5}\\) \\(\\ell\\) of it to make a drink and \\(\\dfrac{1}{4}\\) \\(\\ell\\) of it to water his plants.
(a) How much water did Mr Muthu use altogether?
\\(\\ell\\)
(b) How much water was left?
\\(\\ell\\)","e":"(a) \\(\\dfrac{2}{5} = \\dfrac{8}{20}\\), \\(\\dfrac{1}{4} = \\dfrac{5}{20}\\). Used = \\(\\dfrac{8}{20} + \\dfrac{5}{20} = \\dfrac{13}{20}\\) \\(\\ell\\). (b) Left = 1 - \\(\\dfrac{13}{20} = \\dfrac{7}{20}\\) \\(\\ell\\)."} {"t":"q","id":17042,"q":"Mrs Raja baked some cookies. She gave \\(\\dfrac{1}{3}\\) of the cookies to her daughter, \\(\\dfrac{5}{8}\\) of them to her friend and kept the rest for herself. Mrs Raja gave her friend 42 more cookies than what she had given to her daughter. How many cookies did Mrs Raja bake?
","e":"Friend got \\(\\dfrac{5}{8}\\) and daughter got \\(\\dfrac{1}{3}\\). Difference = \\(\\dfrac{5}{8} - \\dfrac{1}{3} = \\dfrac{15}{24} - \\dfrac{8}{24} = \\dfrac{7}{24}\\) of the cookies = 42. So \\(\\dfrac{1}{24}\\) = 6, and the total (24 units) = 24 x 6 = 144 cookies."} {"t":"q","id":17046,"q":"Cynthia had two times as many $2 notes as $5 notes. The total amount of money that Cynthia had was $243. How many $2 notes did Cynthia have?
","e":"Take 1 group = two $2 notes + one $5 note = $2 + $2 + $5 = $9. Number of groups = $243 \u00f7 $9 = 27. Each group has two $2 notes, so $2 notes = 27 x 2 = 54."} {"t":"q","id":17079,"q":"32 769 rounded to the nearest hundred is .","e":"Look at the tens digit (6). Since 6 \u2265 5, round the hundreds up: 32 769 \u2192 32 800."} {"t":"q","id":17080,"q":"\\(7\\dfrac{4}{5}\\) = \\(\\dfrac{ }{5}\\)
What is the missing number in the box?","e":"Convert the mixed number to an improper fraction: 7 \u00d7 5 + 4 = 39, so \\(7\\dfrac{4}{5}=\\dfrac{39}{5}\\). Missing number = 39."} {"t":"q","id":17081,"q":"Express 0.08 as a fraction in its simplest form.","e":"0.08 = \\(\\dfrac{8}{100}\\). Divide numerator and denominator by 4: \\(\\dfrac{8}{100}=\\dfrac{2}{25}\\)."} {"t":"q","id":17082,"q":"Write \\(6\\dfrac{7}{20}\\) as a decimal.","e":"\\(\\dfrac{7}{20}=\\dfrac{35}{100}=0.35\\). So \\(6\\dfrac{7}{20}=6.35\\)."} {"t":"q","id":17088,"q":"Arrange the following fractions from the greatest to the smallest.
\\(1\\dfrac{1}{9}\\) , \\(\\dfrac{11}{7}\\) , \\(\\dfrac{8}{7}\\)","e":"As decimals: \\(\\dfrac{11}{7}\\approx1.57\\), \\(\\dfrac{8}{7}\\approx1.14\\), \\(1\\dfrac{1}{9}\\approx1.11\\). Greatest to smallest: \\(\\dfrac{11}{7}\\), \\(\\dfrac{8}{7}\\), \\(1\\dfrac{1}{9}\\)."} {"t":"q","id":17091,"q":"Abby reached the bus stop at 12.20 p.m. She waited 15 minutes for the bus and the bus journey was 40 minutes. What time did she reach her destination?","e":"12.20 p.m. = 1220. Add 15 min wait \u2192 1235. Add 40 min journey \u2192 1315 (in 24-hour time)."} {"t":"q","id":17092,"q":"The difference between two numbers is 50. The smaller number is 300. What is the sum of the two numbers?","e":"Larger number = 300 + 50 = 350. Sum = 300 + 350 = 650."} {"t":"q","id":17093,"q":"A flask contained 2 \\(l\\) of hot water. Ms Tan used \\(\\dfrac{3}{4}\\) \\(l\\) of the hot water to make chocolate drinks and \\(\\dfrac{7}{8}\\) \\(l\\) of the hot water to make coffee. How much water was left in the flask?","e":"Used = \\(\\dfrac{3}{4}+\\dfrac{7}{8}=\\dfrac{6}{8}+\\dfrac{7}{8}=\\dfrac{13}{8}=1\\dfrac{5}{8}\\) l. Left = \\(2-1\\dfrac{5}{8}=\\dfrac{3}{8}\\) l."} {"t":"q","id":17096,"q":"There are three electric stars on a Christmas tree. The three electric stars will light up every 3 minutes, 4 minutes, and 6 minutes respectively. The three electric stars are switched on and light up together for the 1st time at 10 00. What time will the electric stars light up together for the 3rd time?","e":"LCM of 3, 4 and 6 = 12, so they light together every 12 min. 1st at 1000, 2nd at 1012, 3rd at 1024."} {"t":"q","id":17098,"q":"Some factors of 12 are 1, 2, 3 and 12. What are the other two factors of 12?
Ans : and ","e":"Factors of 12 are 1, 2, 3, 4, 6, 12. The two not yet listed are 4 and 6."} {"t":"q","id":17100,"q":"Write the missing number in the number pattern.
32 400 , 32 000 , 31 600 , 31 200 , , 30 400","e":"The pattern decreases by 400 each step. 31 200 \u2212 400 = 30 800."} {"t":"q","id":17102,"q":"Which two of the fractions are in the simplest form?
\\(\\dfrac{2}{5}\\) , \\(\\dfrac{3}{6}\\) , \\(\\dfrac{4}{10}\\) , \\(\\dfrac{5}{12}\\)
Ans : and ","e":"A fraction is in simplest form when numerator and denominator share no common factor. \\(\\dfrac{3}{6}=\\dfrac{1}{2}\\) and \\(\\dfrac{4}{10}=\\dfrac{2}{5}\\) can be simplified; \\(\\dfrac{2}{5}\\) and \\(\\dfrac{5}{12}\\) cannot."} {"t":"q","id":17105,"q":"Find the value of 4.72 \u00d7 6.
Answer: ","e":"4.72 \u00d7 6 = 28.32."} {"t":"q","id":17107,"q":"The table shows the times taken by four girls to complete a 100 m race.
Amy: 16.1 , Bess: 17.0 , Cleo: 15.8 , Dawn: 15.9 (time in seconds)
Write down the names of the girls from the 1st to the 4th position.
Ans : (1st) , , , (4th)","e":"The fastest runner (smallest time) is 1st. Times: Cleo 15.8 < Dawn 15.9 < Amy 16.1 < Bess 17.0. So 1st Cleo, 2nd Dawn, 3rd Amy, 4th Bess."} {"t":"q","id":17108,"q":"In a factory, sweets are equally packed into boxes. Bill bought two boxes of sweets. He received 1044 sweets altogether. How many sweets would Bill receive in total, if he buys five more boxes of sweets?
Answer: ","e":"2 boxes = 1044, so 1 box = 1044 \u00f7 2 = 522. Total boxes = 2 + 5 = 7. Total sweets = 7 \u00d7 522 = 3654."} {"t":"q","id":17111,"q":"James took a flight from Singapore to Taiwan. The plane left Singapore 20 min before midnight and he arrived in Taiwan at 04 50. What is the duration of the flight?
Ans : h min","e":"20 min before midnight = 2340. From 2340 to 2400 is 20 min; from 0000 to 0450 is 4 h 50 min. Total = 4 h 50 min + 20 min = 5 h 10 min."} {"t":"q","id":17112,"q":"A number is between 30 and 40. When it is divided by 3, the answer is a whole number. When it is divided by 4, the remainder is 3. What is the number?
Answer: ","e":"Multiples of 3 between 30 and 40: 30, 33, 36, 39. Check remainder 3 when divided by 4: 39 \u00f7 4 = 9 R3. So the number is 39."} {"t":"q","id":17115,"q":"Bill is 4 times as heavy as Charlotte. He is 98.4 kg. What is the total mass of Bill and Charlotte?
Answer: ","e":"Bill = 4 units = 98.4 kg, so 1 unit (Charlotte) = 98.4 \u00f7 4 = 24.6 kg. Total = 5 units = 5 \u00d7 24.6 = 123 kg."} {"t":"q","id":17116,"q":"Ben had a piece of string. He cut it into three pieces, String A, String B and String C. String B is 0.15 m longer than String A and 2.7 m longer than String C. String A is 4.36 m long. What is the length of String C?
Answer: ","e":"String B = String A + 0.15 = 4.36 + 0.15 = 4.51 m. String C = String B \u2212 2.7 = 4.51 \u2212 2.7 = 1.81 m."} {"t":"q","id":17117,"q":"John had some money. He spent \\(\\dfrac{1}{4}\\) of his money on food and \\(\\dfrac{5}{8}\\) of his money on books. He spent $12 more on books than food. How much money did he have at first?
Answer: ","e":"Food = \\(\\dfrac{1}{4}=\\dfrac{2}{8}\\), books = \\(\\dfrac{5}{8}\\). Difference = \\(\\dfrac{5}{8}-\\dfrac{2}{8}=\\dfrac{3}{8}\\) of his money = $12. So \\(\\dfrac{1}{8}\\) = $4, and total \\(\\dfrac{8}{8}\\) = 8 \u00d7 $4 = $32."} {"t":"q","id":17118,"q":"Ravi and Sam had 1780 stickers altogether. After Sam gave Ravi 40 stickers, they had the same number of stickers. How many stickers did Sam have at first?
Answer: ","e":"After the transfer each has 1780 \u00f7 2 = 890. Sam gave away 40, so Sam had 890 + 40 = 930 at first."} {"t":"q","id":17119,"q":"A television costs 10 times as much as a chair. 1 television and 1 table cost $1820. 1 table and 1 chair cost $560. What is the cost of 1 television and 2 tables?
Answer: ","e":"TV = 10 chairs. TV + table = 1820 \u2192 10 chairs + table = 1820. Table + chair = 560. Subtracting: 9 chairs = 1820 \u2212 560 = 1260, so 1 chair = 140. Table = 560 \u2212 140 = 420. TV = 10 \u00d7 140 = 1400. 1 TV + 2 tables = 1400 + 2 \u00d7 420 = 1400 + 840 = $2240."} {"t":"s","id":9282,"s":"For every 5 won, 2 bonus are given, so each group of 5 + 2 = 7 tokens. 150 \/ 7 is not exact; the closest full groups give 21 groups of 7 = 147, with bonus tokens 21 x 2 = 42. So Larry was given 42 bonus tokens."} {"t":"s","id":9283,"s":"Let each colour start with N beads. Red given away = 2\/3 N, yellow given away = 1\/6 N. Total given = 2\/3 N + 1\/6 N = 5\/6 N = 50, so N = 60. Red left = 1\/3 x 60 = 20; yellow left = 5\/6 x 60 = 50. Difference = 50 - 20 = 30."} {"t":"s","id":9286,"s":"Thirteen thousand = 13 000; ninety-two = 92. Together 13 000 + 92 = 13 092."} {"t":"s","id":9287,"s":"Each number decreases by 400. 12 800 - 400 = 12 400 (and 12 400 - 400 = 12 000)."} {"t":"s","id":9290,"s":"6 x 3 = 18, so multiply the numerator by 3: 5 x 3 = 15. So 5\/6 = 15\/18."} {"t":"s","id":9292,"s":"2\/5 = 0.4. Comparing 0.052, 0.4, 0.502 gives smallest to greatest: 0.052, 2\/5, 0.502."} {"t":"s","id":9296,"s":"Daughter 3 years ago = 7, so now = 7 + 3 = 10. Mrs Chan = 5 x 10 = 50 years old."} {"t":"s","id":9297,"s":"Remove the 15 extra green sticks: 41 - 15 = 26. Split equally: 26 \u00f7 2 = 13 blue sticks."} {"t":"s","id":9298,"s":"Largest place value should hold the biggest digit. With 3 decimal places, put 8 as the whole number and arrange the rest in decreasing order: 8.630."} {"t":"s","id":9300,"s":"The pattern repeats every 6 letters: A B B C D A. 70 \u00f7 6 = 11 remainder 4. The 4th letter in the block A B B C D A is C, so the 70th letter is C."} {"t":"s","id":9305,"s":"Let James = 1 unit. Paul = 2 units, Henry = 1 unit - 30. Total = 4 units - 30 = 386, so 4 units = 416, 1 unit = 104. (a) James = 104. (b) Paul = 2 x 104 = 208, Henry = 104 - 30 = 74, Henry + Paul = 208 + 74 = 282."} {"t":"s","id":9306,"s":"Day 1 = 1\/4 m. Day 2 = 1\/4 + 5\/8 = 2\/8 + 5\/8 = 7\/8 m. Total = 1\/4 + 7\/8 = 2\/8 + 7\/8 = 9\/8 = 1 1\/8 m."} {"t":"s","id":9307,"s":"Each of the 2 strings is 1.9 m longer than a ribbon, so the extra length = 2 x 1.9 = 3.8 m. Remove it: 9.12 - 3.8 = 5.32 m for 7 equal ribbon-lengths (2 strings + 5 ribbons all reduced to ribbon length). 5.32 \u00f7 7 = 0.76 m per ribbon."} {"t":"s","id":9308,"s":"(a) From 10 45 to 13 10: 10 45 to 12 45 is 2 h, then to 13 10 is 25 min more = 2 h 25 min. (b) Reached Town B at 13 10, stayed 30 min -> leaves 13 40. Add 4 h 15 min: 13 40 + 4 h = 17 40, + 15 min = 17 55, i.e. 1755 (24-hour clock)."} {"t":"s","id":9310,"s":"42 thousands = 42 000 and 8 tens = 80. 42 000 + 80 = 42 080."} {"t":"s","id":9315,"s":"Factors of 12 are 1, 2, 3, 4, 6, 12; factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, 80. The common factor among the options is 4."} {"t":"s","id":9317,"s":"Oil used = 2\/3 + 1\/12 = 8\/12 + 1\/12 = 9\/12. Oil left = 1 \u2212 9\/12 = 12\/12 \u2212 9\/12 = 3\/12 = 1\/4."} {"t":"s","id":9320,"s":"From 20 30 to 22 30 is 2 h; from 22 30 to 23 15 is a further 45 min. Total = 2 h 45 min."} {"t":"s","id":9323,"s":"Of S, H, I, N, E: H (vertical\/horizontal), I (vertical\/horizontal) and E (horizontal) each have a line of symmetry; S and N do not. So 3 letters."} {"t":"s","id":9329,"s":"Compare digit by digit: 3092 (hundreds 0), then 3902 (hundreds 9, tens 0), then 3920 (hundreds 9, tens 2). Smallest to greatest: 3092, 3902, 3920."} {"t":"s","id":9334,"s":"Using denominator 6: 2\/3 = 4\/6, 1\/2 = 3\/6, 5\/6 = 5\/6. Greatest to smallest: 5\/6, 4\/6, 3\/6, i.e. 5\/6, 2\/3, 1\/2."} {"t":"s","id":9336,"s":"A 1-decimal-place number rounds to 89 if it lies from 88.5 up to 89.4 (88.5 rounds up, 89.4 rounds down, 89.5 would round to 90). Greatest = 89.4; smallest = 88.5."} {"t":"s","id":9339,"s":"Side = 72 \u00f7 4 = 18 cm. Area = 18 \u00d7 18 = 324 cm\u00b2."} {"t":"s","id":9340,"s":"1.50 p.m. + 15 min = 2.05 p.m. In 24-hour clock that is 14 05."} {"t":"s","id":9344,"s":"Let Shop Z = 1 unit. Shop Y = 2 units, Shop X = 4 \u00d7 2 = 8 units. X \u2212 Z = 8 \u2212 1 = 7 units = 602, so 1 unit = 602 \u00f7 7 = 86. Shop Z = 86. Total = (8 + 2 + 1) units = 11 units = 11 \u00d7 86 = 946 cars."} {"t":"s","id":9345,"s":"(a) Total = 8 + 1.43 = 9.43 \u2113. (b) Each jug = 9.43 \u00f7 7 = 1.347... \u2248 1.35 \u2113 (2 d.p.)."} {"t":"s","id":9346,"s":"(a) Monday + Tuesday = 2\/9 + 1\/3 = 2\/9 + 3\/9 = 5\/9, so Wednesday = 1 \u2212 5\/9 = 4\/9. (b) Tuesday \u2212 Monday = 3\/9 \u2212 2\/9 = 1\/9 of the book = 25 pages, so the whole book = 25 \u00d7 9 = 225 pages."} {"t":"s","id":9351,"s":"Add by place value: 50000 + 2000 + 90 + 8 = 52098. There are no hundreds, so the hundreds digit is 0."} {"t":"s","id":9352,"s":"56 = 8x7 = 4x14, so 8, 7 and 4 are factors and 56 is a multiple of each. 56 \/ 9 is not a whole number, so 56 is not a multiple of 9."} {"t":"s","id":9353,"s":"In 6.017 the places after the point are tenths (0), hundredths (1), thousandths (7). The 7 is in the third decimal place, so it stands for 7 thousandths."} {"t":"s","id":9354,"s":"7\/50 = 14\/100 = 0.14 (multiply numerator and denominator by 2). So 4 7\/50 = 4.14."} {"t":"s","id":9356,"s":"Convert the mixed number to an improper fraction: 9 3\/4 = (9x4 + 3)\/4 = (36 + 3)\/4 = 39\/4. So the missing numerator is 39."} {"t":"s","id":9359,"s":"Total stays $348, so after giving each has 348 \/ 2 = $174. Paul gave away $33, so at first Paul had 174 + 33 = $207."} {"t":"s","id":9360,"s":"For a number below 5000 the thousands digit must be 3 (0 not allowed as leading digit; 9 and 7 are too big). The remaining 3 digits (9, 7, 0) can be arranged in 3 x 2 x 1 = 6 ways. So 6 numbers."} {"t":"s","id":9374,"s":"Compare digit by digit after the decimal point: 1.702 has 7 tenths (largest), then 1.207 has 2 tenths, then 1.027 has 0 tenths. Greatest to smallest: 1.702, 1.207, 1.027."} {"t":"s","id":9376,"s":"The numerator goes from 3 to 15, which is x5. Multiply the denominator by 5 too: 8 x 5 = 40. So 3\/8 = 15\/40."} {"t":"s","id":9377,"s":"Make a common denominator of 12: 1\/4 = 3\/12. Then 11\/12 + 3\/12 = 14\/12 = 1 2\/12. (The answer key leaves it as 1 2\/12.)"} {"t":"s","id":9380,"s":"Work backwards from 00 20 by 1 h 55 min. 00 20 minus 1 h = 23 20 (previous day); minus 55 min more = 22 25. The movie started at 2225."} {"t":"s","id":9381,"s":"The factors of 39 are 1, 3, 13 and 39. Their sum = 1 + 3 + 13 + 39 = 56."} {"t":"s","id":9383,"s":"8th multiple minus 3rd multiple = 5 of the number. This equals 35, so the number = 35 \/ 5 = 7."} {"t":"s","id":9385,"s":"Father's mass = 39.8 + 27.35 = 67.15 kg. Total mass = 39.8 + 67.15 = 106.95 kg."} {"t":"s","id":9386,"s":"Lengths from 167.75 up to (but below) 167.85 round to 167.8 (1 d.p.). The least value that rounds up to 167.8 is 167.75 cm."} {"t":"s","id":9390,"s":"(a) Total eggs = 36 x 30 = 1080. Unbroken = 1080 - 82 = 998. (b) 998 \/ 8 = 124 remainder 6, so 124 full cartons and 6 eggs left over (not packed)."} {"t":"s","id":9391,"s":"Let each receive g. Then 392 + g = 6 x (47 + g). 392 + g = 282 + 6g, so 110 = 5g, g = $22. (Check: Terry 392+22=414, Willy 47+22=69, 414 = 6 x 69.)"} {"t":"s","id":9393,"s":"(a) Chocolate + blueberry = 1\/3 + 2\/9 = 3\/9 + 2\/9 = 5\/9. Butter = 1 - 5\/9 = 4\/9. (b) 1\/4 of 108 = 27 cakes sold. Money = 27 x $15 = $405."} {"t":"s","id":9395,"s":"72 thousands = 72 000 and 3 tens = 30. 72 000 + 30 = 72 030."} {"t":"s","id":9396,"s":"Factors of 28: 1,2,4,7,14,28. Factors of 60: 1,2,3,4,5,6,10,12,15,20,30,60. Common factor among options is 4 (4 divides 28 and 60)."} {"t":"s","id":9397,"s":"7\/20 = 35\/100 = 0.35. So 4 7\/20 = 4 + 0.35 = 4.35."} {"t":"s","id":9399,"s":"Convert mixed number to improper fraction: 9 5\/8 = (9\u00d78 + 5)\/8 = (72 + 5)\/8 = 77\/8. Missing number is 77."} {"t":"s","id":9400,"s":"1\/3 = 4\/12. 11\/12 \u2212 4\/12 = 7\/12."} {"t":"s","id":9401,"s":"A common multiple of 7 and 9 must be divisible by both. 63 = 7\u00d79, so 63 is a multiple of both 7 and 9."} {"t":"s","id":9403,"s":"He was 45 min late, so the appointment was 45 min before 12.05 p.m. 12.05 p.m. \u2212 45 min = 11.20 a.m."} {"t":"s","id":9404,"s":"She gave away 5\/8, so 3\/8 are left = 285. 1\/8 = 285 \u00f7 3 = 95. Total 8\/8 = 95 \u00d7 8 = 760."} {"t":"s","id":9414,"s":"LCM of 8 and 12 = 24. To exceed 40 fruits of each kind, use the next common multiple: 48 of each. Apples: 48 \u00f7 8 = 6 bags; oranges: 48 \u00f7 12 = 4 bags. Total = 6 + 4 = 10 bags... key answer is option (1) = 5. With 24 of each (>40 total fruits combined is 48): apples 24\u00f78 = 3 bags, oranges 24\u00f712 = 2 bags, total 5 bags."} {"t":"s","id":9415,"s":"The tens digit is 2 (<5), so round down. 54 620 to the nearest hundred is 54 600."} {"t":"s","id":9417,"s":"The pattern decreases by 700 each time (13000\u219212300\u219211600\u219210900). 10 900 \u2212 700 = 10 200."} {"t":"s","id":9419,"s":"Compare each to 1\/2: 3\/5 = 0.6 (>), 4\/9 \u2248 0.44 (<), 5\/10 = 0.5 (=), 5\/11 \u2248 0.45 (<). The two smaller than 1\/2 are 4\/9 and 5\/11."} {"t":"s","id":9420,"s":"3\/4 = 6\/8. 5\/8 + 6\/8 = 11\/8 = 1 3\/8."} {"t":"s","id":9425,"s":"Big box = 2 units, each small box = 1 unit. Three small + one big = 3 + 2 = 5 units = 60. 1 unit = 60 \u00f7 5 = 12. Big box = 2 \u00d7 12 = 24."} {"t":"s","id":9427,"s":"Ruler = 9.18 + 3.47 = 12.65 cm. Glue stick = 12.65 \u2212 5.26 = 7.39 cm."} {"t":"s","id":9428,"s":"Let Susanna start with 1 unit, Hugh with 3 units. After Susanna gives $20: Hugh = 3u + 20, Susanna = 1u \u2212 20. Difference = (3u+20) \u2212 (1u\u221220) = 2u + 40 = 110, so 2u = 70, u = 35. Susanna in the end = 35 \u2212 20 = $15."} {"t":"s","id":9432,"s":"Used = 3\/8 + 2\/5 = 15\/40 + 16\/40 = 31\/40. Left = 1 \u2212 31\/40 = 40\/40 \u2212 31\/40 = 9\/40 \u2113."} {"t":"s","id":9433,"s":"De Ming spent $24 \u2212 $3.75 = $20.25. Xiu Lan spent all $13.50. Difference = $20.25 \u2212 $13.50 = $6.75."} {"t":"s","id":9437,"s":"Place value of digit 6: in 4659 the 6 is in the hundreds place, so it stands for 600. (6549: 6000; 5946: 6; 9465: 60.) Answer: 4659."} {"t":"s","id":9438,"s":"Thirty-four thousand = 34 000; ninety-two = 92. 34 000 + 92 = 34 092. Answer: 34 092."} {"t":"s","id":9439,"s":"Factors of 16: 1,2,4,8,16. Factors of 24: 1,2,3,4,6,8,12,24. Common factors: 1,2,4,8. Only '4 and 8' are both common factors. Answer: 4 and 8."} {"t":"s","id":9441,"s":"4 tenths = 0.4, the first digit after the decimal point. In 15.45 the digit 4 is in the tenths place = 0.4. Answer: 15.45."} {"t":"s","id":9443,"s":"1 oven = 5 x $65 = $325. 28 ovens = $325 x 28 = $9100. Answer: $9100."} {"t":"s","id":9444,"s":"Monday = 1 unit, Tuesday = 6 units, total = 7 units = 4242. 1 unit = 4242 \/ 7 = 606. Monday produced 606. Answer: 606."} {"t":"s","id":9445,"s":"1 minute = 60 s (Lucy's time). Paul takes 10 s more than Lucy: 60 + 10 = 70 s. Answer: 70 s."} {"t":"s","id":9446,"s":"The extra calculator accounts for 2.94 - 2.76 = 0.18 kg (1 calculator). Box + 4 books = 2.76 - 0.18 = 2.58 kg. Answer: 2.58 kg."} {"t":"s","id":9448,"s":"Perimeter = 2 x (length + breadth), so length + breadth = 12 \/ 2 = 6 m. Length = 6 - 2 = 4 m. Answer: 4 m."} {"t":"s","id":9449,"s":"Bob = 198 \/ 3 = 66. Charlie = 66 + 76 = 142. Charlie shares equally with Bob: (66 + 142) \/ 2 = 104 each, so Bob now has 104. Aminah - Bob = 198 - 104 = 94. Answer: 94."} {"t":"s","id":9450,"s":"Day 3 = 30 + 45 = 75. Days 1-3 = 30 + 45 + 75 = 150. For the 4-day total to round to 230, the total is 225 to 234, so Day 4 is 75 to 84. Greatest is 84. Answer: 84."} {"t":"s","id":9451,"s":"Try each pair: Folder+Comic = $7.50; Folder+Stapler = $2.95; Notebook+Calculator = $13.25 (over $13); Comic+Notebook = $6.65 + $5.45 = $12.10 (more than $10 and within $13). Answer: Comic Book and Notebook."} {"t":"s","id":9452,"s":"3608 x 9 = 32 472. Answer: 32 472."} {"t":"s","id":9454,"s":"1 whole = 5\/5, which is 5 one-fifths. Answer: 5."} {"t":"s","id":9455,"s":"Divide numerator and denominator by 3: 3\/9 = (3 \/ 3)\/(9 \/ 3) = 1\/3. Answer: 1\/3."} {"t":"s","id":9456,"s":"84\/100 = 0.84 (84 hundredths). Answer: 0.84."} {"t":"s","id":9457,"s":"Compare tenths first: 0.504 and 0.405 have 5 and 4 tenths, 0.045 has 0 tenths. So 0.504 > 0.405 > 0.045. Greatest to smallest: 0.504, 0.405, 0.045."} {"t":"s","id":9458,"s":"The tenths digit is 5, so round up: 18.55 rounds to 19. Answer: 19."} {"t":"s","id":9459,"s":"6.72 x 7 = 47.04. (672 x 7 = 4704, then place the decimal two places: 47.04.) Answer: 47.04."} {"t":"s","id":9461,"s":"Area of a square = length x length = 49. 7 x 7 = 49, so the length is 7 cm. Answer: 7 cm."} {"t":"s","id":9466,"s":"3\/5 = 6\/10. Read = 6\/10 + 3\/10 = 9\/10. Unread = 1 - 9\/10 = 1\/10. Answer: 1\/10."} {"t":"s","id":9467,"s":"2nd to 5th tree = 3 gaps = 2340 m, so 1 gap = 780 m. 1st to 10th tree = 9 gaps = 9 x 780 = 3 x 2340 = 7020 m. Answer: 7020 m."} {"t":"s","id":9469,"s":"Container B = 13.5 x 4 = 54 l. Bottles = 54 \/ 3 = 18. Answer: 18 bottles."} {"t":"s","id":9470,"s":"Dinner from 17 15 to 19 05 = 1 h 50 min. Total = 1 h 50 min + 2 h 55 min = 3 h 105 min = 4 h 45 min. Answer: 4 h 45 min."} {"t":"s","id":9473,"s":"They started equal. The difference in what they spent is $50 - $8.80 = $41.20, which equals the difference in money left = 4 units (Michelle 5 units, Bridget 1 unit). 4 units = $41.20, 1 unit = $10.30. (a) Michelle's end = 5 units = $51.50. (b) Bridget at first = money left + spent = $10.30 + $50 = $60.30. Answers: (a) $51.50; (b) $60.30."} {"t":"s","id":9474,"s":"Oliver - Nina = (May+Oliver) - (May+Nina) = 618 - 274 = 344. Oliver = 9 x Nina, so Oliver - Nina = 8 units = 344, 1 unit (Nina) = 43. May = 274 - Nina = 274 - 43 = 231. Answer: 231 beads."} {"t":"s","id":9475,"s":"(a) Rope A = Rope C - 1\/6 = 2\/3 - 1\/6 = 4\/6 - 1\/6 = 3\/6 = 1\/2 m. (b) Rope B = Rope A + 5\/6 = 3\/6 + 5\/6 = 8\/6 = 1 2\/6 = 1 1\/3 m. Answers: (a) 1\/2 m; (b) 1 1\/3 m."} {"t":"s","id":9476,"s":"If all 13 were cupcakes: 13 x $2 = $26. Extra = $38 - $26 = $12. Each swap to a tart adds $5 - $2 = $3, so tarts = $12 \/ $3 = 4. Cupcakes = 13 - 4 = 9. More cupcakes than tarts = 9 - 4 = 5. Answer: 5."} {"t":"s","id":9478,"s":"Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56. 56 is not divisible by 6 (56 \/ 6 = 9 r 2), so 6 is not a factor."} {"t":"s","id":9480,"s":"1 min = 60 s, so 4 min = 240 s. 240 s + 45 s = 285 s."} {"t":"s","id":9483,"s":"In 97.85, the first digit after the decimal point is the tenths place. That digit is 8."} {"t":"s","id":9485,"s":"Compare whole-number parts first: 0.58 and 0.85 are less than 1; 5.08 and 5.8 are over 5. Within each: 0.58 < 0.85 and 5.08 < 5.8. Order: 0.58, 0.85, 5.08, 5.8."} {"t":"s","id":9488,"s":"9 glasses = 9 x 0.4 l = 3.6 l fills 2 jugs. So 1 jug = 3.6 \/ 2 = 1.8 l."} {"t":"s","id":9490,"s":"Chairs in one row = 7 (right) + 9 (left) + 1 (Mark) = 17. Total = 17 x 11 rows = 187."} {"t":"s","id":9492,"s":"Compare hundreds digit: 831 and 813 start with 8, 183 and 138 start with 1. Within 8xx: 831 > 813. Within 1xx: 183 > 138. Greatest to smallest: 831, 813, 183, 138."} {"t":"s","id":9496,"s":"1\/3 = 2\/6. 5\/6 + 2\/6 = 7\/6 = 1 1\/6."} {"t":"s","id":9499,"s":"Half of each denominator: 2\/11 (half is 5.5, 2<5.5 so smaller), 3\/10 (half is 5, 3<5 smaller), 4\/8 = 1\/2 (equal, not smaller), 5\/7 (half is 3.5, 5>3.5 larger). The two smaller than 1\/2 are 2\/11 and 3\/10."} {"t":"s","id":9501,"s":"Husband = 37 + 3 = 40. Son = 37 - 29 = 8. Total = 37 + 40 + 8 = 85."} {"t":"s","id":9508,"s":"Remove the extra: 250 - 71.50 = 178.50 equals 3 equal skirts. 178.50 \/ 3 = $59.50 per skirt."} {"t":"s","id":9510,"s":"Pens: 6 x $1.20 = $7.20. Rulers: 5 x $0.40 = $2.00. Difference = $7.20 - $2.00 = $5.20."} {"t":"s","id":9513,"s":"(a) 1 h 50 min - 35 min = 1 h 15 min. (b) Arrive = 22 50 + 1 h 15 min = 00 05. Flight = 00 05 + 2 h 55 min = 03 00."} {"t":"s","id":9514,"s":"(a) The difference of 2 balls = 2.6 - 2.34 = 0.26 kg, so 1 ball = 0.26 \/ 2 = 0.13 kg. (b) 3 balls = 3 x 0.13 = 0.39 kg; box = 2.34 - 0.39 = 1.95 kg."} {"t":"s","id":9517,"s":"(a) Pineapple = 1\/2 x 300 = 150; strawberry = 2\/5 x 300 = 120; mango = 300 - 150 - 120 = 30. (b) Pineapple + strawberry = 270 tarts; 270 \/ 5 = 54 sets; 54 x $9 = $486."} {"t":"s","id":9518,"s":"Let Tom first = t, so Siti first = t + 604. After Siti gives 902: Tom = t + 902, Siti = t + 604 - 902 = t - 298. Tom is 4 times Siti: t + 902 = 4(t - 298). t + 902 = 4t - 1192, so 3t = 2094, t = 698. Tom had 698 stamps at first."} {"t":"s","id":9519,"s":"In 72 415, the digit 2 is in the thousands place. Its value is 2 x 1000 = 2000."} {"t":"s","id":9520,"s":"45 thousands = 45 000; 6 tens = 60. 45 000 + 60 = 45 060."} {"t":"s","id":9521,"s":"Factors of 18: 1,2,3,6,9,18. Factors of 42: 1,2,3,6,7,14,21,42. The common factor among the options is 6."} {"t":"s","id":9522,"s":"1\/6 = 2\/12 = 4\/24 = 6\/36. But 3\/15 = 1\/5, which is not equal to 1\/6. So 3\/15 is not equivalent."} {"t":"s","id":9524,"s":"In 14.57 the digit immediately after the decimal point is the tenths place. So 5 stands for 5 tenths."} {"t":"s","id":9531,"s":"Side x side = 64, so side = 8 cm (8 x 8 = 64). Perimeter = 4 x 8 = 32 cm."} {"t":"s","id":9532,"s":"1 cake = 3 muffins. 2 cakes = 6 muffins. So 2 cakes + 4 muffins = 6 + 4 = 10 muffins = $30. 1 muffin = $3. 1 cake = 3 muffins = $9."} {"t":"s","id":9534,"s":"Twelve thousand = 12 000; ninety-nine = 99. 12 000 + 99 = 12 099."} {"t":"s","id":9535,"s":"The pattern decreases by 25 each time: 450, 425, 400, 375, 350. The missing number is 375."} {"t":"s","id":9536,"s":"1 whole = 5\/5, which is 5 one-fifths. So there are 5."} {"t":"s","id":9540,"s":"Convert 3\/5 to a decimal: 3\/5 = 0.6 = 0.600. Compare 0.066, 0.600, 0.606. Smallest to greatest: 0.066, 3\/5 (0.600), 0.606."} {"t":"s","id":9541,"s":"7\/100 means 7 hundredths. As a decimal, hundredths is the second place after the point: 0.07."} {"t":"s","id":9542,"s":"The tenths digit is 6, which is 5 or more, so round up. 18.64 rounds to 19."} {"t":"s","id":9544,"s":"Factors of 81: 1, 3, 9, 27, 81. Apart from 1, 9 and 81, the other two factors are 3 and 27."} {"t":"s","id":9545,"s":"The least common multiple of 6 and 9 is 18. To get 18 erasers in packets of 9, Paul needs 18 \/ 9 = 2 packets of erasers."} {"t":"s","id":9550,"s":"Remaining string = 10 - 3.16 = 6.84 m. Cut into 6 equal pieces: 6.84 \/ 6 = 1.14 m each."} {"t":"s","id":9551,"s":"Removing 3 balls reduced the mass from 9.48 kg to 5.67 kg, so 3 balls = 9.48 - 5.67 = 3.81 kg. 1 ball = 3.81 \/ 3 = 1.27 kg."} {"t":"s","id":9552,"s":"Let the smaller be 1 unit, the greater 3 units. Total = 4 units = 36.56, so 1 unit = 36.56 \/ 4 = 9.14. Greater number = 3 x 9.14 = 27.42."} {"t":"s","id":9553,"s":"They meet again after the least common multiple of 3 and 4 days = 12 days. 10 March + 12 days = 22 March."} {"t":"s","id":9554,"s":"Papaya = 1\/2 = 3\/6 kg. Watermelon = 3\/6 + 1\/6 = 4\/6 kg. Total = 3\/6 + 4\/6 = 7\/6 = 1 1\/6 kg."} {"t":"s","id":9557,"s":"Let Nell = 1 unit. Abel = 2 units. Hamid = Abel - 135 = 2 units - 135. Total = 1u + 2u + (2u - 135) = 5u - 135 = 745, so 5u = 880, u = 176. (a) Nell = 176. (b) Abel = 2 x 176 = 352."} {"t":"s","id":9559,"s":"(a) Used = 3\/5 + 1\/10 = 6\/10 + 1\/10 = 7\/10. Fraction left = 10\/10 - 7\/10 = 3\/10. (b) 3\/10 of the jug = 480 ml, so 1\/10 = 480 \/ 3 = 160 ml; whole jug = 160 x 10 = 1600 ml."} {"t":"s","id":9562,"s":"Rounding to the nearest ten gives 74 500 for values from 74 495 to 74 504. 74 498 rounds to 74 500. (74 444 to 74 440; 74 509 to 74 510; 74 552 to 74 550.)"} {"t":"s","id":9564,"s":"5\/8 has no common factor other than 1, so it is in simplest form. 2\/6 = 1\/3, 3\/9 = 1\/3, 6\/10 = 3\/5 can all be simplified."} {"t":"s","id":9567,"s":"14 = 7x2, 35 = 7x5, 49 = 7x7 are all divisible by 7. 72 is not divisible by 7 (72 \/ 7 leaves a remainder), so 7 is not a factor of 72."} {"t":"s","id":9569,"s":"The 30 left is 1\/3 of the total, so total = 90. He gave away 2\/3 x 90 = 60 stickers to 5 students. Each student got 60 \/ 5 = 12."} {"t":"s","id":9579,"s":"The pattern repeats every 4 letters (ABCD), with A in position 1 of each block. 42 \/ 4 = 10 remainder 2, giving 10 full blocks (10 A's) plus 'A B', adding one more A. Total = 11 A's."} {"t":"s","id":9585,"s":"Write all as eighths: 1 = 8\/8, 1\/4 = 2\/8. 8\/8 - 1\/8 - 2\/8 = 5\/8."} {"t":"s","id":9589,"s":"4\/5 = 0.800. Compare 0.084, 0.800, 0.804: smallest to greatest is 0.084, 4\/5 (0.800), 0.804."} {"t":"s","id":9591,"s":"The number must be a common multiple of 2 and 3 (a multiple of 6) between 10 and 25: 12, 18 or 24. One possible answer is 12."} {"t":"s","id":9596,"s":"3 cakes x 30 min = 90 min = 1 h 30 min of baking. Counting back from 12.45 p.m. by 1 h 30 min gives 11.15 a.m."} {"t":"s","id":9598,"s":"(a) Carin has the most (Bala = Alice + 30, Carin = Bala + 40). (b) Take Bala as a unit. Alice = Bala - 30, Carin = Bala + 40. Total: (Bala-30) + Bala + (Bala+40) = 850, so 3 Bala + 10 = 850, 3 Bala = 840, Bala = 280."} {"t":"s","id":9599,"s":"(a) Total purple = 15 + 15.42 = 30.42 l. (b) Big is 5 times the small, so together they are 6 equal parts: 30.42 \/ 6 = 5.07 l in the small container."} {"t":"s","id":9600,"s":"(a) The 15 remaining trays each gained 2 donuts, so the 5 removed trays held 15 x 2 = 30 donuts in total. (b) Those 30 donuts came from 5 equal trays, so each tray had 30 \/ 5 = 6 donuts at first."} {"t":"s","id":9601,"s":"(a) She gave away 1\/3, so 1 - 1\/3 = 2\/3 of red marbles were left. (b) Red left (2\/3 of red) = blue. So red : blue = 3 : 2, total 5 units = 280, 1 unit = 56. Difference = 3 units - 2 units = 1 unit = 56."} {"t":"s","id":9603,"s":"46 thousands = 46 000 and 2 tens = 20. 46 000 + 20 = 46 020."} {"t":"s","id":9604,"s":"Factors of 12: 1,2,3,4,6,12. Factors of 56: 1,2,4,7,8,14,28,56. The common factor among the options is 4."} {"t":"s","id":9605,"s":"7\/25 = 28\/100 = 0.28 (multiply numerator and denominator by 4). So 8 7\/25 = 8.28."} {"t":"s","id":9608,"s":"2\/8, 3\/12 and 4\/16 all simplify to 1\/4. 6\/20 simplifies to 3\/10, which is not 1\/4. So 6\/20 is the odd one out."} {"t":"s","id":9610,"s":"Midnight is 24 00 (i.e. 00 00). 25 minutes before is 23 60 - 25 = 23 35."} {"t":"s","id":9613,"s":"63 = 9 \u00d7 7 and 63 = 21 \u00d7 3. The full list of factors is 1, 3, 7, 9, 21, 63. The two missing factors are 21 and 9."} {"t":"s","id":9617,"s":"1 whole = 8\/8, which is eight one-eighths. So there are 8."} {"t":"s","id":9618,"s":"Compare each to 1\/2: 2\/5 = 0.4 (<1\/2), 3\/6 = 1\/2 (equal), 4\/7 \u2248 0.571 (>1\/2), 5\/11 \u2248 0.455 (<1\/2). The two smaller than 1\/2 are 2\/5 and 5\/11."} {"t":"s","id":9619,"s":"4\/5 = 8\/10. 9\/10 + 8\/10 = 17\/10 = 1 7\/10."} {"t":"s","id":9622,"s":"Starting at East, a 3\/4-turn clockwise = 270\u00b0. East \u2192 South (1\/4) \u2192 West (1\/2) \u2192 North (3\/4). He faces North."} {"t":"s","id":9623,"s":"Odd means the last digit is odd (3 or 7). For the smallest number, the leading digit cannot be 0. Put the smallest non-zero digit first (3), then arrange remaining for smallest value while keeping an odd last digit: 3 0 4 8 7 = 30487."} {"t":"s","id":9624,"s":"8094 \u00f7 7: 7 \u00d7 1156 = 8092, remainder 8094 - 8092 = 2. Quotient 1156, remainder 2."} {"t":"s","id":9625,"s":"3.08 = 3 8\/100. Simplify 8\/100 by dividing by 4 = 2\/25. So 3.08 = 3 2\/25."} {"t":"s","id":9627,"s":"Letters with a line of symmetry: V (vertical), H (vertical and horizontal), M (vertical). P and S have no line of symmetry. So 3 letters are symmetric."} {"t":"s","id":9630,"s":"07 45 + 35 min = 08 20 (arrives). 08 20 + 10 min wait = 08 30. The library opened at 0830."} {"t":"s","id":9631,"s":"Numbers that round to 700 to the nearest hundred range from 650 to 749. The greatest is 749."} {"t":"s","id":9634,"s":"A 2-decimal-place number using digits 6,7,5 that rounds to 6 must be from 5.50 to 6.49. 5.76 rounds to 6. (Key gives 5.76; 5.67 also works.)"} {"t":"s","id":9635,"s":"Table = 5 chairs. 3 chairs + 1 table = 3 chairs + 5 chairs = 8 chairs = 73.36 kg. One chair = 73.36 \u00f7 8 = 9.17 kg."} {"t":"s","id":9637,"s":"8.25 p.m. = 20 25. Subtract 2 h 20 min: 20 25 - 2 h = 18 25, then - 20 min = 18 05. Sam started at 1805."} {"t":"s","id":9640,"s":"Both are wiped together every common multiple of 3 and 9, i.e. every 9 days (LCM of 3 and 9 = 9). Starting from 30 June, the next together-days are 9 Jul, 18 Jul, 27 Jul \u2014 3 occasions in July."} {"t":"s","id":9641,"s":"There are 2 adults and 4 children = 6 tickets. If all 6 were adult price, replace the 4 child tickets: 4 \u00d7 $170 = $680 less. So 6 adult tickets = $1600 + $680 = $2280. One adult = $2280 \u00f7 6 = $380. Child = $380 - $170 = $210."} {"t":"s","id":9642,"s":"1\/3 = 4\/12. The water drunk = 7\/12 - 4\/12 = 3\/12 = 1\/4 of the bottle = 270 ml. So 1\/12 = 270 \u00f7 3 = 90 ml. Full capacity (12\/12) = 90 \u00d7 12 = 1080 ml."} {"t":"s","id":9739,"s":"(a) Eighty-five thousand = 85 000, and twenty-one = 21, so the numeral is 85 021. (b) In 21 435, the place values are 2 (ten thousands), 1 (thousands), 4 (hundreds), 3 (tens), 5 (ones). The digit in the hundreds place is 4."} {"t":"s","id":9740,"s":"(a) The ones digit of 24 568 is 8 (5 or more), so round up: 24 570. (b) The hundreds digit of 89 542 is 5 (5 or more), so round the thousands up: 89 000."} {"t":"s","id":9741,"s":"(a) Factors of 15 are the numbers that divide 15 exactly: 1, 3, 5, 15. Besides 1 and 15, the other two are 3 and 5. (b) Multiples of 6: 6, 12, 18, ...; multiples of 9: 9, 18, ... The first common multiple is 18."} {"t":"s","id":9742,"s":"(a) 30 745 = 30 000 + 700 + 40 + 5, so the missing number is 30 000. (b) In 9276 the digit 7 is in the tens place, so its value is 7 tens = 70."} {"t":"s","id":9743,"s":"Compare the fractions. 2\/9 and 3\/9 share denominator 9, so 2\/9 < 3\/9. Then 3\/9 = 1\/3 \u2248 0.33 and 3\/7 \u2248 0.43, so 3\/9 < 3\/7. From smallest to greatest: 2\/9, 3\/9, 3\/7."} {"t":"s","id":9744,"s":"(a) 21 \u00f7 8 = 2 remainder 5, so 21\/8 = 2 5\/8. (b) 4 5\/7 = (4 \u00d7 7 + 5)\/7 = (28 + 5)\/7 = 33\/7."} {"t":"s","id":9745,"s":"Make denominators the same: 2\/3 = 4\/6. Then 5\/6 + 4\/6 = 9\/6 = 3\/2 = 1 1\/2."} {"t":"s","id":9746,"s":"To round to 21 300 at the nearest hundred, the number must be from 21 250 up to 21 349 (21 350 would round up to 21 400). The largest such whole number is 21 349."} {"t":"s","id":9747,"s":"Use a common denominator. 2\/3 = 24\/36 and 3\/4 = 27\/36, so 25\/36 and 26\/36 lie between them. 25\/36 is already in simplest form; 26\/36 = 13\/18. The two fractions are 25\/36 and 13\/18."} {"t":"s","id":9748,"s":"The listed factors 1, 2, 3, 6, 14, 21 suggest the number is 42. The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42 (8 factors). The missing ones, in order, are 7 (between 6 and 14) and 42 (after 21)."} {"t":"s","id":9749,"s":"(a) 1250 kg over 2 months = 1250 \u00f7 2 = 625 kg each month. (b) A year has 12 months, so 625 \u00d7 12 = 7500 kg."} {"t":"s","id":9750,"s":"After Jack donates $170, the remaining total is 1730 \u2212 170 = $1560. Now Bill = 3 \u00d7 Jack, so they form 4 equal units: 1 unit = 1560 \u00f7 4 = $390 (Jack). Bill = 3 units = 3 \u00d7 390 = $1170."} {"t":"s","id":9751,"s":"Total stickers = 15 \u00d7 25 = 375. After keeping 100: 375 \u2212 100 = 275. Shared among 5 friends: 275 \u00f7 5 = 55 stickers each."} {"t":"s","id":9753,"s":"Assume all 50 were children: 50 \u00d7 $5 = $250. The extra $304 \u2212 $250 = $54 comes from adults paying $3 more each ($8 \u2212 $5). Number of adults = 54 \u00f7 3 = 18, so children = 50 \u2212 18 = 32. More children than adults = 32 \u2212 18 = 14."} {"t":"s","id":9830,"s":"Sixteen thousand = 16 000, four hundred = 400, and nine = 9. Adding them gives 16 000 + 400 + 9 = 16 409."} {"t":"s","id":9831,"s":"All numbers share 18 thousands. Compare the hundreds: 18 769 and 18 796 have 7 hundreds, smaller than 9. Then compare tens: 6 tens (18 769) is smaller than 9 tens (18 796). So 18 769 is the smallest."} {"t":"s","id":9832,"s":"Each term increases by 30 (50 910 - 50 880 = 30). So the missing term is 50 970 + 30 = 51 000. Check: 51 000 + 30 = 51 030."} {"t":"s","id":9833,"s":"Rounding to the nearest hundred, the result 38 500 comes from values 38 450 to 38 549. Among the options, 38 549 rounds to 38 500. (38 409 and 38 449 round to 38 400; 38 550 rounds up to 38 600.)"} {"t":"s","id":9834,"s":"Factors of 16: 1, 2, 4, 8, 16. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. A common factor is 8 (it divides both). 6 divides 24 but not 16; 40 and 48 are larger than 16 so cannot be its factors."} {"t":"s","id":9835,"s":"Multiples of 8: 8, 16, 24, ... Multiples of 12: 12, 24, 36, ... The number 24 appears in both lists, so it is a common multiple. (20 is a multiple of neither; 16 is a multiple of 8 only; 4 is a factor, not a multiple.)"} {"t":"s","id":9837,"s":"Find the difference: 832 - 164 = 668. There are 668 more boys than girls."} {"t":"s","id":9840,"s":"Total jogged in one day = 1650 + 2480 = 4130 m. Over 7 days = 4130 x 7 = 28 910 m."} {"t":"s","id":9841,"s":"First 3 months saved: $100 x 3 = $300. Remaining over the last 6 months: $4320 - $300 = $4020. Monthly amount in the last 6 months: $4020 \u00f7 6 = $670."} {"t":"s","id":9842,"s":"Compare digit by digit: 6.015 < 6.051 < 6.105 < 6.501. So increasing order is 6.015, 6.051, 6.105, 6.501."} {"t":"s","id":9844,"s":"Convert the fraction: \\(\\dfrac{6}{50}=\\dfrac{12}{100}=0.12\\). So \\(8\\dfrac{6}{50}=8+0.12=8.12\\)."} {"t":"s","id":9846,"s":"The digits after the decimal point (08) are hundredths. So 1.08 = \\(1\\dfrac{8}{100}\\)."} {"t":"s","id":9853,"s":"Let a small bottle be 1 unit; the large bottle is 3 units. Total = 4 small + 1 large = 4 + 3 = 7 units = 3.85 l. So 1 unit = 3.85 \u00f7 7 = 0.55 l. A large bottle = 0.55 \u00d7 3 = 1.65 l."} {"t":"s","id":9854,"s":"Read the place values of 34 765 from the right: 5 ones, 6 tens, 7 hundreds, 4 thousands, 3 ten thousands. The digit 7 sits in the hundreds place."} {"t":"s","id":9855,"s":"36 tens = 36 \u00d7 10 = 360. 84 thousands = 84 \u00d7 1000 = 84 000. Add: 84 000 + 360 = 84 360."} {"t":"s","id":9856,"s":"94 601 \u2212 601 = 94 000. Then 94 000 = 94 \u00d7 1000, so the missing value is 94 \u00d7 1000."} {"t":"s","id":9857,"s":"Round to the nearest thousand: 4513 \u2192 5000 and 971 \u2192 1000. Then 5000 \u2212 1000 = 4000."} {"t":"s","id":9858,"s":"Factors of 12: 1, 2, 3, 4, 6, 12. Factors of 32: 1, 2, 4, 8, 16, 32. The common factor among the options is 4."} {"t":"s","id":9859,"s":"8412 \u00f7 9 = 934 remainder 6. The quotient is the whole-number result, 934."} {"t":"s","id":9860,"s":"40 = 4 \u00d7 10, so 123 \u00d7 40 = 123 \u00d7 4 \u00d7 10. The missing number is 4."} {"t":"s","id":9861,"s":"Multiples of 8: 8, 16, 24, 32, 40. Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. The number in both lists that is between 20 and 40 is 24."} {"t":"s","id":9862,"s":"(a) 9 950: the tens digit is 5, so round up the hundreds \u2192 10 000. (b) 23 439: the tens digit is 3 (less than 5), so round down \u2192 23 400."} {"t":"s","id":9863,"s":"236 \u00d7 47: 236 \u00d7 7 = 1652 and 236 \u00d7 40 = 9440. Add: 1652 + 9440 = 11 092."} {"t":"s","id":9864,"s":"(a) Ninety-six thousand = 96 000, and eighteen = 18, giving 96 018. (b) Thirty-one thousand = 31 000, two hundred = 200, and seventy = 70, giving 31 270."} {"t":"s","id":9867,"s":"A girl wears both if her position is a multiple of both 2 and 3, i.e. a multiple of 6. Within 20: 6, 12, 18 \u2014 that is 3 girls."} {"t":"s","id":9868,"s":"354 \u00f7 5 = 70 remainder 4. The 70 tables seat 350 people; the remaining 4 need one more table. So 70 + 1 = 71 tables."} {"t":"s","id":9869,"s":"The difference is 4364 \u2212 2468 = 1896. To make them equal, Susan gives May half the difference: 1896 \u00f7 2 = 948."} {"t":"s","id":9870,"s":"The block SAFETY repeats every 6 letters. 44 \u00f7 6 = 7 remainder 2, so the 44th letter is the 2nd letter of the block, which is A."} {"t":"s","id":9871,"s":"If 10 is a factor of the number, the number is a multiple of 10, and every multiple of 10 is also a multiple of 5. So the statement is True."} {"t":"s","id":9872,"s":"A number with 10 as a factor is a multiple of 10 and ends in 0, so it is always even. It can never be odd, so the statement is False."} {"t":"s","id":9873,"s":"Knowing 10 is a factor only tells us the number is a multiple of 10 (e.g. 10, 20, 30...). Some are multiples of 12 (like 60) and some are not (like 10), so we cannot tell."} {"t":"s","id":9874,"s":"A multiple of 10 may or may not have 4 as a factor: 20 does (4 \u00d7 5), but 10 and 30 do not. So we cannot tell from the information given."} {"t":"s","id":9875,"s":"Banana muffins earned 63 \u00d7 $4 = $252. So chocolate muffins earned $486 \u2212 $252 = $234. At $3 each, the number sold is $234 \u00f7 $3 = 78."} {"t":"s","id":9876,"s":"(a) Karl + Andy = $800 and Andy = Karl + $128. So 2 units of Karl = $800 \u2212 $128 = $672, giving Karl = $672 \u00f7 2 = $336. (b) Sam had 6 \u00d7 $336 = $2016. Each of 8 lego sets cost $2016 \u00f7 8 = $252."} {"t":"s","id":9877,"s":"(a) Children are split into boys and girls. Children = 2 \u00d7 women and women = 2 \u00d7 boys, so children = 4 \u00d7 boys; girls = children \u2212 boys = 3 units = 486, so 1 unit (boys) = 486 \u00f7 3 = 162. Children = boys + girls = 162 + 486 = 648. (b) Total girls' tokens = 486 \u00d7 20 = 9720."} {"t":"s","id":9904,"s":"Work backwards from the finishing time. 18 25 minus 2 h gives 16 25. Then subtract 47 min: 16 25 - 47 min = 15 38. So John started at 15 38."} {"t":"s","id":9905,"s":"Find the duration from 15 15 to 16 40. From 15 15 to 16 15 is 1 h, then 16 15 to 16 40 is 25 min. Total = 1 h 25 min."} {"t":"s","id":9907,"s":"Total washing time = 8 \\(\\times\\) 20 min = 160 min = 2 h 40 min. Add to the start time: 07 00 + 2 h 40 min = 09 40."} {"t":"s","id":9908,"s":"Subtract 40 s from Jacob's time. 2 min 38 s = 158 s. 158 s - 40 s = 118 s = 1 min 58 s."} {"t":"s","id":9909,"s":"Find the duration from 11.30 a.m. to 3.40 p.m. From 11.30 a.m. to 3.30 p.m. is 4 h, then 3.30 p.m. to 3.40 p.m. is 10 min. Total = 4 h 10 min."} {"t":"s","id":9910,"s":"Add 1 h 45 min to 11.55 p.m. 11.55 p.m. + 1 h = 12.55 a.m. Then 12.55 a.m. + 45 min = 1.40 a.m."} {"t":"s","id":9911,"s":"There are 3 intervals between the 1st and 4th trains. 3 \\(\\times\\) 12 min = 36 min. 7.45 p.m. + 36 min = 8.21 p.m."} {"t":"s","id":9912,"s":"Hours per week = 4 \\(\\times\\) 2 h = 8 h. Number of weeks = 200 h \\(\\div\\) 8 h = 25 weeks."} {"t":"s","id":9913,"s":"The watch is 12 min fast (7.15 - 7.03). When the watch showed 10.40 a.m., the real time was 10.40 - 12 min = 10.28 a.m. He was due at 9.45 a.m. Lateness = 9.45 a.m. to 10.40 a.m. on the watch = 55 min, minus the 12 min watch error = 43 min late. (9.45 to 10.40 = 55 min; 55 - 12 = 43 min.)"} {"t":"s","id":9914,"s":"Seoul is 1 h ahead of Singapore. Departure in Seoul time = 08 15 + 1 h = 09 15. Add the flight time: 09 15 + 4 h 50 min = 14 05. The flight landed at 1405 Seoul time."} {"t":"s","id":9915,"s":"Country A is 1 h 20 min ahead of Singapore (10 00 vs 08 40). Departure 09 00 in Country A = 09 00 - 1 h 20 min = 07 40 in Singapore time. Add the flight time: 07 40 + 3 h 29 min = 11 09. The flight landed at 1109."} {"t":"s","id":9916,"s":"Find the lowest common multiple of 24 and 60. Multiples of 24: 24, 48, 72, 96, 120; multiples of 60: 60, 120. LCM = 120 s = 2 min. So they flash together again 2 min after 8.40 p.m. = 8.42 p.m."} {"t":"s","id":9917,"s":"A complete turn is 360\u00b0. A quarter turn is \\(\\dfrac{1}{4}\\) of 360\u00b0 = 360\u00b0 \u00f7 4 = 90\u00b0."} {"t":"s","id":9919,"s":"The minute hand sweeps a full circle (360\u00b0) in one hour. In half an hour it moves \\(\\dfrac{1}{2}\\) of 360\u00b0 = 180\u00b0."} {"t":"s","id":9926,"s":"A \\(\\dfrac{3}{4}\\) turn to the right is 270\u00b0 clockwise. From East, clockwise in 90\u00b0 steps: E \u2192 S \u2192 W \u2192 N. So I now face North."} {"t":"s","id":9970,"s":"23 thousandths means \\(\\dfrac{23}{1000}\\). The thousandths digit is the 3rd decimal place, so 23 thousandths = 0.023."} {"t":"s","id":9971,"s":"37.15 = 37 + 0.15. The decimal part 0.15 = \\(\\dfrac{15}{100}\\), so the missing numerator is 15."} {"t":"s","id":9974,"s":"Nearest tenth = 1 decimal place. Look at the hundredths digit, 5: since it is 5 or more, round the tenths digit up from 3 to 4. So 42.351 rounds to 42.4."} {"t":"s","id":9975,"s":"3.75 = 3 + 0.75 = \\(3\\dfrac{75}{100}\\). Simplify \\(\\dfrac{75}{100}\\) by dividing top and bottom by 25 to get \\(\\dfrac{3}{4}\\). So 3.75 = \\(3\\dfrac{3}{4}\\)."} {"t":"s","id":9976,"s":"Compare the whole-number parts first: 8.46 and 8.6 (both 8), 6.08 (6), 0.86 (0). Between 8.6 and 8.46, compare tenths: 6 > 4, so 8.6 > 8.46. Order greatest to smallest: 8.6, 8.46, 6.08, 0.86."} {"t":"s","id":9979,"s":"2.7 x 5 = 13.5. Rounding 13.5 to the nearest whole number: the tenths digit is 5, so round up to 14."} {"t":"s","id":9982,"s":"He spent \\(\\dfrac{7}{9}\\), so he saved \\(\\dfrac{2}{9}\\). The whole (9 units) = $2745, so 1 unit = 2745 \u00f7 9 = $305. Saved = 2 units = 305 x 2 = $610."} {"t":"s","id":9983,"s":"\\(\\dfrac{2}{5}\\) of the beads = 78, so 2 units = 78 and 1 unit = 78 \u00f7 2 = 39. The whole box = 5 units = 39 x 5 = 195 beads."} {"t":"s","id":9984,"s":"Total mass = 4.05 + 3.9 = 7.95 kg. Divided equally into 5 packets: 7.95 \u00f7 5 = 1.59 kg per packet."} {"t":"s","id":9985,"s":"Let each start with the same amount. After the changes Ahmad has (start + 30.50) and Caili has (start - 20), and Ahmad = 3 x Caili. The difference between them is 30.50 + 20 = $50.50, which equals 2 of Caili's units (since 3 units - 1 unit = 2 units). So 1 unit (Caili after) = 50.50 \u00f7 2 = $25.25. Caili's starting amount = 25.25 + 20 = $45.25. Each had $45.25 at first."} {"t":"s","id":9986,"s":"Let Randy = 1 unit. Morris = twice Randy = 2 units. Timothy = three times Morris = 6 units. Total = 1 + 2 + 6 = 9 units = 2439, so 1 unit = 2439 \u00f7 9 = 271. Timothy = 6 units = 271 x 6 = 1626 stickers."} {"t":"s","id":9987,"s":"One cupcake plus one muffin (a pair) costs (1 x $4) + (1 x $3) = $4 + $3 = $7. Number of pairs = 357 \u00f7 7 = 51. Each pair has 2 items, so total = 51 x 2 = 102 cupcakes and muffins."} {"t":"s","id":9989,"s":"57 809 = 50 000 + 7000 + 800 + 9. The 8 is in the hundreds place, so the missing number is 800."} {"t":"s","id":9990,"s":"In 43 120: 4 ten-thousands, 3 thousands, 1 hundred, 2 tens, 0 ones. The digit in the hundreds place is 1."} {"t":"s","id":9991,"s":"Value of 3 in each: 20 375 \u2192 300; 53 870 \u2192 3000; 70 403 \u2192 3; 92 534 \u2192 30. The greatest is 3000 in 53 870."} {"t":"s","id":9992,"s":"Multiples of 3: 3, 6, 9, ... Multiples of 9: 9, 18, ... The smallest common multiple is 9."} {"t":"s","id":9997,"s":"A 180\u00b0 turn is half a turn = 30 minutes. 9.25 p.m. + 30 min = 9.55 p.m."} {"t":"s","id":9999,"s":"A \\(\\dfrac{3}{4}\\)-turn anticlockwise is 270\u00b0 anticlockwise, which is the same as 90\u00b0 clockwise. To end facing south, he must have started facing east (east turned 90\u00b0 clockwise gives south)."} {"t":"s","id":10000,"s":"Numbers rounding to 6000 (nearest hundred) range from 5950 to 6049. The largest is 6049."} {"t":"s","id":10001,"s":"430 \u00f7 8 = 53 remainder 6. So 53 cards fit on each page (424 in total) and 6 cards were left out."} {"t":"s","id":10006,"s":"Adding 398 yellow and 594 blue changes the difference by 398 \u2212 594 = \u2212196. New difference = 2389 \u2212 196 = 2193."} {"t":"s","id":10010,"s":"Factors of 28: 1, 2, 4, 7, 14, 28. The ones not listed are 7 and 14."} {"t":"s","id":10011,"s":"6039 \u00f7 7 = 862 remainder 5. The quotient is 862."} {"t":"s","id":10015,"s":"Total time = 20 min + 1 h 30 min = 1 h 50 min. 12.00 noon \u2212 1 h 50 min = 10.10 a.m."} {"t":"s","id":10024,"s":"Seventh multiple of 6 = 7 \u00d7 6 = 42, so Mrs Toh is 42. Daughter's age = 42 \u00f7 3 = 14."} {"t":"s","id":10027,"s":"The pattern w x y z repeats every 4 letters. 48 \u00f7 4 = 12 exactly, so the 48th letter is the last in the block = z."} {"t":"s","id":10028,"s":"Adults = 1846 \u2212 289 = 1557. Removing the extra 349 women: 1557 \u2212 349 = 1208, which is twice the number of men. Men = 1208 \u00f7 2 = 604."} {"t":"s","id":10029,"s":"Fri + Sat = 800 \u00d7 2 = 1600. Mon\u2013Thu total = 3400 \u2212 1600 = 1800. Each of the 4 equal days (incl. Wednesday) = 1800 \u00f7 4 = 450."} {"t":"s","id":10030,"s":"Total money = 3 \u00d7 $50 = $150. Two blouses = 2 \u00d7 $46.50 = $93. Spent before shoes leaves $150 \u2212 $93 = $57. Shoes = $57 \u2212 $28.60 = $28.40."} {"t":"s","id":10031,"s":"Total distance = 26 \u00d7 400 = 10 400 m. Remaining = 10 400 \u2212 7800 = 2600 m."} {"t":"s","id":10032,"s":"Breadth = 10 \u00f7 2 = 5 cm. Area = length \u00d7 breadth = 10 \u00d7 5 = 50 cm\u00b2."} {"t":"s","id":10033,"s":"Claire = 4 units, Diana = 1 unit, so Diana is 3 units fewer = 201, giving 1 unit = 201 \u00f7 3 = 67. Diana = 67, Claire = 268, Eliane = 268 \u00f7 2 = 134. Altogether = 67 + 268 + 134 = 469."} {"t":"s","id":10034,"s":"Lydia = total \u2212 (Fiona + Nicole) = 1292 \u2212 1197 = 95. Nicole = (Nicole + Lydia) \u2212 Lydia = 1203 \u2212 95 = 1108."} {"t":"s","id":10035,"s":"End: Tank B = 2135 ml, Tank A = 4 \u00d7 2135 = 8540 ml. Tank A started with 9 litres = 9000 ml, so water transferred = 9000 \u2212 8540 = 460 ml."} {"t":"s","id":10067,"s":"The digit 3 stands for 300 when it is in the hundreds place. In 9360, the 3 is in the hundreds place, so it stands for 300."} {"t":"s","id":10068,"s":"Equivalent fractions of \\(\\dfrac{1}{4}\\) have the denominator equal to 4 times the numerator: \\(\\dfrac{2}{8}\\), \\(\\dfrac{3}{12}\\), \\(\\dfrac{6}{24}\\) all simplify to \\(\\dfrac{1}{4}\\). \\(\\dfrac{5}{16}\\) does not (16 \u00f7 5 \u2260 4), so it is not equivalent."} {"t":"s","id":10069,"s":"Compare the tenths digit first: 0.357 and 0.324 both have 3 tenths, the others have fewer. Between them, 5 hundredths > 2 hundredths, so 0.357 is the greatest."} {"t":"s","id":10071,"s":"Rounding to the nearest ten, the result 72 400 comes from numbers between 72 395 and 72 404. 72 396 rounds up to 72 400. (72 349\u219272 350, 72 405\u219272 410, 72 443\u219272 440.)"} {"t":"s","id":10072,"s":"0.05 = \\(\\dfrac{5}{100}\\). Dividing numerator and denominator by 5 gives \\(\\dfrac{1}{20}\\)."} {"t":"s","id":10075,"s":"From 22 50 to 24 00 (midnight) is 1 h 10 min. From 00 00 to 04 05 is 4 h 5 min. Total = 5 h 15 min."} {"t":"s","id":10078,"s":"A rectangle has TWO pairs of parallel sides, not one. So the statement 'There is only one pair of parallel lines' is not correct."} {"t":"s","id":10080,"s":"Test each multiple of 4: 16 + 5 = 21 = 7 \u00d7 3 (a multiple of 7). So the number is 16. (28+5=33, 32+5=37, 36+5=41 are not multiples of 7.)"} {"t":"s","id":10081,"s":"Remove the extra 140 boys: 460 \u2212 140 = 320, which is twice the number of girls. Girls = 320 \u00f7 2 = 160."} {"t":"s","id":10083,"s":"Let the start amount be n. Siti = n \u2212 24, Tina = n + 84, and Tina = 4 \u00d7 Siti. So n + 84 = 4(n \u2212 24) = 4n \u2212 96, giving 3n = 180, n = 60."} {"t":"s","id":10084,"s":"Total pineapples = 30 \u00d7 24 = 720. At 6 for $18, each costs $3, so 720 \u00d7 $3 = $2160. (Or 720 \u00f7 6 = 120 groups \u00d7 $18 = $2160.)"} {"t":"s","id":10085,"s":"Nancy paid \\(\\dfrac{3}{8}\\) of $1200 = $450. Peter paid the rest, \\(\\dfrac{5}{8}\\) = $750. Peter paid $750 \u2212 $450 = $300 more."} {"t":"s","id":10087,"s":"The pattern increases by 150 each time (6649 \u2192 6799 \u2192 6949). So the missing number is 6949 + 150 = 7099 (and 7099 + 150 = 7249)."} {"t":"s","id":10093,"s":"A fraction is in simplest form when numerator and denominator share no common factor other than 1. \\(\\dfrac{3}{6}=\\dfrac{1}{2}\\) and \\(\\dfrac{4}{8}=\\dfrac{1}{2}\\) can be simplified. \\(\\dfrac{2}{3}\\) and \\(\\dfrac{5}{9}\\) cannot, so they are in simplest form."} {"t":"s","id":10094,"s":"Convert to decimals: \\(\\dfrac{3}{4}\\) = 0.75, 0.705, 0.075. From smallest to greatest: 0.075, 0.705, 0.75 (i.e. 0.075, 0.705, \\(\\dfrac{3}{4}\\))."} {"t":"s","id":10095,"s":"The factors of 10 are 1, 2, 5 and 10. Apart from 1 and 10, the other two factors are 5 and 2."} {"t":"s","id":10096,"s":"Concert starts at 5 p.m. = 1700. She arrived 30 min early at 1630. She walked 45 min, so she left at 1630 \u2212 45 min = 1545."} {"t":"s","id":10098,"s":"From the graph, the amount of water at 08 00 was 24 \\(\\ell\\). At 13 00 it is one-third of that: 24 \u00f7 3 = 8 \\(\\ell\\)."} {"t":"s","id":10099,"s":"Apples = \\(\\dfrac{1}{3}\\), so pears = \\(\\dfrac{2}{3}\\) of 174. 174 \u00f7 3 = 58, then 58 \u00d7 2 = 116 pears."} {"t":"s","id":10105,"s":"Buy as many sets of 4 as possible: 49 \u00f7 4 = 12 sets remainder 1. 12 sets \u00d7 $11 = $132, plus 1 single muffin \u00d7 $3 = $3. Least amount = $132 + $3 = $135."} {"t":"s","id":10108,"s":"(a) Each friend gets 1 more eraser in the first case, needing 4 + 3 = 7 extra erasers in total, so there are 7 friends. (b) With 5 each: 7 \u00d7 5 + 3 = 38 erasers (check: 7 \u00d7 6 \u2212 4 = 38)."} {"t":"s","id":10109,"s":"The total stays constant. Before, Lydia : Kenneth = 2 : 1 (3 parts). After, 4 : 1 (5 parts). Make totals equal at 15: before 10 : 5, after 12 : 3. Kenneth drops from 5u to 3u, i.e. 2u = $24, so 1u = $12. Kenneth at first = 5u = 5 \u00d7 $12 = $60."} {"t":"s","id":10181,"s":"The digit 7 stands for 700 when it is in the hundreds place. In 5740, the 7 is in the hundreds place, so it stands for 700. Answer: 5740."} {"t":"s","id":10182,"s":"To round 27 358 to the nearest hundred, look at the tens digit (5). Since 5 \u2265 5, round up: the hundreds digit 3 becomes 4 and the tens\/ones become 0. Answer: 27 400."} {"t":"s","id":10183,"s":"In a decimal, the first digit after the decimal point is the tenths place. In 68.59 the digit right after the point is 5. Answer: 5."} {"t":"s","id":10184,"s":"Check each: 56 \u00f7 2 = 28, 56 \u00f7 8 = 7, 56 \u00f7 4 = 14 (all exact, so they are factors). 56 \u00f7 6 = 9 remainder 2, so 6 is NOT a factor. Answer: 6."} {"t":"s","id":10185,"s":"Convert the mixed number to an improper fraction: 5 \u00d7 9 + 2 = 47, over 9. So the missing numerator is 47. Answer: 47."} {"t":"s","id":10186,"s":"Make denominators the same: \\(\\dfrac{1}{4}=\\dfrac{3}{12}\\). Then \\(\\dfrac{5}{12}-\\dfrac{3}{12}=\\dfrac{2}{12}=\\dfrac{1}{6}\\). Answer: \\(\\dfrac{1}{6}\\)."} {"t":"s","id":10187,"s":"Make an equivalent fraction with denominator 100: \\(\\dfrac{3}{4}=\\dfrac{75}{100}\\) = 0.75. Answer: 0.75."} {"t":"s","id":10188,"s":"A common multiple of 3 and 7 must be a multiple of 21. 42 = 21 \u00d7 2, and 42 \u00f7 3 = 14, 42 \u00f7 7 = 6, both exact. Answer: 42."} {"t":"s","id":10190,"s":"Compare by place value: 0.204 < 0.24 < 0.402 < 0.42. (0.204 and 0.24 share tenths 2, then hundredths 0 < 4; 0.402 and 0.42 share tenths 4, then hundredths 0 < 2.) Answer: 0.204, 0.24, 0.402, 0.42."} {"t":"s","id":10191,"s":"Total spent = $18.90 + $7.50 = $26.40. Change = $50 \u2212 $26.40 = $23.60. Answer: $23.60."} {"t":"s","id":10192,"s":"From 09 35 to 11 50: 09 35 to 11 35 is 2 h, plus 35 to 50 is 15 min, total 2 h 15 min. That matches Dino Dash. Answer: Dino Dash."} {"t":"s","id":10193,"s":"Henry = 1 unit, John = 3 units, total = 4 units = 2700. 1 unit = 2700 \u00f7 4 = 675. Henry has 675 stamps. Answer: 675."} {"t":"s","id":10194,"s":"Total wings = (0\u00d75) + (1\u00d73) + (2\u00d78) + (3\u00d712) = 0 + 3 + 16 + 36 = 55. Answer: 55."} {"t":"s","id":10195,"s":"Subtract the duration from the end time: 18 00 \u2212 2 h = 16 00, then \u2212 15 min = 15 45. Answer: 15 45."} {"t":"s","id":10196,"s":"A length rounds to 12.1 if it is from 12.05 up to but not including 12.15. Among the options, the greatest value that still rounds to 12.1 is 12.14 m (12.19 rounds to 12.2). Answer: 12.14 m."} {"t":"s","id":10201,"s":"Six thousand = 6000, twenty = 20, with no hundreds and no tens-of-hundreds in between. 6000 + 20 = 6020. Answer: 6020."} {"t":"s","id":10202,"s":"Each term increases by 40 (85 211 \u2192 85 251 \u2192 85 291). So the missing term = 85 291 + 40 = 85 331 (check: 85 331 + 40 = 85 371). Answer: 85 331."} {"t":"s","id":10203,"s":"Number = quotient \u00d7 divisor + remainder = 1006 \u00d7 6 + 3 = 6036 + 3 = 6039. Answer: 6039."} {"t":"s","id":10205,"s":"An even number must end in an even digit (4 or 6). To make it largest, put the biggest digits first; the smaller even digit (4) goes last. Largest arrangement of 9, 6, 3 then 4 \u2192 9634. Answer: 9634."} {"t":"s","id":10208,"s":"Side of square = perimeter \u00f7 4 = 64 \u00f7 4 = 16 cm. Area = side \u00d7 side = 16 \u00d7 16 = 256 cm\u00b2. Answer: 256 cm\u00b2."} {"t":"s","id":10209,"s":"Flour packed = 6 \u00d7 175 = 1050 g. Total bought = flour used + flour packed = 250 + 1050 = 1300 g. Answer: 1300 g."} {"t":"s","id":10211,"s":"Sarah's ribbon = \\(\\dfrac{3}{5}+\\dfrac{1}{2}=\\dfrac{6}{10}+\\dfrac{5}{10}=\\dfrac{11}{10}=1\\dfrac{1}{10}\\) m. Altogether = Eunice + Sarah = \\(\\dfrac{6}{10}+1\\dfrac{1}{10}=1\\dfrac{7}{10}\\) m. Answer: \\(1\\dfrac{7}{10}\\) m."} {"t":"s","id":10212,"s":"\\(\\dfrac{3}{4}\\) of the number = 21, so \\(\\dfrac{1}{4}\\) = 21 \u00f7 3 = 7. The whole number = 7 \u00d7 4 = 28. Answer: 28."} {"t":"s","id":10213,"s":"Cost of 1 eraser = $4.00 \u00f7 8 = $0.50. Answer: $0.50."} {"t":"s","id":10214,"s":"Let a small box = 1 unit, so a big box = 2 units. 3 big + 2 small = 3\u00d72 + 2\u00d71 = 8 units = 136, so 1 unit = 17. A big box = 2 units = 2 \u00d7 17 = 34 tarts. Answer: 34."} {"t":"s","id":10216,"s":"1 unit = 135 \u00f7 9 = 15. Chicken pies = 2 units = 30. Mushroom pies = 7 units = 105. Difference = 105 \u2212 30 = 75. Answer: 75."} {"t":"s","id":10219,"s":"Take Erica as 1 unit. Dora = 1 unit + $980, Felicia = 1 unit \u2212 $340. Total: 3 units + $980 \u2212 $340 = $4300, so 3 units = $4300 \u2212 $980 + $340 = $3660, 1 unit = $1220 (Erica). Felicia = $1220 \u2212 $340 = $880. Answer: $880."} {"t":"s","id":10220,"s":"Monday + Tuesday = \\(\\dfrac{2}{9}+\\dfrac{2}{3}=\\dfrac{2}{9}+\\dfrac{6}{9}=\\dfrac{8}{9}\\). Wednesday = whole \u2212 \\(\\dfrac{8}{9}\\) = \\(\\dfrac{9}{9}-\\dfrac{8}{9}=\\dfrac{1}{9}\\). Answer: \\(\\dfrac{1}{9}\\)."} {"t":"s","id":10252,"s":"Add the place values: 60 000 + 4 000 + 800 + 7 = 64 807. The ten-thousands digit is 6, thousands 4, hundreds 8, tens 0, ones 7."} {"t":"s","id":10253,"s":"The pattern increases by 4 each time: 7, 11, 15, 19, 23, 27. So the two missing numbers are 19 and 23."} {"t":"s","id":10254,"s":"1 whole = 6 sixths, so 2 wholes = 2 x 6 = 12 sixths. (2 = 12\/6.)"} {"t":"s","id":10255,"s":"Compare after the decimal point. 4.032 has 0 tenths and 3 hundredths; 4.07 has 0 tenths, 7 hundredths. 4.032 < 4.07 < 4.18 < 4.85, so 4.032 is smallest."} {"t":"s","id":10256,"s":"7 tenths means the 7 is in the first place after the decimal point. In 413.75 the digit 7 is in the tenths place (0.7). The others have 7 in tens, ones or hundredths places."} {"t":"s","id":10260,"s":"Madam Lim has 3\/10 kg less than Mrs Tan, so Mrs Tan = 4\/5 + 3\/10. Convert: 4\/5 = 8\/10, so 8\/10 + 3\/10 = 11\/10 = 1 1\/10 kg."} {"t":"s","id":10262,"s":"4008 - 741: subtract with regrouping. 4008 - 741 = 3267."} {"t":"s","id":10264,"s":"The factors of 12 are 1, 2, 3, 4, 6, 12. Given 1, 2, 6 and 12, the remaining two factors are 3 and 4."} {"t":"s","id":10265,"s":"A fraction is in simplest form when numerator and denominator share no common factor besides 1. 2\/3 and 3\/7 cannot be simplified. 10\/12 = 5\/6 and 6\/8 = 3\/4 can be simplified."} {"t":"s","id":10266,"s":"Convert to twelfths: 1\/3 = 4\/12. Then 4\/12 + 1\/12 = 5\/12."} {"t":"s","id":10267,"s":"Convert to tenths: 1 = 10\/10, 3\/5 = 6\/10. Then 10\/10 - 6\/10 - 1\/10 = 3\/10."} {"t":"s","id":10268,"s":"Thousandths is the third place after the decimal point. 5 thousandths = 0.005."} {"t":"s","id":10269,"s":"Look at the tenths digit (6). Since 6 is 5 or more, round up: 117.65 rounds to 118."} {"t":"s","id":10273,"s":"Numbers between 10 and 40 leaving remainder 2 when divided by 7: 16, 23, 30, 37. Of these, the one divisible by 3 (no remainder) is 30 (30 = 7x4 + 2 and 30 = 3x10)."} {"t":"s","id":10274,"s":"To round to 10.05 (nearest hundredth), the thousandths digit must be 0-4 to round down. The greatest 3-decimal-place number that rounds to 10.05 is 10.054."} {"t":"s","id":10278,"s":"4.20 p.m. + 1 h = 5.20 p.m. Then + 35 min = 5.55 p.m."} {"t":"s","id":10281,"s":"Let Shop C = x. Then Shop A = 2x. Shop B = A - 50 = 2x - 50. Total: x + 2x + (2x - 50) = 250, so 5x - 50 = 250, 5x = 300, x = 60. Shop C has 60 apples."} {"t":"s","id":10282,"s":"Fraction spent = 1\/3 + 2\/9 = 3\/9 + 2\/9 = 5\/9. Saved = 1 - 5\/9 = 4\/9. So 4\/9 of salary = $2392, meaning 1\/9 = $598 and salary = $5382. Food = 2\/9 = 2 x $598 = $1196."} {"t":"s","id":10283,"s":"Let 1 packet of sugar = 1 unit, so 1 packet of flour = 2 units. Total units = 2 sugar + 2 flour = 2(1) + 2(2) = 6 units = 6.54 kg. 1 unit = 6.54 \/ 6 = 1.09 kg. Flour = 2 units = 2 x 1.09 = 2.18 kg."} {"t":"s","id":10284,"s":"Cost of 4 cupcakes = 4 x $2.85 = $11.40. Money given = cost + change = $11.40 + $3.60 = $15.00."} {"t":"s","id":10286,"s":"(a) Children = total - adults = 2590 - 1770 = 820 children. (b) Boys = adults \/ 3 = 1770 \/ 3 = 590. Girls = children - boys = 820 - 590 = 230 girls."} {"t":"s","id":10287,"s":"Both spent the same amount on plates, so the difference in money stays $304 - $166 = $138. After buying, Larry = 4 x Mary, so the difference = 3 units = $138, 1 unit = $46. (a) Mary had $46 left. (b) Mary spent 166 - 46 = $120 on 5 plates, so 1 plate = 120 \/ 5 = $24."} {"t":"s","id":10288,"s":"Let Amelia = 1 unit, John = 2 units, Max = 2 units + 8.4. Total = 1 + 2 + 2 units + 8.4 = 115.9, so 5 units = 107.5, 1 unit = 21.5. (a) Amelia = 21.5 kg. (b) Max = 2 x 21.5 + 8.4 = 51.4 kg; difference = 51.4 - 21.5 = 29.9 kg."} {"t":"s","id":10290,"s":"(a) From 8.45 a.m. to 5.30 p.m. is 8 h 45 min total. Subtract the 40 min lunch: 8 h 45 min - 40 min = 8 h 5 min working. (b) He reached the gym at 5.45 p.m., exercised 1 h 40 min, finishing at 7.25 p.m. He reached home at 7.50 p.m., so driving took 7.50 - 7.25 = 25 min."} {"t":"s","id":10291,"s":"Ben at first = 1250 + 490 = 1740. Total stickers = 1740 + 1250 = 2990 (unchanged). In the end Ben = Andrew - 626. So Andrew + (Andrew - 626) = 2990, 2 x Andrew = 3616, Andrew = 1808, Ben = 1182. Ben gave away = 1740 - 1182 = 558 stickers."} {"t":"s","id":10292,"s":"Blue = 1\/8, green = blue = 1\/8, red = 7\/12. Pink = 1 - 1\/8 - 1\/8 - 7\/12. Common denom 24: blue 3\/24, green 3\/24, red 14\/24, so pink = 24\/24 - 3\/24 - 3\/24 - 14\/24 = 4\/24. Green + pink = 3\/24 + 4\/24 = 7\/24 = 581, so 1\/24 = 83 and total = 1992. Red = 7\/12 = 14\/24 = 14 x 83 = 1162 marbles."} {"t":"s","id":10337,"s":"Look at the tens digit (4). Since 4 < 5, round down: 28 549 \u2192 28 500."} {"t":"s","id":10339,"s":"Make the denominators the same: \\(\\dfrac{1}{3} = \\dfrac{4}{12}\\). Then \\(\\dfrac{5}{12} - \\dfrac{4}{12} = \\dfrac{1}{12}\\)."} {"t":"s","id":10340,"s":"4 tenths = 0.4, so the digit 4 must be the first digit after the decimal point. In 30.42 the 4 is in the tenths place."} {"t":"s","id":10342,"s":"Use common denominator 24: \\(\\dfrac{3}{4}=\\dfrac{18}{24}\\), \\(\\dfrac{7}{12}=\\dfrac{14}{24}\\), \\(\\dfrac{7}{8}=\\dfrac{21}{24}\\). Greatest to least: \\(\\dfrac{21}{24}, \\dfrac{18}{24}, \\dfrac{14}{24}\\) = \\(\\dfrac{7}{8}, \\dfrac{3}{4}, \\dfrac{7}{12}\\)."} {"t":"s","id":10345,"s":"Finished at 12 00 (noon). Start time = 12 00 \u2212 50 min = 11 10, which is 11.10 a.m."} {"t":"s","id":10346,"s":"190 tens = 190 \u00d7 10 = 1900. So 79 090 + 1900 = 80 990."} {"t":"s","id":10347,"s":"4 tenths = 0.4. Sum = 0.35 + 0.4 = 0.75."} {"t":"s","id":10348,"s":"To round to 5.9, the value must be from 5.85 up to (but not including) 5.95. Only 5.88 lies in this range (5.84 rounds to 5.8; 5.95 and 5.99 round to 6.0)."} {"t":"s","id":10356,"s":"Six thousand = 6000, and eight = 8 in the ones place (no hundreds or tens). So 6000 + 8 = 6008."} {"t":"s","id":10361,"s":"Compare whole-number parts first: 8.4 is largest. Among the others (all 0.something) compare tenths: 0.095 (0 tenths) < 0.784 < 0.804. Order: 0.095, 0.784, 0.804, 8.4."} {"t":"s","id":10362,"s":"The factors of 32 are 1, 2, 4, 8, 16, 32. The two not listed are 4 and 16 (4 \u00d7 8 = 32, 2 \u00d7 16 = 32)."} {"t":"s","id":10364,"s":"A fraction is in simplest form when numerator and denominator share no common factor other than 1. \\(\\dfrac{3}{9}=\\dfrac{1}{3}\\) and \\(\\dfrac{2}{6}=\\dfrac{1}{3}\\) can be simplified, but \\(\\dfrac{2}{5}\\) and \\(\\dfrac{3}{8}\\) cannot."} {"t":"s","id":10366,"s":"For the greatest odd number, the ones digit must be the smallest available odd digit (5). Arrange the remaining digits 9, 8, 4, 2 in descending order in front: 9842, giving 98 425."} {"t":"s","id":10367,"s":"Total mixture = 1.4 + 3.16 = 4.56 \\(l\\). Shared equally into 4 bottles: 4.56 \u00f7 4 = 1.14 \\(l\\) each."} {"t":"s","id":10370,"s":"After selling, pears left = \\(\\dfrac{1}{3}\\) of pears and oranges left = oranges \u2212 14, and these two are equal. The remaining pears (1 unit) plus the sold pears (2 units = 3 units total pears) plus oranges equal the total once the 14 sold oranges are accounted for: 4 units = 170 \u2212 14 = 156, so 1 unit = 156 \u00f7 4 = 39. The oranges left equal the remaining pears = 39."} {"t":"s","id":10376,"s":"(a) Nigel took 1 \u2212 \\(\\dfrac{5}{8}\\) = \\(\\dfrac{3}{8}\\). (b) Evelyn \u2212 Nigel = \\(\\dfrac{5}{8} - \\dfrac{3}{8} = \\dfrac{2}{8}\\) of the sweets = 76, so \\(\\dfrac{1}{8}\\) = 38 and the whole box = 8 \u00d7 38 = 304 sweets."} {"t":"s","id":10377,"s":"The total stays $540. In the end John = 5 units and Peter = 1 unit, so 6 units = $540 and 1 unit = $90. (a) Peter has $90 in the end. (b) John had $490 at first ($90 \u00d7 5 = $450 at the end, plus the $40 he gave away = $490)."} {"t":"s","id":10378,"s":"Let Chinese = 3 units, then English = 6 units (twice Chinese). English + Chinese = 9 units = 720, so 1 unit = 80. Malay = English \u00f7 3 = 6 \u00f7 3 = 2 units. Total = 9 + 2 = 11 units = 11 \u00d7 80 = 880 books."} {"t":"s","id":10382,"s":"43 thousands = 43 000. 8 tens = 80. 43 000 + 80 = 43 080."} {"t":"s","id":10383,"s":"Rounding to the nearest ten, numbers from 72 495 to 72 504 round to 72 500. 72 496 rounds to 72 500. (72 444->72 440; 72 506->72 510; 72 554->72 550.)"} {"t":"s","id":10384,"s":"Convert the mixed number to an improper fraction: \\(6\\dfrac{5}{9} = \\dfrac{6\\times 9 + 5}{9} = \\dfrac{54+5}{9} = \\dfrac{59}{9}\\). The missing numerator is 59."} {"t":"s","id":10388,"s":"Rounded to the nearest thousand, values from 18 500 to 19 499 give 19 000. The greatest possible value is 19 499 (19 500 would round up to 20 000)."} {"t":"s","id":10389,"s":"Both numbers must be divisible by 3 and by 9. 27 = 9x3 and 36 = 9x4, so both share factors 3 and 9. (12, 18, 21 are not multiples of 9.)"} {"t":"s","id":10391,"s":"\\(\\dfrac{4}{5} = \\dfrac{8}{10}\\). Cherries left = \\(\\dfrac{8}{10} - \\dfrac{3}{10} = \\dfrac{5}{10} = \\dfrac{1}{2}\\) kg."} {"t":"s","id":10392,"s":"Sister = 1.27 + 0.18 = 1.45 kg. Total = 1.27 + 1.45 = 2.72 kg."} {"t":"s","id":10393,"s":"Age this year is a multiple of 7; next year (age + 1) is a multiple of 6. 49 is a multiple of 7 and 49 + 1 = 50 is not a multiple of 6... check: 14+1=15 no; 35+1=36 yes (36=6x6, 35=7x5). So 35 works. Re-check key: key gives option 4 = 49? 49+1=50 not multiple of 6. The valid answer is 35."} {"t":"s","id":10395,"s":"Australia is 1 h 30 min ahead of Singapore (10 30 vs 09 00). At 14 50 in Singapore, Australia time = 14 50 + 1 h 30 min = 16 20."} {"t":"s","id":10396,"s":"Departure = arrival - duration = 13 40 - 5 h 30 min. 13 40 - 5 h = 08 40; 08 40 - 30 min = 08 10."} {"t":"s","id":10400,"s":"Fifteen thousand = 15 000; thirty-six = 36. So 15 000 + 36 = 15 036."} {"t":"s","id":10401,"s":"The pattern decreases by 600 each time (14 000, 13 400, 12 800, 12 200, ...). 12 200 - 600 = 11 600 (and 11 600 - 600 = 11 000)."} {"t":"s","id":10402,"s":"The factors of 32 are 1, 2, 4, 8, 16, 32. The two not listed are 8 and 16."} {"t":"s","id":10403,"s":"49 = 7 x 7, so multiply numerator and denominator of \\(\\dfrac{4}{7}\\) by 7: \\(\\dfrac{4\\times 7}{7\\times 7} = \\dfrac{28}{49}\\). The missing numerator is 28."} {"t":"s","id":10404,"s":"Use denominator 12: \\(\\dfrac{1}{2}=\\dfrac{6}{12}\\), \\(\\dfrac{2}{3}=\\dfrac{8}{12}\\), \\(\\dfrac{7}{12}=\\dfrac{7}{12}\\). Greatest to smallest: \\(\\dfrac{8}{12}, \\dfrac{7}{12}, \\dfrac{6}{12}\\), i.e. \\(\\dfrac{2}{3}, \\dfrac{7}{12}, \\dfrac{1}{2}\\)."} {"t":"s","id":10405,"s":"0.6 = \\(\\dfrac{6}{10}\\). Simplify by dividing by 2: \\(\\dfrac{6}{10} = \\dfrac{3}{5}\\)."} {"t":"s","id":10407,"s":"\\(\\dfrac{3}{4} = \\dfrac{6}{8}\\). \\(\\dfrac{5}{8} + \\dfrac{6}{8} = \\dfrac{11}{8} = 1\\dfrac{3}{8}\\)."} {"t":"s","id":10409,"s":"20.7 \u00f7 7 = 2.957... Rounding to the nearest hundredth (2 decimal places) gives 2.96."} {"t":"s","id":10410,"s":"From 11 35 to 14 10. 11 35 to 14 35 is 3 h, but we only need to 14 10, which is 25 min before 14 35... easier: 11 35 to 12 00 = 25 min; 12 00 to 14 00 = 2 h; 14 00 to 14 10 = 10 min. Total = 2 h 35 min."} {"t":"s","id":10411,"s":"Rope A = 2.88 m. Rope B = 2.88 \u00f7 2 = 1.44 m. A + B = 2.88 + 1.44 = 4.32 m. Rope C = 5 - 4.32 = 0.68 m."} {"t":"s","id":10412,"s":"Length + breadth = half the perimeter = 16 cm. With length = 3 x breadth, that is 4 units = 16 cm, so 1 unit (breadth) = 4 cm and length = 12 cm. Area = 12 x 4 = 48 cm\u00b2."} {"t":"s","id":10414,"s":"After selling 46 pears, apples are unchanged and apples = 5 x (remaining pears). Apples are 150 more than the original pears, i.e. 150 + 46 = 196 more than the remaining pears. So 4 units (apples - remaining pears) = 196, 1 unit (remaining pears) = 49. Pears at first = 49 + 46 = 95."} {"t":"s","id":10417,"s":"(a) Cost of erasers = 8 x $1.30 = $10.40. Weijian at first = $10.40 + $3.85 = $14.25. (b) Weijian had 3 times Xavier, so Xavier = $14.25 \u00f7 3 = $4.75."} {"t":"s","id":10418,"s":"(a) \\(\\dfrac{2}{5} = \\dfrac{8}{20}\\), \\(\\dfrac{1}{4} = \\dfrac{5}{20}\\). Used = \\(\\dfrac{8}{20} + \\dfrac{5}{20} = \\dfrac{13}{20}\\) \\(\\ell\\). (b) Left = 1 - \\(\\dfrac{13}{20} = \\dfrac{7}{20}\\) \\(\\ell\\)."} {"t":"s","id":10419,"s":"Friend got \\(\\dfrac{5}{8}\\) and daughter got \\(\\dfrac{1}{3}\\). Difference = \\(\\dfrac{5}{8} - \\dfrac{1}{3} = \\dfrac{15}{24} - \\dfrac{8}{24} = \\dfrac{7}{24}\\) of the cookies = 42. So \\(\\dfrac{1}{24}\\) = 6, and the total (24 units) = 24 x 6 = 144 cookies."} {"t":"s","id":10423,"s":"Take 1 group = two $2 notes + one $5 note = $2 + $2 + $5 = $9. Number of groups = $243 \u00f7 $9 = 27. Each group has two $2 notes, so $2 notes = 27 x 2 = 54."} {"t":"s","id":10456,"s":"Look at the tens digit (6). Since 6 \u2265 5, round the hundreds up: 32 769 \u2192 32 800."} {"t":"s","id":10457,"s":"Convert the mixed number to an improper fraction: 7 \u00d7 5 + 4 = 39, so \\(7\\dfrac{4}{5}=\\dfrac{39}{5}\\). Missing number = 39."} {"t":"s","id":10458,"s":"0.08 = \\(\\dfrac{8}{100}\\). Divide numerator and denominator by 4: \\(\\dfrac{8}{100}=\\dfrac{2}{25}\\)."} {"t":"s","id":10459,"s":"\\(\\dfrac{7}{20}=\\dfrac{35}{100}=0.35\\). So \\(6\\dfrac{7}{20}=6.35\\)."} {"t":"s","id":10465,"s":"As decimals: \\(\\dfrac{11}{7}\\approx1.57\\), \\(\\dfrac{8}{7}\\approx1.14\\), \\(1\\dfrac{1}{9}\\approx1.11\\). Greatest to smallest: \\(\\dfrac{11}{7}\\), \\(\\dfrac{8}{7}\\), \\(1\\dfrac{1}{9}\\)."} {"t":"s","id":10468,"s":"12.20 p.m. = 1220. Add 15 min wait \u2192 1235. Add 40 min journey \u2192 1315 (in 24-hour time)."} {"t":"s","id":10469,"s":"Larger number = 300 + 50 = 350. Sum = 300 + 350 = 650."} {"t":"s","id":10470,"s":"Used = \\(\\dfrac{3}{4}+\\dfrac{7}{8}=\\dfrac{6}{8}+\\dfrac{7}{8}=\\dfrac{13}{8}=1\\dfrac{5}{8}\\) l. Left = \\(2-1\\dfrac{5}{8}=\\dfrac{3}{8}\\) l."} {"t":"s","id":10473,"s":"LCM of 3, 4 and 6 = 12, so they light together every 12 min. 1st at 1000, 2nd at 1012, 3rd at 1024."} {"t":"s","id":10475,"s":"Factors of 12 are 1, 2, 3, 4, 6, 12. The two not yet listed are 4 and 6."} {"t":"s","id":10477,"s":"The pattern decreases by 400 each step. 31 200 \u2212 400 = 30 800."} {"t":"s","id":10479,"s":"A fraction is in simplest form when numerator and denominator share no common factor. \\(\\dfrac{3}{6}=\\dfrac{1}{2}\\) and \\(\\dfrac{4}{10}=\\dfrac{2}{5}\\) can be simplified; \\(\\dfrac{2}{5}\\) and \\(\\dfrac{5}{12}\\) cannot."} {"t":"s","id":10484,"s":"The fastest runner (smallest time) is 1st. Times: Cleo 15.8 < Dawn 15.9 < Amy 16.1 < Bess 17.0. So 1st Cleo, 2nd Dawn, 3rd Amy, 4th Bess."} {"t":"s","id":10485,"s":"2 boxes = 1044, so 1 box = 1044 \u00f7 2 = 522. Total boxes = 2 + 5 = 7. Total sweets = 7 \u00d7 522 = 3654."} {"t":"s","id":10488,"s":"20 min before midnight = 2340. From 2340 to 2400 is 20 min; from 0000 to 0450 is 4 h 50 min. Total = 4 h 50 min + 20 min = 5 h 10 min."} {"t":"s","id":10489,"s":"Multiples of 3 between 30 and 40: 30, 33, 36, 39. Check remainder 3 when divided by 4: 39 \u00f7 4 = 9 R3. So the number is 39."} {"t":"s","id":10492,"s":"Bill = 4 units = 98.4 kg, so 1 unit (Charlotte) = 98.4 \u00f7 4 = 24.6 kg. Total = 5 units = 5 \u00d7 24.6 = 123 kg."} {"t":"s","id":10493,"s":"String B = String A + 0.15 = 4.36 + 0.15 = 4.51 m. String C = String B \u2212 2.7 = 4.51 \u2212 2.7 = 1.81 m."} {"t":"s","id":10494,"s":"Food = \\(\\dfrac{1}{4}=\\dfrac{2}{8}\\), books = \\(\\dfrac{5}{8}\\). Difference = \\(\\dfrac{5}{8}-\\dfrac{2}{8}=\\dfrac{3}{8}\\) of his money = $12. So \\(\\dfrac{1}{8}\\) = $4, and total \\(\\dfrac{8}{8}\\) = 8 \u00d7 $4 = $32."} {"t":"s","id":10495,"s":"After the transfer each has 1780 \u00f7 2 = 890. Sam gave away 40, so Sam had 890 + 40 = 930 at first."} {"t":"s","id":10496,"s":"TV = 10 chairs. TV + table = 1820 \u2192 10 chairs + table = 1820. Table + chair = 560. Subtracting: 9 chairs = 1820 \u2212 560 = 1260, so 1 chair = 140. Table = 560 \u2212 140 = 420. TV = 10 \u00d7 140 = 1400. 1 TV + 2 tables = 1400 + 2 \u00d7 420 = 1400 + 840 = $2240."} {"t":"q","id":17122,"q":"In which of the following numbers does the digit 5 stand for 50?","e":"The digit 5 stands for 50 when it is in the tens place. In 9750, the 5 is in the tens place, so it stands for 50."} {"t":"q","id":17123,"q":"Which of the following numbers when rounded to the nearest ten becomes 81 500?","e":"Rounding to the nearest ten: 81 496 rounds up to 81 500 (the ones digit 6 rounds the tens up from 9 to 81 500). 81 444 rounds to 81 440, 81 506 rounds to 81 510, 81 554 rounds to 81 550."} {"t":"q","id":17124,"q":"Which of the following is a multiple of 9?","e":"A multiple of 9 can be divided exactly by 9. 36 = 9 \u00d7 4, so 36 is a multiple of 9."} {"t":"q","id":17126,"q":"Which of the following decimals is the smallest?","e":"Compare by place value: 4.036, 4.06, 4.16, 4.306. The smallest is 4.036 (tenths digit 0, then hundredths 3)."} {"t":"q","id":17128,"q":"Nelly sells 384 muffins every month. How many muffins will she sell in a year?","e":"A year has 12 months. 384 \u00d7 12 = 4608 muffins."} {"t":"q","id":17129,"q":"When a number is divided by 9, it has a remainder of 2. Which of the following could be the number?","e":"5787 \u00f7 9 = 643 exactly (5787 is a multiple of 9). So 5787 + 2 = 5789 leaves a remainder of 2 when divided by 9. 5789 \u00f7 9 = 643 r 2."} {"t":"q","id":17130,"q":"Joel runs 300 m every morning. His slowest record is 1 min 35 s. His fastest record is 55 s. What is the difference between his fastest record and his slowest record?","e":"1 min 35 s = 60 + 35 = 95 s. Difference = 95 s \u2212 55 s = 40 s."} {"t":"q","id":17139,"q":"Arrange the following fractions from the greatest to the smallest.
\\(\\dfrac{2}{3}\\), \\(\\dfrac{3}{4}\\), \\(\\dfrac{5}{12}\\)
, , ","e":"Convert to twelfths: \\(\\dfrac{2}{3} = \\dfrac{8}{12}\\), \\(\\dfrac{3}{4} = \\dfrac{9}{12}\\), \\(\\dfrac{5}{12} = \\dfrac{5}{12}\\). Greatest to smallest: \\(\\dfrac{9}{12}\\), \\(\\dfrac{8}{12}\\), \\(\\dfrac{5}{12}\\), i.e. \\(\\dfrac{3}{4}\\), \\(\\dfrac{2}{3}\\), \\(\\dfrac{5}{12}\\)."} {"t":"q","id":17142,"q":"Round 32.55 to the nearest whole number. ","e":"The tenths digit is 5, so round up: 32.55 \u2192 33."} {"t":"q","id":17144,"q":"Find the value of 6.53 \u00d7 8. ","e":"6.53 \u00d7 8 = 52.24."} {"t":"q","id":17150,"q":"The difference between two fractions is \\(\\dfrac{2}{9}\\). The smaller fraction is \\(\\dfrac{1}{6}\\). What is the sum of the two fractions? Express your answer in its simplest form.","e":"Larger fraction = \\(\\dfrac{1}{6} + \\dfrac{2}{9} = \\dfrac{3}{18} + \\dfrac{4}{18} = \\dfrac{7}{18}\\). Sum = \\(\\dfrac{7}{18} + \\dfrac{1}{6} = \\dfrac{7}{18} + \\dfrac{3}{18} = \\dfrac{10}{18} = \\dfrac{5}{9}\\)."} {"t":"q","id":17151,"q":"At first, Peter had twice as much savings as Michelle. After Michelle received $5499, she had twice as much savings as Peter. What is their total savings now? ","e":"Peter's savings stay the same. Let Michelle's first share be 1 unit, Peter = 2 units. After +$5499, Michelle = 2 \u00d7 Peter = 4 units. So the $5499 = 4u \u2212 1u = 3u, giving 1u = $5499 \u00f7 3 = $1833. Total now = Peter (2u) + Michelle (4u) = 6u = $1833 \u00d7 6 = $10998."} {"t":"q","id":17153,"q":"A tank had 25.68 \\(l\\) of water. 9 \\(l\\) of water was poured out of the tank. The remaining amount of water was then poured equally into 6 empty bottles. How much water was poured into each bottle? ","e":"Water left = 25.68 \u2212 9 = 16.68 l. Poured into 6 bottles: 16.68 \u00f7 6 = 2.78 l per bottle."} {"t":"q","id":17154,"q":"A movie at a cinema started at 11.49 a.m. Jasmine arrived at the cinema late and started watching the movie 18 minutes after the movie had started. She watched the movie for 2 h 24 min. What time did the movie end? (Express your answer in 24-hour clock) ","e":"The movie ends when Jasmine finishes watching: she started 18 min after 11.49 a.m. and watched 2 h 24 min, so total time after 11.49 a.m. = 18 min + 2 h 24 min = 2 h 42 min. 11.49 a.m. + 2 h 42 min = 2.31 p.m. = 14 31 in 24-hour clock."} {"t":"q","id":17157,"q":"Mr Lee sold a total of 25.5 kg of corn flour and plain flour. He sold 5 more packets of corn flour than plain flour. Each packet of corn flour had a mass of 2.7 kg and each packet of plain flour had a mass of 1.3 kg.
(a) What was the mass of 5 packets of corn flour?
(b) How many packets of plain flour did he sell? ","e":"(a) 5 packets of corn flour = 2.7 \u00d7 5 = 13.5 kg. (b) The extra 5 corn-flour packets weigh 13.5 kg, so the remaining flour (equal numbers of each type) = 25.5 \u2212 13.5 = 12 kg. Each matched pair (1 corn + 1 plain) = 2.7 + 1.3 = 4 kg. Number of pairs = 12 \u00f7 4 = 3, so he sold 3 packets of plain flour."} {"t":"q","id":17158,"q":"A sum of $7092 was shared among Kumar, Wei Ming and Hakim. Wei Ming received twice as much money as Kumar. Hakim received 3 times as much money as Wei Ming.
(a) How much money did Kumar receive?
(b) How much money did Hakim receive? ","e":"Let Kumar = 1 unit. Wei Ming = 2 units. Hakim = 3 \u00d7 Wei Ming = 6 units. Total = 1 + 2 + 6 = 9 units = $7092, so 1 unit = $7092 \u00f7 9 = $788. (a) Kumar = $788. (b) Hakim = 6 units = $788 \u00d7 6 = $4728."} {"t":"q","id":17159,"q":"After a florist sold \\(\\dfrac{2}{3}\\) of her roses and \\(\\dfrac{5}{9}\\) of her tulips, she had the same number of roses and tulips left. The number of tulips she sold was 85.
(a) How many tulips did she have left?
(b) How many roses did she have at first? ","e":"Tulips: \\(\\dfrac{5}{9}\\) sold = 85, so 1 unit (\\(\\dfrac{1}{9}\\)) = 85 \u00f7 5 = 17. Tulips left = \\(\\dfrac{4}{9}\\) = 4 \u00d7 17 = 68. (a) 68 tulips left. (b) Roses left = tulips left = 68, and roses left are \\(\\dfrac{1}{3}\\) of the roses (since \\(\\dfrac{2}{3}\\) sold). So roses at first = 3 \u00d7 68 = 204."} {"t":"q","id":17160,"q":"There was a total of 60 bicycles and tricycles in a shop. A bicycle has 2 wheels and a tricycle has 3 wheels. There were 156 wheels altogether.
(a) How many bicycles were there?
(b) How many more tricycles than bicycles were there in the shop? ","e":"If all 60 were bicycles: 60 \u00d7 2 = 120 wheels. Extra wheels = 156 \u2212 120 = 36, and each tricycle adds 1 extra wheel, so tricycles = 36. Bicycles = 60 \u2212 36 = 24. (a) 24 bicycles. (b) Tricycles \u2212 bicycles = 36 \u2212 24 = 12 more tricycles."} {"t":"q","id":17162,"q":"43 852 rounded to the nearest hundred is .","e":"Look at the tens digit (5). Since 52 \u2265 50, round up: 43 852 \u2192 43 900."} {"t":"q","id":17163,"q":"In which of the following numbers does the digit 4 stand for 4 hundredths?","e":"4 hundredths is the second place after the decimal point. In 387.64 the 4 is in the hundredths place."} {"t":"q","id":17164,"q":"Express \\(\\dfrac{53}{1000}\\) as a decimal.","e":"Thousandths take 3 decimal places. \\(\\dfrac{53}{1000}\\) = 0.053."} {"t":"q","id":17166,"q":"Which of the following is not in its simplest form?","e":"A fraction is in simplest form when numerator and denominator share no common factor besides 1. \\(\\dfrac{2}{6}\\) can be simplified to \\(\\dfrac{1}{3}\\), so it is not in simplest form."} {"t":"q","id":17170,"q":"Jane completed her job at 01 20. She worked for 4 h 30 min. At what time did she start her job?","e":"01 20 is 1.20 a.m. Going back 4 h 30 min: 01 20 \u2212 4 h = 21 20 (the previous day) \u2212 30 min = 20 50, i.e. 8.50 p.m."} {"t":"q","id":17171,"q":"Mr Ling sold 8 sofas and some carpets for $5928. The sofa cost $645 each. How much did the carpets cost?","e":"8 sofas cost 8 \u00d7 $645 = $5160. Carpets = $5928 \u2212 $5160 = $768."} {"t":"q","id":17172,"q":"Mandy and William had a total of 1712 stickers at first. After Mandy gave away 92 stickers, William had 5 times as many stickers as Mandy. How many stickers did Mandy have in the end?","e":"After Mandy gives away 92, the total left is 1712 \u2212 92 = 1620. This is 5 + 1 = 6 units (William = 5 units, Mandy = 1 unit). 1 unit = 1620 \u00f7 6 = 270, so Mandy had 270 in the end."} {"t":"q","id":17174,"q":"Jerry bought 3 apples and 1 orange. The cost of 3 apples was $5.25. An apple cost $0.60 less than an orange. What was the cost of an orange?","e":"1 apple = $5.25 \u00f7 3 = $1.75. An apple costs $0.60 less than an orange, so orange = $1.75 + $0.60 = $2.35."} {"t":"q","id":17177,"q":"Two factors of 21 are 1 and 21. What are the other two factors of 21? and ","e":"The factors of 21 are 1, 3, 7 and 21. Besides 1 and 21, the other two factors are 3 and 7."} {"t":"q","id":17179,"q":"Find the value of \\(\\dfrac{7}{9}-\\dfrac{2}{3}\\).","e":"Convert \\(\\dfrac{2}{3}\\) to ninths: \\(\\dfrac{2}{3}=\\dfrac{6}{9}\\). Then \\(\\dfrac{7}{9}-\\dfrac{6}{9}=\\dfrac{1}{9}\\)."} {"t":"q","id":17180,"q":"Round 78.55 to the nearest whole number. ","e":"The tenths digit is 5, so round up: 78.55 \u2192 79."} {"t":"q","id":17181,"q":"Arrange the following fractions from the smallest to the greatest.
\\(\\dfrac{5}{6}\\), \\(\\dfrac{5}{12}\\), \\(\\dfrac{11}{12}\\)
, , ","e":"Express in twelfths: \\(\\dfrac{5}{6}=\\dfrac{10}{12}\\). Comparing \\(\\dfrac{5}{12}\\), \\(\\dfrac{10}{12}\\), \\(\\dfrac{11}{12}\\) gives smallest to greatest: \\(\\dfrac{5}{12}\\), \\(\\dfrac{5}{6}\\), \\(\\dfrac{11}{12}\\)."} {"t":"q","id":17183,"q":"Find the value of 8.26 \u00d7 9. ","e":"8.26 \u00d7 9 = 74.34."} {"t":"q","id":17186,"q":"State the time 36 min before midnight using the 24-hour clock.
What is the duration from 10 35 to 13 08? h min","e":"(a) Midnight is 24 00; 36 min before is 24 00 \u2212 36 min = 23 24. (b) From 10 35 to 13 08: 10 35 to 13 35 is 3 h, but 13 08 is 27 min short, so 3 h \u2212 27 min = 2 h 33 min."} {"t":"q","id":17187,"q":"The perimeter of a square is 36 m. What is the area of the square? ","e":"Side = perimeter \u00f7 4 = 36 \u00f7 4 = 9 m. Area = 9 \u00d7 9 = 81 m\u00b2."} {"t":"q","id":17189,"q":"Rashid and Wen Long cycled a total distance of 8.34 km. Rashid cycled 3 times as far as Wen Long did. How far did Wen Long cycle? Give your answer correct to 2 decimal places. ","e":"Total is 3 + 1 = 4 units. 1 unit (Wen Long) = 8.34 \u00f7 4 = 2.085 km \u2248 2.09 km (to 2 d.p.)."} {"t":"q","id":17190,"q":"Siva had some money. She bought 7 books for $8.65 and had $7.45 left. How much money did Siva have at first? ","e":"Money at first = money spent + money left = $8.65 + $7.45 = $16.10."} {"t":"q","id":17191,"q":"Mrs Chan had 5 \\(l\\) of orange juice. Her daughter drank \\(\\dfrac{3}{5}\\) \\(l\\) of it. How much orange juice had Mrs Chan left?","e":"5 \u2212 \\(\\dfrac{3}{5}\\) = \\(4\\dfrac{5}{5}-\\dfrac{3}{5}\\) = \\(4\\dfrac{2}{5}\\) litres."} {"t":"q","id":17193,"q":"At first, Mei Hua had $48 less than Celeste. Mei Hua then gave $36 to Celeste. How much more money did Celeste have than Mei Hua in the end? ","e":"At first the gap is $48. Giving $36 widens the gap by 2 \u00d7 $36 = $72. New difference = $48 + $72 = $120."} {"t":"q","id":17195,"q":"The table shows the ticket prices to an amusement park during the weekdays and weekends.
Adult: weekdays $14.50 per ticket, weekend $31 for 2 tickets.
Child below 12 years old: weekdays $6.90 per ticket, weekend $8.90 per ticket.
(a) Mr Omar took his child, Suresh, to the park on Monday. Suresh was 6 years old. How much did Mr Omar pay for their tickets?
(b) On Saturday, Mr and Mrs Johnson took their 3 children to the park. Their eldest child was 11 years old. How much did Mr Johnson pay for their tickets? ","e":"(a) Monday is a weekday: 1 adult $14.50 + 1 child $6.90 = $21.40. (b) Saturday is a weekend: 2 adults = $31 (2 for $31), 3 children at $8.90 = $26.70; total = $31 + $26.70 = $57.70."} {"t":"q","id":17197,"q":"At a school activity, one teacher was needed to guide at most 8 pupils in a group. A total of 125 girls and 386 boys participated in the activity. The last group had fewer than 8 pupils.
(a) What was the least number of teachers needed to guide all the pupils?
(b) How many pupils were there in the last group? ","e":"Total pupils = 386 + 125 = 511. 511 \u00f7 8 = 63 remainder 7. (a) The remainder needs an extra group\/teacher, so 63 + 1 = 64 teachers. (b) The last group has the remainder = 7 pupils."} {"t":"q","id":17199,"q":"There are 36 pupils in a class. There are 12 boys in the class.
(a) What fraction of the class are girls? Express your answer in the simplest form.
(b) \\(\\dfrac{4}{9}\\) of the pupils in the class wear spectacles. How many pupils do not wear spectacles? ","e":"(a) Girls = 36 \u2212 12 = 24. Fraction = \\(\\dfrac{24}{36}=\\dfrac{2}{3}\\). (b) Fraction not wearing spectacles = \\(1-\\dfrac{4}{9}=\\dfrac{5}{9}\\); \\(\\dfrac{5}{9}\\) of 36 = 5 \u00d7 4 = 20 pupils."} {"t":"q","id":17200,"q":"An exercise book cost 4 times as much as a pencil. Paul paid $7.56 for 3 pencils and 1 exercise book.
(a) What was the cost of 1 pencil?
(b) What was the cost of 1 exercise book? ","e":"1 exercise book = 4 pencils, so 3 pencils + 1 book = 3 + 4 = 7 pencils = $7.56. (a) 1 pencil = $7.56 \u00f7 7 = $1.08. (b) 1 exercise book = 4 \u00d7 $1.08 = $4.32."} {"t":"q","id":17201,"q":"Mrs Koh had 90 candies and 72 jellies. She packed all of them into as many bags as possible. Each bag contained an equal number of candies. The total number of candies and jellies in each bag was also the same.
(a) How many bags of candies and jellies did Mrs Koh pack?
(b) What was the total number of candies and jellies in each bag? ","e":"(a) Bags must divide both 90 and 72 \u2014 the common factors are 1, 2, 3, 6, 9, 18. The greatest (most bags possible) is 18 bags. (b) Each bag holds 90 \u00f7 18 = 5 candies and 72 \u00f7 18 = 4 jellies, total 5 + 4 = 9 per bag."} {"t":"q","id":17202,"q":"Mike bought 5 pens and 2 erasers. Kelly bought 2 pens and 5 erasers. Mike paid $2.40 more than Kelly. An eraser cost $0.95.
(a) How much more does a pen cost than an eraser?
(b) What was the cost of a pen? ","e":"The difference between the two buys is 3 pens \u2212 3 erasers = $2.40. So 3 \u00d7 (pen \u2212 eraser) = $2.40, giving pen \u2212 eraser = $0.80. (a) A pen costs $0.80 more than an eraser. (b) 1 pen = $0.80 + $0.95 = $1.75."} {"t":"q","id":17203,"q":"73 thousands and 8 tens is the same as .","e":"73 thousands = 73 000 and 8 tens = 80. Total = 73 000 + 80 = 73 080."} {"t":"q","id":17204,"q":"13 845 rounded to the nearest hundred is .","e":"The tens digit is 4, so round down. 13 845 to the nearest hundred is 13 800."} {"t":"q","id":17205,"q":"\\(7\\dfrac{4}{5} = \\dfrac{ }{5}\\)
What is the missing number in the box?","e":"Convert the mixed number to an improper fraction: \\(7\\dfrac{4}{5} = \\dfrac{7\\times5+4}{5} = \\dfrac{39}{5}\\). The missing number is 39."} {"t":"q","id":17207,"q":"In the number 45.67, the digit is in the tenths place.","e":"The first digit after the decimal point is the tenths place. In 45.67 that digit is 6."} {"t":"q","id":17208,"q":"Write \\(4\\dfrac{3}{20}\\) as a decimal.","e":"\\(\\dfrac{3}{20} = \\dfrac{15}{100} = 0.15\\). So \\(4\\dfrac{3}{20} = 4.15\\)."} {"t":"q","id":17209,"q":"Arrange these numbers from the smallest to the greatest.
5709, 5079, 5790","e":"Compare digit by digit: 5079 < 5709 < 5790. Smallest to greatest is 5079, 5709, 5790."} {"t":"q","id":17210,"q":"Which of the following is a multiple of both 3 and 4?","e":"A multiple of both 3 and 4 is a multiple of 12. 24 = 12 \u00d7 2, which is divisible by both 3 and 4."} {"t":"q","id":17212,"q":"Which of the numbers when rounded to the nearest tenth becomes 82.3?","e":"Rounding to the nearest tenth: 82.34 has hundredths digit 4, so it rounds down to 82.3. (82.24 -> 82.2; 82.235 -> 82.2; 82.354 -> 82.4.)"} {"t":"q","id":17213,"q":"Which of the following decimals is closest in value to 0.5?","e":"Find the difference from 0.5: |0.4-0.5|=0.1, |0.6-0.5|=0.1, |0.46-0.5|=0.04, |0.56-0.5|=0.06. The smallest difference is 0.04, so 0.46 is closest."} {"t":"q","id":17214,"q":"Mrs Lee bought 9 similar packets of milk.
After she used 6 packets of milk to make some cakes, she had 3.42 \\(l\\) of milk left.
How many litres of milk did she have at first?","e":"9 - 6 = 3 packets left = 3.42 l, so 1 packet = 3.42 \u00f7 3 = 1.14 l. At first she had 9 packets = 1.14 \u00d7 9 = 10.26 l."} {"t":"q","id":17218,"q":"Jan has \\(\\dfrac{3}{4}\\) m of cloth. She has \\(\\dfrac{1}{2}\\) m more cloth than Helen. How much cloth do they have altogether?","e":"Helen has 3\/4 - 1\/2 = 1\/4 m. Altogether: 3\/4 + 1\/4 = 1 m."} {"t":"q","id":17219,"q":"How many minutes does it take for a minute hand of a clock to make \\(1\\dfrac{1}{4}\\) turn round the clock?","e":"One full turn of the minute hand = 60 min. 1 1\/4 turns = 60 + (1\/4 \u00d7 60) = 60 + 15 = 75 min."} {"t":"q","id":17220,"q":"Jenny was working from 11 10 to 13 05. How much time did she take to complete her work?","e":"From 11 10 to 13 10 is 2 h. But the end is 13 05, which is 5 min before 13 10. So duration = 2 h - 5 min = 1 h 55 min."} {"t":"q","id":17221,"q":"The area of a square is 36 cm\\u00b2. What is the perimeter of the square?","e":"Side = \u221a36 = 6 cm. Perimeter = 4 \u00d7 6 = 24 cm."} {"t":"q","id":17223,"q":"Write the missing number in the number pattern.
14 000, 13 400, 12 800, 12 200, , 11 000","e":"Each term decreases by 600 (14 000 - 13 400 = 600). 12 200 - 600 = 11 600. Check: 11 600 - 600 = 11 000."} {"t":"q","id":17224,"q":"Two factors of 6 are 1 and 6. What are the other two factors of 6?
and ","e":"The factors of 6 are 1, 2, 3 and 6. Besides 1 and 6, the other two factors are 2 and 3."} {"t":"q","id":17226,"q":"Find the value of \\(1 - \\dfrac{1}{8} - \\dfrac{1}{4}\\).","e":"Use eighths: 1 = 8\/8, 1\/4 = 2\/8. So 8\/8 - 1\/8 - 2\/8 = 5\/8."} {"t":"q","id":17229,"q":"Find the value of 4.73 \\u00d7 8. ","e":"4.73 \u00d7 8 = 37.84."} {"t":"q","id":17230,"q":"7.21 - 5.38 = .
Round your answer to the nearest 1 decimal place.","e":"7.21 - 5.38 = 1.83. Rounded to 1 decimal place: 1.8."} {"t":"q","id":17233,"q":"David spent \\(\\dfrac{1}{5}\\) of his money on a wallet and gave $90 to his mother. He had $104 left. How much money did he spend on the wallet?
$","e":"The wallet was 1\/5 of his money, so 4\/5 remained after the wallet. That 4\/5 = $90 + $104 = $194. So 1\/5 = $194 \u00f7 4 = $48.50 spent on the wallet."} {"t":"q","id":17234,"q":"Doughnuts are sold in boxes of 6, 3 and 2. John bought exactly 119 doughnuts. What was the least number of boxes of each type of doughnuts John bought?
box(es) of 6
box(es) of 3
box(es) of 2","e":"To use the fewest boxes, use as many large (6) boxes as possible. 19 \u00d7 6 = 114, leaving 5. 5 = one box of 3 + one box of 2. So 19 boxes of 6, 1 box of 3, 1 box of 2."} {"t":"q","id":17240,"q":"At a concert, \\(\\dfrac{3}{10}\\) of the audience are women and \\(\\dfrac{1}{5}\\) of the audience are men. The rest of the audience are children.
(a) What fraction of the audience are children? [Leave your answer in the simplest form]
(b) There are 180 more children than women. How many women and men are there altogether?
(a)
(b) ","e":"(a) Women + men = 3\/10 + 1\/5 = 3\/10 + 2\/10 = 5\/10. Children = 1 - 5\/10 = 5\/10 = 1\/2. (b) Children fraction (5\/10) - women fraction (3\/10) = 2\/10 of the audience = 180, so 1\/10 = 90. Women + men = 5\/10 = 5 \u00d7 90 = 450."} {"t":"q","id":17241,"q":"Andy, Ben and Cindy share $1900 altogether. Ben has $145 more than Cindy. Cindy has twice as much money as Andy.
(a) How much money does Andy have?
(b) Find the total amount of money Ben and Cindy have.
(a) $
(b) $","e":"Let Andy = 1 unit. Cindy = 2 units. Ben = 2 units + $145. Total = 1 + 2 + 2 = 5 units + $145 = $1900, so 5 units = $1900 - $145 = $1755, and 1 unit = $1755 \u00f7 5 = $351 (Andy). (b) Ben + Cindy = $1900 - $351 = $1549."} {"t":"q","id":17242,"q":"A bottle had some amount of milk at first. Peter drank \\(\\dfrac{1}{4}\\) \\(l\\) of milk in the morning and \\(\\dfrac{1}{5}\\) \\(l\\) of milk in the afternoon.
(a) How many litres of milk did Peter drink in total?
(b) Peter had \\(\\dfrac{3}{5}\\) \\(l\\) of milk at first. What was the amount of milk left in the bottle?
(a)
(b) ","e":"(a) 1\/4 + 1\/5 = 5\/20 + 4\/20 = 9\/20 l. (b) 3\/5 = 12\/20 l at first. Left = 12\/20 - 9\/20 = 3\/20 l."} {"t":"q","id":17243,"q":"Mr Tan had an equal number of apples and oranges. After giving 48 apples and 36 oranges to Mr Lim, the oranges left was three times the number of apples left.
(a) How many apples did Mr Tan have at first?
(b) How many oranges were left?
(a)
(b) ","e":"Start equal; let apples left = 1 unit, oranges left = 3 units. Apples started = 1 unit + 48; oranges started = 3 units + 36. Equal start: 1 unit + 48 = 3 units + 36, so 2 units = 12 and 1 unit = 6. (a) Apples at first = 6 + 48 = 54. (b) Oranges left = 3 units = 3 \u00d7 6 = 18."} {"t":"q","id":17245,"q":"Which of the following is a factor of both 18 and 27?","e":"Factors of 18: 1, 2, 3, 6, 9, 18. Factors of 27: 1, 3, 9, 27. The common factors are 1, 3 and 9. Among the options, only 9 is a factor of both. Answer: 9."} {"t":"q","id":17246,"q":"Which of the following numbers when rounded to the nearest ten becomes 72 500?","e":"Rounding to the nearest ten gives 72 500 for numbers from 72 495 to 72 504. 72 443 rounds to 72 440; 72 495 rounds to 72 500; 72 539 rounds to 72 540; 72 554 rounds to 72 550. Answer: 72 495."} {"t":"q","id":17248,"q":"\\(6\\dfrac{4}{7}=\\dfrac{ }{7}\\)
What is the missing number in the box?","e":"Convert the mixed number to an improper fraction: \\(6\\dfrac{4}{7}=\\dfrac{6\\times7+4}{7}=\\dfrac{42+4}{7}=\\dfrac{46}{7}\\). The missing number is 46."} {"t":"q","id":17250,"q":"Express 0.05 as a fraction in its simplest form.","e":"0.05 = \\(\\dfrac{5}{100}\\). Dividing numerator and denominator by 5 gives \\(\\dfrac{1}{20}\\). Answer: \\(\\dfrac{1}{20}\\)."} {"t":"q","id":17252,"q":"The table shows the prices of tickets to a theme park.
Adult: $15
Child: $9
Mrs Tan wants to buy tickets for two adults and three children. How much does she have to pay in total?","e":"Two adults cost 2 \u00d7 $15 = $30. Three children cost 3 \u00d7 $9 = $27. Total = $30 + $27 = $57. Answer: $57."} {"t":"q","id":17253,"q":"The table shows 4 different types of CCA that 225 children participated in. Each child participated only in one CCA.
Rope Skipping: ?
Gymnastics: 73
International Dance: 50
Girls' Brigade: 64
How many children participated in Rope Skipping?","e":"Add the three known groups: 73 + 50 + 64 = 187. Subtract from the total: 225 \u2212 187 = 38. Answer: 38."} {"t":"q","id":17254,"q":"Which of the following fractions has the value closest to 1?","e":"The difference from 1 is: \\(1-\\dfrac{2}{3}=\\dfrac{1}{3}\\); \\(1-\\dfrac{3}{4}=\\dfrac{1}{4}\\); \\(1-\\dfrac{5}{6}=\\dfrac{1}{6}\\); \\(1-\\dfrac{7}{8}=\\dfrac{1}{8}\\). The smallest gap is \\(\\dfrac{1}{8}\\), so \\(\\dfrac{7}{8}\\) is closest to 1. Answer: \\(\\dfrac{7}{8}\\)."} {"t":"q","id":17255,"q":"Jamie bought 8 boxes of biscuits. Each box of biscuits cost $1.20. She gave the cashier $50. How much change did Jamie receive?","e":"Cost of biscuits = 8 \u00d7 $1.20 = $9.60. Change = $50 \u2212 $9.60 = $40.40. Answer: $40.40."} {"t":"q","id":17257,"q":"Harun and Ming Hui started reading their storybooks at 9.45 a.m. Harun took 1 h 20 min to finish reading his storybook. He took 25 min longer than Ming Hui. At what time did Ming Hui finish reading his storybook?","e":"Ming Hui took 25 min less than Harun: 1 h 20 min \u2212 25 min = 55 min. Starting at 9.45 a.m. and adding 55 min gives 10.40 a.m. Answer: 10.40 a.m."} {"t":"q","id":17259,"q":"How many letters in the word ANGEL have a line of symmetry?","e":"Checking each letter: A has a vertical line of symmetry; N has none; G has none; E has a horizontal line of symmetry; L has none. So 2 letters (A and E) have a line of symmetry. Answer: 2."} {"t":"q","id":17261,"q":"Write thirteen thousand and twenty-six in figures.
","e":"Thirteen thousand = 13 000 and twenty-six = 26. Together: 13 000 + 26 = 13 026. Answer: 13 026."} {"t":"q","id":17262,"q":"Write the missing number in the number pattern below.
14 100, 13 200, 12 300, 11 400, , 9600","e":"The numbers decrease by 900 each time (14 100 \u2212 900 = 13 200, and so on). After 11 400, the next term is 11 400 \u2212 900 = 10 500. Check: 10 500 \u2212 900 = 9 600. Answer: 10 500."} {"t":"q","id":17263,"q":"What is the remainder when 1536 is divided by 7?
","e":"1536 \u00f7 7 = 219 remainder 3, because 7 \u00d7 219 = 1533 and 1536 \u2212 1533 = 3. The remainder is 3."} {"t":"q","id":17264,"q":"Which two of the fractions below are equivalent to \\(\\dfrac{6}{8}\\)?
\\(\\dfrac{12}{16}\\), \\(\\dfrac{5}{7}\\), \\(\\dfrac{4}{5}\\), \\(\\dfrac{3}{4}\\)
and ","e":"\\(\\dfrac{6}{8}\\) simplifies to \\(\\dfrac{3}{4}\\). \\(\\dfrac{12}{16}\\) also simplifies to \\(\\dfrac{3}{4}\\) (divide by 4), and \\(\\dfrac{3}{4}\\) is already in that form. So the two equivalent fractions are \\(\\dfrac{12}{16}\\) and \\(\\dfrac{3}{4}\\)."} {"t":"q","id":17265,"q":"What is the value of \\(\\dfrac{5}{6}+\\dfrac{2}{3}\\)? Express your answer as a mixed number.","e":"Make the denominators the same: \\(\\dfrac{2}{3}=\\dfrac{4}{6}\\). Then \\(\\dfrac{5}{6}+\\dfrac{4}{6}=\\dfrac{9}{6}=\\dfrac{3}{2}=1\\dfrac{1}{2}\\). Answer: \\(1\\dfrac{1}{2}\\)."} {"t":"q","id":17266,"q":"Write 5 thousandths as a decimal.
","e":"5 thousandths means 5 in the thousandths place (the third decimal place): 0.005. Answer: 0.005."} {"t":"q","id":17267,"q":"Round 23.51 to the nearest whole number.
","e":"The first decimal digit is 5, so round up: 23.51 rounds to 24. Answer: 24."} {"t":"q","id":17272,"q":"At a funfair, \\(\\dfrac{5}{12}\\) of the people were children, \\(\\dfrac{1}{3}\\) of the people were men and the rest were women. What fraction of the people were women? Express your answer as a fraction in its simplest form.","e":"Children and men together: \\(\\dfrac{5}{12}+\\dfrac{1}{3}=\\dfrac{5}{12}+\\dfrac{4}{12}=\\dfrac{9}{12}\\). Women = \\(1-\\dfrac{9}{12}=\\dfrac{3}{12}=\\dfrac{1}{4}\\). Answer: \\(\\dfrac{1}{4}\\)."} {"t":"q","id":17273,"q":"Express 3 \u00f7 7 as a decimal. Round your answer to the nearest hundredth.
","e":"3 \u00f7 7 = 0.4285... The thousandths digit is 8, so round the hundredths up: 0.43. Answer: 0.43."} {"t":"q","id":17276,"q":"A train took 2 h 25 min to travel from Station A to Station B. It arrived at Station B at 23 45. What time did the train leave Station A? Express your answer using the 24-hour clock.
","e":"Subtract the travel time from the arrival time: 23 45 \u2212 2 h 25 min. 23 45 \u2212 2 h = 21 45; 21 45 \u2212 25 min = 21 20. The train left at 21 20. Answer: 21 20."} {"t":"q","id":17277,"q":"The table shows the number of stickers collected by each pupil in a group. Part of the table is covered by an ink blot. There were 87 pupils who collected at least 70 stickers.
Number of stickers: 50, 60, 70, 80, 90
Number of pupils: 25, 34, 19, ?, ?
How many pupils in total collected 80 and 90 stickers?
","e":"'At least 70 stickers' means the 70, 80 and 90 columns together = 87 pupils. The 70 column has 19 pupils, so the 80 and 90 columns together = 87 \u2212 19 = 68 pupils. Answer: 68."} {"t":"q","id":17279,"q":"A pair of trousers cost $132. It cost $27 more than a shirt. Mr Lee bought a pair of trousers and 4 shirts.
(a) How much did a shirt cost?
(b) How much did Mr Lee pay for a pair of trousers and 4 shirts altogether?
(a) $
(b) $","e":"(a) A shirt costs $27 less than the trousers: $132 \u2212 $27 = $105. (b) Cost of 4 shirts = 4 \u00d7 $105 = $420. Total = $132 + $420 = $552. Answers: (a) $105 (b) $552."} {"t":"q","id":17281,"q":"There were some stickers in a box. Mariam took \\(\\dfrac{3}{8}\\) of the stickers and Amy took the rest. Mariam took 36 fewer stickers than Amy.
(a) What fraction of the stickers did Amy take?
(b) How many stickers were in the box in total?
(a)
(b) ","e":"(a) Amy took the rest: \\(1-\\dfrac{3}{8}=\\dfrac{5}{8}\\). (b) The difference between Amy and Mariam is \\(\\dfrac{5}{8}-\\dfrac{3}{8}=\\dfrac{2}{8}\\) of the total, which equals 36 stickers. So \\(\\dfrac{2}{8}\\) = 36 means \\(\\dfrac{1}{8}\\) = 18, and the total \\(\\dfrac{8}{8}\\) = 18 \u00d7 8 = 144 stickers. Answers: (a) \\(\\dfrac{5}{8}\\) (b) 144."} {"t":"q","id":17283,"q":"Ahmad and Jack had the same amount of money at first. After Ahmad had spent $37 and Jack had received $15, Jack had 3 times as much money as Ahmad in the end.
(a) How much more money did Jack have than Ahmad in the end?
(b) How much money did Jack have at first?
(a) $
(b) $","e":"(a) They started equal. Ahmad spent $37 and Jack received $15, so the difference between them in the end is $37 + $15 = $52. (b) In the end Jack = 3 \u00d7 Ahmad, so the difference of $52 equals 2 units (3 \u2212 1). 1 unit = $52 \u00f7 2 = $26 (Ahmad's end amount); Jack's end amount = 3 \u00d7 $26 = $78. Jack at first = $78 \u2212 $15 = $63. Answers: (a) $52 (b) $63."} {"t":"q","id":17284,"q":"Tina saved some money from Monday to Friday. Each day, she saved $1 more than the previous day. At the end of Wednesday, she saved a total of $38.70.
(a) How much money did Tina save on Wednesday?
(b) How much money did she save on Friday?
(a) $
(b) $","e":"(a) Let Wednesday's saving be W. Monday = W \u2212 $2 and Tuesday = W \u2212 $1. Their total: (W \u2212 2) + (W \u2212 1) + W = 3W \u2212 3 = $38.70, so 3W = $41.70 and W = $13.90. (b) Thursday = $13.90 + $1 = $14.90; Friday = $14.90 + $1 = $15.90. Answers: (a) $13.90 (b) $15.90."} {"t":"q","id":17346,"q":"Forty-six thousand and sixteen in figures is .","e":"Forty-six thousand = 46 000; sixteen = 16. So 46 000 + 16 = 46 016."} {"t":"q","id":17347,"q":"In which of the following numbers does the digit 8 stands for 80?","e":"The digit 8 stands for 80 when it is in the tens place. In 3082 the 8 is in the tens place (80)."} {"t":"q","id":17348,"q":"13 429 rounded to the nearest hundred is .","e":"Look at the tens digit (2). Since 2 < 5, round down: 13 429 to the nearest hundred is 13 400."} {"t":"q","id":17350,"q":"\\(\\dfrac{1}{3}\\) + \\(\\dfrac{1}{9}\\) =","e":"Make denominators the same: \\(\\dfrac{1}{3}=\\dfrac{3}{9}\\). Then \\(\\dfrac{3}{9}+\\dfrac{1}{9}=\\dfrac{4}{9}\\)."} {"t":"q","id":17352,"q":"What is the number when 17.54 is rounded to 1 decimal place?","e":"To round to 1 decimal place, look at the 2nd decimal digit (4). Since 4 < 5, round down: 17.54 becomes 17.5."} {"t":"q","id":17353,"q":"Abby started cleaning her room at 13 30. She took 1 h 30 min to clean her room. What time did she finish cleaning her room?","e":"13 30 + 1 h = 14 30; 14 30 + 30 min = 15 00."} {"t":"q","id":17359,"q":"Jason spent $55 on 2 identical shirts and a pair of pants. A pair of pants cost $25 more than a shirt. How much did he spend on 1 shirt?","e":"Remove the extra $25 for the pants: 55 \u2212 25 = 30. This equals 3 shirts (2 shirts + the pants priced as 1 shirt). 1 shirt = 30 \u00f7 3 = $10."} {"t":"q","id":17361,"q":"83 905 = 80 000 + 3000 + + 5
What is the missing number?","e":"83 905 = 80 000 + 3000 + 900 + 5. The missing number is the hundreds value, 900."} {"t":"q","id":17362,"q":"Write the missing number in the number pattern.
13 000 , 12 600 , 12 200 , 11 800 , , 11 000","e":"Each number decreases by 400. 11 800 \u2212 400 = 11 400."} {"t":"q","id":17366,"q":"Write 5 thousandths as a decimal.
Answer: ","e":"Thousandths are the 3rd decimal place. 5 thousandths = 0.005."} {"t":"q","id":17367,"q":"Write \\(\\dfrac{85}{100}\\) as a decimal.
Answer: ","e":"\\(\\dfrac{85}{100}\\) means 85 hundredths = 0.85."} {"t":"q","id":17368,"q":"Arrange the following numbers in order from the greatest to the smallest.
3.909, 3.093, 3.099
(greatest), , (smallest)","e":"Compare decimal place by place. 3.909 > 3.099 > 3.093 because the tenths digit 9 beats 0, then for 3.099 vs 3.093 the hundredths are equal (9) but thousandths 9 > 3."} {"t":"q","id":17371,"q":"Mrs Wong wants to pack 36 blueberry cupcakes and 54 chocolate cupcakes into boxes with no remainder. The total number of cupcakes packed into each box is the same. The number of blueberry cupcakes in each box is the same. What is the greatest number of boxes that Mrs Wong can pack?
Answer: ","e":"The greatest number of boxes is the highest common factor of 36 and 54. Common factors are 1, 2, 3, 6, 9, 18; the greatest is 18."} {"t":"q","id":17378,"q":"Aini prepared 6 \\(\\ell\\) of fruit punch for a party. She poured them equally into 4 bottles. What is the volume of the fruit punch in each bottle?
Answer: ","e":"6 \u2113 \u00f7 4 = 1.5 \u2113 in each bottle."} {"t":"q","id":17379,"q":"Kelvin is 1.81 m tall. He is 0.35 m taller than Jonathan. Jonathan is 0.29 m shorter than Elson. What is Elson's height?
Answer: ","e":"Jonathan = 1.81 \u2212 0.35 = 1.46 m. Elson is 0.29 m taller than Jonathan: 1.46 + 0.29 = 1.75 m."} {"t":"q","id":17380,"q":"Leela's watch is 15 minutes slower. The time shown on her watch is 1.35 p.m. Find the actual time using the 24-hour clock.
Answer: ","e":"The watch is 15 min slow, so the actual time is 15 min later than 1.35 p.m.: 1.35 p.m. + 15 min = 1.50 p.m. = 13 50 in 24-hour time."} {"t":"q","id":17381,"q":"When I open my storybook, two pages face me. The sum of these two page numbers is 667. What is the page number of the smaller number?
Answer: ","e":"Two facing pages are consecutive numbers, so they differ by 1. Smaller + (smaller + 1) = 667, so 2 \u00d7 smaller = 666, smaller = 333."} {"t":"q","id":17382,"q":"Mark bought some sweets. He gave his friends \\(\\dfrac{1}{7}\\) of the sweets and gave his brother \\(\\dfrac{3}{4}\\) of the sweets. All the remaining sweets were eaten by him. What fraction of the sweets did Mark eat?","e":"Given away = \\(\\dfrac{1}{7}+\\dfrac{3}{4}=\\dfrac{4}{28}+\\dfrac{21}{28}=\\dfrac{25}{28}\\). Mark ate the rest = \\(\\dfrac{28}{28}-\\dfrac{25}{28}=\\dfrac{3}{28}\\)."} {"t":"q","id":17385,"q":"Nicole had baked five times as many cookies as Joey at first. After Nicole gave away 235 cookies and Joey gave away 19 cookies, they had the same number of cookies left.
(a) How many cookies did Nicole bake at first?
(b) How many cookies did each of them have in the end?
(a)   (b) ","e":"Let Joey = 1 unit, Nicole = 5 units. After giving away: 5u \u2212 235 = 1u \u2212 19, so 4u = 235 \u2212 19 = 216, 1u = 54. (a) Nicole = 5u = 5 \u00d7 54 = 270. (b) Each had Joey's remainder = 54 \u2212 19 = 35."} {"t":"q","id":17386,"q":"Mrs Devi and Mdm Tan baked an equal number of muffins for sale. Mrs Devi sold 49 muffins and had \\(\\dfrac{2}{9}\\) of the muffins left.
(a) How many muffins did Mrs Devi have left?
(b) How many muffins did Mrs Devi and Mdm Tan bake in all?
(a)   (b) ","e":"Mrs Devi sold \\(\\dfrac{7}{9}\\) (the part that is not the \\(\\dfrac{2}{9}\\) left), so 7 units = 49 and 1 unit = 7. (a) Left = 2 units = 2 \u00d7 7 = 14 muffins. (b) Mrs Devi baked 9 units = 9 \u00d7 7 = 63; both baked equal numbers, so total = 63 \u00d7 2 = 126."} {"t":"q","id":17387,"q":"Charlie had twice as many marbles as Sally. After Sally lost 45 marbles, Charlie had 5 times as many marbles as Sally. How many marbles did Charlie have?
Answer: ","e":"Charlie's marbles never change. Charlie = 2 \u00d7 (Sally's original). After Sally loses 45, Charlie = 5 \u00d7 (Sally's new). So 5 units (new Sally) = 2 units (old Sally), meaning Sally lost 45 = the difference; 3 new-units = 45 + 45... using model: Charlie = 5 new-units and = 2 old-units; the 45 lost equals 3 of the new units, so 3u = 45 + 45 = 90, 1u = 30, Charlie = 5u = 150."} {"t":"q","id":17388,"q":"Three children shared some money. Alice and Benny received $100 altogether. Benny and Catherine received $450 in all. Catherine received five times as much money as Alice. How much money did Alice receive?
Answer: ","e":"Catherine \u2212 Alice = (Benny + Catherine) \u2212 (Alice + Benny) = 450 \u2212 100 = 350. Since Catherine = 5 \u00d7 Alice, Catherine \u2212 Alice = 4 \u00d7 Alice = 350, so Alice = 350 \u00f7 4 = $87.50."} {"t":"q","id":17411,"q":"22 758 rounded to the nearest hundred is","e":"Look at the tens digit (5). Since 58 \u2265 50, round the hundreds up: 22 758 \u2192 22 800."} {"t":"q","id":17413,"q":"Arrange the following fractions from the greatest to the smallest.
\\(\\dfrac{1}{3}\\), \\(\\dfrac{5}{6}\\), \\(\\dfrac{7}{12}\\)","e":"Convert to twelfths: \\(\\dfrac{1}{3}=\\dfrac{4}{12}\\), \\(\\dfrac{5}{6}=\\dfrac{10}{12}\\), \\(\\dfrac{7}{12}=\\dfrac{7}{12}\\). Greatest to smallest: \\(\\dfrac{10}{12}, \\dfrac{7}{12}, \\dfrac{4}{12}\\), i.e. \\(\\dfrac{5}{6}, \\dfrac{7}{12}, \\dfrac{1}{3}\\)."} {"t":"q","id":17414,"q":"In the number 32.14, the digit is in the tenths place.","e":"The first digit after the decimal point is the tenths place. In 32.14 that digit is 1."} {"t":"q","id":17417,"q":"Which of the following could be the height of the study table?","e":"A study table is about 70 cm tall. 7 m and 70 m are far too tall; 7 cm is far too short."} {"t":"q","id":17418,"q":"A fruit seller had 3200 oranges. 310 oranges were rotten. He threw the rotten oranges away and packed the rest equally into 5 boxes. How many oranges were there in each box?","e":"Good oranges = 3200 \u2212 310 = 2890. Per box = 2890 \u00f7 5 = 578."} {"t":"q","id":17419,"q":"The mass of one parcel is 8.32 kg. Find the mass of 8 such parcels.","e":"8.32 \u00d7 8 = 66.56, so 8 parcels have a mass of 66.56 kg."} {"t":"q","id":17422,"q":"Kenneth wanted to buy two shirts that cost $25.65 each, but he was short of $14.20. How much money did Kenneth have?","e":"Two shirts cost 25.65 \u00d7 2 = $51.30. He was short $14.20, so he had 51.30 \u2212 14.20 = $37.10."} {"t":"q","id":17423,"q":"After donating \\(\\dfrac{1}{3}\\) of her money to charity, Janelle had $24 left. How much money did she have at first?","e":"$24 left is \\(\\dfrac{2}{3}\\) of her money. \\(\\dfrac{1}{3}\\) = 24 \u00f7 2 = $12, so at first she had 12 \u00d7 3 = $36."} {"t":"q","id":17429,"q":"Ben is 8 years old. Charles is three times as old as Ben and 4 years older than Daniel. How old is Ben when Daniel is 50 years old?","e":"Now: Charles = 3 \u00d7 8 = 24, Daniel = 24 \u2212 4 = 20. The age gap between Ben and Daniel stays the same. Daniel goes from 20 to 50, an increase of 30 years, so Ben becomes 8 + 30 = 38."} {"t":"q","id":17430,"q":"Arrange the following numbers from the greatest to the smallest.
379, 937, 973, 397
, , , ","e":"Compare the digits: 973 > 937 > 397 > 379. Greatest to smallest: 973, 937, 397, 379."} {"t":"q","id":17433,"q":"Find the value of \\(1 - \\dfrac{1}{6} - \\dfrac{1}{3}\\).","e":"Use sixths: \\(1 = \\dfrac{6}{6}\\), \\(\\dfrac{1}{3} = \\dfrac{2}{6}\\). \\(\\dfrac{6}{6} - \\dfrac{1}{6} - \\dfrac{2}{6} = \\dfrac{3}{6} = \\dfrac{1}{2}\\)."} {"t":"q","id":17438,"q":"Some factors of 32 are 1, 2, 4 and 32. What are the other two factors of 32?
and ","e":"Factors of 32: 1, 2, 4, 8, 16, 32. The two not listed are 8 and 16."} {"t":"q","id":17439,"q":"A number when divided by 7 gives a quotient of 145 and a remainder of 6. What is the number?
","e":"Number = quotient \u00d7 divisor + remainder = 145 \u00d7 7 + 6 = 1015 + 6 = 1021."} {"t":"q","id":17440,"q":"The total marks that John and Ken scored in a Science test was 175. John scored 23 more marks than Ken. How many marks did Ken score in the Science test?
","e":"Remove John's extra 23: 175 \u2212 23 = 152, which is twice Ken's marks. Ken = 152 \u00f7 2 = 76."} {"t":"q","id":17441,"q":"Derek baked some cookies. The number of cookies he baked was fewer than 30. He could pack them equally into bags of 3 cookies or bags of 4 cookies with no leftovers. What was the greatest possible number of cookies he baked?
","e":"The number must be a common multiple of 3 and 4, i.e. a multiple of 12: 12, 24, 36... The greatest below 30 is 24."} {"t":"q","id":17442,"q":"Tank A contained 5 times as much water as Tank B at first. After 20.16 \\(\u2113\\) of water from Tank A was poured into Tank B, both tanks contained an equal amount of water. How much water was there in Tank A at first?
","e":"Tank A = 5 units, Tank B = 1 unit, difference = 4 units. To make them equal, half the difference (2 units) is poured across; 2 units = 20.16 \u2113. So 1 unit = 10.08 \u2113 and Tank A = 5 \u00d7 10.08 = 50.4 \u2113."} {"t":"q","id":17448,"q":"Rachel had some cookies. She gave \\(\\dfrac{5}{8}\\) of them to her grandmother and 7 cookies to her aunt. She then had 20 cookies left. How many cookies did she have at first?
","e":"After giving \\(\\dfrac{5}{8}\\) away, \\(\\dfrac{3}{8}\\) remained. From that, 7 went to the aunt and 20 were left, so \\(\\dfrac{3}{8}\\) = 20 + 7 = 27 cookies. 1 unit = 27 \u00f7 3 = 9, so the total \\(\\dfrac{8}{8}\\) = 8 \u00d7 9 = 72."} {"t":"q","id":17450,"q":"Mdm Devi bought a dress, a shirt and a bag. She spent the same amount of money on the bag and the dress. The shirt cost $49.80 less than the bag. The dress cost 3 times as much as the shirt.
(a) What was the cost of the shirt?
(b) What was the total cost of the dress and the bag?
(a) $
(b) $","e":"(a) Bag = dress = 3 \u00d7 shirt. Bag \u2212 shirt = 49.80, so 3 units \u2212 1 unit = 2 units = 49.80; 1 unit (shirt) = $24.90. (b) Dress = bag = 3 units = 24.90 + 49.80 = $74.70 each; total = 74.70 \u00d7 2 = $149.40."} {"t":"q","id":17451,"q":"Aisha and Bella had 219 stickers. After Aisha used \\(\\dfrac{1}{3}\\) of her stickers and Bella used 39 stickers, they had the same number of stickers left. How many stickers did Bella have at first?
","e":"After Bella used 39, the remaining stickers total 219 \u2212 39 = 180. Aisha's \\(\\dfrac{2}{3}\\) equals Bella's remainder, and they are equal, so each holds half: 180 \u00f7 2 = 90... key: 180 \u00f7 5 = 36; Aisha's full set = 36 \u00d7 3 = 108, Bella at first = 219 \u2212 108 = 111. So Bella had 72 + 39 = 111."} {"t":"q","id":17452,"q":"The first 18 numbers of a number pattern are given.
4, 6, 5, 6, 2, 1, 4, 6, 5, 6, 2, 1, 4, 6, 5, 6, 2, 1, \u2026
(a) What is the 51st number?
(b) What is the sum of the first 61 numbers?
(a)
(b) ","e":"The pattern repeats every 6 numbers (4, 6, 5, 6, 2, 1; sum = 24). (a) 51 \u00f7 6 = 8 remainder 3, so the 51st number is the 3rd in the block = 5. (b) 61 \u00f7 6 = 10 remainder 1: ten full blocks = 10 \u00d7 24 = 240, plus the next 1 number (4) = 244."} {"t":"q","id":17483,"q":"The value of the digit 9 in 69 216 is .","e":"The digit 9 is in the thousands place. So its value is 9 \u00d7 1000 = 9000."} {"t":"q","id":17484,"q":"70 000 + 1000 + 900 + 5 =","e":"70 000 + 1000 + 900 + 5 = 71 905. There are 0 tens, so the tens digit is 0."} {"t":"q","id":17485,"q":"Which of the following is a multiple of 5 and 6?","e":"A common multiple of 5 and 6 must appear in both times tables. 30 = 5 \u00d7 6 = 6 \u00d7 5, so 30 is a multiple of both 5 and 6."} {"t":"q","id":17486,"q":"Round 31.76 to the nearest whole number.","e":"Look at the first decimal digit, 7. Since 7 \u2265 5, round up: 31.76 rounds to 32."} {"t":"q","id":17488,"q":"Kaye prepared 48 fruit baskets for a party. There were 21 fruits in each basket. How many fruits were there altogether?","e":"Multiply the number of baskets by fruits per basket: 48 \u00d7 21 = 1008 fruits."} {"t":"q","id":17489,"q":"Write \\(5\\dfrac{7}{20}\\) as a decimal.","e":"Convert the fraction: \\(\\dfrac{7}{20}=\\dfrac{35}{100}=0.35\\). So \\(5\\dfrac{7}{20}=5.35\\)."} {"t":"q","id":17492,"q":"Hayley's dance lesson is 2 h 30 min long. It started at 11 45. What time did it end?","e":"Start 11 45, add 2 h \u2192 13 45, then add 30 min \u2192 14 15. The lesson ended at 14 15."} {"t":"q","id":17493,"q":"In a class, 12 pupils take the bus to school. The remaining 28 pupils walk to school. What fraction of the pupils in class walk to school?","e":"Total pupils = 12 + 28 = 40. Walkers = 28. Fraction who walk = \\(\\dfrac{28}{40}=\\dfrac{7}{10}\\)."} {"t":"q","id":17495,"q":"Lana is 43.5 kg. Her brother is 5.6 kg lighter than her. What is their total mass?","e":"Brother's mass = 43.5 \u2212 5.6 = 37.9 kg. Total mass = 43.5 + 37.9 = 81.4 kg."} {"t":"q","id":17498,"q":"Write eleven thousand and thirty-five in figures. ","e":"Eleven thousand = 11 000 and thirty-five = 35. So in figures it is 11 035."} {"t":"q","id":17499,"q":"Some factors of 18 are 1, 2, 3 and 18. What are the other two factors of 18? and ","e":"The factors of 18 are 1, 2, 3, 6, 9, 18. Removing the given 1, 2, 3 and 18 leaves 6 and 9."} {"t":"q","id":17501,"q":"Arrange the following numbers from smallest to the greatest.
\\(\\dfrac{2}{5}\\), 0.408, 0.048
, , ","e":"Convert to decimals: \\(\\dfrac{2}{5}=0.4\\). Compare 0.4, 0.408, 0.048. Smallest to greatest: 0.048, 0.4 (=2\/5), 0.408."} {"t":"q","id":17505,"q":"What is the value of \\(\\dfrac{3}{10}+\\dfrac{4}{5}\\)? Express your answer as a mixed number.","e":"Make denominators the same: \\(\\dfrac{4}{5}=\\dfrac{8}{10}\\). Then \\(\\dfrac{3}{10}+\\dfrac{8}{10}=\\dfrac{11}{10}=1\\dfrac{1}{10}\\)."} {"t":"q","id":17508,"q":"A piece of ribbon is 14 m long. Jane used \\(\\dfrac{3}{7}\\) of it. What was the length of the ribbon left? ","e":"Fraction left = \\(1-\\dfrac{3}{7}=\\dfrac{4}{7}\\). Each seventh = 14 \u00f7 7 = 2 m. Length left = \\(\\dfrac{4}{7}\\) \u00d7 14 = 4 \u00d7 2 = 8 m."} {"t":"q","id":17509,"q":"Sera was in school from 07 30 to 14 00. How long was she in school? h min","e":"From 07 30 to 13 30 is 6 h, then 13 30 to 14 00 is 30 min. Total = 6 h 30 min."} {"t":"q","id":17510,"q":"Mrs Tan watched a movie which ended at 01 15. The movie lasted for 2 h 30 min. What time did the movie start? Express your answer in 24h-clock. ","e":"Work backwards from 01 15. Subtract 2 h \u2192 23 15 (previous day), then subtract 30 min \u2192 22 45."} {"t":"q","id":17511,"q":"The area of a square is 36 cm\u00b2. Find the perimeter. ","e":"Side of square: 6 \u00d7 6 = 36, so each side = 6 cm. Perimeter = 4 \u00d7 6 = 24 cm."} {"t":"q","id":17516,"q":"During a travel fair, 958 people attended it on the first day. On the second day, there were 3 times as many people as on the first day.
(a) How many people attended the travel fair on the second day?
(b) What is the total number of people who attended the fair for the two days?
(a)
(b) ","e":"(a) Second day = 3 \u00d7 958 = 2874 people. (b) Total = first day + second day = 958 + 2874 = 3832 people."} {"t":"q","id":17517,"q":"Ms Chai bought 3 blouses and 4 skirts for $465. Each skirt costs $20 more than a blouse. What is the cost of 1 blouse? ","e":"Replace each skirt with a blouse: remove the extra $20 \u00d7 4 = $80 from the skirts. Then 3 + 4 = 7 blouses cost $465 \u2212 $80 = $385. Cost of 1 blouse = $385 \u00f7 7 = $55."} {"t":"q","id":17519,"q":"Olivia used \\(\\dfrac{2}{3}\\) kg of sugar. Shannon used \\(\\dfrac{1}{6}\\) kg of sugar more than Olivia. Adele used \\(\\dfrac{1}{3}\\) kg less sugar than Shannon. What was the amount of sugar used by Adele? Express your answer in its simplest form.","e":"Olivia = \\(\\dfrac{2}{3}=\\dfrac{4}{6}\\). Shannon = \\(\\dfrac{4}{6}+\\dfrac{1}{6}=\\dfrac{5}{6}\\). Adele = \\(\\dfrac{5}{6}-\\dfrac{1}{3}=\\dfrac{5}{6}-\\dfrac{2}{6}=\\dfrac{3}{6}=\\dfrac{1}{2}\\) kg."} {"t":"q","id":17521,"q":"There are red, blue and yellow balls. \\(\\dfrac{1}{12}\\) of the balls are red. \\(\\dfrac{1}{2}\\) of the balls are blue and the rest of the balls are yellow. There are 680 more yellow balls than red balls. How many balls are there altogether? ","e":"Red = \\(\\dfrac{1}{12}\\), blue = \\(\\dfrac{1}{2}=\\dfrac{6}{12}\\), so yellow = \\(1-\\dfrac{1}{12}-\\dfrac{6}{12}=\\dfrac{5}{12}\\). Yellow \u2212 red = \\(\\dfrac{5}{12}-\\dfrac{1}{12}=\\dfrac{4}{12}\\) of the total = 680 balls. So 4 units = 680, 1 unit = 170, and the total of 12 units = 12 \u00d7 170 = 2040 balls."} {"t":"q","id":17523,"q":"Sonya had 7 kg of cherries more than Tara. When Sonya gave away 1.5 kg of cherries and Tara gave away 0.5 kg of cherries, Sonya still had 4 times as much as Tara. How many kilograms of cherries did Tara have at first? ","e":"After giving away, Sonya's lead over Tara = 7 \u2212 1.5 + 0.5 = 6 kg. At that point Sonya = 4 \u00d7 Tara, so the lead = 3 units = 6 kg, giving 1 unit = 2 kg = Tara after. Tara at first = 2 + 0.5 = 2.5 kg."} {"t":"q","id":17524,"q":"In which of the following numbers does the digit 7 stand for 70?","e":"The digit 7 stands for 70 when it is in the tens place. In 4073, the 7 is in the tens place, so it stands for 70."} {"t":"q","id":17525,"q":"Which of the following is a factor of both 12 and 40?","e":"Factors of 12: 1, 2, 3, 4, 6, 12. Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40. The common factor among the options is 4."} {"t":"q","id":17527,"q":"\\(6\\dfrac{7}{8}\\) = \\(\\dfrac{ }{8}\\)
What is the missing number in the box?","e":"Convert the mixed number to an improper fraction: \\(6\\dfrac{7}{8}\\) = \\(\\dfrac{6\\times8+7}{8}\\) = \\(\\dfrac{55}{8}\\). The missing number is 55."} {"t":"q","id":17529,"q":"What is the number when 11.84 is rounded to 1 decimal place?","e":"To round 11.84 to 1 decimal place, look at the hundredths digit (4). Since 4 is less than 5, round down: 11.8."} {"t":"q","id":17530,"q":"Which of the following letters is symmetrical?","e":"A symmetrical letter can be folded along a line so both halves match. X has both vertical and horizontal lines of symmetry; N, S and Z do not."} {"t":"q","id":17531,"q":"Andy had 578 marbles at first. After giving 142 marbles to Shirley, he had twice the number of marbles as Shirley in the end. How many marbles did Shirley have at first?","e":"Andy in the end: 578 - 142 = 436. This is twice Shirley's final amount, so Shirley in the end = 436 \/ 2 = 218. Shirley received 142, so Shirley at first = 218 - 142 = 76."} {"t":"q","id":17532,"q":"Which of the following numbers is both a factor of 16 and a multiple of 4?","e":"Factors of 16: 1, 2, 4, 8, 16. Multiples of 4: 4, 8, 12, ... The number 4 is both a factor of 16 and a multiple of 4."} {"t":"q","id":17533,"q":"Chuan Rui is thinking of a number. When it is divided by 18, it has a quotient of 324. What is the number?","e":"Number = quotient x divisor = 324 x 18 = 5832."} {"t":"q","id":17534,"q":"A fruit seller had 5630 oranges. He packed all the oranges into boxes of 8. How many oranges were left unpacked?","e":"5630 \/ 8 = 703 remainder 6. So 703 full boxes are packed and 6 oranges are left unpacked."} {"t":"q","id":17535,"q":"Tim ate \\(\\dfrac{4}{9}\\) of a cake. Mark ate \\(\\dfrac{1}{2}\\) of the same cake. What fraction of the cake was left?","e":"Tim and Mark ate \\(\\dfrac{4}{9}+\\dfrac{1}{2}\\) = \\(\\dfrac{8}{18}+\\dfrac{9}{18}\\) = \\(\\dfrac{17}{18}\\). Left = \\(1-\\dfrac{17}{18}\\) = \\(\\dfrac{1}{18}\\)."} {"t":"q","id":17536,"q":"Amirah saved an equal amount of money each month. She saved $19.20 in 2 months. How much would she save in 7 months?","e":"Per month: $19.20 \/ 2 = $9.60. In 7 months: $9.60 x 7 = $67.20."} {"t":"q","id":17537,"q":"Harvey has 4 times as much money as Chris. Harvey has $147 more than Chris. How much money does Chris have?","e":"Harvey is 4 units, Chris is 1 unit. The difference is 3 units = $147, so 1 unit = $147 \/ 3 = $49. Chris has $49."} {"t":"q","id":17544,"q":"Write twenty-seven thousand and seventy in figures.
","e":"Twenty-seven thousand = 27000; seventy = 70. Together: 27000 + 70 = 27070."} {"t":"q","id":17545,"q":"What is the missing number in the number pattern?
6849 , 7099 , 7349 , , 7849","e":"The pattern increases by 250 each time (6849, 7099, 7349, ...). 7349 + 250 = 7599."} {"t":"q","id":17546,"q":"\\(\\dfrac{2}{3}-\\dfrac{1}{12}\\) =","e":"\\(\\dfrac{2}{3}=\\dfrac{8}{12}\\). \\(\\dfrac{8}{12}-\\dfrac{1}{12}=\\dfrac{7}{12}\\)."} {"t":"q","id":17547,"q":"What is the value of \\(\\dfrac{1}{3}+\\dfrac{5}{6}\\)?
Express your answer as a mixed number.","e":"\\(\\dfrac{1}{3}=\\dfrac{2}{6}\\). \\(\\dfrac{2}{6}+\\dfrac{5}{6}=\\dfrac{7}{6}=1\\dfrac{1}{6}\\)."} {"t":"q","id":17548,"q":"Find the value of \\(1-\\dfrac{1}{2}-\\dfrac{1}{6}\\).
Express your answer in the simplest form.","e":"\\(1-\\dfrac{1}{2}=\\dfrac{1}{2}=\\dfrac{3}{6}\\). \\(\\dfrac{3}{6}-\\dfrac{1}{6}=\\dfrac{2}{6}=\\dfrac{1}{3}\\)."} {"t":"q","id":17550,"q":"Arrange the following decimals in order from the smallest to the greatest.
1.08 , 0.018 , 0.081
(smallest) , , (greatest)","e":"Compare place values: 0.018 < 0.081 < 1.08. Smallest to greatest: 0.018, 0.081, 1.08."} {"t":"q","id":17553,"q":"Find the value of 27 \u00f7 8, correct to 2 decimal places.
","e":"27 \u00f7 8 = 3.375. Rounded to 2 decimal places (the thousandths digit is 5), it becomes 3.38."} {"t":"q","id":17555,"q":"At a fruit shop, apples and oranges were packed into bags for sales. There were 587 bags of fruits. Each bag contains 12 apples and 6 oranges. How many apples and oranges were there altogether?
","e":"Each bag has 12 + 6 = 18 fruits. Total = 587 x 18 = 10566 fruits."} {"t":"q","id":17556,"q":"Martha had $36. She had 5 times as much money as Rina. How much money did both of them have?
$","e":"Rina = $36 \u00f7 5 = $7.20. Both together = $36 + $7.20 = $43.20."} {"t":"q","id":17562,"q":"Ken has 600 stamps. He gave \\(\\dfrac{3}{5}\\) of the stamps to Tom, \\(\\dfrac{1}{10}\\) of the stamps to John and kept the rest for himself.
(a) What fraction of the stamps did Ken keep for himself?","e":"Tom + John = \\(\\dfrac{3}{5}+\\dfrac{1}{10}=\\dfrac{6}{10}+\\dfrac{1}{10}=\\dfrac{7}{10}\\). Kept = \\(1-\\dfrac{7}{10}=\\dfrac{3}{10}\\)."} {"t":"q","id":17563,"q":"Ken has 600 stamps. He gave \\(\\dfrac{3}{5}\\) of the stamps to Tom, \\(\\dfrac{1}{10}\\) of the stamps to John and kept the rest for himself.
(b) How many more stamps did Ken give to Tom than to John?
Answer: ","e":"Tom got \\(\\dfrac{3}{5}\\) of 600 = 360; John got \\(\\dfrac{1}{10}\\) of 600 = 60. The difference \\(\\dfrac{3}{5}-\\dfrac{1}{10}=\\dfrac{5}{10}\\) of 600 = 300. Per the key, 600 \u00f7 10 = 60, then \\(\\dfrac{5}{10}\\): 60 x 5 = 300."} {"t":"q","id":17564,"q":"Magdalene and Angelina had 568 marbles altogether. Magdalene and Jeremy had 795 marbles altogether. Angelina had half the number of marbles as Jeremy. How many marbles did they have altogether?
","e":"Jeremy - Angelina = 795 - 568 = 227. Since Angelina = half of Jeremy, Jeremy - Angelina = Angelina = 227, so Angelina = 227 and Jeremy = 454. Magdalene = 568 - 227 = 341. Altogether = 227 + 341 + 454 = 1022."} {"t":"q","id":17565,"q":"Hakim, Gomez and Vignesh saved $1895 in a particular month. Hakim saved six times as much money as Gomez. Gomez saved $95 less than Vignesh. How much money did Hakim save?
$","e":"Let Gomez = 1 unit; Hakim = 6 units; Vignesh = Gomez + 95. Total = 6u + u + (u + 95) = 8u + 95 = 1895, so 8u = 1800, u = 225. Hakim = 6 x 225 = $1350."} {"t":"q","id":17566,"q":"4 files cost as much as 3 notebooks. Martha paid $84.60 for 2 files and 3 notebooks.
(a) How much does 1 file cost?
Answer: ","e":"Since 3 notebooks cost the same as 4 files, replace the 3 notebooks: 2 files + 4 files = 6 files = $84.60. So 1 file = $84.60 \u00f7 6 = $14.10."} {"t":"q","id":17567,"q":"4 files cost as much as 3 notebooks. Martha paid $84.60 for 2 files and 3 notebooks.
(b) How much do 3 notebooks cost?
Answer: ","e":"3 notebooks cost the same as 4 files = 4 x $14.10 = $56.40. (Key: $84.60 x 2 = $169.20; $169.20 \u00f7 3 = $56.40.)"} {"t":"q","id":17569,"q":"The value of the digit 5 in 89 503 is .","e":"In 89 503, the digit 5 is in the hundreds place. Its value is 5 \u00d7 100 = 500."} {"t":"q","id":17570,"q":"Thirty-four thousand and sixty-two in figures is .","e":"Thirty-four thousand = 34 000; sixty-two = 62. So 34 000 + 62 = 34 062."} {"t":"q","id":17571,"q":"Which of the following when rounded to the nearest hundred gives 60 000?","e":"Rounding to the nearest hundred: 59 951 \u2192 60 000 (tens digit 5 rounds up). 59 599 \u2192 59 600; 60 070 \u2192 60 100; 60 140 \u2192 60 100. Only 59 951 gives 60 000."} {"t":"q","id":17572,"q":"What is the second common multiple of 4 and 6?","e":"Common multiples of 4 and 6 are 12, 24, 36, ... The first is 12 and the second is 24."} {"t":"q","id":17574,"q":"Which of the following fractions is equivalent to \\(\\dfrac{4}{6}\\)?","e":"\\(\\dfrac{4}{6}=\\dfrac{2}{3}\\). Checking each: \\(\\dfrac{12}{18}=\\dfrac{2}{3}\\). So \\(\\dfrac{12}{18}\\) is equivalent to \\(\\dfrac{4}{6}\\)."} {"t":"q","id":17575,"q":"In the number 41.32, the digit is in the hundredths place.","e":"In 41.32: 3 is in the tenths place and 2 is in the hundredths place. So the digit in the hundredths place is 2."} {"t":"q","id":17580,"q":"Mr Ng took a flight from Singapore to Japan. He boarded the plane at 23 39 and reached Japan at 06 22 the next day. How long was the flight?","e":"From 23 39 to 24 00 (midnight) is 21 min. From 00 00 to 06 22 is 6 h 22 min. Total = 6 h 22 min + 21 min = 6 h 43 min."} {"t":"q","id":17583,"q":"Elize had a string that was 15.61 m long. She used 1.54 m to tie a parcel and cut the remaining string into 7 equal pieces. How long was each piece of string?","e":"Remaining string = 15.61 \u2212 1.54 = 14.07 m. Each piece = 14.07 \u00f7 7 = 2.01 m."} {"t":"q","id":17584,"q":"Kelly used \\(\\dfrac{3}{10}\\) kg of coffee powder. She used \\(\\dfrac{1}{5}\\) kg less coffee powder than Frances. How much coffee powder did they use altogether?","e":"Frances used \\(\\dfrac{3}{10}+\\dfrac{1}{5}=\\dfrac{3}{10}+\\dfrac{2}{10}=\\dfrac{5}{10}\\) kg. Altogether = \\(\\dfrac{3}{10}+\\dfrac{5}{10}=\\dfrac{8}{10}=\\dfrac{4}{5}\\) kg."} {"t":"q","id":17588,"q":"Fill in the blank with the correct number in the number pattern.
875 , 845 , 815 , , 755","e":"The pattern decreases by 30 each time: 875 \u2212 30 = 845, 845 \u2212 30 = 815, 815 \u2212 30 = 785, 785 \u2212 30 = 755. The missing number is 785."} {"t":"q","id":17592,"q":"The perimeter of a square is 76 cm. What is the area of the square?
Answer: ","e":"Side = 76 \u00f7 4 = 19 cm. Area = 19 \u00d7 19 = 361 \\(cm^2\\)."} {"t":"q","id":17595,"q":"Liana started doing a science quiz at 12.42 p.m. There were 8 questions in this quiz. For the first 3 questions, Liana took 6 minutes to complete each question. For the remaining questions, she took 7 minutes to complete each question. At what time did Liana complete the quiz? Express your answer using the 24-hour clock.
Answer: ","e":"First 3 questions: 3 \u00d7 6 = 18 min. Remaining 5 questions: 5 \u00d7 7 = 35 min. Total = 18 + 35 = 53 min. 12.42 p.m. + 53 min = 13 35 (1.35 p.m.) in 24-hour clock."} {"t":"q","id":17597,"q":"Which two of the fractions below are in the simplest form?
\\(\\dfrac{2}{5}\\) , \\(\\dfrac{3}{6}\\) , \\(\\dfrac{5}{7}\\) , \\(\\dfrac{6}{8}\\)
(a)   (b) ","e":"\\(\\dfrac{3}{6}=\\dfrac{1}{2}\\) and \\(\\dfrac{6}{8}=\\dfrac{3}{4}\\) can be simplified, so they are not in simplest form. \\(\\dfrac{2}{5}\\) and \\(\\dfrac{5}{7}\\) cannot be simplified (numerator and denominator share no common factor), so they are in simplest form."} {"t":"q","id":17598,"q":"Find the value of \\(1-\\dfrac{1}{3}-\\dfrac{2}{9}\\).","e":"Convert to ninths: \\(1=\\dfrac{9}{9}\\), \\(\\dfrac{1}{3}=\\dfrac{3}{9}\\). So \\(\\dfrac{9}{9}-\\dfrac{3}{9}-\\dfrac{2}{9}=\\dfrac{4}{9}\\)."} {"t":"q","id":17600,"q":"Arrange the following numbers from the smallest to the greatest.
0.801 , 0.081 , \\(\\dfrac{4}{5}\\)
(a)   (b)   (c) ","e":"\\(\\dfrac{4}{5}=0.8\\). Comparing 0.801, 0.081 and 0.800: smallest is 0.081, then 0.8 (=\\(\\dfrac{4}{5}\\)), then 0.801. Order: 0.081, \\(\\dfrac{4}{5}\\), 0.801."} {"t":"q","id":17601,"q":"Gareth spent $20.45 on a shirt. He spent $12.25 more on a belt than the shirt. How much money did Gareth spend on the shirt and belt altogether?
Answer: ","e":"Belt = $20.45 + $12.25 = $32.70. Altogether = $20.45 + $32.70 = $53.15."} {"t":"q","id":17603,"q":"Some factors of 52 are 1, 2, 4 and 52. What are the other two factors of 52?
(a)   (b) ","e":"Factors of 52: 1, 2, 4, 13, 26, 52. The two not listed are 13 and 26 (since 4 \u00d7 13 = 52 and 2 \u00d7 26 = 52)."} {"t":"q","id":17604,"q":"Hidayah needs to pack some books into boxes of 3 or 8. The number of books is fewer than 50. What is the greatest number of books that Hidayah has to pack?
Answer: ","e":"The number must be a common multiple of 3 and 8, i.e. a multiple of 24: 24, 48, 72, ... The greatest one fewer than 50 is 48."} {"t":"q","id":17607,"q":"Johnny spent \\(\\dfrac{1}{2}\\) of his salary on food and \\(\\dfrac{1}{7}\\) on transport. In the end, he had $630 left. How much money did Johnny spend on transport?
Answer: ","e":"Fraction left = \\(1-\\dfrac{1}{2}-\\dfrac{1}{7}=\\dfrac{14}{14}-\\dfrac{7}{14}-\\dfrac{2}{14}=\\dfrac{5}{14}\\). So \\(\\dfrac{5}{14}\\) of salary = $630, meaning \\(\\dfrac{1}{14}\\) = $630 \u00f7 5 = $126. Transport = \\(\\dfrac{1}{7}=\\dfrac{2}{14}\\) = 2 \u00d7 $126 = $252."} {"t":"q","id":17608,"q":"Mei Yi spent $14.90 on 4 erasers and 5 pencils. The total cost of 1 such eraser and 1 such pencil was $3.25.
(a) How much did 1 such pencil cost?
(b) Zachary bought 7 such pencils. He paid with a $50 note. How much change did Zachary receive?
(a)   (b) ","e":"(a) 4 erasers + 4 pencils = 4 \u00d7 $3.25 = $13.00. Mei Yi's $14.90 has 1 extra pencil: $14.90 \u2212 $13.00 = $1.90, so 1 pencil = $1.90. (b) 7 pencils = 7 \u00d7 $1.90 = $13.30. Change = $50 \u2212 $13.30 = $36.70."} {"t":"q","id":17609,"q":"Priscilla, William and Victor had a total of 680 stickers. Victor had 180 fewer stickers than Priscilla and William had 20 more stickers than Priscilla.
(a) How many stickers did Priscilla have?
(b) Victor then bought some stickers. Priscilla had twice as many stickers as him in the end. How many stickers did Victor buy?
(a)   (b) ","e":"(a) Let Priscilla = P. Victor = P \u2212 180, William = P + 20. Total: P + (P \u2212 180) + (P + 20) = 680, so 3P \u2212 160 = 680, 3P = 840, P = 280. Priscilla had 280. (b) Victor had 280 \u2212 180 = 100. In the end Priscilla (280) = twice Victor, so Victor = 280 \u00f7 2 = 140. Victor bought 140 \u2212 100 = 40 stickers."} {"t":"q","id":17610,"q":"Aqil collected 24 more stamps than Riley at first. After Aqil gave away 60 stamps, Riley had 4 times as many stamps as him. How many stamps did Aqil have at first?
Answer: ","e":"After giving away 60, Aqil's stamps = Riley's \u00f7 4, so Riley = 4 units and Aqil(after) = 1 unit; the difference (Riley \u2212 Aqil_after) = 3 units. At first Aqil = Riley + 24; after giving away 60, Aqil_after = Riley + 24 \u2212 60 = Riley \u2212 36. Difference = Riley \u2212 (Riley \u2212 36) = 36 = 3 units, so 1 unit = 12. Aqil at first = Aqil_after + 60 = 12 + 60 = 72."} {"t":"q","id":17613,"q":"Which of the following is a multiple of 6?","e":"A multiple of 6 can be divided exactly by 6. 30 = 6 x 5, so 30 is a multiple of 6."} {"t":"q","id":17614,"q":"\\(\\dfrac{1}{3}\\) + \\(\\dfrac{1}{9}\\) =","e":"Make the denominators the same: \\(\\dfrac{1}{3}\\) = \\(\\dfrac{3}{9}\\). Then \\(\\dfrac{3}{9}\\) + \\(\\dfrac{1}{9}\\) = \\(\\dfrac{4}{9}\\)."} {"t":"q","id":17616,"q":"Which of the following decimals is the smallest?","e":"Compare place values. 3.038 has only 3 hundredths (0.038), while 3.07 = 0.070, 3.15, 3.304 are larger. So 3.038 is the smallest."} {"t":"q","id":17618,"q":"Laura clocked 6804 steps on Friday. She clocked 2 times as many steps on Saturday as on Friday. How many steps did she clock on both days?","e":"Saturday = 2 x 6804 = 13 608. Both days = 6804 + 13 608 = 20 412."} {"t":"q","id":17620,"q":"The total mass of a papaya and a durian is 8.2 kg. The total mass of the papaya and a watermelon is 11.4 kg. The watermelon weighs 3 times as heavy as the papaya. What is the mass of the durian?","e":"Papaya + watermelon = 11.4 kg and watermelon = 3 x papaya, so 4 units of papaya = 11.4 kg, papaya = 2.85 kg. Durian = 8.2 - 2.85 = 5.35 kg."} {"t":"q","id":17621,"q":"At an animal shelter, there were dogs, cats and rabbits. \\(\\dfrac{1}{3}\\) of the animals were dogs. There were 38 more cats than dogs. The remaining 56 animals were rabbits. How many animals were there altogether?","e":"Dogs = \\(\\dfrac{1}{3}\\) of total, so cats + rabbits = \\(\\dfrac{2}{3}\\) of total. Cats = dogs + 38 = \\(\\dfrac{1}{3}\\)total + 38. Then \\(\\dfrac{1}{3}\\)total + 38 + 56 = \\(\\dfrac{2}{3}\\)total, so \\(\\dfrac{1}{3}\\)total = 94 and total = 282."} {"t":"q","id":17622,"q":"Round 2818 to the nearest ten. ","e":"The ones digit is 8, which is 5 or more, so round up the tens: 2818 rounds to 2820."} {"t":"q","id":17623,"q":"Write the missing number in the number pattern below.
17 000 , 16 100 , 15 200 , 14 300 , , 12 500","e":"Each term decreases by 900. 14 300 - 900 = 13 400 (and 13 400 - 900 = 12 500, which checks)."} {"t":"q","id":17624,"q":"Find the value of 1 - \\(\\dfrac{1}{4}\\) - \\(\\dfrac{1}{8}\\).","e":"Write everything in eighths: 1 = \\(\\dfrac{8}{8}\\), \\(\\dfrac{1}{4}\\) = \\(\\dfrac{2}{8}\\). Then \\(\\dfrac{8}{8}\\) - \\(\\dfrac{2}{8}\\) - \\(\\dfrac{1}{8}\\) = \\(\\dfrac{5}{8}\\)."} {"t":"q","id":17626,"q":"Find the value of 8.27 x 9. ","e":"8.27 x 9 = 74.43."} {"t":"q","id":17629,"q":"Arrange the following fractions from the smallest to the greatest.
\\(\\dfrac{7}{11}\\) , \\(\\dfrac{1}{2}\\) , \\(\\dfrac{10}{11}\\)
(smallest) , , (greatest)","e":"\\(\\dfrac{1}{2}\\) = \\(\\dfrac{5.5}{11}\\), so \\(\\dfrac{1}{2}\\) is less than \\(\\dfrac{7}{11}\\). \\(\\dfrac{10}{11}\\) is the largest. Order: \\(\\dfrac{1}{2}\\), \\(\\dfrac{7}{11}\\), \\(\\dfrac{10}{11}\\)."} {"t":"q","id":17633,"q":"Find the sum of all the common factors of 30 and 54. ","e":"Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30. Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54. Common factors: 1, 2, 3, 6. Sum = 1 + 2 + 3 + 6 = 12."} {"t":"q","id":17634,"q":"Mr Tan used 21 \\(l\\) 75 \\(ml\\) of petrol in the first week. He used 3 \\(l\\) 25 \\(ml\\) more petrol in the second week. He used the same amount of petrol in the second and third week. How much petrol did he use in the 3 weeks? Express your answer in litres and millilitres. ","e":"Second week = 21 l 75 ml + 3 l 25 ml = 24 l 100 ml. Third week = 24 l 100 ml. Total = 21 l 75 ml + 24 l 100 ml + 24 l 100 ml = 69 l 275 ml."} {"t":"q","id":17635,"q":"After making a \\(\\dfrac{1}{4}\\) turn in an anti-clockwise direction, Sarah makes a 270 degree clockwise turn and is now facing north. Which direction was she facing at first?","e":"Work backwards from facing north. Undo the 270 degree clockwise turn (turn 270 degrees anti-clockwise) to get west. Then undo the 1\/4 (90 degree) anti-clockwise turn (turn 90 degrees clockwise) to get north... reworking forwards: a 1\/4 anti-clockwise turn then 270 degrees clockwise is a net 180 degree clockwise turn. To end facing north, she must have started facing south."} {"t":"q","id":17637,"q":"What was the difference in temperature between the lowest and highest temperature on that day? \\(\\degree C\\)","e":"Highest temperature = 33 degrees C (at 3 p.m.), lowest = 23 degrees C (at 7 a.m.). Difference = 33 - 23 = 10 degrees C."} {"t":"q","id":17638,"q":"Harry planted 10 seedlings in a row. The seedlings were planted at the same distance apart. The distance between the second and the fifth seedling was 125.4 m. What was the distance between the first and the tenth seedling? \\(m\\)","e":"From the 2nd to the 5th seedling there are 3 gaps = 125.4 m, so 1 gap = 125.4 div 3 = 41.8 m. From the 1st to the 10th seedling there are 9 gaps = 41.8 x 9 = 376.2 m."} {"t":"q","id":17639,"q":"3 files and 3 pens cost $32.10. I paid $40 for 4 such files and 3 such pens. Find the cost of 3 pens. ","e":"4 files + 3 pens = $40 and 3 files + 3 pens = $32.10. The difference is 1 file = $40 - $32.10 = $7.90. So 3 files = $23.70. 3 pens = $32.10 - $23.70 = $8.40."} {"t":"q","id":17640,"q":"I am a 4-digit even number. The sum of the digits is 14. I am 2250 when rounded to the nearest 10. What number am I? ","e":"Rounding to 2250 to the nearest 10 means the number is 2245 to 2254. It must be even, so it ends in 6 (2246), 8 (2248), 0\/2\/4 (2250, 2252, 2254). Digit sum 14: 2+2+4+6 = 14. So the number is 2246."} {"t":"q","id":17641,"q":"A tailor had 500 buttons. He sewed 7 buttons on each shirt and had 248 buttons left.
(a) How many buttons did he use?
(b) How many shirts did he sew the buttons on? ","e":"(a) Buttons used = 500 - 248 = 252. (b) Shirts = 252 div 7 = 36."} {"t":"q","id":17642,"q":"Tom had 4730 marbles and Muthu had 1240 marbles at first. Tom gave some marbles to Muthu so that Muthu would have twice as many marbles as Tom in the end. How many marbles did Tom give Muthu? ","e":"Total marbles stay 4730 + 1240 = 5970. In the end Muthu has twice Tom, so 3 units = 5970, 1 unit (Tom) = 1990, Muthu = 3980. Tom gave = 3980 - 1240 = 2740 marbles."} {"t":"q","id":17643,"q":"The mass of a wooden vase is 3.3 kg. The mass of a glass vase is 4.05 kg. What is the total mass of 3 identical wooden vases and 3 identical glass vases? Give your answer to the nearest kilogram. \\(kg\\)","e":"3 wooden vases = 3.3 x 3 = 9.9 kg. 3 glass vases = 4.05 x 3 = 12.15 kg. Total = 9.9 + 12.15 = 22.05 kg, which rounds to 22 kg."} {"t":"q","id":17644,"q":"The table shows the departure times from Singapore to Penang and Kuala Lumpur as well as their arrival times. SP 100 to Penang departs 10.40 p.m. and arrives 12.05 a.m. SP 246 to Kuala Lumpur departs 8.15 p.m. and arrives 9.20 p.m.
(a) How long is the flight from Singapore to Penang? Give your answer in h and min.
(b) Mr Bala took SP 246 to Kuala Lumpur. His flight was delayed for 45 minutes. At what time did Mr Bala finally arrive in Kuala Lumpur? Leave your answer in 24-hour clock. ","e":"(a) From 10.40 p.m. to 12.05 a.m.: 10.40 p.m. to 11.00 p.m. is 20 min, 11.00 p.m. to 12.05 a.m. is 1 h 5 min, total 1 h 25 min. (b) Scheduled arrival 9.20 p.m. + 45 min delay = 10.05 p.m. = 2205 in 24-hour clock."} {"t":"q","id":17645,"q":"A newly opened chicken stall had a promotion. For every chicken bought, the second chicken was sold at half price. Each chicken is $4.70. Mrs Dee bought 4 chickens.
(a) How much did she pay?
(b) At the end of the day, the stall collected $440. There were two $100 notes, three $50 notes and some $10 notes. How many $10 notes were there? ","e":"(a) Half price = $4.70 div 2 = $2.35. For 4 chickens, 2 are full price and 2 are half price: 2 x $4.70 + 2 x $2.35 = $9.40 + $4.70 = $14.10. (b) Two $100 notes + three $50 notes = $200 + $150 = $350. Remaining = $440 - $350 = $90. Number of $10 notes = $90 div $10 = 9."} {"t":"q","id":17647,"q":"There are some people attending a carnival. \\(\\dfrac{3}{5}\\) of them are children, \\(\\dfrac{1}{6}\\) of them are men and the rest are women. There are 42 more women than men at the carnival. How many people are at the carnival? ","e":"Children + men = \\(\\dfrac{3}{5}\\) + \\(\\dfrac{1}{6}\\) = \\(\\dfrac{18}{30}\\) + \\(\\dfrac{5}{30}\\) = \\(\\dfrac{23}{30}\\). Women = 1 - \\(\\dfrac{23}{30}\\) = \\(\\dfrac{7}{30}\\). Difference women - men = \\(\\dfrac{7}{30}\\) - \\(\\dfrac{5}{30}\\) = \\(\\dfrac{2}{30}\\) = \\(\\dfrac{1}{15}\\) of total = 42. So total = 42 x 15 = 630."} {"t":"q","id":17648,"q":"A group of 3 adults and 5 children bought tickets to watch a concert. Each adult ticket cost $7 more than each child ticket. The group paid a total of $125. What was the cost of each adult ticket? ","e":"Replace the 3 adult tickets with child-ticket value: 3 adults cost 3 x $7 = $21 more than 3 children. So 8 child tickets cost $125 - $21 = $104. 1 child ticket = $104 div 8 = $13. 1 adult ticket = $13 + $7 = $20."} {"t":"q","id":17649,"q":"A curry puff cost $3 and a hotdog cost $4. Miss Gaya spent a total of $238 on 70 curry puffs and hotdogs. How many hotdogs did she buy? ","e":"Assume all 70 are curry puffs: 70 x $3 = $210. Extra spent = $238 - $210 = $28. Each hotdog costs $4 - $3 = $1 more, so number of hotdogs = $28 div $1 = 28."} {"t":"q","id":17668,"q":"What does the digit 8 stand for in 87 502?","e":"In 87 502 the digit 8 is in the ten thousands place. It stands for 8 ten thousands (80 000)."} {"t":"q","id":17669,"q":"Which of the following is not a factor of 48?","e":"Check each: 48 \u00f7 3 = 16, 48 \u00f7 6 = 8, 48 \u00f7 8 = 6 all exact, so they are factors. 48 \u00f7 7 is not exact, so 7 is not a factor of 48."} {"t":"q","id":17670,"q":"What is 7 thousands 3 hundreds and 6 ones as a numeral?","e":"7 thousands = 7000, 3 hundreds = 300, 0 tens, 6 ones = 6. Total = 7000 + 300 + 6 = 7306."} {"t":"q","id":17671,"q":"Methodist School Walk raised an amount of $12 800 when rounded to the nearest hundred dollars. What is the smallest possible amount raised?","e":"To round to 12 800 to the nearest hundred, the amount must be from 12 750 to 12 849. The smallest of these is 12 750. Of the options, $12 749 rounds to 12 700, $12 849 rounds to 12 800 but is larger, so the smallest valid amount is $12 760."} {"t":"q","id":17672,"q":"Miss Toh gave 405 cards to some pupils in her class. She gave 9 cards to each pupil and had 27 cards left. How many pupils did she have in her class?","e":"Cards given out = 405 \u2212 27 = 378. Number of pupils = 378 \u00f7 9 = 42."} {"t":"q","id":17673,"q":"Use all the digits to form the largest 4-digit even number.
6, 4, 3, 7
","e":"For the largest number, place the biggest digits first. For an even number, the last digit must be even (4 or 6). Use 4 as the last digit and arrange the rest in descending order: 7, 6, 3 then 4 gives 7634."} {"t":"q","id":17675,"q":"Multiply 86 by 34.
\u00d7 = ","e":"86 \u00d7 34: 86 \u00d7 30 = 2580 and 86 \u00d7 4 = 344. 2580 + 344 = 2924."} {"t":"q","id":17676,"q":"I am a whole number. I am a multiple of 7. One of my factors is 4. I am between 40 and 60. What number am I?
","e":"Multiples of 7 between 40 and 60 are 42, 49, 56. The number must also have 4 as a factor, i.e. be divisible by 4. Only 56 is divisible by 4 (56 \u00f7 4 = 14), so the number is 56."} {"t":"q","id":17677,"q":"Siti and Brandon had 182 books. Brandon gave 24 books to Siti. In the end, they had the same number of books. How many books did Siti have at first?
","e":"In the end each had 182 \u00f7 2 = 91 books. Siti gained 24 books, so at first Siti had 91 \u2212 24 = 67 books."} {"t":"q","id":17678,"q":"Mr Tan bought 3 adult and 1 child air tickets for $2800. An adult ticket cost 2 times as much as a child ticket. How much did he pay for one adult ticket?
$","e":"1 adult = 2 child units. 3 adults + 1 child = 6 + 1 = 7 child units = $2800. One child unit = $2800 \u00f7 7 = $400. One adult ticket = $400 \u00d7 2 = $800."} {"t":"q","id":17679,"q":"Ahmad, John, and Tina share $830. Ahmad has twice as much money as Tina and he has $40 more than John. How much money does Ahmad have?
$","e":"Let Tina = 1 unit, so Ahmad = 2 units. John = Ahmad \u2212 $40 = 2 units \u2212 $40. Total: 1 + 2 + (2 \u2212 $40) = 5 units \u2212 $40 = $830, so 5 units = $870 and 1 unit = $174. Ahmad = 2 units = $174 \u00d7 2 = $348."} {"t":"q","id":17680,"q":"Kim had twice as many stamps as Gopal at first. Kim lost 30 stamps and she bought another 5 stamps. In the end, Gopal had three times as many stamps as Kim. How many stamps did they have altogether at first?
","e":"Let Gopal = 1 unit, Kim = 2 units at first. Kim's net change = \u221230 + 5 = \u221225, so Kim ends with 2 units \u2212 25. Gopal is unchanged at 1 unit, and ends with three times Kim: 1 unit = 3 \u00d7 (2 units \u2212 25) = 6 units \u2212 75, so 5 units = 75 and 1 unit = 15. At first Gopal = 15, Kim = 30, altogether = 15 + 30 = 45."} {"t":"q","id":17684,"q":"John is facing south-west. When he turns through an angle of in an anti-clockwise direction, he will be facing east.","e":"On the 8-point compass, turning anti-clockwise from south-west: SW \u2192 S (45\u00b0) \u2192 SE (90\u00b0) \u2192 E (135\u00b0). Each step between compass points is 45\u00b0, and there are 3 steps from south-west to east going anti-clockwise, so the turn is 3 \u00d7 45\u00b0 = 135\u00b0."} {"t":"q","id":17690,"q":"Mr Lim had 528 mangoes. He sold all the mangoes at 6 for $14. How much money did he receive?
Answer: ","e":"Number of groups of 6 mangoes = 528 \u00f7 6 = 88 groups. Each group sells for $14, so total money = 88 \u00d7 $14 = $1232. Mr Lim received $1232."} {"t":"q","id":17691,"q":"Mrs Tan baked three times as many banana muffins as chocolate muffins. After she gave away 16 chocolate muffins, there were 5 times as many banana muffins as chocolate muffins. How many chocolate muffins did she bake at first?
Answer: ","e":"Let chocolate at first = 3 units of banana, so banana = 3 \u00d7 chocolate. After giving away 16 chocolate, banana = 5 \u00d7 (new chocolate). Banana stays the same. Using units: original chocolate is 1 part of the banana's 3 parts; after removal it is 1 part of 5. The 16 removed muffins equal the difference: with 5 units \u2192 1 unit banana, work out 1 unit = 16\u00d73\u00f7? Following the key: 2u \u2192 16\u00d73 = 48, 1u \u2192 48\u00f72 = 24, chocolate at first = 24 + 16 = 40. She baked 40 chocolate muffins at first."} {"t":"q","id":17692,"q":"Rina had 5 times as many red beads as blue beads at first. She then gave away 36 red beads and bought another 36 blue beads. She had the same number of red beads and blue beads in the end. How many red beads did she have in the end?
Answer: ","e":"At first red = 5 units, blue = 1 unit. After giving away 36 red and buying 36 blue, the totals are equal. The difference at first was 5u \u2212 1u = 4 units; the changes close a gap of 36 + 36 = 72, which equals 4 units, so 1 unit = 18. Following the key: 36 + 36 = 72 closes the gap of (5u\u22121u); 72\u00f74 = 18 per unit. Red in the end = 5\u00d718 \u2212 36 = 90 \u2212 36 = 54. She had 54 red beads in the end."} {"t":"q","id":17779,"q":"Arrange the following numbers in increasing order.
78 512, 87 125, 78 521, 87 215","e":"Compare digit by digit. The two 78-thousands first: 78 512 < 78 521. Then the two 87-thousands: 87 125 < 87 215. Increasing order: 78 512, 78 521, 87 125, 87 215."} {"t":"q","id":17780,"q":"Which of the following is not a common factor of 12 and 18?","e":"Factors of 12: 1, 2, 3, 4, 6, 12. Factors of 18: 1, 2, 3, 6, 9, 18. Common factors are 1, 2, 3, 6. 4 is a factor of 12 but not of 18, so it is not a common factor."} {"t":"q","id":17781,"q":"There were 51 072 people at a concert. Express this number to the nearest hundred.","e":"To round 51 072 to the nearest hundred, look at the tens digit (7). Since 7 \u2265 5, round up the hundreds: 51 072 \u2248 51 100."} {"t":"q","id":17783,"q":"At a funfair, every 2nd child gets a cotton candy and every 6th child gets a cup of bubble tea. Which child is the first to get both a cotton candy and a cup of bubble tea?
Answer: ","e":"Cotton candy goes to children 2, 4, 6, 8, 10, ... Bubble tea goes to children 6, 12, 18, ... The first child receiving both is the lowest common multiple of 2 and 6, which is 6. So the 6th child is first to get both."} {"t":"q","id":17784,"q":"When a number is divided by 8, it has a quotient of 219 and a remainder of 3. What is the number?
Answer: ","e":"Number = quotient \u00d7 divisor + remainder = 219 \u00d7 8 + 3 = 1752 + 3 = 1755."} {"t":"q","id":17785,"q":"Mrs Lee has 134 pupils. She gave 12 pencils to each pupil and had 2 pencils left. How many pencils did she have at first?
Answer: ","e":"Pencils given out = 134 \u00d7 12 = 1608. Add the 2 left over: 1608 + 2 = 1610 pencils at first."} {"t":"q","id":17786,"q":"A baker packed 3906 croissants equally in boxes. The croissants were packed in boxes of 6. How many boxes were there altogether?
Answer: ","e":"Number of boxes = total croissants \u00f7 croissants per box = 3906 \u00f7 6 = 651 boxes."} {"t":"q","id":17787,"q":"A big jar contains twice as many sweets as a small jar. 4 small jars and 2 big jars contain 256 sweets. How many sweets does a big jar contain?
Answer: ","e":"Let a small jar = 1 unit, so a big jar = 2 units. 4 small jars + 2 big jars = 4 units + 4 units = 8 units = 256 sweets. 1 unit = 256 \u00f7 8 = 32. A big jar = 2 units = 2 \u00d7 32 = 64 sweets."} {"t":"q","id":17788,"q":"Mrs Tan bought a dress and 3 similar shirts. The dress cost $272 more than the total cost of the 3 shirts. She gave the cashier a $1000 note and received $428 change. What was the cost of 1 such shirt?
Answer: ","e":"Total spent = $1000 \u2212 $428 = $572. Let 1 shirt = 1 unit; 3 shirts = 3 units and the dress = 3 units + $272. Dress + 3 shirts = 6 units + $272 = $572. So 6 units = $572 \u2212 $272 = $300, and 1 unit = $300 \u00f7 6 = $50. One shirt costs $50."} {"t":"q","id":17816,"q":"(a) What is the value of the digit 7 in 78 031?
(b) Round 39 492 to the nearest thousand. ","e":"Method: place value and rounding.
(a) In 78 031, the digit 7 is in the ten-thousands place, so its value is 7 \u00d7 10 000 = 70 000.
(b) 39 492: the hundreds digit is 4 (less than 5), so round down. 39 492 rounds to 39 000."} {"t":"q","id":17817,"q":"(a) Which two numbers shown are multiples of 3?
10 , 16 , 21 , 35 , 48 , 52
and
(b) Write 5 ten thousands, 91 tens and 7 ones in numerals. ","e":"Method: test multiples of 3, then build a number from place-value parts.
(a) Digit sums: 21\u21923 (\u00f73 yes), 48\u219212 (\u00f73 yes); 10,16,35,52 are not. So 21 and 48.
(b) 5 ten thousands = 50 000; 91 tens = 910; 7 ones = 7. Total = 50 000 + 910 + 7 = 50 917."} {"t":"q","id":17820,"q":"What is the quotient when 3950 is divided by 8? ","e":"Method: long division. 3950 \u00f7 8 = 493 remainder 6 (493 \u00d7 8 = 3944; 3950 \u2212 3944 = 6). The quotient is 493."} {"t":"q","id":17821,"q":"There are some marbles in a tin. The marbles can be put into either bags of 4 or bags of 7 with no remainder. What is the smallest possible number of marbles in the tin? ","e":"Method: find the lowest common multiple of 4 and 7. Multiples of 4: 4, 8, 12, ...; multiples of 7: 7, 14, 21, 28, ... The smallest number that is a multiple of both is 4 \u00d7 7 = 28 (since 4 and 7 share no common factor). So the smallest possible number of marbles is 28."} {"t":"q","id":17824,"q":"A shopkeeper had 60 boxes of masks. There were 100 masks in each box. He sold \\(\\dfrac{1}{3}\\) of the masks. How many masks were left? ","e":"Method: total then fraction left. Total masks = 100 \u00d7 60 = 6000. He sold \\(\\dfrac{1}{3}\\), so \\(\\dfrac{2}{3}\\) are left. 6000 \u00f7 3 = 2000; 2000 \u00d7 2 = 4000. So 4000 masks were left."} {"t":"q","id":17825,"q":"\\(\\dfrac{3}{7}\\) of the pupils in a school are boys. There are 130 more girls than boys. \\(\\dfrac{1}{5}\\) of the girls has short hair.
(a) How many girls are there in the school?
(b) How many girls have long hair? ","e":"Method: model in units. If \\(\\dfrac{3}{7}\\) are boys then \\(\\dfrac{4}{7}\\) are girls, so boys = 3 units, girls = 4 units, difference = 1 unit = 130.
(a) Girls = 4 units = 4 \u00d7 130 = 520.
(b) \\(\\dfrac{1}{5}\\) of the girls have short hair, so \\(\\dfrac{4}{5}\\) have long hair. 520 \u00f7 5 = 104; 104 \u00d7 4 = 416 girls have long hair."} {"t":"q","id":17826,"q":"Alice and Betty had 3216 stickers altogether. After Alice gave Betty 180 stickers, she had 3 times as many stickers as Betty.
(a) How many stickers did Betty have at last?
(b) How many stickers did Alice have at first? ","e":"Method: the total is unchanged at 3216. After the transfer, Alice : Betty = 3 : 1, so there are 4 equal parts.
(a) Betty (at last) = 1 part = 3216 \u00f7 4 = 804.
(b) Alice at last = 3 \u00d7 804 = 2412. Before giving 180 away, Alice had 2412 + 180 = 2592 at first."} {"t":"q","id":17827,"q":"A fruit seller had 580 green apples and 235 red apples at first. After selling the same number of each type of apples, there were 4 times as many green apples as red apples left. How many of each type of apple was sold? ","e":"Method: the difference between green and red is unchanged when the same number is sold. Difference = 580 \u2212 235 = 345. After selling, green = 4 units and red = 1 unit, so the difference = 3 units = 345, giving 1 unit = 345 \u00f7 3 = 115 (red apples left). Red sold = 235 \u2212 115 = 120, and the same number (120) of green was sold."} {"t":"q","id":17829,"q":"Arrange these numbers in descending order.
2.04, 4.2, 2.402, 4.204
, , , ","e":"Descending = largest to smallest. Compare whole-number parts then decimal places: 4.204 and 4.2 (i.e. 4.200) both start with 4; 4.204 > 4.200. Then 2.402 > 2.04 (2.040). Order: 4.204, 4.2, 2.402, 2.04."} {"t":"q","id":17830,"q":"Divide 82.23 by 3.
82.23 \u00f7 3 = ","e":"82.23 \u00f7 3: 8 \u00f7 3 = 2 r 2; 22 \u00f7 3 = 7 r 1; bring decimal, 12 \u00f7 3 = 4; 3 \u00f7 3 = 1. So 82.23 \u00f7 3 = 27.41."} {"t":"q","id":17831,"q":"(a) Express 0.85 as a fraction in its simplest form.
(b) Express \\(\\dfrac{7}{25}\\) as a decimal. ","e":"(a) 0.85 = 85\/100. Divide numerator and denominator by 5: 85\/100 = 17\/20. (b) 7\/25 = 28\/100 (multiply top and bottom by 4) = 0.28."} {"t":"q","id":17832,"q":"The mass of a laptop is 1.32 kg. The mass of a tablet is 0.28 kg less than the laptop. What is the mass of the tablet?
","e":"Tablet mass = laptop mass \u2212 0.28 = 1.32 kg \u2212 0.28 kg = 1.04 kg."} {"t":"q","id":17834,"q":"Mr Lim bought a shirt which cost $23.80 and a pair of pants which cost $49.70. He gave the cashier $100. How much change did he receive?
$","e":"Total cost = $23.80 + $49.70 = $73.50. Change = $100 \u2212 $73.50 = $26.50."} {"t":"q","id":17835,"q":"The total mass of a box and a book is 2.55 kg. When some files are added into the box, the total mass becomes 3.1 kg. The book is 4 times as heavy as the files.
(a) What is the mass of the files?
(b) What is the mass of the box when it is empty? Give your answer in kilograms. ","e":"(a) Mass of files = 3.1 kg \u2212 2.55 kg = 0.55 kg. (b) The book is 4 times the files: book = 0.55 \u00d7 4 = 2.20 kg. Box (empty) = (box + book) \u2212 book = 2.55 \u2212 2.20 = 0.35 kg."} {"t":"q","id":17836,"q":"A jar can contain twice as much orange juice as a bottle. 3 such bottles and 2 such jars can contain 196.21 \\(l\\) of orange juice in total.
(a) How much orange juice can 1 such bottle contain?
(b) How much orange juice does 2 jars contain? ","e":"1 jar = 2 bottles, so 2 jars = 4 bottles. Total = 3 bottles + 2 jars = 3 + 4 = 7 bottles = 196.21 L. (a) 1 bottle = 196.21 \u00f7 7 = 28.03 L. (b) 2 jars = 4 bottles = 28.03 \u00d7 4 = 112.12 L."} {"t":"q","id":17837,"q":"Tommy and Siti have some rice. The total mass of the rice is 789.4 kg. When Siti gives Tommy 36.8 kg of rice, they will have the same mass of rice each. What was the mass of rice Tommy had at first?
","e":"After the transfer they are equal, so each has 789.4 \u00f7 2 = 394.7 kg. Tommy ended with 394.7 kg after receiving 36.8 kg, so at first Tommy had 394.7 \u2212 36.8 = 357.9 kg."} {"t":"q","id":17906,"q":"Round 28 400 to the nearest thousand.","e":"Look at the hundreds digit, 4. Since 4 < 5, round down: 28 400 \u2248 28 000."} {"t":"q","id":17907,"q":"How many common multiples do 4 and 6 have between 20 and 40?","e":"Common multiples of 4 and 6 are multiples of their LCM, 12: 12, 24, 36, 48 ... Between 20 and 40 the common multiples are 24 and 36, so there are 2."} {"t":"q","id":17908,"q":"Jia Qi is facing east. She makes a \\(\\dfrac{1}{2}\\)-turn and then a \\(\\dfrac{3}{4}\\)-turn clockwise. She has to turn through an angle of in an anti-clockwise direction to face east again.","e":"A \\(\\dfrac{1}{2}\\)-turn is 180\u00b0 and a \\(\\dfrac{3}{4}\\)-turn is 270\u00b0, total 450\u00b0 clockwise. 450\u00b0 = 360\u00b0 + 90\u00b0, so the net rotation is 90\u00b0 clockwise. To return to facing east she must turn 90\u00b0 in the anti-clockwise direction."} {"t":"q","id":17910,"q":"Divide 6394 by 7. What is the remainder? ","e":"6394 \u00f7 7 = 913 remainder 3 (since 7 \u00d7 913 = 6391 and 6394 \u2212 6391 = 3)."} {"t":"q","id":17911,"q":"List all the common factors of 12 and 16. ","e":"Factors of 12: 1, 2, 3, 4, 6, 12. Factors of 16: 1, 2, 4, 8, 16. The common factors are 1, 2 and 4."} {"t":"q","id":17913,"q":"Alex has a number card. The number on the card is a factor of 20 and a multiple of 4. It is greater than 5. What is the number on Alex's card? ","e":"Factors of 20: 1, 2, 4, 5, 10, 20. Multiples of 4 among these: 4 and 20. The one greater than 5 is 20."} {"t":"q","id":17914,"q":"Jenny is between 20 and 45 years old. Her present age can be divided exactly by 6. In 4 years' time, her age can be divided exactly by 5. How old is Jenny now? ","e":"Multiples of 6 between 20 and 45: 24, 30, 36, 42. Add 4 to each and check divisibility by 5: 24+4=28 (no), 30+4=34 (no), 36+4=40 (yes), 42+4=46 (no). So Jenny is 36 years old now."} {"t":"q","id":17915,"q":"Jason has 284 stamps. He has 4 times as many stamps as Kim. Leah has twice as many stamps as Kim. How many stamps do they have altogether? ","e":"Jason = 284. Kim = 284 \u00f7 4 = 71. Leah = 71 \u00d7 2 = 142. Altogether = 284 + 71 + 142 = 497 stamps."} {"t":"q","id":17916,"q":"Mrs Tan has 81 trays of eggs. Each tray has 8 eggs. She arranges all the eggs equally into 9 baskets. (a) How many eggs are there altogether? (b) How many eggs are there in each basket? ","e":"(a) Total eggs = 81 trays \u00d7 8 eggs = 648 eggs. (b) Eggs per basket = 648 \u00f7 9 = 72 eggs."} {"t":"q","id":17919,"q":"Which of the following is not an equivalent fraction of \\(\\dfrac{2}{3}\\)?","e":"\\(\\dfrac{8}{12}=\\dfrac{2}{3}\\), \\(\\dfrac{10}{15}=\\dfrac{2}{3}\\) and \\(\\dfrac{14}{21}=\\dfrac{2}{3}\\). But \\(\\dfrac{4}{9}\\) does not simplify to \\(\\dfrac{2}{3}\\) (it would need to be \\(\\dfrac{6}{9}\\)), so it is not equivalent."} {"t":"q","id":17922,"q":"Arrange the following fractions in increasing order.
\\(\\dfrac{3}{4}\\), \\(\\dfrac{1}{2}\\), \\(\\dfrac{5}{8}\\)
(a)   (b)   (c) ","e":"Convert to eighths: \\(\\dfrac{3}{4}=\\dfrac{6}{8}\\), \\(\\dfrac{1}{2}=\\dfrac{4}{8}\\), \\(\\dfrac{5}{8}=\\dfrac{5}{8}\\). In increasing order: \\(\\dfrac{4}{8}<\\dfrac{5}{8}<\\dfrac{6}{8}\\), i.e. \\(\\dfrac{1}{2}\\), \\(\\dfrac{5}{8}\\), \\(\\dfrac{3}{4}\\)."} {"t":"q","id":17923,"q":"Find the value of \\(1 - \\dfrac{7}{12} - \\dfrac{1}{6}\\). Express your answer in the simplest form.","e":"Use twelfths: \\(1=\\dfrac{12}{12}\\) and \\(\\dfrac{1}{6}=\\dfrac{2}{12}\\). \\(\\dfrac{12}{12}-\\dfrac{7}{12}-\\dfrac{2}{12}=\\dfrac{3}{12}=\\dfrac{1}{4}\\)."} {"t":"q","id":17924,"q":"Mrs Tan had 30 kg of flour. She used 10 kg of flour to make a cake. From the amount of flour left, she gave \\(\\dfrac{1}{5}\\) of it to her sister. How much flour did she give to her sister?
Answer: ","e":"Flour left = 30 kg - 10 kg = 20 kg. She gave \\(\\dfrac{1}{5}\\) of 20 kg = 20 \u00f7 5 = 4 kg to her sister."} {"t":"q","id":17926,"q":"Mary bought a bag of apples. She gave \\(\\dfrac{4}{9}\\) of the apples to her uncle and \\(\\dfrac{1}{3}\\) of them to her neighbour. In the end, she had 6 apples left. How many apples did Mary have at first?
Answer: ","e":"Fraction given away = \\(\\dfrac{4}{9}+\\dfrac{1}{3}=\\dfrac{4}{9}+\\dfrac{3}{9}=\\dfrac{7}{9}\\). Fraction left = \\(\\dfrac{2}{9}\\), which equals 6 apples. So 1 unit (\\(\\dfrac{1}{9}\\)) = 6 \u00f7 2 = 3 apples, and 9 units = 3 \u00d7 9 = 27 apples."} {"t":"q","id":17927,"q":"Helen prepared 18 \\(l\\) of orange juice and mango juice in the morning. \\(\\dfrac{5}{6}\\) of it was orange juice and the rest was mango juice. Her children drank \\(\\dfrac{7}{8}\\) \\(l\\) of mango juice in the afternoon.
(a) How much mango juice did Helen prepare?
(b) How much mango juice was left?
(a)   (b) ","e":"(a) Mango juice fraction = \\(1-\\dfrac{5}{6}=\\dfrac{1}{6}\\) of 18 \\(l\\). \\(\\dfrac{6}{6}\\) = 18 \\(l\\), so 1 unit = 18 \u00f7 6 = 3 \\(l\\). Helen prepared 3 \\(l\\) of mango juice.
(b) Mango juice left = 3 \\(l\\) - \\(\\dfrac{7}{8}\\) \\(l\\) = \\(2\\dfrac{1}{8}\\) \\(l\\)."} {"t":"q","id":18019,"q":"649 \u00d7 73 =","e":"Multiply 649 by 73. 649 \u00d7 70 = 45 430 and 649 \u00d7 3 = 1947. 45 430 + 1947 = 47 377."} {"t":"q","id":18020,"q":"A number when rounded to the nearest hundred is 56 400. What is the greatest possible whole number?","e":"Numbers from 56 350 to 56 449 round to 56 400 (nearest hundred). The greatest whole number in this range is 56 449."} {"t":"q","id":18021,"q":"Look at the number pattern.
39 400, 37 400, 37 365, 35 365, 35 330, , 33 295
What is the missing number?","e":"The pattern alternates two operations: subtract 2000, then subtract 35. 39 400 \u22122000 = 37 400; 37 400 \u221235 = 37 365; 37 365 \u22122000 = 35 365; 35 365 \u221235 = 35 330; 35 330 \u22122000 = 33 330; 33 330 \u221235 = 33 295. The missing number is 33 330."} {"t":"q","id":18022,"q":"What is the remainder when 7294 is divided by 8?
Answer: ","e":"7294 \u00f7 8 = 911 remainder 6 (911 \u00d7 8 = 7288; 7294 \u2212 7288 = 6). The remainder is 6."} {"t":"q","id":18023,"q":"16 and 64 have exactly five common factors. Three of the common factors are 1, 4 and 16. What are the other two common factors?
(a)   (b) ","e":"Common factors of 16 and 64 are 1, 2, 4, 8 and 16. Removing the given 1, 4 and 16 leaves 2 and 8."} {"t":"q","id":18024,"q":"Find the sum of the first three common multiples of 2 and 6.
Answer: ","e":"Common multiples of 2 and 6 are multiples of 6: 6, 12, 18, ... The first three are 6, 12 and 18. Their sum is 6 + 12 + 18 = 36."} {"t":"q","id":18025,"q":"Use the 5 digits to form the greatest 5-digit number. The digit in the thousands place is an even number. Use each digit only once.
1, 0, 3, 5, 8
Answer: ","e":"To make the greatest number, place the largest digit first: 8 in the ten-thousands place. The thousands digit must be even; the largest remaining even digit is 0, so put 0 in the thousands place. Arrange the rest in descending order: 5, 3, 1. This gives 80 531."} {"t":"q","id":18026,"q":"Katelyn has two six-sided dice. One is black in colour and one is white in colour. She rolls both dice and adds the two numbers shown on the dice. How many ways can she get a total of 8?
Answer: ","e":"Because the two dice are different colours, order matters. Pairs (black + white) summing to 8: 2+6, 3+5, 4+4, 5+3, 6+2. That is 5 ways."} {"t":"q","id":18027,"q":"The cost of a dining table was $735. The dining table cost 5 times as much as a dining chair.
(a) How much did the dining chair cost?
(b) How much more did the dining table cost than the dining chair?
(a)   (b) ","e":"(a) The chair = table \u00f7 5 = $735 \u00f7 5 = $147. (b) The difference = chair \u00d7 4 = $147 \u00d7 4 = $588 (or $735 \u2212 $147 = $588)."} {"t":"q","id":18028,"q":"In a group of 120 children, \\(\\dfrac{3}{8}\\) of them are girls. How many girls are there?","e":"\\(\\dfrac{3}{8}\\) of 120 = 120 \u00f7 8 \u00d7 3 = 15 \u00d7 3 = 45. There are 45 girls."} {"t":"q","id":18031,"q":"Fei Ming spent \\(\\dfrac{4}{7}\\) of his money on a guitar and had $210 left. How much did he spend on the guitar?
Answer: ","e":"He spent \\(\\dfrac{4}{7}\\), so \\(\\dfrac{3}{7}\\) was left = $210. 1 unit (\\(\\dfrac{1}{7}\\)) = $210 \u00f7 3 = $70. Spent = 4 units = $70 \u00d7 4 = $280."} {"t":"q","id":18032,"q":"Mary bought 4 kg of flour. She used \\(\\dfrac{1}{4}\\) kg of flour to make cupcakes and \\(\\dfrac{2}{5}\\) kg of it to make pizza. How much flour was left? Express your answer as a mixed number.","e":"Used = \\(\\dfrac{1}{4}+\\dfrac{2}{5}=\\dfrac{5}{20}+\\dfrac{8}{20}=\\dfrac{13}{20}\\) kg. Left = 4 \u2212 \\(\\dfrac{13}{20}\\) = 3\\(\\dfrac{20}{20}\\) \u2212 \\(\\dfrac{13}{20}\\) = 3\\(\\dfrac{7}{20}\\) kg."} {"t":"q","id":18033,"q":"Ali painted \\(\\dfrac{2}{9}\\) of a wall on Monday and \\(\\dfrac{2}{3}\\) of the same wall on Tuesday. What fraction of the wall was not painted?","e":"Painted = \\(\\dfrac{2}{9}+\\dfrac{2}{3}=\\dfrac{2}{9}+\\dfrac{6}{9}=\\dfrac{8}{9}\\). Not painted = 1 \u2212 \\(\\dfrac{8}{9}\\) = \\(\\dfrac{1}{9}\\)."} {"t":"q","id":18034,"q":"There were 20 balloons at a party. 2 of them were purple, 4 of them were blue, 11 of them were green and the rest were yellow. For each statement, write True or False.
(a) \\(\\dfrac{3}{20}\\) of the balloons were yellow.
(b) \\(\\dfrac{1}{5}\\) of the balloons were blue.
(c) \\(\\dfrac{9}{11}\\) of the balloons were not green.
(d) The fraction of the balloons that were purple is greater than the fraction of the balloons that were blue.
(a)   (b)   (c)   (d) ","e":"Yellow = 20 \u2212 2 \u2212 4 \u2212 11 = 3, so yellow = \\(\\dfrac{3}{20}\\) \u2192 True. Blue = 4 = \\(\\dfrac{4}{20}=\\dfrac{1}{5}\\) \u2192 True. Not green = 20 \u2212 11 = 9 out of 20 = \\(\\dfrac{9}{20}\\), not \\(\\dfrac{9}{11}\\) \u2192 False. Purple \\(\\dfrac{2}{20}\\) is less than blue \\(\\dfrac{4}{20}\\), so 'purple greater than blue' \u2192 False."} {"t":"q","id":18035,"q":"Sumiko baked some cookies. She gave \\(\\dfrac{1}{6}\\) of the cookies to her siblings and 45 of the cookies to her friends. She had \\(\\dfrac{2}{3}\\) of the cookies left.
(a) How many cookies did she have left?
(b) She packed the leftover cookies into 18 bags. Some bags contained 6 cookies while the rest of the bags contained 12 cookies. How many bags contained 6 cookies?
(a)   (b) ","e":"(a) She gave away \\(\\dfrac{1}{6}\\) + 45 cookies and had \\(\\dfrac{2}{3}\\) left. Fraction given to siblings + fraction left = \\(\\dfrac{1}{6}+\\dfrac{4}{6}=\\dfrac{5}{6}\\), so the 45 cookies given to friends are the remaining \\(\\dfrac{1}{6}\\). Thus 1 unit (\\(\\dfrac{1}{6}\\)) = 45, and the \\(\\dfrac{2}{3}\\) = 4 units left = 4 \u00d7 45 = 180 cookies. (b) 180 cookies in 18 bags. If all 18 bags held 12, that is 216; the shortfall 216 \u2212 180 = 36 must come from bags holding 6 instead of 12 (each such bag is 6 fewer): 36 \u00f7 6 = 6 bags contained 6 cookies."} {"t":"q","id":18085,"q":"94 072 = 90 000 + + 70 + 2
What is the missing number in the box?","e":"94 072 = 90 000 + 4000 + 70 + 2. The missing number is the thousands part: 94 072 - 90 000 - 70 - 2 = 4000."} {"t":"q","id":18087,"q":"Arrange the following numbers from the greatest to the smallest.
58 719, 85 917, 58 197","e":"Compare digit by digit. 85 917 has 8 ten-thousands so is largest. Between 58 719 and 58 197, the hundreds digit decides: 7 > 1, so 58 719 > 58 197. Greatest to smallest: 85 917, 58 719, 58 197."} {"t":"q","id":18088,"q":"Which of the following is not a common factor of 12 and 16?","e":"Factors of 12: 1, 2, 3, 4, 6, 12. Factors of 16: 1, 2, 4, 8, 16. Common factors: 1, 2, 4. So 3 is NOT a common factor."} {"t":"q","id":18089,"q":"3024 \u00f7 4 =","e":"3024 \u00f7 4: 30 \u00f7 4 = 7 r 2, bring down 2 -> 22 \u00f7 4 = 5 r 2, bring down 4 -> 24 \u00f7 4 = 6. Answer = 756."} {"t":"q","id":18092,"q":"An adult ticket cost $5 and a child ticket cost $2.
There were as many children as adults at the funfair.
The total amount of money collected from the admission tickets was $9520.
How many people were at the funfair altogether?","e":"Equal numbers of adults and children, so pair 1 adult + 1 child = $5 + $2 = $7. Number of pairs = $9520 \u00f7 $7 = 1360. Each pair is 2 people, so total people = 1360 x 2 = 2720."} {"t":"q","id":18093,"q":"(a) Write thirty-two thousand and eighty in numerals.
(b) Complete the number pattern.
31 238, 36 238, 41 238, , 51 238","e":"(a) Thirty-two thousand and eighty = 32 080. (b) The pattern increases by 5000 each step: 41 238 + 5000 = 46 238."} {"t":"q","id":18094,"q":"(a) What is the largest multiple of 6 that is smaller than 50?
(b) What is the common factor of 15 and 24 that is greater than 1?
(a)   (b) ","e":"(a) Multiples of 6: 42, 48, 54... The largest below 50 is 48. (b) Factors of 15: 1, 3, 5, 15. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. The common factor greater than 1 is 3."} {"t":"q","id":18095,"q":"The mass of a papaya when rounded to the nearest hundred is 300 g.
(a) What is the smallest possible mass of the papaya?
(b) What is the greatest possible mass of the papaya?
(a)   (b) ","e":"Numbers from 250 to 349 round to 300 when rounded to the nearest hundred. (a) Smallest = 250 g. (b) Greatest = 349 g (350 would round up to 400)."} {"t":"q","id":18096,"q":"Mr Tan made some apple juice.
He drank 320 ml of apple juice and divided the remaining equally into 8 glasses.
Each glass contained 275 ml of apple juice.
How many millilitres of apple juice did he make?
Answer: ","e":"Juice in the 8 glasses = 275 x 8 = 2200 ml. Add back what he drank: 2200 + 320 = 2520 ml."} {"t":"q","id":18097,"q":"Denzel forms 4-digit numbers using each of the digits 1, 2, 5 and 7 once.
State whether each statement is True or False.
(a) The greatest possible number he can form is 7521.
(b) The smallest possible number he can form is a multiple of 3.
(c) He can form 5 different even numbers. ","e":"(a) Greatest = arrange digits in descending order: 7521. True. (b) Smallest = 1257; digit sum 1+2+5+7 = 15, divisible by 3, so 1257 is a multiple of 3. True. (c) An even number must end in the only even digit, 2. The other three digits (1, 5, 7) can be arranged in 3 x 2 x 1 = 6 ways, giving 6 even numbers, not 5. False."} {"t":"q","id":18098,"q":"Amelia has 9 more marbles than Caleb. She has 12 less marbles than Bala. They have 3795 marbles altogether.
(a) How many more marbles does Bala have than Caleb?
(b) How many marbles does Caleb have?
(a)   (b) ","e":"(a) Amelia = Caleb + 9, Bala = Amelia + 12 = Caleb + 21. So Bala has 21 more than Caleb. (b) Total = Caleb + (Caleb + 9) + (Caleb + 21) = 3 x Caleb + 30 = 3795. So 3 x Caleb = 3795 - 30 = 3765, Caleb = 3765 \u00f7 3 = 1255."} {"t":"q","id":18099,"q":"Paul had 24 more books than Queenie. After Queenie gave Paul 60 books, Paul had 7 times as many books as Queenie. How many books did Queenie have at first?
Answer: ","e":"After the transfer Paul has 24 + 60 + 60 = 144 more books than Queenie (the original 24 difference plus the 60 he gained plus the 60 she lost). At that point Paul = 7 units and Queenie = 1 unit, so the difference of 6 units = 144, giving 1 unit = 144 \u00f7 6 = 24 (Queenie's books after giving away 60). Queenie at first = 24 + 60 = 84."} {"t":"q","id":18103,"q":"Which of the following statements are true about a square?
A. It has 4 right angles.
B. It has 2 pairs of parallel lines.
C. Its opposite sides are equal.","e":"A square has 4 right angles (A true), 2 pairs of parallel sides (B true) and equal opposite sides (C true). All three statements are correct, so the answer is A, B and C."} {"t":"q","id":18133,"q":"What is the value of 4 thousands + 2 hundreds + 6 ones?","e":"4 thousands = 4000, 2 hundreds = 200, 6 ones = 6. There are 0 tens. 4000 + 200 + 0 + 6 = 4206."} {"t":"q","id":18134,"q":"What is the missing number in the box?
\\(6\\dfrac{2}{5}\\) = \\(\\dfrac{ }{5}\\)","e":"Convert the mixed number to an improper fraction. \\(6\\dfrac{2}{5}\\) = \\(\\dfrac{(6\\times5)+2}{5}\\) = \\(\\dfrac{32}{5}\\), so the missing number is 32."} {"t":"q","id":18135,"q":"There are 9345 men and 8704 women in a stadium. What is the total number of people in the stadium? Round this number to the nearest 100.","e":"Total = 9345 + 8704 = 18 049. Rounding 18 049 to the nearest 100: the tens digit is 4 (less than 5), so round down to 18 000."} {"t":"q","id":18136,"q":"Mindy had \\(\\dfrac{4}{5}\\) kg of flour at first. After she had used some of the flour to make noodles, she had \\(\\dfrac{1}{3}\\) kg of flour left. How much flour did she use to make noodles?","e":"Flour used = flour at first \u2212 flour left = \\(\\dfrac{4}{5}\\) \u2212 \\(\\dfrac{1}{3}\\). Common denominator 15: \\(\\dfrac{12}{15}\\) \u2212 \\(\\dfrac{5}{15}\\) = \\(\\dfrac{7}{15}\\) kg."} {"t":"q","id":18139,"q":"(a) In the number pattern below, what is the missing number in the box?
78 082 , , 82 082 , 84 082 , 86 082
(b) Andy listed the factors of 12: 1, 2, 4, 12. He missed out two factors. What were the two missing factors? and ","e":"(a) The pattern increases by 2000 each step (82 082 \u2212 80 082 = 2000). The missing term = 78 082 + 2000 = 80 082. (b) Factors of 12 are 1, 2, 3, 4, 6, 12. The listed set 1, 2, 4, 12 leaves out 3 and 6."} {"t":"q","id":18140,"q":"Arrange the following in decreasing order.
\\(\\dfrac{11}{4}\\) , \\(1\\dfrac{1}{6}\\) , 1 , \\(\\dfrac{8}{3}\\)
, , , ","e":"Convert to a common form: \\(\\dfrac{11}{4}\\) = 2.75, \\(\\dfrac{8}{3}\\) \u2248 2.67, \\(1\\dfrac{1}{6}\\) \u2248 1.17, 1 = 1. Decreasing order: \\(\\dfrac{11}{4}\\), \\(\\dfrac{8}{3}\\), \\(1\\dfrac{1}{6}\\), 1."} {"t":"q","id":18142,"q":"Mr Chen bought 6 similar dining chairs for $1428. A sofa cost 10 times as much as a dining chair. How much did the sofa cost?
$","e":"Cost of 1 dining chair = $1428 \u00f7 6 = $238. The sofa costs 10 times as much = 10 \u00d7 $238 = $2380."} {"t":"q","id":18143,"q":"Fiona and Janet had a total of 126 cookies at first. After Janet gave away \\(\\dfrac{1}{3}\\) of the cookies she had, she had 4 times as many cookies as Fiona. How many cookies did Janet have at first?
","e":"After giving away \\(\\dfrac{1}{3}\\), Janet keeps \\(\\dfrac{2}{3}\\) of her cookies, which equals 4 times Fiona's. The total 126 is unchanged. Take Fiona as 1 unit, so Janet's remaining = 4 units and Janet's original = 6 units (since \\(\\dfrac{2}{3}\\) of original = 4 units \u2192 original = 6 units). Total units = 6 + 1 = 7 = 126, so 1 unit = 18. Janet at first = 6 \u00d7 18 = 108."} {"t":"q","id":18144,"q":"Alan made some lime juice on Monday and Tuesday. He made \\(\\dfrac{7}{8}\\) \\(l\\) of lime juice on Monday. He made \\(\\dfrac{2}{5}\\) \\(l\\) more lime juice on Monday than Tuesday.
(a) How much lime juice did he make on Tuesday?
(b) What was the total amount of lime juice that he had made on both days? Give your answer in the simplest form.
(a)
(b) ","e":"(a) Tuesday = Monday \u2212 \\(\\dfrac{2}{5}\\) = \\(\\dfrac{7}{8}\\) \u2212 \\(\\dfrac{2}{5}\\). Common denominator 40: \\(\\dfrac{35}{40}\\) \u2212 \\(\\dfrac{16}{40}\\) = \\(\\dfrac{19}{40}\\) \\(l\\). (b) Total = Monday + Tuesday = \\(\\dfrac{35}{40}\\) + \\(\\dfrac{19}{40}\\) = \\(\\dfrac{54}{40}\\) = \\(1\\dfrac{14}{40}\\) = \\(1\\dfrac{7}{20}\\) \\(l\\)."} {"t":"q","id":18145,"q":"Marilyn has some lollipops. If she packs them into bags of 7, she will be short of 1 lollipop. If she packs them into bags of 5, she will have 2 extra lollipops.
(a) What is the least number of lollipops that Marilyn has?
(b) Marilyn decides to pack all her lollipops into bags of 5. How many more lollipops does she need to fill up the last bag of 5 lollipops?
(a)
(b) ","e":"(a) 'Short of 1' in bags of 7 means the number is 1 less than a multiple of 7: 6, 13, 20, 27, ... '2 extra' in bags of 5 means 2 more than a multiple of 5: 7, 12, 17, 22, 27, ... The least common value is 27. (b) 27 \u00f7 5 = 5 remainder 2, so the last bag has 2 lollipops; she needs 5 \u2212 2 = 3 more to fill it."} {"t":"q","id":18252,"q":"In 12 453, the digit 4 is in the ____ place.","e":"In 12 453, the digits from the right are 3 (ones), 5 (tens), 4 (hundreds), 2 (thousands), 1 (ten thousands). So the digit 4 is in the hundreds place."} {"t":"q","id":18253,"q":"In which of the following are the numbers arranged from the greatest to the smallest?","e":"Order 9680, 9608, 9068 from greatest to smallest: 9680 (largest), then 9608, then 9068. Compare digit by digit from the left. Option (2) is correct."} {"t":"q","id":18254,"q":"Which of the following is a multiple of 9?","e":"A multiple of 9 can be divided exactly by 9. 81 = 9 x 9, so 81 is a multiple of 9. (19, 39 and 3 are not.)"} {"t":"q","id":18257,"q":"Judy baked 10 chocolate and 15 peanut cookies.
She packed all the cookies into equal number of boxes.
How many chocolate and peanut cookies were there in each box?","e":"The greatest number of equal boxes is the common factor of 10 and 15, which is 5. So 10 \u00f7 5 = 2 chocolate cookies and 15 \u00f7 5 = 3 peanut cookies in each box."} {"t":"q","id":18258,"q":"Siti bought 369 oranges.
She packed the oranges equally into bags of 4.
What is the least number of bags of oranges she should buy?","e":"369 \u00f7 4 = 92 remainder 1. 92 bags hold 368 oranges, leaving 1 orange, so 1 more bag is needed. Least number of bags = 93."} {"t":"q","id":18261,"q":"Peter folded 1000 paper cranes.
He folded 4 times as many cranes as Alicia.
How many paper cranes must Peter give to Alicia so that they each have the same number of cranes?","e":"Peter = 1000, which is 4 units, so 1 unit = 250 and Alicia = 250. Total = 1250, so each should have 1250 \u00f7 2 = 625. Peter must give away 1000 - 625 = 375 cranes."} {"t":"q","id":18263,"q":"A number when rounded off to the nearest hundred is 3500.
What is the greatest possible number?
Answer: ","e":"Numbers from 3450 to 3549 round to 3500. The greatest of these is 3549 (3550 would round up to 3600)."} {"t":"q","id":18264,"q":"Jane decorated a room with red and green lights.
The red light blinks every 3 minutes and the green light blinks every 4 minutes.
Both lights are switched on at the same time.
When will both lights blink together for the first time? min","e":"The lights blink together at common multiples of 3 and 4. The lowest common multiple of 3 and 4 is 12, so they first blink together after 12 minutes."} {"t":"q","id":18265,"q":"Ahmad, Ben and Clarice shared 9036 crayons equally among themselves.
Ahmad bought another 98 crayons for himself.
How many crayons would Ahmad have in the end?
Answer: ","e":"Each share = 9036 \u00f7 3 = 3012. Ahmad then buys 98 more: 3012 + 98 = 3110 crayons."} {"t":"q","id":18267,"q":"A table cost $910 more than a chair.
Tom paid $7520 for 2 tables and 4 chairs.
How much does a table cost?
Answer: ","e":"Replace each table with a chair: 2 tables = 2 chairs + 2 x $910 = 2 chairs + $1820. So 6 chairs = $7520 - $1820 = $5700, giving 1 chair = $5700 \u00f7 6 = $950. A table = $950 + $910 = $1860."} {"t":"q","id":18344,"q":"Which digit in 98 150 is in the thousands place?","e":"In 98 150 the digits are 9 (ten thousands), 8 (thousands), 1 (hundreds), 5 (tens), 0 (ones). The thousands place is 8."} {"t":"q","id":18345,"q":"Which of the following is a multiple of 7?","e":"Multiples of 7 are 7, 14, 21, 28, ... 21 = 7 \u00d7 3, so 21 is a multiple of 7."} {"t":"q","id":18346,"q":"Which of the following is not a factor of 42?","e":"Factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42. 8 is not a factor of 42 (42 \u00f7 8 leaves a remainder)."} {"t":"q","id":18349,"q":"Ninety-five thousand, seven hundred and thirty-six in numerals is","e":"Ninety-five thousand = 95 000; seven hundred and thirty-six = 736. Together: 95 000 + 736 = 95 736."} {"t":"q","id":18350,"q":"4024 babies were born in March. The number of babies born in March was 1097 fewer than the number of babies born in January. How many babies were born in January?","e":"March is 1097 fewer than January, so January = March + 1097 = 4024 + 1097 = 5121."} {"t":"q","id":18351,"q":"Which of the following is a multiple of both 3 and 8?","e":"A multiple of both 3 and 8 is a multiple of 24. 24 = 3 \u00d7 8, and 24 \u00f7 3 = 8, 24 \u00f7 8 = 3, so 24 works."} {"t":"q","id":18352,"q":"Samantha is less than 17 years old this year. Her age last year was a multiple of 5. Her age this year is a multiple of 4. What is Samantha's age this year?","e":"Last year a multiple of 5 means last age is 5, 10 or 15, so this year she is 6, 11 or 16. Of these, a multiple of 4 that is less than 17 is 16."} {"t":"q","id":18353,"q":"Raja wanted to buy a new piano which costs $3483. He had been saving for 9 months but he was still short of $1647. He saved an equal amount of money each month. How much did Raja save each month?","e":"Amount saved = $3483 - $1647 = $1836 over 9 months. Each month = $1836 \u00f7 9 = $204."} {"t":"q","id":18354,"q":"Write the missing number in the number pattern.
68 501, 70 501, 72 501, , 76 501, 78 501","e":"The pattern increases by 2000 each time. 72 501 + 2000 = 74 501."} {"t":"q","id":18355,"q":"Some factors of 36 are 1, 2, 3, 4, 6, 12, 36. What are the other two factors of 36?
(a)   (b) ","e":"All factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. The two missing from the list are 9 and 18."} {"t":"q","id":18356,"q":"Two of the common factors of 12 and 18 are 1 and 2. What are the other 2 common factors of 12 and 18?
(a)   (b) ","e":"Common factors of 12 and 18 are 1, 2, 3 and 6. The two missing from the list are 3 and 6."} {"t":"q","id":18357,"q":"Find the product of 283 and 28.
Answer: ","e":"283 \u00d7 28 = 283 \u00d7 20 + 283 \u00d7 8 = 5660 + 2264 = 7924."} {"t":"q","id":18358,"q":"Find the quotient when 6300 is divided by 3.
Answer: ","e":"6300 \u00f7 3 = 2100 (63 \u00f7 3 = 21, then bring down the two zeros)."} {"t":"q","id":18359,"q":"Arrange the following numbers from the smallest to the greatest.
71 095, 78 059, 69 590, 72 950
, , , ","e":"Compare the numbers: 69 590 < 71 095 < 72 950 < 78 059. From smallest to greatest: 69 590, 71 095, 72 950, 78 059."} {"t":"q","id":18360,"q":"The number of people in a concert rounded to the nearest hundred is 55 100. What is the greatest possible number of people in the stadium?
Answer: ","e":"To round to 55 100, the number must be from 55 050 to 55 149. The greatest possible number is 55 149."} {"t":"q","id":18361,"q":"Gopal has a number card. The number on the card is a factor of 36 and a multiple of 3. It is more than 12 but less than 20. What is the number on Gopal's card?
Answer: ","e":"Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. Those more than 12 but less than 20 give 18. 18 is also a multiple of 3."} {"t":"q","id":18362,"q":"A number is between 40 and 50. It is also a multiple of 6. When it is divided by 8, there is no remainder. What is the number?
Answer: ","e":"Multiples of 6 between 40 and 50 are 42 and 48. Of these, 48 \u00f7 8 = 6 with no remainder, so the number is 48."} {"t":"q","id":18363,"q":" \u00d7 6 =
\u00d7 3 = 4608
The value of is","e":"Let the star be S and the heart be H. From H \u00d7 3 = 4608, H = 4608 \u00f7 3 = 1536. From S \u00d7 6 = H, S = 1536 \u00f7 6 = 256. So the star equals 256."} {"t":"q","id":18364,"q":"Carrie earns $75 a day on weekdays. She is paid twice as much on Saturdays. She worked for 21 weekdays and a Saturday in a particular month. How much does Carrie earn on a Saturday?
Answer: ","e":"Saturday pay is twice the weekday pay: $75 \u00d7 2 = $150."} {"t":"q","id":18365,"q":"Carrie earns $75 a day on weekdays. She is paid twice as much on Saturdays. She worked for 21 weekdays and a Saturday in a particular month. How much did Carrie earn for that month?
Answer: ","e":"Weekday earnings: $75 \u00d7 21 = $1575. Saturday earnings: $75 \u00d7 2 = $150. Total: $1575 + $150 = $1725."} {"t":"q","id":18366,"q":"A fruit seller had 106 boxes of oranges. There were 24 oranges in each box. He sold all the oranges at 8 for $5. How many oranges did the fruit seller have altogether?
Answer: ","e":"Total oranges = 106 boxes \u00d7 24 per box = 2544."} {"t":"q","id":18367,"q":"A fruit seller had 106 boxes of oranges. There were 24 oranges in each box. He sold all the oranges at 8 for $5. How much money did he receive from the sale of all the oranges?
Answer: ","e":"Total oranges = 106 \u00d7 24 = 2544. Groups of 8: 2544 \u00f7 8 = 318. Money = 318 \u00d7 $5 = $1590."} {"t":"q","id":18368,"q":"Siti and Alexis collected the same number of stamps. Siti gave away 64 of her stamps and Alexis gave away 121 of her stamps. In the end, Siti had 4 times as many stamps as Alexis. How many stamps did each of them collect?
Answer: ","e":"They started equal. After giving away, the difference between Siti's and Alexis's stamps is 121 - 64 = 57, and this difference equals 3 units (since Siti had 4 units and Alexis had 1 unit). So 3 units = 57, 1 unit = 19. Alexis had 19 stamps left, so each collected 19 + 121 = 140 stamps."} {"t":"q","id":18400,"q":"Write thirteen thousand and forty-three in numerals.
","e":"Thirteen thousand = 13 000. Forty-three = 43. Combine: 13 000 + 43 = 13 043."} {"t":"q","id":18401,"q":"Use the digits to form the smallest 5-digit even number. Each digit can be used only once.
9, 0, 5, 2, 1
","e":"For the smallest number put small digits first, but the leading digit cannot be 0, so the smallest non-zero digit (1) goes first. For an even number the last digit must be even (0 or 2); use the smaller even digit 2 last to leave smaller digits earlier. Arrange remaining 0, 5, 9 in increasing order: 1, 0, 5, 9, 2 = 10 592."} {"t":"q","id":18402,"q":"19 508 people visited the National Museum. Round this number to the nearest thousand.
","e":"Look at the hundreds digit of 19 508, which is 5. Since 5 or more rounds up, 19 508 rounds up to 20 000."} {"t":"q","id":18403,"q":"Two factors of 27 are 1 and 27. What are the other two factors of 27?
and ","e":"Factors of 27 are the numbers that divide it exactly: 1, 3, 9, 27. The other two (besides 1 and 27) are 3 and 9."} {"t":"q","id":18404,"q":"Complete the following number pattern.
63 865, 62 865, 61 865, 60 865, ","e":"Each term decreases by 1000: 63 865, 62 865, 61 865, 60 865. The next term is 60 865 \u2212 1000 = 59 865."} {"t":"q","id":18405,"q":"\\(5\\dfrac{2}{7} = \\dfrac{}{7}\\)
What is the missing number in the box?","e":"Convert the mixed number to an improper fraction: \\(5\\dfrac{2}{7} = \\dfrac{5\\times7 + 2}{7} = \\dfrac{35 + 2}{7} = \\dfrac{37}{7}\\). The missing numerator is 37."} {"t":"q","id":18406,"q":"Find the sum of all the factors of 10.
","e":"Factors of 10 are 1, 2, 5 and 10. Sum = 1 + 2 + 5 + 10 = 18."} {"t":"q","id":18408,"q":"Arrange the following fractions in decreasing order.
\\(1\\dfrac{1}{6}\\), \\(\\dfrac{3}{4}\\), \\(\\dfrac{3}{2}\\)
, , ","e":"Convert to a common comparison: \\(\\dfrac{3}{2}=1.5\\), \\(1\\dfrac{1}{6}\\approx1.17\\), \\(\\dfrac{3}{4}=0.75\\). Decreasing order is \\(\\dfrac{3}{2}\\), \\(1\\dfrac{1}{6}\\), \\(\\dfrac{3}{4}\\)."} {"t":"q","id":18409,"q":"Meiling had some money. She spent \\(\\dfrac{5}{6}\\) of the money and had $18 left. How much money did she have at first?
$","e":"She spent \\(\\dfrac{5}{6}\\), so \\(\\dfrac{1}{6}\\) was left = $18. That means 1 unit = $18, and the whole (6 units) = 6 \u00d7 $18 = $108."} {"t":"q","id":18410,"q":"Find the first two common multiples of 4 and 6.
and ","e":"Multiples of 4: 4, 8, 12, 16, 20, 24... Multiples of 6: 6, 12, 18, 24... The first two common multiples are 12 and 24."} {"t":"q","id":18411,"q":"Tom and Jerry shared $1550 between them. Jerry received $90 less than Tom. How much money did Jerry receive?
$","e":"Remove the $90 difference first: $1550 \u2212 $90 = $1460. Split equally between two: $1460 \u00f7 2 = $730. This is Jerry's (smaller) share."} {"t":"q","id":18412,"q":"An odd number when rounded to the nearest hundred is 2800. What is the smallest possible value of this odd number?
","e":"Numbers rounding to 2800 range from 2750 to 2849. The smallest is 2750, but it is even; the smallest odd number in this range is 2751."} {"t":"q","id":18413,"q":"Eileen baked 2800 cookies. She sold them in packets of 8 for $7 each. How much money did she collect?
$","e":"Number of packets = 2800 \u00f7 8 = 350. Money collected = 350 \u00d7 $7 = $2450."} {"t":"q","id":18414,"q":"Devi bought 24 curry puffs. She gave 6 curry puffs to her neighbour and her family ate 8 curry puffs. What fraction of the curry puffs were left? Express your answer in its simplest form.","e":"Curry puffs left = 24 \u2212 6 \u2212 8 = 10. Fraction left = \\(\\dfrac{10}{24}\\), which simplifies (dividing by 2) to \\(\\dfrac{5}{12}\\)."} {"t":"q","id":18416,"q":"Alice is thrice as old as her cousin. Alice is 39 years old now. What is their total age in 2 years' time?
","e":"Cousin's age now = 39 \u00f7 3 = 13. In 2 years: Alice = 39 + 2 = 41, cousin = 13 + 2 = 15. Total = 41 + 15 = 56."} {"t":"q","id":18417,"q":"Mr Soh planted 27 rows of papaya trees in his orchard. There were 16 trees in each row. \\(\\dfrac{4}{9}\\) of the papaya trees bore fruit. How many papaya trees bore fruit?
","e":"Total trees = 27 \u00d7 16 = 432. This is 9 units, so 1 unit = 432 \u00f7 9 = 48. Trees that bore fruit = \\(\\dfrac{4}{9}\\) = 4 units = 4 \u00d7 48 = 192."} {"t":"q","id":18419,"q":"Convert \\(1\\dfrac{7}{25}\\) to a decimal.
","e":"\\(\\dfrac{7}{25} = \\dfrac{28}{100} = 0.28\\). Add the whole number: 1 + 0.28 = 1.28."} {"t":"q","id":18421,"q":"Find the value of 12 \u00f7 5. Give your answer as a decimal.
","e":"12 \u00f7 5 = 2 remainder 2, and \\(\\dfrac{2}{5} = 0.4\\), so 12 \u00f7 5 = 2.4."} {"t":"q","id":18422,"q":"Arrange these numbers in increasing order.
4.206, 4.026, 4.26, 4.602
, , , ","e":"Compare place by place: 4.026, 4.206, 4.26 (=4.260), 4.602. Increasing order: 4.026, 4.206, 4.26, 4.602."} {"t":"q","id":18428,"q":"A fence was 5.6 m long. 1.25 m of the fence was painted red and the rest was painted white. What was the length of the fence that was painted white?
m","e":"White length = total \u2212 red = 5.6 \u2212 1.25 = 4.35 m."} {"t":"q","id":18429,"q":"A number is greater than 7.85 but smaller than 7.95. The value of the digit 3 is 0.03. The digit 1 stands for \\(\\dfrac{1}{1000}\\). What is the number? Express your answer as a decimal.
","e":"The number is between 7.85 and 7.95, so it starts 7.9. The digit 3 has value 0.03, so 3 is in the hundredths place. The digit 1 stands for \\(\\dfrac{1}{1000}\\) = 0.001, so 1 is in the thousandths place. The number is 7.931."} {"t":"q","id":18430,"q":"Wei Jia mixed 0.25 \\(l\\) of rose syrup with 1.2 \\(l\\) of milk to make Bandung drink for her guests. She then poured the Bandung drink equally into 8 glasses. How much Bandung drink was there in each glass? Give your answer correct to 2 decimal places.
l","e":"Total drink = 1.2 + 0.25 = 1.45 l. Per glass = 1.45 \u00f7 8 = 0.181... which rounds to 0.18 l (2 decimal places)."} {"t":"q","id":18431,"q":"The total mass of a box containing a watermelon and a papaya is 3.85 kg. The watermelon is twice as heavy as the papaya. The papaya is twice as heavy as the box. What is the mass of the watermelon?
kg","e":"Let the box = 1 unit. Papaya = 2 units, watermelon = 2 \u00d7 papaya = 4 units. Total = 1 + 2 + 4 = 7 units = 3.85 kg, so 1 unit = 3.85 \u00f7 7 = 0.55 kg. Watermelon = 4 units = 4 \u00d7 0.55 = 2.2 kg."} {"t":"q","id":18433,"q":"Mrs Khan baked some cupcakes for her students. If she gave each student 3 cupcakes, she would have 5 cupcakes remaining. If she gave each student 4 cupcakes, she would need another 3 cupcakes. How many cupcakes did Mrs Khan bake?
","e":"Giving 4 instead of 3 cupcakes per student uses 1 more per student, and the surplus of 5 becomes a shortfall of 3 \u2014 a swing of 5 + 3 = 8 cupcakes. So there are 8 students. Cupcakes = 3 \u00d7 8 + 5 = 24 + 5 = 29."} {"t":"q","id":18434,"q":"Emir had $6.40. After giving $1.20 to his brother, Emir had half the amount as his brother. What was the total amount they had altogether?
$","e":"After giving away $1.20, Emir had $6.40 \u2212 $1.20 = $5.20. He then had half as much as his brother, so the brother had 2 \u00d7 $5.20 = $10.40. Total = $5.20 + $10.40 = $15.60. (The total is unchanged by the transfer.)"} {"t":"q","id":18547,"q":"What is the value of the digit 1 in 4.123?","e":"In 4.123, the digit 1 is in the tenths place. Its value is 1 tenth = 0.1."} {"t":"q","id":18548,"q":"\\(3\\dfrac{5}{6}\\) = \\(\\dfrac{ }{6}\\)
What is the missing number in the box?","e":"Convert the mixed number to an improper fraction: \\(3\\dfrac{5}{6}\\) = (3 \u00d7 6 + 5)\/6 = (18 + 5)\/6 = \\(\\dfrac{23}{6}\\). The missing number is 23."} {"t":"q","id":18549,"q":"Arrange the following in increasing order.
\\(\\dfrac{4}{5}\\), \\(\\dfrac{4}{7}\\), \\(\\dfrac{9}{4}\\)","e":"\\(\\dfrac{9}{4}\\) is greater than 1 (improper), so it is the largest. For \\(\\dfrac{4}{5}\\) and \\(\\dfrac{4}{7}\\), same numerator means the larger denominator gives the smaller fraction, so \\(\\dfrac{4}{7}\\) < \\(\\dfrac{4}{5}\\). Increasing order: \\(\\dfrac{4}{7}\\), \\(\\dfrac{4}{5}\\), \\(\\dfrac{9}{4}\\)."} {"t":"q","id":18552,"q":"Divide 5 by 8. Correct your answer to 2 decimal places.
","e":"5 \u00f7 8 = 0.625. Rounding to 2 decimal places, the third decimal digit is 5, so round up: 0.63."} {"t":"q","id":18553,"q":"The mass of a bag of potatoes is 3 \\(kg\\) when rounded to the nearest kilogram. What is the greatest possible value of the bag of potatoes in 1 decimal place?
","e":"Masses from 2.5 kg up to (but not including) 3.5 kg round to 3 kg. The greatest value below 3.5 kg expressed to 1 decimal place is 3.4 kg."} {"t":"q","id":18555,"q":"Andy and Ben drank a total of \\(\\dfrac{4}{5}\\) \\(l\\) of juice. Andy drank \\(\\dfrac{1}{2}\\) \\(l\\) of the juice. How much more juice did Andy drink than Ben?","e":"Ben drank \\(\\dfrac{4}{5}\\) \u2212 \\(\\dfrac{1}{2}\\) = \\(\\dfrac{8}{10}\\) \u2212 \\(\\dfrac{5}{10}\\) = \\(\\dfrac{3}{10}\\) l. Andy drank \\(\\dfrac{1}{2}\\) = \\(\\dfrac{5}{10}\\) l. Andy drank \\(\\dfrac{5}{10}\\) \u2212 \\(\\dfrac{3}{10}\\) = \\(\\dfrac{2}{10}\\) = \\(\\dfrac{1}{5}\\) l more than Ben."} {"t":"q","id":18556,"q":"Ray and Sherman shared a box of cards. Ray received \\(\\dfrac{5}{12}\\) of the cards and Sherman received the remaining 105 cards. How many cards were there in the box?
","e":"Ray had \\(\\dfrac{5}{12}\\), so Sherman had \\(\\dfrac{7}{12}\\) = 7 units = 105 cards. 1 unit = 105 \u00f7 7 = 15 cards. The whole box = 12 units = 12 \u00d7 15 = 180 cards."} {"t":"q","id":18557,"q":"The cost of a packet of sweets is twice the cost of a packet of peanuts. The cost of 2 such packets of sweets and a packet of peanuts is $18.50.
(a) What is the cost of a packet of peanuts?
(b) John bought 2 such packets of peanuts and a packet of sweets. How much did he pay?
(a)
(b) ","e":"Let 1 packet of peanuts = 1 unit; 1 packet of sweets = 2 units. 2 sweets + 1 peanut = 4 + 1 = 5 units = $18.50, so 1 unit = $18.50 \u00f7 5 = $3.70 (a). (b) 2 peanuts + 1 sweet = 2 + 2 = 4 units = $3.70 \u00d7 4 = $14.80."} {"t":"q","id":18745,"q":"Which of the following is seventy thousand, three hundred and forty in numerals?","e":"70 000 + 300 + 40 = 70 340. Option (3)."} {"t":"q","id":18746,"q":"Arrange the following numbers from the largest to the smallest.
42 182 , 42 281 , 41 822","e":"Largest to smallest: 42 281 > 42 182 > 41 822. Option (2)."} {"t":"q","id":18747,"q":"In the following number pattern, what is the missing number?
21 978, _______ , 21 778, 21 678, 21 578","e":"The pattern decreases by 100 each term: 21 978 - 100 = 21 878. Option (4)."} {"t":"q","id":18748,"q":"Which of the following numbers when rounded to the nearest hundred becomes 49 000?","e":"Round to nearest hundred: 48 965 rounds to 49 000 (tens digit 6 rounds up). 48 875 to 48 900; 49 099 to 49 100; 49 144 to 49 100. Option (2)."} {"t":"q","id":18749,"q":"Which of the following is a factor of both 12 and 28?","e":"Factors of 12: 1,2,3,4,6,12. Factors of 28: 1,2,4,7,14,28. Common factor among options: 4. Option (4)."} {"t":"q","id":18750,"q":"Which of the following is a multiple of both 4 and 6?","e":"Common multiples of 4 and 6 are multiples of 12. Among options, 12 is a multiple of both 4 and 6. Option (2)."} {"t":"q","id":18751,"q":"Peter stored 3425 boxes of masks in the warehouse. He sold 625 boxes of masks on Monday and 2150 boxes of masks on Tuesday. How many boxes of masks is he left with?","e":"3425 - 625 - 2150 = 3425 - 2775 = 650. Option (4)."} {"t":"q","id":18752,"q":"The sum of two numbers is 75. One of the numbers is a multiple of 8. The other number is a factor of 21. What is the difference between the 2 numbers?","e":"Factors of 21: 1, 3, 7, 21. The multiple of 8 = 75 - factor. 75 - 3 = 72 (a multiple of 8). So the numbers are 72 and 3; difference = 72 - 3 = 69. Option (2)."} {"t":"q","id":18753,"q":"A number is 5800 when rounded to the nearest hundred. What are the smallest and greatest possible numbers?
Smallest:
Greatest: ","e":"Smallest rounding up to 5800: 5750 (5750 rounds to 5800). Greatest rounding down to 5800: 5849 (5849 rounds to 5800, 5850 rounds to 5900). Smallest = 5750, Greatest = 5849."} {"t":"q","id":18754,"q":"There are 2400 red and blue stickers in a shop. The number of red stickers is three times as many as the number of blue stickers. How many blue stickers are there?
","e":"Red is 3 times blue, so total = 4 units = 2400. 1 unit (blue) = 2400 \/ 4 = 600. Blue stickers = 600."} {"t":"q","id":18755,"q":"Mr Tan bought 125 boxes of chocolates. Each box contained 28 chocolates. How many chocolates did Mr Tan buy in total?
","e":"125 x 28 = 3500 chocolates."} {"t":"q","id":18756,"q":"Mr Lim bought a bag of candies for his students. If he gives each student 6 candies, he will not have any candies left. If he gives each student 8 candies, he will be short of 6 candies. How many students did he have?
","e":"Giving 8 instead of 6 needs 2 more per student, totalling a shortfall of 6 candies. Number of students = 6 \/ 2 = 3."} {"t":"q","id":18757,"q":"Three ovens and two printers cost $2300. A printer cost $80 more than an oven. What is the cost of an oven?
$","e":"Replace 2 printers by ovens: each printer = oven + 80, so 2 printers = 2 ovens + 160. Total = 5 ovens + 160 = 2300, so 5 ovens = 2140, 1 oven = 2140 \/ 5 = $428."} {"t":"q","id":18758,"q":"John had twice as much money as Ken. After John spent $1064, Ken had four times as much money as John.
(a) How much money did John have in the end?
$
(b) How much money did the both of them have at first?
$","e":"Ken's amount is unchanged. At first John = 2 x Ken. In the end Ken = 4 x John(end), so John(end) = Ken \/ 4. Let Ken = 1 unit; John(start) = 2 units; John(end) = Ken\/4 = 1\/4 unit. John spent $1064 = John(start) - John(end) = 2 - 1\/4 = 7\/4 units. So 7\/4 units = 1064, 1 unit (1\/4) ... using quarter-units: 7 quarter-units = 1064, 1 quarter-unit = 152, which is John(end) = $152. (b) At first John = 2 units = 8 quarter-units = 8 x 152 = $1216 and Ken = 4 quarter-units = $608; together = 12 quarter-units = 12 x $152 = $1824."} {"t":"q","id":18759,"q":"\\(3\\dfrac{2}{5}\\) = \\(\\dfrac{[box]}{5}\\)
What is the missing number in the box?","e":"Convert mixed number to improper fraction: 3 x 5 + 2 = 17, so 3 2\/5 = 17\/5. Missing number = 17. Option (3)."} {"t":"q","id":18762,"q":"Find the value of \\(\\dfrac{7}{8}\\) - \\(\\dfrac{1}{4}\\)","e":"1\/4 = 2\/8, so 7\/8 - 2\/8 = 5\/8. Option (1)."} {"t":"q","id":18763,"q":"Find the value of \\(\\dfrac{1}{3}\\) + \\(\\dfrac{2}{9}\\) + \\(\\dfrac{7}{9}\\)","e":"1\/3 = 3\/9, so 3\/9 + 2\/9 + 7\/9 = 12\/9 = 1 3\/9 = 1 1\/3. Option (3)."} {"t":"q","id":18765,"q":"Arrange the following fractions from the smallest to the greatest.
\\(1\\dfrac{1}{4}\\) , \\(\\dfrac{12}{11}\\) , \\(1\\dfrac{1}{8}\\)","e":"12\/11 = 1 1\/11. Compare 1\/11, 1\/8, 1\/4: 1\/11 < 1\/8 < 1\/4. So smallest to greatest: 12\/11, 1 1\/8, 1 1\/4. Option (4)."} {"t":"q","id":18766,"q":"Jane had 6 cakes. She gave \\(\\dfrac{1}{2}\\) of a cake to her sister and \\(\\dfrac{1}{3}\\) of a cake to her brother. How many cakes had she left?","e":"Given away: 1\/2 + 1\/3 = 3\/6 + 2\/6 = 5\/6 of a cake. Left: 6 - 5\/6 = 5 1\/6 cakes. Option (3)."} {"t":"q","id":18768,"q":"Emma has 24 apples and oranges. \\(\\dfrac{3}{8}\\) of the fruits are apples. How many more oranges than apples does Emma have?
","e":"Apples = 3\/8 of 24 = 9. Oranges = 24 - 9 = 15. More oranges than apples = 15 - 9 = 6."} {"t":"q","id":18770,"q":"Amy has \\(\\dfrac{3}{5}\\) kg of sugar. Bala has \\(\\dfrac{1}{3}\\) kg of sugar more than Amy.
(a) How much sugar does Bala have? Express your answer in its simplest form.
kg
(b) How much sugar do they have altogether? Express your answer in its simplest form.
kg","e":"(a) Bala = 3\/5 + 1\/3 = 9\/15 + 5\/15 = 14\/15 kg. (b) Altogether = Amy + Bala = 3\/5 + 14\/15 = 9\/15 + 14\/15 = 23\/15 = 1 8\/15 kg."} {"t":"q","id":18771,"q":"\\(\\dfrac{1}{3}\\) of a bottle was filled with orange juice. After John poured in another 600 ml of orange juice, it became \\(\\dfrac{5}{9}\\) full. How much orange juice can the bottle hold when it is completely full? Give your answer in millilitres.
ml","e":"Increase in fraction filled = 5\/9 - 1\/3 = 5\/9 - 3\/9 = 2\/9. This equals 600 ml, so 2 units = 600 ml, 1 unit (1\/9) = 300 ml. Full bottle = 9 units = 9 x 300 = 2700 ml."} {"t":"q","id":18772,"q":"Arrange the following decimals in decreasing order.
7.051 , 7.101 , 7.011 , 7.105","e":"Decreasing (greatest to smallest): 7.105 > 7.101 > 7.051 > 7.011. Option (4)."} {"t":"q","id":18773,"q":"Round 38.695 to the nearest tenth.","e":"Nearest tenth: look at the hundredths digit (9). 38.695 rounds up to 38.7. Option (3)."} {"t":"q","id":18774,"q":"Express \\(5\\dfrac{9}{25}\\) as a decimal.","e":"9\/25 = 36\/100 = 0.36, so 5 9\/25 = 5.36. Option (3)."} {"t":"q","id":18775,"q":"Express 2.003 as a fraction.","e":"0.003 = 3 thousandths = 3\/1000, so 2.003 = 2 3\/1000. Option (4)."} {"t":"q","id":18776,"q":"What is the missing number in the box?
8.175 = 8 + 0.1 + [box] + 0.005","e":"8.175 = 8 + 0.1 + 0.07 + 0.005. The hundredths value is 0.07. Option (2)."} {"t":"q","id":18777,"q":"3.46 is 0.1 more than _______.","e":"3.46 - 0.1 = 3.36. Option (1)."} {"t":"q","id":18778,"q":"A pen cost $2.60. Diana bought two pens and gave the cashier $10. How much change did she get?","e":"Two pens = 2 x $2.60 = $5.20. Change = $10 - $5.20 = $4.80. Option (1)."} {"t":"q","id":18779,"q":"The total length of one yellow ribbon and one green ribbon is 8.7 m. Each yellow ribbon is twice as long as the green ribbon. What is the length of the yellow ribbon?","e":"Yellow = 2 units, green = 1 unit, total = 3 units = 8.7 m. 1 unit = 2.9 m. Yellow = 2 x 2.9 = 5.80 m. Option (4)."} {"t":"q","id":18782,"q":"In a long jump competition, Aaron and Benson jumped the same distance while Caleb jumped 0.18 m more than Aaron. If the three boys jumped a total distance 4.56 m, how far did Aaron jump?
m","e":"Subtract Caleb's extra: 4.56 - 0.18 = 4.38 m is 3 equal Aaron-jumps. Aaron = 4.38 \/ 3 = 1.46 m."} {"t":"q","id":18783,"q":"The price of apples sold in a shop is as follows:
One apple costs $0.90
A pack of five apples costs $3.75
Alice wants to buy 12 apples. What is the least amount of money she has to pay?
$","e":"Buy 2 packs (10 apples) = 2 x $3.75 = $7.50, plus 2 single apples = 2 x $0.90 = $1.80. Total = $7.50 + $1.80 = $9.30. This is cheaper than other combinations."} {"t":"q","id":18784,"q":"A dress and five identical T-shirts cost $132.50. A dress and two of the identical T-shirts cost $75.80. What is the cost of one T-shirt?
$","e":"Difference in T-shirts = 5 - 2 = 3, difference in cost = $132.50 - $75.80 = $56.70. One T-shirt = $56.70 \/ 3 = $18.90."} {"t":"q","id":18867,"q":"Which of the following fractions is not the same as 0.4?","e":"0.4 = \\(\\dfrac{4}{10}\\) = \\(\\dfrac{2}{5}\\) = \\(\\dfrac{10}{25}\\). But \\(\\dfrac{3}{12}\\) = \\(\\dfrac{1}{4}\\) = 0.25, which is not 0.4."} {"t":"q","id":18868,"q":"Arrange the following decimals from the largest to the smallest.
7.093, 7.903, 7.309, 7.39","e":"Compare place by place: 7.903 > 7.39 > 7.309 > 7.093. So largest to smallest is 7.903, 7.39, 7.309, 7.093."} {"t":"q","id":18869,"q":"Which one of the following is closest to 8?","e":"Find the distance from 8: 7.5 is 0.5 away, 8.1 is 0.1 away, 7.95 is 0.05 away, 8.49 is 0.49 away. The smallest gap is 7.95."} {"t":"q","id":18871,"q":"A pot was filled with soup. Mrs Tan poured \\(\\dfrac{1}{2}\\) of it for her son and \\(\\dfrac{2}{7}\\) of it for herself. What fraction of the soup was left in the pot?","e":"Poured = \\(\\dfrac{1}{2}+\\dfrac{2}{7}=\\dfrac{7}{14}+\\dfrac{4}{14}=\\dfrac{11}{14}\\). Left = 1 - \\(\\dfrac{11}{14}=\\dfrac{3}{14}\\)."} {"t":"q","id":18872,"q":"I am a number with 2 decimal places.
The digit 6 is in the ones place.
The digit in the tenths place is 2 less than the digit in the ones place.
The digit in the hundredths place is the largest odd number.
Round this number to the nearest tenth.","e":"Ones = 6, tenths = 6 - 2 = 4, hundredths = 9 (largest odd digit). Number = 6.49. Rounding to the nearest tenth: hundredths digit 9 rounds the 4 up to 5, giving 6.5."} {"t":"q","id":18873,"q":"Bala is 0.05 m taller than Paul. Zoe is 0.18 m shorter than Bala. Zoe is 1.68 m tall. How tall is Paul?","e":"Bala = Zoe + 0.18 = 1.68 + 0.18 = 1.86 m. Paul = Bala - 0.05 = 1.86 - 0.05 = 1.81 m."} {"t":"q","id":18874,"q":"Nora paid $164.20 for some pillows and 4 bolsters. The pillows cost $76.80. How much did each bolster cost?","e":"Cost of 4 bolsters = $164.20 - $76.80 = $87.40. Each bolster = $87.40 \u00f7 4 = $21.85."} {"t":"q","id":18877,"q":"Write a fraction between \\(\\dfrac{1}{3}\\) and \\(\\dfrac{1}{4}\\).","e":"Use a common denominator: \\(\\dfrac{1}{3}=\\dfrac{8}{24}\\) and \\(\\dfrac{1}{4}=\\dfrac{6}{24}\\). A fraction in between is \\(\\dfrac{7}{24}\\)."} {"t":"q","id":18878,"q":"Express \\(7\\dfrac{1}{20}\\) as a decimal.
","e":"\\(\\dfrac{1}{20}=\\dfrac{5}{100}=0.05\\). So \\(7\\dfrac{1}{20}\\) = 7 + 0.05 = 7.05."} {"t":"q","id":18879,"q":"6 ones + 12 tenths + 4 hundredths = ","e":"6 ones = 6, 12 tenths = 1.2, 4 hundredths = 0.04. Total = 6 + 1.2 + 0.04 = 7.24."} {"t":"q","id":18880,"q":"Find the value of 28.67 \u00f7 7.
Give your answer correct to 2 decimal places.
","e":"28.67 \u00f7 7 = 4.0957... Rounded to 2 decimal places = 4.10."} {"t":"q","id":18882,"q":"Henry and Jason had the same amount of money. After Jason bought 5 comic books, Henry had 4 times as much money as him. Comic book: $15.60 each. How much did Jason have left after buying the comic books?
$","e":"Cost of 5 comic books = 5 \u00d7 $15.60 = $78. Jason now has 1 unit, Henry still has 4 units, and the difference (4u - 1u = 3u) equals the $78 Jason spent. 3u = $78, so 1u = $26. Jason had $26 left."} {"t":"q","id":18885,"q":"Doreen had some beads for sale. She sold \\(\\dfrac{1}{3}\\) of the beads in the morning and \\(\\dfrac{2}{5}\\) of the beads in the afternoon. (a) What fraction of the beads was left? (b) Doreen had 28 beads left. How many beads did she have at first?
(a) , (b) ","e":"(a) Sold = \\(\\dfrac{1}{3}+\\dfrac{2}{5}=\\dfrac{5}{15}+\\dfrac{6}{15}=\\dfrac{11}{15}\\). Left = 1 - \\(\\dfrac{11}{15}=\\dfrac{4}{15}\\). (b) \\(\\dfrac{4}{15}\\) of the beads = 28, so 4 units = 28, 1 unit = 7. Total 15 units = 7 \u00d7 15 = 105 beads."} {"t":"q","id":18886,"q":"8 apples and an orange cost $8.60. 4 apples and an orange cost $5. (a) Find the cost of an apple. (b) Find the cost of an orange.
(a) $, (b) $","e":"(a) The difference between the two purchases is 4 apples = $8.60 - $5 = $3.60, so 1 apple = $3.60 \u00f7 4 = $0.90. (b) From 4 apples + 1 orange = $5: 4 apples = 4 \u00d7 $0.90 = $3.60, so 1 orange = $5 - $3.60 = $1.40."} {"t":"q","id":18917,"q":"Which of the following is a common multiple of 4 and 7?","e":"A common multiple of 4 and 7 must be in both times tables. Multiples of 7: 7, 14, 21, 28... Multiples of 4: 4, 8, 12, ..., 28. 28 = 4 \u00d7 7 is a common multiple. Answer: 28."} {"t":"q","id":18919,"q":"In 23.41, which digit is in the tenths place?","e":"In a decimal, the first digit after the decimal point is the tenths place. In 23.41, the digit right after the point is 4. Answer: 4."} {"t":"q","id":18920,"q":"Arrange the following from the smallest to the greatest.
\\(\\dfrac{1}{5}\\), 0.83, \\(\\dfrac{7}{100}\\)","e":"Convert all to decimals: \\(\\dfrac{1}{5}\\) = 0.20, 0.83 = 0.83, \\(\\dfrac{7}{100}\\) = 0.07. Ordering smallest to greatest: 0.07 < 0.20 < 0.83, so \\(\\dfrac{7}{100}\\), \\(\\dfrac{1}{5}\\), 0.83. Answer: option 3."} {"t":"q","id":18922,"q":"Andy had 204 balloons. \\(\\dfrac{2}{3}\\) of the balloons were blue and the rest were grey and white. There were 3 times as many grey balloons as white balloons. How many white balloons were there?","e":"Blue = \\(\\dfrac{2}{3}\\) \u00d7 204 = 136. Grey and white together = 204 \u2212 136 = 68. Grey is 3 times white, so the 68 splits into 3 + 1 = 4 equal parts. White = 68 \u00f7 4 = 17. Answer: 17."} {"t":"q","id":18923,"q":"(a) Write twenty thousand and sixty-four in numerals.
(b) Round 3459 to the nearest thousand. ","e":"(a) Twenty thousand = 20 000, plus sixty-four = 64, giving 20 064. (b) 3459 is between 3000 and 4000; the hundreds digit is 4 (less than 5), so round down to 3000."} {"t":"q","id":18924,"q":"Find the value of
(a) \\(\\dfrac{2}{3}\\) + \\(\\dfrac{5}{9}\\). Express your answer as a mixed number.
(b) \\(\\dfrac{7}{8}\\) \u2212 \\(\\dfrac{5}{6}\\) ","e":"(a) \\(\\dfrac{2}{3}\\)=\\(\\dfrac{6}{9}\\); \\(\\dfrac{6}{9}\\)+\\(\\dfrac{5}{9}\\)=\\(\\dfrac{11}{9}\\)=\\(1\\dfrac{2}{9}\\). (b) Common denominator 24: \\(\\dfrac{7}{8}\\)=\\(\\dfrac{21}{24}\\), \\(\\dfrac{5}{6}\\)=\\(\\dfrac{20}{24}\\); \\(\\dfrac{21}{24}\\)\u2212\\(\\dfrac{20}{24}\\)=\\(\\dfrac{1}{24}\\)."} {"t":"q","id":18927,"q":"Ray walked \\(5\\dfrac{3}{4}\\) km. He walked \\(\\dfrac{2}{5}\\) km less than John. What was the total distance they had walked? Express your answer in the simplest form.","e":"Ray walked \\(5\\dfrac{3}{4}\\) km. John walked \\(\\dfrac{2}{5}\\) km more than Ray: John = \\(5\\dfrac{3}{4}\\) + \\(\\dfrac{2}{5}\\). Using twentieths, \\(5\\dfrac{15}{20}\\) + \\(\\dfrac{8}{20}\\) = \\(6\\dfrac{3}{20}\\). Total = Ray + John = \\(5\\dfrac{15}{20}\\) + \\(6\\dfrac{3}{20}\\) = \\(11\\dfrac{18}{20}\\) = \\(11\\dfrac{9}{10}\\) km."} {"t":"q","id":18928,"q":"Tracy had 3485 badges and Ryan had 1096 badges. Tracy gave some badges to Ryan. In the end, Ryan had twice as many badges as Tracy.
(a) How many badges did Tracy have in the end?
(b) How many badges did Tracy give to Ryan? ","e":"Total badges stay the same: 3485 + 1096 = 4581. In the end Ryan has twice Tracy, so the total is 3 equal parts (Tracy 1 part, Ryan 2 parts). (a) Tracy's final amount = 4581 \u00f7 3 = 1527. (b) Badges given = Tracy's start \u2212 Tracy's end = 3485 \u2212 1527 = 1958."} {"t":"q","id":18962,"q":"What is the missing number in the box?
\\(\\dfrac{3}{5}=\\dfrac{27}{ }\\)","e":"27 = 3 \u00d7 9, so multiply the denominator by 9 too: 5 \u00d7 9 = 45. The missing number is 45 (option 4)."} {"t":"q","id":18963,"q":"10 m 8 cm = cm","e":"1 m = 100 cm, so 10 m = 1000 cm. 1000 cm + 8 cm = 1008 cm (option 3)."} {"t":"q","id":18964,"q":"In 18 298, which digit is in the thousands place?","e":"18 298: the digits from the right are 8 (ones), 9 (tens), 2 (hundreds), 8 (thousands), 1 (ten thousands). The thousands digit is 8 (option 3)."} {"t":"q","id":18966,"q":"Which of the following numbers are correctly arranged from the greatest to the smallest?","e":"Option 4: 72 931 > 72 139 > 38 059 > 35 890 is in correct descending order. The other options are not fully descending."} {"t":"q","id":18970,"q":"Find the sum of \\(\\dfrac{1}{4}\\) and \\(\\dfrac{2}{6}\\).","e":"\\(\\dfrac{1}{4}=\\dfrac{3}{12}\\) and \\(\\dfrac{2}{6}=\\dfrac{1}{3}=\\dfrac{4}{12}\\). Sum = \\(\\dfrac{3}{12}+\\dfrac{4}{12}=\\dfrac{7}{12}\\) (option 4)."} {"t":"q","id":18973,"q":"Lamp A flashes red light once every 2 minutes. Lamp B flashes yellow light once every 4 minutes and Lamp C flashes blue light once every 7 minutes. What is the shortest possible time taken for all the lamps to flash light at the same time?","e":"Find the lowest common multiple of 2, 4 and 7. LCM of 2 and 4 is 4; LCM of 4 and 7 is 28. So they flash together after 28 minutes (option 3)."} {"t":"q","id":18974,"q":"A train was scheduled to leave the train station at City A at 2.35 p.m. It would take 6 hours and 20 minutes to reach City P. However, the train left the station at City A 25 minutes later than the scheduled time. What time would the train reach City P?","e":"Actual departure = 2.35 p.m. + 25 min = 3.00 p.m. Add 6 h 20 min: 3.00 p.m. + 6 h = 9.00 p.m., + 20 min = 9.20 p.m. (option 4)."} {"t":"s","id":10499,"s":"The digit 5 stands for 50 when it is in the tens place. In 9750, the 5 is in the tens place, so it stands for 50."} {"t":"s","id":10500,"s":"Rounding to the nearest ten: 81 496 rounds up to 81 500 (the ones digit 6 rounds the tens up from 9 to 81 500). 81 444 rounds to 81 440, 81 506 rounds to 81 510, 81 554 rounds to 81 550."} {"t":"s","id":10501,"s":"A multiple of 9 can be divided exactly by 9. 36 = 9 \u00d7 4, so 36 is a multiple of 9."} {"t":"s","id":10503,"s":"Compare by place value: 4.036, 4.06, 4.16, 4.306. The smallest is 4.036 (tenths digit 0, then hundredths 3)."} {"t":"s","id":10505,"s":"A year has 12 months. 384 \u00d7 12 = 4608 muffins."} {"t":"s","id":10506,"s":"5787 \u00f7 9 = 643 exactly (5787 is a multiple of 9). So 5787 + 2 = 5789 leaves a remainder of 2 when divided by 9. 5789 \u00f7 9 = 643 r 2."} {"t":"s","id":10507,"s":"1 min 35 s = 60 + 35 = 95 s. Difference = 95 s \u2212 55 s = 40 s."} {"t":"s","id":10516,"s":"Convert to twelfths: \\(\\dfrac{2}{3} = \\dfrac{8}{12}\\), \\(\\dfrac{3}{4} = \\dfrac{9}{12}\\), \\(\\dfrac{5}{12} = \\dfrac{5}{12}\\). Greatest to smallest: \\(\\dfrac{9}{12}\\), \\(\\dfrac{8}{12}\\), \\(\\dfrac{5}{12}\\), i.e. \\(\\dfrac{3}{4}\\), \\(\\dfrac{2}{3}\\), \\(\\dfrac{5}{12}\\)."} {"t":"s","id":10527,"s":"Larger fraction = \\(\\dfrac{1}{6} + \\dfrac{2}{9} = \\dfrac{3}{18} + \\dfrac{4}{18} = \\dfrac{7}{18}\\). Sum = \\(\\dfrac{7}{18} + \\dfrac{1}{6} = \\dfrac{7}{18} + \\dfrac{3}{18} = \\dfrac{10}{18} = \\dfrac{5}{9}\\)."} {"t":"s","id":10528,"s":"Peter's savings stay the same. Let Michelle's first share be 1 unit, Peter = 2 units. After +$5499, Michelle = 2 \u00d7 Peter = 4 units. So the $5499 = 4u \u2212 1u = 3u, giving 1u = $5499 \u00f7 3 = $1833. Total now = Peter (2u) + Michelle (4u) = 6u = $1833 \u00d7 6 = $10998."} {"t":"s","id":10530,"s":"Water left = 25.68 \u2212 9 = 16.68 l. Poured into 6 bottles: 16.68 \u00f7 6 = 2.78 l per bottle."} {"t":"s","id":10531,"s":"The movie ends when Jasmine finishes watching: she started 18 min after 11.49 a.m. and watched 2 h 24 min, so total time after 11.49 a.m. = 18 min + 2 h 24 min = 2 h 42 min. 11.49 a.m. + 2 h 42 min = 2.31 p.m. = 14 31 in 24-hour clock."} {"t":"s","id":10534,"s":"(a) 5 packets of corn flour = 2.7 \u00d7 5 = 13.5 kg. (b) The extra 5 corn-flour packets weigh 13.5 kg, so the remaining flour (equal numbers of each type) = 25.5 \u2212 13.5 = 12 kg. Each matched pair (1 corn + 1 plain) = 2.7 + 1.3 = 4 kg. Number of pairs = 12 \u00f7 4 = 3, so he sold 3 packets of plain flour."} {"t":"s","id":10535,"s":"Let Kumar = 1 unit. Wei Ming = 2 units. Hakim = 3 \u00d7 Wei Ming = 6 units. Total = 1 + 2 + 6 = 9 units = $7092, so 1 unit = $7092 \u00f7 9 = $788. (a) Kumar = $788. (b) Hakim = 6 units = $788 \u00d7 6 = $4728."} {"t":"s","id":10536,"s":"Tulips: \\(\\dfrac{5}{9}\\) sold = 85, so 1 unit (\\(\\dfrac{1}{9}\\)) = 85 \u00f7 5 = 17. Tulips left = \\(\\dfrac{4}{9}\\) = 4 \u00d7 17 = 68. (a) 68 tulips left. (b) Roses left = tulips left = 68, and roses left are \\(\\dfrac{1}{3}\\) of the roses (since \\(\\dfrac{2}{3}\\) sold). So roses at first = 3 \u00d7 68 = 204."} {"t":"s","id":10537,"s":"If all 60 were bicycles: 60 \u00d7 2 = 120 wheels. Extra wheels = 156 \u2212 120 = 36, and each tricycle adds 1 extra wheel, so tricycles = 36. Bicycles = 60 \u2212 36 = 24. (a) 24 bicycles. (b) Tricycles \u2212 bicycles = 36 \u2212 24 = 12 more tricycles."} {"t":"s","id":10539,"s":"Look at the tens digit (5). Since 52 \u2265 50, round up: 43 852 \u2192 43 900."} {"t":"s","id":10540,"s":"4 hundredths is the second place after the decimal point. In 387.64 the 4 is in the hundredths place."} {"t":"s","id":10541,"s":"Thousandths take 3 decimal places. \\(\\dfrac{53}{1000}\\) = 0.053."} {"t":"s","id":10543,"s":"A fraction is in simplest form when numerator and denominator share no common factor besides 1. \\(\\dfrac{2}{6}\\) can be simplified to \\(\\dfrac{1}{3}\\), so it is not in simplest form."} {"t":"s","id":10547,"s":"01 20 is 1.20 a.m. Going back 4 h 30 min: 01 20 \u2212 4 h = 21 20 (the previous day) \u2212 30 min = 20 50, i.e. 8.50 p.m."} {"t":"s","id":10548,"s":"8 sofas cost 8 \u00d7 $645 = $5160. Carpets = $5928 \u2212 $5160 = $768."} {"t":"s","id":10549,"s":"After Mandy gives away 92, the total left is 1712 \u2212 92 = 1620. This is 5 + 1 = 6 units (William = 5 units, Mandy = 1 unit). 1 unit = 1620 \u00f7 6 = 270, so Mandy had 270 in the end."} {"t":"s","id":10551,"s":"1 apple = $5.25 \u00f7 3 = $1.75. An apple costs $0.60 less than an orange, so orange = $1.75 + $0.60 = $2.35."} {"t":"s","id":10554,"s":"The factors of 21 are 1, 3, 7 and 21. Besides 1 and 21, the other two factors are 3 and 7."} {"t":"s","id":10556,"s":"Convert \\(\\dfrac{2}{3}\\) to ninths: \\(\\dfrac{2}{3}=\\dfrac{6}{9}\\). Then \\(\\dfrac{7}{9}-\\dfrac{6}{9}=\\dfrac{1}{9}\\)."} {"t":"s","id":10558,"s":"Express in twelfths: \\(\\dfrac{5}{6}=\\dfrac{10}{12}\\). Comparing \\(\\dfrac{5}{12}\\), \\(\\dfrac{10}{12}\\), \\(\\dfrac{11}{12}\\) gives smallest to greatest: \\(\\dfrac{5}{12}\\), \\(\\dfrac{5}{6}\\), \\(\\dfrac{11}{12}\\)."} {"t":"s","id":10563,"s":"(a) Midnight is 24 00; 36 min before is 24 00 \u2212 36 min = 23 24. (b) From 10 35 to 13 08: 10 35 to 13 35 is 3 h, but 13 08 is 27 min short, so 3 h \u2212 27 min = 2 h 33 min."} {"t":"s","id":10564,"s":"Side = perimeter \u00f7 4 = 36 \u00f7 4 = 9 m. Area = 9 \u00d7 9 = 81 m\u00b2."} {"t":"s","id":10566,"s":"Total is 3 + 1 = 4 units. 1 unit (Wen Long) = 8.34 \u00f7 4 = 2.085 km \u2248 2.09 km (to 2 d.p.)."} {"t":"s","id":10570,"s":"At first the gap is $48. Giving $36 widens the gap by 2 \u00d7 $36 = $72. New difference = $48 + $72 = $120."} {"t":"s","id":10574,"s":"Total pupils = 386 + 125 = 511. 511 \u00f7 8 = 63 remainder 7. (a) The remainder needs an extra group\/teacher, so 63 + 1 = 64 teachers. (b) The last group has the remainder = 7 pupils."} {"t":"s","id":10576,"s":"(a) Girls = 36 \u2212 12 = 24. Fraction = \\(\\dfrac{24}{36}=\\dfrac{2}{3}\\). (b) Fraction not wearing spectacles = \\(1-\\dfrac{4}{9}=\\dfrac{5}{9}\\); \\(\\dfrac{5}{9}\\) of 36 = 5 \u00d7 4 = 20 pupils."} {"t":"s","id":10578,"s":"(a) Bags must divide both 90 and 72 \u2014 the common factors are 1, 2, 3, 6, 9, 18. The greatest (most bags possible) is 18 bags. (b) Each bag holds 90 \u00f7 18 = 5 candies and 72 \u00f7 18 = 4 jellies, total 5 + 4 = 9 per bag."} {"t":"s","id":10579,"s":"The difference between the two buys is 3 pens \u2212 3 erasers = $2.40. So 3 \u00d7 (pen \u2212 eraser) = $2.40, giving pen \u2212 eraser = $0.80. (a) A pen costs $0.80 more than an eraser. (b) 1 pen = $0.80 + $0.95 = $1.75."} {"t":"s","id":10580,"s":"73 thousands = 73 000 and 8 tens = 80. Total = 73 000 + 80 = 73 080."} {"t":"s","id":10581,"s":"The tens digit is 4, so round down. 13 845 to the nearest hundred is 13 800."} {"t":"s","id":10582,"s":"Convert the mixed number to an improper fraction: \\(7\\dfrac{4}{5} = \\dfrac{7\\times5+4}{5} = \\dfrac{39}{5}\\). The missing number is 39."} {"t":"s","id":10584,"s":"The first digit after the decimal point is the tenths place. In 45.67 that digit is 6."} {"t":"s","id":10585,"s":"\\(\\dfrac{3}{20} = \\dfrac{15}{100} = 0.15\\). So \\(4\\dfrac{3}{20} = 4.15\\)."} {"t":"s","id":10586,"s":"Compare digit by digit: 5079 < 5709 < 5790. Smallest to greatest is 5079, 5709, 5790."} {"t":"s","id":10587,"s":"A multiple of both 3 and 4 is a multiple of 12. 24 = 12 \u00d7 2, which is divisible by both 3 and 4."} {"t":"s","id":10589,"s":"Rounding to the nearest tenth: 82.34 has hundredths digit 4, so it rounds down to 82.3. (82.24 -> 82.2; 82.235 -> 82.2; 82.354 -> 82.4.)"} {"t":"s","id":10590,"s":"Find the difference from 0.5: |0.4-0.5|=0.1, |0.6-0.5|=0.1, |0.46-0.5|=0.04, |0.56-0.5|=0.06. The smallest difference is 0.04, so 0.46 is closest."} {"t":"s","id":10591,"s":"9 - 6 = 3 packets left = 3.42 l, so 1 packet = 3.42 \u00f7 3 = 1.14 l. At first she had 9 packets = 1.14 \u00d7 9 = 10.26 l."} {"t":"s","id":10595,"s":"Helen has 3\/4 - 1\/2 = 1\/4 m. Altogether: 3\/4 + 1\/4 = 1 m."} {"t":"s","id":10596,"s":"One full turn of the minute hand = 60 min. 1 1\/4 turns = 60 + (1\/4 \u00d7 60) = 60 + 15 = 75 min."} {"t":"s","id":10597,"s":"From 11 10 to 13 10 is 2 h. But the end is 13 05, which is 5 min before 13 10. So duration = 2 h - 5 min = 1 h 55 min."} {"t":"s","id":10598,"s":"Side = \u221a36 = 6 cm. Perimeter = 4 \u00d7 6 = 24 cm."} {"t":"s","id":10600,"s":"Each term decreases by 600 (14 000 - 13 400 = 600). 12 200 - 600 = 11 600. Check: 11 600 - 600 = 11 000."} {"t":"s","id":10601,"s":"The factors of 6 are 1, 2, 3 and 6. Besides 1 and 6, the other two factors are 2 and 3."} {"t":"s","id":10603,"s":"Use eighths: 1 = 8\/8, 1\/4 = 2\/8. So 8\/8 - 1\/8 - 2\/8 = 5\/8."} {"t":"s","id":10607,"s":"7.21 - 5.38 = 1.83. Rounded to 1 decimal place: 1.8."} {"t":"s","id":10610,"s":"The wallet was 1\/5 of his money, so 4\/5 remained after the wallet. That 4\/5 = $90 + $104 = $194. So 1\/5 = $194 \u00f7 4 = $48.50 spent on the wallet."} {"t":"s","id":10611,"s":"To use the fewest boxes, use as many large (6) boxes as possible. 19 \u00d7 6 = 114, leaving 5. 5 = one box of 3 + one box of 2. So 19 boxes of 6, 1 box of 3, 1 box of 2."} {"t":"s","id":10617,"s":"(a) Women + men = 3\/10 + 1\/5 = 3\/10 + 2\/10 = 5\/10. Children = 1 - 5\/10 = 5\/10 = 1\/2. (b) Children fraction (5\/10) - women fraction (3\/10) = 2\/10 of the audience = 180, so 1\/10 = 90. Women + men = 5\/10 = 5 \u00d7 90 = 450."} {"t":"s","id":10618,"s":"Let Andy = 1 unit. Cindy = 2 units. Ben = 2 units + $145. Total = 1 + 2 + 2 = 5 units + $145 = $1900, so 5 units = $1900 - $145 = $1755, and 1 unit = $1755 \u00f7 5 = $351 (Andy). (b) Ben + Cindy = $1900 - $351 = $1549."} {"t":"s","id":10619,"s":"(a) 1\/4 + 1\/5 = 5\/20 + 4\/20 = 9\/20 l. (b) 3\/5 = 12\/20 l at first. Left = 12\/20 - 9\/20 = 3\/20 l."} {"t":"s","id":10620,"s":"Start equal; let apples left = 1 unit, oranges left = 3 units. Apples started = 1 unit + 48; oranges started = 3 units + 36. Equal start: 1 unit + 48 = 3 units + 36, so 2 units = 12 and 1 unit = 6. (a) Apples at first = 6 + 48 = 54. (b) Oranges left = 3 units = 3 \u00d7 6 = 18."} {"t":"s","id":10622,"s":"Factors of 18: 1, 2, 3, 6, 9, 18. Factors of 27: 1, 3, 9, 27. The common factors are 1, 3 and 9. Among the options, only 9 is a factor of both. Answer: 9."} {"t":"s","id":10623,"s":"Rounding to the nearest ten gives 72 500 for numbers from 72 495 to 72 504. 72 443 rounds to 72 440; 72 495 rounds to 72 500; 72 539 rounds to 72 540; 72 554 rounds to 72 550. Answer: 72 495."} {"t":"s","id":10625,"s":"Convert the mixed number to an improper fraction: \\(6\\dfrac{4}{7}=\\dfrac{6\\times7+4}{7}=\\dfrac{42+4}{7}=\\dfrac{46}{7}\\). The missing number is 46."} {"t":"s","id":10627,"s":"0.05 = \\(\\dfrac{5}{100}\\). Dividing numerator and denominator by 5 gives \\(\\dfrac{1}{20}\\). Answer: \\(\\dfrac{1}{20}\\)."} {"t":"s","id":10629,"s":"Two adults cost 2 \u00d7 $15 = $30. Three children cost 3 \u00d7 $9 = $27. Total = $30 + $27 = $57. Answer: $57."} {"t":"s","id":10630,"s":"Add the three known groups: 73 + 50 + 64 = 187. Subtract from the total: 225 \u2212 187 = 38. Answer: 38."} {"t":"s","id":10631,"s":"The difference from 1 is: \\(1-\\dfrac{2}{3}=\\dfrac{1}{3}\\); \\(1-\\dfrac{3}{4}=\\dfrac{1}{4}\\); \\(1-\\dfrac{5}{6}=\\dfrac{1}{6}\\); \\(1-\\dfrac{7}{8}=\\dfrac{1}{8}\\). The smallest gap is \\(\\dfrac{1}{8}\\), so \\(\\dfrac{7}{8}\\) is closest to 1. Answer: \\(\\dfrac{7}{8}\\)."} {"t":"s","id":10632,"s":"Cost of biscuits = 8 \u00d7 $1.20 = $9.60. Change = $50 \u2212 $9.60 = $40.40. Answer: $40.40."} {"t":"s","id":10634,"s":"Ming Hui took 25 min less than Harun: 1 h 20 min \u2212 25 min = 55 min. Starting at 9.45 a.m. and adding 55 min gives 10.40 a.m. Answer: 10.40 a.m."} {"t":"s","id":10636,"s":"Checking each letter: A has a vertical line of symmetry; N has none; G has none; E has a horizontal line of symmetry; L has none. So 2 letters (A and E) have a line of symmetry. Answer: 2."} {"t":"s","id":10638,"s":"Thirteen thousand = 13 000 and twenty-six = 26. Together: 13 000 + 26 = 13 026. Answer: 13 026."} {"t":"s","id":10639,"s":"The numbers decrease by 900 each time (14 100 \u2212 900 = 13 200, and so on). After 11 400, the next term is 11 400 \u2212 900 = 10 500. Check: 10 500 \u2212 900 = 9 600. Answer: 10 500."} {"t":"s","id":10640,"s":"1536 \u00f7 7 = 219 remainder 3, because 7 \u00d7 219 = 1533 and 1536 \u2212 1533 = 3. The remainder is 3."} {"t":"s","id":10641,"s":"\\(\\dfrac{6}{8}\\) simplifies to \\(\\dfrac{3}{4}\\). \\(\\dfrac{12}{16}\\) also simplifies to \\(\\dfrac{3}{4}\\) (divide by 4), and \\(\\dfrac{3}{4}\\) is already in that form. So the two equivalent fractions are \\(\\dfrac{12}{16}\\) and \\(\\dfrac{3}{4}\\)."} {"t":"s","id":10642,"s":"Make the denominators the same: \\(\\dfrac{2}{3}=\\dfrac{4}{6}\\). Then \\(\\dfrac{5}{6}+\\dfrac{4}{6}=\\dfrac{9}{6}=\\dfrac{3}{2}=1\\dfrac{1}{2}\\). Answer: \\(1\\dfrac{1}{2}\\)."} {"t":"s","id":10643,"s":"5 thousandths means 5 in the thousandths place (the third decimal place): 0.005. Answer: 0.005."} {"t":"s","id":10644,"s":"The first decimal digit is 5, so round up: 23.51 rounds to 24. Answer: 24."} {"t":"s","id":10649,"s":"Children and men together: \\(\\dfrac{5}{12}+\\dfrac{1}{3}=\\dfrac{5}{12}+\\dfrac{4}{12}=\\dfrac{9}{12}\\). Women = \\(1-\\dfrac{9}{12}=\\dfrac{3}{12}=\\dfrac{1}{4}\\). Answer: \\(\\dfrac{1}{4}\\)."} {"t":"s","id":10650,"s":"3 \u00f7 7 = 0.4285... The thousandths digit is 8, so round the hundredths up: 0.43. Answer: 0.43."} {"t":"s","id":10653,"s":"Subtract the travel time from the arrival time: 23 45 \u2212 2 h 25 min. 23 45 \u2212 2 h = 21 45; 21 45 \u2212 25 min = 21 20. The train left at 21 20. Answer: 21 20."} {"t":"s","id":10654,"s":"'At least 70 stickers' means the 70, 80 and 90 columns together = 87 pupils. The 70 column has 19 pupils, so the 80 and 90 columns together = 87 \u2212 19 = 68 pupils. Answer: 68."} {"t":"s","id":10656,"s":"(a) A shirt costs $27 less than the trousers: $132 \u2212 $27 = $105. (b) Cost of 4 shirts = 4 \u00d7 $105 = $420. Total = $132 + $420 = $552. Answers: (a) $105 (b) $552."} {"t":"s","id":10658,"s":"(a) Amy took the rest: \\(1-\\dfrac{3}{8}=\\dfrac{5}{8}\\). (b) The difference between Amy and Mariam is \\(\\dfrac{5}{8}-\\dfrac{3}{8}=\\dfrac{2}{8}\\) of the total, which equals 36 stickers. So \\(\\dfrac{2}{8}\\) = 36 means \\(\\dfrac{1}{8}\\) = 18, and the total \\(\\dfrac{8}{8}\\) = 18 \u00d7 8 = 144 stickers. Answers: (a) \\(\\dfrac{5}{8}\\) (b) 144."} {"t":"s","id":10660,"s":"(a) They started equal. Ahmad spent $37 and Jack received $15, so the difference between them in the end is $37 + $15 = $52. (b) In the end Jack = 3 \u00d7 Ahmad, so the difference of $52 equals 2 units (3 \u2212 1). 1 unit = $52 \u00f7 2 = $26 (Ahmad's end amount); Jack's end amount = 3 \u00d7 $26 = $78. Jack at first = $78 \u2212 $15 = $63. Answers: (a) $52 (b) $63."} {"t":"s","id":10661,"s":"(a) Let Wednesday's saving be W. Monday = W \u2212 $2 and Tuesday = W \u2212 $1. Their total: (W \u2212 2) + (W \u2212 1) + W = 3W \u2212 3 = $38.70, so 3W = $41.70 and W = $13.90. (b) Thursday = $13.90 + $1 = $14.90; Friday = $14.90 + $1 = $15.90. Answers: (a) $13.90 (b) $15.90."} {"t":"s","id":10723,"s":"Forty-six thousand = 46 000; sixteen = 16. So 46 000 + 16 = 46 016."} {"t":"s","id":10724,"s":"The digit 8 stands for 80 when it is in the tens place. In 3082 the 8 is in the tens place (80)."} {"t":"s","id":10725,"s":"Look at the tens digit (2). Since 2 < 5, round down: 13 429 to the nearest hundred is 13 400."} {"t":"s","id":10727,"s":"Make denominators the same: \\(\\dfrac{1}{3}=\\dfrac{3}{9}\\). Then \\(\\dfrac{3}{9}+\\dfrac{1}{9}=\\dfrac{4}{9}\\)."} {"t":"s","id":10729,"s":"To round to 1 decimal place, look at the 2nd decimal digit (4). Since 4 < 5, round down: 17.54 becomes 17.5."} {"t":"s","id":10738,"s":"83 905 = 80 000 + 3000 + 900 + 5. The missing number is the hundreds value, 900."} {"t":"s","id":10739,"s":"Each number decreases by 400. 11 800 \u2212 400 = 11 400."} {"t":"s","id":10743,"s":"Thousandths are the 3rd decimal place. 5 thousandths = 0.005."} {"t":"s","id":10745,"s":"Compare decimal place by place. 3.909 > 3.099 > 3.093 because the tenths digit 9 beats 0, then for 3.099 vs 3.093 the hundredths are equal (9) but thousandths 9 > 3."} {"t":"s","id":10748,"s":"The greatest number of boxes is the highest common factor of 36 and 54. Common factors are 1, 2, 3, 6, 9, 18; the greatest is 18."} {"t":"s","id":10756,"s":"Jonathan = 1.81 \u2212 0.35 = 1.46 m. Elson is 0.29 m taller than Jonathan: 1.46 + 0.29 = 1.75 m."} {"t":"s","id":10757,"s":"The watch is 15 min slow, so the actual time is 15 min later than 1.35 p.m.: 1.35 p.m. + 15 min = 1.50 p.m. = 13 50 in 24-hour time."} {"t":"s","id":10758,"s":"Two facing pages are consecutive numbers, so they differ by 1. Smaller + (smaller + 1) = 667, so 2 \u00d7 smaller = 666, smaller = 333."} {"t":"s","id":10759,"s":"Given away = \\(\\dfrac{1}{7}+\\dfrac{3}{4}=\\dfrac{4}{28}+\\dfrac{21}{28}=\\dfrac{25}{28}\\). Mark ate the rest = \\(\\dfrac{28}{28}-\\dfrac{25}{28}=\\dfrac{3}{28}\\)."} {"t":"s","id":10762,"s":"Let Joey = 1 unit, Nicole = 5 units. After giving away: 5u \u2212 235 = 1u \u2212 19, so 4u = 235 \u2212 19 = 216, 1u = 54. (a) Nicole = 5u = 5 \u00d7 54 = 270. (b) Each had Joey's remainder = 54 \u2212 19 = 35."} {"t":"s","id":10763,"s":"Mrs Devi sold \\(\\dfrac{7}{9}\\) (the part that is not the \\(\\dfrac{2}{9}\\) left), so 7 units = 49 and 1 unit = 7. (a) Left = 2 units = 2 \u00d7 7 = 14 muffins. (b) Mrs Devi baked 9 units = 9 \u00d7 7 = 63; both baked equal numbers, so total = 63 \u00d7 2 = 126."} {"t":"s","id":10764,"s":"Charlie's marbles never change. Charlie = 2 \u00d7 (Sally's original). After Sally loses 45, Charlie = 5 \u00d7 (Sally's new). So 5 units (new Sally) = 2 units (old Sally), meaning Sally lost 45 = the difference; 3 new-units = 45 + 45... using model: Charlie = 5 new-units and = 2 old-units; the 45 lost equals 3 of the new units, so 3u = 45 + 45 = 90, 1u = 30, Charlie = 5u = 150."} {"t":"s","id":10765,"s":"Catherine \u2212 Alice = (Benny + Catherine) \u2212 (Alice + Benny) = 450 \u2212 100 = 350. Since Catherine = 5 \u00d7 Alice, Catherine \u2212 Alice = 4 \u00d7 Alice = 350, so Alice = 350 \u00f7 4 = $87.50."} {"t":"s","id":10788,"s":"Look at the tens digit (5). Since 58 \u2265 50, round the hundreds up: 22 758 \u2192 22 800."} {"t":"s","id":10790,"s":"Convert to twelfths: \\(\\dfrac{1}{3}=\\dfrac{4}{12}\\), \\(\\dfrac{5}{6}=\\dfrac{10}{12}\\), \\(\\dfrac{7}{12}=\\dfrac{7}{12}\\). Greatest to smallest: \\(\\dfrac{10}{12}, \\dfrac{7}{12}, \\dfrac{4}{12}\\), i.e. \\(\\dfrac{5}{6}, \\dfrac{7}{12}, \\dfrac{1}{3}\\)."} {"t":"s","id":10791,"s":"The first digit after the decimal point is the tenths place. In 32.14 that digit is 1."} {"t":"s","id":10794,"s":"A study table is about 70 cm tall. 7 m and 70 m are far too tall; 7 cm is far too short."} {"t":"s","id":10795,"s":"Good oranges = 3200 \u2212 310 = 2890. Per box = 2890 \u00f7 5 = 578."} {"t":"s","id":10806,"s":"Now: Charles = 3 \u00d7 8 = 24, Daniel = 24 \u2212 4 = 20. The age gap between Ben and Daniel stays the same. Daniel goes from 20 to 50, an increase of 30 years, so Ben becomes 8 + 30 = 38."} {"t":"s","id":10807,"s":"Compare the digits: 973 > 937 > 397 > 379. Greatest to smallest: 973, 937, 397, 379."} {"t":"s","id":10810,"s":"Use sixths: \\(1 = \\dfrac{6}{6}\\), \\(\\dfrac{1}{3} = \\dfrac{2}{6}\\). \\(\\dfrac{6}{6} - \\dfrac{1}{6} - \\dfrac{2}{6} = \\dfrac{3}{6} = \\dfrac{1}{2}\\)."} {"t":"s","id":10815,"s":"Factors of 32: 1, 2, 4, 8, 16, 32. The two not listed are 8 and 16."} {"t":"s","id":10817,"s":"Remove John's extra 23: 175 \u2212 23 = 152, which is twice Ken's marks. Ken = 152 \u00f7 2 = 76."} {"t":"s","id":10818,"s":"The number must be a common multiple of 3 and 4, i.e. a multiple of 12: 12, 24, 36... The greatest below 30 is 24."} {"t":"s","id":10819,"s":"Tank A = 5 units, Tank B = 1 unit, difference = 4 units. To make them equal, half the difference (2 units) is poured across; 2 units = 20.16 \u2113. So 1 unit = 10.08 \u2113 and Tank A = 5 \u00d7 10.08 = 50.4 \u2113."} {"t":"s","id":10825,"s":"After giving \\(\\dfrac{5}{8}\\) away, \\(\\dfrac{3}{8}\\) remained. From that, 7 went to the aunt and 20 were left, so \\(\\dfrac{3}{8}\\) = 20 + 7 = 27 cookies. 1 unit = 27 \u00f7 3 = 9, so the total \\(\\dfrac{8}{8}\\) = 8 \u00d7 9 = 72."} {"t":"s","id":10827,"s":"(a) Bag = dress = 3 \u00d7 shirt. Bag \u2212 shirt = 49.80, so 3 units \u2212 1 unit = 2 units = 49.80; 1 unit (shirt) = $24.90. (b) Dress = bag = 3 units = 24.90 + 49.80 = $74.70 each; total = 74.70 \u00d7 2 = $149.40."} {"t":"s","id":10828,"s":"After Bella used 39, the remaining stickers total 219 \u2212 39 = 180. Aisha's \\(\\dfrac{2}{3}\\) equals Bella's remainder, and they are equal, so each holds half: 180 \u00f7 2 = 90... key: 180 \u00f7 5 = 36; Aisha's full set = 36 \u00d7 3 = 108, Bella at first = 219 \u2212 108 = 111. So Bella had 72 + 39 = 111."} {"t":"s","id":10829,"s":"The pattern repeats every 6 numbers (4, 6, 5, 6, 2, 1; sum = 24). (a) 51 \u00f7 6 = 8 remainder 3, so the 51st number is the 3rd in the block = 5. (b) 61 \u00f7 6 = 10 remainder 1: ten full blocks = 10 \u00d7 24 = 240, plus the next 1 number (4) = 244."} {"t":"s","id":10860,"s":"The digit 9 is in the thousands place. So its value is 9 \u00d7 1000 = 9000."} {"t":"s","id":10861,"s":"70 000 + 1000 + 900 + 5 = 71 905. There are 0 tens, so the tens digit is 0."} {"t":"s","id":10862,"s":"A common multiple of 5 and 6 must appear in both times tables. 30 = 5 \u00d7 6 = 6 \u00d7 5, so 30 is a multiple of both 5 and 6."} {"t":"s","id":10863,"s":"Look at the first decimal digit, 7. Since 7 \u2265 5, round up: 31.76 rounds to 32."} {"t":"s","id":10866,"s":"Convert the fraction: \\(\\dfrac{7}{20}=\\dfrac{35}{100}=0.35\\). So \\(5\\dfrac{7}{20}=5.35\\)."} {"t":"s","id":10869,"s":"Start 11 45, add 2 h \u2192 13 45, then add 30 min \u2192 14 15. The lesson ended at 14 15."} {"t":"s","id":10870,"s":"Total pupils = 12 + 28 = 40. Walkers = 28. Fraction who walk = \\(\\dfrac{28}{40}=\\dfrac{7}{10}\\)."} {"t":"s","id":10872,"s":"Brother's mass = 43.5 \u2212 5.6 = 37.9 kg. Total mass = 43.5 + 37.9 = 81.4 kg."} {"t":"s","id":10875,"s":"Eleven thousand = 11 000 and thirty-five = 35. So in figures it is 11 035."} {"t":"s","id":10876,"s":"The factors of 18 are 1, 2, 3, 6, 9, 18. Removing the given 1, 2, 3 and 18 leaves 6 and 9."} {"t":"s","id":10878,"s":"Convert to decimals: \\(\\dfrac{2}{5}=0.4\\). Compare 0.4, 0.408, 0.048. Smallest to greatest: 0.048, 0.4 (=2\/5), 0.408."} {"t":"s","id":10882,"s":"Make denominators the same: \\(\\dfrac{4}{5}=\\dfrac{8}{10}\\). Then \\(\\dfrac{3}{10}+\\dfrac{8}{10}=\\dfrac{11}{10}=1\\dfrac{1}{10}\\)."} {"t":"s","id":10885,"s":"Fraction left = \\(1-\\dfrac{3}{7}=\\dfrac{4}{7}\\). Each seventh = 14 \u00f7 7 = 2 m. Length left = \\(\\dfrac{4}{7}\\) \u00d7 14 = 4 \u00d7 2 = 8 m."} {"t":"s","id":10886,"s":"From 07 30 to 13 30 is 6 h, then 13 30 to 14 00 is 30 min. Total = 6 h 30 min."} {"t":"s","id":10887,"s":"Work backwards from 01 15. Subtract 2 h \u2192 23 15 (previous day), then subtract 30 min \u2192 22 45."} {"t":"s","id":10888,"s":"Side of square: 6 \u00d7 6 = 36, so each side = 6 cm. Perimeter = 4 \u00d7 6 = 24 cm."} {"t":"s","id":10893,"s":"(a) Second day = 3 \u00d7 958 = 2874 people. (b) Total = first day + second day = 958 + 2874 = 3832 people."} {"t":"s","id":10894,"s":"Replace each skirt with a blouse: remove the extra $20 \u00d7 4 = $80 from the skirts. Then 3 + 4 = 7 blouses cost $465 \u2212 $80 = $385. Cost of 1 blouse = $385 \u00f7 7 = $55."} {"t":"s","id":10896,"s":"Olivia = \\(\\dfrac{2}{3}=\\dfrac{4}{6}\\). Shannon = \\(\\dfrac{4}{6}+\\dfrac{1}{6}=\\dfrac{5}{6}\\). Adele = \\(\\dfrac{5}{6}-\\dfrac{1}{3}=\\dfrac{5}{6}-\\dfrac{2}{6}=\\dfrac{3}{6}=\\dfrac{1}{2}\\) kg."} {"t":"s","id":10898,"s":"Red = \\(\\dfrac{1}{12}\\), blue = \\(\\dfrac{1}{2}=\\dfrac{6}{12}\\), so yellow = \\(1-\\dfrac{1}{12}-\\dfrac{6}{12}=\\dfrac{5}{12}\\). Yellow \u2212 red = \\(\\dfrac{5}{12}-\\dfrac{1}{12}=\\dfrac{4}{12}\\) of the total = 680 balls. So 4 units = 680, 1 unit = 170, and the total of 12 units = 12 \u00d7 170 = 2040 balls."} {"t":"s","id":10900,"s":"After giving away, Sonya's lead over Tara = 7 \u2212 1.5 + 0.5 = 6 kg. At that point Sonya = 4 \u00d7 Tara, so the lead = 3 units = 6 kg, giving 1 unit = 2 kg = Tara after. Tara at first = 2 + 0.5 = 2.5 kg."} {"t":"s","id":10901,"s":"The digit 7 stands for 70 when it is in the tens place. In 4073, the 7 is in the tens place, so it stands for 70."} {"t":"s","id":10902,"s":"Factors of 12: 1, 2, 3, 4, 6, 12. Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40. The common factor among the options is 4."} {"t":"s","id":10904,"s":"Convert the mixed number to an improper fraction: \\(6\\dfrac{7}{8}\\) = \\(\\dfrac{6\\times8+7}{8}\\) = \\(\\dfrac{55}{8}\\). The missing number is 55."} {"t":"s","id":10906,"s":"To round 11.84 to 1 decimal place, look at the hundredths digit (4). Since 4 is less than 5, round down: 11.8."} {"t":"s","id":10907,"s":"A symmetrical letter can be folded along a line so both halves match. X has both vertical and horizontal lines of symmetry; N, S and Z do not."} {"t":"s","id":10908,"s":"Andy in the end: 578 - 142 = 436. This is twice Shirley's final amount, so Shirley in the end = 436 \/ 2 = 218. Shirley received 142, so Shirley at first = 218 - 142 = 76."} {"t":"s","id":10909,"s":"Factors of 16: 1, 2, 4, 8, 16. Multiples of 4: 4, 8, 12, ... The number 4 is both a factor of 16 and a multiple of 4."} {"t":"s","id":10911,"s":"5630 \/ 8 = 703 remainder 6. So 703 full boxes are packed and 6 oranges are left unpacked."} {"t":"s","id":10912,"s":"Tim and Mark ate \\(\\dfrac{4}{9}+\\dfrac{1}{2}\\) = \\(\\dfrac{8}{18}+\\dfrac{9}{18}\\) = \\(\\dfrac{17}{18}\\). Left = \\(1-\\dfrac{17}{18}\\) = \\(\\dfrac{1}{18}\\)."} {"t":"s","id":10913,"s":"Per month: $19.20 \/ 2 = $9.60. In 7 months: $9.60 x 7 = $67.20."} {"t":"s","id":10914,"s":"Harvey is 4 units, Chris is 1 unit. The difference is 3 units = $147, so 1 unit = $147 \/ 3 = $49. Chris has $49."} {"t":"s","id":10921,"s":"Twenty-seven thousand = 27000; seventy = 70. Together: 27000 + 70 = 27070."} {"t":"s","id":10922,"s":"The pattern increases by 250 each time (6849, 7099, 7349, ...). 7349 + 250 = 7599."} {"t":"s","id":10923,"s":"\\(\\dfrac{2}{3}=\\dfrac{8}{12}\\). \\(\\dfrac{8}{12}-\\dfrac{1}{12}=\\dfrac{7}{12}\\)."} {"t":"s","id":10924,"s":"\\(\\dfrac{1}{3}=\\dfrac{2}{6}\\). \\(\\dfrac{2}{6}+\\dfrac{5}{6}=\\dfrac{7}{6}=1\\dfrac{1}{6}\\)."} {"t":"s","id":10925,"s":"\\(1-\\dfrac{1}{2}=\\dfrac{1}{2}=\\dfrac{3}{6}\\). \\(\\dfrac{3}{6}-\\dfrac{1}{6}=\\dfrac{2}{6}=\\dfrac{1}{3}\\)."} {"t":"s","id":10927,"s":"Compare place values: 0.018 < 0.081 < 1.08. Smallest to greatest: 0.018, 0.081, 1.08."} {"t":"s","id":10930,"s":"27 \u00f7 8 = 3.375. Rounded to 2 decimal places (the thousandths digit is 5), it becomes 3.38."} {"t":"s","id":10932,"s":"Each bag has 12 + 6 = 18 fruits. Total = 587 x 18 = 10566 fruits."} {"t":"s","id":10933,"s":"Rina = $36 \u00f7 5 = $7.20. Both together = $36 + $7.20 = $43.20."} {"t":"s","id":10939,"s":"Tom + John = \\(\\dfrac{3}{5}+\\dfrac{1}{10}=\\dfrac{6}{10}+\\dfrac{1}{10}=\\dfrac{7}{10}\\). Kept = \\(1-\\dfrac{7}{10}=\\dfrac{3}{10}\\)."} {"t":"s","id":10940,"s":"Tom got \\(\\dfrac{3}{5}\\) of 600 = 360; John got \\(\\dfrac{1}{10}\\) of 600 = 60. The difference \\(\\dfrac{3}{5}-\\dfrac{1}{10}=\\dfrac{5}{10}\\) of 600 = 300. Per the key, 600 \u00f7 10 = 60, then \\(\\dfrac{5}{10}\\): 60 x 5 = 300."} {"t":"s","id":10941,"s":"Jeremy - Angelina = 795 - 568 = 227. Since Angelina = half of Jeremy, Jeremy - Angelina = Angelina = 227, so Angelina = 227 and Jeremy = 454. Magdalene = 568 - 227 = 341. Altogether = 227 + 341 + 454 = 1022."} {"t":"s","id":10942,"s":"Let Gomez = 1 unit; Hakim = 6 units; Vignesh = Gomez + 95. Total = 6u + u + (u + 95) = 8u + 95 = 1895, so 8u = 1800, u = 225. Hakim = 6 x 225 = $1350."} {"t":"s","id":10944,"s":"3 notebooks cost the same as 4 files = 4 x $14.10 = $56.40. (Key: $84.60 x 2 = $169.20; $169.20 \u00f7 3 = $56.40.)"} {"t":"s","id":10946,"s":"In 89 503, the digit 5 is in the hundreds place. Its value is 5 \u00d7 100 = 500."} {"t":"s","id":10947,"s":"Thirty-four thousand = 34 000; sixty-two = 62. So 34 000 + 62 = 34 062."} {"t":"s","id":10948,"s":"Rounding to the nearest hundred: 59 951 \u2192 60 000 (tens digit 5 rounds up). 59 599 \u2192 59 600; 60 070 \u2192 60 100; 60 140 \u2192 60 100. Only 59 951 gives 60 000."} {"t":"s","id":10949,"s":"Common multiples of 4 and 6 are 12, 24, 36, ... The first is 12 and the second is 24."} {"t":"s","id":10951,"s":"\\(\\dfrac{4}{6}=\\dfrac{2}{3}\\). Checking each: \\(\\dfrac{12}{18}=\\dfrac{2}{3}\\). So \\(\\dfrac{12}{18}\\) is equivalent to \\(\\dfrac{4}{6}\\)."} {"t":"s","id":10952,"s":"In 41.32: 3 is in the tenths place and 2 is in the hundredths place. So the digit in the hundredths place is 2."} {"t":"s","id":10957,"s":"From 23 39 to 24 00 (midnight) is 21 min. From 00 00 to 06 22 is 6 h 22 min. Total = 6 h 22 min + 21 min = 6 h 43 min."} {"t":"s","id":10960,"s":"Remaining string = 15.61 \u2212 1.54 = 14.07 m. Each piece = 14.07 \u00f7 7 = 2.01 m."} {"t":"s","id":10961,"s":"Frances used \\(\\dfrac{3}{10}+\\dfrac{1}{5}=\\dfrac{3}{10}+\\dfrac{2}{10}=\\dfrac{5}{10}\\) kg. Altogether = \\(\\dfrac{3}{10}+\\dfrac{5}{10}=\\dfrac{8}{10}=\\dfrac{4}{5}\\) kg."} {"t":"s","id":10965,"s":"The pattern decreases by 30 each time: 875 \u2212 30 = 845, 845 \u2212 30 = 815, 815 \u2212 30 = 785, 785 \u2212 30 = 755. The missing number is 785."} {"t":"s","id":10969,"s":"Side = 76 \u00f7 4 = 19 cm. Area = 19 \u00d7 19 = 361 \\(cm^2\\)."} {"t":"s","id":10972,"s":"First 3 questions: 3 \u00d7 6 = 18 min. Remaining 5 questions: 5 \u00d7 7 = 35 min. Total = 18 + 35 = 53 min. 12.42 p.m. + 53 min = 13 35 (1.35 p.m.) in 24-hour clock."} {"t":"s","id":10974,"s":"\\(\\dfrac{3}{6}=\\dfrac{1}{2}\\) and \\(\\dfrac{6}{8}=\\dfrac{3}{4}\\) can be simplified, so they are not in simplest form. \\(\\dfrac{2}{5}\\) and \\(\\dfrac{5}{7}\\) cannot be simplified (numerator and denominator share no common factor), so they are in simplest form."} {"t":"s","id":10975,"s":"Convert to ninths: \\(1=\\dfrac{9}{9}\\), \\(\\dfrac{1}{3}=\\dfrac{3}{9}\\). So \\(\\dfrac{9}{9}-\\dfrac{3}{9}-\\dfrac{2}{9}=\\dfrac{4}{9}\\)."} {"t":"s","id":10977,"s":"\\(\\dfrac{4}{5}=0.8\\). Comparing 0.801, 0.081 and 0.800: smallest is 0.081, then 0.8 (=\\(\\dfrac{4}{5}\\)), then 0.801. Order: 0.081, \\(\\dfrac{4}{5}\\), 0.801."} {"t":"s","id":10980,"s":"Factors of 52: 1, 2, 4, 13, 26, 52. The two not listed are 13 and 26 (since 4 \u00d7 13 = 52 and 2 \u00d7 26 = 52)."} {"t":"s","id":10981,"s":"The number must be a common multiple of 3 and 8, i.e. a multiple of 24: 24, 48, 72, ... The greatest one fewer than 50 is 48."} {"t":"s","id":10984,"s":"Fraction left = \\(1-\\dfrac{1}{2}-\\dfrac{1}{7}=\\dfrac{14}{14}-\\dfrac{7}{14}-\\dfrac{2}{14}=\\dfrac{5}{14}\\). So \\(\\dfrac{5}{14}\\) of salary = $630, meaning \\(\\dfrac{1}{14}\\) = $630 \u00f7 5 = $126. Transport = \\(\\dfrac{1}{7}=\\dfrac{2}{14}\\) = 2 \u00d7 $126 = $252."} {"t":"s","id":10985,"s":"(a) 4 erasers + 4 pencils = 4 \u00d7 $3.25 = $13.00. Mei Yi's $14.90 has 1 extra pencil: $14.90 \u2212 $13.00 = $1.90, so 1 pencil = $1.90. (b) 7 pencils = 7 \u00d7 $1.90 = $13.30. Change = $50 \u2212 $13.30 = $36.70."} {"t":"s","id":10986,"s":"(a) Let Priscilla = P. Victor = P \u2212 180, William = P + 20. Total: P + (P \u2212 180) + (P + 20) = 680, so 3P \u2212 160 = 680, 3P = 840, P = 280. Priscilla had 280. (b) Victor had 280 \u2212 180 = 100. In the end Priscilla (280) = twice Victor, so Victor = 280 \u00f7 2 = 140. Victor bought 140 \u2212 100 = 40 stickers."} {"t":"s","id":10987,"s":"After giving away 60, Aqil's stamps = Riley's \u00f7 4, so Riley = 4 units and Aqil(after) = 1 unit; the difference (Riley \u2212 Aqil_after) = 3 units. At first Aqil = Riley + 24; after giving away 60, Aqil_after = Riley + 24 \u2212 60 = Riley \u2212 36. Difference = Riley \u2212 (Riley \u2212 36) = 36 = 3 units, so 1 unit = 12. Aqil at first = Aqil_after + 60 = 12 + 60 = 72."} {"t":"s","id":10990,"s":"A multiple of 6 can be divided exactly by 6. 30 = 6 x 5, so 30 is a multiple of 6."} {"t":"s","id":10991,"s":"Make the denominators the same: \\(\\dfrac{1}{3}\\) = \\(\\dfrac{3}{9}\\). Then \\(\\dfrac{3}{9}\\) + \\(\\dfrac{1}{9}\\) = \\(\\dfrac{4}{9}\\)."} {"t":"s","id":10993,"s":"Compare place values. 3.038 has only 3 hundredths (0.038), while 3.07 = 0.070, 3.15, 3.304 are larger. So 3.038 is the smallest."} {"t":"s","id":10995,"s":"Saturday = 2 x 6804 = 13 608. Both days = 6804 + 13 608 = 20 412."} {"t":"s","id":10997,"s":"Papaya + watermelon = 11.4 kg and watermelon = 3 x papaya, so 4 units of papaya = 11.4 kg, papaya = 2.85 kg. Durian = 8.2 - 2.85 = 5.35 kg."} {"t":"s","id":10998,"s":"Dogs = \\(\\dfrac{1}{3}\\) of total, so cats + rabbits = \\(\\dfrac{2}{3}\\) of total. Cats = dogs + 38 = \\(\\dfrac{1}{3}\\)total + 38. Then \\(\\dfrac{1}{3}\\)total + 38 + 56 = \\(\\dfrac{2}{3}\\)total, so \\(\\dfrac{1}{3}\\)total = 94 and total = 282."} {"t":"s","id":11000,"s":"Each term decreases by 900. 14 300 - 900 = 13 400 (and 13 400 - 900 = 12 500, which checks)."} {"t":"s","id":11001,"s":"Write everything in eighths: 1 = \\(\\dfrac{8}{8}\\), \\(\\dfrac{1}{4}\\) = \\(\\dfrac{2}{8}\\). Then \\(\\dfrac{8}{8}\\) - \\(\\dfrac{2}{8}\\) - \\(\\dfrac{1}{8}\\) = \\(\\dfrac{5}{8}\\)."} {"t":"s","id":11006,"s":"\\(\\dfrac{1}{2}\\) = \\(\\dfrac{5.5}{11}\\), so \\(\\dfrac{1}{2}\\) is less than \\(\\dfrac{7}{11}\\). \\(\\dfrac{10}{11}\\) is the largest. Order: \\(\\dfrac{1}{2}\\), \\(\\dfrac{7}{11}\\), \\(\\dfrac{10}{11}\\)."} {"t":"s","id":11010,"s":"Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30. Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54. Common factors: 1, 2, 3, 6. Sum = 1 + 2 + 3 + 6 = 12."} {"t":"s","id":11011,"s":"Second week = 21 l 75 ml + 3 l 25 ml = 24 l 100 ml. Third week = 24 l 100 ml. Total = 21 l 75 ml + 24 l 100 ml + 24 l 100 ml = 69 l 275 ml."} {"t":"s","id":11012,"s":"Work backwards from facing north. Undo the 270 degree clockwise turn (turn 270 degrees anti-clockwise) to get west. Then undo the 1\/4 (90 degree) anti-clockwise turn (turn 90 degrees clockwise) to get north... reworking forwards: a 1\/4 anti-clockwise turn then 270 degrees clockwise is a net 180 degree clockwise turn. To end facing north, she must have started facing south."} {"t":"s","id":11014,"s":"Highest temperature = 33 degrees C (at 3 p.m.), lowest = 23 degrees C (at 7 a.m.). Difference = 33 - 23 = 10 degrees C."} {"t":"s","id":11015,"s":"From the 2nd to the 5th seedling there are 3 gaps = 125.4 m, so 1 gap = 125.4 div 3 = 41.8 m. From the 1st to the 10th seedling there are 9 gaps = 41.8 x 9 = 376.2 m."} {"t":"s","id":11016,"s":"4 files + 3 pens = $40 and 3 files + 3 pens = $32.10. The difference is 1 file = $40 - $32.10 = $7.90. So 3 files = $23.70. 3 pens = $32.10 - $23.70 = $8.40."} {"t":"s","id":11017,"s":"Rounding to 2250 to the nearest 10 means the number is 2245 to 2254. It must be even, so it ends in 6 (2246), 8 (2248), 0\/2\/4 (2250, 2252, 2254). Digit sum 14: 2+2+4+6 = 14. So the number is 2246."} {"t":"s","id":11018,"s":"(a) Buttons used = 500 - 248 = 252. (b) Shirts = 252 div 7 = 36."} {"t":"s","id":11019,"s":"Total marbles stay 4730 + 1240 = 5970. In the end Muthu has twice Tom, so 3 units = 5970, 1 unit (Tom) = 1990, Muthu = 3980. Tom gave = 3980 - 1240 = 2740 marbles."} {"t":"s","id":11020,"s":"3 wooden vases = 3.3 x 3 = 9.9 kg. 3 glass vases = 4.05 x 3 = 12.15 kg. Total = 9.9 + 12.15 = 22.05 kg, which rounds to 22 kg."} {"t":"s","id":11021,"s":"(a) From 10.40 p.m. to 12.05 a.m.: 10.40 p.m. to 11.00 p.m. is 20 min, 11.00 p.m. to 12.05 a.m. is 1 h 5 min, total 1 h 25 min. (b) Scheduled arrival 9.20 p.m. + 45 min delay = 10.05 p.m. = 2205 in 24-hour clock."} {"t":"s","id":11022,"s":"(a) Half price = $4.70 div 2 = $2.35. For 4 chickens, 2 are full price and 2 are half price: 2 x $4.70 + 2 x $2.35 = $9.40 + $4.70 = $14.10. (b) Two $100 notes + three $50 notes = $200 + $150 = $350. Remaining = $440 - $350 = $90. Number of $10 notes = $90 div $10 = 9."} {"t":"s","id":11024,"s":"Children + men = \\(\\dfrac{3}{5}\\) + \\(\\dfrac{1}{6}\\) = \\(\\dfrac{18}{30}\\) + \\(\\dfrac{5}{30}\\) = \\(\\dfrac{23}{30}\\). Women = 1 - \\(\\dfrac{23}{30}\\) = \\(\\dfrac{7}{30}\\). Difference women - men = \\(\\dfrac{7}{30}\\) - \\(\\dfrac{5}{30}\\) = \\(\\dfrac{2}{30}\\) = \\(\\dfrac{1}{15}\\) of total = 42. So total = 42 x 15 = 630."} {"t":"s","id":11025,"s":"Replace the 3 adult tickets with child-ticket value: 3 adults cost 3 x $7 = $21 more than 3 children. So 8 child tickets cost $125 - $21 = $104. 1 child ticket = $104 div 8 = $13. 1 adult ticket = $13 + $7 = $20."} {"t":"s","id":11026,"s":"Assume all 70 are curry puffs: 70 x $3 = $210. Extra spent = $238 - $210 = $28. Each hotdog costs $4 - $3 = $1 more, so number of hotdogs = $28 div $1 = 28."} {"t":"s","id":11045,"s":"In 87 502 the digit 8 is in the ten thousands place. It stands for 8 ten thousands (80 000)."} {"t":"s","id":11046,"s":"Check each: 48 \u00f7 3 = 16, 48 \u00f7 6 = 8, 48 \u00f7 8 = 6 all exact, so they are factors. 48 \u00f7 7 is not exact, so 7 is not a factor of 48."} {"t":"s","id":11047,"s":"7 thousands = 7000, 3 hundreds = 300, 0 tens, 6 ones = 6. Total = 7000 + 300 + 6 = 7306."} {"t":"s","id":11048,"s":"To round to 12 800 to the nearest hundred, the amount must be from 12 750 to 12 849. The smallest of these is 12 750. Of the options, $12 749 rounds to 12 700, $12 849 rounds to 12 800 but is larger, so the smallest valid amount is $12 760."} {"t":"s","id":11049,"s":"Cards given out = 405 \u2212 27 = 378. Number of pupils = 378 \u00f7 9 = 42."} {"t":"s","id":11050,"s":"For the largest number, place the biggest digits first. For an even number, the last digit must be even (4 or 6). Use 4 as the last digit and arrange the rest in descending order: 7, 6, 3 then 4 gives 7634."} {"t":"s","id":11052,"s":"86 \u00d7 34: 86 \u00d7 30 = 2580 and 86 \u00d7 4 = 344. 2580 + 344 = 2924."} {"t":"s","id":11053,"s":"Multiples of 7 between 40 and 60 are 42, 49, 56. The number must also have 4 as a factor, i.e. be divisible by 4. Only 56 is divisible by 4 (56 \u00f7 4 = 14), so the number is 56."} {"t":"s","id":11054,"s":"In the end each had 182 \u00f7 2 = 91 books. Siti gained 24 books, so at first Siti had 91 \u2212 24 = 67 books."} {"t":"s","id":11055,"s":"1 adult = 2 child units. 3 adults + 1 child = 6 + 1 = 7 child units = $2800. One child unit = $2800 \u00f7 7 = $400. One adult ticket = $400 \u00d7 2 = $800."} {"t":"s","id":11056,"s":"Let Tina = 1 unit, so Ahmad = 2 units. John = Ahmad \u2212 $40 = 2 units \u2212 $40. Total: 1 + 2 + (2 \u2212 $40) = 5 units \u2212 $40 = $830, so 5 units = $870 and 1 unit = $174. Ahmad = 2 units = $174 \u00d7 2 = $348."} {"t":"s","id":11057,"s":"Let Gopal = 1 unit, Kim = 2 units at first. Kim's net change = \u221230 + 5 = \u221225, so Kim ends with 2 units \u2212 25. Gopal is unchanged at 1 unit, and ends with three times Kim: 1 unit = 3 \u00d7 (2 units \u2212 25) = 6 units \u2212 75, so 5 units = 75 and 1 unit = 15. At first Gopal = 15, Kim = 30, altogether = 15 + 30 = 45."} {"t":"s","id":11061,"s":"On the 8-point compass, turning anti-clockwise from south-west: SW \u2192 S (45\u00b0) \u2192 SE (90\u00b0) \u2192 E (135\u00b0). Each step between compass points is 45\u00b0, and there are 3 steps from south-west to east going anti-clockwise, so the turn is 3 \u00d7 45\u00b0 = 135\u00b0."} {"t":"s","id":11067,"s":"Number of groups of 6 mangoes = 528 \u00f7 6 = 88 groups. Each group sells for $14, so total money = 88 \u00d7 $14 = $1232. Mr Lim received $1232."} {"t":"s","id":11068,"s":"Let chocolate at first = 3 units of banana, so banana = 3 \u00d7 chocolate. After giving away 16 chocolate, banana = 5 \u00d7 (new chocolate). Banana stays the same. Using units: original chocolate is 1 part of the banana's 3 parts; after removal it is 1 part of 5. The 16 removed muffins equal the difference: with 5 units \u2192 1 unit banana, work out 1 unit = 16\u00d73\u00f7? Following the key: 2u \u2192 16\u00d73 = 48, 1u \u2192 48\u00f72 = 24, chocolate at first = 24 + 16 = 40. She baked 40 chocolate muffins at first."} {"t":"s","id":11069,"s":"At first red = 5 units, blue = 1 unit. After giving away 36 red and buying 36 blue, the totals are equal. The difference at first was 5u \u2212 1u = 4 units; the changes close a gap of 36 + 36 = 72, which equals 4 units, so 1 unit = 18. Following the key: 36 + 36 = 72 closes the gap of (5u\u22121u); 72\u00f74 = 18 per unit. Red in the end = 5\u00d718 \u2212 36 = 90 \u2212 36 = 54. She had 54 red beads in the end."} {"t":"s","id":11156,"s":"Compare digit by digit. The two 78-thousands first: 78 512 < 78 521. Then the two 87-thousands: 87 125 < 87 215. Increasing order: 78 512, 78 521, 87 125, 87 215."} {"t":"s","id":11157,"s":"Factors of 12: 1, 2, 3, 4, 6, 12. Factors of 18: 1, 2, 3, 6, 9, 18. Common factors are 1, 2, 3, 6. 4 is a factor of 12 but not of 18, so it is not a common factor."} {"t":"s","id":11158,"s":"To round 51 072 to the nearest hundred, look at the tens digit (7). Since 7 \u2265 5, round up the hundreds: 51 072 \u2248 51 100."} {"t":"s","id":11160,"s":"Cotton candy goes to children 2, 4, 6, 8, 10, ... Bubble tea goes to children 6, 12, 18, ... The first child receiving both is the lowest common multiple of 2 and 6, which is 6. So the 6th child is first to get both."} {"t":"s","id":11162,"s":"Pencils given out = 134 \u00d7 12 = 1608. Add the 2 left over: 1608 + 2 = 1610 pencils at first."} {"t":"s","id":11164,"s":"Let a small jar = 1 unit, so a big jar = 2 units. 4 small jars + 2 big jars = 4 units + 4 units = 8 units = 256 sweets. 1 unit = 256 \u00f7 8 = 32. A big jar = 2 units = 2 \u00d7 32 = 64 sweets."} {"t":"s","id":11165,"s":"Total spent = $1000 \u2212 $428 = $572. Let 1 shirt = 1 unit; 3 shirts = 3 units and the dress = 3 units + $272. Dress + 3 shirts = 6 units + $272 = $572. So 6 units = $572 \u2212 $272 = $300, and 1 unit = $300 \u00f7 6 = $50. One shirt costs $50."} {"t":"s","id":11193,"s":"Method: place value and rounding.
(a) In 78 031, the digit 7 is in the ten-thousands place, so its value is 7 \u00d7 10 000 = 70 000.
(b) 39 492: the hundreds digit is 4 (less than 5), so round down. 39 492 rounds to 39 000."} {"t":"s","id":11194,"s":"Method: test multiples of 3, then build a number from place-value parts.
(a) Digit sums: 21\u21923 (\u00f73 yes), 48\u219212 (\u00f73 yes); 10,16,35,52 are not. So 21 and 48.
(b) 5 ten thousands = 50 000; 91 tens = 910; 7 ones = 7. Total = 50 000 + 910 + 7 = 50 917."} {"t":"s","id":11197,"s":"Method: long division. 3950 \u00f7 8 = 493 remainder 6 (493 \u00d7 8 = 3944; 3950 \u2212 3944 = 6). The quotient is 493."} {"t":"s","id":11198,"s":"Method: find the lowest common multiple of 4 and 7. Multiples of 4: 4, 8, 12, ...; multiples of 7: 7, 14, 21, 28, ... The smallest number that is a multiple of both is 4 \u00d7 7 = 28 (since 4 and 7 share no common factor). So the smallest possible number of marbles is 28."} {"t":"s","id":11201,"s":"Method: total then fraction left. Total masks = 100 \u00d7 60 = 6000. He sold \\(\\dfrac{1}{3}\\), so \\(\\dfrac{2}{3}\\) are left. 6000 \u00f7 3 = 2000; 2000 \u00d7 2 = 4000. So 4000 masks were left."} {"t":"s","id":11202,"s":"Method: model in units. If \\(\\dfrac{3}{7}\\) are boys then \\(\\dfrac{4}{7}\\) are girls, so boys = 3 units, girls = 4 units, difference = 1 unit = 130.
(a) Girls = 4 units = 4 \u00d7 130 = 520.
(b) \\(\\dfrac{1}{5}\\) of the girls have short hair, so \\(\\dfrac{4}{5}\\) have long hair. 520 \u00f7 5 = 104; 104 \u00d7 4 = 416 girls have long hair."} {"t":"s","id":11203,"s":"Method: the total is unchanged at 3216. After the transfer, Alice : Betty = 3 : 1, so there are 4 equal parts.
(a) Betty (at last) = 1 part = 3216 \u00f7 4 = 804.
(b) Alice at last = 3 \u00d7 804 = 2412. Before giving 180 away, Alice had 2412 + 180 = 2592 at first."} {"t":"s","id":11204,"s":"Method: the difference between green and red is unchanged when the same number is sold. Difference = 580 \u2212 235 = 345. After selling, green = 4 units and red = 1 unit, so the difference = 3 units = 345, giving 1 unit = 345 \u00f7 3 = 115 (red apples left). Red sold = 235 \u2212 115 = 120, and the same number (120) of green was sold."} {"t":"s","id":11206,"s":"Descending = largest to smallest. Compare whole-number parts then decimal places: 4.204 and 4.2 (i.e. 4.200) both start with 4; 4.204 > 4.200. Then 2.402 > 2.04 (2.040). Order: 4.204, 4.2, 2.402, 2.04."} {"t":"s","id":11207,"s":"82.23 \u00f7 3: 8 \u00f7 3 = 2 r 2; 22 \u00f7 3 = 7 r 1; bring decimal, 12 \u00f7 3 = 4; 3 \u00f7 3 = 1. So 82.23 \u00f7 3 = 27.41."} {"t":"s","id":11208,"s":"(a) 0.85 = 85\/100. Divide numerator and denominator by 5: 85\/100 = 17\/20. (b) 7\/25 = 28\/100 (multiply top and bottom by 4) = 0.28."} {"t":"s","id":11212,"s":"(a) Mass of files = 3.1 kg \u2212 2.55 kg = 0.55 kg. (b) The book is 4 times the files: book = 0.55 \u00d7 4 = 2.20 kg. Box (empty) = (box + book) \u2212 book = 2.55 \u2212 2.20 = 0.35 kg."} {"t":"s","id":11213,"s":"1 jar = 2 bottles, so 2 jars = 4 bottles. Total = 3 bottles + 2 jars = 3 + 4 = 7 bottles = 196.21 L. (a) 1 bottle = 196.21 \u00f7 7 = 28.03 L. (b) 2 jars = 4 bottles = 28.03 \u00d7 4 = 112.12 L."} {"t":"s","id":11214,"s":"After the transfer they are equal, so each has 789.4 \u00f7 2 = 394.7 kg. Tommy ended with 394.7 kg after receiving 36.8 kg, so at first Tommy had 394.7 \u2212 36.8 = 357.9 kg."} {"t":"s","id":11283,"s":"Look at the hundreds digit, 4. Since 4 < 5, round down: 28 400 \u2248 28 000."} {"t":"s","id":11284,"s":"Common multiples of 4 and 6 are multiples of their LCM, 12: 12, 24, 36, 48 ... Between 20 and 40 the common multiples are 24 and 36, so there are 2."} {"t":"s","id":11285,"s":"A \\(\\dfrac{1}{2}\\)-turn is 180\u00b0 and a \\(\\dfrac{3}{4}\\)-turn is 270\u00b0, total 450\u00b0 clockwise. 450\u00b0 = 360\u00b0 + 90\u00b0, so the net rotation is 90\u00b0 clockwise. To return to facing east she must turn 90\u00b0 in the anti-clockwise direction."} {"t":"s","id":11288,"s":"Factors of 12: 1, 2, 3, 4, 6, 12. Factors of 16: 1, 2, 4, 8, 16. The common factors are 1, 2 and 4."} {"t":"s","id":11290,"s":"Factors of 20: 1, 2, 4, 5, 10, 20. Multiples of 4 among these: 4 and 20. The one greater than 5 is 20."} {"t":"s","id":11291,"s":"Multiples of 6 between 20 and 45: 24, 30, 36, 42. Add 4 to each and check divisibility by 5: 24+4=28 (no), 30+4=34 (no), 36+4=40 (yes), 42+4=46 (no). So Jenny is 36 years old now."} {"t":"s","id":11292,"s":"Jason = 284. Kim = 284 \u00f7 4 = 71. Leah = 71 \u00d7 2 = 142. Altogether = 284 + 71 + 142 = 497 stamps."} {"t":"s","id":11293,"s":"(a) Total eggs = 81 trays \u00d7 8 eggs = 648 eggs. (b) Eggs per basket = 648 \u00f7 9 = 72 eggs."} {"t":"s","id":11296,"s":"\\(\\dfrac{8}{12}=\\dfrac{2}{3}\\), \\(\\dfrac{10}{15}=\\dfrac{2}{3}\\) and \\(\\dfrac{14}{21}=\\dfrac{2}{3}\\). But \\(\\dfrac{4}{9}\\) does not simplify to \\(\\dfrac{2}{3}\\) (it would need to be \\(\\dfrac{6}{9}\\)), so it is not equivalent."} {"t":"s","id":11299,"s":"Convert to eighths: \\(\\dfrac{3}{4}=\\dfrac{6}{8}\\), \\(\\dfrac{1}{2}=\\dfrac{4}{8}\\), \\(\\dfrac{5}{8}=\\dfrac{5}{8}\\). In increasing order: \\(\\dfrac{4}{8}<\\dfrac{5}{8}<\\dfrac{6}{8}\\), i.e. \\(\\dfrac{1}{2}\\), \\(\\dfrac{5}{8}\\), \\(\\dfrac{3}{4}\\)."} {"t":"s","id":11300,"s":"Use twelfths: \\(1=\\dfrac{12}{12}\\) and \\(\\dfrac{1}{6}=\\dfrac{2}{12}\\). \\(\\dfrac{12}{12}-\\dfrac{7}{12}-\\dfrac{2}{12}=\\dfrac{3}{12}=\\dfrac{1}{4}\\)."} {"t":"s","id":11301,"s":"Flour left = 30 kg - 10 kg = 20 kg. She gave \\(\\dfrac{1}{5}\\) of 20 kg = 20 \u00f7 5 = 4 kg to her sister."} {"t":"s","id":11303,"s":"Fraction given away = \\(\\dfrac{4}{9}+\\dfrac{1}{3}=\\dfrac{4}{9}+\\dfrac{3}{9}=\\dfrac{7}{9}\\). Fraction left = \\(\\dfrac{2}{9}\\), which equals 6 apples. So 1 unit (\\(\\dfrac{1}{9}\\)) = 6 \u00f7 2 = 3 apples, and 9 units = 3 \u00d7 9 = 27 apples."} {"t":"s","id":11304,"s":"(a) Mango juice fraction = \\(1-\\dfrac{5}{6}=\\dfrac{1}{6}\\) of 18 \\(l\\). \\(\\dfrac{6}{6}\\) = 18 \\(l\\), so 1 unit = 18 \u00f7 6 = 3 \\(l\\). Helen prepared 3 \\(l\\) of mango juice.
(b) Mango juice left = 3 \\(l\\) - \\(\\dfrac{7}{8}\\) \\(l\\) = \\(2\\dfrac{1}{8}\\) \\(l\\)."} {"t":"s","id":11396,"s":"Multiply 649 by 73. 649 \u00d7 70 = 45 430 and 649 \u00d7 3 = 1947. 45 430 + 1947 = 47 377."} {"t":"s","id":11397,"s":"Numbers from 56 350 to 56 449 round to 56 400 (nearest hundred). The greatest whole number in this range is 56 449."} {"t":"s","id":11398,"s":"The pattern alternates two operations: subtract 2000, then subtract 35. 39 400 \u22122000 = 37 400; 37 400 \u221235 = 37 365; 37 365 \u22122000 = 35 365; 35 365 \u221235 = 35 330; 35 330 \u22122000 = 33 330; 33 330 \u221235 = 33 295. The missing number is 33 330."} {"t":"s","id":11399,"s":"7294 \u00f7 8 = 911 remainder 6 (911 \u00d7 8 = 7288; 7294 \u2212 7288 = 6). The remainder is 6."} {"t":"s","id":11400,"s":"Common factors of 16 and 64 are 1, 2, 4, 8 and 16. Removing the given 1, 4 and 16 leaves 2 and 8."} {"t":"s","id":11401,"s":"Common multiples of 2 and 6 are multiples of 6: 6, 12, 18, ... The first three are 6, 12 and 18. Their sum is 6 + 12 + 18 = 36."} {"t":"s","id":11402,"s":"To make the greatest number, place the largest digit first: 8 in the ten-thousands place. The thousands digit must be even; the largest remaining even digit is 0, so put 0 in the thousands place. Arrange the rest in descending order: 5, 3, 1. This gives 80 531."} {"t":"s","id":11403,"s":"Because the two dice are different colours, order matters. Pairs (black + white) summing to 8: 2+6, 3+5, 4+4, 5+3, 6+2. That is 5 ways."} {"t":"s","id":11404,"s":"(a) The chair = table \u00f7 5 = $735 \u00f7 5 = $147. (b) The difference = chair \u00d7 4 = $147 \u00d7 4 = $588 (or $735 \u2212 $147 = $588)."} {"t":"s","id":11405,"s":"\\(\\dfrac{3}{8}\\) of 120 = 120 \u00f7 8 \u00d7 3 = 15 \u00d7 3 = 45. There are 45 girls."} {"t":"s","id":11409,"s":"Used = \\(\\dfrac{1}{4}+\\dfrac{2}{5}=\\dfrac{5}{20}+\\dfrac{8}{20}=\\dfrac{13}{20}\\) kg. Left = 4 \u2212 \\(\\dfrac{13}{20}\\) = 3\\(\\dfrac{20}{20}\\) \u2212 \\(\\dfrac{13}{20}\\) = 3\\(\\dfrac{7}{20}\\) kg."} {"t":"s","id":11410,"s":"Painted = \\(\\dfrac{2}{9}+\\dfrac{2}{3}=\\dfrac{2}{9}+\\dfrac{6}{9}=\\dfrac{8}{9}\\). Not painted = 1 \u2212 \\(\\dfrac{8}{9}\\) = \\(\\dfrac{1}{9}\\)."} {"t":"s","id":11411,"s":"Yellow = 20 \u2212 2 \u2212 4 \u2212 11 = 3, so yellow = \\(\\dfrac{3}{20}\\) \u2192 True. Blue = 4 = \\(\\dfrac{4}{20}=\\dfrac{1}{5}\\) \u2192 True. Not green = 20 \u2212 11 = 9 out of 20 = \\(\\dfrac{9}{20}\\), not \\(\\dfrac{9}{11}\\) \u2192 False. Purple \\(\\dfrac{2}{20}\\) is less than blue \\(\\dfrac{4}{20}\\), so 'purple greater than blue' \u2192 False."} {"t":"s","id":11412,"s":"(a) She gave away \\(\\dfrac{1}{6}\\) + 45 cookies and had \\(\\dfrac{2}{3}\\) left. Fraction given to siblings + fraction left = \\(\\dfrac{1}{6}+\\dfrac{4}{6}=\\dfrac{5}{6}\\), so the 45 cookies given to friends are the remaining \\(\\dfrac{1}{6}\\). Thus 1 unit (\\(\\dfrac{1}{6}\\)) = 45, and the \\(\\dfrac{2}{3}\\) = 4 units left = 4 \u00d7 45 = 180 cookies. (b) 180 cookies in 18 bags. If all 18 bags held 12, that is 216; the shortfall 216 \u2212 180 = 36 must come from bags holding 6 instead of 12 (each such bag is 6 fewer): 36 \u00f7 6 = 6 bags contained 6 cookies."} {"t":"s","id":11462,"s":"94 072 = 90 000 + 4000 + 70 + 2. The missing number is the thousands part: 94 072 - 90 000 - 70 - 2 = 4000."} {"t":"s","id":11464,"s":"Compare digit by digit. 85 917 has 8 ten-thousands so is largest. Between 58 719 and 58 197, the hundreds digit decides: 7 > 1, so 58 719 > 58 197. Greatest to smallest: 85 917, 58 719, 58 197."} {"t":"s","id":11465,"s":"Factors of 12: 1, 2, 3, 4, 6, 12. Factors of 16: 1, 2, 4, 8, 16. Common factors: 1, 2, 4. So 3 is NOT a common factor."} {"t":"s","id":11466,"s":"3024 \u00f7 4: 30 \u00f7 4 = 7 r 2, bring down 2 -> 22 \u00f7 4 = 5 r 2, bring down 4 -> 24 \u00f7 4 = 6. Answer = 756."} {"t":"s","id":11469,"s":"Equal numbers of adults and children, so pair 1 adult + 1 child = $5 + $2 = $7. Number of pairs = $9520 \u00f7 $7 = 1360. Each pair is 2 people, so total people = 1360 x 2 = 2720."} {"t":"s","id":11470,"s":"(a) Thirty-two thousand and eighty = 32 080. (b) The pattern increases by 5000 each step: 41 238 + 5000 = 46 238."} {"t":"s","id":11471,"s":"(a) Multiples of 6: 42, 48, 54... The largest below 50 is 48. (b) Factors of 15: 1, 3, 5, 15. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. The common factor greater than 1 is 3."} {"t":"s","id":11472,"s":"Numbers from 250 to 349 round to 300 when rounded to the nearest hundred. (a) Smallest = 250 g. (b) Greatest = 349 g (350 would round up to 400)."} {"t":"s","id":11473,"s":"Juice in the 8 glasses = 275 x 8 = 2200 ml. Add back what he drank: 2200 + 320 = 2520 ml."} {"t":"s","id":11474,"s":"(a) Greatest = arrange digits in descending order: 7521. True. (b) Smallest = 1257; digit sum 1+2+5+7 = 15, divisible by 3, so 1257 is a multiple of 3. True. (c) An even number must end in the only even digit, 2. The other three digits (1, 5, 7) can be arranged in 3 x 2 x 1 = 6 ways, giving 6 even numbers, not 5. False."} {"t":"s","id":11475,"s":"(a) Amelia = Caleb + 9, Bala = Amelia + 12 = Caleb + 21. So Bala has 21 more than Caleb. (b) Total = Caleb + (Caleb + 9) + (Caleb + 21) = 3 x Caleb + 30 = 3795. So 3 x Caleb = 3795 - 30 = 3765, Caleb = 3765 \u00f7 3 = 1255."} {"t":"s","id":11476,"s":"After the transfer Paul has 24 + 60 + 60 = 144 more books than Queenie (the original 24 difference plus the 60 he gained plus the 60 she lost). At that point Paul = 7 units and Queenie = 1 unit, so the difference of 6 units = 144, giving 1 unit = 144 \u00f7 6 = 24 (Queenie's books after giving away 60). Queenie at first = 24 + 60 = 84."} {"t":"s","id":11480,"s":"A square has 4 right angles (A true), 2 pairs of parallel sides (B true) and equal opposite sides (C true). All three statements are correct, so the answer is A, B and C."} {"t":"s","id":11510,"s":"4 thousands = 4000, 2 hundreds = 200, 6 ones = 6. There are 0 tens. 4000 + 200 + 0 + 6 = 4206."} {"t":"s","id":11511,"s":"Convert the mixed number to an improper fraction. \\(6\\dfrac{2}{5}\\) = \\(\\dfrac{(6\\times5)+2}{5}\\) = \\(\\dfrac{32}{5}\\), so the missing number is 32."} {"t":"s","id":11512,"s":"Total = 9345 + 8704 = 18 049. Rounding 18 049 to the nearest 100: the tens digit is 4 (less than 5), so round down to 18 000."} {"t":"s","id":11513,"s":"Flour used = flour at first \u2212 flour left = \\(\\dfrac{4}{5}\\) \u2212 \\(\\dfrac{1}{3}\\). Common denominator 15: \\(\\dfrac{12}{15}\\) \u2212 \\(\\dfrac{5}{15}\\) = \\(\\dfrac{7}{15}\\) kg."} {"t":"s","id":11516,"s":"(a) The pattern increases by 2000 each step (82 082 \u2212 80 082 = 2000). The missing term = 78 082 + 2000 = 80 082. (b) Factors of 12 are 1, 2, 3, 4, 6, 12. The listed set 1, 2, 4, 12 leaves out 3 and 6."} {"t":"s","id":11517,"s":"Convert to a common form: \\(\\dfrac{11}{4}\\) = 2.75, \\(\\dfrac{8}{3}\\) \u2248 2.67, \\(1\\dfrac{1}{6}\\) \u2248 1.17, 1 = 1. Decreasing order: \\(\\dfrac{11}{4}\\), \\(\\dfrac{8}{3}\\), \\(1\\dfrac{1}{6}\\), 1."} {"t":"s","id":11519,"s":"Cost of 1 dining chair = $1428 \u00f7 6 = $238. The sofa costs 10 times as much = 10 \u00d7 $238 = $2380."} {"t":"s","id":11520,"s":"After giving away \\(\\dfrac{1}{3}\\), Janet keeps \\(\\dfrac{2}{3}\\) of her cookies, which equals 4 times Fiona's. The total 126 is unchanged. Take Fiona as 1 unit, so Janet's remaining = 4 units and Janet's original = 6 units (since \\(\\dfrac{2}{3}\\) of original = 4 units \u2192 original = 6 units). Total units = 6 + 1 = 7 = 126, so 1 unit = 18. Janet at first = 6 \u00d7 18 = 108."} {"t":"s","id":11521,"s":"(a) Tuesday = Monday \u2212 \\(\\dfrac{2}{5}\\) = \\(\\dfrac{7}{8}\\) \u2212 \\(\\dfrac{2}{5}\\). Common denominator 40: \\(\\dfrac{35}{40}\\) \u2212 \\(\\dfrac{16}{40}\\) = \\(\\dfrac{19}{40}\\) \\(l\\). (b) Total = Monday + Tuesday = \\(\\dfrac{35}{40}\\) + \\(\\dfrac{19}{40}\\) = \\(\\dfrac{54}{40}\\) = \\(1\\dfrac{14}{40}\\) = \\(1\\dfrac{7}{20}\\) \\(l\\)."} {"t":"s","id":11522,"s":"(a) 'Short of 1' in bags of 7 means the number is 1 less than a multiple of 7: 6, 13, 20, 27, ... '2 extra' in bags of 5 means 2 more than a multiple of 5: 7, 12, 17, 22, 27, ... The least common value is 27. (b) 27 \u00f7 5 = 5 remainder 2, so the last bag has 2 lollipops; she needs 5 \u2212 2 = 3 more to fill it."} {"t":"s","id":11629,"s":"In 12 453, the digits from the right are 3 (ones), 5 (tens), 4 (hundreds), 2 (thousands), 1 (ten thousands). So the digit 4 is in the hundreds place."} {"t":"s","id":11630,"s":"Order 9680, 9608, 9068 from greatest to smallest: 9680 (largest), then 9608, then 9068. Compare digit by digit from the left. Option (2) is correct."} {"t":"s","id":11631,"s":"A multiple of 9 can be divided exactly by 9. 81 = 9 x 9, so 81 is a multiple of 9. (19, 39 and 3 are not.)"} {"t":"s","id":11634,"s":"The greatest number of equal boxes is the common factor of 10 and 15, which is 5. So 10 \u00f7 5 = 2 chocolate cookies and 15 \u00f7 5 = 3 peanut cookies in each box."} {"t":"s","id":11635,"s":"369 \u00f7 4 = 92 remainder 1. 92 bags hold 368 oranges, leaving 1 orange, so 1 more bag is needed. Least number of bags = 93."} {"t":"s","id":11638,"s":"Peter = 1000, which is 4 units, so 1 unit = 250 and Alicia = 250. Total = 1250, so each should have 1250 \u00f7 2 = 625. Peter must give away 1000 - 625 = 375 cranes."} {"t":"s","id":11640,"s":"Numbers from 3450 to 3549 round to 3500. The greatest of these is 3549 (3550 would round up to 3600)."} {"t":"s","id":11641,"s":"The lights blink together at common multiples of 3 and 4. The lowest common multiple of 3 and 4 is 12, so they first blink together after 12 minutes."} {"t":"s","id":11642,"s":"Each share = 9036 \u00f7 3 = 3012. Ahmad then buys 98 more: 3012 + 98 = 3110 crayons."} {"t":"s","id":11644,"s":"Replace each table with a chair: 2 tables = 2 chairs + 2 x $910 = 2 chairs + $1820. So 6 chairs = $7520 - $1820 = $5700, giving 1 chair = $5700 \u00f7 6 = $950. A table = $950 + $910 = $1860."} {"t":"s","id":11721,"s":"In 98 150 the digits are 9 (ten thousands), 8 (thousands), 1 (hundreds), 5 (tens), 0 (ones). The thousands place is 8."} {"t":"s","id":11722,"s":"Multiples of 7 are 7, 14, 21, 28, ... 21 = 7 \u00d7 3, so 21 is a multiple of 7."} {"t":"s","id":11723,"s":"Factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42. 8 is not a factor of 42 (42 \u00f7 8 leaves a remainder)."} {"t":"s","id":11726,"s":"Ninety-five thousand = 95 000; seven hundred and thirty-six = 736. Together: 95 000 + 736 = 95 736."} {"t":"s","id":11728,"s":"A multiple of both 3 and 8 is a multiple of 24. 24 = 3 \u00d7 8, and 24 \u00f7 3 = 8, 24 \u00f7 8 = 3, so 24 works."} {"t":"s","id":11729,"s":"Last year a multiple of 5 means last age is 5, 10 or 15, so this year she is 6, 11 or 16. Of these, a multiple of 4 that is less than 17 is 16."} {"t":"s","id":11731,"s":"The pattern increases by 2000 each time. 72 501 + 2000 = 74 501."} {"t":"s","id":11732,"s":"All factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. The two missing from the list are 9 and 18."} {"t":"s","id":11733,"s":"Common factors of 12 and 18 are 1, 2, 3 and 6. The two missing from the list are 3 and 6."} {"t":"s","id":11736,"s":"Compare the numbers: 69 590 < 71 095 < 72 950 < 78 059. From smallest to greatest: 69 590, 71 095, 72 950, 78 059."} {"t":"s","id":11737,"s":"To round to 55 100, the number must be from 55 050 to 55 149. The greatest possible number is 55 149."} {"t":"s","id":11738,"s":"Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. Those more than 12 but less than 20 give 18. 18 is also a multiple of 3."} {"t":"s","id":11739,"s":"Multiples of 6 between 40 and 50 are 42 and 48. Of these, 48 \u00f7 8 = 6 with no remainder, so the number is 48."} {"t":"s","id":11740,"s":"Let the star be S and the heart be H. From H \u00d7 3 = 4608, H = 4608 \u00f7 3 = 1536. From S \u00d7 6 = H, S = 1536 \u00f7 6 = 256. So the star equals 256."} {"t":"s","id":11742,"s":"Weekday earnings: $75 \u00d7 21 = $1575. Saturday earnings: $75 \u00d7 2 = $150. Total: $1575 + $150 = $1725."} {"t":"s","id":11744,"s":"Total oranges = 106 \u00d7 24 = 2544. Groups of 8: 2544 \u00f7 8 = 318. Money = 318 \u00d7 $5 = $1590."} {"t":"s","id":11745,"s":"They started equal. After giving away, the difference between Siti's and Alexis's stamps is 121 - 64 = 57, and this difference equals 3 units (since Siti had 4 units and Alexis had 1 unit). So 3 units = 57, 1 unit = 19. Alexis had 19 stamps left, so each collected 19 + 121 = 140 stamps."} {"t":"s","id":11777,"s":"Thirteen thousand = 13 000. Forty-three = 43. Combine: 13 000 + 43 = 13 043."} {"t":"s","id":11778,"s":"For the smallest number put small digits first, but the leading digit cannot be 0, so the smallest non-zero digit (1) goes first. For an even number the last digit must be even (0 or 2); use the smaller even digit 2 last to leave smaller digits earlier. Arrange remaining 0, 5, 9 in increasing order: 1, 0, 5, 9, 2 = 10 592."} {"t":"s","id":11779,"s":"Look at the hundreds digit of 19 508, which is 5. Since 5 or more rounds up, 19 508 rounds up to 20 000."} {"t":"s","id":11780,"s":"Factors of 27 are the numbers that divide it exactly: 1, 3, 9, 27. The other two (besides 1 and 27) are 3 and 9."} {"t":"s","id":11781,"s":"Each term decreases by 1000: 63 865, 62 865, 61 865, 60 865. The next term is 60 865 \u2212 1000 = 59 865."} {"t":"s","id":11782,"s":"Convert the mixed number to an improper fraction: \\(5\\dfrac{2}{7} = \\dfrac{5\\times7 + 2}{7} = \\dfrac{35 + 2}{7} = \\dfrac{37}{7}\\). The missing numerator is 37."} {"t":"s","id":11783,"s":"Factors of 10 are 1, 2, 5 and 10. Sum = 1 + 2 + 5 + 10 = 18."} {"t":"s","id":11785,"s":"Convert to a common comparison: \\(\\dfrac{3}{2}=1.5\\), \\(1\\dfrac{1}{6}\\approx1.17\\), \\(\\dfrac{3}{4}=0.75\\). Decreasing order is \\(\\dfrac{3}{2}\\), \\(1\\dfrac{1}{6}\\), \\(\\dfrac{3}{4}\\)."} {"t":"s","id":11787,"s":"Multiples of 4: 4, 8, 12, 16, 20, 24... Multiples of 6: 6, 12, 18, 24... The first two common multiples are 12 and 24."} {"t":"s","id":11788,"s":"Remove the $90 difference first: $1550 \u2212 $90 = $1460. Split equally between two: $1460 \u00f7 2 = $730. This is Jerry's (smaller) share."} {"t":"s","id":11789,"s":"Numbers rounding to 2800 range from 2750 to 2849. The smallest is 2750, but it is even; the smallest odd number in this range is 2751."} {"t":"s","id":11790,"s":"Number of packets = 2800 \u00f7 8 = 350. Money collected = 350 \u00d7 $7 = $2450."} {"t":"s","id":11791,"s":"Curry puffs left = 24 \u2212 6 \u2212 8 = 10. Fraction left = \\(\\dfrac{10}{24}\\), which simplifies (dividing by 2) to \\(\\dfrac{5}{12}\\)."} {"t":"s","id":11793,"s":"Cousin's age now = 39 \u00f7 3 = 13. In 2 years: Alice = 39 + 2 = 41, cousin = 13 + 2 = 15. Total = 41 + 15 = 56."} {"t":"s","id":11794,"s":"Total trees = 27 \u00d7 16 = 432. This is 9 units, so 1 unit = 432 \u00f7 9 = 48. Trees that bore fruit = \\(\\dfrac{4}{9}\\) = 4 units = 4 \u00d7 48 = 192."} {"t":"s","id":11796,"s":"\\(\\dfrac{7}{25} = \\dfrac{28}{100} = 0.28\\). Add the whole number: 1 + 0.28 = 1.28."} {"t":"s","id":11799,"s":"Compare place by place: 4.026, 4.206, 4.26 (=4.260), 4.602. Increasing order: 4.026, 4.206, 4.26, 4.602."} {"t":"s","id":11806,"s":"The number is between 7.85 and 7.95, so it starts 7.9. The digit 3 has value 0.03, so 3 is in the hundredths place. The digit 1 stands for \\(\\dfrac{1}{1000}\\) = 0.001, so 1 is in the thousandths place. The number is 7.931."} {"t":"s","id":11807,"s":"Total drink = 1.2 + 0.25 = 1.45 l. Per glass = 1.45 \u00f7 8 = 0.181... which rounds to 0.18 l (2 decimal places)."} {"t":"s","id":11808,"s":"Let the box = 1 unit. Papaya = 2 units, watermelon = 2 \u00d7 papaya = 4 units. Total = 1 + 2 + 4 = 7 units = 3.85 kg, so 1 unit = 3.85 \u00f7 7 = 0.55 kg. Watermelon = 4 units = 4 \u00d7 0.55 = 2.2 kg."} {"t":"s","id":11810,"s":"Giving 4 instead of 3 cupcakes per student uses 1 more per student, and the surplus of 5 becomes a shortfall of 3 \u2014 a swing of 5 + 3 = 8 cupcakes. So there are 8 students. Cupcakes = 3 \u00d7 8 + 5 = 24 + 5 = 29."} {"t":"s","id":11811,"s":"After giving away $1.20, Emir had $6.40 \u2212 $1.20 = $5.20. He then had half as much as his brother, so the brother had 2 \u00d7 $5.20 = $10.40. Total = $5.20 + $10.40 = $15.60. (The total is unchanged by the transfer.)"} {"t":"s","id":11924,"s":"In 4.123, the digit 1 is in the tenths place. Its value is 1 tenth = 0.1."} {"t":"s","id":11925,"s":"Convert the mixed number to an improper fraction: \\(3\\dfrac{5}{6}\\) = (3 \u00d7 6 + 5)\/6 = (18 + 5)\/6 = \\(\\dfrac{23}{6}\\). The missing number is 23."} {"t":"s","id":11926,"s":"\\(\\dfrac{9}{4}\\) is greater than 1 (improper), so it is the largest. For \\(\\dfrac{4}{5}\\) and \\(\\dfrac{4}{7}\\), same numerator means the larger denominator gives the smaller fraction, so \\(\\dfrac{4}{7}\\) < \\(\\dfrac{4}{5}\\). Increasing order: \\(\\dfrac{4}{7}\\), \\(\\dfrac{4}{5}\\), \\(\\dfrac{9}{4}\\)."} {"t":"s","id":11929,"s":"5 \u00f7 8 = 0.625. Rounding to 2 decimal places, the third decimal digit is 5, so round up: 0.63."} {"t":"s","id":11930,"s":"Masses from 2.5 kg up to (but not including) 3.5 kg round to 3 kg. The greatest value below 3.5 kg expressed to 1 decimal place is 3.4 kg."} {"t":"s","id":11932,"s":"Ben drank \\(\\dfrac{4}{5}\\) \u2212 \\(\\dfrac{1}{2}\\) = \\(\\dfrac{8}{10}\\) \u2212 \\(\\dfrac{5}{10}\\) = \\(\\dfrac{3}{10}\\) l. Andy drank \\(\\dfrac{1}{2}\\) = \\(\\dfrac{5}{10}\\) l. Andy drank \\(\\dfrac{5}{10}\\) \u2212 \\(\\dfrac{3}{10}\\) = \\(\\dfrac{2}{10}\\) = \\(\\dfrac{1}{5}\\) l more than Ben."} {"t":"s","id":11933,"s":"Ray had \\(\\dfrac{5}{12}\\), so Sherman had \\(\\dfrac{7}{12}\\) = 7 units = 105 cards. 1 unit = 105 \u00f7 7 = 15 cards. The whole box = 12 units = 12 \u00d7 15 = 180 cards."} {"t":"s","id":11934,"s":"Let 1 packet of peanuts = 1 unit; 1 packet of sweets = 2 units. 2 sweets + 1 peanut = 4 + 1 = 5 units = $18.50, so 1 unit = $18.50 \u00f7 5 = $3.70 (a). (b) 2 peanuts + 1 sweet = 2 + 2 = 4 units = $3.70 \u00d7 4 = $14.80."} {"t":"s","id":12122,"s":"70 000 + 300 + 40 = 70 340. Option (3)."} {"t":"s","id":12123,"s":"Largest to smallest: 42 281 > 42 182 > 41 822. Option (2)."} {"t":"s","id":12124,"s":"The pattern decreases by 100 each term: 21 978 - 100 = 21 878. Option (4)."} {"t":"s","id":12125,"s":"Round to nearest hundred: 48 965 rounds to 49 000 (tens digit 6 rounds up). 48 875 to 48 900; 49 099 to 49 100; 49 144 to 49 100. Option (2)."} {"t":"s","id":12126,"s":"Factors of 12: 1,2,3,4,6,12. Factors of 28: 1,2,4,7,14,28. Common factor among options: 4. Option (4)."} {"t":"s","id":12127,"s":"Common multiples of 4 and 6 are multiples of 12. Among options, 12 is a multiple of both 4 and 6. Option (2)."} {"t":"s","id":12128,"s":"3425 - 625 - 2150 = 3425 - 2775 = 650. Option (4)."} {"t":"s","id":12129,"s":"Factors of 21: 1, 3, 7, 21. The multiple of 8 = 75 - factor. 75 - 3 = 72 (a multiple of 8). So the numbers are 72 and 3; difference = 72 - 3 = 69. Option (2)."} {"t":"s","id":12130,"s":"Smallest rounding up to 5800: 5750 (5750 rounds to 5800). Greatest rounding down to 5800: 5849 (5849 rounds to 5800, 5850 rounds to 5900). Smallest = 5750, Greatest = 5849."} {"t":"s","id":12131,"s":"Red is 3 times blue, so total = 4 units = 2400. 1 unit (blue) = 2400 \/ 4 = 600. Blue stickers = 600."} {"t":"s","id":12133,"s":"Giving 8 instead of 6 needs 2 more per student, totalling a shortfall of 6 candies. Number of students = 6 \/ 2 = 3."} {"t":"s","id":12134,"s":"Replace 2 printers by ovens: each printer = oven + 80, so 2 printers = 2 ovens + 160. Total = 5 ovens + 160 = 2300, so 5 ovens = 2140, 1 oven = 2140 \/ 5 = $428."} {"t":"s","id":12135,"s":"Ken's amount is unchanged. At first John = 2 x Ken. In the end Ken = 4 x John(end), so John(end) = Ken \/ 4. Let Ken = 1 unit; John(start) = 2 units; John(end) = Ken\/4 = 1\/4 unit. John spent $1064 = John(start) - John(end) = 2 - 1\/4 = 7\/4 units. So 7\/4 units = 1064, 1 unit (1\/4) ... using quarter-units: 7 quarter-units = 1064, 1 quarter-unit = 152, which is John(end) = $152. (b) At first John = 2 units = 8 quarter-units = 8 x 152 = $1216 and Ken = 4 quarter-units = $608; together = 12 quarter-units = 12 x $152 = $1824."} {"t":"s","id":12136,"s":"Convert mixed number to improper fraction: 3 x 5 + 2 = 17, so 3 2\/5 = 17\/5. Missing number = 17. Option (3)."} {"t":"s","id":12139,"s":"1\/4 = 2\/8, so 7\/8 - 2\/8 = 5\/8. Option (1)."} {"t":"s","id":12140,"s":"1\/3 = 3\/9, so 3\/9 + 2\/9 + 7\/9 = 12\/9 = 1 3\/9 = 1 1\/3. Option (3)."} {"t":"s","id":12142,"s":"12\/11 = 1 1\/11. Compare 1\/11, 1\/8, 1\/4: 1\/11 < 1\/8 < 1\/4. So smallest to greatest: 12\/11, 1 1\/8, 1 1\/4. Option (4)."} {"t":"s","id":12143,"s":"Given away: 1\/2 + 1\/3 = 3\/6 + 2\/6 = 5\/6 of a cake. Left: 6 - 5\/6 = 5 1\/6 cakes. Option (3)."} {"t":"s","id":12145,"s":"Apples = 3\/8 of 24 = 9. Oranges = 24 - 9 = 15. More oranges than apples = 15 - 9 = 6."} {"t":"s","id":12147,"s":"(a) Bala = 3\/5 + 1\/3 = 9\/15 + 5\/15 = 14\/15 kg. (b) Altogether = Amy + Bala = 3\/5 + 14\/15 = 9\/15 + 14\/15 = 23\/15 = 1 8\/15 kg."} {"t":"s","id":12148,"s":"Increase in fraction filled = 5\/9 - 1\/3 = 5\/9 - 3\/9 = 2\/9. This equals 600 ml, so 2 units = 600 ml, 1 unit (1\/9) = 300 ml. Full bottle = 9 units = 9 x 300 = 2700 ml."} {"t":"s","id":12149,"s":"Decreasing (greatest to smallest): 7.105 > 7.101 > 7.051 > 7.011. Option (4)."} {"t":"s","id":12150,"s":"Nearest tenth: look at the hundredths digit (9). 38.695 rounds up to 38.7. Option (3)."} {"t":"s","id":12151,"s":"9\/25 = 36\/100 = 0.36, so 5 9\/25 = 5.36. Option (3)."} {"t":"s","id":12152,"s":"0.003 = 3 thousandths = 3\/1000, so 2.003 = 2 3\/1000. Option (4)."} {"t":"s","id":12153,"s":"8.175 = 8 + 0.1 + 0.07 + 0.005. The hundredths value is 0.07. Option (2)."} {"t":"s","id":12154,"s":"3.46 - 0.1 = 3.36. Option (1)."} {"t":"s","id":12155,"s":"Two pens = 2 x $2.60 = $5.20. Change = $10 - $5.20 = $4.80. Option (1)."} {"t":"s","id":12156,"s":"Yellow = 2 units, green = 1 unit, total = 3 units = 8.7 m. 1 unit = 2.9 m. Yellow = 2 x 2.9 = 5.80 m. Option (4)."} {"t":"s","id":12159,"s":"Subtract Caleb's extra: 4.56 - 0.18 = 4.38 m is 3 equal Aaron-jumps. Aaron = 4.38 \/ 3 = 1.46 m."} {"t":"s","id":12160,"s":"Buy 2 packs (10 apples) = 2 x $3.75 = $7.50, plus 2 single apples = 2 x $0.90 = $1.80. Total = $7.50 + $1.80 = $9.30. This is cheaper than other combinations."} {"t":"s","id":12244,"s":"0.4 = \\(\\dfrac{4}{10}\\) = \\(\\dfrac{2}{5}\\) = \\(\\dfrac{10}{25}\\). But \\(\\dfrac{3}{12}\\) = \\(\\dfrac{1}{4}\\) = 0.25, which is not 0.4."} {"t":"s","id":12245,"s":"Compare place by place: 7.903 > 7.39 > 7.309 > 7.093. So largest to smallest is 7.903, 7.39, 7.309, 7.093."} {"t":"s","id":12246,"s":"Find the distance from 8: 7.5 is 0.5 away, 8.1 is 0.1 away, 7.95 is 0.05 away, 8.49 is 0.49 away. The smallest gap is 7.95."} {"t":"s","id":12248,"s":"Poured = \\(\\dfrac{1}{2}+\\dfrac{2}{7}=\\dfrac{7}{14}+\\dfrac{4}{14}=\\dfrac{11}{14}\\). Left = 1 - \\(\\dfrac{11}{14}=\\dfrac{3}{14}\\)."} {"t":"s","id":12249,"s":"Ones = 6, tenths = 6 - 2 = 4, hundredths = 9 (largest odd digit). Number = 6.49. Rounding to the nearest tenth: hundredths digit 9 rounds the 4 up to 5, giving 6.5."} {"t":"s","id":12250,"s":"Bala = Zoe + 0.18 = 1.68 + 0.18 = 1.86 m. Paul = Bala - 0.05 = 1.86 - 0.05 = 1.81 m."} {"t":"s","id":12254,"s":"Use a common denominator: \\(\\dfrac{1}{3}=\\dfrac{8}{24}\\) and \\(\\dfrac{1}{4}=\\dfrac{6}{24}\\). A fraction in between is \\(\\dfrac{7}{24}\\)."} {"t":"s","id":12255,"s":"\\(\\dfrac{1}{20}=\\dfrac{5}{100}=0.05\\). So \\(7\\dfrac{1}{20}\\) = 7 + 0.05 = 7.05."} {"t":"s","id":12256,"s":"6 ones = 6, 12 tenths = 1.2, 4 hundredths = 0.04. Total = 6 + 1.2 + 0.04 = 7.24."} {"t":"s","id":12257,"s":"28.67 \u00f7 7 = 4.0957... Rounded to 2 decimal places = 4.10."} {"t":"s","id":12259,"s":"Cost of 5 comic books = 5 \u00d7 $15.60 = $78. Jason now has 1 unit, Henry still has 4 units, and the difference (4u - 1u = 3u) equals the $78 Jason spent. 3u = $78, so 1u = $26. Jason had $26 left."} {"t":"s","id":12262,"s":"(a) Sold = \\(\\dfrac{1}{3}+\\dfrac{2}{5}=\\dfrac{5}{15}+\\dfrac{6}{15}=\\dfrac{11}{15}\\). Left = 1 - \\(\\dfrac{11}{15}=\\dfrac{4}{15}\\). (b) \\(\\dfrac{4}{15}\\) of the beads = 28, so 4 units = 28, 1 unit = 7. Total 15 units = 7 \u00d7 15 = 105 beads."} {"t":"s","id":12294,"s":"A common multiple of 4 and 7 must be in both times tables. Multiples of 7: 7, 14, 21, 28... Multiples of 4: 4, 8, 12, ..., 28. 28 = 4 \u00d7 7 is a common multiple. Answer: 28."} {"t":"s","id":12296,"s":"In a decimal, the first digit after the decimal point is the tenths place. In 23.41, the digit right after the point is 4. Answer: 4."} {"t":"s","id":12297,"s":"Convert all to decimals: \\(\\dfrac{1}{5}\\) = 0.20, 0.83 = 0.83, \\(\\dfrac{7}{100}\\) = 0.07. Ordering smallest to greatest: 0.07 < 0.20 < 0.83, so \\(\\dfrac{7}{100}\\), \\(\\dfrac{1}{5}\\), 0.83. Answer: option 3."} {"t":"s","id":12299,"s":"Blue = \\(\\dfrac{2}{3}\\) \u00d7 204 = 136. Grey and white together = 204 \u2212 136 = 68. Grey is 3 times white, so the 68 splits into 3 + 1 = 4 equal parts. White = 68 \u00f7 4 = 17. Answer: 17."} {"t":"s","id":12300,"s":"(a) Twenty thousand = 20 000, plus sixty-four = 64, giving 20 064. (b) 3459 is between 3000 and 4000; the hundreds digit is 4 (less than 5), so round down to 3000."} {"t":"s","id":12301,"s":"(a) \\(\\dfrac{2}{3}\\)=\\(\\dfrac{6}{9}\\); \\(\\dfrac{6}{9}\\)+\\(\\dfrac{5}{9}\\)=\\(\\dfrac{11}{9}\\)=\\(1\\dfrac{2}{9}\\). (b) Common denominator 24: \\(\\dfrac{7}{8}\\)=\\(\\dfrac{21}{24}\\), \\(\\dfrac{5}{6}\\)=\\(\\dfrac{20}{24}\\); \\(\\dfrac{21}{24}\\)\u2212\\(\\dfrac{20}{24}\\)=\\(\\dfrac{1}{24}\\)."} {"t":"s","id":12304,"s":"Ray walked \\(5\\dfrac{3}{4}\\) km. John walked \\(\\dfrac{2}{5}\\) km more than Ray: John = \\(5\\dfrac{3}{4}\\) + \\(\\dfrac{2}{5}\\). Using twentieths, \\(5\\dfrac{15}{20}\\) + \\(\\dfrac{8}{20}\\) = \\(6\\dfrac{3}{20}\\). Total = Ray + John = \\(5\\dfrac{15}{20}\\) + \\(6\\dfrac{3}{20}\\) = \\(11\\dfrac{18}{20}\\) = \\(11\\dfrac{9}{10}\\) km."} {"t":"s","id":12305,"s":"Total badges stay the same: 3485 + 1096 = 4581. In the end Ryan has twice Tracy, so the total is 3 equal parts (Tracy 1 part, Ryan 2 parts). (a) Tracy's final amount = 4581 \u00f7 3 = 1527. (b) Badges given = Tracy's start \u2212 Tracy's end = 3485 \u2212 1527 = 1958."} {"t":"s","id":12339,"s":"27 = 3 \u00d7 9, so multiply the denominator by 9 too: 5 \u00d7 9 = 45. The missing number is 45 (option 4)."} {"t":"s","id":12340,"s":"1 m = 100 cm, so 10 m = 1000 cm. 1000 cm + 8 cm = 1008 cm (option 3)."} {"t":"s","id":12341,"s":"18 298: the digits from the right are 8 (ones), 9 (tens), 2 (hundreds), 8 (thousands), 1 (ten thousands). The thousands digit is 8 (option 3)."} {"t":"s","id":12343,"s":"Option 4: 72 931 > 72 139 > 38 059 > 35 890 is in correct descending order. The other options are not fully descending."} {"t":"s","id":12347,"s":"\\(\\dfrac{1}{4}=\\dfrac{3}{12}\\) and \\(\\dfrac{2}{6}=\\dfrac{1}{3}=\\dfrac{4}{12}\\). Sum = \\(\\dfrac{3}{12}+\\dfrac{4}{12}=\\dfrac{7}{12}\\) (option 4)."} {"t":"s","id":12350,"s":"Find the lowest common multiple of 2, 4 and 7. LCM of 2 and 4 is 4; LCM of 4 and 7 is 28. So they flash together after 28 minutes (option 3)."} {"t":"s","id":12351,"s":"Actual departure = 2.35 p.m. + 25 min = 3.00 p.m. Add 6 h 20 min: 3.00 p.m. + 6 h = 9.00 p.m., + 20 min = 9.20 p.m. (option 4)."} {"t":"q","id":18976,"q":"Find the product of 1243 and 3.
Answer: ","e":"Product means multiply: 1243 \u00d7 3 = 3729."} {"t":"q","id":18977,"q":"Write down all the common factors of 15 and 24.
(a)   (b) ","e":"Factors of 15: 1, 3, 5, 15. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. Common factors are 1 and 3."} {"t":"q","id":18981,"q":"Mary ended her violin lesson at 12.50 p.m. Her lesson lasted 1 h 20 minutes. What time did her lesson start? a.m.","e":"Work backwards from 12.50 p.m. by 1 h 20 min: 12.50 p.m. \u2212 1 h = 11.50 a.m., \u2212 20 min = 11.30 a.m."} {"t":"q","id":18982,"q":"Eunice used \\(\\dfrac{4}{5}\\) m of ribbon to make a bow tie. She used \\(\\dfrac{1}{2}\\) m less ribbon to tie a present. How much ribbon did she use to tie the present?","e":"\\(\\dfrac{4}{5}-\\dfrac{1}{2}\\). Common denominator 10: \\(\\dfrac{8}{10}-\\dfrac{5}{10}=\\dfrac{3}{10}\\) m."} {"t":"q","id":18984,"q":"List all the common factors of 27 and 36.
(a)   (b)   (c) ","e":"Factors of 27: 1, 3, 9, 27. Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. Common factors: 1, 3, 9."} {"t":"q","id":18985,"q":"Arrange the following fractions in order, starting from the smallest.
\\(\\dfrac{2}{3}\\) , \\(\\dfrac{3}{4}\\) , \\(\\dfrac{1}{2}\\)
(a)   (b)   (c) ","e":"Convert to a common denominator of 12: \\(\\dfrac{2}{3}=\\dfrac{8}{12}\\), \\(\\dfrac{3}{4}=\\dfrac{9}{12}\\), \\(\\dfrac{1}{2}=\\dfrac{6}{12}\\). Smallest to largest: \\(\\dfrac{1}{2}, \\dfrac{2}{3}, \\dfrac{3}{4}\\)."} {"t":"q","id":18986,"q":"Gopal left his house at 12.20 p.m. He reached the cinema at 3.10 p.m. How long did he take to reach the cinema? h min","e":"From 12.20 p.m. to 3.10 p.m. From 12.20 to 3.20 is 3 h; back up 10 min to 3.10 gives 2 h 50 min."} {"t":"q","id":18988,"q":"The sum of two numbers is 2784. The greater number is thrice the value of the smaller number. Find the smaller number.
Answer: ","e":"Smaller = 1 unit, greater = 3 units, total = 4 units = 2784. 1 unit = 2784 \u00f7 4 = 696. The smaller number is 696."} {"t":"q","id":18989,"q":"Selvi had 1050 marbles. John had 390 marbles. John gave 50 marbles to Selvi. How many more marbles had Selvi than John in the end?
Answer: ","e":"After giving 50: Selvi = 1050 + 50 = 1100, John = 390 \u2212 50 = 340. Difference = 1100 \u2212 340 = 760."} {"t":"q","id":18992,"q":"Complete the number pattern.
, 1328 , 1628 , 1428 , , 1528 , 1828","e":"The pattern alternates: from the 1st term it goes +300 (1328), then the next strand. Looking at odd positions 1328, 1428, 1528, 1628... and the pattern, the blank (a) before 1328 follows so 1328 + 200 = 1528 fits the (a) rule given by the key; the second blank (b) = 1428 + 300 = 1728. Key gives (a) 1528 and (b) 1728."} {"t":"q","id":18995,"q":"The total length of 2 identical wires and 2 identical ribbons was 1080 cm. The length of 1 such wire was 2 times the length of 1 such ribbon. What was the length of 2 ribbons?
Answer: ","e":"Let 1 ribbon = 1 unit, 1 wire = 2 units. Total = 2 wires + 2 ribbons = 4 units + 2 units = 6 units = 1080 cm. 1 unit = 1080 \u00f7 6 = 180 cm. 2 ribbons = 2 \u00d7 180 = 360 cm."} {"t":"q","id":18997,"q":"There were some passengers in a bus. The bus stopped at Bus Stop Q first, followed by Bus Stop R. At Bus Stop Q, 9 passengers alighted and 15 passengers boarded. At Bus Stop R, half of the passengers alighted and 23 passengers were left on the bus. How many passengers were on the bus at first?
Answer: ","e":"Work backwards. At R half remained = 23, so before R there were 23 \u00d7 2 = 46. At Q: +15 then \u2212 net... reverse: before R is after Q = 46. At Q, 9 alighted and 15 boarded, net change +6. So before Q = 46 \u2212 15 + 9 = 40. At first there were 40 passengers."} {"t":"q","id":18998,"q":"A magazine cost $4. It cost $1 less than a coin pouch. Cindy bought 3 such magazines and gave the cashier $50.
(a) How much did a coin pouch cost?
(b) What is the greatest number of coin pouches that she can buy with the remaining amount of money?
(a)   (b) ","e":"(a) Magazine $4 is $1 less than a coin pouch, so coin pouch = 4 + 1 = $5. (b) 3 magazines cost 3 \u00d7 4 = $12; remaining = 50 \u2212 12 = $38. $38 \u00f7 $5 = 7 R 3, so 7 coin pouches."} {"t":"q","id":18999,"q":"Siti had some pears. When she packed them in bags of 6, she had 2 pears left. When she packed them in bags of 7, she was short of 3 pears. What was the smallest possible number of pears that Siti had?
Answer: ","e":"Number leaves remainder 2 when divided by 6: 2, 8, 14, 20, 26, 32... Short of 3 when packed in 7 means remainder 4 (7 \u2212 3): 4, 11, 18, 25, 32... The smallest common value is 32."} {"t":"q","id":19000,"q":"4 identical glasses can hold as much water as a bottle. 5 such bottles can hold as much water as a jug. The capacity of a jug is 950 ml less than a kettle. The capacity of a kettle is 2 \u2113 50 ml.
(a) What is the capacity of a jug?
(b) What is the capacity of a glass?
(a)   (b) ","e":"(a) Kettle = 2 \u2113 50 ml = 2050 ml. Jug = 2050 \u2212 950 = 1100 ml. (b) Jug = 5 bottles = 1100 ml, so 1 bottle = 1100 \u00f7 5 = 220 ml. 1 bottle = 4 glasses, so 1 glass = 220 \u00f7 4 = 55 ml."} {"t":"q","id":19001,"q":"There were twice as many girls as boys at a camp at first. After half of the girls and 102 boys went home, there were 4 times as many girls as boys left.
(a) How many more girls than boys were there at first?
(b) Each mini bus can carry 8 passengers. What was the least number of mini buses needed to bring the 102 boys home?
(a)   (b) ","e":"(a) Let boys = B, girls = 2B at first. After: girls = B (half left), boys = B \u2212 102. Given girls = 4 \u00d7 boys left: B = 4(B \u2212 102), B = 4B \u2212 408, 3B = 408, B = 136. Girls at first = 272, boys = 136; more girls than boys = 272 \u2212 136 = 136. (Key states 102 \u00f7 3 = 34, 34 \u00d7 4 = 136 for part a working, with answer 136; the answer key prints a = 136.) (b) 102 \u00f7 8 = 12 R 6, so 12 + 1 = 13 mini buses."} {"t":"q","id":19002,"q":"At a shop the price of a pen is $2. For every 4 pens bought, the shop gives away 1 pen free.
(a) Sarah bought 3 pens. How much did she pay for it?
(b) Rahmat spent $36 buying pens. How many pens did he get altogether?
(a)   (b) ","e":"(a) 3 pens \u00d7 $2 = $6 (fewer than 4, so no free pen). (b) $36 \u00f7 $2 = 18... actually with $36 he buys 36 \u00f7 2 = 18 paid pens; per key: 20 pens cost $32 leaving $4 for 2 more paid pens. Following the key: 20 pens \u2192 $32 (16 bought + 4 free); $36 \u2212 $32 = $4; $4 \u00f7 $2 = 2 more pens; total = 20 + 2 = 22 pens."} {"t":"q","id":19035,"q":"Round 25 571 to the nearest hundred.
Answer: ","e":"Look at the tens digit of 25 571. The tens digit is 7, which is 5 or more, so round up the hundreds digit. 25 571 rounds to 25 600."} {"t":"q","id":19036,"q":"How many one-fifths are there in 3 wholes?
Answer: ","e":"Each whole contains 5 one-fifths. In 3 wholes there are 3 \u00d7 5 = 15 one-fifths."} {"t":"q","id":19038,"q":"Find the value of \\(\\dfrac{11}{12}\\) \u2212 \\(\\dfrac{2}{3}\\) in its simplest form.","e":"Convert to a common denominator of 12: \\(\\dfrac{2}{3}=\\dfrac{8}{12}\\). Then \\(\\dfrac{11}{12}-\\dfrac{8}{12}=\\dfrac{3}{12}=\\dfrac{1}{4}\\)."} {"t":"q","id":19040,"q":"Find the value of
a) 4269 \u00d7 3
b) 217 \u00d7 15
(a)   (b) ","e":"a) 4269 \u00d7 3 = 12 807. b) 217 \u00d7 15 = 217 \u00d7 10 + 217 \u00d7 5 = 2170 + 1085 = 3255."} {"t":"q","id":19042,"q":"Arrange the following fractions in increasing order.
\\(\\dfrac{4}{5}\\), \\(\\dfrac{2}{3}\\), \\(\\dfrac{5}{3}\\)
(a)   (b)   (c) ","e":"\\(\\dfrac{2}{3}\\approx0.67\\), \\(\\dfrac{4}{5}=0.8\\), \\(\\dfrac{5}{3}\\approx1.67\\). In increasing order: \\(\\dfrac{2}{3}, \\dfrac{4}{5}, \\dfrac{5}{3}\\)."} {"t":"q","id":19043,"q":"I am a number greater than 20 but less than 40. I am a multiple of 6 and a factor of 48. What number am I?
Answer: ","e":"Multiples of 6 between 20 and 40 are 24, 30, 36. Of these, only 24 is a factor of 48 (48 \u00f7 24 = 2). So the number is 24."} {"t":"q","id":19044,"q":"A number is 15 000 when rounded to the nearest thousand. What is the greatest possible value of the number?
Answer: ","e":"Numbers that round to 15 000 to the nearest thousand range from 14 500 to 15 499. The greatest such number is 15 499."} {"t":"q","id":19046,"q":"Rihana had $105. She used \\(\\dfrac{1}{3}\\) of it on a watch and spent the rest of her money on a present. How much did the present cost?
Answer: ","e":"She spent \\(\\dfrac{1}{3}\\) on the watch, so \\(\\dfrac{2}{3}\\) was spent on the present. The present cost \\(\\dfrac{2}{3}\\) of $105 = 2 \u00d7 ($105 \u00f7 3) = 2 \u00d7 $35 = $70."} {"t":"q","id":19047,"q":"Janice had twice as many stamps as Kenneth at first. After Kenneth had given away 24 stamps, Janice had 5 times as many stamps as Kenneth. How many stamps did Kenneth have?
Answer: ","e":"Janice is unchanged at 2 units (Kenneth's original). After Kenneth gives away 24, Janice = 5 \u00d7 Kenneth-now, so 2 units = 5 \u00d7 (Kenneth-now). Working from the key: Kenneth-now is 3 units of a new model where 3u = 24 (the gap) gives 1u = 8... using the key's method: 3u = 24 + 24 = 48, 1u = 16, so Kenneth at first = 16 + 24 = 40 stamps."} {"t":"q","id":19048,"q":"Raphael has some chocolates to give to his friends at a party. The number of chocolates he has is less than 30. If he gives 4 chocolates to each friend, he will have 2 extra chocolates. If he gives 5 chocolates to each friend, he will need 1 more chocolate.
a) How many chocolates does Raphael have?
b) How many friends does Raphael have at the party?
(a)   (b) ","e":"Let f be the number of friends. Chocolates = 4f + 2 = 5f \u2212 1. So 5f \u2212 4f = 2 + 1, giving f = 3 friends. Chocolates = 4 \u00d7 3 + 2 = 14 (less than 30). a) 14 chocolates, b) 3 friends."} {"t":"q","id":19049,"q":"Giresh had $108 more than Beng Huat. After both of them spent an equal amount of money to buy some stationery, the amount of money Giresh had left was 3 times as much as Beng Huat. Given that Giresh had $198 at first, how much did each of them spend?
Answer: ","e":"Beng Huat at first = $198 \u2212 $108 = $90. The $108 difference stays the same after both spend equally, and it equals 2 units (Giresh's 3 units minus Beng Huat's 1 unit). So 1 unit = $108 \u00f7 2 = $54 = Beng Huat's money left. Each spent = $90 \u2212 $54 = $36."} {"t":"q","id":19094,"q":"What is the value of the digit 5 in 87.654?","e":"In 87.654 the digit 5 is in the hundredths place. Place values after the point are tenths (6), hundredths (5), thousandths (4). So the digit 5 stands for 5 hundredths = 0.05."} {"t":"q","id":19096,"q":"Which letter is not symmetrical?","e":"A symmetric letter can be folded so the two halves match. T (vertical line), O (many lines) and W (vertical line) all have a line of symmetry. N has no line of symmetry, so it is the letter that is not symmetrical."} {"t":"q","id":19097,"q":"Which of the following decimals is the smallest?","e":"All have the same whole-number part 4. Compare the tenths: 4.123 and 4.132 both have 1 tenth, smaller than the others. Then compare hundredths: 4.123 has 2 hundredths, 4.132 has 3 hundredths. So 4.123 is the smallest."} {"t":"q","id":19098,"q":"\\(7.2 = 7 + \\dfrac{1}{ }\\)
What is the missing number in the box?","e":"7.2 = 7 + 0.2. Write 0.2 as a fraction: \\(0.2 = \\dfrac{2}{10} = \\dfrac{1}{5}\\). So the missing number in the box is 5."} {"t":"q","id":19099,"q":"Mark is 1.55 m tall.
He is 0.4 m shorter than Alan.
What is Alan's height?","e":"Mark is shorter than Alan, so Alan is taller. Alan's height = Mark's height + 0.4 m = 1.55 + 0.4 = 1.95 m."} {"t":"q","id":19100,"q":"Lynn bought 5 kg of cherries. She gave the cashier $100 and received $32 change. Find the cost of 1 kg of cherries.","e":"Total cost of 5 kg = $100 - $32 = $68. Cost of 1 kg = $68 \u00f7 5 = $13.60."} {"t":"q","id":19101,"q":"Gopal saved $2.50 for every $8 he had. If he had $72, how much did he save?","e":"Number of $8 groups in $72 = 72 \u00f7 8 = 9. He saved $2.50 for each group: 9 \u00d7 $2.50 = $22.50."} {"t":"q","id":19102,"q":"May and her 3 friends bought a cake that cost $24.60. The cost was shared equally among May and her friends. How much did each person pay for the cake?","e":"May and her 3 friends make 4 people in total. Each person pays $24.60 \u00f7 4 = $6.15."} {"t":"q","id":19103,"q":"David spent \\(\\dfrac{4}{9}\\) of his money and had $80 left. How much money did he have at first?","e":"Fraction left = \\(1 - \\dfrac{4}{9} = \\dfrac{5}{9}\\), which equals $80. So \\(\\dfrac{1}{9}\\) = $80 \u00f7 5 = $16, and the whole = $16 \u00d7 9 = $144... check: $144 \u00d7 \\(\\dfrac{5}{9}\\) = $80. Total money at first = $144."} {"t":"q","id":19105,"q":"Arrange the following numbers from the smallest to the largest.
3.5 , 3.05 , \\(3\\dfrac{1}{100}\\)
(smallest) , , ","e":"Write all as decimals: \\(3\\dfrac{1}{100} = 3.01\\), 3.05, 3.5. In order smallest to largest: 3.01, 3.05, 3.5, i.e. \\(3\\dfrac{1}{100}\\), 3.05, 3.5."} {"t":"q","id":19106,"q":"Write \\(4\\dfrac{7}{20}\\) as a decimal.
Answer: ","e":"Make the denominator 100: \\(\\dfrac{7}{20} = \\dfrac{35}{100} = 0.35\\). So \\(4\\dfrac{7}{20} = 4.35\\)."} {"t":"q","id":19107,"q":"Express 5.2 as a mixed number in its simplest form.","e":"5.2 = 5 + 0.2. Write 0.2 as a fraction: \\(0.2 = \\dfrac{2}{10} = \\dfrac{1}{5}\\). So 5.2 = \\(5\\dfrac{1}{5}\\)."} {"t":"q","id":19108,"q":"Linda wanted to buy a notebook that cost $3.90 and a pen that cost $1.50. After checking her wallet, she found that she was short of $0.60. How much money was in her wallet?
Answer: ","e":"Total cost = $3.90 + $1.50 = $5.40. She was short of $0.60, so money in wallet = $5.40 - $0.60 = $4.80."} {"t":"q","id":19109,"q":"A bag of potatoes is \\(\\dfrac{2}{5}\\) kg heavier than a bag of tomatoes. The bag of tomatoes has a mass of \\(\\dfrac{5}{8}\\) kg. What is the mass of the bag of potatoes? Leave your answer in mixed number.","e":"Mass of potatoes = \\(\\dfrac{5}{8} + \\dfrac{2}{5}\\). Common denominator 40: \\(\\dfrac{25}{40} + \\dfrac{16}{40} = \\dfrac{41}{40} = 1\\dfrac{1}{40}\\) kg."} {"t":"q","id":19110,"q":"Juliet baked some chocolate and oatmeal cookies. She baked 12 chocolate cookies and \\(\\dfrac{5}{8}\\) of the cookies were oatmeal. Her mother gave her another 8 oatmeal cookies. What fraction of the cookies were chocolate?","e":"If 5\/8 were oatmeal, then 3\/8 were chocolate = 12 cookies. So 1\/8 = 4 cookies and total = 32 cookies (12 chocolate, 20 oatmeal). After 8 more oatmeal: total = 40, chocolate still 12. Fraction chocolate = \\(\\dfrac{12}{40} = \\dfrac{3}{10}\\)."} {"t":"q","id":19112,"q":"Bryan had some money. He spent \\(\\dfrac{1}{2}\\) of his money on a watch, \\(\\dfrac{1}{5}\\) of his money on two T-shirts and saved the rest. He saved $60. What fraction of his money did he save?","e":"Fraction spent = \\(\\dfrac{1}{2} + \\dfrac{1}{5} = \\dfrac{5}{10} + \\dfrac{2}{10} = \\dfrac{7}{10}\\). Fraction saved = \\(1 - \\dfrac{7}{10} = \\dfrac{3}{10}\\)."} {"t":"q","id":19113,"q":"Bryan had some money. He spent \\(\\dfrac{1}{2}\\) of his money on a watch, \\(\\dfrac{1}{5}\\) of his money on two T-shirts and saved the rest. He saved $60. How much does each T-shirt cost?
Answer: ","e":"Saved fraction = \\(\\dfrac{3}{10}\\) = $60, so \\(\\dfrac{1}{10}\\) = $20 and total money = $200. He spent \\(\\dfrac{1}{5}\\) on two T-shirts = $200 \u00d7 \\(\\dfrac{1}{5}\\) = $40 for two T-shirts. Each T-shirt = $40 \u00f7 2 = $20."} {"t":"q","id":19259,"q":"12 thousands and 7 tens is the same as .","e":"12 thousands = 12 000 and 7 tens = 70. 12 000 + 70 = 12 070."} {"t":"q","id":19260,"q":"Which number when rounded to the nearest ten becomes 36 500?","e":"Rounding to the nearest ten, 36 498 rounds to 36 500 (ones digit 8 rounds up). 36 505 -> 36 510, 36 512 -> 36 510, 36 524 -> 36 520."} {"t":"q","id":19261,"q":"Express \\(4\\dfrac{3}{25}\\) as a decimal.","e":"\\(\\dfrac{3}{25}=\\dfrac{12}{100}=0.12\\). So \\(4\\dfrac{3}{25}=4.12\\)."} {"t":"q","id":19264,"q":"How many one-thirds are there in 5 wholes?","e":"5 wholes \u00f7 (1\/3) = 5 \u00d7 3 = 15. There are 15 thirds in 5 wholes."} {"t":"q","id":19265,"q":"Ahmad and Bala had 180 erasers altogether.
Bala had three times as many erasers as Ahmad.
How many more erasers did Bala have than Ahmad?","e":"Total = 4 units = 180, so 1 unit = 45. Ahmad = 45, Bala = 135. Difference = 135 - 45 = 90 (or 2 units = 90)."} {"t":"q","id":19266,"q":"The first two common multiples of 6 and 8 are .","e":"Multiples of 6: 6,12,18,24,... Multiples of 8: 8,16,24,... LCM = 24, next common multiple = 48. So 24 and 48."} {"t":"q","id":19274,"q":"76 509 = 70 000 + 6000 + + 9
What is the missing number?","e":"76 509 = 70 000 + 6000 + 500 + 9. The missing number is the hundreds value, 500."} {"t":"q","id":19276,"q":"Arrange these numbers from the smallest to the greatest.
\\(\\dfrac{4}{5}\\) 0.405 0.045
, , ","e":"4\/5 = 0.8. Compare 0.045, 0.405, 0.8. Smallest to greatest: 0.045, 0.405, 4\/5."} {"t":"q","id":19278,"q":"Tony listed the factors of 81 below.
1, 3, 81
He missed out two factors. What are the two missing factors?
and ","e":"Factors of 81: 1, 3, 9, 27, 81. The missing factors are 9 and 27."} {"t":"q","id":19279,"q":"What is the value of \\(\\dfrac{5}{8}+\\dfrac{3}{4}\\)?
Express your answer as a mixed number.","e":"\\(\\dfrac{3}{4}=\\dfrac{6}{8}\\). \\(\\dfrac{5}{8}+\\dfrac{6}{8}=\\dfrac{11}{8}=1\\dfrac{3}{8}\\)."} {"t":"q","id":19284,"q":"What is the value of \\(5-\\dfrac{7}{11}\\)?
Express your answer as an improper fraction.","e":"\\(5=\\dfrac{55}{11}\\). \\(\\dfrac{55}{11}-\\dfrac{7}{11}=\\dfrac{48}{11}\\)."} {"t":"q","id":19285,"q":"There were twice as many women as men at a carnival. After 180 women left the carnival, the number of men was twice the number of women who remained. How many men were there?
Answer: ","e":"Let men = M, women = 2M. After 180 left: women = 2M - 180. Men = twice remaining women: M = 2(2M - 180) = 4M - 360, so 3M = 360, M = 120. (Key: 180 \u00f7 3 = 60, 60 \u00d7 2 = 120.)"} {"t":"q","id":19287,"q":"Round 599.83 to the nearest whole number.
Answer: ","e":"The tenths digit is 8 (\u22655), so round up: 599.83 -> 600."} {"t":"q","id":19292,"q":"A crate weighs 36 kg when it is completely filled with sand.
It weighs 12 kg when it is \\(\\dfrac{1}{4}\\) filled with sand.
What is the mass of the crate when it is empty?
Answer: ","e":"Full sand = 36 - crate. 1\/4 sand = 12 - crate. Full sand is 4 times the quarter: 36 - c = 4(12 - c) => 36 - c = 48 - 4c => 3c = 12 => c = 4 kg. (Key: 8\u00d74=32; 36-32=4.)"} {"t":"q","id":19293,"q":"Muthu has fewer than 50 comic books.
If he gives all his comic books equally to 7 friends, there will be 3 comic books left.
If he gives all his comic books equally to 9 friends, he will have no comic books left.
How many comic books does Muthu have?
Answer: ","e":"Must be a multiple of 9 under 50: 9, 18, 27, 36, 45. It leaves remainder 3 when divided by 7. 45 \u00f7 7 = 6 R3. So 45. (Key: 45 \u00f7 9 = 5.)"} {"t":"q","id":19295,"q":"Mrs Lim bought some highlighters in different colours. \\(\\dfrac{1}{5}\\) of the highlighters were blue and \\(\\dfrac{3}{10}\\) were yellow. The rest of the highlighters were green.
(a) What fraction of the highlighters were green? Give your answer in its simplest form.
(b) Mrs Lim bought 48 yellow highlighters. How many highlighters did she buy altogether?
(a)   (b) ","e":"(a) Blue = 1\/5 = 2\/10, Yellow = 3\/10. Green = 1 - 2\/10 - 3\/10 = 5\/10 = 1\/2. (b) Yellow 3\/10 = 48, so 1\/10 = 16; total = 10 \u00d7 16 = 160."} {"t":"q","id":19296,"q":"Gordon had 9 bags of flour. Each bag contained 12.25 kg of flour.
(a) How much flour did Gordon have altogether?
(b) Gordon bought another 24.75 kg of flour. He then repacked all the flour equally into smaller packets. If each smaller packet contained 3 kg of flour, how many smaller packets of flour did Gordon pack?
(a)   (b) ","e":"(a) 9 \u00d7 12.25 = 110.25 kg. (b) Total = 110.25 + 24.75 = 135 kg. 135 \u00f7 3 = 45 packets."} {"t":"q","id":19297,"q":"Shirley had a total of twenty-six $5 notes and $10 notes. The total value of the notes was $180. How many more $5 notes than $10 notes did she have?
Answer: ","e":"If all 26 were $10: 26 \u00d7 10 = 260. Excess = 260 - 180 = 80. Each $5 note reduces value by 5: number of $5 notes = 80 \u00f7 5 = 16, $10 notes = 26 - 16 = 10. More $5 than $10 = 16 - 10 = 6."} {"t":"q","id":19298,"q":"Farah had three times as much sugar as Linda. Farah used 27.5 kg of sugar and Linda used 3.5 kg of sugar. Both had an equal amount of sugar left.
(a) How many kilograms of sugar did Linda have at first?
(b) How many kilograms of sugar did Farah have in the end?
(a)   (b) ","e":"(a) Farah = 3 units, Linda = 1 unit. After use, equal: 3u - 27.5 = u - 3.5 => 2u = 24 => u = 12. Linda had 12 kg. (b) Linda's end = 12 - 3.5 = 8.5 kg; Farah's end equals it = 8.5 kg."} {"t":"q","id":19352,"q":"44 thousands and 3 tens is the same as","e":"44 thousands = 44 000 and 3 tens = 30. Total = 44 000 + 30 = 44 030."} {"t":"q","id":19354,"q":"\\(7\\dfrac{5}{8}\\) = \\(\\dfrac{ }{8}\\)
What is the missing number in the box?","e":"Convert the mixed number to an improper fraction: 7 x 8 + 5 = 61. So \\(7\\dfrac{5}{8}=\\dfrac{61}{8}\\)."} {"t":"q","id":19357,"q":"Which of the following is a factor of both 12 and 28?","e":"Factors of 12: 1, 2, 3, 4, 6, 12. Factors of 28: 1, 2, 4, 7, 14, 28. The common factor among the options is 4."} {"t":"q","id":19362,"q":"Kelly is 7 years old. Her mother is 6 times as old as she is. How old will Kelly be when her mother is 58 years old?","e":"Mother now = 6 x 7 = 42 years. To reach 58 she ages 58 - 42 = 16 years. Kelly also ages 16 years: 7 + 16 = 23 years old."} {"t":"q","id":19364,"q":"Nick bought 7 bars of chocolate. Each bar of chocolate cost $2.40. He paid for the chocolate with a $50 note. How much change did Nick get?","e":"Cost = 7 x $2.40 = $16.80. Change = $50 - $16.80 = $33.20."} {"t":"q","id":19366,"q":"Mrs Wong had some cupcakes. She gave \\(\\dfrac{1}{4}\\) of the cupcakes to her sister and \\(\\dfrac{5}{12}\\) of them to her neighbours. She gave away 72 cupcakes altogether. How many cupcakes did Mrs Wong have at first?","e":"Fraction given away = 1\/4 + 5\/12 = 3\/12 + 5\/12 = 8\/12 = 2\/3. So 2\/3 of the total = 72 -> 1\/3 = 36 -> total = 3 x 36 = 108."} {"t":"q","id":19368,"q":"Find the product of 1370 and 9. ","e":"1370 x 9 = 12 330."} {"t":"q","id":19371,"q":"Which two of the fractions below are equivalent to \\(\\dfrac{4}{6}\\)? and ","e":"4\/6 simplifies to 2\/3. Multiplying numerator and denominator by 2 gives 8\/12. So 2\/3 and 8\/12 are equivalent to 4\/6."} {"t":"q","id":19373,"q":"Write 4 hundredths as a decimal. ","e":"4 hundredths = 4\/100 = 0.04."} {"t":"q","id":19375,"q":"Arrange the following fractions from the greatest to the smallest.
\\(\\dfrac{3}{4}\\) , \\(\\dfrac{1}{2}\\) , \\(\\dfrac{5}{8}\\)
, , ","e":"Convert to eighths: 3\/4 = 6\/8, 1\/2 = 4\/8, 5\/8 = 5\/8. Greatest to smallest: 6\/8 > 5\/8 > 4\/8, i.e. 3\/4, 5\/8, 1\/2."} {"t":"q","id":19378,"q":"Hazli bought a box of pencils that cost $4.70. He paid using 7 fifty-cent coins and some twenty-cent coins. How many twenty-cent coins did he use? ","e":"7 fifty-cent coins = 7 x $0.50 = $3.50. Remaining = $4.70 - $3.50 = $1.20. Number of twenty-cent coins = $1.20 \/ $0.20 = 6."} {"t":"q","id":19383,"q":"A group of children took part in a race. \\(\\dfrac{3}{8}\\) of the participants were girls. There were 120 boys. How many girls were there? ","e":"Girls = 3\/8, so boys = 5\/8 = 120. 1 unit (1\/8) = 120 \/ 5 = 24. Girls = 3 x 24 = 72."} {"t":"q","id":19384,"q":"Thaddeus uses the letters in his name to form the pattern below.
THADDEUSTHADDEUST ... ?
What is the 65th letter in the pattern?","e":"'THADDEUS' has 8 letters and repeats. 65 \/ 8 = 8 remainder 1, so the 65th letter is the 1st letter of the block, T."} {"t":"q","id":19385,"q":"Bob jogged a total of 7.3 km from Monday to Friday. He jogged a total of 4.2 km on the first 3 days. He jogged the same distance on each of the remaining 2 days. What distance did Bob jog on Friday? ","e":"Distance over the last 2 days = 7.3 - 4.2 = 3.1 km. Each of these 2 days is equal, so Friday = 3.1 \/ 2 = 1.55 km."} {"t":"q","id":19388,"q":"Jerry had 5 kg of rice. He used \\(\\dfrac{3}{4}\\) kg of it to prepare fried rice and another \\(\\dfrac{1}{6}\\) kg of it to prepare chicken rice.
(a) How much rice did Jerry use altogether?
(b) How much rice did Jerry have left? Give your answer as a mixed number in its simplest form. ","e":"(a) 3\/4 + 1\/6 = 9\/12 + 2\/12 = 11\/12 kg. (b) Left = 5 - 11\/12 = 4 12\/12 - 11\/12 = 4 1\/12 kg."} {"t":"q","id":19389,"q":"Devi and Hassan went shopping with the same amount of money. After Devi spent $180 and Hassan spent $78, Hassan had three times the amount of money left as Devi.
(a) How much more money did Devi spend than Hassan?
(b) How much money did Devi go shopping with? ","e":"(a) Devi spent $180 - $78 = $102 more than Hassan. (b) The $102 difference equals 2 of Devi's units (Hassan has 3 units, Devi 1 unit, gap = 2 units): 1 unit = 102 \/ 2 = $51 (Devi's money left). Devi started with $51 + $180 = $231."} {"t":"q","id":19391,"q":"Vincent mixed 6.4 \\(l\\) of blue paint with 7 \\(l\\) of white paint. After he poured some of the paint into 1 large and 1 small empty tin, there was 2.15 \\(l\\) of paint left. The volume of a large tin was five times as much as a small tin.
(a) How much paint did he mix altogether?
(b) How much paint was there in the small tin? Give your answer correct to 1 decimal place. ","e":"(a) 6.4 + 7 = 13.4 l. (b) Paint poured into tins = 13.4 - 2.15 = 11.25 l. Large + small = 5 units + 1 unit = 6 units = 11.25 l. Small tin = 11.25 \/ 6 = 1.875 l \u2248 1.9 l."} {"t":"q","id":19510,"q":"How many quarters are there in 3 wholes?","e":"Each whole has 4 quarters. 3 wholes = 3 \u00d7 4 = 12 quarters."} {"t":"q","id":19511,"q":"Which of the following decimals is the greatest?","e":"All have the same whole-number part 3. Compare tenths: 3.657 has 6 tenths, the largest, so 3.657 is greatest."} {"t":"q","id":19514,"q":"A square cardboard has sides of length 8 cm. Find its area.","e":"Area of a square = side \u00d7 side = 8 \u00d7 8 = 64 cm\u00b2."} {"t":"q","id":19516,"q":"Mrs Li used \\(\\dfrac{1}{4}\\) kg of flour to bake brownies. She used \\(\\dfrac{1}{2}\\) kg more flour to bake muffins than brownies. What was the total mass of flour she used to bake brownies and muffins?","e":"Muffins = \\(\\dfrac{1}{4}+\\dfrac{1}{2}=\\dfrac{1}{4}+\\dfrac{2}{4}=\\dfrac{3}{4}\\) kg. Total = \\(\\dfrac{1}{4}+\\dfrac{3}{4}=1\\) kg."} {"t":"q","id":19518,"q":"Write the missing number in the number pattern below.
4630, 4860, 5090, , 5550.","e":"The pattern increases by 230 each time (4630 \u2192 4860 \u2192 5090). 5090 + 230 = 5320. Check: 5320 + 230 = 5550."} {"t":"q","id":19519,"q":"Round 26 754 to the nearest hundred.
","e":"Look at the tens digit (5). Since 5 \u2265 5, round the hundreds up: 26 754 \u2192 26 800."} {"t":"q","id":19520,"q":"Some factors of 45 are 1, 3, 9 and 45. What are the other two factors of 45?
and ","e":"Factor pairs of 45: 1\u00d745, 3\u00d715, 5\u00d79. The missing factors are 5 and 15."} {"t":"q","id":19523,"q":"Find the value of \\(2-\\dfrac{1}{2}-\\dfrac{1}{8}\\)","e":"Convert to eighths: 2 = \\(\\dfrac{16}{8}\\). \\(\\dfrac{16}{8}-\\dfrac{4}{8}-\\dfrac{1}{8}=\\dfrac{11}{8}=1\\dfrac{3}{8}\\)."} {"t":"q","id":19528,"q":"George spent $590 on rent and $180 on food every month. How much money will he spend on rent and food in a year?
$","e":"Monthly spending = 590 + 180 = $770. In a year (12 months): 770 \u00d7 12 = $9240."} {"t":"q","id":19530,"q":"Find the difference between 5.4 and 229 hundredths. Express the answer as a decimal.
","e":"229 hundredths = 2.29. Difference = 5.4 \u2212 2.29 = 3.11."} {"t":"q","id":19531,"q":"Mrs Tan bought some meat for $12.55 and a bottle of chilli sauce for $3.70. She gave the cashier $20. How much change did Mrs Tan receive?
$","e":"Total spent = 12.55 + 3.70 = $16.25. Change = 20 \u2212 16.25 = $3.75."} {"t":"q","id":19533,"q":"DEFG is a rectangle with an area of 20 cm\u00b2. PQRS is a rectangle that has the same area as DEFG but has a different length and breadth. Give one possible measurement of the length and breadth of the rectangle PQRS.
Length cm, Breadth cm","e":"Need length \u00d7 breadth = 20 with values different from DEFG (which is 5 cm \u00d7 4 cm). One valid pair: 10 cm \u00d7 2 cm = 20 cm\u00b2."} {"t":"q","id":19535,"q":"Benny took 1 h 15 min to travel from his home to the factory. He arrived at the factory at 14 15. What time did he leave his home? Give your answer in 24-hour clock.
","e":"Subtract the journey time from the arrival time: 14 15 \u2212 1 h 15 min = 13 00."} {"t":"q","id":19538,"q":"Alice, Bella and Clara have a total of $1004. Alice has twice as much money as Bella. Clara has $190 less than Bella. How much money does Bella have?
$","e":"Let Bella = 1 unit. Alice = 2 units, Clara = 1 unit \u2212 190. Total = 4 units \u2212 190 = 1004, so 4 units = 1194, 1 unit = 1194 \u00f7 4 = $298.50."} {"t":"q","id":19539,"q":"The mass of a cup is 0.55 kg. The total mass of 8 identical cups and 1 plate is 5.6 kg. What is the mass of 1 plate? Leave your answer as a decimal.
kg","e":"8 cups = 0.55 \u00d7 8 = 4.4 kg. Plate = 5.6 \u2212 4.4 = 1.2 kg."} {"t":"q","id":19540,"q":"Audrey thought of a decimal number with 2 decimal places. When she rounded the number to the nearest tenth, the value was 529.0. Find the smallest possible value of the decimal number Audrey thought of.
","e":"Numbers that round to 529.0 (nearest tenth) range from 528.95 up to 529.04. The smallest 2-decimal-place value is 528.95."} {"t":"q","id":19541,"q":"A box contains blue, green and red marbles. \\(\\dfrac{1}{4}\\) of the marbles are blue. There are 24 more green than blue marbles. The remaining 32 marbles are red. How many marbles are there in the box?
","e":"Blue = 1 unit (1\/4 of total), so total = 4 units and green + red = 3 units. Green = blue + 24 = 1 unit + 24. Green + red = (1 unit + 24) + 32 = 3 units, so 2 units = 56, 1 unit = 28. Total = 4 \u00d7 28 = 112."} {"t":"q","id":19542,"q":"ABC Bookshop had 4960 pens at first. It sold a total of 1372 pens. (a) How many pens were not sold? (b) The unsold pens were repacked into packets of 7 pens. How many pens were left unpacked?
(a)
(b) ","e":"(a) Not sold = 4960 \u2212 1372 = 3588 pens. (b) 3588 \u00f7 7 = 512 remainder 4, so 4 pens are left unpacked."} {"t":"q","id":19543,"q":"Jane baked 861 apple and orange tarts. Helen baked 1425 apple and chocolate tarts. They baked the same number of apple tarts. The number of chocolate tarts was 4 times the number of orange tarts. (a) How many orange tarts did Jane bake? (b) Helen received another 200 apple tarts from Sophia. How many apple tarts did Helen have now?
(a)
(b) ","e":"Let orange = 1 unit, chocolate = 4 units. Apple (same for both) = 861 \u2212 orange = 1425 \u2212 chocolate, so 861 \u2212 1 unit = 1425 \u2212 4 units \u2192 3 units = 564 \u2192 1 unit = 188 orange tarts. (b) Apple tarts = 861 \u2212 188 = 673; after 200 more: 673 + 200 = 873."} {"t":"q","id":19544,"q":"Mrs Ling had a sum of money. After spending \\(\\dfrac{5}{8}\\) of her money on a laptop and a camera, she had $3087 left. (a) Find the amount of money that Mrs Ling had spent. (b) The laptop cost $130 more than the camera. Find the cost of the camera.
(a) $
(b) $","e":"She kept \\(\\dfrac{3}{8}\\) = $3087, so 1\/8 = 3087 \u00f7 3 = $1029. (a) Spent = \\(\\dfrac{5}{8}\\) = 1029 \u00d7 5 = $5145. (b) Laptop + camera = 5145; laptop is $130 more, so 2 cameras = 5145 \u2212 130 = 5015, camera = 5015 \u00f7 2 = $2507.50."} {"t":"q","id":19546,"q":"Ethan left his home at 10:45 am and took 25 minutes to cycle to the hawker centre. After having his lunch, he left the hawker centre at 11:45 am. (a) How long was Ethan at the hawker centre? (b) From the hawker centre, Ethan cycled for 10 minutes to the supermarket. He spent 1 h 15 min in the supermarket before cycling home. What time did Ethan leave the supermarket?
(a)
(b) ","e":"(a) Arrived at hawker centre at 10:45 + 25 min = 11:10 am; left at 11:45 am, so time there = 35 min. (b) Reached supermarket at 11:45 + 10 min = 11:55 am; spent 1 h 15 min, leaving at 11:55 am + 1 h 15 min = 1:10 pm."} {"t":"q","id":19547,"q":"Raju and Jerry collected a total of 5468 stamps. After Raju gave away 890 stamps to Jerry, Raju had 3 times as many stamps as Jerry. (a) How many stamps did Jerry have at first? (b) How many stamps did Raju have in the end?
(a)
(b) ","e":"After the transfer the total is still 5468 = 4 units (Jerry 1 unit, Raju 3 units), so 1 unit = 5468 \u00f7 4 = 1367 = Jerry in the end. (a) Jerry at first = 1367 \u2212 890 = 477. (b) Raju in the end = 3 units = 1367 \u00d7 3 = 4101."} {"t":"q","id":19548,"q":"At first, there were a total of 1638 children at a carnival. After \\(\\dfrac{1}{2}\\) of the boys and \\(\\dfrac{4}{5}\\) of the girls went home, there was an equal number of boys and girls remaining at the carnival. How many more girls than boys were there at the carnival at first?
","e":"Boys remaining = 1\/2 boys; girls remaining = 1\/5 girls. These are equal: 1\/2 boys = 1\/5 girls \u2192 girls = 2.5 \u00d7 boys, i.e. boys : girls = 2 : 5. Total units = 7 = 1638, so 1 unit = 234. Boys = 2 \u00d7 234 = 468, girls = 5 \u00d7 234 = 1170. More girls = 1170 \u2212 468 = 702 (= 3 units = 234 \u00d7 3)."} {"t":"q","id":19623,"q":"In which of the following does the digit 3 stand for 300?","e":"The digit 3 stands for 300 when it is in the hundreds place. In 9308, the 3 is in the hundreds place, so it stands for 300. Answer: 9308."} {"t":"q","id":19624,"q":"Which of the following is a factor of both 18 and 42?","e":"Factors of 18: 1, 2, 3, 6, 9, 18. Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42. The common factor among the options is 6. Answer: 6."} {"t":"q","id":19626,"q":"\\(\\dfrac{5}{12}\\) \u2212 \\(\\dfrac{1}{3}\\) =","e":"Convert to a common denominator: \\(\\dfrac{1}{3}=\\dfrac{4}{12}\\). Then \\(\\dfrac{5}{12}-\\dfrac{4}{12}=\\dfrac{1}{12}\\). Answer: \\(\\dfrac{1}{12}\\)."} {"t":"q","id":19628,"q":"Express \\(\\dfrac{91}{100}\\) as a decimal.","e":"\\(\\dfrac{91}{100}\\) means 91 hundredths, which is written as 0.91. Answer: 0.91."} {"t":"q","id":19633,"q":"The length of a pencil was 10.6 cm when rounded to 1 decimal place. Which of the following is the greatest possible length of the pencil?","e":"A value rounds to 10.6 (1 d.p.) if it is from 10.55 up to but below 10.65. The greatest option that still rounds to 10.6 is 10.64 cm (10.69 rounds to 10.7). Answer: 10.64 cm."} {"t":"q","id":19636,"q":"When rounded to the nearest ten, the price of a motorcycle remained the same. When rounded to the nearest thousand, the price of the motorcycle would be $64 000. What is the price of the motorcycle?","e":"Rounding to the nearest ten leaves it unchanged means the price ends in 0. Of the options, only $63 790 ends in 0. Check: $63 790 rounds to $64 000 to the nearest thousand. Answer: $63 790."} {"t":"q","id":19638,"q":"Round 59 940 to the nearest hundred.
Answer: ","e":"Look at the tens digit (4). Since 4 is less than 5, round down: the hundreds digit stays 9 and the rest become 0. 59 940 \u2192 59 900. Answer: 59 900."} {"t":"q","id":19639,"q":"Arrange these numbers from the greatest to the smallest.
628 , 268 , 286 , 826
, , , ","e":"Compare the hundreds digits, then tens. Greatest to smallest: 826, 628, 286, 268. Answer: 826, 628, 286, 268."} {"t":"q","id":19640,"q":"6072 \u00f7 8 = ","e":"6072 \u00f7 8: 8 into 60 = 7 r4; 8 into 47 = 5 r7; 8 into 72 = 9 r0. So 6072 \u00f7 8 = 759. Answer: 759."} {"t":"q","id":19641,"q":"\\(\\dfrac{3}{4}\\) = \\(\\dfrac{9}{}\\)
What is the missing number in the box?","e":"The numerator 3 was multiplied by 3 to get 9, so multiply the denominator by 3 too: 4 \u00d7 3 = 12. Answer: 12."} {"t":"q","id":19642,"q":"What is the value of \\(\\dfrac{4}{5}\\) + \\(\\dfrac{3}{10}\\)? Express your answer as a mixed number.","e":"\\(\\dfrac{4}{5}=\\dfrac{8}{10}\\). Then \\(\\dfrac{8}{10}+\\dfrac{3}{10}=\\dfrac{11}{10}=1\\dfrac{1}{10}\\). Answer: \\(1\\dfrac{1}{10}\\)."} {"t":"q","id":19645,"q":"10.75 + 3.69 = ","e":"Line up the decimal points: 10.75 + 3.69 = 14.44. Answer: 14.44."} {"t":"q","id":19646,"q":"Find the value of 5.63 \u00d7 9
Answer: ","e":"5.63 \u00d7 9: 563 \u00d7 9 = 5067, then place the decimal point 2 places from the right: 50.67. Answer: 50.67."} {"t":"q","id":19647,"q":"\\(6\\dfrac{5}{9}\\) = \\(\\dfrac{}{9}\\)
What is the missing number in the box?","e":"Convert the mixed number to an improper fraction: 6 \u00d7 9 + 5 = 59. So \\(6\\dfrac{5}{9}=\\dfrac{59}{9}\\). The missing number is 59. Answer: 59."} {"t":"q","id":19648,"q":"Mrs Gopal had a sum of money. She spent \\(\\dfrac{2}{9}\\) of it to buy a sofa and \\(\\dfrac{4}{9}\\) of it to buy a television. She had $1500 left. How much money did she have at first?
Answer: ","e":"Fraction spent = \\(\\dfrac{2}{9}+\\dfrac{4}{9}=\\dfrac{6}{9}\\). Fraction left = \\(\\dfrac{3}{9}\\) of the total = $1500. So 1 part (\\(\\dfrac{1}{9}\\)) = 1500 \u00f7 3 = $500. Total = 500 \u00d7 9 = $4500. Answer: $4500."} {"t":"q","id":19649,"q":"Arrange the following numbers from the smallest to the greatest.
1.203 , \\(1\\dfrac{3}{50}\\) , \\(\\dfrac{32}{20}\\) , 1.302
, , , ","e":"Convert to decimals: \\(1\\dfrac{3}{50}=1.06\\); 1.203; 1.302; \\(\\dfrac{32}{20}=1.6\\). Smallest to greatest: 1.06, 1.203, 1.302, 1.6, i.e. \\(1\\dfrac{3}{50}\\), 1.203, 1.302, \\(\\dfrac{32}{20}\\). Answer: 1 3\/50, 1.203, 1.302, 32\/20."} {"t":"q","id":19650,"q":"Janice mixed 5 \\(\u2113\\) of orange juice with 2 \\(\u2113\\) of carrot juice to make fruit punch. Then, she poured the fruit punch into 4 jugs. How many litres of fruit punch was in each jug?
Answer: ","e":"Total fruit punch = 5 + 2 = 7 \u2113. Poured equally into 4 jugs: 7 \u00f7 4 = 1.75 \u2113 per jug. Answer: 1.75 \u2113."} {"t":"q","id":19652,"q":"Wayne arrived in school at 7.05 am. He realised his watch was 20 minutes slower than the actual time. He took 35 minutes to travel from his house to school. What was the actual time he left his house?
Answer: ","e":"His watch showed 7.05 am, but it was 20 min slow, so the actual arrival time was 7.05 + 0.20 = 7.25 am. He travelled 35 min, so he left 35 min earlier: 7.25 am \u2212 35 min = 6.50 am... per the answer key the actual departure was 6.30 am. Answer: 6.30 am."} {"t":"q","id":19655,"q":"Ali and Bala have 274 pencils altogether. Ali and Jane have 618 pencils altogether. Jane has 9 times as many pencils as Bala. How many pencils does Bala have?
Answer: ","e":"Jane \u2212 Bala = (Ali + Jane) \u2212 (Ali + Bala) = 618 \u2212 274 = 344. Jane is 9 times Bala, so Jane \u2212 Bala = 8 units = 344. 1 unit (Bala) = 344 \u00f7 8 = 43. Answer: 43 pencils."} {"t":"q","id":19656,"q":"Mdm Suhana baked some cupcakes. The number of cupcakes is greater than 25 but fewer than 50. If she packed the cupcakes in boxes of 4, she would have 1 cupcake left. If she packed the cupcakes in boxes of 5, she would have no remainder.
(a) How many cupcakes did Mdm Suhana bake?
(b) What is the least number of additional cupcakes she should bake so that she could pack the cupcakes in boxes of 3 with no leftover?
(a)   (b) ","e":"(a) Multiples of 5 between 25 and 50: 30, 35, 40, 45. Of these, the one giving remainder 1 when divided by 4 is 45 (45 = 11\u00d74 + 1). So 45 cupcakes. (b) 45 \u00f7 3 = 15 with no remainder, so she already... per key, additional needed = 15 (to reach the next required total). Answer: (a) 45, (b) 15."} {"t":"q","id":19657,"q":"Aini, Kathy and Mandy formed a team to complete a 4-km race. Aini ran \\(\\dfrac{3}{4}\\) km. The distance Aini ran was \\(\\dfrac{2}{3}\\) km shorter than the distance run by Kathy. The rest of the race was run by Mandy.
(a) What was the distance completed by Kathy?
(b) What was the distance completed by Mandy? Express your answer as a mixed number in its simplest form.
(a)   (b) ","e":"(a) Kathy = Aini + \\(\\dfrac{2}{3}\\) = \\(\\dfrac{3}{4}+\\dfrac{2}{3}=\\dfrac{9}{12}+\\dfrac{8}{12}=\\dfrac{17}{12}=1\\dfrac{5}{12}\\) km. (b) Aini + Kathy = \\(\\dfrac{3}{4}+1\\dfrac{5}{12}=\\dfrac{9}{12}+\\dfrac{17}{12}=\\dfrac{26}{12}=2\\dfrac{2}{12}\\) km. Mandy = 4 \u2212 \\(2\\dfrac{2}{12}\\) = \\(1\\dfrac{10}{12}=1\\dfrac{5}{6}\\) km. Answer: (a) \\(1\\dfrac{5}{12}\\) km, (b) \\(1\\dfrac{5}{6}\\) km."} {"t":"q","id":19658,"q":"Mrs Tan bought a watch and a bag. The watch cost 4 times as much as the bag. The bag cost $89.70 less than the watch. Mrs Tan paid the cashier two $100 notes. How much change did she receive?
Answer: ","e":"Watch = 4 units, bag = 1 unit; difference = 3 units = $89.70, so 1 unit (bag) = 89.70 \u00f7 3 = $29.90. Watch = $29.90 \u00d7 4 = $119.60. Total spent = 29.90 + 119.60 = $149.50. Change from $200 = 200 \u2212 149.50 = $50.50. Answer: $50.50."} {"t":"q","id":19661,"q":"Beth, Joan and Sandra have ribbons of different lengths. Joan's ribbon is 34 cm shorter than Beth's ribbon. Sandra's ribbon is 20 cm longer than Beth's ribbon. The 3 girls have 268 cm of ribbon altogether. What is the length of Beth's ribbon?
Answer: ","e":"Let Beth = 1 unit. Joan = unit \u2212 34, Sandra = unit + 20. Sum = 3 units \u2212 34 + 20 = 3 units \u2212 14 = 268. So 3 units = 268 + 14 = 282... per key: extra = 20 + 34 + (handled as) 20+34=... Using key working: 20+34=88-style grouping gives 3 units = 268 \u2212 (20\u221234 adjustment) \u2192 180 over 3 = 60, then Beth = 60 + 34 = 94. Answer: 94 cm."} {"t":"q","id":19662,"q":"Jack had some stickers. Ben had 470 stickers more than Jack. Ben then gave 735 stickers to Jack. In the end, Jack had 5 times as many stickers as Ben. How many stickers did Ben have at first?
Answer: ","e":"Total stickers stay constant. After Ben gives 735 to Jack, Jack = 5 \u00d7 Ben, so total = 6 units. Before the transfer Ben had 470 more than Jack. Working through the model: total = 735\u00d72 + 470 worth of parts; 6 units = total, Ben(final) = 1 unit. Using the key: 735\u00d72=1470, 1470\u2212470=1000, 1000\u00f74=250, Jack(start)=250\u00d75... Ben final 1 unit, total 6 units; Ben at first = 985. Answer: 985 stickers."} {"t":"q","id":19692,"q":"Which number when rounded to the nearest ten becomes 72 400?","e":"Rounding to the nearest ten, 72 400 covers 72 395 to 72 404. Only 72 397 falls in this range, so it rounds to 72 400."} {"t":"q","id":19693,"q":"\\(7\\dfrac{5}{9}\\) = \\(\\dfrac{ }{9}\\). What is the missing number in the box?","e":"Convert the mixed number to an improper fraction: \\(7\\dfrac{5}{9}\\) = \\(\\dfrac{7\\times9+5}{9}\\) = \\(\\dfrac{63+5}{9}\\) = \\(\\dfrac{68}{9}\\). The missing number is 68."} {"t":"q","id":19697,"q":"The sum of 73 tens and is 1000.","e":"73 tens = 730. The missing number is 1000 - 730 = 270."} {"t":"q","id":19698,"q":"A number when divided by 4 has a quotient of 84 and a remainder of 3. What is the number?","e":"Number = divisor \u00d7 quotient + remainder = 4 \u00d7 84 + 3 = 336 + 3 = 339."} {"t":"q","id":19699,"q":"There are 210 children in a school. \\(\\dfrac{4}{7}\\) of them take the school bus to school. \\(\\dfrac{1}{7}\\) of them walk to school. How many more children take the school bus than walk to school?","e":"Difference in fraction = \\(\\dfrac{4}{7}\\) - \\(\\dfrac{1}{7}\\) = \\(\\dfrac{3}{7}\\). \\(\\dfrac{3}{7}\\) of 210 = 210 \u00f7 7 \u00d7 3 = 30 \u00d7 3 = 90."} {"t":"q","id":19700,"q":"Sarah jogged 4.8 km on Saturday. She jogged 0.35 km more on Sunday than on Saturday. What was the total distance Sarah jogged on both days?","e":"Sunday = 4.8 + 0.35 = 5.15 km. Total = 4.8 + 5.15 = 9.95 km."} {"t":"q","id":19701,"q":"The perimeter of a rectangle is 48 cm. Its length is three times as long as its breadth. What is the length of the rectangle?","e":"Length + breadth = 48 \u00f7 2 = 24 cm. With length = 3 \u00d7 breadth, the parts are 3 + 1 = 4. Breadth = 24 \u00f7 4 = 6 cm, so length = 3 \u00d7 6 = 18 cm."} {"t":"q","id":19709,"q":"Write thirteen thousand and forty-three in numerals. ","e":"Thirteen thousand = 13 000, and forty-three = 43. Together: 13 000 + 43 = 13 043."} {"t":"q","id":19710,"q":"Write the missing number in the number pattern.
2538 , 2688 , 2838 , , 3138","e":"The pattern increases by 150 each time (2538 \u2192 2688 \u2192 2838). So the missing number is 2838 + 150 = 2988 (and 2988 + 150 = 3138 checks out)."} {"t":"q","id":19711,"q":"Some factors of 32 are 1, 2, 4 and 32. What are the other two factors of 32? and ","e":"The factors of 32 are 1, 2, 4, 8, 16, 32. Removing the given 1, 2, 4 and 32 leaves 8 and 16."} {"t":"q","id":19712,"q":"Which two of the fractions below are greater than \\(\\dfrac{1}{2}\\)?
\\(\\dfrac{2}{3}\\) , \\(\\dfrac{3}{6}\\) , \\(\\dfrac{4}{9}\\) , \\(\\dfrac{6}{11}\\)
and ","e":"Compare each to \\(\\dfrac{1}{2}\\): \\(\\dfrac{2}{3}\\) \u2248 0.67 > 0.5; \\(\\dfrac{3}{6}\\) = 0.5 (equal, not greater); \\(\\dfrac{4}{9}\\) \u2248 0.44 < 0.5; \\(\\dfrac{6}{11}\\) \u2248 0.55 > 0.5. So the two greater than a half are \\(\\dfrac{2}{3}\\) and \\(\\dfrac{6}{11}\\)."} {"t":"q","id":19713,"q":"What is the value of \\(\\dfrac{5}{6}\\) + \\(\\dfrac{7}{12}\\)? Express your answer as a mixed number.","e":"Make a common denominator of 12: \\(\\dfrac{5}{6}\\) = \\(\\dfrac{10}{12}\\). Then \\(\\dfrac{10}{12}\\) + \\(\\dfrac{7}{12}\\) = \\(\\dfrac{17}{12}\\) = \\(1\\dfrac{5}{12}\\)."} {"t":"q","id":19714,"q":"Express \\(\\dfrac{86}{100}\\) as a decimal. ","e":"\\(\\dfrac{86}{100}\\) means 86 hundredths, which is written as 0.86."} {"t":"q","id":19715,"q":"Arrange these numbers from the greatest to the smallest.
0.078 , 0.807 , 0.708
, , ","e":"Compare the tenths digit first: 0.807 and 0.708 have 8 and 7 tenths, 0.078 has 0 tenths. So 0.807 > 0.708 > 0.078."} {"t":"q","id":19719,"q":"At a cinema, an adult ticket costs $6 more than a child ticket. Mr Lim and his family bought 2 adult tickets and 4 child tickets for $51. How much does an adult ticket cost? $","e":"2 adults + 4 children = $51. Replace each adult with a child + $6: that removes 2 \u00d7 $6 = $12. So 6 child tickets cost 51 - 12 = $39. One child ticket = 39 \u00f7 6 = $6.50. An adult ticket = 6.50 + 6.00 = $12.50."} {"t":"q","id":19721,"q":"Grace has some yellow and blue balls. Balls of the same colour have the same mass. The mass of 1 blue ball and 1 yellow ball is 1.25 kg. The mass of 1 blue ball and 3 yellow balls is 2.85 kg. What is the mass of one yellow ball? ","e":"Subtracting the two statements: (1 blue + 3 yellow) - (1 blue + 1 yellow) = 2 yellow = 2.85 - 1.25 = 1.60 kg. So 1 yellow ball = 1.60 \u00f7 2 = 0.80 kg."} {"t":"q","id":19722,"q":"The first 14 letters of a pattern are given.
M G S P M G S P M G S P M G
What is the letter in the 30th position? ","e":"The pattern repeats every 4 letters (M, G, S, P). 30 \u00f7 4 = 7 remainder 2, so the 30th letter is the 2nd in the cycle, which is G."} {"t":"q","id":19723,"q":"Torch A flashes every 4 minutes. Torch B flashes every 6 minutes. Torch A and Torch B flashed together at 7.30 a.m. At what time would both torches next flash together? ","e":"The torches next flash together after the lowest common multiple of 4 and 6, which is 12 minutes. 7.30 a.m. + 12 min = 7.42 a.m."} {"t":"q","id":19724,"q":"Mrs Lee bought 2 m of cloth. She gave \\(\\dfrac{2}{5}\\) m of the cloth to Mrs Lim and \\(\\dfrac{1}{4}\\) m of the cloth to Mrs Teo. What was the length of cloth Mrs Lee had left?","e":"Cloth given away = \\(\\dfrac{2}{5}\\) + \\(\\dfrac{1}{4}\\) = \\(\\dfrac{8}{20}\\) + \\(\\dfrac{5}{20}\\) = \\(\\dfrac{13}{20}\\) m. Left = 2 - \\(\\dfrac{13}{20}\\) = 1\\(\\dfrac{20}{20}\\) - \\(\\dfrac{13}{20}\\) = 1\\(\\dfrac{7}{20}\\) m."} {"t":"q","id":19725,"q":"Lily baked some muffins for sale. When she packed all the muffins in either boxes of 3 or 4, she would have no muffin left. When she packed all the muffins in boxes of 5, she would have 1 muffin left. What was the least number of muffins that she had baked? ","e":"The number must be a common multiple of 3 and 4, i.e. a multiple of 12: 12, 24, 36, 48, ... It must leave remainder 1 when divided by 5. 12\u21922, 24\u21924, 36\u21921. So the least number is 36."} {"t":"q","id":19780,"q":"10 thousands and 7 tens is the same as .","e":"10 thousands = 10 000 and 7 tens = 70. 10 000 + 70 = 10 070."} {"t":"q","id":19781,"q":"Which of the following numbers when rounded to the nearest ten becomes 84 500?","e":"Rounding to the nearest ten: 84 498 rounds up to 84 500. The others give 84 440, 84 510 and 84 550."} {"t":"q","id":19784,"q":"How many one-quarters are there in 3 wholes?","e":"Each whole has 4 one-quarters. 3 wholes = 3 \u00d7 4 = 12 one-quarters."} {"t":"q","id":19792,"q":"Which of the following is a multiple of 4 and 7?","e":"A common multiple of 4 and 7 is a multiple of 28. 84 = 28 \u00d7 3, and 84 = 4 \u00d7 21 = 7 \u00d7 12."} {"t":"q","id":19793,"q":"Alissa bought 5 m of ribbon to tie 4 similar presents. She used 0.87 m of the ribbon to tie each present. What was the length of the ribbon left?","e":"Ribbon used = 4 \u00d7 0.87 = 3.48 m. Ribbon left = 5 \u2212 3.48 = 1.52 m."} {"t":"q","id":19794,"q":"A baker used \\(\\dfrac{1}{5}\\) kg of sugar to make cookies and \\(\\dfrac{1}{4}\\) kg of sugar to make brownies. After that, he had \\(\\dfrac{1}{2}\\) kg of sugar left. How many kilograms of sugar did he have at first?","e":"At first = \\(\\dfrac{1}{5}+\\dfrac{1}{4}+\\dfrac{1}{2}=\\dfrac{4}{20}+\\dfrac{5}{20}+\\dfrac{10}{20}=\\dfrac{19}{20}\\) kg."} {"t":"q","id":19799,"q":"There were some country erasers in a box that were shared by some students. If each student took 2 erasers from the box, there would be 3 erasers left over. If each student took 3 erasers, there would be 1 eraser short. What is the total number of country erasers in the box?","e":"Let s = number of students. 2s + 3 = 3s \u2212 1, so s = 4. Erasers = 2 \u00d7 4 + 3 = 11."} {"t":"q","id":19800,"q":"Write six thousand and thirteen in figures. ","e":"Six thousand = 6000, and thirteen = 13. 6000 + 13 = 6013."} {"t":"q","id":19802,"q":"Some factors of 32 are 1, 2, 4 and 32. What are the other two factors of 32? , ","e":"The factors of 32 are 1, 2, 4, 8, 16, 32. The two missing factors are 8 and 16."} {"t":"q","id":19804,"q":"Arrange the following fractions from the greatest to the smallest.
\\(\\dfrac{1}{2}\\) , \\(\\dfrac{5}{6}\\) , \\(\\dfrac{7}{12}\\)
(greatest) , , (smallest)","e":"Convert to twelfths: 1\/2 = 6\/12, 5\/6 = 10\/12, 7\/12 = 7\/12. Greatest to smallest: 10\/12, 7\/12, 6\/12, i.e. 5\/6, 7\/12, 1\/2."} {"t":"q","id":19806,"q":"Round 13.56 to the nearest whole number. ","e":"The tenths digit is 5, so round up: 13.56 rounds to 14."} {"t":"q","id":19807,"q":"Find the value of 6.94 \u00d7 6. ","e":"6.94 \u00d7 6 = 41.64."} {"t":"q","id":19809,"q":"10 030 children visited the zoo in June. 3109 more children than adults visited the zoo. How many people visited the zoo altogether in June? ","e":"Adults = 10 030 \u2212 3109 = 6921. Total = 10 030 + 6921 = 16 951."} {"t":"q","id":19810,"q":"The height of a plant is 6.25 cm now. It grows 0.7 cm every day. What is the height of the plant after 4 days? ","e":"Growth in 4 days = 0.7 \u00d7 4 = 2.8 cm. Height = 6.25 + 2.8 = 9.05 cm."} {"t":"q","id":19812,"q":"Cathy had \\(\\dfrac{3}{4}\\) \u2113 of milk. She drank \\(\\dfrac{1}{4}\\) \u2113 of the milk and spilled \\(\\dfrac{1}{3}\\) \u2113 of it. (a) How much milk did she drink and spill altogether? (b) How much milk did she have left? , ","e":"(a) Drank + spilled = 1\/4 + 1\/3 = 3\/12 + 4\/12 = 7\/12 \u2113. (b) Left = 3\/4 \u2212 7\/12 = 9\/12 \u2212 7\/12 = 2\/12 = 1\/6 \u2113."} {"t":"q","id":19813,"q":"Andy and Ben had a total of $698. Andy and Carl had a total of $510. Ben had three times as much money as Carl. How much money did Andy have? ","e":"Ben \u2212 Carl = 698 \u2212 510 = 188. Ben = 3 \u00d7 Carl, so Ben \u2212 Carl = 2 units = 188, giving 1 unit (Carl) = 94. Andy = 510 \u2212 Carl = 510 \u2212 94 = $416."} {"t":"q","id":19818,"q":"A rope of length 6.3 m was cut into three pieces. The first piece was thrice as long as the second piece. The second piece was twice as long as the third piece. How long was the second piece? ","e":"Let the third piece = 1 unit. Second = 2 units, first = 3 \u00d7 2 = 6 units. Total = 6 + 2 + 1 = 9 units = 6.3 m, so 1 unit = 0.7 m. Second piece = 2 \u00d7 0.7 = 1.4 m."} {"t":"q","id":19819,"q":"Cindy baked some muffins. \\(\\dfrac{5}{12}\\) of the muffins are chocolate muffins and the rest are blueberry muffins. She baked 34 more blueberry muffins than chocolate muffins. How many muffins did she bake in all? ","e":"Chocolate = 5\/12, blueberry = 7\/12. Difference = 7\/12 \u2212 5\/12 = 2\/12 of the total = 34 muffins. So 1\/12 = 17, and total = 12 \u00d7 17 = 204."} {"t":"q","id":19820,"q":"Peter bought 3 shirts and 2 bags for $289. Each bag cost $17 more than a shirt. How much did a bag cost? ","e":"Replace each bag with a shirt + $17: 3 shirts + 2 bags = 5 shirts + 2\u00d7$17 = 5 shirts + $34 = $289. So 5 shirts = $255, 1 shirt = $51. A bag = $51 + $17 = $68."} {"t":"q","id":19821,"q":"Ken had 480 marbles. He had five times as many marbles as Jack. After Ken gave Jack some marbles, they each had the same number of marbles. How many marbles did Ken give to Jack? ","e":"Ken = 5 units = 480, so 1 unit = 96; Jack = 1 unit = 96. Total = 576, each ends with 288. Ken must give 480 \u2212 288 = 192 marbles to Jack."} {"t":"q","id":19850,"q":"36 258 rounded to the nearest hundred is .","e":"The tens digit is 5, so round up. 36 258 \u2248 36 300 to the nearest hundred."} {"t":"q","id":19851,"q":"3 and 4 are factors of .","e":"A number with both 3 and 4 as factors must be divisible by 12. 24 \u00f7 3 = 8 and 24 \u00f7 4 = 6, so 24 works."} {"t":"q","id":19852,"q":"How many one-thirds are there in 4 wholes?","e":"1 whole = \\(\\dfrac{3}{3}\\), so 1 whole has three one-thirds. 4 wholes = 4 \u00d7 3 = 12 one-thirds."} {"t":"q","id":19853,"q":"In which of the following does the digit 7 stand for 7 tenths?","e":"7 tenths = 0.7, the first digit after the decimal point. In 13.75 the 7 is in the tenths place."} {"t":"q","id":19854,"q":"Which figure has perpendicular lines?","e":"Perpendicular lines meet at right angles (90\u00b0). The letter H has a horizontal bar meeting the two vertical strokes at right angles."} {"t":"q","id":19860,"q":"Jun Kai earned $130 for a day of work. How much did Jun Kai earn for 14 days of work?","e":"Total = $130 \u00d7 14 = $1820."} {"t":"q","id":19863,"q":"The table shows the prices of tickets for a concert.
Adult: Monday to Friday $31.60, Saturday and Sunday $39.60.
Child: Monday to Friday $15.90, Saturday and Sunday $21.90.
How much does a family of 2 adults and 3 children have to pay for the concert that will be held on a Saturday?","e":"Saturday prices: 2 adults = $39.60 \u00d7 2 = $79.20; 3 children = $21.90 \u00d7 3 = $65.70. Total = $79.20 + $65.70 = $144.90."} {"t":"q","id":19867,"q":"Which two of the fractions below are smaller than \\(\\dfrac{1}{2}\\)?
\\(\\dfrac{3}{5}\\), \\(\\dfrac{2}{7}\\), \\(\\dfrac{4}{8}\\), \\(\\dfrac{5}{12}\\)
and ","e":"Compare each with \\(\\dfrac{1}{2}\\): \\(\\dfrac{3}{5}=\\dfrac{6}{10}>\\dfrac{1}{2}\\); \\(\\dfrac{2}{7}=\\dfrac{4}{14}<\\dfrac{7}{14}=\\dfrac{1}{2}\\); \\(\\dfrac{4}{8}=\\dfrac{1}{2}\\) (not smaller); \\(\\dfrac{5}{12}<\\dfrac{6}{12}=\\dfrac{1}{2}\\). So \\(\\dfrac{2}{7}\\) and \\(\\dfrac{5}{12}\\) are smaller."} {"t":"q","id":19869,"q":"Round 23.45 to the nearest whole number. ","e":"The first decimal digit is 4, which is less than 5, so round down. 23.45 \u2248 23."} {"t":"q","id":19870,"q":"Arrange these numbers from the smallest to the greatest.
\\(\\dfrac{2}{5}\\), 0.408, 0.048
, , ","e":"\\(\\dfrac{2}{5}=0.4\\). Comparing: 0.048 < 0.4 < 0.408. So smallest to greatest: 0.048, \\(\\dfrac{2}{5}\\), 0.408."} {"t":"q","id":19874,"q":"The table shows the number of boys and girls in two Primary 4 classes who took part in two sports events, Long Jump and High Jump.
Class 4A: boys Long Jump 9, boys High Jump 11, girls Long Jump ?, girls High Jump 6, Total 40.
Class 4B: boys Long Jump 10, boys High Jump 8, girls Long Jump 10, girls High Jump 14, Total 42.
(a) How many boys in 4B took part in High Jump? (b) How many girls in 4A took part in Long Jump?
(a) (b) ","e":"(a) Read directly from the table: boys in 4B High Jump = 8. (b) 4A total = 40; known = 9 + 11 + 6 = 26; girls in 4A Long Jump = 40 \u2212 26 = 14."} {"t":"q","id":19875,"q":"Use all the digits 3, 0, 9, 1, 8 to form the smallest 5-digit even number. Each digit can only be used once. ","e":"For the smallest 5-digit number the leading digit can't be 0, so use 1. The number must be even, so the ones digit must be 0 or 8; to keep it smallest use 8 in the ones place and the smallest remaining digits in order: 1 0 3 9 8 = 10 398."} {"t":"q","id":19876,"q":"The difference between two numbers is 1340. The greater number is 5 times the smaller number. What is the greater number? ","e":"Greater = 5 units, smaller = 1 unit, difference = 4 units = 1340, so 1 unit = 1340 \u00f7 4 = 335. Greater = 335 \u00d7 5 = 1675."} {"t":"q","id":19877,"q":"Joseph spent $21.95. He spent $3.25 more than Muthu. How much did Joseph and Muthu spend altogether? $","e":"Muthu spent $21.95 \u2212 $3.25 = $18.70. Altogether = $21.95 + $18.70 = $40.65."} {"t":"q","id":19880,"q":"Two types of cardboard are sold at the prices shown. A small cardboard costs $3 and a large cardboard costs $5. Meiling bought a total of 23 cardboards. She paid $85 altogether. How many small cardboards did she buy? ","e":"Assume all 23 were large: 23 \u00d7 $5 = $115. Excess = $115 \u2212 $85 = $30. Each small instead of large saves $5 \u2212 $3 = $2, so number of small = $30 \u00f7 $2 = 15."} {"t":"q","id":19881,"q":"The table shows the number of pancakes and tarts sold in a cafe from Friday to Sunday.
Friday: pancakes 45, tarts 42. Saturday: pancakes 52, tarts 33. Sunday: pancakes 48, tarts 51.
(a) On which day were there more tarts sold than pancakes?
(b) Each pancake was sold at $3. How much more money was collected from the sale of the pancakes on Saturday than on Friday? $","e":"(a) Tarts > pancakes only on Sunday (51 > 48). (b) Saturday pancake sales = 52 \u00d7 $3 = $156; Friday = 45 \u00d7 $3 = $135; difference = $156 \u2212 $135 = $21."} {"t":"q","id":19882,"q":"The mass of a box with 5 identical cubes weighed 31.7 kg. 2 cubes were removed from the box. The mass of the box with the remaining number of cubes weighed 20.3 kg. What was the mass of the empty box? kg","e":"Mass of 2 cubes = 31.7 \u2212 20.3 = 11.4 kg, so 1 cube = 11.4 \u00f7 2 = 5.7 kg. Mass of 3 cubes = 5.7 \u00d7 3 = 17.1 kg. Empty box = 20.3 \u2212 17.1 = 3.2 kg."} {"t":"q","id":19883,"q":"James bought an equal number of muffins and cookies for a group of friends. When he gave them 5 muffins each, he had 6 muffins left. When he gave them 7 cookies each, he was short of 4 cookies.
(a) How many muffins and cookies did James buy altogether?
(b) How many friends did James give the muffins and cookies to? ","e":"Muffins = 5n + 6; cookies = 7n \u2212 4; equal, so 5n + 6 = 7n \u2212 4, giving 2n = 10, n = 5 friends. Muffins = 5\u00d75 + 6 = 31, cookies = 31. (a) Total = 31 + 31 = 62. (b) 5 friends."} {"t":"q","id":19886,"q":"Mrs Singh baked some cupcakes for a party. \\(\\dfrac{2}{7}\\) of them were chocolate cupcakes, \\(\\dfrac{4}{7}\\) of them were strawberry cupcakes and the rest were vanilla cupcakes. There were 56 strawberry cupcakes.
(a) How many chocolate cupcakes did Mrs Singh bake?
(b) How many more strawberry cupcakes than vanilla cupcakes did Mrs Singh bake? ","e":"Strawberry = \\(\\dfrac{4}{7}\\) = 56, so 1 unit (\\(\\dfrac{1}{7}\\)) = 56 \u00f7 4 = 14. (a) Chocolate = \\(\\dfrac{2}{7}\\) = 2 \u00d7 14 = 28. Vanilla = 1 \u2212 \\(\\dfrac{2}{7}\\) \u2212 \\(\\dfrac{4}{7}\\) = \\(\\dfrac{1}{7}\\) = 14. (b) Strawberry \u2212 vanilla = 56 \u2212 14 = 42 (i.e. 3 units \u00d7 14)."} {"t":"q","id":19887,"q":"Cassie and Eli had some orange juice at first. Cassie gave \\(\\dfrac{3}{4}\\) \u2113 of orange juice to Dayan. Eli then gave Cassie \\(\\dfrac{5}{8}\\) \u2113 of orange juice. Cassie had \\(\\dfrac{9}{10}\\) \u2113 of orange juice in the end. How much orange juice did Cassie have at first? Express your answer as a mixed number.","e":"Before receiving \\(\\dfrac{5}{8}\\) \u2113, Cassie had \\(\\dfrac{9}{10}-\\dfrac{5}{8}=\\dfrac{36}{40}-\\dfrac{25}{40}=\\dfrac{11}{40}\\) \u2113. Adding back the \\(\\dfrac{3}{4}\\) \u2113 she gave away: \\(\\dfrac{11}{40}+\\dfrac{30}{40}=\\dfrac{41}{40}=1\\dfrac{1}{40}\\) \u2113."} {"t":"q","id":19888,"q":"There were 76 more belts than caps at first. After 158 belts and 30 caps were sold, there were 3 times as many caps as belts left.
(a) How many belts were there in the end?
(b) How many caps were there at first? ","e":"Let caps left = c, belts left = b. Belts were 76 more than caps at first; after selling 158 belts and 30 caps, belts left exceed caps left by 76 \u2212 158 + 30 = \u221252, i.e. caps left are 52 more than belts left. Also caps left = 3 \u00d7 belts left, so 2 \u00d7 belts left = 52, belts left = 26. (a) 26 belts in the end. Caps left = 3 \u00d7 26 = 78, so caps at first = 78 + 30 = 108. (b) 108 caps at first."} {"t":"q","id":19992,"q":"Which of the following is a factor of both 18 and 27?","e":"Factors of 18: 1, 2, 3, 6, 9, 18. Factors of 27: 1, 3, 9, 27. The common factors are 1, 3 and 9. Of the options, 9 is a factor of both 18 and 27."} {"t":"q","id":19993,"q":"Which of the following numbers when rounded to the nearest ten becomes 72 500?","e":"Rounding to the nearest ten: 72 443 -> 72 440; 72 495 -> 72 500; 72 539 -> 72 540; 72 554 -> 72 550. Only 72 495 rounds to 72 500."} {"t":"q","id":19995,"q":"\\(6\\dfrac{4}{7} = \\dfrac{ }{7}\\)
What is the missing number in the box?","e":"Convert the mixed number to an improper fraction: \\(6\\dfrac{4}{7} = \\dfrac{6 \\times 7 + 4}{7} = \\dfrac{42 + 4}{7} = \\dfrac{46}{7}\\). The missing number is 46."} {"t":"q","id":19997,"q":"Express 0.05 as a fraction in its simplest form.","e":"0.05 = \\(\\dfrac{5}{100}\\). Dividing numerator and denominator by 5 gives \\(\\dfrac{1}{20}\\)."} {"t":"q","id":19999,"q":"The table shows the prices of tickets to a theme park.
Adult: $15
Child: $9
Mrs Tan wants to buy tickets for two adults and three children. How much does she have to pay in total?","e":"2 adults: 2 \u00d7 $15 = $30. 3 children: 3 \u00d7 $9 = $27. Total = $30 + $27 = $57."} {"t":"q","id":20000,"q":"The table shows 4 different types of CCA that 225 children participated in. Each child participated only in one CCA.
Rope Skipping: ?
Gymnastics: 73
International Dance: 50
Girls' Brigade: 64
How many children participated in Rope Skipping?","e":"Total in the other three CCAs = 73 + 50 + 64 = 187. Rope Skipping = 225 \u2212 187 = 38."} {"t":"q","id":20001,"q":"Which of the following fractions has the value closest to 1?","e":"The distance from 1 is: \\(\\dfrac{1}{3}\\), \\(\\dfrac{1}{4}\\), \\(\\dfrac{1}{6}\\), \\(\\dfrac{1}{8}\\). The smallest gap is \\(\\dfrac{1}{8}\\), so \\(\\dfrac{7}{8}\\) is closest to 1."} {"t":"q","id":20002,"q":"Jamie bought 8 boxes of biscuits. Each box of biscuits cost $1.20. She gave the cashier $50. How much change did Jamie receive?","e":"Cost = 8 \u00d7 $1.20 = $9.60. Change = $50 \u2212 $9.60 = $40.40."} {"t":"q","id":20004,"q":"Harun and Ming Hui started reading their storybooks at 9.45 a.m.. Harun took 1 h 20 min to finish reading his storybook. He took 25 min longer than Ming Hui. At what time did Ming Hui finish reading his storybook?","e":"Ming Hui took 1 h 20 min \u2212 25 min = 55 min. Starting at 9.45 a.m. and adding 55 min gives 10.40 a.m."} {"t":"q","id":20006,"q":"How many letters in the word ANGEL have a line of symmetry?","e":"Checking each letter of ANGEL: A has a vertical line of symmetry, N has none, G has none, E has a horizontal line of symmetry, L has none. So 2 letters (A and E) have a line of symmetry."} {"t":"q","id":20007,"q":"Olivia used sticks to make triangles and squares. She used 6 sticks for each triangle and 8 sticks for each square. Olivia made the same number of triangles and squares. She used 14 more sticks to make the squares than the triangles. How many triangles did she make?","e":"Each square uses 8 \u2212 6 = 2 more sticks than each triangle. With an equal number of each shape, the extra sticks total 14, so the number of squares (and triangles) = 14 \u00f7 2 = 7. She made 7 triangles."} {"t":"q","id":20009,"q":"Write the missing number in the number pattern below.
14 100, 13 200, 12 300, 11 400, , 9600","e":"The pattern decreases by 900 each time (14 100, 13 200, 12 300, 11 400, ...). The missing number is 11 400 \u2212 900 = 10 500 (and 10 500 \u2212 900 = 9 600 confirms it)."} {"t":"q","id":20011,"q":"Which two of the fractions below are equivalent to \\(\\dfrac{6}{8}\\)?
\\(\\dfrac{12}{16}\\), \\(\\dfrac{5}{7}\\), \\(\\dfrac{4}{5}\\), \\(\\dfrac{3}{4}\\)
and ","e":"\\(\\dfrac{6}{8}\\) simplifies to \\(\\dfrac{3}{4}\\). \\(\\dfrac{12}{16}\\) also simplifies to \\(\\dfrac{3}{4}\\). So the two equivalent fractions are \\(\\dfrac{12}{16}\\) and \\(\\dfrac{3}{4}\\)."} {"t":"q","id":20019,"q":"At a funfair, \\(\\dfrac{5}{12}\\) of the people were children, \\(\\dfrac{1}{3}\\) of the people were men and the rest were women. What fraction of the people were women? Express your answer as a fraction in its simplest form.","e":"Children and men make up \\(\\dfrac{5}{12} + \\dfrac{1}{3} = \\dfrac{5}{12} + \\dfrac{4}{12} = \\dfrac{9}{12}\\). Women = \\(1 - \\dfrac{9}{12} = \\dfrac{3}{12} = \\dfrac{1}{4}\\)."} {"t":"q","id":20020,"q":"Express 3 \u00f7 7 as a decimal. Round your answer to the nearest hundredth.
","e":"3 \u00f7 7 = 0.4285... The thousandths digit is 8, so rounding to the nearest hundredth gives 0.43."} {"t":"q","id":20023,"q":"A train took 2 h 25 min to travel from Station A to Station B. It arrived at Station B at 23 45. What time did the train leave Station A? Express your answer using the 24-hour clock.
","e":"Subtract the travelling time from the arrival time: 23 45 \u2212 2 h 25 min. 23 45 \u2212 2 h = 21 45; 21 45 \u2212 25 min = 21 20. The train left at 21 20."} {"t":"q","id":20024,"q":"The table shows the number of stickers collected by each pupil in a group. Part of the table is covered by an ink blot. There were 87 pupils who collected at least 70 stickers.
Number of stickers: 50, 60, 70, 80, 90
Number of pupils: 25, 34, 19, ?, ?
How many pupils in total collected 80 and 90 stickers?
","e":"'At least 70 stickers' means the 70, 80 and 90 groups together = 87. The 70 group is 19, so the 80 and 90 groups together = 87 \u2212 19 = 68."} {"t":"q","id":20026,"q":"A pair of trousers cost $132. It cost $27 more than a shirt. Mr Lee bought a pair of trousers and 4 shirts.
(a) How much did a shirt cost?
(b) How much did Mr Lee pay for a pair of trousers and 4 shirts altogether?
(a) $
(b) $","e":"(a) Shirt = $132 \u2212 $27 = $105. (b) 4 shirts = 4 \u00d7 $105 = $420; total = $132 + $420 = $552."} {"t":"q","id":20028,"q":"There were some stickers in a box. Mariam took \\(\\dfrac{3}{8}\\) of the stickers and Amy took the rest. Mariam took 36 fewer stickers than Amy.
(a) What fraction of the stickers did Amy take?
(b) How many stickers were in the box in total?
(a)
(b) ","e":"(a) Amy took 1 \u2212 \\(\\dfrac{3}{8}\\) = \\(\\dfrac{5}{8}\\). (b) Amy's share minus Mariam's share = \\(\\dfrac{5}{8} - \\dfrac{3}{8} = \\dfrac{2}{8} = \\dfrac{1}{4}\\) of the total = 36 stickers. So total = 36 \u00d7 4 = 144 stickers."} {"t":"q","id":20030,"q":"Ahmad and Jack had the same amount of money at first. After Ahmad had spent $37 and Jack had received $15, Jack had 3 times as much money as Ahmad in the end.
(a) How much more money did Jack have than Ahmad in the end?
(b) How much money did Jack have at first?
(a) $
(b) $","e":"(a) The difference between them grew by $37 (Ahmad spent) + $15 (Jack received) = $52. So in the end Jack had $52 more than Ahmad. (b) In the end Jack = 3 \u00d7 Ahmad, so the $52 difference = 2 units, 1 unit = $26 = Ahmad's end amount; Jack's end = 3 \u00d7 $26 = $78. Jack at first = $78 \u2212 $15 = $63. (Key gives Jack's first amount via 52 \u00f7 2 = 26 = Ahmad's end amount.)"} {"t":"q","id":20031,"q":"Tina saved some money from Monday to Friday. Each day, she saved $1 more than the previous day. At the end of Wednesday, she saved a total of $38.70.
(a) How much money did Tina save on Wednesday?
(b) How much money did she save on Friday?
(a) $
(b) $","e":"(a) Mon, Tue, Wed savings differ by $1. Their total $38.70 minus the extra: Tue = Wed \u2212 1, Mon = Wed \u2212 2. 3 \u00d7 Wed \u2212 3 = 38.70, so 3 \u00d7 Wed = 41.70, Wed = $13.90. (b) Thursday = $14.90, Friday = $15.90."} {"t":"q","id":20147,"q":"Arrange the following numbers from the smallest to the largest.
3.5 , 3.05 , \\(3\\dfrac{1}{100}\\)
(smallest) , , ","e":"Write all as decimals: \\(3\\dfrac{1}{100} = 3.01\\), 3.05, 3.5. In order smallest to largest: 3.01, 3.05, 3.5, i.e. \\(3\\dfrac{1}{100}\\), 3.05, 3.5."} {"t":"q","id":20323,"q":"2 3\/7 = \/7\nWhat is the missing number in the box?","e":"Convert the mixed number to an improper fraction: 2 3\/7 = (2x7 + 3)\/7 = 17\/7. The missing numerator is 17."} {"t":"q","id":20939,"q":"In which of the following are the numbers arranged from the smallest to the greatest?","e":"Order ascending: 6083 < 6803 < 6830. That is option 4."} {"t":"q","id":20940,"q":"Which fraction is in its simplest form?","e":"\\(\\dfrac{5}{7}\\) has no common factor between 5 and 7, so it is already in simplest form. The others simplify: \\(\\dfrac{6}{9}=\\dfrac{2}{3}\\), \\(\\dfrac{3}{6}=\\dfrac{1}{2}\\), \\(\\dfrac{4}{10}=\\dfrac{2}{5}\\)."} {"t":"q","id":20943,"q":"Which of the following decimals is the greatest?","e":"Compare the tenths digit first: 0.369 and 0.346 have 3 tenths, the others have 1 tenth. Between 0.369 and 0.346, the hundredths digit 6 > 4, so 0.369 is greatest."} {"t":"q","id":20944,"q":"Which of the following is a factor of both 12 and 90?","e":"Factors of 12: 1, 2, 3, 4, 6, 12. Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90. The common factor among the options is 6."} {"t":"q","id":20947,"q":"Mrs Lee had some stickers. After she gave 6 stickers to each of her 28 pupils, she had 12 stickers left. How many stickers did Mrs Lee have at first?","e":"Stickers given out = 6 \u00d7 28 = 168. Add the 12 left over: 168 + 12 = 180."} {"t":"q","id":20952,"q":"What could be the mass of a Primary 4 Mathematics textbook?","e":"A textbook has a mass of a few hundred grams. 33 g is far too light, 33 kg and 330 kg are far too heavy. 330 g is the sensible estimate."} {"t":"q","id":20956,"q":"Mei Ling started running a marathon at 6.35 a.m. and finished it at 11.10 a.m. How long did she take to complete the marathon?","e":"From 6.35 a.m. to 11.35 a.m. is 5 h, but she finished at 11.10 a.m., which is 25 min earlier: 5 h \u2212 25 min = 4 h 35 min. (From 6.35 to 11.10 = 4 h to 10.35, plus 35 min to 11.10 = 4 h 35 min.)"} {"t":"q","id":20958,"q":"Write thirteen thousand and ninety-four in numerals. ","e":"Thirteen thousand = 13 000, plus ninety-four = 94, giving 13 094."} {"t":"q","id":20959,"q":"Write the missing number in the number pattern.
14 000, 13 200, 12 400, , 10 800, 10 000","e":"The pattern decreases by 800 each time: 14 000, 13 200, 12 400, 11 600, 10 800, 10 000. The missing number is 11 600."} {"t":"q","id":20960,"q":"Find the sum of 647 and 978. ","e":"647 + 978 = 1625."} {"t":"q","id":20962,"q":"\\(\\dfrac{2}{9}+\\dfrac{1}{3}=\\)","e":"Make the denominators the same: \\(\\dfrac{1}{3}=\\dfrac{3}{9}\\). Then \\(\\dfrac{2}{9}+\\dfrac{3}{9}=\\dfrac{5}{9}\\)."} {"t":"q","id":20963,"q":"\\(0.8=\\dfrac{8}{}\\) What is the missing number in the box?","e":"0.8 means 8 tenths, so \\(0.8=\\dfrac{8}{10}\\). The missing number is 10."} {"t":"q","id":20964,"q":"Round 42.64 to the nearest whole number. ","e":"The tenths digit is 6, which is 5 or more, so round up: 42.64 \u2248 43."} {"t":"q","id":20966,"q":"Which two of the fractions below are smaller than \\(\\dfrac{1}{2}\\)?
\\(\\dfrac{4}{11}\\), \\(\\dfrac{3}{4}\\), \\(\\dfrac{5}{10}\\), \\(\\dfrac{2}{7}\\)
and ","e":"Compare each with \\(\\dfrac{1}{2}\\): \\(\\dfrac{4}{11}<\\dfrac{1}{2}\\) (since 4 < 5.5), \\(\\dfrac{3}{4}>\\dfrac{1}{2}\\), \\(\\dfrac{5}{10}=\\dfrac{1}{2}\\), \\(\\dfrac{2}{7}<\\dfrac{1}{2}\\) (since 2 < 3.5). The two smaller than a half are \\(\\dfrac{4}{11}\\) and \\(\\dfrac{2}{7}\\)."} {"t":"q","id":20967,"q":"Mrs Tan took 20 min to travel from her home to the office. She spent 6 h 30 min in the office. She left her office at 18 15. What time did she leave her home in the morning? Give your answer in 24-hour clock. ","e":"Left office at 18 15. Subtract 6 h 30 min in office: 18 15 \u2212 6 h 30 min = 11 45 (arrived at office). Subtract 20 min travel: 11 45 \u2212 20 min = 11 25. She left home at 11 25."} {"t":"q","id":20968,"q":"PQRS is a square with perimeter 28 cm. Find its area. cm\u00b2","e":"Side of square = 28 \u00f7 4 = 7 cm. Area = 7 \u00d7 7 = 49 cm\u00b2."} {"t":"q","id":20969,"q":"The total cost of a handbag and purse is $242. The handbag costs $20 more than the purse. Find the cost of the handbag. ","e":"Remove the extra $20: 242 \u2212 20 = 222, which is twice the purse. Purse = 222 \u00f7 2 = 111. Handbag = 111 + 20 = 131."} {"t":"q","id":20970,"q":"The chairs in the hall are arranged in rows. Each row has the same number of chairs. When Ali sits at one of the chairs, there are 6 chairs to his right and 5 chairs to his left. There are 8 chairs in front of him and 4 chairs behind him. How many chairs are there in the hall? ","e":"Chairs in Ali's row = 6 + 5 + 1 = 12. Number of rows = 8 + 4 + 1 = 13. Total chairs = 12 \u00d7 13 = 156."} {"t":"q","id":20973,"q":"Mrs Wong baked between 70 to 90 cookies. She could pack all the cookies into boxes of 5 cookies or boxes of 8 cookies without any remainder. How many cookies did Mrs Wong bake? ","e":"The number must be a common multiple of 5 and 8, i.e. a multiple of 40. Between 70 and 90, the multiple of 40 is 80."} {"t":"q","id":20975,"q":"\\(\\dfrac{5}{12}\\) of the passengers on the MRT were female.
(a) What fraction of the passengers were male?
(b) There were 40 female passengers, how many passengers were there on the MRT?
(a) (b) ","e":"(a) Male fraction = \\(\\dfrac{12}{12}-\\dfrac{5}{12}=\\dfrac{7}{12}\\). (b) \\(\\dfrac{5}{12}\\) corresponds to 40 female passengers, so 1 unit = 40 \u00f7 5 = 8, and the total = 8 \u00d7 12 = 96 passengers."} {"t":"q","id":20976,"q":"The total mass of an empty school bag and 5 similar books was 5.4 kg. The total mass of the same school bag and 2 similar books was 3 kg.
(a) What was the mass of 1 book?
(b) What was the mass of the empty school bag?
(a) kg (b) kg","e":"(a) The difference of 3 books = 5.4 \u2212 3 = 2.4 kg, so 1 book = 2.4 \u00f7 3 = 0.8 kg. (b) 2 books = 0.8 \u00d7 2 = 1.6 kg, so the bag = 3 \u2212 1.6 = 1.4 kg."} {"t":"q","id":20977,"q":"Ravi had $92 more than Peter. After Ravi gave $100 to Peter, Peter had 5 times as much as Ravi.
(a) How much money did Ravi have at first?
(b) How much money did Peter have in the end?
(a) (b) ","e":"After the transfer the total is unchanged. Ravi gave away $100, so the difference shifts by $200: originally Ravi had $92 more, after giving $100 Peter has $108 more than Ravi. Peter = 5 \u00d7 Ravi, so the difference = 4 units = $108? Using the key: Ravi's amount after = (total)\u00f76 of a 1:5 split. (100+8)\u00f74 = 27 \u2192 Ravi after = $27, Ravi at first = 27 + 100 = $127. (b) Peter at first = 127 \u2212 92 = $35; Peter in the end = 35 + 100 = $135."} {"t":"q","id":20980,"q":"In which of the following numbers does the digit 6 stand for 600?","e":"The digit 6 stands for 600 when it is in the hundreds place. In 8690, the 6 is in the hundreds place, so it stands for 600."} {"t":"q","id":20981,"q":"Which of the following is not<\/b> a factor of 42?","e":"Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42. 8 is not a factor because 42 \u00f7 8 does not give a whole number."} {"t":"q","id":20988,"q":"Which of the following decimals is the smallest?","e":"All have whole-number part 4. Compare tenths: 4.056 has 0 tenths, which is smallest. So 4.056 is the smallest."} {"t":"q","id":20989,"q":"How many one-fifths are there in 4 wholes?","e":"Each whole has 5 one-fifths. In 4 wholes there are 4 \u00d7 5 = 20 one-fifths."} {"t":"q","id":20991,"q":"The total volume of 2 identical bottles of orange juice is 9.3 litres. What is the volume of 6 such bottles of orange juice?","e":"1 bottle = 9.3 \u00f7 2 = 4.65 litres. 6 bottles = 4.65 \u00d7 6 = 27.9 litres. (Or: 6 bottles = 3 \u00d7 9.3 = 27.9 litres.)"} {"t":"q","id":20993,"q":"Betty and Ken had 180 coins altogether. After Betty gave 25 coins to Ken, Ken had twice as many coins as Betty. How many coins did Ken have at first?","e":"Total stays 180. After giving, Ken = 2 \u00d7 Betty, so 3 units = 180, 1 unit = 60. Betty (after) = 60, Ken (after) = 120. Ken at first = 120 \u2212 25 = 95."} {"t":"q","id":20995,"q":"Arrange the following numbers from the smallest to the greatest.
3504 , 3045 , 3450
, , ","e":"Compare the numbers digit by digit: 3045 < 3450 < 3504. From smallest to greatest: 3045, 3450, 3504."} {"t":"q","id":20996,"q":"Write \\(3\\dfrac{5}{6}\\) as an improper fraction.","e":"Multiply the whole number by the denominator and add the numerator: (3 \u00d7 6) + 5 = 23. So \\(3\\dfrac{5}{6} = \\dfrac{23}{6}\\)."} {"t":"q","id":20999,"q":"\\(\\dfrac{3}{4}\\) \u2212 \\(\\dfrac{5}{8}\\) =","e":"Change to like denominators: \\(\\dfrac{3}{4} = \\dfrac{6}{8}\\). Then \\(\\dfrac{6}{8} - \\dfrac{5}{8} = \\dfrac{1}{8}\\)."} {"t":"q","id":21000,"q":"Round 14 310 to the nearest hundred.
","e":"The tens digit of 14 310 is 1, which is less than 5, so round down. 14 310 rounded to the nearest hundred is 14 300."} {"t":"q","id":21002,"q":"Which two of the fractions below are in the simplest form?
\\(\\dfrac{3}{5}\\) , \\(\\dfrac{4}{6}\\) , \\(\\dfrac{5}{7}\\) , \\(\\dfrac{6}{10}\\)
and ","e":"A fraction is in simplest form when its numerator and denominator share no common factor other than 1. \\(\\dfrac{4}{6}\\) simplifies to \\(\\dfrac{2}{3}\\) and \\(\\dfrac{6}{10}\\) simplifies to \\(\\dfrac{3}{5}\\), so they are not simplest. \\(\\dfrac{3}{5}\\) and \\(\\dfrac{5}{7}\\) cannot be simplified, so they are in simplest form."} {"t":"q","id":21005,"q":"Round 24.85 to 1 decimal place.
","e":"Look at the second decimal place (the hundredths digit) which is 5, so round the tenths up. 24.85 rounded to 1 decimal place is 24.9."} {"t":"q","id":21006,"q":"Jenny took 20 min to walk from her home to school in the morning. She spent 3 h 35 min in school. She left her school at 12 15. What time did she leave her home in the morning? Give your answer in 24-hour clock.
","e":"Work backwards from 12 15. Subtract 3 h 35 min in school: 12 15 \u2212 3 h 35 min = 08 40 (arrival at school). Subtract 20 min walk: 08 40 \u2212 20 min = 08 20. She left home at 08 20."} {"t":"q","id":21011,"q":"Siti paid $30 for 4 chicken pies and 4 tuna pies. Each chicken pie cost $1.20 more than each tuna pie. How much did 1 tuna pie cost?
$","e":"The 4 chicken pies cost 4 \u00d7 $1.20 = $4.80 more than the 4 tuna pies. Remove this extra: $30 \u2212 $4.80 = $25.20, which would be the cost of 8 tuna pies. So 1 tuna pie = $25.20 \u00f7 8 = $3.15."} {"t":"q","id":21012,"q":"Mother gave Ming some money on Monday. She gave him $25 on Tuesday. Ming spent half of the total amount of money he received and had $28 left. How much money did Mother give to Ming on Monday?
$","e":"He had $28 left after spending half, so half the total = $28, meaning the total received = $28 \u00d7 2 = $56. Subtract Tuesday's $25: Monday's amount = $56 \u2212 $25 = $31."} {"t":"q","id":21013,"q":"Taylor, Umar and Victor went for a morning walk. Taylor walked a distance that was 6 times as much as Victor. Umar walked 1.12 km more than Taylor. Umar walked a total distance of 4.6 km. How many kilometres did Victor walk?
km","e":"Taylor's distance = Umar \u2212 1.12 = 4.6 \u2212 1.12 = 3.48 km. Taylor walked 6 times Victor, so Victor = 3.48 \u00f7 6 = 0.58 km."} {"t":"q","id":21015,"q":"A grocer had 25 crates of tomatoes. Each crate contained 60 tomatoes. He threw away 303 rotten tomatoes and repacked the remaining into bags of 7 tomatoes each. How many bags of tomatoes did the grocer pack?
","e":"Total tomatoes = 25 \u00d7 60 = 1500. After throwing away rotten ones: 1500 \u2212 303 = 1197. Bags = 1197 \u00f7 7 = 171 bags."} {"t":"q","id":21017,"q":"Rina bought 30 m of ribbon. After using the ribbon to tie a present and 4 identical parcels, she had 8.81 m of ribbon left. She used 4.75 m of ribbon to tie the present. How many metres of ribbon did she use to tie each parcel?
m","e":"Ribbon used in total = 30 \u2212 8.81 = 21.19 m. Subtract the present: 21.19 \u2212 4.75 = 16.44 m used on the 4 parcels. Each parcel = 16.44 \u00f7 4 = 4.11 m."} {"t":"q","id":21018,"q":"Daniel had 1980 stamps more than Eugene. After Daniel gave away 291 stamps, he had 4 times as many stamps as Eugene.
a) How many more stamps did Daniel have than Eugene in the end?
b) How many stamps did Daniel have at first?
(a)
(b) ","e":"(a) After giving away 291, Daniel's lead over Eugene = 1980 \u2212 291 = 1689 stamps. (b) In the end Daniel = 4 times Eugene, so the 1689 difference = 3 units, 1 unit (Eugene) = 1689 \u00f7 3 = 563. Daniel at first = Eugene + 1980 = 563 + 1980 = 2543 stamps."} {"t":"q","id":21020,"q":"There were 180 flowers at a florist. \\(\\dfrac{2}{3}\\) of them were roses, \\(\\dfrac{2}{9}\\) of them were sunflowers and the remaining were daisies.
a) What fraction of the flowers were daisies?
b) The daisies were sold at 5 for $21. How much was collected from the sale of all the daisies?
(a)
(b) $","e":"(a) Daisies fraction = 1 \u2212 (\\(\\dfrac{2}{3}\\) + \\(\\dfrac{2}{9}\\)) = \\(\\dfrac{9}{9}\\) \u2212 (\\(\\dfrac{6}{9}\\) + \\(\\dfrac{2}{9}\\)) = \\(\\dfrac{9}{9}\\) \u2212 \\(\\dfrac{8}{9}\\) = \\(\\dfrac{1}{9}\\). (b) Number of daisies = \\(\\dfrac{1}{9}\\) \u00d7 180 = 20. Sold at 5 for $21: 20 \u00f7 5 = 4 groups, 4 \u00d7 $21 = $84."} {"t":"q","id":21021,"q":"A baker sold donuts at $2 each. The customers received a free donut for every 4 donuts they bought.
a) What was the least amount of money a customer had to pay if he wanted exactly 15 donuts?
b) How many donuts did a customer receive in total when he paid $40?
(a) $
(b) ","e":"(a) Buy 4, get 1 free = 5 donuts per group. For 15 donuts: 15 \u00f7 5 = 3 groups, so he buys 4 \u00d7 3 = 12 donuts. Cost = 12 \u00d7 $2 = $24. (b) $40 buys 40 \u00f7 2 = 20 donuts. Free donuts = 20 \u00f7 4 = 5. Total = 20 + 5 = 25 donuts."} {"t":"q","id":21022,"q":"Which of the following is a multiple of 6?","e":"A multiple of 6 is a number in the 6 times table: 6, 12, 18, 24, 30, ... Among the options, 24 = 6 \u00d7 4 is a multiple of 6. (32, 3 and 16 are not.) Answer: 24."} {"t":"q","id":21023,"q":"80 000 + 7000 + 300 + 2 =","e":"Add by place value: 80 000 + 7000 + 300 + 0 tens + 2 = 87 302. The tens place is 0, so the answer is 87 302."} {"t":"q","id":21024,"q":"1 min 52 s =","e":"1 min = 60 s. So 1 min 52 s = 60 s + 52 s = 112 s."} {"t":"q","id":21027,"q":"In the number 67.35, the digit ________ is in the tenths place.","e":"In 67.35, the first digit after the decimal point is the tenths place. That digit is 3. (The 5 is hundredths.)"} {"t":"q","id":21029,"q":"Arrange the following decimals from the smallest to the greatest.
4.8 , 0.48 , 4.08 , 0.84","e":"Compare the whole-number parts first: 0.48 and 0.84 (whole part 0) are smaller than 4.08 and 4.8 (whole part 4). Among 0.48 and 0.84, 0.48 < 0.84. Among 4.08 and 4.8, 4.08 < 4.80. Order: 0.48, 0.84, 4.08, 4.8."} {"t":"q","id":21030,"q":"\\(9\\dfrac{3}{5}\\) = \\(\\dfrac{ }{5}\\)
What is the missing number in the box?","e":"Convert the mixed number to an improper fraction with denominator 5: \\(9\\dfrac{3}{5}\\) = \\(\\dfrac{9\\times5+3}{5}\\) = \\(\\dfrac{45+3}{5}\\) = \\(\\dfrac{48}{5}\\). The missing numerator is 48."} {"t":"q","id":21032,"q":"Kumar is 1.53 m tall. His father is 0.28 m taller than him. His mother is 0.13 m shorter than his father. What is his mother's height?","e":"Father's height = 1.53 + 0.28 = 1.81 m. Mother's height = 1.81 \u2212 0.13 = 1.68 m."} {"t":"q","id":21037,"q":"Write \\(\\dfrac{17}{6}\\) as a mixed number.","e":"Divide 17 by 6: 17 \u00f7 6 = 2 remainder 5. So \\(\\dfrac{17}{6}\\) = \\(2\\dfrac{5}{6}\\)."} {"t":"q","id":21039,"q":"Find the value of \\(1 - \\dfrac{1}{8} - \\dfrac{3}{4}\\).","e":"Use a common denominator of 8: 1 = \\(\\dfrac{8}{8}\\), \\(\\dfrac{3}{4}\\) = \\(\\dfrac{6}{8}\\). So \\(\\dfrac{8}{8} - \\dfrac{1}{8} - \\dfrac{6}{8}\\) = \\(\\dfrac{1}{8}\\)."} {"t":"q","id":21040,"q":"Arrange the following numbers from the smallest to the greatest.
3907 , 3079 , 3790
, , ","e":"Compare by place value (all start with 3 thousands): 3079 (0 hundreds) < 3790 (7 hundreds) < 3907 (9 hundreds). Smallest to greatest: 3079, 3790, 3907."} {"t":"q","id":21046,"q":"A ribbon was 27.3 m long. Siti used 2.98 m of it for her project. She then cut the remaining ribbon equally into 8 pieces. What was the length of each piece of ribbon?
","e":"Remaining ribbon = 27.3 \u2212 2.98 = 24.32 m. Each piece = 24.32 \u00f7 8 = 3.04 m."} {"t":"q","id":21047,"q":"Muthu slept at 21 35 on Saturday night and woke up at 06 00 the next day. How long did he sleep?
h min","e":"From 21 35 to 22 00 is 25 min. From 22 00 to 06 00 is 8 h. Total = 8 h 25 min."} {"t":"q","id":21052,"q":"Container X has 96 more balls than Container Y. How many balls must be transferred from Container Y to Container X so that it has 112 balls less than Container X?
","e":"The required new difference is 112. The difference grows by 2 for every ball moved from Y to X (X gains one, Y loses one). Extra difference needed = 112 \u2212 96 = 16. Balls to transfer = 16 \u00f7 2 = 8."} {"t":"q","id":21054,"q":"Factory A and Factory B produce 1508 boxes a day. Factory B produces 3 times as many boxes as Factory A. How many boxes does Factory B produce?
","e":"Factory B is 3 times Factory A, so together they are 3 + 1 = 4 equal units = 1508 boxes. One unit (Factory A) = 1508 \u00f7 4 = 377. Factory B = 3 \u00d7 377 = 1131 boxes."} {"t":"q","id":21056,"q":"Mrs Choo bought a peach, 2 pears and 6 apples for $8.70. The cost of 1 pear and 3 apples was $2.60. What was the cost of the peach?
$","e":"2 pears + 6 apples = 2 \u00d7 (1 pear + 3 apples) = 2 \u00d7 $2.60 = $5.20. Peach = total \u2212 (2 pears + 6 apples) = $8.70 \u2212 $5.20 = $3.50."} {"t":"q","id":21057,"q":"Ali bought 8 kg of flour. He used \\(\\dfrac{2}{5}\\) kg of the flour to bake a cake and \\(\\dfrac{1}{4}\\) kg of it to bake chocolate cookies.
a) What was the total mass of flour he used altogether?

b) What was the mass of flour he had left?
","e":"a) Total used = \\(\\dfrac{2}{5} + \\dfrac{1}{4}\\). Common denominator 20: \\(\\dfrac{8}{20} + \\dfrac{5}{20}\\) = \\(\\dfrac{13}{20}\\) kg. b) Left = 8 \u2212 \\(\\dfrac{13}{20}\\) = \\(7\\dfrac{7}{20}\\) kg."} {"t":"q","id":21058,"q":"Mr Wong earned $0.25 for every newspaper he sold. He earned an additional $1.50 for every 10 copies of newspaper sold.
a) How much did Mr Wong earn in total for selling 10 copies of newspaper?
$
b) He earned $48 one day. How many copies of newspaper did he sell that day?
","e":"a) 10 copies earn 10 \u00d7 $0.25 = $2.50 plus the $1.50 bonus = $4.00. b) Every 10 copies earn $4, so $48 \u00f7 $4 = 12 sets of 10 copies = 12 \u00d7 10 = 120 copies."} {"t":"q","id":21059,"q":"The time in New Zealand is 4 hours ahead of the time in Singapore. When it is 10 00 in Singapore, it is 14 00 in New Zealand. Kathy went to New Zealand for a work trip. She would be taking a flight from New Zealand at 06 40 to come back to Singapore. The flight duration is 9 h 55 min. At what time would Kathy reach Singapore?
","e":"Flight leaves NZ at 06 40. Arrival in NZ time = 06 40 + 9 h 55 min = 16 35 (NZ time). Singapore is 4 h behind NZ, so subtract 4 h: 16 35 \u2212 4 h = 12 35. Kathy reaches Singapore at 12 35."} {"t":"q","id":21061,"q":"Mr Lim had 344 fruits. \\(\\dfrac{3}{4}\\) of the fruits sold were apples. Half of the remaining fruits sold were oranges and the rest were pears.
a) How many apples did he sell?

b) Mr Lim wanted to sell as many oranges as apples. How many more oranges would he need?
","e":"1 unit = 344 \u00f7 4 = 86. a) Apples = \\(\\dfrac{3}{4}\\) = 3 units = 3 \u00d7 86 = 258. b) Remaining = 86; oranges = half = 86 \u00f7 2 = 43. To match the apples (258), more oranges needed = 258 \u2212 43 = 215."} {"t":"q","id":21096,"q":"In which of the following does the digit 5 stand for 500?","e":"Method: the digit 5 stands for 500 when it is in the hundreds place. In 6573, the 5 is in the hundreds place, so it stands for 500. Answer: 6573."} {"t":"q","id":21097,"q":"Which of the following is a factor of both 24 and 30?","e":"Method: find the common factors. Factors of 24: 1,2,3,4,6,8,12,24. Factors of 30: 1,2,3,5,6,10,15,30. 6 is a factor of both. Answer: 6."} {"t":"q","id":21098,"q":"Which number when rounded to the nearest ten becomes 53 200?","e":"Method: rounding to the nearest ten gives 53 200 for numbers from 53 195 to 53 204. 53 196 rounds up to 53 200. Answer: 53 196."} {"t":"q","id":21100,"q":"How many one-fifths are there in 3 wholes?","e":"Method: each whole has 5 one-fifths. 3 wholes = 3 x 5 = 15 one-fifths. Answer: 15."} {"t":"q","id":21101,"q":"The digit 6 in 23.16 stands for 6 ________","e":"Method: in 23.16, the digit after the decimal point is tenths and the next is hundredths. The 6 is in the hundredths place, so it stands for 6 hundredths. Answer: hundredths."} {"t":"q","id":21111,"q":"45 069 = 40 000 + 5000 + + 9","e":"Method: 45 069 = 40 000 + 5000 + ? + 9. Sum of known parts = 40 000 + 5000 + 9 = 45 009. Missing number = 45 069 - 45 009 = 60. Answer: 60."} {"t":"q","id":21112,"q":"Write the missing number in the number pattern below.
11 000 , 10 600 , 10 200 , , 9400","e":"Method: the pattern decreases by 400 each time (11 000 - 10 600 = 400). 10 200 - 400 = 9800. Check: 9800 - 400 = 9400. Answer: 9800."} {"t":"q","id":21113,"q":"Which two of the fractions below are smaller than \\(\\dfrac{1}{2}\\)?
\\(\\dfrac{3}{4}\\) , \\(\\dfrac{4}{9}\\) , \\(\\dfrac{5}{10}\\) , \\(\\dfrac{3}{7}\\)
(a)   (b) ","e":"Method: compare each to \\(\\dfrac{1}{2}\\). \\(\\dfrac{3}{4}\\) > \\(\\dfrac{1}{2}\\); \\(\\dfrac{4}{9}\\) < \\(\\dfrac{1}{2}\\) (since half of 9 is 4.5); \\(\\dfrac{5}{10}\\) = \\(\\dfrac{1}{2}\\); \\(\\dfrac{3}{7}\\) < \\(\\dfrac{1}{2}\\) (since half of 7 is 3.5). The two smaller than a half are \\(\\dfrac{4}{9}\\) and \\(\\dfrac{3}{7}\\). Answer: \\(\\dfrac{4}{9}\\) and \\(\\dfrac{3}{7}\\)."} {"t":"q","id":21114,"q":"What is the value of \\(\\dfrac{2}{3}\\) + \\(\\dfrac{5}{6}\\)? Express your answer as a mixed number.","e":"Method: make the denominators the same. \\(\\dfrac{2}{3}\\) = \\(\\dfrac{4}{6}\\). \\(\\dfrac{4}{6}\\) + \\(\\dfrac{5}{6}\\) = \\(\\dfrac{9}{6}\\) = \\(1\\dfrac{3}{6}\\) = \\(1\\dfrac{1}{2}\\). Answer: \\(1\\dfrac{1}{2}\\)."} {"t":"q","id":21116,"q":"Express 0.15 as a fraction.","e":"Method: 0.15 has 2 decimal places, so it is 15 hundredths = \\(\\dfrac{15}{100}\\). Answer: \\(\\dfrac{15}{100}\\)."} {"t":"q","id":21117,"q":"Round 18.57 to the nearest whole number.
Answer: ","e":"Method: look at the tenths digit. 18.57 has 5 in the tenths place, which is 5 or more, so round up. 18.57 rounds to 19. Answer: 19."} {"t":"q","id":21118,"q":"7.3 \u2212 0.92 = ","e":"Method: align the decimals. 7.30 - 0.92 = 6.38. Answer: 6.38."} {"t":"q","id":21119,"q":"Find the value of 5.79 \u00d7 6.
Answer: ","e":"Method: 5.79 x 6 = 34.74 (since 579 x 6 = 3474, then place the decimal two places). Answer: 34.74."} {"t":"q","id":21121,"q":"The table shows the favourite fruits of a group of students.
Apple: 35, Mango: , Orange: 32, Papaya: 54.
\\(\\dfrac{2}{5}\\) of the students chose papaya as their favourite fruit. How many students chose mango as their favourite fruit?","e":"Method: \\(\\dfrac{2}{5}\\) of the total = 54 (papaya), so total = 54 \u00f7 2 x 5 = 135 students. Mango = total - apple - orange - papaya = 135 - 35 - 32 - 54 = 14. Answer: 14."} {"t":"q","id":21124,"q":"Sally mixed 1.73 \\(l\\) of orange syrup with 4.55 \\(l\\) of water. She poured the mixture equally into 4 bottles. How many litres of the mixture were there in each bottle?
Answer: ","e":"Method: total mixture = 1.73 + 4.55 = 6.28 \\(l\\). Each bottle = 6.28 \u00f7 4 = 1.57 \\(l\\). Answer: 1.57 \\(l\\)."} {"t":"q","id":21125,"q":"The mass of a watermelon is 3.4 kg. It is 5 times as heavy as a pear. What is the total mass of the pear and the watermelon?
Answer: ","e":"Method: pear = 3.4 \u00f7 5 = 0.68 kg. Total = watermelon + pear = 3.4 + 0.68 = 4.08 kg. Answer: 4.08 kg."} {"t":"q","id":21126,"q":"Mr and Mrs Tan took their children to watch a circus show on a Sunday. They bought 5 tickets in total. They had 3 children whose ages were 8, 13 and 14.
Circus Show Ticket Prices \u2014 Adult: Mon\u2013Fri $33.50, Sat\u2013Sun $38.50. Children (12 years and below): Mon\u2013Fri $16, Sat\u2013Sun $22.
How much did the 5 tickets cost altogether?
Answer: ","e":"Method: it is Sunday, so use Sat\u2013Sun prices. The two parents and the two older children (13 and 14, over 12) all pay adult: 4 adults x $38.50 = $154. The 8-year-old pays child: $22. Total = 154 + 22 = $176. Answer: $176."} {"t":"q","id":21130,"q":"The cost of 6 identical laptops is $7692. Find the cost of 5 such laptops.
Answer: ","e":"Method: cost of 1 laptop = 7692 \u00f7 6 = $1282. Cost of 5 laptops = 1282 x 5 = $6410. Answer: $6410."} {"t":"q","id":21131,"q":"Leon has \\(\\dfrac{2}{5}\\) kg of flour in a container. He has \\(\\dfrac{1}{2}\\) kg of flour less than Siti. How much flour do they have altogether? Express your answer as a mixed number in its simplest form.","e":"Method: Siti has \\(\\dfrac{2}{5}\\) + \\(\\dfrac{1}{2}\\) = \\(\\dfrac{4}{10}\\) + \\(\\dfrac{5}{10}\\) = \\(\\dfrac{9}{10}\\) kg. Altogether = Leon + Siti = \\(\\dfrac{4}{10}\\) + \\(\\dfrac{9}{10}\\) = \\(\\dfrac{13}{10}\\) = \\(1\\dfrac{3}{10}\\) kg. Answer: \\(1\\dfrac{3}{10}\\) kg."} {"t":"q","id":21134,"q":"Mrs Lee baked some cookies and ate \\(\\dfrac{2}{9}\\) of the cookies. She gave 12 cookies to her friend and had 9 cookies left.
(a) How many cookies did she bake?
(b) What fraction of the cookies did she have left? Express your answer in its simplest form.
(a)   (b) ","e":"Method: (a) she ate \\(\\dfrac{2}{9}\\), so \\(\\dfrac{7}{9}\\) remained. The 12 given away + 9 left = 21 cookies = \\(\\dfrac{7}{9}\\) of the total. So \\(\\dfrac{1}{9}\\) = 21 \u00f7 7 = 3, and the total = 3 x 9 = 27 cookies. (b) cookies left = 9 out of 27 = \\(\\dfrac{9}{27}\\) = \\(\\dfrac{1}{3}\\). Answer: (a) 27; (b) \\(\\dfrac{1}{3}\\)."} {"t":"q","id":21135,"q":"Sharon and Leo had a total of 3260 stickers. Sharon had 3 times as many stickers as Leo. How many stickers must Sharon give to Leo so that Sharon has 270 more stickers than Leo?
Answer: ","e":"Method: Sharon has 3 units and Leo 1 unit, total 4 units = 3260, so 1 unit = 815. Sharon = 2445, Leo = 815. For Sharon to have 270 more than Leo from a total of 3260: Leo's new amount = (3260 - 270) \u00f7 2 = 2990 \u00f7 2 = 1495, Sharon's new = 1495 + 270 = 1765. Sharon must give = 2445 - 1765 = 680 stickers. Answer: 680."} {"t":"q","id":21136,"q":"A bookshop sells pencils in packs of 4 and erasers in packs of 6. 4 pencils for $3. 6 erasers for $5.
(a) Henry bought an equal number of pencils and erasers. What is the least number of pencils he could have bought?
(b) Liling used all her money to buy 44 pencils. Using the same amount of money, what is the greatest number of erasers she could buy?
(a)   (b) ","e":"Method: (a) pencils come in 4s, erasers in 6s. The least equal number is the lowest common multiple of 4 and 6 = 12. (b) 44 pencils = 11 packs x $3 = $33. With $33, erasers cost $5 per 6: 33 \u00f7 5 = 6 packs ($30) remainder $3, so 6 packs = 36 erasers (the $3 left is not enough for another pack). Answer: (a) 12; (b) 36."} {"t":"q","id":21137,"q":"Keith and Sam had the same amount of money. Keith bought 6 egg tarts and had $1.90 left. Sam wanted to buy 10 egg tarts but was short of $5.50.
(a) What was the cost of 1 egg tart?
(b) How much money did Sam have?
(a)   (b) ","e":"Method: (a) the difference between 10 and 6 egg tarts is 4 egg tarts. Keith had $1.90 left; Sam was short $5.50, so 4 egg tarts cost 1.90 + 5.50 = $7.40. 1 egg tart = 7.40 \u00f7 4 = $1.85. (b) Sam (same money as Keith) = cost of 6 egg tarts + $1.90 = (1.85 x 6) + 1.90 = 11.10 + 1.90 = $13. Answer: (a) $1.85; (b) $13."} {"t":"q","id":21182,"q":"Arrange the following numbers from the smallest to the largest.
3.5 , 3.05 , \\(3\\dfrac{1}{100}\\)
(smallest) , , ","e":"Write all as decimals: \\(3\\dfrac{1}{100} = 3.01\\), 3.05, 3.5. In order smallest to largest: 3.01, 3.05, 3.5, i.e. \\(3\\dfrac{1}{100}\\), 3.05, 3.5."} {"t":"q","id":21238,"q":"In which of the following does the digit 8 stand for 800?","e":"The digit 8 stands for 800 when it is in the hundreds place. In 7 862, the 8 is in the hundreds position, so it stands for 800. Answer: 7 862."} {"t":"q","id":21239,"q":"10000 + 5000 + 600 + 4 =","e":"Add by place value: 10000 + 5000 + 600 + 4 = 15 604. Note there are no tens, so the tens digit is 0. Answer: 15 604."} {"t":"q","id":21240,"q":"2 and 3 are factors of","e":"A number must be divisible by both 2 and 3. 12 = 2 x 6 and 12 = 3 x 4, so both 2 and 3 are factors of 12. Answer: 12."} {"t":"q","id":21241,"q":"Which fraction is not<\/b> in its simplest form?","e":"A fraction is in simplest form when the numerator and denominator share no common factor other than 1. \\(\\dfrac{6}{9}\\) can be simplified by dividing both by 3 to give \\(\\dfrac{2}{3}\\), so it is NOT in simplest form. Answer: \\(\\dfrac{6}{9}\\)."} {"t":"q","id":21242,"q":"Write \\(6\\dfrac{4}{25}\\) as a decimal.","e":"Convert \\(\\dfrac{4}{25}\\) to a decimal: \\(\\dfrac{4}{25}=\\dfrac{16}{100}=0.16\\). So \\(6\\dfrac{4}{25}=6.16\\). Answer: 6.16."} {"t":"q","id":21243,"q":"Arrange these decimals from the smallest to the greatest.
7.3 , 0.73 , 7.03 , 0.75","e":"Compare whole-number parts first: 0.73 and 0.75 are less than 1; 7.03 and 7.3 are over 7. Order the small pair: 0.73 < 0.75. Order the large pair: 7.03 < 7.3. So smallest to greatest: 0.73 , 0.75 , 7.03 , 7.3. Answer: option 2."} {"t":"q","id":21246,"q":"The mass of a pail of sand is 2.5 kg. It is 30.14 kg lighter than a pile of bricks. What is the mass of the bricks?","e":"The sand is 30.14 kg lighter than the bricks, so the bricks are 30.14 kg heavier than the sand. Mass of bricks = 2.5 + 30.14 = 32.64 kg. Answer: 32.64 kg."} {"t":"q","id":21248,"q":"Round off 12.329 \\(l\\) to the nearest tenth.","e":"Rounding to the nearest tenth means keeping 1 decimal place. Look at the hundredths digit (2): since 2 is less than 5, round down. 12.329 rounds to 12.3 l. Answer: 12.3 l."} {"t":"q","id":21253,"q":"Round 8325 to the nearest ten. ","e":"To round to the nearest ten, look at the ones digit (5). Since 5 rounds up, the tens digit goes from 2 to 3. 8325 rounds to 8330. Answer: 8330."} {"t":"q","id":21254,"q":"How many one-elevenths are there in 1 whole? ","e":"One whole = \\(\\dfrac{11}{11}\\), which is eleven groups of \\(\\dfrac{1}{11}\\). So there are 11 one-elevenths in 1 whole. Answer: 11."} {"t":"q","id":21255,"q":"\\(1 - \\dfrac{1}{8} - \\dfrac{1}{4}\\) =","e":"Use a common denominator of 8: \\(1=\\dfrac{8}{8}\\), \\(\\dfrac{1}{4}=\\dfrac{2}{8}\\). So \\(\\dfrac{8}{8}-\\dfrac{1}{8}-\\dfrac{2}{8}=\\dfrac{5}{8}\\). Answer: \\(\\dfrac{5}{8}\\)."} {"t":"q","id":21257,"q":"Find the value of 6.73 x 8. ","e":"Multiply: 6.73 x 8 = 53.84. Answer: 53.84."} {"t":"q","id":21258,"q":"4501 \u00f7 7 = ","e":"Divide: 4501 \u00f7 7 = 643 exactly (7 x 643 = 4501). Answer: 643."} {"t":"q","id":21259,"q":"Write \\(2\\dfrac{2}{3}\\) as an improper fraction.","e":"Multiply the whole number by the denominator and add the numerator: 2 x 3 + 2 = 8. Keep the denominator 3. So \\(2\\dfrac{2}{3}=\\dfrac{8}{3}\\). Answer: \\(\\dfrac{8}{3}\\)."} {"t":"q","id":21262,"q":"Find the sum of the first 2 common multiples of 4 and 6. ","e":"Common multiples of 4 and 6 are multiples of 12. The first two are 12 and 24. Their sum is 12 + 24 = 36. Answer: 36."} {"t":"q","id":21263,"q":"After spilling \\(\\dfrac{2}{3}\\) \\(l\\) of water, John has \\(1\\dfrac{1}{2}\\) \\(l\\) of water left. How much water does he have at first? Give your answer as a mixed number.","e":"At first = water left + water spilled = \\(1\\dfrac{1}{2}+\\dfrac{2}{3}\\). Common denominator 6: \\(1\\dfrac{3}{6}+\\dfrac{4}{6}=1\\dfrac{7}{6}=2\\dfrac{1}{6}\\). Answer: \\(2\\dfrac{1}{6}\\) l."} {"t":"q","id":21266,"q":"The perimeter of a square is 48 cm. Find the area of the square. ","e":"A square has 4 equal sides, so each side = 48 \u00f7 4 = 12 cm. Area = side x side = 12 x 12 = 144 cm^2. Answer: 144 cm^2."} {"t":"q","id":21268,"q":"In a party, the children are told to get into groups to play a game. If they form groups of 5, there will be 2 children left without a group. If they form groups of 6, there will be 4 children left without a group. What is the least number of children at the party? ","e":"The number leaves remainder 2 when divided by 5 (so ends in 2 or 7) and remainder 4 when divided by 6. Check numbers ending in 2 or 7: 22 \u00f7 6 = 3 r 4 and 22 \u00f7 5 = 4 r 2. So the least number is 22. Answer: 22."} {"t":"q","id":21269,"q":"Mrs Tan had $188.70. She spent $39.90 on a blouse. She gave the rest of the money equally to her 3 children. How much did each child receive? ","e":"Money left after the blouse = 188.70 - 39.90 = 148.80. Shared among 3 children: 148.80 \u00f7 3 = 49.60. Each child received $49.60. Answer: $49.60."} {"t":"q","id":21270,"q":"Katherine bought 10.25 \\(l\\) of fruit juice. She fills them into 9 bottles. Each bottle is filled with 0.45 \\(l\\) of fruit juice.
(a) How much fruit juice will be left?
(b) How much did Katherine pay for the fruit juice if it cost $4 per litre?
(a)   (b) ","e":"(a) Juice used = 0.45 x 9 = 4.05 l. Left = 10.25 - 4.05 = 6.20 l. (b) Cost = 10.25 x $4 = $41. Answers: (a) 6.20 l, (b) $41."} {"t":"q","id":21271,"q":"The mass of a bag containing 9 packets of milk is 23.5 kg. After taking out 4 packets, the mass of the bag and remaining packets of milk is 19.36 kg. Find the mass of the bag. ","e":"Mass of 4 packets = 23.5 - 19.36 = 4.14 kg. Mass of 1 packet = 4.14 \u00f7 4 = 1.035 kg. Mass of 9 packets = 1.035 x 9 = 9.315 kg. Mass of bag = 23.5 - 9.315 = 14.185 kg. Answer: 14.185 kg."} {"t":"q","id":21272,"q":"Tom earned $5670 a month. He spent \\(\\dfrac{2}{3}\\) of his salary on food and \\(\\dfrac{1}{9}\\) of it on transport. He saved the rest. How much did he save in a month? ","e":"Fraction spent = \\(\\dfrac{2}{3}+\\dfrac{1}{9}=\\dfrac{6}{9}+\\dfrac{1}{9}=\\dfrac{7}{9}\\). Fraction saved = \\(1-\\dfrac{7}{9}=\\dfrac{2}{9}\\). Saved = \\(\\dfrac{2}{9}\\) of 5670. Since 5670 \u00f7 9 = 630, saved = 630 x 2 = $1260. Answer: $1260."} {"t":"q","id":21276,"q":"Timmy had 4730 marbles and Ahmad had 1240 marbles at first. If Timmy gave some marbles to Ahmad, he would have twice as many marbles as Ahmad in the end. How many marbles did Timmy give Ahmad? ","e":"The total stays the same: 4730 + 1240 = 5970. In the end Timmy has twice Ahmad, so the total is 3 equal parts. Ahmad's final amount = 5970 \u00f7 3 = 1990. Ahmad started with 1240, so he received 1990 - 1240 = 750 marbles. Answer: 750."} {"t":"q","id":21301,"q":"In which of the following does the digit 6 stand for 600?","e":"The digit 6 stands for 600 when it is in the hundreds place. In 7603, the 6 is in the hundreds place (6 hundreds = 600). Answer: 7603."} {"t":"q","id":21302,"q":"Which of the following are common factors of 18 and 24?","e":"Factors of 18: 1, 2, 3, 6, 9, 18. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. Common factors include 1, 2, 3, 6. Among the options, 3 and 6 are both common factors. Answer: 3 and 6."} {"t":"q","id":21303,"q":"How many one-quarters are there in 2 wholes?","e":"Each whole has 4 one-quarters. 2 wholes = 2 \u00d7 4 = 8 one-quarters. Answer: 8."} {"t":"q","id":21304,"q":"\\(7\\dfrac{4}{9}\\) = \\(\\dfrac{ }{9}\\)
What is the missing number in the box?","e":"Convert the mixed number to an improper fraction: 7 \u00d7 9 + 4 = 63 + 4 = 67. So \\(7\\dfrac{4}{9}=\\dfrac{67}{9}\\). Answer: 67."} {"t":"q","id":21306,"q":"What is the number when 223.74 is rounded to 1 decimal place?","e":"To round 223.74 to 1 decimal place, look at the 2nd decimal digit (4). Since 4 < 5, round down: 223.7. Answer: 223.7."} {"t":"q","id":21308,"q":"Mary bought a table and 3 chairs. The table cost $180 more than each chair. She gave the cashier $1000 and received $40 change. What was the cost of each chair?","e":"Total spent = $1000 \u2212 $40 = $960. Table + 3 chairs = $960, and table = 1 chair + $180. So 4 chairs + $180 = $960, 4 chairs = $780, each chair = $780 \u00f7 4 = $195. Answer: $195."} {"t":"q","id":21309,"q":"This number is a factor of 20 and a multiple of 5. It is between 6 and 19. What is this number?","e":"Factors of 20: 1, 2, 4, 5, 10, 20. Multiples of 5: 5, 10, 15, 20. The number is in both lists and between 6 and 19: that is 10. Answer: 10."} {"t":"q","id":21310,"q":"Mrs Tan packed 40 plums into some bags. Each bag contained 7 plums. She sold each bag of plums at $6 and each remaining plum at $1 each. How much would she collect if she sold all the plums?","e":"40 \u00f7 7 = 5 bags with remainder 5 plums. 5 bags \u00d7 $6 = $30, plus 5 plums \u00d7 $1 = $5. Total = $30 + $5 = $35. Answer: $35."} {"t":"q","id":21311,"q":"Ann and David scored a total of 8060 points in a game show. Ann scored 4 times as many points as David. How many points did David score?","e":"David = 1 unit, Ann = 4 units, total = 5 units = 8060. 1 unit = 8060 \u00f7 5 = 1612. David scored 1612 points. Answer: 1612."} {"t":"q","id":21312,"q":"Ethan ate \\(\\dfrac{5}{12}\\) of a pizza. His sister ate \\(\\dfrac{1}{3}\\) of the same pizza. How much more of the pizza did Ethan eat than his sister?","e":"\\(\\dfrac{1}{3}=\\dfrac{4}{12}\\). \\(\\dfrac{5}{12}-\\dfrac{4}{12}=\\dfrac{1}{12}\\). Ethan ate \\(\\dfrac{1}{12}\\) more. Answer: \\(\\dfrac{1}{12}\\)."} {"t":"q","id":21313,"q":"Mr Tan is 1.6 m tall. He is taller than Mdm Siti by 0.02 m. How tall is Mdm Siti?","e":"Mdm Siti is shorter, so subtract: 1.6 \u2212 0.02 = 1.58 m. Answer: 1.58 m."} {"t":"q","id":21314,"q":"The total mass of 5 identical boxes is 11.25 kg. What is the mass of 9 such boxes?","e":"1 box = 11.25 \u00f7 5 = 2.25 kg. 9 boxes = 2.25 \u00d7 9 = 20.25 kg. Answer: 20.25 kg."} {"t":"q","id":21317,"q":"The mass of a durian is 1.7 kg when rounded to 1 decimal place. Which of the following is the maximum possible mass of the durian?","e":"Values from 1.65 up to just below 1.75 round to 1.7. The largest option that still rounds to 1.7 is 1.74. Wait \u2014 1.84 rounds to 1.8, not 1.7. Re-check: the maximum value that rounds to 1.7 is just under 1.75, so 1.74 is the maximum among valid options. The answer key marks option (4) 1.84; however 1.84 rounds to 1.8. Mathematically the maximum that rounds to 1.7 is 1.74 (option 2)."} {"t":"q","id":21321,"q":"Write ninety thousand and sixteen in numerals.
","e":"Ninety thousand = 90 000. Sixteen = 16. Combine: 90 000 + 16 = 90 016. Answer: 90 016."} {"t":"q","id":21322,"q":"Write the missing number in the number pattern.
5624 , 5774 , 5924 , , 6224","e":"The pattern increases by 150 each time (5624 \u2192 5774 \u2192 5924). 5924 + 150 = 6074. Check: 6074 + 150 = 6224. Answer: 6074."} {"t":"q","id":21323,"q":"\\(\\dfrac{11}{12}\\) \u2212 \\(\\dfrac{5}{6}\\) =","e":"\\(\\dfrac{5}{6}=\\dfrac{10}{12}\\). \\(\\dfrac{11}{12}-\\dfrac{10}{12}=\\dfrac{1}{12}\\). Answer: \\(\\dfrac{1}{12}\\)."} {"t":"q","id":21324,"q":"What is the value of \\(\\dfrac{2}{3}\\) + \\(\\dfrac{7}{9}\\)? Express your answer as a mixed number.","e":"\\(\\dfrac{2}{3}=\\dfrac{6}{9}\\). \\(\\dfrac{6}{9}+\\dfrac{7}{9}=\\dfrac{13}{9}=1\\dfrac{4}{9}\\). Answer: \\(1\\dfrac{4}{9}\\)."} {"t":"q","id":21325,"q":"1 \u2212 \\(\\dfrac{1}{2}\\) \u2212 \\(\\dfrac{3}{8}\\) =","e":"1 = \\(\\dfrac{8}{8}\\), \\(\\dfrac{1}{2}=\\dfrac{4}{8}\\). \\(\\dfrac{8}{8}-\\dfrac{4}{8}-\\dfrac{3}{8}=\\dfrac{1}{8}\\). Answer: \\(\\dfrac{1}{8}\\)."} {"t":"q","id":21327,"q":"Arrange these numbers from the greatest to the smallest.
0.065 , 0.605 , 0.506
(greatest) , , (smallest)","e":"Compare tenths first: 0.605 and 0.506 have 6 and 5 tenths; 0.065 has 0 tenths. So 0.605 > 0.506 > 0.065. Greatest to smallest: 0.605, 0.506, 0.065."} {"t":"q","id":21330,"q":"Find the value of 45 \u00f7 7, correct to 2 decimal places.
","e":"45 \u00f7 7 = 6.428... The 3rd decimal digit is 8, so round up the 2nd decimal: 6.43. Answer: 6.43."} {"t":"q","id":21332,"q":"Mr Tay packed pens and pencils into boxes for sale. There are 698 boxes in total. Each box contains 11 pens and 6 pencils. How many pens and pencils are there altogether?
","e":"Each box has 11 + 6 = 17 items. Total = 698 \u00d7 17 = 11 866. Answer: 11 866."} {"t":"q","id":21333,"q":"2 similar spoons and 2 similar mugs cost $27. Each mug costs two times as much as each spoon. How much will 3 such spoons cost?
Ans: $","e":"Let 1 spoon = 1 unit, 1 mug = 2 units. 2 spoons + 2 mugs = 2 + 4 = 6 units = $27, so 1 unit = $4.50. 3 spoons = 3 \u00d7 $4.50 = $13.50. Answer: $13.50."} {"t":"q","id":21340,"q":"Mr Lim had 2 ropes. The first rope was \\(\\dfrac{3}{5}\\) m long. It was \\(\\dfrac{1}{4}\\) m longer than the second rope.
(a) What was the length of the second rope?
(b) What was the total length of the two ropes?
(a) m
(b) m","e":"(a) Second rope = first \u2212 \\(\\dfrac{1}{4}\\) = \\(\\dfrac{3}{5}-\\dfrac{1}{4}=\\dfrac{12}{20}-\\dfrac{5}{20}=\\dfrac{7}{20}\\) m. (b) Total = \\(\\dfrac{3}{5}+\\dfrac{7}{20}=\\dfrac{12}{20}+\\dfrac{7}{20}=\\dfrac{19}{20}\\) m. Answers: (a) \\(\\dfrac{7}{20}\\) m, (b) \\(\\dfrac{19}{20}\\) m."} {"t":"q","id":21341,"q":"Bob and John had a total of $2500 at first. After Bob spent $180 on a watch and John earned $160 from selling some magazines during the holidays, both boys had the same amount of money at the end. How much money did Bob have at first?
Ans: $","e":"Total at end = $2500 \u2212 $180 + $160 = $2480. Equal split = $2480 \u00f7 2 = $1240 each. Bob ended with $1240 after spending $180, so Bob at first = $1240 + $180 = $1420. Answer: $1420."} {"t":"q","id":21342,"q":"There were 1167 buns in a bakery. During a promotion, every customer who bought 2 buns got an additional bun for free. After 140 customers bought 2 buns each and received their additional free buns, the remaining buns were packed equally into 9 bags. How many buns were there in each bag?
","e":"Each of the 140 customers took 2 + 1 free = 3 buns: 140 \u00d7 3 = 420 buns. Remaining = 1167 \u2212 420 = 747. Packed into 9 bags: 747 \u00f7 9 = 83 buns per bag. Answer: 83."} {"t":"q","id":21343,"q":"Mary had $5.20 less than Susan. After Susan's father gave Susan $10, Susan had 5 times as much money as Mary.
(a) How much money did Mary have?
(b) What was the total amount of money both girls had at first?
(a) $
(b) $","e":"(a) Susan at first = Mary + $5.20. After +$10, Susan = Mary + $15.20 = 5 \u00d7 Mary. So 4 \u00d7 Mary = $15.20, Mary = $3.80. (b) Susan at first = $3.80 + $5.20 = $9.00. Total at first = $3.80 + $9.00 = $12.80. Answers: (a) $3.80, (b) $12.80."} {"t":"q","id":21345,"q":"The value of the digit 6 in 48 630 is .","e":"In 48 630, the digit 6 is in the hundreds place. So its value is 6 \u00d7 100 = 600."} {"t":"q","id":21346,"q":"Which of the following are common factors of 9 and 18?","e":"Factors of 9: 1, 3, 9. Factors of 18: 1, 2, 3, 6, 9, 18. Common factors are 1, 3, 9. Of the options, only 3 and 9 are both common factors."} {"t":"q","id":21355,"q":"In which of the following are the numbers arranged from the smallest to the greatest?","e":"Compare the numbers: 17 024 < 17 204 < 17 420. Only option 4 lists them smallest to greatest."} {"t":"q","id":21356,"q":"Complete the number pattern.
50 970 , 50 973 , 50 976 , , , 50 985","e":"The pattern increases by 3 each time: 50 970, 50 973, 50 976, 50 979, 50 982, 50 985. So the two missing numbers are 50 979 and 50 982."} {"t":"q","id":21358,"q":"Find the value of \\(\\dfrac{6}{8}-\\dfrac{1}{2}\\) .","e":"Make denominators the same: \\(\\dfrac{1}{2}=\\dfrac{4}{8}\\). Then \\(\\dfrac{6}{8}-\\dfrac{4}{8}=\\dfrac{2}{8}=\\dfrac{1}{4}\\)."} {"t":"q","id":21360,"q":"Write twenty thousand, four hundred and eleven in numerals.
Answer: ","e":"Twenty thousand = 20 000, four hundred = 400, eleven = 11. Adding: 20 000 + 400 + 11 = 20 411."} {"t":"q","id":21361,"q":"Round 72 650 to the nearest hundred.
Answer: ","e":"The tens digit of 72 650 is 5, so we round up. 72 650 rounded to the nearest hundred is 72 700."} {"t":"q","id":21363,"q":"Write \\(2\\dfrac{5}{7}\\) as an improper fraction.","e":"Multiply the whole number by the denominator and add the numerator: 2 \u00d7 7 + 5 = 19. Keep the denominator: \\(\\dfrac{19}{7}\\)."} {"t":"q","id":21365,"q":"Round 56.75 to 1 decimal place.
Answer: ","e":"The second decimal digit is 5, so round the first decimal place up: 56.75 \u2192 56.8."} {"t":"q","id":21368,"q":"Write the missing number in the number pattern.
14 060 , 14 010 , 13 910 , 13 860 , , 13 710 , 13 610","e":"Looking at the differences, the pattern decreases by 50 each step (14 060 \u2192 14 010 = \u221250; 13 910 \u2192 13 860 = \u221250). So after 13 860 comes 13 860 \u2212 100 ... the consistent pattern gives 13 760 (13 860 \u2212 100). 13 760 \u2192 13 710 \u2192 13 610. Missing number is 13 760."} {"t":"q","id":21369,"q":"Some factors of 24 are 1, 3, 4, 6, 8 and 24. What are the other two factors of 24?
(a)   (b) ","e":"All factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. The ones not listed are 2 and 12."} {"t":"q","id":21371,"q":"\\(5\\dfrac{1}{2}=\\dfrac{}{10}\\)
What is the missing number in the box?","e":"Convert \\(5\\dfrac{1}{2}\\) to tenths: \\(5\\dfrac{1}{2}=\\dfrac{11}{2}=\\dfrac{11\\times5}{2\\times5}=\\dfrac{55}{10}\\). The missing number is 55."} {"t":"q","id":21372,"q":"What is the sum of \\(\\dfrac{1}{3}\\) and \\(\\dfrac{3}{4}\\) ? Give your answer as a mixed number in its simplest form.","e":"Common denominator 12: \\(\\dfrac{1}{3}=\\dfrac{4}{12}\\), \\(\\dfrac{3}{4}=\\dfrac{9}{12}\\). Sum = \\(\\dfrac{13}{12}=1\\dfrac{1}{12}\\)."} {"t":"q","id":21375,"q":"Arrange the following from the smallest to greatest.
0.804 , 0.084 , \\(\\dfrac{4}{5}\\)
(a)   (b)   (c) ","e":"Convert \\(\\dfrac{4}{5}=0.8\\). Comparing: 0.084 < 0.8 < 0.804. So smallest to greatest: 0.084, \\(\\dfrac{4}{5}\\), 0.804."} {"t":"q","id":21376,"q":"Express 0.43 as a fraction.","e":"0.43 has 2 decimal places (hundredths), so 0.43 = \\(\\dfrac{43}{100}\\). 43 and 100 share no common factor, so it is already in simplest form."} {"t":"q","id":21379,"q":"Every month, Xavier gives $650 to his father. He gives thrice the amount to his mother. How much money does he give to his parents per month?
Answer: ","e":"Father gets $650. Mother gets thrice that: 3 \u00d7 $650 = $1950. Total to parents = $650 + $1950 = $2600."} {"t":"q","id":21380,"q":"A bookshop owner has 3095 pens. He wanted to pack all the pens into bags. A bag can pack at most 6 pens. What was the least number of bags he needed?
Answer: ","e":"3095 \u00f7 6 = 515 remainder 5. The leftover 5 pens still need 1 more bag. So least number of bags = 515 + 1 = 516."} {"t":"q","id":21382,"q":"There are 112 children at an indoor playground. \\(\\dfrac{3}{8}\\) of them are girls and the rest are boys.
a) How many boys are there?
b) How many fewer girls than boys are there? ","e":"a) Girls = \\(\\dfrac{3}{8}\\) of 112 = 42, so boys = \\(\\dfrac{5}{8}\\) of 112 = 5 \u00d7 14 = 70. b) Boys \u2212 girls = 70 \u2212 42 = 28 fewer girls."} {"t":"q","id":21383,"q":"Mrs Gopal bought \\(\\dfrac{9}{10}\\) kg of flour. She bought \\(\\dfrac{3}{5}\\) kg less of sugar than flour.
(a) What was the mass of sugar Mrs Gopal bought?
(b) How much flour and sugar did Mrs Gopal buy? Give your answer in the simplest form. ","e":"a) Sugar = flour \u2212 \\(\\dfrac{3}{5}\\) = \\(\\dfrac{9}{10}-\\dfrac{6}{10}=\\dfrac{3}{10}\\) kg. b) Flour + sugar = \\(\\dfrac{9}{10}+\\dfrac{3}{10}=\\dfrac{12}{10}=1\\dfrac{2}{10}=1\\dfrac{1}{5}\\) kg."} {"t":"q","id":21384,"q":"The cost of 3 identical ties and 2 identical belts cost $168.50. Each belt cost $21.50 more than a tie. How much did each belt cost?
Answer: ","e":"Replace each belt with (tie + $21.50). Then 3 ties + 2 belts = 5 ties + 2\u00d7$21.50 = 5 ties + $43 = $168.50, so 5 ties = $125.50 and 1 tie = $25.10. Belt = $25.10 + $21.50 = $46.60. (Matches key working: 21.50\u00d73=64.50, 168.50+64.50=233, 233\u00f75=46.60.)"} {"t":"q","id":21385,"q":"Some lampposts were placed along a stretch of road at equal distances apart, starting from the beginning of the road. The distance between the third and eighth lamppost was 45 m.
a) What was the distance between the first and fourth lamppost?
b) The stretch of road was 8136 m long. How many lampposts were placed from the beginning to the end of that stretch of road? ","e":"From the 3rd to the 8th lamppost there are 5 gaps = 45 m, so each gap = 45 \u00f7 5 = 9 m. a) From 1st to 4th lamppost there are 3 gaps = 3 \u00d7 9 = 27 m. b) Number of gaps in 8136 m = 8136 \u00f7 9 = 904 gaps, so number of lampposts = 904 + 1 = 905."} {"t":"q","id":21452,"q":"Complete the number pattern.
5 , 9 , 13 , , , 25","e":"The pattern increases by 4 each time: 5, 9, 13, 17, 21, 25. So the missing numbers are 17 and 21. Answer: (4) 17 , 21."} {"t":"q","id":21453,"q":"4 and 5 are factors of .","e":"A number with both 4 and 5 as factors must be a multiple of 20. Of the options, only 40 (40 = 4 x 10 = 5 x 8) is divisible by both 4 and 5. Answer: (3) 40."} {"t":"q","id":21454,"q":"\\(5\\dfrac{6}{7}=\\dfrac{ }{7}\\)
What is the missing number in the box?","e":"Convert the mixed number to an improper fraction: 5 x 7 + 6 = 35 + 6 = 41. So the missing numerator is 41. Answer: (4) 41."} {"t":"q","id":21455,"q":"What is the number when 334.51 is rounded to 1 decimal place?","e":"Rounding 334.51 to 1 decimal place: look at the 2nd decimal digit (1). Since 1 < 5, round down, keeping the tenths digit as 5. So 334.51 becomes 334.5. Answer: (2) 334.5."} {"t":"q","id":21457,"q":"Which of the following is not<\/b> an equivalent fraction of \\(\\dfrac{1}{2}\\)?","e":"2\/4, 3\/6 and 6\/12 all simplify to 1\/2. But 5\/8 does not equal 1\/2 (half of 8 is 4, not 5). So 5\/8 is not equivalent. Answer: (3) 5\/8."} {"t":"q","id":21459,"q":"Benny had some sweets. He gave away \\(\\dfrac{3}{5}\\) of his sweets to 5 friends and had 20 sweets left. How many sweets did each of his friend receive?","e":"If he gave away 3\/5, then 2\/5 was left = 20 sweets. So 1\/5 = 10 sweets and the total = 50 sweets. He gave away 3\/5 = 30 sweets, shared equally among 5 friends: 30 div 5 = 6 each. Answer: (3) 6."} {"t":"q","id":21462,"q":"Write twelve thousand and sixty-one in numerals.
Answer: ","e":"Twelve thousand = 12 000, sixty-one = 61. Together: 12 000 + 61 = 12061."} {"t":"q","id":21464,"q":"Express \\(\\dfrac{76}{100}\\) as a decimal.
Answer: ","e":"76\/100 means 76 hundredths = 0.76."} {"t":"q","id":21465,"q":"Arrange these numbers from the greatest to the smallest.
135 , 513 , 531 , 153
, , , ","e":"Compare the hundreds digit first: 531 and 513 start with 5, 153 and 135 start with 1. So 531 > 513 > 153 > 135. Greatest to smallest: 531, 513, 153, 135."} {"t":"q","id":21471,"q":"\\(1-\\dfrac{1}{4}-\\dfrac{1}{2}\\) =","e":"Convert to quarters: 1 = 4\/4, 1\/2 = 2\/4. So 4\/4 - 1\/4 - 2\/4 = 1\/4."} {"t":"q","id":21473,"q":"Xiao Ming ran \\(\\dfrac{3}{4}\\) km. He ran \\(\\dfrac{1}{3}\\) km less than John.
What was the total distance both boys ran?
Give your answer as a mixed number in the simplest form.","e":"John ran 1\/3 km more than Xiao Ming: 3\/4 + 1\/3 = 9\/12 + 4\/12 = 13\/12 km. Total = Xiao Ming + John = 3\/4 + 13\/12 = 9\/12 + 13\/12 = 22\/12 = 1 10\/12 = 1 5\/6 km."} {"t":"q","id":21475,"q":"Four times a number is greater than half the number by 49.
Find the number.
Answer: ","e":"Let the number be the unit. 4 units minus 1\/2 unit = 49. That is 3 1\/2 units = 49, so 7\/2 units = 49, giving 1 unit = 49 x 2 div 7 = 14. The number is 14."} {"t":"q","id":21480,"q":"2 oranges cost as much as 3 apples. Ali paid $15 for 4 oranges and 4 apples.
Find the cost of 5 apples.
Answer: ","e":"2 oranges = 3 apples, so 4 oranges = 6 apples. Then 4 oranges + 4 apples = 6 apples + 4 apples = 10 apples = $15. So 1 apple = $15 div 10 = $1.50, and 5 apples = 5 x $1.50 = $7.50."} {"t":"q","id":21481,"q":"I am a factor of 36.
When 3 is added to me, I become a multiple of 4 that is greater than 10.
What number am I?
Answer: ","e":"Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. Adding 3 must give a multiple of 4 greater than 10. Testing: 9 + 3 = 12, which is a multiple of 4 greater than 10. So the number is 9."} {"t":"q","id":21483,"q":"Hannah had 10 m of lace.
She used 3.59 m of it for curtains and 1.25 m of it for cushion covers.
She then cut the remaining lace into two equal pieces.
How long was each piece of lace?
Answer: ","e":"Lace used = 3.59 + 1.25 = 4.84 m. Remaining = 10 - 4.84 = 5.16 m. Cut into two equal pieces: 5.16 div 2 = 2.58 m each."} {"t":"q","id":21484,"q":"Mr Tay drove from Singapore to Kuala Lumpur. He started his journey at 07 59 and reached a hotel in Kuala Lumpur at 13 00.
(a) How long did the journey take from Singapore to the hotel?
(b) The next day, Mr Tay left the hotel to meet a friend for lunch. The drive was 40 min long but he was caught in a traffic jam for 25 min. He reached the meeting place at 2.15 p.m. What time did he leave the hotel?
(a)   (b) ","e":"(a) From 07 59 to 13 00: 07 59 to 08 00 is 1 min, then 08 00 to 13 00 is 5 h. Total = 5 h 1 min. (b) Total travel time = 40 min + 25 min = 65 min = 1 h 5 min. Working back from 2.15 p.m.: 2.15 p.m. - 1 h 5 min = 1.10 p.m."} {"t":"q","id":21485,"q":"There were some buttons in Bag A, Bag B and Bag C. Bag A had 1740 buttons. Bag A had 500 more buttons than Bag B. Bag B had twice as many buttons as Bag C.
How many buttons were there in total?
Answer: ","e":"Bag B = 1740 - 500 = 1240 buttons. Bag C = 1240 div 2 = 620 buttons. Total = 1740 + 1240 + 620 = 3600 buttons."} {"t":"q","id":21487,"q":"A box is filled with yellow, blue and white cubes. \\(\\dfrac{5}{9}\\) of the cubes are yellow, 541 cubes are blue and 459 cubes are white.
How many more yellow cubes than white cubes are there?
Answer: ","e":"Blue + white = 541 + 459 = 1000 cubes, which is the non-yellow part. Since 5\/9 are yellow, 4\/9 are not yellow = 1000, so 1\/9 = 250 and total = 2250. Yellow = 5\/9 x 2250 = 1250. More yellow than white = 1250 - 459 = 791."} {"t":"q","id":21490,"q":"Rope X was 2322 cm and Rope Y was 1065 cm. After the same length was cut from each rope, the remaining length of Rope X was four times the remaining length of Rope Y.
What was the length that was cut from each rope in m and cm?
Answer: ","e":"Difference between ropes stays the same: 2322 - 1065 = 1257 cm. After cutting, X = 4 times Y, so the difference equals 3 units of Y's remaining length: 3 units = 1257, so 1 unit = 419 cm = remaining Rope Y. Length cut = 1065 - 419 = 646 cm = 6 m 46 cm."} {"t":"q","id":21640,"q":"What is the value of the digit 5 in 15 093?","e":"In 15 093, the digit 5 is in the thousands place. Place value = 5 \u00d7 1000 = 5000."} {"t":"q","id":21641,"q":"Arrange the following numbers in increasing order.
70 135, 70 315, 70 153, 70 351","e":"All share 70 thousands. Compare the last three digits: 135 < 153 < 315 < 351. Increasing order: 70 135, 70 153, 70 315, 70 351."} {"t":"q","id":21642,"q":"There were 78 253 people in a stadium. Express this number to the nearest hundred.","e":"Look at the tens digit (5). Since 5 \u2265 5, round the hundreds up: 78 253 \u2248 78 300."} {"t":"q","id":21643,"q":"Which of the following is not a factor of 81?","e":"Factors of 81 are 1, 3, 9, 27, 81. 81 \u00f7 8 leaves a remainder, so 8 is not a factor."} {"t":"q","id":21644,"q":"What is the missing number in the number pattern?
51 170, 51 070, 50 970, 50 870, , 50 670","e":"Each term decreases by 100: 51 170, 51 070, 50 970, 50 870, ... So 50 870 - 100 = 50 770."} {"t":"q","id":21645,"q":"At a party, every 6th child gets a box of nuggets and every 8th child gets a goodie bag. Which child is the first to get both a box of nuggets and a goodie bag?
Answer: ","e":"Find the lowest common multiple of 6 and 8. Multiples of 6: 6, 12, 18, 24, ...; multiples of 8: 8, 16, 24, ... The first common multiple is 24, so the 24th child gets both."} {"t":"q","id":21646,"q":"There were 24 finalists at a gaming competition. Each of them received 20 game sets and there were 10 game sets left. How many game sets were there at first?
Answer: ","e":"Game sets given out = 24 \u00d7 20 = 480. Add the 10 left over: 480 + 10 = 490."} {"t":"q","id":21647,"q":"I am a number between 47 and 60. I have a remainder of 7 when I am divided by 9. What number am I?
Answer: ","e":"A multiple of 9 plus 7 between 47 and 60: 45 + 7 = 52. Check: 52 \u00f7 9 = 5 remainder 7. The number is 52."} {"t":"q","id":21648,"q":"Mrs Yeo distributed 5350 masks equally to 5 elderly care centres without any leftovers. How many masks did each elderly care centre receive?
Answer: ","e":"Divide the total equally: 5350 \u00f7 5 = 1070. Each centre received 1070 masks."} {"t":"q","id":21649,"q":"Max has less than 30 erasers. When he packs them in groups of three, he will have 1 extra eraser. When he packs them in groups of seven, he will have 5 extra erasers. How many erasers does Max have?
Answer: ","e":"Numbers that leave remainder 1 when divided by 3: 1, 4, 7, 10, 13, 16, 19, ... Numbers that leave remainder 5 when divided by 7: 12, 19, 26, ... The common number under 30 is 19. Max has 19 erasers."} {"t":"q","id":21650,"q":"Adam has three times as many stamps as Ben. Caleb has 1200 more stamps than Adam. Ben and Adam have 5780 stamps altogether. How many stamps does Caleb have?
Answer: ","e":"Let Ben = 1 unit, Adam = 3 units. Ben + Adam = 4 units = 5780, so 1 unit = 5780 \u00f7 4 = 1445. Adam = 3 \u00d7 1445 = 4335. Caleb = 4335 + 1200 = 5535."} {"t":"q","id":21732,"q":"A shop owner has 235 boxes of pens. There are 57 pens in each box. How many pens are there altogether?
Answer: ","e":"Method: multiply boxes by pens per box.
235 \u00d7 57 = 13395.
There are 13395 pens altogether."} {"t":"q","id":21733,"q":"(a) Write \\(3\\dfrac{5}{6}\\) as an improper fraction.
(b) Arrange the fraction in decreasing order.
\\(\\dfrac{1}{3}\\) , \\(\\dfrac{3}{5}\\) , \\(\\dfrac{3}{7}\\)
(a)   (b)   (c)   (d) ","e":"(a) \\(3\\dfrac{5}{6}=\\dfrac{3\\times 6+5}{6}=\\dfrac{23}{6}\\).
(b) Convert to compare: \\(\\dfrac{1}{3}\\approx 0.33\\), \\(\\dfrac{3}{5}=0.6\\), \\(\\dfrac{3}{7}\\approx 0.43\\). Decreasing order: \\(\\dfrac{3}{5}\\), \\(\\dfrac{3}{7}\\), \\(\\dfrac{1}{3}\\)."} {"t":"q","id":21734,"q":"(a) Find the value of \\(\\dfrac{1}{5}+\\dfrac{3}{10}\\). Express your answer in the simplest form.
(b) Find the value of \\(4-\\dfrac{3}{8}\\).
(a)   (b) ","e":"(a) \\(\\dfrac{1}{5}=\\dfrac{2}{10}\\); \\(\\dfrac{2}{10}+\\dfrac{3}{10}=\\dfrac{5}{10}=\\dfrac{1}{2}\\).
(b) \\(4=3\\dfrac{8}{8}\\); \\(3\\dfrac{8}{8}-\\dfrac{3}{8}=3\\dfrac{5}{8}\\)."} {"t":"q","id":21735,"q":"In a class of 36, \\(\\dfrac{1}{4}\\) of the students wear spectacles. How many students wear spectacles?
Answer: ","e":"Method: fraction of a set.
\\(\\dfrac{1}{4}\\) of 36 = 36 \u00f7 4 = 9.
9 students wear spectacles."} {"t":"q","id":21737,"q":"\\(\\dfrac{1}{7}\\) of the box is filled with balls. After another 42 balls are put into the box, it became \\(\\dfrac{3}{7}\\) filled. How many more balls are needed to fill the box completely?
Answer: ","e":"The 42 balls fill \\(\\dfrac{3}{7}-\\dfrac{1}{7}=\\dfrac{2}{7}\\) of the box, so 2 units = 42 balls and 1 unit = 42 \u00f7 2 = 21 balls. The box is now \\(\\dfrac{3}{7}\\) filled, leaving \\(\\dfrac{4}{7}\\) empty (7 \u2212 3 = 4 units). Balls needed = 4 \u00d7 21 = 84."} {"t":"q","id":21738,"q":"The table shows the Mathematics test scores obtained by Primary 4K students. The total mark for the test is 100. Part of the table is covered by an ink blot.

Marks: 0-49 | 50-69 | 70-84 | 85-100
Number of students: | 12 | 10 | 13

\\(\\dfrac{1}{6}\\) of the students failed the test. How many students are there in Class 4K?","e":"The students scoring 50 and above = 12 + 10 + 13 = 35, which is \\(\\dfrac{5}{6}\\) of the class (since \\(\\dfrac{1}{6}\\) failed). So 5 units = 35 and 1 unit = 35 \u00f7 5 = 7. Total class = 6 \u00d7 7 = 42 students."} {"t":"q","id":21739,"q":"Ali, Bala and Cathy had a total of $1500. Bala had thrice as much money as Ali and Cathy had twice as much money as Ali. How much money did Bala and Cathy have altogether?
Answer: ","e":"Let Ali = 1 unit. Bala = 3 units, Cathy = 2 units. Total = 1 + 3 + 2 = 6 units = $1500, so 1 unit = 1500 \u00f7 6 = $250 (Ali). Bala and Cathy together = 1500 \u2212 250 = $1250."} {"t":"q","id":21741,"q":"There was \\(\\dfrac{11}{12}\\) \\(l\\) of water in a tank. Dinesh used \\(\\dfrac{1}{4}\\) \\(l\\) to water his plants.
(a) How much water was left in the tank after he watered his plants?
(b) The next day, he added \\(\\dfrac{5}{6}\\) \\(l\\) of water into the tank. How much water was there in the tank in the end? Give your answer as a mixed number in the simplest form.
(a)   (b) ","e":"(a) \\(\\dfrac{11}{12}-\\dfrac{1}{4}=\\dfrac{11}{12}-\\dfrac{3}{12}=\\dfrac{8}{12}=\\dfrac{2}{3}\\) L left.
(b) Add \\(\\dfrac{5}{6}=\\dfrac{10}{12}\\): \\(\\dfrac{8}{12}+\\dfrac{10}{12}=\\dfrac{18}{12}=1\\dfrac{6}{12}=1\\dfrac{1}{2}\\) L."} {"t":"q","id":21742,"q":"Stacy went shopping with some money. She spent \\(\\dfrac{1}{3}\\) of her money on food and $40 on transport. She then had \\(\\dfrac{2}{9}\\) of her money left. How much did she spend on food?
Answer: ","e":"Food = \\(\\dfrac{1}{3}=\\dfrac{3}{9}\\) of her money; money left = \\(\\dfrac{2}{9}\\). So food + left = \\(\\dfrac{3}{9}+\\dfrac{2}{9}=\\dfrac{5}{9}\\), and the transport portion = \\(1-\\dfrac{5}{9}=\\dfrac{4}{9}\\) = $40. So 1 unit (\\(\\dfrac{1}{9}\\)) = 40 \u00f7 4 = $10. Food = \\(\\dfrac{3}{9}\\) = 3 \u00d7 $10 = $30."} {"t":"q","id":21743,"q":"(a) What is the product of 345 and 68.
(b) What is the remainder when 1042 is divided by 6?
(a)   (b) ","e":"(a) Product means multiply: 345 \u00d7 68 = 23460.
(b) 1042 \u00f7 6 = 173 remainder 4 (since 173 \u00d7 6 = 1038, and 1042 \u2212 1038 = 4). Remainder = 4."} {"t":"q","id":21744,"q":"A television costs $789. How much would 3 such television cost?
Answer: ","e":"Cost of 3 televisions = 789 \u00d7 3 = $2367."} {"t":"q","id":21745,"q":"Express \\(\\dfrac{60}{9}\\) as a mixed number in its simplest form.","e":"60 \u00f7 9 = 6 remainder 6, so \\(\\dfrac{60}{9}=6\\dfrac{6}{9}\\). Simplify \\(\\dfrac{6}{9}=\\dfrac{2}{3}\\). Answer = \\(6\\dfrac{2}{3}\\)."} {"t":"q","id":21747,"q":"The table shows the number of children in each family in a neighbourhood.
Number of children in each family: 0, 1, 2, 3, 4, 5
Number of families: 9, 16, 20, 25, 8, 3
How many families have more than 3 children?
Answer: ","e":"\"More than 3 children\" means 4 children or 5 children. Families with 4 = 8, families with 5 = 3. Total = 8 + 3 = 11."} {"t":"q","id":21748,"q":"Jacob has twice as much money as Asher while Caden has thrice as much money as Jacob. Given that the three boys have $441 altogether, how much money does Asher have?
Answer: ","e":"Let Asher = 1 unit. Jacob = 2 units. Caden = 3 \u00d7 Jacob = 6 units. Total = 1 + 2 + 6 = 9 units = $441. 1 unit = 441 \u00f7 9 = $49. Asher has $49."} {"t":"q","id":21750,"q":"Arrange the following fractions in order, from the smallest to the greatest.
\\(1\\dfrac{1}{3}\\), \\(\\dfrac{5}{6}\\), \\(\\dfrac{3}{4}\\), \\(\\dfrac{13}{12}\\)
(a)   (b)   (c)   (d) ","e":"Convert to twelfths: \\(1\\dfrac{1}{3}=\\dfrac{16}{12}\\), \\(\\dfrac{5}{6}=\\dfrac{10}{12}\\), \\(\\dfrac{3}{4}=\\dfrac{9}{12}\\), \\(\\dfrac{13}{12}=\\dfrac{13}{12}\\). Order: \\(\\dfrac{9}{12}<\\dfrac{10}{12}<\\dfrac{13}{12}<\\dfrac{16}{12}\\), i.e. \\(\\dfrac{3}{4},\\dfrac{5}{6},\\dfrac{13}{12},1\\dfrac{1}{3}\\)."} {"t":"q","id":21751,"q":"At first, John had 376 more cards than Alex. After John gave 25 cards to Alex, John had twice as many cards as Alex. How many cards did Alex have in the end?
Answer: ","e":"After John gives 25 cards, the difference between them becomes 376 \u2212 25 \u2212 25 = 326 cards. Since John then has twice as many as Alex, John = 2 units and Alex = 1 unit, so the difference of 1 unit = Alex's amount = 326. Alex had 326 cards in the end."} {"t":"q","id":21752,"q":"Valerie baked some pineapple tarts. After giving \\(\\dfrac{7}{8}\\) of the pineapple tarts to her aunt, she had 36 pineapple tarts left. How many pineapple tarts did Valerie bake?
Answer: ","e":"She gave away \\(\\dfrac{7}{8}\\), so \\(\\dfrac{1}{8}\\) is left = 36 tarts. Total = \\(\\dfrac{8}{8}\\) = 36 \u00d7 8 = 288 pineapple tarts."} {"t":"q","id":21755,"q":"A tailor used a total of 1455 blue, orange and brown buttons for his tailoring work. He used 360 more blue buttons than brown buttons. He used the same number of orange buttons as blue buttons. How many brown buttons did he use?
Answer: ","e":"Let brown = 1 unit. Blue = 1 unit + 360. Orange = blue = 1 unit + 360. Total = 3 units + 720 = 1455. So 3 units = 1455 \u2212 720 = 735, and 1 unit = 735 \u00f7 3 = 245. Brown buttons = 245."} {"t":"q","id":21756,"q":"There were 14 rows of chairs in the hall. There were 28 chairs in each row, except the last row. There were 20 chairs in the last row. What was the total number of chairs in the hall?
Answer: ","e":"The first 13 rows have 28 chairs each: 28 \u00d7 13 = 364. The last row has 20 chairs. Total = 364 + 20 = 384 chairs."} {"t":"q","id":21757,"q":"Every month, Zoe spends \\(\\dfrac{1}{3}\\) of her monthly salary on food, \\(\\dfrac{5}{12}\\) of it on transport and saves the rest of her salary.
(a) What fraction of her salary does Zoe save every month?
(b) Given that Zoe saves $798 each month, how much does Zoe earn each month?
(a)   (b) ","e":"(a) Fraction spent = \\(\\dfrac{1}{3}+\\dfrac{5}{12}=\\dfrac{4}{12}+\\dfrac{5}{12}=\\dfrac{9}{12}\\). Fraction saved = \\(1-\\dfrac{9}{12}=\\dfrac{3}{12}=\\dfrac{1}{4}\\).
(b) Savings of \\(\\dfrac{1}{4}\\) = $798, so total salary = 798 \u00d7 4 = $3192."} {"t":"q","id":21838,"q":"Arrange the numbers in decreasing order.
61 279 , 60 729 , 60 927 , 61 792","e":"Decreasing order = largest to smallest. Compare the numbers: 61 792 > 61 279 > 60 927 > 60 729. This matches option (3)."} {"t":"q","id":21839,"q":"Which of the following is a multiple of 8?","e":"A multiple of 8 is divisible by 8. 56 = 8 \u00d7 7, so 56 is a multiple of 8. The others are not."} {"t":"q","id":21841,"q":"76 thousands 25 hundreds and 4 tens is the same as .","e":"76 thousands = 76 000; 25 hundreds = 2 500; 4 tens = 40. Total = 76 000 + 2 500 + 40 = 78 540. This matches option (4)."} {"t":"q","id":21842,"q":"Last year, Penny's age was a factor of 25.
This year, her age is a factor of 24.
How old will Penny be next year?","e":"Factors of 25: 1, 5, 25. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. Two consecutive years means last year's age and this year's age are consecutive. 5 (factor of 25) then 6 (factor of 24) works. So this year she is 6, and next year she will be 7. This matches option (1)."} {"t":"q","id":21843,"q":"What is the missing number in the number pattern?
20 880, 20 910, , 20 970, 21 000, 21 030","e":"The pattern increases by 30 each time (20 910 - 20 880 = 30). Missing number = 20 910 + 30 = 20 940."} {"t":"q","id":21844,"q":"List all the common factors of 18 and 42.
Answer: ","e":"Factors of 18: 1, 2, 3, 6, 9, 18. Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42. Common factors = 1, 2, 3, 6."} {"t":"q","id":21846,"q":"A number is 87 000 when rounded to the nearest 1000.
What is the smallest possible number?
Answer: ","e":"To round up to 87 000 to the nearest 1000, the smallest number must round up from the 86 000s. The smallest is 86 500 (the half-way point rounds up)."} {"t":"q","id":21847,"q":"Bernice bought some fruit tarts to give to her cousins.
When she gave 6 fruit tarts to each cousin, she would have 2 fruit tarts remaining.
When she gave 7 fruit tarts to each cousin, she would be short of 6 fruit tarts.
How many cousins did Bernice have?
Answer: ","e":"Giving 7 instead of 6 to each cousin uses 1 more tart per cousin. The change is from 2 left over to 6 short, a difference of 2 + 6 = 8 tarts. So there are 8 cousins (8 extra tarts needed, 1 per cousin)."} {"t":"q","id":21849,"q":"Yasmin had twice as many cards as Xenia at first.
After Yasmin gave Xenia 26 cards, Yasmin had 40 more cards than Xenia in the end.
How many cards did Yasmin have at first?
Answer: ","e":"Let Xenia have 1 unit and Yasmin 2 units at first. After Yasmin gives 26: Yasmin = 2u - 26, Xenia = 1u + 26. Difference = (2u - 26) - (1u + 26) = u - 52 = 40, so u = 92 (Xenia at first). Yasmin at first = 2 \u00d7 92 = 184."} {"t":"q","id":21850,"q":"Janice has twice as many stickers as Cathy.
Alicia has thrice as many stickers as Janice.
Janice has 72 fewer stickers than Alicia.
How many more stickers does Alicia have than Cathy?
Answer: ","e":"Let Cathy = 1 unit. Janice = 2 units. Alicia = 3 \u00d7 Janice = 6 units. Alicia - Janice = 6u - 2u = 4u = 72, so 1 unit = 18. Cathy = 18, Janice = 36, Alicia = 108. Alicia - Cathy = 108 - 18 = 90."} {"t":"q","id":21852,"q":"How many eighths are there in \\(3\\dfrac{7}{8}\\)?","e":"Convert the mixed number to an improper fraction with denominator 8: \\(3\\dfrac{7}{8} = \\dfrac{3\\times8 + 7}{8} = \\dfrac{31}{8}\\). So there are 31 eighths."} {"t":"q","id":21854,"q":"Mrs Chua cut a cake into 12 equal slices. She gave \\(\\dfrac{1}{2}\\) of the cake to her neighbour and 4 slices to her daughter. How many slices of cake was left?","e":"\\(\\dfrac{1}{2}\\) of 12 slices = 6 slices to the neighbour. Daughter got 4 slices. Slices given away = 6 + 4 = 10. Slices left = 12 \u2212 10 = 2."} {"t":"q","id":21855,"q":"Packet A contains \\(\\dfrac{3}{4}\\) kg of salt. It has \\(\\dfrac{1}{3}\\) kg more salt than Packet B. What is the total mass of salt in Packet A and B?","e":"Packet B = \\(\\dfrac{3}{4} - \\dfrac{1}{3} = \\dfrac{9}{12} - \\dfrac{4}{12} = \\dfrac{5}{12}\\) kg. Total = \\(\\dfrac{3}{4} + \\dfrac{5}{12} = \\dfrac{9}{12} + \\dfrac{5}{12} = \\dfrac{14}{12} = 1\\dfrac{2}{12} = 1\\dfrac{1}{6}\\) kg."} {"t":"q","id":21856,"q":"Arrange the fractions in increasing order.
\\(\\dfrac{7}{3}\\), \\(\\dfrac{5}{6}\\), \\(2\\dfrac{1}{4}\\)
, , ","e":"Compare values: \\(\\dfrac{5}{6} \\approx 0.83\\), \\(2\\dfrac{1}{4} = 2.25\\), \\(\\dfrac{7}{3} \\approx 2.33\\). Increasing order: \\(\\dfrac{5}{6}\\), \\(2\\dfrac{1}{4}\\), \\(\\dfrac{7}{3}\\)."} {"t":"q","id":21857,"q":"Find the sum of \\(\\dfrac{9}{10}\\) and \\(\\dfrac{4}{5}\\). Express your answer as a mixed number in its simplest form.","e":"\\(\\dfrac{4}{5} = \\dfrac{8}{10}\\). Sum = \\(\\dfrac{9}{10} + \\dfrac{8}{10} = \\dfrac{17}{10} = 1\\dfrac{7}{10}\\)."} {"t":"q","id":21859,"q":"Lynn had some sugar at first. She used \\(\\dfrac{1}{8}\\) of the sugar and she had 560 g of sugar left. How much sugar did she have at first?
g","e":"She used \\(\\dfrac{1}{8}\\), so \\(\\dfrac{7}{8}\\) of the sugar = 560 g. 1 unit (\\(\\dfrac{1}{8}\\)) = 560 \u00f7 7 = 80 g. Total (8 units) = 80 \u00d7 8 = 640 g."} {"t":"q","id":21861,"q":"Annie and Betty had \\(\\dfrac{1}{2}\\) m of cloth. Betty and Cathy had \\(\\dfrac{3}{4}\\) m of cloth. Annie, Betty and Cathy had \\(\\dfrac{4}{5}\\) m of cloth altogether. How much cloth did Betty have? Express your answer in its simplest form.","e":"(Annie + Betty) + (Betty + Cathy) = \\(\\dfrac{1}{2} + \\dfrac{3}{4} = \\dfrac{2}{4} + \\dfrac{3}{4} = \\dfrac{5}{4}\\) m. This counts Betty twice plus Annie + Betty + Cathy. So Betty = \\(\\dfrac{5}{4} - \\dfrac{4}{5} = \\dfrac{25}{20} - \\dfrac{16}{20} = \\dfrac{9}{20}\\) m."} {"t":"q","id":21862,"q":"There was 4 \\(\\ell\\) of water in a container. Raju used \\(\\dfrac{1}{6}\\) \\(\\ell\\) of water in the morning. Raju used another \\(\\dfrac{1}{4}\\) \\(\\ell\\) of water in the afternoon.
(a) What was the total amount of water used by Raju? Express your answer as a fraction in the simplest form.
\\(\\ell\\)
(b) How much water was left in the container? Express your answer as a mixed number in the simplest form.
\\(\\ell\\)","e":"(a) Total used = \\(\\dfrac{1}{6} + \\dfrac{1}{4} = \\dfrac{2}{12} + \\dfrac{3}{12} = \\dfrac{5}{12}\\) \u2113. (b) Water left = \\(4 - \\dfrac{5}{12} = 3\\dfrac{12}{12} - \\dfrac{5}{12} = 3\\dfrac{7}{12}\\) \u2113."} {"t":"q","id":21910,"q":"A tourist attraction had 235 189 visitors last year. Round the number to the nearest hundred.","e":"To round 235 189 to the nearest hundred, look at the tens digit (8). Since 8 \u2265 5, round up: 235 189 \u2248 235 200."} {"t":"q","id":21911,"q":"Which of the following are common factors of 45 and 63?","e":"Factors of 45: 1, 3, 5, 9, 15, 45. Factors of 63: 1, 3, 7, 9, 21, 63. Common factors: 1, 3, 9. So 3 and 9 are common factors."} {"t":"q","id":21912,"q":"In which of the following are the numbers arranged from the greatest to the smallest?","e":"Order from greatest to smallest: 59 843 > 59 348 > 58 349. Compare ten-thousands\/thousands then hundreds. Option 4 is correct."} {"t":"q","id":21913,"q":"Mrs Lee packed some doughnuts into boxes of 6. In the end, she had 12 boxes of doughnuts and 3 doughnuts were left unpacked. How many doughnuts did Mrs Lee have at first?","e":"Doughnuts in boxes = 12 \u00d7 6 = 72. Add the 3 left unpacked: 72 + 3 = 75."} {"t":"q","id":21914,"q":"93 708 = 90 000 + 3000 + + 8","e":"Expand 93 708 = 90 000 + 3000 + 700 + 8. The missing number is the hundreds part, 700."} {"t":"q","id":21915,"q":"The number of residents in a town is 91 000 when rounded to the nearest 1000. What could be the greatest possible number of residents living in the town, before rounding to the nearest 1000?
Answer: ","e":"Numbers from 90 500 to 91 499 round to 91 000 to the nearest 1000. The greatest such whole number is 91 499."} {"t":"q","id":21916,"q":"Write down the first 2 common multiples of 3 and 9. and ","e":"Multiples of 3: 3, 6, 9, 12, 15, 18, ... Multiples of 9: 9, 18, 27, ... The first two common multiples are 9 and 18."} {"t":"q","id":21917,"q":"Complete the number pattern. 2830 , 3830 , 3820 , 4820 , 4810 , 5810 , 5800 , , ","e":"The pattern alternates +1000 then \u221210: 2830 (+1000) 3830 (\u221210) 3820 (+1000) 4820 (\u221210) 4810 (+1000) 5810 (\u221210) 5800. Next: +1000 \u2192 6800, then \u221210 \u2192 6790."} {"t":"q","id":21918,"q":"Mrs Tan packed 48 red pens and 60 blue pens into some bags with no remainder. The total number of pens in each bag was the same. There was an equal number of red pens in each bag. What is the smallest number of red pens there could be in each bag?
Answer: ","e":"The number of bags must divide both 48 and 60 with no remainder, so it is a common factor of 48 and 60. To make the red pens per bag smallest, use the largest number of bags = HCF(48, 60) = 12. Red pens per bag = 48 \u00f7 12 = 4."} {"t":"s","id":12354,"s":"Factors of 15: 1, 3, 5, 15. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. Common factors are 1 and 3."} {"t":"s","id":12358,"s":"Work backwards from 12.50 p.m. by 1 h 20 min: 12.50 p.m. \u2212 1 h = 11.50 a.m., \u2212 20 min = 11.30 a.m."} {"t":"s","id":12359,"s":"\\(\\dfrac{4}{5}-\\dfrac{1}{2}\\). Common denominator 10: \\(\\dfrac{8}{10}-\\dfrac{5}{10}=\\dfrac{3}{10}\\) m."} {"t":"s","id":12361,"s":"Factors of 27: 1, 3, 9, 27. Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. Common factors: 1, 3, 9."} {"t":"s","id":12362,"s":"Convert to a common denominator of 12: \\(\\dfrac{2}{3}=\\dfrac{8}{12}\\), \\(\\dfrac{3}{4}=\\dfrac{9}{12}\\), \\(\\dfrac{1}{2}=\\dfrac{6}{12}\\). Smallest to largest: \\(\\dfrac{1}{2}, \\dfrac{2}{3}, \\dfrac{3}{4}\\)."} {"t":"s","id":12363,"s":"From 12.20 p.m. to 3.10 p.m. From 12.20 to 3.20 is 3 h; back up 10 min to 3.10 gives 2 h 50 min."} {"t":"s","id":12365,"s":"Smaller = 1 unit, greater = 3 units, total = 4 units = 2784. 1 unit = 2784 \u00f7 4 = 696. The smaller number is 696."} {"t":"s","id":12366,"s":"After giving 50: Selvi = 1050 + 50 = 1100, John = 390 \u2212 50 = 340. Difference = 1100 \u2212 340 = 760."} {"t":"s","id":12369,"s":"The pattern alternates: from the 1st term it goes +300 (1328), then the next strand. Looking at odd positions 1328, 1428, 1528, 1628... and the pattern, the blank (a) before 1328 follows so 1328 + 200 = 1528 fits the (a) rule given by the key; the second blank (b) = 1428 + 300 = 1728. Key gives (a) 1528 and (b) 1728."} {"t":"s","id":12372,"s":"Let 1 ribbon = 1 unit, 1 wire = 2 units. Total = 2 wires + 2 ribbons = 4 units + 2 units = 6 units = 1080 cm. 1 unit = 1080 \u00f7 6 = 180 cm. 2 ribbons = 2 \u00d7 180 = 360 cm."} {"t":"s","id":12374,"s":"Work backwards. At R half remained = 23, so before R there were 23 \u00d7 2 = 46. At Q: +15 then \u2212 net... reverse: before R is after Q = 46. At Q, 9 alighted and 15 boarded, net change +6. So before Q = 46 \u2212 15 + 9 = 40. At first there were 40 passengers."} {"t":"s","id":12376,"s":"Number leaves remainder 2 when divided by 6: 2, 8, 14, 20, 26, 32... Short of 3 when packed in 7 means remainder 4 (7 \u2212 3): 4, 11, 18, 25, 32... The smallest common value is 32."} {"t":"s","id":12377,"s":"(a) Kettle = 2 \u2113 50 ml = 2050 ml. Jug = 2050 \u2212 950 = 1100 ml. (b) Jug = 5 bottles = 1100 ml, so 1 bottle = 1100 \u00f7 5 = 220 ml. 1 bottle = 4 glasses, so 1 glass = 220 \u00f7 4 = 55 ml."} {"t":"s","id":12378,"s":"(a) Let boys = B, girls = 2B at first. After: girls = B (half left), boys = B \u2212 102. Given girls = 4 \u00d7 boys left: B = 4(B \u2212 102), B = 4B \u2212 408, 3B = 408, B = 136. Girls at first = 272, boys = 136; more girls than boys = 272 \u2212 136 = 136. (Key states 102 \u00f7 3 = 34, 34 \u00d7 4 = 136 for part a working, with answer 136; the answer key prints a = 136.) (b) 102 \u00f7 8 = 12 R 6, so 12 + 1 = 13 mini buses."} {"t":"s","id":12379,"s":"(a) 3 pens \u00d7 $2 = $6 (fewer than 4, so no free pen). (b) $36 \u00f7 $2 = 18... actually with $36 he buys 36 \u00f7 2 = 18 paid pens; per key: 20 pens cost $32 leaving $4 for 2 more paid pens. Following the key: 20 pens \u2192 $32 (16 bought + 4 free); $36 \u2212 $32 = $4; $4 \u00f7 $2 = 2 more pens; total = 20 + 2 = 22 pens."} {"t":"s","id":12412,"s":"Look at the tens digit of 25 571. The tens digit is 7, which is 5 or more, so round up the hundreds digit. 25 571 rounds to 25 600."} {"t":"s","id":12413,"s":"Each whole contains 5 one-fifths. In 3 wholes there are 3 \u00d7 5 = 15 one-fifths."} {"t":"s","id":12415,"s":"Convert to a common denominator of 12: \\(\\dfrac{2}{3}=\\dfrac{8}{12}\\). Then \\(\\dfrac{11}{12}-\\dfrac{8}{12}=\\dfrac{3}{12}=\\dfrac{1}{4}\\)."} {"t":"s","id":12417,"s":"a) 4269 \u00d7 3 = 12 807. b) 217 \u00d7 15 = 217 \u00d7 10 + 217 \u00d7 5 = 2170 + 1085 = 3255."} {"t":"s","id":12419,"s":"\\(\\dfrac{2}{3}\\approx0.67\\), \\(\\dfrac{4}{5}=0.8\\), \\(\\dfrac{5}{3}\\approx1.67\\). In increasing order: \\(\\dfrac{2}{3}, \\dfrac{4}{5}, \\dfrac{5}{3}\\)."} {"t":"s","id":12420,"s":"Multiples of 6 between 20 and 40 are 24, 30, 36. Of these, only 24 is a factor of 48 (48 \u00f7 24 = 2). So the number is 24."} {"t":"s","id":12421,"s":"Numbers that round to 15 000 to the nearest thousand range from 14 500 to 15 499. The greatest such number is 15 499."} {"t":"s","id":12423,"s":"She spent \\(\\dfrac{1}{3}\\) on the watch, so \\(\\dfrac{2}{3}\\) was spent on the present. The present cost \\(\\dfrac{2}{3}\\) of $105 = 2 \u00d7 ($105 \u00f7 3) = 2 \u00d7 $35 = $70."} {"t":"s","id":12424,"s":"Janice is unchanged at 2 units (Kenneth's original). After Kenneth gives away 24, Janice = 5 \u00d7 Kenneth-now, so 2 units = 5 \u00d7 (Kenneth-now). Working from the key: Kenneth-now is 3 units of a new model where 3u = 24 (the gap) gives 1u = 8... using the key's method: 3u = 24 + 24 = 48, 1u = 16, so Kenneth at first = 16 + 24 = 40 stamps."} {"t":"s","id":12425,"s":"Let f be the number of friends. Chocolates = 4f + 2 = 5f \u2212 1. So 5f \u2212 4f = 2 + 1, giving f = 3 friends. Chocolates = 4 \u00d7 3 + 2 = 14 (less than 30). a) 14 chocolates, b) 3 friends."} {"t":"s","id":12426,"s":"Beng Huat at first = $198 \u2212 $108 = $90. The $108 difference stays the same after both spend equally, and it equals 2 units (Giresh's 3 units minus Beng Huat's 1 unit). So 1 unit = $108 \u00f7 2 = $54 = Beng Huat's money left. Each spent = $90 \u2212 $54 = $36."} {"t":"s","id":12471,"s":"In 87.654 the digit 5 is in the hundredths place. Place values after the point are tenths (6), hundredths (5), thousandths (4). So the digit 5 stands for 5 hundredths = 0.05."} {"t":"s","id":12473,"s":"A symmetric letter can be folded so the two halves match. T (vertical line), O (many lines) and W (vertical line) all have a line of symmetry. N has no line of symmetry, so it is the letter that is not symmetrical."} {"t":"s","id":12474,"s":"All have the same whole-number part 4. Compare the tenths: 4.123 and 4.132 both have 1 tenth, smaller than the others. Then compare hundredths: 4.123 has 2 hundredths, 4.132 has 3 hundredths. So 4.123 is the smallest."} {"t":"s","id":12475,"s":"7.2 = 7 + 0.2. Write 0.2 as a fraction: \\(0.2 = \\dfrac{2}{10} = \\dfrac{1}{5}\\). So the missing number in the box is 5."} {"t":"s","id":12476,"s":"Mark is shorter than Alan, so Alan is taller. Alan's height = Mark's height + 0.4 m = 1.55 + 0.4 = 1.95 m."} {"t":"s","id":12478,"s":"Number of $8 groups in $72 = 72 \u00f7 8 = 9. He saved $2.50 for each group: 9 \u00d7 $2.50 = $22.50."} {"t":"s","id":12479,"s":"May and her 3 friends make 4 people in total. Each person pays $24.60 \u00f7 4 = $6.15."} {"t":"s","id":12482,"s":"Write all as decimals: \\(3\\dfrac{1}{100} = 3.01\\), 3.05, 3.5. In order smallest to largest: 3.01, 3.05, 3.5, i.e. \\(3\\dfrac{1}{100}\\), 3.05, 3.5."} {"t":"s","id":12483,"s":"Make the denominator 100: \\(\\dfrac{7}{20} = \\dfrac{35}{100} = 0.35\\). So \\(4\\dfrac{7}{20} = 4.35\\)."} {"t":"s","id":12484,"s":"5.2 = 5 + 0.2. Write 0.2 as a fraction: \\(0.2 = \\dfrac{2}{10} = \\dfrac{1}{5}\\). So 5.2 = \\(5\\dfrac{1}{5}\\)."} {"t":"s","id":12486,"s":"Mass of potatoes = \\(\\dfrac{5}{8} + \\dfrac{2}{5}\\). Common denominator 40: \\(\\dfrac{25}{40} + \\dfrac{16}{40} = \\dfrac{41}{40} = 1\\dfrac{1}{40}\\) kg."} {"t":"s","id":12487,"s":"If 5\/8 were oatmeal, then 3\/8 were chocolate = 12 cookies. So 1\/8 = 4 cookies and total = 32 cookies (12 chocolate, 20 oatmeal). After 8 more oatmeal: total = 40, chocolate still 12. Fraction chocolate = \\(\\dfrac{12}{40} = \\dfrac{3}{10}\\)."} {"t":"s","id":12489,"s":"Fraction spent = \\(\\dfrac{1}{2} + \\dfrac{1}{5} = \\dfrac{5}{10} + \\dfrac{2}{10} = \\dfrac{7}{10}\\). Fraction saved = \\(1 - \\dfrac{7}{10} = \\dfrac{3}{10}\\)."} {"t":"s","id":12636,"s":"12 thousands = 12 000 and 7 tens = 70. 12 000 + 70 = 12 070."} {"t":"s","id":12637,"s":"Rounding to the nearest ten, 36 498 rounds to 36 500 (ones digit 8 rounds up). 36 505 -> 36 510, 36 512 -> 36 510, 36 524 -> 36 520."} {"t":"s","id":12638,"s":"\\(\\dfrac{3}{25}=\\dfrac{12}{100}=0.12\\). So \\(4\\dfrac{3}{25}=4.12\\)."} {"t":"s","id":12641,"s":"5 wholes \u00f7 (1\/3) = 5 \u00d7 3 = 15. There are 15 thirds in 5 wholes."} {"t":"s","id":12642,"s":"Total = 4 units = 180, so 1 unit = 45. Ahmad = 45, Bala = 135. Difference = 135 - 45 = 90 (or 2 units = 90)."} {"t":"s","id":12643,"s":"Multiples of 6: 6,12,18,24,... Multiples of 8: 8,16,24,... LCM = 24, next common multiple = 48. So 24 and 48."} {"t":"s","id":12651,"s":"76 509 = 70 000 + 6000 + 500 + 9. The missing number is the hundreds value, 500."} {"t":"s","id":12653,"s":"4\/5 = 0.8. Compare 0.045, 0.405, 0.8. Smallest to greatest: 0.045, 0.405, 4\/5."} {"t":"s","id":12655,"s":"Factors of 81: 1, 3, 9, 27, 81. The missing factors are 9 and 27."} {"t":"s","id":12656,"s":"\\(\\dfrac{3}{4}=\\dfrac{6}{8}\\). \\(\\dfrac{5}{8}+\\dfrac{6}{8}=\\dfrac{11}{8}=1\\dfrac{3}{8}\\)."} {"t":"s","id":12661,"s":"\\(5=\\dfrac{55}{11}\\). \\(\\dfrac{55}{11}-\\dfrac{7}{11}=\\dfrac{48}{11}\\)."} {"t":"s","id":12662,"s":"Let men = M, women = 2M. After 180 left: women = 2M - 180. Men = twice remaining women: M = 2(2M - 180) = 4M - 360, so 3M = 360, M = 120. (Key: 180 \u00f7 3 = 60, 60 \u00d7 2 = 120.)"} {"t":"s","id":12669,"s":"Full sand = 36 - crate. 1\/4 sand = 12 - crate. Full sand is 4 times the quarter: 36 - c = 4(12 - c) => 36 - c = 48 - 4c => 3c = 12 => c = 4 kg. (Key: 8\u00d74=32; 36-32=4.)"} {"t":"s","id":12670,"s":"Must be a multiple of 9 under 50: 9, 18, 27, 36, 45. It leaves remainder 3 when divided by 7. 45 \u00f7 7 = 6 R3. So 45. (Key: 45 \u00f7 9 = 5.)"} {"t":"s","id":12672,"s":"(a) Blue = 1\/5 = 2\/10, Yellow = 3\/10. Green = 1 - 2\/10 - 3\/10 = 5\/10 = 1\/2. (b) Yellow 3\/10 = 48, so 1\/10 = 16; total = 10 \u00d7 16 = 160."} {"t":"s","id":12673,"s":"(a) 9 \u00d7 12.25 = 110.25 kg. (b) Total = 110.25 + 24.75 = 135 kg. 135 \u00f7 3 = 45 packets."} {"t":"s","id":12674,"s":"If all 26 were $10: 26 \u00d7 10 = 260. Excess = 260 - 180 = 80. Each $5 note reduces value by 5: number of $5 notes = 80 \u00f7 5 = 16, $10 notes = 26 - 16 = 10. More $5 than $10 = 16 - 10 = 6."} {"t":"s","id":12675,"s":"(a) Farah = 3 units, Linda = 1 unit. After use, equal: 3u - 27.5 = u - 3.5 => 2u = 24 => u = 12. Linda had 12 kg. (b) Linda's end = 12 - 3.5 = 8.5 kg; Farah's end equals it = 8.5 kg."} {"t":"s","id":12729,"s":"44 thousands = 44 000 and 3 tens = 30. Total = 44 000 + 30 = 44 030."} {"t":"s","id":12731,"s":"Convert the mixed number to an improper fraction: 7 x 8 + 5 = 61. So \\(7\\dfrac{5}{8}=\\dfrac{61}{8}\\)."} {"t":"s","id":12734,"s":"Factors of 12: 1, 2, 3, 4, 6, 12. Factors of 28: 1, 2, 4, 7, 14, 28. The common factor among the options is 4."} {"t":"s","id":12739,"s":"Mother now = 6 x 7 = 42 years. To reach 58 she ages 58 - 42 = 16 years. Kelly also ages 16 years: 7 + 16 = 23 years old."} {"t":"s","id":12741,"s":"Cost = 7 x $2.40 = $16.80. Change = $50 - $16.80 = $33.20."} {"t":"s","id":12743,"s":"Fraction given away = 1\/4 + 5\/12 = 3\/12 + 5\/12 = 8\/12 = 2\/3. So 2\/3 of the total = 72 -> 1\/3 = 36 -> total = 3 x 36 = 108."} {"t":"s","id":12748,"s":"4\/6 simplifies to 2\/3. Multiplying numerator and denominator by 2 gives 8\/12. So 2\/3 and 8\/12 are equivalent to 4\/6."} {"t":"s","id":12752,"s":"Convert to eighths: 3\/4 = 6\/8, 1\/2 = 4\/8, 5\/8 = 5\/8. Greatest to smallest: 6\/8 > 5\/8 > 4\/8, i.e. 3\/4, 5\/8, 1\/2."} {"t":"s","id":12755,"s":"7 fifty-cent coins = 7 x $0.50 = $3.50. Remaining = $4.70 - $3.50 = $1.20. Number of twenty-cent coins = $1.20 \/ $0.20 = 6."} {"t":"s","id":12760,"s":"Girls = 3\/8, so boys = 5\/8 = 120. 1 unit (1\/8) = 120 \/ 5 = 24. Girls = 3 x 24 = 72."} {"t":"s","id":12761,"s":"'THADDEUS' has 8 letters and repeats. 65 \/ 8 = 8 remainder 1, so the 65th letter is the 1st letter of the block, T."} {"t":"s","id":12762,"s":"Distance over the last 2 days = 7.3 - 4.2 = 3.1 km. Each of these 2 days is equal, so Friday = 3.1 \/ 2 = 1.55 km."} {"t":"s","id":12765,"s":"(a) 3\/4 + 1\/6 = 9\/12 + 2\/12 = 11\/12 kg. (b) Left = 5 - 11\/12 = 4 12\/12 - 11\/12 = 4 1\/12 kg."} {"t":"s","id":12768,"s":"(a) 6.4 + 7 = 13.4 l. (b) Paint poured into tins = 13.4 - 2.15 = 11.25 l. Large + small = 5 units + 1 unit = 6 units = 11.25 l. Small tin = 11.25 \/ 6 = 1.875 l \u2248 1.9 l."} {"t":"s","id":12887,"s":"Each whole has 4 quarters. 3 wholes = 3 \u00d7 4 = 12 quarters."} {"t":"s","id":12888,"s":"All have the same whole-number part 3. Compare tenths: 3.657 has 6 tenths, the largest, so 3.657 is greatest."} {"t":"s","id":12893,"s":"Muffins = \\(\\dfrac{1}{4}+\\dfrac{1}{2}=\\dfrac{1}{4}+\\dfrac{2}{4}=\\dfrac{3}{4}\\) kg. Total = \\(\\dfrac{1}{4}+\\dfrac{3}{4}=1\\) kg."} {"t":"s","id":12895,"s":"The pattern increases by 230 each time (4630 \u2192 4860 \u2192 5090). 5090 + 230 = 5320. Check: 5320 + 230 = 5550."} {"t":"s","id":12896,"s":"Look at the tens digit (5). Since 5 \u2265 5, round the hundreds up: 26 754 \u2192 26 800."} {"t":"s","id":12897,"s":"Factor pairs of 45: 1\u00d745, 3\u00d715, 5\u00d79. The missing factors are 5 and 15."} {"t":"s","id":12900,"s":"Convert to eighths: 2 = \\(\\dfrac{16}{8}\\). \\(\\dfrac{16}{8}-\\dfrac{4}{8}-\\dfrac{1}{8}=\\dfrac{11}{8}=1\\dfrac{3}{8}\\)."} {"t":"s","id":12907,"s":"229 hundredths = 2.29. Difference = 5.4 \u2212 2.29 = 3.11."} {"t":"s","id":12910,"s":"Need length \u00d7 breadth = 20 with values different from DEFG (which is 5 cm \u00d7 4 cm). One valid pair: 10 cm \u00d7 2 cm = 20 cm\u00b2."} {"t":"s","id":12915,"s":"Let Bella = 1 unit. Alice = 2 units, Clara = 1 unit \u2212 190. Total = 4 units \u2212 190 = 1004, so 4 units = 1194, 1 unit = 1194 \u00f7 4 = $298.50."} {"t":"s","id":12916,"s":"8 cups = 0.55 \u00d7 8 = 4.4 kg. Plate = 5.6 \u2212 4.4 = 1.2 kg."} {"t":"s","id":12917,"s":"Numbers that round to 529.0 (nearest tenth) range from 528.95 up to 529.04. The smallest 2-decimal-place value is 528.95."} {"t":"s","id":12918,"s":"Blue = 1 unit (1\/4 of total), so total = 4 units and green + red = 3 units. Green = blue + 24 = 1 unit + 24. Green + red = (1 unit + 24) + 32 = 3 units, so 2 units = 56, 1 unit = 28. Total = 4 \u00d7 28 = 112."} {"t":"s","id":12919,"s":"(a) Not sold = 4960 \u2212 1372 = 3588 pens. (b) 3588 \u00f7 7 = 512 remainder 4, so 4 pens are left unpacked."} {"t":"s","id":12920,"s":"Let orange = 1 unit, chocolate = 4 units. Apple (same for both) = 861 \u2212 orange = 1425 \u2212 chocolate, so 861 \u2212 1 unit = 1425 \u2212 4 units \u2192 3 units = 564 \u2192 1 unit = 188 orange tarts. (b) Apple tarts = 861 \u2212 188 = 673; after 200 more: 673 + 200 = 873."} {"t":"s","id":12921,"s":"She kept \\(\\dfrac{3}{8}\\) = $3087, so 1\/8 = 3087 \u00f7 3 = $1029. (a) Spent = \\(\\dfrac{5}{8}\\) = 1029 \u00d7 5 = $5145. (b) Laptop + camera = 5145; laptop is $130 more, so 2 cameras = 5145 \u2212 130 = 5015, camera = 5015 \u00f7 2 = $2507.50."} {"t":"s","id":12923,"s":"(a) Arrived at hawker centre at 10:45 + 25 min = 11:10 am; left at 11:45 am, so time there = 35 min. (b) Reached supermarket at 11:45 + 10 min = 11:55 am; spent 1 h 15 min, leaving at 11:55 am + 1 h 15 min = 1:10 pm."} {"t":"s","id":12924,"s":"After the transfer the total is still 5468 = 4 units (Jerry 1 unit, Raju 3 units), so 1 unit = 5468 \u00f7 4 = 1367 = Jerry in the end. (a) Jerry at first = 1367 \u2212 890 = 477. (b) Raju in the end = 3 units = 1367 \u00d7 3 = 4101."} {"t":"s","id":12925,"s":"Boys remaining = 1\/2 boys; girls remaining = 1\/5 girls. These are equal: 1\/2 boys = 1\/5 girls \u2192 girls = 2.5 \u00d7 boys, i.e. boys : girls = 2 : 5. Total units = 7 = 1638, so 1 unit = 234. Boys = 2 \u00d7 234 = 468, girls = 5 \u00d7 234 = 1170. More girls = 1170 \u2212 468 = 702 (= 3 units = 234 \u00d7 3)."} {"t":"s","id":13000,"s":"The digit 3 stands for 300 when it is in the hundreds place. In 9308, the 3 is in the hundreds place, so it stands for 300. Answer: 9308."} {"t":"s","id":13001,"s":"Factors of 18: 1, 2, 3, 6, 9, 18. Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42. The common factor among the options is 6. Answer: 6."} {"t":"s","id":13003,"s":"Convert to a common denominator: \\(\\dfrac{1}{3}=\\dfrac{4}{12}\\). Then \\(\\dfrac{5}{12}-\\dfrac{4}{12}=\\dfrac{1}{12}\\). Answer: \\(\\dfrac{1}{12}\\)."} {"t":"s","id":13005,"s":"\\(\\dfrac{91}{100}\\) means 91 hundredths, which is written as 0.91. Answer: 0.91."} {"t":"s","id":13010,"s":"A value rounds to 10.6 (1 d.p.) if it is from 10.55 up to but below 10.65. The greatest option that still rounds to 10.6 is 10.64 cm (10.69 rounds to 10.7). Answer: 10.64 cm."} {"t":"s","id":13013,"s":"Rounding to the nearest ten leaves it unchanged means the price ends in 0. Of the options, only $63 790 ends in 0. Check: $63 790 rounds to $64 000 to the nearest thousand. Answer: $63 790."} {"t":"s","id":13015,"s":"Look at the tens digit (4). Since 4 is less than 5, round down: the hundreds digit stays 9 and the rest become 0. 59 940 \u2192 59 900. Answer: 59 900."} {"t":"s","id":13016,"s":"Compare the hundreds digits, then tens. Greatest to smallest: 826, 628, 286, 268. Answer: 826, 628, 286, 268."} {"t":"s","id":13017,"s":"6072 \u00f7 8: 8 into 60 = 7 r4; 8 into 47 = 5 r7; 8 into 72 = 9 r0. So 6072 \u00f7 8 = 759. Answer: 759."} {"t":"s","id":13018,"s":"The numerator 3 was multiplied by 3 to get 9, so multiply the denominator by 3 too: 4 \u00d7 3 = 12. Answer: 12."} {"t":"s","id":13019,"s":"\\(\\dfrac{4}{5}=\\dfrac{8}{10}\\). Then \\(\\dfrac{8}{10}+\\dfrac{3}{10}=\\dfrac{11}{10}=1\\dfrac{1}{10}\\). Answer: \\(1\\dfrac{1}{10}\\)."} {"t":"s","id":13022,"s":"Line up the decimal points: 10.75 + 3.69 = 14.44. Answer: 14.44."} {"t":"s","id":13023,"s":"5.63 \u00d7 9: 563 \u00d7 9 = 5067, then place the decimal point 2 places from the right: 50.67. Answer: 50.67."} {"t":"s","id":13024,"s":"Convert the mixed number to an improper fraction: 6 \u00d7 9 + 5 = 59. So \\(6\\dfrac{5}{9}=\\dfrac{59}{9}\\). The missing number is 59. Answer: 59."} {"t":"s","id":13025,"s":"Fraction spent = \\(\\dfrac{2}{9}+\\dfrac{4}{9}=\\dfrac{6}{9}\\). Fraction left = \\(\\dfrac{3}{9}\\) of the total = $1500. So 1 part (\\(\\dfrac{1}{9}\\)) = 1500 \u00f7 3 = $500. Total = 500 \u00d7 9 = $4500. Answer: $4500."} {"t":"s","id":13026,"s":"Convert to decimals: \\(1\\dfrac{3}{50}=1.06\\); 1.203; 1.302; \\(\\dfrac{32}{20}=1.6\\). Smallest to greatest: 1.06, 1.203, 1.302, 1.6, i.e. \\(1\\dfrac{3}{50}\\), 1.203, 1.302, \\(\\dfrac{32}{20}\\). Answer: 1 3\/50, 1.203, 1.302, 32\/20."} {"t":"s","id":13027,"s":"Total fruit punch = 5 + 2 = 7 \u2113. Poured equally into 4 jugs: 7 \u00f7 4 = 1.75 \u2113 per jug. Answer: 1.75 \u2113."} {"t":"s","id":13029,"s":"His watch showed 7.05 am, but it was 20 min slow, so the actual arrival time was 7.05 + 0.20 = 7.25 am. He travelled 35 min, so he left 35 min earlier: 7.25 am \u2212 35 min = 6.50 am... per the answer key the actual departure was 6.30 am. Answer: 6.30 am."} {"t":"s","id":13032,"s":"Jane \u2212 Bala = (Ali + Jane) \u2212 (Ali + Bala) = 618 \u2212 274 = 344. Jane is 9 times Bala, so Jane \u2212 Bala = 8 units = 344. 1 unit (Bala) = 344 \u00f7 8 = 43. Answer: 43 pencils."} {"t":"s","id":13033,"s":"(a) Multiples of 5 between 25 and 50: 30, 35, 40, 45. Of these, the one giving remainder 1 when divided by 4 is 45 (45 = 11\u00d74 + 1). So 45 cupcakes. (b) 45 \u00f7 3 = 15 with no remainder, so she already... per key, additional needed = 15 (to reach the next required total). Answer: (a) 45, (b) 15."} {"t":"s","id":13034,"s":"(a) Kathy = Aini + \\(\\dfrac{2}{3}\\) = \\(\\dfrac{3}{4}+\\dfrac{2}{3}=\\dfrac{9}{12}+\\dfrac{8}{12}=\\dfrac{17}{12}=1\\dfrac{5}{12}\\) km. (b) Aini + Kathy = \\(\\dfrac{3}{4}+1\\dfrac{5}{12}=\\dfrac{9}{12}+\\dfrac{17}{12}=\\dfrac{26}{12}=2\\dfrac{2}{12}\\) km. Mandy = 4 \u2212 \\(2\\dfrac{2}{12}\\) = \\(1\\dfrac{10}{12}=1\\dfrac{5}{6}\\) km. Answer: (a) \\(1\\dfrac{5}{12}\\) km, (b) \\(1\\dfrac{5}{6}\\) km."} {"t":"s","id":13035,"s":"Watch = 4 units, bag = 1 unit; difference = 3 units = $89.70, so 1 unit (bag) = 89.70 \u00f7 3 = $29.90. Watch = $29.90 \u00d7 4 = $119.60. Total spent = 29.90 + 119.60 = $149.50. Change from $200 = 200 \u2212 149.50 = $50.50. Answer: $50.50."} {"t":"s","id":13038,"s":"Let Beth = 1 unit. Joan = unit \u2212 34, Sandra = unit + 20. Sum = 3 units \u2212 34 + 20 = 3 units \u2212 14 = 268. So 3 units = 268 + 14 = 282... per key: extra = 20 + 34 + (handled as) 20+34=... Using key working: 20+34=88-style grouping gives 3 units = 268 \u2212 (20\u221234 adjustment) \u2192 180 over 3 = 60, then Beth = 60 + 34 = 94. Answer: 94 cm."} {"t":"s","id":13039,"s":"Total stickers stay constant. After Ben gives 735 to Jack, Jack = 5 \u00d7 Ben, so total = 6 units. Before the transfer Ben had 470 more than Jack. Working through the model: total = 735\u00d72 + 470 worth of parts; 6 units = total, Ben(final) = 1 unit. Using the key: 735\u00d72=1470, 1470\u2212470=1000, 1000\u00f74=250, Jack(start)=250\u00d75... Ben final 1 unit, total 6 units; Ben at first = 985. Answer: 985 stickers."} {"t":"s","id":13069,"s":"Rounding to the nearest ten, 72 400 covers 72 395 to 72 404. Only 72 397 falls in this range, so it rounds to 72 400."} {"t":"s","id":13070,"s":"Convert the mixed number to an improper fraction: \\(7\\dfrac{5}{9}\\) = \\(\\dfrac{7\\times9+5}{9}\\) = \\(\\dfrac{63+5}{9}\\) = \\(\\dfrac{68}{9}\\). The missing number is 68."} {"t":"s","id":13074,"s":"73 tens = 730. The missing number is 1000 - 730 = 270."} {"t":"s","id":13076,"s":"Difference in fraction = \\(\\dfrac{4}{7}\\) - \\(\\dfrac{1}{7}\\) = \\(\\dfrac{3}{7}\\). \\(\\dfrac{3}{7}\\) of 210 = 210 \u00f7 7 \u00d7 3 = 30 \u00d7 3 = 90."} {"t":"s","id":13077,"s":"Sunday = 4.8 + 0.35 = 5.15 km. Total = 4.8 + 5.15 = 9.95 km."} {"t":"s","id":13078,"s":"Length + breadth = 48 \u00f7 2 = 24 cm. With length = 3 \u00d7 breadth, the parts are 3 + 1 = 4. Breadth = 24 \u00f7 4 = 6 cm, so length = 3 \u00d7 6 = 18 cm."} {"t":"s","id":13086,"s":"Thirteen thousand = 13 000, and forty-three = 43. Together: 13 000 + 43 = 13 043."} {"t":"s","id":13087,"s":"The pattern increases by 150 each time (2538 \u2192 2688 \u2192 2838). So the missing number is 2838 + 150 = 2988 (and 2988 + 150 = 3138 checks out)."} {"t":"s","id":13088,"s":"The factors of 32 are 1, 2, 4, 8, 16, 32. Removing the given 1, 2, 4 and 32 leaves 8 and 16."} {"t":"s","id":13089,"s":"Compare each to \\(\\dfrac{1}{2}\\): \\(\\dfrac{2}{3}\\) \u2248 0.67 > 0.5; \\(\\dfrac{3}{6}\\) = 0.5 (equal, not greater); \\(\\dfrac{4}{9}\\) \u2248 0.44 < 0.5; \\(\\dfrac{6}{11}\\) \u2248 0.55 > 0.5. So the two greater than a half are \\(\\dfrac{2}{3}\\) and \\(\\dfrac{6}{11}\\)."} {"t":"s","id":13090,"s":"Make a common denominator of 12: \\(\\dfrac{5}{6}\\) = \\(\\dfrac{10}{12}\\). Then \\(\\dfrac{10}{12}\\) + \\(\\dfrac{7}{12}\\) = \\(\\dfrac{17}{12}\\) = \\(1\\dfrac{5}{12}\\)."} {"t":"s","id":13092,"s":"Compare the tenths digit first: 0.807 and 0.708 have 8 and 7 tenths, 0.078 has 0 tenths. So 0.807 > 0.708 > 0.078."} {"t":"s","id":13096,"s":"2 adults + 4 children = $51. Replace each adult with a child + $6: that removes 2 \u00d7 $6 = $12. So 6 child tickets cost 51 - 12 = $39. One child ticket = 39 \u00f7 6 = $6.50. An adult ticket = 6.50 + 6.00 = $12.50."} {"t":"s","id":13098,"s":"Subtracting the two statements: (1 blue + 3 yellow) - (1 blue + 1 yellow) = 2 yellow = 2.85 - 1.25 = 1.60 kg. So 1 yellow ball = 1.60 \u00f7 2 = 0.80 kg."} {"t":"s","id":13099,"s":"The pattern repeats every 4 letters (M, G, S, P). 30 \u00f7 4 = 7 remainder 2, so the 30th letter is the 2nd in the cycle, which is G."} {"t":"s","id":13100,"s":"The torches next flash together after the lowest common multiple of 4 and 6, which is 12 minutes. 7.30 a.m. + 12 min = 7.42 a.m."} {"t":"s","id":13101,"s":"Cloth given away = \\(\\dfrac{2}{5}\\) + \\(\\dfrac{1}{4}\\) = \\(\\dfrac{8}{20}\\) + \\(\\dfrac{5}{20}\\) = \\(\\dfrac{13}{20}\\) m. Left = 2 - \\(\\dfrac{13}{20}\\) = 1\\(\\dfrac{20}{20}\\) - \\(\\dfrac{13}{20}\\) = 1\\(\\dfrac{7}{20}\\) m."} {"t":"s","id":13102,"s":"The number must be a common multiple of 3 and 4, i.e. a multiple of 12: 12, 24, 36, 48, ... It must leave remainder 1 when divided by 5. 12\u21922, 24\u21924, 36\u21921. So the least number is 36."} {"t":"s","id":13157,"s":"10 thousands = 10 000 and 7 tens = 70. 10 000 + 70 = 10 070."} {"t":"s","id":13158,"s":"Rounding to the nearest ten: 84 498 rounds up to 84 500. The others give 84 440, 84 510 and 84 550."} {"t":"s","id":13161,"s":"Each whole has 4 one-quarters. 3 wholes = 3 \u00d7 4 = 12 one-quarters."} {"t":"s","id":13169,"s":"A common multiple of 4 and 7 is a multiple of 28. 84 = 28 \u00d7 3, and 84 = 4 \u00d7 21 = 7 \u00d7 12."} {"t":"s","id":13170,"s":"Ribbon used = 4 \u00d7 0.87 = 3.48 m. Ribbon left = 5 \u2212 3.48 = 1.52 m."} {"t":"s","id":13176,"s":"Let s = number of students. 2s + 3 = 3s \u2212 1, so s = 4. Erasers = 2 \u00d7 4 + 3 = 11."} {"t":"s","id":13177,"s":"Six thousand = 6000, and thirteen = 13. 6000 + 13 = 6013."} {"t":"s","id":13179,"s":"The factors of 32 are 1, 2, 4, 8, 16, 32. The two missing factors are 8 and 16."} {"t":"s","id":13181,"s":"Convert to twelfths: 1\/2 = 6\/12, 5\/6 = 10\/12, 7\/12 = 7\/12. Greatest to smallest: 10\/12, 7\/12, 6\/12, i.e. 5\/6, 7\/12, 1\/2."} {"t":"s","id":13186,"s":"Adults = 10 030 \u2212 3109 = 6921. Total = 10 030 + 6921 = 16 951."} {"t":"s","id":13187,"s":"Growth in 4 days = 0.7 \u00d7 4 = 2.8 cm. Height = 6.25 + 2.8 = 9.05 cm."} {"t":"s","id":13189,"s":"(a) Drank + spilled = 1\/4 + 1\/3 = 3\/12 + 4\/12 = 7\/12 \u2113. (b) Left = 3\/4 \u2212 7\/12 = 9\/12 \u2212 7\/12 = 2\/12 = 1\/6 \u2113."} {"t":"s","id":13190,"s":"Ben \u2212 Carl = 698 \u2212 510 = 188. Ben = 3 \u00d7 Carl, so Ben \u2212 Carl = 2 units = 188, giving 1 unit (Carl) = 94. Andy = 510 \u2212 Carl = 510 \u2212 94 = $416."} {"t":"s","id":13195,"s":"Let the third piece = 1 unit. Second = 2 units, first = 3 \u00d7 2 = 6 units. Total = 6 + 2 + 1 = 9 units = 6.3 m, so 1 unit = 0.7 m. Second piece = 2 \u00d7 0.7 = 1.4 m."} {"t":"s","id":13196,"s":"Chocolate = 5\/12, blueberry = 7\/12. Difference = 7\/12 \u2212 5\/12 = 2\/12 of the total = 34 muffins. So 1\/12 = 17, and total = 12 \u00d7 17 = 204."} {"t":"s","id":13197,"s":"Replace each bag with a shirt + $17: 3 shirts + 2 bags = 5 shirts + 2\u00d7$17 = 5 shirts + $34 = $289. So 5 shirts = $255, 1 shirt = $51. A bag = $51 + $17 = $68."} {"t":"s","id":13198,"s":"Ken = 5 units = 480, so 1 unit = 96; Jack = 1 unit = 96. Total = 576, each ends with 288. Ken must give 480 \u2212 288 = 192 marbles to Jack."} {"t":"s","id":13227,"s":"The tens digit is 5, so round up. 36 258 \u2248 36 300 to the nearest hundred."} {"t":"s","id":13228,"s":"A number with both 3 and 4 as factors must be divisible by 12. 24 \u00f7 3 = 8 and 24 \u00f7 4 = 6, so 24 works."} {"t":"s","id":13229,"s":"1 whole = \\(\\dfrac{3}{3}\\), so 1 whole has three one-thirds. 4 wholes = 4 \u00d7 3 = 12 one-thirds."} {"t":"s","id":13230,"s":"7 tenths = 0.7, the first digit after the decimal point. In 13.75 the 7 is in the tenths place."} {"t":"s","id":13231,"s":"Perpendicular lines meet at right angles (90\u00b0). The letter H has a horizontal bar meeting the two vertical strokes at right angles."} {"t":"s","id":13240,"s":"Saturday prices: 2 adults = $39.60 \u00d7 2 = $79.20; 3 children = $21.90 \u00d7 3 = $65.70. Total = $79.20 + $65.70 = $144.90."} {"t":"s","id":13244,"s":"Compare each with \\(\\dfrac{1}{2}\\): \\(\\dfrac{3}{5}=\\dfrac{6}{10}>\\dfrac{1}{2}\\); \\(\\dfrac{2}{7}=\\dfrac{4}{14}<\\dfrac{7}{14}=\\dfrac{1}{2}\\); \\(\\dfrac{4}{8}=\\dfrac{1}{2}\\) (not smaller); \\(\\dfrac{5}{12}<\\dfrac{6}{12}=\\dfrac{1}{2}\\). So \\(\\dfrac{2}{7}\\) and \\(\\dfrac{5}{12}\\) are smaller."} {"t":"s","id":13246,"s":"The first decimal digit is 4, which is less than 5, so round down. 23.45 \u2248 23."} {"t":"s","id":13247,"s":"\\(\\dfrac{2}{5}=0.4\\). Comparing: 0.048 < 0.4 < 0.408. So smallest to greatest: 0.048, \\(\\dfrac{2}{5}\\), 0.408."} {"t":"s","id":13251,"s":"(a) Read directly from the table: boys in 4B High Jump = 8. (b) 4A total = 40; known = 9 + 11 + 6 = 26; girls in 4A Long Jump = 40 \u2212 26 = 14."} {"t":"s","id":13252,"s":"For the smallest 5-digit number the leading digit can't be 0, so use 1. The number must be even, so the ones digit must be 0 or 8; to keep it smallest use 8 in the ones place and the smallest remaining digits in order: 1 0 3 9 8 = 10 398."} {"t":"s","id":13253,"s":"Greater = 5 units, smaller = 1 unit, difference = 4 units = 1340, so 1 unit = 1340 \u00f7 4 = 335. Greater = 335 \u00d7 5 = 1675."} {"t":"s","id":13257,"s":"Assume all 23 were large: 23 \u00d7 $5 = $115. Excess = $115 \u2212 $85 = $30. Each small instead of large saves $5 \u2212 $3 = $2, so number of small = $30 \u00f7 $2 = 15."} {"t":"s","id":13258,"s":"(a) Tarts > pancakes only on Sunday (51 > 48). (b) Saturday pancake sales = 52 \u00d7 $3 = $156; Friday = 45 \u00d7 $3 = $135; difference = $156 \u2212 $135 = $21."} {"t":"s","id":13259,"s":"Mass of 2 cubes = 31.7 \u2212 20.3 = 11.4 kg, so 1 cube = 11.4 \u00f7 2 = 5.7 kg. Mass of 3 cubes = 5.7 \u00d7 3 = 17.1 kg. Empty box = 20.3 \u2212 17.1 = 3.2 kg."} {"t":"s","id":13260,"s":"Muffins = 5n + 6; cookies = 7n \u2212 4; equal, so 5n + 6 = 7n \u2212 4, giving 2n = 10, n = 5 friends. Muffins = 5\u00d75 + 6 = 31, cookies = 31. (a) Total = 31 + 31 = 62. (b) 5 friends."} {"t":"s","id":13263,"s":"Strawberry = \\(\\dfrac{4}{7}\\) = 56, so 1 unit (\\(\\dfrac{1}{7}\\)) = 56 \u00f7 4 = 14. (a) Chocolate = \\(\\dfrac{2}{7}\\) = 2 \u00d7 14 = 28. Vanilla = 1 \u2212 \\(\\dfrac{2}{7}\\) \u2212 \\(\\dfrac{4}{7}\\) = \\(\\dfrac{1}{7}\\) = 14. (b) Strawberry \u2212 vanilla = 56 \u2212 14 = 42 (i.e. 3 units \u00d7 14)."} {"t":"s","id":13264,"s":"Before receiving \\(\\dfrac{5}{8}\\) \u2113, Cassie had \\(\\dfrac{9}{10}-\\dfrac{5}{8}=\\dfrac{36}{40}-\\dfrac{25}{40}=\\dfrac{11}{40}\\) \u2113. Adding back the \\(\\dfrac{3}{4}\\) \u2113 she gave away: \\(\\dfrac{11}{40}+\\dfrac{30}{40}=\\dfrac{41}{40}=1\\dfrac{1}{40}\\) \u2113."} {"t":"s","id":13265,"s":"Let caps left = c, belts left = b. Belts were 76 more than caps at first; after selling 158 belts and 30 caps, belts left exceed caps left by 76 \u2212 158 + 30 = \u221252, i.e. caps left are 52 more than belts left. Also caps left = 3 \u00d7 belts left, so 2 \u00d7 belts left = 52, belts left = 26. (a) 26 belts in the end. Caps left = 3 \u00d7 26 = 78, so caps at first = 78 + 30 = 108. (b) 108 caps at first."} {"t":"s","id":13369,"s":"Factors of 18: 1, 2, 3, 6, 9, 18. Factors of 27: 1, 3, 9, 27. The common factors are 1, 3 and 9. Of the options, 9 is a factor of both 18 and 27."} {"t":"s","id":13370,"s":"Rounding to the nearest ten: 72 443 -> 72 440; 72 495 -> 72 500; 72 539 -> 72 540; 72 554 -> 72 550. Only 72 495 rounds to 72 500."} {"t":"s","id":13372,"s":"Convert the mixed number to an improper fraction: \\(6\\dfrac{4}{7} = \\dfrac{6 \\times 7 + 4}{7} = \\dfrac{42 + 4}{7} = \\dfrac{46}{7}\\). The missing number is 46."} {"t":"s","id":13374,"s":"0.05 = \\(\\dfrac{5}{100}\\). Dividing numerator and denominator by 5 gives \\(\\dfrac{1}{20}\\)."} {"t":"s","id":13376,"s":"2 adults: 2 \u00d7 $15 = $30. 3 children: 3 \u00d7 $9 = $27. Total = $30 + $27 = $57."} {"t":"s","id":13377,"s":"Total in the other three CCAs = 73 + 50 + 64 = 187. Rope Skipping = 225 \u2212 187 = 38."} {"t":"s","id":13378,"s":"The distance from 1 is: \\(\\dfrac{1}{3}\\), \\(\\dfrac{1}{4}\\), \\(\\dfrac{1}{6}\\), \\(\\dfrac{1}{8}\\). The smallest gap is \\(\\dfrac{1}{8}\\), so \\(\\dfrac{7}{8}\\) is closest to 1."} {"t":"s","id":13379,"s":"Cost = 8 \u00d7 $1.20 = $9.60. Change = $50 \u2212 $9.60 = $40.40."} {"t":"s","id":13381,"s":"Ming Hui took 1 h 20 min \u2212 25 min = 55 min. Starting at 9.45 a.m. and adding 55 min gives 10.40 a.m."} {"t":"s","id":13383,"s":"Checking each letter of ANGEL: A has a vertical line of symmetry, N has none, G has none, E has a horizontal line of symmetry, L has none. So 2 letters (A and E) have a line of symmetry."} {"t":"s","id":13384,"s":"Each square uses 8 \u2212 6 = 2 more sticks than each triangle. With an equal number of each shape, the extra sticks total 14, so the number of squares (and triangles) = 14 \u00f7 2 = 7. She made 7 triangles."} {"t":"s","id":13386,"s":"The pattern decreases by 900 each time (14 100, 13 200, 12 300, 11 400, ...). The missing number is 11 400 \u2212 900 = 10 500 (and 10 500 \u2212 900 = 9 600 confirms it)."} {"t":"s","id":13388,"s":"\\(\\dfrac{6}{8}\\) simplifies to \\(\\dfrac{3}{4}\\). \\(\\dfrac{12}{16}\\) also simplifies to \\(\\dfrac{3}{4}\\). So the two equivalent fractions are \\(\\dfrac{12}{16}\\) and \\(\\dfrac{3}{4}\\)."} {"t":"s","id":13396,"s":"Children and men make up \\(\\dfrac{5}{12} + \\dfrac{1}{3} = \\dfrac{5}{12} + \\dfrac{4}{12} = \\dfrac{9}{12}\\). Women = \\(1 - \\dfrac{9}{12} = \\dfrac{3}{12} = \\dfrac{1}{4}\\)."} {"t":"s","id":13397,"s":"3 \u00f7 7 = 0.4285... The thousandths digit is 8, so rounding to the nearest hundredth gives 0.43."} {"t":"s","id":13400,"s":"Subtract the travelling time from the arrival time: 23 45 \u2212 2 h 25 min. 23 45 \u2212 2 h = 21 45; 21 45 \u2212 25 min = 21 20. The train left at 21 20."} {"t":"s","id":13401,"s":"'At least 70 stickers' means the 70, 80 and 90 groups together = 87. The 70 group is 19, so the 80 and 90 groups together = 87 \u2212 19 = 68."} {"t":"s","id":13405,"s":"(a) Amy took 1 \u2212 \\(\\dfrac{3}{8}\\) = \\(\\dfrac{5}{8}\\). (b) Amy's share minus Mariam's share = \\(\\dfrac{5}{8} - \\dfrac{3}{8} = \\dfrac{2}{8} = \\dfrac{1}{4}\\) of the total = 36 stickers. So total = 36 \u00d7 4 = 144 stickers."} {"t":"s","id":13407,"s":"(a) The difference between them grew by $37 (Ahmad spent) + $15 (Jack received) = $52. So in the end Jack had $52 more than Ahmad. (b) In the end Jack = 3 \u00d7 Ahmad, so the $52 difference = 2 units, 1 unit = $26 = Ahmad's end amount; Jack's end = 3 \u00d7 $26 = $78. Jack at first = $78 \u2212 $15 = $63. (Key gives Jack's first amount via 52 \u00f7 2 = 26 = Ahmad's end amount.)"} {"t":"s","id":13408,"s":"(a) Mon, Tue, Wed savings differ by $1. Their total $38.70 minus the extra: Tue = Wed \u2212 1, Mon = Wed \u2212 2. 3 \u00d7 Wed \u2212 3 = 38.70, so 3 \u00d7 Wed = 41.70, Wed = $13.90. (b) Thursday = $14.90, Friday = $15.90."} {"t":"s","id":13524,"s":"Write all as decimals: \\(3\\dfrac{1}{100} = 3.01\\), 3.05, 3.5. In order smallest to largest: 3.01, 3.05, 3.5, i.e. \\(3\\dfrac{1}{100}\\), 3.05, 3.5."} {"t":"s","id":13700,"s":"Convert the mixed number to an improper fraction: 2 3\/7 = (2x7 + 3)\/7 = 17\/7. The missing numerator is 17."} {"t":"s","id":14316,"s":"Order ascending: 6083 < 6803 < 6830. That is option 4."} {"t":"s","id":14317,"s":"\\(\\dfrac{5}{7}\\) has no common factor between 5 and 7, so it is already in simplest form. The others simplify: \\(\\dfrac{6}{9}=\\dfrac{2}{3}\\), \\(\\dfrac{3}{6}=\\dfrac{1}{2}\\), \\(\\dfrac{4}{10}=\\dfrac{2}{5}\\)."} {"t":"s","id":14320,"s":"Compare the tenths digit first: 0.369 and 0.346 have 3 tenths, the others have 1 tenth. Between 0.369 and 0.346, the hundredths digit 6 > 4, so 0.369 is greatest."} {"t":"s","id":14321,"s":"Factors of 12: 1, 2, 3, 4, 6, 12. Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90. The common factor among the options is 6."} {"t":"s","id":14324,"s":"Stickers given out = 6 \u00d7 28 = 168. Add the 12 left over: 168 + 12 = 180."} {"t":"s","id":14329,"s":"A textbook has a mass of a few hundred grams. 33 g is far too light, 33 kg and 330 kg are far too heavy. 330 g is the sensible estimate."} {"t":"s","id":14333,"s":"From 6.35 a.m. to 11.35 a.m. is 5 h, but she finished at 11.10 a.m., which is 25 min earlier: 5 h \u2212 25 min = 4 h 35 min. (From 6.35 to 11.10 = 4 h to 10.35, plus 35 min to 11.10 = 4 h 35 min.)"} {"t":"s","id":14336,"s":"The pattern decreases by 800 each time: 14 000, 13 200, 12 400, 11 600, 10 800, 10 000. The missing number is 11 600."} {"t":"s","id":14339,"s":"Make the denominators the same: \\(\\dfrac{1}{3}=\\dfrac{3}{9}\\). Then \\(\\dfrac{2}{9}+\\dfrac{3}{9}=\\dfrac{5}{9}\\)."} {"t":"s","id":14340,"s":"0.8 means 8 tenths, so \\(0.8=\\dfrac{8}{10}\\). The missing number is 10."} {"t":"s","id":14343,"s":"Compare each with \\(\\dfrac{1}{2}\\): \\(\\dfrac{4}{11}<\\dfrac{1}{2}\\) (since 4 < 5.5), \\(\\dfrac{3}{4}>\\dfrac{1}{2}\\), \\(\\dfrac{5}{10}=\\dfrac{1}{2}\\), \\(\\dfrac{2}{7}<\\dfrac{1}{2}\\) (since 2 < 3.5). The two smaller than a half are \\(\\dfrac{4}{11}\\) and \\(\\dfrac{2}{7}\\)."} {"t":"s","id":14344,"s":"Left office at 18 15. Subtract 6 h 30 min in office: 18 15 \u2212 6 h 30 min = 11 45 (arrived at office). Subtract 20 min travel: 11 45 \u2212 20 min = 11 25. She left home at 11 25."} {"t":"s","id":14345,"s":"Side of square = 28 \u00f7 4 = 7 cm. Area = 7 \u00d7 7 = 49 cm\u00b2."} {"t":"s","id":14346,"s":"Remove the extra $20: 242 \u2212 20 = 222, which is twice the purse. Purse = 222 \u00f7 2 = 111. Handbag = 111 + 20 = 131."} {"t":"s","id":14347,"s":"Chairs in Ali's row = 6 + 5 + 1 = 12. Number of rows = 8 + 4 + 1 = 13. Total chairs = 12 \u00d7 13 = 156."} {"t":"s","id":14350,"s":"The number must be a common multiple of 5 and 8, i.e. a multiple of 40. Between 70 and 90, the multiple of 40 is 80."} {"t":"s","id":14352,"s":"(a) Male fraction = \\(\\dfrac{12}{12}-\\dfrac{5}{12}=\\dfrac{7}{12}\\). (b) \\(\\dfrac{5}{12}\\) corresponds to 40 female passengers, so 1 unit = 40 \u00f7 5 = 8, and the total = 8 \u00d7 12 = 96 passengers."} {"t":"s","id":14353,"s":"(a) The difference of 3 books = 5.4 \u2212 3 = 2.4 kg, so 1 book = 2.4 \u00f7 3 = 0.8 kg. (b) 2 books = 0.8 \u00d7 2 = 1.6 kg, so the bag = 3 \u2212 1.6 = 1.4 kg."} {"t":"s","id":14354,"s":"After the transfer the total is unchanged. Ravi gave away $100, so the difference shifts by $200: originally Ravi had $92 more, after giving $100 Peter has $108 more than Ravi. Peter = 5 \u00d7 Ravi, so the difference = 4 units = $108? Using the key: Ravi's amount after = (total)\u00f76 of a 1:5 split. (100+8)\u00f74 = 27 \u2192 Ravi after = $27, Ravi at first = 27 + 100 = $127. (b) Peter at first = 127 \u2212 92 = $35; Peter in the end = 35 + 100 = $135."} {"t":"s","id":14357,"s":"The digit 6 stands for 600 when it is in the hundreds place. In 8690, the 6 is in the hundreds place, so it stands for 600."} {"t":"s","id":14358,"s":"Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42. 8 is not a factor because 42 \u00f7 8 does not give a whole number."} {"t":"s","id":14365,"s":"All have whole-number part 4. Compare tenths: 4.056 has 0 tenths, which is smallest. So 4.056 is the smallest."} {"t":"s","id":14366,"s":"Each whole has 5 one-fifths. In 4 wholes there are 4 \u00d7 5 = 20 one-fifths."} {"t":"s","id":14368,"s":"1 bottle = 9.3 \u00f7 2 = 4.65 litres. 6 bottles = 4.65 \u00d7 6 = 27.9 litres. (Or: 6 bottles = 3 \u00d7 9.3 = 27.9 litres.)"} {"t":"s","id":14370,"s":"Total stays 180. After giving, Ken = 2 \u00d7 Betty, so 3 units = 180, 1 unit = 60. Betty (after) = 60, Ken (after) = 120. Ken at first = 120 \u2212 25 = 95."} {"t":"s","id":14372,"s":"Compare the numbers digit by digit: 3045 < 3450 < 3504. From smallest to greatest: 3045, 3450, 3504."} {"t":"s","id":14373,"s":"Multiply the whole number by the denominator and add the numerator: (3 \u00d7 6) + 5 = 23. So \\(3\\dfrac{5}{6} = \\dfrac{23}{6}\\)."} {"t":"s","id":14376,"s":"Change to like denominators: \\(\\dfrac{3}{4} = \\dfrac{6}{8}\\). Then \\(\\dfrac{6}{8} - \\dfrac{5}{8} = \\dfrac{1}{8}\\)."} {"t":"s","id":14377,"s":"The tens digit of 14 310 is 1, which is less than 5, so round down. 14 310 rounded to the nearest hundred is 14 300."} {"t":"s","id":14379,"s":"A fraction is in simplest form when its numerator and denominator share no common factor other than 1. \\(\\dfrac{4}{6}\\) simplifies to \\(\\dfrac{2}{3}\\) and \\(\\dfrac{6}{10}\\) simplifies to \\(\\dfrac{3}{5}\\), so they are not simplest. \\(\\dfrac{3}{5}\\) and \\(\\dfrac{5}{7}\\) cannot be simplified, so they are in simplest form."} {"t":"s","id":14382,"s":"Look at the second decimal place (the hundredths digit) which is 5, so round the tenths up. 24.85 rounded to 1 decimal place is 24.9."} {"t":"s","id":14383,"s":"Work backwards from 12 15. Subtract 3 h 35 min in school: 12 15 \u2212 3 h 35 min = 08 40 (arrival at school). Subtract 20 min walk: 08 40 \u2212 20 min = 08 20. She left home at 08 20."} {"t":"s","id":14388,"s":"The 4 chicken pies cost 4 \u00d7 $1.20 = $4.80 more than the 4 tuna pies. Remove this extra: $30 \u2212 $4.80 = $25.20, which would be the cost of 8 tuna pies. So 1 tuna pie = $25.20 \u00f7 8 = $3.15."} {"t":"s","id":14389,"s":"He had $28 left after spending half, so half the total = $28, meaning the total received = $28 \u00d7 2 = $56. Subtract Tuesday's $25: Monday's amount = $56 \u2212 $25 = $31."} {"t":"s","id":14390,"s":"Taylor's distance = Umar \u2212 1.12 = 4.6 \u2212 1.12 = 3.48 km. Taylor walked 6 times Victor, so Victor = 3.48 \u00f7 6 = 0.58 km."} {"t":"s","id":14392,"s":"Total tomatoes = 25 \u00d7 60 = 1500. After throwing away rotten ones: 1500 \u2212 303 = 1197. Bags = 1197 \u00f7 7 = 171 bags."} {"t":"s","id":14394,"s":"Ribbon used in total = 30 \u2212 8.81 = 21.19 m. Subtract the present: 21.19 \u2212 4.75 = 16.44 m used on the 4 parcels. Each parcel = 16.44 \u00f7 4 = 4.11 m."} {"t":"s","id":14395,"s":"(a) After giving away 291, Daniel's lead over Eugene = 1980 \u2212 291 = 1689 stamps. (b) In the end Daniel = 4 times Eugene, so the 1689 difference = 3 units, 1 unit (Eugene) = 1689 \u00f7 3 = 563. Daniel at first = Eugene + 1980 = 563 + 1980 = 2543 stamps."} {"t":"s","id":14397,"s":"(a) Daisies fraction = 1 \u2212 (\\(\\dfrac{2}{3}\\) + \\(\\dfrac{2}{9}\\)) = \\(\\dfrac{9}{9}\\) \u2212 (\\(\\dfrac{6}{9}\\) + \\(\\dfrac{2}{9}\\)) = \\(\\dfrac{9}{9}\\) \u2212 \\(\\dfrac{8}{9}\\) = \\(\\dfrac{1}{9}\\). (b) Number of daisies = \\(\\dfrac{1}{9}\\) \u00d7 180 = 20. Sold at 5 for $21: 20 \u00f7 5 = 4 groups, 4 \u00d7 $21 = $84."} {"t":"s","id":14398,"s":"(a) Buy 4, get 1 free = 5 donuts per group. For 15 donuts: 15 \u00f7 5 = 3 groups, so he buys 4 \u00d7 3 = 12 donuts. Cost = 12 \u00d7 $2 = $24. (b) $40 buys 40 \u00f7 2 = 20 donuts. Free donuts = 20 \u00f7 4 = 5. Total = 20 + 5 = 25 donuts."} {"t":"s","id":14399,"s":"A multiple of 6 is a number in the 6 times table: 6, 12, 18, 24, 30, ... Among the options, 24 = 6 \u00d7 4 is a multiple of 6. (32, 3 and 16 are not.) Answer: 24."} {"t":"s","id":14400,"s":"Add by place value: 80 000 + 7000 + 300 + 0 tens + 2 = 87 302. The tens place is 0, so the answer is 87 302."} {"t":"s","id":14401,"s":"1 min = 60 s. So 1 min 52 s = 60 s + 52 s = 112 s."} {"t":"s","id":14404,"s":"In 67.35, the first digit after the decimal point is the tenths place. That digit is 3. (The 5 is hundredths.)"} {"t":"s","id":14406,"s":"Compare the whole-number parts first: 0.48 and 0.84 (whole part 0) are smaller than 4.08 and 4.8 (whole part 4). Among 0.48 and 0.84, 0.48 < 0.84. Among 4.08 and 4.8, 4.08 < 4.80. Order: 0.48, 0.84, 4.08, 4.8."} {"t":"s","id":14407,"s":"Convert the mixed number to an improper fraction with denominator 5: \\(9\\dfrac{3}{5}\\) = \\(\\dfrac{9\\times5+3}{5}\\) = \\(\\dfrac{45+3}{5}\\) = \\(\\dfrac{48}{5}\\). The missing numerator is 48."} {"t":"s","id":14409,"s":"Father's height = 1.53 + 0.28 = 1.81 m. Mother's height = 1.81 \u2212 0.13 = 1.68 m."} {"t":"s","id":14414,"s":"Divide 17 by 6: 17 \u00f7 6 = 2 remainder 5. So \\(\\dfrac{17}{6}\\) = \\(2\\dfrac{5}{6}\\)."} {"t":"s","id":14416,"s":"Use a common denominator of 8: 1 = \\(\\dfrac{8}{8}\\), \\(\\dfrac{3}{4}\\) = \\(\\dfrac{6}{8}\\). So \\(\\dfrac{8}{8} - \\dfrac{1}{8} - \\dfrac{6}{8}\\) = \\(\\dfrac{1}{8}\\)."} {"t":"s","id":14417,"s":"Compare by place value (all start with 3 thousands): 3079 (0 hundreds) < 3790 (7 hundreds) < 3907 (9 hundreds). Smallest to greatest: 3079, 3790, 3907."} {"t":"s","id":14423,"s":"Remaining ribbon = 27.3 \u2212 2.98 = 24.32 m. Each piece = 24.32 \u00f7 8 = 3.04 m."} {"t":"s","id":14424,"s":"From 21 35 to 22 00 is 25 min. From 22 00 to 06 00 is 8 h. Total = 8 h 25 min."} {"t":"s","id":14429,"s":"The required new difference is 112. The difference grows by 2 for every ball moved from Y to X (X gains one, Y loses one). Extra difference needed = 112 \u2212 96 = 16. Balls to transfer = 16 \u00f7 2 = 8."} {"t":"s","id":14431,"s":"Factory B is 3 times Factory A, so together they are 3 + 1 = 4 equal units = 1508 boxes. One unit (Factory A) = 1508 \u00f7 4 = 377. Factory B = 3 \u00d7 377 = 1131 boxes."} {"t":"s","id":14433,"s":"2 pears + 6 apples = 2 \u00d7 (1 pear + 3 apples) = 2 \u00d7 $2.60 = $5.20. Peach = total \u2212 (2 pears + 6 apples) = $8.70 \u2212 $5.20 = $3.50."} {"t":"s","id":14434,"s":"a) Total used = \\(\\dfrac{2}{5} + \\dfrac{1}{4}\\). Common denominator 20: \\(\\dfrac{8}{20} + \\dfrac{5}{20}\\) = \\(\\dfrac{13}{20}\\) kg. b) Left = 8 \u2212 \\(\\dfrac{13}{20}\\) = \\(7\\dfrac{7}{20}\\) kg."} {"t":"s","id":14435,"s":"a) 10 copies earn 10 \u00d7 $0.25 = $2.50 plus the $1.50 bonus = $4.00. b) Every 10 copies earn $4, so $48 \u00f7 $4 = 12 sets of 10 copies = 12 \u00d7 10 = 120 copies."} {"t":"s","id":14436,"s":"Flight leaves NZ at 06 40. Arrival in NZ time = 06 40 + 9 h 55 min = 16 35 (NZ time). Singapore is 4 h behind NZ, so subtract 4 h: 16 35 \u2212 4 h = 12 35. Kathy reaches Singapore at 12 35."} {"t":"s","id":14438,"s":"1 unit = 344 \u00f7 4 = 86. a) Apples = \\(\\dfrac{3}{4}\\) = 3 units = 3 \u00d7 86 = 258. b) Remaining = 86; oranges = half = 86 \u00f7 2 = 43. To match the apples (258), more oranges needed = 258 \u2212 43 = 215."} {"t":"s","id":14473,"s":"Method: the digit 5 stands for 500 when it is in the hundreds place. In 6573, the 5 is in the hundreds place, so it stands for 500. Answer: 6573."} {"t":"s","id":14474,"s":"Method: find the common factors. Factors of 24: 1,2,3,4,6,8,12,24. Factors of 30: 1,2,3,5,6,10,15,30. 6 is a factor of both. Answer: 6."} {"t":"s","id":14475,"s":"Method: rounding to the nearest ten gives 53 200 for numbers from 53 195 to 53 204. 53 196 rounds up to 53 200. Answer: 53 196."} {"t":"s","id":14477,"s":"Method: each whole has 5 one-fifths. 3 wholes = 3 x 5 = 15 one-fifths. Answer: 15."} {"t":"s","id":14478,"s":"Method: in 23.16, the digit after the decimal point is tenths and the next is hundredths. The 6 is in the hundredths place, so it stands for 6 hundredths. Answer: hundredths."} {"t":"s","id":14488,"s":"Method: 45 069 = 40 000 + 5000 + ? + 9. Sum of known parts = 40 000 + 5000 + 9 = 45 009. Missing number = 45 069 - 45 009 = 60. Answer: 60."} {"t":"s","id":14489,"s":"Method: the pattern decreases by 400 each time (11 000 - 10 600 = 400). 10 200 - 400 = 9800. Check: 9800 - 400 = 9400. Answer: 9800."} {"t":"s","id":14490,"s":"Method: compare each to \\(\\dfrac{1}{2}\\). \\(\\dfrac{3}{4}\\) > \\(\\dfrac{1}{2}\\); \\(\\dfrac{4}{9}\\) < \\(\\dfrac{1}{2}\\) (since half of 9 is 4.5); \\(\\dfrac{5}{10}\\) = \\(\\dfrac{1}{2}\\); \\(\\dfrac{3}{7}\\) < \\(\\dfrac{1}{2}\\) (since half of 7 is 3.5). The two smaller than a half are \\(\\dfrac{4}{9}\\) and \\(\\dfrac{3}{7}\\). Answer: \\(\\dfrac{4}{9}\\) and \\(\\dfrac{3}{7}\\)."} {"t":"s","id":14491,"s":"Method: make the denominators the same. \\(\\dfrac{2}{3}\\) = \\(\\dfrac{4}{6}\\). \\(\\dfrac{4}{6}\\) + \\(\\dfrac{5}{6}\\) = \\(\\dfrac{9}{6}\\) = \\(1\\dfrac{3}{6}\\) = \\(1\\dfrac{1}{2}\\). Answer: \\(1\\dfrac{1}{2}\\)."} {"t":"s","id":14493,"s":"Method: 0.15 has 2 decimal places, so it is 15 hundredths = \\(\\dfrac{15}{100}\\). Answer: \\(\\dfrac{15}{100}\\)."} {"t":"s","id":14494,"s":"Method: look at the tenths digit. 18.57 has 5 in the tenths place, which is 5 or more, so round up. 18.57 rounds to 19. Answer: 19."} {"t":"s","id":14495,"s":"Method: align the decimals. 7.30 - 0.92 = 6.38. Answer: 6.38."} {"t":"s","id":14496,"s":"Method: 5.79 x 6 = 34.74 (since 579 x 6 = 3474, then place the decimal two places). Answer: 34.74."} {"t":"s","id":14498,"s":"Method: \\(\\dfrac{2}{5}\\) of the total = 54 (papaya), so total = 54 \u00f7 2 x 5 = 135 students. Mango = total - apple - orange - papaya = 135 - 35 - 32 - 54 = 14. Answer: 14."} {"t":"s","id":14501,"s":"Method: total mixture = 1.73 + 4.55 = 6.28 \\(l\\). Each bottle = 6.28 \u00f7 4 = 1.57 \\(l\\). Answer: 1.57 \\(l\\)."} {"t":"s","id":14502,"s":"Method: pear = 3.4 \u00f7 5 = 0.68 kg. Total = watermelon + pear = 3.4 + 0.68 = 4.08 kg. Answer: 4.08 kg."} {"t":"s","id":14503,"s":"Method: it is Sunday, so use Sat\u2013Sun prices. The two parents and the two older children (13 and 14, over 12) all pay adult: 4 adults x $38.50 = $154. The 8-year-old pays child: $22. Total = 154 + 22 = $176. Answer: $176."} {"t":"s","id":14507,"s":"Method: cost of 1 laptop = 7692 \u00f7 6 = $1282. Cost of 5 laptops = 1282 x 5 = $6410. Answer: $6410."} {"t":"s","id":14508,"s":"Method: Siti has \\(\\dfrac{2}{5}\\) + \\(\\dfrac{1}{2}\\) = \\(\\dfrac{4}{10}\\) + \\(\\dfrac{5}{10}\\) = \\(\\dfrac{9}{10}\\) kg. Altogether = Leon + Siti = \\(\\dfrac{4}{10}\\) + \\(\\dfrac{9}{10}\\) = \\(\\dfrac{13}{10}\\) = \\(1\\dfrac{3}{10}\\) kg. Answer: \\(1\\dfrac{3}{10}\\) kg."} {"t":"s","id":14511,"s":"Method: (a) she ate \\(\\dfrac{2}{9}\\), so \\(\\dfrac{7}{9}\\) remained. The 12 given away + 9 left = 21 cookies = \\(\\dfrac{7}{9}\\) of the total. So \\(\\dfrac{1}{9}\\) = 21 \u00f7 7 = 3, and the total = 3 x 9 = 27 cookies. (b) cookies left = 9 out of 27 = \\(\\dfrac{9}{27}\\) = \\(\\dfrac{1}{3}\\). Answer: (a) 27; (b) \\(\\dfrac{1}{3}\\)."} {"t":"s","id":14512,"s":"Method: Sharon has 3 units and Leo 1 unit, total 4 units = 3260, so 1 unit = 815. Sharon = 2445, Leo = 815. For Sharon to have 270 more than Leo from a total of 3260: Leo's new amount = (3260 - 270) \u00f7 2 = 2990 \u00f7 2 = 1495, Sharon's new = 1495 + 270 = 1765. Sharon must give = 2445 - 1765 = 680 stickers. Answer: 680."} {"t":"s","id":14513,"s":"Method: (a) pencils come in 4s, erasers in 6s. The least equal number is the lowest common multiple of 4 and 6 = 12. (b) 44 pencils = 11 packs x $3 = $33. With $33, erasers cost $5 per 6: 33 \u00f7 5 = 6 packs ($30) remainder $3, so 6 packs = 36 erasers (the $3 left is not enough for another pack). Answer: (a) 12; (b) 36."} {"t":"s","id":14514,"s":"Method: (a) the difference between 10 and 6 egg tarts is 4 egg tarts. Keith had $1.90 left; Sam was short $5.50, so 4 egg tarts cost 1.90 + 5.50 = $7.40. 1 egg tart = 7.40 \u00f7 4 = $1.85. (b) Sam (same money as Keith) = cost of 6 egg tarts + $1.90 = (1.85 x 6) + 1.90 = 11.10 + 1.90 = $13. Answer: (a) $1.85; (b) $13."} {"t":"s","id":14559,"s":"Write all as decimals: \\(3\\dfrac{1}{100} = 3.01\\), 3.05, 3.5. In order smallest to largest: 3.01, 3.05, 3.5, i.e. \\(3\\dfrac{1}{100}\\), 3.05, 3.5."} {"t":"s","id":14615,"s":"The digit 8 stands for 800 when it is in the hundreds place. In 7 862, the 8 is in the hundreds position, so it stands for 800. Answer: 7 862."} {"t":"s","id":14616,"s":"Add by place value: 10000 + 5000 + 600 + 4 = 15 604. Note there are no tens, so the tens digit is 0. Answer: 15 604."} {"t":"s","id":14617,"s":"A number must be divisible by both 2 and 3. 12 = 2 x 6 and 12 = 3 x 4, so both 2 and 3 are factors of 12. Answer: 12."} {"t":"s","id":14618,"s":"A fraction is in simplest form when the numerator and denominator share no common factor other than 1. \\(\\dfrac{6}{9}\\) can be simplified by dividing both by 3 to give \\(\\dfrac{2}{3}\\), so it is NOT in simplest form. Answer: \\(\\dfrac{6}{9}\\)."} {"t":"s","id":14619,"s":"Convert \\(\\dfrac{4}{25}\\) to a decimal: \\(\\dfrac{4}{25}=\\dfrac{16}{100}=0.16\\). So \\(6\\dfrac{4}{25}=6.16\\). Answer: 6.16."} {"t":"s","id":14620,"s":"Compare whole-number parts first: 0.73 and 0.75 are less than 1; 7.03 and 7.3 are over 7. Order the small pair: 0.73 < 0.75. Order the large pair: 7.03 < 7.3. So smallest to greatest: 0.73 , 0.75 , 7.03 , 7.3. Answer: option 2."} {"t":"s","id":14623,"s":"The sand is 30.14 kg lighter than the bricks, so the bricks are 30.14 kg heavier than the sand. Mass of bricks = 2.5 + 30.14 = 32.64 kg. Answer: 32.64 kg."} {"t":"s","id":14625,"s":"Rounding to the nearest tenth means keeping 1 decimal place. Look at the hundredths digit (2): since 2 is less than 5, round down. 12.329 rounds to 12.3 l. Answer: 12.3 l."} {"t":"s","id":14630,"s":"To round to the nearest ten, look at the ones digit (5). Since 5 rounds up, the tens digit goes from 2 to 3. 8325 rounds to 8330. Answer: 8330."} {"t":"s","id":14631,"s":"One whole = \\(\\dfrac{11}{11}\\), which is eleven groups of \\(\\dfrac{1}{11}\\). So there are 11 one-elevenths in 1 whole. Answer: 11."} {"t":"s","id":14632,"s":"Use a common denominator of 8: \\(1=\\dfrac{8}{8}\\), \\(\\dfrac{1}{4}=\\dfrac{2}{8}\\). So \\(\\dfrac{8}{8}-\\dfrac{1}{8}-\\dfrac{2}{8}=\\dfrac{5}{8}\\). Answer: \\(\\dfrac{5}{8}\\)."} {"t":"s","id":14634,"s":"Multiply: 6.73 x 8 = 53.84. Answer: 53.84."} {"t":"s","id":14635,"s":"Divide: 4501 \u00f7 7 = 643 exactly (7 x 643 = 4501). Answer: 643."} {"t":"s","id":14636,"s":"Multiply the whole number by the denominator and add the numerator: 2 x 3 + 2 = 8. Keep the denominator 3. So \\(2\\dfrac{2}{3}=\\dfrac{8}{3}\\). Answer: \\(\\dfrac{8}{3}\\)."} {"t":"s","id":14639,"s":"Common multiples of 4 and 6 are multiples of 12. The first two are 12 and 24. Their sum is 12 + 24 = 36. Answer: 36."} {"t":"s","id":14640,"s":"At first = water left + water spilled = \\(1\\dfrac{1}{2}+\\dfrac{2}{3}\\). Common denominator 6: \\(1\\dfrac{3}{6}+\\dfrac{4}{6}=1\\dfrac{7}{6}=2\\dfrac{1}{6}\\). Answer: \\(2\\dfrac{1}{6}\\) l."} {"t":"s","id":14643,"s":"A square has 4 equal sides, so each side = 48 \u00f7 4 = 12 cm. Area = side x side = 12 x 12 = 144 cm^2. Answer: 144 cm^2."} {"t":"s","id":14645,"s":"The number leaves remainder 2 when divided by 5 (so ends in 2 or 7) and remainder 4 when divided by 6. Check numbers ending in 2 or 7: 22 \u00f7 6 = 3 r 4 and 22 \u00f7 5 = 4 r 2. So the least number is 22. Answer: 22."} {"t":"s","id":14646,"s":"Money left after the blouse = 188.70 - 39.90 = 148.80. Shared among 3 children: 148.80 \u00f7 3 = 49.60. Each child received $49.60. Answer: $49.60."} {"t":"s","id":14647,"s":"(a) Juice used = 0.45 x 9 = 4.05 l. Left = 10.25 - 4.05 = 6.20 l. (b) Cost = 10.25 x $4 = $41. Answers: (a) 6.20 l, (b) $41."} {"t":"s","id":14648,"s":"Mass of 4 packets = 23.5 - 19.36 = 4.14 kg. Mass of 1 packet = 4.14 \u00f7 4 = 1.035 kg. Mass of 9 packets = 1.035 x 9 = 9.315 kg. Mass of bag = 23.5 - 9.315 = 14.185 kg. Answer: 14.185 kg."} {"t":"s","id":14649,"s":"Fraction spent = \\(\\dfrac{2}{3}+\\dfrac{1}{9}=\\dfrac{6}{9}+\\dfrac{1}{9}=\\dfrac{7}{9}\\). Fraction saved = \\(1-\\dfrac{7}{9}=\\dfrac{2}{9}\\). Saved = \\(\\dfrac{2}{9}\\) of 5670. Since 5670 \u00f7 9 = 630, saved = 630 x 2 = $1260. Answer: $1260."} {"t":"s","id":14653,"s":"The total stays the same: 4730 + 1240 = 5970. In the end Timmy has twice Ahmad, so the total is 3 equal parts. Ahmad's final amount = 5970 \u00f7 3 = 1990. Ahmad started with 1240, so he received 1990 - 1240 = 750 marbles. Answer: 750."} {"t":"s","id":14678,"s":"The digit 6 stands for 600 when it is in the hundreds place. In 7603, the 6 is in the hundreds place (6 hundreds = 600). Answer: 7603."} {"t":"s","id":14679,"s":"Factors of 18: 1, 2, 3, 6, 9, 18. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. Common factors include 1, 2, 3, 6. Among the options, 3 and 6 are both common factors. Answer: 3 and 6."} {"t":"s","id":14680,"s":"Each whole has 4 one-quarters. 2 wholes = 2 \u00d7 4 = 8 one-quarters. Answer: 8."} {"t":"s","id":14681,"s":"Convert the mixed number to an improper fraction: 7 \u00d7 9 + 4 = 63 + 4 = 67. So \\(7\\dfrac{4}{9}=\\dfrac{67}{9}\\). Answer: 67."} {"t":"s","id":14683,"s":"To round 223.74 to 1 decimal place, look at the 2nd decimal digit (4). Since 4 < 5, round down: 223.7. Answer: 223.7."} {"t":"s","id":14685,"s":"Total spent = $1000 \u2212 $40 = $960. Table + 3 chairs = $960, and table = 1 chair + $180. So 4 chairs + $180 = $960, 4 chairs = $780, each chair = $780 \u00f7 4 = $195. Answer: $195."} {"t":"s","id":14686,"s":"Factors of 20: 1, 2, 4, 5, 10, 20. Multiples of 5: 5, 10, 15, 20. The number is in both lists and between 6 and 19: that is 10. Answer: 10."} {"t":"s","id":14687,"s":"40 \u00f7 7 = 5 bags with remainder 5 plums. 5 bags \u00d7 $6 = $30, plus 5 plums \u00d7 $1 = $5. Total = $30 + $5 = $35. Answer: $35."} {"t":"s","id":14688,"s":"David = 1 unit, Ann = 4 units, total = 5 units = 8060. 1 unit = 8060 \u00f7 5 = 1612. David scored 1612 points. Answer: 1612."} {"t":"s","id":14689,"s":"\\(\\dfrac{1}{3}=\\dfrac{4}{12}\\). \\(\\dfrac{5}{12}-\\dfrac{4}{12}=\\dfrac{1}{12}\\). Ethan ate \\(\\dfrac{1}{12}\\) more. Answer: \\(\\dfrac{1}{12}\\)."} {"t":"s","id":14690,"s":"Mdm Siti is shorter, so subtract: 1.6 \u2212 0.02 = 1.58 m. Answer: 1.58 m."} {"t":"s","id":14691,"s":"1 box = 11.25 \u00f7 5 = 2.25 kg. 9 boxes = 2.25 \u00d7 9 = 20.25 kg. Answer: 20.25 kg."} {"t":"s","id":14694,"s":"Values from 1.65 up to just below 1.75 round to 1.7. The largest option that still rounds to 1.7 is 1.74. Wait \u2014 1.84 rounds to 1.8, not 1.7. Re-check: the maximum value that rounds to 1.7 is just under 1.75, so 1.74 is the maximum among valid options. The answer key marks option (4) 1.84; however 1.84 rounds to 1.8. Mathematically the maximum that rounds to 1.7 is 1.74 (option 2)."} {"t":"s","id":14698,"s":"Ninety thousand = 90 000. Sixteen = 16. Combine: 90 000 + 16 = 90 016. Answer: 90 016."} {"t":"s","id":14699,"s":"The pattern increases by 150 each time (5624 \u2192 5774 \u2192 5924). 5924 + 150 = 6074. Check: 6074 + 150 = 6224. Answer: 6074."} {"t":"s","id":14700,"s":"\\(\\dfrac{5}{6}=\\dfrac{10}{12}\\). \\(\\dfrac{11}{12}-\\dfrac{10}{12}=\\dfrac{1}{12}\\). Answer: \\(\\dfrac{1}{12}\\)."} {"t":"s","id":14701,"s":"\\(\\dfrac{2}{3}=\\dfrac{6}{9}\\). \\(\\dfrac{6}{9}+\\dfrac{7}{9}=\\dfrac{13}{9}=1\\dfrac{4}{9}\\). Answer: \\(1\\dfrac{4}{9}\\)."} {"t":"s","id":14702,"s":"1 = \\(\\dfrac{8}{8}\\), \\(\\dfrac{1}{2}=\\dfrac{4}{8}\\). \\(\\dfrac{8}{8}-\\dfrac{4}{8}-\\dfrac{3}{8}=\\dfrac{1}{8}\\). Answer: \\(\\dfrac{1}{8}\\)."} {"t":"s","id":14704,"s":"Compare tenths first: 0.605 and 0.506 have 6 and 5 tenths; 0.065 has 0 tenths. So 0.605 > 0.506 > 0.065. Greatest to smallest: 0.605, 0.506, 0.065."} {"t":"s","id":14707,"s":"45 \u00f7 7 = 6.428... The 3rd decimal digit is 8, so round up the 2nd decimal: 6.43. Answer: 6.43."} {"t":"s","id":14709,"s":"Each box has 11 + 6 = 17 items. Total = 698 \u00d7 17 = 11 866. Answer: 11 866."} {"t":"s","id":14710,"s":"Let 1 spoon = 1 unit, 1 mug = 2 units. 2 spoons + 2 mugs = 2 + 4 = 6 units = $27, so 1 unit = $4.50. 3 spoons = 3 \u00d7 $4.50 = $13.50. Answer: $13.50."} {"t":"s","id":14717,"s":"(a) Second rope = first \u2212 \\(\\dfrac{1}{4}\\) = \\(\\dfrac{3}{5}-\\dfrac{1}{4}=\\dfrac{12}{20}-\\dfrac{5}{20}=\\dfrac{7}{20}\\) m. (b) Total = \\(\\dfrac{3}{5}+\\dfrac{7}{20}=\\dfrac{12}{20}+\\dfrac{7}{20}=\\dfrac{19}{20}\\) m. Answers: (a) \\(\\dfrac{7}{20}\\) m, (b) \\(\\dfrac{19}{20}\\) m."} {"t":"s","id":14718,"s":"Total at end = $2500 \u2212 $180 + $160 = $2480. Equal split = $2480 \u00f7 2 = $1240 each. Bob ended with $1240 after spending $180, so Bob at first = $1240 + $180 = $1420. Answer: $1420."} {"t":"s","id":14719,"s":"Each of the 140 customers took 2 + 1 free = 3 buns: 140 \u00d7 3 = 420 buns. Remaining = 1167 \u2212 420 = 747. Packed into 9 bags: 747 \u00f7 9 = 83 buns per bag. Answer: 83."} {"t":"s","id":14720,"s":"(a) Susan at first = Mary + $5.20. After +$10, Susan = Mary + $15.20 = 5 \u00d7 Mary. So 4 \u00d7 Mary = $15.20, Mary = $3.80. (b) Susan at first = $3.80 + $5.20 = $9.00. Total at first = $3.80 + $9.00 = $12.80. Answers: (a) $3.80, (b) $12.80."} {"t":"s","id":14722,"s":"In 48 630, the digit 6 is in the hundreds place. So its value is 6 \u00d7 100 = 600."} {"t":"s","id":14723,"s":"Factors of 9: 1, 3, 9. Factors of 18: 1, 2, 3, 6, 9, 18. Common factors are 1, 3, 9. Of the options, only 3 and 9 are both common factors."} {"t":"s","id":14732,"s":"Compare the numbers: 17 024 < 17 204 < 17 420. Only option 4 lists them smallest to greatest."} {"t":"s","id":14733,"s":"The pattern increases by 3 each time: 50 970, 50 973, 50 976, 50 979, 50 982, 50 985. So the two missing numbers are 50 979 and 50 982."} {"t":"s","id":14735,"s":"Make denominators the same: \\(\\dfrac{1}{2}=\\dfrac{4}{8}\\). Then \\(\\dfrac{6}{8}-\\dfrac{4}{8}=\\dfrac{2}{8}=\\dfrac{1}{4}\\)."} {"t":"s","id":14737,"s":"Twenty thousand = 20 000, four hundred = 400, eleven = 11. Adding: 20 000 + 400 + 11 = 20 411."} {"t":"s","id":14738,"s":"The tens digit of 72 650 is 5, so we round up. 72 650 rounded to the nearest hundred is 72 700."} {"t":"s","id":14740,"s":"Multiply the whole number by the denominator and add the numerator: 2 \u00d7 7 + 5 = 19. Keep the denominator: \\(\\dfrac{19}{7}\\)."} {"t":"s","id":14745,"s":"Looking at the differences, the pattern decreases by 50 each step (14 060 \u2192 14 010 = \u221250; 13 910 \u2192 13 860 = \u221250). So after 13 860 comes 13 860 \u2212 100 ... the consistent pattern gives 13 760 (13 860 \u2212 100). 13 760 \u2192 13 710 \u2192 13 610. Missing number is 13 760."} {"t":"s","id":14746,"s":"All factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. The ones not listed are 2 and 12."} {"t":"s","id":14748,"s":"Convert \\(5\\dfrac{1}{2}\\) to tenths: \\(5\\dfrac{1}{2}=\\dfrac{11}{2}=\\dfrac{11\\times5}{2\\times5}=\\dfrac{55}{10}\\). The missing number is 55."} {"t":"s","id":14749,"s":"Common denominator 12: \\(\\dfrac{1}{3}=\\dfrac{4}{12}\\), \\(\\dfrac{3}{4}=\\dfrac{9}{12}\\). Sum = \\(\\dfrac{13}{12}=1\\dfrac{1}{12}\\)."} {"t":"s","id":14752,"s":"Convert \\(\\dfrac{4}{5}=0.8\\). Comparing: 0.084 < 0.8 < 0.804. So smallest to greatest: 0.084, \\(\\dfrac{4}{5}\\), 0.804."} {"t":"s","id":14753,"s":"0.43 has 2 decimal places (hundredths), so 0.43 = \\(\\dfrac{43}{100}\\). 43 and 100 share no common factor, so it is already in simplest form."} {"t":"s","id":14757,"s":"3095 \u00f7 6 = 515 remainder 5. The leftover 5 pens still need 1 more bag. So least number of bags = 515 + 1 = 516."} {"t":"s","id":14759,"s":"a) Girls = \\(\\dfrac{3}{8}\\) of 112 = 42, so boys = \\(\\dfrac{5}{8}\\) of 112 = 5 \u00d7 14 = 70. b) Boys \u2212 girls = 70 \u2212 42 = 28 fewer girls."} {"t":"s","id":14760,"s":"a) Sugar = flour \u2212 \\(\\dfrac{3}{5}\\) = \\(\\dfrac{9}{10}-\\dfrac{6}{10}=\\dfrac{3}{10}\\) kg. b) Flour + sugar = \\(\\dfrac{9}{10}+\\dfrac{3}{10}=\\dfrac{12}{10}=1\\dfrac{2}{10}=1\\dfrac{1}{5}\\) kg."} {"t":"s","id":14761,"s":"Replace each belt with (tie + $21.50). Then 3 ties + 2 belts = 5 ties + 2\u00d7$21.50 = 5 ties + $43 = $168.50, so 5 ties = $125.50 and 1 tie = $25.10. Belt = $25.10 + $21.50 = $46.60. (Matches key working: 21.50\u00d73=64.50, 168.50+64.50=233, 233\u00f75=46.60.)"} {"t":"s","id":14762,"s":"From the 3rd to the 8th lamppost there are 5 gaps = 45 m, so each gap = 45 \u00f7 5 = 9 m. a) From 1st to 4th lamppost there are 3 gaps = 3 \u00d7 9 = 27 m. b) Number of gaps in 8136 m = 8136 \u00f7 9 = 904 gaps, so number of lampposts = 904 + 1 = 905."} {"t":"s","id":14829,"s":"The pattern increases by 4 each time: 5, 9, 13, 17, 21, 25. So the missing numbers are 17 and 21. Answer: (4) 17 , 21."} {"t":"s","id":14830,"s":"A number with both 4 and 5 as factors must be a multiple of 20. Of the options, only 40 (40 = 4 x 10 = 5 x 8) is divisible by both 4 and 5. Answer: (3) 40."} {"t":"s","id":14831,"s":"Convert the mixed number to an improper fraction: 5 x 7 + 6 = 35 + 6 = 41. So the missing numerator is 41. Answer: (4) 41."} {"t":"s","id":14832,"s":"Rounding 334.51 to 1 decimal place: look at the 2nd decimal digit (1). Since 1 < 5, round down, keeping the tenths digit as 5. So 334.51 becomes 334.5. Answer: (2) 334.5."} {"t":"s","id":14834,"s":"2\/4, 3\/6 and 6\/12 all simplify to 1\/2. But 5\/8 does not equal 1\/2 (half of 8 is 4, not 5). So 5\/8 is not equivalent. Answer: (3) 5\/8."} {"t":"s","id":14836,"s":"If he gave away 3\/5, then 2\/5 was left = 20 sweets. So 1\/5 = 10 sweets and the total = 50 sweets. He gave away 3\/5 = 30 sweets, shared equally among 5 friends: 30 div 5 = 6 each. Answer: (3) 6."} {"t":"s","id":14839,"s":"Twelve thousand = 12 000, sixty-one = 61. Together: 12 000 + 61 = 12061."} {"t":"s","id":14842,"s":"Compare the hundreds digit first: 531 and 513 start with 5, 153 and 135 start with 1. So 531 > 513 > 153 > 135. Greatest to smallest: 531, 513, 153, 135."} {"t":"s","id":14848,"s":"Convert to quarters: 1 = 4\/4, 1\/2 = 2\/4. So 4\/4 - 1\/4 - 2\/4 = 1\/4."} {"t":"s","id":14850,"s":"John ran 1\/3 km more than Xiao Ming: 3\/4 + 1\/3 = 9\/12 + 4\/12 = 13\/12 km. Total = Xiao Ming + John = 3\/4 + 13\/12 = 9\/12 + 13\/12 = 22\/12 = 1 10\/12 = 1 5\/6 km."} {"t":"s","id":14852,"s":"Let the number be the unit. 4 units minus 1\/2 unit = 49. That is 3 1\/2 units = 49, so 7\/2 units = 49, giving 1 unit = 49 x 2 div 7 = 14. The number is 14."} {"t":"s","id":14857,"s":"2 oranges = 3 apples, so 4 oranges = 6 apples. Then 4 oranges + 4 apples = 6 apples + 4 apples = 10 apples = $15. So 1 apple = $15 div 10 = $1.50, and 5 apples = 5 x $1.50 = $7.50."} {"t":"s","id":14858,"s":"Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. Adding 3 must give a multiple of 4 greater than 10. Testing: 9 + 3 = 12, which is a multiple of 4 greater than 10. So the number is 9."} {"t":"s","id":14860,"s":"Lace used = 3.59 + 1.25 = 4.84 m. Remaining = 10 - 4.84 = 5.16 m. Cut into two equal pieces: 5.16 div 2 = 2.58 m each."} {"t":"s","id":14861,"s":"(a) From 07 59 to 13 00: 07 59 to 08 00 is 1 min, then 08 00 to 13 00 is 5 h. Total = 5 h 1 min. (b) Total travel time = 40 min + 25 min = 65 min = 1 h 5 min. Working back from 2.15 p.m.: 2.15 p.m. - 1 h 5 min = 1.10 p.m."} {"t":"s","id":14862,"s":"Bag B = 1740 - 500 = 1240 buttons. Bag C = 1240 div 2 = 620 buttons. Total = 1740 + 1240 + 620 = 3600 buttons."} {"t":"s","id":14864,"s":"Blue + white = 541 + 459 = 1000 cubes, which is the non-yellow part. Since 5\/9 are yellow, 4\/9 are not yellow = 1000, so 1\/9 = 250 and total = 2250. Yellow = 5\/9 x 2250 = 1250. More yellow than white = 1250 - 459 = 791."} {"t":"s","id":14867,"s":"Difference between ropes stays the same: 2322 - 1065 = 1257 cm. After cutting, X = 4 times Y, so the difference equals 3 units of Y's remaining length: 3 units = 1257, so 1 unit = 419 cm = remaining Rope Y. Length cut = 1065 - 419 = 646 cm = 6 m 46 cm."} {"t":"s","id":15017,"s":"In 15 093, the digit 5 is in the thousands place. Place value = 5 \u00d7 1000 = 5000."} {"t":"s","id":15018,"s":"All share 70 thousands. Compare the last three digits: 135 < 153 < 315 < 351. Increasing order: 70 135, 70 153, 70 315, 70 351."} {"t":"s","id":15019,"s":"Look at the tens digit (5). Since 5 \u2265 5, round the hundreds up: 78 253 \u2248 78 300."} {"t":"s","id":15020,"s":"Factors of 81 are 1, 3, 9, 27, 81. 81 \u00f7 8 leaves a remainder, so 8 is not a factor."} {"t":"s","id":15021,"s":"Each term decreases by 100: 51 170, 51 070, 50 970, 50 870, ... So 50 870 - 100 = 50 770."} {"t":"s","id":15022,"s":"Find the lowest common multiple of 6 and 8. Multiples of 6: 6, 12, 18, 24, ...; multiples of 8: 8, 16, 24, ... The first common multiple is 24, so the 24th child gets both."} {"t":"s","id":15023,"s":"Game sets given out = 24 \u00d7 20 = 480. Add the 10 left over: 480 + 10 = 490."} {"t":"s","id":15024,"s":"A multiple of 9 plus 7 between 47 and 60: 45 + 7 = 52. Check: 52 \u00f7 9 = 5 remainder 7. The number is 52."} {"t":"s","id":15025,"s":"Divide the total equally: 5350 \u00f7 5 = 1070. Each centre received 1070 masks."} {"t":"s","id":15026,"s":"Numbers that leave remainder 1 when divided by 3: 1, 4, 7, 10, 13, 16, 19, ... Numbers that leave remainder 5 when divided by 7: 12, 19, 26, ... The common number under 30 is 19. Max has 19 erasers."} {"t":"s","id":15027,"s":"Let Ben = 1 unit, Adam = 3 units. Ben + Adam = 4 units = 5780, so 1 unit = 5780 \u00f7 4 = 1445. Adam = 3 \u00d7 1445 = 4335. Caleb = 4335 + 1200 = 5535."} {"t":"s","id":15110,"s":"(a) \\(3\\dfrac{5}{6}=\\dfrac{3\\times 6+5}{6}=\\dfrac{23}{6}\\).
(b) Convert to compare: \\(\\dfrac{1}{3}\\approx 0.33\\), \\(\\dfrac{3}{5}=0.6\\), \\(\\dfrac{3}{7}\\approx 0.43\\). Decreasing order: \\(\\dfrac{3}{5}\\), \\(\\dfrac{3}{7}\\), \\(\\dfrac{1}{3}\\)."} {"t":"s","id":15114,"s":"The 42 balls fill \\(\\dfrac{3}{7}-\\dfrac{1}{7}=\\dfrac{2}{7}\\) of the box, so 2 units = 42 balls and 1 unit = 42 \u00f7 2 = 21 balls. The box is now \\(\\dfrac{3}{7}\\) filled, leaving \\(\\dfrac{4}{7}\\) empty (7 \u2212 3 = 4 units). Balls needed = 4 \u00d7 21 = 84."} {"t":"s","id":15115,"s":"The students scoring 50 and above = 12 + 10 + 13 = 35, which is \\(\\dfrac{5}{6}\\) of the class (since \\(\\dfrac{1}{6}\\) failed). So 5 units = 35 and 1 unit = 35 \u00f7 5 = 7. Total class = 6 \u00d7 7 = 42 students."} {"t":"s","id":15116,"s":"Let Ali = 1 unit. Bala = 3 units, Cathy = 2 units. Total = 1 + 3 + 2 = 6 units = $1500, so 1 unit = 1500 \u00f7 6 = $250 (Ali). Bala and Cathy together = 1500 \u2212 250 = $1250."} {"t":"s","id":15119,"s":"Food = \\(\\dfrac{1}{3}=\\dfrac{3}{9}\\) of her money; money left = \\(\\dfrac{2}{9}\\). So food + left = \\(\\dfrac{3}{9}+\\dfrac{2}{9}=\\dfrac{5}{9}\\), and the transport portion = \\(1-\\dfrac{5}{9}=\\dfrac{4}{9}\\) = $40. So 1 unit (\\(\\dfrac{1}{9}\\)) = 40 \u00f7 4 = $10. Food = \\(\\dfrac{3}{9}\\) = 3 \u00d7 $10 = $30."} {"t":"s","id":15120,"s":"(a) Product means multiply: 345 \u00d7 68 = 23460.
(b) 1042 \u00f7 6 = 173 remainder 4 (since 173 \u00d7 6 = 1038, and 1042 \u2212 1038 = 4). Remainder = 4."} {"t":"s","id":15122,"s":"60 \u00f7 9 = 6 remainder 6, so \\(\\dfrac{60}{9}=6\\dfrac{6}{9}\\). Simplify \\(\\dfrac{6}{9}=\\dfrac{2}{3}\\). Answer = \\(6\\dfrac{2}{3}\\)."} {"t":"s","id":15124,"s":"\"More than 3 children\" means 4 children or 5 children. Families with 4 = 8, families with 5 = 3. Total = 8 + 3 = 11."} {"t":"s","id":15125,"s":"Let Asher = 1 unit. Jacob = 2 units. Caden = 3 \u00d7 Jacob = 6 units. Total = 1 + 2 + 6 = 9 units = $441. 1 unit = 441 \u00f7 9 = $49. Asher has $49."} {"t":"s","id":15127,"s":"Convert to twelfths: \\(1\\dfrac{1}{3}=\\dfrac{16}{12}\\), \\(\\dfrac{5}{6}=\\dfrac{10}{12}\\), \\(\\dfrac{3}{4}=\\dfrac{9}{12}\\), \\(\\dfrac{13}{12}=\\dfrac{13}{12}\\). Order: \\(\\dfrac{9}{12}<\\dfrac{10}{12}<\\dfrac{13}{12}<\\dfrac{16}{12}\\), i.e. \\(\\dfrac{3}{4},\\dfrac{5}{6},\\dfrac{13}{12},1\\dfrac{1}{3}\\)."} {"t":"s","id":15128,"s":"After John gives 25 cards, the difference between them becomes 376 \u2212 25 \u2212 25 = 326 cards. Since John then has twice as many as Alex, John = 2 units and Alex = 1 unit, so the difference of 1 unit = Alex's amount = 326. Alex had 326 cards in the end."} {"t":"s","id":15129,"s":"She gave away \\(\\dfrac{7}{8}\\), so \\(\\dfrac{1}{8}\\) is left = 36 tarts. Total = \\(\\dfrac{8}{8}\\) = 36 \u00d7 8 = 288 pineapple tarts."} {"t":"s","id":15132,"s":"Let brown = 1 unit. Blue = 1 unit + 360. Orange = blue = 1 unit + 360. Total = 3 units + 720 = 1455. So 3 units = 1455 \u2212 720 = 735, and 1 unit = 735 \u00f7 3 = 245. Brown buttons = 245."} {"t":"s","id":15133,"s":"The first 13 rows have 28 chairs each: 28 \u00d7 13 = 364. The last row has 20 chairs. Total = 364 + 20 = 384 chairs."} {"t":"s","id":15134,"s":"(a) Fraction spent = \\(\\dfrac{1}{3}+\\dfrac{5}{12}=\\dfrac{4}{12}+\\dfrac{5}{12}=\\dfrac{9}{12}\\). Fraction saved = \\(1-\\dfrac{9}{12}=\\dfrac{3}{12}=\\dfrac{1}{4}\\).
(b) Savings of \\(\\dfrac{1}{4}\\) = $798, so total salary = 798 \u00d7 4 = $3192."} {"t":"s","id":15215,"s":"Decreasing order = largest to smallest. Compare the numbers: 61 792 > 61 279 > 60 927 > 60 729. This matches option (3)."} {"t":"s","id":15216,"s":"A multiple of 8 is divisible by 8. 56 = 8 \u00d7 7, so 56 is a multiple of 8. The others are not."} {"t":"s","id":15218,"s":"76 thousands = 76 000; 25 hundreds = 2 500; 4 tens = 40. Total = 76 000 + 2 500 + 40 = 78 540. This matches option (4)."} {"t":"s","id":15219,"s":"Factors of 25: 1, 5, 25. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. Two consecutive years means last year's age and this year's age are consecutive. 5 (factor of 25) then 6 (factor of 24) works. So this year she is 6, and next year she will be 7. This matches option (1)."} {"t":"s","id":15220,"s":"The pattern increases by 30 each time (20 910 - 20 880 = 30). Missing number = 20 910 + 30 = 20 940."} {"t":"s","id":15221,"s":"Factors of 18: 1, 2, 3, 6, 9, 18. Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42. Common factors = 1, 2, 3, 6."} {"t":"s","id":15223,"s":"To round up to 87 000 to the nearest 1000, the smallest number must round up from the 86 000s. The smallest is 86 500 (the half-way point rounds up)."} {"t":"s","id":15224,"s":"Giving 7 instead of 6 to each cousin uses 1 more tart per cousin. The change is from 2 left over to 6 short, a difference of 2 + 6 = 8 tarts. So there are 8 cousins (8 extra tarts needed, 1 per cousin)."} {"t":"s","id":15226,"s":"Let Xenia have 1 unit and Yasmin 2 units at first. After Yasmin gives 26: Yasmin = 2u - 26, Xenia = 1u + 26. Difference = (2u - 26) - (1u + 26) = u - 52 = 40, so u = 92 (Xenia at first). Yasmin at first = 2 \u00d7 92 = 184."} {"t":"s","id":15227,"s":"Let Cathy = 1 unit. Janice = 2 units. Alicia = 3 \u00d7 Janice = 6 units. Alicia - Janice = 6u - 2u = 4u = 72, so 1 unit = 18. Cathy = 18, Janice = 36, Alicia = 108. Alicia - Cathy = 108 - 18 = 90."} {"t":"s","id":15229,"s":"Convert the mixed number to an improper fraction with denominator 8: \\(3\\dfrac{7}{8} = \\dfrac{3\\times8 + 7}{8} = \\dfrac{31}{8}\\). So there are 31 eighths."} {"t":"s","id":15231,"s":"\\(\\dfrac{1}{2}\\) of 12 slices = 6 slices to the neighbour. Daughter got 4 slices. Slices given away = 6 + 4 = 10. Slices left = 12 \u2212 10 = 2."} {"t":"s","id":15232,"s":"Packet B = \\(\\dfrac{3}{4} - \\dfrac{1}{3} = \\dfrac{9}{12} - \\dfrac{4}{12} = \\dfrac{5}{12}\\) kg. Total = \\(\\dfrac{3}{4} + \\dfrac{5}{12} = \\dfrac{9}{12} + \\dfrac{5}{12} = \\dfrac{14}{12} = 1\\dfrac{2}{12} = 1\\dfrac{1}{6}\\) kg."} {"t":"s","id":15233,"s":"Compare values: \\(\\dfrac{5}{6} \\approx 0.83\\), \\(2\\dfrac{1}{4} = 2.25\\), \\(\\dfrac{7}{3} \\approx 2.33\\). Increasing order: \\(\\dfrac{5}{6}\\), \\(2\\dfrac{1}{4}\\), \\(\\dfrac{7}{3}\\)."} {"t":"s","id":15234,"s":"\\(\\dfrac{4}{5} = \\dfrac{8}{10}\\). Sum = \\(\\dfrac{9}{10} + \\dfrac{8}{10} = \\dfrac{17}{10} = 1\\dfrac{7}{10}\\)."} {"t":"s","id":15236,"s":"She used \\(\\dfrac{1}{8}\\), so \\(\\dfrac{7}{8}\\) of the sugar = 560 g. 1 unit (\\(\\dfrac{1}{8}\\)) = 560 \u00f7 7 = 80 g. Total (8 units) = 80 \u00d7 8 = 640 g."} {"t":"s","id":15238,"s":"(Annie + Betty) + (Betty + Cathy) = \\(\\dfrac{1}{2} + \\dfrac{3}{4} = \\dfrac{2}{4} + \\dfrac{3}{4} = \\dfrac{5}{4}\\) m. This counts Betty twice plus Annie + Betty + Cathy. So Betty = \\(\\dfrac{5}{4} - \\dfrac{4}{5} = \\dfrac{25}{20} - \\dfrac{16}{20} = \\dfrac{9}{20}\\) m."} {"t":"s","id":15239,"s":"(a) Total used = \\(\\dfrac{1}{6} + \\dfrac{1}{4} = \\dfrac{2}{12} + \\dfrac{3}{12} = \\dfrac{5}{12}\\) \u2113. (b) Water left = \\(4 - \\dfrac{5}{12} = 3\\dfrac{12}{12} - \\dfrac{5}{12} = 3\\dfrac{7}{12}\\) \u2113."} {"t":"s","id":15287,"s":"To round 235 189 to the nearest hundred, look at the tens digit (8). Since 8 \u2265 5, round up: 235 189 \u2248 235 200."} {"t":"s","id":15288,"s":"Factors of 45: 1, 3, 5, 9, 15, 45. Factors of 63: 1, 3, 7, 9, 21, 63. Common factors: 1, 3, 9. So 3 and 9 are common factors."} {"t":"s","id":15289,"s":"Order from greatest to smallest: 59 843 > 59 348 > 58 349. Compare ten-thousands\/thousands then hundreds. Option 4 is correct."} {"t":"s","id":15290,"s":"Doughnuts in boxes = 12 \u00d7 6 = 72. Add the 3 left unpacked: 72 + 3 = 75."} {"t":"s","id":15291,"s":"Expand 93 708 = 90 000 + 3000 + 700 + 8. The missing number is the hundreds part, 700."} {"t":"s","id":15292,"s":"Numbers from 90 500 to 91 499 round to 91 000 to the nearest 1000. The greatest such whole number is 91 499."} {"t":"s","id":15293,"s":"Multiples of 3: 3, 6, 9, 12, 15, 18, ... Multiples of 9: 9, 18, 27, ... The first two common multiples are 9 and 18."} {"t":"s","id":15294,"s":"The pattern alternates +1000 then \u221210: 2830 (+1000) 3830 (\u221210) 3820 (+1000) 4820 (\u221210) 4810 (+1000) 5810 (\u221210) 5800. Next: +1000 \u2192 6800, then \u221210 \u2192 6790."} {"t":"s","id":15295,"s":"The number of bags must divide both 48 and 60 with no remainder, so it is a common factor of 48 and 60. To make the red pens per bag smallest, use the largest number of bags = HCF(48, 60) = 12. Red pens per bag = 48 \u00f7 12 = 4."} {"t":"q","id":21919,"q":"Andy listed the factors of 32. 1 , 2 , 8 , 32 He missed out two factors. What were the two missing factors? and ","e":"All factors of 32 are 1, 2, 4, 8, 16, 32. Andy listed 1, 2, 8, 32, so the missing factors are 4 and 16."} {"t":"q","id":21920,"q":"Jenny has $7500. James has $6850. How much must Jenny give to James so that both of them have the same amount of money?
Answer: ","e":"Difference = $7500 \u2212 $6850 = $650. Jenny gives half the difference so they are equal: $650 \u00f7 2 = $325."} {"t":"q","id":21921,"q":"Ada, Ben and Chris had 720 stickers altogether. Ben had twice as many stickers as Ada, Chris had 40 stickers less than Ada. How many stickers did Ben have?
Answer: ","e":"Let Ada = 1 unit. Ben = 2 units, Chris = 1 unit \u2212 40. Total = 4 units \u2212 40 = 720, so 4 units = 760 and 1 unit = 190. Ben = 2 units = 380."} {"t":"q","id":21922,"q":"Mr Lim bought 5 identical T-shirts and a pair of pants. He paid $120 for the 5 T-shirts. The pair of pants cost 3 times as much as one T-shirt.
(a) How much did one T-shirt cost?
(b) How much did the pair of pants cost?
(a)   (b) ","e":"(a) One T-shirt = $120 \u00f7 5 = $24. (b) The pants cost 3 times one T-shirt = 3 \u00d7 $24 = $72."} {"t":"q","id":22290,"q":"50 000 + 900 + 8 =","e":"Add by place value: 50 000 + 900 + 8 = 50 908. There are 5 ten-thousands, 0 thousands, 9 hundreds, 0 tens and 8 ones. Answer: 50 908."} {"t":"q","id":22291,"q":"Arrange the following numbers from the greatest to the smallest.
9605, 9065, 9506","e":"Compare from the largest place value. All have 9 thousands. Hundreds: 9605 and 9506 have 6 and 5 hundreds; 9065 has 0 hundreds. So 9605 > 9506 > 9065. Greatest to smallest: 9605, 9506, 9065. Answer: option 4."} {"t":"q","id":22292,"q":"Complete the number pattern.
5934, 5634, 5624, 5324, , 5014, 5004","e":"The pattern alternates subtracting 300 then 10: 5934 -300 = 5634, -10 = 5624, -300 = 5324, -10 = 5314, -300 = 5014, -10 = 5004. The missing term is 5314. Answer: option 2."} {"t":"q","id":22293,"q":"3 and 4 are factors of .","e":"A number with both 3 and 4 as factors must be a multiple of 12. Check: 15 (no), 18 (4 is not a factor), 20 (3 is not a factor), 24 = 3 x 8 = 4 x 6. So 24 has both 3 and 4 as factors. Answer: option 4."} {"t":"q","id":22294,"q":"a) Write seventy-eight thousand and twenty in numerals.
b) Round 39 500 to the nearest thousand.
(a)   (b) ","e":"a) Seventy-eight thousand and twenty = 78 000 + 20 = 78 020. b) 39 500 is exactly halfway between 39 000 and 40 000; rounding to the nearest thousand rounds the half up to 40 000."} {"t":"q","id":22295,"q":"Find the product of 8540 and 7.
Answer: ","e":"Product means multiply: 8540 x 7. 8000 x 7 = 56 000; 500 x 7 = 3500; 40 x 7 = 280. Sum: 56 000 + 3500 + 280 = 59 780."} {"t":"q","id":22296,"q":"Ben packed 853 books in boxes of 9. How many books were left unpacked?
Answer: ","e":"Divide 853 by 9 and find the remainder. 9 x 94 = 846, and 853 - 846 = 7. So 94 full boxes are packed and 7 books are left unpacked. Answer: 7 books."} {"t":"q","id":22298,"q":"Andy had $450 more than Betty. Betty gave $35 to Andy. How much more did Andy have than Betty in the end?
Answer: ","e":"When Betty gives $35 to Andy, Andy gains $35 and Betty loses $35, so the gap between them widens by 2 x $35 = $70. New difference = $450 + $70 = $520. Answer: $520."} {"t":"q","id":22299,"q":"At a bookshop, pens are sold in boxes of 6 and pencils are sold in boxes of 8. Miss Nurul bought an equal number of pens and pencils for her class. Find the least total number of pens and pencils Miss Nurul bought.
Answer: ","e":"For an equal number of pens and pencils, the count must be a common multiple of 6 and 8. The least common multiple of 6 and 8 is 24, so the least number of pens is 24 and the least number of pencils is 24. Total = 24 + 24 = 48."} {"t":"q","id":22300,"q":"A fruit seller had 4 times as many durians as watermelons. After he sold 114 durians, he had as many watermelons as durians left. How many fruits did the fruit seller have left in the end?
Answer: ","e":"Let watermelons = 1 unit, durians = 4 units. After selling 114 durians, durians left = watermelons = 1 unit, so 114 durians = 4 units - 1 unit = 3 units. 1 unit = 114 \/ 3 = 38. Watermelons = 38 and durians left = 38, so fruits left = 38 + 38 = 76."} {"t":"q","id":22302,"q":"A school bag costs $60 more than a water bottle. 3 similar school bags and 2 similar water bottles cost $280. How much does each water bottle cost?
Answer: ","e":"Each bag = bottle + $60. So 3 bags = 3 bottles + 3 x $60 = 3 bottles + $180. Then 3 bags + 2 bottles = 5 bottles + $180 = $280. So 5 bottles = $280 - $180 = $100, and 1 bottle = $100 \/ 5 = $20."} {"t":"q","id":22303,"q":"Tammy has 35 $2 and $5 notes. The total value of the notes is $118. How many $5 notes does she have?
Answer: ","e":"Assume all 35 notes are $2: value = 35 x $2 = $70. The actual total is $118, which is $48 more. Each $2 note swapped for a $5 note adds $3. So number of $5 notes = $48 \/ $3 = 16."} {"t":"q","id":22385,"q":"Arrange the following numbers from the smallest to the largest.
3.5 , 3.05 , \\(3\\dfrac{1}{100}\\)
(smallest) , , ","e":"Write all as decimals: \\(3\\dfrac{1}{100} = 3.01\\), 3.05, 3.5. In order smallest to largest: 3.01, 3.05, 3.5, i.e. \\(3\\dfrac{1}{100}\\), 3.05, 3.5."} {"t":"q","id":22521,"q":"List all the common factors of 16 and 28.
(a)   (b)   (c) ","e":"Factors of 16: 1, 2, 4, 8, 16. Factors of 28: 1, 2, 4, 7, 14, 28. The factors common to both are 1, 2 and 4."} {"t":"q","id":22522,"q":"Find the product of 358 and 35.
Answer: ","e":"358 x 35 = 358 x 30 + 358 x 5 = 10 740 + 1 790 = 12 530."} {"t":"q","id":22523,"q":"Find the value of 6793 \u00f7 6
Answer: ","e":"6793 \u00f7 6: 6 \u00f7 6 = 1, 7 \u00f7 6 = 1 r 1, 19 \u00f7 6 = 3 r 1, 13 \u00f7 6 = 2 r 1. Quotient 1132 remainder 1, so 6793 \u00f7 6 = 1132 R1."} {"t":"q","id":22524,"q":"Express \\(\\dfrac{42}{8}\\) as a mixed number in its simplest form.","e":"42 \u00f7 8 = 5 remainder 2, so \\(\\dfrac{42}{8}=5\\dfrac{2}{8}\\). Simplify \\(\\dfrac{2}{8}=\\dfrac{1}{4}\\), giving \\(5\\dfrac{1}{4}\\)."} {"t":"q","id":22525,"q":"Compare the fractions. Use '<' or '>' to indicate which is greater or smaller.
\\(2\\dfrac{5}{8}\\) \\(\\dfrac{5}{2}\\)","e":"\\(\\dfrac{5}{2}=2\\dfrac{1}{2}=2\\dfrac{4}{8}\\). Compare with \\(2\\dfrac{5}{8}\\): the whole parts are equal and \\(\\dfrac{5}{8}>\\dfrac{4}{8}\\), so \\(2\\dfrac{5}{8}>\\dfrac{5}{2}\\)."} {"t":"q","id":22526,"q":"A stadium can seat 52 000 people when rounded to the nearest thousand. What is the greatest possible seating capacity of this stadium?
Answer: ","e":"Numbers from 51 500 to 52 499 round to 52 000. The greatest of these is 52 499."} {"t":"q","id":22527,"q":"I am thinking of a 3-digit number.
When rounded to the hundred, the number is 800.
The digit in the hundreds place is twice that in the tens place.
The sum of all the digits is 15.
What is this number?
Answer: ","e":"Rounds to 800, so the number is 750-849; the hundreds digit is 8, tens digit < 5. Hundreds = twice tens means tens = 4 (8 = 2 x 4). Digits sum to 15: 8 + 4 + ones = 15, so ones = 3. The number is 843."} {"t":"q","id":22528,"q":"James bought an equal number of red and blue marbles. He arranged the red marbles in groups of 5 and the blue marbles in groups of 3. What is the least possible number of red and blue marbles James bought altogether?
Answer: ","e":"The number of each colour must be a common multiple of 5 and 3. The least common multiple is 15, so there are 15 red and 15 blue marbles. Altogether 15 + 15 = 30 marbles."} {"t":"q","id":22529,"q":"Subtract \\(\\dfrac{2}{3}\\) from \\(\\dfrac{6}{7}\\).","e":"\\(\\dfrac{6}{7}-\\dfrac{2}{3}\\). Common denominator 21: \\(\\dfrac{6}{7}=\\dfrac{18}{21}\\) and \\(\\dfrac{2}{3}=\\dfrac{14}{21}\\). \\(\\dfrac{18}{21}-\\dfrac{14}{21}=\\dfrac{4}{21}\\)."} {"t":"q","id":22530,"q":"There were 141 sweets in a box. Melvin gave away \\(\\dfrac{2}{3}\\) of them to his friends and kept the rest. How many sweets did he give away?
Answer: ","e":"\\(\\dfrac{1}{3}\\) of 141 = 141 \u00f7 3 = 47. He gave away \\(\\dfrac{2}{3}\\), so 47 x 2 = 94 sweets."} {"t":"q","id":22531,"q":"A storybook and 2 notepads cost $46 altogether. The 2 notepads cost $10 less than the storybook. How much does 1 notepad cost?
Answer: ","e":"If the 2 notepads cost $10 less than the storybook, then 2 notepads + 2 notepads + $10 = $46. So 4 notepads = $46 - $10 = $36, and 1 notepad = $36 \u00f7 4 = $9."} {"t":"q","id":22533,"q":"Dan had thrice as many erasers as Elijah at first. After their parents gave them an equal number of erasers each, Dan had twice as many erasers as Elijah and they had a total of 84 erasers. How many erasers did Dan have at first?
Answer: ","e":"After receiving erasers, total 84 is split as Dan : Elijah = 2 : 1, i.e. 3 units = 84, so 1 unit = 84 \u00f7 6... working: 84 \u00f7 3 units gives Dan 56 and Elijah 28 after. The equal amount added is x, so Elijah-first = 28 - x and Dan-first = 56 - x = 3(28 - x). Solving: 56 - x = 84 - 3x, 2x = 28, x = 14. Dan at first = 56 - 14 = 42 erasers. (Key working: 84 \u00f7 6 = 14, 14 x 3 = 42.)"} {"t":"q","id":22534,"q":"Nicholas donated some of his savings to charity. He donated \\(\\dfrac{3}{8}\\) of it to Charity A and \\(\\dfrac{1}{4}\\) of it to Charity B. He then donated the rest of his savings equally among 4 other charities. If each of these 4 charities received $60, how much money did he donate to all 6 charities?
Answer: ","e":"The 4 other charities received 4 x $60 = $240, which is the rest of the savings. Fraction left = 1 - \\(\\dfrac{3}{8}\\) - \\(\\dfrac{1}{4}\\) = 1 - \\(\\dfrac{3}{8}\\) - \\(\\dfrac{2}{8}\\) = \\(\\dfrac{3}{8}\\). So \\(\\dfrac{3}{8}\\) of savings = $240, meaning \\(\\dfrac{1}{8}\\) = $80 and total savings = $80 x 8 = $640. All 6 charities together received the whole savings, $640."} {"t":"q","id":22606,"q":"Write the number:
Fifty thousand, eight hundred and three.","e":"Fifty thousand = 50 000, eight hundred = 800, three = 3. So the number is 50 000 + 800 + 3 = 50 803."} {"t":"q","id":22608,"q":"Complete the number pattern.
74 603, 73 603, , 71 603, 70 603, ","e":"Each number decreases by 1000. After 73 603 comes 73 603 - 1000 = 72 603. After 70 603 comes 70 603 - 1000 = 69 603."} {"t":"q","id":22609,"q":"Arrange the numbers in increasing order.
39 039, 40 390, 40 309, 39 309
, , , ","e":"Compare from the largest place value. 39 039 and 39 309 are in the 39-thousands; 39 039 < 39 309. 40 309 and 40 390 are in the 40-thousands; 40 309 < 40 390. Increasing order: 39 039, 39 309, 40 309, 40 390."} {"t":"q","id":22610,"q":"Round 74 945 to the nearest ten.
74 945 \u2248
Round 74 945 to the nearest hundred.
74 945 \u2248 ","e":"Nearest ten: the ones digit is 5, so round up the tens: 74 945 \u2248 74 950. Nearest hundred: the tens digit is 4 (less than 5), so round down: 74 945 \u2248 74 900."} {"t":"q","id":22613,"q":"A given number is a multiple of 7.
The number is between 50 and 60.
What is the number?
Answer: ","e":"Multiples of 7: 49, 56, 63, ... The only one between 50 and 60 is 56 (7 \u00d7 8 = 56)."} {"t":"q","id":22614,"q":"Arrange these fractions from the greatest to the smallest.
\\(\\dfrac{2}{3}\\), \\(\\dfrac{5}{6}\\), \\(\\dfrac{2}{5}\\)
, , ","e":"Convert to a common denominator of 30: \\(\\dfrac{2}{3}=\\dfrac{20}{30}\\), \\(\\dfrac{5}{6}=\\dfrac{25}{30}\\), \\(\\dfrac{2}{5}=\\dfrac{12}{30}\\). Greatest to smallest: \\(\\dfrac{25}{30}, \\dfrac{20}{30}, \\dfrac{12}{30}\\), i.e. \\(\\dfrac{5}{6}, \\dfrac{2}{3}, \\dfrac{2}{5}\\)."} {"t":"q","id":22615,"q":"Find the value of \\(\\dfrac{11}{12}-\\dfrac{1}{4}\\).
Give your answer in its simplest form.","e":"Make the denominators the same: \\(\\dfrac{1}{4}=\\dfrac{3}{12}\\). Then \\(\\dfrac{11}{12}-\\dfrac{3}{12}=\\dfrac{8}{12}\\). Simplify by dividing by 4: \\(\\dfrac{8}{12}=\\dfrac{2}{3}\\)."} {"t":"q","id":22616,"q":"A shop had 162 boxes of mangoes. Each box had 36 mangoes.
(a) How many mangoes were there?
(b) The shop sold 738 mangoes. The rest of the mangoes were packed into bags of 9. How many bags of mangoes were packed?
(a)
(b) ","e":"(a) Total mangoes = 162 \u00d7 36 = 5832. (b) Mangoes left after selling = 5832 - 738 = 5094. Bags = 5094 \u00f7 9 = 566."} {"t":"q","id":22617,"q":"Sam had some game cards at first. He gave 238 cards to his brother. Then he received 648 new cards from his father. Sam had 1330 cards in the end.
How many game cards did he have at first?
Answer: ","e":"Work backwards from the end. Before receiving 648: 1330 - 648 = 682. Before giving away 238: 682 + 238 = 920. So Sam had 920 cards at first."} {"t":"q","id":22618,"q":"School A has 3064 story books in its library. School B has 4 times as many books as School A.
(a) How many more story books does School B have than School A?
(b) How many story books must be moved from School B to School A so that there will be the same number of books in both schools?
(a)
(b) ","e":"School B = 3064 \u00d7 4 = 12 256 books. (a) More books in B than A = 12 256 - 3064 = 9192. (b) To make both equal, move half the difference: 9192 \u00f7 2 = 4596 books."} {"t":"q","id":22619,"q":"A green bulb blinks every 4 minutes, and a red bulb blinks every 6 minutes.
(a) How many times will the red bulb blink in 48 minutes?
(b) The two light bulbs blink together at 8.00 p.m. for the first time. At what time will the two bulbs blink together for the second time?
(a)
(b) ","e":"(a) The red bulb blinks every 6 minutes, so in 48 minutes it blinks 48 \u00f7 6 = 8 times. (b) The bulbs blink together at multiples of the LCM of 4 and 6, which is 12 minutes. After 8.00 p.m., the next time they blink together is 12 minutes later, at 8.12 p.m."} {"t":"q","id":22620,"q":"What is the value of the digit 7 in 38.479?","e":"In 38.479, the digit 7 is in the hundredths place. Its value is 7 hundredths = 0.07."} {"t":"q","id":22621,"q":"Arrange the following decimals in decreasing order.
6.49 , 6.049 , 6.409 , 6.904","e":"Compare place by place: 6.904 > 6.490 > 6.409 > 6.049. Decreasing order: 6.904, 6.49, 6.409, 6.049."} {"t":"q","id":22622,"q":"How many one-fifths are there in \\(1\\dfrac{3}{5}\\)?","e":"Convert \\(1\\dfrac{3}{5}\\) to an improper fraction: \\(1\\dfrac{3}{5}=\\dfrac{8}{5}\\). So there are 8 one-fifths."} {"t":"q","id":22623,"q":"Cindy bought \\(\\dfrac{5}{8}\\) kg of sugar. She bought \\(\\dfrac{1}{4}\\) kg more flour than sugar. How many kilograms of flour did Cindy buy?","e":"Flour = sugar + \\(\\dfrac{1}{4}\\) = \\(\\dfrac{5}{8}+\\dfrac{1}{4}=\\dfrac{5}{8}+\\dfrac{2}{8}=\\dfrac{7}{8}\\) kg."} {"t":"q","id":22624,"q":"10 + 8 + 0.7 + + 0.009 = 18.749
What is the missing number?","e":"Add the known parts: 10 + 8 + 0.7 + 0.009 = 18.709. Missing number = 18.749 - 18.709 = 0.04."} {"t":"q","id":22625,"q":"Round 13.592 to the nearest whole number.
Answer: ","e":"Look at the tenths digit (5). Since 5 \\(\\geq\\) 5, round up: 13.592 rounds to 14."} {"t":"q","id":22627,"q":"What is the sum of 21.73 and 4.98?
Answer: ","e":"21.73 + 4.98 = 26.71. Line up the decimal points and add: 73 + 98 hundredths = 171 hundredths (carry), giving 26.71."} {"t":"q","id":22628,"q":"Arrange the following fractions in ascending order.
\\(\\dfrac{4}{7}\\) , \\(\\dfrac{17}{12}\\) , \\(3\\dfrac{1}{2}\\) , \\(\\dfrac{1}{2}\\)
, , , ","e":"As decimals: \\(\\dfrac{4}{7}\\approx0.57\\), \\(\\dfrac{17}{12}\\approx1.42\\), \\(3\\dfrac{1}{2}=3.5\\), \\(\\dfrac{1}{2}=0.5\\). Ascending: \\(\\dfrac{1}{2}, \\dfrac{4}{7}, \\dfrac{17}{12}, 3\\dfrac{1}{2}\\)."} {"t":"q","id":22629,"q":"Ahmad had some stickers. He lost \\(\\dfrac{2}{5}\\) of the stickers and had 27 stickers left. How many stickers did Ahmad have at first?
Answer: ","e":"Stickers left = \\(1-\\dfrac{2}{5}=\\dfrac{3}{5}\\) of the total = 27. So \\(\\dfrac{1}{5}=27\\div3=9\\), and the total \\(=9\\times5=45\\) stickers."} {"t":"q","id":22630,"q":"Mrs Tan bought some juice. She drank \\(\\dfrac{5}{12}\\) \\(l\\) of juice and gave away \\(\\dfrac{1}{3}\\) \\(l\\) of it. She was left with \\(\\dfrac{7}{12}\\) \\(l\\) of juice.
(a) How many more litres of juice did she drink than she give away?
(b) How many litres of juice did Mrs Tan buy? Give your answer as a mixed number in simplest form.
(a)   (b) ","e":"(a) Drank - gave away = \\(\\dfrac{5}{12}-\\dfrac{1}{3}=\\dfrac{5}{12}-\\dfrac{4}{12}=\\dfrac{1}{12}\\) \\(l\\). (b) Total bought = drank + gave away + left = \\(\\dfrac{5}{12}+\\dfrac{4}{12}+\\dfrac{7}{12}=\\dfrac{16}{12}=1\\dfrac{4}{12}=1\\dfrac{1}{3}\\) \\(l\\)."} {"t":"q","id":22632,"q":"(a) Round 50 185 to the nearest ten.
(b) Round 38 273 to the nearest hundred.
(a)   (b) ","e":"(a) The ones digit of 50 185 is 5, so round up: 50 190.
(b) The tens digit of 38 273 is 7, so round the hundreds up: 38 300."} {"t":"q","id":22633,"q":"Write the missing numerator and denominator.
\\(\\dfrac{}{14}\\) = \\(\\dfrac{3}{7}\\) = \\(\\dfrac{9}{}\\)","e":"\\(\\dfrac{3}{7}\\): multiply numerator and denominator by 2 to get a denominator of 14, so the numerator is 6 (\\(\\dfrac{6}{14}\\)). For \\(\\dfrac{9}{[?]}\\), 9 = 3 x 3, so multiply 7 by 3 to get 21 (\\(\\dfrac{9}{21}\\))."} {"t":"q","id":22634,"q":"Find the value of \\(\\dfrac{2}{3}\\) - \\(\\dfrac{1}{6}\\)
Give your answer as a fraction in the simplest form.","e":"\\(\\dfrac{2}{3}\\) = \\(\\dfrac{4}{6}\\). \\(\\dfrac{4}{6}\\) - \\(\\dfrac{1}{6}\\) = \\(\\dfrac{3}{6}\\) = \\(\\dfrac{1}{2}\\)."} {"t":"q","id":22635,"q":"Find the missing number.
67 852, 67 952, , 68 152, 68 252, 68 352","e":"The sequence increases by 100 each time: 67 852, 67 952, 68 052, 68 152, ... So the missing number is 68 052."} {"t":"q","id":22636,"q":"Arrange the following fractions from the greatest to the smallest.
\\(\\dfrac{5}{12}\\) , \\(\\dfrac{2}{3}\\) , \\(\\dfrac{1}{2}\\)
(a)   (b)   (c) ","e":"Use a common denominator of 12: \\(\\dfrac{5}{12}\\), \\(\\dfrac{2}{3}\\) = \\(\\dfrac{8}{12}\\), \\(\\dfrac{1}{2}\\) = \\(\\dfrac{6}{12}\\). From greatest to smallest: \\(\\dfrac{8}{12}\\) > \\(\\dfrac{6}{12}\\) > \\(\\dfrac{5}{12}\\), i.e. \\(\\dfrac{2}{3}\\), \\(\\dfrac{1}{2}\\), \\(\\dfrac{5}{12}\\)."} {"t":"q","id":22637,"q":"Find the sum of all the common factors of 18 and 27.
Answer: ","e":"Factors of 18: 1, 2, 3, 6, 9, 18. Factors of 27: 1, 3, 9, 27. Common factors: 1, 3, 9. Sum = 1 + 3 + 9 = 13."} {"t":"q","id":22639,"q":"There were 1476 adults and children at a stadium. There were 874 adults and 28 more boys than girls. How many girls were at the stadium?
Answer: ","e":"Children = 1476 - 874 = 602. Boys + girls = 602 and boys = girls + 28, so 2 x girls = 602 - 28 = 574. Girls = 574 \/ 2 = 287."} {"t":"q","id":22640,"q":"Mrs Koh paid $285 for 1 bag and 5 purses. The bag cost $57 more than a purse. How much did she pay for each purse?
Answer: ","e":"Remove the bag's extra cost: 285 - 57 = 228, which is the cost of 6 purses (1 bag now equals 1 purse). Each purse = 228 \/ 6 = $38."} {"t":"q","id":22641,"q":"Mr Tan bought 5 chairs and 9 tables for his office. Each chair costs $354. He paid a total of $5874. How much did he pay in total for the tables?
Answer: ","e":"Cost of chairs = 354 x 5 = $1770. Cost of tables = 5874 - 1770 = $4104."} {"t":"q","id":22642,"q":"Sherry bought the same amount of flour and sugar at first. After using 720 g of flour and 320 g of sugar, she had 6 times as much sugar as flour left. Find the amount of flour that she bought.
Answer: ","e":"She used 720 - 320 = 400 g more flour than sugar, so the sugar left is 400 g more than the flour left. Since sugar left is 6 times the flour left, the 5 extra units = 400 g, so 1 unit (flour left) = 400 \/ 5 = 80 g. Original flour = flour left + flour used = 80 + 720 = 800 g."} {"t":"q","id":22644,"q":"\\(1-\\dfrac{2}{5}-\\dfrac{1}{6}\\) = ______","e":"Use a common denominator of 30: \\(1=\\dfrac{30}{30}\\), \\(\\dfrac{2}{5}=\\dfrac{12}{30}\\), \\(\\dfrac{1}{6}=\\dfrac{5}{30}\\). So \\(\\dfrac{30}{30}-\\dfrac{12}{30}-\\dfrac{5}{30}=\\dfrac{13}{30}\\)."} {"t":"q","id":22645,"q":"Ravi drank \\(\\dfrac{3}{4}\\) \\(\\ell\\) of water. His sister drank \\(\\dfrac{1}{5}\\) \\(\\ell\\) less water than he did. How much water did they drink altogether?","e":"Sister drank \\(\\dfrac{3}{4}-\\dfrac{1}{5}=\\dfrac{15}{20}-\\dfrac{4}{20}=\\dfrac{11}{20}\\) litre. Altogether: \\(\\dfrac{3}{4}+\\dfrac{11}{20}=\\dfrac{15}{20}+\\dfrac{11}{20}=\\dfrac{26}{20}=1\\dfrac{6}{20}=1\\dfrac{3}{10}\\) litre."} {"t":"q","id":22648,"q":"8974 \u00f7 8 = ","e":"8974 \u00f7 8: 8 into 89 is 11 r1; bring down 7 \u2192 17, 8 into 17 is 2 r1; bring down 4 \u2192 14, 8 into 14 is 1 r6. Quotient = 1121 remainder 6."} {"t":"q","id":22650,"q":"\\(1\\dfrac{5}{8}\\) = \\(\\dfrac{}{8}\\) What is the missing value in the box?","e":"Convert the mixed number to an improper fraction: \\(1\\dfrac{5}{8}=\\dfrac{1\\times8+5}{8}=\\dfrac{13}{8}\\). So the missing value is 13."} {"t":"q","id":22651,"q":"Arrange the fractions in decreasing order.
\\(\\dfrac{7}{3}\\) , \\(\\dfrac{11}{5}\\) , \\(2\\dfrac{2}{5}\\)
(a)   (b)   (c) ","e":"Convert to decimals\/like values: \\(\\dfrac{7}{3}\\approx2.33\\), \\(\\dfrac{11}{5}=2.2\\), \\(2\\dfrac{2}{5}=2.4\\). In decreasing order: \\(2\\dfrac{2}{5}\\), \\(\\dfrac{7}{3}\\), \\(\\dfrac{11}{5}\\)."} {"t":"q","id":22652,"q":"There are 56 flowers in a basket. \\(\\dfrac{2}{7}\\) of the flowers are roses. How many roses are there in the basket?
Answer: ","e":"7 units = 56, so 1 unit = 56 \u00f7 7 = 8. Roses = 2 units = 8 \u00d7 2 = 16."} {"t":"q","id":22655,"q":"Kenneth cycled home from school. After completing \\(\\dfrac{7}{10}\\) of the journey, he still needed to cycle another 480 m to reach home. What was the distance between Kenneth's home and his school?
Answer: ","e":"The remaining part of the journey is \\(1-\\dfrac{7}{10}=\\dfrac{3}{10}\\), which equals 480 m. So 3 units = 480 m, 1 unit = 480 \u00f7 3 = 160 m. Whole journey = 10 units = 160 \u00d7 10 = 1600 m."} {"t":"q","id":22656,"q":"Denise, Emily and Fred scored a total of 4490 points in a game. Denise scored 3 times as many points as Emily. Fred scored 550 points less than Denise. How many points did Fred score?
Answer: ","e":"Let Emily = 1 unit, then Denise = 3 units, Fred = 3 units \u2212 550. Total: 1u + 3u + 3u \u2212 550 = 4490, so 7u = 4490 + 550 = 5040, 1u = 5040 \u00f7 7 = 720. Denise = 3 \u00d7 720 = 2160. Fred = 2160 \u2212 550 = 1610."} {"t":"q","id":22657,"q":"Arthur and Ben had the same number of stickers at first. After Arthur gave 72 stickers to Caleb, Ben had 4 times as many stickers as Arthur.
(a) How many stickers did Arthur have left?
(b) Caleb gave \\(\\dfrac{4}{9}\\) of the stickers he received from Arthur to his friends and kept the rest. How many stickers did Caleb keep for himself?
(a)   (b) ","e":"(a) Arthur and Ben started equal. After Arthur gives away 72, Ben = 4 \u00d7 Arthur. The 72 stickers Arthur lost make Ben's amount the extra; the difference 72 equals 3 of Arthur's remaining units, so 3 units = 72, 1 unit = 24. Arthur had 24 stickers left. (b) Caleb received 72 stickers. He gave \\(\\dfrac{4}{9}\\) away and kept \\(\\dfrac{5}{9}\\): 1 unit = 72 \u00f7 9 = 8, kept = 5 units = 8 \u00d7 5 = 40 stickers."} {"t":"q","id":22658,"q":"9 tens 4 tenths 7 thousandths =","e":"9 tens = 90, 4 tenths = 0.4, 7 thousandths = 0.007. Sum = 90 + 0.4 + 0.007 = 90.407."} {"t":"q","id":22661,"q":"Express \\(4\\dfrac{7}{20}\\) as a decimal.
Answer: ","e":"\\(\\dfrac{7}{20}=\\dfrac{35}{100}=0.35\\). So \\(4\\dfrac{7}{20}=4+0.35=4.35\\)."} {"t":"q","id":22663,"q":"Round 43.26 to the nearest tenth.
Answer: ","e":"The tenths digit is 2 and the hundredths digit is 6. Since 6 \u2265 5, round the tenths digit up: 43.26 \u2192 43.3."} {"t":"q","id":22665,"q":"Divide 16 by 7. Give your answer correct to 2 decimal places.
Answer: ","e":"16 \u00f7 7 = 2.2857... To 2 decimal places, look at the 3rd decimal (5), round up: 2.29."} {"t":"q","id":22666,"q":"Arrange these numbers from the greatest to the smallest.
\\(\\dfrac{2}{5}\\) , 0.403 , 0.043
(a)   (b)   (c) ","e":"Convert \\(\\dfrac{2}{5}=0.4\\). Compare 0.403, 0.4, 0.043. Greatest to smallest: 0.403, \\(\\dfrac{2}{5}\\) (0.4), 0.043."} {"t":"q","id":22669,"q":"Megan receives a total of $30 of pocket money for 5 days. Each day, she spends $2.70 on transport, part of the remaining money on food and saves the rest.
(a) How much does Megan spend on transport in 5 days?
(b) Last week, Megan saved $1.80. How much did she spend on food?
(a)   (b) ","e":"(a) Transport in 5 days = $2.70 \u00d7 5 = $13.50. (b) Money left after transport = $30 \u2212 $13.50 = $16.50. Food = remaining \u2212 savings = $16.50 \u2212 $1.80 = $14.70."} {"t":"q","id":22670,"q":"Ken bought 5 kg of sugar. He used 0.32 kg of sugar to make a cake and packed the remaining sugar equally into 6 packets. What was the mass of each packet of sugar?
Answer: ","e":"Remaining sugar = 5 \u2212 0.32 = 4.68 kg. Each packet = 4.68 \u00f7 6 = 0.78 kg."} {"t":"q","id":22671,"q":"Bag A contains 26.5 kg more peanuts than Bag B. After 4.55 kg of peanuts were removed from Bag B and placed into Bag A, the mass of Bag A was five times the mass of Bag B. What was the mass of peanuts in Bag B at first?
Answer: ","e":"After moving 4.55 kg, the difference between the bags becomes 26.5 + 2 \u00d7 4.55 = 35.6 kg. Bag A is now 5 times Bag B, so the difference is 4 units = 35.6 kg, giving 1 unit (Bag B now) = 35.6 \u00f7 4 = 8.90 kg. Bag B at first = 8.90 + 4.55 = 13.45 kg."} {"t":"q","id":22672,"q":"Which of the following is thirteen thousand, eight hundred and fifty in numerals?","e":"Thirteen thousand = 13 000, eight hundred = 800, fifty = 50. 13 000 + 800 + 50 = 13 850."} {"t":"q","id":22673,"q":"Arrange the following numbers from the smallest to the greatest.
47 209, 46 327, 46 825","e":"Compare from the highest place value. Ten-thousands all 4; thousands: 46 327 and 46 825 have 6, 47 209 has 7, so 47 209 is largest. Between 46 327 and 46 825, hundreds 3 < 8, so 46 327 < 46 825. Smallest to greatest: 46 327, 46 825, 47 209."} {"t":"q","id":22674,"q":"In the following number pattern, what is the missing number?
12 878, 12 978, 13 978, 14 078, 15 078, , 16 178, 16 278","e":"The pattern alternates +100 then +1000: 12 878 (+100) 12 978 (+1000) 13 978 (+100) 14 078 (+1000) 15 078 (+100) 15 178 (+1000) 16 178 (+100) 16 278. The missing number is 15 078 + 100 = 15 178."} {"t":"q","id":22675,"q":"Round 39 565 to the nearest thousand.","e":"The hundreds digit is 5, so round up. 39 565 rounds up to 40 000 to the nearest thousand."} {"t":"q","id":22676,"q":"3 and 4 are factors of .","e":"A number with both 3 and 4 as factors must be divisible by both. 24 = 3 \u00d7 8 = 4 \u00d7 6, so both 3 and 4 divide 24. (15 not divisible by 4; 32 not by 3; 38 not by 3 or 4.)"} {"t":"q","id":22677,"q":"Which of the following number is a common multiple of 6 and 9?","e":"A common multiple of 6 and 9 must be in both times tables. 36 = 6 \u00d7 6 = 9 \u00d7 4, so 36 is a multiple of both. (16 is neither; 42 = 6\u00d77 but not a multiple of 9; 63 = 9\u00d77 but not a multiple of 6.)"} {"t":"q","id":22678,"q":"Mary had 3986 erasers. She gave 2013 erasers to her brother and 750 erasers to her sister. How many erasers had she left?
Answer: ","e":"Erasers given away: 3986 - 2013 = 1973. Then 1973 - 750 = 1223. Mary had 1223 erasers left."} {"t":"q","id":22679,"q":"Mr Ahmad spends $346 each month. He spends the same amount of money each month. How much money does he spend in seven months?
Answer: ","e":"Multiply the monthly amount by the number of months: 346 \u00d7 7 = 2422. He spends $2422 in seven months."} {"t":"q","id":22680,"q":"(a) Find the value of 1028 \u00f7 4
(b) Find the product of 45 and 12
(a)   (b) ","e":"(a) 1028 \u00f7 4 = 257. (b) Product means multiply: 45 \u00d7 12 = 540."} {"t":"q","id":22681,"q":"The sum of two numbers is 7293. The greater number is 5485. What is the smaller number?
Answer: ","e":"Smaller number = total - greater number = 7293 - 5485 = 1808."} {"t":"q","id":22682,"q":"30 012 people visited an exhibition. 22 800 of them were adults and the rest were children.
(a) How many children visited the exhibition?
(b) 10 740 women visited the exhibition. How many children and women visited the exhibition?
(a)   (b) ","e":"(a) Children = total - adults = 30 012 - 22 800 = 7212. (b) Children and women = 7212 + 10 740 = 17 952."} {"t":"q","id":22683,"q":"Shop A had 126 boxes of oranges. There were 36 oranges in each box. The shop owner packed the oranges into bags of 8. How many bags of 8 oranges were there?
Answer: ","e":"Total oranges = 126 \u00d7 36 = 4536. Number of bags = 4536 \u00f7 8 = 567. There were 567 bags."} {"t":"q","id":22684,"q":"A watch costs four times as much as a bag. Mr Tan paid $728 for a watch and three bags. How much did the watch cost?
Answer: ","e":"Let 1 bag be 1 unit. Watch = 4 units. Watch + 3 bags = 4 + 3 = 7 units = $728. So 1 unit (1 bag) = 728 \u00f7 7 = $104. Watch = 4 \u00d7 104 = $416."} {"t":"q","id":22686,"q":"Arrange the fractions in increasing order.
\\(1\\dfrac{5}{9}\\) , \\(\\dfrac{15}{7}\\) , \\(1\\dfrac{2}{3}\\)
, , ","e":"Method: convert to a comparable form. \\(1\\dfrac{5}{9}=\\dfrac{14}{9}\\approx1.56\\); \\(1\\dfrac{2}{3}=\\dfrac{5}{3}\\approx1.67\\); \\(\\dfrac{15}{7}\\approx2.14\\). In increasing order: \\(1\\dfrac{5}{9}\\) , \\(1\\dfrac{2}{3}\\) , \\(\\dfrac{15}{7}\\)."} {"t":"q","id":22687,"q":"Subtract \\(\\dfrac{3}{5}\\) from 7.","e":"Method: rename 7 as a fraction with denominator 5. \\(7=\\dfrac{35}{5}\\). Then \\(\\dfrac{35}{5}-\\dfrac{3}{5}=\\dfrac{32}{5}=6\\dfrac{2}{5}\\)."} {"t":"q","id":22691,"q":"Siti jogged \\(\\dfrac{4}{5}\\) km. She jogged \\(\\dfrac{3}{10}\\) km more than Tom. How far did Tom jog?","e":"Method: Tom jogged less than Siti, so subtract. \\(\\dfrac{4}{5}=\\dfrac{8}{10}\\). Tom = \\(\\dfrac{8}{10}-\\dfrac{3}{10}=\\dfrac{5}{10}=\\dfrac{1}{2}\\) km."} {"t":"q","id":22694,"q":"Mrs Tan sold some red and yellow roses. \\(\\dfrac{2}{9}\\) of the roses sold were red. The rest of the roses sold were yellow. 16 red roses were sold. How many yellow roses did Mrs Tan sell? ","e":"Method: \\(\\dfrac{2}{9}\\) of the roses are red = 16, so 1 unit (\\(\\dfrac{1}{9}\\)) = 16 \\(\\div\\) 2 = 8 roses. Yellow is the rest: \\(\\dfrac{9}{9}-\\dfrac{2}{9}=\\dfrac{7}{9}\\) = 7 units. Yellow roses = 8 \\(\\times\\) 7 = 56."} {"t":"q","id":22695,"q":"Jamie had 3 kg of flour. She used \\(\\dfrac{3}{10}\\) kg of flour to bake a cake and \\(\\dfrac{1}{4}\\) kg of flour to bake cookies.
a) What is the total mass of flour Jamie used?
b) What is the mass of flour left after baking the cake and cookies? (Express your answer as a mixed number.)
a) b) ","e":"a) Total used: \\(\\dfrac{3}{10}+\\dfrac{1}{4}=\\dfrac{6}{20}+\\dfrac{5}{20}=\\dfrac{11}{20}\\) kg. b) Flour left: \\(3-\\dfrac{11}{20}\\). Using the key's form, \\(3=\\dfrac{180}{60}\\) and \\(\\dfrac{11}{20}=\\dfrac{33}{60}\\), so \\(\\dfrac{180}{60}-\\dfrac{33}{60}=\\dfrac{147}{60}=2\\dfrac{27}{60}\\) kg (= \\(2\\dfrac{9}{20}\\) kg)."} {"t":"q","id":22696,"q":"Gopal spent \\(\\dfrac{2}{11}\\) of his money and saved the rest. He saved $749 more than the amount he spent. How much did he spend? ","e":"Method: spent = \\(\\dfrac{2}{11}\\) (2 units), saved = \\(\\dfrac{9}{11}\\) (9 units). Saved is $749 more than spent: 9 units - 2 units = 7 units = $749. So 1 unit = 749 \\(\\div\\) 7 = $107. Spent = 2 units = 2 \\(\\times\\) 107 = $214."} {"t":"q","id":22698,"q":"Round 47 832 to the nearest hundred.","e":"The digit in the tens place is 3 (less than 5), so we round down. 47 832 rounds to 47 800."} {"t":"q","id":22699,"q":"Which of the following is not a factor of 18 and 36?","e":"Factors of 18 are 1, 2, 3, 6, 9, 18. 12 is not a factor of 18 (it is a factor of 36 only), so 12 is not a common factor."} {"t":"q","id":22700,"q":"Which fraction is greater than \\(\\dfrac{1}{2}\\)?","e":"Compare each to \\(\\dfrac{1}{2}\\): \\(\\dfrac{2}{3}\\) = 0.67 > 0.5. The others (\\(\\dfrac{1}{3}\\), \\(\\dfrac{3}{7}\\), \\(\\dfrac{4}{9}\\)) are all less than \\(\\dfrac{1}{2}\\)."} {"t":"q","id":22702,"q":"Find the product of 3021 and 7.
Answer: ","e":"3021 \u00d7 7 = 21 147."} {"t":"q","id":22705,"q":"What is the missing number in the box?
\\(\\dfrac{3}{4}\\) = \\(\\dfrac{}{20}\\)","e":"To get from denominator 4 to 20, multiply by 5. So the numerator is 3 \u00d7 5 = 15. \\(\\dfrac{3}{4} = \\dfrac{15}{20}\\)."} {"t":"q","id":22706,"q":"Arrange the following fractions in decreasing order.
\\(\\dfrac{7}{4}\\), \\(\\dfrac{4}{3}\\), \\(1\\dfrac{5}{6}\\)
, , ","e":"Convert to twelfths: \\(\\dfrac{7}{4}=\\dfrac{21}{12}\\), \\(\\dfrac{4}{3}=\\dfrac{16}{12}\\), \\(1\\dfrac{5}{6}=\\dfrac{11}{6}=\\dfrac{22}{12}\\). Decreasing order: \\(1\\dfrac{5}{6}\\) (22\/12), \\(\\dfrac{7}{4}\\) (21\/12), \\(\\dfrac{4}{3}\\) (16\/12)."} {"t":"q","id":22707,"q":"Amelie and Devna had the same number of sweets at first. After Amelie gave 35 sweets to her friends and Devna bought 7 more sweets, Devna had four times as many sweets as Amelie. How many sweets did Amelie have at the end?
Answer: ","e":"Let the start amount be n. Amelie: n \u2212 35. Devna: n + 7 = 4(n \u2212 35). So n + 7 = 4n \u2212 140, giving 147 = 3n, n = 49. Amelie at the end = 49 \u2212 35 = 14. (Check: Devna = 49 + 7 = 56 = 4 \u00d7 14.)"} {"t":"q","id":22709,"q":"Class 4A and 4B borrowed a total of 152 books in the month of May. Class 4A borrowed thrice as many books as Class 4B. Class 4B borrowed twice as many books as Class 4C. How many books did Class 4B and 4C borrow?
Answer: ","e":"Let 4C = 1 unit. Then 4B = 2 units and 4A = 3 \u00d7 4B = 6 units. 4A + 4B = 6 + 2 = 8 units = 152, so 1 unit = 152 \u00f7 8 = 19. 4B = 2 \u00d7 19 = 38, 4C = 19. 4B + 4C = 38 + 19 = 57."} {"t":"q","id":22710,"q":"(a) The smallest factor of a number is 1. The biggest factor of the number is 18. List all the other factors of the number.
, , ,
(b) Wei Ming chose a number between 40 and 70. The number is a multiple of 7. When Janet added 2 to the number, it becomes a multiple of 5. What is the number that Wei Ming chose?
","e":"(a) The number is 18 (its largest factor). Factors of 18 are 1, 2, 3, 6, 9, 18; excluding 1 and 18 the others are 2, 3, 6, 9. (b) Multiples of 7 between 40 and 70: 42, 49, 56, 63. Adding 2 gives 44, 51, 58, 65; only 65 is a multiple of 5, so the number is 63."} {"t":"q","id":22712,"q":"Benny has 345 stamps. Caius has 126 stamps. How many stamps must Benny give to Caius so that Benny has 37 more stamps than Caius?
Answer: ","e":"Total stamps = 345 + 126 = 471 (unchanged when transferred). Current difference = 345 \u2212 126 = 219. We want Benny to have 37 more than Caius, so the difference must drop from 219 to 37, a reduction of 219 \u2212 37 = 182. Each stamp given reduces the gap by 2, so Benny gives 182 \u00f7 2 = 91 stamps."} {"t":"q","id":22713,"q":"Fifty-eight thousand and thirty-nine in numerals is ____________.","e":"Fifty-eight thousand = 58 000; thirty-nine = 39. So 58 000 + 39 = 58 039."} {"t":"q","id":22714,"q":"Which number when rounded to the nearest hundred becomes 72 000?","e":"Rounding to the nearest hundred gives 72 000 for any number from 71 950 to 72 049. 71 952 rounds to 72 000. (71 839 to 71 800; 72 050 to 72 100; 72 499 to 72 500.)"} {"t":"q","id":22715,"q":"Express \\(6\\dfrac{7}{20}\\) as a decimal.","e":"\\(\\dfrac{7}{20}=\\dfrac{35}{100}=0.35\\). So \\(6\\dfrac{7}{20}=6.35\\)."} {"t":"q","id":22716,"q":"In which of the following does the digit 5 stand for 5 tenths?","e":"5 tenths = 0.5, the first digit after the decimal point. In 27.53 the 5 is in the tenths place, so it stands for 5 tenths."} {"t":"q","id":22717,"q":"\\(\\dfrac{7}{12}+\\dfrac{1}{3}\\) = ____________","e":"\\(\\dfrac{1}{3}=\\dfrac{4}{12}\\). \\(\\dfrac{7}{12}+\\dfrac{4}{12}=\\dfrac{11}{12}\\)."} {"t":"q","id":22718,"q":"What is the missing number in the box?
\\(8\\dfrac{4}{9}=\\dfrac{?}{9}\\)","e":"\\(8\\dfrac{4}{9}=\\dfrac{8\\times9+4}{9}=\\dfrac{72+4}{9}=\\dfrac{76}{9}\\). Missing number = 76."} {"t":"q","id":22719,"q":"Noah had 6544 stamps. After giving away 408 stamps, he rearranged the remaining stamps equally into 8 albums. How many stamps were there in each album?","e":"Remaining = 6544 - 408 = 6136. Each album = 6136 \u00f7 8 = 767."} {"t":"q","id":22720,"q":"Which of the following is a common factor of 18 and 24?","e":"Factors of 18: 1,2,3,6,9,18. Factors of 24: 1,2,3,4,6,8,12,24. The common factor among the options is 6."} {"t":"q","id":22723,"q":"Mrs Tan has fewer than 60 lollipops. She can pack them into bags of 3 or 8 without any lollipops left over. How many lollipops does Mrs Tan have?","e":"The number must be a common multiple of 3 and 8, i.e. a multiple of 24, and fewer than 60. 48 is divisible by both 3 and 8 (48 = 3 x 16 = 8 x 6)."} {"t":"q","id":22724,"q":"The perimeter of the garden is 42 m. The breadth of the garden is 6 m. What is the length of the garden?","e":"Perimeter = 2 x (length + breadth). 42 = 2 x (length + 6), so length + 6 = 21, length = 15 m."} {"t":"q","id":22725,"q":"Which of the letter is a symmetrical figure?","e":"The letter T has a vertical line of symmetry (left and right halves are mirror images). F, N and S have no line of symmetry."} {"t":"q","id":22729,"q":"Write the missing number in the number pattern.
34 456 , 34 756 , , 35 356 , 35 656","e":"The pattern increases by 300 each time: 34 456, 34 756, 35 056, 35 356, 35 656. Missing = 34 756 + 300 = 35 056."} {"t":"q","id":22731,"q":"Find the product of 658 and 39.
Answer: ","e":"658 x 39 = 658 x 40 - 658 = 26 320 - 658 = 25 662."} {"t":"q","id":22732,"q":"A number is 2900 when rounded off to the nearest ten. What is the smallest possible number?
Answer: ","e":"Numbers from 2895 to 2904 round to 2900 to the nearest ten. The smallest is 2895."} {"t":"q","id":22737,"q":"Mary poured \\(\\dfrac{1}{3}\\) \\(l\\) of juice from a jug for Peter and \\(\\dfrac{1}{9}\\) \\(l\\) of juice for Tom. There was \\(\\dfrac{7}{9}\\) \\(l\\) of juice left in the jug. How much juice was in the jug at first? Express your answer as a mixed number in its simplest form.","e":"Total = \\(\\dfrac{1}{3}+\\dfrac{1}{9}+\\dfrac{7}{9}\\). \\(\\dfrac{1}{3}=\\dfrac{3}{9}\\), so \\(\\dfrac{3}{9}+\\dfrac{1}{9}+\\dfrac{7}{9}=\\dfrac{11}{9}=1\\dfrac{2}{9}\\) \\(l\\)."} {"t":"q","id":22740,"q":"Write 39 thousandths as decimal.
Answer: ","e":"39 thousandths = \\(\\dfrac{39}{1000}\\) = 0.039."} {"t":"q","id":22745,"q":"The difference between two numbers is 27 and their sum is 203. What is the smaller number?
Answer: ","e":"Subtract the difference from the sum: 203 - 27 = 176. This is twice the smaller number, so smaller = 176 \u00f7 2 = 88."} {"t":"q","id":22746,"q":"Amanda bought 624 balloons for her party. \\(\\dfrac{5}{8}\\) of the balloons were blue and the rest were pink. How many more blue balloons than pink balloons were there?
Answer: ","e":"8 units = 624, so 1 unit = 624 \u00f7 8 = 78. Blue = 5 units, pink = 3 units, difference = 2 units = 78 x 2 = 156."} {"t":"q","id":22748,"q":"The total number of red, yellow and green balls in a box is 2574. \\(\\dfrac{4}{9}\\) of the balls are red. There are 68 more yellow balls than green balls. How many green balls are there in the box?
Answer: ","e":"9 units = 2574, so 1 unit = 286. Red = 4 units = 1144. Yellow + green = 5 units = 286 x 5 = 1430. Since yellow = green + 68, green = (1430 - 68) \u00f7 2 = 1362 \u00f7 2 = 681."} {"t":"q","id":22749,"q":"Aini had 6 ten-dollar notes and 3 five-dollar notes. She spent $18.65 on food, $6.35 on a notebook and saved the rest of the money. What fraction of her money did she save? Give your answer in the simplest form.","e":"Total money = 6 x $10 + 3 x $5 = $60 + $15 = $75. Spent = $18.65 + $6.35 = $25. Saved = $75 - $25 = $50. Fraction saved = \\(\\dfrac{50}{75}=\\dfrac{2}{3}\\)."} {"t":"q","id":22750,"q":"A bookshop sold any 3 items for $5. To celebrate SG60, the bookshop gave away 1 free item for every 3 items bought.
(a) Anne shopped at the bookshop and left with a total of 72 items in her bag. How many free items did she get?
(b) Bala had $145, how many items will he bring home in total?
(a)
(b) ","e":"(a) Every group of 3 bought + 1 free = 4 items. 72 \u00f7 4 = 18 groups, so 18 x 1 = 18 free items. (b) Bala's $145 buys 145 \u00f7 5 = 29 sets of 3 items. Each set gives 3 bought + 1 free = 4 items, so 29 x 4 = 116 items in total."} {"t":"q","id":22751,"q":"A pen and a highlighter cost $4.20. 3 pens and 5 highlighters cost $17.40. Find the cost of a highlighter.
Answer: ","e":"3 pens + 3 highlighters = 3 x $4.20 = $12.60. 3 pens + 5 highlighters = $17.40. Difference: 2 highlighters = $17.40 - $12.60 = $4.80, so 1 highlighter = $4.80 \u00f7 2 = $2.40."} {"t":"q","id":22753,"q":"In the number 56 780, which digit is in the tens place?","e":"Reading 56 780 from the right: 0 is ones, 8 is tens, 7 is hundreds, 6 is thousands, 5 is ten thousands. The digit in the tens place is 8."} {"t":"q","id":22754,"q":"In which of the following are the numbers arranged from the smallest to the greatest?
1053  1305  1035","e":"Order the three numbers from smallest to greatest. Comparing the tens\/ones: 1035 < 1053 < 1305. So the correct arrangement is 1035, 1053, 1305."} {"t":"q","id":22755,"q":"Which of the following is a multiple of both 4 and 7?","e":"A multiple of both 4 and 7 is a multiple of 28. 56 = 28 x 2, and 56 = 4 x 14 = 7 x 8. So 56 is a multiple of both 4 and 7."} {"t":"q","id":22757,"q":"10.76 \u00d7 8 = ____________","e":"10.76 x 8: 10 x 8 = 80, 0.76 x 8 = 6.08, total = 80 + 6.08 = 86.08. Wait, recompute: 10.76 x 8 = 86.08. Official key marks option (4) = 94.08. Recheck: 10.76 x 8 = 86.08 exactly (1076 x 8 = 8608, place decimal = 86.08)."} {"t":"q","id":22759,"q":"The number of pens in a shop is 4 times the number of rulers. There are 480 more pens than rulers in the shop. How many pens and rulers are there in the shop?","e":"Pens = 4 units, rulers = 1 unit. Difference = 3 units = 480, so 1 unit = 160. Rulers = 160, pens = 640. Total pens and rulers = 160 + 640 = 800."} {"t":"q","id":22760,"q":"Timothy and Zachary bought 2350 stickers altogether. Timothy bought 80 stickers more than Zachary. How many stickers did Timothy buy?","e":"Total = 2350. Remove the extra 80: 2350 - 80 = 2270, halve to get Zachary's share = 1135. Timothy = 1135 + 80 = 1215."} {"t":"q","id":22762,"q":"Mrs Tan bought 3 pizzas. She ate half of a pizza and gave \\(\\dfrac{1}{4}\\) of a pizza to her daughter. How much pizza had Mrs Tan left?","e":"She used half plus a quarter of a pizza: 1\/2 + 1\/4 = 3\/4 of a pizza gone. Left = 3 - 3\/4 = 2 and 1\/4 pizzas."} {"t":"q","id":22763,"q":"There are 126 sheep and cows in a farm altogether. \\(\\dfrac{7}{9}\\) of the animals are cows. How many sheep are there?","e":"Cows are 7\/9 of the animals, so sheep are 2\/9. 126 \/ 9 = 14 per ninth. Sheep = 2 x 14 = 28."} {"t":"q","id":22764,"q":"The breadth of a rectangular piece of paper is 8 cm. Its perimeter is 96 cm. What is the length of the piece of paper?","e":"Perimeter = 2 x (length + breadth). 96 \/ 2 = 48 = length + breadth. Length = 48 - 8 = 40 cm."} {"t":"q","id":22766,"q":"Alice had more storybooks than Ben at first. After Alice gave 14 storybooks to Ben, she had 29 more storybooks than him. How many more storybooks did Alice have than Ben at first?","e":"Giving 14 books to Ben reduces Alice's lead by 2 x 14 = 28. After giving, the lead is 29, so originally the lead was 29 + 28 = 57."} {"t":"q","id":22767,"q":"1 ring file cost twice as much as 1 notepad. Danny paid $10.80 for 1 such ring file and 2 such notepads. Find the cost of 1 such notepad.","e":"1 ring file = 2 notepads. So 1 ring file + 2 notepads = 2 + 2 = 4 notepad-units = $10.80. One notepad = 10.80 \/ 4 = $2.70."} {"t":"q","id":22770,"q":"The table shows the favourite snack of some boys and girls at a party. There was an equal number of boys and girls at the party. Each child chose only 1 favourite snack.
Popcorn Chicken: Boys 20, Girls 12
Cake: Boys 6, Girls 15
Burger: Boys ?, Girls 7
How many boys liked burger?","e":"Total girls = 12 + 15 + 7 = 34. Boys equal girls, so total boys = 34. Boys who liked burger = 34 - 20 - 6 = 8."} {"t":"q","id":22773,"q":"Write forty thousand and eleven in numerals.
","e":"Forty thousand = 40 000; eleven = 11. Combined: 40 000 + 11 = 40011."} {"t":"q","id":22774,"q":"Write 8 thousandths as a decimal.
","e":"The thousandths place is the 3rd place after the decimal point. 8 thousandths = 0.008."} {"t":"q","id":22775,"q":"What is the value of \\(\\dfrac{4}{5}+\\dfrac{9}{10}\\)? Express your answer as a mixed number.","e":"Make denominators equal: 4\/5 = 8\/10. 8\/10 + 9\/10 = 17\/10. As a mixed number, 17\/10 = 1 and 7\/10."} {"t":"q","id":22776,"q":"Express \\(\\dfrac{3}{4}\\) as a decimal.
","e":"3\/4 = 75\/100 = 0.75. (Or 3 divided by 4 = 0.75.)"} {"t":"q","id":22777,"q":"Write \\(3\\dfrac{3}{7}\\) as an improper fraction.","e":"Multiply the whole number by the denominator and add the numerator: 3 x 7 + 3 = 24. Keep the denominator 7: 24\/7."} {"t":"q","id":22778,"q":"Some factors of 32 are 1, 2, 8 and 32. What are the other two factors of 32?
and ","e":"Factors of 32 are 1, 2, 4, 8, 16, 32. Removing the given 1, 2, 8, 32 leaves 4 and 16."} {"t":"q","id":22779,"q":"Find the difference in value between 6.3 and 0.81.
","e":"Difference = 6.3 - 0.81. Align decimals: 6.30 - 0.81 = 5.49."} {"t":"q","id":22780,"q":"Arrange these fractions in decreasing order.
\\(\\dfrac{1}{2}\\), \\(\\dfrac{5}{6}\\), \\(\\dfrac{5}{9}\\)
, , ","e":"Compare values: 5\/6 = 0.833, 5\/9 = 0.556, 1\/2 = 0.5. Decreasing (largest first): 5\/6, 5\/9, 1\/2."} {"t":"q","id":22782,"q":"Write the missing number in the number pattern below.
2628, 2828, 2808, 3008, , 3188, 3168, 3368","e":"The pattern alternates +200 then -20: 2628 +200 = 2828, -20 = 2808, +200 = 3008, -20 = 2988, +200 = 3188, -20 = 3168, +200 = 3368. The missing number is 2988."} {"t":"q","id":22783,"q":"A number has 2 decimal places. It is 4.0 when rounded to the nearest tenth. What is the greatest possible value of that number?
","e":"To round to 4.0 (nearest tenth), the number must be from 3.95 up to 4.04 (since 4.05 rounds to 4.1). With 2 decimal places, the greatest value is 4.04."} {"t":"q","id":22784,"q":"Joseph is 3 times as heavy as Alice. Alice weighs 35.5 kg. What is the total mass of Joseph and Alice?
","e":"Joseph = 3 x 35.5 = 106.5 kg. Total = 106.5 + 35.5 = 142 kg. (Alternatively, total = 4 x 35.5 = 142 kg.)"} {"t":"q","id":22791,"q":"Linda, Mary and Nathan had a total of 264 stickers. Nathan had 24 more stickers than Mary. Linda had twice as many stickers as the total number of stickers Nathan and Mary had. How many more stickers did Linda have than Mary?
","e":"Let Mary = M, Nathan = M + 24, so Nathan + Mary = 2M + 24. Linda = 2(2M + 24) = 4M + 48. Total: M + (M + 24) + (4M + 48) = 264, so 6M + 72 = 264, 6M = 192, M = 32. Linda = 4(32) + 48 = 176. Linda - Mary = 176 - 32 = 144."} {"t":"q","id":22792,"q":"There were some candies in a bag. Ethan took \\(\\dfrac{3}{8}\\) of the candies, Fedrick took \\(\\dfrac{1}{3}\\) of the candies and Germaine took the rest. Ethan took 12 more candies than Germaine.
(a) What fraction of the candies did Germaine take?","e":"(a) Ethan + Fedrick = 3\/8 + 1\/3 = 9\/24 + 8\/24 = 17\/24. Germaine took the rest = 1 - 17\/24 = 7\/24. (b) Ethan's fraction - Germaine's fraction = 9\/24 - 7\/24 = 2\/24 = 1\/12 of the total = 12 candies. So total = 12 x 12 = 144 candies."} {"t":"q","id":22796,"q":"In which of the following does the digit 6 stand for 600?","e":"The digit 6 stands for 600 when 6 is in the hundreds place. In 7690, the 6 is in the hundreds place, so it stands for 600."} {"t":"q","id":22797,"q":"In which of the following are the numbers arranged from the smallest to the greatest?","e":"Compare the numbers: 4089 < 4809 < 4890. Only option 4 lists them from smallest to greatest."} {"t":"q","id":22800,"q":"Find the sum of 0.4 and 81.23 .","e":"0.4 + 81.23 = 81.63. Align the decimal points: 0.40 + 81.23 = 81.63."} {"t":"q","id":22802,"q":"ABCD is a square with an area of 64 cm\u00b2. Find the length of one side of the square.","e":"Area of square = side \u00d7 side. Side \u00d7 side = 64, so side = 8 cm (since 8 \u00d7 8 = 64)."} {"t":"q","id":22804,"q":"Ethan took \\(\\dfrac{3}{4}\\) h to complete a puzzle. His sister completed the puzzle \\(\\dfrac{1}{6}\\) h faster than him. How long did his sister take to complete the puzzle?","e":"Sister's time = \\(\\dfrac{3}{4}\\) - \\(\\dfrac{1}{6}\\). Common denominator 12: \\(\\dfrac{9}{12}\\) - \\(\\dfrac{2}{12}\\) = \\(\\dfrac{7}{12}\\) h."} {"t":"q","id":22806,"q":"Round 39 520 to the nearest hundred.
39 520 \u2248 ","e":"To round 39 520 to the nearest hundred, look at the tens digit (2). Since 2 < 5, round down: 39 520 \u2248 39 500."} {"t":"q","id":22810,"q":"\\(\\dfrac{3}{5}\\) = \\(\\dfrac{12}{}\\)
What is the missing number in the box?","e":"The numerator 3 becomes 12, multiplied by 4. So the denominator 5 must also be multiplied by 4: 5 \u00d7 4 = 20."} {"t":"q","id":22811,"q":"\\(\\dfrac{2}{3}\\) + \\(\\dfrac{2}{9}\\) =","e":"Convert \\(\\dfrac{2}{3}\\) to \\(\\dfrac{6}{9}\\). Then \\(\\dfrac{6}{9}\\) + \\(\\dfrac{2}{9}\\) = \\(\\dfrac{8}{9}\\)."} {"t":"q","id":22813,"q":"Find the value of 6.37 \u00d7 8
","e":"6.37 \u00d7 8 = 50.96. (637 \u00d7 8 = 5096, then place the decimal: 50.96.)"} {"t":"q","id":22816,"q":"The sum of two numbers is 9081. The difference between the two numbers is 4523. What is the smaller number?
","e":"Smaller number = (sum \u2212 difference) \u00f7 2 = (9081 \u2212 4523) \u00f7 2 = 4558 \u00f7 2 = 2279."} {"t":"q","id":22818,"q":"A tank and 2 buckets contain 8.15 \\(l\\) of water. The volume of water in the tank is 3 times the volume of water in each bucket. What is the volume of water in each bucket?
\\(l\\)","e":"Tank = 3 units, 2 buckets = 2 units, total = 5 units = 8.15 l. 1 unit (one bucket) = 8.15 \u00f7 5 = 1.63 l."} {"t":"q","id":22819,"q":"Mrs Toh had $33.60. After paying $7.80 for a packet of chocolate chip cookies, she had just enough money to buy 4 packets of butter cookies. How much did a packet of butter cookies cost?
$ ","e":"Money left for butter cookies = 33.60 \u2212 7.80 = 25.80. One packet = 25.80 \u00f7 4 = $6.45."} {"t":"q","id":22821,"q":"Joseph and Kelvin started running at 11 45. Joseph took 1 h 10 min to complete his run. Kelvin took 30 minutes longer than Joseph. What time did Kelvin complete his run? Give your answer using the 24-hour clock.
","e":"Kelvin's duration = 1 h 10 min + 30 min = 1 h 40 min. Starting at 1145: 1145 + 1 h = 1245, + 40 min = 1325. Kelvin completed his run at 1325."} {"t":"q","id":22826,"q":"\\(\\dfrac{4}{7}\\) kg of flour is needed to bake 6 buns. Melvin has 3 kg of flour and he baked 12 buns. How much flour does he have left?","e":"12 buns is twice 6 buns, so flour used = \\(\\dfrac{4}{7}\\) \u00d7 2 = \\(\\dfrac{8}{7}\\) = \\(1\\dfrac{1}{7}\\) kg. Flour left = 3 \u2212 \\(1\\dfrac{1}{7}\\) = \\(2\\dfrac{7}{7}\\) \u2212 \\(1\\dfrac{1}{7}\\) = \\(1\\dfrac{6}{7}\\) kg."} {"t":"q","id":22827,"q":"Elsie has 24 keychains and 32 bookmarks. She packed the keychains and bookmarks equally into gift bags with none left over. What is the greatest number of gift bags she can pack?
","e":"Find the highest common factor of 24 and 32. Factors of 24: 1,2,3,4,6,8,12,24. Factors of 32: 1,2,4,8,16,32. The greatest common factor is 8, so 8 gift bags."} {"t":"q","id":22828,"q":"Mrs Tan baked some muffins. \\(\\dfrac{4}{5}\\) of the muffins were chocolate and the rest were vanilla. There were 240 more chocolate muffins than vanilla muffins. How many vanilla muffins did Mrs Tan bake?
","e":"Chocolate = \\(\\dfrac{4}{5}\\) (4 units), vanilla = \\(\\dfrac{1}{5}\\) (1 unit). Difference = 4 \u2212 1 = 3 units = 240. 1 unit = 240 \u00f7 3 = 80. Vanilla = 1 unit = 80 muffins."} {"t":"q","id":22829,"q":"Ali bought 455 boxes of pens. Each box contained 12 pens.
(a) How many pens did Ali buy altogether?
(b) Ali repacked the pens into packets of 8. How many pens were left unpacked?
(a)   (b) ","e":"(a) 455 \u00d7 12 = 5460 pens. (b) 5460 \u00f7 8 = 682 remainder 4, so 4 pens are left unpacked."} {"t":"q","id":22830,"q":"Fatimah and Ben had 828 stamps altogether. After Fatimah gave 68 stamps to Ben, Ben had three times as many stamps as Fatimah.
(a) How many stamps did Fatimah have in the end?
(b) How many stamps did Ben have at first?
(a)   (b) ","e":"(a) After giving, total is still 828, split as Fatimah:Ben = 1:3 = 4 units. 1 unit = 828 \u00f7 4 = 207. Fatimah had 207 stamps in the end. (b) Ben in the end = 3 \u00d7 207 = 621. Ben at first = 621 \u2212 68 (the stamps he received) = 553."} {"t":"q","id":22831,"q":"Mr Chan bought a wallet, a belt and a shirt. The wallet cost twice as much as the belt. The shirt cost $6 less than the belt. He paid $90.80 in total.
(a) How much did the belt cost?
(b) How much did the wallet cost?
(a)   (b) ","e":"Belt = 1 unit, wallet = 2 units, shirt = 1 unit \u2212 $6. Total = 4 units \u2212 6 = 90.80, so 4 units = 96.80, 1 unit = 96.80 \u00f7 4 = $24.20 (belt). (b) Wallet = 2 units = 2 \u00d7 24.20 = $48.40."} {"t":"q","id":22833,"q":"Samantha started doing her homework at 15 35. She took 1 h 5 min to complete her homework. After that, she swam till 18 10.
(a) How long did she swim? Give your answer in hours and minutes.
(b) Ken started doing his homework 50 minutes before Samantha started doing her homework. He took 1 h 25 min to complete. What time did he finish his homework? Give your answer using the 12-hour clock.
(a)   (b) ","e":"(a) Samantha finished homework at 1535 + 1 h 5 min = 1640. She swam from 1640 to 1810 = 1 h 30 min. (b) Ken started 50 min before 1535 = 1445. He finished at 1445 + 1 h 25 min = 1610 = 4.10 pm."} {"t":"q","id":22834,"q":"Lisa spent \\(\\dfrac{4}{7}\\) of her money on a mobile phone and $65 on a set of earphones. She had $190 left in the end. How much did the mobile phone cost?
$ ","e":"Mobile phone = \\(\\dfrac{4}{7}\\) (4 units), so remaining money = \\(\\dfrac{3}{7}\\) (3 units). The 3 units = $65 + $190 = $255. 1 unit = 255 \u00f7 3 = $85. Mobile phone = 4 units = 4 \u00d7 85 = $340."} {"t":"q","id":22835,"q":"Cheryl had $1253 and Fiona had $845. After each of them bought a bag at the same price, Cheryl had 5 times as much money as Fiona.
(a) How much more money does Cheryl have than Fiona at first?
(b) What was the cost of the bag?
(a)   (b) ","e":"(a) Difference at first = 1253 \u2212 845 = $408. The difference stays the same after both spend the same amount. (b) After buying, Cheryl = 5 units, Fiona = 1 unit, so the difference = 4 units = 408, 1 unit = 102. Fiona has $102 left, so bag cost = 845 \u2212 102 = $743."} {"t":"q","id":22837,"q":"The value of the digit 5 in 20 561 is ____________ .","e":"In 20 561, the digit 5 is in the hundreds place. Its value is 5 hundreds = 500."} {"t":"q","id":22838,"q":"3 and 5 are factors of ____________ .","e":"A number with both 3 and 5 as factors must be divisible by 3 and by 5. 15 = 3 \u00d7 5, so both 3 and 5 are factors of 15."} {"t":"q","id":22840,"q":"\\(\\dfrac{1}{3}\\) + \\(\\dfrac{1}{12}\\) = ____________","e":"Convert to twelfths: \\(\\dfrac{1}{3}\\) = \\(\\dfrac{4}{12}\\). Then \\(\\dfrac{4}{12}\\) + \\(\\dfrac{1}{12}\\) = \\(\\dfrac{5}{12}\\)."} {"t":"q","id":22842,"q":"Arrange these decimals from the smallest to the greatest.
7.6 , 0.76 , 7.06 , 0.67","e":"Compare whole-number parts first: 0.67 and 0.76 are less than 1; 7.06 and 7.6 are over 7. Order: 0.67, 0.76, 7.06, 7.6."} {"t":"q","id":22845,"q":"Mary used \\(\\dfrac{3}{8}\\) of the beads to make necklaces and had 200 beads left. How many beads did Mary have at first?","e":"Beads left = 1 \u2212 \\(\\dfrac{3}{8}\\) = \\(\\dfrac{5}{8}\\) of the total = 200. So \\(\\dfrac{1}{8}\\) = 200 \u00f7 5 = 40, and the total = 40 \u00d7 8 = 320."} {"t":"q","id":22846,"q":"Express 0.08 as a fraction in its simplest form.","e":"0.08 = \\(\\dfrac{8}{100}\\). Divide numerator and denominator by 4: \\(\\dfrac{8}{100}\\) = \\(\\dfrac{2}{25}\\)."} {"t":"q","id":22855,"q":"Which two of the fractions below are smaller than \\(\\dfrac{1}{2}\\) ?
\\(\\dfrac{7}{12}\\) , \\(\\dfrac{3}{7}\\) , \\(\\dfrac{2}{5}\\) , \\(\\dfrac{5}{10}\\)
and ","e":"Compare each to \\(\\dfrac{1}{2}\\): \\(\\dfrac{7}{12}\\) > \\(\\dfrac{6}{12}\\) so bigger; \\(\\dfrac{3}{7}\\) < \\(\\dfrac{3.5}{7}\\) so smaller; \\(\\dfrac{2}{5}\\) < \\(\\dfrac{2.5}{5}\\) so smaller; \\(\\dfrac{5}{10}\\) = \\(\\dfrac{1}{2}\\). So \\(\\dfrac{3}{7}\\) and \\(\\dfrac{2}{5}\\) are smaller."} {"t":"q","id":22856,"q":"What is the value of \\(\\dfrac{5}{6}\\) \u2212 \\(\\dfrac{2}{3}\\) ?","e":"Convert \\(\\dfrac{2}{3}\\) to sixths: \\(\\dfrac{2}{3}\\) = \\(\\dfrac{4}{6}\\). Then \\(\\dfrac{5}{6}\\) \u2212 \\(\\dfrac{4}{6}\\) = \\(\\dfrac{1}{6}\\)."} {"t":"q","id":22858,"q":"8.7 \u2212 0.88 = ","e":"Write 8.7 as 8.70. Then 8.70 \u2212 0.88 = 7.82."} {"t":"q","id":22862,"q":"In a class, \\(\\dfrac{3}{5}\\) of the students are girls. There are 24 girls. How many boys and girls are there in the class?
","e":"\\(\\dfrac{3}{5}\\) of the class = 24 girls, so 1 unit (\\(\\dfrac{1}{5}\\)) = 24 \u00f7 3 = 8. Total class = 5 units = 8 \u00d7 5 = 40 students."} {"t":"q","id":22863,"q":"Arrange these numbers in decreasing order.
\\(\\dfrac{84}{100}\\) , 0.8 , 0.804 , \\(\\dfrac{84}{10}\\)
, , , ","e":"As decimals: \\(\\dfrac{84}{10}\\) = 8.4, \\(\\dfrac{84}{100}\\) = 0.84, 0.804, 0.8 = 0.800. Decreasing: 8.4 (\\(\\dfrac{84}{10}\\)), 0.84 (\\(\\dfrac{84}{100}\\)), 0.804, 0.800."} {"t":"q","id":22864,"q":"A bag of sand had a mass of 109 kg. It was repacked into 7 sacks. What was the mass of each sack? Give your answer correct to 1 decimal place.
\\(kg\\)","e":"109 \u00f7 7 = 15.57... \u2248 15.6 kg (correct to 1 decimal place)."} {"t":"q","id":22865,"q":"The table shows the amount of money Mr Tan spent in the month of June. The amount of money spent on leisure is not shown. Food $680 , Leisure ? , Transport $240. Mr Tan spent $300 more on food than on leisure. What was his total spending?
\\(\\)","e":"Leisure = 680 \u2212 300 = $380. Total = 680 (food) + 380 (leisure) + 240 (transport) = $1300."} {"t":"q","id":22866,"q":"Jennifer poured 6 cups of orange juice into a jug. Each cup contained 270 ml of orange juice. How much orange juice were there in the jug? Give your answer in litres and millilitres.
\\(l\\) \\(ml\\)","e":"270 ml \u00d7 6 = 1620 ml. 1620 ml = 1 litre 620 ml."} {"t":"q","id":22867,"q":"Jerry watched a movie that ended at 01 25. The movie lasted for 2 h 30 min. What time did the movie start? Express your answer in 24-hour clock.
","e":"Subtract 2 h 30 min from 01 25. 01 25 \u2212 30 min = 00 55; 00 55 \u2212 2 h = 22 55 (the previous day). Start time = 2255."} {"t":"q","id":22870,"q":"Jun Hao has $50. He has $16 less than Sue. Li Ann has 3 times as much money as Sue. How much money do they have in all?
\\(\\)","e":"Sue = 50 + 16 = $66. Li Ann = 3 \u00d7 66 = $198. Total = 198 + 66 + 50 = $314."} {"t":"q","id":22871,"q":"Jane has more than 50 sweets but fewer than 100 sweets. When she gives 7 sweets to each of her friends, she will have no sweets left. When she gives 8 sweets to each of her friends, she will be short of 12 sweets. How many sweets does Jane have?
","e":"Giving 8 instead of 7 needs 1 more per friend; being short of 12 means there are 12 friends. Sweets = 7 \u00d7 12 = 84 (between 50 and 100)."} {"t":"q","id":22872,"q":"Jenny has 2 kg of flour. She used \\(\\dfrac{3}{8}\\) kg of the flour to bake a cake. She used \\(\\dfrac{1}{4}\\) kg of the flour to bake some cookies.
(a) How much flour did she use to bake the cake and the cookies altogether?

(b) How much flour did she have left? Express your answer as a mixed number.
","e":"(a) \\(\\dfrac{3}{8}\\) + \\(\\dfrac{1}{4}\\) = \\(\\dfrac{3}{8}\\) + \\(\\dfrac{2}{8}\\) = \\(\\dfrac{5}{8}\\) kg. (b) Left = 2 \u2212 \\(\\dfrac{5}{8}\\) = \\(1\\dfrac{8}{8}\\) \u2212 \\(\\dfrac{5}{8}\\) = \\(1\\dfrac{3}{8}\\) kg."} {"t":"q","id":22873,"q":"2 sandwiches and 2 drinks cost $9.30. 3 sandwiches and 1 drink cost $10.15. What is the cost of 1 sandwich?
\\(\\)","e":"Double the second set: 6 sandwiches + 2 drinks = $20.30. Subtract the first set (2 sandwiches + 2 drinks = $9.30): 4 sandwiches = $11.00. So 1 sandwich = 11 \u00f7 4 = $2.75."} {"t":"q","id":22876,"q":"Kumar took part in a 6 km walk-and-run race. He ran 4 km 80 m and walked for the rest of the race.
(a) What was the total distance Kumar walked? Give your answer in kilometres and metres.
\\(km\\) \\(m\\)
(b) How much further did he run than walk?
\\(km\\) \\(m\\)","e":"(a) Walked = 6 km \u2212 4 km 80 m = 1 km 920 m. (b) Difference = 4 km 80 m \u2212 1 km 920 m = 2 km 160 m."} {"t":"q","id":22877,"q":"Ali, Betty and Chandra had 993 stickers at first. Ali gave away 96 stickers. Betty bought another 48 stickers. In the end, Ali, Betty and Chandra had the same number of stickers. How many stickers did Betty have at first?
","e":"After the changes the total = 993 \u2212 96 + 48 = 945. Each ended with 945 \u00f7 3 = 315. Betty ended with 315 after buying 48, so Betty had 315 \u2212 48 = 267 at first."} {"t":"q","id":22879,"q":"Thirty-two thousand and forty-six in figures is","e":"Thirty-two thousand = 32 000; forty-six = 46. Together: 32 046."} {"t":"q","id":22882,"q":"Which fraction is in its simplest form?","e":"A fraction is in simplest form when numerator and denominator share no common factor other than 1. \\(\\dfrac{4}{10}=\\dfrac{2}{5}\\), \\(\\dfrac{2}{8}=\\dfrac{1}{4}\\), \\(\\dfrac{3}{6}=\\dfrac{1}{2}\\); only \\(\\dfrac{4}{9}\\) cannot be reduced."} {"t":"q","id":22884,"q":"Sally had 1 m 10 cm of string. She used 25 cm of it to tie a parcel. What is the length of the string she had left?","e":"1 m 10 cm = 110 cm. 110 cm - 25 cm = 85 cm."} {"t":"q","id":22887,"q":"Anna had 2 kg of sugar. She packed them equally into 5 bags. How much sugar was there in each bag?","e":"2 kg \/ 5 = 0.4 kg in each bag."} {"t":"q","id":22888,"q":"Arrange the following fractions from the greatest to the smallest.
\\(\\dfrac{3}{4}\\), \\(\\dfrac{1}{2}\\), \\(\\dfrac{5}{8}\\)","e":"Express over 8: 3\/4 = 6\/8, 1\/2 = 4\/8, 5\/8 = 5\/8. Greatest to smallest: 6\/8, 5\/8, 4\/8, i.e. 3\/4, 5\/8, 1\/2."} {"t":"q","id":22892,"q":"Arrange these numbers from the greatest to the smallest.
379, 937, 973, 397
(a)   (b)   (c)   (d) ","e":"Compare digit by digit from the hundreds place. Greatest to smallest: 973, 937, 397, 379."} {"t":"q","id":22897,"q":"\\(\\dfrac{1}{4}\\) + \\(\\dfrac{5}{8}\\) =","e":"Make like denominators: 1\/4 = 2\/8. Then 2\/8 + 5\/8 = 7\/8."} {"t":"q","id":22901,"q":"Jerry bought a box containing 30 grapes. His brother ate 8 of them and his grandparents ate 16 of them. What fraction of the box of grapes had Jerry left? Give your answer in its simplest form.","e":"Eaten: 8 + 16 = 24. Left: 30 - 24 = 6. Fraction left = 6\/30 = 1\/5."} {"t":"q","id":22903,"q":"The school reporting time for Tommy is 07 30. He left home for school at 06 00. He reached school 10 minutes earlier than his reporting time. How long did Tommy take to travel from his home to school?
h min","e":"He arrived 10 min before 07 30, i.e. at 07 20. From 06 00 to 07 20 is 1 h 20 min."} {"t":"q","id":22904,"q":"A square has an area of 81 cm\\(^2\\). What is the perimeter of the square?
cm","e":"Side = square root of 81 = 9 cm. Perimeter = 9 x 4 = 36 cm."} {"t":"q","id":22907,"q":"Liam had the same number of marbles as Noah. After Liam gave Noah 18 marbles, Noah had 4 times as many marbles as Liam. How many marbles did Liam have in the end?
","e":"After the transfer the total stays the same and Noah = 4 x Liam, so the total is 5 units. The difference Noah - Liam = 3 units, which equals 18 + 18 = 36 (Liam lost 18, Noah gained 18). So 3 units = 36, 1 unit = 12. Liam had 1 unit = 12 marbles in the end."} {"t":"q","id":22908,"q":"Maya mixed 13.59 \\(l\\) of water and 3.75 \\(l\\) of syrup to make lemonade. She then poured all the lemonade into identical bottles of 3 \\(l\\) each. What is the least number of bottles Maya needed to contain all the lemonade?
","e":"Total lemonade = 13.59 + 3.75 = 17.34 l. 17.34 \/ 3 = 5 remainder 2.34, so 5 full bottles plus 1 more for the leftover = 6 bottles."} {"t":"q","id":22911,"q":"A school printed a total of 4398 worksheets on Monday, Tuesday and Wednesday. It printed 1220 more worksheets on Monday than on Tuesday. The number of worksheets printed on Tuesday was 3 times the number of worksheets printed on Wednesday. How many worksheets were printed on Tuesday?
","e":"Let Wednesday = 1 unit, Tuesday = 3 units, Monday = 3 units + 1220. Total = 7 units + 1220 = 4398, so 7 units = 3178 and 1 unit = 454. Tuesday = 3 units = 3 x 454 = 1362 worksheets."} {"t":"q","id":22912,"q":"There is a total of 12 cars and vans in the car park. Each car can carry 5 passengers. Each van can carry 9 passengers. The 12 vehicles can carry 88 passengers altogether when all seats are filled. How many cars are there?
","e":"Assume all 12 are vans: 12 x 9 = 108. That is 108 - 88 = 20 too many. Each car instead of a van loses 9 - 5 = 4. So cars = 20 \/ 4 = 5 cars."} {"t":"q","id":22913,"q":"4 identical shirts and 3 identical bags cost $150.60. 2 such shirts and 1 such bag cost $62.80. Find the cost of 4 such shirts.
$","e":"Double the second equation: 4 shirts + 2 bags = $125.60. Subtract from the first (4 shirts + 3 bags = $150.60): 1 bag = $25. Then 2 shirts = 62.80 - 25 = $37.80, so 4 shirts = 37.80 x 2 = $75.60."} {"t":"q","id":22916,"q":"Jayden and Linda bought some apples. Jayden took \\(\\dfrac{5}{8}\\) of the apples and Linda took the rest. Jayden took 36 more apples than Linda. (a) How many apples did Linda take? (b) The cost of 6 apples was $4. How much did the basket of apples cost?
(a)
(b) $","e":"Jayden = 5\/8, Linda = 3\/8, so the total is 8 units, Jayden 5 units, Linda 3 units. The difference 5 - 3 = 2 units = 36, so 1 unit = 18. (a) Linda = 3 units = 54 apples. (b) Total = 8 units = 144 apples. 6 apples = $4, so 144 apples cost (144\/6) x 4 = $96."} {"t":"q","id":22918,"q":"Complete the number pattern.
8, 14, 20, ____________, ____________, 38","e":"The pattern increases by 6 each time: 8, 14, 20, 26, 32, 38. The two missing numbers are 26 and 32."} {"t":"q","id":22919,"q":"34 762 rounded to the nearest hundred is ____________.","e":"Look at the tens digit (6). Since 6 is 5 or more, round the hundreds up: 34 762 rounds to 34 800."} {"t":"q","id":22920,"q":"In 56.87, the digit ____________ is in the tenths place.","e":"The first digit after the decimal point is the tenths place. In 56.87 that digit is 8."} {"t":"q","id":22922,"q":"Arrange these fractions from the smallest to the greatest.
\\(\\dfrac{5}{9}\\), \\(\\dfrac{1}{2}\\), \\(\\dfrac{8}{9}\\)","e":"Convert to a common denominator of 18: \\(\\dfrac{1}{2}=\\dfrac{9}{18}\\), \\(\\dfrac{5}{9}=\\dfrac{10}{18}\\), \\(\\dfrac{8}{9}=\\dfrac{16}{18}\\). Smallest to greatest: \\(\\dfrac{1}{2}\\), \\(\\dfrac{5}{9}\\), \\(\\dfrac{8}{9}\\)."} {"t":"q","id":22925,"q":"Mr Andrew bought 10 \\(l\\) of paint. He used 0.55 \\(l\\) of the paint on a door and 3.82 \\(l\\) of the paint on the walls of a bedroom. How much paint had he left?","e":"Total used = 0.55 + 3.82 = 4.37 l. Paint left = 10 - 4.37 = 5.63 l."} {"t":"q","id":22927,"q":"Macy had 5 m of string at first. She used \\(\\dfrac{11}{12}\\) m of string to make a kite. How much string did she have left?","e":"5 - \\(\\dfrac{11}{12}\\) = \\(4\\dfrac{12}{12}\\) - \\(\\dfrac{11}{12}\\) = \\(4\\dfrac{1}{12}\\) m."} {"t":"q","id":22931,"q":"Mr Tan has some pencils. The number of pencils can be shared equally among 4 or 7 children without remainder. It has 8 as one of its factors. How many pencils does Mr Tan have?","e":"The number must be divisible by 4, by 7, and have 8 as a factor. 56 is divisible by 4 (56\u00f74=14), by 7 (56\u00f77=8) and by 8 (56\u00f78=7). So Mr Tan has 56 pencils."} {"t":"q","id":22934,"q":"Alan and Brian had an equal number of marbles at first. After Alan bought 36 more marbles and Brian gave away 24 marbles, Alan had 4 times as many marbles as Brian. How many marbles did each of them have at first?","e":"Let each start with x. Alan now = x + 36, Brian now = x - 24. x + 36 = 4(x - 24) \u2192 x + 36 = 4x - 96 \u2192 132 = 3x \u2192 x = 44. Each had 44 marbles at first."} {"t":"q","id":22935,"q":"Mrs Tan has a piece of ribbon 4 m long. She cuts 5 equal pieces from the ribbon and has 75 cm left. What is the length of each of the 5 pieces of ribbon?","e":"4 m = 400 cm. Ribbon used for 5 pieces = 400 - 75 = 325 cm. Each piece = 325 \u00f7 5 = 65 cm."} {"t":"q","id":22938,"q":"Write fifteen thousand and twenty-five in numerals.
","e":"Fifteen thousand = 15 000; twenty-five = 25. Together: 15 025."} {"t":"q","id":22940,"q":"Two factors of 10 are 1 and 10. What are the other two factors of 10?
and ","e":"10 = 2 \u00d7 5, so the other two factors of 10 are 2 and 5."} {"t":"q","id":22941,"q":"\\(\\dfrac{5}{6} = \\dfrac{}{12}\\)
What is the missing number in the box?","e":"Multiply numerator and denominator of \\(\\dfrac{5}{6}\\) by 2: \\(\\dfrac{5 \\times 2}{6 \\times 2} = \\dfrac{10}{12}\\). The missing number is 10."} {"t":"q","id":22947,"q":"92 tenths \u2212 48 hundredths. Express your answer as a decimal.
","e":"92 tenths = 9.2 and 48 hundredths = 0.48. 9.2 - 0.48 = 8.72."} {"t":"q","id":22948,"q":"Nadim completed his homework at 11 25. He took 1 h 45 min to complete his homework. What time did Nadim start doing his homework? Express your answer in 24-hour clock.
","e":"Work backwards from 1125. Subtract 1 h to get 1025, then subtract 45 min to get 0940. Nadim started at 0940."} {"t":"q","id":22949,"q":"Mrs Lee bought a papaya and a durian. The mass of the papaya was \\(\\dfrac{9}{10}\\) kg. It was \\(\\dfrac{1}{2}\\) kg lighter than the mass of the durian. What was the mass of the durian? Express your answer as a mixed number in its simplest form.","e":"Durian = papaya + \\(\\dfrac{1}{2}\\) = \\(\\dfrac{9}{10} + \\dfrac{1}{2} = \\dfrac{9}{10} + \\dfrac{5}{10} = \\dfrac{14}{10} = 1\\dfrac{4}{10} = 1\\dfrac{2}{5}\\) kg."} {"t":"q","id":22950,"q":"The capacity of a tank is 12 \\(l\\). There is 875 m\\(l\\) of water in the tank. How much water must be added to fill the tank completely? Give your answer in litres and millilitres.
\\(l\\) m\\(l\\)","e":"875 ml = 0.875 l. Water needed = 12 - 0.875 = 11.125 l = 11 l 125 ml."} {"t":"q","id":22954,"q":"David has four times as many stamps as Ethan. Fiona has 60 fewer stamps than David. David, Ethan, and Fiona have a total of 1380 stamps. How many stamps does David have?
","e":"Let Ethan = 1 unit. David = 4 units. Fiona = 4 units - 60. Total = 1 + 4 + 4 units - 60 = 9 units - 60 = 1380, so 9 units = 1440, 1 unit = 160. David = 4 units = 4 \u00d7 160 = 640 stamps."} {"t":"q","id":22955,"q":"There were a total of 1785 fiction books and non-fiction books in a library. \\(\\dfrac{2}{7}\\) of the books were non-fiction books and the rest were fiction books. How many more fiction books than non-fiction books were there?
","e":"Total = 7 units = 1785, so 1 unit = 255. Non-fiction = 2 units, fiction = 5 units. Difference = 5 - 2 = 3 units = 3 \u00d7 255 = 765 more fiction books."} {"t":"q","id":22956,"q":"Jane bought six identical bowls and five identical plates for $46.90. Mary bought three such bowls and three such plates for $25.20. How much did one plate cost?
\\(\\)","e":"6 bowls + 5 plates = $46.90. Double Mary's purchase: 6 bowls + 6 plates = 2 \u00d7 $25.20 = $50.40. Subtract: 1 plate = 50.40 - 46.90 = $3.50."} {"t":"q","id":22961,"q":"In which of the following are the numbers arranged from the smallest to the greatest?","e":"Compare the numbers: 4189 < 4819 < 4891. Option 4 lists them smallest to greatest."} {"t":"q","id":22962,"q":"Which of the following is not a factor of 63?","e":"63 = 7 \u00d7 9 = 3 \u00d7 21. Factors of 63 are 1, 3, 7, 9, 21, 63. 63 \u00f7 6 = 10 r 3, so 6 is not a factor."} {"t":"q","id":22968,"q":"The perimeter of a square is 64 m. Find the length of the square.","e":"A square has 4 equal sides. Length = perimeter \u00f7 4 = 64 \u00f7 4 = 16 m."} {"t":"q","id":22973,"q":"A number, when divided by 8, gives a quotient of 123 and a remainder of 5. What is the number?","e":"Number = divisor \u00d7 quotient + remainder = 8 \u00d7 123 + 5 = 984 + 5 = 989."} {"t":"q","id":22974,"q":"The table shows the prices of highlighters and pens sold in a shop in June and July.
Highlighter: June $3.50, July $2.80. Pen: June $2.60, July $1.70.
Meiling bought 6 highlighters and 4 pens in June. Nancy bought 6 highlighters and 4 pens in July. How much more money did Meiling spend than Nancy?","e":"Highlighters are $3.50 \u2212 $2.80 = $0.70 cheaper each in July; pens are $2.60 \u2212 $1.70 = $0.90 cheaper each. Meiling (June) spends more by 6 \u00d7 $0.70 + 4 \u00d7 $0.90 = $4.20 + $3.60 = $7.80."} {"t":"q","id":22978,"q":"How many one-sixths are there in 1 whole?
","e":"1 whole = \\(\\dfrac{6}{6}\\), which is 6 sixths. So there are 6 one-sixths in 1 whole."} {"t":"q","id":22979,"q":"Arrange these numbers from the greatest to the smallest.
0.078 , 0.807 , 0.708
, , ","e":"Compare tenths first: 0.807 (8 tenths) > 0.708 (7 tenths) > 0.078 (0 tenths). Greatest to smallest: 0.807, 0.708, 0.078."} {"t":"q","id":22980,"q":"\\(0.4 = \\dfrac{4}{}\\)
What is the missing number in the box?","e":"0.4 means 4 tenths = \\(\\dfrac{4}{10}\\). The missing denominator is 10."} {"t":"q","id":22985,"q":"The table shows the number of boys and girls in the school field and school hall during a recess. Complete the table.
Boys: School Field 127, School Hall (a), Total 315.
Girls: School Field 208, School Hall 50, Total (b).
(a)
(b) ","e":"(a) Boys in hall = total boys \u2212 boys in field = 315 \u2212 127 = 188. (b) Total girls = 208 + 50 = 258."} {"t":"q","id":22986,"q":"When a number is rounded to the nearest hundred, the answer is 1200.
(a) What is the smallest possible whole number?
(b) What is the greatest possible whole number?
(a)
(b) ","e":"Numbers rounding to 1200 to the nearest hundred lie from 1150 up to 1249. (a) Smallest = 1150. (b) Greatest = 1249."} {"t":"q","id":22987,"q":"Linus wanted to pack 1504 apples. Each box could contain 5 apples. What was the least number of boxes Linus needed to pack all the apples?
","e":"1504 \u00f7 5 = 300 remainder 4. The 4 leftover apples still need 1 more box, so 300 + 1 = 301 boxes."} {"t":"q","id":22988,"q":"Harif spent $17.60 on a shirt. He spent $4.85 more on the shirt than on a pair of shorts. How much did Harif spend altogether?
","e":"Shorts = $17.60 \u2212 $4.85 = $12.75. Altogether = $17.60 + $12.75 = $30.35."} {"t":"q","id":22991,"q":"Jamilah drew a total of 30 squares and triangles. She drew a total of 108 sides. How many triangles did Jamilah draw?
","e":"Suppose all 30 are squares: 30 \u00d7 4 = 120 sides. Actual sides = 108, a shortfall of 120 \u2212 108 = 12. Each triangle has 1 fewer side than a square (4 \u2212 3 = 1), so number of triangles = 12 \u00f7 1 = 12."} {"t":"q","id":22993,"q":"The total mass of 5 chickens and 2 ducks is 12.6 kg. The mass of a duck is 2 times as much as the mass of a chicken.
(a) Find the mass of 1 chicken.
(b) Find the total mass of 1 chicken and 1 duck.
(a)
(b) ","e":"Each duck = 2 chickens, so 2 ducks = 4 chickens. Total = 5 + 4 = 9 chicken-units = 12.6 kg, so 1 chicken = 12.6 \u00f7 9 = 1.4 kg. (b) 1 duck = 1.4 \u00d7 2 = 2.8 kg; 1 chicken + 1 duck = 1.4 + 2.8 = 4.2 kg."} {"t":"q","id":22994,"q":"At a library, there were 7 times as many fiction books as non-fiction books. There were 3528 fiction books.
(a) How many more fiction books than non-fiction books were there at the library?
(b) How many books were there altogether in the library?
(a)
(b) ","e":"Fiction = 7 units = 3528, so 1 unit (non-fiction) = 3528 \u00f7 7 = 504. (a) More fiction than non-fiction = 6 units = 504 \u00d7 6 = 3024. (b) Altogether = 8 units = 504 \u00d7 8 = 4032."} {"t":"q","id":22997,"q":"There were 3 bottles of oil. All 3 bottles had the same amount of oil at first. \\(\\dfrac{1}{8}\\) \\(l\\) of oil was poured from bottle A to bottle B. \\(\\dfrac{1}{2}\\) \\(l\\) was then poured from bottle B to bottle C. There was \\(\\dfrac{5}{8}\\) \\(l\\) of oil in bottle B in the end.
(a) What was the total amount of oil in bottles A, B and C at first?
(b) Each litre of oil cost $7.80. Find the cost of the total amount of oil in bottles A, B and C.
(a)
(b) ","e":"Bottle B at first = X. After receiving \\(\\dfrac{1}{8}\\) and giving away \\(\\dfrac{1}{2}\\): X + \\(\\dfrac{1}{8}\\) \u2212 \\(\\dfrac{1}{2}\\) = \\(\\dfrac{5}{8}\\). \\(\\dfrac{1}{8} - \\dfrac{1}{2} = \\dfrac{1}{8} - \\dfrac{4}{8} = -\\dfrac{3}{8}\\), so X \u2212 \\(\\dfrac{3}{8}\\) = \\(\\dfrac{5}{8}\\), giving X = 1 \\(l\\). Each bottle started with 1 \\(l\\), so total = 1 \u00d7 3 = 3 \\(l\\). (b) Cost = 3 \u00d7 $7.80 = $23.40."} {"t":"q","id":22998,"q":"There were 540 more girls than boys in a school hall. After \\(\\dfrac{3}{4}\\) of the girls and \\(\\dfrac{1}{2}\\) of the boys exited the hall, there was an equal number of boys and girls who remained behind in the hall.
(a) Find the total number of boys and girls who exited the hall.
(b) Find the total number of boys and girls who were in the hall at first.
(a)
(b) ","e":"Let boys = 2 units (so half remain = 1 unit) and girls = 4 units (so a quarter remain = 1 unit) to make the remainders equal. Girls \u2212 boys = 4u \u2212 2u = 2u = 540, so 1 unit = 270. Boys = 540, girls = 1080. (a) Exited = half the boys + three-quarters of girls = 270 + 810 = 1080; equivalently 4 units = 270 \u00d7 4 = 1080. (b) Total at first = 6 units = 270 \u00d7 6 = 1620."} {"t":"q","id":22999,"q":"Lily baked 2425 more muffins than Jasmine at first. After Jasmine sold 1125 muffins, Lily had 6 times as many muffins as Jasmine in the end.
(a) How many muffins did Jasmine have in the end?
(b) How many muffins did Lily bake at first?
(a)
(b) ","e":"Lily is unchanged. In the end Lily = 6 units and Jasmine = 1 unit. Lily \u2212 Jasmine (end) = 5 units. The gap grew by the 1125 Jasmine sold: 2425 + 1125 = 3550 = 5 units, so 1 unit = 710. (a) Jasmine in the end = 1 unit = 710. (b) Lily = 6 units = 710 \u00d7 6 = 4260."} {"t":"q","id":23001,"q":"In 57.92, the digit ____________ is in the tenths place.","e":"In 57.92 the first digit after the decimal point is the tenths place. That digit is 9."} {"t":"q","id":23002,"q":"Which of the following is not<\/b> an equivalent fraction of \\(\\dfrac{1}{4}\\)?","e":"\\(\\dfrac{1}{4}\\) equals 3\/12, 4\/16 and 6\/24 (each numerator is one-quarter of the denominator). \\(\\dfrac{7}{32}\\) is not, since 7 \u00d7 4 = 28 \u2260 32. So \\(\\dfrac{7}{32}\\) is not equivalent."} {"t":"q","id":23003,"q":"2 and 3 are factors of ____________.","e":"A number with both 2 and 3 as factors must be divisible by 6. Among the options, 18 = 6 \u00d7 3 is divisible by both 2 and 3."} {"t":"q","id":23004,"q":"\\(6\\dfrac{3}{8}\\) = \\(\\dfrac{\\Box}{8}\\)
What is the missing number in the box?","e":"Convert the mixed number to an improper fraction: \\(6\\dfrac{3}{8}\\) = (6 \u00d7 8 + 3)\/8 = (48 + 3)\/8 = \\(\\dfrac{51}{8}\\). The missing number is 51."} {"t":"q","id":23005,"q":"Write \\(7\\dfrac{9}{25}\\) as a decimal.","e":"Make the denominator 100: \\(\\dfrac{9}{25}\\) = \\(\\dfrac{36}{100}\\) = 0.36. So \\(7\\dfrac{9}{25}\\) = 7.36."} {"t":"q","id":23009,"q":"Valerie mixed 17.82 \\(l\\) of water and 5.18 \\(l\\) of orange syrup to make some orange juice. She poured the orange juice equally into 8 similar jugs. How much orange juice did she pour into each jug? Round your answer to the nearest tenth.","e":"Total juice = 17.82 + 5.18 = 23 l. Each jug = 23 \u00f7 8 = 2.875 l. Rounded to the nearest tenth = 2.9 l."} {"t":"q","id":23010,"q":"Amy took \\(\\dfrac{7}{12}\\) h to fix a jigsaw puzzle. Jenny took \\(\\dfrac{2}{3}\\) h slower to fix the same jigsaw puzzle. How long did Jenny take to fix the puzzle? Express your answer in the simplest form.","e":"Jenny = \\(\\dfrac{7}{12}\\) + \\(\\dfrac{2}{3}\\). Change \\(\\dfrac{2}{3}\\) to \\(\\dfrac{8}{12}\\): \\(\\dfrac{7}{12}\\) + \\(\\dfrac{8}{12}\\) = \\(\\dfrac{15}{12}\\) = \\(1\\dfrac{3}{12}\\) = \\(1\\dfrac{1}{4}\\) h."} {"t":"q","id":23014,"q":"Which of the following letters has at least one line of symmetry?","e":"The letter C has a horizontal line of symmetry (top and bottom halves mirror each other). G, N and K have no line of symmetry."} {"t":"q","id":23015,"q":"Bala is arranging stickers on a display board. He has more than 20 stickers but fewer than 50 stickers. When he arranges them in rows of 6, there are 4 stickers left over. When he arranges them in rows of 8, there are 2 stickers left over. How many stickers does Bala have?","e":"Need a number 20\u201350 that leaves remainder 4 when divided by 6 and remainder 2 when divided by 8. Check 34: 34 \u00f7 6 = 5 r4 \u2713 and 34 \u00f7 8 = 4 r2 \u2713. So Bala has 34 stickers."} {"t":"q","id":23016,"q":"Write twenty thousand and forty-one in numerals.
Ans: ","e":"Twenty thousand = 20 000, and forty-one = 41. Combine: 20 000 + 41 = 20 041."} {"t":"q","id":23017,"q":"Arrange these fractions from the smallest to the greatest.
\\(\\dfrac{8}{11}\\) , \\(\\dfrac{1}{2}\\) , \\(\\dfrac{5}{11}\\)
Ans: (smallest) , , (greatest)","e":"Compare: \\(\\dfrac{5}{11}\\) \u2248 0.45, \\(\\dfrac{1}{2}\\) = 0.5, \\(\\dfrac{8}{11}\\) \u2248 0.73. From smallest to greatest: \\(\\dfrac{5}{11}\\), \\(\\dfrac{1}{2}\\), \\(\\dfrac{8}{11}\\)."} {"t":"q","id":23018,"q":"Round 18 430 to the nearest hundred.
Ans: ","e":"Look at the tens digit of 18 430, which is 3. Since 3 < 5, round down: 18 430 \u2192 18 400."} {"t":"q","id":23024,"q":"Janice bought a roll of ribbon, 3 m long, to wrap some presents. She cut the roll of ribbon into 7 equal pieces. What is the length of each piece of ribbon? Round your answer to the nearest hundredth.
Ans: m","e":"Each piece = 3 \u00f7 7 = 0.428... m. Rounded to the nearest hundredth (2 decimal places) = 0.43 m."} {"t":"q","id":23026,"q":"Gladys jogged a distance of \\(\\dfrac{2}{3}\\) km. She jogged \\(\\dfrac{1}{5}\\) km more than the distance jogged by Ben. What was the total distance Gladys and Ben jogged? Give your answer as a mixed number.","e":"Ben = Gladys \u2212 \\(\\dfrac{1}{5}\\) = \\(\\dfrac{2}{3}\\) \u2212 \\(\\dfrac{1}{5}\\) = \\(\\dfrac{10}{15}\\) \u2212 \\(\\dfrac{3}{15}\\) = \\(\\dfrac{7}{15}\\) km. Total = \\(\\dfrac{2}{3}\\) + \\(\\dfrac{7}{15}\\) = \\(\\dfrac{10}{15}\\) + \\(\\dfrac{7}{15}\\) = \\(\\dfrac{17}{15}\\) = \\(1\\dfrac{2}{15}\\) km."} {"t":"q","id":23033,"q":"Weiling bought 24 packets of sweets. There were 32 sweets in each packet. She gave 12 sweets to each of her 40 classmates.
(a) How many sweets did Weiling buy altogether?
Ans: (a)
(b) How many sweets were left?
Ans: (b) ","e":"(a) Total bought = 24 \u00d7 32 = 768 sweets. (b) Sweets given away = 12 \u00d7 40 = 480. Sweets left = 768 \u2212 480 = 288."} {"t":"q","id":23034,"q":"Farid baked some cookies. He gave away \\(\\dfrac{3}{10}\\) of his cookies to his friends and gave away \\(\\dfrac{1}{2}\\) of his cookies to his siblings. He had 50 cookies left.
(a) What fraction of Farid's cookies was left?","e":"(a) Given away = \\(\\dfrac{3}{10}\\) + \\(\\dfrac{1}{2}\\) = \\(\\dfrac{3}{10}\\) + \\(\\dfrac{5}{10}\\) = \\(\\dfrac{8}{10}\\). Fraction left = \\(\\dfrac{10}{10}\\) \u2212 \\(\\dfrac{8}{10}\\) = \\(\\dfrac{2}{10}\\). (b) \\(\\dfrac{2}{10}\\) \u2192 50 cookies, so \\(\\dfrac{1}{10}\\) \u2192 25, and \\(\\dfrac{10}{10}\\) \u2192 25 \u00d7 10 = 250 cookies."} {"t":"q","id":23037,"q":"Sarah had twice as many blue beads as red beads. She had 3 times as many green beads as blue beads. She had a total of 1728 blue and green beads.
(a) How many green beads did Sarah have?
Ans: (a)
(b) How many fewer red beads than green beads did Sarah have?
Ans: (b) ","e":"Let red = 1 unit. Blue = 2 units, green = 3 \u00d7 blue = 6 units. Blue + green = 2 + 6 = 8 units = 1728, so 1 unit = 1728 \u00f7 8 = 216. (a) Green = 6 units = 6 \u00d7 216 = 1296. (b) Red = 1 unit = 216, so green \u2212 red = 1296 \u2212 216 = 1080."} {"t":"q","id":23038,"q":"The total mass of 3 identical tables and 5 identical stools is 173.1 kg. The total mass of 1 such table and 3 such stools is 65.3 kg.
(a) What is the total mass of a table and a stool?
Ans: (a) kg
(b) What is the mass of 4 stools?
Ans: (b) kg","e":"(a) 3 tables + 5 stools = 173.1; 1 table + 3 stools = 65.3. Tripling the second: 3 tables + 9 stools = 195.9. Subtract the first: 4 stools = 195.9 \u2212 173.1 = 22.8 kg, so 1 stool = 5.7 kg. From the second: 1 table = 65.3 \u2212 3 \u00d7 5.7 = 65.3 \u2212 17.1 = 48.2 kg. Table + stool = 48.2 + 5.7 = 53.9 kg. (b) 4 stools = 4 \u00d7 5.7 = 22.8 kg."} {"t":"q","id":23043,"q":"a) Arrange the following fractions in decreasing order.
\\(\\dfrac{3}{4}\\) , \\(\\dfrac{1}{3}\\) , \\(\\dfrac{7}{12}\\)
, ,
b) Find the value of \\(3 - \\dfrac{5}{6}\\)
","e":"a) Convert to twelfths: \\(\\dfrac{3}{4} = \\dfrac{9}{12}\\), \\(\\dfrac{1}{3} = \\dfrac{4}{12}\\), \\(\\dfrac{7}{12} = \\dfrac{7}{12}\\). Decreasing order: \\(\\dfrac{9}{12} > \\dfrac{7}{12} > \\dfrac{4}{12}\\), i.e. 3\/4, 7\/12, 1\/3.
b) \\(3 - \\dfrac{5}{6} = \\dfrac{18}{6} - \\dfrac{5}{6} = \\dfrac{13}{6} = 2\\dfrac{1}{6}\\)."} {"t":"q","id":23044,"q":"Cookies are sold in packets of 6. Each packet of cookies costs $5. Mdm Rani bought a total of 72 cookies altogether. How much did she pay?
$","e":"Number of packets \\(= 72 \\div 6 = 12\\). Cost \\(= 12 \\times \\$5 = \\$60\\)."} {"t":"q","id":23045,"q":"The table shows the number of boys and girls from Classes 4A and 4B who went on a learning journey.
Class 4A: 21 boys, 15 girls, total 36. Class 4B: ? boys, 17 girls, total 41.
Find the total number of boys who went for the learning journey.
","e":"Boys in 4B \\(= 41 - 17 = 24\\). Total boys \\(= 21 + 24 = 45\\)."} {"t":"q","id":23048,"q":"At first, Dan had the same amount of money as Evan. After Dan spent $480, Evan had three times as much money as Dan.
a) How much did Dan have in the end?
$
b) How much did Dan have at first?
$","e":"Let Dan's amount at the end be 1 unit; then Evan (unchanged) is 3 units. The difference between Evan and Dan-now is the $480 Dan spent, which equals \\(3u - 1u = 2u\\). So \\(2u = \\$480\\), giving \\(1u = \\$240\\) (Dan in the end). Dan at first = Evan = \\(3u = 3 \\times \\$240 = \\$720\\)."} {"t":"q","id":23050,"q":"Mr Lee bought \\(\\dfrac{1}{4}\\) kg of rice. He bought \\(\\dfrac{2}{5}\\) kg more flour than rice. How many kilograms of rice and flour did Mr Lee buy altogether? Express your answer in its simplest form.","e":"Rice \\(= \\dfrac{1}{4}\\) kg. Flour \\(= \\dfrac{1}{4} + \\dfrac{2}{5}\\) kg. Total rice and flour \\(= \\dfrac{1}{4} + \\left(\\dfrac{1}{4} + \\dfrac{2}{5}\\right)\\). Using the key's method: \\(\\dfrac{1}{4} + \\dfrac{2}{5} = \\dfrac{5}{20} + \\dfrac{8}{20} = \\dfrac{13}{20}\\) (flour); then \\(\\dfrac{13}{20} + \\dfrac{5}{20} = \\dfrac{18}{20} = \\dfrac{9}{10}\\) kg altogether."} {"t":"q","id":23051,"q":"On a farm, \\(\\dfrac{1}{6}\\) of the animals are sheep, \\(\\dfrac{1}{3}\\) of them are ducks and \\(\\dfrac{1}{4}\\) of them are horses. The remaining 90 animals are rabbits. How many animals are there in the farm altogether?
","e":"Fraction that are sheep, ducks and horses \\(= \\dfrac{1}{6} + \\dfrac{1}{3} + \\dfrac{1}{4} = \\dfrac{2}{12} + \\dfrac{4}{12} + \\dfrac{3}{12} = \\dfrac{9}{12} = \\dfrac{3}{4}\\). So rabbits are \\(1 - \\dfrac{3}{4} = \\dfrac{1}{4}\\), i.e. 3 of 12 equal units = 90. Per key: take 12 units total, rabbits = 3 units = 90, so 1 unit = 30, total = 12 units = \\(30 \\times 12 = 360\\) animals."} {"t":"q","id":23052,"q":"Ninety-four thousand, eight hundred and seven, written in numeral is","e":"Ninety-four thousand = 94 000; eight hundred = 800; and seven = 7. So \\(94000 + 800 + 7 = 94807\\). The numeral is 94 807."} {"t":"q","id":23053,"q":"Which of the following is a common factor of 4 and 8?","e":"Factors of 4: 1, 2, 4. Factors of 8: 1, 2, 4, 8. A common factor must divide BOTH numbers. Among the options, only 4 divides both 4 and 8. So the answer is 4."} {"t":"q","id":23055,"q":"There were 40 children queuing to enter a room. Every 4th child in the queue received a toy and every 5th child received a sweet. How many children received both a toy and a sweet?","e":"A child gets both if their position is a common multiple of 4 and 5, i.e. a multiple of 20. Within 40, these are positions 20 and 40. So 2 children received both."} {"t":"q","id":23056,"q":"If you add 1 to a certain number and round it to the nearest ten, the answer is 1950. If you add 2 to the number and round it to the nearest ten, the answer is 1960. What is the number?","e":"Try 1953: \\(1953 + 1 = 1954\\), which rounds to 1950. \\(1953 + 2 = 1955\\), which rounds to 1960. Both conditions are satisfied, so the number is 1953."} {"t":"q","id":23057,"q":"What is the largest number that can be formed using the digits 4, 7, 6, and 1? ","e":"To make the largest number, arrange the digits from greatest to smallest: 7, 6, 4, 1. So the largest number is 7641."} {"t":"q","id":23058,"q":"What is the sum of the first two multiples of 5? ","e":"The first two multiples of 5 are 5 and 10. Their sum is \\(5 + 10 = 15\\)."} {"t":"q","id":23060,"q":"When rounded to the nearest hundred, the number of audience at a theatre was 2600. Write down the largest possible number of audience at the theatre. ","e":"Numbers from 2550 to 2649 round to 2600 (to the nearest hundred). The largest of these is 2649."} {"t":"q","id":23062,"q":"Sarah sold a total of 20 bowls and plates for $86. Each bowl was sold at $5 and each plate was sold at $3. How many bowls did Sarah sell? ","e":"If all 20 were plates: \\(20 \\times 3 = 60\\) dollars. The actual total is $86, which is \\(86 - 60 = 26\\) more. Each bowl is \\(5 - 3 = 2\\) dollars more than a plate, so number of bowls = \\(26 \\div 2 = 13\\). Sarah sold 13 bowls."} {"t":"q","id":23063,"q":"Ethan had twice as many beads as Sophie. After Ethan used 36 beads for a bracelet, Sophie had twice as many beads as Ethan. How many beads did Sophie have at first? ","e":"Let Sophie have 1 unit at first, so Ethan had 2 units. After using 36, Ethan had \\(2\\text{ units} - 36\\), and this equals half of Sophie's, i.e. Sophie's 1 unit = \\(2 \\times (2\\text{ units} - 36)\\). So \\(1\\text{ unit} = 4\\text{ units} - 72\\), giving \\(3\\text{ units} = 72\\), so 1 unit = 24. Sophie had 24 beads at first."} {"t":"q","id":23064,"q":"Siti spent a total of $1400 on a bookshelf, a table and a chair. The bookshelf cost $630. The table cost $500 more than the chair.
(a) How much did she spend on the table and the chair altogether?
(b) How much did she spend on the chair? ","e":"(a) Table + chair = total - bookshelf = \\(1400 - 630 = 770\\) dollars. (b) Table = chair + 500, so chair + chair + 500 = 770, giving \\(2 \\times \\text{chair} = 770 - 500 = 270\\), so chair = \\(270 \\div 2 = 135\\) dollars."} {"t":"q","id":23065,"q":"Which of the following is forty-five thousand, nine hundred and six in numerals?","e":"Forty-five thousand = 45 000, nine hundred = 900, and six = 6. Adding these gives 45 000 + 900 + 6 = 45 906. The answer is option (3), 45 906."} {"t":"q","id":23066,"q":"Arrange these numbers in decreasing order.
86 372, 85 327, 86 237","e":"Decreasing order means largest to smallest. Compare the thousands: 86 372 and 86 237 both have 86 thousands, and 85 327 has 85 thousands so it is smallest. Between 86 372 and 86 237, the hundreds 3 > 2, so 86 372 > 86 237. Order: 86 372, 86 237, 85 327. The answer is option (2)."} {"t":"q","id":23067,"q":"In the following number pattern, what is the missing number?
62 831, 62 931, ____________, 63 131, 63 231, 63 331, 63 431","e":"Each term increases by 100: 62 831 + 100 = 62 931, then 62 931 + 100 = 63 031. Checking forward, 63 031 + 100 = 63 131 which matches. The missing number is 63 031, option (3)."} {"t":"q","id":23068,"q":"Which of the following numbers when rounded to the nearest hundred becomes 84 000?","e":"Rounding to the nearest hundred: 83 875 rounds to 83 900; 83 953 rounds to 84 000; 84 092 rounds to 84 100; 84 234 rounds to 84 200. Only 83 953 rounds to 84 000. The answer is option (2)."} {"t":"q","id":23069,"q":"Which of the following has both 4 and 7 as factors?","e":"A number with both 4 and 7 as factors must be a multiple of \\(4 \\times 7 = 28\\). Checking: 11 (no), 21 = 3 x 7 (only 7), 64 = 4 x 16 (only 4), 84 = 28 x 3 (both 4 and 7). The answer is option (4), 84."} {"t":"q","id":23070,"q":"At a party, every 6th guest gets a lollipop and every 8th guest gets a packet of juice. Which guest is the first to get both a lollipop and a packet of juice?","e":"The first guest to get both is the lowest common multiple of 6 and 8. Multiples of 6: 6, 12, 18, 24; multiples of 8: 8, 16, 24. The smallest common multiple is 24, so the 24th guest is first to get both. The answer is option (3)."} {"t":"q","id":23071,"q":"a) What is the value of the digit 7 in 58 701?
b) Round 19 572 to the nearest thousand.
(a)   (b) ","e":"a) In 58 701 the digit 7 is in the hundreds place, so its value is \\(7 \\times 100 = 700\\). b) To round 19 572 to the nearest thousand, look at the hundreds digit 5; since 5 rounds up, 19 572 becomes 20 000."} {"t":"q","id":23072,"q":"a) Write 7 ten thousands, 64 tens and 3 ones in numerals.
b) Find the value of \\(4308 \\times 9\\).
(a)   (b) ","e":"a) 7 ten thousands = 70 000, 64 tens = 640, 3 ones = 3. Sum: 70 000 + 640 + 3 = 70 643. b) \\(4308 \\times 9 = 38772\\)."} {"t":"q","id":23073,"q":"Read the statements made by these 2 students carefully. Ariel says 4 is a factor of 96. Tom says 4 is a factor of 76. One of the following statements is correct.","e":"Check whether 4 divides each number. 96 divided by 4 is 24 with no remainder, so 4 is a factor of 96 (Ariel is correct). 76 divided by 4 is 19 with no remainder, so 4 is a factor of 76 (Tom is correct). Both are correct, so the correct statement is 'Both Ariel and Tom are correct.'"} {"t":"q","id":23074,"q":"Alvin, Simon and Tina shared $6726 equally among themselves. Simon spent $1045 of his money. How much money did Simon have in the end?
Answer: ","e":"Each person's share: \\(6726 \\div 3 = 2242\\), so Simon had $2242. After spending $1045: \\(2242 - 1045 = 1197\\). Simon had $1197 left."} {"t":"q","id":23075,"q":"Mike has 75 packets of stamps. Each packet has 26 stamps. He packs all his stamps into bags of 5. How many bags of 5 stamps are there?
Answer: ","e":"Total stamps: \\(75 \\times 26 = 1950\\). Each bag holds 5 stamps, so number of bags: \\(1950 \\div 5 = 390\\). There are 390 bags."} {"t":"q","id":23076,"q":"A desk cost twice as much as a chair. Daniel spent $2264 on 2 identical desks and 4 identical chairs. What was the total cost of a desk and a chair?
Answer: ","e":"Let a chair be 1 unit; a desk is then 2 units. 2 desks = 4 units and 4 chairs = 4 units, giving \\(4 + 4 = 8\\) units. So 8 units = $2264 and 1 unit = \\(2264 \\div 8 = 283\\). A desk and a chair together = 2 units + 1 unit = 3 units = \\(283 \\times 3 = 849\\). The total cost is $849."} {"t":"q","id":23077,"q":"Sandy had some sweets to give her friends. If she gave each friend 4 sweets, she would have 22 sweets left. If she gave each friend 6 sweets, she would have 8 sweets left. How many sweets did Sandy have?
Answer: ","e":"Each friend gets 2 more sweets in the second case (\\(6 - 4 = 2\\)), and the leftover drops by \\(22 - 8 = 14\\) sweets. So those 14 extra sweets cover the 2-per-friend increase: number of friends = \\(14 \\div 2 = 7\\). Total sweets = (4 sweets x 7 friends) + 22 left over = \\(28 + 22 = 50\\). Sandy had 50 sweets."} {"t":"q","id":23078,"q":"Forty-six thousand and sixteen in figures is .","e":"Forty-six thousand = 46 000, and sixteen = 16. 46 000 + 16 = 46 016. Option (3)."} {"t":"q","id":23079,"q":"In which of the following numbers does the digit 8 stands for 80?","e":"The 8 must be in the tens place to stand for 80. In 3082 the 8 is in the tens place (80). Option (2)."} {"t":"q","id":23080,"q":"13 429 rounded to the nearest hundred is .","e":"Look at the tens digit (2). Since 2 < 5, round down: 13 429 to the nearest hundred is 13 400. Option (3)."} {"t":"q","id":23082,"q":"\\(\\dfrac{1}{3}+\\dfrac{1}{9}=\\)","e":"Make denominators the same: \\(\\dfrac{1}{3}=\\dfrac{3}{9}\\). Then \\(\\dfrac{3}{9}+\\dfrac{1}{9}=\\dfrac{4}{9}\\). Option (4)."} {"t":"q","id":23084,"q":"What is the number when 17.54 is rounded to 1 decimal place?","e":"To round to 1 decimal place, look at the hundredths digit (4). Since 4 < 5, keep the tenths digit: 17.54 to 1 d.p. is 17.5. Option (2)."} {"t":"q","id":23085,"q":"Abby started cleaning her room at 13 30. She took 1 h 30 min to clean her room. What time did she finish cleaning her room?","e":"13 30 + 1 h 30 min = 15 00. Option (4)."} {"t":"q","id":23091,"q":"Jason spent $55 on 2 identical shirts and a pair of pants. A pair of pants cost $25 more than a shirt. How much did he spend on 1 shirt?","e":"$55 - $25 = $30 is the cost of 3 shirts' worth (2 shirts + 1 shirt-equivalent of pants). 3 units = $30, so 1 shirt = $10. Option (1)."} {"t":"q","id":23093,"q":"\\(83\\,905 = 80\\,000 + 3000 +\\) \\(+ 5\\)
What is the missing number?","e":"83 905 = 80 000 + 3000 + 900 + 5. The missing number is 900 (the hundreds value)."} {"t":"q","id":23094,"q":"Write the missing number in the number pattern below.
13 000 , 12 600 , 12 200 , 11 800 , , 11 000","e":"Each term decreases by 400. 11 800 - 400 = 11 400."} {"t":"q","id":23098,"q":"Write 5 thousandths as a decimal.
Answer: ","e":"5 thousandths = 5 \u00f7 1000 = 0.005."} {"t":"q","id":23099,"q":"Write \\(\\dfrac{85}{100}\\) as a decimal.
Answer: ","e":"\\(\\dfrac{85}{100}\\) is 85 hundredths = 0.85."} {"t":"q","id":23100,"q":"Arrange the following numbers in order from the greatest to the smallest.
3.909, 3.093, 3.099
(a)   (b)   (c) ","e":"Compare tenths first: 3.909 has 9 tenths (largest). Then 3.099 vs 3.093 \u2014 hundredths equal (9), thousandths 9 > 3, so 3.099 > 3.093. Order greatest to smallest: 3.909, 3.099, 3.093."} {"t":"q","id":23103,"q":"Mrs Wong wants to pack 36 blueberry cupcakes and 54 chocolate cupcakes into boxes with no remainder. The total number of cupcakes packed into each box is the same. The number of blueberry cupcakes in each box is the same. What is the greatest number of boxes that Mrs Wong can pack?
Answer: ","e":"Find the common factors of 36 and 54: 1, 2, 3, 6, 9, 18. The greatest common factor is 18, so the greatest number of boxes is 18."} {"t":"q","id":23110,"q":"Aini prepared 6 \\(\\ell\\) of fruit punch for a party. She poured them equally into 4 bottles. What is the volume of the fruit punch in each bottle?
Answer: ","e":"6 \\(\\ell\\) \u00f7 4 = 1.5 \\(\\ell\\) in each bottle."} {"t":"q","id":23111,"q":"Kelvin is 1.81 m tall. He is 0.35 m taller than Jonathan. Jonathan is 0.29 m shorter than Elson. What is Elson's height?
Answer: ","e":"Jonathan = 1.81 - 0.35 = 1.46 m. Elson is 0.29 m taller than Jonathan: 1.46 + 0.29 = 1.75 m."} {"t":"q","id":23112,"q":"Leela's watch is 15 minutes slower. The time shown on her watch is 1.35 p.m. Find the actual time using the 24-hour clock.
Answer: ","e":"The watch is 15 min slow, so the actual time is 15 min later: 1.35 p.m. + 15 min = 1.50 p.m. = 13 50 in the 24-hour clock."} {"t":"q","id":23113,"q":"When I open my storybook, two pages face me. The sum of these two page numbers is 667. What is the page number of the smaller number?
Answer: ","e":"Two facing pages are consecutive numbers. Sum = 667, so the smaller page = (667 - 1) \u00f7 2 = 666 \u00f7 2 = 333."} {"t":"q","id":23114,"q":"Mark bought some sweets. He gave his friends \\(\\dfrac{1}{7}\\) of the sweets and gave his brother \\(\\dfrac{3}{4}\\) of the sweets. All the remaining sweets were eaten by him. What fraction of the sweets did Mark eat?","e":"Given away = \\(\\dfrac{1}{7}+\\dfrac{3}{4}=\\dfrac{4}{28}+\\dfrac{21}{28}=\\dfrac{25}{28}\\). Mark ate the rest: \\(\\dfrac{28}{28}-\\dfrac{25}{28}=\\dfrac{3}{28}\\)."} {"t":"q","id":23117,"q":"Nicole had baked five times as many cookies as Joey at first. After Nicole gave away 235 cookies and Joey gave away 19 cookies, they had the same number of cookies left.
(a) How many cookies did Nicole bake at first?
(b) How many cookies did each of them have in the end?
(a)   (b) ","e":"Let Joey = 1 unit, Nicole = 5 units. After giving away: 5u - 235 = 1u - 19, so 4u = 235 - 19 = 216, 1u = 54. (a) Nicole baked 5u = 5 \u00d7 54 = 270. (b) Each had 1u - 19 = 54 - 19 = 35 in the end."} {"t":"q","id":23118,"q":"Mrs Devi and Mdm Tan baked an equal number of muffins for sale. Mrs Devi sold 49 muffins and had \\(\\dfrac{2}{9}\\) of the muffins left.
(a) How many muffins did Mrs Devi have left?
(b) How many muffins did Mrs Devi and Mdm Tan bake in all?
(a)   (b) ","e":"Mrs Devi sold \\(\\dfrac{7}{9}\\) of her muffins (since \\(\\dfrac{2}{9}\\) are left) = 49, so 7 units = 49, 1 unit = 7. (a) Left = 2 units = 2 \u00d7 7 = 14. (b) Each baked 9 units = 9 \u00d7 7 = 63; total for both = 63 \u00d7 2 = 126."} {"t":"q","id":23119,"q":"Charlie had twice as marbles as Sally. After Sally lost 45 marbles, Charlie had 5 times as many marbles as Sally. How many marbles did Charlie have?
Answer: ","e":"Charlie's marbles never change. At first Charlie = 2 \u00d7 Sally. After Sally loses 45, Charlie = 5 \u00d7 (new Sally). Let new Sally = 1 unit, Charlie = 5 units; original Sally = 5u \u00f7 2. Since Sally lost 45: 5u\/2 - 45 = u, giving 3u\/2 = 45, u = 30. Charlie = 5u... using the key: 3u = 45 + 45 = 90, 1u = 30, Charlie = 5 \u00d7 30 = 150."} {"t":"q","id":23120,"q":"Three children shared some money. Alice and Benny received $100 altogether. Benny and Catherine received $450 in all. Catherine received five times as much money as Alice. How much money did Alice receive?
Answer: ","e":"Catherine - Alice = (Benny+Catherine) - (Alice+Benny) = 450 - 100 = 350. Catherine is 5 times Alice, so Catherine - Alice = 4 units = 350, 1 unit = 350 \u00f7 4 = $87.50. Alice (1 unit) received $87.50."} {"t":"q","id":23121,"q":"77 thousands and 3 tens is the same as ____________.","e":"77 thousands = 77 000 and 3 tens = 30. 77 000 + 30 = 77 030."} {"t":"q","id":23122,"q":"Which of the following is not a factor of 56?","e":"Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56. 56 \u00f7 6 = 9 remainder 2, so 6 is not a factor."} {"t":"q","id":23124,"q":"Which of the following fractions is in its simplest form?","e":"4\/9: no common factor of 4 and 9 except 1, so it is in simplest form. 2\/8 = 1\/4, 3\/12 = 1\/4, 6\/10 = 3\/5."} {"t":"q","id":23128,"q":"Arrange these distances from the longest to the shortest.
\\(1340m\\) , \\(1km\\ 304m\\) , \\(1\\dfrac{3}{4}km\\)","e":"Convert all to metres: 1340 m; 1 km 304 m = 1304 m; 1 3\/4 km = 1750 m. Longest to shortest: 1750 m (1 3\/4 km), 1340 m, 1304 m (1 km 304 m)."} {"t":"q","id":23129,"q":"The table shows the number of Pok\u00e9mon cards five boys have.
Ali: 84, Brian: 48, Cheng: 112, Dinesh: 56, Ethan: 102
Which two boys have a total of 150 Pok\u00e9mon cards?","e":"Brian (48) + Ethan (102) = 150. (Ali 84 + Dinesh 56 = 140; Brian 48 + Cheng 112 = 160; Dinesh 56 + Ethan 102 = 158.)"} {"t":"q","id":23130,"q":"A baker bought 5.44 kg of flour. He repacked it equally into 8 packets. How much flour was there in each packet?","e":"5.44 kg \u00f7 8 = 0.68 kg in each packet."} {"t":"q","id":23131,"q":"Ken started painting his bedroom at 9 a.m. He stopped for lunch at 12 p.m. and continued painting at 1.30 p.m. He finished painting his room at 4.30 p.m. How long did he take to paint his room?","e":"Morning: 9 a.m. to 12 p.m. = 3 h. Afternoon: 1.30 p.m. to 4.30 p.m. = 3 h. Total painting time = 3 h + 3 h... wait, 3 h + 3 h would be 6 h, but lunch (12 to 1.30) is excluded. Total = 3 h + 3 h = 6 h? Actual painting: 3 h + 3 h = 6 h. Key gives option 1 (5 h 30 min); morning 9 to 12 = 3 h, afternoon 1.30 to 4.30 = 3 h, total painting 6 h. See notes."} {"t":"q","id":23132,"q":"The figure shows the flight departure details to Hong Kong.
Sunshine Airlines \u2014 Hong Kong, Flight Departure Time: 15 05.
Amber needs to reach the boarding gate at least 30 min before the flight departure time. She takes 20 min to walk to the boarding gate. What is the latest time she should start walking to the boarding gate?","e":"Must reach gate by 30 min before 15 05 = 14 35. She walks 20 min, so she must start by 14 35 - 20 min = 14 15."} {"t":"q","id":23136,"q":"The table shows the number of children and adults who visited the library on a weekday. Part of the table is covered by an ink blot.
Male \u2014 Children 119, Adults [hidden], Total 246.
Female \u2014 Children 123, Adults 230, Total 353.
What is the total number of adults who went to the library on that weekday?","e":"Male adults = total 246 \u2212 children 119 = 127. Total adults = male adults 127 + female adults 230 = 357."} {"t":"q","id":23138,"q":"The first 18 letters of a pattern are given.
C, A, B, C, D, E, C, A, B, C, D, E, C, A, B, C, D, E, ...?
What is the letter in the 50th position?","e":"The pattern repeats every 6 letters: C, A, B, C, D, E. 50 \u00f7 6 = 8 remainder 2, so the 50th letter is the 2nd letter of the block, which is A."} {"t":"q","id":23139,"q":"Tyra paid $9.60 for 4 similar rulers and 4 similar files. Each file cost $0.70 more than each ruler. How much did each ruler cost?","e":"4 files cost 4 \u00d7 $0.70 = $2.80 more than 4 rulers. Remove this: $9.60 \u2212 $2.80 = $6.80 for 8 rulers' worth. $6.80 \u00f7 8 = $0.85 per ruler."} {"t":"q","id":23140,"q":"A player has to play a total of four games in Round 1 of a competition. The scores for Malik's first three games are: 1st 9.3, 2nd 10.1, 3rd 9.5, 4th ?.
Malik will qualify for Round 2 if the total score for three out of the four games is 30 or more. What is the lowest score Malik must get in the 4th game to qualify for Round 2?","e":"Best three of four must total \u2265 30. The two highest existing scores are 10.1 + 9.5 = 19.6. The 4th game must make the best three reach 30: 30 \u2212 19.6 = 10.4. So the lowest 4th-game score is 10.4."} {"t":"q","id":23141,"q":"Round 29 540 to the nearest hundred. ","e":"The tens digit is 4 (less than 5), so round down: 29 540 rounds to 29 500."} {"t":"q","id":23143,"q":"Arrange these fractions from the smallest to the greatest.
\\(\\dfrac{4}{7}\\) , \\(\\dfrac{1}{2}\\) , \\(\\dfrac{6}{7}\\)
, , ","e":"1\/2 = 3.5\/7, so 1\/2 < 4\/7 < 6\/7. Smallest to greatest: 1\/2, 4\/7, 6\/7."} {"t":"q","id":23145,"q":"\\(\\dfrac{3}{4}\\) + \\(\\dfrac{1}{8}\\) =","e":"3\/4 = 6\/8. 6\/8 + 1\/8 = 7\/8."} {"t":"q","id":23147,"q":"Write 64 thousandths as a decimal. ","e":"64 thousandths = 64\/1000 = 0.064."} {"t":"q","id":23149,"q":"Express 0.39 as a fraction.","e":"0.39 = 39 hundredths = 39\/100. 39 and 100 share no common factor, so it is already in simplest form."} {"t":"q","id":23150,"q":"Write the missing number in the number pattern.
11 005 , 10 205 , 9405 , 8605 , , 7005","e":"Each term decreases by 800: 11 005 \u2212 800 = 10 205, ... 8605 \u2212 800 = 7805 (then 7805 \u2212 800 = 7005)."} {"t":"q","id":23151,"q":"Mdm Tan had $7360. She saved $4825 and divided the rest equally among her 3 children. How much did each child receive? $","e":"Remaining after saving: $7360 \u2212 $4825 = $2535. Each child: $2535 \u00f7 3 = $845."} {"t":"q","id":23152,"q":"Sally bought 18 donuts at 3 for $3.95. How much did she pay for the donuts? $","e":"18 donuts \u00f7 3 = 6 sets. 6 \u00d7 $3.95 = $23.70."} {"t":"q","id":23153,"q":"Raju had $50. A bar of chocolate cost $5.50. At a sale (Buy 2 Get 1 Free), Raju took home 6 bars of chocolate. How much change did he receive? $","e":"Buy 2 get 1 free: for 6 bars taken home, Raju pays for only 4 bars. 4 \u00d7 $5.50 = $22. Change = $50 \u2212 $22 = $28."} {"t":"q","id":23156,"q":"Uncle Lee had three times as many apples as Aunt Mei. After he sold 75 apples, Aunt Mei had twice as many apples as him. How many apples did Aunt Mei have? ","e":"Let Aunt Mei have M. Uncle Lee had 3M. After selling 75: 3M \u2212 75. Aunt Mei is now twice his: M = 2(3M \u2212 75) \u2192 M = 6M \u2212 150 \u2192 150 = 5M \u2192 M = 30. (Per key working: 75 \u00f7 5 = 15; total parts give Aunt Mei 30.)"} {"t":"q","id":23160,"q":"In which of the following does the digit 8 stand for 800?","e":"The digit 8 stands for 800 when it sits in the hundreds place. In 5840, the 8 is in the hundreds place, so it stands for 800. In 4058 it is 8, in 5084 it is 80, in 8504 it is 8000."} {"t":"q","id":23161,"q":"45 879 rounded to the nearest hundred is ____________.","e":"To round 45 879 to the nearest hundred, look at the tens digit (7). Since 7 is 5 or more, round the hundreds up: 45 879 rounds to 45 900."} {"t":"q","id":23162,"q":"Arrange these fractions from the smallest to the greatest.
\\(\\dfrac{1}{2}\\) , \\(\\dfrac{4}{9}\\) , \\(\\dfrac{8}{9}\\)","e":"Compare the fractions: 4\/9 is just under a half (4.5\/9 = 1\/2), so 4\/9 < 1\/2. And 8\/9 is the largest. Ordered smallest to greatest: 4\/9, 1\/2, 8\/9."} {"t":"q","id":23164,"q":"Which decimal is the smallest?","e":"Compare the decimals by place value. 3.038 has 0 tenths and 3 hundredths, the smallest of all. 3.07 = 3.070, 3.15, 3.304 are all larger. So 3.038 is smallest."} {"t":"q","id":23165,"q":"Write \\(4\\dfrac{7}{20}\\) as a decimal.","e":"Convert 7\/20 to a decimal: multiply numerator and denominator by 5 to get 35\/100 = 0.35. So 4 7\/20 = 4.35."} {"t":"q","id":23168,"q":"Adam is below 10 years old. His age is a factor of 28 and a multiple of 4. How old is he?","e":"Factors of 28 below 10: 1, 2, 4, 7. Of these, the multiples of 4 are: 4. So Adam is 4 years old. (8 is a multiple of 4 but not a factor of 28.)"} {"t":"q","id":23169,"q":"In a library, there were 2580 fiction books. The number of non-fiction books was 3 times the number of fiction books. How many books were there altogether?","e":"Non-fiction = 3 x 2580 = 7740. Altogether = 2580 + 7740 = 10 320 books."} {"t":"q","id":23170,"q":"Mrs Lim had some money. After buying 48 toy planes at $367 each, she had $10 left. How much money did she have at first?","e":"Cost of planes = 48 x $367 = $17 616. She had $10 left, so at first = $17 616 + $10 = $17 626."} {"t":"q","id":23171,"q":"Azri and Liying had the same number of stamps at first. After Azri gave away 60 stamps, Liying had 5 times as many stamps as Azri. How many stamps did Azri have at first?","e":"Let Azri's amount after giving away be 1 unit; Liying = 5 units. They started equal, so the 60 given away is the difference: 5 units - 1 unit = 4 units = 60, so 1 unit = 15. Azri started with the same as Liying = 5 units = 75 stamps."} {"t":"q","id":23172,"q":"Mrs Lee used \\(\\dfrac{3}{8}\\) kg of flour to bake cookies. The amount of flour used to bake a cake was \\(\\dfrac{1}{5}\\) kg more than the amount used to bake cookies. How much flour did she use altogether?","e":"Cake flour = 3\/8 + 1\/5 = 15\/40 + 8\/40 = 23\/40 kg. Altogether = cookies + cake = 3\/8 + 23\/40 = 15\/40 + 23\/40 = 38\/40 = 19\/20 kg."} {"t":"q","id":23173,"q":"A rope of length 20 m is cut into 8 equal pieces. How long is each piece?","e":"Length of each piece = 20 div 8 = 2.5 m."} {"t":"q","id":23174,"q":"A decimal when rounded to the nearest whole number is 175. Which of the following is the smallest possible decimal?","e":"To round to 175, the decimal must be at least 174.5 (rounds up) and below 175.5. 174.49 rounds to 174 (too small). 174.50 rounds up to 175 and is the smallest of the options that rounds to 175."} {"t":"q","id":23180,"q":"Arrange these numbers from the smallest to the greatest.
5604 , 5064 , 5640
, , ","e":"Compare the numbers by place value. 5064 (thousands 5, hundreds 0), 5604 (hundreds 6), 5640 (hundreds 6, tens 4). Smallest to greatest: 5064, 5604, 5640."} {"t":"q","id":23181,"q":"Some factors of 18 are 1, 2, 3 and 18. What are the other two factors of 18?
and ","e":"The factors of 18 are 1, 2, 3, 6, 9, 18. The ones not listed are 6 and 9."} {"t":"q","id":23182,"q":"Write \\(3\\dfrac{4}{5}\\) as an improper fraction.","e":"Multiply the whole number by the denominator and add the numerator: 3 x 5 + 4 = 19. So 3 4\/5 = 19\/5."} {"t":"q","id":23183,"q":"\\(\\dfrac{1}{4} + \\dfrac{5}{8}\\) =","e":"Make the denominators the same: 1\/4 = 2\/8. Then 2\/8 + 5\/8 = 7\/8."} {"t":"q","id":23184,"q":"\\(1 - \\dfrac{1}{10} - \\dfrac{1}{5}\\) =","e":"Convert to tenths: 1 = 10\/10, 1\/5 = 2\/10. Then 10\/10 - 1\/10 - 2\/10 = 7\/10."} {"t":"q","id":23192,"q":"There are 872 pears and peaches in a box. \\(\\dfrac{3}{8}\\) of them are pears. How many peaches are there?
","e":"Peaches are the remaining fraction: 1 - 3\/8 = 5\/8. Number of peaches = 5\/8 x 872 = 5 x 109 = 545."} {"t":"q","id":23193,"q":"Mrs Tay bought a dress and 2 skirts for $250. The dress cost $65.50 more than a skirt. What was the cost of 1 skirt?
$","e":"Let 1 skirt = 1 unit. Dress = 1 unit + $65.50. Total = 3 units + $65.50 = $250, so 3 units = $184.50, 1 unit = $61.50. One skirt costs $61.50."} {"t":"q","id":23198,"q":"Johnson and Steven have 1200 sweets altogether. Johnson has 5 times as many sweets as Steven. How many sweets must Johnson give to Steven so that they have the same number of sweets?
","e":"Total = 6 units = 1200, so 1 unit = 200. Steven = 200, Johnson = 1000. To be equal each must have 600. Johnson must give Steven 1000 - 600 = 400 sweets. (Equivalently, give 2 units = 400.)"} {"t":"q","id":23199,"q":"In a clothing donation drive, Classes 4A, 4B and 4C collected 3445 kg of clothes in total. Class 4A collected 123 kg less than the combined collection of classes 4B and 4C. Class 4C collected 3 times the amount collected by class 4B. What was the amount of clothes collected by class 4B?
","e":"Let 4B = 1 unit, 4C = 3 units, so 4B+4C = 4 units. 4A = 4 units - 123. Total = (4 units) + (4 units - 123) = 8 units - 123 = 3445. So 8 units = 3568, 1 unit = 446. Class 4B collected 446 kg."} {"t":"q","id":23200,"q":"Joan had some money. She spent \\(\\dfrac{2}{3}\\) of it on a dress and \\(\\dfrac{1}{4}\\) of it on a doll. She had $27 left. How much more money did she spend on the dress than on the doll?
$","e":"Spent = 2\/3 + 1\/4 = 8\/12 + 3\/12 = 11\/12. Left = 1\/12 = $27, so the whole = $324. Dress = 8\/12 = $216, doll = 3\/12 = $81. Difference = 216 - 81 = $135."} {"t":"q","id":23201,"q":"Lisa had 10 kg of grapes more than Zara. When Lisa gave away 1.5 kg of grapes and Zara gave away 0.5 kg of grapes, Lisa still had 4 times as much grapes as Zara. How many kilograms of grapes did Zara have at first?
","e":"After giving away, the difference between Lisa and Zara = 10 - 1.5 + 0.5 = 9 kg. This difference is 4 units - 1 unit = 3 units = 9 kg, so 1 unit = 3 kg (Zara's amount after giving away). Zara at first = 3 + 0.5 = 3.5 kg."} {"t":"q","id":23204,"q":"Thirty-four thousand and sixty-two in figures is .","e":"Thirty-four thousand = 34 000; sixty-two = 62. Together: \\(34\\,000 + 62 = 34\\,062\\)."} {"t":"q","id":23205,"q":"Which of the following when rounded to the nearest hundred gives 60 000?","e":"Rounding to the nearest hundred: 59 951 rounds to 60 000 (the tens digit 5 rounds up). 59 599 rounds to 59 600; 60 070 rounds to 60 100; 60 140 rounds to 60 100."} {"t":"q","id":23206,"q":"What is the second common multiple of 4 and 6?","e":"Common multiples of 4 and 6 are 12, 24, 36, ... The first is 12 and the second is 24."} {"t":"q","id":23208,"q":"Which of the following fractions is equivalent to \\(\\dfrac{4}{6}\\)?","e":"\\(\\dfrac{4}{6} = \\dfrac{2}{3}\\). Checking: \\(\\dfrac{12}{18} = \\dfrac{2}{3}\\), so it is equivalent."} {"t":"q","id":23209,"q":"In the number 41.32, the digit is in the hundredths place.","e":"In 41.32, the first decimal place (tenths) is 3 and the second (hundredths) is 2. So the digit in the hundredths place is 2."} {"t":"q","id":23214,"q":"Mr Ng took a flight from Singapore to Japan. He boarded the plane at 23 39 and reached Japan at 06 22 the next day. How long was the flight?","e":"From 23 39 to 24 00 is 21 min. From 00 00 to 06 22 is 6 h 22 min. Total: \\(6\\ h\\ 22\\ min + 21\\ min = 6\\ h\\ 43\\ min\\)."} {"t":"q","id":23217,"q":"Elize had a string that was 15.61 m long. She used 1.54 m to tie a parcel and cut the remaining string into 7 equal pieces. How long was each piece of string?","e":"Remaining string = \\(15.61 - 1.54 = 14.07\\) m. Each piece = \\(14.07 \\div 7 = 2.01\\) m."} {"t":"q","id":23218,"q":"Kelly used \\(\\dfrac{3}{10}\\) kg of coffee powder. She used \\(\\dfrac{1}{5}\\) kg less coffee powder than Frances. How much coffee powder did they use altogether?","e":"Frances = \\(\\dfrac{3}{10} + \\dfrac{1}{5} = \\dfrac{3}{10} + \\dfrac{2}{10} = \\dfrac{5}{10} = \\dfrac{1}{2}\\) kg. Altogether = \\(\\dfrac{3}{10} + \\dfrac{5}{10} = \\dfrac{8}{10} = \\dfrac{4}{5}\\) kg."} {"t":"q","id":23222,"q":"Fill in the blank with the correct number in the number pattern below.
875 , 845 , 815 , , 755","e":"The pattern decreases by 30 each time: \\(875 - 845 = 30\\). So the missing term is \\(815 - 30 = 785\\) (and \\(785 - 30 = 755\\) checks)."} {"t":"q","id":23226,"q":"The perimeter of a square is 76 cm. What is the area of the square? ","e":"Side = \\(76 \\div 4 = 19\\) cm. Area = \\(19 \\times 19 = 361\\) cm\u00b2. Answer in \\(cm^2\\)."} {"t":"q","id":23229,"q":"Liana started doing a science quiz at 12.42 p.m. There were 8 questions in this quiz. For the first 3 questions, Liana took 6 minutes to complete each question. For the remaining questions, she took 7 minutes to complete each question. At what time did Liana complete the quiz? Express your answer using the 24-hour clock. ","e":"First 3 questions: \\(3 \\times 6 = 18\\) min. Remaining \\(8 - 3 = 5\\) questions: \\(5 \\times 7 = 35\\) min. Total = \\(18 + 35 = 53\\) min. \\(12.42\\ p.m. + 53\\ min = 1.35\\ p.m. = 1335\\)."} {"t":"q","id":23231,"q":"Which two of the fractions below are in the simplest form?
\\(\\dfrac{2}{5}\\) , \\(\\dfrac{3}{6}\\) , \\(\\dfrac{5}{7}\\) , \\(\\dfrac{6}{8}\\)
and ","e":"\\(\\dfrac{3}{6} = \\dfrac{1}{2}\\) and \\(\\dfrac{6}{8} = \\dfrac{3}{4}\\) can be simplified. \\(\\dfrac{2}{5}\\) and \\(\\dfrac{5}{7}\\) cannot, so they are already in simplest form."} {"t":"q","id":23232,"q":"Find the value of \\(1 - \\dfrac{1}{3} - \\dfrac{2}{9}\\).","e":"Use ninths: \\(1 = \\dfrac{9}{9}\\), \\(\\dfrac{1}{3} = \\dfrac{3}{9}\\). \\(\\dfrac{9}{9} - \\dfrac{3}{9} - \\dfrac{2}{9} = \\dfrac{4}{9}\\)."} {"t":"q","id":23234,"q":"Arrange the following numbers from the smallest to the greatest.
\\(0.801\\) , \\(0.081\\) , \\(\\dfrac{4}{5}\\)
, , ","e":"\\(\\dfrac{4}{5} = 0.800\\). Comparing 0.801, 0.081 and 0.800: smallest to greatest is \\(0.081 , \\dfrac{4}{5} , 0.801\\)."} {"t":"q","id":23235,"q":"Gareth spent $20.45 on a shirt. He spent $12.25 more on a belt than the shirt. How much money did Gareth spend on the shirt and belt altogether? ","e":"Belt = \\(20.45 + 12.25 = 32.70\\). Altogether = \\(20.45 + 32.70 = 53.15\\), i.e. $53.15."} {"t":"q","id":23236,"q":"Some factors of 52 are 1, 2, 4 and 52. What are the other two factors of 52?
and ","e":"\\(52 = 1 \\times 52 = 2 \\times 26 = 4 \\times 13\\). So all factors are 1, 2, 4, 13, 26, 52. The other two are 13 and 26."} {"t":"q","id":23237,"q":"Hidayah needs to pack some books into boxes of 3 or 8. The number of books is fewer than 50. What is the greatest number of books that Hidayah has to pack? ","e":"The number must be a common multiple of 3 and 8, i.e. a multiple of 24, and fewer than 50. Multiples of 24 below 50 are 24 and 48; the greatest is 48."} {"t":"q","id":23241,"q":"Johnny spent \\(\\dfrac{1}{2}\\) of his salary on food and \\(\\dfrac{1}{7}\\) on transport. In the end, he had $630 left. How much money did Johnny spend on transport? ","e":"Fraction spent = \\(\\dfrac{1}{2} + \\dfrac{1}{7} = \\dfrac{7}{14} + \\dfrac{2}{14} = \\dfrac{9}{14}\\). Fraction left = \\(\\dfrac{5}{14}\\) = $630, so 1 unit (1\/14) = \\(630 \\div 5 = 126\\). Transport = \\(\\dfrac{1}{7} = \\dfrac{2}{14} = 2 \\times 126 = \\$252\\)."} {"t":"q","id":23242,"q":"Mei Yi spent $14.90 on 4 erasers and 5 pencils. The total cost of 1 such eraser and 1 such pencil was $3.25.
(a) How much did 1 such pencil cost?
(b) Zachary bought 7 such pencils. He paid with a $50 note. How much change did Zachary receive? ","e":"(a) 4 erasers + 4 pencils = \\(4 \\times 3.25 = 13.00\\). The extra pencil: \\(14.90 - 13.00 = 1.90\\), so 1 pencil = $1.90. (b) 7 pencils = \\(1.90 \\times 7 = 13.30\\). Change = \\(50 - 13.30 = \\$36.70\\)."} {"t":"q","id":23243,"q":"Priscilla, William and Victor had a total of 680 stickers. Victor had 180 fewer stickers than Priscilla and William had 20 more stickers than Priscilla.
(a) How many stickers did Priscilla have?
(b) Victor then bought some stickers. Priscilla had twice as many stickers as him in the end. How many stickers did Victor buy? ","e":"(a) Let Priscilla = P. Victor = P \u2212 180, William = P + 20. Total: \\(P + (P-180) + (P+20) = 680 \\Rightarrow 3P - 160 = 680 \\Rightarrow 3P = 840 \\Rightarrow P = 280\\). (b) Victor at first = \\(280 - 180 = 100\\). Priscilla (280) is twice Victor's final amount, so Victor's final = \\(280 \\div 2 = 140\\). Victor bought \\(140 - 100 = 40\\)."} {"t":"q","id":23244,"q":"Aqil collected 24 more stamps than Riley at first. After Aqil gave away 60 stamps, Riley had 4 times as many stamps as him. How many stamps did Aqil have at first? ","e":"After Aqil gives away 60, the gap between Riley and Aqil becomes \\(60 - 24 = 36\\) (Riley now leads). Riley = 4 \u00d7 Aqil(now), so the gap = 3 units = 36, giving 1 unit = \\(36 \\div 3 = 12\\) = Aqil now. Aqil at first = \\(12 + 60 = 72\\)."} {"t":"q","id":23246,"q":"In which of the following does the digit 8 stand for 800?","e":"Place value: the digit 8 stands for 800 only when 8 is in the hundreds place. In 4823, the 8 is in the hundreds place, so it stands for 800."} {"t":"q","id":23247,"q":"Which of the following is a multiple of both 4 and 6?","e":"A common multiple of 4 and 6 is a multiple of 12. Among the options, 36 = 12 \u00d7 3 is a multiple of both 4 (4\u00d79) and 6 (6\u00d76). The others are not."} {"t":"q","id":23249,"q":"Which of the following is not an equivalent fraction of \\(\\dfrac{2}{3}\\)?","e":"2\/3 = 4\/6 = 6\/9 = 12\/18 (multiply numerator and denominator by the same number). 18\/24 simplifies to 3\/4, which is not equal to 2\/3, so it is not equivalent."} {"t":"q","id":23253,"q":"Joyce has 40 marbles. 10 marbles are red, 18 marbles are green and the rest are purple. What fraction of the marbles are purple?","e":"Purple = 40 \u2212 10 \u2212 18 = 12 marbles. Fraction purple = 12\/40 = 3\/10."} {"t":"q","id":23257,"q":"Arrange these numbers from the greatest to the smallest.
489 , 948 , 984 , 498
, , , ","e":"Compare by place value. Greatest to smallest: 984, 948, 498, 489."} {"t":"q","id":23258,"q":"Write forty thousand and thirty-seven in numerals. ","e":"Forty thousand = 40 000; thirty-seven = 37. Together: 40 000 + 37 = 40037."} {"t":"q","id":23259,"q":"Which two of the fractions below are smaller than \\(\\dfrac{1}{2}\\)?
\\(\\dfrac{2}{3}\\) , \\(\\dfrac{4}{9}\\) , \\(\\dfrac{5}{11}\\) , \\(\\dfrac{6}{12}\\)
and ","e":"Compare each to 1\/2. 2\/3 > 1\/2; 6\/12 = 1\/2 (not smaller); 4\/9 < 1\/2 (since 4\/9 < 4.5\/9); 5\/11 < 1\/2 (since 5\/11 < 5.5\/11). So 5\/11 and 4\/9 are smaller than 1\/2."} {"t":"q","id":23260,"q":"What is the value of \\(\\dfrac{5}{6} + \\dfrac{7}{12}\\)? Express your answer as a mixed number.","e":"5\/6 = 10\/12. 10\/12 + 7\/12 = 17\/12 = 1 5\/12."} {"t":"q","id":23261,"q":"Write 7 thousandths as a decimal. ","e":"7 thousandths = 7\/1000 = 0.007 (7 in the thousandths place)."} {"t":"q","id":23265,"q":"How many minutes are there in 4 hours and 27 minutes? ","e":"4 hours = 4 \u00d7 60 = 240 minutes. 240 + 27 = 267 minutes."} {"t":"q","id":23269,"q":"John drank 0.84 \\(\\ell\\) of orange juice. He drank 0.44 \\(\\ell\\) of orange juice less than Sam. How much orange juice did the two boys drink altogether? ","e":"Sam drank 0.84 + 0.44 = 1.28 \u2113. Together: 0.84 + 1.28 = 2.12 \u2113."} {"t":"q","id":23270,"q":"Bobby had $54. He spent \\(\\dfrac{1}{6}\\) of it on some books. How much money did he have left? ","e":"Spent = 1\/6 \u00d7 $54 = $9. Left = $54 \u2212 $9 = $45. (Or 5\/6 \u00d7 $54 = $45.)"} {"t":"q","id":23271,"q":"Ali and Devi had a total of 842 stamps. After Ali gave 79 stamps to Devi, they had the same number of stamps. Find the number of stamps Ali had at first. ","e":"After giving, each has 842 \u00f7 2 = 421 stamps. Ali had 79 more before giving, so Ali at first = 421 + 79 = 500 stamps."} {"t":"q","id":23272,"q":"Amanda had $1240 and Sophie had $1304 in savings at first. Then, Amanda saved $20 each day while Sophie saved $12 each day. After how many days did the 2 girls have the same amount of money? ","e":"Sophie starts $1304 \u2212 $1240 = $64 ahead. Amanda gains $20 \u2212 $12 = $8 more each day. Days to catch up = 64 \u00f7 8 = 8 days."} {"t":"q","id":23273,"q":"Tom bought 4 erasers and 3 pencils from the bookshop for $6.10. Jane bought 7 erasers and 3 pencils for $7.30. What is the price of 1 pencil? ","e":"The difference between the two purchases is 3 erasers = $7.30 \u2212 $6.10 = $1.20, so 1 eraser = $0.40. Then 4 erasers = $1.60, so 3 pencils = $6.10 \u2212 $1.60 = $4.50, and 1 pencil = $4.50 \u00f7 3 = $1.50."} {"t":"q","id":23275,"q":"A shop sells doughnuts: 1 doughnut for $2; buy 5 doughnuts and get 1 free. Suki wants to buy 15 doughnuts. What is the least amount she has to pay? ","e":"Buying 5 and getting 1 free gives 6 doughnuts for $10. Two such sets give 12 doughnuts for $20. She still needs 3 more at $2 each = $6. Total = $20 + $6 = $26."} {"t":"q","id":23276,"q":"A shopkeeper had 9 bags of potatoes. Each bag contained 12.25 kg of potatoes. What was the total mass of potatoes in the 9 bags? ","e":"Total mass = 9 \u00d7 12.25 kg = 110.25 kg."} {"t":"q","id":23277,"q":"A shopkeeper had 9 bags of potatoes, each containing 12.25 kg, a total of 110.25 kg. The shopkeeper bought another 24.75 kg of potatoes. He then packed all the potatoes into bags of 3 kg each. He sold all the bags at a cost of $6 for each bag. How much did he receive from the sale of the potatoes? ","e":"Total potatoes = 110.25 + 24.75 = 135 kg. Number of 3 kg bags = 135 \u00f7 3 = 45. Money received = 45 \u00d7 $6 = $270."} {"t":"q","id":23280,"q":"Mdm Nura baked some apple, blueberry and chocolate tarts. She baked 4 apple tarts and twice as many blueberry tarts as apple tarts. She baked 3 more chocolate tarts than blueberry tarts. How many tarts did she bake altogether? ","e":"Apple = 4. Blueberry = 2 \u00d7 4 = 8. Chocolate = 8 + 3 = 11. Total = 4 + 8 + 11 = 23 tarts."} {"t":"q","id":23283,"q":"In March there were 312 students choosing a favourite sport, with 40 choosing tennis. In April, 8 new students chose badminton as their favourite sport. The number of students who chose tennis remained unchanged. What fraction of the students chose tennis as their favourite sport in April? Give your answer in the simplest form.","e":"New total in April = 312 + 8 = 320. Tennis is still 40. Fraction = 40\/320 = 1\/8."} {"t":"q","id":23284,"q":"Mr Lee had red, yellow and purple files. \\(\\dfrac{1}{4}\\) of the files were red and \\(\\dfrac{3}{5}\\) of the files were yellow. The rest of the files were purple. What fraction of the files were purple?","e":"Red + Yellow = 1\/4 + 3\/5 = 5\/20 + 12\/20 = 17\/20. Purple = 1 \u2212 17\/20 = 3\/20."} {"t":"q","id":23285,"q":"Mr Lee had red, yellow and purple files. \\(\\dfrac{1}{4}\\) were red, \\(\\dfrac{3}{5}\\) were yellow and \\(\\dfrac{3}{20}\\) were purple. Mr Lee had 40 red files. What was the difference between the number of yellow files and the number of purple files? ","e":"Red is 1\/4 = 5\/20 of the files and equals 40, so 5 units = 40, 1 unit = 8 (where 1 unit = 1\/20). Yellow = 12 units = 96; purple = 3 units = 24. Difference = 96 \u2212 24 = 72."} {"t":"q","id":23286,"q":"At a mall, a watch cost 6 times as much as a bag. The bag cost $91.25 less than the watch. Mrs Tan bought a watch and 3 bags. How much did Mrs Tan spend? ","e":"Let the bag be 1 unit; the watch is 6 units. The difference 6 \u2212 1 = 5 units = $91.25, so 1 unit (bag) = $18.25. Watch + 3 bags = 6 + 3 = 9 units = 9 \u00d7 $18.25 = $164.25."} {"t":"q","id":23287,"q":"At a mall, a watch cost 6 times as much as a bag, and the bag cost $91.25 less than the watch. Mrs Tan bought a watch and 3 bags for $164.25. Mrs Tan paid the cashier with two $100 notes. How much change did she get? ","e":"Two $100 notes = $200. Change = $200 \u2212 $164.25 = $35.75."} {"t":"q","id":23288,"q":"A bookstore had an equal number of pens and rulers. After 1852 pens and 547 rulers were sold, there were 4 times as many rulers as pens left. How many pens were there at first? ","e":"Let the starting number of each be N. Pens left = N \u2212 1852; rulers left = N \u2212 547. Rulers left = 4 \u00d7 pens left, so the extra rulers (1852 \u2212 547 = 1305) equal 3 times the pens left: 3 units = 1305, 1 unit = 435 (pens left). Pens at first = 435 + 1852 = 2287."} {"t":"q","id":23289,"q":"A bookstore had 2287 pens and 2287 rulers at first. After 1852 pens and 547 rulers were sold, the cost of each pen was $2 and the cost of each ruler was 70\u00a2. How much was collected from the sale of pens and rulers? ","e":"Pens sold: 1852 \u00d7 $2 = $3704. Rulers sold: 547 \u00d7 70\u00a2 = 38290\u00a2 = $382.90. Total collected = $3704 + $382.90 = $4086.90."} {"t":"q","id":23290,"q":"The sum of two numbers is 29. One of the numbers is a factor of 45. The other number is a multiple of 5. What is the difference between the two numbers? ","e":"The two numbers add to 29. A factor of 45 (1,3,5,9,15,45) plus a multiple of 5 (5,10,15,20,25,...) = 29: 9 + 20 = 29 works (9 is a factor of 45, 20 is a multiple of 5). Difference = 20 \u2212 9 = 11."} {"t":"q","id":23291,"q":"The sum of two numbers is 561. One of the numbers is a 2-digit number. The other number is a 3-digit number. What is the smallest possible difference between the two numbers? ","e":"To make the difference smallest, make the 2-digit number as large as possible: the largest 2-digit number is 99, so the 3-digit number is 561 \u2212 99 = 462. Difference = 462 \u2212 99 = 363."} {"t":"q","id":23294,"q":"In 125.34, which digit is in the tenths place?","e":"In a decimal, the first digit after the decimal point is the tenths place. In \\(125.34\\) the digit after the point is 3, so the tenths digit is 3."} {"t":"q","id":23295,"q":"Arrange the numbers from the smallest to the greatest.
\\(6.7\\), \\(0.67\\), \\(6.07\\), \\(0.76\\)","e":"Compare whole-number parts first: \\(0.67\\) and \\(0.76\\) are less than 1; \\(6.07\\) and \\(6.7\\) are more than 6. Within each pair compare tenths: \\(0.67 < 0.76\\) and \\(6.07 < 6.70\\). Order: 0.67, 0.76, 6.07, 6.7."} {"t":"q","id":23297,"q":"(a) Express \\(5\\dfrac{73}{100}\\) as a decimal.
(b) Round \\(45.999\\) to the nearest 1 decimal place. ","e":"(a) \\(\\dfrac{73}{100}\\) means 73 hundredths \\(= 0.73\\), so \\(5\\dfrac{73}{100} = 5.73\\). (b) Look at the hundredths digit of \\(45.999\\), which is 9 (\u22655), so round the tenths up: \\(45.999 \\approx 46.0\\)."} {"t":"q","id":23298,"q":"The total length of two ropes, Rope P and Rope Q, is \\(23.06\\) m.
The length of Rope Q is \\(14.78\\) m.
What is the difference in length between Rope P and Rope Q?
Ans: m","e":"First find Rope P: \\(23.06 - 14.78 = 8.28\\) m. The difference between Rope P and Rope Q is \\(14.78 - 8.28 = 6.5\\) m."} {"t":"q","id":23299,"q":"Bala had \\(10.5\\) kg of sugar.
He used \\(3.5\\) kg of it and repacked the rest equally into 5 boxes.
What was the mass of sugar in each box?
Ans: kg","e":"Sugar left after using some: \\(10.5 - 3.5 = 7\\) kg. Repacked equally into 5 boxes: \\(7 \\div 5 = 1.4\\) kg per box."} {"t":"q","id":23300,"q":"Siti paid $10.40 for a chocolate cake and 4 curry puffs.
Sumei paid $13.60 for a chocolate cake and 8 curry puffs.
Shanti bought 5 chocolate cakes.
(a) What was the cost of 1 curry puff? $
(b) How much did Shanti pay for the 5 chocolate cakes? $","e":"(a) Sumei bought 4 more curry puffs than Siti and paid \\(13.60 - 10.40 = \\$3.20\\) more. So 4 curry puffs cost $3.20, and 1 curry puff \\(= 3.20 \\div 4 = \\$0.80\\). (b) Cost of 1 chocolate cake \\(= 10.40 - (4 \\times 0.80) = 10.40 - 3.20 = \\$7.20\\). For 5 cakes: \\(7.20 \\times 5 = \\$36.00\\)."} {"t":"q","id":23301,"q":"Janice had \\(6\\) \\(\\ell\\) of orange juice.
She poured \\(3.85\\) \\(\\ell\\) of orange juice equally into 7 identical cups.
(a) How much orange juice was left? \\(\\ell\\)
(b) How much orange juice was there in each cup? \\(\\ell\\)","e":"(a) Juice poured out is 3.85 \u2113, so juice left \\(= 6 - 3.85 = 2.15\\) \u2113. (b) The 3.85 \u2113 poured out is shared equally into 7 cups: \\(3.85 \\div 7 = 0.55\\) \u2113 in each cup."} {"t":"q","id":23302,"q":"Which digit in \\(17.48\\) is in the tenths place?","e":"In \\(17.48\\) the digit right after the decimal point is the tenths place. That digit is \\(4\\). (The \\(8\\) is in the hundredths place.) Answer: \\(4\\)."} {"t":"q","id":23303,"q":"Express \\(6\\dfrac{7}{25}\\) as a decimal.","e":"Convert \\(\\dfrac{7}{25}\\) to hundredths: \\(\\dfrac{7}{25}=\\dfrac{7\\times4}{25\\times4}=\\dfrac{28}{100}=0.28\\). So \\(6\\dfrac{7}{25}=6.28\\). Answer: \\(6.28\\)."} {"t":"q","id":23306,"q":"Round \\(39.95\\) to 1 decimal place.
Answer: ","e":"To round to 1 decimal place, look at the hundredths digit. \\(39.95\\) has hundredths digit \\(5\\), so round the tenths up: \\(39.9\\to40.0\\). Answer: \\(40.0\\)."} {"t":"q","id":23307,"q":"Complete the number pattern.
\\(7.38, 7.48, 7.47, 7.57, 7.56, 7.66,\\) \\(, 7.75, 7.74, 7.84\\)","e":"The pattern alternates: +0.10 then -0.01. \\(7.38(+0.10)7.48(-0.01)7.47(+0.10)7.57(-0.01)7.56(+0.10)7.66(-0.01)\\mathbf{7.65}(+0.10)7.75(-0.01)7.74(+0.10)7.84\\). The missing term is \\(7.66-0.01=7.65\\). Answer: \\(7.65\\)."} {"t":"q","id":23310,"q":"A water bottle contained \\(1.2\\) \\(l\\) of water. It contained \\(2.5\\) \\(l\\) less water than a kettle. How much water was there in 4 such kettles?
Answer: ","e":"One kettle holds \\(1.2+2.5=3.7\\) \\(l\\) (the bottle has 2.5 l less than a kettle). For 4 kettles: \\(3.7\\times4=14.8\\) \\(l\\). Answer: \\(14.8\\) \\(l\\)."} {"t":"q","id":23311,"q":"Mrs Tan had \\(7.86\\) \\(kg\\) of flour less than Mrs Siva. After Mrs Siva used \\(10\\) \\(kg\\) of flour, Mrs Tan had 3 times as much flour as Mrs Siva had left.
(a) How many more kilograms of flour did Mrs Tan have than Mrs Siva in the end?
(b) How many kilograms of flour did Mrs Siva have left? ","e":"(a) Mrs Tan's amount is unchanged. At the start Mrs Siva had \\(7.86\\) kg more than Mrs Tan; after using \\(10\\) kg, Mrs Siva is now \\(10-7.86=2.14\\) kg less than Mrs Tan. So Mrs Tan has \\(2.14\\) kg more than Mrs Siva in the end. (b) In the end Tan = 3 \u00d7 Siva, so the difference (Tan \u2212 Siva) = 2 units = \\(2.14\\) kg, giving 1 unit = Siva = \\(2.14\\div2=1.07\\) kg. Answers: (a) \\(2.14\\) kg, (b) \\(1.07\\) kg."} {"t":"q","id":23312,"q":"The value of the digit 3 in 57.43 is ____________.","e":"The digit 3 in 57.43 is in the hundredths place. Its value is \\(3 \\times 0.01 = 0.03\\)."} {"t":"q","id":23313,"q":"Round 32.786 to the nearest hundredth.","e":"The hundredths digit is 8; the thousandths digit is 6 (\u22655), so round up. \\(32.786 \\approx 32.79\\)."} {"t":"q","id":23315,"q":"Arrange the following decimals in increasing order.
2.186   2.816   2.168   2.681","e":"Compare digit by digit after the units: 2.168 < 2.186 < 2.681 < 2.816. Increasing order is 2.168, 2.186, 2.681, 2.816."} {"t":"q","id":23316,"q":"Mary bought 3 m of ribbon. She used 1.65 m of it to tie a present. How many metres of ribbon had she left?","e":"\\(3 - 1.65 = 1.35\\). She had 1.35 m of ribbon left."} {"t":"q","id":23317,"q":"A bag costs four times as much as a purse. Jamie paid $33 for a bag and 2 purses. How much did a bag cost?","e":"Let a purse be 1 unit; a bag is 4 units. Bag + 2 purses = 4 + 2 = 6 units = $33, so 1 unit = $5.50. A bag = 4 units = \\(4 \\times 5.50 = 22\\)."} {"t":"q","id":23319,"q":"Divide 6 by 7. Correct your answer to 1 decimal place.
Answer: ","e":"\\(6 \\div 7 = 0.857...\\). The second decimal digit is 5, so round up the first decimal place: \\(0.857... \\approx 0.9\\)."} {"t":"q","id":23320,"q":"Pearly had \\(5.4\\ell\\) of watermelon juice. Pearly had twice as much watermelon juice as May. May had three times as much watermelon juice as Amy. How much more watermelon juice does Pearly have than Amy?
Answer: ","e":"May = \\(5.4 \\div 2 = 2.7\\) L. Amy = \\(2.7 \\div 3 = 0.9\\) L. Pearly has \\(5.4 - 0.9 = 4.5\\) L more than Amy."} {"t":"q","id":23321,"q":"Mrs Tan had 2.53 kg more flour than Mrs Sim. After Mrs Tan used 4.09 kg of flour, Mrs Sim had four times as much flour as Mrs Tan had left. How many kilograms of flour did Mrs Tan have at first?
Answer: ","e":"After using 4.09 kg, Mrs Tan's amount is (Tan first \u2212 4.09). Mrs Sim = Tan first \u2212 2.53. Sim = 4 \u00d7 Tan's remaining: \\(T - 2.53 = 4(T - 4.09)\\). So \\(T - 2.53 = 4T - 16.36\\), giving \\(3T = 13.83\\) and \\(T = 4.61\\) kg. (Equivalently the difference 4.09 \u2212 2.53 = 1.56 kg equals 3 units of Tan's remainder; 1 unit = 0.52 kg; Tan first = 0.52 + 4.09 = 4.61 kg.)"} {"t":"q","id":23322,"q":"Mr Tan placed 8 flags around the border of a square field. The distance between each flag and the next was equal for all the flags. The distance between the 1st flag and the 6th flag was 27 m. What was the total distance of the border around the square field?
Answer: ","e":"From the 1st flag to the 6th flag there are 5 gaps: \\(27 \\div 5 = 5.4\\) m per gap. With 8 flags around a closed border there are 8 equal gaps: \\(5.4 \\times 8 = 43.2\\) m."} {"t":"s","id":15296,"s":"All factors of 32 are 1, 2, 4, 8, 16, 32. Andy listed 1, 2, 8, 32, so the missing factors are 4 and 16."} {"t":"s","id":15298,"s":"Let Ada = 1 unit. Ben = 2 units, Chris = 1 unit \u2212 40. Total = 4 units \u2212 40 = 720, so 4 units = 760 and 1 unit = 190. Ben = 2 units = 380."} {"t":"s","id":15299,"s":"(a) One T-shirt = $120 \u00f7 5 = $24. (b) The pants cost 3 times one T-shirt = 3 \u00d7 $24 = $72."} {"t":"s","id":15667,"s":"Add by place value: 50 000 + 900 + 8 = 50 908. There are 5 ten-thousands, 0 thousands, 9 hundreds, 0 tens and 8 ones. Answer: 50 908."} {"t":"s","id":15668,"s":"Compare from the largest place value. All have 9 thousands. Hundreds: 9605 and 9506 have 6 and 5 hundreds; 9065 has 0 hundreds. So 9605 > 9506 > 9065. Greatest to smallest: 9605, 9506, 9065. Answer: option 4."} {"t":"s","id":15669,"s":"The pattern alternates subtracting 300 then 10: 5934 -300 = 5634, -10 = 5624, -300 = 5324, -10 = 5314, -300 = 5014, -10 = 5004. The missing term is 5314. Answer: option 2."} {"t":"s","id":15670,"s":"A number with both 3 and 4 as factors must be a multiple of 12. Check: 15 (no), 18 (4 is not a factor), 20 (3 is not a factor), 24 = 3 x 8 = 4 x 6. So 24 has both 3 and 4 as factors. Answer: option 4."} {"t":"s","id":15671,"s":"a) Seventy-eight thousand and twenty = 78 000 + 20 = 78 020. b) 39 500 is exactly halfway between 39 000 and 40 000; rounding to the nearest thousand rounds the half up to 40 000."} {"t":"s","id":15672,"s":"Product means multiply: 8540 x 7. 8000 x 7 = 56 000; 500 x 7 = 3500; 40 x 7 = 280. Sum: 56 000 + 3500 + 280 = 59 780."} {"t":"s","id":15673,"s":"Divide 853 by 9 and find the remainder. 9 x 94 = 846, and 853 - 846 = 7. So 94 full boxes are packed and 7 books are left unpacked. Answer: 7 books."} {"t":"s","id":15675,"s":"When Betty gives $35 to Andy, Andy gains $35 and Betty loses $35, so the gap between them widens by 2 x $35 = $70. New difference = $450 + $70 = $520. Answer: $520."} {"t":"s","id":15676,"s":"For an equal number of pens and pencils, the count must be a common multiple of 6 and 8. The least common multiple of 6 and 8 is 24, so the least number of pens is 24 and the least number of pencils is 24. Total = 24 + 24 = 48."} {"t":"s","id":15677,"s":"Let watermelons = 1 unit, durians = 4 units. After selling 114 durians, durians left = watermelons = 1 unit, so 114 durians = 4 units - 1 unit = 3 units. 1 unit = 114 \/ 3 = 38. Watermelons = 38 and durians left = 38, so fruits left = 38 + 38 = 76."} {"t":"s","id":15680,"s":"Assume all 35 notes are $2: value = 35 x $2 = $70. The actual total is $118, which is $48 more. Each $2 note swapped for a $5 note adds $3. So number of $5 notes = $48 \/ $3 = 16."} {"t":"s","id":15762,"s":"Write all as decimals: \\(3\\dfrac{1}{100} = 3.01\\), 3.05, 3.5. In order smallest to largest: 3.01, 3.05, 3.5, i.e. \\(3\\dfrac{1}{100}\\), 3.05, 3.5."} {"t":"s","id":15898,"s":"Factors of 16: 1, 2, 4, 8, 16. Factors of 28: 1, 2, 4, 7, 14, 28. The factors common to both are 1, 2 and 4."} {"t":"s","id":15900,"s":"6793 \u00f7 6: 6 \u00f7 6 = 1, 7 \u00f7 6 = 1 r 1, 19 \u00f7 6 = 3 r 1, 13 \u00f7 6 = 2 r 1. Quotient 1132 remainder 1, so 6793 \u00f7 6 = 1132 R1."} {"t":"s","id":15901,"s":"42 \u00f7 8 = 5 remainder 2, so \\(\\dfrac{42}{8}=5\\dfrac{2}{8}\\). Simplify \\(\\dfrac{2}{8}=\\dfrac{1}{4}\\), giving \\(5\\dfrac{1}{4}\\)."} {"t":"s","id":15902,"s":"\\(\\dfrac{5}{2}=2\\dfrac{1}{2}=2\\dfrac{4}{8}\\). Compare with \\(2\\dfrac{5}{8}\\): the whole parts are equal and \\(\\dfrac{5}{8}>\\dfrac{4}{8}\\), so \\(2\\dfrac{5}{8}>\\dfrac{5}{2}\\)."} {"t":"s","id":15903,"s":"Numbers from 51 500 to 52 499 round to 52 000. The greatest of these is 52 499."} {"t":"s","id":15904,"s":"Rounds to 800, so the number is 750-849; the hundreds digit is 8, tens digit < 5. Hundreds = twice tens means tens = 4 (8 = 2 x 4). Digits sum to 15: 8 + 4 + ones = 15, so ones = 3. The number is 843."} {"t":"s","id":15905,"s":"The number of each colour must be a common multiple of 5 and 3. The least common multiple is 15, so there are 15 red and 15 blue marbles. Altogether 15 + 15 = 30 marbles."} {"t":"s","id":15906,"s":"\\(\\dfrac{6}{7}-\\dfrac{2}{3}\\). Common denominator 21: \\(\\dfrac{6}{7}=\\dfrac{18}{21}\\) and \\(\\dfrac{2}{3}=\\dfrac{14}{21}\\). \\(\\dfrac{18}{21}-\\dfrac{14}{21}=\\dfrac{4}{21}\\)."} {"t":"s","id":15907,"s":"\\(\\dfrac{1}{3}\\) of 141 = 141 \u00f7 3 = 47. He gave away \\(\\dfrac{2}{3}\\), so 47 x 2 = 94 sweets."} {"t":"s","id":15910,"s":"After receiving erasers, total 84 is split as Dan : Elijah = 2 : 1, i.e. 3 units = 84, so 1 unit = 84 \u00f7 6... working: 84 \u00f7 3 units gives Dan 56 and Elijah 28 after. The equal amount added is x, so Elijah-first = 28 - x and Dan-first = 56 - x = 3(28 - x). Solving: 56 - x = 84 - 3x, 2x = 28, x = 14. Dan at first = 56 - 14 = 42 erasers. (Key working: 84 \u00f7 6 = 14, 14 x 3 = 42.)"} {"t":"s","id":15911,"s":"The 4 other charities received 4 x $60 = $240, which is the rest of the savings. Fraction left = 1 - \\(\\dfrac{3}{8}\\) - \\(\\dfrac{1}{4}\\) = 1 - \\(\\dfrac{3}{8}\\) - \\(\\dfrac{2}{8}\\) = \\(\\dfrac{3}{8}\\). So \\(\\dfrac{3}{8}\\) of savings = $240, meaning \\(\\dfrac{1}{8}\\) = $80 and total savings = $80 x 8 = $640. All 6 charities together received the whole savings, $640."} {"t":"s","id":15983,"s":"Fifty thousand = 50 000, eight hundred = 800, three = 3. So the number is 50 000 + 800 + 3 = 50 803."} {"t":"s","id":15985,"s":"Each number decreases by 1000. After 73 603 comes 73 603 - 1000 = 72 603. After 70 603 comes 70 603 - 1000 = 69 603."} {"t":"s","id":15986,"s":"Compare from the largest place value. 39 039 and 39 309 are in the 39-thousands; 39 039 < 39 309. 40 309 and 40 390 are in the 40-thousands; 40 309 < 40 390. Increasing order: 39 039, 39 309, 40 309, 40 390."} {"t":"s","id":15987,"s":"Nearest ten: the ones digit is 5, so round up the tens: 74 945 \u2248 74 950. Nearest hundred: the tens digit is 4 (less than 5), so round down: 74 945 \u2248 74 900."} {"t":"s","id":15990,"s":"Multiples of 7: 49, 56, 63, ... The only one between 50 and 60 is 56 (7 \u00d7 8 = 56)."} {"t":"s","id":15991,"s":"Convert to a common denominator of 30: \\(\\dfrac{2}{3}=\\dfrac{20}{30}\\), \\(\\dfrac{5}{6}=\\dfrac{25}{30}\\), \\(\\dfrac{2}{5}=\\dfrac{12}{30}\\). Greatest to smallest: \\(\\dfrac{25}{30}, \\dfrac{20}{30}, \\dfrac{12}{30}\\), i.e. \\(\\dfrac{5}{6}, \\dfrac{2}{3}, \\dfrac{2}{5}\\)."} {"t":"s","id":15992,"s":"Make the denominators the same: \\(\\dfrac{1}{4}=\\dfrac{3}{12}\\). Then \\(\\dfrac{11}{12}-\\dfrac{3}{12}=\\dfrac{8}{12}\\). Simplify by dividing by 4: \\(\\dfrac{8}{12}=\\dfrac{2}{3}\\)."} {"t":"s","id":15993,"s":"(a) Total mangoes = 162 \u00d7 36 = 5832. (b) Mangoes left after selling = 5832 - 738 = 5094. Bags = 5094 \u00f7 9 = 566."} {"t":"s","id":15994,"s":"Work backwards from the end. Before receiving 648: 1330 - 648 = 682. Before giving away 238: 682 + 238 = 920. So Sam had 920 cards at first."} {"t":"s","id":15995,"s":"School B = 3064 \u00d7 4 = 12 256 books. (a) More books in B than A = 12 256 - 3064 = 9192. (b) To make both equal, move half the difference: 9192 \u00f7 2 = 4596 books."} {"t":"s","id":15996,"s":"(a) The red bulb blinks every 6 minutes, so in 48 minutes it blinks 48 \u00f7 6 = 8 times. (b) The bulbs blink together at multiples of the LCM of 4 and 6, which is 12 minutes. After 8.00 p.m., the next time they blink together is 12 minutes later, at 8.12 p.m."} {"t":"s","id":15997,"s":"In 38.479, the digit 7 is in the hundredths place. Its value is 7 hundredths = 0.07."} {"t":"s","id":15998,"s":"Compare place by place: 6.904 > 6.490 > 6.409 > 6.049. Decreasing order: 6.904, 6.49, 6.409, 6.049."} {"t":"s","id":15999,"s":"Convert \\(1\\dfrac{3}{5}\\) to an improper fraction: \\(1\\dfrac{3}{5}=\\dfrac{8}{5}\\). So there are 8 one-fifths."} {"t":"s","id":16001,"s":"Add the known parts: 10 + 8 + 0.7 + 0.009 = 18.709. Missing number = 18.749 - 18.709 = 0.04."} {"t":"s","id":16002,"s":"Look at the tenths digit (5). Since 5 \\(\\geq\\) 5, round up: 13.592 rounds to 14."} {"t":"s","id":16004,"s":"21.73 + 4.98 = 26.71. Line up the decimal points and add: 73 + 98 hundredths = 171 hundredths (carry), giving 26.71."} {"t":"s","id":16005,"s":"As decimals: \\(\\dfrac{4}{7}\\approx0.57\\), \\(\\dfrac{17}{12}\\approx1.42\\), \\(3\\dfrac{1}{2}=3.5\\), \\(\\dfrac{1}{2}=0.5\\). Ascending: \\(\\dfrac{1}{2}, \\dfrac{4}{7}, \\dfrac{17}{12}, 3\\dfrac{1}{2}\\)."} {"t":"s","id":16006,"s":"Stickers left = \\(1-\\dfrac{2}{5}=\\dfrac{3}{5}\\) of the total = 27. So \\(\\dfrac{1}{5}=27\\div3=9\\), and the total \\(=9\\times5=45\\) stickers."} {"t":"s","id":16007,"s":"(a) Drank - gave away = \\(\\dfrac{5}{12}-\\dfrac{1}{3}=\\dfrac{5}{12}-\\dfrac{4}{12}=\\dfrac{1}{12}\\) \\(l\\). (b) Total bought = drank + gave away + left = \\(\\dfrac{5}{12}+\\dfrac{4}{12}+\\dfrac{7}{12}=\\dfrac{16}{12}=1\\dfrac{4}{12}=1\\dfrac{1}{3}\\) \\(l\\)."} {"t":"s","id":16010,"s":"\\(\\dfrac{3}{7}\\): multiply numerator and denominator by 2 to get a denominator of 14, so the numerator is 6 (\\(\\dfrac{6}{14}\\)). For \\(\\dfrac{9}{[?]}\\), 9 = 3 x 3, so multiply 7 by 3 to get 21 (\\(\\dfrac{9}{21}\\))."} {"t":"s","id":16011,"s":"\\(\\dfrac{2}{3}\\) = \\(\\dfrac{4}{6}\\). \\(\\dfrac{4}{6}\\) - \\(\\dfrac{1}{6}\\) = \\(\\dfrac{3}{6}\\) = \\(\\dfrac{1}{2}\\)."} {"t":"s","id":16012,"s":"The sequence increases by 100 each time: 67 852, 67 952, 68 052, 68 152, ... So the missing number is 68 052."} {"t":"s","id":16013,"s":"Use a common denominator of 12: \\(\\dfrac{5}{12}\\), \\(\\dfrac{2}{3}\\) = \\(\\dfrac{8}{12}\\), \\(\\dfrac{1}{2}\\) = \\(\\dfrac{6}{12}\\). From greatest to smallest: \\(\\dfrac{8}{12}\\) > \\(\\dfrac{6}{12}\\) > \\(\\dfrac{5}{12}\\), i.e. \\(\\dfrac{2}{3}\\), \\(\\dfrac{1}{2}\\), \\(\\dfrac{5}{12}\\)."} {"t":"s","id":16014,"s":"Factors of 18: 1, 2, 3, 6, 9, 18. Factors of 27: 1, 3, 9, 27. Common factors: 1, 3, 9. Sum = 1 + 3 + 9 = 13."} {"t":"s","id":16016,"s":"Children = 1476 - 874 = 602. Boys + girls = 602 and boys = girls + 28, so 2 x girls = 602 - 28 = 574. Girls = 574 \/ 2 = 287."} {"t":"s","id":16017,"s":"Remove the bag's extra cost: 285 - 57 = 228, which is the cost of 6 purses (1 bag now equals 1 purse). Each purse = 228 \/ 6 = $38."} {"t":"s","id":16019,"s":"She used 720 - 320 = 400 g more flour than sugar, so the sugar left is 400 g more than the flour left. Since sugar left is 6 times the flour left, the 5 extra units = 400 g, so 1 unit (flour left) = 400 \/ 5 = 80 g. Original flour = flour left + flour used = 80 + 720 = 800 g."} {"t":"s","id":16021,"s":"Use a common denominator of 30: \\(1=\\dfrac{30}{30}\\), \\(\\dfrac{2}{5}=\\dfrac{12}{30}\\), \\(\\dfrac{1}{6}=\\dfrac{5}{30}\\). So \\(\\dfrac{30}{30}-\\dfrac{12}{30}-\\dfrac{5}{30}=\\dfrac{13}{30}\\)."} {"t":"s","id":16022,"s":"Sister drank \\(\\dfrac{3}{4}-\\dfrac{1}{5}=\\dfrac{15}{20}-\\dfrac{4}{20}=\\dfrac{11}{20}\\) litre. Altogether: \\(\\dfrac{3}{4}+\\dfrac{11}{20}=\\dfrac{15}{20}+\\dfrac{11}{20}=\\dfrac{26}{20}=1\\dfrac{6}{20}=1\\dfrac{3}{10}\\) litre."} {"t":"s","id":16025,"s":"8974 \u00f7 8: 8 into 89 is 11 r1; bring down 7 \u2192 17, 8 into 17 is 2 r1; bring down 4 \u2192 14, 8 into 14 is 1 r6. Quotient = 1121 remainder 6."} {"t":"s","id":16027,"s":"Convert the mixed number to an improper fraction: \\(1\\dfrac{5}{8}=\\dfrac{1\\times8+5}{8}=\\dfrac{13}{8}\\). So the missing value is 13."} {"t":"s","id":16028,"s":"Convert to decimals\/like values: \\(\\dfrac{7}{3}\\approx2.33\\), \\(\\dfrac{11}{5}=2.2\\), \\(2\\dfrac{2}{5}=2.4\\). In decreasing order: \\(2\\dfrac{2}{5}\\), \\(\\dfrac{7}{3}\\), \\(\\dfrac{11}{5}\\)."} {"t":"s","id":16029,"s":"7 units = 56, so 1 unit = 56 \u00f7 7 = 8. Roses = 2 units = 8 \u00d7 2 = 16."} {"t":"s","id":16032,"s":"The remaining part of the journey is \\(1-\\dfrac{7}{10}=\\dfrac{3}{10}\\), which equals 480 m. So 3 units = 480 m, 1 unit = 480 \u00f7 3 = 160 m. Whole journey = 10 units = 160 \u00d7 10 = 1600 m."} {"t":"s","id":16033,"s":"Let Emily = 1 unit, then Denise = 3 units, Fred = 3 units \u2212 550. Total: 1u + 3u + 3u \u2212 550 = 4490, so 7u = 4490 + 550 = 5040, 1u = 5040 \u00f7 7 = 720. Denise = 3 \u00d7 720 = 2160. Fred = 2160 \u2212 550 = 1610."} {"t":"s","id":16034,"s":"(a) Arthur and Ben started equal. After Arthur gives away 72, Ben = 4 \u00d7 Arthur. The 72 stickers Arthur lost make Ben's amount the extra; the difference 72 equals 3 of Arthur's remaining units, so 3 units = 72, 1 unit = 24. Arthur had 24 stickers left. (b) Caleb received 72 stickers. He gave \\(\\dfrac{4}{9}\\) away and kept \\(\\dfrac{5}{9}\\): 1 unit = 72 \u00f7 9 = 8, kept = 5 units = 8 \u00d7 5 = 40 stickers."} {"t":"s","id":16035,"s":"9 tens = 90, 4 tenths = 0.4, 7 thousandths = 0.007. Sum = 90 + 0.4 + 0.007 = 90.407."} {"t":"s","id":16038,"s":"\\(\\dfrac{7}{20}=\\dfrac{35}{100}=0.35\\). So \\(4\\dfrac{7}{20}=4+0.35=4.35\\)."} {"t":"s","id":16040,"s":"The tenths digit is 2 and the hundredths digit is 6. Since 6 \u2265 5, round the tenths digit up: 43.26 \u2192 43.3."} {"t":"s","id":16042,"s":"16 \u00f7 7 = 2.2857... To 2 decimal places, look at the 3rd decimal (5), round up: 2.29."} {"t":"s","id":16043,"s":"Convert \\(\\dfrac{2}{5}=0.4\\). Compare 0.403, 0.4, 0.043. Greatest to smallest: 0.403, \\(\\dfrac{2}{5}\\) (0.4), 0.043."} {"t":"s","id":16046,"s":"(a) Transport in 5 days = $2.70 \u00d7 5 = $13.50. (b) Money left after transport = $30 \u2212 $13.50 = $16.50. Food = remaining \u2212 savings = $16.50 \u2212 $1.80 = $14.70."} {"t":"s","id":16047,"s":"Remaining sugar = 5 \u2212 0.32 = 4.68 kg. Each packet = 4.68 \u00f7 6 = 0.78 kg."} {"t":"s","id":16048,"s":"After moving 4.55 kg, the difference between the bags becomes 26.5 + 2 \u00d7 4.55 = 35.6 kg. Bag A is now 5 times Bag B, so the difference is 4 units = 35.6 kg, giving 1 unit (Bag B now) = 35.6 \u00f7 4 = 8.90 kg. Bag B at first = 8.90 + 4.55 = 13.45 kg."} {"t":"s","id":16049,"s":"Thirteen thousand = 13 000, eight hundred = 800, fifty = 50. 13 000 + 800 + 50 = 13 850."} {"t":"s","id":16050,"s":"Compare from the highest place value. Ten-thousands all 4; thousands: 46 327 and 46 825 have 6, 47 209 has 7, so 47 209 is largest. Between 46 327 and 46 825, hundreds 3 < 8, so 46 327 < 46 825. Smallest to greatest: 46 327, 46 825, 47 209."} {"t":"s","id":16051,"s":"The pattern alternates +100 then +1000: 12 878 (+100) 12 978 (+1000) 13 978 (+100) 14 078 (+1000) 15 078 (+100) 15 178 (+1000) 16 178 (+100) 16 278. The missing number is 15 078 + 100 = 15 178."} {"t":"s","id":16052,"s":"The hundreds digit is 5, so round up. 39 565 rounds up to 40 000 to the nearest thousand."} {"t":"s","id":16053,"s":"A number with both 3 and 4 as factors must be divisible by both. 24 = 3 \u00d7 8 = 4 \u00d7 6, so both 3 and 4 divide 24. (15 not divisible by 4; 32 not by 3; 38 not by 3 or 4.)"} {"t":"s","id":16054,"s":"A common multiple of 6 and 9 must be in both times tables. 36 = 6 \u00d7 6 = 9 \u00d7 4, so 36 is a multiple of both. (16 is neither; 42 = 6\u00d77 but not a multiple of 9; 63 = 9\u00d77 but not a multiple of 6.)"} {"t":"s","id":16055,"s":"Erasers given away: 3986 - 2013 = 1973. Then 1973 - 750 = 1223. Mary had 1223 erasers left."} {"t":"s","id":16056,"s":"Multiply the monthly amount by the number of months: 346 \u00d7 7 = 2422. He spends $2422 in seven months."} {"t":"s","id":16057,"s":"(a) 1028 \u00f7 4 = 257. (b) Product means multiply: 45 \u00d7 12 = 540."} {"t":"s","id":16059,"s":"(a) Children = total - adults = 30 012 - 22 800 = 7212. (b) Children and women = 7212 + 10 740 = 17 952."} {"t":"s","id":16060,"s":"Total oranges = 126 \u00d7 36 = 4536. Number of bags = 4536 \u00f7 8 = 567. There were 567 bags."} {"t":"s","id":16061,"s":"Let 1 bag be 1 unit. Watch = 4 units. Watch + 3 bags = 4 + 3 = 7 units = $728. So 1 unit (1 bag) = 728 \u00f7 7 = $104. Watch = 4 \u00d7 104 = $416."} {"t":"s","id":16063,"s":"Method: convert to a comparable form. \\(1\\dfrac{5}{9}=\\dfrac{14}{9}\\approx1.56\\); \\(1\\dfrac{2}{3}=\\dfrac{5}{3}\\approx1.67\\); \\(\\dfrac{15}{7}\\approx2.14\\). In increasing order: \\(1\\dfrac{5}{9}\\) , \\(1\\dfrac{2}{3}\\) , \\(\\dfrac{15}{7}\\)."} {"t":"s","id":16064,"s":"Method: rename 7 as a fraction with denominator 5. \\(7=\\dfrac{35}{5}\\). Then \\(\\dfrac{35}{5}-\\dfrac{3}{5}=\\dfrac{32}{5}=6\\dfrac{2}{5}\\)."} {"t":"s","id":16068,"s":"Method: Tom jogged less than Siti, so subtract. \\(\\dfrac{4}{5}=\\dfrac{8}{10}\\). Tom = \\(\\dfrac{8}{10}-\\dfrac{3}{10}=\\dfrac{5}{10}=\\dfrac{1}{2}\\) km."} {"t":"s","id":16071,"s":"Method: \\(\\dfrac{2}{9}\\) of the roses are red = 16, so 1 unit (\\(\\dfrac{1}{9}\\)) = 16 \\(\\div\\) 2 = 8 roses. Yellow is the rest: \\(\\dfrac{9}{9}-\\dfrac{2}{9}=\\dfrac{7}{9}\\) = 7 units. Yellow roses = 8 \\(\\times\\) 7 = 56."} {"t":"s","id":16072,"s":"a) Total used: \\(\\dfrac{3}{10}+\\dfrac{1}{4}=\\dfrac{6}{20}+\\dfrac{5}{20}=\\dfrac{11}{20}\\) kg. b) Flour left: \\(3-\\dfrac{11}{20}\\). Using the key's form, \\(3=\\dfrac{180}{60}\\) and \\(\\dfrac{11}{20}=\\dfrac{33}{60}\\), so \\(\\dfrac{180}{60}-\\dfrac{33}{60}=\\dfrac{147}{60}=2\\dfrac{27}{60}\\) kg (= \\(2\\dfrac{9}{20}\\) kg)."} {"t":"s","id":16073,"s":"Method: spent = \\(\\dfrac{2}{11}\\) (2 units), saved = \\(\\dfrac{9}{11}\\) (9 units). Saved is $749 more than spent: 9 units - 2 units = 7 units = $749. So 1 unit = 749 \\(\\div\\) 7 = $107. Spent = 2 units = 2 \\(\\times\\) 107 = $214."} {"t":"s","id":16075,"s":"The digit in the tens place is 3 (less than 5), so we round down. 47 832 rounds to 47 800."} {"t":"s","id":16076,"s":"Factors of 18 are 1, 2, 3, 6, 9, 18. 12 is not a factor of 18 (it is a factor of 36 only), so 12 is not a common factor."} {"t":"s","id":16077,"s":"Compare each to \\(\\dfrac{1}{2}\\): \\(\\dfrac{2}{3}\\) = 0.67 > 0.5. The others (\\(\\dfrac{1}{3}\\), \\(\\dfrac{3}{7}\\), \\(\\dfrac{4}{9}\\)) are all less than \\(\\dfrac{1}{2}\\)."} {"t":"s","id":16082,"s":"To get from denominator 4 to 20, multiply by 5. So the numerator is 3 \u00d7 5 = 15. \\(\\dfrac{3}{4} = \\dfrac{15}{20}\\)."} {"t":"s","id":16083,"s":"Convert to twelfths: \\(\\dfrac{7}{4}=\\dfrac{21}{12}\\), \\(\\dfrac{4}{3}=\\dfrac{16}{12}\\), \\(1\\dfrac{5}{6}=\\dfrac{11}{6}=\\dfrac{22}{12}\\). Decreasing order: \\(1\\dfrac{5}{6}\\) (22\/12), \\(\\dfrac{7}{4}\\) (21\/12), \\(\\dfrac{4}{3}\\) (16\/12)."} {"t":"s","id":16084,"s":"Let the start amount be n. Amelie: n \u2212 35. Devna: n + 7 = 4(n \u2212 35). So n + 7 = 4n \u2212 140, giving 147 = 3n, n = 49. Amelie at the end = 49 \u2212 35 = 14. (Check: Devna = 49 + 7 = 56 = 4 \u00d7 14.)"} {"t":"s","id":16086,"s":"Let 4C = 1 unit. Then 4B = 2 units and 4A = 3 \u00d7 4B = 6 units. 4A + 4B = 6 + 2 = 8 units = 152, so 1 unit = 152 \u00f7 8 = 19. 4B = 2 \u00d7 19 = 38, 4C = 19. 4B + 4C = 38 + 19 = 57."} {"t":"s","id":16087,"s":"(a) The number is 18 (its largest factor). Factors of 18 are 1, 2, 3, 6, 9, 18; excluding 1 and 18 the others are 2, 3, 6, 9. (b) Multiples of 7 between 40 and 70: 42, 49, 56, 63. Adding 2 gives 44, 51, 58, 65; only 65 is a multiple of 5, so the number is 63."} {"t":"s","id":16089,"s":"Total stamps = 345 + 126 = 471 (unchanged when transferred). Current difference = 345 \u2212 126 = 219. We want Benny to have 37 more than Caius, so the difference must drop from 219 to 37, a reduction of 219 \u2212 37 = 182. Each stamp given reduces the gap by 2, so Benny gives 182 \u00f7 2 = 91 stamps."} {"t":"s","id":16090,"s":"Fifty-eight thousand = 58 000; thirty-nine = 39. So 58 000 + 39 = 58 039."} {"t":"s","id":16091,"s":"Rounding to the nearest hundred gives 72 000 for any number from 71 950 to 72 049. 71 952 rounds to 72 000. (71 839 to 71 800; 72 050 to 72 100; 72 499 to 72 500.)"} {"t":"s","id":16092,"s":"\\(\\dfrac{7}{20}=\\dfrac{35}{100}=0.35\\). So \\(6\\dfrac{7}{20}=6.35\\)."} {"t":"s","id":16093,"s":"5 tenths = 0.5, the first digit after the decimal point. In 27.53 the 5 is in the tenths place, so it stands for 5 tenths."} {"t":"s","id":16094,"s":"\\(\\dfrac{1}{3}=\\dfrac{4}{12}\\). \\(\\dfrac{7}{12}+\\dfrac{4}{12}=\\dfrac{11}{12}\\)."} {"t":"s","id":16095,"s":"\\(8\\dfrac{4}{9}=\\dfrac{8\\times9+4}{9}=\\dfrac{72+4}{9}=\\dfrac{76}{9}\\). Missing number = 76."} {"t":"s","id":16096,"s":"Remaining = 6544 - 408 = 6136. Each album = 6136 \u00f7 8 = 767."} {"t":"s","id":16097,"s":"Factors of 18: 1,2,3,6,9,18. Factors of 24: 1,2,3,4,6,8,12,24. The common factor among the options is 6."} {"t":"s","id":16100,"s":"The number must be a common multiple of 3 and 8, i.e. a multiple of 24, and fewer than 60. 48 is divisible by both 3 and 8 (48 = 3 x 16 = 8 x 6)."} {"t":"s","id":16101,"s":"Perimeter = 2 x (length + breadth). 42 = 2 x (length + 6), so length + 6 = 21, length = 15 m."} {"t":"s","id":16102,"s":"The letter T has a vertical line of symmetry (left and right halves are mirror images). F, N and S have no line of symmetry."} {"t":"s","id":16106,"s":"The pattern increases by 300 each time: 34 456, 34 756, 35 056, 35 356, 35 656. Missing = 34 756 + 300 = 35 056."} {"t":"s","id":16109,"s":"Numbers from 2895 to 2904 round to 2900 to the nearest ten. The smallest is 2895."} {"t":"s","id":16114,"s":"Total = \\(\\dfrac{1}{3}+\\dfrac{1}{9}+\\dfrac{7}{9}\\). \\(\\dfrac{1}{3}=\\dfrac{3}{9}\\), so \\(\\dfrac{3}{9}+\\dfrac{1}{9}+\\dfrac{7}{9}=\\dfrac{11}{9}=1\\dfrac{2}{9}\\) \\(l\\)."} {"t":"s","id":16122,"s":"Subtract the difference from the sum: 203 - 27 = 176. This is twice the smaller number, so smaller = 176 \u00f7 2 = 88."} {"t":"s","id":16123,"s":"8 units = 624, so 1 unit = 624 \u00f7 8 = 78. Blue = 5 units, pink = 3 units, difference = 2 units = 78 x 2 = 156."} {"t":"s","id":16125,"s":"9 units = 2574, so 1 unit = 286. Red = 4 units = 1144. Yellow + green = 5 units = 286 x 5 = 1430. Since yellow = green + 68, green = (1430 - 68) \u00f7 2 = 1362 \u00f7 2 = 681."} {"t":"s","id":16126,"s":"Total money = 6 x $10 + 3 x $5 = $60 + $15 = $75. Spent = $18.65 + $6.35 = $25. Saved = $75 - $25 = $50. Fraction saved = \\(\\dfrac{50}{75}=\\dfrac{2}{3}\\)."} {"t":"s","id":16127,"s":"(a) Every group of 3 bought + 1 free = 4 items. 72 \u00f7 4 = 18 groups, so 18 x 1 = 18 free items. (b) Bala's $145 buys 145 \u00f7 5 = 29 sets of 3 items. Each set gives 3 bought + 1 free = 4 items, so 29 x 4 = 116 items in total."} {"t":"s","id":16128,"s":"3 pens + 3 highlighters = 3 x $4.20 = $12.60. 3 pens + 5 highlighters = $17.40. Difference: 2 highlighters = $17.40 - $12.60 = $4.80, so 1 highlighter = $4.80 \u00f7 2 = $2.40."} {"t":"s","id":16130,"s":"Reading 56 780 from the right: 0 is ones, 8 is tens, 7 is hundreds, 6 is thousands, 5 is ten thousands. The digit in the tens place is 8."} {"t":"s","id":16131,"s":"Order the three numbers from smallest to greatest. Comparing the tens\/ones: 1035 < 1053 < 1305. So the correct arrangement is 1035, 1053, 1305."} {"t":"s","id":16132,"s":"A multiple of both 4 and 7 is a multiple of 28. 56 = 28 x 2, and 56 = 4 x 14 = 7 x 8. So 56 is a multiple of both 4 and 7."} {"t":"s","id":16134,"s":"10.76 x 8: 10 x 8 = 80, 0.76 x 8 = 6.08, total = 80 + 6.08 = 86.08. Wait, recompute: 10.76 x 8 = 86.08. Official key marks option (4) = 94.08. Recheck: 10.76 x 8 = 86.08 exactly (1076 x 8 = 8608, place decimal = 86.08)."} {"t":"s","id":16136,"s":"Pens = 4 units, rulers = 1 unit. Difference = 3 units = 480, so 1 unit = 160. Rulers = 160, pens = 640. Total pens and rulers = 160 + 640 = 800."} {"t":"s","id":16137,"s":"Total = 2350. Remove the extra 80: 2350 - 80 = 2270, halve to get Zachary's share = 1135. Timothy = 1135 + 80 = 1215."} {"t":"s","id":16139,"s":"She used half plus a quarter of a pizza: 1\/2 + 1\/4 = 3\/4 of a pizza gone. Left = 3 - 3\/4 = 2 and 1\/4 pizzas."} {"t":"s","id":16140,"s":"Cows are 7\/9 of the animals, so sheep are 2\/9. 126 \/ 9 = 14 per ninth. Sheep = 2 x 14 = 28."} {"t":"s","id":16141,"s":"Perimeter = 2 x (length + breadth). 96 \/ 2 = 48 = length + breadth. Length = 48 - 8 = 40 cm."} {"t":"s","id":16143,"s":"Giving 14 books to Ben reduces Alice's lead by 2 x 14 = 28. After giving, the lead is 29, so originally the lead was 29 + 28 = 57."} {"t":"s","id":16144,"s":"1 ring file = 2 notepads. So 1 ring file + 2 notepads = 2 + 2 = 4 notepad-units = $10.80. One notepad = 10.80 \/ 4 = $2.70."} {"t":"s","id":16147,"s":"Total girls = 12 + 15 + 7 = 34. Boys equal girls, so total boys = 34. Boys who liked burger = 34 - 20 - 6 = 8."} {"t":"s","id":16150,"s":"Forty thousand = 40 000; eleven = 11. Combined: 40 000 + 11 = 40011."} {"t":"s","id":16151,"s":"The thousandths place is the 3rd place after the decimal point. 8 thousandths = 0.008."} {"t":"s","id":16152,"s":"Make denominators equal: 4\/5 = 8\/10. 8\/10 + 9\/10 = 17\/10. As a mixed number, 17\/10 = 1 and 7\/10."} {"t":"s","id":16153,"s":"3\/4 = 75\/100 = 0.75. (Or 3 divided by 4 = 0.75.)"} {"t":"s","id":16154,"s":"Multiply the whole number by the denominator and add the numerator: 3 x 7 + 3 = 24. Keep the denominator 7: 24\/7."} {"t":"s","id":16155,"s":"Factors of 32 are 1, 2, 4, 8, 16, 32. Removing the given 1, 2, 8, 32 leaves 4 and 16."} {"t":"s","id":16156,"s":"Difference = 6.3 - 0.81. Align decimals: 6.30 - 0.81 = 5.49."} {"t":"s","id":16157,"s":"Compare values: 5\/6 = 0.833, 5\/9 = 0.556, 1\/2 = 0.5. Decreasing (largest first): 5\/6, 5\/9, 1\/2."} {"t":"s","id":16159,"s":"The pattern alternates +200 then -20: 2628 +200 = 2828, -20 = 2808, +200 = 3008, -20 = 2988, +200 = 3188, -20 = 3168, +200 = 3368. The missing number is 2988."} {"t":"s","id":16160,"s":"To round to 4.0 (nearest tenth), the number must be from 3.95 up to 4.04 (since 4.05 rounds to 4.1). With 2 decimal places, the greatest value is 4.04."} {"t":"s","id":16161,"s":"Joseph = 3 x 35.5 = 106.5 kg. Total = 106.5 + 35.5 = 142 kg. (Alternatively, total = 4 x 35.5 = 142 kg.)"} {"t":"s","id":16168,"s":"Let Mary = M, Nathan = M + 24, so Nathan + Mary = 2M + 24. Linda = 2(2M + 24) = 4M + 48. Total: M + (M + 24) + (4M + 48) = 264, so 6M + 72 = 264, 6M = 192, M = 32. Linda = 4(32) + 48 = 176. Linda - Mary = 176 - 32 = 144."} {"t":"s","id":16169,"s":"(a) Ethan + Fedrick = 3\/8 + 1\/3 = 9\/24 + 8\/24 = 17\/24. Germaine took the rest = 1 - 17\/24 = 7\/24. (b) Ethan's fraction - Germaine's fraction = 9\/24 - 7\/24 = 2\/24 = 1\/12 of the total = 12 candies. So total = 12 x 12 = 144 candies."} {"t":"s","id":16173,"s":"The digit 6 stands for 600 when 6 is in the hundreds place. In 7690, the 6 is in the hundreds place, so it stands for 600."} {"t":"s","id":16174,"s":"Compare the numbers: 4089 < 4809 < 4890. Only option 4 lists them from smallest to greatest."} {"t":"s","id":16177,"s":"0.4 + 81.23 = 81.63. Align the decimal points: 0.40 + 81.23 = 81.63."} {"t":"s","id":16179,"s":"Area of square = side \u00d7 side. Side \u00d7 side = 64, so side = 8 cm (since 8 \u00d7 8 = 64)."} {"t":"s","id":16181,"s":"Sister's time = \\(\\dfrac{3}{4}\\) - \\(\\dfrac{1}{6}\\). Common denominator 12: \\(\\dfrac{9}{12}\\) - \\(\\dfrac{2}{12}\\) = \\(\\dfrac{7}{12}\\) h."} {"t":"s","id":16183,"s":"To round 39 520 to the nearest hundred, look at the tens digit (2). Since 2 < 5, round down: 39 520 \u2248 39 500."} {"t":"s","id":16187,"s":"The numerator 3 becomes 12, multiplied by 4. So the denominator 5 must also be multiplied by 4: 5 \u00d7 4 = 20."} {"t":"s","id":16188,"s":"Convert \\(\\dfrac{2}{3}\\) to \\(\\dfrac{6}{9}\\). Then \\(\\dfrac{6}{9}\\) + \\(\\dfrac{2}{9}\\) = \\(\\dfrac{8}{9}\\)."} {"t":"s","id":16190,"s":"6.37 \u00d7 8 = 50.96. (637 \u00d7 8 = 5096, then place the decimal: 50.96.)"} {"t":"s","id":16195,"s":"Tank = 3 units, 2 buckets = 2 units, total = 5 units = 8.15 l. 1 unit (one bucket) = 8.15 \u00f7 5 = 1.63 l."} {"t":"s","id":16196,"s":"Money left for butter cookies = 33.60 \u2212 7.80 = 25.80. One packet = 25.80 \u00f7 4 = $6.45."} {"t":"s","id":16198,"s":"Kelvin's duration = 1 h 10 min + 30 min = 1 h 40 min. Starting at 1145: 1145 + 1 h = 1245, + 40 min = 1325. Kelvin completed his run at 1325."} {"t":"s","id":16203,"s":"12 buns is twice 6 buns, so flour used = \\(\\dfrac{4}{7}\\) \u00d7 2 = \\(\\dfrac{8}{7}\\) = \\(1\\dfrac{1}{7}\\) kg. Flour left = 3 \u2212 \\(1\\dfrac{1}{7}\\) = \\(2\\dfrac{7}{7}\\) \u2212 \\(1\\dfrac{1}{7}\\) = \\(1\\dfrac{6}{7}\\) kg."} {"t":"s","id":16204,"s":"Find the highest common factor of 24 and 32. Factors of 24: 1,2,3,4,6,8,12,24. Factors of 32: 1,2,4,8,16,32. The greatest common factor is 8, so 8 gift bags."} {"t":"s","id":16205,"s":"Chocolate = \\(\\dfrac{4}{5}\\) (4 units), vanilla = \\(\\dfrac{1}{5}\\) (1 unit). Difference = 4 \u2212 1 = 3 units = 240. 1 unit = 240 \u00f7 3 = 80. Vanilla = 1 unit = 80 muffins."} {"t":"s","id":16206,"s":"(a) 455 \u00d7 12 = 5460 pens. (b) 5460 \u00f7 8 = 682 remainder 4, so 4 pens are left unpacked."} {"t":"s","id":16207,"s":"(a) After giving, total is still 828, split as Fatimah:Ben = 1:3 = 4 units. 1 unit = 828 \u00f7 4 = 207. Fatimah had 207 stamps in the end. (b) Ben in the end = 3 \u00d7 207 = 621. Ben at first = 621 \u2212 68 (the stamps he received) = 553."} {"t":"s","id":16208,"s":"Belt = 1 unit, wallet = 2 units, shirt = 1 unit \u2212 $6. Total = 4 units \u2212 6 = 90.80, so 4 units = 96.80, 1 unit = 96.80 \u00f7 4 = $24.20 (belt). (b) Wallet = 2 units = 2 \u00d7 24.20 = $48.40."} {"t":"s","id":16210,"s":"(a) Samantha finished homework at 1535 + 1 h 5 min = 1640. She swam from 1640 to 1810 = 1 h 30 min. (b) Ken started 50 min before 1535 = 1445. He finished at 1445 + 1 h 25 min = 1610 = 4.10 pm."} {"t":"s","id":16211,"s":"Mobile phone = \\(\\dfrac{4}{7}\\) (4 units), so remaining money = \\(\\dfrac{3}{7}\\) (3 units). The 3 units = $65 + $190 = $255. 1 unit = 255 \u00f7 3 = $85. Mobile phone = 4 units = 4 \u00d7 85 = $340."} {"t":"s","id":16214,"s":"In 20 561, the digit 5 is in the hundreds place. Its value is 5 hundreds = 500."} {"t":"s","id":16215,"s":"A number with both 3 and 5 as factors must be divisible by 3 and by 5. 15 = 3 \u00d7 5, so both 3 and 5 are factors of 15."} {"t":"s","id":16217,"s":"Convert to twelfths: \\(\\dfrac{1}{3}\\) = \\(\\dfrac{4}{12}\\). Then \\(\\dfrac{4}{12}\\) + \\(\\dfrac{1}{12}\\) = \\(\\dfrac{5}{12}\\)."} {"t":"s","id":16219,"s":"Compare whole-number parts first: 0.67 and 0.76 are less than 1; 7.06 and 7.6 are over 7. Order: 0.67, 0.76, 7.06, 7.6."} {"t":"s","id":16222,"s":"Beads left = 1 \u2212 \\(\\dfrac{3}{8}\\) = \\(\\dfrac{5}{8}\\) of the total = 200. So \\(\\dfrac{1}{8}\\) = 200 \u00f7 5 = 40, and the total = 40 \u00d7 8 = 320."} {"t":"s","id":16223,"s":"0.08 = \\(\\dfrac{8}{100}\\). Divide numerator and denominator by 4: \\(\\dfrac{8}{100}\\) = \\(\\dfrac{2}{25}\\)."} {"t":"s","id":16232,"s":"Compare each to \\(\\dfrac{1}{2}\\): \\(\\dfrac{7}{12}\\) > \\(\\dfrac{6}{12}\\) so bigger; \\(\\dfrac{3}{7}\\) < \\(\\dfrac{3.5}{7}\\) so smaller; \\(\\dfrac{2}{5}\\) < \\(\\dfrac{2.5}{5}\\) so smaller; \\(\\dfrac{5}{10}\\) = \\(\\dfrac{1}{2}\\). So \\(\\dfrac{3}{7}\\) and \\(\\dfrac{2}{5}\\) are smaller."} {"t":"s","id":16233,"s":"Convert \\(\\dfrac{2}{3}\\) to sixths: \\(\\dfrac{2}{3}\\) = \\(\\dfrac{4}{6}\\). Then \\(\\dfrac{5}{6}\\) \u2212 \\(\\dfrac{4}{6}\\) = \\(\\dfrac{1}{6}\\)."} {"t":"s","id":16235,"s":"Write 8.7 as 8.70. Then 8.70 \u2212 0.88 = 7.82."} {"t":"s","id":16239,"s":"\\(\\dfrac{3}{5}\\) of the class = 24 girls, so 1 unit (\\(\\dfrac{1}{5}\\)) = 24 \u00f7 3 = 8. Total class = 5 units = 8 \u00d7 5 = 40 students."} {"t":"s","id":16240,"s":"As decimals: \\(\\dfrac{84}{10}\\) = 8.4, \\(\\dfrac{84}{100}\\) = 0.84, 0.804, 0.8 = 0.800. Decreasing: 8.4 (\\(\\dfrac{84}{10}\\)), 0.84 (\\(\\dfrac{84}{100}\\)), 0.804, 0.800."} {"t":"s","id":16241,"s":"109 \u00f7 7 = 15.57... \u2248 15.6 kg (correct to 1 decimal place)."} {"t":"s","id":16243,"s":"270 ml \u00d7 6 = 1620 ml. 1620 ml = 1 litre 620 ml."} {"t":"s","id":16244,"s":"Subtract 2 h 30 min from 01 25. 01 25 \u2212 30 min = 00 55; 00 55 \u2212 2 h = 22 55 (the previous day). Start time = 2255."} {"t":"s","id":16247,"s":"Sue = 50 + 16 = $66. Li Ann = 3 \u00d7 66 = $198. Total = 198 + 66 + 50 = $314."} {"t":"s","id":16248,"s":"Giving 8 instead of 7 needs 1 more per friend; being short of 12 means there are 12 friends. Sweets = 7 \u00d7 12 = 84 (between 50 and 100)."} {"t":"s","id":16249,"s":"(a) \\(\\dfrac{3}{8}\\) + \\(\\dfrac{1}{4}\\) = \\(\\dfrac{3}{8}\\) + \\(\\dfrac{2}{8}\\) = \\(\\dfrac{5}{8}\\) kg. (b) Left = 2 \u2212 \\(\\dfrac{5}{8}\\) = \\(1\\dfrac{8}{8}\\) \u2212 \\(\\dfrac{5}{8}\\) = \\(1\\dfrac{3}{8}\\) kg."} {"t":"s","id":16253,"s":"(a) Walked = 6 km \u2212 4 km 80 m = 1 km 920 m. (b) Difference = 4 km 80 m \u2212 1 km 920 m = 2 km 160 m."} {"t":"s","id":16254,"s":"After the changes the total = 993 \u2212 96 + 48 = 945. Each ended with 945 \u00f7 3 = 315. Betty ended with 315 after buying 48, so Betty had 315 \u2212 48 = 267 at first."} {"t":"s","id":16256,"s":"Thirty-two thousand = 32 000; forty-six = 46. Together: 32 046."} {"t":"s","id":16259,"s":"A fraction is in simplest form when numerator and denominator share no common factor other than 1. \\(\\dfrac{4}{10}=\\dfrac{2}{5}\\), \\(\\dfrac{2}{8}=\\dfrac{1}{4}\\), \\(\\dfrac{3}{6}=\\dfrac{1}{2}\\); only \\(\\dfrac{4}{9}\\) cannot be reduced."} {"t":"s","id":16261,"s":"1 m 10 cm = 110 cm. 110 cm - 25 cm = 85 cm."} {"t":"s","id":16265,"s":"Express over 8: 3\/4 = 6\/8, 1\/2 = 4\/8, 5\/8 = 5\/8. Greatest to smallest: 6\/8, 5\/8, 4\/8, i.e. 3\/4, 5\/8, 1\/2."} {"t":"s","id":16269,"s":"Compare digit by digit from the hundreds place. Greatest to smallest: 973, 937, 397, 379."} {"t":"s","id":16274,"s":"Make like denominators: 1\/4 = 2\/8. Then 2\/8 + 5\/8 = 7\/8."} {"t":"s","id":16278,"s":"Eaten: 8 + 16 = 24. Left: 30 - 24 = 6. Fraction left = 6\/30 = 1\/5."} {"t":"s","id":16280,"s":"He arrived 10 min before 07 30, i.e. at 07 20. From 06 00 to 07 20 is 1 h 20 min."} {"t":"s","id":16281,"s":"Side = square root of 81 = 9 cm. Perimeter = 9 x 4 = 36 cm."} {"t":"s","id":16284,"s":"After the transfer the total stays the same and Noah = 4 x Liam, so the total is 5 units. The difference Noah - Liam = 3 units, which equals 18 + 18 = 36 (Liam lost 18, Noah gained 18). So 3 units = 36, 1 unit = 12. Liam had 1 unit = 12 marbles in the end."} {"t":"s","id":16285,"s":"Total lemonade = 13.59 + 3.75 = 17.34 l. 17.34 \/ 3 = 5 remainder 2.34, so 5 full bottles plus 1 more for the leftover = 6 bottles."} {"t":"s","id":16288,"s":"Let Wednesday = 1 unit, Tuesday = 3 units, Monday = 3 units + 1220. Total = 7 units + 1220 = 4398, so 7 units = 3178 and 1 unit = 454. Tuesday = 3 units = 3 x 454 = 1362 worksheets."} {"t":"s","id":16289,"s":"Assume all 12 are vans: 12 x 9 = 108. That is 108 - 88 = 20 too many. Each car instead of a van loses 9 - 5 = 4. So cars = 20 \/ 4 = 5 cars."} {"t":"s","id":16293,"s":"Jayden = 5\/8, Linda = 3\/8, so the total is 8 units, Jayden 5 units, Linda 3 units. The difference 5 - 3 = 2 units = 36, so 1 unit = 18. (a) Linda = 3 units = 54 apples. (b) Total = 8 units = 144 apples. 6 apples = $4, so 144 apples cost (144\/6) x 4 = $96."} {"t":"s","id":16295,"s":"The pattern increases by 6 each time: 8, 14, 20, 26, 32, 38. The two missing numbers are 26 and 32."} {"t":"s","id":16296,"s":"Look at the tens digit (6). Since 6 is 5 or more, round the hundreds up: 34 762 rounds to 34 800."} {"t":"s","id":16297,"s":"The first digit after the decimal point is the tenths place. In 56.87 that digit is 8."} {"t":"s","id":16299,"s":"Convert to a common denominator of 18: \\(\\dfrac{1}{2}=\\dfrac{9}{18}\\), \\(\\dfrac{5}{9}=\\dfrac{10}{18}\\), \\(\\dfrac{8}{9}=\\dfrac{16}{18}\\). Smallest to greatest: \\(\\dfrac{1}{2}\\), \\(\\dfrac{5}{9}\\), \\(\\dfrac{8}{9}\\)."} {"t":"s","id":16302,"s":"Total used = 0.55 + 3.82 = 4.37 l. Paint left = 10 - 4.37 = 5.63 l."} {"t":"s","id":16308,"s":"The number must be divisible by 4, by 7, and have 8 as a factor. 56 is divisible by 4 (56\u00f74=14), by 7 (56\u00f77=8) and by 8 (56\u00f78=7). So Mr Tan has 56 pencils."} {"t":"s","id":16311,"s":"Let each start with x. Alan now = x + 36, Brian now = x - 24. x + 36 = 4(x - 24) \u2192 x + 36 = 4x - 96 \u2192 132 = 3x \u2192 x = 44. Each had 44 marbles at first."} {"t":"s","id":16312,"s":"4 m = 400 cm. Ribbon used for 5 pieces = 400 - 75 = 325 cm. Each piece = 325 \u00f7 5 = 65 cm."} {"t":"s","id":16315,"s":"Fifteen thousand = 15 000; twenty-five = 25. Together: 15 025."} {"t":"s","id":16318,"s":"Multiply numerator and denominator of \\(\\dfrac{5}{6}\\) by 2: \\(\\dfrac{5 \\times 2}{6 \\times 2} = \\dfrac{10}{12}\\). The missing number is 10."} {"t":"s","id":16324,"s":"92 tenths = 9.2 and 48 hundredths = 0.48. 9.2 - 0.48 = 8.72."} {"t":"s","id":16325,"s":"Work backwards from 1125. Subtract 1 h to get 1025, then subtract 45 min to get 0940. Nadim started at 0940."} {"t":"s","id":16327,"s":"875 ml = 0.875 l. Water needed = 12 - 0.875 = 11.125 l = 11 l 125 ml."} {"t":"s","id":16331,"s":"Let Ethan = 1 unit. David = 4 units. Fiona = 4 units - 60. Total = 1 + 4 + 4 units - 60 = 9 units - 60 = 1380, so 9 units = 1440, 1 unit = 160. David = 4 units = 4 \u00d7 160 = 640 stamps."} {"t":"s","id":16332,"s":"Total = 7 units = 1785, so 1 unit = 255. Non-fiction = 2 units, fiction = 5 units. Difference = 5 - 2 = 3 units = 3 \u00d7 255 = 765 more fiction books."} {"t":"s","id":16338,"s":"Compare the numbers: 4189 < 4819 < 4891. Option 4 lists them smallest to greatest."} {"t":"s","id":16339,"s":"63 = 7 \u00d7 9 = 3 \u00d7 21. Factors of 63 are 1, 3, 7, 9, 21, 63. 63 \u00f7 6 = 10 r 3, so 6 is not a factor."} {"t":"s","id":16345,"s":"A square has 4 equal sides. Length = perimeter \u00f7 4 = 64 \u00f7 4 = 16 m."} {"t":"s","id":16351,"s":"Highlighters are $3.50 \u2212 $2.80 = $0.70 cheaper each in July; pens are $2.60 \u2212 $1.70 = $0.90 cheaper each. Meiling (June) spends more by 6 \u00d7 $0.70 + 4 \u00d7 $0.90 = $4.20 + $3.60 = $7.80."} {"t":"s","id":16355,"s":"1 whole = \\(\\dfrac{6}{6}\\), which is 6 sixths. So there are 6 one-sixths in 1 whole."} {"t":"s","id":16356,"s":"Compare tenths first: 0.807 (8 tenths) > 0.708 (7 tenths) > 0.078 (0 tenths). Greatest to smallest: 0.807, 0.708, 0.078."} {"t":"s","id":16357,"s":"0.4 means 4 tenths = \\(\\dfrac{4}{10}\\). The missing denominator is 10."} {"t":"s","id":16362,"s":"(a) Boys in hall = total boys \u2212 boys in field = 315 \u2212 127 = 188. (b) Total girls = 208 + 50 = 258."} {"t":"s","id":16363,"s":"Numbers rounding to 1200 to the nearest hundred lie from 1150 up to 1249. (a) Smallest = 1150. (b) Greatest = 1249."} {"t":"s","id":16364,"s":"1504 \u00f7 5 = 300 remainder 4. The 4 leftover apples still need 1 more box, so 300 + 1 = 301 boxes."} {"t":"s","id":16368,"s":"Suppose all 30 are squares: 30 \u00d7 4 = 120 sides. Actual sides = 108, a shortfall of 120 \u2212 108 = 12. Each triangle has 1 fewer side than a square (4 \u2212 3 = 1), so number of triangles = 12 \u00f7 1 = 12."} {"t":"s","id":16370,"s":"Each duck = 2 chickens, so 2 ducks = 4 chickens. Total = 5 + 4 = 9 chicken-units = 12.6 kg, so 1 chicken = 12.6 \u00f7 9 = 1.4 kg. (b) 1 duck = 1.4 \u00d7 2 = 2.8 kg; 1 chicken + 1 duck = 1.4 + 2.8 = 4.2 kg."} {"t":"s","id":16371,"s":"Fiction = 7 units = 3528, so 1 unit (non-fiction) = 3528 \u00f7 7 = 504. (a) More fiction than non-fiction = 6 units = 504 \u00d7 6 = 3024. (b) Altogether = 8 units = 504 \u00d7 8 = 4032."} {"t":"s","id":16374,"s":"Bottle B at first = X. After receiving \\(\\dfrac{1}{8}\\) and giving away \\(\\dfrac{1}{2}\\): X + \\(\\dfrac{1}{8}\\) \u2212 \\(\\dfrac{1}{2}\\) = \\(\\dfrac{5}{8}\\). \\(\\dfrac{1}{8} - \\dfrac{1}{2} = \\dfrac{1}{8} - \\dfrac{4}{8} = -\\dfrac{3}{8}\\), so X \u2212 \\(\\dfrac{3}{8}\\) = \\(\\dfrac{5}{8}\\), giving X = 1 \\(l\\). Each bottle started with 1 \\(l\\), so total = 1 \u00d7 3 = 3 \\(l\\). (b) Cost = 3 \u00d7 $7.80 = $23.40."} {"t":"s","id":16375,"s":"Let boys = 2 units (so half remain = 1 unit) and girls = 4 units (so a quarter remain = 1 unit) to make the remainders equal. Girls \u2212 boys = 4u \u2212 2u = 2u = 540, so 1 unit = 270. Boys = 540, girls = 1080. (a) Exited = half the boys + three-quarters of girls = 270 + 810 = 1080; equivalently 4 units = 270 \u00d7 4 = 1080. (b) Total at first = 6 units = 270 \u00d7 6 = 1620."} {"t":"s","id":16376,"s":"Lily is unchanged. In the end Lily = 6 units and Jasmine = 1 unit. Lily \u2212 Jasmine (end) = 5 units. The gap grew by the 1125 Jasmine sold: 2425 + 1125 = 3550 = 5 units, so 1 unit = 710. (a) Jasmine in the end = 1 unit = 710. (b) Lily = 6 units = 710 \u00d7 6 = 4260."} {"t":"s","id":16378,"s":"In 57.92 the first digit after the decimal point is the tenths place. That digit is 9."} {"t":"s","id":16379,"s":"\\(\\dfrac{1}{4}\\) equals 3\/12, 4\/16 and 6\/24 (each numerator is one-quarter of the denominator). \\(\\dfrac{7}{32}\\) is not, since 7 \u00d7 4 = 28 \u2260 32. So \\(\\dfrac{7}{32}\\) is not equivalent."} {"t":"s","id":16380,"s":"A number with both 2 and 3 as factors must be divisible by 6. Among the options, 18 = 6 \u00d7 3 is divisible by both 2 and 3."} {"t":"s","id":16381,"s":"Convert the mixed number to an improper fraction: \\(6\\dfrac{3}{8}\\) = (6 \u00d7 8 + 3)\/8 = (48 + 3)\/8 = \\(\\dfrac{51}{8}\\). The missing number is 51."} {"t":"s","id":16382,"s":"Make the denominator 100: \\(\\dfrac{9}{25}\\) = \\(\\dfrac{36}{100}\\) = 0.36. So \\(7\\dfrac{9}{25}\\) = 7.36."} {"t":"s","id":16386,"s":"Total juice = 17.82 + 5.18 = 23 l. Each jug = 23 \u00f7 8 = 2.875 l. Rounded to the nearest tenth = 2.9 l."} {"t":"s","id":16387,"s":"Jenny = \\(\\dfrac{7}{12}\\) + \\(\\dfrac{2}{3}\\). Change \\(\\dfrac{2}{3}\\) to \\(\\dfrac{8}{12}\\): \\(\\dfrac{7}{12}\\) + \\(\\dfrac{8}{12}\\) = \\(\\dfrac{15}{12}\\) = \\(1\\dfrac{3}{12}\\) = \\(1\\dfrac{1}{4}\\) h."} {"t":"s","id":16391,"s":"The letter C has a horizontal line of symmetry (top and bottom halves mirror each other). G, N and K have no line of symmetry."} {"t":"s","id":16392,"s":"Need a number 20\u201350 that leaves remainder 4 when divided by 6 and remainder 2 when divided by 8. Check 34: 34 \u00f7 6 = 5 r4 \u2713 and 34 \u00f7 8 = 4 r2 \u2713. So Bala has 34 stickers."} {"t":"s","id":16393,"s":"Twenty thousand = 20 000, and forty-one = 41. Combine: 20 000 + 41 = 20 041."} {"t":"s","id":16394,"s":"Compare: \\(\\dfrac{5}{11}\\) \u2248 0.45, \\(\\dfrac{1}{2}\\) = 0.5, \\(\\dfrac{8}{11}\\) \u2248 0.73. From smallest to greatest: \\(\\dfrac{5}{11}\\), \\(\\dfrac{1}{2}\\), \\(\\dfrac{8}{11}\\)."} {"t":"s","id":16395,"s":"Look at the tens digit of 18 430, which is 3. Since 3 < 5, round down: 18 430 \u2192 18 400."} {"t":"s","id":16401,"s":"Each piece = 3 \u00f7 7 = 0.428... m. Rounded to the nearest hundredth (2 decimal places) = 0.43 m."} {"t":"s","id":16403,"s":"Ben = Gladys \u2212 \\(\\dfrac{1}{5}\\) = \\(\\dfrac{2}{3}\\) \u2212 \\(\\dfrac{1}{5}\\) = \\(\\dfrac{10}{15}\\) \u2212 \\(\\dfrac{3}{15}\\) = \\(\\dfrac{7}{15}\\) km. Total = \\(\\dfrac{2}{3}\\) + \\(\\dfrac{7}{15}\\) = \\(\\dfrac{10}{15}\\) + \\(\\dfrac{7}{15}\\) = \\(\\dfrac{17}{15}\\) = \\(1\\dfrac{2}{15}\\) km."} {"t":"s","id":16410,"s":"(a) Total bought = 24 \u00d7 32 = 768 sweets. (b) Sweets given away = 12 \u00d7 40 = 480. Sweets left = 768 \u2212 480 = 288."} {"t":"s","id":16411,"s":"(a) Given away = \\(\\dfrac{3}{10}\\) + \\(\\dfrac{1}{2}\\) = \\(\\dfrac{3}{10}\\) + \\(\\dfrac{5}{10}\\) = \\(\\dfrac{8}{10}\\). Fraction left = \\(\\dfrac{10}{10}\\) \u2212 \\(\\dfrac{8}{10}\\) = \\(\\dfrac{2}{10}\\). (b) \\(\\dfrac{2}{10}\\) \u2192 50 cookies, so \\(\\dfrac{1}{10}\\) \u2192 25, and \\(\\dfrac{10}{10}\\) \u2192 25 \u00d7 10 = 250 cookies."} {"t":"s","id":16414,"s":"Let red = 1 unit. Blue = 2 units, green = 3 \u00d7 blue = 6 units. Blue + green = 2 + 6 = 8 units = 1728, so 1 unit = 1728 \u00f7 8 = 216. (a) Green = 6 units = 6 \u00d7 216 = 1296. (b) Red = 1 unit = 216, so green \u2212 red = 1296 \u2212 216 = 1080."} {"t":"s","id":16415,"s":"(a) 3 tables + 5 stools = 173.1; 1 table + 3 stools = 65.3. Tripling the second: 3 tables + 9 stools = 195.9. Subtract the first: 4 stools = 195.9 \u2212 173.1 = 22.8 kg, so 1 stool = 5.7 kg. From the second: 1 table = 65.3 \u2212 3 \u00d7 5.7 = 65.3 \u2212 17.1 = 48.2 kg. Table + stool = 48.2 + 5.7 = 53.9 kg. (b) 4 stools = 4 \u00d7 5.7 = 22.8 kg."} {"t":"s","id":16420,"s":"a) Convert to twelfths: \\(\\dfrac{3}{4} = \\dfrac{9}{12}\\), \\(\\dfrac{1}{3} = \\dfrac{4}{12}\\), \\(\\dfrac{7}{12} = \\dfrac{7}{12}\\). Decreasing order: \\(\\dfrac{9}{12} > \\dfrac{7}{12} > \\dfrac{4}{12}\\), i.e. 3\/4, 7\/12, 1\/3.
b) \\(3 - \\dfrac{5}{6} = \\dfrac{18}{6} - \\dfrac{5}{6} = \\dfrac{13}{6} = 2\\dfrac{1}{6}\\)."} {"t":"s","id":16421,"s":"Number of packets \\(= 72 \\div 6 = 12\\). Cost \\(= 12 \\times \\$5 = \\$60\\)."} {"t":"s","id":16422,"s":"Boys in 4B \\(= 41 - 17 = 24\\). Total boys \\(= 21 + 24 = 45\\)."} {"t":"s","id":16425,"s":"Let Dan's amount at the end be 1 unit; then Evan (unchanged) is 3 units. The difference between Evan and Dan-now is the $480 Dan spent, which equals \\(3u - 1u = 2u\\). So \\(2u = \\$480\\), giving \\(1u = \\$240\\) (Dan in the end). Dan at first = Evan = \\(3u = 3 \\times \\$240 = \\$720\\)."} {"t":"s","id":16427,"s":"Rice \\(= \\dfrac{1}{4}\\) kg. Flour \\(= \\dfrac{1}{4} + \\dfrac{2}{5}\\) kg. Total rice and flour \\(= \\dfrac{1}{4} + \\left(\\dfrac{1}{4} + \\dfrac{2}{5}\\right)\\). Using the key's method: \\(\\dfrac{1}{4} + \\dfrac{2}{5} = \\dfrac{5}{20} + \\dfrac{8}{20} = \\dfrac{13}{20}\\) (flour); then \\(\\dfrac{13}{20} + \\dfrac{5}{20} = \\dfrac{18}{20} = \\dfrac{9}{10}\\) kg altogether."} {"t":"s","id":16428,"s":"Fraction that are sheep, ducks and horses \\(= \\dfrac{1}{6} + \\dfrac{1}{3} + \\dfrac{1}{4} = \\dfrac{2}{12} + \\dfrac{4}{12} + \\dfrac{3}{12} = \\dfrac{9}{12} = \\dfrac{3}{4}\\). So rabbits are \\(1 - \\dfrac{3}{4} = \\dfrac{1}{4}\\), i.e. 3 of 12 equal units = 90. Per key: take 12 units total, rabbits = 3 units = 90, so 1 unit = 30, total = 12 units = \\(30 \\times 12 = 360\\) animals."} {"t":"s","id":16429,"s":"Ninety-four thousand = 94 000; eight hundred = 800; and seven = 7. So \\(94000 + 800 + 7 = 94807\\). The numeral is 94 807."} {"t":"s","id":16430,"s":"Factors of 4: 1, 2, 4. Factors of 8: 1, 2, 4, 8. A common factor must divide BOTH numbers. Among the options, only 4 divides both 4 and 8. So the answer is 4."} {"t":"s","id":16432,"s":"A child gets both if their position is a common multiple of 4 and 5, i.e. a multiple of 20. Within 40, these are positions 20 and 40. So 2 children received both."} {"t":"s","id":16433,"s":"Try 1953: \\(1953 + 1 = 1954\\), which rounds to 1950. \\(1953 + 2 = 1955\\), which rounds to 1960. Both conditions are satisfied, so the number is 1953."} {"t":"s","id":16434,"s":"To make the largest number, arrange the digits from greatest to smallest: 7, 6, 4, 1. So the largest number is 7641."} {"t":"s","id":16435,"s":"The first two multiples of 5 are 5 and 10. Their sum is \\(5 + 10 = 15\\)."} {"t":"s","id":16437,"s":"Numbers from 2550 to 2649 round to 2600 (to the nearest hundred). The largest of these is 2649."} {"t":"s","id":16439,"s":"If all 20 were plates: \\(20 \\times 3 = 60\\) dollars. The actual total is $86, which is \\(86 - 60 = 26\\) more. Each bowl is \\(5 - 3 = 2\\) dollars more than a plate, so number of bowls = \\(26 \\div 2 = 13\\). Sarah sold 13 bowls."} {"t":"s","id":16440,"s":"Let Sophie have 1 unit at first, so Ethan had 2 units. After using 36, Ethan had \\(2\\text{ units} - 36\\), and this equals half of Sophie's, i.e. Sophie's 1 unit = \\(2 \\times (2\\text{ units} - 36)\\). So \\(1\\text{ unit} = 4\\text{ units} - 72\\), giving \\(3\\text{ units} = 72\\), so 1 unit = 24. Sophie had 24 beads at first."} {"t":"s","id":16441,"s":"(a) Table + chair = total - bookshelf = \\(1400 - 630 = 770\\) dollars. (b) Table = chair + 500, so chair + chair + 500 = 770, giving \\(2 \\times \\text{chair} = 770 - 500 = 270\\), so chair = \\(270 \\div 2 = 135\\) dollars."} {"t":"s","id":16442,"s":"Forty-five thousand = 45 000, nine hundred = 900, and six = 6. Adding these gives 45 000 + 900 + 6 = 45 906. The answer is option (3), 45 906."} {"t":"s","id":16443,"s":"Decreasing order means largest to smallest. Compare the thousands: 86 372 and 86 237 both have 86 thousands, and 85 327 has 85 thousands so it is smallest. Between 86 372 and 86 237, the hundreds 3 > 2, so 86 372 > 86 237. Order: 86 372, 86 237, 85 327. The answer is option (2)."} {"t":"s","id":16444,"s":"Each term increases by 100: 62 831 + 100 = 62 931, then 62 931 + 100 = 63 031. Checking forward, 63 031 + 100 = 63 131 which matches. The missing number is 63 031, option (3)."} {"t":"s","id":16445,"s":"Rounding to the nearest hundred: 83 875 rounds to 83 900; 83 953 rounds to 84 000; 84 092 rounds to 84 100; 84 234 rounds to 84 200. Only 83 953 rounds to 84 000. The answer is option (2)."} {"t":"s","id":16446,"s":"A number with both 4 and 7 as factors must be a multiple of \\(4 \\times 7 = 28\\). Checking: 11 (no), 21 = 3 x 7 (only 7), 64 = 4 x 16 (only 4), 84 = 28 x 3 (both 4 and 7). The answer is option (4), 84."} {"t":"s","id":16447,"s":"The first guest to get both is the lowest common multiple of 6 and 8. Multiples of 6: 6, 12, 18, 24; multiples of 8: 8, 16, 24. The smallest common multiple is 24, so the 24th guest is first to get both. The answer is option (3)."} {"t":"s","id":16448,"s":"a) In 58 701 the digit 7 is in the hundreds place, so its value is \\(7 \\times 100 = 700\\). b) To round 19 572 to the nearest thousand, look at the hundreds digit 5; since 5 rounds up, 19 572 becomes 20 000."} {"t":"s","id":16449,"s":"a) 7 ten thousands = 70 000, 64 tens = 640, 3 ones = 3. Sum: 70 000 + 640 + 3 = 70 643. b) \\(4308 \\times 9 = 38772\\)."} {"t":"s","id":16450,"s":"Check whether 4 divides each number. 96 divided by 4 is 24 with no remainder, so 4 is a factor of 96 (Ariel is correct). 76 divided by 4 is 19 with no remainder, so 4 is a factor of 76 (Tom is correct). Both are correct, so the correct statement is 'Both Ariel and Tom are correct.'"} {"t":"s","id":16451,"s":"Each person's share: \\(6726 \\div 3 = 2242\\), so Simon had $2242. After spending $1045: \\(2242 - 1045 = 1197\\). Simon had $1197 left."} {"t":"s","id":16452,"s":"Total stamps: \\(75 \\times 26 = 1950\\). Each bag holds 5 stamps, so number of bags: \\(1950 \\div 5 = 390\\). There are 390 bags."} {"t":"s","id":16453,"s":"Let a chair be 1 unit; a desk is then 2 units. 2 desks = 4 units and 4 chairs = 4 units, giving \\(4 + 4 = 8\\) units. So 8 units = $2264 and 1 unit = \\(2264 \\div 8 = 283\\). A desk and a chair together = 2 units + 1 unit = 3 units = \\(283 \\times 3 = 849\\). The total cost is $849."} {"t":"s","id":16454,"s":"Each friend gets 2 more sweets in the second case (\\(6 - 4 = 2\\)), and the leftover drops by \\(22 - 8 = 14\\) sweets. So those 14 extra sweets cover the 2-per-friend increase: number of friends = \\(14 \\div 2 = 7\\). Total sweets = (4 sweets x 7 friends) + 22 left over = \\(28 + 22 = 50\\). Sandy had 50 sweets."} {"t":"s","id":16455,"s":"Forty-six thousand = 46 000, and sixteen = 16. 46 000 + 16 = 46 016. Option (3)."} {"t":"s","id":16456,"s":"The 8 must be in the tens place to stand for 80. In 3082 the 8 is in the tens place (80). Option (2)."} {"t":"s","id":16457,"s":"Look at the tens digit (2). Since 2 < 5, round down: 13 429 to the nearest hundred is 13 400. Option (3)."} {"t":"s","id":16459,"s":"Make denominators the same: \\(\\dfrac{1}{3}=\\dfrac{3}{9}\\). Then \\(\\dfrac{3}{9}+\\dfrac{1}{9}=\\dfrac{4}{9}\\). Option (4)."} {"t":"s","id":16461,"s":"To round to 1 decimal place, look at the hundredths digit (4). Since 4 < 5, keep the tenths digit: 17.54 to 1 d.p. is 17.5. Option (2)."} {"t":"s","id":16462,"s":"13 30 + 1 h 30 min = 15 00. Option (4)."} {"t":"s","id":16468,"s":"$55 - $25 = $30 is the cost of 3 shirts' worth (2 shirts + 1 shirt-equivalent of pants). 3 units = $30, so 1 shirt = $10. Option (1)."} {"t":"s","id":16470,"s":"83 905 = 80 000 + 3000 + 900 + 5. The missing number is 900 (the hundreds value)."} {"t":"s","id":16471,"s":"Each term decreases by 400. 11 800 - 400 = 11 400."} {"t":"s","id":16477,"s":"Compare tenths first: 3.909 has 9 tenths (largest). Then 3.099 vs 3.093 \u2014 hundredths equal (9), thousandths 9 > 3, so 3.099 > 3.093. Order greatest to smallest: 3.909, 3.099, 3.093."} {"t":"s","id":16480,"s":"Find the common factors of 36 and 54: 1, 2, 3, 6, 9, 18. The greatest common factor is 18, so the greatest number of boxes is 18."} {"t":"s","id":16488,"s":"Jonathan = 1.81 - 0.35 = 1.46 m. Elson is 0.29 m taller than Jonathan: 1.46 + 0.29 = 1.75 m."} {"t":"s","id":16489,"s":"The watch is 15 min slow, so the actual time is 15 min later: 1.35 p.m. + 15 min = 1.50 p.m. = 13 50 in the 24-hour clock."} {"t":"s","id":16490,"s":"Two facing pages are consecutive numbers. Sum = 667, so the smaller page = (667 - 1) \u00f7 2 = 666 \u00f7 2 = 333."} {"t":"s","id":16491,"s":"Given away = \\(\\dfrac{1}{7}+\\dfrac{3}{4}=\\dfrac{4}{28}+\\dfrac{21}{28}=\\dfrac{25}{28}\\). Mark ate the rest: \\(\\dfrac{28}{28}-\\dfrac{25}{28}=\\dfrac{3}{28}\\)."} {"t":"s","id":16494,"s":"Let Joey = 1 unit, Nicole = 5 units. After giving away: 5u - 235 = 1u - 19, so 4u = 235 - 19 = 216, 1u = 54. (a) Nicole baked 5u = 5 \u00d7 54 = 270. (b) Each had 1u - 19 = 54 - 19 = 35 in the end."} {"t":"s","id":16495,"s":"Mrs Devi sold \\(\\dfrac{7}{9}\\) of her muffins (since \\(\\dfrac{2}{9}\\) are left) = 49, so 7 units = 49, 1 unit = 7. (a) Left = 2 units = 2 \u00d7 7 = 14. (b) Each baked 9 units = 9 \u00d7 7 = 63; total for both = 63 \u00d7 2 = 126."} {"t":"s","id":16496,"s":"Charlie's marbles never change. At first Charlie = 2 \u00d7 Sally. After Sally loses 45, Charlie = 5 \u00d7 (new Sally). Let new Sally = 1 unit, Charlie = 5 units; original Sally = 5u \u00f7 2. Since Sally lost 45: 5u\/2 - 45 = u, giving 3u\/2 = 45, u = 30. Charlie = 5u... using the key: 3u = 45 + 45 = 90, 1u = 30, Charlie = 5 \u00d7 30 = 150."} {"t":"s","id":16497,"s":"Catherine - Alice = (Benny+Catherine) - (Alice+Benny) = 450 - 100 = 350. Catherine is 5 times Alice, so Catherine - Alice = 4 units = 350, 1 unit = 350 \u00f7 4 = $87.50. Alice (1 unit) received $87.50."} {"t":"s","id":16498,"s":"77 thousands = 77 000 and 3 tens = 30. 77 000 + 30 = 77 030."} {"t":"s","id":16499,"s":"Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56. 56 \u00f7 6 = 9 remainder 2, so 6 is not a factor."} {"t":"s","id":16501,"s":"4\/9: no common factor of 4 and 9 except 1, so it is in simplest form. 2\/8 = 1\/4, 3\/12 = 1\/4, 6\/10 = 3\/5."} {"t":"s","id":16505,"s":"Convert all to metres: 1340 m; 1 km 304 m = 1304 m; 1 3\/4 km = 1750 m. Longest to shortest: 1750 m (1 3\/4 km), 1340 m, 1304 m (1 km 304 m)."} {"t":"s","id":16506,"s":"Brian (48) + Ethan (102) = 150. (Ali 84 + Dinesh 56 = 140; Brian 48 + Cheng 112 = 160; Dinesh 56 + Ethan 102 = 158.)"} {"t":"s","id":16508,"s":"Morning: 9 a.m. to 12 p.m. = 3 h. Afternoon: 1.30 p.m. to 4.30 p.m. = 3 h. Total painting time = 3 h + 3 h... wait, 3 h + 3 h would be 6 h, but lunch (12 to 1.30) is excluded. Total = 3 h + 3 h = 6 h? Actual painting: 3 h + 3 h = 6 h. Key gives option 1 (5 h 30 min); morning 9 to 12 = 3 h, afternoon 1.30 to 4.30 = 3 h, total painting 6 h. See notes."} {"t":"s","id":16509,"s":"Must reach gate by 30 min before 15 05 = 14 35. She walks 20 min, so she must start by 14 35 - 20 min = 14 15."} {"t":"s","id":16513,"s":"Male adults = total 246 \u2212 children 119 = 127. Total adults = male adults 127 + female adults 230 = 357."} {"t":"s","id":16515,"s":"The pattern repeats every 6 letters: C, A, B, C, D, E. 50 \u00f7 6 = 8 remainder 2, so the 50th letter is the 2nd letter of the block, which is A."} {"t":"s","id":16516,"s":"4 files cost 4 \u00d7 $0.70 = $2.80 more than 4 rulers. Remove this: $9.60 \u2212 $2.80 = $6.80 for 8 rulers' worth. $6.80 \u00f7 8 = $0.85 per ruler."} {"t":"s","id":16517,"s":"Best three of four must total \u2265 30. The two highest existing scores are 10.1 + 9.5 = 19.6. The 4th game must make the best three reach 30: 30 \u2212 19.6 = 10.4. So the lowest 4th-game score is 10.4."} {"t":"s","id":16520,"s":"1\/2 = 3.5\/7, so 1\/2 < 4\/7 < 6\/7. Smallest to greatest: 1\/2, 4\/7, 6\/7."} {"t":"s","id":16522,"s":"3\/4 = 6\/8. 6\/8 + 1\/8 = 7\/8."} {"t":"s","id":16526,"s":"0.39 = 39 hundredths = 39\/100. 39 and 100 share no common factor, so it is already in simplest form."} {"t":"s","id":16527,"s":"Each term decreases by 800: 11 005 \u2212 800 = 10 205, ... 8605 \u2212 800 = 7805 (then 7805 \u2212 800 = 7005)."} {"t":"s","id":16529,"s":"18 donuts \u00f7 3 = 6 sets. 6 \u00d7 $3.95 = $23.70."} {"t":"s","id":16530,"s":"Buy 2 get 1 free: for 6 bars taken home, Raju pays for only 4 bars. 4 \u00d7 $5.50 = $22. Change = $50 \u2212 $22 = $28."} {"t":"s","id":16533,"s":"Let Aunt Mei have M. Uncle Lee had 3M. After selling 75: 3M \u2212 75. Aunt Mei is now twice his: M = 2(3M \u2212 75) \u2192 M = 6M \u2212 150 \u2192 150 = 5M \u2192 M = 30. (Per key working: 75 \u00f7 5 = 15; total parts give Aunt Mei 30.)"} {"t":"s","id":16537,"s":"The digit 8 stands for 800 when it sits in the hundreds place. In 5840, the 8 is in the hundreds place, so it stands for 800. In 4058 it is 8, in 5084 it is 80, in 8504 it is 8000."} {"t":"s","id":16538,"s":"To round 45 879 to the nearest hundred, look at the tens digit (7). Since 7 is 5 or more, round the hundreds up: 45 879 rounds to 45 900."} {"t":"s","id":16539,"s":"Compare the fractions: 4\/9 is just under a half (4.5\/9 = 1\/2), so 4\/9 < 1\/2. And 8\/9 is the largest. Ordered smallest to greatest: 4\/9, 1\/2, 8\/9."} {"t":"s","id":16541,"s":"Compare the decimals by place value. 3.038 has 0 tenths and 3 hundredths, the smallest of all. 3.07 = 3.070, 3.15, 3.304 are all larger. So 3.038 is smallest."} {"t":"s","id":16542,"s":"Convert 7\/20 to a decimal: multiply numerator and denominator by 5 to get 35\/100 = 0.35. So 4 7\/20 = 4.35."} {"t":"s","id":16545,"s":"Factors of 28 below 10: 1, 2, 4, 7. Of these, the multiples of 4 are: 4. So Adam is 4 years old. (8 is a multiple of 4 but not a factor of 28.)"} {"t":"s","id":16546,"s":"Non-fiction = 3 x 2580 = 7740. Altogether = 2580 + 7740 = 10 320 books."} {"t":"s","id":16547,"s":"Cost of planes = 48 x $367 = $17 616. She had $10 left, so at first = $17 616 + $10 = $17 626."} {"t":"s","id":16548,"s":"Let Azri's amount after giving away be 1 unit; Liying = 5 units. They started equal, so the 60 given away is the difference: 5 units - 1 unit = 4 units = 60, so 1 unit = 15. Azri started with the same as Liying = 5 units = 75 stamps."} {"t":"s","id":16549,"s":"Cake flour = 3\/8 + 1\/5 = 15\/40 + 8\/40 = 23\/40 kg. Altogether = cookies + cake = 3\/8 + 23\/40 = 15\/40 + 23\/40 = 38\/40 = 19\/20 kg."} {"t":"s","id":16551,"s":"To round to 175, the decimal must be at least 174.5 (rounds up) and below 175.5. 174.49 rounds to 174 (too small). 174.50 rounds up to 175 and is the smallest of the options that rounds to 175."} {"t":"s","id":16557,"s":"Compare the numbers by place value. 5064 (thousands 5, hundreds 0), 5604 (hundreds 6), 5640 (hundreds 6, tens 4). Smallest to greatest: 5064, 5604, 5640."} {"t":"s","id":16558,"s":"The factors of 18 are 1, 2, 3, 6, 9, 18. The ones not listed are 6 and 9."} {"t":"s","id":16559,"s":"Multiply the whole number by the denominator and add the numerator: 3 x 5 + 4 = 19. So 3 4\/5 = 19\/5."} {"t":"s","id":16560,"s":"Make the denominators the same: 1\/4 = 2\/8. Then 2\/8 + 5\/8 = 7\/8."} {"t":"s","id":16561,"s":"Convert to tenths: 1 = 10\/10, 1\/5 = 2\/10. Then 10\/10 - 1\/10 - 2\/10 = 7\/10."} {"t":"s","id":16569,"s":"Peaches are the remaining fraction: 1 - 3\/8 = 5\/8. Number of peaches = 5\/8 x 872 = 5 x 109 = 545."} {"t":"s","id":16570,"s":"Let 1 skirt = 1 unit. Dress = 1 unit + $65.50. Total = 3 units + $65.50 = $250, so 3 units = $184.50, 1 unit = $61.50. One skirt costs $61.50."} {"t":"s","id":16575,"s":"Total = 6 units = 1200, so 1 unit = 200. Steven = 200, Johnson = 1000. To be equal each must have 600. Johnson must give Steven 1000 - 600 = 400 sweets. (Equivalently, give 2 units = 400.)"} {"t":"s","id":16576,"s":"Let 4B = 1 unit, 4C = 3 units, so 4B+4C = 4 units. 4A = 4 units - 123. Total = (4 units) + (4 units - 123) = 8 units - 123 = 3445. So 8 units = 3568, 1 unit = 446. Class 4B collected 446 kg."} {"t":"s","id":16577,"s":"Spent = 2\/3 + 1\/4 = 8\/12 + 3\/12 = 11\/12. Left = 1\/12 = $27, so the whole = $324. Dress = 8\/12 = $216, doll = 3\/12 = $81. Difference = 216 - 81 = $135."} {"t":"s","id":16578,"s":"After giving away, the difference between Lisa and Zara = 10 - 1.5 + 0.5 = 9 kg. This difference is 4 units - 1 unit = 3 units = 9 kg, so 1 unit = 3 kg (Zara's amount after giving away). Zara at first = 3 + 0.5 = 3.5 kg."} {"t":"s","id":16581,"s":"Thirty-four thousand = 34 000; sixty-two = 62. Together: \\(34\\,000 + 62 = 34\\,062\\)."} {"t":"s","id":16582,"s":"Rounding to the nearest hundred: 59 951 rounds to 60 000 (the tens digit 5 rounds up). 59 599 rounds to 59 600; 60 070 rounds to 60 100; 60 140 rounds to 60 100."} {"t":"s","id":16583,"s":"Common multiples of 4 and 6 are 12, 24, 36, ... The first is 12 and the second is 24."} {"t":"s","id":16585,"s":"\\(\\dfrac{4}{6} = \\dfrac{2}{3}\\). Checking: \\(\\dfrac{12}{18} = \\dfrac{2}{3}\\), so it is equivalent."} {"t":"s","id":16586,"s":"In 41.32, the first decimal place (tenths) is 3 and the second (hundredths) is 2. So the digit in the hundredths place is 2."} {"t":"s","id":16591,"s":"From 23 39 to 24 00 is 21 min. From 00 00 to 06 22 is 6 h 22 min. Total: \\(6\\ h\\ 22\\ min + 21\\ min = 6\\ h\\ 43\\ min\\)."} {"t":"s","id":16594,"s":"Remaining string = \\(15.61 - 1.54 = 14.07\\) m. Each piece = \\(14.07 \\div 7 = 2.01\\) m."} {"t":"s","id":16595,"s":"Frances = \\(\\dfrac{3}{10} + \\dfrac{1}{5} = \\dfrac{3}{10} + \\dfrac{2}{10} = \\dfrac{5}{10} = \\dfrac{1}{2}\\) kg. Altogether = \\(\\dfrac{3}{10} + \\dfrac{5}{10} = \\dfrac{8}{10} = \\dfrac{4}{5}\\) kg."} {"t":"s","id":16599,"s":"The pattern decreases by 30 each time: \\(875 - 845 = 30\\). So the missing term is \\(815 - 30 = 785\\) (and \\(785 - 30 = 755\\) checks)."} {"t":"s","id":16603,"s":"Side = \\(76 \\div 4 = 19\\) cm. Area = \\(19 \\times 19 = 361\\) cm\u00b2. Answer in \\(cm^2\\)."} {"t":"s","id":16606,"s":"First 3 questions: \\(3 \\times 6 = 18\\) min. Remaining \\(8 - 3 = 5\\) questions: \\(5 \\times 7 = 35\\) min. Total = \\(18 + 35 = 53\\) min. \\(12.42\\ p.m. + 53\\ min = 1.35\\ p.m. = 1335\\)."} {"t":"s","id":16608,"s":"\\(\\dfrac{3}{6} = \\dfrac{1}{2}\\) and \\(\\dfrac{6}{8} = \\dfrac{3}{4}\\) can be simplified. \\(\\dfrac{2}{5}\\) and \\(\\dfrac{5}{7}\\) cannot, so they are already in simplest form."} {"t":"s","id":16609,"s":"Use ninths: \\(1 = \\dfrac{9}{9}\\), \\(\\dfrac{1}{3} = \\dfrac{3}{9}\\). \\(\\dfrac{9}{9} - \\dfrac{3}{9} - \\dfrac{2}{9} = \\dfrac{4}{9}\\)."} {"t":"s","id":16611,"s":"\\(\\dfrac{4}{5} = 0.800\\). Comparing 0.801, 0.081 and 0.800: smallest to greatest is \\(0.081 , \\dfrac{4}{5} , 0.801\\)."} {"t":"s","id":16612,"s":"Belt = \\(20.45 + 12.25 = 32.70\\). Altogether = \\(20.45 + 32.70 = 53.15\\), i.e. $53.15."} {"t":"s","id":16613,"s":"\\(52 = 1 \\times 52 = 2 \\times 26 = 4 \\times 13\\). So all factors are 1, 2, 4, 13, 26, 52. The other two are 13 and 26."} {"t":"s","id":16614,"s":"The number must be a common multiple of 3 and 8, i.e. a multiple of 24, and fewer than 50. Multiples of 24 below 50 are 24 and 48; the greatest is 48."} {"t":"s","id":16618,"s":"Fraction spent = \\(\\dfrac{1}{2} + \\dfrac{1}{7} = \\dfrac{7}{14} + \\dfrac{2}{14} = \\dfrac{9}{14}\\). Fraction left = \\(\\dfrac{5}{14}\\) = $630, so 1 unit (1\/14) = \\(630 \\div 5 = 126\\). Transport = \\(\\dfrac{1}{7} = \\dfrac{2}{14} = 2 \\times 126 = \\$252\\)."} {"t":"s","id":16619,"s":"(a) 4 erasers + 4 pencils = \\(4 \\times 3.25 = 13.00\\). The extra pencil: \\(14.90 - 13.00 = 1.90\\), so 1 pencil = $1.90. (b) 7 pencils = \\(1.90 \\times 7 = 13.30\\). Change = \\(50 - 13.30 = \\$36.70\\)."} {"t":"s","id":16620,"s":"(a) Let Priscilla = P. Victor = P \u2212 180, William = P + 20. Total: \\(P + (P-180) + (P+20) = 680 \\Rightarrow 3P - 160 = 680 \\Rightarrow 3P = 840 \\Rightarrow P = 280\\). (b) Victor at first = \\(280 - 180 = 100\\). Priscilla (280) is twice Victor's final amount, so Victor's final = \\(280 \\div 2 = 140\\). Victor bought \\(140 - 100 = 40\\)."} {"t":"s","id":16621,"s":"After Aqil gives away 60, the gap between Riley and Aqil becomes \\(60 - 24 = 36\\) (Riley now leads). Riley = 4 \u00d7 Aqil(now), so the gap = 3 units = 36, giving 1 unit = \\(36 \\div 3 = 12\\) = Aqil now. Aqil at first = \\(12 + 60 = 72\\)."} {"t":"s","id":16623,"s":"Place value: the digit 8 stands for 800 only when 8 is in the hundreds place. In 4823, the 8 is in the hundreds place, so it stands for 800."} {"t":"s","id":16624,"s":"A common multiple of 4 and 6 is a multiple of 12. Among the options, 36 = 12 \u00d7 3 is a multiple of both 4 (4\u00d79) and 6 (6\u00d76). The others are not."} {"t":"s","id":16626,"s":"2\/3 = 4\/6 = 6\/9 = 12\/18 (multiply numerator and denominator by the same number). 18\/24 simplifies to 3\/4, which is not equal to 2\/3, so it is not equivalent."} {"t":"s","id":16630,"s":"Purple = 40 \u2212 10 \u2212 18 = 12 marbles. Fraction purple = 12\/40 = 3\/10."} {"t":"s","id":16634,"s":"Compare by place value. Greatest to smallest: 984, 948, 498, 489."} {"t":"s","id":16635,"s":"Forty thousand = 40 000; thirty-seven = 37. Together: 40 000 + 37 = 40037."} {"t":"s","id":16636,"s":"Compare each to 1\/2. 2\/3 > 1\/2; 6\/12 = 1\/2 (not smaller); 4\/9 < 1\/2 (since 4\/9 < 4.5\/9); 5\/11 < 1\/2 (since 5\/11 < 5.5\/11). So 5\/11 and 4\/9 are smaller than 1\/2."} {"t":"s","id":16637,"s":"5\/6 = 10\/12. 10\/12 + 7\/12 = 17\/12 = 1 5\/12."} {"t":"s","id":16642,"s":"4 hours = 4 \u00d7 60 = 240 minutes. 240 + 27 = 267 minutes."} {"t":"s","id":16646,"s":"Sam drank 0.84 + 0.44 = 1.28 \u2113. Together: 0.84 + 1.28 = 2.12 \u2113."} {"t":"s","id":16647,"s":"Spent = 1\/6 \u00d7 $54 = $9. Left = $54 \u2212 $9 = $45. (Or 5\/6 \u00d7 $54 = $45.)"} {"t":"s","id":16648,"s":"After giving, each has 842 \u00f7 2 = 421 stamps. Ali had 79 more before giving, so Ali at first = 421 + 79 = 500 stamps."} {"t":"s","id":16649,"s":"Sophie starts $1304 \u2212 $1240 = $64 ahead. Amanda gains $20 \u2212 $12 = $8 more each day. Days to catch up = 64 \u00f7 8 = 8 days."} {"t":"s","id":16650,"s":"The difference between the two purchases is 3 erasers = $7.30 \u2212 $6.10 = $1.20, so 1 eraser = $0.40. Then 4 erasers = $1.60, so 3 pencils = $6.10 \u2212 $1.60 = $4.50, and 1 pencil = $4.50 \u00f7 3 = $1.50."} {"t":"s","id":16652,"s":"Buying 5 and getting 1 free gives 6 doughnuts for $10. Two such sets give 12 doughnuts for $20. She still needs 3 more at $2 each = $6. Total = $20 + $6 = $26."} {"t":"s","id":16654,"s":"Total potatoes = 110.25 + 24.75 = 135 kg. Number of 3 kg bags = 135 \u00f7 3 = 45. Money received = 45 \u00d7 $6 = $270."} {"t":"s","id":16657,"s":"Apple = 4. Blueberry = 2 \u00d7 4 = 8. Chocolate = 8 + 3 = 11. Total = 4 + 8 + 11 = 23 tarts."} {"t":"s","id":16660,"s":"New total in April = 312 + 8 = 320. Tennis is still 40. Fraction = 40\/320 = 1\/8."} {"t":"s","id":16661,"s":"Red + Yellow = 1\/4 + 3\/5 = 5\/20 + 12\/20 = 17\/20. Purple = 1 \u2212 17\/20 = 3\/20."} {"t":"s","id":16662,"s":"Red is 1\/4 = 5\/20 of the files and equals 40, so 5 units = 40, 1 unit = 8 (where 1 unit = 1\/20). Yellow = 12 units = 96; purple = 3 units = 24. Difference = 96 \u2212 24 = 72."} {"t":"s","id":16663,"s":"Let the bag be 1 unit; the watch is 6 units. The difference 6 \u2212 1 = 5 units = $91.25, so 1 unit (bag) = $18.25. Watch + 3 bags = 6 + 3 = 9 units = 9 \u00d7 $18.25 = $164.25."} {"t":"s","id":16664,"s":"Two $100 notes = $200. Change = $200 \u2212 $164.25 = $35.75."} {"t":"s","id":16665,"s":"Let the starting number of each be N. Pens left = N \u2212 1852; rulers left = N \u2212 547. Rulers left = 4 \u00d7 pens left, so the extra rulers (1852 \u2212 547 = 1305) equal 3 times the pens left: 3 units = 1305, 1 unit = 435 (pens left). Pens at first = 435 + 1852 = 2287."} {"t":"s","id":16666,"s":"Pens sold: 1852 \u00d7 $2 = $3704. Rulers sold: 547 \u00d7 70\u00a2 = 38290\u00a2 = $382.90. Total collected = $3704 + $382.90 = $4086.90."} {"t":"s","id":16667,"s":"The two numbers add to 29. A factor of 45 (1,3,5,9,15,45) plus a multiple of 5 (5,10,15,20,25,...) = 29: 9 + 20 = 29 works (9 is a factor of 45, 20 is a multiple of 5). Difference = 20 \u2212 9 = 11."} {"t":"s","id":16668,"s":"To make the difference smallest, make the 2-digit number as large as possible: the largest 2-digit number is 99, so the 3-digit number is 561 \u2212 99 = 462. Difference = 462 \u2212 99 = 363."} {"t":"s","id":16671,"s":"In a decimal, the first digit after the decimal point is the tenths place. In \\(125.34\\) the digit after the point is 3, so the tenths digit is 3."} {"t":"s","id":16672,"s":"Compare whole-number parts first: \\(0.67\\) and \\(0.76\\) are less than 1; \\(6.07\\) and \\(6.7\\) are more than 6. Within each pair compare tenths: \\(0.67 < 0.76\\) and \\(6.07 < 6.70\\). Order: 0.67, 0.76, 6.07, 6.7."} {"t":"s","id":16674,"s":"(a) \\(\\dfrac{73}{100}\\) means 73 hundredths \\(= 0.73\\), so \\(5\\dfrac{73}{100} = 5.73\\). (b) Look at the hundredths digit of \\(45.999\\), which is 9 (\u22655), so round the tenths up: \\(45.999 \\approx 46.0\\)."} {"t":"s","id":16675,"s":"First find Rope P: \\(23.06 - 14.78 = 8.28\\) m. The difference between Rope P and Rope Q is \\(14.78 - 8.28 = 6.5\\) m."} {"t":"s","id":16676,"s":"Sugar left after using some: \\(10.5 - 3.5 = 7\\) kg. Repacked equally into 5 boxes: \\(7 \\div 5 = 1.4\\) kg per box."} {"t":"s","id":16677,"s":"(a) Sumei bought 4 more curry puffs than Siti and paid \\(13.60 - 10.40 = \\$3.20\\) more. So 4 curry puffs cost $3.20, and 1 curry puff \\(= 3.20 \\div 4 = \\$0.80\\). (b) Cost of 1 chocolate cake \\(= 10.40 - (4 \\times 0.80) = 10.40 - 3.20 = \\$7.20\\). For 5 cakes: \\(7.20 \\times 5 = \\$36.00\\)."} {"t":"s","id":16678,"s":"(a) Juice poured out is 3.85 \u2113, so juice left \\(= 6 - 3.85 = 2.15\\) \u2113. (b) The 3.85 \u2113 poured out is shared equally into 7 cups: \\(3.85 \\div 7 = 0.55\\) \u2113 in each cup."} {"t":"s","id":16679,"s":"In \\(17.48\\) the digit right after the decimal point is the tenths place. That digit is \\(4\\). (The \\(8\\) is in the hundredths place.) Answer: \\(4\\)."} {"t":"s","id":16680,"s":"Convert \\(\\dfrac{7}{25}\\) to hundredths: \\(\\dfrac{7}{25}=\\dfrac{7\\times4}{25\\times4}=\\dfrac{28}{100}=0.28\\). So \\(6\\dfrac{7}{25}=6.28\\). Answer: \\(6.28\\)."} {"t":"s","id":16683,"s":"To round to 1 decimal place, look at the hundredths digit. \\(39.95\\) has hundredths digit \\(5\\), so round the tenths up: \\(39.9\\to40.0\\). Answer: \\(40.0\\)."} {"t":"s","id":16684,"s":"The pattern alternates: +0.10 then -0.01. \\(7.38(+0.10)7.48(-0.01)7.47(+0.10)7.57(-0.01)7.56(+0.10)7.66(-0.01)\\mathbf{7.65}(+0.10)7.75(-0.01)7.74(+0.10)7.84\\). The missing term is \\(7.66-0.01=7.65\\). Answer: \\(7.65\\)."} {"t":"s","id":16687,"s":"One kettle holds \\(1.2+2.5=3.7\\) \\(l\\) (the bottle has 2.5 l less than a kettle). For 4 kettles: \\(3.7\\times4=14.8\\) \\(l\\). Answer: \\(14.8\\) \\(l\\)."} {"t":"s","id":16688,"s":"(a) Mrs Tan's amount is unchanged. At the start Mrs Siva had \\(7.86\\) kg more than Mrs Tan; after using \\(10\\) kg, Mrs Siva is now \\(10-7.86=2.14\\) kg less than Mrs Tan. So Mrs Tan has \\(2.14\\) kg more than Mrs Siva in the end. (b) In the end Tan = 3 \u00d7 Siva, so the difference (Tan \u2212 Siva) = 2 units = \\(2.14\\) kg, giving 1 unit = Siva = \\(2.14\\div2=1.07\\) kg. Answers: (a) \\(2.14\\) kg, (b) \\(1.07\\) kg."} {"t":"s","id":16689,"s":"The digit 3 in 57.43 is in the hundredths place. Its value is \\(3 \\times 0.01 = 0.03\\)."} {"t":"s","id":16690,"s":"The hundredths digit is 8; the thousandths digit is 6 (\u22655), so round up. \\(32.786 \\approx 32.79\\)."} {"t":"s","id":16692,"s":"Compare digit by digit after the units: 2.168 < 2.186 < 2.681 < 2.816. Increasing order is 2.168, 2.186, 2.681, 2.816."} {"t":"s","id":16693,"s":"\\(3 - 1.65 = 1.35\\). She had 1.35 m of ribbon left."} {"t":"s","id":16694,"s":"Let a purse be 1 unit; a bag is 4 units. Bag + 2 purses = 4 + 2 = 6 units = $33, so 1 unit = $5.50. A bag = 4 units = \\(4 \\times 5.50 = 22\\)."} {"t":"s","id":16696,"s":"\\(6 \\div 7 = 0.857...\\). The second decimal digit is 5, so round up the first decimal place: \\(0.857... \\approx 0.9\\)."} {"t":"s","id":16697,"s":"May = \\(5.4 \\div 2 = 2.7\\) L. Amy = \\(2.7 \\div 3 = 0.9\\) L. Pearly has \\(5.4 - 0.9 = 4.5\\) L more than Amy."} {"t":"s","id":16698,"s":"After using 4.09 kg, Mrs Tan's amount is (Tan first \u2212 4.09). Mrs Sim = Tan first \u2212 2.53. Sim = 4 \u00d7 Tan's remaining: \\(T - 2.53 = 4(T - 4.09)\\). So \\(T - 2.53 = 4T - 16.36\\), giving \\(3T = 13.83\\) and \\(T = 4.61\\) kg. (Equivalently the difference 4.09 \u2212 2.53 = 1.56 kg equals 3 units of Tan's remainder; 1 unit = 0.52 kg; Tan first = 0.52 + 4.09 = 4.61 kg.)"} {"t":"s","id":16699,"s":"From the 1st flag to the 6th flag there are 5 gaps: \\(27 \\div 5 = 5.4\\) m per gap. With 8 flags around a closed border there are 8 equal gaps: \\(5.4 \\times 8 = 43.2\\) m."} {"t":"q","id":23323,"q":"What is the product of 454 and 18?","e":"Multiply 454 by 18. \\(454 \\times 18 = 454 \\times 10 + 454 \\times 8 = 4540 + 3632 = 8172\\). The product is 8172."} {"t":"q","id":23324,"q":"The number of beads Mrs Tan bought when rounded to the nearest hundred is 4500. What is the greatest possible number of beads that she bought?","e":"A number rounds to 4500 to the nearest hundred when it is from 4450 to 4549. The greatest such number is 4549, since 4550 would round up to 4600."} {"t":"q","id":23325,"q":"Look at the number sequence carefully.
24, 28, 32, 36, 40, \u2026 \u2026
What is the 20th number?","e":"The sequence increases by 4 each time, starting at 24. The number of 4s added is 1 less than the position, so the 20th term adds \\(19 \\times 4 = 76\\). Then \\(76 + 24 = 100\\)."} {"t":"q","id":23326,"q":"What is the remainder when 5729 is divided by 9?
Answer: ","e":"Divide 5729 by 9: \\(5729 \\div 9 = 636\\) remainder 5, since \\(636 \\times 9 = 5724\\) and \\(5729 - 5724 = 5\\). The remainder is 5."} {"t":"q","id":23327,"q":"List down all the common factors of 15 and 42.
Answer: ","e":"Factors of 15: 1, 3, 5, 15. Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42. The common factors are 1 and 3."} {"t":"q","id":23328,"q":"(a) Find the 7th multiple of 4.
(b) List down the second common multiple of 6 and 9.
(a)   (b) ","e":"(a) The 7th multiple of 4 is \\(7 \\times 4 = 28\\). (b) Multiples of 6: 6, 12, 18, 24, 30, 36, \u2026; multiples of 9: 9, 18, 27, 36, \u2026. Common multiples are 18 (1st) and 36 (2nd), so the second common multiple is 36."} {"t":"q","id":23330,"q":"Denise has some stamps and pens. She has as many stamps as pens. When she gives each friend 3 pens, she will have 9 pens left. When each friend gets 4 stamps from Denise, she will have 6 extra stamps. How many friends does Denise have?
Answer: ","e":"Let the number of friends be a value. Pens = \\(3 \\times \\text{friends} + 9\\) and stamps = \\(4 \\times \\text{friends} + 6\\). Since stamps equal pens, \\(3 \\times \\text{friends} + 9 = 4 \\times \\text{friends} + 6\\), so \\(9 - 6 = 4 \\times \\text{friends} - 3 \\times \\text{friends}\\), giving friends = 3. (Check: 3 friends \u2192 pens = \\(3 \\times 3 + 9 = 18\\), stamps = \\(4 \\times 3 + 6 = 18\\).)"} {"t":"q","id":23331,"q":"Devi baked 675 cookies on Saturday. She baked 4 times as many cookies on Sunday as on Saturday.
(a) How many cookies did she bake on Sunday?
(b) Devi packed all the cookies that she baked on Saturday into boxes. Each box had 5 cookies. How many boxes of cookies did she pack? Round your answer to the nearest ten.
(a)   (b) ","e":"(a) Sunday = 4 times Saturday = \\(675 \\times 4 = 2700\\) cookies. (b) Boxes = \\(675 \\div 5 = 135\\) boxes; rounded to the nearest ten this is 140."} {"t":"q","id":23332,"q":"\\(12\\,608 = 10\\,000 + 2000 + + 8\\)
What is the missing number in the box?","e":"Method: subtract the known parts from the total. \\(12\\,608 - 10\\,000 - 2000 - 8 = 600\\). The missing number is 600 (the hundreds place value of 12 608)."} {"t":"q","id":23333,"q":"What is the missing numerator in the box?
\\(4\\dfrac{1}{3} = \\dfrac{ }{3}\\)","e":"Method: convert the mixed number to an improper fraction. \\(4\\dfrac{1}{3} = \\dfrac{4 \\times 3 + 1}{3} = \\dfrac{13}{3}\\). The missing numerator is 13."} {"t":"q","id":23336,"q":"4 is not<\/b> a factor of ____________.","e":"Method: test divisibility by 4. \\(16 = 4 \\times 4\\), \\(32 = 4 \\times 8\\), \\(60 = 4 \\times 15\\) \u2014 all divisible. \\(27 \\div 4 = 6\\,R3\\), so 4 is not a factor of 27."} {"t":"q","id":23338,"q":"(a) What is the first common multiple of 3 and 7?
(b) Round 18 067 to the nearest hundred. ","e":"(a) List multiples: 3, 6, 9, 12, 15, 18, 21... and 7, 14, 21... The first common multiple is 21 (\\(3 \\times 7\\)). (b) The tens digit of 18 067 is 6, which is 5 or more, so round up: 18 067 rounds to 18 100."} {"t":"q","id":23341,"q":"Harry bought some brownies. He packed them into boxes of 6. Then, he had 48 boxes of brownies and 5 brownies were left unpacked. How many brownies did Harry buy? ","e":"Method: brownies in full boxes \\(= 48 \\times 6 = 288\\). Add the 5 unpacked: \\(288 + 5 = 293\\). Harry bought 293 brownies."} {"t":"q","id":23344,"q":"Jenny bought 2 tables and 3 chairs. Each table cost twice as much as a chair. Jenny spent a total of $378.
(a) Find the cost of a chair. \\(\\\\)
(b) Find the cost of the 2 tables. \\(\\\\)","e":"Method (units): a table = 2 chair-units. 2 tables = 4 units, 3 chairs = 3 units, total = 7 units = $378. (a) 1 chair = \\(378 \\div 7 = \\$54\\). (b) 2 tables = 4 units = \\(54 \\times 4 = \\$216\\)."} {"t":"q","id":23346,"q":"Which of the following is thirteen thousand, nine hundred and twenty in numerals?","e":"Thirteen thousand = 13 000, nine hundred = 900, twenty = 20. Combine: 13 000 + 900 + 20 = 13 920. Answer: 13 920."} {"t":"q","id":23347,"q":"In 72 140, which digit is in the tens place?","e":"In 72 140, reading from the right: 0 is ones, 4 is tens, 1 is hundreds, 2 is thousands, 7 is ten thousands. The tens digit is 4."} {"t":"q","id":23348,"q":"In which of the following numbers does the digit 3 have the greatest value?","e":"Find the place value of digit 3 in each: 30 275 -> 30 000; 53 980 -> 3 000; 72 403 -> 3; 90 635 -> 30. The greatest is 30 000 in 30 275."} {"t":"q","id":23349,"q":"Which of the following numbers when rounded off to the nearest ten becomes 72 500?","e":"Round each to the nearest ten: 72 444 -> 72 440; 72 496 -> 72 500; 72 506 -> 72 510; 72 554 -> 72 550. Only 72 496 rounds to 72 500."} {"t":"q","id":23350,"q":"Peter drew a repeated pattern using some letters on his drawing paper. The first 21 letters are A B C D C B A A B C D C B A A B C D C B A. What is the 80th letter?","e":"The pattern repeats in blocks of 7 letters: A B C D C B A. 80 divided by 7 = 11 remainder 3. The remainder 3 points to the 3rd letter of the block, which is C."} {"t":"q","id":23351,"q":"(a) Arrange the following numbers from the greatest to the smallest.
3899, 9938, 9983, 3998
, , ,
(b) Write the missing number in the number pattern.
4549, 4699, 4849, , 5149, 5299","e":"(a) Compare the numbers: the two starting with 9 are larger. 9983 > 9938; then 3998 > 3899. Greatest to smallest: 9983, 9938, 3998, 3899. (b) The pattern increases by 150 each step (4549, 4699, 4849, ...). 4849 + 150 = 4999."} {"t":"q","id":23352,"q":"(a) Some factors of 28 are 1, 2, 4 and 28. What are the other two factors of 28?
and
(b) Find the first common multiple of 4 and 6.
","e":"(a) The factors of 28 are 1, 2, 4, 7, 14, 28. The two not listed are 7 and 14. (b) Multiples of 4: 4, 8, 12, ...; multiples of 6: 6, 12, ... The first common multiple is 12."} {"t":"q","id":23353,"q":"(a) What is the product of 207 and 86?

(b) What is the quotient when 8017 is divided by 9?
","e":"(a) 207 x 86 = 207 x 80 + 207 x 6 = 16 560 + 1 242 = 17 802. (b) 8017 divided by 9 = 890 remainder 7. The quotient is 890."} {"t":"q","id":23356,"q":"Ali bought a packet of sweets. When he put the sweets into bags of 6, he would have no sweets left. When he put them into bags of 8, he would have 4 sweets left. The packet contained more than 40 but less than 70 sweets. How many sweets were there in the packet?
","e":"A multiple of 6 between 40 and 70: 42, 48, 54, 60, 66. Numbers that leave remainder 4 when divided by 8 (i.e. 4 more than a multiple of 8: 44, 52, 60, 68). The number in both lists is 60."} {"t":"q","id":23357,"q":"Eileen has 4 times as many beads as Fiona. Eileen has twice as many beads as Giselle. Fiona has 207 fewer beads than Eileen. How many beads do they have altogether?
","e":"Let Fiona = 1 unit, so Eileen = 4 units. The difference is 4 - 1 = 3 units = 207, so 1 unit = 207 divided by 3 = 69. Fiona = 69, Eileen = 276, Giselle = half of Eileen = 138. Total = 69 + 276 + 138 = 483. (Equivalently, in units: Fiona 1u + Eileen 4u + Giselle 2u = 7u = 7 x 69 = 483.)"} {"t":"q","id":23358,"q":"Jeanette and Nicole have a total of 197 stickers. Nicole and Scarlett have a total of 203 stickers. The 3 girls have a total of 292 stickers.
(a) How many stickers does Scarlett have?

(b) How many stickers does Jeanette have?
","e":"(a) Jeanette + Nicole = 197, so Scarlett = total 292 - 197 = 95. (b) Nicole + Scarlett = 203, so Jeanette = total 292 - 203 = 89."} {"t":"q","id":23359,"q":"The amount of sugar in Box A is 250 \\(g\\) more than the amount of sugar in Box B. After Mrs Lim used 350 \\(g\\) of sugar in Box B to bake some cupcakes, the amount of sugar in Box A is 5 times as much as the amount of sugar in Box B.
(a) How much sugar is left in Box B?
\\(g\\)
(b) How much sugar is there in Box A?
\\(g\\)","e":"After Box B loses 350 g, let Box B = 1 unit and Box A = 5 units. Box A is unchanged, so the difference is now 250 + 350 = 600 g = 4 units. 1 unit = 600 divided by 4 = 150 g, so (a) Box B has 150 g left. (b) Box A = 5 units = 5 x 150 = 750 g."} {"t":"q","id":23361,"q":"What is the value of the digit 7 in \\(70\\ 246\\)?","e":"The digit 7 is in the ten-thousands place. Its value is \\(7 \\times 10\\,000 = 70\\ 000\\)."} {"t":"q","id":23362,"q":"Which of the following is a multiple of 8?","e":"A multiple of 8 can be divided exactly by 8. \\(32 = 8 \\times 4\\), so 32 is a multiple of 8."} {"t":"q","id":23364,"q":"Which of the following is a multiple of both 4 and 5?","e":"A common multiple of 4 and 5 must be in both times tables. \\(40 = 4 \\times 10 = 5 \\times 8\\), so 40 is a multiple of both."} {"t":"q","id":23365,"q":"Sarah and Tom had the same amount of money. After Sarah spent $336, Tom had 7 times as much money as Sarah in the end. How much money did Sarah have left?","e":"Tom's money never changed, and at first both were equal. Let the starting amount be the whole. After Sarah spends $336, Tom = 7 units and Sarah = 1 unit, so 6 units = $336 \u2192 1 unit = $56. Sarah had $56 left."} {"t":"q","id":23367,"q":"Arrange the following numbers from the smallest to the greatest.
\\(54\\ 678\\), \\(54\\ 867\\), \\(45\\ 876\\)
, , ","e":"Compare digit by digit from the left. 45 876 starts with 4 (smallest). Between 54 678 and 54 867, compare hundreds: 6 < 8, so 54 678 < 54 867. Order: 45 876, 54 678, 54 867."} {"t":"q","id":23368,"q":"Write the missing number in the number pattern.
\\(88\\ 520\\), \\(88\\ 720\\), \\(88\\ 920\\), , \\(89\\ 320\\),","e":"The pattern increases by 200 each step. \\(88\\ 920 + 200 = 89\\ 120\\) (and \\(89\\ 320 - 200 = 89\\ 120\\))."} {"t":"q","id":23369,"q":"A number is \\(29\\ 800\\) when rounded to the nearest 100. What is the greatest possible whole number? ","e":"Numbers that round to 29 800 (nearest 100) range from 29 750 up to 29 849. The greatest whole number is 29 849 (29 850 would round up to 29 900)."} {"t":"q","id":23370,"q":"Some factors of 32 are 1, 2, 4 and 32. What are the other two factors of 32? and ","e":"The factors of 32 are 1, 2, 4, 8, 16, 32. The two not listed are 8 and 16 (\\(8 \\times 4 = 32\\), \\(16 \\times 2 = 32\\))."} {"t":"q","id":23371,"q":"A shop had 104 boxes of oranges. Each box had 73 oranges. How many oranges were there altogether? ","e":"Multiply boxes by oranges per box: \\(104 \\times 73 = 7592\\)."} {"t":"q","id":23372,"q":"A given number is a common factor of 12 and 21. It is greater than 1. What is the number? ","e":"Factors of 12: 1, 2, 3, 4, 6, 12. Factors of 21: 1, 3, 7, 21. The common factors are 1 and 3. The one greater than 1 is 3."} {"t":"q","id":23373,"q":"I am a number between 25 and 35. I am a multiple of 3. One of my factors is 5. What number am I? ","e":"Multiples of 3 between 25 and 35: 27, 30, 33. Of these, only 30 has 5 as a factor (\\(30 \\div 5 = 6\\)). The number is 30."} {"t":"q","id":23374,"q":"Alex and Betty had a total of 308 stickers at first. After Alex gave away 56 stickers, Betty had 3 times as many stickers as Alex. How many stickers did Alex have at first? ","e":"After Alex gives away 56, the remaining total is \\(308 - 56 = 252\\). Then Betty : Alex = 3 : 1, so 4 units = 252 \u2192 1 unit = 63. Alex had 63 after, so at first \\(63 + 56 = 119\\)."} {"t":"q","id":23375,"q":"A chair costs $280 lesser than a bed. A bed and 4 identical chairs cost $880. How much does each chair cost? ","e":"A bed = 1 chair + $280. So 1 bed + 4 chairs = 5 chairs + $280 = $880 \u2192 5 chairs = $600 \u2192 1 chair = $120."} {"t":"q","id":23376,"q":"Ryan baked 3 times as many cookies as Chloe. Ryan sold 66 of his cookies and Chloe sold 10 of her cookies. They then had the same number of cookies left. How many cookies did Ryan bake? ","e":"Ryan = 3 units, Chloe = 1 unit. After selling, 3 units \u2212 66 = 1 unit \u2212 10, so 2 units = 66 \u2212 10 = 56 \u2192 1 unit = 28. Ryan baked 3 units = \\(28 \\times 3 = 84\\)."} {"t":"q","id":23377,"q":"Write the missing number in the number pattern.
3489, 3639, 3789, , 4089","e":"The pattern increases by 150 each step: 3489, 3639, 3789, ... The missing term = 3789 + 150 = 3939 (and 3939 + 150 = 4089, confirming)."} {"t":"q","id":23378,"q":"Write \\(4\\dfrac{2}{3}\\) as an improper fraction.","e":"Multiply the whole number by the denominator and add the numerator: 4 x 3 + 2 = 14. Keep the denominator: 14\/3."} {"t":"q","id":23379,"q":"Round 34 578 to the nearest 100.
","e":"Look at the tens digit (7). Since 7 is 5 or more, round the hundreds up: 34 578 rounds to 34 600."} {"t":"q","id":23380,"q":"Write 14 043 in words.","e":"14 043 = 14 thousands and 43 ones = Fourteen thousand and forty-three. There are no hundreds."} {"t":"q","id":23381,"q":"What is the first common multiple of 6 and 9?
","e":"Multiples of 6: 6, 12, 18, ... Multiples of 9: 9, 18, ... The first (lowest) common multiple is 18."} {"t":"q","id":23384,"q":"Find the value of \\(1 - \\dfrac{1}{4} - \\dfrac{5}{12}\\)
Express your answer in the simplest form.","e":"Use twelfths: 1 = 12\/12. 12\/12 - 3\/12 - 5\/12 = 4\/12 = 1\/3."} {"t":"q","id":23385,"q":"Which two of the fractions are equivalent?
\\(\\dfrac{8}{12}\\), \\(\\dfrac{3}{9}\\), \\(\\dfrac{4}{6}\\), \\(\\dfrac{6}{8}\\)
and ","e":"Simplify each: 8\/12 = 2\/3, 3\/9 = 1\/3, 4\/6 = 2\/3, 6\/8 = 3\/4. Both 8\/12 and 4\/6 equal 2\/3, so they are equivalent."} {"t":"q","id":23386,"q":"There are 75 fruits in a box. \\(\\dfrac{1}{5}\\) of the fruits are apples and the rest are oranges. How many oranges are there?
","e":"1\/5 of 75 = 75 \/ 5 = 15 apples. Oranges = 4\/5 of 75 = 15 x 4 = 60."} {"t":"q","id":23387,"q":"At a party, there were 3 times as many boys as girls. There were 30 more boys than girls. How many girls were there?
","e":"Boys = 3 units, girls = 1 unit, so boys are 2 units more than girls. 2 units = 30, so 1 unit = 30 \/ 2 = 15 girls."} {"t":"q","id":23389,"q":"Mrs Lee is planning a class activity. She has 18 students and wants to divide them into equal groups. Each group must have more than 1 student and there must be more than 1 group. List down 3 possible groupings she can make.
(i) groups of students
(ii) groups of students
(iii) groups of students","e":"18 can be split into equal groups whose factors are both greater than 1: 2 x 9, 3 x 6, and 6 x 3 (also 9 x 2). Any three valid factor pairs are accepted. Key gives: 2 groups of 9, 3 groups of 6, 6 groups of 3."} {"t":"q","id":23390,"q":"Ali, Bobby and Calvin had $4000 altogether. Ali had $1000 more than Bobby. Calvin had $300 less than Bobby. How much money did Calvin have?
","e":"Let Bobby = 1 unit. Ali = 1 unit + 1000, Calvin = 1 unit - 300. Total = 3 units + 1000 - 300 = 4000, so 3 units = 4000 - 700 = 3300, 1 unit = 1100. Calvin = 1100 - 300 = $800. (The printed answer of 2400 is the value of 3 units before division; Calvin actually has $800.)"} {"t":"q","id":23391,"q":"Mary had some money. She spent \\(\\dfrac{1}{4}\\) of her money on food and \\(\\dfrac{5}{8}\\) of her money on books. She spent $24 more on books than food. How much money did she have at first?
","e":"Food = 1\/4 = 2\/8, books = 5\/8. Difference = 5\/8 - 2\/8 = 3\/8 of her money = $24, so 1\/8 = 24 \/ 3 = $8. Total money = 8\/8 = 8 x 8 = $64."} {"t":"q","id":23392,"q":"Cathy and Donna had 465 stickers. After Cathy used \\(\\dfrac{1}{3}\\) of her stickers and Donna used 30 stickers, they had the same number of stickers left. How many stickers did Donna have at first?
","e":"After Donna uses 30, the remaining total = 465 - 30 = 435. Cathy keeps 2\/3 of her stickers; this 2\/3 of Cathy equals Donna's remaining (Donna - 30 originally... ). Using the key method: 435 \/ 5 = 87 (one part), so Cathy's 1\/3 = 87 used. Donna's stickers left = 87 x 2 = 174, and Donna at first = 174 + 30 = 204."} {"t":"q","id":23393,"q":"The table shows the favourite colours of some children.
Colour: Red, Green, Blue, Black, Yellow
Number of children: 12, 9, 13, 3, 6
Which colour is liked by twice as many children as those who like the colour yellow?","e":"Yellow is liked by 6 children. Twice 6 is \\(2 \\times 6 = 12\\). Red is liked by 12 children, so the answer is Red."} {"t":"q","id":23394,"q":"Express \\(3\\dfrac{1}{8}\\) as an improper fraction.","e":"Multiply the whole number by the denominator and add the numerator: \\(3 \\times 8 + 1 = 25\\). So \\(3\\dfrac{1}{8} = \\dfrac{25}{8}\\)."} {"t":"q","id":23395,"q":"Which of the following is not an equivalent fraction of \\(\\dfrac{3}{4}\\)?","e":"\\(\\dfrac{6}{8}, \\dfrac{9}{12}, \\dfrac{15}{20}\\) all simplify to \\(\\dfrac{3}{4}\\). \\(\\dfrac{13}{14}\\) does not, so it is not equivalent."} {"t":"q","id":23396,"q":"Find the difference between \\(\\dfrac{1}{3}\\) and \\(\\dfrac{5}{8}\\).","e":"Use a common denominator of 24: \\(\\dfrac{5}{8} = \\dfrac{15}{24}\\) and \\(\\dfrac{1}{3} = \\dfrac{8}{24}\\). The difference is \\(\\dfrac{15}{24} - \\dfrac{8}{24} = \\dfrac{7}{24}\\)."} {"t":"q","id":23397,"q":"The table shows the number of pupils in two CCAs.
Concert Band: 15 girls, 17 boys, total ?
Robotics Club: 17 girls, ? boys, total 97
How many more boys than girls are there in Robotics Club? ","e":"Number of boys in Robotics Club \\(= 97 - 17 = 80\\). More boys than girls \\(= 80 - 17 = 63\\)."} {"t":"q","id":23398,"q":"The table shows the number of pupils in two CCAs.
Concert Band: 15 girls, 17 boys, total ?
Robotics Club: 17 girls, ? boys, total 97
How many fewer pupils joined Concert Band than Robotics Club? ","e":"Concert Band total \\(= 17 + 15 = 32\\) pupils. Robotics Club has 97 pupils. Fewer \\(= 97 - 32 = 65\\)."} {"t":"q","id":23399,"q":"What is the value of \\(\\dfrac{3}{5} + \\dfrac{5}{8}\\)? Express your answer as a mixed number.","e":"Use a common denominator of 40: \\(\\dfrac{3}{5} = \\dfrac{24}{40}\\) and \\(\\dfrac{5}{8} = \\dfrac{25}{40}\\). Sum \\(= \\dfrac{49}{40} = 1\\dfrac{9}{40}\\)."} {"t":"q","id":23401,"q":"The table shows the number of P4 pupils who took part in different activities at 'Sports Day'.
Relay Race: 48, Soccer: 36, Tug-of-war: 52, Volleyball: 64
(a) How many pupils took part in the activities?
(b) Some pupils took part in an activity at 'Sports Day' that had \\(\\dfrac{3}{4}\\) as many pupils who took part in Volleyball. Which activity was it? ","e":"(a) Total \\(= 48 + 36 + 52 + 64 = 200\\) pupils. (b) \\(\\dfrac{3}{4}\\) of Volleyball \\(= 64 \\div 4 = 16\\), then \\(16 \\times 3 = 48\\). The activity with 48 pupils is Relay Race."} {"t":"q","id":23402,"q":"\\(\\dfrac{3}{8}\\) of counters in a container are red and the rest are blue.
(a) What fraction of the counters are blue?","e":"(a) Blue \\(= 1 - \\dfrac{3}{8} = \\dfrac{5}{8}\\). (b) Blue minus red \\(= \\dfrac{5}{8} - \\dfrac{3}{8} = \\dfrac{2}{8}\\), so 2 units \\(= 34\\), 1 unit \\(= 17\\). Total is 8 units \\(= 17 \\times 8 = 136\\) counters."} {"t":"q","id":23403,"q":"Rena and Sebastian shared 72 stickers. Rena had \\(\\dfrac{4}{9}\\) of the stickers.
(a) How many stickers did Rena have?
(b) How many stickers would Sebastian give to Rena so that both had an equal number of stickers? ","e":"(a) 9 units \\(= 72\\), so 1 unit \\(= 8\\); Rena \\(= 4 \\times 8 = 32\\) stickers. (b) Sebastian has \\(72 - 32 = 40\\). Equal share \\(= 72 \\div 2 = 36\\), so Sebastian gives \\(40 - 36 = 4\\) (i.e. \\(8 \\div 2 = 4\\))."} {"t":"q","id":23407,"q":"(a) Round 168.205 to 2 decimal places.
(b) Express \\(\\dfrac{3}{25}\\) as a decimal.
(a)
(b) ","e":"(a) The digit in the 3rd decimal place is 5, so round the 2nd decimal place up: \\(168.205 \\approx 168.21\\). (b) Make the denominator 100: \\(\\dfrac{3}{25} = \\dfrac{12}{100} = 0.12\\)."} {"t":"q","id":23408,"q":"Find the value of \\(3.9 + 15.72\\). Round your answer to the nearest tenth.
","e":"\\(3.90 + 15.72 = 19.62\\). The hundredths digit is 2, so it rounds down: \\(19.62 \\approx 19.6\\) to the nearest tenth."} {"t":"q","id":23410,"q":"What is the product of 6 ones and 72 hundredths?
","e":"6 ones = 6 and 72 hundredths = 0.72. The product is \\(6 \\times 0.72 = 4.32\\)."} {"t":"q","id":23411,"q":"Arrange the following in increasing order.
\\(4\\dfrac{3}{4}\\) , 4.90, \\(4\\dfrac{7}{10}\\) , 4.65
, , ,
(smallest)","e":"Convert all to decimals: \\(4\\dfrac{3}{4}=4.75\\), \\(4.90\\), \\(4\\dfrac{7}{10}=4.70\\), \\(4.65\\). In increasing order: 4.65, 4.70, 4.75, 4.90, i.e. 4.65, \\(4\\dfrac{7}{10}\\), \\(4\\dfrac{3}{4}\\), 4.9."} {"t":"q","id":23412,"q":"5 identical bags of flour weigh \\(28.15\\) \\(kg\\) in total. How much do 8 identical bags of flour weigh?
kg","e":"1 bag = \\(28.15 \\div 5 = 5.63\\) kg. 8 bags = \\(5.63 \\times 8 = 45.04\\) kg."} {"t":"q","id":23414,"q":"A tailor used \\(42.1\\) \\(m\\) of fabric on Monday. He used \\(28.62\\) \\(m\\) more fabric on Monday than on Tuesday.
(a) How many metres of fabric did the tailor use on Tuesday?
(b) How many metres of fabric did he use altogether over the two days?
(a) m
(b) m","e":"(a) Tuesday = Monday \u2212 28.62 = \\(42.10 - 28.62 = 13.48\\) m. (b) Total = Monday + Tuesday = \\(42.10 + 13.48 = 55.58\\) m."} {"t":"q","id":23415,"q":"James had 3 times as much money as Sally at first. When Mrs Lee gave $7.20 to James and $22.50 to Sally, both James and Sally had the same amount of money.
(a) Find the amount of money Sally had at first.
(b) Find the amount of money James had at first.
(a) $
(b) $","e":"Let Sally = 1 unit, James = 3 units. After: Sally has 1u + $22.50, James has 3u + $7.20, and they are equal. So 3u + 7.20 = 1u + 22.50, giving 2u = 22.50 \u2212 7.20 = $15.30. (a) Sally at first = 1u = $15.30 \u00f7 2 = $7.65. (b) James at first = 3u = $7.65 \u00d7 3 = $22.95."} {"t":"q","id":23417,"q":"Which of the following is not true about both squares and rectangles?","e":"A rectangle has its two pairs of opposite sides equal but not all four sides equal, so 'All the sides are equal' is true only for squares, not both shapes. The other three statements hold for both."} {"t":"q","id":23419,"q":"A bag of flour has a mass of \\(\\dfrac{3}{4}\\) \\(kg\\). The bag of flour is \\(\\dfrac{1}{8}\\) \\(kg\\) heavier than a bag of sugar. What is the total mass of the two bags?","e":"Sugar = \\(\\dfrac{3}{4} - \\dfrac{1}{8} = \\dfrac{6}{8} - \\dfrac{1}{8} = \\dfrac{5}{8}\\) kg. Total = \\(\\dfrac{3}{4} + \\dfrac{5}{8} = \\dfrac{6}{8} + \\dfrac{5}{8} = \\dfrac{11}{8} = 1\\dfrac{3}{8}\\) kg."} {"t":"q","id":23420,"q":"There are 72 black and white buttons in a box. \\(\\dfrac{5}{6}\\) of them are white buttons and the rest are black buttons. How many more white than black buttons are there?","e":"White = \\(\\dfrac{5}{6} \\times 72 = 60\\). Black = \\(72 - 60 = 12\\). More white than black = \\(60 - 12 = 48\\)."} {"t":"q","id":23423,"q":"Mr Pang sold some packets of sugar and 24 packets of salt. \\(\\dfrac{4}{7}\\) of the total packets sold were sugar. How many packets of sugar were sold? ","e":"Sugar is \\(\\dfrac{4}{7}\\) of the total, so salt is \\(\\dfrac{3}{7}\\) of the total. 3 units = 24, so 1 unit = \\(24 \\div 3 = 8\\). Sugar = 4 units = \\(8 \\times 4 = 32\\) packets."} {"t":"q","id":23426,"q":"Gabby gave \\(\\dfrac{5}{8}\\) of her stickers to Hani and \\(\\dfrac{1}{4}\\) of them to Ivy. Ivy received 12 fewer stickers than Hani. How many stickers did Gabby have at first? ","e":"Hani got \\(\\dfrac{5}{8}\\) and Ivy got \\(\\dfrac{1}{4} = \\dfrac{2}{8}\\). The difference is \\(\\dfrac{5}{8} - \\dfrac{2}{8} = \\dfrac{3}{8}\\), which equals 12 stickers. So 3 units = 12, 1 unit = \\(12 \\div 3 = 4\\). Total = 8 units = \\(8 \\times 4 = 32\\) stickers."} {"t":"q","id":23427,"q":"Mrs Goh had some tea. She poured \\(\\dfrac{2}{5}\\) \\(\\ell\\) of it into a jug. She then poured the remaining amount of tea into 2 equal cups. Each cup contained \\(\\dfrac{3}{10}\\) \\(\\ell\\) less amount of tea than the amount of tea in the jug. (a) How much tea did she pour into each cup? (b) How much tea did she make? Express your answer in its simplest form.
(a)   (b) ","e":"(a) Each cup = jug \u2212 \\(\\dfrac{3}{10}\\) = \\(\\dfrac{2}{5} - \\dfrac{3}{10} = \\dfrac{4}{10} - \\dfrac{3}{10} = \\dfrac{1}{10}\\) \u2113. (b) Total = jug + 2 cups = \\(\\dfrac{2}{5} + \\dfrac{1}{10} + \\dfrac{1}{10} = \\dfrac{4}{10} + \\dfrac{1}{10} + \\dfrac{1}{10} = \\dfrac{6}{10} = \\dfrac{3}{5}\\) \u2113."} {"t":"q","id":23428,"q":"Write twenty-seven thousand, three hundred and nine in numerals.
Answer: ","e":"Twenty-seven thousand = 27000, three hundred = 300, nine = 9. Combine: 27000 + 300 + 9 = 27309."} {"t":"q","id":23429,"q":"Round 10 247 to the nearest ten.
Answer: ","e":"Look at the ones digit of 10247, which is 7. Since 7 is 5 or more, round the tens digit up: 10247 rounds to 10250."} {"t":"q","id":23430,"q":"Write down the common factors of 15 and 20.
(a)   (b) ","e":"Factors of 15: 1, 3, 5, 15. Factors of 20: 1, 2, 4, 5, 10, 20. The common factors are 1 and 5."} {"t":"q","id":23431,"q":"Arrange the following fractions from the smallest to the greatest.
\\(\\dfrac{1}{3}\\) \\(\\dfrac{1}{10}\\) \\(\\dfrac{1}{6}\\)
(a)   (b)   (c) ","e":"For unit fractions, the larger the denominator, the smaller the fraction. Denominators are 3, 10, 6. From smallest to greatest fraction: 1\/10 (denom 10), 1\/6 (denom 6), 1\/3 (denom 3)."} {"t":"q","id":23432,"q":"What is the remainder when 5840 is divided by 7?
Answer: ","e":"5840 \\(\\div\\) 7 = 834 with a remainder. 834 \\(\\times\\) 7 = 5838, and 5840 \\(-\\) 5838 = 2. The remainder is 2."} {"t":"q","id":23433,"q":"\\(\\dfrac{1}{2} - \\dfrac{3}{8} =\\)","e":"Make the denominators the same: \\(\\dfrac{1}{2} = \\dfrac{4}{8}\\). Then \\(\\dfrac{4}{8} - \\dfrac{3}{8} = \\dfrac{1}{8}\\)."} {"t":"q","id":23434,"q":"What is the missing number in the box?
\\(\\dfrac{1}{3} = \\dfrac{}{12}\\)","e":"To change the denominator from 3 to 12, multiply by 4. Multiply the numerator by the same: 1 \\(\\times\\) 4 = 4. So \\(\\dfrac{1}{3} = \\dfrac{4}{12}\\)."} {"t":"q","id":23438,"q":"A number is a multiple of 9 and a factor of 6.
It is between 60 and 80.
What is the number?
Answer: ","e":"Multiples of 9 between 60 and 80: 63 and 72. The number must also be a multiple of 6. 63 \\(\\div\\) 6 = 10 remainder 3 (not a multiple of 6); 72 \\(\\div\\) 6 = 12 (a multiple of 6). So the number is 72."} {"t":"q","id":23439,"q":"The sum of two numbers is 7390.
The greater number is 4 times the smaller number.
What is the greater number?
Answer: ","e":"Let the smaller number be 1 unit; the greater is 4 units. Together 5 units = 7390. 1 unit = 7390 \\(\\div\\) 5 = 1478. Greater number = 4 units = 1478 \\(\\times\\) 4 = 5912."} {"t":"q","id":23443,"q":"Xavier, Yusof and Zachary scored a total of 561 points in a game.
Xavier scored 93 more than Yusof.
Zachary scored twice the total number of points Xavier and Yusof scored.
How many points did Xavier score?
Answer: ","e":"Let Xavier + Yusof = 1 unit. Zachary = 2 units. Total = 3 units = 561, so 1 unit = 561 \\(\\div\\) 3 = 187 (Xavier + Yusof). Xavier is 93 more than Yusof: Yusof = (187 - 93) \\(\\div\\) 2 = 47, Xavier = 47 + 93 = 140."} {"t":"q","id":23444,"q":"Aisyah sold some cupcakes at a carnival. For every 30 cupcakes sold, she would donate $5 to a charity. In the end, Aisyah donated $80 to the charity.
(a) How many cupcakes did Aisyah sell?
(b) Aisyah sold each cupcake for $3. After donating $80, how much did she earn from the sale?
(a)   (b) ","e":"(a) $80 donated at $5 per 30 cupcakes: 80 \\(\\div\\) 5 = 16 sets, 16 \\(\\times\\) 30 = 480 cupcakes. (b) Sales = 480 \\(\\times\\) $3 = $1440. After donating $80: 1440 - 80 = $1360."} {"t":"q","id":23447,"q":"Arrange the fractions in increasing order.
\\(\\dfrac{15}{7}\\), \\(1\\dfrac{4}{9}\\), \\(\\dfrac{5}{3}\\)","e":"Convert to decimals: \\(1\\dfrac{4}{9}\\approx1.44\\), \\(\\dfrac{5}{3}\\approx1.67\\), \\(\\dfrac{15}{7}\\approx2.14\\). Increasing order: \\(1\\dfrac{4}{9}\\), \\(\\dfrac{5}{3}\\), \\(\\dfrac{15}{7}\\) (option 2)."} {"t":"q","id":23450,"q":"Ms Lim is planning for a class party. She wants to buy enough pizza such that each of her 35 students can have \\(\\dfrac{1}{6}\\) of a pizza. The shop only sells whole pizza. What is the least number of whole pizza Ms Lim need to buy?","e":"Total pizza needed = \\(35\\times\\dfrac{1}{6} = \\dfrac{35}{6} = 5\\dfrac{5}{6}\\) pizzas. Since only whole pizzas are sold, round up to 6 (option 2)."} {"t":"q","id":23451,"q":"(a) Express \\(\\dfrac{22}{4}\\) as a mixed number in its simplest form.
(b) \\(\\dfrac{2}{9}\\) of 63 = ","e":"(a) \\(\\dfrac{22}{4} = 5\\dfrac{2}{4} = 5\\dfrac{1}{2}\\). (b) \\(\\dfrac{2}{9}\\) of 63: \\(63\\div9 = 7\\), then \\(7\\times2 = 14\\)."} {"t":"q","id":23452,"q":"Mdm Siti had 5 \\(l\\) of orange juice. She drank \\(\\dfrac{3}{8}\\) \\(l\\) of orange juice. How much orange juice did she have left?","e":"\\(5 - \\dfrac{3}{8} = 4\\dfrac{8}{8} - \\dfrac{3}{8} = 4\\dfrac{5}{8}\\) litres."} {"t":"q","id":23456,"q":"Alice jogs \\(\\dfrac{3}{4}\\) \\(km\\) at a park. She walks \\(\\dfrac{5}{12}\\) \\(km\\) less than the distance she jogs. What is the total distance she jogs and walks?","e":"Walk = \\(\\dfrac{3}{4} - \\dfrac{5}{12} = \\dfrac{9}{12} - \\dfrac{5}{12} = \\dfrac{4}{12}\\) km. Total = \\(\\dfrac{3}{4} + \\dfrac{4}{12} = \\dfrac{9}{12} + \\dfrac{4}{12} = \\dfrac{13}{12} = 1\\dfrac{1}{12}\\) km."} {"t":"q","id":23457,"q":"A box is filled with some balls. \\(\\dfrac{4}{11}\\) of the balls are yellow and the rest of the balls are red. There are 42 more red balls than yellow balls. How many balls are there in the box altogether? ","e":"Yellow = 4 units, red = 11 \u2212 4 = 7 units. Difference = 7 \u2212 4 = 3 units = 42, so 1 unit = 14. Total = 11 units = 14 \u00d7 11 = 154 balls."} {"t":"q","id":23462,"q":"Lucy had \\$954. She spent \\(\\dfrac{5}{9}\\) of her money to buy a pair of shoes. How much had she left after buying the pair of shoes?
Answer: ","e":"Method: the money is 9 equal units. She spent \\(\\dfrac{5}{9}\\), so \\(\\dfrac{4}{9}\\) is left. 9 units = \\$954, so 1 unit = \\(954\\div9=106\\)... using the unitary method 4 units left = \\$424. The answer is \\$424."} {"t":"q","id":23463,"q":"Bag A weighs \\(\\dfrac{1}{4}\\) kg. Bag B weighs \\(\\dfrac{3}{5}\\) kg. Bag C weighs \\(\\dfrac{5}{8}\\) kg.
(a) Which 2 bags, when added together, will be heavier than 1 kg? Answer: Bag and Bag
(b) Muthu puts a laptop into Bag B. The total mass of Bag B and the laptop is 3 kg. What is the mass of the laptop, in kg?","e":"(a) Check each pair against 1 kg. Bag B + Bag C = \\(\\dfrac{3}{5}+\\dfrac{5}{8}=\\dfrac{24}{40}+\\dfrac{25}{40}=\\dfrac{49}{40}\\) which is more than 1 kg; the other pairs are less. So Bag B and Bag C. (b) Laptop mass = total minus Bag B = \\(3-\\dfrac{3}{5}=2\\dfrac{2}{5}\\) kg."} {"t":"q","id":23464,"q":"Ali drank \\(\\dfrac{7}{10}\\) \\(\\ell\\) of water. He drank \\(\\dfrac{1}{5}\\) \\(\\ell\\) of water more than Harry. How much water did Ali and Harry drink in total? Give your answer as a mixed number.","e":"Method: Harry = Ali minus \\(\\dfrac{1}{5}\\) = \\(\\dfrac{7}{10}-\\dfrac{2}{10}=\\dfrac{5}{10}\\). Total = Ali + Harry = \\(\\dfrac{7}{10}+\\dfrac{5}{10}=\\dfrac{12}{10}=1\\dfrac{2}{10}\\) litres."} {"t":"q","id":23465,"q":"Jim had 3 pieces of rope. Rope A is the longest. Its length is \\(\\dfrac{9}{10}\\) m. The difference between the lengths of Rope A and Rope B is \\(\\dfrac{3}{4}\\) m.
(a) What is the length of Rope B, in m? Give your answer in its simplest form.
(b) Rope B is the shortest. The difference between the lengths of Rope B and Rope C is \\(\\dfrac{1}{2}\\) m. What is the length of Rope C, in m?
(a)   (b) ","e":"(a) Rope B = Rope A minus the difference = \\(\\dfrac{9}{10}-\\dfrac{3}{4}=\\dfrac{18}{20}-\\dfrac{15}{20}=\\dfrac{3}{20}\\) m. (b) Rope C is longer than Rope B by \\(\\dfrac{1}{2}\\), so Rope C = \\(\\dfrac{3}{20}+\\dfrac{1}{2}=\\dfrac{3}{20}+\\dfrac{10}{20}=\\dfrac{13}{20}\\) m."} {"t":"q","id":23466,"q":"A fruit seller sold some apples, pears and watermelons. \\(\\dfrac{2}{7}\\) of the fruits sold were pears, \\(\\dfrac{4}{7}\\) of the fruits sold were apples and the rest of the fruits sold were watermelons. He sold 360 more apples than watermelons.
(a) How many pears did the fruit seller sell?
(b) How many apples, pears and watermelons did the fruit seller sell in total?
(a)   (b) ","e":"Method: treat the total as 7 units. Pears = 2 units, apples = 4 units, watermelons = \\(7-2-4=1\\) unit. Apples minus watermelons = \\(4-1=3\\) units = 360, so 1 unit = \\(360\\div3=120\\). (a) Pears = 2 units = \\(2\\times120=240\\). (b) Total = 7 units = \\(7\\times120=840\\)."} {"t":"q","id":23467,"q":"Which number has the digit 3 in the thousands place?","e":"The thousands place is the 4th digit from the right. In 73 648 the digits are 7 (ten thousands), 3 (thousands), 6 (hundreds), 4 (tens), 8 (ones). So 73 648 has 3 in the thousands place."} {"t":"q","id":23468,"q":"Which of the following is not an equivalent fraction of \\(\\dfrac{1}{4}\\)?","e":"Equivalent fractions of 1\/4: multiply top and bottom by the same number. 2\/8 (x2), 3\/12 (x3), 5\/20 (x5) all equal 1\/4. But 4\/12 = 1\/3, not 1\/4. So 4\/12 is the odd one out."} {"t":"q","id":23469,"q":"Which of the following decimals is the greatest?","e":"Compare the tenths digit first: 0.030 (0 tenths), 0.42 (4 tenths), 0.176 (1 tenth), 0.234 (2 tenths). The largest tenths value is 4, so 0.42 is the greatest."} {"t":"q","id":23470,"q":"At a carnival, every 6th participant receives a cup of drink and every 8th participant receives a key chain. Which is the first participant to receive both a cup of drink and a key chain?","e":"Find the lowest common multiple of 6 and 8. Multiples of 6: 6, 12, 18, 24... Multiples of 8: 8, 16, 24... The smallest common multiple is 24, so the 24th participant receives both."} {"t":"q","id":23471,"q":"Arrange the following from the greatest to the smallest.
\\(1\\dfrac{1}{9}\\), \\(\\dfrac{4}{5}\\), \\(\\dfrac{7}{6}\\)
Greatest: , , :Smallest","e":"Convert to decimals: 1 1\/9 = 1.11, 4\/5 = 0.8, 7\/6 = 1.166... Ordering greatest to smallest: 7\/6 (1.166), 1 1\/9 (1.11), 4\/5 (0.8)."} {"t":"q","id":23473,"q":"Use all the digits 5, 2, 7, 0, 4 to form
(a) the largest 5-digit number
(b) the smallest 5-digit even number ","e":"(a) Largest: arrange digits from greatest to least: 7, 5, 4, 2, 0 = 75420. (b) Smallest even: the number must end in an even digit and cannot start with 0. Smallest leading digit is 2, then smallest remaining with an even last digit gives 20574 (ends in 4)."} {"t":"q","id":23474,"q":"What is the value of \\(\\dfrac{5}{6}+\\dfrac{2}{3}\\)? Express your answer as a mixed number.","e":"Make denominators the same: 2\/3 = 4\/6. Then 5\/6 + 4\/6 = 9\/6 = 3\/2. As a mixed number, 3\/2 = 1 1\/2."} {"t":"q","id":23475,"q":"What is the value of \\(4 \\div 7\\)? Correct your answer to 1 decimal place.
","e":"4 \/ 7 = 0.5714... To 1 decimal place, look at the second decimal digit (7), which rounds up. So 0.57... rounds to 0.6."} {"t":"q","id":23476,"q":"The table shows the number of times Primary Four students in a school jog in a week.
Number of times jogged in a week: 1, 2, 3, 4, 5
Number of students: 61, 50, 42, 75, 80
How many students jogged more than 2 times in a week?
","e":"More than 2 times means 3, 4 or 5 times. Add those student counts: 42 + 75 + 80 = 197."} {"t":"q","id":23477,"q":"Tina baked some cookies. She gave \\(\\dfrac{3}{10}\\) of the cookies to her neighbour and had 84 cookies left. How many cookies did she give to her neighbour?
","e":"She gave 3\/10, so the 84 left represent the remaining 7\/10. 1\/10 = 84 \/ 7 = 12. She gave 3\/10 = 3 x 12 = 36 cookies."} {"t":"q","id":23478,"q":"\\(\\dfrac{13}{25}=0.5+\\) ","e":"Convert 13\/25 to a decimal: 13\/25 = 52\/100 = 0.52. Then 0.52 = 0.5 + 0.02, so the missing decimal is 0.02."} {"t":"q","id":23479,"q":"Joseph had 1378 marbles and Kumar had 1490 marbles. Kumar gave some marbles to Joseph. In the end Joseph had twice as many marbles as Kumar.
(a) How many marbles did Kumar have in the end?
(b) How many marbles did Kumar give Joseph? ","e":"Total marbles stay the same: 1378 + 1490 = 2868. In the end Joseph = twice Kumar, so they share into 3 equal parts. (a) Kumar's end = 2868 \/ 3 = 956. (b) Kumar gave away = his start minus his end = 1490 - 956 = 534."} {"t":"q","id":23480,"q":"Amy read \\(\\dfrac{1}{4}\\) of a book on Saturday, \\(\\dfrac{1}{8}\\) of the book on Sunday and the remaining pages on Monday. She read 72 fewer pages on Saturday than on Monday. How many pages were there in the book?
","e":"Saturday = 1\/4 = 2\/8, Sunday = 1\/8. Together = 3\/8, so Monday = 8\/8 - 3\/8 = 5\/8. Difference between Monday and Saturday = 5\/8 - 2\/8 = 3\/8, which equals 72 pages. So 1\/8 = 72 \/ 3 = 24, and the whole book = 8\/8 = 24 x 8 = 192 pages."} {"t":"q","id":23481,"q":"Round 25 571 to the nearest hundred.
Answer: ","e":"The hundreds digit of 25 571 is 5. The digit after it (tens) is 7, which is 5 or more, so round up. 25 571 rounds to 25 600."} {"t":"q","id":23482,"q":"How many one-fifths are there in 3 wholes?
Answer: ","e":"Each whole contains 5 one-fifths. For 3 wholes: \\(3 \\times 5 = 15\\) one-fifths."} {"t":"q","id":23484,"q":"Find the value of \\(\\dfrac{11}{12} - \\dfrac{2}{3}\\) in its simplest form.","e":"Make a common denominator: \\(\\dfrac{2}{3} = \\dfrac{8}{12}\\). Then \\(\\dfrac{11}{12} - \\dfrac{8}{12} = \\dfrac{3}{12} = \\dfrac{1}{4}\\)."} {"t":"q","id":23486,"q":"Find the value of
a) \\(4269 \\times 3\\)
b) \\(217 \\times 15\\)
(a)   (b) ","e":"a) \\(4269 \\times 3 = 12807\\). b) \\(217 \\times 15 = 217 \\times 10 + 217 \\times 5 = 2170 + 1085 = 3255\\)."} {"t":"q","id":23488,"q":"Arrange the following fractions in increasing order.
\\(\\dfrac{4}{5}\\) , \\(\\dfrac{2}{3}\\) , \\(\\dfrac{5}{3}\\)
(a)   (b)   (c) ","e":"Compare values: \\(\\dfrac{2}{3} \\approx 0.67\\), \\(\\dfrac{4}{5} = 0.8\\), \\(\\dfrac{5}{3} \\approx 1.67\\). Increasing order: 2\/3, 4\/5, 5\/3."} {"t":"q","id":23489,"q":"I am a number greater than 20 but less than 40. I am a multiple of 6 and a factor of 48. What number am I?
Answer: ","e":"Multiples of 6 between 20 and 40: 24, 30, 36. Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. The only number in both lists is 24."} {"t":"q","id":23490,"q":"A number is 15 000 when rounded to the nearest thousand. What is the greatest possible value of the number?
Answer: ","e":"To round to 15 000, the number must be from 14 500 to 15 499. The greatest whole number that still rounds down to 15 000 is 15 499."} {"t":"q","id":23491,"q":"Find the quotient and remainder when 4505 is divided by 6.
(a)   (b) ","e":"\\(4505 \\div 6 = 750\\) remainder \\(5\\), since \\(6 \\times 750 = 4500\\) and \\(4505 - 4500 = 5\\)."} {"t":"q","id":23492,"q":"Rihana had $105. She used \\(\\dfrac{1}{3}\\) of it on a watch and spent the rest of her money on a present. How much did the present cost?
Answer: ","e":"Watch cost \\(\\dfrac{1}{3} \\times 105 = \\$35\\). The rest (present) is \\(\\dfrac{2}{3}\\) of 105, i.e. \\(105 - 35 = \\$70\\)."} {"t":"q","id":23493,"q":"Janice had twice as many stamps as Kenneth at first. After Kenneth had given away 24 stamps, Janice had 5 times as many stamps as Kenneth. How many stamps did Kenneth have?
Answer: ","e":"Janice is unchanged. Let Kenneth's start = K, so Janice = 2K. After giving away 24, Kenneth = K - 24 and 2K = 5(K - 24). So \\(2K = 5K - 120\\), \\(3K = 120\\), \\(K = 40\\). Kenneth had 40 stamps."} {"t":"q","id":23494,"q":"Raphael has some chocolates to give to his friends at a party. The number of chocolates he has is less than 30. If he gives 4 chocolates to each friend, he will have 2 extra chocolates. If he gives 5 chocolates to each friend, he will need 1 more chocolate.
a) How many chocolates does Raphael have?
b) How many friends does Raphael have at the party?
(a)   (b) ","e":"Let f = number of friends. Chocolates = \\(4f + 2\\) (2 extra) and also \\(5f - 1\\) (needs 1 more). So \\(4f + 2 = 5f - 1\\), giving \\(f = 3\\). Chocolates \\(= 4 \\times 3 + 2 = 14\\) (less than 30, checks out)."} {"t":"q","id":23495,"q":"Giresh had $108 more than Beng Huat. After both of them spent an equal amount of money to buy some stationery, the amount of money Giresh had left was 3 times as much as Beng Huat. Given that Giresh had $198 at first, how much did each of them spend?
Answer: ","e":"Beng Huat at first \\(= 198 - 108 = \\$90\\). After spending the same amount, Giresh = 3 units and Beng Huat = 1 unit, so the difference of 2 units still equals $108 (the difference is unchanged). \\(1 \\text{ unit} = 108 \\div 2 = \\$54\\) = Beng Huat's money left. So each spent \\(90 - 54 = \\$36\\)."} {"t":"q","id":23498,"q":"In which of the following does the digit '4' stand for 4 hundredths?","e":"Hundredths is the second place after the decimal point. In 92.54, the 4 is in the hundredths place, so it stands for 4 hundredths (0.04)."} {"t":"q","id":23501,"q":"(a) Write \\(\\dfrac{15}{7}\\) as a mixed number.
(b) Express 0.75 as a fraction in its simplest form. ","e":"(a) \\(15 \\div 7 = 2\\) remainder \\(1\\), so \\(\\dfrac{15}{7} = 2\\dfrac{1}{7}\\). (b) \\(0.75 = \\dfrac{75}{100} = \\dfrac{3}{4}\\) after dividing numerator and denominator by 25."} {"t":"q","id":23502,"q":"(a) Arrange the following in decreasing order. \\(\\dfrac{13}{5}\\), \\(2\\dfrac{3}{4}\\), \\(\\dfrac{7}{8}\\)
, ,
(b) What is the missing number in the box? \\(\\dfrac{15}{24} = \\dfrac{}{8}\\)","e":"(a) Convert to decimals: \\(\\dfrac{13}{5}=2.6\\), \\(2\\dfrac{3}{4}=2.75\\), \\(\\dfrac{7}{8}=0.875\\). In decreasing order: \\(2\\dfrac{3}{4}\\), \\(\\dfrac{13}{5}\\), \\(\\dfrac{7}{8}\\). (b) \\(\\dfrac{15}{24}=\\dfrac{5}{8}\\) (divide top and bottom by 3), so the missing number is 5."} {"t":"q","id":23505,"q":"Leonard had $120. He spent \\(\\dfrac{5}{8}\\) of his money and saved the rest. How much did Leonard save? $","e":"He saved \\(1-\\dfrac{5}{8}=\\dfrac{3}{8}\\) of his money. \\(\\dfrac{1}{8}\\) of $120 = $120 \\div 8 = $15. Saved = \\(\\dfrac{3}{8}\\) = $15 \\times 3 = $45."} {"t":"q","id":23507,"q":"Sophia drank \\(\\dfrac{7}{10}\\) \\(\\ell\\) of apple juice. John drank \\(\\dfrac{1}{5}\\) \\(\\ell\\) of apple juice less than her. How much apple juice did they drink altogether? Give your answer as a decimal. \\(\\ell\\)","e":"John drank \\(\\dfrac{7}{10}-\\dfrac{1}{5}=\\dfrac{7}{10}-\\dfrac{2}{10}=\\dfrac{5}{10}\\) \\(\\ell\\). Together: \\(\\dfrac{7}{10}+\\dfrac{5}{10}=\\dfrac{12}{10}=1.2\\) \\(\\ell\\)."} {"t":"q","id":23508,"q":"Helen was preparing for her Science examination. She managed to revise \\(\\dfrac{1}{4}\\) of her textbook on Saturday and \\(\\dfrac{1}{6}\\) of it on Sunday. She had 98 more pages to read. How many pages were there in the textbook? ","e":"Revised over the weekend: \\(\\dfrac{1}{4}+\\dfrac{1}{6}=\\dfrac{3}{12}+\\dfrac{2}{12}=\\dfrac{5}{12}\\). Left to read: \\(1-\\dfrac{5}{12}=\\dfrac{7}{12}\\), which equals 98 pages. So \\(\\dfrac{1}{12}=98\\div7=14\\) pages, and the whole textbook = \\(14\\times12=168\\) pages."} {"t":"q","id":23509,"q":"Ali, Benny and Charles have some marbles. Benny has three times as many marbles as Ali. Charles has \\(\\dfrac{1}{2}\\) of the total number of marbles that Ali and Benny have altogether.
(a) The total number of marbles the 3 boys have is 1260. How many marbles does Benny have?
(b) Charles gave \\(\\dfrac{5}{6}\\) of his marbles to his brother. How many marbles did he have left? ","e":"(a) Let Ali = 1 unit, then Benny = 3 units, Ali+Benny = 4 units, Charles = half of that = 2 units. Total = 1+3+2 = 6 units = 1260, so 1 unit = 1260 \u00f7 6 = 210. Benny = 3 \u00d7 210 = 630. (b) Charles = 2 units = 420 marbles. He gave away \\(\\dfrac{5}{6}\\), so he kept \\(\\dfrac{1}{6}\\) = 420 \u00f7 6 = 70 marbles."} {"t":"q","id":23510,"q":"There are some beads in a box. \\(\\dfrac{7}{9}\\) of them are red beads and the rest are blue beads. There are 130 more red beads than blue beads.
(a) What fraction of the beads are blue?","e":"(a) Blue fraction = \\(1-\\dfrac{7}{9}=\\dfrac{2}{9}\\). (b) Red is \\(\\dfrac{7}{9}\\) and blue is \\(\\dfrac{2}{9}\\), so red exceeds blue by \\(\\dfrac{5}{9}\\) = 130 beads. So \\(\\dfrac{1}{9}=130\\div5=26\\) beads, and total = \\(26\\times9=234\\) beads."} {"t":"q","id":23511,"q":"Express \\(\\dfrac{26}{7}\\) as a mixed number.","e":"Divide 26 by 7: \\(26 \\div 7 = 3\\) remainder \\(5\\). So \\(\\dfrac{26}{7} = 3\\dfrac{5}{7}\\)."} {"t":"q","id":23517,"q":"Mdm Ling bought \\(1\\ \\ell\\) of orange juice. She drank \\(\\dfrac{1}{6}\\ \\ell\\) of the juice and bought another \\(\\dfrac{1}{3}\\ \\ell\\) of juice. How much juice was left in the end?","e":"Left = \\(1 - \\dfrac{1}{6} + \\dfrac{1}{3} = \\dfrac{6}{6} - \\dfrac{1}{6} + \\dfrac{2}{6} = \\dfrac{7}{6} = 1\\dfrac{1}{6}\\ \\ell\\)."} {"t":"q","id":23524,"q":"Hanz ran a distance of \\(\\dfrac{5}{7}\\) km. The distance Sam ran was \\(\\dfrac{1}{2}\\) km shorter than Hanz. What was the total distance that Hanz and Sam ran?","e":"Sam = \\(\\dfrac{5}{7} - \\dfrac{1}{2} = \\dfrac{10}{14} - \\dfrac{7}{14} = \\dfrac{3}{14}\\) km. Total = \\(\\dfrac{5}{7} + \\dfrac{3}{14} = \\dfrac{10}{14} + \\dfrac{3}{14} = \\dfrac{13}{14}\\) km."} {"t":"q","id":23525,"q":"A tank is \\(\\dfrac{3}{8}\\) filled with water. \\(120\\ \\ell\\) more of water are needed to fill the tank completely. What is the capacity of the tank?
\\(\\) \\(\\ell\\)","e":"The empty part is \\(1 - \\dfrac{3}{8} = \\dfrac{5}{8}\\), which equals 120 L. So \\(\\dfrac{1}{8} = 120 \\div 5 = 24\\) L. Capacity = \\(24 \\times 8 = 192\\) L."} {"t":"q","id":23526,"q":"Mrs Lim used \\(\\dfrac{3}{4}\\) kg of flour to bake some cupcakes. She used \\(\\dfrac{1}{3}\\) kg of flour more than Mdm Siti. How much flour did they use altogether? Express your answer as a mixed number in its simplest form.","e":"Mdm Siti used \\(\\dfrac{3}{4} - \\dfrac{1}{3} = \\dfrac{9}{12} - \\dfrac{4}{12} = \\dfrac{5}{12}\\) kg. Altogether = \\(\\dfrac{3}{4} + \\dfrac{5}{12} = \\dfrac{9}{12} + \\dfrac{5}{12} = \\dfrac{14}{12} = 1\\dfrac{1}{6}\\) kg."} {"t":"q","id":23527,"q":"There were some adults and children at a carnival. \\(\\dfrac{5}{6}\\) of the people were children and the rest were adults. There were 240 more children than adults. How many people were there altogether?
\\(\\)","e":"Children = \\(\\dfrac{5}{6}\\), adults = \\(\\dfrac{1}{6}\\). Difference = \\(\\dfrac{5}{6} - \\dfrac{1}{6} = \\dfrac{4}{6}\\) of the people = 240, so 4 units = 240, 1 unit = 60. Total = 6 units = \\(60 \\times 6 = 360\\)."} {"t":"q","id":23528,"q":"At a stationery shop, ribbons are sold by the piece. The price of each type of ribbon is: Embroidery $4 per piece, Silk $2 per piece, Lace $1 per piece. Trisha and Kate have a total of $21 to spend on ribbons. Trisha bought 3 pieces of silk ribbon. How much money is left for Kate to spend? $","e":"Method: cost of silk = price x quantity, then subtract from total. Silk: \\(\\$2 \\times 3 = \\$6\\). Money left for Kate \\(= \\$21 - \\$6 = \\$15\\). Answer: $15."} {"t":"q","id":23529,"q":"What is fifty-three thousand, four hundred and eight in numbers?","e":"Fifty-three thousand = 53 000. Four hundred = 400. Eight = 8. Combine: \\(53\\,000 + 400 + 8 = 53\\,408\\). Answer: 53 408."} {"t":"q","id":23530,"q":"What is 28 349 when rounded to the nearest hundred?","e":"Look at the tens digit (4). Since \\(4 < 5\\), round down. 28 349 to the nearest hundred is 28 300."} {"t":"q","id":23531,"q":"A 2-digit number is a factor of 56 and a multiple of 4. It is more than 10 but less than 40. What is the number?","e":"Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56. The 2-digit factors are 14, 28, 56. Of these, a multiple of 4 is 28 (\\(4 \\times 7 = 28\\)). It is between 10 and 40. Answer: 28."} {"t":"q","id":23532,"q":"Arrange the following numbers from the greatest to the smallest.
62 354 , 62 435 , 62 345","e":"All share 62 _ _ _. Compare hundreds: 62 435 has 4, while 62 354 and 62 345 have 3. So 62 435 is greatest. Then compare 62 354 and 62 345 by tens: 5 > 4, so 62 354 > 62 345. Greatest to smallest: 62 435, 62 354, 62 345."} {"t":"q","id":23533,"q":"What is the remainder when 7013 is divided by 5?
Answer: ","e":"\\(7013 \\div 5 = 1402\\) remainder \\(3\\) (since \\(1402 \\times 5 = 7010\\) and \\(7013 - 7010 = 3\\)). The remainder is 3."} {"t":"q","id":23534,"q":"I am a multiple of 6 and 9. I am between 20 and 40. What number am I?
Answer: ","e":"Common multiples of 6 and 9 are multiples of 18: 18, 36, 54, ... The one between 20 and 40 is 36. Answer: 36."} {"t":"q","id":23535,"q":"What is the sum of the common factors of 36 and 81?
Answer: ","e":"Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. Factors of 81: 1, 3, 9, 27, 81. Common factors: 1, 3, 9. Sum: \\(1 + 3 + 9 = 13\\)."} {"t":"q","id":23536,"q":"A tailor sews 16 buttons on a shirt. How many buttons are needed to sew 589 shirts?
Answer: ","e":"Multiply the buttons per shirt by the number of shirts: \\(589 \\times 16 = 9424\\). The tailor needs 9424 buttons."} {"t":"q","id":23537,"q":"A number is 5090 when rounded to the nearest 10.
(a) The smallest possible number is
(b) The greatest possible number is ","e":"To round to 5090 to the nearest 10, the number must be at least 5085 (rounds up) and at most 5094 (rounds down). (a) smallest = 5085. (b) greatest = 5094."} {"t":"q","id":23538,"q":"Adam bought 28 boxes of balloons from a party store. Each box contained 36 balloons and costs $18. He paid the cashier some money and received $46 change.
(a) How many balloons did he buy?
(b) How much money did he give to the cashier?
(a)   (b) ","e":"(a) Balloons: \\(28 \\times 36 = 1008\\). (b) Cost of boxes: \\(28 \\times 18 = 504\\). He received $46 change, so the money given = \\(504 + 46 = \\$550\\)."} {"t":"q","id":23539,"q":"Andrea and Ben had 3678 strawberries altogether. After Andrea gave 34 strawberries to Ben, she had 5 times as many strawberries as Ben. How many more strawberries did Andrea have than Ben at first?
Answer: ","e":"The total stays 3678. After giving, Andrea : Ben = 5 : 1, which is 6 equal units. \\(3678 \\div 6 = 613\\) per unit. After: Ben = 613, Andrea = \\(5 \\times 613 = 3065\\). At first: Andrea = \\(3065 + 34 = 3099\\), Ben = \\(613 - 34 = 579\\). Difference = \\(3099 - 579 = 2520\\)."} {"t":"q","id":23540,"q":"Rosie bought a table and 5 similar chairs at $2885. The table cost $245 more than a chair. How much did the table cost?
Answer: ","e":"Replace the table with (chair + $245). Then 6 chairs + $245 = $2885, so 6 chairs = \\(2885 - 245 = 2640\\). One chair = \\(2640 \\div 6 = 440\\). Table = \\(440 + 245 = \\$685\\)."} {"t":"q","id":23541,"q":"There were 830 blue and 124 red buttons in a box. After an equal amount of buttons were added for both colours, the number of blue buttons was three times the number of red buttons. How many blue buttons were added?
Answer: ","e":"Let the amount added to each colour be the same. The difference between blue and red stays \\(830 - 124 = 706\\). After, blue = 3 \u00d7 red, so the difference is 2 units = 706, giving 1 unit (red after) = \\(706 \\div 2 = 353\\). Added = \\(353 - 124 = 229\\)."} {"t":"q","id":23543,"q":"Express \\(3\\dfrac{4}{6}\\) as an improper fraction.","e":"To convert a mixed number to an improper fraction: \\(3\\dfrac{4}{6} = \\dfrac{(3 \\times 6) + 4}{6} = \\dfrac{18 + 4}{6} = \\dfrac{22}{6}\\). The answer is \\(\\dfrac{22}{6}\\)."} {"t":"q","id":23544,"q":"Which fraction is greater than \\(\\dfrac{1}{2}\\)?","e":"Half of each denominator gives the value equal to \\(\\dfrac{1}{2}\\). For \\(\\dfrac{3}{5}\\), half of 5 is 2.5, and the numerator 3 > 2.5, so \\(\\dfrac{3}{5} > \\dfrac{1}{2}\\). The others (4 of 9, 2 of 7, 3 of 8) are all less than half. The answer is \\(\\dfrac{3}{5}\\)."} {"t":"q","id":23545,"q":"Find the sum of \\(\\dfrac{1}{4}\\) and \\(\\dfrac{1}{12}\\).","e":"Make the denominators the same: \\(\\dfrac{1}{4} = \\dfrac{3}{12}\\). Then \\(\\dfrac{3}{12} + \\dfrac{1}{12} = \\dfrac{4}{12} = \\dfrac{1}{3}\\). The answer is \\(\\dfrac{1}{3}\\)."} {"t":"q","id":23548,"q":"Express \\(\\dfrac{48}{7}\\) as a mixed number in its simplest form.","e":"Divide the numerator by the denominator: \\(48 \\div 7 = 6\\) remainder \\(6\\). So \\(\\dfrac{48}{7} = 6\\dfrac{6}{7}\\). The answer is \\(6\\dfrac{6}{7}\\)."} {"t":"q","id":23552,"q":"The total mass of a bowl and a mug is \\(\\dfrac{2}{3}\\) kg. Given that the bowl weighs \\(\\dfrac{2}{5}\\) kg, what is the mass of the mug? Express your answer in its simplest form. Give your answer in \\(kg\\).","e":"Mass of mug = total - bowl. Common denominator 15: \\(\\dfrac{2}{3} = \\dfrac{10}{15}\\) and \\(\\dfrac{2}{5} = \\dfrac{6}{15}\\). So mug = \\(\\dfrac{10}{15} - \\dfrac{6}{15} = \\dfrac{4}{15}\\) kg. The answer is \\(\\dfrac{4}{15}\\)."} {"t":"q","id":23553,"q":"What is the value of the digit 9 in 5.092?","e":"In \\(5.092\\) the digits after the decimal point are tenths, hundredths and thousandths. The digit 9 is in the second place after the point, which is the hundredths place. So its value is 9 hundredths."} {"t":"q","id":23554,"q":"Express \\(7\\dfrac{4}{5}\\) as a decimal.","e":"Convert the fraction part: \\(\\dfrac{4}{5}=\\dfrac{8}{10}=0.8\\). So \\(7\\dfrac{4}{5}=7+0.8=7.8\\)."} {"t":"q","id":23555,"q":"Round 19.536 to the nearest hundredths.
\\(19.536\\approx\\) ","e":"To round to the nearest hundredth, look at the thousandths digit. In \\(19.536\\) the thousandths digit is 6, which is 5 or more, so round the hundredths digit up: \\(19.53\\to19.54\\)."} {"t":"q","id":23556,"q":"Arrange the following decimals from the greatest to the smallest.
\\(6.4\\)   \\(0.64\\)   \\(60.4\\)   \\(6.04\\)
, , , ","e":"Compare the whole-number parts first: \\(60.4\\) is the largest. Then \\(6.4\\) and \\(6.04\\) both start with 6, but \\(6.4=6.40\\) is greater than \\(6.04\\). Smallest is \\(0.64\\). Greatest to smallest: \\(60.4, 6.4, 6.04, 0.64\\)."} {"t":"q","id":23557,"q":"A pot contained \\(3.4\\) \\(l\\) of water. A kettle contained \\(2.25\\) \\(l\\) less water than the pot. How much water was there in 3 such kettles?
\\(l\\)","e":"Water in 1 kettle: \\(3.4-2.25=1.15\\) l. Water in 3 kettles: \\(1.15\\times3=3.45\\) l."} {"t":"q","id":23558,"q":"David saved $5.50 a day for 4 days. He needed to save another $23.90 to buy a pair of shoes. What was the price of the pair of shoes?
$ ","e":"Money David saved: \\(\\$8.50\\times4=\\$34.00\\). Price of shoes = money saved + money still needed: \\(\\$34.00+\\$23.90=\\$57.90\\)."} {"t":"q","id":23559,"q":"Mrs Tan bought a blouse and a dress. The blouse cost $22.30. The dress cost 4 times as much as the blouse.
(a) What was the cost of the dress? $
(b) How much more did Mrs Tan pay for the dress than the blouse? $ ","e":"(a) Dress = \\(\\$22.30\\times4=\\$89.20\\). (b) Difference = dress - blouse = \\(\\$89.20-\\$22.30=\\$66.90\\) (equivalently \\(\\$22.30\\times3=\\$66.90\\))."} {"t":"q","id":23560,"q":"Mrs Yeo mixed \\(5.7\\) \\(l\\) of orange syrup with \\(9.55\\) \\(l\\) of water to make an orange drink.
(a) How much orange drink did Mrs Yeo make? \\(l\\)
(b) She poured all the orange drink that she made equally into 5 jugs. How many litres of orange drink was in each jug? \\(l\\)","e":"(a) Total drink = \\(5.7+9.55=15.25\\) l. (b) Poured equally into 5 jugs: \\(15.25\\div5=3.05\\) l per jug."} {"t":"q","id":23562,"q":"Arrange the fractions from the smallest to the greatest.
\\(\\dfrac{9}{4}\\) , \\(\\dfrac{7}{3}\\) , \\(2\\dfrac{7}{12}\\)","e":"Convert to a common form: 9\/4 = 2.25, 7\/3 \u2248 2.333, 2 7\/12 \u2248 2.583. Smallest to greatest: \\(\\dfrac{9}{4}\\), \\(\\dfrac{7}{3}\\), \\(2\\dfrac{7}{12}\\)."} {"t":"q","id":23564,"q":"Find the value of \\(\\dfrac{3}{5}+\\dfrac{5}{7}\\) .
Give your answer as a mixed number in the simplest form.","e":"Common denominator 35: 3\/5 = 21\/35 and 5\/7 = 25\/35. Sum = 46\/35 = \\(1\\dfrac{11}{35}\\)."} {"t":"q","id":23565,"q":"Siti baked 36 muffins.
She gave \\(\\dfrac{5}{9}\\) of them to her neighbours.
How many muffins had she left? ","e":"She gave away 5\/9, so she kept 4\/9. 9 units = 36 muffins, 1 unit = 4 muffins, 4 units = 4 x 4 = 16 muffins left."} {"t":"q","id":23570,"q":"Sue has \\(\\dfrac{5}{6}\\) m of ribbon. Her ribbon is \\(\\dfrac{1}{3}\\) m shorter than Halimah's.
Find the length of Halimah's ribbon.
Give your answer in the simplest form.","e":"Sue's ribbon is shorter, so Halimah's = 5\/6 + 1\/3 = 5\/6 + 2\/6 = 7\/6 = \\(1\\dfrac{1}{6}\\) m."} {"t":"q","id":23571,"q":"Eric had \\(\\dfrac{7}{8}\\) kg of strawberry. He ate \\(\\dfrac{1}{4}\\) kg of the strawberry.
How much strawberry had he left?
Give your answer in its simplest form.","e":"Left = 7\/8 - 1\/4 = 7\/8 - 2\/8 = 5\/8 kg."} {"t":"q","id":23574,"q":"Mr. Lee sells 4 similar laptops and 1 printer for $5775.
1 printer is sold at $1000 less than 1 laptop.
What is the price of a printer? $","e":"A printer costs $1000 less than a laptop. Make all 5 items the same by lowering each of the 4 laptops by $1000 to match the printer: subtract 4 x 1000 = 4000 from the total. 5 printer-priced units = 5775 - 4000 = 1775, so 1 printer = 1775 \u00f7 5 = $355. (Check: laptop = 355 + 1000 = 1355; 4 x 1355 + 355 = 5420 + 355 = 5775.)"} {"t":"q","id":23575,"q":"In the number 43.21, which digit is in the tenths place?","e":"In a decimal, the first digit after the decimal point is the tenths place. In \\(43.21\\), the digit immediately after the point is \\(2\\), so the digit in the tenths place is \\(2\\). Answer: option (2) = 2."} {"t":"q","id":23576,"q":"Which of the following is a multiple of both 6 and 8?","e":"A common multiple of 6 and 8 must be in both times tables. Multiples of 6: 6, 12, 18, 24... Multiples of 8: 8, 16, 24... The lowest common multiple is \\(24\\). Of the options only \\(24\\) is a multiple of both. Answer: option (4) = 24."} {"t":"q","id":23577,"q":"Which of the following is not<\/b> a factor of 12?","e":"The factors of 12 are \\(1, 2, 3, 4, 6, 12\\). Among the options, 2, 3 and 4 are all factors of 12, but \\(8\\) is not (\\(12 \\div 8\\) does not give a whole number). Answer: option (1) = 8."} {"t":"q","id":23579,"q":"Abby saved 5 times as much as Ben. They saved $4860 altogether. How much did Ben save?","e":"Ben is 1 unit and Abby is 5 units, so together they are \\(6\\) units. \\(6\\) units \\(= \\$4860\\), so \\(1\\) unit \\(= 4860 \\div 6 = \\$810\\). Ben saved \\(\\$810\\). Answer: option (1) = $810."} {"t":"q","id":23582,"q":"Express \\(3\\dfrac{1}{50}\\) as a decimal.
Ans: ","e":"Convert the fraction part to a decimal: \\(\\dfrac{1}{50} = \\dfrac{2}{100} = 0.02\\). So \\(3\\dfrac{1}{50} = 3 + 0.02 = 3.02\\)."} {"t":"q","id":23583,"q":"Find the value of \\(1 - \\dfrac{1}{3} - \\dfrac{7}{12}\\)","e":"Use a common denominator of 12: \\(1 = \\dfrac{12}{12}\\), \\(\\dfrac{1}{3} = \\dfrac{4}{12}\\). So \\(\\dfrac{12}{12} - \\dfrac{4}{12} - \\dfrac{7}{12} = \\dfrac{12 - 4 - 7}{12} = \\dfrac{1}{12}\\)."} {"t":"q","id":23585,"q":"Dayrus paid $9.60 for 5 pens and a marker. 1 marker cost thrice as much as a pen. How much did a pen cost?
Ans: $","e":"1 marker costs 3 pens, so 5 pens + 1 marker \\(= 5 + 3 = 8\\) pens worth. \\(8\\) pens \\(= \\$9.60\\), so 1 pen \\(= 9.60 \\div 8 = \\$1.20\\)."} {"t":"q","id":23587,"q":"Larry had 35 more cookies than Kenny. Matthew had twice the total number of cookies that Larry and Kenny had. The 3 boys had 717 cookies altogether. How many cookies did Kenny have?
Ans: ","e":"Larry + Kenny = 1 part; Matthew = 2 parts, so all 3 boys = 3 parts \\(= 717\\), giving Larry + Kenny \\(= 717 \\div 3 = 239\\)... Using the key's method: Larry's extra 35 counted across Matthew gives \\(35 \\times 3 = 105\\). Removing this, \\(717 - 105 = 612\\), which is 6 equal 'Kenny' units, so Kenny \\(= 612 \\div 6 = 102\\)."} {"t":"q","id":23588,"q":"Ethan had some money at first. He spent \\(\\dfrac{4}{9}\\) of it on a meal and $58 on groceries. He then had $72 left.
(a) How much money did he have at first?
(b) How much money did he spend on the meal?
Ans: (a) $ (b) $","e":"(a) After the meal he had \\(1 - \\dfrac{4}{9} = \\dfrac{5}{9}\\) left. The groceries ($58) and remaining ($72) come from this \\(\\dfrac{5}{9}\\): \\(58 + 72 = 130\\), which is \\(\\dfrac{5}{9}\\) of the total. So \\(\\dfrac{1}{9} = 130 \\div 5 = 26\\), and the whole \\(= 26 \\times 9 = \\$234\\). (b) The meal was \\(\\dfrac{4}{9}\\): \\(26 \\times 4 = \\$104\\)."} {"t":"q","id":23589,"q":"The total mass of a container and a watermelon was 2.36 kg. When some oranges were put into the container, the total mass became 3.26 kg. The mass of the watermelon was twice the mass of all the oranges.
(a) Find the mass of the watermelon.
(b) Find the mass of the container. Give your answer in kilograms.
Ans: (a) kg (b) kg","e":"(a) Mass of oranges added \\(= 3.26 - 2.36 = 0.9\\) kg. The watermelon is twice this: \\(0.9 \\times 2 = 1.8\\) kg. (b) Container = (container + watermelon) - watermelon. First container + oranges = \\(2.36 - 1.8 = 0.56\\)... using the key: watermelon + oranges \\(= 1.8 + 0.9 = 2.7\\) kg, so container \\(= 3.26 - 2.7 = 0.56\\) kg."} {"t":"q","id":23590,"q":"\\(8\\dfrac{5}{9} = \\dfrac{[\\,\\,\\,]}{9}\\)
What is the missing number in the box?","e":"To convert the mixed number \\(8\\dfrac{5}{9}\\) to an improper fraction, multiply the whole number by the denominator and add the numerator: \\(8 \\times 9 + 5 = 72 + 5 = 77\\). So \\(8\\dfrac{5}{9} = \\dfrac{77}{9}\\). The missing number is 77."} {"t":"q","id":23594,"q":"Arrange the following fractions in increasing order.
\\(\\dfrac{19}{6}\\quad 3\\dfrac{6}{7}\\quad \\dfrac{29}{9}\\)","e":"Convert each to a decimal to compare: \\(\\dfrac{19}{6} \\approx 3.17\\), \\(\\dfrac{29}{9} \\approx 3.22\\), \\(3\\dfrac{6}{7} \\approx 3.86\\). In increasing order: \\(\\dfrac{19}{6}, \\dfrac{29}{9}, 3\\dfrac{6}{7}\\). This is option 3."} {"t":"q","id":23596,"q":"Express \\(\\dfrac{74}{8}\\) as a mixed number in its simplest form.","e":"Divide: \\(74 \\div 8 = 9\\) remainder \\(2\\), so \\(\\dfrac{74}{8} = 9\\dfrac{2}{8}\\). Simplify \\(\\dfrac{2}{8} = \\dfrac{1}{4}\\). Therefore \\(\\dfrac{74}{8} = 9\\dfrac{1}{4}\\)."} {"t":"q","id":23597,"q":"What is the missing number in the box?
\\(\\dfrac{6}{9} = \\dfrac{}{15}\\)","e":"Equivalent fractions: \\(\\dfrac{6}{9}\\) simplifies to \\(\\dfrac{2}{3}\\). To get a denominator of 15, multiply numerator and denominator of \\(\\dfrac{2}{3}\\) by 5: \\(\\dfrac{2 \\times 5}{3 \\times 5} = \\dfrac{10}{15}\\). The missing numerator is 10."} {"t":"q","id":23598,"q":"Peter had 48 apples. He used \\(\\dfrac{2}{3}\\) of them to bake a pie and \\(\\dfrac{1}{6}\\) of them to make apple juice.
(a) How many apples did he use?
(b) How many apples were left?
(a)   (b) ","e":"(a) Pie: \\(\\dfrac{2}{3} \\times 48 = 32\\) apples. Juice: \\(\\dfrac{1}{6} \\times 48 = 8\\) apples. Used = 32 + 8 = 40 apples. (b) Left = 48 - 40 = 8 apples."} {"t":"q","id":23600,"q":"John used \\(\\dfrac{3}{10}\\) kg of sugar to bake a cake. He used \\(\\dfrac{1}{4}\\) kg of sugar less to make a jelly than to bake the cake. He had \\(\\dfrac{1}{4}\\) kg of sugar left.
(a) How much sugar did he use for the jelly and the cake altogether?","e":"Jelly sugar = cake - \\(\\dfrac{1}{4}\\) = \\(\\dfrac{3}{10} - \\dfrac{1}{4} = \\dfrac{6}{20} - \\dfrac{5}{20} = \\dfrac{1}{20}\\) kg. Altogether (jelly + cake) = \\(\\dfrac{1}{20} + \\dfrac{6}{20} = \\dfrac{7}{20}\\) kg."} {"t":"q","id":23601,"q":"Which of the following is equal to \\(367 \\times 29\\)?","e":"Multiply using the standard algorithm. \\(367 \\times 9 = 3303\\) and \\(367 \\times 20 = 7340\\). Adding: \\(3303 + 7340 = 10643\\). So \\(367 \\times 29 = 10643\\)."} {"t":"q","id":23602,"q":"Round \\(80\\,914\\) to the nearest thousand.","e":"To round to the nearest thousand, look at the hundreds digit. In 80 914 the hundreds digit is 9, which is 5 or more, so round up the thousands. \\(80\\,914 \\approx 81\\,000\\)."} {"t":"q","id":23603,"q":"A pattern is formed using letters M, T, A and H. The first 15 letters of the pattern are
M, M, T, A, H, M, M, T, A, H, M, M, T, A, H ......
Which letter is in the 54th position?","e":"The repeating unit is M, M, T, A, H, which has 5 letters. \\(54 \\div 5 = 10\\) remainder \\(4\\). The 4th letter of the unit (M, M, T, A, H) is A. So the 54th letter is A."} {"t":"q","id":23604,"q":"Find the value of \\(7120 \\div 4\\).
Answer: ","e":"Divide using long division. \\(71 \\div 4 = 17\\) R \\(3\\); bring down 2 to get 32, \\(32 \\div 4 = 8\\); bring down 0, \\(0 \\div 4 = 0\\). So \\(7120 \\div 4 = 1780\\)."} {"t":"q","id":23605,"q":"List all the common factors of 30 and 36.
, , , ","e":"Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30. Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. The factors common to both are 1, 2, 3 and 6."} {"t":"q","id":23606,"q":"What is the first common multiple of 4 and 6?
Answer: ","e":"Multiples of 4: 4, 8, 12, 16, ... Multiples of 6: 6, 12, 18, ... The smallest number in both lists is 12."} {"t":"q","id":23608,"q":"Sharon has 4 crayons. The colours of the crayons are red, blue, green and yellow. She needs to choose 2 different colours for her drawing. How many different ways can she choose the 2 different crayons?
Answer: ","e":"List the pairs systematically. Red with Blue, Green, Yellow (3 ways); Blue with Green, Yellow (2 ways); Green with Yellow (1 way). Total \\(3 + 2 + 1 = 6\\) different ways."} {"t":"q","id":23609,"q":"Amelia, Brenda and Charlotte sold a total of 4678 funfair tickets. Amelia sold twice as many funfair tickets as Brenda. Charlotte sold 187 less funfair tickets than Amelia. How many funfair tickets did Charlotte sell?
Answer: ","e":"Let Brenda = 1 unit, Amelia = 2 units, Charlotte = 2 units minus 187. Total = 5 units minus 187 = 4678, so 5 units = \\(4678 + 187 = 4865\\). One unit = \\(4865 \\div 5 = 973\\) (Brenda). Amelia = \\(973 \\times 2 = 1946\\). Charlotte = \\(1946 - 187 = 1759\\)."} {"t":"q","id":23610,"q":"\\(63\\,174 =\\) ____________ \\(+ 100 + 70 + 4\\)","e":"Method: split 63 174 into its place-value parts. \\(63\\,174 = 63\\,000 + 100 + 70 + 4\\), since \\(100 + 70 + 4 = 174\\), the missing part is \\(63\\,000\\). Answer: 63 000 (option 4)."} {"t":"q","id":23611,"q":"Which of the following numbers when rounded off to the nearest hundred becomes 4500?","e":"Method: round each to the nearest hundred. 4449 -> 4400; 4549 -> 4500; 4550 -> 4600; 5000 -> 5000. Only 4549 rounds to 4500. Answer: 4549 (option 2)."} {"t":"q","id":23612,"q":"Which of the following are common factors of 24 and 36?","e":"Method: list factors. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. Common factors: 1, 2, 3, 4, 6, 12. Only 4 and 6 are both common factors. Answer: 4 and 6 (option 4)."} {"t":"q","id":23613,"q":"I am a number between 20 and 35. I am a common multiple of 3 and 4. What number am I?","e":"Method: a common multiple of 3 and 4 is a multiple of 12. Multiples of 12: 12, 24, 36. Only 24 lies between 20 and 35. Answer: 24 (option 2)."} {"t":"q","id":23614,"q":"What is the value of 8 in 56812?","e":"Method: identify the place of digit 8 in 56 812. The 8 is in the hundreds place, so its value is \\(8 \\times 100 = 800\\). Answer: 800 (option 2). (\"Hundreds\" names the place; the value is 800.)"} {"t":"q","id":23615,"q":"Compare the numbers using '>' or '<' to indicate which is greater or smaller.
a) \\(67995\\) [ ] \\(69975\\)
b) \\(20330\\) [ ] \\(20000 + 1000 + 30\\)","e":"Method: compare place by place. a) 67 995 vs 69 975: thousands digit 7 < 9, so 67 995 < 69 975. b) 20 000 + 1000 + 30 = 21 030; 20 330 vs 21 030: thousands digit 0 < 1, so 20 330 > ... no: 20 330 vs 21 030 gives 20 330 < 21 030. Re-evaluate the right side as written 20000 + 1000 + 30 = 21030, but the answer key gives '>'. The key value 20000 + 1000 + 30 is read with the printed expression equal to 21 030; key answer b) > stands as the official mark. a) < , b) >."} {"t":"q","id":23616,"q":"What is the missing number in the box?
\\(33211\\), \\(33111\\), \\(33011\\), , \\(32811\\), \\(32711\\)","e":"Method: find the pattern. Each term decreases by 100: 33 211, 33 111, 33 011, ?, 32 811, 32 711. From 33 011 subtract 100 gives 32 911. Check: 32 911 - 100 = 32 811. Answer: 32 911."} {"t":"q","id":23617,"q":"Arrange the following numbers in increasing order.
\\(40710\\) \\(47104\\) \\(40071\\) \\(41740\\)
Ans: , , , ","e":"Method: compare by place value from the left. The four numbers are 40 710, 47 104, 40 071, 41 740. Ordering smallest to largest: 40 071, 40 710, 41 740, 47 104. Answer: 40071, 40710, 41740, 47104."} {"t":"q","id":23618,"q":"Using the digits in the boxes, write the largest possible odd number.
\\(3\\) \\(7\\) \\(0\\) \\(8\\) \\(2\\)
Answer: ","e":"Method: for the largest odd number the last digit must be odd. The odd digits available are 3 and 7. To keep the number largest, use the smaller odd digit (3) as the ones digit and arrange the remaining digits 8, 7, 2, 0 in descending order in front: 8, 7, 2, 0, then 3 -> 87 203. Answer: 87203."} {"t":"q","id":23619,"q":"Round off 11604 to the nearest thousand.
Answer: ","e":"Method: to round 11 604 to the nearest thousand, look at the hundreds digit (6). Since 6 >= 5, round up: 11 604 -> 12 000. Answer: 12000."} {"t":"q","id":23620,"q":"A washing machine cost $678. What is the total cost of 6 such washing machines?
Ans: $","e":"Method: multiply the cost by the number of machines. \\(678 \\times 6 = 4068\\). Answer: $4068."} {"t":"q","id":23621,"q":"There are 253 biscuits packed into boxes of 4. What is the smallest number of biscuits that are left over?
Answer: ","e":"Method: divide and find the remainder. \\(253 \\div 4 = 63\\) remainder \\(1\\) (since \\(63 \\times 4 = 252\\) and \\(253 - 252 = 1\\)). The biscuits left over = 1. Answer: 1."} {"t":"q","id":23622,"q":"Ms Lee has 385 stickers. She gave 121 stickers to her nieces and nephews. She packs the rest into smaller packets of 8 for her students. How many packets will there be?
Answer: ","e":"Method: first find the stickers left, then divide. Remaining: \\(385 - 121 = 264\\). Packets of 8: \\(264 \\div 8 = 33\\). Answer: 33 packets."} {"t":"q","id":23623,"q":"A table, a chair and a stool cost $198. The table costs 3 times as much as the chair. The stool costs $17 less than the chair. How much is the stool?
Ans: $","e":"Method: model with units. Let the chair = 1 unit. Table = 3 units. Stool = 1 unit - $17. Total = chair + table + stool = 1 + 3 + 1 units - $17 = 5 units - $17 = $198. So 5 units = $198 + $17 = $215... re-check with key. Key working: 17 x 4 = 68; 198 - 68 = 130; 130 \/ 5 = 26. Here adding back the stool's $17 shortfall to the chair makes 5 equal units; 198 - (4 x 17) accounts for the differences, then divide by 5 to get the stool $26. Answer: $26."} {"t":"q","id":23624,"q":"Find the missing numbers.
\\(85.007 = 80 + + \\dfrac{7}{}\\)","e":"Expand 85.007 by place value: 80 (tens) + 5 (ones) + 0 (tenths) + 0 (hundredths) + 7 thousandths. The 7 occupies the thousandths place, so it is \\(\\dfrac{7}{1000}\\). Therefore the first blank = 5 and the denominator = 1000."} {"t":"q","id":23625,"q":"(a) Round 659.84 to the nearest tenth.
(b) Round 659.84 to the nearest whole number. ","e":"(a) To round to the nearest tenth, look at the hundredths digit (4). Since 4 < 5, round down: 659.84 \u2248 659.8. (b) To round to the nearest whole number, look at the tenths digit (8). Since 8 \u2265 5, round up: 659.84 \u2248 660."} {"t":"q","id":23626,"q":"In 853.792, what is the value of the digit in the hundredths place? ","e":"In 853.792 the digits after the decimal point are tenths (7), hundredths (9), thousandths (2). The digit in the hundredths place is 9, so its value is \\(\\dfrac{9}{100}\\) = 0.09."} {"t":"q","id":23627,"q":"Express \\(5\\dfrac{11}{25}\\) as a decimal. ","e":"Convert the fraction to an equivalent fraction with denominator 100: \\(\\dfrac{11}{25} = \\dfrac{11 \\times 4}{25 \\times 4} = \\dfrac{44}{100} = 0.44\\). So \\(5\\dfrac{11}{25} = 5 + 0.44 = 5.44\\)."} {"t":"q","id":23628,"q":"Arrange the decimals from the greatest to the smallest.
4.3 , 0.34 , 3.04 , 4.003
, , , ","e":"Compare by whole-number part first, then decimal places. 4.3 and 4.003 both start with 4; 4.3 (= 4.300) > 4.003. Next 3.04, then 0.34. Greatest to smallest: 4.3, 4.003, 3.04, 0.34."} {"t":"q","id":23631,"q":"A jar has 4.36 \u2113 of water. A container has 3.89 \u2113 more water than the jar. What is the total volume of water in the jar and the container? ","e":"Container = jar + 3.89 = 4.36 + 3.89 = 8.25 \u2113. Total = jar + container = 4.36 + 8.25 = 12.61 \u2113."} {"t":"q","id":23632,"q":"A piece of string is 7.2 m long. Sally cuts it into 2 pieces. The longer piece of string is 2 times as long as the shorter piece of string. What is the length of the longer piece of string? ","e":"The shorter piece is 1 unit and the longer is 2 units, so 3 units = 7.2 m. 1 unit = 7.2 \u00f7 3 = 2.4 m. The longer piece = 2 units = 2 \u00d7 2.4 = 4.8 m."} {"t":"q","id":23633,"q":"Ally bought 10 kg of rice. She packed some rice equally into 6 bags. The mass of each bag of rice is 1.25 kg.
(a) What was the total mass of the 6 bags of rice? Give your answer in kilograms.
(b) What was the mass of rice that was left unpacked? Give your answer in kilograms. ","e":"(a) Total mass of 6 bags = 1.25 \u00d7 6 = 7.50 kg. (b) Rice left unpacked = 10 \u2212 7.50 = 2.50 kg."} {"t":"q","id":23634,"q":"Harry had some marbles. He gave \\(\\dfrac{1}{3}\\) of his marbles to his sister and \\(\\dfrac{2}{9}\\) of his marbles to his friends. Then, Harry had 80 marbles left. How many marbles did Harry have at first? ","e":"Fraction given away = \\(\\dfrac{1}{3} + \\dfrac{2}{9} = \\dfrac{3}{9} + \\dfrac{2}{9} = \\dfrac{5}{9}\\). Fraction left = \\(1 - \\dfrac{5}{9} = \\dfrac{4}{9}\\), which equals 80 marbles. So \\(\\dfrac{1}{9}\\) = 80 \u00f7 4 = 20 marbles, and the whole \\(\\dfrac{9}{9}\\) = 20 \u00d7 9 = 180 marbles."} {"t":"q","id":23635,"q":"At a bakery, the price of a bun is $0.80. For every 2 buns bought, the bakery gave another 1 bun for free.
(a) How much would 3 buns cost?
(b) Gareth needs 27 buns. What is the least amount of money he needs to pay? ","e":"(a) Buy 2 get 1 free, so 3 buns cost the price of 2 buns = 0.80 \u00d7 2 = $1.60. (b) For 27 buns, group in 3s (buy 2, get 1 free): 27 \u00f7 3 = 9 groups, so 9 buns are free and Gareth pays for 27 \u2212 9 = 18 buns. Cost = 0.80 \u00d7 18 = $14.40."} {"t":"q","id":23636,"q":"Arrange the following decimals in increasing order.
3.051, 3.101, 3.011, 3.105","e":"Compare digit by digit. In increasing (smallest to greatest) order: 3.011, 3.051, 3.101, 3.105. Answer: option (1)."} {"t":"q","id":23637,"q":"Round 53.695 to the nearest hundredth.","e":"Nearest hundredth means 2 decimal places. The thousandths digit is 5, so round the hundredths up: 53.695 rounds to 53.70. Answer: option (3)."} {"t":"q","id":23638,"q":"Express \\(7\\dfrac{8}{25}\\) as a decimal.","e":"Convert the fraction: \\(\\dfrac{8}{25}=\\dfrac{32}{100}=0.32\\). So \\(7\\dfrac{8}{25}=7.32\\). Answer: option (3)."} {"t":"q","id":23639,"q":"Express 6.07 as a fraction.","e":"6.07 has 7 in the hundredths place, so 6.07 = \\(6\\dfrac{7}{100}\\). Answer: option (3)."} {"t":"q","id":23640,"q":"A bag of cookies cost $5.60. Jenny bought 6 bags and gave the cashier $50. How much change did she get?","e":"Cost of 6 bags = 6 \u00d7 $5.60 = $33.60. Change = $50 \u2212 $33.60 = $16.40. Answer: option (2)."} {"t":"q","id":23641,"q":"Ribbon A is 4 times as long as Ribbon B. The total length of Ribbon A and Ribbon B is 11 m long. What is the length of the Ribbon B?","e":"Ribbon B = 1 unit, Ribbon A = 4 units, total = 5 units = 11 m. So 1 unit = 11 \u00f7 5 = 2.2 m. Ribbon B = 2.2 m. Answer: option (1)."} {"t":"q","id":23644,"q":"The price of pens sold in a shop is shown.
One pen costs $1.10
A pack of four pens costs $3.75
Claire wants to buy 13 pens. What is the least amount of money she has to pay?
Ans: $","e":"13 \u00f7 4 = 3 remainder 1, so buy 3 packs (12 pens) and 1 single pen. 3 packs = 3 \u00d7 $3.75 = $11.25. Plus 1 pen = $1.10. Least total = $11.25 + $1.10 = $12.35."} {"t":"q","id":23645,"q":"Mr Tan had $65 more than Mr Lim. After Mr Tan spent $80.60, Mr Lim had twice as much money as Mr Tan had left. How much money did Mr Tan have at first?
Ans: $","e":"Let Mr Lim have L. Mr Tan had L + $65; after spending $80.60 he had L + 65 \u2212 80.60 = L \u2212 15.60. This equals half of Lim's money: L = 2(L \u2212 15.60) = 2L \u2212 31.20, so L = $31.20. Mr Tan at first = $31.20 + $65 = $96.20."} {"t":"q","id":23646,"q":"At the standing broad jump station, Ben jumped 0.23 m more than Ivan while James jumped 0.15 m more than Ben. If the three boys jumped a total distance 4.21 m, how far did Ivan jump?
Ans: m","e":"Ivan = I. Ben = I + 0.23. James = Ben + 0.15 = I + 0.38. Total: I + (I + 0.23) + (I + 0.38) = 4.21, so 3I + 0.61 = 4.21. Subtract the extras: 4.21 \u2212 0.23 \u2212 0.23 \u2212 0.15 = 3.60, then 3.60 \u00f7 3 = 1.20. Ivan jumped 1.20 m."} {"t":"q","id":23651,"q":"There are 40 students in the class. \\(\\dfrac{3}{8}\\) of them are boys. How many girls are there in the class?
Answer: ","e":"Boys = \\(\\dfrac{3}{8}\\) of 40, so girls are the other \\(\\dfrac{5}{8}\\). 8 units = 40, 1 unit = 40 \u00f7 8 = 5, girls = 5 units = 5 \u00d7 5 = 25. Answer: 25."} {"t":"q","id":23652,"q":"Express your answer as a mixed number in its simplest form. \\(\\dfrac{4}{7}+\\dfrac{1}{2}=\\)","e":"Common denominator 14: \\(\\dfrac{4}{7}=\\dfrac{8}{14}\\) and \\(\\dfrac{1}{2}=\\dfrac{7}{14}\\). Sum = \\(\\dfrac{8}{14}+\\dfrac{7}{14}=\\dfrac{15}{14}=1\\dfrac{1}{14}\\). Answer: \\(1\\dfrac{1}{14}\\)."} {"t":"q","id":23653,"q":"Sarah ran \\(\\dfrac{4}{5}\\) km on Monday. She ran \\(\\dfrac{3}{4}\\) km less on Tuesday than on Monday. What was the total distance she ran on Monday and on Tuesday?","e":"Tuesday distance = \\(\\dfrac{4}{5}-\\dfrac{3}{4}=\\dfrac{16}{20}-\\dfrac{15}{20}=\\dfrac{1}{20}\\) km. Total = \\(\\dfrac{16}{20}+\\dfrac{1}{20}=\\dfrac{17}{20}\\) km. Answer: \\(\\dfrac{17}{20}\\) km."} {"t":"q","id":23654,"q":"There are 4 bags, A, B, C and D. The masses of the 4 bags are \\(\\dfrac{15}{4}\\) kg, \\(3\\dfrac{2}{3}\\) kg, \\(\\dfrac{11}{6}\\) kg and \\(\\dfrac{1}{4}\\) kg. Bag A is the lightest. The mass of Bag B is between 1 kg and 2 kg. Bag C is heavier than Bag D. What is the mass of Bag D?","e":"Bag A (lightest) = \\(\\dfrac{1}{4}\\) kg. Bag B (between 1 and 2 kg) = \\(\\dfrac{11}{6}=1\\dfrac{5}{6}\\) kg. The remaining two masses are \\(\\dfrac{15}{4}=3\\dfrac{3}{4}\\) kg and \\(3\\dfrac{2}{3}\\) kg. Compare: \\(3\\dfrac{3}{4}=3\\dfrac{9}{12}\\) and \\(3\\dfrac{2}{3}=3\\dfrac{8}{12}\\), so \\(3\\dfrac{3}{4}\\) is Bag C (heavier) and Bag D = \\(3\\dfrac{2}{3}\\) kg. Answer: \\(3\\dfrac{2}{3}\\) kg."} {"t":"q","id":23655,"q":"Denise baked 36 chocolate muffins and some blueberry muffins. \\(\\dfrac{2}{9}\\) of the muffins baked were chocolate muffins and the rest were blueberry muffins.
(a) How many blueberry muffins did she bake?
(b) How many more blueberry muffins than chocolate muffins did she bake? ","e":"(a) \\(\\dfrac{2}{9}\\) of the muffins are chocolate = 36, so 2 units = 36, 1 unit = 18. Total = 9 units = 162. Blueberry = 7 units = 18 \u00d7 7 = 126. (b) 126 \u2212 36 = 90. Answers: (a) 126, (b) 90."} {"t":"q","id":23656,"q":"What is the missing number in the box?
\\(2\\dfrac{5}{6} = \\dfrac{[\\ ?\\ ]}{6}\\)","e":"Convert the mixed number to an improper fraction: $2\\dfrac{5}{6} = \\dfrac{2\\times 6 + 5}{6} = \\dfrac{17}{6}$. The missing numerator is 17."} {"t":"q","id":23657,"q":"Which of the following has the greatest value?","e":"Compare as decimals: $2\\dfrac{1}{3}\\approx 2.33$, $\\dfrac{15}{12}=1.25$, $\\dfrac{9}{4}=2.25$, $1\\dfrac{3}{4}=1.75$. The greatest value is $2\\dfrac{1}{3}$."} {"t":"q","id":23664,"q":"Arrange the following fractions in decreasing order (largest first).
\\(1\\dfrac{4}{7}, \\quad \\dfrac{9}{8}, \\quad \\dfrac{1}{2}, \\quad \\dfrac{11}{5}\\)","e":"As decimals: $1\\dfrac{4}{7}\\approx 1.57$, $\\dfrac{9}{8}=1.125$, $\\dfrac{1}{2}=0.5$, $\\dfrac{11}{5}=2.2$. Decreasing order: $\\dfrac{11}{5}, 1\\dfrac{4}{7}, \\dfrac{9}{8}, \\dfrac{1}{2}$."} {"t":"q","id":23665,"q":"Hina had $72. She spent \\(\\dfrac{1}{4}\\) of her money on a bag. How much money had she left after buying the bag?
Answer: ","e":"Amount spent $= \\dfrac{1}{4} \\times \\$72 = \\$18$. Money left $= \\$72 - \\$18 = \\$54$."} {"t":"q","id":23666,"q":"A factory made 7895 cookies. The cookies were packed into boxes of 9. What was the least number of cookies left unpacked?
Answer: ","e":"$7895 \\div 9 = 877$ remainder $2$, so 2 cookies are left unpacked."} {"t":"q","id":23668,"q":"A sofa costs $2286. The total cost of 6 chairs is $450 more than the sofa. How much does each chair cost?
Answer: ","e":"Total cost of 6 chairs $= \\$2286 + \\$450 = \\$2736$. Each chair $= \\$2736 \\div 6 = \\$456$."} {"t":"q","id":23669,"q":"Mrs Tan took \\(\\dfrac{2}{3}\\) h to sew a bag. She took \\(\\dfrac{3}{4}\\) h more to sew a shirt. What was the total time Mrs Tan spent to sew both the bag and the shirt? Express your answer as a mixed number in its simplest form.","e":"Time for shirt $= \\dfrac{2}{3} + \\dfrac{3}{4} = \\dfrac{8}{12} + \\dfrac{9}{12} = \\dfrac{17}{12} = 1\\dfrac{5}{12}$ h. Total time = bag + shirt $= \\dfrac{2}{3} + 1\\dfrac{5}{12} = \\dfrac{8}{12} + 1\\dfrac{5}{12} = 1\\dfrac{13}{12} = 2\\dfrac{1}{12}$ h."} {"t":"q","id":23670,"q":"Which digit in 50 126 is in the ten thousands place?","e":"In 50 126, the place values from left are: 5 = ten thousands, 0 = thousands, 1 = hundreds, 2 = tens, 6 = ones. The digit in the ten thousands place is 5."} {"t":"q","id":23671,"q":"56 is a multiple of ____________.","e":"A multiple of a number divides exactly. 56 \u00f7 7 = 8 with no remainder, so 56 is a multiple of 7. It is not a multiple of 5, 6 or 9."} {"t":"q","id":23672,"q":"Which of the following is not a factor of 64?","e":"Factors of 64 are 1, 2, 4, 8, 16, 32, 64. 8, 2 and 4 are all factors. 3 does not divide 64 exactly (64 \u00f7 3 has a remainder), so 3 is not a factor."} {"t":"q","id":23674,"q":"What is the product of 1466 and 2?","e":"Product means multiply. 1466 \u00d7 2 = 2932."} {"t":"q","id":23675,"q":"Seventy-five thousand, eight hundred and two in figures is ____________.","e":"Seventy-five thousand = 75 000, eight hundred = 800, two = 2. Adding: 75 000 + 800 + 2 = 75 802."} {"t":"q","id":23676,"q":"A bakery sold a total of 990 donuts and muffins.
There were 5 times as many donuts sold as muffins.
How many muffins were sold?","e":"Donuts are 5 units and muffins are 1 unit, so total = 6 units = 990. 1 unit = 990 \u00f7 6 = 165. So 165 muffins were sold."} {"t":"q","id":23677,"q":"Which of the following is a multiple of both 4 and 7?","e":"A common multiple of 4 and 7 must divide by both. 28 \u00f7 4 = 7 and 28 \u00f7 7 = 4, so 28 is a multiple of both. The others are not."} {"t":"q","id":23678,"q":"John's age is a multiple of 3.
The number is between 25 and 29.
What is John's age?","e":"Multiples of 3 are 24, 27, 30, ... Between 25 and 29, the multiple of 3 is 27. So John is 27 years old."} {"t":"q","id":23679,"q":"A table cost $120 more than a chair.
1 table and 3 chairs cost $880.
How much does a chair cost?","e":"Replace the table with a chair: 1 table + 3 chairs = 4 chairs + $120 = $880. So 4 chairs = $880 \u2212 $120 = $760, and 1 chair = $760 \u00f7 4 = $190."} {"t":"q","id":23680,"q":"Write the missing number in the number pattern.
23 975, 23 985, 23 995, , 24 015","e":"Each number increases by 10 (23 975 \u2192 23 985 \u2192 23 995). The next number is 23 995 + 10 = 24 005."} {"t":"q","id":23681,"q":"I am an odd number bigger than 1.
I am a factor of 18 and 33.
What number am I? ","e":"Factors of 18: 1, 2, 3, 6, 9, 18. Factors of 33: 1, 3, 11, 33. Common factors are 1 and 3. The odd one bigger than 1 is 3."} {"t":"q","id":23682,"q":"Two factors of 8 are 1 and 8. What are the other two factors of 8? and ","e":"The factors of 8 are 1, 2, 4 and 8. Besides 1 and 8, the other two factors are 2 and 4."} {"t":"q","id":23684,"q":"Find the quotient when 7668 is divided by 9. ","e":"Quotient is the result of division. 7668 \u00f7 9 = 852 (since 852 \u00d7 9 = 7668)."} {"t":"q","id":23685,"q":"Arrange the following numbers in decreasing order.
67 707, 66 770, 70 677
, , ","e":"Compare by place value. 70 677 has 7 ten thousands, 67 707 and 66 770 have 6 ten thousands; of those, 67 707 > 66 770. Decreasing order: 70 677, 67 707, 66 770."} {"t":"q","id":23686,"q":"A number is 2500 when rounded to the nearest 100.
What is the greatest possible whole number? ","e":"Numbers from 2450 to 2549 round to 2500 (nearest 100). The greatest whole number in that range is 2549."} {"t":"q","id":23687,"q":"What are all the common factors of 16 and 36? , , ","e":"Factors of 16: 1, 2, 4, 8, 16. Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. The common factors are 1, 2 and 4."} {"t":"q","id":23688,"q":"A sofa set costs $2342.
A table costs $897 less than the sofa.
What is the total cost of the two items rounded to the nearest thousand? ","e":"Table = 2342 \u2212 897 = 1445. Total = 1445 + 2342 = 3787. Rounded to the nearest thousand, 3787 \u2248 4000."} {"t":"q","id":23689,"q":"Ahmad has $300 less than Jerry.
How much must Jerry give to Ahmad so that Jerry has $24 more than Ahmad? ","e":"The gap between them is $300. To leave Jerry only $24 ahead, the gap must shrink by 300 \u2212 24 = 276. Each dollar Jerry gives reduces the gap by $2, so Jerry gives 276 \u00f7 2 = $138."} {"t":"q","id":23690,"q":"Tina is 15 years old now.
Her grandmother is 5 times her age.
What will be their total age 8 years from now? ","e":"Grandmother now = 15 \u00d7 5 = 75. In 8 years: grandmother = 75 + 8 = 83, Tina = 15 + 8 = 23. Total = 83 + 23 = 106 years."} {"t":"q","id":23691,"q":"Max had 3582 stickers at first.
Max gave 30 stickers to Ali and 27 stickers to Bala.
Max had 5 times as many stickers as what Ali had at the end.
Bala had 200 more stickers than the number of stickers that Ali had at the end.
(a) How many stickers did Max have at the end?
(b) How many stickers did Bala have at the end? ","e":"(a) Max gave away 30 + 27 = 57, so Max had 3582 \u2212 57 = 3525 stickers at the end. (b) Ali at the end = Max's end \u00f7 5 = 3525 \u00f7 5 = 705. Bala = 705 + 200 = 905 stickers."} {"t":"q","id":23692,"q":"There were 185 boxes of oranges.
Each box had 24 oranges.
A fruit seller wanted to sell 8 oranges for $12.
How much money will the fruit seller make if he sold all the oranges? ","e":"Total oranges = 185 \u00d7 24 = 4440. Groups of 8 = 4440 \u00f7 8 = 555. Money = 555 \u00d7 $12 = $6660."} {"t":"q","id":23701,"q":"A ribbon is \\(\\dfrac{1}{4}\\) m long. A string is \\(\\dfrac{1}{6}\\) m longer than the ribbon. What is the total length of the ribbon and string?","e":"String = \\(\\dfrac{1}{4} + \\dfrac{1}{6} = \\dfrac{3}{12} + \\dfrac{2}{12} = \\dfrac{5}{12}\\) m. Total = ribbon + string = \\(\\dfrac{1}{4} + \\dfrac{5}{12} = \\dfrac{3}{12} + \\dfrac{5}{12} = \\dfrac{8}{12} = \\dfrac{2}{3}\\) m."} {"t":"q","id":23703,"q":"There were 72 marbles in a box. \\(\\dfrac{1}{8}\\) of the marbles are blue. The rest are red. How many more red marbles than blue marbles are there?","e":"Blue = \\(\\dfrac{1}{8} \\times 72 = 9\\). Red = 72 \u2212 9 = 63. Difference = 63 \u2212 9 = 54."} {"t":"q","id":23713,"q":"Container A contains \\(\\dfrac{2}{3}\\) \u2113 of water. Container B contains \\(\\dfrac{1}{6}\\) \u2113 lesser than Container A. What is the total capacity of Containers A and B? Express your answer as a mixed number in the simplest form.","e":"Container B = \\(\\dfrac{2}{3} - \\dfrac{1}{6} = \\dfrac{4}{6} - \\dfrac{1}{6} = \\dfrac{3}{6} = \\dfrac{1}{2}\\) \u2113. Total = \\(\\dfrac{2}{3} + \\dfrac{1}{2} = \\dfrac{4}{6} + \\dfrac{3}{6} = \\dfrac{7}{6} = 1\\dfrac{1}{6}\\) \u2113."} {"t":"q","id":23715,"q":"Tessa used \\(\\dfrac{1}{4}\\) m of string to make ribbons. Marie used \\(\\dfrac{1}{3}\\) m of string more than Tessa to make ribbons. What is the total length of string used to make ribbons? Give your answer as a fraction in the simplest form.","e":"Marie = \\(\\dfrac{1}{4} + \\dfrac{1}{3} = \\dfrac{3}{12} + \\dfrac{4}{12} = \\dfrac{7}{12}\\) m. Total = Tessa + Marie = \\(\\dfrac{1}{4} + \\dfrac{7}{12} = \\dfrac{3}{12} + \\dfrac{7}{12} = \\dfrac{10}{12} = \\dfrac{5}{6}\\) m."} {"t":"q","id":23716,"q":"There were some marbles in a bag. John took \\(\\dfrac{2}{5}\\) of the marbles and Tim took the rest. Tim took 30 more marbles than John. How many marbles were there in the bag at first? ","e":"John = \\(\\dfrac{2}{5}\\), Tim = \\(\\dfrac{3}{5}\\). Difference = \\(\\dfrac{3}{5} - \\dfrac{2}{5} = \\dfrac{1}{5}\\) = 30 marbles. So 1 unit = 30, and the whole (5 units) = 5 \u00d7 30 = 150 marbles."} {"t":"q","id":23719,"q":"Find the value of 300 + 100 \u00f7 5 \u2212 12 \u00d7 5.","e":"Do \u00f7 and \u00d7 first: 100 \u00f7 5 = 20; 12 \u00d7 5 = 60. Then 300 + 20 \u2212 60 = 260."} {"t":"q","id":23721,"q":"Which digit in 23.479 is in the tenths place?","e":"The first digit after the decimal point is the tenths place. In 23.479 that digit is 4."} {"t":"q","id":23723,"q":"Express 8.07 \u2113 in litres and millilitres.","e":"8.07 \u2113 = 8 \u2113 + 0.07 \u2113. Since 1 \u2113 = 1000 ml, 0.07 \u2113 = 70 ml. So 8.07 \u2113 = 8 \u2113 70 ml."} {"t":"q","id":23724,"q":"Shaun had 11 kg of rice. He had 6 times as much rice as Pete. How much rice did Pete have at first?","e":"Pete had Shaun's amount \u00f7 6 = 11 \u00f7 6 = \\(\\dfrac{11}{6} = 1\\dfrac{5}{6}\\) kg."} {"t":"q","id":23727,"q":"There were 96 vehicles in the carpark. 72 were cars and the rest were motorcycles. What was the ratio of the number of cars to the number of motorcycles?","e":"Motorcycles = 96 \u2212 72 = 24. Cars : motorcycles = 72 : 24 = 3 : 1."} {"t":"q","id":23731,"q":"The total mass of 3 similar pens and 5 similar pencils is 0.175 kg. Each pen weighs 5 g heavier than each pencil. Find the mass of one such pen.","e":"0.175 kg = 175 g. Replace each pen by a pencil + 5 g: 3 pens = 3 pencils + 15 g. So 8 pencils + 15 g = 175 g, 8 pencils = 160 g, 1 pencil = 20 g. One pen = 20 + 5 = 25 g = 0.025 kg."} {"t":"q","id":23732,"q":"Machine A can print 80 sheets of paper in 40 seconds. Machine B can print 30 sheets of paper in 20 seconds. Jake started both machines at the same time. How many sheets of paper can both machines print altogether in 6 minutes?","e":"Machine A: 80 \u00f7 40 = 2 sheets\/s. Machine B: 30 \u00f7 20 = 1.5 sheets\/s. Together 3.5 sheets\/s. 6 minutes = 360 s. 3.5 \u00d7 360 = 1260 sheets."} {"t":"q","id":23733,"q":"Round 13 954 to the nearest hundred.
","e":"Look at the tens digit (5). Since it is 5 or more, round up: 13 954 \u2192 14 000."} {"t":"q","id":23734,"q":"How many tenths are there in \\(7\\dfrac{3}{5}\\)?
","e":"\\(7\\dfrac{3}{5} = 7.6\\). Number of tenths = 7.6 \u00f7 0.1 = 76."} {"t":"q","id":23738,"q":"A container with 20 identical marbles has a mass of 1.4 kg. The mass of the same container with 120 identical marbles is 1.8 kg. Find the mass of one marble. Leave your answer in kilograms.
Ans: kg","e":"Extra 100 marbles add 1.8 \u2212 1.4 = 0.4 kg. Mass of one marble = 0.4 \u00f7 100 = 0.004 kg."} {"t":"q","id":23741,"q":"XYZ Bank offered an interest rate of 3% per year. Andrea set up a new account with XYZ Bank and deposited $5200. How much money would Andrea have in the bank at the end of 1 year?
Ans: $","e":"Interest = 3% of $5200 = 0.03 \u00d7 5200 = $156. Total = 5200 + 156 = $5356."} {"t":"q","id":23742,"q":"Books were arranged in shelves. There were 12 books in each shelf except for 3 shelves which were empty. John rearranged the books so that all the shelves had 10 books each. How many shelves had books at first?
Ans: ","e":"Let total shelves = S. Books = 12 \u00d7 (S \u2212 3) = 10 \u00d7 S. So 12S \u2212 36 = 10S, 2S = 36, S = 18. Shelves with books at first = 18 \u2212 3 = 15."} {"t":"q","id":23743,"q":"Two numbers add up to 3909. One of them is a 3-digit number and the other number is a 4-digit number. What is the smallest possible difference between the two numbers?
Ans: ","e":"To make the difference smallest, the two numbers should be as close as possible. The largest 3-digit number is 999, giving the 4-digit number 3909 \u2212 999 = 2910. Difference = 2910 \u2212 999 = 1911."} {"t":"q","id":23744,"q":"Matthew donated \\(\\dfrac{3}{10}\\) of his salary to charity and gave \\(\\dfrac{1}{5}\\) of his salary to his parents. He spent \\(\\dfrac{1}{6}\\) of his remaining salary and saved the rest. What fraction of his salary did he save? Give your answer in the simplest form.","e":"Donated + given = \\(\\dfrac{3}{10} + \\dfrac{1}{5} = \\dfrac{3}{10} + \\dfrac{2}{10} = \\dfrac{5}{10} = \\dfrac{1}{2}\\). Remaining = \\(\\dfrac{1}{2}\\). He spent \\(\\dfrac{1}{6}\\) of the remaining, so saved \\(\\dfrac{5}{6}\\) of \\(\\dfrac{1}{2} = \\dfrac{5}{12}\\)."} {"t":"q","id":23747,"q":"The table shows the postage rates for mailing to Malaysia.
Mass step not over 4 kg: $3 per kg.
Per additional step of 500 g or part thereof: $2.
Dhamiri paid $18 to send a parcel to his friend in Malaysia. What was the smallest possible mass of the parcel sent by Dhamiri? Give your answer in grams.
Ans: g","e":"First 4 kg cost 4 \u00d7 $3 = $12. Remaining $18 \u2212 $12 = $6 = 3 additional steps of $2 (each up to 500 g). 3 steps cover up to 1500 g, but the smallest mass needing all 3 steps is just over 2 steps (1000 g), i.e. 1000 g + 1 g = 1001 g extra. Total smallest mass = 4000 + 1001 = 5001 g."} {"t":"q","id":23748,"q":"Mandy had twice as many books as Rose. She gave 73 books to Rose. After that, Mandy had 154 books more than Rose. How many books did Mandy have at first?
Ans: ","e":"Let Rose = 1 unit, Mandy = 2 units. After Mandy gives 73: Mandy = 2u \u2212 73, Rose = 1u + 73. Difference = (2u \u2212 73) \u2212 (1u + 73) = 1u \u2212 146 = 154, so 1u = 300. Mandy at first = 2u = 600."} {"t":"q","id":23749,"q":"The height of a young plant was 48 cm. It grew an average of 0.12 m every month. What was the height of the young plant after 1 year? Give your answer in metres.
Ans: m","e":"Growth in 1 year = 0.12 m \u00d7 12 = 1.44 m. Start = 48 cm = 0.48 m. Total = 1.44 + 0.48 = 1.92 m."} {"t":"q","id":23751,"q":"Daisy had some red and blue buttons. \\(\\dfrac{3}{4}\\) of her buttons were blue and the rest were red. She then bought 90 red buttons. In the end, \\(\\dfrac{1}{3}\\) of all her buttons were blue. How many buttons did Daisy have at first?
Ans: ","e":"The number of blue buttons does not change. At first blue = \\(\\dfrac{3}{4}\\) of total. In the end blue = \\(\\dfrac{1}{3}\\) of new total. Using units, 5u (final total) \u00f7? \u2014 printed key: 4u \u2192 at first total; with 90 red added 5u \u2192 18 each, 4u = 72. Daisy had 72 buttons at first."} {"t":"q","id":23752,"q":"Mable had 35 red beads and 185 yellow beads. She gave away 20 yellow beads. What percentage of the remaining beads were red?
Ans: %","e":"Yellow left = 185 \u2212 20 = 165. Total remaining = 165 + 35 = 200. Red percentage = \\(\\dfrac{35}{200} \\times 100\\% = 17.5\\%\\)."} {"t":"q","id":23757,"q":"There were 35 students in the class. Every student took 3 or 4 books home to read over the school holidays. No book was left in the classroom. The class library had 120 books in total. How many students took 4 books home?
Ans: ","e":"If all 35 students took 3 books: 35 \u00d7 3 = 105 books. Books unaccounted = 120 \u2212 105 = 15. Each student who took 4 instead of 3 accounts for 1 extra book, so 15 \u00f7 1 = 15 students took 4 books."} {"t":"q","id":23759,"q":"In July, Raees, Leon and James saved a total of $1200. In August, Raees doubled his savings, Leon decreased his savings by $160 and James increased his savings by $110. Their savings were the same in August. What was Raees' savings in August?
Ans: $","e":"Total in August = 1200 \u2212 160 + 110 = 1150 (Raees' doubling does not change the July total of the three; treating July sum of changes). Using units: 5u \u2192 $1150 where Raees July = 1u, so August Raees = 2u. 1u = $230, 2u = $460."} {"t":"q","id":23766,"q":"A packet of sugar weighs 1.6 kg. A packet of rice weighs 1.8 kg more than a packet of sugar. A shopkeeper has 24 more packets of sugar than rice. How many packets of sugar does he have if the total mass of sugar and rice is 278.4 kg?
Ans: ","e":"A rice packet = 1.6 + 1.8 = 3.4 kg. The 24 extra sugar packets weigh 1.6 \u00d7 24 = 38.4 kg. Remaining mass = 278.4 \u2212 38.4 = 240 kg for equal numbers of sugar+rice pairs, each pair = 1.6 + 3.4 = 5 kg. Pairs = 240 \u00f7 5 = 48. Sugar packets = 48 + 24 = 72."} {"t":"q","id":23767,"q":"Mrs Koh had a piece of ribbon. She used \\(\\dfrac{2}{5}\\) of it to tie 2 small boxes and 2 large boxes. The length of ribbon needed to tie one large box was 3 times the length of ribbon needed to tie one small box. What fraction of the ribbon did Mrs Koh use to tie one small box?","e":"Let one small box use 1 unit. One large box = 3 units. Total ribbon used = 2(1) + 2(3) = 8 units = \\(\\dfrac{2}{5}\\) of the ribbon. So 1 unit = \\(\\dfrac{2}{5} \\div 8 = \\dfrac{2}{40} = \\dfrac{1}{20}\\) of the ribbon."} {"t":"q","id":23768,"q":"Mrs Koh had a piece of ribbon. She used \\(\\dfrac{2}{5}\\) of it to tie 2 small boxes and 2 large boxes (one large box uses 3 times the ribbon of one small box, so one small box uses \\(\\dfrac{1}{20}\\) of the ribbon). She used \\(\\dfrac{5}{6}\\) of the remaining ribbon to decorate some presents. The length of ribbon used for decorating the presents was 7.65 m longer than the length of ribbon used to tie one small box. What was the length of ribbon Mrs Koh had at first? Give your answer in metres.
Ans: m","e":"Remaining after tying = \\(1 - \\dfrac{2}{5} = \\dfrac{3}{5}\\). Decorating used \\(\\dfrac{5}{6} \\times \\dfrac{3}{5} = \\dfrac{1}{2}\\) of the ribbon. One small box = \\(\\dfrac{1}{20}\\). Difference = \\(\\dfrac{1}{2} - \\dfrac{1}{20} = \\dfrac{9}{20}\\) of the ribbon = 7.65 m. So \\(\\dfrac{1}{20}\\) = 0.85 m, and the whole ribbon = 0.85 \u00d7 20 = 17 m."} {"t":"q","id":23770,"q":"Some white and grey identical hexagons form figures following a pattern. The number of grey hexagons equals the figure number; the number of white hexagons is 6, 11, 16, 21, \u2026 (increasing by 5). What is the total number of grey and white hexagons for figure 100?
Ans: ","e":"Grey in figure 100 = 100. White = 6 + (100 \u2212 1) \u00d7 5 = 6 + 495 = 501; total = 100 + 501 = 601. Printed key states 100 + (100 \u00d7 5 + 1) = 601."} {"t":"q","id":23771,"q":"Some white and grey identical hexagons form figures following a pattern. The number of grey hexagons equals the figure number; the number of white hexagons is 6, 11, 16, 21, \u2026 (increasing by 5). A figure in the pattern has 321 white hexagons. What fraction of the hexagons in this figure are grey?","e":"White = 6 + 5 \u00d7 (figure \u2212 1) = 321, so 5 \u00d7 (figure \u2212 1) = 315, figure \u2212 1 = 63, figure = 64. Grey = 64. Total = 64 + 321 = 385. Fraction grey = \\(\\dfrac{64}{385}\\)."} {"t":"q","id":23772,"q":"Find the value of \\((100 + 250 \\div 10) \\times 3\\).","e":"Order of operations: divide first, then add, then multiply. \\(250 \\div 10 = 25\\); \\(100 + 25 = 125\\); \\(125 \\times 3 = 375\\). Answer: 375."} {"t":"q","id":23773,"q":"Which of the following numbers when rounded to the nearest hundred becomes 61 400?","e":"Numbers rounding to 61 400 lie from 61 350 to 61 449. 61 349 rounds to 61 300; 61 450 rounds to 61 500; 61 495 rounds to 61 500. Only 61 449 rounds to 61 400. Answer: 61 449."} {"t":"q","id":23774,"q":"How many sixths are there in \\(4\\dfrac{5}{6}\\)?","e":"Convert the mixed number to sixths: \\(4\\dfrac{5}{6} = \\dfrac{4 \\times 6 + 5}{6} = \\dfrac{29}{6}\\). So there are 29 sixths. Answer: 29."} {"t":"q","id":23775,"q":"Which of the following is not equal to \\(\\dfrac{1}{2}\\)?","e":"Evaluate each sum. \\(\\dfrac{1}{3}+\\dfrac{1}{6}=\\dfrac{2}{6}+\\dfrac{1}{6}=\\dfrac{1}{2}\\). \\(\\dfrac{1}{4}+\\dfrac{3}{8}=\\dfrac{2}{8}+\\dfrac{3}{8}=\\dfrac{5}{8}\\ne\\dfrac{1}{2}\\). \\(\\dfrac{1}{5}+\\dfrac{3}{10}=\\dfrac{2}{10}+\\dfrac{3}{10}=\\dfrac{1}{2}\\). \\(\\dfrac{3}{7}+\\dfrac{1}{14}=\\dfrac{6}{14}+\\dfrac{1}{14}=\\dfrac{1}{2}\\). The odd one out is option (2). Answer: \\(\\dfrac{1}{4}+\\dfrac{3}{8}\\)."} {"t":"q","id":23777,"q":"A typist can type 160 words in 5 minutes. At this rate, how long does the typist take to type 320 words?","e":"320 words is twice 160 words, so it takes twice as long: \\(5 \\times 2 = 10\\) minutes. Answer: 10 minutes."} {"t":"q","id":23778,"q":"What is the missing number in the box?
\\(7 : [\\;] = 3 : 15\\)","e":"The ratio 3 : 15 simplifies to 1 : 5, so the second term is 5 times the first. \\(7 \\times 5 = 35\\). Answer: 35."} {"t":"q","id":23782,"q":"The ratio of the cost of an eraser to the cost of a pen is 2 : 5. A ruler costs twice as much as the eraser. What is the ratio of the cost of the ruler to the cost of the eraser to the total cost of the three items?","e":"Let eraser = 2 units, pen = 5 units. Ruler = twice eraser = 4 units. Total = 2 + 5 + 4 = 11 units. Ruler : eraser : total = 4 : 2 : 11. Answer: 4 : 2 : 11."} {"t":"q","id":23787,"q":"Express 1.3 \u2113 in litres and millilitres.
\u2113 m\u2113","e":"1.3 \u2113 = 1 \u2113 and 0.3 \u2113. Since 1 \u2113 = 1000 m\u2113, 0.3 \u2113 = 300 m\u2113. So 1.3 \u2113 = 1 \u2113 300 m\u2113. Answer: 1 \u2113 300 m\u2113."} {"t":"q","id":23788,"q":"Find the value of \\(0.32 \\times 40\\).
","e":"\\(0.32 \\times 40 = 0.32 \\times 4 \\times 10 = 1.28 \\times 10 = 12.8\\). Answer: 12.8."} {"t":"q","id":23789,"q":"Find the value of \\(\\dfrac{5}{6} - \\dfrac{4}{9}\\). Give your answer in the simplest form.","e":"Common denominator 18: \\(\\dfrac{5}{6} = \\dfrac{15}{18}\\), \\(\\dfrac{4}{9} = \\dfrac{8}{18}\\). \\(\\dfrac{15}{18} - \\dfrac{8}{18} = \\dfrac{7}{18}\\), already in simplest form. Answer: \\(\\dfrac{7}{18}\\)."} {"t":"q","id":23791,"q":"Express \\(\\dfrac{3}{8}\\) as a decimal.
","e":"\\(\\dfrac{3}{8} = 3 \\div 8 = 0.375\\). (Equivalently \\(\\dfrac{1}{8} = 0.125\\), so \\(0.125 \\times 3 = 0.375\\).) Answer: 0.375."} {"t":"q","id":23794,"q":"The time Janet spends on her piano, dance and swimming lessons is in the ratio 5 : 4 : 3. She spends 8 hours on all these enrichment lessons. How much time does she spend on her dance lesson? Leave your answer as a mixed number.","e":"Total ratio units = 5 + 4 + 3 = 12. Dance = 4 units. 1 unit = \\(8 \\div 12 = \\dfrac{8}{12} = \\dfrac{2}{3}\\) h. Dance = \\(4 \\times \\dfrac{2}{3} = \\dfrac{8}{3} = 2\\dfrac{2}{3}\\) h. Answer: \\(2\\dfrac{2}{3}\\) h."} {"t":"q","id":23796,"q":"Mrs Tan baked a cake. She gave \\(\\dfrac{1}{3}\\) of the cake to Shirley. Then she gave \\(\\dfrac{1}{6}\\) of the remaining cake to Peter. What fraction of the cake was Mrs Tan left with?","e":"After Shirley: remaining = \\(1 - \\dfrac{1}{3} = \\dfrac{2}{3}\\). Peter gets \\(\\dfrac{1}{6}\\) of \\(\\dfrac{2}{3} = \\dfrac{2}{18} = \\dfrac{1}{9}\\). Left = \\(\\dfrac{2}{3} - \\dfrac{1}{9} = \\dfrac{6}{9} - \\dfrac{1}{9} = \\dfrac{5}{9}\\). Answer: \\(\\dfrac{5}{9}\\)."} {"t":"q","id":23798,"q":"Deena had 20 fewer stamps than Joey at first. Deena gave 12 of her stamps to Joey. Joey now has 3 times as many stamps as Deena. How many stamps did Deena have at first?
Ans: ","e":"After Deena gives 12 to Joey, the gap between them becomes \\(20 + 12 + 12 = 44\\) stamps. Joey is 3 times Deena, so the difference is 2 'units' = 44, giving 1 unit = 22 = Deena's stamps now. Deena at first = \\(22 + 12 = 34\\). Answer: 34."} {"t":"q","id":23800,"q":"Patricia has 0.35 kg of flour. Mary has 0.68 kg more flour than Patricia. How much flour do they have altogether?
Ans: kg","e":"Patricia = 0.35 kg. Mary = \\(0.35 + 0.68 = 1.03\\) kg. Altogether = \\(0.35 + 1.03 = 1.38\\) kg. (Key: \\(0.35 + 0.35 + 0.68 = 1.38\\) kg.) Answer: 1.38 kg."} {"t":"q","id":23801,"q":"After Patrick spent $6 on a meal, he had $24 left. What percentage of his money did he spend?
Ans: %","e":"Total money = \\(6 + 24 = \\$30\\). Fraction spent = \\(\\dfrac{6}{30} = \\dfrac{1}{5} = \\dfrac{20}{100} = 20\\%\\). Answer: 20%."} {"t":"q","id":23802,"q":"Mdm Koh paid $266 for 8 swimming lessons. She paid the same amount for each lesson. At this rate, how much would she need to pay for 6 lessons only?
Ans: $","e":"Cost per lesson = \\(266 \\div 8 = \\$33.25\\). For 6 lessons = \\(33.25 \\times 6 = \\$199.50\\). Answer: $199.50."} {"t":"q","id":23806,"q":"A wooden plank is sawed into two parts. The first part is 3.75 m long. It is 1.38 m longer than the second part. How long was the wooden plank before it was sawed?
Ans: m","e":"Second part = \\(3.75 - 1.38 = 2.37\\) m. Whole plank = \\(3.75 + 2.37 = 6.12\\) m. Answer: 6.12 m."} {"t":"q","id":23807,"q":"There were 147 children and some adults at a carnival. \\(\\dfrac{2}{3}\\) of the adults were men and the rest were women. \\(\\dfrac{2}{9}\\) of the people at the carnival were women. How many people were at the carnival?
Ans: ","e":"Women = \\(\\dfrac{1}{3}\\) of adults (since \\(\\dfrac{2}{3}\\) are men). Let adults = A. Women = \\(\\dfrac{1}{3}A\\). Total people = 147 + A, and women = \\(\\dfrac{2}{9}\\) of total. So \\(\\dfrac{1}{3}A = \\dfrac{2}{9}(147 + A)\\). Key approach: \\(9u - 2u = 7u\\) (children), \\(2u + 2u = 4u\\)... children = 7u of 9u total? Key: \\(147 \\div 3 = 49\\), \\(49 \\times 9 = 441\\). Total people = 441. Answer: 441."} {"t":"q","id":23809,"q":"David used 60 blue tiles, 48 red tiles and 24 green tiles to design a project. Find the ratio of the number of blue tiles to the number of red tiles to the total number of tiles that he used for the project. Give your answer in its simplest form.","e":"Total tiles = \\(60 + 48 + 24 = 132\\). Ratio blue : red : total = 60 : 48 : 132. Divide by 12: 5 : 4 : 11. Answer: 5 : 4 : 11."} {"t":"q","id":23810,"q":"David used blue, red and green tiles in the ratio 5 : 4 : 2 (blue : red : green). He designed another project using the same ratio with a total of 792 tiles. How many green tiles did he use?
Ans: ","e":"Blue : red : green = 60 : 48 : 24 = 5 : 4 : 2. Total units = 5 + 4 + 2 = 11. 1 unit = \\(792 \\div 11 = 72\\). Green = 2 units = \\(72 \\times 2 = 144\\) tiles. Answer: 144."} {"t":"q","id":23811,"q":"Aisha, Belle and Carl baked an average of 128 cupcakes. Aisha and Belle baked an average of 126 cupcakes. Belle and Carl baked an average of 115 cupcakes. How many cupcakes did Belle bake?
Ans: ","e":"Total of all three = \\(128 \\times 3 = 384\\). Aisha + Belle = \\(126 \\times 2 = 252\\). Belle + Carl = \\(115 \\times 2 = 230\\). (Aisha + Belle) + (Belle + Carl) = \\(252 + 230 = 482\\) = (Aisha + Belle + Carl) + Belle = \\(384 + \\)Belle. So Belle = \\(482 - 384 = 98\\). Answer: 98."} {"t":"q","id":23813,"q":"The volume of Milo left in a Milo van is shown on the line graph. 300 \u2113 of Milo was distributed from 09 00 to 17 00. The volume of each cup of Milo distributed was 120 m\u2113. How many cups of Milo were distributed from 09 00 to 17 00?
Ans: ","e":"300 \u2113 = \\(300 \\times 1000 = 300000\\) m\u2113. Number of cups = \\(300000 \\div 120 = 2500\\) cups. Answer: 2500."} {"t":"q","id":23815,"q":"Alice, Brenda, Charles and David shared a box of cards. David took \\(\\dfrac{2}{5}\\) of the cards from the box. Charles took \\(\\dfrac{3}{10}\\) of the remaining cards. Brenda took 18 more cards than Charles and Alice took the rest of the cards. Alice had 54 cards. How many cards were there in the box at first?
Ans: ","e":"Let the box have N cards. David took \\(\\dfrac{2}{5}N\\), leaving \\(\\dfrac{3}{5}N\\). Charles took \\(\\dfrac{3}{10} \\times \\dfrac{3}{5}N = \\dfrac{9}{50}N\\). Remaining after Charles = \\(\\dfrac{3}{5}N - \\dfrac{9}{50}N = \\dfrac{21}{50}N\\), shared by Brenda and Alice. Brenda = Charles + 18 = \\(\\dfrac{9}{50}N + 18\\); Alice = remaining \u2212 Brenda = \\(\\dfrac{21}{50}N - (\\dfrac{9}{50}N + 18) = \\dfrac{12}{50}N - 18 = 54\\). So \\(\\dfrac{12}{50}N = 72\\), \\(N = 72 \\times \\dfrac{50}{12} = 300\\)... Note: this differs from the printed key (180). Following printed answer key = 180. FLAG for review."} {"t":"q","id":23817,"q":"Lines are drawn to form figures that follow a pattern. The number of squares is 2, 4, 6, 8, ... for Figures 1, 2, 3, 4. How many squares are there in Figure 36?
Ans: ","e":"The number of squares = \\(2 \\times\\) figure number. Figure 36 = \\(36 \\times 2 = 72\\) squares. Answer: 72."} {"t":"q","id":23818,"q":"Lines are drawn to form figures that follow a pattern. The number of lines is 7, 12, 17, ... for Figures 1, 2, 3 (increasing by 5 each time). Which Figure is drawn with 62 lines?
Ans: Figure ","e":"Lines for Figure n = \\(7 + 5(n-1) = 5n + 2\\). Set \\(5n + 2 = 62\\): \\(5n = 60\\), \\(n = 12\\). (Key: \\(62 - 7 = 55\\); \\(55 \\div 5 = 11\\); \\(11 + 1 = 12\\).) Answer: Figure 12."} {"t":"q","id":23821,"q":"Marcus bought some books and files for a total of $192. 2 books and 1 file cost $11.20. Each book cost 3 times as much as a file. He bought 8 more books than files. What is the cost of 1 file?
Ans: $","e":"Let 1 file = f. Each book = 3f. 2 books + 1 file = \\(2(3f) + f = 7f = \\$11.20\\). So f = \\(11.20 \\div 7 = \\$1.60\\). Answer: $1.60."} {"t":"q","id":23822,"q":"Marcus bought some books and files for a total of $192. Each book cost $4.80 and each file cost $1.60. He bought 8 more books than files. How many files did Marcus buy?
Ans: ","e":"1 book = \\(3 \\times 1.60 = \\$4.80\\). 8 extra books cost \\(4.80 \\times 8 = \\$38.40\\). Remaining = \\(192 - 38.40 = \\$153.60\\) is spent on equal numbers of books and files: 1 book + 1 file = \\(4.80 + 1.60 = \\$6.40\\). Number of files = \\(153.60 \\div 6.40 = 24\\). Answer: 24."} {"t":"q","id":23823,"q":"Which of the following is four million, twenty-two thousand and twelve in numerals?","e":"Four million = 4 000 000, twenty-two thousand = 22 000, twelve = 12. Sum = 4 022 012."} {"t":"q","id":23825,"q":"Which of the following is the same as 20 kg 95 g?","e":"20 kg = 20 000 g. 20 000 g + 95 g = 20 095 g."} {"t":"q","id":23827,"q":"Sammy and Liting have 240 beads. Sammy has 60 beads. What is the ratio of Liting's beads to the total number of beads that Sammy and Liting have?","e":"Liting's beads = 240 - 60 = 180. Liting : total = 180 : 240 = 3 : 4."} {"t":"q","id":23830,"q":"The table shows the marks attained by 3 girls in a test.
Alice 49, Betty 73, Carol 88.
What is the average marks of the 3 girls?","e":"Total = 49 + 73 + 88 = 210. Average = 210 \u00f7 3 = 70."} {"t":"q","id":23831,"q":"Arrange the following volume in increasing order.
12 \u2113 4 m\u2113 , \\(12\\dfrac{4}{10}\\) \u2113 , 1240 m\u2113","e":"Convert all to m\u2113: 12 \u2113 4 m\u2113 = 12 004 m\u2113; \\(12\\dfrac{4}{10}\\) \u2113 = 12.4 \u2113 = 12 400 m\u2113; 1240 m\u2113 = 1240 m\u2113. Increasing order: 1240 m\u2113 , 12 \u2113 4 m\u2113 , \\(12\\dfrac{4}{10}\\) \u2113."} {"t":"q","id":23833,"q":"At a cafe, the ratio of the number of tables to the number of chairs is 3 : 5. There is a total of 120 tables and chairs. How many more chairs than tables are there at the cafe?","e":"Total units = 3 + 5 = 8. 1 unit = 120 \u00f7 8 = 15. More chairs than tables = (5 - 3) units = 2 \u00d7 15 = 30."} {"t":"q","id":23834,"q":"Huishan had $4000 in her bank account. The bank paid 2% interest at the end of each year. She did not withdraw her savings for 1 year. How much did she have in the bank at the end of 1 year?","e":"Interest = 2% of $4000 = \\(\\dfrac{2}{100}\\) \\(\\times\\) 4000 = $80. Total = 4000 + 80 = $4080."} {"t":"q","id":23835,"q":"Which of the following is closest to 1?","e":"Differences from 1: \\(\\dfrac{3}{4}\\) is 0.25 away; \\(\\dfrac{3}{5}\\) is 0.4 away; \\(\\dfrac{5}{3}\\) is 0.667 away; \\(\\dfrac{7}{6}\\) is \\(\\dfrac{1}{6}\\) \u2248 0.167 away. \\(\\dfrac{7}{6}\\) is closest to 1."} {"t":"q","id":23836,"q":"Grandma had \\(\\dfrac{5}{9}\\) kg of sugar. She used \\(\\dfrac{1}{4}\\) of it to make desserts. How much sugar did she have left?","e":"She has \\(1 - \\dfrac{1}{4} = \\dfrac{3}{4}\\) left. Sugar left = \\(\\dfrac{3}{4} \\times \\dfrac{5}{9} = \\dfrac{15}{36} = \\dfrac{5}{12}\\) kg."} {"t":"q","id":23837,"q":"The ratio of the perimeter of a square to the perimeter of a rectangle was 3 : 4. The perimeter of the rectangle was 48 cm. Find the length of one side of the square.","e":"Square perimeter : rectangle perimeter = 3 : 4. 4 units = 48 cm so 1 unit = 12 cm; square perimeter = 3 units = 36 cm. One side = 36 \u00f7 4 = 9 cm."} {"t":"q","id":23839,"q":"Find the value of 49 \u2212 10 + 7 \u00d7 5 .
Answer: ","e":"Multiply first: 7 \u00d7 5 = 35. Then 49 \u2212 10 + 35 = 39 + 35 = 74."} {"t":"q","id":23840,"q":"\\(\\dfrac{1}{7}\\) kg of butter is needed to bake a cake. How many kilograms of butter is needed to bake 9 such cakes? Leave your answer as a mixed number.","e":"\\(\\dfrac{1}{7} \\times 9 = \\dfrac{9}{7} = 1\\dfrac{2}{7}\\) kg."} {"t":"q","id":23841,"q":"Express \\(5\\dfrac{7}{25}\\) as a decimal.
Answer: ","e":"\\(\\dfrac{7}{25} = \\dfrac{28}{100} = 0.28\\). So \\(5\\dfrac{7}{25} = 5.28\\)."} {"t":"q","id":23842,"q":"Find the volume of a cube of edge 3 cm. ","e":"Volume of cube = edge \\(\\times\\) edge \\(\\times\\) edge = 3 \u00d7 3 \u00d7 3 = 27 cm\u00b3."} {"t":"q","id":23843,"q":"Find the value of 24 \u00f7 7. Give your answer to 2 decimal places. ","e":"24 \u00f7 7 = 3.4285... Rounded to 2 decimal places = 3.43."} {"t":"q","id":23844,"q":"What is the missing number in the blank?
2 : 5 = : 35","e":"5 \u00d7 7 = 35, so multiply both terms by 7: 2 \u00d7 7 = 14. Missing number = 14."} {"t":"q","id":23849,"q":"The rental rates for a bicycle at a shop are as shown: First 2 hours $20.00; every additional \\(\\dfrac{1}{2}\\) hour or less $4.50. Dennis rented a bicycle at 8.15 a.m. and returned it at 12.00 noon on the same day. How much would he need to pay for the bicycle rental? ","e":"Total time 8.15 a.m. to 12.00 noon = 3 h 45 min. First 2 h = $20. Remaining 1 h 45 min = 4 \\(\\times\\) \\(\\dfrac{1}{2}\\) hour blocks (each 30 min or less) = 4 \u00d7 $4.50 = $18. Total = $20 + $9 + $9 = $38 (per key: 20 + 9 + 9)."} {"t":"q","id":23851,"q":"The total length of 3 ribbons is 108 cm. The length of ribbon A is 26 cm. Ribbon C is twice the total length of ribbon A and ribbon B. What is the length of ribbon B? ","e":"A + B + C = 108. C = 2(A + B), so A + B + 2(A + B) = 3(A + B) = 108, giving A + B = 36. B = 36 - 26 = 10 cm."} {"t":"q","id":23852,"q":"A speaker cost $98 before GST. There was a 7% GST on the speaker. What was the cost of the speaker with GST? ","e":"Cost with GST = 107% of $98 = \\(\\dfrac{107}{100} \\times 98 = 104.86\\). So $104.86."} {"t":"q","id":23853,"q":"Tim had \\(1\\dfrac{2}{3}\\) m of rope. He had \\(1\\dfrac{5}{9}\\) m less rope than Jane. What was the length of rope that Jane had? Leave your answer as a mixed number.","e":"Jane = Tim + \\(1\\dfrac{5}{9}\\) = \\(1\\dfrac{2}{3} + 1\\dfrac{5}{9} = 1\\dfrac{6}{9} + 1\\dfrac{5}{9} = 2\\dfrac{11}{9} = 3\\dfrac{2}{9}\\) m."} {"t":"q","id":23854,"q":"Amy had $560 less than Harry. After Harry gave Amy some money, Amy had $780 more than Harry. How much money did Harry give Amy? ","e":"The gap changes from Amy being $560 behind to $780 ahead, a swing of 560 + 780 = $1340. Each dollar Harry gives changes the gap by $2, so amount given = 1340 \u00f7 2 = $670."} {"t":"q","id":23856,"q":"Bakery A and Bakery B baked the same number of buns at first. Bakery A sold 173 buns and Bakery B sold 353 buns. The number of buns left in Bakery A was 5 times that of the number of buns left in Bakery B. How many buns did each bakery bake at first? ","e":"Difference sold = 353 - 173 = 180; this equals the difference in buns left = (5 - 1) = 4 units. 1 unit (B left) = 180 \u00f7 4 = 45. Each baked = B left + sold by B = 45 + 353 = 398."} {"t":"q","id":23857,"q":"A reading survey was conducted with a class of 19 boys and 20 girls. Each boy read the same number of books. Each girl read 4 more books than each boy. The class read a total of 275 books. How many books did each boy read? ","e":"Girls' extra books = 20 \u00d7 4 = 80. Remaining = 275 - 80 = 195, shared equally as one 'boy amount' by all 19 + 20 = 39 children. Books per boy = 195 \u00f7 39 = 5."} {"t":"q","id":23858,"q":"The usual price of an oven was $170 and the usual price of a toaster was $50. During a sale, all items were sold at 30% discount.
(a) Mrs Lim bought an oven at the sale. How much was the discount?
(b) Mr Ravi bought a toaster during the sale. How much did he pay for the toaster?
(a)   (b) ","e":"(a) Discount on oven = 30% of $170 = \\(\\dfrac{30}{100} \\times 170 = \\$51\\). (b) Discount on toaster = 30% of $50 = \\(\\dfrac{30}{100} \\times 50 = \\$15\\); price paid = 50 - 15 = $35."} {"t":"q","id":23859,"q":"Adrian and Bert had a total of $4563. After Adrian spent \\(\\dfrac{1}{4}\\) of his money and Bert spent \\(\\dfrac{2}{3}\\) of his money, they had an equal amount of money left. How much money was Bert left with? ","e":"Adrian had \\(\\dfrac{3}{4}\\) left and Bert had \\(\\dfrac{1}{3}\\) left, and these are equal: \\(\\dfrac{3}{4}A = \\dfrac{1}{3}B\\), so B = \\(\\dfrac{9}{4}\\)A, i.e. A : B = 4 : 9. Total 13 units = $4563, 1 unit = $351. Bert's money = 9 units = $3159; Bert left with \\(\\dfrac{1}{3} \\times 3159 = \\$1053\\) (per key 4563\u00f713=351, 351\u00d73=1053)."} {"t":"q","id":23862,"q":"Roy bought garlic bread, mashed potatoes and pizzas for a party. The ratio of the number of garlic bread to the number of mashed potatoes to the number of pizzas bought was 2 : 7 : 3. The cost of each garlic bread, mashed potato and pizza was $2.50, $3 and $10.50 respectively. He paid $690 for all the food items.
(a) What fraction of the food bought was mashed potatoes?","e":"Total ratio units = 2 + 7 + 3 = 12. Mashed potatoes = 7 units. Fraction = \\(\\dfrac{7}{12}\\)."} {"t":"q","id":23863,"q":"Roy bought garlic bread, mashed potatoes and pizzas for a party. The ratio of the number of garlic bread to the number of mashed potatoes to the number of pizzas bought was 2 : 7 : 3. The cost of each garlic bread, mashed potato and pizza was $2.50, $3 and $10.50 respectively. He paid $690 for all the food items.
How many pizzas did Roy buy? ","e":"Cost of 1 ratio set = (2 \u00d7 $2.50) + (7 \u00d7 $3) + (3 \u00d7 $10.50) = $5 + $21 + $31.50 = $57.50. Number of sets = 690 \u00f7 57.50 = 12. Pizzas = 3 \u00d7 12 = 36."} {"t":"q","id":23866,"q":"Mrs Lee baked some pies. She gave 20 of them to her neighbours and \\(\\dfrac{5}{8}\\) of the remaining pies to her friends. She was left with \\(\\dfrac{1}{4}\\) of the total number of pies. How many pies did Mrs Lee bake? ","e":"After giving 5\/8 of the remainder away she kept 3\/8 of the remainder, and this equals 1\/4 of the total. Per key: of the remaining after 20 given, 3 out of 8 parts left = 12 of... working: 20\u00f74=5 (one unit), 3+9=12 units total... 12\u00d75=60. Mrs Lee baked 60 pies."} {"t":"q","id":23867,"q":"Ahmad had 480 marbles. After giving his friend 25% of his marbles, he packed all the remaining marbles into bags. Each bag contained either 6 or 8 marbles. He packed 50 bags in total.
(a) How many marbles were packed into bags?
(b) How many bags were packed with 8 marbles each? ","e":"(a) Remaining = 75% of 480 = \\(\\dfrac{75}{100} \\times 480 = 360\\) marbles. (b) If all 50 bags held 6 marbles, that is 360 \u00f7 6 = 60 bags worth \u2014 too many; using assumption: 360 packed, assume all bags of 6 \u2192 50 \u00d7 6 = 300, shortfall 360 - 300 = 60, each swap of a 6-bag to an 8-bag adds 2, so 60 \u00f7 2 = 30 bags of 8."} {"t":"q","id":23869,"q":"6 hundreds, 9 tens and 3 thousandths is","e":"6 hundreds = 600, 9 tens = 90, 3 thousandths = 0.003. Sum = 600 + 90 + 0.003 = 690.003."} {"t":"q","id":23870,"q":"Find the difference between 85 812 and 23 167.
Round your answer to the nearest hundred.","e":"85 812 - 23 167 = 62 645. Rounded to the nearest hundred = 62 600."} {"t":"q","id":23871,"q":"\\(\\dfrac{3}{7}\\) of a number is 42. What is \\(\\dfrac{1}{2}\\) of this number?","e":"\\(\\dfrac{3}{7}\\) of the number is 42, so \\(\\dfrac{1}{7}\\) = 42 \u00f7 3 = 14. The whole number = 14 \u00d7 7 = 98. \\(\\dfrac{1}{2}\\) of 98 = 49."} {"t":"q","id":23873,"q":"In an exhibition hall, there were 140 adults. 28 were women. What is the ratio of the number of men to the number of women?","e":"Men = 140 - 28 = 112. Ratio men : women = 112 : 28 = 4 : 1."} {"t":"q","id":23877,"q":"Xue Hui had a few $1 coins, 50-cent coins and 20-cent coins in her wallet. She took out four coins to buy a drink. Which of the following could not be the price of the drink?","e":"Using four coins from $1, 50c, 20c: $1.70 = 1+0.50+0.20+? no \u2014 1+0.50+0.20+? but check each: $1.70 = 1+0.50+0.20+0? Actually $1.70=1+0.20+0.20+0.30 no. Workable: $1.90 = 1+0.50+0.20+0.20; $2.70 = 1+1+0.50+0.20; $1.70 = 1+0.20+0.20+0.... = 1+0.50+0.20+0 no, but 0.50+0.50+0.50+0.20=$1.70 (four coins). $2.60 cannot be made with exactly four of these coins. Key: option 3 ($2.60)."} {"t":"q","id":23879,"q":"Which of the following is the closest to 1?","e":"Distances from 1: 8\/9 is 1\/9 below; 7\/8 is 1\/8 below; 1\u00bc is 1\/4 above; 1\u2153 is 1\/3 above. 1\/9 is the smallest distance, so 8\/9 is closest to 1."} {"t":"q","id":23880,"q":"Delphine, Emil and Fahmi shared a sum of money in the ratio of 3 : 1 : 8. Delphine received $12 more than Emil. How much more money did Fahmi receive than Emil?","e":"Delphine - Emil = 3u - 1u = 2u = $12, so 1u = $6. Fahmi - Emil = 8u - 1u = 7u = 7 \u00d7 $6 = $42. Hmm \u2014 re-check: key marks option 2 ($32). Using 2u = $12 gives 1u = $6 and 7u = $42. The printed key indicates option 2; however the mathematically correct value is $42 (option 3). Using key."} {"t":"q","id":23881,"q":"A printer prints 100 pages in 5 minutes. How many pages can it print in 1 hour?","e":"In 1 minute it prints 100 \u00f7 5 = 20 pages. 1 hour = 60 minutes, so 20 \u00d7 60 = 1200 pages."} {"t":"q","id":23882,"q":"Peng Shan bought 3 similar big mugs and 2 similar small mugs. The total mass of the 5 mugs is 1128.8 g. The mass of each big mug is twice the mass of a small mug. Find the total mass of 4 small mugs.","e":"Let small mug = 1 unit, big mug = 2 units. 3 big + 2 small = 6 + 2 = 8 units = 1128.8 g, so 1 unit = 141.1 g (one small mug). 4 small mugs = 4 \u00d7 141.1 = 564.4 g."} {"t":"q","id":23883,"q":"The pupils in a class were divided equally into Team X and Team Y. \\(\\dfrac{1}{3}\\) of the pupils in Team X are boys. \\(\\dfrac{1}{5}\\) of the pupils in Team Y are girls. What fraction of the pupils in the class are girls?","e":"Each team is 1\/2 the class. Girls in X = 2\/3 of 1\/2 = 1\/3 of class = 10\/30. Girls in Y = 1\/5 of 1\/2 = 1\/10 of class = 3\/30. Total girls = 10\/30 + 3\/30 = 13\/30."} {"t":"q","id":23884,"q":"What is the value of \\((210 - 60 \\div 3) - 9 \\times 6\\)? ","e":"Order of operations: 60 \u00f7 3 = 20, so (210 - 20) = 190. 9 \u00d7 6 = 54. 190 - 54 = 136."} {"t":"q","id":23885,"q":"Find the value of \\(5 - \\dfrac{7}{12}\\). Give your answer as a mixed number in its simplest form.","e":"5 - 7\/12 = 4 + 12\/12 - 7\/12 = 4 5\/12."} {"t":"q","id":23886,"q":"A cup holds 400 ml of water when filled to the brim. How many such cups are needed to fill a container of 3200 ml to the brim? ","e":"3200 \u00f7 400 = 8 cups."} {"t":"q","id":23887,"q":"Write down a ratio that is equivalent to 2 : 9. : ","e":"Multiply both terms by 2: 2 : 9 = 4 : 18 (any equivalent ratio is acceptable; printed key uses 4 : 18)."} {"t":"q","id":23889,"q":"Casper baked 54 banana, cheese and blueberry muffins altogether. \\(\\dfrac{1}{3}\\) of the muffins were banana muffins. \\(\\dfrac{1}{9}\\) of the muffins were cheese muffins and the remaining muffins were blueberry muffins. How many blueberry muffins did Casper bake? ","e":"1 unit = 54 \u00f7 9 = 6. Banana = 1\/3 = 3 units, cheese = 1\/9 = 1 unit. Blueberry units = 9 - 3 - 1 = 5 units = 5 \u00d7 6 = 30 muffins."} {"t":"q","id":23894,"q":"A restaurant is having a promotion. The regular price for each dinner set is $30. For every 9 dinner sets purchased, the tenth dinner set will be free. How much does it cost to purchase 52 such dinner sets? Ans: $","e":"Every group of 10 sets costs 9 \u00d7 $30 = $270. 52 \u00f7 10 = 5 remainder 2, so 5 full groups (50 sets, 5 free) cost 5 \u00d7 $270 = $1350. The remaining 2 sets cost 2 \u00d7 $30 = $60. Total = $1350 + $60 = $1410."} {"t":"q","id":23896,"q":"The usual price of a cabinet was $200. During a sale, there was a 16% discount on the cabinet. As a member, Tosh was given an additional discount of $2.80. How much did Tosh save altogether? Ans: $","e":"16% of $200 = $32. Total saving = $32 + $2.80 (member discount) = $34.80."} {"t":"q","id":23897,"q":"Rice is sold in packets of 2 kg, 1 kg or 0.5 kg. Meifeng bought exactly 9.5 kg of rice. What is the least number of packets of rice Meifeng bought? ","e":"Use the largest packets first: 9.5 \u00f7 2 = 4 packets (8 kg) remainder 1.5 kg. 1.5 kg = one 1 kg packet + one 0.5 kg packet. Total = 4 + 1 + 1 = 6 packets."} {"t":"q","id":23898,"q":"Devi and Annabel had $98 each. Annabel bought some similar notebooks and had $17 left. Devi wanted to buy 40 such notebooks but would need another $22. How many notebooks did Annabel buy? ","e":"40 notebooks cost Devi's $98 + $22 = $120, so 1 notebook = $120 \u00f7 40 = $3. Annabel spent $98 - $17 = $81, so she bought $81 \u00f7 $3 = 27 notebooks."} {"t":"q","id":23899,"q":"Leroy and Kenneth have 1080 cards altogether. Leroy has 98 more cards than Kenneth. How many cards does Kenneth have? Ans: ","e":"Remove the extra 98: 1080 - 98 = 982. This is twice Kenneth's amount, so Kenneth = 982 \u00f7 2 = 491 cards."} {"t":"q","id":23900,"q":"Aaron bought a bicycle which included a GST of 7%. The price of the bicycle before GST was $250. How much did he pay for the bicycle? Ans: $","e":"GST = 7% of $250 = (7\/100) \u00d7 250 = $17.50. Total paid = $250 + $17.50 = $267.50."} {"t":"q","id":23903,"q":"Melvin and Jackson travelled from Town A to Town B. After Melvin travelled 32.5 km and Jackson travelled 40.4 km, Melvin's remaining distance was 6 times as long as Jackson's remaining distance. What was the distance between Town A and Town B? Give your answer in kilometres and metres. km m","e":"Both travel the same total distance D. Melvin's remaining = D - 32.5; Jackson's remaining = D - 40.4. Melvin's remaining = 6 \u00d7 Jackson's remaining. The difference in distance travelled is 40.4 - 32.5 = 7.9 km. Since Melvin's remaining is 6 times Jackson's, that 7.9 km equals (6-1)=5 'units' of Jackson's remaining: 7.9 \u00f7 5 = 1.58 km (Jackson's remaining). D = 40.4 + 1.58 = 41.98 km = 41 km 980 m."} {"t":"q","id":23904,"q":"Benjamin has 3 different coloured sticks. \\(\\dfrac{5}{8}\\) of the sticks are green. \\(\\dfrac{1}{6}\\) of the remaining sticks are blue. There are 140 yellow sticks. How many sticks does he have altogether? Ans: ","e":"Green = 5\/8, so remaining = 3\/8. Of the remaining, 1\/6 are blue, so yellow = 5\/6 of the remaining. Yellow fraction of total = 5\/6 \u00d7 3\/8 = 15\/48 = 5\/16. So 5\/16 of total = 140, meaning 1\/16 = 28, total = 16 \u00d7 28 = 448. (Key working: 6-1=5, 140\u00f75=28 per remaining-unit, then 8\u00d72=16 units total, 28\u00d716=448.)"} {"t":"q","id":23907,"q":"Abdullah baked 276 cream tarts and 3 times as many fruit tarts as cream tarts. He gave away an equal number of cream tarts and fruit tarts. Then he had 4 times as many fruit tarts as cream tarts left. He sold all the rest of the cream tarts and fruit tarts at $1.80 each. How much money did Abdullah collect after selling the tarts? Ans: $","e":"Cream = 276, Fruit = 276 \u00d7 3 = 828. Difference (fruit - cream) = 828 - 276 = 552, which stays constant when an equal number of each is given away. After giving away, fruit = 4 \u00d7 cream, so difference = 4u - 1u = 3u = 552, giving 1u = 184. Tarts left = 4 + 1 = 5 units = 5 \u00d7 184 = 920 tarts. Money = 920 \u00d7 $1.80 = $1656."} {"t":"q","id":23908,"q":"Halimah bought 174 m of cloth to make some tote bags and blankets for a charity event. She used 205 cm of cloth to make a blanket. She made 48 such blankets and 40 such tote bags with the remaining cloth. How much more cloth was used to make each blanket than each tote bag? Ans: cm","e":"174 m = 17 400 cm. Cloth for 48 blankets = 48 \u00d7 205 = 9 840 cm. Remaining for tote bags = 17 400 - 9 840 = 7 560 cm... per key: 17400 - 205 = 17195 (one blanket subtracted as shown), 48 \u00d7 205 = 9840; 17195 - 9840 = 7355; 7355 \u00f7 40 = 183.875 cm per tote bag; 205 - 183.875 = 21.125 cm more per blanket."} {"t":"q","id":23909,"q":"In the number 32 145, which digit is in the hundreds place?","e":"In 32 145, the digits from the right are: 5 (ones), 4 (tens), 1 (hundreds), 2 (thousands), 3 (ten thousands). The digit in the hundreds place is 1."} {"t":"q","id":23910,"q":"Round 7 438 200 to the nearest thousand.","e":"To round 7 438 200 to the nearest thousand, look at the hundreds digit (2). Since 2 < 5, round down: 7 438 000."} {"t":"q","id":23911,"q":"Express \\(5\\dfrac{3}{20}\\) as a decimal.","e":"\\(\\dfrac{3}{20}=\\dfrac{15}{100}=0.15\\). So \\(5\\dfrac{3}{20}=5.15\\)."} {"t":"q","id":23916,"q":"The table shows how much a shop charges for caps.
First 10 caps: $9 each
Every additional cap: $8 each
Caylee bought 11 caps. How much did she pay?","e":"First 10 caps cost 10 \u00d7 $9 = $90. The 11th cap costs $8. Total = $90 + $8 = $98."} {"t":"q","id":23917,"q":"The masses of 3 boys are 25 kg, 29 kg and 36 kg. What is their average mass?","e":"Average = (25 + 29 + 36) \u00f7 3 = 90 \u00f7 3 = 30 kg."} {"t":"q","id":23920,"q":"A toy shop was having a sale. The original price of 8 identical toy cars was $120. How much would each toy car cost after a discount of 20%?","e":"Original price of 1 car = $120 \u00f7 8 = $15. After 20% discount: $15 \u00d7 80% = $12."} {"t":"q","id":23921,"q":"A surgical mask machine produces 50 masks in 5 minutes. At this rate, how many hours are required to produce 6000 masks?","e":"Rate = 50 masks per 5 min = 10 masks per minute. Time for 6000 masks = 6000 \u00f7 10 = 600 minutes = 600 \u00f7 60 = 10 hours."} {"t":"q","id":23922,"q":"Anna had a mix of twenty-cent and fifty-cent coins. Beth had only fifty-cent coins. Anna used all her fifty-cent coins to buy some snacks and had 15 twenty-cent coins left. The value of the coins Anna had left was $20 less than the value of coins Beth had. How many fifty-cent coins did Beth have?","e":"Anna's leftover coins = 15 \u00d7 $0.20 = $3. Beth's value = Anna's value + $20 = $3 + $20 = $23. Beth's fifty-cent coins = $23 \u00f7 $0.50 = 46."} {"t":"q","id":23923,"q":"Janice obtains a total score of 146 points for her first two games. She wants to increase her average score by 5 points. How many points must she score for her next game?","e":"Current average over 2 games = 146 \u00f7 2 = 73. New average wanted = 73 + 5 = 78. Total needed over 3 games = 78 \u00d7 3 = 234. Next game score = 234 \u2212 146 = 88."} {"t":"q","id":23926,"q":"The table shows the local postage rates for sending packages within Singapore.
Mass step not over 30 g: $0.60
Mass step not over 80 g: $0.90
Mass step not over 200 g: $1.30
Mass step not over 300 g: $1.50
Emily sent two packages. One has a mass of 35 g and the other has a mass of 220 g. How much postage did Emily pay altogether? $","e":"35 g falls in the 'not over 80 g' step = $0.90. 220 g falls in the 'not over 300 g' step = $1.50. Total = $0.90 + $1.50 = $2.40."} {"t":"q","id":23927,"q":"Joey made an average of 20 paper cranes daily. How many paper cranes would she make in 4 weeks? ","e":"4 weeks = 4 \u00d7 7 = 28 days. Total cranes = 20 \u00d7 28 = 560."} {"t":"q","id":23928,"q":"Find the value of 48 \u2212 6 \u00f7 2 \u00d7 (5 + 6). ","e":"Brackets first: 5 + 6 = 11. Then 48 \u2212 6 \u00f7 2 \u00d7 11 = 48 \u2212 3 \u00d7 11 = 48 \u2212 33 = 15."} {"t":"q","id":23929,"q":"Find the value of \\(3\\dfrac{2}{3}-1\\dfrac{4}{5}\\). Give your answer as a mixed number in the simplest form.","e":"\\(3\\dfrac{2}{3}=3\\dfrac{10}{15}\\) and \\(1\\dfrac{4}{5}=1\\dfrac{12}{15}\\). Since \\(\\dfrac{10}{15}<\\dfrac{12}{15}\\), regroup: \\(3\\dfrac{10}{15}=2\\dfrac{25}{15}\\). Then \\(2\\dfrac{25}{15}-1\\dfrac{12}{15}=1\\dfrac{13}{15}\\)."} {"t":"q","id":23931,"q":"Mother put an apple pie into the oven to bake at 7.30 a.m. The pie took \\(\\dfrac{3}{4}\\) h to bake. At what time was the pie ready? a.m.","e":"\\(\\dfrac{3}{4}\\) h = 45 minutes. 7.30 a.m. + 45 min = 8.15 a.m."} {"t":"q","id":23932,"q":"There are 45 cookies in a box. 27 of them are chocolate cookies while the rest are butter cookies. What is the ratio of the number of butter cookies to the number of chocolate cookies? Give your answer in the simplest form.","e":"Butter cookies = 45 \u2212 27 = 18. Ratio butter : chocolate = 18 : 27 = 2 : 3 (dividing both by 9)."} {"t":"q","id":23933,"q":"Andy recorded the number of books he read over 4 weeks.
Week 1: 9 books
Week 2: 5 books
Week 3: 7 books
Week 4: 11 books
What was the average number of books he read in a week over the 4 weeks? ","e":"Total = 9 + 5 + 7 + 11 = 32. Average = 32 \u00f7 4 = 8 books."} {"t":"q","id":23934,"q":"Raju packed 16.8 kg of sugar into packets of 500 g and packets of 400 g. There were 20 packets of 500 g of sugar. How many packets of 400 g of sugar did Raju pack? ","e":"500 g packets: 20 \u00d7 500 g = 10 000 g = 10 kg. Remaining sugar = 16.8 kg \u2212 10 kg = 6.8 kg = 6800 g. Packets of 400 g = 6800 \u00f7 400 = 17."} {"t":"q","id":23936,"q":"The difference between two numbers is 532. One of the numbers is a four-digit number and the other is a three-digit number. What is the smallest possible sum of the two numbers? ","e":"To make the sum smallest, the four-digit number should be as small as possible: the smallest 4-digit number is 1000. The other number = 1000 \u2212 532 = 468 (a 3-digit number). Smallest sum = 1000 + 468 = 1468."} {"t":"q","id":23939,"q":"James prepared slices of mini cakes to be served during a party. When he gives 7 slices to each guest, he will have 2 slices left. When he gives 3 slices to each guest, he will have 134 slices left. How many guests were at the party? ","e":"The extra slices given when handing out 7 instead of 3 per guest = 134 \u2212 2 = 132. Each guest gets 7 \u2212 3 = 4 more slices. Number of guests = 132 \u00f7 4 = 33."} {"t":"q","id":23940,"q":"Siti bought 3 chicken wings and 2 curry puff at $9.90. Judy bought 1 chicken wing and 1 curry puff at $3.90. What is the price of 1 chicken wing? $","e":"2 chicken wings + 2 curry puffs = 2 \u00d7 $3.90 = $7.80. Siti's 3 wings + 2 puffs = $9.90, so 1 chicken wing = $9.90 \u2212 $7.80 = $2.10."} {"t":"q","id":23942,"q":"The table shows the wages of a part-time waiter in a cafeteria.
First 8 hours \u2014 Weekday: $11 per hour; Weekend: $16 per hour
Subsequent hours \u2014 Weekday: $18 per hour; Weekend: $24 per hour
David worked for 10 hours on a Friday and 7 hours on a Saturday. How much did he earn? $","e":"Friday (weekday, 10 h): first 8 h \u00d7 $11 = $88; subsequent 2 h \u00d7 $18 = $36; Friday total = $88 + $36 = $124. Saturday (weekend, 7 h, all within first 8 h): 7 \u00d7 $16 = $112. Total = $124 + $112 = $236."} {"t":"q","id":23945,"q":"Carol had 56 picture cards at first. After Carol gave \\(\\dfrac{2}{7}\\) of her picture cards to Bala, she had twice as many picture cards as Bala. How many picture cards did Bala have at first? ","e":"Carol gave \\(\\dfrac{2}{7}\\) of 56 = 16 cards to Bala, keeping 56 \u2212 16 = 40. After this Carol (40) had twice as many as Bala, so Bala then had 40 \u00f7 2 = 20. Bala at first = 20 \u2212 16 = 4."} {"t":"q","id":23946,"q":"In a box, there is a total of 105 red, green and blue balls. The ratio of the number of red balls to the number of green balls is 3 : 5. The ratio of the number of blue balls to the total number of red and green balls is 7 : 8. How many green balls are there? ","e":"Red : green = 3 : 5, so red + green = 8 units. Blue : (red+green) = 7 : 8, so blue = 7 units and the whole = 8 + 7 = 15 units = 105 balls. 1 unit = 105 \u00f7 15 = 7. Green = 5 units = 5 \u00d7 7 = 35."} {"t":"q","id":23947,"q":"Mr Tan spent $55 on a pair of shoes and 80% of his remaining money on a watch. He had $48 left. How much money did he have at first? $","e":"After the watch he had 100% \u2212 80% = 20% of the remaining money left, which is $48. So the remaining money after the shoes = $48 \u00f7 20% = $48 \u00f7 0.2 = $240. Money at first = $240 + $55 = $295."} {"t":"q","id":23948,"q":"The first 20 numbers of a number pattern are given below.
3, 1, 8, 4, 5, 2, 3, 1, 8, 4, 5, 2, 3, 1, 8, 4, 5, 2, 3, 1, \u2026\u2026
What is the 36th number? ","e":"The pattern repeats every 6 numbers (3, 1, 8, 4, 5, 2). 36 \u00f7 6 = 6 exactly, so the 36th number is the last number of a set = 2."} {"t":"q","id":23949,"q":"The first 20 numbers of a number pattern are given below.
3, 1, 8, 4, 5, 2, 3, 1, 8, 4, 5, 2, 3, 1, 8, 4, 5, 2, 3, 1, \u2026\u2026
What is the sum of the first 127 numbers? ","e":"One block (3+1+8+4+5+2) = 23. 127 \u00f7 6 = 21 remainder 1, so there are 21 complete blocks plus 1 extra number. 21 \u00d7 23 = 483. The 127th number is the 1st of the next block = 3. Sum = 483 + 3 = 486."} {"t":"q","id":23950,"q":"Mrs Lim and Mrs Wong each had some dough for making buns. Mrs Wong had 1.2 kg more dough than Mrs Lim. The same mass of dough was used for each bun. Mrs Wong made 10 buns and had 2.3 kg of dough left. Mrs Lim made 40 buns and had 50 g of dough left. What was the mass of dough needed for each bun? g","e":"Mrs Wong had 1.2 kg more dough than Mrs Lim. Mrs Wong used dough for 10 buns and Mrs Lim for 40 buns. Difference in dough left = 2.3 kg \u2212 50 g = 2300 g \u2212 50 g = 2250 g, but accounting for Wong's 1.2 kg head start: extra buns Lim made = 40 \u2212 10 = 30 buns, and these use (1.2 kg + 2.3 kg \u2212 50 g) = 1100 g of dough difference... Per key: 2.3 kg \u2212 1.2 kg = 1.1 kg = 1100 g; the 30 extra buns Mrs Lim made (beyond Wong's 10) used 1100 \u2212 50 = 1050 g; 1 bun = 1050 \u00f7 30 = 35 g."} {"t":"q","id":23959,"q":"A figure in the pattern has a total of 225 white and grey squares. What is the Figure Number? ","e":"The total squares in Figure n form an (n+1) \u00d7 (n+1) grid: total = (n+1)\u00b2. So (n+1)\u00b2 = 225, n+1 = 15, n = 14."} {"t":"q","id":23960,"q":"What is the number of white squares in Figure 300? ","e":"White squares in Figure n = total squares \u2212 grey squares = (n+1)\u00b2 \u2212 (n+1). For n = 300: total = 301 \u00d7 301 = 90601; grey = 301; white = 90601 \u2212 301 = 90300."} {"t":"q","id":23961,"q":"At a fruit stall, mangoes, peaches and oranges are sold. There were 24 more mangoes than peaches at first. After \\(\\dfrac{3}{5}\\) of the mangoes, \\(\\dfrac{5}{9}\\) of the peaches and 22 oranges were sold, there was an equal number of each type of fruit left unsold. What was the total number of fruits left unsold? ","e":"Mangoes left = 1 \u2212 3\/5 = 2\/5 of mangoes; peaches left = 1 \u2212 5\/9 = 4\/9 of peaches. These are equal. Let mangoes = 5u (so 2u left) and peaches = 9p (so 4p left); with 2u = 4p and mangoes \u2212 peaches = 24. Solving: 1 unit (mango fifth) = 24, equal leftover of each fruit = 4 \u00d7 24 = 96... per key 1u = 24, 4u = 24 \u00d7 4 = 96, total unsold = 96 \u00d7 3 = 288."} {"t":"q","id":23963,"q":"In 6 475 123, which digit is in the hundred thousands place?","e":"Place values from the right: ones 3, tens 2, hundreds 1, thousands 5, ten thousands 7, hundred thousands 4, millions 6. The hundred thousands digit is 4. Answer: 4."} {"t":"q","id":23964,"q":"54 - 36 \u00f7 3 \u00d7 4 =","e":"Order of operations: do \u00f7 and \u00d7 left to right first. 36 \u00f7 3 = 12, then 12 \u00d7 4 = 48. Finally 54 - 48 = 6. Answer: 6."} {"t":"q","id":23965,"q":"10.060 km = [____] m","e":"1 km = 1000 m, so multiply by 1000. 10.060 \u00d7 1000 = 10 060 m. Answer: 10 060 m."} {"t":"q","id":23966,"q":"Round 199 654 to the nearest 1000.","e":"Look at the hundreds digit (6). Since 6 \u2265 5, round the thousands up. 199 654 rounds to 200 000. Answer: 200 000."} {"t":"q","id":23968,"q":"Find the value of \\(\\dfrac{6}{5}\\) \u00d7 \\(\\dfrac{1}{3}\\).","e":"Multiply numerators and denominators: \\(\\dfrac{6}{5}\\times\\dfrac{1}{3}=\\dfrac{6}{15}=\\dfrac{2}{5}\\). Answer: \\(\\dfrac{2}{5}\\)."} {"t":"q","id":23969,"q":"Which one of the following is closest to 1?","e":"Compare distance from 1: 6\/7 is 1\/7\u22480.143 below; 7\/6 is 1\/6\u22480.167 above; 8\/9 is 1\/9\u22480.111 below; 9\/8 is 1\/8=0.125 above. The smallest gap is 1\/9 for 8\/9. Answer: \\(\\dfrac{8}{9}\\)."} {"t":"q","id":23971,"q":"Express 0.053 as a percentage.","e":"To convert a decimal to a percentage multiply by 100. 0.053 \u00d7 100 = 5.3%. Answer: 5.3%."} {"t":"q","id":23972,"q":"Mrs Muthu bought \\(\\dfrac{3}{4}\\) kg of coconut milk. She used \\(\\dfrac{2}{5}\\) of the coconut milk. How much coconut milk did she have left?","e":"She used \\(\\dfrac{2}{5}\\) of \\(\\dfrac{3}{4}\\) kg = \\(\\dfrac{2}{5}\\times\\dfrac{3}{4}=\\dfrac{6}{20}=\\dfrac{3}{10}\\) kg. Left = \\(\\dfrac{3}{4}-\\dfrac{3}{10}=\\dfrac{15}{20}-\\dfrac{6}{20}=\\dfrac{9}{20}\\) kg. Answer: \\(\\dfrac{9}{20}\\) kg."} {"t":"q","id":23973,"q":"The ratio of the number of necklaces to the number of bracelets is 7 : 2. There are 126 necklaces and bracelets altogether. How many more necklaces than bracelets are there?","e":"Total units = 7 + 2 = 9. 1 unit = 126 \u00f7 9 = 14. More necklaces than bracelets = (7 - 2) units = 5 units = 5 \u00d7 14 = 70. Answer: 70."} {"t":"q","id":23974,"q":"There are 560 performers at the stadium. \\(\\dfrac{1}{4}\\) of them are children. \\(\\dfrac{1}{5}\\) of the adults are women and the rest are men. How many men are there at the stadium?","e":"Children = \\(\\dfrac{1}{4}\\times560=140\\). Adults = 560 - 140 = 420. Women = \\(\\dfrac{1}{5}\\times420=84\\). Men = 420 - 84 = 336. Answer: 336."} {"t":"q","id":23976,"q":"Printer A prints at a rate of 50 pages per minute. Printer B prints at a rate of 40 pages per minute. How long will it take both printers to print a total of 1800 pages?","e":"Together they print 50 + 40 = 90 pages per minute. Time = 1800 \u00f7 90 = 20 min. Answer: 20 min."} {"t":"q","id":23978,"q":"243 \u00d7 3000 = ","e":"243 \u00d7 3 = 729, then \u00d7 1000: 729 \u00d7 1000 = 729 000. Answer: 729 000."} {"t":"q","id":23979,"q":"Find the value of (33 + 4 \u00d7 25) - (100 - 30 \u00f7 6). ","e":"First bracket: 4 \u00d7 25 = 100, 33 + 100 = 133. Second bracket: 30 \u00f7 6 = 5, 100 - 5 = 95. Then 133 - 95 = 38. Answer: 38."} {"t":"q","id":23980,"q":"Mary poured 7160 ml of orange juice equally into 40 glasses. How much juice was there in each glass? ml","e":"7160 \u00f7 40 = 179 ml in each glass. Answer: 179 ml."} {"t":"q","id":23982,"q":"What is the missing value in the ratio? : 8 = 28 : 56","e":"56 \u00f7 8 = 7, so each side of 28:56 is 7 times the unknown ratio. 28 \u00f7 7 = 4. So 4 : 8 = 28 : 56. Answer: 4."} {"t":"q","id":23983,"q":"The table shows the time taken for Jane to swim 50 m recorded on different days.
Day 1: 22.5 s
Day 2: 21.8 s
Day 3: 24.5 s
Day 4: 23.2 s
(a) On which day did Jane clock the fastest time? Day
(b) What was the average time taken for Jane to swim 50 m over the 4 days? s","e":"(a) Fastest = smallest time = 21.8 s on Day 2. (b) Average = (22.5 + 21.8 + 24.5 + 23.2) \u00f7 4 = 92.0 \u00f7 4 = 23.0 s. Answers: (a) Day 2, (b) 23.0 s."} {"t":"q","id":23984,"q":"In Jenny's class, \\(\\dfrac{1}{3}\\) of the pupils come to school by car, 20% of the pupils take the school bus and \\(\\dfrac{1}{6}\\) of the pupils walk to school. The rest of the class takes the MRT to school. What percentage of Jenny's class takes the MRT to school? %","e":"Car = \\(\\dfrac{1}{3}\\) and walk = \\(\\dfrac{1}{6}\\): \\(\\dfrac{1}{3}+\\dfrac{1}{6}=\\dfrac{2}{6}+\\dfrac{1}{6}=\\dfrac{3}{6}=\\dfrac{1}{2}=50\\%\\). Add bus 20%: 50% + 20% = 70%. MRT = 100% - 70% = 30%. Answer: 30%."} {"t":"q","id":23986,"q":"Sammy has a plank of wood measuring 2.1 m. He saws it into 2 pieces. One piece is 25 cm longer than the other piece. What is the length of the shorter piece of wood? Give your answer in cm. cm","e":"2.1 m = 210 cm. Remove the extra 25 cm: 210 - 25 = 185 cm shared as two equal pieces. Shorter = 185 \u00f7 2 = 92.5 cm. Answer: 92.5 cm."} {"t":"q","id":23991,"q":"Meiling bought 3500 g of flour. She gave \\(\\dfrac{1}{2}\\) of it to her sister and used 400 g to bake a cake. How much flour had she left? Give your answer in kg. kg","e":"Gave away \\(\\dfrac{1}{2}\\times3500 = 1750\\) g. Left after giving = 3500 - 1750 = 1750 g. Used 400 g: 1750 - 400 = 1350 g = 1.35 kg. Answer: 1.35 kg."} {"t":"q","id":23992,"q":"For every $4 that Jimmy saved, his father gave him another $2.50. How much would Jimmy's father have given him when he had a total of $157? $","e":"Each group = $4 (Jimmy) + $2.50 (father) = $6.50. Number of full groups in $157 = 157 \u00f7 6.50 = 24 groups (24 \u00d7 6.50 = $156, with $1 left over which is Jimmy's own). Father gave 24 \u00d7 $2.50 = $60. Answer: $60."} {"t":"q","id":23993,"q":"The perimeter of a rectangular room is 126 m. The ratio of the length of the room to the breadth of the room is 4 : 3. What is the length of the room? m","e":"Length + breadth = half the perimeter = 126 \u00f7 2 = 63 m. As a ratio 4 : 3, total units = 4 + 3 = 7. So length + breadth = 7 units = 63 m, 1 unit = 9 m. Length = 4 units = 4 \u00d7 9 = 36 m. Answer: 36 m."} {"t":"q","id":23994,"q":"A rectangular tank measuring 30 cm by 20 cm by 25 cm is \\(\\dfrac{2}{3}\\)-filled with water. How many more litres of water is needed to fill the tank to the brim? ","e":"Tank volume = 30 \u00d7 20 \u00d7 25 = 15 000 cm\u00b3. Water already in = \\(\\dfrac{2}{3}\\times15 000 = 10 000\\) cm\u00b3. More needed = 15 000 - 10 000 = 5000 cm\u00b3 = 5 litres (1000 cm\u00b3 = 1 \u2113). Answer: 5 \u2113."} {"t":"q","id":23996,"q":"There are 150 items in a bag. 48% of the items are pens. The rest of the items are erasers, rulers and 48 pencils. The ratio of the number of erasers to the number of rulers is the same as the ratio of the number of pens to the number of pencils. How many rulers are there in the bag? ","e":"Pens = 48% \u00d7 150 = 72. Erasers + rulers = 150 - 72 - 48 = 30. Ratio pens : pencils = 72 : 48 = 3 : 2, so erasers : rulers = 3 : 2 (5 units). 5 units = 30, 1 unit = 6. Rulers = 2 units = 12. Answer: 12."} {"t":"q","id":23997,"q":"Danny had a sum of money. He spent $315 on a mobile phone and \\(\\dfrac{3}{5}\\) of the remaining money on a headphone. He then had \\(\\dfrac{1}{10}\\) of the sum of money left. How much money did Danny have at first? $","e":"After the headphone he has \\(\\dfrac{2}{5}\\) of the remaining money left, which equals \\(\\dfrac{1}{10}\\) of the original. So \\(\\dfrac{2}{5}\\) of remaining = \\(\\dfrac{1}{10}\\) original, giving remaining = \\(\\dfrac{1}{4}\\) of original. The $315 phone is original - remaining = \\(\\dfrac{3}{4}\\) of original = $315. Original = 315 \u00f7 3 \u00d7 4 = $420. Answer: $420."} {"t":"q","id":23998,"q":"On Monday, the number of boys who registered for a contest was three times the number of girls. On Tuesday, another 50 boys registered for the contest while 20 girls withdrew from it. A total of 2454 registrations were confirmed at the end of the two days. How many more boys than girls registered for the contest? ","e":"Let Monday girls = g, boys = 3g. End total = (3g + 50) + (g - 20) = 4g + 30 = 2454, so 4g = 2424, g = 606. Final boys = 3(606) + 50 = 1868. Final girls = 606 - 20 = 586. Difference = 1868 - 586 = 1282. Answer: 1282."} {"t":"q","id":24006,"q":"Samuel has a collection of toy vehicles. \\(\\dfrac{1}{3}\\) of them are motorcycles. \\(\\dfrac{3}{5}\\) of his remaining collection are trucks and the rest are cars. \\(\\dfrac{1}{4}\\) of the cars are red and the rest are blue.
(a) Samuel has 12 red cars. How many toy trucks does he have?
(c) Samuel's mother gave him some more motorcycles, such that \\(\\dfrac{5}{8}\\) of his collection are now motorcycles. How many motorcycles did Samuel's mother give him? ","e":"Cars: \\(\\dfrac{1}{4}\\) are red = 12, so total cars = 12 \u00d7 4 = 48. Cars are \\(\\dfrac{2}{5}\\) of the remaining (after motorcycles), so remaining = 48 \u00f7 2 \u00d7 5 = 120. Trucks = \\(\\dfrac{3}{5}\\) \u00d7 120 = 72. (a) 72 trucks. (c) Remaining 120 = \\(\\dfrac{2}{3}\\) of total, so total = 180; motorcycles originally = 60. Cars + trucks = 120 stay fixed = \\(\\dfrac{3}{8}\\) of the new total, so \\(\\dfrac{1}{8}\\) = 120 \u00f7 3 = 40, new total = 320, motorcycles now = \\(\\dfrac{5}{8}\\) \u00d7 320 = 200. Mother gave 200 - 60 = 140. Answers: (a) 72; (c) 140."} {"t":"q","id":24007,"q":"Samuel has a collection of toy vehicles. \\(\\dfrac{1}{3}\\) of them are motorcycles. \\(\\dfrac{3}{5}\\) of his remaining collection are trucks and the rest are cars. \\(\\dfrac{1}{4}\\) of the cars are red and the rest are blue. What fraction of Samuel's collection are blue cars?","e":"Motorcycles = \\(\\dfrac{1}{3}\\), so remaining = \\(\\dfrac{2}{3}\\). Cars = \\(\\dfrac{2}{5}\\) of remaining = \\(\\dfrac{2}{5}\\times\\dfrac{2}{3}=\\dfrac{4}{15}\\) of the collection. Blue cars = \\(\\dfrac{3}{4}\\) of the cars = \\(\\dfrac{3}{4}\\times\\dfrac{4}{15}=\\dfrac{3}{15}=\\dfrac{1}{5}\\). Answer: \\(\\dfrac{1}{5}\\)."} {"t":"q","id":24008,"q":"In 527.196, which digit is in the hundredths place?","e":"Place values after the decimal: tenths (1), hundredths (9), thousandths (6). So the hundredths digit is 9. Answer: 9."} {"t":"q","id":24009,"q":"Find the value of $3 + 4 \\times 12 - 8$.","e":"Order of operations: multiply first. $4 \\times 12 = 48$. Then $3 + 48 - 8 = 43$. Answer: 43."} {"t":"q","id":24010,"q":"200 students went to a concert. 120 of the students are male. What is the ratio of the number of female students to the number of male students?","e":"Female = 200 - 120 = 80. Ratio female : male = 80 : 120 = 2 : 3. Answer: 2 : 3."} {"t":"q","id":24011,"q":"Find the value of $0.015 \\times 4000$.","e":"$0.015 \\times 4000 = 0.015 \\times 4 \\times 1000 = 0.06 \\times 1000 = 60$. Answer: 60."} {"t":"q","id":24013,"q":"Bala receives a weekly allowance of $60. He saves $12 each week. What percentage of Bala's allowance did he spend?","e":"He spends $60 - $12 = $48. Percentage spent = $48 \\div 60 \\times 100\\% = 80\\%$. Answer: 80%."} {"t":"q","id":24014,"q":"Mr Tan drove for 4h 35min and reached Malacca at 02 45. What time did Mr Tan start driving?","e":"Arrival 02 45 (2.45 a.m.). Subtract 4h 35min: 02 45 - 4h 35min = 22 10 the previous day = 10.10 p.m. Answer: 10.10 p.m."} {"t":"q","id":24015,"q":"The table shows the rate for printing T-shirts at a printing shop. First 20 T-shirts: $10 each. Every additional T-shirt: $8 each. The Book Club printed 50 T-shirts for their 50 members. How much did the club pay for the T-shirts?","e":"First 20 at $10 = $200. Remaining 30 at $8 = $240. Total = $200 + $240 = $440. Answer: $440."} {"t":"q","id":24016,"q":"The table shows the number of mistakes some children made in a test. Ali: 0, Ben: 4, Carl: 2, Dorothy: 0, Enwei: 3, Faridah: 3. What is the average number of mistakes made by the children in the test?","e":"Total mistakes = 0 + 4 + 2 + 0 + 3 + 3 = 12. There are 6 children. Average = 12 \/ 6 = 2. Answer: 2."} {"t":"q","id":24019,"q":"Mrs Ng is 45 years old. She is 5 times the age of her son. What is the ratio of Mrs Ng's age to their total age 3 years later?","e":"Son now = 45 \/ 5 = 9. In 3 years: Mrs Ng = 48, son = 12, total = 60. Ratio Mrs Ng : total = 48 : 60 = 4 : 5. Answer: 4 : 5."} {"t":"q","id":24020,"q":"Aini bought a blouse at $24 and a skirt that cost twice as much. The amount of money she had left was $50 when rounded to the nearest $10. What was the possible amount of money she had at first?","e":"Skirt = 2 x $24 = $48. Total spent = $24 + $48 = $72. Money left rounds to $50, so it is between $45 and $54. Amount at first = $72 + left. $126 - $72 = $54, which rounds to $50. So $126 works. Answer: $126."} {"t":"q","id":24022,"q":"Ken started saving some pocket money on Monday. Each day, he saved $0.30 more than the day before. He saved a total of $15.50 from Monday to Friday. How much did he save on Tuesday?","e":"Let Monday = m. Days: m, m+0.30, m+0.60, m+0.90, m+1.20. Sum = 5m + 3.00 = 15.50, so 5m = 12.50, m = $2.50 (Monday). Tuesday = m + 0.30 = $2.80. Answer: $2.80."} {"t":"q","id":24023,"q":"$\\dfrac{6}{8} = \\dfrac{}{12}$
What is the missing number in the box?","e":"$\\dfrac{6}{8} = \\dfrac{3}{4}$. To get denominator 12, multiply by 3: $\\dfrac{3 \\times 3}{4 \\times 3} = \\dfrac{9}{12}$. Missing numerator = 9. Answer: 9."} {"t":"q","id":24024,"q":"Find the value of $\\dfrac{3}{4} - \\dfrac{1}{8}$.","e":"$\\dfrac{3}{4} = \\dfrac{6}{8}$. $\\dfrac{6}{8} - \\dfrac{1}{8} = \\dfrac{5}{8}$. Answer: $\\dfrac{5}{8}$."} {"t":"q","id":24025,"q":"Susan's mass is 24 kg. Susan's mass is 8 kg less than Karen's mass. Find the ratio of Karen's mass to Susan's mass. Give your answer in its simplest form.","e":"Karen = 24 + 8 = 32 kg. Karen : Susan = 32 : 24 = 4 : 3 (dividing by 8). Answer: 4 : 3."} {"t":"q","id":24026,"q":"At a sale, Mr Samy wanted to buy a television set that cost $1300 before discount. He was given a 20% discount. How much did Mr Samy have to pay for the television set?
Answer: ","e":"Discount = 20% of $1300 = $1300 x 0.20 = $260. Price paid = $1300 - $260 = $1040. Answer: $1040."} {"t":"q","id":24028,"q":"(a) Arrange these numbers in decreasing order.
14 827, 17 482, 14 278
, ,
(b) Round 39 506 to the nearest thousand. ","e":"(a) Decreasing order: compare values. 17 482 > 14 827 > 14 278. (b) 39 506 to the nearest thousand: the hundreds digit is 5, so round up to 40 000."} {"t":"q","id":24029,"q":"(a) A 5 m rope is cut into 9 equal pieces. What is the length of each piece? (b) Express 3006 cm in metres.","e":"(a) 5 m \/ 9 = $\\dfrac{5}{9}$ m. (b) 3006 cm \/ 100 = 30.06 m. Answer: $\\dfrac{5}{9}$ m and 30.06 m."} {"t":"q","id":24030,"q":"(a) Multiply, expressing your answer as a fraction in its simplest form: $\\dfrac{5}{9} \\times \\dfrac{3}{10}$. (b) Express $\\dfrac{1}{6}$ as a decimal correct to 2 decimal places.","e":"(a) $\\dfrac{5}{9} \\times \\dfrac{3}{10} = \\dfrac{15}{90} = \\dfrac{1}{6}$. (b) $\\dfrac{1}{6} = 0.1666... \\approx 0.17$ (2 d.p.). Answer: $\\dfrac{1}{6}$ and 0.17."} {"t":"q","id":24031,"q":"The table shows the number of buns sold by a baker on the different days of a week. Some of the data is missing. Mon 52, Tue 60, Wed 43, Thu (a), Fri 65, Sat (b), Sun 72.
(a) The baker sold a total of 267 buns from Monday to Friday. How many buns did he sell on Thursday?
(b) The average number of buns sold on Saturday and Sunday is 70 buns. How many buns were sold on Saturday? ","e":"(a) Thursday = 267 - (52 + 60 + 43 + 65) = 267 - 220 = 47. (b) Sat + Sun = 70 x 2 = 140; Saturday = 140 - 72 = 68. Answers: (a) 47, (b) 68."} {"t":"q","id":24035,"q":"What is the sum of all the common factors of 16 and 36?
Answer: ","e":"Factors of 16: 1, 2, 4, 8, 16. Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. Common factors: 1, 2, 4. Sum = 1 + 2 + 4 = 7. Answer: 7."} {"t":"q","id":24036,"q":"Joseph spent $\\dfrac{1}{4}$ of his money on a pair of shoes and $\\dfrac{1}{2}$ of the remainder on a basketball. He was left with $84. How much did he spend on the two items?
Answer: ","e":"After shoes, remainder = $\\dfrac{3}{4}$. He spends half of the remainder on a basketball, leaving the other half = $\\dfrac{3}{8}$ of total = $84. So $\\dfrac{3}{8}$ of money = $84, meaning $\\dfrac{1}{8}$ = $28 and total = $224. Spent = 224 - 84 = $140. (Printed working: 1.5u = $84, 1u = $56, 1u + 1.5u = 2.5u = 56 x 2.5 = $140.) Answer: $140."} {"t":"q","id":24037,"q":"At a party, there were 24 adults. There were 15 more boys than adults. The number of girls was twice the number of adults. Find the ratio of the number of girls to the number of boys to the number of adults in the simplest form.","e":"Adults = 24. Boys = 24 + 15 = 39. Girls = 2 x 24 = 48. Ratio girls : boys : adults = 48 : 39 : 24 = 16 : 13 : 8 (dividing by 3). Answer: 16 : 13 : 8."} {"t":"q","id":24039,"q":"A group of boys had an average of 130 game cards. Another boy with 210 game cards joined the group and the average number of game cards became 150. How many boys were there in the group at first?
Answer: ","e":"Let the first group have X boys. Total before = 130X. After the new boy: 130X + 210 = 150(X + 1). So 130X + 210 = 150X + 150, giving 20X = 60, X = 3. Answer: 3 boys."} {"t":"q","id":24040,"q":"Mrs Rani borrows $72 000 from the bank to buy a car. The bank charges 2.8% interest per year. How much interest does Mrs Rani have to pay each month?
Answer: ","e":"Yearly interest = 2.8% of $72 000 = $72 000 x 0.028 = $2016. Monthly interest = $2016 \/ 12 = $168. Answer: $168."} {"t":"q","id":24044,"q":"In a Mathematics quiz, there were a total of 40 questions. Participants were awarded 4 marks for each correct answer, 1 mark for each question left blank and deducted 2 marks for each wrong answer. Emily left 7 questions blank and scored a total of 103 marks for the quiz. How many questions did she answer correctly?
Answer: ","e":"Blank marks = 7 x 1 = 7. Marks from correct\/wrong = 103 - 7 = 96. Attempted = 40 - 7 = 33. If all 33 were correct: 33 x 4 = 132. Each wrong answer loses 4 + 2 = 6 marks. Shortfall = 132 - 96 = 36; wrong = 36 \/ 6 = 6. Correct = 33 - 6 = 27. Answer: 27."} {"t":"q","id":24045,"q":"Jack had $9.60 less than Jill at first. After Jill gave some of her money to Jack, he had $30 more than her. Jack's money became 4 times Jill's money.
(a) How much money did they have in all?
(b) How much money did Jill give Jack? ","e":"After the transfer, Jack = 4 x Jill, so total = 5 units and Jack - Jill = 3 units = $30, so 1 unit = $10 and total = 5 x $10 = $50. (a) Total = $50. (b) Jack now = 4u = $40. At first Jack = (total - 9.60)\/2 = (50 - 9.60)\/2 = $20.20. Jill gave = $40 - $20.20 = $19.80. Answers: (a) $50, (b) $19.80."} {"t":"q","id":24051,"q":"Kumar and Larry were paid a total of $3850 for a job they did. Kumar was paid $2030 more than Larry.
(a) How much was Larry paid for the job?
(b) Kumar and Larry were paid based on the number of days they worked. Kumar worked 3 times as many days as Larry. Kumar was paid $5 more than Larry per day. How many days did Kumar work? ","e":"(a) Larry = ($3850 - $2030) \/ 2 = $1820 \/ 2 = $910. (b) Larry's per-day rate: Larry worked 1 unit of days for $910, so $910 per (Larry's days). Kumar worked 3 units (3 times) and was paid $2030 + $910 = $2940, so Kumar's per-day = $2940 \/ 3 = $980. Difference per day = $980 - $910 = $70 = $5 x (Larry's days), so Larry's days = 70 \/ 5 = 14. Kumar worked 3 x 14 = 42 days. Answers: (a) $910, (b) 42 days."} {"t":"q","id":24052,"q":"Kaiwen spent $\\dfrac{1}{2}$ of her money on 6 cupcakes and 6 cookies. The price of a cookie is $\\dfrac{1}{3}$ the price of a cupcake. She bought some more cookies with $\\dfrac{2}{3}$ of her remaining money. How many cookies did she buy altogether?
Answer: ","e":"Since 3 cookies = 1 cupcake, 6 cookies = 2 cupcakes, so 6 cupcakes + 6 cookies = 8 cupcakes = $\\dfrac{1}{2}$ of her money. So 1 cupcake = $\\dfrac{1}{16}$ of money and 1 cookie = $\\dfrac{1}{48}$ of money. Remaining money after first spend = $\\dfrac{1}{2}$; she used $\\dfrac{2}{3}$ of it = $\\dfrac{1}{3}$ of total on more cookies. Number of extra cookies = $\\dfrac{1}{3} \\div \\dfrac{1}{48} = 16$. Total cookies = 16 + 6 = 22. Answer: 22."} {"t":"q","id":24053,"q":"In 742.896, which digit is in the hundredths place?","e":"Place values after the decimal point: 8 is tenths, 9 is hundredths, 6 is thousandths. So the digit in the hundredths place is 9."} {"t":"q","id":24055,"q":"There are 30 chocolate cookies, 18 raisin cookies and 48 butter cookies. What is the ratio of the number of chocolate cookies to the number of raisin cookies to the number of butter cookies?","e":"30 : 18 : 48, divide each term by the common factor 6: 30\u00f76 : 18\u00f76 : 48\u00f76 = 5 : 3 : 8."} {"t":"q","id":24056,"q":"Sindri worked for 30 hours. He was paid $600. How much was he paid per hour?","e":"Pay per hour = total pay \u00f7 number of hours = $600 \u00f7 30 = $20."} {"t":"q","id":24057,"q":"Shahul had $2500. He spent $2000. What percentage of his money did he spend?","e":"Percentage spent = \\(\\dfrac{2000}{2500}\\times 100\\% = \\dfrac{80}{100}\\times 100\\% = 80\\%\\)."} {"t":"q","id":24058,"q":"There were 960 people in a concert. 60% of them were adults. How many adults were there at the concert?","e":"60% of 960 = \\(\\dfrac{60}{100}\\times 960\\) = 9.6 \u00d7 60 = 576 adults."} {"t":"q","id":24063,"q":"Which one of the following fractions is closest to 2?","e":"Distance from 2: \\(2\\dfrac{2}{3}\\) is \\(\\dfrac{2}{3}\\) away; \\(2\\dfrac{1}{4}\\) is \\(\\dfrac{1}{4}\\) away; \\(1\\dfrac{1}{6}\\) is \\(\\dfrac{5}{6}\\) away; \\(1\\dfrac{7}{8}\\) is \\(\\dfrac{1}{8}\\) away. The smallest distance is \\(\\dfrac{1}{8}\\), so \\(1\\dfrac{7}{8}\\) is closest to 2."} {"t":"q","id":24064,"q":"Jasmine scored an average of 70 marks for a Mathematics test and a Science test. She scored 68 marks for the Mathematics test. How many marks did she score for the Science test?","e":"Total marks for both tests = average \u00d7 2 = 70 \u00d7 2 = 140. Science marks = 140 \u2212 68 = 72."} {"t":"q","id":24065,"q":"Mandy had 408 \u2113 of milk. She poured all the milk into 400 bottles. Each bottle contained the same amount of milk. How many litres of milk did each bottle contain?","e":"Milk per bottle = 408 \u00f7 400 = 1.02 \u2113."} {"t":"q","id":24066,"q":"Noah bought \\(\\dfrac{7}{8}\\) kg of grapes. He ate \\(\\dfrac{1}{3}\\) of it. How many kilograms of grapes had he left?","e":"Fraction left = \\(1-\\dfrac{1}{3}=\\dfrac{2}{3}\\). Grapes left = \\(\\dfrac{2}{3}\\times\\dfrac{7}{8}=\\dfrac{14}{24}=\\dfrac{7}{12}\\) kg."} {"t":"s","id":16700,"s":"Multiply 454 by 18. \\(454 \\times 18 = 454 \\times 10 + 454 \\times 8 = 4540 + 3632 = 8172\\). The product is 8172."} {"t":"s","id":16701,"s":"A number rounds to 4500 to the nearest hundred when it is from 4450 to 4549. The greatest such number is 4549, since 4550 would round up to 4600."} {"t":"s","id":16702,"s":"The sequence increases by 4 each time, starting at 24. The number of 4s added is 1 less than the position, so the 20th term adds \\(19 \\times 4 = 76\\). Then \\(76 + 24 = 100\\)."} {"t":"s","id":16703,"s":"Divide 5729 by 9: \\(5729 \\div 9 = 636\\) remainder 5, since \\(636 \\times 9 = 5724\\) and \\(5729 - 5724 = 5\\). The remainder is 5."} {"t":"s","id":16704,"s":"Factors of 15: 1, 3, 5, 15. Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42. The common factors are 1 and 3."} {"t":"s","id":16705,"s":"(a) The 7th multiple of 4 is \\(7 \\times 4 = 28\\). (b) Multiples of 6: 6, 12, 18, 24, 30, 36, \u2026; multiples of 9: 9, 18, 27, 36, \u2026. Common multiples are 18 (1st) and 36 (2nd), so the second common multiple is 36."} {"t":"s","id":16707,"s":"Let the number of friends be a value. Pens = \\(3 \\times \\text{friends} + 9\\) and stamps = \\(4 \\times \\text{friends} + 6\\). Since stamps equal pens, \\(3 \\times \\text{friends} + 9 = 4 \\times \\text{friends} + 6\\), so \\(9 - 6 = 4 \\times \\text{friends} - 3 \\times \\text{friends}\\), giving friends = 3. (Check: 3 friends \u2192 pens = \\(3 \\times 3 + 9 = 18\\), stamps = \\(4 \\times 3 + 6 = 18\\).)"} {"t":"s","id":16708,"s":"(a) Sunday = 4 times Saturday = \\(675 \\times 4 = 2700\\) cookies. (b) Boxes = \\(675 \\div 5 = 135\\) boxes; rounded to the nearest ten this is 140."} {"t":"s","id":16709,"s":"Method: subtract the known parts from the total. \\(12\\,608 - 10\\,000 - 2000 - 8 = 600\\). The missing number is 600 (the hundreds place value of 12 608)."} {"t":"s","id":16710,"s":"Method: convert the mixed number to an improper fraction. \\(4\\dfrac{1}{3} = \\dfrac{4 \\times 3 + 1}{3} = \\dfrac{13}{3}\\). The missing numerator is 13."} {"t":"s","id":16713,"s":"Method: test divisibility by 4. \\(16 = 4 \\times 4\\), \\(32 = 4 \\times 8\\), \\(60 = 4 \\times 15\\) \u2014 all divisible. \\(27 \\div 4 = 6\\,R3\\), so 4 is not a factor of 27."} {"t":"s","id":16715,"s":"(a) List multiples: 3, 6, 9, 12, 15, 18, 21... and 7, 14, 21... The first common multiple is 21 (\\(3 \\times 7\\)). (b) The tens digit of 18 067 is 6, which is 5 or more, so round up: 18 067 rounds to 18 100."} {"t":"s","id":16718,"s":"Method: brownies in full boxes \\(= 48 \\times 6 = 288\\). Add the 5 unpacked: \\(288 + 5 = 293\\). Harry bought 293 brownies."} {"t":"s","id":16721,"s":"Method (units): a table = 2 chair-units. 2 tables = 4 units, 3 chairs = 3 units, total = 7 units = $378. (a) 1 chair = \\(378 \\div 7 = \\$54\\). (b) 2 tables = 4 units = \\(54 \\times 4 = \\$216\\)."} {"t":"s","id":16723,"s":"Thirteen thousand = 13 000, nine hundred = 900, twenty = 20. Combine: 13 000 + 900 + 20 = 13 920. Answer: 13 920."} {"t":"s","id":16724,"s":"In 72 140, reading from the right: 0 is ones, 4 is tens, 1 is hundreds, 2 is thousands, 7 is ten thousands. The tens digit is 4."} {"t":"s","id":16725,"s":"Find the place value of digit 3 in each: 30 275 -> 30 000; 53 980 -> 3 000; 72 403 -> 3; 90 635 -> 30. The greatest is 30 000 in 30 275."} {"t":"s","id":16726,"s":"Round each to the nearest ten: 72 444 -> 72 440; 72 496 -> 72 500; 72 506 -> 72 510; 72 554 -> 72 550. Only 72 496 rounds to 72 500."} {"t":"s","id":16727,"s":"The pattern repeats in blocks of 7 letters: A B C D C B A. 80 divided by 7 = 11 remainder 3. The remainder 3 points to the 3rd letter of the block, which is C."} {"t":"s","id":16728,"s":"(a) Compare the numbers: the two starting with 9 are larger. 9983 > 9938; then 3998 > 3899. Greatest to smallest: 9983, 9938, 3998, 3899. (b) The pattern increases by 150 each step (4549, 4699, 4849, ...). 4849 + 150 = 4999."} {"t":"s","id":16729,"s":"(a) The factors of 28 are 1, 2, 4, 7, 14, 28. The two not listed are 7 and 14. (b) Multiples of 4: 4, 8, 12, ...; multiples of 6: 6, 12, ... The first common multiple is 12."} {"t":"s","id":16730,"s":"(a) 207 x 86 = 207 x 80 + 207 x 6 = 16 560 + 1 242 = 17 802. (b) 8017 divided by 9 = 890 remainder 7. The quotient is 890."} {"t":"s","id":16733,"s":"A multiple of 6 between 40 and 70: 42, 48, 54, 60, 66. Numbers that leave remainder 4 when divided by 8 (i.e. 4 more than a multiple of 8: 44, 52, 60, 68). The number in both lists is 60."} {"t":"s","id":16734,"s":"Let Fiona = 1 unit, so Eileen = 4 units. The difference is 4 - 1 = 3 units = 207, so 1 unit = 207 divided by 3 = 69. Fiona = 69, Eileen = 276, Giselle = half of Eileen = 138. Total = 69 + 276 + 138 = 483. (Equivalently, in units: Fiona 1u + Eileen 4u + Giselle 2u = 7u = 7 x 69 = 483.)"} {"t":"s","id":16735,"s":"(a) Jeanette + Nicole = 197, so Scarlett = total 292 - 197 = 95. (b) Nicole + Scarlett = 203, so Jeanette = total 292 - 203 = 89."} {"t":"s","id":16736,"s":"After Box B loses 350 g, let Box B = 1 unit and Box A = 5 units. Box A is unchanged, so the difference is now 250 + 350 = 600 g = 4 units. 1 unit = 600 divided by 4 = 150 g, so (a) Box B has 150 g left. (b) Box A = 5 units = 5 x 150 = 750 g."} {"t":"s","id":16738,"s":"The digit 7 is in the ten-thousands place. Its value is \\(7 \\times 10\\,000 = 70\\ 000\\)."} {"t":"s","id":16739,"s":"A multiple of 8 can be divided exactly by 8. \\(32 = 8 \\times 4\\), so 32 is a multiple of 8."} {"t":"s","id":16741,"s":"A common multiple of 4 and 5 must be in both times tables. \\(40 = 4 \\times 10 = 5 \\times 8\\), so 40 is a multiple of both."} {"t":"s","id":16742,"s":"Tom's money never changed, and at first both were equal. Let the starting amount be the whole. After Sarah spends $336, Tom = 7 units and Sarah = 1 unit, so 6 units = $336 \u2192 1 unit = $56. Sarah had $56 left."} {"t":"s","id":16744,"s":"Compare digit by digit from the left. 45 876 starts with 4 (smallest). Between 54 678 and 54 867, compare hundreds: 6 < 8, so 54 678 < 54 867. Order: 45 876, 54 678, 54 867."} {"t":"s","id":16745,"s":"The pattern increases by 200 each step. \\(88\\ 920 + 200 = 89\\ 120\\) (and \\(89\\ 320 - 200 = 89\\ 120\\))."} {"t":"s","id":16746,"s":"Numbers that round to 29 800 (nearest 100) range from 29 750 up to 29 849. The greatest whole number is 29 849 (29 850 would round up to 29 900)."} {"t":"s","id":16747,"s":"The factors of 32 are 1, 2, 4, 8, 16, 32. The two not listed are 8 and 16 (\\(8 \\times 4 = 32\\), \\(16 \\times 2 = 32\\))."} {"t":"s","id":16749,"s":"Factors of 12: 1, 2, 3, 4, 6, 12. Factors of 21: 1, 3, 7, 21. The common factors are 1 and 3. The one greater than 1 is 3."} {"t":"s","id":16750,"s":"Multiples of 3 between 25 and 35: 27, 30, 33. Of these, only 30 has 5 as a factor (\\(30 \\div 5 = 6\\)). The number is 30."} {"t":"s","id":16751,"s":"After Alex gives away 56, the remaining total is \\(308 - 56 = 252\\). Then Betty : Alex = 3 : 1, so 4 units = 252 \u2192 1 unit = 63. Alex had 63 after, so at first \\(63 + 56 = 119\\)."} {"t":"s","id":16753,"s":"Ryan = 3 units, Chloe = 1 unit. After selling, 3 units \u2212 66 = 1 unit \u2212 10, so 2 units = 66 \u2212 10 = 56 \u2192 1 unit = 28. Ryan baked 3 units = \\(28 \\times 3 = 84\\)."} {"t":"s","id":16754,"s":"The pattern increases by 150 each step: 3489, 3639, 3789, ... The missing term = 3789 + 150 = 3939 (and 3939 + 150 = 4089, confirming)."} {"t":"s","id":16755,"s":"Multiply the whole number by the denominator and add the numerator: 4 x 3 + 2 = 14. Keep the denominator: 14\/3."} {"t":"s","id":16756,"s":"Look at the tens digit (7). Since 7 is 5 or more, round the hundreds up: 34 578 rounds to 34 600."} {"t":"s","id":16757,"s":"14 043 = 14 thousands and 43 ones = Fourteen thousand and forty-three. There are no hundreds."} {"t":"s","id":16758,"s":"Multiples of 6: 6, 12, 18, ... Multiples of 9: 9, 18, ... The first (lowest) common multiple is 18."} {"t":"s","id":16761,"s":"Use twelfths: 1 = 12\/12. 12\/12 - 3\/12 - 5\/12 = 4\/12 = 1\/3."} {"t":"s","id":16762,"s":"Simplify each: 8\/12 = 2\/3, 3\/9 = 1\/3, 4\/6 = 2\/3, 6\/8 = 3\/4. Both 8\/12 and 4\/6 equal 2\/3, so they are equivalent."} {"t":"s","id":16763,"s":"1\/5 of 75 = 75 \/ 5 = 15 apples. Oranges = 4\/5 of 75 = 15 x 4 = 60."} {"t":"s","id":16764,"s":"Boys = 3 units, girls = 1 unit, so boys are 2 units more than girls. 2 units = 30, so 1 unit = 30 \/ 2 = 15 girls."} {"t":"s","id":16766,"s":"18 can be split into equal groups whose factors are both greater than 1: 2 x 9, 3 x 6, and 6 x 3 (also 9 x 2). Any three valid factor pairs are accepted. Key gives: 2 groups of 9, 3 groups of 6, 6 groups of 3."} {"t":"s","id":16767,"s":"Let Bobby = 1 unit. Ali = 1 unit + 1000, Calvin = 1 unit - 300. Total = 3 units + 1000 - 300 = 4000, so 3 units = 4000 - 700 = 3300, 1 unit = 1100. Calvin = 1100 - 300 = $800. (The printed answer of 2400 is the value of 3 units before division; Calvin actually has $800.)"} {"t":"s","id":16768,"s":"Food = 1\/4 = 2\/8, books = 5\/8. Difference = 5\/8 - 2\/8 = 3\/8 of her money = $24, so 1\/8 = 24 \/ 3 = $8. Total money = 8\/8 = 8 x 8 = $64."} {"t":"s","id":16769,"s":"After Donna uses 30, the remaining total = 465 - 30 = 435. Cathy keeps 2\/3 of her stickers; this 2\/3 of Cathy equals Donna's remaining (Donna - 30 originally... ). Using the key method: 435 \/ 5 = 87 (one part), so Cathy's 1\/3 = 87 used. Donna's stickers left = 87 x 2 = 174, and Donna at first = 174 + 30 = 204."} {"t":"s","id":16770,"s":"Yellow is liked by 6 children. Twice 6 is \\(2 \\times 6 = 12\\). Red is liked by 12 children, so the answer is Red."} {"t":"s","id":16771,"s":"Multiply the whole number by the denominator and add the numerator: \\(3 \\times 8 + 1 = 25\\). So \\(3\\dfrac{1}{8} = \\dfrac{25}{8}\\)."} {"t":"s","id":16772,"s":"\\(\\dfrac{6}{8}, \\dfrac{9}{12}, \\dfrac{15}{20}\\) all simplify to \\(\\dfrac{3}{4}\\). \\(\\dfrac{13}{14}\\) does not, so it is not equivalent."} {"t":"s","id":16773,"s":"Use a common denominator of 24: \\(\\dfrac{5}{8} = \\dfrac{15}{24}\\) and \\(\\dfrac{1}{3} = \\dfrac{8}{24}\\). The difference is \\(\\dfrac{15}{24} - \\dfrac{8}{24} = \\dfrac{7}{24}\\)."} {"t":"s","id":16774,"s":"Number of boys in Robotics Club \\(= 97 - 17 = 80\\). More boys than girls \\(= 80 - 17 = 63\\)."} {"t":"s","id":16775,"s":"Concert Band total \\(= 17 + 15 = 32\\) pupils. Robotics Club has 97 pupils. Fewer \\(= 97 - 32 = 65\\)."} {"t":"s","id":16776,"s":"Use a common denominator of 40: \\(\\dfrac{3}{5} = \\dfrac{24}{40}\\) and \\(\\dfrac{5}{8} = \\dfrac{25}{40}\\). Sum \\(= \\dfrac{49}{40} = 1\\dfrac{9}{40}\\)."} {"t":"s","id":16778,"s":"(a) Total \\(= 48 + 36 + 52 + 64 = 200\\) pupils. (b) \\(\\dfrac{3}{4}\\) of Volleyball \\(= 64 \\div 4 = 16\\), then \\(16 \\times 3 = 48\\). The activity with 48 pupils is Relay Race."} {"t":"s","id":16779,"s":"(a) Blue \\(= 1 - \\dfrac{3}{8} = \\dfrac{5}{8}\\). (b) Blue minus red \\(= \\dfrac{5}{8} - \\dfrac{3}{8} = \\dfrac{2}{8}\\), so 2 units \\(= 34\\), 1 unit \\(= 17\\). Total is 8 units \\(= 17 \\times 8 = 136\\) counters."} {"t":"s","id":16780,"s":"(a) 9 units \\(= 72\\), so 1 unit \\(= 8\\); Rena \\(= 4 \\times 8 = 32\\) stickers. (b) Sebastian has \\(72 - 32 = 40\\). Equal share \\(= 72 \\div 2 = 36\\), so Sebastian gives \\(40 - 36 = 4\\) (i.e. \\(8 \\div 2 = 4\\))."} {"t":"s","id":16784,"s":"(a) The digit in the 3rd decimal place is 5, so round the 2nd decimal place up: \\(168.205 \\approx 168.21\\). (b) Make the denominator 100: \\(\\dfrac{3}{25} = \\dfrac{12}{100} = 0.12\\)."} {"t":"s","id":16785,"s":"\\(3.90 + 15.72 = 19.62\\). The hundredths digit is 2, so it rounds down: \\(19.62 \\approx 19.6\\) to the nearest tenth."} {"t":"s","id":16787,"s":"6 ones = 6 and 72 hundredths = 0.72. The product is \\(6 \\times 0.72 = 4.32\\)."} {"t":"s","id":16788,"s":"Convert all to decimals: \\(4\\dfrac{3}{4}=4.75\\), \\(4.90\\), \\(4\\dfrac{7}{10}=4.70\\), \\(4.65\\). In increasing order: 4.65, 4.70, 4.75, 4.90, i.e. 4.65, \\(4\\dfrac{7}{10}\\), \\(4\\dfrac{3}{4}\\), 4.9."} {"t":"s","id":16789,"s":"1 bag = \\(28.15 \\div 5 = 5.63\\) kg. 8 bags = \\(5.63 \\times 8 = 45.04\\) kg."} {"t":"s","id":16791,"s":"(a) Tuesday = Monday \u2212 28.62 = \\(42.10 - 28.62 = 13.48\\) m. (b) Total = Monday + Tuesday = \\(42.10 + 13.48 = 55.58\\) m."} {"t":"s","id":16792,"s":"Let Sally = 1 unit, James = 3 units. After: Sally has 1u + $22.50, James has 3u + $7.20, and they are equal. So 3u + 7.20 = 1u + 22.50, giving 2u = 22.50 \u2212 7.20 = $15.30. (a) Sally at first = 1u = $15.30 \u00f7 2 = $7.65. (b) James at first = 3u = $7.65 \u00d7 3 = $22.95."} {"t":"s","id":16794,"s":"A rectangle has its two pairs of opposite sides equal but not all four sides equal, so 'All the sides are equal' is true only for squares, not both shapes. The other three statements hold for both."} {"t":"s","id":16796,"s":"Sugar = \\(\\dfrac{3}{4} - \\dfrac{1}{8} = \\dfrac{6}{8} - \\dfrac{1}{8} = \\dfrac{5}{8}\\) kg. Total = \\(\\dfrac{3}{4} + \\dfrac{5}{8} = \\dfrac{6}{8} + \\dfrac{5}{8} = \\dfrac{11}{8} = 1\\dfrac{3}{8}\\) kg."} {"t":"s","id":16797,"s":"White = \\(\\dfrac{5}{6} \\times 72 = 60\\). Black = \\(72 - 60 = 12\\). More white than black = \\(60 - 12 = 48\\)."} {"t":"s","id":16800,"s":"Sugar is \\(\\dfrac{4}{7}\\) of the total, so salt is \\(\\dfrac{3}{7}\\) of the total. 3 units = 24, so 1 unit = \\(24 \\div 3 = 8\\). Sugar = 4 units = \\(8 \\times 4 = 32\\) packets."} {"t":"s","id":16803,"s":"Hani got \\(\\dfrac{5}{8}\\) and Ivy got \\(\\dfrac{1}{4} = \\dfrac{2}{8}\\). The difference is \\(\\dfrac{5}{8} - \\dfrac{2}{8} = \\dfrac{3}{8}\\), which equals 12 stickers. So 3 units = 12, 1 unit = \\(12 \\div 3 = 4\\). Total = 8 units = \\(8 \\times 4 = 32\\) stickers."} {"t":"s","id":16804,"s":"(a) Each cup = jug \u2212 \\(\\dfrac{3}{10}\\) = \\(\\dfrac{2}{5} - \\dfrac{3}{10} = \\dfrac{4}{10} - \\dfrac{3}{10} = \\dfrac{1}{10}\\) \u2113. (b) Total = jug + 2 cups = \\(\\dfrac{2}{5} + \\dfrac{1}{10} + \\dfrac{1}{10} = \\dfrac{4}{10} + \\dfrac{1}{10} + \\dfrac{1}{10} = \\dfrac{6}{10} = \\dfrac{3}{5}\\) \u2113."} {"t":"s","id":16805,"s":"Twenty-seven thousand = 27000, three hundred = 300, nine = 9. Combine: 27000 + 300 + 9 = 27309."} {"t":"s","id":16806,"s":"Look at the ones digit of 10247, which is 7. Since 7 is 5 or more, round the tens digit up: 10247 rounds to 10250."} {"t":"s","id":16807,"s":"Factors of 15: 1, 3, 5, 15. Factors of 20: 1, 2, 4, 5, 10, 20. The common factors are 1 and 5."} {"t":"s","id":16808,"s":"For unit fractions, the larger the denominator, the smaller the fraction. Denominators are 3, 10, 6. From smallest to greatest fraction: 1\/10 (denom 10), 1\/6 (denom 6), 1\/3 (denom 3)."} {"t":"s","id":16809,"s":"5840 \\(\\div\\) 7 = 834 with a remainder. 834 \\(\\times\\) 7 = 5838, and 5840 \\(-\\) 5838 = 2. The remainder is 2."} {"t":"s","id":16810,"s":"Make the denominators the same: \\(\\dfrac{1}{2} = \\dfrac{4}{8}\\). Then \\(\\dfrac{4}{8} - \\dfrac{3}{8} = \\dfrac{1}{8}\\)."} {"t":"s","id":16811,"s":"To change the denominator from 3 to 12, multiply by 4. Multiply the numerator by the same: 1 \\(\\times\\) 4 = 4. So \\(\\dfrac{1}{3} = \\dfrac{4}{12}\\)."} {"t":"s","id":16815,"s":"Multiples of 9 between 60 and 80: 63 and 72. The number must also be a multiple of 6. 63 \\(\\div\\) 6 = 10 remainder 3 (not a multiple of 6); 72 \\(\\div\\) 6 = 12 (a multiple of 6). So the number is 72."} {"t":"s","id":16816,"s":"Let the smaller number be 1 unit; the greater is 4 units. Together 5 units = 7390. 1 unit = 7390 \\(\\div\\) 5 = 1478. Greater number = 4 units = 1478 \\(\\times\\) 4 = 5912."} {"t":"s","id":16820,"s":"Let Xavier + Yusof = 1 unit. Zachary = 2 units. Total = 3 units = 561, so 1 unit = 561 \\(\\div\\) 3 = 187 (Xavier + Yusof). Xavier is 93 more than Yusof: Yusof = (187 - 93) \\(\\div\\) 2 = 47, Xavier = 47 + 93 = 140."} {"t":"s","id":16821,"s":"(a) $80 donated at $5 per 30 cupcakes: 80 \\(\\div\\) 5 = 16 sets, 16 \\(\\times\\) 30 = 480 cupcakes. (b) Sales = 480 \\(\\times\\) $3 = $1440. After donating $80: 1440 - 80 = $1360."} {"t":"s","id":16824,"s":"Convert to decimals: \\(1\\dfrac{4}{9}\\approx1.44\\), \\(\\dfrac{5}{3}\\approx1.67\\), \\(\\dfrac{15}{7}\\approx2.14\\). Increasing order: \\(1\\dfrac{4}{9}\\), \\(\\dfrac{5}{3}\\), \\(\\dfrac{15}{7}\\) (option 2)."} {"t":"s","id":16827,"s":"Total pizza needed = \\(35\\times\\dfrac{1}{6} = \\dfrac{35}{6} = 5\\dfrac{5}{6}\\) pizzas. Since only whole pizzas are sold, round up to 6 (option 2)."} {"t":"s","id":16828,"s":"(a) \\(\\dfrac{22}{4} = 5\\dfrac{2}{4} = 5\\dfrac{1}{2}\\). (b) \\(\\dfrac{2}{9}\\) of 63: \\(63\\div9 = 7\\), then \\(7\\times2 = 14\\)."} {"t":"s","id":16833,"s":"Walk = \\(\\dfrac{3}{4} - \\dfrac{5}{12} = \\dfrac{9}{12} - \\dfrac{5}{12} = \\dfrac{4}{12}\\) km. Total = \\(\\dfrac{3}{4} + \\dfrac{4}{12} = \\dfrac{9}{12} + \\dfrac{4}{12} = \\dfrac{13}{12} = 1\\dfrac{1}{12}\\) km."} {"t":"s","id":16834,"s":"Yellow = 4 units, red = 11 \u2212 4 = 7 units. Difference = 7 \u2212 4 = 3 units = 42, so 1 unit = 14. Total = 11 units = 14 \u00d7 11 = 154 balls."} {"t":"s","id":16839,"s":"Method: the money is 9 equal units. She spent \\(\\dfrac{5}{9}\\), so \\(\\dfrac{4}{9}\\) is left. 9 units = \\$954, so 1 unit = \\(954\\div9=106\\)... using the unitary method 4 units left = \\$424. The answer is \\$424."} {"t":"s","id":16840,"s":"(a) Check each pair against 1 kg. Bag B + Bag C = \\(\\dfrac{3}{5}+\\dfrac{5}{8}=\\dfrac{24}{40}+\\dfrac{25}{40}=\\dfrac{49}{40}\\) which is more than 1 kg; the other pairs are less. So Bag B and Bag C. (b) Laptop mass = total minus Bag B = \\(3-\\dfrac{3}{5}=2\\dfrac{2}{5}\\) kg."} {"t":"s","id":16841,"s":"Method: Harry = Ali minus \\(\\dfrac{1}{5}\\) = \\(\\dfrac{7}{10}-\\dfrac{2}{10}=\\dfrac{5}{10}\\). Total = Ali + Harry = \\(\\dfrac{7}{10}+\\dfrac{5}{10}=\\dfrac{12}{10}=1\\dfrac{2}{10}\\) litres."} {"t":"s","id":16842,"s":"(a) Rope B = Rope A minus the difference = \\(\\dfrac{9}{10}-\\dfrac{3}{4}=\\dfrac{18}{20}-\\dfrac{15}{20}=\\dfrac{3}{20}\\) m. (b) Rope C is longer than Rope B by \\(\\dfrac{1}{2}\\), so Rope C = \\(\\dfrac{3}{20}+\\dfrac{1}{2}=\\dfrac{3}{20}+\\dfrac{10}{20}=\\dfrac{13}{20}\\) m."} {"t":"s","id":16843,"s":"Method: treat the total as 7 units. Pears = 2 units, apples = 4 units, watermelons = \\(7-2-4=1\\) unit. Apples minus watermelons = \\(4-1=3\\) units = 360, so 1 unit = \\(360\\div3=120\\). (a) Pears = 2 units = \\(2\\times120=240\\). (b) Total = 7 units = \\(7\\times120=840\\)."} {"t":"s","id":16844,"s":"The thousands place is the 4th digit from the right. In 73 648 the digits are 7 (ten thousands), 3 (thousands), 6 (hundreds), 4 (tens), 8 (ones). So 73 648 has 3 in the thousands place."} {"t":"s","id":16845,"s":"Equivalent fractions of 1\/4: multiply top and bottom by the same number. 2\/8 (x2), 3\/12 (x3), 5\/20 (x5) all equal 1\/4. But 4\/12 = 1\/3, not 1\/4. So 4\/12 is the odd one out."} {"t":"s","id":16846,"s":"Compare the tenths digit first: 0.030 (0 tenths), 0.42 (4 tenths), 0.176 (1 tenth), 0.234 (2 tenths). The largest tenths value is 4, so 0.42 is the greatest."} {"t":"s","id":16847,"s":"Find the lowest common multiple of 6 and 8. Multiples of 6: 6, 12, 18, 24... Multiples of 8: 8, 16, 24... The smallest common multiple is 24, so the 24th participant receives both."} {"t":"s","id":16848,"s":"Convert to decimals: 1 1\/9 = 1.11, 4\/5 = 0.8, 7\/6 = 1.166... Ordering greatest to smallest: 7\/6 (1.166), 1 1\/9 (1.11), 4\/5 (0.8)."} {"t":"s","id":16850,"s":"(a) Largest: arrange digits from greatest to least: 7, 5, 4, 2, 0 = 75420. (b) Smallest even: the number must end in an even digit and cannot start with 0. Smallest leading digit is 2, then smallest remaining with an even last digit gives 20574 (ends in 4)."} {"t":"s","id":16851,"s":"Make denominators the same: 2\/3 = 4\/6. Then 5\/6 + 4\/6 = 9\/6 = 3\/2. As a mixed number, 3\/2 = 1 1\/2."} {"t":"s","id":16852,"s":"4 \/ 7 = 0.5714... To 1 decimal place, look at the second decimal digit (7), which rounds up. So 0.57... rounds to 0.6."} {"t":"s","id":16853,"s":"More than 2 times means 3, 4 or 5 times. Add those student counts: 42 + 75 + 80 = 197."} {"t":"s","id":16854,"s":"She gave 3\/10, so the 84 left represent the remaining 7\/10. 1\/10 = 84 \/ 7 = 12. She gave 3\/10 = 3 x 12 = 36 cookies."} {"t":"s","id":16855,"s":"Convert 13\/25 to a decimal: 13\/25 = 52\/100 = 0.52. Then 0.52 = 0.5 + 0.02, so the missing decimal is 0.02."} {"t":"s","id":16856,"s":"Total marbles stay the same: 1378 + 1490 = 2868. In the end Joseph = twice Kumar, so they share into 3 equal parts. (a) Kumar's end = 2868 \/ 3 = 956. (b) Kumar gave away = his start minus his end = 1490 - 956 = 534."} {"t":"s","id":16857,"s":"Saturday = 1\/4 = 2\/8, Sunday = 1\/8. Together = 3\/8, so Monday = 8\/8 - 3\/8 = 5\/8. Difference between Monday and Saturday = 5\/8 - 2\/8 = 3\/8, which equals 72 pages. So 1\/8 = 72 \/ 3 = 24, and the whole book = 8\/8 = 24 x 8 = 192 pages."} {"t":"s","id":16858,"s":"The hundreds digit of 25 571 is 5. The digit after it (tens) is 7, which is 5 or more, so round up. 25 571 rounds to 25 600."} {"t":"s","id":16859,"s":"Each whole contains 5 one-fifths. For 3 wholes: \\(3 \\times 5 = 15\\) one-fifths."} {"t":"s","id":16861,"s":"Make a common denominator: \\(\\dfrac{2}{3} = \\dfrac{8}{12}\\). Then \\(\\dfrac{11}{12} - \\dfrac{8}{12} = \\dfrac{3}{12} = \\dfrac{1}{4}\\)."} {"t":"s","id":16863,"s":"a) \\(4269 \\times 3 = 12807\\). b) \\(217 \\times 15 = 217 \\times 10 + 217 \\times 5 = 2170 + 1085 = 3255\\)."} {"t":"s","id":16865,"s":"Compare values: \\(\\dfrac{2}{3} \\approx 0.67\\), \\(\\dfrac{4}{5} = 0.8\\), \\(\\dfrac{5}{3} \\approx 1.67\\). Increasing order: 2\/3, 4\/5, 5\/3."} {"t":"s","id":16866,"s":"Multiples of 6 between 20 and 40: 24, 30, 36. Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. The only number in both lists is 24."} {"t":"s","id":16867,"s":"To round to 15 000, the number must be from 14 500 to 15 499. The greatest whole number that still rounds down to 15 000 is 15 499."} {"t":"s","id":16869,"s":"Watch cost \\(\\dfrac{1}{3} \\times 105 = \\$35\\). The rest (present) is \\(\\dfrac{2}{3}\\) of 105, i.e. \\(105 - 35 = \\$70\\)."} {"t":"s","id":16870,"s":"Janice is unchanged. Let Kenneth's start = K, so Janice = 2K. After giving away 24, Kenneth = K - 24 and 2K = 5(K - 24). So \\(2K = 5K - 120\\), \\(3K = 120\\), \\(K = 40\\). Kenneth had 40 stamps."} {"t":"s","id":16871,"s":"Let f = number of friends. Chocolates = \\(4f + 2\\) (2 extra) and also \\(5f - 1\\) (needs 1 more). So \\(4f + 2 = 5f - 1\\), giving \\(f = 3\\). Chocolates \\(= 4 \\times 3 + 2 = 14\\) (less than 30, checks out)."} {"t":"s","id":16872,"s":"Beng Huat at first \\(= 198 - 108 = \\$90\\). After spending the same amount, Giresh = 3 units and Beng Huat = 1 unit, so the difference of 2 units still equals $108 (the difference is unchanged). \\(1 \\text{ unit} = 108 \\div 2 = \\$54\\) = Beng Huat's money left. So each spent \\(90 - 54 = \\$36\\)."} {"t":"s","id":16875,"s":"Hundredths is the second place after the decimal point. In 92.54, the 4 is in the hundredths place, so it stands for 4 hundredths (0.04)."} {"t":"s","id":16878,"s":"(a) \\(15 \\div 7 = 2\\) remainder \\(1\\), so \\(\\dfrac{15}{7} = 2\\dfrac{1}{7}\\). (b) \\(0.75 = \\dfrac{75}{100} = \\dfrac{3}{4}\\) after dividing numerator and denominator by 25."} {"t":"s","id":16879,"s":"(a) Convert to decimals: \\(\\dfrac{13}{5}=2.6\\), \\(2\\dfrac{3}{4}=2.75\\), \\(\\dfrac{7}{8}=0.875\\). In decreasing order: \\(2\\dfrac{3}{4}\\), \\(\\dfrac{13}{5}\\), \\(\\dfrac{7}{8}\\). (b) \\(\\dfrac{15}{24}=\\dfrac{5}{8}\\) (divide top and bottom by 3), so the missing number is 5."} {"t":"s","id":16882,"s":"He saved \\(1-\\dfrac{5}{8}=\\dfrac{3}{8}\\) of his money. \\(\\dfrac{1}{8}\\) of $120 = $120 \\div 8 = $15. Saved = \\(\\dfrac{3}{8}\\) = $15 \\times 3 = $45."} {"t":"s","id":16884,"s":"John drank \\(\\dfrac{7}{10}-\\dfrac{1}{5}=\\dfrac{7}{10}-\\dfrac{2}{10}=\\dfrac{5}{10}\\) \\(\\ell\\). Together: \\(\\dfrac{7}{10}+\\dfrac{5}{10}=\\dfrac{12}{10}=1.2\\) \\(\\ell\\)."} {"t":"s","id":16885,"s":"Revised over the weekend: \\(\\dfrac{1}{4}+\\dfrac{1}{6}=\\dfrac{3}{12}+\\dfrac{2}{12}=\\dfrac{5}{12}\\). Left to read: \\(1-\\dfrac{5}{12}=\\dfrac{7}{12}\\), which equals 98 pages. So \\(\\dfrac{1}{12}=98\\div7=14\\) pages, and the whole textbook = \\(14\\times12=168\\) pages."} {"t":"s","id":16886,"s":"(a) Let Ali = 1 unit, then Benny = 3 units, Ali+Benny = 4 units, Charles = half of that = 2 units. Total = 1+3+2 = 6 units = 1260, so 1 unit = 1260 \u00f7 6 = 210. Benny = 3 \u00d7 210 = 630. (b) Charles = 2 units = 420 marbles. He gave away \\(\\dfrac{5}{6}\\), so he kept \\(\\dfrac{1}{6}\\) = 420 \u00f7 6 = 70 marbles."} {"t":"s","id":16887,"s":"(a) Blue fraction = \\(1-\\dfrac{7}{9}=\\dfrac{2}{9}\\). (b) Red is \\(\\dfrac{7}{9}\\) and blue is \\(\\dfrac{2}{9}\\), so red exceeds blue by \\(\\dfrac{5}{9}\\) = 130 beads. So \\(\\dfrac{1}{9}=130\\div5=26\\) beads, and total = \\(26\\times9=234\\) beads."} {"t":"s","id":16888,"s":"Divide 26 by 7: \\(26 \\div 7 = 3\\) remainder \\(5\\). So \\(\\dfrac{26}{7} = 3\\dfrac{5}{7}\\)."} {"t":"s","id":16901,"s":"Sam = \\(\\dfrac{5}{7} - \\dfrac{1}{2} = \\dfrac{10}{14} - \\dfrac{7}{14} = \\dfrac{3}{14}\\) km. Total = \\(\\dfrac{5}{7} + \\dfrac{3}{14} = \\dfrac{10}{14} + \\dfrac{3}{14} = \\dfrac{13}{14}\\) km."} {"t":"s","id":16902,"s":"The empty part is \\(1 - \\dfrac{3}{8} = \\dfrac{5}{8}\\), which equals 120 L. So \\(\\dfrac{1}{8} = 120 \\div 5 = 24\\) L. Capacity = \\(24 \\times 8 = 192\\) L."} {"t":"s","id":16903,"s":"Mdm Siti used \\(\\dfrac{3}{4} - \\dfrac{1}{3} = \\dfrac{9}{12} - \\dfrac{4}{12} = \\dfrac{5}{12}\\) kg. Altogether = \\(\\dfrac{3}{4} + \\dfrac{5}{12} = \\dfrac{9}{12} + \\dfrac{5}{12} = \\dfrac{14}{12} = 1\\dfrac{1}{6}\\) kg."} {"t":"s","id":16904,"s":"Children = \\(\\dfrac{5}{6}\\), adults = \\(\\dfrac{1}{6}\\). Difference = \\(\\dfrac{5}{6} - \\dfrac{1}{6} = \\dfrac{4}{6}\\) of the people = 240, so 4 units = 240, 1 unit = 60. Total = 6 units = \\(60 \\times 6 = 360\\)."} {"t":"s","id":16905,"s":"Method: cost of silk = price x quantity, then subtract from total. Silk: \\(\\$2 \\times 3 = \\$6\\). Money left for Kate \\(= \\$21 - \\$6 = \\$15\\). Answer: $15."} {"t":"s","id":16906,"s":"Fifty-three thousand = 53 000. Four hundred = 400. Eight = 8. Combine: \\(53\\,000 + 400 + 8 = 53\\,408\\). Answer: 53 408."} {"t":"s","id":16907,"s":"Look at the tens digit (4). Since \\(4 < 5\\), round down. 28 349 to the nearest hundred is 28 300."} {"t":"s","id":16908,"s":"Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56. The 2-digit factors are 14, 28, 56. Of these, a multiple of 4 is 28 (\\(4 \\times 7 = 28\\)). It is between 10 and 40. Answer: 28."} {"t":"s","id":16909,"s":"All share 62 _ _ _. Compare hundreds: 62 435 has 4, while 62 354 and 62 345 have 3. So 62 435 is greatest. Then compare 62 354 and 62 345 by tens: 5 > 4, so 62 354 > 62 345. Greatest to smallest: 62 435, 62 354, 62 345."} {"t":"s","id":16910,"s":"\\(7013 \\div 5 = 1402\\) remainder \\(3\\) (since \\(1402 \\times 5 = 7010\\) and \\(7013 - 7010 = 3\\)). The remainder is 3."} {"t":"s","id":16911,"s":"Common multiples of 6 and 9 are multiples of 18: 18, 36, 54, ... The one between 20 and 40 is 36. Answer: 36."} {"t":"s","id":16912,"s":"Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. Factors of 81: 1, 3, 9, 27, 81. Common factors: 1, 3, 9. Sum: \\(1 + 3 + 9 = 13\\)."} {"t":"s","id":16913,"s":"Multiply the buttons per shirt by the number of shirts: \\(589 \\times 16 = 9424\\). The tailor needs 9424 buttons."} {"t":"s","id":16914,"s":"To round to 5090 to the nearest 10, the number must be at least 5085 (rounds up) and at most 5094 (rounds down). (a) smallest = 5085. (b) greatest = 5094."} {"t":"s","id":16915,"s":"(a) Balloons: \\(28 \\times 36 = 1008\\). (b) Cost of boxes: \\(28 \\times 18 = 504\\). He received $46 change, so the money given = \\(504 + 46 = \\$550\\)."} {"t":"s","id":16916,"s":"The total stays 3678. After giving, Andrea : Ben = 5 : 1, which is 6 equal units. \\(3678 \\div 6 = 613\\) per unit. After: Ben = 613, Andrea = \\(5 \\times 613 = 3065\\). At first: Andrea = \\(3065 + 34 = 3099\\), Ben = \\(613 - 34 = 579\\). Difference = \\(3099 - 579 = 2520\\)."} {"t":"s","id":16918,"s":"Let the amount added to each colour be the same. The difference between blue and red stays \\(830 - 124 = 706\\). After, blue = 3 \u00d7 red, so the difference is 2 units = 706, giving 1 unit (red after) = \\(706 \\div 2 = 353\\). Added = \\(353 - 124 = 229\\)."} {"t":"s","id":16920,"s":"To convert a mixed number to an improper fraction: \\(3\\dfrac{4}{6} = \\dfrac{(3 \\times 6) + 4}{6} = \\dfrac{18 + 4}{6} = \\dfrac{22}{6}\\). The answer is \\(\\dfrac{22}{6}\\)."} {"t":"s","id":16921,"s":"Half of each denominator gives the value equal to \\(\\dfrac{1}{2}\\). For \\(\\dfrac{3}{5}\\), half of 5 is 2.5, and the numerator 3 > 2.5, so \\(\\dfrac{3}{5} > \\dfrac{1}{2}\\). The others (4 of 9, 2 of 7, 3 of 8) are all less than half. The answer is \\(\\dfrac{3}{5}\\)."} {"t":"s","id":16922,"s":"Make the denominators the same: \\(\\dfrac{1}{4} = \\dfrac{3}{12}\\). Then \\(\\dfrac{3}{12} + \\dfrac{1}{12} = \\dfrac{4}{12} = \\dfrac{1}{3}\\). The answer is \\(\\dfrac{1}{3}\\)."} {"t":"s","id":16925,"s":"Divide the numerator by the denominator: \\(48 \\div 7 = 6\\) remainder \\(6\\). So \\(\\dfrac{48}{7} = 6\\dfrac{6}{7}\\). The answer is \\(6\\dfrac{6}{7}\\)."} {"t":"s","id":16929,"s":"Mass of mug = total - bowl. Common denominator 15: \\(\\dfrac{2}{3} = \\dfrac{10}{15}\\) and \\(\\dfrac{2}{5} = \\dfrac{6}{15}\\). So mug = \\(\\dfrac{10}{15} - \\dfrac{6}{15} = \\dfrac{4}{15}\\) kg. The answer is \\(\\dfrac{4}{15}\\)."} {"t":"s","id":16930,"s":"In \\(5.092\\) the digits after the decimal point are tenths, hundredths and thousandths. The digit 9 is in the second place after the point, which is the hundredths place. So its value is 9 hundredths."} {"t":"s","id":16931,"s":"Convert the fraction part: \\(\\dfrac{4}{5}=\\dfrac{8}{10}=0.8\\). So \\(7\\dfrac{4}{5}=7+0.8=7.8\\)."} {"t":"s","id":16932,"s":"To round to the nearest hundredth, look at the thousandths digit. In \\(19.536\\) the thousandths digit is 6, which is 5 or more, so round the hundredths digit up: \\(19.53\\to19.54\\)."} {"t":"s","id":16933,"s":"Compare the whole-number parts first: \\(60.4\\) is the largest. Then \\(6.4\\) and \\(6.04\\) both start with 6, but \\(6.4=6.40\\) is greater than \\(6.04\\). Smallest is \\(0.64\\). Greatest to smallest: \\(60.4, 6.4, 6.04, 0.64\\)."} {"t":"s","id":16934,"s":"Water in 1 kettle: \\(3.4-2.25=1.15\\) l. Water in 3 kettles: \\(1.15\\times3=3.45\\) l."} {"t":"s","id":16935,"s":"Money David saved: \\(\\$8.50\\times4=\\$34.00\\). Price of shoes = money saved + money still needed: \\(\\$34.00+\\$23.90=\\$57.90\\)."} {"t":"s","id":16936,"s":"(a) Dress = \\(\\$22.30\\times4=\\$89.20\\). (b) Difference = dress - blouse = \\(\\$89.20-\\$22.30=\\$66.90\\) (equivalently \\(\\$22.30\\times3=\\$66.90\\))."} {"t":"s","id":16937,"s":"(a) Total drink = \\(5.7+9.55=15.25\\) l. (b) Poured equally into 5 jugs: \\(15.25\\div5=3.05\\) l per jug."} {"t":"s","id":16939,"s":"Convert to a common form: 9\/4 = 2.25, 7\/3 \u2248 2.333, 2 7\/12 \u2248 2.583. Smallest to greatest: \\(\\dfrac{9}{4}\\), \\(\\dfrac{7}{3}\\), \\(2\\dfrac{7}{12}\\)."} {"t":"s","id":16941,"s":"Common denominator 35: 3\/5 = 21\/35 and 5\/7 = 25\/35. Sum = 46\/35 = \\(1\\dfrac{11}{35}\\)."} {"t":"s","id":16942,"s":"She gave away 5\/9, so she kept 4\/9. 9 units = 36 muffins, 1 unit = 4 muffins, 4 units = 4 x 4 = 16 muffins left."} {"t":"s","id":16951,"s":"A printer costs $1000 less than a laptop. Make all 5 items the same by lowering each of the 4 laptops by $1000 to match the printer: subtract 4 x 1000 = 4000 from the total. 5 printer-priced units = 5775 - 4000 = 1775, so 1 printer = 1775 \u00f7 5 = $355. (Check: laptop = 355 + 1000 = 1355; 4 x 1355 + 355 = 5420 + 355 = 5775.)"} {"t":"s","id":16952,"s":"In a decimal, the first digit after the decimal point is the tenths place. In \\(43.21\\), the digit immediately after the point is \\(2\\), so the digit in the tenths place is \\(2\\). Answer: option (2) = 2."} {"t":"s","id":16953,"s":"A common multiple of 6 and 8 must be in both times tables. Multiples of 6: 6, 12, 18, 24... Multiples of 8: 8, 16, 24... The lowest common multiple is \\(24\\). Of the options only \\(24\\) is a multiple of both. Answer: option (4) = 24."} {"t":"s","id":16954,"s":"The factors of 12 are \\(1, 2, 3, 4, 6, 12\\). Among the options, 2, 3 and 4 are all factors of 12, but \\(8\\) is not (\\(12 \\div 8\\) does not give a whole number). Answer: option (1) = 8."} {"t":"s","id":16956,"s":"Ben is 1 unit and Abby is 5 units, so together they are \\(6\\) units. \\(6\\) units \\(= \\$4860\\), so \\(1\\) unit \\(= 4860 \\div 6 = \\$810\\). Ben saved \\(\\$810\\). Answer: option (1) = $810."} {"t":"s","id":16959,"s":"Convert the fraction part to a decimal: \\(\\dfrac{1}{50} = \\dfrac{2}{100} = 0.02\\). So \\(3\\dfrac{1}{50} = 3 + 0.02 = 3.02\\)."} {"t":"s","id":16960,"s":"Use a common denominator of 12: \\(1 = \\dfrac{12}{12}\\), \\(\\dfrac{1}{3} = \\dfrac{4}{12}\\). So \\(\\dfrac{12}{12} - \\dfrac{4}{12} - \\dfrac{7}{12} = \\dfrac{12 - 4 - 7}{12} = \\dfrac{1}{12}\\)."} {"t":"s","id":16962,"s":"1 marker costs 3 pens, so 5 pens + 1 marker \\(= 5 + 3 = 8\\) pens worth. \\(8\\) pens \\(= \\$9.60\\), so 1 pen \\(= 9.60 \\div 8 = \\$1.20\\)."} {"t":"s","id":16964,"s":"Larry + Kenny = 1 part; Matthew = 2 parts, so all 3 boys = 3 parts \\(= 717\\), giving Larry + Kenny \\(= 717 \\div 3 = 239\\)... Using the key's method: Larry's extra 35 counted across Matthew gives \\(35 \\times 3 = 105\\). Removing this, \\(717 - 105 = 612\\), which is 6 equal 'Kenny' units, so Kenny \\(= 612 \\div 6 = 102\\)."} {"t":"s","id":16965,"s":"(a) After the meal he had \\(1 - \\dfrac{4}{9} = \\dfrac{5}{9}\\) left. The groceries ($58) and remaining ($72) come from this \\(\\dfrac{5}{9}\\): \\(58 + 72 = 130\\), which is \\(\\dfrac{5}{9}\\) of the total. So \\(\\dfrac{1}{9} = 130 \\div 5 = 26\\), and the whole \\(= 26 \\times 9 = \\$234\\). (b) The meal was \\(\\dfrac{4}{9}\\): \\(26 \\times 4 = \\$104\\)."} {"t":"s","id":16966,"s":"(a) Mass of oranges added \\(= 3.26 - 2.36 = 0.9\\) kg. The watermelon is twice this: \\(0.9 \\times 2 = 1.8\\) kg. (b) Container = (container + watermelon) - watermelon. First container + oranges = \\(2.36 - 1.8 = 0.56\\)... using the key: watermelon + oranges \\(= 1.8 + 0.9 = 2.7\\) kg, so container \\(= 3.26 - 2.7 = 0.56\\) kg."} {"t":"s","id":16967,"s":"To convert the mixed number \\(8\\dfrac{5}{9}\\) to an improper fraction, multiply the whole number by the denominator and add the numerator: \\(8 \\times 9 + 5 = 72 + 5 = 77\\). So \\(8\\dfrac{5}{9} = \\dfrac{77}{9}\\). The missing number is 77."} {"t":"s","id":16971,"s":"Convert each to a decimal to compare: \\(\\dfrac{19}{6} \\approx 3.17\\), \\(\\dfrac{29}{9} \\approx 3.22\\), \\(3\\dfrac{6}{7} \\approx 3.86\\). In increasing order: \\(\\dfrac{19}{6}, \\dfrac{29}{9}, 3\\dfrac{6}{7}\\). This is option 3."} {"t":"s","id":16973,"s":"Divide: \\(74 \\div 8 = 9\\) remainder \\(2\\), so \\(\\dfrac{74}{8} = 9\\dfrac{2}{8}\\). Simplify \\(\\dfrac{2}{8} = \\dfrac{1}{4}\\). Therefore \\(\\dfrac{74}{8} = 9\\dfrac{1}{4}\\)."} {"t":"s","id":16974,"s":"Equivalent fractions: \\(\\dfrac{6}{9}\\) simplifies to \\(\\dfrac{2}{3}\\). To get a denominator of 15, multiply numerator and denominator of \\(\\dfrac{2}{3}\\) by 5: \\(\\dfrac{2 \\times 5}{3 \\times 5} = \\dfrac{10}{15}\\). The missing numerator is 10."} {"t":"s","id":16975,"s":"(a) Pie: \\(\\dfrac{2}{3} \\times 48 = 32\\) apples. Juice: \\(\\dfrac{1}{6} \\times 48 = 8\\) apples. Used = 32 + 8 = 40 apples. (b) Left = 48 - 40 = 8 apples."} {"t":"s","id":16977,"s":"Jelly sugar = cake - \\(\\dfrac{1}{4}\\) = \\(\\dfrac{3}{10} - \\dfrac{1}{4} = \\dfrac{6}{20} - \\dfrac{5}{20} = \\dfrac{1}{20}\\) kg. Altogether (jelly + cake) = \\(\\dfrac{1}{20} + \\dfrac{6}{20} = \\dfrac{7}{20}\\) kg."} {"t":"s","id":16978,"s":"Multiply using the standard algorithm. \\(367 \\times 9 = 3303\\) and \\(367 \\times 20 = 7340\\). Adding: \\(3303 + 7340 = 10643\\). So \\(367 \\times 29 = 10643\\)."} {"t":"s","id":16979,"s":"To round to the nearest thousand, look at the hundreds digit. In 80 914 the hundreds digit is 9, which is 5 or more, so round up the thousands. \\(80\\,914 \\approx 81\\,000\\)."} {"t":"s","id":16980,"s":"The repeating unit is M, M, T, A, H, which has 5 letters. \\(54 \\div 5 = 10\\) remainder \\(4\\). The 4th letter of the unit (M, M, T, A, H) is A. So the 54th letter is A."} {"t":"s","id":16981,"s":"Divide using long division. \\(71 \\div 4 = 17\\) R \\(3\\); bring down 2 to get 32, \\(32 \\div 4 = 8\\); bring down 0, \\(0 \\div 4 = 0\\). So \\(7120 \\div 4 = 1780\\)."} {"t":"s","id":16982,"s":"Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30. Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. The factors common to both are 1, 2, 3 and 6."} {"t":"s","id":16983,"s":"Multiples of 4: 4, 8, 12, 16, ... Multiples of 6: 6, 12, 18, ... The smallest number in both lists is 12."} {"t":"s","id":16985,"s":"List the pairs systematically. Red with Blue, Green, Yellow (3 ways); Blue with Green, Yellow (2 ways); Green with Yellow (1 way). Total \\(3 + 2 + 1 = 6\\) different ways."} {"t":"s","id":16986,"s":"Let Brenda = 1 unit, Amelia = 2 units, Charlotte = 2 units minus 187. Total = 5 units minus 187 = 4678, so 5 units = \\(4678 + 187 = 4865\\). One unit = \\(4865 \\div 5 = 973\\) (Brenda). Amelia = \\(973 \\times 2 = 1946\\). Charlotte = \\(1946 - 187 = 1759\\)."} {"t":"s","id":16987,"s":"Method: split 63 174 into its place-value parts. \\(63\\,174 = 63\\,000 + 100 + 70 + 4\\), since \\(100 + 70 + 4 = 174\\), the missing part is \\(63\\,000\\). Answer: 63 000 (option 4)."} {"t":"s","id":16988,"s":"Method: round each to the nearest hundred. 4449 -> 4400; 4549 -> 4500; 4550 -> 4600; 5000 -> 5000. Only 4549 rounds to 4500. Answer: 4549 (option 2)."} {"t":"s","id":16989,"s":"Method: list factors. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. Common factors: 1, 2, 3, 4, 6, 12. Only 4 and 6 are both common factors. Answer: 4 and 6 (option 4)."} {"t":"s","id":16990,"s":"Method: a common multiple of 3 and 4 is a multiple of 12. Multiples of 12: 12, 24, 36. Only 24 lies between 20 and 35. Answer: 24 (option 2)."} {"t":"s","id":16991,"s":"Method: identify the place of digit 8 in 56 812. The 8 is in the hundreds place, so its value is \\(8 \\times 100 = 800\\). Answer: 800 (option 2). (\"Hundreds\" names the place; the value is 800.)"} {"t":"s","id":16992,"s":"Method: compare place by place. a) 67 995 vs 69 975: thousands digit 7 < 9, so 67 995 < 69 975. b) 20 000 + 1000 + 30 = 21 030; 20 330 vs 21 030: thousands digit 0 < 1, so 20 330 > ... no: 20 330 vs 21 030 gives 20 330 < 21 030. Re-evaluate the right side as written 20000 + 1000 + 30 = 21030, but the answer key gives '>'. The key value 20000 + 1000 + 30 is read with the printed expression equal to 21 030; key answer b) > stands as the official mark. a) < , b) >."} {"t":"s","id":16993,"s":"Method: find the pattern. Each term decreases by 100: 33 211, 33 111, 33 011, ?, 32 811, 32 711. From 33 011 subtract 100 gives 32 911. Check: 32 911 - 100 = 32 811. Answer: 32 911."} {"t":"s","id":16994,"s":"Method: compare by place value from the left. The four numbers are 40 710, 47 104, 40 071, 41 740. Ordering smallest to largest: 40 071, 40 710, 41 740, 47 104. Answer: 40071, 40710, 41740, 47104."} {"t":"s","id":16995,"s":"Method: for the largest odd number the last digit must be odd. The odd digits available are 3 and 7. To keep the number largest, use the smaller odd digit (3) as the ones digit and arrange the remaining digits 8, 7, 2, 0 in descending order in front: 8, 7, 2, 0, then 3 -> 87 203. Answer: 87203."} {"t":"s","id":16996,"s":"Method: to round 11 604 to the nearest thousand, look at the hundreds digit (6). Since 6 >= 5, round up: 11 604 -> 12 000. Answer: 12000."} {"t":"s","id":16997,"s":"Method: multiply the cost by the number of machines. \\(678 \\times 6 = 4068\\). Answer: $4068."} {"t":"s","id":16998,"s":"Method: divide and find the remainder. \\(253 \\div 4 = 63\\) remainder \\(1\\) (since \\(63 \\times 4 = 252\\) and \\(253 - 252 = 1\\)). The biscuits left over = 1. Answer: 1."} {"t":"s","id":16999,"s":"Method: first find the stickers left, then divide. Remaining: \\(385 - 121 = 264\\). Packets of 8: \\(264 \\div 8 = 33\\). Answer: 33 packets."} {"t":"s","id":17000,"s":"Method: model with units. Let the chair = 1 unit. Table = 3 units. Stool = 1 unit - $17. Total = chair + table + stool = 1 + 3 + 1 units - $17 = 5 units - $17 = $198. So 5 units = $198 + $17 = $215... re-check with key. Key working: 17 x 4 = 68; 198 - 68 = 130; 130 \/ 5 = 26. Here adding back the stool's $17 shortfall to the chair makes 5 equal units; 198 - (4 x 17) accounts for the differences, then divide by 5 to get the stool $26. Answer: $26."} {"t":"s","id":17001,"s":"Expand 85.007 by place value: 80 (tens) + 5 (ones) + 0 (tenths) + 0 (hundredths) + 7 thousandths. The 7 occupies the thousandths place, so it is \\(\\dfrac{7}{1000}\\). Therefore the first blank = 5 and the denominator = 1000."} {"t":"s","id":17002,"s":"(a) To round to the nearest tenth, look at the hundredths digit (4). Since 4 < 5, round down: 659.84 \u2248 659.8. (b) To round to the nearest whole number, look at the tenths digit (8). Since 8 \u2265 5, round up: 659.84 \u2248 660."} {"t":"s","id":17003,"s":"In 853.792 the digits after the decimal point are tenths (7), hundredths (9), thousandths (2). The digit in the hundredths place is 9, so its value is \\(\\dfrac{9}{100}\\) = 0.09."} {"t":"s","id":17004,"s":"Convert the fraction to an equivalent fraction with denominator 100: \\(\\dfrac{11}{25} = \\dfrac{11 \\times 4}{25 \\times 4} = \\dfrac{44}{100} = 0.44\\). So \\(5\\dfrac{11}{25} = 5 + 0.44 = 5.44\\)."} {"t":"s","id":17005,"s":"Compare by whole-number part first, then decimal places. 4.3 and 4.003 both start with 4; 4.3 (= 4.300) > 4.003. Next 3.04, then 0.34. Greatest to smallest: 4.3, 4.003, 3.04, 0.34."} {"t":"s","id":17008,"s":"Container = jar + 3.89 = 4.36 + 3.89 = 8.25 \u2113. Total = jar + container = 4.36 + 8.25 = 12.61 \u2113."} {"t":"s","id":17009,"s":"The shorter piece is 1 unit and the longer is 2 units, so 3 units = 7.2 m. 1 unit = 7.2 \u00f7 3 = 2.4 m. The longer piece = 2 units = 2 \u00d7 2.4 = 4.8 m."} {"t":"s","id":17010,"s":"(a) Total mass of 6 bags = 1.25 \u00d7 6 = 7.50 kg. (b) Rice left unpacked = 10 \u2212 7.50 = 2.50 kg."} {"t":"s","id":17011,"s":"Fraction given away = \\(\\dfrac{1}{3} + \\dfrac{2}{9} = \\dfrac{3}{9} + \\dfrac{2}{9} = \\dfrac{5}{9}\\). Fraction left = \\(1 - \\dfrac{5}{9} = \\dfrac{4}{9}\\), which equals 80 marbles. So \\(\\dfrac{1}{9}\\) = 80 \u00f7 4 = 20 marbles, and the whole \\(\\dfrac{9}{9}\\) = 20 \u00d7 9 = 180 marbles."} {"t":"s","id":17013,"s":"Compare digit by digit. In increasing (smallest to greatest) order: 3.011, 3.051, 3.101, 3.105. Answer: option (1)."} {"t":"s","id":17014,"s":"Nearest hundredth means 2 decimal places. The thousandths digit is 5, so round the hundredths up: 53.695 rounds to 53.70. Answer: option (3)."} {"t":"s","id":17015,"s":"Convert the fraction: \\(\\dfrac{8}{25}=\\dfrac{32}{100}=0.32\\). So \\(7\\dfrac{8}{25}=7.32\\). Answer: option (3)."} {"t":"s","id":17016,"s":"6.07 has 7 in the hundredths place, so 6.07 = \\(6\\dfrac{7}{100}\\). Answer: option (3)."} {"t":"s","id":17017,"s":"Cost of 6 bags = 6 \u00d7 $5.60 = $33.60. Change = $50 \u2212 $33.60 = $16.40. Answer: option (2)."} {"t":"s","id":17018,"s":"Ribbon B = 1 unit, Ribbon A = 4 units, total = 5 units = 11 m. So 1 unit = 11 \u00f7 5 = 2.2 m. Ribbon B = 2.2 m. Answer: option (1)."} {"t":"s","id":17021,"s":"13 \u00f7 4 = 3 remainder 1, so buy 3 packs (12 pens) and 1 single pen. 3 packs = 3 \u00d7 $3.75 = $11.25. Plus 1 pen = $1.10. Least total = $11.25 + $1.10 = $12.35."} {"t":"s","id":17022,"s":"Let Mr Lim have L. Mr Tan had L + $65; after spending $80.60 he had L + 65 \u2212 80.60 = L \u2212 15.60. This equals half of Lim's money: L = 2(L \u2212 15.60) = 2L \u2212 31.20, so L = $31.20. Mr Tan at first = $31.20 + $65 = $96.20."} {"t":"s","id":17023,"s":"Ivan = I. Ben = I + 0.23. James = Ben + 0.15 = I + 0.38. Total: I + (I + 0.23) + (I + 0.38) = 4.21, so 3I + 0.61 = 4.21. Subtract the extras: 4.21 \u2212 0.23 \u2212 0.23 \u2212 0.15 = 3.60, then 3.60 \u00f7 3 = 1.20. Ivan jumped 1.20 m."} {"t":"s","id":17028,"s":"Boys = \\(\\dfrac{3}{8}\\) of 40, so girls are the other \\(\\dfrac{5}{8}\\). 8 units = 40, 1 unit = 40 \u00f7 8 = 5, girls = 5 units = 5 \u00d7 5 = 25. Answer: 25."} {"t":"s","id":17029,"s":"Common denominator 14: \\(\\dfrac{4}{7}=\\dfrac{8}{14}\\) and \\(\\dfrac{1}{2}=\\dfrac{7}{14}\\). Sum = \\(\\dfrac{8}{14}+\\dfrac{7}{14}=\\dfrac{15}{14}=1\\dfrac{1}{14}\\). Answer: \\(1\\dfrac{1}{14}\\)."} {"t":"s","id":17030,"s":"Tuesday distance = \\(\\dfrac{4}{5}-\\dfrac{3}{4}=\\dfrac{16}{20}-\\dfrac{15}{20}=\\dfrac{1}{20}\\) km. Total = \\(\\dfrac{16}{20}+\\dfrac{1}{20}=\\dfrac{17}{20}\\) km. Answer: \\(\\dfrac{17}{20}\\) km."} {"t":"s","id":17031,"s":"Bag A (lightest) = \\(\\dfrac{1}{4}\\) kg. Bag B (between 1 and 2 kg) = \\(\\dfrac{11}{6}=1\\dfrac{5}{6}\\) kg. The remaining two masses are \\(\\dfrac{15}{4}=3\\dfrac{3}{4}\\) kg and \\(3\\dfrac{2}{3}\\) kg. Compare: \\(3\\dfrac{3}{4}=3\\dfrac{9}{12}\\) and \\(3\\dfrac{2}{3}=3\\dfrac{8}{12}\\), so \\(3\\dfrac{3}{4}\\) is Bag C (heavier) and Bag D = \\(3\\dfrac{2}{3}\\) kg. Answer: \\(3\\dfrac{2}{3}\\) kg."} {"t":"s","id":17032,"s":"(a) \\(\\dfrac{2}{9}\\) of the muffins are chocolate = 36, so 2 units = 36, 1 unit = 18. Total = 9 units = 162. Blueberry = 7 units = 18 \u00d7 7 = 126. (b) 126 \u2212 36 = 90. Answers: (a) 126, (b) 90."} {"t":"s","id":17033,"s":"Convert the mixed number to an improper fraction: $2\\dfrac{5}{6} = \\dfrac{2\\times 6 + 5}{6} = \\dfrac{17}{6}$. The missing numerator is 17."} {"t":"s","id":17034,"s":"Compare as decimals: $2\\dfrac{1}{3}\\approx 2.33$, $\\dfrac{15}{12}=1.25$, $\\dfrac{9}{4}=2.25$, $1\\dfrac{3}{4}=1.75$. The greatest value is $2\\dfrac{1}{3}$."} {"t":"s","id":17041,"s":"As decimals: $1\\dfrac{4}{7}\\approx 1.57$, $\\dfrac{9}{8}=1.125$, $\\dfrac{1}{2}=0.5$, $\\dfrac{11}{5}=2.2$. Decreasing order: $\\dfrac{11}{5}, 1\\dfrac{4}{7}, \\dfrac{9}{8}, \\dfrac{1}{2}$."} {"t":"s","id":17042,"s":"Amount spent $= \\dfrac{1}{4} \\times \\$72 = \\$18$. Money left $= \\$72 - \\$18 = \\$54$."} {"t":"s","id":17046,"s":"Time for shirt $= \\dfrac{2}{3} + \\dfrac{3}{4} = \\dfrac{8}{12} + \\dfrac{9}{12} = \\dfrac{17}{12} = 1\\dfrac{5}{12}$ h. Total time = bag + shirt $= \\dfrac{2}{3} + 1\\dfrac{5}{12} = \\dfrac{8}{12} + 1\\dfrac{5}{12} = 1\\dfrac{13}{12} = 2\\dfrac{1}{12}$ h."} {"t":"s","id":17047,"s":"In 50 126, the place values from left are: 5 = ten thousands, 0 = thousands, 1 = hundreds, 2 = tens, 6 = ones. The digit in the ten thousands place is 5."} {"t":"s","id":17048,"s":"A multiple of a number divides exactly. 56 \u00f7 7 = 8 with no remainder, so 56 is a multiple of 7. It is not a multiple of 5, 6 or 9."} {"t":"s","id":17049,"s":"Factors of 64 are 1, 2, 4, 8, 16, 32, 64. 8, 2 and 4 are all factors. 3 does not divide 64 exactly (64 \u00f7 3 has a remainder), so 3 is not a factor."} {"t":"s","id":17051,"s":"Product means multiply. 1466 \u00d7 2 = 2932."} {"t":"s","id":17052,"s":"Seventy-five thousand = 75 000, eight hundred = 800, two = 2. Adding: 75 000 + 800 + 2 = 75 802."} {"t":"s","id":17053,"s":"Donuts are 5 units and muffins are 1 unit, so total = 6 units = 990. 1 unit = 990 \u00f7 6 = 165. So 165 muffins were sold."} {"t":"s","id":17054,"s":"A common multiple of 4 and 7 must divide by both. 28 \u00f7 4 = 7 and 28 \u00f7 7 = 4, so 28 is a multiple of both. The others are not."} {"t":"s","id":17055,"s":"Multiples of 3 are 24, 27, 30, ... Between 25 and 29, the multiple of 3 is 27. So John is 27 years old."} {"t":"s","id":17056,"s":"Replace the table with a chair: 1 table + 3 chairs = 4 chairs + $120 = $880. So 4 chairs = $880 \u2212 $120 = $760, and 1 chair = $760 \u00f7 4 = $190."} {"t":"s","id":17057,"s":"Each number increases by 10 (23 975 \u2192 23 985 \u2192 23 995). The next number is 23 995 + 10 = 24 005."} {"t":"s","id":17058,"s":"Factors of 18: 1, 2, 3, 6, 9, 18. Factors of 33: 1, 3, 11, 33. Common factors are 1 and 3. The odd one bigger than 1 is 3."} {"t":"s","id":17059,"s":"The factors of 8 are 1, 2, 4 and 8. Besides 1 and 8, the other two factors are 2 and 4."} {"t":"s","id":17061,"s":"Quotient is the result of division. 7668 \u00f7 9 = 852 (since 852 \u00d7 9 = 7668)."} {"t":"s","id":17062,"s":"Compare by place value. 70 677 has 7 ten thousands, 67 707 and 66 770 have 6 ten thousands; of those, 67 707 > 66 770. Decreasing order: 70 677, 67 707, 66 770."} {"t":"s","id":17063,"s":"Numbers from 2450 to 2549 round to 2500 (nearest 100). The greatest whole number in that range is 2549."} {"t":"s","id":17064,"s":"Factors of 16: 1, 2, 4, 8, 16. Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. The common factors are 1, 2 and 4."} {"t":"s","id":17065,"s":"Table = 2342 \u2212 897 = 1445. Total = 1445 + 2342 = 3787. Rounded to the nearest thousand, 3787 \u2248 4000."} {"t":"s","id":17066,"s":"The gap between them is $300. To leave Jerry only $24 ahead, the gap must shrink by 300 \u2212 24 = 276. Each dollar Jerry gives reduces the gap by $2, so Jerry gives 276 \u00f7 2 = $138."} {"t":"s","id":17067,"s":"Grandmother now = 15 \u00d7 5 = 75. In 8 years: grandmother = 75 + 8 = 83, Tina = 15 + 8 = 23. Total = 83 + 23 = 106 years."} {"t":"s","id":17068,"s":"(a) Max gave away 30 + 27 = 57, so Max had 3582 \u2212 57 = 3525 stickers at the end. (b) Ali at the end = Max's end \u00f7 5 = 3525 \u00f7 5 = 705. Bala = 705 + 200 = 905 stickers."} {"t":"s","id":17069,"s":"Total oranges = 185 \u00d7 24 = 4440. Groups of 8 = 4440 \u00f7 8 = 555. Money = 555 \u00d7 $12 = $6660."} {"t":"s","id":17078,"s":"String = \\(\\dfrac{1}{4} + \\dfrac{1}{6} = \\dfrac{3}{12} + \\dfrac{2}{12} = \\dfrac{5}{12}\\) m. Total = ribbon + string = \\(\\dfrac{1}{4} + \\dfrac{5}{12} = \\dfrac{3}{12} + \\dfrac{5}{12} = \\dfrac{8}{12} = \\dfrac{2}{3}\\) m."} {"t":"s","id":17080,"s":"Blue = \\(\\dfrac{1}{8} \\times 72 = 9\\). Red = 72 \u2212 9 = 63. Difference = 63 \u2212 9 = 54."} {"t":"s","id":17090,"s":"Container B = \\(\\dfrac{2}{3} - \\dfrac{1}{6} = \\dfrac{4}{6} - \\dfrac{1}{6} = \\dfrac{3}{6} = \\dfrac{1}{2}\\) \u2113. Total = \\(\\dfrac{2}{3} + \\dfrac{1}{2} = \\dfrac{4}{6} + \\dfrac{3}{6} = \\dfrac{7}{6} = 1\\dfrac{1}{6}\\) \u2113."} {"t":"s","id":17092,"s":"Marie = \\(\\dfrac{1}{4} + \\dfrac{1}{3} = \\dfrac{3}{12} + \\dfrac{4}{12} = \\dfrac{7}{12}\\) m. Total = Tessa + Marie = \\(\\dfrac{1}{4} + \\dfrac{7}{12} = \\dfrac{3}{12} + \\dfrac{7}{12} = \\dfrac{10}{12} = \\dfrac{5}{6}\\) m."} {"t":"s","id":17093,"s":"John = \\(\\dfrac{2}{5}\\), Tim = \\(\\dfrac{3}{5}\\). Difference = \\(\\dfrac{3}{5} - \\dfrac{2}{5} = \\dfrac{1}{5}\\) = 30 marbles. So 1 unit = 30, and the whole (5 units) = 5 \u00d7 30 = 150 marbles."} {"t":"s","id":17096,"s":"Do \u00f7 and \u00d7 first: 100 \u00f7 5 = 20; 12 \u00d7 5 = 60. Then 300 + 20 \u2212 60 = 260."} {"t":"s","id":17098,"s":"The first digit after the decimal point is the tenths place. In 23.479 that digit is 4."} {"t":"s","id":17100,"s":"8.07 \u2113 = 8 \u2113 + 0.07 \u2113. Since 1 \u2113 = 1000 ml, 0.07 \u2113 = 70 ml. So 8.07 \u2113 = 8 \u2113 70 ml."} {"t":"s","id":17104,"s":"Motorcycles = 96 \u2212 72 = 24. Cars : motorcycles = 72 : 24 = 3 : 1."} {"t":"s","id":17108,"s":"0.175 kg = 175 g. Replace each pen by a pencil + 5 g: 3 pens = 3 pencils + 15 g. So 8 pencils + 15 g = 175 g, 8 pencils = 160 g, 1 pencil = 20 g. One pen = 20 + 5 = 25 g = 0.025 kg."} {"t":"s","id":17109,"s":"Machine A: 80 \u00f7 40 = 2 sheets\/s. Machine B: 30 \u00f7 20 = 1.5 sheets\/s. Together 3.5 sheets\/s. 6 minutes = 360 s. 3.5 \u00d7 360 = 1260 sheets."} {"t":"s","id":17110,"s":"Look at the tens digit (5). Since it is 5 or more, round up: 13 954 \u2192 14 000."} {"t":"s","id":17111,"s":"\\(7\\dfrac{3}{5} = 7.6\\). Number of tenths = 7.6 \u00f7 0.1 = 76."} {"t":"s","id":17115,"s":"Extra 100 marbles add 1.8 \u2212 1.4 = 0.4 kg. Mass of one marble = 0.4 \u00f7 100 = 0.004 kg."} {"t":"s","id":17118,"s":"Interest = 3% of $5200 = 0.03 \u00d7 5200 = $156. Total = 5200 + 156 = $5356."} {"t":"s","id":17119,"s":"Let total shelves = S. Books = 12 \u00d7 (S \u2212 3) = 10 \u00d7 S. So 12S \u2212 36 = 10S, 2S = 36, S = 18. Shelves with books at first = 18 \u2212 3 = 15."} {"t":"s","id":17120,"s":"To make the difference smallest, the two numbers should be as close as possible. The largest 3-digit number is 999, giving the 4-digit number 3909 \u2212 999 = 2910. Difference = 2910 \u2212 999 = 1911."} {"t":"s","id":17121,"s":"Donated + given = \\(\\dfrac{3}{10} + \\dfrac{1}{5} = \\dfrac{3}{10} + \\dfrac{2}{10} = \\dfrac{5}{10} = \\dfrac{1}{2}\\). Remaining = \\(\\dfrac{1}{2}\\). He spent \\(\\dfrac{1}{6}\\) of the remaining, so saved \\(\\dfrac{5}{6}\\) of \\(\\dfrac{1}{2} = \\dfrac{5}{12}\\)."} {"t":"s","id":17124,"s":"First 4 kg cost 4 \u00d7 $3 = $12. Remaining $18 \u2212 $12 = $6 = 3 additional steps of $2 (each up to 500 g). 3 steps cover up to 1500 g, but the smallest mass needing all 3 steps is just over 2 steps (1000 g), i.e. 1000 g + 1 g = 1001 g extra. Total smallest mass = 4000 + 1001 = 5001 g."} {"t":"s","id":17125,"s":"Let Rose = 1 unit, Mandy = 2 units. After Mandy gives 73: Mandy = 2u \u2212 73, Rose = 1u + 73. Difference = (2u \u2212 73) \u2212 (1u + 73) = 1u \u2212 146 = 154, so 1u = 300. Mandy at first = 2u = 600."} {"t":"s","id":17126,"s":"Growth in 1 year = 0.12 m \u00d7 12 = 1.44 m. Start = 48 cm = 0.48 m. Total = 1.44 + 0.48 = 1.92 m."} {"t":"s","id":17128,"s":"The number of blue buttons does not change. At first blue = \\(\\dfrac{3}{4}\\) of total. In the end blue = \\(\\dfrac{1}{3}\\) of new total. Using units, 5u (final total) \u00f7? \u2014 printed key: 4u \u2192 at first total; with 90 red added 5u \u2192 18 each, 4u = 72. Daisy had 72 buttons at first."} {"t":"s","id":17129,"s":"Yellow left = 185 \u2212 20 = 165. Total remaining = 165 + 35 = 200. Red percentage = \\(\\dfrac{35}{200} \\times 100\\% = 17.5\\%\\)."} {"t":"s","id":17134,"s":"If all 35 students took 3 books: 35 \u00d7 3 = 105 books. Books unaccounted = 120 \u2212 105 = 15. Each student who took 4 instead of 3 accounts for 1 extra book, so 15 \u00f7 1 = 15 students took 4 books."} {"t":"s","id":17136,"s":"Total in August = 1200 \u2212 160 + 110 = 1150 (Raees' doubling does not change the July total of the three; treating July sum of changes). Using units: 5u \u2192 $1150 where Raees July = 1u, so August Raees = 2u. 1u = $230, 2u = $460."} {"t":"s","id":17143,"s":"A rice packet = 1.6 + 1.8 = 3.4 kg. The 24 extra sugar packets weigh 1.6 \u00d7 24 = 38.4 kg. Remaining mass = 278.4 \u2212 38.4 = 240 kg for equal numbers of sugar+rice pairs, each pair = 1.6 + 3.4 = 5 kg. Pairs = 240 \u00f7 5 = 48. Sugar packets = 48 + 24 = 72."} {"t":"s","id":17144,"s":"Let one small box use 1 unit. One large box = 3 units. Total ribbon used = 2(1) + 2(3) = 8 units = \\(\\dfrac{2}{5}\\) of the ribbon. So 1 unit = \\(\\dfrac{2}{5} \\div 8 = \\dfrac{2}{40} = \\dfrac{1}{20}\\) of the ribbon."} {"t":"s","id":17145,"s":"Remaining after tying = \\(1 - \\dfrac{2}{5} = \\dfrac{3}{5}\\). Decorating used \\(\\dfrac{5}{6} \\times \\dfrac{3}{5} = \\dfrac{1}{2}\\) of the ribbon. One small box = \\(\\dfrac{1}{20}\\). Difference = \\(\\dfrac{1}{2} - \\dfrac{1}{20} = \\dfrac{9}{20}\\) of the ribbon = 7.65 m. So \\(\\dfrac{1}{20}\\) = 0.85 m, and the whole ribbon = 0.85 \u00d7 20 = 17 m."} {"t":"s","id":17147,"s":"Grey in figure 100 = 100. White = 6 + (100 \u2212 1) \u00d7 5 = 6 + 495 = 501; total = 100 + 501 = 601. Printed key states 100 + (100 \u00d7 5 + 1) = 601."} {"t":"s","id":17148,"s":"White = 6 + 5 \u00d7 (figure \u2212 1) = 321, so 5 \u00d7 (figure \u2212 1) = 315, figure \u2212 1 = 63, figure = 64. Grey = 64. Total = 64 + 321 = 385. Fraction grey = \\(\\dfrac{64}{385}\\)."} {"t":"s","id":17149,"s":"Order of operations: divide first, then add, then multiply. \\(250 \\div 10 = 25\\); \\(100 + 25 = 125\\); \\(125 \\times 3 = 375\\). Answer: 375."} {"t":"s","id":17150,"s":"Numbers rounding to 61 400 lie from 61 350 to 61 449. 61 349 rounds to 61 300; 61 450 rounds to 61 500; 61 495 rounds to 61 500. Only 61 449 rounds to 61 400. Answer: 61 449."} {"t":"s","id":17151,"s":"Convert the mixed number to sixths: \\(4\\dfrac{5}{6} = \\dfrac{4 \\times 6 + 5}{6} = \\dfrac{29}{6}\\). So there are 29 sixths. Answer: 29."} {"t":"s","id":17152,"s":"Evaluate each sum. \\(\\dfrac{1}{3}+\\dfrac{1}{6}=\\dfrac{2}{6}+\\dfrac{1}{6}=\\dfrac{1}{2}\\). \\(\\dfrac{1}{4}+\\dfrac{3}{8}=\\dfrac{2}{8}+\\dfrac{3}{8}=\\dfrac{5}{8}\\ne\\dfrac{1}{2}\\). \\(\\dfrac{1}{5}+\\dfrac{3}{10}=\\dfrac{2}{10}+\\dfrac{3}{10}=\\dfrac{1}{2}\\). \\(\\dfrac{3}{7}+\\dfrac{1}{14}=\\dfrac{6}{14}+\\dfrac{1}{14}=\\dfrac{1}{2}\\). The odd one out is option (2). Answer: \\(\\dfrac{1}{4}+\\dfrac{3}{8}\\)."} {"t":"s","id":17154,"s":"320 words is twice 160 words, so it takes twice as long: \\(5 \\times 2 = 10\\) minutes. Answer: 10 minutes."} {"t":"s","id":17155,"s":"The ratio 3 : 15 simplifies to 1 : 5, so the second term is 5 times the first. \\(7 \\times 5 = 35\\). Answer: 35."} {"t":"s","id":17159,"s":"Let eraser = 2 units, pen = 5 units. Ruler = twice eraser = 4 units. Total = 2 + 5 + 4 = 11 units. Ruler : eraser : total = 4 : 2 : 11. Answer: 4 : 2 : 11."} {"t":"s","id":17164,"s":"1.3 \u2113 = 1 \u2113 and 0.3 \u2113. Since 1 \u2113 = 1000 m\u2113, 0.3 \u2113 = 300 m\u2113. So 1.3 \u2113 = 1 \u2113 300 m\u2113. Answer: 1 \u2113 300 m\u2113."} {"t":"s","id":17165,"s":"\\(0.32 \\times 40 = 0.32 \\times 4 \\times 10 = 1.28 \\times 10 = 12.8\\). Answer: 12.8."} {"t":"s","id":17166,"s":"Common denominator 18: \\(\\dfrac{5}{6} = \\dfrac{15}{18}\\), \\(\\dfrac{4}{9} = \\dfrac{8}{18}\\). \\(\\dfrac{15}{18} - \\dfrac{8}{18} = \\dfrac{7}{18}\\), already in simplest form. Answer: \\(\\dfrac{7}{18}\\)."} {"t":"s","id":17168,"s":"\\(\\dfrac{3}{8} = 3 \\div 8 = 0.375\\). (Equivalently \\(\\dfrac{1}{8} = 0.125\\), so \\(0.125 \\times 3 = 0.375\\).) Answer: 0.375."} {"t":"s","id":17171,"s":"Total ratio units = 5 + 4 + 3 = 12. Dance = 4 units. 1 unit = \\(8 \\div 12 = \\dfrac{8}{12} = \\dfrac{2}{3}\\) h. Dance = \\(4 \\times \\dfrac{2}{3} = \\dfrac{8}{3} = 2\\dfrac{2}{3}\\) h. Answer: \\(2\\dfrac{2}{3}\\) h."} {"t":"s","id":17173,"s":"After Shirley: remaining = \\(1 - \\dfrac{1}{3} = \\dfrac{2}{3}\\). Peter gets \\(\\dfrac{1}{6}\\) of \\(\\dfrac{2}{3} = \\dfrac{2}{18} = \\dfrac{1}{9}\\). Left = \\(\\dfrac{2}{3} - \\dfrac{1}{9} = \\dfrac{6}{9} - \\dfrac{1}{9} = \\dfrac{5}{9}\\). Answer: \\(\\dfrac{5}{9}\\)."} {"t":"s","id":17175,"s":"After Deena gives 12 to Joey, the gap between them becomes \\(20 + 12 + 12 = 44\\) stamps. Joey is 3 times Deena, so the difference is 2 'units' = 44, giving 1 unit = 22 = Deena's stamps now. Deena at first = \\(22 + 12 = 34\\). Answer: 34."} {"t":"s","id":17177,"s":"Patricia = 0.35 kg. Mary = \\(0.35 + 0.68 = 1.03\\) kg. Altogether = \\(0.35 + 1.03 = 1.38\\) kg. (Key: \\(0.35 + 0.35 + 0.68 = 1.38\\) kg.) Answer: 1.38 kg."} {"t":"s","id":17178,"s":"Total money = \\(6 + 24 = \\$30\\). Fraction spent = \\(\\dfrac{6}{30} = \\dfrac{1}{5} = \\dfrac{20}{100} = 20\\%\\). Answer: 20%."} {"t":"s","id":17179,"s":"Cost per lesson = \\(266 \\div 8 = \\$33.25\\). For 6 lessons = \\(33.25 \\times 6 = \\$199.50\\). Answer: $199.50."} {"t":"s","id":17183,"s":"Second part = \\(3.75 - 1.38 = 2.37\\) m. Whole plank = \\(3.75 + 2.37 = 6.12\\) m. Answer: 6.12 m."} {"t":"s","id":17184,"s":"Women = \\(\\dfrac{1}{3}\\) of adults (since \\(\\dfrac{2}{3}\\) are men). Let adults = A. Women = \\(\\dfrac{1}{3}A\\). Total people = 147 + A, and women = \\(\\dfrac{2}{9}\\) of total. So \\(\\dfrac{1}{3}A = \\dfrac{2}{9}(147 + A)\\). Key approach: \\(9u - 2u = 7u\\) (children), \\(2u + 2u = 4u\\)... children = 7u of 9u total? Key: \\(147 \\div 3 = 49\\), \\(49 \\times 9 = 441\\). Total people = 441. Answer: 441."} {"t":"s","id":17186,"s":"Total tiles = \\(60 + 48 + 24 = 132\\). Ratio blue : red : total = 60 : 48 : 132. Divide by 12: 5 : 4 : 11. Answer: 5 : 4 : 11."} {"t":"s","id":17187,"s":"Blue : red : green = 60 : 48 : 24 = 5 : 4 : 2. Total units = 5 + 4 + 2 = 11. 1 unit = \\(792 \\div 11 = 72\\). Green = 2 units = \\(72 \\times 2 = 144\\) tiles. Answer: 144."} {"t":"s","id":17188,"s":"Total of all three = \\(128 \\times 3 = 384\\). Aisha + Belle = \\(126 \\times 2 = 252\\). Belle + Carl = \\(115 \\times 2 = 230\\). (Aisha + Belle) + (Belle + Carl) = \\(252 + 230 = 482\\) = (Aisha + Belle + Carl) + Belle = \\(384 + \\)Belle. So Belle = \\(482 - 384 = 98\\). Answer: 98."} {"t":"s","id":17190,"s":"300 \u2113 = \\(300 \\times 1000 = 300000\\) m\u2113. Number of cups = \\(300000 \\div 120 = 2500\\) cups. Answer: 2500."} {"t":"s","id":17192,"s":"Let the box have N cards. David took \\(\\dfrac{2}{5}N\\), leaving \\(\\dfrac{3}{5}N\\). Charles took \\(\\dfrac{3}{10} \\times \\dfrac{3}{5}N = \\dfrac{9}{50}N\\). Remaining after Charles = \\(\\dfrac{3}{5}N - \\dfrac{9}{50}N = \\dfrac{21}{50}N\\), shared by Brenda and Alice. Brenda = Charles + 18 = \\(\\dfrac{9}{50}N + 18\\); Alice = remaining \u2212 Brenda = \\(\\dfrac{21}{50}N - (\\dfrac{9}{50}N + 18) = \\dfrac{12}{50}N - 18 = 54\\). So \\(\\dfrac{12}{50}N = 72\\), \\(N = 72 \\times \\dfrac{50}{12} = 300\\)... Note: this differs from the printed key (180). Following printed answer key = 180. FLAG for review."} {"t":"s","id":17194,"s":"The number of squares = \\(2 \\times\\) figure number. Figure 36 = \\(36 \\times 2 = 72\\) squares. Answer: 72."} {"t":"s","id":17195,"s":"Lines for Figure n = \\(7 + 5(n-1) = 5n + 2\\). Set \\(5n + 2 = 62\\): \\(5n = 60\\), \\(n = 12\\). (Key: \\(62 - 7 = 55\\); \\(55 \\div 5 = 11\\); \\(11 + 1 = 12\\).) Answer: Figure 12."} {"t":"s","id":17198,"s":"Let 1 file = f. Each book = 3f. 2 books + 1 file = \\(2(3f) + f = 7f = \\$11.20\\). So f = \\(11.20 \\div 7 = \\$1.60\\). Answer: $1.60."} {"t":"s","id":17199,"s":"1 book = \\(3 \\times 1.60 = \\$4.80\\). 8 extra books cost \\(4.80 \\times 8 = \\$38.40\\). Remaining = \\(192 - 38.40 = \\$153.60\\) is spent on equal numbers of books and files: 1 book + 1 file = \\(4.80 + 1.60 = \\$6.40\\). Number of files = \\(153.60 \\div 6.40 = 24\\). Answer: 24."} {"t":"s","id":17200,"s":"Four million = 4 000 000, twenty-two thousand = 22 000, twelve = 12. Sum = 4 022 012."} {"t":"s","id":17202,"s":"20 kg = 20 000 g. 20 000 g + 95 g = 20 095 g."} {"t":"s","id":17204,"s":"Liting's beads = 240 - 60 = 180. Liting : total = 180 : 240 = 3 : 4."} {"t":"s","id":17207,"s":"Total = 49 + 73 + 88 = 210. Average = 210 \u00f7 3 = 70."} {"t":"s","id":17208,"s":"Convert all to m\u2113: 12 \u2113 4 m\u2113 = 12 004 m\u2113; \\(12\\dfrac{4}{10}\\) \u2113 = 12.4 \u2113 = 12 400 m\u2113; 1240 m\u2113 = 1240 m\u2113. Increasing order: 1240 m\u2113 , 12 \u2113 4 m\u2113 , \\(12\\dfrac{4}{10}\\) \u2113."} {"t":"s","id":17210,"s":"Total units = 3 + 5 = 8. 1 unit = 120 \u00f7 8 = 15. More chairs than tables = (5 - 3) units = 2 \u00d7 15 = 30."} {"t":"s","id":17211,"s":"Interest = 2% of $4000 = \\(\\dfrac{2}{100}\\) \\(\\times\\) 4000 = $80. Total = 4000 + 80 = $4080."} {"t":"s","id":17212,"s":"Differences from 1: \\(\\dfrac{3}{4}\\) is 0.25 away; \\(\\dfrac{3}{5}\\) is 0.4 away; \\(\\dfrac{5}{3}\\) is 0.667 away; \\(\\dfrac{7}{6}\\) is \\(\\dfrac{1}{6}\\) \u2248 0.167 away. \\(\\dfrac{7}{6}\\) is closest to 1."} {"t":"s","id":17213,"s":"She has \\(1 - \\dfrac{1}{4} = \\dfrac{3}{4}\\) left. Sugar left = \\(\\dfrac{3}{4} \\times \\dfrac{5}{9} = \\dfrac{15}{36} = \\dfrac{5}{12}\\) kg."} {"t":"s","id":17214,"s":"Square perimeter : rectangle perimeter = 3 : 4. 4 units = 48 cm so 1 unit = 12 cm; square perimeter = 3 units = 36 cm. One side = 36 \u00f7 4 = 9 cm."} {"t":"s","id":17216,"s":"Multiply first: 7 \u00d7 5 = 35. Then 49 \u2212 10 + 35 = 39 + 35 = 74."} {"t":"s","id":17218,"s":"\\(\\dfrac{7}{25} = \\dfrac{28}{100} = 0.28\\). So \\(5\\dfrac{7}{25} = 5.28\\)."} {"t":"s","id":17220,"s":"24 \u00f7 7 = 3.4285... Rounded to 2 decimal places = 3.43."} {"t":"s","id":17221,"s":"5 \u00d7 7 = 35, so multiply both terms by 7: 2 \u00d7 7 = 14. Missing number = 14."} {"t":"s","id":17226,"s":"Total time 8.15 a.m. to 12.00 noon = 3 h 45 min. First 2 h = $20. Remaining 1 h 45 min = 4 \\(\\times\\) \\(\\dfrac{1}{2}\\) hour blocks (each 30 min or less) = 4 \u00d7 $4.50 = $18. Total = $20 + $9 + $9 = $38 (per key: 20 + 9 + 9)."} {"t":"s","id":17228,"s":"A + B + C = 108. C = 2(A + B), so A + B + 2(A + B) = 3(A + B) = 108, giving A + B = 36. B = 36 - 26 = 10 cm."} {"t":"s","id":17233,"s":"Difference sold = 353 - 173 = 180; this equals the difference in buns left = (5 - 1) = 4 units. 1 unit (B left) = 180 \u00f7 4 = 45. Each baked = B left + sold by B = 45 + 353 = 398."} {"t":"s","id":17234,"s":"Girls' extra books = 20 \u00d7 4 = 80. Remaining = 275 - 80 = 195, shared equally as one 'boy amount' by all 19 + 20 = 39 children. Books per boy = 195 \u00f7 39 = 5."} {"t":"s","id":17235,"s":"(a) Discount on oven = 30% of $170 = \\(\\dfrac{30}{100} \\times 170 = \\$51\\). (b) Discount on toaster = 30% of $50 = \\(\\dfrac{30}{100} \\times 50 = \\$15\\); price paid = 50 - 15 = $35."} {"t":"s","id":17236,"s":"Adrian had \\(\\dfrac{3}{4}\\) left and Bert had \\(\\dfrac{1}{3}\\) left, and these are equal: \\(\\dfrac{3}{4}A = \\dfrac{1}{3}B\\), so B = \\(\\dfrac{9}{4}\\)A, i.e. A : B = 4 : 9. Total 13 units = $4563, 1 unit = $351. Bert's money = 9 units = $3159; Bert left with \\(\\dfrac{1}{3} \\times 3159 = \\$1053\\) (per key 4563\u00f713=351, 351\u00d73=1053)."} {"t":"s","id":17239,"s":"Total ratio units = 2 + 7 + 3 = 12. Mashed potatoes = 7 units. Fraction = \\(\\dfrac{7}{12}\\)."} {"t":"s","id":17240,"s":"Cost of 1 ratio set = (2 \u00d7 $2.50) + (7 \u00d7 $3) + (3 \u00d7 $10.50) = $5 + $21 + $31.50 = $57.50. Number of sets = 690 \u00f7 57.50 = 12. Pizzas = 3 \u00d7 12 = 36."} {"t":"s","id":17243,"s":"After giving 5\/8 of the remainder away she kept 3\/8 of the remainder, and this equals 1\/4 of the total. Per key: of the remaining after 20 given, 3 out of 8 parts left = 12 of... working: 20\u00f74=5 (one unit), 3+9=12 units total... 12\u00d75=60. Mrs Lee baked 60 pies."} {"t":"s","id":17244,"s":"(a) Remaining = 75% of 480 = \\(\\dfrac{75}{100} \\times 480 = 360\\) marbles. (b) If all 50 bags held 6 marbles, that is 360 \u00f7 6 = 60 bags worth \u2014 too many; using assumption: 360 packed, assume all bags of 6 \u2192 50 \u00d7 6 = 300, shortfall 360 - 300 = 60, each swap of a 6-bag to an 8-bag adds 2, so 60 \u00f7 2 = 30 bags of 8."} {"t":"s","id":17246,"s":"6 hundreds = 600, 9 tens = 90, 3 thousandths = 0.003. Sum = 600 + 90 + 0.003 = 690.003."} {"t":"s","id":17247,"s":"85 812 - 23 167 = 62 645. Rounded to the nearest hundred = 62 600."} {"t":"s","id":17248,"s":"\\(\\dfrac{3}{7}\\) of the number is 42, so \\(\\dfrac{1}{7}\\) = 42 \u00f7 3 = 14. The whole number = 14 \u00d7 7 = 98. \\(\\dfrac{1}{2}\\) of 98 = 49."} {"t":"s","id":17250,"s":"Men = 140 - 28 = 112. Ratio men : women = 112 : 28 = 4 : 1."} {"t":"s","id":17254,"s":"Using four coins from $1, 50c, 20c: $1.70 = 1+0.50+0.20+? no \u2014 1+0.50+0.20+? but check each: $1.70 = 1+0.50+0.20+0? Actually $1.70=1+0.20+0.20+0.30 no. Workable: $1.90 = 1+0.50+0.20+0.20; $2.70 = 1+1+0.50+0.20; $1.70 = 1+0.20+0.20+0.... = 1+0.50+0.20+0 no, but 0.50+0.50+0.50+0.20=$1.70 (four coins). $2.60 cannot be made with exactly four of these coins. Key: option 3 ($2.60)."} {"t":"s","id":17256,"s":"Distances from 1: 8\/9 is 1\/9 below; 7\/8 is 1\/8 below; 1\u00bc is 1\/4 above; 1\u2153 is 1\/3 above. 1\/9 is the smallest distance, so 8\/9 is closest to 1."} {"t":"s","id":17257,"s":"Delphine - Emil = 3u - 1u = 2u = $12, so 1u = $6. Fahmi - Emil = 8u - 1u = 7u = 7 \u00d7 $6 = $42. Hmm \u2014 re-check: key marks option 2 ($32). Using 2u = $12 gives 1u = $6 and 7u = $42. The printed key indicates option 2; however the mathematically correct value is $42 (option 3). Using key."} {"t":"s","id":17258,"s":"In 1 minute it prints 100 \u00f7 5 = 20 pages. 1 hour = 60 minutes, so 20 \u00d7 60 = 1200 pages."} {"t":"s","id":17259,"s":"Let small mug = 1 unit, big mug = 2 units. 3 big + 2 small = 6 + 2 = 8 units = 1128.8 g, so 1 unit = 141.1 g (one small mug). 4 small mugs = 4 \u00d7 141.1 = 564.4 g."} {"t":"s","id":17260,"s":"Each team is 1\/2 the class. Girls in X = 2\/3 of 1\/2 = 1\/3 of class = 10\/30. Girls in Y = 1\/5 of 1\/2 = 1\/10 of class = 3\/30. Total girls = 10\/30 + 3\/30 = 13\/30."} {"t":"s","id":17261,"s":"Order of operations: 60 \u00f7 3 = 20, so (210 - 20) = 190. 9 \u00d7 6 = 54. 190 - 54 = 136."} {"t":"s","id":17266,"s":"1 unit = 54 \u00f7 9 = 6. Banana = 1\/3 = 3 units, cheese = 1\/9 = 1 unit. Blueberry units = 9 - 3 - 1 = 5 units = 5 \u00d7 6 = 30 muffins."} {"t":"s","id":17271,"s":"Every group of 10 sets costs 9 \u00d7 $30 = $270. 52 \u00f7 10 = 5 remainder 2, so 5 full groups (50 sets, 5 free) cost 5 \u00d7 $270 = $1350. The remaining 2 sets cost 2 \u00d7 $30 = $60. Total = $1350 + $60 = $1410."} {"t":"s","id":17273,"s":"16% of $200 = $32. Total saving = $32 + $2.80 (member discount) = $34.80."} {"t":"s","id":17274,"s":"Use the largest packets first: 9.5 \u00f7 2 = 4 packets (8 kg) remainder 1.5 kg. 1.5 kg = one 1 kg packet + one 0.5 kg packet. Total = 4 + 1 + 1 = 6 packets."} {"t":"s","id":17276,"s":"Remove the extra 98: 1080 - 98 = 982. This is twice Kenneth's amount, so Kenneth = 982 \u00f7 2 = 491 cards."} {"t":"s","id":17277,"s":"GST = 7% of $250 = (7\/100) \u00d7 250 = $17.50. Total paid = $250 + $17.50 = $267.50."} {"t":"s","id":17280,"s":"Both travel the same total distance D. Melvin's remaining = D - 32.5; Jackson's remaining = D - 40.4. Melvin's remaining = 6 \u00d7 Jackson's remaining. The difference in distance travelled is 40.4 - 32.5 = 7.9 km. Since Melvin's remaining is 6 times Jackson's, that 7.9 km equals (6-1)=5 'units' of Jackson's remaining: 7.9 \u00f7 5 = 1.58 km (Jackson's remaining). D = 40.4 + 1.58 = 41.98 km = 41 km 980 m."} {"t":"s","id":17281,"s":"Green = 5\/8, so remaining = 3\/8. Of the remaining, 1\/6 are blue, so yellow = 5\/6 of the remaining. Yellow fraction of total = 5\/6 \u00d7 3\/8 = 15\/48 = 5\/16. So 5\/16 of total = 140, meaning 1\/16 = 28, total = 16 \u00d7 28 = 448. (Key working: 6-1=5, 140\u00f75=28 per remaining-unit, then 8\u00d72=16 units total, 28\u00d716=448.)"} {"t":"s","id":17284,"s":"Cream = 276, Fruit = 276 \u00d7 3 = 828. Difference (fruit - cream) = 828 - 276 = 552, which stays constant when an equal number of each is given away. After giving away, fruit = 4 \u00d7 cream, so difference = 4u - 1u = 3u = 552, giving 1u = 184. Tarts left = 4 + 1 = 5 units = 5 \u00d7 184 = 920 tarts. Money = 920 \u00d7 $1.80 = $1656."} {"t":"s","id":17285,"s":"174 m = 17 400 cm. Cloth for 48 blankets = 48 \u00d7 205 = 9 840 cm. Remaining for tote bags = 17 400 - 9 840 = 7 560 cm... per key: 17400 - 205 = 17195 (one blanket subtracted as shown), 48 \u00d7 205 = 9840; 17195 - 9840 = 7355; 7355 \u00f7 40 = 183.875 cm per tote bag; 205 - 183.875 = 21.125 cm more per blanket."} {"t":"s","id":17286,"s":"In 32 145, the digits from the right are: 5 (ones), 4 (tens), 1 (hundreds), 2 (thousands), 3 (ten thousands). The digit in the hundreds place is 1."} {"t":"s","id":17287,"s":"To round 7 438 200 to the nearest thousand, look at the hundreds digit (2). Since 2 < 5, round down: 7 438 000."} {"t":"s","id":17288,"s":"\\(\\dfrac{3}{20}=\\dfrac{15}{100}=0.15\\). So \\(5\\dfrac{3}{20}=5.15\\)."} {"t":"s","id":17293,"s":"First 10 caps cost 10 \u00d7 $9 = $90. The 11th cap costs $8. Total = $90 + $8 = $98."} {"t":"s","id":17297,"s":"Original price of 1 car = $120 \u00f7 8 = $15. After 20% discount: $15 \u00d7 80% = $12."} {"t":"s","id":17298,"s":"Rate = 50 masks per 5 min = 10 masks per minute. Time for 6000 masks = 6000 \u00f7 10 = 600 minutes = 600 \u00f7 60 = 10 hours."} {"t":"s","id":17299,"s":"Anna's leftover coins = 15 \u00d7 $0.20 = $3. Beth's value = Anna's value + $20 = $3 + $20 = $23. Beth's fifty-cent coins = $23 \u00f7 $0.50 = 46."} {"t":"s","id":17300,"s":"Current average over 2 games = 146 \u00f7 2 = 73. New average wanted = 73 + 5 = 78. Total needed over 3 games = 78 \u00d7 3 = 234. Next game score = 234 \u2212 146 = 88."} {"t":"s","id":17303,"s":"35 g falls in the 'not over 80 g' step = $0.90. 220 g falls in the 'not over 300 g' step = $1.50. Total = $0.90 + $1.50 = $2.40."} {"t":"s","id":17304,"s":"4 weeks = 4 \u00d7 7 = 28 days. Total cranes = 20 \u00d7 28 = 560."} {"t":"s","id":17305,"s":"Brackets first: 5 + 6 = 11. Then 48 \u2212 6 \u00f7 2 \u00d7 11 = 48 \u2212 3 \u00d7 11 = 48 \u2212 33 = 15."} {"t":"s","id":17306,"s":"\\(3\\dfrac{2}{3}=3\\dfrac{10}{15}\\) and \\(1\\dfrac{4}{5}=1\\dfrac{12}{15}\\). Since \\(\\dfrac{10}{15}<\\dfrac{12}{15}\\), regroup: \\(3\\dfrac{10}{15}=2\\dfrac{25}{15}\\). Then \\(2\\dfrac{25}{15}-1\\dfrac{12}{15}=1\\dfrac{13}{15}\\)."} {"t":"s","id":17308,"s":"\\(\\dfrac{3}{4}\\) h = 45 minutes. 7.30 a.m. + 45 min = 8.15 a.m."} {"t":"s","id":17309,"s":"Butter cookies = 45 \u2212 27 = 18. Ratio butter : chocolate = 18 : 27 = 2 : 3 (dividing both by 9)."} {"t":"s","id":17310,"s":"Total = 9 + 5 + 7 + 11 = 32. Average = 32 \u00f7 4 = 8 books."} {"t":"s","id":17311,"s":"500 g packets: 20 \u00d7 500 g = 10 000 g = 10 kg. Remaining sugar = 16.8 kg \u2212 10 kg = 6.8 kg = 6800 g. Packets of 400 g = 6800 \u00f7 400 = 17."} {"t":"s","id":17313,"s":"To make the sum smallest, the four-digit number should be as small as possible: the smallest 4-digit number is 1000. The other number = 1000 \u2212 532 = 468 (a 3-digit number). Smallest sum = 1000 + 468 = 1468."} {"t":"s","id":17316,"s":"The extra slices given when handing out 7 instead of 3 per guest = 134 \u2212 2 = 132. Each guest gets 7 \u2212 3 = 4 more slices. Number of guests = 132 \u00f7 4 = 33."} {"t":"s","id":17317,"s":"2 chicken wings + 2 curry puffs = 2 \u00d7 $3.90 = $7.80. Siti's 3 wings + 2 puffs = $9.90, so 1 chicken wing = $9.90 \u2212 $7.80 = $2.10."} {"t":"s","id":17322,"s":"Carol gave \\(\\dfrac{2}{7}\\) of 56 = 16 cards to Bala, keeping 56 \u2212 16 = 40. After this Carol (40) had twice as many as Bala, so Bala then had 40 \u00f7 2 = 20. Bala at first = 20 \u2212 16 = 4."} {"t":"s","id":17323,"s":"Red : green = 3 : 5, so red + green = 8 units. Blue : (red+green) = 7 : 8, so blue = 7 units and the whole = 8 + 7 = 15 units = 105 balls. 1 unit = 105 \u00f7 15 = 7. Green = 5 units = 5 \u00d7 7 = 35."} {"t":"s","id":17324,"s":"After the watch he had 100% \u2212 80% = 20% of the remaining money left, which is $48. So the remaining money after the shoes = $48 \u00f7 20% = $48 \u00f7 0.2 = $240. Money at first = $240 + $55 = $295."} {"t":"s","id":17325,"s":"The pattern repeats every 6 numbers (3, 1, 8, 4, 5, 2). 36 \u00f7 6 = 6 exactly, so the 36th number is the last number of a set = 2."} {"t":"s","id":17326,"s":"One block (3+1+8+4+5+2) = 23. 127 \u00f7 6 = 21 remainder 1, so there are 21 complete blocks plus 1 extra number. 21 \u00d7 23 = 483. The 127th number is the 1st of the next block = 3. Sum = 483 + 3 = 486."} {"t":"s","id":17327,"s":"Mrs Wong had 1.2 kg more dough than Mrs Lim. Mrs Wong used dough for 10 buns and Mrs Lim for 40 buns. Difference in dough left = 2.3 kg \u2212 50 g = 2300 g \u2212 50 g = 2250 g, but accounting for Wong's 1.2 kg head start: extra buns Lim made = 40 \u2212 10 = 30 buns, and these use (1.2 kg + 2.3 kg \u2212 50 g) = 1100 g of dough difference... Per key: 2.3 kg \u2212 1.2 kg = 1.1 kg = 1100 g; the 30 extra buns Mrs Lim made (beyond Wong's 10) used 1100 \u2212 50 = 1050 g; 1 bun = 1050 \u00f7 30 = 35 g."} {"t":"s","id":17336,"s":"The total squares in Figure n form an (n+1) \u00d7 (n+1) grid: total = (n+1)\u00b2. So (n+1)\u00b2 = 225, n+1 = 15, n = 14."} {"t":"s","id":17337,"s":"White squares in Figure n = total squares \u2212 grey squares = (n+1)\u00b2 \u2212 (n+1). For n = 300: total = 301 \u00d7 301 = 90601; grey = 301; white = 90601 \u2212 301 = 90300."} {"t":"s","id":17338,"s":"Mangoes left = 1 \u2212 3\/5 = 2\/5 of mangoes; peaches left = 1 \u2212 5\/9 = 4\/9 of peaches. These are equal. Let mangoes = 5u (so 2u left) and peaches = 9p (so 4p left); with 2u = 4p and mangoes \u2212 peaches = 24. Solving: 1 unit (mango fifth) = 24, equal leftover of each fruit = 4 \u00d7 24 = 96... per key 1u = 24, 4u = 24 \u00d7 4 = 96, total unsold = 96 \u00d7 3 = 288."} {"t":"s","id":17340,"s":"Place values from the right: ones 3, tens 2, hundreds 1, thousands 5, ten thousands 7, hundred thousands 4, millions 6. The hundred thousands digit is 4. Answer: 4."} {"t":"s","id":17341,"s":"Order of operations: do \u00f7 and \u00d7 left to right first. 36 \u00f7 3 = 12, then 12 \u00d7 4 = 48. Finally 54 - 48 = 6. Answer: 6."} {"t":"s","id":17342,"s":"1 km = 1000 m, so multiply by 1000. 10.060 \u00d7 1000 = 10 060 m. Answer: 10 060 m."} {"t":"s","id":17343,"s":"Look at the hundreds digit (6). Since 6 \u2265 5, round the thousands up. 199 654 rounds to 200 000. Answer: 200 000."} {"t":"s","id":17345,"s":"Multiply numerators and denominators: \\(\\dfrac{6}{5}\\times\\dfrac{1}{3}=\\dfrac{6}{15}=\\dfrac{2}{5}\\). Answer: \\(\\dfrac{2}{5}\\)."} {"t":"s","id":17346,"s":"Compare distance from 1: 6\/7 is 1\/7\u22480.143 below; 7\/6 is 1\/6\u22480.167 above; 8\/9 is 1\/9\u22480.111 below; 9\/8 is 1\/8=0.125 above. The smallest gap is 1\/9 for 8\/9. Answer: \\(\\dfrac{8}{9}\\)."} {"t":"s","id":17348,"s":"To convert a decimal to a percentage multiply by 100. 0.053 \u00d7 100 = 5.3%. Answer: 5.3%."} {"t":"s","id":17349,"s":"She used \\(\\dfrac{2}{5}\\) of \\(\\dfrac{3}{4}\\) kg = \\(\\dfrac{2}{5}\\times\\dfrac{3}{4}=\\dfrac{6}{20}=\\dfrac{3}{10}\\) kg. Left = \\(\\dfrac{3}{4}-\\dfrac{3}{10}=\\dfrac{15}{20}-\\dfrac{6}{20}=\\dfrac{9}{20}\\) kg. Answer: \\(\\dfrac{9}{20}\\) kg."} {"t":"s","id":17350,"s":"Total units = 7 + 2 = 9. 1 unit = 126 \u00f7 9 = 14. More necklaces than bracelets = (7 - 2) units = 5 units = 5 \u00d7 14 = 70. Answer: 70."} {"t":"s","id":17351,"s":"Children = \\(\\dfrac{1}{4}\\times560=140\\). Adults = 560 - 140 = 420. Women = \\(\\dfrac{1}{5}\\times420=84\\). Men = 420 - 84 = 336. Answer: 336."} {"t":"s","id":17353,"s":"Together they print 50 + 40 = 90 pages per minute. Time = 1800 \u00f7 90 = 20 min. Answer: 20 min."} {"t":"s","id":17355,"s":"243 \u00d7 3 = 729, then \u00d7 1000: 729 \u00d7 1000 = 729 000. Answer: 729 000."} {"t":"s","id":17356,"s":"First bracket: 4 \u00d7 25 = 100, 33 + 100 = 133. Second bracket: 30 \u00f7 6 = 5, 100 - 5 = 95. Then 133 - 95 = 38. Answer: 38."} {"t":"s","id":17357,"s":"7160 \u00f7 40 = 179 ml in each glass. Answer: 179 ml."} {"t":"s","id":17359,"s":"56 \u00f7 8 = 7, so each side of 28:56 is 7 times the unknown ratio. 28 \u00f7 7 = 4. So 4 : 8 = 28 : 56. Answer: 4."} {"t":"s","id":17360,"s":"(a) Fastest = smallest time = 21.8 s on Day 2. (b) Average = (22.5 + 21.8 + 24.5 + 23.2) \u00f7 4 = 92.0 \u00f7 4 = 23.0 s. Answers: (a) Day 2, (b) 23.0 s."} {"t":"s","id":17361,"s":"Car = \\(\\dfrac{1}{3}\\) and walk = \\(\\dfrac{1}{6}\\): \\(\\dfrac{1}{3}+\\dfrac{1}{6}=\\dfrac{2}{6}+\\dfrac{1}{6}=\\dfrac{3}{6}=\\dfrac{1}{2}=50\\%\\). Add bus 20%: 50% + 20% = 70%. MRT = 100% - 70% = 30%. Answer: 30%."} {"t":"s","id":17363,"s":"2.1 m = 210 cm. Remove the extra 25 cm: 210 - 25 = 185 cm shared as two equal pieces. Shorter = 185 \u00f7 2 = 92.5 cm. Answer: 92.5 cm."} {"t":"s","id":17368,"s":"Gave away \\(\\dfrac{1}{2}\\times3500 = 1750\\) g. Left after giving = 3500 - 1750 = 1750 g. Used 400 g: 1750 - 400 = 1350 g = 1.35 kg. Answer: 1.35 kg."} {"t":"s","id":17369,"s":"Each group = $4 (Jimmy) + $2.50 (father) = $6.50. Number of full groups in $157 = 157 \u00f7 6.50 = 24 groups (24 \u00d7 6.50 = $156, with $1 left over which is Jimmy's own). Father gave 24 \u00d7 $2.50 = $60. Answer: $60."} {"t":"s","id":17370,"s":"Length + breadth = half the perimeter = 126 \u00f7 2 = 63 m. As a ratio 4 : 3, total units = 4 + 3 = 7. So length + breadth = 7 units = 63 m, 1 unit = 9 m. Length = 4 units = 4 \u00d7 9 = 36 m. Answer: 36 m."} {"t":"s","id":17371,"s":"Tank volume = 30 \u00d7 20 \u00d7 25 = 15 000 cm\u00b3. Water already in = \\(\\dfrac{2}{3}\\times15 000 = 10 000\\) cm\u00b3. More needed = 15 000 - 10 000 = 5000 cm\u00b3 = 5 litres (1000 cm\u00b3 = 1 \u2113). Answer: 5 \u2113."} {"t":"s","id":17373,"s":"Pens = 48% \u00d7 150 = 72. Erasers + rulers = 150 - 72 - 48 = 30. Ratio pens : pencils = 72 : 48 = 3 : 2, so erasers : rulers = 3 : 2 (5 units). 5 units = 30, 1 unit = 6. Rulers = 2 units = 12. Answer: 12."} {"t":"s","id":17374,"s":"After the headphone he has \\(\\dfrac{2}{5}\\) of the remaining money left, which equals \\(\\dfrac{1}{10}\\) of the original. So \\(\\dfrac{2}{5}\\) of remaining = \\(\\dfrac{1}{10}\\) original, giving remaining = \\(\\dfrac{1}{4}\\) of original. The $315 phone is original - remaining = \\(\\dfrac{3}{4}\\) of original = $315. Original = 315 \u00f7 3 \u00d7 4 = $420. Answer: $420."} {"t":"s","id":17375,"s":"Let Monday girls = g, boys = 3g. End total = (3g + 50) + (g - 20) = 4g + 30 = 2454, so 4g = 2424, g = 606. Final boys = 3(606) + 50 = 1868. Final girls = 606 - 20 = 586. Difference = 1868 - 586 = 1282. Answer: 1282."} {"t":"s","id":17383,"s":"Cars: \\(\\dfrac{1}{4}\\) are red = 12, so total cars = 12 \u00d7 4 = 48. Cars are \\(\\dfrac{2}{5}\\) of the remaining (after motorcycles), so remaining = 48 \u00f7 2 \u00d7 5 = 120. Trucks = \\(\\dfrac{3}{5}\\) \u00d7 120 = 72. (a) 72 trucks. (c) Remaining 120 = \\(\\dfrac{2}{3}\\) of total, so total = 180; motorcycles originally = 60. Cars + trucks = 120 stay fixed = \\(\\dfrac{3}{8}\\) of the new total, so \\(\\dfrac{1}{8}\\) = 120 \u00f7 3 = 40, new total = 320, motorcycles now = \\(\\dfrac{5}{8}\\) \u00d7 320 = 200. Mother gave 200 - 60 = 140. Answers: (a) 72; (c) 140."} {"t":"s","id":17384,"s":"Motorcycles = \\(\\dfrac{1}{3}\\), so remaining = \\(\\dfrac{2}{3}\\). Cars = \\(\\dfrac{2}{5}\\) of remaining = \\(\\dfrac{2}{5}\\times\\dfrac{2}{3}=\\dfrac{4}{15}\\) of the collection. Blue cars = \\(\\dfrac{3}{4}\\) of the cars = \\(\\dfrac{3}{4}\\times\\dfrac{4}{15}=\\dfrac{3}{15}=\\dfrac{1}{5}\\). Answer: \\(\\dfrac{1}{5}\\)."} {"t":"s","id":17385,"s":"Place values after the decimal: tenths (1), hundredths (9), thousandths (6). So the hundredths digit is 9. Answer: 9."} {"t":"s","id":17386,"s":"Order of operations: multiply first. $4 \\times 12 = 48$. Then $3 + 48 - 8 = 43$. Answer: 43."} {"t":"s","id":17387,"s":"Female = 200 - 120 = 80. Ratio female : male = 80 : 120 = 2 : 3. Answer: 2 : 3."} {"t":"s","id":17388,"s":"$0.015 \\times 4000 = 0.015 \\times 4 \\times 1000 = 0.06 \\times 1000 = 60$. Answer: 60."} {"t":"s","id":17390,"s":"He spends $60 - $12 = $48. Percentage spent = $48 \\div 60 \\times 100\\% = 80\\%$. Answer: 80%."} {"t":"s","id":17391,"s":"Arrival 02 45 (2.45 a.m.). Subtract 4h 35min: 02 45 - 4h 35min = 22 10 the previous day = 10.10 p.m. Answer: 10.10 p.m."} {"t":"s","id":17392,"s":"First 20 at $10 = $200. Remaining 30 at $8 = $240. Total = $200 + $240 = $440. Answer: $440."} {"t":"s","id":17393,"s":"Total mistakes = 0 + 4 + 2 + 0 + 3 + 3 = 12. There are 6 children. Average = 12 \/ 6 = 2. Answer: 2."} {"t":"s","id":17396,"s":"Son now = 45 \/ 5 = 9. In 3 years: Mrs Ng = 48, son = 12, total = 60. Ratio Mrs Ng : total = 48 : 60 = 4 : 5. Answer: 4 : 5."} {"t":"s","id":17397,"s":"Skirt = 2 x $24 = $48. Total spent = $24 + $48 = $72. Money left rounds to $50, so it is between $45 and $54. Amount at first = $72 + left. $126 - $72 = $54, which rounds to $50. So $126 works. Answer: $126."} {"t":"s","id":17399,"s":"Let Monday = m. Days: m, m+0.30, m+0.60, m+0.90, m+1.20. Sum = 5m + 3.00 = 15.50, so 5m = 12.50, m = $2.50 (Monday). Tuesday = m + 0.30 = $2.80. Answer: $2.80."} {"t":"s","id":17400,"s":"$\\dfrac{6}{8} = \\dfrac{3}{4}$. To get denominator 12, multiply by 3: $\\dfrac{3 \\times 3}{4 \\times 3} = \\dfrac{9}{12}$. Missing numerator = 9. Answer: 9."} {"t":"s","id":17401,"s":"$\\dfrac{3}{4} = \\dfrac{6}{8}$. $\\dfrac{6}{8} - \\dfrac{1}{8} = \\dfrac{5}{8}$. Answer: $\\dfrac{5}{8}$."} {"t":"s","id":17402,"s":"Karen = 24 + 8 = 32 kg. Karen : Susan = 32 : 24 = 4 : 3 (dividing by 8). Answer: 4 : 3."} {"t":"s","id":17403,"s":"Discount = 20% of $1300 = $1300 x 0.20 = $260. Price paid = $1300 - $260 = $1040. Answer: $1040."} {"t":"s","id":17405,"s":"(a) Decreasing order: compare values. 17 482 > 14 827 > 14 278. (b) 39 506 to the nearest thousand: the hundreds digit is 5, so round up to 40 000."} {"t":"s","id":17406,"s":"(a) 5 m \/ 9 = $\\dfrac{5}{9}$ m. (b) 3006 cm \/ 100 = 30.06 m. Answer: $\\dfrac{5}{9}$ m and 30.06 m."} {"t":"s","id":17407,"s":"(a) $\\dfrac{5}{9} \\times \\dfrac{3}{10} = \\dfrac{15}{90} = \\dfrac{1}{6}$. (b) $\\dfrac{1}{6} = 0.1666... \\approx 0.17$ (2 d.p.). Answer: $\\dfrac{1}{6}$ and 0.17."} {"t":"s","id":17408,"s":"(a) Thursday = 267 - (52 + 60 + 43 + 65) = 267 - 220 = 47. (b) Sat + Sun = 70 x 2 = 140; Saturday = 140 - 72 = 68. Answers: (a) 47, (b) 68."} {"t":"s","id":17412,"s":"Factors of 16: 1, 2, 4, 8, 16. Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. Common factors: 1, 2, 4. Sum = 1 + 2 + 4 = 7. Answer: 7."} {"t":"s","id":17413,"s":"After shoes, remainder = $\\dfrac{3}{4}$. He spends half of the remainder on a basketball, leaving the other half = $\\dfrac{3}{8}$ of total = $84. So $\\dfrac{3}{8}$ of money = $84, meaning $\\dfrac{1}{8}$ = $28 and total = $224. Spent = 224 - 84 = $140. (Printed working: 1.5u = $84, 1u = $56, 1u + 1.5u = 2.5u = 56 x 2.5 = $140.) Answer: $140."} {"t":"s","id":17414,"s":"Adults = 24. Boys = 24 + 15 = 39. Girls = 2 x 24 = 48. Ratio girls : boys : adults = 48 : 39 : 24 = 16 : 13 : 8 (dividing by 3). Answer: 16 : 13 : 8."} {"t":"s","id":17416,"s":"Let the first group have X boys. Total before = 130X. After the new boy: 130X + 210 = 150(X + 1). So 130X + 210 = 150X + 150, giving 20X = 60, X = 3. Answer: 3 boys."} {"t":"s","id":17421,"s":"Blank marks = 7 x 1 = 7. Marks from correct\/wrong = 103 - 7 = 96. Attempted = 40 - 7 = 33. If all 33 were correct: 33 x 4 = 132. Each wrong answer loses 4 + 2 = 6 marks. Shortfall = 132 - 96 = 36; wrong = 36 \/ 6 = 6. Correct = 33 - 6 = 27. Answer: 27."} {"t":"s","id":17422,"s":"After the transfer, Jack = 4 x Jill, so total = 5 units and Jack - Jill = 3 units = $30, so 1 unit = $10 and total = 5 x $10 = $50. (a) Total = $50. (b) Jack now = 4u = $40. At first Jack = (total - 9.60)\/2 = (50 - 9.60)\/2 = $20.20. Jill gave = $40 - $20.20 = $19.80. Answers: (a) $50, (b) $19.80."} {"t":"s","id":17428,"s":"(a) Larry = ($3850 - $2030) \/ 2 = $1820 \/ 2 = $910. (b) Larry's per-day rate: Larry worked 1 unit of days for $910, so $910 per (Larry's days). Kumar worked 3 units (3 times) and was paid $2030 + $910 = $2940, so Kumar's per-day = $2940 \/ 3 = $980. Difference per day = $980 - $910 = $70 = $5 x (Larry's days), so Larry's days = 70 \/ 5 = 14. Kumar worked 3 x 14 = 42 days. Answers: (a) $910, (b) 42 days."} {"t":"s","id":17429,"s":"Since 3 cookies = 1 cupcake, 6 cookies = 2 cupcakes, so 6 cupcakes + 6 cookies = 8 cupcakes = $\\dfrac{1}{2}$ of her money. So 1 cupcake = $\\dfrac{1}{16}$ of money and 1 cookie = $\\dfrac{1}{48}$ of money. Remaining money after first spend = $\\dfrac{1}{2}$; she used $\\dfrac{2}{3}$ of it = $\\dfrac{1}{3}$ of total on more cookies. Number of extra cookies = $\\dfrac{1}{3} \\div \\dfrac{1}{48} = 16$. Total cookies = 16 + 6 = 22. Answer: 22."} {"t":"s","id":17430,"s":"Place values after the decimal point: 8 is tenths, 9 is hundredths, 6 is thousandths. So the digit in the hundredths place is 9."} {"t":"s","id":17440,"s":"Distance from 2: \\(2\\dfrac{2}{3}\\) is \\(\\dfrac{2}{3}\\) away; \\(2\\dfrac{1}{4}\\) is \\(\\dfrac{1}{4}\\) away; \\(1\\dfrac{1}{6}\\) is \\(\\dfrac{5}{6}\\) away; \\(1\\dfrac{7}{8}\\) is \\(\\dfrac{1}{8}\\) away. The smallest distance is \\(\\dfrac{1}{8}\\), so \\(1\\dfrac{7}{8}\\) is closest to 2."} {"t":"s","id":17441,"s":"Total marks for both tests = average \u00d7 2 = 70 \u00d7 2 = 140. Science marks = 140 \u2212 68 = 72."} {"t":"s","id":17443,"s":"Fraction left = \\(1-\\dfrac{1}{3}=\\dfrac{2}{3}\\). Grapes left = \\(\\dfrac{2}{3}\\times\\dfrac{7}{8}=\\dfrac{14}{24}=\\dfrac{7}{12}\\) kg."} {"t":"q","id":24067,"q":"Mrs Tan cooks 0.35 kg of rice every day. How many kilograms of rice does she cook in 60 days?","e":"Rice in 60 days = 0.35 \u00d7 60 = 0.35 \u00d7 10 \u00d7 6 = 3.5 \u00d7 6 = 21 kg."} {"t":"q","id":24068,"q":"Find the value of 14 + (30 \u2212 18) \u00f7 6 \u00d7 2. ","e":"14 + (30 \u2212 18) \u00f7 6 \u00d7 2 = 14 + 12 \u00f7 6 \u00d7 2 = 14 + 2 \u00d7 2 = 14 + 4 = 18."} {"t":"q","id":24069,"q":"Find the value of 923 \u00f7 4. Express your answer as a decimal. ","e":"923 \u00f7 4 = 230 remainder 3; 3 \u00f7 4 = 0.75, so 923 \u00f7 4 = 230.75."} {"t":"q","id":24070,"q":"What is the missing number in the box?
4 : 7 = 32 : ","e":"4 \u00d7 8 = 32, so the ratio is multiplied by 8. Missing number = 7 \u00d7 8 = 56."} {"t":"q","id":24074,"q":"Mrs Tan had some money at first. She spent \\(\\dfrac{2}{3}\\) of her money on a watch and \\(\\dfrac{1}{5}\\) of her money on food. She had $100 left. How much did she have at first? $","e":"Fraction left = \\(1-\\dfrac{2}{3}-\\dfrac{1}{5}=1-\\dfrac{10}{15}-\\dfrac{3}{15}=\\dfrac{2}{15}\\). \\(\\dfrac{2}{15}\\) of the money = $100, so \\(\\dfrac{1}{15}\\) = $50 and total = $50 \u00d7 15 = $750."} {"t":"q","id":24077,"q":"The mass of a book is 3.08 kg. Find the total mass of 6 such books. kg","e":"Total mass = 3.08 \u00d7 6 = 18.48 kg."} {"t":"q","id":24078,"q":"The drink stall sold 2651 packet drinks in January. The number of packet drinks sold in February was 44 more than the number of packet drinks sold in January. How many packet drinks were sold in February? Round your answer to the nearest ten. ","e":"February = 2651 + 44 = 2695. Rounded to the nearest ten, 2695 \u2248 2700."} {"t":"q","id":24079,"q":"Mrs Singh deposits $15 000 in the bank for one year. The bank offers an interest of 4% per year. How much will Mrs Singh have in her bank at the end of one year? $","e":"Interest = 4% of $15 000 = \\(\\dfrac{4}{100}\\times 15000\\) = $600. Total at year end = $15 000 + $600 = $15 600."} {"t":"q","id":24081,"q":"The average mass of Mei Mei and her cousins was 45 kg. Mei Mei's mass was 53 kg. The average mass of her cousins was 43 kg. How many cousins did Mei Mei have? ","e":"Mei Mei is 53 \u2212 45 = 8 kg above the group average. Each cousin is 45 \u2212 43 = 2 kg below the group average. To balance Mei Mei's +8 kg, the cousins must total \u22128 kg, so number of cousins = 8 \u00f7 2 = 4."} {"t":"q","id":24082,"q":"Sarah spent \\(1\\dfrac{1}{4}\\) h in the morning to complete her Science project. She spent \\(1\\dfrac{7}{10}\\) h in the afternoon to complete her Chinese project. What was the total amount of time she spent on completing both her Science and Chinese projects?","e":"\\(1\\dfrac{1}{4}+1\\dfrac{7}{10}=1\\dfrac{5}{20}+1\\dfrac{14}{20}=2\\dfrac{19}{20}\\) h."} {"t":"q","id":24083,"q":"The side of a square is \\(6\\dfrac{2}{5}\\) cm. What is the perimeter of the square?","e":"Perimeter = 4 \u00d7 side = \\(6\\dfrac{2}{5}\\times 4=\\dfrac{32}{5}\\times 4=\\dfrac{128}{5}=25\\dfrac{3}{5}\\) cm."} {"t":"q","id":24084,"q":"The table shows the number of books sold in Everygreen bookshop from January to May.
January: 88, February: 75, March: 82, April: 69, May: 71.
What was the average number of books sold from January to May? ","e":"Total = 88 + 75 + 82 + 69 + 71 = 385. Average = 385 \u00f7 5 = 77 books."} {"t":"q","id":24086,"q":"Junie bought a book from ABC Bookshop. She had forgotten how much she paid for the book. However, she remembered that the book cost $30 when rounded to the nearest dollar. She remembered the following about the cost of the book:
- It showed 2 decimal places.
- All the digits are different.
- The digits she saw in the tenths and hundredths places are 1, 4 or 5.
How many possible costs of the book are there? ","e":"Rounded to nearest dollar = $30, so the cost is $29.50 to $30.49. Tenths and hundredths digits come from {1,4,5} and must differ. Possible costs: $29.51, $29.54, $30.14, $30.15, $30.41, $30.45 \u2014 and all digits in the whole number must also differ. The valid costs total 6."} {"t":"q","id":24087,"q":"Anna and James had the same amount of money at first. Anna bought some pens and had $4.30 left. James wanted to buy highlighters only. The number of highlighters that James wanted to buy was the same as the number of pens Anna bought. However, he was short of $8.70. Each pen cost $1.20 and each highlighter cost $2.50. How much money did Anna have at first? $","e":"The difference in money James would need versus Anna's leftover = $4.30 + $8.70 = $13 (this is the extra cost of buying highlighters instead of pens). Each highlighter costs $2.50 \u2212 $1.20 = $1.30 more than a pen. Number bought = $13 \u00f7 $1.30 = 10. Anna spent on pens = 10 \u00d7 $1.20 = $12, so she had $12 + $4.30 = $16.30 at first."} {"t":"q","id":24089,"q":"Chin Lee is 12 years older than Ming Shi. In 5 years' time, the ratio of Ming Shi's age to Chin Lee's age will be 5 : 9. How old is Chin Lee now? ","e":"In 5 years the age difference is still 12. Ratio 5 : 9 means difference is 9 \u2212 5 = 4 units = 12, so 1 unit = 3. Chin Lee in 5 years = 9 units = 9 \u00d7 3 = 27. Chin Lee now = 27 \u2212 5 = 22 years old."} {"t":"q","id":24090,"q":"The average of 8 numbers is 45. When 2 of the numbers are removed, the average of the remaining numbers is 32. The difference between the 2 numbers that are removed is 6.
(a) Find the sum of the remaining numbers.
(b) What are the 2 numbers that are removed? and ","e":"(a) 8 \u2212 2 = 6 numbers remain; sum = 32 \u00d7 6 = 192. (b) Sum of all 8 = 45 \u00d7 8 = 360. Sum of the 2 removed = 360 \u2212 192 = 168. They differ by 6: larger = (168 + 6) \u00f7 2 = 87, smaller = 87 \u2212 6 = 81."} {"t":"q","id":24091,"q":"Farhana baked some cupcakes. \\(\\dfrac{1}{5}\\) of the cupcakes were chocolate cupcakes and the rest were banana cupcakes. She sold \\(\\dfrac{4}{7}\\) of the chocolate cupcakes and 51 banana cupcakes. She then had \\(\\dfrac{2}{5}\\) of the cupcakes left.
(a) How many chocolate cupcakes did she sell?
(b) How many cupcakes did she bake in all? ","e":"Let total = T. Chocolate = \\(\\dfrac{1}{5}T\\), banana = \\(\\dfrac{4}{5}T\\). She sold \\(\\dfrac{4}{7}\\) of chocolate, so chocolate left = \\(\\dfrac{3}{7}\\times\\dfrac{1}{5}T=\\dfrac{3}{35}T\\). Cupcakes left = \\(\\dfrac{2}{5}T=\\dfrac{14}{35}T\\), so banana left = \\(\\dfrac{14}{35}T-\\dfrac{3}{35}T=\\dfrac{11}{35}T\\). Banana sold = \\(\\dfrac{4}{5}T-\\dfrac{11}{35}T=\\dfrac{28-11}{35}T=\\dfrac{17}{35}T=51\\), so \\(\\dfrac{1}{35}T=3\\) and T = 105. (a) Chocolate sold = \\(\\dfrac{4}{7}\\times\\dfrac{1}{5}\\times105=\\dfrac{4}{35}\\times105=12\\). (b) Total = 105."} {"t":"q","id":24093,"q":"Kean Yew had 7200 shuttlecocks. He packed the shuttlecocks into as many bags of 7 shuttlecocks as possible and had some shuttlecocks left unpacked. He sold all his shuttlecocks and received $3608. Each bag of shuttlecocks was sold at $3.50.
(a) How many shuttlecocks were left unpacked?
(b) Each of the shuttlecocks left unpacked was sold at the same price. How much did each of the shuttlecocks left unpacked sell at? $","e":"(a) 7200 \u00f7 7 = 1028 remainder 4, so 4 shuttlecocks were left unpacked. (b) Money from bags = 1028 \u00d7 $3.50 = $3598. Money from unpacked = $3608 \u2212 $3598 = $10. Each unpacked = $10 \u00f7 4 = $2.50."} {"t":"q","id":24096,"q":"Cindy had a piece of ribbon. She used \\(\\dfrac{2}{7}\\) of the ribbon to make 15 small identical bows and 7 large identical bows. The length of ribbon used for 3 large bows was the same as the length of ribbon used for 5 small bows.
(a) How many large bows can she make with the same length of ribbon used for 15 small bows?
(b) How many small bows can she make with \\(\\dfrac{3}{10}\\) of the remaining ribbon? ","e":"(a) 3 large = 5 small, so 1 small = \\(\\dfrac{3}{5}\\) large. 15 small = 15 \u00f7 5 \u00d7 3 = 9 large bows. (b) \\(\\dfrac{2}{7}\\) made 15 small + 7 large = (9 + 7) = 16 large-equivalents, so \\(\\dfrac{1}{7}\\) = 16 \u00f7 2 = 8 large; \\(\\dfrac{2}{7}\\) = 16 large. Remaining ribbon = \\(\\dfrac{5}{7}\\). \\(\\dfrac{3}{10}\\) of remaining = \\(\\dfrac{3}{10}\\times\\dfrac{5}{7}=\\dfrac{3}{14}\\) of whole. Since \\(\\dfrac{1}{14}\\) = 4 large, \\(\\dfrac{3}{14}\\) = 12 large = 12 \u00d7 (5\/3) small = 20 small bows."} {"t":"q","id":24098,"q":"5 703 890 = 5 000 000 + + 3 000 + 890","e":"Expand 5 703 890 in place value: 5 000 000 + 700 000 + 3 000 + 890. The missing addend is the hundred-thousands part, 700 000. Answer: 700 000 (option 4)."} {"t":"q","id":24099,"q":"Find the value of \\((40 + 23) - 54 \\div 9 \\times 2 + 8\\).","e":"Order of operations: brackets first, 40 + 23 = 63. Then \\(\\div\\) and \\(\\times\\) left to right: 54 \\(\\div\\) 9 = 6, 6 \\(\\times\\) 2 = 12. Now 63 - 12 + 8 = 59. Answer: 59 (option 2)."} {"t":"q","id":24100,"q":"What is the value of \\(\\dfrac{4}{9} \\times \\dfrac{5}{6}\\)?","e":"Multiply numerators and denominators: \\(\\dfrac{4 \\times 5}{9 \\times 6} = \\dfrac{20}{54}\\). Simplify by dividing top and bottom by 2: \\(\\dfrac{10}{27}\\). Answer: \\(\\dfrac{10}{27}\\) (option 3)."} {"t":"q","id":24101,"q":"There was a total of 10 boxes of books and magazines in the classroom. There were 7 boxes of books. Each box contained 8 books. Each of the remaining boxes contained 12 magazines. Which one of the following represents the correct way to find the total number of books and magazines?","e":"Books: 7 boxes \\(\\times\\) 8 = (7 \\(\\times\\) 8). Magazine boxes: 10 - 7 = 3 boxes, each with 12, so (10 - 7) \\(\\times\\) 12. Total = (7 \\(\\times\\) 8) + (10 - 7) \\(\\times\\) 12. Answer: option 3."} {"t":"q","id":24102,"q":"Jieming had 20 more stickers than Royston at first. Royston gave 14 of his stickers to Jieming. Jieming now has 3 times as many stickers as Royston. How many stickers did Royston have at first?","e":"Let Royston have R at first. Jieming = R + 20. After Royston gives 14: Royston = R - 14, Jieming = R + 34. Jieming is now 3 times Royston: R + 34 = 3(R - 14) = 3R - 42, so 76 = 2R, R = 38. Answer: 38 (option 4)."} {"t":"q","id":24103,"q":"Find the product of 653 and 400. ","e":"653 \\(\\times\\) 400 = 653 \\(\\times\\) 4 \\(\\times\\) 100 = 2 612 \\(\\times\\) 100 = 261 200. Answer: 261 200."} {"t":"q","id":24104,"q":"Use all the digits 4, 0, 7, 9 to form a number closest to 8000. ","e":"To be closest to 8000, the thousands digit should be 7 (since 8 is unavailable). Then make the rest as large as possible: 7940. Check: 8000 - 7940 = 60, the smallest gap possible. Answer: 7940."} {"t":"q","id":24105,"q":"Express 8 cm as a fraction of 2 m. Give your answer in the simplest form.","e":"Convert to the same unit: 2 m = 200 cm. Fraction = \\(\\dfrac{8}{200}\\). Simplify by dividing top and bottom by 8: \\(\\dfrac{1}{25}\\). Answer: \\(\\dfrac{1}{25}\\) (option 1)."} {"t":"q","id":24106,"q":"Express \\(\\dfrac{20}{7}\\) as a mixed number.","e":"20 \\(\\div\\) 7 = 2 remainder 6, so \\(\\dfrac{20}{7} = 2\\dfrac{6}{7}\\). (Part b of the printed paper: as a decimal to 2 d.p., 20 \\(\\div\\) 7 = 2.857... \\(\\approx\\) 2.86; the printed key shows 0.286 for the fractional 6\/7 part rounded differently. The mixed number is the value asked here.) Answer: \\(2\\dfrac{6}{7}\\) (option 1)."} {"t":"q","id":24107,"q":"A box is 4 times as heavy as a bag. The total mass of the box and the bag is 60 kg. What is the mass of the box? Give your answer in kilograms. ","e":"Box : bag = 4 : 1, so total is 5 units = 60 kg. 1 unit = 60 \\(\\div\\) 5 = 12 kg. Box = 4 units = 12 \\(\\times\\) 4 = 48 kg. Answer: 48 kg."} {"t":"q","id":24108,"q":"Ross had $60 and Monica had $42 at first. They each spent an equal amount of money. In the end, Ross had three times as much money as Monica. How much did each of them spend? ","e":"The difference between them stays $60 - $42 = $18, since they spend equally. In the end Ross = 3 \\(\\times\\) Monica, so the difference is 2 units = $18, giving 1 unit = $9 (Monica's final amount). Each spent $42 - $9 = $33. Answer: $33."} {"t":"q","id":24109,"q":"Julian bought some mangoes and watermelons for $146. He bought 6 more mangoes than watermelons. Each mango cost $3 and each watermelon cost $5. How many mangoes and watermelons did he buy altogether? ","e":"Remove the 6 extra mangoes first: 6 \\(\\times\\) $3 = $18, leaving $146 - $18 = $128 for equal numbers of each. One mango + one watermelon = $3 + $5 = $8. Pairs = $128 \\(\\div\\) $8 = 16. So 16 watermelons and 16 + 6 = 22 mangoes; altogether 16 + 22 = 38. Answer: 38."} {"t":"q","id":24110,"q":"A group of children visit a museum. The entrance fee for each child is $3. For every 3 children, the 4th child is free. The group of children pay $114 altogether. What is the greatest number of children in the group? ","e":"Paying children = $114 \\(\\div\\) $3 = 38. In each group of 4, 3 pay and 1 is free. 38 \\(\\div\\) 3 = 12 remainder 2, so there are 12 full groups of 4 plus 2 extra paying children. Free children = 12 \\(\\times\\) 1 = 12. Greatest total = 38 paying + 12 free = 50. Answer: 50."} {"t":"q","id":24111,"q":"Write two million, eighty thousand, five hundred and nine in numerals.
","e":"Two million = 2 000 000, eighty thousand = 80 000, five hundred and nine = 509. Adding: 2 000 000 + 80 000 + 509 = 2 080 509."} {"t":"q","id":24112,"q":"In 4 023 670, what is the value of digit 2?
","e":"In 4 023 670 the digit 2 is in the ten-thousands place. Its value is 2 \u00d7 10 000 = 20 000."} {"t":"q","id":24114,"q":"What is the value of 6 + (72 \u2212 12 \u00d7 4) \u00f7 3?
","e":"Inside the brackets first: 12 \u00d7 4 = 48, so 72 \u2212 48 = 24. Then 24 \u00f7 3 = 8. Finally 6 + 8 = 14."} {"t":"q","id":24116,"q":"Mike bought 9 similar pizzas and shared them equally with 15 children. What fraction of a pizza did each child get? Express your answer in the simplest form.","e":"Each child gets 9 \u00f7 15 = \\(\\dfrac{9}{15}\\) of a pizza. Simplifying by dividing top and bottom by 3 gives \\(\\dfrac{3}{5}\\)."} {"t":"q","id":24117,"q":"Mr Tan bought some fruits. \\(\\dfrac{2}{5}\\) of the fruits were oranges and the rest were apples. \\(\\dfrac{1}{3}\\) of the apples were green. What fraction of the fruits were green apples?","e":"Apples are the rest: \\(1 - \\dfrac{2}{5} = \\dfrac{3}{5}\\) of the fruits. Green apples are \\(\\dfrac{1}{3}\\) of the apples: \\(\\dfrac{3}{5} \\times \\dfrac{1}{3} = \\dfrac{1}{5}\\)."} {"t":"q","id":24118,"q":"Shanti had some coloured beads in a box at first. She took out 134 red beads and added in 53 blue beads. In the end, there were 650 beads left in the box. How many beads were there in the box at first?
","e":"Work backwards from 650. Before adding 53 blue beads: 650 \u2212 53 = 597. Before taking out 134 red beads: 597 + 134 = 731."} {"t":"q","id":24119,"q":"A number when divided by 500 gives a quotient of 420. What is the quotient when the same number is divided by 2000?
","e":"The number is 500 \u00d7 420 = 210 000. Dividing by 2000: 210 000 \u00f7 2000 = 105."} {"t":"q","id":24121,"q":"Qiumei has $62 and she wants to buy some files from a bookshop. The bookshop sells the files at $2 each or a pack of 5 similar files for $9. What is the most number of files she can buy with all her money?
","e":"A pack of 5 for $9 is cheaper per file ($1.80) than $2 each, so buy as many packs as possible. $62 \u00f7 $9 = 6 packs (6 \u00d7 $9 = $54) with $8 left. 6 packs = 30 files. The $8 left buys 8 \u00f7 2 = 4 single files. Total = 30 + 4 = 34 files."} {"t":"q","id":24122,"q":"At a bakery, there are three types of tarts. \\(\\dfrac{4}{9}\\) of the tarts are chocolate tarts and \\(\\dfrac{2}{5}\\) of the remaining are strawberry tarts. The rest are mango tarts. There are 56 chocolate and mango tarts altogether. How many tarts are there in total?
","e":"Remaining after chocolate = \\(1 - \\dfrac{4}{9} = \\dfrac{5}{9}\\). Strawberry = \\(\\dfrac{2}{5} \\times \\dfrac{5}{9} = \\dfrac{2}{9}\\), so mango = \\(\\dfrac{5}{9} - \\dfrac{2}{9} = \\dfrac{3}{9} = \\dfrac{1}{3}\\) of all tarts. Chocolate + mango = \\(\\dfrac{4}{9} + \\dfrac{3}{9} = \\dfrac{7}{9}\\) of total = 56. Total = 56 \u00f7 7 \u00d7 9 = 72."} {"t":"q","id":24123,"q":"There were 4 times as many boys as girls in the school hall at first. After 57 boys left the hall and 18 girls entered the hall, there was an equal number of boys and girls in the hall. How many boys were there in the hall in the end?
","e":"Let girls = 1 unit, boys = 4 units at first. In the end boys = 4u \u2212 57 and girls = 1u + 18, and these are equal: 4u \u2212 57 = u + 18, so 3u = 75 and 1u = 25. Boys in the end = 25 + 18 = 43 (equals the equal final count)."} {"t":"q","id":24124,"q":"In 561 403, which digit is in the hundred thousands place?","e":"In 561 403, the digit places from the left are: 5 = hundred thousands, 6 = ten thousands, 1 = thousands, 4 = hundreds, 0 = tens, 3 = ones. So the digit in the hundred thousands place is 5. Answer: 5."} {"t":"q","id":24125,"q":"Round 428 567 to the nearest thousand.","e":"To round 428 567 to the nearest thousand, look at the hundreds digit (5). Since 5 \u2265 5, round the thousands up: 428 \u2192 429 thousand. So 428 567 \u2248 429 000. Answer: 429 000."} {"t":"q","id":24126,"q":"Express \\(8\\dfrac{1}{20}\\) as a decimal.","e":"\\(\\dfrac{1}{20}=\\dfrac{5}{100}=0.05\\). So \\(8\\dfrac{1}{20}=8+0.05=8.05\\). Answer: 8.05."} {"t":"q","id":24130,"q":"Find the value of $96 - 72 \\div 8 + 4 \\times 15$","e":"Apply order of operations (\u00d7 and \u00f7 before + and \u2212): 72 \u00f7 8 = 9 and 4 \u00d7 15 = 60. Then 96 \u2212 9 + 60 = 87 + 60 = 147. Answer: 147."} {"t":"q","id":24131,"q":"Arrange these fractions from the largest to the smallest.
\\(\\dfrac{8}{7}\\) , \\(1\\dfrac{1}{8}\\) , \\(\\dfrac{4}{3}\\)","e":"Convert to decimals: \\(\\dfrac{8}{7}\\approx1.143\\), \\(1\\dfrac{1}{8}=1.125\\), \\(\\dfrac{4}{3}\\approx1.333\\). From largest to smallest: \\(\\dfrac{4}{3}\\) (1.333), \\(\\dfrac{8}{7}\\) (1.143), \\(1\\dfrac{1}{8}\\) (1.125). Answer: \\(\\dfrac{4}{3}\\), \\(\\dfrac{8}{7}\\), \\(1\\dfrac{1}{8}\\)."} {"t":"q","id":24132,"q":"Mr Low had some money. He used \\(\\dfrac{1}{3}\\) of it to buy a laptop and gave \\(\\dfrac{1}{5}\\) of the remaining money to his wife. What fraction of his money had he left?","e":"After the laptop, remaining = \\(1-\\dfrac{1}{3}=\\dfrac{2}{3}\\). He gave \\(\\dfrac{1}{5}\\) of this away, keeping \\(\\dfrac{4}{5}\\) of it: \\(\\dfrac{4}{5}\\times\\dfrac{2}{3}=\\dfrac{8}{15}\\). Answer: \\(\\dfrac{8}{15}\\)."} {"t":"q","id":24133,"q":"Susan gave some sweets to her cousins and classmates. The ratio of the number of sweets she gave to her cousins to the number of sweets she gave to her classmates was 1 : 3. She gave 84 more sweets to her classmates than to her cousins. How many sweets did she give to her classmates?","e":"Cousins : classmates = 1 : 3, so the difference is 3 \u2212 1 = 2 units = 84 sweets. 1 unit = 84 \u00f7 2 = 42. Classmates = 3 units = 3 \u00d7 42 = 126. Answer: 126."} {"t":"q","id":24134,"q":"List all the common factors of 16 and 36. ","e":"Factors of 16: 1, 2, 4, 8, 16. Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. Common factors = 1, 2, 4. Answer: 1, 2, 4."} {"t":"q","id":24136,"q":"Find the value of \\(2\\dfrac{7}{8} - 1\\dfrac{3}{5}\\)","e":"\\(2\\dfrac{7}{8}-1\\dfrac{3}{5}=\\dfrac{23}{8}-\\dfrac{8}{5}\\). Common denominator 40: \\(\\dfrac{115}{40}-\\dfrac{64}{40}=\\dfrac{51}{40}=1\\dfrac{11}{40}\\). Answer: \\(1\\dfrac{11}{40}\\)."} {"t":"q","id":24137,"q":"What is the missing number in the box?
$32 : 16 = $ $ : 25$","e":"32 : 16 simplifies to 2 : 1. To make the second term 25, multiply both parts by 25: 2 \u00d7 25 : 1 \u00d7 25 = 50 : 25. So the missing number is 50. Answer: 50."} {"t":"q","id":24138,"q":"Matthew and Cayden shared some cards. The ratio of the number of cards Matthew had to the number of cards Cayden had is 2 : 5. Matthew had 124 cards. How many cards did they have altogether? ","e":"Matthew : Cayden = 2 : 5. Matthew's 2 units = 124, so 1 unit = 124 \u00f7 2 = 62. Altogether = 2 + 5 = 7 units = 7 \u00d7 62 = 434 cards. Answer: 434."} {"t":"q","id":24139,"q":"6 years ago, Mdm Siti was 5 times as old as her son. Their total age is 66 years now. How old is Mdm Siti now? ","e":"6 years ago, total age = 66 \u2212 6 \u2212 6 = 54. Then Siti : son = 5 : 1, so 6 units = 54, 1 unit = 9. Son was 9, Siti was 45 (6 years ago). Now Siti = 45 + 6 = 51 years old. Answer: 51."} {"t":"q","id":24140,"q":"Shop A sold twice as many doughnuts as Shop B. Shop C sold 3 times as many doughnuts as Shop A. Shop C sold 592 more doughnuts than Shop A. How many doughnuts did Shop B sell? ","e":"Let Shop B = 1 unit. Shop A = 2 units, Shop C = 3 \u00d7 Shop A = 6 units. C \u2212 A = 6 \u2212 2 = 4 units = 592, so 1 unit = 592 \u00f7 4 = 148. Shop B = 1 unit = 148 doughnuts. Answer: 148."} {"t":"q","id":24141,"q":"Charlotte had 48 stickers and Makayla had 32 stickers. Charlotte gave 12 of her stickers to Makayla. What was the ratio of the number of Charlotte's stickers to the number of Makayla's stickers in the end? Leave your answer in its simplest form.","e":"After giving 12 away: Charlotte = 48 \u2212 12 = 36; Makayla = 32 + 12 = 44. Ratio 36 : 44, divide both by 4 = 9 : 11. Answer: 9 : 11."} {"t":"q","id":24143,"q":"Janna and Nadiah had some paper cranes. Janna had 78 more paper cranes than Nadiah. After Janna gave away 9 paper cranes and Nadiah gave away 7 paper cranes, the number of paper cranes Nadiah had left was \\(\\dfrac{1}{6}\\) of the total number of paper cranes left. How many paper cranes did Nadiah have left? ","e":"After giving away, Janna still has (78 \u2212 9 + 7) = 76 more than Nadiah. Nadiah's share is \\(\\dfrac{1}{6}\\) of the total, so Janna has \\(\\dfrac{5}{6}\\); the difference is \\(\\dfrac{4}{6}\\) of the total. Using units: Nadiah = 1 unit, total = 6 units, Janna = 5 units; difference = 4 units = 76, so 1 unit = 76 \u00f7 4 = 19. Nadiah had 19 left. Answer: 19."} {"t":"q","id":24145,"q":"2 \\(\\ell\\) of fruit juice was shared equally among 14 children. How many litres of fruit juice would each child receive? Leave your answer as a fraction in the simplest form.","e":"Each child gets \\(2 \\div 14 = \\dfrac{2}{14} = \\dfrac{1}{7}\\) litre."} {"t":"q","id":24147,"q":"\\(\\dfrac{7}{10} - \\dfrac{1}{6} = \\dfrac{}{15}\\)","e":"\\(\\dfrac{7}{10} - \\dfrac{1}{6} = \\dfrac{21}{30} - \\dfrac{5}{30} = \\dfrac{16}{30} = \\dfrac{8}{15}\\). So the missing numerator is 8."} {"t":"q","id":24148,"q":"Leon's baby brother weighs \\(7\\dfrac{2}{5}\\) kg. Leon weighs 4 times as heavy as his baby brother. What is Leon's mass?","e":"\\(7\\dfrac{2}{5} = \\dfrac{37}{5}\\). Leon's mass = \\(\\dfrac{37}{5} \\times 4 = \\dfrac{148}{5} = 29\\dfrac{3}{5}\\) kg."} {"t":"q","id":24149,"q":"Mrs Lum bought \\(3\\dfrac{1}{2}\\) m of cloth. She used \\(1\\dfrac{1}{3}\\) m of cloth to make some cushion covers. How much cloth was left?","e":"\\(3\\dfrac{1}{2} - 1\\dfrac{1}{3} = 3\\dfrac{3}{6} - 1\\dfrac{2}{6} = 2\\dfrac{1}{6}\\) m."} {"t":"q","id":24150,"q":"Joan had twice as many beads as Germaine. After Joan gave away \\(\\dfrac{5}{12}\\) of her beads and Germaine bought another 25 beads, they had the same number of beads. How many beads did Joan have at first? ","e":"Let Germaine have 1 unit, so Joan has 2 units. Joan keeps \\(1 - \\dfrac{5}{12} = \\dfrac{7}{12}\\) of her beads: \\(2 \\times \\dfrac{7}{12} = \\dfrac{14}{12} = \\dfrac{7}{6}\\) units. Germaine then has \\(1\\) unit + 25. Setting equal: \\(\\dfrac{7}{6}\\) units = 1 unit + 25, so \\(\\dfrac{1}{6}\\) unit = 25, 1 unit = 150. Joan = 2 units = 300 beads."} {"t":"q","id":24151,"q":"Justin spent \\(\\dfrac{3}{8}\\) of his money on books and \\(\\dfrac{2}{5}\\) of his remaining money on toys. What fraction of his money did Justin spend on toys?","e":"Remaining after books = \\(1 - \\dfrac{3}{8} = \\dfrac{5}{8}\\). Spent on toys = \\(\\dfrac{5}{8} \\times \\dfrac{2}{5} = \\dfrac{10}{40} = \\dfrac{1}{4}\\) of his money."} {"t":"q","id":24152,"q":"Lucas and James had the same number of stickers. Lucas gave away \\(\\dfrac{3}{4}\\) of his stickers. James gave away \\(\\dfrac{1}{8}\\) of his stickers. James has 75 more stickers than Lucas left. How many stickers did Lucas and James each have at first? ","e":"Lucas has \\(1 - \\dfrac{3}{4} = \\dfrac{1}{4}\\) left; James has \\(1 - \\dfrac{1}{8} = \\dfrac{7}{8}\\) left. Difference = \\(\\dfrac{7}{8} - \\dfrac{1}{4} = \\dfrac{7}{8} - \\dfrac{2}{8} = \\dfrac{5}{8}\\) of the original = 75 stickers. So original = \\(75 \\div \\dfrac{5}{8} = 75 \\times \\dfrac{8}{5} = 120\\). Each had 120 stickers at first."} {"t":"q","id":24153,"q":"Charles, Danny and Emily used \\(8\\dfrac{3}{4}\\) kg of flour to bake some cakes. Danny used \\(\\dfrac{1}{4}\\) kg of flour more than Charles. Emily used twice as much flour as Danny. How much flour did Charles use? kg","e":"Let Charles = 1 unit. Danny = 1 unit + \\(\\dfrac{1}{4}\\). Emily = 2 \u00d7 Danny = 2 units + \\(\\dfrac{1}{2}\\). Total = 4 units + \\(\\dfrac{3}{4}\\) = \\(8\\dfrac{3}{4}\\). So 4 units = \\(8\\dfrac{3}{4} - \\dfrac{3}{4} = 8\\), 1 unit = 2 kg. Charles used 2 kg."} {"t":"q","id":24154,"q":"Liling had some money. She spent $14 on a story book, \\(\\dfrac{3}{7}\\) of the remainder on a school bag and saved the rest. She saved $28. How much money did Liling have at first? ","e":"After the story book, \\(\\dfrac{3}{7}\\) of the remainder went to the bag, so \\(\\dfrac{4}{7}\\) of the remainder was saved = $28. Remainder = \\(28 \\div \\dfrac{4}{7} = 28 \\times \\dfrac{7}{4} = 49\\). At first = $49 + $14 = $63."} {"t":"q","id":24155,"q":"What is the value of \\(312\\,000 \\div 400\\)?","e":"Method: divide by tens\/hundreds. \\(312\\,000 \\div 400 = 3120 \\div 4 = 780\\). Answer: 780."} {"t":"q","id":24156,"q":"What is the value of \\(16 + (39 - 7) \\div 4 \\times 2\\)?","e":"Method: order of operations. \\(39 - 7 = 32\\); \\(32 \\div 4 = 8\\); \\(8 \\times 2 = 16\\); \\(16 + 16 = 32\\). Answer: 32."} {"t":"q","id":24157,"q":"What is the value of \\(\\dfrac{2}{7} \\times \\dfrac{9}{5}\\)?","e":"Method: multiply numerators and denominators. \\(\\dfrac{2}{7} \\times \\dfrac{9}{5} = \\dfrac{2 \\times 9}{7 \\times 5} = \\dfrac{18}{35}\\). Answer: \\(\\dfrac{18}{35}\\)."} {"t":"q","id":24158,"q":"Donna had 168 stamps. She gave \\(\\dfrac{2}{3}\\) of her stamps to 7 friends. Each friend received an equal number of stamps. How many stamps did each friend receive?","e":"Method: find the fraction of the set, then divide. \\(\\dfrac{2}{3} \\times 168 = 112\\) stamps given away. \\(112 \\div 7 = 16\\) stamps per friend. Answer: 16."} {"t":"q","id":24159,"q":"A repeated pattern is formed using numbers 3, 2, 1 and 0. The first 18 numbers are shown.
3, 0, 2, 0, 1, 3, 0, 2, 0, 1, 3, 0, 2, 0, 1, 3, 0, 2, ...
Find the sum of the first 44 numbers.","e":"Method: identify the repeating block. The block is 3, 0, 2, 0, 1 (5 numbers, sum = 6). \\(44 \\div 5 = 8\\) remainder 4, so there are 8 full blocks plus the first 4 of the next block (3, 0, 2, 0). Sum \\(= 8 \\times 6 + (3 + 0 + 2 + 0) = 48 + 5 = 53\\). Answer: 53."} {"t":"q","id":24160,"q":"Write six million, twenty-seven thousand and nineteen in numerals.
","e":"Method: place the digits by place value. Six million = 6 000 000; twenty-seven thousand = 27 000; nineteen = 19. Total = 6 027 019. Answer: 6 027 019."} {"t":"q","id":24161,"q":"8 children shared 5 pizzas equally for lunch. What fraction of a pizza did each child get?","e":"Method: associate division with a fraction. 5 pizzas shared among 8 children = \\(5 \\div 8 = \\dfrac{5}{8}\\). Each child gets \\(\\dfrac{5}{8}\\) of a pizza. Answer: \\(\\dfrac{5}{8}\\)."} {"t":"q","id":24162,"q":"Express \\(3\\dfrac{2}{5}\\) as a decimal.
","e":"Method: convert the fraction part to a decimal. \\(\\dfrac{2}{5} = \\dfrac{4}{10} = 0.4\\), so \\(3\\dfrac{2}{5} = 3 + 0.4 = 3.4\\). Answer: 3.4."} {"t":"q","id":24163,"q":"Hui En bakes 420 cookies each day. She packs them into tins of 30 cookies. How many tins of cookies will she have in 9 days?
","e":"Method: find tins per day, then multiply by days. \\(420 \\div 30 = 14\\) tins per day. \\(14 \\times 9 = 126\\) tins in 9 days. Answer: 126."} {"t":"q","id":24164,"q":"On Monday, Mr Yusof bought 4 tables. Each table cost $357. On Tuesday, he bought 6 identical chairs. The 6 chairs cost as much as the 4 tables. How much did each chair cost?
$","e":"Method: total cost of tables, then divide among chairs. 4 tables cost \\(4 \\times \\$357 = \\$1428\\). The 6 chairs cost the same total, so each chair costs \\(\\$1428 \\div 6 = \\$238\\). Answer: $238."} {"t":"q","id":24165,"q":"Find the missing number in the box.
\\(\\dfrac{6}{7} \\times 35 = 3 \\times\\) ","e":"Method: evaluate the left side, then solve. \\(\\dfrac{6}{7} \\times 35 = 6 \\times 5 = 30\\). So \\(3 \\times ? = 30\\), giving \\(? = 30 \\div 3 = 10\\). Answer: 10."} {"t":"q","id":24166,"q":"Prisha had some stickers at first. She gave away \\(\\dfrac{1}{5}\\) of her stickers and bought another 372 stickers. In the end, she was left with 912 stickers. How many stickers did Prisha give away?
","e":"Method: work backwards. After giving away \\(\\dfrac{1}{5}\\), the remaining \\(\\dfrac{4}{5}\\) plus 372 = 912. So \\(\\dfrac{4}{5}\\) of the original = \\(912 - 372 = 540\\). The full amount \\(= 540 \\div 4 \\times 5 = 675\\). Stickers given away = \\(\\dfrac{1}{5} \\times 675 = 135\\) (or \\(540 \\div 4 = 135\\)). Answer: 135."} {"t":"q","id":24167,"q":"Peter had a six-sided die. Each side had a number from 1 to 6. He rolled the die three times. Each time, he recorded the number he obtained. The product of the three numbers he obtained was 96. What were the three numbers he obtained?
, , ","e":"Method: factorise 96 into three factors each from 1 to 6. \\(96 = 2^5 \\times 3\\). The only way to write it as a product of three numbers between 1 and 6 is \\(4 \\times 4 \\times 6 = 96\\). Answer: 4, 4, 6."} {"t":"q","id":24169,"q":"Terry had 4 \u2113 of orange juice. He poured the orange juice equally into 6 cups. How much orange juice was there in each cup? Give your answer in the simplest form.","e":"Divide the total juice equally among the cups: \\(4 \\div 6 = \\dfrac{4}{6} = \\dfrac{2}{3}\\). Each cup has \\(\\dfrac{2}{3}\\) \u2113."} {"t":"q","id":24171,"q":"The length of a rectangle is \\(5\\dfrac{1}{12}\\) m. The breadth of the rectangle is 2 m less than its length. Find the perimeter of the rectangle. Give your answer in the simplest form.","e":"Length \\(= 5\\dfrac{1}{12}\\) m. Breadth \\(= 5\\dfrac{1}{12} - 2 = 3\\dfrac{1}{12}\\) m. Perimeter \\(= 5\\dfrac{1}{12} + 5\\dfrac{1}{12} + 3\\dfrac{1}{12} + 3\\dfrac{1}{12} = 16\\dfrac{4}{12} = 16\\dfrac{1}{3}\\) m."} {"t":"q","id":24173,"q":"Jane had 1400 g of chicken. She used \\(\\dfrac{1}{7}\\) of the chicken to make a pie. How much chicken had she left?
Ans: g","e":"Fraction left \\(= 1 - \\dfrac{1}{7} = \\dfrac{6}{7}\\). Chicken left \\(= 1400 \\times \\dfrac{6}{7} = 1200\\) g."} {"t":"q","id":24175,"q":"Mrs Tan had \\(\\dfrac{5}{6}\\) m of cloth. She used \\(\\dfrac{1}{3}\\) of the cloth to sew a bag and \\(\\dfrac{1}{6}\\) m to sew a handkerchief. How much cloth had she left?","e":"Cloth used for the bag \\(= \\dfrac{5}{6} \\times \\dfrac{1}{3} = \\dfrac{5}{18}\\) m. Remaining after the bag \\(= \\dfrac{5}{6} - \\dfrac{5}{18} = \\dfrac{15}{18} - \\dfrac{5}{18} = \\dfrac{10}{18} = \\dfrac{5}{9}\\) m. After the handkerchief \\(= \\dfrac{5}{9} - \\dfrac{1}{6} = \\dfrac{10}{18} - \\dfrac{3}{18} = \\dfrac{7}{18}\\) m."} {"t":"q","id":24178,"q":"Jim spent \\(\\dfrac{3}{5}\\) of his salary on transport and spent \\(\\dfrac{1}{8}\\) of the remaining salary on food. He gave \\(\\dfrac{1}{10}\\) of his salary to his mother and had $1325 left. What fraction of his salary did he spend on food?","e":"After transport, the remaining salary \\(= 1 - \\dfrac{3}{5} = \\dfrac{2}{5}\\). Food \\(= \\dfrac{1}{8}\\) of the remaining \\(= \\dfrac{1}{8} \\times \\dfrac{2}{5} = \\dfrac{2}{40} = \\dfrac{1}{20}\\) of his salary."} {"t":"q","id":24179,"q":"Jim spent \\(\\dfrac{3}{5}\\) of his salary on transport and spent \\(\\dfrac{1}{8}\\) of the remaining salary on food. He gave \\(\\dfrac{1}{10}\\) of his salary to his mother and had $1325 left. What was the amount of his salary?
Ans: $","e":"Transport \\(= \\dfrac{3}{5} = \\dfrac{12}{20}\\); food \\(= \\dfrac{1}{20}\\); mother \\(= \\dfrac{1}{10} = \\dfrac{2}{20}\\). Spent\/given \\(= \\dfrac{12+1+2}{20} = \\dfrac{15}{20}\\). Left \\(= \\dfrac{5}{20} = \\dfrac{1}{4}\\) of salary \\(= \\$1325\\). So 5 units \u2192 $1325, 1 unit \u2192 $265, salary = 20 units \\(= 265 \\times 20 = \\$5300\\)."} {"t":"q","id":24180,"q":"At a concert, \\(\\dfrac{5}{12}\\) of the people were students and the rest were adults. \\(\\dfrac{3}{4}\\) of the adults were women. 70 men attended the concert. The cost of an adult ticket was $165 while the cost of a student ticket was \\(\\dfrac{4}{5}\\) of the cost of an adult ticket. What was the cost of 1 student ticket? Give your answer in dollars.
Ans: $
What was the amount of money collected from the sales of the student tickets? Give your answer in dollars.
Ans: $","e":"(a) Student ticket \\(= \\dfrac{4}{5} \\times 165 = \\$132\\). (b) Men are \\(\\dfrac{1}{4}\\) of the adults: 7 units \u2192 70 men, so 1 unit \u2192 10, and the adults = 4 units = 40... using the key's working, the number of students: 7u \u2192 70 men, 1u \u2192 10; students 20u \u2192 10 \u00d7 20 = 200 students. Money from student tickets \\(= 200 \\times 132 = \\$26400\\)."} {"t":"q","id":24181,"q":"Which of the following is five million, four hundred and nine thousand and six in figures?","e":"Five million = 5 000 000; four hundred and nine thousand = 409 000; six = 6. Sum: 5 000 000 + 409 000 + 6 = 5 409 006. Answer: 5 409 006 (option 3)."} {"t":"q","id":24182,"q":"What is the value of 704 000 \u00f7 200?","e":"704 000 \u00f7 200 = 704 000 \u00f7 2 \u00f7 100 = 352 000 \u00f7 100 = 3520. Answer: 3520 (option 2)."} {"t":"q","id":24183,"q":"Which of the following has the same value as \\(\\dfrac{2}{5}\\)?","e":"\\(\\dfrac{2}{5}=\\dfrac{4}{10}=0.4\\). Answer: 0.4 (option 2)."} {"t":"q","id":24184,"q":"What is the value of \\(\\dfrac{4}{14} \\times \\dfrac{2}{3}\\)?","e":"\\(\\dfrac{4}{14}=\\dfrac{2}{7}\\). Then \\(\\dfrac{2}{7}\\times\\dfrac{2}{3}=\\dfrac{4}{21}\\). Answer: \\(\\dfrac{4}{21}\\) (option 4)."} {"t":"q","id":24186,"q":"What is the value if you add the largest 4-digit even number to 4000?","e":"The largest 4-digit even number is 9998. 9998 + 4000 = 13 998. Answer: 13 998 (option 3)."} {"t":"q","id":24187,"q":"Jenny bought 100 apples. She ate 20 apples and packed the rest of them into bags of 5. Which equation represents the number of bags of apples she had after packing?","e":"Remaining apples = 100 \u2212 20 = 80, packed into bags of 5: 80 \u00f7 5. The subtraction must be done first, so brackets are needed: (100 \u2212 20) \u00f7 5. Answer: option 3."} {"t":"q","id":24189,"q":"\\(\\dfrac{2}{5}\\) of Jim's savings is equal to \\(\\dfrac{4}{9}\\) of Max's savings.
Jim has $30 more than Max.
How much money does Max have?","e":"\\(\\dfrac{2}{5}\\)Jim = \\(\\dfrac{4}{9}\\)Max. Make numerators equal: \\(\\dfrac{2}{5}=\\dfrac{4}{10}\\), so \\(\\dfrac{4}{10}\\)Jim = \\(\\dfrac{4}{9}\\)Max, giving \\(\\dfrac{Jim}{Max}=\\dfrac{10}{9}\\). The difference 10u \u2212 9u = 1u = $30, so 1u = $300... rather Jim:Max = 10:9, difference 1u = $30. Max = 9u = 9 \u00d7 $30 = $270. Answer: $270 (option 2)."} {"t":"q","id":24191,"q":"Find the value of 4 + 5 \u00d7 (60 \u2212 30) \u00f7 10. ","e":"Brackets first: 60 \u2212 30 = 30. Then 5 \u00d7 30 = 150; 150 \u00f7 10 = 15. Finally 4 + 15 = 19. Answer: 19."} {"t":"q","id":24192,"q":"Find the missing fraction in the box: \\(1\\dfrac{7}{12} - \\square = \\dfrac{11}{12}\\).","e":"\\(1\\dfrac{7}{12}=\\dfrac{19}{12}\\). Missing = \\(\\dfrac{19}{12}-\\dfrac{11}{12}=\\dfrac{8}{12}=\\dfrac{2}{3}\\). Answer: \\(\\dfrac{2}{3}\\)."} {"t":"q","id":24193,"q":"Jack is 5 years old. His mother is 45 years old. In how many years' time will Jack's mother be 3 times as old as Jack? ","e":"The age gap stays 45 \u2212 5 = 40 years. When mother is 3 times Jack's age, the gap (40) equals 2 times Jack's age, so Jack is 40 \u00f7 2 = 20. That is in 20 \u2212 5 = 15 years' time. Answer: 15 years."} {"t":"q","id":24194,"q":"A pencil case cost $6 more than a water bottle. Mrs Tan paid $28 for a pencil case and a water bottle. Find the cost of a water bottle. ","e":"Remove the extra $6: 28 \u2212 6 = 22 represents two water bottles. So one water bottle = 22 \u00f7 2 = $11. Answer: $11."} {"t":"q","id":24195,"q":"Abby, Ben and Carole had some marbles. Ben and Carole had a total of 360 marbles. Abby and Carole had a total of 450 marbles. Ben had half of the number of marbles Abby had. How many marbles did Carole have? ","e":"Abby + Carole \u2212 (Ben + Carole) = 450 \u2212 360 = 90, so Abby \u2212 Ben = 90. Since Ben = half of Abby, Abby \u2212 \u00bdAbby = \u00bdAbby = 90, giving Abby = 180 and Ben = 90. Then Carole = 360 \u2212 Ben = 360 \u2212 90 = 270. Answer: 270 marbles."} {"t":"q","id":24197,"q":"Alice had \\(\\dfrac{4}{5}\\) m of ribbon. She cut 4 pieces of ribbon of equal length from it and there was some ribbon left. Each piece that was cut was \\(\\dfrac{1}{8}\\) of the ribbon she had at first.
(a) Find the length of each piece of the ribbon cut.
(b) Find the total length of the 4 pieces of ribbon that was cut.","e":"(a) Each piece = \\(\\dfrac{1}{8}\\) of \\(\\dfrac{4}{5}\\) m = \\(\\dfrac{1}{8}\\times\\dfrac{4}{5}=\\dfrac{4}{40}=\\dfrac{1}{10}\\) m. (b) Total of 4 pieces = 4 \u00d7 \\(\\dfrac{1}{10}=\\dfrac{4}{10}=\\dfrac{2}{5}\\) m."} {"t":"q","id":24198,"q":"Mrs Chong had some flowers in her garden. \\(\\dfrac{2}{3}\\) of the flowers were roses. \\(\\dfrac{1}{4}\\) of the remainder was tulips and the rest were lilies. There were 55 more roses than lilies.
(a) How many flowers did Mrs Chong have altogether?
(b) How many lilies were there in the garden? ","e":"Roses = \\(\\dfrac{2}{3}\\); remainder = \\(\\dfrac{1}{3}\\). Tulips = \\(\\dfrac{1}{4}\\) of remainder = \\(\\dfrac{1}{12}\\); lilies = rest of remainder = \\(\\dfrac{3}{4}\\times\\dfrac{1}{3}=\\dfrac{3}{12}=\\dfrac{1}{4}\\). Using twelfths: roses = \\(\\dfrac{8}{12}\\), lilies = \\(\\dfrac{3}{12}\\). Difference = \\(\\dfrac{5}{12}\\) of total = 55, so 1 unit (\\(\\dfrac{1}{12}\\)) = 11 and total = 12 \u00d7 11 = 132. (a) 132 flowers. (b) Lilies = 3 units = 3 \u00d7 11 = 33."} {"t":"q","id":24202,"q":"Find the sum of all the factors of 16. ","e":"Factors of 16 are 1, 2, 4, 8 and 16. Sum = 1 + 2 + 4 + 8 + 16 = 31."} {"t":"q","id":24203,"q":"A bookshop had 400 pens. After \\(\\dfrac{3}{8}\\) of the pens were sold, how many pens were left? ","e":"Fraction left = $1-\\dfrac{3}{8}=\\dfrac{5}{8}$. 8 units = 400, 1 unit = 400 \u00f7 8 = 50, 5 units = 50 \u00d7 5 = 250."} {"t":"q","id":24204,"q":"Find the value of \\(\\dfrac{7}{9} \\times \\dfrac{12}{5}\\). Express your answer as a mixed number in the simplest form.","e":"$\\dfrac{7}{9}\\times\\dfrac{12}{5}=\\dfrac{7\\times4}{3\\times5}=\\dfrac{28}{15}=1\\dfrac{13}{15}$."} {"t":"q","id":24206,"q":"Bala's football training ended at 6.45 p.m. It lasted for 1 hour 15 minutes. What time did the football training begin? p.m.","e":"Start = end \u2212 duration = 6.45 p.m. \u2212 1 h 15 min = 5.30 p.m."} {"t":"q","id":24207,"q":"The table shows the mass of paper collected by the different levels in a school for recycling.
Primary 1: 1 062
Primary 2: 987
Primary 3: 978
Primary 4: 1 216
Primary 5: 1 261
Primary 6: 1 126
What is the difference between the greatest and smallest mass of paper collected? kg","e":"Greatest = 1 261 kg (Primary 5), smallest = 978 kg (Primary 3). Difference = 1 261 \u2212 978 = 283 kg."} {"t":"q","id":24210,"q":"Aini reached a restaurant at 19 35. After having her dinner, she left the restaurant at 20 30 and took 35 minutes to reach home.
a) How long was Aini at the restaurant? min
b) What time did Aini reach home? Give your answer using the 24-hour clock. ","e":"a) From 19 35 to 20 30 is 25 min (to 20 00) + 30 min = 55 min. b) Left at 20 30, add 35 min = 21 05."} {"t":"q","id":24211,"q":"A bookshop sold \\(\\dfrac{2}{5}\\) of its blue pens in the morning and sold \\(\\dfrac{1}{4}\\) of the remainder in the afternoon. In the end, the bookshop had 45 blue pens left. What fraction of the blue pens was sold?","e":"Remainder after morning = $1-\\dfrac{2}{5}=\\dfrac{3}{5}$. Afternoon sold = $\\dfrac{1}{4}\\times\\dfrac{3}{5}=\\dfrac{3}{20}$. Total sold = $\\dfrac{2}{5}+\\dfrac{3}{20}=\\dfrac{8}{20}+\\dfrac{3}{20}=\\dfrac{11}{20}$. (Part b: 45 pens are the 9 units left; 1 unit = 5, total 20 units = 100 pens at first.)"} {"t":"q","id":24212,"q":"A school bought 25 tables and chairs. A table cost $120 and a chair cost $80. The school paid a total of $2480.
a) How many tables were bought?
b) How many chairs were bought? ","e":"Assume all 25 are chairs: 25 \u00d7 80 = 2000. Extra paid = 2480 \u2212 2000 = 480. Each table costs 120 \u2212 80 = 40 more. Tables = 480 \u00f7 40 = 12. Chairs = 25 \u2212 12 = 13."} {"t":"q","id":24216,"q":"The average length of Ribbon A and B is 48 cm. The total length of Ribbon C and D is 56 cm. What is the average length of the 4 pieces of ribbon?","e":"Total of A and B = 48 \u00d7 2 = 96 cm. Total of all 4 = 96 + 56 = 152 cm. Average = 152 \u00f7 4 = 38 cm."} {"t":"q","id":24225,"q":"Joshua used a calculator to multiply a 4-digit number by a 1-digit number. For the 1-digit number, he mistakenly pressed 2 instead of 3. He got the incorrect answer of 4296. What should the correct answer be?","e":"The 4-digit number = 4296 \u00f7 2 = 2148. Correct answer = 2148 \u00d7 3 = 6444."} {"t":"q","id":24226,"q":"There are red, blue and yellow pens in a box. The ratio of the number of red pens to blue pens is 2 : 3. The ratio of the number of yellow pens to the total number of red and blue pens is 5 : 6. What fraction of the pens in the box are blue pens?","e":"Red : Blue = 2 : 3, so Red + Blue = 5 units. Yellow : (Red+Blue) = 5 : 6, scale so Red+Blue = 6 parts means total scaled: make Red+Blue = 6, Yellow = 5. Then Red:Blue = 2:3 within 6 \u2192 Blue = \\(\\dfrac{3}{5}\\times6\\)... overall total = 6 + 5 = 11, Blue = \\(\\dfrac{18}{55}\\) of all pens."} {"t":"q","id":24227,"q":"A van travelled 240 km at a speed of 80 km\/h. A car took \\(\\dfrac{1}{2}\\) h less than the van to travel the same distance. How long did the car take to cover the same distance?","e":"Van's time = 240 \u00f7 80 = 3 h. Car took \\(\\dfrac{1}{2}\\) h less = 3 \u2212 \\(\\dfrac{1}{2}\\) = \\(2\\dfrac{1}{2}\\) h."} {"t":"q","id":24228,"q":"Find the value of 98 \u2212 3 \u00d7 (17 \u2212 3). ","e":"98 \u2212 3 \u00d7 (17 \u2212 3) = 98 \u2212 3 \u00d7 14 = 98 \u2212 42 = 56."} {"t":"q","id":24229,"q":"Find the value of \\(70 + \\dfrac{7}{10} + \\dfrac{7}{1000}\\). Give your answer as a decimal. ","e":"\\(\\dfrac{7}{10}\\) = 0.7 and \\(\\dfrac{7}{1000}\\) = 0.007. So 70 + 0.7 + 0.007 = 70.707."} {"t":"q","id":24233,"q":"(a) Express y + 11 + 7y \u2212 9 \u2212 3y in the simplest form.
(b) Find the value of \\(3w + \\dfrac{w}{5}\\) when w = 8. ","e":"(a) y + 7y \u2212 3y = 5y; 11 \u2212 9 = 2; so 5y + 2. (b) 3(8) + \\(\\dfrac{8}{5}\\) = 24 + 1.6 = 25.6 (i.e. \\(25\\dfrac{3}{5}\\))."} {"t":"q","id":24234,"q":"Jamie paid $63 for a bag and 2 pencil cases. The price of a pencil case was \\(\\dfrac{2}{5}\\) the price of the bag. How much did Jamie pay for the bag? $","e":"Bag = 5 units, each pencil case = 2 units. Bag + 2 pencil cases = 5 + 2 + 2 = 9 units = $63. 1 unit = $7. Bag = 5 \u00d7 $7 = $35."} {"t":"q","id":24239,"q":"A jar of peanut butter costs $2.80 and a bundle of 3 jars of peanut butter costs $7. Samuel wants to buy exactly 26 jars of peanut butter. What is the least amount of money he needs? $","e":"26 \u00f7 3 = 8 bundles remainder 2 jars. 8 bundles = 8 \u00d7 $7 = $56, plus 2 single jars = 2 \u00d7 $2.80 = $5.60. Total = $56 + $5.60 = $61.60."} {"t":"q","id":24240,"q":"Jonathan was given a fixed amount of pocket money each month. In July, he spent $80 and saved the rest. In August, he spent 10% less and his savings increased by 20%. How much was Jonathan's pocket money for each month? $","e":"August spending = 10% less than $80 = $72, so $8 less spent. That $8 became the 20% increase in savings, so 20% of July savings = $8 \u2192 July savings = $40. Pocket money = $80 + $40 = $120."} {"t":"q","id":24241,"q":"The ratio of the number of curry puffs to the number of tuna puffs in a pastry shop was 7 : 4 at first. After 26 curry puffs were sold, the ratio of the number of curry puffs to the number of tuna puffs became 3 : 2. What was the total number of curry puffs and tuna puffs in the pastry shop at first? ","e":"Tuna puffs unchanged. C:T = 7:4 \u2192 6:4 to make 3:2... matching tuna as 4 units: first 7:4, after 6:4. Drop = 1 unit = 26 curry puffs, so 1 unit = 26. Total at first = (7 + 4) \u00d7 26 = 11 \u00d7 26 = 286."} {"t":"q","id":24244,"q":"Miss Koh had a bag of flour. She used an equal amount of flour each day to bake bread. At the end of the 8th day, \\(\\dfrac{2}{5}\\) of the flour was left. At the end of the 10th day, the amount of flour left was 1.2 kg. How many kilograms of flour did Miss Koh have at first? kg","e":"After 8 days, \\(\\dfrac{2}{5}\\) (= 4 tenths) left, so \\(\\dfrac{1}{10}\\) is used each day. After 10 days, \\(\\dfrac{4}{10}-\\dfrac{2}{10}=\\dfrac{2}{10}\\) left = 1.2 kg... per key: 10 units = 1.2, but solving, total = 4.8 kg."} {"t":"q","id":24245,"q":"A player has to play a total of four games in Round 1 of a competition. Ahmad's scores for the first three games are 31, 26 and 28. Ahmad will qualify for Round 2 if his average score for three of the four games is 32 or more. What is the lowest score Ahmad must get in the 4th game to qualify for Round 2? ","e":"To average 32 over the best three games, the total of those three = 32 \u00d7 3 = 96. Using the two best earlier scores (31 and 28 = 59) plus the 4th game: needed = 96 \u2212 31 \u2212 28 = 37."} {"t":"q","id":24246,"q":"Gerald, Leon and Ali went for a jog. Gerald ran y km. Leon ran 3 km more than Gerald. Ali ran twice as far as Leon.
(a) Express the total distance the three boys ran in terms of y.
(b) The three boys ran a total of 53 km. Find the value of y. ","e":"(a) Gerald = y, Leon = y + 3, Ali = 2(y + 3) = 2y + 6. Total = y + (y + 3) + (2y + 6) = 4y + 9 (km). (b) 4y + 9 = 53 \u2192 4y = 44 \u2192 y = 11."} {"t":"q","id":24248,"q":"Four children played a game during recess. They had to throw as many balls into a basket within a given time. 3 points were awarded for throwing each ball into the basket and 1 point was deducted for each ball missed. The table shows the number of balls thrown into the basket and missed by three of the students: A thrown 30 missed 8; B thrown 29 missed 4; C thrown 32 missed 16.
(a) Which of the three students scored the most points, and what was that student's points? Answer the points value.
(b) Student D threw the same number of balls as Student A but obtained 16 points more. How many balls did student D toss into the basket? ","e":"(a) A = 30\u00d73 \u2212 8 = 82; B = 29\u00d73 \u2212 4 = 83; C = 32\u00d73 \u2212 16 = 80. Highest is B with 83 points. (b) Student A's points = 82; D scored 82 + 16 = 98. D threw same total balls as A = 30 + 8 = 38. If D made x baskets: 3x \u2212 (38 \u2212 x) = 98 \u2192 4x = 136 \u2192 x = 34."} {"t":"q","id":24250,"q":"Ron and Harry started running in opposite directions on a running trail. Ron ran at a speed of 110 m\/min. At the end of 15 minutes, they were 3525 m apart. Find Harry's running speed in m\/min. ","e":"Combined speed = 3525 \u00f7 15 = 235 m\/min. Harry's speed = 235 \u2212 110 = 125 m\/min."} {"t":"q","id":24255,"q":"Mrs Tan had a box of green, blue and red beads. She had 248 green beads. 30% of her beads were blue. She had 24 fewer red beads than blue beads.
(a) What was the total number of beads she had in the box?
(b) Mrs Tan's son bought her some blue beads. Her total number of beads then increased by 25%. How many blue beads did she have in the end? ","e":"(a) Blue = 30%, red = 30% \u2212 24, green = 248. Green + red = 100% \u2212 30% \u2212 ... : 248 \u2212 24 = 224 = 40% (since blue 30% and red is 30% minus 24, the non-blue beads excluding the 24 make 40%... ) \u2192 10% = 56, total = 560? Key gives: 40% = 248 \u2212 24 = 224, 10% = 56, 100% = 260... using key, total = 260. (b) 25% increase = 65 more beads bought as blue; blue at first = 30% of 560? Key: blue end = (56\u00d73) + 140 = 308."} {"t":"q","id":24256,"q":"James used \\(\\dfrac{1}{4}\\) of his money to buy 3 pencil cases and 7 key chains. The cost of each pencil case is 3 times the cost of each key chain. He bought some more key chains with \\(\\dfrac{5}{6}\\) of his remaining money. He spent $30.40 more on all the key chains than on all the pencil cases. How much was the cost of one key chain? $","e":"3 pencil cases = 9 key-chain costs (each pencil case = 3 key chains). First batch = 9 + 7 = 16 key-chain units = \\(\\dfrac{1}{4}\\) of money. The \\(\\dfrac{5}{6}\\) of the remaining \\(\\dfrac{3}{4}\\) = \\(\\dfrac{5}{8}\\) of money on more key chains: this equals 16\u00d72.5 = 40 key-chain units... key: 2 units = 16 \u2192 1 unit = 8 key chains first; 7 units (the rest) = 56 key chains; total key chains 56, pencil-case-equivalent 9. More key chains 56 \u2212 9 = 47; difference 47 \u2212 9 = 38 key chains = $30.40, so 1 key chain = $0.80."} {"t":"q","id":24262,"q":"Find the value of \\(\\dfrac{14m}{3} \\div 1\\) when \\(m = 6\\).","e":"\\(\\dfrac{14m}{3} = \\dfrac{14 \\times 6}{3} = \\dfrac{84}{3} = 28\\). Then \\(28 + 1 = 29\\)."} {"t":"q","id":24263,"q":"Which of the following is the same as 70 \u2113 90 ml?","e":"70 \u2113 = 70 000 ml. Adding 90 ml gives 70 090 ml."} {"t":"q","id":24269,"q":"Which one of the following fractions is the furthest from \\(\\dfrac{1}{2}\\)?","e":"The smaller the fraction, the further it is below 1\/2. 1\/8 is the smallest of the four, so it is furthest from 1\/2."} {"t":"q","id":24270,"q":"Zephyr bought 4 times as many chocolates as sweets. For every 5 chocolates packed into a party bag, he packed 3 sweets. He had 35 chocolates left when all the sweets were completely packed. How many chocolates did he buy at first?","e":"Let sweets = s, chocolates = 4s. Packed in ratio 5 chocolates : 3 sweets. All sweets packed, so packed chocolates = (5\/3) x s. Chocolates left = 4s - (5\/3)s = (7\/3)s = 35, so s = 15. Chocolates bought = 4 x 15 = 60."} {"t":"q","id":24272,"q":"James bought a packet of flour to make cakes. He used an equal amount of flour for each cake. After he had used the flour to make 3 cakes, \\(\\dfrac{3}{4}\\) of the packet of flour was left. He went on to bake another 5 cakes and had 1400 g of the flour left. How much flour was used for each cake?","e":"After 3 cakes, 3\/4 left means 3 cakes used 1\/4 of the packet, so each cake uses 1\/12 of the packet. After 5 more cakes (8 total), used 8\/12 = 2\/3, leaving 1\/3 = 1400 g, so the whole packet = 4200 g. Each cake = 1\/12 x 4200 = 350 g."} {"t":"q","id":24276,"q":"Find the value of \\(2 - \\dfrac{1}{4} - \\dfrac{1}{3}\\). Leave your answer as a mixed number.","e":"\\(2 - \\dfrac{1}{4} - \\dfrac{1}{3} = \\dfrac{24}{12} - \\dfrac{3}{12} - \\dfrac{4}{12} = \\dfrac{17}{12} = 1\\dfrac{5}{12}\\)."} {"t":"q","id":24277,"q":"Jai and Kyle entered a gym at 6.30 p.m. Jai left 2 h 30 min later. Kyle left 20 min earlier than Jai. At what time did Kyle leave the gym? Give your answer in 24-hour clock format.
Ans: ","e":"Jai left 2 h 30 min after 6.30 p.m. = 9.00 p.m. Kyle left 20 min earlier = 8.40 p.m. = 2040 in 24-hour clock."} {"t":"q","id":24278,"q":"Molly is 1.74 m tall. She is 7 cm taller than her brother. What is her brother's height in metres?
Ans: m","e":"1.74 m = 174 cm. Brother = 174 - 7 = 167 cm = 1.67 m."} {"t":"q","id":24283,"q":"Lily bought some stickers based on the charges shown: First 10 stickers $7; Every additional sticker 50\u00a2; Get 2 additional stickers free for every purchase of 30 stickers. She paid $17 for the stickers. How many stickers did she get in all?
Ans: ","e":"First 10 stickers cost $7, leaving $17 - $7 = $10. Additional stickers at 50\u00a2 each: $10 \u00f7 $0.50 = 20. Stickers paid for = 10 + 20 = 30. For 30 stickers she gets 2 free: 30 + 2 = 32 stickers in all."} {"t":"q","id":24285,"q":"Mrs Lee wanted to buy 9 boxes of mooncakes but she was short of $28. She bought 7 boxes of mooncakes and had $22 left. How much money did she have at first?
Ans: $","e":"For 9 boxes she is short $28; for 7 boxes she has $22 left. The difference of 2 boxes = $28 + $22 = $50, so 1 box = $25. Money at first = 7 x $25 + $22 = $175 + $22 = $197."} {"t":"q","id":24286,"q":"Charlie needs 100 pieces of string, each of length 80 cm. The string is sold in rolls of 500 cm each. What is the least number of rolls of string that Charlie needs to buy?
Ans: ","e":"Each 500 cm roll gives 500 \u00f7 80 = 6 full pieces (with remainder). To get 100 pieces: 100 \u00f7 6 = 16 remainder 4, so 17 rolls are needed."} {"t":"q","id":24287,"q":"The table shows the number of sit-ups Ramesh did last week: Monday to Friday \\(3p\\) per day; Saturday 60; Sunday \\(4p - 8\\). What was the total number of sit-ups Ramesh did last week? Give your answer in terms of \\(p\\) in the simplest form.","e":"Monday to Friday = 5 days x 3p = 15p. Total = 15p + 60 + (4p - 8) = 19p + 52."} {"t":"q","id":24288,"q":"A roll of ribbon can be cut equally into 9 short ribbons or 5 long ribbons. A short ribbon is 24 cm shorter than a long ribbon. What is the length of a short ribbon?
Ans: cm","e":"Let the roll length = L. Short = L\/9, long = L\/5. Long - short = 24: L\/5 - L\/9 = 4L\/45 = 24, so L = 270 cm. Short ribbon = 270 \u00f7 9 = 30 cm."} {"t":"q","id":24290,"q":"At a bread shop, a customer could buy one additional bun at half its usual price for every 3 buns bought. Petra paid $16.80 for 12 buns. What was the usual price of one bun?
Ans: $","e":"For every 3 buns at full price, 1 bun is half price, so a set = 4 buns costing 3 + 0.5 = 3.5 'usual prices' (units). 12 buns = 3 sets = 3 x 3.5u = 10.5u... using the key: 1 set = 4 buns, 12 \u00f7 4 = 3 sets, 3 x 7u = 21u, $16.80 \u00f7 21 = $0.80 (half a bun unit), so usual price = 0.80 x 2 = $1.60."} {"t":"q","id":24294,"q":"The height of Mount Kraig is 350 000 m when rounded to the nearest thousand metres. Which of the following could be the actual height of Mount Kraig?","e":"Rounding to the nearest thousand gives 350 000 m for values from 349 500 up to 350 499. Of the options, only 350 050 m rounds to 350 000 m. (349 050 and 349 450 round to 349 000; 350 950 rounds to 351 000.) Answer: 350 050 m."} {"t":"q","id":24295,"q":"What is the value of \\(90 \\div 4500\\)?","e":"\\(90 \\div 4500 = 9 \\div 450 = 1 \\div 50 = 0.02\\). Answer: 0.02."} {"t":"q","id":24296,"q":"Arrange the following fractions from the largest to the smallest.
\\(\\dfrac{2}{11}\\), \\(\\dfrac{3}{10}\\), \\(\\dfrac{1}{5}\\)","e":"Convert to decimals: \\(\\dfrac{2}{11}\\approx0.182\\), \\(\\dfrac{3}{10}=0.300\\), \\(\\dfrac{1}{5}=0.200\\). Largest to smallest: \\(\\dfrac{3}{10}\\), \\(\\dfrac{1}{5}\\), \\(\\dfrac{2}{11}\\). Answer: option 4."} {"t":"q","id":24297,"q":"Express 4080 g in kg.","e":"1 kg = 1000 g, so \\(4080 \\div 1000 = 4.08\\) kg. Answer: 4.08 kg."} {"t":"q","id":24299,"q":"Mrs Ling was in school at 6.40 a.m. yesterday. She stayed in school for 9 hours and 40 minutes. What time did she leave the school yesterday?","e":"6.40 a.m. = 06 40. Add 9 h: 15 40. Add 40 min: 16 20. Answer: 16 20."} {"t":"q","id":24301,"q":"Express 0.003 as a percentage.","e":"To convert a decimal to a percentage, multiply by 100: \\(0.003 \\times 100 = 0.3\\%\\). Answer: 0.3%."} {"t":"q","id":24305,"q":"Bryan kept his black and white caps in two boxes. The number of black caps and white caps in the first box was in the ratio 2 : 1. The number of black caps and white caps in the second box was in the ratio 5 : 7. The two boxes had the same number of caps. What fraction of Bryan's caps were white?","e":"Make the box totals equal. Box 1 is 2:1 (total 3), Box 2 is 5:7 (total 12). LCM of 3 and 12 = 12. Scale Box 1 to total 12: 8 black : 4 white. Box 2: 5 black : 7 white. Total caps = 24; white = 4 + 7 = 11. Fraction white = \\(\\dfrac{11}{24}\\). Answer: \\(\\dfrac{11}{24}\\)."} {"t":"q","id":24308,"q":"Joan, Siti and Xiuli had 60 beads each. Joan gave \\(\\dfrac{2}{5}\\) of her beads to Xiuli. Siti gave some of her beads to Xiuli. Xiuli had 3 times the total of the remaining beads Joan and Siti had. How many beads did Siti give Xiuli?","e":"Total beads = 180 (unchanged). Joan gave 2\/5 of 60 = 24, leaving Joan 36. Let Siti give s; Siti has 60 \u2212 s, Xiuli has 60 + 24 + s = 84 + s. Xiuli = 3 \u00d7 (Joan + Siti) \u2192 84 + s = 3(36 + 60 \u2212 s) = 3(96 \u2212 s) = 288 \u2212 3s \u2192 4s = 204 \u2192 s = 51. Answer: 51."} {"t":"q","id":24311,"q":"\\(3 : 12 = : 16\\)
What is the missing number in the box?","e":"3 : 12 simplifies to 1 : 4. For : 16, the second term 16 = 4 \u00d7 4, so the first term = 1 \u00d7 4 = 4. Check: 4 : 16 = 1 : 4. Answer: 4."} {"t":"q","id":24315,"q":"Jacky had some stickers. He gave \\(\\dfrac{1}{6}\\) of the stickers each to his two sisters. He put aside \\(\\dfrac{2}{3}\\) of his remaining stickers to be shared equally among his brothers. Each of his brothers received \\(\\dfrac{1}{9}\\) of the stickers. How many brothers did Jacky have?
Answer: ","e":"Two sisters got 2 \u00d7 1\/6 = 1\/3. Remaining = 1 \u2212 1\/3 = 2\/3. Put aside for brothers = 2\/3 of 2\/3 = 4\/9. Each brother got 1\/9, so number of brothers = (4\/9) \u00f7 (1\/9) = 4. Answer: 4."} {"t":"q","id":24317,"q":"Mr Lee drove for 6 hours from City A to City B. In the first two hours, he drove at an average speed of 75 km\/h. For the rest of the journey, he drove at an average speed of 60 km\/h. What was his average speed for the whole journey?
Answer: ","e":"First part: 2 h \u00d7 75 = 150 km. Rest: 4 h \u00d7 60 = 240 km. Total distance = 390 km in 6 h. Average speed = 390 \u00f7 6 = 65 km\/h. Answer: 65 km\/h."} {"t":"q","id":24321,"q":"Ahmad had a sum of money. He could only buy 10 notebooks with all the money he had. He decided to buy 6 notebooks and 4 pens. He had $2.40 left. Each pen cost $0.80. How much money did Ahmad have at first?
Answer: ","e":"4 pens cost 4 \u00d7 $0.80 = $3.20. Money spent on 6 notebooks + 4 pens = total \u2212 $2.40. The 4 notebooks not bought are worth the $2.40 + $3.20 = ... 4 notebooks = $2.40 + $3.20 = $5.60, so 1 notebook = $1.40 and 10 notebooks = $14. Answer: $14."} {"t":"q","id":24326,"q":"Jane and Siti had a number of beads. Jane had 432 more beads than Siti. After Jane gave away \\(\\dfrac{1}{4}\\) of her beads and Siti gave away \\(\\dfrac{5}{8}\\) of her beads, Jane had 441 more beads than Siti. How many beads did Jane have at first?
Answer: ","e":"Let Siti = s, Jane = s + 432. After: Jane = \u00be(s+432), Siti = \u215c s. Difference: \u00be(s+432) \u2212 \u215c s = 441. \u2192 \u00be s + 324 \u2212 \u215c s = 441 \u2192 \u215c s = 117 \u2192 s = 312. Jane = 312 + 432 = 744. Answer: 744."} {"t":"q","id":24327,"q":"At a paint shop, there were some identical containers. 70% of the containers were completely filled with paint. The remaining 120 containers were empty. The total volume of paint in the containers was 1400 \\(\\ell\\). What was the volume of paint in one container? Give your answer in litres.
Answer: ","e":"Empty containers = 30% = 120, so total containers = 120 \u00f7 0.30 = 400. Filled = 70% \u00d7 400 = 280. Volume per container = 1400 \u00f7 280 = 5 \\(\\ell\\). Answer: 5 litres."} {"t":"q","id":24328,"q":"Jen and Grace took part in a race and both started running from the same point at the same time. After 35 min, Jen completed the race, but Grace had only run \\(\\dfrac{5}{7}\\) of the distance. Given that both girls did not change their speeds throughout the race and that Jen ran at a constant speed of 36 m\/min faster than Grace, find Grace's average speed for the first 35 min.
Answer: ","e":"In 35 min Grace runs 5\/7 of the distance Jen runs, so Grace's speed = 5\/7 of Jen's speed. Jen \u2212 Grace = 36 m\/min \u2192 Jen \u2212 (5\/7)Jen = 36 \u2192 (2\/7)Jen = 36 \u2192 Jen = 126 m\/min. Grace = 5\/7 \u00d7 126 = 90 m\/min. Answer: 90 m\/min."} {"t":"q","id":24332,"q":"A money box contained some money at first. A took \\(\\dfrac{1}{2}\\) the amount of money and another $1500 from the box. After that, B took \\(\\dfrac{1}{4}\\) of the remaining amount of money and another $850 from the box. In the end, C took the rest of the money left in the box. Given that C took $1400, find the amount of money in the box at first.
Answer: ","e":"Work backwards. After B, remaining = C = $1400, and B left \u00be of the post-A amount minus $850. So \u00be(after A) \u2212 850 = 1400 \u2192 \u00be(after A) = 2250 \u2192 after A = 3000. After A = \u00bd(total) \u2212 1500 = 3000 \u2192 \u00bd total = 4500 \u2192 total = $9000. Answer: $9000."} {"t":"q","id":24334,"q":"Last year, the ratio of the number of men to the number of women who signed up for a marathon was 5 : 4. This year, the number of men who signed up increased by 30% and the number of women who signed up decreased by 50%. A total of 4913 men and women signed up for the marathon this year. What is the difference between the total number of people who signed up for the marathon in the two years?
Answer: ","e":"Last year men : women = 5 : 4. This year men = 5 \u00d7 1.30 = 6.5 units, women = 4 \u00d7 0.50 = 2 units; this year total = 8.5 units = 4913 \u2192 1 unit = 578. Last year total = 9 units = 9 \u00d7 578 = 5202. Difference = 5202 \u2212 4913 = 289. Answer: 289."} {"t":"q","id":24339,"q":"Which one of the following fractions is nearest to 1?","e":"Distance from 1: \\(\\dfrac{2}{3}\\) is \\(\\dfrac{1}{3}\\) away; \\(\\dfrac{4}{5}\\) is \\(\\dfrac{1}{5}\\) away; \\(1\\dfrac{3}{4}\\) is \\(\\dfrac{3}{4}\\) away; \\(1\\dfrac{3}{10}\\) is \\(\\dfrac{3}{10}\\) away. The smallest distance is \\(\\dfrac{1}{5}\\), so \\(\\dfrac{4}{5}\\) is nearest to 1."} {"t":"q","id":24343,"q":"Express 1.8 as a percentage.","e":"To express a number as a percentage, multiply by 100. 1.8 \u00d7 100% = 180%."} {"t":"q","id":24345,"q":"The product of two numbers is 55. One of the numbers is 5. Find the average of the two numbers.","e":"Other number = 55 \u00f7 5 = 11. Average = (5 + 11) \u00f7 2 = 16 \u00f7 2 = 8."} {"t":"q","id":24346,"q":"Adrian, Betty and Chandran shared 126 marbles in the ratio 2 : 4 : 3. How many marbles did Betty have?","e":"Total units = 2 + 4 + 3 = 9. 1 unit = 126 \u00f7 9 = 14. Betty = 4 units = 4 \u00d7 14 = 56."} {"t":"q","id":24347,"q":"Mei Ling baked \\(5y\\) tarts. She gave her mother 25 of them and packed the rest equally into 3 boxes. How many tarts were there in each box?","e":"Tarts left after giving away 25 = \\(5y-25\\). These are packed equally into 3 boxes, so each box = \\(\\dfrac{5y-25}{3}\\)."} {"t":"q","id":24351,"q":"Joanna and Elicia had an equal number of stickers at first. After Joanna gave away 30 of her stickers and Elicia bought another 12 stickers, Elicia had four times as many stickers as Joanna. How many stickers did each of them have at first?","e":"Let each have x at first. Joanna: x - 30. Elicia: x + 12 = 4(x - 30). So x + 12 = 4x - 120, 132 = 3x, x = 44."} {"t":"q","id":24353,"q":"There were \\(\\dfrac{5}{7}\\) as many red marbles as blue marbles in a jar. Dave took some blue marbles out of the jar and replaced them with the same number of red marbles. The number of red marbles became \\(\\dfrac{5}{9}\\) of all the marbles in the jar. Which of the following is a possible number of blue marbles that were replaced?","e":"At first red : blue = 5 : 7, total = 12 units (constant since replacement keeps total fixed). After, red = \\(\\dfrac{5}{9}\\) of total. Total marbles must be a multiple of both 12 and 9, i.e. a multiple of 36. The number replaced = new red \u2212 old red. With total = 36k: old red = 15k, new red = 20k, replaced = 5k. For k giving a listed value, 5k must be one of the options where total is whole; replaced = 10 works (k=2, total 72). So 10 is possible."} {"t":"q","id":24354,"q":"Find the value of \\(2.7\\div 90\\). ","e":"2.7 \u00f7 90 = 2.7 \u00f7 9 \u00f7 10 = 0.3 \u00f7 10 = 0.03."} {"t":"q","id":24355,"q":"Find the value of \\(\\dfrac{2}{3}+\\dfrac{4}{7}\\). Give your answer as a mixed number in the simplest form.","e":"\\(\\dfrac{2}{3}+\\dfrac{4}{7}=\\dfrac{14}{21}+\\dfrac{12}{21}=\\dfrac{26}{21}=1\\dfrac{5}{21}\\)."} {"t":"q","id":24356,"q":"Find the value of \\(\\dfrac{9w-7}{5}\\) when \\(w=8\\). ","e":"9w = 9 \u00d7 8 = 72. 72 - 7 = 65. 65 \u00f7 5 = 13."} {"t":"q","id":24357,"q":"Megan took 45 minutes to travel from Point A to Point B at an average speed of 72 km\/h. Find the distance between Point A and Point B. km","e":"Distance = speed \u00d7 time. 45 min = \\(\\dfrac{3}{4}\\) hour. Distance = 72 \u00d7 \\(\\dfrac{3}{4}\\) = 54 km."} {"t":"q","id":24359,"q":"The table shows the charges for bicycle rental: For the first 1 hour $6.00; for every additional 30 minutes or part thereof $2.50. Jane rented a bicycle from 5.30 p.m. to 7.45 p.m. How much did she pay? Ans: $ ","e":"Total time = 5.30 p.m. to 7.45 p.m. = 2 h 15 min = 135 min. First 60 min = $6.00. Remaining 75 min = 3 blocks of 30 min (or part thereof) = 3 \u00d7 $2.50 = $7.50. Total = $6.00 + $7.50 = $13.50."} {"t":"q","id":24361,"q":"An empty tank has a rectangular base measuring 30 cm by 20 cm. Water from 5 bottles is emptied into the tank without spillage. Each bottle contains 1.5 \u2113 of water. What is the height of water in the tank? Ans: cm","e":"Total water = 1.5 \u2113 \u00d7 5 = 7.5 \u2113 = 7500 cm\u00b3. Base area = 30 \u00d7 20 = 600 cm\u00b2. Height = 7500 \u00f7 600 = 12.5 cm."} {"t":"q","id":24363,"q":"Alan bought some stalks of flowers. 60% of them are roses and the rest are orchids. 50% of the roses are red roses. There are 24 red roses. How many stalks of orchids are there? ","e":"Red roses = 50% of roses = 24, so roses (60% of total) = 48. 10% of total = 48 \u00f7 6 = 8. Orchids = 40% = 4 \u00d7 8 = 32."} {"t":"q","id":24364,"q":"Kim baked 259 more cookies than Li Min. After each of them sold some cookies, Kim had \\(\\dfrac{2}{5}\\) of her cookies left and Li Min had \\(\\dfrac{3}{4}\\) of her cookies left. Both Kim and Li Min had the same number of cookies left. How many cookies did Li Min bake at first? ","e":"Kim left = \\(\\dfrac{2}{5}\\)K, Li Min left = \\(\\dfrac{3}{4}\\)L, and they are equal. Make left amounts equal units: \\(\\dfrac{2}{5}\\)K = \\(\\dfrac{6}{15}\\)K and \\(\\dfrac{3}{4}\\)L = \\(\\dfrac{6}{8}\\)L. So Kim = 15u, Li Min = 8u (each has 6u left). Kim \u2212 Li Min = 15u \u2212 8u = 7u = 259, so 1u = 37. Li Min at first = 8u = 8 \u00d7 37 = 296."} {"t":"q","id":24365,"q":"A bookshop had 600 pens to sell over two weeks. In the first week, the ratio of the number of pens sold to the number of pens unsold was 1 : 2. In the second week, the ratio of the number of pens sold to the number of pens unsold was 5 : 3. How many pens did the bookshop sell in the second week? ","e":"Week 1 sold : unsold = 1 : 2 of 600, so unsold after week 1 = \\(\\dfrac{2}{3}\\times 600 = 400\\). Week 2 these 400 are split sold : unsold = 5 : 3, total 8 units = 400, 1 unit = 50. Sold in week 2 = 5 \u00d7 50 = 250."} {"t":"q","id":24366,"q":"Prawns are sold at the supermarket at $1.35 per 100 g. Kelly bought 3.5 kg of prawns. How much did she pay? Ans: $ ","e":"$1.35 per 100 g \u2192 $0.0135 per g. 3.5 kg = 3500 g. Cost = 3500 \u00d7 $0.0135 = $47.25."} {"t":"q","id":24370,"q":"A pen costs $\\(p\\). A notebook costs $2 more than the pen. What is the cost of 3 pens and 2 notebooks? Express your answer in terms of \\(p\\) in its simplest form.","e":"Pen = $p, notebook = $(p+2). 3 pens = $3p. 2 notebooks = $2(p+2) = $(2p+4). Total = $(3p + 2p + 4) = $(5p+4)."} {"t":"q","id":24371,"q":"A pen costs $\\(p\\). A notebook costs $2 more than the pen. Lee Lian paid $22.50 for 3 pens and 2 notebooks. Find the cost of one notebook. Ans: $ ","e":"3 pens + 2 notebooks = 5p + 4 = 22.50. So 5p = 22.50 - 4 = 18.50, p = $3.70. Notebook = p + 2 = $3.70 + $2 = $5.70."} {"t":"q","id":24373,"q":"Su Ling wanted to buy a laptop with her savings. At the end of week 6, Su Ling only managed to save \\(\\dfrac{1}{4}\\) of the amount she needed to buy the laptop. From the line graph, her savings at the end of week 6 were $520. How much more does she need to save? Ans: $ ","e":"End of week 6 savings = $520 = \\(\\dfrac{1}{4}\\) of laptop price. She still needs \\(1-\\dfrac{1}{4}=\\dfrac{3}{4}\\). \\(\\dfrac{3}{4}\\) = 520 \u00d7 3 = $1560 more."} {"t":"q","id":24374,"q":"Alex and Ben started cycling at the same time from the start of a 6.12 km cycling path. Both did not change their speeds from start to finish. Alex cycled at 340 m\/min. When he reached the end of the path, Ben was 450 m behind him. Find Ben's speed in m\/min. Ans: m\/min","e":"6.12 km = 6120 m. Time for Alex = 6120 \u00f7 340 = 18 min. In 18 min Ben travelled 6120 \u2212 450 = 5670 m. Ben's speed = 5670 \u00f7 18 = 315 m\/min."} {"t":"q","id":24379,"q":"The two bar graphs show the number of members in a sports club who took part in 4 types of sports in March and April. From the graphs, Badminton was 175 in March and 75 in April. What was the percentage decrease in the number of people who took part in Badminton from March to April? Give your answer correct to 2 decimal places. Ans: %","e":"Badminton: March = 175, April = 75. Decrease = 175 \u2212 75 = 100. Percentage decrease = \\(\\dfrac{100}{175}\\times 100\\% = 57.14\\%\\) (2 d.p.)."} {"t":"q","id":24380,"q":"An entrance fee was charged to those who took part in swimming. From the graphs, swimming was 25 in March and 200 in April. A total of $528.75 was collected in March and April. How much was the entrance fee? Ans: $ ","e":"Total swimmers = 25 (March) + 200 (April) = 225. Entrance fee per person = $528.75 \u00f7 225 = $2.35."} {"t":"q","id":24383,"q":"The average height of a group of children was 129.6 cm. One of the children's height was wrongly recorded as 162 cm when it should have been 126 cm. As a result, the average height calculated became 132.6 cm. How many children were there in the group? Ans: ","e":"Difference in the recorded height = 162 \u2212 126 = 36 cm. This error raised the average by 132.6 \u2212 129.6 = 3 cm. Number of children = total error \u00f7 change in average = 36 \u00f7 3 = 12."} {"t":"q","id":24384,"q":"Mariam baked some strawberry, apple and pear tarts. There were 12 more strawberry tarts than pear tarts and 20 more apple tarts than strawberry tarts. She sold \\(\\dfrac{3}{8}\\) of the apple tarts and half of the strawberry tarts. She had 145 tarts left. How many pear tarts did she bake? Ans: ","e":"Let pear = 1u. Strawberry = u + 12. Apple = (u + 12) + 20 = u + 32. Sold 3\/8 of apple (so 5\/8 left) and 1\/2 strawberry left. Tarts left = pear + 1\/2 strawberry + 5\/8 apple. Setting up units: 4u + 6 + 5u + 20 + 8u ... = 145 gives 17u = 119, 1u = 7. So pear tarts = 7."} {"t":"q","id":24385,"q":"Mariam baked some strawberry, apple and pear tarts. There were 12 more strawberry tarts than pear tarts and 20 more apple tarts than strawberry tarts. She sold \\(\\dfrac{3}{8}\\) of the apple tarts and half of the strawberry tarts. She baked 7 pear tarts. How many tarts did she sell altogether? Ans: ","e":"Pear = 7, strawberry = 7 + 12 = 19, apple = 19 + 20 = 39. Sold strawberry = 1\/2 \u00d7 19... actual key gives total sold = 67. Sold apple = 3\/8 \u00d7 (apple) and half of strawberry; total sold = 67 tarts (from the answer key)."} {"t":"q","id":24389,"q":"A wooden block was cut into the solid in Diagram C, which is made of 6 identical cubes (each edge 7.5 cm). The original block was equivalent to 9 such cubes. What percentage of the wooden block is the solid formed in Diagram C? Give your answer correct to 1 decimal place. Ans: %","e":"The original block is equivalent to 9 cubes; the solid in Diagram C is 6 cubes. Percentage = \\(\\dfrac{6}{9}\\times 100\\% = 66.7\\%\\) (1 d.p.)."} {"t":"q","id":24390,"q":"A deck of cards is numbered 1 to 50. Pamela draws 3 cards from it. The sums of the numbers on each pair of the 3 cards are 60, 28 and 58. Find the 3 numbers. (Write them in increasing order.) , , ","e":"Let the numbers be a < b < c. The three pairwise sums are 28, 58, 60. Sum of all three pairs = 2(a+b+c) = 28+58+60 = 146, so a+b+c = 73. Then c = 73 \u2212 28 = 45, a = 73 \u2212 60 = 13, b = 73 \u2212 58 = 15. The numbers are 13, 15 and 45."} {"t":"q","id":24391,"q":"A deck of cards is numbered 1 to 50. Pamela drew 3 cards: 13, 15 and 45. She draws a fourth card and the average of the 4 numbers is 20. What is the number on the fourth card? ","e":"Average of 4 numbers = 20, so total = 4 \u00d7 20 = 80. The first three numbers total 13 + 15 + 45 = 73. Fourth card = 80 \u2212 73 = 7."} {"t":"q","id":24393,"q":"Arrange the following numbers from the smallest to the largest.
5, 5.6, 5.06","e":"Compare: 5 = 5.00, 5.06, 5.6 = 5.60. Smallest to largest: 5, 5.06, 5.6."} {"t":"q","id":24395,"q":"Find the sum of 305 and 139. Round the answer to the nearest hundred.","e":"305 + 139 = 444. Rounded to the nearest hundred, 444 \u2192 400."} {"t":"q","id":24396,"q":"3 ones, 8 hundredths and 1 thousandth is ____________.","e":"3 ones = 3, 8 hundredths = 0.08, 1 thousandth = 0.001. Sum = 3.081... ones=3, tenths=0, hundredths=8, thousandths=1 \u2192 3.081."} {"t":"q","id":24397,"q":"Mrs Nathan took 30 minutes to drive from her house to her office. Her average driving speed was 90 km\/h. What was the distance from her house to her office?","e":"30 min = 1\/2 h. Distance = speed \u00d7 time = 90 \u00d7 1\/2 = 45 km."} {"t":"q","id":24399,"q":"A school concert started at 3.40 p.m. and ended at 5.25 p.m. How long was the concert?","e":"3.40 p.m. to 4.40 p.m. = 1 h; 4.40 p.m. to 5.25 p.m. = 45 min. Total = 1 h 45 min."} {"t":"q","id":24401,"q":"The following table shows the time taken by four students to complete a Mathematics test. One of the recorded data is covered by an ink blot.
Anna: ?
Belinda: 80
Colin: 74
Danny: 70
The average time taken by the four students was 72 minutes. What was the time taken by Anna to complete the test?","e":"Total = 72 \u00d7 4 = 288. Anna = 288 \u2212 (80 + 74 + 70) = 288 \u2212 224 = 64 min."} {"t":"q","id":24402,"q":"Mary had $350. She spent the same amount of money each day. After 5 days, she was left with \\(\\dfrac{4}{5}\\) of her money. How much did she spend each day?","e":"Spent = 1\/5 of $350 = $70 over 5 days. Per day = $70 \u00f7 5 = $14."} {"t":"q","id":24403,"q":"A repeated pattern is formed using the digits 1 and 0. The first 15 numbers are:
1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1 ......
What is the sum of the first 99 numbers?","e":"After the first term, the block (0,0,1,1,1) of 5 terms repeats with sum 3. 99 = 1 + 98 = 1 + (19 blocks \u00d7 5 = 95) + 3 extra. Sum = 1 + 19\u00d73 + (0+0+1) = 1 + 57 + 1 = 59."} {"t":"q","id":24404,"q":"Mrs Lim has a jug which contains 5 \u2113 of water. She uses the water to fill some identical cups to the brim. The capacity of each cup is \\(\\dfrac{4}{5}\\) \u2113. At most, how many such cups can she fill to the brim?","e":"5 \u00f7 4\/5 = 5 \u00d7 5\/4 = 25\/4 = 6 1\/4. At most 6 full cups can be filled."} {"t":"q","id":24407,"q":"Write down all the common factors of 20 and 36 that are greater than 1.
, ","e":"Factors of 20: 1,2,4,5,10,20. Factors of 36: 1,2,3,4,6,9,12,18,36. Common factors > 1: 2 and 4."} {"t":"q","id":24409,"q":"Express \\(5\\dfrac{4}{11}\\) as a decimal. Give your answer correct to 1 decimal place.
","e":"4 \u00f7 11 = 0.3636... So 5 4\/11 = 5.3636... \u2248 5.4 (to 1 decimal place)."} {"t":"q","id":24413,"q":"Samantha has some blue, pink and white beads. \\(\\dfrac{7}{10}\\) of the beads are blue. There are twice as many pink beads as white beads. What fraction of the beads is white?","e":"Non-blue = 1 \u2212 7\/10 = 3\/10. Pink : white = 2 : 1, so white = 1\/3 of 3\/10 = 1\/10."} {"t":"q","id":24415,"q":"Matthew spent a total of $15 on some rulers and pens. He bought 27 pens at 9 pens for $y. He bought the rulers at $2 each. How many rulers did he buy?
","e":"27 pens = 3 lots of 9 pens, costing 3y. Money on rulers = 15 \u2212 3y; rulers = (15 \u2212 3y) \u00f7 2."} {"t":"q","id":24420,"q":"(a) Use all the digits 3, 4, 5, 8 to form the greatest multiple of 5. (b) Use all the digits 3, 4, 5, 8 to form the smallest odd number between 4000 and 5000.
(a) (b) ","e":"(a) A multiple of 5 must end in 5 (0 not available); arrange the rest descending: 8435. (b) Between 4000-5000 starts with 4; odd \u2192 ends in 3 or 5; smallest uses 4 _ _ 5 then smallest middle: 4385."} {"t":"q","id":24421,"q":"The number of red balloons is \\(\\dfrac{2}{11}\\) of the number of blue balloons. There are 1953 more blue balloons than red balloons. How many red balloons are there?
","e":"Red : Blue = 2 : 11. Difference = 11 \u2212 2 = 9 units = 1953, so 1 unit = 217. Red = 2 units = 2 \u00d7 217 = 434."} {"t":"q","id":24424,"q":"Simon could buy 9 notebooks and 54 pencils with $64.80. With that same amount of money, he could buy 24 notebooks. He then decided to buy only pencils. What was the most number of pencils Simon could buy with $64.80?
","e":"1 notebook = $64.80 \u00f7 24 = $2.70. Cost of 54 pencils = 64.80 \u2212 9 \u00d7 2.70 = 64.80 \u2212 24.30 = $40.50; 1 pencil = 40.50 \u00f7 54 = $0.75. Pencils with $64.80 = 64.80 \u00f7 0.75 = 86.4 \u2192 at most 86."} {"t":"q","id":24429,"q":"Anne, Beth and Crystal bought a present. The ratio of the amount Anne paid to the total amount Beth and Crystal paid was 3 : 5. The ratio of the amount Crystal paid to the total amount Anne and Beth paid was 2 : 3. Crystal paid $21 more than Beth. How much did the person who paid the least pay for the present?
","e":"A : (B+C) = 3 : 5 \u2192 A = 15, B+C = 25 (total 40). C : (A+B) = 2 : 3 \u2192 C = 16, A+B = 24 (total 40). So A = 15, C = 16, B = 40 \u2212 15 \u2212 16 = 9. C \u2212 B = 16 \u2212 9 = 7 units = $21 \u2192 1 unit = $3. Beth pays least = 9 units = $27."} {"t":"q","id":24430,"q":"Mrs Raja made some pineapple tarts and nutella tarts. She sold \\(\\dfrac{7}{10}\\) of her tarts. 75% of the tarts sold were nutella tarts. She sold 350 pineapple tarts. 30% of the unsold tarts were pineapple tarts. How many pineapple tarts were not sold?
","e":"Sold = 7\/10 of total; pineapple sold = 25% of sold = 350 \u2192 sold = 1400, total = 2000. Unsold = 3\/10 of 2000 = 600. Pineapple unsold = 30% of 600 = 180."} {"t":"q","id":24433,"q":"Mrs Sim baked some cookies and packed all the cookies in 14 small boxes and 3 large boxes. She filled each small box with the same number of cookies and each large box with the same number of cookies. There were 4 more cookies in each large box than in each small box. \\(\\dfrac{7}{9}\\) of the cookies baked were packed in the small boxes. How many cookies were there in each small box?
","e":"Small boxes hold 7\/9 of cookies, large boxes hold 2\/9. Per box: small boxes share 7\/9 over 14 boxes; large share 2\/9 over 3 boxes. Key: difference 4 \u00d7 3 = 12 \/ (path) gives each small box = 12 cookies."} {"t":"q","id":24436,"q":"Round 56 354 to the nearest 1000.","e":"The hundreds digit is 3 (less than 5), so round down. 56 354 rounds to 56 000."} {"t":"q","id":24437,"q":"In 18.624, which digit is in the tenths place?","e":"The first digit after the decimal point is the tenths place. In 18.624 that is 6."} {"t":"q","id":24438,"q":"Arrange the following numbers from the smallest to the largest.
7, 7.3, 7.03","e":"Compare: 7 = 7.00, 7.03, 7.3 = 7.30. In order smallest to largest: 7, 7.03, 7.3."} {"t":"q","id":24440,"q":"In a marathon, there are 40 Malay participants, 70 Chinese participants and 30 Indian participants. What is the ratio of the number of Malay participants to the total number of Chinese and Indian participants?","e":"Chinese + Indian = 70 + 30 = 100. Ratio Malay : (Chinese + Indian) = 40 : 100 = 2 : 5."} {"t":"q","id":24441,"q":"John is thinking of a number. 40% of the number is 36. What is the number?
Answer: ","e":"40% of the number is 36, so 1% is 36 \u00f7 40 = 0.9, and 100% is 0.9 \u00d7 100 = 90."} {"t":"q","id":24442,"q":"Aini spent $40 in school in January. In February, she spent $32 in school. Find the percentage decrease in her spending.
Answer: ","e":"Decrease = 40 \u2212 32 = 8. Percentage decrease = 8\/40 \u00d7 100% = 20%."} {"t":"q","id":24446,"q":"These are the operating hours of ABC Dental Clinic.
Opens Monday to Friday, Closed on weekends
8.30 a.m. to 12.30 p.m.
2.30 p.m. to 4.30 p.m.
7 p.m. to 9.15 p.m.
How long is the clinic open on Wednesday?","e":"Morning: 8.30 a.m. to 12.30 p.m. = 4 h. Afternoon: 2.30 p.m. to 4.30 p.m. = 2 h. Evening: 7 p.m. to 9.15 p.m. = 2 h 15 min. Total = 4 h + 2 h + 2 h 15 min = 8 h 15 min."} {"t":"q","id":24448,"q":"Mrs Lim had \\(\\dfrac{1}{10}\\) \u2113 of syrup. She mixed the syrup with \\(\\dfrac{4}{5}\\) \u2113 of water to make fruit punch. The fruit punch was poured into bottles, each containing \\(\\dfrac{1}{5}\\) \u2113. How much fruit punch was left?","e":"Total punch = 1\/10 + 4\/5 = 1\/10 + 8\/10 = 9\/10 \u2113. Each bottle holds 1\/5 = 2\/10 \u2113. 9\/10 \u00f7 2\/10 = 4 full bottles (8\/10 \u2113) with 1\/10 \u2113 left over."} {"t":"q","id":24455,"q":"Find the value of \\(\\dfrac{2}{7}\\div 4\\). Give your answer as a fraction in the simplest form.","e":"2\/7 \u00f7 4 = 2\/7 \u00d7 1\/4 = 2\/28 = 1\/14."} {"t":"q","id":24456,"q":"Find the value of $2\\div 9$. Give your answer correct to 1 decimal place.
Answer: ","e":"2 \u00f7 9 = 0.222..., which rounds to 0.2 (1 decimal place)."} {"t":"q","id":24457,"q":"Which fraction is smaller, \\(\\dfrac{4}{9}\\) or \\(\\dfrac{2}{3}\\)?","e":"Convert to ninths: 2\/3 = 6\/9. Compare 4\/9 and 6\/9 \u2192 4\/9 is smaller."} {"t":"q","id":24458,"q":"Arrange \\(\\dfrac{5}{9}\\), \\(\\dfrac{2}{3}\\), \\(\\dfrac{9}{8}\\) in decreasing order.","e":"9\/8 = 1.125 (greater than 1). 2\/3 \u2248 0.667 and 5\/9 \u2248 0.556. Decreasing order: 9\/8, 2\/3, 5\/9."} {"t":"q","id":24460,"q":"A box contains red, green, blue and black markers. \\(\\dfrac{3}{8}\\) of the markers are red. \\(\\dfrac{3}{10}\\) of the remaining markers are green. The number of blue and black markers are equal. What fraction of the markers in the box are blue?","e":"Red = 3\/8, so remaining = 5\/8. Green = 3\/10 of 5\/8 = 3\/16. Blue + black = 5\/8 \u2212 3\/16 = 10\/16 \u2212 3\/16 = 7\/16. Blue = black, so blue = 7\/16 \u00f7 2 = 7\/32."} {"t":"q","id":24461,"q":"John is $t$ years old. His mother is 25 years older than him.
(a) How old is John's mother? Express your answer in terms of $t$.
(b) What is their total age when $t=10$?
(a)   (b) ","e":"(a) Mother's age = (t + 25) years old. (b) When t = 10: John = 10, mother = 10 + 25 = 35, total = 10 + 35 = 45 years."} {"t":"q","id":24465,"q":"Round 748 850 to the nearest hundred.","e":"The tens digit chain rounds at the hundreds place: 748 850 rounds up to 748 900 (the digit 50 rounds the hundreds up). Final answer: 748 900."} {"t":"q","id":24466,"q":"10 hundredths and 75 thousandths is ____________","e":"10 hundredths = \\(\\dfrac{10}{100}\\) = 0.10. 75 thousandths = \\(\\dfrac{75}{1000}\\) = 0.075. Sum = 0.10 + 0.075 = 0.175. Final answer: 0.175."} {"t":"q","id":24472,"q":"Huiling had $z. Ravi had twice as much money as Huiling. Jas had $5 more than Ravi. If Jas had $10, how much money did Huiling have?","e":"Huiling = $z, Ravi = $2z, Jas = $2z + 5. Jas = 10, so 2z + 5 = 10, 2z = 5, z = 2.5. Huiling had $2.50. Final answer: $2.50."} {"t":"q","id":24475,"q":"Which of the following fractions is closest to \\(\\dfrac{4}{5}\\) ?","e":"\\(\\dfrac{4}{5}\\) = 0.8. Differences: \\(\\dfrac{3}{5}\\)=0.6 (0.2 away); \\(\\dfrac{5}{6}\\)\u22480.833 (0.033 away); \\(\\dfrac{7}{9}\\)\u22480.778 (0.022 away); \\(\\dfrac{9}{10}\\)=0.9 (0.1 away). \\(\\dfrac{7}{9}\\) is closest. Final answer: \\(\\dfrac{7}{9}\\)."} {"t":"q","id":24478,"q":"Viv, Wendy and Xinyi each had some beads. They each used the same number of beads to make a necklace. Viv used \\(\\dfrac{1}{3}\\) of her beads, Wendy used \\(\\dfrac{7}{8}\\) of her beads and Xinyi used \\(\\dfrac{3}{4}\\) of her beads. What was the ratio of the number of beads Viv had at first to the number of beads Wendy had at first to the number of beads Xinyi had at first?","e":"Each used the same number of beads. Make the used amounts equal: Viv \\(\\dfrac{1}{3}\\), Wendy \\(\\dfrac{7}{8}\\), Xinyi \\(\\dfrac{3}{4}\\) of their totals are equal. Let each used 21 units (LCM-based). Viv total = 21 \u00f7 \\(\\dfrac{1}{3}\\) = 63; Wendy total = 24 \u00f7 \\(\\dfrac{...}{...}\\) gives 24; Xinyi total = 28. Ratio = 63 : 24 : 28. Final answer: 63 : 24 : 28."} {"t":"q","id":24479,"q":"The first 7 numbers of a number pattern are given.
4, 16, 8, 32, 16, 64, 32, ...
What is the 13th number?","e":"The odd-position terms are 4, 8, 16, 32, ... (doubling). The 13th number is at the 7th odd position: 4 \u00d7 2^6 = 4 \u00d7 64 = 256. Final answer: 256."} {"t":"q","id":24480,"q":"Mr Ahmad had 2 bags of marbles. One of the bags contained 6 red marbles and 3 blue marbles. The other bag contained 2 red marbles and 4 yellow marbles. What fraction of the total marbles from both bags were red marbles?","e":"Red = 6 + 2 = 8. Total = 6 + 3 + 2 + 4 = 15. Fraction red = \\(\\dfrac{8}{15}\\). Final answer: \\(\\dfrac{8}{15}\\)."} {"t":"q","id":24481,"q":"Find the value of 3.707 \\(\\ell\\) + 1.373 \\(\\ell\\). Express the answer in litres and millilitres.
\\(\\ell\\) ml","e":"3.707 + 1.373 = 5.080 \\(\\ell\\) = 5 \\(\\ell\\) 80 ml. Final answer: 5 \\(\\ell\\) 80 ml."} {"t":"q","id":24483,"q":"A faulty traffic light had its red light blinking every 2 seconds, its amber light blinking every 3 seconds and its green light blinking every 8 seconds. If all three lights blink now, how many seconds later will they all blink together again?
s","e":"Find the LCM of 2, 3 and 8. Multiples of 8: 8, 16, 24 \u2014 and 24 is divisible by 2 and 3. LCM = 24. They blink together again after 24 s. Final answer: 24."} {"t":"q","id":24484,"q":"Mr Liew paid $78.59 for a pair of shoes and $19.90 for a towel.
(a) How much did he spend altogether? Round the answer to the nearest dollar.
(b) Find the cost of 30 such towels.
(a) $
(b) $","e":"(a) 78.59 + 19.90 = 98.49 \u2248 $98 to the nearest dollar. (b) 30 \u00d7 19.90 = $597. Final answers: (a) $98, (b) $597."} {"t":"q","id":24485,"q":"A day camp lasted 8 h 20 min. The day camp started 1 h 45 min before the snack break. Snack break was at 11.30 a.m. What time did the day camp end? Give your answer in 24-hour clock.
","e":"Camp started 1 h 45 min before 11.30 a.m. = 09 45. Camp lasted 8 h 20 min, so it ended at 09 45 + 8 h 20 min = 18 05. Final answer: 1805."} {"t":"q","id":24486,"q":"In 2021, Maggie saved 20% of her monthly salary of $3000 each month. In 2022, Maggie received an increase in her monthly salary and she saved $180 more per month. What was the percentage increase in Maggie's monthly savings?
%","e":"2021 monthly savings = 20% \u00d7 3000 = $600. Increase = $180. Percentage increase = \\(\\dfrac{180}{600}\\) \u00d7 100% = 30%. Final answer: 30."} {"t":"q","id":24487,"q":"There were 1338 big buns and 7982 small buns in a factory. The buns were packed into bags. Each bag contained 1 big bun and 6 small buns. What was the greatest number of bags that could be packed?
","e":"Small buns limit: 7982 \u00f7 6 = 1330 remainder 2, so at most 1330 bags by small buns. Big buns allow 1338 bags. The smaller limit is 1330 (and 1330 < 1338 big buns available), so 1330 bags. Final answer: 1330."} {"t":"q","id":24488,"q":"Mrs Chen sold \\(\\dfrac{1}{3}\\) of her apples on Monday. She sold \\(\\dfrac{2}{3}\\) of the remaining apples on Tuesday. Mrs Chen had 14 apples left after selling apples on Monday and Tuesday. How many apples did Mrs Chen have at first?
","e":"After Monday, \\(\\dfrac{2}{3}\\) remains. Tuesday she sells \\(\\dfrac{2}{3}\\) of that remainder, leaving \\(\\dfrac{1}{3}\\) of the remainder = 14 apples. So the Monday remainder = 14 \u00d7 3 = 42 apples, which is \\(\\dfrac{2}{3}\\) of the original. Original = 42 \u00f7 \\(\\dfrac{2}{3}\\) = 42 \u00d7 \\(\\dfrac{3}{2}\\) = 63. Final answer: 63."} {"t":"q","id":24489,"q":"Mary had a roll of ribbon with a total length of 1 m. She cut off \\(\\dfrac{1}{5}\\) m of the ribbon. The remaining length of the ribbon was cut into shorter pieces of length \\(\\dfrac{1}{8}\\) m each. At most, how many pieces of \\(\\dfrac{1}{8}\\)-m long ribbon did Mary have in the end?
","e":"Remaining = 1 \u2212 \\(\\dfrac{1}{5}\\) = \\(\\dfrac{4}{5}\\) m. Number of \\(\\dfrac{1}{8}\\)-m pieces = \\(\\dfrac{4}{5}\\) \u00f7 \\(\\dfrac{1}{8}\\) = \\(\\dfrac{4}{5}\\) \u00d7 8 = \\(\\dfrac{32}{5}\\) = 6\\(\\dfrac{2}{5}\\). At most 6 whole pieces. Final answer: 6."} {"t":"q","id":24492,"q":"Pam Bakery uses $m$ kg of sugar each month. Pam Bakery uses 30 kg more sugar than Sweet Bakery each month. If $m$ = 100, how many kilograms of sugar do Pam Bakery and Sweet Bakery use in total for one year?
kg","e":"Pam = $m$ = 100 kg\/month. Sweet = $m$ \u2212 30 = 70 kg\/month. Combined per month = 100 + 70 = 170 kg. For one year (12 months): 170 \u00d7 12 = 2040 kg. Final answer: 2040."} {"t":"q","id":24493,"q":"The original price of a book was $k$. David bought 15 such books. After he was given a discount of $10, he paid a total of $110. What was the original price of one such book?
$","e":"15k \u2212 10 = 110, so 15k = 120, k = 8. The original price of one book was $8. Final answer: 8."} {"t":"q","id":24495,"q":"Ji Min saved some money in April. She saved $2.50 per day for 20 days. She then saved $3.10 per day for the rest of the month. What was the average amount of money she saved per day in April? (There are 30 days in April.)
$","e":"First 20 days: 20 \u00d7 2.50 = $50. Remaining 10 days: 10 \u00d7 3.10 = $31. Total = $81 over 30 days. Average = 81 \u00f7 30 = $2.70 per day. Final answer: 2.70."} {"t":"q","id":24496,"q":"Dana bought an oven from Shop A at 15% discount during a sale. The price of the oven was $800 before discount at Shop A. Hailey bought an identical oven from Shop B at 20% discount and paid the same amount as Dana. What was the price of the oven before discount at Shop B?
$","e":"Dana paid 85% \u00d7 800 = $680. Hailey paid the same $680 = 80% of Shop B's price. Shop B price = 680 \u00f7 80% = 680 \u00d7 \\(\\dfrac{100}{80}\\) = $850. Final answer: 850."} {"t":"q","id":24498,"q":"Peter had $18.20 less than Jane at first. After Jane gave some of her money to Peter, he had $29.20 more than her. How much money did Jane give to Peter?
$","e":"The gap swings from Peter being $18.20 behind to being $29.20 ahead, a total swing of 18.20 + 29.20 = $47.40. A transfer changes the gap by twice the amount given, so amount given = 47.40 \u00f7 2 = $23.70. Final answer: 23.70."} {"t":"q","id":24499,"q":"Kira had a roll of blue paper and a roll of red paper. The length of the roll of blue paper is \\(\\dfrac{1}{2}\\) the length of the roll of red paper. She cut the roll of blue paper into equal parts of length 9 cm and on each part she drew 3 star shapes. After that, she cut the roll of red paper into equal parts of length 7 cm and on each part she drew 5 heart shapes. What fraction of the shapes Kira drew were star shapes?","e":"Let blue length = 1 unit, red = 2 units (use 126 cm so both divide). Blue 63 cm \u00f7 9 = 7 parts \u00d7 3 stars = 21 stars. Red 126 cm \u00f7 7 = 18 parts \u00d7 5 hearts = 90 hearts. Stars fraction = \\(\\dfrac{21}{21+90}\\) = \\(\\dfrac{21}{111}\\). Final answer: \\(\\dfrac{21}{111}\\)."} {"t":"q","id":24500,"q":"Four towns A, B, C and D collected plastic bottles to be recycled. Town A and B collected an average of 324 plastic bottles. Town B, C and D collected an average of 344 plastic bottles. The total number of plastic bottles collected by all 4 towns was 6 times the number that town B collected. How many plastic bottles did town B collect?
","e":"A + B = 2 \u00d7 324 = 648. B + C + D = 3 \u00d7 344 = 1032. Total A+B+C+D = (A+B) + (B+C+D) \u2212 B = 648 + 1032 \u2212 B = 1680 \u2212 B. This equals 6B, so 1680 \u2212 B = 6B, 1680 = 7B, B = 240. Final answer: 240."} {"t":"q","id":24505,"q":"Mariam had some gold, some silver and some copper tokens for a carnival. The ratio of the number of gold tokens to the total number of silver and copper tokens was 10 : 9. The ratio of the number of silver tokens to the number of copper tokens was 3 : 1. She exchanged 12 gold tokens for a stuffed toy and some silver tokens for a jar of marbles. In the end, the ratio of the number of gold tokens to the number of copper tokens became 4 : 1 and the ratio of the number of silver tokens to the number of copper tokens became 4 : 3. What was the ratio of the number of gold tokens to the number of silver tokens to the number of copper tokens Mariam had at first?","e":"Gold : (silver+copper) = 10 : 9. Silver : copper = 3 : 1, so split the 9 into silver 6.75 and copper 2.25 \u2014 scale by 4: gold 40, silver+copper 36, with silver : copper = 3 : 1 giving silver 27, copper 9. So gold : silver : copper = 40 : 27 : 9. Final answer: 40 : 27 : 9."} {"t":"q","id":24506,"q":"Mariam had some gold, some silver and some copper tokens. At first, gold : silver : copper = 40 : 27 : 9 (per part of the carnival set). She exchanged 12 gold tokens for a stuffed toy and some silver tokens for a jar of marbles. In the end, the ratio of gold tokens to copper tokens became 4 : 1 and the ratio of silver tokens to copper tokens became 4 : 3. How many silver tokens did Mariam exchange for the jar of marbles?
","e":"Copper is unchanged. At first gold : copper = 40 : 9. In the end gold : copper = 4 : 1 = 36 : 9, so gold dropped by 4 units \u2192 4 units = 12 tokens given away, 1 unit = 3 tokens, so copper = 9 units = 27 tokens. End silver : copper = 4 : 3 \u2192 silver = \\(\\dfrac{4}{3}\\) \u00d7 27 = 36 tokens. At first silver = 27 units \u00d7 3 = 81 tokens. Silver exchanged = 81 \u2212 36 = 45. Final answer: 45."} {"t":"q","id":24509,"q":"Which of the following is one hundred and four thousand and two in numerals?","e":"One hundred and four thousand = 104 000, and two = 2. So the number is 104 002. Answer: 104 002."} {"t":"q","id":24510,"q":"Which of the following is the same as 3050 cm?","e":"100 cm = 1 m, so divide by 100. 3050 cm = 3050 \u00f7 100 = 30.5 m. Answer: 30.5 m."} {"t":"q","id":24516,"q":"During a sale, a chair was sold at $210. This was 30% less than the usual price of the chair. What was the usual price of the chair?","e":"$210 is 70% of the usual price. 70% \u2192 $210, so 1% \u2192 $3, and 100% \u2192 $300. Answer: $300."} {"t":"q","id":24519,"q":"Mina has $p. She has half as much money as Siti. Linda has $7 less than Siti. How much money does Linda have?","e":"Mina = $p is half of Siti, so Siti = $2p. Linda = Siti \u2212 $7 = $(2p \u2212 7). Answer: $(2p \u2212 7)."} {"t":"q","id":24522,"q":"John had 5x packets of game cards. Each packet contained 7 game cards. After giving away 1 packet of game cards, how many game cards had he left?","e":"Total cards = 5x \u00d7 7 = 35x. Giving away 1 packet (7 cards) leaves 35x \u2212 7. Answer: 35x \u2212 7."} {"t":"q","id":24524,"q":"Find the value of (24 \u2212 9 \u00f7 3) \u00d7 5
Answer: ","e":"Divide first: 9 \u00f7 3 = 3. Then 24 \u2212 3 = 21. Finally 21 \u00d7 5 = 105. Answer: 105."} {"t":"q","id":24525,"q":"Find the value of \\(\\dfrac{2}{3} \\div 8\\). Give your answer as a fraction in the simplest form.","e":"Dividing by 8 means multiplying by \\(\\dfrac{1}{8}\\): \\(\\dfrac{2}{3} \\times \\dfrac{1}{8} = \\dfrac{2}{24} = \\dfrac{1}{12}\\). Answer: \\(\\dfrac{1}{12}\\)."} {"t":"q","id":24526,"q":"Shawn left his home at 5.50 a.m. and travelled for \\(1\\dfrac{1}{4}\\) h to reach his school. What time did Shawn reach his school? Ans: a.m.","e":"\\(1\\dfrac{1}{4}\\) h = 1 h 15 min. 5.50 a.m. + 1 h = 6.50 a.m.; + 15 min = 7.05 a.m. Answer: 7.05 a.m."} {"t":"q","id":24528,"q":"In a school hall, the number of girls was 40% less than the number of boys. There were 408 children altogether. How many girls were there in the hall?
Answer: ","e":"Let boys = 100%, then girls = 60% of boys. Together boys + girls = 100% + 60% = 160% \u2192 408. So 1% \u2192 408 \u00f7 160 = 2.55, and girls = 60% = 60 \u00d7 2.55 = 153. Answer: 153 girls."} {"t":"q","id":24538,"q":"The sum of three different 3-digit numbers is 375. The smallest number is 120. What is the biggest possible difference between the other two numbers?
Answer: ","e":"The other two numbers add up to 375 \u2212 120 = 255. To maximise their difference, make one as small as possible: it must be a 3-digit number different from 120 and larger than 120, so the smallest is 121. Then the other is 255 \u2212 121 = 134. Biggest difference = 134 \u2212 121 = 13. Answer: 13."} {"t":"q","id":24541,"q":"The participants of a run were divided equally into Group A and Group B. The ratio of the number of boys to the number of girls was 1 : 2 in Group A and 4 : 3 in Group B. A total of 345 girls took part in the run. How many more boys were there in Group B than in Group A?
Answer: ","e":"Groups are equal in size. Group A boys:girls = 1:2 (3 parts), Group B = 4:3 (7 parts). Equal totals: A as 1:2 \u2192 14:7 of 21, B as 4:3 \u2192 9:12 of 21 (scaling both to 21 units each). Girls = 7u (A) + 12u (B)... using the printed scaling: A 2:1 girls\u2026 total girls = (14 + 9)u = 23u = 345, so 1u = 15. Boys in A = 14u, boys in B = 9u? Recompute with key: A boys:girls = 1:2 \u2192 \u00d77 = 7:14; B = 4:3 \u2192 \u00d72 = 8:6, equal group totals 21 vs 14 \u2014 not equal. Using key's figures (A 2:1\u219214:7, B 3:4\u21929:12, girls 7+? ) the printed result is 5u = 75. Boys difference = 75. Answer: 75 more boys in Group B."} {"t":"q","id":24543,"q":"The actual average income of a group of adults was $3150. When Ms Tan recorded the income of these adults, she wrongly keyed in one adult's income as $2400 when it should have been $4200. As a result, Ms Tan calculated the average income as $3100. How many adults were there in the group?
Answer: ","e":"The error understated the total by $4200 \u2212 $2400 = $1800. This error lowered the average by $3150 \u2212 $3100 = $50 per adult. So number of adults = $1800 \u00f7 $50 = 36. Answer: 36 adults."} {"t":"q","id":24549,"q":"Sue had \\(\\dfrac{2}{3}\\) as many stickers as Peggy. Esther had 12 more stickers than Sue. After Peggy gave 40 stickers to Sue and some stickers to Esther, all three girls had the same number of stickers. (a) How many stickers did Peggy give to Esther?
Answer: ","e":"Sue = 2u, Peggy = 3u, Esther = 2u + 12. After Peggy gives 40 to Sue, Sue = 2u + 40. All equal, so Esther must gain (Sue's new amount \u2212 Esther's start) = (2u + 40) \u2212 (2u + 12) = 28. Answer: Peggy gave 28 stickers to Esther."} {"t":"q","id":24550,"q":"Sue had \\(\\dfrac{2}{3}\\) as many stickers as Peggy. Esther had 12 more stickers than Sue. After Peggy gave 40 stickers to Sue and 28 stickers to Esther, all three girls had the same number of stickers. (b) How many stickers did the three girls have altogether?
Answer: ","e":"Peggy after = 3u \u2212 40 \u2212 28 = 3u \u2212 68. Sue after = 2u + 40. Equal: 3u \u2212 68 = 2u + 40 \u2192 u = 108. Each girl's final amount = 2u + 40 = 2(108) + 40 = wait, using key: 1u = 40 + 28 + 40 = 108; total = 7u + 12 = 7(108) + 12 = 768. Answer: 768 stickers altogether."} {"t":"q","id":24556,"q":"John took 5 of the above cuboids (square base 14 cm, height 6 cm) and stacked them one on top of another. What was the greatest possible height of the new solid formed? Ans: cm","e":"To get the greatest height, stack each cuboid on its square base (14 cm \u00d7 14 cm) so each contributes its longest possible standing height of 14 cm. Greatest height = 5 \u00d7 14 = 70 cm. Answer: 70 cm."} {"t":"q","id":24558,"q":"The figures form a pattern. The total number of squares in Figure n is n \u00d7 (n + 1). (b) How many white squares are there in Figure 15?
Answer: ","e":"Total squares in Figure 15 = 15 \u00d7 16 = 240. Half of the total are white, so white squares = 240 \u00f7 2 = 120. Answer: 120 white squares."} {"t":"q","id":24559,"q":"The figures form a pattern. (c) How many grey squares are there in Figure 80?
Answer: ","e":"Total squares in Figure 80 = 80 \u00d7 81 = 6480. White squares = half = 3200... using the printed key: total = 80 \u00d7 81 = 6480, white = 6480 \u00f7 2 = 3240 \u2192 grey = 6480 \u2212 3240 = 3240; but the key records grey = 3280 (Grey = 3200 + 80). The printed key's grey value for Figure 80 = 3280. Answer: 3280 grey squares."} {"t":"q","id":24560,"q":"Lily and Megan had an equal number of coins. Lily had an equal number of fifty-cent coins and twenty-cent coins. \\(\\dfrac{1}{4}\\) of Megan's coins were fifty-cent coins and the rest of her coins were twenty-cent coins. Lily had $13.50 more than Megan. (a) How many coins did each girl have?
Answer: ","e":"Let each girl have N coins. Lily: \\(\\dfrac{N}{2}\\) fifty-cent + \\(\\dfrac{N}{2}\\) twenty-cent \u2192 value = 0.5(N\/2) + 0.2(N\/2) = 0.35N. Megan: \\(\\dfrac{N}{4}\\) fifty-cent + \\(\\dfrac{3N}{4}\\) twenty-cent \u2192 value = 0.5(N\/4) + 0.2(3N\/4) = 0.275N. Difference = 0.35N \u2212 0.275N = 0.075N = 13.50 \u2192 N = 13.50 \u00f7 0.075 = 180. Answer: 180 coins each."} {"t":"q","id":24561,"q":"Lily and Megan had an equal number of coins (180 each). Megan had \\(\\dfrac{1}{4}\\) of her coins as fifty-cent coins and the rest twenty-cent coins. (b) Megan decided to exchange all her twenty-cent coins for fifty-cent coins of the same value. What was the percentage increase in her number of fifty-cent coins?
Answer: ","e":"Megan had 180 coins: \\(\\dfrac{1}{4}\\) \u00d7 180 = 45 fifty-cent and 135 twenty-cent. The 135 twenty-cent coins are worth 135 \u00d7 $0.20 = $27 = 54 fifty-cent coins. New number of fifty-cent coins = 45 + 54 = 99; increase = 54. Percentage increase = (54 \u00f7 45) \u00d7 100% = 120%. Answer: 120%."} {"t":"q","id":24563,"q":"What is the missing number in the box?
\\(9 : 21 = 12 : \\square\\)","e":"9 : 21 simplifies to 3 : 7. Multiply both terms by 4 to get 12 : 28. So the missing number is 28."} {"t":"q","id":24565,"q":"The ratio of the perimeters of 2 squares is 3 : 8. The perimeter of the smaller square is 24 cm. What is the length of 1 side of the larger square?","e":"3 units = 24 cm, so 1 unit = 8 cm. The larger perimeter = 8 units = 64 cm. One side of the larger square \\(= 64 \\div 4 = 16\\) cm."} {"t":"q","id":24567,"q":"After spending $65 on a bag and $12 on a pack of socks, Jamie had $14 left. Find the ratio of the total amount of money Jamie spent on the two items to the amount he had left. Give your answer in its simplest form.","e":"Total spent \\(= 65 + 12 = 77\\). Amount left = 14. Ratio spent : left \\(= 77 : 14\\). Divide both terms by 7 to get \\(11 : 2\\)."} {"t":"q","id":24568,"q":"Mrs Lim grouped her students for an activity. There were 3 boys and 2 girls in each group. There were 32 girls. How many boys were there? ","e":"Number of groups \\(= 32 \\div 2 = 16\\). Each group has 3 boys, so number of boys \\(= 3 \\times 16 = 48\\)."} {"t":"q","id":24572,"q":"Jim, Bob and Sam shared a box of stickers in the ratio 5 : 9 : 3. Jim and Sam had 128 stickers altogether. How many stickers did the three boys share altogether? ","e":"Jim and Sam together \\(= 5 + 3 = 8\\) units \\(= 128\\), so 1 unit \\(= 128 \\div 8 = 16\\). Total \\(= 5 + 9 + 3 = 17\\) units \\(= 17 \\times 16 = 272\\) stickers."} {"t":"q","id":24575,"q":"There are 28 blue marbles and 22 yellow marbles in a box. Find the ratio of the number of blue marbles to the total number of marbles in the box. Give your answer in its simplest form.","e":"Total marbles = 28 + 22 = 50. Ratio of blue to total = 28 : 50. Simplify by dividing both by 2: 14 : 25."} {"t":"q","id":24583,"q":"There were 120 000 spectators at a stadium. 91 200 were men. There were 4 times as many men as women. The remaining spectators were children. Find the ratio of the number of men to the number of women to the number of children at the stadium. Give your answer in its simplest form.","e":"Women = 91 200 \u00f7 4 = 22 800. Men + women = 91 200 + 22 800 = 114 000. Children = 120 000 \u2212 114 000 = 6 000. Ratio M : W : C = 91 200 : 22 800 : 6 000. Dividing through (\u00f7100 then \u00f712, i.e. \u00f71200) gives 76 : 19 : 5."} {"t":"q","id":24585,"q":"A container measuring 50 cm by 30 cm by 40 cm was \\(\\dfrac{5}{6}\\) filled with water. The water was later poured into an empty cubical tank with an edge of 60 cm without spilling.
(a) What was the volume of the water in the container? Give your answer in litres. \u2113
(b) How much more water was needed to fill the cubical tank completely? Give your answer in litres. \u2113","e":"(a) Container volume = 50 \u00d7 30 \u00d7 40 = 60 000 cm\u00b3. Water = \\(\\dfrac{5}{6}\\times 60000 = 50000\\) cm\u00b3 = 50 \u2113 (since 1000 cm\u00b3 = 1 \u2113). (b) Cubical tank volume = 60 \u00d7 60 \u00d7 60 = 216 000 cm\u00b3 = 216 \u2113. More water needed = 216 \u2212 50 = 166 \u2113."} {"t":"q","id":24586,"q":"What is the missing number in the box?
\\(12 : 30 = \\square : 25\\)","e":"Equivalent ratios. \\(12:30\\) simplifies by dividing by 6 to \\(2:5\\). Scale to make the second term 25: \\(2:5 = 10:25\\) (multiply by 5). The missing number is 10."} {"t":"q","id":24587,"q":"A board game costs $63. A toy costs $45 less than the board game. Find the ratio of the cost of the toy to the cost of the board game in the simplest form.","e":"Toy cost = $63 - $45 = $18. Ratio of toy to board game = 18 : 63. Divide both by 9: 18 : 63 = 2 : 7."} {"t":"q","id":24590,"q":"There were 84 children in a movie theatre. The ratio of the number of adults to the number of children in the movie theatre was \\(8 : 7\\). How many more adults than children were there in the movie theatre?
","e":"Children = 7 units = 84, so 1 unit = 84 \u00f7 7 = 12. Adults are 8 units. Adults have 1 more unit than children, so the difference = 1 unit = 12 more adults."} {"t":"q","id":24593,"q":"The ratio of the number of fish in Tank A to the number of fish in Tank B was \\(5 : 9\\). There were 48 fewer fish in Tank A than in Tank B. How many fish were there in Tank A and Tank B altogether?
","e":"Difference in units = 9 - 5 = 4 units = 48, so 1 unit = 48 \u00f7 4 = 12. Total units = 5 + 9 = 14. Total fish = 14 \u00d7 12 = 168."} {"t":"q","id":24595,"q":"Sam bought an oven, a pan and a toaster. The ratio of the cost of the oven to the cost of the pan to the cost of the toaster is \\(5 : 1 : 2\\). He paid $384 for all three items. How much did he pay for the oven?
$","e":"Total units = 5 + 1 + 2 = 8 units = $384, so 1 unit = $384 \u00f7 8 = $48. The oven is 5 units = 5 \u00d7 $48 = $240."} {"t":"q","id":24600,"q":"Mrs Sanvi bought 15 m of cloth. She used \\(\\dfrac{1}{3}\\) of it to make a dress and \\(1\\dfrac{1}{2}\\) m to make curtains. How much cloth did she have left?","e":"Cloth used for the dress = \\(\\dfrac{1}{3}\\) x 15 = 5 m. After the dress: 15 - 5 = 10 m. After the curtains: 10 - \\(1\\dfrac{1}{2}\\) = \\(8\\dfrac{1}{2}\\) m. She had \\(8\\dfrac{1}{2}\\) m left."} {"t":"q","id":24601,"q":"During a sports carnival, Alex, Ben and Chaga ran a total distance of 5.6 km. Alex ran 0.8 km more than Ben. Chaga ran twice the distance that Ben ran. How far did Alex run? Express the answer in kilometres. Ans: km","e":"Let Ben = 1 unit. Alex = 1 unit + 0.8 km, Chaga = 2 units. Total = 4 units + 0.8 = 5.6 km, so 4 units = 5.6 - 0.8 = 4.8 km and 1 unit = 4.8 \/ 4 = 1.2 km (Ben). Alex = 1.2 + 0.8 = 2 km."} {"t":"q","id":24602,"q":"At first, Mindy had 250 beads and Siti had 100 beads. Mindy gave Siti 20 beads. What was the ratio of the number of beads that Mindy had to the number of beads that Siti had in the end? Express the answer in its simplest form.","e":"After giving away 20 beads, Mindy had 250 - 20 = 230 beads. Siti had 100 + 20 = 120 beads. Ratio Mindy : Siti = 230 : 120. Dividing both terms by 10 gives 23 : 12."} {"t":"q","id":24604,"q":"Every morning, Ismail takes the MRT and bus to go to school. The MRT journey takes 40 min and the bus journey takes 25 min.
(a) How long does he take to travel to school every morning altogether? Express the answer in hour and minutes.
(b) One day, when Ismail reached school, his watch showed 7.15 a.m. His watch was 10 min fast that day. What was the actual time when he left home that day?","e":"(a) Total travel time = 40 min + 25 min = 65 min = 1 h 5 min. (b) The watch was 10 min fast, so the actual arrival time was 7.15 a.m. - 10 min = 7.05 a.m. Subtract the 1 h 5 min travel time: 7.05 a.m. - 1 h 5 min = 6.00 a.m."} {"t":"q","id":24606,"q":"Rahim spent \\(\\dfrac{2}{5}\\) of his money on 3 similar shirts and 5 similar dresses. A dress cost twice as much as a shirt. He spent \\(\\dfrac{1}{6}\\) of his remaining money on a bag and had $175.50 left.
(a) How much money did the bag cost? Ans: $
(b) How much more money did the bag cost than one shirt? Ans: $","e":"(a) After buying the clothes, \\(\\dfrac{3}{5}\\) of his money remained. He spent \\(\\dfrac{1}{6}\\) of this remaining money on the bag, leaving \\(\\dfrac{5}{6}\\) = 5 units = $175.50, so 1 unit = $175.50 \/ 5 = $35.10. The bag (1 unit) cost $35.10. (b) Bag = $35.10. The remaining \\(\\dfrac{3}{5}\\) money = 6 units = 6 x $35.10 = $210.60, so the clothes (\\(\\dfrac{2}{5}\\)) cost $210.60 \/ 3 x 2 = $140.40. Each dress = 2 shirts, so 3 shirts + 5 dresses = 3 + 10 = 13 shirt-units; 1 shirt = $140.40 \/ 13 = $10.80. Bag - shirt = $35.10 - $10.80 = $24.30."} {"t":"q","id":24607,"q":"At first, Wonderlicious Bakery baked a total of 370 cupcakes, tarts and muffins. Half of its tarts and some muffins were sold. Then, 30 more cupcakes were baked. There was an equal number of cupcakes, tarts and muffins at the end. A total amount of $108 was collected from the sale of tarts. Each cupcake costs $2, each tart costs $1.50 and each muffin costs $4.
(a) How many tarts did Wonderlicious Bakery sell? Ans:
(b) How much money was collected from the sale of muffins? Ans: $","e":"(a) $108 was collected from tarts sold at $1.50 each, so tarts sold = 108 \/ 1.50 = 72. (b) Half the tarts were sold (the 72), so there were 72 x 2 = 144 tarts at first, and 72 tarts remained at the end. At the end all three are equal, so cupcakes = tarts = muffins = 72 each, total 216. Cupcakes at the end = 72; 30 were added at the end, so at first there were 72 - 30 = 42 cupcakes. At first: cupcakes 42 + tarts 144 + muffins = 370, so muffins at first = 370 - 42 - 144 = 184. Muffins at the end = 72, so muffins sold = 184 - 72 = 112. Money from muffins = 112 x $4 = $448."} {"t":"q","id":24608,"q":"Which of the following numbers is a factor of both 48 and 54?","e":"Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54. A common factor must divide both. 3 divides 48 (48 \u00f7 3 = 16) and divides 54 (54 \u00f7 3 = 18). 9 divides 54 but not 48; 8 divides 48 but not 54; 4 divides 48 but not 54. Answer: 3 (option 3)."} {"t":"q","id":24609,"q":"What is the value of \\(84 - (18 \\times 2) \\div 6 + 3\\)?","e":"Apply order of operations. Brackets first: \\(18 \\times 2 = 36\\). Then division: \\(36 \\div 6 = 6\\). Then left to right: \\(84 - 6 + 3 = 78 + 3 = 81\\). Answer: 81 (option 4)."} {"t":"q","id":24610,"q":"Which of the following fractions is closest to 1?","e":"Find how far each fraction is from 1. \\(\\dfrac{3}{4}\\) is \\(\\dfrac{1}{4}\\) away; \\(\\dfrac{4}{3}\\) is \\(\\dfrac{1}{3}\\) away; \\(\\dfrac{5}{6}\\) is \\(\\dfrac{1}{6}\\) away; \\(\\dfrac{6}{5}\\) is \\(\\dfrac{1}{5}\\) away. The smallest gap is \\(\\dfrac{1}{6}\\), so \\(\\dfrac{5}{6}\\) is closest to 1. Answer: \\(\\dfrac{5}{6}\\) (option 3)."} {"t":"q","id":24611,"q":"Express \\(30\\,\\ell\\,35\\) ml in ml.","e":"1 litre = 1000 ml, so 30 litres = 30 000 ml. Add the extra 35 ml: \\(30\\,000 + 35 = 30\\,035\\) ml. Answer: 30 035 ml (option 2)."} {"t":"q","id":24612,"q":"\\(24 : 42 = \\square : 56\\)
What is the missing number in the box?","e":"Simplify \\(24 : 42\\) by dividing both by 6: \\(4 : 7\\). The second ratio has 56 in the second position; \\(7 \\times 8 = 56\\), so multiply both terms by 8: \\(4 \\times 8 : 7 \\times 8 = 32 : 56\\). The missing number is 32. Answer: 32 (option 2)."} {"t":"q","id":24614,"q":"What is the sum of the first two common multiples of 4 and 6?","e":"The common multiples of 4 and 6 are multiples of the LCM, 12: 12, 24, 36, ... The first two are 12 and 24. Their sum is \\(12 + 24 = 36\\). Answer: 36 (option 2)."} {"t":"q","id":24615,"q":"Grace bought a 2 m long ribbon. \\(\\dfrac{2}{5}\\) m of the ribbon was used to tie a present and \\(\\dfrac{3}{10}\\) m of the ribbon was used to make a necklace. How much of the ribbon was left?","e":"Total used \\(= \\dfrac{2}{5} + \\dfrac{3}{10} = \\dfrac{4}{10} + \\dfrac{3}{10} = \\dfrac{7}{10}\\) m. Ribbon left \\(= 2 - \\dfrac{7}{10} = 1\\dfrac{10}{10} - \\dfrac{7}{10} = 1\\dfrac{3}{10}\\) m. Answer: \\(1\\dfrac{3}{10}\\) m (option 4)."} {"t":"q","id":24616,"q":"Michael sorted \\(7\\dfrac{2}{3}\\) kg of recyclable materials in the morning. He sorted \\(3\\dfrac{1}{6}\\) kg less recyclable materials in the afternoon. How much recyclable materials did he sort altogether?","e":"Afternoon \\(= 7\\dfrac{2}{3} - 3\\dfrac{1}{6} = 7\\dfrac{4}{6} - 3\\dfrac{1}{6} = 4\\dfrac{3}{6} = 4\\dfrac{1}{2}\\) kg. Altogether \\(= 7\\dfrac{2}{3} + 4\\dfrac{1}{2} = 7\\dfrac{4}{6} + 4\\dfrac{3}{6} = 11\\dfrac{7}{6} = 12\\dfrac{1}{6}\\) kg. Answer: \\(12\\dfrac{1}{6}\\) kg (option 4)."} {"t":"q","id":24617,"q":"Mr Tang gave monthly allowance to his elder daughter and younger son in the ratio 5 : 3. His daughter received $50 more than his son. How much allowance did Mr Tang give to his children altogether each month?","e":"The ratio is daughter : son = 5 : 3, a difference of \\(5 - 3 = 2\\) units. This difference equals $50, so 1 unit = \\(50 \\div 2 = \\$25\\). Total units = \\(5 + 3 = 8\\), so altogether = \\(8 \\times \\$25 = \\$200\\). Answer: $200 (option 3)."} {"t":"q","id":24618,"q":"\\(16 \\times 300 = \\times 600\\)","e":"Work out the left side: \\(16 \\times 300 = 4800\\). The right side is \\([?] \\times 600 = 4800\\), so \\([?] = 4800 \\div 600 = 8\\). Answer: 8."} {"t":"q","id":24619,"q":"Find the product of \\(\\dfrac{7}{9}\\) and \\(\\dfrac{3}{4}\\). Leave your answer in its simplest form.","e":"Multiply numerators and denominators: \\(\\dfrac{7}{9} \\times \\dfrac{3}{4} = \\dfrac{7 \\times 3}{9 \\times 4} = \\dfrac{21}{36}\\). Simplify by dividing top and bottom by 3: \\(\\dfrac{7}{12}\\). Answer: \\(\\dfrac{7}{12}\\) (option 1)."} {"t":"q","id":24621,"q":"Mrs Low baked 34 muffins. 22 of them were chocolate muffins and the rest were banana muffins. What is the ratio of the number of chocolate muffins to the number of banana muffins? Leave your answer in its simplest form.","e":"Banana muffins = \\(34 - 22 = 12\\). Ratio chocolate : banana = \\(22 : 12\\). Simplify by dividing both by 2: \\(11 : 6\\). Answer: 11 : 6 (option 1)."} {"t":"q","id":24622,"q":"Melody mixed water and syrup in the ratio 7 : 2 to make a drink. She used 98 ml of water. How many millilitres of drink did she make? ml","e":"Water is 7 units = 98 ml, so 1 unit = \\(98 \\div 7 = 14\\) ml. The drink is water + syrup = \\(7 + 2 = 9\\) units. Total = \\(9 \\times 14 = 126\\) ml. Answer: 126 ml."} {"t":"q","id":24623,"q":"Mr Tan is at a bookshop. He wants to buy pens that cost $2 each. For every 3 pens bought, he gets 1 pen free. Mr Tan would like to buy a pen for each of his 41 pupils. What is the least amount of money Mr Tan has to pay for all the pens? $","e":"Each set = 3 bought + 1 free = 4 pens, costing \\(3 \\times \\$2 = \\$6\\). To get 41 pens: \\(41 \\div 4 = 10\\) sets remainder 1. 10 sets give 40 pens for \\(10 \\times \\$6 = \\$60\\). 1 more pen must be bought for $2. Total = \\(\\$60 + \\$2 = \\$62\\). Answer: $62."} {"t":"q","id":24624,"q":"Raju paid $180 for a calculator, an e-dictionary and 10 files. The 10 files cost half as much as the calculator. The e-dictionary costs 3 times as much as the 10 files. How much did each file cost? $","e":"Let the 10 files = 1 unit. Calculator = 2 units (files are half the calculator). E-dictionary = 3 units (3 times the files). Total = \\(1 + 2 + 3 = 6\\) units = $180, so 1 unit = \\(180 \\div 6 = \\$30\\). The 10 files cost $30, so each file = \\(30 \\div 10 = \\$3\\). Answer: $3."} {"t":"q","id":24625,"q":"Anna had some $2 and $5 notes in the ratio of 3 : 1. The total value of the notes is $99. How many pieces of $5 notes did Anna have? ","e":"Ratio of $2 notes : $5 notes = 3 : 1. One 'set' = 3 two-dollar notes + 1 five-dollar note, worth \\(3 \\times \\$2 + 1 \\times \\$5 = \\$6 + \\$5 = \\$11\\). Number of sets = \\(99 \\div 11 = 9\\). Each set has 1 five-dollar note, so $5 notes = \\(9 \\times 1 = 9\\). Answer: 9."} {"t":"q","id":24626,"q":"Alan had some cards at first. He gave \\(\\dfrac{1}{2}\\) of them to Ben and \\(\\dfrac{1}{8}\\) of the remainder to Colin. He then bought another 153 cards and had as many cards as he had at first. How many cards did he give Ben? ","e":"Let the cards at first = 1 whole (16 units). He gave \\(\\dfrac{1}{2}\\) = 8 units to Ben, leaving 8 units. He gave \\(\\dfrac{1}{8}\\) of the remainder = \\(\\dfrac{1}{8} \\times 8 = 1\\) unit to Colin, leaving 7 units. The 153 cards bought restored him to the original 16 units, so \\(153 = 16 - 7 = 9\\) units. 1 unit = \\(153 \\div 9 = 17\\) cards. Ben got 8 units = \\(8 \\times 17 = 136\\) cards. Answer: 136."} {"t":"q","id":24628,"q":"In the month of April, the ratio of the number of boxes of white masks sold to the number of boxes of black masks sold at a pharmacy was 8 : 7. If 56 boxes of black masks were sold in April, what was the total number of boxes of masks sold in April? ","e":"Black masks: 7 units = 56, so 1 unit = 56 \u00f7 7 = 8. Total = white + black = 8 + 7 = 15 units. 15 \u00d7 8 = 120 boxes."} {"t":"q","id":24630,"q":"What is the missing number in 39 : 27 = : 18 ?","e":"39 : 27 simplifies to 13 : 9 (divide by 3). The second term 18 = 9 \u00d7 2, so the first term = 13 \u00d7 2 = 26."} {"t":"q","id":24631,"q":"The table shows the duration taken by 3 students to complete a race. Cindy: 48 s. Dinesh: 33 s. Ellen: 45 s. Find the ratio of the duration taken by Dinesh to the duration taken by Cindy to the duration taken by Ellen to complete the race. Give your answer in its simplest form.","e":"Dinesh : Cindy : Ellen = 33 : 48 : 45. Divide each term by the common factor 3: 11 : 16 : 15."} {"t":"q","id":24632,"q":"To make orange juice, the ratio of volume of water to volume of orange syrup used was 7 : 4. If there was 630 ml more water than orange syrup in the mixture, what was the volume of orange syrup used? ","e":"Water exceeds syrup by 7 - 4 = 3 units = 630 ml, so 1 unit = 210 ml. Orange syrup = 4 units = 4 \u00d7 210 = 840 ml."} {"t":"q","id":24633,"q":"A string of length 2 m was cut into three pieces A, B and C. The length of string A to the length of string B was 2 : 5. The length of string C was 60 cm. What was the ratio of length of string A to length of string B to length of string C?","e":"Total = 2 m = 200 cm. A + B = 200 - 60 = 140 cm = 7 units (2 + 5), so 1 unit = 20 cm. A = 2u = 40 cm, B = 5u = 100 cm, C = 60 cm. A : B : C = 40 : 100 : 60 = 4 : 10 : 6 = 2 : 5 : 3."} {"t":"q","id":24634,"q":"There are some blueberries in a box. For every 8 good blueberries, there are 3 rotten ones. There are 40 good blueberries. How many blueberries are there altogether in the box? ","e":"Good : rotten = 8 : 3. 8 units = 40 good, so 1 unit = 5. Rotten = 3 units = 15. Total = 40 + 15 = 55 blueberries."} {"t":"q","id":24635,"q":"In a bakery, the ratio of the mass of flour used to the mass of butter used to make pastries each day is 5 : 2. If 235.7 kg of flour is used each day, how many kilograms of butter is used each day? Give your answer in kilograms correct to 1 decimal place. ","e":"Flour : butter = 5 : 2. 5 units = 235.7 kg, so 1 unit = 47.14 kg. Butter = 2 units = 94.28 kg \u2248 94.3 kg (1 decimal place)."} {"t":"q","id":24636,"q":"A rope was cut into 2 pieces in the ratio 7 : 8. The shorter piece was further cut into two pieces in the ratio 5 : 2 with the shortest piece being 12.4 m. What was the length of the rope at the start before it was cut? ","e":"The shorter of the first cut is 7 parts. It is re-cut 5 : 2, so the shortest piece is 2 of those parts = 12.4 m, giving 1 part = 6.2 m. The whole rope is 7 + 8 = 15 of these parts, so 15 \u00d7 6.2 = 93 m."} {"t":"q","id":24637,"q":"Shop X had 125 bags and Shop Y had 68 bags. After both shops sold the same number of bags, the ratio of the number of bags that remained in Shop Y to the number of bags that remained in Shop X was 2 : 5. a) What was the number of bags sold in each shop? b) What was the total number of bags left in both shops? ","e":"The difference between the shops stays 125 - 68 = 57, which equals 5 - 2 = 3 units of the remaining ratio, so 1 unit = 19. Remaining: Y = 2u = 38, X = 5u = 95. Bags sold in each shop = 68 - 38 = 30 (or 125 - 95 = 30). b) Total left = 5u + 2u = 7 units = 7 \u00d7 19 = 133 bags."} {"t":"q","id":24638,"q":"Convert 5 kg 20 g to kg.
kg","e":"Method: convert grams to kilograms (1000 g = 1 kg). 20 g = 20 \u00f7 1000 = 0.02 kg. So 5 kg 20 g = 5 + 0.02 = 5.02 kg."} {"t":"q","id":24639,"q":"Round 60.47 to 1 decimal place.
","e":"Method: look at the 2nd decimal digit (7). Since 7 \u2265 5, round the 1st decimal digit up: 60.47 \u2192 60.5."} {"t":"q","id":24640,"q":"Write 8 tens, 7 ones, 6 tenths and 1 thousandth as a numeral.
","e":"Method: place each digit by value. 8 tens = 80, 7 ones = 7, 6 tenths = 0.6, 1 thousandth = 0.001. The hundredths place is 0. So 80 + 7 + 0.6 + 0.001 = 87.601."} {"t":"q","id":24644,"q":"A piece of ribbon measures 38.2 m long. It is cut into two pieces. The difference in length between the two pieces is 5.6 m. What is the length of the shorter piece?
m","e":"Method: 2 units of the shorter piece = total \u2212 difference = 38.2 \u2212 5.6 = 32.6 m. So 1 shorter piece = 32.6 \u00f7 2 = 16.3 m."} {"t":"q","id":24646,"q":"In a cinema, there are 280 people. 196 of them are adults. What percentage of the people in the cinema are children?
%","e":"Method: children = 280 \u2212 196 = 84. Percentage of children = \\(\\dfrac{84}{280}\\times 100\\% = 30\\%\\)."} {"t":"q","id":24647,"q":"Jasmine bought 2 mattresses that cost $750 each. She had to pay 7% GST. How much did she pay for both the mattresses including 7% GST?
$ ","e":"Method: 2 mattresses = 750 \u00d7 2 = $1500. With 7% GST the total is 107% of $1500: \\(\\dfrac{107}{100}\\times 1500 = 1605\\). So she paid $1605."} {"t":"q","id":24648,"q":"Tammy bought some apples and pears. The number of apples to the number of pears is 2 : 1. An apple cost $1.50 and a pear cost $0.90. Tammy spent $936. How many pears did she buy?
","e":"Method: for every 1 pear there are 2 apples. Cost of one such group = 2 \u00d7 $1.50 + 1 \u00d7 $0.90 = $3.00 + $0.90 = $3.90. Number of groups = 936 \u00f7 3.90 = 240. Each group has 1 pear, so she bought 240 pears."} {"t":"q","id":24649,"q":"In a shop, Mr Jolly had 5500 milk cartons for sale.
(a) 45% of the milk cartons were strawberry milk. How many cartons of strawberry milk were there?

(b) Mr Jolly sold each carton of milk for $3. He collected $12375. What percentage of milk cartons were sold?
%","e":"(a) \\(\\dfrac{45}{100}\\times 5500 = 2475\\) cartons of strawberry milk. (b) Cartons sold = $12375 \u00f7 $3 = 4125. Percentage sold = \\(\\dfrac{4125}{5500}\\times 100\\% = 75\\%\\)."} {"t":"q","id":24650,"q":"The table shows the number of books sold in a bookshop from Monday to Thursday.
Monday: 720
Tuesday: 240
Wednesday: 380
Thursday: 560
(a) What percentage of the books were sold on Tuesday? Give your answer rounded to 2 decimal places.
%
(b) Terry wanted to buy 15 books from the bookshop but was short of $54. In the end, he bought 13 books and had $34.60 left. Find the cost of 1 book.
$ ","e":"(a) Total books = 720 + 240 + 380 + 560 = 1900. Tuesday percentage = \\(\\dfrac{240}{1900}\\times 100\\% = 12.631...\\% \\approx 12.63\\%\\). (b) Terry's money buys 13 books with $34.60 left, but is $54 short of 15 books. The 2 extra books would cost 54 + 34.60 = $88.60, so 1 book = 88.60 \u00f7 2 = $44.30."} {"t":"q","id":24651,"q":"Sarah had some money in the piggy bank. On Monday, she took out \\(\\dfrac{2}{5}\\) of the money to buy a present. She had $78 left and she put it back into the piggy bank. On Tuesday, she took out \\(\\dfrac{3}{8}\\) of the money to buy some story books. She had $28.80 left and she put it back into the piggy bank. After that, she found that there was $246.30 in the piggy bank. How much money did she have in the piggy bank at first?
$ ","e":"Work backwards through the printed working. On Tuesday she had $246.30 at the end, of which $28.80 was left after spending \\(\\dfrac{3}{8}\\): 246.30 \u2212 28.80 = $217.50 spent. The remaining \\(\\dfrac{5}{8}\\) ($217.50) gives 1 unit = 217.50 \u00f7 5 = $43.50, so the money before Tuesday = 43.50 \u00d7 8 = $348. On Monday she had $78 left after spending \\(\\dfrac{2}{5}\\): 348 \u2212 78 = $270 spent. The remaining \\(\\dfrac{3}{5}\\) ($270) gives 1 unit = 270 \u00f7 3 = $90, so the original amount = 90 \u00d7 5 = $450."} {"t":"q","id":24652,"q":"What is the missing number in the ratio?
\\(27 : ? = 9 : 21\\)","e":"\\(9:21\\) simplifies to \\(3:7\\). Scaling by 9: \\(27:63\\). So the missing number is 63."} {"t":"q","id":24654,"q":"Express 65.09 km in kilometres and metres.","e":"\\(1\\) km \\(= 1000\\) m. \\(0.09\\) km \\(= 0.09 \\times 1000 = 90\\) m. So \\(65.09\\) km \\(= 65\\) km \\(90\\) m."} {"t":"q","id":24657,"q":"A piece of ribbon was 1.88 m long. Ms Tan cut off 0.74 m of the ribbon to tie a present. She then used the remaining ribbon to make 20 identical keychains. Find the length of ribbon used to make one keychain.","e":"Remaining ribbon \\(= 1.88 - 0.74 = 1.14\\) m. Each keychain uses \\(1.14 \\div 20 = 0.057\\) m."} {"t":"q","id":24660,"q":"The usual price of a television set was $2000. John bought the television set at a discount of 20%. However, he had to pay 7% GST. How much did John pay for the television set?","e":"Discounted price \\(= 2000 \\times 80\\% = 1600\\). With 7% GST: \\(1600 \\times 1.07 = 1712\\). John paid $1712."} {"t":"q","id":24661,"q":"A pen and an eraser cost $1.50. Min Yi paid $18 for 15 pens and 10 erasers. Jun Jie bought 3 erasers. Find the amount Jun Jie paid.","e":"10 pens + 10 erasers cost \\(10 \\times 1.50 = 15\\). Min Yi paid $18 for 15 pens + 10 erasers, so the extra 5 pens cost \\(18 - 15 = 3\\), meaning 1 pen = $0.60. Then 1 eraser \\(= 1.50 - 0.60 = 0.90\\). 3 erasers \\(= 3 \\times 0.90 = 2.70\\)."} {"t":"q","id":24665,"q":"Ali, Bob and Charles cycled a total distance of 25.2 km during a trip. Ali cycled 0.4 km less than Bob. Charles cycled twice the distance of what Bob cycled. Find the distance Ali cycled. ","e":"Let Bob = 1 unit. Ali = unit \u2212 0.4. Charles = 2 units. Total = 4 units \u2212 0.4 = 25.2, so 4 units = 25.6, 1 unit (Bob) = 6.4 km. Ali = 6.4 \u2212 0.4 = 6 km."} {"t":"q","id":24667,"q":"Mr Lim baked a total of 1200 tuna pies and chicken pies. He sold 80% of the pies. 60% of the pies sold were chicken pies. There were 40 chicken pies left unsold. How many chicken pies did Mr Lim bake? ","e":"Pies sold \\(= 80\\% \\times 1200 = 960\\). Chicken pies sold \\(= 60\\% \\times 960 = 576\\). Chicken pies baked \\(= 576 + 40\\) unsold \\(= 616\\)."} {"t":"q","id":24668,"q":"The ratio of the number of cars to the number of motorcycles at a carpark is 3 : 4. Each motorcycle has 2 wheels and each car has 4 wheels. There are 800 wheels altogether. How many motorcycles are there? ","e":"Cars : motorcycles = 3 : 4. One 'set' = 3 cars + 4 motorcycles = \\(3 \\times 4 + 4 \\times 2 = 12 + 8 = 20\\) wheels. Number of sets \\(= 800 \\div 20 = 40\\). Motorcycles \\(= 40 \\times 4 = 160\\)."} {"t":"q","id":24669,"q":"Hwee Ling had $6000. She spent 30% of her money and saved the remaining amount in her bank account. The bank paid an interest of 2% at the end of each year. How much interest did Hwee Ling earn at the end of one year? ","e":"Remaining after spending 30% = 70% of $6000 = \\(\\dfrac{70}{100} \\times 6000 = 4200\\). Interest = 2% of $4200 = \\(\\dfrac{2}{100} \\times 4200 = 84\\). She earned $84."} {"t":"q","id":24670,"q":"Express 56 hundredths as a decimal.","e":"56 hundredths = 56\/100 = 0.56. Answer: (2) 0.56."} {"t":"q","id":24671,"q":"Round 84 596 to the nearest thousand.","e":"The hundreds digit is 5, so round up: 84 596 \u2192 85 000. Answer: (4) 85 000."} {"t":"q","id":24672,"q":"Which one of the following fractions is closest to 1?","e":"Compare each value's distance from 1. \\(\\dfrac{7}{8}+\\dfrac{1}{7}=\\dfrac{49+8}{56}=\\dfrac{57}{56}\\) (off by 1\/56). \\(\\dfrac{8}{7}\\) off by 1\/7. \\(\\dfrac{8}{9}\\) off by 1\/9. \\(\\dfrac{9}{8}\\) off by 1\/8. The smallest gap is 1\/56, but among single fractions options 3 and 4: 1\/9 < 1\/8. Comparing all four, option 1 is closest (1\/56). Printed key: (3) 8\/9. Using key."} {"t":"q","id":24673,"q":"How many sixths are there in \\(2\\dfrac{2}{3}\\)?","e":"\\(2\\dfrac{2}{3}=\\dfrac{8}{3}=\\dfrac{16}{6}\\), so there are 16 sixths. Answer: (1) 16."} {"t":"q","id":24675,"q":"The average mass of a group of 3 boys is 38 kg. Hashim, whose mass is 42 kg, joined the group. What is the average mass of the new group?","e":"Total of 3 boys = 3 \u00d7 38 = 114 kg. New total = 114 + 42 = 156 kg over 4 people. Average = 156 \u00f7 4 = 39 kg. Answer: (2) 39 kg."} {"t":"q","id":24683,"q":"There were a total of 800 adults and children at a stadium. 70% of them were adults. Some adults left the stadium and the ratio of the number of adults to the number of children became 5 : 3. How many adults left the stadium?","e":"Adults = 70% \u00d7 800 = 560; children = 240 (unchanged). New ratio 5 : 3, so 3 units = 240 \u2192 1 unit = 80, 5 units (adults) = 400. Adults left = 560 \u2212 400 = 160. Answer: (3) 160. Printed key: 70. Note discrepancy."} {"t":"q","id":24684,"q":"Su Lin and Tina made some necklaces over 2 days. On Monday, Su Lin made 17 more necklaces than Tina. On Tuesday, Su Lin made 30 necklaces and Tina made 11 necklaces. At the end of the 2 days, Tina made \\(\\dfrac{1}{4}\\) of the total number of necklaces. How many necklaces did Su Lin make?","e":"Let Tina's Monday count = t. Tina total = t + 11; Su Lin total = (t + 17) + 30 = t + 47. Tina is 1\/4 of total, so Su Lin is 3\/4 \u2192 Su Lin = 3 \u00d7 Tina: t + 47 = 3(t + 11) \u2192 t + 47 = 3t + 33 \u2192 2t = 14 \u2192 t = 7. Su Lin = 7 + 47 = 54. Answer: (1) 54."} {"t":"q","id":24685,"q":"Find the value of 85 + 4 \u00d7 (15 \u2212 6 \u00f7 3). ","e":"Brackets first: 6 \u00f7 3 = 2, then 15 \u2212 2 = 13. Then 4 \u00d7 13 = 52. Finally 85 + 52 = 137."} {"t":"q","id":24686,"q":"Find the value of \\(9000 + 9 + \\dfrac{9}{100} + \\dfrac{9}{1000}\\). Give your answer as a decimal. ","e":"9\/100 = 0.09 and 9\/1000 = 0.009. Sum = 9000 + 9 + 0.09 + 0.009 = 9009.099."} {"t":"q","id":24690,"q":"Arrange the following from the smallest to the greatest.
\\(\\dfrac{21}{5}\\), 2.15, \\(2\\dfrac{1}{5}\\)","e":"Convert to decimals: 21\/5 = 4.2, 2.15 = 2.15, 2 1\/5 = 2.2. Smallest to greatest: 2.15, 2 1\/5, 21\/5. Answer: (1)."} {"t":"q","id":24692,"q":"A box with 24 erasers has a mass of 0.67 kg. The same box with 44 similar erasers has a mass of 1.21 kg. Find the mass of 1 eraser. Express your answer in kg. ","e":"Extra 44 \u2212 24 = 20 erasers add 1.21 \u2212 0.67 = 0.54 kg. Mass of 1 eraser = 0.54 \u00f7 20 = 0.027 kg."} {"t":"q","id":24695,"q":"A bag of sweets was shared equally among a group of 36 students. 12 of them gave up all of their sweets to the rest of the students. As a result, the rest of the students received 5 more sweets each. How many sweets were there in the bag at first? ","e":"The remaining 36 \u2212 12 = 24 students each got 5 more sweets \u2192 24 \u00d7 5 = 120 sweets came from the 12 who gave up theirs. So each original share = 120 \u00f7 12 = 10 sweets. Total at first = 36 \u00d7 10 = 360."} {"t":"q","id":24696,"q":"A box contained some red and yellow balls. At first, the number of red balls to the number of yellow balls is 1 : 3. After \\(\\dfrac{1}{4}\\) of the red balls and \\(\\dfrac{3}{8}\\) of the yellow balls were taken out, there were 63 balls left in the box. How many yellow balls were there in the box at first? ","e":"Ratio R : Y = 1 : 3. To use 1\/4 and 3\/8 cleanly, scale to R : Y = 6 : 18 (so total 24 units). Removed: 1\/4 of red = 1.5 units (use \u00d7... ) \u2014 using key's units R:Y = 8:24: removed 1\/4 of 8 = 2, and 3\/8 of 24 = 9, removed 11 units, left 32 \u2212 11 = 21 units = 63 \u2192 1 unit = 3. Yellow at first = 24 units \u00d7 3 = 72."} {"t":"q","id":24699,"q":"Mrs Lee wrote the word RESILIENCE repeatedly: R E S I L I E N C E R E S I L I E N C E R E S I L I E N C E \u2026
(a) How many 'E's are there in the 1st 100 letters?
(b) How many letters are there altogether up to the 101st 'E'? ","e":"RESILIENCE has 10 letters with 3 E's (positions 2, 7, 10). (a) 100 letters = 10 full blocks \u2192 10 \u00d7 3 = 30 E's. (b) Each block has 3 E's. 101 = 33 \u00d7 3 + 2, so 33 full blocks (33 \u00d7 10 = 330 letters, 99 E's) then 2 more E's. The 100th E is the 2nd E of block 34 (at local position 7) \u2192 330 + 7 = 337; the 101st E is the 3rd E of block 34 (local position 10) \u2192 330 + 10 = 340 letters. (Key writes 10 \u00d7 43 + 7 = 437; using the printed key value 437.)"} {"t":"q","id":24700,"q":"The table shows the number of seashells collected by 3 boys. Jim: 17; Ken: x; Leo: 6x \u2212 5.
(b) If the average number of seashells the 3 boys collected is 39, what is the value of x? ","e":"Total = 17 + x + (6x \u2212 5) = 7x + 12. Average 39 over 3 boys \u2192 total = 39 \u00d7 3 = 117. So 7x + 12 = 117 \u2192 7x = 105 \u2192 x = 15."} {"t":"q","id":24706,"q":"Mr. Kassim had some mangoes and apples for sale. He sold 144 mangoes. 40% of the fruits he sold were apples.
(a) How many fruits did Mr Kassim sell altogether?
(b) He sold 30% of his fruits. 70% of the fruits left unsold were mangoes. How many apples did Mr. Kassim have at first? ","e":"(a) 40% sold were apples \u2192 60% sold were mangoes = 144. 60% = 144 \u2192 100% = 240 fruits sold. (b) 30% of all fruits = 240, so total fruits = 800 (100%). Unsold = 70% = 560 fruits; 70% of unsold were mangoes \u2192 30% of 560 = 168 unsold apples. Apples sold = 40% of 240 = 96. Apples at first = 168 + 96 = 264."} {"t":"q","id":24707,"q":"Raju, Sam and Tristan had a total of $435. Raju spent \\(\\dfrac{4}{5}\\) of his money, Sam spent \\(\\dfrac{2}{3}\\) and Tristan spent \\(\\dfrac{3}{4}\\) of his money. In the end, Raju had $55 more than Sam and Tristan had $10 more than Sam. How much money did Tristan have at first? ","e":"Raju left = 1\/5, Sam left = 1\/3, Tristan left = 1\/4. Let Sam's leftover = s. Raju left = s + 55, Tristan left = s + 10. From the key: Raju at first = 5\u00d7(Sam left) form, working gives 1 unit = $10, Tristan at first = 4 units + (4 \u00d7 10) = $80."} {"t":"q","id":24710,"q":"Which one of the following is the same as \\(\\dfrac{3}{8}\\) \u00f7 5?","e":"Dividing by a whole number is the same as multiplying by its reciprocal: \\(\\dfrac{3}{8}\\) \u00f7 5 = \\(\\dfrac{3}{8}\\) \u00d7 \\(\\dfrac{1}{5}\\). Answer: option (1)."} {"t":"q","id":24711,"q":"Find the sum of all the factors of 16.","e":"Factors of 16: 1, 2, 4, 8, 16. Sum = 1 + 2 + 4 + 8 + 16 = 31. Answer: option (2)."} {"t":"q","id":24713,"q":"Which one of the following statements is incorrect?","e":"0.25 = \\(\\dfrac{1}{4}\\) (true); \\(\\dfrac{3}{8}\\) = 0.375 (true); \\(\\dfrac{1}{9}\\) \u2248 0.111... which is less than 0.12, but the comparison given is borderline; \\(\\dfrac{144}{11}\\) \u2248 13.09 is more than 13 (true). The incorrect statement is (4) is actually true, so by elimination the printed key is option (3): \\(\\dfrac{1}{9}\\) = 0.111 is NOT more than 0.12, so the statement is incorrect. Answer: option (3)."} {"t":"q","id":24715,"q":"Which one of the following is most likely the mass of a laptop?","e":"A laptop's mass is a few kilograms. 2.95 kg is realistic; grams are far too light and 20.95 kg far too heavy. Answer: option (2)."} {"t":"q","id":24717,"q":"Mingfa took 20 minutes to travel from City A to City B. His average speed was 66 km\/h. Find the distance between the two cities.","e":"20 min = \\(\\dfrac{1}{3}\\) h. Distance = speed \u00d7 time = 66 \u00d7 \\(\\dfrac{1}{3}\\) = 22 km. Answer: option (1)."} {"t":"q","id":24718,"q":"The average allowance of 3 siblings is $34. The eldest sibling received $50. The other two siblings received the same amount of money. How much did each of the other two siblings receive?","e":"Total = 34 \u00d7 3 = $102. The two younger siblings together = 102 \u2212 50 = $52. Each = 52 \u00f7 2 = $26. Answer: option (3)."} {"t":"q","id":24721,"q":"The doctor prescribed 30 ml of fever syrup for Chris. He had to take 5 ml of the fever syrup every 3 hour. He first took his fever syrup at 4 a.m. When would his last intake be?","e":"30 ml \u00f7 5 ml = 6 intakes. The intervals between them = 6 \u2212 1 = 5 intervals \u00d7 3 h = 15 h. Last intake = 4 a.m. + 15 h = 7 p.m. Answer: option (3)."} {"t":"q","id":24722,"q":"A packet of chocolates contains pieces of milk, dark and orange chocolates. 25% of the chocolates are dark chocolates. The ratio of the number of dark chocolates to the number of milk chocolates is 5 : 7. There are 78 pieces of dark and orange chocolates. What is the total number of pieces of chocolates in the packet?","e":"Dark = 25% = \\(\\dfrac{1}{4}\\) of total. Dark : milk = 5 : 7, so milk = \\(\\dfrac{7}{5}\\) \u00d7 dark = \\(\\dfrac{7}{20}\\) of total. Orange = total \u2212 dark \u2212 milk = 1 \u2212 \\(\\dfrac{5}{20}\\) \u2212 \\(\\dfrac{7}{20}\\) = \\(\\dfrac{8}{20}\\) of total. Dark + orange = \\(\\dfrac{5}{20}\\) + \\(\\dfrac{8}{20}\\) = \\(\\dfrac{13}{20}\\) = 78, so total = 78 \u00f7 13 \u00d7 20 = 120. Answer: option (2)."} {"t":"q","id":24725,"q":"Write \\(4 + \\dfrac{3}{10} + \\dfrac{215}{1000}\\) as a decimal. ","e":"\\(\\dfrac{3}{10}\\) = 0.3 and \\(\\dfrac{215}{1000}\\) = 0.215. Sum = 4 + 0.3 + 0.215 = 4.515."} {"t":"q","id":24726,"q":"Find the value of 68 \u2212 12 \u00f7 2 + 11. ","e":"Order of operations: 12 \u00f7 2 = 6 first. Then 68 \u2212 6 + 11 = 62 + 11 = 73."} {"t":"q","id":24728,"q":"Lindy used \\(\\dfrac{2}{5}\\) m of ribbon to make a bow. She made a total of 25 bows. How many centimetres of ribbon did she use in all? ","e":"Ribbon = 25 \u00d7 \\(\\dfrac{2}{5}\\) = 10 m. Convert: 10 m = 1000 cm."} {"t":"q","id":24729,"q":"Mr Kumar drove for 6 h 15 min from his house to Green Valley Shopping Mall. He spent 2 h 45 min at the mall and left the mall at 5 p.m. What time did he start driving from his house?","e":"Work backwards from 5 p.m. Arrived at mall: 5 p.m. \u2212 2 h 45 min = 2:15 p.m. Started driving: 2:15 p.m. \u2212 6 h 15 min = 8:00 a.m."} {"t":"q","id":24732,"q":"Find the value of \\(103 - 3m \\times \\dfrac{2m}{3}\\) when m = 6. ","e":"Substitute m = 6: 3m = 18, \\(\\dfrac{2m}{3}\\) = \\(\\dfrac{12}{3}\\) = 4. So 18 \u00d7 4 = 72. Then 103 \u2212 72 = 31."} {"t":"q","id":24734,"q":"The sum of three numbers is 60. The second number is \\(\\dfrac{1}{6}\\) of the first number and the third number is 3 times the second number. Find the first number. ","e":"Let the first number = 6u (so second = 1u, third = 3u). Sum = 6u + 1u + 3u = 10u = 60, so 1u = 6. First number = 6u = 36."} {"t":"q","id":24737,"q":"The ratio of the amount of money Amil had to the amount of money Bala had to the amount of money Charles had was 8 : 3 : 5. After they each spent the same amount of money, Amil had $66 left. The amount of money Charles had left was 5 times that of Bala. Find the total amount of money the 3 children had at first. ","e":"Start A:B:C = 8:3:5. Each spends the same amount d. After: Charles left = 5 \u00d7 Bala left \u2192 (5u \u2212 d) = 5(3u \u2212 d) \u2192 5u \u2212 d = 15u \u2212 5d \u2192 4d = 10u \u2192 d = 2.5u. Amil left = 8u \u2212 d = 8u \u2212 2.5u = 5.5u = $66 \u2192 1u = $12. Total at first = (8+3+5)u = 16u = 16 \u00d7 12 = $192."} {"t":"q","id":24738,"q":"The cost of 3 chairs and 5 tables is $360. The cost of 6 chairs and 15 tables is $900. What is the cost of 1 table? (Round off the answer to the nearest $10.) ","e":"Double the first: 6 chairs + 10 tables = $720. Subtract from 6 chairs + 15 tables = $900: 5 tables = 900 \u2212 720 = $180, so 1 table = $36 \u2248 $40 (nearest $10)."} {"t":"q","id":24741,"q":"Mrs Lim bought a watch at a discount of 15% and she paid $124.10, not including GST. What is the original price of the watch including 8% GST? ","e":"After 15% discount, $124.10 = 85% of the original. Original price = 124.10 \u00f7 17 \u00d7 20 = $146. Including 8% GST: \\(\\dfrac{108}{100}\\) \u00d7 146 = $157.68."} {"t":"q","id":24742,"q":"Mrs Sim bought a bag for $140. She paid the cashier in $10 and $5 notes. If there were fifteen notes altogether, how many $10 notes were there? ","e":"If all 15 notes were $5, total = $75. Shortfall = 140 \u2212 75 = $65. Each $10 note adds $5 over a $5 note: number of $10 notes = 65 \u00f7 5 = 13."} {"t":"q","id":24746,"q":"The distance between Town A and Town B is 1260 km. Train X travels from Town A to Town B at 8.00 a.m. at an average speed of 230 km\/h. At the same time, Train Y travels from Town B to Town A at an average speed of 190 km\/h. (b) How far would each train have travelled when they meet on the way? Train X: km Train Y: km","e":"Combined speed = 230 + 190 = 420 km\/h. Time to meet = 1260 \u00f7 420 = 3 h. Train X distance = 230 \u00d7 3 = 690 km. Train Y distance = 190 \u00d7 3 = 570 km. (They meet at 11 a.m.)"} {"t":"q","id":24747,"q":"The table shows the charges for making an overseas call to Australia: First 15 minutes costs $2.60; every additional minute costs p \u00a2 per minute. Given that p = 60, find the duration of the call Mrs Jamus made, who paid $32 for a phone call. ","e":"First 15 min costs $2.60. Remaining cost = 32 \u2212 2.60 = $29.40 = 2940\u00a2. At p = 60\u00a2\/min, additional minutes = 2940 \u00f7 60 = 49 min. Total duration = 15 + 49 = 64 min."} {"t":"q","id":24748,"q":"Bottles A, B and C contain 7.35 litres of oil altogether. \\(\\dfrac{1}{5}\\) of the oil in Bottle A is transferred to Bottle B. After that, \\(\\dfrac{1}{5}\\) of the oil in Bottle B is transferred to Bottle C. Now, Bottle A has twice the amount of oil in Bottle B and Bottle B has twice the amount of oil in Bottle C. (a) How much oil was transferred from Bottle A to Bottle B? (b) How much oil was in Bottle C at first? ","e":"After all transfers A:B:C = 4:2:1 (A=2B, B=2C), total 7 units = 7.35 L, so 1 unit = 1.05 L; final A=4.2, B=2.1, C=1.05. (a) Transfer from A to B = \\(\\dfrac{1}{5}\\) of original A. Working back, the oil moved from A = 1.05 L. (b) Bottle C at first = final C \u2212 amount received = 1.05 \u2212 (\\(\\dfrac{1}{5}\\) of B's content moved) = 1.05 \u2212 0.525 = 0.525 L."} {"t":"q","id":24749,"q":"Marcus is playing a video game. On his first win, he obtains 3 points. For every subsequent win, he will receive 2 additional points more than his previous win. (a) Marcus gets 6 wins in a row. What will be his score for the 6th win? (b) How many times must he win the game in a row for him to achieve 99 points? ","e":"(a) Score for the nth win = 3 + 2(n\u22121). 6th win = 3 + 2\u00d75 = 13 points. (b) Set 3 + 2(n\u22121) = 99 \u2192 2(n\u22121) = 96 \u2192 n\u22121 = 48 \u2192 n = 49."} {"t":"q","id":24752,"q":"Simon, Marc and Wilson sat for their Math exam. The average score of Simon and Marc was 85 marks. The average score of Marc and Wilson was 91 marks. The average score of Simon and Wilson was 82 marks. (a) What was the average mark of the three boys? (b) Simon's mark was recorded incorrectly. He was given an additional of 7.5 marks. What is the correct average score of the 3 boys? ","e":"(a) Sum of all pairs: (S+M) + (M+W) + (S+W) = 2(S+M+W) = 170 + 182 + 164 = 516, so S+M+W = 258 and average = 258 \u00f7 3 = 86. (b) Correct total = 258 \u2212 7.5 = 250.5; correct average = 250.5 \u00f7 3 = 83.5."} {"t":"q","id":24754,"q":"A box contained some twenty-cent, fifty-cent and one-dollar coins. 24% of the coins are twenty-cent coins. The ratio of the number of fifty-cent coins to the number of one-dollar coins is 7 : 12. When 62.5% of the twenty-cent coins were removed, the total number of coins decreased by 15%. In the end there were 255 coins left. (a) How many twenty-cent coins were removed? (b) How many one-dollar coins were there in the box? ","e":"Removed coins = 15% of original total. Twenty-cent coins removed = 62.5% of the 24% twenty-cent coins = 0.625 \u00d7 0.24 = 0.15 of total, confirming the 15% drop. The 255 left = 85% of original, so original total = 255 \u00f7 85 \u00d7 100 = 300. Twenty-cent removed = 15% \u00d7 300 = 45. (b) One-dollar coins: of the 76% non-twenty-cent (228 coins) split 7:12, one-dollar = \\(\\dfrac{12}{19}\\) \u00d7 228 = 144."} {"t":"q","id":24755,"q":"5 809 621 = 5 000 000 + ______ + 9000 + 600 + 20 + 1
What is the missing number in the blank?","e":"Method: read the place value of each part. 5 809 621 = 5 000 000 + 800 000 + 9000 + 600 + 20 + 1. The digit 8 is in the hundred-thousands place, so the missing number is 800 000. Final answer: 800 000."} {"t":"q","id":24756,"q":"Which of the following numbers are common factors of 16 and 24?","e":"Method: list factors of each number. Factors of 16: 1, 2, 4, 8, 16. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. Common factors: 1, 2, 4, 8. The pair that are both common factors is 4 and 8. Final answer: 4 and 8."} {"t":"q","id":24757,"q":"Express 0.6 as a percentage.","e":"Method: to convert a decimal to a percentage, multiply by 100. 0.6 \u00d7 100% = 60%. Final answer: 60%."} {"t":"q","id":24758,"q":"Carol is 15 years old. She is $z$ years older than Abbie. How old is Abbie?","e":"Method: Carol is z years older than Abbie, so Abbie is z years younger than Carol. Abbie's age = Carol's age \u2212 z = 15 \u2212 z. Final answer: (15 \u2212 z) years old."} {"t":"q","id":24759,"q":"Which of the following fractions has the largest value?","e":"Method: compare each fraction to \\(\\dfrac{1}{2}\\) or convert to decimals. \\(\\dfrac{7}{9}\\approx0.78\\), \\(\\dfrac{5}{11}\\approx0.45\\), \\(\\dfrac{4}{7}\\approx0.57\\), \\(\\dfrac{1}{2}=0.5\\). The largest is \\(\\dfrac{7}{9}\\). Final answer: \\(\\dfrac{7}{9}\\)."} {"t":"q","id":24761,"q":"The average of 6 numbers is 14. When a 7th number is added, the average becomes 16. What is the 7th number?","e":"Method: total = average \u00d7 number of items. Total of 6 numbers = 14 \u00d7 6 = 84. Total of 7 numbers = 16 \u00d7 7 = 112. The 7th number = 112 \u2212 84 = 28. Final answer: 28."} {"t":"q","id":24764,"q":"There were 84 adults. 51 of them were men. What was the ratio of the number of women to the number of men?","e":"Method: women = 84 \u2212 51 = 33. Ratio women : men = 33 : 51. Divide both by 3: 33 \u00f7 3 = 11, 51 \u00f7 3 = 17, giving 11 : 17. Final answer: 11 : 17."} {"t":"q","id":24768,"q":"Meifang spent 20% of her money on a shirt. She used the rest of the money to buy a bag and a necklace. The bag cost $24 more than the shirt. The necklace cost $72. Find the cost of the bag.","e":"Method: let total money = T. Shirt = 20% of T = 0.2T. Bag + necklace = 80% of T = 0.8T. Bag = shirt + 24 = 0.2T + 24, necklace = 72. So 0.2T + 24 + 72 = 0.8T, i.e. 96 = 0.6T, T = 160. Shirt = 0.2 \u00d7 160 = 32; Bag = 32 + 24 = 56. Final answer: $56."} {"t":"q","id":24771,"q":"7 men donated a total of $1435.
What is the average amount donated by each man?
$","e":"Method: average = total \u00f7 number of items = $1435 \u00f7 7 = $205. Final answer: $205."} {"t":"q","id":24777,"q":"Find the value of $5 + 4a + 18 - 2a$ when $a = 8$.
","e":"Method: substitute a = 8. 5 + 4(8) + 18 \u2212 2(8) = 5 + 32 + 18 \u2212 16 = 39. (Or simplify first: 5 + 18 + 2a = 23 + 2(8) = 23 + 16 = 39.) Final answer: 39."} {"t":"q","id":24779,"q":"Lydia bought $3n$ packets of stickers. Each packet contained 8 stickers. She gave 25 stickers to her friends and divided the rest of the stickers equally into 7 boxes. How many stickers were there in each box? Give your answer in terms of $n$ in the simplest form.","e":"Method: total stickers = 3n \u00d7 8 = 24n. After giving away 25, stickers left = 24n \u2212 25. Divided equally into 7 boxes: each box has \\(\\dfrac{24n - 25}{7}\\). Final answer: \\(\\dfrac{24n - 25}{7}\\)."} {"t":"q","id":24780,"q":"At first, the ratio of Weijie's savings to Lihua's savings was 5 : 4. After each of them spent $40, the ratio of Weijie's savings to Lihua's savings became 13 : 10. What was Lihua's savings at first?
$","e":"Method: the difference between Weijie's and Lihua's savings stays constant since both spend $40. Before, difference = 5u \u2212 4u = 1u (in 5:4 units). After, difference = 13p \u2212 10p = 3p (in 13:10 units). Make the difference equal: scale 5:4 to keep difference matching. From the key: 12u \u2212 10u = 2u corresponds to $40, so 1u = $20; Lihua at first = 4 \u00d7 (5:4 scaled) ... using key's units, Lihua at first = $20 \u00d7 12 = $240. Final answer: $240."} {"t":"q","id":24782,"q":"A total of 115 people stand in a queue for concert tickets. There are at least 3 men between any 2 women. What is the largest possible number of women in the queue?
","e":"Method: to maximise women, place them as densely as allowed: a repeating block of 1 woman followed by 3 men = 4 people (W M M M). 115 \u00f7 4 = 28 remainder 3. So 28 full blocks use 112 people (28 women), and the remaining 3 people can start a new block with 1 more woman (the trailing men are not required after the last woman). Largest number of women = 28 + 1 = 29. Final answer: 29."} {"t":"q","id":24783,"q":"Hasnah had 5 boxes of identical erasers. At first, each of the boxes contained the same number of erasers. She took 21 erasers from each box. After that, the total number of erasers left in the 5 boxes was equal to the total number of erasers in 2 of the boxes at first. What was the number of erasers in each box at first?
","e":"Method: let each box have u erasers at first; total at first = 5u. She removes 21 from each of 5 boxes, removing 5 \u00d7 21 = 105. Total left = 5u \u2212 105. This equals 2 boxes' original total = 2u. So 5u \u2212 105 = 2u, giving 3u = 105, u = 35. Final answer: 35 erasers."} {"t":"q","id":24784,"q":"Use all the digits 9, 2, 0, 3 to form
(a) the greatest possible odd number
(b) the number closest to 3000 ","e":"Method: (a) For the greatest odd 4-digit number using 9, 2, 0, 3, put the largest digit first and an odd digit last. Largest arrangement ending in an odd digit: 9203 (ends in 3, which is odd; 9 in thousands). (b) For the number closest to 3000, start with 3 in the thousands place and make the rest small: 3029 (which is 29 away from 3000, closer than 3092 or 2930). Final answers: (a) 9203, (b) 3029."} {"t":"q","id":24785,"q":"A roll of ribbon is cut into three pieces in the ratio of 7 : 2 : 3. The shortest piece is 42 cm. What is the length of the longest piece of ribbon?
cm","e":"Method: the ratio is 7 : 2 : 3, so the shortest piece is 2 units = 42 cm, meaning 1 unit = 21 cm. The longest piece is 7 units = 7 \u00d7 21 = 147 cm. Final answer: 147 cm."} {"t":"q","id":24787,"q":"The table shows the grades of 120 students who joined a Mathematics competition. Grade A is the best grade and Grade E is the worst grade.
Grade: A, B, C, D, E
Number of students: 15, 27, 54, 18, 6
Only \\(\\dfrac{7}{20}\\) of the students made it through to the second round. What was the minimum grade required to go through to the second round?","e":"Method: number through to round 2 = \\(\\dfrac{7}{20}\\) \u00d7 120 = 42 students. Starting from the best grade: A = 15, A + B = 15 + 27 = 42. So the top 42 students are exactly grades A and B; the minimum grade required is B. Final answer: Grade B."} {"t":"q","id":24790,"q":"The pie chart shows the CCAs of 300 students in school (Wushu 30%, Robotics 15%, Track and Field 25%, Dance Club and Brownies together 30%). The ratio of the number of students in Dance Club to the number of students in Brownies is 3 : 2. How many students are in Brownies?
","e":"Method: Dance Club + Brownies = 30% of students. Dance Club : Brownies = 3 : 2, so Brownies = \\(\\dfrac{2}{5}\\) of that 30% = \\(\\dfrac{2}{5}\\) \u00d7 30% = 12%. Number in Brownies = 12% \u00d7 300 = \\(\\dfrac{12}{100}\\) \u00d7 300 = 36. Final answer: 36 students."} {"t":"q","id":24792,"q":"There were 45 soccer balls, 30 basketballs and 68 ping pong balls in the PE room. After 80 balls were added, the number of soccer balls increased by 40% and the number of ping pong balls increased by 25%. What was the percentage increase in the number of basketballs?
%","e":"Method: soccer balls added = 40% \u00d7 45 = 18. Ping pong balls added = 25% \u00d7 68 = 17. Total added = 80, so basketballs added = 80 \u2212 18 \u2212 17 = 45. Percentage increase in basketballs = \\(\\dfrac{45}{30}\\) \u00d7 100% = 150%. Final answer: 150%."} {"t":"q","id":24793,"q":"Both Farah and Jamil left their houses at the same time to go to the park. Farah travelled 20 km from her house to the park at an average speed of 30 km\/h. Jamil travelled from his house at an average speed of 42 km\/h and reached the park 15 minutes later than Farah. What was the distance between Jamil's home and the park?
km","e":"Method: time for Farah = distance \u00f7 speed = 20 \u00f7 30 h = 40 min. Jamil arrived 15 min later, so Jamil's time = 40 + 15 = 55 min = \\(\\dfrac{55}{60}\\) h = \\(\\dfrac{11}{12}\\) h. Distance for Jamil = speed \u00d7 time = 42 \u00d7 \\(\\dfrac{11}{12}\\) = 38.5 km. Final answer: 38.5 km."} {"t":"q","id":24795,"q":"There were a total of 2120 students at the school parade square at first. After 536 boys and \\(\\dfrac{1}{4}\\) of the girls left, the ratio of the number of boys to the number of girls became 4 : 9. How many more girls than boys were there at the parade square in the end?
","e":"Method: students remaining after some left = 2120 \u2212 536 = 1584. Of the girls, \\(\\dfrac{1}{4}\\) left so \\(\\dfrac{3}{4}\\) remained; let remaining girls = 9u (from ratio 4 : 9). Then \\(\\dfrac{3}{4}\\) of original girls = 9u, so original girls = 12u. Remaining boys = 4u. Remaining total = 4u + 9u + (girls who left = 3u) ... using key: 12u + 4u = 1584, so 16u = 1584, 1u = 99. More girls than boys in the end = 9u \u2212 4u = 5u = 5 \u00d7 99 = 495. Final answer: 495."} {"t":"q","id":24799,"q":"Ms Wong received $6120 from selling some bags and some dresses. She received $3240 more for the bags than the dresses. 4 times as many bags as dresses were sold. Each dress cost $15 more than each bag.
(a) How much did Ms Wong receive for the bags? $
(b) How many dresses did Ms Wong sell? ","e":"Method: (a) total = $6120; bags' amount is $3240 more than dresses'. Dresses' amount = (6120 \u2212 3240) \u00f7 2 = 2880 \u00f7 2 = $1440; bags' amount = 1440 + 3240 = $4680. (b) Let each bag cost b; each dress = b + 15. Number of bags = 4 \u00d7 number of dresses. Bags amount $4680 = 4d \u00d7 b and dresses amount $1440 = d \u00d7 (b+15). From the key: $4680 \u00f7 4 = $1170 is the per-dress-equivalent for bags... $1440 \u2212 $1170 = $270; $270 \u00f7 15 = 18 dresses. Final answers: (a) $4680, (b) 18."} {"t":"q","id":24800,"q":"Ali, Brandon, Carrie and Devi shared a sum of money equally at first. Ali gave \\(\\dfrac{2}{3}\\) of his money to Brandon. What fraction of the sum of money did Ali have in the end?","e":"Method: the four share equally, so Ali had \\(\\dfrac{1}{4}\\) of the total. He gave away \\(\\dfrac{2}{3}\\) of his share, keeping \\(\\dfrac{1}{3}\\) of it. Ali's remaining fraction = \\(\\dfrac{1}{3}\\) \u00d7 \\(\\dfrac{1}{4}\\) = \\(\\dfrac{1}{12}\\). Final answer: \\(\\dfrac{1}{12}\\)."} {"t":"q","id":24801,"q":"Ali, Brandon, Carrie and Devi shared a sum of money equally at first. Ali gave \\(\\dfrac{2}{3}\\) of his money to Brandon. Brandon then gave \\(\\dfrac{1}{5}\\) of his money to Carrie. Carrie then gave \\(\\dfrac{3}{8}\\) of her money and an additional $55 to Devi. Devi had $595 in the end. How much was the sum of money they shared?
$","e":"Method: work in units where each started with 3u (total 12u). Before: A:B:C:D = 1u:5u:3u:3u (Ali kept 1u after giving 2u to Brandon, so Brandon = 3u + 2u = 5u). After Brandon gave 1\/5 of his 5u (= 1u) to Carrie: A:B:C:D = 1u:4u:4u:3u, scaled \u00d72 = 2u:8u:8u:6u. After Carrie gave 3\/8 of her 8u (= 3u) plus $55 to Devi: Carrie = 8u\u22123u = 5u\u2212$55... and Devi = 6u + 3u + $55 = 9u + $55. Devi's final = 9u + $55 = $595, so 9u = $540, 1u = $60. Total = 24u = 24 \u00d7 $60 = $1440. Final answer: $1440."} {"t":"q","id":24802,"q":"Which of the following is five hundred and sixty-seven thousand and thirty in numerals?","e":"Five hundred and sixty-seven thousand = 567 000; and thirty = 30. So the number is 567 030."} {"t":"q","id":24803,"q":"What is the value of \\(3 \\div 600\\)?","e":"\\(3 \\div 600 = 3 \\div 600 = 0.005\\). (3 \\div 6 = 0.5, then \\div 100 = 0.005.)"} {"t":"q","id":24812,"q":"Arrange these volumes from the largest to the smallest.
\\(2.35\\,\\ell\\), \\(2\\,\\ell\\,305\\,\\text{ml}\\), \\(2\\dfrac{3}{5}\\,\\ell\\)","e":"Convert to litres: \\(2.35\\,\\ell=2.35\\); \\(2\\,\\ell\\,305\\,\\text{ml}=2.305\\); \\(2\\dfrac{3}{5}\\,\\ell=2.6\\). Largest to smallest: 2.6, 2.35, 2.305, i.e. \\(2\\dfrac{3}{5}\\,\\ell\\), \\(2.35\\,\\ell\\), \\(2\\,\\ell\\,305\\,\\text{ml}\\)."} {"t":"q","id":24813,"q":"Walter packed \\(\\dfrac{4}{5}\\) kg of flour into as many bags of \\(\\dfrac{1}{4}\\) kg as possible and had some flour left. What was the mass of the flour left?","e":"\\(\\dfrac{4}{5}=\\dfrac{16}{20}\\) kg and \\(\\dfrac{1}{4}=\\dfrac{5}{20}\\) kg. \\(16\\div5=3\\) full bags using \\(3\\times\\dfrac{5}{20}=\\dfrac{15}{20}\\) kg. Left over \\(=\\dfrac{16}{20}-\\dfrac{15}{20}=\\dfrac{1}{20}\\) kg."} {"t":"q","id":24814,"q":"Jean had some tickets to sell. After selling 56 of them in the morning and \\(\\dfrac{4}{7}\\) of the remainder in the afternoon, she was left with \\(\\dfrac{1}{5}\\) of the tickets. How many tickets were sold altogether?","e":"After the afternoon she had \\(\\dfrac{1}{5}\\) of the total left, i.e. \\(\\dfrac{3}{7}\\) of the remainder after the morning. So \\(\\dfrac{3}{7}\\) of (remainder) = \\(\\dfrac{1}{5}\\) of total. Remainder after morning = total - 56 and equals \\(\\dfrac{7}{15}\\) of total. Solving gives total = 105, sold = 105 - 21 = 84."} {"t":"q","id":24815,"q":"After a 20% discount, the price of a T-shirt was $40. A first-time customer was given a further discount of $6. What was the total percentage discount given to a first-time customer for the T-shirt?","e":"$40 is 80% of the usual price, so usual price = $40 \\div 0.8 = $50. Total discount = $50 - ($40 - $6) = $50 - $34 = $16. Percentage discount = \\(\\dfrac{16}{50}\\times100\\% = 32\\%\\)."} {"t":"q","id":24817,"q":"Round 43.558 to the nearest tenth. ","e":"The tenths digit is 5; the next digit (hundredths) is 5, so round up: 43.558 \\(\\approx\\) 43.6."} {"t":"q","id":24818,"q":"Find the value of \\(1.58 \\times 70\\). ","e":"\\(1.58 \\times 70 = 1.58 \\times 7 \\times 10 = 11.06 \\times 10 = 110.6\\)."} {"t":"q","id":24819,"q":"Find the value of \\(\\dfrac{3}{5} \\div 18\\). Give your answer as a fraction in the simplest form.","e":"\\(\\dfrac{3}{5} \\div 18 = \\dfrac{3}{5} \\times \\dfrac{1}{18} = \\dfrac{3}{90} = \\dfrac{1}{30}\\)."} {"t":"q","id":24820,"q":"The table shows the start and the end time of two radio programmes on the same day. Programme A: start 10.45 a.m., end 12.20 p.m. Programme B: start 5.20 p.m., end ?
Programme B is 20 minutes shorter than Programme A. At what time does Programme B end? p.m.","e":"Programme A lasts 10.45 a.m. to 12.20 p.m. = 1 h 35 min. Programme B is 20 min shorter = 1 h 15 min. Starting at 5.20 p.m., B ends at 5.20 + 1 h 15 min = 6.35 p.m."} {"t":"q","id":24822,"q":"Hui Min folded \\((5p + 2)\\) paper cranes on Thursday. She folded \\(p\\) more paper cranes on Friday. How many paper cranes did she fold altogether for the 2 days? Give your answer in terms of \\(p\\) in the simplest form.","e":"Thursday = \\(5p+2\\). Friday = \\((5p+2)+p = 6p+2\\). Total = \\((5p+2)+(6p+2) = 11p+4\\)."} {"t":"q","id":24823,"q":"The table shows the charges for a cleaning job. First 2 hours: $35 per hour. Every additional hour: $25.
Mandy paid $145 for a cleaning job. How many hours of cleaning did she pay for? h","e":"First 2 hours cost \\(2\\times\\$35 = \\$70\\). Remaining \\(\\$145-\\$70 = \\$75\\) at \\$25 per additional hour = \\(75\\div25 = 3\\) hours. Total = \\(2+3 = 5\\) hours."} {"t":"q","id":24826,"q":"The difference between two whole numbers is 45. One of them is a 2-digit number and the other is a 3-digit number. What is the smallest possible sum of the two numbers? ","e":"To make the sum smallest, the 3-digit number should be as small as possible. The smallest 3-digit number is 100; then the 2-digit number is \\(100-45 = 55\\). Sum = \\(100+55 = 155\\)."} {"t":"q","id":24828,"q":"Batteries were sold in packs of 9 batteries and 5 batteries. Adam bought 12 packs with a total 88 batteries. How many packs of 5 batteries did Adam buy? ","e":"If all 12 packs were 9-battery packs: \\(12\\times9 = 108\\). That is \\(108-88 = 20\\) too many. Swapping a 9-pack for a 5-pack reduces the count by 4, so number of 5-packs = \\(20\\div4 = 5\\)."} {"t":"q","id":24829,"q":"Mr Lim packed 284 eggs on large trays and small trays to sell. He filled each large tray with 8 eggs and each small tray with 5 eggs. All the trays were full and there was no egg left over. What was the least total number of trays used by Mr Lim? ","e":"To use the fewest trays, use as many large (8-egg) trays as possible. \\(284\\div8 = 35\\) R 4; reduce large trays until the remainder is a multiple of 5. With 33 large trays: \\(33\\times8 = 264\\), leaving \\(284-264 = 20 = 4\\times5\\) small trays. Total = \\(33+4 = 37\\) trays."} {"t":"q","id":24832,"q":"30 pupils were each assigned to fold an equal number of paper hearts for a charity drive. 3 of them were unwell and did not fold any paper hearts. The remaining pupils had to fold an additional 5 paper hearts each. How many paper hearts did each pupil have to fold at first? ","e":"The 27 remaining pupils each fold 5 extra, covering the share of the 3 absent pupils: total extra = \\(27\\times5 = 135\\) hearts, which equals the 3 absentees' share = \\(3\\times\\)(original each). So original each = \\(135\\div3 = 45\\) paper hearts."} {"t":"q","id":24833,"q":"Zach had 80 more guppies than Ken at first. Ken gave 24 of his guppies to Zach. Zach had 3 times as many guppies as Ken after that. How many guppies did Zach have at first? ","e":"The total is unchanged. After Ken gives 24 to Zach, the difference becomes \\(80+48 = 128\\) and Zach = 3 \\times Ken, so the difference is 2 units = 128, 1 unit = 64. Ken after = 64, Zach after = 192. Zach at first = \\(192-24 = 168\\)."} {"t":"q","id":24834,"q":"Forrest bought \\(3k\\) boxes of chocolates. Each box contained 8 chocolates. After eating 2 boxes of chocolates, he had 200 chocolates left. What is the value of \\(k\\)? ","e":"Eating 2 boxes removes \\(2\\times8 = 16\\) chocolates, so he started with \\(200+16 = 216\\) chocolates. Boxes = \\(216\\div8 = 27\\), and \\(3k = 27\\), so \\(k = 9\\)."} {"t":"q","id":24836,"q":"At first, Nathan had $92 and Mabel had $50. Each of them bought a book at the same price. The ratio of the amount of money Nathan and Mabel had left was 5 : 2. How much did the book cost? ","e":"The difference in their money stays $92 - $50 = $42 after both spend the same. The ratio 5 : 2 has difference 3 units = $42, so 1 unit = $14. Mabel's 2 units = $28 left, so the book = $50 - $28 = $22."} {"t":"q","id":24841,"q":"Maverick and Nathan started jogging from the start point of a 3-km track at the same time and in the same direction. After jogging for 15 min, Nathan was 825 m ahead of Maverick. Both did not change their speeds throughout. Maverick took 24 min to reach the end point of the track. What was Nathan's jogging speed in m\/min? ","e":"Maverick: 3 km = 3000 m in 24 min, so speed = \\(3000\\div24 = 125\\) m\/min. In 15 min Maverick runs \\(125\\times15 = 1875\\) m; Nathan is 825 m ahead = 2700 m in 15 min, so Nathan's speed = \\(2700\\div15 = 180\\) m\/min. (125 + 825\\div15 = 125 + 55 = 180.)"} {"t":"q","id":24843,"q":"After the 5-day sale, a customer paid $4600 for all the remaining laptops in Shop A at a discount of $50 for every $300 spent. How much would the customer pay for the remaining laptops without the discount? ","e":"For every $300 of full price, $50 is taken off, so the customer pays $250 per $300 block. $4600 \\div 250 = 18.4 blocks; using the printed working $4600 \\div 250 = 18 sets, 18 \\times $300 = $5400, plus the remaining $100 = $5500 full price."} {"t":"q","id":24846,"q":"Abel, Ben and Chris had 448 tarts altogether. Abel gave \\(\\dfrac{1}{7}\\) of his tarts to Ben and \\(\\dfrac{2}{5}\\) of his tarts to Chris. After that, the ratio of the number of tarts Abel had to Ben had to Chris had was 4 : 3 : 9. What fraction of his tarts did Abel have left after giving some tarts to Ben and Chris?","e":"Abel gave away \\(\\dfrac{1}{7} + \\dfrac{2}{5} = \\dfrac{5}{35} + \\dfrac{14}{35} = \\dfrac{19}{35}\\) of his tarts. Fraction left = \\(1 - \\dfrac{19}{35} = \\dfrac{16}{35}\\)."} {"t":"q","id":24847,"q":"Abel, Ben and Chris had 448 tarts altogether. Abel gave \\(\\dfrac{1}{7}\\) of his tarts to Ben and \\(\\dfrac{2}{5}\\) of his tarts to Chris. After that, the ratio of the number of tarts Abel had to Ben had to Chris had was 4 : 3 : 9. How many more tarts did Chris have than Ben at first? ","e":"Abel kept \\(\\dfrac{16}{35}\\); after giving, ratio A:B:C = 4:3:9 with total 16 units = 448, so 1 unit = 28. Abel before = \\(\\dfrac{16}{35}\\) corresponds to 4 units = 112 \u2192 Abel's original = \\(112\\times\\dfrac{35}{16} = 245\\). Abel gave Ben \\(\\dfrac{1}{7}\\times245 = 35\\) and Chris \\(\\dfrac{2}{5}\\times245 = 98\\). Ben before = \\(3\\times28 - 35 = 49\\); Chris before = \\(9\\times28 - 98 = 154\\). Chris - Ben = \\(154 - 49 = 105\\)."} {"t":"q","id":24852,"q":"Andrew had a collection of gold, silver and bronze stars. He had 100 gold stars. 30% of his collection was silver stars. He had 12 more bronze stars than silver stars. What was the total number of gold and bronze stars Andrew had in his collection? ","e":"Gold = 100. Let total = T. Silver = 30% of T; bronze = silver + 12; gold = 100% - 30% - bronze%. Solving (gold = 40% of T after accounting for bronze): silver = 84, total = 280, so gold + bronze = 100 + 96 = 196. (Printed: 30% = 84, total 280; gold+bronze = 84 + 12 + 100 = 196.)"} {"t":"q","id":24853,"q":"Andrew had 100 gold stars, with silver being 30% of his collection and bronze 12 more than silver (total collection 280 stars: 100 gold, 84 silver, 96 bronze). Andrew's uncle gave him some silver stars. After that, 44% of his collection was silver stars. How many silver stars did Andrew receive from his uncle? ","e":"Gold and bronze stay fixed = 196, which is now 100% - 44% = 56% of the new collection. New total = \\(196 \\div 0.56 = 350\\). New silver = 44% of 350 = 154. Silver received = 154 - 84 = 70."} {"t":"q","id":24857,"q":"Round 4.567 to 2 decimal places.","e":"To round 4.567 to 2 decimal places, look at the 3rd decimal (7). Since 7 \u2265 5, round up the hundredths: 4.567 \u2248 4.57."} {"t":"q","id":24862,"q":"Arrange the following fractions from the smallest to the largest.
\\(\\dfrac{3}{2}\\), \\(1\\dfrac{5}{9}\\), \\(\\dfrac{6}{5}\\)","e":"As decimals: \\(\\dfrac{6}{5}=1.2\\), \\(\\dfrac{3}{2}=1.5\\), \\(1\\dfrac{5}{9}\\approx1.56\\). Smallest to largest: \\(\\dfrac{6}{5}\\), \\(\\dfrac{3}{2}\\), \\(1\\dfrac{5}{9}\\)."} {"t":"q","id":24864,"q":"There are 36 pens in a box. \\(\\dfrac{1}{3}\\) of them are red, 50% are blue and the rest are green. Express the number of green pens as a fraction of the number of blue pens.","e":"Red = \\(\\dfrac{1}{3}\\times36=12\\). Blue = 50% of 36 = 18. Green = 36 \u2212 12 \u2212 18 = 6. Green as a fraction of blue = \\(\\dfrac{6}{18}=\\dfrac{1}{3}\\)."} {"t":"q","id":24866,"q":"Sandy is given a total of $30 to spend from Monday to Friday. Every day, she spends $4 on food, $q on transport and saves the rest. How much does she save each week?","e":"Each day she spends $(4 + q), over 5 days that is $(20 + 5q). Savings = 30 \u2212 (20 + 5q) = $(10 \u2212 5q)."} {"t":"q","id":24867,"q":"Lisa paid $18.90 for 3 identical files and 3 identical pencils. Howard paid $10.50 for 2 such files and 1 such pencil. How much did each file cost?","e":"Lisa: 3 files + 3 pencils = $18.90, so 1 file + 1 pencil = $6.30. Howard: 2 files + 1 pencil = $10.50. Subtracting: 1 file = $10.50 \u2212 $6.30 = $4.20."} {"t":"q","id":24868,"q":"The ratio of Tianwei's height to Bala's height is 6 : 5. Bala is \\(\\dfrac{10}{11}\\) as tall as Chelsea. What is the ratio of Tianwei's height to Chelsea's height?","e":"Bala : Chelsea = 10 : 11. Tianwei : Bala = 6 : 5 = 12 : 10. Making Bala common (10): Tianwei : Bala : Chelsea = 12 : 10 : 11, so Tianwei : Chelsea = 12 : 11."} {"t":"q","id":24870,"q":"Dalia has 30 more stickers than Huda at first. Dalia gave 40% of her stickers to Huda. Then, Huda gave 50% of her stickers to Dalia. In the end, Dalia has 48 more stickers than Huda. How many stickers did Dalia have at first?","e":"Let Dalia = D at first, Huda = D \u2212 30. Dalia gives 40%: Dalia keeps 0.6D, Huda has D\u221230+0.4D=1.4D\u221230. Huda gives 50% to Dalia: Dalia = 0.6D+0.5(1.4D\u221230)=1.3D\u221215, Huda = 0.7D\u221215. Difference = (1.3D\u221215)\u2212(0.7D\u221215)=0.6D=48, so D=80."} {"t":"q","id":24871,"q":"Express \\(6\\dfrac{7}{100}\\) as a decimal. ","e":"\\(\\dfrac{7}{100}=0.07\\), so \\(6\\dfrac{7}{100}=6.07\\)."} {"t":"q","id":24872,"q":"Write down all the common multiples of 3 and 5 that are smaller than 40. ","e":"Common multiples of 3 and 5 are multiples of 15: 15, 30, 45, ... Those smaller than 40 are 15 and 30."} {"t":"q","id":24880,"q":"Lishi pressed a calculator to multiply a 3-digit number by a 1-digit number. For the 1-digit number, she made a mistake by pressing a wrong number. She obtained an incorrect product of 624 which is \\(\\dfrac{3}{4}\\) of the correct product. What is the smallest possible value of the 3-digit number? ","e":"Correct product = 624 \u00f7 \\(\\dfrac{3}{4}\\) = 832. The 3-digit number must divide both 624 and 832; the largest 1-digit factors give the smallest 3-digit number. 624 \u00f7 6 = 104 and 832 \u00f7 8 = 104, so the smallest 3-digit number is 104."} {"t":"q","id":24884,"q":"Kenny took 3 hours to paint 3 bedrooms. He took the same amount of time to paint the first 2 bedrooms. He took 15 minutes longer to paint the third bedroom than the first. How many minutes did he take to paint the third bedroom? ","e":"3 hours = 180 min. First 2 bedrooms take equal time, and the third = first + 15 min. So 180 \u2212 15 = 165 min split equally over 3 equal portions \u2192 165 \u00f7 3 = 55 min (the first\/each base portion). Third bedroom = 55 + 15 = 70 min."} {"t":"q","id":24887,"q":"Mr Raja paid a total of $1406.40 for a laptop and a camera at a sale. The price of the camera before discount was $864. Sale terms: 1st item 10% discount; 2nd item 20% discount (price of the 2nd item must be equal to or less than the 1st item). What was the price of the laptop before discount? $","e":"The camera ($864) is the cheaper 2nd item at 20% off: 90% of $864 is the 1st item only if it is the 1st. Here camera at 10%? Key: 1st item (laptop) at 10% off = 90% \u00d7 $864? No \u2014 work: 90% \u00d7 $864 = $777.60 is the discounted 1st item portion attributed; $1406.40 \u2212 $777.60 = $628.80 is the laptop at 80%. Laptop before discount = $628.80 \u00f7 80 \u00d7 100 = $786."} {"t":"q","id":24889,"q":"Kelly bought a total of 40 pieces of squares and rectangular craft paper. She cut all the squares into 3 rectangles. She now has a total of 92 rectangles. How many pieces of rectangular craft paper did she buy? ","e":"Each square becomes 3 rectangles, adding 2 extra pieces per square. Total increase = 92 \u2212 40 = 52, so squares = 52 \u00f7 2 = 26. Rectangular papers = 40 \u2212 26 = 14."} {"t":"q","id":24896,"q":"The ratio of the number of girls to boys in Hall A is 7 : 3. The ratio of the number of girls to boys in Hall B is 2 : 7. The total number of pupils in Hall A is \\(\\dfrac{2}{3}\\) of the total number of pupils in Hall B. What is the ratio of the number of boys in Hall A to the number of boys in Hall B? Express your answer in the simplest form.","e":"Total A : Total B = 2 : 3 = 30 : 45 (using units). Hall A girls:boys = 7:3 \u2192 scale total 10 to 30: 21 : 9. Hall B girls:boys = 2:7 \u2192 scale total 9 to 45: 10 : 35. Boys A : Boys B = 9 : 35."} {"t":"q","id":24897,"q":"The ratio of the number of girls to boys in Hall A is 7 : 3. The ratio of the number of girls to boys in Hall B is 2 : 7. The total number of pupils in Hall A is \\(\\dfrac{2}{3}\\) of the total number of pupils in Hall B. The number of boys in Hall A to boys in Hall B is 9 : 35. After a total of 375 boys left the hall, the percentage of all the girls became 62%. How many boys remained in the hall? ","e":"Total girls : total boys across both halls = (21+10) : (9+35) = 31 : 44, total 75 units. After 375 boys leave, girls are 62%, so boys = 38%. Girls 62% \u2192 31 units, so 1% = \\(\\dfrac{1}{2}\\) unit; boys 38% = 19 units. Boys who left = 44u \u2212 19u = 25u = 375, so 1u = 15. Boys remaining = 19 \u00d7 15 = 285."} {"t":"q","id":24898,"q":"At a concert, $9180 was collected from the sale of adult and child tickets. The ratio of the money collected from adult to child tickets is 14 : 3. \\(\\dfrac{1}{5}\\) of the tickets sold were child tickets. Each adult ticket is $9 more than each child ticket. How many child tickets were sold? ","e":"Money A : C = 14 : 3, total 17 units = $9180, so 1 unit = $540. Adult money = $7560, child money = $1620. \\(\\dfrac{1}{5}\\) of tickets are child, so adults : children = 4 : 1; adult ticket price = $7560 \u00f7 4u and child = $1620 \u00f7 1u, with adult \u2212 child = $9. Solving: child tickets = 30."} {"t":"q","id":24900,"q":"Which of the following is seventy-five thousand and thirty in numerals?","e":"Seventy-five thousand = 75 000; and thirty = 30. So the number is 75 000 + 30 = 75 030. Answer: 75 030."} {"t":"q","id":24902,"q":"Arrange these fractions from the smallest to the largest.
\\(\\dfrac{4}{5}\\) \\(\\dfrac{3}{7}\\) \\(\\dfrac{2}{3}\\)","e":"Convert to a common denominator 105: \\(\\dfrac{4}{5}=\\dfrac{84}{105}\\), \\(\\dfrac{3}{7}=\\dfrac{45}{105}\\), \\(\\dfrac{2}{3}=\\dfrac{70}{105}\\). Ordering smallest to largest: 45, 70, 84 gives \\(\\dfrac{3}{7}\\), \\(\\dfrac{2}{3}\\), \\(\\dfrac{4}{5}\\). Answer: option (3)."} {"t":"q","id":24903,"q":"Which number is the largest?","e":"Compare digit by digit. Tenths: 0.87 has 8, 0.807 has 8, 0.78 has 7, 0.708 has 7. Among the two with 8 tenths, hundredths: 0.87 has 7, 0.807 has 0. So 0.87 is the largest. Answer: 0.87."} {"t":"q","id":24904,"q":"Express \\(3\\dfrac{2}{25}\\) as a decimal.","e":"\\(\\dfrac{2}{25}=\\dfrac{8}{100}=0.08\\). So \\(3\\dfrac{2}{25}=3+0.08=3.08\\). Answer: 3.08."} {"t":"q","id":24905,"q":"Express 3080 cm in m.","e":"100 cm = 1 m, so divide by 100: 3080 cm \u00f7 100 = 30.8 m. Answer: 30.8 m."} {"t":"q","id":24906,"q":"Round 3.465 to 2 decimal places.","e":"To round to 2 decimal places, look at the 3rd decimal digit (5). Since it is 5, round up the 2nd decimal digit: 3.465 -> 3.47. Answer: 3.47."} {"t":"q","id":24907,"q":"In a basket, there were 4 apples, 8 pears and 12 papayas. What is the ratio of the number of apples to the total number of pears and papayas?","e":"Pears + papayas = 8 + 12 = 20. Ratio of apples to (pears + papayas) = 4 : 20 = 1 : 5. Answer: 1 : 5."} {"t":"q","id":24913,"q":"The table below shows the range of marks scored by a group of 220 students in a competition.
Marks: 70, 75, 80, 85, 90
Number of students: 24, 44, 108, 36, 8
20% of the students in this group qualified for the next round. What is the minimum score needed to qualify for the next round?","e":"20% of 220 = 44 students qualify, i.e. the top 44 scorers. Counting from the highest: 90 has 8, 85 has 36; 8 + 36 = 44. So the top 44 scored 85 or 90. The minimum qualifying score is 85. Answer: 85."} {"t":"q","id":24914,"q":"At a party, 20% of the people were men, 55% of the remaining people were women and the rest were children. There were 100 men. How many children were there at the party?","e":"Men = 20% = 100, so total people = 100 \u00f7 0.2 = 500. Remaining = 500 \u2212 100 = 400. Women = 55% of 400 = 220. Children = 400 \u2212 220 = 180. Answer: 180."} {"t":"q","id":24915,"q":"Find the value of (74 \u2212 36) \u00d7 10 + 6 \u00f7 2 = ","e":"Brackets first: 74 \u2212 36 = 38. Then \u00d7 and \u00f7 before +: 38 \u00d7 10 = 380 and 6 \u00f7 2 = 3. Finally 380 + 3 = 383. Answer: 383."} {"t":"q","id":24916,"q":"How many sixths are there in \\(5\\dfrac{1}{3}\\)? ","e":"\\(5\\dfrac{1}{3}=\\dfrac{16}{3}=\\dfrac{32}{6}\\). So there are 32 sixths. Equivalently \\(5\\dfrac{1}{3}\\div\\dfrac{1}{6}=\\dfrac{16}{3}\\times 6=32\\). Answer: 32."} {"t":"q","id":24917,"q":"Find the value of 12.2 \u2212 5.47 = ","e":"Align decimals: 12.20 \u2212 5.47 = 6.73. Answer: 6.73."} {"t":"q","id":24919,"q":"(a) Find the value of \\(1-\\dfrac{1}{3}-\\dfrac{1}{5}\\). (b) Find the value of \\(11\\div\\dfrac{3}{5}\\).","e":"(a) Common denominator 15: \\(1=\\dfrac{15}{15}\\), so \\(\\dfrac{15}{15}-\\dfrac{5}{15}-\\dfrac{3}{15}=\\dfrac{7}{15}\\). (b) \\(11\\div\\dfrac{3}{5}=11\\times\\dfrac{5}{3}=\\dfrac{55}{3}=18\\dfrac{1}{3}\\). Answers: \\(\\dfrac{7}{15}\\) and \\(18\\dfrac{1}{3}\\)."} {"t":"q","id":24920,"q":"Denise answered 20 questions in a survey. She took 3 min for each of the first 10 questions and twice as long for each of the remaining questions. She started her survey at 1.20 p.m. At what time did she complete her survey? p.m.","e":"First 10 questions: 10 \u00d7 3 = 30 min. Remaining 10 questions: 6 min each, 10 \u00d7 6 = 60 min. Total = 30 + 60 = 90 min = 1 h 30 min. Start 1.20 p.m. + 1 h 30 min = 2.50 p.m. Answer: 2.50 p.m."} {"t":"q","id":24922,"q":"The ratio of the number of stickers Kingston had to the number of stickers Tim had was 8 : 5. After Kingston gave away 44 stickers, Tim had twice as many stickers as Kingston. How many stickers did they have at first? ","e":"Let Kingston = 8u, Tim = 5u. After giving away 44, Tim = 2 \u00d7 (new Kingston): 5u = 2(8u \u2212 44) = 16u \u2212 88, so 88 = 11u, u = 8. Total at first = 8u + 5u = 13u = 13 \u00d7 8 = 104. Answer: 104."} {"t":"q","id":24923,"q":"Pauline drove from her home to her office. The distance between her home and her office was 24 km. The average speed of her car was 60 km\/h. Pauline left home at 0815, what time did she reach her office? ","e":"Time = distance \u00f7 speed = 24 \u00f7 60 = 0.4 h = 24 min. Start 0815 + 24 min = 0839. Answer: 0839."} {"t":"q","id":24924,"q":"Andy had $5x. After buying apples at 60\u00a2 each, he had $2x left. How many apples did Andy buy?","e":"Money spent on apples = $5x \u2212 $2x = $3x. Each apple costs 60\u00a2 = $0.60. Number of apples = \\(\\dfrac{3x}{0.6}\\). Answer: \\(\\dfrac{3x}{0.6}\\) (= 5x)."} {"t":"q","id":24929,"q":"Jimmy gave his mother $1200 of his salary. He gave \\(\\dfrac{5}{8}\\) of the remainder of his salary to his brother and had \\(\\dfrac{1}{4}\\) of his salary left. What was Jimmy's salary? $","e":"After giving the brother \\(\\dfrac{5}{8}\\) of the remainder, \\(\\dfrac{3}{8}\\) of the remainder is left, which equals \\(\\dfrac{1}{4}\\) of the salary. So remainder = $1200 corresponds to: \\(\\dfrac{3}{8}\\) of remainder = \\(\\dfrac{1}{4}\\) salary. The $1200 given to mother is \\(\\dfrac{1}{3}\\) of the salary, so salary = 1200 \u00d7 3 = $3600. Answer: $3600."} {"t":"q","id":24932,"q":"Mr Lee had a piece of wire 26y cm long. He used the wire to form a rectangle, with length and breadth measuring 2y cm and 20 cm. (a) Express the length of the remaining wire in terms of y. (b) Mr Lee used the remaining wire to make a square. If y = 4, what was the length of one side of the square? cm","e":"(a) Perimeter of rectangle = 2(2y + 20) = 4y + 40. Remaining wire = 26y \u2212 (4y + 40) = 22y \u2212 40 cm. (b) When y = 4: remaining = 22(4) \u2212 40 = 88 \u2212 40 = 48 cm. A square has 4 equal sides, so one side = 48 \u00f7 4 = 12 cm. Answers: (a) (22y \u2212 40) cm, (b) 12 cm."} {"t":"q","id":24935,"q":"At 8 a.m., Joey travelled from Town X to Town Y at a constant speed of 120 km\/h. At the same time, Madeline travelled from Town Y to Town X at a constant speed of 90 km\/h. At 9.20 a.m., they were 50 km apart after driving past each other. What is the distance between Town X and Town Y? km","e":"Time travelled = 8 a.m. to 9.20 a.m. = 1 h 20 min = \\(1\\dfrac{1}{3}\\) h. Joey's distance = 120 \u00d7 4\/3 = 160 km. Madeline's distance = 90 \u00d7 4\/3 = 120 km. They have passed each other and are 50 km apart, so distance XY = 160 + 120 \u2212 50 = 230 km. Answer: 230 km."} {"t":"q","id":24937,"q":"The table shows the scores of 4 students in a Math test. Some of the scores are covered by an ink patch.
Aloysius = 6_, Benedict = 8_, Charles = 7_, Dominic = 82.
The average score of Charles and Dominic is 80. The average score of Aloysius, Benedict and Charles is 74. What is the largest possible score that Benedict has achieved? ","e":"Charles + Dominic = 80 \u00d7 2 = 160, and Dominic = 82, so Charles = 78. Aloysius + Benedict + Charles = 74 \u00d7 3 = 222, so Aloysius + Benedict = 222 \u2212 78 = 144. Aloysius is 6_ (smallest possible 60) to make Benedict largest: Benedict = 144 \u2212 60 = 84. Answer: 84."} {"t":"q","id":24938,"q":"Peter had some stickers. He gave half of them and an additional 60 stickers to Samuel. Next, he gave half of the remainder of the stickers and an additional 30 stickers to Troy. He then gave 40 stickers to each of his 3 siblings and had 100 stickers left. How many stickers did Peter have at first? ","e":"Work backwards. After siblings: 100 + 3\u00d740 = 100 + 120 = 220 before the siblings. Before Troy: (220 + 30) \u00d7 2 = 250 \u00d7 2 = 500. Before Samuel: (500 + 60) \u00d7 2 = 560 \u00d7 2 = 1120. Answer: 1120. (Key working: 120 + 30 + 100 = 250; 60 + 250 + 250 = 560; 560 \u00d7 2 = 1120.)"} {"t":"q","id":24939,"q":"There were 400 adults attending a concert in a stadium. During the break, \\(\\dfrac{1}{3}\\) of the men and \\(\\dfrac{3}{5}\\) of the women left the stadium. 224 adults remained in the stadium. How many women were there in the stadium at first? ","e":"Let m = men, w = women, m + w = 400. Remaining = \\(\\dfrac{2}{3}m + \\dfrac{2}{5}w = 224\\). Multiply by 3\/2: m + \\(\\dfrac{3}{5}w = 336\\). Subtract from m + w = 400: \\(\\dfrac{2}{5}w = 64\\), so \\(\\dfrac{1}{5}w = 32\\), w = 160. Answer: 160 women."} {"t":"q","id":24941,"q":"In the morning, Mrs Chen baked muffins of 3 different flavours \u2014 chocolate, strawberry and vanilla. The ratio of the number of chocolate muffins to the number of strawberry muffins was 3 : 5. There were 28 more strawberry muffins than chocolate muffins. There were 10 more vanilla muffins than strawberry muffins. How many vanilla muffins did she bake in the morning? ","e":"Chocolate : strawberry = 3 : 5, difference = 2 units = 28, so 1 unit = 14. Strawberry = 5 \u00d7 14 = 70. Vanilla = strawberry + 10 = 70 + 10 = 80. Answer: 80 vanilla muffins."} {"t":"q","id":24942,"q":"Mrs Chen baked chocolate, strawberry and vanilla muffins. In the morning there were 42 chocolate, 70 strawberry and 80 vanilla muffins. In the afternoon, she baked some more chocolate and vanilla muffins. The total number of chocolate and vanilla muffins became thrice the number of strawberry muffins. The percentage increase of the chocolate muffins was between 8% to 10%. How many vanilla muffins did she bake in the afternoon? ","e":"Strawberry stays 70, so chocolate + vanilla total = 3 \u00d7 70 = 210. Chocolate increase 8\u201310% of 42 is 3.36\u20134.2, so chocolate increased by 4 (42 \u2192 46). Vanilla total = 210 \u2212 46 = 164. Vanilla baked in afternoon = 164 \u2212 80 = 84. Answer: 84. (Key: 70\u00d73 = 210; 8% = 3.20, 10% = 4.20, so +4 \u2192 46; 210 \u2212 46 \u2212 80 = 84.)"} {"t":"q","id":24945,"q":"In June, Mr Tan saved 20% of his salary. In July, his monthly salary increased by $600 and he saved 15% of his new monthly salary. Given that Mr Tan saved the same amount of money in both months, find the percentage increase in Mr Tan's salary.","e":"15% of $600 = $90, which is the extra 'saving slack' \u2014 set up: June saving 20% of S = July saving 15% of (S + 600). So 0.20S = 0.15(S + 600) \u2192 0.20S = 0.15S + 90 \u2192 0.05S = 90 \u2192 S = $1800. Increase = 600\/1800 = \\(33\\dfrac{1}{3}\\)%. Answer: \\(33\\dfrac{1}{3}\\)%."} {"t":"q","id":24946,"q":"How many hundredths are there in 0.8?","e":"0.8 = 0.80 = 80 hundredths. Final answer: 80."} {"t":"q","id":24947,"q":"What is the sum of all the factors of 9?","e":"Factors of 9 are 1, 3 and 9. Sum = 1 + 3 + 9 = 13. Final answer: 13."} {"t":"q","id":24948,"q":"Express 8 km 20 m in km.","e":"20 m = 20 \u00f7 1000 km = 0.02 km. So 8 km 20 m = 8.02 km. Final answer: 8.02 km."} {"t":"q","id":24949,"q":"Express \\(\\dfrac{3}{8}\\) as a decimal correct to 2 decimal places.","e":"3 \u00f7 8 = 0.375. Rounded to 2 decimal places = 0.38. Final answer: 0.38."} {"t":"q","id":24951,"q":"A movie started at 10.35 p.m. and ended at 1.15 a.m. How long did the movie last?","e":"10.35 p.m. to 12 midnight = 1 h 25 min. Midnight to 1.15 a.m. = 1 h 15 min. Total = 1 h 25 min + 1 h 15 min = 2 h 40 min. Final answer: 2 h 40 min."} {"t":"q","id":24953,"q":"Which of the following is the most likely mass of an apple?","e":"A typical apple has a mass of about 200 g. 20 kg and 2 kg are far too heavy and 20 g is too light. Final answer: 200 g."} {"t":"q","id":24954,"q":"James paid $20 for 40 rulers. How much did each ruler cost?","e":"$20 \u00f7 40 = $0.50 = 50 cents per ruler. Final answer: 50 cents."} {"t":"q","id":24956,"q":"Two years ago, Andy was n years older than Belle. Andy is twice her age now, how old was Belle 2 years ago?","e":"Let Belle's age now = B, Andy's age now = 2B. Two years ago: Belle = B \u2212 2, Andy = 2B \u2212 2. Andy was n older: (2B \u2212 2) \u2212 (B \u2212 2) = n, so B = n. Belle 2 years ago = B \u2212 2 = n \u2212 2. Final answer: n \u2212 2."} {"t":"q","id":24959,"q":"There were a total of 50 blue, red and white marbles in a box. The number of blue and red marbles was \\(\\dfrac{2}{5}\\) of the total number of marbles. The number of red and white marbles was \\(\\dfrac{9}{10}\\) of the total number of marbles. Find the number of red marbles.","e":"Total = 50. Blue + Red = \\(\\dfrac{2}{5}\\) \u00d7 50 = 20. Red + White = \\(\\dfrac{9}{10}\\) \u00d7 50 = 45. (Blue+Red) + (Red+White) = 20 + 45 = 65 = Total + Red = 50 + Red. So Red = 65 \u2212 50 = 15. Final answer: 15."} {"t":"q","id":24960,"q":"In a school, 40% of the pupils are boys.
5% of the boys and 20% of the girls walk to school.
What percentage of the pupils in the school walk to school?","e":"Boys = 40%, Girls = 60%. Boys who walk = 5% of 40% = 2%. Girls who walk = 20% of 60% = 12%. Total walking = 2% + 12% = 14%. Final answer: 14%."} {"t":"q","id":24961,"q":"Express 8% as a fraction. Give your answer in its simplest form.","e":"8% = \\(\\dfrac{8}{100}\\). Divide numerator and denominator by 4: \\(\\dfrac{2}{25}\\). Final answer: \\(\\dfrac{2}{25}\\)."} {"t":"q","id":24962,"q":"Round 589.02 to the nearest tenth.
Answer: ","e":"The hundredths digit is 2 (less than 5), so the tenths digit stays. 589.02 rounded to the nearest tenth = 589.0. Final answer: 589.0."} {"t":"q","id":24964,"q":"What is the greatest possible whole number that gives 9300 when rounded to the nearest ten?
Answer: ","e":"Numbers rounding to 9300 (nearest ten) range from 9295 to 9304. The greatest whole number is 9304 (9305 would round to 9310). Final answer: 9304."} {"t":"q","id":24965,"q":"Give a fraction that is halfway between \\(\\dfrac{1}{5}\\) and \\(\\dfrac{1}{3}\\).","e":"Halfway = average = \\(\\dfrac{1}{2}\\)(\\(\\dfrac{1}{5}\\) + \\(\\dfrac{1}{3}\\)) = \\(\\dfrac{1}{2}\\)(\\(\\dfrac{3}{15}\\) + \\(\\dfrac{5}{15}\\)) = \\(\\dfrac{1}{2}\\) \u00d7 \\(\\dfrac{8}{15}\\) = \\(\\dfrac{4}{15}\\). Final answer: \\(\\dfrac{4}{15}\\)."} {"t":"q","id":24967,"q":"Study the pattern below carefully. If the pattern continues, what is the 99th letter?
S Q U A R E S Q U A R E S Q U A R E ........","e":"The word SQUARE repeats every 6 letters. 99 \u00f7 6 = 16 remainder 3. The 3rd letter of SQUARE is U. Final answer: U."} {"t":"q","id":24971,"q":"Jack and Keith left Town X at the same time and travelled in opposite directions along a straight road. If Jack travelled at 7 km\/h and Keith travelled at 5 km\/h, how far apart would they be 2 hours later?
Answer: km","e":"Jack's distance = 7 \u00d7 2 = 14 km. Keith's distance = 5 \u00d7 2 = 10 km. Travelling in opposite directions, distance apart = 14 + 10 = 24 km. Final answer: 24 km."} {"t":"q","id":24972,"q":"A group of 5 boys rented a paddle boat for 2 hours and took turns to play. At any one time, there were 3 boys paddling the boat. On average, how long did each boy play on the paddle boat?
Answer: min","e":"Total paddling time = 3 boys \u00d7 2 hours = 3 \u00d7 120 min = 360 boy-minutes. Shared equally among 5 boys: 360 \u00f7 5 = 72 min each. Final answer: 72 min."} {"t":"q","id":24973,"q":"Two numbers X and Y are in the ratio of 3 : 7. After Y is halved and X is increased by 4, the ratio became 1 : 1. What is the original value of X?
Answer: ","e":"X : Y = 3 : 7, so let X = 3u, Y = 7u. After: X+4 : Y\u00f72 = (3u+4) : 3.5u and this equals 1 : 1, so 3u + 4 = 3.5u, giving 0.5u = 4, u = 8. X = 3u = 3 \u00d7 8 = 24. Final answer: 24."} {"t":"q","id":24974,"q":"John has just enough money to buy either 6 rulers and 3 erasers or 4 rulers and 8 erasers. He spends all the money on erasers, how many erasers can he buy?
Answer: ","e":"6 rulers + 3 erasers = 4 rulers + 8 erasers, so 2 rulers = 5 erasers. Total money = 6 rulers + 3 erasers = 3 \u00d7 (2 rulers) + 3 erasers = 3 \u00d7 5 erasers + 3 erasers = 15 + 3 = 18 erasers. Final answer: 18."} {"t":"s","id":17447,"s":"4 \u00d7 8 = 32, so the ratio is multiplied by 8. Missing number = 7 \u00d7 8 = 56."} {"t":"s","id":17451,"s":"Fraction left = \\(1-\\dfrac{2}{3}-\\dfrac{1}{5}=1-\\dfrac{10}{15}-\\dfrac{3}{15}=\\dfrac{2}{15}\\). \\(\\dfrac{2}{15}\\) of the money = $100, so \\(\\dfrac{1}{15}\\) = $50 and total = $50 \u00d7 15 = $750."} {"t":"s","id":17455,"s":"February = 2651 + 44 = 2695. Rounded to the nearest ten, 2695 \u2248 2700."} {"t":"s","id":17456,"s":"Interest = 4% of $15 000 = \\(\\dfrac{4}{100}\\times 15000\\) = $600. Total at year end = $15 000 + $600 = $15 600."} {"t":"s","id":17458,"s":"Mei Mei is 53 \u2212 45 = 8 kg above the group average. Each cousin is 45 \u2212 43 = 2 kg below the group average. To balance Mei Mei's +8 kg, the cousins must total \u22128 kg, so number of cousins = 8 \u00f7 2 = 4."} {"t":"s","id":17461,"s":"Total = 88 + 75 + 82 + 69 + 71 = 385. Average = 385 \u00f7 5 = 77 books."} {"t":"s","id":17463,"s":"Rounded to nearest dollar = $30, so the cost is $29.50 to $30.49. Tenths and hundredths digits come from {1,4,5} and must differ. Possible costs: $29.51, $29.54, $30.14, $30.15, $30.41, $30.45 \u2014 and all digits in the whole number must also differ. The valid costs total 6."} {"t":"s","id":17464,"s":"The difference in money James would need versus Anna's leftover = $4.30 + $8.70 = $13 (this is the extra cost of buying highlighters instead of pens). Each highlighter costs $2.50 \u2212 $1.20 = $1.30 more than a pen. Number bought = $13 \u00f7 $1.30 = 10. Anna spent on pens = 10 \u00d7 $1.20 = $12, so she had $12 + $4.30 = $16.30 at first."} {"t":"s","id":17466,"s":"In 5 years the age difference is still 12. Ratio 5 : 9 means difference is 9 \u2212 5 = 4 units = 12, so 1 unit = 3. Chin Lee in 5 years = 9 units = 9 \u00d7 3 = 27. Chin Lee now = 27 \u2212 5 = 22 years old."} {"t":"s","id":17467,"s":"(a) 8 \u2212 2 = 6 numbers remain; sum = 32 \u00d7 6 = 192. (b) Sum of all 8 = 45 \u00d7 8 = 360. Sum of the 2 removed = 360 \u2212 192 = 168. They differ by 6: larger = (168 + 6) \u00f7 2 = 87, smaller = 87 \u2212 6 = 81."} {"t":"s","id":17468,"s":"Let total = T. Chocolate = \\(\\dfrac{1}{5}T\\), banana = \\(\\dfrac{4}{5}T\\). She sold \\(\\dfrac{4}{7}\\) of chocolate, so chocolate left = \\(\\dfrac{3}{7}\\times\\dfrac{1}{5}T=\\dfrac{3}{35}T\\). Cupcakes left = \\(\\dfrac{2}{5}T=\\dfrac{14}{35}T\\), so banana left = \\(\\dfrac{14}{35}T-\\dfrac{3}{35}T=\\dfrac{11}{35}T\\). Banana sold = \\(\\dfrac{4}{5}T-\\dfrac{11}{35}T=\\dfrac{28-11}{35}T=\\dfrac{17}{35}T=51\\), so \\(\\dfrac{1}{35}T=3\\) and T = 105. (a) Chocolate sold = \\(\\dfrac{4}{7}\\times\\dfrac{1}{5}\\times105=\\dfrac{4}{35}\\times105=12\\). (b) Total = 105."} {"t":"s","id":17470,"s":"(a) 7200 \u00f7 7 = 1028 remainder 4, so 4 shuttlecocks were left unpacked. (b) Money from bags = 1028 \u00d7 $3.50 = $3598. Money from unpacked = $3608 \u2212 $3598 = $10. Each unpacked = $10 \u00f7 4 = $2.50."} {"t":"s","id":17473,"s":"(a) 3 large = 5 small, so 1 small = \\(\\dfrac{3}{5}\\) large. 15 small = 15 \u00f7 5 \u00d7 3 = 9 large bows. (b) \\(\\dfrac{2}{7}\\) made 15 small + 7 large = (9 + 7) = 16 large-equivalents, so \\(\\dfrac{1}{7}\\) = 16 \u00f7 2 = 8 large; \\(\\dfrac{2}{7}\\) = 16 large. Remaining ribbon = \\(\\dfrac{5}{7}\\). \\(\\dfrac{3}{10}\\) of remaining = \\(\\dfrac{3}{10}\\times\\dfrac{5}{7}=\\dfrac{3}{14}\\) of whole. Since \\(\\dfrac{1}{14}\\) = 4 large, \\(\\dfrac{3}{14}\\) = 12 large = 12 \u00d7 (5\/3) small = 20 small bows."} {"t":"s","id":17475,"s":"Expand 5 703 890 in place value: 5 000 000 + 700 000 + 3 000 + 890. The missing addend is the hundred-thousands part, 700 000. Answer: 700 000 (option 4)."} {"t":"s","id":17476,"s":"Order of operations: brackets first, 40 + 23 = 63. Then \\(\\div\\) and \\(\\times\\) left to right: 54 \\(\\div\\) 9 = 6, 6 \\(\\times\\) 2 = 12. Now 63 - 12 + 8 = 59. Answer: 59 (option 2)."} {"t":"s","id":17477,"s":"Multiply numerators and denominators: \\(\\dfrac{4 \\times 5}{9 \\times 6} = \\dfrac{20}{54}\\). Simplify by dividing top and bottom by 2: \\(\\dfrac{10}{27}\\). Answer: \\(\\dfrac{10}{27}\\) (option 3)."} {"t":"s","id":17478,"s":"Books: 7 boxes \\(\\times\\) 8 = (7 \\(\\times\\) 8). Magazine boxes: 10 - 7 = 3 boxes, each with 12, so (10 - 7) \\(\\times\\) 12. Total = (7 \\(\\times\\) 8) + (10 - 7) \\(\\times\\) 12. Answer: option 3."} {"t":"s","id":17479,"s":"Let Royston have R at first. Jieming = R + 20. After Royston gives 14: Royston = R - 14, Jieming = R + 34. Jieming is now 3 times Royston: R + 34 = 3(R - 14) = 3R - 42, so 76 = 2R, R = 38. Answer: 38 (option 4)."} {"t":"s","id":17480,"s":"653 \\(\\times\\) 400 = 653 \\(\\times\\) 4 \\(\\times\\) 100 = 2 612 \\(\\times\\) 100 = 261 200. Answer: 261 200."} {"t":"s","id":17481,"s":"To be closest to 8000, the thousands digit should be 7 (since 8 is unavailable). Then make the rest as large as possible: 7940. Check: 8000 - 7940 = 60, the smallest gap possible. Answer: 7940."} {"t":"s","id":17482,"s":"Convert to the same unit: 2 m = 200 cm. Fraction = \\(\\dfrac{8}{200}\\). Simplify by dividing top and bottom by 8: \\(\\dfrac{1}{25}\\). Answer: \\(\\dfrac{1}{25}\\) (option 1)."} {"t":"s","id":17483,"s":"20 \\(\\div\\) 7 = 2 remainder 6, so \\(\\dfrac{20}{7} = 2\\dfrac{6}{7}\\). (Part b of the printed paper: as a decimal to 2 d.p., 20 \\(\\div\\) 7 = 2.857... \\(\\approx\\) 2.86; the printed key shows 0.286 for the fractional 6\/7 part rounded differently. The mixed number is the value asked here.) Answer: \\(2\\dfrac{6}{7}\\) (option 1)."} {"t":"s","id":17484,"s":"Box : bag = 4 : 1, so total is 5 units = 60 kg. 1 unit = 60 \\(\\div\\) 5 = 12 kg. Box = 4 units = 12 \\(\\times\\) 4 = 48 kg. Answer: 48 kg."} {"t":"s","id":17485,"s":"The difference between them stays $60 - $42 = $18, since they spend equally. In the end Ross = 3 \\(\\times\\) Monica, so the difference is 2 units = $18, giving 1 unit = $9 (Monica's final amount). Each spent $42 - $9 = $33. Answer: $33."} {"t":"s","id":17486,"s":"Remove the 6 extra mangoes first: 6 \\(\\times\\) $3 = $18, leaving $146 - $18 = $128 for equal numbers of each. One mango + one watermelon = $3 + $5 = $8. Pairs = $128 \\(\\div\\) $8 = 16. So 16 watermelons and 16 + 6 = 22 mangoes; altogether 16 + 22 = 38. Answer: 38."} {"t":"s","id":17487,"s":"Paying children = $114 \\(\\div\\) $3 = 38. In each group of 4, 3 pay and 1 is free. 38 \\(\\div\\) 3 = 12 remainder 2, so there are 12 full groups of 4 plus 2 extra paying children. Free children = 12 \\(\\times\\) 1 = 12. Greatest total = 38 paying + 12 free = 50. Answer: 50."} {"t":"s","id":17488,"s":"Two million = 2 000 000, eighty thousand = 80 000, five hundred and nine = 509. Adding: 2 000 000 + 80 000 + 509 = 2 080 509."} {"t":"s","id":17489,"s":"In 4 023 670 the digit 2 is in the ten-thousands place. Its value is 2 \u00d7 10 000 = 20 000."} {"t":"s","id":17491,"s":"Inside the brackets first: 12 \u00d7 4 = 48, so 72 \u2212 48 = 24. Then 24 \u00f7 3 = 8. Finally 6 + 8 = 14."} {"t":"s","id":17493,"s":"Each child gets 9 \u00f7 15 = \\(\\dfrac{9}{15}\\) of a pizza. Simplifying by dividing top and bottom by 3 gives \\(\\dfrac{3}{5}\\)."} {"t":"s","id":17494,"s":"Apples are the rest: \\(1 - \\dfrac{2}{5} = \\dfrac{3}{5}\\) of the fruits. Green apples are \\(\\dfrac{1}{3}\\) of the apples: \\(\\dfrac{3}{5} \\times \\dfrac{1}{3} = \\dfrac{1}{5}\\)."} {"t":"s","id":17495,"s":"Work backwards from 650. Before adding 53 blue beads: 650 \u2212 53 = 597. Before taking out 134 red beads: 597 + 134 = 731."} {"t":"s","id":17496,"s":"The number is 500 \u00d7 420 = 210 000. Dividing by 2000: 210 000 \u00f7 2000 = 105."} {"t":"s","id":17498,"s":"A pack of 5 for $9 is cheaper per file ($1.80) than $2 each, so buy as many packs as possible. $62 \u00f7 $9 = 6 packs (6 \u00d7 $9 = $54) with $8 left. 6 packs = 30 files. The $8 left buys 8 \u00f7 2 = 4 single files. Total = 30 + 4 = 34 files."} {"t":"s","id":17499,"s":"Remaining after chocolate = \\(1 - \\dfrac{4}{9} = \\dfrac{5}{9}\\). Strawberry = \\(\\dfrac{2}{5} \\times \\dfrac{5}{9} = \\dfrac{2}{9}\\), so mango = \\(\\dfrac{5}{9} - \\dfrac{2}{9} = \\dfrac{3}{9} = \\dfrac{1}{3}\\) of all tarts. Chocolate + mango = \\(\\dfrac{4}{9} + \\dfrac{3}{9} = \\dfrac{7}{9}\\) of total = 56. Total = 56 \u00f7 7 \u00d7 9 = 72."} {"t":"s","id":17500,"s":"Let girls = 1 unit, boys = 4 units at first. In the end boys = 4u \u2212 57 and girls = 1u + 18, and these are equal: 4u \u2212 57 = u + 18, so 3u = 75 and 1u = 25. Boys in the end = 25 + 18 = 43 (equals the equal final count)."} {"t":"s","id":17501,"s":"In 561 403, the digit places from the left are: 5 = hundred thousands, 6 = ten thousands, 1 = thousands, 4 = hundreds, 0 = tens, 3 = ones. So the digit in the hundred thousands place is 5. Answer: 5."} {"t":"s","id":17502,"s":"To round 428 567 to the nearest thousand, look at the hundreds digit (5). Since 5 \u2265 5, round the thousands up: 428 \u2192 429 thousand. So 428 567 \u2248 429 000. Answer: 429 000."} {"t":"s","id":17503,"s":"\\(\\dfrac{1}{20}=\\dfrac{5}{100}=0.05\\). So \\(8\\dfrac{1}{20}=8+0.05=8.05\\). Answer: 8.05."} {"t":"s","id":17507,"s":"Apply order of operations (\u00d7 and \u00f7 before + and \u2212): 72 \u00f7 8 = 9 and 4 \u00d7 15 = 60. Then 96 \u2212 9 + 60 = 87 + 60 = 147. Answer: 147."} {"t":"s","id":17508,"s":"Convert to decimals: \\(\\dfrac{8}{7}\\approx1.143\\), \\(1\\dfrac{1}{8}=1.125\\), \\(\\dfrac{4}{3}\\approx1.333\\). From largest to smallest: \\(\\dfrac{4}{3}\\) (1.333), \\(\\dfrac{8}{7}\\) (1.143), \\(1\\dfrac{1}{8}\\) (1.125). Answer: \\(\\dfrac{4}{3}\\), \\(\\dfrac{8}{7}\\), \\(1\\dfrac{1}{8}\\)."} {"t":"s","id":17509,"s":"After the laptop, remaining = \\(1-\\dfrac{1}{3}=\\dfrac{2}{3}\\). He gave \\(\\dfrac{1}{5}\\) of this away, keeping \\(\\dfrac{4}{5}\\) of it: \\(\\dfrac{4}{5}\\times\\dfrac{2}{3}=\\dfrac{8}{15}\\). Answer: \\(\\dfrac{8}{15}\\)."} {"t":"s","id":17510,"s":"Cousins : classmates = 1 : 3, so the difference is 3 \u2212 1 = 2 units = 84 sweets. 1 unit = 84 \u00f7 2 = 42. Classmates = 3 units = 3 \u00d7 42 = 126. Answer: 126."} {"t":"s","id":17511,"s":"Factors of 16: 1, 2, 4, 8, 16. Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. Common factors = 1, 2, 4. Answer: 1, 2, 4."} {"t":"s","id":17513,"s":"\\(2\\dfrac{7}{8}-1\\dfrac{3}{5}=\\dfrac{23}{8}-\\dfrac{8}{5}\\). Common denominator 40: \\(\\dfrac{115}{40}-\\dfrac{64}{40}=\\dfrac{51}{40}=1\\dfrac{11}{40}\\). Answer: \\(1\\dfrac{11}{40}\\)."} {"t":"s","id":17514,"s":"32 : 16 simplifies to 2 : 1. To make the second term 25, multiply both parts by 25: 2 \u00d7 25 : 1 \u00d7 25 = 50 : 25. So the missing number is 50. Answer: 50."} {"t":"s","id":17515,"s":"Matthew : Cayden = 2 : 5. Matthew's 2 units = 124, so 1 unit = 124 \u00f7 2 = 62. Altogether = 2 + 5 = 7 units = 7 \u00d7 62 = 434 cards. Answer: 434."} {"t":"s","id":17516,"s":"6 years ago, total age = 66 \u2212 6 \u2212 6 = 54. Then Siti : son = 5 : 1, so 6 units = 54, 1 unit = 9. Son was 9, Siti was 45 (6 years ago). Now Siti = 45 + 6 = 51 years old. Answer: 51."} {"t":"s","id":17517,"s":"Let Shop B = 1 unit. Shop A = 2 units, Shop C = 3 \u00d7 Shop A = 6 units. C \u2212 A = 6 \u2212 2 = 4 units = 592, so 1 unit = 592 \u00f7 4 = 148. Shop B = 1 unit = 148 doughnuts. Answer: 148."} {"t":"s","id":17518,"s":"After giving 12 away: Charlotte = 48 \u2212 12 = 36; Makayla = 32 + 12 = 44. Ratio 36 : 44, divide both by 4 = 9 : 11. Answer: 9 : 11."} {"t":"s","id":17520,"s":"After giving away, Janna still has (78 \u2212 9 + 7) = 76 more than Nadiah. Nadiah's share is \\(\\dfrac{1}{6}\\) of the total, so Janna has \\(\\dfrac{5}{6}\\); the difference is \\(\\dfrac{4}{6}\\) of the total. Using units: Nadiah = 1 unit, total = 6 units, Janna = 5 units; difference = 4 units = 76, so 1 unit = 76 \u00f7 4 = 19. Nadiah had 19 left. Answer: 19."} {"t":"s","id":17524,"s":"\\(\\dfrac{7}{10} - \\dfrac{1}{6} = \\dfrac{21}{30} - \\dfrac{5}{30} = \\dfrac{16}{30} = \\dfrac{8}{15}\\). So the missing numerator is 8."} {"t":"s","id":17525,"s":"\\(7\\dfrac{2}{5} = \\dfrac{37}{5}\\). Leon's mass = \\(\\dfrac{37}{5} \\times 4 = \\dfrac{148}{5} = 29\\dfrac{3}{5}\\) kg."} {"t":"s","id":17527,"s":"Let Germaine have 1 unit, so Joan has 2 units. Joan keeps \\(1 - \\dfrac{5}{12} = \\dfrac{7}{12}\\) of her beads: \\(2 \\times \\dfrac{7}{12} = \\dfrac{14}{12} = \\dfrac{7}{6}\\) units. Germaine then has \\(1\\) unit + 25. Setting equal: \\(\\dfrac{7}{6}\\) units = 1 unit + 25, so \\(\\dfrac{1}{6}\\) unit = 25, 1 unit = 150. Joan = 2 units = 300 beads."} {"t":"s","id":17528,"s":"Remaining after books = \\(1 - \\dfrac{3}{8} = \\dfrac{5}{8}\\). Spent on toys = \\(\\dfrac{5}{8} \\times \\dfrac{2}{5} = \\dfrac{10}{40} = \\dfrac{1}{4}\\) of his money."} {"t":"s","id":17529,"s":"Lucas has \\(1 - \\dfrac{3}{4} = \\dfrac{1}{4}\\) left; James has \\(1 - \\dfrac{1}{8} = \\dfrac{7}{8}\\) left. Difference = \\(\\dfrac{7}{8} - \\dfrac{1}{4} = \\dfrac{7}{8} - \\dfrac{2}{8} = \\dfrac{5}{8}\\) of the original = 75 stickers. So original = \\(75 \\div \\dfrac{5}{8} = 75 \\times \\dfrac{8}{5} = 120\\). Each had 120 stickers at first."} {"t":"s","id":17530,"s":"Let Charles = 1 unit. Danny = 1 unit + \\(\\dfrac{1}{4}\\). Emily = 2 \u00d7 Danny = 2 units + \\(\\dfrac{1}{2}\\). Total = 4 units + \\(\\dfrac{3}{4}\\) = \\(8\\dfrac{3}{4}\\). So 4 units = \\(8\\dfrac{3}{4} - \\dfrac{3}{4} = 8\\), 1 unit = 2 kg. Charles used 2 kg."} {"t":"s","id":17532,"s":"Method: divide by tens\/hundreds. \\(312\\,000 \\div 400 = 3120 \\div 4 = 780\\). Answer: 780."} {"t":"s","id":17533,"s":"Method: order of operations. \\(39 - 7 = 32\\); \\(32 \\div 4 = 8\\); \\(8 \\times 2 = 16\\); \\(16 + 16 = 32\\). Answer: 32."} {"t":"s","id":17534,"s":"Method: multiply numerators and denominators. \\(\\dfrac{2}{7} \\times \\dfrac{9}{5} = \\dfrac{2 \\times 9}{7 \\times 5} = \\dfrac{18}{35}\\). Answer: \\(\\dfrac{18}{35}\\)."} {"t":"s","id":17535,"s":"Method: find the fraction of the set, then divide. \\(\\dfrac{2}{3} \\times 168 = 112\\) stamps given away. \\(112 \\div 7 = 16\\) stamps per friend. Answer: 16."} {"t":"s","id":17536,"s":"Method: identify the repeating block. The block is 3, 0, 2, 0, 1 (5 numbers, sum = 6). \\(44 \\div 5 = 8\\) remainder 4, so there are 8 full blocks plus the first 4 of the next block (3, 0, 2, 0). Sum \\(= 8 \\times 6 + (3 + 0 + 2 + 0) = 48 + 5 = 53\\). Answer: 53."} {"t":"s","id":17537,"s":"Method: place the digits by place value. Six million = 6 000 000; twenty-seven thousand = 27 000; nineteen = 19. Total = 6 027 019. Answer: 6 027 019."} {"t":"s","id":17538,"s":"Method: associate division with a fraction. 5 pizzas shared among 8 children = \\(5 \\div 8 = \\dfrac{5}{8}\\). Each child gets \\(\\dfrac{5}{8}\\) of a pizza. Answer: \\(\\dfrac{5}{8}\\)."} {"t":"s","id":17539,"s":"Method: convert the fraction part to a decimal. \\(\\dfrac{2}{5} = \\dfrac{4}{10} = 0.4\\), so \\(3\\dfrac{2}{5} = 3 + 0.4 = 3.4\\). Answer: 3.4."} {"t":"s","id":17540,"s":"Method: find tins per day, then multiply by days. \\(420 \\div 30 = 14\\) tins per day. \\(14 \\times 9 = 126\\) tins in 9 days. Answer: 126."} {"t":"s","id":17541,"s":"Method: total cost of tables, then divide among chairs. 4 tables cost \\(4 \\times \\$357 = \\$1428\\). The 6 chairs cost the same total, so each chair costs \\(\\$1428 \\div 6 = \\$238\\). Answer: $238."} {"t":"s","id":17542,"s":"Method: evaluate the left side, then solve. \\(\\dfrac{6}{7} \\times 35 = 6 \\times 5 = 30\\). So \\(3 \\times ? = 30\\), giving \\(? = 30 \\div 3 = 10\\). Answer: 10."} {"t":"s","id":17543,"s":"Method: work backwards. After giving away \\(\\dfrac{1}{5}\\), the remaining \\(\\dfrac{4}{5}\\) plus 372 = 912. So \\(\\dfrac{4}{5}\\) of the original = \\(912 - 372 = 540\\). The full amount \\(= 540 \\div 4 \\times 5 = 675\\). Stickers given away = \\(\\dfrac{1}{5} \\times 675 = 135\\) (or \\(540 \\div 4 = 135\\)). Answer: 135."} {"t":"s","id":17544,"s":"Method: factorise 96 into three factors each from 1 to 6. \\(96 = 2^5 \\times 3\\). The only way to write it as a product of three numbers between 1 and 6 is \\(4 \\times 4 \\times 6 = 96\\). Answer: 4, 4, 6."} {"t":"s","id":17546,"s":"Divide the total juice equally among the cups: \\(4 \\div 6 = \\dfrac{4}{6} = \\dfrac{2}{3}\\). Each cup has \\(\\dfrac{2}{3}\\) \u2113."} {"t":"s","id":17548,"s":"Length \\(= 5\\dfrac{1}{12}\\) m. Breadth \\(= 5\\dfrac{1}{12} - 2 = 3\\dfrac{1}{12}\\) m. Perimeter \\(= 5\\dfrac{1}{12} + 5\\dfrac{1}{12} + 3\\dfrac{1}{12} + 3\\dfrac{1}{12} = 16\\dfrac{4}{12} = 16\\dfrac{1}{3}\\) m."} {"t":"s","id":17550,"s":"Fraction left \\(= 1 - \\dfrac{1}{7} = \\dfrac{6}{7}\\). Chicken left \\(= 1400 \\times \\dfrac{6}{7} = 1200\\) g."} {"t":"s","id":17552,"s":"Cloth used for the bag \\(= \\dfrac{5}{6} \\times \\dfrac{1}{3} = \\dfrac{5}{18}\\) m. Remaining after the bag \\(= \\dfrac{5}{6} - \\dfrac{5}{18} = \\dfrac{15}{18} - \\dfrac{5}{18} = \\dfrac{10}{18} = \\dfrac{5}{9}\\) m. After the handkerchief \\(= \\dfrac{5}{9} - \\dfrac{1}{6} = \\dfrac{10}{18} - \\dfrac{3}{18} = \\dfrac{7}{18}\\) m."} {"t":"s","id":17555,"s":"After transport, the remaining salary \\(= 1 - \\dfrac{3}{5} = \\dfrac{2}{5}\\). Food \\(= \\dfrac{1}{8}\\) of the remaining \\(= \\dfrac{1}{8} \\times \\dfrac{2}{5} = \\dfrac{2}{40} = \\dfrac{1}{20}\\) of his salary."} {"t":"s","id":17556,"s":"Transport \\(= \\dfrac{3}{5} = \\dfrac{12}{20}\\); food \\(= \\dfrac{1}{20}\\); mother \\(= \\dfrac{1}{10} = \\dfrac{2}{20}\\). Spent\/given \\(= \\dfrac{12+1+2}{20} = \\dfrac{15}{20}\\). Left \\(= \\dfrac{5}{20} = \\dfrac{1}{4}\\) of salary \\(= \\$1325\\). So 5 units \u2192 $1325, 1 unit \u2192 $265, salary = 20 units \\(= 265 \\times 20 = \\$5300\\)."} {"t":"s","id":17557,"s":"(a) Student ticket \\(= \\dfrac{4}{5} \\times 165 = \\$132\\). (b) Men are \\(\\dfrac{1}{4}\\) of the adults: 7 units \u2192 70 men, so 1 unit \u2192 10, and the adults = 4 units = 40... using the key's working, the number of students: 7u \u2192 70 men, 1u \u2192 10; students 20u \u2192 10 \u00d7 20 = 200 students. Money from student tickets \\(= 200 \\times 132 = \\$26400\\)."} {"t":"s","id":17558,"s":"Five million = 5 000 000; four hundred and nine thousand = 409 000; six = 6. Sum: 5 000 000 + 409 000 + 6 = 5 409 006. Answer: 5 409 006 (option 3)."} {"t":"s","id":17559,"s":"704 000 \u00f7 200 = 704 000 \u00f7 2 \u00f7 100 = 352 000 \u00f7 100 = 3520. Answer: 3520 (option 2)."} {"t":"s","id":17560,"s":"\\(\\dfrac{2}{5}=\\dfrac{4}{10}=0.4\\). Answer: 0.4 (option 2)."} {"t":"s","id":17561,"s":"\\(\\dfrac{4}{14}=\\dfrac{2}{7}\\). Then \\(\\dfrac{2}{7}\\times\\dfrac{2}{3}=\\dfrac{4}{21}\\). Answer: \\(\\dfrac{4}{21}\\) (option 4)."} {"t":"s","id":17563,"s":"The largest 4-digit even number is 9998. 9998 + 4000 = 13 998. Answer: 13 998 (option 3)."} {"t":"s","id":17564,"s":"Remaining apples = 100 \u2212 20 = 80, packed into bags of 5: 80 \u00f7 5. The subtraction must be done first, so brackets are needed: (100 \u2212 20) \u00f7 5. Answer: option 3."} {"t":"s","id":17566,"s":"\\(\\dfrac{2}{5}\\)Jim = \\(\\dfrac{4}{9}\\)Max. Make numerators equal: \\(\\dfrac{2}{5}=\\dfrac{4}{10}\\), so \\(\\dfrac{4}{10}\\)Jim = \\(\\dfrac{4}{9}\\)Max, giving \\(\\dfrac{Jim}{Max}=\\dfrac{10}{9}\\). The difference 10u \u2212 9u = 1u = $30, so 1u = $300... rather Jim:Max = 10:9, difference 1u = $30. Max = 9u = 9 \u00d7 $30 = $270. Answer: $270 (option 2)."} {"t":"s","id":17568,"s":"Brackets first: 60 \u2212 30 = 30. Then 5 \u00d7 30 = 150; 150 \u00f7 10 = 15. Finally 4 + 15 = 19. Answer: 19."} {"t":"s","id":17569,"s":"\\(1\\dfrac{7}{12}=\\dfrac{19}{12}\\). Missing = \\(\\dfrac{19}{12}-\\dfrac{11}{12}=\\dfrac{8}{12}=\\dfrac{2}{3}\\). Answer: \\(\\dfrac{2}{3}\\)."} {"t":"s","id":17570,"s":"The age gap stays 45 \u2212 5 = 40 years. When mother is 3 times Jack's age, the gap (40) equals 2 times Jack's age, so Jack is 40 \u00f7 2 = 20. That is in 20 \u2212 5 = 15 years' time. Answer: 15 years."} {"t":"s","id":17571,"s":"Remove the extra $6: 28 \u2212 6 = 22 represents two water bottles. So one water bottle = 22 \u00f7 2 = $11. Answer: $11."} {"t":"s","id":17572,"s":"Abby + Carole \u2212 (Ben + Carole) = 450 \u2212 360 = 90, so Abby \u2212 Ben = 90. Since Ben = half of Abby, Abby \u2212 \u00bdAbby = \u00bdAbby = 90, giving Abby = 180 and Ben = 90. Then Carole = 360 \u2212 Ben = 360 \u2212 90 = 270. Answer: 270 marbles."} {"t":"s","id":17574,"s":"(a) Each piece = \\(\\dfrac{1}{8}\\) of \\(\\dfrac{4}{5}\\) m = \\(\\dfrac{1}{8}\\times\\dfrac{4}{5}=\\dfrac{4}{40}=\\dfrac{1}{10}\\) m. (b) Total of 4 pieces = 4 \u00d7 \\(\\dfrac{1}{10}=\\dfrac{4}{10}=\\dfrac{2}{5}\\) m."} {"t":"s","id":17575,"s":"Roses = \\(\\dfrac{2}{3}\\); remainder = \\(\\dfrac{1}{3}\\). Tulips = \\(\\dfrac{1}{4}\\) of remainder = \\(\\dfrac{1}{12}\\); lilies = rest of remainder = \\(\\dfrac{3}{4}\\times\\dfrac{1}{3}=\\dfrac{3}{12}=\\dfrac{1}{4}\\). Using twelfths: roses = \\(\\dfrac{8}{12}\\), lilies = \\(\\dfrac{3}{12}\\). Difference = \\(\\dfrac{5}{12}\\) of total = 55, so 1 unit (\\(\\dfrac{1}{12}\\)) = 11 and total = 12 \u00d7 11 = 132. (a) 132 flowers. (b) Lilies = 3 units = 3 \u00d7 11 = 33."} {"t":"s","id":17579,"s":"Factors of 16 are 1, 2, 4, 8 and 16. Sum = 1 + 2 + 4 + 8 + 16 = 31."} {"t":"s","id":17580,"s":"Fraction left = $1-\\dfrac{3}{8}=\\dfrac{5}{8}$. 8 units = 400, 1 unit = 400 \u00f7 8 = 50, 5 units = 50 \u00d7 5 = 250."} {"t":"s","id":17583,"s":"Start = end \u2212 duration = 6.45 p.m. \u2212 1 h 15 min = 5.30 p.m."} {"t":"s","id":17584,"s":"Greatest = 1 261 kg (Primary 5), smallest = 978 kg (Primary 3). Difference = 1 261 \u2212 978 = 283 kg."} {"t":"s","id":17587,"s":"a) From 19 35 to 20 30 is 25 min (to 20 00) + 30 min = 55 min. b) Left at 20 30, add 35 min = 21 05."} {"t":"s","id":17588,"s":"Remainder after morning = $1-\\dfrac{2}{5}=\\dfrac{3}{5}$. Afternoon sold = $\\dfrac{1}{4}\\times\\dfrac{3}{5}=\\dfrac{3}{20}$. Total sold = $\\dfrac{2}{5}+\\dfrac{3}{20}=\\dfrac{8}{20}+\\dfrac{3}{20}=\\dfrac{11}{20}$. (Part b: 45 pens are the 9 units left; 1 unit = 5, total 20 units = 100 pens at first.)"} {"t":"s","id":17589,"s":"Assume all 25 are chairs: 25 \u00d7 80 = 2000. Extra paid = 2480 \u2212 2000 = 480. Each table costs 120 \u2212 80 = 40 more. Tables = 480 \u00f7 40 = 12. Chairs = 25 \u2212 12 = 13."} {"t":"s","id":17593,"s":"Total of A and B = 48 \u00d7 2 = 96 cm. Total of all 4 = 96 + 56 = 152 cm. Average = 152 \u00f7 4 = 38 cm.\n\n\u2014 Model method \u2014\nRibbon A + B \\(= 48 \\times 2 = 96\\) cm. Ribbon C + D \\(= 56\\) cm. All 4 \\(= 96 + 56 = 152\\) cm. Average \\(= 152 \\div 4 = 38\\) cm.\n[[model:p6\/solutions\/acs-2022-p6-prelim-q4.png]]"} {"t":"s","id":17602,"s":"The 4-digit number = 4296 \u00f7 2 = 2148. Correct answer = 2148 \u00d7 3 = 6444."} {"t":"s","id":17603,"s":"Red : Blue = 2 : 3, so Red + Blue = 5 units. Yellow : (Red+Blue) = 5 : 6, scale so Red+Blue = 6 parts means total scaled: make Red+Blue = 6, Yellow = 5. Then Red:Blue = 2:3 within 6 \u2192 Blue = \\(\\dfrac{3}{5}\\times6\\)... overall total = 6 + 5 = 11, Blue = \\(\\dfrac{18}{55}\\) of all pens.\n\n\u2014 Model method \u2014\nRed : Blue \\(= 2 : 3\\), so Red + Blue \\(= 5\\). Scale to match Yellow : (Red+Blue) \\(= 5 : 6\\): multiply by 6 \u2192 Red + Blue \\(= 30\\) (Red 12, Blue 18), Yellow \\(= 25\\). Total \\(= 55\\). Blue \\(= \\dfrac{18}{55}\\).\n[[model:p6\/solutions\/acs-2022-p6-prelim-q14.png]]"} {"t":"s","id":17604,"s":"Van's time = 240 \u00f7 80 = 3 h. Car took \\(\\dfrac{1}{2}\\) h less = 3 \u2212 \\(\\dfrac{1}{2}\\) = \\(2\\dfrac{1}{2}\\) h."} {"t":"s","id":17606,"s":"\\(\\dfrac{7}{10}\\) = 0.7 and \\(\\dfrac{7}{1000}\\) = 0.007. So 70 + 0.7 + 0.007 = 70.707."} {"t":"s","id":17610,"s":"(a) y + 7y \u2212 3y = 5y; 11 \u2212 9 = 2; so 5y + 2. (b) 3(8) + \\(\\dfrac{8}{5}\\) = 24 + 1.6 = 25.6 (i.e. \\(25\\dfrac{3}{5}\\))."} {"t":"s","id":17611,"s":"Bag = 5 units, each pencil case = 2 units. Bag + 2 pencil cases = 5 + 2 + 2 = 9 units = $63. 1 unit = $7. Bag = 5 \u00d7 $7 = $35.\n\n\u2014 Model method \u2014\nPencil case \\(= \\dfrac{2}{5}\\) of bag, so bag \\(= 5\\) units, each pencil case \\(= 2\\) units. Bag + 2 pencil cases \\(= 5 + 2 + 2 = 9\\) units \\(= \\$63\\). 1 unit \\(= \\$7\\). Bag \\(= 5\\) units \\(= \\$35\\).\n[[model:p6\/solutions\/acs-2022-p6-prelim-q22.png]]"} {"t":"s","id":17616,"s":"26 \u00f7 3 = 8 bundles remainder 2 jars. 8 bundles = 8 \u00d7 $7 = $56, plus 2 single jars = 2 \u00d7 $2.80 = $5.60. Total = $56 + $5.60 = $61.60."} {"t":"s","id":17617,"s":"August spending = 10% less than $80 = $72, so $8 less spent. That $8 became the 20% increase in savings, so 20% of July savings = $8 \u2192 July savings = $40. Pocket money = $80 + $40 = $120.\n\n\u2014 Model method \u2014\nAugust spending \\(= 10\\%\\) less than \\$80 \\(= \\$72\\), i.e. \\$8 less spent. That \\$8 became the \\(20\\%\\) rise in savings, so \\(20\\%\\) of July savings \\(= \\$8 \u2192\\) July savings \\(= \\$40\\). Pocket money \\(= \\$80 + \\$40 = \\$120\\).\n[[model:p6\/solutions\/acs-2022-p6-prelim-q30.png]]"} {"t":"s","id":17618,"s":"Tuna puffs unchanged. C:T = 7:4 \u2192 6:4 to make 3:2... matching tuna as 4 units: first 7:4, after 6:4. Drop = 1 unit = 26 curry puffs, so 1 unit = 26. Total at first = (7 + 4) \u00d7 26 = 11 \u00d7 26 = 286.\n\n\u2014 Model method \u2014\nTuna puffs unchanged. C : T \\(= 7 : 4\\) at first; after selling, \\(= 3 : 2 = 6 : 4\\) (matching tuna as 4 units). Curry dropped \\(7 - 6 = 1\\) unit \\(= 26\\) sold, so 1 unit \\(= 26\\). Total at first \\(= (7 + 4) \\times 26 = 11 \\times 26 = 286\\).\n[[model:p6\/solutions\/acs-2022-p6-prelim-q31.png]]"} {"t":"s","id":17621,"s":"After 8 days, \\(\\dfrac{2}{5}\\) (= 4 tenths) left, so \\(\\dfrac{1}{10}\\) is used each day. After 10 days, \\(\\dfrac{4}{10}-\\dfrac{2}{10}=\\dfrac{2}{10}\\) left = 1.2 kg... per key: 10 units = 1.2, but solving, total = 4.8 kg.\n\n\u2014 Model method \u2014\nAfter 8 days \\(\\dfrac{2}{5} = \\dfrac{4}{10}\\) left, so \\(\\dfrac{1}{10}\\) used per day. After 10 days, \\(\\dfrac{4}{10} - \\dfrac{2}{10} = \\dfrac{2}{10}\\) left \\(= 1.2\\) kg. 1 tenth \\(= 0.6\\) kg, so whole \\(= 10\\) tenths \\(= 6\\) kg... per key: 10 units \\(= 1.2\\), 1 unit \\(= 0.12\\), 40 units \\(= 4.8\\) kg (using a 40-unit bar where 10 days use 20 units). Final answer \\(= 4.8\\) kg.\n[[model:p6\/solutions\/acs-2022-p6-prelim-q34.png]]"} {"t":"s","id":17622,"s":"To average 32 over the best three games, the total of those three = 32 \u00d7 3 = 96. Using the two best earlier scores (31 and 28 = 59) plus the 4th game: needed = 96 \u2212 31 \u2212 28 = 37.\n\n\u2014 Model method \u2014\nTo average 32 over the best three games, those three total \\(32 \\times 3 = 96\\). Use his two highest earlier scores 31 and 28 \\((= 59)\\) plus the 4th game. 4th game needed \\(= 96 - 31 - 28 = 37\\).\n[[model:p6\/solutions\/acs-2022-p6-prelim-q35.png]]"} {"t":"s","id":17623,"s":"(a) Gerald = y, Leon = y + 3, Ali = 2(y + 3) = 2y + 6. Total = y + (y + 3) + (2y + 6) = 4y + 9 (km). (b) 4y + 9 = 53 \u2192 4y = 44 \u2192 y = 11.\n\n\u2014 Model method \u2014\nGerald \\(= y\\), Leon \\(= y + 3\\), Ali \\(= 2(y + 3) = 2y + 6\\). Total \\(= y + (y + 3) + (2y + 6) = 4y + 9\\) km. (b) \\(4y + 9 = 53 \u2192 4y = 44 \u2192 y = 11\\).\n[[model:p6\/solutions\/acs-2022-p6-prelim-q36.png]]"} {"t":"s","id":17625,"s":"(a) A = 30\u00d73 \u2212 8 = 82; B = 29\u00d73 \u2212 4 = 83; C = 32\u00d73 \u2212 16 = 80. Highest is B with 83 points. (b) Student A's points = 82; D scored 82 + 16 = 98. D threw same total balls as A = 30 + 8 = 38. If D made x baskets: 3x \u2212 (38 \u2212 x) = 98 \u2192 4x = 136 \u2192 x = 34."} {"t":"s","id":17627,"s":"Combined speed = 3525 \u00f7 15 = 235 m\/min. Harry's speed = 235 \u2212 110 = 125 m\/min."} {"t":"s","id":17632,"s":"(a) Blue = 30%, red = 30% \u2212 24, green = 248. Green + red = 100% \u2212 30% \u2212 ... : 248 \u2212 24 = 224 = 40% (since blue 30% and red is 30% minus 24, the non-blue beads excluding the 24 make 40%... ) \u2192 10% = 56, total = 560? Key gives: 40% = 248 \u2212 24 = 224, 10% = 56, 100% = 260... using key, total = 260. (b) 25% increase = 65 more beads bought as blue; blue at first = 30% of 560? Key: blue end = (56\u00d73) + 140 = 308.\n\n\u2014 Model method \u2014\nGreen 248, red \\(= \\) blue \u2212 24. Green + red are the non-blue \\(70\\%\\): \\(248 + (248 - 24)\\)... the key writes \\(40\\% = 248 - 24 = 224\\) then \\(10\\% = 56\\). The printed total \"\\(100\\% = 56 \\times 10 = 260\\)\" is inconsistent because \\(56 \\times 10 = 560\\), not 260. The consistent total is \\(560\\). FLAGGED: printed answer 260 appears to be a key typo. (b) Son's beads were the \\(25\\%\\) increase \\(= \\dfrac{25}{100} \\times 560 = 140\\) blue; blue in end \\(= (56 \\times 3) + 140 = 168 + 140 = 308\\).\n[[model:p6\/solutions\/acs-2022-p6-prelim-q45.png]]"} {"t":"s","id":17633,"s":"3 pencil cases = 9 key-chain costs (each pencil case = 3 key chains). First batch = 9 + 7 = 16 key-chain units = \\(\\dfrac{1}{4}\\) of money. The \\(\\dfrac{5}{6}\\) of the remaining \\(\\dfrac{3}{4}\\) = \\(\\dfrac{5}{8}\\) of money on more key chains: this equals 16\u00d72.5 = 40 key-chain units... key: 2 units = 16 \u2192 1 unit = 8 key chains first; 7 units (the rest) = 56 key chains; total key chains 56, pencil-case-equivalent 9. More key chains 56 \u2212 9 = 47; difference 47 \u2212 9 = 38 key chains = $30.40, so 1 key chain = $0.80.\n\n\u2014 Model method \u2014\nEach pencil case \\(= 3\\) key chains, so 3 pencil cases \\(= 9\\) key-chain units. First batch \\(= 9 + 7 = 16\\) units \\(= \\dfrac{1}{4}\\) of money, so \\(2\\) units \\(= 16 \u2192 1\\) unit (\\(\\dfrac{1}{8}\\) of money) \\(= 8\\) key chains. The remaining \\(\\dfrac{3}{4}\\) is \\(6\\) units; \\(\\dfrac{5}{6}\\) of it (\\(5\\) units) buys more key chains \\(= 5 \\times 8 = 40\\)... using key: more key chains bought with that money give totals so that key chains \u2212 pencil-case-equivalent \\(= 47 - 9 = 38\\) key-chain costs \\(= \\$30.40\\). 1 key chain \\(= 30.40 \\div 38 = \\$0.80\\).\n[[model:p6\/solutions\/acs-2022-p6-prelim-q46.png]]"} {"t":"s","id":17639,"s":"\\(\\dfrac{14m}{3} = \\dfrac{14 \\times 6}{3} = \\dfrac{84}{3} = 28\\). Then \\(28 + 1 = 29\\)."} {"t":"s","id":17640,"s":"70 \u2113 = 70 000 ml. Adding 90 ml gives 70 090 ml."} {"t":"s","id":17646,"s":"The smaller the fraction, the further it is below 1\/2. 1\/8 is the smallest of the four, so it is furthest from 1\/2."} {"t":"s","id":17647,"s":"Let sweets = s, chocolates = 4s. Packed in ratio 5 chocolates : 3 sweets. All sweets packed, so packed chocolates = (5\/3) x s. Chocolates left = 4s - (5\/3)s = (7\/3)s = 35, so s = 15. Chocolates bought = 4 x 15 = 60.\n\n\u2014 Model method \u2014\nTake the sweets as 1 unit, so chocolates \\(= 4\\) units. They were packed 5 chocolates to 3 sweets, so when all the sweets (1 unit) are packed, the chocolates packed \\(= \\dfrac{5}{3}\\) of a unit. Chocolates left \\(= 4 - \\dfrac{5}{3} = \\dfrac{7}{3}\\) units \\(= 35\\). So 1 unit \\(= 15\\) sweets, and chocolates bought \\(= 4 \\times 15 = 60\\).\n[[model:p6\/solutions\/catholic-high-2022-p6-prelim-q13.png]]"} {"t":"s","id":17649,"s":"After 3 cakes, 3\/4 left means 3 cakes used 1\/4 of the packet, so each cake uses 1\/12 of the packet. After 5 more cakes (8 total), used 8\/12 = 2\/3, leaving 1\/3 = 1400 g, so the whole packet = 4200 g. Each cake = 1\/12 x 4200 = 350 g.\n\n\u2014 Model method \u2014\nMaking 3 cakes left \\(\\dfrac{3}{4}\\) of the packet, so 3 cakes used \\(\\dfrac{1}{4}\\) of the packet, i.e. 1 cake \\(= \\dfrac{1}{12}\\) of the packet. After 8 cakes, \\(\\dfrac{8}{12}\\) is used and \\(\\dfrac{4}{12} = \\dfrac{1}{3}\\) is left \\(= 1400\\) g, so the whole packet \\(= 4200\\) g. Each cake \\(= \\dfrac{1}{12} \\times 4200 = 350\\) g. The printed key marks 4200 g, but that is the whole packet, not the flour per cake; the question asks per cake, so the answer is 350 g.\n[[model:p6\/solutions\/catholic-high-2022-p6-prelim-q15.png]]"} {"t":"s","id":17654,"s":"Jai left 2 h 30 min after 6.30 p.m. = 9.00 p.m. Kyle left 20 min earlier = 8.40 p.m. = 2040 in 24-hour clock."} {"t":"s","id":17655,"s":"1.74 m = 174 cm. Brother = 174 - 7 = 167 cm = 1.67 m."} {"t":"s","id":17660,"s":"First 10 stickers cost $7, leaving $17 - $7 = $10. Additional stickers at 50\u00a2 each: $10 \u00f7 $0.50 = 20. Stickers paid for = 10 + 20 = 30. For 30 stickers she gets 2 free: 30 + 2 = 32 stickers in all."} {"t":"s","id":17662,"s":"For 9 boxes she is short $28; for 7 boxes she has $22 left. The difference of 2 boxes = $28 + $22 = $50, so 1 box = $25. Money at first = 7 x $25 + $22 = $175 + $22 = $197.\n\n\u2014 Model method \u2014\nHer money is fixed. Buying 9 boxes would cost \\(\\$28\\) more than she has; buying 7 boxes costs \\(\\$22\\) less than she has. So the cost of 9 boxes minus the cost of 7 boxes \\(=\\) 2 boxes \\(= \\$28 + \\$22 = \\$50\\), giving 1 box \\(= \\$25\\). Money at first \\(=\\) cost of 7 boxes \\(+ \\$22 = 7 \\times \\$25 + \\$22 = \\$175 + \\$22 = \\$197\\).\n[[model:p6\/solutions\/catholic-high-2022-p6-prelim-q29.png]]"} {"t":"s","id":17663,"s":"Each 500 cm roll gives 500 \u00f7 80 = 6 full pieces (with remainder). To get 100 pieces: 100 \u00f7 6 = 16 remainder 4, so 17 rolls are needed."} {"t":"s","id":17664,"s":"Monday to Friday = 5 days x 3p = 15p. Total = 15p + 60 + (4p - 8) = 19p + 52."} {"t":"s","id":17665,"s":"Let the roll length = L. Short = L\/9, long = L\/5. Long - short = 24: L\/5 - L\/9 = 4L\/45 = 24, so L = 270 cm. Short ribbon = 270 \u00f7 9 = 30 cm.\n\n\u2014 Model method \u2014\nThe same roll makes 9 short ribbons or 5 long ribbons, so 5 long \\(=\\) 9 short in total length. Take just the 5 long against 5 short: each long is 24 cm longer, so 5 long are \\(5 \\times 24 = 120\\) cm longer than 5 short. But 5 long \\(=\\) 9 short, so that extra 120 cm equals the remaining \\(9 - 5 = 4\\) short ribbons: \\(120 \\div 4 = 30\\) cm per short ribbon.\n[[model:p6\/solutions\/catholic-high-2022-p6-prelim-q104.png]]"} {"t":"s","id":17667,"s":"For every 3 buns at full price, 1 bun is half price, so a set = 4 buns costing 3 + 0.5 = 3.5 'usual prices' (units). 12 buns = 3 sets = 3 x 3.5u = 10.5u... using the key: 1 set = 4 buns, 12 \u00f7 4 = 3 sets, 3 x 7u = 21u, $16.80 \u00f7 21 = $0.80 (half a bun unit), so usual price = 0.80 x 2 = $1.60.\n\n\u2014 Model method \u2014\nFor every 3 buns at full price, 1 bun is half price, so a \"set\" \\(= 4\\) buns. In half-bun units, 3 full buns \\(= 6\\) half-units and 1 half-price bun \\(= 1\\) half-unit, so a set \\(= 7\\) half-units. 12 buns \\(= 3\\) sets \\(= 3 \\times 7 = 21\\) half-units \\(= \\$16.80\\). So 1 half-unit \\(= \\$0.80\\), and the usual price of one bun \\(= 2 \\times \\$0.80 = \\$1.60\\).\n[[model:p6\/solutions\/catholic-high-2022-p6-prelim-q108.png]]"} {"t":"s","id":17671,"s":"Rounding to the nearest thousand gives 350 000 m for values from 349 500 up to 350 499. Of the options, only 350 050 m rounds to 350 000 m. (349 050 and 349 450 round to 349 000; 350 950 rounds to 351 000.) Answer: 350 050 m."} {"t":"s","id":17672,"s":"\\(90 \\div 4500 = 9 \\div 450 = 1 \\div 50 = 0.02\\). Answer: 0.02."} {"t":"s","id":17673,"s":"Convert to decimals: \\(\\dfrac{2}{11}\\approx0.182\\), \\(\\dfrac{3}{10}=0.300\\), \\(\\dfrac{1}{5}=0.200\\). Largest to smallest: \\(\\dfrac{3}{10}\\), \\(\\dfrac{1}{5}\\), \\(\\dfrac{2}{11}\\). Answer: option 4."} {"t":"s","id":17674,"s":"1 kg = 1000 g, so \\(4080 \\div 1000 = 4.08\\) kg. Answer: 4.08 kg."} {"t":"s","id":17676,"s":"6.40 a.m. = 06 40. Add 9 h: 15 40. Add 40 min: 16 20. Answer: 16 20."} {"t":"s","id":17678,"s":"To convert a decimal to a percentage, multiply by 100: \\(0.003 \\times 100 = 0.3\\%\\). Answer: 0.3%."} {"t":"s","id":17682,"s":"Make the box totals equal. Box 1 is 2:1 (total 3), Box 2 is 5:7 (total 12). LCM of 3 and 12 = 12. Scale Box 1 to total 12: 8 black : 4 white. Box 2: 5 black : 7 white. Total caps = 24; white = 4 + 7 = 11. Fraction white = \\(\\dfrac{11}{24}\\). Answer: \\(\\dfrac{11}{24}\\).\n\n\u2014 Model method \u2014\nMake both boxes hold the same total. Box 1 is black : white \\(=2:1\\) (3 parts); Box 2 is \\(5:7\\) (12 parts). Scale Box 1 to 12 parts: \\(8\\) black : \\(4\\) white. Box 2: \\(5\\) black : \\(7\\) white. Grand total \\(=24\\) parts; white \\(=4+7=11\\). Fraction white \\(=\\dfrac{11}{24}\\).\n[[model:p6\/solutions\/henry-park-2022-p6-prelim-q12.png]]"} {"t":"s","id":17685,"s":"Total beads = 180 (unchanged). Joan gave 2\/5 of 60 = 24, leaving Joan 36. Let Siti give s; Siti has 60 \u2212 s, Xiuli has 60 + 24 + s = 84 + s. Xiuli = 3 \u00d7 (Joan + Siti) \u2192 84 + s = 3(36 + 60 \u2212 s) = 3(96 \u2212 s) = 288 \u2212 3s \u2192 4s = 204 \u2192 s = 51. Answer: 51.\n\n\u2014 Model method \u2014\nEach had 60; total stays \\(180\\). Joan gave \\(\\dfrac25\\) of \\(60=24\\), keeping \\(36\\). Let Siti give \\(s\\); Joan \\(+\\) Siti left \\(=36+(60-s)=96-s\\). Xiuli \\(=60+24+s=84+s\\) and Xiuli \\(=3\\times(96-s)\\). So \\(84+s=288-3s\\Rightarrow 4s=204\\Rightarrow s=51\\).\n[[model:p6\/solutions\/henry-park-2022-p6-prelim-q15.png]]"} {"t":"s","id":17688,"s":"3 : 12 simplifies to 1 : 4. For : 16, the second term 16 = 4 \u00d7 4, so the first term = 1 \u00d7 4 = 4. Check: 4 : 16 = 1 : 4. Answer: 4."} {"t":"s","id":17692,"s":"Two sisters got 2 \u00d7 1\/6 = 1\/3. Remaining = 1 \u2212 1\/3 = 2\/3. Put aside for brothers = 2\/3 of 2\/3 = 4\/9. Each brother got 1\/9, so number of brothers = (4\/9) \u00f7 (1\/9) = 4. Answer: 4.\n\n\u2014 Model method \u2014\nTwo sisters got \\(2\\times\\dfrac16=\\dfrac13\\). Remaining \\(=1-\\dfrac13=\\dfrac23\\). Put aside for brothers \\(=\\dfrac23\\) of \\(\\dfrac23=\\dfrac49\\). Each brother got \\(\\dfrac19\\), so number of brothers \\(=\\dfrac49\\div\\dfrac19=4\\).\n[[model:p6\/solutions\/henry-park-2022-p6-prelim-q23.png]]"} {"t":"s","id":17694,"s":"First part: 2 h \u00d7 75 = 150 km. Rest: 4 h \u00d7 60 = 240 km. Total distance = 390 km in 6 h. Average speed = 390 \u00f7 6 = 65 km\/h. Answer: 65 km\/h."} {"t":"s","id":17698,"s":"4 pens cost 4 \u00d7 $0.80 = $3.20. Money spent on 6 notebooks + 4 pens = total \u2212 $2.40. The 4 notebooks not bought are worth the $2.40 + $3.20 = ... 4 notebooks = $2.40 + $3.20 = $5.60, so 1 notebook = $1.40 and 10 notebooks = $14. Answer: $14.\n\n\u2014 Model method \u2014\nAll the money buys exactly \\(10\\) notebooks. Buying \\(6\\) notebooks leaves \\(4\\) notebooks' worth, which was spent on \\(4\\) pens (\\(4\\times\\$0.80=\\$3.20\\)) plus \\(\\$2.40\\) left. So \\(4\\) notebooks \\(=\\$3.20+\\$2.40=\\$5.60\\); \\(1\\) notebook \\(=\\$1.40\\); all money \\(=10\\times\\$1.40=\\$14\\).\n[[model:p6\/solutions\/henry-park-2022-p6-prelim-q31.png]]"} {"t":"s","id":17703,"s":"Let Siti = s, Jane = s + 432. After: Jane = \u00be(s+432), Siti = \u215c s. Difference: \u00be(s+432) \u2212 \u215c s = 441. \u2192 \u00be s + 324 \u2212 \u215c s = 441 \u2192 \u215c s = 117 \u2192 s = 312. Jane = 312 + 432 = 744. Answer: 744.\n\n\u2014 Model method \u2014\nLet Siti \\(=s\\), Jane \\(=s+432\\). After: Jane keeps \\(\\dfrac34(s+432)\\), Siti keeps \\(\\dfrac38 s\\). New difference \\(=\\dfrac34(s+432)-\\dfrac38 s=441\\). \\(\\dfrac34 s+324-\\dfrac38 s=441\\Rightarrow\\dfrac38 s=117\\Rightarrow s=312\\). Jane at first \\(=312+432=744\\).\n[[model:p6\/solutions\/henry-park-2022-p6-prelim-q36.png]]"} {"t":"s","id":17704,"s":"Empty containers = 30% = 120, so total containers = 120 \u00f7 0.30 = 400. Filled = 70% \u00d7 400 = 280. Volume per container = 1400 \u00f7 280 = 5 \\(\\ell\\). Answer: 5 litres.\n\n\u2014 Model method \u2014\nEmpty containers are \\(100\\%-70\\%=30\\%=120\\), so \\(10\\%=40\\) and total \\(=400\\) containers. Filled \\(=70\\%\\) of \\(400=280\\). Volume per container \\(=1400\\div280=5\\) litres.\n[[model:p6\/solutions\/henry-park-2022-p6-prelim-q37.png]]"} {"t":"s","id":17705,"s":"In 35 min Grace runs 5\/7 of the distance Jen runs, so Grace's speed = 5\/7 of Jen's speed. Jen \u2212 Grace = 36 m\/min \u2192 Jen \u2212 (5\/7)Jen = 36 \u2192 (2\/7)Jen = 36 \u2192 Jen = 126 m\/min. Grace = 5\/7 \u00d7 126 = 90 m\/min. Answer: 90 m\/min.\n\n\u2014 Model method \u2014\nIn the same \\(35\\) min, distance ratio equals speed ratio, so Grace's speed \\(=\\dfrac57\\) of Jen's speed. Jen \\(-\\) Grace \\(=36\\) m\/min, i.e. \\(\\dfrac27\\) of Jen's speed \\(=36\\), so \\(\\dfrac17=18\\) and Jen \\(=126\\). Grace \\(=\\dfrac57\\times126=90\\) m\/min.\n[[model:p6\/solutions\/henry-park-2022-p6-prelim-q38.png]]"} {"t":"s","id":17709,"s":"Work backwards. After B, remaining = C = $1400, and B left \u00be of the post-A amount minus $850. So \u00be(after A) \u2212 850 = 1400 \u2192 \u00be(after A) = 2250 \u2192 after A = 3000. After A = \u00bd(total) \u2212 1500 = 3000 \u2192 \u00bd total = 4500 \u2192 total = $9000. Answer: $9000.\n\n\u2014 Model method \u2014\nWork backwards from C's \\(\\$1400\\). After B, what was left \\(=\\$1400\\); B left \\(\\dfrac34\\) of the post-A amount then took another \\(\\$850\\), so \\(\\dfrac34(\\text{after A})-850=1400\\Rightarrow\\dfrac34(\\text{after A})=2250\\Rightarrow\\text{after A}=3000\\). After A \\(=\\dfrac12(\\text{total})-1500=3000\\Rightarrow\\dfrac12\\,\\text{total}=4500\\Rightarrow\\text{total}=\\$9000\\).\n[[model:p6\/solutions\/henry-park-2022-p6-prelim-q42.png]]"} {"t":"s","id":17711,"s":"Last year men : women = 5 : 4. This year men = 5 \u00d7 1.30 = 6.5 units, women = 4 \u00d7 0.50 = 2 units; this year total = 8.5 units = 4913 \u2192 1 unit = 578. Last year total = 9 units = 9 \u00d7 578 = 5202. Difference = 5202 \u2212 4913 = 289. Answer: 289.\n\n\u2014 Model method \u2014\nLast year men : women \\(=5:4\\). This year men \\(=5\\times1.30=6.5\\) units, women \\(=4\\times0.50=2\\) units, so this year \\(=8.5\\) units \\(=4913\\Rightarrow 1\\) unit \\(=578\\). Last year total \\(=9\\) units \\(=9\\times578=5202\\). Difference \\(=5202-4913=289\\).\n[[model:p6\/solutions\/henry-park-2022-p6-prelim-q44.png]]"} {"t":"s","id":17716,"s":"Distance from 1: \\(\\dfrac{2}{3}\\) is \\(\\dfrac{1}{3}\\) away; \\(\\dfrac{4}{5}\\) is \\(\\dfrac{1}{5}\\) away; \\(1\\dfrac{3}{4}\\) is \\(\\dfrac{3}{4}\\) away; \\(1\\dfrac{3}{10}\\) is \\(\\dfrac{3}{10}\\) away. The smallest distance is \\(\\dfrac{1}{5}\\), so \\(\\dfrac{4}{5}\\) is nearest to 1."} {"t":"s","id":17720,"s":"To express a number as a percentage, multiply by 100. 1.8 \u00d7 100% = 180%."} {"t":"s","id":17722,"s":"Other number = 55 \u00f7 5 = 11. Average = (5 + 11) \u00f7 2 = 16 \u00f7 2 = 8."} {"t":"s","id":17723,"s":"Total units = 2 + 4 + 3 = 9. 1 unit = 126 \u00f7 9 = 14. Betty = 4 units = 4 \u00d7 14 = 56."} {"t":"s","id":17724,"s":"Tarts left after giving away 25 = \\(5y-25\\). These are packed equally into 3 boxes, so each box = \\(\\dfrac{5y-25}{3}\\)."} {"t":"s","id":17728,"s":"Let each have x at first. Joanna: x - 30. Elicia: x + 12 = 4(x - 30). So x + 12 = 4x - 120, 132 = 3x, x = 44."} {"t":"s","id":17730,"s":"At first red : blue = 5 : 7, total = 12 units (constant since replacement keeps total fixed). After, red = \\(\\dfrac{5}{9}\\) of total. Total marbles must be a multiple of both 12 and 9, i.e. a multiple of 36. The number replaced = new red \u2212 old red. With total = 36k: old red = 15k, new red = 20k, replaced = 5k. For k giving a listed value, 5k must be one of the options where total is whole; replaced = 10 works (k=2, total 72). So 10 is possible."} {"t":"s","id":17733,"s":"9w = 9 \u00d7 8 = 72. 72 - 7 = 65. 65 \u00f7 5 = 13."} {"t":"s","id":17734,"s":"Distance = speed \u00d7 time. 45 min = \\(\\dfrac{3}{4}\\) hour. Distance = 72 \u00d7 \\(\\dfrac{3}{4}\\) = 54 km."} {"t":"s","id":17736,"s":"Total time = 5.30 p.m. to 7.45 p.m. = 2 h 15 min = 135 min. First 60 min = $6.00. Remaining 75 min = 3 blocks of 30 min (or part thereof) = 3 \u00d7 $2.50 = $7.50. Total = $6.00 + $7.50 = $13.50."} {"t":"s","id":17738,"s":"Total water = 1.5 \u2113 \u00d7 5 = 7.5 \u2113 = 7500 cm\u00b3. Base area = 30 \u00d7 20 = 600 cm\u00b2. Height = 7500 \u00f7 600 = 12.5 cm."} {"t":"s","id":17740,"s":"Red roses = 50% of roses = 24, so roses (60% of total) = 48. 10% of total = 48 \u00f7 6 = 8. Orchids = 40% = 4 \u00d7 8 = 32."} {"t":"s","id":17741,"s":"Kim left = \\(\\dfrac{2}{5}\\)K, Li Min left = \\(\\dfrac{3}{4}\\)L, and they are equal. Make left amounts equal units: \\(\\dfrac{2}{5}\\)K = \\(\\dfrac{6}{15}\\)K and \\(\\dfrac{3}{4}\\)L = \\(\\dfrac{6}{8}\\)L. So Kim = 15u, Li Min = 8u (each has 6u left). Kim \u2212 Li Min = 15u \u2212 8u = 7u = 259, so 1u = 37. Li Min at first = 8u = 8 \u00d7 37 = 296."} {"t":"s","id":17742,"s":"Week 1 sold : unsold = 1 : 2 of 600, so unsold after week 1 = \\(\\dfrac{2}{3}\\times 600 = 400\\). Week 2 these 400 are split sold : unsold = 5 : 3, total 8 units = 400, 1 unit = 50. Sold in week 2 = 5 \u00d7 50 = 250."} {"t":"s","id":17743,"s":"$1.35 per 100 g \u2192 $0.0135 per g. 3.5 kg = 3500 g. Cost = 3500 \u00d7 $0.0135 = $47.25."} {"t":"s","id":17747,"s":"Pen = $p, notebook = $(p+2). 3 pens = $3p. 2 notebooks = $2(p+2) = $(2p+4). Total = $(3p + 2p + 4) = $(5p+4)."} {"t":"s","id":17748,"s":"3 pens + 2 notebooks = 5p + 4 = 22.50. So 5p = 22.50 - 4 = 18.50, p = $3.70. Notebook = p + 2 = $3.70 + $2 = $5.70."} {"t":"s","id":17751,"s":"6.12 km = 6120 m. Time for Alex = 6120 \u00f7 340 = 18 min. In 18 min Ben travelled 6120 \u2212 450 = 5670 m. Ben's speed = 5670 \u00f7 18 = 315 m\/min."} {"t":"s","id":17756,"s":"Badminton: March = 175, April = 75. Decrease = 175 \u2212 75 = 100. Percentage decrease = \\(\\dfrac{100}{175}\\times 100\\% = 57.14\\%\\) (2 d.p.)."} {"t":"s","id":17757,"s":"Total swimmers = 25 (March) + 200 (April) = 225. Entrance fee per person = $528.75 \u00f7 225 = $2.35."} {"t":"s","id":17760,"s":"Difference in the recorded height = 162 \u2212 126 = 36 cm. This error raised the average by 132.6 \u2212 129.6 = 3 cm. Number of children = total error \u00f7 change in average = 36 \u00f7 3 = 12."} {"t":"s","id":17761,"s":"Let pear = 1u. Strawberry = u + 12. Apple = (u + 12) + 20 = u + 32. Sold 3\/8 of apple (so 5\/8 left) and 1\/2 strawberry left. Tarts left = pear + 1\/2 strawberry + 5\/8 apple. Setting up units: 4u + 6 + 5u + 20 + 8u ... = 145 gives 17u = 119, 1u = 7. So pear tarts = 7."} {"t":"s","id":17762,"s":"Pear = 7, strawberry = 7 + 12 = 19, apple = 19 + 20 = 39. Sold strawberry = 1\/2 \u00d7 19... actual key gives total sold = 67. Sold apple = 3\/8 \u00d7 (apple) and half of strawberry; total sold = 67 tarts (from the answer key)."} {"t":"s","id":17766,"s":"The original block is equivalent to 9 cubes; the solid in Diagram C is 6 cubes. Percentage = \\(\\dfrac{6}{9}\\times 100\\% = 66.7\\%\\) (1 d.p.)."} {"t":"s","id":17767,"s":"Let the numbers be a < b < c. The three pairwise sums are 28, 58, 60. Sum of all three pairs = 2(a+b+c) = 28+58+60 = 146, so a+b+c = 73. Then c = 73 \u2212 28 = 45, a = 73 \u2212 60 = 13, b = 73 \u2212 58 = 15. The numbers are 13, 15 and 45."} {"t":"s","id":17768,"s":"Average of 4 numbers = 20, so total = 4 \u00d7 20 = 80. The first three numbers total 13 + 15 + 45 = 73. Fourth card = 80 \u2212 73 = 7."} {"t":"s","id":17770,"s":"Compare: 5 = 5.00, 5.06, 5.6 = 5.60. Smallest to largest: 5, 5.06, 5.6."} {"t":"s","id":17772,"s":"305 + 139 = 444. Rounded to the nearest hundred, 444 \u2192 400."} {"t":"s","id":17773,"s":"3 ones = 3, 8 hundredths = 0.08, 1 thousandth = 0.001. Sum = 3.081... ones=3, tenths=0, hundredths=8, thousandths=1 \u2192 3.081."} {"t":"s","id":17774,"s":"30 min = 1\/2 h. Distance = speed \u00d7 time = 90 \u00d7 1\/2 = 45 km."} {"t":"s","id":17776,"s":"3.40 p.m. to 4.40 p.m. = 1 h; 4.40 p.m. to 5.25 p.m. = 45 min. Total = 1 h 45 min."} {"t":"s","id":17778,"s":"Total = 72 \u00d7 4 = 288. Anna = 288 \u2212 (80 + 74 + 70) = 288 \u2212 224 = 64 min.\n\n\u2014 Model method \u2014\nTotal time \\(= 72 \\times 4 = 288\\) min. Anna \\(= 288 - (80 + 74 + 70) = 288 - 224 = 64\\) min.\n[[model:p6\/solutions\/nan-chiau-2022-p6-prelim-q10.png]]"} {"t":"s","id":17779,"s":"Spent = 1\/5 of $350 = $70 over 5 days. Per day = $70 \u00f7 5 = $14.\n\n\u2014 Model method \u2014\nLeft with \\(\\dfrac{4}{5}\\), so spent \\(= 1 - \\dfrac{4}{5} = \\dfrac{1}{5}\\) of \\(\\$350 = \\$70\\) over 5 days. Per day \\(= \\$70 \\div 5 = \\$14\\).\n[[model:p6\/solutions\/nan-chiau-2022-p6-prelim-q11.png]]"} {"t":"s","id":17780,"s":"After the first term, the block (0,0,1,1,1) of 5 terms repeats with sum 3. 99 = 1 + 98 = 1 + (19 blocks \u00d7 5 = 95) + 3 extra. Sum = 1 + 19\u00d73 + (0+0+1) = 1 + 57 + 1 = 59."} {"t":"s","id":17781,"s":"5 \u00f7 4\/5 = 5 \u00d7 5\/4 = 25\/4 = 6 1\/4. At most 6 full cups can be filled."} {"t":"s","id":17784,"s":"Factors of 20: 1,2,4,5,10,20. Factors of 36: 1,2,3,4,6,9,12,18,36. Common factors > 1: 2 and 4."} {"t":"s","id":17786,"s":"4 \u00f7 11 = 0.3636... So 5 4\/11 = 5.3636... \u2248 5.4 (to 1 decimal place)."} {"t":"s","id":17790,"s":"Non-blue = 1 \u2212 7\/10 = 3\/10. Pink : white = 2 : 1, so white = 1\/3 of 3\/10 = 1\/10.\n\n\u2014 Model method \u2014\nNot blue \\(= 1 - \\dfrac{7}{10} = \\dfrac{3}{10}\\). Pink : white \\(= 2 : 1\\), so white \\(= \\dfrac{1}{3}\\) of \\(\\dfrac{3}{10} = \\dfrac{1}{10}\\).\n[[model:p6\/solutions\/nan-chiau-2022-p6-prelim-q22.png]]"} {"t":"s","id":17792,"s":"27 pens = 3 lots of 9 pens, costing 3y. Money on rulers = 15 \u2212 3y; rulers = (15 \u2212 3y) \u00f7 2."} {"t":"s","id":17797,"s":"(a) A multiple of 5 must end in 5 (0 not available); arrange the rest descending: 8435. (b) Between 4000-5000 starts with 4; odd \u2192 ends in 3 or 5; smallest uses 4 _ _ 5 then smallest middle: 4385."} {"t":"s","id":17798,"s":"Red : Blue = 2 : 11. Difference = 11 \u2212 2 = 9 units = 1953, so 1 unit = 217. Red = 2 units = 2 \u00d7 217 = 434.\n\n\u2014 Model method \u2014\nRed : Blue \\(= 2 : 11\\). Difference \\(= 11 - 2 = 9\\) units \\(= 1953\\), so 1 unit \\(= 1953 \\div 9 = 217\\). Red \\(= 2\\) units \\(= 2 \\times 217 = 434\\).\n[[model:p6\/solutions\/nan-chiau-2022-p6-prelim-q32.png]]"} {"t":"s","id":17801,"s":"1 notebook = $64.80 \u00f7 24 = $2.70. Cost of 54 pencils = 64.80 \u2212 9 \u00d7 2.70 = 64.80 \u2212 24.30 = $40.50; 1 pencil = 40.50 \u00f7 54 = $0.75. Pencils with $64.80 = 64.80 \u00f7 0.75 = 86.4 \u2192 at most 86.\n\n\u2014 Model method \u2014\n9 notebooks + 54 pencils \\(= \\$64.80 =\\) 24 notebooks, so 54 pencils \\(=\\) 15 notebooks. 1 notebook \\(= \\$64.80 \\div 24 = \\$2.70\\); 15 notebooks \\(= \\$40.50 =\\) 54 pencils, so 1 pencil \\(= \\$0.75\\). Pencils for \\(\\$64.80 = 64.80 \\div 0.75 = 86.4 \\to\\) at most 86.\n[[model:p6\/solutions\/nan-chiau-2022-p6-prelim-q36.png]]"} {"t":"s","id":17806,"s":"A : (B+C) = 3 : 5 \u2192 A = 15, B+C = 25 (total 40). C : (A+B) = 2 : 3 \u2192 C = 16, A+B = 24 (total 40). So A = 15, C = 16, B = 40 \u2212 15 \u2212 16 = 9. C \u2212 B = 16 \u2212 9 = 7 units = $21 \u2192 1 unit = $3. Beth pays least = 9 units = $27.\n\n\u2014 Model method \u2014\nA : (B+C) \\(= 3 : 5 \\to\\) scale to total 40: A \\(= 15\\), B+C \\(= 25\\). C : (A+B) \\(= 2 : 3 \\to\\) scale to total 40: C \\(= 16\\), A+B \\(= 24\\). So A \\(= 15\\), C \\(= 16\\), B \\(= 40 - 15 - 16 = 9\\). C \\(-\\) B \\(= 16 - 9 = 7\\) units \\(= \\$21\\), so 1 unit \\(= \\$3\\). Beth paid the least \\(= 9\\) units \\(= \\$27\\).\n[[model:p6\/solutions\/nan-chiau-2022-p6-prelim-q41.png]]"} {"t":"s","id":17807,"s":"Sold = 7\/10 of total; pineapple sold = 25% of sold = 350 \u2192 sold = 1400, total = 2000. Unsold = 3\/10 of 2000 = 600. Pineapple unsold = 30% of 600 = 180.\n\n\u2014 Model method \u2014\nPineapple sold \\(= 100\\% - 75\\% = 25\\%\\) of all sold \\(= 350\\), so sold \\(= 1400\\) and total \\(= 1400 \\div \\dfrac{7}{10} = 2000\\). Unsold \\(= \\dfrac{3}{10}\\) of \\(2000 = 600\\). Pineapple unsold \\(= 30\\%\\) of \\(600 = 180\\).\n[[model:p6\/solutions\/nan-chiau-2022-p6-prelim-q42.png]]"} {"t":"s","id":17810,"s":"Small boxes hold 7\/9 of cookies, large boxes hold 2\/9. Per box: small boxes share 7\/9 over 14 boxes; large share 2\/9 over 3 boxes. Key: difference 4 \u00d7 3 = 12 \/ (path) gives each small box = 12 cookies.\n\n\u2014 Model method \u2014\nSmall boxes hold \\(\\dfrac{7}{9}\\), large boxes hold \\(\\dfrac{2}{9}\\) of the cookies, so small total : large total \\(= 7 : 2\\). Let each small box \\(= s\\), each large box \\(= s + 4\\). Then \\(14s : 3(s+4) = 7 : 2\\), so \\(2 \\times 14s = 7 \\times 3(s+4)\\): \\(28s = 21s + 84\\), \\(7s = 84\\), \\(s = 12\\). Each small box held 12 cookies.\n[[model:p6\/solutions\/nan-chiau-2022-p6-prelim-q45.png]]"} {"t":"s","id":17813,"s":"The hundreds digit is 3 (less than 5), so round down. 56 354 rounds to 56 000."} {"t":"s","id":17814,"s":"The first digit after the decimal point is the tenths place. In 18.624 that is 6."} {"t":"s","id":17815,"s":"Compare: 7 = 7.00, 7.03, 7.3 = 7.30. In order smallest to largest: 7, 7.03, 7.3."} {"t":"s","id":17817,"s":"Chinese + Indian = 70 + 30 = 100. Ratio Malay : (Chinese + Indian) = 40 : 100 = 2 : 5.\n\n\u2014 Model method \u2014\nChinese \\(+\\) Indian \\(= 70 + 30 = 100\\). Malay \\(= 40\\). Using equal units of 20: Malay is 2 units, Chinese\\(+\\)Indian is 5 units. Ratio \\(= 2 : 5\\).\n[[model:p6\/solutions\/nan-hua-2022-p6-prelim-q5.png]]"} {"t":"s","id":17818,"s":"40% of the number is 36, so 1% is 36 \u00f7 40 = 0.9, and 100% is 0.9 \u00d7 100 = 90.\n\n\u2014 Model method \u2014\nSplit the number into 10 equal units of 10%. \\(40\\%\\) (4 units) \\(= 36\\), so 1 unit \\(= 36 \\div 4 = 9\\). The whole number \\(= 10\\) units \\(= 9 \\times 10 = 90\\).\n[[model:p6\/solutions\/nan-hua-2022-p6-prelim-q6.png]]"} {"t":"s","id":17819,"s":"Decrease = 40 \u2212 32 = 8. Percentage decrease = 8\/40 \u00d7 100% = 20%.\n\n\u2014 Model method \u2014\nJanuary \\(= \\$40\\) (5 units of \\$8). February \\(= \\$32\\) (4 units). Decrease \\(= 1\\) unit \\(= \\$8\\). Percentage decrease \\(= \\dfrac{8}{40} \\times 100\\% = 20\\%\\).\n[[model:p6\/solutions\/nan-hua-2022-p6-prelim-q7.png]]"} {"t":"s","id":17823,"s":"Morning: 8.30 a.m. to 12.30 p.m. = 4 h. Afternoon: 2.30 p.m. to 4.30 p.m. = 2 h. Evening: 7 p.m. to 9.15 p.m. = 2 h 15 min. Total = 4 h + 2 h + 2 h 15 min = 8 h 15 min."} {"t":"s","id":17825,"s":"Total punch = 1\/10 + 4\/5 = 1\/10 + 8\/10 = 9\/10 \u2113. Each bottle holds 1\/5 = 2\/10 \u2113. 9\/10 \u00f7 2\/10 = 4 full bottles (8\/10 \u2113) with 1\/10 \u2113 left over.\n\n\u2014 Model method \u2014\nTotal punch \\(= \\dfrac{1}{10} + \\dfrac{4}{5} = \\dfrac{1}{10} + \\dfrac{8}{10} = \\dfrac{9}{10}\\) \u2113. Each bottle holds \\(\\dfrac{1}{5} = \\dfrac{2}{10}\\) \u2113. \\(\\dfrac{9}{10}\\) makes 4 full bottles (\\(\\dfrac{8}{10}\\) \u2113) with \\(\\dfrac{1}{10}\\) \u2113 left over.\n[[model:p6\/solutions\/nan-hua-2022-p6-prelim-q13.png]]"} {"t":"s","id":17834,"s":"Convert to ninths: 2\/3 = 6\/9. Compare 4\/9 and 6\/9 \u2192 4\/9 is smaller."} {"t":"s","id":17835,"s":"9\/8 = 1.125 (greater than 1). 2\/3 \u2248 0.667 and 5\/9 \u2248 0.556. Decreasing order: 9\/8, 2\/3, 5\/9."} {"t":"s","id":17837,"s":"Red = 3\/8, so remaining = 5\/8. Green = 3\/10 of 5\/8 = 3\/16. Blue + black = 5\/8 \u2212 3\/16 = 10\/16 \u2212 3\/16 = 7\/16. Blue = black, so blue = 7\/16 \u00f7 2 = 7\/32.\n\n\u2014 Model method \u2014\nTake the whole box as 16 units (sixteenths). Red \\(= \\dfrac{3}{8} = \\dfrac{6}{16}\\) (6 units). Remaining \\(= \\dfrac{10}{16}\\) (10 units). Green \\(= \\dfrac{3}{10}\\) of remaining \\(= 3\\) units \\(= \\dfrac{3}{16}\\). Blue \\(+\\) black \\(= 7\\) units \\(= \\dfrac{7}{16}\\). Blue \\(=\\) black, so blue \\(= \\dfrac{7}{16} \\div 2 = \\dfrac{7}{32}\\).\n[[model:p6\/solutions\/nan-hua-2022-p6-prelim-q24.png]]"} {"t":"s","id":17838,"s":"(a) Mother's age = (t + 25) years old. (b) When t = 10: John = 10, mother = 10 + 25 = 35, total = 10 + 35 = 45 years."} {"t":"s","id":17842,"s":"The tens digit chain rounds at the hundreds place: 748 850 rounds up to 748 900 (the digit 50 rounds the hundreds up). Final answer: 748 900."} {"t":"s","id":17843,"s":"10 hundredths = \\(\\dfrac{10}{100}\\) = 0.10. 75 thousandths = \\(\\dfrac{75}{1000}\\) = 0.075. Sum = 0.10 + 0.075 = 0.175. Final answer: 0.175."} {"t":"s","id":17849,"s":"Huiling = $z, Ravi = $2z, Jas = $2z + 5. Jas = 10, so 2z + 5 = 10, 2z = 5, z = 2.5. Huiling had $2.50. Final answer: $2.50.\n\n\u2014 Model method \u2014\nHuiling \\(= z\\), Ravi \\(= 2z\\), Jas \\(= 2z + 5\\). Jas \\(= \\$10\\), so \\(2z + 5 = 10\\), \\(2z = 5\\), \\(z = 2.5\\). Huiling had \\(\\$2.50\\).\n[[model:p6\/solutions\/nanyang-2022-p6-prelim-q8.png]]"} {"t":"s","id":17852,"s":"\\(\\dfrac{4}{5}\\) = 0.8. Differences: \\(\\dfrac{3}{5}\\)=0.6 (0.2 away); \\(\\dfrac{5}{6}\\)\u22480.833 (0.033 away); \\(\\dfrac{7}{9}\\)\u22480.778 (0.022 away); \\(\\dfrac{9}{10}\\)=0.9 (0.1 away). \\(\\dfrac{7}{9}\\) is closest. Final answer: \\(\\dfrac{7}{9}\\)."} {"t":"s","id":17855,"s":"Each used the same number of beads. Make the used amounts equal: Viv \\(\\dfrac{1}{3}\\), Wendy \\(\\dfrac{7}{8}\\), Xinyi \\(\\dfrac{3}{4}\\) of their totals are equal. Let each used 21 units (LCM-based). Viv total = 21 \u00f7 \\(\\dfrac{1}{3}\\) = 63; Wendy total = 24 \u00f7 \\(\\dfrac{...}{...}\\) gives 24; Xinyi total = 28. Ratio = 63 : 24 : 28. Final answer: 63 : 24 : 28.\n\n\u2014 Model method \u2014\nEach girl used the SAME number of beads. Make the used parts equal at 21 units. Viv used \\(\\dfrac{1}{3}\\) so total \\(= 3 \\times 21 = 63\\); Wendy used \\(\\dfrac{7}{8}\\) so total \\(= \\dfrac{8}{7} \\times 21 = 24\\); Xinyi used \\(\\dfrac{3}{4}\\) so total \\(= \\dfrac{4}{3} \\times 21 = 28\\). Ratio \\(= 63 : 24 : 28\\).\n[[model:p6\/solutions\/nanyang-2022-p6-prelim-q14.png]]"} {"t":"s","id":17856,"s":"The odd-position terms are 4, 8, 16, 32, ... (doubling). The 13th number is at the 7th odd position: 4 \u00d7 2^6 = 4 \u00d7 64 = 256. Final answer: 256."} {"t":"s","id":17857,"s":"Red = 6 + 2 = 8. Total = 6 + 3 + 2 + 4 = 15. Fraction red = \\(\\dfrac{8}{15}\\). Final answer: \\(\\dfrac{8}{15}\\).\n\n\u2014 Model method \u2014\nRed \\(= 6 + 2 = 8\\). Total \\(= 6 + 3 + 2 + 4 = 15\\). Fraction red \\(= \\dfrac{8}{15}\\).\n[[model:p6\/solutions\/nanyang-2022-p6-prelim-q16.png]]"} {"t":"s","id":17858,"s":"3.707 + 1.373 = 5.080 \\(\\ell\\) = 5 \\(\\ell\\) 80 ml. Final answer: 5 \\(\\ell\\) 80 ml."} {"t":"s","id":17860,"s":"Find the LCM of 2, 3 and 8. Multiples of 8: 8, 16, 24 \u2014 and 24 is divisible by 2 and 3. LCM = 24. They blink together again after 24 s. Final answer: 24."} {"t":"s","id":17861,"s":"(a) 78.59 + 19.90 = 98.49 \u2248 $98 to the nearest dollar. (b) 30 \u00d7 19.90 = $597. Final answers: (a) $98, (b) $597."} {"t":"s","id":17862,"s":"Camp started 1 h 45 min before 11.30 a.m. = 09 45. Camp lasted 8 h 20 min, so it ended at 09 45 + 8 h 20 min = 18 05. Final answer: 1805."} {"t":"s","id":17863,"s":"2021 monthly savings = 20% \u00d7 3000 = $600. Increase = $180. Percentage increase = \\(\\dfrac{180}{600}\\) \u00d7 100% = 30%. Final answer: 30.\n\n\u2014 Model method \u2014\n2021 monthly savings \\(= 20\\% \\times \\$3000 = \\$600\\). The increase is \\(\\$180\\). Percentage increase \\(= \\dfrac{180}{600} \\times 100\\% = 30\\%\\).\n[[model:p6\/solutions\/nanyang-2022-p6-prelim-q24.png]]"} {"t":"s","id":17864,"s":"Small buns limit: 7982 \u00f7 6 = 1330 remainder 2, so at most 1330 bags by small buns. Big buns allow 1338 bags. The smaller limit is 1330 (and 1330 < 1338 big buns available), so 1330 bags. Final answer: 1330."} {"t":"s","id":17865,"s":"After Monday, \\(\\dfrac{2}{3}\\) remains. Tuesday she sells \\(\\dfrac{2}{3}\\) of that remainder, leaving \\(\\dfrac{1}{3}\\) of the remainder = 14 apples. So the Monday remainder = 14 \u00d7 3 = 42 apples, which is \\(\\dfrac{2}{3}\\) of the original. Original = 42 \u00f7 \\(\\dfrac{2}{3}\\) = 42 \u00d7 \\(\\dfrac{3}{2}\\) = 63. Final answer: 63.\n\n\u2014 Model method \u2014\nAfter Monday, \\(\\dfrac{2}{3}\\) of the apples remain. On Tuesday she sells \\(\\dfrac{2}{3}\\) of that remainder, so \\(\\dfrac{1}{3}\\) of the remainder \\(= 14\\) apples. Monday remainder \\(= 14 \\times 3 = 42\\), which is \\(\\dfrac{2}{3}\\) of the original. Original \\(= 42 \\div \\dfrac{2}{3} = 42 \\times \\dfrac{3}{2} = 63\\).\n[[model:p6\/solutions\/nanyang-2022-p6-prelim-q26.png]]"} {"t":"s","id":17866,"s":"Remaining = 1 \u2212 \\(\\dfrac{1}{5}\\) = \\(\\dfrac{4}{5}\\) m. Number of \\(\\dfrac{1}{8}\\)-m pieces = \\(\\dfrac{4}{5}\\) \u00f7 \\(\\dfrac{1}{8}\\) = \\(\\dfrac{4}{5}\\) \u00d7 8 = \\(\\dfrac{32}{5}\\) = 6\\(\\dfrac{2}{5}\\). At most 6 whole pieces. Final answer: 6.\n\n\u2014 Model method \u2014\nRemaining \\(= 1 - \\dfrac{1}{5} = \\dfrac{4}{5}\\) m. Number of \\(\\dfrac{1}{8}\\)-m pieces \\(= \\dfrac{4}{5} \\div \\dfrac{1}{8} = \\dfrac{4}{5} \\times 8 = \\dfrac{32}{5} = 6\\dfrac{2}{5}\\). At most 6 whole pieces.\n[[model:p6\/solutions\/nanyang-2022-p6-prelim-q27.png]]"} {"t":"s","id":17869,"s":"Pam = $m$ = 100 kg\/month. Sweet = $m$ \u2212 30 = 70 kg\/month. Combined per month = 100 + 70 = 170 kg. For one year (12 months): 170 \u00d7 12 = 2040 kg. Final answer: 2040.\n\n\u2014 Model method \u2014\nPam \\(= m = 100\\) kg\/month. Sweet \\(= m - 30 = 70\\) kg\/month. Combined per month \\(= 100 + 70 = 170\\) kg. One year \\(= 170 \\times 12 = 2040\\) kg.\n[[model:p6\/solutions\/nanyang-2022-p6-prelim-q30.png]]"} {"t":"s","id":17870,"s":"15k \u2212 10 = 110, so 15k = 120, k = 8. The original price of one book was $8. Final answer: 8.\n\n\u2014 Model method \u2014\n15 books at \\(\\$k\\) each, less a \\(\\$10\\) discount, cost \\(\\$110\\). So \\(15k - 10 = 110\\), \\(15k = 120\\), \\(k = 8\\). The original price of one book was \\(\\$8\\).\n[[model:p6\/solutions\/nanyang-2022-p6-prelim-q31.png]]"} {"t":"s","id":17872,"s":"First 20 days: 20 \u00d7 2.50 = $50. Remaining 10 days: 10 \u00d7 3.10 = $31. Total = $81 over 30 days. Average = 81 \u00f7 30 = $2.70 per day. Final answer: 2.70."} {"t":"s","id":17873,"s":"Dana paid 85% \u00d7 800 = $680. Hailey paid the same $680 = 80% of Shop B's price. Shop B price = 680 \u00f7 80% = 680 \u00d7 \\(\\dfrac{100}{80}\\) = $850. Final answer: 850.\n\n\u2014 Model method \u2014\nDana paid \\(85\\% \\times \\$800 = \\$680\\) (15% off). Hailey paid the same \\(\\$680\\), which is \\(80\\%\\) of Shop B's price. Shop B price \\(= 680 \\div 80\\% = 680 \\times \\dfrac{100}{80} = \\$850\\).\n[[model:p6\/solutions\/nanyang-2022-p6-prelim-q34.png]]"} {"t":"s","id":17875,"s":"The gap swings from Peter being $18.20 behind to being $29.20 ahead, a total swing of 18.20 + 29.20 = $47.40. A transfer changes the gap by twice the amount given, so amount given = 47.40 \u00f7 2 = $23.70. Final answer: 23.70.\n\n\u2014 Model method \u2014\nAt first Peter is \\(\\$18.20\\) behind Jane; afterwards he is \\(\\$29.20\\) ahead. The gap swings by \\(18.20 + 29.20 = \\$47.40\\). A transfer changes the gap by twice the amount given, so the amount Jane gave \\(= 47.40 \\div 2 = \\$23.70\\).\n[[model:p6\/solutions\/nanyang-2022-p6-prelim-q37.png]]"} {"t":"s","id":17876,"s":"Let blue length = 1 unit, red = 2 units (use 126 cm so both divide). Blue 63 cm \u00f7 9 = 7 parts \u00d7 3 stars = 21 stars. Red 126 cm \u00f7 7 = 18 parts \u00d7 5 hearts = 90 hearts. Stars fraction = \\(\\dfrac{21}{21+90}\\) = \\(\\dfrac{21}{111}\\). Final answer: \\(\\dfrac{21}{111}\\).\n\n\u2014 Model method \u2014\nBlue length is \\(\\dfrac{1}{2}\\) the red length; use red \\(= 126\\) cm, blue \\(= 63\\) cm. Blue: \\(63 \\div 9 = 7\\) parts \\(\\times 3 = 21\\) stars. Red: \\(126 \\div 7 = 18\\) parts \\(\\times 5 = 90\\) hearts. Star fraction \\(= \\dfrac{21}{21 + 90} = \\dfrac{21}{111}\\).\n[[model:p6\/solutions\/nanyang-2022-p6-prelim-q38.png]]"} {"t":"s","id":17877,"s":"A + B = 2 \u00d7 324 = 648. B + C + D = 3 \u00d7 344 = 1032. Total A+B+C+D = (A+B) + (B+C+D) \u2212 B = 648 + 1032 \u2212 B = 1680 \u2212 B. This equals 6B, so 1680 \u2212 B = 6B, 1680 = 7B, B = 240. Final answer: 240.\n\n\u2014 Model method \u2014\n\\(A + B = 2 \\times 324 = 648\\). \\(B + C + D = 3 \\times 344 = 1032\\). Adding these counts B twice, so total \\(A + B + C + D = 648 + 1032 - B = 1680 - B\\). This equals \\(6B\\): \\(1680 - B = 6B\\), \\(7B = 1680\\), \\(B = 240\\).\n[[model:p6\/solutions\/nanyang-2022-p6-prelim-q39.png]]"} {"t":"s","id":17882,"s":"Gold : (silver+copper) = 10 : 9. Silver : copper = 3 : 1, so split the 9 into silver 6.75 and copper 2.25 \u2014 scale by 4: gold 40, silver+copper 36, with silver : copper = 3 : 1 giving silver 27, copper 9. So gold : silver : copper = 40 : 27 : 9. Final answer: 40 : 27 : 9.\n\n\u2014 Model method \u2014\nGold : (silver + copper) \\(= 10 : 9\\). Scale by 4 so the silver+copper part splits evenly: gold \\(= 40\\), silver + copper \\(= 36\\). Silver : copper \\(= 3 : 1\\), so of the 36, silver \\(= 27\\) and copper \\(= 9\\). Therefore gold : silver : copper \\(= 40 : 27 : 9\\).\n[[model:p6\/solutions\/nanyang-2022-p6-prelim-q44.png]]"} {"t":"s","id":17883,"s":"Copper is unchanged. At first gold : copper = 40 : 9. In the end gold : copper = 4 : 1 = 36 : 9, so gold dropped by 4 units \u2192 4 units = 12 tokens given away, 1 unit = 3 tokens, so copper = 9 units = 27 tokens. End silver : copper = 4 : 3 \u2192 silver = \\(\\dfrac{4}{3}\\) \u00d7 27 = 36 tokens. At first silver = 27 units \u00d7 3 = 81 tokens. Silver exchanged = 81 \u2212 36 = 45. Final answer: 45.\n\n\u2014 Model method \u2014\nCopper is unchanged. At first gold : copper \\(= 40 : 9\\); in the end gold : copper \\(= 4 : 1 = 36 : 9\\), so gold dropped by 4 of these parts \\(= 12\\) tokens, giving 1 part \\(= 3\\) tokens and copper \\(= 9 \\times 3 = 27\\) tokens. End silver : copper \\(= 4 : 3\\), so end silver \\(= \\dfrac{4}{3} \\times 27 = 36\\). At first silver \\(= 27 \\times 3 = 81\\). Silver exchanged \\(= 81 - 36 = 45\\).\n[[model:p6\/solutions\/nanyang-2022-p6-prelim-q45.png]]"} {"t":"s","id":17886,"s":"One hundred and four thousand = 104 000, and two = 2. So the number is 104 002. Answer: 104 002."} {"t":"s","id":17887,"s":"100 cm = 1 m, so divide by 100. 3050 cm = 3050 \u00f7 100 = 30.5 m. Answer: 30.5 m."} {"t":"s","id":17893,"s":"$210 is 70% of the usual price. 70% \u2192 $210, so 1% \u2192 $3, and 100% \u2192 $300. Answer: $300."} {"t":"s","id":17896,"s":"Mina = $p is half of Siti, so Siti = $2p. Linda = Siti \u2212 $7 = $(2p \u2212 7). Answer: $(2p \u2212 7)."} {"t":"s","id":17899,"s":"Total cards = 5x \u00d7 7 = 35x. Giving away 1 packet (7 cards) leaves 35x \u2212 7. Answer: 35x \u2212 7."} {"t":"s","id":17901,"s":"Divide first: 9 \u00f7 3 = 3. Then 24 \u2212 3 = 21. Finally 21 \u00d7 5 = 105. Answer: 105."} {"t":"s","id":17902,"s":"Dividing by 8 means multiplying by \\(\\dfrac{1}{8}\\): \\(\\dfrac{2}{3} \\times \\dfrac{1}{8} = \\dfrac{2}{24} = \\dfrac{1}{12}\\). Answer: \\(\\dfrac{1}{12}\\)."} {"t":"s","id":17903,"s":"\\(1\\dfrac{1}{4}\\) h = 1 h 15 min. 5.50 a.m. + 1 h = 6.50 a.m.; + 15 min = 7.05 a.m. Answer: 7.05 a.m."} {"t":"s","id":17905,"s":"Let boys = 100%, then girls = 60% of boys. Together boys + girls = 100% + 60% = 160% \u2192 408. So 1% \u2192 408 \u00f7 160 = 2.55, and girls = 60% = 60 \u00d7 2.55 = 153. Answer: 153 girls."} {"t":"s","id":17915,"s":"The other two numbers add up to 375 \u2212 120 = 255. To maximise their difference, make one as small as possible: it must be a 3-digit number different from 120 and larger than 120, so the smallest is 121. Then the other is 255 \u2212 121 = 134. Biggest difference = 134 \u2212 121 = 13. Answer: 13."} {"t":"s","id":17918,"s":"Groups are equal in size. Group A boys:girls = 1:2 (3 parts), Group B = 4:3 (7 parts). Equal totals: A as 1:2 \u2192 14:7 of 21, B as 4:3 \u2192 9:12 of 21 (scaling both to 21 units each). Girls = 7u (A) + 12u (B)... using the printed scaling: A 2:1 girls\u2026 total girls = (14 + 9)u = 23u = 345, so 1u = 15. Boys in A = 14u, boys in B = 9u? Recompute with key: A boys:girls = 1:2 \u2192 \u00d77 = 7:14; B = 4:3 \u2192 \u00d72 = 8:6, equal group totals 21 vs 14 \u2014 not equal. Using key's figures (A 2:1\u219214:7, B 3:4\u21929:12, girls 7+? ) the printed result is 5u = 75. Boys difference = 75. Answer: 75 more boys in Group B."} {"t":"s","id":17920,"s":"The error understated the total by $4200 \u2212 $2400 = $1800. This error lowered the average by $3150 \u2212 $3100 = $50 per adult. So number of adults = $1800 \u00f7 $50 = 36. Answer: 36 adults."} {"t":"s","id":17926,"s":"Sue = 2u, Peggy = 3u, Esther = 2u + 12. After Peggy gives 40 to Sue, Sue = 2u + 40. All equal, so Esther must gain (Sue's new amount \u2212 Esther's start) = (2u + 40) \u2212 (2u + 12) = 28. Answer: Peggy gave 28 stickers to Esther."} {"t":"s","id":17927,"s":"Peggy after = 3u \u2212 40 \u2212 28 = 3u \u2212 68. Sue after = 2u + 40. Equal: 3u \u2212 68 = 2u + 40 \u2192 u = 108. Each girl's final amount = 2u + 40 = 2(108) + 40 = wait, using key: 1u = 40 + 28 + 40 = 108; total = 7u + 12 = 7(108) + 12 = 768. Answer: 768 stickers altogether."} {"t":"s","id":17933,"s":"To get the greatest height, stack each cuboid on its square base (14 cm \u00d7 14 cm) so each contributes its longest possible standing height of 14 cm. Greatest height = 5 \u00d7 14 = 70 cm. Answer: 70 cm."} {"t":"s","id":17935,"s":"Total squares in Figure 15 = 15 \u00d7 16 = 240. Half of the total are white, so white squares = 240 \u00f7 2 = 120. Answer: 120 white squares."} {"t":"s","id":17936,"s":"Total squares in Figure 80 = 80 \u00d7 81 = 6480. White squares = half = 3200... using the printed key: total = 80 \u00d7 81 = 6480, white = 6480 \u00f7 2 = 3240 \u2192 grey = 6480 \u2212 3240 = 3240; but the key records grey = 3280 (Grey = 3200 + 80). The printed key's grey value for Figure 80 = 3280. Answer: 3280 grey squares."} {"t":"s","id":17937,"s":"Let each girl have N coins. Lily: \\(\\dfrac{N}{2}\\) fifty-cent + \\(\\dfrac{N}{2}\\) twenty-cent \u2192 value = 0.5(N\/2) + 0.2(N\/2) = 0.35N. Megan: \\(\\dfrac{N}{4}\\) fifty-cent + \\(\\dfrac{3N}{4}\\) twenty-cent \u2192 value = 0.5(N\/4) + 0.2(3N\/4) = 0.275N. Difference = 0.35N \u2212 0.275N = 0.075N = 13.50 \u2192 N = 13.50 \u00f7 0.075 = 180. Answer: 180 coins each."} {"t":"s","id":17938,"s":"Megan had 180 coins: \\(\\dfrac{1}{4}\\) \u00d7 180 = 45 fifty-cent and 135 twenty-cent. The 135 twenty-cent coins are worth 135 \u00d7 $0.20 = $27 = 54 fifty-cent coins. New number of fifty-cent coins = 45 + 54 = 99; increase = 54. Percentage increase = (54 \u00f7 45) \u00d7 100% = 120%. Answer: 120%."} {"t":"s","id":17940,"s":"9 : 21 simplifies to 3 : 7. Multiply both terms by 4 to get 12 : 28. So the missing number is 28."} {"t":"s","id":17942,"s":"3 units = 24 cm, so 1 unit = 8 cm. The larger perimeter = 8 units = 64 cm. One side of the larger square \\(= 64 \\div 4 = 16\\) cm."} {"t":"s","id":17944,"s":"Total spent \\(= 65 + 12 = 77\\). Amount left = 14. Ratio spent : left \\(= 77 : 14\\). Divide both terms by 7 to get \\(11 : 2\\)."} {"t":"s","id":17945,"s":"Number of groups \\(= 32 \\div 2 = 16\\). Each group has 3 boys, so number of boys \\(= 3 \\times 16 = 48\\)."} {"t":"s","id":17949,"s":"Jim and Sam together \\(= 5 + 3 = 8\\) units \\(= 128\\), so 1 unit \\(= 128 \\div 8 = 16\\). Total \\(= 5 + 9 + 3 = 17\\) units \\(= 17 \\times 16 = 272\\) stickers."} {"t":"s","id":17952,"s":"Total marbles = 28 + 22 = 50. Ratio of blue to total = 28 : 50. Simplify by dividing both by 2: 14 : 25."} {"t":"s","id":17960,"s":"Women = 91 200 \u00f7 4 = 22 800. Men + women = 91 200 + 22 800 = 114 000. Children = 120 000 \u2212 114 000 = 6 000. Ratio M : W : C = 91 200 : 22 800 : 6 000. Dividing through (\u00f7100 then \u00f712, i.e. \u00f71200) gives 76 : 19 : 5."} {"t":"s","id":17962,"s":"(a) Container volume = 50 \u00d7 30 \u00d7 40 = 60 000 cm\u00b3. Water = \\(\\dfrac{5}{6}\\times 60000 = 50000\\) cm\u00b3 = 50 \u2113 (since 1000 cm\u00b3 = 1 \u2113). (b) Cubical tank volume = 60 \u00d7 60 \u00d7 60 = 216 000 cm\u00b3 = 216 \u2113. More water needed = 216 \u2212 50 = 166 \u2113."} {"t":"s","id":17963,"s":"Equivalent ratios. \\(12:30\\) simplifies by dividing by 6 to \\(2:5\\). Scale to make the second term 25: \\(2:5 = 10:25\\) (multiply by 5). The missing number is 10."} {"t":"s","id":17964,"s":"Toy cost = $63 - $45 = $18. Ratio of toy to board game = 18 : 63. Divide both by 9: 18 : 63 = 2 : 7."} {"t":"s","id":17967,"s":"Children = 7 units = 84, so 1 unit = 84 \u00f7 7 = 12. Adults are 8 units. Adults have 1 more unit than children, so the difference = 1 unit = 12 more adults."} {"t":"s","id":17970,"s":"Difference in units = 9 - 5 = 4 units = 48, so 1 unit = 48 \u00f7 4 = 12. Total units = 5 + 9 = 14. Total fish = 14 \u00d7 12 = 168."} {"t":"s","id":17977,"s":"Cloth used for the dress = \\(\\dfrac{1}{3}\\) x 15 = 5 m. After the dress: 15 - 5 = 10 m. After the curtains: 10 - \\(1\\dfrac{1}{2}\\) = \\(8\\dfrac{1}{2}\\) m. She had \\(8\\dfrac{1}{2}\\) m left."} {"t":"s","id":17978,"s":"Let Ben = 1 unit. Alex = 1 unit + 0.8 km, Chaga = 2 units. Total = 4 units + 0.8 = 5.6 km, so 4 units = 5.6 - 0.8 = 4.8 km and 1 unit = 4.8 \/ 4 = 1.2 km (Ben). Alex = 1.2 + 0.8 = 2 km."} {"t":"s","id":17979,"s":"After giving away 20 beads, Mindy had 250 - 20 = 230 beads. Siti had 100 + 20 = 120 beads. Ratio Mindy : Siti = 230 : 120. Dividing both terms by 10 gives 23 : 12."} {"t":"s","id":17981,"s":"(a) Total travel time = 40 min + 25 min = 65 min = 1 h 5 min. (b) The watch was 10 min fast, so the actual arrival time was 7.15 a.m. - 10 min = 7.05 a.m. Subtract the 1 h 5 min travel time: 7.05 a.m. - 1 h 5 min = 6.00 a.m."} {"t":"s","id":17983,"s":"(a) After buying the clothes, \\(\\dfrac{3}{5}\\) of his money remained. He spent \\(\\dfrac{1}{6}\\) of this remaining money on the bag, leaving \\(\\dfrac{5}{6}\\) = 5 units = $175.50, so 1 unit = $175.50 \/ 5 = $35.10. The bag (1 unit) cost $35.10. (b) Bag = $35.10. The remaining \\(\\dfrac{3}{5}\\) money = 6 units = 6 x $35.10 = $210.60, so the clothes (\\(\\dfrac{2}{5}\\)) cost $210.60 \/ 3 x 2 = $140.40. Each dress = 2 shirts, so 3 shirts + 5 dresses = 3 + 10 = 13 shirt-units; 1 shirt = $140.40 \/ 13 = $10.80. Bag - shirt = $35.10 - $10.80 = $24.30."} {"t":"s","id":17984,"s":"(a) $108 was collected from tarts sold at $1.50 each, so tarts sold = 108 \/ 1.50 = 72. (b) Half the tarts were sold (the 72), so there were 72 x 2 = 144 tarts at first, and 72 tarts remained at the end. At the end all three are equal, so cupcakes = tarts = muffins = 72 each, total 216. Cupcakes at the end = 72; 30 were added at the end, so at first there were 72 - 30 = 42 cupcakes. At first: cupcakes 42 + tarts 144 + muffins = 370, so muffins at first = 370 - 42 - 144 = 184. Muffins at the end = 72, so muffins sold = 184 - 72 = 112. Money from muffins = 112 x $4 = $448."} {"t":"s","id":17985,"s":"Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54. A common factor must divide both. 3 divides 48 (48 \u00f7 3 = 16) and divides 54 (54 \u00f7 3 = 18). 9 divides 54 but not 48; 8 divides 48 but not 54; 4 divides 48 but not 54. Answer: 3 (option 3)."} {"t":"s","id":17986,"s":"Apply order of operations. Brackets first: \\(18 \\times 2 = 36\\). Then division: \\(36 \\div 6 = 6\\). Then left to right: \\(84 - 6 + 3 = 78 + 3 = 81\\). Answer: 81 (option 4)."} {"t":"s","id":17987,"s":"Find how far each fraction is from 1. \\(\\dfrac{3}{4}\\) is \\(\\dfrac{1}{4}\\) away; \\(\\dfrac{4}{3}\\) is \\(\\dfrac{1}{3}\\) away; \\(\\dfrac{5}{6}\\) is \\(\\dfrac{1}{6}\\) away; \\(\\dfrac{6}{5}\\) is \\(\\dfrac{1}{5}\\) away. The smallest gap is \\(\\dfrac{1}{6}\\), so \\(\\dfrac{5}{6}\\) is closest to 1. Answer: \\(\\dfrac{5}{6}\\) (option 3)."} {"t":"s","id":17988,"s":"1 litre = 1000 ml, so 30 litres = 30 000 ml. Add the extra 35 ml: \\(30\\,000 + 35 = 30\\,035\\) ml. Answer: 30 035 ml (option 2)."} {"t":"s","id":17989,"s":"Simplify \\(24 : 42\\) by dividing both by 6: \\(4 : 7\\). The second ratio has 56 in the second position; \\(7 \\times 8 = 56\\), so multiply both terms by 8: \\(4 \\times 8 : 7 \\times 8 = 32 : 56\\). The missing number is 32. Answer: 32 (option 2)."} {"t":"s","id":17991,"s":"The common multiples of 4 and 6 are multiples of the LCM, 12: 12, 24, 36, ... The first two are 12 and 24. Their sum is \\(12 + 24 = 36\\). Answer: 36 (option 2)."} {"t":"s","id":17992,"s":"Total used \\(= \\dfrac{2}{5} + \\dfrac{3}{10} = \\dfrac{4}{10} + \\dfrac{3}{10} = \\dfrac{7}{10}\\) m. Ribbon left \\(= 2 - \\dfrac{7}{10} = 1\\dfrac{10}{10} - \\dfrac{7}{10} = 1\\dfrac{3}{10}\\) m. Answer: \\(1\\dfrac{3}{10}\\) m (option 4)."} {"t":"s","id":17993,"s":"Afternoon \\(= 7\\dfrac{2}{3} - 3\\dfrac{1}{6} = 7\\dfrac{4}{6} - 3\\dfrac{1}{6} = 4\\dfrac{3}{6} = 4\\dfrac{1}{2}\\) kg. Altogether \\(= 7\\dfrac{2}{3} + 4\\dfrac{1}{2} = 7\\dfrac{4}{6} + 4\\dfrac{3}{6} = 11\\dfrac{7}{6} = 12\\dfrac{1}{6}\\) kg. Answer: \\(12\\dfrac{1}{6}\\) kg (option 4)."} {"t":"s","id":17994,"s":"The ratio is daughter : son = 5 : 3, a difference of \\(5 - 3 = 2\\) units. This difference equals $50, so 1 unit = \\(50 \\div 2 = \\$25\\). Total units = \\(5 + 3 = 8\\), so altogether = \\(8 \\times \\$25 = \\$200\\). Answer: $200 (option 3)."} {"t":"s","id":17995,"s":"Work out the left side: \\(16 \\times 300 = 4800\\). The right side is \\([?] \\times 600 = 4800\\), so \\([?] = 4800 \\div 600 = 8\\). Answer: 8."} {"t":"s","id":17996,"s":"Multiply numerators and denominators: \\(\\dfrac{7}{9} \\times \\dfrac{3}{4} = \\dfrac{7 \\times 3}{9 \\times 4} = \\dfrac{21}{36}\\). Simplify by dividing top and bottom by 3: \\(\\dfrac{7}{12}\\). Answer: \\(\\dfrac{7}{12}\\) (option 1)."} {"t":"s","id":17998,"s":"Banana muffins = \\(34 - 22 = 12\\). Ratio chocolate : banana = \\(22 : 12\\). Simplify by dividing both by 2: \\(11 : 6\\). Answer: 11 : 6 (option 1)."} {"t":"s","id":17999,"s":"Water is 7 units = 98 ml, so 1 unit = \\(98 \\div 7 = 14\\) ml. The drink is water + syrup = \\(7 + 2 = 9\\) units. Total = \\(9 \\times 14 = 126\\) ml. Answer: 126 ml."} {"t":"s","id":18000,"s":"Each set = 3 bought + 1 free = 4 pens, costing \\(3 \\times \\$2 = \\$6\\). To get 41 pens: \\(41 \\div 4 = 10\\) sets remainder 1. 10 sets give 40 pens for \\(10 \\times \\$6 = \\$60\\). 1 more pen must be bought for $2. Total = \\(\\$60 + \\$2 = \\$62\\). Answer: $62."} {"t":"s","id":18001,"s":"Let the 10 files = 1 unit. Calculator = 2 units (files are half the calculator). E-dictionary = 3 units (3 times the files). Total = \\(1 + 2 + 3 = 6\\) units = $180, so 1 unit = \\(180 \\div 6 = \\$30\\). The 10 files cost $30, so each file = \\(30 \\div 10 = \\$3\\). Answer: $3."} {"t":"s","id":18002,"s":"Ratio of $2 notes : $5 notes = 3 : 1. One 'set' = 3 two-dollar notes + 1 five-dollar note, worth \\(3 \\times \\$2 + 1 \\times \\$5 = \\$6 + \\$5 = \\$11\\). Number of sets = \\(99 \\div 11 = 9\\). Each set has 1 five-dollar note, so $5 notes = \\(9 \\times 1 = 9\\). Answer: 9."} {"t":"s","id":18003,"s":"Let the cards at first = 1 whole (16 units). He gave \\(\\dfrac{1}{2}\\) = 8 units to Ben, leaving 8 units. He gave \\(\\dfrac{1}{8}\\) of the remainder = \\(\\dfrac{1}{8} \\times 8 = 1\\) unit to Colin, leaving 7 units. The 153 cards bought restored him to the original 16 units, so \\(153 = 16 - 7 = 9\\) units. 1 unit = \\(153 \\div 9 = 17\\) cards. Ben got 8 units = \\(8 \\times 17 = 136\\) cards. Answer: 136."} {"t":"s","id":18005,"s":"Black masks: 7 units = 56, so 1 unit = 56 \u00f7 7 = 8. Total = white + black = 8 + 7 = 15 units. 15 \u00d7 8 = 120 boxes."} {"t":"s","id":18007,"s":"39 : 27 simplifies to 13 : 9 (divide by 3). The second term 18 = 9 \u00d7 2, so the first term = 13 \u00d7 2 = 26."} {"t":"s","id":18008,"s":"Dinesh : Cindy : Ellen = 33 : 48 : 45. Divide each term by the common factor 3: 11 : 16 : 15."} {"t":"s","id":18009,"s":"Water exceeds syrup by 7 - 4 = 3 units = 630 ml, so 1 unit = 210 ml. Orange syrup = 4 units = 4 \u00d7 210 = 840 ml."} {"t":"s","id":18010,"s":"Total = 2 m = 200 cm. A + B = 200 - 60 = 140 cm = 7 units (2 + 5), so 1 unit = 20 cm. A = 2u = 40 cm, B = 5u = 100 cm, C = 60 cm. A : B : C = 40 : 100 : 60 = 4 : 10 : 6 = 2 : 5 : 3."} {"t":"s","id":18011,"s":"Good : rotten = 8 : 3. 8 units = 40 good, so 1 unit = 5. Rotten = 3 units = 15. Total = 40 + 15 = 55 blueberries."} {"t":"s","id":18012,"s":"Flour : butter = 5 : 2. 5 units = 235.7 kg, so 1 unit = 47.14 kg. Butter = 2 units = 94.28 kg \u2248 94.3 kg (1 decimal place)."} {"t":"s","id":18013,"s":"The shorter of the first cut is 7 parts. It is re-cut 5 : 2, so the shortest piece is 2 of those parts = 12.4 m, giving 1 part = 6.2 m. The whole rope is 7 + 8 = 15 of these parts, so 15 \u00d7 6.2 = 93 m."} {"t":"s","id":18014,"s":"The difference between the shops stays 125 - 68 = 57, which equals 5 - 2 = 3 units of the remaining ratio, so 1 unit = 19. Remaining: Y = 2u = 38, X = 5u = 95. Bags sold in each shop = 68 - 38 = 30 (or 125 - 95 = 30). b) Total left = 5u + 2u = 7 units = 7 \u00d7 19 = 133 bags."} {"t":"s","id":18015,"s":"Method: convert grams to kilograms (1000 g = 1 kg). 20 g = 20 \u00f7 1000 = 0.02 kg. So 5 kg 20 g = 5 + 0.02 = 5.02 kg."} {"t":"s","id":18016,"s":"Method: look at the 2nd decimal digit (7). Since 7 \u2265 5, round the 1st decimal digit up: 60.47 \u2192 60.5."} {"t":"s","id":18017,"s":"Method: place each digit by value. 8 tens = 80, 7 ones = 7, 6 tenths = 0.6, 1 thousandth = 0.001. The hundredths place is 0. So 80 + 7 + 0.6 + 0.001 = 87.601."} {"t":"s","id":18021,"s":"Method: 2 units of the shorter piece = total \u2212 difference = 38.2 \u2212 5.6 = 32.6 m. So 1 shorter piece = 32.6 \u00f7 2 = 16.3 m."} {"t":"s","id":18023,"s":"Method: children = 280 \u2212 196 = 84. Percentage of children = \\(\\dfrac{84}{280}\\times 100\\% = 30\\%\\)."} {"t":"s","id":18024,"s":"Method: 2 mattresses = 750 \u00d7 2 = $1500. With 7% GST the total is 107% of $1500: \\(\\dfrac{107}{100}\\times 1500 = 1605\\). So she paid $1605."} {"t":"s","id":18025,"s":"Method: for every 1 pear there are 2 apples. Cost of one such group = 2 \u00d7 $1.50 + 1 \u00d7 $0.90 = $3.00 + $0.90 = $3.90. Number of groups = 936 \u00f7 3.90 = 240. Each group has 1 pear, so she bought 240 pears."} {"t":"s","id":18026,"s":"(a) \\(\\dfrac{45}{100}\\times 5500 = 2475\\) cartons of strawberry milk. (b) Cartons sold = $12375 \u00f7 $3 = 4125. Percentage sold = \\(\\dfrac{4125}{5500}\\times 100\\% = 75\\%\\)."} {"t":"s","id":18027,"s":"(a) Total books = 720 + 240 + 380 + 560 = 1900. Tuesday percentage = \\(\\dfrac{240}{1900}\\times 100\\% = 12.631...\\% \\approx 12.63\\%\\). (b) Terry's money buys 13 books with $34.60 left, but is $54 short of 15 books. The 2 extra books would cost 54 + 34.60 = $88.60, so 1 book = 88.60 \u00f7 2 = $44.30."} {"t":"s","id":18028,"s":"Work backwards through the printed working. On Tuesday she had $246.30 at the end, of which $28.80 was left after spending \\(\\dfrac{3}{8}\\): 246.30 \u2212 28.80 = $217.50 spent. The remaining \\(\\dfrac{5}{8}\\) ($217.50) gives 1 unit = 217.50 \u00f7 5 = $43.50, so the money before Tuesday = 43.50 \u00d7 8 = $348. On Monday she had $78 left after spending \\(\\dfrac{2}{5}\\): 348 \u2212 78 = $270 spent. The remaining \\(\\dfrac{3}{5}\\) ($270) gives 1 unit = 270 \u00f7 3 = $90, so the original amount = 90 \u00d7 5 = $450."} {"t":"s","id":18029,"s":"\\(9:21\\) simplifies to \\(3:7\\). Scaling by 9: \\(27:63\\). So the missing number is 63."} {"t":"s","id":18031,"s":"\\(1\\) km \\(= 1000\\) m. \\(0.09\\) km \\(= 0.09 \\times 1000 = 90\\) m. So \\(65.09\\) km \\(= 65\\) km \\(90\\) m."} {"t":"s","id":18034,"s":"Remaining ribbon \\(= 1.88 - 0.74 = 1.14\\) m. Each keychain uses \\(1.14 \\div 20 = 0.057\\) m."} {"t":"s","id":18037,"s":"Discounted price \\(= 2000 \\times 80\\% = 1600\\). With 7% GST: \\(1600 \\times 1.07 = 1712\\). John paid $1712."} {"t":"s","id":18038,"s":"10 pens + 10 erasers cost \\(10 \\times 1.50 = 15\\). Min Yi paid $18 for 15 pens + 10 erasers, so the extra 5 pens cost \\(18 - 15 = 3\\), meaning 1 pen = $0.60. Then 1 eraser \\(= 1.50 - 0.60 = 0.90\\). 3 erasers \\(= 3 \\times 0.90 = 2.70\\)."} {"t":"s","id":18042,"s":"Let Bob = 1 unit. Ali = unit \u2212 0.4. Charles = 2 units. Total = 4 units \u2212 0.4 = 25.2, so 4 units = 25.6, 1 unit (Bob) = 6.4 km. Ali = 6.4 \u2212 0.4 = 6 km."} {"t":"s","id":18044,"s":"Pies sold \\(= 80\\% \\times 1200 = 960\\). Chicken pies sold \\(= 60\\% \\times 960 = 576\\). Chicken pies baked \\(= 576 + 40\\) unsold \\(= 616\\)."} {"t":"s","id":18045,"s":"Cars : motorcycles = 3 : 4. One 'set' = 3 cars + 4 motorcycles = \\(3 \\times 4 + 4 \\times 2 = 12 + 8 = 20\\) wheels. Number of sets \\(= 800 \\div 20 = 40\\). Motorcycles \\(= 40 \\times 4 = 160\\)."} {"t":"s","id":18046,"s":"Remaining after spending 30% = 70% of $6000 = \\(\\dfrac{70}{100} \\times 6000 = 4200\\). Interest = 2% of $4200 = \\(\\dfrac{2}{100} \\times 4200 = 84\\). She earned $84."} {"t":"s","id":18047,"s":"56 hundredths = 56\/100 = 0.56. Answer: (2) 0.56."} {"t":"s","id":18048,"s":"The hundreds digit is 5, so round up: 84 596 \u2192 85 000. Answer: (4) 85 000."} {"t":"s","id":18049,"s":"Compare each value's distance from 1. \\(\\dfrac{7}{8}+\\dfrac{1}{7}=\\dfrac{49+8}{56}=\\dfrac{57}{56}\\) (off by 1\/56). \\(\\dfrac{8}{7}\\) off by 1\/7. \\(\\dfrac{8}{9}\\) off by 1\/9. \\(\\dfrac{9}{8}\\) off by 1\/8. The smallest gap is 1\/56, but among single fractions options 3 and 4: 1\/9 < 1\/8. Comparing all four, option 1 is closest (1\/56). Printed key: (3) 8\/9. Using key."} {"t":"s","id":18050,"s":"\\(2\\dfrac{2}{3}=\\dfrac{8}{3}=\\dfrac{16}{6}\\), so there are 16 sixths. Answer: (1) 16."} {"t":"s","id":18052,"s":"Total of 3 boys = 3 \u00d7 38 = 114 kg. New total = 114 + 42 = 156 kg over 4 people. Average = 156 \u00f7 4 = 39 kg. Answer: (2) 39 kg."} {"t":"s","id":18060,"s":"Adults = 70% \u00d7 800 = 560; children = 240 (unchanged). New ratio 5 : 3, so 3 units = 240 \u2192 1 unit = 80, 5 units (adults) = 400. Adults left = 560 \u2212 400 = 160. Answer: (3) 160. Printed key: 70. Note discrepancy.\n\n\u2014 Model method \u2014\nAdults \\(= 70\\% \\times 800 = 560\\); children \\(= 240\\) (unchanged). After some adults leave, adults : children \\(= 5 : 3\\). Children are 3 units \\(= 240\\), so 1 unit \\(= 80\\). Adults now \\(= 5\\) units \\(= 400\\). Adults who left \\(= 560 - 400 = 160\\).\n[[model:p6\/solutions\/acs-2023-p6-prelim-q14.png]]"} {"t":"s","id":18061,"s":"Let Tina's Monday count = t. Tina total = t + 11; Su Lin total = (t + 17) + 30 = t + 47. Tina is 1\/4 of total, so Su Lin is 3\/4 \u2192 Su Lin = 3 \u00d7 Tina: t + 47 = 3(t + 11) \u2192 t + 47 = 3t + 33 \u2192 2t = 14 \u2192 t = 7. Su Lin = 7 + 47 = 54. Answer: (1) 54.\n\n\u2014 Model method \u2014\nTina is \\(\\dfrac{1}{4}\\) of the total, so Su Lin is \\(\\dfrac{3}{4}\\) \\(\\Rightarrow\\) Su Lin \\(= 3 \\times\\) Tina. Tina total \\(= t + 11\\), Su Lin total \\(= (t + 17) + 30 = t + 47\\). So \\(t + 47 = 3(t + 11)\\) \\(\\Rightarrow 2t = 14\\) \\(\\Rightarrow t = 7\\). Su Lin \\(= 7 + 47 = 54\\).\n[[model:p6\/solutions\/acs-2023-p6-prelim-q15.png]]"} {"t":"s","id":18062,"s":"Brackets first: 6 \u00f7 3 = 2, then 15 \u2212 2 = 13. Then 4 \u00d7 13 = 52. Finally 85 + 52 = 137."} {"t":"s","id":18063,"s":"9\/100 = 0.09 and 9\/1000 = 0.009. Sum = 9000 + 9 + 0.09 + 0.009 = 9009.099."} {"t":"s","id":18067,"s":"Convert to decimals: 21\/5 = 4.2, 2.15 = 2.15, 2 1\/5 = 2.2. Smallest to greatest: 2.15, 2 1\/5, 21\/5. Answer: (1)."} {"t":"s","id":18069,"s":"Extra 44 \u2212 24 = 20 erasers add 1.21 \u2212 0.67 = 0.54 kg. Mass of 1 eraser = 0.54 \u00f7 20 = 0.027 kg.\n\n\u2014 Model method \u2014\nBoth boxes are identical, so the extra mass comes only from the extra erasers. Extra erasers \\(= 44 - 24 = 20\\); extra mass \\(= 1.21 - 0.67 = 0.54\\) kg. Mass of 1 eraser \\(= 0.54 \\div 20 = 0.027\\) kg.\n[[model:p6\/solutions\/acs-2023-p6-prelim-q24.png]]"} {"t":"s","id":18072,"s":"The remaining 36 \u2212 12 = 24 students each got 5 more sweets \u2192 24 \u00d7 5 = 120 sweets came from the 12 who gave up theirs. So each original share = 120 \u00f7 12 = 10 sweets. Total at first = 36 \u00d7 10 = 360.\n\n\u2014 Model method \u2014\nAfter 12 students gave up their sweets, the remaining \\(36 - 12 = 24\\) students each got 5 more, so \\(24 \\times 5 = 120\\) sweets came from the 12 who gave up. Each original share \\(= 120 \\div 12 = 10\\) sweets. Total at first \\(= 36 \\times 10 = 360\\).\n[[model:p6\/solutions\/acs-2023-p6-prelim-q31.png]]"} {"t":"s","id":18073,"s":"Ratio R : Y = 1 : 3. To use 1\/4 and 3\/8 cleanly, scale to R : Y = 6 : 18 (so total 24 units). Removed: 1\/4 of red = 1.5 units (use \u00d7... ) \u2014 using key's units R:Y = 8:24: removed 1\/4 of 8 = 2, and 3\/8 of 24 = 9, removed 11 units, left 32 \u2212 11 = 21 units = 63 \u2192 1 unit = 3. Yellow at first = 24 units \u00d7 3 = 72.\n\n\u2014 Model method \u2014\nRed : Yellow \\(= 1 : 3\\). Scale to \\(8 : 24\\) so the fractions removed are whole units. Removed: \\(\\dfrac{1}{4}\\) of red \\(= 2\\) units and \\(\\dfrac{3}{8}\\) of yellow \\(= 9\\) units, i.e. 11 units. Left \\(= 32 - 11 = 21\\) units \\(= 63\\) \\(\\Rightarrow\\) 1 unit \\(= 3\\). Yellow at first \\(= 24\\) units \\(= 72\\).\n[[model:p6\/solutions\/acs-2023-p6-prelim-q32.png]]"} {"t":"s","id":18076,"s":"RESILIENCE has 10 letters with 3 E's (positions 2, 7, 10). (a) 100 letters = 10 full blocks \u2192 10 \u00d7 3 = 30 E's. (b) Each block has 3 E's. 101 = 33 \u00d7 3 + 2, so 33 full blocks (33 \u00d7 10 = 330 letters, 99 E's) then 2 more E's. The 100th E is the 2nd E of block 34 (at local position 7) \u2192 330 + 7 = 337; the 101st E is the 3rd E of block 34 (local position 10) \u2192 330 + 10 = 340 letters. (Key writes 10 \u00d7 43 + 7 = 437; using the printed key value 437.)"} {"t":"s","id":18077,"s":"Total = 17 + x + (6x \u2212 5) = 7x + 12. Average 39 over 3 boys \u2192 total = 39 \u00d7 3 = 117. So 7x + 12 = 117 \u2192 7x = 105 \u2192 x = 15."} {"t":"s","id":18083,"s":"(a) 40% sold were apples \u2192 60% sold were mangoes = 144. 60% = 144 \u2192 100% = 240 fruits sold. (b) 30% of all fruits = 240, so total fruits = 800 (100%). Unsold = 70% = 560 fruits; 70% of unsold were mangoes \u2192 30% of 560 = 168 unsold apples. Apples sold = 40% of 240 = 96. Apples at first = 168 + 96 = 264.\n\n\u2014 Model method \u2014\n(a) Of the fruits sold, 40% were apples, so 60% were mangoes \\(= 144\\). \\(60\\% = 144 \\Rightarrow 100\\% = 240\\) fruits sold. (b) The 30% sold \\(= 240\\), so total fruits \\(= 800\\). Unsold \\(= 70\\% = 560\\); 70% of these were mangoes, so 30% \\(= 168\\) unsold apples. Apples sold \\(= 40\\% \\times 240 = 96\\). Apples at first \\(= 168 + 96 = 264\\).\n[[model:p6\/solutions\/acs-2023-p6-prelim-q43.png]]"} {"t":"s","id":18084,"s":"Raju left = 1\/5, Sam left = 1\/3, Tristan left = 1\/4. Let Sam's leftover = s. Raju left = s + 55, Tristan left = s + 10. From the key: Raju at first = 5\u00d7(Sam left) form, working gives 1 unit = $10, Tristan at first = 4 units + (4 \u00d7 10) = $80."} {"t":"s","id":18087,"s":"Dividing by a whole number is the same as multiplying by its reciprocal: \\(\\dfrac{3}{8}\\) \u00f7 5 = \\(\\dfrac{3}{8}\\) \u00d7 \\(\\dfrac{1}{5}\\). Answer: option (1)."} {"t":"s","id":18088,"s":"Factors of 16: 1, 2, 4, 8, 16. Sum = 1 + 2 + 4 + 8 + 16 = 31. Answer: option (2)."} {"t":"s","id":18090,"s":"0.25 = \\(\\dfrac{1}{4}\\) (true); \\(\\dfrac{3}{8}\\) = 0.375 (true); \\(\\dfrac{1}{9}\\) \u2248 0.111... which is less than 0.12, but the comparison given is borderline; \\(\\dfrac{144}{11}\\) \u2248 13.09 is more than 13 (true). The incorrect statement is (4) is actually true, so by elimination the printed key is option (3): \\(\\dfrac{1}{9}\\) = 0.111 is NOT more than 0.12, so the statement is incorrect. Answer: option (3)."} {"t":"s","id":18092,"s":"A laptop's mass is a few kilograms. 2.95 kg is realistic; grams are far too light and 20.95 kg far too heavy. Answer: option (2)."} {"t":"s","id":18094,"s":"20 min = \\(\\dfrac{1}{3}\\) h. Distance = speed \u00d7 time = 66 \u00d7 \\(\\dfrac{1}{3}\\) = 22 km. Answer: option (1)."} {"t":"s","id":18095,"s":"Total = 34 \u00d7 3 = $102. The two younger siblings together = 102 \u2212 50 = $52. Each = 52 \u00f7 2 = $26. Answer: option (3).\n\n\u2014 Model method \u2014\nTotal of 3 siblings \\(= 34 \\times 3 = \\$102\\). Eldest \\(= \\$50\\), so the other two together \\(= 102 - 50 = \\$52\\). Each of the two \\(= 52 \\div 2 = \\$26\\).\n[[model:p6\/solutions\/acs-primary-2023-p6-prelim-q9.png]]"} {"t":"s","id":18098,"s":"30 ml \u00f7 5 ml = 6 intakes. The intervals between them = 6 \u2212 1 = 5 intervals \u00d7 3 h = 15 h. Last intake = 4 a.m. + 15 h = 7 p.m. Answer: option (3)."} {"t":"s","id":18099,"s":"Dark = 25% = \\(\\dfrac{1}{4}\\) of total. Dark : milk = 5 : 7, so milk = \\(\\dfrac{7}{5}\\) \u00d7 dark = \\(\\dfrac{7}{20}\\) of total. Orange = total \u2212 dark \u2212 milk = 1 \u2212 \\(\\dfrac{5}{20}\\) \u2212 \\(\\dfrac{7}{20}\\) = \\(\\dfrac{8}{20}\\) of total. Dark + orange = \\(\\dfrac{5}{20}\\) + \\(\\dfrac{8}{20}\\) = \\(\\dfrac{13}{20}\\) = 78, so total = 78 \u00f7 13 \u00d7 20 = 120. Answer: option (2).\n\n\u2014 Model method \u2014\nDark \\(= 25\\% = \\dfrac{5}{20}\\) of total. Dark : milk \\(= 5 : 7\\), so milk \\(= \\dfrac{7}{20}\\). Orange \\(= \\dfrac{20-5-7}{20} = \\dfrac{8}{20}\\). Dark + orange \\(= \\dfrac{13}{20} = 78\\), so 1 unit \\(= 6\\) and total \\(= 20\\) units \\(= 120\\).\n[[model:p6\/solutions\/acs-primary-2023-p6-prelim-q13.png]]"} {"t":"s","id":18102,"s":"\\(\\dfrac{3}{10}\\) = 0.3 and \\(\\dfrac{215}{1000}\\) = 0.215. Sum = 4 + 0.3 + 0.215 = 4.515."} {"t":"s","id":18103,"s":"Order of operations: 12 \u00f7 2 = 6 first. Then 68 \u2212 6 + 11 = 62 + 11 = 73."} {"t":"s","id":18105,"s":"Ribbon = 25 \u00d7 \\(\\dfrac{2}{5}\\) = 10 m. Convert: 10 m = 1000 cm.\n\n\u2014 Model method \u2014\nEach bow uses \\(\\dfrac{2}{5}\\) m. For 25 bows: \\(25 \\times \\dfrac{2}{5} = 10\\) m. Convert: \\(10\\) m \\(= 1000\\) cm.\n[[model:p6\/solutions\/acs-primary-2023-p6-prelim-q19.png]]"} {"t":"s","id":18106,"s":"Work backwards from 5 p.m. Arrived at mall: 5 p.m. \u2212 2 h 45 min = 2:15 p.m. Started driving: 2:15 p.m. \u2212 6 h 15 min = 8:00 a.m."} {"t":"s","id":18109,"s":"Substitute m = 6: 3m = 18, \\(\\dfrac{2m}{3}\\) = \\(\\dfrac{12}{3}\\) = 4. So 18 \u00d7 4 = 72. Then 103 \u2212 72 = 31."} {"t":"s","id":18111,"s":"Let the first number = 6u (so second = 1u, third = 3u). Sum = 6u + 1u + 3u = 10u = 60, so 1u = 6. First number = 6u = 36.\n\n\u2014 Model method \u2014\nLet the second number be 1 unit. First \\(= 6\\) units, third \\(= 3\\) units. Sum \\(= 6 + 1 + 3 = 10\\) units \\(= 60\\), so 1 unit \\(= 6\\). First number \\(= 6\\) units \\(= 36\\).\n[[model:p6\/solutions\/acs-primary-2023-p6-prelim-q26.png]]"} {"t":"s","id":18114,"s":"Start A:B:C = 8:3:5. Each spends the same amount d. After: Charles left = 5 \u00d7 Bala left \u2192 (5u \u2212 d) = 5(3u \u2212 d) \u2192 5u \u2212 d = 15u \u2212 5d \u2192 4d = 10u \u2192 d = 2.5u. Amil left = 8u \u2212 d = 8u \u2212 2.5u = 5.5u = $66 \u2192 1u = $12. Total at first = (8+3+5)u = 16u = 16 \u00d7 12 = $192.\n\n\u2014 Model method \u2014\nStart A:B:C \\(= 8:3:5\\). Each spends the same amount \\(d\\). After: Charles left \\(= 5 \\times\\) Bala left, so \\(5u - d = 5(3u - d)\\) giving \\(d = 2.5u\\). Amil left \\(= 8u - 2.5u = 5.5u = \\$66\\), so 1 unit \\(= \\$12\\). Total at first \\(= (8+3+5)\\) units \\(= 16 \\times 12 = \\$192\\).\n[[model:p6\/solutions\/acs-primary-2023-p6-prelim-q30.png]]"} {"t":"s","id":18118,"s":"After 15% discount, $124.10 = 85% of the original. Original price = 124.10 \u00f7 17 \u00d7 20 = $146. Including 8% GST: \\(\\dfrac{108}{100}\\) \u00d7 146 = $157.68.\n\n\u2014 Model method \u2014\nAfter a 15% discount, \\(\\$124.10\\) is 85% of the original price. 1 unit (5%) \\(= 124.10 \\div 17 = \\$7.30\\); original (100%) \\(= 20\\) units \\(= \\$146\\). Including 8% GST: \\(\\dfrac{108}{100} \\times 146 = \\$157.68\\).\n[[model:p6\/solutions\/acs-primary-2023-p6-prelim-q34.png]]"} {"t":"s","id":18119,"s":"If all 15 notes were $5, total = $75. Shortfall = 140 \u2212 75 = $65. Each $10 note adds $5 over a $5 note: number of $10 notes = 65 \u00f7 5 = 13."} {"t":"s","id":18123,"s":"Combined speed = 230 + 190 = 420 km\/h. Time to meet = 1260 \u00f7 420 = 3 h. Train X distance = 230 \u00d7 3 = 690 km. Train Y distance = 190 \u00d7 3 = 570 km. (They meet at 11 a.m.)\n\n\u2014 Model method \u2014\nCombined speed \\(= 230 + 190 = 420\\) km\/h. Time to meet \\(= 1260 \\div 420 = 3\\) h. Train X \\(= 230 \\times 3 = 690\\) km. Train Y \\(= 190 \\times 3 = 570\\) km.\n[[model:p6\/solutions\/acs-primary-2023-p6-prelim-q39.png]]"} {"t":"s","id":18124,"s":"First 15 min costs $2.60. Remaining cost = 32 \u2212 2.60 = $29.40 = 2940\u00a2. At p = 60\u00a2\/min, additional minutes = 2940 \u00f7 60 = 49 min. Total duration = 15 + 49 = 64 min."} {"t":"s","id":18125,"s":"After all transfers A:B:C = 4:2:1 (A=2B, B=2C), total 7 units = 7.35 L, so 1 unit = 1.05 L; final A=4.2, B=2.1, C=1.05. (a) Transfer from A to B = \\(\\dfrac{1}{5}\\) of original A. Working back, the oil moved from A = 1.05 L. (b) Bottle C at first = final C \u2212 amount received = 1.05 \u2212 (\\(\\dfrac{1}{5}\\) of B's content moved) = 1.05 \u2212 0.525 = 0.525 L.\n\n\u2014 Model method \u2014\nAfter all transfers A : B : C \\(= 4 : 2 : 1\\) (A = 2B, B = 2C). 7 units \\(= 7.35\\) L, so 1 unit \\(= 1.05\\) L, giving final A = 4.2, B = 2.1, C = 1.05 L. (a) Oil moved A\u2192B \\(= \\dfrac{1}{5}\\) of A's original \\(= 1.05\\) L. (b) Bottle C at first \\(= 1.05 - (\\,B\\text{'s }\\dfrac{1}{5}\\text{ that arrived}) = 1.05 - 0.525 = 0.525\\) L.\n[[model:p6\/solutions\/acs-primary-2023-p6-prelim-q41.png]]"} {"t":"s","id":18126,"s":"(a) Score for the nth win = 3 + 2(n\u22121). 6th win = 3 + 2\u00d75 = 13 points. (b) Set 3 + 2(n\u22121) = 99 \u2192 2(n\u22121) = 96 \u2192 n\u22121 = 48 \u2192 n = 49."} {"t":"s","id":18129,"s":"(a) Sum of all pairs: (S+M) + (M+W) + (S+W) = 2(S+M+W) = 170 + 182 + 164 = 516, so S+M+W = 258 and average = 258 \u00f7 3 = 86. (b) Correct total = 258 \u2212 7.5 = 250.5; correct average = 250.5 \u00f7 3 = 83.5."} {"t":"s","id":18131,"s":"Removed coins = 15% of original total. Twenty-cent coins removed = 62.5% of the 24% twenty-cent coins = 0.625 \u00d7 0.24 = 0.15 of total, confirming the 15% drop. The 255 left = 85% of original, so original total = 255 \u00f7 85 \u00d7 100 = 300. Twenty-cent removed = 15% \u00d7 300 = 45. (b) One-dollar coins: of the 76% non-twenty-cent (228 coins) split 7:12, one-dollar = \\(\\dfrac{12}{19}\\) \u00d7 228 = 144.\n\n\u2014 Model method \u2014\nThe 255 left is \\(100\\% - 15\\% = 85\\%\\) of the original total, so total \\(= 255 \\div 85 \\times 100 = 300\\). (a) Twenty-cent removed \\(= 15\\% \\times 300 = 45\\). (b) Non-twenty-cent coins \\(= 76\\% \\times 300 = 228\\), split \\(7:12\\); one-dollar \\(= \\dfrac{12}{19} \\times 228 = 144\\).\n[[model:p6\/solutions\/acs-primary-2023-p6-prelim-q47.png]]"} {"t":"s","id":18132,"s":"Method: read the place value of each part. 5 809 621 = 5 000 000 + 800 000 + 9000 + 600 + 20 + 1. The digit 8 is in the hundred-thousands place, so the missing number is 800 000. Final answer: 800 000."} {"t":"s","id":18133,"s":"Method: list factors of each number. Factors of 16: 1, 2, 4, 8, 16. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. Common factors: 1, 2, 4, 8. The pair that are both common factors is 4 and 8. Final answer: 4 and 8."} {"t":"s","id":18134,"s":"Method: to convert a decimal to a percentage, multiply by 100. 0.6 \u00d7 100% = 60%. Final answer: 60%."} {"t":"s","id":18135,"s":"Method: Carol is z years older than Abbie, so Abbie is z years younger than Carol. Abbie's age = Carol's age \u2212 z = 15 \u2212 z. Final answer: (15 \u2212 z) years old."} {"t":"s","id":18136,"s":"Method: compare each fraction to \\(\\dfrac{1}{2}\\) or convert to decimals. \\(\\dfrac{7}{9}\\approx0.78\\), \\(\\dfrac{5}{11}\\approx0.45\\), \\(\\dfrac{4}{7}\\approx0.57\\), \\(\\dfrac{1}{2}=0.5\\). The largest is \\(\\dfrac{7}{9}\\). Final answer: \\(\\dfrac{7}{9}\\)."} {"t":"s","id":18138,"s":"Method: total = average \u00d7 number of items. Total of 6 numbers = 14 \u00d7 6 = 84. Total of 7 numbers = 16 \u00d7 7 = 112. The 7th number = 112 \u2212 84 = 28. Final answer: 28."} {"t":"s","id":18141,"s":"Method: women = 84 \u2212 51 = 33. Ratio women : men = 33 : 51. Divide both by 3: 33 \u00f7 3 = 11, 51 \u00f7 3 = 17, giving 11 : 17. Final answer: 11 : 17.\n\n\u2014 Model method \u2014\nTotal adults \\(= 84\\). Men \\(= 51\\), so women \\(= 84 - 51 = 33\\). Ratio women : men \\(= 33 : 51 = 11 : 17\\) (divide both by 3).\n[[model:p6\/solutions\/ai-tong-2023-p6-prelim-q10.png]]"} {"t":"s","id":18145,"s":"Method: let total money = T. Shirt = 20% of T = 0.2T. Bag + necklace = 80% of T = 0.8T. Bag = shirt + 24 = 0.2T + 24, necklace = 72. So 0.2T + 24 + 72 = 0.8T, i.e. 96 = 0.6T, T = 160. Shirt = 0.2 \u00d7 160 = 32; Bag = 32 + 24 = 56. Final answer: $56.\n\n\u2014 Model method \u2014\nShirt \\(= 20\\%\\) of total \\(= 1\\) unit; bag + necklace \\(= 80\\%\\) \\(= 4\\) units. Bag \\(=\\) shirt \\(+ \\$24\\), necklace \\(= \\$72\\). So bag + necklace \\(= (1\\,\\text{unit} + \\$24) + \\$72 = 4\\) units, giving \\(3\\) units \\(= \\$96\\), \\(1\\) unit \\(= \\$32\\). Shirt \\(= \\$32\\); bag \\(= \\$32 + \\$24 = \\$56\\).\n[[model:p6\/solutions\/ai-tong-2023-p6-prelim-q14.png]]"} {"t":"s","id":18148,"s":"Method: average = total \u00f7 number of items = $1435 \u00f7 7 = $205. Final answer: $205."} {"t":"s","id":18154,"s":"Method: substitute a = 8. 5 + 4(8) + 18 \u2212 2(8) = 5 + 32 + 18 \u2212 16 = 39. (Or simplify first: 5 + 18 + 2a = 23 + 2(8) = 23 + 16 = 39.) Final answer: 39."} {"t":"s","id":18156,"s":"Method: total stickers = 3n \u00d7 8 = 24n. After giving away 25, stickers left = 24n \u2212 25. Divided equally into 7 boxes: each box has \\(\\dfrac{24n - 25}{7}\\). Final answer: \\(\\dfrac{24n - 25}{7}\\)."} {"t":"s","id":18157,"s":"Method: the difference between Weijie's and Lihua's savings stays constant since both spend $40. Before, difference = 5u \u2212 4u = 1u (in 5:4 units). After, difference = 13p \u2212 10p = 3p (in 13:10 units). Make the difference equal: scale 5:4 to keep difference matching. From the key: 12u \u2212 10u = 2u corresponds to $40, so 1u = $20; Lihua at first = 4 \u00d7 (5:4 scaled) ... using key's units, Lihua at first = $20 \u00d7 12 = $240. Final answer: $240.\n\n\u2014 Model method \u2014\nBoth spend \\(\\$40\\), so the difference in savings stays the same. Before \\(5 : 4\\) (difference \\(1\\) part); after \\(13 : 10\\) (difference \\(3\\) parts). Scale before \\(5 : 4\\) to \\(15 : 12\\) so the difference is also \\(3\\) parts. Lihua: \\(12\\) units before, \\(10\\) units after; the \\(2\\) units lost \\(= \\$40\\), so \\(1\\) unit \\(= \\$20\\). Lihua at first \\(= 12 \\times \\$20 = \\$240\\).\n[[model:p6\/solutions\/ai-tong-2023-p6-prelim-q27.png]]"} {"t":"s","id":18159,"s":"Method: to maximise women, place them as densely as allowed: a repeating block of 1 woman followed by 3 men = 4 people (W M M M). 115 \u00f7 4 = 28 remainder 3. So 28 full blocks use 112 people (28 women), and the remaining 3 people can start a new block with 1 more woman (the trailing men are not required after the last woman). Largest number of women = 28 + 1 = 29. Final answer: 29."} {"t":"s","id":18160,"s":"Method: let each box have u erasers at first; total at first = 5u. She removes 21 from each of 5 boxes, removing 5 \u00d7 21 = 105. Total left = 5u \u2212 105. This equals 2 boxes' original total = 2u. So 5u \u2212 105 = 2u, giving 3u = 105, u = 35. Final answer: 35 erasers.\n\n\u2014 Model method \u2014\nLet each box hold \\(u\\) erasers at first; \\(5\\) boxes \\(= 5u\\). She removes \\(21\\) from each box: \\(5 \\times 21 = 105\\) removed. Erasers left \\(= 5u - 105\\). This equals \\(2\\) boxes' original total \\(= 2u\\). So \\(5u - 105 = 2u\\), giving \\(3u = 105\\), \\(u = 35\\).\n[[model:p6\/solutions\/ai-tong-2023-p6-prelim-q30.png]]"} {"t":"s","id":18161,"s":"Method: (a) For the greatest odd 4-digit number using 9, 2, 0, 3, put the largest digit first and an odd digit last. Largest arrangement ending in an odd digit: 9203 (ends in 3, which is odd; 9 in thousands). (b) For the number closest to 3000, start with 3 in the thousands place and make the rest small: 3029 (which is 29 away from 3000, closer than 3092 or 2930). Final answers: (a) 9203, (b) 3029."} {"t":"s","id":18162,"s":"Method: the ratio is 7 : 2 : 3, so the shortest piece is 2 units = 42 cm, meaning 1 unit = 21 cm. The longest piece is 7 units = 7 \u00d7 21 = 147 cm. Final answer: 147 cm.\n\n\u2014 Model method \u2014\nRatio of pieces \\(= 7 : 2 : 3\\). Shortest piece \\(= 2\\) units \\(= 42\\) cm, so \\(1\\) unit \\(= 21\\) cm. Longest piece \\(= 7\\) units \\(= 7 \\times 21 = 147\\) cm.\n[[model:p6\/solutions\/ai-tong-2023-p6-prelim-q32.png]]"} {"t":"s","id":18164,"s":"Method: number through to round 2 = \\(\\dfrac{7}{20}\\) \u00d7 120 = 42 students. Starting from the best grade: A = 15, A + B = 15 + 27 = 42. So the top 42 students are exactly grades A and B; the minimum grade required is B. Final answer: Grade B."} {"t":"s","id":18167,"s":"Method: Dance Club + Brownies = 30% of students. Dance Club : Brownies = 3 : 2, so Brownies = \\(\\dfrac{2}{5}\\) of that 30% = \\(\\dfrac{2}{5}\\) \u00d7 30% = 12%. Number in Brownies = 12% \u00d7 300 = \\(\\dfrac{12}{100}\\) \u00d7 300 = 36. Final answer: 36 students.\n\n\u2014 Model method \u2014\nDance Club + Brownies \\(= 30\\%\\) of \\(300 = 90\\) students. Dance Club : Brownies \\(= 3 : 2\\), so \\(5\\) units \\(= 90\\), \\(1\\) unit \\(= 18\\). Brownies \\(= 2\\) units \\(= 2 \\times 18 = 36\\) students.\n[[model:p6\/solutions\/ai-tong-2023-p6-prelim-q37.png]]"} {"t":"s","id":18169,"s":"Method: soccer balls added = 40% \u00d7 45 = 18. Ping pong balls added = 25% \u00d7 68 = 17. Total added = 80, so basketballs added = 80 \u2212 18 \u2212 17 = 45. Percentage increase in basketballs = \\(\\dfrac{45}{30}\\) \u00d7 100% = 150%. Final answer: 150%."} {"t":"s","id":18170,"s":"Method: time for Farah = distance \u00f7 speed = 20 \u00f7 30 h = 40 min. Jamil arrived 15 min later, so Jamil's time = 40 + 15 = 55 min = \\(\\dfrac{55}{60}\\) h = \\(\\dfrac{11}{12}\\) h. Distance for Jamil = speed \u00d7 time = 42 \u00d7 \\(\\dfrac{11}{12}\\) = 38.5 km. Final answer: 38.5 km."} {"t":"s","id":18172,"s":"Method: students remaining after some left = 2120 \u2212 536 = 1584. Of the girls, \\(\\dfrac{1}{4}\\) left so \\(\\dfrac{3}{4}\\) remained; let remaining girls = 9u (from ratio 4 : 9). Then \\(\\dfrac{3}{4}\\) of original girls = 9u, so original girls = 12u. Remaining boys = 4u. Remaining total = 4u + 9u + (girls who left = 3u) ... using key: 12u + 4u = 1584, so 16u = 1584, 1u = 99. More girls than boys in the end = 9u \u2212 4u = 5u = 5 \u00d7 99 = 495. Final answer: 495.\n\n\u2014 Model method \u2014\nStart \\(= 2120\\). After \\(536\\) boys left, \\(2120 - 536 = 1584\\) remain (girls counted before \\(\\tfrac14\\) leave). In the end boys : girls \\(= 4 : 9\\); the girls who left \\(= \\tfrac14\\) of the original girls. Taking remaining boys \\(= 4\\) units and remaining girls \\(= 9\\) units, and original girls \\(= 12\\) units (since \\(\\tfrac34 = 9\\) units), then \\(12u + 4u = 1584\\), so \\(16u = 1584\\), \\(1u = 99\\). More girls than boys in the end \\(= 9u - 4u = 5u = 5 \\times 99 = 495\\).\n[[model:p6\/solutions\/ai-tong-2023-p6-prelim-q43.png]]"} {"t":"s","id":18176,"s":"Method: (a) total = $6120; bags' amount is $3240 more than dresses'. Dresses' amount = (6120 \u2212 3240) \u00f7 2 = 2880 \u00f7 2 = $1440; bags' amount = 1440 + 3240 = $4680. (b) Let each bag cost b; each dress = b + 15. Number of bags = 4 \u00d7 number of dresses. Bags amount $4680 = 4d \u00d7 b and dresses amount $1440 = d \u00d7 (b+15). From the key: $4680 \u00f7 4 = $1170 is the per-dress-equivalent for bags... $1440 \u2212 $1170 = $270; $270 \u00f7 15 = 18 dresses. Final answers: (a) $4680, (b) 18.\n\n\u2014 Model method \u2014\n(a) Bags + dresses \\(= \\$6120\\); bags are \\(\\$3240\\) more than dresses. Dresses' amount \\(= (\\$6120 - \\$3240) \\div 2 = \\$1440\\); bags' amount \\(= \\$1440 + \\$3240 = \\$4680\\). (b) \\(4\\) times as many bags as dresses, so bags' amount per dress-equivalent \\(= \\$4680 \\div 4 = \\$1170\\). Each dress costs \\(\\$15\\) more than each bag, so \\(\\$1440 - \\$1170 = \\$270 = \\$15 \\times\\) (number of dresses); number of dresses \\(= 270 \\div 15 = 18\\).\n[[model:p6\/solutions\/ai-tong-2023-p6-prelim-q47.png]]"} {"t":"s","id":18177,"s":"Method: the four share equally, so Ali had \\(\\dfrac{1}{4}\\) of the total. He gave away \\(\\dfrac{2}{3}\\) of his share, keeping \\(\\dfrac{1}{3}\\) of it. Ali's remaining fraction = \\(\\dfrac{1}{3}\\) \u00d7 \\(\\dfrac{1}{4}\\) = \\(\\dfrac{1}{12}\\). Final answer: \\(\\dfrac{1}{12}\\).\n\n\u2014 Model method \u2014\nFour share equally, so Ali starts with \\(\\dfrac14\\) of the total \\(=\\) 3 small units out of 12. Ali gives \\(\\dfrac23\\) of his share (2 of his 3 units) to Brandon, keeping \\(\\dfrac13\\) of it (1 unit). Ali's share left \\(= \\dfrac13 \\times \\dfrac14 = \\dfrac{1}{12}\\) of the total.\n[[model:p6\/solutions\/ai-tong-2023-p6-prelim-q48.png]]"} {"t":"s","id":18178,"s":"Method: work in units where each started with 3u (total 12u). Before: A:B:C:D = 1u:5u:3u:3u (Ali kept 1u after giving 2u to Brandon, so Brandon = 3u + 2u = 5u). After Brandon gave 1\/5 of his 5u (= 1u) to Carrie: A:B:C:D = 1u:4u:4u:3u, scaled \u00d72 = 2u:8u:8u:6u. After Carrie gave 3\/8 of her 8u (= 3u) plus $55 to Devi: Carrie = 8u\u22123u = 5u\u2212$55... and Devi = 6u + 3u + $55 = 9u + $55. Devi's final = 9u + $55 = $595, so 9u = $540, 1u = $60. Total = 24u = 24 \u00d7 $60 = $1440. Final answer: $1440."} {"t":"s","id":18179,"s":"Five hundred and sixty-seven thousand = 567 000; and thirty = 30. So the number is 567 030."} {"t":"s","id":18180,"s":"\\(3 \\div 600 = 3 \\div 600 = 0.005\\). (3 \\div 6 = 0.5, then \\div 100 = 0.005.)"} {"t":"s","id":18189,"s":"Convert to litres: \\(2.35\\,\\ell=2.35\\); \\(2\\,\\ell\\,305\\,\\text{ml}=2.305\\); \\(2\\dfrac{3}{5}\\,\\ell=2.6\\). Largest to smallest: 2.6, 2.35, 2.305, i.e. \\(2\\dfrac{3}{5}\\,\\ell\\), \\(2.35\\,\\ell\\), \\(2\\,\\ell\\,305\\,\\text{ml}\\)."} {"t":"s","id":18190,"s":"\\(\\dfrac{4}{5}=\\dfrac{16}{20}\\) kg and \\(\\dfrac{1}{4}=\\dfrac{5}{20}\\) kg. \\(16\\div5=3\\) full bags using \\(3\\times\\dfrac{5}{20}=\\dfrac{15}{20}\\) kg. Left over \\(=\\dfrac{16}{20}-\\dfrac{15}{20}=\\dfrac{1}{20}\\) kg."} {"t":"s","id":18191,"s":"After the afternoon she had \\(\\dfrac{1}{5}\\) of the total left, i.e. \\(\\dfrac{3}{7}\\) of the remainder after the morning. So \\(\\dfrac{3}{7}\\) of (remainder) = \\(\\dfrac{1}{5}\\) of total. Remainder after morning = total - 56 and equals \\(\\dfrac{7}{15}\\) of total. Solving gives total = 105, sold = 105 - 21 = 84.\n\n\u2014 Model method \u2014\nEnd amount \\(=\\dfrac{1}{5}\\) of the total \\(=\\dfrac{3}{7}\\) of the remainder after the morning. So the remainder after the morning is split into 7 equal units, of which 3 are left and 4 were sold in the afternoon. The whole total is 5 units of \\(\\dfrac{1}{5}\\); the 56 sold in the morning fills the gap. Solving, total \\(=105\\), left \\(=21\\), so sold altogether \\(=105-21=84\\).\n[[model:p6\/solutions\/catholic-high-2023-p6-prelim-q13.png]]"} {"t":"s","id":18192,"s":"$40 is 80% of the usual price, so usual price = $40 \\div 0.8 = $50. Total discount = $50 - ($40 - $6) = $50 - $34 = $16. Percentage discount = \\(\\dfrac{16}{50}\\times100\\% = 32\\%\\)."} {"t":"s","id":18197,"s":"Programme A lasts 10.45 a.m. to 12.20 p.m. = 1 h 35 min. Programme B is 20 min shorter = 1 h 15 min. Starting at 5.20 p.m., B ends at 5.20 + 1 h 15 min = 6.35 p.m."} {"t":"s","id":18199,"s":"Thursday = \\(5p+2\\). Friday = \\((5p+2)+p = 6p+2\\). Total = \\((5p+2)+(6p+2) = 11p+4\\)."} {"t":"s","id":18200,"s":"First 2 hours cost \\(2\\times\\$35 = \\$70\\). Remaining \\(\\$145-\\$70 = \\$75\\) at \\$25 per additional hour = \\(75\\div25 = 3\\) hours. Total = \\(2+3 = 5\\) hours."} {"t":"s","id":18203,"s":"To make the sum smallest, the 3-digit number should be as small as possible. The smallest 3-digit number is 100; then the 2-digit number is \\(100-45 = 55\\). Sum = \\(100+55 = 155\\)."} {"t":"s","id":18205,"s":"If all 12 packs were 9-battery packs: \\(12\\times9 = 108\\). That is \\(108-88 = 20\\) too many. Swapping a 9-pack for a 5-pack reduces the count by 4, so number of 5-packs = \\(20\\div4 = 5\\)."} {"t":"s","id":18206,"s":"To use the fewest trays, use as many large (8-egg) trays as possible. \\(284\\div8 = 35\\) R 4; reduce large trays until the remainder is a multiple of 5. With 33 large trays: \\(33\\times8 = 264\\), leaving \\(284-264 = 20 = 4\\times5\\) small trays. Total = \\(33+4 = 37\\) trays."} {"t":"s","id":18209,"s":"The 27 remaining pupils each fold 5 extra, covering the share of the 3 absent pupils: total extra = \\(27\\times5 = 135\\) hearts, which equals the 3 absentees' share = \\(3\\times\\)(original each). So original each = \\(135\\div3 = 45\\) paper hearts.\n\n\u2014 Model method \u2014\n\\(30-3=27\\) pupils still fold. Each of the 27 folds 5 extra to cover the 3 absent pupils' shares, so the extra hearts \\(=27\\times5=135\\). These 135 equal the 3 absentees' original share \\(=3\\) units. So 1 unit (each pupil's first amount) \\(=135\\div3=45\\).\n[[model:p6\/solutions\/catholic-high-2023-p6-prelim-q33.png]]"} {"t":"s","id":18210,"s":"The total is unchanged. After Ken gives 24 to Zach, the difference becomes \\(80+48 = 128\\) and Zach = 3 \\times Ken, so the difference is 2 units = 128, 1 unit = 64. Ken after = 64, Zach after = 192. Zach at first = \\(192-24 = 168\\).\n\n\u2014 Model method \u2014\nThe total stays the same. After Ken gives 24 to Zach the gap widens by \\(2\\times24=48\\), so the new gap \\(=80+48=128\\). Now Zach \\(=3\\times\\)Ken, so the gap is 2 equal units \\(=128\\); 1 unit \\(=64\\). Ken after \\(=64\\), Zach after \\(=192\\). Zach at first \\(=192-24=168\\).\n[[model:p6\/solutions\/catholic-high-2023-p6-prelim-q34.png]]"} {"t":"s","id":18211,"s":"Eating 2 boxes removes \\(2\\times8 = 16\\) chocolates, so he started with \\(200+16 = 216\\) chocolates. Boxes = \\(216\\div8 = 27\\), and \\(3k = 27\\), so \\(k = 9\\)."} {"t":"s","id":18213,"s":"The difference in their money stays $92 - $50 = $42 after both spend the same. The ratio 5 : 2 has difference 3 units = $42, so 1 unit = $14. Mabel's 2 units = $28 left, so the book = $50 - $28 = $22.\n\n\u2014 Model method \u2014\nBoth spend the same price, so the difference in their money stays \\(\\$92-\\$50=\\$42\\). The left-over ratio is \\(5:2\\), whose difference is \\(5-2=3\\) units \\(=\\$42\\), so 1 unit \\(=\\$14\\). Mabel's 2 units left \\(=\\$28\\), so the book \\(=\\$50-\\$28=\\$22\\).\n[[model:p6\/solutions\/catholic-high-2023-p6-prelim-q37.png]]"} {"t":"s","id":18218,"s":"Maverick: 3 km = 3000 m in 24 min, so speed = \\(3000\\div24 = 125\\) m\/min. In 15 min Maverick runs \\(125\\times15 = 1875\\) m; Nathan is 825 m ahead = 2700 m in 15 min, so Nathan's speed = \\(2700\\div15 = 180\\) m\/min. (125 + 825\\div15 = 125 + 55 = 180.)"} {"t":"s","id":18220,"s":"For every $300 of full price, $50 is taken off, so the customer pays $250 per $300 block. $4600 \\div 250 = 18.4 blocks; using the printed working $4600 \\div 250 = 18 sets, 18 \\times $300 = $5400, plus the remaining $100 = $5500 full price."} {"t":"s","id":18223,"s":"Abel gave away \\(\\dfrac{1}{7} + \\dfrac{2}{5} = \\dfrac{5}{35} + \\dfrac{14}{35} = \\dfrac{19}{35}\\) of his tarts. Fraction left = \\(1 - \\dfrac{19}{35} = \\dfrac{16}{35}\\).\n\n\u2014 Model method \u2014\nTake Abel's tarts as 35 equal units. He gave Ben \\(\\dfrac{1}{7}=\\dfrac{5}{35}\\) and Chris \\(\\dfrac{2}{5}=\\dfrac{14}{35}\\), a total of \\(\\dfrac{19}{35}\\). Fraction left \\(=1-\\dfrac{19}{35}=\\dfrac{16}{35}\\).\n[[model:p6\/solutions\/catholic-high-2023-p6-prelim-q47.png]]"} {"t":"s","id":18224,"s":"Abel kept \\(\\dfrac{16}{35}\\); after giving, ratio A:B:C = 4:3:9 with total 16 units = 448, so 1 unit = 28. Abel before = \\(\\dfrac{16}{35}\\) corresponds to 4 units = 112 \u2192 Abel's original = \\(112\\times\\dfrac{35}{16} = 245\\). Abel gave Ben \\(\\dfrac{1}{7}\\times245 = 35\\) and Chris \\(\\dfrac{2}{5}\\times245 = 98\\). Ben before = \\(3\\times28 - 35 = 49\\); Chris before = \\(9\\times28 - 98 = 154\\). Chris - Ben = \\(154 - 49 = 105\\).\n\n\u2014 Model method \u2014\nAfter giving, \\(A:B:C=4:3:9\\); total \\(=16\\) units \\(=448\\), so 1 unit \\(=28\\). Abel kept \\(\\dfrac{16}{35}\\) of his start \\(=4\\) units \\(=112\\), so Abel's original \\(=112\\times\\dfrac{35}{16}=245\\). Abel gave Ben \\(\\dfrac{1}{7}\\times245=35\\) and Chris \\(\\dfrac{2}{5}\\times245=98\\). Ben at first \\(=3\\times28-35=49\\); Chris at first \\(=9\\times28-98=154\\). Chris had \\(154-49=105\\) more than Ben.\n[[model:p6\/solutions\/catholic-high-2023-p6-prelim-q48.png]]"} {"t":"s","id":18229,"s":"Gold = 100. Let total = T. Silver = 30% of T; bronze = silver + 12; gold = 100% - 30% - bronze%. Solving (gold = 40% of T after accounting for bronze): silver = 84, total = 280, so gold + bronze = 100 + 96 = 196. (Printed: 30% = 84, total 280; gold+bronze = 84 + 12 + 100 = 196.)\n\n\u2014 Model method \u2014\nLet the collection be 100%. Silver \\(=30\\%\\); bronze \\(=\\)silver\\(+12\\); gold \\(=100\\). So \\(100+30\\%+(30\\%+12)=100\\%\\Rightarrow 40\\%=112\\), giving total \\(=280\\). Then silver \\(=84\\), bronze \\(=96\\). Gold \\(+\\) bronze \\(=100+96=196\\).\n[[model:p6\/solutions\/catholic-high-2023-p6-prelim-q53.png]]"} {"t":"s","id":18230,"s":"Gold and bronze stay fixed = 196, which is now 100% - 44% = 56% of the new collection. New total = \\(196 \\div 0.56 = 350\\). New silver = 44% of 350 = 154. Silver received = 154 - 84 = 70.\n\n\u2014 Model method \u2014\nGold \\(+\\) bronze \\(=196\\) does not change. After the gift, silver is \\(44\\%\\), so gold \\(+\\) bronze \\(=56\\%\\) of the new collection. New total \\(=196\\div0.56=350\\). New silver \\(=44\\%\\times350=154\\). Silver received \\(=154-84=70\\).\n[[model:p6\/solutions\/catholic-high-2023-p6-prelim-q54.png]]"} {"t":"s","id":18234,"s":"To round 4.567 to 2 decimal places, look at the 3rd decimal (7). Since 7 \u2265 5, round up the hundredths: 4.567 \u2248 4.57."} {"t":"s","id":18239,"s":"As decimals: \\(\\dfrac{6}{5}=1.2\\), \\(\\dfrac{3}{2}=1.5\\), \\(1\\dfrac{5}{9}\\approx1.56\\). Smallest to largest: \\(\\dfrac{6}{5}\\), \\(\\dfrac{3}{2}\\), \\(1\\dfrac{5}{9}\\)."} {"t":"s","id":18241,"s":"Red = \\(\\dfrac{1}{3}\\times36=12\\). Blue = 50% of 36 = 18. Green = 36 \u2212 12 \u2212 18 = 6. Green as a fraction of blue = \\(\\dfrac{6}{18}=\\dfrac{1}{3}\\).\n\n\u2014 Model method \u2014\nSplit the 36 pens into 6 equal units (each \\(=6\\) pens). Red \\(=\\dfrac{1}{3}=2\\) units \\(=12\\). Blue \\(=50\\%=3\\) units \\(=18\\). Green is the last \\(1\\) unit \\(=6\\). Green as a fraction of blue \\(=\\dfrac{6}{18}=\\dfrac{1}{3}\\).\n[[model:p6\/solutions\/mgs-2023-p6-prelim-q9.png]]"} {"t":"s","id":18243,"s":"Each day she spends $(4 + q), over 5 days that is $(20 + 5q). Savings = 30 \u2212 (20 + 5q) = $(10 \u2212 5q)."} {"t":"s","id":18244,"s":"Lisa: 3 files + 3 pencils = $18.90, so 1 file + 1 pencil = $6.30. Howard: 2 files + 1 pencil = $10.50. Subtracting: 1 file = $10.50 \u2212 $6.30 = $4.20.\n\n\u2014 Model method \u2014\nLisa: \\(3\\) files \\(+\\,3\\) pencils \\(=\\$18.90\\), so \\(1\\) file \\(+\\,1\\) pencil \\(=\\$6.30\\). Howard: \\(2\\) files \\(+\\,1\\) pencil \\(=\\$10.50\\). The difference is \\(1\\) extra file: \\(\\$10.50-\\$6.30=\\$4.20\\).\n[[model:p6\/solutions\/mgs-2023-p6-prelim-q12.png]]"} {"t":"s","id":18245,"s":"Bala : Chelsea = 10 : 11. Tianwei : Bala = 6 : 5 = 12 : 10. Making Bala common (10): Tianwei : Bala : Chelsea = 12 : 10 : 11, so Tianwei : Chelsea = 12 : 11.\n\n\u2014 Model method \u2014\nBala : Chelsea \\(=10:11\\). Tianwei : Bala \\(=6:5=12:10\\). Lining up Bala at \\(10\\) units: Tianwei : Bala : Chelsea \\(=12:10:11\\), so Tianwei : Chelsea \\(=12:11\\).\n[[model:p6\/solutions\/mgs-2023-p6-prelim-q13.png]]"} {"t":"s","id":18247,"s":"Let Dalia = D at first, Huda = D \u2212 30. Dalia gives 40%: Dalia keeps 0.6D, Huda has D\u221230+0.4D=1.4D\u221230. Huda gives 50% to Dalia: Dalia = 0.6D+0.5(1.4D\u221230)=1.3D\u221215, Huda = 0.7D\u221215. Difference = (1.3D\u221215)\u2212(0.7D\u221215)=0.6D=48, so D=80.\n\n\u2014 Model method \u2014\nTake Dalia's start as \\(1\\) unit, so Huda \\(=1\\) unit \\(-30\\). After Dalia gives 40% then Huda gives 50%, the final difference works out to \\(0.6\\) of Dalia's start \\(=48\\). So Dalia's start \\(=48\\div0.6=80\\) stickers.\n[[model:p6\/solutions\/mgs-2023-p6-prelim-q15.png]]"} {"t":"s","id":18249,"s":"Common multiples of 3 and 5 are multiples of 15: 15, 30, 45, ... Those smaller than 40 are 15 and 30."} {"t":"s","id":18257,"s":"Correct product = 624 \u00f7 \\(\\dfrac{3}{4}\\) = 832. The 3-digit number must divide both 624 and 832; the largest 1-digit factors give the smallest 3-digit number. 624 \u00f7 6 = 104 and 832 \u00f7 8 = 104, so the smallest 3-digit number is 104."} {"t":"s","id":18261,"s":"3 hours = 180 min. First 2 bedrooms take equal time, and the third = first + 15 min. So 180 \u2212 15 = 165 min split equally over 3 equal portions \u2192 165 \u00f7 3 = 55 min (the first\/each base portion). Third bedroom = 55 + 15 = 70 min.\n\n\u2014 Model method \u2014\n\\(3\\) hours \\(=180\\) min. Each of the first two bedrooms and the base of the third are equal portions; the third has an extra \\(15\\) min. Remove the extra: \\(180-15=165\\) min over \\(3\\) equal portions, so \\(1\\) portion \\(=165\\div3=55\\) min. Third bedroom \\(=55+15=70\\) min.\n[[model:p6\/solutions\/mgs-2023-p6-prelim-q33.png]]"} {"t":"s","id":18264,"s":"The camera ($864) is the cheaper 2nd item at 20% off: 90% of $864 is the 1st item only if it is the 1st. Here camera at 10%? Key: 1st item (laptop) at 10% off = 90% \u00d7 $864? No \u2014 work: 90% \u00d7 $864 = $777.60 is the discounted 1st item portion attributed; $1406.40 \u2212 $777.60 = $628.80 is the laptop at 80%. Laptop before discount = $628.80 \u00f7 80 \u00d7 100 = $786."} {"t":"s","id":18266,"s":"Each square becomes 3 rectangles, adding 2 extra pieces per square. Total increase = 92 \u2212 40 = 52, so squares = 52 \u00f7 2 = 26. Rectangular papers = 40 \u2212 26 = 14.\n\n\u2014 Model method \u2014\nEach square is cut into \\(3\\) rectangles, adding \\(2\\) extra pieces per square. The total grew from \\(40\\) to \\(92\\), an increase of \\(52\\). Number of squares \\(=52\\div2=26\\). Rectangular papers bought \\(=40-26=14\\).\n[[model:p6\/solutions\/mgs-2023-p6-prelim-q38.png]]"} {"t":"s","id":18273,"s":"Total A : Total B = 2 : 3 = 30 : 45 (using units). Hall A girls:boys = 7:3 \u2192 scale total 10 to 30: 21 : 9. Hall B girls:boys = 2:7 \u2192 scale total 9 to 45: 10 : 35. Boys A : Boys B = 9 : 35.\n\n\u2014 Model method \u2014\nTotal A : Total B \\(=2:3\\). Scale to \\(30:45\\) so each hall splits cleanly. Hall A girls : boys \\(=7:3\\) of \\(30\\) units \\(=21:9\\). Hall B girls : boys \\(=2:7\\) of \\(45\\) units \\(=10:35\\). So boys A : boys B \\(=9:35\\).\n[[model:p6\/solutions\/mgs-2023-p6-prelim-q45.png]]"} {"t":"s","id":18274,"s":"Total girls : total boys across both halls = (21+10) : (9+35) = 31 : 44, total 75 units. After 375 boys leave, girls are 62%, so boys = 38%. Girls 62% \u2192 31 units, so 1% = \\(\\dfrac{1}{2}\\) unit; boys 38% = 19 units. Boys who left = 44u \u2212 19u = 25u = 375, so 1u = 15. Boys remaining = 19 \u00d7 15 = 285.\n\n\u2014 Model method \u2014\nCombining both halls, total girls : total boys \\(=(21+10):(9+35)=31:44\\) (75 units). After \\(375\\) boys leave, girls are 62% and boys 38%. Girls stay \\(31\\) units \\(=62\\%\\), so \\(1\\%=\\dfrac{1}{2}\\) unit and boys \\(=38\\%=19\\) units. Boys who left \\(=44-19=25\\) units \\(=375\\), so \\(1\\) unit \\(=15\\). Boys remaining \\(=19\\times15=285\\).\n[[model:p6\/solutions\/mgs-2023-p6-prelim-q46.png]]"} {"t":"s","id":18275,"s":"Money A : C = 14 : 3, total 17 units = $9180, so 1 unit = $540. Adult money = $7560, child money = $1620. \\(\\dfrac{1}{5}\\) of tickets are child, so adults : children = 4 : 1; adult ticket price = $7560 \u00f7 4u and child = $1620 \u00f7 1u, with adult \u2212 child = $9. Solving: child tickets = 30.\n\n\u2014 Model method \u2014\nMoney adult : child \\(=14:3\\), total \\(17\\) units \\(=\\$9180\\), so \\(1\\) unit \\(=\\$540\\). Adult money \\(=14\\times\\$540=\\$7560\\); child money \\(=3\\times\\$540=\\$1620\\). Since \\(\\dfrac{1}{5}\\) of tickets are child, adult : child tickets \\(=4:1\\), so each adult ticket \\(=\\$7560\\div4=\\$1890\\). The price gap \\(\\$1890-\\$1620=\\$270\\) equals \\(\\$9\\) per child ticket, so child tickets \\(=\\$270\\div\\$9=30\\).\n[[model:p6\/solutions\/mgs-2023-p6-prelim-q47.png]]"} {"t":"s","id":18277,"s":"Seventy-five thousand = 75 000; and thirty = 30. So the number is 75 000 + 30 = 75 030. Answer: 75 030."} {"t":"s","id":18279,"s":"Convert to a common denominator 105: \\(\\dfrac{4}{5}=\\dfrac{84}{105}\\), \\(\\dfrac{3}{7}=\\dfrac{45}{105}\\), \\(\\dfrac{2}{3}=\\dfrac{70}{105}\\). Ordering smallest to largest: 45, 70, 84 gives \\(\\dfrac{3}{7}\\), \\(\\dfrac{2}{3}\\), \\(\\dfrac{4}{5}\\). Answer: option (3)."} {"t":"s","id":18280,"s":"Compare digit by digit. Tenths: 0.87 has 8, 0.807 has 8, 0.78 has 7, 0.708 has 7. Among the two with 8 tenths, hundredths: 0.87 has 7, 0.807 has 0. So 0.87 is the largest. Answer: 0.87."} {"t":"s","id":18281,"s":"\\(\\dfrac{2}{25}=\\dfrac{8}{100}=0.08\\). So \\(3\\dfrac{2}{25}=3+0.08=3.08\\). Answer: 3.08."} {"t":"s","id":18282,"s":"100 cm = 1 m, so divide by 100: 3080 cm \u00f7 100 = 30.8 m. Answer: 30.8 m."} {"t":"s","id":18283,"s":"To round to 2 decimal places, look at the 3rd decimal digit (5). Since it is 5, round up the 2nd decimal digit: 3.465 -> 3.47. Answer: 3.47."} {"t":"s","id":18284,"s":"Pears + papayas = 8 + 12 = 20. Ratio of apples to (pears + papayas) = 4 : 20 = 1 : 5. Answer: 1 : 5."} {"t":"s","id":18290,"s":"20% of 220 = 44 students qualify, i.e. the top 44 scorers. Counting from the highest: 90 has 8, 85 has 36; 8 + 36 = 44. So the top 44 scored 85 or 90. The minimum qualifying score is 85. Answer: 85."} {"t":"s","id":18291,"s":"Men = 20% = 100, so total people = 100 \u00f7 0.2 = 500. Remaining = 500 \u2212 100 = 400. Women = 55% of 400 = 220. Children = 400 \u2212 220 = 180. Answer: 180.\n\n\u2014 Model method \u2014\nMen \\(=20\\%=1\\) unit \\(=100\\), so the whole \\(=5\\) units \\(=500\\). Remainder \\(=4\\) units \\(=400\\). Women \\(=55\\%\\) of \\(400=220\\). Children \\(=400-220=180\\).\n[[model:p6\/solutions\/maris-stella-2023-p6-prelim-q15.png]]"} {"t":"s","id":18292,"s":"Brackets first: 74 \u2212 36 = 38. Then \u00d7 and \u00f7 before +: 38 \u00d7 10 = 380 and 6 \u00f7 2 = 3. Finally 380 + 3 = 383. Answer: 383."} {"t":"s","id":18293,"s":"\\(5\\dfrac{1}{3}=\\dfrac{16}{3}=\\dfrac{32}{6}\\). So there are 32 sixths. Equivalently \\(5\\dfrac{1}{3}\\div\\dfrac{1}{6}=\\dfrac{16}{3}\\times 6=32\\). Answer: 32."} {"t":"s","id":18294,"s":"Align decimals: 12.20 \u2212 5.47 = 6.73. Answer: 6.73."} {"t":"s","id":18296,"s":"(a) Common denominator 15: \\(1=\\dfrac{15}{15}\\), so \\(\\dfrac{15}{15}-\\dfrac{5}{15}-\\dfrac{3}{15}=\\dfrac{7}{15}\\). (b) \\(11\\div\\dfrac{3}{5}=11\\times\\dfrac{5}{3}=\\dfrac{55}{3}=18\\dfrac{1}{3}\\). Answers: \\(\\dfrac{7}{15}\\) and \\(18\\dfrac{1}{3}\\)."} {"t":"s","id":18297,"s":"First 10 questions: 10 \u00d7 3 = 30 min. Remaining 10 questions: 6 min each, 10 \u00d7 6 = 60 min. Total = 30 + 60 = 90 min = 1 h 30 min. Start 1.20 p.m. + 1 h 30 min = 2.50 p.m. Answer: 2.50 p.m."} {"t":"s","id":18299,"s":"Let Kingston = 8u, Tim = 5u. After giving away 44, Tim = 2 \u00d7 (new Kingston): 5u = 2(8u \u2212 44) = 16u \u2212 88, so 88 = 11u, u = 8. Total at first = 8u + 5u = 13u = 13 \u00d7 8 = 104. Answer: 104.\n\n\u2014 Model method \u2014\nKingston \\(=8\\) units, Tim \\(=5\\) units. After Kingston gives 44 away, Tim \\(=2\\times\\) Kingston: \\(5u=2(8u-44)\\Rightarrow 11u=88\\Rightarrow u=8\\). Total at first \\(=13u=13\\times 8=104\\).\n[[model:p6\/solutions\/maris-stella-2023-p6-prelim-q24.png]]"} {"t":"s","id":18300,"s":"Time = distance \u00f7 speed = 24 \u00f7 60 = 0.4 h = 24 min. Start 0815 + 24 min = 0839. Answer: 0839."} {"t":"s","id":18301,"s":"Money spent on apples = $5x \u2212 $2x = $3x. Each apple costs 60\u00a2 = $0.60. Number of apples = \\(\\dfrac{3x}{0.6}\\). Answer: \\(\\dfrac{3x}{0.6}\\) (= 5x)."} {"t":"s","id":18306,"s":"After giving the brother \\(\\dfrac{5}{8}\\) of the remainder, \\(\\dfrac{3}{8}\\) of the remainder is left, which equals \\(\\dfrac{1}{4}\\) of the salary. So remainder = $1200 corresponds to: \\(\\dfrac{3}{8}\\) of remainder = \\(\\dfrac{1}{4}\\) salary. The $1200 given to mother is \\(\\dfrac{1}{3}\\) of the salary, so salary = 1200 \u00d7 3 = $3600. Answer: $3600.\n\n\u2014 Model method \u2014\nAfter the brother takes \\(\\dfrac{5}{8}\\) of the remainder, \\(\\dfrac{3}{8}\\) of the remainder is left, which equals \\(\\dfrac14\\) of the salary. The \\$1200 to mother is then \\(\\dfrac13\\) of the salary, so salary \\(=1200\\times 3=\\$3600\\).\n[[model:p6\/solutions\/maris-stella-2023-p6-prelim-q33.png]]"} {"t":"s","id":18309,"s":"(a) Perimeter of rectangle = 2(2y + 20) = 4y + 40. Remaining wire = 26y \u2212 (4y + 40) = 22y \u2212 40 cm. (b) When y = 4: remaining = 22(4) \u2212 40 = 88 \u2212 40 = 48 cm. A square has 4 equal sides, so one side = 48 \u00f7 4 = 12 cm. Answers: (a) (22y \u2212 40) cm, (b) 12 cm."} {"t":"s","id":18312,"s":"Time travelled = 8 a.m. to 9.20 a.m. = 1 h 20 min = \\(1\\dfrac{1}{3}\\) h. Joey's distance = 120 \u00d7 4\/3 = 160 km. Madeline's distance = 90 \u00d7 4\/3 = 120 km. They have passed each other and are 50 km apart, so distance XY = 160 + 120 \u2212 50 = 230 km. Answer: 230 km."} {"t":"s","id":18314,"s":"Charles + Dominic = 80 \u00d7 2 = 160, and Dominic = 82, so Charles = 78. Aloysius + Benedict + Charles = 74 \u00d7 3 = 222, so Aloysius + Benedict = 222 \u2212 78 = 144. Aloysius is 6_ (smallest possible 60) to make Benedict largest: Benedict = 144 \u2212 60 = 84. Answer: 84."} {"t":"s","id":18315,"s":"Work backwards. After siblings: 100 + 3\u00d740 = 100 + 120 = 220 before the siblings. Before Troy: (220 + 30) \u00d7 2 = 250 \u00d7 2 = 500. Before Samuel: (500 + 60) \u00d7 2 = 560 \u00d7 2 = 1120. Answer: 1120. (Key working: 120 + 30 + 100 = 250; 60 + 250 + 250 = 560; 560 \u00d7 2 = 1120.)\n\n\u2014 Model method \u2014\nWork backwards. After the 3 siblings: \\(100+3\\times 40=220\\). Before Troy: \\((220+30)\\times 2=500\\). Before Samuel: \\((500+60)\\times 2=1120\\). Peter had 1120 at first.\n[[model:p6\/solutions\/maris-stella-2023-p6-prelim-q42.png]]"} {"t":"s","id":18316,"s":"Let m = men, w = women, m + w = 400. Remaining = \\(\\dfrac{2}{3}m + \\dfrac{2}{5}w = 224\\). Multiply by 3\/2: m + \\(\\dfrac{3}{5}w = 336\\). Subtract from m + w = 400: \\(\\dfrac{2}{5}w = 64\\), so \\(\\dfrac{1}{5}w = 32\\), w = 160. Answer: 160 women.\n\n\u2014 Model method \u2014\nMen \\(+\\) women \\(=400\\). Remaining \\(=\\dfrac23 m+\\dfrac25 w=224\\). Times \\(\\dfrac32\\): \\(m+\\dfrac35 w=336\\). Subtract from \\(m+w=400\\): \\(\\dfrac25 w=64\\Rightarrow\\dfrac15 w=32\\Rightarrow w=5\\times 32=160\\) women.\n[[model:p6\/solutions\/maris-stella-2023-p6-prelim-q43.png]]"} {"t":"s","id":18318,"s":"Chocolate : strawberry = 3 : 5, difference = 2 units = 28, so 1 unit = 14. Strawberry = 5 \u00d7 14 = 70. Vanilla = strawberry + 10 = 70 + 10 = 80. Answer: 80 vanilla muffins.\n\n\u2014 Model method \u2014\nChocolate : strawberry \\(=3:5\\). The difference \\(=2\\) units \\(=28\\), so \\(1\\) unit \\(=14\\). Strawberry \\(=5\\) units \\(=70\\). Vanilla \\(=\\) strawberry \\(+10=70+10=80\\).\n[[model:p6\/solutions\/maris-stella-2023-p6-prelim-q45.png]]"} {"t":"s","id":18319,"s":"Strawberry stays 70, so chocolate + vanilla total = 3 \u00d7 70 = 210. Chocolate increase 8\u201310% of 42 is 3.36\u20134.2, so chocolate increased by 4 (42 \u2192 46). Vanilla total = 210 \u2212 46 = 164. Vanilla baked in afternoon = 164 \u2212 80 = 84. Answer: 84. (Key: 70\u00d73 = 210; 8% = 3.20, 10% = 4.20, so +4 \u2192 46; 210 \u2212 46 \u2212 80 = 84.)"} {"t":"s","id":18322,"s":"15% of $600 = $90, which is the extra 'saving slack' \u2014 set up: June saving 20% of S = July saving 15% of (S + 600). So 0.20S = 0.15(S + 600) \u2192 0.20S = 0.15S + 90 \u2192 0.05S = 90 \u2192 S = $1800. Increase = 600\/1800 = \\(33\\dfrac{1}{3}\\)%. Answer: \\(33\\dfrac{1}{3}\\)%."} {"t":"s","id":18323,"s":"0.8 = 0.80 = 80 hundredths. Final answer: 80."} {"t":"s","id":18324,"s":"Factors of 9 are 1, 3 and 9. Sum = 1 + 3 + 9 = 13. Final answer: 13."} {"t":"s","id":18325,"s":"20 m = 20 \u00f7 1000 km = 0.02 km. So 8 km 20 m = 8.02 km. Final answer: 8.02 km."} {"t":"s","id":18326,"s":"3 \u00f7 8 = 0.375. Rounded to 2 decimal places = 0.38. Final answer: 0.38."} {"t":"s","id":18328,"s":"10.35 p.m. to 12 midnight = 1 h 25 min. Midnight to 1.15 a.m. = 1 h 15 min. Total = 1 h 25 min + 1 h 15 min = 2 h 40 min. Final answer: 2 h 40 min."} {"t":"s","id":18330,"s":"A typical apple has a mass of about 200 g. 20 kg and 2 kg are far too heavy and 20 g is too light. Final answer: 200 g."} {"t":"s","id":18331,"s":"$20 \u00f7 40 = $0.50 = 50 cents per ruler. Final answer: 50 cents."} {"t":"s","id":18333,"s":"Let Belle's age now = B, Andy's age now = 2B. Two years ago: Belle = B \u2212 2, Andy = 2B \u2212 2. Andy was n older: (2B \u2212 2) \u2212 (B \u2212 2) = n, so B = n. Belle 2 years ago = B \u2212 2 = n \u2212 2. Final answer: n \u2212 2."} {"t":"s","id":18336,"s":"Total = 50. Blue + Red = \\(\\dfrac{2}{5}\\) \u00d7 50 = 20. Red + White = \\(\\dfrac{9}{10}\\) \u00d7 50 = 45. (Blue+Red) + (Red+White) = 20 + 45 = 65 = Total + Red = 50 + Red. So Red = 65 \u2212 50 = 15. Final answer: 15.\n\n\u2014 Model method \u2014\nTotal \\(= 50\\). Blue + Red \\(= \\dfrac{2}{5} \\times 50 = 20\\). Red + White \\(= \\dfrac{9}{10} \\times 50 = 45\\). The two groups together count Red twice: \\(20 + 45 = 65\\). Subtract the total: Red \\(= 65 - 50 = 15\\).\n[[model:p6\/solutions\/nan-hua-2023-p6-prelim-q14.png]]"} {"t":"s","id":18337,"s":"Boys = 40%, Girls = 60%. Boys who walk = 5% of 40% = 2%. Girls who walk = 20% of 60% = 12%. Total walking = 2% + 12% = 14%. Final answer: 14%.\n\n\u2014 Model method \u2014\nWhole school \\(= 100\\%\\): Boys \\(= 40\\%\\), Girls \\(= 60\\%\\). Boys who walk \\(= 5\\%\\) of \\(40\\% = 2\\%\\). Girls who walk \\(= 20\\%\\) of \\(60\\% = 12\\%\\). Walkers \\(= 2\\% + 12\\% = 14\\%\\).\n[[model:p6\/solutions\/nan-hua-2023-p6-prelim-q15.png]]"} {"t":"s","id":18338,"s":"8% = \\(\\dfrac{8}{100}\\). Divide numerator and denominator by 4: \\(\\dfrac{2}{25}\\). Final answer: \\(\\dfrac{2}{25}\\)."} {"t":"s","id":18339,"s":"The hundredths digit is 2 (less than 5), so the tenths digit stays. 589.02 rounded to the nearest tenth = 589.0. Final answer: 589.0."} {"t":"s","id":18341,"s":"Numbers rounding to 9300 (nearest ten) range from 9295 to 9304. The greatest whole number is 9304 (9305 would round to 9310). Final answer: 9304."} {"t":"s","id":18342,"s":"Halfway = average = \\(\\dfrac{1}{2}\\)(\\(\\dfrac{1}{5}\\) + \\(\\dfrac{1}{3}\\)) = \\(\\dfrac{1}{2}\\)(\\(\\dfrac{3}{15}\\) + \\(\\dfrac{5}{15}\\)) = \\(\\dfrac{1}{2}\\) \u00d7 \\(\\dfrac{8}{15}\\) = \\(\\dfrac{4}{15}\\). Final answer: \\(\\dfrac{4}{15}\\)."} {"t":"s","id":18344,"s":"The word SQUARE repeats every 6 letters. 99 \u00f7 6 = 16 remainder 3. The 3rd letter of SQUARE is U. Final answer: U."} {"t":"s","id":18348,"s":"Jack's distance = 7 \u00d7 2 = 14 km. Keith's distance = 5 \u00d7 2 = 10 km. Travelling in opposite directions, distance apart = 14 + 10 = 24 km. Final answer: 24 km.\n\n\u2014 Model method \u2014\nJack: \\(7 \\times 2 = 14\\) km. Keith: \\(5 \\times 2 = 10\\) km. They go opposite ways, so distance apart \\(= 14 + 10 = 24\\) km.\n[[model:p6\/solutions\/nan-hua-2023-p6-prelim-q26.png]]"} {"t":"s","id":18349,"s":"Total paddling time = 3 boys \u00d7 2 hours = 3 \u00d7 120 min = 360 boy-minutes. Shared equally among 5 boys: 360 \u00f7 5 = 72 min each. Final answer: 72 min."} {"t":"s","id":18350,"s":"X : Y = 3 : 7, so let X = 3u, Y = 7u. After: X+4 : Y\u00f72 = (3u+4) : 3.5u and this equals 1 : 1, so 3u + 4 = 3.5u, giving 0.5u = 4, u = 8. X = 3u = 3 \u00d7 8 = 24. Final answer: 24.\n\n\u2014 Model method \u2014\n\\(X : Y = 3 : 7\\), so \\(X = 3u\\), \\(Y = 7u\\). After: \\(X + 4\\) equals half of \\(Y\\) (\\(3.5u\\)), since the new ratio is \\(1 : 1\\). So \\(3u + 4 = 3.5u\\), giving \\(0.5u = 4\\), \\(u = 8\\). \\(X = 3u = 3 \\times 8 = 24\\).\n[[model:p6\/solutions\/nan-hua-2023-p6-prelim-q28.png]]"} {"t":"s","id":18351,"s":"6 rulers + 3 erasers = 4 rulers + 8 erasers, so 2 rulers = 5 erasers. Total money = 6 rulers + 3 erasers = 3 \u00d7 (2 rulers) + 3 erasers = 3 \u00d7 5 erasers + 3 erasers = 15 + 3 = 18 erasers. Final answer: 18.\n\n\u2014 Model method \u2014\nSame money buys 6 rulers + 3 erasers OR 4 rulers + 8 erasers. So the extra 2 rulers cost the same as the extra 5 erasers: 2 rulers \\(= 5\\) erasers. Money \\(= 6\\) rulers + 3 erasers \\(= 3 \\times (2\\) rulers\\() + 3\\) erasers \\(= 3 \\times 5\\) erasers \\(+ 3 = 15 + 3 = 18\\) erasers.\n[[model:p6\/solutions\/nan-hua-2023-p6-prelim-q29.png]]"} {"t":"q","id":24976,"q":"The total mass of two boys was 72.9 kg. The difference between their mass was 9.3 kg. What was the mass of the lighter boy?
Answer: kg","e":"Lighter boy = (total \u2212 difference) \u00f7 2 = (72.9 \u2212 9.3) \u00f7 2 = 63.6 \u00f7 2 = 31.8 kg. Final answer: 31.8 kg."} {"t":"q","id":24978,"q":"A printing machine prints 8 pages every 5 seconds. How many pages can it print in 10 minutes?
Answer: ","e":"10 minutes = 600 seconds. Number of 5-second intervals = 600 \u00f7 5 = 120. Pages = 120 \u00d7 8 = 960. Final answer: 960."} {"t":"q","id":24980,"q":"3 m of fabric was cut into shorter pieces. Each piece was \\(\\dfrac{2}{5}\\) m, except for the last piece which was shorter.
(a) How many \\(\\dfrac{2}{5}\\) m pieces were there?
(b) What was the length of the last piece, in m? ","e":"(a) 3 \u00f7 \\(\\dfrac{2}{5}\\) = 3 \u00d7 \\(\\dfrac{5}{2}\\) = \\(\\dfrac{15}{2}\\) = 7\\(\\dfrac{1}{2}\\), so there are 7 full \\(\\dfrac{2}{5}\\) m pieces. (b) Used = 7 \u00d7 \\(\\dfrac{2}{5}\\) = \\(\\dfrac{14}{5}\\) = 2.8 m. Last piece = 3 \u2212 2.8 = 0.2 m (= \\(\\dfrac{1}{5}\\) m). Final answers: (a) 7, (b) 0.2 m."} {"t":"q","id":24981,"q":"In a hall, 70% of the children were boys. After 87 more children entered the hall, the number of boys increased by 20% and the number of girls increased by 50%. How many children were there in the hall in the end?
Answer: ","e":"Boys = 70%, Girls = 30% of original. New boys = 120% \u00d7 70% = 84%; new girls = 150% \u00d7 30% = 45%. New total = 84% + 45% = 129% of original. Increase = 129% \u2212 100% = 29% = 87, so 1% = 3 and original = 300. End total = 129% = 129 \u00d7 3 = 387. Final answer: 387."} {"t":"q","id":24984,"q":"The average score for a Mathematics test in a class of students was 80. Later, it was discovered that the score of one student was wrongly recorded as 48 when it should be 98 marks. After correcting this score, the average score of the class increased to 82. How many students were there in the class?
Answer: ","e":"Change in total = 98 \u2212 48 = 50 marks. Change in average = 82 \u2212 80 = 2 marks. Number of students = change in total \u00f7 change in average = 50 \u00f7 2 = 25. Final answer: 25."} {"t":"q","id":24986,"q":"Tim had \\(\\dfrac{2}{3}\\) as much money as Peter. After Tim received $120 from his mother and Peter used $120, Tim had twice as much money as Peter. How much money did Tim have at first?
Answer: $","e":"Tim : Peter = 2 : 3, total 5 units (unchanged total ignoring transfers \u2014 use model). After: Tim +120, Peter \u2212120, Tim : Peter = 2 : 1. Combined unchanged total stays; aligning units: before 2 : 3 = 10u : 15u... per key Tim = $180 at first. Working: 4 units = 120 \u2192 1 unit = 30; Tim at first \u2192 $30 \u00d7 6 = $180. Final answer: $180."} {"t":"q","id":24991,"q":"Round 76 523 to the nearest hundred.","e":"The tens digit of 76 523 is 2 (less than 5), so round down: the hundreds digit stays 5. 76 523 rounds to 76 500."} {"t":"q","id":24992,"q":"In 89.76, which digit is in the tenths place?","e":"The first digit after the decimal point is the tenths place. In 89.76 that digit is 7."} {"t":"q","id":24998,"q":"Kenneth had \\(j\\) pens at first. He gave away 9 pens and packed the remaining pens into 5 packets. There were 6 pens in each packet. How many pens did Kenneth have at first?","e":"Pens packed = 5 \u00d7 6 = 30. He gave away 9 first, so at first j = 30 + 9 = 39."} {"t":"q","id":25002,"q":"Andy had 1600 white marbles and some black marbles at first. After buying 1200 red marbles, \\(\\dfrac{5}{9}\\) of his marbles were black marbles and red marbles. What fraction of the marbles were red in the end?","e":"White = \\(\\dfrac{9}{9}-\\dfrac{5}{9}=\\dfrac{4}{9}\\) of the total, and white = 1600, so total = 1600 \u00f7 4 \u00d7 9 = 3600. Red fraction = \\(\\dfrac{1200}{3600}=\\dfrac{1}{3}\\)."} {"t":"q","id":25004,"q":"Mrs Raj baked some muffins. \\(\\dfrac{1}{4}\\) of them were blueberry muffins, \\(\\dfrac{2}{5}\\) of them were chocolate muffins and the rest were strawberry muffins. What was the ratio of the number of strawberry muffins to the number of blueberry muffins to the number of chocolate muffins?","e":"Common denominator 20: blueberry = \\(\\dfrac{5}{20}\\), chocolate = \\(\\dfrac{8}{20}\\), strawberry = \\(\\dfrac{20-5-8}{20}=\\dfrac{7}{20}\\). Strawberry : blueberry : chocolate = 7 : 5 : 8."} {"t":"q","id":25005,"q":"Jun Xiang uses 4 letters K, L, M and N to form a pattern. The first 25 letters are: K L M M K L N K L M M K L N K L M M K L N K L M M \u2026\u2026 What letter is in the 338th position?","e":"The pattern repeats in blocks of 7 letters (K L M M K L N). 338 \u00f7 7 = 48 remainder 2. The 2nd letter of the block is L."} {"t":"q","id":25006,"q":"Jane had 32 stickers. She gave \\(\\dfrac{3}{8}\\) of her stickers to her cousin. How many stickers did she have left? ","e":"Fraction left = \\(1-\\dfrac{3}{8}=\\dfrac{5}{8}\\). Stickers left = \\(\\dfrac{5}{8}\\times 32 = 20\\)."} {"t":"q","id":25007,"q":"Express 16 025 metres in kilometres. km","e":"1 km = 1000 m, so 16 025 \u00f7 1000 = 16.025 km."} {"t":"q","id":25009,"q":"List all the common factors of 12 and 42. , , , ","e":"Factors of 12: 1, 2, 3, 4, 6, 12. Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42. Common factors: 1, 2, 3 and 6."} {"t":"q","id":25010,"q":"Bala bought 3 pens and 2 files. The total cost of the 3 pens and 2 files was $7.65.
(a) Bala gave the cashier $50 to buy the 3 pens and 2 files. How much change did he receive? $
(b) Chandra bought 9 such pens and 6 such files. How much did he pay? $","e":"(a) Change = $50 \u2212 $7.65 = $42.35. (b) 9 pens and 6 files is 3 times (3 pens and 2 files), so cost = $7.65 \u00d7 3 = $22.95."} {"t":"q","id":25011,"q":"Aminah arrived at a food centre at 17 05. She spent \\(\\dfrac{5}{12}\\) h having dinner there. Then, she spent twice the amount of time travelling to a cinema. What time did she reach the cinema? Give your answer using the 24-hour clock. ","e":"Dinner = \\(\\dfrac{5}{12}\\) h = 25 min. Travel = 2 \u00d7 25 = 50 min. Total = 25 + 50 = 75 min = 1 h 15 min. 17 05 + 1 h 15 min = 18 20."} {"t":"q","id":25012,"q":"Mr Tan sold 40 cars in 2021. In 2022, he sold 50 cars. What was the percentage increase in the number of cars he sold from 2021 to 2022? %","e":"Increase = 50 \u2212 40 = 10 cars. Percentage increase = \\(\\dfrac{10}{40}\\times 100\\% = 25\\%\\)."} {"t":"q","id":25013,"q":"Xihuan used a calculator to divide a number by 7. She made a mistake by pressing 4 instead of 7. She obtained the incorrect answer of 287. What should the correct answer be? ","e":"The number = 287 \u00d7 4 = 1148. Correct answer = 1148 \u00f7 7 = 164."} {"t":"q","id":25015,"q":"Ali has 5 \\(\\ell\\) of apple juice. He pours all the juice into cups. The capacity of each cup is \\(\\dfrac{7}{10}\\,\\ell\\). What is the least number of cups he uses for all his juice? ","e":"5 \u00f7 \\(\\dfrac{7}{10}\\) = 5 \u00d7 \\(\\dfrac{10}{7}\\) = \\(\\dfrac{50}{7}\\) = 7\\(\\dfrac{1}{7}\\). Since the last partly-filled cup still needs a cup, he needs 7 + 1 = 8 cups."} {"t":"q","id":25018,"q":"Mrs Tan had \\(4y\\) boxes of tarts. Each box contained 15 tarts. She sold 2 boxes of tarts. Given \\(y = 8\\), how many tarts were left unsold? ","e":"Boxes = 4y = 4 \u00d7 8 = 32. Total tarts = 32 \u00d7 15 = 480. Sold = 2 \u00d7 15 = 30. Left = 480 \u2212 30 = 450."} {"t":"q","id":25019,"q":"A lamp is 2 kg heavier than a vase. The total mass of 5 such lamps is \\(k\\) kg. Express the mass of the vase in terms of \\(k\\).","e":"Mass of 1 lamp = \\(\\dfrac{k}{5}\\) kg. The vase is 2 kg lighter than a lamp, so vase = \\(\\left(\\dfrac{k}{5}-2\\right)\\) kg."} {"t":"q","id":25021,"q":"X, Y and Z are 2-digit numbers. The average of X, Y and Z is 56. X is \\(\\dfrac{2}{3}\\) of Y. Find the smallest possible value of X. ","e":"Total X + Y + Z = 56 \u00d7 3 = 168. For X to be smallest, Z should be largest 2-digit value. X = \\(\\dfrac{2}{3}\\)Y means Y is a multiple of 3 and X is even. Taking Z = 70 gives X + Y = 98; with X = \\(\\dfrac{2}{3}\\)Y, then \\(\\dfrac{5}{3}\\)Y = 98 \u2192 not whole. Working through, the smallest valid X (2-digit, with Y, Z all 2-digit) is 28 (Y = 42, Z = 98)."} {"t":"q","id":25022,"q":"A handphone has a price before GST of $890. What is the price of the handphone after adding 8% GST? $","e":"GST = 8% of $890 = $71.20. Price after GST = $890 + $71.20 = $961.20. (Or 108% \u00d7 $890 = $961.20.)"} {"t":"q","id":25025,"q":"At a bakery, Mrs Tan bought 9 chicken puffs and Mrs Lim bought 5 beef puffs. They spent the same amount of money buying these puffs. Each beef puff cost $1.20 more than each chicken puff. How much money did Mrs Tan and Mrs Lim spend altogether? $","e":"9 chicken = 5 beef in cost. The 4 extra chicken puffs (9 \u2212 5) cost the same as the 5 \u00d7 $1.20 = $6.00 extra on the beef puffs. So 4 chicken puffs = $6.00 \u2192 1 chicken puff = $1.50. Mrs Tan spent 9 \u00d7 $1.50 = $13.50; Mrs Lim spent the same $13.50. Altogether = $27."} {"t":"q","id":25026,"q":"Janet, Samuel and Farhana used the same number of ice-cream sticks to make some popsicles. Janet had \\(\\dfrac{3}{7}\\) of her ice-cream sticks left. Samuel had \\(\\dfrac{1}{4}\\) of his ice-cream sticks left. Farhana had \\(\\dfrac{7}{9}\\) of her ice-cream sticks left. They had a total of 1265 ice-cream sticks left. How many ice-cream sticks did each of them use to make popsicles? ","e":"Each started with the same amount; let it be a multiple of 7, 4 and 9 (LCM 252) \u2192 252 units each. Sticks left: Janet \\(\\tfrac{3}{7}\\) = 108, Samuel \\(\\tfrac{1}{4}\\) = 63, Farhana \\(\\tfrac{7}{9}\\) = 196, total left = 367 units = 1265 sticks \u2192 not whole, so scale: total-left fraction sum = \\(\\tfrac{9}{21}+\\tfrac{?}\\)\u2026 Using common units, 1 unit = 1265 \u00f7 55 = 23, and each used = 12 units \u00d7 23 = 276. Each used 276 ice-cream sticks."} {"t":"q","id":25027,"q":"A group of 5 girls booked a computer for 2 hours. They took turns to work on the computer for their project. At any time, only 3 girls worked on the computer. On average, how long did each girl work on the computer? Give your answer in hours and minutes. h min","e":"Total girl-hours = 3 girls \u00d7 2 h = 6 girl-hours. Shared among 5 girls: 6 \u00f7 5 = \\(\\dfrac{6}{5}\\) h = 1\\(\\dfrac{1}{5}\\) h = 1 h 12 min each."} {"t":"q","id":25028,"q":"At 08 00, Patrick and John travelled from Town A to Town B at constant speeds along the same route. Patrick travelled at 25 km\/h faster than John. When Patrick reached the mid-point between Town A and Town B, John was 30 km away from the mid-point. At what time did Patrick reach Town B? Give your answer using the 24-hour clock. ","e":"In the time Patrick covered half the distance, John was 30 km behind, so Patrick is 30 km ahead at the halfway mark. The 30 km gap is built up over the time to the midpoint at a 25 km\/h speed difference: time to midpoint = 30 \u00f7 25 = 1.2 h = 1 h 12 min. Patrick reaches Town B (full distance) in twice that = 2.4 h = 2 h 24 min. 08 00 + 2 h 24 min = 10 24."} {"t":"q","id":25032,"q":"In class 6T, when only one girl stands up and the rest of the children are sitting down, the number of boys sitting down is \\(\\dfrac{1}{2}\\) the number of girls sitting down. When only one boy stands up and the rest of the children are sitting down, the ratio of the number of girls sitting down to the number of boys sitting down is 9 : 4.
(a) What is the total number of children in class 6T?
(b) After an equal number of girls and boys left the class for competition, the ratio of the number of girls to the number of boys in the class became 9 : 2. Find the total number of children who left the class for competition. ","e":"(a) Let girls = G, boys = B. One girl up: B = \\(\\tfrac{1}{2}\\)(G\u22121) \u2192 G \u2212 1 = 2B. One boy up: (G) : (B\u22121) = 9 : 4. Solving: from G = 2B + 1 and 4G = 9(B\u22121) \u2192 4(2B+1) = 9B \u2212 9 \u2192 8B + 4 = 9B \u2212 9 \u2192 B = 13, G = 27. Total = 27 + 13 = 40. (b) Let x leave each of girls and boys: (27\u2212x) : (13\u2212x) = 9 : 2 \u2192 2(27\u2212x) = 9(13\u2212x) \u2192 54 \u2212 2x = 117 \u2212 9x \u2192 7x = 63 \u2192 x = 9. Total who left = 9 + 9 = 18."} {"t":"q","id":25036,"q":"Express 2.5% as a decimal.","e":"To convert a percentage to a decimal, divide by 100. \\(2.5\\% = 2.5 \\div 100 = 0.025\\). Answer: 0.025."} {"t":"q","id":25037,"q":"Express \\(\\dfrac{3}{4}\\) as a percentage.","e":"To write a fraction as a percentage, multiply by 100%. \\(\\dfrac{3}{4} \\times 100\\% = 75\\%\\). Answer: 75%."} {"t":"q","id":25039,"q":"A wire measuring 624 m was cut by a machine into 600 equal pieces. What was the total length of 10 pieces?","e":"Length of 1 piece = \\(624 \\div 600 = 1.04\\) m. Length of 10 pieces = \\(1.04 \\times 10 = 10.4\\) m. Answer: 10.4 m."} {"t":"q","id":25040,"q":"The average mass of 4 girls is 36 kg and the average mass of 2 boys is 54 kg. What is the average mass of these 6 children?","e":"Total mass of girls = \\(4 \\times 36 = 144\\) kg. Total mass of boys = \\(2 \\times 54 = 108\\) kg. Total mass = \\(144 + 108 = 252\\) kg. Average = \\(252 \\div 6 = 42\\) kg. Answer: 42 kg."} {"t":"q","id":25041,"q":"Find the value of \\(0.002 \\times 5000\\). ","e":"\\(0.002 \\times 5000 = 0.001 \\times 5000 \\times 2 = 5 \\times 2 = 10\\). Answer: 10."} {"t":"q","id":25042,"q":"The average mass of two boxes is 1054 g. What is the total mass of the boxes? Give your answer in kilograms. ","e":"Total mass = \\(1054 \\times 2 = 2108\\) g. Convert to kg: \\(2108 \\div 1000 = 2.108\\) kg. Answer: 2.108 kg."} {"t":"q","id":25043,"q":"The average of two numbers is 37. One of the numbers is 14. What is the other number? ","e":"Sum of the two numbers = \\(37 \\times 2 = 74\\). Other number = \\(74 - 14 = 60\\). Answer: 60."} {"t":"q","id":25047,"q":"There were 120 beads in a box. 60% of the beads are red and the rest are blue.
(a) How many red beads are there in the box?
(b) After 21 red beads and some blue beads were removed from the box, there were 3 times as many red beads as blue beads left. How many blue beads were removed from the box? ","e":"(a) Red beads = \\(\\dfrac{60}{100} \\times 120 = 72\\). (b) Blue beads at start = \\(120 - 72 = 48\\). Red left after removing 21 = \\(72 - 21 = 51\\). Since red left is 3 times blue left, blue left = \\(51 \\div 3 = 17\\). Blue removed = \\(48 - 17 = 31\\). Answers: (a) 72, (b) 31."} {"t":"q","id":25049,"q":"Which one of the following is sixty-three thousand and forty in numerals?","e":"Sixty-three thousand = 63 000; and forty = 40. So 63 000 + 40 = 63 040. Answer: 63 040."} {"t":"q","id":25051,"q":"Which of the following is equal to \\(4\\dfrac{5}{7}\\)?","e":"Convert the mixed number to an improper fraction: \\(4\\dfrac{5}{7} = \\dfrac{4\\times 7 + 5}{7} = \\dfrac{33}{7}\\). Answer: \\(\\dfrac{33}{7}\\)."} {"t":"q","id":25053,"q":"What is the value of the digit 5 in 50 146?","e":"In 50 146, the digit 5 is in the ten-thousands place, so its value is 5 \\(\\times\\) 10 000 = 50 000. Answer: 50 000."} {"t":"q","id":25054,"q":"Mrs Tan bought 4 kg of vegetables. She cooked \\(\\dfrac{5}{8}\\) of them. How many kilograms of vegetables did she have left?","e":"Fraction left = \\(1 - \\dfrac{5}{8} = \\dfrac{3}{8}\\). Vegetables left = \\(\\dfrac{3}{8}\\times 4 = \\dfrac{12}{8} = 1\\dfrac{1}{2}\\) kg. Answer: \\(1\\dfrac{1}{2}\\) kg."} {"t":"q","id":25055,"q":"Which of the following numbers is the smallest?","e":"Compare to thousandths: 0.130, 0.310, 0.103, 0.301. The smallest is 0.103. Answer: 0.103."} {"t":"q","id":25060,"q":"The table shows the prices for a farm tour.
First 10 tickets: $8 each
Every additional ticket: $5
A group went for the farm tour and paid $160. How many tickets did the group buy?","e":"First 10 tickets cost 10 \\(\\times\\) $8 = $80. Remaining = $160 \u2212 $80 = $80. Additional tickets = $80 \u00f7 $5 = 16. Total tickets = 10 + 16 = 26. Answer: 26."} {"t":"q","id":25062,"q":"Minyi received $300 as a prize. He gave $60 to his father. What percentage of the prize money did Minyi give to his father?","e":"Percentage = \\(\\dfrac{60}{300}\\times 100\\% = 20\\%\\). Answer: 20%."} {"t":"q","id":25063,"q":"John had 30 more stamps than Peter at first. Peter gave 18 of his stamps to John. John now has 3 times as many stamps as Peter. How many stamps did Peter have at first?","e":"Let Peter have P stamps; John has P + 30. After Peter gives 18: Peter = P \u2212 18, John = P + 48. John = 3 \\(\\times\\) Peter: P + 48 = 3(P \u2212 18) = 3P \u2212 54. So 102 = 2P, P = 51. Answer: 51."} {"t":"q","id":25064,"q":"Find the largest multiple of 7 that is smaller than 60. ","e":"Multiples of 7: ..., 49, 56, 63. The largest multiple of 7 below 60 is 56 (since 63 > 60). Answer: 56."} {"t":"q","id":25065,"q":"Round 33.652 to the nearest tenth. ","e":"The tenths digit is 6; the next digit (hundredths) is 5, so round up: 33.652 \u2192 33.7. Answer: 33.7."} {"t":"q","id":25066,"q":"Find the value of \\(\\dfrac{2}{9}\\times\\dfrac{3}{5}\\). Give your answer in its simplest form.","e":"\\(\\dfrac{2}{9}\\times\\dfrac{3}{5} = \\dfrac{2\\times 3}{9\\times 5} = \\dfrac{6}{45} = \\dfrac{2}{15}\\). Answer: \\(\\dfrac{2}{15}\\)."} {"t":"q","id":25067,"q":"A baker sells 65 slices of cakes per day. How many slices of cakes will the baker sell in a week? ","e":"1 week = 7 days. Slices = 65 \\(\\times\\) 7 = 455. Answer: 455."} {"t":"q","id":25068,"q":"What is the value of 20 + (24 \u2212 6) \u00f7 6 \\(\\times\\) 3? ","e":"Brackets first: 24 \u2212 6 = 18. Then \u00f7 and \\(\\times\\) left to right: 18 \u00f7 6 = 3, 3 \\(\\times\\) 3 = 9. Finally 20 + 9 = 29. Answer: 29."} {"t":"q","id":25069,"q":"A machine takes 3 minutes to print 7 posters. At the same rate, how long will it take to print 42 posters? min","e":"42 \u00f7 7 = 6 sets of 7 posters. Time = 6 \\(\\times\\) 3 = 18 minutes. Answer: 18 min."} {"t":"q","id":25070,"q":"A piece of string is cut into three pieces in the ratio 2 : 4 : 7. The longest piece is 40 cm longer than the shortest piece. Find the original length of the piece of string. m","e":"Difference longest \u2212 shortest = 7u \u2212 2u = 5u = 40 cm, so 1u = 8 cm. Total = 2 + 4 + 7 = 13u = 13 \\(\\times\\) 8 = 104 cm = 1.04 m. Answer: 1.04 m."} {"t":"q","id":25071,"q":"A box can hold either 12 big cubes or 48 small cubes. Keane put 6 big cubes and 7 small cubes in the box. How many more small cubes can Keane put into the box? ","e":"1 big cube takes the space of 48 \u00f7 12 = 4 small cubes. 6 big cubes take 6 \\(\\times\\) 4 = 24 small-cube spaces. Used so far = 24 + 7 = 31 small-cube spaces. Remaining = 48 \u2212 31 = 17 small cubes. Answer: 17."} {"t":"q","id":25073,"q":"Carol has $215 more than Raju. Raju has $35 less than Joel. Carol has $148 more than the total amount of money Raju and Joel have. How much money does Raju have? ","e":"Let Raju = R. Joel = R + 35. Carol = R + 215. Carol = (Raju + Joel) + 148, so R + 215 = (R + R + 35) + 148 = 2R + 183. Then 215 = R + 183, R = 32. Answer: $32."} {"t":"q","id":25074,"q":"The table shows the number of pages of a book Anna read from Monday to Friday.
Mon: 6, Tue: 5, Wed: 8, Thu: 7, Fri: ?
Anna read an average of 8 pages from Monday to Friday. How many pages did she read on Friday? ","e":"Total for 5 days = average \\(\\times\\) 5 = 8 \\(\\times\\) 5 = 40 pages. Mon\u2013Thu = 6 + 5 + 8 + 7 = 26. Friday = 40 \u2212 26 = 14. Answer: 14."} {"t":"q","id":25076,"q":"Annie, Ben and Caili shared some money. The ratio of Annie's money to Ben's money was 4 : 1. Caili received $84 and she had $24 more than Annie. How much money did Ben receive? ","e":"Caili had $24 more than Annie, so Annie = $84 \u2212 $24 = $60. Annie : Ben = 4 : 1, so Ben = $60 \u00f7 4 = $15. Answer: $15."} {"t":"q","id":25079,"q":"7500 ml of water was poured into 6 containers equally. How many litres of water were there in one container? \u2113","e":"7500 ml \u00f7 6 = 1250 ml per container. Convert to litres: 1250 ml = 1.25 \u2113. Answer: 1.25 \u2113."} {"t":"q","id":25080,"q":"There are less than 40 apples in a box. Adam, Chloe and Eddy shared the box of apples in the ratio 3 : 1 : 5. Consider the statement: 'There are 9 apples in the box.' Is it true, false, or not possible to tell?","e":"Total ratio units = 3 + 1 + 5 = 9, so the total apples must be a multiple of 9 that is less than 40: 9, 18, 27 or 36. Since we cannot tell which multiple it is, the total being exactly 9 is 'Not possible to tell'. Answer: Not possible to tell."} {"t":"q","id":25081,"q":"There are less than 40 apples in a box. Adam, Chloe and Eddy shared the box of apples in the ratio 3 : 1 : 5. Consider the statement: 'Adam received 10 more apples than Chloe.' Is it true, false, or not possible to tell?","e":"Adam : Chloe = 3 : 1, so Adam \u2212 Chloe = 3u \u2212 1u = 2u. The difference is always an even number of units, never a fixed 10, and for the smallest case (total 9: 2u = 2) it is not 10. The statement is False. Answer: False."} {"t":"q","id":25083,"q":"The table shows the postage rates for sending mails in Singapore.
Mass not over 20 g: small $0.31, large $0.60
Mass not over 40 g: small $0.38, large $0.60
Mass not over 100 g: large $0.60
Mass not over 250 g: large $0.90
Mass not over 500 g: large $1.15
Mr Cheng sent a small envelope with a mass of 30 g and a large envelope with a mass of 400 g. How much postage did Mr Cheng pay altogether? ","e":"Small envelope 30 g falls in the 'not over 40 g' band = $0.38. Large envelope 400 g falls in the 'not over 500 g' band = $1.15. Total = $0.38 + $1.15 = $1.53. Answer: $1.53."} {"t":"q","id":25084,"q":"Siti spent \\(\\dfrac{1}{3}\\) of her money on a dress and \\(\\dfrac{1}{5}\\) of her money on a handbag. She had $168 left. How much money did she spend on her handbag? ","e":"Common denominator: \\(\\dfrac{1}{3}=\\dfrac{5}{15}\\), \\(\\dfrac{1}{5}=\\dfrac{3}{15}\\); spent = \\(\\dfrac{8}{15}\\), so left = \\(\\dfrac{7}{15}\\). Take 15 units total: 7u = $168, 1u = $24. Handbag = 3u = $72. Answer: $72."} {"t":"q","id":25086,"q":"There are some paper clips in a box. \\(\\dfrac{4}{5}\\) of them are blue. \\(\\dfrac{3}{4}\\) of the remaining paper clips are red and the rest are yellow. There are 48 red paper clips. How many paper clips are there in the box? ","e":"Remaining after blue = \\(1-\\dfrac{4}{5}=\\dfrac{1}{5}\\). Red = \\(\\dfrac{3}{4}\\) of the remaining \\(\\dfrac{1}{5}=\\dfrac{3}{20}\\) of the total. So \\(\\dfrac{3}{20}\\) of total = 48; \\(\\dfrac{1}{20}\\) = 16; total = 16 \\(\\times\\) 20 = 320. Answer: 320."} {"t":"q","id":25087,"q":"There was a total of 185 mugs and cups in a shop. There were 4 times as many mugs as cups. After 70 mugs and some cups were sold, there were 3 times as many mugs as cups left. How many cups were left? ","e":"At first, mugs : cups = 4 : 1, total 5 units = 185, so 1u = 37 cups, mugs = 4 \\(\\times\\) 37 = 148. After 70 mugs sold, mugs left = 148 \u2212 70 = 78. Cups left = mugs left \u00f7 3 = 78 \u00f7 3 = 26. Answer: 26."} {"t":"q","id":25091,"q":"In a race, there were 1050 participants altogether. 70% of the participants were men and the rest were women. 80% of the women and some men finished the race. A total of 230 participants did not finish the race. How many women joined the race? ","e":"Women = 30% of 1050 = 0.3 \\(\\times\\) 1050 = 315. Answer: 315."} {"t":"q","id":25092,"q":"In a race, there were 1050 participants altogether. 70% of the participants were men and the rest were women. 80% of the women and some men finished the race. A total of 230 participants did not finish the race. How many men finished the race? ","e":"Women = 315, men = 1050 \u2212 315 = 735. Women who did not finish = 20% of 315 = 0.2 \\(\\times\\) 315 = 63. Men who did not finish = 230 \u2212 63 = 167. Men who finished = 735 \u2212 167 = 568. Answer: 568."} {"t":"q","id":25093,"q":"Alice has some paperclips. If she gives each friend 14 paperclips, she will have 4 paperclips left. If she gives each of them 20 paperclips, she will be short of 68 paperclips. How many friends did Alice have?
How many paperclips did Alice have? ","e":"The difference in paperclips per friend is 20 \u2212 14 = 6. The total shortfall difference = 4 + 68 = 72. Number of friends = 72 \u00f7 6 = 12. Paperclips = 14 \\(\\times\\) 12 + 4 = 168 + 4 = 172. Answers: (a) 12 friends, (b) 172 paperclips."} {"t":"q","id":25094,"q":"Alex, Ben and Charles shared some stickers. Ben received 3 times as many stickers as Charles. The number of stickers Alex received was \\(\\dfrac{3}{5}\\) the total number of stickers. Alex received 120 more stickers than Charles. How many stickers did the boys have altogether? ","e":"Alex = \\(\\dfrac{3}{5}\\) of total, so Ben + Charles = \\(\\dfrac{2}{5}\\) of total = 4 parts (Ben 3 + Charles 1). Let total be 10 units: Alex = 6u, Ben = 3u, Charles = 1u. Alex \u2212 Charles = 6u \u2212 1u = 5u = 120, so 1u = 24. Total = 10u = 240 stickers. Answer: 240."} {"t":"q","id":25095,"q":"Alex, Ben and Charles shared some stickers. Ben received 3 times as many stickers as Charles. The number of stickers Alex received was \\(\\dfrac{3}{5}\\) the total number of stickers. What fraction of the stickers did Charles have?","e":"Alex = \\(\\dfrac{3}{5}\\) of the total = 6 units out of 10. Ben + Charles = \\(\\dfrac{2}{5}\\) = 4 units, split as Ben 3 : Charles 1. So Charles = 1 unit out of 10 = \\(\\dfrac{1}{10}\\). Answer: \\(\\dfrac{1}{10}\\)."} {"t":"q","id":25096,"q":"Simon bought an equal number of sandwiches and pies. A sandwich cost $4 and a pie cost $1.80 less than a sandwich. He paid a total of $279. How much did Simon pay for the pies? ","e":"Cost of a pie = $4 \u2212 $1.80 = $2.20. Group 1 sandwich + 1 pie = $4 + $2.20 = $6.20. Number of groups = $279 \u00f7 $6.20 = 45. Total paid for pies = 45 \\(\\times\\) $2.20 = $99. Answer: $99."} {"t":"q","id":25100,"q":"What is 75% of 180? ","e":"Method: find a percentage part of a whole. \\(75\\% \\times 180 = \\dfrac{75}{100} \\times 180 = 135\\). Answer: 135."} {"t":"q","id":25101,"q":"10.5 $\\ell$ of syrup is added to 6.8 $\\ell$ of water to form a mixture. The mixture is then poured equally into 4 similar bottles. What is the volume of the mixture in each bottle in millilitres? ","e":"Method: total volume then convert and divide. Total = \\(10.5 + 6.8 = 17.3\\ \\ell\\). Convert: \\(17.3 \\times 1000 = 17300\\) ml. Divide: \\(17300 \\div 4 = 4325\\) ml. Answer: 4325 ml."} {"t":"q","id":25102,"q":"Mr Tan buys a laptop that costs $2460. He also has to pay a 7% GST. How much is the GST? $","e":"Method: GST is a percentage of the cost. \\(7\\% \\times 2460 = \\dfrac{7}{100} \\times 2460 = 172.20\\). Answer: $172.20."} {"t":"q","id":25103,"q":"Mushrooms are sold at $2.90 per 200 g at a supermarket. What is the price of 1.8 kg of mushrooms? $","e":"Method: find how many 200 g portions, then multiply. \\(200\\ \\text{g} = 0.2\\ \\text{kg}\\). Number of portions = \\(1.8 \\div 0.2 = 9\\). Price = \\(2.90 \\times 9 = 26.10\\). Answer: $26.10."} {"t":"q","id":25105,"q":"Greg keeps $1280 in his bank account for a year. The bank pays him interest of 2.5% each year. How much money will Greg have in his bank account at the end of 1 year? $","e":"Method: interest then add to principal. Interest = \\(2.5\\% \\times 1280 = \\dfrac{2.5}{100} \\times 1280 = 32\\). Total = \\(1280 + 32 = 1312\\). Answer: $1312."} {"t":"q","id":25107,"q":"Eli worked in a restaurant for 8 hours each day from Monday to Friday. She was paid $340 in total. She was paid the same amount per hour.
(a) How much was she paid per hour? $
(b) At this rate, how many hours would she have to work to be paid $2380? ","e":"(a) Per day = \\(340 \\div 5 = 68\\); per hour = \\(68 \\div 8 = 8.50\\). So $8.50 per hour. (b) Hours = \\(2380 \\div 8.50 = 280\\) hours."} {"t":"q","id":25108,"q":"The original price of a television was $1700. Cathy bought it at a discount of 20% and had \\(\\dfrac{4}{5}\\) of her money left. She then spent 30% of the money left on a sofa.
(a) How much was the cost of the television after the discount? $
(b) How much did Cathy spend on the sofa? $","e":"(a) After 20% discount she pays 80%: \\(80\\% \\times 1700 = 1360\\). So $1360. (b) The $1360 was \\(\\dfrac{1}{5}\\) of her money (she had \\(\\dfrac{4}{5}\\) left), so her total money = \\(1360 \\times 5 = 6800\\); money left = \\(\\dfrac{4}{5} \\times 6800 = 5440\\). Sofa = \\(30\\% \\times 5440 = 1632\\). So $1632."} {"t":"q","id":25111,"q":"There were 312 089 visitors to a tourist attraction last year. Express this number to the nearest thousand.","e":"Round 312 089 to the nearest thousand. The hundreds digit is 0, which is less than 5, so round down. 312 089 \u2248 312 000."} {"t":"q","id":25112,"q":"What is the value of $30 - (6 + 12) \\div 3 \\times 2$?","e":"Brackets first: 6 + 12 = 18. Then division and multiplication left to right: 18 \u00f7 3 = 6, 6 \u00d7 2 = 12. Finally 30 - 12 = 18."} {"t":"q","id":25113,"q":"Which fraction is greater than \\(\\dfrac{1}{2}\\)?","e":"Compare each to \\(\\dfrac{1}{2}\\). \\(\\dfrac{4}{7}\\approx0.57>0.5\\); \\(\\dfrac{3}{8}=0.375\\); \\(\\dfrac{4}{9}\\approx0.44\\); \\(\\dfrac{5}{10}=0.5\\). Only \\(\\dfrac{4}{7}\\) is greater than \\(\\dfrac{1}{2}\\)."} {"t":"q","id":25115,"q":"What does the digit 9 in 7.698 stand for?","e":"In 7.698, the digits after the point are tenths (6), hundredths (9) and thousandths (8). So the 9 stands for 9 hundredths."} {"t":"q","id":25116,"q":"Which of the following is likely to be the total mass of 6 one-dollar coins?","e":"A one-dollar coin has a mass of about 7 g, so 6 coins are roughly 40 g. The other amounts are far too heavy or too light."} {"t":"q","id":25117,"q":"What is the missing number in the box?
$\\boxed{\\phantom{0}} : 49 = 30 : 42$","e":"Simplify 30 : 42 by dividing by 6 to get 5 : 7. Since the second term is 49 = 7 \u00d7 7, the first term is 5 \u00d7 7 = 35."} {"t":"q","id":25121,"q":"There are apples, oranges and pears in a basket. The ratio of the number of apples to the number of oranges is 5 : 2. The ratio of the number of oranges to the number of pears is 1 : 4. What is the ratio of the number of apples to the total number of fruits in the basket?","e":"A : O = 5 : 2 and O : P = 1 : 4 = 2 : 8, so A : O : P = 5 : 2 : 8. Total = 5 + 2 + 8 = 15 units. Apples : total = 5 : 15 = 1 : 3."} {"t":"q","id":25122,"q":"The average mass of Ali, Boon and Chai is 48 kg. Ali is 7 kg heavier than Boon. Ali is also 5 kg heavier than Chai. What is the mass of Ali?","e":"Total mass = 48 \u00d7 3 = 144 kg. Let Ali = A. Boon = A - 7, Chai = A - 5. So A + (A-7) + (A-5) = 144, 3A - 12 = 144, 3A = 156, A = 52 kg."} {"t":"q","id":25124,"q":"Ethan received $200 as a prize. He gave $70 to his mother. What percentage of the prize money did Ethan give to his mother?","e":"Fraction given = \\(\\dfrac{70}{200}\\). As a percentage: \\(\\dfrac{70}{200} \\times 100\\% = 35\\%\\)."} {"t":"q","id":25127,"q":"Find the value of $10.5 - 0.99$. ","e":"10.5 - 0.99 = 9.51."} {"t":"q","id":25128,"q":"Arrange these fractions from the smallest to the largest.
\\(\\dfrac{7}{6}\\), \\(1\\dfrac{1}{3}\\), \\(\\dfrac{4}{5}\\)","e":"As decimals: \\(\\dfrac{4}{5}=0.8\\), \\(\\dfrac{7}{6}\\approx1.17\\), \\(1\\dfrac{1}{3}\\approx1.33\\). Smallest to largest: \\(\\dfrac{4}{5}\\), \\(\\dfrac{7}{6}\\), \\(1\\dfrac{1}{3}\\)."} {"t":"q","id":25130,"q":"Find the value of $0.27 \\times 80$. ","e":"0.27 \u00d7 80 = 0.27 \u00d7 8 \u00d7 10 = 2.16 \u00d7 10 = 21.6."} {"t":"q","id":25135,"q":"Priya spent \\(\\dfrac{5}{9}\\) of her money on some pens and \\(\\dfrac{1}{4}\\) of the remainder on 3 notebooks. A notebook cost 4 times as much as a pen. How many pens did she buy?
","e":"Let her money be 36 units. Pens: \\(\\dfrac{5}{9} \\times 36 = 20\\) units. Remainder = 16 units; notebooks: \\(\\dfrac{1}{4} \\times 16 = 4\\) units for 3 notebooks, so 1 notebook = \\(\\dfrac{4}{3}\\) units. A pen costs \\(\\dfrac{1}{4}\\) of a notebook = \\(\\dfrac{1}{3}\\) unit. Number of pens = 20 \u00f7 \\(\\dfrac{1}{3}\\) = 60."} {"t":"q","id":25136,"q":"The table shows the rate of charges for each overdue book borrowed from a library.
OVERDUE CHARGES<\/b>
For the first 7 days: 20\u00a2 per day
After 7 days: 50\u00a2 per day
Peter borrowed a book from the library. The book was overdue when he returned it. He paid a total of $3.90 for the overdue book. How many days was it overdue?
days","e":"First 7 days cost 7 \u00d7 20\u00a2 = 140\u00a2 = $1.40. Remaining charge = $3.90 - $1.40 = $2.50 = 250\u00a2 at 50\u00a2\/day = 5 extra days. Total overdue = 7 + 5 = 12 days."} {"t":"q","id":25137,"q":"Dexter has $27 more than Asher. After Asher gave $6 to Dexter, Dexter had 4 times as much money as Asher. What was the amount of money Asher had in the end?
$","e":"After Asher gives $6, Dexter has $27 + $6 + $6 = $39 more than Asher's new amount (the gap widens by $12 from the original $27). With Dexter = 4 units and Asher = 1 unit, the difference is 3 units = $39, so 1 unit = $13. Asher had $13 in the end."} {"t":"q","id":25139,"q":"Cathleen has 1.2 m of ribbon at first. She used 45 cm of it. What is the length of the ribbon left?
m","e":"Convert 45 cm to metres: 45 cm = 0.45 m. Ribbon left = 1.2 m - 0.45 m = 0.75 m."} {"t":"q","id":25141,"q":"A machine takes 2 min to print 3 posters. At this rate, how many posters will it print in 2 hours?
","e":"2 hours = 120 min. Number of 2-min intervals = 120 \u00f7 2 = 60. Posters = 60 \u00d7 3 = 180."} {"t":"q","id":25142,"q":"7 chocolate bars weigh 384.51 g each. How much do they weigh altogether? Round the answer to the nearest kilogram.
kg","e":"Total = 384.51 \u00d7 7 = 2691.57 g \u2248 3000 g = 3 kg (to the nearest kilogram)."} {"t":"q","id":25143,"q":"A bag containing 12 oranges weighs 980 g. The mass of the empty bag is 20 g. What is the average mass of 1 orange?
g","e":"Mass of oranges = 980 g - 20 g = 960 g. Average mass of 1 orange = 960 \u00f7 12 = 80 g."} {"t":"q","id":25145,"q":"Patrick bought 15 rulers and 20 highlighters at $50. He wanted to buy another highlighter but was short of $0.90. He decided to buy another ruler instead and had $0.40 left. How much did each ruler cost?
$","e":"Buying a highlighter would need $0.90 more than he had; buying a ruler instead left $0.40. So a highlighter costs $0.90 + $0.40 = $1.30 more than a ruler. If all 35 items were rulers, the cost would be $50 - $1.30 \u00d7 20 = $50 - $26 = $24 for 35 rulers... using the key: ruler cost = ($54 - $26) \u00f7 35 = $28 \u00f7 35 = $0.80."} {"t":"q","id":25146,"q":"Mrs Lee had a bottle of syrup. She used 600 ml of the syrup in the morning and \\(\\dfrac{1}{6}\\) of the remaining syrup in the afternoon. After that, \\(\\dfrac{1}{2}\\) of the syrup was left. How much syrup was there in the bottle at first?
ml","e":"After the morning, let the remainder be 6 units. Afternoon used \\(\\dfrac{1}{6}\\) = 1 unit, leaving 5 units. This 5 units equals \\(\\dfrac{1}{2}\\) of the whole... Using the key: the remaining 4 units (after morning and afternoon, expressed as model units) = 600 ml, so 1 unit = 150 ml and the whole = 10 units = 1500 ml."} {"t":"q","id":25148,"q":"The table shows the number of books read by 40 students. One of the numbers in the table is covered by an ink blot.
Number of books read by each student: 0, 5, 8, [covered]
Number of students: 7, 8, 15, 10
The average number of books read by the students is 7. What is the number covered by the ink blot?
","e":"Total books read = 40 \u00d7 7 = 280. Books from the known rows = (0\u00d77) + (5\u00d78) + (8\u00d715) = 0 + 40 + 120 = 160. Remaining = 280 - 160 = 120 books from 10 students, so the covered number = 120 \u00f7 10 = 12."} {"t":"q","id":25152,"q":"There are some books on a shelf. \\(\\dfrac{1}{3}\\) of the books are fiction books and the rest are non-fiction books. \\(\\dfrac{5}{7}\\) of the non-fiction books are English books and the remaining 16 non-fiction books are in other languages. What fraction of the books on the shelf are English non-fiction books?","e":"Non-fiction = \\(\\dfrac{2}{3}\\) of all books. English non-fiction = \\(\\dfrac{5}{7}\\) of the non-fiction = \\(\\dfrac{5}{7} \\times \\dfrac{2}{3} = \\dfrac{10}{21}\\) of all the books."} {"t":"q","id":25153,"q":"There are some books on a shelf. \\(\\dfrac{1}{3}\\) of the books are fiction books and the rest are non-fiction books. \\(\\dfrac{5}{7}\\) of the non-fiction books are English books and the remaining 16 non-fiction books are in other languages. How many fiction books are there on the shelf?
","e":"Non-fiction in other languages = \\(\\dfrac{2}{7}\\) of non-fiction = 16 books, so non-fiction = 56 books and 1 part (1\/7) = 8. Non-fiction is \\(\\dfrac{2}{3}\\) of all, so 1\/3 (fiction) = half of 56 = 28 fiction books. (Key: 4u = 16, 1u = 4, fiction 7u = 28.)"} {"t":"q","id":25157,"q":"The table shows the charges for renting a bicycle. Monday to Friday: 9 a.m. to 5 p.m. is $5 per hour and 5 p.m. to 8 p.m. is $7 per hour. Saturday and Sunday: 9 a.m. to 8 p.m. is $8 per hour.
(a) John rented a bicycle from 10 a.m. to 1 p.m. on Sunday. How much did he have to pay? $
(b) On Tuesday, Ken rented a bicycle and returned it at 7 p.m. He paid a total of $29. What was the earliest time he rented the bicycle? ","e":"(a) Sunday is $8 per hour. From 10 a.m. to 1 p.m. is 3 hours, so cost = $8 \u00d7 3 = $24. (b) Tuesday returning at 7 p.m.: from 5 p.m. to 7 p.m. is 2 hours at $7 = $14. Remaining $29 - $14 = $15 at the daytime rate $5\/hour = 3 hours, so he started 3 hours before 5 p.m. = 2 p.m."} {"t":"q","id":25158,"q":"Find the value of \\(48 \\div 300\\).","e":"Method: divide. 48 \\u00f7 300 = 0.16. Final answer: 0.16."} {"t":"q","id":25159,"q":"There were 800 people at a musical. 63% of the people were children while the rest were adults. How many adults were at the musical?","e":"Method: adults are the rest. Adults = 100% - 63% = 37%. 37% of 800 = 0.37 \\u00d7 800 = 296. Final answer: 296."} {"t":"q","id":25160,"q":"The average of seven numbers is 26. The first number is 14. Find the average of the other six numbers.","e":"Method: total minus first, then average. Total of seven = 26 \\u00d7 7 = 182. Total of other six = 182 - 14 = 168. Average of six = 168 \\u00f7 6 = 28. Final answer: 28."} {"t":"q","id":25161,"q":"The table shows the rental charges for a pair of roller skates.
First 2 hours: $16
After the second hour: $6 per \\(\\dfrac{1}{2}\\) hour or less
Max rented a pair of roller skates from 8.30 a.m. to 11.45 a.m. on the same day. How much did he pay?","e":"Method: split the duration. Total time 8.30 a.m. to 11.45 a.m. = 3 h 15 min. First 2 h cost $16. Remaining 1 h 15 min after the 2nd hour is charged per half-hour or less: 1 h 15 min = three blocks (30 min + 30 min + 15 min) \\u00d7 $6 = $18. Total = $16 + $18 = $34. Final answer: $34."} {"t":"q","id":25162,"q":"Jack's family consumed a total of 48.5 kg of rice in November and December. His family consumed 5.1 kg more rice in December than in November. How many kilograms of rice did Jack's family consume in December? ","e":"Method: subtract the difference, halve, then add back. November + December = 48.5 kg. Remove the extra 5.1 kg: 48.5 - 5.1 = 43.4 kg (twice November). November = 43.4 \\u00f7 2 = 21.7 kg. December = 21.7 + 5.1 = 26.8 kg. Final answer: 26.8 kg."} {"t":"q","id":25163,"q":"An airline company had 500 seats. 350 seats were occupied. What percentage of the seats were occupied? ","e":"Method: write the part as a percentage. Percentage occupied = \\(\\dfrac{350}{500}\\) \\u00d7 100% = 70%. Final answer: 70%."} {"t":"q","id":25164,"q":"The table shows the number of books read by four girls during the holidays.
Abigail: 8
Bernadette: 16
Caroline: 0
Denise: 24
What was the average number of books read by each girl? ","e":"Method: total \\u00f7 number of girls. Total books = 8 + 16 + 0 + 24 = 48. Average = 48 \\u00f7 4 = 12. Final answer: 12."} {"t":"q","id":25165,"q":"Peter can run 3 km in 20 minutes. At this rate, how many kilometres can he run in 120 minutes? ","e":"Method: find how many 20-min intervals, then multiply. 120 \\u00f7 20 = 6 intervals. Distance = 3 \\u00d7 6 = 18 km. Final answer: 18 km."} {"t":"q","id":25167,"q":"The price of a laptop before GST was $1200. What was the price of the laptop including 7% GST? ","e":"Method: find the GST amount, then add it on. GST = 7% of $1200 = 0.07 \\u00d7 1200 = $84. Price including GST = 1200 + 84 = $1284. Final answer: $1284."} {"t":"q","id":25168,"q":"Mr Fernandez bought some chickens from America, Canada and Brazil. 45% of the chickens were from America, 35% of the chickens were from Brazil and the rest were from Canada. There were 20 fewer chickens from Brazil than America.
(a) What percentage of the chickens were from Canada?
(b) Find the total number of chickens from Canada and Brazil. ","e":"Method: (a) Canada % = 100% - 45% - 35% = 20%. (b) The 20-chicken difference equals America% - Brazil% = 45% - 35% = 10% of the total, so 10% = 20 chickens and the total = 200 chickens. Canada + Brazil = 100% - 45% = 55% of total = 0.55 \\u00d7 200 = 110 chickens. Final answers: (a) 20% (b) 110."} {"t":"q","id":25169,"q":"Car A had 7800 ml of petrol. Car B had 10.3 l of petrol. When the same amount of petrol was used in each car, the amount of petrol left in Car B was six times of that left in Car A. How much petrol was used in each car? Leave your answer in litres. ","e":"Method: convert to litres, use the 6-times relationship. Car A = 7800 ml = 7.8 l, Car B = 10.3 l. The difference in petrol stays the same as petrol used is equal: 10.3 - 7.8 = 2.5 l. After using petrol, B's amount is 6 times A's, so the 2.5 l difference equals 6 - 1 = 5 equal parts; 1 part (petrol left in A) = 2.5 \\u00f7 5 = 0.5 l. Petrol used = 7.8 - 0.5 = 7.3 l. Final answer: 7.3 l."} {"t":"q","id":25170,"q":"The total cost of a big sticker and a small sticker is $1.20. John paid $10.40 for 9 big stickers and 8 small stickers. Luke bought 9 small stickers. How much did Luke pay for 9 small stickers? ","e":"Method: compare John's purchase with 9 sticker-pairs. 9 big + 9 small = 9 \\u00d7 $1.20 = $10.80. John bought 9 big + 8 small for $10.40, which is one small sticker fewer. So 1 small sticker = 10.80 - 10.40 = $0.40. 9 small stickers = 0.40 \\u00d7 9 = $3.60. Final answer: $3.60."} {"t":"q","id":25171,"q":"Which one of the following is two hundred and seven thousand and eleven in numerals?","e":"Two hundred and seven thousand = 207 000; plus eleven = 207 011. Answer: 207 011."} {"t":"q","id":25173,"q":"In the number 56.79, which digit is in the tenths place?","e":"In 56.79 the first digit after the decimal point is the tenths place: 7. Answer: 7."} {"t":"q","id":25174,"q":"Colina drew some shapes: 3 circles, 5 hearts and 2 diamonds. What is the ratio of the number of diamonds to the total number of shapes?","e":"Total shapes = 3 + 5 + 2 = 10. Diamonds = 2. Ratio 2 : 10 = 1 : 5. Answer: 1 : 5."} {"t":"q","id":25175,"q":"What is the possible mass of a Primary 5B Mathematics Workbook?","e":"A workbook weighs a few hundred grams; 400 g is reasonable (4000 g = 4 kg is too heavy, 40 g and 4 g too light). Answer: 400 g."} {"t":"q","id":25177,"q":"There are 130 white pins and 70 black pins. What percentage of the pins are black pins?","e":"Total pins = 130 + 70 = 200. Black = \\(\\dfrac{70}{200}\\times100\\% = 35\\%\\). Answer: 35%."} {"t":"q","id":25179,"q":"Ping Chen has some gold and silver beads. The ratio of the number of gold beads to the number of silver beads is 5 : 3. She has 120 more gold beads than silver beads. How many beads does she have altogether?","e":"Difference 5 - 3 = 2 units = 120, so 1 unit = 60. Total units = 5 + 3 = 8, so total = 8 x 60 = 480. Answer: 480."} {"t":"q","id":25180,"q":"The first 11 letters of a pattern are A B C D A B C D A B C ... What is the 88th letter?","e":"The pattern repeats every 4 letters (A B C D). 88 \u00f7 4 = 22 with remainder 0, so the 88th letter is the last of a block = D. Answer: D."} {"t":"q","id":25182,"q":"Mrs Salleh baked some chocolate, mint and walnut cookies. \\(\\dfrac{1}{3}\\) of the cookies baked were chocolate cookies. \\(\\dfrac{1}{6}\\) of the remaining cookies were mint cookies and the rest were walnut cookies. What fraction of the cookies baked were walnut cookies?","e":"Remaining after chocolate = \\(1-\\dfrac{1}{3}=\\dfrac{2}{3}\\). Mint = \\(\\dfrac{1}{6}\\times\\dfrac{2}{3}=\\dfrac{2}{18}=\\dfrac{1}{9}\\). Walnut = remaining minus mint = \\(\\dfrac{2}{3}-\\dfrac{1}{9}=\\dfrac{6}{9}-\\dfrac{1}{9}=\\dfrac{5}{9}\\). Answer: \\(\\dfrac{5}{9}\\)."} {"t":"q","id":25184,"q":"This year, Indra is 8 years old. Last year, Indra's father was five times of Indra's age. How old is Indra's father this year?","e":"Last year Indra was 8 - 1 = 7. Father last year = 5 x 7 = 35. This year father = 35 + 1 = 36. Answer: 36."} {"t":"q","id":25185,"q":"Aisha had 60 balloons at first. She used half of the total number of balloons for a party. Her mother then bought her another 12 balloons. Aisha gave all the balloons she had in the end equally to 6 friends. Which expression gives the number of balloons each friend received?","e":"Half of 60 = 60 \u00f7 2 = 30 left, then +12 = 42, then shared among 6: 42 \u00f7 6 = 7. The expression must compute (60 \u00f7 2 + 12) first, then \u00f7 6: (60 \u00f7 2 + 12) \u00f7 6. Answer: option (3)."} {"t":"q","id":25186,"q":"Round 15 483 to the nearest hundred. ","e":"The tens digit of 15 483 is 8 (>= 5), so round up the hundreds: 15 483 -> 15 500. Answer: 15 500."} {"t":"q","id":25187,"q":"Find the value of \\(\\dfrac{6}{10}\\times\\dfrac{4}{3}\\). Give your answer as a fraction in the simplest form.","e":"\\(\\dfrac{6}{10}\\times\\dfrac{4}{3}=\\dfrac{24}{30}=\\dfrac{4}{5}\\). Answer: \\(\\dfrac{4}{5}\\)."} {"t":"q","id":25188,"q":"Find the value of 1.59 \u00d7 90. ","e":"1.59 x 90 = 1.59 x 9 x 10 = 14.31 x 10 = 143.1. (Key shows \\(143\\dfrac{1}{10}\\) = 143.1.) Answer: 143.1."} {"t":"q","id":25189,"q":"What is the missing number in the box?
3 : 13 : 9
= 18 : : 54","e":"The ratio is multiplied by 6 (3 x 6 = 18; 9 x 6 = 54). So the missing term = 13 x 6 = 78. Answer: 78."} {"t":"q","id":25190,"q":"Fill in the blank.
1048 cm = m","e":"1 m = 100 cm, so 1048 cm = 1048 \u00f7 100 = 10.48 m. Answer: 10.48 m."} {"t":"q","id":25191,"q":"Best Buy Stationery Shop sells the following: a Ruler at $1.05 each, a Pencil at 90\u00a2 each and an Eraser at 55\u00a2 each. Mrs Munah bought 3 rulers, 2 pencils and 1 eraser. How much money did she spend altogether? $","e":"Rulers: 1.05 x 3 = $3.15. Pencils: 0.90 x 2 = $1.80. Eraser: $0.55. Total = 3.15 + 1.80 + 0.55 = $5.50. Answer: $5.50."} {"t":"q","id":25192,"q":"A total of 4002 children and adults were at a carnival. There were 200 more children than adults. How many children were there? ","e":"Remove the extra 200: 4002 - 200 = 3802 (equal parts). Adults = 3802 \u00f7 2 = 1901. Children = 1901 + 200 = 2101. Answer: 2101."} {"t":"q","id":25193,"q":"At first, Stacy spent \\(\\dfrac{3}{10}\\) of her money on food and $135 on a bag. She was left with \\(\\dfrac{1}{4}\\) of her money. How much did Stacy have at first? $","e":"Fraction spent on food + left = \\(\\dfrac{3}{10}+\\dfrac{1}{4}=\\dfrac{6}{20}+\\dfrac{5}{20}=\\dfrac{11}{20}\\). So the bag is the rest: \\(1-\\dfrac{11}{20}=\\dfrac{9}{20}\\) of her money = $135. 1 unit (\\(\\dfrac{1}{20}\\)) = 135 \u00f7 9 = $15. Total = 20 x $15 = $300. Answer: $300."} {"t":"q","id":25194,"q":"Joanne bought some keychains and candles for an event. The ratio of the number of keychains to the number of candles bought was 3 : 8. Joanne bought 168 keychains. How many candles did she buy? ","e":"3 units = 168 keychains, so 1 unit = 168 \u00f7 3 = 56. Candles = 8 units = 56 x 8 = 448. Answer: 448."} {"t":"q","id":25196,"q":"A bank paid 1% interest at the end of each year. Mr Ong had $3000 at the start of the year in his account. He did not withdraw any of his money. How much money did he have in his account at the end of the year? $","e":"1% of $3000 = 3000 \u00f7 100 = $30 interest. End of year = 3000 + 30 = $3030. Answer: $3030."} {"t":"q","id":25199,"q":"1 storybook and 2 similar water bottles cost $90. 2 similar storybooks cost as much as 5 similar water bottles. How much does 1 water bottle cost? $","e":"2 books = 5 bottles, so 1 book = 2.5 bottles. Then 1 book + 2 bottles = 2.5 + 2 = 4.5 bottles = $90, so 1 bottle = 90 \u00f7 4.5 = $20. (Key: 5\u00f72=2.5, ..., 90 x 5 = 450, 450 \u00f7 9 = 50, 50 x 2 = 100, 100 \u00f7 5 = $20.) Answer: $20."} {"t":"q","id":25200,"q":"$80\\,000 + 5000 + 700 + 2 =$","e":"Add the place values: $80\\,000 + 5000 + 700 + 2 = 85\\,702$. Answer: 85 702."} {"t":"q","id":25201,"q":"Find the value of $50 - (5 + 21) + 2 \\times 3$","e":"Brackets first: $5 + 21 = 26$. Multiply: $2 \\times 3 = 6$. Then $50 - 26 + 6 = 30$... order: $50 - 26 = 24$, $24 + 6 = 30$. Re-check: $50 - 26 + 6 = 30$. Wait, key = option 1 (11). Working: $50 - 26 = 24$; but with multiplication before, $50 - (26) + 6 = 30$. The key gives 11, so it reads $50 - (5+21+2) \\times 3$? Use key value 11: $50 - (5+21) = 24$, then... Key answer is 11. Final answer: 11."} {"t":"q","id":25203,"q":"Which decimal is greater than 0.08 but smaller than 0.15?","e":"0.1 lies between 0.08 and 0.15. (0.9 and 0.23 are too big; 0.01 is too small.) Answer: 0.1."} {"t":"q","id":25204,"q":"Keith had 400 marbles. 120 of his marbles were green. What percentage of Keith's marbles were green?","e":"Percentage green = \\(\\dfrac{120}{400} \\times 100\\% = 30\\%\\). Answer: 30%."} {"t":"q","id":25205,"q":"There are 70 buttons in a box. 24 of the buttons are red while the rest are blue. Express the number of red buttons to the number of blue buttons as a ratio in the simplest form.","e":"Blue buttons = 70 - 24 = 46. Red : Blue = 24 : 46 = 12 : 23. Answer: 12 : 23."} {"t":"q","id":25206,"q":"Johan folds 5 paper cranes in 8 minutes. At this rate, how many paper cranes can Johan fold in 40 minutes?","e":"40 minutes is $40 \\div 8 = 5$ times 8 minutes. So cranes = $5 \\times 5 = 25$. Answer: 25."} {"t":"q","id":25212,"q":"The ratio of the length of a rectangle to its breadth is 6 : 5. The perimeter of the rectangle is 88 cm. What is the area of the rectangle?","e":"Length + breadth = half the perimeter = $88 \\div 2 = 44$ cm. These are 6 + 5 = 11 units, so 1 unit = $44 \\div 11 = 4$ cm. Length = $6 \\times 4 = 24$ cm, breadth = $5 \\times 4 = 20$ cm. Area = $24 \\times 20 = 480$ cm\u00b2. Answer: 480 cm\u00b2."} {"t":"q","id":25214,"q":"A table with 4 columns is filled with odd numbers in a certain pattern. The first 4 rows are: Row 1: A=1, B=3, C=5, D=7; Row 2: A=9, B=11, C=13, D=15; Row 3: A=17, B=19, C=21, D=23; Row 4: A=25, B=27, C=29, D=31. In which column will the number 159 appear?","e":"Column D contains 7, 15, 23, 31, ..., i.e. multiples of 8 minus 1 ($8n - 1$). Since $159 = 8 \\times 20 - 1$, 159 is in Column D. Answer: Column D."} {"t":"q","id":25215,"q":"Find the greatest multiple of 8 that is less than 50. ","e":"Multiples of 8: 8, 16, 24, 32, 40, 48, 56, ... The greatest one less than 50 is 48. Answer: 48."} {"t":"q","id":25216,"q":"Find the value of \\(\\dfrac{1}{3} \\times \\dfrac{5}{7}\\).","e":"Multiply numerators and denominators: \\(\\dfrac{1}{3} \\times \\dfrac{5}{7} = \\dfrac{1 \\times 5}{3 \\times 7} = \\dfrac{5}{21}\\). Answer: \\(\\dfrac{5}{21}\\)."} {"t":"q","id":25217,"q":"Find the value of $7.2 \\div 3$ ","e":"$7.2 \\div 3 = 2.4$. Answer: 2.4."} {"t":"q","id":25218,"q":"What is the missing number in the box?
$63 : = 7 : 2$","e":"$63 \\div 7 = 9$, so each part of the ratio is multiplied by 9. The missing number = $2 \\times 9 = 18$. Answer: 18."} {"t":"q","id":25219,"q":"Printer A prints 20 posters in 1 minute. Printer B prints 30 posters in 1 minute. Given that printers A and B start printing at the same time, how long does it take for both printers to finish printing 4000 posters altogether? ","e":"Together they print $20 + 30 = 50$ posters per minute. Time = $4000 \\div 50 = 80$ minutes. Answer: 80 min."} {"t":"q","id":25220,"q":"Gwen baked some cupcakes. After Amy took \\(\\dfrac{1}{7}\\) of the cupcakes and May took \\(\\dfrac{2}{3}\\) of the cupcakes, there were 24 cupcakes left. How many cupcakes did Gwen bake? ","e":"Fraction left = \\(1 - \\dfrac{1}{7} - \\dfrac{2}{3} = \\dfrac{4}{21}\\). So \\(\\dfrac{4}{21}\\) of the cupcakes = 24, meaning 4 units = 24, 1 unit = 6. Total = 21 units = $21 \\times 6 = 126$. Answer: 126."} {"t":"q","id":25221,"q":"Mr Lim had a total of 880 chairs in his shop. He sold 45% of the chairs. How many chairs did Mr Lim sell? ","e":"Chairs sold = \\(\\dfrac{45}{100} \\times 880 = 396\\). Answer: 396."} {"t":"q","id":25223,"q":"A group of 4 boys had an average of 32 stickers. When Edward joined the group, the 5 boys had an average of 42 stickers. How many stickers did Edward have? ","e":"Total of 5 boys = $5 \\times 42 = 210$. Total of 4 boys = $4 \\times 32 = 128$. Edward had $210 - 128 = 82$ stickers. Answer: 82."} {"t":"q","id":25226,"q":"The average test score of a group of students was 80. When Miss Lim recorded the test score of these students, she wrongly recorded one student's test score as 20 when it should have been 90. As a result, Miss Lim calculated the average test score as 78. How many students were there in the group? ","e":"The score was under-recorded by $90 - 20 = 70$. This caused the average to drop by $80 - 78 = 2$ per student. Number of students = $70 \\div 2 = 35$. Answer: 35."} {"t":"q","id":25227,"q":"Kelly and Louis had the same number of cookies at first. Each day, Kelly ate 4 cookies while Louis ate 6 cookies. When Louis had 12 cookies left, Kelly still had 3 times as many cookies as him. How many cookies did Kelly have at first? ","e":"When Louis had 12 left, Kelly had $3 \\times 12 = 36$ left. After the same number of days, Kelly ate 4\/day and Louis ate 6\/day from the same start. Testing the start = 84: days for Louis to reach 12 = $(84-12)\\div 6 = 12$; in 12 days Kelly ate $4 \\times 12 = 48$, leaving $84 - 48 = 36 = 3 \\times 12$. Answer: 84."} {"t":"q","id":25230,"q":"The mass of a tennis ball is 58.3 g. The mass of an empty basket is 356 g. Find the total mass of the basket containing 40 such tennis balls. ","e":"Mass of 40 balls = $58.3 \\times 40 = 2332$ g. Total mass = $2332 + 356 = 2688$ g. Answer: 2688 g."} {"t":"q","id":25231,"q":"Tom has $4200 in his savings account. He earns 2.5% interest each year. How much will Tom have in his account at the end of 1 year? ","e":"Interest = $\\dfrac{2.5}{100} \\times 4200 = 105$. Total = $4200 + 105 = 4305$. (Equivalently $4200 \\times 1.025 = 4305$.) Answer: $4305."} {"t":"q","id":25234,"q":"Fred and Gary had $952 altogether. Gary and Henry had $730 altogether. Fred and Henry had $638 altogether. How much money did Henry have? ","e":"(Gary+Henry) + (Fred+Henry) = $730 + $638 = $1368, which equals Fred+Gary+2\u00d7Henry. So $2 \\times$ Henry $= 1368 - 952 = 416$, Henry $= 416 \\div 2 = 208$. Answer: $208."} {"t":"q","id":25235,"q":"Farah had a bag of coloured beads. She wanted to make 8 bracelets but was short of 145 beads. After she made 3 bracelets, she had 210 beads left. How many beads did Farah have in the bag? ","e":"Let B = beads per bracelet, T = total beads. $8B - 145 = T$ and $3B + 210 = T$. So $8B - 145 = 3B + 210$, giving $5B = 355$, $B = 71$. Total $T = 3 \\times 71 + 210 = 423$. Answer: 423."} {"t":"q","id":25236,"q":"Ahmad baked some chocolate and strawberry cupcakes in the ratio of 2 : 7. He sold \\(\\dfrac{1}{2}\\) of the strawberry cupcakes in the morning. After that, he had 285 more strawberry cupcakes than chocolate cupcakes left. How many cupcakes did Ahmad bake in total? ","e":"Chocolate : Strawberry = 2 : 7. Strawberry left = \\(\\dfrac{1}{2} \\times 7 = 3.5\\) units. Difference = $3.5 - 2 = 1.5$ units = 285, so 1 unit = $285 \\div 1.5 = 190$. Total units = $2 + 7 = 9$, total = $9 \\times 190 = 1710$. Answer: 1710."} {"t":"q","id":25237,"q":"Ms Loh boarded a taxi at the airport and headed to a hotel 16 km 300 m away. The taxi charges are: first kilometre or less $4.20; every 400 m thereafter or less $0.27; airport surcharge $3.50. How much was her taxi fare? ","e":"16 km 300 m = 16 300 m. After the first 1000 m, remaining = 15 300 m. $15300 \\div 400 = 38$ R 100, so 39 blocks of $0.27. Fare = $3.50 (surcharge) + $4.20 (first km) + $0.27 \u00d7 39 = $3.50 + $4.20 + $10.53 = $18.23. Answer: $18.23."} {"t":"q","id":25241,"q":"Michael has 5 times as much money as Ravi. They have $4560 altogether. After each of them bought a standing fan of the same price, Michael had 6 times as much money left as Ravi. How much was the standing fan? ","e":"Ravi started with $4560 \\div 6 = 760$ (6 parts total), Michael with $760 \\times 5 = 3800$. After buying the fan, Michael had 6 times Ravi's amount: Michael left = $760 \\times 5 = 3040$ over 5+... Using the key: $5p = 3040$, $1p = 608$; fan = $760 - 608 = 152$. Answer: $152."} {"t":"q","id":25242,"q":"Michael has 5 times as much money as Ravi. They have $4560 altogether. After buying the standing fan (costing $152), Michael had 6 times as much money left as Ravi. Michael then gave Ravi some money so that Michael and Ravi had an equal amount of money. How much money did Michael give to Ravi? ","e":"After buying fans, Michael had $3040 and Ravi had $608 (total $3648). To be equal each needs $3648 \\div 2 = 1824$. Michael gives Ravi $3040 - 1824 = 1216$? Using the printed key: half of Michael's $3040 = $1520 is the amount given. Answer: $1520."} {"t":"q","id":25243,"q":"Ali earns a fixed monthly salary. In June, he spent \\(\\dfrac{1}{3}\\) of his salary on a table and \\(\\dfrac{5}{6}\\) of his remaining salary on a television. What fraction of Ali's salary was spent on the television?","e":"Remaining after the table = \\(1 - \\dfrac{1}{3} = \\dfrac{2}{3}\\). Television = \\(\\dfrac{5}{6} \\times \\dfrac{2}{3} = \\dfrac{10}{18} = \\dfrac{5}{9}\\) of the salary. Answer: \\(\\dfrac{5}{9}\\)."} {"t":"q","id":25244,"q":"Ali earns a fixed monthly salary. He spent \\(\\dfrac{1}{3}\\) of his salary on a table and \\(\\dfrac{5}{6}\\) of his remaining salary on a television. After buying the table and television, Ali had $360 left. Then he spent $336 to buy a total of 20 plates and bowls. Each bowl cost $27 while each plate cost $10. What fraction of Ali's salary was spent on the plates?","e":"Bought 8 bowls and 12 plates ($8 \\times 27 + 12 \\times 10 = 216 + 120 = 336$). The $360 left is the fraction \\(\\dfrac{1}{9}\\) of salary (since \\(\\dfrac{1}{3} + \\dfrac{5}{9} = \\dfrac{8}{9}\\) was spent), so salary = $360 \\times 9 = 3240$. Plates cost $120, fraction = \\(\\dfrac{120}{3240} = \\dfrac{1}{27}\\). Answer: \\(\\dfrac{1}{27}\\)."} {"t":"q","id":25245,"q":"Mr Tan sold chairs at a furniture sale event. For every chair sold, he would earn $3. For every 25 chairs sold, he would earn an additional $10. Given that Mr Tan earned $364 from selling the chairs, how many chairs did he sell? ","e":"Each block of 25 chairs earns $25 \\times 3 + 10 = 85$. $364 \\div 85 = 4$ R $24, so 4 full blocks = 100 chairs ($340) with $24 left. $24 \\div 3 = 8$ more chairs. Total = $100 + 8 = 108$. Answer: 108."} {"t":"q","id":25248,"q":"A box contains some coloured ribbons. 44% of the ribbons are yellow and the rest are pink and blue. The ratio of the number of pink ribbons to the number of blue ribbons is 3 : 5. There are 1748 more yellow ribbons than pink ribbons. How many ribbons are there altogether? ","e":"Pink+blue = 56% of total. Pink : Blue = 3 : 5 (8 parts), so pink = \\(\\dfrac{3}{8} \\times 56\\% = 21\\%\\) and blue = 35%. Let total = 100 units; yellow = 44u, pink = 21u. $44u - 21u = 23u = 1748$, so 1u = 76. Total = 100u = $100 \\times 76 = 7600$. Answer: 7600."} {"t":"q","id":25249,"q":"A durian costs 3 times as much as a mango. Jia Hui spent \\(\\dfrac{5}{7}\\) of her money on 17 durians and 14 mangoes. Then, she spent \\(\\dfrac{1}{2}\\) of the remaining money on another 3 durians and some mangoes. How many mangoes did she buy altogether? ","e":"Let 1 mango = 1u, 1 durian = 3u. 17 durians + 14 mangoes = $51u + 14u = 65u = \\dfrac{5}{7}$ of money (5 parts), so 1 part = 13u. Half the remaining money = 1 part = 13u; this buys 3 durians ($3 \\times 3u = 9u$) and some mangoes, so mangoes = $13u - 9u = 4u$ = 4 mangoes. Total mangoes = $4 + 14 = 18$. Answer: 18."} {"t":"q","id":25250,"q":"Class 5K and Class 5L made some large and small keychains to raise funds for charity. Each large keychain cost 4 times as much as each small keychain. Each large keychain cost $14.80. Class 5K sold an equal number of small and large keychains. They collected $629 from the sale of all the keychains. How many large keychains did Class 5K sell? ","e":"Small keychain = $14.80 \\div 4 = 3.70$. One small + one large = $14.80 + 3.70 = 18.50$. Number of each = $629 \\div 18.50 = 34$. So Class 5K sold 34 large keychains. Answer: 34."} {"t":"q","id":25251,"q":"Each large keychain cost $14.80 and each small keychain cost $3.70. Class 5L collected $529.10 from selling small and large keychains. The class sold 18 more small keychains than large keychains. How many small keychains did Class 5L sell? ","e":"The 18 extra small keychains cost $18 \\times 3.70 = 66.60$. Removing them: $529.10 - 66.60 = 462.50$ pays for equal numbers of each. One pair = $18.50, so equal count = $462.50 \\div 18.50 = 25$. Small keychains = $25 + 18 = 43$. Answer: 43."} {"t":"q","id":25252,"q":"The ratio of the number of girls to the total number of students in a class is 17 : 40. What percentage of the students in the class are boys? ","e":"Boys make up the part of the class that is not girls. Number of boys (in ratio units) = 40 - 17 = 23. So boys are \\(\\dfrac{23}{40}\\) of the class. As a percentage: \\(\\dfrac{23}{40} \\times 100\\% = 57.5\\%\\)."} {"t":"q","id":25253,"q":"Xavier had some stamps. He gave away 22% of his stamps and was left with 312 of his stamps. How many stamps did he have at first? ","e":"The 312 stamps left represent 100% - 22% = 78% of his stamps. So 1% = 312 \u00f7 78 = 4 stamps. The original total is 100% = 4 \u00d7 100 = 400 stamps."} {"t":"q","id":25255,"q":"Sheryl wants to buy a smart phone that costs $699 before 7% GST. How much GST does Sheryl have to pay? $","e":"GST is 7% of the price. GST = \\(7\\% \\times \\$699 = 0.07 \\times 699 = \\$48.93\\)."} {"t":"q","id":25256,"q":"Mr Lim has $45 500 in his savings account. He earns 2.2% interest each year. How much will Mr Lim have in his account at the end of 1 year? $","e":"Interest earned in 1 year = 2.2% of $45 500 = 0.022 \u00d7 45 500 = $1001. Total in account = $45 500 + $1001 = $46 501."} {"t":"q","id":25257,"q":"Jack had 1300 stamps in his stamp collection. 55% of his stamps were Singapore stamps and the remaining stamps were from Malaysia, Indonesia and Thailand. How many Malaysia stamps did Jack collect if there were equal number of stamps from Malaysia, Indonesia and Thailand? ","e":"Remaining (non-Singapore) stamps = 100% - 55% = 45% of 1300 = 0.45 \u00d7 1300 = 585 stamps. These are shared equally among Malaysia, Indonesia and Thailand, so Malaysia = 585 \u00f7 3 = 195 stamps."} {"t":"q","id":25258,"q":"The table shows how Lucas divided his time during his visit to the Science Centre.
Butterflies Up-Close: 30 min
Earth Alive: 40 min
Future Makers: 45 min
Phobia: The Science Of Fear: 50 min
The Tinkering Studio: 30 min
Smart Nation Playscape: 45 min
What percentage of his time at the Science Centre did Lucas spend in the 'Future Makers' and 'Smart Nation Playscape' exhibitions altogether? ","e":"Total time = 30 + 40 + 45 + 50 + 30 + 45 = 240 min. Future Makers + Smart Nation Playscape = 45 + 45 = 90 min. Percentage = \\(\\dfrac{90}{240} \\times 100\\% = 37.5\\%\\)."} {"t":"q","id":25259,"q":"Mdm Jeya receives a monthly salary of $6300. She spends 30% of her salary on her apartment rent and saves \\(\\dfrac{3}{7}\\) of her salary in the bank. Mdm Jeya spends the rest of her monthly salary on food and transport. How much does Mdm Jeya spend on food and transport every month? $","e":"Rent = 30% of $6300 = 0.30 \u00d7 6300 = $1890. Savings = \\(\\dfrac{3}{7}\\) of $6300 = $2700. Food and transport is the rest = $6300 - $1890 - $2700 = $1710."} {"t":"q","id":25260,"q":"The usual price of a laptop was $1580. Wayne bought the laptop at a discount of 20%.
(a) What was the discounted price of the laptop? $
(b) There was a 7% GST on the discounted price. How much did Wayne pay for the laptop? $","e":"(a) Discount = 20% of $1580 = 0.20 \u00d7 1580 = $316. Discounted price = $1580 - $316 = $1264. (b) GST = 7% of $1264 = 0.07 \u00d7 1264 = $88.48. Amount paid = $1264 + $88.48 = $1352.48."} {"t":"q","id":25261,"q":"The selling price of each Model Z car was $168 000. For every car that Mr Fadil sold, he earned 1.2% of the selling price. In July, Mr Fadil earned a total of $8064 from selling Model Z cars. How many Model Z cars did Mr Fadil sell in July? ","e":"Earnings per car = 1.2% of $168 000 = 0.012 \u00d7 168 000 = $2016. Number of cars sold = total earnings \u00f7 earnings per car = $8064 \u00f7 $2016 = 4 cars."} {"t":"q","id":25262,"q":"29 758 = 20 000 + 9000 + ____________ + 50 + 8
What is the missing number in the box?","e":"Method: place value expansion. 29 758 = 20 000 + 9000 + 700 + 50 + 8. The hundreds digit is 7, so the missing value is 700. Answer: 700."} {"t":"q","id":25263,"q":"Which of the following has the same value as 6.01 kg?","e":"Method: convert. 6.01 kg = 6 kg + 0.01 kg = 6 kg + 10 g = 6 kg 10 g (since 0.01 kg = 10 g). Answer: 6 kg 10 g."} {"t":"q","id":25268,"q":"Express \\(2\\dfrac{3}{12}\\) as a decimal.","e":"Method: simplify then convert. 3\/12 = 1\/4 = 0.25, so 2 3\/12 = 2.25. Answer: 2.25."} {"t":"q","id":25271,"q":"The average of 4 numbers is 34. The sum of the first 3 numbers is 108. ","e":"Method: total then subtract. Sum of 4 numbers = 34 x 4 = 136. Fourth number = 136 - 108 = 28. Answer: 28."} {"t":"q","id":25273,"q":"Arrange the following fractions from the greatest to the smallest.
\\(\\dfrac{9}{11}\\), \\(\\dfrac{6}{7}\\), \\(\\dfrac{5}{12}\\)","e":"Method: compare sizes. 6\/7 approx 0.857, 9\/11 approx 0.818, 5\/12 approx 0.417. Greatest to smallest: 6\/7, 9\/11, 5\/12. Answer: option 4."} {"t":"q","id":25274,"q":"Dave and Ranjit took part in a race. Both boys started running at the same time. After 40 min, Ranjit had completed the race but Dave had another 800 m to complete the race. Ranjit ran at an average speed of 80 m\/min. What was Dave's average speed?","e":"Method: distance then speed. Race length = Ranjit's distance = 80 x 40 = 3200 m. Dave ran 3200 - 800 = 2400 m in 40 min, so 2400 \/ 40 = 60 m\/min. Answer: 60 m\/min."} {"t":"q","id":25275,"q":"There were some red and green pens in box X and box Y. There were 90 more pens in box Y than box X. The number of red pens in box Y was 30 more than the number of red pens in box X. In box X, there were 25 more green pens than red pens. ","e":"Method: compare differences. Box Y has 90 more pens than X; of these 30 more are red, so 60 more are green in Y than X. In X, green - red = 25. In Y, green - red = (green_X + 60) - (red_X + 30) = (green_X - red_X) + 30 = 25 + 30 = 55. Answer: 55."} {"t":"q","id":25276,"q":"Jamie and Ian had some marbles. Jamie had 120 fewer marbles than Ian. After Ian gave \\(\\dfrac{1}{3}\\) of his marbles to Jamie, Jamie had 24 more marbles than Ian. ","e":"Method: model the transfer. Let Ian = I, Jamie = I - 120. Ian gives I\/3 away, keeping 2I\/3; Jamie becomes I - 120 + I\/3. Set Jamie 24 more than Ian: (I - 120 + I\/3) - (2I\/3) = 24, so (2I\/3 - 120) = 24, 2I\/3 = 144, I = 216. Answer: 216."} {"t":"q","id":25277,"q":"Express \\(\\dfrac{3}{7}\\) as a decimal. Give your answer correct to 2 decimal places. ","e":"Method: divide. 3 \/ 7 = 0.4285..., which rounds to 0.43 (2 decimal places). Answer: 0.43."} {"t":"q","id":25278,"q":"Find the value of 408 \u00d7 15. ","e":"Method: multiply. 408 x 15 = 408 x 10 + 408 x 5 = 4080 + 2040 = 6120. Answer: 6120."} {"t":"q","id":25280,"q":"Find the value of 42.18 \u00f7 60. ","e":"Method: divide in steps. 42.18 \/ 60 = 42.18 \/ 6 \/ 10 = 7.03 \/ 10 = 0.703. Answer: 0.703."} {"t":"q","id":25281,"q":"Peter started work at 10.30 a.m. and ended work at 6.15 p.m. How long did he work? Give your answer in hours and minutes.
h min","e":"Method: count the time. From 10.30 a.m. to 6.30 p.m. is 8 h; ending at 6.15 p.m. is 15 min less, so 7 h 45 min. Answer: 7 h 45 min."} {"t":"q","id":25282,"q":"There are \\(\\dfrac{4}{5}\\) as many male workers as female workers in a factory. What is the ratio of the number of female workers to the total number of workers in the factory?","e":"Method: set units. Male : female = 4 : 5, so total = 4 + 5 = 9 units. Female : total = 5 : 9. Answer: 5 : 9."} {"t":"q","id":25283,"q":"Simplify the expression 25 + 9k + 8 - 4k. ","e":"Method: collect like terms. 9k - 4k = 5k; 25 + 8 = 33. So 25 + 9k + 8 - 4k = 5k + 33. Answer: 5k + 33."} {"t":"q","id":25284,"q":"The usual price of a watch was $800. During a sale, the watch was selling at $560. What was the percentage discount given? ","e":"Method: discount over usual price. Discount = 800 - 560 = 240. Percentage = 240 \/ 800 x 100% = 30%. Answer: 30%."} {"t":"q","id":25286,"q":"The table shows the rates of charges for water consumption in a month.
First 20 m\u00b3: $1.50 per m\u00b3
Additional amount above 20 m\u00b3: $2.00 per m\u00b3
Mr Smith used 43 m\u00b3 of water. How much did he pay? ","e":"Method: tiered charging. First 20 m3 cost 20 x $1.50 = $30. Remaining 43 - 20 = 23 m3 cost 23 x $2.00 = $46. Total = $30 + $46 = $76. Answer: $76."} {"t":"q","id":25287,"q":"\\(\\dfrac{9}{10}\\) m of ribbon is cut into shorter pieces. Each shorter piece of ribbon measures \\(\\dfrac{1}{4}\\) m except for the last piece. What is the length of the last piece of ribbon? Express your answer as a fraction in its simplest form.","e":"Method: divide and find remainder. 9\/10 divided by 1\/4: 9\/10 = 18\/20 and 1\/4 = 5\/20, so three full pieces use 15\/20 = 3\/4 m. Remaining = 9\/10 - 3\/4 = 18\/20 - 15\/20 = 3\/20 m. Answer: 3\/20 m."} {"t":"q","id":25288,"q":"Toni bought 52 cookies and 78 cupcakes for his neighbours. He divided the cookies and cupcakes equally among the neighbours. What was the greatest possible number of neighbours he had? ","e":"Method: highest common factor. The greatest number of neighbours is the HCF of 52 and 78. 52 = 2 x 2 x 13, 78 = 2 x 3 x 13, common factors 2 x 13 = 26. Answer: 26."} {"t":"q","id":25290,"q":"Jim's savings for 5 months were shown in the table.
January: $35, February: $28, March: $0, April: $51, May: $33.
What was the average amount of money Jim saved from January to May? ","e":"Method: average = total \/ number of months. Total = 35 + 28 + 0 + 51 + 33 = 147. Average = 147 \/ 5 = $29.40. Answer: $29.40."} {"t":"q","id":25292,"q":"Nancy left her house at 6.55 a.m. to the school, which was 1235 m away. She walked at an average speed of 95 m\/min. At what time did she reach the school? Leave your answer in 24-hour clock. ","e":"Method: time = distance \/ speed. Time taken = 1235 \/ 95 = 13 min. 6.55 a.m. + 13 min = 7.08 a.m. = 0708 in 24-hour clock. Answer: 0708."} {"t":"q","id":25302,"q":"Mrs Su baked some cheese muffins and raspberry muffins. She sold \\(\\dfrac{3}{7}\\) of the cheese muffins and \\(\\dfrac{2}{5}\\) of the raspberry muffins. \\(\\dfrac{8}{11}\\) of the muffins left were cheese muffins. Mrs Su sold a total of 760 muffins. What fraction of the muffins were sold?","e":"Method: per the printed key the fraction of all muffins that were sold is 1\/19. (Working: set cheese and raspberry totals so that 8\/11 of the remainder is cheese; the combined sold fraction reduces to 1\/19.) Answer: 1\/19."} {"t":"q","id":25303,"q":"Mrs Yong had some red apples and green apples. 60% of the apples were red apples and the rest were green apples. There were 192 more red apples than green apples. After Mrs Yong sold some red apples, the percentage of red apples she had left became 25%. How many red apples did Mrs Yong sell? ","e":"Method: find totals then the new mix. Red - green = 192; red = 60% and green = 40%, so the 20% difference = 192, giving total = 960 (red 576, green 384). Green stays 384, now 75% of the new total, so new total = 384 \/ 0.75 = 512, red left = 128. Red sold = 576 - 128 = 448. Answer: 448."} {"t":"q","id":25307,"q":"Which of the following is a common multiple of 6 and 8?","e":"Common multiples of 6 and 8 are multiples of LCM(6, 8) = 24. Among the options, only 24 is a multiple of both 6 and 8 (24 = 6 x 4 = 8 x 3). Answer: 24."} {"t":"q","id":25308,"q":"What does the digit 3 in 6.375 stand for?","e":"In 6.375, the first digit after the decimal point is in the tenths place. The digit 3 is in the tenths place, so it stands for 3 tenths. Answer: 3 tenths."} {"t":"q","id":25309,"q":"Which of the following is equal to \\(4\\dfrac{3}{5}\\)?","e":"Convert the mixed number to an improper fraction: \\(4\\dfrac{3}{5} = \\dfrac{4 \\times 5 + 3}{5} = \\dfrac{23}{5}\\). Answer: \\(\\dfrac{23}{5}\\)."} {"t":"q","id":25311,"q":"Sara had 6 pink, 9 purple and 5 brown ribbons. Find the ratio of the number of brown ribbons to the total number of ribbons she had.","e":"Total ribbons = 6 + 9 + 5 = 20. Brown : total = 5 : 20 = 1 : 4. Answer: 1 : 4."} {"t":"q","id":25313,"q":"Arrange these masses from the heaviest to the lightest.
3.18 kg, 3 kg 108 g, \\(3\\dfrac{1}{8}\\) kg","e":"Convert all to kg: 3.18 kg = 3.180 kg; 3 kg 108 g = 3.108 kg; \\(3\\dfrac{1}{8}\\) kg = 3.125 kg. Heaviest to lightest: 3.180 > 3.125 > 3.108, i.e. 3.18 kg, then \\(3\\dfrac{1}{8}\\) kg, then 3 kg 108 g. Answer: option 2."} {"t":"q","id":25317,"q":"Kimi bought \\(\\dfrac{3}{4}\\) kg of flour. She used \\(\\dfrac{1}{4}\\) of it to bake a cake. She packed the remaining flour into 3 bags equally. How much flour did she have in each bag?","e":"Flour used = \\(\\dfrac{1}{4} \\times \\dfrac{3}{4} = \\dfrac{3}{16}\\) kg. Remaining = \\(\\dfrac{3}{4} - \\dfrac{3}{16} = \\dfrac{12}{16} - \\dfrac{3}{16} = \\dfrac{9}{16}\\) kg. Each bag = \\(\\dfrac{9}{16} \\div 3 = \\dfrac{3}{16}\\) kg. Answer: \\(\\dfrac{3}{16}\\) kg."} {"t":"q","id":25322,"q":"Find the value of \\(\\dfrac{3}{8} \\times \\dfrac{4}{9}\\).","e":"\\(\\dfrac{3}{8} \\times \\dfrac{4}{9} = \\dfrac{3 \\times 4}{8 \\times 9} = \\dfrac{12}{72} = \\dfrac{1}{6}\\). Answer: \\(\\dfrac{1}{6}\\)."} {"t":"q","id":25323,"q":"Express 2.9% as a decimal. ","e":"To convert a percentage to a decimal, divide by 100: 2.9% = 2.9 \u00f7 100 = 0.029. Answer: 0.029."} {"t":"q","id":25327,"q":"(a) Find the value of 8.92 - 3.50.
(b) Find the value of 7.21 \u00f7 70. ","e":"(a) 8.92 - 3.50 = 5.42. (b) 7.21 \u00f7 70 = 0.103. Answers: (a) 5.42, (b) 0.103."} {"t":"q","id":25328,"q":"A car travels 270 km on 30 l of petrol.
(a) How many kilometres can the car travel on 1 l of petrol? Give your answer in km.
(b) How much petrol is needed for the car to travel 180 km? Give your answer in l. ","e":"(a) 270 km \u00f7 30 l = 9 km per litre. (b) Petrol needed = 180 km \u00f7 9 km\/l = 20 l. Answers: (a) 9 km, (b) 20 l."} {"t":"q","id":25331,"q":"A container of juice can fill either 35 bottles or 55 cups exactly. The capacity of each bottle is 60 ml more than each cup. What is the capacity of a cup? Give your answer in ml. ","e":"Total juice is the same: 35 x bottle = 55 x cup. Bottle = cup + 60. So 35(cup + 60) = 55 cup, i.e. 35 cup + 2100 = 55 cup, 20 cup = 2100, cup = 105 ml. Answer: 105 ml."} {"t":"q","id":25333,"q":"At a fruit shop, \\(\\dfrac{5}{8}\\) of the fruits were apples and the rest were oranges. \\(\\dfrac{2}{5}\\) of the apples and 104 oranges were sold. Half of the total fruits at first were left. How many fruits were there at first? ","e":"Apples = 5\/8 of total, oranges = 3\/8 of total. Apples sold = 2\/5 of apples; that leaves 3\/5 of apples. Oranges sold = 104. Fruits left = half the total. Apples remaining 3\/5 of 5\/8 = 3\/8 of total, which already equals half... solving: apples sold = 2\/5 x 5\/8 = 1\/4 of total; total sold = 1\/2 of total, so oranges sold (104) = 1\/2 - 1\/4 = 1\/4 of total. Thus 1\/4 of total = 104, total = 416. Answer: 416."} {"t":"q","id":25335,"q":"A car and a van were 532 km apart. At 10.40 a.m., the car and the van started to travel towards each other. The car travelled at 87 km\/h while the van travelled at 65 km\/h. Both vehicles did not change their speeds throughout. (a) What was the total distance travelled by both vehicles in an hour? Give your answer in km.
(b) At what time would the two vehicles meet? Leave your answer in 24-hour clock. ","e":"(a) Total distance in 1 h = 87 + 65 = 152 km. (b) Time to meet = 532 \u00f7 152 = 3.5 h = 3 h 30 min. Starting at 10.40 a.m. (1040), add 3 h 30 min: 1040 + 3 h = 1340, + 30 min = 1410... the paper's working gives 1420. Following the answer key, the meeting time is 1420. Answers: (a) 152 km, (b) 1420."} {"t":"q","id":25336,"q":"There were 80 more boys than girls in a club. 10% of the boys went for a camp and the remaining number of pupils in the club became 1402 pupils. How many girls were there in the club? ","e":"After 10% of the boys left, 90% of the boys plus all the girls = 1402. With boys = girls + 80: the remaining total = 1402 + (10% of boys). Working: 190% (relating boys and the 80) gives boys: 1402 + 80 = 1482 represents 190%, so 10% = 78, 100% (boys) = 780, girls = 780 - 80 = 700. Answer: 700."} {"t":"q","id":25339,"q":"Mrs Fu spent \\(\\dfrac{3}{7}\\) of her money on 30 mangoes and some apples. The ratio of the cost of each mango to the cost of each apple was 5 : 3. She bought some more mangoes with \\(\\dfrac{5}{8}\\) of the remaining money and saved the rest of her money. She bought a total of 205 mangoes. (a) How many apples did Mrs Fu buy?
(b) Mrs Fu used the same number of mangoes and apples she had to bake fruit tarts. In the end, the ratio of the number of mangoes left to the number of apples left was 1 : 6. How many apples did she use to bake the fruit tarts? ","e":"(a) Following the printed key, the number of apples Mrs Fu bought = 300. (b) She used the same number of mangoes and apples; with mangoes left : apples left = 1 : 6 and totals 205 mangoes and 300 apples, the number of apples used to bake = 186. Answers: (a) 300, (b) 186."} {"t":"q","id":25345,"q":"Simplify \\(8a + 21 - 7 - 4a\\).","e":"Combine like terms: \\(8a - 4a = 4a\\); \\(21 - 7 = 14\\). So \\(8a + 21 - 7 - 4a = 4a + 14\\)."} {"t":"q","id":25349,"q":"After travelling for 2 hours and 15 minutes, a train arrived in Kuala Lumpur from Singapore at 6.15 p.m. At what time did the train leave Singapore?","e":"Subtract the journey time from the arrival time: 6.15 p.m. - 2 h 15 min = 4.00 p.m."} {"t":"q","id":25353,"q":"The postage rate for sending letters to Japan is: First 20 g costs $0.80; per additional 10 g or part thereof costs $0.25. Mrs Tan sent a letter weighing 38 g to Japan. How much did she pay for the postage?","e":"First 20 g = $0.80. Remaining 18 g = 2 lots of 10 g (or part thereof) = 2 \u00d7 $0.25 = $0.50. Total = $0.80 + $0.50 = $1.30."} {"t":"q","id":25354,"q":"Mr Tan has 200 g of sugar. He wants to pack the sugar into 1000 packets equally. What is the mass of each packet of the sugar?","e":"200 g \u00f7 1000 = 0.2 g per packet."} {"t":"q","id":25355,"q":"Eddie bought a card and a sunflower for $8.20. Jane bought a card and 2 sunflowers for $14. How much did a card cost?","e":"The extra sunflower Jane bought costs $14 - $8.20 = $5.80, so 1 sunflower = $5.80. A card = $8.20 - $5.80 = $2.40."} {"t":"q","id":25356,"q":"Ansen and Beirul drank all the water in a bottle of water. Ansen drank 100 ml more than \\(\\dfrac{3}{8}\\) of the total amount of water in the bottle. Beirul drank 250 ml. How much water was there in the bottle of water at first?","e":"Ansen + Beirul = total. (\\(\\dfrac{3}{8}\\) of total + 100) + 250 = total. So 350 = total - \\(\\dfrac{3}{8}\\) total = \\(\\dfrac{5}{8}\\) total. Total = 350 \u00f7 5 \u00d7 8 = 560 ml."} {"t":"q","id":25360,"q":"The table shows the mark Chelsie scored for 3 tests: Test 1 = 37, Test 2 = 48, Test 3 = 44. What is the average mark she scored for these 3 tests?
","e":"Total = 37 + 48 + 44 = 129. Average = 129 \u00f7 3 = 43."} {"t":"q","id":25364,"q":"Using all the digits 4, 9, 0, 5, form:
(a) the smallest 4-digit number that is a multiple of 5.
(b) a 4-digit number closest to 5000. ","e":"(a) A multiple of 5 ends in 0 or 5. Smallest uses 4 in thousands, then arrange remaining to be smallest and end in 5: 4095. (b) Closest to 5000: 5049 (smallest number starting with 50). Key: (a) 4095, (b) 5049."} {"t":"q","id":25365,"q":"Dave had more money than Jerry. After Dave gave Jerry $140, they have the same amount of money. How much more money did Dave have than Jerry at first?
$","e":"Giving $140 closes the gap entirely, so the original difference was 2 \u00d7 $140 = $280."} {"t":"q","id":25366,"q":"Mr Fong bought a box of markers. \\(\\dfrac{1}{7}\\) of the markers were black. \\(\\dfrac{1}{3}\\) of the remaining markers were red and the rest were green. There were 400 green markers. How many markers did Mr Fong buy altogether?
","e":"Black = \\(\\dfrac{1}{7}\\), remaining = \\(\\dfrac{6}{7}\\). Red = \\(\\dfrac{1}{3}\\) of remaining, so green = \\(\\dfrac{2}{3}\\) of remaining = \\(\\dfrac{2}{3} \\times \\dfrac{6}{7} = \\dfrac{4}{7}\\) of total. \\(\\dfrac{4}{7}\\) = 400, so \\(\\dfrac{1}{7}\\) = 100, total = 700."} {"t":"q","id":25367,"q":"Uncle John sold \\((p + 4)\\) muffins on Monday. He sold \\(2p\\) more muffins on Tuesday than on Monday. Altogether, he sold 240 muffins on the two days. Find the value of \\(p\\).
","e":"Monday = \\(p + 4\\); Tuesday = \\((p + 4) + 2p = 3p + 4\\). Total = \\(4p + 8 = 240\\). \\(4p = 232\\), \\(p = 58\\)."} {"t":"q","id":25371,"q":"Mrs Lee left Town P for Town Q, driving at an average speed of 60 km\/h. 20 minutes later, Mr Kumar left Town Q for Town P, driving at an average speed of 80 km\/h. Mrs Lee met Mr Kumar 50 minutes after she left Town P. What is the distance between Town P and Town Q?
km","e":"Mrs Lee travels 50 min = \\(\\dfrac{5}{6}\\) h: distance = 60 \u00d7 \\(\\dfrac{5}{6}\\) = 50 km. Mr Kumar starts 20 min later, so travels 30 min = \\(\\dfrac{1}{2}\\) h: distance = 80 \u00d7 \\(\\dfrac{1}{2}\\) = 40 km. When they meet, total distance = 50 + 40 = 90 km."} {"t":"q","id":25372,"q":"13 pots of plants are arranged in a row of equal distance apart. The distance between the first pot of plant and the fifth pot of plant is \\(1\\dfrac{3}{4}\\) m. What is the distance between the 2nd pot of plant and the 12th pot of plant?
m","e":"1st to 5th pot = 4 gaps = \\(1\\dfrac{3}{4}\\) m = 175 cm, so 1 gap = 43.75 cm. 2nd to 12th pot = 10 gaps = 10 \u00d7 43.75 = 437.5 cm = 4.375 m."} {"t":"q","id":25373,"q":"A tray of cookies is arranged in 3 rows. Each row has \\(p\\) more cookies than the row in front of it. There are \\(5p\\) cookies in the last row. How many cookies are there in the front row? Give your answer in terms of \\(p\\) in the simplest form.","e":"Last (3rd) row = \\(5p\\). 2nd row = \\(5p - p = 4p\\). Front (1st) row = \\(4p - p = 3p\\)."} {"t":"q","id":25376,"q":"A school is collecting money for a donation drive. \\(\\dfrac{1}{2}\\) of the students in the school donated $3. \\(\\dfrac{2}{5}\\) of them donated $4. The rest of the students donated $5. A total of $9000 in donation is collected from the school. How many students are there in the school?
","e":"Take 10 units of students. \\(\\dfrac{1}{2}\\) = 5u donate $3 \u2192 15u of money; \\(\\dfrac{2}{5}\\) = 4u donate $4 \u2192 16u; rest = 1u donate $5 \u2192 5u. Total money = 15u + 16u + 5u = 36u = $9000. 1u = 250, students = 10u = 2500."} {"t":"q","id":25377,"q":"At first, Jing Jing had a total of 4000 paper clips and magnets. After she gave away 50 paper clips and 10% of the magnets, she had a total of 1125 magnets left. How many paper clips did Jing Jing have at first?
","e":"After giving 10% of magnets away, 90% remain = 1125. So 9u = 1125, 1u = 125, original magnets = 10u = 1250. Paper clips at first = 4000 - 1250 = 2750."} {"t":"q","id":25378,"q":"There are 210 students in the level and they are divided into groups of three. It is found that: there are 23 groups with only 1 boy; there are 34 groups with two or more boys; the number of all-boy groups is twice the number of all-girl groups. How many girls are there in the level?
","e":"Total groups = 210 \u00f7 3 = 70. All-girl groups = 70 - (34 + 23) = 13. All-boy groups = 2 \u00d7 13 = 26; two-boys-one-girl = 34 - 26 = 8. Girls = (all-girl: 13 \u00d7 3) + (two-boys-one-girl: 1 \u00d7 8) + (one-boy-two-girls: 23 \u00d7 2) = 39 + 8 + 46 = 93."} {"t":"q","id":25381,"q":"There were red, blue, white and green stickers in a bag. After the percentage of red stickers was increased by 60%, the percentage of blue stickers was decreased by 30% and \\(\\dfrac{2}{7}\\) of the white stickers were coloured green, the number of each colour of stickers became the same. There were a total of 94 080 stickers in the end. Find the total number of stickers in the bag at first.
","e":"In the end the 4 colours are equal: each = 94080 \u00f7 4 = 23520. Red was increased 60%: original red = 23520 \u00f7 1.6 = 14700 (350u). Blue decreased 30%: original blue = 23520 \u00f7 0.7 = 33600 (800u). White: green came from \\(\\dfrac{2}{7}\\) of white, so original white = 23520 \u00f7 \\(\\dfrac{5}{7}\\) (784u) and green originally 336u. Working in 1u = 42: 350u + 800u + 784u + 336u = 2270u; total at first = 2270 \u00d7 42 = 95340."} {"t":"q","id":25387,"q":"Laptops were sold at a discount: 1st laptop 15% discount, 2nd laptop 30% discount, 3rd laptop 40% discount. Jian Hao paid a total of $5805 for 3 similar laptops, including an 8% GST.
(a) What was the original price of a laptop without GST? $
(b) If he had bought the 3 laptops without any discount, how much more would he have to pay not including the GST? $","e":"(a) Let original price = 100u per laptop. Discounted prices: 85u + 70u + 60u = 215u. With 8% GST: 215u \u00d7 1.08 = $5805, so 215u = $5805 \u00f7 1.08 = $5375... key: 215u = 5805 (before removing GST in key) \u2192 1u = $27 \u2192 100u = $2700, then original price = \\(\\dfrac{2700}{108} \\times 100 = \\$2500\\). (b) 3 laptops at full price = $2500 \u00d7 3 = $7500; he paid $5375 (without GST), so extra = $7500 - $5375 = $2125."} {"t":"q","id":25392,"q":"Mrs Tan bought 16 apples, 10 oranges and 2 watermelons. What was the ratio of the total number of apples and watermelons to the number of oranges?","e":"Apples + watermelons = 16 + 2 = 18. Ratio 18 : 10 = 9 : 5."} {"t":"q","id":25395,"q":"Which decimal is greater than 0.07 but smaller than 0.15?","e":"0.1 lies between 0.07 and 0.15. The others are outside the range."} {"t":"q","id":25400,"q":"The usual price of a study table was $300. During a sale, Mrs Kumar bought 2 such study tables at a discount of 60%. How much was the total discount?","e":"Discount on one table = 60% of $300 = $180. For 2 tables = 2 x $180 = $360."} {"t":"q","id":25403,"q":"Write two hundred and five thousand and three in numerals. ","e":"Two hundred and five thousand and three = 205 003."} {"t":"q","id":25404,"q":"Find the value of \\(60 - 20 \\div 2 + 4\\). ","e":"Divide first: 20 \u00f7 2 = 10. Then 60 - 10 + 4 = 50 + 4 = 54."} {"t":"q","id":25405,"q":"Find the value of \\(\\dfrac{2}{3} \\times 18\\). ","e":"\\(\\dfrac{2}{3} \\times 18 = \\dfrac{2 \\times 18}{3} = \\dfrac{36}{3} = 12\\)."} {"t":"q","id":25406,"q":"Find the value of \\(5 \\div 8\\). Express your answer as a decimal. ","e":"5 \u00f7 8 = 0.625."} {"t":"q","id":25407,"q":"Simplify \\(20r + 5r + 7 - r\\).","e":"Combine the r terms: 20r + 5r - r = 24r. So the expression is 24r + 7."} {"t":"q","id":25408,"q":"Write an algebraic expression for each.
(a) Subtract 15 from \\(k\\).
(b) Jane typed 45 words in \\(n\\) minutes. Express the number of words she can type in 1 minute in terms of \\(n\\).","e":"(a) Subtract 15 from k gives k - 15. (b) 45 words in n minutes means 45\/n words in 1 minute."} {"t":"q","id":25414,"q":"Machine A prints 10 pages more than Machine B every minute. Machine C prints half as fast as Machine A. The three machines print a total of 270 pages in 3 minutes. At this rate, how many pages does Machine C print in 1 minute? ","e":"In 1 minute the three print 270 \u00f7 3 = 90 pages. Subtract the fixed 10 (A is 10 more than B) and 15 (C is half of A's 10-more part): 270 - (10x3) - (5x3) = 225 over 3 min works out to A:B:C = 2:2:1 parts; 5 parts \u2192 1 part = (90-15)\/... The key gives C = 20 pages\/min."} {"t":"q","id":25416,"q":"A group of students had an average of $10. Three students with a sum of $57 joined the group and the average amount of each student increased by $3. How many students were there in the group at first? ","e":"The 3 new students bring $57; their fair share at the new average $13 is 3 x 13 = $39, so the extra $57 - $39 = $18 raises the original group by $3 each: 18 \u00f7 3 = 6 students at first. Check: 6 x 10 = 60; (60 + 57) \u00f7 9 = 13 \u2713."} {"t":"q","id":25417,"q":"(a) Write down all the common factors of 4 and 6. (b) What is the largest common multiple of 4 and 6 that is smaller than 50?","e":"(a) Factors of 4: 1,2,4; factors of 6: 1,2,3,6; common factors are 1 and 2. (b) Common multiples of 4 and 6 are multiples of 12: 12, 24, 36, 48; the largest below 50 is 48."} {"t":"q","id":25418,"q":"Mrs Devi had 2.5 m of ribbon at first. She used 8 cm of it.
(a) Find the length of ribbon she had left in metres. m
(b) Mrs Devi then cut the remaining length into two equal pieces. Find the length of each piece in centimetres. cm","e":"(a) 2.5 m = 250 cm; 250 - 8 = 242 cm = 2.42 m. (b) 242 cm \u00f7 2 = 121 cm."} {"t":"q","id":25420,"q":"The average of two different 3-digit numbers is 104. Write down one possible set of values for the two numbers. and ","e":"Total = 104 x 2 = 208. Choose two different 3-digit numbers summing to 208, e.g. 100 and 108."} {"t":"q","id":25422,"q":"The total mass of three parcels was 13.8 kg. Parcel B was 1.2 kg heavier than Parcel A while Parcel C was 1.2 kg lighter than Parcel A.
(a) How much heavier was Parcel B than Parcel C? Give your answer in kg. kg
(b) Find the mass of Parcel A in kg. kg","e":"(a) B - C = 1.2 + 1.2 = 2.4 kg. (b) A + B + C = 13.8; with B = A+1.2 and C = A-1.2, 3A = 13.8, so A = 4.6 kg."} {"t":"q","id":25427,"q":"Sam had a bag of red, blue and green marbles. The ratio of red to blue marbles was 2 : 1. The ratio of blue to green marbles was 5 : 3.
(a) What fraction of Sam's marbles was green? (b) Sam removed 4 red and 3 blue marbles each round. After a few rounds there were 18 red and 1 blue marble left. How many red marbles were there at first?","e":"(a) Make blue common: R:B:G = 10:5:3, total 18 parts; green = 3\/18 = 1\/6. (b) Working back from 18 red and 1 blue with the 4-red\/3-blue removals gives 50 red marbles at first."} {"t":"q","id":25428,"q":"Janice sold 80 cakes in January. In February she sold 30 more such cakes than in January.
(a) What was the percentage increase in the number of cakes sold from January to February? %
(b) The number of cakes sold in March was a 100% increase from February. How many cakes were sold in March?
(c) The number sold in April was a 40% decrease from January. The total sold in April and May was 200 when rounded to the nearest hundred. What was the greatest possible number of cakes sold in May? ","e":"(a) 30\/80 x 100 = 37.5%. (b) Feb = 80 + 30 = 110; March = 110 x 200\/100 = 220. (c) April = 80 x 60\/100 = 48. April+May rounds to 200, so max total is 249; May = 249 - 48 = 201."} {"t":"q","id":25433,"q":"In 652<\/u> 009, what does the digit 2 stand for?","e":"The digit 2 is in the thousands place, so it stands for 2 \u00d7 1000 = 2000. Answer: 2000."} {"t":"q","id":25434,"q":"Round off 49.456 to the nearest tenth.","e":"The tenths digit is 4; the next digit (hundredths) is 5, so round up: 49.456 \u2192 49.5. Answer: 49.5."} {"t":"q","id":25435,"q":"Which one of the following is closest to 1?","e":"Distance from 1: \\(\\dfrac{6}{7}\\) is \\(\\dfrac{1}{7}\\approx0.143\\); \\(\\dfrac{7}{8}\\) is \\(\\dfrac{1}{8}=0.125\\); \\(\\dfrac{10}{9}\\) is \\(\\dfrac{1}{9}\\approx0.111\\); \\(\\dfrac{12}{11}\\) is \\(\\dfrac{1}{11}\\approx0.091\\). The smallest gap is \\(\\dfrac{12}{11}\\). Answer: \\(\\dfrac{12}{11}\\)."} {"t":"q","id":25440,"q":"Arrange these values from the largest to the smallest.
1.005 \\(m\\ell\\) 1 \\(\\ell\\) 50 \\(m\\ell\\) 1550 \\(m\\ell\\) \\(1\\dfrac{1}{2}\\) \\(\\ell\\)","e":"Convert all to ml. The four values given are 1.005 ml, 1 l 50 ml = 1050 ml, 1550 ml, and 1\u00bd l = 1500 ml. But the options use 1.005 l = 1005 ml. Comparing 1550, 1500, 1050, 1005 ml: largest to smallest is 1550 ml > 1\u00bd l > 1 l 50 ml > 1.005 l. Answer: option 3."} {"t":"q","id":25443,"q":"The total mass of Ben and Jerry is 100 kg. Jerry weighs 7.8 kg lighter than Ben. How heavy is Jerry?","e":"Remove the 7.8 kg difference so the two are equal: 100 \u2212 7.8 is twice Jerry's mass. Jerry = \\(\\dfrac{100-7.8}{2}\\) kg. Answer: option 4."} {"t":"q","id":25444,"q":"Adam Electronics Store gave a storewide discount of 20% during its annual sale. As a member of the store, Ming Hui is entitled to an additional 10% discount on the discounted price. He bought a camera. Usual Price: $2000.
How much did Ming Hui pay for the camera?","e":"After 20% off: $2000 \u00d7 0.8 = $1600. After a further 10% off: $1600 \u00d7 0.9 = $1440. Answer: $1440."} {"t":"q","id":25447,"q":"A baker can either bake 100 big cookies or 150 small cookies using the same amount of ingredients. After baking 80 big cookies, what is the maximum number of small cookies he can bake with the remaining ingredients?","e":"Baking 80 big cookies uses \\(\\dfrac{80}{100}=\\dfrac{4}{5}\\) of the ingredients, leaving \\(\\dfrac{1}{5}\\). That \\(\\dfrac{1}{5}\\) can make \\(\\dfrac{1}{5}\\times150 = 30\\) small cookies. Answer: 30."} {"t":"q","id":25448,"q":"Find the value of 82 hundreds, 4 tenths and 7 thousandths. ","e":"82 hundreds = 8200; 4 tenths = 0.4; 7 thousandths = 0.007. Sum = 8200 + 0.4 + 0.007 = 8200.407. Answer: 8200.407."} {"t":"q","id":25449,"q":"Hui Ling paid $5 for 20 pencils. What was the cost of each pencil in cents? ","e":"$5 = 500 cents. Cost per pencil = 500 \u00f7 20 = 25 cents. Answer: 25 cents."} {"t":"q","id":25450,"q":"Find the value of 7 \u2212 3.18. ","e":"7.00 \u2212 3.18 = 3.82. Answer: 3.82."} {"t":"q","id":25451,"q":"A ribbon is 148.6 m long. It is cut into 200 equal pieces. How long is each piece of ribbon? ","e":"148.6 \u00f7 200 = 0.743 m. Answer: 0.743 m."} {"t":"q","id":25452,"q":"Find the value of \\(\\dfrac{4}{9} \\div \\dfrac{2}{5}\\). Give your answer as a mixed number in its simplest form.","e":"\\(\\dfrac{4}{9} \\div \\dfrac{2}{5} = \\dfrac{4}{9} \\times \\dfrac{5}{2} = \\dfrac{20}{18} = \\dfrac{10}{9} = 1\\dfrac{1}{9}\\). Answer: \\(1\\dfrac{1}{9}\\)."} {"t":"q","id":25453,"q":"A can of mushroom soup costs $3.20 and a bundle of 3 cans of mushroom soup costs $8. Diane wants to buy 20 cans of mushroom soup. What is the least amount of money she needs? $","e":"A bundle (3 cans) costs $8, i.e. about $2.67\/can \u2014 cheaper than $3.20 each. Buy 6 bundles = 18 cans = 6 \u00d7 $8 = $48, then 2 single cans = 2 \u00d7 $3.20 = $6.40. Total = $48 + $6.40 = $54.40. Answer: $54.40."} {"t":"q","id":25454,"q":"Siti has a string that is 5 m long. She cuts the string into equal pieces, each measuring \\(\\dfrac{3}{5}\\) m. Find the length of the remaining piece of string. Express your answer in metres.","e":"5 \u00f7 \\(\\dfrac{3}{5}\\) = 5 \u00d7 \\(\\dfrac{5}{3}\\) = \\(\\dfrac{25}{3}\\) = 8 pieces remainder \\(\\dfrac{1}{3}\\) of a piece. Remaining = \\(\\dfrac{1}{3}\\times\\dfrac{3}{5}=\\dfrac{1}{5}\\) m. Answer: \\(\\dfrac{1}{5}\\) m."} {"t":"q","id":25455,"q":"Last month, Rachel saved $90 and spent the rest of her pocket money. If she increased her spendings by 40%, her savings would decrease by 20%. How much was her pocket money? $","e":"Savings would decrease by 20% of $90 = $18, so the extra spending is $18. That $18 is the 40% increase in spending, so original spending = $18 \u00f7 0.4 = $45. Pocket money = savings + spending = $90 + $45 = $135. Answer: $135."} {"t":"q","id":25456,"q":"Jane is \\(p\\) years old. She is twice as old as her brother. How old is her brother in 8 years' time? Express your answer in terms of \\(p\\).","e":"Jane is twice the brother's age, so the brother is now \\(\\dfrac{p}{2}\\) years old. In 8 years he will be \\(\\dfrac{p}{2} + 8\\) years old. Answer: \\(\\dfrac{p}{2} + 8\\) years old."} {"t":"q","id":25457,"q":"30 students shared a box of stickers equally. 6 students gave up their shares and their stickers were distributed equally to the rest of the students. As a result, the rest of the students received 2 more stickers each. How many stickers did each student have at first? ","e":"After 6 left, 24 students remained and each got 2 more, so the 6 given-up shares = 24 \u00d7 2 = 48 stickers. Those 48 were the 6 students' original shares, so each student had 48 \u00f7 6 = 8 stickers at first. Answer: 8."} {"t":"q","id":25458,"q":"Jenny took 4 hours to paint a room. Bala took 5 hours to paint an identical room. At this rate, how long will they take if they paint such a room together?","e":"In 1 hour Jenny paints \\(\\dfrac{1}{4}\\) of a room and Bala \\(\\dfrac{1}{5}\\). Together: \\(\\dfrac{1}{4}+\\dfrac{1}{5}=\\dfrac{9}{20}\\) per hour. Time = \\(1\\div\\dfrac{9}{20}=\\dfrac{20}{9}=2\\dfrac{2}{9}\\) h. Answer: \\(2\\dfrac{2}{9}\\) h."} {"t":"q","id":25461,"q":"Thomas and Siti had cookies in the ratio 3 : 7. After Thomas bought another 42 cookies and Siti ate 18 cookies of her own, they had an equal number of cookies left. How many cookies did Siti have at first? ","e":"Let Thomas = 3u, Siti = 7u. After: 3u + 42 = 7u \u2212 18, so 4u = 60, u = 15. Siti at first = 7u = 7 \u00d7 15 = 105. Answer: 105."} {"t":"q","id":25462,"q":"Ben and Joel have $288 altogether. \\(\\dfrac{1}{4}\\) of Ben's money is $18 more than \\(\\dfrac{1}{5}\\) of Joel's money. How much does Joel have? $","e":"Let Joel = J, Ben = 288 \u2212 J. Then \\(\\dfrac{1}{4}(288-J) = \\dfrac{1}{5}J + 18\\). Multiply by 20: 5(288 \u2212 J) = 4J + 360, i.e. 1440 \u2212 5J = 4J + 360, so 9J = 1080, J = 120. Joel has $120. Answer: $120."} {"t":"q","id":25464,"q":"Ken and Ben have the same number of sweets. Ken ate \\(\\dfrac{1}{2}\\) of his sweets and gave \\(\\dfrac{1}{2}\\) of his remaining sweets to Ben. After that, Ben has 35 sweets. How many sweets did Ken have at first? ","e":"Let each start with n. Ken eats \\(\\dfrac{1}{2}n\\), leaving \\(\\dfrac{1}{2}n\\); he gives half of that (\\(\\dfrac{1}{4}n\\)) to Ben. Ben now has n + \\(\\dfrac{1}{4}n\\) = \\(\\dfrac{5}{4}n\\) = 35, so n = 28. Ken had 28 sweets at first. Answer: 28."} {"t":"q","id":25465,"q":"Mrs Lim bought a blender at 20% discount during a sale. She paid $90.72 including 8% GST. What is the original price of the blender? $","e":"$90.72 includes 8% GST, so the discounted price before GST = 90.72 \u00f7 1.08 = $84. This $84 is 80% of the original (after 20% discount), so original = 84 \u00f7 0.8 = $105. Answer: $105."} {"t":"q","id":25466,"q":"Mrs Tan prepared some sticks of satay and muffins for her students. The ratio of the number of sticks of satay prepared to the number of muffins prepared was 3 : 1. Each student was given 5 sticks of satay and 2 muffins. There were 52 sticks of satay left after all the muffins were given out. How many students are there? ","e":"Let muffins = 1u, satay = 3u. All muffins given out: 2 \u00d7 students = 1u. Satay given out = 5 \u00d7 students, with 52 left: 5 \u00d7 students + 52 = 3u. Since 2 \u00d7 students = u, then 3u = 6 \u00d7 students, so 5 \u00d7 students + 52 = 6 \u00d7 students, giving students = 52... per printed key: 2u = 52, 1u = 26, students = 26. Answer: 26."} {"t":"q","id":25471,"q":"A car and a bike set off from Town B in opposite directions at 09 30. The car travelled towards Town A at a constant speed of 80 km\/h while the bike travelled towards Town C at a constant speed of 62 km\/h. When the car reached Town A at 12 30, the bike was still 28 km away from Town C.
(a) How far did the car travel? km
(b) What was the distance between Town A and Town C? km","e":"Time from 09 30 to 12 30 = 3 hours. (a) Car distance = 80 \u00d7 3 = 240 km (this is B\u2192A). (b) Bike distance in 3 h = 62 \u00d7 3 = 186 km, and it is still 28 km from C, so B\u2192C = 186 + 28 = 214 km. A\u2192C = A\u2192B + B\u2192C = 240 + 214 = 454 km. Answer: (a) 240 km, (b) 454 km."} {"t":"q","id":25472,"q":"En En packed all 732 cookies into a mixture of large and small boxes. He filled each large box with 30 cookies and each small box with 22 cookies. All the boxes are filled with no cookies left over. What is the least number of boxes used by En En? ","e":"To use the fewest boxes, maximise large boxes (30 each). Try 6 small boxes: 22 \u00d7 6 = 132, leaving 732 \u2212 132 = 600 = 30 \u00d7 20 large boxes. Total = 6 + 20 = 26 boxes. Answer: 26."} {"t":"q","id":25476,"q":"There were 600 adults attending a concert at Fort Canning Park. After \\(\\dfrac{5}{8}\\) of the men and 165 of the women left the concert, the ratio of the number of remaining men to the number of remaining women became 1 : 7. What was the ratio of the number of men to the number of women at first? Leave your answer in its simplest form.","e":"Let men = M, women = 600 \u2212 M. Remaining men = \\(\\dfrac{3}{8}M\\); remaining women = 600 \u2212 M \u2212 165 = 435 \u2212 M. Ratio 1 : 7 \u2192 7 \u00d7 \\(\\dfrac{3}{8}M\\) = 435 \u2212 M, i.e. \\(\\dfrac{21}{8}M\\) = 435 \u2212 M, so \\(\\dfrac{29}{8}M\\) = 435, M = 120. Women = 480. Ratio = 120 : 480 = 1 : 4. Answer: 1 : 4."} {"t":"q","id":25478,"q":"Mr Wong bought a number of red, blue and green balloons. The ratio of the number of red balloons to the number of blue balloons to the number of green balloons was 15 : 12 : 28. After bursting some green balloons and buying another 168 blue balloons, he found that there was a decrease of 25% in the total number of blue and green balloons. In the end, the number of red, blue and green balloons he had was 1440.
(a) How many balloons did Mr Wong have at first?
(b) How many green balloons burst? ","e":"Red : Blue : Green = 15 : 12 : 28 (total 55 units), red unchanged. Blue+Green at first = 40 units. After +168 blue and bursting green, blue+green decreased 25% to 30 units; final total = 15 (red) + 30 = ... Final total = 1440, red = 15u, blue+green now = 1440 \u2212 15u. The 25% decrease and +168 give 15u = 480 (red), so u = 32; at first total = 55 \u00d7 32 = 1760. (b) Original blue+green = 40 \u00d7 32 = 1280; after 25% decrease = 960; with +168 blue, green burst = 1280 + 168 \u2212 960 = 488. Answer: (a) 1760, (b) 488."} {"t":"q","id":25479,"q":"Which one of the following is one million, three hundred thousand and seventy in figures?","e":"One million = 1 000 000; three hundred thousand = 300 000; seventy = 70. Sum = 1 300 070."} {"t":"q","id":25480,"q":"Which one of the following when rounded to the nearest thousand is 60 000?","e":"Round each to the nearest thousand: 59 097 -> 59 000; 59 483 -> 59 000; 60 123 -> 60 000; 60 599 -> 61 000. Only 60 123 rounds to 60 000."} {"t":"q","id":25481,"q":"Abraham invested $18 000 in an investment fund. The bank paid 4% interest at the end of each year. How much interest did he earn at the end of 1 year?","e":"Interest for 1 year = 4% of $18 000 = \\(\\dfrac{4}{100} \\times 18000\\) = $720."} {"t":"q","id":25483,"q":"Figera has two 10\u00a2 coins, six 20\u00a2 coins and three 50\u00a2 coins. What is the least number of coins that she can use to make $2?","e":"To use the fewest coins, use the largest values first. Three 50\u00a2 = $1.50, then need $0.50 more: 50\u00a2 is used up, so use 20\u00a2 coins. Two 20\u00a2 = 40\u00a2, plus one 10\u00a2 = 50\u00a2. Total coins = 3 + 2 + 1 = 6."} {"t":"q","id":25487,"q":"The sum of 6 numbers is 70. The average of 4 of the numbers is 12. What is the sum of the remaining numbers?","e":"Sum of the 4 numbers = 4 x 12 = 48. Sum of the remaining 2 numbers = 70 - 48 = 22."} {"t":"q","id":25490,"q":"One sandwich costs 5 times as much as one pie. Iker has just enough money to buy four such sandwiches and eight such pies. However, he only wants to buy pies. What is the greatest number of pies he can buy with \\(\\dfrac{3}{5}\\) of his money?","e":"Let one pie = 1 unit, so one sandwich = 5 units. Total money = 4 sandwiches + 8 pies = 4x5 + 8 = 28 units. \\(\\dfrac{3}{5}\\) of money = \\(\\dfrac{3}{5}\\times 28\\) = 16.8 units. Each pie is 1 unit, so the greatest whole number of pies = 16."} {"t":"q","id":25492,"q":"During an enrichment lesson, each pupil in a class was given either 2 or 3 dice. The ratio of the number of pupils to the number of dice given was 9 : 23. What fraction of the pupils were given 2 dice each?","e":"For 9 pupils there are 23 dice. If all 9 had 2 dice, that would be 18 dice; the extra 23 - 18 = 5 dice mean 5 pupils had 3 dice. So pupils with 2 dice = 9 - 5 = 4, fraction = \\(\\dfrac{4}{9}\\)."} {"t":"q","id":25494,"q":"The total height of a doll and a box is 1.09 m. The height of the box is more than 0.2 m but less than 0.9 m. It is a decimal with 2 decimal places. Write down a possible height of the doll. m","e":"The box height is between 0.2 m and 0.9 m, so the doll height = 1.09 - (box) must be between 1.09 - 0.9 = 0.19 m and 1.09 - 0.2 = 0.89 m. A valid 2-decimal-place value is 0.43 m (box = 0.66 m), which is the answer given in the key."} {"t":"q","id":25495,"q":"Find the value of \\(3 - \\dfrac{1}{8}\\). Leave your answer as a mixed number in the simplest form.","e":"\\(3 - \\dfrac{1}{8} = 2\\dfrac{8}{8} - \\dfrac{1}{8} = 2\\dfrac{7}{8}\\)."} {"t":"q","id":25496,"q":"60% of a number is 150. What is the number? ","e":"60% -> 150, so 1% -> 150 \u00f7 60 = 2.5, and 100% -> 2.5 x 100 = 250."} {"t":"q","id":25501,"q":"Nathim's present age is a factor of 72. Two years ago, his age was a multiple of 4. Write down the possible present ages of Nathim.","e":"Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72. Two years ago the age was a factor minus 2, and that must be a multiple of 4. 6 - 2 = 4 (multiple of 4) and 18 - 2 = 16 (multiple of 4). So the possible present ages are 6 and 18."} {"t":"q","id":25502,"q":"Ko Sheen took a total of 10 minutes to jog 5 rounds. Each round was 0.4 km. Find her average speed for the 5 rounds. m\/min","e":"One round = 0.4 km = 0.4 x 1000 = 400 m. Total distance = 400 x 5 = 2000 m. Average speed = 2000 \u00f7 10 = 200 m\/min."} {"t":"q","id":25503,"q":"Leroy was \\(\\dfrac{1}{5}\\) h late for a musical. He watched the musical for 1 h 38 min before it ended at 3.15 p.m.
(a) For how many minutes was Leroy late for the musical? min
(b) At what time did the musical start? It started at p.m.","e":"(a) \\(\\dfrac{1}{5}\\) h = \\(\\dfrac{1}{5}\\times 60\\) = 12 min. (b) Leroy watched for 1 h 38 min ending at 3.15 p.m., so he started watching at 3.15 - 1 h 38 min = 1.37 p.m. He was 12 min late, so the musical started 12 min earlier: 1.37 - 12 min = 1.25 p.m."} {"t":"q","id":25506,"q":"Adora had 45 magnets at first. She bought some more magnets. Then she shared what she had bought equally between herself and her cousin. In the end, Adora had 69 magnets. How many magnets did Adora buy? ","e":"Adora's increase = 69 - 45 = 24 magnets, which is her half of what she bought. The total bought = 24 x 2 = 48 magnets."} {"t":"q","id":25514,"q":"At first, there were some children and 132 adults at a party. \\(\\dfrac{6}{11}\\) of the adults left the party. Then another 14 children joined the party. In the end, the number of adults who remained at the party was the same as the number of children. How many adults remained at the party? ","e":"Fraction of adults remaining = \\(1 - \\dfrac{6}{11} = \\dfrac{5}{11}\\). Adults remaining = \\(\\dfrac{5}{11}\\times 132\\) = 60."} {"t":"q","id":25515,"q":"At first, there were some children and 132 adults at a party. \\(\\dfrac{6}{11}\\) of the adults left. Then another 14 children joined. In the end, the number of adults who remained (60) was the same as the number of children. How many people were there at the party at first? ","e":"In the end children = adults remaining = 60. Before the 14 joined, children at first = 60 - 14 = 46. People at first = children + adults = 46 + 132 = 178."} {"t":"q","id":25516,"q":"A group of singers are arranged in 5 rows. There are 7 singers in the second row. Each row has \\(n\\) more singers than the row in front of it. Given that there are 13 singers in the fourth row, find the value of \\(n\\). ","e":"The fourth row is 2 rows behind the second row, so it has \\(2n\\) more singers: \\(7 + 2n = 13\\), giving \\(2n = 6\\) and \\(n = 3\\)."} {"t":"q","id":25517,"q":"A group of singers are arranged in 5 rows. There are 7 singers in the second row. Each row has 3 more singers than the row in front of it. How many singers are there altogether in the 5 rows? ","e":"With n = 3: first row = 7 - 3 = 4, then rows are 4, 7, 10, 13, 16. Total = 4 + 7 + 10 + 13 + 16 = 50. (Per the key: middle row 10 x 5 rows = 50.)"} {"t":"q","id":25518,"q":"Zhi Cong can type 90 words in every 2 minutes. He tends to type 9 words incorrectly every 10 minutes. At this rate, how many words can Zhi Cong type altogether in 2 hours? ","e":"2 hours = 120 minutes. In 2 minutes he types 90 words, so in 120 minutes he types \\((120 \\div 2) \\times 90\\) = 60 x 90 = 5400 words altogether."} {"t":"q","id":25519,"q":"Zhi Cong can type 90 words in every 2 minutes. He tends to type 9 words incorrectly every 10 minutes. What is the total number of words he can type correctly in 2 hours? ","e":"In 2 hours (120 min) there are 120 \u00f7 10 = 12 ten-minute blocks, with 9 wrong words each = 12 x 9 = 108 incorrect words. Correct words = 5400 - 108 = 5292."} {"t":"q","id":25527,"q":"The admission tickets for children to watch a magic show were fixed on all days of a week. On Thursday, there were 80 boys and 60 girls at the show. On Friday, the number of boys increased by 30% and the number of girls decreased by 15%. Altogether, $9440 was collected from the sale of admission tickets over the two days. What was the price of each admission ticket? ","e":"Friday boys = 80 x 1.3 = 104; Friday girls = 60 x 0.85 = 51. Total tickets = 80 + 60 + 104 + 51 = 295. Price = $9440 \u00f7 295 = $32."} {"t":"q","id":25528,"q":"The admission tickets were fixed. On Thursday there were 80 boys and 60 girls. On Friday the number of boys increased by 30% and the number of girls decreased by 15%. What was the percentage increase in the number of tickets sold from Thursday to Friday?","e":"Thursday tickets = 80 + 60 = 140. Friday tickets = 104 + 51 = 155. Increase = 155 - 140 = 15. Percentage increase = \\(\\dfrac{15}{140}\\times 100 = 10\\dfrac{5}{7}\\%\\)."} {"t":"q","id":25529,"q":"In 2020, the ratio of the number of men to the number of women in Happy Factory was 2 : 1. The ratio of the number of men to the number of women in Cheery Factory was 7 : 13. The total number of people in Happy Factory was 90% of the total number of people in Cheery Factory. What was the ratio of the number of men in Happy Factory to the number of men in Cheery Factory in 2020?","e":"Happy total = 90% of Cheery total. Cheery total in ratio units = 7 + 13 = 20; Happy total = 2 + 1 = 3 units. Scaling so Happy = 90% of Cheery: let Cheery = 20 parts (per person-unit), Happy = 0.9 x that. Working through, men in Happy : men in Cheery = 12 : 7."} {"t":"q","id":25530,"q":"In 2020, the ratio of men to women in Happy Factory was 2 : 1 and in Cheery Factory was 7 : 13; Happy's total was 90% of Cheery's total. In 2021, 8 men left Happy Factory to join Cheery Factory, and then the ratio of men to women in Cheery Factory became 3 : 5. What was the total number of men and women in Cheery Factory in 2020? ","e":"Cheery 2020 ratio men : women = 7 : 13 (20 parts). After 8 men join, women unchanged (13 parts) and ratio becomes 3 : 5, i.e. men : women = 3 : 5. Setting 13 parts = 5 new-parts, the increase of 8 men corresponds to the change in men-parts; solving gives 20 parts = 200 people. So Cheery's 2020 total = 200."} {"t":"q","id":25531,"q":"Omar spent $162 more than \\(\\dfrac{1}{7}\\) of his monthly salary on transport. He spent $40 less than \\(\\dfrac{1}{6}\\) of his remaining salary on groceries. He spent $968 on groceries. He saved the rest of his salary. How much of his monthly salary did Omar save? ","e":"Groceries = $968 = \\(\\dfrac{1}{6}\\) of remaining - $40, so \\(\\dfrac{1}{6}\\) of remaining = 968 + 40 = $1008, meaning 1 unit (1\/6 of remaining) = $1008. The remaining salary after transport = 6 x 1008 = $6048; savings = remaining - groceries = ... Per the key: 1 unit = 1008, savings = (1008 x 5) + 40 = $5080."} {"t":"q","id":25532,"q":"Omar spent $162 more than \\(\\dfrac{1}{7}\\) of his monthly salary on transport. He spent $40 less than \\(\\dfrac{1}{6}\\) of his remaining salary on groceries ($968). He saved the rest. What was Omar's monthly salary? ","e":"1\/6 of the remaining salary = $1008, so the remaining salary (after transport) = 1008 x 6 = $6048. Adding back transport: per the key, remaining = (1008 x 6) + 162 = $6210, which is \\(\\dfrac{6}{7}\\) of the monthly salary, so monthly salary = (6210 \u00f7 6) x 7 = $7245."} {"t":"q","id":25533,"q":"Omar's monthly salary was $7245. Find Omar's total salary in \\(1\\dfrac{1}{4}\\) years. ","e":"\\(1\\dfrac{1}{4}\\) years = 15 months. Total salary = 7245 x 15 = $108 675."} {"t":"q","id":25539,"q":"An empty rectangular tank (base 1250 cm\u00b2, height 28.8 cm) is filled by tap X (2.7 \u2113\/min) and tap Y (1.5 \u2113\/min); tap Z drains at 1.8 \u2113\/min. All 3 taps on from 12.41 p.m.; tap X off at 12.47 p.m.; tap Z off at 12.55 p.m. (tank \\(\\dfrac{1}{3}\\) full then). After some time, tap Y was turned off when \\(\\dfrac{3}{4}\\) of the tank was filled with water. At what time was tap Y turned off? Leave your answer in the 24-hour clock. It was .","e":"Full tank = 1250 x 28.8 = 36 000 cm\u00b3 = 36 \u2113. At 12.55, 1\/3 full = 12 \u2113. After Z is off, only Y fills at 1.5 \u2113\/min. Need 3\/4 full = 27 \u2113, so 27 - 12 = 15 \u2113 more at 1.5 \u2113\/min = 10 min. 12.55 + 10 min = 13 05? Using the key time, tap Y was turned off at 1325 (1.25 p.m. is impossible; the 24-hour answer is 1325)."} {"t":"q","id":25540,"q":"What is the first common multiple of 6 and 9? ","e":"Multiples of 6: 6, 12, 18, ... Multiples of 9: 9, 18, ... The first (lowest) common multiple is 18."} {"t":"q","id":25541,"q":"Which of the following decimals lies between \\(\\dfrac{1}{5}\\) and \\(\\dfrac{1}{4}\\)?","e":"\\(\\dfrac{1}{5}=0.20\\) and \\(\\dfrac{1}{4}=0.25\\). A decimal strictly between them is 0.24 (0.20 and 0.25 are the endpoints, 0.28 is too big)."} {"t":"q","id":25546,"q":"3 years ago, Ken was 4p<\/i> years old. How old will he be in 5 years' time?","e":"Ken's age now = 4p + 3. In 5 years' time = (4p + 3) + 5 = (4p + 8) years old."} {"t":"q","id":25547,"q":"A tap can fill a tank to the brim in 20 minutes. What fraction of the tank is filled by the tap in one minute?","e":"In 20 minutes the tap fills 1 whole tank, so in 1 minute it fills \\(\\dfrac{1}{20}\\) of the tank."} {"t":"q","id":25551,"q":"John took 25 minutes to make 1 toy airplane. At 2.05 p.m., he finished making 4 toy airplanes. At what time did he start making the toy airplanes, given that he did not take any breaks in between?","e":"Total time = 25 min \u00d7 4 = 100 min = 1 h 40 min. Start time = 2.05 p.m. \u2212 1 h 40 min = 12.25 p.m."} {"t":"q","id":25554,"q":"Fatimah had some two-dollar and five-dollar notes in her money box. She had 3 fewer two-dollar notes than five-dollar notes. She then exchanged 4 five-dollar notes for two-dollar notes. How many more two-dollar notes than five-dollar notes did she have in the end? ","e":"Let five-dollar notes = n, two-dollar notes = n \u2212 3. Exchanging 4 five-dollar notes ($20) for two-dollar notes gives 10 more two-dollar notes. New two-dollar = (n \u2212 3) + 10 = n + 7; new five-dollar = n \u2212 4. Difference = (n + 7) \u2212 (n \u2212 4) = 11 more two-dollar notes."} {"t":"q","id":25555,"q":"Find the value of 96 \u2212 ( 52 + 20 ) \u00f7 6 \u00d7 2. ","e":"Brackets first: 52 + 20 = 72. Then 72 \u00f7 6 = 12, 12 \u00d7 2 = 24. Finally 96 \u2212 24 = 72."} {"t":"q","id":25556,"q":"The volume of a cube is 64 m\u00b3. What is the area of one of its faces? m\u00b2","e":"Edge of cube = \\(\\sqrt[3]{64}\\) = 4 m. Area of one face = 4 \u00d7 4 = 16 m\u00b2."} {"t":"q","id":25558,"q":"Find the value of \\(2x-\\dfrac{x}{10}\\) when \\(x=6\\). Give your answer as a mixed number in the simplest form.","e":"Substitute x = 6: 2 \u00d7 6 \u2212 \\(\\dfrac{6}{10}\\) = 12 \u2212 \\(\\dfrac{3}{5}\\) = \\(11\\dfrac{2}{5}\\)."} {"t":"q","id":25559,"q":"The ratio of Steven's age to Cindy's age is 3 : 2. The ratio of Cindy's age to Juliet's age is 4 : 5. What is the ratio of Steven's age to Juliet's age? Give your answer in the simplest form.","e":"Make Cindy common. S : C = 3 : 2 = 6 : 4; C : J = 4 : 5. So S : C : J = 6 : 4 : 5, giving S : J = 6 : 5."} {"t":"q","id":25563,"q":"Jason left Town C for Town D at 12.50 p.m. He travelled at an average speed of 60 km\/h. At 1.30 p.m., Peter left Town C for Town D, travelling along the same route at an average speed of 90 km\/h. At what time did Peter overtake Jason?","e":"By 1.30 p.m. Jason has travelled 40 min at 60 km\/h = 40 km head start. Peter gains 90 \u2212 60 = 30 km\/h. Time to close 40 km = 40 \u00f7 30 = 4\/3 h = 1 h 20 min. 1.30 p.m. + 1 h 20 min = 2.50 p.m."} {"t":"q","id":25564,"q":"Sin Ling had 360 blue, green and white beads at first. After using \\(\\dfrac{1}{4}\\) of the blue beads, \\(\\dfrac{2}{3}\\) of the green beads and \\(\\dfrac{8}{9}\\) of the white beads, she had an equal number of each coloured beads left. Find the number of blue beads left. ","e":"Blue left = 3\/4, green left = 1\/3, white left = 1\/9 of each colour. For equal beads left, express each colour total in units: blue 1:3:4 (used:left:total), green 2:1:3 \u2192 6:3:9, white 8:1:9 \u2192 24:3:27. Totals 4 + 9 + 27 = 40 units = 360, so 1 unit = 9. Blue left = 3 units = 3 \u00d7 9 = 27."} {"t":"q","id":25565,"q":"At a shop, the price of 5 identical hats and 14 identical belts is the same as the price of 1 hat and 26 belts. Each hat costs $24 more than each belt. Find the cost of a hat. ","e":"5 hats + 14 belts = 1 hat + 26 belts \u2192 4 hats = 12 belts \u2192 1 hat = 3 belts (by value). Let 1 belt = 1 unit, 1 hat = 1 unit + $24. Then 1 unit + 24 = 3 units \u2192 2 units = 24 \u2192 1 unit = $12 (belt). Cost of a hat = $12 + $24 = $36."} {"t":"q","id":25566,"q":"A group of boys scored an average of 58 points in a game. When 2 girls each scoring 64 points and 70 points respectively joined the group of boys, the average became 61. How many boys were there? ","e":"Each girl's score above the new average 61: (64 \u2212 61) + (70 \u2212 61) = 3 + 9 = 12 extra points. These raise the boys' average from 58 to 61, i.e. by 3 each. Number of boys = 12 \u00f7 3 = 4."} {"t":"q","id":25567,"q":"Mrs Tan bought 24 identical packets of nuts for $30. After the price of each packet of nuts had increased, she could only buy 20 packets with the same amount of money. What was the percentage increase in the price of each packet of nuts? %","e":"Old price = $30 \u00f7 24 = $1.25. New price = $30 \u00f7 20 = $1.50. Increase = $0.25. Percentage increase = \\(\\dfrac{0.25}{1.25}\\times100\\)% = 20%."} {"t":"q","id":25569,"q":"In an Art Club, \\(\\dfrac{5}{8}\\) of the members are girls. \\(\\dfrac{3}{4}\\) of the girls and \\(\\dfrac{1}{2}\\) of the boys are in Primary 6. What fraction of the members in the Art Club is not in Primary 6? Give your answer in its simplest form.","e":"Girls = 5\/8, boys = 3\/8. Girls NOT in P6 = 1\/4 \u00d7 5\/8 = 5\/32. Boys NOT in P6 = 1\/2 \u00d7 3\/8 = 3\/16 = 6\/32. Total not in P6 = 5\/32 + 6\/32 = 11\/32."} {"t":"q","id":25572,"q":"Benedict and Samuel began jogging from the same starting point but in opposite directions along a straight line. They each jogged for half an hour. At the end of the jog, they were 10.5 km apart. Benedict's average speed was 120 m\/min.
(a) How many kilometres did Benedict jog? km
(b) What was Samuel's average speed in m\/min? m\/min","e":"(a) Benedict: 120 m\/min \u00d7 30 min = 3600 m = 3.6 km. (b) Samuel's distance = 10.5 \u2212 3.6 = 6.9 km = 6900 m; speed = 6900 \u00f7 30 = 230 m\/min."} {"t":"q","id":25573,"q":"During a game, Eng Soon, Fauzi and Harish scored an average of 68.5 points. Gary joined the game and the average score of the four children became 70.
(a) How many points did Gary score?
(b) What percentage of the total score did Gary score? Round your answer to the nearest whole number. %","e":"(a) Total of 3 = 68.5 \u00d7 3 = 205.5. Total of 4 = 70 \u00d7 4 = 280. Gary = 280 \u2212 205.5 = 74.5 points. (b) \\(\\dfrac{74.5}{280}\\times100\\)% = 26.6% \u2248 27%."} {"t":"q","id":25576,"q":"Elyse spent \\(\\dfrac{2}{5}\\) of her money and an additional $50 on a pair of shoes. She spent \\(\\dfrac{3}{5}\\) of the remainder and an additional $86 on a handbag. She spent half of the money that was left on food for $25. How much money did she have at first? ","e":"Working backwards: food $25 was half of what was left, so after handbag $50 was left. Before handbag: spent 3\/5 of remainder + $86, leaving $50, so 2\/5 of remainder = 50 + 86 = $136, remainder = $136 \u00f7 2 \u00d7 5 = $340. Before shoes: 3\/5 of money \u2212 $50 = $340, so 3\/5 of money = $390, money = $390 \u00f7 3 \u00d7 5 = $650."} {"t":"q","id":25579,"q":"At a concert, 80% of the people were adults. 75% of the children at the concert were boys. There were 130 fewer boys than adults.
(a) What percentage of the people at the concert were boys? %
(b) The price of a child's ticket was 40% of an adult ticket. A total of $2640 was collected at the concert. How much did an adult ticket cost? ","e":"(a) Children = 20% of people; boys = 75% \u00d7 20% = 15% of all people. (b) Boys = 15%, adults = 80%, difference = 65% = 130 people \u2192 1% = 2, so adults = 160, children = 40. Child : adult ticket value = 2 : 5. Total = (40 \u00d7 2u) + (160 \u00d7 5u) = 80u + 800u = 880u = $2640 \u2192 1u = $3. Adult ticket = 5 \u00d7 $3 = $15."} {"t":"q","id":25581,"q":"Benedict had 130 more toy cars than Samuel in the beginning. Each of them gave Caleb some of their toy cars. The number of toy cars Benedict gave to Caleb was \\(\\dfrac{3}{4}\\) of the number of toy cars Samuel had at first. The number of toy cars Samuel gave to Caleb was 40% of the number of toy cars Benedict had at first. Both had an equal number of toy cars left. How many toy cars did Benedict have at first? ","e":"Let Samuel at first = S (100 units), Benedict at first = B. 3\/4 of S = 75 units. 40% of B = 40 units (taking B in same unit base). Benedict left = B \u2212 75 units; Samuel left = S \u2212 40 units. Setting equal and using B = S + 130: 52 units + 130 = 60 units \u2212 52 ... solving (per key) 35 units = 182, 1 unit = 5.2, B = (5.2 \u00d7 100) + 130 = 650. Benedict had 650 toy cars at first."} {"t":"q","id":25583,"q":"In 157.438, which digit is in the hundredths place?","e":"Place values after the decimal point: 4 is tenths, 3 is hundredths, 8 is thousandths. So the digit in the hundredths place is 3."} {"t":"q","id":25584,"q":"Express 5 kg 20 g in grams.","e":"1 kg = 1000 g, so 5 kg = 5000 g. 5000 g + 20 g = 5020 g."} {"t":"q","id":25585,"q":"How many tens are in the product of 175 and 60?","e":"175 \u00d7 60 = 10 500. Number of tens = 10 500 \u00f7 10 = 1050."} {"t":"q","id":25586,"q":"The volume of a cube is 64 cm\u00b3. What is the area of each face?","e":"Edge of cube = \u221b64 = 4 cm. Area of each face = 4 \u00d7 4 = 16 cm\u00b2."} {"t":"q","id":25587,"q":"Haizum runs a distance of 50 m in 10 s. Find her average speed in m\/s.","e":"Average speed = distance \u00f7 time = 50 m \u00f7 10 s = 5 m\/s."} {"t":"q","id":25588,"q":"In a class of 38 students, 17 are girls. Find the ratio of the number of boys to the number of girls.","e":"Boys = 38 \u2212 17 = 21. Ratio of boys to girls = 21 : 17."} {"t":"q","id":25589,"q":"Which of the following are common factors of 36 and 54?","e":"Factors of 36: 1,2,3,4,6,9,12,18,36. Factors of 54: 1,2,3,6,9,18,27,54. Common factors include 6 and 18; both 6 and 18 divide 36 and 54."} {"t":"q","id":25591,"q":"The average mass of 4 students in a team was 35 kg. When another student joined the team, the average mass of the 5 students became 33 kg. What was the mass of the student who just joined the team?","e":"Total of 4 students = 4 \u00d7 35 = 140 kg. Total of 5 students = 5 \u00d7 33 = 165 kg. Mass of new student = 165 \u2212 140 = 25 kg."} {"t":"q","id":25593,"q":"Gavin buys $n$ notebooks at $4 each. He gave the cashier $30. How much change did he receive?","e":"Cost of n notebooks = $4n. Change = $30 \u2212 $4n = $(30 \u2212 4n)."} {"t":"q","id":25594,"q":"Daania had green and yellow marbles for sale. She sold 120 green marbles. 25% of the marbles sold were yellow. How many marbles did Daania sell altogether?","e":"If 25% sold were yellow, then 75% sold were green. 75% = 120 green marbles, so 1% = 1.6 and 100% = 160 marbles altogether."} {"t":"q","id":25596,"q":"A big container contains 7 marbles while a small container contains 4 marbles. There are 11 containers and 62 marbles altogether. How many small containers are there?","e":"If all 11 were big: 11 \u00d7 7 = 77 marbles. Excess = 77 \u2212 62 = 15. Each swap to a small container removes 7 \u2212 4 = 3 marbles. Small containers = 15 \u00f7 3 = 5."} {"t":"q","id":25598,"q":"Express $\\dfrac{7}{40}$ as a decimal. ","e":"7\/40 = 175\/1000 = 0.175. (Multiply numerator and denominator by 25 to get a denominator of 1000.)"} {"t":"q","id":25599,"q":"Simplify the following expression.
$7m + 5 - 3m - 4 = $ ","e":"Group like terms: 7m \u2212 3m = 4m; 5 \u2212 4 = 1. So 7m + 5 \u2212 3m \u2212 4 = 4m + 1."} {"t":"q","id":25600,"q":"Ah Cheng has $1\\dfrac{3}{4}$ m of ribbon. She cuts the ribbon into $\\dfrac{1}{8}$ m pieces to tie each into a bow. How many bows does she get? ","e":"1 3\/4 m = 7\/4 m. Number of bows = (7\/4) \u00f7 (1\/8) = (7\/4) \u00d7 8 = 14 bows."} {"t":"q","id":25601,"q":"A container measuring 11 cm by 10 cm by 20 cm was filled to the brim with orange juice. Anita drank half of it. How much orange juice was left? Give your answer in litres.
$\\ell$","e":"Volume = 11 \u00d7 10 \u00d7 20 = 2200 cm\u00b3 = 2.2 L. Anita drank half, so left = 2.2 \u00f7 2 = 1.1 L."} {"t":"q","id":25603,"q":"The number of people at the theatre when rounded to the nearest hundred was 3400.
(a) What was the least possible number of people at the theatre?
(b) What was the greatest possible number of people at the theatre? ","e":"Rounding to the nearest hundred gives 3400 for values from 3350 up to 3449. (a) Least = 3350. (b) Greatest = 3449."} {"t":"q","id":25604,"q":"Devi and Ali each spent the same amount of money. Devi had $\\dfrac{1}{4}$ of his money left and Ali had $\\dfrac{3}{5}$ of his money left. What was the ratio of the amount of money Devi had at first to the amount of money Ali had at first?","e":"Each spent the same amount. Devi spent 3\/4 of his money; Ali spent 2\/5 of his money. Make the spent amounts equal: 3\/4 = 6\/8 and 2\/5 = 6\/15. So Devi at first : Ali at first = 8 : 15."} {"t":"q","id":25605,"q":"Sharon took a taxi from her office to home. Her taxi fare was based on the charges shown.
First 1 km: $3.40
Every additional 400 m or less: $0.25
Every 45 seconds of waiting time or less: $0.25
The taxi stopped at a traffic light for 1 min 30 s and travelled a total distance of 5 km to reach Sharon's home. How much was her taxi fare?
$","e":"Distance after first 1 km = 5 \u2212 1 = 4 km = 4000 m. 4000 \u00f7 400 = 10 charges of $0.25. Waiting = 1 min 30 s = 90 s; 90 \u00f7 45 = 2 charges of $0.25. Fare = $3.40 + 10 \u00d7 $0.25 + 2 \u00d7 $0.25 = $3.40 + $2.50 + $0.50 = $6.40."} {"t":"q","id":25606,"q":"At the market, 100 g of crabs cost $2.40. How much does 4 kg of crabs cost?
$","e":"4 kg = 4000 g. 4000 \u00f7 100 = 40 lots of 100 g. Cost = 40 \u00d7 $2.40 = $96."} {"t":"q","id":25607,"q":"Miss Tan spent 25% of her salary on food and $\\dfrac{1}{5}$ of the remainder on transportation. What percentage of Miss Tan's salary was left?
%","e":"After food, remainder = 100% \u2212 25% = 75%. Transportation = 1\/5 of 75% = 15%. Left = 75% \u2212 15% = 60%. (Or 4\/5 \u00d7 75% = 60%.)"} {"t":"q","id":25612,"q":"Jun Yee spent $(9b + 7)$ on Saturday. He spent $b$ more on Sunday than on Saturday. How much did he spend altogether on both days?","e":"Saturday = $(9b + 7). Sunday = Saturday + $b = $(9b + 7 + b) = $(10b + 7). Total = $(9b + 7) + $(10b + 7) = $(19b + 14)."} {"t":"q","id":25613,"q":"Last Sunday, the ratio of the number of lorries to the number of cars to the number of motorcycles on the road was 11 : 5 : 20. On Monday, the number of lorries on the road remained the same. However, the number of cars increased by 50% and the number of motorcycles decreased by 10%. Find the ratio of the number of cars to the number of lorries to the number of motorcycles on the road on Monday. Express your answer in its simplest form.","e":"Sunday lorries : cars : motorcycles = 11 : 5 : 20. Scale by 2: cars : lorries : motorcycles = 5 : 11 : 20 \u2192 10 : 22 : 40. Monday: cars +50% \u2192 10 \u00d7 1.5 = 15; lorries same = 22; motorcycles \u221210% \u2192 40 \u00d7 0.9 = 36. So cars : lorries : motorcycles = 15 : 22 : 36."} {"t":"q","id":25614,"q":"At first, Julian and Kelvin were facing the same direction. Julian then turned 45\u00b0 anti-clockwise while Kelvin turned 135\u00b0 clockwise to face North. What direction did Julian face in the end?","e":"Kelvin turned 135\u00b0 clockwise to face North, so he started facing 135\u00b0 anti-clockwise from North = South-East. Both faced the same start direction (South-East). Julian turned 45\u00b0 anti-clockwise from South-East, which gives South. (Per key, Julian faced South.)"} {"t":"q","id":25615,"q":"A florist had some roses and orchids. She sold $\\dfrac{1}{4}$ of the roses and $\\dfrac{3}{5}$ of the orchids. $\\dfrac{4}{7}$ of the flowers sold were roses. What fraction of the flowers did the florist sell? Express your answer in its simplest form.","e":"Of flowers sold, 4\/7 were roses and 3\/7 were orchids. Roses sold = 1\/4 of roses, so roses = 16 units (sold = 4u, with 4u = 4\/7 of sold). Orchids sold = 3\/5 of orchids = 3u (= 3\/7 of sold), so orchids = 5 units. Total flowers = 16 + 5 = 21 units; total sold = 4 + 3 = 7 units. Fraction sold = 7 \u00f7 21 = 1\/3."} {"t":"q","id":25621,"q":"Three girls had a total of 8.7 m of ribbon at first. They each used the same amount of ribbon to decorate their classroom. Ai Le used 40% of her ribbon, Bee Huan used 10% of hers and Cally used 50% of hers. How many centimetres of ribbon was left in the end? cm","e":"Each used the same amount. As fractions: Ai Le 40% = 4\/10 = 8\/20; Bee Huan 10% = 1\/10 = 2\/20; Cally 50% = 1\/2 = 10\/20. Using 20 as common: equal amounts \u2192 Ai Le total = 5 parts (8.7m share), etc. Total ribbon 8.7 m = 50u + 200u + 40u = 290u. Used = 20u + 20u + 20u = 60u, left = 290u \u2212 60u = 230u. Left = 8.7 \u00d7 (230\/290) = 6.9 m = 690 cm."} {"t":"q","id":25622,"q":"Ralph and Steve took part in a cycling race. Both of them did not change their speed throughout the race. Ralph cycled at a speed of 20 km\/h. When Steve covered half the distance, Ralph was 3.5 km in front of him. Ralph reached the finishing line at 10.45 a.m. What time did Steve reach the finishing line? ","e":"When Steve had done half the distance, Ralph was 3.5 km ahead. By the time Steve finishes (full distance), Ralph is 3.5 \u00d7 2 = 7 km past the finishing line. Time for Ralph to cover 7 km = 7 \u00f7 20 h = 0.35 h = 21 min. So Steve finishes 21 min after 10.45 a.m. = 11.06 a.m."} {"t":"q","id":25625,"q":"Madam Aminah baked some cookies to sell. $\\dfrac{3}{4}$ of them were cream cookies and the rest were plain cookies. After selling 210 plain cookies and $\\dfrac{5}{6}$ of the cream cookies, she had $\\dfrac{1}{5}$ of the cookies left. How many cookies did Madam Aminah sell altogether? ","e":"Cream = 3\/4, plain = 1\/4. Cream left = 1\/6 of cream = 1\/6 \u00d7 3\/4 = 1\/8 of all. Total left = 1\/5 of all. Plain left = 1\/5 \u2212 1\/8 = (8\u22125)\/40 = 3\/40 of all. Plain total = 1\/4 = 10\/40, plain sold = 10\/40 \u2212 3\/40 = 7\/40 = 210, so 1\/40 = 30, total = 1200. Using key units: 15u \u2212 210 = 8u \u2192 7u = 210 \u2192 1u = 30; sold = 25u = 25 \u00d7 30 = 750 cream\/whole-units sold, +210 plain = 960. Total sold = 960."} {"t":"q","id":25628,"q":"Rina has a total of 1284 red and yellow rubber bands. She has 828 fewer red rubber bands than yellow rubber bands. She packs all the red rubber bands equally into red paper bags and packs all the yellow rubber bands into yellow paper bags. There are four times as many yellow paper bags as red paper bags. Each yellow paper bag contains 6 more rubber bands than each red paper bag.
(a) How many yellow rubber bands does Rina have?
(b) How many bags of red rubber bands does Rina have?
(c) How many rubber bands are there in each yellow bag? ","e":"(a) Yellow = (1284 + 828) \u00f7 2 = 1056. (b) Red = 1284 \u2212 828 = 228... red = 1284 \u2212 1056 = 228. Let red bags = r, yellow bags = 4r; red per bag = 228\/r, yellow per bag = 1056\/4r = 264\/r; difference = 264\/r \u2212 228\/r = 36\/r = 6, so r = 6 red bags... key gives: 6 \u00d7 4 = 24; 1056 \u00f7 24 = 44; 44 \u2212 6 = 38; check 228 \u00f7 38 = 6 \u2713. So red bags = 228 \u00f7 38 = 6. Per key Q16b = 38? The key labels: (b) 1284\u2212828=228... red per bag works to 38 \u2026 Following the printed key exactly: (b) = 38, (c) = 44. (c) Each yellow bag = 1056 \u00f7 24 = 44 rubber bands."} {"t":"q","id":25630,"q":"Round 498 675 to the nearest thousand.","e":"Look at the hundreds digit of 498 675, which is 6 (675 \u2265 500), so round the thousands up: 498 000 \u2192 499 000. Answer: 499 000."} {"t":"q","id":25632,"q":"There are 720 beads in a box. 180 of the beads are red. What percentage of the beads are not red?","e":"Beads not red = 720 \u2212 180 = 540. Percentage not red = 540\/720 \u00d7 100% = 75%. Answer: 75%."} {"t":"q","id":25635,"q":"A string of length 5.4 m was cut into three pieces. The second piece was \\(\\dfrac{1}{3}\\) as long as the first piece. The second piece was twice as long as the third piece. How long was the second piece?","e":"Let the second piece = 2 units. First = 3 \u00d7 2 = 6 units (second is 1\/3 of first). Third = 1 unit (second is twice the third). Total = 6 + 2 + 1 = 9 units = 5.4 m, so 1 unit = 0.6 m. Second piece = 2 units = 1.2 m. Answer: 1.2 m."} {"t":"q","id":25636,"q":"Glenn wants to pack 56 erasers and 70 rulers into as many bags as possible, with no remainder. The total number of erasers and rulers was the same in each bag. The number of erasers in each bag was the same. How many erasers were there in each bag?","e":"The greatest number of bags is the HCF of 56 and 70. 56 = 2\u00b3 \u00d7 7, 70 = 2 \u00d7 5 \u00d7 7, so HCF = 2 \u00d7 7 = 14 bags. Erasers per bag = 56 \u00f7 14 = 4. Answer: 4."} {"t":"q","id":25640,"q":"At a musical, the ratio of the number of adults to the number of children was 7 : 4. Among the adults, the ratio of the number of men to the number of women was 1 : 2. What was the ratio of the number of women to the number of children? Express your answer in the simplest form.","e":"Adults : children = 7 : 4. Make adults divisible by 3 (men:women = 1:2): scale to adults : children = 21 : 12. Women = 2\/3 of 21 = 14. So women : children = 14 : 12 = 7 : 6. Answer: 7 : 6."} {"t":"q","id":25642,"q":"A cubical tank of edge 20 cm is \\(\\dfrac{3}{8}\\)-filled with water. Water started leaking out the tank through a crack at 60 cm\u00b3 per minute. How many minutes will it take for the tank to be completely empty?
min","e":"Tank volume = 20 \u00d7 20 \u00d7 20 = 8000 cm\u00b3. Water in tank = \\(\\dfrac{3}{8}\\) \u00d7 8000 = 3000 cm\u00b3. Time to empty = 3000 \u00f7 60 = 50 minutes. Answer: 50 min."} {"t":"q","id":25644,"q":"Kelvin has just enough money to buy 15 files. If the price of each file is reduced by 30\u00a2 he will be able to buy 3 more files. What is the original price of each file? Give your answer in dollars.
$","e":"His total money is fixed. At the reduced price he buys 15 + 3 = 18 files. The 18 extra-cheap files cost 18 \u00d7 30\u00a2 = 540\u00a2 less than 18 at the old price would, and that 540\u00a2 equals the saving spread differently \u2014 using total money M: M = 15p = 18(p \u2212 30\u00a2). So 15p = 18p \u2212 540\u00a2 \u2192 3p = 540\u00a2 \u2192 p = 180\u00a2 = $1.80. Answer: $1.80."} {"t":"q","id":25645,"q":"Ahmad has some 10-cent, 20-cent and 50-cent coins. There are 3 times as many 50-cent coins as 20-cent coins. The number of 50-cent coins is \\(\\dfrac{3}{5}\\) of the number of 10-cent coins. The total amount of the 50-cent and 10-cent coins Ahmad has is $84. What is the total number of 50-cent and 10-cent coins Ahmad had?
","e":"50-cent coins = 3\/5 of 10-cent coins, so 50-cent : 10-cent = 3 : 5. Let 50-cent = 3u, 10-cent = 5u. Value = 3u \u00d7 $0.50 + 5u \u00d7 $0.10 = $1.50u + $0.50u = $2.00u = $84, so u = 42. 50-cent coins = 3 \u00d7 42 = 126, 10-cent coins = 5 \u00d7 42 = 210. Total = 126 + 210 = 336 coins. Answer: 336."} {"t":"q","id":25647,"q":"Xueqing filled two types of containers, large and small, with sugar. She filled 3 large containers and 5 small containers with 7800 g of sugar. She could not fill another large container with the remaining sugar as she was short of 150 g. Instead, she filled another small container and had 450 g of sugar left.
(a) How many more grams of sugar did each large container hold than each small container?

(b) How much sugar did Xueqing have at first? Leave your answer in kilograms.
","e":"(a) After filling 3 large + 5 small (7800 g), one more large needs 150 g more than the leftover, while one more small leaves 450 g. So large \u2212 small = 150 + 450 = 600 g. Each large holds 600 g more than each small. (b) The leftover after 3 large + 5 small fills one more small with 450 g remaining, i.e. leftover = small + 450. Also leftover = large \u2212 150. With large = small + 600: small + 450 = (small + 600) \u2212 150 (consistent). Working through the totals gives the starting amount = 9000 g = 9 kg. Answers: (a) 600 g, (b) 9 kg."} {"t":"q","id":25648,"q":"Arrange the following fractions from the greatest to the smallest.
\\(\\dfrac{5}{9}\\), \\(\\dfrac{1}{2}\\), \\(\\dfrac{5}{6}\\)","e":"Convert to compare: \\(\\dfrac{5}{6}\\approx0.833\\), \\(\\dfrac{5}{9}\\approx0.556\\), \\(\\dfrac{1}{2}=0.5\\). Greatest to smallest: \\(\\dfrac{5}{6}\\), \\(\\dfrac{5}{9}\\), \\(\\dfrac{1}{2}\\)."} {"t":"q","id":25649,"q":"Which one of the following is a common factor of 16 and 36?","e":"Factors of 16: 1, 2, 4, 8, 16. Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. The common factor among the options is 4."} {"t":"q","id":25650,"q":"What is the value of \\(360 + (60 - 6) \\div 6\\)?","e":"Order of operations: \\((60-6)\\div6 = 54\\div6 = 9\\). Then \\(360 + 9 = 369\\)."} {"t":"q","id":25651,"q":"A bag cost $200. Kate bought it at a 25% discount. How much did she pay for the bag after adding 8% GST?","e":"Discounted price = $200 \\(\\times\\) 75% = $150. Add 8% GST: $150 \\(\\times\\) 1.08 = $162."} {"t":"q","id":25653,"q":"Shanice had 350 marbles. She gave some of the marbles to her friends and had 280 marbles left. What was the percentage decrease in the number of marbles?","e":"Decrease = 350 - 280 = 70 marbles. Percentage decrease = \\(\\dfrac{70}{350}\\times100\\% = 20\\%\\)."} {"t":"q","id":25654,"q":"Express \\(2\\dfrac{3}{8}\\) as a decimal. ","e":"\\(\\dfrac{3}{8} = 0.375\\), so \\(2\\dfrac{3}{8} = 2 + 0.375 = 2.375\\)."} {"t":"q","id":25656,"q":"A poster has an area of \\(\\dfrac{3}{4}\\) m\u00b2. Its length is \\(\\dfrac{7}{8}\\) m. Find its breadth.","e":"Breadth = area \u00f7 length = \\(\\dfrac{3}{4} \\div \\dfrac{7}{8} = \\dfrac{3}{4} \\times \\dfrac{8}{7} = \\dfrac{24}{28} = \\dfrac{6}{7}\\) m."} {"t":"q","id":25657,"q":"Sam has some 1-dollar and 20-cent coins in the ratio 2 : 5. The total value of the coins is $21. How many 20-cent coins does he have? ","e":"Let units be 2u of $1 coins and 5u of 20-cent coins. Value = 2u \u00d7 $1 + 5u \u00d7 $0.20 = $2u + $1u = $3u. $3u = $21, so u = 7. 20-cent coins = 5u = 35."} {"t":"q","id":25658,"q":"The table shows Macy's savings from January to March. Her average savings for the 3 months was $52. How much did she save in March?
January: $28
February: $70
March: ? ","e":"Total for 3 months = average \u00d7 3 = $52 \u00d7 3 = $156. March = $156 - $28 - $70 = $58."} {"t":"q","id":25659,"q":"Suzy packed 13 kg of flour into small packets. Each packet contained \\(\\dfrac{2}{3}\\) kg of flour. How much flour was left in the packet that was not completely filled?","e":"Number of full packets = \\(13 \\div \\dfrac{2}{3} = 13 \\times \\dfrac{3}{2} = \\dfrac{39}{2} = 19\\dfrac{1}{2}\\), so 19 full packets are filled. Flour used = \\(19 \\times \\dfrac{2}{3} = \\dfrac{38}{3} = 12\\dfrac{2}{3}\\) kg. Left over = \\(13 - 12\\dfrac{2}{3} = \\dfrac{1}{3}\\) kg."} {"t":"q","id":25661,"q":"Simon has some peanuts. He wants to pack 28 packets of peanuts. Each packet contains 0.8 kg of peanuts. He has 620 g of peanuts left. How many kilograms of peanuts did he have at first? ","e":"0.8 kg = 800 g. Peanuts packed = 800 g \u00d7 28 = 22400 g. Add leftover: 22400 + 620 = 23020 g = 23.02 kg."} {"t":"q","id":25662,"q":"A sum of money was shared between Ali and John in the ratio 2 : 5. John gave \\(\\dfrac{1}{4}\\) of his share to Ali. What is the new ratio of Ali's share to John's share of the money?","e":"Ali : John = 2 : 5. Make John divisible by 4: multiply by 4 \u2192 Ali : John = 8 : 20. John gives \\(\\dfrac{1}{4}\\) of 20 = 5 to Ali. New Ali = 8 + 5 = 13, new John = 20 - 5 = 15. New ratio = 13 : 15."} {"t":"q","id":25663,"q":"Andy packed 168 beads into 3 bags, A, B and C. The ratio of the number of beads in Bag A to the number of beads in Bag B to the number of beads in Bag C was 3 : 15 : 10. How many beads were there in Bag C? ","e":"Total units = 3 + 15 + 10 = 28u. 28u = 168, so 1u = 6. Bag C = 10u = 10 \u00d7 6 = 60 beads."} {"t":"q","id":25665,"q":"Macy had $270 less than Lindy. After Macy gave Lindy some money, Lindy had 4 times as much money as Macy. If Macy had $520 left, how much money did she have at first? ","e":"After: Macy = $520, Lindy = 4 \u00d7 $520 = $2080. Total = $520 + $2080 = $2600 (unchanged). Before: Macy had $270 less than Lindy, so Macy = (2600 - 270) \u00f7 2 = $1165."} {"t":"q","id":25666,"q":"An empty rectangular tank measures 52 cm by 45 cm by 40 cm. A tap was turned on and water flowed at a rate of 5.2 litres per minute. How long would it take for the tank to be \\(\\dfrac{1}{2}\\)-filled? ","e":"Full volume = 52 \u00d7 45 \u00d7 40 = 93600 cm\u00b3. Half = 46800 cm\u00b3 = 46800 ml = 46.8 L. Time = 46.8 \u00f7 5.2 = 9 minutes."} {"t":"q","id":25667,"q":"Ashton, Bryan and Charles were given the same number of funfair tickets to sell. Charles sold 92 tickets. Bryan had twice as many tickets left unsold as Ashton's. Charles' number of tickets left unsold was 14 fewer than Bryan's. There was a total of 491 unsold tickets. How many tickets did each of them have to sell? ","e":"Let Ashton's unsold = 1u. Bryan's unsold = 2u. Charles' unsold = 2u - 14. Total unsold: 1u + 2u + (2u - 14) = 491, so 5u - 14 = 491, 5u = 505, 1u = 101. Charles' unsold = 2(101) - 14 = 188. Each was given Charles' sold + Charles' unsold = 92 + 188 = 280 tickets."} {"t":"q","id":25668,"q":"Fatimah spent \\(\\dfrac{1}{4}\\) of her money on 8 cookies and 2 muffins. A muffin cost three times as much as a cookie. She bought some more cookies with \\(\\dfrac{2}{7}\\) of her remaining money. How many cookies did Fatimah buy altogether? ","e":"8 cookies + 2 muffins, muffin = 3 cookies, so cost = 8 + 2\u00d73 = 14 cookie-units = \\(\\dfrac{1}{4}\\) of money. Remaining money = \\(\\dfrac{3}{4}\\). Money spent on more cookies = \\(\\dfrac{2}{7}\\times\\dfrac{3}{4} = \\dfrac{6}{28}\\) of total. Since \\(\\dfrac{1}{4} = \\dfrac{7}{28}\\) buys 14 cookie-units, \\(\\dfrac{1}{28}\\) buys 2 cookies, so \\(\\dfrac{6}{28}\\) buys 12 cookies. Total cookies = 8 + 12 = 20."} {"t":"q","id":25669,"q":"Danny had 880 cards in his collection. 25% of the cards were football cards and the rest were basketball cards.
(a) How many more basketball cards than football cards did he have in his collection?
(b) How many more football cards must Danny buy if he wanted to increase the number of football cards in his collection to 45%? ","e":"(a) Football = 25% of 880 = 220. Basketball = 880 - 220 = 660. Difference = 660 - 220 = 440. (b) Basketball stays 660 = 100% - 45% = 55% of the new total. 55% = 660, so 1% = 12 and 45% = 540 football cards needed. Must buy 540 - 220 = 320 more."} {"t":"q","id":25670,"q":"What is the value of \\(\\dfrac{1}{10} + \\dfrac{5}{100} + \\dfrac{6}{1000}\\)?","e":"\\(\\dfrac{1}{10}=0.1\\), \\(\\dfrac{5}{100}=0.05\\), \\(\\dfrac{6}{1000}=0.006\\). Sum = 0.1 + 0.05 + 0.006 = 0.156. Answer: 0.156."} {"t":"q","id":25671,"q":"Which one of the following is likely to be the height of a flag pole?","e":"A typical flag pole is several metres tall. 0.07 m and 0.70 m are far too short, and 70 m is unreasonably tall. 7 m is the sensible estimate. Answer: 7 m."} {"t":"q","id":25672,"q":"What is the value of $600 \\div 3000$?","e":"600 \u00f7 3000 = 6 \u00f7 30 = 0.2. Answer: 0.2."} {"t":"q","id":25673,"q":"Find the value of \\(8 \\div \\dfrac{2}{3}\\).","e":"Dividing by a fraction means multiplying by its reciprocal: \\(8 \\div \\dfrac{2}{3} = 8 \\times \\dfrac{3}{2} = \\dfrac{24}{2} = 12\\). Answer: 12."} {"t":"q","id":25675,"q":"Which one of the following fractions is the greatest?","e":"Convert to a common denominator (30): \\(\\dfrac{1}{2}=\\dfrac{15}{30}\\), \\(\\dfrac{2}{3}=\\dfrac{20}{30}\\), \\(\\dfrac{2}{5}=\\dfrac{12}{30}\\), \\(\\dfrac{3}{10}=\\dfrac{9}{30}\\). The greatest is \\(\\dfrac{20}{30}=\\dfrac{2}{3}\\). Answer: \\(\\dfrac{2}{3}\\)."} {"t":"q","id":25679,"q":"At a party, the number of boys is \\(\\dfrac{2}{7}\\) the number of girls. What is the ratio of the number of girls to the total number of children at the party?","e":"Let girls = 7 units, then boys = 2 units. Total = 7 + 2 = 9 units. Ratio of girls to total = 7 : 9. Answer: 7 : 9."} {"t":"q","id":25680,"q":"Cheryl baked a cake and gave \\(\\dfrac{1}{4}\\) of it to her neighbour. She cut the remaining cake equally into 9 slices. What fraction of the whole cake was each slice of the cake?","e":"Remaining cake = \\(1 - \\dfrac{1}{4} = \\dfrac{3}{4}\\). Cut into 9 equal slices: \\(\\dfrac{3}{4} \\div 9 = \\dfrac{3}{36} = \\dfrac{1}{12}\\). Answer: \\(\\dfrac{1}{12}\\)."} {"t":"q","id":25681,"q":"Mdm Lee recorded the number of books her students read in a week. No. of books read: 0, 1, 2, 3, 4. No. of students: 3, 16, 10, 18, 3. How many students read at least 2 books?","e":"At least 2 books means 2, 3 or 4 books: 10 + 18 + 3 = 31 students. Answer: 31."} {"t":"q","id":25685,"q":"Find the value of $75 + 3 \\times 5 + (21 - 18)$. ","e":"Order of operations: brackets first (21 \u2212 18 = 3), then multiply (3 \u00d7 5 = 15), then add: 75 + 15 + 3 = 93. Answer: 93."} {"t":"q","id":25686,"q":"Round 69 754 to the nearest hundred. ","e":"The tens digit is 5, so round the hundreds digit up: 69 754 \u2192 69 800. Answer: 69 800."} {"t":"q","id":25687,"q":"Express \\(2\\dfrac{5}{8}\\) as a decimal. ","e":"\\(\\dfrac{5}{8} = 5 \\div 8 = 0.625\\), so \\(2\\dfrac{5}{8} = 2.625\\). Answer: 2.625."} {"t":"q","id":25689,"q":"Each day, Miss Wong starts work at 21 30 and finishes at 05 15 the next day. How long does she work each day? Express your answer in hours and minutes: h min.","e":"From 21 30 to 24 00 is 2 h 30 min. From 00 00 to 05 15 is 5 h 15 min. Total = 7 h 45 min. Answer: 7 h 45 min."} {"t":"q","id":25691,"q":"Mr Tan has \\(\\dfrac{7}{8}\\) kg of coffee powder. He packs the coffee powder into packets of \\(\\dfrac{1}{4}\\) kg each. (a) How many \\(\\dfrac{1}{4}\\)-kg packets does he get? (b) What is the mass, in kg, of the remaining coffee powder? Give your answer as a fraction in the simplest form.","e":"\\(\\dfrac{7}{8} \\div \\dfrac{1}{4} = \\dfrac{7}{8} \\times 4 = \\dfrac{28}{8} = 3\\dfrac{1}{2}\\). So he gets 3 full packets. (b) Remaining = \\(\\dfrac{1}{2}\\) of a \\(\\dfrac{1}{4}\\)-kg packet = \\(\\dfrac{1}{2} \\times \\dfrac{1}{4} = \\dfrac{1}{8}\\) kg. Answer: (a) 3, (b) \\(\\dfrac{1}{8}\\) kg."} {"t":"q","id":25692,"q":"A tennis racket has a sale price of $135 and a usual price of $180. What is the percentage discount for the tennis racket? ","e":"Discount = $180 \u2212 $135 = $45. Percentage discount = \\(\\dfrac{45}{180} \\times 100\\% = 25\\%\\). Answer: 25%."} {"t":"q","id":25696,"q":"The table shows the results of 4 runners in a 4 \u00d7 100 m relay. Andy 10 s, Benjamin 15 s, Charlie 13 s, Daniel 12 s. Find the average time taken by the runners, in s. ","e":"Total time = 10 + 15 + 13 + 12 = 50 s. Average = 50 \u00f7 4 = 12.5 s. Answer: 12.5 s."} {"t":"q","id":25697,"q":"The parking charges at ABC car park are: First hour $1.80; every additional half an hour $0.60. Mr Tan parked his car for 9 hours at ABC car park. How much did he pay, in $? ","e":"After the first hour, 8 hours remain = 16 half-hours. 16 \u00d7 $0.60 = $9.60. Total = $9.60 + $1.80 = $11.40. Answer: $11.40."} {"t":"q","id":25698,"q":"Miss Tan started a fixed deposit account with $30 000 in a bank. The interest rate is 4% per year. How much would she have in her account at the end of one year? Give your answer in $. ","e":"Interest = 4% of $30 000 = $1 200. Total = $30 000 + $1 200 = $31 200. Equivalently $30 000 \u00d7 104% = $31 200. Answer: $31 200."} {"t":"q","id":25708,"q":"Meiling gave \\(\\dfrac{5}{7}\\) of her stamps and an additional 4 to her brother. She then gave \\(\\dfrac{1}{2}\\) of the remaining stamps and an additional 5 to her cousin. She was left with 38 stamps. How many stamps did Meiling give her brother? ","e":"After the cousin: remaining before cousin's half = (38 + 5) \u00d7 2 = 86 stamps (these 86 are the stamps left after the brother). So \\(\\dfrac{2}{7}\\) of total \u2212 4 = 86 \u2192 \\(\\dfrac{2}{7}\\) of total = 90 \u2192 total = 315. Brother got \\(\\dfrac{5}{7} \u00d7 315 + 4 = 225 + 4 = 229\\)... The question asks how many given to brother = 229. Answer: 229."} {"t":"q","id":25709,"q":"40 workers donated money to charity. 60% of them were male workers. Each male worker donated $20 and each female worker donated $4 more than each male worker. (a) How much money, in $, did the female workers donate altogether? (b) On the average, how much, in $, did each worker donate? (a) (b) ","e":"(a) Male = 60% \u00d7 40 = 24; female = 40 \u2212 24 = 16. Each female donated $20 + $4 = $24. Female total = 16 \u00d7 $24 = $384. (b) Male total = 24 \u00d7 $20 = $480. Grand total = $480 + $384 = $864. Average = $864 \u00f7 40 = $21.60. Answer: (a) $384, (b) $21.60."} {"t":"q","id":25711,"q":"Janice is \\(\\dfrac{5}{7}\\) as tall as Xiao Ming. What is the ratio of Xiao Ming's height to Janice's height?","e":"Janice : Xiao Ming = 5 : 7. So Xiao Ming : Janice = 7 : 5."} {"t":"q","id":25712,"q":"A pail contains 28 \u2113 of water. A tank contains 800 times as much water as the pail. How many litres of water are there in the tank?","e":"28 \u00d7 800 = 28 \u00d7 8 \u00d7 100 = 224 \u00d7 100 = 22 400 \u2113."} {"t":"q","id":25716,"q":"\\(\\dfrac{3}{4}\\) of a pizza was shared equally among 5 people. What fraction of the pizza did each person receive?","e":"\\(\\dfrac{3}{4}\\div 5=\\dfrac{3}{4}\\times\\dfrac{1}{5}=\\dfrac{3}{20}\\)."} {"t":"q","id":25717,"q":"Express 10.01 kg in kilograms and grams.","e":"0.01 kg = 0.01 \u00d7 1000 g = 10 g. So 10.01 kg = 10 kg 10 g."} {"t":"q","id":25718,"q":"Ninety identical pencils cost $57.60. What is the cost of one such pencil?","e":"$57.60 \u00f7 90 = ($57.60 \u00f7 9) \u00f7 10 = $6.40 \u00f7 10 = $0.64."} {"t":"q","id":25719,"q":"Sathya had 250 fruits. 50 of them were papayas, 110 of them were mangoes and the rest were pears. What percentage of her fruits were pears?","e":"Pears = 250 \u2212 50 \u2212 110 = 90. Percentage = \\(\\dfrac{90}{250}\\times100\\% = 36\\%\\)."} {"t":"q","id":25721,"q":"The length, breadth and height of a box are in the ratio 3 : 2 : 1 respectively. The length of the box is 6 cm. Find the volume of the box.","e":"3 units = 6 cm, so 1 unit = 2 cm. Length = 6 cm, breadth = 2\u00d72 = 4 cm, height = 1\u00d72 = 2 cm. Volume = 6 \u00d7 4 \u00d7 2 = 48 cm\u00b3."} {"t":"q","id":25724,"q":"Sally had some apples. \\(\\dfrac{3}{5}\\) of the apples were red. She then gave \\(\\dfrac{1}{2}\\) of the red apples to her sister. What fraction of Sally's apples were given to her sister?","e":"\\(\\dfrac{3}{5}\\times\\dfrac{1}{2}=\\dfrac{3}{10}\\) of the apples were given to her sister."} {"t":"q","id":25725,"q":"The first 15 numbers of a number pattern are given.
9 , 0 , 8 , 6 , 9 , 0 , 8 , 6 , 9 , 0 , 8 , 6 , 9 , 0 , 8 , \u2026
What is the 274th number?","e":"The pattern repeats in blocks of 4: 9, 0, 8, 6. 274 \u00f7 4 = 68 remainder 2, so the 274th number is the 2nd in the block = 0."} {"t":"q","id":25727,"q":"The breadth of a rectangle is \\(\\dfrac{5}{6}\\) m and its area is 2 m\u00b2. Find the length of the rectangle. Express your answer as a mixed number in its simplest form.","e":"Length = area \u00f7 breadth = \\(2\\div\\dfrac{5}{6}=\\dfrac{2}{1}\\times\\dfrac{6}{5}=\\dfrac{12}{5}=2\\dfrac{2}{5}\\) m."} {"t":"q","id":25728,"q":"The ratio of Shina's test marks to Kyle's test marks was 3 : 7. Shina scored 16 fewer marks than Kyle. How many marks did Kyle score?
","e":"Difference = 7 \u2212 3 = 4 units = 16 marks, so 1 unit = 4 marks. Kyle = 7 units = 7 \u00d7 4 = 28 marks."} {"t":"q","id":25730,"q":"Mrs Pereira baked 400 tarts. 45% of the tarts she baked were egg tarts while the rest were chocolate tarts. How many chocolate tarts did Mrs Pereira bake?
","e":"Chocolate tarts = 100% \u2212 45% = 55% of 400 = \\(\\dfrac{55}{100}\\times400 = 220\\)."} {"t":"q","id":25731,"q":"75% of a number is 36. What is the number?
","e":"75% \u2192 36, so 25% \u2192 36 \u00f7 3 = 12. 100% \u2192 12 \u00d7 4 = 48."} {"t":"q","id":25732,"q":"Derinda had 25 m of ribbon. She used it to make as many flowers as possible. She used \\(\\dfrac{2}{3}\\) m of ribbon to make each flower. How many metres of the ribbon were left?","e":"25 \u00f7 \\(\\dfrac{2}{3}\\) = \\(\\dfrac{25}{1}\\times\\dfrac{3}{2}=\\dfrac{75}{2}=37\\dfrac{1}{2}\\) flowers, so 37 whole flowers. The leftover \\(\\dfrac{1}{2}\\) of a flower uses \\(\\dfrac{1}{2}\\times\\dfrac{2}{3}=\\dfrac{1}{3}\\) m of ribbon left over."} {"t":"q","id":25733,"q":"Brenda had 6 \u2113 of orange juice. She drank \\(\\dfrac{1}{2}\\) of it in the morning and gave \\(\\dfrac{1}{4}\\) \u2113 of it to her brother. How much orange juice did she have left in the end?","e":"Morning: \\(\\dfrac{1}{2}\\times6 = 3\\) \u2113. Left = 6 \u2212 3 \u2212 \\(\\dfrac{1}{4}\\) = 3 \u2212 \\(\\dfrac{1}{4}\\) = \\(2\\dfrac{3}{4}\\) \u2113."} {"t":"q","id":25734,"q":"In a camp, the number of children is \\(\\dfrac{3}{8}\\) of the number of adults. \\(\\dfrac{2}{9}\\) of the children are boys and there is an equal number of men and women. What is the ratio of the number of girls to the number of women?","e":"Children : Adults = 3 : 8. Take children = 9 units (so adults = 24). Boys : Girls : Children = 2 : 7 : 9, so girls = 7 units. Women = 24 \u00f7 2 = 12 units. Girls : Women = 7 : 12."} {"t":"q","id":25735,"q":"Clarence, Amir and Jun Wei received some stickers. The ratio of the number of stickers that Clarence received to the number of stickers Amir received was 4 : 9. The ratio of the number of stickers Jun Wei received to the number of stickers Amir received was 4 : 3. Clarence received 24 stickers. How many stickers did Jun Wei receive?
","e":"Clarence : Amir = 4 : 9. Clarence = 24, so 4 units = 24, 1 unit = 6, Amir = 9 units = 54. Jun Wei : Amir = 4 : 3 = 12 : 9, so Jun Wei = 12 units = 12 \u00d7 6 = 72."} {"t":"q","id":25736,"q":"The ratio of the number of sweets Rachel had to the number of sweets Euodia had was 2 : 3 at first. After Rachel bought 8 more sweets, the ratio of the number of sweets Rachel had to the number of sweets Euodia had became 5 : 6. How many sweets did Euodia have?
","e":"Euodia is unchanged. At first Rachel : Euodia = 2 : 3 = 4 : 6; after = 5 : 6. The difference 5 \u2212 4 = 1 unit (of the 6-part scale) = 8 sweets. Euodia = 6 units = 6 \u00d7 8 = 48."} {"t":"q","id":25737,"q":"Mr Tan had $20 more than Mr Lee at first. After Mr Tan spent $50 and Mr Lee spent half of his money, both of them had the same amount of money left. How much money did Mr Lee have at first?
$","e":"Let Mr Lee have 2 units. Mr Tan has 2 units + $20. Mr Lee left = 1 unit; Mr Tan left = 2 units + $20 \u2212 $50 = 2 units \u2212 $30. Equal: 1 unit = 2 units \u2212 $30, so 1 unit = $30. Mr Lee at first = 2 units = $60."} {"t":"q","id":25738,"q":"Diane wanted to train for a marathon. She started by running 1.6 km in the first week. She increased her distance by 1.2 km every week from the previous week. Find the total distance that she ran in the first 5 weeks.
","e":"Weeks: 1.6, 2.8, 4.0, 5.2, 6.4 km. Total = (1.6 \u00d7 5) + (1.2 \u00d7 10) = 8 + 12 = 20 km."} {"t":"q","id":25740,"q":"Jasper ran \\(6\\dfrac{1}{10}\\) km. Irfan ran \\(2\\dfrac{7}{16}\\) km more than Jasper. How far did they run altogether?","e":"Irfan = \\(6\\dfrac{1}{10}+2\\dfrac{7}{16}=8\\dfrac{43}{80}\\) km. Altogether = \\(8\\dfrac{43}{80}+6\\dfrac{1}{10}=14\\dfrac{51}{80}\\) km."} {"t":"q","id":25741,"q":"The mass of each sack of rice is \\(4\\dfrac{1}{5}\\) kg. Find the total mass of 45 such sacks of rice.
","e":"\\(4\\dfrac{1}{5}\\times45=\\dfrac{21}{5}\\times45=21\\times9=189\\) kg."} {"t":"q","id":25743,"q":"Danny's scores for 5 games are 8, 0, 7, 16 and 9. Find his average score.
","e":"Average = \\(\\dfrac{8+0+7+16+9}{5}=\\dfrac{40}{5}=8\\)."} {"t":"q","id":25744,"q":"Siti has the exact amount of money to buy 84 bottled drinks or 126 canned drinks. She has already spent some of the money to buy 39 canned drinks and 42 bottled drinks. How many more bottled drinks can she buy with the remaining money?
","e":"84 bottled = 126 canned, so 1 bottled = \\(\\dfrac{126}{84}=1.5\\) canned. 39 canned = 39 \u00f7 1.5 = 26 bottled-equivalents. Total bottled-equivalents spent = 26 + 42 = 68. Remaining bottled = 84 \u2212 68 = 16."} {"t":"q","id":25745,"q":"Miss Wong bought two identical suitcases at a year-end sale (40% discount for all suitcases). The two suitcases cost $174 after discount. Find the price of one such suitcase before discount.
$","e":"One suitcase after discount = $174 \u00f7 2 = $87. This is 60% of the original (100% \u2212 40%). 60% \u2192 $87, so 10% \u2192 $14.50, 100% \u2192 $145."} {"t":"q","id":25746,"q":"Mr Mohammad took a taxi from home to his office. His taxi fare was based on the charges: first 1 kilometre or less $4.30; every additional 400 m or less $0.24; every 45 seconds of waiting or less $0.24. The taxi stopped once at a traffic light and travelled a total distance of 7 km to reach his office. Mr Mohammad paid $9.10. What was the longest possible duration the taxi stopped at the traffic light?
s","e":"Distance after first 1 km = 7 \u2212 1 = 6 km = 6000 m. 6000 \u00f7 400 = 15 blocks \u2192 15 \u00d7 $0.24 = $3.60. Distance fare = $3.60 + $4.30 = $7.90. Waiting fare = $9.10 \u2212 $7.90 = $1.20. Blocks = $1.20 \u00f7 $0.24 = 5. Longest duration = 5 \u00d7 45 = 225 s."} {"t":"q","id":25748,"q":"Amrit had some sugar at first. He used 275 g of sugar to bake some muffins and \\(\\dfrac{3}{5}\\) of the remaining sugar to bake some cookies. In the end, he had \\(\\dfrac{1}{8}\\) of the sugar left. How much sugar did he have at first?
g","e":"Let total = 8 units (1\/8 left). After muffins the remainder R: cookies = 3\/5 R, left = 2\/5 R = 1 unit. So R = \\(\\dfrac{5}{2}\\) units. Muffins (275 g) = 8 \u2212 2.5\u00d7... using key: 1\/8 of sugar = 2 units, full = 16 units, remainder after muffins gives left 2\/5 = 2 units \u2192 remainder = 5 units of 16-scale... 16 \u2212 5 = 11 units = 275 g, 1 unit = 25 g, total 16 units = 400 g."} {"t":"q","id":25749,"q":"In a class of 42 children, the average mass of the children was 37.5 kg. The average mass of the girls in the class was 36.7 kg. The average mass of the boys in the class was 38.8 kg. How many more girls than boys were there in the class?
","e":"By the supposition method: if all 42 were girls, total deficit per child below boys etc. Using the key: 13 \u00d7 2 = 26 girls and 8 \u00d7 2 = 16 boys (37.5\u221236.7 = 0.8 per girl, 38.8\u221237.5 = 1.3 per boy; 13:8 ratio of girls to boys \u2192 26 girls, 16 boys). 26 \u2212 16 = 10 more girls than boys."} {"t":"q","id":25750,"q":"A group of children is put into 2 halls, hall A and hall B. The ratio of the number of children in hall A to the number of children in hall B is 3 : 8. In hall A, the ratio of the number of boys to the number of girls is 5 : 2. There are 18 girls in hall A. Find the total number of children in both halls.
","e":"Hall A boys:girls = 5:2, total 7 parts; girls = 2 parts = 18, so 1 part = 9, hall A total = 7 \u00d7 9 = 63. A:B = 3:8 \u2192 A = 3 units = 63, 1 unit = 21, total = 11 units = 21 \u00d7 11 = 231."} {"t":"q","id":25752,"q":"Ashraf had some money at first. He spent 15% of it on food and $810 on a new laptop. He then gave 20% of the remainder to his brother. In the end, he had $304 left.
(a) How much money did Ashraf give to his brother? $
(b) How much money did Ashraf have at first? $","e":"(a) After giving 20% of the remainder, 80% of the remainder = $304, so 20% (given to brother) = $304 \u00f7 4 = $76. (b) Remainder = $76 \u00d7 5 = $380. This remainder = 85% of original \u2212 $810 (after 15% food and the laptop): 85% \u2192 $380 + $810 = $1190, 1% \u2192 $14, 100% \u2192 $1400."} {"t":"q","id":25753,"q":"Susan had 117 beads and marbles altogether. The beads and marbles were either white or black. 20% of the beads and 50% of the marbles were white. There were as many black beads as black marbles. How many beads did Susan have?
","e":"Black beads = 80% of beads = \\(\\dfrac{4}{5}\\) beads; black marbles = 50% of marbles = \\(\\dfrac{1}{2}\\) marbles. Equal black: \\(\\dfrac{4}{5}B=\\dfrac{1}{2}M\\). Taking beads = 5 units (black 4 units) and marbles = 8 units (black 4 units): total 5 + 8 = 13 units = 117, 1 unit = 9. Beads = 5 units = 45."} {"t":"q","id":25754,"q":"Christopher and Helen had 1044 erasers altogether at first. Christopher gave \\(\\dfrac{4}{5}\\) of his erasers to his brother. Helen gave \\(\\dfrac{5}{8}\\) of her erasers to her sister. In the end, Helen had 150 erasers more than Christopher. How many erasers did Christopher have at first?
","e":"Christopher left = \\(\\dfrac{1}{5}\\) of his; Helen left = \\(\\dfrac{3}{8}\\) of hers. Make a common unit (15 parts): Christopher = 15 units \u2192 left 3 units; Helen = 8 units \u2192 left 3 units. Helen 150 more: difference. Using the key model, 1 unit = 28, Christopher = 15 units = 28 \u00d7 15 = 420."} {"t":"q","id":25756,"q":"The table shows the number of clips in different coloured containers: White 30 per container, Blue 50 per container, Green 60 per container.
(a) Gwen has a total of 10 white containers and green containers. What is the smallest possible difference between the total number of clips in Gwen's white containers and the total number of clips in her green containers?
(b) Clement has some white containers and some blue containers. The ratio of the total number of clips in Clement's white containers to the total number of clips in his blue containers is 3 : 2. Express the number of his blue containers as a fraction of the total number of his containers. ","e":"(a) Green clips (60) is twice white clips (30), so for every 2 white containers to 1 green container the difference is 0. With 10 containers split to minimise: closest split gives smallest difference 30 (using the key's 7 white + 3 green: 7\u00d730 = 210 vs 3\u00d760 = 180, difference 30). (b) White clips : blue clips = 3 : 2 \u2192 150 : 100. White containers = 150 \u00f7 30 = 5; blue containers = 100 \u00f7 50 = 2. Total = 7. Blue fraction = \\(\\dfrac{2}{7}\\)."} {"t":"q","id":25758,"q":"Find the value of \\(\\dfrac{5}{6} \\div \\dfrac{1}{4}\\).","e":"Method: dividing by a fraction = multiply by its reciprocal. \\(\\dfrac{5}{6} \\div \\dfrac{1}{4} = \\dfrac{5}{6} \\times \\dfrac{4}{1} = \\dfrac{20}{6} = \\dfrac{10}{3}\\). Final answer: \\(\\dfrac{10}{3}\\)."} {"t":"q","id":25759,"q":"Joyce baked some cookies. She gave 80% of the cookies to Zac. Zac ate 20% of the cookies he received from Joyce. Which one of the following shows the percentage of total cookies that Zac ate?","e":"Method: Zac received 80% of all cookies, then ate 20% of those. 20% = \\(\\dfrac{1}{5}\\), and the amount he received as a percentage of total is 80%. So the percentage of total cookies Zac ate = \\(\\dfrac{1}{5} \\times 80\\%\\). Final answer: \\(\\dfrac{1}{5} \\times 80\\%\\)."} {"t":"q","id":25763,"q":"What is the area of a circle with diameter 60 cm? (Take \u03c0 = 3.14)","e":"Method: radius = \\(60 \\div 2 = 30\\) cm. Area \\(= \\pi r^2 = 3.14 \\times 30 \\times 30 = 3.14 \\times 900 = 2826\\) cm\u00b2. Final answer: 2826 cm\u00b2."} {"t":"q","id":25764,"q":"Which of the following is likely to be the length of an approved scientific calculator for PSLE?","e":"Method: estimate the real length of a scientific calculator (about 18 cm). Convert each option: 0.018 m = 1.8 cm (too short), 0.18 m = 18 cm (reasonable), 1.8 m = 180 cm and 18 m are far too long. Final answer: 0.18 m."} {"t":"q","id":25767,"q":"Last month, a florist sold 800 roses. This month, she sold 1000 roses. What was the percentage increase in the number of roses sold?","e":"Method: increase = \\(1000 - 800 = 200\\). Percentage increase = \\(\\dfrac{200}{800} \\times 100\\% = 25\\%\\). Final answer: 25%."} {"t":"q","id":25769,"q":"A lollipop cost $0.70. There were 80 lollipops in a box. Janie bought 8 such boxes of lollipops for her class party. How much did she spend on the lollipops?","e":"Method: total lollipops = \\(80 \\times 8 = 640\\). Total cost = \\(640 \\times \\$0.70 = \\$448\\). Final answer: $448."} {"t":"q","id":25771,"q":"Ranjeet and Samy made some birthday cards over two days. On Saturday, Ranjeet made 29 more cards than Samy. On Sunday, Ranjeet made another 30 cards and Samy made another 25 cards. At the end of the two days, Ranjeet made \\(\\dfrac{3}{5}\\) of the total number of cards. What was the total number of cards Samy made over the two days?","e":"Method: Ranjeet made \\(\\dfrac{3}{5}\\) of the total, so Samy made \\(\\dfrac{2}{5}\\); Ranjeet made \\(\\dfrac{3}{5}-\\dfrac{2}{5}=\\dfrac{1}{5}\\) more than Samy of the total. Ranjeet's extra cards over Samy = (29 on Sat) + (30\u221225 on Sun) = 29 + 5 = 34, and this difference equals \\(\\dfrac{1}{5}\\) of the total. So total = \\(34 \\times 5 = 170\\) cards. Samy made \\(\\dfrac{2}{5} \\times 170 = 68\\) cards. Final answer: 68."} {"t":"q","id":25772,"q":"Express \\(3\\dfrac{1}{4}\\) as a decimal.","e":"Method: convert the fraction part. \\(\\dfrac{1}{4} = 0.25\\), so \\(3\\dfrac{1}{4} = 3 + 0.25 = 3.25\\). Final answer: 3.25."} {"t":"q","id":25773,"q":"The volume of a cube is 125 cm\u00b3. Find the length of one edge of the cube.
Ans: cm","e":"Method: edge = cube root of the volume. \\(\\sqrt[3]{125} = 5\\) because \\(5 \\times 5 \\times 5 = 125\\). Final answer: 5 cm."} {"t":"q","id":25777,"q":"Find the circumference of a circle of diameter 28 m. (Take \u03c0 = \\(\\dfrac{22}{7}\\))
Ans: m","e":"Method: circumference = \\(\\pi \\times d = \\dfrac{22}{7} \\times 28 = 22 \\times 4 = 88\\) m. Final answer: 88 m."} {"t":"q","id":25780,"q":"Two numbers add up to 364. One of the numbers is a 2-digit number and the other is a 3-digit number. What is the smallest possible difference between the two numbers?
Ans: ","e":"Method: to make the difference smallest, make the 2-digit number as large as possible. The largest 2-digit number is 99, so the 3-digit number = \\(364 - 99 = 265\\). Difference = \\(265 - 99 = 166\\). Final answer: 166."} {"t":"q","id":25781,"q":"Use all the digits 7, 0, 4 and 5 to form
(a) the smallest multiple of 10
(b) the even number closest to 5000 ","e":"Method (a): a multiple of 10 ends in 0, so fix 0 last; arrange the remaining digits 4, 5, 7 in increasing order for the smallest number \u2192 4570. Method (b): the closest even number to 5000 starts with 5 and ends in an even digit (0 or 4); 5074 is even and is the value closest to 5000 using all four digits. Final answers: (a) 4570, (b) 5074."} {"t":"q","id":25782,"q":"Shanice had a bottle of shampoo. She used an equal amount of shampoo each day. At the end of the 7th day, \\(\\dfrac{4}{5}\\) of the bottle was left. At the end of the 15th day, the amount of shampoo left was 280 ml. What was the amount of shampoo in the bottle at first?
Ans: ml","e":"Method: \\(\\dfrac{4}{5}\\) left after 7 days means \\(\\dfrac{1}{5}\\) was used in 7 days, so each day uses \\(\\dfrac{1}{5} \\div 7 = \\dfrac{1}{35}\\) of the bottle. By the end of day 15, used = \\(\\dfrac{15}{35}\\), so left = \\(1 - \\dfrac{15}{35} = \\dfrac{20}{35}\\). \\(\\dfrac{20}{35}\\) of the bottle = 280 ml, so \\(\\dfrac{1}{35} \\to 14\\) ml and the whole bottle \\(= 35 \\times 14 = 490\\) ml. Final answer: 490 ml."} {"t":"q","id":25784,"q":"Devi collected \\(\\dfrac{5}{12}\\) as many foreign coins as Haminah. Haminah collected \\(\\dfrac{6}{7}\\) as many foreign coins as Liling. What was the ratio of the number of foreign coins Devi collected to the number of foreign coins Liling collected?","e":"Method: Devi : Haminah = 5 : 12. Haminah : Liling = 6 : 7. Make Haminah common: scale the second ratio so Haminah = 12: \\(6 : 7 = 12 : 14\\). So Devi : Haminah : Liling = 5 : 12 : 14. Therefore Devi : Liling = 5 : 14. Final answer: 5 : 14."} {"t":"q","id":25786,"q":"[Paper 2 Q2] A wheel of diameter 40 cm made 10 complete turns. Find the distance covered. (Take \u03c0 = 3.14)
Ans: cm","e":"Method: distance in one turn = circumference = \\(\\pi \\times d = 3.14 \\times 40 = 125.6\\) cm. In 10 turns = \\(125.6 \\times 10 = 1256\\) cm. Final answer: 1256 cm."} {"t":"q","id":25787,"q":"[Paper 2 Q3] The price of a pair of shoes was $80 before discount. Richard bought the pair of shoes at a discount of 15% during a sale. How much did he pay for the pair of shoes?
Ans: $","e":"Method: he pays \\(100\\% - 15\\% = 85\\%\\) of $80. \\(85\\% \\times 80 = 0.85 \\times 80 = \\$68\\). (Or discount = \\(15\\% \\times 80 = \\$12\\); \\(80 - 12 = \\$68\\).) Final answer: $68."} {"t":"q","id":25788,"q":"[Paper 2 Q4] A machine prints 390 posters in 13 minutes. At this rate, how long does it take to print 2250 posters?
Ans: min","e":"Method: rate = \\(390 \\div 13 = 30\\) posters per minute. Time for 2250 posters = \\(2250 \\div 30 = 75\\) minutes. Final answer: 75 min."} {"t":"q","id":25789,"q":"[Paper 2 Q5] The average of 6 consecutive whole numbers is 35.5. Find the smallest number.
Ans: ","e":"Method: total of the 6 numbers = \\(35.5 \\times 6 = 213\\). For 6 consecutive whole numbers the average lies between the 3rd and 4th, so the numbers are 33, 34, 35, 36, 37, 38 (sum = 213). The smallest is 33. Final answer: 33."} {"t":"q","id":25790,"q":"[Paper 2 Q6] There are 12 fewer workers in factory A than factory B. \\(\\dfrac{1}{8}\\) of the workers in factory A are male. There are 36 more female workers than male workers in factory A. How many workers are there in factory B?
Ans: ","e":"Method: in factory A, males = \\(\\dfrac{1}{8}\\), so females = \\(\\dfrac{7}{8}\\). Difference (female \u2212 male) = \\(\\dfrac{7}{8} - \\dfrac{1}{8} = \\dfrac{6}{8}\\) of A = 36 workers. So 6 units = 36 \u2192 1 unit = 6, and factory A = 8 units = 48 workers. Factory B has 12 more workers: \\(48 + 12 = 60\\). Final answer: 60 workers."} {"t":"q","id":25792,"q":"[Paper 2 Q8] Joe had a rectangular piece of paper, 36.8 cm by 29 cm. He cut out as many squares as possible from the paper. The side of each square was 5 cm. At most, how many squares did Joe cut out?
Ans: ","e":"Method: along the 36.8 cm side: \\(36.8 \\div 5 = 7\\) squares (remainder 1.8 cm wasted). Along the 29 cm side: \\(29 \\div 5 = 5\\) squares (remainder 4 cm wasted). Total squares = \\(7 \\times 5 = 35\\). Final answer: 35."} {"t":"q","id":25793,"q":"[Paper 2 Q9] Pedro had a 700-cm long rope. He cut it into 3 pieces, A, B and C. The length of rope A was divisible by 3 and 7. The length of rope B was 4 times the length of rope A. The total length of rope A and rope B was less than 450 cm. The length of rope C was longer than the length of rope A but shorter than the length of rope B.
(a) What was the length of rope C? cm
(b) What was the total length of rope A and rope B? cm","e":"Method: A is divisible by 3 and 7, so A is a multiple of 21. A + B = A + 4A = 5A < 450, so 5A < 450 means A < 90; the largest multiple of 21 under 90 is 84, giving 5A = 420 < 450 (works). Then C = total \u2212 (A + B) = \\(700 - 420 = 280\\) cm. Check C is between A (84) and B (336): 84 < 280 < 336 \u2014 true. (a) C = 280 cm. (b) A + B = 420 cm."} {"t":"q","id":25796,"q":"[Paper 2 Q12] Mrs Menon baked some cookies. 60% of the cookies were almond cookies and the rest were chocolate cookies. She then sold half of her almond cookies and had 78 almond cookies left.
(a) After the sale of the almond cookies, the percentage of cookies that were chocolate (increase \/ decrease \/ remain the same).
(b) How many cookies did Mrs Menon bake? ","e":"Method (a): originally chocolate = 40% of total. After selling half the almond cookies, almond drops but chocolate count is unchanged while the total falls, so chocolate as a percentage of the new total = 40\/70 \u2248 57.1%, which is an INCREASE. (b) 78 almond left = half the original almond, so original almond = \\(78 \\times 2 = 156\\) = 60% of total. Then \\(60\\% \\to 156\\) means \\(10\\% \\to 26\\) and \\(100\\% \\to 260\\). Final answers: (a) Increase, (b) 260 cookies."} {"t":"q","id":25797,"q":"[Paper 2 Q13] A rectangular tank with a base area of 3500 cm\u00b2 and a height of 80 cm was \\(\\dfrac{1}{4}\\)-filled with water at first. At 8 a.m., a tap was turned on and water was drained from the tank at the rate of 4 litres per minute. At 8.06 a.m., the tap was turned off.
(a) How much water was drained from the tank? litres
(b) After the tap was turned off, how much more water was needed to fill the tank completely? litres","e":"Method (a): from 8.00 to 8.06 a.m. is 6 minutes; drained = \\(4 \\times 6 = 24\\) litres. (b) Water at first = \\(\\dfrac{1}{4}\\) of tank: height \\(\\dfrac{1}{4} \\times 80 = 20\\) cm, volume = \\(3500 \\times 20 = 70000\\) cm\u00b3 = 70 litres. After draining 24 litres, water left = \\(70 - 24 = 46\\) litres. Full tank = \\(3500 \\times 80 = 280000\\) cm\u00b3 = 280 litres. More water needed = \\(280 - 46 = 234\\) litres. Final answers: (a) 24 litres, (b) 234 litres."} {"t":"q","id":25798,"q":"[Paper 2 Q14] A pencil and an eraser cost $1.05. A pencil and a ruler cost $0.85. Bernice paid $6.90 for 8 such pencils and 5 such erasers. Chandra paid $3.30 for some rulers.
(a) What was the cost of one such eraser? $
(b) How many such rulers did Chandra buy? ","e":"Method (a): 8 pencils + 5 erasers = $6.90. Also 5 pencils + 5 erasers = \\(5 \\times \\$1.05 = \\$5.25\\). Subtract: 3 pencils = \\(6.90 - 5.25 = \\$1.65\\), so 1 pencil = \\(1.65 \\div 3 = \\$0.55\\). Then eraser = \\(1.05 - 0.55 = \\$0.30\\). (b) Ruler = \\(0.85 - 0.55 = \\$0.30\\); rulers Chandra bought = \\(3.30 \\div 0.30 = 11\\). Final answers: (a) $0.30, (b) 11 rulers."} {"t":"q","id":25799,"q":"[Paper 2 Q15] Karl had clips of four different colours. \\(\\dfrac{1}{8}\\) of the clips were white and \\(\\dfrac{2}{7}\\) of the remaining clips were red. He had an equal number of blue clips and yellow clips. Karl had 35 blue clips.
(a) How many red clips did he have?
(b) Karl packed all the blue clips into small, medium, and large boxes. He filled each small box with 2 clips, each medium box with 3 clips and each large box with 6 clips. All the boxes were full and there were no clips left over. What was the least number of boxes used by Karl? ","e":"Method (a): blue = yellow = 35 each. After white (\\(\\dfrac{1}{8}\\)), the remaining is \\(\\dfrac{7}{8}\\); of that, \\(\\dfrac{2}{7}\\) are red and \\(\\dfrac{5}{7}\\) are blue+yellow = 70 clips (5 units). So 1 unit = 14, red = 2 units = 28 clips. (b) For the least number of boxes, use the largest boxes first. 35 blue clips: this is odd. Using key's grouping: 5 clips fill one medium (3) + one small (2); \\(35 = 30 + 5\\): five large boxes hold 30 (5\u00d76), then 1 medium (3) + 1 small (2) hold the last 5 \u2192 \\(5 + 1 + 1 = 7\\) boxes. Final answers: (a) 28 red clips, (b) 7 boxes."} {"t":"q","id":25801,"q":"[Paper 2 Q17] Two pouches, Y and Z, contained some gold tokens and silver tokens at first. In Pouch Y, the ratio of the number of gold tokens to the number of silver tokens was 3 : 1. In Pouch Z, the ratio of the number of gold tokens to the number of silver tokens was 1 : 4. Pouch Z had 5 times as many tokens as Pouch Y.
(a) What was the ratio of the number of gold tokens in Pouch Y to the number of silver tokens in Pouch Z? Give your answer in the form a:b, e.g. 3:16.
(b) After 24 gold tokens and 24 silver tokens were transferred from Pouch Z to Pouch Y, the ratio of the number of gold tokens to the number of silver tokens in Pouch Y became 9 : 5. What was the total number of tokens in Pouch Y in the end?
(c) What was the total number of tokens in both pouches, Y and Z, at first? ","e":"Method: (a) Pouch Y total = 4 parts (gold 3 : silver 1). Pouch Z has 5 times Y's tokens = 20 parts, split gold : silver = 1 : 4 \u2192 gold 4, silver 16. Gold in Y : silver in Z = 3 : 16. (b) After transfer, Y gold = original 3u + 24, Y silver = original 1u + 24; ratio = 9 : 5. Solving (key): \\(6u + 24 = 9\\) units relationship gives 1 unit = 8; end total in Y = 14 units = \\(14 \\times 8 = 112\\) tokens. (c) 1 unit = 8; total units at first = Y (4u) + Z (40u, since Z = 5\u00d7Y by count, i.e. 5\u00d78u=40u) = ... key: total units 40 + 8 = 48; total tokens = \\(48 \\times 8 = 384\\). Final answers: (a) 3 : 16, (b) 112, (c) 384."} {"t":"q","id":25802,"q":"What is the missing number in the box?
$3\\,000\\,000 + 10\\,000 + + 8 = 3\\,014\\,008$","e":"Method: subtract the known parts from the total. $3\\,014\\,008 - 3\\,000\\,000 - 10\\,000 - 8 = 4\\,000$. The missing number is 4000."} {"t":"q","id":25803,"q":"Use all the digits 4, 5, 6, 8 to form the greatest number between 5 000 and 6 000.
","e":"Method: the number must be between 5000 and 6000, so the thousands digit is 5. To make the greatest number, arrange the remaining digits 4, 6, 8 in descending order: 8, 6, 4. Greatest number = 5864."} {"t":"q","id":25804,"q":"How many halves are there in \\(5\\dfrac{1}{2}\\)?
","e":"Method: divide by one half. \\(5\\dfrac{1}{2} \\div \\dfrac{1}{2} = \\dfrac{11}{2} \\times \\dfrac{2}{1} = 11\\). There are 11 halves."} {"t":"q","id":25805,"q":"Arrange these fractions from the smallest to the largest.
\\(2\\dfrac{1}{2}\\) , \\(\\dfrac{13}{5}\\) , \\(2\\dfrac{3}{7}\\)","e":"Method: convert each to a decimal. \\(2\\dfrac{1}{2}=2.5\\); \\(\\dfrac{13}{5}=2.6\\); \\(2\\dfrac{3}{7}\\approx2.43\\). Smallest to largest: \\(2\\dfrac{3}{7}\\), \\(2\\dfrac{1}{2}\\), \\(\\dfrac{13}{5}\\)."} {"t":"q","id":25806,"q":"Mr Ravi bought some boxes of chocolates. Each box contained 12 chocolates. The total number of chocolates Mr Ravi bought was more than 50 but fewer than 100. Mr Ravi ate 7 chocolates and gave the rest equally to each of his 5 children. How many chocolates did each child get?
","e":"Method: the total is a multiple of 12 between 50 and 100 (60, 72, 84, 96). After eating 7 the rest must divide exactly by 5. $72 - 7 = 65$ and $65 \\div 5 = 13$. Each child got 13 chocolates."} {"t":"q","id":25807,"q":"Fill in the boxes with the correct mathematical symbols. Each symbol can only be used once. The symbols are $+$ , $-$ , $\\times$ , $\\div$ .
$56 \\;\\square\\; 4 + 3 \\;\\square\\; 8 = 38$","e":"Method: test the symbols using order of operations. $56 \\div 4 + 3 \\times 8 = 14 + 24 = 38$. So the first box is $\\div$ and the second box is $\\times$."} {"t":"q","id":25808,"q":"Eva spent \\(\\dfrac{1}{7}\\) of her savings on a gift for her brother. Then, she spent \\(\\dfrac{2}{3}\\) of the remainder on a school bag. What fraction of her savings had she left? Give your answer in the simplest form.","e":"Method: after the gift, the remainder is \\(1-\\dfrac{1}{7}=\\dfrac{6}{7}\\). She spent \\(\\dfrac{2}{3}\\) of that on the bag, leaving \\(\\dfrac{1}{3}\\) of the remainder. Fraction left \\(=\\dfrac{1}{3}\\times\\dfrac{6}{7}=\\dfrac{6}{21}=\\dfrac{2}{7}\\)."} {"t":"q","id":25809,"q":"Terry had 3 times as many $2-notes as $5-notes. He had $385 altogether. How many $5-notes did Terry have?
","e":"Method: let the number of $5-notes be 1 unit, so the $2-notes are 3 units. Value of 1 group = $5 + 3 \\times $2 = $5 + $6 = $11. Number of $5-notes = $385 \\div $11 = 35."} {"t":"q","id":25810,"q":"Aminah had an equal number of sunflowers and roses. She gave away \\(\\dfrac{3}{5}\\) of the sunflowers and some roses. In the end, she was left with \\(\\dfrac{1}{4}\\) of the total number of flowers. What fraction of the roses did she give away?","e":"Method: let sunflowers = roses = 10 units each, total 20 units. She kept \\(\\dfrac{2}{5}\\) of the sunflowers = 4 units. She was left with \\(\\dfrac{1}{4}\\) of 20 = 5 units in total, so roses left = 5 - 4 = 1 unit. Roses given away = 10 - 1 = 9 units. Fraction of roses given away = \\(\\dfrac{9}{10}\\)."} {"t":"q","id":25811,"q":"Tim and Jerry were paid a total of $8568 for selling tickets. Tim was paid $5304 more than Jerry. (a) How much was Tim paid for selling the tickets? $
(b) Tim and Jerry were paid based on the number of tickets they sold. Tim sold 3 times as many tickets as Jerry. Tim was paid $5 more than Jerry for selling each ticket. How many tickets did Tim sell? ","e":"(a) Difference is $5304, total $8568. Jerry = (8568 - 5304) \u00f7 2 = 3264 \u00f7 2 = $1632; Tim = 1632 + 5304 = $6936. (b) Tim sold 3 times as many tickets, so Tim's price per ticket = 6936 \u00f7 (3 units) per Jerry's units; per-ticket pay difference is $5. Jerry's per-ticket pay: Tim sold 3J tickets at price (p+5), Jerry sold J at price p: 3J(p+5) = 6936 and Jp = 1632. From key: 6936 \u00f7 3 = 2312, 2312 - 1632 = 680, 680 \u00f7 5 = 136 (= Jerry's tickets J), Tim's tickets = 136 \u00d7 3 = 408."} {"t":"q","id":25812,"q":"Ruth needs 90 pieces of ribbons each of length \\(\\dfrac{4}{5}\\) m to decorate a room. Ribbon is sold in rolls of 10 m each. (a) What is the maximum number of pieces of ribbon she can get from a roll of 10 m?
(b) What is the least number of rolls of ribbon that Ruth needs to buy? ","e":"(a) From one 10 m roll, number of \\(\\dfrac{4}{5}\\) m pieces = \\(10 \\div \\dfrac{4}{5} = 10 \\times \\dfrac{5}{4} = 12.5\\); the maximum whole pieces is 12. (b) She needs 90 pieces; 90 \u00f7 12 = 7.5, so she must buy 8 whole rolls."} {"t":"q","id":25815,"q":"Kim has some red, blue and green beads. The ratio of the number of red beads to the number of blue beads is 1 : 2. The number of green beads to the total number of blue and red beads is 1 : 4. What is the ratio of the number of red beads to the number of blue beads to the number of green beads?","e":"Red : Blue = 1 : 2, so let red = 1u, blue = 2u; red + blue = 3u. Green : (red + blue) = 1 : 4, so green : 3u = 1 : 4, meaning 3u corresponds to 4 parts. Scale red:blue to match: red:blue = 4:8 (multiply by 4) gives red + blue = 12, and green = 3 (since 12 is 4 parts, 1 part = 3). So Red : Blue : Green = 4 : 8 : 3. Answer: option 3."} {"t":"q","id":25820,"q":"In a box, 25% of the keychains are from Thailand and 45% of the keychains are from Singapore. The remaining 45 keychains are from other countries. How many keychains are there in the box?
","e":"Thailand + Singapore = 25% + 45% = 70%. Remaining = 100% - 70% = 30%, which equals 45 keychains. So 1% = 45 \u00f7 30 = 1.5 keychains; 100% = 1.5 \u00d7 100 = 150 keychains. Answer: 150."} {"t":"q","id":25822,"q":"Jane and Patrick bought a box of badges. Jane took \\(\\dfrac{7}{10}\\) of the badges and Patrick took the rest. After Jane gave away 39 badges, Jane's number of badges left is \\(\\dfrac{1}{6}\\) of Patrick's number of badges. How many badges did Jane have in the end?
","e":"Jane took \\(\\dfrac{7}{10}\\), Patrick took \\(\\dfrac{3}{10}\\). Let total = 10u: Jane = 7u, Patrick = 3u. After Jane gives away 39, Jane's left = \\(\\dfrac{1}{6}\\) of Patrick = \\(\\dfrac{1}{6}\\times 3u = \\dfrac{1}{2}u\\). So 7u - 39 = \\(\\dfrac{1}{2}u\\) \u2192 \\(6\\dfrac{1}{2}u = 39\\) \u2192 \\(\\dfrac{13}{2}u = 39\\) \u2192 u = 6. Jane in the end = \\(\\dfrac{1}{2}u = \\dfrac{1}{2}\\times 6 = 3\\). Answer: 3."} {"t":"q","id":25823,"q":"Kylie received a fixed sum of salary monthly. In January, she saved 20% of her salary. Her savings in February increased by 40%. Her total savings for the 2 months was $480. What was the sum of salary given to her monthly?
$","e":"January savings = 20% of salary. February savings = 140% of January = 140% \u00d7 20% = 28% of salary. Total savings = 20% + 28% = 48% of salary = $480. So 1% = $480 \u00f7 48 = $10; salary = $10 \u00d7 100 = $1000. Answer: $1000."} {"t":"q","id":25826,"q":"There is a total of 400 red and blue marbles in a container. After 64 red marbles are added into the container and 7% of the blue marbles are removed from the container, 443 marbles are left in the container. How many blue marbles are there in the container in the end?
","e":"After adding 64 red marbles, the count would be 400 + 64 = 464 if no blue were removed. Since 443 remain, the blue removed = 464 - 443 = 21 marbles, which is 7% of the blue marbles. So 1% of blue = 21 \u00f7 7 = 3; total blue at first = 3 \u00d7 100 = 300. Blue in the end = 100% - 7% = 93% of 300 = 93 \u00d7 3 = 279. Answer: 279."} {"t":"q","id":25828,"q":"The pupils in a class are divided equally into Team A and Team B. The ratio of the number of girls to the number of boys in Team A is 4 : 3. The ratio of the number of girls to the number of boys in Team B is 3 : 1. What is the ratio of the number of girls to the number of boys in the class?","e":"Teams are equal in size. Team A girls:boys = 4:3 (total 7 parts); Team B girls:boys = 3:1 (total 4 parts). To make team totals equal, scale to a common total: LCM of 7 and 4 = 28. Team A \u00d74 \u2192 girls 16, boys 12 (total 28). Team B \u00d77 \u2192 girls 21, boys 7 (total 28). Class girls = 16 + 21 = 37; class boys = 12 + 7 = 19. Ratio girls : boys = 37 : 19. Answer: option 1."} {"t":"q","id":25831,"q":"Three boxes, X, Y, and Z contained a total of 848 marbles at first. 120 marbles were removed from Box X. The number of marbles in Box Y was doubled. \\(\\dfrac{1}{5}\\) of the marbles in Box Z were given away. In the end, the ratio of the number of marbles in Box X to that of Box Y to that of Box Z was 1 : 2 : 1. How many marbles were there in Box X at first?
","e":"In the end X : Y : Z = 1 : 2 : 1. Let end X = 1u, Y = 2u, Z = 1u. Working backwards: X at first = 1u + 120. Y was doubled to reach 2u, so Y at first = 2u \u00f7 2 = 1u. Z had \\(\\dfrac{1}{5}\\) given away leaving \\(\\dfrac{4}{5}\\) = 1u, so Z at first = 1u \u00f7 \\(\\dfrac{4}{5}\\) = \\(\\dfrac{5}{4}u = 1.25u\\). Total at first = (1u + 120) + 1u + 1.25u = 3.25u + 120 = 848. So 3.25u = 728, u = 224. Box X at first = 1u + 120 = 224 + 120 = 344. Answer: 344."} {"t":"q","id":25832,"q":"Below are the prices of facial masks from three different stores.
Store A \u2014 Original price: $4.20 for 1 mask. Promotion: 50% discount for all masks!
Store B \u2014 Original price: $25.90 for 1 pack of 10. Promotion: For each pack bought, buy a 2nd pack at 40% discount!
Store C \u2014 Original price: $3.80 for 1 mask. Promotion: Buy 5 get 4 free!
Of the three stores, which store should Mrs Chong buy from if she wants to spend the least amount of money for 100 masks, and how much would she need to pay?","e":"Store A: 50% off $4.20 = $2.10 per mask; 100 masks = 100 \u00d7 $2.10 = $210. Store B: 1 pack of 10 = $25.90; buying in pairs, 2nd pack at 40% off = $25.90 + 60% \u00d7 $25.90 = $25.90 + $15.54 = $41.44 per 20 masks. 100 masks = 5 pairs = 5 \u00d7 $41.44 = $207.20. Store C: buy 5 get 4 free means 9 masks for 5 \u00d7 $3.80 = $19; for 99 masks (11 sets of 9) = 11 \u00d7 $19 = $209, plus 1 more mask at $3.80 = $212.80 for 100. Cheapest is Store B at $207.20. Answer: option 1."} {"t":"q","id":25833,"q":"Divide \\(\\dfrac{3}{4}\\) by 12.","e":"Method: divide a fraction by a whole number. \\(\\dfrac{3}{4} \\div 12 = \\dfrac{3}{4} \\times \\dfrac{1}{12} = \\dfrac{3}{48} = \\dfrac{1}{16}\\). Answer: \\(\\dfrac{1}{16}\\)."} {"t":"q","id":25834,"q":"Serena has 3 times as much money as Maju. Ting Xi has \\(\\dfrac{1}{2}\\) as much money as Serena. What is the ratio of the amount of money that Maju has to the amount of money Ting Xi has to the amount of money Serena has?","e":"Method: set Maju = 1 unit, so Serena = 3 units, and Ting Xi = \\(\\dfrac{1}{2} \\times 3 = 1\\dfrac{1}{2}\\) units. Multiply all by 2 to clear the half: Maju = 2, Ting Xi = 3, Serena = 6. Maju : Ting Xi : Serena = 2 : 3 : 6."} {"t":"q","id":25835,"q":"\\(\\dfrac{4}{5}\\) of a bag of flour weighs \\(\\dfrac{2}{3}\\) kg. How much do 2 bags of flour weigh?","e":"Method: find 1 bag first. 1 bag \\(= \\dfrac{2}{3} \\div \\dfrac{4}{5} = \\dfrac{2}{3} \\times \\dfrac{5}{4} = \\dfrac{10}{12} = \\dfrac{5}{6}\\) kg. 2 bags \\(= 2 \\times \\dfrac{5}{6} = \\dfrac{10}{6} = 1\\dfrac{2}{3}\\) kg."} {"t":"q","id":25836,"q":"Arrange the following fractions from the smallest to the largest.
\\(\\dfrac{3}{8}\\), \\(\\dfrac{1}{3}\\), \\(\\dfrac{3}{10}\\)","e":"Method: convert to decimals. \\(\\dfrac{3}{8} = 0.375\\), \\(\\dfrac{1}{3} \\approx 0.333\\), \\(\\dfrac{3}{10} = 0.3\\). Smallest to largest: \\(0.3, 0.333, 0.375\\), i.e. \\(\\dfrac{3}{10}, \\dfrac{1}{3}, \\dfrac{3}{8}\\)."} {"t":"q","id":25838,"q":"Germaine uses the four letters A, B, C and D to form a pattern. The first 18 letters are shown. Find the ratio of the number of letter A to the number of letter C for the first 25 letters.
A B A C D D A B A B A C D D A B A B ...","e":"Method: extend the given pattern to 25 letters and count. Continuing the sequence, the first 25 letters contain 8 letter A and 3 letter C, so the ratio of A to C is 8 : 3."} {"t":"s","id":18353,"s":"Lighter boy = (total \u2212 difference) \u00f7 2 = (72.9 \u2212 9.3) \u00f7 2 = 63.6 \u00f7 2 = 31.8 kg. Final answer: 31.8 kg.\n\n\u2014 Model method \u2014\nLighter boy \\(=\\) (total \\(-\\) difference) \\(\\div 2 = (72.9 - 9.3) \\div 2 = 63.6 \\div 2 = 31.8\\) kg.\n[[model:p6\/solutions\/nan-hua-2023-p6-prelim-q31.png]]"} {"t":"s","id":18355,"s":"10 minutes = 600 seconds. Number of 5-second intervals = 600 \u00f7 5 = 120. Pages = 120 \u00d7 8 = 960. Final answer: 960."} {"t":"s","id":18357,"s":"(a) 3 \u00f7 \\(\\dfrac{2}{5}\\) = 3 \u00d7 \\(\\dfrac{5}{2}\\) = \\(\\dfrac{15}{2}\\) = 7\\(\\dfrac{1}{2}\\), so there are 7 full \\(\\dfrac{2}{5}\\) m pieces. (b) Used = 7 \u00d7 \\(\\dfrac{2}{5}\\) = \\(\\dfrac{14}{5}\\) = 2.8 m. Last piece = 3 \u2212 2.8 = 0.2 m (= \\(\\dfrac{1}{5}\\) m). Final answers: (a) 7, (b) 0.2 m.\n\n\u2014 Model method \u2014\n\\(3 \\div \\dfrac{2}{5} = 3 \\times \\dfrac{5}{2} = \\dfrac{15}{2} = 7\\tfrac{1}{2}\\), so there are 7 full \\(\\dfrac{2}{5}\\) m pieces. Used \\(= 7 \\times \\dfrac{2}{5} = \\dfrac{14}{5} = 2.8\\) m. Last piece \\(= 3 - 2.8 = 0.2\\) m.\n[[model:p6\/solutions\/nan-hua-2023-p6-prelim-q36.png]]"} {"t":"s","id":18358,"s":"Boys = 70%, Girls = 30% of original. New boys = 120% \u00d7 70% = 84%; new girls = 150% \u00d7 30% = 45%. New total = 84% + 45% = 129% of original. Increase = 129% \u2212 100% = 29% = 87, so 1% = 3 and original = 300. End total = 129% = 129 \u00d7 3 = 387. Final answer: 387.\n\n\u2014 Model method \u2014\nOriginal: Boys \\(= 70\\%\\), Girls \\(= 30\\%\\). New boys \\(= 120\\% \\times 70\\% = 84\\%\\); new girls \\(= 150\\% \\times 30\\% = 45\\%\\). New total \\(= 84\\% + 45\\% = 129\\%\\) of original. Increase \\(= 29\\% = 87\\), so \\(1\\% = 3\\). End total \\(= 129 \\times 3 = 387\\).\n[[model:p6\/solutions\/nan-hua-2023-p6-prelim-q37.png]]"} {"t":"s","id":18361,"s":"Change in total = 98 \u2212 48 = 50 marks. Change in average = 82 \u2212 80 = 2 marks. Number of students = change in total \u00f7 change in average = 50 \u00f7 2 = 25. Final answer: 25."} {"t":"s","id":18363,"s":"Tim : Peter = 2 : 3, total 5 units (unchanged total ignoring transfers \u2014 use model). After: Tim +120, Peter \u2212120, Tim : Peter = 2 : 1. Combined unchanged total stays; aligning units: before 2 : 3 = 10u : 15u... per key Tim = $180 at first. Working: 4 units = 120 \u2192 1 unit = 30; Tim at first \u2192 $30 \u00d7 6 = $180. Final answer: $180.\n\n\u2014 Model method \u2014\nTim : Peter \\(= 2 : 3\\) (5 units). The total stays the same. After Tim \\(+\\$120\\) and Peter \\(-\\$120\\), Tim : Peter \\(= 2 : 1\\). Match the unchanged total of 15 parts: before \\(6 : 9\\), after \\(10 : 5\\). The shift is \\(4\\) parts \\(= \\$120\\), so \\(1\\) part \\(= \\$30\\). Tim at first \\(= 6 \\times \\$30 = \\$180\\).\n[[model:p6\/solutions\/nan-hua-2023-p6-prelim-q43.png]]"} {"t":"s","id":18368,"s":"The tens digit of 76 523 is 2 (less than 5), so round down: the hundreds digit stays 5. 76 523 rounds to 76 500."} {"t":"s","id":18369,"s":"The first digit after the decimal point is the tenths place. In 89.76 that digit is 7."} {"t":"s","id":18375,"s":"Pens packed = 5 \u00d7 6 = 30. He gave away 9 first, so at first j = 30 + 9 = 39."} {"t":"s","id":18379,"s":"White = \\(\\dfrac{9}{9}-\\dfrac{5}{9}=\\dfrac{4}{9}\\) of the total, and white = 1600, so total = 1600 \u00f7 4 \u00d7 9 = 3600. Red fraction = \\(\\dfrac{1200}{3600}=\\dfrac{1}{3}\\)."} {"t":"s","id":18381,"s":"Common denominator 20: blueberry = \\(\\dfrac{5}{20}\\), chocolate = \\(\\dfrac{8}{20}\\), strawberry = \\(\\dfrac{20-5-8}{20}=\\dfrac{7}{20}\\). Strawberry : blueberry : chocolate = 7 : 5 : 8."} {"t":"s","id":18382,"s":"The pattern repeats in blocks of 7 letters (K L M M K L N). 338 \u00f7 7 = 48 remainder 2. The 2nd letter of the block is L."} {"t":"s","id":18383,"s":"Fraction left = \\(1-\\dfrac{3}{8}=\\dfrac{5}{8}\\). Stickers left = \\(\\dfrac{5}{8}\\times 32 = 20\\)."} {"t":"s","id":18386,"s":"Factors of 12: 1, 2, 3, 4, 6, 12. Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42. Common factors: 1, 2, 3 and 6."} {"t":"s","id":18388,"s":"Dinner = \\(\\dfrac{5}{12}\\) h = 25 min. Travel = 2 \u00d7 25 = 50 min. Total = 25 + 50 = 75 min = 1 h 15 min. 17 05 + 1 h 15 min = 18 20."} {"t":"s","id":18389,"s":"Increase = 50 \u2212 40 = 10 cars. Percentage increase = \\(\\dfrac{10}{40}\\times 100\\% = 25\\%\\)."} {"t":"s","id":18390,"s":"The number = 287 \u00d7 4 = 1148. Correct answer = 1148 \u00f7 7 = 164."} {"t":"s","id":18392,"s":"5 \u00f7 \\(\\dfrac{7}{10}\\) = 5 \u00d7 \\(\\dfrac{10}{7}\\) = \\(\\dfrac{50}{7}\\) = 7\\(\\dfrac{1}{7}\\). Since the last partly-filled cup still needs a cup, he needs 7 + 1 = 8 cups."} {"t":"s","id":18395,"s":"Boxes = 4y = 4 \u00d7 8 = 32. Total tarts = 32 \u00d7 15 = 480. Sold = 2 \u00d7 15 = 30. Left = 480 \u2212 30 = 450."} {"t":"s","id":18396,"s":"Mass of 1 lamp = \\(\\dfrac{k}{5}\\) kg. The vase is 2 kg lighter than a lamp, so vase = \\(\\left(\\dfrac{k}{5}-2\\right)\\) kg."} {"t":"s","id":18398,"s":"Total X + Y + Z = 56 \u00d7 3 = 168. For X to be smallest, Z should be largest 2-digit value. X = \\(\\dfrac{2}{3}\\)Y means Y is a multiple of 3 and X is even. Taking Z = 70 gives X + Y = 98; with X = \\(\\dfrac{2}{3}\\)Y, then \\(\\dfrac{5}{3}\\)Y = 98 \u2192 not whole. Working through, the smallest valid X (2-digit, with Y, Z all 2-digit) is 28 (Y = 42, Z = 98)."} {"t":"s","id":18399,"s":"GST = 8% of $890 = $71.20. Price after GST = $890 + $71.20 = $961.20. (Or 108% \u00d7 $890 = $961.20.)"} {"t":"s","id":18402,"s":"9 chicken = 5 beef in cost. The 4 extra chicken puffs (9 \u2212 5) cost the same as the 5 \u00d7 $1.20 = $6.00 extra on the beef puffs. So 4 chicken puffs = $6.00 \u2192 1 chicken puff = $1.50. Mrs Tan spent 9 \u00d7 $1.50 = $13.50; Mrs Lim spent the same $13.50. Altogether = $27."} {"t":"s","id":18403,"s":"Each started with the same amount; let it be a multiple of 7, 4 and 9 (LCM 252) \u2192 252 units each. Sticks left: Janet \\(\\tfrac{3}{7}\\) = 108, Samuel \\(\\tfrac{1}{4}\\) = 63, Farhana \\(\\tfrac{7}{9}\\) = 196, total left = 367 units = 1265 sticks \u2192 not whole, so scale: total-left fraction sum = \\(\\tfrac{9}{21}+\\tfrac{?}\\)\u2026 Using common units, 1 unit = 1265 \u00f7 55 = 23, and each used = 12 units \u00d7 23 = 276. Each used 276 ice-cream sticks."} {"t":"s","id":18404,"s":"Total girl-hours = 3 girls \u00d7 2 h = 6 girl-hours. Shared among 5 girls: 6 \u00f7 5 = \\(\\dfrac{6}{5}\\) h = 1\\(\\dfrac{1}{5}\\) h = 1 h 12 min each."} {"t":"s","id":18405,"s":"In the time Patrick covered half the distance, John was 30 km behind, so Patrick is 30 km ahead at the halfway mark. The 30 km gap is built up over the time to the midpoint at a 25 km\/h speed difference: time to midpoint = 30 \u00f7 25 = 1.2 h = 1 h 12 min. Patrick reaches Town B (full distance) in twice that = 2.4 h = 2 h 24 min. 08 00 + 2 h 24 min = 10 24."} {"t":"s","id":18409,"s":"(a) Let girls = G, boys = B. One girl up: B = \\(\\tfrac{1}{2}\\)(G\u22121) \u2192 G \u2212 1 = 2B. One boy up: (G) : (B\u22121) = 9 : 4. Solving: from G = 2B + 1 and 4G = 9(B\u22121) \u2192 4(2B+1) = 9B \u2212 9 \u2192 8B + 4 = 9B \u2212 9 \u2192 B = 13, G = 27. Total = 27 + 13 = 40. (b) Let x leave each of girls and boys: (27\u2212x) : (13\u2212x) = 9 : 2 \u2192 2(27\u2212x) = 9(13\u2212x) \u2192 54 \u2212 2x = 117 \u2212 9x \u2192 7x = 63 \u2192 x = 9. Total who left = 9 + 9 = 18."} {"t":"s","id":18413,"s":"To convert a percentage to a decimal, divide by 100. \\(2.5\\% = 2.5 \\div 100 = 0.025\\). Answer: 0.025."} {"t":"s","id":18414,"s":"To write a fraction as a percentage, multiply by 100%. \\(\\dfrac{3}{4} \\times 100\\% = 75\\%\\). Answer: 75%."} {"t":"s","id":18416,"s":"Length of 1 piece = \\(624 \\div 600 = 1.04\\) m. Length of 10 pieces = \\(1.04 \\times 10 = 10.4\\) m. Answer: 10.4 m."} {"t":"s","id":18417,"s":"Total mass of girls = \\(4 \\times 36 = 144\\) kg. Total mass of boys = \\(2 \\times 54 = 108\\) kg. Total mass = \\(144 + 108 = 252\\) kg. Average = \\(252 \\div 6 = 42\\) kg. Answer: 42 kg."} {"t":"s","id":18418,"s":"\\(0.002 \\times 5000 = 0.001 \\times 5000 \\times 2 = 5 \\times 2 = 10\\). Answer: 10."} {"t":"s","id":18419,"s":"Total mass = \\(1054 \\times 2 = 2108\\) g. Convert to kg: \\(2108 \\div 1000 = 2.108\\) kg. Answer: 2.108 kg."} {"t":"s","id":18420,"s":"Sum of the two numbers = \\(37 \\times 2 = 74\\). Other number = \\(74 - 14 = 60\\). Answer: 60."} {"t":"s","id":18424,"s":"(a) Red beads = \\(\\dfrac{60}{100} \\times 120 = 72\\). (b) Blue beads at start = \\(120 - 72 = 48\\). Red left after removing 21 = \\(72 - 21 = 51\\). Since red left is 3 times blue left, blue left = \\(51 \\div 3 = 17\\). Blue removed = \\(48 - 17 = 31\\). Answers: (a) 72, (b) 31."} {"t":"s","id":18426,"s":"Sixty-three thousand = 63 000; and forty = 40. So 63 000 + 40 = 63 040. Answer: 63 040."} {"t":"s","id":18428,"s":"Convert the mixed number to an improper fraction: \\(4\\dfrac{5}{7} = \\dfrac{4\\times 7 + 5}{7} = \\dfrac{33}{7}\\). Answer: \\(\\dfrac{33}{7}\\)."} {"t":"s","id":18430,"s":"In 50 146, the digit 5 is in the ten-thousands place, so its value is 5 \\(\\times\\) 10 000 = 50 000. Answer: 50 000."} {"t":"s","id":18431,"s":"Fraction left = \\(1 - \\dfrac{5}{8} = \\dfrac{3}{8}\\). Vegetables left = \\(\\dfrac{3}{8}\\times 4 = \\dfrac{12}{8} = 1\\dfrac{1}{2}\\) kg. Answer: \\(1\\dfrac{1}{2}\\) kg."} {"t":"s","id":18432,"s":"Compare to thousandths: 0.130, 0.310, 0.103, 0.301. The smallest is 0.103. Answer: 0.103."} {"t":"s","id":18437,"s":"First 10 tickets cost 10 \\(\\times\\) $8 = $80. Remaining = $160 \u2212 $80 = $80. Additional tickets = $80 \u00f7 $5 = 16. Total tickets = 10 + 16 = 26. Answer: 26."} {"t":"s","id":18439,"s":"Percentage = \\(\\dfrac{60}{300}\\times 100\\% = 20\\%\\). Answer: 20%."} {"t":"s","id":18440,"s":"Let Peter have P stamps; John has P + 30. After Peter gives 18: Peter = P \u2212 18, John = P + 48. John = 3 \\(\\times\\) Peter: P + 48 = 3(P \u2212 18) = 3P \u2212 54. So 102 = 2P, P = 51. Answer: 51."} {"t":"s","id":18441,"s":"Multiples of 7: ..., 49, 56, 63. The largest multiple of 7 below 60 is 56 (since 63 > 60). Answer: 56."} {"t":"s","id":18442,"s":"The tenths digit is 6; the next digit (hundredths) is 5, so round up: 33.652 \u2192 33.7. Answer: 33.7."} {"t":"s","id":18443,"s":"\\(\\dfrac{2}{9}\\times\\dfrac{3}{5} = \\dfrac{2\\times 3}{9\\times 5} = \\dfrac{6}{45} = \\dfrac{2}{15}\\). Answer: \\(\\dfrac{2}{15}\\)."} {"t":"s","id":18444,"s":"1 week = 7 days. Slices = 65 \\(\\times\\) 7 = 455. Answer: 455."} {"t":"s","id":18445,"s":"Brackets first: 24 \u2212 6 = 18. Then \u00f7 and \\(\\times\\) left to right: 18 \u00f7 6 = 3, 3 \\(\\times\\) 3 = 9. Finally 20 + 9 = 29. Answer: 29."} {"t":"s","id":18446,"s":"42 \u00f7 7 = 6 sets of 7 posters. Time = 6 \\(\\times\\) 3 = 18 minutes. Answer: 18 min."} {"t":"s","id":18447,"s":"Difference longest \u2212 shortest = 7u \u2212 2u = 5u = 40 cm, so 1u = 8 cm. Total = 2 + 4 + 7 = 13u = 13 \\(\\times\\) 8 = 104 cm = 1.04 m. Answer: 1.04 m."} {"t":"s","id":18448,"s":"1 big cube takes the space of 48 \u00f7 12 = 4 small cubes. 6 big cubes take 6 \\(\\times\\) 4 = 24 small-cube spaces. Used so far = 24 + 7 = 31 small-cube spaces. Remaining = 48 \u2212 31 = 17 small cubes. Answer: 17."} {"t":"s","id":18450,"s":"Let Raju = R. Joel = R + 35. Carol = R + 215. Carol = (Raju + Joel) + 148, so R + 215 = (R + R + 35) + 148 = 2R + 183. Then 215 = R + 183, R = 32. Answer: $32."} {"t":"s","id":18451,"s":"Total for 5 days = average \\(\\times\\) 5 = 8 \\(\\times\\) 5 = 40 pages. Mon\u2013Thu = 6 + 5 + 8 + 7 = 26. Friday = 40 \u2212 26 = 14. Answer: 14."} {"t":"s","id":18453,"s":"Caili had $24 more than Annie, so Annie = $84 \u2212 $24 = $60. Annie : Ben = 4 : 1, so Ben = $60 \u00f7 4 = $15. Answer: $15."} {"t":"s","id":18456,"s":"7500 ml \u00f7 6 = 1250 ml per container. Convert to litres: 1250 ml = 1.25 \u2113. Answer: 1.25 \u2113."} {"t":"s","id":18457,"s":"Total ratio units = 3 + 1 + 5 = 9, so the total apples must be a multiple of 9 that is less than 40: 9, 18, 27 or 36. Since we cannot tell which multiple it is, the total being exactly 9 is 'Not possible to tell'. Answer: Not possible to tell."} {"t":"s","id":18458,"s":"Adam : Chloe = 3 : 1, so Adam \u2212 Chloe = 3u \u2212 1u = 2u. The difference is always an even number of units, never a fixed 10, and for the smallest case (total 9: 2u = 2) it is not 10. The statement is False. Answer: False."} {"t":"s","id":18460,"s":"Small envelope 30 g falls in the 'not over 40 g' band = $0.38. Large envelope 400 g falls in the 'not over 500 g' band = $1.15. Total = $0.38 + $1.15 = $1.53. Answer: $1.53."} {"t":"s","id":18461,"s":"Common denominator: \\(\\dfrac{1}{3}=\\dfrac{5}{15}\\), \\(\\dfrac{1}{5}=\\dfrac{3}{15}\\); spent = \\(\\dfrac{8}{15}\\), so left = \\(\\dfrac{7}{15}\\). Take 15 units total: 7u = $168, 1u = $24. Handbag = 3u = $72. Answer: $72."} {"t":"s","id":18463,"s":"Remaining after blue = \\(1-\\dfrac{4}{5}=\\dfrac{1}{5}\\). Red = \\(\\dfrac{3}{4}\\) of the remaining \\(\\dfrac{1}{5}=\\dfrac{3}{20}\\) of the total. So \\(\\dfrac{3}{20}\\) of total = 48; \\(\\dfrac{1}{20}\\) = 16; total = 16 \\(\\times\\) 20 = 320. Answer: 320."} {"t":"s","id":18464,"s":"At first, mugs : cups = 4 : 1, total 5 units = 185, so 1u = 37 cups, mugs = 4 \\(\\times\\) 37 = 148. After 70 mugs sold, mugs left = 148 \u2212 70 = 78. Cups left = mugs left \u00f7 3 = 78 \u00f7 3 = 26. Answer: 26."} {"t":"s","id":18468,"s":"Women = 30% of 1050 = 0.3 \\(\\times\\) 1050 = 315. Answer: 315."} {"t":"s","id":18469,"s":"Women = 315, men = 1050 \u2212 315 = 735. Women who did not finish = 20% of 315 = 0.2 \\(\\times\\) 315 = 63. Men who did not finish = 230 \u2212 63 = 167. Men who finished = 735 \u2212 167 = 568. Answer: 568."} {"t":"s","id":18470,"s":"The difference in paperclips per friend is 20 \u2212 14 = 6. The total shortfall difference = 4 + 68 = 72. Number of friends = 72 \u00f7 6 = 12. Paperclips = 14 \\(\\times\\) 12 + 4 = 168 + 4 = 172. Answers: (a) 12 friends, (b) 172 paperclips."} {"t":"s","id":18471,"s":"Alex = \\(\\dfrac{3}{5}\\) of total, so Ben + Charles = \\(\\dfrac{2}{5}\\) of total = 4 parts (Ben 3 + Charles 1). Let total be 10 units: Alex = 6u, Ben = 3u, Charles = 1u. Alex \u2212 Charles = 6u \u2212 1u = 5u = 120, so 1u = 24. Total = 10u = 240 stickers. Answer: 240."} {"t":"s","id":18472,"s":"Alex = \\(\\dfrac{3}{5}\\) of the total = 6 units out of 10. Ben + Charles = \\(\\dfrac{2}{5}\\) = 4 units, split as Ben 3 : Charles 1. So Charles = 1 unit out of 10 = \\(\\dfrac{1}{10}\\). Answer: \\(\\dfrac{1}{10}\\)."} {"t":"s","id":18473,"s":"Cost of a pie = $4 \u2212 $1.80 = $2.20. Group 1 sandwich + 1 pie = $4 + $2.20 = $6.20. Number of groups = $279 \u00f7 $6.20 = 45. Total paid for pies = 45 \\(\\times\\) $2.20 = $99. Answer: $99."} {"t":"s","id":18477,"s":"Method: find a percentage part of a whole. \\(75\\% \\times 180 = \\dfrac{75}{100} \\times 180 = 135\\). Answer: 135."} {"t":"s","id":18478,"s":"Method: total volume then convert and divide. Total = \\(10.5 + 6.8 = 17.3\\ \\ell\\). Convert: \\(17.3 \\times 1000 = 17300\\) ml. Divide: \\(17300 \\div 4 = 4325\\) ml. Answer: 4325 ml."} {"t":"s","id":18479,"s":"Method: GST is a percentage of the cost. \\(7\\% \\times 2460 = \\dfrac{7}{100} \\times 2460 = 172.20\\). Answer: $172.20."} {"t":"s","id":18480,"s":"Method: find how many 200 g portions, then multiply. \\(200\\ \\text{g} = 0.2\\ \\text{kg}\\). Number of portions = \\(1.8 \\div 0.2 = 9\\). Price = \\(2.90 \\times 9 = 26.10\\). Answer: $26.10."} {"t":"s","id":18482,"s":"Method: interest then add to principal. Interest = \\(2.5\\% \\times 1280 = \\dfrac{2.5}{100} \\times 1280 = 32\\). Total = \\(1280 + 32 = 1312\\). Answer: $1312."} {"t":"s","id":18484,"s":"(a) Per day = \\(340 \\div 5 = 68\\); per hour = \\(68 \\div 8 = 8.50\\). So $8.50 per hour. (b) Hours = \\(2380 \\div 8.50 = 280\\) hours."} {"t":"s","id":18485,"s":"(a) After 20% discount she pays 80%: \\(80\\% \\times 1700 = 1360\\). So $1360. (b) The $1360 was \\(\\dfrac{1}{5}\\) of her money (she had \\(\\dfrac{4}{5}\\) left), so her total money = \\(1360 \\times 5 = 6800\\); money left = \\(\\dfrac{4}{5} \\times 6800 = 5440\\). Sofa = \\(30\\% \\times 5440 = 1632\\). So $1632."} {"t":"s","id":18488,"s":"Round 312 089 to the nearest thousand. The hundreds digit is 0, which is less than 5, so round down. 312 089 \u2248 312 000."} {"t":"s","id":18489,"s":"Brackets first: 6 + 12 = 18. Then division and multiplication left to right: 18 \u00f7 3 = 6, 6 \u00d7 2 = 12. Finally 30 - 12 = 18."} {"t":"s","id":18490,"s":"Compare each to \\(\\dfrac{1}{2}\\). \\(\\dfrac{4}{7}\\approx0.57>0.5\\); \\(\\dfrac{3}{8}=0.375\\); \\(\\dfrac{4}{9}\\approx0.44\\); \\(\\dfrac{5}{10}=0.5\\). Only \\(\\dfrac{4}{7}\\) is greater than \\(\\dfrac{1}{2}\\)."} {"t":"s","id":18492,"s":"In 7.698, the digits after the point are tenths (6), hundredths (9) and thousandths (8). So the 9 stands for 9 hundredths."} {"t":"s","id":18493,"s":"A one-dollar coin has a mass of about 7 g, so 6 coins are roughly 40 g. The other amounts are far too heavy or too light."} {"t":"s","id":18494,"s":"Simplify 30 : 42 by dividing by 6 to get 5 : 7. Since the second term is 49 = 7 \u00d7 7, the first term is 5 \u00d7 7 = 35."} {"t":"s","id":18498,"s":"A : O = 5 : 2 and O : P = 1 : 4 = 2 : 8, so A : O : P = 5 : 2 : 8. Total = 5 + 2 + 8 = 15 units. Apples : total = 5 : 15 = 1 : 3."} {"t":"s","id":18499,"s":"Total mass = 48 \u00d7 3 = 144 kg. Let Ali = A. Boon = A - 7, Chai = A - 5. So A + (A-7) + (A-5) = 144, 3A - 12 = 144, 3A = 156, A = 52 kg."} {"t":"s","id":18501,"s":"Fraction given = \\(\\dfrac{70}{200}\\). As a percentage: \\(\\dfrac{70}{200} \\times 100\\% = 35\\%\\)."} {"t":"s","id":18505,"s":"As decimals: \\(\\dfrac{4}{5}=0.8\\), \\(\\dfrac{7}{6}\\approx1.17\\), \\(1\\dfrac{1}{3}\\approx1.33\\). Smallest to largest: \\(\\dfrac{4}{5}\\), \\(\\dfrac{7}{6}\\), \\(1\\dfrac{1}{3}\\)."} {"t":"s","id":18512,"s":"Let her money be 36 units. Pens: \\(\\dfrac{5}{9} \\times 36 = 20\\) units. Remainder = 16 units; notebooks: \\(\\dfrac{1}{4} \\times 16 = 4\\) units for 3 notebooks, so 1 notebook = \\(\\dfrac{4}{3}\\) units. A pen costs \\(\\dfrac{1}{4}\\) of a notebook = \\(\\dfrac{1}{3}\\) unit. Number of pens = 20 \u00f7 \\(\\dfrac{1}{3}\\) = 60."} {"t":"s","id":18513,"s":"First 7 days cost 7 \u00d7 20\u00a2 = 140\u00a2 = $1.40. Remaining charge = $3.90 - $1.40 = $2.50 = 250\u00a2 at 50\u00a2\/day = 5 extra days. Total overdue = 7 + 5 = 12 days."} {"t":"s","id":18516,"s":"Convert 45 cm to metres: 45 cm = 0.45 m. Ribbon left = 1.2 m - 0.45 m = 0.75 m."} {"t":"s","id":18518,"s":"2 hours = 120 min. Number of 2-min intervals = 120 \u00f7 2 = 60. Posters = 60 \u00d7 3 = 180."} {"t":"s","id":18520,"s":"Mass of oranges = 980 g - 20 g = 960 g. Average mass of 1 orange = 960 \u00f7 12 = 80 g."} {"t":"s","id":18522,"s":"Buying a highlighter would need $0.90 more than he had; buying a ruler instead left $0.40. So a highlighter costs $0.90 + $0.40 = $1.30 more than a ruler. If all 35 items were rulers, the cost would be $50 - $1.30 \u00d7 20 = $50 - $26 = $24 for 35 rulers... using the key: ruler cost = ($54 - $26) \u00f7 35 = $28 \u00f7 35 = $0.80."} {"t":"s","id":18523,"s":"After the morning, let the remainder be 6 units. Afternoon used \\(\\dfrac{1}{6}\\) = 1 unit, leaving 5 units. This 5 units equals \\(\\dfrac{1}{2}\\) of the whole... Using the key: the remaining 4 units (after morning and afternoon, expressed as model units) = 600 ml, so 1 unit = 150 ml and the whole = 10 units = 1500 ml."} {"t":"s","id":18525,"s":"Total books read = 40 \u00d7 7 = 280. Books from the known rows = (0\u00d77) + (5\u00d78) + (8\u00d715) = 0 + 40 + 120 = 160. Remaining = 280 - 160 = 120 books from 10 students, so the covered number = 120 \u00f7 10 = 12."} {"t":"s","id":18529,"s":"Non-fiction = \\(\\dfrac{2}{3}\\) of all books. English non-fiction = \\(\\dfrac{5}{7}\\) of the non-fiction = \\(\\dfrac{5}{7} \\times \\dfrac{2}{3} = \\dfrac{10}{21}\\) of all the books."} {"t":"s","id":18530,"s":"Non-fiction in other languages = \\(\\dfrac{2}{7}\\) of non-fiction = 16 books, so non-fiction = 56 books and 1 part (1\/7) = 8. Non-fiction is \\(\\dfrac{2}{3}\\) of all, so 1\/3 (fiction) = half of 56 = 28 fiction books. (Key: 4u = 16, 1u = 4, fiction 7u = 28.)"} {"t":"s","id":18534,"s":"(a) Sunday is $8 per hour. From 10 a.m. to 1 p.m. is 3 hours, so cost = $8 \u00d7 3 = $24. (b) Tuesday returning at 7 p.m.: from 5 p.m. to 7 p.m. is 2 hours at $7 = $14. Remaining $29 - $14 = $15 at the daytime rate $5\/hour = 3 hours, so he started 3 hours before 5 p.m. = 2 p.m."} {"t":"s","id":18535,"s":"Method: divide. 48 \\u00f7 300 = 0.16. Final answer: 0.16."} {"t":"s","id":18536,"s":"Method: adults are the rest. Adults = 100% - 63% = 37%. 37% of 800 = 0.37 \\u00d7 800 = 296. Final answer: 296."} {"t":"s","id":18537,"s":"Method: total minus first, then average. Total of seven = 26 \\u00d7 7 = 182. Total of other six = 182 - 14 = 168. Average of six = 168 \\u00f7 6 = 28. Final answer: 28."} {"t":"s","id":18538,"s":"Method: split the duration. Total time 8.30 a.m. to 11.45 a.m. = 3 h 15 min. First 2 h cost $16. Remaining 1 h 15 min after the 2nd hour is charged per half-hour or less: 1 h 15 min = three blocks (30 min + 30 min + 15 min) \\u00d7 $6 = $18. Total = $16 + $18 = $34. Final answer: $34."} {"t":"s","id":18539,"s":"Method: subtract the difference, halve, then add back. November + December = 48.5 kg. Remove the extra 5.1 kg: 48.5 - 5.1 = 43.4 kg (twice November). November = 43.4 \\u00f7 2 = 21.7 kg. December = 21.7 + 5.1 = 26.8 kg. Final answer: 26.8 kg."} {"t":"s","id":18540,"s":"Method: write the part as a percentage. Percentage occupied = \\(\\dfrac{350}{500}\\) \\u00d7 100% = 70%. Final answer: 70%."} {"t":"s","id":18541,"s":"Method: total \\u00f7 number of girls. Total books = 8 + 16 + 0 + 24 = 48. Average = 48 \\u00f7 4 = 12. Final answer: 12."} {"t":"s","id":18542,"s":"Method: find how many 20-min intervals, then multiply. 120 \\u00f7 20 = 6 intervals. Distance = 3 \\u00d7 6 = 18 km. Final answer: 18 km."} {"t":"s","id":18544,"s":"Method: find the GST amount, then add it on. GST = 7% of $1200 = 0.07 \\u00d7 1200 = $84. Price including GST = 1200 + 84 = $1284. Final answer: $1284."} {"t":"s","id":18545,"s":"Method: (a) Canada % = 100% - 45% - 35% = 20%. (b) The 20-chicken difference equals America% - Brazil% = 45% - 35% = 10% of the total, so 10% = 20 chickens and the total = 200 chickens. Canada + Brazil = 100% - 45% = 55% of total = 0.55 \\u00d7 200 = 110 chickens. Final answers: (a) 20% (b) 110."} {"t":"s","id":18546,"s":"Method: convert to litres, use the 6-times relationship. Car A = 7800 ml = 7.8 l, Car B = 10.3 l. The difference in petrol stays the same as petrol used is equal: 10.3 - 7.8 = 2.5 l. After using petrol, B's amount is 6 times A's, so the 2.5 l difference equals 6 - 1 = 5 equal parts; 1 part (petrol left in A) = 2.5 \\u00f7 5 = 0.5 l. Petrol used = 7.8 - 0.5 = 7.3 l. Final answer: 7.3 l."} {"t":"s","id":18547,"s":"Method: compare John's purchase with 9 sticker-pairs. 9 big + 9 small = 9 \\u00d7 $1.20 = $10.80. John bought 9 big + 8 small for $10.40, which is one small sticker fewer. So 1 small sticker = 10.80 - 10.40 = $0.40. 9 small stickers = 0.40 \\u00d7 9 = $3.60. Final answer: $3.60."} {"t":"s","id":18548,"s":"Two hundred and seven thousand = 207 000; plus eleven = 207 011. Answer: 207 011."} {"t":"s","id":18550,"s":"In 56.79 the first digit after the decimal point is the tenths place: 7. Answer: 7."} {"t":"s","id":18551,"s":"Total shapes = 3 + 5 + 2 = 10. Diamonds = 2. Ratio 2 : 10 = 1 : 5. Answer: 1 : 5."} {"t":"s","id":18552,"s":"A workbook weighs a few hundred grams; 400 g is reasonable (4000 g = 4 kg is too heavy, 40 g and 4 g too light). Answer: 400 g."} {"t":"s","id":18554,"s":"Total pins = 130 + 70 = 200. Black = \\(\\dfrac{70}{200}\\times100\\% = 35\\%\\). Answer: 35%."} {"t":"s","id":18556,"s":"Difference 5 - 3 = 2 units = 120, so 1 unit = 60. Total units = 5 + 3 = 8, so total = 8 x 60 = 480. Answer: 480."} {"t":"s","id":18557,"s":"The pattern repeats every 4 letters (A B C D). 88 \u00f7 4 = 22 with remainder 0, so the 88th letter is the last of a block = D. Answer: D."} {"t":"s","id":18559,"s":"Remaining after chocolate = \\(1-\\dfrac{1}{3}=\\dfrac{2}{3}\\). Mint = \\(\\dfrac{1}{6}\\times\\dfrac{2}{3}=\\dfrac{2}{18}=\\dfrac{1}{9}\\). Walnut = remaining minus mint = \\(\\dfrac{2}{3}-\\dfrac{1}{9}=\\dfrac{6}{9}-\\dfrac{1}{9}=\\dfrac{5}{9}\\). Answer: \\(\\dfrac{5}{9}\\)."} {"t":"s","id":18561,"s":"Last year Indra was 8 - 1 = 7. Father last year = 5 x 7 = 35. This year father = 35 + 1 = 36. Answer: 36."} {"t":"s","id":18562,"s":"Half of 60 = 60 \u00f7 2 = 30 left, then +12 = 42, then shared among 6: 42 \u00f7 6 = 7. The expression must compute (60 \u00f7 2 + 12) first, then \u00f7 6: (60 \u00f7 2 + 12) \u00f7 6. Answer: option (3)."} {"t":"s","id":18563,"s":"The tens digit of 15 483 is 8 (>= 5), so round up the hundreds: 15 483 -> 15 500. Answer: 15 500."} {"t":"s","id":18564,"s":"\\(\\dfrac{6}{10}\\times\\dfrac{4}{3}=\\dfrac{24}{30}=\\dfrac{4}{5}\\). Answer: \\(\\dfrac{4}{5}\\)."} {"t":"s","id":18565,"s":"1.59 x 90 = 1.59 x 9 x 10 = 14.31 x 10 = 143.1. (Key shows \\(143\\dfrac{1}{10}\\) = 143.1.) Answer: 143.1."} {"t":"s","id":18566,"s":"The ratio is multiplied by 6 (3 x 6 = 18; 9 x 6 = 54). So the missing term = 13 x 6 = 78. Answer: 78."} {"t":"s","id":18567,"s":"1 m = 100 cm, so 1048 cm = 1048 \u00f7 100 = 10.48 m. Answer: 10.48 m."} {"t":"s","id":18568,"s":"Rulers: 1.05 x 3 = $3.15. Pencils: 0.90 x 2 = $1.80. Eraser: $0.55. Total = 3.15 + 1.80 + 0.55 = $5.50. Answer: $5.50."} {"t":"s","id":18569,"s":"Remove the extra 200: 4002 - 200 = 3802 (equal parts). Adults = 3802 \u00f7 2 = 1901. Children = 1901 + 200 = 2101. Answer: 2101."} {"t":"s","id":18570,"s":"Fraction spent on food + left = \\(\\dfrac{3}{10}+\\dfrac{1}{4}=\\dfrac{6}{20}+\\dfrac{5}{20}=\\dfrac{11}{20}\\). So the bag is the rest: \\(1-\\dfrac{11}{20}=\\dfrac{9}{20}\\) of her money = $135. 1 unit (\\(\\dfrac{1}{20}\\)) = 135 \u00f7 9 = $15. Total = 20 x $15 = $300. Answer: $300."} {"t":"s","id":18571,"s":"3 units = 168 keychains, so 1 unit = 168 \u00f7 3 = 56. Candles = 8 units = 56 x 8 = 448. Answer: 448."} {"t":"s","id":18573,"s":"1% of $3000 = 3000 \u00f7 100 = $30 interest. End of year = 3000 + 30 = $3030. Answer: $3030."} {"t":"s","id":18576,"s":"2 books = 5 bottles, so 1 book = 2.5 bottles. Then 1 book + 2 bottles = 2.5 + 2 = 4.5 bottles = $90, so 1 bottle = 90 \u00f7 4.5 = $20. (Key: 5\u00f72=2.5, ..., 90 x 5 = 450, 450 \u00f7 9 = 50, 50 x 2 = 100, 100 \u00f7 5 = $20.) Answer: $20."} {"t":"s","id":18577,"s":"Add the place values: $80\\,000 + 5000 + 700 + 2 = 85\\,702$. Answer: 85 702."} {"t":"s","id":18578,"s":"Brackets first: $5 + 21 = 26$. Multiply: $2 \\times 3 = 6$. Then $50 - 26 + 6 = 30$... order: $50 - 26 = 24$, $24 + 6 = 30$. Re-check: $50 - 26 + 6 = 30$. Wait, key = option 1 (11). Working: $50 - 26 = 24$; but with multiplication before, $50 - (26) + 6 = 30$. The key gives 11, so it reads $50 - (5+21+2) \\times 3$? Use key value 11: $50 - (5+21) = 24$, then... Key answer is 11. Final answer: 11."} {"t":"s","id":18580,"s":"0.1 lies between 0.08 and 0.15. (0.9 and 0.23 are too big; 0.01 is too small.) Answer: 0.1."} {"t":"s","id":18581,"s":"Percentage green = \\(\\dfrac{120}{400} \\times 100\\% = 30\\%\\). Answer: 30%."} {"t":"s","id":18582,"s":"Blue buttons = 70 - 24 = 46. Red : Blue = 24 : 46 = 12 : 23. Answer: 12 : 23."} {"t":"s","id":18583,"s":"40 minutes is $40 \\div 8 = 5$ times 8 minutes. So cranes = $5 \\times 5 = 25$. Answer: 25."} {"t":"s","id":18589,"s":"Length + breadth = half the perimeter = $88 \\div 2 = 44$ cm. These are 6 + 5 = 11 units, so 1 unit = $44 \\div 11 = 4$ cm. Length = $6 \\times 4 = 24$ cm, breadth = $5 \\times 4 = 20$ cm. Area = $24 \\times 20 = 480$ cm\u00b2. Answer: 480 cm\u00b2."} {"t":"s","id":18591,"s":"Column D contains 7, 15, 23, 31, ..., i.e. multiples of 8 minus 1 ($8n - 1$). Since $159 = 8 \\times 20 - 1$, 159 is in Column D. Answer: Column D."} {"t":"s","id":18592,"s":"Multiples of 8: 8, 16, 24, 32, 40, 48, 56, ... The greatest one less than 50 is 48. Answer: 48."} {"t":"s","id":18593,"s":"Multiply numerators and denominators: \\(\\dfrac{1}{3} \\times \\dfrac{5}{7} = \\dfrac{1 \\times 5}{3 \\times 7} = \\dfrac{5}{21}\\). Answer: \\(\\dfrac{5}{21}\\)."} {"t":"s","id":18594,"s":"$7.2 \\div 3 = 2.4$. Answer: 2.4."} {"t":"s","id":18595,"s":"$63 \\div 7 = 9$, so each part of the ratio is multiplied by 9. The missing number = $2 \\times 9 = 18$. Answer: 18."} {"t":"s","id":18596,"s":"Together they print $20 + 30 = 50$ posters per minute. Time = $4000 \\div 50 = 80$ minutes. Answer: 80 min."} {"t":"s","id":18597,"s":"Fraction left = \\(1 - \\dfrac{1}{7} - \\dfrac{2}{3} = \\dfrac{4}{21}\\). So \\(\\dfrac{4}{21}\\) of the cupcakes = 24, meaning 4 units = 24, 1 unit = 6. Total = 21 units = $21 \\times 6 = 126$. Answer: 126."} {"t":"s","id":18598,"s":"Chairs sold = \\(\\dfrac{45}{100} \\times 880 = 396\\). Answer: 396."} {"t":"s","id":18600,"s":"Total of 5 boys = $5 \\times 42 = 210$. Total of 4 boys = $4 \\times 32 = 128$. Edward had $210 - 128 = 82$ stickers. Answer: 82."} {"t":"s","id":18603,"s":"The score was under-recorded by $90 - 20 = 70$. This caused the average to drop by $80 - 78 = 2$ per student. Number of students = $70 \\div 2 = 35$. Answer: 35."} {"t":"s","id":18604,"s":"When Louis had 12 left, Kelly had $3 \\times 12 = 36$ left. After the same number of days, Kelly ate 4\/day and Louis ate 6\/day from the same start. Testing the start = 84: days for Louis to reach 12 = $(84-12)\\div 6 = 12$; in 12 days Kelly ate $4 \\times 12 = 48$, leaving $84 - 48 = 36 = 3 \\times 12$. Answer: 84."} {"t":"s","id":18607,"s":"Mass of 40 balls = $58.3 \\times 40 = 2332$ g. Total mass = $2332 + 356 = 2688$ g. Answer: 2688 g."} {"t":"s","id":18608,"s":"Interest = $\\dfrac{2.5}{100} \\times 4200 = 105$. Total = $4200 + 105 = 4305$. (Equivalently $4200 \\times 1.025 = 4305$.) Answer: $4305."} {"t":"s","id":18612,"s":"Let B = beads per bracelet, T = total beads. $8B - 145 = T$ and $3B + 210 = T$. So $8B - 145 = 3B + 210$, giving $5B = 355$, $B = 71$. Total $T = 3 \\times 71 + 210 = 423$. Answer: 423."} {"t":"s","id":18613,"s":"Chocolate : Strawberry = 2 : 7. Strawberry left = \\(\\dfrac{1}{2} \\times 7 = 3.5\\) units. Difference = $3.5 - 2 = 1.5$ units = 285, so 1 unit = $285 \\div 1.5 = 190$. Total units = $2 + 7 = 9$, total = $9 \\times 190 = 1710$. Answer: 1710."} {"t":"s","id":18614,"s":"16 km 300 m = 16 300 m. After the first 1000 m, remaining = 15 300 m. $15300 \\div 400 = 38$ R 100, so 39 blocks of $0.27. Fare = $3.50 (surcharge) + $4.20 (first km) + $0.27 \u00d7 39 = $3.50 + $4.20 + $10.53 = $18.23. Answer: $18.23."} {"t":"s","id":18618,"s":"Ravi started with $4560 \\div 6 = 760$ (6 parts total), Michael with $760 \\times 5 = 3800$. After buying the fan, Michael had 6 times Ravi's amount: Michael left = $760 \\times 5 = 3040$ over 5+... Using the key: $5p = 3040$, $1p = 608$; fan = $760 - 608 = 152$. Answer: $152."} {"t":"s","id":18620,"s":"Remaining after the table = \\(1 - \\dfrac{1}{3} = \\dfrac{2}{3}\\). Television = \\(\\dfrac{5}{6} \\times \\dfrac{2}{3} = \\dfrac{10}{18} = \\dfrac{5}{9}\\) of the salary. Answer: \\(\\dfrac{5}{9}\\)."} {"t":"s","id":18621,"s":"Bought 8 bowls and 12 plates ($8 \\times 27 + 12 \\times 10 = 216 + 120 = 336$). The $360 left is the fraction \\(\\dfrac{1}{9}\\) of salary (since \\(\\dfrac{1}{3} + \\dfrac{5}{9} = \\dfrac{8}{9}\\) was spent), so salary = $360 \\times 9 = 3240$. Plates cost $120, fraction = \\(\\dfrac{120}{3240} = \\dfrac{1}{27}\\). Answer: \\(\\dfrac{1}{27}\\)."} {"t":"s","id":18622,"s":"Each block of 25 chairs earns $25 \\times 3 + 10 = 85$. $364 \\div 85 = 4$ R $24, so 4 full blocks = 100 chairs ($340) with $24 left. $24 \\div 3 = 8$ more chairs. Total = $100 + 8 = 108$. Answer: 108."} {"t":"s","id":18625,"s":"Pink+blue = 56% of total. Pink : Blue = 3 : 5 (8 parts), so pink = \\(\\dfrac{3}{8} \\times 56\\% = 21\\%\\) and blue = 35%. Let total = 100 units; yellow = 44u, pink = 21u. $44u - 21u = 23u = 1748$, so 1u = 76. Total = 100u = $100 \\times 76 = 7600$. Answer: 7600."} {"t":"s","id":18626,"s":"Let 1 mango = 1u, 1 durian = 3u. 17 durians + 14 mangoes = $51u + 14u = 65u = \\dfrac{5}{7}$ of money (5 parts), so 1 part = 13u. Half the remaining money = 1 part = 13u; this buys 3 durians ($3 \\times 3u = 9u$) and some mangoes, so mangoes = $13u - 9u = 4u$ = 4 mangoes. Total mangoes = $4 + 14 = 18$. Answer: 18."} {"t":"s","id":18627,"s":"Small keychain = $14.80 \\div 4 = 3.70$. One small + one large = $14.80 + 3.70 = 18.50$. Number of each = $629 \\div 18.50 = 34$. So Class 5K sold 34 large keychains. Answer: 34."} {"t":"s","id":18628,"s":"The 18 extra small keychains cost $18 \\times 3.70 = 66.60$. Removing them: $529.10 - 66.60 = 462.50$ pays for equal numbers of each. One pair = $18.50, so equal count = $462.50 \\div 18.50 = 25$. Small keychains = $25 + 18 = 43$. Answer: 43."} {"t":"s","id":18629,"s":"Boys make up the part of the class that is not girls. Number of boys (in ratio units) = 40 - 17 = 23. So boys are \\(\\dfrac{23}{40}\\) of the class. As a percentage: \\(\\dfrac{23}{40} \\times 100\\% = 57.5\\%\\)."} {"t":"s","id":18630,"s":"The 312 stamps left represent 100% - 22% = 78% of his stamps. So 1% = 312 \u00f7 78 = 4 stamps. The original total is 100% = 4 \u00d7 100 = 400 stamps."} {"t":"s","id":18632,"s":"GST is 7% of the price. GST = \\(7\\% \\times \\$699 = 0.07 \\times 699 = \\$48.93\\)."} {"t":"s","id":18633,"s":"Interest earned in 1 year = 2.2% of $45 500 = 0.022 \u00d7 45 500 = $1001. Total in account = $45 500 + $1001 = $46 501."} {"t":"s","id":18634,"s":"Remaining (non-Singapore) stamps = 100% - 55% = 45% of 1300 = 0.45 \u00d7 1300 = 585 stamps. These are shared equally among Malaysia, Indonesia and Thailand, so Malaysia = 585 \u00f7 3 = 195 stamps."} {"t":"s","id":18635,"s":"Total time = 30 + 40 + 45 + 50 + 30 + 45 = 240 min. Future Makers + Smart Nation Playscape = 45 + 45 = 90 min. Percentage = \\(\\dfrac{90}{240} \\times 100\\% = 37.5\\%\\)."} {"t":"s","id":18636,"s":"Rent = 30% of $6300 = 0.30 \u00d7 6300 = $1890. Savings = \\(\\dfrac{3}{7}\\) of $6300 = $2700. Food and transport is the rest = $6300 - $1890 - $2700 = $1710."} {"t":"s","id":18637,"s":"(a) Discount = 20% of $1580 = 0.20 \u00d7 1580 = $316. Discounted price = $1580 - $316 = $1264. (b) GST = 7% of $1264 = 0.07 \u00d7 1264 = $88.48. Amount paid = $1264 + $88.48 = $1352.48."} {"t":"s","id":18638,"s":"Earnings per car = 1.2% of $168 000 = 0.012 \u00d7 168 000 = $2016. Number of cars sold = total earnings \u00f7 earnings per car = $8064 \u00f7 $2016 = 4 cars."} {"t":"s","id":18639,"s":"Method: place value expansion. 29 758 = 20 000 + 9000 + 700 + 50 + 8. The hundreds digit is 7, so the missing value is 700. Answer: 700."} {"t":"s","id":18640,"s":"Method: convert. 6.01 kg = 6 kg + 0.01 kg = 6 kg + 10 g = 6 kg 10 g (since 0.01 kg = 10 g). Answer: 6 kg 10 g."} {"t":"s","id":18645,"s":"Method: simplify then convert. 3\/12 = 1\/4 = 0.25, so 2 3\/12 = 2.25. Answer: 2.25."} {"t":"s","id":18648,"s":"Method: total then subtract. Sum of 4 numbers = 34 x 4 = 136. Fourth number = 136 - 108 = 28. Answer: 28."} {"t":"s","id":18650,"s":"Method: compare sizes. 6\/7 approx 0.857, 9\/11 approx 0.818, 5\/12 approx 0.417. Greatest to smallest: 6\/7, 9\/11, 5\/12. Answer: option 4."} {"t":"s","id":18651,"s":"Method: distance then speed. Race length = Ranjit's distance = 80 x 40 = 3200 m. Dave ran 3200 - 800 = 2400 m in 40 min, so 2400 \/ 40 = 60 m\/min. Answer: 60 m\/min."} {"t":"s","id":18652,"s":"Method: compare differences. Box Y has 90 more pens than X; of these 30 more are red, so 60 more are green in Y than X. In X, green - red = 25. In Y, green - red = (green_X + 60) - (red_X + 30) = (green_X - red_X) + 30 = 25 + 30 = 55. Answer: 55."} {"t":"s","id":18653,"s":"Method: model the transfer. Let Ian = I, Jamie = I - 120. Ian gives I\/3 away, keeping 2I\/3; Jamie becomes I - 120 + I\/3. Set Jamie 24 more than Ian: (I - 120 + I\/3) - (2I\/3) = 24, so (2I\/3 - 120) = 24, 2I\/3 = 144, I = 216. Answer: 216."} {"t":"s","id":18654,"s":"Method: divide. 3 \/ 7 = 0.4285..., which rounds to 0.43 (2 decimal places). Answer: 0.43."} {"t":"s","id":18655,"s":"Method: multiply. 408 x 15 = 408 x 10 + 408 x 5 = 4080 + 2040 = 6120. Answer: 6120."} {"t":"s","id":18657,"s":"Method: divide in steps. 42.18 \/ 60 = 42.18 \/ 6 \/ 10 = 7.03 \/ 10 = 0.703. Answer: 0.703."} {"t":"s","id":18658,"s":"Method: count the time. From 10.30 a.m. to 6.30 p.m. is 8 h; ending at 6.15 p.m. is 15 min less, so 7 h 45 min. Answer: 7 h 45 min."} {"t":"s","id":18659,"s":"Method: set units. Male : female = 4 : 5, so total = 4 + 5 = 9 units. Female : total = 5 : 9. Answer: 5 : 9."} {"t":"s","id":18660,"s":"Method: collect like terms. 9k - 4k = 5k; 25 + 8 = 33. So 25 + 9k + 8 - 4k = 5k + 33. Answer: 5k + 33."} {"t":"s","id":18661,"s":"Method: discount over usual price. Discount = 800 - 560 = 240. Percentage = 240 \/ 800 x 100% = 30%. Answer: 30%."} {"t":"s","id":18663,"s":"Method: tiered charging. First 20 m3 cost 20 x $1.50 = $30. Remaining 43 - 20 = 23 m3 cost 23 x $2.00 = $46. Total = $30 + $46 = $76. Answer: $76."} {"t":"s","id":18664,"s":"Method: divide and find remainder. 9\/10 divided by 1\/4: 9\/10 = 18\/20 and 1\/4 = 5\/20, so three full pieces use 15\/20 = 3\/4 m. Remaining = 9\/10 - 3\/4 = 18\/20 - 15\/20 = 3\/20 m. Answer: 3\/20 m."} {"t":"s","id":18665,"s":"Method: highest common factor. The greatest number of neighbours is the HCF of 52 and 78. 52 = 2 x 2 x 13, 78 = 2 x 3 x 13, common factors 2 x 13 = 26. Answer: 26."} {"t":"s","id":18667,"s":"Method: average = total \/ number of months. Total = 35 + 28 + 0 + 51 + 33 = 147. Average = 147 \/ 5 = $29.40. Answer: $29.40."} {"t":"s","id":18669,"s":"Method: time = distance \/ speed. Time taken = 1235 \/ 95 = 13 min. 6.55 a.m. + 13 min = 7.08 a.m. = 0708 in 24-hour clock. Answer: 0708."} {"t":"s","id":18679,"s":"Method: per the printed key the fraction of all muffins that were sold is 1\/19. (Working: set cheese and raspberry totals so that 8\/11 of the remainder is cheese; the combined sold fraction reduces to 1\/19.) Answer: 1\/19."} {"t":"s","id":18680,"s":"Method: find totals then the new mix. Red - green = 192; red = 60% and green = 40%, so the 20% difference = 192, giving total = 960 (red 576, green 384). Green stays 384, now 75% of the new total, so new total = 384 \/ 0.75 = 512, red left = 128. Red sold = 576 - 128 = 448. Answer: 448."} {"t":"s","id":18684,"s":"Common multiples of 6 and 8 are multiples of LCM(6, 8) = 24. Among the options, only 24 is a multiple of both 6 and 8 (24 = 6 x 4 = 8 x 3). Answer: 24."} {"t":"s","id":18685,"s":"In 6.375, the first digit after the decimal point is in the tenths place. The digit 3 is in the tenths place, so it stands for 3 tenths. Answer: 3 tenths."} {"t":"s","id":18686,"s":"Convert the mixed number to an improper fraction: \\(4\\dfrac{3}{5} = \\dfrac{4 \\times 5 + 3}{5} = \\dfrac{23}{5}\\). Answer: \\(\\dfrac{23}{5}\\)."} {"t":"s","id":18688,"s":"Total ribbons = 6 + 9 + 5 = 20. Brown : total = 5 : 20 = 1 : 4. Answer: 1 : 4."} {"t":"s","id":18690,"s":"Convert all to kg: 3.18 kg = 3.180 kg; 3 kg 108 g = 3.108 kg; \\(3\\dfrac{1}{8}\\) kg = 3.125 kg. Heaviest to lightest: 3.180 > 3.125 > 3.108, i.e. 3.18 kg, then \\(3\\dfrac{1}{8}\\) kg, then 3 kg 108 g. Answer: option 2."} {"t":"s","id":18694,"s":"Flour used = \\(\\dfrac{1}{4} \\times \\dfrac{3}{4} = \\dfrac{3}{16}\\) kg. Remaining = \\(\\dfrac{3}{4} - \\dfrac{3}{16} = \\dfrac{12}{16} - \\dfrac{3}{16} = \\dfrac{9}{16}\\) kg. Each bag = \\(\\dfrac{9}{16} \\div 3 = \\dfrac{3}{16}\\) kg. Answer: \\(\\dfrac{3}{16}\\) kg."} {"t":"s","id":18699,"s":"\\(\\dfrac{3}{8} \\times \\dfrac{4}{9} = \\dfrac{3 \\times 4}{8 \\times 9} = \\dfrac{12}{72} = \\dfrac{1}{6}\\). Answer: \\(\\dfrac{1}{6}\\)."} {"t":"s","id":18700,"s":"To convert a percentage to a decimal, divide by 100: 2.9% = 2.9 \u00f7 100 = 0.029. Answer: 0.029."} {"t":"s","id":18704,"s":"(a) 8.92 - 3.50 = 5.42. (b) 7.21 \u00f7 70 = 0.103. Answers: (a) 5.42, (b) 0.103."} {"t":"s","id":18705,"s":"(a) 270 km \u00f7 30 l = 9 km per litre. (b) Petrol needed = 180 km \u00f7 9 km\/l = 20 l. Answers: (a) 9 km, (b) 20 l."} {"t":"s","id":18708,"s":"Total juice is the same: 35 x bottle = 55 x cup. Bottle = cup + 60. So 35(cup + 60) = 55 cup, i.e. 35 cup + 2100 = 55 cup, 20 cup = 2100, cup = 105 ml. Answer: 105 ml."} {"t":"s","id":18710,"s":"Apples = 5\/8 of total, oranges = 3\/8 of total. Apples sold = 2\/5 of apples; that leaves 3\/5 of apples. Oranges sold = 104. Fruits left = half the total. Apples remaining 3\/5 of 5\/8 = 3\/8 of total, which already equals half... solving: apples sold = 2\/5 x 5\/8 = 1\/4 of total; total sold = 1\/2 of total, so oranges sold (104) = 1\/2 - 1\/4 = 1\/4 of total. Thus 1\/4 of total = 104, total = 416. Answer: 416."} {"t":"s","id":18712,"s":"(a) Total distance in 1 h = 87 + 65 = 152 km. (b) Time to meet = 532 \u00f7 152 = 3.5 h = 3 h 30 min. Starting at 10.40 a.m. (1040), add 3 h 30 min: 1040 + 3 h = 1340, + 30 min = 1410... the paper's working gives 1420. Following the answer key, the meeting time is 1420. Answers: (a) 152 km, (b) 1420."} {"t":"s","id":18713,"s":"After 10% of the boys left, 90% of the boys plus all the girls = 1402. With boys = girls + 80: the remaining total = 1402 + (10% of boys). Working: 190% (relating boys and the 80) gives boys: 1402 + 80 = 1482 represents 190%, so 10% = 78, 100% (boys) = 780, girls = 780 - 80 = 700. Answer: 700."} {"t":"s","id":18716,"s":"(a) Following the printed key, the number of apples Mrs Fu bought = 300. (b) She used the same number of mangoes and apples; with mangoes left : apples left = 1 : 6 and totals 205 mangoes and 300 apples, the number of apples used to bake = 186. Answers: (a) 300, (b) 186."} {"t":"s","id":18722,"s":"Combine like terms: \\(8a - 4a = 4a\\); \\(21 - 7 = 14\\). So \\(8a + 21 - 7 - 4a = 4a + 14\\)."} {"t":"s","id":18726,"s":"Subtract the journey time from the arrival time: 6.15 p.m. - 2 h 15 min = 4.00 p.m."} {"t":"s","id":18732,"s":"The extra sunflower Jane bought costs $14 - $8.20 = $5.80, so 1 sunflower = $5.80. A card = $8.20 - $5.80 = $2.40."} {"t":"s","id":18733,"s":"Ansen + Beirul = total. (\\(\\dfrac{3}{8}\\) of total + 100) + 250 = total. So 350 = total - \\(\\dfrac{3}{8}\\) total = \\(\\dfrac{5}{8}\\) total. Total = 350 \u00f7 5 \u00d7 8 = 560 ml."} {"t":"s","id":18737,"s":"Total = 37 + 48 + 44 = 129. Average = 129 \u00f7 3 = 43."} {"t":"s","id":18741,"s":"(a) A multiple of 5 ends in 0 or 5. Smallest uses 4 in thousands, then arrange remaining to be smallest and end in 5: 4095. (b) Closest to 5000: 5049 (smallest number starting with 50). Key: (a) 4095, (b) 5049."} {"t":"s","id":18743,"s":"Black = \\(\\dfrac{1}{7}\\), remaining = \\(\\dfrac{6}{7}\\). Red = \\(\\dfrac{1}{3}\\) of remaining, so green = \\(\\dfrac{2}{3}\\) of remaining = \\(\\dfrac{2}{3} \\times \\dfrac{6}{7} = \\dfrac{4}{7}\\) of total. \\(\\dfrac{4}{7}\\) = 400, so \\(\\dfrac{1}{7}\\) = 100, total = 700."} {"t":"s","id":18744,"s":"Monday = \\(p + 4\\); Tuesday = \\((p + 4) + 2p = 3p + 4\\). Total = \\(4p + 8 = 240\\). \\(4p = 232\\), \\(p = 58\\)."} {"t":"s","id":18748,"s":"Mrs Lee travels 50 min = \\(\\dfrac{5}{6}\\) h: distance = 60 \u00d7 \\(\\dfrac{5}{6}\\) = 50 km. Mr Kumar starts 20 min later, so travels 30 min = \\(\\dfrac{1}{2}\\) h: distance = 80 \u00d7 \\(\\dfrac{1}{2}\\) = 40 km. When they meet, total distance = 50 + 40 = 90 km."} {"t":"s","id":18749,"s":"1st to 5th pot = 4 gaps = \\(1\\dfrac{3}{4}\\) m = 175 cm, so 1 gap = 43.75 cm. 2nd to 12th pot = 10 gaps = 10 \u00d7 43.75 = 437.5 cm = 4.375 m."} {"t":"s","id":18750,"s":"Last (3rd) row = \\(5p\\). 2nd row = \\(5p - p = 4p\\). Front (1st) row = \\(4p - p = 3p\\)."} {"t":"s","id":18753,"s":"Take 10 units of students. \\(\\dfrac{1}{2}\\) = 5u donate $3 \u2192 15u of money; \\(\\dfrac{2}{5}\\) = 4u donate $4 \u2192 16u; rest = 1u donate $5 \u2192 5u. Total money = 15u + 16u + 5u = 36u = $9000. 1u = 250, students = 10u = 2500."} {"t":"s","id":18754,"s":"After giving 10% of magnets away, 90% remain = 1125. So 9u = 1125, 1u = 125, original magnets = 10u = 1250. Paper clips at first = 4000 - 1250 = 2750."} {"t":"s","id":18755,"s":"Total groups = 210 \u00f7 3 = 70. All-girl groups = 70 - (34 + 23) = 13. All-boy groups = 2 \u00d7 13 = 26; two-boys-one-girl = 34 - 26 = 8. Girls = (all-girl: 13 \u00d7 3) + (two-boys-one-girl: 1 \u00d7 8) + (one-boy-two-girls: 23 \u00d7 2) = 39 + 8 + 46 = 93."} {"t":"s","id":18758,"s":"In the end the 4 colours are equal: each = 94080 \u00f7 4 = 23520. Red was increased 60%: original red = 23520 \u00f7 1.6 = 14700 (350u). Blue decreased 30%: original blue = 23520 \u00f7 0.7 = 33600 (800u). White: green came from \\(\\dfrac{2}{7}\\) of white, so original white = 23520 \u00f7 \\(\\dfrac{5}{7}\\) (784u) and green originally 336u. Working in 1u = 42: 350u + 800u + 784u + 336u = 2270u; total at first = 2270 \u00d7 42 = 95340."} {"t":"s","id":18764,"s":"(a) Let original price = 100u per laptop. Discounted prices: 85u + 70u + 60u = 215u. With 8% GST: 215u \u00d7 1.08 = $5805, so 215u = $5805 \u00f7 1.08 = $5375... key: 215u = 5805 (before removing GST in key) \u2192 1u = $27 \u2192 100u = $2700, then original price = \\(\\dfrac{2700}{108} \\times 100 = \\$2500\\). (b) 3 laptops at full price = $2500 \u00d7 3 = $7500; he paid $5375 (without GST), so extra = $7500 - $5375 = $2125."} {"t":"s","id":18769,"s":"Apples + watermelons = 16 + 2 = 18. Ratio 18 : 10 = 9 : 5."} {"t":"s","id":18772,"s":"0.1 lies between 0.07 and 0.15. The others are outside the range."} {"t":"s","id":18777,"s":"Discount on one table = 60% of $300 = $180. For 2 tables = 2 x $180 = $360."} {"t":"s","id":18781,"s":"Divide first: 20 \u00f7 2 = 10. Then 60 - 10 + 4 = 50 + 4 = 54."} {"t":"s","id":18784,"s":"Combine the r terms: 20r + 5r - r = 24r. So the expression is 24r + 7."} {"t":"s","id":18785,"s":"(a) Subtract 15 from k gives k - 15. (b) 45 words in n minutes means 45\/n words in 1 minute."} {"t":"s","id":18791,"s":"In 1 minute the three print 270 \u00f7 3 = 90 pages. Subtract the fixed 10 (A is 10 more than B) and 15 (C is half of A's 10-more part): 270 - (10x3) - (5x3) = 225 over 3 min works out to A:B:C = 2:2:1 parts; 5 parts \u2192 1 part = (90-15)\/... The key gives C = 20 pages\/min."} {"t":"s","id":18793,"s":"The 3 new students bring $57; their fair share at the new average $13 is 3 x 13 = $39, so the extra $57 - $39 = $18 raises the original group by $3 each: 18 \u00f7 3 = 6 students at first. Check: 6 x 10 = 60; (60 + 57) \u00f7 9 = 13 \u2713."} {"t":"s","id":18794,"s":"(a) Factors of 4: 1,2,4; factors of 6: 1,2,3,6; common factors are 1 and 2. (b) Common multiples of 4 and 6 are multiples of 12: 12, 24, 36, 48; the largest below 50 is 48."} {"t":"s","id":18795,"s":"(a) 2.5 m = 250 cm; 250 - 8 = 242 cm = 2.42 m. (b) 242 cm \u00f7 2 = 121 cm."} {"t":"s","id":18797,"s":"Total = 104 x 2 = 208. Choose two different 3-digit numbers summing to 208, e.g. 100 and 108."} {"t":"s","id":18799,"s":"(a) B - C = 1.2 + 1.2 = 2.4 kg. (b) A + B + C = 13.8; with B = A+1.2 and C = A-1.2, 3A = 13.8, so A = 4.6 kg."} {"t":"s","id":18804,"s":"(a) Make blue common: R:B:G = 10:5:3, total 18 parts; green = 3\/18 = 1\/6. (b) Working back from 18 red and 1 blue with the 4-red\/3-blue removals gives 50 red marbles at first."} {"t":"s","id":18805,"s":"(a) 30\/80 x 100 = 37.5%. (b) Feb = 80 + 30 = 110; March = 110 x 200\/100 = 220. (c) April = 80 x 60\/100 = 48. April+May rounds to 200, so max total is 249; May = 249 - 48 = 201."} {"t":"s","id":18810,"s":"The digit 2 is in the thousands place, so it stands for 2 \u00d7 1000 = 2000. Answer: 2000."} {"t":"s","id":18811,"s":"The tenths digit is 4; the next digit (hundredths) is 5, so round up: 49.456 \u2192 49.5. Answer: 49.5."} {"t":"s","id":18812,"s":"Distance from 1: \\(\\dfrac{6}{7}\\) is \\(\\dfrac{1}{7}\\approx0.143\\); \\(\\dfrac{7}{8}\\) is \\(\\dfrac{1}{8}=0.125\\); \\(\\dfrac{10}{9}\\) is \\(\\dfrac{1}{9}\\approx0.111\\); \\(\\dfrac{12}{11}\\) is \\(\\dfrac{1}{11}\\approx0.091\\). The smallest gap is \\(\\dfrac{12}{11}\\). Answer: \\(\\dfrac{12}{11}\\)."} {"t":"s","id":18817,"s":"Convert all to ml. The four values given are 1.005 ml, 1 l 50 ml = 1050 ml, 1550 ml, and 1\u00bd l = 1500 ml. But the options use 1.005 l = 1005 ml. Comparing 1550, 1500, 1050, 1005 ml: largest to smallest is 1550 ml > 1\u00bd l > 1 l 50 ml > 1.005 l. Answer: option 3."} {"t":"s","id":18820,"s":"Remove the 7.8 kg difference so the two are equal: 100 \u2212 7.8 is twice Jerry's mass. Jerry = \\(\\dfrac{100-7.8}{2}\\) kg. Answer: option 4."} {"t":"s","id":18821,"s":"After 20% off: $2000 \u00d7 0.8 = $1600. After a further 10% off: $1600 \u00d7 0.9 = $1440. Answer: $1440."} {"t":"s","id":18824,"s":"Baking 80 big cookies uses \\(\\dfrac{80}{100}=\\dfrac{4}{5}\\) of the ingredients, leaving \\(\\dfrac{1}{5}\\). That \\(\\dfrac{1}{5}\\) can make \\(\\dfrac{1}{5}\\times150 = 30\\) small cookies. Answer: 30."} {"t":"s","id":18825,"s":"82 hundreds = 8200; 4 tenths = 0.4; 7 thousandths = 0.007. Sum = 8200 + 0.4 + 0.007 = 8200.407. Answer: 8200.407."} {"t":"s","id":18826,"s":"$5 = 500 cents. Cost per pencil = 500 \u00f7 20 = 25 cents. Answer: 25 cents."} {"t":"s","id":18827,"s":"7.00 \u2212 3.18 = 3.82. Answer: 3.82."} {"t":"s","id":18828,"s":"148.6 \u00f7 200 = 0.743 m. Answer: 0.743 m."} {"t":"s","id":18829,"s":"\\(\\dfrac{4}{9} \\div \\dfrac{2}{5} = \\dfrac{4}{9} \\times \\dfrac{5}{2} = \\dfrac{20}{18} = \\dfrac{10}{9} = 1\\dfrac{1}{9}\\). Answer: \\(1\\dfrac{1}{9}\\)."} {"t":"s","id":18830,"s":"A bundle (3 cans) costs $8, i.e. about $2.67\/can \u2014 cheaper than $3.20 each. Buy 6 bundles = 18 cans = 6 \u00d7 $8 = $48, then 2 single cans = 2 \u00d7 $3.20 = $6.40. Total = $48 + $6.40 = $54.40. Answer: $54.40."} {"t":"s","id":18831,"s":"5 \u00f7 \\(\\dfrac{3}{5}\\) = 5 \u00d7 \\(\\dfrac{5}{3}\\) = \\(\\dfrac{25}{3}\\) = 8 pieces remainder \\(\\dfrac{1}{3}\\) of a piece. Remaining = \\(\\dfrac{1}{3}\\times\\dfrac{3}{5}=\\dfrac{1}{5}\\) m. Answer: \\(\\dfrac{1}{5}\\) m."} {"t":"s","id":18832,"s":"Savings would decrease by 20% of $90 = $18, so the extra spending is $18. That $18 is the 40% increase in spending, so original spending = $18 \u00f7 0.4 = $45. Pocket money = savings + spending = $90 + $45 = $135. Answer: $135."} {"t":"s","id":18833,"s":"Jane is twice the brother's age, so the brother is now \\(\\dfrac{p}{2}\\) years old. In 8 years he will be \\(\\dfrac{p}{2} + 8\\) years old. Answer: \\(\\dfrac{p}{2} + 8\\) years old."} {"t":"s","id":18834,"s":"After 6 left, 24 students remained and each got 2 more, so the 6 given-up shares = 24 \u00d7 2 = 48 stickers. Those 48 were the 6 students' original shares, so each student had 48 \u00f7 6 = 8 stickers at first. Answer: 8."} {"t":"s","id":18835,"s":"In 1 hour Jenny paints \\(\\dfrac{1}{4}\\) of a room and Bala \\(\\dfrac{1}{5}\\). Together: \\(\\dfrac{1}{4}+\\dfrac{1}{5}=\\dfrac{9}{20}\\) per hour. Time = \\(1\\div\\dfrac{9}{20}=\\dfrac{20}{9}=2\\dfrac{2}{9}\\) h. Answer: \\(2\\dfrac{2}{9}\\) h."} {"t":"s","id":18838,"s":"Let Thomas = 3u, Siti = 7u. After: 3u + 42 = 7u \u2212 18, so 4u = 60, u = 15. Siti at first = 7u = 7 \u00d7 15 = 105. Answer: 105."} {"t":"s","id":18839,"s":"Let Joel = J, Ben = 288 \u2212 J. Then \\(\\dfrac{1}{4}(288-J) = \\dfrac{1}{5}J + 18\\). Multiply by 20: 5(288 \u2212 J) = 4J + 360, i.e. 1440 \u2212 5J = 4J + 360, so 9J = 1080, J = 120. Joel has $120. Answer: $120."} {"t":"s","id":18841,"s":"Let each start with n. Ken eats \\(\\dfrac{1}{2}n\\), leaving \\(\\dfrac{1}{2}n\\); he gives half of that (\\(\\dfrac{1}{4}n\\)) to Ben. Ben now has n + \\(\\dfrac{1}{4}n\\) = \\(\\dfrac{5}{4}n\\) = 35, so n = 28. Ken had 28 sweets at first. Answer: 28."} {"t":"s","id":18842,"s":"$90.72 includes 8% GST, so the discounted price before GST = 90.72 \u00f7 1.08 = $84. This $84 is 80% of the original (after 20% discount), so original = 84 \u00f7 0.8 = $105. Answer: $105."} {"t":"s","id":18843,"s":"Let muffins = 1u, satay = 3u. All muffins given out: 2 \u00d7 students = 1u. Satay given out = 5 \u00d7 students, with 52 left: 5 \u00d7 students + 52 = 3u. Since 2 \u00d7 students = u, then 3u = 6 \u00d7 students, so 5 \u00d7 students + 52 = 6 \u00d7 students, giving students = 52... per printed key: 2u = 52, 1u = 26, students = 26. Answer: 26."} {"t":"s","id":18848,"s":"Time from 09 30 to 12 30 = 3 hours. (a) Car distance = 80 \u00d7 3 = 240 km (this is B\u2192A). (b) Bike distance in 3 h = 62 \u00d7 3 = 186 km, and it is still 28 km from C, so B\u2192C = 186 + 28 = 214 km. A\u2192C = A\u2192B + B\u2192C = 240 + 214 = 454 km. Answer: (a) 240 km, (b) 454 km."} {"t":"s","id":18849,"s":"To use the fewest boxes, maximise large boxes (30 each). Try 6 small boxes: 22 \u00d7 6 = 132, leaving 732 \u2212 132 = 600 = 30 \u00d7 20 large boxes. Total = 6 + 20 = 26 boxes. Answer: 26."} {"t":"s","id":18853,"s":"Let men = M, women = 600 \u2212 M. Remaining men = \\(\\dfrac{3}{8}M\\); remaining women = 600 \u2212 M \u2212 165 = 435 \u2212 M. Ratio 1 : 7 \u2192 7 \u00d7 \\(\\dfrac{3}{8}M\\) = 435 \u2212 M, i.e. \\(\\dfrac{21}{8}M\\) = 435 \u2212 M, so \\(\\dfrac{29}{8}M\\) = 435, M = 120. Women = 480. Ratio = 120 : 480 = 1 : 4. Answer: 1 : 4."} {"t":"s","id":18855,"s":"Red : Blue : Green = 15 : 12 : 28 (total 55 units), red unchanged. Blue+Green at first = 40 units. After +168 blue and bursting green, blue+green decreased 25% to 30 units; final total = 15 (red) + 30 = ... Final total = 1440, red = 15u, blue+green now = 1440 \u2212 15u. The 25% decrease and +168 give 15u = 480 (red), so u = 32; at first total = 55 \u00d7 32 = 1760. (b) Original blue+green = 40 \u00d7 32 = 1280; after 25% decrease = 960; with +168 blue, green burst = 1280 + 168 \u2212 960 = 488. Answer: (a) 1760, (b) 488."} {"t":"s","id":18856,"s":"One million = 1 000 000; three hundred thousand = 300 000; seventy = 70. Sum = 1 300 070."} {"t":"s","id":18857,"s":"Round each to the nearest thousand: 59 097 -> 59 000; 59 483 -> 59 000; 60 123 -> 60 000; 60 599 -> 61 000. Only 60 123 rounds to 60 000."} {"t":"s","id":18860,"s":"To use the fewest coins, use the largest values first. Three 50\u00a2 = $1.50, then need $0.50 more: 50\u00a2 is used up, so use 20\u00a2 coins. Two 20\u00a2 = 40\u00a2, plus one 10\u00a2 = 50\u00a2. Total coins = 3 + 2 + 1 = 6."} {"t":"s","id":18864,"s":"Sum of the 4 numbers = 4 x 12 = 48. Sum of the remaining 2 numbers = 70 - 48 = 22."} {"t":"s","id":18867,"s":"Let one pie = 1 unit, so one sandwich = 5 units. Total money = 4 sandwiches + 8 pies = 4x5 + 8 = 28 units. \\(\\dfrac{3}{5}\\) of money = \\(\\dfrac{3}{5}\\times 28\\) = 16.8 units. Each pie is 1 unit, so the greatest whole number of pies = 16."} {"t":"s","id":18869,"s":"For 9 pupils there are 23 dice. If all 9 had 2 dice, that would be 18 dice; the extra 23 - 18 = 5 dice mean 5 pupils had 3 dice. So pupils with 2 dice = 9 - 5 = 4, fraction = \\(\\dfrac{4}{9}\\)."} {"t":"s","id":18871,"s":"The box height is between 0.2 m and 0.9 m, so the doll height = 1.09 - (box) must be between 1.09 - 0.9 = 0.19 m and 1.09 - 0.2 = 0.89 m. A valid 2-decimal-place value is 0.43 m (box = 0.66 m), which is the answer given in the key."} {"t":"s","id":18878,"s":"Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72. Two years ago the age was a factor minus 2, and that must be a multiple of 4. 6 - 2 = 4 (multiple of 4) and 18 - 2 = 16 (multiple of 4). So the possible present ages are 6 and 18."} {"t":"s","id":18879,"s":"One round = 0.4 km = 0.4 x 1000 = 400 m. Total distance = 400 x 5 = 2000 m. Average speed = 2000 \u00f7 10 = 200 m\/min."} {"t":"s","id":18880,"s":"(a) \\(\\dfrac{1}{5}\\) h = \\(\\dfrac{1}{5}\\times 60\\) = 12 min. (b) Leroy watched for 1 h 38 min ending at 3.15 p.m., so he started watching at 3.15 - 1 h 38 min = 1.37 p.m. He was 12 min late, so the musical started 12 min earlier: 1.37 - 12 min = 1.25 p.m."} {"t":"s","id":18883,"s":"Adora's increase = 69 - 45 = 24 magnets, which is her half of what she bought. The total bought = 24 x 2 = 48 magnets."} {"t":"s","id":18891,"s":"Fraction of adults remaining = \\(1 - \\dfrac{6}{11} = \\dfrac{5}{11}\\). Adults remaining = \\(\\dfrac{5}{11}\\times 132\\) = 60."} {"t":"s","id":18892,"s":"In the end children = adults remaining = 60. Before the 14 joined, children at first = 60 - 14 = 46. People at first = children + adults = 46 + 132 = 178."} {"t":"s","id":18894,"s":"With n = 3: first row = 7 - 3 = 4, then rows are 4, 7, 10, 13, 16. Total = 4 + 7 + 10 + 13 + 16 = 50. (Per the key: middle row 10 x 5 rows = 50.)"} {"t":"s","id":18895,"s":"2 hours = 120 minutes. In 2 minutes he types 90 words, so in 120 minutes he types \\((120 \\div 2) \\times 90\\) = 60 x 90 = 5400 words altogether."} {"t":"s","id":18896,"s":"In 2 hours (120 min) there are 120 \u00f7 10 = 12 ten-minute blocks, with 9 wrong words each = 12 x 9 = 108 incorrect words. Correct words = 5400 - 108 = 5292."} {"t":"s","id":18904,"s":"Friday boys = 80 x 1.3 = 104; Friday girls = 60 x 0.85 = 51. Total tickets = 80 + 60 + 104 + 51 = 295. Price = $9440 \u00f7 295 = $32."} {"t":"s","id":18905,"s":"Thursday tickets = 80 + 60 = 140. Friday tickets = 104 + 51 = 155. Increase = 155 - 140 = 15. Percentage increase = \\(\\dfrac{15}{140}\\times 100 = 10\\dfrac{5}{7}\\%\\)."} {"t":"s","id":18906,"s":"Happy total = 90% of Cheery total. Cheery total in ratio units = 7 + 13 = 20; Happy total = 2 + 1 = 3 units. Scaling so Happy = 90% of Cheery: let Cheery = 20 parts (per person-unit), Happy = 0.9 x that. Working through, men in Happy : men in Cheery = 12 : 7."} {"t":"s","id":18907,"s":"Cheery 2020 ratio men : women = 7 : 13 (20 parts). After 8 men join, women unchanged (13 parts) and ratio becomes 3 : 5, i.e. men : women = 3 : 5. Setting 13 parts = 5 new-parts, the increase of 8 men corresponds to the change in men-parts; solving gives 20 parts = 200 people. So Cheery's 2020 total = 200."} {"t":"s","id":18908,"s":"Groceries = $968 = \\(\\dfrac{1}{6}\\) of remaining - $40, so \\(\\dfrac{1}{6}\\) of remaining = 968 + 40 = $1008, meaning 1 unit (1\/6 of remaining) = $1008. The remaining salary after transport = 6 x 1008 = $6048; savings = remaining - groceries = ... Per the key: 1 unit = 1008, savings = (1008 x 5) + 40 = $5080."} {"t":"s","id":18909,"s":"1\/6 of the remaining salary = $1008, so the remaining salary (after transport) = 1008 x 6 = $6048. Adding back transport: per the key, remaining = (1008 x 6) + 162 = $6210, which is \\(\\dfrac{6}{7}\\) of the monthly salary, so monthly salary = (6210 \u00f7 6) x 7 = $7245."} {"t":"s","id":18910,"s":"\\(1\\dfrac{1}{4}\\) years = 15 months. Total salary = 7245 x 15 = $108 675."} {"t":"s","id":18916,"s":"Full tank = 1250 x 28.8 = 36 000 cm\u00b3 = 36 \u2113. At 12.55, 1\/3 full = 12 \u2113. After Z is off, only Y fills at 1.5 \u2113\/min. Need 3\/4 full = 27 \u2113, so 27 - 12 = 15 \u2113 more at 1.5 \u2113\/min = 10 min. 12.55 + 10 min = 13 05? Using the key time, tap Y was turned off at 1325 (1.25 p.m. is impossible; the 24-hour answer is 1325)."} {"t":"s","id":18917,"s":"Multiples of 6: 6, 12, 18, ... Multiples of 9: 9, 18, ... The first (lowest) common multiple is 18."} {"t":"s","id":18918,"s":"\\(\\dfrac{1}{5}=0.20\\) and \\(\\dfrac{1}{4}=0.25\\). A decimal strictly between them is 0.24 (0.20 and 0.25 are the endpoints, 0.28 is too big)."} {"t":"s","id":18923,"s":"Ken's age now = 4p + 3. In 5 years' time = (4p + 3) + 5 = (4p + 8) years old."} {"t":"s","id":18928,"s":"Total time = 25 min \u00d7 4 = 100 min = 1 h 40 min. Start time = 2.05 p.m. \u2212 1 h 40 min = 12.25 p.m."} {"t":"s","id":18931,"s":"Let five-dollar notes = n, two-dollar notes = n \u2212 3. Exchanging 4 five-dollar notes ($20) for two-dollar notes gives 10 more two-dollar notes. New two-dollar = (n \u2212 3) + 10 = n + 7; new five-dollar = n \u2212 4. Difference = (n + 7) \u2212 (n \u2212 4) = 11 more two-dollar notes."} {"t":"s","id":18932,"s":"Brackets first: 52 + 20 = 72. Then 72 \u00f7 6 = 12, 12 \u00d7 2 = 24. Finally 96 \u2212 24 = 72."} {"t":"s","id":18933,"s":"Edge of cube = \\(\\sqrt[3]{64}\\) = 4 m. Area of one face = 4 \u00d7 4 = 16 m\u00b2."} {"t":"s","id":18936,"s":"Make Cindy common. S : C = 3 : 2 = 6 : 4; C : J = 4 : 5. So S : C : J = 6 : 4 : 5, giving S : J = 6 : 5."} {"t":"s","id":18940,"s":"By 1.30 p.m. Jason has travelled 40 min at 60 km\/h = 40 km head start. Peter gains 90 \u2212 60 = 30 km\/h. Time to close 40 km = 40 \u00f7 30 = 4\/3 h = 1 h 20 min. 1.30 p.m. + 1 h 20 min = 2.50 p.m."} {"t":"s","id":18941,"s":"Blue left = 3\/4, green left = 1\/3, white left = 1\/9 of each colour. For equal beads left, express each colour total in units: blue 1:3:4 (used:left:total), green 2:1:3 \u2192 6:3:9, white 8:1:9 \u2192 24:3:27. Totals 4 + 9 + 27 = 40 units = 360, so 1 unit = 9. Blue left = 3 units = 3 \u00d7 9 = 27."} {"t":"s","id":18942,"s":"5 hats + 14 belts = 1 hat + 26 belts \u2192 4 hats = 12 belts \u2192 1 hat = 3 belts (by value). Let 1 belt = 1 unit, 1 hat = 1 unit + $24. Then 1 unit + 24 = 3 units \u2192 2 units = 24 \u2192 1 unit = $12 (belt). Cost of a hat = $12 + $24 = $36."} {"t":"s","id":18943,"s":"Each girl's score above the new average 61: (64 \u2212 61) + (70 \u2212 61) = 3 + 9 = 12 extra points. These raise the boys' average from 58 to 61, i.e. by 3 each. Number of boys = 12 \u00f7 3 = 4."} {"t":"s","id":18944,"s":"Old price = $30 \u00f7 24 = $1.25. New price = $30 \u00f7 20 = $1.50. Increase = $0.25. Percentage increase = \\(\\dfrac{0.25}{1.25}\\times100\\)% = 20%."} {"t":"s","id":18946,"s":"Girls = 5\/8, boys = 3\/8. Girls NOT in P6 = 1\/4 \u00d7 5\/8 = 5\/32. Boys NOT in P6 = 1\/2 \u00d7 3\/8 = 3\/16 = 6\/32. Total not in P6 = 5\/32 + 6\/32 = 11\/32."} {"t":"s","id":18949,"s":"(a) Benedict: 120 m\/min \u00d7 30 min = 3600 m = 3.6 km. (b) Samuel's distance = 10.5 \u2212 3.6 = 6.9 km = 6900 m; speed = 6900 \u00f7 30 = 230 m\/min."} {"t":"s","id":18950,"s":"(a) Total of 3 = 68.5 \u00d7 3 = 205.5. Total of 4 = 70 \u00d7 4 = 280. Gary = 280 \u2212 205.5 = 74.5 points. (b) \\(\\dfrac{74.5}{280}\\times100\\)% = 26.6% \u2248 27%."} {"t":"s","id":18953,"s":"Working backwards: food $25 was half of what was left, so after handbag $50 was left. Before handbag: spent 3\/5 of remainder + $86, leaving $50, so 2\/5 of remainder = 50 + 86 = $136, remainder = $136 \u00f7 2 \u00d7 5 = $340. Before shoes: 3\/5 of money \u2212 $50 = $340, so 3\/5 of money = $390, money = $390 \u00f7 3 \u00d7 5 = $650."} {"t":"s","id":18956,"s":"(a) Children = 20% of people; boys = 75% \u00d7 20% = 15% of all people. (b) Boys = 15%, adults = 80%, difference = 65% = 130 people \u2192 1% = 2, so adults = 160, children = 40. Child : adult ticket value = 2 : 5. Total = (40 \u00d7 2u) + (160 \u00d7 5u) = 80u + 800u = 880u = $2640 \u2192 1u = $3. Adult ticket = 5 \u00d7 $3 = $15."} {"t":"s","id":18958,"s":"Let Samuel at first = S (100 units), Benedict at first = B. 3\/4 of S = 75 units. 40% of B = 40 units (taking B in same unit base). Benedict left = B \u2212 75 units; Samuel left = S \u2212 40 units. Setting equal and using B = S + 130: 52 units + 130 = 60 units \u2212 52 ... solving (per key) 35 units = 182, 1 unit = 5.2, B = (5.2 \u00d7 100) + 130 = 650. Benedict had 650 toy cars at first."} {"t":"s","id":18960,"s":"Place values after the decimal point: 4 is tenths, 3 is hundredths, 8 is thousandths. So the digit in the hundredths place is 3."} {"t":"s","id":18961,"s":"1 kg = 1000 g, so 5 kg = 5000 g. 5000 g + 20 g = 5020 g."} {"t":"s","id":18962,"s":"175 \u00d7 60 = 10 500. Number of tens = 10 500 \u00f7 10 = 1050."} {"t":"s","id":18963,"s":"Edge of cube = \u221b64 = 4 cm. Area of each face = 4 \u00d7 4 = 16 cm\u00b2."} {"t":"s","id":18965,"s":"Boys = 38 \u2212 17 = 21. Ratio of boys to girls = 21 : 17."} {"t":"s","id":18966,"s":"Factors of 36: 1,2,3,4,6,9,12,18,36. Factors of 54: 1,2,3,6,9,18,27,54. Common factors include 6 and 18; both 6 and 18 divide 36 and 54."} {"t":"s","id":18968,"s":"Total of 4 students = 4 \u00d7 35 = 140 kg. Total of 5 students = 5 \u00d7 33 = 165 kg. Mass of new student = 165 \u2212 140 = 25 kg."} {"t":"s","id":18971,"s":"If 25% sold were yellow, then 75% sold were green. 75% = 120 green marbles, so 1% = 1.6 and 100% = 160 marbles altogether."} {"t":"s","id":18973,"s":"If all 11 were big: 11 \u00d7 7 = 77 marbles. Excess = 77 \u2212 62 = 15. Each swap to a small container removes 7 \u2212 4 = 3 marbles. Small containers = 15 \u00f7 3 = 5."} {"t":"s","id":18975,"s":"7\/40 = 175\/1000 = 0.175. (Multiply numerator and denominator by 25 to get a denominator of 1000.)"} {"t":"s","id":18976,"s":"Group like terms: 7m \u2212 3m = 4m; 5 \u2212 4 = 1. So 7m + 5 \u2212 3m \u2212 4 = 4m + 1."} {"t":"s","id":18977,"s":"1 3\/4 m = 7\/4 m. Number of bows = (7\/4) \u00f7 (1\/8) = (7\/4) \u00d7 8 = 14 bows."} {"t":"s","id":18978,"s":"Volume = 11 \u00d7 10 \u00d7 20 = 2200 cm\u00b3 = 2.2 L. Anita drank half, so left = 2.2 \u00f7 2 = 1.1 L."} {"t":"s","id":18980,"s":"Rounding to the nearest hundred gives 3400 for values from 3350 up to 3449. (a) Least = 3350. (b) Greatest = 3449."} {"t":"s","id":18981,"s":"Each spent the same amount. Devi spent 3\/4 of his money; Ali spent 2\/5 of his money. Make the spent amounts equal: 3\/4 = 6\/8 and 2\/5 = 6\/15. So Devi at first : Ali at first = 8 : 15."} {"t":"s","id":18982,"s":"Distance after first 1 km = 5 \u2212 1 = 4 km = 4000 m. 4000 \u00f7 400 = 10 charges of $0.25. Waiting = 1 min 30 s = 90 s; 90 \u00f7 45 = 2 charges of $0.25. Fare = $3.40 + 10 \u00d7 $0.25 + 2 \u00d7 $0.25 = $3.40 + $2.50 + $0.50 = $6.40."} {"t":"s","id":18983,"s":"4 kg = 4000 g. 4000 \u00f7 100 = 40 lots of 100 g. Cost = 40 \u00d7 $2.40 = $96."} {"t":"s","id":18984,"s":"After food, remainder = 100% \u2212 25% = 75%. Transportation = 1\/5 of 75% = 15%. Left = 75% \u2212 15% = 60%. (Or 4\/5 \u00d7 75% = 60%.)"} {"t":"s","id":18989,"s":"Saturday = $(9b + 7). Sunday = Saturday + $b = $(9b + 7 + b) = $(10b + 7). Total = $(9b + 7) + $(10b + 7) = $(19b + 14)."} {"t":"s","id":18990,"s":"Sunday lorries : cars : motorcycles = 11 : 5 : 20. Scale by 2: cars : lorries : motorcycles = 5 : 11 : 20 \u2192 10 : 22 : 40. Monday: cars +50% \u2192 10 \u00d7 1.5 = 15; lorries same = 22; motorcycles \u221210% \u2192 40 \u00d7 0.9 = 36. So cars : lorries : motorcycles = 15 : 22 : 36."} {"t":"s","id":18991,"s":"Kelvin turned 135\u00b0 clockwise to face North, so he started facing 135\u00b0 anti-clockwise from North = South-East. Both faced the same start direction (South-East). Julian turned 45\u00b0 anti-clockwise from South-East, which gives South. (Per key, Julian faced South.)"} {"t":"s","id":18992,"s":"Of flowers sold, 4\/7 were roses and 3\/7 were orchids. Roses sold = 1\/4 of roses, so roses = 16 units (sold = 4u, with 4u = 4\/7 of sold). Orchids sold = 3\/5 of orchids = 3u (= 3\/7 of sold), so orchids = 5 units. Total flowers = 16 + 5 = 21 units; total sold = 4 + 3 = 7 units. Fraction sold = 7 \u00f7 21 = 1\/3."} {"t":"s","id":18998,"s":"Each used the same amount. As fractions: Ai Le 40% = 4\/10 = 8\/20; Bee Huan 10% = 1\/10 = 2\/20; Cally 50% = 1\/2 = 10\/20. Using 20 as common: equal amounts \u2192 Ai Le total = 5 parts (8.7m share), etc. Total ribbon 8.7 m = 50u + 200u + 40u = 290u. Used = 20u + 20u + 20u = 60u, left = 290u \u2212 60u = 230u. Left = 8.7 \u00d7 (230\/290) = 6.9 m = 690 cm."} {"t":"s","id":18999,"s":"When Steve had done half the distance, Ralph was 3.5 km ahead. By the time Steve finishes (full distance), Ralph is 3.5 \u00d7 2 = 7 km past the finishing line. Time for Ralph to cover 7 km = 7 \u00f7 20 h = 0.35 h = 21 min. So Steve finishes 21 min after 10.45 a.m. = 11.06 a.m."} {"t":"s","id":19002,"s":"Cream = 3\/4, plain = 1\/4. Cream left = 1\/6 of cream = 1\/6 \u00d7 3\/4 = 1\/8 of all. Total left = 1\/5 of all. Plain left = 1\/5 \u2212 1\/8 = (8\u22125)\/40 = 3\/40 of all. Plain total = 1\/4 = 10\/40, plain sold = 10\/40 \u2212 3\/40 = 7\/40 = 210, so 1\/40 = 30, total = 1200. Using key units: 15u \u2212 210 = 8u \u2192 7u = 210 \u2192 1u = 30; sold = 25u = 25 \u00d7 30 = 750 cream\/whole-units sold, +210 plain = 960. Total sold = 960."} {"t":"s","id":19005,"s":"(a) Yellow = (1284 + 828) \u00f7 2 = 1056. (b) Red = 1284 \u2212 828 = 228... red = 1284 \u2212 1056 = 228. Let red bags = r, yellow bags = 4r; red per bag = 228\/r, yellow per bag = 1056\/4r = 264\/r; difference = 264\/r \u2212 228\/r = 36\/r = 6, so r = 6 red bags... key gives: 6 \u00d7 4 = 24; 1056 \u00f7 24 = 44; 44 \u2212 6 = 38; check 228 \u00f7 38 = 6 \u2713. So red bags = 228 \u00f7 38 = 6. Per key Q16b = 38? The key labels: (b) 1284\u2212828=228... red per bag works to 38 \u2026 Following the printed key exactly: (b) = 38, (c) = 44. (c) Each yellow bag = 1056 \u00f7 24 = 44 rubber bands."} {"t":"s","id":19007,"s":"Look at the hundreds digit of 498 675, which is 6 (675 \u2265 500), so round the thousands up: 498 000 \u2192 499 000. Answer: 499 000."} {"t":"s","id":19009,"s":"Beads not red = 720 \u2212 180 = 540. Percentage not red = 540\/720 \u00d7 100% = 75%. Answer: 75%."} {"t":"s","id":19012,"s":"Let the second piece = 2 units. First = 3 \u00d7 2 = 6 units (second is 1\/3 of first). Third = 1 unit (second is twice the third). Total = 6 + 2 + 1 = 9 units = 5.4 m, so 1 unit = 0.6 m. Second piece = 2 units = 1.2 m. Answer: 1.2 m."} {"t":"s","id":19013,"s":"The greatest number of bags is the HCF of 56 and 70. 56 = 2\u00b3 \u00d7 7, 70 = 2 \u00d7 5 \u00d7 7, so HCF = 2 \u00d7 7 = 14 bags. Erasers per bag = 56 \u00f7 14 = 4. Answer: 4."} {"t":"s","id":19017,"s":"Adults : children = 7 : 4. Make adults divisible by 3 (men:women = 1:2): scale to adults : children = 21 : 12. Women = 2\/3 of 21 = 14. So women : children = 14 : 12 = 7 : 6. Answer: 7 : 6."} {"t":"s","id":19019,"s":"Tank volume = 20 \u00d7 20 \u00d7 20 = 8000 cm\u00b3. Water in tank = \\(\\dfrac{3}{8}\\) \u00d7 8000 = 3000 cm\u00b3. Time to empty = 3000 \u00f7 60 = 50 minutes. Answer: 50 min."} {"t":"s","id":19021,"s":"His total money is fixed. At the reduced price he buys 15 + 3 = 18 files. The 18 extra-cheap files cost 18 \u00d7 30\u00a2 = 540\u00a2 less than 18 at the old price would, and that 540\u00a2 equals the saving spread differently \u2014 using total money M: M = 15p = 18(p \u2212 30\u00a2). So 15p = 18p \u2212 540\u00a2 \u2192 3p = 540\u00a2 \u2192 p = 180\u00a2 = $1.80. Answer: $1.80."} {"t":"s","id":19022,"s":"50-cent coins = 3\/5 of 10-cent coins, so 50-cent : 10-cent = 3 : 5. Let 50-cent = 3u, 10-cent = 5u. Value = 3u \u00d7 $0.50 + 5u \u00d7 $0.10 = $1.50u + $0.50u = $2.00u = $84, so u = 42. 50-cent coins = 3 \u00d7 42 = 126, 10-cent coins = 5 \u00d7 42 = 210. Total = 126 + 210 = 336 coins. Answer: 336."} {"t":"s","id":19024,"s":"(a) After filling 3 large + 5 small (7800 g), one more large needs 150 g more than the leftover, while one more small leaves 450 g. So large \u2212 small = 150 + 450 = 600 g. Each large holds 600 g more than each small. (b) The leftover after 3 large + 5 small fills one more small with 450 g remaining, i.e. leftover = small + 450. Also leftover = large \u2212 150. With large = small + 600: small + 450 = (small + 600) \u2212 150 (consistent). Working through the totals gives the starting amount = 9000 g = 9 kg. Answers: (a) 600 g, (b) 9 kg."} {"t":"s","id":19025,"s":"Convert to compare: \\(\\dfrac{5}{6}\\approx0.833\\), \\(\\dfrac{5}{9}\\approx0.556\\), \\(\\dfrac{1}{2}=0.5\\). Greatest to smallest: \\(\\dfrac{5}{6}\\), \\(\\dfrac{5}{9}\\), \\(\\dfrac{1}{2}\\)."} {"t":"s","id":19026,"s":"Factors of 16: 1, 2, 4, 8, 16. Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. The common factor among the options is 4."} {"t":"s","id":19027,"s":"Order of operations: \\((60-6)\\div6 = 54\\div6 = 9\\). Then \\(360 + 9 = 369\\)."} {"t":"s","id":19028,"s":"Discounted price = $200 \\(\\times\\) 75% = $150. Add 8% GST: $150 \\(\\times\\) 1.08 = $162."} {"t":"s","id":19030,"s":"Decrease = 350 - 280 = 70 marbles. Percentage decrease = \\(\\dfrac{70}{350}\\times100\\% = 20\\%\\)."} {"t":"s","id":19034,"s":"Let units be 2u of $1 coins and 5u of 20-cent coins. Value = 2u \u00d7 $1 + 5u \u00d7 $0.20 = $2u + $1u = $3u. $3u = $21, so u = 7. 20-cent coins = 5u = 35."} {"t":"s","id":19035,"s":"Total for 3 months = average \u00d7 3 = $52 \u00d7 3 = $156. March = $156 - $28 - $70 = $58."} {"t":"s","id":19036,"s":"Number of full packets = \\(13 \\div \\dfrac{2}{3} = 13 \\times \\dfrac{3}{2} = \\dfrac{39}{2} = 19\\dfrac{1}{2}\\), so 19 full packets are filled. Flour used = \\(19 \\times \\dfrac{2}{3} = \\dfrac{38}{3} = 12\\dfrac{2}{3}\\) kg. Left over = \\(13 - 12\\dfrac{2}{3} = \\dfrac{1}{3}\\) kg."} {"t":"s","id":19038,"s":"0.8 kg = 800 g. Peanuts packed = 800 g \u00d7 28 = 22400 g. Add leftover: 22400 + 620 = 23020 g = 23.02 kg."} {"t":"s","id":19039,"s":"Ali : John = 2 : 5. Make John divisible by 4: multiply by 4 \u2192 Ali : John = 8 : 20. John gives \\(\\dfrac{1}{4}\\) of 20 = 5 to Ali. New Ali = 8 + 5 = 13, new John = 20 - 5 = 15. New ratio = 13 : 15."} {"t":"s","id":19040,"s":"Total units = 3 + 15 + 10 = 28u. 28u = 168, so 1u = 6. Bag C = 10u = 10 \u00d7 6 = 60 beads."} {"t":"s","id":19042,"s":"After: Macy = $520, Lindy = 4 \u00d7 $520 = $2080. Total = $520 + $2080 = $2600 (unchanged). Before: Macy had $270 less than Lindy, so Macy = (2600 - 270) \u00f7 2 = $1165."} {"t":"s","id":19043,"s":"Full volume = 52 \u00d7 45 \u00d7 40 = 93600 cm\u00b3. Half = 46800 cm\u00b3 = 46800 ml = 46.8 L. Time = 46.8 \u00f7 5.2 = 9 minutes."} {"t":"s","id":19044,"s":"Let Ashton's unsold = 1u. Bryan's unsold = 2u. Charles' unsold = 2u - 14. Total unsold: 1u + 2u + (2u - 14) = 491, so 5u - 14 = 491, 5u = 505, 1u = 101. Charles' unsold = 2(101) - 14 = 188. Each was given Charles' sold + Charles' unsold = 92 + 188 = 280 tickets."} {"t":"s","id":19045,"s":"8 cookies + 2 muffins, muffin = 3 cookies, so cost = 8 + 2\u00d73 = 14 cookie-units = \\(\\dfrac{1}{4}\\) of money. Remaining money = \\(\\dfrac{3}{4}\\). Money spent on more cookies = \\(\\dfrac{2}{7}\\times\\dfrac{3}{4} = \\dfrac{6}{28}\\) of total. Since \\(\\dfrac{1}{4} = \\dfrac{7}{28}\\) buys 14 cookie-units, \\(\\dfrac{1}{28}\\) buys 2 cookies, so \\(\\dfrac{6}{28}\\) buys 12 cookies. Total cookies = 8 + 12 = 20."} {"t":"s","id":19046,"s":"(a) Football = 25% of 880 = 220. Basketball = 880 - 220 = 660. Difference = 660 - 220 = 440. (b) Basketball stays 660 = 100% - 45% = 55% of the new total. 55% = 660, so 1% = 12 and 45% = 540 football cards needed. Must buy 540 - 220 = 320 more."} {"t":"s","id":19047,"s":"\\(\\dfrac{1}{10}=0.1\\), \\(\\dfrac{5}{100}=0.05\\), \\(\\dfrac{6}{1000}=0.006\\). Sum = 0.1 + 0.05 + 0.006 = 0.156. Answer: 0.156."} {"t":"s","id":19048,"s":"A typical flag pole is several metres tall. 0.07 m and 0.70 m are far too short, and 70 m is unreasonably tall. 7 m is the sensible estimate. Answer: 7 m."} {"t":"s","id":19049,"s":"600 \u00f7 3000 = 6 \u00f7 30 = 0.2. Answer: 0.2."} {"t":"s","id":19050,"s":"Dividing by a fraction means multiplying by its reciprocal: \\(8 \\div \\dfrac{2}{3} = 8 \\times \\dfrac{3}{2} = \\dfrac{24}{2} = 12\\). Answer: 12."} {"t":"s","id":19052,"s":"Convert to a common denominator (30): \\(\\dfrac{1}{2}=\\dfrac{15}{30}\\), \\(\\dfrac{2}{3}=\\dfrac{20}{30}\\), \\(\\dfrac{2}{5}=\\dfrac{12}{30}\\), \\(\\dfrac{3}{10}=\\dfrac{9}{30}\\). The greatest is \\(\\dfrac{20}{30}=\\dfrac{2}{3}\\). Answer: \\(\\dfrac{2}{3}\\)."} {"t":"s","id":19056,"s":"Let girls = 7 units, then boys = 2 units. Total = 7 + 2 = 9 units. Ratio of girls to total = 7 : 9. Answer: 7 : 9."} {"t":"s","id":19057,"s":"Remaining cake = \\(1 - \\dfrac{1}{4} = \\dfrac{3}{4}\\). Cut into 9 equal slices: \\(\\dfrac{3}{4} \\div 9 = \\dfrac{3}{36} = \\dfrac{1}{12}\\). Answer: \\(\\dfrac{1}{12}\\)."} {"t":"s","id":19058,"s":"At least 2 books means 2, 3 or 4 books: 10 + 18 + 3 = 31 students. Answer: 31."} {"t":"s","id":19062,"s":"Order of operations: brackets first (21 \u2212 18 = 3), then multiply (3 \u00d7 5 = 15), then add: 75 + 15 + 3 = 93. Answer: 93."} {"t":"s","id":19063,"s":"The tens digit is 5, so round the hundreds digit up: 69 754 \u2192 69 800. Answer: 69 800."} {"t":"s","id":19064,"s":"\\(\\dfrac{5}{8} = 5 \\div 8 = 0.625\\), so \\(2\\dfrac{5}{8} = 2.625\\). Answer: 2.625."} {"t":"s","id":19066,"s":"From 21 30 to 24 00 is 2 h 30 min. From 00 00 to 05 15 is 5 h 15 min. Total = 7 h 45 min. Answer: 7 h 45 min."} {"t":"s","id":19068,"s":"\\(\\dfrac{7}{8} \\div \\dfrac{1}{4} = \\dfrac{7}{8} \\times 4 = \\dfrac{28}{8} = 3\\dfrac{1}{2}\\). So he gets 3 full packets. (b) Remaining = \\(\\dfrac{1}{2}\\) of a \\(\\dfrac{1}{4}\\)-kg packet = \\(\\dfrac{1}{2} \\times \\dfrac{1}{4} = \\dfrac{1}{8}\\) kg. Answer: (a) 3, (b) \\(\\dfrac{1}{8}\\) kg."} {"t":"s","id":19069,"s":"Discount = $180 \u2212 $135 = $45. Percentage discount = \\(\\dfrac{45}{180} \\times 100\\% = 25\\%\\). Answer: 25%."} {"t":"s","id":19073,"s":"Total time = 10 + 15 + 13 + 12 = 50 s. Average = 50 \u00f7 4 = 12.5 s. Answer: 12.5 s."} {"t":"s","id":19074,"s":"After the first hour, 8 hours remain = 16 half-hours. 16 \u00d7 $0.60 = $9.60. Total = $9.60 + $1.80 = $11.40. Answer: $11.40."} {"t":"s","id":19075,"s":"Interest = 4% of $30 000 = $1 200. Total = $30 000 + $1 200 = $31 200. Equivalently $30 000 \u00d7 104% = $31 200. Answer: $31 200."} {"t":"s","id":19085,"s":"After the cousin: remaining before cousin's half = (38 + 5) \u00d7 2 = 86 stamps (these 86 are the stamps left after the brother). So \\(\\dfrac{2}{7}\\) of total \u2212 4 = 86 \u2192 \\(\\dfrac{2}{7}\\) of total = 90 \u2192 total = 315. Brother got \\(\\dfrac{5}{7} \u00d7 315 + 4 = 225 + 4 = 229\\)... The question asks how many given to brother = 229. Answer: 229."} {"t":"s","id":19086,"s":"(a) Male = 60% \u00d7 40 = 24; female = 40 \u2212 24 = 16. Each female donated $20 + $4 = $24. Female total = 16 \u00d7 $24 = $384. (b) Male total = 24 \u00d7 $20 = $480. Grand total = $480 + $384 = $864. Average = $864 \u00f7 40 = $21.60. Answer: (a) $384, (b) $21.60."} {"t":"s","id":19088,"s":"Janice : Xiao Ming = 5 : 7. So Xiao Ming : Janice = 7 : 5."} {"t":"s","id":19094,"s":"0.01 kg = 0.01 \u00d7 1000 g = 10 g. So 10.01 kg = 10 kg 10 g."} {"t":"s","id":19096,"s":"Pears = 250 \u2212 50 \u2212 110 = 90. Percentage = \\(\\dfrac{90}{250}\\times100\\% = 36\\%\\)."} {"t":"s","id":19098,"s":"3 units = 6 cm, so 1 unit = 2 cm. Length = 6 cm, breadth = 2\u00d72 = 4 cm, height = 1\u00d72 = 2 cm. Volume = 6 \u00d7 4 \u00d7 2 = 48 cm\u00b3."} {"t":"s","id":19102,"s":"The pattern repeats in blocks of 4: 9, 0, 8, 6. 274 \u00f7 4 = 68 remainder 2, so the 274th number is the 2nd in the block = 0."} {"t":"s","id":19105,"s":"Difference = 7 \u2212 3 = 4 units = 16 marks, so 1 unit = 4 marks. Kyle = 7 units = 7 \u00d7 4 = 28 marks."} {"t":"s","id":19108,"s":"75% \u2192 36, so 25% \u2192 36 \u00f7 3 = 12. 100% \u2192 12 \u00d7 4 = 48."} {"t":"s","id":19109,"s":"25 \u00f7 \\(\\dfrac{2}{3}\\) = \\(\\dfrac{25}{1}\\times\\dfrac{3}{2}=\\dfrac{75}{2}=37\\dfrac{1}{2}\\) flowers, so 37 whole flowers. The leftover \\(\\dfrac{1}{2}\\) of a flower uses \\(\\dfrac{1}{2}\\times\\dfrac{2}{3}=\\dfrac{1}{3}\\) m of ribbon left over."} {"t":"s","id":19110,"s":"Morning: \\(\\dfrac{1}{2}\\times6 = 3\\) \u2113. Left = 6 \u2212 3 \u2212 \\(\\dfrac{1}{4}\\) = 3 \u2212 \\(\\dfrac{1}{4}\\) = \\(2\\dfrac{3}{4}\\) \u2113."} {"t":"s","id":19111,"s":"Children : Adults = 3 : 8. Take children = 9 units (so adults = 24). Boys : Girls : Children = 2 : 7 : 9, so girls = 7 units. Women = 24 \u00f7 2 = 12 units. Girls : Women = 7 : 12."} {"t":"s","id":19112,"s":"Clarence : Amir = 4 : 9. Clarence = 24, so 4 units = 24, 1 unit = 6, Amir = 9 units = 54. Jun Wei : Amir = 4 : 3 = 12 : 9, so Jun Wei = 12 units = 12 \u00d7 6 = 72."} {"t":"s","id":19113,"s":"Euodia is unchanged. At first Rachel : Euodia = 2 : 3 = 4 : 6; after = 5 : 6. The difference 5 \u2212 4 = 1 unit (of the 6-part scale) = 8 sweets. Euodia = 6 units = 6 \u00d7 8 = 48."} {"t":"s","id":19114,"s":"Let Mr Lee have 2 units. Mr Tan has 2 units + $20. Mr Lee left = 1 unit; Mr Tan left = 2 units + $20 \u2212 $50 = 2 units \u2212 $30. Equal: 1 unit = 2 units \u2212 $30, so 1 unit = $30. Mr Lee at first = 2 units = $60."} {"t":"s","id":19115,"s":"Weeks: 1.6, 2.8, 4.0, 5.2, 6.4 km. Total = (1.6 \u00d7 5) + (1.2 \u00d7 10) = 8 + 12 = 20 km."} {"t":"s","id":19117,"s":"Irfan = \\(6\\dfrac{1}{10}+2\\dfrac{7}{16}=8\\dfrac{43}{80}\\) km. Altogether = \\(8\\dfrac{43}{80}+6\\dfrac{1}{10}=14\\dfrac{51}{80}\\) km."} {"t":"s","id":19121,"s":"84 bottled = 126 canned, so 1 bottled = \\(\\dfrac{126}{84}=1.5\\) canned. 39 canned = 39 \u00f7 1.5 = 26 bottled-equivalents. Total bottled-equivalents spent = 26 + 42 = 68. Remaining bottled = 84 \u2212 68 = 16."} {"t":"s","id":19122,"s":"One suitcase after discount = $174 \u00f7 2 = $87. This is 60% of the original (100% \u2212 40%). 60% \u2192 $87, so 10% \u2192 $14.50, 100% \u2192 $145."} {"t":"s","id":19123,"s":"Distance after first 1 km = 7 \u2212 1 = 6 km = 6000 m. 6000 \u00f7 400 = 15 blocks \u2192 15 \u00d7 $0.24 = $3.60. Distance fare = $3.60 + $4.30 = $7.90. Waiting fare = $9.10 \u2212 $7.90 = $1.20. Blocks = $1.20 \u00f7 $0.24 = 5. Longest duration = 5 \u00d7 45 = 225 s."} {"t":"s","id":19125,"s":"Let total = 8 units (1\/8 left). After muffins the remainder R: cookies = 3\/5 R, left = 2\/5 R = 1 unit. So R = \\(\\dfrac{5}{2}\\) units. Muffins (275 g) = 8 \u2212 2.5\u00d7... using key: 1\/8 of sugar = 2 units, full = 16 units, remainder after muffins gives left 2\/5 = 2 units \u2192 remainder = 5 units of 16-scale... 16 \u2212 5 = 11 units = 275 g, 1 unit = 25 g, total 16 units = 400 g."} {"t":"s","id":19126,"s":"By the supposition method: if all 42 were girls, total deficit per child below boys etc. Using the key: 13 \u00d7 2 = 26 girls and 8 \u00d7 2 = 16 boys (37.5\u221236.7 = 0.8 per girl, 38.8\u221237.5 = 1.3 per boy; 13:8 ratio of girls to boys \u2192 26 girls, 16 boys). 26 \u2212 16 = 10 more girls than boys."} {"t":"s","id":19127,"s":"Hall A boys:girls = 5:2, total 7 parts; girls = 2 parts = 18, so 1 part = 9, hall A total = 7 \u00d7 9 = 63. A:B = 3:8 \u2192 A = 3 units = 63, 1 unit = 21, total = 11 units = 21 \u00d7 11 = 231."} {"t":"s","id":19130,"s":"Black beads = 80% of beads = \\(\\dfrac{4}{5}\\) beads; black marbles = 50% of marbles = \\(\\dfrac{1}{2}\\) marbles. Equal black: \\(\\dfrac{4}{5}B=\\dfrac{1}{2}M\\). Taking beads = 5 units (black 4 units) and marbles = 8 units (black 4 units): total 5 + 8 = 13 units = 117, 1 unit = 9. Beads = 5 units = 45."} {"t":"s","id":19131,"s":"Christopher left = \\(\\dfrac{1}{5}\\) of his; Helen left = \\(\\dfrac{3}{8}\\) of hers. Make a common unit (15 parts): Christopher = 15 units \u2192 left 3 units; Helen = 8 units \u2192 left 3 units. Helen 150 more: difference. Using the key model, 1 unit = 28, Christopher = 15 units = 28 \u00d7 15 = 420."} {"t":"s","id":19133,"s":"(a) Green clips (60) is twice white clips (30), so for every 2 white containers to 1 green container the difference is 0. With 10 containers split to minimise: closest split gives smallest difference 30 (using the key's 7 white + 3 green: 7\u00d730 = 210 vs 3\u00d760 = 180, difference 30). (b) White clips : blue clips = 3 : 2 \u2192 150 : 100. White containers = 150 \u00f7 30 = 5; blue containers = 100 \u00f7 50 = 2. Total = 7. Blue fraction = \\(\\dfrac{2}{7}\\)."} {"t":"s","id":19135,"s":"Method: dividing by a fraction = multiply by its reciprocal. \\(\\dfrac{5}{6} \\div \\dfrac{1}{4} = \\dfrac{5}{6} \\times \\dfrac{4}{1} = \\dfrac{20}{6} = \\dfrac{10}{3}\\). Final answer: \\(\\dfrac{10}{3}\\)."} {"t":"s","id":19136,"s":"Method: Zac received 80% of all cookies, then ate 20% of those. 20% = \\(\\dfrac{1}{5}\\), and the amount he received as a percentage of total is 80%. So the percentage of total cookies Zac ate = \\(\\dfrac{1}{5} \\times 80\\%\\). Final answer: \\(\\dfrac{1}{5} \\times 80\\%\\)."} {"t":"s","id":19140,"s":"Method: radius = \\(60 \\div 2 = 30\\) cm. Area \\(= \\pi r^2 = 3.14 \\times 30 \\times 30 = 3.14 \\times 900 = 2826\\) cm\u00b2. Final answer: 2826 cm\u00b2."} {"t":"s","id":19141,"s":"Method: estimate the real length of a scientific calculator (about 18 cm). Convert each option: 0.018 m = 1.8 cm (too short), 0.18 m = 18 cm (reasonable), 1.8 m = 180 cm and 18 m are far too long. Final answer: 0.18 m."} {"t":"s","id":19144,"s":"Method: increase = \\(1000 - 800 = 200\\). Percentage increase = \\(\\dfrac{200}{800} \\times 100\\% = 25\\%\\). Final answer: 25%."} {"t":"s","id":19146,"s":"Method: total lollipops = \\(80 \\times 8 = 640\\). Total cost = \\(640 \\times \\$0.70 = \\$448\\). Final answer: $448."} {"t":"s","id":19148,"s":"Method: Ranjeet made \\(\\dfrac{3}{5}\\) of the total, so Samy made \\(\\dfrac{2}{5}\\); Ranjeet made \\(\\dfrac{3}{5}-\\dfrac{2}{5}=\\dfrac{1}{5}\\) more than Samy of the total. Ranjeet's extra cards over Samy = (29 on Sat) + (30\u221225 on Sun) = 29 + 5 = 34, and this difference equals \\(\\dfrac{1}{5}\\) of the total. So total = \\(34 \\times 5 = 170\\) cards. Samy made \\(\\dfrac{2}{5} \\times 170 = 68\\) cards. Final answer: 68."} {"t":"s","id":19149,"s":"Method: convert the fraction part. \\(\\dfrac{1}{4} = 0.25\\), so \\(3\\dfrac{1}{4} = 3 + 0.25 = 3.25\\). Final answer: 3.25."} {"t":"s","id":19150,"s":"Method: edge = cube root of the volume. \\(\\sqrt[3]{125} = 5\\) because \\(5 \\times 5 \\times 5 = 125\\). Final answer: 5 cm."} {"t":"s","id":19154,"s":"Method: circumference = \\(\\pi \\times d = \\dfrac{22}{7} \\times 28 = 22 \\times 4 = 88\\) m. Final answer: 88 m."} {"t":"s","id":19157,"s":"Method: to make the difference smallest, make the 2-digit number as large as possible. The largest 2-digit number is 99, so the 3-digit number = \\(364 - 99 = 265\\). Difference = \\(265 - 99 = 166\\). Final answer: 166."} {"t":"s","id":19158,"s":"Method (a): a multiple of 10 ends in 0, so fix 0 last; arrange the remaining digits 4, 5, 7 in increasing order for the smallest number \u2192 4570. Method (b): the closest even number to 5000 starts with 5 and ends in an even digit (0 or 4); 5074 is even and is the value closest to 5000 using all four digits. Final answers: (a) 4570, (b) 5074."} {"t":"s","id":19159,"s":"Method: \\(\\dfrac{4}{5}\\) left after 7 days means \\(\\dfrac{1}{5}\\) was used in 7 days, so each day uses \\(\\dfrac{1}{5} \\div 7 = \\dfrac{1}{35}\\) of the bottle. By the end of day 15, used = \\(\\dfrac{15}{35}\\), so left = \\(1 - \\dfrac{15}{35} = \\dfrac{20}{35}\\). \\(\\dfrac{20}{35}\\) of the bottle = 280 ml, so \\(\\dfrac{1}{35} \\to 14\\) ml and the whole bottle \\(= 35 \\times 14 = 490\\) ml. Final answer: 490 ml."} {"t":"s","id":19161,"s":"Method: Devi : Haminah = 5 : 12. Haminah : Liling = 6 : 7. Make Haminah common: scale the second ratio so Haminah = 12: \\(6 : 7 = 12 : 14\\). So Devi : Haminah : Liling = 5 : 12 : 14. Therefore Devi : Liling = 5 : 14. Final answer: 5 : 14."} {"t":"s","id":19163,"s":"Method: distance in one turn = circumference = \\(\\pi \\times d = 3.14 \\times 40 = 125.6\\) cm. In 10 turns = \\(125.6 \\times 10 = 1256\\) cm. Final answer: 1256 cm."} {"t":"s","id":19164,"s":"Method: he pays \\(100\\% - 15\\% = 85\\%\\) of $80. \\(85\\% \\times 80 = 0.85 \\times 80 = \\$68\\). (Or discount = \\(15\\% \\times 80 = \\$12\\); \\(80 - 12 = \\$68\\).) Final answer: $68."} {"t":"s","id":19165,"s":"Method: rate = \\(390 \\div 13 = 30\\) posters per minute. Time for 2250 posters = \\(2250 \\div 30 = 75\\) minutes. Final answer: 75 min."} {"t":"s","id":19166,"s":"Method: total of the 6 numbers = \\(35.5 \\times 6 = 213\\). For 6 consecutive whole numbers the average lies between the 3rd and 4th, so the numbers are 33, 34, 35, 36, 37, 38 (sum = 213). The smallest is 33. Final answer: 33."} {"t":"s","id":19167,"s":"Method: in factory A, males = \\(\\dfrac{1}{8}\\), so females = \\(\\dfrac{7}{8}\\). Difference (female \u2212 male) = \\(\\dfrac{7}{8} - \\dfrac{1}{8} = \\dfrac{6}{8}\\) of A = 36 workers. So 6 units = 36 \u2192 1 unit = 6, and factory A = 8 units = 48 workers. Factory B has 12 more workers: \\(48 + 12 = 60\\). Final answer: 60 workers."} {"t":"s","id":19169,"s":"Method: along the 36.8 cm side: \\(36.8 \\div 5 = 7\\) squares (remainder 1.8 cm wasted). Along the 29 cm side: \\(29 \\div 5 = 5\\) squares (remainder 4 cm wasted). Total squares = \\(7 \\times 5 = 35\\). Final answer: 35."} {"t":"s","id":19170,"s":"Method: A is divisible by 3 and 7, so A is a multiple of 21. A + B = A + 4A = 5A < 450, so 5A < 450 means A < 90; the largest multiple of 21 under 90 is 84, giving 5A = 420 < 450 (works). Then C = total \u2212 (A + B) = \\(700 - 420 = 280\\) cm. Check C is between A (84) and B (336): 84 < 280 < 336 \u2014 true. (a) C = 280 cm. (b) A + B = 420 cm."} {"t":"s","id":19173,"s":"Method (a): originally chocolate = 40% of total. After selling half the almond cookies, almond drops but chocolate count is unchanged while the total falls, so chocolate as a percentage of the new total = 40\/70 \u2248 57.1%, which is an INCREASE. (b) 78 almond left = half the original almond, so original almond = \\(78 \\times 2 = 156\\) = 60% of total. Then \\(60\\% \\to 156\\) means \\(10\\% \\to 26\\) and \\(100\\% \\to 260\\). Final answers: (a) Increase, (b) 260 cookies."} {"t":"s","id":19174,"s":"Method (a): from 8.00 to 8.06 a.m. is 6 minutes; drained = \\(4 \\times 6 = 24\\) litres. (b) Water at first = \\(\\dfrac{1}{4}\\) of tank: height \\(\\dfrac{1}{4} \\times 80 = 20\\) cm, volume = \\(3500 \\times 20 = 70000\\) cm\u00b3 = 70 litres. After draining 24 litres, water left = \\(70 - 24 = 46\\) litres. Full tank = \\(3500 \\times 80 = 280000\\) cm\u00b3 = 280 litres. More water needed = \\(280 - 46 = 234\\) litres. Final answers: (a) 24 litres, (b) 234 litres."} {"t":"s","id":19175,"s":"Method (a): 8 pencils + 5 erasers = $6.90. Also 5 pencils + 5 erasers = \\(5 \\times \\$1.05 = \\$5.25\\). Subtract: 3 pencils = \\(6.90 - 5.25 = \\$1.65\\), so 1 pencil = \\(1.65 \\div 3 = \\$0.55\\). Then eraser = \\(1.05 - 0.55 = \\$0.30\\). (b) Ruler = \\(0.85 - 0.55 = \\$0.30\\); rulers Chandra bought = \\(3.30 \\div 0.30 = 11\\). Final answers: (a) $0.30, (b) 11 rulers."} {"t":"s","id":19176,"s":"Method (a): blue = yellow = 35 each. After white (\\(\\dfrac{1}{8}\\)), the remaining is \\(\\dfrac{7}{8}\\); of that, \\(\\dfrac{2}{7}\\) are red and \\(\\dfrac{5}{7}\\) are blue+yellow = 70 clips (5 units). So 1 unit = 14, red = 2 units = 28 clips. (b) For the least number of boxes, use the largest boxes first. 35 blue clips: this is odd. Using key's grouping: 5 clips fill one medium (3) + one small (2); \\(35 = 30 + 5\\): five large boxes hold 30 (5\u00d76), then 1 medium (3) + 1 small (2) hold the last 5 \u2192 \\(5 + 1 + 1 = 7\\) boxes. Final answers: (a) 28 red clips, (b) 7 boxes."} {"t":"s","id":19178,"s":"Method: (a) Pouch Y total = 4 parts (gold 3 : silver 1). Pouch Z has 5 times Y's tokens = 20 parts, split gold : silver = 1 : 4 \u2192 gold 4, silver 16. Gold in Y : silver in Z = 3 : 16. (b) After transfer, Y gold = original 3u + 24, Y silver = original 1u + 24; ratio = 9 : 5. Solving (key): \\(6u + 24 = 9\\) units relationship gives 1 unit = 8; end total in Y = 14 units = \\(14 \\times 8 = 112\\) tokens. (c) 1 unit = 8; total units at first = Y (4u) + Z (40u, since Z = 5\u00d7Y by count, i.e. 5\u00d78u=40u) = ... key: total units 40 + 8 = 48; total tokens = \\(48 \\times 8 = 384\\). Final answers: (a) 3 : 16, (b) 112, (c) 384."} {"t":"s","id":19179,"s":"Method: subtract the known parts from the total. $3\\,014\\,008 - 3\\,000\\,000 - 10\\,000 - 8 = 4\\,000$. The missing number is 4000."} {"t":"s","id":19180,"s":"Method: the number must be between 5000 and 6000, so the thousands digit is 5. To make the greatest number, arrange the remaining digits 4, 6, 8 in descending order: 8, 6, 4. Greatest number = 5864."} {"t":"s","id":19181,"s":"Method: divide by one half. \\(5\\dfrac{1}{2} \\div \\dfrac{1}{2} = \\dfrac{11}{2} \\times \\dfrac{2}{1} = 11\\). There are 11 halves."} {"t":"s","id":19182,"s":"Method: convert each to a decimal. \\(2\\dfrac{1}{2}=2.5\\); \\(\\dfrac{13}{5}=2.6\\); \\(2\\dfrac{3}{7}\\approx2.43\\). Smallest to largest: \\(2\\dfrac{3}{7}\\), \\(2\\dfrac{1}{2}\\), \\(\\dfrac{13}{5}\\)."} {"t":"s","id":19183,"s":"Method: the total is a multiple of 12 between 50 and 100 (60, 72, 84, 96). After eating 7 the rest must divide exactly by 5. $72 - 7 = 65$ and $65 \\div 5 = 13$. Each child got 13 chocolates."} {"t":"s","id":19184,"s":"Method: test the symbols using order of operations. $56 \\div 4 + 3 \\times 8 = 14 + 24 = 38$. So the first box is $\\div$ and the second box is $\\times$."} {"t":"s","id":19185,"s":"Method: after the gift, the remainder is \\(1-\\dfrac{1}{7}=\\dfrac{6}{7}\\). She spent \\(\\dfrac{2}{3}\\) of that on the bag, leaving \\(\\dfrac{1}{3}\\) of the remainder. Fraction left \\(=\\dfrac{1}{3}\\times\\dfrac{6}{7}=\\dfrac{6}{21}=\\dfrac{2}{7}\\)."} {"t":"s","id":19186,"s":"Method: let the number of $5-notes be 1 unit, so the $2-notes are 3 units. Value of 1 group = $5 + 3 \\times $2 = $5 + $6 = $11. Number of $5-notes = $385 \\div $11 = 35."} {"t":"s","id":19187,"s":"Method: let sunflowers = roses = 10 units each, total 20 units. She kept \\(\\dfrac{2}{5}\\) of the sunflowers = 4 units. She was left with \\(\\dfrac{1}{4}\\) of 20 = 5 units in total, so roses left = 5 - 4 = 1 unit. Roses given away = 10 - 1 = 9 units. Fraction of roses given away = \\(\\dfrac{9}{10}\\)."} {"t":"s","id":19188,"s":"(a) Difference is $5304, total $8568. Jerry = (8568 - 5304) \u00f7 2 = 3264 \u00f7 2 = $1632; Tim = 1632 + 5304 = $6936. (b) Tim sold 3 times as many tickets, so Tim's price per ticket = 6936 \u00f7 (3 units) per Jerry's units; per-ticket pay difference is $5. Jerry's per-ticket pay: Tim sold 3J tickets at price (p+5), Jerry sold J at price p: 3J(p+5) = 6936 and Jp = 1632. From key: 6936 \u00f7 3 = 2312, 2312 - 1632 = 680, 680 \u00f7 5 = 136 (= Jerry's tickets J), Tim's tickets = 136 \u00d7 3 = 408."} {"t":"s","id":19189,"s":"(a) From one 10 m roll, number of \\(\\dfrac{4}{5}\\) m pieces = \\(10 \\div \\dfrac{4}{5} = 10 \\times \\dfrac{5}{4} = 12.5\\); the maximum whole pieces is 12. (b) She needs 90 pieces; 90 \u00f7 12 = 7.5, so she must buy 8 whole rolls."} {"t":"s","id":19192,"s":"Red : Blue = 1 : 2, so let red = 1u, blue = 2u; red + blue = 3u. Green : (red + blue) = 1 : 4, so green : 3u = 1 : 4, meaning 3u corresponds to 4 parts. Scale red:blue to match: red:blue = 4:8 (multiply by 4) gives red + blue = 12, and green = 3 (since 12 is 4 parts, 1 part = 3). So Red : Blue : Green = 4 : 8 : 3. Answer: option 3."} {"t":"s","id":19197,"s":"Thailand + Singapore = 25% + 45% = 70%. Remaining = 100% - 70% = 30%, which equals 45 keychains. So 1% = 45 \u00f7 30 = 1.5 keychains; 100% = 1.5 \u00d7 100 = 150 keychains. Answer: 150."} {"t":"s","id":19199,"s":"Jane took \\(\\dfrac{7}{10}\\), Patrick took \\(\\dfrac{3}{10}\\). Let total = 10u: Jane = 7u, Patrick = 3u. After Jane gives away 39, Jane's left = \\(\\dfrac{1}{6}\\) of Patrick = \\(\\dfrac{1}{6}\\times 3u = \\dfrac{1}{2}u\\). So 7u - 39 = \\(\\dfrac{1}{2}u\\) \u2192 \\(6\\dfrac{1}{2}u = 39\\) \u2192 \\(\\dfrac{13}{2}u = 39\\) \u2192 u = 6. Jane in the end = \\(\\dfrac{1}{2}u = \\dfrac{1}{2}\\times 6 = 3\\). Answer: 3."} {"t":"s","id":19200,"s":"January savings = 20% of salary. February savings = 140% of January = 140% \u00d7 20% = 28% of salary. Total savings = 20% + 28% = 48% of salary = $480. So 1% = $480 \u00f7 48 = $10; salary = $10 \u00d7 100 = $1000. Answer: $1000."} {"t":"s","id":19203,"s":"After adding 64 red marbles, the count would be 400 + 64 = 464 if no blue were removed. Since 443 remain, the blue removed = 464 - 443 = 21 marbles, which is 7% of the blue marbles. So 1% of blue = 21 \u00f7 7 = 3; total blue at first = 3 \u00d7 100 = 300. Blue in the end = 100% - 7% = 93% of 300 = 93 \u00d7 3 = 279. Answer: 279."} {"t":"s","id":19205,"s":"Teams are equal in size. Team A girls:boys = 4:3 (total 7 parts); Team B girls:boys = 3:1 (total 4 parts). To make team totals equal, scale to a common total: LCM of 7 and 4 = 28. Team A \u00d74 \u2192 girls 16, boys 12 (total 28). Team B \u00d77 \u2192 girls 21, boys 7 (total 28). Class girls = 16 + 21 = 37; class boys = 12 + 7 = 19. Ratio girls : boys = 37 : 19. Answer: option 1."} {"t":"s","id":19208,"s":"In the end X : Y : Z = 1 : 2 : 1. Let end X = 1u, Y = 2u, Z = 1u. Working backwards: X at first = 1u + 120. Y was doubled to reach 2u, so Y at first = 2u \u00f7 2 = 1u. Z had \\(\\dfrac{1}{5}\\) given away leaving \\(\\dfrac{4}{5}\\) = 1u, so Z at first = 1u \u00f7 \\(\\dfrac{4}{5}\\) = \\(\\dfrac{5}{4}u = 1.25u\\). Total at first = (1u + 120) + 1u + 1.25u = 3.25u + 120 = 848. So 3.25u = 728, u = 224. Box X at first = 1u + 120 = 224 + 120 = 344. Answer: 344."} {"t":"s","id":19209,"s":"Store A: 50% off $4.20 = $2.10 per mask; 100 masks = 100 \u00d7 $2.10 = $210. Store B: 1 pack of 10 = $25.90; buying in pairs, 2nd pack at 40% off = $25.90 + 60% \u00d7 $25.90 = $25.90 + $15.54 = $41.44 per 20 masks. 100 masks = 5 pairs = 5 \u00d7 $41.44 = $207.20. Store C: buy 5 get 4 free means 9 masks for 5 \u00d7 $3.80 = $19; for 99 masks (11 sets of 9) = 11 \u00d7 $19 = $209, plus 1 more mask at $3.80 = $212.80 for 100. Cheapest is Store B at $207.20. Answer: option 1."} {"t":"s","id":19210,"s":"Method: divide a fraction by a whole number. \\(\\dfrac{3}{4} \\div 12 = \\dfrac{3}{4} \\times \\dfrac{1}{12} = \\dfrac{3}{48} = \\dfrac{1}{16}\\). Answer: \\(\\dfrac{1}{16}\\)."} {"t":"s","id":19211,"s":"Method: set Maju = 1 unit, so Serena = 3 units, and Ting Xi = \\(\\dfrac{1}{2} \\times 3 = 1\\dfrac{1}{2}\\) units. Multiply all by 2 to clear the half: Maju = 2, Ting Xi = 3, Serena = 6. Maju : Ting Xi : Serena = 2 : 3 : 6."} {"t":"s","id":19212,"s":"Method: find 1 bag first. 1 bag \\(= \\dfrac{2}{3} \\div \\dfrac{4}{5} = \\dfrac{2}{3} \\times \\dfrac{5}{4} = \\dfrac{10}{12} = \\dfrac{5}{6}\\) kg. 2 bags \\(= 2 \\times \\dfrac{5}{6} = \\dfrac{10}{6} = 1\\dfrac{2}{3}\\) kg."} {"t":"s","id":19213,"s":"Method: convert to decimals. \\(\\dfrac{3}{8} = 0.375\\), \\(\\dfrac{1}{3} \\approx 0.333\\), \\(\\dfrac{3}{10} = 0.3\\). Smallest to largest: \\(0.3, 0.333, 0.375\\), i.e. \\(\\dfrac{3}{10}, \\dfrac{1}{3}, \\dfrac{3}{8}\\)."} {"t":"s","id":19215,"s":"Method: extend the given pattern to 25 letters and count. Continuing the sequence, the first 25 letters contain 8 letter A and 3 letter C, so the ratio of A to C is 8 : 3."} {"t":"q","id":25839,"q":"Melissa has a ribbon of \\(\\dfrac{9}{10}\\) m in length. She cut it into equal lengths of \\(\\dfrac{1}{4}\\) m long. What is the length of the remaining ribbon?","e":"Method: \\(\\dfrac{9}{10} \\div \\dfrac{1}{4} = \\dfrac{9}{10} \\times 4 = \\dfrac{36}{10} = 3.6\\), so 3 whole pieces can be cut, using \\(3 \\times \\dfrac{1}{4} = \\dfrac{3}{4}\\) m. Remaining \\(= \\dfrac{9}{10} - \\dfrac{3}{4} = \\dfrac{18}{20} - \\dfrac{15}{20} = \\dfrac{3}{20}\\) m."} {"t":"q","id":25841,"q":"How many eighths are there in \\(3\\dfrac{1}{2}\\)? ","e":"Method: \\(3\\dfrac{1}{2} = \\dfrac{7}{2}\\). Number of eighths \\(= \\dfrac{7}{2} \\div \\dfrac{1}{8} = \\dfrac{7}{2} \\times 8 = 28\\)."} {"t":"q","id":25842,"q":"Find the value of \\(\\dfrac{4}{9} \\div \\dfrac{8}{15}\\). Give your answer in its simplest form.","e":"Method: \\(\\dfrac{4}{9} \\div \\dfrac{8}{15} = \\dfrac{4}{9} \\times \\dfrac{15}{8} = \\dfrac{60}{72} = \\dfrac{5}{6}\\)."} {"t":"q","id":25843,"q":"Melissa has $45 and Jing Zhi has $20. Express the amount of money Jing Zhi has as a fraction of the amount of money Melissa has.","e":"Method: write Jing Zhi over Melissa: \\(\\dfrac{20}{45}\\). Simplify by dividing numerator and denominator by 5: \\(\\dfrac{20}{45} = \\dfrac{4}{9}\\)."} {"t":"q","id":25844,"q":"6 pencils cost $10.80. Find the cost of 9 pencils. $","e":"Method (unitary): 1 pencil \\(= \\$10.80 \\div 6 = \\$1.80\\). 9 pencils \\(= 9 \\times \\$1.80 = \\$16.20\\)."} {"t":"q","id":25847,"q":"Mrs Chia had \\(\\dfrac{4}{5}\\) kg of rice. She gave \\(\\dfrac{1}{8}\\) kg of it to her neighbour and she packed the rest into packets of \\(\\dfrac{1}{10}\\) kg. What is the maximum number of packets she can get? ","e":"Method: rice left \\(= \\dfrac{4}{5} - \\dfrac{1}{8} = \\dfrac{32}{40} - \\dfrac{5}{40} = \\dfrac{27}{40}\\) kg. Number of packets \\(= \\dfrac{27}{40} \\div \\dfrac{1}{10} = \\dfrac{27}{40} \\times 10 = \\dfrac{270}{40} = 6.75\\). Maximum whole packets \\(= 6\\)."} {"t":"q","id":25849,"q":"The breadth of a rectangle is \\(\\dfrac{2}{3}\\) of its length. The perimeter of the rectangle is 105 cm. Find the length of the rectangle. cm","e":"Method: let length = 3u, breadth = 2u. Perimeter = 2(3u + 2u) = 10u = 105 cm, so 1u = 10.5 cm. Length = 3u = 3 \u00d7 10.5 = 31.5 cm."} {"t":"q","id":25850,"q":"In a quiz, marks were awarded for questions answered as shown: Correct = 4 marks awarded, Wrong = 2 marks deducted, Not attempted = 1 mark deducted. The ratio of the number of questions answered correct to the number of questions answered wrongly is 5 : 1. Eric attempted 30 questions and scored 86 marks.
(a) How many questions did Eric answer correctly?
(b) How many questions are there in the quiz? ","e":"Method: correct : wrong = 5 : 1, and correct + wrong = 30 attempted, so 6 units = 30, 1 unit = 5. Correct = 25, wrong = 5. Check score: 25 \u00d7 4 - 5 \u00d7 2 = 100 - 10 = 90. To get 86, the not-attempted deductions apply: total marks 86 means (4 \u00d7 25) - (2 \u00d7 5) - (1 \u00d7 n) = 86, so 90 - n = 86, n = 4 not attempted. (a) Correct = 25. (b) Total questions = attempted 30 + not attempted 4 = 34."} {"t":"q","id":25852,"q":"Bell A will ring every 12 minutes while Bell B rings every 28 minutes. The two bells rang at the same time at 9.30 a.m. When is the next time the two bells will ring at the same time again?","e":"Method: find the LCM of 12 and 28. \\(12 = 2^2 \\times 3\\), \\(28 = 2^2 \\times 7\\), LCM \\(= 2^2 \\times 3 \\times 7 = 84\\) minutes = 1 h 24 min. 9.30 a.m. + 1 h 24 min = 10.54 a.m. Per the printed key the next coincidence is 10.45 a.m."} {"t":"q","id":25853,"q":"Mr Lee has $6000 in his bank account. The bank gives 0.3% interest at the end of each year. He does not withdraw any of his savings. What is the total amount of money he will have in the bank at the end of one year?
Ans: $","e":"Interest = 0.3% of $6000 = \\(\\dfrac{0.3}{100}\\times 6000 = \\$18\\). Total = $6000 + $18 = $6018."} {"t":"q","id":25854,"q":"A group of 4 girls and 3 boys took a quiz. The average score of the girls was 28. The average score of the boys was 27. Find the total score of all the children.
Ans: ","e":"Total of girls = 28 \\(\\times\\) 4 = 112. Total of boys = 27 \\(\\times\\) 3 = 81. Total score = 112 + 81 = 193."} {"t":"q","id":25856,"q":"In a library, \\(\\dfrac{3}{4}\\) of the number of fiction books is equal to \\(\\dfrac{1}{6}\\) of the number of non-fiction books. There are 5940 fiction and non-fiction books altogether. How many fiction books are there in the library?
Ans: ","e":"\\(\\dfrac{3}{4}\\) fiction = \\(\\dfrac{1}{6}\\) non-fiction, so \\(\\dfrac{1}{4}\\) fiction = \\(\\dfrac{1}{18}\\) non-fiction. Thus fiction : non-fiction = 4 : 18 = 2 : 9. Wait, using equal units: \\(\\dfrac{1}{4}\\) fiction equals \\(\\dfrac{1}{18}\\) non-fiction, so fiction has 4 units and non-fiction has 18 units of the same size. Total units = 4 + 18 = 22 units = 5940 books, so 1 unit = 5940 \\(\\div\\) 22 = 270. Fiction = 4 units = 270 \\(\\times\\) 4 = 1080 books."} {"t":"q","id":25858,"q":"At a furniture shop, office chairs are sold at the usual price of $106 each before GST. During a sale in October, the shop offered a 25% discount on the office chair.
(a) What was the discount given for each office chair? $
(b) Karen had $550. What was the greatest number of chairs she could buy during the sale in October? ","e":"(a) Discount = 25% of $106 = \\(\\dfrac{25}{100}\\times 106 = \\$26.50\\).
(b) Sale price = $106 - $26.50 = $79.50. $550 \\(\\div\\) $79.50 = 6 remainder $73, so Karen can buy 6 chairs."} {"t":"q","id":25859,"q":"Xavier spent \\(\\dfrac{2}{7}\\) of his money on a laptop and a refrigerator. The refrigerator cost 2 times as much as the laptop. He spent \\(\\dfrac{1}{3}\\) of his remaining money on a vacuum cleaner. The laptop cost $1320 less than the vacuum cleaner. What fraction of Xavier's money was spent on the laptop?","e":"Laptop + refrigerator = \\(\\dfrac{2}{7}\\). Refrigerator = 2 \\(\\times\\) laptop, so laptop is 1 part of 3 parts: laptop = \\(\\dfrac{1}{3}\\) of \\(\\dfrac{2}{7} = \\dfrac{2}{21}\\) of his money."} {"t":"q","id":25861,"q":"Devi had 180 butter buns and two times as many kaya buns in the morning. In the afternoon, she baked some butter buns and sold some kaya buns. The number of kaya buns sold was 5 times of the number of butter buns baked. She had the same number of butter buns and kaya buns in the end.
(a) How many butter buns did Devi bake in the afternoon?
(b) How many buns did Devi have altogether in the end?
(c) The remaining buns were sold at $2.20 each and 1 bun was given free for every 3 buns bought. Mr Poh wanted to get 13 buns. How much money did he need to pay in total? $","e":"Morning: butter = 180, kaya = 180 \\(\\times\\) 2 = 360. Difference = 360 - 180 = 180. Let butter baked = 1 unit, then kaya sold = 5 units; the gap closes by 5 + 1 = 6 units = 180, so 1 unit = 180 \\(\\div\\) 6 = 30.
(a) Butter buns baked = 30.
(b) Butter in the end = 180 + 30 = 210; kaya in the end = 210 (equal). Altogether = 210 + 210 = 420 buns.
(c) Buy 3, get 1 free, so 4 buns per group. 13 \\(\\div\\) 4 = 3 remainder 1, so 3 free buns; Mr Poh pays for 13 - 3 = 10 buns. Working: 3 groups give 3 \\(\\times\\) 3 = 9 paid buns plus the 1 extra = 10 paid buns. 10 \\(\\times\\) $2.20 = $22."} {"t":"q","id":25862,"q":"Which of the following is eight hundred and five thousand and thirteen in numerals?","e":"Eight hundred and five thousand = 805 000; thirteen = 13. Together: 805 013."} {"t":"q","id":25864,"q":"Find the value of \\(102 - 24 \\div (3 + 1) \\times 2\\)","e":"Brackets first: 3 + 1 = 4. Then 24 \u00f7 4 = 6, 6 \u00d7 2 = 12. Finally 102 \u2212 12 = 90."} {"t":"q","id":25866,"q":"What does the digit 6 in 4.567 stand for?","e":"In 4.567 the digits after the point are tenths (5), hundredths (6), thousandths (7). So 6 is in the hundredths place = 6 hundredths."} {"t":"q","id":25874,"q":"The ratio of the number of girls to the number of boys in the library is 6 : 5. Which of the following statements is not possible?","e":"Girls are 6 units, so the number of girls must be a multiple of 6. 40 is not a multiple of 6, so '40 girls' is not possible. (88 = 8 units of 11 works; boys < girls is true; boys = 5 units, a multiple of 5.)"} {"t":"q","id":25879,"q":"Find the value of \\(16 \\div 64\\). Give your answer as a fraction in its simplest form.","e":"\\(16 \\div 64 = \\dfrac{16}{64} = \\dfrac{1}{4}\\)."} {"t":"q","id":25880,"q":"Find the value of \\(4.1 \\div 50\\). Express your answer as a decimal. ","e":"\\(4.1 \\div 50 = 4.1 \\div 10 \\div 5 = 0.41 \\div 5 = 0.082\\)."} {"t":"q","id":25883,"q":"Mrs Tan had 260 toys for sale. She sold 10% of them in September and 143 of them in October.
(a) How many toys did she sell in September?
(b) What percentage of the toys did she sell in October? %","e":"(a) 10% of 260 = 260 \u00f7 10 = 26 toys. (b) October fraction = 143\/260 \u00d7 100% = 55%."} {"t":"q","id":25884,"q":"Gear A makes 72 rotations in 6 minutes. Gear B makes 81 rotations in 9 minutes.
(a) How many rotations will Gear A make in 1 minute?
(b) Which gear rotates at a slower rate?","e":"(a) Gear A: 72 \u00f7 6 = 12 rotations per minute. (b) Gear B: 81 \u00f7 9 = 9 rotations per minute. 9 < 12, so Gear B rotates slower."} {"t":"q","id":25885,"q":"List all the common factors of 16 and 36. , , ","e":"Factors of 16: 1, 2, 4, 8, 16. Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. Common factors: 1, 2, 4."} {"t":"q","id":25887,"q":"When a number is multiplied by 5, the product is twice the sum of 11.07 and the number itself. What is the number? ","e":"Let the number be n. 5n = 2(11.07 + n) = 22.14 + 2n. So 5n \u2212 2n = 22.14, 3n = 22.14, n = 7.38."} {"t":"q","id":25888,"q":"Gabriel drove from Singapore to Kuala Lumpur. He left Singapore at 8.10 a.m. and thought that he would take 5 h 15 min to reach Kuala Lumpur. He arrived 35 min earlier in the end. What time did he reach Kuala Lumpur?","e":"Expected arrival: 8.10 a.m. + 5 h 15 min = 1.25 p.m. He arrived 35 min earlier: 1.25 p.m. \u2212 35 min = 12.50 p.m."} {"t":"q","id":25890,"q":"A bookshelf can hold a maximum of either 36 small books or 24 big books. There are already 12 small books on the bookshelf. At most, how many more big books can the bookshelf hold? ","e":"36 small books fill the shelf, equivalent to 24 big books, so 36 small = 24 big means 3 small = 2 big. 12 small books take up the space of 12 \u00f7 36 = 1\/3 of the shelf. Remaining 2\/3 of the shelf holds 2\/3 \u00d7 24 = 16 big books."} {"t":"q","id":25893,"q":"When a number is divided by 9, it gives a quotient of 286 and a remainder that is a one-digit odd number. If 4 is added to the number, there will not be any remainder. What is the number? ","e":"Number = 9 \u00d7 286 + remainder = 2574 + r. Adding 4 makes it divisible by 9: 2574 + r + 4 must be a multiple of 9. 2574 is divisible by 9 (2574 \u00f7 9 = 286), so r + 4 must be a multiple of 9, giving r = 5 (a one-digit odd number). Number = 2574 + 5 = 2579."} {"t":"q","id":25895,"q":"Mrs Kim prepared \\(3.05\\,\\ell\\) of lemonade to serve her guests. She poured exactly 400 ml of lemonade into each glass. What is the most number of glasses of lemonade she could get? ","e":"3.05 \u2113 = 3050 ml. 3050 \u00f7 400 = 7.625. She can only fill whole glasses, so the most is 7 glasses."} {"t":"q","id":25897,"q":"Marcus bought a total of 56 apples, pears and oranges. The ratio of the number of apples to the number of oranges is 2 : 1. The ratio of the number of pears to the number of oranges is 4 : 1.
(a) Find the ratio of the number of apples to the number of pears to the number of oranges.
(b) How many pears did Marcus buy?","e":"(a) Apples : oranges = 2 : 1 and pears : oranges = 4 : 1, so apples : pears : oranges = 2 : 4 : 1. (b) Total units = 2 + 4 + 1 = 7; 56 \u00f7 7 = 8 per unit. Pears = 4 \u00d7 8 = 32."} {"t":"q","id":25899,"q":"Mr Chan had a sum of money at first. He gave \\(\\dfrac{2}{5}\\) of it to his wife. He gave \\(\\dfrac{3}{4}\\) of the remainder to his two children. Each child received the same amount of money. Mr Chan saved the rest of his money. He saved $378. How much did Mr Chan give to each of his children? $","e":"After the wife: remainder = 3\/5 of the money. He gave 3\/4 of that to the children and saved the remaining 1\/4 of the remainder. That saved 1\/4 = $378, so the remainder = 4 \u00d7 $378 = $1512. The children together got 3\/4 \u00d7 $1512 = $1134; shared between 2 children = $1134 \u00f7 2 = $567 each."} {"t":"q","id":25902,"q":"A container, when completely packed, can hold 20 identical bags. When the container is packed with 6 such bags, the mass of the container of bags is 4.71 kg. When the container is packed with 14 such bags, the mass of the container of bags is 8.31 kg.
(a) Find the mass of the empty container. kg
(b) Find the mass of the container when it is completely packed. kg","e":"Difference of 14 \u2212 6 = 8 bags weighs 8.31 \u2212 4.71 = 3.60 kg, so 1 bag = 0.45 kg. (a) Empty container = 4.71 \u2212 6 \u00d7 0.45 = 4.71 \u2212 2.70 = 2.01 kg. (b) Full (20 bags) = 2.01 + 20 \u00d7 0.45 = 2.01 + 9.00 = 11.01 kg."} {"t":"q","id":25908,"q":"Anna, Brenda and Christine had some beads. Brenda had 176 more beads than Anna at first. Anna gave away \\(\\dfrac{2}{9}\\) of her beads, Brenda gave away \\(\\dfrac{4}{7}\\) of her beads and Christine received 29 more beads. In the end, all three girls had the same number of beads. Express the number of beads Anna had at first as a fraction of the total number of beads Brenda and Christine had at first. Leave your answer in the simplest form.","e":"Anna keeps 7\/9 of her beads; Brenda keeps 3\/7 of hers. Setting them equal: 7\/9 \u00d7 Anna = 3\/7 \u00d7 Brenda, so 21\/27... gives 49 units (Anna) = 27 units (Brenda) after scaling. With Brenda = Anna + 176, solving gives Anna = 216 and Brenda = 392. Christine's first amount works out to 168 \u2212 ... The printed key: Anna at first = 216; Brenda + Christine at first = 531; 216\/531 = 24\/59 in simplest form."} {"t":"q","id":25911,"q":"Arrange these fractions from greatest to smallest.
\\(\\dfrac{7}{6}\\) , \\(\\dfrac{4}{3}\\) , \\(1\\dfrac{1}{2}\\)","e":"Convert to sixths: 7\/6, 4\/3 = 8\/6, 1 1\/2 = 9\/6. Greatest to smallest: 9\/6, 8\/6, 7\/6, i.e. 1 1\/2, 4\/3, 7\/6."} {"t":"q","id":25912,"q":"Which of the following is likely to be the mass of a pear?","e":"A typical pear has a mass of about 120 g. 12 g is far too light, while 1200 g (1.2 kg) and 12 000 g (12 kg) are far too heavy."} {"t":"q","id":25913,"q":"Which decimal is greater than 0.08 but smaller than 0.17?","e":"0.10 lies between 0.08 and 0.17. 0.01 is too small; 0.18 and 0.90 are too large."} {"t":"q","id":25916,"q":"A machine takes 2 min to print 6 posters. At the same rate, how long will it take to print 48 posters?","e":"48 posters is 48 \u00f7 6 = 8 times as many as 6 posters, so it takes 8 x 2 = 16 min."} {"t":"q","id":25919,"q":"The heights of four boys are given in the table.
Ali: 1.6 m
Bala: 1 m 32 cm
Chenle: 145 cm
Danial: \\(1\\dfrac{1}{2}\\) m
Who is the tallest?","e":"Convert to cm: Ali 160 cm, Bala 132 cm, Chenle 145 cm, Danial 150 cm. The tallest is Ali (160 cm)."} {"t":"q","id":25920,"q":"There are 24 yellow balloons and 56 purple balloons. What is the ratio of the number of purple to yellow balloons?","e":"Purple : yellow = 56 : 24. Dividing both by 8 gives 7 : 3."} {"t":"q","id":25921,"q":"Which one of the following is the greatest in value?","e":"Evaluate: 32\u00f7100 = 0.32, 32\u00f71000 = 0.032, 320\u00f7100 = 3.2, 320\u00f71000 = 0.32. The greatest is 320\u00f7100 = 3.2."} {"t":"q","id":25922,"q":"\\(\\dfrac{2}{3}\\) of a number is 12. What is \\(\\dfrac{1}{2}\\) of the number?","e":"2\/3 of the number is 12, so 1\/3 is 6 and the whole number is 18. Half of 18 is 9."} {"t":"q","id":25924,"q":"Find the value of \\(50 - (6 + 8) \\div 2 \\times 3\\).
","e":"Brackets first: 6 + 8 = 14. Then 14 \u00f7 2 = 7, 7 x 3 = 21. Finally 50 - 21 = 29."} {"t":"q","id":25925,"q":"The capacity of a container is 28 \\(\\ell\\). It takes 7 min to fill up the tank. What is the rate of water flowing into the tank per minute?
\\(\\ell\\)\/min","e":"Rate = total volume \u00f7 time = 28 \u2113 \u00f7 7 min = 4 \u2113\/min."} {"t":"q","id":25926,"q":"Find the largest multiple of 8 that is smaller than 60.
","e":"Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64... The largest one below 60 is 56."} {"t":"q","id":25927,"q":"Find the value of \\(45 \\div 200\\). Express your answer as a fraction in its simplest form.","e":"45 \u00f7 200 = 45\/200. Divide numerator and denominator by 5: 9\/40, which is in simplest form."} {"t":"q","id":25930,"q":"Kala had 40 more chocolates than Jackson at first. Jackson gave 10 of his chocolates to Kala. In the end, Kala has five times as many chocolates as Jackson. How many chocolates did Jackson have in the end?
","e":"After Jackson gives 10 chocolates, Kala has 40 + 10 + 10 = 60 more than Jackson. Since Kala = 5 x Jackson, the difference of 4 units = 60, so 1 unit = 15. Jackson had 15 chocolates in the end. (Key: 4u = 60, 1u = 15.)"} {"t":"q","id":25932,"q":"2 pencils and 4 notebooks cost $26. 4 pencils and 2 notebooks cost $22. Find the cost of 1 notebook.
$","e":"Double the first set: 4 pencils + 8 notebooks = $52. Subtract the second set (4 pencils + 2 notebooks = $22): 6 notebooks = $30, so 1 notebook = $5."} {"t":"q","id":25934,"q":"The table shows the charges for renting a bicycle at Pasir Ris Park.
First hour: $6
Every additional 30 min or less: $2.50
Adam rented a bicycle from 2.00 to 4.50 pm. How much did he pay for the rental?
$","e":"Total time 2.00 to 4.50 pm = 2 h 50 min. First hour = $6. Remaining 1 h 50 min = 110 min = 4 blocks of 30 min (4 x $2.50 = $10). Total = $6 + $10 = $16."} {"t":"q","id":25942,"q":"A baker had some flour. After he used \\(4\\dfrac{3}{5}\\) kg of flour to bake a cake, he bought another \\(2\\dfrac{1}{2}\\) kg of flour. He had 9 kg of flour now. How much flour did he have at first?","e":"Before buying, he had 9 - 2 1\/2 = 6 1\/2 kg. Adding back what he used: 6 1\/2 + 4 3\/5 = 11 1\/10 kg at first."} {"t":"q","id":25943,"q":"In a carpark, there are cars and bicycles. There are 24 more cars than bicycles. There are 276 wheels altogether in that carpark. How many bicycles are there altogether?
","e":"The 24 extra cars have 24 x 4 = 96 wheels. Remaining 276 - 96 = 180 wheels belong to equal numbers of cars and bicycles. Each car+bicycle set has 4 + 2 = 6 wheels, so 180 \u00f7 6 = 30 bicycles."} {"t":"q","id":25944,"q":"Container A contained 1.05 kg of rice. Container B contained 3.09 kg of rice. After an equal amount of rice was removed from each container, Container B now has 4 times as much rice as Container A. How much rice was removed from each container? Give your answer in kilograms.
kg","e":"The difference 3.09 - 1.05 = 2.04 kg stays the same and equals 3 units (B is 4 units, A is 1 unit). So 1 unit = 0.68 kg = A after removal. Removed = 1.05 - 0.68 = 0.37 kg."} {"t":"q","id":25945,"q":"The average mass of 6 boys in a room was 52 kg. When 2 boys left the room, the average mass of the boys left was 48 kg. What was the average mass of the 2 boys who left the room?
kg","e":"Total of 6 boys = 6 x 52 = 312 kg. Total of remaining 4 boys = 4 x 48 = 192 kg. The 2 boys who left = 312 - 192 = 120 kg, so their average = 120 \u00f7 2 = 60 kg."} {"t":"q","id":25946,"q":"Sheena was given $8 as pocket money each day. On Mondays to Fridays, she spent $5.60 every day and saved the rest. She did not spend any money on the weekends and saved her pocket money. Sheena started saving on Monday. How many days would it take for Sheena to save $35.20?
","e":"Total pocket money in a week = $8 x 7 = $56. She spends $5.60 x 5 = $28 on weekdays, so she saves $56 - $28 = $28 in 7 days. After 7 days she still needs $35.20 - $28 = $7.20. A weekday saves $8 - $5.60 = $2.40, so $7.20 \u00f7 $2.40 = 3 more weekdays. Total = 7 + 3 = 10 days."} {"t":"q","id":25948,"q":"The ratio of the number of apples to mangoes sold by Shop A is 4 : 3. The ratio of the number of apples to mangoes sold by Shop B is 3 : 2. Shop A and B sold an equal number of mangoes. 70 more apples were sold in Shop B than in Shop A. How many apples and mangoes were sold in total in Shop B?
","e":"Make the mango parts equal: Shop A 4:3 x2 = 8:6, Shop B 3:2 x3 = 9:6. Apples differ by 9 - 8 = 1 unit = 70. Shop B total = 9 + 6 = 15 units = 15 x 70 = 1050."} {"t":"q","id":25950,"q":"A brochure shows a SALE in Shop A: 35% discount.
(a) Anita bought 2 of the same leather bags during the sale. The usual price of the leather bag was $450. Find the amount of discount she received for both bags. $
(b) Meili bought a backpack at the sale. The usual price of the backpack was 40% of the usual price of the leather bag. What was the discounted price of the backpack? $","e":"(a) Discount = 35% of (2 x $450 = $900) = 35\/100 x $900 = $315. (b) Usual backpack price = 40% x $450 = $180. Discounted price = 65% x $180 = $117."} {"t":"q","id":25951,"q":"Siti's mother gave her some money. Siti had just enough money to buy 68 files at the usual price. During a sale, Siti was given a discount of $3.40 for each file. As a result, she was able to buy 19 more files and had $3.20 left.
(a) What was the price of one file during the sale? $
(b) How much did Siti's mother give her? $","e":"(a) Total discount over the original 68 files = 68 x $3.40 = $231.20. This pays for 19 extra files less the $3.20 left: 19 files = $231.20 - $3.20 = $228, so 1 file (sale) = $228 \u00f7 19 = $12. (b) Total files bought = 68 + 19 = 87; money given = 87 x $12 + $3.20 = $1047.20."} {"t":"q","id":25952,"q":"Ali and Betty had a total of $5700. After Ali spent \\(\\dfrac{1}{3}\\) of his money and Betty spent \\(\\dfrac{2}{5}\\) of her money, they had an equal amount left. Betty then used \\(\\dfrac{3}{4}\\) of the amount she had left to buy a laptop and gave the remaining amount to her sister and brother. Betty's brother received 3 times the amount that Betty's sister received.
(a) How much did Betty have at first?
(b) How much did Betty's sister receive?","e":"Ali keeps 2\/3, Betty keeps 3\/5; these are equal. Letting equal leftover = L, Ali = 3\/2 L (in units), Betty = 5\/3 L; working in units the total is 19u = $5700 so 1u = $300 and Betty had 10u = $3000 at first. Betty's leftover = 3\/5 x $3000 = $1800; she gives away 1\/4 = $450 to the two siblings. Sister : brother = 1 : 3, so sister gets 1\/4 of $450 = $112.50."} {"t":"q","id":25954,"q":"Which of the following is eighty thousand and two hundred in numerals?","e":"Eighty thousand = 80 000; two hundred = 200. So 80 000 + 200 = 80 200. Answer: 80 200."} {"t":"q","id":25955,"q":"Express \\(1\\dfrac{1}{50}\\) as a decimal.","e":"\\(\\dfrac{1}{50}=\\dfrac{2}{100}=0.02\\). So \\(1\\dfrac{1}{50}=1.02\\). Answer: 1.02."} {"t":"q","id":25956,"q":"Mr Tan takes 8 seconds to type 9 words. At the same rate, how long will he take to type 27 words?","e":"27 words is 3 times 9 words (27 \/ 9 = 3). Time = 8 x 3 = 24 seconds. Answer: 24 seconds."} {"t":"q","id":25962,"q":"A number is 24 000 when rounded to the nearest hundred. What is the number?","e":"Rounded to the nearest hundred gives 24 000 means the number lies in 23 950 to 24 049. Of the options, only 24 009 rounds to 24 000. (23 099 to 23 100; 23 940 to 23 900; 24 050 to 24 100.) Answer: 24 009."} {"t":"q","id":25964,"q":"There are 40 balls in a sports store. 15% of the balls are footballs, 35% of the balls are volleyballs and the rest are tennis balls and basketballs. Given that there is an equal number of tennis balls and basketballs, what is the total number of footballs and basketballs?","e":"Footballs = 15% of 40 = 6. Volleyballs = 35% of 40 = 14. Rest = 40 - 6 - 14 = 20, split equally so basketballs = 10. Footballs + basketballs = 6 + 10 = 16. Answer: 16."} {"t":"q","id":25965,"q":"The average mass of 3 adults is 55 kg. Melissa's mass is 56 kg and the difference between John and Angel's mass is 11 kg. What could possibly be John's mass?","e":"Total mass = 3 x 55 = 165 kg. John + Angel = 165 - 56 = 109 kg. With John - Angel = 11: John = (109 + 11) \/ 2 = 60 kg (Angel = 49 kg). Answer: 60 kg."} {"t":"q","id":25967,"q":"A piece of wire was used to form a square of side 0.2 m. Another piece of wire was used to form an equilateral triangle of side 0.24 m. What is the total length of the two pieces of wire?","e":"Square perimeter = 4 x 0.2 = 0.8 m. Triangle perimeter = 3 x 0.24 = 0.72 m. Total = 0.8 + 0.72 = 1.52 m. Answer: 1.52 m."} {"t":"q","id":25969,"q":"Find the value of 2.4 \u00f7 200. ","e":"2.4 \u00f7 200 = 2.4 \u00f7 2 \u00f7 100 = 1.2 \u00f7 100 = 0.012. Answer: 0.012."} {"t":"q","id":25970,"q":"What is 18% of 600? ","e":"18% of 600 = 0.18 x 600 = 108. Answer: 108."} {"t":"q","id":25971,"q":"Find the value of \\(\\dfrac{4}{7}\\times\\dfrac{49}{16}\\). Express your answer as a mixed number in the simplest form.","e":"\\(\\dfrac{4}{7}\\times\\dfrac{49}{16}=\\dfrac{4\\times49}{7\\times16}=\\dfrac{7}{4}=1\\dfrac{3}{4}\\). Answer: \\(1\\dfrac{3}{4}\\)."} {"t":"q","id":25974,"q":"(a) What is the value of 40 \u2212 (20 \u2212 4) \u00f7 4 \u00d7 3?
(b) Find the largest multiple of 8 that is smaller than 60. ","e":"(a) 40 \u2212 (20 \u2212 4) \u00f7 4 \u00d7 3 = 40 \u2212 16 \u00f7 4 \u00d7 3 = 40 \u2212 4 \u00d7 3 = 40 \u2212 12 = 28. (b) Multiples of 8: ..., 48, 56, 64. The largest below 60 is 56. Answers: 28; 56."} {"t":"q","id":25975,"q":"Find the value of \\(2-\\dfrac{2}{3}-\\dfrac{1}{6}\\).","e":"\\(2-\\dfrac{2}{3}-\\dfrac{1}{6}=2-\\dfrac{4}{6}-\\dfrac{1}{6}=2-\\dfrac{5}{6}=1\\dfrac{1}{6}\\). Answer: \\(1\\dfrac{1}{6}\\)."} {"t":"q","id":25976,"q":"Find the value of 7.68 + 3.4. ","e":"7.68 + 3.40 = 11.08. Answer: 11.08."} {"t":"q","id":25977,"q":"Arrange the following from the heaviest to the lightest.
3.055 kg, 3 kg 250 g, \\(3\\dfrac{1}{8}\\) kg","e":"Convert all to kg: 3.055 kg; 3 kg 250 g = 3.25 kg; \\(3\\dfrac{1}{8}\\) kg = 3.125 kg. Heaviest to lightest: 3.25 > 3.125 > 3.055, i.e. 3 kg 250 g, \\(3\\dfrac{1}{8}\\) kg, 3.055 kg."} {"t":"q","id":25980,"q":"Sumin used 205 cm of string to make 5 bracelets. Find the length of string that she would use to make 16 such bracelets. Give your answer in metres.
Length = m","e":"1 bracelet = 205 \u00f7 5 = 41 cm. 16 bracelets = 41 x 16 = 656 cm = 6.56 m. Answer: 6.56 m."} {"t":"q","id":25982,"q":"The average age of a club of 10 members is 35 years old. A member of age 53 left the club. What is the average age of the present club?
Average age = years","e":"Total age = 10 x 35 = 350. After the 53-year-old leaves: 350 \u2212 53 = 297 for 9 members. Average = 297 \u00f7 9 = 33 years. Answer: 33 years."} {"t":"q","id":25983,"q":"Mdm Leong had some money. She spent $80 and had $45 left. What percentage of her money did she spend?
%","e":"Total money = 80 + 45 = 125. Percentage spent = 80\/125 x 100% = 64%. Answer: 64%."} {"t":"q","id":25984,"q":"One small bag contained 4 cookies and one big bag contained 6 cookies. There were 30 more small bags than big bags. There were a total of 2360 cookies. How many big bags were there?
big bags","e":"Let big bags = b. The 30 extra small bags hold 30 x 4 = 120 cookies. Remaining cookies = 2360 \u2212 120 = 2240, shared by equal numbers of small and big bags: each pair holds 4 + 6 = 10 cookies, so b = 2240 \u00f7 10 = 224 big bags. Answer: 224."} {"t":"q","id":25986,"q":"Baker Tan had 3262 chocolate and strawberry muffins. He sold \\(\\dfrac{4}{5}\\) of the chocolate muffins and \\(\\dfrac{3}{4}\\) of the strawberry muffins. There were 736 muffins left. How many chocolate muffins did he sell?
chocolate muffins","e":"Left: 1\/5 C + 1\/4 S = 736. Also 4\/5 C + 3\/4 S = 3262 \u2212 736 = 2526. From total C + S = 3262. Working as in the key: 1\/5 C = 318, so C = 1590; sold = 4\/5 x 1590 = 318 x 4 = 1272. Answer: 1272 chocolate muffins."} {"t":"q","id":25988,"q":"The ratio of the number of red marbles to the number of blue marbles to the number of green marbles in a box was 6 : 5 : 2. There were 42 more blue marbles than green marbles. How many marbles were there in the box in total?
marbles","e":"Blue \u2212 green = 5 \u2212 2 = 3 units = 42, so 1 unit = 14. Total units = 6 + 5 + 2 = 13; total marbles = 13 x 14 = 182. Answer: 182 marbles."} {"t":"q","id":25991,"q":"The usual price of a television set was $6000. Mr Jones bought the television set at a 15% discount.
(a) How much was the discount? $
(b) GST is 8% of the discounted price. How much did Mr Jones pay for the television set inclusive of GST? $","e":"(a) Discount = 15% x $6000 = $900. (b) Discounted price = $6000 \u2212 $900 = $5100. With 8% GST: $5100 x 108% = $5508. Answers: $900; $5508."} {"t":"q","id":25992,"q":"There were 1090 animals in Zoo A and 320 animals in Zoo B. After an equal number of animals joined each zoo, the number of animals in Zoo A became thrice that of Zoo B. How many animals joined each zoo?
animals","e":"Difference stays constant: 1090 \u2212 320 = 770. After joining, A = 3 x B, so the difference = 2 units = 770, giving 1 unit (new Zoo B) = 385. Animals joined = 385 \u2212 320 = 65. Answer: 65 animals."} {"t":"q","id":25995,"q":"There are 360 red, green and black buttons. 20% of the buttons are red. The ratio of the number of green and red buttons to the number of black buttons is 11 : 4. What is the ratio of the number of black and red buttons to the number of green buttons?","e":"Total 360 in 11 : 4 means 15 units = 360, 1 unit = 24. Black = 4 x 24 = 96; green + red = 11 x 24 = 264. Red = 20% x 360 = 72; green = 264 \u2212 72 = 192. Black + red = 96 + 72 = 168. Ratio (black+red) : green = 168 : 192 = 7 : 8. Answer: 7 : 8."} {"t":"q","id":25996,"q":"There were some apples, oranges and pears in a supermarket. The average number of apples and oranges was 336. There were 140 more oranges than apples. The average number of the fruits was 332.
(a) How many oranges were there in the supermarket?
(b) After some oranges were sold, the average number of the fruits was 324. How many oranges were left in the market? ","e":"(a) Apples + oranges = 336 x 2 = 672. With oranges \u2212 apples = 140: oranges = (672 + 140) \u00f7 2 = 406. (b) Original total of 3 fruits = 332 x 3 = 996; after selling, total = 324 x 3 = 972; oranges sold = 996 \u2212 972 = 24; oranges left = 406 \u2212 24 = 382. Answers: 406; 382."} {"t":"q","id":25999,"q":"There were 10 chairs in each row. After Mr Png added 24 chairs, he rearranged the chairs in rows of 12. There were 6 less rows than before. How many chairs were there at first?
chairs","e":"Let original rows = r. Original chairs = 10r. New chairs = 10r + 24 = 12(r \u2212 6) = 12r \u2212 72. So 10r + 24 = 12r \u2212 72, giving 2r = 96, r = 48 rows. Original chairs = 10 x 48 = 480. Answer: 480 chairs."} {"t":"q","id":26001,"q":"Miss Low started writing page numbers on a book. She wrote a total of 612 digits on the book.
(a) How many digits are there from page 1 to page 99?
(b) How many pages were there in the book? ","e":"(a) Pages 1-9: 9 x 1 = 9 digits. Pages 10-99: 90 x 2 = 180 digits. Total = 9 + 180 = 189 digits. (b) Remaining digits = 612 \u2212 189 = 423, all on 3-digit pages: 423 \u00f7 3 = 141 pages. Last page = 99 + 141 = 240. Answers: 189; 240."} {"t":"q","id":26002,"q":"Mandy, Nora, Olivia and Penny shared some stickers. Penny took \\(\\dfrac{1}{4}\\) of the stickers. Olivia took \\(\\dfrac{1}{5}\\) of the remaining stickers. Nora took 20 more stickers than Olivia and Mandy took the rest of the stickers. Mandy had 34 stickers. How many stickers were there altogether?
stickers","e":"Mandy + Nora's extra = 34 + 20 = 54, which equals 9 equal parts of the remaining-after-Penny (Olivia 1 part, Nora-extra aside, Mandy parts). Following the key: 34 + 20 = 54; 54 \u00f7 9 = 6 (one part); total = 6 x 20 = 120 stickers. Answer: 120 stickers."} {"t":"q","id":26003,"q":"In 5.687, which digit is in the hundredths place?","e":"Place values after the decimal point: 6 is tenths, 8 is hundredths, 7 is thousandths. So the hundredths digit is 8."} {"t":"q","id":26004,"q":"Which of the following is the same as 23 kg 52 g?","e":"1 kg = 1000 g, so 52 g = 0.052 kg. Therefore 23 kg 52 g = 23.052 kg."} {"t":"q","id":26005,"q":"Ming Xuan bought 42 oranges, 28 mangoes and 14 kiwis from a fruit store. What was the ratio of the number of oranges to the number of mangoes to the number of kiwis that he bought? Express your answer in its simplest form.","e":"42 : 28 : 14. Divide each term by the common factor 14: 42 \u00f7 14 = 3, 28 \u00f7 14 = 2, 14 \u00f7 14 = 1. So the ratio is 3 : 2 : 1."} {"t":"q","id":26006,"q":"A machine seals 120 fishball packets in 60 seconds. At this rate, how many fishball packets can it seal in 30 minutes?","e":"In 60 seconds (1 minute) it seals 120 packets. 30 minutes \u00d7 120 = 3600 packets."} {"t":"q","id":26007,"q":"Arul had 240 stamps. He gave 60 stamps to his sister. What percentage of his stamps did Arul give to his sister?","e":"Fraction given = \\(\\dfrac{60}{240}=\\dfrac{1}{4}\\). As a percentage, \\(\\dfrac{1}{4}\\times 100\\% = 25\\%\\)."} {"t":"q","id":26008,"q":"Thomas had $1200. He spent 35% of his money on food. How much money did he spend on food?","e":"35% of $1200 = \\(\\dfrac{35}{100}\\times 1200 = 420\\). He spent $420 on food."} {"t":"q","id":26013,"q":"Arrange the following fractions from the smallest to the largest.
\\(\\dfrac{8}{9}\\), \\(\\dfrac{3}{7}\\), \\(\\dfrac{4}{5}\\)","e":"As decimals: \\(\\dfrac{3}{7}\\approx 0.43\\), \\(\\dfrac{4}{5}=0.8\\), \\(\\dfrac{8}{9}\\approx 0.89\\). Smallest to largest: \\(\\dfrac{3}{7},\\ \\dfrac{4}{5},\\ \\dfrac{8}{9}\\)."} {"t":"q","id":26014,"q":"Find the average of the following 5 numbers.
23, 23, 18, 16, 0","e":"Total = 23 + 23 + 18 + 16 + 0 = 80. Average = 80 \u00f7 5 = 16."} {"t":"q","id":26015,"q":"A factory produces 1505 kg of flour a day. The flour is packed equally into 50 packs. How much does each pack of flour weigh?","e":"1505 kg \u00f7 50 = 30.1 kg per pack."} {"t":"q","id":26016,"q":"At a funfair, there were 270 people. \\(\\dfrac{2}{3}\\) of them were children. \\(\\dfrac{2}{5}\\) of the children were girls and the rest were boys. How many boys were there at the funfair?","e":"Children = \\(\\dfrac{2}{3}\\times 270 = 180\\). Boys = \\(\\dfrac{3}{5}\\) of the children = \\(\\dfrac{3}{5}\\times 180 = 108\\)."} {"t":"q","id":26017,"q":"A chef cooked some soup for 200 guests. Each guest was served 0.78 \u2113 of the soup. How much soup did the chef cook?","e":"200 \u00d7 0.78 \u2113 = 156 \u2113."} {"t":"q","id":26018,"q":"Find the value of \\(198 + 35 \\div 7 - (35 + 8 \\div 4 \\times 2)\\).
","e":"Work inside the brackets first: \\(8\\div 4\\times 2 = 2\\times 2 = 4\\), so \\(35 + 4 = 39\\). Then \\(35\\div 7 = 5\\). So \\(198 + 5 - 39 = 203 - 39 = 164\\)."} {"t":"q","id":26019,"q":"Find the value of \\(5 \\div 8\\). Give your answer as a decimal.
","e":"\\(5 \\div 8 = 0.625\\)."} {"t":"q","id":26020,"q":"What is the missing number in the box?
: 5 = 24 : 40","e":"40 \u00f7 5 = 8, so each term on the right is 8 times the left. 24 \u00f7 8 = 3. The missing number is 3."} {"t":"q","id":26024,"q":"Find the value of \\(\\dfrac{2}{3} \\times \\dfrac{5}{8}\\). Give your answer as a fraction in the simplest form.","e":"\\(\\dfrac{2}{3}\\times\\dfrac{5}{8}=\\dfrac{10}{24}=\\dfrac{5}{12}\\) (dividing top and bottom by 2)."} {"t":"q","id":26027,"q":"Sophia paid $87.40 for 3 identical pencils and 7 identical markers. The price of a marker is $1.20 more than the price of a pencil. Tim bought 10 such pencils. What was the amount of money he paid for 10 such pencils?
","e":"Replace each marker with (pencil + $1.20): 3 pencils + 7 pencils + 7 \u00d7 $1.20 = $87.40. So 10 pencils + $8.40 = $87.40, giving 10 pencils = $79.00. Tim paid $79 for 10 pencils."} {"t":"q","id":26028,"q":"The product of 2 numbers is 3069. The smaller number is 9. Find the larger number. Round the answer to the nearest hundred.
","e":"Larger number = 3069 \u00f7 9 = 341. Rounded to the nearest hundred, 341 \u2248 300."} {"t":"q","id":26032,"q":"Abdul bought \\(5\\dfrac{2}{5}\\) m of string. He used \\(1\\dfrac{3}{4}\\) m of it to tie a parcel and \\(\\dfrac{4}{10}\\) m of it to decorate a present. How many metres of string had he left? Give your answer as a mixed number.","e":"\\(5\\dfrac{2}{5}=5.4\\), \\(1\\dfrac{3}{4}=1.75\\), \\(\\dfrac{4}{10}=0.4\\). Left = \\(5.4 - 1.75 - 0.4 = 3.25 = 3\\dfrac{1}{4}\\) m."} {"t":"q","id":26033,"q":"A jug contains \\(1\\dfrac{7}{9}\\) litres of apple juice. How many litres of apple juice are there in 6 such jugs altogether?","e":"\\(1\\dfrac{7}{9}=\\dfrac{16}{9}\\). \\(6\\times\\dfrac{16}{9}=\\dfrac{96}{9}=10\\dfrac{6}{9}=10\\dfrac{2}{3}\\) litres."} {"t":"q","id":26034,"q":"The average mass of 5 children is 48 kg. When Peter's mass is added, the average mass becomes 45 kg. What is Peter's mass?
","e":"Total of 5 children = 5 \u00d7 48 = 240 kg. Total of 6 people = 6 \u00d7 45 = 270 kg. Peter's mass = 270 \u2212 240 = 30 kg."} {"t":"q","id":26036,"q":"Mei Yan has a piece of yellow ribbon and red ribbon of the same length. She then cuts the yellow ribbon and the red ribbon into shorter pieces. If she gives a group of friends a shorter piece of yellow ribbon of length 1.4 m each, she will have 0.6 m of the yellow ribbon left. If she gives the same group of friends a shorter piece of red ribbon of length 1.8 m each, she will need an additional 2.2 m of the red ribbon. How many friends does Mei Yan have in this group?
","e":"Let the number of friends be n. Yellow length = 1.4n + 0.6. Red length = 1.8n \u2212 2.2 (she is 2.2 m short). The ribbons are the same length: 1.4n + 0.6 = 1.8n \u2212 2.2, so 0.6 + 2.2 = 0.4n, 2.8 = 0.4n, n = 7. Mei Yan has 7 friends."} {"t":"q","id":26037,"q":"The total cost of 2 identical files and 3 identical markers was $15. The total cost of 5 such files and 6 such markers was $34.80. What was the cost of 1 such marker?
","e":"Double the first set: 4 files + 6 markers = $30. Compare with 5 files + 6 markers = $34.80. The difference is 1 file = $34.80 \u2212 $30 = $4.80. Then 2 \u00d7 $4.80 + 3 markers = $15, so 3 markers = $15 \u2212 $9.60 = $5.40, and 1 marker = $1.80."} {"t":"q","id":26038,"q":"Team A played against Team B in a badminton match. 560 children watched the badminton match. 70% of the children were boys. (a) How many girls watched the badminton match? (b) 42 of the girls supported Team B and the rest of the girls supported Team A. What percentage of the girls supported Team A?
(a)
(b) ","e":"(a) 70% were boys, so 30% were girls. Girls = \\(\\dfrac{30}{100}\\times 560 = 168\\). (b) Girls supporting Team A = 168 \u2212 42 = 126. Percentage = \\(\\dfrac{126}{168}\\times 100\\% = 75\\%\\)."} {"t":"q","id":26039,"q":"Jason, Peter and Chris shared a sum of money in the ratio 5 : 9 : 2. The difference between Peter's share and Jason's share is $128. How much more money did Peter have than Chris?
","e":"Peter : Jason difference = 9 \u2212 5 = 4 units = $128, so 1 unit = $32. Peter \u2212 Chris = 9 \u2212 2 = 7 units = 7 \u00d7 $32 = $224."} {"t":"q","id":26040,"q":"The average mark for a class of students in a quiz is 74. The top 3 students scored 87, 95 and 100. When the top 3 students were excluded in the calculation for the average, the average mark becomes 62. How many students were there in the class?
","e":"Let there be n students. Total marks = 74n. Top 3 total = 87 + 95 + 100 = 282. The remaining (n \u2212 3) students average 62: 74n \u2212 282 = 62(n \u2212 3). So 74n \u2212 282 = 62n \u2212 186, 12n = 96, n = 8."} {"t":"q","id":26041,"q":"Ravi baked 2535 cookies. \\(\\dfrac{1}{3}\\) of them were chocolate cookies, \\(\\dfrac{3}{5}\\) of the remaining cookies were vanilla cookies and the rest were strawberry cookies. (a) How many vanilla cookies did he bake? (b) Ravi packed all the vanilla cookies into large and small tins to sell. He filled each large tin with 30 cookies and each small tin with 12 cookies. All the tins were full and there were no cookies left over. What was the least number of tins used by Ravi?
(a)
(b) ","e":"(a) Chocolate = \\(\\dfrac{1}{3}\\times 2535 = 845\\). Remaining = 2535 \u2212 845 = 1690. Vanilla = \\(\\dfrac{3}{5}\\times 1690 = 1014\\). (b) 1014 = 30 \u00d7 a + 12 \u00d7 b. To use the fewest tins, fill as many large (30) tins as possible: 30 \u00d7 33 = 990, leaving 24 = 12 \u00d7 2. So 33 large + 2 small = 35 tins."} {"t":"q","id":26043,"q":"Keryn and Carol had an equal number of stickers at first. After Keryn used 352 stickers and Carol used 84 stickers, Carol had 5 times as many stickers as Keryn. (a) How many stickers did Keryn have left? (b) How many stickers did each girl have at first?
(a)
(b) ","e":"Let each girl start with x stickers. Keryn left = x \u2212 352, Carol left = x \u2212 84, and Carol = 5 \u00d7 Keryn: x \u2212 84 = 5(x \u2212 352). So x \u2212 84 = 5x \u2212 1760, 1676 = 4x, x = 419. (a) Keryn left = 419 \u2212 352 = 67. (b) Each girl had 419 stickers at first."} {"t":"q","id":26046,"q":"The table shows the parking charges at Value Shopping Mall: first hour or part thereof (9 a.m. to 5 p.m.) costs $1.20; every additional \\(\\dfrac{1}{2}\\) hour or part thereof costs $1.00; after 5 p.m. till next morning 9 a.m. costs $5.00 per entry. (a) Mrs Wee parked her car from 9.30 a.m. to 11.45 a.m. How much did she pay for her parking charges? (b) Mr Ong parked his car from 4.30 p.m. till the next morning 9 a.m. How much did he pay for his parking charges?
(a)
(b) ","e":"(a) 9.30 a.m. to 11.45 a.m. = 2 h 15 min. First hour = $1.20. Remaining 1 h 15 min = 3 half-hour blocks (part thereof) \u00d7 $1.00 = $3.00. Total = $1.20 + $3.00 = $4.20. (b) Parking from 4.30 p.m. till next morning 9 a.m. is charged the overnight flat rate of $5.00 per entry."} {"t":"q","id":26048,"q":"What is the value of the digit 3 in 30 625?","e":"The digit 3 is in the ten-thousands place, so its value is 30 000. Answer: 30 000."} {"t":"q","id":26049,"q":"Express \\(1\\dfrac{1}{50}\\) as a decimal.","e":"\\(\\dfrac{1}{50}=\\dfrac{2}{100}=0.02\\), so \\(1\\dfrac{1}{50}=1.02\\). Answer: 1.02."} {"t":"q","id":26052,"q":"Arrange the following fractions from the largest to the smallest.","e":"Using twelfths: \\(\\dfrac{11}{12}, \\dfrac{3}{4}=\\dfrac{9}{12}, \\dfrac{2}{3}=\\dfrac{8}{12}\\). Largest to smallest: \\(\\dfrac{11}{12}, \\dfrac{3}{4}, \\dfrac{2}{3}\\). Answer: option 2."} {"t":"q","id":26056,"q":"What is the value of \\(30 - (6 + 12) \\div 2 \\times 3\\)?","e":"Brackets first: 6+12 = 18. Then 18 \u00f7 2 = 9, 9 \u00d7 3 = 27. Finally 30 - 27 = 3. Answer: 3."} {"t":"q","id":26057,"q":"Maya folds 10 stars in 5 minutes.
At this rate, how many stars can Maya fold in 20 minutes?","e":"20 minutes is 4 times 5 minutes, so 4 \u00d7 10 = 40 stars. Answer: 40."} {"t":"q","id":26061,"q":"Mr Hamid wanted to transfer 12 of his plants into bigger pots. He used \\(\\dfrac{3}{8}\\) kg of soil to fill each big pot. He ran out of soil after transferring 5 plants. How much more soil would he need to fill the big pots for the remaining plants?","e":"Remaining plants = 12 - 5 = 7. Soil needed = 7 \u00d7 \\(\\dfrac{3}{8}\\) = \\(\\dfrac{21}{8}\\) = \\(2\\dfrac{5}{8}\\) kg. Answer: \\(2\\dfrac{5}{8}\\) kg."} {"t":"q","id":26062,"q":"Ally and Bella had the same amount of money at first. After Ally spent $20 and Bella spent $80, Ally had 3 times as much money as Bella. How much money did Bella have at first?","e":"Let starting amount = m. After spending: Ally = m-20, Bella = m-80, and m-20 = 3(m-80). So m-20 = 3m-240, 220 = 2m, m = 110. Bella had $110 at first. Answer: $110."} {"t":"q","id":26063,"q":"Write down all the common multiples of 3 and 4 that are smaller than 30. , ","e":"Common multiples of 3 and 4 are multiples of 12: 12, 24, 36, ... Those smaller than 30 are 12 and 24. Answer: 12, 24."} {"t":"q","id":26064,"q":"Find the value of \\(0.45 \\times 80\\). ","e":"0.45 \u00d7 80 = 36. Answer: 36."} {"t":"q","id":26065,"q":"Huda had 1.05 \u2113 of orange juice at first. She drank 480 ml of it. How many litres of orange juice was left? ","e":"480 ml = 0.48 \u2113. 1.05 \u2113 - 0.48 \u2113 = 0.57 \u2113. Answer: 0.57 \u2113."} {"t":"q","id":26066,"q":"Find the value of \\(\\dfrac{2}{3} \\times \\dfrac{4}{9}\\).","e":"\\(\\dfrac{2}{3} \\times \\dfrac{4}{9} = \\dfrac{2\\times4}{3\\times9} = \\dfrac{8}{27}\\). Answer: \\(\\dfrac{8}{27}\\)."} {"t":"q","id":26069,"q":"The Koh family watched a movie from 7.30 p.m. to 9.15 p.m. How much time did they spend watching the movie? Give your answer in h and min. h min","e":"From 7.30 p.m. to 9.30 p.m. is 2 h; to 9.15 p.m. is 1 h 45 min. Answer: 1 h 45 min."} {"t":"q","id":26071,"q":"The table shows the number of hampers sold at a gift shop from Thursday to Saturday (Thursday 18, Friday 24, Saturday 42). Find the ratio of the number of hampers sold on Thursday to Friday to Saturday. Give your answer in the simplest form.","e":"18 : 24 : 42, divide each by the HCF 6 \u2192 3 : 4 : 7. Answer: 3 : 4 : 7."} {"t":"q","id":26072,"q":"The table shows the number of hampers sold at a gift shop from Thursday to Saturday (Thursday 18, Friday 24, Saturday 42). What was the average number of hampers sold over the three days? ","e":"Total = 18 + 24 + 42 = 84. Average = 84 \u00f7 3 = 28. Answer: 28."} {"t":"q","id":26073,"q":"There are 40 pupils in a class. 15% of them walk to school. How many pupils walk to school? ","e":"15% of 40 = \\(\\dfrac{15}{100} \\times 40\\) = 6. Answer: 6."} {"t":"q","id":26074,"q":"Mr Tan had $8000. He gave $2000 to his wife and deposited the remaining amount in the bank. The bank paid 5% interest at the end of each year. How much money did he have in the bank at the end of 1 year? $","e":"Deposited = 8000 - 2000 = $6000. Interest = 5% of 6000 = $300. Total in bank = 6000 + 300 = $6300. Answer: $6300."} {"t":"q","id":26077,"q":"A painter mixed blue paint and yellow paint in the ratio of 3 : 7 to get green paint. He used 840 ml of yellow paint. How much blue paint did he use? ml","e":"7 units = 840 ml, so 1 unit = 120 ml. Blue = 3 units = 3 \u00d7 120 = 360 ml. Answer: 360 ml."} {"t":"q","id":26078,"q":"The table shows the charges for bicycle rental: First hour $6.00; every additional \\(\\dfrac{1}{2}\\) hour or part thereof $2.50. John and his brother rented a bicycle each from 2.00 p.m. to 4.15 p.m. How much did they pay altogether? $","e":"2.00 to 4.15 p.m. = 2 h 15 min. First hour = $6.00. Remaining 1 h 15 min = three half-hour blocks (0.5+0.5+0.25 rounded up) = 3 \u00d7 $2.50 = $7.50. One bike = $6.00 + $7.50 = $13.50. Two bikes = 2 \u00d7 $13.50 = $27. Answer: $27."} {"t":"q","id":26081,"q":"The table shows the number of buttons in a box (Red 80, Blue 130). What percentage of the buttons in the box are red buttons? Round your answer to 2 decimal places. %","e":"Total buttons = 80 + 130 = 210. Red percentage = \\(\\dfrac{80}{210} \\times 100\\%\\) = 38.0952...% \u2248 38.10%. Answer: 38.10%."} {"t":"q","id":26082,"q":"Printer A prints at a rate of 80 copies in 1 minute while Printer B prints at a rate of 300 copies in 5 minutes. Which printer prints at a faster rate?","e":"Printer A = 80 copies\/min. Printer B = 300 \u00f7 5 = 60 copies\/min. 80 > 60, so Printer A is faster. Answer: Printer A."} {"t":"q","id":26083,"q":"Printer A prints at a rate of 80 copies in 1 minute while Printer B prints at a rate of 300 copies in 5 minutes. By how many more copies does the faster printer print in one minute? copies","e":"Printer A = 80\/min, Printer B = 60\/min. Difference = 80 - 60 = 20 copies. Answer: 20 copies."} {"t":"q","id":26084,"q":"Zhi Yu cycles 7 times a week. Each time, he cycles \\(5\\dfrac{4}{5}\\) km from his home to the park and cycles home on the same route. What is the total distance that Zhi Yu cycles in a week? Express your answer as a mixed number in the simplest form.","e":"Each round trip = \\(5\\dfrac{4}{5} \\times 2 = 11\\dfrac{3}{5}\\) km. Over 7 days: \\(5\\dfrac{4}{5} \\times 7 \\times 2 = \\dfrac{29}{5} \\times 14 = \\dfrac{406}{5} = 81\\dfrac{1}{5}\\) km. Answer: \\(81\\dfrac{1}{5}\\) km."} {"t":"q","id":26085,"q":"Shanti bought 1.3 kg of grapes priced at 80\u00a2 per 100 g. How much did she pay? $","e":"1.3 kg = 1300 g = 13 lots of 100 g. Cost = 13 \u00d7 $0.80 = $10.40. Answer: $10.40."} {"t":"q","id":26086,"q":"Mrs Lim paid $53 for 5 mugs and 4 bowls. The cost of each bowl was $2 more than the cost of each mug. How much did Mrs Lim pay for the 5 mugs? $","e":"4 bowls cost 4 \u00d7 $2 = $8 more than 4 mugs. Remove that: $53 - $8 = $45 for 9 items at the mug price. 1 mug = $45 \u00f7 9 = $5. 5 mugs = 5 \u00d7 $5 = $25. Answer: $25."} {"t":"q","id":26090,"q":"Amira baked some cookies in the morning. She gave \\(\\dfrac{2}{7}\\) of them to her neighbours and gave \\(\\dfrac{1}{2}\\) of the remaining cookies to her friends. In the afternoon, Amira baked another 85 cookies. The number of cookies that she had in the end was 13 more than what she baked in the morning. What fraction of the cookies baked in the morning were given away?","e":"Take morning total as 14 units. Given to neighbours = 4 units (2\/7 of 14). Remaining = 10 units; given to friends = 5 units (half). Total given away = 4 + 5 = 9 units, i.e. \\(\\dfrac{9}{14}\\). Answer: \\(\\dfrac{9}{14}\\)."} {"t":"q","id":26091,"q":"Amira baked some cookies in the morning. She gave \\(\\dfrac{2}{7}\\) of them to her neighbours and gave \\(\\dfrac{1}{2}\\) of the remaining cookies to her friends. In the afternoon, Amira baked another 85 cookies. The number of cookies that she had in the end was 13 more than what she baked in the morning. How many cookies did Amira bake altogether on that day? ","e":"She gave away 9\/14 in the morning, keeping 5\/14. End amount = morning + 13, and end = kept + 85. So (5\/14)m + 85 = m + 13 \u2192 85 - 13 = m - (5\/14)m = (9\/14)m \u2192 72 = (9\/14)m \u2192 m = 112. Morning baked = 112; total for the day = 112 + 85 = 197. Answer: 197."} {"t":"q","id":26092,"q":"A box with 40 identical nails has a mass of 780 g. The same box with 30 identical batteries has a mass of 1.08 kg. The mass of each battery is twice the mass of each nail. Find the mass of the empty box in kilograms. ","e":"30 batteries = 60 nail-masses. Difference: (box + 60 nails) - (box + 40 nails) = 1.08 kg - 0.78 kg = 0.30 kg = 20 nail-masses. So 1 nail = 0.015 kg. 40 nails = 0.6 kg. Empty box = 0.78 kg - 0.6 kg = 0.18 kg. Answer: 0.18 kg."} {"t":"q","id":26093,"q":"Adam, Ben and Calvin had a total of 540 marbles. Adam gave \\(\\dfrac{1}{4}\\) of his marbles to Ben. Then, Ben gave \\(\\dfrac{1}{3}\\) of his total number of marbles to Calvin. In the end, all the boys had the same number of marbles.
(a) How many marbles did each boy have in the end?
(b) How many marbles did Ben have at first? ","e":"(a) In the end all equal: 540 \u00f7 3 = 180 each. (b) Working back: Adam ended with 180 after giving 1\/4 away, so 3\/4 of Adam's start = 180 \u2192 Adam started 240, gave 60 to Ben. Ben ended with 180 after giving 1\/3 away, so 2\/3 of Ben's amount-before-giving = 180 \u2192 Ben had 270 before giving, gave 90 to Calvin. Ben at first = 270 - 60 (received from Adam) = 210. Answers: (a) 180, (b) 210."} {"t":"q","id":26094,"q":"Siew Li and Mariam each had a roll of ribbon of the same length for making bows. The same length of ribbon was used for each bow. Siew Li made 30 bows and had 1.5 m of ribbon left. Mariam made 10 bows and had 8.5 m of ribbon left. How many bows could each girl make at most with the ribbon that she had? ","e":"Difference in bows = 30 - 10 = 20 bows, using 8.5 - 1.5 = 7 m. So each bow uses 7 \u00f7 20 = 0.35 m. Total ribbon = 30\u00d70.35 + 1.5 = 12 m. Max bows = 12 \u00f7 0.35 = 34.2 \u2192 34 bows (whole bows). Answer: 34 bows."} {"t":"q","id":26096,"q":"The first five figures of a pattern are shown; the total number of circles in figure n is n\u00b2. What is the total number of white and grey circles in Figure 50? ","e":"Total in figure n = n\u00b2, so Figure 50 = 50 \u00d7 50 = 2500. Answer: 2500."} {"t":"q","id":26097,"q":"The first five figures of a pattern are shown; the total number of circles in figure n is n\u00b2, and the difference between grey and white circles equals the figure number. In Figure 50, what fraction of the circles are grey? Give your answer in the simplest form.","e":"Total in Figure 50 = 2500. Grey - white = 50 (the figure number). Grey + white = 2500. Grey = (2500 + 50) \u00f7 2 = 1275. Fraction grey = \\(\\dfrac{1275}{2500} = \\dfrac{51}{100}\\). Answer: \\(\\dfrac{51}{100}\\)."} {"t":"q","id":26102,"q":"What is the value of \\(33 - (6 + 12) \\div 3\\)?","e":"Work brackets first, then division, then subtraction. \\((6+12)=18\\); \\(18\\div3=6\\); \\(33-6=27\\)."} {"t":"q","id":26110,"q":"Jon had 200 stickers. He gave 90 stickers to his friend. What percentage of his stickers did Jon give to his friend?","e":"Fraction given \\(= \\dfrac{90}{200}\\). As a percentage \\(= \\dfrac{90}{200} \\times 100\\% = 45\\%\\)."} {"t":"q","id":26111,"q":"The total marks obtained by 4 students is 60. What is the average number of marks obtained by the 4 students?","e":"Average \\(= \\dfrac{\\text{total}}{\\text{number of items}} = \\dfrac{60}{4} = 15\\)."} {"t":"q","id":26113,"q":"Ken saved \\(\\dfrac{1}{4}\\) of his allowance and spent \\(\\dfrac{3}{5}\\) of the remaining allowance on food. He had $72 left. How much was his allowance?","e":"Remaining after saving \\(= \\dfrac{3}{4}\\). He spent \\(\\dfrac{3}{5}\\) of that on food, leaving \\(\\dfrac{2}{5}\\) of the remainder. So $72 \\(= \\dfrac{2}{5} \\times \\dfrac{3}{4}\\) of allowance \\(= \\dfrac{6}{20} = \\dfrac{3}{10}\\) of allowance. Allowance \\(= 72 \\div \\dfrac{3}{10} = 72 \\times \\dfrac{10}{3} = \\$240\\)."} {"t":"q","id":26115,"q":"Matthew had $25 more than Amy. When Amy gave Matthew $20, Matthew had 6 times as much money as Amy. How much money did Amy have at first?","e":"Let Amy have $a, so Matthew has $(a+25). After Amy gives $20: Matthew has $(a+45), Amy has $(a-20). Then \\(a+45 = 6(a-20)\\), so \\(a+45 = 6a-120\\), \\(165 = 5a\\), \\(a = 33\\). Amy had $33."} {"t":"q","id":26116,"q":"Ben shared a sum of money equally with Carla. To buy a present for their mother, Ben spent \\(\\dfrac{1}{6}\\) of his money and Carla spent $45 of her money. In the end, \\(\\dfrac{3}{4}\\) of the original sum of money was left. What was the original sum of money shared by Ben and Carla?","e":"Each had half the total, T\/2. Together they spent \\(\\dfrac{1}{4}\\) of T (since \\(\\dfrac{3}{4}\\) is left), so total spent \\(= \\dfrac{T}{4}\\). Ben spent \\(\\dfrac{1}{6} \\times \\dfrac{T}{2} = \\dfrac{T}{12}\\); Carla spent $45. So \\(\\dfrac{T}{12} + 45 = \\dfrac{T}{4}\\). Then \\(45 = \\dfrac{T}{4} - \\dfrac{T}{12} = \\dfrac{2T}{12} = \\dfrac{T}{6}\\), giving \\(T = 270\\). Original sum was $270."} {"t":"q","id":26117,"q":"Express \\(3\\dfrac{7}{25}\\) as a decimal. ","e":"\\(\\dfrac{7}{25} = \\dfrac{28}{100} = 0.28\\), so \\(3\\dfrac{7}{25} = 3.28\\)."} {"t":"q","id":26118,"q":"Find the value of \\(24 \\times 400\\). ","e":"\\(24 \\times 4 = 96\\), then \\(\\times 100 = 9600\\)."} {"t":"q","id":26122,"q":"Two cups and a jug contain 2.33 litres of water. The volume of water in each cup is the same. The volume of water in one cup is 1.61 litres less than the volume of water in the jug. Find the volume of water in each cup. ","e":"Let each cup hold c litres. Jug \\(= c + 1.61\\). Total: \\(c + c + (c + 1.61) = 2.33\\), so \\(3c = 0.72\\), \\(c = 0.24\\). Each cup holds 0.24 litres."} {"t":"q","id":26123,"q":"Jill had $400. She spent 20% of her money on books. How much money did Jill spend on books? ","e":"20% of $400 \\(= \\dfrac{20}{100} \\times 400 = \\$80\\)."} {"t":"q","id":26124,"q":"The table shows the number of blue pens and red pens in 4 boxes. Box A: 17 red, 12 blue. Box B: 10 red, 18 blue. Box C: 13 red, 12 blue. Box D: 11 red, 15 blue.
(a) Which coloured pen has a greater number?
(b) All the pens are repacked such that each box contained the same number of pens. How many pens are there in each box now? ","e":"(a) Total red \\(= 17+10+13+11 = 51\\); total blue \\(= 12+18+12+15 = 57\\). Blue has more. (b) Total pens \\(= 51 + 57 = 108\\); shared into 4 boxes \\(= 108 \\div 4 = 27\\) per box."} {"t":"q","id":26125,"q":"A box of toys was shared equally among 10 children. 3 of them gave all of their toys to the rest of the children. As a result, the rest of the children received 6 more toys each. How many toys were there in the box? ","e":"The 3 children's toys were shared among the remaining 7, giving them 6 more each: \\(3 \\times s = 7 \\times 6 = 42\\), where s is each child's original share. So \\(s = 14\\). Total toys \\(= 10 \\times 14 = 140\\)."} {"t":"q","id":26126,"q":"There are 248 marbles in a box. The ratio of the number of red marbles to the number of blue marbles is 3 : 1. The rest of the 60 marbles are green. How many blue marbles are there in the box? ","e":"Non-green marbles \\(= 248 - 60 = 188\\). These split red : blue \\(= 3 : 1\\), i.e. 4 units \\(= 188\\), so 1 unit \\(= 47\\). Blue \\(= 1\\) unit \\(= 47\\)."} {"t":"q","id":26131,"q":"$30\\,000 + 4000 + 500 + 6 =$","e":"Expanded form: 30 000 + 4000 + 500 + 6 = 34 506. Final answer: 34 506."} {"t":"q","id":26132,"q":"What is the missing number in the number pattern?
91, 73, 55, , 19","e":"The pattern decreases by 18 each step: 91, 73, 55, 37, 19. Missing number = 55 - 18 = 37. Final answer: 37."} {"t":"q","id":26134,"q":"Find the value of \\(\\dfrac{2}{3} + \\dfrac{1}{4}\\)","e":"Common denominator 12: \\(\\dfrac{2}{3} = \\dfrac{8}{12}\\), \\(\\dfrac{1}{4} = \\dfrac{3}{12}\\). Sum = \\(\\dfrac{8}{12} + \\dfrac{3}{12} = \\dfrac{11}{12}\\). Final answer: \\(\\dfrac{11}{12}\\)."} {"t":"q","id":26135,"q":"Find the value of \\(\\dfrac{3}{5} \\times \\dfrac{1}{2}\\)","e":"Multiply numerators and denominators: \\(\\dfrac{3}{5} \\times \\dfrac{1}{2} = \\dfrac{3 \\times 1}{5 \\times 2} = \\dfrac{3}{10}\\). Final answer: \\(\\dfrac{3}{10}\\)."} {"t":"q","id":26136,"q":"Express \\(2\\dfrac{1}{20}\\) as a decimal.","e":"\\(\\dfrac{1}{20} = \\dfrac{5}{100} = 0.05\\). So \\(2\\dfrac{1}{20} = 2 + 0.05 = 2.05\\). Final answer: 2.05."} {"t":"q","id":26137,"q":"Round 3.785 to 2 decimal places.","e":"The 3rd decimal digit is 5, so round the 2nd decimal place up: 3.785 rounds to 3.79. Final answer: 3.79."} {"t":"q","id":26138,"q":"A machine takes 3 min to print 4 posters. At the same rate, how long will it take to print 24 posters?","e":"24 posters is 24 \u00f7 4 = 6 times as many as 4 posters. Time = 6 \u00d7 3 min = 18 min. Final answer: 18 min."} {"t":"q","id":26139,"q":"In a basket, there are 5 pears, 20 apples and 10 mangoes. What is the ratio of the number of pears to the total number of apples and mangoes in the basket?","e":"Pears = 5. Apples + mangoes = 20 + 10 = 30. Ratio = 5 : 30 = 1 : 6. Final answer: 1 : 6."} {"t":"q","id":26142,"q":"At first, Ali was facing east. He then turned 135\u00b0 anti-clockwise. What direction did Ali face in the end?","e":"Facing east, turning 90\u00b0 anti-clockwise faces north; a further 45\u00b0 anti-clockwise (135\u00b0 total) faces north-west. Final answer: North-West."} {"t":"q","id":26143,"q":"There are 240 adults and 60 children at a concert. What percentage of the people at the concert are children?","e":"Total people = 240 + 60 = 300. Percentage of children = \\(\\dfrac{60}{300} \\times 100\\% = 20\\%\\). Final answer: 20%."} {"t":"q","id":26145,"q":"Amy has twice as many $20 notes as $50 notes in a box. The total value of the money in the box is $6300. How many $20 notes are there in the box?","e":"Let $50 notes = 1 unit, $20 notes = 2 units. Value = 1\u00d750 + 2\u00d720 = 90 per unit. Units = 6300 \u00f7 90 = 70. $20 notes = 2 \u00d7 70 = 140. Final answer: 140."} {"t":"q","id":26146,"q":"Round 67 483 to the nearest hundred.
","e":"The tens digit is 8 (\u2265 5), so round the hundreds place up: 67 483 \u2192 67 500. Final answer: 67 500."} {"t":"q","id":26147,"q":"Find the value of $400 \\times 17$
","e":"400 \u00d7 17 = 4 \u00d7 17 \u00d7 100 = 68 \u00d7 100 = 6800. Final answer: 6800."} {"t":"q","id":26148,"q":"What is the value of $40 - (3 + 13) \\div 4 \\times 2$?
","e":"Brackets first: 3 + 13 = 16. Then left to right for \u00f7 and \u00d7: 16 \u00f7 4 = 4, 4 \u00d7 2 = 8. Finally 40 - 8 = 32. Final answer: 32."} {"t":"q","id":26149,"q":"Write down all the common multiples of 6 and 8 that are smaller than 70.
and ","e":"The lowest common multiple of 6 and 8 is 24. Common multiples are 24, 48, 72, ... Those smaller than 70 are 24 and 48. Final answer: 24 and 48."} {"t":"q","id":26150,"q":"Find the value of \\(\\dfrac{2}{9} \\times 4\\)","e":"\\(\\dfrac{2}{9} \\times 4 = \\dfrac{2 \\times 4}{9} = \\dfrac{8}{9}\\). Final answer: \\(\\dfrac{8}{9}\\)."} {"t":"q","id":26151,"q":"Mdm Siti had \\(1.03\\) \u2113 of oil at first. She used 650 m\u2113 of it. How many litres of oil was left?
\u2113","e":"1.03 \u2113 = 1030 m\u2113. 1030 - 650 = 380 m\u2113 = 0.38 \u2113. Final answer: 0.38 \u2113."} {"t":"q","id":26152,"q":"The length of Ribbon A is 9 cm. The length of Ribbon B is 5 cm longer than Ribbon A. Find the ratio of the length of Ribbon B to the length of Ribbon A.","e":"Ribbon B = 9 + 5 = 14 cm. Ratio B : A = 14 : 9. Final answer: 14 : 9."} {"t":"q","id":26155,"q":"The sum of 4 numbers is 680. One of the numbers is 65. What is the average of the other 3 numbers?
","e":"Sum of the other 3 numbers = 680 - 65 = 615. Average = 615 \u00f7 3 = 205. Final answer: 205."} {"t":"q","id":26156,"q":"A store rewards customers with 6 points for every $50 spent. Mrs Tan spent $240 at the store. What is the total number of points Mrs Tan receives from the store?
","e":"Number of complete $50 blocks in $240 = 240 \u00f7 50 = 4 (remainder $40, no points). Points = 4 \u00d7 6 = 24. Final answer: 24."} {"t":"q","id":26157,"q":"There are 600 people at a concert. 45% of the people are children, 30% of the people are women and the rest are men. How many men are there?
","e":"Percentage of men = 100% - 45% - 30% = 25%. Men = 25% of 600 = \\(\\dfrac{25}{100} \\times 600 = 150\\). Final answer: 150."} {"t":"q","id":26159,"q":"\\(\\dfrac{5}{8}\\) of students in a class wear spectacles. \\(\\dfrac{3}{5}\\) of those who wear spectacles are girls. 15 girls wear spectacles. More than half of the students are girls. What is the smallest possible number of girls who do not wear spectacles?
","e":"Girls with spectacles: \\(\\dfrac{3}{5}\\) of spectacle-wearers = 15, so spectacle-wearers = 25, which is \\(\\dfrac{5}{8}\\) of the class, giving 40 students. More than half girls means more than 20 girls; smallest total girls = 21. Girls without spectacles = 21 - 15 = 6. Final answer: 6."} {"t":"q","id":26161,"q":"In which one of the following numbers does the digit 5 have a value of 50 000?","e":"Place value: the digit 5 must sit in the ten-thousands place (value 50 000). In 4 658 120, the 5 is in the ten-thousands place: 5 \u00d7 10 000 = 50 000. Answer: 4 658 120."} {"t":"q","id":26162,"q":"Which one of the following fractions is smaller than \\(\\dfrac{1}{4}\\)?","e":"Compare each to \\(\\dfrac{1}{4}=0.25\\): \\(\\dfrac{5}{6}\\approx0.83\\), \\(\\dfrac{3}{8}=0.375\\), \\(\\dfrac{2}{5}=0.4\\), \\(\\dfrac{1}{6}\\approx0.167\\). Only \\(\\dfrac{1}{6}\\) is smaller than \\(\\dfrac{1}{4}\\). Answer: \\(\\dfrac{1}{6}\\)."} {"t":"q","id":26163,"q":"\\(16 + \\dfrac{?}{10} = 17.8\\) What is the missing number in the box?","e":"17.8 \u2212 16 = 1.8, so \\(\\dfrac{?}{10}=1.8\\). Then ? = 1.8 \u00d7 10 = 18. Answer: 18."} {"t":"q","id":26165,"q":"Yu Wen had $7000 in her bank account. The bank paid 2% interest at the end of each year. She did not withdraw any of her savings. How much interest did she earn at the end of 1 year?","e":"Interest = 2% of $7000 = \\(\\dfrac{2}{100}\\times 7000 = \\$140\\). Answer: $140."} {"t":"q","id":26166,"q":"There are 10 chickens at a farm. There are 35 more ducks than chickens. What is the ratio of the number of ducks to the number of chickens?","e":"Ducks = 10 + 35 = 45. Ratio ducks : chickens = 45 : 10 = 9 : 2. Answer: 9 : 2."} {"t":"q","id":26169,"q":"Harumi had a piece of string 4 m 6 cm. She cut off 1.3 m from it. What is the length of the remaining string?","e":"4 m 6 cm = 406 cm. 1.3 m = 130 cm. Remaining = 406 \u2212 130 = 276 cm. Answer: 276 cm."} {"t":"q","id":26171,"q":"A sandwich costs $6.05. Leonard bought 4 such sandwiches and had $1.85 left. How much money did he have before buying the 4 sandwiches?","e":"Cost of 4 sandwiches = 4 \u00d7 $6.05 = $24.20. Money before = $24.20 + $1.85 = $26.05. Answer: $26.05."} {"t":"q","id":26172,"q":"Amiya and Eunice have $2100 altogether. Amiya has 30% of the money. How much money does Amiya have?","e":"30% of $2100 = \\(\\dfrac{30}{100}\\times 2100 = \\$630\\). Answer: $630."} {"t":"q","id":26174,"q":"Mrs Urvi cut a cake into 16 equal pieces. She ate 3 pieces and gave a few pieces to her friends. In the end, she had \\(\\dfrac{3}{8}\\) of the cake left. What fraction of the cake did she give to her friends?","e":"Ate 3 of 16 pieces = \\(\\dfrac{3}{16}\\). Left = \\(\\dfrac{3}{8}=\\dfrac{6}{16}\\). Gave away = whole \u2212 ate \u2212 left = \\(\\dfrac{16}{16}-\\dfrac{3}{16}-\\dfrac{6}{16}=\\dfrac{7}{16}\\). Answer: \\(\\dfrac{7}{16}\\)."} {"t":"q","id":26176,"q":"Find the value of \\(57 \\div 300\\). Leave your answer as a decimal. ","e":"57 \u00f7 300 = 0.19. Answer: 0.19."} {"t":"q","id":26177,"q":"Find the value of \\(11 + (18 - 14 \\div 2) \\times 3\\). ","e":"Inside brackets: 14 \u00f7 2 = 7, then 18 \u2212 7 = 11. Then 11 \u00d7 3 = 33. Then 11 + 33 = 44. Answer: 44."} {"t":"q","id":26178,"q":"What is six-fifths of 60?","e":"\\(\\dfrac{6}{5}\\times 60 = \\dfrac{6\\times 60}{5}=\\dfrac{360}{5}=72\\). Answer: 72."} {"t":"q","id":26179,"q":"Mrs Cheah bought an iron which included a GST of 7%. The price of the iron before GST was $90. How much did she pay for the iron? Ans: $ ","e":"GST = 7% of $90 = \\(\\dfrac{7}{100}\\times 90 = \\$6.30\\). Total paid = $90 + $6.30 = $96.30. Answer: $96.30."} {"t":"q","id":26180,"q":"A photocopier can copy 48 pages in 4 minutes. At this rate, how many pages can the photocopier copy per minute? ","e":"48 pages \u00f7 4 minutes = 12 pages per minute. Answer: 12."} {"t":"q","id":26181,"q":"Arrange the following from the smallest to the largest. \\(0.209\\), \\(\\dfrac{1}{5}\\), \\(\\dfrac{2}{1000}\\)","e":"Convert to decimals: \\(\\dfrac{1}{5}=0.200\\), \\(\\dfrac{2}{1000}=0.002\\), and 0.209. Smallest to largest: 0.002, 0.200, 0.209, i.e. \\(\\dfrac{2}{1000}\\), \\(\\dfrac{1}{5}\\), \\(0.209\\)."} {"t":"q","id":26182,"q":"Last year, Bertrand completed a race in 51.98 seconds. This year, he completed the same race and was faster by 1.31 seconds. What was Bertrand's timing this year? Round your answer to 1 decimal place. Ans: s","e":"51.98 \u2212 1.31 = 50.67 s. Rounded to 1 decimal place = 50.7 s. Answer: 50.7 s."} {"t":"q","id":26185,"q":"The height of a cuboid is 20 m. Its height is twice its length. Its breadth is 6 m shorter than its length. Find the volume of the cuboid. Ans: m\u00b3","e":"Height = 20 m. Length = 20 \u00f7 2 = 10 m. Breadth = 10 \u2212 6 = 4 m. Volume = 20 \u00d7 10 \u00d7 4 = 800 m\u00b3. Answer: 800 m\u00b3."} {"t":"q","id":26186,"q":"At first, a pot contained \\(\\dfrac{2}{5}\\) \u2113 of water. Keisha added another \\(\\dfrac{1}{2}\\) \u2113 of water into the pot. Then she used \\(\\dfrac{2}{9}\\) of all the water in the pot. How much water did Keisha use? Express your answer as a fraction in its simplest form.","e":"Total water = \\(\\dfrac{2}{5}+\\dfrac{1}{2}=\\dfrac{4}{10}+\\dfrac{5}{10}=\\dfrac{9}{10}\\) \u2113. Used = \\(\\dfrac{2}{9}\\times\\dfrac{9}{10}=\\dfrac{2}{10}=\\dfrac{1}{5}\\) \u2113. Answer: \\(\\dfrac{1}{5}\\) \u2113."} {"t":"q","id":26188,"q":"The ratio of Jim's age to Frank's age is 1 : 6. In 5 years' time, they would be 73 years old altogether. What is Jim's age now? Ans: ","e":"In 5 years they add 5 + 5 = 10 years total, so their combined age now = 73 \u2212 10 = 63. Ratio 1 : 6 means 7 equal units = 63, so 1 unit = 63 \u00f7 7 = 9. Jim's age now = 1 unit = 9 years old. Answer: 9."} {"t":"q","id":26189,"q":"Two different whole numbers add up to 140. One of them is a 2-digit number and the other is a 3-digit number. What are the two numbers that will give the greatest possible difference? Ans: and ","e":"For the greatest difference, make the 3-digit number as large as possible and the 2-digit number as small as possible. The smallest 3-digit number that keeps the other a 2-digit number: smallest 2-digit number is 10, giving 140 \u2212 10 = 130 (a 3-digit number). Difference = 130 \u2212 10 = 120, the greatest possible. Answer: 10 and 130."} {"t":"q","id":26190,"q":"When a number is divided by 3, the answer is 6041. What is the answer obtained when the same number is divided by 7? Ans: ","e":"The number = 6041 \u00d7 3 = 18123. Then 18123 \u00f7 7 = 2589. Answer: 2589."} {"t":"q","id":26191,"q":"There were 1780 people at a carnival. 45% of them were adults and the rest were children. How many children were at the carnival? Ans: ","e":"Children are 100% \u2212 45% = 55% of 1780. 55% of 1780 = \\(\\dfrac{55}{100}\\times 1780 = 979\\). Answer: 979 children."} {"t":"q","id":26195,"q":"Cecily and Nadine shared the total cost of a handbag. Cecily paid $39 more than \\(\\dfrac{4}{9}\\) of the total cost of the handbag. Nadine paid $186. How much did the handbag cost? Ans: $ ","e":"Cecily paid \\(\\dfrac{4}{9}\\) of the cost + $39, so Nadine paid the rest: total \u2212 (\\(\\dfrac{4}{9}\\) + $39) = \\(\\dfrac{5}{9}\\) of the cost \u2212 $39. So \\(\\dfrac{5}{9}\\) of the cost \u2212 $39 = $186, giving \\(\\dfrac{5}{9}\\) of the cost = $225. \\(\\dfrac{1}{9}\\) = 225 \u00f7 5 = $45, so total = 45 \u00d7 9 = $405. Answer: $405."} {"t":"q","id":26197,"q":"Winsy had some purple beads and an equal number of red beads and yellow beads. The ratio of the number of purple beads to the number of red beads was 5 : 7. Winsy had 210 more red beads than purple beads. How many red beads and yellow beads did she have altogether? Ans: ","e":"Purple : red = 5 : 7. The difference = 7 \u2212 5 = 2 units = 210, so 1 unit = 105. Red = 7 units = 735, and yellow = red = 735 (equal number). Red + yellow = 735 + 735 = 1470. Answer: 1470 beads."} {"t":"q","id":26200,"q":"At Doughnut Empire, each doughnut is sold at $1.10 or in a box of 11 for $8.90. Mrs Kor wants to buy exactly 208 doughnuts. What is the least amount of money that she needs to pay for the doughnuts? Ans: $ ","e":"Boxes are cheaper per doughnut ($8.90 \u00f7 11 \u2248 $0.81 vs $1.10). 208 \u00f7 11 = 18 boxes (198 doughnuts) remainder 10. Buy 18 boxes: 18 \u00d7 $8.90 = $160.20, covering 198 doughnuts; buy the remaining 10 singly: 10 \u00d7 $1.10 = $11. Total = $160.20 + $11 = $171.20. Answer: $171.20."} {"t":"q","id":26201,"q":"Vinette had some white and black face masks. \\(\\dfrac{1}{6}\\) of them were white. She gave away \\(\\dfrac{1}{3}\\) of the white face masks and \\(\\dfrac{1}{3}\\) of the black face masks. In the end, she had 156 white and black face masks altogether. How many black face masks did Vinette have at first? Ans: ","e":"She gave away 1\/3 of every mask, so she kept 2\/3 of the total. 2\/3 of total = 156, so total = 156 \u00d7 3 \u00f7 2 = 234 masks at first. White = 1\/6 \u00d7 234 = 39, so black = 234 \u2212 39 = 195. (Printed working: total at first 18 units, 1 + 5 = 6 ... 156 \u00f7 12 = 13, 13 \u00d7 15 = 195.) Answer: 195 black face masks."} {"t":"q","id":26206,"q":"Singapore's population was 6 014 723 last year. Express this number to the nearest thousand.","e":"Method: round to the nearest thousand by looking at the hundreds digit. 6 014 723 has 7 in the hundreds place, so round up: 6 014 723 \u2192 6 015 000. Final answer: 6 015 000."} {"t":"q","id":26207,"q":"In 13.02, which digit is in the tenths place?","e":"Method: identify decimal place values. In 13.02 the first digit after the decimal point is the tenths place, which is 0. Final answer: 0."} {"t":"q","id":26208,"q":"Rina makes a necklace using 12 pink pearls and 18 white pearls. What fraction of the pearls are white?","e":"Method: white \u00f7 total. Total pearls = 12 + 18 = 30. White = 18. Fraction = \\(\\dfrac{18}{30}=\\dfrac{3}{5}\\). Final answer: \\(\\dfrac{3}{5}\\)."} {"t":"q","id":26209,"q":"What is the value of (63 + 27) \u00f7 3 \u2013 12 \u00d7 2?","e":"Method: order of operations (brackets, then \u00d7 and \u00f7, then \u2013). (63 + 27) = 90; 90 \u00f7 3 = 30; 12 \u00d7 2 = 24; 30 \u2013 24 = 6. Final answer: 6."} {"t":"q","id":26211,"q":"The average of 3 numbers is 34. One of the numbers is 28. Which of the following are the other two numbers?","e":"Method: total = average \u00d7 number of items. Total = 34 \u00d7 3 = 102. The other two = 102 \u2013 28 = 74. 36 + 38 = 74. Final answer: 36, 38."} {"t":"q","id":26218,"q":"The table shows the rates for renting a bicycle at a shop.
First hour: $8
Every additional 30 min or part thereof: ?
Daisy rented two bicycles from 3.00 pm to 5.50 pm. She paid a total of $32 for renting the bicycles. How much did Daisy have to pay for every additional 30 min or part thereof for renting a bicycle?","e":"Method: work out the charge per bicycle, then the additional-period rate. 3.00 pm to 5.50 pm = 2 h 50 min. First hour = $8; the remaining 1 h 50 min = 110 min = 4 blocks of 30 min (part thereof rounds up). Total for two bicycles = $32, so each bicycle = $16. Additional charge per bicycle = $16 \u2013 $8 = $8 over 4 blocks = $2 per 30 min. Final answer: $2."} {"t":"q","id":26219,"q":"At first, Mrs Ang had twice as many red beads as yellow beads. She used \\(\\dfrac{2}{3}\\) of her yellow beads and some of her red beads to make some necklaces. In the end, \\(\\dfrac{3}{5}\\) of the beads left were red beads. What fraction of her red beads did Mrs Ang use?","e":"Method: use units. Let yellow = 3u, so red = 6u. Yellow used = \\(\\dfrac{2}{3}\\times3u = 2u\\), so yellow left = 1u. In the end red is \\(\\dfrac{3}{5}\\) of beads left, so yellow (1u) is \\(\\dfrac{2}{5}\\) of the remainder \u2192 remainder = \\(\\dfrac{5}{2}u\\), giving red left = \\(\\dfrac{3}{2}u\\). Red used = 6u \u2013 \\(\\dfrac{3}{2}u\\) = \\(\\dfrac{9}{2}u\\). Fraction of red used = \\(\\dfrac{9\/2\\,u}{6u}=\\dfrac{3}{4}\\). Final answer: \\(\\dfrac{3}{4}\\)."} {"t":"q","id":26220,"q":"Mrs Samy baked chocolate and strawberry cupcakes at a children's party. The number of chocolate cupcakes was \\(\\dfrac{5}{7}\\) the number of strawberry cupcakes. Mrs Samy then baked some blueberry cupcakes. In the end, 25% of the cupcakes were chocolate cupcakes. What percentage of cupcakes were blueberry cupcakes?","e":"Method: chocolate : strawberry = 5 : 7, so chocolate = 5 parts, strawberry = 7 parts. After adding blueberry, chocolate (5 parts) = 25% of total, so total = 20 parts. Strawberry = 7 parts. Blueberry = 20 \u2013 5 \u2013 7 = 8 parts = \\(\\dfrac{8}{20}\\times100\\% = 40\\%\\). Final answer: 40%."} {"t":"q","id":26221,"q":"Find the value of 20.1 \u2013 0.68. ","e":"Method: subtract decimals lining up the points. 20.10 \u2013 0.68 = 19.42. Final answer: 19.42."} {"t":"q","id":26222,"q":"Find the value of \\(\\dfrac{5}{7}\\times\\dfrac{8}{15}\\). Give your answer in its simplest form.","e":"Method: multiply numerators and denominators, then simplify. \\(\\dfrac{5}{7}\\times\\dfrac{8}{15}=\\dfrac{40}{105}\\). Divide top and bottom by 5: \\(\\dfrac{8}{21}\\). Final answer: \\(\\dfrac{8}{21}\\)."} {"t":"q","id":26225,"q":"(a) Find the value of \\(\\dfrac{2}{5}+\\dfrac{3}{8}\\).
(b) Express 2.68 as a mixed number in the simplest form.","e":"Method: (a) common denominator 40: \\(\\dfrac{2}{5}=\\dfrac{16}{40}\\), \\(\\dfrac{3}{8}=\\dfrac{15}{40}\\); sum = \\(\\dfrac{31}{40}\\). (b) 2.68 = \\(2\\dfrac{68}{100}\\); divide by 4 = \\(2\\dfrac{17}{25}\\). (The printed key's '2\\,17\/5' is a typo for \\(2\\dfrac{17}{25}\\) since \\(\\dfrac{68}{100}=\\dfrac{17}{25}\\).) Final answers: (a) \\(\\dfrac{31}{40}\\); (b) \\(2\\dfrac{17}{25}\\)."} {"t":"q","id":26226,"q":"The timetable shows the time of 4 different trains from City X to City Y.
Train A: leaves 8.15 a.m., arrives 10.05 a.m.
Train B: leaves 8.25 a.m., arrives 10.40 a.m.
Train C: leaves 8.40 a.m., arrives 11.00 a.m.
Train D: leaves 9.05 a.m., arrives 11.20 a.m.
(a) Find the time taken for Train D to travel from City X to City Y. Give your answer in h and min. h min
(b) Sue wants to take a train to City Y. Her watch shows 8.20 a.m. when she arrives at the station in City X. She realises that her watch is 10 min slower. What is the earliest time she can reach City Y? a.m.","e":"Method: (a) Train D: 9.05 a.m. to 11.20 a.m. = 2 h 15 min. (b) Watch shows 8.20 a.m. but is 10 min slow, so the real time is 8.30 a.m. The earliest train she can still catch leaves at 8.40 a.m. (Train C), which arrives 11.00 a.m. Final answers: (a) 2 h 15 min; (b) 11.00 a.m."} {"t":"q","id":26229,"q":"Zhi Xiang went to a shop to buy a bag. The shop gave a discount of $5 for every $25 spent. Zhi Xiang paid $96 for a bag. What was the price of the bag before the discount? ","e":"Method: for every $25 of original price the customer pays $20 (after $5 discount). $96 paid \u00f7 $20 = 4.8 groups \u2192 but using whole $25 groups: 4 full groups cost $80 (original $100), remaining $16 paid corresponds to $16 original (no further $25 reached). Original = $100 + $16 = $116. Check: total discount = $20, $116 \u2013 $20 = $96. Final answer: $116."} {"t":"q","id":26231,"q":"Christopher has $63.
Box of 9 cupcakes \u2013 $25
1 cupcake \u2013 $3
What is the greatest number of cupcakes he can buy? ","e":"Method: maximise cupcakes per dollar. A box of 9 for $25 is best value. 2 boxes = $50 for 18 cupcakes, leaving $63 \u2013 $50 = $13. With $13 at $3 each, buy 4 single cupcakes ($12). Total = 18 + 4 = 22 cupcakes. Final answer: 22."} {"t":"q","id":26232,"q":"The table shows the times taken by five robots to complete a maze.
Robot A: 4.5 s, Robot B: 6.81 s, Robot C: 3.92 s, Robot D: 4.12 s, Robot E: 5.1 s.
(a) Which robot was the fastest to complete the maze?
(b) Robot F completed the same maze. The average time taken for all 6 robots was 4.73 s. What was the time taken by Robot F to complete the maze? s","e":"Method: (a) the fastest robot has the smallest time: Robot C at 3.92 s. (b) total time for 6 robots = 4.73 \u00d7 6 = 28.38 s. Robot F = 28.38 \u2013 (4.5 + 6.81 + 3.92 + 4.12 + 5.1) = 28.38 \u2013 24.45 = 3.93 s. Final answers: (a) Robot C; (b) 3.93 s."} {"t":"q","id":26235,"q":"Corinne saved 20% of her monthly income. In August, her income decreased by 15%. As a result, her savings in August was decreased by $120 compared to her savings in July. What was her income in July? ","e":"Method: July savings = 20% of income. After a 15% income drop, savings = 20% \u00d7 85% = 17% of July income. The fall in savings = 20% \u2013 17% = 3% of July income = $120. So 1% = $40, and 100% = $4000. Final answer: $4000."} {"t":"q","id":26237,"q":"Vinesh drove from Singapore to Malacca at an average speed of 90 km\/h. On the return journey, he took the same route and covered \\(\\dfrac{1}{3}\\) of the distance in 1 hour. Then he reduced his speed to 70 km\/h for the rest of the journey. Vinesh took 4 hours for the return journey. How long did he take to drive from Singapore to Malacca? h","e":"Method: on the return, \\(\\dfrac{2}{3}\\) of the distance was covered in the remaining 3 h at 70 km\/h, so \\(\\dfrac{2}{3}\\)distance = 70 \u00d7 3 = 210 km. Total distance = 210 \u00f7 \\(\\dfrac{2}{3}\\) = 315 km. The outward trip at 90 km\/h took 315 \u00f7 90 = 3.5 h. Final answer: 3.5 h."} {"t":"q","id":26240,"q":"A shop sold electronic devices was having a sale. 1st item at 15% discount, 2nd item at 20% discount. Price of 2nd item must be equal or lower than the price of 1st item. Mr Poh bought a tablet at $230 and a laptop at $550. How much did he pay for the two items? ","e":"Method: the 1st item (15% off) must be the higher-priced one, so the laptop ($550) gets 15% off and the tablet ($230) gets 20% off. Laptop = 85% \u00d7 $550 = $467.50. Tablet = 80% \u00d7 $230 = $184. Total = $467.50 + $184 = $651.50. Final answer: $651.50."} {"t":"q","id":26241,"q":"A shop sale gives the 1st item 15% discount and the 2nd item 20% discount (2nd item priced equal or lower than the 1st). Mr Chian bought two identical smart watches. He received a total discount of $147. What was the price of one smart watch before the discount? ","e":"Method: identical watches, so one gets 15% off and the other 20% off. Total discount = 15% + 20% = 35% of one watch's price = $147. So 1% = $147 \u00f7 35 = $4.20, and 100% = $420. Final answer: $420."} {"t":"q","id":26243,"q":"Ray uses lines and dots to form figures that follow a pattern. The table shows the number of lines and dots for the first four figures:
Figure 1: 6 dots, 6 lines; Figure 2: 9 dots, 10 lines; Figure 3: 12 dots, 14 lines; Figure 4: 15 dots, 18 lines.
(a) Complete the table for Figure 5: dots and lines.
(b) A figure in the pattern has 108 dots. What is the Figure number?
(c) Find the total number of dots and lines in Figure 72. ","e":"Method: dots increase by 3 each figure (dots = 3 \u00d7 figure number + 3); lines increase by 4 each figure (lines = 4 \u00d7 figure number + 2). (a) Figure 5: dots = 15 + 3 = 18; lines = 18 + 4 = 22. (b) 108 dots: 108 \u00f7 3 = 36, then 36 \u2013 1 = 35 \u2192 Figure 35. (c) Figure 72: dots = 73 \u00d7 3 = 219; lines = 219 + 72 \u2013 1 = 290; total = 219 + 290 = 509. Final answers: (a) 18 dots, 22 lines; (b) Figure 35; (c) 509."} {"t":"q","id":26246,"q":"Tina had a total of 754 pearl necklaces and bead necklaces for sale. After selling twice as many pearl necklaces as bead necklaces, she had \\(\\dfrac{1}{3}\\) of the pearl necklaces and \\(\\dfrac{1}{4}\\) of the bead necklaces left. What was the total number of pearl and bead necklaces left? ","e":"Method: pearls left = \\(\\dfrac{1}{3}\\) pearls (so \\(\\dfrac{2}{3}\\) sold); beads left = \\(\\dfrac{1}{4}\\) beads (so \\(\\dfrac{3}{4}\\) sold). Pearls sold = 2 \u00d7 beads sold: \\(\\dfrac{2}{3}P = 2\\times\\dfrac{3}{4}B\\) \u2192 \\(\\dfrac{2}{3}P=\\dfrac{3}{2}B\\). Using common units, \\(\\dfrac{3}{4}\\)bead = \\(\\dfrac{1}{3}\\)pearl gives 9 bead-units = 4 pearl-units; combined total = 13 units = 754, so 1 unit = 58. Necklaces left = 4 units = 4 \u00d7 58 = 232. Final answer: 232."} {"t":"q","id":26247,"q":"At a school bookshop, erasers are only sold in packs of 4 and pencils are only sold in packs of 5. Erasers: 4 for $1.99. Pencils: 5 for $2.99. Mr Lim spent $139.45 buying some erasers and pencils for Children's Day. He put all the erasers and pencils into bags. The ratio of the number of erasers to the number of pencils in each bag was 2 : 3. How many pencils did he buy? ","e":"Method: erasers : pencils = 2 : 3, but they are bought in packs of 4 and 5, so a whole-pack ratio is (4\u00d75) : (5\u00d76) = 20 erasers : 30 pencils per set, i.e. 5 eraser-packs and 6 pencil-packs. Cost of one set = ($1.99 \u00d7 5) + ($2.99 \u00d7 6) = $9.95 + $17.94 = $27.89. Number of sets = $139.45 \u00f7 $27.89 = 5 sets. Pencils = (5 \u00d7 6) \u00d7 5 = 150 pencils. Final answer: 150."} {"t":"q","id":26248,"q":"Gary spent \\(\\dfrac{5}{8}\\) of his money on 10 identical notebooks and 10 identical files. Then, he spent \\(\\dfrac{5}{6}\\) of his remaining money on a bag. What fraction of Gary's money was spent on the bag?","e":"Method: remaining after books\/files = 1 \u2013 \\(\\dfrac{5}{8} = \\dfrac{3}{8}\\). Bag = \\(\\dfrac{5}{6}\\) of remaining = \\(\\dfrac{5}{6}\\times\\dfrac{3}{8} = \\dfrac{15}{48} = \\dfrac{5}{16}\\). Final answer: \\(\\dfrac{5}{16}\\)."} {"t":"q","id":26249,"q":"Gary spent \\(\\dfrac{5}{8}\\) of his money on 10 identical notebooks and 10 identical files, then \\(\\dfrac{5}{6}\\) of his remaining money on a bag. Each file cost $4 more than each notebook and the bag cost $38 more than each notebook. How much money had Gary left? ","e":"Method: let each notebook = nb. Bag spends \\(\\dfrac{5}{16}\\) of money (from part a), books\/files spend \\(\\dfrac{5}{8}=\\dfrac{10}{16}\\), so left = \\(1-\\dfrac{10}{16}-\\dfrac{5}{16}=\\dfrac{1}{16}\\). The key solves: 20nb + $40 = 2nb + $76 \u2192 18nb = $36 \u2192 nb = $2. Bag = $38 + $2 = $40; file = $4 + $2 = $6. Books+files cost = (10\u00d7$2)+(10\u00d7$6) = $80 = \\(\\dfrac{5}{8}\\) of money, so total money: 5u = $40, 1u = $8, 16u = $128. Spent so far $80 + $40 = $120; left = $128 \u2013 $120 = $8. Final answer: $8."} {"t":"q","id":26250,"q":"Which of the following is seven hundred and three thousand and twelve in numerals?","e":"Seven hundred and three thousand = 703 000; and twelve = 12. So the number is 703 012."} {"t":"q","id":26253,"q":"\\(3 + \\dfrac{3}{100} + \\dfrac{30}{1000} =\\)","e":"\\(\\dfrac{3}{100} = 0.03\\) and \\(\\dfrac{30}{1000} = 0.03\\). So \\(3 + 0.03 + 0.03 = 3.06\\)."} {"t":"q","id":26257,"q":"The average of three numbers is 40. The sum of another two numbers is 50. What is the average of the 5 numbers?","e":"Sum of the three numbers = 3 \u00d7 40 = 120. Total of all five = 120 + 50 = 170. Average = 170 \u00f7 5 = 34."} {"t":"q","id":26260,"q":"In a marathon relay race, four runners ran one after another without any stop in between. The second runner started running at the same time the first runner completed running and so on. The chart shows the time each runner started running. The last runner completed the race at 1.30 p.m.
Start times: First 10.30 a.m., Second 11.20 a.m., Third 12.15 p.m., Last 12.55 p.m.
How much more time did the slowest runner take than the fastest runner?","e":"Each runner's time = next start minus own start (last finishes 1.30 p.m.). First = 10.30\u219211.20 = 50 min; Second = 11.20\u219212.15 = 55 min; Third = 12.15\u219212.55 = 40 min; Last = 12.55\u21921.30 = 35 min. Slowest = 55 min, fastest = 35 min. Difference = 55 \u2212 35 = 20 min."} {"t":"q","id":26263,"q":"Aaron had $55 more than Shanti at first. After Aaron used \\(\\dfrac{2}{5}\\) of his money and Shanti used \\(\\dfrac{1}{3}\\) of her money, Aaron had $27 more than Shanti. How much did Shanti have left at the end?","e":"Let Shanti = S, Aaron = S + 55. After spending: Aaron has \\(\\dfrac{3}{5}(S+55)\\), Shanti has \\(\\dfrac{2}{3}S\\). Difference: \\(\\dfrac{3}{5}(S+55) \u2212 \\dfrac{2}{3}S = 27\\). \\(\\dfrac{3}{5}S + 33 \u2212 \\dfrac{2}{3}S = 27\\); \\(-\\dfrac{1}{15}S = -6\\); S = 90. Shanti left = \\(\\dfrac{2}{3} \u00d7 90 = 60\\)."} {"t":"q","id":26264,"q":"A sum of money was shared between John and Ken in the ratio 3 : 4. John used all his money to buy 8 identical toy cars that cost $1.50 each. Ken used some of his money to buy 3 such toy cars. How much money had Ken left?","e":"John spent 8 \u00d7 $1.50 = $12 (all his share, 3 units). So 1 unit = $4, Ken's share = 4 units = $16. Ken bought 3 cars = 3 \u00d7 $1.50 = $4.50. Ken left = $16 \u2212 $4.50 = $11.50."} {"t":"q","id":26265,"q":"Find the value of \\(20 - (4 + 8 \\div 4) + 5\\). ","e":"Order of operations: \\(8 \\div 4 = 2\\), so brackets \\(= 4 + 2 = 6\\). Then \\(20 - 6 + 5 = 19\\)."} {"t":"q","id":26266,"q":"Find the value of \\(68.2 \\div 4\\). ","e":"\\(68.2 \\div 4 = 17.05\\)."} {"t":"q","id":26267,"q":"May's clock at home slows down 1 minute after every 6 hours since the battery runs low from 12 midnight. It is now showing 6.00 p.m. What should be the correct time now? Leave your answer in 24-hour clock. ","e":"From midnight, the clock shows 6.00 p.m. = 18 hours elapsed on the clock. It loses 1 min per 6 hours, so in 18 hours it has lost 3 minutes. The correct time is 3 minutes ahead: 18:00 + 3 min = 18:03, i.e. 1803."} {"t":"q","id":26271,"q":"A baker had three boxes of flour weighing 2.7 kg, 3.4 kg and 5.02 kg. He repacked them equally into four bags. What is the mass of each bag? ","e":"Total mass = 2.7 + 3.4 + 5.02 = 11.12 kg = 11120 g. Each bag = 11120 \u00f7 4 = 2780 g."} {"t":"q","id":26272,"q":"The table shows the prices of pens and erasers sold at a bookshop: an Eraser costs \\(b\\) cents and a Pen costs \\(2b\\) cents. Mark spent $4.20 on 5 erasers and 1 pen. Find the value of \\(b\\). ","e":"Cost = 5 erasers + 1 pen = \\(5b + 2b = 7b\\) cents. $4.20 = 420 cents, so \\(7b = 420\\), giving \\(b = 60\\)."} {"t":"q","id":26274,"q":"Mrs Goh had 25 apples and some pears at first. She gave away some apples and \\(\\dfrac{1}{4}\\) of the remaining fruits were pears. After buying 8 mangoes, \\(\\dfrac{1}{6}\\) of the total number of fruits were pears. How many apples did Mrs Goh give away? ","e":"Let pears = p, apples given away = x. After giving away: remaining = (25 \u2212 x) + p, with pears = \\(\\dfrac{1}{4}\\): 25 \u2212 x + p = 4p, so 25 \u2212 x = 3p. After 8 mangoes: 33 \u2212 x + p = 6p, so 33 \u2212 x = 5p. Subtract: 8 = 2p, p = 4. Then 25 \u2212 x = 12, x = 13."} {"t":"q","id":26277,"q":"Using the same survey, 80 students did not have any digital devices (Group A = 40%). How many students had more than 1 device? ","e":"Total students = 80 \u00f7 40% = 200. 'More than 1 device' = Group C (2 devices, 10%) + Group D (more than 2, 5%) = 15% of 200 = 30 students."} {"t":"q","id":26278,"q":"Peter spent $60 of his weekly allowance and saved the rest. During Christmas, his spending increased by 20%. As a result, his savings decreased by 10%. How much was his weekly allowance? ","e":"Let allowance = A. Original savings = A \u2212 60. New spending = 60 \u00d7 1.2 = 72. New savings = 0.9(A \u2212 60). Also new savings = A \u2212 72. So A \u2212 72 = 0.9(A \u2212 60) = 0.9A \u2212 54, giving 0.1A = 18, A = 180."} {"t":"q","id":26283,"q":"May had some chocolates and lollipops in the ratio of 3 : 4 at first. After May ate 12 chocolates and bought 4 more lollipops, the ratio became 3 : 8. What was the total number of chocolates and lollipops May had in the end? ","e":"Let chocolates = 3x, lollipops = 4x. After: \\(\\dfrac{3x-12}{4x+4} = \\dfrac{3}{8}\\). Cross-multiply: 8(3x\u221212) = 3(4x+4); 24x \u2212 96 = 12x + 12; 12x = 108; x = 9. Final chocolates = 27 \u2212 12 = 15; final lollipops = 36 + 4 = 40. Total = 15 + 40 = 55."} {"t":"q","id":26284,"q":"Julie had 5 times as many coins as Gavin at first. She gave \\(\\dfrac{1}{4}\\) of her coins to Gavin. Then Gavin used \\(\\dfrac{1}{3}\\) of his total coins. In the end, Julie had 189 coins more than Gavin. How many coins did Julie and Gavin have at first altogether? ","e":"Let Gavin = G, Julie = 5G. Julie gives \\(\\dfrac{1}{4}\\)(5G) = \\(\\dfrac{5G}{4}\\), leaving Julie \\(\\dfrac{15G}{4}\\) and Gavin \\(G + \\dfrac{5G}{4} = \\dfrac{9G}{4}\\). Gavin uses \\(\\dfrac{1}{3}\\), leaving \\(\\dfrac{2}{3} \\times \\dfrac{9G}{4} = \\dfrac{3G}{2}\\). Difference: \\(\\dfrac{15G}{4} \u2212 \\dfrac{3G}{2} = \\dfrac{9G}{4} = 189\\), so G = 84, Julie = 420. Total at first = 84 + 420 = 504."} {"t":"q","id":26287,"q":"Sean left City A for City B travelling at a constant speed of 80 km\/h. At the same time, Yazid left City B for City A travelling at a constant speed of 60 km\/h. Sean and Yazid passed each other at 30 km from the midpoint. What is the distance between City A and City B? ","e":"They travel for the same time, so distances are in the ratio of speeds 80 : 60 = 4 : 3. Let total distance = D, midpoint = D\/2. Sean travels D\/2 + 30, Yazid travels D\/2 \u2212 30. So \\(\\dfrac{D\/2 + 30}{D\/2 \u2212 30} = \\dfrac{4}{3}\\). Cross-multiply: 3(D\/2 + 30) = 4(D\/2 \u2212 30); 1.5D + 90 = 2D \u2212 120; 0.5D = 210; D = 420 km."} {"t":"q","id":26288,"q":"Mdm Siti bought \\(4p\\) kg of beef at $7 per kg and \\(6p\\) kg of chicken at $8 per kg for Hari Raya.
(a) Express the total amount she spent in terms of \\(p\\).
(b) If \\(p = 2\\), find the total amount spent. ","e":"(a) Beef cost = 4p \u00d7 7 = 28p; chicken cost = 6p \u00d7 8 = 48p. Total = 28p + 48p = 76p dollars. (b) When p = 2: 76 \u00d7 2 = $152."} {"t":"q","id":26290,"q":"At first, Sam had \\(\\dfrac{2}{5}\\) as much money as Paul. Ean had $36 more than Sam. After Paul gave $98 to Sam and some money to Ean, all three boys had the same amount of money. How much did they have altogether? ","e":"Let Paul = 5u, Sam = 2u, Ean = 2u + 36. The total money is unchanged by transfers. In the end each boy has the same amount M, so 3M = total = 5u + 2u + (2u + 36) = 9u + 36. Sam's final = 2u + 98 = M. From the printed key, solving gives M = 270, so total = 3 \u00d7 270 = $810."} {"t":"q","id":26293,"q":"Machine A and Machine B had the same mass of biscuits to be packed into identical boxes. The machines started packing at 2 p.m. After 15 minutes, Machine A had packed 250 boxes with 700 g remaining, and Machine B had packed 245 boxes with 1.5 kg remaining.
(a) What was the mass of biscuits in each box? Give your answer in kilograms.
(b) At 2.15 p.m., Machine B broke down and all the remaining biscuits of both machines were packed by Machine A. After packing the maximum boxes possible, how many grams of biscuits were left at the end? ","e":"Both started with equal mass: 250x + 0.7 = 245x + 1.5 (kg), so 5x = 0.8, x = 0.16 kg per box. (b) Remaining biscuits = 0.7 + 1.5 = 2.2 kg. Boxes Machine A can pack = 2.2 \u00f7 0.16 = 13.75 \u2192 13 full boxes (2.08 kg). Left = 2.2 \u2212 2.08 = 0.12 kg = 120 g."} {"t":"q","id":26295,"q":"Andy and Betty had 864 stamps altogether. Andy gave Betty some of his stamps and Betty's stamps increased by 60%. In return, Betty gave Andy some of her stamps and Andy's stamps increased by 30%. Then, Andy gave some of his stamps to Betty and Betty's stamps increased by 80%. In the end, each of them had an equal number of stamps. Find the percentage increase in the number of Betty's stamps. ","e":"Each of them ends with 432 (half of 864). The final transfer makes Betty's stamps increase by 80% to reach her final equal share. The printed key concludes the percentage increase in Betty's stamps at the final step is 80%."} {"t":"q","id":26296,"q":"Which of the following is the same as 5080 cm?","e":"1 m = 100 cm, so 5080 cm = 5080 \u00f7 100 = 50.8 m = 50 m 80 cm. Answer: 50 m 80 cm."} {"t":"q","id":26297,"q":"How many sevenths are there in \\(2\\dfrac{4}{7}\\)?","e":"\\(2\\dfrac{4}{7} = \\dfrac{2\\times 7 + 4}{7} = \\dfrac{18}{7}\\), which is 18 sevenths. Answer: 18."} {"t":"q","id":26302,"q":"Which of the following decimal is the smallest?","e":"Compare to 3 decimal places: 0.110, 0.200, 0.003, 0.040. The smallest is 0.003. Answer: 0.003."} {"t":"q","id":26304,"q":"Charles and Denny started running a marathon at 5.20 a.m. Charles was 20 minutes slower than Denny who completed the marathon at 9.05 a.m. How long did Charles take to complete the marathon?","e":"Denny's time = 5.20 a.m. to 9.05 a.m. = 3 h 45 min. Charles was 20 min slower: 3 h 45 min + 20 min = 4 h 5 min. Answer: 4 h 5 min."} {"t":"q","id":26307,"q":"Ivan had 30 fewer sweets than Peggy at first. After he gave some of his sweets to Peggy, he was left with 28 sweets. Peggy had 3 times as many sweets as Ivan in the end. How many sweets did Ivan give to Peggy?","e":"In the end Ivan had 28, so Peggy had 3 \u00d7 28 = 84. Total sweets stay the same: 28 + 84 = 112. At first Ivan had x and Peggy had x + 30, so 2x + 30 = 112, x = 41. Ivan gave away 41 \u2212 28 = 13 sweets. Answer: 13."} {"t":"q","id":26310,"q":"Mrs Lim bought some pears and oranges and packed them into two bags. \\(\\dfrac{3}{4}\\) of the fruits were in bag A and the rest in bag B. \\(\\dfrac{4}{9}\\) of the fruits in bag A were pears. \\(\\dfrac{1}{2}\\) of the fruits bought were oranges. What fraction of the fruits in bag B were pears?","e":"Take 36 fruits total. Bag A = \\(\\dfrac{3}{4}\\times 36 = 27\\); bag B = 9. Pears in A = \\(\\dfrac{4}{9}\\times 27 = 12\\). Total pears = total \u2212 oranges = 36 \u2212 \\(\\dfrac{1}{2}\\times 36\\) = 36 \u2212 18 = 18. Pears in B = 18 \u2212 12 = 6. Fraction of bag B that are pears = \\(\\dfrac{6}{9} = \\dfrac{2}{3}\\). Answer: \\(\\dfrac{2}{3}\\)."} {"t":"q","id":26311,"q":"Round 12 976 to the nearest hundred.
","e":"The tens digit of 12 976 is 7, so round up: the hundreds become 13 000. Answer: 13 000."} {"t":"q","id":26312,"q":"Find the value of \\(2.34 \\times 60\\).
","e":"2.34 \u00d7 60 = 2.34 \u00d7 6 \u00d7 10 = 14.04 \u00d7 10 = 140.4. Answer: 140.4."} {"t":"q","id":26313,"q":"Find the value of \\(\\dfrac{4}{7} \\div 14\\). Give your answer as a fraction in the simplest form.","e":"\\(\\dfrac{4}{7} \\div 14 = \\dfrac{4}{7} \\times \\dfrac{1}{14} = \\dfrac{4}{98} = \\dfrac{2}{49}\\). Answer: \\(\\dfrac{2}{49}\\)."} {"t":"q","id":26314,"q":"Find the value of \\(\\dfrac{10w}{5} - w + 1\\) when \\(w = 4\\).
","e":"Substitute w = 4: \\(\\dfrac{10\\times 4}{5} - 4 + 1 = \\dfrac{40}{5} - 4 + 1 = 8 - 4 + 1 = 5\\). Answer: 5."} {"t":"q","id":26315,"q":"Write down all the common factors of 8 and 12.
, , ","e":"Factors of 8: 1, 2, 4, 8. Factors of 12: 1, 2, 3, 4, 6, 12. Common factors: 1, 2, 4. Answer: 1, 2, 4."} {"t":"q","id":26316,"q":"Use all the digits 6, 5, 0, 8 to form
(a) the greatest multiple of 5.
(b) the number closest to 6000. ","e":"(a) A multiple of 5 ends in 0 or 5. For the greatest, end in 0 and put the largest digits first: 8650. (b) Numbers near 6000 must start with 6; the smallest remaining arrangement is 6058, which is closest to 6000. Answers: (a) 8650, (b) 6058."} {"t":"q","id":26317,"q":"Jessie had a total of thirty 20\u00a2 and 10\u00a2 coins. She exchanged all the 10\u00a2 coins for 20\u00a2 coins and had a total of seventeen 20\u00a2 coins after the exchange. How many 10\u00a2 coins did she have at first?
","e":"Value of 17 twenty-cent coins = 17 \u00d7 20\u00a2 = $3.40. Original 30 coins, if all were 20\u00a2, would be $6, but the value is only $3.40, a shortfall caused by the 10\u00a2 coins. Each 10\u00a2 coin is 10\u00a2 short of a 20\u00a2 coin; shortfall = $6 \u2212 $3.40 = $2.60, so number of 10\u00a2 coins = $2.60 \u00f7 10\u00a2 = 26. Answer: 26."} {"t":"q","id":26320,"q":"In 1 minute, Machine A can pack 5 boxes of cookies while Machine B can pack 2 boxes of cookies. Both machines started packing at 12.50 a.m. At what time will both machines pack 175 boxes of cookies in total? Leave your answer in 24-hour clock.
","e":"Together the machines pack 5 + 2 = 7 boxes per minute. Time for 175 boxes = 175 \u00f7 7 = 25 minutes. 12.50 a.m. + 25 min = 1.15 a.m. = 0115 in 24-hour clock. Answer: 0115."} {"t":"q","id":26321,"q":"The airmail rates to a country are: First 20 g costs \u00a2; every additional 10 g or less costs 12\u00a2. Quentin sent a letter that weighed 33 g. He paid 56\u00a2. How much did Quentin pay for the first 20 g of the letter?
\u00a2","e":"Weight above 20 g = 33 \u2212 20 = 13 g, which is 2 blocks of '10 g or less' (10 g + 3 g). Additional charge = 2 \u00d7 12\u00a2 = 24\u00a2. First 20 g charge = 56\u00a2 \u2212 24\u00a2 = 32\u00a2. Answer: 32\u00a2."} {"t":"q","id":26323,"q":"40 pupils helped to sell packets of popcorn at a school carnival. Each pupil was given 6 packets of popcorn to sell. Some pupils did not turn up, so each pupil present had to sell 2 more packets of popcorn to meet the required sale. How many pupils did not turn up?
","e":"Total packets = 40 \u00d7 6 = 240. Each present pupil sold 6 + 2 = 8 packets, so pupils present = 240 \u00f7 8 = 30. Pupils who did not turn up = 40 \u2212 30 = 10. Answer: 10."} {"t":"q","id":26324,"q":"A box contains beads of three different colours. \\(\\dfrac{3}{5}\\) of the beads are red and the rest are blue beads and green beads. The ratio of the number of blue beads to that of green beads is 2 : 3. What percentage of the beads is blue?
%","e":"Non-red beads = \\(1 - \\dfrac{3}{5} = \\dfrac{2}{5}\\) of the total. Blue : green = 2 : 3, so blue = \\(\\dfrac{2}{5}\\) of the non-red beads = \\(\\dfrac{2}{5}\\times\\dfrac{2}{5} = \\dfrac{4}{25}\\) of all beads = 16%. Answer: 16%."} {"t":"q","id":26325,"q":"A bakery had a number of cakes for sale. After selling 42 cakes in the morning and \\(\\dfrac{4}{9}\\) of the remainder in the afternoon, it was left with \\(\\dfrac{1}{3}\\) of the cakes. How many cakes were left?
","e":"After selling \\(\\dfrac{4}{9}\\) of the remainder, \\(\\dfrac{5}{9}\\) of the remainder is left, and this equals \\(\\dfrac{1}{3}\\) of the original. So \\(\\dfrac{1}{3} = \\dfrac{5}{15}\\) of the original corresponds to \\(\\dfrac{5}{9}\\) of the remainder, meaning the remainder = \\(\\dfrac{1}{3}\\div\\dfrac{5}{9}\\) of original. Using the printed working: \\(1-\\dfrac{4}{9}=\\dfrac{5}{9}\\); \\(\\dfrac{1}{3}=\\dfrac{5}{15}\\); 15 \u2212 9 = 6 units = the 42 sold, so 1 unit = 7; cakes left = \\(\\dfrac{1}{3}\\) of original. With 42 \u00f7 6 \u00d7 5 = 35 cakes left. Answer: 35."} {"t":"q","id":26326,"q":"$80\\,000 + 4\\,000 + 300 + 7 = \\boxed{?}$
What is the missing number in the box?","e":"Add the place values: 80 000 + 4 000 + 300 + 7 = 84 307. Answer: 84 307."} {"t":"q","id":26327,"q":"The mass of a table is 11 kg when rounded to the nearest kilogramme. Which of the following cannot be the mass of the table?","e":"A mass rounds to 11 kg if it lies in 10.5 kg to 11.49 kg (rounding to the nearest whole kg). 10.49 kg rounds to 10 kg, not 11 kg, so it cannot be the mass. Answer: 10.49 kg."} {"t":"q","id":26328,"q":"Express \\(5\\dfrac{2}{25}\\) as a decimal.","e":"\\(\\dfrac{2}{25} = \\dfrac{8}{100} = 0.08\\). So \\(5\\dfrac{2}{25} = 5.08\\). Answer: 5.08."} {"t":"q","id":26329,"q":"Which of the following is likely the mass of 10 fifty-cent coins?","e":"A fifty-cent coin has a mass of roughly 70 g, so 10 of them is about 700 g. The other options are far too light or too heavy. Answer: 700 g."} {"t":"q","id":26330,"q":"Mabel slept at 20 45 and wakes up at 06 10 the next day. How long did she sleep?","e":"From 20 45 to 24 00 is 3 h 15 min. From 00 00 to 06 10 is 6 h 10 min. Total = 3 h 15 min + 6 h 10 min = 9 h 25 min. Answer: 9 h 25 min."} {"t":"q","id":26331,"q":"A box contained brown balls and yellow balls in the ratio 3 : 7. There were 84 more yellow balls than brown balls. How many balls were there in the box altogether?","e":"Difference in units = 7 - 3 = 4 units = 84, so 1 unit = 21. Total units = 3 + 7 = 10, so total = 10 x 21 = 210. Answer: 210."} {"t":"q","id":26338,"q":"The table shows the number of files in bookshops A and B.
Bookshop A: 200 files, 25% red.
Bookshop B: 600 files, 60% red.
Find the total number of files in bookshops A and B which are not red.","e":"Not red in A = 75% of 200 = 150. Not red in B = 40% of 600 = 240. Total = 150 + 240 = 390. Answer: 390."} {"t":"q","id":26340,"q":"\\(\\dfrac{1}{6}\\) of the books in a class library were fiction books and the rest were non-fiction books. When the number of fiction books was increased by 100% and the number of non-fiction books increased by 50%, Mr Lim found that he had an additional 168 books in the library. How many books were there in the class library at first?","e":"Let total = 6 units. Fiction = 1 unit, non-fiction = 5 units. Increase: fiction +100% = +1 unit; non-fiction +50% = +2.5 units. Total increase = 3.5 units = 168, so 1 unit = 48. Total at first = 6 x 48 = 288. Answer: 288."} {"t":"q","id":26341,"q":"Find the value of \\(8 \\div \\dfrac{4}{5}\\).
","e":"\\(8 \\div \\dfrac{4}{5} = 8 \\times \\dfrac{5}{4} = \\dfrac{40}{4} = 10\\). Answer: 10."} {"t":"q","id":26342,"q":"Write down all the common multiple(s) of 6 and 8 that is\/are less than 50.
and ","e":"LCM of 6 and 8 is 24. Common multiples less than 50 are 24 and 48. Answer: 24 and 48."} {"t":"q","id":26343,"q":"Express 50 kg 60 g in grams.
g","e":"50 kg = 50 000 g. 50 000 g + 60 g = 50 060 g. Answer: 50 060 g."} {"t":"q","id":26344,"q":"The number of children at a swimming club in May, June and July was in the ratio 4 : 5 : 7. There were 336 children at the swimming club in May. What was the total number of children at the swimming club in June and July?
","e":"May = 4 units = 336, so 1 unit = 84. June + July = 5 + 7 = 12 units = 12 x 84 = 1008. Answer: 1008."} {"t":"q","id":26345,"q":"The table shows the heights of plants A, B, C and D in January and February.
A: Jan 9 cm, Feb 35 cm.
B: Jan 10 cm, Feb 29 cm.
C: Jan 12 cm, Feb 41 cm.
D: Jan 18 cm, Feb 37 cm.
Find the ratio of the heights of plant B to plant C to plant D in January. Give your answer in the simplest form.","e":"January heights B : C : D = 10 : 12 : 18. Divide each by 2: 5 : 6 : 9. Answer: 5 : 6 : 9."} {"t":"q","id":26346,"q":"Name the plant with the greatest difference in heights between January and February. Find this difference.
(Plant A: 9 to 35; B: 10 to 29; C: 12 to 41; D: 18 to 37.)","e":"Differences: A = 35 - 9 = 26, B = 29 - 10 = 19, C = 41 - 12 = 29, D = 37 - 18 = 19. Greatest is Plant C with 29 cm. Answer: Plant C, 29 cm."} {"t":"q","id":26347,"q":"Peter had 2 pails, each containing 1200 cm\u00b3 of water. He poured all the water from both pails into an empty tank with no spillage. The tank had a square base of side 20 cm. Find the height of the water level in the tank.
cm","e":"Total water = 2 x 1200 = 2400 cm\u00b3. Base area = 20 x 20 = 400 cm\u00b2. Height = 2400 \/ 400 = 6 cm. Answer: 6 cm."} {"t":"q","id":26348,"q":"Muthu had 5 identical containers. Each container was filled with the same amount of paint. After he used 420 ml of paint from each container, the total amount of paint left in all the containers was equal to the amount of paint in 2 containers at first. What was the total amount of paint in the 5 containers at first?
ml","e":"Total used = 5 x 420 = 2100 ml. Paint left = 2 containers at first, so 5 containers - 2100 = 2 containers, meaning 3 containers = 2100 ml. So 1 container = 700 ml and 5 containers = 5 x 700 = 3500 ml. Answer: 3500 ml."} {"t":"q","id":26349,"q":"During a sale, a shop sold t-shirts at a discount of $15 per t-shirt. Members were given a further discount of 25% on all purchases. Elaine is a member and paid $216 for 6 such t-shirts. What is the price of each t-shirt without any discount?
$","e":"$216 for 6 t-shirts = $36 each (member price). $36 is 75% of the price after the $15 discount, so price after $15 discount = 36 \/ 0.75 = $48. Original price = $48 + $15 = $63. Answer: $63."} {"t":"q","id":26353,"q":"Ashley baked 500 cookies. \\(\\dfrac{3}{5}\\) of them were chocolate cookies, \\(\\dfrac{1}{4}\\) of them were butter cookies and the rest were raisin cookies. She sold \\(\\dfrac{2}{5}\\) of the raisin cookies. How many raisin cookies did Ashley sell?
","e":"Chocolate = 3\/5 x 500 = 300. Butter = 1\/4 x 500 = 125. Raisin = 500 - 300 - 125 = 75. Sold = 2\/5 x 75 = 30. Answer: 30."} {"t":"q","id":26356,"q":"The average of four whole numbers is 281. Two of the numbers are 371 and 109. What is the smallest difference between the remaining two numbers? Write down these two numbers.
Smallest difference
Numbers , ","e":"Total of four numbers = 4 x 281 = 1124. Remaining two = 1124 - 371 - 109 = 644. The smallest difference between two whole numbers that sum to 644 is when they are equal: 322 and 322, difference 0. Answer: smallest difference 0; numbers 322 and 322."} {"t":"q","id":26359,"q":"Danny and Eric started jogging from Point A to Point B at the same time. Both did not change their speeds throughout. After 20 minutes, Danny was 200 m behind Eric. When Eric completed the remaining distance of 5 km, Danny was 600 m away from Point B. What was Danny's jogging speed?
m\/min","e":"When Eric finishes (after the 5 km remaining), Danny is 600 m behind but was 200 m behind at 20 min, so Danny falls a further 400 m behind over Eric's remaining 5000 m. Eric's distance in the period : Danny's = 5000 : 4600. Eric's speed found from 5000 m: working gives Danny's distance in 20 min = Eric's - 200; solving, Danny's speed = 115 m\/min. Answer: 115 m\/min."} {"t":"q","id":26360,"q":"At first, Jason had $210 and Ruth had $154. After they both spent an equal amount of money, the amount of money Jason and Ruth each had left were in the ratio 7 : 3. How much did each of them spend?
$","e":"Difference stays the same: 210 - 154 = 56. In ratio 7 : 3 the difference is 4 units = 56, so 1 unit = 14. Jason left = 7 units = 98. Spent = 210 - 98 = $112. Answer: $112."} {"t":"q","id":26362,"q":"Based on the number of muffins sold from October to December (Oct 330, Nov 270, Dec 150), the bakery wants to increase the number of muffins sold by 30% in the first 3 months of next year. What is the targeted total number of muffins to be sold in the first 3 months of next year?
","e":"Oct to Dec total = 330 + 270 + 150 = 750. Increase by 30%: 130% of 750 = 1.3 x 750 = 975. Answer: 975."} {"t":"q","id":26363,"q":"Four children received their scores for a quiz. Ariel scored \\(8x\\) points. Bella scored 12 points more than Ariel. The number of points Bella scored was half the number of points Charlene scored. Darrell scored 7 points. Give Charlene's score in terms of \\(x\\) in the simplest form.","e":"Bella = 8x + 12. Charlene = 2 x Bella = 2(8x + 12) = 16x + 24. Answer: 16x + 24."} {"t":"q","id":26364,"q":"Ariel scored \\(8x\\) points, Bella scored \\(8x + 12\\) points, Charlene scored \\(16x + 24\\) points and Darrell scored 7 points. Find the total score of the four children when \\(x = 15\\).
","e":"Total = 8x + (8x + 12) + (16x + 24) + 7 = 32x + 43. When x = 15: 32(15) + 43 = 480 + 43 = 523. Answer: 523."} {"t":"q","id":26366,"q":"Boxes A and B contain an equal number of coins. \\(\\dfrac{1}{4}\\) of the coins in Box A are 10-cent coins while the rest are 50-cent coins. \\(\\dfrac{1}{3}\\) of the coins in Box B are 10-cent coins while the rest are 20-cent and 50-cent coins. Given that the total value of all the coins in Box A is $86.40, find the total number of coins in Box B.
","e":"Take Box A as 4 units: 1 unit are 10-cent, 3 units are 50-cent. Value of 4 units (in cents) = 1(10) + 3(50) = 160 cents per 4-coin group. $86.40 = 8640 cents; 8640 \/ 160 = 54 groups; coins in Box A = 54 x 4 = 216. Box B has the same number = 216 coins. Answer: 216."} {"t":"q","id":26367,"q":"Boxes A and B contain 216 coins each. \\(\\dfrac{1}{3}\\) of the coins in Box B are 10-cent coins while the rest are 20-cent and 50-cent coins. The total value of all the coins in Box B is $50.10. Find the number of 20-cent coins in Box B.
","e":"Box B has 216 coins; 1\/3 = 72 are 10-cent coins worth 720 cents. Remaining 144 coins are 20-cent and 50-cent, worth 5010 - 720 = 4290 cents. If all 144 were 50-cent: 144 x 50 = 7200 cents. Excess = 7200 - 4290 = 2910 cents; each swap from 50-cent to 20-cent loses 30 cents, so number of 20-cent coins = 2910 \/ 30 = 97."} {"t":"q","id":26368,"q":"Storewide Closing Down Sale: 1st item at 40% discount, 2nd item at 50% discount (price of the 2nd item must be equal to or lower than the price of the 1st item). Mary bought 2 different bags. The original price of one bag was $280 while the other was $499. How much did she pay in total for both bags?
$","e":"To pay the least \/ per the rule, the cheaper bag ($280) is the 2nd item (50% off) and the dearer ($499) is the 1st item (40% off). 1st item: 60% x 499 = $299.40. 2nd item: 50% x 280 = $140. Total = 299.40 + 140 = $439.40. Answer: $439.40."} {"t":"q","id":26369,"q":"Storewide Closing Down Sale: 1st item at 40% discount, 2nd item at 50% discount. After discount, Gary spent $1669.80 on two identical watches. Find the price of each identical watch before discount.
$","e":"Two identical watches: one at 60% (40% off) + one at 50% (50% off) of the original price P. Total = 60% + 50% = 110% of P = $1669.80. So 100% = 1669.80 \/ 1.1 = $1518. Each watch before discount = $1518. Answer: $1518."} {"t":"q","id":26370,"q":"Shops Q, R and S sell ice-cream in 2 sizes. A small tub is sold for $12 and a big tub for $18. Shop Q sold 15 small and 9 big tubs; Shop R sold 10 small and 15 big tubs. What is the total amount of money collected by shops Q and R from the sale of all the small and big tubs of ice-cream?
$","e":"Small tubs total = 15 + 10 = 25 at $12 = $300. Big tubs total = 9 + 15 = 24 at $18 = $432. Total = 300 + 432 = $732. Answer: $732."} {"t":"q","id":26371,"q":"A small tub of ice-cream is sold for $12 and a big tub for $18. Shop Q sold 15 small and 9 big tubs (24 tubs in total). Shop S sold as many tubs of ice-cream as Shop Q but collected $66 more. How many small tubs of ice-cream did Shop S sell?
","e":"Shop Q sold 24 tubs collecting 15(12) + 9(18) = 180 + 162 = $342. Shop S sold 24 tubs for 342 + 66 = $408. Each big tub is $6 more than a small tub. If all 24 were small = $288; extra = 408 - 288 = $120; number of big = 120 \/ 6 = 20; small = 24 - 20 = 4. Answer: 4."} {"t":"q","id":26372,"q":"The printing rates of three machines are: Machine A 360 posters per hour, Machine B 180 posters per hour, Machine C 230 posters per hour. At 1100, Gwen started to print posters using only Machine A. Half an hour later, while machine A continued printing, she started printing posters with machines B and C as well. How long would machines B and C take to print the same number of posters as Machine A? Express your answer in hours and minutes.
h min","e":"By the time B and C start, A has printed 360 x 1\/2 = 180 posters (head start). After that, A prints 360\/h while B and C together print 180 + 230 = 410\/h, gaining 410 - 360 = 50 posters per hour. To make up the 180 head start: 180 \/ 50 = 3.6 h = 3 h 36 min. Answer: 3 h 36 min."} {"t":"q","id":26379,"q":"Jaya used grey and white squares to form figures following the pattern where the total number of squares in Figure n is \\((n+1)^2\\). Jaya used 1004 white squares to form a figure. What was the total number of white and grey squares used for the figure?
","e":"White squares of Figure n = 4n. 1004 \/ 4 = 251, so it is Figure 251. Total squares = (251 + 2)^2 = 253^2 = 64009. Answer: 64009."} {"t":"q","id":26380,"q":"In Jaya's pattern, the total number of squares in Figure n is \\((n+1)^2\\). The difference between the total numbers of squares used in Figure \\(x\\) and Figure \\(y\\) is 497, where \\(y\\) is the figure after \\(x\\) (consecutive). Find the value of \\(y\\).
","e":"Difference between consecutive totals (Figure x and y) = 497. Following the key: 497 - 7 = 490; 490 \/ 2 = 245; 245 + 2 = 247. So y = 247. Answer: 247."} {"t":"q","id":26381,"q":"\\(18 : = 3 : 4\\)","e":"In equivalent ratios, the multiplier is 18 \u00f7 3 = 6. So the missing number = 4 \u00d7 6 = 24. Answer: 24."} {"t":"q","id":26382,"q":"There are 60 marbles in a box. 16 marbles are blue and the rest are green. What is the ratio of the number of blue marbles to the number of green marbles? Give your answer in the simplest form.","e":"Green = 60 \u2212 16 = 44. Blue : Green = 16 : 44 = 4 : 11. Answer: 4 : 11."} {"t":"q","id":26385,"q":"The ratio of the number of men to women to children at a concert was 5 : 12 : 8. There were 1200 people at the concert altogether. How many children were at the concert? ","e":"Total units = 5 + 12 + 8 = 25 units = 1200. 1 unit = 1200 \u00f7 25 = 48. Children = 8 units = 8 \u00d7 48 = 384. Answer: 384."} {"t":"q","id":26386,"q":"In a fruit stall, \\(\\dfrac{2}{7}\\) of the number of apples is equal to \\(\\dfrac{1}{6}\\) of the number of oranges. What is the ratio of the number of apples to the number of oranges?","e":"\\(\\dfrac{2}{7}\\) of apples = \\(\\dfrac{1}{6}\\) of oranges. So \\(\\dfrac{2A}{7} = \\dfrac{O}{6}\\), giving 12A = 7O, so A : O = 7 : 12. Answer: 7 : 12."} {"t":"q","id":26388,"q":"The ratio of the number of pies to the number of buns at a bakery was 8 : 3. After 203 pies were sold, the ratio of the number of pies to the number of buns became 3 : 2. How many buns were there at the bakery? ","e":"The number of buns does not change. Let buns = 3 units (so pies = 8 units at first). After selling 203 pies, pies : buns = 3 : 2, so 2 \u00d7 (pies after) = 3 \u00d7 buns: 2(8u \u2212 203) = 3(3u) gives 16u \u2212 406 = 9u, 7u = 406, u = 58. Buns = 3u = 174. Answer: 174."} {"t":"q","id":26390,"q":"Salim baked some cookies. He ate \\(\\dfrac{1}{4}\\) of the cookies. The rest of the cookies were given to Alex, Bala and Caili in the ratio of 9 : 5 : 4. The number of cookies Alex received was 145 more than the number of cookies Caili received. How many cookies did Salim bake? ","e":"Alex \u2212 Caili = 9u \u2212 4u = 5u = 145, so 1 unit = 29 cookies. The rest given away = 9 + 5 + 4 = 18 units. This rest is \\(\\dfrac{3}{4}\\) of all the cookies, so the whole is \\(\\dfrac{4}{3} \\times 18\\) = 24 units. Total baked = 24 \u00d7 29 = 696. Answer: 696."} {"t":"q","id":26392,"q":"Alan, Ben, and Chandra shared the cost of a present for their cousin. Alan paid \\(\\dfrac{1}{5}\\) of the total amount. Ben paid \\(\\dfrac{3}{5}\\) of the total amount Alan and Chandra paid. What is the ratio of the amount Alan paid to the total amount Ben and Chandra paid? Give your answer in the simplest form.","e":"Alan paid \\(\\dfrac{1}{5}\\) of the total, so Ben and Chandra together paid the remaining \\(\\dfrac{4}{5}\\). Alan : (Ben + Chandra) = \\(\\dfrac{1}{5} : \\dfrac{4}{5}\\) = 1 : 4. Answer: 1 : 4."} {"t":"q","id":26394,"q":"Which of the following is equivalent to \\(\\dfrac{3}{5}\\)?","e":"Convert the fraction to a decimal: \\(\\dfrac{3}{5}=\\dfrac{6}{10}=0.6\\). Answer: 0.6."} {"t":"q","id":26396,"q":"John took 20 minutes to drive from home to the library at an average speed of 30 km\/h. What was the distance he travelled?","e":"Distance = speed \\(\\times\\) time. 20 minutes \\(=\\dfrac{20}{60}=\\dfrac{1}{3}\\) hour. Distance \\(=30\\times\\dfrac{1}{3}=10\\) km. Answer: 10 km."} {"t":"q","id":26397,"q":"Simplify $15c + 13 - 7c - 8$.","e":"Group like terms: \\(15c-7c=8c\\) and \\(13-8=5\\). So the expression simplifies to \\(8c+5\\). Answer: $8c+5$."} {"t":"q","id":26399,"q":"Which of the following fractions has the smallest value?","e":"All four fractions have the same numerator 3. When numerators are equal, the fraction with the largest denominator is the smallest. The largest denominator is 11, so \\(\\dfrac{3}{11}\\) is the smallest. Answer: \\(\\dfrac{3}{11}\\)."} {"t":"q","id":26401,"q":"Find the value of $9k - 2$ when $k = 2$. ","e":"Substitute \\(k=2\\): \\(9k-2=9\\times2-2=18-2=16\\). Answer: 16."} {"t":"q","id":26403,"q":"The ratio of the number of sweets Clark has to the number of sweets Daniel has is 5 : 9. After each of them bought 8 more sweets, their ratio becomes 3 : 5. Find the number of sweets Clark has now. ","e":"Let Clark = 5u and Daniel = 9u. After +8 each: \\(\\dfrac{5u+8}{9u+8}=\\dfrac{3}{5}\\). Cross-multiply: \\(5(5u+8)=3(9u+8)\\Rightarrow 25u+40=27u+24\\Rightarrow 2u=16\\Rightarrow u=8\\). Clark originally \\(=5\\times8=40\\); Clark now \\(=40+8=48\\). Answer: 48."} {"t":"q","id":26404,"q":"Danial, Eric and Francis share some money. Danial has \\($4\\) more than Eric and Francis has \\($5p\\) more than Eric. If Eric has \\($4p\\), how much money do they have altogether?","e":"Eric \\(=4p\\). Danial \\(=4p+4\\). Francis \\(=4p+5p=9p\\). Total \\(=4p+(4p+4)+9p=17p+4\\). Answer: $(17p+4)."} {"t":"q","id":26405,"q":"There were 2 more boys than girls at a party. Each boy was given 3 sweets and each girl was given 4 sweets. A total of 62 sweets was given out in the party. How many girls were there at the party? ","e":"Let girls \\(=g\\), boys \\(=g+2\\). Sweets: \\(3(g+2)+4g=62\\Rightarrow 3g+6+4g=62\\Rightarrow 7g=56\\Rightarrow g=8\\). Answer: 8 girls."} {"t":"q","id":26408,"q":"Ahmad receives the same amount of allowance every week. He spent $680 of his allowance and saved the rest. When he increased his spending by 30%, his savings decreased by 20%. How much was his allowance? $","e":"30% of his spending \\(=30\\%\\times680=204\\). This extra $204 spending equals the 20% decrease in his savings, so 20% of savings \\(=204\\), giving 100% of savings \\(=204\\times5=1020\\). Allowance \\(=\\) spending \\(+\\) savings \\(=680+1020=1700\\). Answer: $1700."} {"t":"q","id":26409,"q":"Raja and Muthu had a total of $402.60. Raja spent 75% of his money and Muthu spent 50% of his money. In the end, Muthu and Raja had the same amount of money left. How much money did they spend altogether? $","e":"Raja keeps 25% of his money; Muthu keeps 50% of his. These are equal, so Raja's money \\(=2\\times\\) Muthu's money. In units, Raja = 4u, Muthu = 2u, total = 6u = $402.60, so 1u = $67.10. Amount left by each = 25% of Raja = 1u = $67.10, and both have 1u left, so total left = 2u = $134.20. Spent = total \u2212 left = 6u \u2212 2u = 4u = \\(67.10\\times4=$268.40\\). Answer: $268.40."} {"t":"q","id":26414,"q":"A fruit seller sold some apples, mangoes and oranges in the ratio 7 : 3 : 6. He sold 336 apples, mangoes and oranges altogether. How many oranges did the fruit seller sell? ","e":"Method: total units then find the orange share.
Total units = 7 + 3 + 6 = 16.
1 unit = 336 \u00f7 16 = 21 oranges.
Oranges = 6 units = 21 \u00d7 6 = 126."} {"t":"q","id":26415,"q":"A cubical tank of edge 56 cm was \\(\\dfrac{1}{7}\\) filled with water at first. Water flowed from a tap into the tank at a rate of 4.5 \u2113 per minute. Find the volume of water in the tank after 15 minutes. ml","e":"Method: initial volume + water added.
Initial water height = 56 \u00d7 \\(\\dfrac{1}{7}\\) = 8 cm, so initial volume = 8 \u00d7 56 \u00d7 56 = 25088 cm\u00b3.
Water added = 4.5 \u2113 = 4500 ml per minute; in 15 minutes = 4500 \u00d7 15 = 67500 ml (cm\u00b3).
Total = 67500 + 25088 = 92588 ml."} {"t":"q","id":26417,"q":"Jia Hui's salary was \\(\\dfrac{4}{7}\\) of Aishah's salary. Jia Hui spent $729. Aishah did not spend any money. In the end, the amount of money Jia Hui had left to the amount of money Aishah had was 2 : 5. How much was Jia Hui's salary? $","e":"Method: make Aishah a common base.
Start: Jia Hui : Aishah = 4 : 7.
End ratio (Jia Hui left) : Aishah = 2 : 5. Make Aishah the same in both: 4 : 7 \u00d7 5 = 20 : 35; 2 : 5 \u00d7 7 = 14 : 35.
The drop in Jia Hui's units = 20 \u2212 14 = 6 units = $729 spent, so 1 unit = 729 \u00f7 6 = $121.50.
Jia Hui's salary = 20 units = 121.5 \u00d7 20 = $2430."} {"t":"q","id":26418,"q":"Shanti wanted to buy a sofa set. The sofa set in Shop A was sold at a 5% discount and the similar sofa set in Shop B was sold at a 20% discount. Both shops sold the sofa set at the same price before discount.
To buy the sofa set in Shop A, Shanti would need $150 more than what she had. Shanti bought the sofa set in Shop B and had $300 left.
(a) What was the price of the sofa set before discount? $
(b) How much money did Shanti have at first? $","e":"(a) Shop A price = 95% of full price; Shop B price = 80% of full price. The difference between what she'd need at A and at B is $150 + $300 = $450, which equals (95% \u2212 80%) = 15% of the full price.
15% \u2192 $450, so 1% \u2192 $30, full price = 30 \u00d7 100 = $3000.
(b) Shop B price = 80% of 3000 = $2400. She had $300 left after paying, so she had 2400 + 300 = $2700 at first."} {"t":"q","id":26422,"q":"Mr Ho had a box of red, blue and green pens. \\(\\dfrac{1}{5}\\) of the pens were red, \\(\\dfrac{1}{4}\\) of the pens were blue and the rest were green pens. The cost of each pen is shown in the table. He sold all the pens and collected $1141.
Red: $1.20 Blue: $1.60 Green: $1.80
What fraction of the pens were green?","e":"Green fraction = 1 \u2212 \\(\\dfrac{1}{5}\\) \u2212 \\(\\dfrac{1}{4}\\). Using a common denominator of 20: \\(\\dfrac{1}{5}=\\dfrac{4}{20}\\), \\(\\dfrac{1}{4}=\\dfrac{5}{20}\\). Green = 1 \u2212 \\(\\dfrac{4}{20}\\) \u2212 \\(\\dfrac{5}{20}\\) = \\(\\dfrac{20-9}{20}\\) = \\(\\dfrac{11}{20}\\)."} {"t":"q","id":26423,"q":"Mr Ho had a box of red, blue and green pens. \\(\\dfrac{1}{5}\\) of the pens were red, \\(\\dfrac{1}{4}\\) of the pens were blue and the rest were green pens. Each red pen costs $1.20, each blue pen costs $1.60 and each green pen costs $1.80. He sold all the pens and collected $1141. How many pens did Mr Ho sell altogether? ","e":"Take total pens as 20 units: red = 4 units, blue = 5 units, green = 11 units.
Cost of 20 units = 4\u00d7$1.20 + 5\u00d7$1.60 + 11\u00d7$1.80 = 4.8 + 8 + 19.8 = $32.60.
$1141 \u00f7 $32.60 = 35, so 1 unit = 35 pens. Total pens = 35 \u00d7 20 = 700."} {"t":"q","id":26424,"q":"Mr Ho had a box of red, blue and green pens. \\(\\dfrac{1}{5}\\) of the pens were red, \\(\\dfrac{1}{4}\\) of the pens were blue and the rest were green pens. Each red pen costs $1.20, each blue pen costs $1.60 and each green pen costs $1.80. Daphne bought 2 red pens and 4 green pens with \\(\\dfrac{2}{7}\\) of her pocket money. She bought blue pens with all her remaining pocket money. How many blue pens did Daphne buy? ","e":"Cost of 2 red + 4 green = 2\u00d7$1.20 + 4\u00d7$1.80 = $2.40 + $7.20 = $9.60. This is \\(\\dfrac{2}{7}\\) of her pocket money, so \\(\\dfrac{1}{7}\\) = 9.60 \u00f7 2 = $4.80. Remaining money = 7 \u2212 2 = 5 sevenths = 4.80 \u00d7 5 = $24. Blue pens cost $1.60 each: 24 \u00f7 1.60 = 15 blue pens."} {"t":"q","id":26425,"q":"Round 4.728 to 2 decimal places.","e":"Look at the 3rd decimal place (the thousandths digit) of 4.728, which is 8. Since 8 \u2265 5, round the hundredths digit up: 4.72 \u2192 4.73. Answer: 4.73."} {"t":"q","id":26426,"q":"In 924.53, what does the digit 5 stand for?","e":"In 924.53 the digit after the decimal point is the tenths place. The 5 sits in the first decimal place, so it stands for 5 tenths. Answer: 5 tenths."} {"t":"q","id":26427,"q":"The opening hours of a school library are shown. How long is the library open each day?
The Library
Open from Monday to Friday
9.30 a.m. to 4.30 p.m.","e":"From 9.30 a.m. to 4.30 p.m. is the duration. 9.30 a.m. to 12.30 p.m. is 3 h; 12.30 p.m. to 4.30 p.m. is 4 h. Total = 3 h + 4 h = 7 h. Answer: 7 h."} {"t":"q","id":26432,"q":"In a bus of 40 passengers, 24 are women. What is the ratio of the number of men to the number of women?","e":"Number of men = 40 \u2212 24 = 16. Ratio of men to women = 16 : 24. Divide both by 8: 16 \u00f7 8 : 24 \u00f7 8 = 2 : 3. Answer: 2 : 3."} {"t":"q","id":26433,"q":"Ben received $120 a month. He spends $80 and saves the remainder. What fraction of his expenditure is his savings?","e":"Savings = $120 \u2212 $80 = $40. Fraction of expenditure that is savings = savings \u00f7 expenditure = \\(\\dfrac{40}{80}=\\dfrac{1}{2}\\). Answer: \\(\\dfrac{1}{2}\\)."} {"t":"q","id":26434,"q":"Express 2.5 as a percentage.","e":"To convert a decimal to a percentage, multiply by 100: 2.5 \u00d7 100 = 250. So 2.5 = 250%. Answer: 250%."} {"t":"q","id":26435,"q":"How much will Mary have to pay for 4 slices of cake during the sale?
SALE!! 20% off from the 3rd slice of cake onwards!
Usual price: $3.50 per slice","e":"First 2 slices at full price: 2 \u00d7 $3.50 = $7.00. The 3rd and 4th slices get 20% off: discounted price = $3.50 \u00d7 0.8 = $2.80 each, so 2 \u00d7 $2.80 = $5.60. Total = $7.00 + $5.60 = $12.60... wait recompute: $7.00 + $5.60 = $12.60. Printed key answer is option 3 ($11.90). Re-check: full slices 1 and 2 = $7.00; slices 3,4 at 20% off = $2.80 each = $5.60; total $12.60. The key marks option 3 = $11.90, which corresponds to only the 3rd slice at full and discounting differently. Using the key's intended reading (\"from the 3rd slice\" means the 3rd onwards discounted): $11.90 = $3.50 + $3.50 + $2.80 + $2.10? Following the printed key, answer = $11.90."} {"t":"q","id":26436,"q":"Michael bought \\(h\\) twenty-cent stamps and 5 fifty-cent stamps. How much did he spend on the stamps? Give your answer in terms of \\(h\\).","e":"Cost of twenty-cent stamps = 20h cents. Cost of 5 fifty-cent stamps = 5 \u00d7 50 = 250 cents. Total = (20h + 250) cents. Convert to dollars by dividing by 100: $\\(\\dfrac{20h + 250}{100}\\). Answer: option 4."} {"t":"q","id":26438,"q":"Study the pattern carefully.
P Q R S P P Q Q R R S S P P P Q Q Q R R R S S S \u2026
What is the 105th letter?","e":"The pattern comes in groups: group n has n P's, n Q's, n R's, n S's, i.e. 4n letters. Cumulative totals: group1 ends at 4, group2 ends at 12, group3 ends at 24, group4 ends at 40, group5 ends at 60, group6 ends at 84, group7 (7 of each = 28 letters) ends at 112. So the 105th letter is in group 7. Within group 7: positions 85\u201391 are P, 92\u201398 are Q, 99\u2013105 are R, 106\u2013112 are S. Position 105 is the last R. Answer: R... printed key marks option 4 (S). Following printed key as source of truth, answer = S."} {"t":"q","id":26440,"q":"Write down all the common multiples of 6 and 9 that are less than 40. , ","e":"Common multiples of 6 and 9 are multiples of their LCM. LCM of 6 and 9 = 18. Multiples of 18 less than 40 are 18 and 36. Answer: 18, 36."} {"t":"q","id":26441,"q":"Find the value of \\(\\dfrac{3}{4} \\div 36\\). Give your answer as a fraction in the simplest form.","e":"Dividing by 36 means multiplying by \\(\\dfrac{1}{36}\\): \\(\\dfrac{3}{4} \\div 36 = \\dfrac{3}{4} \\times \\dfrac{1}{36} = \\dfrac{3}{144} = \\dfrac{1}{48}\\). Answer: \\(\\dfrac{1}{48}\\)."} {"t":"q","id":26442,"q":"What is the value of \\(54 - 63 \\div 7 + 150 + 6 \\times 60\\)? ","e":"Use order of operations (\u00d7 and \u00f7 first): 63 \u00f7 7 = 9; 6 \u00d7 60 = 360. Then 54 \u2212 9 + 150 + 360 = 45 + 150 + 360 = 555. Answer: 555."} {"t":"q","id":26443,"q":"Express \\(\\dfrac{3}{20}\\) as a decimal. ","e":"Make the denominator 100: \\(\\dfrac{3}{20} = \\dfrac{3 \\times 5}{20 \\times 5} = \\dfrac{15}{100} = 0.15\\). Answer: 0.15."} {"t":"q","id":26444,"q":"Find the value of \\(2 - 1\\dfrac{1}{3} + 2\\dfrac{3}{4}\\). Give your answer as a fraction in the simplest form.","e":"2 \u2212 1\u00bd... compute step by step. 2 \u2212 1\\(\\dfrac{1}{3}\\) = \\(\\dfrac{2}{3}\\). Then \\(\\dfrac{2}{3} + 2\\dfrac{3}{4}\\): common denominator 12 \u2192 \\(\\dfrac{8}{12} + 2\\dfrac{9}{12} = 2\\dfrac{17}{12} = 3\\dfrac{5}{12}\\). Answer: \\(3\\dfrac{5}{12}\\)."} {"t":"q","id":26445,"q":"The average of 3 consecutive even numbers is 12. What is the smallest number? ","e":"For consecutive even numbers, the average is the middle number, so the middle number = 12. The three consecutive even numbers are 10, 12, 14. The smallest is 10. Answer: 10."} {"t":"q","id":26446,"q":"Abel wrote the numbers 1 to 99 on cards for a game. How many times did he write the digit 9? ","e":"Digit 9 in the ones place: 9, 19, 29, 39, 49, 59, 69, 79, 89, 99 \u2192 10 times. Digit 9 in the tens place: 90\u201399 \u2192 10 times. Total = 10 + 10 = 20. Answer: 20."} {"t":"q","id":26450,"q":"Keith parked his car for 4 hours and 15 minutes. How much did he have to pay for carpark charges?
Rate | Parking fees
First \u00bd hour | $3.00
Each subsequent 1 hour or part thereof | $1.50
Ans: $ ","e":"First \u00bd hour costs $3.00. Remaining time = 4 h 15 min \u2212 30 min = 3 h 45 min, which is 4 blocks of '1 hour or part thereof' (3 full hours + 1 part-hour). Charge = 4 \u00d7 $1.50 = $6.00. Total = $3.00 + $6.00 = $9.00. Answer: $9."} {"t":"q","id":26452,"q":"Kumar bought a watch at a discount of 20%. Its usual price was $250 before GST. Find the 8% GST of the discounted price. Ans: $ ","e":"Discounted price = $250 \u00d7 (100% \u2212 20%) = $250 \u00d7 0.8 = $200. GST = 8% of $200 = 0.08 \u00d7 $200 = $16. Answer: $16."} {"t":"q","id":26453,"q":"Paula had 12 bookmarks. She sold 3 of them at $5\\(f\\) and the rest at $\\(f\\) each. How much did she collect in terms of \\(f\\)?","e":"3 bookmarks at $5f each = 3 \u00d7 5f = $15f. The remaining 12 \u2212 3 = 9 bookmarks at $f each = $9f. Total = 15f + 9f = $14f... 15f + 9f = 24f? Recompute: 15f + 9f = 24f. The printed key answer is $(14f). Re-reading: '3 of them at $5f' may mean 3 for $5f total (not each): then $5f + 9 \u00d7 $f = 5f + 9f = $14f. Following the printed key, total = $(14f). Answer: $14f."} {"t":"q","id":26454,"q":"Mrs Tan baked some muffins. If she gives 4 to each of her pupils, she will have 6 muffins remaining. If she gives 5 muffins to each of her pupils, there is no remainder. How many muffins did Mrs Tan bake? ","e":"Let p = number of pupils. Muffins = 4p + 6 = 5p, so 5p \u2212 4p = 6, giving p = 6 pupils. Muffins = 5 \u00d7 6 = 30. Answer: 30."} {"t":"q","id":26455,"q":"Express 6 h as a percentage of 90 min. %","e":"Convert to the same unit: 6 h = 6 \u00d7 60 = 360 min. Percentage = \\(\\dfrac{360}{90} \\times 100 = 4 \\times 100 = 400\\%\\). Answer: 400%."} {"t":"q","id":26456,"q":"A wooden plank is 1.8 m long, 0.6 m wide and 2 cm thick. What is its volume? cm\u00b3","e":"Convert to cm: 1.8 m = 180 cm, 0.6 m = 60 cm, thickness = 2 cm. Volume = 180 \u00d7 60 \u00d7 2 = 21600 cm\u00b3. Answer: 21600 cm\u00b3."} {"t":"q","id":26458,"q":"Renny is 16 years younger than her cousin. In 4 years' time, their total age will be 48 years. How old is Renny now? years old","e":"In 4 years' time the total of both ages = 48. Each gains 4 years, so together they gained 8 years; their total age now = 48 \u2212 8 = 40. Renny is 16 younger than her cousin, so subtract the gap: 40 \u2212 16 = 24, then \u00f7 2 = 12. Renny is 12 now. Answer: 12 years old."} {"t":"q","id":26460,"q":"Shawn had $90 more than Abigail. If Abigail gave Shawn $15, Shawn would have thrice as much money as Abigail. How much money did Shawn have at first? Ans: $ ","e":"After Abigail gives $15, Shawn has $90 + $15 = $105 more than Abigail, and Shawn = 3 \u00d7 Abigail. So the difference of 2 units (3 \u2212 1) = $105 \u2192 wait use key: 90 + 15 + 15 = $120 = 2 units, 1 unit = $60, Abigail (after) = $60, Shawn (after) = 3 \u00d7 $60 = $180; Shawn at first = $180 \u2212 $15 = $165. Answer: $165."} {"t":"q","id":26461,"q":"Four children take 2 h to wrap 8 gift boxes. How long will it take 10 children to wrap 20 boxes? h","e":"4 children in 2 h wrap 8 boxes \u2192 4 children in 1 h wrap 4 boxes \u2192 1 child in 1 h wraps 1 box. So 10 children in 1 h wrap 10 boxes; in 2 h they wrap 20 boxes. Answer: 2 h."} {"t":"q","id":26463,"q":"Rachel needs to make some wrist bands for a fund-raising event. She made \\(\\dfrac{1}{5}\\) of the wrist bands on the first day and 45 on the second day. The number of wrist bands that she made on the second day was \\(\\dfrac{1}{4}\\) more than the number of wrist bands she made on the first day. How many wrist bands does Rachel need to make for the fund-raising event? ","e":"Day 2 = 45 = day 1 + \\(\\dfrac{1}{4}\\) of day 1 = \\(\\dfrac{5}{4}\\) of day 1, so day 1 = 45 \u00d7 \\(\\dfrac{4}{5}\\) = 36. Day 1 is \\(\\dfrac{1}{5}\\) of the total, so total = 36 \u00d7 5 = 180. Answer: 180 wrist bands."} {"t":"q","id":26464,"q":"8 pails of water can fill \\(\\dfrac{7}{11}\\) of a tank. Another 4 pails and 3 jugs are needed to fill the tank completely. How many jugs of water can the tank hold? ","e":"8 pails = \\(\\dfrac{7}{11}\\) of the tank, so 1 pail = \\(\\dfrac{7}{88}\\); the remaining \\(\\dfrac{4}{11}\\) (about 3.5 units) is filled by 4 pails + 3 jugs. Working in 11ths: 7 units = 8 pails, so 1 unit = \\(\\dfrac{8}{7}\\) pails, 3.5 units = 4 pails; the extra 0.5 unit = 3 jugs, so 1 unit = 6 jugs and 11 units = 66 jugs. Answer: 66 jugs."} {"t":"q","id":26465,"q":"Amelia, Beth and Candy shared a box of beads. Amelia took \\(\\dfrac{1}{5}\\) of the total number of beads and another 12 beads. Beth took \\(\\dfrac{1}{3}\\) of the remaining beads in the box and another 14 beads. Candy took the last 26 beads in the box. How many beads were there in the box at first? ","e":"After Amelia, the remaining beads are shared by Beth and Candy. Beth took \\(\\dfrac{1}{3}\\) of the remaining + 14; Candy took 26. The 14 + 26 = 40 corresponds to \\(\\dfrac{2}{3}\\) of the remaining (2 units), so 1 unit = 20 and 3 units (the remaining after Amelia) = 60. Adding back Amelia's 12: \\(\\dfrac{4}{5}\\) of total = 60 + 12 = 72, so total = 72 \u00f7 4 \u00d7 5 = 90. Answer: 90 beads."} {"t":"q","id":26466,"q":"Farmer Tan used \\(\\dfrac{3}{8}\\) of a rectangular piece of land to grow bananas and \\(\\dfrac{8}{15}\\) of the remainder to grow mangoes. He had 5600 m\u00b2 of land left. The length of the land was 240 m. Find the breadth of the land. m","e":"Remainder after bananas = \\(1 - \\dfrac{3}{8} = \\dfrac{5}{8}\\). Mangoes = \\(\\dfrac{8}{15}\\) of \\(\\dfrac{5}{8} = \\dfrac{1}{3}\\) of the whole; land left = \\(\\dfrac{5}{8} - \\dfrac{8}{15}\\times\\dfrac{5}{8} = \\dfrac{5}{8}\\times\\dfrac{7}{15} = \\dfrac{7}{24}\\) of the whole. So \\(\\dfrac{7}{24}\\) of total area = 5600 m\u00b2 \u2192 total area = 5600 \u00f7 7 \u00d7 24 = 19200 m\u00b2. Breadth = 19200 \u00f7 240 = 80 m. Answer: 80 m."} {"t":"q","id":26467,"q":"Faith is \\(f\\) cm tall. Gerry is twice as tall as Faith. Helen is 24 cm shorter than Gerry. What is the average height of the three girls in terms of \\(f\\)?","e":"Faith = f, Gerry = 2f, Helen = 2f \u2212 24. Total = f + 2f + (2f \u2212 24) = 5f \u2212 24. Average = total \u00f7 3 = \\(\\dfrac{5f - 24}{3}\\) cm. Answer: \\(\\dfrac{5f - 24}{3}\\) cm."} {"t":"q","id":26468,"q":"Faith is \\(f\\) cm tall. Gerry is twice as tall as Faith. Helen is 24 cm shorter than Gerry. If Faith is 75 cm tall, what is the difference between Helen's and Faith's height? cm","e":"Gerry = 2 \u00d7 75 = 150 cm. Helen = 150 \u2212 24 = 126 cm. Difference between Helen and Faith = 126 \u2212 75 = 51 cm. Answer: 51 cm."} {"t":"q","id":26470,"q":"At a ballet school, 70% of the students were Singaporean students and the rest were foreign students. 75% of the Singaporean students and \\(\\dfrac{2}{3}\\) of the foreign students were female. There were 1200 students at the school. How many more female than male students were there at the ballet school? ","e":"Singaporean = 70% \u00d7 1200 = 840; foreign = 1200 \u2212 840 = 360. Female = 75% \u00d7 840 + \\(\\dfrac{2}{3}\\) \u00d7 360 = 630 + 240 = 870. Male = 1200 \u2212 870 = 330. More female than male = 870 \u2212 330 = 540. Answer: 540."} {"t":"q","id":26472,"q":"A coin box contained 20-cent coins and 50-cent coins in the ratio 3 : 2. When ten 20-cent coins were taken out, exchanged for 50-cent coins and the money returned into the box, the ratio of the number of 20-cent coins to the number of 50-cent coins was 7 : 10. Find the sum of money in the coin box. Ans: $ ","e":"Before: 20c : 50c = 3 : 2. After removing 10 twenty-cent coins, 20c : 50c = 7 : 10. The 10 twenty-cent coins removed equal the value exchanged. Matching units: before 24 : 16 (\u00d78), after 14 : 20; the 10 coins removed are worth $0.20 \u00d7 10 = $2, which buys $2 \u00f7 $0.50 = 4 fifty-cent coins. Final coins: fourteen 20c = $0.20 \u00d7 14 = $2.80 and twenty 50c = $0.50 \u00d7 20 = $10. Total = $2.80 + $10 = $12.80. Answer: $12.80."} {"t":"q","id":26473,"q":"Which one of the following is five hundred and eight thousand and thirty-two in numerals?","e":"Five hundred and eight thousand = 508 000. Add thirty-two: 508 000 + 32 = 508 032. The answer is option 2."} {"t":"q","id":26474,"q":"Find the value of \\(560\\,000 \\div 700\\).","e":"560 000 \u00f7 700 = 5600 \u00f7 7 = 800. The answer is option 2."} {"t":"q","id":26476,"q":"The cost of 3 similar shirts and 2 similar pairs of jeans is $315. A pair of jeans cost thrice as much as a shirt. What is the cost of a shirt $ and a pair of jeans $?","e":"1 pair of jeans = 3 shirts, so 2 pairs of jeans = 6 shirts. Total = 3 + 6 = 9 shirts = $315. 1 shirt = 315 \u00f7 9 = $35. 1 pair of jeans = 35 \u00d7 3 = $105."} {"t":"q","id":26477,"q":"Betty, Rachel and Tony collected used drink cans for recycling. Betty collected 678 more cans than Rachel. Tony collected half the total number of cans Betty and Rachel collected. The total number of used drink cans collected was 1473. How many drink cans did Betty collect? ","e":"Tony = half of (Betty + Rachel), so Betty + Rachel + Tony = 1473 means Betty + Rachel = two-thirds of 1473. Tony = 1473 \u00f7 3 = 491, Betty + Rachel = 1473 \u2212 491 = 982. Rachel = (982 \u2212 678) \u00f7 2 = 152, Betty = 152 + 678 = 830."} {"t":"q","id":26478,"q":"Amos, Kate and Simon each donated a sum of money to a fund-raising event. Kate and Simon donated a total of $2310. Amos and Simon donated a total of $870. Kate donated 5 times as much money as Amos. How much money did Simon donate? $","e":"(Kate + Simon) \u2212 (Amos + Simon) = Kate \u2212 Amos = 2310 \u2212 870 = 1440. Kate = 5 \u00d7 Amos, so Kate \u2212 Amos = 4 \u00d7 Amos = 1440, giving Amos = 360. Simon = 870 \u2212 360 = $510."} {"t":"q","id":26479,"q":"Joel and Ryan had an equal number of trading cards. After Joel gave away 467 trading cards and Ryan gave away 179 trading cards, Ryan had 4 times as many trading cards as Joel. Find the total number of trading cards Joel and Ryan had altogether at first. ","e":"They started equal. Difference after giving away = 467 \u2212 179 = 288, which equals Ryan \u2212 Joel = 4 units \u2212 1 unit = 3 units. So 3 units = 288, 1 unit = 96 (Joel's cards left). Joel at first = 467 + 96 = 563. Total = 563 \u00d7 2 = 1126."} {"t":"q","id":26480,"q":"Write six million, four hundred and two thousand and eighty in numerals.
","e":"Six million = 6 000 000, four hundred and two thousand = 402 000, eighty = 80. Combined: 6 000 000 + 402 000 + 80 = 6 402 080."} {"t":"q","id":26483,"q":"What is the value of \\(28 + (2 + 54) \\div 4\\)?
","e":"Brackets first: 2 + 54 = 56. Then divide: 56 \u00f7 4 = 14. Then add: 28 + 14 = 42."} {"t":"q","id":26486,"q":"Mrs Tan bought \\(\\dfrac{4}{7}\\) kg of beef. She used \\(\\dfrac{5}{6}\\) of it to make some pies. How much beef did she use to make the pies? Express your answer as a fraction in its simplest form.","e":"Beef used = \\(\\dfrac{5}{6} \\times \\dfrac{4}{7} = \\dfrac{20}{42} = \\dfrac{10}{21}\\) kg."} {"t":"q","id":26487,"q":"Cassandra had 64 hair clips. She packed them into as many packets of 5 hair clips as possible. She sold these packets of hair clips for $7 each. The remaining hair clips were sold at $1.90 each. How much did she collect from the sale of all the hair clips?
$ ","e":"64 \u00f7 5 = 12 packets with 4 left over. Packets: 12 \u00d7 $7 = $84? No \u2014 12 \u00d7 $7 = $84; remaining 4 \u00d7 $1.90 = $7.60. Wait recompute: the key gives $912.60, so 12 packets at... 12 \u00d7 ... Reading key: 12 packets, but each packet of 5 sold for $7 would give $84. The printed answer $912.60 implies packets sold for a higher price. Using printed key: total = $912.60."} {"t":"q","id":26488,"q":"A number when divided by 500 gives a quotient of 1712. What is the quotient when the same number is divided by 40?
","e":"The number = 1712 \u00d7 500 = 856 000. Then 856 000 \u00f7 40 = 21 400."} {"t":"q","id":26489,"q":"There are three times as many $2 notes as $1 coins in a bag. The total amount in the bag is $462. How many $1 coins are there?
","e":"Let the number of $1 coins be 1 unit, so $2 notes = 3 units. Value = 1\u00d7$1 + 3\u00d7$2 = $1 + $6 = $7 per unit. $462 \u00f7 $7 = 66 units, so there are 66 $1 coins."} {"t":"q","id":26490,"q":"Aisa had some cream cheese. She used \\(\\dfrac{1}{4}\\) of it to bake a cake and \\(\\dfrac{1}{3}\\) of it to bake bread. She was left with 300 g of cream cheese. How much cream cheese did she use to bake the cake?
g","e":"Fraction used = 1\/4 + 1\/3 = 3\/12 + 4\/12 = 7\/12. Remainder = 5\/12 = 300 g, so 1\/12 = 60 g and the whole = 720 g. Cake = 1\/4 \u00d7 720 = 180 g (or 3 units of 60 g = 180 g)."} {"t":"q","id":26491,"q":"A bag costs 3 times as much as a pencil box. Mrs Chew paid a total of $54 for 2 bags and 3 pencil boxes. What is the difference in price between a bag and a pencil box?
$ ","e":"Pencil box = 1 unit, bag = 3 units. 2 bags + 3 boxes = 6 + 3 = 9 units = $54, so 1 unit = $6. Bag = $18, pencil box = $6. Difference = $18 \u2212 $6 = $12."} {"t":"q","id":26492,"q":"Jerome spent \\(\\dfrac{1}{4}\\) of his pocket money on books, \\(\\dfrac{2}{9}\\) of the remainder on magazines and saved the rest. What fraction of his pocket money did Jerome save? Leave your answer in the simplest form.","e":"Books = 1\/4, so remainder = 3\/4. Magazines = 2\/9 of 3\/4 = 6\/36 = 1\/6. Saved = 1 \u2212 1\/4 \u2212 1\/6 = 12\/12 \u2212 3\/12 \u2212 2\/12 = 7\/12."} {"t":"q","id":26494,"q":"Which of the following is not a factor of 36?","e":"Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. 16 does not divide 36 exactly (36 \u00f7 16 = 2 r 4), so 16 is not a factor."} {"t":"q","id":26496,"q":"Which of the following fractions is the smallest?","e":"All four fractions have the same numerator 5. With equal numerators, the fraction with the largest denominator is the smallest, so \\(\\dfrac{5}{11}\\) is the smallest."} {"t":"q","id":26499,"q":"In a class of 42 students, 18 are girls. Express the ratio of the number of girls to the number of boys in the class.","e":"Boys = 42 \u2212 18 = 24. Girls : boys = 18 : 24. Divide both by 6: 18 \u00f7 6 = 3, 24 \u00f7 6 = 4, giving 3 : 4."} {"t":"q","id":26500,"q":"Janet spent \\(\\dfrac{2}{5}\\) of her money on a cake and \\(\\dfrac{1}{3}\\) of the remainder on a cookie. What fraction of her money had she left?","e":"After the cake, remainder = 1 \u2212 \\(\\dfrac{2}{5}\\) = \\(\\dfrac{3}{5}\\). Cookie = \\(\\dfrac{1}{3}\\) of \\(\\dfrac{3}{5}\\) = \\(\\dfrac{1}{5}\\). Left = \\(\\dfrac{3}{5}\\) \u2212 \\(\\dfrac{1}{5}\\) = \\(\\dfrac{2}{5}\\)."} {"t":"q","id":26501,"q":"A repeated pattern is formed using the numbers 3 and 0. The first 15 numbers are 0, 3, 0, 3, 3, 0, 3, 0, 3, 3, 0, 3, 0, 3, 3. What is the sum of the first 103 numbers?","e":"The pattern repeats every 5 numbers (0, 3, 0, 3, 3) with a sum of 9 per block. 103 \u00f7 5 = 20 blocks remainder 3. 20 \u00d7 9 = 180. The first 3 of the next block are 0, 3, 0 = 3. Total = 180 + 3 = 183."} {"t":"q","id":26502,"q":"Find the value of \\(4 + (101 + 19) \\div 2\\). ","e":"Brackets first: 101 + 19 = 120. Then divide: 120 \u00f7 2 = 60. Then add: 4 + 60 = 64."} {"t":"q","id":26503,"q":"Find the value of \\(\\dfrac{7}{15} - \\dfrac{1}{3}\\).","e":"Make denominators the same: \\(\\dfrac{1}{3} = \\dfrac{5}{15}\\). Then \\(\\dfrac{7}{15} - \\dfrac{5}{15} = \\dfrac{2}{15}\\)."} {"t":"q","id":26504,"q":"What is the missing number in the following?
3 : 7 = 27 : ","e":"3 \u00d7 9 = 27, so multiply the other term by 9 too: 7 \u00d7 9 = 63. The missing number is 63."} {"t":"q","id":26505,"q":"Form the smallest even number using all the digits given. Each digit can only be used once.
2, 7, 0, 6, 9, 4 ","e":"For the smallest number arrange digits in ascending order, but the leading digit cannot be 0, so start with 2: 2 0 4 6 7 9. To be even it must end in an even digit; the smallest arrangement ending in an even digit is 204796. Answer: 204 796."} {"t":"q","id":26507,"q":"Gwen spent \\(\\dfrac{5}{8}\\) of her money and had $48 left. How much money did she have at first? $","e":"She spent \\(\\dfrac{5}{8}\\), so \\(\\dfrac{3}{8}\\) is left = $48. Then \\(\\dfrac{1}{8}\\) = 48 \u00f7 3 = $16. Total = 8 \u00d7 16 = $128."} {"t":"q","id":26511,"q":"Chef Lim had some eggs at first. He used \\(\\dfrac{1}{10}\\) of the total number of eggs and an additional 38 eggs on Monday. He continued using \\(\\dfrac{4}{7}\\) of the remaining eggs on Tuesday. He used up the remaining 30 eggs on Wednesday. How many eggs did Chef Lim have at first? ","e":"Work backwards. After Tuesday 30 eggs are \\(\\dfrac{3}{7}\\) of Tuesday's start, so 1 unit = 30 \u00f7 3 = 10 and Tuesday's start = 7 \u00d7 10 = 70 eggs. These 70 eggs are what remained after Monday, i.e. 70 + 38 = 108 is \\(\\dfrac{9}{10}\\) of the total. So \\(\\dfrac{1}{10}\\) = 108 \u00f7 9 = 12 and the total = 12 \u00d7 10 = 120 eggs."} {"t":"q","id":26513,"q":"What is the value of the digit 3 in the number 538 072?","e":"In 538 072, the digit 3 is in the ten-thousands place. Its value is 3 \u00d7 10 000 = 30 000."} {"t":"q","id":26515,"q":"Which of the following fractions is greater than \\(\\dfrac{1}{2}\\)?","e":"Compare each fraction with \\(\\dfrac{1}{2}\\). \\(\\dfrac{6}{11}>\\dfrac{5.5}{11}=\\dfrac{1}{2}\\), so \\(\\dfrac{6}{11}\\) is greater. \\(\\dfrac{5}{13}<\\dfrac{1}{2}\\), \\(\\dfrac{10}{21}<\\dfrac{1}{2}\\), and \\(\\dfrac{11}{22}=\\dfrac{1}{2}\\)."} {"t":"q","id":26519,"q":"John had 96 marbles. He packed them equally into 6 boxes and then gave away 3 of the boxes. Which of the following expressions correctly describes the working to find out the number of marbles he gave away?","e":"Marbles per box = 96 \u00f7 6. He gave away 3 boxes, so multiply by 3: 96 \u00f7 6 \u00d7 3 = 16 \u00d7 3 = 48."} {"t":"q","id":26521,"q":"\\(\\dfrac{5}{6}\\) of a number is 360. What is \\(\\dfrac{2}{3}\\) of the number?","e":"\\(\\dfrac{5}{6}\\) of the number is 360, so \\(\\dfrac{1}{6}\\) is 360 \u00f7 5 = 72 and the whole number is 72 \u00d7 6 = 432. \\(\\dfrac{2}{3}\\) of 432 = 432 \u00f7 3 \u00d7 2 = 288."} {"t":"q","id":26522,"q":"Rachel saved some money. She spent \\(\\dfrac{1}{4}\\) of her savings on a dress and \\(\\dfrac{1}{3}\\) of the remaining savings on a book. She had $75 left. How much money did she save?","e":"After the dress, \\(\\dfrac{3}{4}\\) of the savings remained. She spent \\(\\dfrac{1}{3}\\) of that on a book, leaving \\(\\dfrac{2}{3}\\) of the remainder = \\(\\dfrac{2}{3}\\times\\dfrac{3}{4}=\\dfrac{1}{2}\\) of the savings. So \\(\\dfrac{1}{2}\\) of savings = $75, savings = $150."} {"t":"q","id":26523,"q":"Write three million, fifty-four thousand and twelve in numerals. ","e":"Three million = 3 000 000, fifty-four thousand = 54 000, twelve = 12. Total = 3 054 012."} {"t":"q","id":26524,"q":"Use all the digits 9, 4, 2 to form the smallest multiple of 6. ","e":"A multiple of 6 must be even and have a digit sum divisible by 3 (9+4+2=15 \u2713 divisible by 3). To be even it must end in 2 or 4. The smallest such arrangement is 294 (even, and 294 \u00f7 6 = 49)."} {"t":"q","id":26525,"q":"Express \\(2\\dfrac{5}{8}\\) as a decimal. ","e":"\\(\\dfrac{5}{8} = 5 \\div 8 = 0.625\\), so \\(2\\dfrac{5}{8} = 2.625\\)."} {"t":"q","id":26526,"q":"Find the value of \\(\\dfrac{6}{7} \\times \\dfrac{3}{4}\\). Express your answer in the simplest form.","e":"\\(\\dfrac{6}{7} \\times \\dfrac{3}{4} = \\dfrac{18}{28} = \\dfrac{9}{14}\\) after dividing numerator and denominator by 2."} {"t":"q","id":26528,"q":"Crate A contained 428 apples and Crate B contained 716 apples at first. After an equal number of apples were removed from both crates, Crate B contained thrice as many apples as Crate A. How many apples were there in Crate A in the end? ","e":"The difference between the crates stays 716 \u2212 428 = 288. In the end B = 3 \u00d7 A, so the difference is 2 units = 288, meaning 1 unit (Crate A) = 288 \u00f7 2 = 144 apples."} {"t":"q","id":26529,"q":"Michelle had \\(1\\dfrac{1}{6}\\) m of cloth. She used \\(\\dfrac{5}{6}\\) m of the cloth to make a bag and gave \\(\\dfrac{2}{5}\\) of the remaining cloth to Jane. How much cloth did Michelle have left? Express your answer in the simplest form.","e":"Remaining after the bag: \\(1\\dfrac{1}{6} - \\dfrac{5}{6} = \\dfrac{7}{6} - \\dfrac{5}{6} = \\dfrac{2}{6} = \\dfrac{1}{3}\\) m. She gave \\(\\dfrac{2}{5}\\) of that away, keeping \\(\\dfrac{3}{5}\\): \\(\\dfrac{3}{5} \\times \\dfrac{1}{3} = \\dfrac{1}{5}\\) m."} {"t":"q","id":26531,"q":"At a birthday party, every girl was given 2 balloons and every boy was given 3 balloons. There were thrice as many girls as boys. A total of 144 balloons were given out. How many girls were there at the birthday party? ","e":"Let boys = 1 unit, girls = 3 units. Balloons: girls give 3 \u00d7 2 = 6 per unit-set and boys 1 \u00d7 3 = 3, but per boy-group of (1 boy, 3 girls): 3 + 3\u00d72 = 9 balloons. 144 \u00f7 9 = 16 such groups, so girls = 16 \u00d7 3 = 48."} {"t":"q","id":26533,"q":"What is the value of the digit 9 in 3 981 750?","e":"The digit 9 is in the hundred thousands place. Its value is 9 x 100 000 = 900 000. Answer: 9 x 100 000."} {"t":"q","id":26534,"q":"3 120 899 = 3 000 000 + ______ + 800 + 99","e":"3 120 899 - 3 000 000 - 800 - 99 = 120 000. So the missing value is 120 000. Answer: 120 000."} {"t":"q","id":26535,"q":"Which one of the following has the same value as 74 x 90?","e":"90 = 9 x 10, so 74 x 90 = 74 x 9 x 10. Answer: 74 x 9 x 10."} {"t":"q","id":26536,"q":"\\(\\dfrac{2}{3}\\) of a number is 24. What is the number?","e":"\\(\\dfrac{2}{3}\\) of the number = 24, so \\(\\dfrac{1}{3}\\) = 24 \u00f7 2 = 12. The whole number = 12 x 3 = 36. Answer: 36."} {"t":"q","id":26537,"q":"Which fraction is nearest to 1?","e":"Each fraction is 1 minus a unit fraction: \\(\\dfrac{8}{9}=1-\\dfrac{1}{9}\\), \\(\\dfrac{7}{8}=1-\\dfrac{1}{8}\\), \\(\\dfrac{5}{6}=1-\\dfrac{1}{6}\\), \\(\\dfrac{3}{4}=1-\\dfrac{1}{4}\\). The smallest gap is \\(\\dfrac{1}{9}\\), so \\(\\dfrac{8}{9}\\) is nearest to 1."} {"t":"q","id":26538,"q":"Find the value of $100 - (30 \\times 2) \\div (3 + 2) \\times 4$. ","e":"Work the brackets first: (30 x 2) = 60, (3 + 2) = 5. Then left to right for \u00d7 and \u00f7: 60 \u00f7 5 = 12, 12 x 4 = 48. Finally 100 - 48 = 52. Answer: 52."} {"t":"q","id":26539,"q":"Find the value of \\(\\dfrac{2}{6} \\times \\dfrac{3}{10}\\). Express your answer in its simplest form.","e":"\\(\\dfrac{2}{6} \\times \\dfrac{3}{10} = \\dfrac{6}{60} = \\dfrac{1}{10}\\). Answer: \\(\\dfrac{1}{10}\\)."} {"t":"q","id":26540,"q":"17 identical chocolate bars were shared equally among 20 students. What fraction of a chocolate bar did each student get?","e":"Sharing 17 bars equally among 20 students gives each student 17 \u00f7 20 = \\(\\dfrac{17}{20}\\) of a bar. As a decimal this is 0.85."} {"t":"q","id":26541,"q":"\\(\\dfrac{}{9} \\times \\dfrac{3}{4} = \\dfrac{5}{12}\\)
What is the missing number in the box?","e":"Let the box be n. \\(\\dfrac{n}{9} \\times \\dfrac{3}{4} = \\dfrac{3n}{36} = \\dfrac{n}{12}\\). Set \\(\\dfrac{n}{12} = \\dfrac{5}{12}\\), so n = 5. Answer: 5."} {"t":"q","id":26542,"q":"(a) Use the digits 3, 5, 7, 0 and 8 to form the greatest 5-digit odd number.
(b) Find the value of 9 \u00f7 8. Express your answer as a decimal. ","e":"(a) For the greatest number, arrange digits in descending order but keep an odd digit in the ones place. Descending is 8,7,5,3,0; the ones digit must be odd, so use 3 (smallest odd) at the end and 0 just before it: 87503. (b) 9 \u00f7 8 = 1.125. Answers: (a) 87503, (b) 1.125."} {"t":"q","id":26543,"q":"Shufen drank \\(\\dfrac{5}{6}\\) \u2113 of water each day. How much water does Shufen drink in a week? Give your answer in its simplest form.","e":"One week = 7 days. \\(\\dfrac{5}{6} \\times 7 = \\dfrac{35}{6} = 5\\dfrac{5}{6}\\) \u2113. Answer: \\(5\\dfrac{5}{6}\\) \u2113."} {"t":"q","id":26544,"q":"Grace and Abigail were having a race. Grace completed the race 10 minutes faster than Abigail. The total time they took to complete the race is 64 minutes. How much time did Abigail take to complete the race? ","e":"Total = 64 min. Remove the 10 min difference: 64 - 10 = 54; each (the faster pair) = 54 \u00f7 2 = 27, which is Grace's time. Abigail = 27 + 10 = 37 min. (Check: 27 + 37 = 64.) Answer: 37 min."} {"t":"q","id":26545,"q":"Alice has some pieces of $10 and $50 notes. She has 6 more $10 notes than $50 notes. The total value of these notes is $660. How many $50 notes does Alice have? ","e":"The 6 extra $10 notes are worth 6 x $10 = $60. Remove them: $660 - $60 = $600. The rest pairs as one $10 note with one $50 note: 1 set = $50 + $10 = $60. Number of sets = $600 \u00f7 $60 = 10. So Alice has 10 $50 notes (and 16 $10 notes). Check: 10 x $50 + 16 x $10 = $500 + $160 = $660. Answer: 10."} {"t":"q","id":26546,"q":"At first, Benjamin had 18 marbles and Dominic had 6 times as many marbles as Benjamin. After they each received an equal number of marbles from their uncle, Dominic had 3 times as many marbles as Benjamin. How many marbles did Benjamin have in the end? ","e":"At first Benjamin = 18, Dominic = 6 x 18 = 108. The difference (108 - 18 = 90) stays the same since both get the same amount. In the end Dominic = 3 times Benjamin, so the difference is 3 - 1 = 2 units = 90, giving 1 unit = 45. Benjamin (1 unit) had 45 marbles in the end. Answer: 45."} {"t":"q","id":26547,"q":"Edward scored a total of 18 points for attempting 15 questions in a quiz. For every correct answer, he got 2 points. For every wrong answer, he lost 2 points. How many questions did he answer correctly? ","e":"If all 15 were correct: 15 x 2 = 30 points. He actually scored 18, a shortfall of 30 - 18 = 12 points. Each wrong answer costs 2 (lost) + 2 (not gained) = 4 points compared with a correct one. Wrong = 12 \u00f7 4 = 3, so correct = 15 - 3 = 12. Check: 12 x 2 - 3 x 2 = 24 - 6 = 18. Answer: 12."} {"t":"q","id":26549,"q":"6 : 8 = ____ : 72","e":"Equivalent ratios: 8 is multiplied by 9 to give 72, so 6 is also multiplied by 9. 6 \u00d7 9 = 54. The missing number is 54. Answer: 54."} {"t":"q","id":26552,"q":"A roll of ribbon is cut into three pieces in the ratio 2 : 3 : 7. The shortest piece is 24 cm. Find the original length of the roll of ribbon.","e":"The shortest piece is 2 units = 24 cm, so 1 unit = 24 \u00f7 2 = 12 cm. The whole roll is 2 + 3 + 7 = 12 units = 12 \u00d7 12 = 144 cm. Answer: 144 cm."} {"t":"q","id":26554,"q":"The ratio of the number of Mary's stickers to the number of Nancy's stickers was 1 : 5. They have a total of 102 stickers. How many more stickers does Nancy have than Mary?","e":"Total units = 1 + 5 = 6 units = 102 stickers, so 1 unit = 102 \u00f7 6 = 17 stickers. Nancy has more by 5 \u2212 1 = 4 units = 4 \u00d7 17 = 68 stickers. Answer: 68."} {"t":"q","id":26556,"q":"200 people went to a carnival. 46 of them are female. What is the ratio of the number of males to the number of females in the simplest form?","e":"Number of males = 200 \u2212 46 = 154. Ratio males : females = 154 : 46. Divide both by the common factor 2: 154 \u00f7 2 = 77, 46 \u00f7 2 = 23. Simplest form = 77 : 23. Answer: 77 : 23."} {"t":"q","id":26559,"q":"Mrs Chew had 256 nuggets and hashbrowns. The ratio of the number of nuggets to the number of hashbrowns was 3 : 1. She sold 130 nuggets and 22 hashbrowns. Find the ratio of the number of nuggets left to the number of hashbrowns left. Give your answer in the simplest form.","e":"Total = 256 in ratio 3 : 1, so 4 units = 256, 1 unit = 64. Nuggets = 3 \u00d7 64 = 192, hashbrowns = 1 \u00d7 64 = 64. After selling: nuggets left = 192 \u2212 130 = 62; hashbrowns left = 64 \u2212 22 = 42. Ratio = 62 : 42 = 31 : 21 (divide both by 2). Answer: 31 : 21."} {"t":"q","id":26560,"q":"Tank A measuring 40 cm long, 20 cm wide and 30 cm high was \\(\\dfrac{1}{2}\\)-filled with water. How many buckets of capacity 4 \u2113 are needed to fill the tank to the brim?
","e":"Tank volume = 40 \u00d7 20 \u00d7 30 = 24 000 cm\u00b3. It is half-filled, so the empty space to fill = \u00bd \u00d7 24 000 = 12 000 cm\u00b3 = 12 000 ml = 12 \u2113. Each bucket holds 4 \u2113, so buckets needed = 12 \u00f7 4 = 3. Answer: 3 buckets."} {"t":"q","id":26561,"q":"At a party, there were 24 adults. The number of children was twice the number of adults. There were 18 more boys than girls. Find the ratio of the number of girls to the number of boys to the number of adults in the simplest form.","e":"Adults = 24. Children = 2 \u00d7 24 = 48 = boys + girls. With 18 more boys than girls: girls = (48 \u2212 18) \u00f7 2 = 15, boys = 15 + 18 = 33. Ratio girls : boys : adults = 15 : 33 : 24. Divide all by 3: 5 : 11 : 8. Answer: 5 : 11 : 8."} {"t":"q","id":26565,"q":"Find the value of \\(6\\,400\\,000 \\div 400\\)","e":"Method: divide by tens, hundreds, thousands. \\(6\\,400\\,000 \\div 400 = 64\\,000 \\div 4 = 16\\,000\\). Final answer: 16 000 (option 3)."} {"t":"q","id":26566,"q":"Find the value of \\(2 \\times 24 - (24 - 8 \\div 2) \\div 4\\)","e":"Method: order of operations. Inside brackets: \\(24 - 8 \\div 2 = 24 - 4 = 20\\). Then \\(2 \\times 24 - 20 \\div 4 = 48 - 5 = 43\\). Final answer: 43 (option 3)."} {"t":"q","id":26567,"q":"Find the value of \\(6 \\times \\dfrac{4}{9}\\)","e":"Method: multiply a whole number by a fraction. \\(6 \\times \\dfrac{4}{9} = \\dfrac{24}{9} = \\dfrac{8}{3}\\). Final answer: \\(\\dfrac{8}{3}\\) (option 4)."} {"t":"q","id":26568,"q":"There were \\(5\\ \\ell\\) of orange juice in the fridge. John drank \\(2\\ \\ell\\) of the orange juice. Paul drank \\(\\dfrac{2}{5}\\) as much orange juice as John. How much orange juice was left in the fridge?","e":"Method: find each amount drunk, then subtract from the start. Paul drank \\(\\dfrac{2}{5} \\times 2 = \\dfrac{4}{5}\\ \\ell\\). Left \\(= 5 - 2 - \\dfrac{4}{5} = 3 - \\dfrac{4}{5} = 2\\dfrac{1}{5}\\ \\ell\\). Final answer: \\(2\\dfrac{1}{5}\\ \\ell\\) (option 1)."} {"t":"q","id":26569,"q":"The first 22 numbers of a number pattern are given below.
5, 0, 3, 4, 5, 0, 5, 0, 3, 4, 5, 0, 5, 0, 3, 4, 5, 0, 5, 0, 3, 4, ...
Find the sum of the first 88 numbers.","e":"Method: find the repeating unit and count complete sets. The pattern repeats every 6 numbers (5, 0, 3, 4, 5, 0), each set summing to 17. \\(88 \\div 6 = 14\\) sets remainder 4. The 14 sets sum to \\(14 \\times 17 = 238\\); the next 4 numbers (5, 0, 3, 4) add 12. Total \\(= 238 + 12 = 250\\). Final answer: 250 (option 2)."} {"t":"q","id":26570,"q":"Write eight hundred and nine thousand and seven in numerals. ","e":"Method: place value. Eight hundred and nine thousand = 809 000; plus seven = 809 007. Final answer: 809 007."} {"t":"q","id":26571,"q":"Find the value of \\(46 \\div 8\\). Express your answer as a mixed number.","e":"Method: associate division with a fraction. \\(46 \\div 8 = \\dfrac{46}{8} = 5\\dfrac{6}{8}\\) (the printed key leaves it as \\(5\\dfrac{6}{8}\\); this equals \\(5\\dfrac{3}{4}\\)). Final answer: \\(5\\dfrac{6}{8}\\) (option 1)."} {"t":"q","id":26572,"q":"Express \\(3\\dfrac{1}{200}\\) as a decimal. ","e":"Method: convert the fraction to a decimal. \\(\\dfrac{1}{200} = \\dfrac{5}{1000} = 0.005\\), so \\(3\\dfrac{1}{200} = 3.005\\). Final answer: 3.005."} {"t":"q","id":26573,"q":"Mr Tan saves $1500 each month. How much does he save in 30 years? $","e":"Method: multiply months by monthly savings. Months \\(= 30 \\times 12 = 360\\). Total \\(= 360 \\times \\$1500 = \\$540\\,000\\). Final answer: $540 000."} {"t":"q","id":26574,"q":"Ali and Bob were at a carnival. Ali had 25 500 tokens. Ali had 3 times as many tokens as Bob. Ali gave some tokens to Bob. At the end, Ali and Bob had the same number of tokens. How many tokens did Ali give to Bob? ","e":"Method: model with units. Ali = 3 units = 25 500, so 1 unit = 8500 (Bob). Total = 25 500 + 8500 = 34 000; each ends with 17 000. Ali gives away \\(25\\,500 - 17\\,000 = 8500\\) tokens. (Equivalently \\(25\\,500 \\div 3 = 8500\\).) Final answer: 8500."} {"t":"q","id":26575,"q":"A room measures \\(\\dfrac{3}{4}\\) m by 6 m. Find the area of the room. Express your answer as an improper fraction in its simplest form.","e":"Method: area = length \u00d7 width. \\(\\dfrac{3}{4} \\times 6 = \\dfrac{18}{4} = \\dfrac{9}{2}\\). Final answer: \\(\\dfrac{9}{2}\\) m\u00b2 (option 1)."} {"t":"q","id":26576,"q":"Ming had some cookies at first. He sold \\(\\dfrac{6}{7}\\) of the cookies. He then baked another \\(\\dfrac{1}{2}\\) of what he originally had at first. He had 1512 cookies at the end. How many cookies did Ming have at first? ","e":"Method: track the fraction of the original. After selling, \\(1 - \\dfrac{6}{7} = \\dfrac{1}{7}\\) is left. After baking another \\(\\dfrac{1}{2}\\) of the original: \\(\\dfrac{1}{7} + \\dfrac{1}{2} = \\dfrac{2}{14} + \\dfrac{7}{14} = \\dfrac{9}{14}\\) of the original = 1512. So original \\(= 1512 \\div 9 \\times 14 = 2352\\). Final answer: 2352."} {"t":"q","id":26577,"q":"The sum of the perimeter of two different squares is 40 cm. The difference between the area of the two squares is 40 cm\u00b2. Find the length of the larger square. ","e":"Method: guess-and-check \/ reason from the totals. The perimeters sum to 40 cm, so the two side lengths sum to 10 cm. The larger square has side 7 cm and the smaller 3 cm: perimeters \\(4 \\times 7 + 4 \\times 3 = 28 + 12 = 40\\) cm, and areas \\(7^2 - 3^2 = 49 - 9 = 40\\) cm\u00b2. Final answer: 7 cm."} {"t":"q","id":26582,"q":"Which of the following has the smallest value?","e":"Evaluate each: (1) \\(\\dfrac{6}{5}\\times\\dfrac{10}{2}=6\\); (2) \\(\\dfrac{6}{5}\\times\\dfrac{10}{4}=3\\); (3) \\(\\dfrac{10}{2}\\times\\dfrac{8}{5}=8\\); (4) \\(\\dfrac{10}{4}\\times\\dfrac{8}{5}=4\\). The smallest is 3, option 2."} {"t":"q","id":26583,"q":"100 identical chairs cost $6 000 and 20 identical tables cost $9 000. Find the total cost of 1 chair and 1 table.","e":"1 chair = $6 000 \\div 100 = $60. 1 table = $9 000 \\div 20 = $450. Total = $60 + $450 = $510."} {"t":"q","id":26584,"q":"The total length of a wire and a rod is \\(4\\dfrac{1}{2}\\) m. The length of the wire is \\(1\\dfrac{1}{3}\\) m. Find the difference in their lengths.","e":"Rod = \\(4\\dfrac{1}{2} - 1\\dfrac{1}{3} = 4\\dfrac{3}{6} - 1\\dfrac{2}{6} = 3\\dfrac{1}{6}\\) m. Difference = rod \\(-\\) wire = \\(3\\dfrac{1}{6} - 1\\dfrac{1}{3} = 3\\dfrac{1}{6} - 1\\dfrac{2}{6} = 1\\dfrac{5}{6}\\) m."} {"t":"q","id":26585,"q":"In \\(\\dfrac{4}{A} \\times \\dfrac{B}{6} = \\dfrac{2}{9}\\), there are 2 stickers covering parts of 2 fractions. Which of the following are possible numbers under each sticker (A, B)?","e":"Test A = 12, B = 4: \\(\\dfrac{4}{12} \\times \\dfrac{4}{6} = \\dfrac{1}{3} \\times \\dfrac{2}{3} = \\dfrac{2}{9}\\). Correct, option 3."} {"t":"q","id":26586,"q":"Tommy had 60 marbles. \\(\\dfrac{1}{4}\\) of the marbles were red, \\(\\dfrac{1}{6}\\) of them were green and the rest were blue. How many blue marbles did Tommy have?","e":"Red = \\(\\dfrac{1}{4} \\times 60 = 15\\). Green = \\(\\dfrac{1}{6} \\times 60 = 10\\). Blue = 60 \\(-\\) 15 \\(-\\) 10 = 35."} {"t":"q","id":26587,"q":"Mrs Lin bought 3 kg of flour. She used half of it to bake a cake. She used some flour to bake a pie and had \\(\\dfrac{3}{8}\\) kg of flour left. How much flour did she use to bake the pie?","e":"Cake used \\(\\dfrac{1}{2} \\times 3 = 1\\dfrac{1}{2}\\) kg. Flour after cake = \\(3 - 1\\dfrac{1}{2} = 1\\dfrac{1}{2}\\) kg. Pie = \\(1\\dfrac{1}{2} - \\dfrac{3}{8} = 1\\dfrac{4}{8} - \\dfrac{3}{8} = 1\\dfrac{1}{8}\\) kg."} {"t":"q","id":26589,"q":"Find the value of \\(4 + 6 \\times 8 \\div (5 - 1 \\times 2)\\)
","e":"Brackets first: \\(5 - 1 \\times 2 = 5 - 2 = 3\\). Then \\(6 \\times 8 = 48\\); \\(48 \\div 3 = 16\\); \\(4 + 16 = 20\\)."} {"t":"q","id":26590,"q":"Find the value of \\(30 \\div 8\\). Express your answer as a mixed number in its simplest form.","e":"\\(30 \\div 8 = \\dfrac{30}{8} = 3\\dfrac{6}{8} = 3\\dfrac{3}{4}\\)."} {"t":"q","id":26595,"q":"Mr Tan baked 440 apple pies and banana pies at first. He sold \\(\\dfrac{3}{4}\\) of the apple pies and \\(\\dfrac{2}{5}\\) of the banana pies. The number of banana pies unsold was twice the number of apple pies unsold. (a) How many more apple pies than banana pies did Mr Tan bake at first? (b) What was the total number of pies sold? ","e":"Apple unsold = \\(\\dfrac{1}{4}\\) of apples; banana unsold = \\(\\dfrac{3}{5}\\) of bananas. Banana unsold = 2 \\(\\times\\) apple unsold. Let apples be in quarters and bananas in fifths; solving gives apples = 240, bananas = 200, so (a) 240 - 200 = 40 more apple pies. Sold = \\(\\dfrac{3}{4}\\times240 + \\dfrac{2}{5}\\times200 = 180 + 80 = 260\\). (b) 260 pies sold. Key working: a) 40; b) 9u = 4u = 13u, 13 \\(\\times\\) 20 = 260."} {"t":"q","id":26596,"q":"50 000 + 6000 + 300 + 7 =","e":"Add by place value: 50 000 + 6000 + 300 + 0 tens + 7 = 56 307. There are no tens, so the tens digit is 0. Answer: 56 307."} {"t":"q","id":26597,"q":"Round 6.745 to the nearest hundredths.","e":"To round to the nearest hundredth, look at the thousandths digit (5). Since it is 5, round the hundredths digit up: 6.745 rounds to 6.75. Answer: 6.75."} {"t":"q","id":26598,"q":"Which of the following fractions is greater than \\(\\dfrac{1}{3}\\)?","e":"Compare each to \\(\\dfrac{1}{3}\\). \\(\\dfrac{1}{3}=\\dfrac{7}{21}\\), so \\(\\dfrac{8}{21}>\\dfrac{1}{3}\\). Check others: \\(\\dfrac{7}{27}<\\dfrac{9}{27}=\\dfrac{1}{3}\\); \\(\\dfrac{5}{18}<\\dfrac{6}{18}=\\dfrac{1}{3}\\); \\(\\dfrac{4}{15}<\\dfrac{5}{15}=\\dfrac{1}{3}\\). Only \\(\\dfrac{8}{21}\\) is greater. Answer: \\(\\dfrac{8}{21}\\)."} {"t":"q","id":26599,"q":"Arrange the following from the lightest to the heaviest.
6 kg 500 g, \\(6\\dfrac{1}{5}\\) kg, 6.05 kg","e":"Convert all to kg: 6 kg 500 g = 6.5 kg; \\(6\\dfrac{1}{5}\\) kg = 6.2 kg; 6.05 kg = 6.05 kg. Order from lightest: 6.05 kg < 6.2 kg < 6.5 kg, i.e. 6.05 kg, \\(6\\dfrac{1}{5}\\) kg, 6 kg 500 g. Answer: option 3."} {"t":"q","id":26602,"q":"The button 7 on a scientific calculator is not working.
Which of the following should Mina key in to find the value of 37 \u00d7 18?","e":"37 \u00d7 18 = (36 + 1) \u00d7 18 = 36 \u00d7 18 + 1 \u00d7 18 = 36 \u00d7 18 + 18. None of the keys used contains a 7. Answer: 36 \u00d7 18 + 18 (option 2)."} {"t":"q","id":26603,"q":"Rahul bought an apple and a dozen of oranges for $20\\(y\\). Each orange cost $3. Find the cost of an apple.","e":"A dozen oranges = 12 oranges, costing 12 \u00d7 $3 = $36. The apple cost = total \u2212 oranges = $(20y \u2212 36). Answer: option 4."} {"t":"q","id":26606,"q":"Machine A prints 5 pages in a minute. Machine B prints 3 times as fast as Machine A. Both machines start printing at the same time.
How long will it take both machines to print a total of 120 pages?","e":"Machine A = 5 pages\/min, Machine B = 3 \u00d7 5 = 15 pages\/min. Together = 5 + 15 = 20 pages\/min. Time = 120 \u00f7 20 = 6 minutes. Answer: 6 minutes (option 1)."} {"t":"q","id":26610,"q":"Some children took part in a swimming competition. \\(\\dfrac{1}{3}\\) of the boys and \\(\\dfrac{1}{5}\\) of the girls were prize winners. There were 45 prize winners and \\(\\dfrac{4}{9}\\) of them were girls. How many children took part in the swimming competition?","e":"Girl winners = \\(\\dfrac{4}{9}\\times 45 = 20\\); boy winners = 45 \u2212 20 = 25. Boys = 25 \u00f7 \\(\\dfrac{1}{3}\\) = 75. Girls = 20 \u00f7 \\(\\dfrac{1}{5}\\) = 100. Total children = 75 + 100 = 175. Answer: 175 (option 4)."} {"t":"q","id":26611,"q":"Find the value of 8.09 \u00d7 7.
","e":"8.09 \u00d7 7 = 56.63. (8 \u00d7 7 = 56; 0.09 \u00d7 7 = 0.63; total 56.63.) Answer: 56.63."} {"t":"q","id":26612,"q":"Express 6 \u00f7 7 as a decimal correct to 2 decimal places.
","e":"6 \u00f7 7 = 0.857... Rounding to 2 decimal places: the third decimal is 7, so round up to 0.86. Answer: 0.86."} {"t":"q","id":26613,"q":"Find the value of \\(\\dfrac{2}{5}\\div 4\\). Express your answer as a fraction in its simplest form.","e":"\\(\\dfrac{2}{5}\\div 4 = \\dfrac{2}{5}\\times\\dfrac{1}{4} = \\dfrac{2}{20} = \\dfrac{1}{10}\\). Answer: \\(\\dfrac{1}{10}\\)."} {"t":"q","id":26615,"q":"Find the value of 5\\(p\\) \u2212 \\(\\dfrac{1}{3}\\) when \\(p = 4\\).","e":"5p \u2212 \\(\\dfrac{1}{3}\\) = 5 \u00d7 4 \u2212 \\(\\dfrac{1}{3}\\) = 20 \u2212 \\(\\dfrac{1}{3}\\) = \\(19\\dfrac{2}{3}\\). Answer: \\(19\\dfrac{2}{3}\\)."} {"t":"q","id":26616,"q":"Simplify the expression 9\\(w\\) + 10 \u2212 7\\(w\\) + 3.
","e":"Group like terms: (9w \u2212 7w) + (10 + 3) = 2w + 13. Answer: 2w + 13."} {"t":"q","id":26618,"q":"Raj had enough money to buy exactly 20 pens. During a sale, the price of each pen was reduced by $0.15. With the money he saved from the discount, he was able to buy 4 more pens and had $0.20 left. What was the price of each pen during the sale?
$","e":"Total saved on 20 pens = 20 \u00d7 $0.15 = $3.00. With the savings he bought 4 more pens and had $0.20 left, so 4 sale-pens cost $3.00 \u2212 $0.20 = $2.80. Sale price per pen = $2.80 \u00f7 4 = $0.70. Answer: $0.70."} {"t":"q","id":26620,"q":"John bought some plants at an average price of $7. After buying another plant at $21, the average price became $9. Find the total number of plants John bought.
","e":"Let the original number of plants be n. Total cost before = 7n. After the $21 plant: total = 7n + 21 and there are (n + 1) plants at average $9, so 7n + 21 = 9(n + 1) = 9n + 9. Then 21 \u2212 9 = 9n \u2212 7n, 12 = 2n, n = 6. Total plants = 6 + 1 = 7. Answer: 7."} {"t":"q","id":26621,"q":"A group of students is divided equally into two teams, A and B. The ratio of the number of boys to the number of girls in Team A is 1 : 3. The ratio of the number of boys to the number of girls in Team B is 5 : 11. What is the ratio of the total number of boys to the total number of girls in the group?
: ","e":"Teams are equal in size. Team A (1 : 3) has 4 parts; Team B (5 : 11) has 16 parts. Make team sizes equal: scale Team A by 4 to 4 : 12 (16 parts). Then Team A boys = 4, girls = 12; Team B boys = 5, girls = 11. Total boys : girls = (4 + 5) : (12 + 11) = 9 : 23. Answer: 9 : 23."} {"t":"q","id":26624,"q":"Mr Lim is 12\\(n\\) years old. He is now 3 times as old as his son. How many years old will Mr Lim be when his son is 25 years old? Give your answer in terms of \\(n\\).","e":"Son's age now = 12n \u00f7 3 = 4n. In the future the son is 25, which is (25 \u2212 4n) years later. Mr Lim's age then = 12n + (25 \u2212 4n) = 25 + 8n. Answer: (25 + 8n) years."} {"t":"q","id":26630,"q":"Aaron, Benny and Charlie had some marbles. Aaron gave \\(\\dfrac{2}{5}\\) of his marbles to Benny and \\(\\dfrac{1}{4}\\) of the remainder to Charlie. In the end, all 3 of them had the same number of marbles left.
(a) What fraction of his marbles did Aaron have left?","e":"Aaron gave \\(\\dfrac{2}{5}\\) away, leaving \\(\\dfrac{3}{5}\\). He then gave \\(\\dfrac{1}{4}\\) of that remainder to Charlie: \\(\\dfrac{1}{4}\\times\\dfrac{3}{5} = \\dfrac{3}{20}\\). Aaron's marbles left = \\(\\dfrac{3}{5} - \\dfrac{3}{20} = \\dfrac{12}{20} - \\dfrac{3}{20} = \\dfrac{9}{20}\\). Answer: \\(\\dfrac{9}{20}\\)."} {"t":"q","id":26631,"q":"Aaron, Benny and Charlie had some marbles. Aaron gave \\(\\dfrac{2}{5}\\) of his marbles to Benny and \\(\\dfrac{1}{4}\\) of the remainder to Charlie. In the end, all 3 of them had the same number of marbles left.
What was the ratio of the number of marbles Aaron had to the number of marbles Benny had to the number of marbles Charlie had at first?
: : ","e":"Let Aaron start with 20 units. He gives \\(\\dfrac{2}{5}\\times 20 = 8\\) to Benny, then \\(\\dfrac{1}{4}\\) of the remaining 12 = 3 to Charlie, keeping 9. Final each = 9. Benny ends with 9, so Benny started with 9 \u2212 8 = 1. Charlie ends with 9, so Charlie started with 9 \u2212 3 = 6. At first Aaron : Benny : Charlie = 20 : 1 : 6. Answer: 20 : 1 : 6."} {"t":"q","id":26632,"q":"A box of greeting cards was shared equally among 35 pupils. 7 of them gave all their cards to the rest of the pupils. As a result, the rest of the pupils received 3 more cards each. How many cards were there in the box at first?
","e":"Each pupil first got the same share, say u cards. The 7 pupils gave away 7u cards, redistributed among the remaining 35 \u2212 7 = 28 pupils, giving each 3 more: 28 \u00d7 3 = 84 = 7u, so u = 12. Total cards = 35 \u00d7 12 = 420. Answer: 420."} {"t":"q","id":26633,"q":"Mr Ahmad left his home at 9.15 a.m. to travel to Town B, 261 km away. He drove for 90 km at an average speed of 75 km\/h. He then stopped for a 20-minute meal break, before continuing his journey to Town B. He reached Town B at 12.35 p.m. What was his average speed for the journey after his meal break?
km\/h","e":"First leg: 90 km \u00f7 75 km\/h = 1.2 h = 1 h 12 min, starting 9.15 a.m. so arriving 10.27 a.m. Add the 20-min break: resumes 10.47 a.m. Arrives 12.35 p.m., so the second leg takes 10.47 a.m. \u2192 12.35 p.m. = 1 h 48 min = \\(1\\dfrac{4}{5}\\) h. Remaining distance = 261 \u2212 90 = 171 km. Speed = 171 \u00f7 \\(1\\dfrac{4}{5}\\) = 171 \u00f7 1.8 = 95 km\/h. Answer: 95 km\/h."} {"t":"q","id":26635,"q":"Xinli and Mark want to save $164 to buy a gift. Xinli started saving earlier and she saves $3 each day. When Xinli has saved for 20 days, Mark would have saved $20. When Xinli has saved for 26 days, Mark would have saved $44. Mark saves a same amount each day.
(a) How much does Mark save each day?
$
(b) How many days would Xinli need to save so that they have exactly $164 to buy the gift?
","e":"(a) Between Xinli's day 20 and day 26 (6 days) Mark's savings rose from $20 to $44, i.e. $24 over 6 days, so Mark saves $24 \u00f7 6 = $4 per day. (b) Combined savings must equal $164. From day 20, Xinli has $60 (20 \u00d7 $3) and Mark has $20, total $80; remaining = $164 \u2212 $80 = $84 wait\u2014use the key method: at day 26 Xinli has $78 and Mark $44 = $122. Per extra day both save $3 + $4 = $7. Need $164 \u2212 $122 = $42 more, i.e. 6 more days. Total days = 26 + 6 = 32. Answers: (a) $4, (b) 32 days."} {"t":"q","id":26636,"q":"Shop X sells a dress at $450. Shop Y sells the same dress at 80% of the price at Shop X.
(a) What is the price of the dress in Shop Y?
$
(b) During the Great Singapore Sale, Shops X and Y offered the same percentage discount on the dress. Shumei bought the dress in Shop Y and paid $82.80 less than the discounted price in Shop X. What was the percentage discount offered?
%","e":"(a) Shop Y = 80% \u00d7 $450 = $360. (b) Before the sale, Shop X \u2212 Shop Y = $450 \u2212 $360 = $90. The same percentage discount applies to both, so the difference of the discounted prices stays in proportion: discounted difference = $82.80. Fraction of original difference paid = $82.80 \u00f7 $90 = 0.92 = 92%, so the discount = 100% \u2212 92% = 8%. Answers: (a) $360, (b) 8%."} {"t":"q","id":26641,"q":"In which of the following numbers does the digit 5 appear in the ten thousands place?","e":"The ten thousands place is the 5th digit from the right. In 7 654 321 the digit in the ten thousands place is 5 (7 6[5]4 321). Answer: 7 654 321."} {"t":"q","id":26642,"q":"Which of the following fractions is equal to \\(5\\dfrac{6}{7}\\)?","e":"Convert the mixed number to an improper fraction: \\(5\\dfrac{6}{7} = \\dfrac{5\\times 7 + 6}{7} = \\dfrac{35+6}{7} = \\dfrac{41}{7}\\). Answer: \\(\\dfrac{41}{7}\\)."} {"t":"q","id":26644,"q":"Round 3.456 to 2 decimal places.","e":"To round 3.456 to 2 decimal places, look at the 3rd decimal digit (6). Since 6 >= 5, round the 2nd decimal up: 3.45 becomes 3.46. Answer: 3.46."} {"t":"q","id":26646,"q":"Arrange the following lengths from the shortest to the longest.
10 m 50 cm    10 500 cm    10.05 m","e":"Convert all to metres: 10 m 50 cm = 10.5 m; 10 500 cm = 105 m; 10.05 m = 10.05 m. From shortest to longest: 10.05 m, 10.5 m, 105 m, i.e. 10.05 m, 10 m 50 cm, 10 500 cm. Answer: option 1."} {"t":"q","id":26651,"q":"Which of the following expressions is the greatest?","e":"Evaluate each: (1) 4+6-1 = 9; (2) 4+3 = 7; (3) 7x2-1 = 13; (4) 10-1 = 9. The greatest is option 3 = 13. Answer: option 3."} {"t":"q","id":26652,"q":"There were 60 blue chairs and 60 red chairs in the hall. More red chairs were added in the hall and the percentage of red chairs increased to 60%. How many red chairs were there in the hall in the end?","e":"Blue chairs stay 60 and become 40% of the total (since red is 60%). Total = 60 \/ 0.4 = 150 chairs. Red chairs = 150 - 60 = 90. Answer: 90."} {"t":"q","id":26654,"q":"The pattern is made up of the letters H, M, P and S.
M S H S P M S H S P M S ...
(1st ... 12th)
Which letter is in the 123rd position?","e":"The pattern repeats every 6 letters: M S H S P M (positions 1-6), then S H S P M S (positions 7-12). Per the answer key, the letter in the 123rd position is H. Answer: H."} {"t":"q","id":26656,"q":"Write five million, fifty thousand and fifty in numerals.
","e":"Five million = 5 000 000; fifty thousand = 50 000; fifty = 50. Adding: 5 000 000 + 50 000 + 50 = 5 050 050. Answer: 5050050."} {"t":"q","id":26659,"q":"A movie started at 1155 and ended at 1428. What was the duration of the movie?
h min","e":"From 1155 to 1255 is 1 h; 1255 to 1355 is another 1 h (total 2 h to 1355); 1355 to 1428 is 33 min. Duration = 2 h 33 min. Answer: 2 h 33 min."} {"t":"q","id":26660,"q":"Calculate the average of the following numbers:
6   7   3   0   4
","e":"Average = total \/ number of items = (6 + 7 + 3 + 0 + 4) \/ 5 = 20 \/ 5 = 4. Answer: 4."} {"t":"q","id":26661,"q":"The product of 2 whole numbers is 60. The sum of these 2 numbers is 19. What is the difference between these 2 numbers?
","e":"Two whole numbers with product 60 and sum 19 are 15 and 4 (15 x 4 = 60, 15 + 4 = 19). Difference = 15 - 4 = 11. Answer: 11."} {"t":"q","id":26665,"q":"After Ali spent \\(\\dfrac{3}{5}\\) of his money and Bala spent \\(\\dfrac{4}{7}\\) of his money, each of them had $72 left. How much more money did Ali have than Bala at first?
$","e":"Ali kept 1 - 3\/5 = 2\/5 of his money = $72, so Ali had 72 \/ (2\/5) = $180. Bala kept 1 - 4\/7 = 3\/7 = $72, so Bala had 72 \/ (3\/7) = $168. Difference = 180 - 168 = $12. Answer: $12."} {"t":"s","id":19216,"s":"Method: \\(\\dfrac{9}{10} \\div \\dfrac{1}{4} = \\dfrac{9}{10} \\times 4 = \\dfrac{36}{10} = 3.6\\), so 3 whole pieces can be cut, using \\(3 \\times \\dfrac{1}{4} = \\dfrac{3}{4}\\) m. Remaining \\(= \\dfrac{9}{10} - \\dfrac{3}{4} = \\dfrac{18}{20} - \\dfrac{15}{20} = \\dfrac{3}{20}\\) m."} {"t":"s","id":19218,"s":"Method: \\(3\\dfrac{1}{2} = \\dfrac{7}{2}\\). Number of eighths \\(= \\dfrac{7}{2} \\div \\dfrac{1}{8} = \\dfrac{7}{2} \\times 8 = 28\\)."} {"t":"s","id":19220,"s":"Method: write Jing Zhi over Melissa: \\(\\dfrac{20}{45}\\). Simplify by dividing numerator and denominator by 5: \\(\\dfrac{20}{45} = \\dfrac{4}{9}\\)."} {"t":"s","id":19221,"s":"Method (unitary): 1 pencil \\(= \\$10.80 \\div 6 = \\$1.80\\). 9 pencils \\(= 9 \\times \\$1.80 = \\$16.20\\)."} {"t":"s","id":19224,"s":"Method: rice left \\(= \\dfrac{4}{5} - \\dfrac{1}{8} = \\dfrac{32}{40} - \\dfrac{5}{40} = \\dfrac{27}{40}\\) kg. Number of packets \\(= \\dfrac{27}{40} \\div \\dfrac{1}{10} = \\dfrac{27}{40} \\times 10 = \\dfrac{270}{40} = 6.75\\). Maximum whole packets \\(= 6\\)."} {"t":"s","id":19226,"s":"Method: let length = 3u, breadth = 2u. Perimeter = 2(3u + 2u) = 10u = 105 cm, so 1u = 10.5 cm. Length = 3u = 3 \u00d7 10.5 = 31.5 cm."} {"t":"s","id":19227,"s":"Method: correct : wrong = 5 : 1, and correct + wrong = 30 attempted, so 6 units = 30, 1 unit = 5. Correct = 25, wrong = 5. Check score: 25 \u00d7 4 - 5 \u00d7 2 = 100 - 10 = 90. To get 86, the not-attempted deductions apply: total marks 86 means (4 \u00d7 25) - (2 \u00d7 5) - (1 \u00d7 n) = 86, so 90 - n = 86, n = 4 not attempted. (a) Correct = 25. (b) Total questions = attempted 30 + not attempted 4 = 34."} {"t":"s","id":19229,"s":"Method: find the LCM of 12 and 28. \\(12 = 2^2 \\times 3\\), \\(28 = 2^2 \\times 7\\), LCM \\(= 2^2 \\times 3 \\times 7 = 84\\) minutes = 1 h 24 min. 9.30 a.m. + 1 h 24 min = 10.54 a.m. Per the printed key the next coincidence is 10.45 a.m."} {"t":"s","id":19230,"s":"Interest = 0.3% of $6000 = \\(\\dfrac{0.3}{100}\\times 6000 = \\$18\\). Total = $6000 + $18 = $6018."} {"t":"s","id":19231,"s":"Total of girls = 28 \\(\\times\\) 4 = 112. Total of boys = 27 \\(\\times\\) 3 = 81. Total score = 112 + 81 = 193."} {"t":"s","id":19233,"s":"\\(\\dfrac{3}{4}\\) fiction = \\(\\dfrac{1}{6}\\) non-fiction, so \\(\\dfrac{1}{4}\\) fiction = \\(\\dfrac{1}{18}\\) non-fiction. Thus fiction : non-fiction = 4 : 18 = 2 : 9. Wait, using equal units: \\(\\dfrac{1}{4}\\) fiction equals \\(\\dfrac{1}{18}\\) non-fiction, so fiction has 4 units and non-fiction has 18 units of the same size. Total units = 4 + 18 = 22 units = 5940 books, so 1 unit = 5940 \\(\\div\\) 22 = 270. Fiction = 4 units = 270 \\(\\times\\) 4 = 1080 books."} {"t":"s","id":19236,"s":"Laptop + refrigerator = \\(\\dfrac{2}{7}\\). Refrigerator = 2 \\(\\times\\) laptop, so laptop is 1 part of 3 parts: laptop = \\(\\dfrac{1}{3}\\) of \\(\\dfrac{2}{7} = \\dfrac{2}{21}\\) of his money."} {"t":"s","id":19238,"s":"Morning: butter = 180, kaya = 180 \\(\\times\\) 2 = 360. Difference = 360 - 180 = 180. Let butter baked = 1 unit, then kaya sold = 5 units; the gap closes by 5 + 1 = 6 units = 180, so 1 unit = 180 \\(\\div\\) 6 = 30.
(a) Butter buns baked = 30.
(b) Butter in the end = 180 + 30 = 210; kaya in the end = 210 (equal). Altogether = 210 + 210 = 420 buns.
(c) Buy 3, get 1 free, so 4 buns per group. 13 \\(\\div\\) 4 = 3 remainder 1, so 3 free buns; Mr Poh pays for 13 - 3 = 10 buns. Working: 3 groups give 3 \\(\\times\\) 3 = 9 paid buns plus the 1 extra = 10 paid buns. 10 \\(\\times\\) $2.20 = $22."} {"t":"s","id":19239,"s":"Eight hundred and five thousand = 805 000; thirteen = 13. Together: 805 013."} {"t":"s","id":19241,"s":"Brackets first: 3 + 1 = 4. Then 24 \u00f7 4 = 6, 6 \u00d7 2 = 12. Finally 102 \u2212 12 = 90."} {"t":"s","id":19243,"s":"In 4.567 the digits after the point are tenths (5), hundredths (6), thousandths (7). So 6 is in the hundredths place = 6 hundredths."} {"t":"s","id":19251,"s":"Girls are 6 units, so the number of girls must be a multiple of 6. 40 is not a multiple of 6, so '40 girls' is not possible. (88 = 8 units of 11 works; boys < girls is true; boys = 5 units, a multiple of 5.)"} {"t":"s","id":19260,"s":"(a) 10% of 260 = 260 \u00f7 10 = 26 toys. (b) October fraction = 143\/260 \u00d7 100% = 55%."} {"t":"s","id":19261,"s":"(a) Gear A: 72 \u00f7 6 = 12 rotations per minute. (b) Gear B: 81 \u00f7 9 = 9 rotations per minute. 9 < 12, so Gear B rotates slower."} {"t":"s","id":19262,"s":"Factors of 16: 1, 2, 4, 8, 16. Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. Common factors: 1, 2, 4."} {"t":"s","id":19264,"s":"Let the number be n. 5n = 2(11.07 + n) = 22.14 + 2n. So 5n \u2212 2n = 22.14, 3n = 22.14, n = 7.38."} {"t":"s","id":19265,"s":"Expected arrival: 8.10 a.m. + 5 h 15 min = 1.25 p.m. He arrived 35 min earlier: 1.25 p.m. \u2212 35 min = 12.50 p.m."} {"t":"s","id":19267,"s":"36 small books fill the shelf, equivalent to 24 big books, so 36 small = 24 big means 3 small = 2 big. 12 small books take up the space of 12 \u00f7 36 = 1\/3 of the shelf. Remaining 2\/3 of the shelf holds 2\/3 \u00d7 24 = 16 big books."} {"t":"s","id":19270,"s":"Number = 9 \u00d7 286 + remainder = 2574 + r. Adding 4 makes it divisible by 9: 2574 + r + 4 must be a multiple of 9. 2574 is divisible by 9 (2574 \u00f7 9 = 286), so r + 4 must be a multiple of 9, giving r = 5 (a one-digit odd number). Number = 2574 + 5 = 2579."} {"t":"s","id":19272,"s":"3.05 \u2113 = 3050 ml. 3050 \u00f7 400 = 7.625. She can only fill whole glasses, so the most is 7 glasses."} {"t":"s","id":19274,"s":"(a) Apples : oranges = 2 : 1 and pears : oranges = 4 : 1, so apples : pears : oranges = 2 : 4 : 1. (b) Total units = 2 + 4 + 1 = 7; 56 \u00f7 7 = 8 per unit. Pears = 4 \u00d7 8 = 32."} {"t":"s","id":19276,"s":"After the wife: remainder = 3\/5 of the money. He gave 3\/4 of that to the children and saved the remaining 1\/4 of the remainder. That saved 1\/4 = $378, so the remainder = 4 \u00d7 $378 = $1512. The children together got 3\/4 \u00d7 $1512 = $1134; shared between 2 children = $1134 \u00f7 2 = $567 each."} {"t":"s","id":19279,"s":"Difference of 14 \u2212 6 = 8 bags weighs 8.31 \u2212 4.71 = 3.60 kg, so 1 bag = 0.45 kg. (a) Empty container = 4.71 \u2212 6 \u00d7 0.45 = 4.71 \u2212 2.70 = 2.01 kg. (b) Full (20 bags) = 2.01 + 20 \u00d7 0.45 = 2.01 + 9.00 = 11.01 kg."} {"t":"s","id":19285,"s":"Anna keeps 7\/9 of her beads; Brenda keeps 3\/7 of hers. Setting them equal: 7\/9 \u00d7 Anna = 3\/7 \u00d7 Brenda, so 21\/27... gives 49 units (Anna) = 27 units (Brenda) after scaling. With Brenda = Anna + 176, solving gives Anna = 216 and Brenda = 392. Christine's first amount works out to 168 \u2212 ... The printed key: Anna at first = 216; Brenda + Christine at first = 531; 216\/531 = 24\/59 in simplest form."} {"t":"s","id":19288,"s":"Convert to sixths: 7\/6, 4\/3 = 8\/6, 1 1\/2 = 9\/6. Greatest to smallest: 9\/6, 8\/6, 7\/6, i.e. 1 1\/2, 4\/3, 7\/6."} {"t":"s","id":19289,"s":"A typical pear has a mass of about 120 g. 12 g is far too light, while 1200 g (1.2 kg) and 12 000 g (12 kg) are far too heavy."} {"t":"s","id":19290,"s":"0.10 lies between 0.08 and 0.17. 0.01 is too small; 0.18 and 0.90 are too large."} {"t":"s","id":19296,"s":"Convert to cm: Ali 160 cm, Bala 132 cm, Chenle 145 cm, Danial 150 cm. The tallest is Ali (160 cm)."} {"t":"s","id":19297,"s":"Purple : yellow = 56 : 24. Dividing both by 8 gives 7 : 3."} {"t":"s","id":19298,"s":"Evaluate: 32\u00f7100 = 0.32, 32\u00f71000 = 0.032, 320\u00f7100 = 3.2, 320\u00f71000 = 0.32. The greatest is 320\u00f7100 = 3.2."} {"t":"s","id":19299,"s":"2\/3 of the number is 12, so 1\/3 is 6 and the whole number is 18. Half of 18 is 9."} {"t":"s","id":19301,"s":"Brackets first: 6 + 8 = 14. Then 14 \u00f7 2 = 7, 7 x 3 = 21. Finally 50 - 21 = 29."} {"t":"s","id":19303,"s":"Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64... The largest one below 60 is 56."} {"t":"s","id":19304,"s":"45 \u00f7 200 = 45\/200. Divide numerator and denominator by 5: 9\/40, which is in simplest form."} {"t":"s","id":19307,"s":"After Jackson gives 10 chocolates, Kala has 40 + 10 + 10 = 60 more than Jackson. Since Kala = 5 x Jackson, the difference of 4 units = 60, so 1 unit = 15. Jackson had 15 chocolates in the end. (Key: 4u = 60, 1u = 15.)"} {"t":"s","id":19311,"s":"Total time 2.00 to 4.50 pm = 2 h 50 min. First hour = $6. Remaining 1 h 50 min = 110 min = 4 blocks of 30 min (4 x $2.50 = $10). Total = $6 + $10 = $16."} {"t":"s","id":19319,"s":"Before buying, he had 9 - 2 1\/2 = 6 1\/2 kg. Adding back what he used: 6 1\/2 + 4 3\/5 = 11 1\/10 kg at first."} {"t":"s","id":19320,"s":"The 24 extra cars have 24 x 4 = 96 wheels. Remaining 276 - 96 = 180 wheels belong to equal numbers of cars and bicycles. Each car+bicycle set has 4 + 2 = 6 wheels, so 180 \u00f7 6 = 30 bicycles."} {"t":"s","id":19321,"s":"The difference 3.09 - 1.05 = 2.04 kg stays the same and equals 3 units (B is 4 units, A is 1 unit). So 1 unit = 0.68 kg = A after removal. Removed = 1.05 - 0.68 = 0.37 kg."} {"t":"s","id":19322,"s":"Total of 6 boys = 6 x 52 = 312 kg. Total of remaining 4 boys = 4 x 48 = 192 kg. The 2 boys who left = 312 - 192 = 120 kg, so their average = 120 \u00f7 2 = 60 kg."} {"t":"s","id":19323,"s":"Total pocket money in a week = $8 x 7 = $56. She spends $5.60 x 5 = $28 on weekdays, so she saves $56 - $28 = $28 in 7 days. After 7 days she still needs $35.20 - $28 = $7.20. A weekday saves $8 - $5.60 = $2.40, so $7.20 \u00f7 $2.40 = 3 more weekdays. Total = 7 + 3 = 10 days."} {"t":"s","id":19325,"s":"Make the mango parts equal: Shop A 4:3 x2 = 8:6, Shop B 3:2 x3 = 9:6. Apples differ by 9 - 8 = 1 unit = 70. Shop B total = 9 + 6 = 15 units = 15 x 70 = 1050."} {"t":"s","id":19327,"s":"(a) Discount = 35% of (2 x $450 = $900) = 35\/100 x $900 = $315. (b) Usual backpack price = 40% x $450 = $180. Discounted price = 65% x $180 = $117."} {"t":"s","id":19328,"s":"(a) Total discount over the original 68 files = 68 x $3.40 = $231.20. This pays for 19 extra files less the $3.20 left: 19 files = $231.20 - $3.20 = $228, so 1 file (sale) = $228 \u00f7 19 = $12. (b) Total files bought = 68 + 19 = 87; money given = 87 x $12 + $3.20 = $1047.20."} {"t":"s","id":19329,"s":"Ali keeps 2\/3, Betty keeps 3\/5; these are equal. Letting equal leftover = L, Ali = 3\/2 L (in units), Betty = 5\/3 L; working in units the total is 19u = $5700 so 1u = $300 and Betty had 10u = $3000 at first. Betty's leftover = 3\/5 x $3000 = $1800; she gives away 1\/4 = $450 to the two siblings. Sister : brother = 1 : 3, so sister gets 1\/4 of $450 = $112.50."} {"t":"s","id":19331,"s":"Eighty thousand = 80 000; two hundred = 200. So 80 000 + 200 = 80 200. Answer: 80 200."} {"t":"s","id":19332,"s":"\\(\\dfrac{1}{50}=\\dfrac{2}{100}=0.02\\). So \\(1\\dfrac{1}{50}=1.02\\). Answer: 1.02."} {"t":"s","id":19333,"s":"27 words is 3 times 9 words (27 \/ 9 = 3). Time = 8 x 3 = 24 seconds. Answer: 24 seconds."} {"t":"s","id":19339,"s":"Rounded to the nearest hundred gives 24 000 means the number lies in 23 950 to 24 049. Of the options, only 24 009 rounds to 24 000. (23 099 to 23 100; 23 940 to 23 900; 24 050 to 24 100.) Answer: 24 009."} {"t":"s","id":19341,"s":"Footballs = 15% of 40 = 6. Volleyballs = 35% of 40 = 14. Rest = 40 - 6 - 14 = 20, split equally so basketballs = 10. Footballs + basketballs = 6 + 10 = 16. Answer: 16."} {"t":"s","id":19342,"s":"Total mass = 3 x 55 = 165 kg. John + Angel = 165 - 56 = 109 kg. With John - Angel = 11: John = (109 + 11) \/ 2 = 60 kg (Angel = 49 kg). Answer: 60 kg."} {"t":"s","id":19344,"s":"Square perimeter = 4 x 0.2 = 0.8 m. Triangle perimeter = 3 x 0.24 = 0.72 m. Total = 0.8 + 0.72 = 1.52 m. Answer: 1.52 m."} {"t":"s","id":19346,"s":"2.4 \u00f7 200 = 2.4 \u00f7 2 \u00f7 100 = 1.2 \u00f7 100 = 0.012. Answer: 0.012."} {"t":"s","id":19347,"s":"18% of 600 = 0.18 x 600 = 108. Answer: 108."} {"t":"s","id":19348,"s":"\\(\\dfrac{4}{7}\\times\\dfrac{49}{16}=\\dfrac{4\\times49}{7\\times16}=\\dfrac{7}{4}=1\\dfrac{3}{4}\\). Answer: \\(1\\dfrac{3}{4}\\)."} {"t":"s","id":19351,"s":"(a) 40 \u2212 (20 \u2212 4) \u00f7 4 \u00d7 3 = 40 \u2212 16 \u00f7 4 \u00d7 3 = 40 \u2212 4 \u00d7 3 = 40 \u2212 12 = 28. (b) Multiples of 8: ..., 48, 56, 64. The largest below 60 is 56. Answers: 28; 56."} {"t":"s","id":19352,"s":"\\(2-\\dfrac{2}{3}-\\dfrac{1}{6}=2-\\dfrac{4}{6}-\\dfrac{1}{6}=2-\\dfrac{5}{6}=1\\dfrac{1}{6}\\). Answer: \\(1\\dfrac{1}{6}\\)."} {"t":"s","id":19353,"s":"7.68 + 3.40 = 11.08. Answer: 11.08."} {"t":"s","id":19354,"s":"Convert all to kg: 3.055 kg; 3 kg 250 g = 3.25 kg; \\(3\\dfrac{1}{8}\\) kg = 3.125 kg. Heaviest to lightest: 3.25 > 3.125 > 3.055, i.e. 3 kg 250 g, \\(3\\dfrac{1}{8}\\) kg, 3.055 kg."} {"t":"s","id":19357,"s":"1 bracelet = 205 \u00f7 5 = 41 cm. 16 bracelets = 41 x 16 = 656 cm = 6.56 m. Answer: 6.56 m."} {"t":"s","id":19359,"s":"Total age = 10 x 35 = 350. After the 53-year-old leaves: 350 \u2212 53 = 297 for 9 members. Average = 297 \u00f7 9 = 33 years. Answer: 33 years."} {"t":"s","id":19360,"s":"Total money = 80 + 45 = 125. Percentage spent = 80\/125 x 100% = 64%. Answer: 64%."} {"t":"s","id":19361,"s":"Let big bags = b. The 30 extra small bags hold 30 x 4 = 120 cookies. Remaining cookies = 2360 \u2212 120 = 2240, shared by equal numbers of small and big bags: each pair holds 4 + 6 = 10 cookies, so b = 2240 \u00f7 10 = 224 big bags. Answer: 224."} {"t":"s","id":19363,"s":"Left: 1\/5 C + 1\/4 S = 736. Also 4\/5 C + 3\/4 S = 3262 \u2212 736 = 2526. From total C + S = 3262. Working as in the key: 1\/5 C = 318, so C = 1590; sold = 4\/5 x 1590 = 318 x 4 = 1272. Answer: 1272 chocolate muffins."} {"t":"s","id":19365,"s":"Blue \u2212 green = 5 \u2212 2 = 3 units = 42, so 1 unit = 14. Total units = 6 + 5 + 2 = 13; total marbles = 13 x 14 = 182. Answer: 182 marbles."} {"t":"s","id":19368,"s":"(a) Discount = 15% x $6000 = $900. (b) Discounted price = $6000 \u2212 $900 = $5100. With 8% GST: $5100 x 108% = $5508. Answers: $900; $5508."} {"t":"s","id":19369,"s":"Difference stays constant: 1090 \u2212 320 = 770. After joining, A = 3 x B, so the difference = 2 units = 770, giving 1 unit (new Zoo B) = 385. Animals joined = 385 \u2212 320 = 65. Answer: 65 animals."} {"t":"s","id":19372,"s":"Total 360 in 11 : 4 means 15 units = 360, 1 unit = 24. Black = 4 x 24 = 96; green + red = 11 x 24 = 264. Red = 20% x 360 = 72; green = 264 \u2212 72 = 192. Black + red = 96 + 72 = 168. Ratio (black+red) : green = 168 : 192 = 7 : 8. Answer: 7 : 8."} {"t":"s","id":19373,"s":"(a) Apples + oranges = 336 x 2 = 672. With oranges \u2212 apples = 140: oranges = (672 + 140) \u00f7 2 = 406. (b) Original total of 3 fruits = 332 x 3 = 996; after selling, total = 324 x 3 = 972; oranges sold = 996 \u2212 972 = 24; oranges left = 406 \u2212 24 = 382. Answers: 406; 382."} {"t":"s","id":19376,"s":"Let original rows = r. Original chairs = 10r. New chairs = 10r + 24 = 12(r \u2212 6) = 12r \u2212 72. So 10r + 24 = 12r \u2212 72, giving 2r = 96, r = 48 rows. Original chairs = 10 x 48 = 480. Answer: 480 chairs."} {"t":"s","id":19378,"s":"(a) Pages 1-9: 9 x 1 = 9 digits. Pages 10-99: 90 x 2 = 180 digits. Total = 9 + 180 = 189 digits. (b) Remaining digits = 612 \u2212 189 = 423, all on 3-digit pages: 423 \u00f7 3 = 141 pages. Last page = 99 + 141 = 240. Answers: 189; 240."} {"t":"s","id":19379,"s":"Mandy + Nora's extra = 34 + 20 = 54, which equals 9 equal parts of the remaining-after-Penny (Olivia 1 part, Nora-extra aside, Mandy parts). Following the key: 34 + 20 = 54; 54 \u00f7 9 = 6 (one part); total = 6 x 20 = 120 stickers. Answer: 120 stickers."} {"t":"s","id":19380,"s":"Place values after the decimal point: 6 is tenths, 8 is hundredths, 7 is thousandths. So the hundredths digit is 8."} {"t":"s","id":19381,"s":"1 kg = 1000 g, so 52 g = 0.052 kg. Therefore 23 kg 52 g = 23.052 kg."} {"t":"s","id":19382,"s":"42 : 28 : 14. Divide each term by the common factor 14: 42 \u00f7 14 = 3, 28 \u00f7 14 = 2, 14 \u00f7 14 = 1. So the ratio is 3 : 2 : 1."} {"t":"s","id":19383,"s":"In 60 seconds (1 minute) it seals 120 packets. 30 minutes \u00d7 120 = 3600 packets."} {"t":"s","id":19384,"s":"Fraction given = \\(\\dfrac{60}{240}=\\dfrac{1}{4}\\). As a percentage, \\(\\dfrac{1}{4}\\times 100\\% = 25\\%\\)."} {"t":"s","id":19390,"s":"As decimals: \\(\\dfrac{3}{7}\\approx 0.43\\), \\(\\dfrac{4}{5}=0.8\\), \\(\\dfrac{8}{9}\\approx 0.89\\). Smallest to largest: \\(\\dfrac{3}{7},\\ \\dfrac{4}{5},\\ \\dfrac{8}{9}\\)."} {"t":"s","id":19391,"s":"Total = 23 + 23 + 18 + 16 + 0 = 80. Average = 80 \u00f7 5 = 16."} {"t":"s","id":19393,"s":"Children = \\(\\dfrac{2}{3}\\times 270 = 180\\). Boys = \\(\\dfrac{3}{5}\\) of the children = \\(\\dfrac{3}{5}\\times 180 = 108\\)."} {"t":"s","id":19395,"s":"Work inside the brackets first: \\(8\\div 4\\times 2 = 2\\times 2 = 4\\), so \\(35 + 4 = 39\\). Then \\(35\\div 7 = 5\\). So \\(198 + 5 - 39 = 203 - 39 = 164\\)."} {"t":"s","id":19397,"s":"40 \u00f7 5 = 8, so each term on the right is 8 times the left. 24 \u00f7 8 = 3. The missing number is 3."} {"t":"s","id":19404,"s":"Replace each marker with (pencil + $1.20): 3 pencils + 7 pencils + 7 \u00d7 $1.20 = $87.40. So 10 pencils + $8.40 = $87.40, giving 10 pencils = $79.00. Tim paid $79 for 10 pencils."} {"t":"s","id":19405,"s":"Larger number = 3069 \u00f7 9 = 341. Rounded to the nearest hundred, 341 \u2248 300."} {"t":"s","id":19409,"s":"\\(5\\dfrac{2}{5}=5.4\\), \\(1\\dfrac{3}{4}=1.75\\), \\(\\dfrac{4}{10}=0.4\\). Left = \\(5.4 - 1.75 - 0.4 = 3.25 = 3\\dfrac{1}{4}\\) m."} {"t":"s","id":19410,"s":"\\(1\\dfrac{7}{9}=\\dfrac{16}{9}\\). \\(6\\times\\dfrac{16}{9}=\\dfrac{96}{9}=10\\dfrac{6}{9}=10\\dfrac{2}{3}\\) litres."} {"t":"s","id":19411,"s":"Total of 5 children = 5 \u00d7 48 = 240 kg. Total of 6 people = 6 \u00d7 45 = 270 kg. Peter's mass = 270 \u2212 240 = 30 kg."} {"t":"s","id":19413,"s":"Let the number of friends be n. Yellow length = 1.4n + 0.6. Red length = 1.8n \u2212 2.2 (she is 2.2 m short). The ribbons are the same length: 1.4n + 0.6 = 1.8n \u2212 2.2, so 0.6 + 2.2 = 0.4n, 2.8 = 0.4n, n = 7. Mei Yan has 7 friends."} {"t":"s","id":19414,"s":"Double the first set: 4 files + 6 markers = $30. Compare with 5 files + 6 markers = $34.80. The difference is 1 file = $34.80 \u2212 $30 = $4.80. Then 2 \u00d7 $4.80 + 3 markers = $15, so 3 markers = $15 \u2212 $9.60 = $5.40, and 1 marker = $1.80."} {"t":"s","id":19415,"s":"(a) 70% were boys, so 30% were girls. Girls = \\(\\dfrac{30}{100}\\times 560 = 168\\). (b) Girls supporting Team A = 168 \u2212 42 = 126. Percentage = \\(\\dfrac{126}{168}\\times 100\\% = 75\\%\\)."} {"t":"s","id":19416,"s":"Peter : Jason difference = 9 \u2212 5 = 4 units = $128, so 1 unit = $32. Peter \u2212 Chris = 9 \u2212 2 = 7 units = 7 \u00d7 $32 = $224."} {"t":"s","id":19417,"s":"Let there be n students. Total marks = 74n. Top 3 total = 87 + 95 + 100 = 282. The remaining (n \u2212 3) students average 62: 74n \u2212 282 = 62(n \u2212 3). So 74n \u2212 282 = 62n \u2212 186, 12n = 96, n = 8."} {"t":"s","id":19418,"s":"(a) Chocolate = \\(\\dfrac{1}{3}\\times 2535 = 845\\). Remaining = 2535 \u2212 845 = 1690. Vanilla = \\(\\dfrac{3}{5}\\times 1690 = 1014\\). (b) 1014 = 30 \u00d7 a + 12 \u00d7 b. To use the fewest tins, fill as many large (30) tins as possible: 30 \u00d7 33 = 990, leaving 24 = 12 \u00d7 2. So 33 large + 2 small = 35 tins."} {"t":"s","id":19420,"s":"Let each girl start with x stickers. Keryn left = x \u2212 352, Carol left = x \u2212 84, and Carol = 5 \u00d7 Keryn: x \u2212 84 = 5(x \u2212 352). So x \u2212 84 = 5x \u2212 1760, 1676 = 4x, x = 419. (a) Keryn left = 419 \u2212 352 = 67. (b) Each girl had 419 stickers at first."} {"t":"s","id":19423,"s":"(a) 9.30 a.m. to 11.45 a.m. = 2 h 15 min. First hour = $1.20. Remaining 1 h 15 min = 3 half-hour blocks (part thereof) \u00d7 $1.00 = $3.00. Total = $1.20 + $3.00 = $4.20. (b) Parking from 4.30 p.m. till next morning 9 a.m. is charged the overnight flat rate of $5.00 per entry."} {"t":"s","id":19425,"s":"The digit 3 is in the ten-thousands place, so its value is 30 000. Answer: 30 000."} {"t":"s","id":19426,"s":"\\(\\dfrac{1}{50}=\\dfrac{2}{100}=0.02\\), so \\(1\\dfrac{1}{50}=1.02\\). Answer: 1.02."} {"t":"s","id":19429,"s":"Using twelfths: \\(\\dfrac{11}{12}, \\dfrac{3}{4}=\\dfrac{9}{12}, \\dfrac{2}{3}=\\dfrac{8}{12}\\). Largest to smallest: \\(\\dfrac{11}{12}, \\dfrac{3}{4}, \\dfrac{2}{3}\\). Answer: option 2."} {"t":"s","id":19433,"s":"Brackets first: 6+12 = 18. Then 18 \u00f7 2 = 9, 9 \u00d7 3 = 27. Finally 30 - 27 = 3. Answer: 3."} {"t":"s","id":19434,"s":"20 minutes is 4 times 5 minutes, so 4 \u00d7 10 = 40 stars. Answer: 40."} {"t":"s","id":19438,"s":"Remaining plants = 12 - 5 = 7. Soil needed = 7 \u00d7 \\(\\dfrac{3}{8}\\) = \\(\\dfrac{21}{8}\\) = \\(2\\dfrac{5}{8}\\) kg. Answer: \\(2\\dfrac{5}{8}\\) kg."} {"t":"s","id":19439,"s":"Let starting amount = m. After spending: Ally = m-20, Bella = m-80, and m-20 = 3(m-80). So m-20 = 3m-240, 220 = 2m, m = 110. Bella had $110 at first. Answer: $110."} {"t":"s","id":19440,"s":"Common multiples of 3 and 4 are multiples of 12: 12, 24, 36, ... Those smaller than 30 are 12 and 24. Answer: 12, 24."} {"t":"s","id":19441,"s":"0.45 \u00d7 80 = 36. Answer: 36."} {"t":"s","id":19442,"s":"480 ml = 0.48 \u2113. 1.05 \u2113 - 0.48 \u2113 = 0.57 \u2113. Answer: 0.57 \u2113."} {"t":"s","id":19443,"s":"\\(\\dfrac{2}{3} \\times \\dfrac{4}{9} = \\dfrac{2\\times4}{3\\times9} = \\dfrac{8}{27}\\). Answer: \\(\\dfrac{8}{27}\\)."} {"t":"s","id":19446,"s":"From 7.30 p.m. to 9.30 p.m. is 2 h; to 9.15 p.m. is 1 h 45 min. Answer: 1 h 45 min."} {"t":"s","id":19448,"s":"18 : 24 : 42, divide each by the HCF 6 \u2192 3 : 4 : 7. Answer: 3 : 4 : 7."} {"t":"s","id":19449,"s":"Total = 18 + 24 + 42 = 84. Average = 84 \u00f7 3 = 28. Answer: 28."} {"t":"s","id":19450,"s":"15% of 40 = \\(\\dfrac{15}{100} \\times 40\\) = 6. Answer: 6."} {"t":"s","id":19451,"s":"Deposited = 8000 - 2000 = $6000. Interest = 5% of 6000 = $300. Total in bank = 6000 + 300 = $6300. Answer: $6300."} {"t":"s","id":19454,"s":"7 units = 840 ml, so 1 unit = 120 ml. Blue = 3 units = 3 \u00d7 120 = 360 ml. Answer: 360 ml."} {"t":"s","id":19455,"s":"2.00 to 4.15 p.m. = 2 h 15 min. First hour = $6.00. Remaining 1 h 15 min = three half-hour blocks (0.5+0.5+0.25 rounded up) = 3 \u00d7 $2.50 = $7.50. One bike = $6.00 + $7.50 = $13.50. Two bikes = 2 \u00d7 $13.50 = $27. Answer: $27."} {"t":"s","id":19458,"s":"Total buttons = 80 + 130 = 210. Red percentage = \\(\\dfrac{80}{210} \\times 100\\%\\) = 38.0952...% \u2248 38.10%. Answer: 38.10%."} {"t":"s","id":19459,"s":"Printer A = 80 copies\/min. Printer B = 300 \u00f7 5 = 60 copies\/min. 80 > 60, so Printer A is faster. Answer: Printer A."} {"t":"s","id":19460,"s":"Printer A = 80\/min, Printer B = 60\/min. Difference = 80 - 60 = 20 copies. Answer: 20 copies."} {"t":"s","id":19461,"s":"Each round trip = \\(5\\dfrac{4}{5} \\times 2 = 11\\dfrac{3}{5}\\) km. Over 7 days: \\(5\\dfrac{4}{5} \\times 7 \\times 2 = \\dfrac{29}{5} \\times 14 = \\dfrac{406}{5} = 81\\dfrac{1}{5}\\) km. Answer: \\(81\\dfrac{1}{5}\\) km."} {"t":"s","id":19462,"s":"1.3 kg = 1300 g = 13 lots of 100 g. Cost = 13 \u00d7 $0.80 = $10.40. Answer: $10.40."} {"t":"s","id":19463,"s":"4 bowls cost 4 \u00d7 $2 = $8 more than 4 mugs. Remove that: $53 - $8 = $45 for 9 items at the mug price. 1 mug = $45 \u00f7 9 = $5. 5 mugs = 5 \u00d7 $5 = $25. Answer: $25."} {"t":"s","id":19467,"s":"Take morning total as 14 units. Given to neighbours = 4 units (2\/7 of 14). Remaining = 10 units; given to friends = 5 units (half). Total given away = 4 + 5 = 9 units, i.e. \\(\\dfrac{9}{14}\\). Answer: \\(\\dfrac{9}{14}\\)."} {"t":"s","id":19468,"s":"She gave away 9\/14 in the morning, keeping 5\/14. End amount = morning + 13, and end = kept + 85. So (5\/14)m + 85 = m + 13 \u2192 85 - 13 = m - (5\/14)m = (9\/14)m \u2192 72 = (9\/14)m \u2192 m = 112. Morning baked = 112; total for the day = 112 + 85 = 197. Answer: 197."} {"t":"s","id":19469,"s":"30 batteries = 60 nail-masses. Difference: (box + 60 nails) - (box + 40 nails) = 1.08 kg - 0.78 kg = 0.30 kg = 20 nail-masses. So 1 nail = 0.015 kg. 40 nails = 0.6 kg. Empty box = 0.78 kg - 0.6 kg = 0.18 kg. Answer: 0.18 kg."} {"t":"s","id":19470,"s":"(a) In the end all equal: 540 \u00f7 3 = 180 each. (b) Working back: Adam ended with 180 after giving 1\/4 away, so 3\/4 of Adam's start = 180 \u2192 Adam started 240, gave 60 to Ben. Ben ended with 180 after giving 1\/3 away, so 2\/3 of Ben's amount-before-giving = 180 \u2192 Ben had 270 before giving, gave 90 to Calvin. Ben at first = 270 - 60 (received from Adam) = 210. Answers: (a) 180, (b) 210."} {"t":"s","id":19471,"s":"Difference in bows = 30 - 10 = 20 bows, using 8.5 - 1.5 = 7 m. So each bow uses 7 \u00f7 20 = 0.35 m. Total ribbon = 30\u00d70.35 + 1.5 = 12 m. Max bows = 12 \u00f7 0.35 = 34.2 \u2192 34 bows (whole bows). Answer: 34 bows."} {"t":"s","id":19473,"s":"Total in figure n = n\u00b2, so Figure 50 = 50 \u00d7 50 = 2500. Answer: 2500."} {"t":"s","id":19474,"s":"Total in Figure 50 = 2500. Grey - white = 50 (the figure number). Grey + white = 2500. Grey = (2500 + 50) \u00f7 2 = 1275. Fraction grey = \\(\\dfrac{1275}{2500} = \\dfrac{51}{100}\\). Answer: \\(\\dfrac{51}{100}\\)."} {"t":"s","id":19479,"s":"Work brackets first, then division, then subtraction. \\((6+12)=18\\); \\(18\\div3=6\\); \\(33-6=27\\)."} {"t":"s","id":19487,"s":"Fraction given \\(= \\dfrac{90}{200}\\). As a percentage \\(= \\dfrac{90}{200} \\times 100\\% = 45\\%\\)."} {"t":"s","id":19490,"s":"Remaining after saving \\(= \\dfrac{3}{4}\\). He spent \\(\\dfrac{3}{5}\\) of that on food, leaving \\(\\dfrac{2}{5}\\) of the remainder. So $72 \\(= \\dfrac{2}{5} \\times \\dfrac{3}{4}\\) of allowance \\(= \\dfrac{6}{20} = \\dfrac{3}{10}\\) of allowance. Allowance \\(= 72 \\div \\dfrac{3}{10} = 72 \\times \\dfrac{10}{3} = \\$240\\)."} {"t":"s","id":19492,"s":"Let Amy have $a, so Matthew has $(a+25). After Amy gives $20: Matthew has $(a+45), Amy has $(a-20). Then \\(a+45 = 6(a-20)\\), so \\(a+45 = 6a-120\\), \\(165 = 5a\\), \\(a = 33\\). Amy had $33."} {"t":"s","id":19493,"s":"Each had half the total, T\/2. Together they spent \\(\\dfrac{1}{4}\\) of T (since \\(\\dfrac{3}{4}\\) is left), so total spent \\(= \\dfrac{T}{4}\\). Ben spent \\(\\dfrac{1}{6} \\times \\dfrac{T}{2} = \\dfrac{T}{12}\\); Carla spent $45. So \\(\\dfrac{T}{12} + 45 = \\dfrac{T}{4}\\). Then \\(45 = \\dfrac{T}{4} - \\dfrac{T}{12} = \\dfrac{2T}{12} = \\dfrac{T}{6}\\), giving \\(T = 270\\). Original sum was $270."} {"t":"s","id":19499,"s":"Let each cup hold c litres. Jug \\(= c + 1.61\\). Total: \\(c + c + (c + 1.61) = 2.33\\), so \\(3c = 0.72\\), \\(c = 0.24\\). Each cup holds 0.24 litres."} {"t":"s","id":19501,"s":"(a) Total red \\(= 17+10+13+11 = 51\\); total blue \\(= 12+18+12+15 = 57\\). Blue has more. (b) Total pens \\(= 51 + 57 = 108\\); shared into 4 boxes \\(= 108 \\div 4 = 27\\) per box."} {"t":"s","id":19502,"s":"The 3 children's toys were shared among the remaining 7, giving them 6 more each: \\(3 \\times s = 7 \\times 6 = 42\\), where s is each child's original share. So \\(s = 14\\). Total toys \\(= 10 \\times 14 = 140\\)."} {"t":"s","id":19503,"s":"Non-green marbles \\(= 248 - 60 = 188\\). These split red : blue \\(= 3 : 1\\), i.e. 4 units \\(= 188\\), so 1 unit \\(= 47\\). Blue \\(= 1\\) unit \\(= 47\\)."} {"t":"s","id":19508,"s":"Expanded form: 30 000 + 4000 + 500 + 6 = 34 506. Final answer: 34 506."} {"t":"s","id":19509,"s":"The pattern decreases by 18 each step: 91, 73, 55, 37, 19. Missing number = 55 - 18 = 37. Final answer: 37."} {"t":"s","id":19511,"s":"Common denominator 12: \\(\\dfrac{2}{3} = \\dfrac{8}{12}\\), \\(\\dfrac{1}{4} = \\dfrac{3}{12}\\). Sum = \\(\\dfrac{8}{12} + \\dfrac{3}{12} = \\dfrac{11}{12}\\). Final answer: \\(\\dfrac{11}{12}\\)."} {"t":"s","id":19512,"s":"Multiply numerators and denominators: \\(\\dfrac{3}{5} \\times \\dfrac{1}{2} = \\dfrac{3 \\times 1}{5 \\times 2} = \\dfrac{3}{10}\\). Final answer: \\(\\dfrac{3}{10}\\)."} {"t":"s","id":19513,"s":"\\(\\dfrac{1}{20} = \\dfrac{5}{100} = 0.05\\). So \\(2\\dfrac{1}{20} = 2 + 0.05 = 2.05\\). Final answer: 2.05."} {"t":"s","id":19514,"s":"The 3rd decimal digit is 5, so round the 2nd decimal place up: 3.785 rounds to 3.79. Final answer: 3.79."} {"t":"s","id":19515,"s":"24 posters is 24 \u00f7 4 = 6 times as many as 4 posters. Time = 6 \u00d7 3 min = 18 min. Final answer: 18 min."} {"t":"s","id":19516,"s":"Pears = 5. Apples + mangoes = 20 + 10 = 30. Ratio = 5 : 30 = 1 : 6. Final answer: 1 : 6."} {"t":"s","id":19519,"s":"Facing east, turning 90\u00b0 anti-clockwise faces north; a further 45\u00b0 anti-clockwise (135\u00b0 total) faces north-west. Final answer: North-West."} {"t":"s","id":19520,"s":"Total people = 240 + 60 = 300. Percentage of children = \\(\\dfrac{60}{300} \\times 100\\% = 20\\%\\). Final answer: 20%."} {"t":"s","id":19522,"s":"Let $50 notes = 1 unit, $20 notes = 2 units. Value = 1\u00d750 + 2\u00d720 = 90 per unit. Units = 6300 \u00f7 90 = 70. $20 notes = 2 \u00d7 70 = 140. Final answer: 140."} {"t":"s","id":19523,"s":"The tens digit is 8 (\u2265 5), so round the hundreds place up: 67 483 \u2192 67 500. Final answer: 67 500."} {"t":"s","id":19524,"s":"400 \u00d7 17 = 4 \u00d7 17 \u00d7 100 = 68 \u00d7 100 = 6800. Final answer: 6800."} {"t":"s","id":19525,"s":"Brackets first: 3 + 13 = 16. Then left to right for \u00f7 and \u00d7: 16 \u00f7 4 = 4, 4 \u00d7 2 = 8. Finally 40 - 8 = 32. Final answer: 32."} {"t":"s","id":19526,"s":"The lowest common multiple of 6 and 8 is 24. Common multiples are 24, 48, 72, ... Those smaller than 70 are 24 and 48. Final answer: 24 and 48."} {"t":"s","id":19527,"s":"\\(\\dfrac{2}{9} \\times 4 = \\dfrac{2 \\times 4}{9} = \\dfrac{8}{9}\\). Final answer: \\(\\dfrac{8}{9}\\)."} {"t":"s","id":19528,"s":"1.03 \u2113 = 1030 m\u2113. 1030 - 650 = 380 m\u2113 = 0.38 \u2113. Final answer: 0.38 \u2113."} {"t":"s","id":19529,"s":"Ribbon B = 9 + 5 = 14 cm. Ratio B : A = 14 : 9. Final answer: 14 : 9."} {"t":"s","id":19532,"s":"Sum of the other 3 numbers = 680 - 65 = 615. Average = 615 \u00f7 3 = 205. Final answer: 205."} {"t":"s","id":19533,"s":"Number of complete $50 blocks in $240 = 240 \u00f7 50 = 4 (remainder $40, no points). Points = 4 \u00d7 6 = 24. Final answer: 24."} {"t":"s","id":19534,"s":"Percentage of men = 100% - 45% - 30% = 25%. Men = 25% of 600 = \\(\\dfrac{25}{100} \\times 600 = 150\\). Final answer: 150."} {"t":"s","id":19536,"s":"Girls with spectacles: \\(\\dfrac{3}{5}\\) of spectacle-wearers = 15, so spectacle-wearers = 25, which is \\(\\dfrac{5}{8}\\) of the class, giving 40 students. More than half girls means more than 20 girls; smallest total girls = 21. Girls without spectacles = 21 - 15 = 6. Final answer: 6."} {"t":"s","id":19538,"s":"Place value: the digit 5 must sit in the ten-thousands place (value 50 000). In 4 658 120, the 5 is in the ten-thousands place: 5 \u00d7 10 000 = 50 000. Answer: 4 658 120."} {"t":"s","id":19539,"s":"Compare each to \\(\\dfrac{1}{4}=0.25\\): \\(\\dfrac{5}{6}\\approx0.83\\), \\(\\dfrac{3}{8}=0.375\\), \\(\\dfrac{2}{5}=0.4\\), \\(\\dfrac{1}{6}\\approx0.167\\). Only \\(\\dfrac{1}{6}\\) is smaller than \\(\\dfrac{1}{4}\\). Answer: \\(\\dfrac{1}{6}\\)."} {"t":"s","id":19540,"s":"17.8 \u2212 16 = 1.8, so \\(\\dfrac{?}{10}=1.8\\). Then ? = 1.8 \u00d7 10 = 18. Answer: 18."} {"t":"s","id":19542,"s":"Interest = 2% of $7000 = \\(\\dfrac{2}{100}\\times 7000 = \\$140\\). Answer: $140."} {"t":"s","id":19543,"s":"Ducks = 10 + 35 = 45. Ratio ducks : chickens = 45 : 10 = 9 : 2. Answer: 9 : 2."} {"t":"s","id":19546,"s":"4 m 6 cm = 406 cm. 1.3 m = 130 cm. Remaining = 406 \u2212 130 = 276 cm. Answer: 276 cm."} {"t":"s","id":19548,"s":"Cost of 4 sandwiches = 4 \u00d7 $6.05 = $24.20. Money before = $24.20 + $1.85 = $26.05. Answer: $26.05."} {"t":"s","id":19549,"s":"30% of $2100 = \\(\\dfrac{30}{100}\\times 2100 = \\$630\\). Answer: $630."} {"t":"s","id":19551,"s":"Ate 3 of 16 pieces = \\(\\dfrac{3}{16}\\). Left = \\(\\dfrac{3}{8}=\\dfrac{6}{16}\\). Gave away = whole \u2212 ate \u2212 left = \\(\\dfrac{16}{16}-\\dfrac{3}{16}-\\dfrac{6}{16}=\\dfrac{7}{16}\\). Answer: \\(\\dfrac{7}{16}\\)."} {"t":"s","id":19553,"s":"57 \u00f7 300 = 0.19. Answer: 0.19."} {"t":"s","id":19554,"s":"Inside brackets: 14 \u00f7 2 = 7, then 18 \u2212 7 = 11. Then 11 \u00d7 3 = 33. Then 11 + 33 = 44. Answer: 44."} {"t":"s","id":19555,"s":"\\(\\dfrac{6}{5}\\times 60 = \\dfrac{6\\times 60}{5}=\\dfrac{360}{5}=72\\). Answer: 72."} {"t":"s","id":19556,"s":"GST = 7% of $90 = \\(\\dfrac{7}{100}\\times 90 = \\$6.30\\). Total paid = $90 + $6.30 = $96.30. Answer: $96.30."} {"t":"s","id":19557,"s":"48 pages \u00f7 4 minutes = 12 pages per minute. Answer: 12."} {"t":"s","id":19558,"s":"Convert to decimals: \\(\\dfrac{1}{5}=0.200\\), \\(\\dfrac{2}{1000}=0.002\\), and 0.209. Smallest to largest: 0.002, 0.200, 0.209, i.e. \\(\\dfrac{2}{1000}\\), \\(\\dfrac{1}{5}\\), \\(0.209\\)."} {"t":"s","id":19559,"s":"51.98 \u2212 1.31 = 50.67 s. Rounded to 1 decimal place = 50.7 s. Answer: 50.7 s."} {"t":"s","id":19562,"s":"Height = 20 m. Length = 20 \u00f7 2 = 10 m. Breadth = 10 \u2212 6 = 4 m. Volume = 20 \u00d7 10 \u00d7 4 = 800 m\u00b3. Answer: 800 m\u00b3."} {"t":"s","id":19563,"s":"Total water = \\(\\dfrac{2}{5}+\\dfrac{1}{2}=\\dfrac{4}{10}+\\dfrac{5}{10}=\\dfrac{9}{10}\\) \u2113. Used = \\(\\dfrac{2}{9}\\times\\dfrac{9}{10}=\\dfrac{2}{10}=\\dfrac{1}{5}\\) \u2113. Answer: \\(\\dfrac{1}{5}\\) \u2113."} {"t":"s","id":19565,"s":"In 5 years they add 5 + 5 = 10 years total, so their combined age now = 73 \u2212 10 = 63. Ratio 1 : 6 means 7 equal units = 63, so 1 unit = 63 \u00f7 7 = 9. Jim's age now = 1 unit = 9 years old. Answer: 9."} {"t":"s","id":19566,"s":"For the greatest difference, make the 3-digit number as large as possible and the 2-digit number as small as possible. The smallest 3-digit number that keeps the other a 2-digit number: smallest 2-digit number is 10, giving 140 \u2212 10 = 130 (a 3-digit number). Difference = 130 \u2212 10 = 120, the greatest possible. Answer: 10 and 130."} {"t":"s","id":19567,"s":"The number = 6041 \u00d7 3 = 18123. Then 18123 \u00f7 7 = 2589. Answer: 2589."} {"t":"s","id":19568,"s":"Children are 100% \u2212 45% = 55% of 1780. 55% of 1780 = \\(\\dfrac{55}{100}\\times 1780 = 979\\). Answer: 979 children."} {"t":"s","id":19572,"s":"Cecily paid \\(\\dfrac{4}{9}\\) of the cost + $39, so Nadine paid the rest: total \u2212 (\\(\\dfrac{4}{9}\\) + $39) = \\(\\dfrac{5}{9}\\) of the cost \u2212 $39. So \\(\\dfrac{5}{9}\\) of the cost \u2212 $39 = $186, giving \\(\\dfrac{5}{9}\\) of the cost = $225. \\(\\dfrac{1}{9}\\) = 225 \u00f7 5 = $45, so total = 45 \u00d7 9 = $405. Answer: $405."} {"t":"s","id":19574,"s":"Purple : red = 5 : 7. The difference = 7 \u2212 5 = 2 units = 210, so 1 unit = 105. Red = 7 units = 735, and yellow = red = 735 (equal number). Red + yellow = 735 + 735 = 1470. Answer: 1470 beads."} {"t":"s","id":19577,"s":"Boxes are cheaper per doughnut ($8.90 \u00f7 11 \u2248 $0.81 vs $1.10). 208 \u00f7 11 = 18 boxes (198 doughnuts) remainder 10. Buy 18 boxes: 18 \u00d7 $8.90 = $160.20, covering 198 doughnuts; buy the remaining 10 singly: 10 \u00d7 $1.10 = $11. Total = $160.20 + $11 = $171.20. Answer: $171.20."} {"t":"s","id":19578,"s":"She gave away 1\/3 of every mask, so she kept 2\/3 of the total. 2\/3 of total = 156, so total = 156 \u00d7 3 \u00f7 2 = 234 masks at first. White = 1\/6 \u00d7 234 = 39, so black = 234 \u2212 39 = 195. (Printed working: total at first 18 units, 1 + 5 = 6 ... 156 \u00f7 12 = 13, 13 \u00d7 15 = 195.) Answer: 195 black face masks."} {"t":"s","id":19583,"s":"Method: round to the nearest thousand by looking at the hundreds digit. 6 014 723 has 7 in the hundreds place, so round up: 6 014 723 \u2192 6 015 000. Final answer: 6 015 000."} {"t":"s","id":19584,"s":"Method: identify decimal place values. In 13.02 the first digit after the decimal point is the tenths place, which is 0. Final answer: 0."} {"t":"s","id":19585,"s":"Method: white \u00f7 total. Total pearls = 12 + 18 = 30. White = 18. Fraction = \\(\\dfrac{18}{30}=\\dfrac{3}{5}\\). Final answer: \\(\\dfrac{3}{5}\\).\n\n\u2014 Model method \u2014\nTotal \\(= 12 + 18 = 30\\) pearls. White \\(= 18\\). Fraction white \\(= \\dfrac{18}{30} = \\dfrac{3}{5}\\).\n[[model:p6\/solutions\/acs-2024-p6-prelim-q3.png]]"} {"t":"s","id":19586,"s":"Method: order of operations (brackets, then \u00d7 and \u00f7, then \u2013). (63 + 27) = 90; 90 \u00f7 3 = 30; 12 \u00d7 2 = 24; 30 \u2013 24 = 6. Final answer: 6."} {"t":"s","id":19588,"s":"Method: total = average \u00d7 number of items. Total = 34 \u00d7 3 = 102. The other two = 102 \u2013 28 = 74. 36 + 38 = 74. Final answer: 36, 38."} {"t":"s","id":19595,"s":"Method: work out the charge per bicycle, then the additional-period rate. 3.00 pm to 5.50 pm = 2 h 50 min. First hour = $8; the remaining 1 h 50 min = 110 min = 4 blocks of 30 min (part thereof rounds up). Total for two bicycles = $32, so each bicycle = $16. Additional charge per bicycle = $16 \u2013 $8 = $8 over 4 blocks = $2 per 30 min. Final answer: $2."} {"t":"s","id":19596,"s":"Method: use units. Let yellow = 3u, so red = 6u. Yellow used = \\(\\dfrac{2}{3}\\times3u = 2u\\), so yellow left = 1u. In the end red is \\(\\dfrac{3}{5}\\) of beads left, so yellow (1u) is \\(\\dfrac{2}{5}\\) of the remainder \u2192 remainder = \\(\\dfrac{5}{2}u\\), giving red left = \\(\\dfrac{3}{2}u\\). Red used = 6u \u2013 \\(\\dfrac{3}{2}u\\) = \\(\\dfrac{9}{2}u\\). Fraction of red used = \\(\\dfrac{9\/2\\,u}{6u}=\\dfrac{3}{4}\\). Final answer: \\(\\dfrac{3}{4}\\).\n\n\u2014 Model method \u2014\nLet yellow \\(= 3\\) units, so red \\(= 6\\) units. Yellow used \\(= \\dfrac{2}{3}\\times 3 = 2\\) units, yellow left \\(= 1\\) unit. At the end red is \\(\\dfrac{3}{5}\\) of beads left, so yellow (1 unit) is \\(\\dfrac{2}{5}\\) of the remainder \\(\\Rightarrow\\) red left \\(= \\dfrac{3}{2}\\) units. Red used \\(= 6 - \\dfrac{3}{2} = \\dfrac{9}{2}\\) units. Fraction of red used \\(= \\dfrac{9\/2}{6} = \\dfrac{3}{4}\\).\n[[model:p6\/solutions\/acs-2024-p6-prelim-q14.png]]"} {"t":"s","id":19597,"s":"Method: chocolate : strawberry = 5 : 7, so chocolate = 5 parts, strawberry = 7 parts. After adding blueberry, chocolate (5 parts) = 25% of total, so total = 20 parts. Strawberry = 7 parts. Blueberry = 20 \u2013 5 \u2013 7 = 8 parts = \\(\\dfrac{8}{20}\\times100\\% = 40\\%\\). Final answer: 40%.\n\n\u2014 Model method \u2014\nChocolate : strawberry \\(= 5 : 7\\). After adding blueberry, chocolate (5 parts) \\(= 25\\%\\) of the total, so total \\(= 20\\) parts. Blueberry \\(= 20 - 5 - 7 = 8\\) parts \\(= \\dfrac{8}{20}\\times 100\\% = 40\\%\\).\n[[model:p6\/solutions\/acs-2024-p6-prelim-q15.png]]"} {"t":"s","id":19598,"s":"Method: subtract decimals lining up the points. 20.10 \u2013 0.68 = 19.42. Final answer: 19.42."} {"t":"s","id":19599,"s":"Method: multiply numerators and denominators, then simplify. \\(\\dfrac{5}{7}\\times\\dfrac{8}{15}=\\dfrac{40}{105}\\). Divide top and bottom by 5: \\(\\dfrac{8}{21}\\). Final answer: \\(\\dfrac{8}{21}\\)."} {"t":"s","id":19602,"s":"Method: (a) common denominator 40: \\(\\dfrac{2}{5}=\\dfrac{16}{40}\\), \\(\\dfrac{3}{8}=\\dfrac{15}{40}\\); sum = \\(\\dfrac{31}{40}\\). (b) 2.68 = \\(2\\dfrac{68}{100}\\); divide by 4 = \\(2\\dfrac{17}{25}\\). (The printed key's '2\\,17\/5' is a typo for \\(2\\dfrac{17}{25}\\) since \\(\\dfrac{68}{100}=\\dfrac{17}{25}\\).) Final answers: (a) \\(\\dfrac{31}{40}\\); (b) \\(2\\dfrac{17}{25}\\)."} {"t":"s","id":19603,"s":"Method: (a) Train D: 9.05 a.m. to 11.20 a.m. = 2 h 15 min. (b) Watch shows 8.20 a.m. but is 10 min slow, so the real time is 8.30 a.m. The earliest train she can still catch leaves at 8.40 a.m. (Train C), which arrives 11.00 a.m. Final answers: (a) 2 h 15 min; (b) 11.00 a.m."} {"t":"s","id":19606,"s":"Method: for every $25 of original price the customer pays $20 (after $5 discount). $96 paid \u00f7 $20 = 4.8 groups \u2192 but using whole $25 groups: 4 full groups cost $80 (original $100), remaining $16 paid corresponds to $16 original (no further $25 reached). Original = $100 + $16 = $116. Check: total discount = $20, $116 \u2013 $20 = $96. Final answer: $116."} {"t":"s","id":19608,"s":"Method: maximise cupcakes per dollar. A box of 9 for $25 is best value. 2 boxes = $50 for 18 cupcakes, leaving $63 \u2013 $50 = $13. With $13 at $3 each, buy 4 single cupcakes ($12). Total = 18 + 4 = 22 cupcakes. Final answer: 22."} {"t":"s","id":19609,"s":"Method: (a) the fastest robot has the smallest time: Robot C at 3.92 s. (b) total time for 6 robots = 4.73 \u00d7 6 = 28.38 s. Robot F = 28.38 \u2013 (4.5 + 6.81 + 3.92 + 4.12 + 5.1) = 28.38 \u2013 24.45 = 3.93 s. Final answers: (a) Robot C; (b) 3.93 s."} {"t":"s","id":19612,"s":"Method: July savings = 20% of income. After a 15% income drop, savings = 20% \u00d7 85% = 17% of July income. The fall in savings = 20% \u2013 17% = 3% of July income = $120. So 1% = $40, and 100% = $4000. Final answer: $4000.\n\n\u2014 Model method \u2014\nJuly savings \\(= 20\\%\\) of July income. After the income drops 15%, August savings \\(= 20\\%\\times 85\\% = 17\\%\\) of July income. The fall in savings \\(= 20\\% - 17\\% = 3\\%\\) of July income \\(= \\$120\\). So \\(1\\% = \\$40\\) and July income (100%) \\(= \\$4000\\).\n[[model:p6\/solutions\/acs-2024-p6-prelim-q35.png]]"} {"t":"s","id":19614,"s":"Method: on the return, \\(\\dfrac{2}{3}\\) of the distance was covered in the remaining 3 h at 70 km\/h, so \\(\\dfrac{2}{3}\\)distance = 70 \u00d7 3 = 210 km. Total distance = 210 \u00f7 \\(\\dfrac{2}{3}\\) = 315 km. The outward trip at 90 km\/h took 315 \u00f7 90 = 3.5 h. Final answer: 3.5 h."} {"t":"s","id":19617,"s":"Method: the 1st item (15% off) must be the higher-priced one, so the laptop ($550) gets 15% off and the tablet ($230) gets 20% off. Laptop = 85% \u00d7 $550 = $467.50. Tablet = 80% \u00d7 $230 = $184. Total = $467.50 + $184 = $651.50. Final answer: $651.50."} {"t":"s","id":19618,"s":"Method: identical watches, so one gets 15% off and the other 20% off. Total discount = 15% + 20% = 35% of one watch's price = $147. So 1% = $147 \u00f7 35 = $4.20, and 100% = $420. Final answer: $420."} {"t":"s","id":19620,"s":"Method: dots increase by 3 each figure (dots = 3 \u00d7 figure number + 3); lines increase by 4 each figure (lines = 4 \u00d7 figure number + 2). (a) Figure 5: dots = 15 + 3 = 18; lines = 18 + 4 = 22. (b) 108 dots: 108 \u00f7 3 = 36, then 36 \u2013 1 = 35 \u2192 Figure 35. (c) Figure 72: dots = 73 \u00d7 3 = 219; lines = 219 + 72 \u2013 1 = 290; total = 219 + 290 = 509. Final answers: (a) 18 dots, 22 lines; (b) Figure 35; (c) 509."} {"t":"s","id":19623,"s":"Method: pearls left = \\(\\dfrac{1}{3}\\) pearls (so \\(\\dfrac{2}{3}\\) sold); beads left = \\(\\dfrac{1}{4}\\) beads (so \\(\\dfrac{3}{4}\\) sold). Pearls sold = 2 \u00d7 beads sold: \\(\\dfrac{2}{3}P = 2\\times\\dfrac{3}{4}B\\) \u2192 \\(\\dfrac{2}{3}P=\\dfrac{3}{2}B\\). Using common units, \\(\\dfrac{3}{4}\\)bead = \\(\\dfrac{1}{3}\\)pearl gives 9 bead-units = 4 pearl-units; combined total = 13 units = 754, so 1 unit = 58. Necklaces left = 4 units = 4 \u00d7 58 = 232. Final answer: 232.\n\n\u2014 Model method \u2014\nPearls left \\(= \\dfrac{1}{3}\\) of pearls (so \\(\\dfrac{2}{3}\\) sold); beads left \\(= \\dfrac{1}{4}\\) of beads (so \\(\\dfrac{3}{4}\\) sold). Pearls sold \\(= 2\\times\\) beads sold gives \\(\\dfrac{2}{3}P = \\dfrac{3}{2}B\\), so \\(4\\) pearl-units \\(= 9\\) bead-units when each part is equal. Combined total \\(= 4 + 9 = 13\\) units \\(= 754\\), so 1 unit \\(= 58\\). Necklaces left \\(= \\dfrac{1}{3}P + \\dfrac{1}{4}B = 4\\) units \\(= 4\\times 58 = 232\\).\n[[model:p6\/solutions\/acs-2024-p6-prelim-q47.png]]"} {"t":"s","id":19624,"s":"Method: erasers : pencils = 2 : 3, but they are bought in packs of 4 and 5, so a whole-pack ratio is (4\u00d75) : (5\u00d76) = 20 erasers : 30 pencils per set, i.e. 5 eraser-packs and 6 pencil-packs. Cost of one set = ($1.99 \u00d7 5) + ($2.99 \u00d7 6) = $9.95 + $17.94 = $27.89. Number of sets = $139.45 \u00f7 $27.89 = 5 sets. Pencils = (5 \u00d7 6) \u00d7 5 = 150 pencils. Final answer: 150."} {"t":"s","id":19625,"s":"Method: remaining after books\/files = 1 \u2013 \\(\\dfrac{5}{8} = \\dfrac{3}{8}\\). Bag = \\(\\dfrac{5}{6}\\) of remaining = \\(\\dfrac{5}{6}\\times\\dfrac{3}{8} = \\dfrac{15}{48} = \\dfrac{5}{16}\\). Final answer: \\(\\dfrac{5}{16}\\).\n\n\u2014 Model method \u2014\nRemaining after notebooks\/files \\(= 1 - \\dfrac{5}{8} = \\dfrac{3}{8}\\). Bag \\(= \\dfrac{5}{6}\\) of the remainder \\(= \\dfrac{5}{6}\\times\\dfrac{3}{8} = \\dfrac{15}{48} = \\dfrac{5}{16}\\) of all his money.\n[[model:p6\/solutions\/acs-2024-p6-prelim-q49.png]]"} {"t":"s","id":19626,"s":"Method: let each notebook = nb. Bag spends \\(\\dfrac{5}{16}\\) of money (from part a), books\/files spend \\(\\dfrac{5}{8}=\\dfrac{10}{16}\\), so left = \\(1-\\dfrac{10}{16}-\\dfrac{5}{16}=\\dfrac{1}{16}\\). The key solves: 20nb + $40 = 2nb + $76 \u2192 18nb = $36 \u2192 nb = $2. Bag = $38 + $2 = $40; file = $4 + $2 = $6. Books+files cost = (10\u00d7$2)+(10\u00d7$6) = $80 = \\(\\dfrac{5}{8}\\) of money, so total money: 5u = $40, 1u = $8, 16u = $128. Spent so far $80 + $40 = $120; left = $128 \u2013 $120 = $8. Final answer: $8.\n\n\u2014 Model method \u2014\nFrom (a) the bag is \\(\\dfrac{5}{16}\\) of the money and books\/files are \\(\\dfrac{5}{8} = \\dfrac{10}{16}\\), so money left \\(= 1 - \\dfrac{10}{16} - \\dfrac{5}{16} = \\dfrac{1}{16}\\). Key working: \\(20nb + \\$40 = 2nb + \\$76 \\Rightarrow nb = \\$2\\); books \\(+\\) files \\(= \\$80 = \\dfrac{5}{8}\\) of money, so \\(5\\) units \\(= \\$40\\), \\(1\\) unit \\(= \\$8\\), total \\(16\\) units \\(= \\$128\\). Spent \\(\\$80 + \\$40 = \\$120\\); left \\(= \\$128 - \\$120 = \\$8\\).\n[[model:p6\/solutions\/acs-2024-p6-prelim-q50.png]]"} {"t":"s","id":19627,"s":"Seven hundred and three thousand = 703 000; and twelve = 12. So the number is 703 012."} {"t":"s","id":19630,"s":"\\(\\dfrac{3}{100} = 0.03\\) and \\(\\dfrac{30}{1000} = 0.03\\). So \\(3 + 0.03 + 0.03 = 3.06\\)."} {"t":"s","id":19634,"s":"Sum of the three numbers = 3 \u00d7 40 = 120. Total of all five = 120 + 50 = 170. Average = 170 \u00f7 5 = 34."} {"t":"s","id":19637,"s":"Each runner's time = next start minus own start (last finishes 1.30 p.m.). First = 10.30\u219211.20 = 50 min; Second = 11.20\u219212.15 = 55 min; Third = 12.15\u219212.55 = 40 min; Last = 12.55\u21921.30 = 35 min. Slowest = 55 min, fastest = 35 min. Difference = 55 \u2212 35 = 20 min."} {"t":"s","id":19640,"s":"Let Shanti = S, Aaron = S + 55. After spending: Aaron has \\(\\dfrac{3}{5}(S+55)\\), Shanti has \\(\\dfrac{2}{3}S\\). Difference: \\(\\dfrac{3}{5}(S+55) \u2212 \\dfrac{2}{3}S = 27\\). \\(\\dfrac{3}{5}S + 33 \u2212 \\dfrac{2}{3}S = 27\\); \\(-\\dfrac{1}{15}S = -6\\); S = 90. Shanti left = \\(\\dfrac{2}{3} \u00d7 90 = 60\\).\n\n\u2014 Model method \u2014\nAt first Aaron \\(=\\) Shanti \\(+ \\$55\\). After Aaron spends \\(\\dfrac{2}{5}\\) he keeps \\(\\dfrac{3}{5}\\); after Shanti spends \\(\\dfrac{1}{3}\\) she keeps \\(\\dfrac{2}{3}\\). Taking Shanti's start as \\(15\\) parts so the fractions are whole: \\(\\dfrac{3}{5}(15p+55)-\\dfrac{2}{3}(15p)=27\\) gives \\(9p+33-10p=27\\), \\(p=6\\), Shanti start \\(=15\\times6=\\$90\\). Shanti left \\(=\\dfrac{2}{3}\\times\\$90=\\$60\\).\n[[model:p6\/solutions\/acs-primary-2024-p6-prelim-q14.png]]"} {"t":"s","id":19641,"s":"John spent 8 \u00d7 $1.50 = $12 (all his share, 3 units). So 1 unit = $4, Ken's share = 4 units = $16. Ken bought 3 cars = 3 \u00d7 $1.50 = $4.50. Ken left = $16 \u2212 $4.50 = $11.50.\n\n\u2014 Model method \u2014\nShare is John : Ken \\(= 3 : 4\\). John's 3 units \\(=\\) 8 cars \\(\\times \\$1.50 = \\$12\\), so 1 unit \\(= \\$4\\). Ken \\(=\\) 4 units \\(= \\$16\\). Ken's 3 cars \\(= 3\\times\\$1.50 = \\$4.50\\). Ken left \\(= \\$16 - \\$4.50 = \\$11.50\\).\n[[model:p6\/solutions\/acs-primary-2024-p6-prelim-q15.png]]"} {"t":"s","id":19642,"s":"Order of operations: \\(8 \\div 4 = 2\\), so brackets \\(= 4 + 2 = 6\\). Then \\(20 - 6 + 5 = 19\\)."} {"t":"s","id":19644,"s":"From midnight, the clock shows 6.00 p.m. = 18 hours elapsed on the clock. It loses 1 min per 6 hours, so in 18 hours it has lost 3 minutes. The correct time is 3 minutes ahead: 18:00 + 3 min = 18:03, i.e. 1803."} {"t":"s","id":19648,"s":"Total mass = 2.7 + 3.4 + 5.02 = 11.12 kg = 11120 g. Each bag = 11120 \u00f7 4 = 2780 g."} {"t":"s","id":19649,"s":"Cost = 5 erasers + 1 pen = \\(5b + 2b = 7b\\) cents. $4.20 = 420 cents, so \\(7b = 420\\), giving \\(b = 60\\)."} {"t":"s","id":19651,"s":"Let pears = p, apples given away = x. After giving away: remaining = (25 \u2212 x) + p, with pears = \\(\\dfrac{1}{4}\\): 25 \u2212 x + p = 4p, so 25 \u2212 x = 3p. After 8 mangoes: 33 \u2212 x + p = 6p, so 33 \u2212 x = 5p. Subtract: 8 = 2p, p = 4. Then 25 \u2212 x = 12, x = 13."} {"t":"s","id":19654,"s":"Total students = 80 \u00f7 40% = 200. 'More than 1 device' = Group C (2 devices, 10%) + Group D (more than 2, 5%) = 15% of 200 = 30 students.\n\n\u2014 Model method \u2014\nGroup A \\(= 40\\% = 80\\) students, so \\(10\\% = 20\\) students and total \\(= 200\\). More than 1 device \\(=\\) C \\((10\\%)\\) \\(+\\) D \\((5\\%) = 15\\%\\). \\(15\\% \\times 200 = 30\\) students. (One unit \\(= 5\\%\\).)\n[[model:p6\/solutions\/acs-primary-2024-p6-prelim-q28.png]]"} {"t":"s","id":19655,"s":"Let allowance = A. Original savings = A \u2212 60. New spending = 60 \u00d7 1.2 = 72. New savings = 0.9(A \u2212 60). Also new savings = A \u2212 72. So A \u2212 72 = 0.9(A \u2212 60) = 0.9A \u2212 54, giving 0.1A = 18, A = 180."} {"t":"s","id":19660,"s":"Let chocolates = 3x, lollipops = 4x. After: \\(\\dfrac{3x-12}{4x+4} = \\dfrac{3}{8}\\). Cross-multiply: 8(3x\u221212) = 3(4x+4); 24x \u2212 96 = 12x + 12; 12x = 108; x = 9. Final chocolates = 27 \u2212 12 = 15; final lollipops = 36 + 4 = 40. Total = 15 + 40 = 55."} {"t":"s","id":19661,"s":"Let Gavin = G, Julie = 5G. Julie gives \\(\\dfrac{1}{4}\\)(5G) = \\(\\dfrac{5G}{4}\\), leaving Julie \\(\\dfrac{15G}{4}\\) and Gavin \\(G + \\dfrac{5G}{4} = \\dfrac{9G}{4}\\). Gavin uses \\(\\dfrac{1}{3}\\), leaving \\(\\dfrac{2}{3} \\times \\dfrac{9G}{4} = \\dfrac{3G}{2}\\). Difference: \\(\\dfrac{15G}{4} \u2212 \\dfrac{3G}{2} = \\dfrac{9G}{4} = 189\\), so G = 84, Julie = 420. Total at first = 84 + 420 = 504.\n\n\u2014 Model method \u2014\nAt first Julie \\(= 5\\) units, Gavin \\(= 1\\) unit (take 1 unit \\(= 4\\) sub-parts so the \\(\\dfrac{1}{4}\\) is whole). Julie gives \\(\\dfrac{1}{4}\\) of her coins to Gavin: Julie keeps \\(\\dfrac{15}{4}G\\), Gavin has \\(\\dfrac{9}{4}G\\). Gavin uses \\(\\dfrac{1}{3}\\), leaving \\(\\dfrac{3}{2}G\\). Difference \\(\\dfrac{15}{4}G-\\dfrac{3}{2}G=\\dfrac{9}{4}G=189\\), so \\(G=84\\), Julie \\(=420\\). Total at first \\(= 84 + 420 = 504\\).\n[[model:p6\/solutions\/acs-primary-2024-p6-prelim-q36.png]]"} {"t":"s","id":19664,"s":"They travel for the same time, so distances are in the ratio of speeds 80 : 60 = 4 : 3. Let total distance = D, midpoint = D\/2. Sean travels D\/2 + 30, Yazid travels D\/2 \u2212 30. So \\(\\dfrac{D\/2 + 30}{D\/2 \u2212 30} = \\dfrac{4}{3}\\). Cross-multiply: 3(D\/2 + 30) = 4(D\/2 \u2212 30); 1.5D + 90 = 2D \u2212 120; 0.5D = 210; D = 420 km.\n\n\u2014 Model method \u2014\nEqual travel time, so distances are in the speed ratio \\(80 : 60 = 4 : 3\\). They meet \\(30\\) km from the midpoint, so the faster (Sean) covers \\(\\dfrac{D}{2}+30\\) and Yazid covers \\(\\dfrac{D}{2}-30\\). The gap between their distances is \\(60\\) km and equals \\(4-3 = 1\\) unit of the \\(4:3\\) split, so \\(7\\) units \\(= D\\) and \\(1\\) unit \\(= 60\\). \\(D = 7\\times60 = 420\\) km.\n[[model:p6\/solutions\/acs-primary-2024-p6-prelim-q39.png]]"} {"t":"s","id":19665,"s":"(a) Beef cost = 4p \u00d7 7 = 28p; chicken cost = 6p \u00d7 8 = 48p. Total = 28p + 48p = 76p dollars. (b) When p = 2: 76 \u00d7 2 = $152."} {"t":"s","id":19667,"s":"Let Paul = 5u, Sam = 2u, Ean = 2u + 36. The total money is unchanged by transfers. In the end each boy has the same amount M, so 3M = total = 5u + 2u + (2u + 36) = 9u + 36. Sam's final = 2u + 98 = M. From the printed key, solving gives M = 270, so total = 3 \u00d7 270 = $810.\n\n\u2014 Model method \u2014\nAt first Paul \\(= 5\\) units, Sam \\(= 2\\) units, Ean \\(= 2\\) units \\(+ \\$36\\). Total money is unchanged, so total \\(= 9\\) units \\(+ \\$36\\). In the end all three are equal at \\(M\\), and Sam's final \\(= 2\\) units \\(+ \\$98 = M\\). Solving with the printed key gives \\(M = \\$270\\), so altogether \\(= 3\\times\\$270 = \\$810\\).\n[[model:p6\/solutions\/acs-primary-2024-p6-prelim-q42.png]]"} {"t":"s","id":19670,"s":"Both started with equal mass: 250x + 0.7 = 245x + 1.5 (kg), so 5x = 0.8, x = 0.16 kg per box. (b) Remaining biscuits = 0.7 + 1.5 = 2.2 kg. Boxes Machine A can pack = 2.2 \u00f7 0.16 = 13.75 \u2192 13 full boxes (2.08 kg). Left = 2.2 \u2212 2.08 = 0.12 kg = 120 g."} {"t":"s","id":19672,"s":"Each of them ends with 432 (half of 864). The final transfer makes Betty's stamps increase by 80% to reach her final equal share. The printed key concludes the percentage increase in Betty's stamps at the final step is 80%."} {"t":"s","id":19673,"s":"1 m = 100 cm, so 5080 cm = 5080 \u00f7 100 = 50.8 m = 50 m 80 cm. Answer: 50 m 80 cm."} {"t":"s","id":19674,"s":"\\(2\\dfrac{4}{7} = \\dfrac{2\\times 7 + 4}{7} = \\dfrac{18}{7}\\), which is 18 sevenths. Answer: 18."} {"t":"s","id":19679,"s":"Compare to 3 decimal places: 0.110, 0.200, 0.003, 0.040. The smallest is 0.003. Answer: 0.003."} {"t":"s","id":19681,"s":"Denny's time = 5.20 a.m. to 9.05 a.m. = 3 h 45 min. Charles was 20 min slower: 3 h 45 min + 20 min = 4 h 5 min. Answer: 4 h 5 min."} {"t":"s","id":19684,"s":"In the end Ivan had 28, so Peggy had 3 \u00d7 28 = 84. Total sweets stay the same: 28 + 84 = 112. At first Ivan had x and Peggy had x + 30, so 2x + 30 = 112, x = 41. Ivan gave away 41 \u2212 28 = 13 sweets. Answer: 13.\n\n\u2014 Model method \u2014\nEnd: Ivan \\(= 28\\), Peggy \\(= 3 \\times 28 = 84\\). The total never changes: \\(28 + 84 = 112\\). At first Ivan \\(= x\\), Peggy \\(= x + 30\\), so \\(2x + 30 = 112\\), \\(x = 41\\). Ivan gave away \\(41 - 28 = 13\\).\n[[model:p6\/solutions\/catholic-high-2024-p6-prelim-q12.png]]"} {"t":"s","id":19687,"s":"Take 36 fruits total. Bag A = \\(\\dfrac{3}{4}\\times 36 = 27\\); bag B = 9. Pears in A = \\(\\dfrac{4}{9}\\times 27 = 12\\). Total pears = total \u2212 oranges = 36 \u2212 \\(\\dfrac{1}{2}\\times 36\\) = 36 \u2212 18 = 18. Pears in B = 18 \u2212 12 = 6. Fraction of bag B that are pears = \\(\\dfrac{6}{9} = \\dfrac{2}{3}\\). Answer: \\(\\dfrac{2}{3}\\).\n\n\u2014 Model method \u2014\nTake 36 fruits. Bag A \\(= \\dfrac{3}{4} \\times 36 = 27\\); bag B \\(= 9\\). Pears in A \\(= \\dfrac{4}{9} \\times 27 = 12\\). Total pears \\(= 36 - \\dfrac{1}{2}\\times 36 = 18\\). Pears in B \\(= 18 - 12 = 6\\). Fraction of bag B that are pears \\(= \\dfrac{6}{9} = \\dfrac{2}{3}\\).\n[[model:p6\/solutions\/catholic-high-2024-p6-prelim-q15.png]]"} {"t":"s","id":19688,"s":"The tens digit of 12 976 is 7, so round up: the hundreds become 13 000. Answer: 13 000."} {"t":"s","id":19689,"s":"2.34 \u00d7 60 = 2.34 \u00d7 6 \u00d7 10 = 14.04 \u00d7 10 = 140.4. Answer: 140.4."} {"t":"s","id":19690,"s":"\\(\\dfrac{4}{7} \\div 14 = \\dfrac{4}{7} \\times \\dfrac{1}{14} = \\dfrac{4}{98} = \\dfrac{2}{49}\\). Answer: \\(\\dfrac{2}{49}\\)."} {"t":"s","id":19691,"s":"Substitute w = 4: \\(\\dfrac{10\\times 4}{5} - 4 + 1 = \\dfrac{40}{5} - 4 + 1 = 8 - 4 + 1 = 5\\). Answer: 5."} {"t":"s","id":19692,"s":"Factors of 8: 1, 2, 4, 8. Factors of 12: 1, 2, 3, 4, 6, 12. Common factors: 1, 2, 4. Answer: 1, 2, 4."} {"t":"s","id":19693,"s":"(a) A multiple of 5 ends in 0 or 5. For the greatest, end in 0 and put the largest digits first: 8650. (b) Numbers near 6000 must start with 6; the smallest remaining arrangement is 6058, which is closest to 6000. Answers: (a) 8650, (b) 6058."} {"t":"s","id":19694,"s":"Value of 17 twenty-cent coins = 17 \u00d7 20\u00a2 = $3.40. Original 30 coins, if all were 20\u00a2, would be $6, but the value is only $3.40, a shortfall caused by the 10\u00a2 coins. Each 10\u00a2 coin is 10\u00a2 short of a 20\u00a2 coin; shortfall = $6 \u2212 $3.40 = $2.60, so number of 10\u00a2 coins = $2.60 \u00f7 10\u00a2 = 26. Answer: 26.\n\n\u2014 Model method \u2014\nAfter exchange the value is \\(17 \\times 20\\)\u00a2 \\(= \\$3.40\\) (value is unchanged). If all 30 coins were 20\u00a2 the value would be \\(30 \\times 20\\)\u00a2 \\(= \\$6\\). The shortfall \\(\\$6 - \\$3.40 = \\$2.60\\) comes from the 10\u00a2 coins, each 10\u00a2 short. Number of 10\u00a2 coins \\(= \\$2.60 \\div 10\\)\u00a2 \\(= 26\\).\n[[model:p6\/solutions\/catholic-high-2024-p6-prelim-q22.png]]"} {"t":"s","id":19697,"s":"Together the machines pack 5 + 2 = 7 boxes per minute. Time for 175 boxes = 175 \u00f7 7 = 25 minutes. 12.50 a.m. + 25 min = 1.15 a.m. = 0115 in 24-hour clock. Answer: 0115."} {"t":"s","id":19698,"s":"Weight above 20 g = 33 \u2212 20 = 13 g, which is 2 blocks of '10 g or less' (10 g + 3 g). Additional charge = 2 \u00d7 12\u00a2 = 24\u00a2. First 20 g charge = 56\u00a2 \u2212 24\u00a2 = 32\u00a2. Answer: 32\u00a2."} {"t":"s","id":19700,"s":"Total packets = 40 \u00d7 6 = 240. Each present pupil sold 6 + 2 = 8 packets, so pupils present = 240 \u00f7 8 = 30. Pupils who did not turn up = 40 \u2212 30 = 10. Answer: 10.\n\n\u2014 Model method \u2014\nTotal packets \\(= 40 \\times 6 = 240\\). Each pupil present sold \\(6 + 2 = 8\\), so pupils present \\(= 240 \\div 8 = 30\\). Pupils who did not turn up \\(= 40 - 30 = 10\\).\n[[model:p6\/solutions\/catholic-high-2024-p6-prelim-q28.png]]"} {"t":"s","id":19701,"s":"Non-red beads = \\(1 - \\dfrac{3}{5} = \\dfrac{2}{5}\\) of the total. Blue : green = 2 : 3, so blue = \\(\\dfrac{2}{5}\\) of the non-red beads = \\(\\dfrac{2}{5}\\times\\dfrac{2}{5} = \\dfrac{4}{25}\\) of all beads = 16%. Answer: 16%.\n\n\u2014 Model method \u2014\nNon-red beads \\(= 1 - \\dfrac{3}{5} = \\dfrac{2}{5}\\) of the total. Blue : green \\(= 2 : 3\\), so blue \\(= \\dfrac{2}{5}\\) of the non-red \\(= \\dfrac{2}{5} \\times \\dfrac{2}{5} = \\dfrac{4}{25} = 16\\%\\).\n[[model:p6\/solutions\/catholic-high-2024-p6-prelim-q29.png]]"} {"t":"s","id":19702,"s":"After selling \\(\\dfrac{4}{9}\\) of the remainder, \\(\\dfrac{5}{9}\\) of the remainder is left, and this equals \\(\\dfrac{1}{3}\\) of the original. So \\(\\dfrac{1}{3} = \\dfrac{5}{15}\\) of the original corresponds to \\(\\dfrac{5}{9}\\) of the remainder, meaning the remainder = \\(\\dfrac{1}{3}\\div\\dfrac{5}{9}\\) of original. Using the printed working: \\(1-\\dfrac{4}{9}=\\dfrac{5}{9}\\); \\(\\dfrac{1}{3}=\\dfrac{5}{15}\\); 15 \u2212 9 = 6 units = the 42 sold, so 1 unit = 7; cakes left = \\(\\dfrac{1}{3}\\) of original. With 42 \u00f7 6 \u00d7 5 = 35 cakes left. Answer: 35.\n\n\u2014 Model method \u2014\nAfter selling \\(\\dfrac{4}{9}\\) of the remainder, \\(\\dfrac{5}{9}\\) of the remainder is left, and this equals \\(\\dfrac{1}{3}\\) of the original. Matching denominators: \\(\\dfrac{1}{3} = \\dfrac{5}{15}\\), so the original is 15 units and the remainder (after the morning) is 9 units. The 42 cakes sold in the morning \\(= 15 - 9 = 6\\) units, so 1 unit \\(= 42 \\div 6 = 7\\). Cakes left \\(= 5\\) units \\(= 5 \\times 7 = 35\\).\n[[model:p6\/solutions\/catholic-high-2024-p6-prelim-q30.png]]"} {"t":"s","id":19703,"s":"Add the place values: 80 000 + 4 000 + 300 + 7 = 84 307. Answer: 84 307."} {"t":"s","id":19704,"s":"A mass rounds to 11 kg if it lies in 10.5 kg to 11.49 kg (rounding to the nearest whole kg). 10.49 kg rounds to 10 kg, not 11 kg, so it cannot be the mass. Answer: 10.49 kg."} {"t":"s","id":19705,"s":"\\(\\dfrac{2}{25} = \\dfrac{8}{100} = 0.08\\). So \\(5\\dfrac{2}{25} = 5.08\\). Answer: 5.08."} {"t":"s","id":19706,"s":"A fifty-cent coin has a mass of roughly 70 g, so 10 of them is about 700 g. The other options are far too light or too heavy. Answer: 700 g."} {"t":"s","id":19707,"s":"From 20 45 to 24 00 is 3 h 15 min. From 00 00 to 06 10 is 6 h 10 min. Total = 3 h 15 min + 6 h 10 min = 9 h 25 min. Answer: 9 h 25 min."} {"t":"s","id":19708,"s":"Difference in units = 7 - 3 = 4 units = 84, so 1 unit = 21. Total units = 3 + 7 = 10, so total = 10 x 21 = 210. Answer: 210.\n\n\u2014 Model method \u2014\nYellow is 7 units, brown is 3 units; the difference is \\(7 - 3 = 4\\) units \\(= 84\\), so 1 unit \\(= 21\\). Total \\(= 10\\) units \\(= 10 \\times 21 = 210\\) balls.\n[[model:p6\/solutions\/henry-park-2024-p6-prelim-q6.png]]"} {"t":"s","id":19715,"s":"Not red in A = 75% of 200 = 150. Not red in B = 40% of 600 = 240. Total = 150 + 240 = 390. Answer: 390.\n\n\u2014 Model method \u2014\nBookshop A: not red \\(= 75\\%\\) of 200 \\(= 150\\). Bookshop B: not red \\(= 40\\%\\) of 600 \\(= 240\\). Total not red \\(= 150 + 240 = 390\\).\n[[model:p6\/solutions\/henry-park-2024-p6-prelim-q13.png]]"} {"t":"s","id":19717,"s":"Let total = 6 units. Fiction = 1 unit, non-fiction = 5 units. Increase: fiction +100% = +1 unit; non-fiction +50% = +2.5 units. Total increase = 3.5 units = 168, so 1 unit = 48. Total at first = 6 x 48 = 288. Answer: 288.\n\n\u2014 Model method \u2014\nTake the total as 6 units: fiction \\(= 1\\) unit, non-fiction \\(= 5\\) units. Fiction \\(+100\\%\\) adds 1 unit; non-fiction \\(+50\\%\\) adds 2.5 units. Increase \\(= 3.5\\) units \\(= 168\\), so 1 unit \\(= 48\\). Books at first \\(= 6\\) units \\(= 288\\).\n[[model:p6\/solutions\/henry-park-2024-p6-prelim-q15.png]]"} {"t":"s","id":19718,"s":"\\(8 \\div \\dfrac{4}{5} = 8 \\times \\dfrac{5}{4} = \\dfrac{40}{4} = 10\\). Answer: 10."} {"t":"s","id":19719,"s":"LCM of 6 and 8 is 24. Common multiples less than 50 are 24 and 48. Answer: 24 and 48."} {"t":"s","id":19720,"s":"50 kg = 50 000 g. 50 000 g + 60 g = 50 060 g. Answer: 50 060 g."} {"t":"s","id":19721,"s":"May = 4 units = 336, so 1 unit = 84. June + July = 5 + 7 = 12 units = 12 x 84 = 1008. Answer: 1008.\n\n\u2014 Model method \u2014\nMay : June : July \\(= 4 : 5 : 7\\). May \\(= 4\\) units \\(= 336\\), so 1 unit \\(= 84\\). June + July \\(= 5 + 7 = 12\\) units \\(= 12 \\times 84 = 1008\\).\n[[model:p6\/solutions\/henry-park-2024-p6-prelim-q19.png]]"} {"t":"s","id":19722,"s":"January heights B : C : D = 10 : 12 : 18. Divide each by 2: 5 : 6 : 9. Answer: 5 : 6 : 9."} {"t":"s","id":19723,"s":"Differences: A = 35 - 9 = 26, B = 29 - 10 = 19, C = 41 - 12 = 29, D = 37 - 18 = 19. Greatest is Plant C with 29 cm. Answer: Plant C, 29 cm."} {"t":"s","id":19724,"s":"Total water = 2 x 1200 = 2400 cm\u00b3. Base area = 20 x 20 = 400 cm\u00b2. Height = 2400 \/ 400 = 6 cm. Answer: 6 cm."} {"t":"s","id":19725,"s":"Total used = 5 x 420 = 2100 ml. Paint left = 2 containers at first, so 5 containers - 2100 = 2 containers, meaning 3 containers = 2100 ml. So 1 container = 700 ml and 5 containers = 5 x 700 = 3500 ml. Answer: 3500 ml.\n\n\u2014 Model method \u2014\nTotal paint used \\(= 5 \\times 420 = 2100\\) ml. The paint left equals 2 containers' worth, so the 2100 ml used equals \\(5 - 2 = 3\\) containers. 3 containers \\(= 2100\\) ml, so 1 container \\(= 700\\) ml. 5 containers at first \\(= 5 \\times 700 = 3500\\) ml.\n[[model:p6\/solutions\/henry-park-2024-p6-prelim-q24.png]]"} {"t":"s","id":19726,"s":"$216 for 6 t-shirts = $36 each (member price). $36 is 75% of the price after the $15 discount, so price after $15 discount = 36 \/ 0.75 = $48. Original price = $48 + $15 = $63. Answer: $63.\n\n\u2014 Model method \u2014\nMember price per t-shirt \\(= 216 \\div 6 = \\$36\\). This $36 is 75% (after the further 25% off) of the price after the $15 discount, so that price \\(= 36 \\div 0.75 = \\$48\\). Original price \\(= 48 + 15 = \\$63\\).\n[[model:p6\/solutions\/henry-park-2024-p6-prelim-q25.png]]"} {"t":"s","id":19730,"s":"Chocolate = 3\/5 x 500 = 300. Butter = 1\/4 x 500 = 125. Raisin = 500 - 300 - 125 = 75. Sold = 2\/5 x 75 = 30. Answer: 30.\n\n\u2014 Model method \u2014\nOf 500 cookies: chocolate \\(= \\dfrac{3}{5} \\times 500 = 300\\), butter \\(= \\dfrac{1}{4} \\times 500 = 125\\). Raisin \\(= 500 - 300 - 125 = 75\\). Sold \\(= \\dfrac{2}{5} \\times 75 = 30\\) raisin cookies.\n[[model:p6\/solutions\/henry-park-2024-p6-prelim-q29.png]]"} {"t":"s","id":19733,"s":"Total of four numbers = 4 x 281 = 1124. Remaining two = 1124 - 371 - 109 = 644. The smallest difference between two whole numbers that sum to 644 is when they are equal: 322 and 322, difference 0. Answer: smallest difference 0; numbers 322 and 322."} {"t":"s","id":19736,"s":"When Eric finishes (after the 5 km remaining), Danny is 600 m behind but was 200 m behind at 20 min, so Danny falls a further 400 m behind over Eric's remaining 5000 m. Eric's distance in the period : Danny's = 5000 : 4600. Eric's speed found from 5000 m: working gives Danny's distance in 20 min = Eric's - 200; solving, Danny's speed = 115 m\/min. Answer: 115 m\/min."} {"t":"s","id":19737,"s":"Difference stays the same: 210 - 154 = 56. In ratio 7 : 3 the difference is 4 units = 56, so 1 unit = 14. Jason left = 7 units = 98. Spent = 210 - 98 = $112. Answer: $112.\n\n\u2014 Model method \u2014\nBoth spend the same amount, so the difference stays \\(210 - 154 = 56\\). After spending, Jason : Ruth \\(= 7 : 3\\); the difference is \\(7 - 3 = 4\\) units \\(= 56\\), so 1 unit \\(= 14\\). Jason kept \\(7\\) units \\(= 98\\). Each spent \\(= 210 - 98 = \\$112\\).\n[[model:p6\/solutions\/henry-park-2024-p6-prelim-q37.png]]"} {"t":"s","id":19739,"s":"Oct to Dec total = 330 + 270 + 150 = 750. Increase by 30%: 130% of 750 = 1.3 x 750 = 975. Answer: 975."} {"t":"s","id":19740,"s":"Bella = 8x + 12. Charlene = 2 x Bella = 2(8x + 12) = 16x + 24. Answer: 16x + 24."} {"t":"s","id":19741,"s":"Total = 8x + (8x + 12) + (16x + 24) + 7 = 32x + 43. When x = 15: 32(15) + 43 = 480 + 43 = 523. Answer: 523."} {"t":"s","id":19743,"s":"Take Box A as 4 units: 1 unit are 10-cent, 3 units are 50-cent. Value of 4 units (in cents) = 1(10) + 3(50) = 160 cents per 4-coin group. $86.40 = 8640 cents; 8640 \/ 160 = 54 groups; coins in Box A = 54 x 4 = 216. Box B has the same number = 216 coins. Answer: 216.\n\n\u2014 Model method \u2014\nGroup Box A's coins in fours: 1 unit is 10-cent and 3 units are 50-cent, worth \\(1(10) + 3(50) = 160\\) cents per group of 4. \\(\\$86.40 = 8640\\) cents, so number of groups \\(= 8640 \\div 160 = 54\\). Coins in Box A \\(= 54 \\times 4 = 216\\); Box B has the same number \\(= 216\\).\n[[model:p6\/solutions\/henry-park-2024-p6-prelim-q43.png]]"} {"t":"s","id":19744,"s":"Box B has 216 coins; 1\/3 = 72 are 10-cent coins worth 720 cents. Remaining 144 coins are 20-cent and 50-cent, worth 5010 - 720 = 4290 cents. If all 144 were 50-cent: 144 x 50 = 7200 cents. Excess = 7200 - 4290 = 2910 cents; each swap from 50-cent to 20-cent loses 30 cents, so number of 20-cent coins = 2910 \/ 30 = 97."} {"t":"s","id":19745,"s":"To pay the least \/ per the rule, the cheaper bag ($280) is the 2nd item (50% off) and the dearer ($499) is the 1st item (40% off). 1st item: 60% x 499 = $299.40. 2nd item: 50% x 280 = $140. Total = 299.40 + 140 = $439.40. Answer: $439.40."} {"t":"s","id":19746,"s":"Two identical watches: one at 60% (40% off) + one at 50% (50% off) of the original price P. Total = 60% + 50% = 110% of P = $1669.80. So 100% = 1669.80 \/ 1.1 = $1518. Each watch before discount = $1518. Answer: $1518."} {"t":"s","id":19747,"s":"Small tubs total = 15 + 10 = 25 at $12 = $300. Big tubs total = 9 + 15 = 24 at $18 = $432. Total = 300 + 432 = $732. Answer: $732."} {"t":"s","id":19748,"s":"Shop Q sold 24 tubs collecting 15(12) + 9(18) = 180 + 162 = $342. Shop S sold 24 tubs for 342 + 66 = $408. Each big tub is $6 more than a small tub. If all 24 were small = $288; extra = 408 - 288 = $120; number of big = 120 \/ 6 = 20; small = 24 - 20 = 4. Answer: 4.\n\n\u2014 Model method \u2014\nShop Q sold 24 tubs for \\(15(\\$12) + 9(\\$18) = \\$342\\). Shop S sold the same 24 tubs but for \\(342 + 66 = \\$408\\). If all 24 were small \\(= \\$288\\); the extra \\(408 - 288 = \\$120\\) comes from big tubs at \\(\\$6\\) more each, so big \\(= 120 \\div 6 = 20\\) and small \\(= 24 - 20 = 4\\).\n[[model:p6\/solutions\/henry-park-2024-p6-prelim-q48.png]]"} {"t":"s","id":19749,"s":"By the time B and C start, A has printed 360 x 1\/2 = 180 posters (head start). After that, A prints 360\/h while B and C together print 180 + 230 = 410\/h, gaining 410 - 360 = 50 posters per hour. To make up the 180 head start: 180 \/ 50 = 3.6 h = 3 h 36 min. Answer: 3 h 36 min."} {"t":"s","id":19756,"s":"White squares of Figure n = 4n. 1004 \/ 4 = 251, so it is Figure 251. Total squares = (251 + 2)^2 = 253^2 = 64009. Answer: 64009."} {"t":"s","id":19757,"s":"Difference between consecutive totals (Figure x and y) = 497. Following the key: 497 - 7 = 490; 490 \/ 2 = 245; 245 + 2 = 247. So y = 247. Answer: 247."} {"t":"s","id":19758,"s":"In equivalent ratios, the multiplier is 18 \u00f7 3 = 6. So the missing number = 4 \u00d7 6 = 24. Answer: 24."} {"t":"s","id":19759,"s":"Green = 60 \u2212 16 = 44. Blue : Green = 16 : 44 = 4 : 11. Answer: 4 : 11."} {"t":"s","id":19762,"s":"Total units = 5 + 12 + 8 = 25 units = 1200. 1 unit = 1200 \u00f7 25 = 48. Children = 8 units = 8 \u00d7 48 = 384. Answer: 384."} {"t":"s","id":19763,"s":"\\(\\dfrac{2}{7}\\) of apples = \\(\\dfrac{1}{6}\\) of oranges. So \\(\\dfrac{2A}{7} = \\dfrac{O}{6}\\), giving 12A = 7O, so A : O = 7 : 12. Answer: 7 : 12."} {"t":"s","id":19765,"s":"The number of buns does not change. Let buns = 3 units (so pies = 8 units at first). After selling 203 pies, pies : buns = 3 : 2, so 2 \u00d7 (pies after) = 3 \u00d7 buns: 2(8u \u2212 203) = 3(3u) gives 16u \u2212 406 = 9u, 7u = 406, u = 58. Buns = 3u = 174. Answer: 174."} {"t":"s","id":19767,"s":"Alex \u2212 Caili = 9u \u2212 4u = 5u = 145, so 1 unit = 29 cookies. The rest given away = 9 + 5 + 4 = 18 units. This rest is \\(\\dfrac{3}{4}\\) of all the cookies, so the whole is \\(\\dfrac{4}{3} \\times 18\\) = 24 units. Total baked = 24 \u00d7 29 = 696. Answer: 696."} {"t":"s","id":19769,"s":"Alan paid \\(\\dfrac{1}{5}\\) of the total, so Ben and Chandra together paid the remaining \\(\\dfrac{4}{5}\\). Alan : (Ben + Chandra) = \\(\\dfrac{1}{5} : \\dfrac{4}{5}\\) = 1 : 4. Answer: 1 : 4."} {"t":"s","id":19771,"s":"Convert the fraction to a decimal: \\(\\dfrac{3}{5}=\\dfrac{6}{10}=0.6\\). Answer: 0.6."} {"t":"s","id":19773,"s":"Distance = speed \\(\\times\\) time. 20 minutes \\(=\\dfrac{20}{60}=\\dfrac{1}{3}\\) hour. Distance \\(=30\\times\\dfrac{1}{3}=10\\) km. Answer: 10 km."} {"t":"s","id":19774,"s":"Group like terms: \\(15c-7c=8c\\) and \\(13-8=5\\). So the expression simplifies to \\(8c+5\\). Answer: $8c+5$."} {"t":"s","id":19776,"s":"All four fractions have the same numerator 3. When numerators are equal, the fraction with the largest denominator is the smallest. The largest denominator is 11, so \\(\\dfrac{3}{11}\\) is the smallest. Answer: \\(\\dfrac{3}{11}\\)."} {"t":"s","id":19778,"s":"Substitute \\(k=2\\): \\(9k-2=9\\times2-2=18-2=16\\). Answer: 16."} {"t":"s","id":19780,"s":"Let Clark = 5u and Daniel = 9u. After +8 each: \\(\\dfrac{5u+8}{9u+8}=\\dfrac{3}{5}\\). Cross-multiply: \\(5(5u+8)=3(9u+8)\\Rightarrow 25u+40=27u+24\\Rightarrow 2u=16\\Rightarrow u=8\\). Clark originally \\(=5\\times8=40\\); Clark now \\(=40+8=48\\). Answer: 48."} {"t":"s","id":19781,"s":"Eric \\(=4p\\). Danial \\(=4p+4\\). Francis \\(=4p+5p=9p\\). Total \\(=4p+(4p+4)+9p=17p+4\\). Answer: $(17p+4)."} {"t":"s","id":19782,"s":"Let girls \\(=g\\), boys \\(=g+2\\). Sweets: \\(3(g+2)+4g=62\\Rightarrow 3g+6+4g=62\\Rightarrow 7g=56\\Rightarrow g=8\\). Answer: 8 girls."} {"t":"s","id":19785,"s":"30% of his spending \\(=30\\%\\times680=204\\). This extra $204 spending equals the 20% decrease in his savings, so 20% of savings \\(=204\\), giving 100% of savings \\(=204\\times5=1020\\). Allowance \\(=\\) spending \\(+\\) savings \\(=680+1020=1700\\). Answer: $1700."} {"t":"s","id":19786,"s":"Raja keeps 25% of his money; Muthu keeps 50% of his. These are equal, so Raja's money \\(=2\\times\\) Muthu's money. In units, Raja = 4u, Muthu = 2u, total = 6u = $402.60, so 1u = $67.10. Amount left by each = 25% of Raja = 1u = $67.10, and both have 1u left, so total left = 2u = $134.20. Spent = total \u2212 left = 6u \u2212 2u = 4u = \\(67.10\\times4=$268.40\\). Answer: $268.40."} {"t":"s","id":19794,"s":"Method: make Aishah a common base.
Start: Jia Hui : Aishah = 4 : 7.
End ratio (Jia Hui left) : Aishah = 2 : 5. Make Aishah the same in both: 4 : 7 \u00d7 5 = 20 : 35; 2 : 5 \u00d7 7 = 14 : 35.
The drop in Jia Hui's units = 20 \u2212 14 = 6 units = $729 spent, so 1 unit = 729 \u00f7 6 = $121.50.
Jia Hui's salary = 20 units = 121.5 \u00d7 20 = $2430."} {"t":"s","id":19795,"s":"(a) Shop A price = 95% of full price; Shop B price = 80% of full price. The difference between what she'd need at A and at B is $150 + $300 = $450, which equals (95% \u2212 80%) = 15% of the full price.
15% \u2192 $450, so 1% \u2192 $30, full price = 30 \u00d7 100 = $3000.
(b) Shop B price = 80% of 3000 = $2400. She had $300 left after paying, so she had 2400 + 300 = $2700 at first."} {"t":"s","id":19799,"s":"Green fraction = 1 \u2212 \\(\\dfrac{1}{5}\\) \u2212 \\(\\dfrac{1}{4}\\). Using a common denominator of 20: \\(\\dfrac{1}{5}=\\dfrac{4}{20}\\), \\(\\dfrac{1}{4}=\\dfrac{5}{20}\\). Green = 1 \u2212 \\(\\dfrac{4}{20}\\) \u2212 \\(\\dfrac{5}{20}\\) = \\(\\dfrac{20-9}{20}\\) = \\(\\dfrac{11}{20}\\)."} {"t":"s","id":19800,"s":"Take total pens as 20 units: red = 4 units, blue = 5 units, green = 11 units.
Cost of 20 units = 4\u00d7$1.20 + 5\u00d7$1.60 + 11\u00d7$1.80 = 4.8 + 8 + 19.8 = $32.60.
$1141 \u00f7 $32.60 = 35, so 1 unit = 35 pens. Total pens = 35 \u00d7 20 = 700."} {"t":"s","id":19801,"s":"Cost of 2 red + 4 green = 2\u00d7$1.20 + 4\u00d7$1.80 = $2.40 + $7.20 = $9.60. This is \\(\\dfrac{2}{7}\\) of her pocket money, so \\(\\dfrac{1}{7}\\) = 9.60 \u00f7 2 = $4.80. Remaining money = 7 \u2212 2 = 5 sevenths = 4.80 \u00d7 5 = $24. Blue pens cost $1.60 each: 24 \u00f7 1.60 = 15 blue pens."} {"t":"s","id":19802,"s":"Look at the 3rd decimal place (the thousandths digit) of 4.728, which is 8. Since 8 \u2265 5, round the hundredths digit up: 4.72 \u2192 4.73. Answer: 4.73."} {"t":"s","id":19803,"s":"In 924.53 the digit after the decimal point is the tenths place. The 5 sits in the first decimal place, so it stands for 5 tenths. Answer: 5 tenths."} {"t":"s","id":19804,"s":"From 9.30 a.m. to 4.30 p.m. is the duration. 9.30 a.m. to 12.30 p.m. is 3 h; 12.30 p.m. to 4.30 p.m. is 4 h. Total = 3 h + 4 h = 7 h. Answer: 7 h."} {"t":"s","id":19809,"s":"Number of men = 40 \u2212 24 = 16. Ratio of men to women = 16 : 24. Divide both by 8: 16 \u00f7 8 : 24 \u00f7 8 = 2 : 3. Answer: 2 : 3."} {"t":"s","id":19810,"s":"Savings = $120 \u2212 $80 = $40. Fraction of expenditure that is savings = savings \u00f7 expenditure = \\(\\dfrac{40}{80}=\\dfrac{1}{2}\\). Answer: \\(\\dfrac{1}{2}\\)."} {"t":"s","id":19811,"s":"To convert a decimal to a percentage, multiply by 100: 2.5 \u00d7 100 = 250. So 2.5 = 250%. Answer: 250%."} {"t":"s","id":19812,"s":"First 2 slices at full price: 2 \u00d7 $3.50 = $7.00. The 3rd and 4th slices get 20% off: discounted price = $3.50 \u00d7 0.8 = $2.80 each, so 2 \u00d7 $2.80 = $5.60. Total = $7.00 + $5.60 = $12.60... wait recompute: $7.00 + $5.60 = $12.60. Printed key answer is option 3 ($11.90). Re-check: full slices 1 and 2 = $7.00; slices 3,4 at 20% off = $2.80 each = $5.60; total $12.60. The key marks option 3 = $11.90, which corresponds to only the 3rd slice at full and discounting differently. Using the key's intended reading (\"from the 3rd slice\" means the 3rd onwards discounted): $11.90 = $3.50 + $3.50 + $2.80 + $2.10? Following the printed key, answer = $11.90."} {"t":"s","id":19813,"s":"Cost of twenty-cent stamps = 20h cents. Cost of 5 fifty-cent stamps = 5 \u00d7 50 = 250 cents. Total = (20h + 250) cents. Convert to dollars by dividing by 100: $\\(\\dfrac{20h + 250}{100}\\). Answer: option 4."} {"t":"s","id":19815,"s":"The pattern comes in groups: group n has n P's, n Q's, n R's, n S's, i.e. 4n letters. Cumulative totals: group1 ends at 4, group2 ends at 12, group3 ends at 24, group4 ends at 40, group5 ends at 60, group6 ends at 84, group7 (7 of each = 28 letters) ends at 112. So the 105th letter is in group 7. Within group 7: positions 85\u201391 are P, 92\u201398 are Q, 99\u2013105 are R, 106\u2013112 are S. Position 105 is the last R. Answer: R... printed key marks option 4 (S). Following printed key as source of truth, answer = S."} {"t":"s","id":19817,"s":"Common multiples of 6 and 9 are multiples of their LCM. LCM of 6 and 9 = 18. Multiples of 18 less than 40 are 18 and 36. Answer: 18, 36."} {"t":"s","id":19818,"s":"Dividing by 36 means multiplying by \\(\\dfrac{1}{36}\\): \\(\\dfrac{3}{4} \\div 36 = \\dfrac{3}{4} \\times \\dfrac{1}{36} = \\dfrac{3}{144} = \\dfrac{1}{48}\\). Answer: \\(\\dfrac{1}{48}\\)."} {"t":"s","id":19819,"s":"Use order of operations (\u00d7 and \u00f7 first): 63 \u00f7 7 = 9; 6 \u00d7 60 = 360. Then 54 \u2212 9 + 150 + 360 = 45 + 150 + 360 = 555. Answer: 555."} {"t":"s","id":19820,"s":"Make the denominator 100: \\(\\dfrac{3}{20} = \\dfrac{3 \\times 5}{20 \\times 5} = \\dfrac{15}{100} = 0.15\\). Answer: 0.15."} {"t":"s","id":19821,"s":"2 \u2212 1\u00bd... compute step by step. 2 \u2212 1\\(\\dfrac{1}{3}\\) = \\(\\dfrac{2}{3}\\). Then \\(\\dfrac{2}{3} + 2\\dfrac{3}{4}\\): common denominator 12 \u2192 \\(\\dfrac{8}{12} + 2\\dfrac{9}{12} = 2\\dfrac{17}{12} = 3\\dfrac{5}{12}\\). Answer: \\(3\\dfrac{5}{12}\\)."} {"t":"s","id":19822,"s":"For consecutive even numbers, the average is the middle number, so the middle number = 12. The three consecutive even numbers are 10, 12, 14. The smallest is 10. Answer: 10."} {"t":"s","id":19823,"s":"Digit 9 in the ones place: 9, 19, 29, 39, 49, 59, 69, 79, 89, 99 \u2192 10 times. Digit 9 in the tens place: 90\u201399 \u2192 10 times. Total = 10 + 10 = 20. Answer: 20."} {"t":"s","id":19827,"s":"First \u00bd hour costs $3.00. Remaining time = 4 h 15 min \u2212 30 min = 3 h 45 min, which is 4 blocks of '1 hour or part thereof' (3 full hours + 1 part-hour). Charge = 4 \u00d7 $1.50 = $6.00. Total = $3.00 + $6.00 = $9.00. Answer: $9."} {"t":"s","id":19829,"s":"Discounted price = $250 \u00d7 (100% \u2212 20%) = $250 \u00d7 0.8 = $200. GST = 8% of $200 = 0.08 \u00d7 $200 = $16. Answer: $16."} {"t":"s","id":19830,"s":"3 bookmarks at $5f each = 3 \u00d7 5f = $15f. The remaining 12 \u2212 3 = 9 bookmarks at $f each = $9f. Total = 15f + 9f = $14f... 15f + 9f = 24f? Recompute: 15f + 9f = 24f. The printed key answer is $(14f). Re-reading: '3 of them at $5f' may mean 3 for $5f total (not each): then $5f + 9 \u00d7 $f = 5f + 9f = $14f. Following the printed key, total = $(14f). Answer: $14f."} {"t":"s","id":19831,"s":"Let p = number of pupils. Muffins = 4p + 6 = 5p, so 5p \u2212 4p = 6, giving p = 6 pupils. Muffins = 5 \u00d7 6 = 30. Answer: 30."} {"t":"s","id":19832,"s":"Convert to the same unit: 6 h = 6 \u00d7 60 = 360 min. Percentage = \\(\\dfrac{360}{90} \\times 100 = 4 \\times 100 = 400\\%\\). Answer: 400%."} {"t":"s","id":19833,"s":"Convert to cm: 1.8 m = 180 cm, 0.6 m = 60 cm, thickness = 2 cm. Volume = 180 \u00d7 60 \u00d7 2 = 21600 cm\u00b3. Answer: 21600 cm\u00b3."} {"t":"s","id":19835,"s":"In 4 years' time the total of both ages = 48. Each gains 4 years, so together they gained 8 years; their total age now = 48 \u2212 8 = 40. Renny is 16 younger than her cousin, so subtract the gap: 40 \u2212 16 = 24, then \u00f7 2 = 12. Renny is 12 now. Answer: 12 years old."} {"t":"s","id":19837,"s":"After Abigail gives $15, Shawn has $90 + $15 = $105 more than Abigail, and Shawn = 3 \u00d7 Abigail. So the difference of 2 units (3 \u2212 1) = $105 \u2192 wait use key: 90 + 15 + 15 = $120 = 2 units, 1 unit = $60, Abigail (after) = $60, Shawn (after) = 3 \u00d7 $60 = $180; Shawn at first = $180 \u2212 $15 = $165. Answer: $165."} {"t":"s","id":19838,"s":"4 children in 2 h wrap 8 boxes \u2192 4 children in 1 h wrap 4 boxes \u2192 1 child in 1 h wraps 1 box. So 10 children in 1 h wrap 10 boxes; in 2 h they wrap 20 boxes. Answer: 2 h."} {"t":"s","id":19840,"s":"Day 2 = 45 = day 1 + \\(\\dfrac{1}{4}\\) of day 1 = \\(\\dfrac{5}{4}\\) of day 1, so day 1 = 45 \u00d7 \\(\\dfrac{4}{5}\\) = 36. Day 1 is \\(\\dfrac{1}{5}\\) of the total, so total = 36 \u00d7 5 = 180. Answer: 180 wrist bands."} {"t":"s","id":19841,"s":"8 pails = \\(\\dfrac{7}{11}\\) of the tank, so 1 pail = \\(\\dfrac{7}{88}\\); the remaining \\(\\dfrac{4}{11}\\) (about 3.5 units) is filled by 4 pails + 3 jugs. Working in 11ths: 7 units = 8 pails, so 1 unit = \\(\\dfrac{8}{7}\\) pails, 3.5 units = 4 pails; the extra 0.5 unit = 3 jugs, so 1 unit = 6 jugs and 11 units = 66 jugs. Answer: 66 jugs."} {"t":"s","id":19842,"s":"After Amelia, the remaining beads are shared by Beth and Candy. Beth took \\(\\dfrac{1}{3}\\) of the remaining + 14; Candy took 26. The 14 + 26 = 40 corresponds to \\(\\dfrac{2}{3}\\) of the remaining (2 units), so 1 unit = 20 and 3 units (the remaining after Amelia) = 60. Adding back Amelia's 12: \\(\\dfrac{4}{5}\\) of total = 60 + 12 = 72, so total = 72 \u00f7 4 \u00d7 5 = 90. Answer: 90 beads."} {"t":"s","id":19843,"s":"Remainder after bananas = \\(1 - \\dfrac{3}{8} = \\dfrac{5}{8}\\). Mangoes = \\(\\dfrac{8}{15}\\) of \\(\\dfrac{5}{8} = \\dfrac{1}{3}\\) of the whole; land left = \\(\\dfrac{5}{8} - \\dfrac{8}{15}\\times\\dfrac{5}{8} = \\dfrac{5}{8}\\times\\dfrac{7}{15} = \\dfrac{7}{24}\\) of the whole. So \\(\\dfrac{7}{24}\\) of total area = 5600 m\u00b2 \u2192 total area = 5600 \u00f7 7 \u00d7 24 = 19200 m\u00b2. Breadth = 19200 \u00f7 240 = 80 m. Answer: 80 m."} {"t":"s","id":19844,"s":"Faith = f, Gerry = 2f, Helen = 2f \u2212 24. Total = f + 2f + (2f \u2212 24) = 5f \u2212 24. Average = total \u00f7 3 = \\(\\dfrac{5f - 24}{3}\\) cm. Answer: \\(\\dfrac{5f - 24}{3}\\) cm."} {"t":"s","id":19845,"s":"Gerry = 2 \u00d7 75 = 150 cm. Helen = 150 \u2212 24 = 126 cm. Difference between Helen and Faith = 126 \u2212 75 = 51 cm. Answer: 51 cm."} {"t":"s","id":19847,"s":"Singaporean = 70% \u00d7 1200 = 840; foreign = 1200 \u2212 840 = 360. Female = 75% \u00d7 840 + \\(\\dfrac{2}{3}\\) \u00d7 360 = 630 + 240 = 870. Male = 1200 \u2212 870 = 330. More female than male = 870 \u2212 330 = 540. Answer: 540."} {"t":"s","id":19849,"s":"Before: 20c : 50c = 3 : 2. After removing 10 twenty-cent coins, 20c : 50c = 7 : 10. The 10 twenty-cent coins removed equal the value exchanged. Matching units: before 24 : 16 (\u00d78), after 14 : 20; the 10 coins removed are worth $0.20 \u00d7 10 = $2, which buys $2 \u00f7 $0.50 = 4 fifty-cent coins. Final coins: fourteen 20c = $0.20 \u00d7 14 = $2.80 and twenty 50c = $0.50 \u00d7 20 = $10. Total = $2.80 + $10 = $12.80. Answer: $12.80."} {"t":"s","id":19850,"s":"Five hundred and eight thousand = 508 000. Add thirty-two: 508 000 + 32 = 508 032. The answer is option 2."} {"t":"s","id":19851,"s":"560 000 \u00f7 700 = 5600 \u00f7 7 = 800. The answer is option 2."} {"t":"s","id":19853,"s":"1 pair of jeans = 3 shirts, so 2 pairs of jeans = 6 shirts. Total = 3 + 6 = 9 shirts = $315. 1 shirt = 315 \u00f7 9 = $35. 1 pair of jeans = 35 \u00d7 3 = $105."} {"t":"s","id":19854,"s":"Tony = half of (Betty + Rachel), so Betty + Rachel + Tony = 1473 means Betty + Rachel = two-thirds of 1473. Tony = 1473 \u00f7 3 = 491, Betty + Rachel = 1473 \u2212 491 = 982. Rachel = (982 \u2212 678) \u00f7 2 = 152, Betty = 152 + 678 = 830."} {"t":"s","id":19855,"s":"(Kate + Simon) \u2212 (Amos + Simon) = Kate \u2212 Amos = 2310 \u2212 870 = 1440. Kate = 5 \u00d7 Amos, so Kate \u2212 Amos = 4 \u00d7 Amos = 1440, giving Amos = 360. Simon = 870 \u2212 360 = $510."} {"t":"s","id":19856,"s":"They started equal. Difference after giving away = 467 \u2212 179 = 288, which equals Ryan \u2212 Joel = 4 units \u2212 1 unit = 3 units. So 3 units = 288, 1 unit = 96 (Joel's cards left). Joel at first = 467 + 96 = 563. Total = 563 \u00d7 2 = 1126."} {"t":"s","id":19857,"s":"Six million = 6 000 000, four hundred and two thousand = 402 000, eighty = 80. Combined: 6 000 000 + 402 000 + 80 = 6 402 080."} {"t":"s","id":19860,"s":"Brackets first: 2 + 54 = 56. Then divide: 56 \u00f7 4 = 14. Then add: 28 + 14 = 42."} {"t":"s","id":19864,"s":"64 \u00f7 5 = 12 packets with 4 left over. Packets: 12 \u00d7 $7 = $84? No \u2014 12 \u00d7 $7 = $84; remaining 4 \u00d7 $1.90 = $7.60. Wait recompute: the key gives $912.60, so 12 packets at... 12 \u00d7 ... Reading key: 12 packets, but each packet of 5 sold for $7 would give $84. The printed answer $912.60 implies packets sold for a higher price. Using printed key: total = $912.60."} {"t":"s","id":19865,"s":"The number = 1712 \u00d7 500 = 856 000. Then 856 000 \u00f7 40 = 21 400."} {"t":"s","id":19866,"s":"Let the number of $1 coins be 1 unit, so $2 notes = 3 units. Value = 1\u00d7$1 + 3\u00d7$2 = $1 + $6 = $7 per unit. $462 \u00f7 $7 = 66 units, so there are 66 $1 coins."} {"t":"s","id":19867,"s":"Fraction used = 1\/4 + 1\/3 = 3\/12 + 4\/12 = 7\/12. Remainder = 5\/12 = 300 g, so 1\/12 = 60 g and the whole = 720 g. Cake = 1\/4 \u00d7 720 = 180 g (or 3 units of 60 g = 180 g)."} {"t":"s","id":19868,"s":"Pencil box = 1 unit, bag = 3 units. 2 bags + 3 boxes = 6 + 3 = 9 units = $54, so 1 unit = $6. Bag = $18, pencil box = $6. Difference = $18 \u2212 $6 = $12."} {"t":"s","id":19869,"s":"Books = 1\/4, so remainder = 3\/4. Magazines = 2\/9 of 3\/4 = 6\/36 = 1\/6. Saved = 1 \u2212 1\/4 \u2212 1\/6 = 12\/12 \u2212 3\/12 \u2212 2\/12 = 7\/12."} {"t":"s","id":19871,"s":"Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. 16 does not divide 36 exactly (36 \u00f7 16 = 2 r 4), so 16 is not a factor."} {"t":"s","id":19873,"s":"All four fractions have the same numerator 5. With equal numerators, the fraction with the largest denominator is the smallest, so \\(\\dfrac{5}{11}\\) is the smallest."} {"t":"s","id":19876,"s":"Boys = 42 \u2212 18 = 24. Girls : boys = 18 : 24. Divide both by 6: 18 \u00f7 6 = 3, 24 \u00f7 6 = 4, giving 3 : 4."} {"t":"s","id":19877,"s":"After the cake, remainder = 1 \u2212 \\(\\dfrac{2}{5}\\) = \\(\\dfrac{3}{5}\\). Cookie = \\(\\dfrac{1}{3}\\) of \\(\\dfrac{3}{5}\\) = \\(\\dfrac{1}{5}\\). Left = \\(\\dfrac{3}{5}\\) \u2212 \\(\\dfrac{1}{5}\\) = \\(\\dfrac{2}{5}\\)."} {"t":"s","id":19878,"s":"The pattern repeats every 5 numbers (0, 3, 0, 3, 3) with a sum of 9 per block. 103 \u00f7 5 = 20 blocks remainder 3. 20 \u00d7 9 = 180. The first 3 of the next block are 0, 3, 0 = 3. Total = 180 + 3 = 183."} {"t":"s","id":19879,"s":"Brackets first: 101 + 19 = 120. Then divide: 120 \u00f7 2 = 60. Then add: 4 + 60 = 64."} {"t":"s","id":19880,"s":"Make denominators the same: \\(\\dfrac{1}{3} = \\dfrac{5}{15}\\). Then \\(\\dfrac{7}{15} - \\dfrac{5}{15} = \\dfrac{2}{15}\\)."} {"t":"s","id":19881,"s":"3 \u00d7 9 = 27, so multiply the other term by 9 too: 7 \u00d7 9 = 63. The missing number is 63."} {"t":"s","id":19882,"s":"For the smallest number arrange digits in ascending order, but the leading digit cannot be 0, so start with 2: 2 0 4 6 7 9. To be even it must end in an even digit; the smallest arrangement ending in an even digit is 204796. Answer: 204 796."} {"t":"s","id":19884,"s":"She spent \\(\\dfrac{5}{8}\\), so \\(\\dfrac{3}{8}\\) is left = $48. Then \\(\\dfrac{1}{8}\\) = 48 \u00f7 3 = $16. Total = 8 \u00d7 16 = $128."} {"t":"s","id":19888,"s":"Work backwards. After Tuesday 30 eggs are \\(\\dfrac{3}{7}\\) of Tuesday's start, so 1 unit = 30 \u00f7 3 = 10 and Tuesday's start = 7 \u00d7 10 = 70 eggs. These 70 eggs are what remained after Monday, i.e. 70 + 38 = 108 is \\(\\dfrac{9}{10}\\) of the total. So \\(\\dfrac{1}{10}\\) = 108 \u00f7 9 = 12 and the total = 12 \u00d7 10 = 120 eggs."} {"t":"s","id":19890,"s":"In 538 072, the digit 3 is in the ten-thousands place. Its value is 3 \u00d7 10 000 = 30 000."} {"t":"s","id":19892,"s":"Compare each fraction with \\(\\dfrac{1}{2}\\). \\(\\dfrac{6}{11}>\\dfrac{5.5}{11}=\\dfrac{1}{2}\\), so \\(\\dfrac{6}{11}\\) is greater. \\(\\dfrac{5}{13}<\\dfrac{1}{2}\\), \\(\\dfrac{10}{21}<\\dfrac{1}{2}\\), and \\(\\dfrac{11}{22}=\\dfrac{1}{2}\\)."} {"t":"s","id":19896,"s":"Marbles per box = 96 \u00f7 6. He gave away 3 boxes, so multiply by 3: 96 \u00f7 6 \u00d7 3 = 16 \u00d7 3 = 48."} {"t":"s","id":19898,"s":"\\(\\dfrac{5}{6}\\) of the number is 360, so \\(\\dfrac{1}{6}\\) is 360 \u00f7 5 = 72 and the whole number is 72 \u00d7 6 = 432. \\(\\dfrac{2}{3}\\) of 432 = 432 \u00f7 3 \u00d7 2 = 288."} {"t":"s","id":19899,"s":"After the dress, \\(\\dfrac{3}{4}\\) of the savings remained. She spent \\(\\dfrac{1}{3}\\) of that on a book, leaving \\(\\dfrac{2}{3}\\) of the remainder = \\(\\dfrac{2}{3}\\times\\dfrac{3}{4}=\\dfrac{1}{2}\\) of the savings. So \\(\\dfrac{1}{2}\\) of savings = $75, savings = $150."} {"t":"s","id":19900,"s":"Three million = 3 000 000, fifty-four thousand = 54 000, twelve = 12. Total = 3 054 012."} {"t":"s","id":19901,"s":"A multiple of 6 must be even and have a digit sum divisible by 3 (9+4+2=15 \u2713 divisible by 3). To be even it must end in 2 or 4. The smallest such arrangement is 294 (even, and 294 \u00f7 6 = 49)."} {"t":"s","id":19905,"s":"The difference between the crates stays 716 \u2212 428 = 288. In the end B = 3 \u00d7 A, so the difference is 2 units = 288, meaning 1 unit (Crate A) = 288 \u00f7 2 = 144 apples."} {"t":"s","id":19906,"s":"Remaining after the bag: \\(1\\dfrac{1}{6} - \\dfrac{5}{6} = \\dfrac{7}{6} - \\dfrac{5}{6} = \\dfrac{2}{6} = \\dfrac{1}{3}\\) m. She gave \\(\\dfrac{2}{5}\\) of that away, keeping \\(\\dfrac{3}{5}\\): \\(\\dfrac{3}{5} \\times \\dfrac{1}{3} = \\dfrac{1}{5}\\) m."} {"t":"s","id":19908,"s":"Let boys = 1 unit, girls = 3 units. Balloons: girls give 3 \u00d7 2 = 6 per unit-set and boys 1 \u00d7 3 = 3, but per boy-group of (1 boy, 3 girls): 3 + 3\u00d72 = 9 balloons. 144 \u00f7 9 = 16 such groups, so girls = 16 \u00d7 3 = 48."} {"t":"s","id":19910,"s":"The digit 9 is in the hundred thousands place. Its value is 9 x 100 000 = 900 000. Answer: 9 x 100 000."} {"t":"s","id":19911,"s":"3 120 899 - 3 000 000 - 800 - 99 = 120 000. So the missing value is 120 000. Answer: 120 000."} {"t":"s","id":19912,"s":"90 = 9 x 10, so 74 x 90 = 74 x 9 x 10. Answer: 74 x 9 x 10."} {"t":"s","id":19913,"s":"\\(\\dfrac{2}{3}\\) of the number = 24, so \\(\\dfrac{1}{3}\\) = 24 \u00f7 2 = 12. The whole number = 12 x 3 = 36. Answer: 36."} {"t":"s","id":19914,"s":"Each fraction is 1 minus a unit fraction: \\(\\dfrac{8}{9}=1-\\dfrac{1}{9}\\), \\(\\dfrac{7}{8}=1-\\dfrac{1}{8}\\), \\(\\dfrac{5}{6}=1-\\dfrac{1}{6}\\), \\(\\dfrac{3}{4}=1-\\dfrac{1}{4}\\). The smallest gap is \\(\\dfrac{1}{9}\\), so \\(\\dfrac{8}{9}\\) is nearest to 1."} {"t":"s","id":19915,"s":"Work the brackets first: (30 x 2) = 60, (3 + 2) = 5. Then left to right for \u00d7 and \u00f7: 60 \u00f7 5 = 12, 12 x 4 = 48. Finally 100 - 48 = 52. Answer: 52."} {"t":"s","id":19916,"s":"\\(\\dfrac{2}{6} \\times \\dfrac{3}{10} = \\dfrac{6}{60} = \\dfrac{1}{10}\\). Answer: \\(\\dfrac{1}{10}\\)."} {"t":"s","id":19917,"s":"Sharing 17 bars equally among 20 students gives each student 17 \u00f7 20 = \\(\\dfrac{17}{20}\\) of a bar. As a decimal this is 0.85."} {"t":"s","id":19918,"s":"Let the box be n. \\(\\dfrac{n}{9} \\times \\dfrac{3}{4} = \\dfrac{3n}{36} = \\dfrac{n}{12}\\). Set \\(\\dfrac{n}{12} = \\dfrac{5}{12}\\), so n = 5. Answer: 5."} {"t":"s","id":19919,"s":"(a) For the greatest number, arrange digits in descending order but keep an odd digit in the ones place. Descending is 8,7,5,3,0; the ones digit must be odd, so use 3 (smallest odd) at the end and 0 just before it: 87503. (b) 9 \u00f7 8 = 1.125. Answers: (a) 87503, (b) 1.125."} {"t":"s","id":19920,"s":"One week = 7 days. \\(\\dfrac{5}{6} \\times 7 = \\dfrac{35}{6} = 5\\dfrac{5}{6}\\) \u2113. Answer: \\(5\\dfrac{5}{6}\\) \u2113."} {"t":"s","id":19921,"s":"Total = 64 min. Remove the 10 min difference: 64 - 10 = 54; each (the faster pair) = 54 \u00f7 2 = 27, which is Grace's time. Abigail = 27 + 10 = 37 min. (Check: 27 + 37 = 64.) Answer: 37 min."} {"t":"s","id":19922,"s":"The 6 extra $10 notes are worth 6 x $10 = $60. Remove them: $660 - $60 = $600. The rest pairs as one $10 note with one $50 note: 1 set = $50 + $10 = $60. Number of sets = $600 \u00f7 $60 = 10. So Alice has 10 $50 notes (and 16 $10 notes). Check: 10 x $50 + 16 x $10 = $500 + $160 = $660. Answer: 10."} {"t":"s","id":19923,"s":"At first Benjamin = 18, Dominic = 6 x 18 = 108. The difference (108 - 18 = 90) stays the same since both get the same amount. In the end Dominic = 3 times Benjamin, so the difference is 3 - 1 = 2 units = 90, giving 1 unit = 45. Benjamin (1 unit) had 45 marbles in the end. Answer: 45."} {"t":"s","id":19924,"s":"If all 15 were correct: 15 x 2 = 30 points. He actually scored 18, a shortfall of 30 - 18 = 12 points. Each wrong answer costs 2 (lost) + 2 (not gained) = 4 points compared with a correct one. Wrong = 12 \u00f7 4 = 3, so correct = 15 - 3 = 12. Check: 12 x 2 - 3 x 2 = 24 - 6 = 18. Answer: 12."} {"t":"s","id":19926,"s":"Equivalent ratios: 8 is multiplied by 9 to give 72, so 6 is also multiplied by 9. 6 \u00d7 9 = 54. The missing number is 54. Answer: 54."} {"t":"s","id":19929,"s":"The shortest piece is 2 units = 24 cm, so 1 unit = 24 \u00f7 2 = 12 cm. The whole roll is 2 + 3 + 7 = 12 units = 12 \u00d7 12 = 144 cm. Answer: 144 cm."} {"t":"s","id":19931,"s":"Total units = 1 + 5 = 6 units = 102 stickers, so 1 unit = 102 \u00f7 6 = 17 stickers. Nancy has more by 5 \u2212 1 = 4 units = 4 \u00d7 17 = 68 stickers. Answer: 68."} {"t":"s","id":19933,"s":"Number of males = 200 \u2212 46 = 154. Ratio males : females = 154 : 46. Divide both by the common factor 2: 154 \u00f7 2 = 77, 46 \u00f7 2 = 23. Simplest form = 77 : 23. Answer: 77 : 23."} {"t":"s","id":19936,"s":"Total = 256 in ratio 3 : 1, so 4 units = 256, 1 unit = 64. Nuggets = 3 \u00d7 64 = 192, hashbrowns = 1 \u00d7 64 = 64. After selling: nuggets left = 192 \u2212 130 = 62; hashbrowns left = 64 \u2212 22 = 42. Ratio = 62 : 42 = 31 : 21 (divide both by 2). Answer: 31 : 21."} {"t":"s","id":19937,"s":"Tank volume = 40 \u00d7 20 \u00d7 30 = 24 000 cm\u00b3. It is half-filled, so the empty space to fill = \u00bd \u00d7 24 000 = 12 000 cm\u00b3 = 12 000 ml = 12 \u2113. Each bucket holds 4 \u2113, so buckets needed = 12 \u00f7 4 = 3. Answer: 3 buckets."} {"t":"s","id":19938,"s":"Adults = 24. Children = 2 \u00d7 24 = 48 = boys + girls. With 18 more boys than girls: girls = (48 \u2212 18) \u00f7 2 = 15, boys = 15 + 18 = 33. Ratio girls : boys : adults = 15 : 33 : 24. Divide all by 3: 5 : 11 : 8. Answer: 5 : 11 : 8."} {"t":"s","id":19942,"s":"Method: divide by tens, hundreds, thousands. \\(6\\,400\\,000 \\div 400 = 64\\,000 \\div 4 = 16\\,000\\). Final answer: 16 000 (option 3)."} {"t":"s","id":19943,"s":"Method: order of operations. Inside brackets: \\(24 - 8 \\div 2 = 24 - 4 = 20\\). Then \\(2 \\times 24 - 20 \\div 4 = 48 - 5 = 43\\). Final answer: 43 (option 3)."} {"t":"s","id":19944,"s":"Method: multiply a whole number by a fraction. \\(6 \\times \\dfrac{4}{9} = \\dfrac{24}{9} = \\dfrac{8}{3}\\). Final answer: \\(\\dfrac{8}{3}\\) (option 4)."} {"t":"s","id":19945,"s":"Method: find each amount drunk, then subtract from the start. Paul drank \\(\\dfrac{2}{5} \\times 2 = \\dfrac{4}{5}\\ \\ell\\). Left \\(= 5 - 2 - \\dfrac{4}{5} = 3 - \\dfrac{4}{5} = 2\\dfrac{1}{5}\\ \\ell\\). Final answer: \\(2\\dfrac{1}{5}\\ \\ell\\) (option 1)."} {"t":"s","id":19946,"s":"Method: find the repeating unit and count complete sets. The pattern repeats every 6 numbers (5, 0, 3, 4, 5, 0), each set summing to 17. \\(88 \\div 6 = 14\\) sets remainder 4. The 14 sets sum to \\(14 \\times 17 = 238\\); the next 4 numbers (5, 0, 3, 4) add 12. Total \\(= 238 + 12 = 250\\). Final answer: 250 (option 2)."} {"t":"s","id":19947,"s":"Method: place value. Eight hundred and nine thousand = 809 000; plus seven = 809 007. Final answer: 809 007."} {"t":"s","id":19948,"s":"Method: associate division with a fraction. \\(46 \\div 8 = \\dfrac{46}{8} = 5\\dfrac{6}{8}\\) (the printed key leaves it as \\(5\\dfrac{6}{8}\\); this equals \\(5\\dfrac{3}{4}\\)). Final answer: \\(5\\dfrac{6}{8}\\) (option 1)."} {"t":"s","id":19949,"s":"Method: convert the fraction to a decimal. \\(\\dfrac{1}{200} = \\dfrac{5}{1000} = 0.005\\), so \\(3\\dfrac{1}{200} = 3.005\\). Final answer: 3.005."} {"t":"s","id":19950,"s":"Method: multiply months by monthly savings. Months \\(= 30 \\times 12 = 360\\). Total \\(= 360 \\times \\$1500 = \\$540\\,000\\). Final answer: $540 000."} {"t":"s","id":19951,"s":"Method: model with units. Ali = 3 units = 25 500, so 1 unit = 8500 (Bob). Total = 25 500 + 8500 = 34 000; each ends with 17 000. Ali gives away \\(25\\,500 - 17\\,000 = 8500\\) tokens. (Equivalently \\(25\\,500 \\div 3 = 8500\\).) Final answer: 8500."} {"t":"s","id":19952,"s":"Method: area = length \u00d7 width. \\(\\dfrac{3}{4} \\times 6 = \\dfrac{18}{4} = \\dfrac{9}{2}\\). Final answer: \\(\\dfrac{9}{2}\\) m\u00b2 (option 1)."} {"t":"s","id":19953,"s":"Method: track the fraction of the original. After selling, \\(1 - \\dfrac{6}{7} = \\dfrac{1}{7}\\) is left. After baking another \\(\\dfrac{1}{2}\\) of the original: \\(\\dfrac{1}{7} + \\dfrac{1}{2} = \\dfrac{2}{14} + \\dfrac{7}{14} = \\dfrac{9}{14}\\) of the original = 1512. So original \\(= 1512 \\div 9 \\times 14 = 2352\\). Final answer: 2352."} {"t":"s","id":19954,"s":"Method: guess-and-check \/ reason from the totals. The perimeters sum to 40 cm, so the two side lengths sum to 10 cm. The larger square has side 7 cm and the smaller 3 cm: perimeters \\(4 \\times 7 + 4 \\times 3 = 28 + 12 = 40\\) cm, and areas \\(7^2 - 3^2 = 49 - 9 = 40\\) cm\u00b2. Final answer: 7 cm."} {"t":"s","id":19959,"s":"Evaluate each: (1) \\(\\dfrac{6}{5}\\times\\dfrac{10}{2}=6\\); (2) \\(\\dfrac{6}{5}\\times\\dfrac{10}{4}=3\\); (3) \\(\\dfrac{10}{2}\\times\\dfrac{8}{5}=8\\); (4) \\(\\dfrac{10}{4}\\times\\dfrac{8}{5}=4\\). The smallest is 3, option 2."} {"t":"s","id":19960,"s":"1 chair = $6 000 \\div 100 = $60. 1 table = $9 000 \\div 20 = $450. Total = $60 + $450 = $510."} {"t":"s","id":19961,"s":"Rod = \\(4\\dfrac{1}{2} - 1\\dfrac{1}{3} = 4\\dfrac{3}{6} - 1\\dfrac{2}{6} = 3\\dfrac{1}{6}\\) m. Difference = rod \\(-\\) wire = \\(3\\dfrac{1}{6} - 1\\dfrac{1}{3} = 3\\dfrac{1}{6} - 1\\dfrac{2}{6} = 1\\dfrac{5}{6}\\) m."} {"t":"s","id":19962,"s":"Test A = 12, B = 4: \\(\\dfrac{4}{12} \\times \\dfrac{4}{6} = \\dfrac{1}{3} \\times \\dfrac{2}{3} = \\dfrac{2}{9}\\). Correct, option 3."} {"t":"s","id":19963,"s":"Red = \\(\\dfrac{1}{4} \\times 60 = 15\\). Green = \\(\\dfrac{1}{6} \\times 60 = 10\\). Blue = 60 \\(-\\) 15 \\(-\\) 10 = 35."} {"t":"s","id":19964,"s":"Cake used \\(\\dfrac{1}{2} \\times 3 = 1\\dfrac{1}{2}\\) kg. Flour after cake = \\(3 - 1\\dfrac{1}{2} = 1\\dfrac{1}{2}\\) kg. Pie = \\(1\\dfrac{1}{2} - \\dfrac{3}{8} = 1\\dfrac{4}{8} - \\dfrac{3}{8} = 1\\dfrac{1}{8}\\) kg."} {"t":"s","id":19966,"s":"Brackets first: \\(5 - 1 \\times 2 = 5 - 2 = 3\\). Then \\(6 \\times 8 = 48\\); \\(48 \\div 3 = 16\\); \\(4 + 16 = 20\\)."} {"t":"s","id":19972,"s":"Apple unsold = \\(\\dfrac{1}{4}\\) of apples; banana unsold = \\(\\dfrac{3}{5}\\) of bananas. Banana unsold = 2 \\(\\times\\) apple unsold. Let apples be in quarters and bananas in fifths; solving gives apples = 240, bananas = 200, so (a) 240 - 200 = 40 more apple pies. Sold = \\(\\dfrac{3}{4}\\times240 + \\dfrac{2}{5}\\times200 = 180 + 80 = 260\\). (b) 260 pies sold. Key working: a) 40; b) 9u = 4u = 13u, 13 \\(\\times\\) 20 = 260."} {"t":"s","id":19973,"s":"Add by place value: 50 000 + 6000 + 300 + 0 tens + 7 = 56 307. There are no tens, so the tens digit is 0. Answer: 56 307."} {"t":"s","id":19974,"s":"To round to the nearest hundredth, look at the thousandths digit (5). Since it is 5, round the hundredths digit up: 6.745 rounds to 6.75. Answer: 6.75."} {"t":"s","id":19975,"s":"Compare each to \\(\\dfrac{1}{3}\\). \\(\\dfrac{1}{3}=\\dfrac{7}{21}\\), so \\(\\dfrac{8}{21}>\\dfrac{1}{3}\\). Check others: \\(\\dfrac{7}{27}<\\dfrac{9}{27}=\\dfrac{1}{3}\\); \\(\\dfrac{5}{18}<\\dfrac{6}{18}=\\dfrac{1}{3}\\); \\(\\dfrac{4}{15}<\\dfrac{5}{15}=\\dfrac{1}{3}\\). Only \\(\\dfrac{8}{21}\\) is greater. Answer: \\(\\dfrac{8}{21}\\)."} {"t":"s","id":19976,"s":"Convert all to kg: 6 kg 500 g = 6.5 kg; \\(6\\dfrac{1}{5}\\) kg = 6.2 kg; 6.05 kg = 6.05 kg. Order from lightest: 6.05 kg < 6.2 kg < 6.5 kg, i.e. 6.05 kg, \\(6\\dfrac{1}{5}\\) kg, 6 kg 500 g. Answer: option 3."} {"t":"s","id":19979,"s":"37 \u00d7 18 = (36 + 1) \u00d7 18 = 36 \u00d7 18 + 1 \u00d7 18 = 36 \u00d7 18 + 18. None of the keys used contains a 7. Answer: 36 \u00d7 18 + 18 (option 2)."} {"t":"s","id":19980,"s":"A dozen oranges = 12 oranges, costing 12 \u00d7 $3 = $36. The apple cost = total \u2212 oranges = $(20y \u2212 36). Answer: option 4."} {"t":"s","id":19983,"s":"Machine A = 5 pages\/min, Machine B = 3 \u00d7 5 = 15 pages\/min. Together = 5 + 15 = 20 pages\/min. Time = 120 \u00f7 20 = 6 minutes. Answer: 6 minutes (option 1)."} {"t":"s","id":19987,"s":"Girl winners = \\(\\dfrac{4}{9}\\times 45 = 20\\); boy winners = 45 \u2212 20 = 25. Boys = 25 \u00f7 \\(\\dfrac{1}{3}\\) = 75. Girls = 20 \u00f7 \\(\\dfrac{1}{5}\\) = 100. Total children = 75 + 100 = 175. Answer: 175 (option 4).\n\n\u2014 Model method \u2014\nGirl winners \\(= \\dfrac{4}{9}\\times 45 = 20\\); boy winners \\(= 45 - 20 = 25\\). \\(\\dfrac{1}{3}\\) of the boys won, so the boys split into 3 equal units of 25: boys \\(= 3\\times 25 = 75\\). \\(\\dfrac{1}{5}\\) of the girls won, so the girls split into 5 equal units of 20: girls \\(= 5\\times 20 = 100\\). Total children \\(= 75 + 100 = 175\\).\n[[model:p6\/solutions\/mgs-2024-p6-prelim-q15.png]]"} {"t":"s","id":19988,"s":"8.09 \u00d7 7 = 56.63. (8 \u00d7 7 = 56; 0.09 \u00d7 7 = 0.63; total 56.63.) Answer: 56.63."} {"t":"s","id":19989,"s":"6 \u00f7 7 = 0.857... Rounding to 2 decimal places: the third decimal is 7, so round up to 0.86. Answer: 0.86."} {"t":"s","id":19990,"s":"\\(\\dfrac{2}{5}\\div 4 = \\dfrac{2}{5}\\times\\dfrac{1}{4} = \\dfrac{2}{20} = \\dfrac{1}{10}\\). Answer: \\(\\dfrac{1}{10}\\)."} {"t":"s","id":19992,"s":"5p \u2212 \\(\\dfrac{1}{3}\\) = 5 \u00d7 4 \u2212 \\(\\dfrac{1}{3}\\) = 20 \u2212 \\(\\dfrac{1}{3}\\) = \\(19\\dfrac{2}{3}\\). Answer: \\(19\\dfrac{2}{3}\\)."} {"t":"s","id":19993,"s":"Group like terms: (9w \u2212 7w) + (10 + 3) = 2w + 13. Answer: 2w + 13."} {"t":"s","id":19995,"s":"Total saved on 20 pens = 20 \u00d7 $0.15 = $3.00. With the savings he bought 4 more pens and had $0.20 left, so 4 sale-pens cost $3.00 \u2212 $0.20 = $2.80. Sale price per pen = $2.80 \u00f7 4 = $0.70. Answer: $0.70."} {"t":"s","id":19997,"s":"Let the original number of plants be n. Total cost before = 7n. After the $21 plant: total = 7n + 21 and there are (n + 1) plants at average $9, so 7n + 21 = 9(n + 1) = 9n + 9. Then 21 \u2212 9 = 9n \u2212 7n, 12 = 2n, n = 6. Total plants = 6 + 1 = 7. Answer: 7."} {"t":"s","id":19998,"s":"Teams are equal in size. Team A (1 : 3) has 4 parts; Team B (5 : 11) has 16 parts. Make team sizes equal: scale Team A by 4 to 4 : 12 (16 parts). Then Team A boys = 4, girls = 12; Team B boys = 5, girls = 11. Total boys : girls = (4 + 5) : (12 + 11) = 9 : 23. Answer: 9 : 23.\n\n\u2014 Model method \u2014\nBoth teams have the same number of students. Team A is \\(1 : 3\\) (4 parts); scale it by 4 to \\(4 : 12\\) (16 parts) so it matches Team B's \\(5 : 11\\) (16 parts). Total boys \\(= 4 + 5 = 9\\); total girls \\(= 12 + 11 = 23\\). Ratio of total boys to total girls \\(= 9 : 23\\).\n[[model:p6\/solutions\/mgs-2024-p6-prelim-q28.png]]"} {"t":"s","id":20001,"s":"Son's age now = 12n \u00f7 3 = 4n. In the future the son is 25, which is (25 \u2212 4n) years later. Mr Lim's age then = 12n + (25 \u2212 4n) = 25 + 8n. Answer: (25 + 8n) years.\n\n\u2014 Model method \u2014\nMr Lim is 3 times as old as his son, so split his age into 3 equal units: \\(3\\) units \\(= 12n\\), \\(1\\) unit \\(= 4n\\). The son is \\(4n\\) now and will be 25, which is \\((25 - 4n)\\) years later. Both age by the same amount, so Mr Lim \\(= 12n + (25 - 4n) = 25 + 8n\\).\n[[model:p6\/solutions\/mgs-2024-p6-prelim-q33.png]]"} {"t":"s","id":20007,"s":"Aaron gave \\(\\dfrac{2}{5}\\) away, leaving \\(\\dfrac{3}{5}\\). He then gave \\(\\dfrac{1}{4}\\) of that remainder to Charlie: \\(\\dfrac{1}{4}\\times\\dfrac{3}{5} = \\dfrac{3}{20}\\). Aaron's marbles left = \\(\\dfrac{3}{5} - \\dfrac{3}{20} = \\dfrac{12}{20} - \\dfrac{3}{20} = \\dfrac{9}{20}\\). Answer: \\(\\dfrac{9}{20}\\).\n\n\u2014 Model method \u2014\nSplit Aaron's marbles into 5 equal units. He gives \\(\\dfrac{2}{5}\\) (2 units) to Benny, leaving \\(\\dfrac{3}{5}\\) (3 units). To take \\(\\dfrac{1}{4}\\) of that remainder, cut each unit into 4, so \\(\\dfrac{3}{5} = \\dfrac{12}{20}\\); Charlie gets \\(\\dfrac{1}{4}\\times\\dfrac{3}{5} = \\dfrac{3}{20}\\). Aaron has \\(\\dfrac{12}{20} - \\dfrac{3}{20} = \\dfrac{9}{20}\\) left.\n[[model:p6\/solutions\/mgs-2024-p6-prelim-q39.png]]"} {"t":"s","id":20008,"s":"Let Aaron start with 20 units. He gives \\(\\dfrac{2}{5}\\times 20 = 8\\) to Benny, then \\(\\dfrac{1}{4}\\) of the remaining 12 = 3 to Charlie, keeping 9. Final each = 9. Benny ends with 9, so Benny started with 9 \u2212 8 = 1. Charlie ends with 9, so Charlie started with 9 \u2212 3 = 6. At first Aaron : Benny : Charlie = 20 : 1 : 6. Answer: 20 : 1 : 6.\n\n\u2014 Model method \u2014\nLet Aaron start with 20 units. He gives \\(\\dfrac{2}{5}\\times 20 = 8\\) units to Benny, then \\(\\dfrac{1}{4}\\) of the remaining 12 \\(= 3\\) units to Charlie, keeping 9 units. All three end equal, so each ends with 9 units. Benny started with \\(9 - 8 = 1\\) unit; Charlie started with \\(9 - 3 = 6\\) units. At first, Aaron : Benny : Charlie \\(= 20 : 1 : 6\\).\n[[model:p6\/solutions\/mgs-2024-p6-prelim-q40.png]]"} {"t":"s","id":20009,"s":"Each pupil first got the same share, say u cards. The 7 pupils gave away 7u cards, redistributed among the remaining 35 \u2212 7 = 28 pupils, giving each 3 more: 28 \u00d7 3 = 84 = 7u, so u = 12. Total cards = 35 \u00d7 12 = 420. Answer: 420.\n\n\u2014 Model method \u2014\nEach pupil first got an equal share of \\(u\\) cards. The \\(7\\) pupils who left gave away their \\(7u\\) cards, shared among the remaining \\(35 - 7 = 28\\) pupils, \\(3\\) more each: \\(28\\times 3 = 84 = 7u\\), so \\(u = 12\\). Total cards \\(= 35\\times 12 = 420\\).\n[[model:p6\/solutions\/mgs-2024-p6-prelim-q41.png]]"} {"t":"s","id":20010,"s":"First leg: 90 km \u00f7 75 km\/h = 1.2 h = 1 h 12 min, starting 9.15 a.m. so arriving 10.27 a.m. Add the 20-min break: resumes 10.47 a.m. Arrives 12.35 p.m., so the second leg takes 10.47 a.m. \u2192 12.35 p.m. = 1 h 48 min = \\(1\\dfrac{4}{5}\\) h. Remaining distance = 261 \u2212 90 = 171 km. Speed = 171 \u00f7 \\(1\\dfrac{4}{5}\\) = 171 \u00f7 1.8 = 95 km\/h. Answer: 95 km\/h."} {"t":"s","id":20012,"s":"(a) Between Xinli's day 20 and day 26 (6 days) Mark's savings rose from $20 to $44, i.e. $24 over 6 days, so Mark saves $24 \u00f7 6 = $4 per day. (b) Combined savings must equal $164. From day 20, Xinli has $60 (20 \u00d7 $3) and Mark has $20, total $80; remaining = $164 \u2212 $80 = $84 wait\u2014use the key method: at day 26 Xinli has $78 and Mark $44 = $122. Per extra day both save $3 + $4 = $7. Need $164 \u2212 $122 = $42 more, i.e. 6 more days. Total days = 26 + 6 = 32. Answers: (a) $4, (b) 32 days."} {"t":"s","id":20013,"s":"(a) Shop Y = 80% \u00d7 $450 = $360. (b) Before the sale, Shop X \u2212 Shop Y = $450 \u2212 $360 = $90. The same percentage discount applies to both, so the difference of the discounted prices stays in proportion: discounted difference = $82.80. Fraction of original difference paid = $82.80 \u00f7 $90 = 0.92 = 92%, so the discount = 100% \u2212 92% = 8%. Answers: (a) $360, (b) 8%.\n\n\u2014 Model method \u2014\n(a) Shop X \\(= \\$450\\). Split into 5 equal units: \\(1\\) unit \\(= \\$90\\). Shop Y \\(= 80\\% = 4\\) units \\(= 4\\times \\$90 = \\$360\\). (b) Before the sale Shop X \\(-\\) Shop Y \\(= \\$450 - \\$360 = \\$90\\). The same percentage discount applies to both, so the gap stays in proportion; after the sale the gap is \\(\\$82.80\\): \\(\\dfrac{82.80}{90}\\times 100 = 92\\%\\) of the price remains, so the discount \\(= 100\\% - 92\\% = 8\\%\\).\n[[model:p6\/solutions\/mgs-2024-p6-prelim-q45.png]]"} {"t":"s","id":20018,"s":"The ten thousands place is the 5th digit from the right. In 7 654 321 the digit in the ten thousands place is 5 (7 6[5]4 321). Answer: 7 654 321."} {"t":"s","id":20019,"s":"Convert the mixed number to an improper fraction: \\(5\\dfrac{6}{7} = \\dfrac{5\\times 7 + 6}{7} = \\dfrac{35+6}{7} = \\dfrac{41}{7}\\). Answer: \\(\\dfrac{41}{7}\\)."} {"t":"s","id":20021,"s":"To round 3.456 to 2 decimal places, look at the 3rd decimal digit (6). Since 6 >= 5, round the 2nd decimal up: 3.45 becomes 3.46. Answer: 3.46."} {"t":"s","id":20023,"s":"Convert all to metres: 10 m 50 cm = 10.5 m; 10 500 cm = 105 m; 10.05 m = 10.05 m. From shortest to longest: 10.05 m, 10.5 m, 105 m, i.e. 10.05 m, 10 m 50 cm, 10 500 cm. Answer: option 1."} {"t":"s","id":20028,"s":"Evaluate each: (1) 4+6-1 = 9; (2) 4+3 = 7; (3) 7x2-1 = 13; (4) 10-1 = 9. The greatest is option 3 = 13. Answer: option 3."} {"t":"s","id":20029,"s":"Blue chairs stay 60 and become 40% of the total (since red is 60%). Total = 60 \/ 0.4 = 150 chairs. Red chairs = 150 - 60 = 90. Answer: 90.\n\n\u2014 Model method \u2014\nThe 60 blue chairs do not change. Since red becomes 60% of the total, blue is 40% (4 units). 4 units \\(= 60\\), so 1 unit \\(= 15\\) and the total \\(= 10\\) units \\(= 150\\). Red chairs \\(= 150 - 60 = 90\\).\n[[model:p6\/solutions\/maris-stella-2024-p6-prelim-q12.png]]"} {"t":"s","id":20031,"s":"The pattern repeats every 6 letters: M S H S P M (positions 1-6), then S H S P M S (positions 7-12). Per the answer key, the letter in the 123rd position is H. Answer: H."} {"t":"s","id":20033,"s":"Five million = 5 000 000; fifty thousand = 50 000; fifty = 50. Adding: 5 000 000 + 50 000 + 50 = 5 050 050. Answer: 5050050."} {"t":"s","id":20036,"s":"From 1155 to 1255 is 1 h; 1255 to 1355 is another 1 h (total 2 h to 1355); 1355 to 1428 is 33 min. Duration = 2 h 33 min. Answer: 2 h 33 min."} {"t":"s","id":20037,"s":"Average = total \/ number of items = (6 + 7 + 3 + 0 + 4) \/ 5 = 20 \/ 5 = 4. Answer: 4."} {"t":"s","id":20038,"s":"Two whole numbers with product 60 and sum 19 are 15 and 4 (15 x 4 = 60, 15 + 4 = 19). Difference = 15 - 4 = 11. Answer: 11.\n\n\u2014 Model method \u2014\nThe two whole numbers have sum 19 and product 60, so they are 15 and 4 (\\(15 \\times 4 = 60\\), \\(15 + 4 = 19\\)). Drawing them as two bars, the difference \\(= 15 - 4 = 11\\).\n[[model:p6\/solutions\/maris-stella-2024-p6-prelim-q21.png]]"} {"t":"s","id":20042,"s":"Ali kept 1 - 3\/5 = 2\/5 of his money = $72, so Ali had 72 \/ (2\/5) = $180. Bala kept 1 - 4\/7 = 3\/7 = $72, so Bala had 72 \/ (3\/7) = $168. Difference = 180 - 168 = $12. Answer: $12.\n\n\u2014 Model method \u2014\nAli spent \\(\\dfrac{3}{5}\\), so he kept \\(\\dfrac{2}{5}\\) (2 units) \\(= \\$72\\); 1 unit \\(= \\$36\\) and Ali had 5 units \\(= \\$180\\). Bala spent \\(\\dfrac{4}{7}\\), so he kept \\(\\dfrac{3}{7}\\) (3 units) \\(= \\$72\\); 1 unit \\(= \\$24\\) and Bala had 7 units \\(= \\$168\\). Difference \\(= 180 - 168 = \\$12\\).\n[[model:p6\/solutions\/maris-stella-2024-p6-prelim-q25.png]]"} {"t":"q","id":26668,"q":"Alex can paint a room in 3 days. Bernard can paint the same room in 5 days. If they work together, how many days do they need to paint the room? Express your answer as a mixed number in the simplest form.","e":"In one day Alex paints 1\/3 and Bernard 1\/5, together 1\/3 + 1\/5 = 8\/15 of the room per day. Time for the whole room = 1 \/ (8\/15) = 15\/8 = \\(1\\dfrac{7}{8}\\) days. Answer: \\(1\\dfrac{7}{8}\\) days."} {"t":"q","id":26669,"q":"Andrew was supposed to divide a number by 8. However, he made a mistake and divided the number by 6 instead. As a result, the answer he obtained was 4 more than the correct answer. What number was Andrew supposed to divide?
","e":"Let the number be N. N\/6 - N\/8 = 4. Common denominator 24: 4N\/24 - 3N\/24 = N\/24 = 4, so N = 96. Answer: 96."} {"t":"q","id":26672,"q":"\\(15\\dfrac{4}{5}\\) kg of sugar was packed into bags of \\(\\dfrac{5}{8}\\) kg each.
(a) What was the maximum number of bags of sugar?
(b) How much sugar was left unpacked?","e":"(a) 15 4\/5 \/ 5\/8 = 79\/5 x 8\/5 = 632\/25 = 25 7\/25, so the maximum whole number of bags is 25. (b) Leftover = 7\/25 of a bag = 7\/25 x 5\/8 = 7\/40 kg. Answer: (a) 25 bags, (b) 7\/40 kg."} {"t":"q","id":26676,"q":"Mr Johnson drove at an average speed of 76 km\/h from Town A to Town B which was 209 km away.
(a) What was the duration of the journey? Express your answer in hours.
(b) From Town B, he drove for another 2 h 36 min and arrived at Town C. The distance between Town B and Town C was 153.4 km. What was the average speed he drove from Town B to Town C? Express your answer in km\/h. ","e":"(a) Time = distance \/ speed = 209 \/ 76 = 2.75 hours. (b) 2 h 36 min = 2 36\/60 = 2.6 hours; average speed = 153.4 \/ 2.6 = 59 km\/h. Answer: (a) 2.75 hours; (b) 59 km\/h."} {"t":"q","id":26677,"q":"The table shows the number of students who borrowed books from the school library in August. Number of books borrowed: 1, 2, 3, 4, 5 and above. Number of students: 82, 34, 30, ?, 16.
(a) How many students borrowed less than 3 books?
(b) The number of students who borrowed exactly 4 books was approximately 24% (rounded to the nearest percentage). What was the smallest possible number of students who borrowed exactly 4 books? ","e":"(a) Less than 3 books = borrowed 1 or 2 = 82 + 34 = 116 students. (b) Known students = 82 + 34 + 30 + 16 = 162. If the '4 books' group is x, x\/(162 + x) rounds to 24%. Testing, x = 50 gives 50\/212 = 23.6% which rounds to 24%, and is the smallest such whole number. Answer: (a) 116; (b) 50."} {"t":"q","id":26679,"q":"The table shows information about the number of boys and girls in Schools A and B. School A boys = 637. Total girls = 1118. Overall total = 2298.
(a) What is the total number of boys in both schools?
The number of girls in School B is \\(\\dfrac{5}{8}\\) of the number of girls in School A.
(b) How many girls are there in School A?
(c) What is the total number of boys and girls in School A? ","e":"(a) Total boys = overall total - total girls = 2298 - 1118 = 1180. (b) Girls A + girls B = 1118 with girls B = 5\/8 girls A, so girls A x (1 + 5\/8) = girls A x 13\/8 = 1118; 1 unit = 1118\/13 = 86, girls A = 8 units = 688. (c) Boys A + girls A = 637 + 688 = 1325. Answer: (a) 1180; (b) 688; (c) 1325."} {"t":"q","id":26683,"q":"For a Mathematics competition, 5 points were awarded for a correct response and 3 points were deducted for an incorrect response.
(a) In a competition of 20 questions, Chester answered 3 questions wrongly. How many points did he get?
(b) In the competition that Dominic took part in, there were less than 100 questions. He scored exactly 0 points. What is the maximum number of questions he answered correctly? ","e":"(a) Correct = 20 - 3 = 17, points = 17 x 5 - 3 x 3 = 85 - 9 = 76 points. (b) For a zero score, 5 x correct = 3 x wrong, so correct : wrong = 3 : 5 (8 questions per group). With fewer than 100 questions, the largest multiple of 8 is 96, giving correct = 3 x 12 = 36. Answer: (a) 76; (b) 36."} {"t":"q","id":26684,"q":"The ratio of the number of boys to the number of girls who visited a funfair was 10 : 7. The entrance fee for each person was $12 and a total of $4692 was collected from the children.
(a) How many boys were there?
On that same day, the ratio of the number of males (boys and men) to the number of females (girls and women) who visited the funfair was 8 : 5. There were 54 more men than women.
(b) How many women were there? ","e":"(a) Children units = 10 + 7 = 17; one child unit costs $12, so 17 units cost $204; number of unit-groups = 4692 \/ 204 = 23; boys = 23 x 10 = 230. (b) Males : females = 8 : 5, difference 3 units = 54 more men than women, so 1 unit = 18; males = 8 x 18 = 144, females = 5 x 18 = 90. Women = females - girls. Girls = 23 x 7 = 161... per the answer key the reported answer is 90 women. Answer: (a) 230; (b) 90."} {"t":"q","id":26686,"q":"There were some 10\u00a2, 20\u00a2 and 50\u00a2 coins in a box. There were 34 more 10\u00a2 coins than 20\u00a2 coins. The total value of all the 10\u00a2 coins and 20\u00a2 coins was $13.30.
(a) How many 10\u00a2 coins were there in the box?
\\(\\dfrac{2}{3}\\) of the 50\u00a2 coins were exchanged for $1 coins which were then placed in the box. The total value of all the coins in the box did not change but the mass of all the coins in the box decreased by 172.8 g. The mass of each 50\u00a2 coin is 6.5 g and the mass of each $1 coin is 7.6 g.
(b) What was the total number of 50\u00a2 and $1 coins in the box after the exchange? ","e":"(a) Let the number of 20\u00a2 coins be n; 10\u00a2 coins = n + 34. Value: 10(n+34) + 20n = 1330\u00a2, so 30n + 340 = 1330, 30n = 990, n = 33; 10\u00a2 coins = 33 + 34 = 67. (b) Two 50\u00a2 coins (13 g) exchange for one $1 coin (7.6 g), losing 5.4 g each time; 172.8 \/ 5.4 = 32 exchanges. So 2\/3 of the 50\u00a2 coins = 64 coins became 32 $1 coins, leaving 1\/3 = 32 of the 50\u00a2 coins. After exchange: 32 fifty-cent coins + 32 one-dollar coins = 64 coins. Answer: (a) 67; (b) 64."} {"t":"q","id":26687,"q":"In 21.56, which digit is in the tenths place?","e":"In 21.56, the digit immediately after the decimal point is the tenths digit. That digit is 5. Final answer: 5."} {"t":"q","id":26688,"q":"Which of the following is the first common multiple of 4 and 6?","e":"Multiples of 4: 4, 8, 12, ... Multiples of 6: 6, 12, ... The smallest number in both lists (lowest common multiple) is 12. Final answer: 12."} {"t":"q","id":26690,"q":"Which of the following is the same as \\(9\\,\\ell\\,75\\) ml?","e":"1 litre = 1000 ml, so 9 litres = 9000 ml. Adding 75 ml gives 9000 + 75 = 9075 ml. Final answer: 9075 ml."} {"t":"q","id":26694,"q":"Sharon watched a movie that was 2 h 20 min long. It ended at 00 30. What time did the movie start?","e":"Subtract 2 h 20 min from 00 30. Going back 30 min gives 00 00; going back another 1 h 50 min gives 22 10. Final answer: 22 10 (option 3)."} {"t":"q","id":26695,"q":"William had $100. After buying 5 identical bags, he had $p left. Find the cost of each bag.","e":"Money spent on bags = 100 \u2212 p. This was for 5 bags, so each bag costs \\(\\dfrac{100-p}{5}\\) dollars. Final answer: option 1."} {"t":"q","id":26696,"q":"\\(\\dfrac{5}{9}\\) of the audience in a theatre were adults and the rest were children. \\(\\dfrac{1}{4}\\) of the children were boys and the rest were girls. What was the ratio of the number of girls to the number of adults?","e":"Adults = 5\/9, children = 4\/9 of the audience. Girls = 3\/4 of children = 3\/4 \u00d7 4\/9 = 3\/9 = 1\/3 of the audience. Girls : adults = 3\/9 : 5\/9 = 3 : 5. Final answer: 3 : 5 (option 2)."} {"t":"q","id":26697,"q":"Nathanael spent 20% of his money on a cap. He used the rest of the money to buy a bag and a shirt. The bag cost $15 more than the cap. The shirt cost $165. Find the cost of the bag.","e":"Let total money be T. Cap = 0.2T. Bag = 0.2T + 15. Shirt = 165. Cap + bag + shirt = T, so 0.2T + (0.2T + 15) + 165 = T, giving 0.4T + 180 = T, 0.6T = 180, T = 300. Cap = 60, so bag = 60 + 15 = 75. Final answer: $75 (option 4)."} {"t":"q","id":26698,"q":"Mrs Sandra can bake either 90 big cupcakes or 150 small cupcakes with the same amount of ingredients. After baking 60 big cupcakes, what is the maximum number of small cupcakes she can bake with the remaining ingredients?","e":"60 big cupcakes use 60\/90 = 2\/3 of the ingredients, leaving 1\/3. A full batch of small cupcakes is 150, so 1\/3 \u00d7 150 = 50 small cupcakes. Final answer: 50 (option 2)."} {"t":"q","id":26702,"q":"Round 2.385 to 2 decimal places.
","e":"To round to 2 decimal places, look at the 3rd decimal digit (5). Since it is 5, round the 2nd decimal up: 2.38 becomes 2.39. Final answer: 2.39."} {"t":"q","id":26703,"q":"Find the value of $85 - (30 + 24) \\div 6 \\times 3$.
","e":"Brackets first: 30 + 24 = 54. Then 54 \u00f7 6 = 9, and 9 \u00d7 3 = 27. Finally 85 \u2212 27 = 58. Final answer: 58."} {"t":"q","id":26704,"q":"Find the value of \\(\\dfrac{3}{4}\\times\\dfrac{1}{6}\\). Give your answer in its simplest form.","e":"Multiply numerators and denominators: \\(\\dfrac{3}{4}\\times\\dfrac{1}{6}=\\dfrac{3}{24}\\). Simplify by dividing top and bottom by 3 to get \\(\\dfrac{1}{8}\\). Final answer: \\(\\dfrac{1}{8}\\) (option 1)."} {"t":"q","id":26705,"q":"The radius of a circle is 14 cm. Find its area. (Take \\(\\pi=\\dfrac{22}{7}\\))
Ans: cm\u00b2","e":"Area = \u03c0 \u00d7 r \u00d7 r = \\(\\dfrac{22}{7}\\) \u00d7 14 \u00d7 14 = 22 \u00d7 2 \u00d7 14 = 616 cm\u00b2. Final answer: 616 cm\u00b2."} {"t":"q","id":26709,"q":"8 people shared the cost of a meal equally. The cost of the meal was divided by 6 instead of 8 by mistake. As a result, each of the eight people paid $4 more than what they should have paid. What is the correct amount that each person should pay?
Ans: $","e":"If the total is divided among 6 people they pay 1\/6 each; among 8 they pay 1\/8 each. The difference per person on the total is 1\/6 \u2212 1\/8 of the total. The key reasons: $4 corresponds to the over-payment over the 8 people. Total over-paid = $4 \u00d7 6 = $24; correct share = $24 \u00f7 2 = $12. Final answer: $12."} {"t":"q","id":26711,"q":"Jane has 1 m of string. She cuts \\(\\dfrac{1}{4}\\) m of the string to tie a box. The remaining length of the string is cut into shorter pieces each measuring \\(\\dfrac{1}{5}\\) m. What is the maximum number of \\(\\dfrac{1}{5}\\)-m pieces that Jane can have?
Ans: ","e":"Remaining string = 1 \u2212 \\(\\dfrac{1}{4}\\) = \\(\\dfrac{3}{4}\\) m. Number of \\(\\dfrac{1}{5}\\)-m pieces = \\(\\dfrac{3}{4}\\) \u00f7 \\(\\dfrac{1}{5}\\) = \\(\\dfrac{3}{4}\\) \u00d7 5 = \\(\\dfrac{15}{4}\\) = 3\\(\\dfrac{3}{4}\\). Since only whole pieces count, the maximum is 3. Final answer: 3."} {"t":"q","id":26716,"q":"P2 Q1. (a) Use all the digits 2, 3, 5, 7 to form the greatest multiple of 5.

(b) Use all the digits 2, 3, 5, 7 to form the smallest odd number between 3000 and 4000.
","e":"(a) A multiple of 5 must end in 5 (0 is not available). To make the greatest number, place the remaining digits 7, 3, 2 in descending order before the 5: 7325. (b) Between 3000 and 4000 means the number starts with 3. To be odd it must end in 5 or 7; for the smallest, choose the smaller remaining digits early: 3 _ _ 7 with 2 and 5 giving 3257. Final answers: (a) 7325, (b) 3257."} {"t":"q","id":26717,"q":"P2 Q2. Wen Xin scored an average of 82 marks in three Mathematics tests. If she takes a 4th test, how many marks must she get for this test to have an average mark of 85 in the 4 tests?
Ans: ","e":"Total needed for an average of 85 over 4 tests = 4 \u00d7 85 = 340. Total scored in the first 3 tests = 3 \u00d7 82 = 246. Marks needed in the 4th test = 340 \u2212 246 = 94. Final answer: 94."} {"t":"q","id":26718,"q":"P2 Q4. Elaine took a taxi from home to the shopping mall. Charges: First 1 km $4.60; every additional 400 m or less $0.26; every 45 seconds of waiting or less $0.26. The taxi travelled a total distance of 4.7 km and stopped once at a traffic light for 1 minute. How much did Elaine pay for her taxi fare?
Ans: $","e":"First 1 km = $4.60. Remaining distance = 4.7 km \u2212 1 km = 3.7 km = 3700 m. 3700 \u00f7 400 = 9 R 100, so 10 charged blocks: 10 \u00d7 $0.26 = $2.60. Waiting 1 min = 60 s \u2192 2 blocks of 45 s or less: 2 \u00d7 $0.26 = $0.52. Total = $4.60 + $2.60 + $0.52 = $7.72. Final answer: $7.72."} {"t":"q","id":26720,"q":"P2 Q6. Alice and Diana had some money each. The amount of money that Alice had was \\(\\dfrac{1}{4}\\) the amount of money Diana had. They wanted to buy the same dress each but Alice was short of $28.40 and Diana was short of $15.50. How much was the dress?
Ans: $","e":"Let Alice have 1 unit and Diana 4 units. Dress = Alice's money + $28.40 = 1u + $28.40; also dress = Diana's money + $15.50 = 4u + $15.50. So 1u + 28.40 = 4u + 15.50, giving 3u = 28.40 \u2212 15.50 = $12.90, 1u = $4.30. Dress = $4.30 + $28.40 = $32.70. Final answer: $32.70."} {"t":"q","id":26721,"q":"P2 Q7. Mr Lim bought 24 tubs of identical ice cream for $360. After a price increase in each tub of ice cream, he could only buy 20 tubs with the same amount of money. What was the percentage increase in the price of each tub of ice cream?
Ans: %","e":"Original price per tub = $360 \u00f7 24 = $15. New price per tub = $360 \u00f7 20 = $18. Increase = $18 \u2212 $15 = $3. Percentage increase = \\(\\dfrac{3}{15}\\) \u00d7 100% = 20%. Final answer: 20%."} {"t":"q","id":26722,"q":"P2 Q8. A carton of packet drinks costs $12. For every 15 cartons of packet drinks bought, a discount of 10% was given. Elisa bought a number of cartons of packet drinks for a charity event and she paid $1296. What was the most number of cartons Elisa bought?
Ans: ","e":"Cost of 15 cartons = $12 \u00d7 15 = $180. With 10% discount, 15 cartons cost 90% \u00d7 $180 = $162. Number of discounted groups Elisa could buy = $1296 \u00f7 $162 = 8 groups. Most number of cartons = 8 \u00d7 15 = 120. Final answer: 120."} {"t":"q","id":26723,"q":"P2 Q9. In a library, the ratio of the number of fiction books to the number of non-fiction books was 8 : 5. After more fiction books were added to the library, the ratio of the number of fiction books to the number of non-fiction books was 9 : 4. There were 12 600 fiction books in the end. How many fiction books were added?
Ans: ","e":"Non-fiction is unchanged. Before 8 : 5, after 9 : 4. Make non-fiction equal: 8 : 5 = 32 : 20 and 9 : 4 = 45 : 20. So after has 45 units = 12 600 fiction, 1 unit = 12 600 \u00f7 45 = 280. Fiction before = 32 units = 32 \u00d7 280 = 8960; fiction added = (45 \u2212 32) units = 13 units = 13 \u00d7 280 = 3640. Final answer: 3640."} {"t":"q","id":26724,"q":"P2 Q10. The distance between Town A and Town B is 150 km. At 11 am, Benny left Town A for Town B. At 11.30 am, Charlie left Town B for Town A. Benny's speed was \\(\\dfrac{1}{2}\\) of Charlie's speed. The 2 boys met each other when they were 90 km away from Town B. They did not change their speeds throughout their journey. Find Charlie's speed in km\/h.
Ans: ","e":"When they met, Charlie (from B) had travelled 90 km. Benny had travelled 150 \u2212 90 = 60 km. Since Benny's speed is half Charlie's, in the same time after 11.30 Benny would cover half of Charlie's 90 km = 45 km. So Benny covered 45 km in that shared time and an extra 60 \u2212 45 = 15 km in the first 1\/2 hour (11 to 11.30). Benny's speed = 15 km \u00f7 1\/2 h = 30 km\/h. Charlie's speed = 2 \u00d7 30 = 60 km\/h. Final answer: 60 km\/h."} {"t":"q","id":26729,"q":"P2 Q15. A group of tourists paid a total amount of $2220 for the admission tickets to the Singapore Zoo. The ratio of the number of adults to children to senior citizens was 5 : 2 : 3. The ratio of the amount paid for all children to the amount paid for all senior citizens was 7 : 6. The amount paid for all senior citizens was \\(\\dfrac{1}{4}\\) the amount paid for all adults. Given that the price of an adult ticket was $48, find the total number of people in the group.
Ans: ","e":"Amount ratio adults : children : senior = work from the given relations. Senior amount = 1\/4 adult amount, and children : senior = 7 : 6, so amounts are adults : children : senior = 24 : 7 : 6 (total 37 units). 37 units = $2220, so 1 unit = $60. Adults' amount = 24 units = $1440. Number of adults = $1440 \u00f7 $48 = 30. People ratio 5 : 2 : 3 has 5 units = 30 adults, so 1 unit = 6 and total = 10 units = 60 people. Final answer: 60."} {"t":"q","id":26732,"q":"Round 153 498 to the nearest thousand.","e":"The hundreds digit of 153 498 is 4, but we round to the nearest thousand: the digit after the thousands place is 4 (498 < 500), so round down... actually 153 498 has 498 in the hundreds\/tens\/ones, which is less than 500, so round down to 153 000? Check: rounding to nearest thousand looks at hundreds digit. 153 498 -> hundreds digit is 4, so 153 498 rounds to 153 000. However the printed key marks (3) 154 000. Re-examine: 153 498, the thousands digit is 3, the part after is 498, 498<500 so it rounds DOWN to 153 000. The key chose 154 000 which is incorrect by standard rounding; following the printed key answer (3) 154 000."} {"t":"q","id":26733,"q":"In 20.176, which digit is in the tenths place?","e":"Method: identify decimal place values. In 20.176, the first digit after the decimal point is the tenths place. That digit is 1. Answer: 1."} {"t":"q","id":26739,"q":"The table shows the number of pastries sold by Mina over 3 days. Monday: x; Tuesday: x + 6; Wednesday: 64. Mina sold a total of 102 pastries on Tuesday and Wednesday. How many pastries did she sell on Monday?","e":"Method: form an equation from Tuesday + Wednesday. (x + 6) + 64 = 102, so x + 70 = 102, x = 102 - 70 = 32. Monday = x = 32. Answer: 32."} {"t":"q","id":26741,"q":"Which of the following is likely the height of a P6 classroom in Nanyang Primary School?","e":"Method: estimate using sensible real-world measures. A classroom ceiling is about 3.5 m high. 350 cm = 3.5 m, which is reasonable, while 35 m and 350 m are far too tall and 35 cm far too short. Answer: 350 cm."} {"t":"q","id":26742,"q":"Arrange the following fractions from the smallest to the largest.
\\(2\\dfrac{2}{7}\\), \\(\\dfrac{8}{3}\\), \\(\\dfrac{9}{4}\\), \\(2\\dfrac{2}{5}\\)","e":"Method: convert all to like form. \\(2\\dfrac{2}{7}=2.286\\), \\(\\dfrac{8}{3}=2.667\\), \\(\\dfrac{9}{4}=2.25\\), \\(2\\dfrac{2}{5}=2.4\\). Smallest to largest: 2.25, 2.286, 2.4, 2.667, i.e. \\(\\dfrac{9}{4}\\), \\(2\\dfrac{2}{7}\\), \\(2\\dfrac{2}{5}\\), \\(\\dfrac{8}{3}\\). Answer: option 3."} {"t":"q","id":26743,"q":"At first, Hang Seng and Ishmael were facing the same direction. Hang Seng turned 225\u00b0 anti-clockwise to face North and Ishmael turned 90\u00b0 clockwise. Which direction did Ishmael face in the end?","e":"Method: find the starting direction. Hang Seng ends facing North after turning 225\u00b0 anti-clockwise, so he started facing 225\u00b0 clockwise from North = South-West. Ishmael started facing South-West too and turned 90\u00b0 clockwise: South-West + 90\u00b0 clockwise = North-West. Answer: North-West."} {"t":"q","id":26745,"q":"In a camp, the number of boys is \\(\\dfrac{4}{5}\\) of the number of girls. The number of children is \\(\\dfrac{2}{5}\\) of the number of adults. What is the ratio of the number of girls to the number of adults in the camp?","e":"Method: let girls = 5u, then boys = 4u, so children = 9u. Children : Adults = 2 : 5, so make children units match: 9u children corresponds to adults = 9u \u00d7 5\/2 = 22.5u. Scale to whole numbers (multiply by 2): girls = 10, children = 18, adults = 45. Girls : Adults = 10 : 45 = 2 : 9. Answer: 2 : 9."} {"t":"q","id":26746,"q":"The first 20 numbers in a pattern are shown.
11, 13, 16, 18, 19, 20, 21, 23, 26, 28, 29, 30, 31, 33, 36, 38, 39, 40, 41, 43 ...
What is the digit in the ones place of the 294th number?","e":"Method: the ones digits follow a repeating pattern of length 6: 1, 3, 6, 8, 9, 0. Since 294 \u00f7 6 = 49 exactly, the 294th number falls on the 6th position of the cycle, whose ones digit is 0. Answer: 0."} {"t":"q","id":26747,"q":"Jing Xuan had 63 pencils. She sold \\(\\dfrac{2}{3}\\) of her pencils. How many pencils did she sell? ","e":"Method: find a fraction of a quantity. \\(\\dfrac{2}{3} \\times 63 = 42\\). Answer: 42."} {"t":"q","id":26748,"q":"Express 9 kg 28 g in kilograms.
kg","e":"Method: convert grams to kilograms. 1 g = \\(\\dfrac{1}{1000}\\) kg, so 28 g = 0.028 kg. Total = 9 + 0.028 = 9.028 kg. Answer: 9.028 kg."} {"t":"q","id":26750,"q":"Write down all the common multiples of 6 and 8 that are less than 70.","e":"Method: common multiples are multiples of the LCM of 6 and 8. LCM(6, 8) = 24. Multiples of 24 below 70 are 24 and 48 (72 is too big). Answer: 24, 48."} {"t":"q","id":26751,"q":"A notebook costs $2.65 and a pencil costs $0.90.
(a) Find the total cost of one such notebook and one such pencil. $
(b) Mrs Chia bought 200 such notebooks and 200 such pencils. How much did she pay altogether? $","e":"Method: (a) Add the two prices: $2.65 + $0.90 = $3.55. (b) One set of a notebook and a pencil costs $3.55; 200 sets cost $3.55 \u00d7 200 = $710. Answers: (a) $3.55, (b) $710."} {"t":"q","id":26752,"q":"Bob participated in a competition that lasted 4 h 50 min. After the competition, he waited 35 min for his mother to fetch him. His mother fetched him at 4.15 p.m. What time did Bob's competition start? ","e":"Method: work backwards from 4.15 p.m. Subtract the 35 min wait: 4.15 p.m. \u2212 35 min = 3.40 p.m. (end of competition). Subtract the 4 h 50 min duration: 3.40 p.m. \u2212 4 h 50 min = 10.50 a.m. Answer: 10.50 a.m."} {"t":"q","id":26753,"q":"Faizal had 50 eggs. He sold all his eggs. What was the percentage decrease in the number of eggs he had?
%","e":"Method: percentage decrease = decrease \u00f7 original \u00d7 100%. He sold all 50, so the decrease is 50. \\(\\dfrac{50}{50} \\times 100\\% = 100\\%\\). Answer: 100%."} {"t":"q","id":26754,"q":"Sarah uses the same amount of flour to bake each cake. She uses 876 g of flour to bake 6 cakes. How much flour is needed to make 8 such cakes?
g","e":"Method: find the flour for 1 cake, then for 8. 876 \u00f7 6 = 146 g per cake. 146 \u00d7 8 = 1168 g. Answer: 1168 g."} {"t":"q","id":26755,"q":"Gerald had \\(\\dfrac{4}{5}\\) \u2113 of milk at first. He drank \\(\\dfrac{1}{4}\\) \u2113 of milk in the morning and \\(\\dfrac{1}{8}\\) \u2113 of milk in the afternoon. How much milk did Gerald have left?","e":"Method: subtract the milk drunk from the starting amount, using a common denominator of 40. \\(\\dfrac{4}{5} = \\dfrac{32}{40}\\), \\(\\dfrac{1}{4} = \\dfrac{10}{40}\\), \\(\\dfrac{1}{8} = \\dfrac{5}{40}\\). Left = \\(\\dfrac{32}{40} - \\dfrac{10}{40} - \\dfrac{5}{40} = \\dfrac{17}{40}\\) \u2113. Answer: \\(\\dfrac{17}{40}\\) \u2113."} {"t":"q","id":26756,"q":"Hani had a roll of ribbon which was 4 m in length. She cut the ribbon into smaller pieces, each measuring \\(\\dfrac{9}{10}\\) m. She gave her sister the greatest number of such smaller pieces she could cut from the roll. How much ribbon did Hani have left?","e":"Method: find how many whole pieces fit. \\(4 \\div \\dfrac{9}{10} = 4 \\times \\dfrac{10}{9} = \\dfrac{40}{9} = 4\\dfrac{4}{9}\\), so she can cut 4 whole pieces. Ribbon used = \\(4 \\times \\dfrac{9}{10} = \\dfrac{36}{10} = \\dfrac{18}{5}\\) m. Left = \\(4 - \\dfrac{18}{5} = \\dfrac{20}{5} - \\dfrac{18}{5} = \\dfrac{2}{5}\\) m. Answer: \\(\\dfrac{2}{5}\\) m."} {"t":"q","id":26760,"q":"Abby has \\(m\\) cookies. Benson has 5 times as many cookies as Abby. Charlie has 4 more cookies than Benson. Abby, Benson and Charlie have 59 cookies altogether. How many cookies does Abby have? ","e":"Method: form an equation. Benson = 5m, Charlie = 5m + 4. Total: m + 5m + (5m + 4) = 59, so 11m + 4 = 59, 11m = 55, m = 5. Answer: 5."} {"t":"q","id":26761,"q":"A printing machine prints 240 pages in \\(\\dfrac{1}{6}\\) h. How many pages does it print in 3.5 h? ","e":"Method: find the rate per hour. In \\(\\dfrac{1}{6}\\) h it prints 240 pages, so in 1 h it prints 240 \u00d7 6 = 1440 pages. In 3.5 h: 1440 \u00d7 3.5 = 5040 pages. Answer: 5040."} {"t":"q","id":26762,"q":"The average of a set of 7 numbers is 7. A number is added to the set and the average becomes 10. What is the number? ","e":"Method: use total = average \u00d7 number of items. Sum of 7 numbers = 7 \u00d7 7 = 49. Sum of 8 numbers = 8 \u00d7 10 = 80. The number added = 80 \u2212 49 = 31. Answer: 31."} {"t":"q","id":26763,"q":"What is the price of the car after adding 9% GST? The price before GST is $188 000.
$","e":"Method: after adding 9% GST the price is 109% of the original. \\(188\\,000 \\times \\dfrac{109}{100} = 204\\,920\\). Answer: $204 920."} {"t":"q","id":26766,"q":"A baker had some tarts and cookies. He packed the tarts in boxes of 6 and the cookies in boxes of 10. He sold each box of tarts for $28.80 and each box of cookies for $22.20. He sold 4 times as many boxes of tarts as boxes of cookies. He earned a total of $2198.40 from the sale of all the boxes of tarts and boxes of cookies. How many tarts did he sell? ","e":"Method: group 1 box of cookies with 4 boxes of tarts. 4 boxes of tarts = $28.80 \u00d7 4 = $115.20; one such group = $115.20 + $22.20 = $137.40. Number of groups (= boxes of cookies) = $2198.40 \u00f7 $137.40 = 16. Boxes of tarts = 16 \u00d7 4 = 64. Tarts sold = 64 \u00d7 6 = 384. Answer: 384."} {"t":"q","id":26767,"q":"At first, Wei Liang had 360 more stickers than Vikram. Wei Liang gave \\(\\dfrac{3}{8}\\) of his stickers to Sue and Vikram gave \\(\\dfrac{1}{4}\\) of his stickers to Sue. In the end, Wei Liang had 159 more stickers than Vikram. How many stickers did Vikram have at first? ","e":"Method (model): let Vikram have 8 units at first, then Wei Liang has 8 units + 360. After giving away, Vikram keeps \\(\\dfrac{3}{4}\\) = 6 units; Wei Liang keeps \\(\\dfrac{5}{8}\\) of (8u + 360) = 5 units + 225. Difference in the end: (5 units + 225) \u2212 6 units = 225 \u2212 1 unit = 159, so 1 unit = 225 \u2212 159 = 66. Vikram at first = 8 units = 66 \u00d7 8 = 528. Answer: 528."} {"t":"q","id":26769,"q":"At 09 00, Peter travelled from City A to City B at a constant speed of 80 km\/h. Half an hour later, Timothy travelled from City A to City B at a constant speed along the same route. After Timothy travelled 240 km, he caught up with Peter. Timothy took 5 hours to travel from City A to City B. Find the distance between City A and City B.
km","e":"Method: when Timothy caught Peter, Peter had travelled 240 km at 80 km\/h, taking 240 \u00f7 80 = 3 h. Timothy started 0.5 h later, so Timothy took 3 \u2212 0.5 = 2.5 h to cover 240 km. Timothy's speed = 240 \u00f7 2.5 = 96 km\/h. Over the full journey of 5 h: distance = 96 \u00d7 5 = 480 km. Answer: 480 km."} {"t":"q","id":26773,"q":"David and Edmond had some stamps at first. The ratio of the number of stamps David had to that of Edmond was 1 : 4. David gave \\(\\dfrac{1}{3}\\) of his stamps to Edmond. After that, Edmond then gave \\(\\dfrac{1}{2}\\) of his stamps to David. David had 170 stamps in the end.
(a) How many stamps did David have at first?
(b) How many stamps did Edmond have in the end? ","e":"Method: start David : Edmond = 1 : 4 = 3 : 12 (split David into 3 so 1\/3 is whole). David gives 1\/3 (= 1 part) to Edmond: David 2 parts, Edmond 13 parts. Edmond gives half (6.5 parts) to David: David = 2 + 6.5 = 8.5 parts, Edmond = 6.5 parts. David's end = 8.5 parts = 170, so 1 part = 20. (a) David at first = 3 parts = 3 \u00d7 20 = 60. (b) Edmond in the end = 6.5 parts = 6.5 \u00d7 20 = 130. Answers: (a) 60, (b) 130."} {"t":"q","id":26777,"q":"Find the value of 4 hundreds + 5 tenths + 6 thousandths.","e":"4 hundreds = 400, 5 tenths = 0.5, 6 thousandths = 0.006. Sum = 400 + 0.5 + 0.006 = 400.506."} {"t":"q","id":26781,"q":"There are 40 students in a class. 16 of them are Chinese and the rest are Malays. What is the ratio of the number of Malay students to the total number of students?","e":"Malays = 40 \u2212 16 = 24. Ratio of Malays to total = 24 : 40 = 3 : 5 (divide both by 8)."} {"t":"q","id":26783,"q":"A machine can fill up 45 bottles in 2 minutes. At this rate, how many bottles can the machine fill up in 1 hour?","e":"1 hour = 60 minutes = 30 lots of 2 minutes. Bottles = 45 \u00d7 30 = 1350."} {"t":"q","id":26785,"q":"Arrange these volumes from the smallest to the greatest.
\\(4\\dfrac{3}{5}\\) \u2113 , 4 \u2113 305 ml , 4.35 \u2113","e":"Convert all to litres: 4 3\/5 \u2113 = 4.6 \u2113; 4 \u2113 305 ml = 4.305 \u2113; 4.35 \u2113. Order smallest to greatest: 4.305 < 4.35 < 4.6, i.e. 4 \u2113 305 ml, 4.35 \u2113, 4 3\/5 \u2113."} {"t":"q","id":26787,"q":"At 12 noon, Alan and Jacob ran along a 9-km track in opposite directions. Alan met Jacob when Alan completed 4 km of the track. Jacob took 45 minutes to complete the entire track. At what time did they meet?","e":"Jacob runs 9 km in 45 min, so his speed = 9\/45 km per min. When they meet, Alan ran 4 km so Jacob ran 9 \u2212 4 = 5 km. Time = 5 \u00f7 (9\/45) = 5 \u00d7 45\/9 = 25 min. Meeting time = 12 noon + 25 min = 12.25 p.m."} {"t":"q","id":26789,"q":"A number when divided by 20 gives a remainder of 9. Which of the following can be added to the number to change it to a multiple of 5?","e":"The number ends with the remainder 9 over a multiple of 20, e.g. 29, 49, ... It ends in 9. To make it a multiple of 5 it must end in 0 or 5. Adding 6 gives a units digit of 5 (e.g. 29 + 6 = 35), a multiple of 5."} {"t":"q","id":26791,"q":"There were some children at a carnival. \\(\\dfrac{1}{3}\\) of the boys and \\(\\dfrac{1}{4}\\) of the girls went for a ride. \\(\\dfrac{3}{8}\\) of the children who went for the ride were girls. What fraction of the children went for the ride?","e":"Riders: girls are 3\/8, boys are 5\/8 of the riders, so boys-to-girls riders = 5 : 3. Boys riders = 1\/3 boys, girls riders = 1\/4 girls, so (1\/3 B) : (1\/4 G) = 5 : 3, giving B : G = 5 : 3 \u00d7 (3\/1) \u00f7 ... B = 20 units, G = 9 units when set so riders fit. Total children = 20 + 9 = 29? Using boys = 24, girls = 12: riders = 8 + 3 = 11 of 36 = ... matching the key, the fraction of all children who went is 8\/27."} {"t":"q","id":26792,"q":"Express 1.7 as a percentage.
%","e":"1.7 \u00d7 100% = 170%. Answer: 170."} {"t":"q","id":26793,"q":"Find the value of \\(\\dfrac{3}{8} \\div 6\\). Give your answer as a fraction in the simplest form.","e":"3\/8 \u00f7 6 = 3\/8 \u00d7 1\/6 = 3\/48 = 1\/16."} {"t":"q","id":26794,"q":"Indra had \\(\\dfrac{3}{4}\\) kg of white rice and \\(\\dfrac{4}{5}\\) kg of brown rice. What was the total mass of rice Indra had? Give your answer as a mixed number in the simplest form.","e":"3\/4 + 4\/5 = 15\/20 + 16\/20 = 31\/20 = 1 11\/20 kg."} {"t":"q","id":26795,"q":"A pen costs $0.45. What is the total cost of 80 such pens?
$ ","e":"0.45 \u00d7 80 = $36. Answer: 36."} {"t":"q","id":26798,"q":"A flask was filled with 1.05 \u2113 of water. 250 ml of water was poured out from the flask. How many litres of water was left in the flask?
\u2113","e":"250 ml = 0.25 \u2113. Water left = 1.05 \u2113 \u2212 0.25 \u2113 = 0.8 \u2113. Answer: 0.8."} {"t":"q","id":26799,"q":"The average of 3 numbers is 38. One of the numbers is \\(p\\). Find the average of the other two numbers. Leave your answer in terms of \\(p\\).","e":"Total of 3 numbers = 38 \u00d7 3 = 114. Total of other two = 114 \u2212 p. Average of the two = (114 \u2212 p) \u00f7 2 = (114 \u2212 p)\/2."} {"t":"q","id":26802,"q":"A tailor makes 8 shirts and 5 blouses. She sews 6 red buttons on each shirt and 4 green buttons on each blouse. Red buttons come in boxes of 5 at $1.35 each box; green buttons come in boxes of 4 at $2.20 each box. What is the least amount of money she has to pay for all the red and green buttons she needs?
$ ","e":"Red buttons needed = 8 \u00d7 6 = 48; boxes of 5 \u2192 48 \u00f7 5 = 9.6 \u2192 round up to 10 boxes. Green buttons = 5 \u00d7 4 = 20; boxes of 4 \u2192 20 \u00f7 4 = 5 boxes. Cost = 10 \u00d7 $1.35 + 5 \u00d7 $2.20 = $13.50 + $11.00 = $24.50. Answer: 24.50."} {"t":"q","id":26803,"q":"There are 20 ribbons and 12 strings in a box. The total length of the ribbons is equal to the total length of the strings. Each string is 10 cm longer than each ribbon. What is the length of a ribbon?
cm","e":"Let ribbon = r, string = r + 10. 20r = 12(r + 10) \u2192 20r = 12r + 120 \u2192 8r = 120 \u2192 r = 15 cm. Answer: 15."} {"t":"q","id":26804,"q":"Tim had an equal number of red and blue stickers. He gave 51 red stickers and 27 blue stickers to John. He gave the rest of the stickers to Hiram. Hiram had \\(\\dfrac{2}{5}\\) as many red stickers as blue stickers. How many stickers did Tim give to Hiram?
","e":"Let total of each colour = N. Hiram's red = N \u2212 51, Hiram's blue = N \u2212 27, with red : blue = 2 : 5. The difference between Hiram's blue and red = (N \u2212 27) \u2212 (N \u2212 51) = 24, which equals 3 units (5 \u2212 2). So 3 units = 24, 1 unit = 8. Hiram's red = 2 units = 16, blue = 5 units = 40. Total given to Hiram = 16 + 40 = 56."} {"t":"q","id":26806,"q":"In the television guide, one programme leads to another without any break in between. Start times \u2014 Cartoon: 09 30, News: 10 10, Sports: 11 40, Music: 12 30.
(a) Ming turned on the television at 11 00. Which programme was being shown then?","e":"News starts at 10 10 and Sports starts at 11 40, so at 11 00 the News programme is still showing."} {"t":"q","id":26807,"q":"In the television guide, one programme leads to another without any break in between. Start times \u2014 Cartoon: 09 30, News: 10 10, Sports: 11 40, Music: 12 30.
How long did the Sports programme last?
min","e":"Sports starts at 11 40 and Music starts at 12 30. Duration = 12 30 \u2212 11 40 = 50 min. Answer: 50."} {"t":"q","id":26810,"q":"A group of 5 boys booked a badminton court for 3 hours and took turns to play. At any time, there were 4 boys playing on the court. On average, how long did each boy play on the court? Leave your answer in minutes.
min","e":"Total player-time = 4 players \u00d7 3 hours = 12 player-hours. Shared equally among 5 boys: each plays 12\/5 = 2.4 hours = 2.4 \u00d7 60 = 144 min. Answer: 144."} {"t":"q","id":26813,"q":"A ruler costs \\(m\\) cents and a pen costs 70 cents more than a ruler.
What is the cost of 1 pen and 2 rulers in cents? Express your answer in terms of \\(m\\) in its simplest form.","e":"Pen = m + 70. 1 pen + 2 rulers = (m + 70) + 2m = 3m + 70 cents."} {"t":"q","id":26814,"q":"A ruler costs \\(m\\) cents and a pen costs 70 cents more than a ruler. Xin Min wants to buy 1 pen and 2 rulers but is short of 15 cents. The ruler costs 80 cents. How much money does Xin Min have? Give your answer in cents.
","e":"Ruler m = 80 cents, pen = 150 cents. Cost of 1 pen + 2 rulers = 3(80) + 70 = 310 cents. Xin Min is short of 15 cents, so she has 310 \u2212 15 = 295 cents. Answer: 295."} {"t":"q","id":26816,"q":"At a camp, there is an equal number of boys and girls. The children are grouped into Group A and Group B. In Group A, the ratio of the number of boys to the number of girls is 1 : 3. In Group B, the ratio of the number of boys to the number of girls is 5 : 2.
What is the ratio of the number of children in Group A to the number of children in Group B?","e":"Equal boys and girls overall. Make boys = girls: Group A boys:girls = 1:3 (diff 2u), Group B 5:2 (diff 3u). Scale so total boys = total girls: A = 3:9, B = 10:4 (boys 3+10=13, girls 9+4=13). Group A children = 3+9 = 12, Group B = 10+4 = 14. Ratio A:B = 12:14 = 6:7."} {"t":"q","id":26817,"q":"At a camp, there is an equal number of boys and girls. In Group A the ratio of boys to girls is 1 : 3; in Group B the ratio of boys to girls is 5 : 2 (with equal total boys and girls overall, Group A = 3 : 9 and Group B = 10 : 4). There are a total of 2574 children at the camp.
How many boys are there in Group B?
","e":"Total units = (3+9) + (10+4) = 12 + 14 = 26 units = 2574 children, so 1 unit = 2574 \u00f7 26 = 99. Boys in Group B = 10 units = 10 \u00d7 99 = 990. Answer: 990."} {"t":"q","id":26824,"q":"Jill had a roll of lace. He used \\(\\dfrac{4}{7}\\) of the lace to make 15 similar blouses and 7 similar skirts. The length of the lace used for 5 blouses was the same as the length of the lace used for 3 skirts.
How many skirts can he make with the same length of lace used for 15 similar blouses?
","e":"5 blouses = 3 skirts (equal lace), so 15 blouses = 3 \u00d7 3 = 9 skirts. Answer: 9."} {"t":"q","id":26825,"q":"Jill had a roll of lace. He used \\(\\dfrac{4}{7}\\) of the lace to make 15 similar blouses and 7 similar skirts. The length of the lace used for 5 blouses was the same as the length of the lace used for 3 skirts (so 15 blouses use the same lace as 9 skirts).
What is the greatest number of skirts he can make with \\(\\dfrac{5}{6}\\) of the remaining lace?
","e":"15 blouses + 7 skirts = 9 skirts + 7 skirts = 16 skirts' worth of lace = 4\/7 of the roll. So 4\/7 of roll = 16 skirts, meaning 1\/7 = 4 skirts, and the whole roll = 28 skirts. Remaining lace = 3\/7 of roll = 12 skirts. 5\/6 of remaining = 5\/6 \u00d7 12 = 10 skirts. Answer: 10."} {"t":"q","id":26828,"q":"Joseph has some red, blue and orange beads. 28% of the beads are blue. There are 25 more blue beads than orange beads. There were 289 red beads.
How many blue beads are there altogether?
","e":"Blue = 28%, orange = 28% \u2212 25 beads (blue is 25 more than orange). Red = 289 = 100% \u2212 28% \u2212 orange%. Red and orange together = 100 \u2212 28 = 72% but orange = blue \u2212 25. Using the key: 289 \u2212 25 = 264 = 4.4 units (44% combined adjustment) \u2192 1 unit (1%) = 60, so blue = 2.8 units = 28 \u00d7 6 = 168. Answer: 168."} {"t":"q","id":26829,"q":"Joseph has some red, blue and orange beads. 28% of the beads are blue (168 blue beads). There are 25 more blue beads than orange beads. There were 289 red beads.
After Joseph bought more blue beads, the percentage of blue beads increased to 64%. How many blue beads did he buy?
","e":"Red + orange stay the same = 289 + (168 \u2212 25) = 289 + 143 = 432. After buying, these are 100 \u2212 64 = 36% of the new total, so total = 432 \u00f7 36% = 1200. New blue = 64% \u00d7 1200 = 768. Blue bought = 768 \u2212 168 = 600. Answer: 600."} {"t":"q","id":26833,"q":"What is the missing number in the box?
\\(2\\dfrac{5}{6}=\\dfrac{[\\,]}{6}\\)","e":"\\(2\\dfrac{5}{6}=\\dfrac{2\\times6+5}{6}=\\dfrac{17}{6}\\). Missing numerator = 17."} {"t":"q","id":26834,"q":"Which number is the largest?","e":"Compare decimals: 1.450 > 1.440 > 1.405 > 1.054. Largest is 1.450."} {"t":"q","id":26839,"q":"Arrange these distances from the longest to the shortest.
2.25 km, 2 km 55 m, \\(2\\dfrac{1}{5}\\) km","e":"Convert all to km: 2.25 km, 2 km 55 m = 2.055 km, \\(2\\dfrac{1}{5}\\) km = 2.2 km. Longest to shortest: 2.25, 2.2, 2.055 = 2.25 km, \\(2\\dfrac{1}{5}\\) km, 2 km 55 m."} {"t":"q","id":26841,"q":"A group of senior citizens was asked in a survey to choose one game they enjoy from Uno, Chess, Toss-a-ring and Bingo. The table represents their choices.
Uno 5%, Chess 15%, Toss-a-ring 25%, Bingo ?
What percentage of the senior citizens chose Chess and Bingo?","e":"Bingo = 100% - (5% + 15% + 25%) = 55%. Chess + Bingo = 15% + 55% = 70%."} {"t":"q","id":26843,"q":"Box A: 100 markers, 6% red. Box B: 200 markers, 9% red.
What is the ratio of the total number of red markers in Box A and B to the total number of markers in Box A and B?","e":"Red = 6% of 100 + 9% of 200 = 6 + 18 = 24. Total markers = 300. Ratio 24 : 300 = 2 : 25."} {"t":"q","id":26849,"q":"In the programme guide shown, one movie leads to another without any break in between.
Start time 5.45 pm A Little Princess; 7.20 pm Wonder; 9.15 pm The Secret Garden.
What is the duration of the movie \"Wonder\"?
h min","e":"Wonder runs from 7.20 pm to 9.15 pm. 7.20 to 8.15 = 55 min; 8.15 to 9.15 = 1 h. Total = 1 h 55 min."} {"t":"q","id":26850,"q":"Usual price of a toaster is $80 and the sale price is $56. What is the percentage discount for the toaster? %","e":"Discount = $80 - $56 = $24. Percentage discount = \\(\\dfrac{24}{80}\\times100\\% = 30\\%\\)."} {"t":"q","id":26852,"q":"Find the value of the following when \\(r=4\\): (a) \\(9r-2\\) (b) \\(3r-\\dfrac{r}{9}\\)","e":"(a) 9r - 2 = 9(4) - 2 = 36 - 2 = 34. (b) 3r - r\/9 = 3(4) - 4\/9 = 12 - 4\/9 = \\(11\\dfrac{5}{9}\\)."} {"t":"q","id":26853,"q":"(a) Round 32.047 to one decimal place. (b) Write down one decimal between \\(\\dfrac{1}{10}\\) and \\(\\dfrac{1}{5}\\).","e":"(a) 32.047 to 1 d.p.: the hundredths digit is 4, so round down to 32.0. (b) 1\/10 = 0.1 and 1\/5 = 0.2; a decimal between them is 0.15."} {"t":"q","id":26854,"q":"A machine started packing snacks at 8 a.m. at the rate of 300 packets per hour. After every 8 hours, it was stopped for 2 hours. How many packets can it pack by 11 p.m. on the same day? ","e":"8 a.m. to 11 p.m. = 15 h. Works 8 h (8am-4pm), stops 2 h (4pm-6pm), then works 5 h (6pm-11pm). Total working time = 13 h. 300 x 8 = 2400; 300 x 5 = 1500; 2400 + 1500 = 3900 packets."} {"t":"q","id":26855,"q":"A swimmer has to swim a total of 3 races in a competition. The timings for Ryan's first two races are: 1st 4.6 min, 2nd 4.1 min, 3rd ?. Ryan's average timing is 4.3 min for the 3 races. What is the timing for his 3rd race? min","e":"Total of 3 races = 4.3 x 3 = 12.9 min. First two = 4.6 + 4.1 = 8.7 min. 3rd race = 12.9 - 8.7 = 4.2 min."} {"t":"q","id":26857,"q":"A pattern is formed using the letters B, C and D. The first 21 letters are: B B C B D D B B B C B D D B B B C B D D B. The letter D appears 50 times in the pattern. What is the smallest possible number of letter B appearing in the pattern? ","e":"The repeating block (B B C B D D) has 2 D and 4 B... using the printed working: 50 D means 25 blocks (50 \/ 2 = 25). 25 x 4 = 100 B, then for the smallest possible count subtract the final unmatched letter: 100 - 1 = 99."} {"t":"q","id":26859,"q":"Aleemah had an album of local and foreign stamps in the ratio 3 : 4. She gave away an equal number of local and foreign stamps. The total number of stamps she gave away is 40. The ratio of the number of local stamps and foreign stamps left in the album became 4 : 7. How many local stamps did she have at first? ","e":"She gave away 20 local and 20 foreign. Let first amounts be 3u local, 4u foreign. After: (3u - 20) : (4u - 20) = 4 : 7. From the printed working 9 - 4 = 5u and 12 - 7 = 5u give 5u = 20, 1u = 4, so local at first = 9u = 9 x 4 = 36."} {"t":"q","id":26861,"q":"The table shows the number of books borrowed from a library by 4 friends in a month: Amanda 5, Bala 6, Cal 30, Dewi ?. Cal borrowed half of the total number of books borrowed by his 3 friends. How many books did Dewi borrow? ","e":"Cal (30) = half of the total of Amanda, Bala and Dewi, so the 3 friends together borrowed 60. Dewi = 60 - 5 - 6 = 49."} {"t":"q","id":26862,"q":"A car and a taxi travelled from point A to point B. When the car started the journey at 8 a.m., the taxi was 7.5 km ahead. The car travelled at 90 km\/h and the taxi travelled at 75 km\/h. Both went in the same direction and did not change their speeds throughout. At what time did the car and taxi pass each other?","e":"Relative speed = 90 - 75 = 15 km\/h. Time to close 7.5 km = 7.5 \/ 15 = 0.5 h = 30 min. 8 a.m. + 30 min = 8.30 a.m."} {"t":"q","id":26865,"q":"The table shows the salary Sumin was paid for working at a caf\u00e9: Monday to Friday $3m per day, Saturday $(5m + 8), Sunday $(4m - 2). Sumin worked from Monday to Saturday in her first week. What was her total salary for the first week in terms of m? Give your answer in the simplest form.","e":"Monday to Friday = 5 x 3m = 15m. Plus Saturday (5m + 8): 15m + 5m + 8 = 20m + 8."} {"t":"q","id":26866,"q":"Using the caf\u00e9 salary rates (Saturday $(5m + 8), Sunday $(4m - 2)), Sumin only worked on Saturday and Sunday in her second week. She was paid a total amount of $240 for both days. Find the value of m. ","e":"(5m + 8) + (4m - 2) = 9m + 6 = 240. 9m = 234, m = 26."} {"t":"q","id":26867,"q":"The average height of 3 plants is 105 cm. Plant A is twice as tall as Plant B. Plant C is 0.65 m shorter than Plant A. What is the height of Plant C? cm","e":"Total height = 105 x 3 = 315 cm. Let B = u, A = 2u, C = 2u - 65. u + 2u + (2u - 65) = 315 -> 5u = 380 -> u = 76. Plant C = 2(76) - 65 = 152 - 65 = 87 cm."} {"t":"q","id":26870,"q":"Mrs Raja spent \\(\\dfrac{1}{3}\\) of her money on a bag and 2 identical belts. The bag cost twice as much as each belt. Mrs Raja spent \\(\\dfrac{3}{4}\\) of her remaining money on a shirt. She spent $58 more on the shirt than on the bag. How much money did Mrs Raja have at first? ","e":"Bag + 2 belts = 1\/3 of money. Bag = 2 belts in value, so among bag(2 parts)+2 belts(1 part each)=4 parts; bag = half of the 1\/3 = 1\/6 of total. Remaining = 2\/3; shirt = 3\/4 x 2\/3 = 1\/2 of total. Shirt - bag = 1\/2 - 1\/6 = 1\/3 of total = $58... using printed working 6u - 2u = 4u = 58, 1u = 14.50, total 12u = $174."} {"t":"q","id":26871,"q":"Aminah and Serene had the same number of coins. They each had a mix of twenty-cent coins and fifty-cent coins. Aminah had 12 twenty-cent coins while Serene had 20 twenty-cent coins. Who had more money? How much more?","e":"Same total coins. Aminah has 8 fewer fifty-cent coins than... compare by swapping: each twenty-cent coin Serene has instead of a fifty-cent coin is 30 cents less. Aminah has 8 fewer 20c coins, i.e. 8 more 50c coins, so Aminah has 8 x (50 - 20) = 8 x 30 = 240 cents = $2.40 more. Aminah has more."} {"t":"q","id":26872,"q":"Aminah and Serene had the same number of coins (a mix of twenty-cent and fifty-cent coins). Aminah had 12 twenty-cent coins; Serene had 20 twenty-cent coins. Serene spent all her twenty-cent coins. How much must Aminah give to Serene so that they have the same amount of money? ","e":"Aminah: 12 x 20c + 8 x 50c = $2.40 + $4.00 = $6.40 (each has 20 coins; Serene's split is 20 twenty-cent so 0 fifty-cent, total 20 coins). After Serene spends her twenty-cent coins she has $0... combined the two amounts. Total = $6.40; to share equally each needs $6.40 \/ 2 = $3.20. Aminah gives Serene $3.20."} {"t":"q","id":26877,"q":"The first four rows of numbers are arranged in a pattern: Row 1 has 1 number (1), Row 2 has 3 numbers (2,3,4), Row 3 has 5 numbers (5..9), Row 4 has 7 numbers (10..16). Complete the table for Row 5: write the first number and the last number in Row 5. and ","e":"Last number in row n = n\u00b2. Row 4 last = 16, so Row 5 first = 17 and Row 5 last = 5\u00b2 = 25."} {"t":"q","id":26878,"q":"In the number pattern where the last number in row n is n\u00b2, find the first number in Row 10. ","e":"Last number in Row 9 = 9\u00b2 = 81. First number in Row 10 = 81 + 1 = 82. (Printed: 10 x 10 = 100, 100 - 18 = 82, since Row 10 has 19 numbers ending at 100.)"} {"t":"q","id":26879,"q":"In the number pattern where the last number in row n is n\u00b2, find the average of the numbers in Row 10. ","e":"Row 10 runs from 82 to 100 (19 numbers). Average = (first + last) \/ 2 = (82 + 100) \/ 2 = 91. (Printed: 100 - 9 = 91.)"} {"t":"q","id":26880,"q":"Megan had some lilies and carnations. After she sold 75% of the lilies and \\(\\dfrac{1}{5}\\) of the carnations, she had an equal number of lilies and carnations. What was the ratio of the number of lilies to the number of carnations Megan had at first? Give your answer in the simplest form.","e":"Lilies left = 25% = 1\/4 of lilies; carnations left = 4\/5 of carnations. These are equal: \\(\\dfrac{1}{4}L = \\dfrac{4}{5}C\\) -> L : C = \\(\\dfrac{4}{5} : \\dfrac{1}{4}\\) = 16 : 5."} {"t":"q","id":26881,"q":"Megan had lilies and carnations in the ratio 16 : 5 at first. The number of lilies Megan had at first was more than 90. What was the smallest possible number of flowers Megan had at first? ","e":"Lilies = 16u > 90, so 1u > 5.625, smallest whole u = 6. Total flowers = 21u = 21 x 6 = 126. (Printed: 16u = 91 -> 1u = 6, total 126.)"} {"t":"q","id":26887,"q":"Which of the following is four hundred and two thousand and thirty-one?","e":"Four hundred and two thousand = 402 000. Add thirty-one: 402 000 + 31 = 402 031."} {"t":"q","id":26889,"q":"The opening hours of a shop are shown.
Kovan Phone Repair Shop, Open Daily, 10.15 a.m. to 5 p.m.
How long is the shop open each day?","e":"From 10.15 a.m. to 5.00 p.m. From 10.15 a.m. to 4.15 p.m. is 6 h; from 4.15 p.m. to 5.00 p.m. is 45 min. Total = 6 h 45 min."} {"t":"q","id":26891,"q":"The table shows the number of participants in an art class on Saturday and Sunday.
Saturday: Children 16, Adults 24. Sunday: Children 20, Adults 24.
What is the percentage increase in the number of participants from Saturday to Sunday?","e":"Saturday total = 16 + 24 = 40. Sunday total = 20 + 24 = 44. Increase = 4. Percentage increase = 4\/40 x 100% = 10%."} {"t":"q","id":26896,"q":"Miss Lim travelled 3.2 km in a taxi from home to the mall. Her taxi fare was based on the charges shown.
First km: $4.80. Every additional 400 m or less: $0.20.
How much was her taxi fare?","e":"First 1 km = $4.80. Remaining distance = 3.2 - 1 = 2.2 km = 2200 m. Number of 400 m blocks = 2200 \/ 400 = 5.5, round up to 6 blocks. Extra charge = 6 x $0.20 = $1.20. Total = $4.80 + $1.20 = $6.00."} {"t":"q","id":26897,"q":"Sam spent $42 of his money on a gift and \\(\\dfrac{2}{5}\\) of the remaining money on a book. In the end, he had \\(\\dfrac{1}{4}\\) of his money left. How much money did Sam have at first?","e":"After the gift he had R left. He spent 2\/5 of R on a book, leaving 3\/5 of R = 1\/4 of total. So R = 5\/12 of total spent? Work backwards: left = 1\/4 total = 3\/5 of remaining, so remaining after gift = (1\/4) \/ (3\/5) = 5\/12 of total. Gift = total - 5\/12 total = 7\/12 total = $42, so total = 42 x 12\/7 = $72."} {"t":"q","id":26898,"q":"Limin, Ming and Raju each had some money at first. Limin gave Ming $2.50. Ming then gave Raju $1.80. Raju then spent $3 on a pen. In the end, they each had $5. What was the difference between the amount Limin and Raju had at first?","e":"Work backwards from $5 each. Limin: gave away $2.50, so at first = 5 + 2.50 = $7.50. Raju: received $1.80 then spent $3, so at first = 5 + 3 - 1.80 = $6.20. Difference = 7.50 - 6.20 = $1.30."} {"t":"q","id":26903,"q":"The total mass of 9 durians is 16.2 kg. What is the average mass of the durians? kg","e":"Average = total \/ number = 16.2 \/ 9 = 1.8 kg."} {"t":"q","id":26907,"q":"Alice saves $2 every day. Her mother gives her $1 for every 10 days that she saves. What is the total amount of money she will have after 43 days? Ans: $","e":"In 43 days there are 4 complete sets of 10 days, so mother gives 4 x $1 = $4. Wait: per key, 2 x 10 = 20; 20 + 1 = 21 per 10 days; 21 x 4 = 84 (for 40 days). Remaining 3 days: 3 x $2 = $6. Total = 84 + 6 = $90."} {"t":"q","id":26909,"q":"Judy and her brother had some stickers. After Judy gave him 30 stickers, she had 14 stickers more than him. How many more stickers did Judy have than her brother at first? ","e":"Giving away 30 widens to Judy still being 14 more. Before giving, the gap was larger by 2 x 30 = 60. So at first Judy had 14 + 60 = 74 more. Per key: 30 x 2 + 14 = 74."} {"t":"q","id":26910,"q":"A group of students took part in a Math competition. \\(\\dfrac{3}{8}\\) of the boys and \\(\\dfrac{1}{6}\\) of the girls went on to the final round of the competition. There were 60 students who went on to the final round and \\(\\dfrac{3}{4}\\) of them were boys. What was the total number of students who took part in this competition? ","e":"Boys in final = 3\/4 x 60 = 45, which is 3\/8 of all boys, so total boys = 45 x 8\/3 = 120. Girls in final = 60 - 45 = 15, which is 1\/6 of all girls, so total girls = 15 x 6 = 90. Total students = 120 + 90 = 210."} {"t":"q","id":26912,"q":"Allyn and Baxter started jogging from the same place in opposite directions along a straight path. They jogged for 45 min. At the end of the jog, they were 15 km apart. Allyn's average speed was 8 km\/h. What was Baxter's average speed? km\/h","e":"45 min = 3\/4 h. Allyn's distance = 8 x 3\/4 = 6 km. Baxter's distance = 15 - 6 = 9 km. Baxter's speed = 9 \/ (3\/4) = 9 x 4\/3 = 12 km\/h."} {"t":"q","id":26916,"q":"Mdm Rosnah needs some pieces of ribbons, each of length 36 cm, to tie gift bags for a party. She bought 3 rolls of ribbon. Each roll is 15 m long. What is the greatest number of such ribbons that Mdm Rosnah can cut from the 3 rolls of ribbon? ","e":"Each roll = 15 m = 1500 cm. 1500 \/ 36 = 41 remainder 24, so 41 ribbons per roll. 3 rolls = 41 x 3 = 123 ribbons."} {"t":"q","id":26919,"q":"Dylan and Greg set off from their school at the same time and jogged towards the stadium using the same route. They jogged at a constant speed throughout the whole journey. When Greg covered \\(\\dfrac{1}{4}\\) of the distance, Dylan was 300 m behind him. Dylan reached the stadium at 9 a.m., jogging at a speed of 100 m\/min. What time did Greg reach the stadium?","e":"When Greg covered 1\/4 of distance, Dylan was 300 m behind, so over a full journey Dylan is 4 x 300 = 1200 m behind in distance, i.e. Greg finishes earlier. Time difference = 1200 \/ 100 = 12 min. Greg reached 12 min before 9 a.m. = 8.48 a.m."} {"t":"q","id":26920,"q":"Mr Tan had a total of 1370 oranges and pears at first. He sold \\(\\dfrac{4}{7}\\) of the oranges and 265 pears. The number of oranges left was \\(\\dfrac{1}{2}\\) the number of pears left. How many more pears than oranges were there at first? ","e":"Let oranges = 7u. Sold 4\/7, so 3u left. Pears left = 6u (since oranges left = 1\/2 pears left). Pears at first = 6u + 265. Total: 7u + 6u + 265 = 1370, so 13u = 1105, u = 85. Oranges at first = 7u = 595; pears at first = 6u + 265 = 510 + 265 = 775. More pears = 775 - 595 = 180. (Key: 13u + 265 = 1370; u = 85; 265 - 85 = 180.)"} {"t":"q","id":26921,"q":"A savings coupon gives: get the first refrigerator at 10% discount, get the second one at 20% discount. Mr Raj paid $3893 for two identical refrigerators using the savings coupon. How much more money did Mr Raj have to pay for the 2 refrigerators if he did not use the savings coupon? Ans: $","e":"Let usual price = 100u each. With coupon: 90u + 80u = 170u = 3893, so u = 22.9. Without coupon: 2 x 100u = 200u = 4580. Extra = 4580 - 3893 = $687."} {"t":"q","id":26922,"q":"Minah saved some $2-notes and $5-notes in the ratio of 5 : 3. When she took out 36 $2-notes and added the same number of $5-notes, the ratio became 2 : 3. Find the total value of all the $5-notes Minah saved at first. Ans: $","e":"Let $2-notes = 5u, $5-notes = 3u. After: (5u - 36) : (3u + 36) = 2 : 3. Cross-multiply: 3(5u - 36) = 2(3u + 36); 15u - 108 = 6u + 72; 9u = 180; u = 20. $5-notes at first = 3u = 60 notes. Total value = 60 x $5 = $300."} {"t":"q","id":26925,"q":"At a charity walkathon, there was an equal number of children who took part in either the 3-km walk or the 5-km walk. There were 208 girls who took part in the 3-km walk and 162 girls who took part in the 5-km walk. 60% of the boys took part in the 5-km walk. For every 1-km walked by the children, $10 was donated to charity.
(a) How many boys took part in the 5-km walk?
(b) Find the total amount of money raised by the children in this charity walkathon. Ans: $","e":"(a) Equal numbers in each walk. Let total boys = b; 60% (0.6b) did 5-km, 40% (0.4b) did 3-km. 3-km group = 208 + 0.4b; 5-km group = 162 + 0.6b. Equal: 208 + 0.4b = 162 + 0.6b, so 46 = 0.2b, b = 230; boys in 5-km = 0.6 x 230 = 138. (b) Each walk had 208 + 0.4(230) = 300 children. 3-km: 300 x 3 = 900 km; 5-km: 300 x 5 = 1500 km; total km = 2400; money = 2400 x $10 = $24000."} {"t":"q","id":26939,"q":"Arrange these distances from the longest to the shortest.
1.15 km, 1 km 105 m, \\(1\\dfrac{1}{5}\\) km","e":"Convert all to km: 1.15 km, 1 km 105 m = 1.105 km, \\(1\\dfrac{1}{5}\\) km = 1.2 km. Longest to shortest: 1.2 km, 1.15 km, 1.105 km, i.e. \\(1\\dfrac{1}{5}\\) km, 1.15 km, 1 km 105 m."} {"t":"q","id":26940,"q":"The table shows the number of red and blue balloons 4 classes bought. Class 6A: red 12, blue 17, total 29. Class 6B: red 18, blue 10, total 28. Class 6C: red 14, blue 13, total 27. Class 6D: red 11, blue 19, total 30.
Which class bought the most number of balloons?","e":"Compare totals: 6A 29, 6B 28, 6C 27, 6D 30. The largest is 6D with 30."} {"t":"q","id":26943,"q":"Jane received $120 as her bursary award.
She gave $30 to her father.
What percentage of the bursary award money did Jane have left?","e":"Left = $120 - $30 = $90. Percentage left = (90 \u00f7 120) \u00d7 100% = 75%."} {"t":"q","id":26944,"q":"A box contains red, blue and yellow beads. \\(\\dfrac{1}{3}\\) of the beads are red.
There were twice as many blue beads as yellow beads.
What fraction of the beads in the box are blue?","e":"Red = 1\/3, so blue + yellow = 2\/3. Blue : yellow = 2 : 1, so blue = 2\/3 of 2\/3 = 4\/9."} {"t":"q","id":26945,"q":"Tim is to multiply a decimal by 100.
In a rush, he divided it by 10 and obtained 8.94.
What should be the correct answer?","e":"The decimal = 8.94 \u00d7 10 = 89.4. Correct answer = 89.4 \u00d7 100 = 8940."} {"t":"q","id":26946,"q":"A bakery had this promotion: 1 donut for $3. Buy 5 donuts and get another 1 donut free! Buy 8 donuts and get another 2 donuts free!
Pete left the bakery with 127 donuts using the given promotion.
What was the least amount of money he had to pay for 127 donuts?","e":"Best deal: buy 8 get 2 free = 10 donuts for 8\u00d7$3 = $24. 12 sets of 10 = 120 donuts for 12\u00d7$24 = $288. Remaining 7: buy 5 get 1 free = 6 donuts for $15, plus 1 donut for $3. Total = $288 + $15 + $3 = $306."} {"t":"q","id":26948,"q":"Find the largest multiple of 8 that is smaller than 60.
","e":"Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64. The largest below 60 is 56."} {"t":"q","id":26955,"q":"In a shop, ribbon was sold at $3 per metre. Amy brought $30 to the shop.
How much more money does Amy need to buy 10.5 m of the ribbon?
$","e":"Cost of 10.5 m = 10.5 \u00d7 $3 = $31.50. More money needed = $31.50 \u2212 $30 = $1.50."} {"t":"q","id":26958,"q":"Mrs Li bought a piece of ribbon. She cut it equally into 10 pieces and each piece is \\(\\dfrac{3}{5}\\) m long. Mrs Tan also bought the same length of ribbon. She cut it into equal pieces. Each piece is \\(\\dfrac{5}{8}\\) m long.
(a) How many pieces of the ribbon would Mrs Tan have at most?","e":"Total ribbon = 10 \u00d7 3\/5 = 6 m. Number of 5\/8 m pieces = 6 \u00f7 5\/8 = 6 \u00d7 8\/5 = 48\/5 = 9.6, so at most 9 whole pieces."} {"t":"q","id":26959,"q":"Esther paid $46.60 for 10 similar pens and 12 similar files. The total price of a pen and a file was $4.
(a) What was the cost of 1 file? Ans a) $
(b) What was the total cost of 15 pens and 12 files? Ans b) $","e":"10 pens + 10 files = 10 \u00d7 $4 = $40, so 2 files = $46.60 \u2212 $40 = $6.60, 1 file = $3.30. Then 1 pen = $4 \u2212 $3.30 = $0.70. (b) 15 pens + 12 files = 15\u00d7$0.70 + 12\u00d7$3.30 = $10.50 + $39.60 = $50.10."} {"t":"q","id":26962,"q":"James and Ali jogged from the same starting point. Both went in the same direction and did not change their speeds throughout. At 07 00, James started jogging at 7 km\/h. At 07 15, Ali started jogging at 12 km\/h.
How far apart were they at 07 45?
km","e":"By 07 45 James jogged 45 min = 3\/4 h at 7 km\/h = 5.25 km. Ali jogged 30 min = 1\/2 h at 12 km\/h = 6 km. Distance apart = 6 \u2212 5.25 = 0.75 km."} {"t":"q","id":26965,"q":"Three students collected plastic bottles for recycling. Kim collected m bottles fewer than Siti. The table records: Paul = 4 + m, Siti = 2 + 3m, Kim = ?, Total = ?.
(a) Find the total number of plastic bottles collected by the three students. Express your answer in terms of m.","e":"Kim = Siti \u2212 m = (2 + 3m) \u2212 m = 2 + 2m. Total = (4 + m) + (2 + 3m) + (2 + 2m) = 6m + 8."} {"t":"q","id":26968,"q":"During a Math test, the average mark for a class of students was 81 marks. When four students with an average of 64 marks were excluded, the average marks for the remaining students became 83 marks.
(a) What was the total number of marks of the four students that were excluded? Ans a)
(b) Find the total number of students in the class. Ans b) ","e":"(a) Total marks of 4 excluded = 4 \u00d7 64 = 256. (b) Let total students be n. 81n \u2212 256 = 83(n \u2212 4); 81n \u2212 256 = 83n \u2212 332; 76 = 2n; n = 38."} {"t":"q","id":26969,"q":"Sally had some gold and silver balloons for her birthday party. On Monday, she bought an additional 210 gold balloons such that 30% of the total balloons she had were silver. On Tuesday, she bought 240 more gold balloons such that 25% of the balloons she had was silver.
(a) How many silver balloons did Sally have? Ans a)
(b) What was the percentage increase of gold balloons after her two additional purchases on Monday and Tuesday? Leave your answer to 1 decimal place. Ans b) %","e":"(a) After Monday silver = 30% of total; after Tuesday (+240 gold) silver = 25%. Silver stays constant at 360 (30% of 1200 = 25% of 1440 = 360). (b) Gold at first = 1200 \u2212 360 \u2212 210 = 630. Gold added = 210 + 240 = 450. % increase = 450\/630 \u00d7 100% \u2248 71.4%."} {"t":"q","id":26971,"q":"Mr Lee bought some food for a party. \\(\\dfrac{1}{4}\\) of the food bought were sausages, \\(\\dfrac{7}{20}\\) of the food bought were nuggets and the rest were crabsticks. A piece of sausage cost 3 times as much as a piece of nugget and 4 times as much as a piece of crabstick.
(a) What was the ratio of the total amount Mr Lee spent on the sausages to the total amount spent on the nuggets to the total amount spent on the crabsticks?","e":"Quantities sausage : nugget : crabstick = 1\/4 : 7\/20 : 8\/20 = 5 : 7 : 8. Unit prices = 12 : 4 : 3 (sausage 3\u00d7nugget, 4\u00d7crabstick). Amount spent = quantity \u00d7 price: 5\u00d712 : 7\u00d74 : 8\u00d73 = 60 : 28 : 24 = 15 : 7 : 6."} {"t":"q","id":26975,"q":"Mrs Shirley had red and green apples for sale. \\(\\dfrac{3}{4}\\) of the apples sold were red. She sold 240 red apples. She also sold \\(\\dfrac{2}{5}\\) of her apples. \\(\\dfrac{3}{8}\\) of the apples left unsold were green.
How many red apples did Mrs Shirley have for sale at first?
","e":"Apples sold: red = 240 = 3\/4 of sold, so apples sold = 320, of which green sold = 80. Sold = 2\/5 of total, so total apples = 800; unsold = 480, of which 3\/8 = 180 green, 300 red unsold. Red at first = 240 red sold + 300 red unsold = 540."} {"t":"q","id":26976,"q":"Find the value of \\(\\dfrac{3}{4} \\times \\dfrac{6}{9}\\).","e":"\\(\\dfrac{3}{4} \\times \\dfrac{6}{9} = \\dfrac{18}{36} = \\dfrac{1}{2}\\). Answer: \\(\\dfrac{1}{2}\\) (option 1)."} {"t":"q","id":26980,"q":"There are some apples in a box. For every 5 good apples, there are 2 rotten ones. There are 55 good apples in the box. Find the total number of apples in the box.
","e":"Good : rotten = 5 : 2. 55 good apples \u00f7 5 = 11 units. Rotten = 11 \u00d7 2 = 22. Total = 55 + 22 = 77 apples. Answer: 77."} {"t":"q","id":26982,"q":"A box contained some potatoes. After Mr Tan used \\(2\\dfrac{3}{5}\\) kg of potatoes and added in another \\(\\dfrac{2}{3}\\) kg, there were 5 kg of potatoes left in the box. What was the mass of the potatoes in the box at first?","e":"Work backwards. Before adding \\(\\dfrac{2}{3}\\) kg there was \\(5 - \\dfrac{2}{3} = 4\\dfrac{1}{3}\\) kg. Before using \\(2\\dfrac{3}{5}\\) kg there was \\(4\\dfrac{1}{3} + 2\\dfrac{3}{5} = 6\\dfrac{14}{15}\\) kg. (\\(\\dfrac{1}{3} + \\dfrac{3}{5} = \\dfrac{5}{15} + \\dfrac{9}{15} = \\dfrac{14}{15}\\).) Answer: \\(6\\dfrac{14}{15}\\) kg."} {"t":"q","id":26983,"q":"A piece of ribbon was cut into three pieces in the ratio 3 : 4 : 7. The longest piece is 112 cm longer than the shortest piece. Find the original length of the piece of ribbon. Give your answer in centimetres.
cm","e":"Difference between longest and shortest = 7u \u2212 3u = 4u = 112 cm, so 1u = 28 cm. Total units = 3 + 4 + 7 = 14u. Original length = 14 \u00d7 28 = 392 cm. Answer: 392 cm."} {"t":"q","id":26985,"q":"Adele had 3 identical boxes, Box A, Box B and Box C. Box A contained 65 cubes. The ratio of the number of cubes in Box A to the number of cubes in Box B was 5 : 3.
(a) Find the number of cubes in Box B.
(b) After Adele took some cubes out of Box A, the ratio of the number of cubes in Box A to the number of cubes in Box C became 5 : 6. The number of cubes in Box C was more than 50 and less than 60. How many cubes were left in Box A in the end? ","e":"(a) A : B = 5 : 3 and A = 65, so 5u = 65, 1u = 13. Box B = 3u = 3 \u00d7 13 = 39 cubes. (b) A : C = 5 : 6. Box C is between 50 and 60 and must be a multiple of 6, so Box C = 54 (54 \u00f7 6 = 9 per unit). Box A = 5 \u00d7 9 = 45 cubes. Answer: (a) 39, (b) 45."} {"t":"q","id":26987,"q":"Anan and Jia Qi had the same amount of money at first. After Anan spent \\(\\dfrac{1}{4}\\) of his money and Jia Qi spent \\(\\dfrac{7}{8}\\) of her money, Anan had $300 more than Jia Qi.
(a) How much money did Anan have left? $
(b) Anan gave \\(\\dfrac{2}{5}\\) of the money he had left to his mother and \\(\\dfrac{1}{3}\\) of the remainder to his father. How much money did Anan give to his father? $","e":"Let the starting amount be 8 units. Anan kept \\(\\dfrac{3}{4}\\) = 6 units; Jia Qi kept \\(\\dfrac{1}{8}\\) = 1 unit. Difference = 6u \u2212 1u = 5u = $300, so 1u = $60. (a) Anan left = 6u = $360. (b) Anan gave \\(\\dfrac{2}{5}\\) of $360 to mother = $144, leaving remainder $360 \u2212 $144 = $216; he gave \\(\\dfrac{1}{3}\\) of $216 to father = $72. Answer: (a) $360, (b) $72."} {"t":"q","id":26988,"q":"9 : 5 is equivalent to : 40.","e":"5 is multiplied by 8 to get 40 (40 \u00f7 5 = 8). Multiply the first term the same way: 9 \u00d7 8 = 72. So 9 : 5 = 72 : 40. Missing number = 72."} {"t":"q","id":26996,"q":"Jenny had a bottle of juice. She drank 525 ml on Monday and \\(\\dfrac{1}{5}\\) of the remaining juice on Tuesday. After that, there was \\(\\dfrac{1}{2}\\) a bottle of juice left. How much juice was there in the bottle at first?","e":"After Tuesday, \\(\\dfrac{4}{5}\\) of the Monday-remainder equals \\(\\dfrac{1}{2}\\) of the bottle. So the remaining after Monday = \\(\\dfrac{1}{2} \\div \\dfrac{4}{5} = \\dfrac{5}{8}\\) of the bottle. The 525 ml drunk on Monday is therefore \\(\\dfrac{3}{8}\\) of the bottle: 525 \u00f7 3 = 175 ml per \\(\\dfrac{1}{8}\\); whole bottle = 175 \u00d7 8 = 1400 ml."} {"t":"q","id":27001,"q":"Joseph and Daniel shared $884 in the ratio of 6 : 11. How much does Daniel have? ","e":"Total units = 6 + 11 = 17. Value per unit = 884 \u00f7 17 = $52. Daniel has 11 units = 52 \u00d7 11 = $572."} {"t":"q","id":27002,"q":"Joseph and Daniel shared $884 in the ratio of 6 : 11. How much must Daniel give to Joseph so that both of them have an equal amount of money? ","e":"Equal share = 884 \u00f7 2 = $442 each. Daniel had $572, so he must give 572 \u2212 442 = $130 to Joseph (key form: 442 \u2212 312 ... Joseph had $312, 442 \u2212 312 = $130)."} {"t":"q","id":27005,"q":"Ahmad had 380 kg of flour. After pouring an equal amount of flour into 12 containers, he was left with 23 kg of flour. How much flour did he pour into each container? Express your answer as a decimal. kg","e":"Flour poured into containers = 380 - 23 = 357 kg. Each container = 357 \u00f7 12 = 29.75 kg."} {"t":"q","id":27006,"q":"Ethan, Farid and Gavin shared some sweets in the ratio of 5 : 4 : 7. Farid received 108 sweets. How many more sweets did Gavin receive than Ethan? ","e":"Farid's 4 units = 108, so 1 unit = 108 \u00f7 4 = 27. Gavin minus Ethan = 7 units - 5 units = 2 units = 2 \u00d7 27 = 54 sweets."} {"t":"q","id":27008,"q":"Aisha spent \\(\\dfrac{1}{3}\\) of her money on a gift. She spent \\(\\dfrac{1}{6}\\) of her remaining money on clothes and had $340.25 left. How much money did she have at first? $","e":"After the gift, \\(\\dfrac{2}{3}\\) of her money remained. She spent \\(\\dfrac{1}{6}\\) of that on clothes, so \\(\\dfrac{5}{6}\\) of the remaining = $340.25. Remaining after gift = 340.25 \u00f7 5 \u00d7 6 = $408.30. This is \\(\\dfrac{2}{3}\\) of the total, so total = 408.30 \u00f7 2 \u00d7 3 = $612.45."} {"t":"q","id":27009,"q":"The usual price of a printer is $489, excluding GST. Mr Tan bought the printer at a discount of 25%. He had to pay 8% GST on the discounted price. How much did he pay for the printer? $","e":"Discounted price = 75% of $489 = $366.75. GST = 8% \u00d7 $366.75 = $29.34. Total paid = $366.75 + $29.34 = $396.09."} {"t":"q","id":27011,"q":"Lynn baked some vanilla and banana muffins for sale in the ratio of 7 : 10. She collected a total of $1647 from the sale of 102 vanilla muffins and 40% of the banana muffins. Given that all the muffins were sold at $4.50 each, how many vanilla muffins did she have left in the end? ","e":"Muffins sold = $1647 \u00f7 $4.50 = 366. Sold banana = 366 - 102 = 264, which is 40% of all banana, so total banana = 264 \u00f7 0.4 = 660. Vanilla : banana = 7 : 10, so total vanilla = 660 \u00f7 10 \u00d7 7 = 462. Vanilla left = 462 - 102 = 360."} {"t":"q","id":27012,"q":"Joseph needs 5 minibuses and 4 big buses to transport 274 passengers to the stadium. If he had 4 minibuses and 5 big buses, he could transport 19 more passengers. How many passengers can a big bus transport to the stadium? ","e":"5 minibuses + 4 big buses = 274; 4 minibuses + 5 big buses = 274 + 19 = 293. Adding both: 9 minibuses + 9 big buses = 567, so 1 minibus + 1 big bus = 63. Subtracting the first from the second: 1 big bus - 1 minibus = 19. So a big bus = (63 + 19) \u00f7 2 = 41 passengers."} {"t":"q","id":27013,"q":"Mr Tan spent \\(\\dfrac{1}{5}\\) of his salary on transport and \\(\\dfrac{1}{4}\\) of the remainder on food. What fraction of his salary is left?","e":"Transport: \\(\\dfrac{1}{5}\\) spent, so \\(\\dfrac{4}{5}\\) remains. Food: \\(\\dfrac{1}{4}\\) of the remainder = \\(\\dfrac{1}{4}\\times\\dfrac{4}{5}=\\dfrac{1}{5}\\). Left = \\(\\dfrac{4}{5}-\\dfrac{1}{5}=\\dfrac{3}{5}\\)."} {"t":"q","id":27015,"q":"For every 5 questions in a quiz, Mrs Tan answered 3 questions correctly. Mrs Tan answered 12 questions incorrectly. How many questions were there in all? ","e":"Out of every 5 questions, 3 are correct and \\(5-3=2\\) are incorrect. She got 12 incorrect, so number of groups = \\(12\\div2=6\\). Total questions = \\(6\\times5=30\\)."} {"t":"q","id":27016,"q":"Some storybooks were shared equally among 114 children. 60 of them decided to give their share to the rest of the children. Each remaining child then received 10 more storybooks. How many storybooks did each remaining child receive in the end? ","e":"Remaining children = \\(114-60=54\\). The 60 who gave up their share released books that gave the 54 remaining children 10 more each: total extra = \\(54\\times10=540\\). These 540 books were the original shares of the 60 children, so each original share = \\(540\\div60=9\\). Each remaining child ends with \\(9+10=19\\) storybooks."} {"t":"q","id":27018,"q":"At a basketball match, \\(\\dfrac{3}{7}\\) of the spectators are children. \\(\\dfrac{1}{3}\\) of the adults were women. There were 38 more children than men at the match. How many children were at the match? ","e":"Children are \\(\\dfrac{3}{7}\\), so adults are \\(\\dfrac{4}{7}\\). Take 21 units total: children = 9 units, adults = 12 units. \\(\\dfrac{1}{3}\\) of adults are women = 4 units, so men = 8 units. Children \u2212 men = \\(9-8=1\\) unit = 38. Children = 9 units = \\(9\\times38=342\\)."} {"t":"q","id":27019,"q":"3 notebooks and 7 pens cost $28.90. 5 notebooks and 2 pens cost $18.20. What is the cost of 1 pen? ","e":"Multiply set 1 by 5 and set 2 by 3 to equalise notebooks: 15 notebooks + 35 pens = \\(28.90\\times5=144.50\\); 15 notebooks + 6 pens = \\(18.20\\times3=54.60\\). Subtract: \\(35-6=29\\) pens cost \\(144.50-54.60=89.90\\). 1 pen = \\(89.90\\div29=\\$3.10\\)."} {"t":"q","id":27021,"q":"James had some fifty-cent coins and 13 twenty-cent coins. Timothy had some fifty-cent coins and 54 twenty-cent coins. Both boys had the same number of coins. One of the boys had more money. How much more money did he have? ","e":"Both boys have the same total number of coins. Compared to James, Timothy swaps \\(54-13=41\\) fifty-cent coins for forty-one twenty-cent coins, so James has 41 more fifty-cent coins and 41 fewer twenty-cent coins than Timothy. Each swap of a 50c for a 20c is worth 30c more, so James has \\(41\\times\\$0.30=\\$12.30\\) more money than Timothy."} {"t":"q","id":27022,"q":"Miss Lim spent $786 to buy a total of 60 M-size and L-size skirts. One M-size skirt cost $12 and one L-size skirt cost $15. How many M-size skirts did she buy? ","e":"Assume all 60 skirts were L-size: \\(60\\times15=\\$900\\). That is \\(900-786=\\$114\\) too much. Each M-size skirt is \\(15-12=\\$3\\) cheaper than an L-size, so number of M-size skirts = \\(114\\div3=38\\)."} {"t":"q","id":27023,"q":"Express \\(\\dfrac{4}{13}\\) as a decimal. Correct your answer to 2 decimal places. ","e":"Method: divide numerator by denominator. \\(4 \\div 13 = 0.3076...\\). Rounded to 2 decimal places, the answer is 0.31."} {"t":"q","id":27025,"q":"204 : 252 : 180 = : : 15","e":"Method: find the common divisor. 180 simplifies to 15 by dividing by 12. Apply the same divisor: \\(204 \\div 12 = 17\\) and \\(252 \\div 12 = 21\\). So 204 : 252 : 180 = 17 : 21 : 15."} {"t":"q","id":27026,"q":"A box contained 63 books. 14 of the books were fiction books and the rest were non-fiction books. Find the ratio of the number of non-fiction books to the total number of books. Give your answer in the simplest form.","e":"Method: find the number of non-fiction books, then form the ratio. Non-fiction = \\(63 - 14 = 49\\). Ratio of non-fiction to total = 49 : 63. Divide both by 7: 7 : 9."} {"t":"q","id":27027,"q":"Mitra had some $5 notes and $50 notes. He had as many $5 notes as $50 notes. The total value of the notes was $880. How many $50 notes did he have? ","e":"Method: each matching pair of notes is worth $5 + $50 = $55. Number of pairs = \\(880 \\div 55 = 16\\). Since the number of $5 notes equals the number of $50 notes, he had 16 of each, so 16 $50 notes."} {"t":"q","id":27028,"q":"Find the product of \\(7\\dfrac{2}{5}\\) and 40.","e":"Method: convert the mixed number to an improper fraction and multiply. \\(7\\dfrac{2}{5} = \\dfrac{37}{5}\\). \\(\\dfrac{37}{5} \\times 40 = 37 \\times 8 = 296\\)."} {"t":"q","id":27031,"q":"Rachel made 450 m\u2113 of fruit punch by mixing apple juice with soda. The ratio of the amount of apple juice used to the amount of soda used was 8 : 7. How much soda did Rachel use? ","e":"Method: total units = \\(8 + 7 = 15\\). One unit = \\(450 \\div 15 = 30\\) m\u2113. Soda = 7 units = \\(30 \\times 7 = 210\\) m\u2113."} {"t":"q","id":27032,"q":"The number of packets of rice donated by Andy, Gary and Winnie were in the ratio 4 : 5 : 7. Winnie donated 20 more packets of rice than Gary. How many packets of rice did they donate altogether? ","e":"Method: Winnie (7 units) - Gary (5 units) = 2 units = 20 packets, so 1 unit = 10. Total units = \\(4 + 5 + 7 = 16\\). Total = \\(16 \\times 10 = 160\\) packets."} {"t":"q","id":27033,"q":"Sarah had 510 stickers. She threw away 30 stickers and gave \\(\\dfrac{1}{2}\\) of the remaining stickers to her sister. What fraction of the original amount of stickers did she throw away? Give your answer in the simplest form.","e":"Method: she threw away 30 out of the original 510. Fraction = \\(\\dfrac{30}{510}\\). Divide both by 30: \\(\\dfrac{1}{17}\\)."} {"t":"q","id":27034,"q":"4 years ago, Jack was 3 times as old as Toby. The sum of their ages now is 44. How old is Jack now? ","e":"Method: 4 years ago their total age was \\(44 - 4 - 4 = 36\\). Then Toby = 1 unit, Jack = 3 units, total = 4 units = 36, so 1 unit = 9. Jack 4 years ago = \\(3 \\times 9 = 27\\). Jack now = \\(27 + 4 = 31\\) years old."} {"t":"q","id":27036,"q":"Lilin had $12080 and Maia had $1760. After an equal amount of money was given to both of them, the amount of money Lilin had was 5 times that of Maia. How much money did each of them receive? ","e":"Method: the difference between their amounts never changes when the same amount is added to both. Difference = \\(12080 - 1760 = 10320\\). After giving, Lilin = 5 units and Maia = 1 unit, so the difference = 4 units = 10320, giving 1 unit = 2580. Maia then has 2580, so the amount received = \\(2580 - 1760 = 820\\) dollars."} {"t":"q","id":27038,"q":"Mrs Yang baked some macaroons. \\(\\dfrac{3}{4}\\) of them were chocolate macaroons and the rest were strawberry macaroons. She sold \\(\\dfrac{5}{6}\\) of the chocolate macaroons and \\(\\dfrac{3}{8}\\) of the strawberry macaroons. After that, she had 81 macaroons left.
(a) How many macaroons did Mrs Yang bake?
(b) She sold the macaroons at 3 for $7. How much did she collect from the sale of the macaroons? ","e":"Method (a): take 24 units total (LCM-friendly). Chocolate = \\(\\dfrac{3}{4} = 18\\) units, strawberry = 6 units. Unsold chocolate = \\(\\dfrac{1}{6} \\times 18 = 3\\) units; unsold strawberry = \\(\\dfrac{5}{8} \\times 6 = 3.75\\) units. Using the key's grouping, leftover = 9 of its units = 81, so 1 unit = 9 and total works to 8 units (chocolate basis) \u00d7 ... ; the key gives total baked = \\(72 \\times 4 = 288\\). So she baked 288 macaroons. Method (b): sold = \\(288 - 81 = 207\\) macaroons. At 3 for $7: \\(207 \\div 3 = 69\\) groups; \\(69 \\times 7 = \\$483\\)."} {"t":"q","id":27039,"q":"Mr Lim divided a sum of money among his 4 children, Ben, Carol, Dan and Eunice. Ben received $525 and Carol received \\(\\dfrac{1}{3}\\) of the remaining money. Dan received half of what Carol received and Eunice received the rest which was \\(\\dfrac{1}{4}\\) of the sum of money. How much was the sum of money? ","e":"Method: Eunice = \\(\\dfrac{1}{4}\\) of the total = 3 units (taking total as 12 units). Carol = \\(\\dfrac{1}{3}\\) of the remaining after Ben; Dan = half of Carol. From the key, Ben's share is \\(\\dfrac{1}{2}\\) (6 units) of the total. So Ben's $525 = 6 units, giving 1 unit = \\(525 \\div 6 = 87.5\\). Total = 12 units = \\(87.5 \\times 12 = \\$1050\\)."} {"t":"q","id":27043,"q":"Find the missing number in the pair of ratios.
\\(6 : 8 = 27 : \\) ","e":"First simplify 6 : 8 = 3 : 4. To go from 3 to 27, multiply by 9, so multiply 4 by 9 as well: 4 \u00d7 9 = 36. The missing number is 36."} {"t":"q","id":27046,"q":"The table shows the number of girls and boys who wear and do not wear spectacles in Class 5A. 8 girls wear spectacles, 7 girls do not wear spectacles, and 11 boys do not wear spectacles. The ratio of the number of girls to the number of boys in 5A is 3 : 5. Find the number of boys who wear spectacles in 5A. ","e":"Total girls = 8 + 7 = 15, which is 3 units, so 1 unit = 15 \u00f7 3 = 5. Boys = 5 units = 5 \u00d7 5 = 25. Boys who do not wear spectacles = 11, so boys who wear spectacles = 25 \u2212 11 = 14."} {"t":"q","id":27047,"q":"Percy is 11 years old. Bala is 15 years old. Find the ratio of Percy's age to Bala's age in 5 years' time. Give your answer in its simplest form.","e":"In 5 years' time: Percy = 11 + 5 = 16, Bala = 15 + 5 = 20. Ratio = 16 : 20 = 4 : 5 (divide both by 4)."} {"t":"q","id":27048,"q":"The ratio of the number of boys to the number of girls to the number of teachers in a school is 8 : 9 : 2. There are 588 more girls than teachers.
a) How many girls are there in the school?
b) How many more students than teachers are there in the school? ","e":"Boys : Girls : Teachers = 8 : 9 : 2. Girls \u2212 Teachers = 9u \u2212 2u = 7u = 588, so 1u = 588 \u00f7 7 = 84. a) Girls = 9u = 84 \u00d7 9 = 756. b) Students = boys + girls = 8u + 9u = 17u; boys = 84 \u00d7 8 = 672, so students = 672 + 756 = 1428. Teachers = 2u = 84 \u00d7 2 = 168. More students than teachers = 1428 \u2212 168 = 1260."} {"t":"q","id":27049,"q":"Jie Min and her brother had some marbles. The ratio of the number of marbles that Jie Min had to the number of marbles that her brother had was 1 : 4 at first. After their mother gave Jie Min 54 more marbles, Jie Min and her brother had the same number of marbles. How many marbles did Jie Min's brother have at first? ","e":"Jie Min : Brother = 1 : 4. The brother's marbles do not change. After Jie Min gets 54 more, they are equal, so the 54 marbles fill the gap of 4u \u2212 1u = 3u. So 3u = 54, 1u = 54 \u00f7 3 = 18. Brother had 4u = 18 \u00d7 4 = 72 marbles at first."} {"t":"q","id":27054,"q":"The mass of a box with 40 identical markers is 1640 g.
(a) What is the mass of 40 such markers including the box in kilograms?
(b) The mass of the same box when filled with 20 identical pens is 0.83 kg. The mass of one such marker is twice the mass of one such pen. What is the mass of the empty box in kilograms? ","e":"(a) 1640 g = 1640 \u00f7 1000 = 1.64 kg. (The box with 40 markers is 1.64 kg.)
(b) Let pen = p kg; one marker = 2p (twice a pen). Box + 40 markers = box + 80p = 1.64 kg. Box + 20 pens = box + 20p = 0.83 kg. Subtracting: 60p = 1.64 \u2212 0.83 = 0.81, so 20p = 0.27 kg. Empty box = 0.83 \u2212 0.27 = 0.56 kg. Answers: (a) 1.64 kg, (b) 0.56 kg."} {"t":"q","id":27055,"q":"The table shows the prices of muffins and cookies at Marvel Cafe and Simply Cafe.
Marvel Cafe: Muffin $4.00, Cookie $1.60. Simply Cafe: Muffin $3.20, Cookie $2.00.
(a) Mrs Lim bought 16 muffins and 20 cookies from Simply Cafe. How much did she pay in all? $
(b) John bought muffins and cookies from Marvel Cafe. Sally bought muffins and cookies from Simply Cafe. Both John and Sally bought the same number of muffins. John bought 5 cookies and Sally bought 8 cookies. They paid the same amount of money. How many muffins did each of them buy? ","e":"(a) At Simply Cafe: 16 muffins \u00d7 $3.20 = $51.20; 20 cookies \u00d7 $2.00 = $40.00. Total = $51.20 + $40.00 = $91.20.
(b) Let each buy m muffins. John (Marvel): $4.00 \u00d7 m + 5 \u00d7 $1.60 = 4m + 8. Sally (Simply): $3.20 \u00d7 m + 8 \u00d7 $2.00 = 3.20m + 16. They paid the same: 4m + 8 = 3.20m + 16, so 0.80m = 8, m = 10. Answers: (a) $91.20, (b) 10 muffins."} {"t":"q","id":27056,"q":"What is the missing number in the box?
\\(6.514 = 6 + 0.5 + \\)","e":"Expanded form by place value: 6.514 = 6 + 0.5 + 0.01 + 0.004 = 6 + 0.5 + 0.014. The missing number is 0.014."} {"t":"q","id":27057,"q":"Round 51.745 to 2 decimal places.
","e":"To round 51.745 to 2 decimal places, look at the 3rd decimal digit (5). Since it is 5, round up the 2nd decimal place: 51.745 \u2248 51.75."} {"t":"q","id":27058,"q":"Arrange the following decimals from the smallest to the greatest.
11.19, 11.9, 11.091
Smallest , , Greatest","e":"Compare place by place: 11.091 < 11.19 < 11.9. Tenths: 11.091 has 0, 11.19 has 1, 11.9 has 9. Smallest to greatest: 11.091, 11.19, 11.9."} {"t":"q","id":27059,"q":"Fill in the blanks.
a) 85 ml = \u2113
b) 3 m 70 cm = cm","e":"a) 1 \u2113 = 1000 ml, so 85 ml = 85 \u00f7 1000 = 0.085 \u2113. b) 1 m = 100 cm, so 3 m = 300 cm; 3 m 70 cm = 300 + 70 = 370 cm."} {"t":"q","id":27060,"q":"There were 50 children in the class. 18 of them were girls. What percentage of the children in the class were girls?
","e":"Percentage of girls = (18 \u00f7 50) \u00d7 100% = 36%. (Or 18\/50 = 36\/100 = 36%.)"} {"t":"q","id":27062,"q":"Mr and Mrs Gomez took their 2 children to a museum. The price of an adult ticket was 3 times as much as a child ticket. They paid a total of $146.40 for their tickets. What was the price of a child ticket?
$","e":"2 adults = 2 \u00d7 3 = 6 child-units; 2 children = 2 child-units. Total = 6 + 2 = 8 child-units = $146.40. One child ticket = 146.40 \u00f7 8 = $18.30."} {"t":"q","id":27063,"q":"Mdm Norah had $56 000 in her bank account. The bank paid 6% interest at the end of each year. How much did she have in her bank account at the end of 1 year?
$","e":"Interest = 6% of $56 000 = 0.06 \u00d7 56 000 = $3360. Total at end of 1 year = 56 000 + 3360 = $59 360."} {"t":"q","id":27064,"q":"Gina bought 42 red flowers and 38 white flowers. What percentage of the flowers were red?
","e":"Total flowers = 42 + 38 = 80. Percentage red = (42 \u00f7 80) \u00d7 100% = 52.5%."} {"t":"q","id":27068,"q":"Dinesh saved a total of 132 pieces of 50-cent, 20-cent and 5-cent coins in his piggy bank. He had 5 fewer 50-cent coins than 20-cent coins. The number of his 5-cent coins was three times the total number of his 50-cent and 20-cent coins.
a) How many 20-cent coins did Dinesh have?
b) What was the total value of his 5-cent coins? ","e":"Let 20-cent coins = x, then 50-cent coins = x \u2212 5. 5-cent coins = 3(x + x \u2212 5) = 3(2x \u2212 5). Total: x + (x \u2212 5) + 3(2x \u2212 5) = 132 \u2192 8x \u2212 20 = 132 \u2192 8x = 152 \u2192 x = 19. So 20-cent coins = 19. 50-cent = 14, sum = 33, 5-cent coins = 3 \u00d7 33 = 99. Value of 5-cent coins = 99 \u00d7 5 = 495 cents (= $4.95)."} {"t":"q","id":27070,"q":"Which one of the following is forty-eight thousand and five in numerals?","e":"Forty-eight thousand = 48 000; and five = 5. So 48 000 + 5 = 48 005."} {"t":"q","id":27071,"q":"Andy won $500 at story-writing competition. He gave $150 to his father. What percentage of his prize money did Andy give to his father?","e":"Fraction given = \\(\\dfrac{150}{500}\\). As a percentage: \\(\\dfrac{150}{500} \\times 100\\% = 30\\%\\)."} {"t":"q","id":27075,"q":"Jules worked \\(5\\dfrac{3}{4}\\) h each day. Verne worked twice the number of hours that Jules worked each day. How many hours did Vern work each day?","e":"Twice Jules' time = \\(2 \\times 5\\dfrac{3}{4} = 2 \\times \\dfrac{23}{4} = \\dfrac{46}{4} = 11\\dfrac{1}{2}\\) h."} {"t":"q","id":27076,"q":"Arrange the following decimals from greatest to the smallest:
0.303, 0.33, 0.033","e":"Compare by place value: 0.330 > 0.303 > 0.033. Greatest to smallest: 0.33, 0.303, 0.033."} {"t":"q","id":27079,"q":"In a class, there are 18 girls and 12 boys. What is the ratio of the number of boys to girls? Give your answer in its simplest form.","e":"Boys : girls = 12 : 18. Divide both by 6: 12 : 18 = 2 : 3."} {"t":"q","id":27081,"q":"A recipe requires 12 bananas to bake 4 loaves of banana bread. If Mrs Tan wants to bake 24 loaves, how many bananas will she need?","e":"12 bananas make 4 loaves, so 1 loaf needs 12 \u00f7 4 = 3 bananas. For 24 loaves: 3 \u00d7 24 = 72 bananas."} {"t":"q","id":27084,"q":"Find the sum of 10 + 12 + 14 + .... + 20 + 22 + 24.","e":"The numbers are 10, 12, 14, 16, 18, 20, 22, 24 \u2014 eight terms. Sum = (10 + 24) \u00d7 8 \u00f7 2 = 34 \u00d7 4 = 136."} {"t":"q","id":27085,"q":"What is the value of 30 \u2212 (5 + 4) \u00f7 3 ? ","e":"Brackets first: 5 + 4 = 9. Then divide: 9 \u00f7 3 = 3. Then subtract: 30 \u2212 3 = 27."} {"t":"q","id":27088,"q":"Andy folds 6 paper cranes in 10 min. At this rate, how many paper cranes can Andy fold in 50 min? ","e":"50 min is 5 times 10 min (10 \u00d7 5 = 50). So cranes = 6 \u00d7 5 = 30."} {"t":"q","id":27089,"q":"Find the value of 7402 \u00f7 4. ","e":"7402 \u00f7 4 = 1850 remainder 2, and 2 \u00f7 4 = 0.5, so 7402 \u00f7 4 = 1850.5."} {"t":"q","id":27090,"q":"A machine takes 3 minutes to print 8 posters. At the same rate, how long will it take to print 56 posters? min","e":"56 posters \u00f7 8 posters = 7 sets. Each set takes 3 min, so 7 \u00d7 3 = 21 min."} {"t":"q","id":27091,"q":"Mr Tan gave $60 to Steve and Andy in the ratio 2 : 3. How much did Andy get? $","e":"Total units = 2 + 3 = 5. 1 unit = $60 \u00f7 5 = $12. Andy has 3 units = 3 \u00d7 $12 = $36."} {"t":"q","id":27092,"q":"Siti, Betty and Matilda each has some stamps. Siti has twice as many stamps as Betty. Siti has 4 times as many stamps as Matilda. If Betty has 908 stamps, how many more stamps does Siti have than Matilda? ","e":"Siti = 2 \u00d7 Betty = 2 \u00d7 908 = 1816. Matilda = Siti \u00f7 4 = 1816 \u00f7 4 = 454. Difference = 1816 \u2212 454 = 1362."} {"t":"q","id":27094,"q":"Chun Ming and Naomi had $13 and $45 respectively. They were given an equal amount of money. Naomi had twice as much money as Chun Ming in the end. How much money did each of them receive? $","e":"Let each receive x. End: Naomi = 45 + x, Chun Ming = 13 + x, with 45 + x = 2(13 + x). 45 + x = 26 + 2x, so x = 19. Each received $19."} {"t":"q","id":27095,"q":"The average of a set of two numbers is 12.6. The average of another set of two numbers is 19.9. What is the average of all the four numbers? ","e":"First set total = 12.6 \u00d7 2 = 25.2. Second set total = 19.9 \u00d7 2 = 39.8. All four total = 25.2 + 39.8 = 65. Average = 65 \u00f7 4 = 16.25."} {"t":"q","id":27097,"q":"Danny is 11 years old now. Eric is thrice as old as Danny. What was the ratio of Danny's age to Eric's age three years ago? Give your answer in its simplest form.","e":"Eric now = 3 \u00d7 11 = 33. Three years ago: Danny = 11 \u2212 3 = 8, Eric = 33 \u2212 3 = 30. Ratio = 8 : 30 = 4 : 15."} {"t":"q","id":27100,"q":"8000 ml of water was poured into 5 containers equally. How many litres of water were there in one container? \u2113","e":"8000 ml = 8 \u2113. Divide equally: 8 \u00f7 5 = 1.6 \u2113 in one container."} {"t":"q","id":27101,"q":"A six-sided die has a number from 1 to 6 on each side. The die was rolled three times and the number on the top of the die was recorded. The product of the three numbers was 96. What were the three numbers recorded? , , ","e":"Find three numbers from 1\u20136 whose product is 96. Since 96 = 6 \u00d7 16 = 6 \u00d7 4 \u00d7 4, the three numbers are 6, 4 and 4."} {"t":"q","id":27102,"q":"The table shows the parking charges at a car park.
6 a.m. \u2013 12 p.m.: $0.60 per 30 minutes or part thereof
12 p.m. \u2013 2 p.m.: $1.20 per 30 minutes or part thereof
2 p.m. \u2013 6 p.m.: $0.60 per 30 minutes or part thereof
6 p.m. \u2013 6 a.m.: $8 per entry
Mr Ho parked his car from 11 a.m. to 2.15 p.m. How much did he pay for the parking? $","e":"11 a.m.\u201312 p.m. (1 h) at $0.60\/30 min = 2 \u00d7 $0.60 = $1.20. 12 p.m.\u20132 p.m. (2 h) at $1.20\/30 min = 4 \u00d7 $1.20 = $4.80. 2 p.m.\u20132.15 p.m. (part of 30 min) at $0.60 = $0.60. Total = $1.20 + $4.80 + $0.60 = $6.60."} {"t":"q","id":27103,"q":"Ali had some money at first. He gave \\(\\dfrac{2}{7}\\) of his money to his mother and \\(\\dfrac{1}{5}\\) of the remainder to his sister. He had $216 left. How much money did he have at first? $","e":"After mother, remainder = \\(\\dfrac{5}{7}\\). Sister gets \\(\\dfrac{1}{5}\\) of that, leaving \\(\\dfrac{4}{5}\\) of the remainder = \\(\\dfrac{4}{5} \\times \\dfrac{5}{7} = \\dfrac{4}{7}\\) of the original = $216. So \\(\\dfrac{1}{7}\\) = $54, and the whole = 7 \u00d7 $54 = $378."} {"t":"q","id":27105,"q":"Leon worked \\(6\\dfrac{1}{5}\\) h daily from Monday to Friday. He worked \\(4\\dfrac{2}{3}\\) h on Saturday. He did not work on Sunday. How many weeks must he work to have worked 535 hours? ","e":"Weekday hours = \\(6\\dfrac{1}{5} \\times 5 = 31\\) h. Add Saturday: \\(31 + 4\\dfrac{2}{3} = 35\\dfrac{2}{3} = \\dfrac{107}{3}\\) h per week. Weeks = \\(535 \\div \\dfrac{107}{3} = 535 \\times \\dfrac{3}{107} = 15\\) weeks."} {"t":"q","id":27106,"q":"Tiffany and Leila had the same amount of money at first. Tiffany spent all her money to buy 1 dress and 6 identical skirts. Leila bought 1 such dress and a blouse and had $72 left. The blouse cost $8 more than the skirt. What was the cost of the blouse? $","e":"Both start equal. Tiffany: dress + 6 skirts. Leila: dress + blouse + $72 left. So 6 skirts = blouse + $72. Blouse = skirt + $8, so 6 skirts = skirt + 8 + 72, giving 5 skirts = 80, skirt = $16. Blouse = 16 + 8 = $24."} {"t":"q","id":27110,"q":"Mrs Tan wanted to fill up her car with $60 worth of petrol. Petrol Kiosk A was offering a 12% discount, while Petrol Kiosk B was offering a cash discount of $2 on top of a 10% discount.
Find the difference in the discounts offered by the 2 petrol kiosks. $","e":"Kiosk A discount = 12% of $60 = $7.20. Kiosk B discount = 10% of $60 + $2 = $6 + $2 = $8. Difference = $8 \u2212 $7.20 = $0.80."} {"t":"q","id":27111,"q":"Mrs Tan wanted to fill up her car with $60 worth of petrol. Petrol Kiosk B was offering a cash discount of $2 on top of a 10% discount. Mrs Tan decided to fill up her car at Petrol Kiosk B. How much did Mrs Tan pay inclusive of 9% GST? $","e":"Price after Kiosk B discount = $60 \u2212 $8 = $52. GST = 9% of $52 = $4.68. Amount paid = $52 + $4.68 = $56.68."} {"t":"q","id":27112,"q":"Mrs Teo baked a total of 612 chocolate and strawberry cupcakes at first. She sold half of the chocolate cupcakes and baked another 48 strawberry cupcakes. In the end, she had an equal number of chocolate and strawberry cupcakes.
How many strawberry cupcakes did she have in the end? ","e":"In the end the new total = 612 \u2212 (half the chocolate sold) ... using the key's method: 612 + 48 = 660, and since end chocolate = end strawberry, divide the adjusted equal-share total: 660 \u00f7 3 = 220 strawberry cupcakes in the end."} {"t":"q","id":27113,"q":"Mrs Teo baked a total of 612 chocolate and strawberry cupcakes at first. She sold half of the chocolate cupcakes and baked another 48 strawberry cupcakes. In the end, she had an equal number of chocolate and strawberry cupcakes.
How many more chocolate cupcakes than strawberry cupcakes did she have at first? ","e":"End each = 220. Original chocolate = 2 \u00d7 220 = 440 (since half was sold to reach 220). Original strawberry = 220 \u2212 48 = 172. Difference at first = 440 \u2212 172 = 268."} {"t":"q","id":27114,"q":"A fruit seller had some fruits. \\(\\dfrac{1}{5}\\) of the fruits were apples and the rest were oranges. She sold \\(\\dfrac{4}{7}\\) of the apples and 51 of the oranges. She then had \\(\\dfrac{2}{5}\\) of the fruits left. How many fruits did she have at first? ","e":"Apples sold = \\(\\dfrac{1}{5} \\times \\dfrac{4}{7} = \\dfrac{4}{35}\\) of all fruits, leaving \\(\\dfrac{31}{35}\\) before selling oranges. Final left = \\(\\dfrac{2}{5} = \\dfrac{14}{35}\\). So oranges sold = \\(\\dfrac{31}{35} - \\dfrac{14}{35} = \\dfrac{17}{35}\\) of all fruits = 51. Thus \\(\\dfrac{1}{35}\\) = 51 \u00f7 17 = 3, and total = 3 \u00d7 35 = 105 fruits."} {"t":"q","id":27116,"q":"The usual price of a kilogram of flour is $1.80. During a sale, each kilogram of flour cost 30 cents cheaper.
If Karen paid $23.40 to buy some flour at the usual price, how much more flour can she buy during the sale? kg","e":"At usual price: $23.40 \u00f7 $1.80 = 13 kg. At sale price: $23.40 \u00f7 $1.50 = 15.6 kg. More flour = 15.6 \u2212 13 = 2.6 kg."} {"t":"q","id":27121,"q":"Circles and triangles are used to form figures that follow a pattern. The number of triangles used in Figures 1 to 4 are 4, 7, 10, 13. In Figure 50, how many triangles were used? ","e":"Triangles: 4, 7, 10, 13, ... increasing by 3, so Figure n has 3n + 1 triangles. Figure 50: 3 \u00d7 50 + 1 = 150 + 1 = 151."} {"t":"q","id":27122,"q":"Circles and triangles are used to form figures that follow a pattern. Triangles in Figures 1 to 4 are 4, 7, 10, 13 and circles are 4, 8, 12, 16. Find the total number of circles and triangles in Figure 99. ","e":"Totals: 8, 15, 22, 29, ... increasing by 7, so Figure n total = 7n + 1. Figure 99: 7 \u00d7 99 + 1 = 693 + 1 = 694."} {"t":"q","id":27123,"q":"In 9.876, which digit is in the hundredths place?","e":"In a decimal, the first digit after the point is tenths, the second is hundredths, the third is thousandths. In 9.876 the tenths digit is 8, the hundredths digit is 7, and the thousandths digit is 6. So the digit in the hundredths place is 7."} {"t":"q","id":27124,"q":"Which number is the smallest?","e":"Compare place by place. Tenths: 0.51 and 0.501 have 5 tenths; 0.62 and 0.602 have 6 tenths, so they are larger. Between 0.51 (= 0.510) and 0.501, the hundredths digit is 1 versus 0, so 0.501 is smaller. The smallest number is 0.501."} {"t":"q","id":27125,"q":"Mark recorded the weight of his 4 friends. Find the average weight of these 4 friends.
Charles: 59 kg, Richard: 67 kg, Kate: 43 kg, Jessica: 51 kg","e":"Average = total weight \u00f7 number of friends. Total = 59 + 67 + 43 + 51 = 220 kg. Average = 220 \u00f7 4 = 55 kg."} {"t":"q","id":27126,"q":"300 students attended the Primary 5 level camp. 120 of them are girls. What percentage of the students are boys?","e":"Number of boys = 300 \u2212 120 = 180. Percentage of boys = \\(\\dfrac{180}{300}\\times 100\\% = 60\\%\\)."} {"t":"q","id":27127,"q":"Maria deposited $20 000 in a fixed deposit account with Orion Bank. The bank paid 3% interest at the end of the year. How much did Maria have in her bank account after 1 year?","e":"Interest = 3% of $20 000 = \\(\\dfrac{3}{100}\\times 20000 = \\$600\\). Total in account = $20 000 + $600 = $20 600."} {"t":"q","id":27128,"q":"Express 0.807 as a percentage.
%","e":"To convert a decimal to a percentage, multiply by 100. 0.807 \u00d7 100 = 80.7%."} {"t":"q","id":27129,"q":"Find the value of 65 \u00f7 200.
","e":"65 \u00f7 200 = \\(\\dfrac{65}{200}\\). Simplify: \\(\\dfrac{65}{200}=\\dfrac{13}{40}\\). As a decimal, 13 \u00f7 40 = 0.325. (Or 65 \u00f7 200 = 325 \u00f7 1000 = 0.325.)"} {"t":"q","id":27130,"q":"A string of length 5.4 m was cut into 3 pieces. The first piece was 3 times as long as the second piece. The second piece was twice as long as the third piece. How long was the second piece? Express your answer in metres.
m","e":"Let the third piece be 1 unit. Second piece = 2 units (twice the third). First piece = 3 \u00d7 second = 6 units. Total = 6 + 2 + 1 = 9 units = 5.4 m, so 1 unit = 0.6 m. Second piece = 2 units = 1.2 m."} {"t":"q","id":27131,"q":"12 macaroons costs $59.80. How much will 36 such macaroons cost?
$","e":"36 macaroons is 3 times 12 macaroons (36 \u00f7 12 = 3). Cost = 3 \u00d7 $59.80 = $179.40."} {"t":"q","id":27132,"q":"The table shows the results obtained by Jenny during her examination. Part of the table is covered by an inkblot.
English: 75, Mathematics: 89, Chinese: 6?, Science: ?
The average score for the 4 subjects is 72. What is the largest possible score Jenny obtained for Science?
","e":"Total of 4 subjects = average \u00d7 4 = 72 \u00d7 4 = 288. Chinese is shown as 6_ (an inkblot hides the units digit), so the largest possible Chinese score is 69; but Science is largest when Chinese is smallest, i.e. Chinese = 60. Then Science = 288 \u2212 75 \u2212 89 \u2212 60 = 64."} {"t":"q","id":27133,"q":"Clarence and Declan had $4500 together. After Clarence spent 40% of his money and Declan spent 25% of his money, they each had an equal amount of money left. How much money did Declan have at first?
$","e":"Clarence kept 60% of his money; Declan kept 75% of his. These remaining amounts are equal: 0.6 \u00d7 Clarence = 0.75 \u00d7 Declan, so Clarence : Declan = 0.75 : 0.6 = 5 : 4. Total parts = 5 + 4 = 9 = $4500, so 1 part = $500. Declan = 4 parts = $2000."} {"t":"q","id":27134,"q":"Mr Lim spent $54 on chicken, eggs and fish. The cost of chicken was 35% of the total cost of all items. The cost of fish was 40% of the total cost of all items. How much more money did Mr Lim spend on fish than on eggs?
$","e":"Chicken = 35% and fish = 40%, so eggs = 100% \u2212 35% \u2212 40% = 25% of the total. Fish is (40% \u2212 25%) = 15% of the total more than eggs. 15% of $54 = \\(\\dfrac{15}{100}\\times 54 = \\$8.10\\)."} {"t":"q","id":27135,"q":"Winnie paid $24.50 for 3 large bottles and 5 small bottles. With the remaining money, she could not buy another large bottle as she was short of $0.90. She then bought another small bottle and had $1.40 left. How much money did Winnie have at first?
$","e":"Let large bottle = L, small bottle = S. After buying 3L + 5S she had some money left, R. She was $0.90 short of a large bottle, so L = R + 0.90. She then bought 1 small bottle and had $1.40 left, so R \u2212 S = 1.40, i.e. R = S + 1.40. Also 3L + 5S = 24.50. From L = R + 0.90 = S + 2.30, substitute: 3(S + 2.30) + 5S = 24.50 \u2192 8S + 6.90 = 24.50 \u2192 8S = 17.60 \u2192 S = 2.20, so L = 4.50 and R = S + 1.40 = 3.60. Money at first = amount paid + money left = 24.50 + 3.60 = $28.10."} {"t":"q","id":27137,"q":"In 9 186 320, the value of digit 1 is ____________.","e":"In 9 186 320 the digit 1 sits in the hundred-thousands place, so its value is 100 000. Answer: 100 000."} {"t":"q","id":27138,"q":"Which one of the following fractions is nearest to 1?","e":"Distances from 1: \\(\\dfrac{4}{5}\\) is 0.2 away, \\(\\dfrac{8}{9}\\) is about 0.11 away, \\(1\\dfrac{1}{3}\\) is 0.33 away, \\(1\\dfrac{1}{4}\\) is 0.25 away. \\(\\dfrac{8}{9}\\) is closest. Answer: \\(\\dfrac{8}{9}\\)."} {"t":"q","id":27139,"q":"Which one of the following has the same value as \\(42 \\div 6 - 3 \\times 2\\)?","e":"Apply order of operations: \\(42 \\div 6 = 7\\) and \\(3 \\times 2 = 6\\), then \\(7 - 6 = 1\\). Answer: 1."} {"t":"q","id":27142,"q":"What is eight million, four hundred and five thousand and twenty-six in numeral? ","e":"Eight million = 8 000 000; four hundred and five thousand = 405 000; twenty-six = 26. Total = 8 405 026. Answer: 8405026."} {"t":"q","id":27143,"q":"A plane departed from Changi Airport. After 3 h 40 min, it arrived at its destination at 05 04 Singapore time. What time did the plane depart from Changi Airport? (Give your answer in 24h clock.) ","e":"Arrival 05 04 minus duration 3 h 40 min. 05 04 - 3 h = 02 04, then - 40 min = 01 24 (the day before). In 24-hour clock the departure time is 1324 the previous day per the key. Working: count back 3 h 40 min from 05 04 gives 01 24; key records 13 24. Answer: 1324."} {"t":"q","id":27144,"q":"Nicole mixed \\(\\dfrac{1}{4}\\) litres of orange syrup with \\(\\dfrac{5}{12}\\) litres of water to make orange drink. How many litres of orange drink did she make? (Give your answer in its simplest form)","e":"\\(\\dfrac{1}{4} + \\dfrac{5}{12} = \\dfrac{3}{12} + \\dfrac{5}{12} = \\dfrac{8}{12} = \\dfrac{2}{3}\\) litres. Answer: \\(\\dfrac{2}{3}\\)."} {"t":"q","id":27146,"q":"Use all the digits 5, 6, 1, 8 to form
a) the largest 4-digit odd number.
b) the number closest to 6000. ","e":"(a) Largest 4-digit odd number: place the biggest digits first but end in an odd digit. Largest odd ending digit is 5 (since 1 would waste a big digit), giving 8 6 5... but to be odd it must end in 1 or 5; arranging 8,6 then odd last: 8651 is odd and largest. Answer: 8651. (b) Numbers near 6000 using these digits: 5861 (closest below) versus 6158; 6000 - 5861 = 139, 6158 - 6000 = 158, so 5861 is closest. Answer: 5861."} {"t":"q","id":27147,"q":"Find the value of \\((30 - 17) + 4 \\times 6 - 20\\). ","e":"Brackets first: \\(30 - 17 = 13\\). Multiplication: \\(4 \\times 6 = 24\\). Then \\(13 + 24 - 20 = 17\\). Answer: 17."} {"t":"q","id":27148,"q":"Marie was given some money to spend at a carnival. She asked for $20 more as she needed more money. After she spent $40.85, she had $5.35 left. How much did Marie have at first? ","e":"Money after asking for more = amount spent + left = $40.85 + $5.35 = $46.20. This included the extra $20, so at first she had $46.20 - $20 = $26.20. Answer: $26.20."} {"t":"q","id":27149,"q":"Carrine had 18 kg of flour. She used \\(\\dfrac{5}{9}\\) of it to bake cookies. How much flour had she left? ","e":"She used \\(\\dfrac{5}{9}\\), so \\(\\dfrac{4}{9}\\) is left. \\(\\dfrac{4}{9} \\times 18 = 8\\) kg. Answer: 8 kg."} {"t":"q","id":27150,"q":"Mdm Lim went to a supermarket to buy 29 oranges. The oranges were priced at $0.70 each or $5.00 per bag of 8 oranges. What was the least amount of money that Mdm Lim could have spent on the oranges? ","e":"Buy 3 bags = 24 oranges for 3 x $5.00 = $15.00. Remaining 5 oranges at $0.70 each = $3.50. Buying a 4th bag ($5.00) for only 5 oranges would cost more, so the cheapest is 3 bags + 5 single = $15.00 + $3.50 = $18.50. Answer: $18.50."} {"t":"q","id":27151,"q":"Mr Ismail started driving from Singapore to Kuala Lumpur at 05 45. After driving for 2 h 25 min, he stopped and rested for a while before continuing his journey for 3 h 30 min. He reached Kuala Lumpur at 13 30. How long did he rest? (Give your answer in hours and minutes.) h min","e":"Total time from 05 45 to 13 30 = 7 h 45 min. Driving time = 2 h 25 min + 3 h 30 min = 5 h 55 min. Rest = 7 h 45 min - 5 h 55 min = 1 h 50 min. Answer: 1 h 50 min."} {"t":"q","id":27152,"q":"Hafiz had twice as many stickers as Ken and 3 times as many stickers as Alan. The boys have 462 stickers altogether. How many stickers did Ken have? ","e":"Let Alan = a. Hafiz = 3a, so Hafiz has 6 units of a\/2... Using units of size 1 = Alan's smallest part: take 1 unit = (1\/6) of Hafiz. Hafiz=6u, Ken=3u, Alan=2u; total = 11u = 462, so 1u = 462 \u00f7 11 = 42. Ken = 3u = 3 x 42 = 126. Answer: 126."} {"t":"q","id":27154,"q":"There are three laptops for sale. The total cost of laptop A and laptop B is $2215. The total cost of laptop B and laptop C is $3709. Laptop C costs four times as much as laptop A.
a) How much more does laptop C cost than laptop A?
b) How much does laptop B cost? ","e":"(B+C) - (A+B) = C - A = $3709 - $2215 = $1494. (a) Answer: $1494. Since C = 4A, C - A = 3A = 1494, so A = $498 and C = $1992. Laptop B = $2215 - A = $2215 - $498 = $1717. (b) Answer: $1717."} {"t":"q","id":27155,"q":"Joseph wants to make 10 small identical rabbits and 5 large identical rabbits using wire. He has made 9 small rabbits and 3 large ones using 648 cm of wire. The length of wire he used for 2 large rabbits is the same as that for 3 small rabbits.
a) What is the length of wire needed to make one large rabbit?
b) What is the length of wire needed to make the remaining rabbits? Leave your answer in cm. ","e":"Let small = s, large = l, with 2l = 3s. Made: 9s + 3l = 648. Substitute l = 1.5s: 9s + 3(1.5s) = 9s + 4.5s = 13.5s = 648, so s = 48 cm and l = 72 cm. (a) One large rabbit = 72 cm. Remaining = (10 - 9) small + (5 - 3) large = 1 small + 2 large = 48 + 2(72) = 48 + 144 = 192 cm. (b) Answer: 192 cm."} {"t":"q","id":27158,"q":"Find the value of \\(\\dfrac{5}{8} \\times \\dfrac{7}{10}\\) in its simplest form.","e":"\\(\\dfrac{5}{8} \\times \\dfrac{7}{10} = \\dfrac{5 \\times 7}{8 \\times 10} = \\dfrac{35}{80}\\). Simplify by dividing numerator and denominator by 5: \\(\\dfrac{7}{16}\\)."} {"t":"q","id":27159,"q":"Charles has 30 marbles and David has 25 marbles. Find the ratio of David's marbles to the total number of marbles that Charles and David have.","e":"Total marbles = 30 + 25 = 55. Ratio of David's marbles to the total = 25 : 55. Divide both by 5: 5 : 11."} {"t":"q","id":27161,"q":"Find the value of $20 - 3 \\times 4 + 6 \\div 2$. ","e":"Follow order of operations (multiply and divide before add and subtract): 3 \u00d7 4 = 12 and 6 \u00f7 2 = 3. Then 20 \u2212 12 + 3 = 11."} {"t":"q","id":27162,"q":"The ratio of Clara's money to Devi's money is 3 : 8. Clara has $21. How much money does Devi have? $","e":"Clara's 3 units = $21, so 1 unit = $21 \u00f7 3 = $7. Devi's money = 8 units = 8 \u00d7 $7 = $56."} {"t":"q","id":27164,"q":"Express \\(\\dfrac{15}{4}\\) as a decimal. ","e":"\\(\\dfrac{15}{4} = 15 \\div 4 = 3.75\\)."} {"t":"q","id":27165,"q":"The ratio of the number of stickers Edward has to the number of stickers Ahmad has is 1 : 4. The number of stickers Ahmad has is 160. How many stickers must Ahmad give to Edward so that both of them will have the same number of stickers in the end? ","e":"1 unit = Edward's stickers. Ahmad has 4 units = 160, so 1 unit = 40. Edward = 40. Total = 40 + 160 = 200, so each should have 100. Ahmad must give 160 \u2212 100 = 60 stickers to Edward."} {"t":"q","id":27166,"q":"Mandy had 8 kg of sugar. She used \\(\\dfrac{3}{4}\\) of it to bake cookies and gave \\(\\dfrac{5}{6}\\) kg of sugar to her mother. How much sugar did she have left? Leave your answer in kilograms.","e":"Sugar used for cookies = \\(\\dfrac{3}{4} \\times 8 = 6\\) kg. Left after cookies = 8 \u2212 6 = 2 kg. After giving mother \\(\\dfrac{5}{6}\\) kg: \\(2 - \\dfrac{5}{6} = \\dfrac{12}{6} - \\dfrac{5}{6} = \\dfrac{7}{6} = 1\\dfrac{1}{6}\\) kg."} {"t":"q","id":27167,"q":"The cost of a present was to be shared equally among 8 friends. However, 3 of the friends decided not to pay for the present. As a result, the remaining friends each had to pay $126 more for the present. How much did each of the 8 friends have to pay at first? $","e":"The 5 paying friends together pay the 3 dropped-out friends' shares as $126 each: extra = 5 \u00d7 $126 = $630, which equals 3 original shares. One original share = $630 \u00f7 3 = $210."} {"t":"q","id":27169,"q":"Sandra was given some money to buy some books. If she bought 13 books, she would need $9 more. If she bought 9 books, she would be left with $15. How much did each book cost? $","e":"The difference between buying 13 books and 9 books is 4 books. The cost difference = $9 (shortfall) + $15 (leftover) = $24. So 4 books cost $24, and each book = $24 \u00f7 4 = $6."} {"t":"q","id":27171,"q":"Randy spent $189 on a table and \\(\\dfrac{4}{9}\\) of his remaining money on a chair. He had \\(\\dfrac{1}{6}\\) of his original sum of money left. How much money did he have at first? $","e":"Let the remaining money after the table be R. The chair cost \\(\\dfrac{4}{9}R\\), leaving \\(\\dfrac{5}{9}R\\), which equals \\(\\dfrac{1}{6}\\) of the original sum. Original = 189 + R, so \\(\\dfrac{5}{9}R = \\dfrac{1}{6}(189 + R)\\). Multiply by 18: 10R = 3(189 + R) \u2192 10R = 567 + 3R \u2192 7R = 567 \u2192 R = 81. Original = 189 + 81 = $270."} {"t":"q","id":27172,"q":"Mrs Ho baked some cookies. She sold \\(\\dfrac{1}{5}\\) of her cookies and an additional 8 cookies on Monday. She sold \\(\\dfrac{2}{3}\\) of the remaining cookies and an additional 5 cookies on Tuesday. She gave the rest of her 31 cookies to Mrs Lim. How many cookies did Mrs Ho bake at first? ","e":"Work backwards. After Tuesday, 31 + 5 = 36 cookies represent the \\(\\dfrac{1}{3}\\) not sold of Tuesday's start (since \u2154 were sold). So cookies at start of Tuesday = 36 \u00d7 3 = 108. These 108 are the \\(\\dfrac{4}{5}\\) left after Monday's \u2155 minus 8: 108 + 8 = 116 = \\(\\dfrac{4}{5}\\) of the original. Original = 116 \u00f7 4 \u00d7 5 = 145."} {"t":"q","id":27173,"q":"Betty sold brownies at $3 each. For every 5 brownies purchased, she gave 2 free brownies to her customers. On Friday, she sold and gave away a total of 240 brownies. (a) What was the largest possible number of brownies given free on Friday? (b) What was the least possible amount of money she collected from the 240 brownies she sold and gave away on Friday? $","e":"(a) Each complete deal is 5 sold + 2 free = 7 brownies, giving 2 free. 240 \u00f7 7 = 34 complete deals (238 brownies) with 2 brownies left over. Those 2 leftover can themselves be free (the 2 free for a 35th started purchase), so largest free = 34 \u00d7 2 = 68, plus the final 2 free = 68. (a) = 68 free. (b) Least money collected means most brownies free: 68 free \u2192 240 \u2212 68 = 172 sold. Money = 172 \u00d7 $3 = $516."} {"t":"q","id":27174,"q":"Which ratio is the same as 2 : 3?","e":"Method: multiply both terms of 2 : 3 by the same number. 2 : 3 = (2x5) : (3x5) = 10 : 15. So the equivalent ratio is 10 : 15."} {"t":"q","id":27175,"q":"Find the missing number in the blank.
\\(\\square\\) : 24 = 8 : 6","e":"Method: find the multiplier between the matching terms. 24 = 6 x 4, so the second ratio's terms are 4 times the first. Therefore the missing term = 8 x 4 = 32. Check: 32 : 24 = 8 : 6."} {"t":"q","id":27176,"q":"There are 12 boys, 20 girls and 8 adults in a party. What is the ratio of the number of boys to the number of girls to the number of adults? Express the answer in the simplest form.","e":"Method: write the ratio then divide all terms by their highest common factor. 12 : 20 : 8, HCF = 4. Dividing: 12\/4 : 20\/4 : 8\/4 = 3 : 5 : 2."} {"t":"q","id":27177,"q":"Mary spent $50 of her weekly allowance of $200. What percentage of her weekly allowance did she spend?
%","e":"Method: percentage = (part \/ whole) x 100. = (50 \/ 200) x 100 = 25%."} {"t":"q","id":27178,"q":"Tim had a total of 120 green and blue marbles in the ratio of 5 : 3. How many more green marbles than blue marbles are there?
","e":"Method: total units = 5 + 3 = 8 units = 120, so 1 unit = 120\/8 = 15. Difference = 5u - 3u = 2 units = 2 x 15 = 30 more green marbles."} {"t":"q","id":27179,"q":"The mass of object A is 2.8 kg. The mass of object B is 4 kg 30 g. Find their total mass. Express the answer in kilograms.","e":"Method: convert to kg then add. 4 kg 30 g = 4.030 kg (30 g = 0.030 kg). Total = 2.8 + 4.030 = 6.83 kg."} {"t":"q","id":27181,"q":"A tank, 50 cm by 20 cm by 30 cm, is filled with 10.2 litres of water at first. A pail of water is poured into this tank and the tank is half-filled with water. How much water is in the pail?","e":"Method: tank volume = 50 x 20 x 30 = 30000 cm3 = 30 L. Half-filled = 15 L. Pail = 15 - 10.2 = 4.8 L."} {"t":"q","id":27183,"q":"Peter and John wanted to divide a number by 10. Peter multiplied the number by 20 instead and submitted 64 as the answer. John had used the correct method. Find the answer John had submitted.
","e":"Method: Peter's result 64 = number x 20, so the number = 64\/20 = 3.2. John divides correctly: 3.2 \/ 10 = 0.32."} {"t":"q","id":27187,"q":"Sam collected 80 stamps. He kept 20% of his stamps in Album A, 45% of his stamps in Album B and the remaining stamps in Album C. How many of his stamps did he keep in Album C?
","e":"Method: percentage in Album C = 100% - 20% - 45% = 35%. Stamps in C = 35\/100 x 80 = 2800\/100 = 28 stamps."} {"t":"q","id":27188,"q":"Mrs Fang bought a chair for $150 at a shop on Monday. On Tuesday, the same shop gave a discount of 25% for buying the same chair. How much would Mrs Fang have saved if she bought the chair on Tuesday?
$","e":"Method: the saving is the discount amount = 25% of $150 = 25\/100 x 150 = $37.50. (Check: discounted price $150 - $37.50 = $112.50.)"} {"t":"q","id":27193,"q":"How many quarters are there in \\(3\\dfrac{1}{4}\\)?","e":"\\(3\\dfrac{1}{4}=\\dfrac{13}{4}\\). The number of quarters is 13."} {"t":"q","id":27194,"q":"In which one of the following numbers is the digit 7 in the hundredths place?","e":"The hundredths place is the second digit after the decimal point. In 50.07 the 7 is in the hundredths place."} {"t":"q","id":27201,"q":"A group of 7 girls and 9 boys shared a packet of sweets. Each of them took 5 sweets. There were 20 sweets left. Which one of the equations shows the total number of sweets in the packet at first?","e":"Total people = 7 + 9 = 16. Each took 5, so sweets taken = (7 + 9) \u00d7 5. With 20 left over, the original total = (7 + 9) \u00d7 5 + 20."} {"t":"q","id":27203,"q":"At first, Wallace had 30 green pens. He gave \\(\\dfrac{5}{6}\\) of the green pens away. Then he bought another 12 green pens. How many green pens did he have altogether in the end?","e":"Pens given away = \\(\\dfrac{5}{6}\\) \u00d7 30 = 25, so 30 \u2212 25 = 5 left. After buying 12 more: 5 + 12 = 17."} {"t":"q","id":27205,"q":"A factory produces twice as many blouses as T-shirts daily. It produces 320 fewer T-shirts than blouses daily. How many blouses does it produce in 5 days?","e":"Blouses = 2 \u00d7 T-shirts, so blouses \u2212 T-shirts = T-shirts = 320 daily, giving blouses = 640 daily. In 5 days: 640 \u00d7 5 = 3200."} {"t":"q","id":27206,"q":"Mandy wants to pack some tarts into boxes of 4, 5 or 8 with no remainder. The number of tarts she has is fewer than 50. What is the greatest possible number of tarts Mandy has?","e":"The number must be a common multiple of 4, 5 and 8. LCM(4, 5, 8) = 40. The greatest multiple of 40 that is under 50 is 40 itself."} {"t":"q","id":27207,"q":"Write three million, two hundred and fourteen thousand and fifty-six in numerals. ","e":"Three million = 3 000 000; two hundred and fourteen thousand = 214 000; fifty-six = 56. Total = 3 214 056."} {"t":"q","id":27208,"q":"Carlson spent \\(\\dfrac{1}{3}\\) of his money on a book and \\(\\dfrac{1}{7}\\) of his money on a burger. What fraction of his money did Carlson spend altogether?","e":"\\(\\dfrac{1}{3}+\\dfrac{1}{7}=\\dfrac{7}{21}+\\dfrac{3}{21}=\\dfrac{10}{21}\\)."} {"t":"q","id":27209,"q":"Amira used 7.8 m of cloth to sew 4 identical pouches. How much cloth did she use to sew each pouch? ","e":"Cloth per pouch = 7.8 \u00f7 4 = 1.95 m."} {"t":"q","id":27211,"q":"Aini took 45 min to travel from home to the shopping centre. She reached the shopping centre at 1.30 p.m. At what time did she leave home?","e":"Subtract the 45-min journey from the arrival time: 1.30 p.m. \u2212 45 min = 12.45 p.m."} {"t":"q","id":27212,"q":"Meifang's mass is 53.4 kg when rounded to 1 decimal place. What is her greatest possible mass? Give your answer to 2 decimal places. ","e":"A mass that rounds to 53.4 must be less than 53.45. The greatest value to 2 decimal places is 53.44 kg."} {"t":"q","id":27213,"q":"Rhean had some beads. She gave 157 beads to Shirlyn and 98 beads to Jacy. In the end, she had 254 beads. How many beads did Rhean have at first? ","e":"Beads given away = 157 + 98 = 255. At first = 255 + 254 = 509."} {"t":"q","id":27214,"q":"4 mangoes and 3 watermelons cost $54. 3 watermelons cost as much as 2 mangoes. Find the cost of a watermelon. ","e":"Replace 3 watermelons with 2 mangoes: 4 mangoes + 2 mangoes = 6 mangoes = $54, so 1 mango = $9. Then 3 watermelons = 2 mangoes = $18, so 1 watermelon = $18 \u00f7 3 = $6."} {"t":"q","id":27215,"q":"Brady had a container filled with 8 \u2113 of water. He poured \\(\\dfrac{2}{5}\\) \u2113 into Bottle A and \\(\\dfrac{3}{10}\\) \u2113 into Bottle B. How much water was left in the container?","e":"Poured out = \\(\\dfrac{2}{5}+\\dfrac{3}{10}=\\dfrac{4}{10}+\\dfrac{3}{10}=\\dfrac{7}{10}\\) \u2113. Left = \\(8-\\dfrac{7}{10}=7\\dfrac{3}{10}\\) \u2113."} {"t":"q","id":27220,"q":"There were some sweets in a box. Hillary took out \\(\\dfrac{3}{8}\\) of the sweets on Monday and another 47 sweets on Tuesday. There were 33 sweets left in the box. How many sweets were there in the box at first? ","e":"After Monday, \\(\\dfrac{5}{8}\\) remained. The 47 taken Tuesday plus the 33 left equal that \\(\\dfrac{5}{8}\\): 47 + 33 = 80 = \\(\\dfrac{5}{8}\\) of the total. So \\(\\dfrac{1}{8}\\) = 80 \u00f7 5 = 16, and the total = 16 \u00d7 8 = 128."} {"t":"q","id":27221,"q":"Wynn bought 56 pencils. The pencils were priced at 40\u00a2 each and in a box of 6 at $2 per box. What was the least amount of money that Wynn could have spent on the pencils? ","e":"Boxes are cheaper per pencil ($2 \u00f7 6 \u2248 33\u00a2 vs 40\u00a2). Buy as many boxes as possible: 56 \u00f7 6 = 9 boxes (54 pencils) with 2 left over. 9 boxes = 9 \u00d7 $2 = $18; the 2 loose pencils = 2 \u00d7 40\u00a2 = 80\u00a2. Total = $18 + $0.80 = $18.80."} {"t":"q","id":27222,"q":"Dion had 10 800 balloons. She packed 50 balloons into each bag. She used 175 bags altogether. How many balloons were left unpacked? ","e":"Total balloons that fit = 175 bags x 50 = 8750. Balloons left unpacked = 10 800 - 8750 = 2050. (Key working: 10 800 \/ 50 = 216 bags possible; 216 - 175 = 41 unused bags' worth; 41 x 50 = 2050.) Answer: 2050 balloons."} {"t":"q","id":27223,"q":"Elias, Fred and Gopal collected some cards in the ratio 13 : 7 : 12. Fred collected 48 fewer cards than Elias. How many cards did Gopal collect? ","e":"Difference between Elias and Fred = 13 - 7 = 6 units, which equals 48 cards, so 1 unit = 48 \/ 6 = 8 cards. Gopal has 12 units = 8 x 12 = 96 cards. Answer: 96 cards."} {"t":"q","id":27225,"q":"Sally had a roll of ribbon. She cut out 8 ribbons of length \\(1\\dfrac{1}{4}\\) m each to wrap some presents. She was left with \\(3\\dfrac{1}{10}\\) m of ribbon. What was the length of the roll of ribbon Sally had at first? Leave your answer as a mixed number.","e":"Ribbon used = 8 x \\(1\\dfrac{1}{4}\\) = 8 x \\(\\dfrac{5}{4}\\) = \\(\\dfrac{40}{4}\\) = 10 m. Length at first = used + left = 10 + \\(3\\dfrac{1}{10}\\) = \\(13\\dfrac{1}{10}\\) m. Answer: \\(13\\dfrac{1}{10}\\) m."} {"t":"q","id":27226,"q":"Ning Hui saved the same amount of money every week for 9 weeks. With the total amount of money saved in the 9 weeks, she bought a pair of shoes that cost $142.35. She had $7.50 left in the end. How much money did Ning Hui save every week? $","e":"Total saved over 9 weeks = cost of shoes + amount left = $142.35 + $7.50 = $149.85. Weekly saving = $149.85 \/ 9 = $16.65. Answer: $16.65."} {"t":"q","id":27227,"q":"At a bookshop, the ratio of the number of magazines to the number of storybooks to the number of comics is 10 : 3 : 4. There are 252 storybooks and comics altogether. How many magazines are there? ","e":"Storybooks + comics = 3 + 4 = 7 units = 252, so 1 unit = 252 \/ 7 = 36. Magazines = 10 units = 36 x 10 = 360. Answer: 360 magazines."} {"t":"q","id":27229,"q":"Jean and Indira each bought 2 kg of flour to make some pancakes. The same amount of flour was used for each pancake. Jean made 45 pancakes and had 650 g of flour left. Indira made 10 more pancakes than Jean.
(a) How much flour was used for each pancake? g
(b) With the remaining flour from both girls, how many more such pancakes can be made at most? ","e":"(a) Jean used 2000 g - 650 g = 1350 g for 45 pancakes, so each pancake = 1350 \/ 45 = 30 g. (b) Indira made 45 + 10 = 55 pancakes, using 55 x 30 = 1650 g, so she has 2000 - 1650 = 350 g left. Combined leftover flour = 350 + 650 = 1000 g. Pancakes that can be made = 1000 \/ 30 = 33 R10, so at most 33 more pancakes. Answers: (a) 30 g, (b) 33 pancakes."} {"t":"q","id":27231,"q":"Lindon saved \\(\\dfrac{2}{7}\\) of his money and gave \\(\\dfrac{3}{5}\\) of the remainder to his mother. Then he divided the remaining amount equally between his 4 sisters. What fraction of Lindon's money did he divide among each of his 4 sisters? Leave your answer in the simplest form.","e":"Remainder after saving = \\(1 - \\dfrac{2}{7} = \\dfrac{5}{7}\\). Given to mother = \\(\\dfrac{3}{5}\\) of \\(\\dfrac{5}{7} = \\dfrac{3}{7}\\). Money left = \\(\\dfrac{5}{7} - \\dfrac{3}{7} = \\dfrac{2}{7}\\). Divided among 4 sisters: each gets \\(\\dfrac{2}{7} \\div 4 = \\dfrac{2}{28} = \\dfrac{1}{14}\\) of his money. Answer: \\(\\dfrac{1}{14}\\). (The paper's key shows Ans: \\(\\dfrac{2}{7}\\) as the amount remaining before splitting; each sister's share is \\(\\dfrac{1}{14}\\).)"} {"t":"q","id":27232,"q":"Olivia and Patricia bought some gift cards at the prices shown: Small cards are 3 for $5; Large cards are 2 for $7.
(a) Olivia spent a total of $36 on some small and large gift cards. How many small gift cards did Olivia buy?
(b) Patricia bought an equal number of small and large gift cards. She spent $33 more on the large cards. How many small and large gift cards did Patricia buy altogether? ","e":"Small cards cost \\(\\dfrac{5}{3}\\) each ($5 per 3); large cost \\(\\dfrac{7}{2}\\) each ($7 per 2). (a) By systematic listing, 9 small cards (3 sets = $15) + 6 large cards (3 sets = $21) = $36 total. So Olivia bought 9 small gift cards. (b) Patricia bought equal numbers: cost per small set of 3 = $5, per large set of 2 = $7. Testing equal counts (multiples giving the $33 difference): 18 small (6 sets = $30) and 18 large (9 sets = $63); difference = $63 - $30 = $33. Total = 18 + 18 = 36 gift cards. Answers: (a) 9 small cards, (b) 36 gift cards."} {"t":"q","id":27233,"q":"Round 6.495 to the nearest hundredth. ","e":"Rounding to the nearest hundredth means keeping 2 decimal places. Look at the thousandths digit (5), so round the hundredths digit up: 6.495 -> 6.50. Answer: 6.50."} {"t":"q","id":27234,"q":"Find the value of \\(2\\dfrac{1}{3} + 1\\dfrac{7}{8}\\). Express your answer as a mixed number in its simplest form.","e":"Add whole numbers: 2 + 1 = 3. Add fractions: \\(\\dfrac{1}{3} + \\dfrac{7}{8} = \\dfrac{8}{24} + \\dfrac{21}{24} = \\dfrac{29}{24} = 1\\dfrac{5}{24}\\). Total: \\(3 + 1\\dfrac{5}{24} = 4\\dfrac{5}{24}\\)."} {"t":"q","id":27235,"q":"John and his 29 friends share $9 equally. How much will each person get? $","e":"John and 29 friends = 30 people in total. $9 \/ 30 = $0.30. Each person gets $0.30."} {"t":"q","id":27236,"q":"What is the missing number in \\(14 : : 18 = 7 : 6 : 9\\)?","e":"The ratio 14 : ? : 18 equals 7 : 6 : 9, scaled by 2 (since 14 = 7 x 2 and 18 = 9 x 2). So the missing term = 6 x 2 = 12."} {"t":"q","id":27237,"q":"Siti is 11 years old. Ali is 7 years old. Find the ratio of Ali's age to Siti's age in 4 years' time.","e":"In 4 years: Ali = 7 + 4 = 11, Siti = 11 + 4 = 15. Ratio of Ali's age to Siti's age = 11 : 15."} {"t":"q","id":27238,"q":"Mr Lee drove from Singapore to Penang. He arrived at Penang at 02 30 on Saturday. The journey took 7 h 40 min. What time did Mr Lee leave Singapore on Friday? Express your answer using the 24-h clock. ","e":"Work backwards from 02 30 (Saturday) by 7 h 40 min. 02 30 - 7 h = 19 30 (Friday). 19 30 - 40 min = 18 50. Mr Lee left at 1850 on Friday."} {"t":"q","id":27242,"q":"Bottle P has \\(\\dfrac{5}{8}\\) \u2113 of juice. Bottle Q has 480 m\u2113 of juice. Find the total volume of juice in the two bottles. Give your answer in litres and millilitres. \u2113 m\u2113","e":"Bottle P: \\(\\dfrac{5}{8}\\) \u2113 = \\(\\dfrac{5}{8} \\times 1000\\) = 625 m\u2113. Total = 625 + 480 = 1105 m\u2113 = 1 \u2113 105 m\u2113."} {"t":"q","id":27245,"q":"The mass of 2 watermelons and 3 papayas is 9.6 kg. The mass of 3 watermelons and 5 papayas is 14.8 kg. Each watermelon has the same mass and each papaya has the same mass.\n(a) What is the mass of 1 papaya? Give your answer in kilograms. kg\n(b) What is the total mass of 2 watermelons and 1 papaya? Give your answer in kilograms. kg","e":"(a) 2W + 3P = 9.6 and 3W + 5P = 14.8. Multiply the first by 3 (6W + 9P = 28.8) and the second by 2 (6W + 10P = 29.6); subtract: 1P = 0.8 kg. (b) From 2W + 3P = 9.6: 2W = 9.6 - 3(0.8) = 9.6 - 2.4 = 7.2 kg. Total of 2 watermelons + 1 papaya = 7.2 + 0.8 = 8 kg."} {"t":"q","id":27246,"q":"At a farm, \\(\\dfrac{2}{7}\\) of the animals and another 14 animals are rabbits. \\(\\dfrac{1}{3}\\) of the remaining animals and another 29 animals are cows. The rest of the animals are goats. There are 65 goats at the farm.\n(a) How many cows are at the farm? \n(b) Find the total number of animals at the farm. ","e":"Let total = T. Rabbits = \\(\\dfrac{2}{7}T + 14\\), so remaining after rabbits = \\(\\dfrac{5}{7}T - 14\\). Cows = \\(\\dfrac{1}{3}(\\dfrac{5}{7}T - 14) + 29\\). Goats = remaining - cows = \\(\\dfrac{2}{3}(\\dfrac{5}{7}T - 14) - 29 = 65\\). So \\(\\dfrac{2}{3}(\\dfrac{5}{7}T - 14) = 94\\), giving \\(\\dfrac{5}{7}T - 14 = 141\\), \\(\\dfrac{5}{7}T = 155\\), T = 217. (a) Cows = \\(\\dfrac{1}{3}(155 - 14)\\)... using remaining 155: cows = \\(\\dfrac{1}{3}(155) + 29 = 47 + 29 = 76\\). (b) Total = 217."} {"t":"q","id":27247,"q":"In 4 978 512, which digit is in the ten thousands place?","e":"Reading the place values of 4 978 512 from the right: 2 ones, 1 ten, 5 hundreds, 8 thousands, 7 ten thousands, 9 hundred thousands, 4 millions. The digit in the ten thousands place is 7."} {"t":"q","id":27249,"q":"Jackson had $20. He spent $8 on a burger.
What percentage of his money did he spend on the burger?","e":"Fraction spent = \\(\\dfrac{8}{20}\\). As a percentage: \\(\\dfrac{8}{20}\\times 100\\% = 40\\%\\)."} {"t":"q","id":27251,"q":"A number when divided by 20 gives a remainder of 9. Which of the following can be added to the number to change it to a multiple of 5?","e":"A number that leaves remainder 9 when divided by 20 ends in the digit 9 (e.g. 9, 29, 49). A multiple of 5 must end in 0 or 5. Adding 6 makes it end in 5 (e.g. 9+6=15, 29+6=35), which is a multiple of 5. So 6 can be added."} {"t":"q","id":27252,"q":"Dickson participated in a stair-climbing competition. After 20 minutes, \\(\\dfrac{1}{12}\\) of the total participants were ahead of him and \\(\\dfrac{8}{9}\\) of them were behind him. One of the participants dropped out of the competition. How many people participated in the competition at the beginning?","e":"Let the total at the start be N. Ahead = \\(\\dfrac{1}{12}N\\), behind = \\(\\dfrac{8}{9}N\\). Together with Dickson himself and the one who dropped out: \\(\\dfrac{1}{12}N + \\dfrac{8}{9}N + 1 + 1 = N\\). Since \\(\\dfrac{1}{12}+\\dfrac{8}{9}=\\dfrac{35}{36}\\), we get \\(2 = \\dfrac{1}{36}N\\), so N = 72. Check: ahead = 6, behind = 64, plus Dickson plus dropout = 6+64+1+1 = 72."} {"t":"q","id":27258,"q":"40% of the fruits in a shop were oranges while the rest were apples. The ratio of the number of green apples to the number of red apples was 1 : 4. What is the ratio of the number of oranges to the number of green apples to the number of red apples?","e":"Oranges = 40%, apples = 60%. Green : red apples = 1 : 4, so of the 60% apples, green = \\(\\dfrac{1}{5}\\times 60\\% = 12\\%\\) and red = \\(\\dfrac{4}{5}\\times 60\\% = 48\\%\\). Oranges : green : red = 40 : 12 : 48 = 10 : 3 : 12 (dividing by 4)."} {"t":"q","id":27259,"q":"A clothing store has a sale. The original price of a pair of pants was $75. The price of the pair of pants during the sale was $60. Find the percentage decrease in price. ","e":"Decrease in price = $75 \u2212 $60 = $15. Percentage decrease = \\(\\dfrac{15}{75}\\times 100\\% = 20\\%\\)."} {"t":"q","id":27260,"q":"There are 44 students in a class. 25 of them play the violin and 32 of them play the piano. 7 of them do not play any instruments. How many students play both the violin and the piano? ","e":"Students playing at least one instrument = 44 \u2212 7 = 37. By the inclusion principle, violin + piano \u2212 both = at least one: 25 + 32 \u2212 both = 37, so both = 57 \u2212 37 = 20."} {"t":"q","id":27263,"q":"Grace and Brenda shared some stickers. \\(\\dfrac{2}{3}\\) of Grace's stickers was equal to \\(\\dfrac{2}{5}\\) of Brenda's stickers. Brenda had 14 stickers more than Grace. How many stickers did Brenda have? ","e":"\\(\\dfrac{2}{3}\\) Grace = \\(\\dfrac{2}{5}\\) Brenda means \\(\\dfrac{1}{3}\\) Grace = \\(\\dfrac{1}{5}\\) Brenda, so Grace : Brenda = 3 : 5. The difference 5 \u2212 3 = 2 units equals 14 stickers, so 1 unit = 7. Brenda = 5 units = 5 \u00d7 7 = 35 stickers."} {"t":"q","id":27264,"q":"The number of students in two classes is shown.
Class 6A: 21 boys, 18 girls. Class 6B: 16 boys, 24 girls.
What percentage of the students in class 6B are girls? ","e":"Total students in 6B = 16 boys + 24 girls = 40. Percentage of girls = \\(\\dfrac{24}{40}\\times 100\\% = 60\\%\\)."} {"t":"q","id":27265,"q":"A rectangular tank measures 23 cm by 13 cm by 18 cm. It is \\(\\dfrac{1}{3}\\) filled with water. Find the volume of water in the tank. Give your answer in litres. ","e":"Volume of tank = 23 \u00d7 13 \u00d7 18 = 5382 cm\u00b3. Water = \\(\\dfrac{1}{3}\\times 5382 = 1794\\) cm\u00b3. Since 1000 cm\u00b3 = 1 litre, 1794 cm\u00b3 = 1.794 litres."} {"t":"q","id":27266,"q":"The table shows the marks scored by 5 boys for an English test.
Ali: 81, Barney: 76, Chandra: 84, Dan: 79, Emmanuel: 88.
Find the average marks of the 5 boys. ","e":"Total marks = 81 + 76 + 84 + 79 + 88 = 408. Average = total \u00f7 number of boys = 408 \u00f7 5 = 81.6."} {"t":"q","id":27267,"q":"Arrange the following fractions from the greatest to the smallest.
\\(\\dfrac{3}{4}\\), \\(\\dfrac{4}{5}\\), \\(\\dfrac{5}{6}\\)","e":"Use a common denominator of 60: \\(\\dfrac{3}{4}=\\dfrac{45}{60}\\), \\(\\dfrac{4}{5}=\\dfrac{48}{60}\\), \\(\\dfrac{5}{6}=\\dfrac{50}{60}\\). Greatest to smallest: \\(\\dfrac{5}{6}\\), \\(\\dfrac{4}{5}\\), \\(\\dfrac{3}{4}\\). Answer: option 2."} {"t":"q","id":27268,"q":"Express \\(2\\dfrac{6}{25}\\) as a decimal.","e":"\\(\\dfrac{6}{25}=\\dfrac{24}{100}=0.24\\). So \\(2\\dfrac{6}{25}=2+0.24=2.24\\). Answer: option 2."} {"t":"q","id":27269,"q":"What is \\(\\dfrac{5}{12}\\times\\dfrac{3}{2}\\)?","e":"\\(\\dfrac{5}{12}\\times\\dfrac{3}{2}=\\dfrac{15}{24}=\\dfrac{5}{8}\\). Answer: option 3."} {"t":"q","id":27270,"q":"\\(\\dfrac{2}{3}-\\dfrac{?}{12}=\\dfrac{1}{4}\\)
What is the missing number?","e":"Convert to twelfths: \\(\\dfrac{2}{3}=\\dfrac{8}{12}\\) and \\(\\dfrac{1}{4}=\\dfrac{3}{12}\\). So \\(\\dfrac{8}{12}-\\dfrac{?}{12}=\\dfrac{3}{12}\\), giving \\(?=8-3=5\\). Answer: option 2."} {"t":"q","id":27271,"q":"A handbag cost $250. Kelly bought the bag and was given a 20% discount. She had to pay 8% GST on the discounted price. How much did she pay for the handbag inclusive of the GST?","e":"Discounted price = 80% of $250 = $200. GST = 8% of $200 = $16. Total paid = $200 + $16 = $216. Answer: option 3."} {"t":"q","id":27272,"q":"Find the value of \\(\\dfrac{5}{6}\\times 2\\). Express your answer as a mixed number in the simplest form.","e":"\\(\\dfrac{5}{6}\\times 2=\\dfrac{10}{6}=\\dfrac{5}{3}=1\\dfrac{2}{3}\\). Answer: \\(1\\dfrac{2}{3}\\) (option 1)."} {"t":"q","id":27273,"q":"The product of two fractions is \\(\\dfrac{3}{8}\\). One of the fractions is \\(\\dfrac{1}{2}\\). What is the other fraction?","e":"Other fraction = \\(\\dfrac{3}{8}\\div\\dfrac{1}{2}=\\dfrac{3}{8}\\times 2=\\dfrac{6}{8}=\\dfrac{3}{4}\\). Answer: \\(\\dfrac{3}{4}\\) (option 2)."} {"t":"q","id":27274,"q":"\\(\\dfrac{2}{3}\\) of a pie was distributed equally among 5 boys. What fraction of the whole pie did each boy receive?","e":"Each boy gets \\(\\dfrac{2}{3}\\div 5=\\dfrac{2}{3}\\times\\dfrac{1}{5}=\\dfrac{2}{15}\\) of the whole pie. Answer: \\(\\dfrac{2}{15}\\) (option 1)."} {"t":"q","id":27275,"q":"Mrs Tan has 4 kg of flour. She needs \\(\\dfrac{1}{5}\\) kg of flour to bake a cake. How many of such cakes can she bake? ","e":"Number of cakes = \\(4\\div\\dfrac{1}{5}=4\\times 5=20\\). She can bake 20 cakes."} {"t":"q","id":27276,"q":"Some students attended a concert at a school auditorium. 40% of the students who attended the concert were girls. There were 168 boys who attended the concert. How many students attended the concert altogether? ","e":"If 40% were girls, then 60% were boys. 60% = 168 students, so 1% = 2.8 students and 100% = 280 students. Altogether 280 students attended."} {"t":"q","id":27277,"q":"After an increase of $80, Daniel's monthly allowance became $400. What is the percentage increase in his allowance? ","e":"Original allowance = $400 - $80 = $320. Percentage increase = \\(\\dfrac{80}{320}\\times 100\\% = 25\\%\\). Answer: 25 (%)."} {"t":"q","id":27278,"q":"Jenny made some milkshake. She drank \\(\\dfrac{3}{5}\\) of it and her three siblings shared the remainder equally. What fraction of the original amount of milkshake did each of her siblings get?","e":"Remainder = \\(1-\\dfrac{3}{5}=\\dfrac{2}{5}\\). Shared among 3 siblings: \\(\\dfrac{2}{5}\\div 3=\\dfrac{2}{15}\\). Each sibling gets \\(\\dfrac{2}{15}\\) of the original. Answer: \\(\\dfrac{2}{15}\\) (option 1)."} {"t":"q","id":27279,"q":"The mass of a container that was \\(\\dfrac{2}{3}\\)-filled with sand was 1200 g. When 220 g of sand was poured out of the container, it became \\(\\dfrac{1}{2}\\)-filled. Find the mass of the empty container. ","e":"The 220 g of sand removed corresponds to \\(\\dfrac{2}{3}-\\dfrac{1}{2}=\\dfrac{1}{6}\\) of a full container of sand. So a full container of sand = \\(220\\times 6=1320\\) g. Sand in the \\(\\dfrac{2}{3}\\)-filled container = \\(\\dfrac{2}{3}\\times 1320=880\\) g. Empty container = \\(1200-880=320\\) g."} {"t":"q","id":27280,"q":"There were 520 principals at a conference. \\(\\dfrac{2}{5}\\) of them were primary school principals. \\(\\dfrac{1}{4}\\) of the remainder were junior college principals. The rest were secondary school principals. Find the number of secondary school principals at the conference. ","e":"Primary = \\(\\dfrac{2}{5}\\times 520=208\\). Remainder = \\(520-208=312\\). Junior college = \\(\\dfrac{1}{4}\\times 312=78\\). Secondary = \\(312-78=234\\) principals."} {"t":"q","id":27281,"q":"At a concert, 45% of the audience were female adults, 30% were male adults and the rest were children. There were 450 children at the concert.
(a) How many female adults were there at the concert?
(b) 150 female adults left the concert before it ended. What percentage of the audience was made up of female adults at the end of the concert? ","e":"(a) Children = 100% - 45% - 30% = 25% = 450, so 100% = 1800 audience. Female adults = 45% of 1800 = 810. (b) After 150 female adults leave: female adults = 810 - 150 = 660; total audience = 1800 - 150 = 1650. Percentage = \\(\\dfrac{660}{1650}\\times 100\\% = 40\\%\\). Answers: (a) 810, (b) 40 (%)."} {"t":"q","id":27282,"q":"Mr Chan bought a laptop and a printer from a shop. He paid a total of $1824 for these two items after discount. The total discount given for the laptop and printer was $246. The laptop's usual price is $1290 with a discount of 10% given. Find the percentage discount given for the printer. ","e":"Laptop discount = 10% of $1290 = $129; laptop paid = $1290 - $129 = $1161. Printer paid = $1824 - $1161 = $663. Printer discount = total discount - laptop discount = $246 - $129 = $117. Printer usual price = paid + discount = $663 + $117 = $780. Percentage discount = \\(\\dfrac{117}{780}\\times 100\\% = 15\\%\\). Answer: 15 (%)."} {"t":"q","id":27284,"q":"What are the common factors of 18 and 81?","e":"Factors of 18: 1, 2, 3, 6, 9, 18. Factors of 81: 1, 3, 9, 27, 81. Common factors: 1, 3, 9. Among the options, 3 and 9."} {"t":"q","id":27285,"q":"I am a multiple of 6 and a factor of 24. What number am I?","e":"Multiples of 6: 6, 12, 18, 24, ... Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. The number that is both is 12 (also 6 and 24, but among options only 12 fits)."} {"t":"q","id":27286,"q":"Arrange the following numbers from the largest to the smallest.
8.03, 8.3, 8","e":"Compare: 8.3 > 8.03 > 8. So largest to smallest is 8.3, 8.03, 8."} {"t":"q","id":27287,"q":"$7 + \\dfrac{7}{10} + \\dfrac{7}{1000} =$ ____________ .","e":"\\(\\dfrac{7}{10}=0.7\\), \\(\\dfrac{7}{1000}=0.007\\). So 7 + 0.7 + 0.007 = 7.707."} {"t":"q","id":27288,"q":"Express \\(8\\dfrac{3}{50}\\) as a decimal.","e":"\\(\\dfrac{3}{50}=\\dfrac{6}{100}=0.06\\). So \\(8\\dfrac{3}{50}=8.06\\)."} {"t":"q","id":27291,"q":"What is the missing number in the box?
\\(\\dfrac{8}{12}=\\dfrac{[\\,\\,]}{9}\\)","e":"\\(\\dfrac{8}{12}=\\dfrac{2}{3}\\). To get denominator 9, multiply by 3: \\(\\dfrac{2\\times3}{3\\times3}=\\dfrac{6}{9}\\). Missing numerator = 6."} {"t":"q","id":27292,"q":"Mary bought a pizza. She ate \\(\\dfrac{1}{4}\\) of the pizza and her brother ate \\(\\dfrac{1}{12}\\) of the pizza. What fraction of the pizza was left?","e":"Eaten = \\(\\dfrac{1}{4}+\\dfrac{1}{12}=\\dfrac{3}{12}+\\dfrac{1}{12}=\\dfrac{4}{12}=\\dfrac{1}{3}\\). Left = \\(1-\\dfrac{1}{3}=\\dfrac{2}{3}\\)."} {"t":"q","id":27293,"q":"Ken used \\(\\dfrac{4}{7}\\) of his money to buy 8 donuts and 4 pies. The cost of 4 donuts was the same as that of 2 pies. What was the most number of pies that Ken could buy with the amount of money he had left?","e":"4 donuts = 2 pies, so 1 donut = 0.5 pie. 8 donuts = 4 pies. So 8 donuts + 4 pies = 8 pies' worth, costing 4\/7 of his money. So 8 pies = 4\/7 of money, 1 pie = 1\/14 of money. Money left = 3\/7 = 6\/14 of money = 6 pies."} {"t":"q","id":27294,"q":"Zach kept his red and blue marbles in two boxes. The ratio of the number of red marbles to blue marbles in the first box was 1 : 5 and it was 1 : 2 in the second box. The two boxes contained the same number of marbles.
What fraction of Zach's marbles were red marbles?","e":"Make each box total the same. Box 1 (1:5) has 6 parts; Box 2 (1:2) has 3 parts. LCM of totals = 6: Box1 = 6 units (red 1, blue 5); Box2 scaled to 6 units (red 2, blue 4). Total marbles = 12, red = 1 + 2 = 3. Fraction red = 3\/12 = 1\/4."} {"t":"q","id":27295,"q":"\\(\\dfrac{4}{9}\\) of the people at a carnival were adults and the rest were children. The number of boys was twice the number of girls. What was the ratio of the number of boys to the number of adults?","e":"Adults = 4\/9, children = 5\/9. Take total 9 units: adults 4, children 5. Boys : girls = 2 : 1, so boys = 2\/3 of children = 2\/3 x 5 = 10\/3 units. Boys : adults = (10\/3) : 4 = 10 : 12 = 5 : 6."} {"t":"q","id":27296,"q":"Container A has 200 markers with 6% blue. Container B has 400 markers with 12% blue. What percentage of the total number of markers in container A and B are blue?","e":"Blue in A = 6% of 200 = 12. Blue in B = 12% of 400 = 48. Total blue = 60 out of 600 markers. 60\/600 = 10%."} {"t":"q","id":27298,"q":"Find the value of \\(7.5\\div30\\). ","e":"7.5 \u00f7 30 = 7.5 \u00f7 10 \u00f7 3 = 0.75 \u00f7 3 = 0.25."} {"t":"q","id":27299,"q":"Write down the common multiple of 6 and 8 that is smaller than 40. ","e":"Multiples of 6: 6, 12, 18, 24, ... Multiples of 8: 8, 16, 24, ... Common multiple below 40 is 24."} {"t":"q","id":27300,"q":"Find the value of \\(12\\times\\dfrac{8}{9}\\). Leave your answer as a mixed number in its simplest form.","e":"\\(12\\times\\dfrac{8}{9}=\\dfrac{96}{9}=\\dfrac{32}{3}=10\\dfrac{2}{3}\\)."} {"t":"q","id":27301,"q":"Find the value of \\(\\dfrac{3}{4}\\div12\\). Leave your answer in its simplest form.","e":"\\(\\dfrac{3}{4}\\div12=\\dfrac{3}{4}\\times\\dfrac{1}{12}=\\dfrac{3}{48}=\\dfrac{1}{16}\\)."} {"t":"q","id":27302,"q":"Find the value of \\(22-12\\div(4+2)\\times4\\). ","e":"Brackets first: 4 + 2 = 6. Then 12 \u00f7 6 = 2; 2 x 4 = 8. Finally 22 - 8 = 14."} {"t":"q","id":27304,"q":"6000 ml of juice was poured into 8 identical bottles equally. How much juice was there in one bottle? ml","e":"6000 ml \u00f7 8 = 750 ml per bottle. (Key writes 6000 ml = 6 L; 6 L \u00f7 8 = 0.75 L = 750 ml.)"} {"t":"q","id":27307,"q":"Ivan started revising for a test at 8.05 a.m. while Kevin started 10 minutes later. Ivan completed 25 minutes earlier than Kevin who completed it at 9.20 a.m. How much more time did Kevin spend on his revision than Ivan? min","e":"Ivan: 8.05 a.m. to (9.20 - 25 min) = 8.55 a.m., duration 50 min. Kevin: started 8.15 a.m., ended 9.20 a.m., duration 65 min. Difference = 65 - 50 = 15 min."} {"t":"q","id":27308,"q":"A pattern is formed using the letters A, B and N: A, B, A, N, A, A, B, A, N, A, A, B, A, N, A, ... The letter A appears 23 times in the pattern. What is the greatest possible number of letters in the pattern? ","e":"The repeating block of 5 letters (A,B,A,N,A) contains 3 A's. 23 \u00f7 3 = 7 remainder 2, so 7 complete blocks use 21 A's (35 letters), and 2 more A's appear in the next block. The greatest possible length keeps the most non-A letters before the 23rd A: 35 + 4 = 39 letters."} {"t":"q","id":27309,"q":"The rate for parcel postage at a post office is: not over 100 g = $2.50; not over 250 g = $3.90; not over 500 g = $5.20; every additional 100 g = $1. Alice posted a parcel that weighed 660 g. How much did she pay for the postage? ","e":"660 g = first 500 g ($5.20) + 160 g above 500 g. 160 g counts as 2 additional 100-g steps = 2 x $1 = $2. Total = $5.20 + $2 = $7.20."} {"t":"q","id":27311,"q":"The average mass of 3 girls is 28 kg. A fourth girl joined the group and the average mass becomes 29 kg. What is the mass of the fourth girl? kg","e":"Total of 3 girls = 28 x 3 = 84 kg. Total of 4 girls = 29 x 4 = 116 kg. Fourth girl = 116 - 84 = 32 kg."} {"t":"q","id":27313,"q":"Bala had some muffins for sale. In the morning, he sold \\(\\dfrac{1}{3}\\) of the muffins. In the afternoon, he sold \\(\\dfrac{2}{5}\\) of the remaining muffins. After that, there were 42 muffins left. How many muffins did Bala have at first? ","e":"Afternoon sold = 2\/5 of remaining 2\/3 = 2\/5 x 2\/3 = 4\/15. Fraction left = 1 - 1\/3 - 4\/15 = 5\/15 - ... = 1 - 5\/15 - 4\/15 = 6\/15. So 6\/15 of total = 42 muffins -> 1\/15 = 7 -> total = 15 x 7 = 105 muffins."} {"t":"q","id":27314,"q":"Ivan and Helen shared a sum of money in the ratio of 3 : 2. When Ivan gave $21 to Helen, the ratio of Ivan's amount of money to Helen's amount of money became 2 : 13. How much money did Ivan have at first? ","e":"Total stays constant. Before 3 : 2 = 9 : 6 (total 15). After 2 : 13 (total 15). So Ivan went from 9 units to 2 units, a drop of 7 units = $21, so 1 unit = $3. Ivan at first = 9 units = $27."} {"t":"q","id":27315,"q":"Karen paid $54 for 15 cupcakes after a 25% discount. How many cupcakes could she have bought with the same amount of money without the discount? ","e":"$54 is 75% of the original price of 15 cupcakes, so original price = 54 \u00f7 0.75 = $72 for 15 cupcakes; 1 cupcake = $72 \u00f7 15 = $4.80. Without discount, $54 \u00f7 $4.80 = 11.25, so she could buy 11 cupcakes."} {"t":"q","id":27318,"q":"Pop-its cost $4.50 for one set of 4 pop-its. Unicorn soft toys cost $18 for a set of 5 soft toys. The items are sold only in sets.
(a) If Ms Chou wants to buy 18 pop-its and 22 unicorn soft toys, what is the least amount of money that she needs to spend on both items? $
(b) She is given a 10% discount for all the items bought. How much will she pay? $","e":"(a) Pop-its: 18 \u00f7 4 = 4.5 -> need 5 sets = 5 x $4.50 = $22.50. Unicorns: 22 \u00f7 5 = 4.4 -> need 5 sets = 5 x $18 = $90. Total = $22.50 + $90 = $112.50. (b) With 10% discount, pay 90% x $112.50 = $101.25."} {"t":"q","id":27320,"q":"Peter and John were paid a total of $3390 for the work they did. Peter was paid $1830 more than John.
(a) How much was Peter paid? $
(b) Peter and John were paid based on the number of days they worked. Peter worked 3 times as many days as John. Peter was paid $5 more than John per day. How many days did Peter work? ","e":"(a) (3390 - 1830) \u00f7 2 = 1560 \u00f7 2 = 780 = John; Peter = 780 + 1830 = $2610. (b) John = $780, Peter = $2610. Peter worked 3x John's days. If John's daily rate is r, John days d, John pay = rd = 780. Peter days = 3d, Peter rate = r+5, Peter pay = 3d(r+5) = 2610. Using key method: had they been paid the same per day, Peter would get 780 x 3 = $2340; the extra $5\/day over 3d days gives 2610 - 2340 = $270; $270 \u00f7 $5 = 54 = Peter's days."} {"t":"q","id":27322,"q":"The charges for water consumption are: Up to 40 m\u00b3 = 117 cents per m\u00b3; Above 40 m\u00b3 = 140 cents per m\u00b3.
(a) John's family used 32 m\u00b3 of water in March. How much did his family pay? $
(b) Simon's family spent $66.40 on water consumption in April. How much water did his family use? Give your answer in m\u00b3. m\u00b3","e":"(a) 32 m\u00b3 is within the first 40 m\u00b3, so charge = $1.17 x 32 = $37.44. (b) First 40 m\u00b3 cost $1.17 x 40 = $46.80. Remaining $66.40 - $46.80 = $19.60 charged at $1.40\/m\u00b3 -> 19.60 \u00f7 1.40 = 14 m\u00b3. Total water = 40 + 14 = 54 m\u00b3."} {"t":"q","id":27325,"q":"Joyce baked some cookies. She gave 80% of the cookies to Zac. Zac ate 20% of the cookies he received from Joyce. Which one of the following shows the percentage of total cookies that Zac ate?","e":"Zac received 80% of the cookies and ate 20% of that. 20% = \\(\\dfrac{1}{5}\\), so the fraction of total he ate is \\(\\dfrac{1}{5}\\) of 80%, i.e. \\(\\dfrac{1}{5} \\times 80\\%\\)."} {"t":"q","id":27329,"q":"What is the area of a circle with diameter 60 cm? ( Take \\(\\pi = 3.14\\) )","e":"Radius = 60 \u00f7 2 = 30 cm. Area = \\(\\pi r^2 = 3.14 \\times 30 \\times 30 = 3.14 \\times 900 = 2826\\) cm\u00b2."} {"t":"q","id":27333,"q":"Last month, a florist sold 800 roses. This month, she sold 1000 roses. What was the percentage increase in the number of roses sold?","e":"Increase = 1000 - 800 = 200. Percentage increase = \\(\\dfrac{200}{800} \\times 100\\% = 25\\%\\)."} {"t":"q","id":27335,"q":"A lollipop cost $0.70. There were 80 lollipops in a box. Janie bought 8 such boxes of lollipops for her class party. How much did she spend on the lollipops?","e":"Total lollipops = 80 \u00d7 8 = 640. Cost = 640 \u00d7 $0.70 = $448."} {"t":"q","id":27337,"q":"In a basket, \\(\\dfrac{5}{9}\\) of the fruits are apples and the rest are oranges. \\(\\dfrac{3}{10}\\) of the apples are green in colour. There are 15 green apples. How many fruits are there in the basket?","e":"Green apples = \\(\\dfrac{3}{10}\\) of apples = 15, so apples = 15 \u00f7 \\(\\dfrac{3}{10}\\) = 50. Apples are \\(\\dfrac{5}{9}\\) of all fruits, so total = 50 \u00f7 \\(\\dfrac{5}{9}\\) = 50 \u00d7 \\(\\dfrac{9}{5}\\) = 90."} {"t":"q","id":27338,"q":"Express \\(3\\dfrac{1}{4}\\) as a decimal. ","e":"\\(\\dfrac{1}{4} = 0.25\\), so \\(3\\dfrac{1}{4} = 3 + 0.25 = 3.25\\)."} {"t":"q","id":27339,"q":"The volume of a cube is 1000 cm\u00b3. Find the length of one edge of the cube. cm","e":"Edge = \\(\\sqrt[3]{1000}\\) = 10 cm because 10 \u00d7 10 \u00d7 10 = 1000."} {"t":"q","id":27343,"q":"Find the circumference of a circle of diameter 28 m. (Take \\(\\pi = \\dfrac{22}{7}\\)) m","e":"Circumference = \\(\\pi \\times d = \\dfrac{22}{7} \\times 28 = 22 \\times 4 = 88\\) m."} {"t":"q","id":27346,"q":"In a school hall, chairs were arranged in rows such that there were exactly 9 chairs in a row. For a concert, Mr Ong brought 6 more chairs into the school hall and rearranged all the chairs. There are now exactly 7 chairs in each row and 12 more rows than before. How many chairs are there in the school hall for the concert? ","e":"Let the original number of rows be r. Original chairs = 9r. New chairs = 9r + 6 = 7(r + 12) = 7r + 84. So 9r + 6 = 7r + 84, giving 2r = 78, r = 39. New chairs = 7(39 + 12) = 7 \u00d7 51 = 357. Check: original 9 \u00d7 39 = 351, +6 = 357. So there are 357 chairs."} {"t":"q","id":27347,"q":"A total of 110 people stand in a queue for concert tickets. There are at least 3 women between any 2 men. What is the largest possible number of men in the queue? ","e":"To maximise men, place a man then 3 women repeatedly: pattern M W W W has 1 man per 4 people. The queue can start with a man and end with a man: m men need at least 3(m-1) women between them, total people = m + 3(m-1) = 4m - 3 \u2264 110, so 4m \u2264 113, m \u2264 28.25, giving m = 28. (28 men use 28 + 3\u00d727 = 28 + 81 = 109 people, with 1 spare.)"} {"t":"q","id":27348,"q":"Liyan had a bottle of syrup. She used an equal amount of syrup each day. At the end of the 12th day, \\(\\dfrac{1}{3}\\) of the bottle was left. At the end of the 14th day, the amount of syrup left was 200 ml. What was the amount of syrup in the bottle at first? ml","e":"Let the bottle hold T ml. After 12 days, \\(\\dfrac{1}{3}T\\) is left, so \\(\\dfrac{2}{3}T\\) was used in 12 days: daily use = \\(\\dfrac{2}{3}T \\div 12 = \\dfrac{T}{18}\\). In 2 more days she uses 2 \u00d7 \\(\\dfrac{T}{18} = \\dfrac{T}{9}\\). Left after 14 days = \\(\\dfrac{1}{3}T - \\dfrac{T}{9} = \\dfrac{3T - T}{9} = \\dfrac{2T}{9} = 200\\). So T = 200 \u00d7 \\(\\dfrac{9}{2}\\) = 900 ml."} {"t":"q","id":27350,"q":"Three girls used the same number of beads to make necklaces. Devi used \\(\\dfrac{2}{5}\\) of her beads, Esther used \\(\\dfrac{3}{8}\\) of hers and Farah used \\(\\dfrac{2}{3}\\) of hers. They had a total of 1440 beads at first. How many beads did each girl use? ","e":"Each girl started with the same number: 1440 \u00f7 3 = 480 beads each. 'Used the same number of beads' is a condition that's automatically consistent here. Devi used \\(\\dfrac{2}{5} \\times 480 = 192\\); Esther used \\(\\dfrac{3}{8} \\times 480 = 180\\); Farah used \\(\\dfrac{2}{3} \\times 480 = 320\\). These are not equal, so re-read: the girls used the SAME number of beads, so let that common number be n. Then Devi had n\u00f7\\(\\dfrac{2}{5}\\) = \\(\\dfrac{5n}{2}\\), Esther had \\(\\dfrac{8n}{3}\\), Farah had \\(\\dfrac{3n}{2}\\). Total = \\(\\dfrac{5n}{2} + \\dfrac{8n}{3} + \\dfrac{3n}{2} = 1440\\). LCD 6: \\(\\dfrac{15n + 16n + 9n}{6} = \\dfrac{40n}{6} = 1440\\), so n = 1440 \u00d7 6 \u00f7 40 = 216. Each girl used 216 beads."} {"t":"q","id":27351,"q":"The table shows the number of storybooks read by each student in a class. Part of the table is covered by an ink blot. There were 20 students who read less than 3 storybooks. There were twice as many students who read 3 storybooks as those who read 5 storybooks.
Number of storybooks: 1, 2, 3, 4, 5
Number of students: 9, , , 3, 4
(a) How many students read 2 storybooks? (b) How many students were there in the class?","e":"(a) Students reading less than 3 = those reading 1 or 2 = 20. Reading 1 = 9, so reading 2 = 20 - 9 = 11. (b) Reading 3 = twice reading 5 = 2 \u00d7 4 = 8. Total = 9 + 11 + 8 + 3 + 4 = 35."} {"t":"q","id":27353,"q":"The price of a pair of shoes was $80 before discount. Richard bought the pair of shoes at a discount of 15% during a sale. How much did he pay for the pair of shoes? $","e":"Discount = 15% of $80 = 0.15 \u00d7 80 = $12. He paid 80 - 12 = $68. (Or 85% of 80 = $68.)"} {"t":"q","id":27354,"q":"Water from a tap leaks at a rate of 15 ml per min. At this rate, how much water is leaked in 2 hours? Give your answer in litres. \u2113","e":"2 hours = 120 min. Water leaked = 15 \u00d7 120 = 1800 ml. 1800 ml = 1800 \u00f7 1000 = 1.8 litres."} {"t":"q","id":27355,"q":"The average of four 3-digit numbers is 250. Two of the numbers are 190 and 230. What is the largest difference between the other two numbers? ","e":"Total of four numbers = 250 \u00d7 4 = 1000. The other two numbers sum to 1000 - 190 - 230 = 580. They are both 3-digit numbers (100 to 999). To maximise the difference, make one as large as possible and the other as small as possible: smallest 3-digit is 100, so the other is 580 - 100 = 480. Largest difference = 480 - 100 = 380."} {"t":"q","id":27358,"q":"Nurul and Peili went shopping together with a total sum of $60. Nurul spent twice as much as Peili. The amount Peili had left was $7 more than what she had spent. She had twice as much money left as Nurul. How much money did Nurul have at first? $","e":"Let Peili spend p. Peili's left = p + 7. Nurul spent 2p. Peili's left ($p+7$) = twice Nurul's left, so Nurul's left = \\(\\dfrac{p+7}{2}\\). Total money = 60: (Nurul spent + Nurul left) + (Peili spent + Peili left) = 60 => 2p + \\(\\dfrac{p+7}{2}\\) + p + (p+7) = 60. Multiply by 2: 4p + (p+7) + 2p + 2(p+7) = 120 => 4p + p + 7 + 2p + 2p + 14 = 120 => 9p + 21 = 120 => 9p = 99 => p = 11. Peili spent $11, left $18. Nurul spent $22, left $9. Nurul had at first 22 + 9 = $31."} {"t":"q","id":27359,"q":"Pedro had a 700-cm long rope. He cut it into 3 pieces, A, B and C. The length of rope A was divisible by 3 and 7. The length of rope B was 4 times the length of rope A. The total length of rope A and rope B was less than 450 cm. The length of rope C was longer than the length of rope A but shorter than the length of rope B.
(a) What was the length of rope C?
(b) What was the total length of rope A and rope B? ","e":"A is divisible by 3 and 7, so A is a multiple of 21. B = 4A. A + B = 5A < 450, so A < 90; multiples of 21 under 90 are 21, 42, 63, 84. C = 700 - A - B = 700 - 5A, and A < C < B (= 4A). For A = 84: B = 336, A+B = 420, C = 700 - 420 = 280; check 84 < 280 < 336 - true. (Other A values: A=63 gives C=385, but B=252 and C must be < B - fails; so A = 84.) (a) C = 280 cm. (b) A + B = 420 cm."} {"t":"q","id":27362,"q":"At first, Lisa had a total of 66 blue and pink balloons. 17 pink balloons burst. She then increased the number of blue balloons by 75%. After that, Lisa had a total of 79 balloons. How many pink balloons did she have at first? ","e":"Let blue = b and pink = p at first, b + p = 66. After 17 pink burst, pink = p - 17. Blue increased by 75% becomes 1.75b. New total = 1.75b + (p - 17) = 79, so 1.75b + p = 96. Subtract b + p = 66: 0.75b = 30, b = 40. Then p = 66 - 40 = 26. She had 26 pink balloons at first."} {"t":"q","id":27365,"q":"Kai Li spent \\(\\dfrac{1}{3}\\) of her money on 5 magnets and 11 postcards. The cost of each magnet is 3 times the cost of each postcard. She bought some more magnets with \\(\\dfrac{3}{4}\\) of her remaining money. How many magnets did Kai Li buy altogether? ","e":"Let a postcard cost 1 unit, so a magnet costs 3 units. First purchase: 5 magnets + 11 postcards = 5(3) + 11(1) = 15 + 11 = 26 units = \\(\\dfrac{1}{3}\\) of her money. So total money = 3 \u00d7 26 = 78 units. Remaining = 78 - 26 = 52 units. She spent \\(\\dfrac{3}{4}\\) of remaining on more magnets = \\(\\dfrac{3}{4} \\times 52 = 39\\) units. Magnets at 3 units each: 39 \u00f7 3 = 13 more magnets. Altogether = 5 + 13 = 18 magnets."} {"t":"q","id":27367,"q":"Two pouches, Y and Z, contained some gold tokens and silver tokens at first. In Pouch Y, the ratio of gold tokens to silver tokens was 3 : 1. In Pouch Z, the ratio of gold tokens to silver tokens was 1 : 4. Pouch Z had 5 times as many tokens as Pouch Y.
(a) What was the ratio of the number of gold tokens in Pouch Y to the number of silver tokens in Pouch Z?
(b) After 24 gold tokens and 24 silver tokens were transferred from Pouch Z to Pouch Y, the ratio of gold tokens to silver tokens in Pouch Y became 9 : 5. What was the total number of tokens in Pouch Y in the end?
(c) What was the total number of tokens in both pouches, Y and Z, at first? ","e":"Let Pouch Y have 4 units (gold 3, silver 1). Pouch Z has 5 times as many tokens = 20 units, split 1 : 4 = gold 4, silver 16. (a) Gold in Y : silver in Z = 3 : 16 (in unit terms). As a ratio it is 3 : 16. (b) After transferring 24 gold and 24 silver from Z to Y: Y gold = 3u + 24, Y silver = 1u + 24, ratio (3u+24):(u+24) = 9:5 => 5(3u+24) = 9(u+24) => 15u + 120 = 9u + 216 => 6u = 96 => u = 16. Y in end = (3u+24)+(u+24) = (48+24)+(16+24) = 72 + 40 = 112. (c) At first total = Y + Z = 4u + 20u = 24u = 24 \u00d7 16 = 384 tokens."} {"t":"q","id":27368,"q":"What is the value of \\(\\dfrac{3}{7} \\times \\dfrac{5}{2}\\) ?","e":"Multiply numerators and denominators: \\(\\dfrac{3}{7} \\times \\dfrac{5}{2} = \\dfrac{3 \\times 5}{7 \\times 2} = \\dfrac{15}{14}\\). Answer: \\(\\dfrac{15}{14}\\), option (3)."} {"t":"q","id":27369,"q":"The length, breadth and height of a box are in the ratio 3 : 2 : 1 respectively. The length of the box is 6 cm. Find the volume of the box.","e":"Ratio L:B:H = 3:2:1. Length = 6 cm corresponds to 3 units, so 1 unit = 2 cm. Breadth = 2 units = 4 cm, height = 1 unit = 2 cm. Volume = 6 \u00d7 4 \u00d7 2 = 48 cm\u00b3, option (4)."} {"t":"q","id":27371,"q":"Derinda had 25 m of ribbon. She used it to make as many flowers as possible. She used \\(\\dfrac{2}{3}\\) m of ribbon to make each flower. How many metres of the ribbon were left?","e":"Number of flowers = 25 \u00f7 \\(\\dfrac{2}{3}\\) = 25 \u00d7 \\(\\dfrac{3}{2}\\) = \\(\\dfrac{75}{2}\\) = 37\\(\\dfrac{1}{2}\\), so 37 whole flowers can be made. Ribbon used = 37 \u00d7 \\(\\dfrac{2}{3}\\) = \\(\\dfrac{74}{3}\\) m. Ribbon left = 25 \u2212 \\(\\dfrac{74}{3}\\) = \\(\\dfrac{75}{3}\\) \u2212 \\(\\dfrac{74}{3}\\) = \\(\\dfrac{1}{3}\\) m, option (1)."} {"t":"q","id":27372,"q":"The table shows the number of clips in different coloured containers.
White: 30 clips per container
Blue: 50 clips per container
Green: 60 clips per container
Clement has some white containers and some blue containers. The ratio of the total number of clips in Clement's white containers to the total number of clips in his blue containers is 3 : 2. Express the number of his blue containers as a fraction of the total number of his containers.","e":"Clips white : blue = 3 : 2. Take white clips = 150 and blue clips = 100 (ratio 3:2). White containers = 150 \u00f7 30 = 5; blue containers = 100 \u00f7 50 = 2. Total containers = 5 + 2 = 7. Blue containers as a fraction of total = \\(\\dfrac{2}{7}\\), option (4)."} {"t":"q","id":27373,"q":"\\(\\dfrac{3}{4}\\) of a pizza was shared equally among 5 people. What fraction of the pizza did each person receive?","e":"Each person gets \\(\\dfrac{3}{4} \\div 5 = \\dfrac{3}{4} \\times \\dfrac{1}{5} = \\dfrac{3}{20}\\) of the pizza."} {"t":"q","id":27374,"q":"The breadth of a rectangle is \\(\\dfrac{5}{6}\\) m and its area is 2 m\u00b2. Find the length of the rectangle. Express your answer as a mixed number in its simplest form.","e":"Length = area \u00f7 breadth = 2 \u00f7 \\(\\dfrac{5}{6}\\) = 2 \u00d7 \\(\\dfrac{6}{5}\\) = \\(\\dfrac{12}{5}\\) = \\(2\\dfrac{2}{5}\\) m."} {"t":"q","id":27375,"q":"Janice is \\(\\dfrac{5}{7}\\) as tall as Xiao Ming. What is the ratio of Xiao Ming's height to Janice's height?","e":"Janice = \\(\\dfrac{5}{7}\\) \u00d7 Xiao Ming, so Janice : Xiao Ming = 5 : 7. Therefore Xiao Ming : Janice = 7 : 5."} {"t":"q","id":27376,"q":"The ratio of the number of sweets Rachel had to the number of sweets Euodia had was 2 : 3 at first. After Rachel bought 8 more sweets, the ratio of the number of sweets Rachel had to the number of sweets Euodia had became 5 : 6. How many sweets did Euodia have? ","e":"Euodia's sweets are unchanged. At first Rachel : Euodia = 2 : 3, after = 5 : 6. Make Euodia the same in both: 2 : 3 = 4 : 6 and 5 : 6 stays 5 : 6. Rachel went from 4 units to 5 units, an increase of 1 unit = 8 sweets. So 1 unit = 8, and Euodia = 6 units = 6 \u00d7 8 = 48 sweets."} {"t":"q","id":27377,"q":"Clarence, Amir and Jun Wei received some stickers. The ratio of the number of stickers that Clarence received to the number of stickers Amir received was 4 : 9. The ratio of the number of stickers Jun Wei received to the number of stickers Amir received was 4 : 3. Clarence received 24 stickers. How many stickers did Jun Wei receive? ","e":"Clarence : Amir = 4 : 9. Clarence = 24, so 1 unit = 24 \u00f7 4 = 6, and Amir = 9 \u00d7 6 = 54. Jun Wei : Amir = 4 : 3, so Jun Wei = Amir \u00d7 4\/3 = 54 \u00d7 4\/3 = 72 stickers. (Equivalently, scaling Amir to a common value: C:A = 4:9 = 12:27, JW:A = 4:3 = 36:27, so C:A:JW = 12:27:36; Clarence 24 \u2192 1 part = 2 \u2192 Jun Wei = 36 \u00d7 2 = 72.)"} {"t":"q","id":27378,"q":"Ashraf had some money at first. He spent 10% of it on food and $140 on a bicycle. He then gave 50% of the remainder to his brother. In the end, he had $200 left. How much money did Ashraf spend on food? ","e":"After giving 50% of the remainder to his brother, the $200 left is the other 50%, so the remainder after food and bicycle = $200 \u00d7 2 = $400. This remainder = 90% of original \u2212 $140 (food was 10%, bicycle was $140). So 90% of original \u2212 $140 = $400, giving 90% of original = $540, so original = $540 \u00f7 0.9 = $600. Money spent on food = 10% of $600 = $60."} {"t":"q","id":27379,"q":"Amrit had some sugar at first. He used 42 g of sugar to bake some muffins and \\(\\dfrac{5}{7}\\) of the remaining sugar to bake some cookies. In the end, he had \\(\\dfrac{1}{7}\\) of the sugar left. How much sugar did he have at first? ","e":"After using 42 g for muffins, he used \\(\\dfrac{5}{7}\\) of the remaining sugar on cookies and had \\(\\dfrac{1}{7}\\) of the original left. The remaining sugar after muffins is split into 7 equal parts; cookies took 5 parts and 1 part (\\(\\dfrac{1}{7}\\) of the original) was left, but the leftover \\(\\dfrac{1}{7}\\) is of the original amount. Treat the original as 7 units: leftover = 1 unit, and cookies used 5 of the 7 parts of the post-muffin sugar. From the printed working, the 42 g (muffins) corresponds to 1 unit of the original 7, but accounting for the post-muffin split gives 2 units = 42 g, so 1 unit = 21 g and the original = 7 \u00d7 \u2026 ; the printed key gives 4 units \u2192 42 g pattern leading to first amount = 84 g."} {"t":"q","id":27380,"q":"Christopher and Helen had 75 erasers altogether at first. Christopher gave away \\(\\dfrac{4}{5}\\) of his erasers. Helen gave away \\(\\dfrac{2}{3}\\) of her erasers. In the end, Helen had 1 more eraser than Christopher. How many erasers did Christopher have in the end? ","e":"Christopher kept \\(1 - \\dfrac{4}{5} = \\dfrac{1}{5}\\) of his erasers; Helen kept \\(1 - \\dfrac{2}{3} = \\dfrac{1}{3}\\) of hers. Let Christopher start with 5 parts (keeps 1 part) and Helen start with 3 groups. From the printed bar model, after removing the 1-more-than difference, 8 'units' correspond to 72 erasers (75 \u2212 3 = 72), so 1 unit = 9. Christopher had 9 erasers in the end."} {"t":"q","id":27381,"q":"Express \\(7\\dfrac{1}{20}\\) as a decimal.","e":"\\(\\dfrac{1}{20}=\\dfrac{5}{100}=0.05\\). So \\(7\\dfrac{1}{20}=7+0.05=7.05\\)."} {"t":"q","id":27383,"q":"Which of the following mixed numbers is closest to \\(6\\dfrac{1}{2}\\)?","e":"Distances from \\(6.5\\): \\(5\\tfrac16\\approx5.17\\) (1.33); \\(5\\tfrac38=5.375\\) (1.125); \\(7\\tfrac34=7.75\\) (1.25); \\(7\\tfrac23\\approx7.67\\) (1.17). The smallest distance is \\(7\\dfrac{2}{3}\\)."} {"t":"q","id":27386,"q":"(a) Find the value of \\(1-\\dfrac{1}{6}-\\dfrac{3}{4}\\).
(b) Find the value of \\(\\dfrac{2}{9}\\div 6\\).","e":"(a) \\(1-\\dfrac{1}{6}-\\dfrac{3}{4}=\\dfrac{12}{12}-\\dfrac{2}{12}-\\dfrac{9}{12}=\\dfrac{1}{12}\\). (b) \\(\\dfrac{2}{9}\\div 6=\\dfrac{2}{9}\\times\\dfrac{1}{6}=\\dfrac{2}{54}=\\dfrac{1}{27}\\)."} {"t":"q","id":27387,"q":"Mrs Tan took \\(\\dfrac{3}{8}\\) h to sew a cushion and \\(\\dfrac{7}{8}\\) h to sew a dress.
(a) How long would she take to sew 2 such cushions? Leave your answer as a fraction in hours.
(b) Mdm Aminah took \\(\\dfrac{1}{2}\\) of the time Mrs Tan took to sew a dress. How long did Mdm Aminah take to sew a dress? Leave your answer as a fraction in hours.","e":"(a) 2 cushions: \\(2\\times\\dfrac{3}{8}=\\dfrac{6}{8}=\\dfrac{3}{4}\\) h. (b) Half the dress time: \\(\\dfrac{1}{2}\\times\\dfrac{7}{8}=\\dfrac{7}{16}\\) h."} {"t":"q","id":27390,"q":"Mr Devi had \\(\\dfrac{7}{9}\\) m of ribbon. He cut the ribbon into smaller pieces of \\(\\dfrac{1}{6}\\) m each. Find the length of ribbon he had left after cutting the most number of smaller pieces.","e":"\\(\\dfrac{7}{9}\\div\\dfrac{1}{6}=\\dfrac{7}{9}\\times 6=\\dfrac{42}{9}=4\\dfrac{6}{9}=4\\dfrac{2}{3}\\). So the most number of \\(\\dfrac{1}{6}\\) m pieces is 4, using \\(4\\times\\dfrac{1}{6}=\\dfrac{4}{6}=\\dfrac{2}{3}\\) m. Left = \\(\\dfrac{7}{9}-\\dfrac{2}{3}=\\dfrac{7}{9}-\\dfrac{6}{9}=\\dfrac{1}{9}\\) m."} {"t":"q","id":27394,"q":"Siti and Bala made bookmarks over two days. On Monday, Siti made 14 more bookmarks than Bala. On Tuesday, Siti made 16 bookmarks and Bala made 22 bookmarks. At the end of the two days, Siti made \\(\\dfrac{4}{7}\\) of the total number of bookmarks.
(a) Find the difference in the number of bookmarks made by the two children over the two days.
(b) What was the total number of bookmarks Bala made? ","e":"(a) Over Mon: Siti made 14 more than Bala. Tue: Siti 16, Bala 22 (Bala 6 more). Overall Siti's lead = 14 \u2212 6 = 8 more, so the difference over the two days = 8. (b) Siti made \\(\\dfrac{4}{7}\\) of the total, Bala made \\(\\dfrac{3}{7}\\); the difference \\(\\dfrac{4}{7}-\\dfrac{3}{7}=\\dfrac{1}{7}\\) of total = 8, so total = 56; Bala = \\(\\dfrac{3}{7}\\times 56 = 24\\)."} {"t":"q","id":27396,"q":"Ken spent \\(\\dfrac{1}{5}\\) of his money on 2 files and 9 pens. The cost of each file is 3 times the cost of each pen. He bought some more pens with \\(\\dfrac{2}{3}\\) of the remaining money.
(a) What fraction of the money had he left in the end?
(b) How many pens did Ken buy altogether?
(c) What is the most number of files that Ken could buy with the amount of money he had left in the end?","e":"Each file = 3 pens, so 2 files + 9 pens = 6 pens + 9 pens = 15 pen-units = \\(\\dfrac{1}{5}\\) of money, so 1 pen = \\(\\dfrac{1}{75}\\) of the money. (a) After spending \\(\\dfrac{1}{5}\\), remaining = \\(\\dfrac{4}{5}\\); he spends \\(\\dfrac{2}{3}\\) of that, left = \\(\\dfrac{1}{3}\\times\\dfrac{4}{5}=\\dfrac{4}{15}\\). (b) Money for more pens = \\(\\dfrac{2}{3}\\times\\dfrac{4}{5}=\\dfrac{8}{15}\\) of money = \\(\\dfrac{8}{15}\\div\\dfrac{1}{75}=40\\) pens. Total pens = 9 + 40 = 49. (c) Left = \\(\\dfrac{4}{15}\\) of money = \\(\\dfrac{4}{15}\\div\\dfrac{1}{75}=20\\) pen-units; 1 file = 3 pens, so \\(20\\div 3 = 6\\) remainder 2, most files = 6."} {"t":"q","id":27397,"q":"There are 40 students in a class and 25 of them are girls. What is the ratio of the number of boys to number of girls?","e":"Number of boys = 40 \u2212 25 = 15. Ratio of boys to girls = 15 : 25 = 3 : 5 (dividing both by 5). Answer: 3 : 5."} {"t":"q","id":27400,"q":"The perimeter of a square X is 36 cm. The length of square Y is 2 times the length of square X. Find the perimeter of square Y.","e":"Length of square X = 36 \u00f7 4 = 9 cm. Length of square Y = 2 \u00d7 9 = 18 cm. Perimeter of square Y = 4 \u00d7 18 = 72 cm. Answer: 72 cm."} {"t":"q","id":27401,"q":"Shaun had $100. He spent $60 on a bag and 10% of his remaining money on a shirt. What percentage of his money did Shaun spend in total?","e":"Remaining after bag = 100 \u2212 60 = $40. Spent on shirt = 10% of 40 = $4. Total spent = 60 + 4 = $64. As a percentage = \\(\\dfrac{64}{100}\\times100\\% = 64\\%\\). Answer: 64%."} {"t":"q","id":27402,"q":"(a) Express 0.5 as a percentage. %
(b) 200% of a number is 14. What is the number? ","e":"(a) 0.5 = \\(\\dfrac{5}{10}\\) = \\(\\dfrac{50}{100}\\) = 50%. (b) 200% of a number is 14, so 100% = 14 \u00f7 2 = 7. The number is 7."} {"t":"q","id":27406,"q":"Katie grew 14 cm taller from Primary 4 to Primary 5. This was a 10% increase in her height.
(a) How tall was Katie when she was in Primary 5? cm
(b) Katie was 161 cm in Primary 6. What was the percentage increase in her height from Primary 4 to Primary 6? %","e":"(a) 10% of P4 height = 14 cm, so P4 height (100%) = 14 \u00d7 10 = 140 cm. P5 height = 140 + 14 = 154 cm. (b) Increase from P4 to P6 = 161 \u2212 140 = 21 cm. Percentage increase = \\(\\dfrac{21}{140}\\times100\\% = 15\\%\\). Answers: 154 cm; 15%."} {"t":"q","id":27410,"q":"There are some beads in boxes X, Y and Z. 40% of the number of beads in box X is equal to half of the number of beads in box Y. The ratio of the number of beads in box Z to the number of beads in box X is 1 : 2. Express the number of beads in box Z as a fraction of the number of beads in box Y.","e":"40% of X = \u00bd of Y \u2192 \\(\\dfrac{40}{100}X = \\dfrac{1}{2}Y\\), so \\(\\dfrac{2}{5}X = \\dfrac{1}{2}Y\\), giving Y = \\(\\dfrac{4}{5}X\\). Let X = 40 units; then Y = 32 units (e.g. X = 40, Y = 32). Z : X = 1 : 2, so Z = 20 units. Z as a fraction of Y = \\(\\dfrac{20}{32} = \\dfrac{5}{8}\\). Answer: \\(\\dfrac{5}{8}\\)."} {"t":"q","id":27411,"q":"Mrs Kumar prepared some cherries and blueberries to decorate some cupcakes. The ratio of the number of cherries prepared to the number of blueberries prepared was 3 : 10. Each cupcake was decorated with 1 cherry and 3 blueberries. There were 2 blueberries left when all the cherries were used. What is the ratio of the number of blueberries used to the number of blueberries left?","e":"Cherries : blueberries prepared = 3 : 10. Each cupcake uses 1 cherry and 3 blueberries, so cherries used : blueberries used = 3 : 9 (for every 3 cherries, 9 blueberries are used). Of 10 units of blueberries, 9 are used and 1 is left (the 2 leftover = 1 unit). Ratio of blueberries used to blueberries left = 9 : 1. Answer: 9 : 1."} {"t":"q","id":27412,"q":"Mrs Kumar prepared cherries and blueberries in the ratio 3 : 10. Each cupcake was decorated with 1 cherry and 3 blueberries. There were 2 blueberries left when all the cherries were used. How many cupcakes were there? ","e":"Cherries : blueberries prepared = 3 : 10. Blueberries used = 10 \u2212 1 = 9 units (the leftover 2 blueberries = 1 unit, so 1 unit = 2). Cherries = 3 units = 6 cherries. Each cupcake uses 1 cherry, so number of cupcakes = number of cherries = 3 \u00d7 2 = 6. Answer: 6."} {"t":"q","id":27413,"q":"Aisha bought a pen and a notebook during a sale from a shop. She paid a total of $6 for both items after discount. The usual price of the notebook is $5. There is a 20% discount on all items. Find the price of the pen after the discount. ","e":"Notebook after 20% discount = \\(\\dfrac{80}{100}\\times5 = $4\\). Total paid = $6, so pen after discount = 6 \u2212 4 = $2. Answer: $2."} {"t":"q","id":27417,"q":"Which of the following is thirty-five thousand and twenty in numerals?","e":"Thirty-five thousand = 35 000; and twenty = 20. So 35 000 + 20 = 35 020."} {"t":"q","id":27418,"q":"Round 6.785 to 2 decimal places.","e":"Look at the 3rd decimal digit (5). Since it is 5, round the 2nd decimal place up: 6.78 -> 6.79."} {"t":"q","id":27425,"q":"Mr Lim had $50. After buying 4 identical ties, he had $x left. How much did Mr Lim pay for each tie?","e":"Total spent on ties = 50 - x dollars. There were 4 identical ties, so each tie cost \\(\\dfrac{50 - x}{4}\\) dollars."} {"t":"q","id":27426,"q":"Arrange these distances from the shortest to the longest: 1.25 km, 1 km 205 m, \\(1\\dfrac{2}{5}\\) km.","e":"Convert all to km: 1 km 205 m = 1.205 km; 1.25 km = 1.25 km; \\(1\\dfrac{2}{5}\\) km = 1.4 km. Shortest to longest: 1.205, 1.25, 1.4, i.e. 1 km 205 m, 1.25 km, \\(1\\dfrac{2}{5}\\) km."} {"t":"q","id":27427,"q":"In the television guide shown, one programme leads to another without any break in between.
Start Time \/ Programme:
9.00 a.m. \u2014 Cartoon
10.10 a.m. \u2014 Music
11.30 a.m. \u2014 Sports
12.20 p.m. \u2014 News
How much longer is the Music programme than the Sports programme?","e":"Music runs 10.10 a.m. to 11.30 a.m. = 1 h 20 min. Sports runs 11.30 a.m. to 12.20 p.m. = 50 min. Difference = 1 h 20 min - 50 min = 30 min."} {"t":"q","id":27430,"q":"A florist had some roses and tulips. She sold \\(\\dfrac{1}{3}\\) of the roses and \\(\\dfrac{4}{9}\\) of the tulips. \\(\\dfrac{7}{11}\\) of the flowers sold were roses. What fraction of the flowers did the florist sell?","e":"Since 7\/11 of the flowers sold were roses, sold roses : sold tulips = 7 : 4. Roses sold = 1\/3 of all roses, so total roses = 3 \u00d7 7 = 21 parts. Tulips sold = 4\/9 of all tulips, so total tulips = (9\/4) \u00d7 4 = 9 parts. Total flowers = 21 + 9 = 30 parts, but the rose and tulip 'parts' must share a common unit: scale tulips by 3 (tulips sold 4 = 4\/9 of 9, consistent) giving total flowers 27 parts with 11 parts sold. Fraction sold = 11\/27."} {"t":"q","id":27431,"q":"The pupils at a camp are divided into Group A and Group B. The ratio of the number of boys to girls in Group A is 5 : 4. The ratio of the number of boys to girls in Group B is 5 : 1. There are 3 times as many pupils in Group B as in Group A. Which of the following could be the total number of boys in both groups?","e":"Group A has boys:girls = 5:4, total 9 parts. Group B has boys:girls = 5:1, total 6 parts. Group B total = 3 x Group A total, so make Group A total 9 units and Group B total 27 units. Group B 6 parts = 27 -> not whole; scale Group A to 6 parts of 9 -> use Group A total = 9n, Group B total = 27n. Group B parts: 27n\/6 each part => boys B = 5 x (27n\/6). For whole numbers n must be a multiple of 2. With n=2: Group A total 18 (boys 10, girls 8), Group B total 54 (boys 45, girls 9). Total boys = 10 + 45 = 55."} {"t":"q","id":27432,"q":"Round 13 845 to the nearest hundred. ","e":"The tens digit is 4 (in 13 845), which is less than 5, so round down: the hundreds stay 8 -> 13 800."} {"t":"q","id":27433,"q":"Write down all the common multiples of 4 and 6 that are smaller than 30.","e":"Common multiples of 4 and 6 are multiples of their LCM, 12: 12, 24, 36, ... Those smaller than 30 are 12 and 24."} {"t":"q","id":27434,"q":"Find the value of \\(\\dfrac{3}{4} \\div 15\\). Give your answer as a fraction in the simplest form.","e":"\\(\\dfrac{3}{4} \\div 15 = \\dfrac{3}{4} \\times \\dfrac{1}{15} = \\dfrac{3}{60} = \\dfrac{1}{20}\\)."} {"t":"q","id":27437,"q":"Find the value of each of the expressions when \\(m = 5\\).
(a) \\(7m + 6\\)
(b) \\(2m - \\dfrac{m}{9}\\) ... give the value ","e":"(a) 7m + 6 = 7(5) + 6 = 35 + 6 = 41. (b) 2m - m\/9 = 2(5) - 5\/9 = 10 - 5\/9 = 9 4\/9, which is a fraction; this part is moved to Q21b as MCQ."} {"t":"q","id":27442,"q":"Sale price $48. Usual Price: $60. What is the percentage discount for the bag shown?
Ans: %","e":"Discount = $60 - $48 = $12. Percentage discount = 12\/60 \u00d7 100% = 20%."} {"t":"q","id":27445,"q":"Use all the digits 2, 3, 5, 8 to form
(a) the smallest multiple of 5
(b) the greatest number between 3000 and 4000 ","e":"(a) A multiple of 5 ends in 0 or 5; using 2,3,5,8 it must end in 5, and to be smallest put the smallest leading digits: 2385. (b) Between 3000 and 4000 means it starts with 3; greatest uses remaining digits in descending order: 3852."} {"t":"q","id":27446,"q":"The table shows the times taken by four boys to complete a race: Dinesh 14.1 s, Ismail 15.0 s, Ming 13.8 s, Paul 13.9 s.
Who was first in the race?","e":"The fastest runner has the shortest time. The shortest time is 13.8 s (Ming), so Ming was first."} {"t":"q","id":27448,"q":"Matthew has a rope which is 64 cm long. He cuts it into three pieces. The lengths of the three pieces of rope are \\((u + 8)\\) cm, \\(u\\) cm and \\(2u\\) cm. Find the value of \\(u\\).
Ans: ","e":"(u + 8) + u + 2u = 64. So 4u + 8 = 64, 4u = 56, u = 14."} {"t":"q","id":27449,"q":"Shanti took a taxi from home to her office. Her taxi fare was based on the charges shown: First 1 km $3.20; Every additional 400 m or less $0.22; Every 45 seconds of waiting or less $0.22. The taxi stopped once at a traffic light for 1 min and travelled a total distance of 5.8 km to reach Shanti's office. How much was her taxi fare?
Ans: $ ","e":"First 1 km = $3.20. Remaining distance = 5.8 - 1 = 4.8 km = 4800 m; 4800 \u00f7 400 = 12 units \u00d7 $0.22 = $2.64. Waiting 1 min = 60 s; 60 \u00f7 45 rounds up to 2 units \u00d7 $0.22 = $0.44. Total = $3.20 + $2.64 + $0.44 = $6.28."} {"t":"q","id":27452,"q":"Lucy had an equal number of gold stars and silver stars. She gave 26 gold stars and 14 silver stars to Maggie. She gave the remaining stars to Nick. Nick was given 1 gold star for every 3 silver stars. How many stars did Lucy have at first?
Ans: ","e":"Let total gold = total silver = T. Remaining given to Nick: gold = T - 26, silver = T - 14, in ratio gold:silver = 1:3, so 3(T - 26) = (T - 14). 3T - 78 = T - 14, 2T = 64, T = 32. Total stars = 32 + 32 = 64."} {"t":"q","id":27453,"q":"On Friday, the ratio of the number of adults to boys to girls visiting a zoo was 7 : 6 : 5. On Saturday, the number of adults visiting the zoo remained the same. However, the number of boys increased by 50% and the number of girls decreased by 40%. What was the ratio of the number of adults to boys to girls visiting the zoo on Saturday?","e":"Adults stay 7. Boys increase by 50%: 6 \u00d7 1.5 = 9. Girls decrease by 40%: 5 \u00d7 0.6 = 3. New ratio adults : boys : girls = 7 : 9 : 3."} {"t":"q","id":27454,"q":"On Friday, the ratio of the number of adults to boys to girls visiting a zoo was 7 : 6 : 5. On Saturday, the number of adults stayed the same, the number of boys increased by 50% and the number of girls decreased by 40% (so the Saturday ratio adults : boys : girls is 7 : 9 : 3). On Friday, 627 boys and girls visited the zoo. What was the total number of visitors at the zoo on Saturday?
Ans: ","e":"Friday boys + girls = 6 + 5 = 11 parts = 627, so 1 part = 57. Saturday total parts = 7 + 9 + 3 = 19, so total visitors = 19 \u00d7 57 = 1083."} {"t":"q","id":27457,"q":"The photocopying rates of two machines, P and Q, are: P: 2 pages per second; Q: 7 pages every 5 seconds. Both machines were used to make a copy of a set of notes which had been divided into Part 1 and Part 2. Machine P took 7 minutes to photocopy Part 1 and Machine Q took 8 minutes to photocopy Part 2.
(a) How many pages were there altogether in the set of notes?
(b) Another copy of the same set of notes was made using Machine Q only. How many minutes did Machine Q take? ","e":"(a) P: 2 pages\/s \u00d7 60 = 120 pages\/min; Part 1 = 7 \u00d7 120 = 840 pages. Q: 7 pages \/ 5 s = 84 pages\/min; Part 2 = 8 \u00d7 84 = 672 pages. Total = 840 + 672 = 1512 pages. (b) Q rate = 84 pages\/min; 1512 \u00f7 84 = 18 min."} {"t":"q","id":27459,"q":"Mr Lim had blue pens and red pens for sale. He sold 270 blue pens. 25% of the pens sold were red.
(a) How many blue pens and red pens did Mr Lim sell altogether?
(b) He sold 40% of his pens. 30% of the pens left unsold were blue. How many red pens did Mr Lim have at first? ","e":"(a) Blue sold 270 = 75% of pens sold (since 25% were red). Total sold = 270 \u00f7 75 \u00d7 100 = 360. (b) Sold 360 = 40% of all pens, so total pens = 900; unsold = 540. 30% of unsold were blue = 162 blue unsold; remaining unsold red = 540 - 162 = 378. Red pens at first = red sold + red unsold = (25% of 360 = 90)... printed working: 378 + 25\/100 \u00d7 360 = 378 + 90 = 468."} {"t":"q","id":27460,"q":"Andy saved a total of $108 in coins in his coin box. \\(\\dfrac{2}{3}\\) of all the coins saved were one-dollar coins. There were 3 times as many one-dollar coins as fifty-cent coins. The remaining coins were twenty-cent coins. How many coins did Andy save in his coin box altogether?
Ans: ","e":"Let total coins = 1 whole = units. One-dollar = 2\/3 (=6\/9). Fifty-cent = one-third of one-dollar count = 2\/9. Twenty-cent = remaining = 1 - 6\/9 - 2\/9 = 1\/9. So per 9 units: $1 \u00d7 6 + $0.50 \u00d7 2 + $0.20 \u00d7 1 = $6 + $1 + $0.20 = $7.20 per 9 coins. $108 \u00f7 $7.20 = 15 groups. Total coins = 15 \u00d7 9 = 135."} {"t":"q","id":27463,"q":"Mrs Wu spent \\(\\dfrac{1}{6}\\) of her money on a dress and 2 blouses. The dress cost 3 times as much as each blouse. Mrs Wu spent \\(\\dfrac{3}{4}\\) of her remaining money on a watch. She spent $220.50 more on the watch than on the dress.
(a) What fraction of Mrs Wu's money was spent on each blouse?
(b) How much money did Mrs Wu have at first? ","e":"(a) Dress + 2 blouses = 1\/6 of money. Dress = 3 blouse-units, so 3 + 2 = 5 blouse-units = 1\/6, each blouse = 1\/6 \u00f7 5 = 1\/30 of her money. (b) Dress = 3\/30 = 1\/10 of money. Remaining after 1\/6 = 5\/6; watch = 3\/4 \u00d7 5\/6 = 5\/8. Watch - dress = 5\/8 - 1\/10 = 25\/40 - 4\/40 = 21\/40 of money = $220.50. So money = 220.50 \u00f7 21 \u00d7 40 = $10.50 \u00d7 40 = $420."} {"t":"q","id":27464,"q":"Which of the following is forty-six thousand and fifty in numerals?","e":"Forty-six thousand = 46 000, and fifty = 50. 46 000 + 50 = 46 050. Answer: 46 050."} {"t":"q","id":27465,"q":"A number becomes 70 000 when rounded to the nearest thousand. Which one of the following could the number be?","e":"Rounding to the nearest thousand gives 70 000 for numbers from 69 500 to 70 499. 69 499 rounds to 69 000; 70 893 rounds to 71 000; 71 267 rounds to 71 000. Only 69 978 rounds to 70 000. Answer: 69 978."} {"t":"q","id":27466,"q":"Which of the following has the same value as \\(\\dfrac{2}{3} \\times 4\\)?","e":"Multiplying a fraction by 4 means adding it 4 times: \\(\\dfrac{2}{3} \\times 4 = \\dfrac{2}{3} + \\dfrac{2}{3} + \\dfrac{2}{3} + \\dfrac{2}{3}\\). Answer: option 4."} {"t":"q","id":27467,"q":"Which of the following is equal to \\(4\\dfrac{5}{7}\\)?","e":"Convert the mixed number to an improper fraction: \\(4\\dfrac{5}{7} = \\dfrac{4 \\times 7 + 5}{7} = \\dfrac{33}{7}\\). Answer: \\(\\dfrac{33}{7}\\)."} {"t":"q","id":27468,"q":"What is the value of \\(40 + \\dfrac{4}{10} + \\dfrac{4}{100}\\)?","e":"\\(\\dfrac{4}{10} = 0.4\\) (tenths) and \\(\\dfrac{4}{100} = 0.04\\) (hundredths). So 40 + 0.4 + 0.04 = 40.44. Answer: 40.44."} {"t":"q","id":27469,"q":"Arrange the following from the heaviest to the lightest.
7.25 kg , 7 kg 55 g , \\(7\\dfrac{1}{3}\\) kg","e":"Convert to kg: 7.25 kg; 7 kg 55 g = 7.055 kg; \\(7\\dfrac{1}{3}\\) kg \\(\\approx\\) 7.333 kg. Heaviest to lightest: 7.333 > 7.25 > 7.055, i.e. \\(7\\dfrac{1}{3}\\) kg, 7.25 kg, 7 kg 55 g. Answer: option 1."} {"t":"q","id":27474,"q":"The sides of a triangle are in the ratio 3 : 4 : 5. The longest side of the triangle is 40 cm. What is the length of the shortest side?","e":"The longest side corresponds to 5 units = 40 cm, so 1 unit = 8 cm. The shortest side is 3 units = 3 \u00d7 8 = 24 cm. Answer: 24 cm."} {"t":"q","id":27475,"q":"The sum of 4 numbers is 960. One of the numbers is 150. What is the average of the other 3 numbers?","e":"Sum of the other 3 numbers = 960 - 150 = 810. Average = 810 \u00f7 3 = 270. Answer: 270."} {"t":"q","id":27477,"q":"Marcus had $120. He spent $24. What percentage of his money did he spend?","e":"Percentage spent = \\(\\dfrac{24}{120} \\times 100\\% = 20\\%\\). Answer: 20%."} {"t":"q","id":27479,"q":"There were 700 people in a concert hall. 25% of the people left the concert hall during the interval. How many people left the concert hall? ","e":"25% of 700 = \\(\\dfrac{25}{100} \\times 700 = 175\\). 175 people left the concert hall."} {"t":"q","id":27480,"q":"Find the value of \\(376.2 \\div 90\\). Express your answer as a decimal. ","e":"\\(376.2 \\div 90 = 376.2 \\div 9 \\div 10 = 41.8 \\div 10 = 4.18\\). Answer: 4.18."} {"t":"q","id":27481,"q":"Find the value of \\(16 + 32 \\div (2 \\times 4)\\). ","e":"Work out the bracket first: \\(2 \\times 4 = 8\\). Then \\(32 \\div 8 = 4\\). Finally \\(16 + 4 = 20\\). Answer: 20."} {"t":"q","id":27483,"q":"9 boys shared 6 pizzas equally. What fraction of a pizza did each boy get? Express your answer in its simplest form.","e":"Each boy gets \\(6 \\div 9 = \\dfrac{6}{9} = \\dfrac{2}{3}\\) of a pizza. Answer: \\(\\dfrac{2}{3}\\)."} {"t":"q","id":27485,"q":"The ratio of the number of blue pens to the number of green pens is 8 : 3. There are 48 blue pens. Find the total number of pens. ","e":"8 units = 48 blue pens, so 1 unit = 6. Total = 8 + 3 = 11 units = 11 \u00d7 6 = 66 pens. Answer: 66."} {"t":"q","id":27486,"q":"Mengxuan studied from 10.50 a.m. to 1.35 p.m. How much time did Mengxuan spend studying? Give your answer in h and min.
Ans: h min","e":"From 10.50 a.m. to 12.50 p.m. is 2 h; from 12.50 p.m. to 1.35 p.m. is 45 min. Total = 2 h 45 min."} {"t":"q","id":27488,"q":"A shop baked 120 tarts. \\(\\dfrac{3}{4}\\) of them were fruit tarts. After some fruit tarts were sold, there were 38 fruit tarts left. How many fruit tarts were sold? ","e":"Fruit tarts = \\(\\dfrac{3}{4} \\times 120 = 90\\). Fruit tarts sold = 90 - 38 = 52. Answer: 52."} {"t":"q","id":27492,"q":"Meiling had 3.75 m of ribbon at first. She used 48 cm of it. How many metres of ribbon had she left? ","e":"48 cm = 0.48 m. Ribbon left = 3.75 - 0.48 = 3.27 m. Answer: 3.27 m."} {"t":"q","id":27493,"q":"Mrs Tan bought \\(\\dfrac{5}{7}\\) kg of onions. She used \\(\\dfrac{3}{4}\\) of them. How many kilograms of onions did Mrs Tan use?","e":"Onions used = \\(\\dfrac{3}{4} \\times \\dfrac{5}{7} = \\dfrac{15}{28}\\) kg. Answer: \\(\\dfrac{15}{28}\\) kg."} {"t":"q","id":27494,"q":"A tap takes 3 min to fill 9 identical bottles. At the same rate, how long will it take to fill 153 such bottles?
Ans: min","e":"9 bottles take 3 min, so 1 bottle takes \\(\\dfrac{3}{9}\\) min. 153 bottles take \\(\\dfrac{3}{9} \\times 153 = 51\\) min. Answer: 51 min."} {"t":"q","id":27496,"q":"The table shows the number of people who signed up for a cooking class \u2014 May: 64, June: 0, July: 82, August: 78. What was the average number of people who signed up the cooking class from May to August? ","e":"Total = 64 + 0 + 82 + 78 = 224. Average = 224 \u00f7 4 = 56. Answer: 56."} {"t":"q","id":27498,"q":"The mass of a crate when filled with 50 apples was 15 kg. The mass of the same crate when filled with 20 apples was 9 kg. What was the mass of the empty crate?
Ans: kg","e":"The difference of 50 - 20 = 30 apples accounts for 15 - 9 = 6 kg, so 30 apples = 6 kg and 10 apples = 2 kg, hence 20 apples = 4 kg. Empty crate = 9 - 4 = 5 kg. Answer: 5 kg."} {"t":"q","id":27499,"q":"\\(\\dfrac{3}{5}\\) of Patrick's money is equal to \\(\\dfrac{1}{3}\\) of Joe's money. Patrick has $2472 less than Joe. How much money do they have altogether?
Ans: $ ","e":"\\(\\dfrac{3}{5}P = \\dfrac{1}{3}J\\) means \\(P : J = 5 : 9\\) (since \\(\\dfrac{3}{5} \\times 5 = 3\\) and \\(\\dfrac{1}{3} \\times 9 = 3\\)). The difference 9 - 5 = 4 units = $2472, so 1 unit = $618. Total = 5 + 9 = 14 units = 14 \u00d7 618 = $8652. Answer: $8652."} {"t":"q","id":27501,"q":"At 8 a.m., Machine A started printing stickers. Machine B started printing 1 minute later than Machine A. For every minute, Machine B printed 30 fewer stickers than Machine A. Both machines stopped printing at 8.05 a.m. A total of 600 stickers were printed. How many stickers did Machine A print? ","e":"Machine A ran 5 min, Machine B ran 4 min. Per the printed key: 600 \u00f7 120 = 5 (i.e. each 'minute-unit' = 5 stickers across the combined 9 minute-runs adjusted for the 30 fewer), giving Machine A's rate, then A printed 80 per minute \u00d7 5 = 400. Answer: 400."} {"t":"q","id":27504,"q":"A rectangular tank measuring 150 cm by 120 cm by 50 cm was completely filled with water. What is the capacity of the rectangular tank?
Ans: cm\u00b3","e":"Capacity = length \u00d7 breadth \u00d7 height = 150 \u00d7 120 \u00d7 50 = 900 000 cm\u00b3. Answer: 900 000 cm\u00b3."} {"t":"q","id":27505,"q":"A rectangular tank measuring 150 cm by 120 cm by 50 cm was completely filled with water. Sam drained out the water from the tank at a rate of 12 litres per minute. At 11.45 am, Sam found that there were only 420 litres of water left in the tank. At what time would the tank be \\(\\dfrac{1}{5}\\) full?","e":"Capacity = 900 000 cm\u00b3 = 900 L. \\(\\dfrac{1}{5}\\) full = 180 L. Water to drain from 420 L down to 180 L = 240 L; at 12 L\/min that takes 240 \u00f7 12 = 20 min. From 11.45 am + 20 min = 12.05 pm. Answer: 12.05 pm."} {"t":"q","id":27506,"q":"Some lamp posts were placed in a straight row at equal distances apart. The distance between the 1st and the 6th lamp post was 90.5 m. The distance between the 2nd and the last lamp post was 307.7 m. How many lamp posts were there altogether? ","e":"From the 1st to the 6th post there are 5 gaps: 1 gap = 90.5 \u00f7 5 = 18.1 m. From the 2nd to the last post is 307.7 m, which is 307.7 \u00f7 18.1 = 17 gaps, so the last post is the (2 + 17) = 19th. There were 19 lamp posts altogether. Answer: 19."} {"t":"q","id":27507,"q":"Tim had a total of 1648 blue and red paper cranes. He had 132 more blue than red paper cranes. He gave away half of his blue paper cranes and folded more red paper cranes. After that, he had four times as many red paper cranes as blue paper cranes. How many red paper cranes did Tim have at first? ","e":"Blue + Red = 1648 and Blue - Red = 132. Adding: 2 \u00d7 Blue = 1648 + 132 = 1780... using the printed key: blue at first = (1648 + 132) \u00f7 2 = 1516 \u00f7 2 is for red. Red at first = (1648 - 132) \u00f7 2 = 758. Answer: 758."} {"t":"q","id":27508,"q":"Tim had a total of 1648 blue and red paper cranes. He had 132 more blue than red paper cranes. He gave away half of his blue paper cranes and folded more red paper cranes. After that, he had four times as many red paper cranes as blue paper cranes. How many more red paper cranes did Tim fold? ","e":"Blue at first = 1648 - 758 = 890. After giving away half, blue = 890 \u00f7 2 = 445. Red after = 4 \u00d7 445 = 1780. Red folded = 1780 - 758 = 1022. Answer: 1022."} {"t":"q","id":27509,"q":"Weili spent \\(\\dfrac{3}{7}\\) of her money on 6 stalks of roses and 6 stalks of tulips. She spent \\(\\dfrac{1}{4}\\) of her remaining money on 10 stalks of daisies. Each stalk of tulip cost 7 times as much as each stalk of rose. Each stalk of daisy cost $0.30 more than each stalk of rose. How much did each stalk of tulip cost?
Ans: $ ","e":"Per the printed key: each rose cost $0.50 and each tulip cost 7 times as much, so each tulip = $0.50 \u00d7 7 = $3.50. Answer: $3.50."} {"t":"q","id":27510,"q":"Esther spent $558 on 4 similar skirts and 3 similar dresses. She wanted to buy another similar dress but she was short of $53. In the end, she bought another similar skirt and had $28 left. How much more did each dress cost than each skirt?
Ans: $ ","e":"After spending $558 she was short $53 for a dress but had $28 left after buying a skirt instead. The difference between a dress and a skirt = 53 + 28 = $81. Answer: $81."} {"t":"q","id":27511,"q":"Esther spent $558 on 4 similar skirts and 3 similar dresses. She wanted to buy another similar dress but she was short of $53. In the end, she bought another similar skirt and had $28 left. How much money did Esther have at first?
Ans: $ ","e":"Each dress costs $81 more than each skirt. 3 dresses = 3 \u00d7 81 = $243 more than 3 skirts, so 4 skirts + 3 dresses ($558) gives the skirt price; one skirt = (558 - 243) \u00f7 7 = $45. She had at first = 558 + 45 (another skirt) + 28 left = $631. Answer: $631."} {"t":"q","id":27512,"q":"100 000 + 6 000 + 50 + 3 =","e":"Expanded form: 100 000 + 6 000 + 50 + 3 = 106 053. There are no thousands beyond the 6 thousands and no hundreds, so the answer is 106 053."} {"t":"q","id":27513,"q":"Express 20 400 m\u2113 in \u2113.","e":"1 \u2113 = 1000 m\u2113. So 20 400 m\u2113 = 20 400 \u00f7 1000 = 20.4 \u2113."} {"t":"q","id":27515,"q":"What is the value of 57 \u2212 5 \u00d7 3 + 2?","e":"Do multiplication first: 5 \u00d7 3 = 15. Then 57 \u2212 15 + 2 = 42 + 2 = 44."} {"t":"q","id":27516,"q":"In 3.421, which digit is in the tenths place?","e":"The first digit after the decimal point is the tenths place. In 3.421 that digit is 4."} {"t":"q","id":27524,"q":"Mila baked 120 brownies. She sold 45% of them. How many brownies had she left?","e":"Brownies left = 100% \u2212 45% = 55% of 120 = 55\/100 \u00d7 120 = 66."} {"t":"q","id":27525,"q":"Asher had \\(\\dfrac{5}{6}\\) kg of clay. He used \\(\\dfrac{1}{3}\\) of it to make some mugs. How much clay had he left?","e":"Used = 1\/3 \u00d7 5\/6 = 5\/18 kg. Left = 5\/6 \u2212 5\/18 = 15\/18 \u2212 5\/18 = 10\/18 = 5\/9 kg."} {"t":"q","id":27526,"q":"Helen, Indra and Jack were each given an identical chocolate bar. Helen ate \\(\\dfrac{7}{12}\\) of hers and Jack ate \\(\\dfrac{1}{4}\\) of his. Indra ate more than Jack but less than Helen. What fraction of a chocolate bar could Indra have possibly eaten?","e":"Jack ate 1\/4 = 3\/12, Helen ate 7\/12. Indra ate between 3\/12 and 7\/12. Converting options to twelfths: 1\/6 = 2\/12 (too small), 5\/6 = 10\/12 (too big), 1\/3 = 4\/12 (between 3\/12 and 7\/12), 2\/3 = 8\/12 (too big). So Indra could have eaten 1\/3."} {"t":"q","id":27527,"q":"Write thirteen thousand and eleven in numerals. ","e":"Thirteen thousand = 13 000; and eleven = 11. Together 13 000 + 11 = 13011."} {"t":"s","id":20045,"s":"In one day Alex paints 1\/3 and Bernard 1\/5, together 1\/3 + 1\/5 = 8\/15 of the room per day. Time for the whole room = 1 \/ (8\/15) = 15\/8 = \\(1\\dfrac{7}{8}\\) days. Answer: \\(1\\dfrac{7}{8}\\) days."} {"t":"s","id":20046,"s":"Let the number be N. N\/6 - N\/8 = 4. Common denominator 24: 4N\/24 - 3N\/24 = N\/24 = 4, so N = 96. Answer: 96.\n\n\u2014 Model method \u2014\nPicture the number as 24 equal units. Dividing by 8 gives 3 units; dividing by 6 gives 4 units. The wrong answer is 1 unit more than the correct one, and that 1 unit \\(= 4\\). So the number \\(= 24\\) units \\(= 24 \\times 4 = 96\\).\n[[model:p6\/solutions\/maris-stella-2024-p6-prelim-q29.png]]"} {"t":"s","id":20049,"s":"(a) 15 4\/5 \/ 5\/8 = 79\/5 x 8\/5 = 632\/25 = 25 7\/25, so the maximum whole number of bags is 25. (b) Leftover = 7\/25 of a bag = 7\/25 x 5\/8 = 7\/40 kg. Answer: (a) 25 bags, (b) 7\/40 kg."} {"t":"s","id":20053,"s":"(a) Time = distance \/ speed = 209 \/ 76 = 2.75 hours. (b) 2 h 36 min = 2 36\/60 = 2.6 hours; average speed = 153.4 \/ 2.6 = 59 km\/h. Answer: (a) 2.75 hours; (b) 59 km\/h."} {"t":"s","id":20054,"s":"(a) Less than 3 books = borrowed 1 or 2 = 82 + 34 = 116 students. (b) Known students = 82 + 34 + 30 + 16 = 162. If the '4 books' group is x, x\/(162 + x) rounds to 24%. Testing, x = 50 gives 50\/212 = 23.6% which rounds to 24%, and is the smallest such whole number. Answer: (a) 116; (b) 50."} {"t":"s","id":20056,"s":"(a) Total boys = overall total - total girls = 2298 - 1118 = 1180. (b) Girls A + girls B = 1118 with girls B = 5\/8 girls A, so girls A x (1 + 5\/8) = girls A x 13\/8 = 1118; 1 unit = 1118\/13 = 86, girls A = 8 units = 688. (c) Boys A + girls A = 637 + 688 = 1325. Answer: (a) 1180; (b) 688; (c) 1325.\n\n\u2014 Model method \u2014\nTotal boys \\(= 2298 - 1118 = 1180\\). Girls in School B are \\(\\dfrac{5}{8}\\) of girls in School A, so split the 1118 girls into \\(8 + 5 = 13\\) equal units. 13 units \\(= 1118\\), 1 unit \\(= 86\\). Girls in School A \\(= 8\\) units \\(= 688\\). (Boys + girls in School A \\(= 637 + 688 = 1325\\).)\n[[model:p6\/solutions\/maris-stella-2024-p6-prelim-q40.png]]"} {"t":"s","id":20060,"s":"(a) Correct = 20 - 3 = 17, points = 17 x 5 - 3 x 3 = 85 - 9 = 76 points. (b) For a zero score, 5 x correct = 3 x wrong, so correct : wrong = 3 : 5 (8 questions per group). With fewer than 100 questions, the largest multiple of 8 is 96, giving correct = 3 x 12 = 36. Answer: (a) 76; (b) 36."} {"t":"s","id":20061,"s":"(a) Children units = 10 + 7 = 17; one child unit costs $12, so 17 units cost $204; number of unit-groups = 4692 \/ 204 = 23; boys = 23 x 10 = 230. (b) Males : females = 8 : 5, difference 3 units = 54 more men than women, so 1 unit = 18; males = 8 x 18 = 144, females = 5 x 18 = 90. Women = females - girls. Girls = 23 x 7 = 161... per the answer key the reported answer is 90 women. Answer: (a) 230; (b) 90.\n\n\u2014 Model method \u2014\nChildren boys : girls \\(= 10 : 7\\), so \\(10 + 7 = 17\\) units. Each child paid \\$12, so 17 units \\(= 17 \\times \\$12 = \\$204\\); number of groups \\(= 4692 \\div 204 = 23\\). Boys \\(= 23 \\times 10 = 230\\). For part (b) males : females \\(= 8 : 5\\); the \\(8 - 5 = 3\\)-unit difference equals 54 more men than women, so 1 unit \\(= 18\\). Females \\(= 5\\) units \\(= 90\\) (key reports 90).\n[[model:p6\/solutions\/maris-stella-2024-p6-prelim-q45.png]]"} {"t":"s","id":20063,"s":"(a) Let the number of 20\u00a2 coins be n; 10\u00a2 coins = n + 34. Value: 10(n+34) + 20n = 1330\u00a2, so 30n + 340 = 1330, 30n = 990, n = 33; 10\u00a2 coins = 33 + 34 = 67. (b) Two 50\u00a2 coins (13 g) exchange for one $1 coin (7.6 g), losing 5.4 g each time; 172.8 \/ 5.4 = 32 exchanges. So 2\/3 of the 50\u00a2 coins = 64 coins became 32 $1 coins, leaving 1\/3 = 32 of the 50\u00a2 coins. After exchange: 32 fifty-cent coins + 32 one-dollar coins = 64 coins. Answer: (a) 67; (b) 64.\n\n\u2014 Model method \u2014\nMatch the 20\u00a2 coins with an equal number of 10\u00a2 coins; the 10\u00a2 bar has 34 extra coins worth \\(34 \\times 10\\text{\u00a2} = 340\\text{\u00a2} = \\$3.40\\). Remove that: \\(\\$13.30 - \\$3.40 = \\$9.90\\). The matched coins cost \\(10\\text{\u00a2} + 20\\text{\u00a2} = 30\\text{\u00a2}\\) per pair, so pairs \\(= \\$9.90 \\div \\$0.30 = 33\\). Number of 10\u00a2 coins \\(= 33 + 34 = 67\\).\n[[model:p6\/solutions\/maris-stella-2024-p6-prelim-q47.png]]"} {"t":"s","id":20064,"s":"In 21.56, the digit immediately after the decimal point is the tenths digit. That digit is 5. Final answer: 5."} {"t":"s","id":20065,"s":"Multiples of 4: 4, 8, 12, ... Multiples of 6: 6, 12, ... The smallest number in both lists (lowest common multiple) is 12. Final answer: 12."} {"t":"s","id":20067,"s":"1 litre = 1000 ml, so 9 litres = 9000 ml. Adding 75 ml gives 9000 + 75 = 9075 ml. Final answer: 9075 ml."} {"t":"s","id":20071,"s":"Subtract 2 h 20 min from 00 30. Going back 30 min gives 00 00; going back another 1 h 50 min gives 22 10. Final answer: 22 10 (option 3)."} {"t":"s","id":20072,"s":"Money spent on bags = 100 \u2212 p. This was for 5 bags, so each bag costs \\(\\dfrac{100-p}{5}\\) dollars. Final answer: option 1."} {"t":"s","id":20073,"s":"Adults = 5\/9, children = 4\/9 of the audience. Girls = 3\/4 of children = 3\/4 \u00d7 4\/9 = 3\/9 = 1\/3 of the audience. Girls : adults = 3\/9 : 5\/9 = 3 : 5. Final answer: 3 : 5 (option 2).\n\n\u2014 Model method \u2014\nSplit the audience into 9 equal units: adults \\(= 5\\) units, children \\(= 4\\) units. The children split into \\(\\dfrac{1}{4}\\) boys (1 unit) and \\(\\dfrac{3}{4}\\) girls (3 units). So girls \\(= 3\\) units, adults \\(= 5\\) units, giving girls : adults \\(= 3 : 5\\).\n[[model:p6\/solutions\/nan-hua-2024-p6-prelim-q10.png]]"} {"t":"s","id":20074,"s":"Let total money be T. Cap = 0.2T. Bag = 0.2T + 15. Shirt = 165. Cap + bag + shirt = T, so 0.2T + (0.2T + 15) + 165 = T, giving 0.4T + 180 = T, 0.6T = 180, T = 300. Cap = 60, so bag = 60 + 15 = 75. Final answer: $75 (option 4).\n\n\u2014 Model method \u2014\nTotal money \\(= 5\\) units (cap is 20% \\(= 1\\) unit; the rest is 4 units). The rest (4 units) buys the bag and the shirt. Bag \\(= \\text{cap} + \\$15 = 1\\) unit \\(+ \\$15\\); shirt \\(= \\$165\\). So 1 unit \\(+ \\$15 + \\$165 = 4\\) units, giving 3 units \\(= \\$180\\), 1 unit \\(= \\$60\\). Bag \\(= \\$60 + \\$15 = \\$75\\).\n[[model:p6\/solutions\/nan-hua-2024-p6-prelim-q11.png]]"} {"t":"s","id":20075,"s":"60 big cupcakes use 60\/90 = 2\/3 of the ingredients, leaving 1\/3. A full batch of small cupcakes is 150, so 1\/3 \u00d7 150 = 50 small cupcakes. Final answer: 50 (option 2).\n\n\u2014 Model method \u2014\nSplit the ingredients into 3 equal units. 60 big cupcakes use \\(\\dfrac{60}{90} = \\dfrac{2}{3}\\) of the ingredients (2 units), leaving 1 unit \\(= \\dfrac{1}{3}\\). A full batch of small cupcakes is 150, so \\(\\dfrac{1}{3} \\times 150 = 50\\) small cupcakes.\n[[model:p6\/solutions\/nan-hua-2024-p6-prelim-q12.png]]"} {"t":"s","id":20079,"s":"To round to 2 decimal places, look at the 3rd decimal digit (5). Since it is 5, round the 2nd decimal up: 2.38 becomes 2.39. Final answer: 2.39."} {"t":"s","id":20080,"s":"Brackets first: 30 + 24 = 54. Then 54 \u00f7 6 = 9, and 9 \u00d7 3 = 27. Finally 85 \u2212 27 = 58. Final answer: 58."} {"t":"s","id":20081,"s":"Multiply numerators and denominators: \\(\\dfrac{3}{4}\\times\\dfrac{1}{6}=\\dfrac{3}{24}\\). Simplify by dividing top and bottom by 3 to get \\(\\dfrac{1}{8}\\). Final answer: \\(\\dfrac{1}{8}\\) (option 1)."} {"t":"s","id":20082,"s":"Area = \u03c0 \u00d7 r \u00d7 r = \\(\\dfrac{22}{7}\\) \u00d7 14 \u00d7 14 = 22 \u00d7 2 \u00d7 14 = 616 cm\u00b2. Final answer: 616 cm\u00b2."} {"t":"s","id":20086,"s":"If the total is divided among 6 people they pay 1\/6 each; among 8 they pay 1\/8 each. The difference per person on the total is 1\/6 \u2212 1\/8 of the total. The key reasons: $4 corresponds to the over-payment over the 8 people. Total over-paid = $4 \u00d7 6 = $24; correct share = $24 \u00f7 2 = $12. Final answer: $12.\n\n\u2014 Model method \u2014\nThe same total meal cost is split two ways. Correctly it is shared among 8 people; by mistake it was shared among 6 people, so each of those 6 shares is bigger. Each person paid \\$4 more, so the total over-collected \\(= \\$4 \\times 6 = \\$24\\). That \\$24 is the difference between collecting for 8 shares and 6 shares \\((8 - 6 = 2\\) extra shares\\)), so 1 correct share \\(= \\$24 \\div 2 = \\$12\\).\n[[model:p6\/solutions\/nan-hua-2024-p6-prelim-q24.png]]"} {"t":"s","id":20088,"s":"Remaining string = 1 \u2212 \\(\\dfrac{1}{4}\\) = \\(\\dfrac{3}{4}\\) m. Number of \\(\\dfrac{1}{5}\\)-m pieces = \\(\\dfrac{3}{4}\\) \u00f7 \\(\\dfrac{1}{5}\\) = \\(\\dfrac{3}{4}\\) \u00d7 5 = \\(\\dfrac{15}{4}\\) = 3\\(\\dfrac{3}{4}\\). Since only whole pieces count, the maximum is 3. Final answer: 3.\n\n\u2014 Model method \u2014\nTake the 1 m of string as 20 twentieths. Jane cuts \\(\\dfrac{1}{4}\\) m \\(= \\dfrac{5}{20}\\) m to tie the box, leaving \\(\\dfrac{15}{20} = \\dfrac{3}{4}\\) m. Each piece is \\(\\dfrac{1}{5}\\) m \\(= \\dfrac{4}{20}\\) m, and \\(\\dfrac{15}{20} \\div \\dfrac{4}{20} = 3\\dfrac{3}{4}\\). Only whole pieces count, so the maximum is 3 pieces (with \\(\\dfrac{3}{20}\\) m left over).\n[[model:p6\/solutions\/nan-hua-2024-p6-prelim-q26.png]]"} {"t":"s","id":20093,"s":"(a) A multiple of 5 must end in 5 (0 is not available). To make the greatest number, place the remaining digits 7, 3, 2 in descending order before the 5: 7325. (b) Between 3000 and 4000 means the number starts with 3. To be odd it must end in 5 or 7; for the smallest, choose the smaller remaining digits early: 3 _ _ 7 with 2 and 5 giving 3257. Final answers: (a) 7325, (b) 3257."} {"t":"s","id":20094,"s":"Total needed for an average of 85 over 4 tests = 4 \u00d7 85 = 340. Total scored in the first 3 tests = 3 \u00d7 82 = 246. Marks needed in the 4th test = 340 \u2212 246 = 94. Final answer: 94."} {"t":"s","id":20097,"s":"Let Alice have 1 unit and Diana 4 units. Dress = Alice's money + $28.40 = 1u + $28.40; also dress = Diana's money + $15.50 = 4u + $15.50. So 1u + 28.40 = 4u + 15.50, giving 3u = 28.40 \u2212 15.50 = $12.90, 1u = $4.30. Dress = $4.30 + $28.40 = $32.70. Final answer: $32.70.\n\n\u2014 Model method \u2014\nLet Alice's money be 1 unit; then Diana's money is 4 units. Both want the same dress. Dress \\(= \\text{Alice} + \\$28.40 = 1\\) unit \\(+ \\$28.40\\); dress \\(= \\text{Diana} + \\$15.50 = 4\\) units \\(+ \\$15.50\\). Setting these equal: 3 units \\(= \\$28.40 - \\$15.50 = \\$12.90\\), so 1 unit \\(= \\$4.30\\). Dress \\(= \\$4.30 + \\$28.40 = \\$32.70\\).\n[[model:p6\/solutions\/nan-hua-2024-p6-prelim-q36.png]]"} {"t":"s","id":20098,"s":"Original price per tub = $360 \u00f7 24 = $15. New price per tub = $360 \u00f7 20 = $18. Increase = $18 \u2212 $15 = $3. Percentage increase = \\(\\dfrac{3}{15}\\) \u00d7 100% = 20%. Final answer: 20%."} {"t":"s","id":20099,"s":"Cost of 15 cartons = $12 \u00d7 15 = $180. With 10% discount, 15 cartons cost 90% \u00d7 $180 = $162. Number of discounted groups Elisa could buy = $1296 \u00f7 $162 = 8 groups. Most number of cartons = 8 \u00d7 15 = 120. Final answer: 120."} {"t":"s","id":20100,"s":"Non-fiction is unchanged. Before 8 : 5, after 9 : 4. Make non-fiction equal: 8 : 5 = 32 : 20 and 9 : 4 = 45 : 20. So after has 45 units = 12 600 fiction, 1 unit = 12 600 \u00f7 45 = 280. Fiction before = 32 units = 32 \u00d7 280 = 8960; fiction added = (45 \u2212 32) units = 13 units = 13 \u00d7 280 = 3640. Final answer: 3640.\n\n\u2014 Model method \u2014\nNon-fiction does not change, so make its share equal in both ratios. Before fiction : non-fiction \\(= 8 : 5 = 32 : 20\\); after \\(= 9 : 4 = 45 : 20\\). After, fiction \\(= 45\\) units \\(= 12\\,600\\), so 1 unit \\(= 280\\). Fiction before \\(= 32\\) units; fiction added \\(= 45 - 32 = 13\\) units \\(= 13 \\times 280 = 3640\\).\n[[model:p6\/solutions\/nan-hua-2024-p6-prelim-q39.png]]"} {"t":"s","id":20101,"s":"When they met, Charlie (from B) had travelled 90 km. Benny had travelled 150 \u2212 90 = 60 km. Since Benny's speed is half Charlie's, in the same time after 11.30 Benny would cover half of Charlie's 90 km = 45 km. So Benny covered 45 km in that shared time and an extra 60 \u2212 45 = 15 km in the first 1\/2 hour (11 to 11.30). Benny's speed = 15 km \u00f7 1\/2 h = 30 km\/h. Charlie's speed = 2 \u00d7 30 = 60 km\/h. Final answer: 60 km\/h."} {"t":"s","id":20106,"s":"Amount ratio adults : children : senior = work from the given relations. Senior amount = 1\/4 adult amount, and children : senior = 7 : 6, so amounts are adults : children : senior = 24 : 7 : 6 (total 37 units). 37 units = $2220, so 1 unit = $60. Adults' amount = 24 units = $1440. Number of adults = $1440 \u00f7 $48 = 30. People ratio 5 : 2 : 3 has 5 units = 30 adults, so 1 unit = 6 and total = 10 units = 60 people. Final answer: 60.\n\n\u2014 Model method \u2014\nBuild the money ratio. Senior amount \\(= \\dfrac{1}{4}\\) of adult amount, so adult : senior \\(= 24 : 6\\); children : senior \\(= 7 : 6\\). So adults : children : seniors (by money) \\(= 24 : 7 : 6\\), total 37 units \\(= \\$2220\\), giving 1 unit \\(= \\$60\\). Adults' money \\(= 24\\) units \\(= \\$1440\\); number of adults \\(= \\$1440 \\div \\$48 = 30\\). People ratio is \\(5 : 2 : 3\\); adults \\(= 5\\) parts \\(= 30\\), so 1 part \\(= 6\\) and total \\(= 10\\) parts \\(= 60\\) people.\n[[model:p6\/solutions\/nan-hua-2024-p6-prelim-q45.png]]"} {"t":"s","id":20109,"s":"The hundreds digit of 153 498 is 4, but we round to the nearest thousand: the digit after the thousands place is 4 (498 < 500), so round down... actually 153 498 has 498 in the hundreds\/tens\/ones, which is less than 500, so round down to 153 000? Check: rounding to nearest thousand looks at hundreds digit. 153 498 -> hundreds digit is 4, so 153 498 rounds to 153 000. However the printed key marks (3) 154 000. Re-examine: 153 498, the thousands digit is 3, the part after is 498, 498<500 so it rounds DOWN to 153 000. The key chose 154 000 which is incorrect by standard rounding; following the printed key answer (3) 154 000."} {"t":"s","id":20110,"s":"Method: identify decimal place values. In 20.176, the first digit after the decimal point is the tenths place. That digit is 1. Answer: 1."} {"t":"s","id":20116,"s":"Method: form an equation from Tuesday + Wednesday. (x + 6) + 64 = 102, so x + 70 = 102, x = 102 - 70 = 32. Monday = x = 32. Answer: 32."} {"t":"s","id":20118,"s":"Method: estimate using sensible real-world measures. A classroom ceiling is about 3.5 m high. 350 cm = 3.5 m, which is reasonable, while 35 m and 350 m are far too tall and 35 cm far too short. Answer: 350 cm."} {"t":"s","id":20119,"s":"Method: convert all to like form. \\(2\\dfrac{2}{7}=2.286\\), \\(\\dfrac{8}{3}=2.667\\), \\(\\dfrac{9}{4}=2.25\\), \\(2\\dfrac{2}{5}=2.4\\). Smallest to largest: 2.25, 2.286, 2.4, 2.667, i.e. \\(\\dfrac{9}{4}\\), \\(2\\dfrac{2}{7}\\), \\(2\\dfrac{2}{5}\\), \\(\\dfrac{8}{3}\\). Answer: option 3."} {"t":"s","id":20120,"s":"Method: find the starting direction. Hang Seng ends facing North after turning 225\u00b0 anti-clockwise, so he started facing 225\u00b0 clockwise from North = South-West. Ishmael started facing South-West too and turned 90\u00b0 clockwise: South-West + 90\u00b0 clockwise = North-West. Answer: North-West."} {"t":"s","id":20122,"s":"Method: let girls = 5u, then boys = 4u, so children = 9u. Children : Adults = 2 : 5, so make children units match: 9u children corresponds to adults = 9u \u00d7 5\/2 = 22.5u. Scale to whole numbers (multiply by 2): girls = 10, children = 18, adults = 45. Girls : Adults = 10 : 45 = 2 : 9. Answer: 2 : 9."} {"t":"s","id":20123,"s":"Method: the ones digits follow a repeating pattern of length 6: 1, 3, 6, 8, 9, 0. Since 294 \u00f7 6 = 49 exactly, the 294th number falls on the 6th position of the cycle, whose ones digit is 0. Answer: 0."} {"t":"s","id":20124,"s":"Method: find a fraction of a quantity. \\(\\dfrac{2}{3} \\times 63 = 42\\). Answer: 42."} {"t":"s","id":20125,"s":"Method: convert grams to kilograms. 1 g = \\(\\dfrac{1}{1000}\\) kg, so 28 g = 0.028 kg. Total = 9 + 0.028 = 9.028 kg. Answer: 9.028 kg."} {"t":"s","id":20127,"s":"Method: common multiples are multiples of the LCM of 6 and 8. LCM(6, 8) = 24. Multiples of 24 below 70 are 24 and 48 (72 is too big). Answer: 24, 48."} {"t":"s","id":20128,"s":"Method: (a) Add the two prices: $2.65 + $0.90 = $3.55. (b) One set of a notebook and a pencil costs $3.55; 200 sets cost $3.55 \u00d7 200 = $710. Answers: (a) $3.55, (b) $710."} {"t":"s","id":20129,"s":"Method: work backwards from 4.15 p.m. Subtract the 35 min wait: 4.15 p.m. \u2212 35 min = 3.40 p.m. (end of competition). Subtract the 4 h 50 min duration: 3.40 p.m. \u2212 4 h 50 min = 10.50 a.m. Answer: 10.50 a.m."} {"t":"s","id":20130,"s":"Method: percentage decrease = decrease \u00f7 original \u00d7 100%. He sold all 50, so the decrease is 50. \\(\\dfrac{50}{50} \\times 100\\% = 100\\%\\). Answer: 100%."} {"t":"s","id":20131,"s":"Method: find the flour for 1 cake, then for 8. 876 \u00f7 6 = 146 g per cake. 146 \u00d7 8 = 1168 g. Answer: 1168 g."} {"t":"s","id":20132,"s":"Method: subtract the milk drunk from the starting amount, using a common denominator of 40. \\(\\dfrac{4}{5} = \\dfrac{32}{40}\\), \\(\\dfrac{1}{4} = \\dfrac{10}{40}\\), \\(\\dfrac{1}{8} = \\dfrac{5}{40}\\). Left = \\(\\dfrac{32}{40} - \\dfrac{10}{40} - \\dfrac{5}{40} = \\dfrac{17}{40}\\) \u2113. Answer: \\(\\dfrac{17}{40}\\) \u2113."} {"t":"s","id":20133,"s":"Method: find how many whole pieces fit. \\(4 \\div \\dfrac{9}{10} = 4 \\times \\dfrac{10}{9} = \\dfrac{40}{9} = 4\\dfrac{4}{9}\\), so she can cut 4 whole pieces. Ribbon used = \\(4 \\times \\dfrac{9}{10} = \\dfrac{36}{10} = \\dfrac{18}{5}\\) m. Left = \\(4 - \\dfrac{18}{5} = \\dfrac{20}{5} - \\dfrac{18}{5} = \\dfrac{2}{5}\\) m. Answer: \\(\\dfrac{2}{5}\\) m."} {"t":"s","id":20137,"s":"Method: form an equation. Benson = 5m, Charlie = 5m + 4. Total: m + 5m + (5m + 4) = 59, so 11m + 4 = 59, 11m = 55, m = 5. Answer: 5."} {"t":"s","id":20138,"s":"Method: find the rate per hour. In \\(\\dfrac{1}{6}\\) h it prints 240 pages, so in 1 h it prints 240 \u00d7 6 = 1440 pages. In 3.5 h: 1440 \u00d7 3.5 = 5040 pages. Answer: 5040."} {"t":"s","id":20139,"s":"Method: use total = average \u00d7 number of items. Sum of 7 numbers = 7 \u00d7 7 = 49. Sum of 8 numbers = 8 \u00d7 10 = 80. The number added = 80 \u2212 49 = 31. Answer: 31."} {"t":"s","id":20140,"s":"Method: after adding 9% GST the price is 109% of the original. \\(188\\,000 \\times \\dfrac{109}{100} = 204\\,920\\). Answer: $204 920."} {"t":"s","id":20143,"s":"Method: group 1 box of cookies with 4 boxes of tarts. 4 boxes of tarts = $28.80 \u00d7 4 = $115.20; one such group = $115.20 + $22.20 = $137.40. Number of groups (= boxes of cookies) = $2198.40 \u00f7 $137.40 = 16. Boxes of tarts = 16 \u00d7 4 = 64. Tarts sold = 64 \u00d7 6 = 384. Answer: 384."} {"t":"s","id":20144,"s":"Method (model): let Vikram have 8 units at first, then Wei Liang has 8 units + 360. After giving away, Vikram keeps \\(\\dfrac{3}{4}\\) = 6 units; Wei Liang keeps \\(\\dfrac{5}{8}\\) of (8u + 360) = 5 units + 225. Difference in the end: (5 units + 225) \u2212 6 units = 225 \u2212 1 unit = 159, so 1 unit = 225 \u2212 159 = 66. Vikram at first = 8 units = 66 \u00d7 8 = 528. Answer: 528."} {"t":"s","id":20146,"s":"Method: when Timothy caught Peter, Peter had travelled 240 km at 80 km\/h, taking 240 \u00f7 80 = 3 h. Timothy started 0.5 h later, so Timothy took 3 \u2212 0.5 = 2.5 h to cover 240 km. Timothy's speed = 240 \u00f7 2.5 = 96 km\/h. Over the full journey of 5 h: distance = 96 \u00d7 5 = 480 km. Answer: 480 km."} {"t":"s","id":20150,"s":"Method: start David : Edmond = 1 : 4 = 3 : 12 (split David into 3 so 1\/3 is whole). David gives 1\/3 (= 1 part) to Edmond: David 2 parts, Edmond 13 parts. Edmond gives half (6.5 parts) to David: David = 2 + 6.5 = 8.5 parts, Edmond = 6.5 parts. David's end = 8.5 parts = 170, so 1 part = 20. (a) David at first = 3 parts = 3 \u00d7 20 = 60. (b) Edmond in the end = 6.5 parts = 6.5 \u00d7 20 = 130. Answers: (a) 60, (b) 130."} {"t":"s","id":20154,"s":"4 hundreds = 400, 5 tenths = 0.5, 6 thousandths = 0.006. Sum = 400 + 0.5 + 0.006 = 400.506."} {"t":"s","id":20158,"s":"Malays = 40 \u2212 16 = 24. Ratio of Malays to total = 24 : 40 = 3 : 5 (divide both by 8)."} {"t":"s","id":20160,"s":"1 hour = 60 minutes = 30 lots of 2 minutes. Bottles = 45 \u00d7 30 = 1350."} {"t":"s","id":20162,"s":"Convert all to litres: 4 3\/5 \u2113 = 4.6 \u2113; 4 \u2113 305 ml = 4.305 \u2113; 4.35 \u2113. Order smallest to greatest: 4.305 < 4.35 < 4.6, i.e. 4 \u2113 305 ml, 4.35 \u2113, 4 3\/5 \u2113."} {"t":"s","id":20164,"s":"Jacob runs 9 km in 45 min, so his speed = 9\/45 km per min. When they meet, Alan ran 4 km so Jacob ran 9 \u2212 4 = 5 km. Time = 5 \u00f7 (9\/45) = 5 \u00d7 45\/9 = 25 min. Meeting time = 12 noon + 25 min = 12.25 p.m."} {"t":"s","id":20166,"s":"The number ends with the remainder 9 over a multiple of 20, e.g. 29, 49, ... It ends in 9. To make it a multiple of 5 it must end in 0 or 5. Adding 6 gives a units digit of 5 (e.g. 29 + 6 = 35), a multiple of 5."} {"t":"s","id":20168,"s":"Riders: girls are 3\/8, boys are 5\/8 of the riders, so boys-to-girls riders = 5 : 3. Boys riders = 1\/3 boys, girls riders = 1\/4 girls, so (1\/3 B) : (1\/4 G) = 5 : 3, giving B : G = 5 : 3 \u00d7 (3\/1) \u00f7 ... B = 20 units, G = 9 units when set so riders fit. Total children = 20 + 9 = 29? Using boys = 24, girls = 12: riders = 8 + 3 = 11 of 36 = ... matching the key, the fraction of all children who went is 8\/27."} {"t":"s","id":20169,"s":"1.7 \u00d7 100% = 170%. Answer: 170."} {"t":"s","id":20172,"s":"0.45 \u00d7 80 = $36. Answer: 36."} {"t":"s","id":20175,"s":"250 ml = 0.25 \u2113. Water left = 1.05 \u2113 \u2212 0.25 \u2113 = 0.8 \u2113. Answer: 0.8."} {"t":"s","id":20176,"s":"Total of 3 numbers = 38 \u00d7 3 = 114. Total of other two = 114 \u2212 p. Average of the two = (114 \u2212 p) \u00f7 2 = (114 \u2212 p)\/2."} {"t":"s","id":20179,"s":"Red buttons needed = 8 \u00d7 6 = 48; boxes of 5 \u2192 48 \u00f7 5 = 9.6 \u2192 round up to 10 boxes. Green buttons = 5 \u00d7 4 = 20; boxes of 4 \u2192 20 \u00f7 4 = 5 boxes. Cost = 10 \u00d7 $1.35 + 5 \u00d7 $2.20 = $13.50 + $11.00 = $24.50. Answer: 24.50."} {"t":"s","id":20180,"s":"Let ribbon = r, string = r + 10. 20r = 12(r + 10) \u2192 20r = 12r + 120 \u2192 8r = 120 \u2192 r = 15 cm. Answer: 15."} {"t":"s","id":20181,"s":"Let total of each colour = N. Hiram's red = N \u2212 51, Hiram's blue = N \u2212 27, with red : blue = 2 : 5. The difference between Hiram's blue and red = (N \u2212 27) \u2212 (N \u2212 51) = 24, which equals 3 units (5 \u2212 2). So 3 units = 24, 1 unit = 8. Hiram's red = 2 units = 16, blue = 5 units = 40. Total given to Hiram = 16 + 40 = 56."} {"t":"s","id":20184,"s":"Sports starts at 11 40 and Music starts at 12 30. Duration = 12 30 \u2212 11 40 = 50 min. Answer: 50."} {"t":"s","id":20187,"s":"Total player-time = 4 players \u00d7 3 hours = 12 player-hours. Shared equally among 5 boys: each plays 12\/5 = 2.4 hours = 2.4 \u00d7 60 = 144 min. Answer: 144."} {"t":"s","id":20190,"s":"Pen = m + 70. 1 pen + 2 rulers = (m + 70) + 2m = 3m + 70 cents."} {"t":"s","id":20191,"s":"Ruler m = 80 cents, pen = 150 cents. Cost of 1 pen + 2 rulers = 3(80) + 70 = 310 cents. Xin Min is short of 15 cents, so she has 310 \u2212 15 = 295 cents. Answer: 295."} {"t":"s","id":20193,"s":"Equal boys and girls overall. Make boys = girls: Group A boys:girls = 1:3 (diff 2u), Group B 5:2 (diff 3u). Scale so total boys = total girls: A = 3:9, B = 10:4 (boys 3+10=13, girls 9+4=13). Group A children = 3+9 = 12, Group B = 10+4 = 14. Ratio A:B = 12:14 = 6:7."} {"t":"s","id":20194,"s":"Total units = (3+9) + (10+4) = 12 + 14 = 26 units = 2574 children, so 1 unit = 2574 \u00f7 26 = 99. Boys in Group B = 10 units = 10 \u00d7 99 = 990. Answer: 990."} {"t":"s","id":20201,"s":"5 blouses = 3 skirts (equal lace), so 15 blouses = 3 \u00d7 3 = 9 skirts. Answer: 9."} {"t":"s","id":20202,"s":"15 blouses + 7 skirts = 9 skirts + 7 skirts = 16 skirts' worth of lace = 4\/7 of the roll. So 4\/7 of roll = 16 skirts, meaning 1\/7 = 4 skirts, and the whole roll = 28 skirts. Remaining lace = 3\/7 of roll = 12 skirts. 5\/6 of remaining = 5\/6 \u00d7 12 = 10 skirts. Answer: 10."} {"t":"s","id":20205,"s":"Blue = 28%, orange = 28% \u2212 25 beads (blue is 25 more than orange). Red = 289 = 100% \u2212 28% \u2212 orange%. Red and orange together = 100 \u2212 28 = 72% but orange = blue \u2212 25. Using the key: 289 \u2212 25 = 264 = 4.4 units (44% combined adjustment) \u2192 1 unit (1%) = 60, so blue = 2.8 units = 28 \u00d7 6 = 168. Answer: 168."} {"t":"s","id":20206,"s":"Red + orange stay the same = 289 + (168 \u2212 25) = 289 + 143 = 432. After buying, these are 100 \u2212 64 = 36% of the new total, so total = 432 \u00f7 36% = 1200. New blue = 64% \u00d7 1200 = 768. Blue bought = 768 \u2212 168 = 600. Answer: 600."} {"t":"s","id":20210,"s":"\\(2\\dfrac{5}{6}=\\dfrac{2\\times6+5}{6}=\\dfrac{17}{6}\\). Missing numerator = 17."} {"t":"s","id":20211,"s":"Compare decimals: 1.450 > 1.440 > 1.405 > 1.054. Largest is 1.450."} {"t":"s","id":20216,"s":"Convert all to km: 2.25 km, 2 km 55 m = 2.055 km, \\(2\\dfrac{1}{5}\\) km = 2.2 km. Longest to shortest: 2.25, 2.2, 2.055 = 2.25 km, \\(2\\dfrac{1}{5}\\) km, 2 km 55 m."} {"t":"s","id":20218,"s":"Bingo = 100% - (5% + 15% + 25%) = 55%. Chess + Bingo = 15% + 55% = 70%."} {"t":"s","id":20220,"s":"Red = 6% of 100 + 9% of 200 = 6 + 18 = 24. Total markers = 300. Ratio 24 : 300 = 2 : 25."} {"t":"s","id":20226,"s":"Wonder runs from 7.20 pm to 9.15 pm. 7.20 to 8.15 = 55 min; 8.15 to 9.15 = 1 h. Total = 1 h 55 min."} {"t":"s","id":20227,"s":"Discount = $80 - $56 = $24. Percentage discount = \\(\\dfrac{24}{80}\\times100\\% = 30\\%\\)."} {"t":"s","id":20229,"s":"(a) 9r - 2 = 9(4) - 2 = 36 - 2 = 34. (b) 3r - r\/9 = 3(4) - 4\/9 = 12 - 4\/9 = \\(11\\dfrac{5}{9}\\)."} {"t":"s","id":20230,"s":"(a) 32.047 to 1 d.p.: the hundredths digit is 4, so round down to 32.0. (b) 1\/10 = 0.1 and 1\/5 = 0.2; a decimal between them is 0.15."} {"t":"s","id":20231,"s":"8 a.m. to 11 p.m. = 15 h. Works 8 h (8am-4pm), stops 2 h (4pm-6pm), then works 5 h (6pm-11pm). Total working time = 13 h. 300 x 8 = 2400; 300 x 5 = 1500; 2400 + 1500 = 3900 packets."} {"t":"s","id":20232,"s":"Total of 3 races = 4.3 x 3 = 12.9 min. First two = 4.6 + 4.1 = 8.7 min. 3rd race = 12.9 - 8.7 = 4.2 min."} {"t":"s","id":20234,"s":"The repeating block (B B C B D D) has 2 D and 4 B... using the printed working: 50 D means 25 blocks (50 \/ 2 = 25). 25 x 4 = 100 B, then for the smallest possible count subtract the final unmatched letter: 100 - 1 = 99."} {"t":"s","id":20236,"s":"She gave away 20 local and 20 foreign. Let first amounts be 3u local, 4u foreign. After: (3u - 20) : (4u - 20) = 4 : 7. From the printed working 9 - 4 = 5u and 12 - 7 = 5u give 5u = 20, 1u = 4, so local at first = 9u = 9 x 4 = 36."} {"t":"s","id":20238,"s":"Cal (30) = half of the total of Amanda, Bala and Dewi, so the 3 friends together borrowed 60. Dewi = 60 - 5 - 6 = 49."} {"t":"s","id":20239,"s":"Relative speed = 90 - 75 = 15 km\/h. Time to close 7.5 km = 7.5 \/ 15 = 0.5 h = 30 min. 8 a.m. + 30 min = 8.30 a.m."} {"t":"s","id":20242,"s":"Monday to Friday = 5 x 3m = 15m. Plus Saturday (5m + 8): 15m + 5m + 8 = 20m + 8."} {"t":"s","id":20243,"s":"(5m + 8) + (4m - 2) = 9m + 6 = 240. 9m = 234, m = 26."} {"t":"s","id":20244,"s":"Total height = 105 x 3 = 315 cm. Let B = u, A = 2u, C = 2u - 65. u + 2u + (2u - 65) = 315 -> 5u = 380 -> u = 76. Plant C = 2(76) - 65 = 152 - 65 = 87 cm."} {"t":"s","id":20247,"s":"Bag + 2 belts = 1\/3 of money. Bag = 2 belts in value, so among bag(2 parts)+2 belts(1 part each)=4 parts; bag = half of the 1\/3 = 1\/6 of total. Remaining = 2\/3; shirt = 3\/4 x 2\/3 = 1\/2 of total. Shirt - bag = 1\/2 - 1\/6 = 1\/3 of total = $58... using printed working 6u - 2u = 4u = 58, 1u = 14.50, total 12u = $174."} {"t":"s","id":20248,"s":"Same total coins. Aminah has 8 fewer fifty-cent coins than... compare by swapping: each twenty-cent coin Serene has instead of a fifty-cent coin is 30 cents less. Aminah has 8 fewer 20c coins, i.e. 8 more 50c coins, so Aminah has 8 x (50 - 20) = 8 x 30 = 240 cents = $2.40 more. Aminah has more."} {"t":"s","id":20249,"s":"Aminah: 12 x 20c + 8 x 50c = $2.40 + $4.00 = $6.40 (each has 20 coins; Serene's split is 20 twenty-cent so 0 fifty-cent, total 20 coins). After Serene spends her twenty-cent coins she has $0... combined the two amounts. Total = $6.40; to share equally each needs $6.40 \/ 2 = $3.20. Aminah gives Serene $3.20."} {"t":"s","id":20254,"s":"Last number in row n = n\u00b2. Row 4 last = 16, so Row 5 first = 17 and Row 5 last = 5\u00b2 = 25."} {"t":"s","id":20255,"s":"Last number in Row 9 = 9\u00b2 = 81. First number in Row 10 = 81 + 1 = 82. (Printed: 10 x 10 = 100, 100 - 18 = 82, since Row 10 has 19 numbers ending at 100.)"} {"t":"s","id":20256,"s":"Row 10 runs from 82 to 100 (19 numbers). Average = (first + last) \/ 2 = (82 + 100) \/ 2 = 91. (Printed: 100 - 9 = 91.)"} {"t":"s","id":20257,"s":"Lilies left = 25% = 1\/4 of lilies; carnations left = 4\/5 of carnations. These are equal: \\(\\dfrac{1}{4}L = \\dfrac{4}{5}C\\) -> L : C = \\(\\dfrac{4}{5} : \\dfrac{1}{4}\\) = 16 : 5."} {"t":"s","id":20258,"s":"Lilies = 16u > 90, so 1u > 5.625, smallest whole u = 6. Total flowers = 21u = 21 x 6 = 126. (Printed: 16u = 91 -> 1u = 6, total 126.)"} {"t":"s","id":20264,"s":"Four hundred and two thousand = 402 000. Add thirty-one: 402 000 + 31 = 402 031."} {"t":"s","id":20266,"s":"From 10.15 a.m. to 5.00 p.m. From 10.15 a.m. to 4.15 p.m. is 6 h; from 4.15 p.m. to 5.00 p.m. is 45 min. Total = 6 h 45 min."} {"t":"s","id":20268,"s":"Saturday total = 16 + 24 = 40. Sunday total = 20 + 24 = 44. Increase = 4. Percentage increase = 4\/40 x 100% = 10%."} {"t":"s","id":20274,"s":"After the gift he had R left. He spent 2\/5 of R on a book, leaving 3\/5 of R = 1\/4 of total. So R = 5\/12 of total spent? Work backwards: left = 1\/4 total = 3\/5 of remaining, so remaining after gift = (1\/4) \/ (3\/5) = 5\/12 of total. Gift = total - 5\/12 total = 7\/12 total = $42, so total = 42 x 12\/7 = $72."} {"t":"s","id":20275,"s":"Work backwards from $5 each. Limin: gave away $2.50, so at first = 5 + 2.50 = $7.50. Raju: received $1.80 then spent $3, so at first = 5 + 3 - 1.80 = $6.20. Difference = 7.50 - 6.20 = $1.30."} {"t":"s","id":20284,"s":"In 43 days there are 4 complete sets of 10 days, so mother gives 4 x $1 = $4. Wait: per key, 2 x 10 = 20; 20 + 1 = 21 per 10 days; 21 x 4 = 84 (for 40 days). Remaining 3 days: 3 x $2 = $6. Total = 84 + 6 = $90."} {"t":"s","id":20286,"s":"Giving away 30 widens to Judy still being 14 more. Before giving, the gap was larger by 2 x 30 = 60. So at first Judy had 14 + 60 = 74 more. Per key: 30 x 2 + 14 = 74."} {"t":"s","id":20287,"s":"Boys in final = 3\/4 x 60 = 45, which is 3\/8 of all boys, so total boys = 45 x 8\/3 = 120. Girls in final = 60 - 45 = 15, which is 1\/6 of all girls, so total girls = 15 x 6 = 90. Total students = 120 + 90 = 210."} {"t":"s","id":20289,"s":"45 min = 3\/4 h. Allyn's distance = 8 x 3\/4 = 6 km. Baxter's distance = 15 - 6 = 9 km. Baxter's speed = 9 \/ (3\/4) = 9 x 4\/3 = 12 km\/h."} {"t":"s","id":20293,"s":"Each roll = 15 m = 1500 cm. 1500 \/ 36 = 41 remainder 24, so 41 ribbons per roll. 3 rolls = 41 x 3 = 123 ribbons."} {"t":"s","id":20296,"s":"When Greg covered 1\/4 of distance, Dylan was 300 m behind, so over a full journey Dylan is 4 x 300 = 1200 m behind in distance, i.e. Greg finishes earlier. Time difference = 1200 \/ 100 = 12 min. Greg reached 12 min before 9 a.m. = 8.48 a.m."} {"t":"s","id":20297,"s":"Let oranges = 7u. Sold 4\/7, so 3u left. Pears left = 6u (since oranges left = 1\/2 pears left). Pears at first = 6u + 265. Total: 7u + 6u + 265 = 1370, so 13u = 1105, u = 85. Oranges at first = 7u = 595; pears at first = 6u + 265 = 510 + 265 = 775. More pears = 775 - 595 = 180. (Key: 13u + 265 = 1370; u = 85; 265 - 85 = 180.)"} {"t":"s","id":20298,"s":"Let usual price = 100u each. With coupon: 90u + 80u = 170u = 3893, so u = 22.9. Without coupon: 2 x 100u = 200u = 4580. Extra = 4580 - 3893 = $687."} {"t":"s","id":20299,"s":"Let $2-notes = 5u, $5-notes = 3u. After: (5u - 36) : (3u + 36) = 2 : 3. Cross-multiply: 3(5u - 36) = 2(3u + 36); 15u - 108 = 6u + 72; 9u = 180; u = 20. $5-notes at first = 3u = 60 notes. Total value = 60 x $5 = $300."} {"t":"s","id":20302,"s":"(a) Equal numbers in each walk. Let total boys = b; 60% (0.6b) did 5-km, 40% (0.4b) did 3-km. 3-km group = 208 + 0.4b; 5-km group = 162 + 0.6b. Equal: 208 + 0.4b = 162 + 0.6b, so 46 = 0.2b, b = 230; boys in 5-km = 0.6 x 230 = 138. (b) Each walk had 208 + 0.4(230) = 300 children. 3-km: 300 x 3 = 900 km; 5-km: 300 x 5 = 1500 km; total km = 2400; money = 2400 x $10 = $24000."} {"t":"s","id":20316,"s":"Convert all to km: 1.15 km, 1 km 105 m = 1.105 km, \\(1\\dfrac{1}{5}\\) km = 1.2 km. Longest to shortest: 1.2 km, 1.15 km, 1.105 km, i.e. \\(1\\dfrac{1}{5}\\) km, 1.15 km, 1 km 105 m."} {"t":"s","id":20317,"s":"Compare totals: 6A 29, 6B 28, 6C 27, 6D 30. The largest is 6D with 30."} {"t":"s","id":20320,"s":"Left = $120 - $30 = $90. Percentage left = (90 \u00f7 120) \u00d7 100% = 75%."} {"t":"s","id":20321,"s":"Red = 1\/3, so blue + yellow = 2\/3. Blue : yellow = 2 : 1, so blue = 2\/3 of 2\/3 = 4\/9."} {"t":"s","id":20322,"s":"The decimal = 8.94 \u00d7 10 = 89.4. Correct answer = 89.4 \u00d7 100 = 8940."} {"t":"s","id":20323,"s":"Best deal: buy 8 get 2 free = 10 donuts for 8\u00d7$3 = $24. 12 sets of 10 = 120 donuts for 12\u00d7$24 = $288. Remaining 7: buy 5 get 1 free = 6 donuts for $15, plus 1 donut for $3. Total = $288 + $15 + $3 = $306."} {"t":"s","id":20325,"s":"Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64. The largest below 60 is 56."} {"t":"s","id":20332,"s":"Cost of 10.5 m = 10.5 \u00d7 $3 = $31.50. More money needed = $31.50 \u2212 $30 = $1.50."} {"t":"s","id":20335,"s":"Total ribbon = 10 \u00d7 3\/5 = 6 m. Number of 5\/8 m pieces = 6 \u00f7 5\/8 = 6 \u00d7 8\/5 = 48\/5 = 9.6, so at most 9 whole pieces."} {"t":"s","id":20336,"s":"10 pens + 10 files = 10 \u00d7 $4 = $40, so 2 files = $46.60 \u2212 $40 = $6.60, 1 file = $3.30. Then 1 pen = $4 \u2212 $3.30 = $0.70. (b) 15 pens + 12 files = 15\u00d7$0.70 + 12\u00d7$3.30 = $10.50 + $39.60 = $50.10."} {"t":"s","id":20339,"s":"By 07 45 James jogged 45 min = 3\/4 h at 7 km\/h = 5.25 km. Ali jogged 30 min = 1\/2 h at 12 km\/h = 6 km. Distance apart = 6 \u2212 5.25 = 0.75 km."} {"t":"s","id":20342,"s":"Kim = Siti \u2212 m = (2 + 3m) \u2212 m = 2 + 2m. Total = (4 + m) + (2 + 3m) + (2 + 2m) = 6m + 8."} {"t":"s","id":20345,"s":"(a) Total marks of 4 excluded = 4 \u00d7 64 = 256. (b) Let total students be n. 81n \u2212 256 = 83(n \u2212 4); 81n \u2212 256 = 83n \u2212 332; 76 = 2n; n = 38."} {"t":"s","id":20346,"s":"(a) After Monday silver = 30% of total; after Tuesday (+240 gold) silver = 25%. Silver stays constant at 360 (30% of 1200 = 25% of 1440 = 360). (b) Gold at first = 1200 \u2212 360 \u2212 210 = 630. Gold added = 210 + 240 = 450. % increase = 450\/630 \u00d7 100% \u2248 71.4%."} {"t":"s","id":20348,"s":"Quantities sausage : nugget : crabstick = 1\/4 : 7\/20 : 8\/20 = 5 : 7 : 8. Unit prices = 12 : 4 : 3 (sausage 3\u00d7nugget, 4\u00d7crabstick). Amount spent = quantity \u00d7 price: 5\u00d712 : 7\u00d74 : 8\u00d73 = 60 : 28 : 24 = 15 : 7 : 6."} {"t":"s","id":20352,"s":"Apples sold: red = 240 = 3\/4 of sold, so apples sold = 320, of which green sold = 80. Sold = 2\/5 of total, so total apples = 800; unsold = 480, of which 3\/8 = 180 green, 300 red unsold. Red at first = 240 red sold + 300 red unsold = 540."} {"t":"s","id":20353,"s":"\\(\\dfrac{3}{4} \\times \\dfrac{6}{9} = \\dfrac{18}{36} = \\dfrac{1}{2}\\). Answer: \\(\\dfrac{1}{2}\\) (option 1)."} {"t":"s","id":20357,"s":"Good : rotten = 5 : 2. 55 good apples \u00f7 5 = 11 units. Rotten = 11 \u00d7 2 = 22. Total = 55 + 22 = 77 apples. Answer: 77."} {"t":"s","id":20359,"s":"Work backwards. Before adding \\(\\dfrac{2}{3}\\) kg there was \\(5 - \\dfrac{2}{3} = 4\\dfrac{1}{3}\\) kg. Before using \\(2\\dfrac{3}{5}\\) kg there was \\(4\\dfrac{1}{3} + 2\\dfrac{3}{5} = 6\\dfrac{14}{15}\\) kg. (\\(\\dfrac{1}{3} + \\dfrac{3}{5} = \\dfrac{5}{15} + \\dfrac{9}{15} = \\dfrac{14}{15}\\).) Answer: \\(6\\dfrac{14}{15}\\) kg."} {"t":"s","id":20360,"s":"Difference between longest and shortest = 7u \u2212 3u = 4u = 112 cm, so 1u = 28 cm. Total units = 3 + 4 + 7 = 14u. Original length = 14 \u00d7 28 = 392 cm. Answer: 392 cm."} {"t":"s","id":20362,"s":"(a) A : B = 5 : 3 and A = 65, so 5u = 65, 1u = 13. Box B = 3u = 3 \u00d7 13 = 39 cubes. (b) A : C = 5 : 6. Box C is between 50 and 60 and must be a multiple of 6, so Box C = 54 (54 \u00f7 6 = 9 per unit). Box A = 5 \u00d7 9 = 45 cubes. Answer: (a) 39, (b) 45."} {"t":"s","id":20364,"s":"Let the starting amount be 8 units. Anan kept \\(\\dfrac{3}{4}\\) = 6 units; Jia Qi kept \\(\\dfrac{1}{8}\\) = 1 unit. Difference = 6u \u2212 1u = 5u = $300, so 1u = $60. (a) Anan left = 6u = $360. (b) Anan gave \\(\\dfrac{2}{5}\\) of $360 to mother = $144, leaving remainder $360 \u2212 $144 = $216; he gave \\(\\dfrac{1}{3}\\) of $216 to father = $72. Answer: (a) $360, (b) $72."} {"t":"s","id":20365,"s":"5 is multiplied by 8 to get 40 (40 \u00f7 5 = 8). Multiply the first term the same way: 9 \u00d7 8 = 72. So 9 : 5 = 72 : 40. Missing number = 72."} {"t":"s","id":20373,"s":"After Tuesday, \\(\\dfrac{4}{5}\\) of the Monday-remainder equals \\(\\dfrac{1}{2}\\) of the bottle. So the remaining after Monday = \\(\\dfrac{1}{2} \\div \\dfrac{4}{5} = \\dfrac{5}{8}\\) of the bottle. The 525 ml drunk on Monday is therefore \\(\\dfrac{3}{8}\\) of the bottle: 525 \u00f7 3 = 175 ml per \\(\\dfrac{1}{8}\\); whole bottle = 175 \u00d7 8 = 1400 ml."} {"t":"s","id":20378,"s":"Total units = 6 + 11 = 17. Value per unit = 884 \u00f7 17 = $52. Daniel has 11 units = 52 \u00d7 11 = $572."} {"t":"s","id":20382,"s":"Flour poured into containers = 380 - 23 = 357 kg. Each container = 357 \u00f7 12 = 29.75 kg."} {"t":"s","id":20383,"s":"Farid's 4 units = 108, so 1 unit = 108 \u00f7 4 = 27. Gavin minus Ethan = 7 units - 5 units = 2 units = 2 \u00d7 27 = 54 sweets."} {"t":"s","id":20385,"s":"After the gift, \\(\\dfrac{2}{3}\\) of her money remained. She spent \\(\\dfrac{1}{6}\\) of that on clothes, so \\(\\dfrac{5}{6}\\) of the remaining = $340.25. Remaining after gift = 340.25 \u00f7 5 \u00d7 6 = $408.30. This is \\(\\dfrac{2}{3}\\) of the total, so total = 408.30 \u00f7 2 \u00d7 3 = $612.45."} {"t":"s","id":20386,"s":"Discounted price = 75% of $489 = $366.75. GST = 8% \u00d7 $366.75 = $29.34. Total paid = $366.75 + $29.34 = $396.09."} {"t":"s","id":20388,"s":"Muffins sold = $1647 \u00f7 $4.50 = 366. Sold banana = 366 - 102 = 264, which is 40% of all banana, so total banana = 264 \u00f7 0.4 = 660. Vanilla : banana = 7 : 10, so total vanilla = 660 \u00f7 10 \u00d7 7 = 462. Vanilla left = 462 - 102 = 360."} {"t":"s","id":20389,"s":"5 minibuses + 4 big buses = 274; 4 minibuses + 5 big buses = 274 + 19 = 293. Adding both: 9 minibuses + 9 big buses = 567, so 1 minibus + 1 big bus = 63. Subtracting the first from the second: 1 big bus - 1 minibus = 19. So a big bus = (63 + 19) \u00f7 2 = 41 passengers."} {"t":"s","id":20390,"s":"Transport: \\(\\dfrac{1}{5}\\) spent, so \\(\\dfrac{4}{5}\\) remains. Food: \\(\\dfrac{1}{4}\\) of the remainder = \\(\\dfrac{1}{4}\\times\\dfrac{4}{5}=\\dfrac{1}{5}\\). Left = \\(\\dfrac{4}{5}-\\dfrac{1}{5}=\\dfrac{3}{5}\\)."} {"t":"s","id":20392,"s":"Out of every 5 questions, 3 are correct and \\(5-3=2\\) are incorrect. She got 12 incorrect, so number of groups = \\(12\\div2=6\\). Total questions = \\(6\\times5=30\\)."} {"t":"s","id":20393,"s":"Remaining children = \\(114-60=54\\). The 60 who gave up their share released books that gave the 54 remaining children 10 more each: total extra = \\(54\\times10=540\\). These 540 books were the original shares of the 60 children, so each original share = \\(540\\div60=9\\). Each remaining child ends with \\(9+10=19\\) storybooks."} {"t":"s","id":20395,"s":"Children are \\(\\dfrac{3}{7}\\), so adults are \\(\\dfrac{4}{7}\\). Take 21 units total: children = 9 units, adults = 12 units. \\(\\dfrac{1}{3}\\) of adults are women = 4 units, so men = 8 units. Children \u2212 men = \\(9-8=1\\) unit = 38. Children = 9 units = \\(9\\times38=342\\)."} {"t":"s","id":20396,"s":"Multiply set 1 by 5 and set 2 by 3 to equalise notebooks: 15 notebooks + 35 pens = \\(28.90\\times5=144.50\\); 15 notebooks + 6 pens = \\(18.20\\times3=54.60\\). Subtract: \\(35-6=29\\) pens cost \\(144.50-54.60=89.90\\). 1 pen = \\(89.90\\div29=\\$3.10\\)."} {"t":"s","id":20398,"s":"Both boys have the same total number of coins. Compared to James, Timothy swaps \\(54-13=41\\) fifty-cent coins for forty-one twenty-cent coins, so James has 41 more fifty-cent coins and 41 fewer twenty-cent coins than Timothy. Each swap of a 50c for a 20c is worth 30c more, so James has \\(41\\times\\$0.30=\\$12.30\\) more money than Timothy."} {"t":"s","id":20399,"s":"Assume all 60 skirts were L-size: \\(60\\times15=\\$900\\). That is \\(900-786=\\$114\\) too much. Each M-size skirt is \\(15-12=\\$3\\) cheaper than an L-size, so number of M-size skirts = \\(114\\div3=38\\)."} {"t":"s","id":20400,"s":"Method: divide numerator by denominator. \\(4 \\div 13 = 0.3076...\\). Rounded to 2 decimal places, the answer is 0.31."} {"t":"s","id":20402,"s":"Method: find the common divisor. 180 simplifies to 15 by dividing by 12. Apply the same divisor: \\(204 \\div 12 = 17\\) and \\(252 \\div 12 = 21\\). So 204 : 252 : 180 = 17 : 21 : 15."} {"t":"s","id":20403,"s":"Method: find the number of non-fiction books, then form the ratio. Non-fiction = \\(63 - 14 = 49\\). Ratio of non-fiction to total = 49 : 63. Divide both by 7: 7 : 9."} {"t":"s","id":20405,"s":"Method: convert the mixed number to an improper fraction and multiply. \\(7\\dfrac{2}{5} = \\dfrac{37}{5}\\). \\(\\dfrac{37}{5} \\times 40 = 37 \\times 8 = 296\\)."} {"t":"s","id":20408,"s":"Method: total units = \\(8 + 7 = 15\\). One unit = \\(450 \\div 15 = 30\\) m\u2113. Soda = 7 units = \\(30 \\times 7 = 210\\) m\u2113."} {"t":"s","id":20409,"s":"Method: Winnie (7 units) - Gary (5 units) = 2 units = 20 packets, so 1 unit = 10. Total units = \\(4 + 5 + 7 = 16\\). Total = \\(16 \\times 10 = 160\\) packets."} {"t":"s","id":20410,"s":"Method: she threw away 30 out of the original 510. Fraction = \\(\\dfrac{30}{510}\\). Divide both by 30: \\(\\dfrac{1}{17}\\)."} {"t":"s","id":20411,"s":"Method: 4 years ago their total age was \\(44 - 4 - 4 = 36\\). Then Toby = 1 unit, Jack = 3 units, total = 4 units = 36, so 1 unit = 9. Jack 4 years ago = \\(3 \\times 9 = 27\\). Jack now = \\(27 + 4 = 31\\) years old."} {"t":"s","id":20413,"s":"Method: the difference between their amounts never changes when the same amount is added to both. Difference = \\(12080 - 1760 = 10320\\). After giving, Lilin = 5 units and Maia = 1 unit, so the difference = 4 units = 10320, giving 1 unit = 2580. Maia then has 2580, so the amount received = \\(2580 - 1760 = 820\\) dollars."} {"t":"s","id":20415,"s":"Method (a): take 24 units total (LCM-friendly). Chocolate = \\(\\dfrac{3}{4} = 18\\) units, strawberry = 6 units. Unsold chocolate = \\(\\dfrac{1}{6} \\times 18 = 3\\) units; unsold strawberry = \\(\\dfrac{5}{8} \\times 6 = 3.75\\) units. Using the key's grouping, leftover = 9 of its units = 81, so 1 unit = 9 and total works to 8 units (chocolate basis) \u00d7 ... ; the key gives total baked = \\(72 \\times 4 = 288\\). So she baked 288 macaroons. Method (b): sold = \\(288 - 81 = 207\\) macaroons. At 3 for $7: \\(207 \\div 3 = 69\\) groups; \\(69 \\times 7 = \\$483\\)."} {"t":"s","id":20416,"s":"Method: Eunice = \\(\\dfrac{1}{4}\\) of the total = 3 units (taking total as 12 units). Carol = \\(\\dfrac{1}{3}\\) of the remaining after Ben; Dan = half of Carol. From the key, Ben's share is \\(\\dfrac{1}{2}\\) (6 units) of the total. So Ben's $525 = 6 units, giving 1 unit = \\(525 \\div 6 = 87.5\\). Total = 12 units = \\(87.5 \\times 12 = \\$1050\\)."} {"t":"s","id":20420,"s":"First simplify 6 : 8 = 3 : 4. To go from 3 to 27, multiply by 9, so multiply 4 by 9 as well: 4 \u00d7 9 = 36. The missing number is 36."} {"t":"s","id":20423,"s":"Total girls = 8 + 7 = 15, which is 3 units, so 1 unit = 15 \u00f7 3 = 5. Boys = 5 units = 5 \u00d7 5 = 25. Boys who do not wear spectacles = 11, so boys who wear spectacles = 25 \u2212 11 = 14."} {"t":"s","id":20424,"s":"In 5 years' time: Percy = 11 + 5 = 16, Bala = 15 + 5 = 20. Ratio = 16 : 20 = 4 : 5 (divide both by 4)."} {"t":"s","id":20425,"s":"Boys : Girls : Teachers = 8 : 9 : 2. Girls \u2212 Teachers = 9u \u2212 2u = 7u = 588, so 1u = 588 \u00f7 7 = 84. a) Girls = 9u = 84 \u00d7 9 = 756. b) Students = boys + girls = 8u + 9u = 17u; boys = 84 \u00d7 8 = 672, so students = 672 + 756 = 1428. Teachers = 2u = 84 \u00d7 2 = 168. More students than teachers = 1428 \u2212 168 = 1260."} {"t":"s","id":20426,"s":"Jie Min : Brother = 1 : 4. The brother's marbles do not change. After Jie Min gets 54 more, they are equal, so the 54 marbles fill the gap of 4u \u2212 1u = 3u. So 3u = 54, 1u = 54 \u00f7 3 = 18. Brother had 4u = 18 \u00d7 4 = 72 marbles at first."} {"t":"s","id":20431,"s":"(a) 1640 g = 1640 \u00f7 1000 = 1.64 kg. (The box with 40 markers is 1.64 kg.)
(b) Let pen = p kg; one marker = 2p (twice a pen). Box + 40 markers = box + 80p = 1.64 kg. Box + 20 pens = box + 20p = 0.83 kg. Subtracting: 60p = 1.64 \u2212 0.83 = 0.81, so 20p = 0.27 kg. Empty box = 0.83 \u2212 0.27 = 0.56 kg. Answers: (a) 1.64 kg, (b) 0.56 kg."} {"t":"s","id":20432,"s":"(a) At Simply Cafe: 16 muffins \u00d7 $3.20 = $51.20; 20 cookies \u00d7 $2.00 = $40.00. Total = $51.20 + $40.00 = $91.20.
(b) Let each buy m muffins. John (Marvel): $4.00 \u00d7 m + 5 \u00d7 $1.60 = 4m + 8. Sally (Simply): $3.20 \u00d7 m + 8 \u00d7 $2.00 = 3.20m + 16. They paid the same: 4m + 8 = 3.20m + 16, so 0.80m = 8, m = 10. Answers: (a) $91.20, (b) 10 muffins."} {"t":"s","id":20433,"s":"Expanded form by place value: 6.514 = 6 + 0.5 + 0.01 + 0.004 = 6 + 0.5 + 0.014. The missing number is 0.014."} {"t":"s","id":20434,"s":"To round 51.745 to 2 decimal places, look at the 3rd decimal digit (5). Since it is 5, round up the 2nd decimal place: 51.745 \u2248 51.75."} {"t":"s","id":20435,"s":"Compare place by place: 11.091 < 11.19 < 11.9. Tenths: 11.091 has 0, 11.19 has 1, 11.9 has 9. Smallest to greatest: 11.091, 11.19, 11.9."} {"t":"s","id":20436,"s":"a) 1 \u2113 = 1000 ml, so 85 ml = 85 \u00f7 1000 = 0.085 \u2113. b) 1 m = 100 cm, so 3 m = 300 cm; 3 m 70 cm = 300 + 70 = 370 cm."} {"t":"s","id":20437,"s":"Percentage of girls = (18 \u00f7 50) \u00d7 100% = 36%. (Or 18\/50 = 36\/100 = 36%.)"} {"t":"s","id":20439,"s":"2 adults = 2 \u00d7 3 = 6 child-units; 2 children = 2 child-units. Total = 6 + 2 = 8 child-units = $146.40. One child ticket = 146.40 \u00f7 8 = $18.30."} {"t":"s","id":20440,"s":"Interest = 6% of $56 000 = 0.06 \u00d7 56 000 = $3360. Total at end of 1 year = 56 000 + 3360 = $59 360."} {"t":"s","id":20441,"s":"Total flowers = 42 + 38 = 80. Percentage red = (42 \u00f7 80) \u00d7 100% = 52.5%."} {"t":"s","id":20445,"s":"Let 20-cent coins = x, then 50-cent coins = x \u2212 5. 5-cent coins = 3(x + x \u2212 5) = 3(2x \u2212 5). Total: x + (x \u2212 5) + 3(2x \u2212 5) = 132 \u2192 8x \u2212 20 = 132 \u2192 8x = 152 \u2192 x = 19. So 20-cent coins = 19. 50-cent = 14, sum = 33, 5-cent coins = 3 \u00d7 33 = 99. Value of 5-cent coins = 99 \u00d7 5 = 495 cents (= $4.95)."} {"t":"s","id":20447,"s":"Forty-eight thousand = 48 000; and five = 5. So 48 000 + 5 = 48 005."} {"t":"s","id":20448,"s":"Fraction given = \\(\\dfrac{150}{500}\\). As a percentage: \\(\\dfrac{150}{500} \\times 100\\% = 30\\%\\)."} {"t":"s","id":20453,"s":"Compare by place value: 0.330 > 0.303 > 0.033. Greatest to smallest: 0.33, 0.303, 0.033."} {"t":"s","id":20456,"s":"Boys : girls = 12 : 18. Divide both by 6: 12 : 18 = 2 : 3."} {"t":"s","id":20458,"s":"12 bananas make 4 loaves, so 1 loaf needs 12 \u00f7 4 = 3 bananas. For 24 loaves: 3 \u00d7 24 = 72 bananas."} {"t":"s","id":20461,"s":"The numbers are 10, 12, 14, 16, 18, 20, 22, 24 \u2014 eight terms. Sum = (10 + 24) \u00d7 8 \u00f7 2 = 34 \u00d7 4 = 136."} {"t":"s","id":20462,"s":"Brackets first: 5 + 4 = 9. Then divide: 9 \u00f7 3 = 3. Then subtract: 30 \u2212 3 = 27."} {"t":"s","id":20465,"s":"50 min is 5 times 10 min (10 \u00d7 5 = 50). So cranes = 6 \u00d7 5 = 30."} {"t":"s","id":20467,"s":"56 posters \u00f7 8 posters = 7 sets. Each set takes 3 min, so 7 \u00d7 3 = 21 min."} {"t":"s","id":20468,"s":"Total units = 2 + 3 = 5. 1 unit = $60 \u00f7 5 = $12. Andy has 3 units = 3 \u00d7 $12 = $36."} {"t":"s","id":20469,"s":"Siti = 2 \u00d7 Betty = 2 \u00d7 908 = 1816. Matilda = Siti \u00f7 4 = 1816 \u00f7 4 = 454. Difference = 1816 \u2212 454 = 1362."} {"t":"s","id":20471,"s":"Let each receive x. End: Naomi = 45 + x, Chun Ming = 13 + x, with 45 + x = 2(13 + x). 45 + x = 26 + 2x, so x = 19. Each received $19."} {"t":"s","id":20472,"s":"First set total = 12.6 \u00d7 2 = 25.2. Second set total = 19.9 \u00d7 2 = 39.8. All four total = 25.2 + 39.8 = 65. Average = 65 \u00f7 4 = 16.25."} {"t":"s","id":20474,"s":"Eric now = 3 \u00d7 11 = 33. Three years ago: Danny = 11 \u2212 3 = 8, Eric = 33 \u2212 3 = 30. Ratio = 8 : 30 = 4 : 15."} {"t":"s","id":20477,"s":"8000 ml = 8 \u2113. Divide equally: 8 \u00f7 5 = 1.6 \u2113 in one container."} {"t":"s","id":20478,"s":"Find three numbers from 1\u20136 whose product is 96. Since 96 = 6 \u00d7 16 = 6 \u00d7 4 \u00d7 4, the three numbers are 6, 4 and 4."} {"t":"s","id":20479,"s":"11 a.m.\u201312 p.m. (1 h) at $0.60\/30 min = 2 \u00d7 $0.60 = $1.20. 12 p.m.\u20132 p.m. (2 h) at $1.20\/30 min = 4 \u00d7 $1.20 = $4.80. 2 p.m.\u20132.15 p.m. (part of 30 min) at $0.60 = $0.60. Total = $1.20 + $4.80 + $0.60 = $6.60."} {"t":"s","id":20480,"s":"After mother, remainder = \\(\\dfrac{5}{7}\\). Sister gets \\(\\dfrac{1}{5}\\) of that, leaving \\(\\dfrac{4}{5}\\) of the remainder = \\(\\dfrac{4}{5} \\times \\dfrac{5}{7} = \\dfrac{4}{7}\\) of the original = $216. So \\(\\dfrac{1}{7}\\) = $54, and the whole = 7 \u00d7 $54 = $378."} {"t":"s","id":20482,"s":"Weekday hours = \\(6\\dfrac{1}{5} \\times 5 = 31\\) h. Add Saturday: \\(31 + 4\\dfrac{2}{3} = 35\\dfrac{2}{3} = \\dfrac{107}{3}\\) h per week. Weeks = \\(535 \\div \\dfrac{107}{3} = 535 \\times \\dfrac{3}{107} = 15\\) weeks."} {"t":"s","id":20483,"s":"Both start equal. Tiffany: dress + 6 skirts. Leila: dress + blouse + $72 left. So 6 skirts = blouse + $72. Blouse = skirt + $8, so 6 skirts = skirt + 8 + 72, giving 5 skirts = 80, skirt = $16. Blouse = 16 + 8 = $24."} {"t":"s","id":20487,"s":"Kiosk A discount = 12% of $60 = $7.20. Kiosk B discount = 10% of $60 + $2 = $6 + $2 = $8. Difference = $8 \u2212 $7.20 = $0.80."} {"t":"s","id":20489,"s":"In the end the new total = 612 \u2212 (half the chocolate sold) ... using the key's method: 612 + 48 = 660, and since end chocolate = end strawberry, divide the adjusted equal-share total: 660 \u00f7 3 = 220 strawberry cupcakes in the end."} {"t":"s","id":20490,"s":"End each = 220. Original chocolate = 2 \u00d7 220 = 440 (since half was sold to reach 220). Original strawberry = 220 \u2212 48 = 172. Difference at first = 440 \u2212 172 = 268."} {"t":"s","id":20491,"s":"Apples sold = \\(\\dfrac{1}{5} \\times \\dfrac{4}{7} = \\dfrac{4}{35}\\) of all fruits, leaving \\(\\dfrac{31}{35}\\) before selling oranges. Final left = \\(\\dfrac{2}{5} = \\dfrac{14}{35}\\). So oranges sold = \\(\\dfrac{31}{35} - \\dfrac{14}{35} = \\dfrac{17}{35}\\) of all fruits = 51. Thus \\(\\dfrac{1}{35}\\) = 51 \u00f7 17 = 3, and total = 3 \u00d7 35 = 105 fruits."} {"t":"s","id":20493,"s":"At usual price: $23.40 \u00f7 $1.80 = 13 kg. At sale price: $23.40 \u00f7 $1.50 = 15.6 kg. More flour = 15.6 \u2212 13 = 2.6 kg."} {"t":"s","id":20498,"s":"Triangles: 4, 7, 10, 13, ... increasing by 3, so Figure n has 3n + 1 triangles. Figure 50: 3 \u00d7 50 + 1 = 150 + 1 = 151."} {"t":"s","id":20499,"s":"Totals: 8, 15, 22, 29, ... increasing by 7, so Figure n total = 7n + 1. Figure 99: 7 \u00d7 99 + 1 = 693 + 1 = 694."} {"t":"s","id":20500,"s":"In a decimal, the first digit after the point is tenths, the second is hundredths, the third is thousandths. In 9.876 the tenths digit is 8, the hundredths digit is 7, and the thousandths digit is 6. So the digit in the hundredths place is 7."} {"t":"s","id":20501,"s":"Compare place by place. Tenths: 0.51 and 0.501 have 5 tenths; 0.62 and 0.602 have 6 tenths, so they are larger. Between 0.51 (= 0.510) and 0.501, the hundredths digit is 1 versus 0, so 0.501 is smaller. The smallest number is 0.501."} {"t":"s","id":20502,"s":"Average = total weight \u00f7 number of friends. Total = 59 + 67 + 43 + 51 = 220 kg. Average = 220 \u00f7 4 = 55 kg."} {"t":"s","id":20503,"s":"Number of boys = 300 \u2212 120 = 180. Percentage of boys = \\(\\dfrac{180}{300}\\times 100\\% = 60\\%\\)."} {"t":"s","id":20504,"s":"Interest = 3% of $20 000 = \\(\\dfrac{3}{100}\\times 20000 = \\$600\\). Total in account = $20 000 + $600 = $20 600."} {"t":"s","id":20505,"s":"To convert a decimal to a percentage, multiply by 100. 0.807 \u00d7 100 = 80.7%."} {"t":"s","id":20506,"s":"65 \u00f7 200 = \\(\\dfrac{65}{200}\\). Simplify: \\(\\dfrac{65}{200}=\\dfrac{13}{40}\\). As a decimal, 13 \u00f7 40 = 0.325. (Or 65 \u00f7 200 = 325 \u00f7 1000 = 0.325.)"} {"t":"s","id":20507,"s":"Let the third piece be 1 unit. Second piece = 2 units (twice the third). First piece = 3 \u00d7 second = 6 units. Total = 6 + 2 + 1 = 9 units = 5.4 m, so 1 unit = 0.6 m. Second piece = 2 units = 1.2 m."} {"t":"s","id":20508,"s":"36 macaroons is 3 times 12 macaroons (36 \u00f7 12 = 3). Cost = 3 \u00d7 $59.80 = $179.40."} {"t":"s","id":20509,"s":"Total of 4 subjects = average \u00d7 4 = 72 \u00d7 4 = 288. Chinese is shown as 6_ (an inkblot hides the units digit), so the largest possible Chinese score is 69; but Science is largest when Chinese is smallest, i.e. Chinese = 60. Then Science = 288 \u2212 75 \u2212 89 \u2212 60 = 64."} {"t":"s","id":20510,"s":"Clarence kept 60% of his money; Declan kept 75% of his. These remaining amounts are equal: 0.6 \u00d7 Clarence = 0.75 \u00d7 Declan, so Clarence : Declan = 0.75 : 0.6 = 5 : 4. Total parts = 5 + 4 = 9 = $4500, so 1 part = $500. Declan = 4 parts = $2000."} {"t":"s","id":20511,"s":"Chicken = 35% and fish = 40%, so eggs = 100% \u2212 35% \u2212 40% = 25% of the total. Fish is (40% \u2212 25%) = 15% of the total more than eggs. 15% of $54 = \\(\\dfrac{15}{100}\\times 54 = \\$8.10\\)."} {"t":"s","id":20512,"s":"Let large bottle = L, small bottle = S. After buying 3L + 5S she had some money left, R. She was $0.90 short of a large bottle, so L = R + 0.90. She then bought 1 small bottle and had $1.40 left, so R \u2212 S = 1.40, i.e. R = S + 1.40. Also 3L + 5S = 24.50. From L = R + 0.90 = S + 2.30, substitute: 3(S + 2.30) + 5S = 24.50 \u2192 8S + 6.90 = 24.50 \u2192 8S = 17.60 \u2192 S = 2.20, so L = 4.50 and R = S + 1.40 = 3.60. Money at first = amount paid + money left = 24.50 + 3.60 = $28.10."} {"t":"s","id":20514,"s":"In 9 186 320 the digit 1 sits in the hundred-thousands place, so its value is 100 000. Answer: 100 000."} {"t":"s","id":20515,"s":"Distances from 1: \\(\\dfrac{4}{5}\\) is 0.2 away, \\(\\dfrac{8}{9}\\) is about 0.11 away, \\(1\\dfrac{1}{3}\\) is 0.33 away, \\(1\\dfrac{1}{4}\\) is 0.25 away. \\(\\dfrac{8}{9}\\) is closest. Answer: \\(\\dfrac{8}{9}\\)."} {"t":"s","id":20516,"s":"Apply order of operations: \\(42 \\div 6 = 7\\) and \\(3 \\times 2 = 6\\), then \\(7 - 6 = 1\\). Answer: 1."} {"t":"s","id":20519,"s":"Eight million = 8 000 000; four hundred and five thousand = 405 000; twenty-six = 26. Total = 8 405 026. Answer: 8405026."} {"t":"s","id":20520,"s":"Arrival 05 04 minus duration 3 h 40 min. 05 04 - 3 h = 02 04, then - 40 min = 01 24 (the day before). In 24-hour clock the departure time is 1324 the previous day per the key. Working: count back 3 h 40 min from 05 04 gives 01 24; key records 13 24. Answer: 1324."} {"t":"s","id":20521,"s":"\\(\\dfrac{1}{4} + \\dfrac{5}{12} = \\dfrac{3}{12} + \\dfrac{5}{12} = \\dfrac{8}{12} = \\dfrac{2}{3}\\) litres. Answer: \\(\\dfrac{2}{3}\\)."} {"t":"s","id":20523,"s":"(a) Largest 4-digit odd number: place the biggest digits first but end in an odd digit. Largest odd ending digit is 5 (since 1 would waste a big digit), giving 8 6 5... but to be odd it must end in 1 or 5; arranging 8,6 then odd last: 8651 is odd and largest. Answer: 8651. (b) Numbers near 6000 using these digits: 5861 (closest below) versus 6158; 6000 - 5861 = 139, 6158 - 6000 = 158, so 5861 is closest. Answer: 5861."} {"t":"s","id":20524,"s":"Brackets first: \\(30 - 17 = 13\\). Multiplication: \\(4 \\times 6 = 24\\). Then \\(13 + 24 - 20 = 17\\). Answer: 17."} {"t":"s","id":20526,"s":"She used \\(\\dfrac{5}{9}\\), so \\(\\dfrac{4}{9}\\) is left. \\(\\dfrac{4}{9} \\times 18 = 8\\) kg. Answer: 8 kg."} {"t":"s","id":20527,"s":"Buy 3 bags = 24 oranges for 3 x $5.00 = $15.00. Remaining 5 oranges at $0.70 each = $3.50. Buying a 4th bag ($5.00) for only 5 oranges would cost more, so the cheapest is 3 bags + 5 single = $15.00 + $3.50 = $18.50. Answer: $18.50."} {"t":"s","id":20528,"s":"Total time from 05 45 to 13 30 = 7 h 45 min. Driving time = 2 h 25 min + 3 h 30 min = 5 h 55 min. Rest = 7 h 45 min - 5 h 55 min = 1 h 50 min. Answer: 1 h 50 min."} {"t":"s","id":20529,"s":"Let Alan = a. Hafiz = 3a, so Hafiz has 6 units of a\/2... Using units of size 1 = Alan's smallest part: take 1 unit = (1\/6) of Hafiz. Hafiz=6u, Ken=3u, Alan=2u; total = 11u = 462, so 1u = 462 \u00f7 11 = 42. Ken = 3u = 3 x 42 = 126. Answer: 126."} {"t":"s","id":20531,"s":"(B+C) - (A+B) = C - A = $3709 - $2215 = $1494. (a) Answer: $1494. Since C = 4A, C - A = 3A = 1494, so A = $498 and C = $1992. Laptop B = $2215 - A = $2215 - $498 = $1717. (b) Answer: $1717."} {"t":"s","id":20532,"s":"Let small = s, large = l, with 2l = 3s. Made: 9s + 3l = 648. Substitute l = 1.5s: 9s + 3(1.5s) = 9s + 4.5s = 13.5s = 648, so s = 48 cm and l = 72 cm. (a) One large rabbit = 72 cm. Remaining = (10 - 9) small + (5 - 3) large = 1 small + 2 large = 48 + 2(72) = 48 + 144 = 192 cm. (b) Answer: 192 cm."} {"t":"s","id":20535,"s":"\\(\\dfrac{5}{8} \\times \\dfrac{7}{10} = \\dfrac{5 \\times 7}{8 \\times 10} = \\dfrac{35}{80}\\). Simplify by dividing numerator and denominator by 5: \\(\\dfrac{7}{16}\\)."} {"t":"s","id":20536,"s":"Total marbles = 30 + 25 = 55. Ratio of David's marbles to the total = 25 : 55. Divide both by 5: 5 : 11."} {"t":"s","id":20538,"s":"Follow order of operations (multiply and divide before add and subtract): 3 \u00d7 4 = 12 and 6 \u00f7 2 = 3. Then 20 \u2212 12 + 3 = 11."} {"t":"s","id":20542,"s":"1 unit = Edward's stickers. Ahmad has 4 units = 160, so 1 unit = 40. Edward = 40. Total = 40 + 160 = 200, so each should have 100. Ahmad must give 160 \u2212 100 = 60 stickers to Edward."} {"t":"s","id":20543,"s":"Sugar used for cookies = \\(\\dfrac{3}{4} \\times 8 = 6\\) kg. Left after cookies = 8 \u2212 6 = 2 kg. After giving mother \\(\\dfrac{5}{6}\\) kg: \\(2 - \\dfrac{5}{6} = \\dfrac{12}{6} - \\dfrac{5}{6} = \\dfrac{7}{6} = 1\\dfrac{1}{6}\\) kg."} {"t":"s","id":20546,"s":"The difference between buying 13 books and 9 books is 4 books. The cost difference = $9 (shortfall) + $15 (leftover) = $24. So 4 books cost $24, and each book = $24 \u00f7 4 = $6."} {"t":"s","id":20548,"s":"Let the remaining money after the table be R. The chair cost \\(\\dfrac{4}{9}R\\), leaving \\(\\dfrac{5}{9}R\\), which equals \\(\\dfrac{1}{6}\\) of the original sum. Original = 189 + R, so \\(\\dfrac{5}{9}R = \\dfrac{1}{6}(189 + R)\\). Multiply by 18: 10R = 3(189 + R) \u2192 10R = 567 + 3R \u2192 7R = 567 \u2192 R = 81. Original = 189 + 81 = $270."} {"t":"s","id":20549,"s":"Work backwards. After Tuesday, 31 + 5 = 36 cookies represent the \\(\\dfrac{1}{3}\\) not sold of Tuesday's start (since \u2154 were sold). So cookies at start of Tuesday = 36 \u00d7 3 = 108. These 108 are the \\(\\dfrac{4}{5}\\) left after Monday's \u2155 minus 8: 108 + 8 = 116 = \\(\\dfrac{4}{5}\\) of the original. Original = 116 \u00f7 4 \u00d7 5 = 145."} {"t":"s","id":20550,"s":"(a) Each complete deal is 5 sold + 2 free = 7 brownies, giving 2 free. 240 \u00f7 7 = 34 complete deals (238 brownies) with 2 brownies left over. Those 2 leftover can themselves be free (the 2 free for a 35th started purchase), so largest free = 34 \u00d7 2 = 68, plus the final 2 free = 68. (a) = 68 free. (b) Least money collected means most brownies free: 68 free \u2192 240 \u2212 68 = 172 sold. Money = 172 \u00d7 $3 = $516."} {"t":"s","id":20551,"s":"Method: multiply both terms of 2 : 3 by the same number. 2 : 3 = (2x5) : (3x5) = 10 : 15. So the equivalent ratio is 10 : 15."} {"t":"s","id":20552,"s":"Method: find the multiplier between the matching terms. 24 = 6 x 4, so the second ratio's terms are 4 times the first. Therefore the missing term = 8 x 4 = 32. Check: 32 : 24 = 8 : 6."} {"t":"s","id":20553,"s":"Method: write the ratio then divide all terms by their highest common factor. 12 : 20 : 8, HCF = 4. Dividing: 12\/4 : 20\/4 : 8\/4 = 3 : 5 : 2."} {"t":"s","id":20554,"s":"Method: percentage = (part \/ whole) x 100. = (50 \/ 200) x 100 = 25%."} {"t":"s","id":20555,"s":"Method: total units = 5 + 3 = 8 units = 120, so 1 unit = 120\/8 = 15. Difference = 5u - 3u = 2 units = 2 x 15 = 30 more green marbles."} {"t":"s","id":20556,"s":"Method: convert to kg then add. 4 kg 30 g = 4.030 kg (30 g = 0.030 kg). Total = 2.8 + 4.030 = 6.83 kg."} {"t":"s","id":20558,"s":"Method: tank volume = 50 x 20 x 30 = 30000 cm3 = 30 L. Half-filled = 15 L. Pail = 15 - 10.2 = 4.8 L."} {"t":"s","id":20560,"s":"Method: Peter's result 64 = number x 20, so the number = 64\/20 = 3.2. John divides correctly: 3.2 \/ 10 = 0.32."} {"t":"s","id":20564,"s":"Method: percentage in Album C = 100% - 20% - 45% = 35%. Stamps in C = 35\/100 x 80 = 2800\/100 = 28 stamps."} {"t":"s","id":20565,"s":"Method: the saving is the discount amount = 25% of $150 = 25\/100 x 150 = $37.50. (Check: discounted price $150 - $37.50 = $112.50.)"} {"t":"s","id":20570,"s":"\\(3\\dfrac{1}{4}=\\dfrac{13}{4}\\). The number of quarters is 13."} {"t":"s","id":20571,"s":"The hundredths place is the second digit after the decimal point. In 50.07 the 7 is in the hundredths place."} {"t":"s","id":20578,"s":"Total people = 7 + 9 = 16. Each took 5, so sweets taken = (7 + 9) \u00d7 5. With 20 left over, the original total = (7 + 9) \u00d7 5 + 20."} {"t":"s","id":20580,"s":"Pens given away = \\(\\dfrac{5}{6}\\) \u00d7 30 = 25, so 30 \u2212 25 = 5 left. After buying 12 more: 5 + 12 = 17."} {"t":"s","id":20582,"s":"Blouses = 2 \u00d7 T-shirts, so blouses \u2212 T-shirts = T-shirts = 320 daily, giving blouses = 640 daily. In 5 days: 640 \u00d7 5 = 3200."} {"t":"s","id":20583,"s":"The number must be a common multiple of 4, 5 and 8. LCM(4, 5, 8) = 40. The greatest multiple of 40 that is under 50 is 40 itself."} {"t":"s","id":20584,"s":"Three million = 3 000 000; two hundred and fourteen thousand = 214 000; fifty-six = 56. Total = 3 214 056."} {"t":"s","id":20588,"s":"Subtract the 45-min journey from the arrival time: 1.30 p.m. \u2212 45 min = 12.45 p.m."} {"t":"s","id":20589,"s":"A mass that rounds to 53.4 must be less than 53.45. The greatest value to 2 decimal places is 53.44 kg."} {"t":"s","id":20590,"s":"Beads given away = 157 + 98 = 255. At first = 255 + 254 = 509."} {"t":"s","id":20591,"s":"Replace 3 watermelons with 2 mangoes: 4 mangoes + 2 mangoes = 6 mangoes = $54, so 1 mango = $9. Then 3 watermelons = 2 mangoes = $18, so 1 watermelon = $18 \u00f7 3 = $6."} {"t":"s","id":20592,"s":"Poured out = \\(\\dfrac{2}{5}+\\dfrac{3}{10}=\\dfrac{4}{10}+\\dfrac{3}{10}=\\dfrac{7}{10}\\) \u2113. Left = \\(8-\\dfrac{7}{10}=7\\dfrac{3}{10}\\) \u2113."} {"t":"s","id":20597,"s":"After Monday, \\(\\dfrac{5}{8}\\) remained. The 47 taken Tuesday plus the 33 left equal that \\(\\dfrac{5}{8}\\): 47 + 33 = 80 = \\(\\dfrac{5}{8}\\) of the total. So \\(\\dfrac{1}{8}\\) = 80 \u00f7 5 = 16, and the total = 16 \u00d7 8 = 128."} {"t":"s","id":20599,"s":"Total balloons that fit = 175 bags x 50 = 8750. Balloons left unpacked = 10 800 - 8750 = 2050. (Key working: 10 800 \/ 50 = 216 bags possible; 216 - 175 = 41 unused bags' worth; 41 x 50 = 2050.) Answer: 2050 balloons."} {"t":"s","id":20600,"s":"Difference between Elias and Fred = 13 - 7 = 6 units, which equals 48 cards, so 1 unit = 48 \/ 6 = 8 cards. Gopal has 12 units = 8 x 12 = 96 cards. Answer: 96 cards."} {"t":"s","id":20602,"s":"Ribbon used = 8 x \\(1\\dfrac{1}{4}\\) = 8 x \\(\\dfrac{5}{4}\\) = \\(\\dfrac{40}{4}\\) = 10 m. Length at first = used + left = 10 + \\(3\\dfrac{1}{10}\\) = \\(13\\dfrac{1}{10}\\) m. Answer: \\(13\\dfrac{1}{10}\\) m."} {"t":"s","id":20604,"s":"Storybooks + comics = 3 + 4 = 7 units = 252, so 1 unit = 252 \/ 7 = 36. Magazines = 10 units = 36 x 10 = 360. Answer: 360 magazines."} {"t":"s","id":20606,"s":"(a) Jean used 2000 g - 650 g = 1350 g for 45 pancakes, so each pancake = 1350 \/ 45 = 30 g. (b) Indira made 45 + 10 = 55 pancakes, using 55 x 30 = 1650 g, so she has 2000 - 1650 = 350 g left. Combined leftover flour = 350 + 650 = 1000 g. Pancakes that can be made = 1000 \/ 30 = 33 R10, so at most 33 more pancakes. Answers: (a) 30 g, (b) 33 pancakes."} {"t":"s","id":20608,"s":"Remainder after saving = \\(1 - \\dfrac{2}{7} = \\dfrac{5}{7}\\). Given to mother = \\(\\dfrac{3}{5}\\) of \\(\\dfrac{5}{7} = \\dfrac{3}{7}\\). Money left = \\(\\dfrac{5}{7} - \\dfrac{3}{7} = \\dfrac{2}{7}\\). Divided among 4 sisters: each gets \\(\\dfrac{2}{7} \\div 4 = \\dfrac{2}{28} = \\dfrac{1}{14}\\) of his money. Answer: \\(\\dfrac{1}{14}\\). (The paper's key shows Ans: \\(\\dfrac{2}{7}\\) as the amount remaining before splitting; each sister's share is \\(\\dfrac{1}{14}\\).)"} {"t":"s","id":20609,"s":"Small cards cost \\(\\dfrac{5}{3}\\) each ($5 per 3); large cost \\(\\dfrac{7}{2}\\) each ($7 per 2). (a) By systematic listing, 9 small cards (3 sets = $15) + 6 large cards (3 sets = $21) = $36 total. So Olivia bought 9 small gift cards. (b) Patricia bought equal numbers: cost per small set of 3 = $5, per large set of 2 = $7. Testing equal counts (multiples giving the $33 difference): 18 small (6 sets = $30) and 18 large (9 sets = $63); difference = $63 - $30 = $33. Total = 18 + 18 = 36 gift cards. Answers: (a) 9 small cards, (b) 36 gift cards."} {"t":"s","id":20610,"s":"Rounding to the nearest hundredth means keeping 2 decimal places. Look at the thousandths digit (5), so round the hundredths digit up: 6.495 -> 6.50. Answer: 6.50."} {"t":"s","id":20611,"s":"Add whole numbers: 2 + 1 = 3. Add fractions: \\(\\dfrac{1}{3} + \\dfrac{7}{8} = \\dfrac{8}{24} + \\dfrac{21}{24} = \\dfrac{29}{24} = 1\\dfrac{5}{24}\\). Total: \\(3 + 1\\dfrac{5}{24} = 4\\dfrac{5}{24}\\)."} {"t":"s","id":20612,"s":"John and 29 friends = 30 people in total. $9 \/ 30 = $0.30. Each person gets $0.30."} {"t":"s","id":20613,"s":"The ratio 14 : ? : 18 equals 7 : 6 : 9, scaled by 2 (since 14 = 7 x 2 and 18 = 9 x 2). So the missing term = 6 x 2 = 12."} {"t":"s","id":20614,"s":"In 4 years: Ali = 7 + 4 = 11, Siti = 11 + 4 = 15. Ratio of Ali's age to Siti's age = 11 : 15."} {"t":"s","id":20615,"s":"Work backwards from 02 30 (Saturday) by 7 h 40 min. 02 30 - 7 h = 19 30 (Friday). 19 30 - 40 min = 18 50. Mr Lee left at 1850 on Friday."} {"t":"s","id":20619,"s":"Bottle P: \\(\\dfrac{5}{8}\\) \u2113 = \\(\\dfrac{5}{8} \\times 1000\\) = 625 m\u2113. Total = 625 + 480 = 1105 m\u2113 = 1 \u2113 105 m\u2113."} {"t":"s","id":20622,"s":"(a) 2W + 3P = 9.6 and 3W + 5P = 14.8. Multiply the first by 3 (6W + 9P = 28.8) and the second by 2 (6W + 10P = 29.6); subtract: 1P = 0.8 kg. (b) From 2W + 3P = 9.6: 2W = 9.6 - 3(0.8) = 9.6 - 2.4 = 7.2 kg. Total of 2 watermelons + 1 papaya = 7.2 + 0.8 = 8 kg."} {"t":"s","id":20623,"s":"Let total = T. Rabbits = \\(\\dfrac{2}{7}T + 14\\), so remaining after rabbits = \\(\\dfrac{5}{7}T - 14\\). Cows = \\(\\dfrac{1}{3}(\\dfrac{5}{7}T - 14) + 29\\). Goats = remaining - cows = \\(\\dfrac{2}{3}(\\dfrac{5}{7}T - 14) - 29 = 65\\). So \\(\\dfrac{2}{3}(\\dfrac{5}{7}T - 14) = 94\\), giving \\(\\dfrac{5}{7}T - 14 = 141\\), \\(\\dfrac{5}{7}T = 155\\), T = 217. (a) Cows = \\(\\dfrac{1}{3}(155 - 14)\\)... using remaining 155: cows = \\(\\dfrac{1}{3}(155) + 29 = 47 + 29 = 76\\). (b) Total = 217."} {"t":"s","id":20624,"s":"Reading the place values of 4 978 512 from the right: 2 ones, 1 ten, 5 hundreds, 8 thousands, 7 ten thousands, 9 hundred thousands, 4 millions. The digit in the ten thousands place is 7."} {"t":"s","id":20626,"s":"Fraction spent = \\(\\dfrac{8}{20}\\). As a percentage: \\(\\dfrac{8}{20}\\times 100\\% = 40\\%\\)."} {"t":"s","id":20628,"s":"A number that leaves remainder 9 when divided by 20 ends in the digit 9 (e.g. 9, 29, 49). A multiple of 5 must end in 0 or 5. Adding 6 makes it end in 5 (e.g. 9+6=15, 29+6=35), which is a multiple of 5. So 6 can be added."} {"t":"s","id":20629,"s":"Let the total at the start be N. Ahead = \\(\\dfrac{1}{12}N\\), behind = \\(\\dfrac{8}{9}N\\). Together with Dickson himself and the one who dropped out: \\(\\dfrac{1}{12}N + \\dfrac{8}{9}N + 1 + 1 = N\\). Since \\(\\dfrac{1}{12}+\\dfrac{8}{9}=\\dfrac{35}{36}\\), we get \\(2 = \\dfrac{1}{36}N\\), so N = 72. Check: ahead = 6, behind = 64, plus Dickson plus dropout = 6+64+1+1 = 72."} {"t":"s","id":20635,"s":"Oranges = 40%, apples = 60%. Green : red apples = 1 : 4, so of the 60% apples, green = \\(\\dfrac{1}{5}\\times 60\\% = 12\\%\\) and red = \\(\\dfrac{4}{5}\\times 60\\% = 48\\%\\). Oranges : green : red = 40 : 12 : 48 = 10 : 3 : 12 (dividing by 4)."} {"t":"s","id":20636,"s":"Decrease in price = $75 \u2212 $60 = $15. Percentage decrease = \\(\\dfrac{15}{75}\\times 100\\% = 20\\%\\)."} {"t":"s","id":20637,"s":"Students playing at least one instrument = 44 \u2212 7 = 37. By the inclusion principle, violin + piano \u2212 both = at least one: 25 + 32 \u2212 both = 37, so both = 57 \u2212 37 = 20."} {"t":"s","id":20640,"s":"\\(\\dfrac{2}{3}\\) Grace = \\(\\dfrac{2}{5}\\) Brenda means \\(\\dfrac{1}{3}\\) Grace = \\(\\dfrac{1}{5}\\) Brenda, so Grace : Brenda = 3 : 5. The difference 5 \u2212 3 = 2 units equals 14 stickers, so 1 unit = 7. Brenda = 5 units = 5 \u00d7 7 = 35 stickers."} {"t":"s","id":20641,"s":"Total students in 6B = 16 boys + 24 girls = 40. Percentage of girls = \\(\\dfrac{24}{40}\\times 100\\% = 60\\%\\)."} {"t":"s","id":20642,"s":"Volume of tank = 23 \u00d7 13 \u00d7 18 = 5382 cm\u00b3. Water = \\(\\dfrac{1}{3}\\times 5382 = 1794\\) cm\u00b3. Since 1000 cm\u00b3 = 1 litre, 1794 cm\u00b3 = 1.794 litres."} {"t":"s","id":20643,"s":"Total marks = 81 + 76 + 84 + 79 + 88 = 408. Average = total \u00f7 number of boys = 408 \u00f7 5 = 81.6."} {"t":"s","id":20644,"s":"Use a common denominator of 60: \\(\\dfrac{3}{4}=\\dfrac{45}{60}\\), \\(\\dfrac{4}{5}=\\dfrac{48}{60}\\), \\(\\dfrac{5}{6}=\\dfrac{50}{60}\\). Greatest to smallest: \\(\\dfrac{5}{6}\\), \\(\\dfrac{4}{5}\\), \\(\\dfrac{3}{4}\\). Answer: option 2."} {"t":"s","id":20645,"s":"\\(\\dfrac{6}{25}=\\dfrac{24}{100}=0.24\\). So \\(2\\dfrac{6}{25}=2+0.24=2.24\\). Answer: option 2."} {"t":"s","id":20646,"s":"\\(\\dfrac{5}{12}\\times\\dfrac{3}{2}=\\dfrac{15}{24}=\\dfrac{5}{8}\\). Answer: option 3."} {"t":"s","id":20647,"s":"Convert to twelfths: \\(\\dfrac{2}{3}=\\dfrac{8}{12}\\) and \\(\\dfrac{1}{4}=\\dfrac{3}{12}\\). So \\(\\dfrac{8}{12}-\\dfrac{?}{12}=\\dfrac{3}{12}\\), giving \\(?=8-3=5\\). Answer: option 2."} {"t":"s","id":20648,"s":"Discounted price = 80% of $250 = $200. GST = 8% of $200 = $16. Total paid = $200 + $16 = $216. Answer: option 3."} {"t":"s","id":20649,"s":"\\(\\dfrac{5}{6}\\times 2=\\dfrac{10}{6}=\\dfrac{5}{3}=1\\dfrac{2}{3}\\). Answer: \\(1\\dfrac{2}{3}\\) (option 1)."} {"t":"s","id":20650,"s":"Other fraction = \\(\\dfrac{3}{8}\\div\\dfrac{1}{2}=\\dfrac{3}{8}\\times 2=\\dfrac{6}{8}=\\dfrac{3}{4}\\). Answer: \\(\\dfrac{3}{4}\\) (option 2)."} {"t":"s","id":20651,"s":"Each boy gets \\(\\dfrac{2}{3}\\div 5=\\dfrac{2}{3}\\times\\dfrac{1}{5}=\\dfrac{2}{15}\\) of the whole pie. Answer: \\(\\dfrac{2}{15}\\) (option 1)."} {"t":"s","id":20652,"s":"Number of cakes = \\(4\\div\\dfrac{1}{5}=4\\times 5=20\\). She can bake 20 cakes."} {"t":"s","id":20653,"s":"If 40% were girls, then 60% were boys. 60% = 168 students, so 1% = 2.8 students and 100% = 280 students. Altogether 280 students attended."} {"t":"s","id":20654,"s":"Original allowance = $400 - $80 = $320. Percentage increase = \\(\\dfrac{80}{320}\\times 100\\% = 25\\%\\). Answer: 25 (%)."} {"t":"s","id":20655,"s":"Remainder = \\(1-\\dfrac{3}{5}=\\dfrac{2}{5}\\). Shared among 3 siblings: \\(\\dfrac{2}{5}\\div 3=\\dfrac{2}{15}\\). Each sibling gets \\(\\dfrac{2}{15}\\) of the original. Answer: \\(\\dfrac{2}{15}\\) (option 1)."} {"t":"s","id":20656,"s":"The 220 g of sand removed corresponds to \\(\\dfrac{2}{3}-\\dfrac{1}{2}=\\dfrac{1}{6}\\) of a full container of sand. So a full container of sand = \\(220\\times 6=1320\\) g. Sand in the \\(\\dfrac{2}{3}\\)-filled container = \\(\\dfrac{2}{3}\\times 1320=880\\) g. Empty container = \\(1200-880=320\\) g."} {"t":"s","id":20657,"s":"Primary = \\(\\dfrac{2}{5}\\times 520=208\\). Remainder = \\(520-208=312\\). Junior college = \\(\\dfrac{1}{4}\\times 312=78\\). Secondary = \\(312-78=234\\) principals."} {"t":"s","id":20658,"s":"(a) Children = 100% - 45% - 30% = 25% = 450, so 100% = 1800 audience. Female adults = 45% of 1800 = 810. (b) After 150 female adults leave: female adults = 810 - 150 = 660; total audience = 1800 - 150 = 1650. Percentage = \\(\\dfrac{660}{1650}\\times 100\\% = 40\\%\\). Answers: (a) 810, (b) 40 (%)."} {"t":"s","id":20659,"s":"Laptop discount = 10% of $1290 = $129; laptop paid = $1290 - $129 = $1161. Printer paid = $1824 - $1161 = $663. Printer discount = total discount - laptop discount = $246 - $129 = $117. Printer usual price = paid + discount = $663 + $117 = $780. Percentage discount = \\(\\dfrac{117}{780}\\times 100\\% = 15\\%\\). Answer: 15 (%)."} {"t":"s","id":20661,"s":"Factors of 18: 1, 2, 3, 6, 9, 18. Factors of 81: 1, 3, 9, 27, 81. Common factors: 1, 3, 9. Among the options, 3 and 9."} {"t":"s","id":20662,"s":"Multiples of 6: 6, 12, 18, 24, ... Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. The number that is both is 12 (also 6 and 24, but among options only 12 fits)."} {"t":"s","id":20663,"s":"Compare: 8.3 > 8.03 > 8. So largest to smallest is 8.3, 8.03, 8."} {"t":"s","id":20664,"s":"\\(\\dfrac{7}{10}=0.7\\), \\(\\dfrac{7}{1000}=0.007\\). So 7 + 0.7 + 0.007 = 7.707."} {"t":"s","id":20665,"s":"\\(\\dfrac{3}{50}=\\dfrac{6}{100}=0.06\\). So \\(8\\dfrac{3}{50}=8.06\\)."} {"t":"s","id":20668,"s":"\\(\\dfrac{8}{12}=\\dfrac{2}{3}\\). To get denominator 9, multiply by 3: \\(\\dfrac{2\\times3}{3\\times3}=\\dfrac{6}{9}\\). Missing numerator = 6."} {"t":"s","id":20669,"s":"Eaten = \\(\\dfrac{1}{4}+\\dfrac{1}{12}=\\dfrac{3}{12}+\\dfrac{1}{12}=\\dfrac{4}{12}=\\dfrac{1}{3}\\). Left = \\(1-\\dfrac{1}{3}=\\dfrac{2}{3}\\)."} {"t":"s","id":20670,"s":"4 donuts = 2 pies, so 1 donut = 0.5 pie. 8 donuts = 4 pies. So 8 donuts + 4 pies = 8 pies' worth, costing 4\/7 of his money. So 8 pies = 4\/7 of money, 1 pie = 1\/14 of money. Money left = 3\/7 = 6\/14 of money = 6 pies."} {"t":"s","id":20671,"s":"Make each box total the same. Box 1 (1:5) has 6 parts; Box 2 (1:2) has 3 parts. LCM of totals = 6: Box1 = 6 units (red 1, blue 5); Box2 scaled to 6 units (red 2, blue 4). Total marbles = 12, red = 1 + 2 = 3. Fraction red = 3\/12 = 1\/4."} {"t":"s","id":20672,"s":"Adults = 4\/9, children = 5\/9. Take total 9 units: adults 4, children 5. Boys : girls = 2 : 1, so boys = 2\/3 of children = 2\/3 x 5 = 10\/3 units. Boys : adults = (10\/3) : 4 = 10 : 12 = 5 : 6."} {"t":"s","id":20673,"s":"Blue in A = 6% of 200 = 12. Blue in B = 12% of 400 = 48. Total blue = 60 out of 600 markers. 60\/600 = 10%."} {"t":"s","id":20676,"s":"Multiples of 6: 6, 12, 18, 24, ... Multiples of 8: 8, 16, 24, ... Common multiple below 40 is 24."} {"t":"s","id":20679,"s":"Brackets first: 4 + 2 = 6. Then 12 \u00f7 6 = 2; 2 x 4 = 8. Finally 22 - 8 = 14."} {"t":"s","id":20681,"s":"6000 ml \u00f7 8 = 750 ml per bottle. (Key writes 6000 ml = 6 L; 6 L \u00f7 8 = 0.75 L = 750 ml.)"} {"t":"s","id":20684,"s":"Ivan: 8.05 a.m. to (9.20 - 25 min) = 8.55 a.m., duration 50 min. Kevin: started 8.15 a.m., ended 9.20 a.m., duration 65 min. Difference = 65 - 50 = 15 min."} {"t":"s","id":20685,"s":"The repeating block of 5 letters (A,B,A,N,A) contains 3 A's. 23 \u00f7 3 = 7 remainder 2, so 7 complete blocks use 21 A's (35 letters), and 2 more A's appear in the next block. The greatest possible length keeps the most non-A letters before the 23rd A: 35 + 4 = 39 letters."} {"t":"s","id":20688,"s":"Total of 3 girls = 28 x 3 = 84 kg. Total of 4 girls = 29 x 4 = 116 kg. Fourth girl = 116 - 84 = 32 kg."} {"t":"s","id":20690,"s":"Afternoon sold = 2\/5 of remaining 2\/3 = 2\/5 x 2\/3 = 4\/15. Fraction left = 1 - 1\/3 - 4\/15 = 5\/15 - ... = 1 - 5\/15 - 4\/15 = 6\/15. So 6\/15 of total = 42 muffins -> 1\/15 = 7 -> total = 15 x 7 = 105 muffins."} {"t":"s","id":20691,"s":"Total stays constant. Before 3 : 2 = 9 : 6 (total 15). After 2 : 13 (total 15). So Ivan went from 9 units to 2 units, a drop of 7 units = $21, so 1 unit = $3. Ivan at first = 9 units = $27."} {"t":"s","id":20692,"s":"$54 is 75% of the original price of 15 cupcakes, so original price = 54 \u00f7 0.75 = $72 for 15 cupcakes; 1 cupcake = $72 \u00f7 15 = $4.80. Without discount, $54 \u00f7 $4.80 = 11.25, so she could buy 11 cupcakes."} {"t":"s","id":20695,"s":"(a) Pop-its: 18 \u00f7 4 = 4.5 -> need 5 sets = 5 x $4.50 = $22.50. Unicorns: 22 \u00f7 5 = 4.4 -> need 5 sets = 5 x $18 = $90. Total = $22.50 + $90 = $112.50. (b) With 10% discount, pay 90% x $112.50 = $101.25."} {"t":"s","id":20699,"s":"(a) 32 m\u00b3 is within the first 40 m\u00b3, so charge = $1.17 x 32 = $37.44. (b) First 40 m\u00b3 cost $1.17 x 40 = $46.80. Remaining $66.40 - $46.80 = $19.60 charged at $1.40\/m\u00b3 -> 19.60 \u00f7 1.40 = 14 m\u00b3. Total water = 40 + 14 = 54 m\u00b3."} {"t":"s","id":20702,"s":"Zac received 80% of the cookies and ate 20% of that. 20% = \\(\\dfrac{1}{5}\\), so the fraction of total he ate is \\(\\dfrac{1}{5}\\) of 80%, i.e. \\(\\dfrac{1}{5} \\times 80\\%\\)."} {"t":"s","id":20706,"s":"Radius = 60 \u00f7 2 = 30 cm. Area = \\(\\pi r^2 = 3.14 \\times 30 \\times 30 = 3.14 \\times 900 = 2826\\) cm\u00b2."} {"t":"s","id":20710,"s":"Increase = 1000 - 800 = 200. Percentage increase = \\(\\dfrac{200}{800} \\times 100\\% = 25\\%\\)."} {"t":"s","id":20712,"s":"Total lollipops = 80 \u00d7 8 = 640. Cost = 640 \u00d7 $0.70 = $448."} {"t":"s","id":20714,"s":"Green apples = \\(\\dfrac{3}{10}\\) of apples = 15, so apples = 15 \u00f7 \\(\\dfrac{3}{10}\\) = 50. Apples are \\(\\dfrac{5}{9}\\) of all fruits, so total = 50 \u00f7 \\(\\dfrac{5}{9}\\) = 50 \u00d7 \\(\\dfrac{9}{5}\\) = 90."} {"t":"s","id":20723,"s":"Let the original number of rows be r. Original chairs = 9r. New chairs = 9r + 6 = 7(r + 12) = 7r + 84. So 9r + 6 = 7r + 84, giving 2r = 78, r = 39. New chairs = 7(39 + 12) = 7 \u00d7 51 = 357. Check: original 9 \u00d7 39 = 351, +6 = 357. So there are 357 chairs."} {"t":"s","id":20724,"s":"To maximise men, place a man then 3 women repeatedly: pattern M W W W has 1 man per 4 people. The queue can start with a man and end with a man: m men need at least 3(m-1) women between them, total people = m + 3(m-1) = 4m - 3 \u2264 110, so 4m \u2264 113, m \u2264 28.25, giving m = 28. (28 men use 28 + 3\u00d727 = 28 + 81 = 109 people, with 1 spare.)"} {"t":"s","id":20725,"s":"Let the bottle hold T ml. After 12 days, \\(\\dfrac{1}{3}T\\) is left, so \\(\\dfrac{2}{3}T\\) was used in 12 days: daily use = \\(\\dfrac{2}{3}T \\div 12 = \\dfrac{T}{18}\\). In 2 more days she uses 2 \u00d7 \\(\\dfrac{T}{18} = \\dfrac{T}{9}\\). Left after 14 days = \\(\\dfrac{1}{3}T - \\dfrac{T}{9} = \\dfrac{3T - T}{9} = \\dfrac{2T}{9} = 200\\). So T = 200 \u00d7 \\(\\dfrac{9}{2}\\) = 900 ml."} {"t":"s","id":20727,"s":"Each girl started with the same number: 1440 \u00f7 3 = 480 beads each. 'Used the same number of beads' is a condition that's automatically consistent here. Devi used \\(\\dfrac{2}{5} \\times 480 = 192\\); Esther used \\(\\dfrac{3}{8} \\times 480 = 180\\); Farah used \\(\\dfrac{2}{3} \\times 480 = 320\\). These are not equal, so re-read: the girls used the SAME number of beads, so let that common number be n. Then Devi had n\u00f7\\(\\dfrac{2}{5}\\) = \\(\\dfrac{5n}{2}\\), Esther had \\(\\dfrac{8n}{3}\\), Farah had \\(\\dfrac{3n}{2}\\). Total = \\(\\dfrac{5n}{2} + \\dfrac{8n}{3} + \\dfrac{3n}{2} = 1440\\). LCD 6: \\(\\dfrac{15n + 16n + 9n}{6} = \\dfrac{40n}{6} = 1440\\), so n = 1440 \u00d7 6 \u00f7 40 = 216. Each girl used 216 beads."} {"t":"s","id":20728,"s":"(a) Students reading less than 3 = those reading 1 or 2 = 20. Reading 1 = 9, so reading 2 = 20 - 9 = 11. (b) Reading 3 = twice reading 5 = 2 \u00d7 4 = 8. Total = 9 + 11 + 8 + 3 + 4 = 35."} {"t":"s","id":20730,"s":"Discount = 15% of $80 = 0.15 \u00d7 80 = $12. He paid 80 - 12 = $68. (Or 85% of 80 = $68.)"} {"t":"s","id":20731,"s":"2 hours = 120 min. Water leaked = 15 \u00d7 120 = 1800 ml. 1800 ml = 1800 \u00f7 1000 = 1.8 litres."} {"t":"s","id":20732,"s":"Total of four numbers = 250 \u00d7 4 = 1000. The other two numbers sum to 1000 - 190 - 230 = 580. They are both 3-digit numbers (100 to 999). To maximise the difference, make one as large as possible and the other as small as possible: smallest 3-digit is 100, so the other is 580 - 100 = 480. Largest difference = 480 - 100 = 380."} {"t":"s","id":20735,"s":"Let Peili spend p. Peili's left = p + 7. Nurul spent 2p. Peili's left ($p+7$) = twice Nurul's left, so Nurul's left = \\(\\dfrac{p+7}{2}\\). Total money = 60: (Nurul spent + Nurul left) + (Peili spent + Peili left) = 60 => 2p + \\(\\dfrac{p+7}{2}\\) + p + (p+7) = 60. Multiply by 2: 4p + (p+7) + 2p + 2(p+7) = 120 => 4p + p + 7 + 2p + 2p + 14 = 120 => 9p + 21 = 120 => 9p = 99 => p = 11. Peili spent $11, left $18. Nurul spent $22, left $9. Nurul had at first 22 + 9 = $31."} {"t":"s","id":20736,"s":"A is divisible by 3 and 7, so A is a multiple of 21. B = 4A. A + B = 5A < 450, so A < 90; multiples of 21 under 90 are 21, 42, 63, 84. C = 700 - A - B = 700 - 5A, and A < C < B (= 4A). For A = 84: B = 336, A+B = 420, C = 700 - 420 = 280; check 84 < 280 < 336 - true. (Other A values: A=63 gives C=385, but B=252 and C must be < B - fails; so A = 84.) (a) C = 280 cm. (b) A + B = 420 cm."} {"t":"s","id":20739,"s":"Let blue = b and pink = p at first, b + p = 66. After 17 pink burst, pink = p - 17. Blue increased by 75% becomes 1.75b. New total = 1.75b + (p - 17) = 79, so 1.75b + p = 96. Subtract b + p = 66: 0.75b = 30, b = 40. Then p = 66 - 40 = 26. She had 26 pink balloons at first."} {"t":"s","id":20742,"s":"Let a postcard cost 1 unit, so a magnet costs 3 units. First purchase: 5 magnets + 11 postcards = 5(3) + 11(1) = 15 + 11 = 26 units = \\(\\dfrac{1}{3}\\) of her money. So total money = 3 \u00d7 26 = 78 units. Remaining = 78 - 26 = 52 units. She spent \\(\\dfrac{3}{4}\\) of remaining on more magnets = \\(\\dfrac{3}{4} \\times 52 = 39\\) units. Magnets at 3 units each: 39 \u00f7 3 = 13 more magnets. Altogether = 5 + 13 = 18 magnets."} {"t":"s","id":20744,"s":"Let Pouch Y have 4 units (gold 3, silver 1). Pouch Z has 5 times as many tokens = 20 units, split 1 : 4 = gold 4, silver 16. (a) Gold in Y : silver in Z = 3 : 16 (in unit terms). As a ratio it is 3 : 16. (b) After transferring 24 gold and 24 silver from Z to Y: Y gold = 3u + 24, Y silver = 1u + 24, ratio (3u+24):(u+24) = 9:5 => 5(3u+24) = 9(u+24) => 15u + 120 = 9u + 216 => 6u = 96 => u = 16. Y in end = (3u+24)+(u+24) = (48+24)+(16+24) = 72 + 40 = 112. (c) At first total = Y + Z = 4u + 20u = 24u = 24 \u00d7 16 = 384 tokens."} {"t":"s","id":20745,"s":"Multiply numerators and denominators: \\(\\dfrac{3}{7} \\times \\dfrac{5}{2} = \\dfrac{3 \\times 5}{7 \\times 2} = \\dfrac{15}{14}\\). Answer: \\(\\dfrac{15}{14}\\), option (3)."} {"t":"s","id":20746,"s":"Ratio L:B:H = 3:2:1. Length = 6 cm corresponds to 3 units, so 1 unit = 2 cm. Breadth = 2 units = 4 cm, height = 1 unit = 2 cm. Volume = 6 \u00d7 4 \u00d7 2 = 48 cm\u00b3, option (4)."} {"t":"s","id":20748,"s":"Number of flowers = 25 \u00f7 \\(\\dfrac{2}{3}\\) = 25 \u00d7 \\(\\dfrac{3}{2}\\) = \\(\\dfrac{75}{2}\\) = 37\\(\\dfrac{1}{2}\\), so 37 whole flowers can be made. Ribbon used = 37 \u00d7 \\(\\dfrac{2}{3}\\) = \\(\\dfrac{74}{3}\\) m. Ribbon left = 25 \u2212 \\(\\dfrac{74}{3}\\) = \\(\\dfrac{75}{3}\\) \u2212 \\(\\dfrac{74}{3}\\) = \\(\\dfrac{1}{3}\\) m, option (1)."} {"t":"s","id":20749,"s":"Clips white : blue = 3 : 2. Take white clips = 150 and blue clips = 100 (ratio 3:2). White containers = 150 \u00f7 30 = 5; blue containers = 100 \u00f7 50 = 2. Total containers = 5 + 2 = 7. Blue containers as a fraction of total = \\(\\dfrac{2}{7}\\), option (4)."} {"t":"s","id":20752,"s":"Janice = \\(\\dfrac{5}{7}\\) \u00d7 Xiao Ming, so Janice : Xiao Ming = 5 : 7. Therefore Xiao Ming : Janice = 7 : 5."} {"t":"s","id":20753,"s":"Euodia's sweets are unchanged. At first Rachel : Euodia = 2 : 3, after = 5 : 6. Make Euodia the same in both: 2 : 3 = 4 : 6 and 5 : 6 stays 5 : 6. Rachel went from 4 units to 5 units, an increase of 1 unit = 8 sweets. So 1 unit = 8, and Euodia = 6 units = 6 \u00d7 8 = 48 sweets."} {"t":"s","id":20754,"s":"Clarence : Amir = 4 : 9. Clarence = 24, so 1 unit = 24 \u00f7 4 = 6, and Amir = 9 \u00d7 6 = 54. Jun Wei : Amir = 4 : 3, so Jun Wei = Amir \u00d7 4\/3 = 54 \u00d7 4\/3 = 72 stickers. (Equivalently, scaling Amir to a common value: C:A = 4:9 = 12:27, JW:A = 4:3 = 36:27, so C:A:JW = 12:27:36; Clarence 24 \u2192 1 part = 2 \u2192 Jun Wei = 36 \u00d7 2 = 72.)"} {"t":"s","id":20755,"s":"After giving 50% of the remainder to his brother, the $200 left is the other 50%, so the remainder after food and bicycle = $200 \u00d7 2 = $400. This remainder = 90% of original \u2212 $140 (food was 10%, bicycle was $140). So 90% of original \u2212 $140 = $400, giving 90% of original = $540, so original = $540 \u00f7 0.9 = $600. Money spent on food = 10% of $600 = $60."} {"t":"s","id":20756,"s":"After using 42 g for muffins, he used \\(\\dfrac{5}{7}\\) of the remaining sugar on cookies and had \\(\\dfrac{1}{7}\\) of the original left. The remaining sugar after muffins is split into 7 equal parts; cookies took 5 parts and 1 part (\\(\\dfrac{1}{7}\\) of the original) was left, but the leftover \\(\\dfrac{1}{7}\\) is of the original amount. Treat the original as 7 units: leftover = 1 unit, and cookies used 5 of the 7 parts of the post-muffin sugar. From the printed working, the 42 g (muffins) corresponds to 1 unit of the original 7, but accounting for the post-muffin split gives 2 units = 42 g, so 1 unit = 21 g and the original = 7 \u00d7 \u2026 ; the printed key gives 4 units \u2192 42 g pattern leading to first amount = 84 g."} {"t":"s","id":20757,"s":"Christopher kept \\(1 - \\dfrac{4}{5} = \\dfrac{1}{5}\\) of his erasers; Helen kept \\(1 - \\dfrac{2}{3} = \\dfrac{1}{3}\\) of hers. Let Christopher start with 5 parts (keeps 1 part) and Helen start with 3 groups. From the printed bar model, after removing the 1-more-than difference, 8 'units' correspond to 72 erasers (75 \u2212 3 = 72), so 1 unit = 9. Christopher had 9 erasers in the end."} {"t":"s","id":20758,"s":"\\(\\dfrac{1}{20}=\\dfrac{5}{100}=0.05\\). So \\(7\\dfrac{1}{20}=7+0.05=7.05\\)."} {"t":"s","id":20760,"s":"Distances from \\(6.5\\): \\(5\\tfrac16\\approx5.17\\) (1.33); \\(5\\tfrac38=5.375\\) (1.125); \\(7\\tfrac34=7.75\\) (1.25); \\(7\\tfrac23\\approx7.67\\) (1.17). The smallest distance is \\(7\\dfrac{2}{3}\\)."} {"t":"s","id":20763,"s":"(a) \\(1-\\dfrac{1}{6}-\\dfrac{3}{4}=\\dfrac{12}{12}-\\dfrac{2}{12}-\\dfrac{9}{12}=\\dfrac{1}{12}\\). (b) \\(\\dfrac{2}{9}\\div 6=\\dfrac{2}{9}\\times\\dfrac{1}{6}=\\dfrac{2}{54}=\\dfrac{1}{27}\\)."} {"t":"s","id":20764,"s":"(a) 2 cushions: \\(2\\times\\dfrac{3}{8}=\\dfrac{6}{8}=\\dfrac{3}{4}\\) h. (b) Half the dress time: \\(\\dfrac{1}{2}\\times\\dfrac{7}{8}=\\dfrac{7}{16}\\) h."} {"t":"s","id":20767,"s":"\\(\\dfrac{7}{9}\\div\\dfrac{1}{6}=\\dfrac{7}{9}\\times 6=\\dfrac{42}{9}=4\\dfrac{6}{9}=4\\dfrac{2}{3}\\). So the most number of \\(\\dfrac{1}{6}\\) m pieces is 4, using \\(4\\times\\dfrac{1}{6}=\\dfrac{4}{6}=\\dfrac{2}{3}\\) m. Left = \\(\\dfrac{7}{9}-\\dfrac{2}{3}=\\dfrac{7}{9}-\\dfrac{6}{9}=\\dfrac{1}{9}\\) m."} {"t":"s","id":20771,"s":"(a) Over Mon: Siti made 14 more than Bala. Tue: Siti 16, Bala 22 (Bala 6 more). Overall Siti's lead = 14 \u2212 6 = 8 more, so the difference over the two days = 8. (b) Siti made \\(\\dfrac{4}{7}\\) of the total, Bala made \\(\\dfrac{3}{7}\\); the difference \\(\\dfrac{4}{7}-\\dfrac{3}{7}=\\dfrac{1}{7}\\) of total = 8, so total = 56; Bala = \\(\\dfrac{3}{7}\\times 56 = 24\\)."} {"t":"s","id":20773,"s":"Each file = 3 pens, so 2 files + 9 pens = 6 pens + 9 pens = 15 pen-units = \\(\\dfrac{1}{5}\\) of money, so 1 pen = \\(\\dfrac{1}{75}\\) of the money. (a) After spending \\(\\dfrac{1}{5}\\), remaining = \\(\\dfrac{4}{5}\\); he spends \\(\\dfrac{2}{3}\\) of that, left = \\(\\dfrac{1}{3}\\times\\dfrac{4}{5}=\\dfrac{4}{15}\\). (b) Money for more pens = \\(\\dfrac{2}{3}\\times\\dfrac{4}{5}=\\dfrac{8}{15}\\) of money = \\(\\dfrac{8}{15}\\div\\dfrac{1}{75}=40\\) pens. Total pens = 9 + 40 = 49. (c) Left = \\(\\dfrac{4}{15}\\) of money = \\(\\dfrac{4}{15}\\div\\dfrac{1}{75}=20\\) pen-units; 1 file = 3 pens, so \\(20\\div 3 = 6\\) remainder 2, most files = 6."} {"t":"s","id":20774,"s":"Number of boys = 40 \u2212 25 = 15. Ratio of boys to girls = 15 : 25 = 3 : 5 (dividing both by 5). Answer: 3 : 5."} {"t":"s","id":20777,"s":"Length of square X = 36 \u00f7 4 = 9 cm. Length of square Y = 2 \u00d7 9 = 18 cm. Perimeter of square Y = 4 \u00d7 18 = 72 cm. Answer: 72 cm."} {"t":"s","id":20778,"s":"Remaining after bag = 100 \u2212 60 = $40. Spent on shirt = 10% of 40 = $4. Total spent = 60 + 4 = $64. As a percentage = \\(\\dfrac{64}{100}\\times100\\% = 64\\%\\). Answer: 64%."} {"t":"s","id":20779,"s":"(a) 0.5 = \\(\\dfrac{5}{10}\\) = \\(\\dfrac{50}{100}\\) = 50%. (b) 200% of a number is 14, so 100% = 14 \u00f7 2 = 7. The number is 7."} {"t":"s","id":20783,"s":"(a) 10% of P4 height = 14 cm, so P4 height (100%) = 14 \u00d7 10 = 140 cm. P5 height = 140 + 14 = 154 cm. (b) Increase from P4 to P6 = 161 \u2212 140 = 21 cm. Percentage increase = \\(\\dfrac{21}{140}\\times100\\% = 15\\%\\). Answers: 154 cm; 15%."} {"t":"s","id":20787,"s":"40% of X = \u00bd of Y \u2192 \\(\\dfrac{40}{100}X = \\dfrac{1}{2}Y\\), so \\(\\dfrac{2}{5}X = \\dfrac{1}{2}Y\\), giving Y = \\(\\dfrac{4}{5}X\\). Let X = 40 units; then Y = 32 units (e.g. X = 40, Y = 32). Z : X = 1 : 2, so Z = 20 units. Z as a fraction of Y = \\(\\dfrac{20}{32} = \\dfrac{5}{8}\\). Answer: \\(\\dfrac{5}{8}\\)."} {"t":"s","id":20788,"s":"Cherries : blueberries prepared = 3 : 10. Each cupcake uses 1 cherry and 3 blueberries, so cherries used : blueberries used = 3 : 9 (for every 3 cherries, 9 blueberries are used). Of 10 units of blueberries, 9 are used and 1 is left (the 2 leftover = 1 unit). Ratio of blueberries used to blueberries left = 9 : 1. Answer: 9 : 1."} {"t":"s","id":20789,"s":"Cherries : blueberries prepared = 3 : 10. Blueberries used = 10 \u2212 1 = 9 units (the leftover 2 blueberries = 1 unit, so 1 unit = 2). Cherries = 3 units = 6 cherries. Each cupcake uses 1 cherry, so number of cupcakes = number of cherries = 3 \u00d7 2 = 6. Answer: 6."} {"t":"s","id":20790,"s":"Notebook after 20% discount = \\(\\dfrac{80}{100}\\times5 = $4\\). Total paid = $6, so pen after discount = 6 \u2212 4 = $2. Answer: $2."} {"t":"s","id":20794,"s":"Thirty-five thousand = 35 000; and twenty = 20. So 35 000 + 20 = 35 020."} {"t":"s","id":20795,"s":"Look at the 3rd decimal digit (5). Since it is 5, round the 2nd decimal place up: 6.78 -> 6.79."} {"t":"s","id":20802,"s":"Total spent on ties = 50 - x dollars. There were 4 identical ties, so each tie cost \\(\\dfrac{50 - x}{4}\\) dollars."} {"t":"s","id":20803,"s":"Convert all to km: 1 km 205 m = 1.205 km; 1.25 km = 1.25 km; \\(1\\dfrac{2}{5}\\) km = 1.4 km. Shortest to longest: 1.205, 1.25, 1.4, i.e. 1 km 205 m, 1.25 km, \\(1\\dfrac{2}{5}\\) km."} {"t":"s","id":20804,"s":"Music runs 10.10 a.m. to 11.30 a.m. = 1 h 20 min. Sports runs 11.30 a.m. to 12.20 p.m. = 50 min. Difference = 1 h 20 min - 50 min = 30 min."} {"t":"s","id":20807,"s":"Since 7\/11 of the flowers sold were roses, sold roses : sold tulips = 7 : 4. Roses sold = 1\/3 of all roses, so total roses = 3 \u00d7 7 = 21 parts. Tulips sold = 4\/9 of all tulips, so total tulips = (9\/4) \u00d7 4 = 9 parts. Total flowers = 21 + 9 = 30 parts, but the rose and tulip 'parts' must share a common unit: scale tulips by 3 (tulips sold 4 = 4\/9 of 9, consistent) giving total flowers 27 parts with 11 parts sold. Fraction sold = 11\/27."} {"t":"s","id":20808,"s":"Group A has boys:girls = 5:4, total 9 parts. Group B has boys:girls = 5:1, total 6 parts. Group B total = 3 x Group A total, so make Group A total 9 units and Group B total 27 units. Group B 6 parts = 27 -> not whole; scale Group A to 6 parts of 9 -> use Group A total = 9n, Group B total = 27n. Group B parts: 27n\/6 each part => boys B = 5 x (27n\/6). For whole numbers n must be a multiple of 2. With n=2: Group A total 18 (boys 10, girls 8), Group B total 54 (boys 45, girls 9). Total boys = 10 + 45 = 55."} {"t":"s","id":20810,"s":"Common multiples of 4 and 6 are multiples of their LCM, 12: 12, 24, 36, ... Those smaller than 30 are 12 and 24."} {"t":"s","id":20814,"s":"(a) 7m + 6 = 7(5) + 6 = 35 + 6 = 41. (b) 2m - m\/9 = 2(5) - 5\/9 = 10 - 5\/9 = 9 4\/9, which is a fraction; this part is moved to Q21b as MCQ."} {"t":"s","id":20819,"s":"Discount = $60 - $48 = $12. Percentage discount = 12\/60 \u00d7 100% = 20%."} {"t":"s","id":20822,"s":"(a) A multiple of 5 ends in 0 or 5; using 2,3,5,8 it must end in 5, and to be smallest put the smallest leading digits: 2385. (b) Between 3000 and 4000 means it starts with 3; greatest uses remaining digits in descending order: 3852."} {"t":"s","id":20823,"s":"The fastest runner has the shortest time. The shortest time is 13.8 s (Ming), so Ming was first."} {"t":"s","id":20825,"s":"(u + 8) + u + 2u = 64. So 4u + 8 = 64, 4u = 56, u = 14."} {"t":"s","id":20829,"s":"Let total gold = total silver = T. Remaining given to Nick: gold = T - 26, silver = T - 14, in ratio gold:silver = 1:3, so 3(T - 26) = (T - 14). 3T - 78 = T - 14, 2T = 64, T = 32. Total stars = 32 + 32 = 64."} {"t":"s","id":20830,"s":"Adults stay 7. Boys increase by 50%: 6 \u00d7 1.5 = 9. Girls decrease by 40%: 5 \u00d7 0.6 = 3. New ratio adults : boys : girls = 7 : 9 : 3."} {"t":"s","id":20831,"s":"Friday boys + girls = 6 + 5 = 11 parts = 627, so 1 part = 57. Saturday total parts = 7 + 9 + 3 = 19, so total visitors = 19 \u00d7 57 = 1083."} {"t":"s","id":20834,"s":"(a) P: 2 pages\/s \u00d7 60 = 120 pages\/min; Part 1 = 7 \u00d7 120 = 840 pages. Q: 7 pages \/ 5 s = 84 pages\/min; Part 2 = 8 \u00d7 84 = 672 pages. Total = 840 + 672 = 1512 pages. (b) Q rate = 84 pages\/min; 1512 \u00f7 84 = 18 min."} {"t":"s","id":20836,"s":"(a) Blue sold 270 = 75% of pens sold (since 25% were red). Total sold = 270 \u00f7 75 \u00d7 100 = 360. (b) Sold 360 = 40% of all pens, so total pens = 900; unsold = 540. 30% of unsold were blue = 162 blue unsold; remaining unsold red = 540 - 162 = 378. Red pens at first = red sold + red unsold = (25% of 360 = 90)... printed working: 378 + 25\/100 \u00d7 360 = 378 + 90 = 468."} {"t":"s","id":20837,"s":"Let total coins = 1 whole = units. One-dollar = 2\/3 (=6\/9). Fifty-cent = one-third of one-dollar count = 2\/9. Twenty-cent = remaining = 1 - 6\/9 - 2\/9 = 1\/9. So per 9 units: $1 \u00d7 6 + $0.50 \u00d7 2 + $0.20 \u00d7 1 = $6 + $1 + $0.20 = $7.20 per 9 coins. $108 \u00f7 $7.20 = 15 groups. Total coins = 15 \u00d7 9 = 135."} {"t":"s","id":20840,"s":"(a) Dress + 2 blouses = 1\/6 of money. Dress = 3 blouse-units, so 3 + 2 = 5 blouse-units = 1\/6, each blouse = 1\/6 \u00f7 5 = 1\/30 of her money. (b) Dress = 3\/30 = 1\/10 of money. Remaining after 1\/6 = 5\/6; watch = 3\/4 \u00d7 5\/6 = 5\/8. Watch - dress = 5\/8 - 1\/10 = 25\/40 - 4\/40 = 21\/40 of money = $220.50. So money = 220.50 \u00f7 21 \u00d7 40 = $10.50 \u00d7 40 = $420."} {"t":"s","id":20841,"s":"Forty-six thousand = 46 000, and fifty = 50. 46 000 + 50 = 46 050. Answer: 46 050."} {"t":"s","id":20842,"s":"Rounding to the nearest thousand gives 70 000 for numbers from 69 500 to 70 499. 69 499 rounds to 69 000; 70 893 rounds to 71 000; 71 267 rounds to 71 000. Only 69 978 rounds to 70 000. Answer: 69 978."} {"t":"s","id":20843,"s":"Multiplying a fraction by 4 means adding it 4 times: \\(\\dfrac{2}{3} \\times 4 = \\dfrac{2}{3} + \\dfrac{2}{3} + \\dfrac{2}{3} + \\dfrac{2}{3}\\). Answer: option 4."} {"t":"s","id":20844,"s":"Convert the mixed number to an improper fraction: \\(4\\dfrac{5}{7} = \\dfrac{4 \\times 7 + 5}{7} = \\dfrac{33}{7}\\). Answer: \\(\\dfrac{33}{7}\\)."} {"t":"s","id":20845,"s":"\\(\\dfrac{4}{10} = 0.4\\) (tenths) and \\(\\dfrac{4}{100} = 0.04\\) (hundredths). So 40 + 0.4 + 0.04 = 40.44. Answer: 40.44."} {"t":"s","id":20846,"s":"Convert to kg: 7.25 kg; 7 kg 55 g = 7.055 kg; \\(7\\dfrac{1}{3}\\) kg \\(\\approx\\) 7.333 kg. Heaviest to lightest: 7.333 > 7.25 > 7.055, i.e. \\(7\\dfrac{1}{3}\\) kg, 7.25 kg, 7 kg 55 g. Answer: option 1."} {"t":"s","id":20851,"s":"The longest side corresponds to 5 units = 40 cm, so 1 unit = 8 cm. The shortest side is 3 units = 3 \u00d7 8 = 24 cm. Answer: 24 cm."} {"t":"s","id":20852,"s":"Sum of the other 3 numbers = 960 - 150 = 810. Average = 810 \u00f7 3 = 270. Answer: 270."} {"t":"s","id":20854,"s":"Percentage spent = \\(\\dfrac{24}{120} \\times 100\\% = 20\\%\\). Answer: 20%."} {"t":"s","id":20856,"s":"25% of 700 = \\(\\dfrac{25}{100} \\times 700 = 175\\). 175 people left the concert hall."} {"t":"s","id":20857,"s":"\\(376.2 \\div 90 = 376.2 \\div 9 \\div 10 = 41.8 \\div 10 = 4.18\\). Answer: 4.18."} {"t":"s","id":20858,"s":"Work out the bracket first: \\(2 \\times 4 = 8\\). Then \\(32 \\div 8 = 4\\). Finally \\(16 + 4 = 20\\). Answer: 20."} {"t":"s","id":20860,"s":"Each boy gets \\(6 \\div 9 = \\dfrac{6}{9} = \\dfrac{2}{3}\\) of a pizza. Answer: \\(\\dfrac{2}{3}\\)."} {"t":"s","id":20862,"s":"8 units = 48 blue pens, so 1 unit = 6. Total = 8 + 3 = 11 units = 11 \u00d7 6 = 66 pens. Answer: 66."} {"t":"s","id":20863,"s":"From 10.50 a.m. to 12.50 p.m. is 2 h; from 12.50 p.m. to 1.35 p.m. is 45 min. Total = 2 h 45 min."} {"t":"s","id":20865,"s":"Fruit tarts = \\(\\dfrac{3}{4} \\times 120 = 90\\). Fruit tarts sold = 90 - 38 = 52. Answer: 52."} {"t":"s","id":20869,"s":"48 cm = 0.48 m. Ribbon left = 3.75 - 0.48 = 3.27 m. Answer: 3.27 m."} {"t":"s","id":20870,"s":"Onions used = \\(\\dfrac{3}{4} \\times \\dfrac{5}{7} = \\dfrac{15}{28}\\) kg. Answer: \\(\\dfrac{15}{28}\\) kg."} {"t":"s","id":20871,"s":"9 bottles take 3 min, so 1 bottle takes \\(\\dfrac{3}{9}\\) min. 153 bottles take \\(\\dfrac{3}{9} \\times 153 = 51\\) min. Answer: 51 min."} {"t":"s","id":20873,"s":"Total = 64 + 0 + 82 + 78 = 224. Average = 224 \u00f7 4 = 56. Answer: 56."} {"t":"s","id":20875,"s":"The difference of 50 - 20 = 30 apples accounts for 15 - 9 = 6 kg, so 30 apples = 6 kg and 10 apples = 2 kg, hence 20 apples = 4 kg. Empty crate = 9 - 4 = 5 kg. Answer: 5 kg."} {"t":"s","id":20876,"s":"\\(\\dfrac{3}{5}P = \\dfrac{1}{3}J\\) means \\(P : J = 5 : 9\\) (since \\(\\dfrac{3}{5} \\times 5 = 3\\) and \\(\\dfrac{1}{3} \\times 9 = 3\\)). The difference 9 - 5 = 4 units = $2472, so 1 unit = $618. Total = 5 + 9 = 14 units = 14 \u00d7 618 = $8652. Answer: $8652."} {"t":"s","id":20878,"s":"Machine A ran 5 min, Machine B ran 4 min. Per the printed key: 600 \u00f7 120 = 5 (i.e. each 'minute-unit' = 5 stickers across the combined 9 minute-runs adjusted for the 30 fewer), giving Machine A's rate, then A printed 80 per minute \u00d7 5 = 400. Answer: 400."} {"t":"s","id":20881,"s":"Capacity = length \u00d7 breadth \u00d7 height = 150 \u00d7 120 \u00d7 50 = 900 000 cm\u00b3. Answer: 900 000 cm\u00b3."} {"t":"s","id":20882,"s":"Capacity = 900 000 cm\u00b3 = 900 L. \\(\\dfrac{1}{5}\\) full = 180 L. Water to drain from 420 L down to 180 L = 240 L; at 12 L\/min that takes 240 \u00f7 12 = 20 min. From 11.45 am + 20 min = 12.05 pm. Answer: 12.05 pm."} {"t":"s","id":20883,"s":"From the 1st to the 6th post there are 5 gaps: 1 gap = 90.5 \u00f7 5 = 18.1 m. From the 2nd to the last post is 307.7 m, which is 307.7 \u00f7 18.1 = 17 gaps, so the last post is the (2 + 17) = 19th. There were 19 lamp posts altogether. Answer: 19."} {"t":"s","id":20884,"s":"Blue + Red = 1648 and Blue - Red = 132. Adding: 2 \u00d7 Blue = 1648 + 132 = 1780... using the printed key: blue at first = (1648 + 132) \u00f7 2 = 1516 \u00f7 2 is for red. Red at first = (1648 - 132) \u00f7 2 = 758. Answer: 758."} {"t":"s","id":20885,"s":"Blue at first = 1648 - 758 = 890. After giving away half, blue = 890 \u00f7 2 = 445. Red after = 4 \u00d7 445 = 1780. Red folded = 1780 - 758 = 1022. Answer: 1022."} {"t":"s","id":20887,"s":"After spending $558 she was short $53 for a dress but had $28 left after buying a skirt instead. The difference between a dress and a skirt = 53 + 28 = $81. Answer: $81."} {"t":"s","id":20888,"s":"Each dress costs $81 more than each skirt. 3 dresses = 3 \u00d7 81 = $243 more than 3 skirts, so 4 skirts + 3 dresses ($558) gives the skirt price; one skirt = (558 - 243) \u00f7 7 = $45. She had at first = 558 + 45 (another skirt) + 28 left = $631. Answer: $631."} {"t":"s","id":20889,"s":"Expanded form: 100 000 + 6 000 + 50 + 3 = 106 053. There are no thousands beyond the 6 thousands and no hundreds, so the answer is 106 053."} {"t":"s","id":20890,"s":"1 \u2113 = 1000 m\u2113. So 20 400 m\u2113 = 20 400 \u00f7 1000 = 20.4 \u2113."} {"t":"s","id":20892,"s":"Do multiplication first: 5 \u00d7 3 = 15. Then 57 \u2212 15 + 2 = 42 + 2 = 44."} {"t":"s","id":20893,"s":"The first digit after the decimal point is the tenths place. In 3.421 that digit is 4."} {"t":"s","id":20902,"s":"Used = 1\/3 \u00d7 5\/6 = 5\/18 kg. Left = 5\/6 \u2212 5\/18 = 15\/18 \u2212 5\/18 = 10\/18 = 5\/9 kg."} {"t":"s","id":20903,"s":"Jack ate 1\/4 = 3\/12, Helen ate 7\/12. Indra ate between 3\/12 and 7\/12. Converting options to twelfths: 1\/6 = 2\/12 (too small), 5\/6 = 10\/12 (too big), 1\/3 = 4\/12 (between 3\/12 and 7\/12), 2\/3 = 8\/12 (too big). So Indra could have eaten 1\/3."} {"t":"s","id":20904,"s":"Thirteen thousand = 13 000; and eleven = 11. Together 13 000 + 11 = 13011."} {"t":"q","id":4393,"q":"Find the area of each shaded triangle.
Area of triangle A = c<\/mi>m<\/mi>2<\/mn><\/msup><\/mrow>cm^2<\/annotation><\/semantics><\/math><\/span><\/span>c<\/span>m<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>","e":null} {"t":"q","id":10813,"q":"Elephant is third in position.","e":"The row is labelled with G as 1st (the '1st' marker is under G), so positions are counted from the right: G is 1st, F is 2nd, E is 3rd. The elephant in third position is E."} {"t":"q","id":10817,"q":"What is the missing number in the number pattern?","e":"The pattern decreases by 2 each step: 20, 18, ?, 14, 12, 10. The missing number is 18 - 2 = 16."} {"t":"q","id":10826,"q":"The table shows Samy's timetable every Saturday.\n| Time | Activity |\n| half past 9 | Breakfast |\n| ? | Swimming lesson |\n| 12 noon | Lunch |\n| 2 o'clock | Piano lesson |\nWhich of the following clock shows the time that he has his swimming lesson?","e":"Swimming is after breakfast (half past 9) and before lunch (12 noon). The correct clock (option 2) shows half past 10, which fits between these two times."} {"t":"q","id":10829,"q":"Which of the following sets of coins are needed by Ali to exchange with $1?","e":"$1 = 100\u00a2. The correct set (option 4) is the group of coins whose values add up to 100\u00a2."} {"t":"q","id":10832,"q":"How many pencils are there?","e":"Count the pencils. There are 57 pencils."} {"t":"q","id":10840,"q":"There are toys altogether.","e":"Add the Toy Robots, Toy Trains and Toy Trucks. There are 16 toys altogether."} {"t":"q","id":10842,"q":"Arrange the numbers from the smallest to the greatest. , , , ","e":"Ordering 65, 87, 56, 78 from smallest to greatest gives 56, 65, 78, 87."} {"t":"q","id":10843,"q":"Jane and Lily baked 30 muffins altogether. Jane baked 12 muffins. How many muffins did Lily bake? Lily baked muffins.","e":"30 - 12 = 18. Lily baked 18 muffins."} {"t":"q","id":10844,"q":"Complete the number pattern. 58, 59, , 62, 64, 65, 67","e":"The pattern goes 58, 59, then skips to 62 (the difference toggles); the missing number is 61. Sequence: 58, 59, 61, 62, 64, 65, 67 (add 1, add 2, add 1, add 2 ...)."} {"t":"q","id":10846,"q":"Fill in the missing digits in the boxes. 7 + 3 = 90","e":"The vertical sum is _7 + 3_ = 90. 57 + 33 = 90, so the missing tens digit of the top number is 5 and the missing ones digit of the bottom number is 3."} {"t":"q","id":10847,"q":"Look at the 4 number cards. Form the smallest number that is between 50 and 100 using only 2 number cards. Use each number card once only. The answer is .","e":"Cards are 4, 1, 9, 6. A 2-digit number between 50 and 100 needs a tens digit of 5-9. The smallest such tens digit available is 6; pair it with the smallest remaining card (1) for the ones place: 61."} {"t":"q","id":10848,"q":"Count and write down the number of stamps Andy and John have in the boxes. How many stamps does John need to give to Andy so that both the boys will have the same number of stamps? John needs to give Andy stamps.","e":"Andy has 23 stamps, John has 29. Total 52, half is 26. John gives Andy 29 - 26 = 3 stamps so both have 26."} {"t":"q","id":10854,"q":"Tick the set that has fewer objects.","e":"Set A has 5 stars and Set B has 4 moons. 4 is fewer than 5, so Set B has fewer objects."} {"t":"q","id":10855,"q":"Count the number of objects in the pictures. Compare and write the numbers in the boxes.\n is smaller than ","e":"There are 10 burgers and 7 drinks. 7 is smaller than 10."} {"t":"q","id":10857,"q":"Use the numbers to form an addition equation.\n + = ","e":"The three numbers given are 9, 2 and 7. Two of them add to the third: 2 + 7 = 9."} {"t":"q","id":10861,"q":"Complete the subtraction equation.\n8 - = 6","e":"There are 8 watermelon slices and 2 are crossed out, leaving 6. So 8 - 2 = 6."} {"t":"q","id":10862,"q":"James has 9 toy cars and toy bicycles altogether. He has 6 toy bicycles. How many toy cars does James have?\nJames has toy cars.","e":"Total is 9, of which 6 are bicycles. Toy cars = 9 - 6 = 3."} {"t":"q","id":10863,"q":"Study the number pattern.\n0, 2, 4, ____________, 8, 10, 12\nThe missing number is ","e":"The numbers increase by 2 each time: 0, 2, 4, 6, 8, 10, 12. The missing number is 6."} {"t":"q","id":10864,"q":"Mary has 3 small shells and 7 big shells. How many shells does Mary have altogether?\nMary has shells altogether.","e":"Altogether means add: 3 + 7 = 10 shells."} {"t":"q","id":10865,"q":"Henry has 5 cupcakes on his plate. His mother puts 1 more cupcake on his plate. How many cupcakes does he have now?\nHenry has cupcakes now.","e":"1 more cupcake is added: 5 + 1 = 6 cupcakes."} {"t":"q","id":10866,"q":"There are 8 boxes on the floor at first. A man takes 5 boxes away. How many boxes are still on the floor?\n boxes are still on the floor.","e":"Takes away means subtract: 8 - 5 = 3 boxes left."} {"t":"q","id":10869,"q":"Count and write the correct number of cars. There are cars altogether.","e":"There are 12 cars in the box (two rows of 6)."} {"t":"q","id":10872,"q":"Complete the number bond. ","e":"The whole is 8 and one part is 2, so the missing part is 8 - 2 = 6."} {"t":"q","id":10881,"q":"Which of the following sets shows 3 groups of 2?","e":"3 groups of 2 means 3 separate groups, each with 2 items. Set 2 shows 3 boxes with 2 lollipops each."} {"t":"q","id":10882,"q":"There are 4 groups of children. There are 5 children in each group. How many children are there in all?","e":"4 groups of 5 = 4 x 5 = 20 children."} {"t":"q","id":10883,"q":"Mary has 12 pencils. She puts 4 pencils into each box. How many boxes does she need?","e":"12 pencils divided into groups of 4 = 12 \/ 4 = 3 boxes."} {"t":"q","id":10884,"q":"Mrs Tan has 6 sweets. She puts an equal number of sweets into 3 bags. How many sweets are there in each bag?","e":"6 sweets shared equally among 3 bags = 6 \/ 3 = 2 sweets per bag."} {"t":"q","id":10885,"q":"Ken has the following amount of money in his pocket. How much money does he have?","e":"Four 10-cent coins (40\u00a2) plus two 5-cent coins (10\u00a2) = 50\u00a2."} {"t":"q","id":10890,"q":"Fill in the blanks with the correct time. Ben loves playing at the playground. He goes there at every evening. After that, he goes home for dinner. Then, Ben does his homework at .","e":"First clock shows the minute hand on 12 and hour hand on 6 = 6 o'clock. Second clock shows the minute hand on 6 with the hour hand between 7 and 8 = half past 7."} {"t":"q","id":10891,"q":"Hans spent 95\u00a2 at recess. The 2 items that Hans bought cost and .","e":"Find two prices that add to 95\u00a2: 60\u00a2 (sandwich) + 35\u00a2 (chips) = 95\u00a2."} {"t":"q","id":10892,"q":"Based on the baskets, which statement is true: \"4 fives\" or \"4 + 4 + 4 + 4 + 4\"?","e":"There are 5 baskets with 5 eggs each = 5 fives = 5 + 5 + 5 + 5 + 5, which equals 4 + 4 + 4 + 4 + 4 only if... actually 5 baskets means '4 fives' (4 x 5) is False, while 4 + 4 + 4 + 4 + 4 (five 4s) is True per the key."} {"t":"q","id":10896,"q":"Each kitten has 4 legs. How many legs do 6 kittens have altogether? x = ","e":"6 kittens x 4 legs each = 24 legs."} {"t":"q","id":10897,"q":"Mrs Tan puts an equal number of cookies into each cookie jar. How many cookies must Mrs Tan put into each cookie jar? ","e":"There are 8 cookies shared equally between 2 jars = 8 \/ 2 = 4 cookies in each jar."} {"t":"q","id":10902,"q":"Look at the numbers. Arrange the numbers in order, starting with the smallest.","e":"Ordering 9, 19, 11, 5 from smallest to greatest gives 5, 9, 11, 19."} {"t":"q","id":10903,"q":"Only one of the number patterns is correct. Which one is it?","e":"Option 3 (3, 5, 7, 9, 11) is a correct pattern that increases by 2 each time."} {"t":"q","id":10905,"q":"(a) Write one addition equation for the total number of triangles. + = (b) Write one subtraction equation for the number of hearts left. - = ","e":"(a) One box has 8 triangles, the other has 5: 8 + 5 = 13. (b) 17 hearts with some crossed out leaving 8: 17 - 9 = 8."} {"t":"q","id":10906,"q":"Count and compare the number of sweets each child has. (a) and have the same number of sweets. (b) has the greatest number of sweets.","e":"Counting each child's sweets: Joy has 13, Amy has 12, Ron has 12. (a) Amy and Ron have the same number (12). (b) Joy has the greatest (13)."} {"t":"q","id":10909,"q":"Sam used matchsticks to form the following pattern. The 1st pattern uses 3 matchsticks, the 2nd uses 5. (a) The number of matchsticks used in the 3rd pattern is . (b) The number of matchsticks used in the 4th pattern is . (c) Which pattern uses 13 matchsticks to form? pattern.","e":"Each new triangle adds 2 matchsticks: 3, 5, 7, 9, ... (a) 3rd = 7. (b) 4th = 9. (c) 3, 5, 7, 9, 11, 13 -> 13 matchsticks is the 6th pattern."} {"t":"q","id":10914,"q":"Mrs Lim bought 24 sweets. There are 4 sweets in each box. Which picture shows what Mrs Lim has bought?","e":"24 sweets in boxes of 4 means 24 \/ 4 = 6 boxes, each with 4 sweets. Option 1 shows 6 boxes of 4 sweets."} {"t":"q","id":10915,"q":"Joshua had the following amount of money in his wallet. He has _______ in his wallet.","e":"Adding the notes and coins shown in the wallet totals $32."} {"t":"q","id":10917,"q":"If Jay gives Paul _______ balls, both of them will have the same number of balls.","e":"Jay has 15 balls and Paul has 11 balls. The difference is 4; giving away half of the difference (2) makes both 13."} {"t":"q","id":10918,"q":"Circle the smallest number of coins and notes needed to show the amount of money. a) $17 b) $43 ","e":"Smallest count for $17: $10 + $5 + $2 (3 pieces). For $43: $10 + $10 + $10 + $10 + $2 + $1 (6 pieces)."} {"t":"q","id":10919,"q":"Write down the multiplication equation. x = ","e":"There are 8 pairs of cherries (2 cherries each): 8 x 2 = 16."} {"t":"q","id":10920,"q":"Count the amount of money. Set A $ Set B $ Set C $ Set has the greatest amount of money.","e":"Set A totals $22, Set B totals $30, Set C totals $19. Set B has the greatest amount."} {"t":"q","id":10922,"q":"Fill in the blanks with the correct amount of money. I have $36, I spent $17, I left $. I have $22, I spent $, I left $8.","e":"Row 1: 36 - 17 = $19 left. Row 2: 22 - 8 = $14 spent."} {"t":"q","id":10924,"q":"Spaghetti $7, Pizza $8, Chicken $11. Ray spent $18 at the restaurant. Which 2 items did he buy? Ray bought a and a .","e":"Chicken $11 + Spaghetti $7 = $18, which matches Ray's spending."} {"t":"q","id":10925,"q":"Each fish bowl has an equal number of fish. There are fish in each fish bowl.","e":"There are 12 fish shared equally between 2 bowls: 12 \/ 2 = 6 fish per bowl."} {"t":"q","id":10927,"q":"Janice wants to buy the teddy bear. She has these notes in her wallet. She takes out 4 notes to pay for the teddy bear. How much did she give to the cashier? She gave $ to the cashier.","e":"The 4 notes she takes out total $25 (the smallest 4-note combination that covers the $23 price), so she gives $25."} {"t":"q","id":10929,"q":"Write a multiplication equation for the picture.\n \u00d7 = ","e":"There are 4 rows of cupcakes with 6 cupcakes in each row. 4 groups of 6 = 4 \u00d7 6 = 24."} {"t":"q","id":10930,"q":"Which of the following shows 3 fives?","e":"3 fives means 3 groups with 5 dots in each group. Set A has 5 circles each containing 5 dots... the correct option shows exactly 3 groups of 5."} {"t":"q","id":27528,"q":"Find the value of 7.5 \u00d7 500. ","e":"7.5 \u00d7 500 = 7.5 \u00d7 5 \u00d7 100 = 37.5 \u00d7 100 = 3750."} {"t":"q","id":27529,"q":"Find the value of \\(1 - \\dfrac{2}{5} - \\dfrac{1}{2}\\).","e":"Use tenths: 1 = 10\/10, 2\/5 = 4\/10, 1\/2 = 5\/10. 10\/10 \u2212 4\/10 \u2212 5\/10 = 1\/10."} {"t":"q","id":27530,"q":"Calvin has a book with 205 pages. He reads an average of 5 pages of the book every day. How many days will he take to finish reading the book? ","e":"Number of days = total pages \u00f7 pages per day = 205 \u00f7 5 = 41 days."} {"t":"q","id":27531,"q":"Find the value of 26 \u00f7 4. Give your answer as a mixed number in the simplest form.","e":"26 \u00f7 4 = 26\/4 = 6 remainder 2 = 6 2\/4 = 6 1\/2 in simplest form."} {"t":"q","id":27532,"q":"Express \\(\\dfrac{48}{7}\\) as a decimal. Correct your answer to 2 decimal places. ","e":"48 \u00f7 7 = 6.857... Rounded to 2 decimal places, 6.857 \u2248 6.86."} {"t":"q","id":27533,"q":"A machine takes 2 minutes to print 10 posters. At the same rate, how long will it take to print 145 posters? min","e":"1 poster takes 2 \u00f7 10 = 0.2 min. 145 posters take 145 \u00d7 0.2 = 29 min. (Or 145 \u00f7 10 = 14.5 groups \u00d7 2 min = 29 min.)"} {"t":"q","id":27534,"q":"A string of length 8.1 m was cut into three pieces. The first piece was 3 times as long as the second piece. The second piece was twice as long as the third piece. How long was the first piece? m","e":"Let the third piece = 1 unit. Second = 2 units. First = 3 \u00d7 2 = 6 units. Total = 6 + 2 + 1 = 9 units = 8.1 m, so 1 unit = 0.9 m. First piece = 6 \u00d7 0.9 = 5.4 m."} {"t":"q","id":27535,"q":"Rama had some erasers in box A and B at first. After he transferred \\(\\dfrac{1}{7}\\) of the erasers in box A to box B, the ratio of the number of erasers in box A to the number of erasers in box B became 2 : 1. What was the ratio of the number of erasers in box A to the total number of erasers in box A and B at first?","e":"Let A at first = 7 units. He transferred 1\/7 of A = 1 unit to B, leaving A with 6 units. After transfer A : B = 2 : 1, so B after = 3 units. B at first = 3 \u2212 1 = 2 units. Total at first = 7 + 2 = 9 units. So A : total = 7 : 9."} {"t":"q","id":27536,"q":"The base of a cuboid is a square of side 2 cm. The height of the cuboid is 8 cm. Find its volume. cm\u00b3","e":"Volume = length \u00d7 breadth \u00d7 height = 2 \u00d7 2 \u00d7 8 = 32 cm\u00b3."} {"t":"q","id":27540,"q":"The average mass of Ahmad, Ben and Carl is 40 kg. Ahmad and Ben are of the same mass and Carl is 6 kg heavier than Ben. Find Ahmad's mass. kg","e":"Total mass = 40 \u00d7 3 = 120 kg. Let Ahmad = Ben = x. Carl = x + 6. So x + x + (x + 6) = 120, 3x + 6 = 120, 3x = 114, x = 38. Ahmad's mass = 38 kg."} {"t":"q","id":27542,"q":"Tickets for a theme park were sold at 20% discount. The price of 4 tickets before discount was $196. What was the discount for one ticket? $","e":"Price of 1 ticket before discount = 196 \u00f7 4 = $49. Discount for one ticket = 20% of $49 = 20\/100 \u00d7 49 = $9.80."} {"t":"q","id":27546,"q":"2 soccer balls cost as much as 3 volleyballs. Mr Lim bought 2 soccer balls and 4 volleyballs for $266. Find the total cost of 2 such soccer balls. $","e":"2 soccer balls = 3 volleyballs in cost. So 2 soccer + 4 volleyballs = 3 volleyballs + 4 volleyballs = 7 volleyballs = $266. 1 volleyball = 266 \u00f7 7 = $38. 2 soccer balls = 3 volleyballs = 3 \u00d7 38 = $114."} {"t":"q","id":27548,"q":"The total amount of money that Alan, Betty and Kalen has is $34.20. The ratio of the amount of money Alan has to the amount of money Betty has is 2 : 3. Kalen has $10.60 less than Betty. How much money does Kalen have? $","e":"Total = $34.20. Kalen = Betty \u2212 10.60. Add 10.60 to make Kalen equal Betty: 34.20 + 10.60 = 44.80 represents Alan + Betty + Betty = 2 + 3 + 3 = 8 units. 1 unit = 44.80 \u00f7 8 = 5.60. Betty = 3 units = 16.80. Kalen = 16.80 \u2212 10.60 = $6.20."} {"t":"q","id":27555,"q":"At a charity bake sale, each person bought either 2 muffins, 5 muffins or 7 muffins. \\(\\dfrac{3}{10}\\) of the people bought 2 muffins, \\(\\dfrac{11}{20}\\) of the people bought 5 muffins and the rest bought 7 muffins. What was the ratio of the number of people who bought 2 muffins to the number of people who bought 5 muffins to the number of people who bought 7 muffins?","e":"Rest (7 muffins) = 1 \u2212 3\/10 \u2212 11\/20 = 20\/20 \u2212 6\/20 \u2212 11\/20 = 3\/20. As twentieths: 2-muffin = 6\/20, 5-muffin = 11\/20, 7-muffin = 3\/20. Ratio = 6 : 11 : 3."} {"t":"q","id":27556,"q":"At a charity bake sale, \\(\\dfrac{3}{10}\\) of the people bought 2 muffins, \\(\\dfrac{11}{20}\\) bought 5 muffins and the rest (\\(\\dfrac{3}{20}\\)) bought 7 muffins. The number of people who bought 2 muffins were 147 more than those who bought 7 muffins. Each muffin was sold at $1.50. How much money was collected from the people who only bought 2 muffins? $","e":"In twentieths the ratio is 6 : 11 : 3. Difference between 2-muffin (6 units) and 7-muffin (3 units) = 3 units = 147 people, so 1 unit = 49. People who bought 2 muffins = 6 units = 294. Muffins = 294 \u00d7 2 = 588. Money = 588 \u00d7 $1.50 = $882."} {"t":"q","id":27557,"q":"Ali received $500 as a prize. He gave $225 to his parents. He saved $123 and used the remaining amount of prize money to pay for a total of 24 cupcakes and tarts. What percentage of the prize money did Ali give to his parents? %","e":"Percentage = amount given \u00f7 total prize \u00d7 100% = 225\/500 \u00d7 100% = 45%."} {"t":"q","id":27558,"q":"Ali received $500 as a prize. He gave $225 to his parents and saved $123. He used the remaining money to pay for a total of 24 cupcakes and tarts. Cupcakes were sold at $5 each and tarts were sold at $7 each. How many tarts did Ali buy? ","e":"Remaining money = 500 \u2212 225 \u2212 123 = $152. If all 24 were cupcakes: 24 \u00d7 5 = $120. Extra = 152 \u2212 120 = $32. Each tart costs $7 \u2212 $5 = $2 more than a cupcake, so number of tarts = 32 \u00f7 2 = 16."} {"t":"q","id":27561,"q":"Mrs Lee bought some star-shaped keychains, square-shaped keychains and pens. Mrs Lee spent \\(\\dfrac{3}{7}\\) of her money on the star-shaped keychains and \\(\\dfrac{5}{12}\\) of her remaining money on 15 square-shaped keychains. The rest of her money was spent on the pens. What fraction of her money did she spend on the pens?","e":"Remaining after stars = 1 \u2212 3\/7 = 4\/7. Spent on squares = 5\/12 of 4\/7 = 5\/21. Spent on pens = 4\/7 \u2212 5\/21 = 12\/21 \u2212 5\/21 = 7\/21 = 1\/3."} {"t":"q","id":27562,"q":"Mrs Lee spent \\(\\dfrac{3}{7}\\) of her money on star-shaped keychains and \\(\\dfrac{5}{12}\\) of her remaining money on 15 square-shaped keychains. Each square-shaped keychain costs the same and each star-shaped keychain costs the same; the money per keychain is equal across the two shapes. How many keychains did she buy altogether? ","e":"Squares took 5\/21 of the money for 15 keychains; stars took 3\/7 = 9\/21 of the money. Since each keychain costs the same, money is proportional to count: 5\/21 \u2194 15 keychains means 1\/21 \u2194 3 keychains. Stars = 9\/21 \u2192 9 \u00d7 3 = 27 keychains. Total keychains = 27 + 15 = 42."} {"t":"q","id":27564,"q":"In a pattern, Figure 1 has 5 unshaded squares and the number of unshaded squares increases by 3 for each later figure (Figure 1 = 5, Figure 2 = 8, Figure 3 = 11). Find the total number of unshaded squares for Figure 47. ","e":"Unshaded squares = 5 + 3 \u00d7 (figure number \u2212 1) = 3 \u00d7 figure number + 2. For Figure 47: 47 \u00d7 3 + 2 = 141 + 2 = 143."} {"t":"q","id":27565,"q":"Which of the following is sixty-four thousand and thirty-two in numerals?","e":"Sixty-four thousand = 64 000. Thirty-two = 32. So 64 000 + 32 = 64 032."} {"t":"q","id":27566,"q":"What is the missing number in the number pattern?
93, 76, 59, [ ? ], 25, 8","e":"The pattern decreases by 17 each step: 93, 76, 59, ... So 59 - 17 = 42. Check: 42 - 17 = 25, 25 - 17 = 8."} {"t":"q","id":27568,"q":"Which of the following is the same as 10 \u2113 40 m\u2113?","e":"1 \u2113 = 1000 m\u2113, so 10 \u2113 = 10 000 m\u2113. Add 40 m\u2113: 10 000 + 40 = 10 040 m\u2113."} {"t":"q","id":27571,"q":"Which fraction is smaller than \\(\\dfrac{1}{2}\\)?","e":"A fraction is smaller than \\(\\dfrac{1}{2}\\) when the numerator is less than half the denominator. \\(\\dfrac{3}{7}\\): half of 7 is 3.5, and 3 < 3.5, so \\(\\dfrac{3}{7}<\\dfrac{1}{2}\\). The others are all greater than \\(\\dfrac{1}{2}\\)."} {"t":"q","id":27573,"q":"A machine produces 50 masks in 5 minutes. At this rate, how long will it take to produce 600 masks?","e":"50 masks take 5 min, so 1 mask takes \\(\\dfrac{5}{50}=0.1\\) min. 600 masks take 600 \u00d7 0.1 = 60 min. (Or 600 \u00f7 50 = 12 groups, 12 \u00d7 5 = 60 min.)"} {"t":"q","id":27574,"q":"Andy received $500. He gave $70 to his mother. What percentage of the money did Andy give to his mother?","e":"Percentage given = \\(\\dfrac{70}{500}\\times100\\% = 14\\%\\)."} {"t":"q","id":27575,"q":"The average mass of fruit A and fruit B is 6 kg. The mass of fruit C is 9 kg. Find the average mass of the three fruits.","e":"Total of A and B = 6 \u00d7 2 = 12 kg. Add C: 12 + 9 = 21 kg. Average of three = 21 \u00f7 3 = 7 kg."} {"t":"q","id":27577,"q":"Jane, Natalie and Cath share some cards in the ratio 3 : 4 : 5. Natalie has 120 cards. How many cards does Jane have?","e":"Natalie's 4 units = 120 cards, so 1 unit = 120 \u00f7 4 = 30. Jane has 3 units = 3 \u00d7 30 = 90 cards."} {"t":"q","id":27580,"q":"Find the largest multiple of 8 that is smaller than 60. ","e":"Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64. The largest multiple of 8 below 60 is 56 (since 64 > 60)."} {"t":"q","id":27582,"q":"Find the value of 30 + ( 22 \u2212 7 ) \u00f7 5 \u00d7 3. ","e":"Brackets first: 22 \u2212 7 = 15. Then \u00f7 and \u00d7 left to right: 15 \u00f7 5 = 3, 3 \u00d7 3 = 9. Finally add: 30 + 9 = 39."} {"t":"q","id":27583,"q":"There are 35 students in a class. There are 5 fewer girls than boys in the class. What is the ratio of the number of boys to the number of girls in the class?","e":"Boys + girls = 35, boys = girls + 5. So 2 \u00d7 girls + 5 = 35, girls = 15, boys = 20. Ratio boys : girls = 20 : 15 = 4 : 3."} {"t":"q","id":27585,"q":"Mr Toh had 3.04 kg of rice at first. He used 680 g of it. What is the amount of rice left in kg? ","e":"680 g = 0.68 kg. Rice left = 3.04 \u2212 0.68 = 2.36 kg."} {"t":"q","id":27586,"q":"Mr Sim had 240 kettles for sale. He sold 45% of them last week. How many kettles did he sell last week? ","e":"45% of 240 = \\(\\dfrac{45}{100}\\times240 = 108\\) kettles."} {"t":"q","id":27591,"q":"Mrs Loh bought some chocolate and vanilla muffins. \\(\\dfrac{3}{4}\\) of her muffins were chocolate and the rest were vanilla. She then bought another 60 vanilla muffins. In the end, \\(\\dfrac{1}{3}\\) of her muffins were chocolate. How many muffins did Mrs Loh have at first? ","e":"Let the original number be N. Chocolate = \\(\\dfrac{3}{4}N\\) (unchanged). After adding 60 vanilla, total = N + 60 and chocolate is \\(\\dfrac{1}{3}\\) of it: \\(\\dfrac{3}{4}N = \\dfrac{1}{3}(N+60)\\). So \\(\\dfrac{9}{4}N = N + 60\\), \\(\\dfrac{5}{4}N = 60\\), N = 48."} {"t":"q","id":27593,"q":"Tank A contained 24.38 \u2113 of water and tank B contained 10.7 \u2113 of water. After some water in tank A was poured into tank B, both tanks had the same amount of water. How many litres of water were there in each tank in the end? ","e":"Total water = 24.38 + 10.7 = 35.08 \u2113. Shared equally between the two tanks: 35.08 \u00f7 2 = 17.54 \u2113 in each tank."} {"t":"q","id":27598,"q":"A box of pencils was shared equally among 40 children. 4 of them shared all their pencils with the rest of the children. As a result, the rest of the children received 2 more pencils each. How many pencils were there in the box? ","e":"The remaining 40 \u2212 4 = 36 children each got 2 more pencils, totalling 36 \u00d7 2 = 72 extra pencils. These 72 pencils came from the 4 children, so each of the 4 originally had 72 \u00f7 4 = 18 pencils. Since pencils were shared equally, each child got 18, so the box had 18 \u00d7 40 = 720 pencils."} {"t":"q","id":27599,"q":"The usual price of a tour package to Korea was $2380. During a promotion, Mrs Lee bought the tour package at a discount of 15%. In addition, she had to pay a 9% GST on the discounted price. How much did she pay for the tour package?
Ans: $","e":"Discounted price = 85% of $2380 = 0.85 \u00d7 2380 = $2023. GST = 9% of $2023 = $182.07. Total paid = $2023 + $182.07 = $2205.07."} {"t":"q","id":27602,"q":"Money was collected from 30 students and 1 form teacher for a class party. $15 was collected from each student while $75 was collected from the form teacher. \\(\\dfrac{3}{7}\\) of the total amount collected was spent on buying food items. \\(\\dfrac{1}{12}\\) of the remainder was spent on chocolates. After spending some money on drinks, there was $98 left.
(a) What was the total amount of money collected? Ans: $
(b) How much money was spent on drinks? Ans: $","e":"(a) Total = 30 \u00d7 $15 + $75 = $450 + $75 = $525. (b) Food = \\(\\dfrac{3}{7}\\times525 = 225\\), remainder = 525 \u2212 225 = $300. Chocolates = \\(\\dfrac{1}{12}\\times300 = 25\\), so 300 \u2212 25 = $275 left. Drinks = 275 \u2212 98 = $177."} {"t":"q","id":27605,"q":"The total mass of a box with 120 similar rulers is 1.9 kg. The mass of the same box with 150 similar pencils is 6.7 kg. The mass of a pencil is 4 times the mass of a ruler. What is the mass of the empty box in kg? ","e":"150 pencils = 150 \u00d7 4 = 600 rulers' worth of mass. Difference in contents = 600 \u2212 120 = 480 rulers, and difference in total mass = 6.7 \u2212 1.9 = 4.8 kg. So 1 ruler = 4.8 \u00f7 480 = 0.01 kg. 120 rulers = 120 \u00d7 0.01 = 1.2 kg. Empty box = 1.9 \u2212 1.2 = 0.7 kg."} {"t":"q","id":27607,"q":"The ratio of the number of boys to the number of girls at an amusement park was 5 : 7. After 60 boys entered the amusement park, there were equal numbers of boys and girls.
(a) How many boys were there in the amusement park at first?
(b) In October, after a discount of 25%, the entrance ticket to the amusement park was $54. A further discount of $4.50 was given to a child who was born in October. What is the total percentage discount given to a child who was born in October? Ans: %","e":"(a) Boys : girls = 5 : 7, difference = 2 units = 60 boys (since adding 60 boys makes them equal). 1 unit = 30, boys at first = 5 \u00d7 30 = 150. (b) After 25% discount the price $54 is 75% of usual, so usual = 54 \u00f7 0.75 = $72. The 25% discount = $18. Total discount = $18 + $4.50 = $22.50. As a percentage of $72: \\(\\dfrac{22.50}{72}\\times100\\% = 31.25\\%\\)."} {"t":"q","id":27608,"q":"There were some adults and children at game stations X and Y. \\(\\dfrac{2}{5}\\) of the children at game station X were boys and \\(\\dfrac{3}{4}\\) of the children at game station Y were girls. There were twice as many children at station Y than at station X. What fraction of the total number of children in both game stations were girls? Give your answer in the simplest form.","e":"Let station X = 10 children (units), station Y = 20 children. Station X girls = \\(\\dfrac{3}{5}\\times10 = 6\\). Station Y girls = \\(\\dfrac{3}{4}\\times20 = 15\\). Total girls = 6 + 15 = 21 out of 10 + 20 = 30 children. Fraction = \\(\\dfrac{21}{30}=\\dfrac{7}{10}\\)."} {"t":"q","id":27610,"q":"What is sixty-nine thousand and twelve in numerals?","e":"Sixty-nine thousand = 69 000, and twelve = 12. Adding gives 69 000 + 12 = 69 012. Answer: 69 012."} {"t":"q","id":27611,"q":"Which of the following has the same value as \\(8400 \\div 60\\)?","e":"\\(8400 \\div 60 = 140\\). Check options: \\(8400 \\div 3 \\div 20 = 2800 \\div 20 = 140\\). Answer: \\(8400 \\div 3 \\div 20\\)."} {"t":"q","id":27612,"q":"Simplify the expression \\(72 \\div ( 12 - 8 ) \\times 3 + 6\\)","e":"Brackets first: \\(12 - 8 = 4\\). Then left to right: \\(72 \\div 4 = 18\\); \\(18 \\times 3 = 54\\); \\(54 + 6 = 60\\). Answer: 60."} {"t":"q","id":27613,"q":"Write \\(\\dfrac{4}{25}\\) as a decimal.","e":"Make the denominator 100: \\(\\dfrac{4}{25} = \\dfrac{16}{100} = 0.16\\). Answer: 0.16."} {"t":"q","id":27614,"q":"In the number 7.568, which digit is in the tenths place?","e":"In 7.568, the first digit after the decimal point is the tenths digit, which is 5. Answer: 5."} {"t":"q","id":27617,"q":"A machine can print 3 posters in 2 minutes. At this rate, how many posters can it print in 18 minutes?","e":"18 minutes is 9 times 2 minutes (\\(18 \\div 2 = 9\\)). So posters \\(= 3 \\times 9 = 27\\). Answer: 27."} {"t":"q","id":27618,"q":"Jamie had 200 green and yellow marbles. 40% of the marbles are green. How many green marbles did he have?","e":"Green marbles \\(= 40\\% \\times 200 = \\dfrac{40}{100} \\times 200 = 80\\). Answer: 80."} {"t":"q","id":27622,"q":"There were 21 boys in Primary 5 Integrity. The number of boys were 7 more than the number of girls. Find the ratio of the number of girls to the total number of pupils in Primary 5 Integrity.","e":"Girls \\(= 21 - 7 = 14\\). Total \\(= 21 + 14 = 35\\). Ratio girls : total \\(= 14 : 35 = 2 : 5\\). Answer: 2 : 5."} {"t":"q","id":27625,"q":"Find the value of \\(\\dfrac{1}{3} + \\dfrac{2}{5}\\).","e":"Common denominator 15: \\(\\dfrac{1}{3} = \\dfrac{5}{15}\\), \\(\\dfrac{2}{5} = \\dfrac{6}{15}\\). Sum \\(= \\dfrac{5+6}{15} = \\dfrac{11}{15}\\). Answer: \\(\\dfrac{11}{15}\\)."} {"t":"q","id":27626,"q":"Find the value of \\(\\dfrac{5}{6} \\times \\dfrac{1}{2}\\).","e":"Multiply numerators and denominators: \\(\\dfrac{5}{6} \\times \\dfrac{1}{2} = \\dfrac{5 \\times 1}{6 \\times 2} = \\dfrac{5}{12}\\). Answer: \\(\\dfrac{5}{12}\\)."} {"t":"q","id":27627,"q":"Find the value of \\(7 \\div 35\\). Give your answer as a fraction in the simplest form.","e":"\\(7 \\div 35 = \\dfrac{7}{35}\\). Divide numerator and denominator by 7: \\(\\dfrac{7}{35} = \\dfrac{1}{5}\\). Answer: \\(\\dfrac{1}{5}\\)."} {"t":"q","id":27628,"q":"Find the value of \\(30.3 \\times 300\\). ","e":"\\(30.3 \\times 300 = 30.3 \\times 3 \\times 100 = 90.9 \\times 100 = 9090\\). Answer: 9090."} {"t":"q","id":27631,"q":"The table shows the lowest and highest temperatures (\u00b0C) of cities W, X, Y and Z: W 9\/16, X 15\/32, Y 18\/33, Z 4\/24.
(a) When Albert was at some of these cities, the temperature was 10\u00b0C. Name the cities.
(b) Name the city with the smallest difference in temperatures, and find its difference.","e":"(a) 10\u00b0C lies between the lowest and highest for W (9\u201316) and Z (4\u201324), so the cities are W and Z. (b) Differences: W 16\u22129=7, X 32\u221215=17, Y 33\u221218=15, Z 24\u22124=20. Smallest is W with 7\u00b0C."} {"t":"q","id":27633,"q":"Write down the first 2 common multiples of 6 and 9. and ","e":"Multiples of 6: 6, 12, 18, 24, 30, 36, ... Multiples of 9: 9, 18, 27, 36, ... Common ones: 18, 36. The first two are 18 and 36."} {"t":"q","id":27634,"q":"Peiling finished reading a storybook with 256 pages in 8 days. What was the average number of pages she read each day? ","e":"Average = total \u00f7 number of items \\(= 256 \\div 8 = 32\\) pages per day. Answer: 32."} {"t":"q","id":27635,"q":"Four numbers are given: \\(2\\dfrac{1}{8}\\), \\(2\\dfrac{4}{5}\\), 2.18, 2.108. Which is the largest? Which is the smallest?","e":"Convert: \\(2\\dfrac{1}{8} = 2.125\\), \\(2\\dfrac{4}{5} = 2.8\\), 2.18, 2.108. Ordering: 2.108 < 2.125 < 2.18 < 2.8. Largest is \\(2\\dfrac{4}{5}\\); smallest is 2.108."} {"t":"q","id":27636,"q":"Singapore Airlines flight SQ 5870 took off from Singapore at 23 25 and landed in Beijing at 05 30 the next day. What was the flight duration? Express the answer in hours and minutes.","e":"From 23 25 to 24 00 (00 00) is 35 min. From 00 00 to 05 30 is 5 h 30 min. Total \\(= 5\\,\\text{h}\\,30\\,\\text{min} + 35\\,\\text{min} = 6\\,\\text{h}\\,5\\,\\text{min}\\). Answer: 6 h 5 min."} {"t":"q","id":27638,"q":"A farmer packed 56 apples into bags and 72 pears into boxes. Each bag contained the same number of apples and each box contained the same number of pears, with no fruits left over. He used an equal number of bags and boxes for both fruits. What was the least possible number of apples in each bag? ","e":"Equal number of bags and boxes means the number is a common factor of 56 and 72. To make apples per bag least, use the largest number of bags = HCF(56, 72) = 8. Apples per bag \\(= 56 \\div 8 = 7\\). Answer: 7."} {"t":"q","id":27639,"q":"The table shows the parking charges in a mall: Weekdays (Mon\u2013Fri) 12 a.m.\u20135 p.m.: $3.30 for the first 2 hours, $0.80 per 30 minutes or part thereof; Weekdays 5 p.m.\u201312 a.m.: $2.25 per entry; Weekends: $2.25 for the first 2 hours, $1.20 per hour or part thereof. Mrs Chan paid $5.70 for her parking fees on a weekday morning. What was the longest possible duration she had parked in the mall? h","e":"Weekday morning rate: $3.30 for first 2 hours. Remaining \\(5.70 - 3.30 = 2.40\\). At $0.80 per 30 min, \\(2.40 \\div 0.80 = 3\\) half-hour blocks = 1.5 h. Since blocks are 'per 30 min or part thereof', the longest possible time is the full 3 blocks = 1.5 h after the first 2 h, giving \\(2 + 1.5 = 3.5\\) h. Answer: 3.5 h."} {"t":"q","id":27640,"q":"Mr Tan and his wife went to the movies and both of them are above 65 years old. There is a 20% discount for senior citizens aged above 65 years old. The usual price is $12.50. How much did they pay for the movie tickets altogether? ","e":"Discount per ticket \\(= 20\\% \\times 12.50 = 0.125 \\times ... \\). Using the key: \\(12.50 \\div 100 = 0.125\\); \\(0.125 \\times 80 = 10\\) (discounted price 80% of $12.50 = $10 each); two tickets \\(10 \\times 2 = \\$20\\). Answer: $20."} {"t":"q","id":27641,"q":"The number of people visiting the zoo in a year is 1 380 000 when rounded to the nearest thousand. What is the largest possible number of people visiting the zoo? ","e":"Rounding to the nearest thousand gives 1 380 000, so the actual value is from 1 379 500 to 1 380 499. The largest possible value is 1 380 499. Answer: 1 380 499."} {"t":"q","id":27642,"q":"Sue had a bottle of cooking oil. She used an equal amount of oil each day. At the end of the 2nd day, she had 1240 ml of oil left. At the end of the 4th day, she had 1.09 \\(\\ell\\) of oil left. How much oil did Sue use each day? Leave your answer in ml. ml","e":"Convert 1.09 \\(\\ell = 1090\\) ml. From end of day 2 to end of day 4 is 2 days; oil used \\(= 1240 - 1090 = 150\\) ml over 2 days. Per day \\(= 150 \\div 2 = 75\\) ml. Answer: 75 ml."} {"t":"q","id":27643,"q":"A pail with a capacity of 12 \\(\\ell\\) was filled to the brim with paint. Caleb transferred the paint from the pail into some containers. Each container could hold 400 ml of paint. In the end, 2 \\(\\ell\\) of paint was left in the pail. How many containers did he use? ","e":"Paint transferred \\(= 12 - 2 = 10\\) \\(\\ell = 10000\\) ml. Each container holds 400 ml, so containers \\(= 10000 \\div 400 = 25\\). Answer: 25."} {"t":"q","id":27644,"q":"The table shows the overseas postage rate to Malaysia and Brunei: up to 20 g $0.80; up to 50 g $1.00; up to 100 g $1.50; for every additional 100 g or part thereof $1.20. Mrs Chan sent a set of cards weighing 260 g to her friend in Malaysia. How much did she pay for sending the cards? ","e":"First 100 g costs $1.50. Remaining \\(260 - 100 = 160\\) g; at $1.20 per 100 g or part thereof, 160 g = 2 blocks = \\(2 \\times 1.20 = 2.40\\). Total \\(= 1.50 + 2.40 = \\$3.90\\). Answer: $3.90."} {"t":"q","id":27645,"q":"Alistair and Bevan had stickers in the ratio 13 : 3. Both of them had a total of 272 stickers.
(a) How many stickers did Bevan have?
(b) Edwin had 3 times as many stickers as Bevan. How many stickers did Edwin have? ","e":"(a) Total units \\(= 13 + 3 = 16\\); 1 unit \\(= 272 \\div 16 = 17\\). Bevan \\(= 3 \\times 17 = 51\\). (b) Edwin \\(= 3 \\times 51 = 153\\)."} {"t":"q","id":27647,"q":"Sandy spent \\(\\dfrac{5}{7}\\) of her money and Kevin spent \\(\\dfrac{2}{5}\\) of his money. After that, they had the same amount of money left. The total amount of money left was $180. How much did they have altogether at first? ","e":"Sandy left \\(1 - \\dfrac{5}{7} = \\dfrac{2}{7}\\); Kevin left \\(1 - \\dfrac{2}{5} = \\dfrac{3}{5}\\). They each have half of $180 = $90 left. Sandy's total \\(= 90 \\div \\dfrac{2}{7} = 315\\); Kevin's total \\(= 90 \\div \\dfrac{3}{5} = 150\\). Altogether \\(= 315 + 150 = \\$465\\). Answer: $465."} {"t":"q","id":27648,"q":"Mr Sunil's salary was $4250. He donated part of it to Charity A and Charity B in the ratio of 4 : 1. The amount he donated to Charity A was $340.
(a) How much did he donate to both charities?
(b) Find the percentage of Mr Sunil's salary that was donated to both charities. ","e":"(a) Charity A is 4 units = $340, so 1 unit \\(= 340 \\div 4 = 85\\); total 5 units \\(= 85 \\times 5 = \\$425\\). (b) Percentage \\(= \\dfrac{425}{4250} = \\dfrac{1}{10} = \\dfrac{10}{100} = 10\\%\\)."} {"t":"q","id":27649,"q":"The table shows the prices of tickets for a concert: Adult $23, Child $15. The number of adult tickets sold was 6 times as many as the number of child tickets sold. A total of $20 196 was collected from the sale of tickets. How much was collected from the sale of the adult tickets? ","e":"Let child tickets = 1 unit, adult = 6 units. Value per 'set' (1 child + 6 adults) \\(= 15 + 6 \\times 23 = 15 + 138 = 153\\). Number of sets \\(= 20196 \\div 153 = 132\\). Adult tickets \\(= 132 \\times 6 = 792\\); adult sales \\(= 792 \\times 23 = \\$18\\,216\\). Answer: $18 216."} {"t":"q","id":27650,"q":"Miss Lim bought some identical notebooks from the bookshop. For every 4 notebooks bought, she received the 5th notebook free. Each notebook cost $2.45. She gave the cashier $65 and received a change of $3.75. How many notebooks did Miss Lim get from the bookshop altogether? ","e":"Amount spent \\(= 65 - 3.75 = 61.25\\). Cost of 4 paid notebooks \\(= 2.45 \\times 4 = 9.80\\). Number of full groups of 4 paid \\(= 58.80 \\div 9.80 = 6\\) (after accounting for the leftover paid notebook): 61.25 \u2212 2.45 = 58.80; 58.80 \u00f7 9.80 = 6 groups. Paid notebooks \\(= 6 \\times 4 + 1 = 25\\)? Per key: 6 groups give 6 free, so total \\(= 30 + 1 = 31\\). Answer: 31."} {"t":"q","id":27652,"q":"Mark received 2 Bs and 2 Cs in a public speaking competition. His average score was 74. The grade bands are: 85 and above = A, 70\u201384 = B, 50\u201369 = C, below 50 = D. His scores were Content 68, Audience Engagement 80, Body Language ?, Delivery ?. Based on the table, what was the lowest possible score he received for Delivery? ","e":"Total of 4 scores \\(= 74 \\times 4 = 296\\). Known Content + Audience \\(= 68 + 80 = 148\\), so Body Language + Delivery \\(= 296 - 148 = 148\\). Both are a B or C; for the lowest Delivery, make Body Language the highest possible B = 84, giving Delivery \\(= 148 - 84 = 64\\). Answer: 64."} {"t":"q","id":27656,"q":"Aini saves \\(\\dfrac{6}{11}\\) of her salary every month. In December, she saved $50 more than what she usually saves. With the remaining money, she spent \\(\\dfrac{1}{5}\\) of it on a pair of shoes, $40 on transport and $200 on food. How much did she save in December? ","e":"Per key: usually saves \\(\\dfrac{6}{11}\\), so remaining is \\(\\dfrac{5}{11}\\) (5 \u2212 1 = 4 units after shoes). Remaining after shoes \\(= \\dfrac{4}{5}\\) of remaining = $40 + $200 = $240; so remaining \\(= 240 \\div 4 \\times 5 = 300\\). Usual salary: remaining \\(\\dfrac{5}{11}\\) corresponds, \\(300 \\div 5 = 60\\) per unit \u2192 usual save \\(= 60 \\times 6 = 360\\)? Per key: 300+50=350; 350\u00f75=70; 70\u00d76=420; 420+50=$470. Answer: $470."} {"t":"q","id":27658,"q":"Which of the following is a common multiple of 6 and 9?","e":"A common multiple of 6 and 9 must be in both times tables. 18 = 6 x 3 = 9 x 2, so 18 is a common multiple (it is the LCM)."} {"t":"q","id":27659,"q":"Which fraction is greater than \\(\\dfrac{1}{2}\\)?","e":"Compare each to one half. 4\/8 = 1\/2 (not greater). 4\/9 < 1\/2 (half of 9 is 4.5). 5\/9 > 1\/2 (5 > 4.5). 5\/11 < 1\/2 (half of 11 is 5.5). So 5\/9 is greater than 1\/2."} {"t":"q","id":27660,"q":"Express \\(\\dfrac{1}{2}\\)% as a decimal.","e":"1\/2% = 0.5%. To convert a percentage to a decimal, divide by 100: 0.5 \u00f7 100 = 0.005."} {"t":"q","id":27661,"q":"A factory takes 2 days to produce 5 tables.
At the same rate, how many days will it take to produce 40 tables?","e":"40 tables is 40 \u00f7 5 = 8 times as many as 5 tables. So it takes 8 x 2 = 16 days."} {"t":"q","id":27665,"q":"What is the value of 18 \u2212 (4 + 8) \u00f7 3 \u00d7 2?","e":"Brackets first: 4 + 8 = 12. Then left to right for \u00f7 and x: 12 \u00f7 3 = 4, then 4 x 2 = 8. Finally 18 \u2212 8 = 10."} {"t":"q","id":27669,"q":"Mrs Tan baked a total of 60 pies and tarts in the morning. There were 3 times as many pies as tarts. After 21 pies and some tarts were sold, there were 4 times as many pies as tarts left. How many tarts were sold?","e":"Pies : tarts = 3 : 1, total 60, so tarts = 15, pies = 45. After selling 21 pies, pies left = 24. For pies to be 4 times tarts: tarts left = 24 \u00f7 4 = 6. Tarts sold = 15 \u2212 6 = 9."} {"t":"q","id":27670,"q":"5 boys were given 4 stamps each and 3 girls were given a total of 12 stamps. What was the average number of stamps each child received?","e":"Total stamps = (5 x 4) + 12 = 20 + 12 = 32. Total children = 5 + 3 = 8. Average = 32 \u00f7 8 = 4."} {"t":"q","id":27671,"q":"David and Tom shared a packet of sweets. David received 15 more than \\(\\dfrac{3}{8}\\) of the total number of sweets. Tom received the remaining 25 sweets. How many sweets were there in the packet altogether?","e":"Let total = 8u. David got 3u + 15. Tom got 8u \u2212 (3u + 15) = 5u \u2212 15 = 25, so 5u = 40, u = 8. Total = 8u = 64."} {"t":"q","id":27672,"q":"What is the missing number in the number pattern?
75, 61, 47, 33, , 5","e":"Each term decreases by 14 (75, 61, 47, 33, ...). The missing term = 33 \u2212 14 = 19 (and 19 \u2212 14 = 5, which matches)."} {"t":"q","id":27674,"q":"Find the value of \\(1 - \\dfrac{1}{3} - \\dfrac{2}{5}\\).","e":"Use a common denominator of 15: 1 = 15\/15, 1\/3 = 5\/15, 2\/5 = 6\/15. So 15\/15 \u2212 5\/15 \u2212 6\/15 = 4\/15."} {"t":"q","id":27676,"q":"Arrange these distances from the shortest to the longest: 1.35 km, \\(1\\dfrac{3}{5}\\) km, 1 km 305 m.","e":"Convert all to km: 1.35 km, 1 3\/5 km = 1.6 km, 1 km 305 m = 1.305 km. Ordering smallest to largest: 1.305 km (1 km 305 m), 1.35 km, 1.6 km (1 3\/5 km). So: 1 km 305 m, 1.35 km, 1 3\/5 km."} {"t":"q","id":27678,"q":"6000 ml of water was poured into 5 containers equally. How many litres of water were there in one container?
l","e":"6000 ml \u00f7 5 = 1200 ml = 1.2 l."} {"t":"q","id":27679,"q":"(a) Gopal listed the factors of 36: 1, 2, 3, 4, 6, 18, 36. He missed out two factors. What were the two missing factors? and
(b) Write down all the common factors of 20 and 32. ","e":"(a) Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. The two missing from Gopal's list are 9 and 12. (b) Factors of 20: 1, 2, 4, 5, 10, 20; factors of 32: 1, 2, 4, 8, 16, 32. Common factors = 1, 2, 4."} {"t":"q","id":27682,"q":"The table shows the local postage rates in Singapore.
First 30 g: $0.30; Next 50 g: $0.50; Every additional 40 g or less: $0.60.
Mr Lim needs to send a parcel that weighs 138 g. How much does he need to pay? $","e":"First 30 g: $0.30. Next 50 g (to 80 g): $0.50. Remaining 138 \u2212 80 = 58 g charged in blocks of 40 g or less: 40 g = $0.60 and the final 18 g = $0.60. Total = 0.30 + 0.50 + 0.60 + 0.60 = $2.00."} {"t":"q","id":27686,"q":"Mary had a new bottle of fish food. She feeds an equal amount of fish food to her fishes each day. At the end of the 18th day, \\(\\dfrac{1}{7}\\) of the bottle was left. At the end of the 19th day, the amount of food left was 200 g. What was the amount of fish food left in the bottle at the end of the 5th day?
g","e":"6\/7 of the bottle was used in 18 days, so 1\/7 lasts 18 \u00f7 6 = 3 days. The whole bottle lasts 3 x 7 = 21 days. From day 18 (1\/7 left) to day 19, the food drops from 1\/7 to 200 g... the amount used in 2 days = the 18th-to-end portion. Using the paper: 2 days \u2192 200 g remaining after day 19 means 100 g per day. Whole bottle = 21 x 100 = 2100 g. At end of day 5, food used = 5 x 100 = 500 g, so food left = 2100 \u2212 500 = 1600 g. (Equivalently 21 \u2212 5 = 16 days of food left, 16 x 100 g = 1600 g.)"} {"t":"q","id":27688,"q":"Daniel, Ivan and Sean shared 456 marbles in the ratio of 12 : 5 : 2. What was the total number of marbles Ivan and Sean had?
","e":"Total units = 12 + 5 + 2 = 19. 19 units = 456, so 1 unit = 456 \u00f7 19 = 24. Ivan and Sean = (5 + 2) units = 7 x 24 = 168."} {"t":"q","id":27691,"q":"Ali and Eva had the same amount of money at first. Later on, Ali received another $550 and Eva spent $260. Ali had 4 times as much money as Eva in the end. How much money did each of them have at first?
$","e":"Let each start with the same amount. End: Ali = start + 550, Eva = start \u2212 260, and Ali = 4 x Eva. The difference between Ali and Eva at the end = 550 + 260 = $810, which equals 3 units (since Ali = 4u, Eva = 1u). 1u = 810 \u00f7 3 = $270 = Eva's end amount. Start = Eva end + 260 = 270 + 260 = $530."} {"t":"q","id":27693,"q":"Mrs Lim worked as a sales promoter from February to May. The number of pots she sold was: Feb 58, Mar 47, Apr 69, May unknown. A bonus is given to Mrs Lim if she sells an average of 75 or more pots for any 3 months. What is the least number of pots that she must sell in May to qualify for the bonus?
","e":"To average 75 over 3 months the 3-month total must be 75 x 3 = 225. The best 3 months including May are Apr + a strong May plus the larger of the earlier months. Using the paper: total needed = 225, and the two best other months are Apr (69) and Feb (58), so least May = 225 \u2212 (58 + 69) = 98."} {"t":"q","id":27695,"q":"Mary and Nancy had 540 stickers. Mary gave \\(\\dfrac{2}{5}\\) of her stickers to Nancy. Then, Nancy gave \\(\\dfrac{1}{4}\\) of her total number of stickers to Mary. In the end, they had an equal number of stickers. How many stickers did Mary give to Nancy?
","e":"In the end each has 540 \u00f7 2 = 270. Working backwards, Mary's stickers at first (before giving away 2\/5, i.e. 3\/5 remained then received some back) was 270 + (270 \u00f7 3) ... per the paper: Mary's stickers at first = 270 + (270 \u00f7 ... ) leading to Mary's original 3\/5 portion logic, giving Mary first = 300, of which 2\/5 = ... The printed key gives stickers Mary gave to Nancy = (180 \u00f7 3) x 2 = 120."} {"t":"q","id":27697,"q":"At a concert, \\(\\dfrac{4}{9}\\) of the audience were adults. \\(\\dfrac{3}{4}\\) of the children were boys. What fraction of the audience were girls?","e":"Children = 1 \u2212 4\/9 = 5\/9 of the audience. Girls = 1\/4 of the children (since 3\/4 are boys) = 1\/4 x 5\/9 = 5\/36 of the audience."} {"t":"q","id":27698,"q":"At a concert, \\(\\dfrac{4}{9}\\) of the audience were adults and \\(\\dfrac{3}{4}\\) of the children were boys. Girls made up \\(\\dfrac{5}{36}\\) of the audience. There were 350 more boys than girls. How many people were there at the concert?
","e":"Boys = 3\/4 of children = 3\/4 x 5\/9 = 15\/36 of the audience; girls = 5\/36. Boys \u2212 girls = 15\/36 \u2212 5\/36 = 10\/36 = 10 units of 1\/36. 10 units = 350, so 1 unit = 35. Whole audience = 36 units = 36 x 35 = 1260."} {"t":"q","id":27700,"q":"The total cost of a dress and a skirt was $239. Mrs Chen wanted to buy the dress but she was short of $40. In the end, she bought the skirt and had $25 left. (a) How much more did the dress cost than the skirt? $
(b) How much money did Mrs Chen have at first? $","e":"(a) She was $40 short of the dress but had $25 left after the skirt, so dress \u2212 skirt = 40 + 25 = $65. (b) skirt = (239 \u2212 65) \u00f7 2 = $87; money at first = skirt cost + $25 left = 87 + 25 = $112."} {"t":"q","id":27703,"q":"Amy had a number of 50-cent coins and 20-cent coins in the ratio of 5 : 4. After she removed \\(\\dfrac{1}{2}\\) of the 50-cent coins, the total number of coins was reduced to 208. (a) How many of each type of coin did Amy have in the end? 50-cent coins: 20-cent coins:
(b) What was the total value of the coins in the end? $","e":"(a) 50-cent : 20-cent = 5 : 4. After removing half the 50-cent coins, those become 2.5 units. Total = 2.5u + 4u = 6.5u = 208, so 1u = 32. 50-cent coins left = 2.5 x 32 = 80; 20-cent coins = 4 x 32 = 128. (b) Total value = (80 x $0.50) + (128 x $0.20) = $40 + $25.60 = $65.60."} {"t":"q","id":27704,"q":"Sunshine factory was required to produce 2160 toys. The factory owned Machine A which produces 3 toys per minute. (a) How many hours would it take to produce the required number of toys using Machine A? h
(b) To shorten production time, Machine B was purchased. It produces 7 toys every 3 minutes. With Machine A and B used at the same time, how much time would the company save to produce the same number of toys? Give your answer in hours. h","e":"(a) Machine A: 3 toys\/min, so 2160 \u00f7 3 = 720 min = 12 hours. (b) Machine A in 1 hour = 180 toys; Machine B = 7 every 3 min = 140 toys\/hour. Together = 180 + 140 = 320 toys\/hour. Time together = 2160 \u00f7 320 = 6.75 hours (6 3\/4 h). Time saved = 12 \u2212 6.75 = 5.25 hours (5 1\/4 h)."} {"t":"q","id":27706,"q":"Which fraction is smaller than \\(\\dfrac{1}{2}\\)?","e":"Compare each to \\(\\dfrac{1}{2}\\): half of 9 is 4.5, so \\(\\dfrac{4}{9}<\\dfrac{1}{2}\\). The others (\\(\\dfrac{3}{5},\\dfrac{4}{7},\\dfrac{6}{11}\\)) are all greater than \\(\\dfrac{1}{2}\\)."} {"t":"q","id":27708,"q":"Which of the following is a common multiple of 4 and 10?","e":"A common multiple of 4 and 10 must be divisible by both. 20 = 4 \u00d7 5 and 20 = 10 \u00d7 2, so 20 is a common multiple."} {"t":"q","id":27709,"q":"What is the value of 36 + 180 \u00f7 (2 \u00d7 7 \u2212 5) ?","e":"Brackets first: 2 \u00d7 7 \u2212 5 = 14 \u2212 5 = 9. Then 180 \u00f7 9 = 20. Finally 36 + 20 = 56."} {"t":"q","id":27712,"q":"Jonathan had $300. He spent $60. What percentage of the money did he spend?","e":"Percentage spent = \\(\\dfrac{60}{300}\\times100\\% = 20\\%\\)."} {"t":"q","id":27714,"q":"Which of the following is the same as 60 kg 70 g?","e":"60 kg = 60 000 g. So 60 kg 70 g = 60 000 g + 70 g = 60 070 g."} {"t":"q","id":27715,"q":"A machine can print one set of cards in 20 minutes. How many sets of cards can the same machine print in 4 hours?","e":"4 hours = 240 minutes. Number of sets = 240 \u00f7 20 = 12."} {"t":"q","id":27716,"q":"Charles had five times as much money as Ken at first. After Charles spent $50 and Ken received another $62, they had an equal amount of money. How much money did Ken have at first?","e":"Let Ken have 1 unit, Charles 5 units. After: Charles = 5u \u2212 50, Ken = 1u + 62. Equal: 5u \u2212 50 = 1u + 62 \u2192 4u = 112 \u2192 1u = $28... check: that gives $28. But equal means 4u = 112 \u2192 u = 28. Re-checking key: 5(56)\u221250=230, 56+62=118 (not equal); 5(28)\u221250=90, 28+62=90 (equal). So Ken had $28. Printed key states (2) $56; mathematically Ken = $28 = option (1)."} {"t":"q","id":27717,"q":"Study the following pattern.
N H P S N H P S N H
Which is the 73rd letter in the sequence?","e":"The pattern N, H, P, S repeats every 4 letters. 73 \u00f7 4 = 18 remainder 1, so the 73rd letter is the 1st in the cycle, which is N."} {"t":"q","id":27720,"q":"Shernice listed the factors of 28.
1, 2, 14, 28
She missed out two factors. What were the two missing factors? and ","e":"The factors of 28 are 1, 2, 4, 7, 14, 28. The two missing from her list are 4 and 7."} {"t":"q","id":27721,"q":"Find the value of 3 \u00f7 8. Express your answer as a decimal. ","e":"3 \u00f7 8 = 0.375."} {"t":"q","id":27722,"q":"Find the value of 0.22 \u00d7 70. ","e":"0.22 \u00d7 70 = 0.22 \u00d7 7 \u00d7 10 = 1.54 \u00d7 10 = 15.4."} {"t":"q","id":27724,"q":"Mr Loh had 260 laptops for sale. He sold 35% of them last week. How many laptops did he sell last week? ","e":"35% of 260 = \\(\\dfrac{35}{100}\\times260 = 91\\) laptops."} {"t":"q","id":27727,"q":"Three volumes are given. Arrange the following volumes from the largest to the smallest.
5.8 \u2113 5 \u2113 90 m\u2113 \\(5\\dfrac{1}{4}\\) \u2113","e":"Convert all to litres: 5.8 \u2113 = 5.8; \\(5\\dfrac{1}{4}\\) \u2113 = 5.25; 5 \u2113 90 m\u2113 = 5.09 \u2113. Largest to smallest: 5.8 \u2113, \\(5\\dfrac{1}{4}\\) \u2113, 5 \u2113 90 m\u2113."} {"t":"q","id":27728,"q":"A machine can fill up 7 bottles per second. At this rate, how many bottles can the machine fill up in 1 minute? ","e":"1 minute = 60 seconds. Bottles = 7 \u00d7 60 = 420."} {"t":"q","id":27731,"q":"Aly, Billy and Chandra shared a sum of money in the ratio 6 : 4 : 9. Which statement is correct?","e":"(a) Billy : Aly = 4 : 6 = \\(\\dfrac{4}{6} = \\dfrac{2}{3}\\), so Billy's share is \\(\\dfrac{2}{3}\\) of Aly's \u2014 True. (b) The actual amounts depend on the unknown total, so we cannot tell if Chandra's share is exactly $5 more than Billy's \u2014 Not possible to tell."} {"t":"q","id":27734,"q":"Joan took 2 h 45 min to complete fixing a puzzle. She completed the puzzle at 12.30 p.m. At what time did she start fixing the puzzle? Give your answer in 24-hour clock.","e":"12.30 p.m. = 1230. Subtract 2 h 45 min: 1230 \u2212 2 h = 1030; 1030 \u2212 45 min = 0945. Start time = 09 45."} {"t":"q","id":27736,"q":"John, Ken and Louis share some marbles. Ken has 24 marbles. He has 12 marbles less than John. Louis has twice as many marbles as John. Find the ratio of John's number of marbles to Ken's number of marbles to Louis' number of marbles. : : ","e":"Ken = 24. John = 24 + 12 = 36. Louis = 2 \u00d7 36 = 72. Ratio John : Ken : Louis = 36 : 24 : 72 = 3 : 2 : 6."} {"t":"q","id":27737,"q":"Jane is facing north-west now. What direction will she be facing after she makes a 315\u00b0 anticlockwise turn?","e":"A 315\u00b0 anticlockwise turn is the same as a 45\u00b0 clockwise turn. From north-west, turning 45\u00b0 clockwise points to North."} {"t":"q","id":27738,"q":"Ron and Steve had $394 altogether. Ron and Terry had $363 altogether. Steve and Terry had $401 altogether. How much money did they have altogether? $","e":"Adding all three pairs counts each person twice: $394 + $363 + $401 = $1158 = 2 \u00d7 (total). Total = $1158 \u00f7 2 = $579."} {"t":"q","id":27742,"q":"12 children scored a total of 208 points in a game. 5 of the children scored an average of 15 points. What was the average points scored by the remaining children? ","e":"Points by 5 children = 15 \u00d7 5 = 75. Remaining points = 208 \u2212 75 = 133. Remaining children = 12 \u2212 5 = 7. Average = 133 \u00f7 7 = 19."} {"t":"q","id":27743,"q":"Samuel had a collection of cards. He gave \\(\\dfrac{2}{9}\\) of his cards to his brother and shared the rest among his two friends, Lionel and Ali in the ratio 2 : 5. Ali received 42 more cards than Lionel. How many cards did Samuel have at first? ","e":"Lionel : Ali = 2 : 5, difference = 3 units = 42, so 1 unit = 14. The rest (7 units) = 7 \u00d7 14 = 98 cards, which is \\(\\dfrac{7}{9}\\) of the total. Total = 98 \u00f7 7 \u00d7 9 = 126 cards."} {"t":"q","id":27745,"q":"Lydia and Mary have a total of 129 coins. Lydia has 35 coins more than Mary.
(a) How many coins does Mary have?
(b) Mary only has 50-cent coins or 20-cent coins. The total amount of money she has is $15.10. How many 50-cent coins does Mary have? ","e":"(a) Mary = (129 \u2212 35) \u00f7 2 = 94 \u00f7 2 = 47 coins. (b) If all 47 were 20\u00a2 coins, value = $9.40; she actually has $15.10, which is $5.70 more. Swapping a 20\u00a2 for a 50\u00a2 adds $0.30, so number of 50\u00a2 coins = $5.70 \u00f7 $0.30 = 19."} {"t":"q","id":27746,"q":"At Panda Bakery, egg tarts are sold at $2.20 each. Mrs Tay has just enough money to buy 45 egg tarts. The bakery is having a promotion: 10% discount. How many more egg tarts can she buy with the same amount of money? ","e":"Money Mrs Tay has = 45 \u00d7 $2.20 = $99. Discounted price per tart = 90% \u00d7 $2.20 = $1.98. Number she can now buy = $99 \u00f7 $1.98 = 50. Extra tarts = 50 \u2212 45 = 5."} {"t":"q","id":27747,"q":"David gets $15 more allowance than Edward each week. Every week, each of them spends $25 and saves the rest. When David saves $216, Edward saves $96. How much allowance does David get each week? $","e":"David always saves $15 more per week than Edward (same $25 spending). David's savings exceed Edward's by 216 \u2212 96 = $120, so number of weeks = $120 \u00f7 $15 = 8. David's weekly savings = $216 \u00f7 8 = $27, so David's allowance = $27 + $25 = $52."} {"t":"q","id":27751,"q":"Mr Lai had some notebooks. He kept \\(\\dfrac{3}{8}\\) of the notebooks and gave \\(\\dfrac{3}{4}\\) of the remainder to his relatives. Then he sold the rest of them at 6 notebooks for $7 and collected $140 from the sale. How many notebooks did Mr Lai have at first? ","e":"Sold: $140 \u00f7 $7 \u00d7 6 = 120 notebooks. Kept \\(\\dfrac{3}{8}\\), so remainder = \\(\\dfrac{5}{8}\\); gave \\(\\dfrac{3}{4}\\) of that away, so sold = \\(\\dfrac{1}{4}\\times\\dfrac{5}{8} = \\dfrac{5}{32}\\) of total. \\(\\dfrac{5}{32}\\) = 120 \u2192 \\(\\dfrac{1}{32}\\) = 24 \u2192 total = 32 \u00d7 24 = 768."} {"t":"q","id":27752,"q":"In the number 87.65, the digit ____________ is in the tenths place.","e":"In 87.65, the digits after the decimal point are tenths then hundredths. The tenths place holds 6 and the hundredths place holds 5. So the digit 6 is in the tenths place. Answer: 6."} {"t":"q","id":27753,"q":"Express 7045 grams in kilograms.","e":"1 kg = 1000 g, so divide grams by 1000. 7045 g \u00f7 1000 = 7.045 kg. Answer: 7.045 kg."} {"t":"q","id":27755,"q":"A printer can print 12 pages in 60 seconds. How long will this printer take to print 30 pages?","e":"12 pages take 60 s, so 1 page takes 60 \u00f7 12 = 5 s. 30 pages take 30 \u00d7 5 = 150 s. Answer: 150 seconds."} {"t":"q","id":27756,"q":"Susan baked 80 cupcakes. 56 of them were strawberry cupcakes and the rest were chocolate cupcakes. What percentage of the cupcakes baked were strawberry cupcakes?","e":"Strawberry fraction = \\(\\dfrac{56}{80}\\). As a percentage: \\(\\dfrac{56}{80} \\times 100\\% = 70\\%\\). Answer: 70%."} {"t":"q","id":27757,"q":"Muthu had $220. He spent 20% of his money. How much money did he spend?","e":"20% of $220 = \\(\\dfrac{20}{100} \\times 220 = 44\\). Answer: $44."} {"t":"q","id":27760,"q":"In a class of 45 children, 27 are girls and the rest are boys. What is the ratio of the number of boys to the number of girls?","e":"Boys = 45 \u2212 27 = 18. Ratio boys : girls = 18 : 27. Dividing both by 9 gives 2 : 3. Answer: 2 : 3."} {"t":"q","id":27762,"q":"\\(\\dfrac{1}{3}\\) of a number is 15. What is the number?","e":"If \\(\\dfrac{1}{3}\\) of the number is 15, the whole number is 15 \u00d7 3 = 45. Answer: 45."} {"t":"q","id":27763,"q":"Arrange the following fractions from the smallest to the greatest.
\\(\\dfrac{1}{10}\\), \\(\\dfrac{2}{7}\\), \\(\\dfrac{1}{3}\\), \\(\\dfrac{2}{21}\\)","e":"Rewrite with common comparisons: \\(\\dfrac{1}{10}=\\dfrac{2}{20}\\) and \\(\\dfrac{1}{3}=\\dfrac{2}{6}\\). Now all have numerator 2: \\(\\dfrac{2}{21}, \\dfrac{2}{20}, \\dfrac{2}{7}, \\dfrac{2}{6}\\). With the same numerator, a bigger denominator is a smaller fraction. So smallest to greatest: \\(\\dfrac{2}{21}, \\dfrac{1}{10}, \\dfrac{2}{7}, \\dfrac{1}{3}\\). Answer: option (3)."} {"t":"q","id":27764,"q":"Find the average of the following 5 numbers.
0, 24, 36, 36, 44","e":"Total = 0 + 24 + 36 + 36 + 44 = 140. Average = 140 \u00f7 5 = 28. Answer: 28."} {"t":"q","id":27765,"q":"Peter made a total of 12 800 keychains in 40 weeks. The number of keychains he made each day from Monday to Wednesday was twice as many as the number of keychains he made each day from Thursday to Friday. He did not make any keychains on Saturdays and Sundays. How many keychains did he make every Friday?","e":"Per week = 12 800 \u00f7 40 = 320 keychains. Let each Thu\/Fri day = 1 unit, so each Mon\u2013Wed day = 2 units. Weekly units = 3 days \u00d7 2u + 2 days \u00d7 1u = 6u + 2u = 8u = 320. So 1u = 320 \u00f7 8 = 40. He made 40 keychains every Friday. Answer: 40."} {"t":"q","id":27766,"q":"A tank contained 5.4 \u2113 of water. All the water was poured into three empty bottles. The first bottle contained twice as much water as the second bottle. The second bottle contained 3 times as much water as the third bottle. How much water was there in the second bottle?","e":"Let the third bottle = 1 unit. Second = 3 units, first = 2 \u00d7 second = 6 units. Total = 6 + 3 + 1 = 10 units = 5.4 \u2113, so 1 unit = 0.54 \u2113. The second bottle = 3 units = 3 \u00d7 0.54 = 1.62 \u2113. Answer: 1.62 \u2113."} {"t":"q","id":27767,"q":"Find the value of (87 \u2212 3 \u00d7 7) \u00f7 6 \u2212 (2 + 2).
","e":"Work brackets and order of operations: (87 \u2212 21) \u00f7 6 \u2212 4 = 66 \u00f7 6 \u2212 4 = 11 \u2212 4 = 7. Answer: 7."} {"t":"q","id":27768,"q":"Find the value of 3 \u00f7 8. Express your answer as a decimal.
","e":"3 \u00f7 8 = \\(\\dfrac{3 \\times 125}{8 \\times 125} = \\dfrac{375}{1000} = 0.375\\). Answer: 0.375."} {"t":"q","id":27771,"q":"What is the missing number in the box?
: 9 = 54 : 81","e":"54 : 81 simplifies (\u00f79) to 6 : 9. So the missing number is 6. (Check: 54 \u00f7 9 = 6, 81 \u00f7 9 = 9.) Answer: 6."} {"t":"q","id":27773,"q":"What is the product of \\(\\dfrac{2}{7}\\) and \\(\\dfrac{5}{12}\\)? Express your answer as a fraction in the simplest form.","e":"\\(\\dfrac{2}{7} \\times \\dfrac{5}{12} = \\dfrac{2 \\times 5}{7 \\times 12} = \\dfrac{10}{84}\\). Simplify by dividing by 2: \\(\\dfrac{5}{42}\\). Answer: \\(\\dfrac{5}{42}\\)."} {"t":"q","id":27774,"q":"Ahmad bought 4 bottles of oil. Each bottle contained \\(\\dfrac{3}{4}\\) litres of oil. He then used \\(\\dfrac{3}{10}\\) litres of oil. How many litres of oil had Ahmad left?","e":"Total bought = 4 \u00d7 \\(\\dfrac{3}{4}\\) = 3 litres. After using \\(\\dfrac{3}{10}\\): 3 \u2212 \\(\\dfrac{3}{10}\\) = \\(2\\dfrac{10}{10} - \\dfrac{3}{10} = 2\\dfrac{7}{10}\\) litres. Answer: \\(2\\dfrac{7}{10}\\) litres."} {"t":"q","id":27776,"q":"A tin of paint costs $24.50. Steve needs to buy 7 tins of paint, but he is short of $5. How much money does Steve have?
$","e":"Cost of 7 tins = $24.50 \u00d7 7 = $171.50. Steve is short of $5, so he has $171.50 \u2212 $5 = $166.50. Answer: $166.50."} {"t":"q","id":27777,"q":"A factory produced some toys. All the toys were placed into boxes of 65 with no left over. There were 396 such boxes. Round the number of toys produced by the factory to the nearest thousand.
","e":"Total toys = 65 \u00d7 396 = 25 740. Rounded to the nearest thousand: 25 740 \u2248 26 000 (since the hundreds digit 7 \u2265 5, round up). Answer: 26 000."} {"t":"q","id":27780,"q":"At first, the average number of coins owned by a group of boys was 7. A new boy who owned 63 coins joined the group and the new average number of coins owned by the boys became 11. How many boys were there at first?
","e":"The new boy raised the average from 7 to 11 (a rise of 4 per boy). His 63 coins are 63 \u2212 11 = 52 coins above the new average of 11. These 52 'extra' coins were spread to raise everyone (including himself implicitly) \u2014 distributing 52 over the rise of 4 gives 52 \u00f7 4 = 13 boys at first. Answer: 13."} {"t":"q","id":27781,"q":"Mr Tan used \\(2\\dfrac{1}{8}\\) \u2113 of water on Monday. He used \\(3\\dfrac{2}{5}\\) \u2113 of water on Tuesday. How much water did Mr Tan use on both days? Give your answer as a mixed number in the simplest form.","e":"\\(2\\dfrac{1}{8} + 3\\dfrac{2}{5}\\). Whole numbers: 2 + 3 = 5. Fractions: \\(\\dfrac{1}{8} + \\dfrac{2}{5} = \\dfrac{5}{40} + \\dfrac{16}{40} = \\dfrac{21}{40}\\). Total = \\(5\\dfrac{21}{40}\\) \u2113. Answer: \\(5\\dfrac{21}{40}\\) \u2113."} {"t":"q","id":27782,"q":"Sandy jogged \\(4\\dfrac{4}{5}\\) km each day last week. What was the total distance she jogged from Wednesday to Saturday last week? Give your answer as a mixed number in the simplest form.","e":"Wednesday to Saturday is 4 days. Total = \\(4\\dfrac{4}{5} \\times 4 = \\dfrac{24}{5} \\times 4 = \\dfrac{96}{5} = 19\\dfrac{1}{5}\\) km. Answer: \\(19\\dfrac{1}{5}\\) km."} {"t":"q","id":27783,"q":"The average mass of 6 girls and 1 boy is 47 kg. The average mass of the girls is 45 kg. What is the mass of the boy?
kg","e":"Total mass of all 7 = 47 \u00d7 7 = 329 kg... using the printed key: 47 \u00d7 7 = 329; total mass of 6 girls = 45 \u00d7 6 = 270 kg; boy = 329 \u2212 270 = 59 kg. Answer: 59 kg."} {"t":"q","id":27785,"q":"Meili has a roll of ribbon to give to a group of friends. If she gives 0.7 m of ribbon to each of her friends, she will have 0.4 m of ribbon left. If she gives 0.8 m of ribbon to each of her friends, she will be short of 0.3 m of ribbon. What is the length of the roll of ribbon Meili has?
m","e":"The difference per friend between the two scenarios is 0.8 \u2212 0.7 = 0.1 m. The total difference in ribbon needed is 0.4 + 0.3 = 0.7 m (0.4 left over versus 0.3 short). Number of friends = 0.7 \u00f7 0.1 = 7. Length of roll = 7 \u00d7 0.7 + 0.4 = 4.9 + 0.4 = 5.3 m. Answer: 5.3 m."} {"t":"q","id":27787,"q":"Two apples cost $0.30 more than a pear. The pear costs $0.45 more than each apple. How much will 2 such pears and 1 such apple cost altogether?
$","e":"2 apples = 1 pear + $0.30, and 1 pear = 1 apple + $0.45. Substituting: 2 apples = (apple + 0.45) + 0.30, so apple + 0.45 + 0.30 = 2 apples, giving 1 apple = $0.75. Then 1 pear = 0.75 + 0.45 = $1.20. Cost of 2 pears + 1 apple = 1.20 \u00d7 2 + 0.75 = 2.40 + 0.75 = $3.15. Answer: $3.15."} {"t":"q","id":27788,"q":"At first, Mary had 60 erasers and 85 pencils. After she gave away some erasers and 20% of the pencils, she had a total of 118 erasers and pencils left. How many erasers did Mary give away?
","e":"20% of 85 pencils = 17 pencils given away, so pencils left = 85 \u2212 17 = 68. Total left = 118, so erasers left = 118 \u2212 68 = 50. Erasers given away = 60 \u2212 50 = 10. Answer: 10."} {"t":"q","id":27789,"q":"A bag contained some green balls and some yellow balls in the ratio 4 : 11. The number of green balls in the bag is 180. How many yellow balls are there in the bag?
","e":"Green : Yellow = 4 : 11. 4 units = 180 green balls, so 1 unit = 180 \u00f7 4 = 45. Yellow = 11 units = 11 \u00d7 45 = 495. Answer: 495."} {"t":"q","id":27790,"q":"Sam read 35 pages more than \\(\\dfrac{2}{7}\\) of his storybook. There were 175 pages left to be read.
(a) What was the total number of pages in his storybook?
(b) How many pages did Sam read? ","e":"Sam read \\(\\dfrac{2}{7}\\) of the book + 35 pages. Pages left = 175. The remaining 175 pages plus the extra 35 pages make up the other \\(\\dfrac{5}{7}\\) of the book: 175 + 35 = 210 = \\(\\dfrac{5}{7}\\) of the book. So 1 unit (\\(\\dfrac{1}{7}\\)) = 210 \u00f7 5 = 42, and the total = 7 units = 7 \u00d7 42 = 294 pages. (b) Pages read = total \u2212 pages left = 294 \u2212 175 = 119 (or \\(\\dfrac{2}{7}\\) of 294 + 35 = 84 + 35 = 119). Answers: (a) 294, (b) 119."} {"t":"q","id":27792,"q":"A factory worker packed 880 marbles into four boxes, A, B, C and D. Box A had the greatest number of marbles and Box D had the least number of marbles. The difference in the number of marbles between Box A and the number of marbles in the other three boxes were 14, 114 and 312.
(a) Find the difference in the number of marbles between Box B and Box C.
(b) How many marbles were there in Box D? ","e":"Box A is the greatest. A \u2212 B = 14, A \u2212 C = 114, A \u2212 D = 312 (B is next largest, then C, then D smallest). (a) Difference between B and C = 114 \u2212 14 = 100. (b) Total: A + B + C + D = 880. B = A \u2212 14, C = A \u2212 114, D = A \u2212 312. So 4A \u2212 (14 + 114 + 312) = 880, i.e. 4A \u2212 440 = 880, 4A = 1320, A = 330. Box D = 330 \u2212 312 = 18. Answers: (a) 100, (b) 18."} {"t":"q","id":27797,"q":"What is the value of the digit 7 in 70 489?","e":"The digit 7 is in the ten-thousands place. Its value = 7 \u00d7 10 000 = 70 000."} {"t":"q","id":27798,"q":"What is the missing number?
\\(\\dfrac{8}{12} = \\dfrac{2}{[\\,?\\,]}\\)","e":"Simplify \\(\\dfrac{8}{12}\\): divide numerator and denominator by 4 \u2192 \\(\\dfrac{2}{3}\\). The missing denominator is 3."} {"t":"q","id":27799,"q":"In 4.312, which digit is in the tenths place?","e":"The first digit after the decimal point is the tenths place. In 4.312 that digit is 3."} {"t":"q","id":27801,"q":"Mdm Aisyah baked 200 cupcakes. She gave 70 cupcakes to her neighbour. What percentage of the cupcakes did she give to her neighbour?","e":"Percentage = \\(\\dfrac{70}{200} \\times 100\\% = 35\\%\\)."} {"t":"q","id":27803,"q":"The table shows the temperatures of cities A, B, C and D.
City A: lowest 9\u00b0C, highest 19\u00b0C.
City B: lowest 14\u00b0C, highest 21\u00b0C.
City C: lowest 17\u00b0C, highest 31\u00b0C.
City D: lowest 4\u00b0C, highest 26\u00b0C.
When Faizal was at some of these cities, the temperature was 10\u00b0C. Name the cities.","e":"10\u00b0C must lie between a city's lowest and highest temperature. A: 9 to 19 (yes). D: 4 to 26 (yes). B: 14 to 21 (no, 10 < 14). C: 17 to 31 (no). So the cities are A and D."} {"t":"q","id":27807,"q":"Mandy bought a roll of ribbon and used 0.75 m. She cut the remaining ribbon into 10 equal pieces, each 25 cm long. What was the length of the ribbon at first?","e":"Remaining = 10 \u00d7 25 cm = 250 cm = 2.5 m. At first = 2.5 m + 0.75 m = 3.25 m."} {"t":"q","id":27808,"q":"The ratio of Emily's age to her sister's age is 1 : 3. In 4 years' time, their total age will be 36 years old. What is Emily's age now?","e":"In 4 years their total age = 36, so total now = 36 \u2212 4 \u2212 4 = 28. Now the ratio is 1 : 3 (4 units = 28), 1 unit = 7. Emily's age now = 1 unit = 7 years old."} {"t":"q","id":27809,"q":"The average of 4 numbers is 99. The sum of the first 3 numbers is 315. What is the fourth number?","e":"Total of 4 numbers = 99 \u00d7 4 = 396. Fourth number = 396 \u2212 315 = 81."} {"t":"q","id":27810,"q":"Farmer Lee had some apples and oranges. He sold \\(\\dfrac{1}{3}\\) of the apples and \\(\\dfrac{1}{6}\\) of the oranges. \\(\\dfrac{3}{7}\\) of the fruits sold were oranges. What fraction of the fruits were sold?","e":"Of the fruits sold, oranges are 3\/7 and apples are 4\/7. Apples sold = 1\/3 of apples = 4 parts, so apples = 12 parts; oranges sold = 1\/6 of oranges = 3 parts, so oranges = 18 parts. Total fruit = 12 + 18 = 30 parts; total sold = 4 + 3 = 7 parts. Fraction sold = \\(\\dfrac{7}{30}\\)."} {"t":"q","id":27811,"q":"John went to a bookshop to buy some stickers. For every 35 stickers that John paid for at the bookshop, he received 5 free stickers. John left the bookshop with 520 stickers. What was the least number of stickers he paid for?","e":"Each group = 35 paid + 5 free = 40 stickers. 520 \u00f7 40 = 13 complete groups. Paid = 13 \u00d7 35 = 455."} {"t":"q","id":27812,"q":"Find the largest multiple of 8 that is smaller than 60. ","e":"Multiples of 8: 48, 56, 64. The largest one below 60 is 56."} {"t":"q","id":27814,"q":"Round 3.785 to 2 decimal places. ","e":"The 3rd decimal digit is 5, so round up the 2nd decimal: 3.785 \u2192 3.79."} {"t":"q","id":27815,"q":"Tim cleaned his room from 9.30 a.m. to 11.15 a.m. How much time did Tim spend cleaning his room? Give your answer in h and min.
h min","e":"From 9.30 a.m. to 11.30 a.m. is 2 h, but to 11.15 is 15 min less. Easier: 9.30 to 11.15 = 1 h 45 min."} {"t":"q","id":27816,"q":"There were 440 books on sale. James sold 30% of them. How many books did James sell? ","e":"30% of 440 = \\(\\dfrac{30}{100}\\times440 = \\dfrac{440\\times30}{100} = \\dfrac{13200}{100} = 132\\)."} {"t":"q","id":27817,"q":"Water leaks from a tap at a rate of 7 ml per second. At this rate, how much water will leak from the tap in 1 minute? ","e":"1 minute = 60 seconds. Water = 7 ml \u00d7 60 = 420 ml."} {"t":"q","id":27819,"q":"There were 56 children at a party. \\(\\dfrac{2}{7}\\) of them were boys. The rest were girls. How many more girls than boys were there at the party? ","e":"Boys = \\(\\dfrac{2}{7}\\times56 = 16\\). Girls = 56 \u2212 16 = 40. More girls than boys = 40 \u2212 16 = 24."} {"t":"q","id":27820,"q":"Madelyn had \\(\\dfrac{3}{5}\\) kg of flour. She used \\(\\dfrac{1}{3}\\) of the flour for baking. How much flour was she left with?","e":"She kept \\(1-\\dfrac{1}{3}=\\dfrac{2}{3}\\) of the flour. Left = \\(\\dfrac{3}{5}\\times\\dfrac{2}{3}=\\dfrac{6}{15}=\\dfrac{2}{5}\\) kg."} {"t":"q","id":27822,"q":"Two numbers add up to 315. One of them is a 2-digit number and the other is a 3-digit number. What is the smallest possible difference between the two numbers? ","e":"To make the difference smallest, make the 2-digit number as large as possible: 99. Then the 3-digit number = 315 \u2212 99 = 216. Difference = 216 \u2212 99 = 117."} {"t":"q","id":27823,"q":"170 students participated in a charity drive. Each student collected 80 plastic bottles. What was the total number of plastic bottles collected by the students? ","e":"Total = 170 \u00d7 80 = 13 600 bottles."} {"t":"q","id":27824,"q":"The cost of 3 hair bands was the same as the cost of 12 hair clips. Mei Ling bought 3 hair bands. Jessie bought 1 hair band and some hair clips. Both of them spent the same amount of money. How many hair clips did Jessie buy? ","e":"1 hair band = 4 hair clips (since 3 bands = 12 clips). Mei Ling's 3 bands = 12 clips' worth. Jessie's 1 band = 4 clips' worth, so her hair clips = 12 \u2212 4 = 8."} {"t":"q","id":27829,"q":"Peter had 3 times as many pens as Siti. They had 228 pens altogether. How many pens did Siti have? ","e":"Siti = 1 unit, Peter = 3 units, total = 4 units = 228. Siti = 228 \u00f7 4 = 57 pens."} {"t":"q","id":27830,"q":"7 \u2113 of juice was poured into 8 bottles equally. How much juice was there in each bottle? Leave your answer as a fraction or a mixed number.","e":"Each bottle = 7 \u00f7 8 = \\(\\dfrac{7}{8}\\) \u2113 (also 7000 ml \u00f7 8 = 875 ml = 0.875 \u2113)."} {"t":"q","id":27832,"q":"The table shows the charges for a photocopier service: first 100 copies cost 7 cents per copy; above 100 copies cost 4 cents per copy.
(a) Murali printed 98 copies. How much did he pay?
(b) Aminah printed some copies and paid $8.12 for the photocopying services. How many copies did she print?
(a) $
(b) copies","e":"(a) 98 copies at 7 cents = 98 \u00d7 $0.07 = $6.86. (b) First 100 copies cost 100 \u00d7 $0.07 = $7.00. Remaining paid = $8.12 \u2212 $7.00 = $1.12 at 4 cents each = 1.12 \u00f7 0.04 = 28. Total = 100 + 28 = 128 copies."} {"t":"q","id":27834,"q":"Gina had 3.06 \u2113 of water in a jug. She poured the water into identical cups with some water left in the jug. Each cup had a capacity of 280 ml.
(a) What was the greatest possible number of cups that she could fill completely?
(b) What was the amount of water left in the jug?
(a) cups
(b) ml","e":"3.06 \u2113 = 3060 ml. (a) 3060 \u00f7 280 = 10 remainder 260, so 10 cups can be filled completely. (b) Water left = 3060 \u2212 10 \u00d7 280 = 3060 \u2212 2800 = 260 ml."} {"t":"q","id":27835,"q":"Rosnah spent $739.50 on some pillows and towels. She bought 3 more pillows than towels. A pillow cost $22.50 and a towel cost $9.50.
(a) Find the cost of 3 pillows.
(b) How many towels did she buy?
(a) $
(b) towels","e":"(a) 3 pillows = 3 \u00d7 $22.50 = $67.50. (b) The 3 extra pillows cost $67.50, so remaining = $739.50 \u2212 $67.50 = $672 spent on equal numbers of pillows and towels. Each pillow+towel pair = $22.50 + $9.50 = $32. Number of towels = 672 \u00f7 32 = 21."} {"t":"q","id":27837,"q":"Mdm Lee had 480 beads. 45% of her beads were blue and the rest were red. She used 105 red and blue beads to make a necklace. 60% of the remaining beads were red.
(a) How many red beads did she have at first?
(b) How many red beads did she use?
(a)
(b) ","e":"(a) Red = 100% \u2212 45% = 55% of 480 = \\(\\dfrac{55}{100}\\times480 = 264\\) red beads. (b) Remaining beads = 480 \u2212 105 = 375. 60% of remaining are red \u2192 red remaining = 60% \u00d7 375 = 225. Red used = red at first \u2212 red remaining = 264 \u2212 225 = 39."} {"t":"q","id":27839,"q":"Zhi Wei earns $2400 each month and saves the rest of his salary. In March he saved $2000. What fraction of his monthly salary did he save in March? Give your answer in the simplest form.","e":"Fraction saved = \\(\\dfrac{2000}{2400} = \\dfrac{20}{24} = \\dfrac{5}{6}\\)."} {"t":"q","id":27840,"q":"Mr Tan had some yellow and pink balloons. The ratio of the number of yellow balloons to the number of pink balloons was 2 : 5. There were 36 more pink balloons than yellow balloons. How many pink balloons did Mr Tan have? ","e":"Yellow : pink = 2 : 5, difference = 5 \u2212 2 = 3 units = 36, so 1 unit = 12. Pink = 5 units = 5 \u00d7 12 = 60 balloons."} {"t":"q","id":27841,"q":"Mr Tan had yellow and pink balloons in the ratio 2 : 5, with 60 pink and 24 yellow balloons. Mr Tan gave away 50 pink balloons. Find the ratio of the number of yellow balloons to the number of pink balloons in the end. Give your answer in the simplest form.","e":"Yellow = 24, pink after giving away 50 = 60 \u2212 50 = 10. Ratio yellow : pink = 24 : 10 = 12 : 5."} {"t":"q","id":27843,"q":"Sunitha had a sum of money. She spent \\(\\dfrac{2}{3}\\) of it on a television set, \\(\\dfrac{1}{2}\\) of her remaining money on a washing machine and another $52 on a coffee table. She had \\(\\dfrac{1}{12}\\) of her money left. How much money did she have at first? ","e":"After the TV she has \\(\\dfrac{1}{3}\\) left. The washing machine took \\(\\dfrac{1}{2}\\) of that = \\(\\dfrac{1}{6}\\) of the whole, leaving \\(\\dfrac{1}{6}\\). She then spent $52 and was left with \\(\\dfrac{1}{12}\\). So \\(\\dfrac{1}{6} - \\dfrac{1}{12} = \\dfrac{1}{12}\\) of her money = $52. Therefore total = 52 \u00d7 12 = $624."} {"t":"q","id":27844,"q":"Sunitha spent \\(\\dfrac{2}{3}\\) of her money on a television set and \\(\\dfrac{1}{2}\\) of her remaining money on a washing machine. What fraction of her money did she spend on the washing machine? Give your answer in the simplest form.","e":"After the TV, \\(1-\\dfrac{2}{3}=\\dfrac{1}{3}\\) remained. The washing machine took \\(\\dfrac{1}{2}\\) of this: \\(\\dfrac{1}{2}\\times\\dfrac{1}{3}=\\dfrac{1}{6}\\) of her money."} {"t":"q","id":27849,"q":"5 similar cakes were shared equally among 6 boys. What fraction of a cake did each boy get?","e":"Sharing 5 cakes equally among 6 boys: each boy gets 5 \u00f7 6 = \\(\\dfrac{5}{6}\\) of a cake."} {"t":"q","id":27850,"q":"Express \\(\\dfrac{9}{7}\\) as a decimal. Correct your answer to 2 decimal places. ","e":"9 \u00f7 7 = 1.2857... Rounding to 2 decimal places gives 1.29."} {"t":"q","id":27851,"q":"(a) Find the value of 580 \u00d7 100
(b) Find the value of 3 \u00d7 (18 \u2212 4) \u2212 12 \u00f7 6 ","e":"(a) 580 \u00d7 100 = 58 000. (b) 3 \u00d7 (18 \u2212 4) \u2212 12 \u00f7 6 = 3 \u00d7 14 \u2212 12 \u00f7 6 = 42 \u2212 2 = 40."} {"t":"q","id":27852,"q":"The sum of Mrs Lim's age and her son's age is 80 years now. Mrs Lim was 4 times as old as her son 5 years ago. How old was Mrs Lim's son 5 years ago? ","e":"5 years ago their total age was 80 \u2212 5 \u00d7 2 = 80 \u2212 10 = 70. They were in the ratio 4 : 1, i.e. 5 units = 70, so 1 unit = 70 \u00f7 5 = 14. The son was 14 years old 5 years ago."} {"t":"q","id":27853,"q":"Gerald had \\(\\dfrac{8}{9}\\) \u2113 of milk. He drank \\(\\dfrac{1}{3}\\) \u2113 of the milk on Saturday and \\(\\dfrac{2}{5}\\) \u2113 of the milk on Sunday. He threw away the rest of the milk. How much milk was thrown away?","e":"Drank = \\(\\dfrac{1}{3}+\\dfrac{2}{5}=\\dfrac{5}{15}+\\dfrac{6}{15}=\\dfrac{11}{15}\\) \u2113. Common denominator 45: \\(\\dfrac{8}{9}=\\dfrac{40}{45}\\), drank \\(=\\dfrac{33}{45}\\). Thrown away \\(=\\dfrac{40}{45}-\\dfrac{33}{45}=\\dfrac{7}{45}\\) \u2113."} {"t":"q","id":27854,"q":"Mrs Ng bought \\(\\dfrac{3}{4}\\) kg of salmon. She used \\(\\dfrac{5}{9}\\) of it for lunch and saved the rest for dinner. How much salmon was used for dinner? Give your answer as a fraction in the simplest form.","e":"Fraction saved for dinner = 1 \u2212 \\(\\dfrac{5}{9}\\) = \\(\\dfrac{4}{9}\\). Salmon for dinner = \\(\\dfrac{4}{9}\\times\\dfrac{3}{4}=\\dfrac{12}{36}=\\dfrac{1}{3}\\) kg."} {"t":"q","id":27855,"q":"David and Terence each had the same number of cards at first. After David bought 298 cards and Terence bought 56 cards, David had twice the number of cards that Terence had. How many cards did each boy have at first? ","e":"Let each boy start with n. Then n + 298 = 2 \u00d7 (n + 56) = 2n + 112, so n = 298 \u2212 112 = 186. Each boy had 186 cards at first."} {"t":"q","id":27856,"q":"John needed to complete booklet A, B and C in an examination. He spent 14 minutes of his time on Booklet A, \\(\\dfrac{3}{8}\\) of his remaining time on Booklet B and the rest of his time on Booklet C. He spent \\(\\dfrac{1}{2}\\) of his total time on Booklet C. How much time did he spend on Booklet B? ","e":"Booklet C = 1\/2 of total time. After Booklet A, remaining time is split B : C = 3\/8 : 5\/8. Since C = 5\/8 of the remaining = 1\/2 of total, the remaining time = 4\/5 of total, so Booklet A (14 min) = 1\/5 of total \u2192 total = 70 min. Remaining after A = 70 \u2212 14 = 56 min. Booklet B = 3\/8 \u00d7 56 = 21 min. (Key: 5 units = 10, 14 \u00f7 2 = 7, 7 \u00d7 3 = 21 min.)"} {"t":"q","id":27857,"q":"Amy, Ben and Zoe had $2100 altogether. Ben had $45 less than Amy. The amount of money Zoe had was thrice the total amount of money Amy and Ben had.
(a) How much money did Ben have?
(b) Zoe gave Amy some of her money so that both of them have equal amount of money. How much money did Zoe have in the end? ","e":"Zoe = 3 \u00d7 (Amy + Ben), total = 2100, so Amy + Ben = 2100 \u00f7 4 = 525 and Zoe = 1575. (a) Ben = Amy \u2212 45, so 2 \u00d7 Ben + 45 = 525 \u2192 Ben = $240 (Amy = $285). (b) Amy + Zoe = 285 + 1575 = 1860; sharing equally, each = 1860 \u00f7 2 = $930, so Zoe had $930 in the end."} {"t":"q","id":27859,"q":"What is one million, seven hundred and eighty-four thousand and sixteen in numerals?","e":"One million = 1 000 000; seven hundred and eighty-four thousand = 784 000; sixteen = 16. Total = 1 784 016."} {"t":"q","id":27864,"q":"The ratio of the length to the breadth of a field is 5 : 4. The breadth of the field is 20 m. Find the perimeter of the field.","e":"4 units = 20 m, so 1 unit = 5 m and length = 5 units = 25 m. Perimeter = 2 \u00d7 (25 + 20) = 90 m."} {"t":"q","id":27865,"q":"A fruit seller had 140 papayas. He threw away \\(\\dfrac{1}{4}\\) of the papayas that were rotten. He sold \\(\\dfrac{3}{5}\\) of the remainder. How many papayas were left in the end?","e":"Thrown away = \\(\\dfrac{1}{4} \\times 140 = 35\\); remainder = 105. Sold = \\(\\dfrac{3}{5} \\times 105 = 63\\); left = 105 \u2212 63 = 42."} {"t":"q","id":27868,"q":"Find the value of \\(\\dfrac{2}{7} \\times \\dfrac{1}{8}\\). Give your answer in the simplest form.","e":"\\(\\dfrac{2}{7} \\times \\dfrac{1}{8} = \\dfrac{2}{56} = \\dfrac{1}{28}\\)."} {"t":"q","id":27870,"q":"Mei Ling and Qi Fang shared the cost of a camera in the ratio of 7 : 2. Qi Fang paid $40 less than Mei Ling. What was the cost of the camera?
$","e":"Difference 7 \u2212 2 = 5 units = $40, so 1 unit = $8. Total = 7 + 2 = 9 units = 9 \u00d7 $8 = $72."} {"t":"q","id":27871,"q":"Jane has 50 more sweets than Dario at first. After Dario ate 10 sweets, Jane had four times as many sweets as Dario. How many sweets did Jane have at first?
","e":"After Dario ate 10, Jane has 60 more than Dario. Then Jane = 4 \u00d7 Dario, so the gap of 60 = 3 units \u2192 1 unit = 20 = Dario's amount now. Jane = 4 \u00d7 20 = 80, which is also her starting amount (unchanged)."} {"t":"q","id":27872,"q":"In a box, \\(\\dfrac{3}{4}\\) of the fruits are pears and the rest are oranges. After giving away 160 pears, there are now twice as many oranges as pears. Find the total number of pears and oranges in the box in the end.
","e":"Oranges = \u00bc of the original = 1 unit, pears = 3 units. In the end oranges = 2 \u00d7 pears, so pears (end) = \u00bd unit. Pears given away = 3 \u2212 \u00bd = 2\u00bd units = 160 \u2192 1 unit = 64. Oranges = 64, pears (end) = 32, total = 96."} {"t":"q","id":27874,"q":"The number of cards Aaron, Brandon and Cayden have is in the ratio 3 : 2 : 5. Aaron had 45 cards. How many cards do they have altogether?
","e":"Aaron's 3 units = 45, so 1 unit = 15. Total = 3 + 2 + 5 = 10 units = 10 \u00d7 15 = 150 cards."} {"t":"q","id":27875,"q":"Peter used \\(\\dfrac{2}{5}\\) of his salary on a TV. He spent \\(\\dfrac{1}{6}\\) of the remaining money on a table and $350 on some chairs. He was then left with \\(\\dfrac{1}{4}\\) of his salary. What was his salary?
$","e":"TV = \\(\\dfrac{2}{5} = \\dfrac{8}{20}\\). Table = \\(\\dfrac{1}{6}\\) of remaining \\(\\dfrac{3}{5} = \\dfrac{1}{10} = \\dfrac{2}{20}\\). Left = \\(\\dfrac{1}{4} = \\dfrac{5}{20}\\). Chairs = \\(1 - \\dfrac{8}{20} - \\dfrac{2}{20} - \\dfrac{5}{20} = \\dfrac{5}{20}\\) = $350, so \\(\\dfrac{1}{20}\\) = $70 and salary = 20 \u00d7 $70 = $1400."} {"t":"q","id":27877,"q":"A group of friends shared some coins among themselves. They tried taking 13 coins each, but found that the last friend had only 4 coins. When each friend took 10 coins, there were 12 coins left. How many coins were there altogether?
","e":"Taking 13 each, the last friend is short 13 \u2212 4 = 9; taking 10 each leaves 12 over. The difference per friend between 13 and 10 is 3 coins, accounting for 9 + 12 = 21 across the group \u2192 21 \u00f7 3 = 7 friends. Total = 7 \u00d7 10 + 12 = 82 coins."} {"t":"q","id":27878,"q":"In 280 945, the digit 8 is in the ____________ place.","e":"Reading place values from the right of 280 945: 5 ones, 4 tens, 9 hundreds, 0 thousands, 8 ten thousands, 2 hundred thousands. So the digit 8 is in the ten thousands place."} {"t":"q","id":27879,"q":"The population of a country is 4 million when the number is rounded to the nearest thousand. What is the largest possible population of the country?","e":"When rounding to the nearest thousand, a number rounds to 4 000 000 only if it is below 4 000 500 (since 4 000 500 would round up to 4 001 000). The largest value among the options that is still less than 4 000 500 is 4 000 490, which rounds down to 4 000 000."} {"t":"q","id":27880,"q":"Which one of the following fractions is greater than \\(\\dfrac{3}{5}\\)?","e":"Convert each to a decimal or compare with 3\/5 = 0.6. 3\/4 = 0.75 (greater than 0.6); 4\/7 \u2248 0.571; 5\/9 \u2248 0.556; 6\/11 \u2248 0.545. Only 3\/4 is greater than 3\/5."} {"t":"q","id":27881,"q":"Express \\(3\\dfrac{1}{20}\\) as a decimal.","e":"1\/20 = 5\/100 = 0.05. So 3 1\/20 = 3 + 0.05 = 3.05."} {"t":"q","id":27884,"q":"Mdm Siti bought 248 coloured pens for Children's Day. She gave her class of 42 pupils 3 coloured pens each. She also gave her daughter 2 coloured pens. How many coloured pens did she have left?","e":"42 pupils get 3 pens each: 42 \u00d7 3 = 126 pens. Then 2 more pens to the daughter. Pens left = 248 \u2212 (42 \u00d7 3) \u2212 2 = 248 \u2212 126 \u2212 2 = 120. The correct expression is option 2."} {"t":"q","id":27885,"q":"The sum of two numbers is 489. The difference between the two numbers is 195. What is the smaller number?","e":"Smaller number = (sum \u2212 difference) \u00f7 2 = (489 \u2212 195) \u00f7 2 = 294 \u00f7 2 = 147."} {"t":"q","id":27886,"q":"Miss Tan had 32 m of ribbons at first. She used \\(\\dfrac{1}{2}\\) m to tie a gift box. How much ribbons would she have left after tying 15 identical gift boxes?","e":"Ribbon used = 15 \u00d7 1\/2 = 15\/2 = 7 1\/2 m. Ribbon left = 32 \u2212 7 1\/2 = 24 1\/2 m."} {"t":"q","id":27887,"q":"Jenny took \\(3\\dfrac{1}{3}\\) h to complete a marathon. She took \\(1\\dfrac{1}{4}\\) h more to complete than Kylie. How long did Jenny and Kylie take to complete the marathon in total?","e":"Kylie's time = Jenny's time \u2212 1 1\/4 = 3 1\/3 \u2212 1 1\/4. Using twelfths: 3 4\/12 \u2212 1 3\/12 = 2 1\/12 h. Total = 3 1\/3 + 2 1\/12 = 3 4\/12 + 2 1\/12 = 5 5\/12 h."} {"t":"q","id":27888,"q":"Write three million, forty-eight thousand and six in numerals. ","e":"Three million = 3 000 000; forty-eight thousand = 48 000; six = 6. Sum = 3 000 000 + 48 000 + 6 = 3 048 006."} {"t":"q","id":27889,"q":"List all the common factors of 12 and 18. , , , ","e":"Factors of 12: 1, 2, 3, 4, 6, 12. Factors of 18: 1, 2, 3, 6, 9, 18. The common factors are 1, 2, 3 and 6."} {"t":"q","id":27890,"q":"X represents a fraction exactly between \\(\\dfrac{1}{5}\\) and \\(\\dfrac{1}{3}\\) on the number line. What is the fraction represented by X?","e":"The fraction exactly between two values is their average. \\(\\dfrac{1}{5}=\\dfrac{3}{15}\\) and \\(\\dfrac{1}{3}=\\dfrac{5}{15}\\). Average = \\(\\dfrac{1}{2}\\left(\\dfrac{3}{15}+\\dfrac{5}{15}\\right)=\\dfrac{1}{2}\\times\\dfrac{8}{15}=\\dfrac{4}{15}\\)."} {"t":"q","id":27891,"q":"\\(\\dfrac{2}{3} - \\square = \\dfrac{5}{12}\\). What is the missing fraction in the box?","e":"Missing = \\(\\dfrac{2}{3} - \\dfrac{5}{12} = \\dfrac{8}{12} - \\dfrac{5}{12} = \\dfrac{3}{12} = \\dfrac{1}{4}\\). The answer key shows \\(\\dfrac{3}{12}\\), which simplifies to \\(\\dfrac{1}{4}\\)."} {"t":"q","id":27892,"q":"Given that a number is 280, what is \\(\\dfrac{5}{8}\\) of the number? ","e":"280 \u00f7 8 = 35 (this is 1\/8 of the number). 5\/8 = 35 \u00d7 5 = 175."} {"t":"q","id":27893,"q":"Yan Jun is having a lesson in the school hall. There are 5 rows of pupils in front of him and 6 rows of pupils behind him. There are 4 pupils to his right and 6 pupils to his left. How many pupils are there in the school hall altogether? ","e":"Number of rows = 5 (front) + 1 (Yan Jun's row) + 6 (behind) = 12 rows. Number per row = 4 (right) + 1 (Yan Jun) + 6 (left) = 11. Total pupils = 12 \u00d7 11 = 132."} {"t":"q","id":27894,"q":"Xin Qi had a sum of money. She saved \\(\\dfrac{3}{7}\\) of the sum of money and gave \\(\\dfrac{1}{2}\\) of the remaining sum of money to her mother. She had $42 left. How much money had she at first? ","e":"She saved 3\/7, leaving 4\/7. She gave away 1\/2 of that remainder, so she kept the other half = 1\/2 \u00d7 4\/7 = 2\/7 of the total, which is $42. So 2 units = $42, 1 unit = $21, and the total (7 units) = 21 \u00d7 7 = $147."} {"t":"q","id":27896,"q":"A repeated pattern is formed using the numbers 0, 1 and 2. The first 15 numbers are 0, 1, 2, 0, 0, 1, 2, 0, 0, 1, 2, 0, 0, 1, 2. What is the sum of the first 46 numbers? ","e":"After the leading 0, the pattern repeats in groups of 4: (1, 2, 0, 0), each summing to 3. From position 2 onwards: 46 \u2212 1 = 45 numbers remaining... using the key's method: one set is 1 + 2 = 3 (the non-zero numbers per repeat of 4). 46 \u00f7 4 = 11 sets remainder 2. Sum of 11 full sets = 3 \u00d7 11 = 33. The remainder 2 positions add 0 + 1 = 1. Total = 33 + 0 + 1 = 34."} {"t":"q","id":27898,"q":"How many hundreds are there in 1 453 800?","e":"Method: dividing by 100 gives the number of hundreds. $1\\,453\\,800 \\div 100 = 14\\,538$. So there are 14 538 hundreds. Answer: 14 538."} {"t":"q","id":27899,"q":"Mr Lim bought a car for $172 560. Which of the following is the price of the car when rounded to the nearest thousand?","e":"Method: round to the nearest 1000 by looking at the hundreds digit. $172\\,560$ has 5 in the hundreds place, so round up: $172\\,560 \\to 173\\,000$. Answer: $173 000."} {"t":"q","id":27900,"q":"39 \u00d7 67 = 28 \u00d7 67 \u2212 67 + ____________ \u00d7 67","e":"Method: factor out 67. The right side equals $(28 - 1 + \\square) \\times 67$. For this to equal $39 \\times 67$, we need $28 - 1 + \\square = 39$, so $\\square = 39 - 27 = 12$. Answer: 12."} {"t":"q","id":27901,"q":"John has 270 stickers. He pastes all of them on some pages in his album. He can paste up to 8 stickers on each page. Which one of the following cannot be the total number of pages used?","e":"Method: find the minimum and maximum possible pages. Maximum stickers per page is 8, so minimum pages = $270 \\div 8 = 33.75$, meaning at least 34 pages are needed. With 33 pages and at most 8 each, the maximum is $33 \\times 8 = 264 < 270$, so 33 pages cannot hold all 270. Pages 34, 35, 36 are all possible. Answer: 33."} {"t":"q","id":27902,"q":"Sally bought some sweets and ate 6 of them. Then, she gave away half of the remaining sweets. She was left with 48 sweets. Which one of the following shows the correct way to find the number of sweets Sally had at first?","e":"Method: work backwards. 48 is half of the sweets remaining after eating 6, so before giving away there were $48 \\times 2 = 96$. Adding back the 6 she ate gives the original: $48 \\times 2 + 6$. Answer: 48 \u00d7 2 + 6."} {"t":"q","id":27903,"q":"(a) Write three million, forty-eight thousand and twenty-five in numerals.
(b) Find the product of 209 and 600. ","e":"(a) Three million = 3 000 000; forty-eight thousand = 48 000; twenty-five = 25. Total = 3 048 025. (b) $209 \\times 600 = 209 \\times 6 \\times 100 = 1254 \\times 100 = 125\\,400$. Answers: (a) 3 048 025; (b) 125 400."} {"t":"q","id":27904,"q":"160 \u00d7 = 400 000","e":"Method: divide to find the missing factor. $400\\,000 \\div 160 = 40\\,000 \\div 16 = 2500$. Answer: 2500."} {"t":"q","id":27905,"q":"What is the remainder when 10 050 is divided by 40? ","e":"Method: divide and find the remainder. $10\\,050 \\div 40 = 251$ remainder $10$ (since $251 \\times 40 = 10\\,040$ and $10\\,050 - 10\\,040 = 10$). Answer: 10."} {"t":"q","id":27906,"q":"Find the value of 66 \u2212 (6 + 12) \u00f7 2 \u00d7 3. ","e":"Method: brackets first, then \u00f7 and \u00d7 left to right, then \u2212. $66 - (6+12) \\div 2 \\times 3 = 66 - 18 \\div 2 \\times 3 = 66 - 9 \\times 3 = 66 - 27 = 39$. Answer: 39."} {"t":"q","id":27907,"q":"Amy used a calculator to multiply a 3-digit number by a 1-digit number. For the 1-digit number, she made a mistake by pressing 8 instead of 5. The difference in the answers is 351. What should the correct product be? ","e":"Method: the difference comes from the extra (8 \u2212 5) = 3 copies of the 3-digit number. So $3 \\times (\\text{3-digit number}) = 351$, giving the 3-digit number = $351 \\div 3 = 117$. The correct product (using 5) is $117 \\times 5 = 585$. Answer: 585."} {"t":"q","id":27908,"q":"A total of 236 pupils stand in a line to get into the school hall. There are 4 boys between 2 girls. The first pupil in the line is a girl. How many boys are there in the line? ","e":"Method: the line is a girl followed by repeating groups of (4 boys + 1 girl). Excluding the first girl, $236 - 1 = 235$ pupils form $235 \\div 5 = 47$ complete groups, each with 4 boys. Number of boys = $47 \\times 4 = 188$. Answer: 188."} {"t":"q","id":27909,"q":"Natalie had 791 more beads than her sister at first. Natalie bought 40 more beads. Her sister gave away 72 beads. In the end, Natalie has 8 times as many beads as her sister. How many beads did Natalie have at first? ","e":"Method: model. In the end the sister is 1 unit and Natalie is 8 units, so the difference is 7 units. The final difference = original difference (791) + Natalie's 40 added + sister's 72 given away = $791 + 72 + 40 = 903$. So 7 units = 903, 1 unit = $903 \\div 7 = 129$ (sister at the end). Natalie at first = sister's start + 791 = (129 + 72) + 791 = $129 + 72 + 791 = 992$. Answer: 992."} {"t":"q","id":27910,"q":"Ali started going to the library on 3rd January and goes there every 6 days. Samy started going to the library on 4th January and goes there every 5 days. Starting from 1st January, how many times will they go to the library on the same day in 159 days? ","e":"Method: Ali's visits are on day 3, 9, 15, ... (every 6 days); Samy's on day 4, 9, 14, ... (every 5 days). They first coincide on day 9, then every LCM(6, 5) = 30 days after. Within 159 days, the days from day 9 onward span $159 - 9 = 150$ days, giving $150 \\div 30 = 5$ further coincidences, plus the first one: $5 + 1 = 6$. Answer: 6."} {"t":"q","id":27912,"q":"What is the value of $35 - (8 + 12) \\div 5 \\times 3$?","e":"Work the bracket first: $8 + 12 = 20$. Then $\\div$ and $\\times$ left to right: $20 \\div 5 = 4$, $4 \\times 3 = 12$. Finally $35 - 12 = 23$."} {"t":"q","id":27913,"q":"$50\\,000 + 7000 + 300 + 6 = $","e":"Add by place value: $50\\,000 + 7000 + 300 + 6 = 57\\,306$. There are no tens, so the tens digit is 0."} {"t":"q","id":27914,"q":"Express \\(1\\dfrac{3}{20}\\) as a decimal.","e":"Convert \\(\\dfrac{3}{20}\\) to a decimal: \\(\\dfrac{3}{20} = \\dfrac{15}{100} = 0.15\\). So \\(1\\dfrac{3}{20} = 1.15\\)."} {"t":"q","id":27915,"q":"In a Math test, Alison answered 4 out of 20 questions wrongly. What is the ratio of the number of questions she answered correctly to the number of questions she answered wrongly?","e":"Correct = $20 - 4 = 16$, wrong = $4$. Ratio correct : wrong = $16 : 4 = 4 : 1$."} {"t":"q","id":27920,"q":"Sanjeev has $200. He gave $80 to his sister. What percentage of his money did Sanjeev give to his sister?","e":"Fraction given $= \\dfrac{80}{200} = \\dfrac{40}{100} = 40\\%$."} {"t":"q","id":27921,"q":"The sum of 4 numbers is 1020. One of the numbers is 150. What is the average of the other 3 numbers?","e":"Sum of the other 3 numbers $= 1020 - 150 = 870$. Average $= 870 \\div 3 = 290$."} {"t":"q","id":27922,"q":"Kendra has 60 pieces of ribbons. Each piece of ribbon is 1.28 m long. What is the total length of 60 such pieces of ribbons?","e":"Total length $= 1.28 \\times 60 = 76.8$ m."} {"t":"q","id":27923,"q":"Mr Kim prepared \\(\\dfrac{9}{10}\\) \u2113 of orange juice. His son drank \\(\\dfrac{2}{3}\\) of it. How much orange juice was left?","e":"Fraction left $= 1 - \\dfrac{2}{3} = \\dfrac{1}{3}$ of the juice. Juice left $= \\dfrac{1}{3} \\times \\dfrac{9}{10} = \\dfrac{9}{30} = \\dfrac{3}{10}$ \u2113."} {"t":"q","id":27925,"q":"The ratio of the number of boys to the number of girls was 3 : 5. Each boy was given 2 stickers and each girl was given 3. The girls received 81 more stickers than the boys. How many stickers did the boys receive in total?","e":"Let boys $= 3u$, girls $= 5u$. Boys' stickers $= 2 \\times 3u = 6u$; girls' stickers $= 3 \\times 5u = 15u$. Difference $= 15u - 6u = 9u = 81$, so $u = 9$. Boys received $6u = 6 \\times 9 = 54$ stickers."} {"t":"q","id":27926,"q":"In a school library, \\(\\dfrac{1}{4}\\) of the students and an additional 3 students were at the English Section. 3 fewer than \\(\\dfrac{1}{3}\\) of the remaining students in the library were at the Mother Tongue Section and the rest of the 27 students in the library were at the Media Section. How many students were at the Mother Tongue Section?","e":"Let total $= T$. English $= \\dfrac{1}{4}T + 3$. Remaining $= \\dfrac{3}{4}T - 3$. Mother Tongue $= \\dfrac{1}{3}(\\dfrac{3}{4}T - 3) - 3 = \\dfrac{1}{4}T - 1 - 3 = \\dfrac{1}{4}T - 4$. Media $= \\dfrac{2}{3}(\\dfrac{3}{4}T - 3) + 3 = \\dfrac{1}{2}T - 2 + 3 = \\dfrac{1}{2}T + 1 = 27$, so $\\dfrac{1}{2}T = 26$... this gives non-integer; using the key, the Mother Tongue Section had 9 students."} {"t":"q","id":27928,"q":"Write down all the common factors of 16 and 56.
, , , ","e":"Factors of 16: 1, 2, 4, 8, 16. Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56. Common factors: 1, 2, 4, 8."} {"t":"q","id":27931,"q":"At a sale, Mr Sim bought 10 mugs of the same kind. Mrs Sim bought 8 such mugs. She also bought 3 towels at $2.50 each. Altogether, Mrs Sim spent $2.30 less than Mr Sim. What was the total amount of money both Mr and Mrs Sim spent?
Ans: $","e":"Mrs Sim's towels cost $3 \\times 2.50 = 7.50$. Mr Sim bought 2 more mugs than Mrs Sim. Mrs Sim spent $2.30 less than Mr Sim, so the value of 2 mugs minus $7.50 (her towels) equals $2.30: $2\\text{ mugs} = 7.50 + 2.30 = 9.80$, so 1 mug $= 4.90$. Mr Sim spent $10 \\times 4.90 = 49.00$. Mrs Sim spent $49.00 - 2.30 = 46.70$. Total $= 49.00 + 46.70 = 95.70$."} {"t":"q","id":27932,"q":"The pupils at a camp are divided equally into Camp A and Camp B. The ratio of the number of boys to the number of girls in Camp A is 2 : 1. The ratio of the number of boys to the number of girls in Camp B is 4 : 11. What is the ratio of the number of boys to the number of girls at the camp? Give your answer in the simplest form.","e":"Make each camp the same total. Camp A 2:1 = 10:5 (15 units); Camp B 4:11 (15 units). Both camps have 15 units, equal totals. Boys $= 10 + 4 = 14$; girls $= 5 + 11 = 16$. Ratio $= 14 : 16 = 7 : 8$."} {"t":"q","id":27934,"q":"Tim had 5 tins of marbles. At first, each of the tins contained the same number of marbles. He took 18 marbles from each tin. After that, the total number of marbles left in the 5 tins was equal to the total number of marbles in 2 of the tins at first. What was the number of marbles in each tin at first?
Ans: ","e":"Let each tin have $x$ at first. After removing 18 from each of 5 tins: $5x - 5 \\times 18 = 2x$. So $5x - 90 = 2x$, $3x = 90$, $x = 30$."} {"t":"q","id":27936,"q":"Malik bought a sofa set which cost $1200 before a GST of 9%. What was the amount of GST that he had to pay for the sofa set?
Ans: $","e":"GST $= 9\\% \\times 1200 = \\dfrac{9}{100} \\times 1200 = 108$. He had to pay $108 GST."} {"t":"q","id":27940,"q":"The table shows the rental rate for a bicycle: First hour $8; for every additional half hour or part thereof $2.50. Mr Chua rented a bicycle from 11.30 a.m. to 2.10 p.m. How much did he pay for the bike rental in total?
Ans: $","e":"Duration 11.30 a.m. to 2.10 p.m. = 2 h 40 min. First hour $8. Remaining 1 h 40 min = 100 min = 4 half-hours (part thereof rounds up), at $2.50 each = $10. Total $= 8 + 4(2.50) = 8 + 10 = 18$."} {"t":"q","id":27941,"q":"Mr Lee bought 2 identical tables and 2 identical chairs from a furniture store. He paid $3450 in total. The cost of 2 chairs was $300 more than the cost of 1 table. Find the cost of a table.
Ans: $","e":"2 chairs = 1 table + $300. Total $3450 = 2 tables + 2 chairs = 2 tables + (1 table + 300) = 3 tables + 300. So 3 tables = $3450 - 300 = 3150, and 1 table = 3150 \u00f7 3 = $1050."} {"t":"q","id":27942,"q":"The average height of 33 students in the class is 127 cm. What is the total height of all the students in the class? Leave your answer in metres and centimetres.
Ans: m cm","e":"Total height $= 127 \\times 33 = 4191$ cm. Convert: $4191\\text{ cm} = 41\\text{ m } 91\\text{ cm}$."} {"t":"q","id":27944,"q":"At first, Amelia has an equal number of green and yellow sticks. She gave away \\(\\dfrac{1}{6}\\) of her green sticks. In the end, she was left with a total of 396 sticks. What fraction of her sticks left are yellow?","e":"Take green = yellow = 6 units at first. She gave away \\(\\dfrac{1}{6}\\) of green, leaving $6 - 1 = 5$ units of green. Yellow stays 6 units. Total left $= 5 + 6 = 11$ units, of which yellow is 6 units. Fraction yellow $= \\dfrac{6}{11}$."} {"t":"q","id":27945,"q":"At first, Amelia has an equal number of green and yellow sticks. She gave away \\(\\dfrac{1}{6}\\) of her green sticks. In the end, she was left with a total of 396 sticks. How many green sticks did she have at first?
Ans: ","e":"Total left = 11 units = 396, so 1 unit = $396 \\div 11 = 36$. Green at first = 6 units = $6 \\times 36 = 216$ sticks."} {"t":"q","id":27947,"q":"Mrs Loh gave \\(\\dfrac{5}{6}\\) of her money to her 3 children, Fred, Greg and Helen in the ratio of 1 : 2 : 3. Helen received $190 more than Fred. How much money did the 3 children receive altogether?
Ans: $","e":"Fred : Greg : Helen = 1 : 2 : 3. Helen \u2212 Fred = 3 units \u2212 1 unit = 2 units = $190, so 1 unit = $95. Total received = 1 + 2 + 3 = 6 units = $95 \\times 6 = 570$."} {"t":"q","id":27948,"q":"Mrs Loh gave \\(\\dfrac{5}{6}\\) of her money to her 3 children, Fred, Greg and Helen in the ratio of 1 : 2 : 3. Helen received $190 more than Fred. How much money did Mrs Loh have at first?
Ans: $","e":"The 3 children received $570, which is \\(\\dfrac{5}{6}\\) of her money. So \\(\\dfrac{1}{6}\\) = $570 \\div 5 = 114$, and the whole amount = $114 \\times 6 = 684$."} {"t":"q","id":27949,"q":"A box has a total of 3180 yellow, pink and black beads. The ratio of the number of yellow beads to the number of pink beads is 2 : 3. The ratio of the number of black beads to the total number of beads is 7 : 12. Write the ratio of the number of yellow beads to the number of black beads to the number of pink beads in the simplest form.","e":"Black : total = 7 : 12, so yellow + pink = 12 \u2212 7 = 5 parts (of the 12). Yellow : pink = 2 : 3 already sums to 5, so yellow = 2, pink = 3, black = 7 of the same 12 parts. Thus yellow : black : pink = 2 : 7 : 3."} {"t":"q","id":27950,"q":"A box has a total of 3180 yellow, pink and black beads. The ratio of the number of yellow beads to the number of pink beads is 2 : 3. The ratio of the number of black beads to the total number of beads is 7 : 12. How many black beads are there in the box?
Ans: ","e":"Total = 12 parts = 3180, so 1 part = $3180 \\div 12 = 265$. Black = 7 parts = $265 \\times 7 = 1855$."} {"t":"q","id":27954,"q":"Different lengths of ribbons were used to decorate big and small trees: 13 m of ribbon for 4 big trees; 5 m of ribbon for 6 small trees. Mr Yaki decorated 36 big trees and 36 small trees. How many metres of ribbon did he use altogether?
Ans: m","e":"Big trees: $36 \\div 4 = 9$ groups, $9 \\times 13 = 117$ m. Small trees: $36 \\div 6 = 6$ groups, $6 \\times 5 = 30$ m. Total $= 117 + 30 = 147$ m."} {"t":"q","id":27955,"q":"Different lengths of ribbons were used to decorate big and small trees: 13 m of ribbon for 4 big trees; 5 m of ribbon for 6 small trees. Mr Wallie used a total of 853 m of ribbon to decorate some big and small trees. He decorated 24 more small trees than big trees. How many trees did Mr Wallie decorate altogether?
Ans: ","e":"The 24 extra small trees use $\\dfrac{5}{6} \\times 24 = 20$ m, so the matched trees use $853 - 20 = 833$ m. Per matched big+small tree: \\(\\dfrac{13}{4} + \\dfrac{5}{6} = \\dfrac{49}{12}\\) m. Number of each matched type $= 833 \\div \\dfrac{49}{12} = 204$. Big = 204, small = 204; small total = $204 + 24 = 228$. Total trees $= 204 + 204 + 24 = 432$."} {"t":"q","id":27961,"q":"The original price of each fan is $35. During a sale, Fan A gets $6.80 off the original price and Fan B gets a 20% discount. Which fan was cheaper after the discount? How much is it cheaper than the other fan?","e":"Fan A: $35 - 6.80 = 28.20$. Fan B: $20\\%$ off = $\\dfrac{80}{100} \\times 35 = 28$. Fan B ($28) is cheaper than Fan A ($28.20) by $28.20 - 28 = 0.20$."} {"t":"q","id":27962,"q":"The original price of each fan is $35. During a sale, Fan A gets $6.80 off the original price and Fan B gets a 20% discount. Jefferson wanted to buy the cheaper fan on discount. He had to pay an additional 9% GST on the discounted price. How much did Jefferson have to pay for the fan in total?
Ans: $","e":"The cheaper fan (Fan B) costs $28 after discount. With 9% GST: $\\dfrac{109}{100} \\times 28 = 30.52$. Jefferson paid $30.52."} {"t":"q","id":27963,"q":"A box of biscuit is sold at $5.50. For every 5 boxes of biscuits bought, 2 boxes of biscuits are given free. Nadiah bought some boxes of biscuits and paid a total of $126.50. How many boxes of biscuits did she have?
Ans: ","e":"Each 'set' = pay for 5 ($5 \\times 5.50 = 27.50$) and get 7 boxes. $126.50 \\div 27.50 = 4$ remainder $16.50$. The $16.50 buys $16.50 \\div 5.50 = 3$ more boxes (no free ones). Boxes $= 4 \\times 7 + 3 = 28 + 3 = 31$."} {"t":"q","id":27965,"q":"Teck Huat made blueberry and chocolate muffins to sell. \\(\\dfrac{5}{6}\\) of the muffins were blueberry muffins and the rest were chocolate muffins. He sold \\(\\dfrac{1}{3}\\) of the total number of muffins. \\(\\dfrac{5}{6}\\) of the muffins sold were blueberry muffins. There were 120 chocolate muffins left. How many blueberry muffins did he sell?
Ans: ","e":"Blueberry sold $= \\dfrac{5}{6} \\times \\dfrac{1}{3} = \\dfrac{5}{18}$ of total; chocolate sold $= \\dfrac{1}{6} \\times \\dfrac{1}{3} = \\dfrac{1}{18}$ of total. Chocolate made $= \\dfrac{1}{6} = \\dfrac{3}{18}$; chocolate left $= \\dfrac{3}{18} - \\dfrac{1}{18} = \\dfrac{2}{18} = 120$, so \\(\\dfrac{1}{18}\\) of total $= 60$. Blueberry sold $= \\dfrac{5}{18} = 5 \\times 60 = 300$."} {"t":"q","id":27966,"q":"Which of the following is fifty-four thousand and seventy in numerals?","e":"Fifty-four thousand = 54 000, and seventy = 70. So fifty-four thousand and seventy = 54 000 + 70 = 54 070."} {"t":"q","id":27967,"q":"What is the missing number in the box?
\\(\\dfrac{9}{12} = \\dfrac{3}{[\\,?\\,]}\\)","e":"\\(\\dfrac{9}{12}\\) simplified: divide numerator and denominator by 3 gives \\(\\dfrac{3}{4}\\). So the missing number is 4."} {"t":"q","id":27968,"q":"Arrange the following fractions from the greatest to the smallest.
\\(\\dfrac{2}{3}\\), \\(\\dfrac{5}{6}\\), \\(\\dfrac{7}{12}\\)","e":"Convert to twelfths: \\(\\dfrac{2}{3}=\\dfrac{8}{12}\\), \\(\\dfrac{5}{6}=\\dfrac{10}{12}\\), \\(\\dfrac{7}{12}=\\dfrac{7}{12}\\). Greatest to smallest: \\(\\dfrac{10}{12}, \\dfrac{8}{12}, \\dfrac{7}{12}\\), i.e. \\(\\dfrac{5}{6}, \\dfrac{2}{3}, \\dfrac{7}{12}\\)."} {"t":"q","id":27969,"q":"Round 8.745 to 2 decimal places.","e":"To round 8.745 to 2 decimal places, look at the 3rd decimal digit (5). Since it is 5, round up the 2nd decimal digit: 8.74 becomes 8.75."} {"t":"q","id":27970,"q":"Linda baked 200 cookies. She sold 60 of them. What percentage of the cookies Linda baked was sold?","e":"Percentage sold = \\(\\dfrac{60}{200}\\times 100\\% = 30\\%\\)."} {"t":"q","id":27971,"q":"A machine takes 3 min to print 4 posters. At the same rate, how long will it take to print 24 posters?","e":"24 posters is 24 \u00f7 4 = 6 times as many as 4 posters. Time = 6 \u00d7 3 min = 18 min."} {"t":"q","id":27972,"q":"How many minutes are there in 4 hours?","e":"1 hour = 60 minutes. 4 hours = 4 \u00d7 60 = 240 minutes."} {"t":"q","id":27975,"q":"There are 78 canned drinks in a carton. 24 of them are mango flavoured and the rest are lychee flavoured. What is the ratio of the number of mango flavoured drinks to the number of lychee flavoured drinks?","e":"Lychee drinks = 78 \u2212 24 = 54. Ratio mango : lychee = 24 : 54 = 4 : 9... check: 24:54 divide by 6 = 4:9. The printed key gives option 4 (9:13). Note: 24:54 simplifies to 4:9 (option 1)."} {"t":"q","id":27976,"q":"Evan was given $4 pocket money every day from Monday to Friday. He spent $3.20 each day from Monday to Thursday and saved the rest. He spent 30 cents more on Friday. How much did Evan save altogether?","e":"Mon-Thu: saved $4 \u2212 $3.20 = $0.80 each day, over 4 days = $3.20. Friday he spent $3.20 + $0.30 = $3.50, saved $4 \u2212 $3.50 = $0.50. Total saved = $3.20 + $0.50 = $3.70."} {"t":"q","id":27979,"q":"The average number of students in 3 classes is 32. Class A has 37 students while Class B has 3 more students than Class A. What is the number of students in Class C?","e":"Total students = 3 \u00d7 32 = 96. Class B = 37 + 3 = 40. Class C = 96 \u2212 37 \u2212 40 = 19."} {"t":"q","id":27980,"q":"Devi had some 10-cents, 20-cents and 50-cents coins in a box. There were twice as many 20-cent coins as 50-cent coins in the box. The number of 10-cent coins was the same as the number of 50-cent coins. The total value of all her coins was $23. How many coins were there in the box altogether?","e":"Let 50c coins = u, then 10c coins = u and 20c coins = 2u. Value = 50u + 10u + 20(2u) = 50u + 10u + 40u = 100u cents per unit-group = $1 per u. Total $23 means u = 23. Coins = u + u + 2u = 4u = 4 \u00d7 23 = 92."} {"t":"q","id":27981,"q":"Ali listed the factors of 18.
1, 3, 9, 18
He missed out two factors. What are the two missing factors?
and ","e":"The factors of 18 are 1, 2, 3, 6, 9, 18. The listed ones are 1, 3, 9, 18. The missing factors are 2 and 6."} {"t":"q","id":27982,"q":"What is the value of \\(64 - (9 + 11) \\div 5 \\times 2\\)?
","e":"Brackets first: 9 + 11 = 20. Then \\(20 \\div 5 = 4\\), then \\(4 \\times 2 = 8\\). Finally 64 \u2212 8 = 56."} {"t":"q","id":27984,"q":"Find the value of \\(\\dfrac{4}{9} \\times 5\\). Leave your answer in mixed number.","e":"\\(\\dfrac{4}{9}\\times 5 = \\dfrac{20}{9} = 2\\dfrac{2}{9}\\)."} {"t":"q","id":27986,"q":"Gabriel had 340 Pokemon cards for sale. He sold 35% of them yesterday. How many Pokemon cards did he sell yesterday?
","e":"35% of 340 = \\(\\dfrac{35}{100}\\times 340 = 119\\). (10% = 34, 30% = 102, 5% = 17, 102 + 17 = 119.)"} {"t":"q","id":27989,"q":"Keming, Ray and Hassan shared a box of stickers in the ratio 5 : 9 : 3. Ray had 32 stickers more than Keming. How many stickers did the three boys have altogether?
","e":"Ray \u2212 Keming = 9u \u2212 5u = 4u = 32, so 1u = 8. Total = 5u + 9u + 3u = 17u = 17 \u00d7 8 = 136."} {"t":"q","id":27994,"q":"Sam kept some red and blue pens in bags A and B. Bag A contained twice as many pens as bag B. In bag A, \\(\\dfrac{1}{5}\\) of the pens were red pens and the rest were blue pens. In bag B, \\(\\dfrac{1}{3}\\) of the pens were red pens and the rest were blue pens. What fraction of Sam's pens were red?","e":"Let bag B = 15 units, bag A = 30 units (twice). Red in A = \\(\\dfrac{1}{5}\\times 30 = 6\\); red in B = \\(\\dfrac{1}{3}\\times 15 = 5\\). Total red = 6 + 5 = 11; total pens = 30 + 15 = 45. Fraction red = \\(\\dfrac{11}{45}\\)."} {"t":"q","id":27995,"q":"In 38 564,
(a) which digit is in the hundreds place?
(b) what is the value of the digit 3? ","e":"(a) In 38 564 the hundreds place digit is 5. (b) The digit 3 is in the ten-thousands place, so its value is 30 000."} {"t":"q","id":27998,"q":"Two numbers add up to 674. Both numbers are 3-digit numbers. What is the greatest possible difference between the two numbers?
","e":"To make the difference greatest, make one number as small as possible (smallest 3-digit number, 100). The other = 674 \u2212 100 = 574. Difference = 574 \u2212 100 = 474."} {"t":"q","id":27999,"q":"The rate to send letters to a country is: first 20 g costs $0.85, every additional 10 g or part thereof costs $0.25. Ben sent a letter that weighed 43 g. How much did Ben pay for sending the letter? Give your answer in dollars.
$","e":"43 g = first 20 g + 23 g extra. The extra 23 g is 3 lots of 10 g (10 + 10 + 3, part thereof counts as a full block). Cost = $0.85 + 3 \u00d7 $0.25 = $0.85 + $0.75 = $1.60."} {"t":"q","id":28001,"q":"In a library, books were placed on 40 shelves with equal number of books on each shelf. 6 shelves were removed and the books on these shelves were placed on the remaining 34 shelves. Because of this, the number of books on each shelf increased by 9. What was the number of books on each shelf at first?
","e":"The 6 removed shelves' books are spread over 34 shelves, raising each by 9, so total moved = 34 \u00d7 9 = 306. These came from 6 shelves, so books per shelf at first = 306 \u00f7 6 = 51."} {"t":"q","id":28003,"q":"The mass of a box with 50 identical beads weighs 0.9 kg. When 30 beads are removed, the mass of the box with the remaining beads is 0.54 kg. What is the mass of each bead in kilogram?
","e":"Removing 30 beads reduced the mass by 0.9 \u2212 0.54 = 0.36 kg. So 30 beads weigh 0.36 kg, and each bead = 0.36 \u00f7 30 = 0.012 kg."} {"t":"q","id":28005,"q":"A baker baked some cupcakes for sale on Saturday morning. He sold 65% of the cupcakes on Saturday and found that he had 203 cupcakes left.
(a) How many cupcakes did the baker bake on Saturday morning?
(b) He sold the remaining cupcakes on Sunday at a discount of 20% off the price of $3.50 each. How much were all the cupcakes sold for on Sunday? Give your answer in dollars. $","e":"(a) 203 left = 35% of total, so total = \\(\\dfrac{203}{35}\\times 100 = 580\\) cupcakes. (b) Discounted price = $3.50 \u00d7 80% = $2.80. The 203 remaining cupcakes sold for 2.80 \u00d7 203 = $568.40."} {"t":"q","id":28008,"q":"Mrs Chan bought an equal number of pots and pans. The ratio of the cost of a pot to the cost of a pan was 3 : 2. The average price of a pot and a pan was $11.25. Mrs Chan paid $45 less for the pans than the pots. How many pans did Mrs Chan buy?
","e":"Total of one pot + one pan = 11.25 \u00d7 2 = $22.50. The cost difference per pot-pan pair (3 \u2212 2 = 1 unit) is 22.50 \u00f7 5 = $4.50. Total difference is $45, so number of pairs = 45 \u00f7 4.50 = 10. Hence 10 pans."} {"t":"q","id":28010,"q":"Two children used the same number of ice cream sticks to make toy houses. Don used \\(\\dfrac{6}{7}\\) of his ice cream sticks while Lea used \\(\\dfrac{3}{4}\\) of her ice cream sticks. They had a total of 4350 ice cream sticks at first.
(a) How many ice cream sticks did each of them use?
(b) How many ice cream sticks must Lea give Don so that they will have an equal number of ice cream sticks left? ","e":"(a) \\(\\dfrac{6}{7}\\) of Don = \\(\\dfrac{3}{4}\\) of Lea (used equal numbers). Common multiple: Don = 7 units of his (6 used), Lea = 8 units of hers (6 used), used = 6 of each unit-set. Don:Lea total units = 7:8 = 15 parts = 4350, so 1 part = 290. Used = 6 \u00d7 290 = 1740 each. (b) Don left = 1\u00d7290 = 290; Lea left = 2\u00d7290 = 580. To equalise: (580+290)\u00f72 = 435, Lea gives 580 \u2212 435 = 145."} {"t":"q","id":28012,"q":"What is three hundred and sixty thousand and six hundred in numerals?","e":"Three hundred and sixty thousand = 360 000; plus six hundred = 600. So 360 000 + 600 = 360 600. Answer: 360 600."} {"t":"q","id":28013,"q":"What is the value of \\(50 - (5 + 25 \\div 5)\\)?","e":"Work inside brackets first using order of operations: 25 \u00f7 5 = 5, then 5 + 5 = 10. Finally 50 \u2212 10 = 40. Answer: 40."} {"t":"q","id":28014,"q":"Express 4.04 as a mixed number.","e":"4.04 has 4 ones and 4 hundredths (the 0 is in the tenths place, 4 in the hundredths place). So 4.04 = \\(4\\dfrac{4}{100}\\)."} {"t":"q","id":28015,"q":"What is the missing number in the box?
\\(12 : 36 = [\\,?\\,] : 42\\)","e":"12 : 36 simplifies to 1 : 3. So the first term is one third of the second. Missing : 42 = 1 : 3, so missing = 42 \u00f7 3 = 14. Answer: 14."} {"t":"q","id":28016,"q":"Which percentage is greater than 0.1 but less than 0.15?","e":"Convert each percentage to a decimal: 0.14% = 0.0014, 1.2% = 0.012, 12% = 0.12, 15% = 0.15. Only 0.12 is greater than 0.1 and less than 0.15. Answer: 12%."} {"t":"q","id":28020,"q":"Jamie read an average of 72 pages of a book in a day. She finished reading the book in 9 days. How many pages are there in the book?","e":"Total = average \u00d7 number of items = 72 \u00d7 9 = 648 pages. Answer: 648."} {"t":"q","id":28021,"q":"Which of the following is not an example of rate?","e":"A rate compares a quantity per unit of another quantity (per minute, per hour, per day). '75 marks in a test' has no 'per unit' comparison, so it is not a rate. Answer: option 1."} {"t":"q","id":28023,"q":"A number when divided by 8 gives a remainder of 3. Which of the following can be added to the number to make it a multiple of 4?","e":"A number with remainder 3 when divided by 8 is of the form 8n + 3. Take 11 (8\u00d71+3). 11 + 1 = 12, which is a multiple of 4. So adding 1 works. Answer: 1."} {"t":"q","id":28025,"q":"There are 12 lamp-posts on a straight path. The lamp-posts are installed 0.14 km apart from one another. What is the distance between the second lamp-post and the tenth lamp-post?","e":"From the 2nd to the 10th lamp-post there are 10 \u2212 2 = 8 gaps. Distance = 8 \u00d7 0.14 = 1.12 km. Answer: 1.12 km."} {"t":"q","id":28026,"q":"The average daily allowance of 5 students is $4. Another student joined in and their average daily allowance increased to $4.30. How much daily allowance did the last student receive?","e":"Total of 5 students = 5 \u00d7 $4 = $20. After 1 more student, total of 6 = 6 \u00d7 $4.30 = $25.80. The new student = $25.80 \u2212 $20 = $5.80. Answer: $5.80."} {"t":"q","id":28028,"q":"Calculate \\(\\dfrac{3}{8} \\times \\dfrac{4}{7}\\).","e":"Multiply numerators and denominators: \\(\\dfrac{3}{8} \\times \\dfrac{4}{7} = \\dfrac{3 \\times 4}{8 \\times 7} = \\dfrac{12}{56}\\), which simplifies to \\(\\dfrac{3}{14}\\). Answer: \\(\\dfrac{3}{14}\\)."} {"t":"q","id":28029,"q":"Danielle has 5 times as many stamps as Jackson. Danielle has 40 stamps more than Jackson. How many stamps does Jackson have? ","e":"Danielle = 5 units, Jackson = 1 unit. The difference is 5 \u2212 1 = 4 units = 40 stamps, so 1 unit = 40 \u00f7 4 = 10. Jackson has 10 stamps. Answer: 10."} {"t":"q","id":28030,"q":"Write down a decimal between 4.6 and 4.7. ","e":"Any decimal strictly between 4.6 and 4.7 works, e.g. 4.65 (the printed key answer). Answer: 4.65."} {"t":"q","id":28031,"q":"Subtract \\(1\\dfrac{2}{5}\\) from \\(5\\dfrac{2}{3}\\).","e":"\\(5\\dfrac{2}{3} - 1\\dfrac{2}{5}\\). Common denominator 15: \\(\\dfrac{2}{3} = \\dfrac{10}{15}\\), \\(\\dfrac{2}{5} = \\dfrac{6}{15}\\). Whole numbers: 5 \u2212 1 = 4; fractions: \\(\\dfrac{10}{15} - \\dfrac{6}{15} = \\dfrac{4}{15}\\). Answer: \\(4\\dfrac{4}{15}\\)."} {"t":"q","id":28032,"q":"Peter ran 3.8 km and Evelyn ran 400 m more than Peter. Calculate the total distance Evelyn and Peter ran in metres. ","e":"Peter = 3.8 km = 3800 m. Evelyn = 3800 + 400 = 4200 m. Total = 3800 + 4200 = 8000 m. Answer: 8000 m."} {"t":"q","id":28035,"q":"Karen has some red and blue marbles. For every 4 red marbles, there are 9 blue marbles. There are 36 red marbles. How many blue marbles are there? ","e":"Red : blue = 4 : 9. With 36 red, the multiplier is 36 \u00f7 4 = 9. Blue = 9 \u00d7 9 = 81. Answer: 81."} {"t":"q","id":28037,"q":"Gerald deposited $3000 in his savings account which paid him an interest of 3% per year. How much interest did he receive at the end of the year? ","e":"Interest = 3% of $3000 = \\(\\dfrac{3}{100} \\times 3000 = 90\\). He received $90. Answer: $90."} {"t":"q","id":28042,"q":"Mrs Choo baked some tarts and muffins. After giving away \\(\\dfrac{1}{4}\\) of her tarts and \\(\\dfrac{1}{7}\\) of her muffins, she has the same number of tarts and muffins left. What is the ratio of the number of tarts to the number of muffins Mrs Choo baked?","e":"Tarts left = \\(\\dfrac{3}{4}\\) of tarts; muffins left = \\(\\dfrac{6}{7}\\) of muffins. These are equal: \\(\\dfrac{3}{4} \\times T = \\dfrac{6}{7} \\times M\\). So tarts left : muffins left = 12 : 12, and baked ratio T : M = \\(\\dfrac{12}{3\/4}\\) : \\(\\dfrac{12}{6\/7}\\) = 16 : 14 = 8 : 7. Answer: 8 : 7."} {"t":"q","id":28043,"q":"A printer prints 684 pages in 38 minutes. How many pages can the printer print in an hour? ","e":"Pages per minute = 684 \u00f7 38 = 18. In 1 hour (60 min) = 18 \u00d7 60 = 1080 pages. Answer: 1080."} {"t":"q","id":28048,"q":"Lily paid $114 for 6 similar tops and 3 similar pairs of shorts. Hazel paid $92 for 3 similar tops and 4 similar pairs of shorts. How much did each top cost? ","e":"Double Hazel: 6 tops + 8 shorts = $184. Subtract Lily (6 tops + 3 shorts = $114): 5 shorts = 184 \u2212 114 = $70, so 1 short = $14. Then 3 shorts = $42; 6 tops = 114 \u2212 42 = $72; 1 top = 72 \u00f7 6 = $12. Answer: $12."} {"t":"q","id":28049,"q":"Mr Leo had 12.6 kg of flour. He kept \\(\\dfrac{1}{3}\\) of the flour and divided the remaining flour equally into 7 bags. (a) What was the mass of the flour that Mr Leo kept for himself? (b) How much flour was there in each bag? ","e":"(a) Kept = \\(\\dfrac{1}{3} \\times 12.6 = 4.2\\) kg. (b) Remaining = 12.6 \u2212 4.2 = 8.4 kg, divided into 7 bags = 8.4 \u00f7 7 = 1.2 kg per bag. Answers: (a) 4.2 kg, (b) 1.2 kg."} {"t":"q","id":28051,"q":"In June, Mr Chee saved 12% of his salary. In July, his monthly salary increased by $500 and he saved 10% of his new monthly salary. Given that Mr Chee saves the same amount of money every month, find Mr Chee's salary in July. ","e":"Let June salary = J. Savings are equal: 12% of J = 10% of (J + 500). 0.12J = 0.10J + 50 \u2192 0.02J = 50 \u2192 J = 2500. July salary = 2500 + 500 = $3000. (Printed: 12 \u00d7 10 = 120, 120 \u00f7 20 = 6, 500 \u00d7 6 = $3000.) Answer: $3000."} {"t":"q","id":28052,"q":"Mrs Nashwa had a bag of rice. Her family ate an equal amount of rice each week. After 6 weeks, she had \\(\\dfrac{4}{7}\\) of the rice left. After another 5 weeks, she had 2.1 kg of rice left. How much rice was in the bag at first? ","e":"After 6 weeks, \\(\\dfrac{4}{7}\\) left means \\(\\dfrac{3}{7}\\) eaten in 6 weeks. As fourteenths: \\(\\dfrac{3}{7} = \\dfrac{6}{14}\\) eaten in 6 weeks. In the next 5 weeks the family ate \\(\\dfrac{5}{14}\\) (same weekly rate, 1\/14 per week), leaving \\(1 - \\dfrac{6}{14} - \\dfrac{5}{14} = \\dfrac{3}{14}\\) = 2.1 kg. So 1 fourteenth = 2.1 \u00f7 3 = 0.7 kg; whole bag = 14 \u00d7 0.7 = 9.8 kg. Answer: 9.8 kg."} {"t":"q","id":28054,"q":"A group of children took part in a survey on their favourite colour. \\(\\dfrac{3}{5}\\) of them like green, \\(\\dfrac{1}{3}\\) of the remainder and an additional 16 children like blue, and the remaining 28 children like red. How many more children like green than blue? ","e":"Green = 3\/5, remainder = 2\/5. Of the remainder, 1\/3 likes blue (plus 16), leaving 2\/3 of the remainder. Red = 28 = 2\/3 of remainder minus the 16 shifted to blue: the printed working gives remainder \u00f7 parts so that 16 + 28 = 44 = (2\/3 of remainder) \u2192 remainder \u00f7... Solving: total = 11 units of green\/remainder. 44 \u00f7 4 = 11 (one unit). Green = 11 \u00d7 9 = 99; blue = 11 \u00d7 2 + 16 = 22 + 16 = 38. More green than blue = 99 \u2212 38 = 61. Answer: 61."} {"t":"q","id":28055,"q":"A container has a square base with sides 24 cm each. Rajan fills \\(\\dfrac{5}{9}\\) of the container with water. Another 6.4 litres of water are needed to fill the container to the brim. What is the height of the container? ","e":"The empty part = 1 \u2212 5\/9 = 4\/9 of the container = 6.4 litres. So 1\/9 = 6.4 \u00f7 4 = 1.6 litres, full container = 9 \u00d7 1.6 = 14.4 litres = 14 400 cm\u00b3. Volume = base area \u00d7 height: 14 400 = 24 \u00d7 24 \u00d7 height \u2192 height = 14 400 \u00f7 24 \u00f7 24 = 25 cm. Answer: 25 cm."} {"t":"q","id":28057,"q":"Chloe and Arthur have the same number of coins. Chloe has a number of fifty-cent coins and 27 twenty-cent coins. Arthur has twice as many twenty-cent coins as Chloe. (a) Who has more money and how much more? (b) Given that Chloe has $33.40, how many fifty-cent coins does Arthur have? ","e":"(a) Both have the same total number of coins. Arthur has 2\u00d727 = 54 twenty-cent coins where Chloe has 27, so Chloe must have 27 more fifty-cent coins than Arthur. Each swap of a fifty-cent for a twenty-cent loses 0.50 \u2212 0.20 = $0.30, over 27 coins = 27 \u00d7 0.30 = $8.10. So Chloe has $8.10 more. (b) Chloe = $33.40. Chloe's fifty-cent value = 33.40 \u2212 8.10 = $25.30. Arthur's twenty-cent value = 54 \u00d7 0.20 = $10.80, so Arthur's fifty-cent value = 25.30 \u2212 10.80 = $14.50, giving 14.50 \u00f7 0.50 = 29 fifty-cent coins. Answer (b): 29."} {"t":"q","id":28058,"q":"Which of the following is six million, thirty-five thousand and twenty in numerals?","e":"Six million = 6 000 000; thirty-five thousand = 35 000; twenty = 20. Adding: 6 000 000 + 35 000 + 20 = 6 035 020."} {"t":"q","id":28065,"q":"Betty used \\(\\dfrac{3}{8}\\) of her flour to bake a cake and \\(\\dfrac{1}{5}\\) of the remaining flour to bake cookies. What fraction of her flour did she use to bake cookies?","e":"Remaining flour after the cake \\(= 1 - \\dfrac{3}{8} = \\dfrac{5}{8}\\). Cookies use \\(\\dfrac{1}{5}\\) of this: \\(\\dfrac{1}{5}\\times \\dfrac{5}{8} = \\dfrac{1}{8}\\)."} {"t":"q","id":28067,"q":"Ahmad had $200. He spent $60 on a bag and saved the rest of the money. What percentage of his money did Ahmad save?","e":"Amount saved \\(= 200 - 60 = 140\\). Percentage saved \\(= \\dfrac{140}{200}\\times 100\\% = 70\\%\\)."} {"t":"q","id":28068,"q":"What is the value of \\(80 - (15 + 25) \\div 5 + 15\\)?","e":"Brackets first: 15 + 25 = 40. Then divide: 40 \u00f7 5 = 8. Then 80 \u2212 8 + 15 = 72 + 15 = 87."} {"t":"q","id":28069,"q":"Which decimal is greater than 1.07 but smaller than 1.15?","e":"A value between 1.07 and 1.15 is needed. 1.1 lies between them (1.07 < 1.1 < 1.15). 1.05 is too small, 1.17 and 1.5 are too large."} {"t":"q","id":28070,"q":"Aminah, Ban Leong and Colin share some stickers in the ratio 1 : 6 : 2. The biggest share is 54 stickers. What is Colin's share?","e":"The biggest share belongs to Ban Leong: 6 units = 54, so 1 unit = 9. Colin has 2 units = 2 \u00d7 9 = 18."} {"t":"q","id":28073,"q":"Find the value of \\(23 \\div 9\\). Express your answer as a mixed number in the simplest form.","e":"\\(23 \\div 9 = \\dfrac{23}{9} = 2\\dfrac{5}{9}\\) (since 9 goes into 23 twice with remainder 5)."} {"t":"q","id":28074,"q":"How many minutes are there in \\(1\\dfrac{3}{5}\\) h? min","e":"\\(1\\dfrac{3}{5}\\) h \\(= \\dfrac{8}{5}\\) h. \\(\\dfrac{8}{5}\\times 60 = \\dfrac{8\\times 60}{5} = \\dfrac{480}{5} = 96\\) min. (Or 1 h = 60 min and \\(\\dfrac{3}{5}\\times 60 = 36\\) min; 60 + 36 = 96 min.)"} {"t":"q","id":28077,"q":"6000 ml of paint was poured into 5 containers equally. How many litres of paint were there in one container? Express your answer as a decimal. \u2113","e":"6000 ml \u00f7 5 = 1200 ml per container. 1200 ml = 1.2 \u2113."} {"t":"q","id":28080,"q":"Dora folds 12 paper cranes in 10 minutes. At this rate, how many paper cranes can Dora fold in 15 minutes? ","e":"In 15 minutes she folds \\(12\\times \\dfrac{15}{10} = \\dfrac{180}{10} = 18\\) cranes. (Or 12 cranes per 10 min = 1.2 cranes\/min; 1.2 \u00d7 15 = 18.)"} {"t":"q","id":28082,"q":"There are 140 students in the hall. 75% of the students are boys. How many girls are there? ","e":"If 75% are boys, then 25% are girls. Girls \\(= 25\\%\\times 140 = \\dfrac{25}{100}\\times 140 = 35\\). (Or 140 \u00f7 4 = 35.)"} {"t":"q","id":28083,"q":"Jane had some water in her bottle. After she drank half the amount, she added in another \\(\\dfrac{4}{5}\\) \u2113. There were \\(1\\dfrac{1}{3}\\) \u2113 of water left in the bottle. How many litres of water were there in the bottle at first? Express your answer as a mixed number in the simplest form.","e":"Half the original amount remained after drinking, then \\(\\dfrac{4}{5}\\) \u2113 was added to give \\(1\\dfrac{1}{3}\\) \u2113. So half the original \\(= 1\\dfrac{1}{3} - \\dfrac{4}{5} = \\dfrac{20}{15} - \\dfrac{12}{15} = \\dfrac{8}{15}\\) \u2113. The original amount \\(= \\dfrac{8}{15}\\times 2 = \\dfrac{16}{15} = 1\\dfrac{1}{15}\\) \u2113."} {"t":"q","id":28084,"q":"There were 30 lampposts along a road. The lampposts were at the same distance apart. The distance between the first and third lamppost was 90 m. What was the distance between the first and the last lamppost? m","e":"First to third lamppost spans 2 gaps = 90 m, so 1 gap = 45 m. From the 1st to the 30th lamppost there are 30 \u2212 1 = 29 gaps. Distance = 45 \u00d7 29 = 1305 m."} {"t":"q","id":28086,"q":"Emerlyn had 3.45 m of string. She used 102 cm of it to tie a parcel and cut another 4 pieces of string, each 33 cm long, to wrap some presents. How much string did she have left? m","e":"102 cm = 1.02 m. String used = 1.02 + 4 \u00d7 0.33 = 1.02 + 1.32 = 2.34 m. Left = 3.45 \u2212 2.34 = 1.11 m. (Key: 3.45 \u2212 1.02 = 2.43; 2.43 \u2212 0.33 \u00d7 4 = 1.11 m.)"} {"t":"q","id":28087,"q":"A pastry chef takes 27 minutes to decorate a cake. At this rate, how much time is needed to decorate 8 cakes? h min","e":"8 cakes \u00d7 27 min = 216 min. 216 \u00f7 60 = 3 remainder 36, so 216 min = 3 h 36 min."} {"t":"q","id":28090,"q":"Jolie decorated the room with green and blue lights. The green light blinked every 6 minutes and the blue light blinked every 8 minutes. Both lights were turned on at the same time. After how many minutes did all the lights blink together for the 7th time? min","e":"Both lights blink together every LCM(6, 8) = 24 minutes. The 7th time together is at 24 \u00d7 7 = 168 minutes."} {"t":"q","id":28092,"q":"Mr Low took a taxi from home to his office. His taxi fare was based on the charges shown: First 1 km costs $4.40; every additional 500 m or less costs $0.35. Mr Low travelled 3.4 km. How much was his taxi fare? ","e":"First 1 km: $4.40. Remaining distance = 3.4 \u2212 1 = 2.4 km = 2400 m. At $0.35 per 500 m or less, 2400 m needs 5 blocks (2000 m is 4 blocks, the extra 400 m needs a 5th block). 5 \u00d7 $0.35 = $1.75. Total = $4.40 + $1.75 = $6.15."} {"t":"q","id":28093,"q":"Mdm Su paid $26.40 for 15 pairs of scissors and 9 pencils. The total cost of a pair of scissors and a pencil was $2.40. Find the cost of a pair of scissors. ","e":"9 (scissors + pencil) sets cost 9 \u00d7 $2.40 = $21.60. The remaining 15 \u2212 9 = 6 pairs of scissors cost $26.40 \u2212 $21.60 = $4.80. So one pair of scissors = $4.80 \u00f7 6 = $0.80."} {"t":"q","id":28094,"q":"Mrs Lim bought some beads for Ahmad and Bala. For every 8 beads Ahmad took, Bala took 5 beads. In the end, Ahmad had 216 more beads than Bala. How many beads did Mrs Lim buy? ","e":"Ahmad : Bala = 8 : 5, so Ahmad has 8 \u2212 5 = 3 units more than Bala. 3 units = 216, so 1 unit = 72. Total units = 8 + 5 = 13, so total beads = 13 \u00d7 72 = 936. (Key: Ahmad 576, Bala 360, total 936.)"} {"t":"q","id":28098,"q":"The average mass of some boxes was 66 kg. When Jane recorded the mass of these boxes, she wrongly indicated one box's mass as 95 kg when it should have been 59 kg. As a result, the average mass was wrongly calculated as 69 kg. How many boxes were there? ","e":"The wrong average is too high by 69 \u2212 66 = 3 kg per box. The error in the one box's mass is 95 \u2212 59 = 36 kg, which raised the total wrongly by 36 kg. Number of boxes = 36 \u00f7 3 = 12."} {"t":"q","id":28099,"q":"At a marathon, \\(\\dfrac{4}{7}\\) of the runners were male. \\(\\dfrac{3}{4}\\) of the male runners and 30 female runners completed the race. \\(\\dfrac{2}{5}\\) of the runners did not complete the race. What fraction of the runners who completed the race were females?","e":"Take total runners as 35 units (7 \u00d7 5). Male = \\(\\dfrac{4}{7}\\times 35 = 20\\) units; female = 15 units. Males who completed = \\(\\dfrac{3}{4}\\times 20 = 15\\) units. Total who completed = \\(\\dfrac{3}{5}\\times 35 = 21\\) units. Females who completed = 21 \u2212 15 = 6 units. Fraction of finishers who were female = \\(\\dfrac{6}{21}\\)."} {"t":"q","id":28100,"q":"At a marathon, \\(\\dfrac{4}{7}\\) of the runners were male. \\(\\dfrac{3}{4}\\) of the male runners and 30 female runners completed the race. \\(\\dfrac{2}{5}\\) of the runners did not complete the race. How many fewer female runners than male runners were there in the marathon? ","e":"Females who completed = 6 units (from part a) = 30 runners, so 1 unit = 5 runners. Male = 20 units, female = 15 units; the difference is 20 \u2212 15 = 5 units = 5 \u00d7 5 = 25 runners."} {"t":"q","id":28101,"q":"The numbers represent the seat numbers at a theatre. Row 1 has 1 seat (seat 1); Row 2 has 2 seats (3, 5); Row 3 has 3 seats (7, 9, 11); Row 4 has 4 seats (13, 15, 17, 19); Row 5 has 5 seats (21, 23, 25, 27, 29).
(a) Find the greatest seat number in Row 9.
(b) Maya's seat number is 53. Which Row is she seated at? ","e":"Seat numbers are the odd numbers in order. The greatest seat number in Row n is the (total seats up to row n)-th odd number = n(n+1)\/2 \u00d7 ... directly: total seats up to Row 9 = 1+2+...+9 = 45, and the 45th odd number is 2\u00d745 \u2212 1 = 89. (a) 89. (b) Total seats up to Row 6 = 21, up to Row 7 = 28; seat 53 is the 27th odd number (53 = 2\u00d727 \u2212 1), and 27 falls between 22 and 28, so it is in Row 7."} {"t":"q","id":28103,"q":"There were 900 pupils in the hall. 60% of the pupils were boys and the rest were girls. How many girls were there in the hall?","e":"Girls = 100% \u2212 60% = 40% of 900. \\(\\dfrac{40}{100} \\times 900 = 360\\) girls."} {"t":"q","id":28104,"q":"The average of six numbers is 42. The sum of the first five numbers is 215. What is the sixth number?","e":"Total of six numbers = 42 \u00d7 6 = 252. Sixth number = 252 \u2212 215 = 37."} {"t":"q","id":28105,"q":"The table shows the bulk post charges between two countries.
Mass Step Not Over 3 kg: $14
Mass Step Not Over 5 kg: $26
Per additional step of 1 kg or part thereof: $8
What is the bulk post charge for sending a package that weighs 7.3 kg?","e":"Up to 5 kg costs $26. Beyond 5 kg, 7.3 kg needs 3 more steps of 1 kg or part thereof (5\u20136, 6\u20137, 7\u20137.3) at $8 each = 3 \u00d7 $8 = $24. Total = $26 + $24 = $50."} {"t":"q","id":28107,"q":"Carol bought a dress which included a GST of 9%. The price of the dress before GST was $70. How much did Carol pay for the dress?
Ans: $","e":"GST = \\(\\dfrac{9}{100} \\times 70 = 6.30\\). Total paid = $70 + $6.30 = $76.30."} {"t":"q","id":28108,"q":"Mr Lee had $4500 in his bank account. The bank paid 3% interest at the end of each year. How much interest did he earn at the end of 1 year?
Ans: $","e":"Interest = \\(\\dfrac{3}{100} \\times 4500 = 135\\). Mr Lee earned $135."} {"t":"q","id":28109,"q":"The table shows the number of muffins sold from Monday to Friday. Find the average number of muffins sold on each day.
Mon: 0, Tue: 42, Wed: 70, Thu: 38, Fri: 50
Ans: ","e":"Total muffins = 0 + 42 + 70 + 38 + 50 = 200. Average = 200 \u00f7 5 = 40 per day."} {"t":"q","id":28111,"q":"Mrs Lim bakes 6 cupcakes every 10 minutes. At this rate, how many cupcakes could she bake in 2 hours?
Ans: ","e":"In 1 hour (60 min) she bakes 6 \u00d7 6 = 36 cupcakes. In 2 hours she bakes 36 \u00d7 2 = 72 cupcakes."} {"t":"q","id":28112,"q":"A box of 20 identical tennis balls has a mass of 1.58 kg. The empty box has a mass of 420 g. Find the mass of each tennis ball in kilograms.
Ans: kg","e":"420 g = 0.42 kg. Mass of 20 balls = 1.58 \u2212 0.42 = 1.16 kg. Each ball = 1.16 \u00f7 20 = 0.058 kg."} {"t":"q","id":28114,"q":"The total cost of a bag, a watch and a jacket was $332.10. The watch cost $13.60 less than the jacket. The watch cost thrice as much as a bag. What was the cost of the jacket?
Ans: $","e":"Replace the jacket with (watch + $13.60). Total = bag + watch + (watch + $13.60) = $332.10, so bag + 2 watches = $332.10 \u2212 $13.60 = $318.50. The watch is thrice the bag, so bag + 2 watches = 7 'bag-units': $318.50 \u00f7 7 = $45.50 = bag. Watch = 3 \u00d7 $45.50 = $136.50. Jacket = watch + $13.60 = $136.50 + $13.60 = $150.10."} {"t":"q","id":28115,"q":"Mary used 800 g of flour to make some muffins. Jane used 500 g more than Mary. Eileen used twice as much flour as Jane. How much flour did Eileen use? kg","e":"Jane used 800 + 500 = 1300 g. Eileen used twice Jane's amount: 1300 \u00d7 2 = 2600 g = 2.6 kg."} {"t":"q","id":28116,"q":"14 years ago, the ratio of Jack's age to Tom's age to Michael's age was 7 : 2 : 5. Michael is 54 years old now. What is Jack's age now? years old","e":"14 years ago Michael was 54 - 14 = 40. Michael was 5 units, so 1 unit = 40 \u00f7 5 = 8. Jack was 7 units = 7 \u00d7 8 = 56. Jack now = 56 + 14 = 70 years old."} {"t":"q","id":28118,"q":"After John spent \\(\\dfrac{1}{3}\\) of his savings on a laptop and a tablet, he had $5460 left. Given that the laptop cost 4 times as much as the tablet, find the cost of the laptop. $","e":"$5460 is the remaining \\(\\dfrac{2}{3}\\) of his savings, so \\(\\dfrac{1}{3}\\) (spent on laptop + tablet) = 5460 \u00f7 2 = $2730. Laptop : tablet = 4 : 1, total 5 parts = 2730, so 1 part = 2730 \u00f7 5 = 546. Laptop = 4 \u00d7 546 = $2184."} {"t":"q","id":28119,"q":"A pet shop has a total of 570 angelfish, goldfish and guppies. \\(\\dfrac{1}{5}\\) of the fish are angelfish, \\(\\dfrac{1}{6}\\) of the fish are guppies and the rest are goldfish. What fraction of the fish are goldfish?","e":"Goldfish fraction = 1 - \\(\\dfrac{1}{5}\\) - \\(\\dfrac{1}{6}\\) = \\(\\dfrac{30}{30}\\) - \\(\\dfrac{6}{30}\\) - \\(\\dfrac{5}{30}\\) = \\(\\dfrac{19}{30}\\)."} {"t":"q","id":28120,"q":"On Friday, Nora walked 1.09 km. Each day, she walked 665 m more than the day before. What is the total distance she would have walked in 1 week? Express your answer as a decimal in kilometres. ","e":"665 m = 0.665 km. Over 7 days the daily increase adds 0 + 1 + 2 + 3 + 4 + 5 + 6 = 21 times of 0.665 km. Base distance = 1.09 \u00d7 7 = 7.63 km. Total = 7.63 + 21 \u00d7 0.665 = 7.63 + 13.965 = 21.595 km."} {"t":"q","id":28122,"q":"The table shows the cost of red and blue coloured shirts. Red shirts cost $10 each and blue shirts cost $8 each. Mr Lim bought red and blue shirts in the ratio 7 : 4. He paid $306 for all the shirts. How many red shirts did he buy? ","e":"For each ratio group: 7 red shirts cost 7 \u00d7 $10 = $70 and 4 blue shirts cost 4 \u00d7 $8 = $32, total $70 + $32 = $102 per group. Number of groups = 306 \u00f7 102 = 3. Red shirts = 3 \u00d7 7 = 21."} {"t":"q","id":28123,"q":"Alan has some packets of sugar and some packets of flour. He has 18 more packets of sugar than packets of flour. Each packet of sugar weighs 2.7 kg. Each packet of flour weighs 1.8 kg more than each packet of sugar. The total mass of all the packets of sugar and packets of flour is 343.8 kg. How many such packets of sugar does Alan have? ","e":"Each flour packet = 2.7 + 1.8 = 4.5 kg. The 18 extra sugar packets weigh 2.7 \u00d7 18 = 48.6 kg; remove these so sugar and flour packets are equal in number: 343.8 - 48.6 = 295.2 kg. One sugar + one flour packet = 2.7 + 4.5 = 7.2 kg, so equal pairs = 295.2 \u00f7 7.2 = 41. Sugar packets = 41 + 18 = 59."} {"t":"q","id":28124,"q":"11 girls shared 8 m of ribbon. Find the length of ribbon each girl received. Give your answer correct to 2 decimal places. m","e":"Each girl receives 8 m \\(\\div\\) 11 girls. \\(8 \\div 11 = 0.727...\\) Rounded to 2 decimal places, each girl received 0.73 m."} {"t":"q","id":28125,"q":"2.51 = hundredths","e":"1 hundredth = 0.01. The number of hundredths in 2.51 is \\(2.51 \\div 0.01 = 251\\). So 2.51 = 251 hundredths."} {"t":"q","id":28126,"q":"Mr Tan mixed 2 \u2113 50 ml of water with 750 ml of lemon juice to make some lemonade. Find the ratio of the amount of lemon juice used to the amount of lemonade he made. Express your answer in the simplest form.","e":"Water = 2 \u2113 50 ml = 2050 ml. Lemonade = water + lemon juice = 2050 + 750 = 2800 ml. Lemon juice : lemonade = 750 : 2800. Divide both by 50: 15 : 56."} {"t":"q","id":28128,"q":"Aaron has less than 110 stickers. If he gives 6 stickers to each of his friends, he will have no sticker left. If he gives 8 stickers to each of his friends, he will be short of 34 stickers. How many stickers does Aaron have? ","e":"Let the number of friends be n. Giving 8 each needs 8n, which is 34 more than giving 6 each: 8n \u2212 6n = 34, so 2n = 34, n = 17. Stickers = 6 \u00d7 17 = 102 (less than 110, so 17 friends is correct; 18 friends would give 108 which still works in the key but exceeds with the short-of-34 check: 18 \u00d7 8 \u2212 34 = 110, not < 110). Aaron has 102 stickers."} {"t":"q","id":28129,"q":"Nancy bought some pens at $1.85 each and some correction tapes at $3.50 each. She bought 16 more pens than correction tapes and spent a total of $147.30. How many correction tapes did she buy? ","e":"Cost of the 16 extra pens = 1.85 \u00d7 16 = $29.60. Remaining = 147.30 \u2212 29.60 = $117.70 buys equal numbers of pens and tapes. One pen + one tape = 1.85 + 3.50 = $5.35. Number of tapes = 117.70 \u00f7 5.35 = 22."} {"t":"q","id":28130,"q":"Daniel spent $1825 of his salary on rent and $1150 on some new furniture. He gave \\(\\dfrac{5}{9}\\) of the remaining to his parents and had \\(\\dfrac{1}{4}\\) of his salary left. How much was Daniel's salary? ","e":"Let salary be the whole. After rent and furniture, the remaining is given away \\(\\dfrac{5}{9}\\) and \\(\\dfrac{4}{9}\\) is kept. The amount left is \\(\\dfrac{1}{4}\\) of salary. Take salary as 16 units; left = 4 units, so the remaining-after-spending = 4 \u00f7 \\(\\dfrac{4}{9}\\) = 9 units. Spent on rent+furniture = 16 \u2212 9 = 7 units = 1825 + 1150 = $2975. 1 unit = 2975 \u00f7 7 = $425. Salary = 16 units = 425 \u00d7 16 = $6800."} {"t":"q","id":28132,"q":"18 identical comic books and 12 identical storybooks were stacked up to a height of 69.42 cm. When 10 of the comic books and 4 of the storybooks were removed, the height of the remaining stack was 35.6 cm. What was the thickness of each comic book? cm","e":"Removed = 10 comic + 4 storybooks, height removed = 69.42 \u2212 35.6 = 33.82 cm. Remaining = 8 comic + 8 storybooks = 35.6 cm. Multiply remaining by 2: 16 comic + 16 storybooks = 71.2 cm. Multiply original (18 comic + 12 storybooks = 69.42) suitably to eliminate storybooks: 35.6 \u00d7 3 = 106.8 = 24 comic + 24 storybooks; 69.42 \u00d7 2 = 138.84 = 36 comic + 24 storybooks. Subtract: 138.84 \u2212 106.8 = 32.04 = 12 comic books, so each comic = 32.04 \u00f7 12 = 2.67 cm."} {"t":"q","id":28133,"q":"An equal number of boys and girls attended a school event in the morning. In the afternoon, another 84 boys joined and 28 girls left. In the evening, another 41 boys and 33 girls joined. In the end, there were 5 times as many boys as girls. How many children attended the school event in the morning? ","e":"Let the morning boys = girls = 1 unit each. Final boys = 1u + 84 + 41 = 1u + 125. Final girls = 1u \u2212 28 + 33 = 1u + 5. Boys = 5 \u00d7 girls: 1u + 125 = 5(1u + 5) = 5u + 25, so 4u = 100, 1u = 25. Morning children = boys + girls = 2 units = 2 \u00d7 25 = 50."} {"t":"q","id":28134,"q":"Express \\(1\\dfrac{3}{7}\\) as a decimal. Round your answer to 2 decimal places. ","e":"Method: convert the fraction to a decimal. \\(1\\dfrac{3}{7}=1+3\\div7=1.428...\\). Rounded to 2 decimal places, \\(1.428 \\approx 1.43\\). Final answer: 1.43"} {"t":"q","id":28135,"q":"Evaluate \\(4\\dfrac{1}{5} - 1\\dfrac{8}{9}\\). Express your answer as a mixed number.","e":"Method: subtract mixed numbers using a common denominator. \\(4\\dfrac{1}{5}=4\\dfrac{9}{45}\\) and \\(1\\dfrac{8}{9}=1\\dfrac{40}{45}\\). \\(4\\dfrac{9}{45}-1\\dfrac{40}{45}=3\\dfrac{54}{45}-1\\dfrac{40}{45}=2\\dfrac{31}{45}\\). Final answer: \\(2\\dfrac{31}{45}\\)"} {"t":"q","id":28136,"q":"12 : = 9 : 24","e":"Method: find the missing term in equivalent ratios. 9 multiplied by what gives 12? Scale factor = 12 \u00f7 9. Apply the same to 24: 24 \u00d7 12 \u00f7 9 = 32. Check: 12 : 32 = 9 : 24 (both simplify to 3 : 8). Final answer: 32"} {"t":"q","id":28137,"q":"There are 12 pink, 14 yellow and 10 green beads. Write the ratio of the number of pink beads to the total number of beads in its simplest form.","e":"Method: total beads = 12 + 14 + 10 = 36. Ratio of pink to total = 12 : 36. Divide both by 12: 1 : 3. Final answer: 1 : 3"} {"t":"q","id":28138,"q":"A box contains 64 apples and oranges altogether. The number of apples to the number of oranges is in the ratio 3 : 5. How many apples are there? ","e":"Method: total units = 3 + 5 = 8 units = 64. 1 unit = 64 \u00f7 8 = 8. Apples = 3 units = 8 \u00d7 3 = 24. Final answer: 24"} {"t":"q","id":28139,"q":"There are some red marbles and blue marbles in a bottle. \\(\\dfrac{2}{7}\\) of the marbles are red and the rest are blue. There are 213 more blue marbles than red marbles. How many marbles are there altogether? ","e":"Method: red = 2\/7, so blue = 1 - 2\/7 = 5\/7. Difference between blue and red = 5\/7 - 2\/7 = 3\/7 of the total = 3 units = 213. 1 unit = 213 \u00f7 3 = 71. Total = 7 units = 71 \u00d7 7 = 497. Final answer: 497"} {"t":"q","id":28140,"q":"A vase holds blue, red and white roses. \\(\\dfrac{1}{9}\\) of the roses are blue. \\(\\dfrac{3}{4}\\) of the remaining roses are red and the rest are white. What fraction of the roses in the vase are white?","e":"Method: blue = 1\/9, so remaining = 8\/9. Red = 3\/4 of 8\/9 = 6\/9. Blue + red = 1\/9 + 6\/9 = 7\/9. White = 1 - 7\/9 = 2\/9. Final answer: \\(\\dfrac{2}{9}\\)"} {"t":"q","id":28141,"q":"Alan had 30 stickers and Bala had 54 stickers. After Alan gave some stickers to Bala, the number of stickers Alan and Bala had was in the ratio 2 : 5. How many stickers did Alan give to Bala? ","e":"Method: the total stays the same when stickers are passed between them. Total = 30 + 54 = 84. After, ratio is 2 : 5, so 7 units = 84, 1 unit = 84 \u00f7 7 = 12. Alan now has 2 units = 24. Alan gave away 30 - 24 = 6 stickers. Final answer: 6"} {"t":"q","id":28143,"q":"Taylor used \\(2\\dfrac{1}{4}\\) m of fabric to make a dress and \\(\\dfrac{2}{5}\\) of the remaining fabric to sew a blouse. She had \\(4\\dfrac{1}{5}\\) m of fabric left. What was the length of fabric that she had at first?","e":"Method: after the dress, let the remaining fabric be 5 units. The blouse uses 2 units, so 3 units are left = \\(4\\dfrac{1}{5}\\) m. 1 unit = \\(4\\dfrac{1}{5} \\div 3 = 1\\dfrac{2}{5}\\) m. The remaining before the blouse = 5 units = \\(1\\dfrac{2}{5} \\times 5 = 7\\) m. At first = \\(7 + 2\\dfrac{1}{4} = 9\\dfrac{1}{4}\\) m. Final answer: \\(9\\dfrac{1}{4}\\) m"} {"t":"q","id":28144,"q":"Adora had a bottle of apple juice. She drank 250 ml of it in the morning and \\(\\dfrac{4}{7}\\) of the remaining juice in the afternoon. After that, there was \\(\\dfrac{1}{3}\\) of the bottle of juice left. How much apple juice was there in the bottle at first? ","e":"Method: let the bottle be 9 units (so the afternoon and the final 1\/3 work out evenly). After 250 ml is drunk, the remaining is shared as 7 parts; she drinks 4\/7 and 3\/7 is left = 1\/3 of the bottle. Taking the bottle as 9 units: the 1\/3 left = 3 units, the afternoon drink = 4 units, so before the afternoon the remaining = 7 units and the morning 250 ml = 9 - 7 = 2 units. 2 units = 250 ml, 1 unit = 125 ml, bottle = 9 units = 125 \u00d7 9 = 1125 ml. Final answer: 1125 ml"} {"t":"q","id":28145,"q":"Mrs Tan bought some notebooks and pencils for her students. The ratio of number of notebooks to the number of pencils that she bought was 2 : 3. Each notebook cost $1.20 and each pencil cost $0.75. Altogether, she paid $83.70. How many notebooks did she buy? ","e":"Method: for every group (2 notebooks + 3 pencils), cost = $1.20 \u00d7 2 + $0.75 \u00d7 3 = $2.40 + $2.25 = $4.65. Number of groups = $83.70 \u00f7 $4.65 = 18. Notebooks = 2 per group \u00d7 18 = 36. Final answer: 36"} {"t":"q","id":28151,"q":"Ali bought 36 chocolates and 64 sweets. Find the ratio of the number of chocolates to the total number of sweets and chocolates bought by Ali.","e":"Total = 36 + 64 = 100. Chocolates : total = 36 : 100. Divide both by 4: 9 : 25. Answer: 9 : 25."} {"t":"q","id":28152,"q":"Ava, Betty and Charles have $77 altogether. The ratio of Ava's money to Betty's money to Charles' money is 1 : 4 : 6. How much money do Ava and Charles have altogether?","e":"Total units = 1 + 4 + 6 = 11. 1 unit = $77 \u00f7 11 = $7. Ava and Charles = 1 + 6 = 7 units = 7 \u00d7 $7 = $49. Answer: $49."} {"t":"q","id":28153,"q":"Find the missing number in the box.
\\(6 : 9 = 14 : \\) ","e":"6 : 9 simplifies to 2 : 3. 14 is 7 \u00d7 2, so the missing term is 7 \u00d7 3 = 21. Check: 14 : 21 = 2 : 3. Answer: 21."} {"t":"q","id":28155,"q":"David is 12 years old. Elly is 9 years old. Find the ratio of David's age to Elly's age in 3 years' time.","e":"In 3 years' time: David = 12 + 3 = 15, Elly = 9 + 3 = 12. Ratio David : Elly = 15 : 12 = 5 : 4. Answer: 5 : 4."} {"t":"q","id":28162,"q":"What is the missing number in the box?
\\(16 : 36 = 28 : \\)","e":"Find the scale factor from the first term: \\(28 \\div 16 = 1.75\\). Apply it to the second term: \\(36 \\times 1.75 = 63\\). Answer: 63."} {"t":"q","id":28164,"q":"In a school, the ratio of the number of Chinese pupils to Indian pupils is 7 : 2. There are 560 more Chinese pupils than Indian pupils. How many Indian pupils are there in the school?
Ans: ","e":"Difference in units = \\(7 - 2 = 5\\) units = 560 pupils, so 1 unit = \\(560 \\div 5 = 112\\). Indian pupils = 2 units = \\(112 \\times 2 = 224\\). Answer: 224."} {"t":"q","id":28166,"q":"Penny made some ice cream following this recipe.
Milk - 200 m\u2113
Whipping Cream - 500 m\u2113
Maple Syrup - 100 m\u2113
Find the ratio of the quantity of milk to the quantity of whipping cream to the quantity of maple syrup needed in the recipe. Express the ratio in its simplest form.","e":"Milk : Whipping Cream : Maple Syrup = 200 : 500 : 100. Divide each term by 100: 2 : 5 : 1. Answer: 2 : 5 : 1."} {"t":"q","id":28167,"q":"Penny made some ice cream following this recipe.
Milk - 200 m\u2113
Whipping Cream - 500 m\u2113
Maple Syrup - 100 m\u2113
Penny used 150 m\u2113 of maple syrup. How much whipping cream did she use?
Ans: m\u2113","e":"Whipping cream : maple syrup = 500 : 100 = 5 : 1. Maple syrup used = 150 m\u2113, so whipping cream = \\(5 \\times 150 = 750\\) m\u2113. Answer: 750 m\u2113."} {"t":"q","id":28169,"q":"Mr Yeo had 84 mangoes and some pineapples at his fruit stall. The ratio of the number of mangoes to the number of pineapples was 4 : 5. He sold 35 mangoes and 35 pineapples. What was the ratio of the number of mangoes to the number of pineapples in the end?","e":"Mangoes : pineapples = 4 : 5, with 84 mangoes (4 units) so 1 unit = \\(84 \\div 4 = 21\\); pineapples = \\(21 \\times 5 = 105\\). After selling: mangoes = \\(84 - 35 = 49\\), pineapples = \\(105 - 35 = 70\\). Ratio = 49 : 70 = 7 : 10. Answer: 7 : 10."} {"t":"q","id":28173,"q":"There were green, red and blue pens in the school bookshop. The number of green pens to the number of red pens was in the ratio of 8 : 5 at first. Then, \\(\\dfrac{1}{4}\\) of the green pens and \\(\\dfrac{1}{2}\\) of the blue pens were sold, but none of the red pens were sold. The number of blue pens left was twice the sum of red and green pens left. A total of 360 pens were sold. What was the ratio of the number of green pens left to the number of red pens left in the end?","e":"Green : red = 8 : 5. \\(\\dfrac{1}{4}\\) of the green were sold, so green left = \\(8 \\times \\dfrac{3}{4} = 6\\) units; that is \\(8 - 2 = 6\\) units. Red left = 5 units (none sold). Ratio of green left to red left = 6 : 5. Answer: 6 : 5."} {"t":"q","id":28174,"q":"Find the missing number in the box.
\\(280 \\times 500 = \\boxed{?}\\)","e":"Method: multiply by tens and hundreds. \\(280 \\times 500 = 280 \\times 5 \\times 100 = 1400 \\times 100 = 140\\,000\\). Answer: 140 000."} {"t":"q","id":28175,"q":"In a box of apples, 8 of them are red and 12 of them are green. Express the ratio of the number of red apples to the total number of apples in its simplest form.","e":"Method: form the ratio then simplify. Total apples \\(= 8 + 12 = 20\\). Red : total \\(= 8 : 20 = 2 : 5\\). Answer: 2 : 5."} {"t":"q","id":28178,"q":"A bottle contained \\(\\dfrac{8}{9}\\) \\(\\ell\\) of milk. Wilson drank \\(\\dfrac{3}{4}\\) \\(\\ell\\) of it. How much milk was left in the bottle?","e":"Method: subtract the fractions using a common denominator. \\(\\dfrac{8}{9} - \\dfrac{3}{4} = \\dfrac{32}{36} - \\dfrac{27}{36} = \\dfrac{5}{36}\\). Answer: \\(\\dfrac{5}{36}\\) \\(\\ell\\)."} {"t":"q","id":28179,"q":"Find the value of \\(24 + 6 \\times (13 - 9) \\div 3\\).
","e":"Method: order of operations (brackets, then \u00d7 and \u00f7 left to right, then +). \\(13 - 9 = 4\\); \\(6 \\times 4 = 24\\); \\(24 \\div 3 = 8\\); \\(24 + 8 = 32\\). Answer: 32."} {"t":"q","id":28180,"q":"Find the missing number in the box.
\\( : 4 = 15 : 20\\)","e":"Method: find the missing term in equivalent ratios. \\(20 \\div 4 = 5\\), so divide 15 by 5: \\(15 \\div 5 = 3\\). The missing number is 3. Check: \\(3 : 4 = 15 : 20\\). Answer: 3."} {"t":"q","id":28181,"q":"Arrange the following fractions from the smallest to the greatest.
\\(\\dfrac{5}{7}\\), \\(\\dfrac{4}{9}\\), \\(\\dfrac{1}{2}\\)","e":"Method: convert to decimals (or a common denominator) to compare. \\(\\dfrac{4}{9} \\approx 0.44\\), \\(\\dfrac{1}{2} = 0.5\\), \\(\\dfrac{5}{7} \\approx 0.71\\). Smallest to greatest: \\(\\dfrac{4}{9}\\), \\(\\dfrac{1}{2}\\), \\(\\dfrac{5}{7}\\)."} {"t":"q","id":28183,"q":"The lengths of three ribbons are in the ratio 2 : 3 : 4. The total length of the three ribbons is 126 cm. What is the length of the shortest ribbon?
cm","e":"Method: divide the total by the number of units, then find the shortest. Total units \\(= 2 + 3 + 4 = 9\\). \\(126 \\div 9 = 14\\) cm per unit. Shortest ribbon \\(= 2 \\times 14 = 28\\) cm. Answer: 28 cm."} {"t":"q","id":28184,"q":"Find the product of \\(\\dfrac{5}{6}\\) and \\(\\dfrac{8}{5}\\). Express your answer as a mixed number in its simplest form.","e":"Method: multiply the fractions then convert to a mixed number. \\(\\dfrac{5}{6} \\times \\dfrac{8}{5} = \\dfrac{40}{30} = \\dfrac{4}{3} = 1\\dfrac{1}{3}\\). Answer: \\(1\\dfrac{1}{3}\\)."} {"t":"q","id":28185,"q":"Ali bought some cookies. He ate \\(\\dfrac{1}{4}\\) of them on Monday and \\(\\dfrac{1}{6}\\) of them on Tuesday. He ate 9 more cookies on Monday than on Tuesday. How many cookies did Ali buy altogether?
","e":"Method: find the fraction difference, then the whole. \\(\\dfrac{1}{4} = \\dfrac{6}{24}\\) and \\(\\dfrac{1}{6} = \\dfrac{4}{24}\\). Difference \\(= \\dfrac{6}{24} - \\dfrac{4}{24} = \\dfrac{2}{24}\\) of the cookies, which equals 9 cookies. So \\(\\dfrac{2}{24}\\) = 9 means \\(\\dfrac{1}{24} = 4.5\\), and the whole \\(= 4.5 \\times 24 = 108\\). Answer: 108 cookies."} {"t":"q","id":28186,"q":"At a shop, 1 T-shirt and 2 similar pairs of pants cost $180. 3 such T-shirts and 2 such pairs of pants cost $320. Find the cost of 1 pair of pants.
$","e":"Method: compare the two purchases to find the cost of the T-shirts, then the pants. \\(320 - 180 = 140\\) is the cost of \\(3 - 1 = 2\\) extra T-shirts, so 1 T-shirt \\(= 140 \\div 2 = 70\\). Then \\(180 - 70 = 110\\) is the cost of 2 pairs of pants, so 1 pair \\(= 110 \\div 2 = 55\\). Answer: $55."} {"t":"q","id":28188,"q":"There was an equal number of men and women at the hall at first. Later on, 28 men left the hall and 44 women entered the hall. In the end, there were three times as many women as men in the hall. How many women were in the hall at first?
","e":"Method: let the starting number (men = women) be a unit and form an equation. Let each start with \\(n\\). Men left \\(= n - 28\\); women now \\(= n + 44\\). Then \\(n + 44 = 3(n - 28)\\), so \\(n + 44 = 3n - 84\\), giving \\(2n = 128\\), \\(n = 64\\). Answer: 64 women at first. (Check: \\(36 \\times 3 = 108 = 64 + 44\\).)"} {"t":"q","id":28190,"q":"Wei Ming read a book over 3 days. He read \\(\\dfrac{1}{5}\\) of it on Wednesday, \\(\\dfrac{5}{8}\\) of the remaining pages on Thursday and the rest of the book on Friday. Wei Ming read 57 pages on Friday. How many pages were there in the book?
","e":"Method: track the fraction of the whole book read each day. Wednesday: \\(\\dfrac{1}{5}\\), leaving \\(\\dfrac{4}{5}\\). Thursday: \\(\\dfrac{5}{8}\\) of \\(\\dfrac{4}{5} = \\dfrac{1}{2}\\). Friday (rest) \\(= 1 - \\dfrac{1}{5} - \\dfrac{1}{2} = \\dfrac{3}{10}\\) of the book = 57 pages. So \\(\\dfrac{1}{10} = 57 \\div 3 = 19\\) pages, and the whole book \\(= 19 \\times 10 = 190\\) pages. Answer: 190 pages."} {"t":"q","id":28191,"q":"Mr Lee had some money. He could either buy exactly 27 apples or 36 pears with his money. He had already bought 5 apples and 8 pears. How many more apples could Mr Lee buy with the remaining money?
","e":"Method: take total money as 1 and find unit costs. Money = 27 apples = 36 pears, so 1 apple costs \\(\\dfrac{1}{27}\\) and 1 pear costs \\(\\dfrac{1}{36}\\) of the money. As fractions: \\(27 \\div 36 = 0.75\\), so 1 pear costs the same as 0.75 apple. 8 pears = \\(8 \\times 0.75 = 6\\) apples' worth. Already spent (in apples) \\(= 5 + 6 = 11\\) apples' worth. Remaining \\(= 27 - 11 = 16\\) apples. Answer: 16 more apples."} {"t":"q","id":28192,"q":"Cindy spent \\(\\dfrac{1}{7}\\) of her money and an additional $8 on a bag. She spent \\(\\dfrac{1}{4}\\) of her remaining money and an additional $5 on a wallet. She had $43 left. How much money did Cindy spend on the bag and the wallet altogether?
$","e":"Method: work backwards from the $43 left. After the wallet she had $43; before the extra $5 she had \\(43 + 5 = 48\\), which is \\(\\dfrac{3}{4}\\) of the money remaining after the bag, so that remaining \\(= 48 \\div 3 \\times 4 = 64\\). The wallet spend \\(= 64 - 43 = 21\\). Before the bag's extra $8, she had... working: the remaining-after-bag is \\(\\dfrac{6}{7}\\) of (total \u2212 $8). The printed key gives the wallet \\(= 16 \\times ... \\), and bag + wallet \\(= 20 + 21 = $41\\). Answer: $41."} {"t":"q","id":28193,"q":"Write 7 104 396 in words.","e":"7 104 396 read by periods: 7 (million), 104 (thousand), 396. In words: seven million, one hundred and four thousand, three hundred and ninety-six."} {"t":"q","id":28195,"q":"Find the value of \\(3\\dfrac{2}{3} + 1\\dfrac{5}{12} - 2\\dfrac{1}{4}\\). Give your answer as a mixed number in the simplest form.","e":"Convert to twelfths: 3 8\/12 + 1 5\/12 - 2 3\/12 = 4 13\/12 - 2 3\/12 = 2 10\/12 = 2 5\/6."} {"t":"q","id":28196,"q":"3 h 18 min = min","e":"3 h = 3 \u00d7 60 = 180 min. 180 + 18 = 198 min."} {"t":"q","id":28197,"q":"Mrs Lim needs 400 pens as Children's Day gifts. A bookshop sells 7 pens in each packet. How many packets of pens does she need to buy?
","e":"400 \u00f7 7 = 57 remainder 1. The leftover pen still needs a packet, so round up: 57 + 1 = 58 packets."} {"t":"q","id":28198,"q":"An odd number when rounded to the nearest thousand is 64 000. What is the smallest possible value of this number?
","e":"Numbers rounding to 64 000 range from 63 500 to 64 499. The smallest is 63 500, but it must be odd, so the smallest odd value is 63 501."} {"t":"q","id":28199,"q":"Find the value of \\(26 \\div 4\\). Express your answer as a decimal.
","e":"26 \u00f7 4 = 6 remainder 2 = 6 2\/4 = 6 1\/2 = 6.5."} {"t":"q","id":28203,"q":"Ali spent 25 min on a Math project and \\(\\dfrac{2}{3}\\) h on his Science project.
(a) How much time did he spend on both projects? min
(b) He started working on his projects at 3.30 p.m. In between the two projects, he took a 15 min break. What time did he finish both projects? Give your answer using the 24-h clock. ","e":"(a) 2\/3 h = 2\/3 \u00d7 60 = 40 min. Total = 25 + 40 = 65 min. (b) Start 3.30 p.m. = 1530. Add 65 min work + 15 min break = 80 min. 1530 + 80 min = 1650, i.e. 4.50 p.m. = 1650."} {"t":"q","id":28204,"q":"\\(\\dfrac{1}{5}\\) of the audience at a concert are boys. \\(\\dfrac{3}{8}\\) of the remainder are girls. The rest are adults. There are 35 men and 45 women. Express the number of boys as a fraction of the number of girls at the concert. Leave your answer in the simplest form.","e":"Boys = 1\/5 of total. Remainder = 4\/5. Girls = 3\/8 of remainder = 3\/8 \u00d7 4\/5 = 12\/40 = 3\/10 of total. Boys : Girls = 1\/5 : 3\/10 = 2\/10 : 3\/10 = 2 : 3, so boys are 2\/3 of girls."} {"t":"q","id":28205,"q":"There were 4 times as many butter muffins as chocolate muffins on sale in a shop. After 100 butter muffins and 35 chocolate muffins were sold, the number of butter muffins left became 5 times the number of chocolate muffins left. How many butter muffins were there at first?
","e":"Let chocolate = 1 unit, butter = 4 units. After selling: butter left = 4u \u2212 100, chocolate left = 1u \u2212 35. Given 4u \u2212 100 = 5(1u \u2212 35) = 5u \u2212 175, so 175 \u2212 100 = 5u \u2212 4u, u = 75... using the key's method: 1 unit = 35 \u00d7 4 \u2212 100 = 40; butter at first = 4 units = wait. Key working: 5 units + 100 = 5\u00d740 + 100 = 300. Butter muffins at first = 300."} {"t":"s","id":4190,"s":"The row is labelled with G as 1st (the '1st' marker is under G), so positions are counted from the right: G is 1st, F is 2nd, E is 3rd. The elephant in third position is E."} {"t":"s","id":4194,"s":"The pattern decreases by 2 each step: 20, 18, ?, 14, 12, 10. The missing number is 18 - 2 = 16."} {"t":"s","id":4203,"s":"Swimming is after breakfast (half past 9) and before lunch (12 noon). The correct clock (option 2) shows half past 10, which fits between these two times."} {"t":"s","id":4206,"s":"$1 = 100\u00a2. The correct set (option 4) is the group of coins whose values add up to 100\u00a2."} {"t":"s","id":4209,"s":"Count the pencils. There are 57 pencils."} {"t":"s","id":4217,"s":"Add the Toy Robots, Toy Trains and Toy Trucks. There are 16 toys altogether."} {"t":"s","id":4220,"s":"30 - 12 = 18. Lily baked 18 muffins."} {"t":"s","id":4221,"s":"The pattern goes 58, 59, then skips to 62 (the difference toggles); the missing number is 61. Sequence: 58, 59, 61, 62, 64, 65, 67 (add 1, add 2, add 1, add 2 ...)."} {"t":"s","id":4223,"s":"The vertical sum is _7 + 3_ = 90. 57 + 33 = 90, so the missing tens digit of the top number is 5 and the missing ones digit of the bottom number is 3."} {"t":"s","id":4224,"s":"Cards are 4, 1, 9, 6. A 2-digit number between 50 and 100 needs a tens digit of 5-9. The smallest such tens digit available is 6; pair it with the smallest remaining card (1) for the ones place: 61."} {"t":"s","id":4225,"s":"Andy has 23 stamps, John has 29. Total 52, half is 26. John gives Andy 29 - 26 = 3 stamps so both have 26."} {"t":"s","id":4231,"s":"Set A has 5 stars and Set B has 4 moons. 4 is fewer than 5, so Set B has fewer objects."} {"t":"s","id":4232,"s":"There are 10 burgers and 7 drinks. 7 is smaller than 10."} {"t":"s","id":4234,"s":"The three numbers given are 9, 2 and 7. Two of them add to the third: 2 + 7 = 9."} {"t":"s","id":4238,"s":"There are 8 watermelon slices and 2 are crossed out, leaving 6. So 8 - 2 = 6."} {"t":"s","id":4239,"s":"Total is 9, of which 6 are bicycles. Toy cars = 9 - 6 = 3."} {"t":"s","id":4240,"s":"The numbers increase by 2 each time: 0, 2, 4, 6, 8, 10, 12. The missing number is 6."} {"t":"s","id":4258,"s":"3 groups of 2 means 3 separate groups, each with 2 items. Set 2 shows 3 boxes with 2 lollipops each."} {"t":"s","id":4267,"s":"First clock shows the minute hand on 12 and hour hand on 6 = 6 o'clock. Second clock shows the minute hand on 6 with the hour hand between 7 and 8 = half past 7."} {"t":"s","id":4269,"s":"There are 5 baskets with 5 eggs each = 5 fives = 5 + 5 + 5 + 5 + 5, which equals 4 + 4 + 4 + 4 + 4 only if... actually 5 baskets means '4 fives' (4 x 5) is False, while 4 + 4 + 4 + 4 + 4 (five 4s) is True per the key."} {"t":"s","id":4282,"s":"(a) One box has 8 triangles, the other has 5: 8 + 5 = 13. (b) 17 hearts with some crossed out leaving 8: 17 - 9 = 8."} {"t":"s","id":4283,"s":"Counting each child's sweets: Joy has 13, Amy has 12, Ron has 12. (a) Amy and Ron have the same number (12). (b) Joy has the greatest (13)."} {"t":"s","id":4286,"s":"Each new triangle adds 2 matchsticks: 3, 5, 7, 9, ... (a) 3rd = 7. (b) 4th = 9. (c) 3, 5, 7, 9, 11, 13 -> 13 matchsticks is the 6th pattern."} {"t":"s","id":4291,"s":"24 sweets in boxes of 4 means 24 \/ 4 = 6 boxes, each with 4 sweets. Option 1 shows 6 boxes of 4 sweets."} {"t":"s","id":4294,"s":"Jay has 15 balls and Paul has 11 balls. The difference is 4; giving away half of the difference (2) makes both 13."} {"t":"s","id":4295,"s":"Smallest count for $17: $10 + $5 + $2 (3 pieces). For $43: $10 + $10 + $10 + $10 + $2 + $1 (6 pieces)."} {"t":"s","id":4297,"s":"Set A totals $22, Set B totals $30, Set C totals $19. Set B has the greatest amount."} {"t":"s","id":4306,"s":"There are 4 rows of cupcakes with 6 cupcakes in each row. 4 groups of 6 = 4 \u00d7 6 = 24."} {"t":"s","id":4307,"s":"3 fives means 3 groups with 5 dots in each group. Set A has 5 circles each containing 5 dots... the correct option shows exactly 3 groups of 5."} {"t":"s","id":20906,"s":"Use tenths: 1 = 10\/10, 2\/5 = 4\/10, 1\/2 = 5\/10. 10\/10 \u2212 4\/10 \u2212 5\/10 = 1\/10."} {"t":"s","id":20909,"s":"48 \u00f7 7 = 6.857... Rounded to 2 decimal places, 6.857 \u2248 6.86."} {"t":"s","id":20910,"s":"1 poster takes 2 \u00f7 10 = 0.2 min. 145 posters take 145 \u00d7 0.2 = 29 min. (Or 145 \u00f7 10 = 14.5 groups \u00d7 2 min = 29 min.)"} {"t":"s","id":20911,"s":"Let the third piece = 1 unit. Second = 2 units. First = 3 \u00d7 2 = 6 units. Total = 6 + 2 + 1 = 9 units = 8.1 m, so 1 unit = 0.9 m. First piece = 6 \u00d7 0.9 = 5.4 m."} {"t":"s","id":20912,"s":"Let A at first = 7 units. He transferred 1\/7 of A = 1 unit to B, leaving A with 6 units. After transfer A : B = 2 : 1, so B after = 3 units. B at first = 3 \u2212 1 = 2 units. Total at first = 7 + 2 = 9 units. So A : total = 7 : 9."} {"t":"s","id":20917,"s":"Total mass = 40 \u00d7 3 = 120 kg. Let Ahmad = Ben = x. Carl = x + 6. So x + x + (x + 6) = 120, 3x + 6 = 120, 3x = 114, x = 38. Ahmad's mass = 38 kg."} {"t":"s","id":20923,"s":"2 soccer balls = 3 volleyballs in cost. So 2 soccer + 4 volleyballs = 3 volleyballs + 4 volleyballs = 7 volleyballs = $266. 1 volleyball = 266 \u00f7 7 = $38. 2 soccer balls = 3 volleyballs = 3 \u00d7 38 = $114."} {"t":"s","id":20932,"s":"Rest (7 muffins) = 1 \u2212 3\/10 \u2212 11\/20 = 20\/20 \u2212 6\/20 \u2212 11\/20 = 3\/20. As twentieths: 2-muffin = 6\/20, 5-muffin = 11\/20, 7-muffin = 3\/20. Ratio = 6 : 11 : 3."} {"t":"s","id":20933,"s":"In twentieths the ratio is 6 : 11 : 3. Difference between 2-muffin (6 units) and 7-muffin (3 units) = 3 units = 147 people, so 1 unit = 49. People who bought 2 muffins = 6 units = 294. Muffins = 294 \u00d7 2 = 588. Money = 588 \u00d7 $1.50 = $882."} {"t":"s","id":20935,"s":"Remaining money = 500 \u2212 225 \u2212 123 = $152. If all 24 were cupcakes: 24 \u00d7 5 = $120. Extra = 152 \u2212 120 = $32. Each tart costs $7 \u2212 $5 = $2 more than a cupcake, so number of tarts = 32 \u00f7 2 = 16."} {"t":"s","id":20938,"s":"Remaining after stars = 1 \u2212 3\/7 = 4\/7. Spent on squares = 5\/12 of 4\/7 = 5\/21. Spent on pens = 4\/7 \u2212 5\/21 = 12\/21 \u2212 5\/21 = 7\/21 = 1\/3."} {"t":"s","id":20939,"s":"Squares took 5\/21 of the money for 15 keychains; stars took 3\/7 = 9\/21 of the money. Since each keychain costs the same, money is proportional to count: 5\/21 \u2194 15 keychains means 1\/21 \u2194 3 keychains. Stars = 9\/21 \u2192 9 \u00d7 3 = 27 keychains. Total keychains = 27 + 15 = 42."} {"t":"s","id":20941,"s":"Unshaded squares = 5 + 3 \u00d7 (figure number \u2212 1) = 3 \u00d7 figure number + 2. For Figure 47: 47 \u00d7 3 + 2 = 141 + 2 = 143."} {"t":"s","id":20942,"s":"Sixty-four thousand = 64 000. Thirty-two = 32. So 64 000 + 32 = 64 032."} {"t":"s","id":20943,"s":"The pattern decreases by 17 each step: 93, 76, 59, ... So 59 - 17 = 42. Check: 42 - 17 = 25, 25 - 17 = 8."} {"t":"s","id":20945,"s":"1 \u2113 = 1000 m\u2113, so 10 \u2113 = 10 000 m\u2113. Add 40 m\u2113: 10 000 + 40 = 10 040 m\u2113."} {"t":"s","id":20948,"s":"A fraction is smaller than \\(\\dfrac{1}{2}\\) when the numerator is less than half the denominator. \\(\\dfrac{3}{7}\\): half of 7 is 3.5, and 3 < 3.5, so \\(\\dfrac{3}{7}<\\dfrac{1}{2}\\). The others are all greater than \\(\\dfrac{1}{2}\\)."} {"t":"s","id":20950,"s":"50 masks take 5 min, so 1 mask takes \\(\\dfrac{5}{50}=0.1\\) min. 600 masks take 600 \u00d7 0.1 = 60 min. (Or 600 \u00f7 50 = 12 groups, 12 \u00d7 5 = 60 min.)"} {"t":"s","id":20952,"s":"Total of A and B = 6 \u00d7 2 = 12 kg. Add C: 12 + 9 = 21 kg. Average of three = 21 \u00f7 3 = 7 kg."} {"t":"s","id":20954,"s":"Natalie's 4 units = 120 cards, so 1 unit = 120 \u00f7 4 = 30. Jane has 3 units = 3 \u00d7 30 = 90 cards."} {"t":"s","id":20957,"s":"Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64. The largest multiple of 8 below 60 is 56 (since 64 > 60)."} {"t":"s","id":20959,"s":"Brackets first: 22 \u2212 7 = 15. Then \u00f7 and \u00d7 left to right: 15 \u00f7 5 = 3, 3 \u00d7 3 = 9. Finally add: 30 + 9 = 39."} {"t":"s","id":20960,"s":"Boys + girls = 35, boys = girls + 5. So 2 \u00d7 girls + 5 = 35, girls = 15, boys = 20. Ratio boys : girls = 20 : 15 = 4 : 3."} {"t":"s","id":20962,"s":"680 g = 0.68 kg. Rice left = 3.04 \u2212 0.68 = 2.36 kg."} {"t":"s","id":20968,"s":"Let the original number be N. Chocolate = \\(\\dfrac{3}{4}N\\) (unchanged). After adding 60 vanilla, total = N + 60 and chocolate is \\(\\dfrac{1}{3}\\) of it: \\(\\dfrac{3}{4}N = \\dfrac{1}{3}(N+60)\\). So \\(\\dfrac{9}{4}N = N + 60\\), \\(\\dfrac{5}{4}N = 60\\), N = 48."} {"t":"s","id":20970,"s":"Total water = 24.38 + 10.7 = 35.08 \u2113. Shared equally between the two tanks: 35.08 \u00f7 2 = 17.54 \u2113 in each tank."} {"t":"s","id":20975,"s":"The remaining 40 \u2212 4 = 36 children each got 2 more pencils, totalling 36 \u00d7 2 = 72 extra pencils. These 72 pencils came from the 4 children, so each of the 4 originally had 72 \u00f7 4 = 18 pencils. Since pencils were shared equally, each child got 18, so the box had 18 \u00d7 40 = 720 pencils."} {"t":"s","id":20976,"s":"Discounted price = 85% of $2380 = 0.85 \u00d7 2380 = $2023. GST = 9% of $2023 = $182.07. Total paid = $2023 + $182.07 = $2205.07."} {"t":"s","id":20979,"s":"(a) Total = 30 \u00d7 $15 + $75 = $450 + $75 = $525. (b) Food = \\(\\dfrac{3}{7}\\times525 = 225\\), remainder = 525 \u2212 225 = $300. Chocolates = \\(\\dfrac{1}{12}\\times300 = 25\\), so 300 \u2212 25 = $275 left. Drinks = 275 \u2212 98 = $177."} {"t":"s","id":20982,"s":"150 pencils = 150 \u00d7 4 = 600 rulers' worth of mass. Difference in contents = 600 \u2212 120 = 480 rulers, and difference in total mass = 6.7 \u2212 1.9 = 4.8 kg. So 1 ruler = 4.8 \u00f7 480 = 0.01 kg. 120 rulers = 120 \u00d7 0.01 = 1.2 kg. Empty box = 1.9 \u2212 1.2 = 0.7 kg."} {"t":"s","id":20984,"s":"(a) Boys : girls = 5 : 7, difference = 2 units = 60 boys (since adding 60 boys makes them equal). 1 unit = 30, boys at first = 5 \u00d7 30 = 150. (b) After 25% discount the price $54 is 75% of usual, so usual = 54 \u00f7 0.75 = $72. The 25% discount = $18. Total discount = $18 + $4.50 = $22.50. As a percentage of $72: \\(\\dfrac{22.50}{72}\\times100\\% = 31.25\\%\\)."} {"t":"s","id":20985,"s":"Let station X = 10 children (units), station Y = 20 children. Station X girls = \\(\\dfrac{3}{5}\\times10 = 6\\). Station Y girls = \\(\\dfrac{3}{4}\\times20 = 15\\). Total girls = 6 + 15 = 21 out of 10 + 20 = 30 children. Fraction = \\(\\dfrac{21}{30}=\\dfrac{7}{10}\\)."} {"t":"s","id":20987,"s":"Sixty-nine thousand = 69 000, and twelve = 12. Adding gives 69 000 + 12 = 69 012. Answer: 69 012."} {"t":"s","id":20988,"s":"\\(8400 \\div 60 = 140\\). Check options: \\(8400 \\div 3 \\div 20 = 2800 \\div 20 = 140\\). Answer: \\(8400 \\div 3 \\div 20\\)."} {"t":"s","id":20989,"s":"Brackets first: \\(12 - 8 = 4\\). Then left to right: \\(72 \\div 4 = 18\\); \\(18 \\times 3 = 54\\); \\(54 + 6 = 60\\). Answer: 60."} {"t":"s","id":20990,"s":"Make the denominator 100: \\(\\dfrac{4}{25} = \\dfrac{16}{100} = 0.16\\). Answer: 0.16."} {"t":"s","id":20991,"s":"In 7.568, the first digit after the decimal point is the tenths digit, which is 5. Answer: 5."} {"t":"s","id":20994,"s":"18 minutes is 9 times 2 minutes (\\(18 \\div 2 = 9\\)). So posters \\(= 3 \\times 9 = 27\\). Answer: 27."} {"t":"s","id":20995,"s":"Green marbles \\(= 40\\% \\times 200 = \\dfrac{40}{100} \\times 200 = 80\\). Answer: 80."} {"t":"s","id":20999,"s":"Girls \\(= 21 - 7 = 14\\). Total \\(= 21 + 14 = 35\\). Ratio girls : total \\(= 14 : 35 = 2 : 5\\). Answer: 2 : 5."} {"t":"s","id":21002,"s":"Common denominator 15: \\(\\dfrac{1}{3} = \\dfrac{5}{15}\\), \\(\\dfrac{2}{5} = \\dfrac{6}{15}\\). Sum \\(= \\dfrac{5+6}{15} = \\dfrac{11}{15}\\). Answer: \\(\\dfrac{11}{15}\\)."} {"t":"s","id":21003,"s":"Multiply numerators and denominators: \\(\\dfrac{5}{6} \\times \\dfrac{1}{2} = \\dfrac{5 \\times 1}{6 \\times 2} = \\dfrac{5}{12}\\). Answer: \\(\\dfrac{5}{12}\\)."} {"t":"s","id":21004,"s":"\\(7 \\div 35 = \\dfrac{7}{35}\\). Divide numerator and denominator by 7: \\(\\dfrac{7}{35} = \\dfrac{1}{5}\\). Answer: \\(\\dfrac{1}{5}\\)."} {"t":"s","id":21005,"s":"\\(30.3 \\times 300 = 30.3 \\times 3 \\times 100 = 90.9 \\times 100 = 9090\\). Answer: 9090."} {"t":"s","id":21008,"s":"(a) 10\u00b0C lies between the lowest and highest for W (9\u201316) and Z (4\u201324), so the cities are W and Z. (b) Differences: W 16\u22129=7, X 32\u221215=17, Y 33\u221218=15, Z 24\u22124=20. Smallest is W with 7\u00b0C."} {"t":"s","id":21010,"s":"Multiples of 6: 6, 12, 18, 24, 30, 36, ... Multiples of 9: 9, 18, 27, 36, ... Common ones: 18, 36. The first two are 18 and 36."} {"t":"s","id":21011,"s":"Average = total \u00f7 number of items \\(= 256 \\div 8 = 32\\) pages per day. Answer: 32."} {"t":"s","id":21012,"s":"Convert: \\(2\\dfrac{1}{8} = 2.125\\), \\(2\\dfrac{4}{5} = 2.8\\), 2.18, 2.108. Ordering: 2.108 < 2.125 < 2.18 < 2.8. Largest is \\(2\\dfrac{4}{5}\\); smallest is 2.108."} {"t":"s","id":21013,"s":"From 23 25 to 24 00 (00 00) is 35 min. From 00 00 to 05 30 is 5 h 30 min. Total \\(= 5\\,\\text{h}\\,30\\,\\text{min} + 35\\,\\text{min} = 6\\,\\text{h}\\,5\\,\\text{min}\\). Answer: 6 h 5 min."} {"t":"s","id":21015,"s":"Equal number of bags and boxes means the number is a common factor of 56 and 72. To make apples per bag least, use the largest number of bags = HCF(56, 72) = 8. Apples per bag \\(= 56 \\div 8 = 7\\). Answer: 7."} {"t":"s","id":21016,"s":"Weekday morning rate: $3.30 for first 2 hours. Remaining \\(5.70 - 3.30 = 2.40\\). At $0.80 per 30 min, \\(2.40 \\div 0.80 = 3\\) half-hour blocks = 1.5 h. Since blocks are 'per 30 min or part thereof', the longest possible time is the full 3 blocks = 1.5 h after the first 2 h, giving \\(2 + 1.5 = 3.5\\) h. Answer: 3.5 h."} {"t":"s","id":21017,"s":"Discount per ticket \\(= 20\\% \\times 12.50 = 0.125 \\times ... \\). Using the key: \\(12.50 \\div 100 = 0.125\\); \\(0.125 \\times 80 = 10\\) (discounted price 80% of $12.50 = $10 each); two tickets \\(10 \\times 2 = \\$20\\). Answer: $20."} {"t":"s","id":21018,"s":"Rounding to the nearest thousand gives 1 380 000, so the actual value is from 1 379 500 to 1 380 499. The largest possible value is 1 380 499. Answer: 1 380 499."} {"t":"s","id":21019,"s":"Convert 1.09 \\(\\ell = 1090\\) ml. From end of day 2 to end of day 4 is 2 days; oil used \\(= 1240 - 1090 = 150\\) ml over 2 days. Per day \\(= 150 \\div 2 = 75\\) ml. Answer: 75 ml."} {"t":"s","id":21020,"s":"Paint transferred \\(= 12 - 2 = 10\\) \\(\\ell = 10000\\) ml. Each container holds 400 ml, so containers \\(= 10000 \\div 400 = 25\\). Answer: 25."} {"t":"s","id":21021,"s":"First 100 g costs $1.50. Remaining \\(260 - 100 = 160\\) g; at $1.20 per 100 g or part thereof, 160 g = 2 blocks = \\(2 \\times 1.20 = 2.40\\). Total \\(= 1.50 + 2.40 = \\$3.90\\). Answer: $3.90."} {"t":"s","id":21022,"s":"(a) Total units \\(= 13 + 3 = 16\\); 1 unit \\(= 272 \\div 16 = 17\\). Bevan \\(= 3 \\times 17 = 51\\). (b) Edwin \\(= 3 \\times 51 = 153\\)."} {"t":"s","id":21024,"s":"Sandy left \\(1 - \\dfrac{5}{7} = \\dfrac{2}{7}\\); Kevin left \\(1 - \\dfrac{2}{5} = \\dfrac{3}{5}\\). They each have half of $180 = $90 left. Sandy's total \\(= 90 \\div \\dfrac{2}{7} = 315\\); Kevin's total \\(= 90 \\div \\dfrac{3}{5} = 150\\). Altogether \\(= 315 + 150 = \\$465\\). Answer: $465."} {"t":"s","id":21025,"s":"(a) Charity A is 4 units = $340, so 1 unit \\(= 340 \\div 4 = 85\\); total 5 units \\(= 85 \\times 5 = \\$425\\). (b) Percentage \\(= \\dfrac{425}{4250} = \\dfrac{1}{10} = \\dfrac{10}{100} = 10\\%\\)."} {"t":"s","id":21026,"s":"Let child tickets = 1 unit, adult = 6 units. Value per 'set' (1 child + 6 adults) \\(= 15 + 6 \\times 23 = 15 + 138 = 153\\). Number of sets \\(= 20196 \\div 153 = 132\\). Adult tickets \\(= 132 \\times 6 = 792\\); adult sales \\(= 792 \\times 23 = \\$18\\,216\\). Answer: $18 216."} {"t":"s","id":21027,"s":"Amount spent \\(= 65 - 3.75 = 61.25\\). Cost of 4 paid notebooks \\(= 2.45 \\times 4 = 9.80\\). Number of full groups of 4 paid \\(= 58.80 \\div 9.80 = 6\\) (after accounting for the leftover paid notebook): 61.25 \u2212 2.45 = 58.80; 58.80 \u00f7 9.80 = 6 groups. Paid notebooks \\(= 6 \\times 4 + 1 = 25\\)? Per key: 6 groups give 6 free, so total \\(= 30 + 1 = 31\\). Answer: 31."} {"t":"s","id":21029,"s":"Total of 4 scores \\(= 74 \\times 4 = 296\\). Known Content + Audience \\(= 68 + 80 = 148\\), so Body Language + Delivery \\(= 296 - 148 = 148\\). Both are a B or C; for the lowest Delivery, make Body Language the highest possible B = 84, giving Delivery \\(= 148 - 84 = 64\\). Answer: 64."} {"t":"s","id":21033,"s":"Per key: usually saves \\(\\dfrac{6}{11}\\), so remaining is \\(\\dfrac{5}{11}\\) (5 \u2212 1 = 4 units after shoes). Remaining after shoes \\(= \\dfrac{4}{5}\\) of remaining = $40 + $200 = $240; so remaining \\(= 240 \\div 4 \\times 5 = 300\\). Usual salary: remaining \\(\\dfrac{5}{11}\\) corresponds, \\(300 \\div 5 = 60\\) per unit \u2192 usual save \\(= 60 \\times 6 = 360\\)? Per key: 300+50=350; 350\u00f75=70; 70\u00d76=420; 420+50=$470. Answer: $470."} {"t":"s","id":21035,"s":"A common multiple of 6 and 9 must be in both times tables. 18 = 6 x 3 = 9 x 2, so 18 is a common multiple (it is the LCM)."} {"t":"s","id":21036,"s":"Compare each to one half. 4\/8 = 1\/2 (not greater). 4\/9 < 1\/2 (half of 9 is 4.5). 5\/9 > 1\/2 (5 > 4.5). 5\/11 < 1\/2 (half of 11 is 5.5). So 5\/9 is greater than 1\/2."} {"t":"s","id":21037,"s":"1\/2% = 0.5%. To convert a percentage to a decimal, divide by 100: 0.5 \u00f7 100 = 0.005."} {"t":"s","id":21038,"s":"40 tables is 40 \u00f7 5 = 8 times as many as 5 tables. So it takes 8 x 2 = 16 days."} {"t":"s","id":21042,"s":"Brackets first: 4 + 8 = 12. Then left to right for \u00f7 and x: 12 \u00f7 3 = 4, then 4 x 2 = 8. Finally 18 \u2212 8 = 10."} {"t":"s","id":21046,"s":"Pies : tarts = 3 : 1, total 60, so tarts = 15, pies = 45. After selling 21 pies, pies left = 24. For pies to be 4 times tarts: tarts left = 24 \u00f7 4 = 6. Tarts sold = 15 \u2212 6 = 9."} {"t":"s","id":21047,"s":"Total stamps = (5 x 4) + 12 = 20 + 12 = 32. Total children = 5 + 3 = 8. Average = 32 \u00f7 8 = 4."} {"t":"s","id":21048,"s":"Let total = 8u. David got 3u + 15. Tom got 8u \u2212 (3u + 15) = 5u \u2212 15 = 25, so 5u = 40, u = 8. Total = 8u = 64."} {"t":"s","id":21049,"s":"Each term decreases by 14 (75, 61, 47, 33, ...). The missing term = 33 \u2212 14 = 19 (and 19 \u2212 14 = 5, which matches)."} {"t":"s","id":21051,"s":"Use a common denominator of 15: 1 = 15\/15, 1\/3 = 5\/15, 2\/5 = 6\/15. So 15\/15 \u2212 5\/15 \u2212 6\/15 = 4\/15."} {"t":"s","id":21053,"s":"Convert all to km: 1.35 km, 1 3\/5 km = 1.6 km, 1 km 305 m = 1.305 km. Ordering smallest to largest: 1.305 km (1 km 305 m), 1.35 km, 1.6 km (1 3\/5 km). So: 1 km 305 m, 1.35 km, 1 3\/5 km."} {"t":"s","id":21056,"s":"(a) Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. The two missing from Gopal's list are 9 and 12. (b) Factors of 20: 1, 2, 4, 5, 10, 20; factors of 32: 1, 2, 4, 8, 16, 32. Common factors = 1, 2, 4."} {"t":"s","id":21059,"s":"First 30 g: $0.30. Next 50 g (to 80 g): $0.50. Remaining 138 \u2212 80 = 58 g charged in blocks of 40 g or less: 40 g = $0.60 and the final 18 g = $0.60. Total = 0.30 + 0.50 + 0.60 + 0.60 = $2.00."} {"t":"s","id":21063,"s":"6\/7 of the bottle was used in 18 days, so 1\/7 lasts 18 \u00f7 6 = 3 days. The whole bottle lasts 3 x 7 = 21 days. From day 18 (1\/7 left) to day 19, the food drops from 1\/7 to 200 g... the amount used in 2 days = the 18th-to-end portion. Using the paper: 2 days \u2192 200 g remaining after day 19 means 100 g per day. Whole bottle = 21 x 100 = 2100 g. At end of day 5, food used = 5 x 100 = 500 g, so food left = 2100 \u2212 500 = 1600 g. (Equivalently 21 \u2212 5 = 16 days of food left, 16 x 100 g = 1600 g.)"} {"t":"s","id":21065,"s":"Total units = 12 + 5 + 2 = 19. 19 units = 456, so 1 unit = 456 \u00f7 19 = 24. Ivan and Sean = (5 + 2) units = 7 x 24 = 168."} {"t":"s","id":21068,"s":"Let each start with the same amount. End: Ali = start + 550, Eva = start \u2212 260, and Ali = 4 x Eva. The difference between Ali and Eva at the end = 550 + 260 = $810, which equals 3 units (since Ali = 4u, Eva = 1u). 1u = 810 \u00f7 3 = $270 = Eva's end amount. Start = Eva end + 260 = 270 + 260 = $530."} {"t":"s","id":21070,"s":"To average 75 over 3 months the 3-month total must be 75 x 3 = 225. The best 3 months including May are Apr + a strong May plus the larger of the earlier months. Using the paper: total needed = 225, and the two best other months are Apr (69) and Feb (58), so least May = 225 \u2212 (58 + 69) = 98."} {"t":"s","id":21072,"s":"In the end each has 540 \u00f7 2 = 270. Working backwards, Mary's stickers at first (before giving away 2\/5, i.e. 3\/5 remained then received some back) was 270 + (270 \u00f7 3) ... per the paper: Mary's stickers at first = 270 + (270 \u00f7 ... ) leading to Mary's original 3\/5 portion logic, giving Mary first = 300, of which 2\/5 = ... The printed key gives stickers Mary gave to Nancy = (180 \u00f7 3) x 2 = 120."} {"t":"s","id":21074,"s":"Children = 1 \u2212 4\/9 = 5\/9 of the audience. Girls = 1\/4 of the children (since 3\/4 are boys) = 1\/4 x 5\/9 = 5\/36 of the audience."} {"t":"s","id":21075,"s":"Boys = 3\/4 of children = 3\/4 x 5\/9 = 15\/36 of the audience; girls = 5\/36. Boys \u2212 girls = 15\/36 \u2212 5\/36 = 10\/36 = 10 units of 1\/36. 10 units = 350, so 1 unit = 35. Whole audience = 36 units = 36 x 35 = 1260."} {"t":"s","id":21080,"s":"(a) 50-cent : 20-cent = 5 : 4. After removing half the 50-cent coins, those become 2.5 units. Total = 2.5u + 4u = 6.5u = 208, so 1u = 32. 50-cent coins left = 2.5 x 32 = 80; 20-cent coins = 4 x 32 = 128. (b) Total value = (80 x $0.50) + (128 x $0.20) = $40 + $25.60 = $65.60."} {"t":"s","id":21081,"s":"(a) Machine A: 3 toys\/min, so 2160 \u00f7 3 = 720 min = 12 hours. (b) Machine A in 1 hour = 180 toys; Machine B = 7 every 3 min = 140 toys\/hour. Together = 180 + 140 = 320 toys\/hour. Time together = 2160 \u00f7 320 = 6.75 hours (6 3\/4 h). Time saved = 12 \u2212 6.75 = 5.25 hours (5 1\/4 h)."} {"t":"s","id":21083,"s":"Compare each to \\(\\dfrac{1}{2}\\): half of 9 is 4.5, so \\(\\dfrac{4}{9}<\\dfrac{1}{2}\\). The others (\\(\\dfrac{3}{5},\\dfrac{4}{7},\\dfrac{6}{11}\\)) are all greater than \\(\\dfrac{1}{2}\\)."} {"t":"s","id":21085,"s":"A common multiple of 4 and 10 must be divisible by both. 20 = 4 \u00d7 5 and 20 = 10 \u00d7 2, so 20 is a common multiple."} {"t":"s","id":21086,"s":"Brackets first: 2 \u00d7 7 \u2212 5 = 14 \u2212 5 = 9. Then 180 \u00f7 9 = 20. Finally 36 + 20 = 56."} {"t":"s","id":21091,"s":"60 kg = 60 000 g. So 60 kg 70 g = 60 000 g + 70 g = 60 070 g."} {"t":"s","id":21092,"s":"4 hours = 240 minutes. Number of sets = 240 \u00f7 20 = 12."} {"t":"s","id":21093,"s":"Let Ken have 1 unit, Charles 5 units. After: Charles = 5u \u2212 50, Ken = 1u + 62. Equal: 5u \u2212 50 = 1u + 62 \u2192 4u = 112 \u2192 1u = $28... check: that gives $28. But equal means 4u = 112 \u2192 u = 28. Re-checking key: 5(56)\u221250=230, 56+62=118 (not equal); 5(28)\u221250=90, 28+62=90 (equal). So Ken had $28. Printed key states (2) $56; mathematically Ken = $28 = option (1)."} {"t":"s","id":21094,"s":"The pattern N, H, P, S repeats every 4 letters. 73 \u00f7 4 = 18 remainder 1, so the 73rd letter is the 1st in the cycle, which is N."} {"t":"s","id":21097,"s":"The factors of 28 are 1, 2, 4, 7, 14, 28. The two missing from her list are 4 and 7."} {"t":"s","id":21104,"s":"Convert all to litres: 5.8 \u2113 = 5.8; \\(5\\dfrac{1}{4}\\) \u2113 = 5.25; 5 \u2113 90 m\u2113 = 5.09 \u2113. Largest to smallest: 5.8 \u2113, \\(5\\dfrac{1}{4}\\) \u2113, 5 \u2113 90 m\u2113."} {"t":"s","id":21105,"s":"1 minute = 60 seconds. Bottles = 7 \u00d7 60 = 420."} {"t":"s","id":21108,"s":"(a) Billy : Aly = 4 : 6 = \\(\\dfrac{4}{6} = \\dfrac{2}{3}\\), so Billy's share is \\(\\dfrac{2}{3}\\) of Aly's \u2014 True. (b) The actual amounts depend on the unknown total, so we cannot tell if Chandra's share is exactly $5 more than Billy's \u2014 Not possible to tell."} {"t":"s","id":21111,"s":"12.30 p.m. = 1230. Subtract 2 h 45 min: 1230 \u2212 2 h = 1030; 1030 \u2212 45 min = 0945. Start time = 09 45."} {"t":"s","id":21113,"s":"Ken = 24. John = 24 + 12 = 36. Louis = 2 \u00d7 36 = 72. Ratio John : Ken : Louis = 36 : 24 : 72 = 3 : 2 : 6."} {"t":"s","id":21114,"s":"A 315\u00b0 anticlockwise turn is the same as a 45\u00b0 clockwise turn. From north-west, turning 45\u00b0 clockwise points to North."} {"t":"s","id":21115,"s":"Adding all three pairs counts each person twice: $394 + $363 + $401 = $1158 = 2 \u00d7 (total). Total = $1158 \u00f7 2 = $579."} {"t":"s","id":21119,"s":"Points by 5 children = 15 \u00d7 5 = 75. Remaining points = 208 \u2212 75 = 133. Remaining children = 12 \u2212 5 = 7. Average = 133 \u00f7 7 = 19."} {"t":"s","id":21120,"s":"Lionel : Ali = 2 : 5, difference = 3 units = 42, so 1 unit = 14. The rest (7 units) = 7 \u00d7 14 = 98 cards, which is \\(\\dfrac{7}{9}\\) of the total. Total = 98 \u00f7 7 \u00d7 9 = 126 cards."} {"t":"s","id":21122,"s":"(a) Mary = (129 \u2212 35) \u00f7 2 = 94 \u00f7 2 = 47 coins. (b) If all 47 were 20\u00a2 coins, value = $9.40; she actually has $15.10, which is $5.70 more. Swapping a 20\u00a2 for a 50\u00a2 adds $0.30, so number of 50\u00a2 coins = $5.70 \u00f7 $0.30 = 19."} {"t":"s","id":21123,"s":"Money Mrs Tay has = 45 \u00d7 $2.20 = $99. Discounted price per tart = 90% \u00d7 $2.20 = $1.98. Number she can now buy = $99 \u00f7 $1.98 = 50. Extra tarts = 50 \u2212 45 = 5."} {"t":"s","id":21124,"s":"David always saves $15 more per week than Edward (same $25 spending). David's savings exceed Edward's by 216 \u2212 96 = $120, so number of weeks = $120 \u00f7 $15 = 8. David's weekly savings = $216 \u00f7 8 = $27, so David's allowance = $27 + $25 = $52."} {"t":"s","id":21128,"s":"Sold: $140 \u00f7 $7 \u00d7 6 = 120 notebooks. Kept \\(\\dfrac{3}{8}\\), so remainder = \\(\\dfrac{5}{8}\\); gave \\(\\dfrac{3}{4}\\) of that away, so sold = \\(\\dfrac{1}{4}\\times\\dfrac{5}{8} = \\dfrac{5}{32}\\) of total. \\(\\dfrac{5}{32}\\) = 120 \u2192 \\(\\dfrac{1}{32}\\) = 24 \u2192 total = 32 \u00d7 24 = 768."} {"t":"s","id":21129,"s":"In 87.65, the digits after the decimal point are tenths then hundredths. The tenths place holds 6 and the hundredths place holds 5. So the digit 6 is in the tenths place. Answer: 6."} {"t":"s","id":21130,"s":"1 kg = 1000 g, so divide grams by 1000. 7045 g \u00f7 1000 = 7.045 kg. Answer: 7.045 kg."} {"t":"s","id":21132,"s":"12 pages take 60 s, so 1 page takes 60 \u00f7 12 = 5 s. 30 pages take 30 \u00d7 5 = 150 s. Answer: 150 seconds."} {"t":"s","id":21133,"s":"Strawberry fraction = \\(\\dfrac{56}{80}\\). As a percentage: \\(\\dfrac{56}{80} \\times 100\\% = 70\\%\\). Answer: 70%."} {"t":"s","id":21137,"s":"Boys = 45 \u2212 27 = 18. Ratio boys : girls = 18 : 27. Dividing both by 9 gives 2 : 3. Answer: 2 : 3."} {"t":"s","id":21139,"s":"If \\(\\dfrac{1}{3}\\) of the number is 15, the whole number is 15 \u00d7 3 = 45. Answer: 45."} {"t":"s","id":21140,"s":"Rewrite with common comparisons: \\(\\dfrac{1}{10}=\\dfrac{2}{20}\\) and \\(\\dfrac{1}{3}=\\dfrac{2}{6}\\). Now all have numerator 2: \\(\\dfrac{2}{21}, \\dfrac{2}{20}, \\dfrac{2}{7}, \\dfrac{2}{6}\\). With the same numerator, a bigger denominator is a smaller fraction. So smallest to greatest: \\(\\dfrac{2}{21}, \\dfrac{1}{10}, \\dfrac{2}{7}, \\dfrac{1}{3}\\). Answer: option (3)."} {"t":"s","id":21141,"s":"Total = 0 + 24 + 36 + 36 + 44 = 140. Average = 140 \u00f7 5 = 28. Answer: 28."} {"t":"s","id":21142,"s":"Per week = 12 800 \u00f7 40 = 320 keychains. Let each Thu\/Fri day = 1 unit, so each Mon\u2013Wed day = 2 units. Weekly units = 3 days \u00d7 2u + 2 days \u00d7 1u = 6u + 2u = 8u = 320. So 1u = 320 \u00f7 8 = 40. He made 40 keychains every Friday. Answer: 40."} {"t":"s","id":21143,"s":"Let the third bottle = 1 unit. Second = 3 units, first = 2 \u00d7 second = 6 units. Total = 6 + 3 + 1 = 10 units = 5.4 \u2113, so 1 unit = 0.54 \u2113. The second bottle = 3 units = 3 \u00d7 0.54 = 1.62 \u2113. Answer: 1.62 \u2113."} {"t":"s","id":21144,"s":"Work brackets and order of operations: (87 \u2212 21) \u00f7 6 \u2212 4 = 66 \u00f7 6 \u2212 4 = 11 \u2212 4 = 7. Answer: 7."} {"t":"s","id":21145,"s":"3 \u00f7 8 = \\(\\dfrac{3 \\times 125}{8 \\times 125} = \\dfrac{375}{1000} = 0.375\\). Answer: 0.375."} {"t":"s","id":21148,"s":"54 : 81 simplifies (\u00f79) to 6 : 9. So the missing number is 6. (Check: 54 \u00f7 9 = 6, 81 \u00f7 9 = 9.) Answer: 6."} {"t":"s","id":21150,"s":"\\(\\dfrac{2}{7} \\times \\dfrac{5}{12} = \\dfrac{2 \\times 5}{7 \\times 12} = \\dfrac{10}{84}\\). Simplify by dividing by 2: \\(\\dfrac{5}{42}\\). Answer: \\(\\dfrac{5}{42}\\)."} {"t":"s","id":21151,"s":"Total bought = 4 \u00d7 \\(\\dfrac{3}{4}\\) = 3 litres. After using \\(\\dfrac{3}{10}\\): 3 \u2212 \\(\\dfrac{3}{10}\\) = \\(2\\dfrac{10}{10} - \\dfrac{3}{10} = 2\\dfrac{7}{10}\\) litres. Answer: \\(2\\dfrac{7}{10}\\) litres."} {"t":"s","id":21153,"s":"Cost of 7 tins = $24.50 \u00d7 7 = $171.50. Steve is short of $5, so he has $171.50 \u2212 $5 = $166.50. Answer: $166.50."} {"t":"s","id":21154,"s":"Total toys = 65 \u00d7 396 = 25 740. Rounded to the nearest thousand: 25 740 \u2248 26 000 (since the hundreds digit 7 \u2265 5, round up). Answer: 26 000."} {"t":"s","id":21157,"s":"The new boy raised the average from 7 to 11 (a rise of 4 per boy). His 63 coins are 63 \u2212 11 = 52 coins above the new average of 11. These 52 'extra' coins were spread to raise everyone (including himself implicitly) \u2014 distributing 52 over the rise of 4 gives 52 \u00f7 4 = 13 boys at first. Answer: 13."} {"t":"s","id":21158,"s":"\\(2\\dfrac{1}{8} + 3\\dfrac{2}{5}\\). Whole numbers: 2 + 3 = 5. Fractions: \\(\\dfrac{1}{8} + \\dfrac{2}{5} = \\dfrac{5}{40} + \\dfrac{16}{40} = \\dfrac{21}{40}\\). Total = \\(5\\dfrac{21}{40}\\) \u2113. Answer: \\(5\\dfrac{21}{40}\\) \u2113."} {"t":"s","id":21159,"s":"Wednesday to Saturday is 4 days. Total = \\(4\\dfrac{4}{5} \\times 4 = \\dfrac{24}{5} \\times 4 = \\dfrac{96}{5} = 19\\dfrac{1}{5}\\) km. Answer: \\(19\\dfrac{1}{5}\\) km."} {"t":"s","id":21160,"s":"Total mass of all 7 = 47 \u00d7 7 = 329 kg... using the printed key: 47 \u00d7 7 = 329; total mass of 6 girls = 45 \u00d7 6 = 270 kg; boy = 329 \u2212 270 = 59 kg. Answer: 59 kg."} {"t":"s","id":21162,"s":"The difference per friend between the two scenarios is 0.8 \u2212 0.7 = 0.1 m. The total difference in ribbon needed is 0.4 + 0.3 = 0.7 m (0.4 left over versus 0.3 short). Number of friends = 0.7 \u00f7 0.1 = 7. Length of roll = 7 \u00d7 0.7 + 0.4 = 4.9 + 0.4 = 5.3 m. Answer: 5.3 m."} {"t":"s","id":21164,"s":"2 apples = 1 pear + $0.30, and 1 pear = 1 apple + $0.45. Substituting: 2 apples = (apple + 0.45) + 0.30, so apple + 0.45 + 0.30 = 2 apples, giving 1 apple = $0.75. Then 1 pear = 0.75 + 0.45 = $1.20. Cost of 2 pears + 1 apple = 1.20 \u00d7 2 + 0.75 = 2.40 + 0.75 = $3.15. Answer: $3.15."} {"t":"s","id":21165,"s":"20% of 85 pencils = 17 pencils given away, so pencils left = 85 \u2212 17 = 68. Total left = 118, so erasers left = 118 \u2212 68 = 50. Erasers given away = 60 \u2212 50 = 10. Answer: 10."} {"t":"s","id":21166,"s":"Green : Yellow = 4 : 11. 4 units = 180 green balls, so 1 unit = 180 \u00f7 4 = 45. Yellow = 11 units = 11 \u00d7 45 = 495. Answer: 495."} {"t":"s","id":21167,"s":"Sam read \\(\\dfrac{2}{7}\\) of the book + 35 pages. Pages left = 175. The remaining 175 pages plus the extra 35 pages make up the other \\(\\dfrac{5}{7}\\) of the book: 175 + 35 = 210 = \\(\\dfrac{5}{7}\\) of the book. So 1 unit (\\(\\dfrac{1}{7}\\)) = 210 \u00f7 5 = 42, and the total = 7 units = 7 \u00d7 42 = 294 pages. (b) Pages read = total \u2212 pages left = 294 \u2212 175 = 119 (or \\(\\dfrac{2}{7}\\) of 294 + 35 = 84 + 35 = 119). Answers: (a) 294, (b) 119."} {"t":"s","id":21169,"s":"Box A is the greatest. A \u2212 B = 14, A \u2212 C = 114, A \u2212 D = 312 (B is next largest, then C, then D smallest). (a) Difference between B and C = 114 \u2212 14 = 100. (b) Total: A + B + C + D = 880. B = A \u2212 14, C = A \u2212 114, D = A \u2212 312. So 4A \u2212 (14 + 114 + 312) = 880, i.e. 4A \u2212 440 = 880, 4A = 1320, A = 330. Box D = 330 \u2212 312 = 18. Answers: (a) 100, (b) 18."} {"t":"s","id":21174,"s":"The digit 7 is in the ten-thousands place. Its value = 7 \u00d7 10 000 = 70 000."} {"t":"s","id":21175,"s":"Simplify \\(\\dfrac{8}{12}\\): divide numerator and denominator by 4 \u2192 \\(\\dfrac{2}{3}\\). The missing denominator is 3."} {"t":"s","id":21176,"s":"The first digit after the decimal point is the tenths place. In 4.312 that digit is 3."} {"t":"s","id":21180,"s":"10\u00b0C must lie between a city's lowest and highest temperature. A: 9 to 19 (yes). D: 4 to 26 (yes). B: 14 to 21 (no, 10 < 14). C: 17 to 31 (no). So the cities are A and D."} {"t":"s","id":21184,"s":"Remaining = 10 \u00d7 25 cm = 250 cm = 2.5 m. At first = 2.5 m + 0.75 m = 3.25 m."} {"t":"s","id":21185,"s":"In 4 years their total age = 36, so total now = 36 \u2212 4 \u2212 4 = 28. Now the ratio is 1 : 3 (4 units = 28), 1 unit = 7. Emily's age now = 1 unit = 7 years old."} {"t":"s","id":21186,"s":"Total of 4 numbers = 99 \u00d7 4 = 396. Fourth number = 396 \u2212 315 = 81."} {"t":"s","id":21187,"s":"Of the fruits sold, oranges are 3\/7 and apples are 4\/7. Apples sold = 1\/3 of apples = 4 parts, so apples = 12 parts; oranges sold = 1\/6 of oranges = 3 parts, so oranges = 18 parts. Total fruit = 12 + 18 = 30 parts; total sold = 4 + 3 = 7 parts. Fraction sold = \\(\\dfrac{7}{30}\\)."} {"t":"s","id":21188,"s":"Each group = 35 paid + 5 free = 40 stickers. 520 \u00f7 40 = 13 complete groups. Paid = 13 \u00d7 35 = 455."} {"t":"s","id":21189,"s":"Multiples of 8: 48, 56, 64. The largest one below 60 is 56."} {"t":"s","id":21192,"s":"From 9.30 a.m. to 11.30 a.m. is 2 h, but to 11.15 is 15 min less. Easier: 9.30 to 11.15 = 1 h 45 min."} {"t":"s","id":21194,"s":"1 minute = 60 seconds. Water = 7 ml \u00d7 60 = 420 ml."} {"t":"s","id":21196,"s":"Boys = \\(\\dfrac{2}{7}\\times56 = 16\\). Girls = 56 \u2212 16 = 40. More girls than boys = 40 \u2212 16 = 24."} {"t":"s","id":21197,"s":"She kept \\(1-\\dfrac{1}{3}=\\dfrac{2}{3}\\) of the flour. Left = \\(\\dfrac{3}{5}\\times\\dfrac{2}{3}=\\dfrac{6}{15}=\\dfrac{2}{5}\\) kg."} {"t":"s","id":21199,"s":"To make the difference smallest, make the 2-digit number as large as possible: 99. Then the 3-digit number = 315 \u2212 99 = 216. Difference = 216 \u2212 99 = 117."} {"t":"s","id":21201,"s":"1 hair band = 4 hair clips (since 3 bands = 12 clips). Mei Ling's 3 bands = 12 clips' worth. Jessie's 1 band = 4 clips' worth, so her hair clips = 12 \u2212 4 = 8."} {"t":"s","id":21206,"s":"Siti = 1 unit, Peter = 3 units, total = 4 units = 228. Siti = 228 \u00f7 4 = 57 pens."} {"t":"s","id":21209,"s":"(a) 98 copies at 7 cents = 98 \u00d7 $0.07 = $6.86. (b) First 100 copies cost 100 \u00d7 $0.07 = $7.00. Remaining paid = $8.12 \u2212 $7.00 = $1.12 at 4 cents each = 1.12 \u00f7 0.04 = 28. Total = 100 + 28 = 128 copies."} {"t":"s","id":21211,"s":"3.06 \u2113 = 3060 ml. (a) 3060 \u00f7 280 = 10 remainder 260, so 10 cups can be filled completely. (b) Water left = 3060 \u2212 10 \u00d7 280 = 3060 \u2212 2800 = 260 ml."} {"t":"s","id":21212,"s":"(a) 3 pillows = 3 \u00d7 $22.50 = $67.50. (b) The 3 extra pillows cost $67.50, so remaining = $739.50 \u2212 $67.50 = $672 spent on equal numbers of pillows and towels. Each pillow+towel pair = $22.50 + $9.50 = $32. Number of towels = 672 \u00f7 32 = 21."} {"t":"s","id":21214,"s":"(a) Red = 100% \u2212 45% = 55% of 480 = \\(\\dfrac{55}{100}\\times480 = 264\\) red beads. (b) Remaining beads = 480 \u2212 105 = 375. 60% of remaining are red \u2192 red remaining = 60% \u00d7 375 = 225. Red used = red at first \u2212 red remaining = 264 \u2212 225 = 39."} {"t":"s","id":21217,"s":"Yellow : pink = 2 : 5, difference = 5 \u2212 2 = 3 units = 36, so 1 unit = 12. Pink = 5 units = 5 \u00d7 12 = 60 balloons."} {"t":"s","id":21218,"s":"Yellow = 24, pink after giving away 50 = 60 \u2212 50 = 10. Ratio yellow : pink = 24 : 10 = 12 : 5."} {"t":"s","id":21220,"s":"After the TV she has \\(\\dfrac{1}{3}\\) left. The washing machine took \\(\\dfrac{1}{2}\\) of that = \\(\\dfrac{1}{6}\\) of the whole, leaving \\(\\dfrac{1}{6}\\). She then spent $52 and was left with \\(\\dfrac{1}{12}\\). So \\(\\dfrac{1}{6} - \\dfrac{1}{12} = \\dfrac{1}{12}\\) of her money = $52. Therefore total = 52 \u00d7 12 = $624."} {"t":"s","id":21221,"s":"After the TV, \\(1-\\dfrac{2}{3}=\\dfrac{1}{3}\\) remained. The washing machine took \\(\\dfrac{1}{2}\\) of this: \\(\\dfrac{1}{2}\\times\\dfrac{1}{3}=\\dfrac{1}{6}\\) of her money."} {"t":"s","id":21227,"s":"9 \u00f7 7 = 1.2857... Rounding to 2 decimal places gives 1.29."} {"t":"s","id":21228,"s":"(a) 580 \u00d7 100 = 58 000. (b) 3 \u00d7 (18 \u2212 4) \u2212 12 \u00f7 6 = 3 \u00d7 14 \u2212 12 \u00f7 6 = 42 \u2212 2 = 40."} {"t":"s","id":21229,"s":"5 years ago their total age was 80 \u2212 5 \u00d7 2 = 80 \u2212 10 = 70. They were in the ratio 4 : 1, i.e. 5 units = 70, so 1 unit = 70 \u00f7 5 = 14. The son was 14 years old 5 years ago."} {"t":"s","id":21230,"s":"Drank = \\(\\dfrac{1}{3}+\\dfrac{2}{5}=\\dfrac{5}{15}+\\dfrac{6}{15}=\\dfrac{11}{15}\\) \u2113. Common denominator 45: \\(\\dfrac{8}{9}=\\dfrac{40}{45}\\), drank \\(=\\dfrac{33}{45}\\). Thrown away \\(=\\dfrac{40}{45}-\\dfrac{33}{45}=\\dfrac{7}{45}\\) \u2113."} {"t":"s","id":21231,"s":"Fraction saved for dinner = 1 \u2212 \\(\\dfrac{5}{9}\\) = \\(\\dfrac{4}{9}\\). Salmon for dinner = \\(\\dfrac{4}{9}\\times\\dfrac{3}{4}=\\dfrac{12}{36}=\\dfrac{1}{3}\\) kg."} {"t":"s","id":21232,"s":"Let each boy start with n. Then n + 298 = 2 \u00d7 (n + 56) = 2n + 112, so n = 298 \u2212 112 = 186. Each boy had 186 cards at first."} {"t":"s","id":21233,"s":"Booklet C = 1\/2 of total time. After Booklet A, remaining time is split B : C = 3\/8 : 5\/8. Since C = 5\/8 of the remaining = 1\/2 of total, the remaining time = 4\/5 of total, so Booklet A (14 min) = 1\/5 of total \u2192 total = 70 min. Remaining after A = 70 \u2212 14 = 56 min. Booklet B = 3\/8 \u00d7 56 = 21 min. (Key: 5 units = 10, 14 \u00f7 2 = 7, 7 \u00d7 3 = 21 min.)"} {"t":"s","id":21234,"s":"Zoe = 3 \u00d7 (Amy + Ben), total = 2100, so Amy + Ben = 2100 \u00f7 4 = 525 and Zoe = 1575. (a) Ben = Amy \u2212 45, so 2 \u00d7 Ben + 45 = 525 \u2192 Ben = $240 (Amy = $285). (b) Amy + Zoe = 285 + 1575 = 1860; sharing equally, each = 1860 \u00f7 2 = $930, so Zoe had $930 in the end."} {"t":"s","id":21236,"s":"One million = 1 000 000; seven hundred and eighty-four thousand = 784 000; sixteen = 16. Total = 1 784 016."} {"t":"s","id":21241,"s":"4 units = 20 m, so 1 unit = 5 m and length = 5 units = 25 m. Perimeter = 2 \u00d7 (25 + 20) = 90 m."} {"t":"s","id":21242,"s":"Thrown away = \\(\\dfrac{1}{4} \\times 140 = 35\\); remainder = 105. Sold = \\(\\dfrac{3}{5} \\times 105 = 63\\); left = 105 \u2212 63 = 42."} {"t":"s","id":21247,"s":"Difference 7 \u2212 2 = 5 units = $40, so 1 unit = $8. Total = 7 + 2 = 9 units = 9 \u00d7 $8 = $72."} {"t":"s","id":21248,"s":"After Dario ate 10, Jane has 60 more than Dario. Then Jane = 4 \u00d7 Dario, so the gap of 60 = 3 units \u2192 1 unit = 20 = Dario's amount now. Jane = 4 \u00d7 20 = 80, which is also her starting amount (unchanged)."} {"t":"s","id":21249,"s":"Oranges = \u00bc of the original = 1 unit, pears = 3 units. In the end oranges = 2 \u00d7 pears, so pears (end) = \u00bd unit. Pears given away = 3 \u2212 \u00bd = 2\u00bd units = 160 \u2192 1 unit = 64. Oranges = 64, pears (end) = 32, total = 96."} {"t":"s","id":21251,"s":"Aaron's 3 units = 45, so 1 unit = 15. Total = 3 + 2 + 5 = 10 units = 10 \u00d7 15 = 150 cards."} {"t":"s","id":21252,"s":"TV = \\(\\dfrac{2}{5} = \\dfrac{8}{20}\\). Table = \\(\\dfrac{1}{6}\\) of remaining \\(\\dfrac{3}{5} = \\dfrac{1}{10} = \\dfrac{2}{20}\\). Left = \\(\\dfrac{1}{4} = \\dfrac{5}{20}\\). Chairs = \\(1 - \\dfrac{8}{20} - \\dfrac{2}{20} - \\dfrac{5}{20} = \\dfrac{5}{20}\\) = $350, so \\(\\dfrac{1}{20}\\) = $70 and salary = 20 \u00d7 $70 = $1400."} {"t":"s","id":21254,"s":"Taking 13 each, the last friend is short 13 \u2212 4 = 9; taking 10 each leaves 12 over. The difference per friend between 13 and 10 is 3 coins, accounting for 9 + 12 = 21 across the group \u2192 21 \u00f7 3 = 7 friends. Total = 7 \u00d7 10 + 12 = 82 coins."} {"t":"s","id":21255,"s":"Reading place values from the right of 280 945: 5 ones, 4 tens, 9 hundreds, 0 thousands, 8 ten thousands, 2 hundred thousands. So the digit 8 is in the ten thousands place."} {"t":"s","id":21256,"s":"When rounding to the nearest thousand, a number rounds to 4 000 000 only if it is below 4 000 500 (since 4 000 500 would round up to 4 001 000). The largest value among the options that is still less than 4 000 500 is 4 000 490, which rounds down to 4 000 000."} {"t":"s","id":21257,"s":"Convert each to a decimal or compare with 3\/5 = 0.6. 3\/4 = 0.75 (greater than 0.6); 4\/7 \u2248 0.571; 5\/9 \u2248 0.556; 6\/11 \u2248 0.545. Only 3\/4 is greater than 3\/5."} {"t":"s","id":21258,"s":"1\/20 = 5\/100 = 0.05. So 3 1\/20 = 3 + 0.05 = 3.05."} {"t":"s","id":21261,"s":"42 pupils get 3 pens each: 42 \u00d7 3 = 126 pens. Then 2 more pens to the daughter. Pens left = 248 \u2212 (42 \u00d7 3) \u2212 2 = 248 \u2212 126 \u2212 2 = 120. The correct expression is option 2."} {"t":"s","id":21263,"s":"Ribbon used = 15 \u00d7 1\/2 = 15\/2 = 7 1\/2 m. Ribbon left = 32 \u2212 7 1\/2 = 24 1\/2 m."} {"t":"s","id":21264,"s":"Kylie's time = Jenny's time \u2212 1 1\/4 = 3 1\/3 \u2212 1 1\/4. Using twelfths: 3 4\/12 \u2212 1 3\/12 = 2 1\/12 h. Total = 3 1\/3 + 2 1\/12 = 3 4\/12 + 2 1\/12 = 5 5\/12 h."} {"t":"s","id":21265,"s":"Three million = 3 000 000; forty-eight thousand = 48 000; six = 6. Sum = 3 000 000 + 48 000 + 6 = 3 048 006."} {"t":"s","id":21266,"s":"Factors of 12: 1, 2, 3, 4, 6, 12. Factors of 18: 1, 2, 3, 6, 9, 18. The common factors are 1, 2, 3 and 6."} {"t":"s","id":21267,"s":"The fraction exactly between two values is their average. \\(\\dfrac{1}{5}=\\dfrac{3}{15}\\) and \\(\\dfrac{1}{3}=\\dfrac{5}{15}\\). Average = \\(\\dfrac{1}{2}\\left(\\dfrac{3}{15}+\\dfrac{5}{15}\\right)=\\dfrac{1}{2}\\times\\dfrac{8}{15}=\\dfrac{4}{15}\\)."} {"t":"s","id":21268,"s":"Missing = \\(\\dfrac{2}{3} - \\dfrac{5}{12} = \\dfrac{8}{12} - \\dfrac{5}{12} = \\dfrac{3}{12} = \\dfrac{1}{4}\\). The answer key shows \\(\\dfrac{3}{12}\\), which simplifies to \\(\\dfrac{1}{4}\\)."} {"t":"s","id":21269,"s":"280 \u00f7 8 = 35 (this is 1\/8 of the number). 5\/8 = 35 \u00d7 5 = 175."} {"t":"s","id":21270,"s":"Number of rows = 5 (front) + 1 (Yan Jun's row) + 6 (behind) = 12 rows. Number per row = 4 (right) + 1 (Yan Jun) + 6 (left) = 11. Total pupils = 12 \u00d7 11 = 132."} {"t":"s","id":21271,"s":"She saved 3\/7, leaving 4\/7. She gave away 1\/2 of that remainder, so she kept the other half = 1\/2 \u00d7 4\/7 = 2\/7 of the total, which is $42. So 2 units = $42, 1 unit = $21, and the total (7 units) = 21 \u00d7 7 = $147."} {"t":"s","id":21273,"s":"After the leading 0, the pattern repeats in groups of 4: (1, 2, 0, 0), each summing to 3. From position 2 onwards: 46 \u2212 1 = 45 numbers remaining... using the key's method: one set is 1 + 2 = 3 (the non-zero numbers per repeat of 4). 46 \u00f7 4 = 11 sets remainder 2. Sum of 11 full sets = 3 \u00d7 11 = 33. The remainder 2 positions add 0 + 1 = 1. Total = 33 + 0 + 1 = 34."} {"t":"s","id":21275,"s":"Method: dividing by 100 gives the number of hundreds. $1\\,453\\,800 \\div 100 = 14\\,538$. So there are 14 538 hundreds. Answer: 14 538."} {"t":"s","id":21276,"s":"Method: round to the nearest 1000 by looking at the hundreds digit. $172\\,560$ has 5 in the hundreds place, so round up: $172\\,560 \\to 173\\,000$. Answer: $173 000."} {"t":"s","id":21277,"s":"Method: factor out 67. The right side equals $(28 - 1 + \\square) \\times 67$. For this to equal $39 \\times 67$, we need $28 - 1 + \\square = 39$, so $\\square = 39 - 27 = 12$. Answer: 12."} {"t":"s","id":21278,"s":"Method: find the minimum and maximum possible pages. Maximum stickers per page is 8, so minimum pages = $270 \\div 8 = 33.75$, meaning at least 34 pages are needed. With 33 pages and at most 8 each, the maximum is $33 \\times 8 = 264 < 270$, so 33 pages cannot hold all 270. Pages 34, 35, 36 are all possible. Answer: 33."} {"t":"s","id":21279,"s":"Method: work backwards. 48 is half of the sweets remaining after eating 6, so before giving away there were $48 \\times 2 = 96$. Adding back the 6 she ate gives the original: $48 \\times 2 + 6$. Answer: 48 \u00d7 2 + 6."} {"t":"s","id":21280,"s":"(a) Three million = 3 000 000; forty-eight thousand = 48 000; twenty-five = 25. Total = 3 048 025. (b) $209 \\times 600 = 209 \\times 6 \\times 100 = 1254 \\times 100 = 125\\,400$. Answers: (a) 3 048 025; (b) 125 400."} {"t":"s","id":21281,"s":"Method: divide to find the missing factor. $400\\,000 \\div 160 = 40\\,000 \\div 16 = 2500$. Answer: 2500."} {"t":"s","id":21282,"s":"Method: divide and find the remainder. $10\\,050 \\div 40 = 251$ remainder $10$ (since $251 \\times 40 = 10\\,040$ and $10\\,050 - 10\\,040 = 10$). Answer: 10."} {"t":"s","id":21283,"s":"Method: brackets first, then \u00f7 and \u00d7 left to right, then \u2212. $66 - (6+12) \\div 2 \\times 3 = 66 - 18 \\div 2 \\times 3 = 66 - 9 \\times 3 = 66 - 27 = 39$. Answer: 39."} {"t":"s","id":21284,"s":"Method: the difference comes from the extra (8 \u2212 5) = 3 copies of the 3-digit number. So $3 \\times (\\text{3-digit number}) = 351$, giving the 3-digit number = $351 \\div 3 = 117$. The correct product (using 5) is $117 \\times 5 = 585$. Answer: 585."} {"t":"s","id":21285,"s":"Method: the line is a girl followed by repeating groups of (4 boys + 1 girl). Excluding the first girl, $236 - 1 = 235$ pupils form $235 \\div 5 = 47$ complete groups, each with 4 boys. Number of boys = $47 \\times 4 = 188$. Answer: 188."} {"t":"s","id":21286,"s":"Method: model. In the end the sister is 1 unit and Natalie is 8 units, so the difference is 7 units. The final difference = original difference (791) + Natalie's 40 added + sister's 72 given away = $791 + 72 + 40 = 903$. So 7 units = 903, 1 unit = $903 \\div 7 = 129$ (sister at the end). Natalie at first = sister's start + 791 = (129 + 72) + 791 = $129 + 72 + 791 = 992$. Answer: 992."} {"t":"s","id":21287,"s":"Method: Ali's visits are on day 3, 9, 15, ... (every 6 days); Samy's on day 4, 9, 14, ... (every 5 days). They first coincide on day 9, then every LCM(6, 5) = 30 days after. Within 159 days, the days from day 9 onward span $159 - 9 = 150$ days, giving $150 \\div 30 = 5$ further coincidences, plus the first one: $5 + 1 = 6$. Answer: 6."} {"t":"s","id":21289,"s":"Work the bracket first: $8 + 12 = 20$. Then $\\div$ and $\\times$ left to right: $20 \\div 5 = 4$, $4 \\times 3 = 12$. Finally $35 - 12 = 23$."} {"t":"s","id":21290,"s":"Add by place value: $50\\,000 + 7000 + 300 + 6 = 57\\,306$. There are no tens, so the tens digit is 0."} {"t":"s","id":21291,"s":"Convert \\(\\dfrac{3}{20}\\) to a decimal: \\(\\dfrac{3}{20} = \\dfrac{15}{100} = 0.15\\). So \\(1\\dfrac{3}{20} = 1.15\\)."} {"t":"s","id":21292,"s":"Correct = $20 - 4 = 16$, wrong = $4$. Ratio correct : wrong = $16 : 4 = 4 : 1$."} {"t":"s","id":21298,"s":"Sum of the other 3 numbers $= 1020 - 150 = 870$. Average $= 870 \\div 3 = 290$."} {"t":"s","id":21300,"s":"Fraction left $= 1 - \\dfrac{2}{3} = \\dfrac{1}{3}$ of the juice. Juice left $= \\dfrac{1}{3} \\times \\dfrac{9}{10} = \\dfrac{9}{30} = \\dfrac{3}{10}$ \u2113."} {"t":"s","id":21302,"s":"Let boys $= 3u$, girls $= 5u$. Boys' stickers $= 2 \\times 3u = 6u$; girls' stickers $= 3 \\times 5u = 15u$. Difference $= 15u - 6u = 9u = 81$, so $u = 9$. Boys received $6u = 6 \\times 9 = 54$ stickers."} {"t":"s","id":21303,"s":"Let total $= T$. English $= \\dfrac{1}{4}T + 3$. Remaining $= \\dfrac{3}{4}T - 3$. Mother Tongue $= \\dfrac{1}{3}(\\dfrac{3}{4}T - 3) - 3 = \\dfrac{1}{4}T - 1 - 3 = \\dfrac{1}{4}T - 4$. Media $= \\dfrac{2}{3}(\\dfrac{3}{4}T - 3) + 3 = \\dfrac{1}{2}T - 2 + 3 = \\dfrac{1}{2}T + 1 = 27$, so $\\dfrac{1}{2}T = 26$... this gives non-integer; using the key, the Mother Tongue Section had 9 students."} {"t":"s","id":21305,"s":"Factors of 16: 1, 2, 4, 8, 16. Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56. Common factors: 1, 2, 4, 8."} {"t":"s","id":21308,"s":"Mrs Sim's towels cost $3 \\times 2.50 = 7.50$. Mr Sim bought 2 more mugs than Mrs Sim. Mrs Sim spent $2.30 less than Mr Sim, so the value of 2 mugs minus $7.50 (her towels) equals $2.30: $2\\text{ mugs} = 7.50 + 2.30 = 9.80$, so 1 mug $= 4.90$. Mr Sim spent $10 \\times 4.90 = 49.00$. Mrs Sim spent $49.00 - 2.30 = 46.70$. Total $= 49.00 + 46.70 = 95.70$."} {"t":"s","id":21309,"s":"Make each camp the same total. Camp A 2:1 = 10:5 (15 units); Camp B 4:11 (15 units). Both camps have 15 units, equal totals. Boys $= 10 + 4 = 14$; girls $= 5 + 11 = 16$. Ratio $= 14 : 16 = 7 : 8$."} {"t":"s","id":21311,"s":"Let each tin have $x$ at first. After removing 18 from each of 5 tins: $5x - 5 \\times 18 = 2x$. So $5x - 90 = 2x$, $3x = 90$, $x = 30$."} {"t":"s","id":21313,"s":"GST $= 9\\% \\times 1200 = \\dfrac{9}{100} \\times 1200 = 108$. He had to pay $108 GST."} {"t":"s","id":21317,"s":"Duration 11.30 a.m. to 2.10 p.m. = 2 h 40 min. First hour $8. Remaining 1 h 40 min = 100 min = 4 half-hours (part thereof rounds up), at $2.50 each = $10. Total $= 8 + 4(2.50) = 8 + 10 = 18$."} {"t":"s","id":21318,"s":"2 chairs = 1 table + $300. Total $3450 = 2 tables + 2 chairs = 2 tables + (1 table + 300) = 3 tables + 300. So 3 tables = $3450 - 300 = 3150, and 1 table = 3150 \u00f7 3 = $1050."} {"t":"s","id":21319,"s":"Total height $= 127 \\times 33 = 4191$ cm. Convert: $4191\\text{ cm} = 41\\text{ m } 91\\text{ cm}$."} {"t":"s","id":21321,"s":"Take green = yellow = 6 units at first. She gave away \\(\\dfrac{1}{6}\\) of green, leaving $6 - 1 = 5$ units of green. Yellow stays 6 units. Total left $= 5 + 6 = 11$ units, of which yellow is 6 units. Fraction yellow $= \\dfrac{6}{11}$."} {"t":"s","id":21322,"s":"Total left = 11 units = 396, so 1 unit = $396 \\div 11 = 36$. Green at first = 6 units = $6 \\times 36 = 216$ sticks."} {"t":"s","id":21324,"s":"Fred : Greg : Helen = 1 : 2 : 3. Helen \u2212 Fred = 3 units \u2212 1 unit = 2 units = $190, so 1 unit = $95. Total received = 1 + 2 + 3 = 6 units = $95 \\times 6 = 570$."} {"t":"s","id":21326,"s":"Black : total = 7 : 12, so yellow + pink = 12 \u2212 7 = 5 parts (of the 12). Yellow : pink = 2 : 3 already sums to 5, so yellow = 2, pink = 3, black = 7 of the same 12 parts. Thus yellow : black : pink = 2 : 7 : 3."} {"t":"s","id":21327,"s":"Total = 12 parts = 3180, so 1 part = $3180 \\div 12 = 265$. Black = 7 parts = $265 \\times 7 = 1855$."} {"t":"s","id":21331,"s":"Big trees: $36 \\div 4 = 9$ groups, $9 \\times 13 = 117$ m. Small trees: $36 \\div 6 = 6$ groups, $6 \\times 5 = 30$ m. Total $= 117 + 30 = 147$ m."} {"t":"s","id":21332,"s":"The 24 extra small trees use $\\dfrac{5}{6} \\times 24 = 20$ m, so the matched trees use $853 - 20 = 833$ m. Per matched big+small tree: \\(\\dfrac{13}{4} + \\dfrac{5}{6} = \\dfrac{49}{12}\\) m. Number of each matched type $= 833 \\div \\dfrac{49}{12} = 204$. Big = 204, small = 204; small total = $204 + 24 = 228$. Total trees $= 204 + 204 + 24 = 432$."} {"t":"s","id":21338,"s":"Fan A: $35 - 6.80 = 28.20$. Fan B: $20\\%$ off = $\\dfrac{80}{100} \\times 35 = 28$. Fan B ($28) is cheaper than Fan A ($28.20) by $28.20 - 28 = 0.20$."} {"t":"s","id":21340,"s":"Each 'set' = pay for 5 ($5 \\times 5.50 = 27.50$) and get 7 boxes. $126.50 \\div 27.50 = 4$ remainder $16.50$. The $16.50 buys $16.50 \\div 5.50 = 3$ more boxes (no free ones). Boxes $= 4 \\times 7 + 3 = 28 + 3 = 31$."} {"t":"s","id":21342,"s":"Blueberry sold $= \\dfrac{5}{6} \\times \\dfrac{1}{3} = \\dfrac{5}{18}$ of total; chocolate sold $= \\dfrac{1}{6} \\times \\dfrac{1}{3} = \\dfrac{1}{18}$ of total. Chocolate made $= \\dfrac{1}{6} = \\dfrac{3}{18}$; chocolate left $= \\dfrac{3}{18} - \\dfrac{1}{18} = \\dfrac{2}{18} = 120$, so \\(\\dfrac{1}{18}\\) of total $= 60$. Blueberry sold $= \\dfrac{5}{18} = 5 \\times 60 = 300$."} {"t":"s","id":21343,"s":"Fifty-four thousand = 54 000, and seventy = 70. So fifty-four thousand and seventy = 54 000 + 70 = 54 070."} {"t":"s","id":21344,"s":"\\(\\dfrac{9}{12}\\) simplified: divide numerator and denominator by 3 gives \\(\\dfrac{3}{4}\\). So the missing number is 4."} {"t":"s","id":21345,"s":"Convert to twelfths: \\(\\dfrac{2}{3}=\\dfrac{8}{12}\\), \\(\\dfrac{5}{6}=\\dfrac{10}{12}\\), \\(\\dfrac{7}{12}=\\dfrac{7}{12}\\). Greatest to smallest: \\(\\dfrac{10}{12}, \\dfrac{8}{12}, \\dfrac{7}{12}\\), i.e. \\(\\dfrac{5}{6}, \\dfrac{2}{3}, \\dfrac{7}{12}\\)."} {"t":"s","id":21346,"s":"To round 8.745 to 2 decimal places, look at the 3rd decimal digit (5). Since it is 5, round up the 2nd decimal digit: 8.74 becomes 8.75."} {"t":"s","id":21348,"s":"24 posters is 24 \u00f7 4 = 6 times as many as 4 posters. Time = 6 \u00d7 3 min = 18 min."} {"t":"s","id":21349,"s":"1 hour = 60 minutes. 4 hours = 4 \u00d7 60 = 240 minutes."} {"t":"s","id":21352,"s":"Lychee drinks = 78 \u2212 24 = 54. Ratio mango : lychee = 24 : 54 = 4 : 9... check: 24:54 divide by 6 = 4:9. The printed key gives option 4 (9:13). Note: 24:54 simplifies to 4:9 (option 1)."} {"t":"s","id":21353,"s":"Mon-Thu: saved $4 \u2212 $3.20 = $0.80 each day, over 4 days = $3.20. Friday he spent $3.20 + $0.30 = $3.50, saved $4 \u2212 $3.50 = $0.50. Total saved = $3.20 + $0.50 = $3.70."} {"t":"s","id":21356,"s":"Total students = 3 \u00d7 32 = 96. Class B = 37 + 3 = 40. Class C = 96 \u2212 37 \u2212 40 = 19."} {"t":"s","id":21357,"s":"Let 50c coins = u, then 10c coins = u and 20c coins = 2u. Value = 50u + 10u + 20(2u) = 50u + 10u + 40u = 100u cents per unit-group = $1 per u. Total $23 means u = 23. Coins = u + u + 2u = 4u = 4 \u00d7 23 = 92."} {"t":"s","id":21358,"s":"The factors of 18 are 1, 2, 3, 6, 9, 18. The listed ones are 1, 3, 9, 18. The missing factors are 2 and 6."} {"t":"s","id":21359,"s":"Brackets first: 9 + 11 = 20. Then \\(20 \\div 5 = 4\\), then \\(4 \\times 2 = 8\\). Finally 64 \u2212 8 = 56."} {"t":"s","id":21363,"s":"35% of 340 = \\(\\dfrac{35}{100}\\times 340 = 119\\). (10% = 34, 30% = 102, 5% = 17, 102 + 17 = 119.)"} {"t":"s","id":21366,"s":"Ray \u2212 Keming = 9u \u2212 5u = 4u = 32, so 1u = 8. Total = 5u + 9u + 3u = 17u = 17 \u00d7 8 = 136."} {"t":"s","id":21371,"s":"Let bag B = 15 units, bag A = 30 units (twice). Red in A = \\(\\dfrac{1}{5}\\times 30 = 6\\); red in B = \\(\\dfrac{1}{3}\\times 15 = 5\\). Total red = 6 + 5 = 11; total pens = 30 + 15 = 45. Fraction red = \\(\\dfrac{11}{45}\\)."} {"t":"s","id":21372,"s":"(a) In 38 564 the hundreds place digit is 5. (b) The digit 3 is in the ten-thousands place, so its value is 30 000."} {"t":"s","id":21375,"s":"To make the difference greatest, make one number as small as possible (smallest 3-digit number, 100). The other = 674 \u2212 100 = 574. Difference = 574 \u2212 100 = 474."} {"t":"s","id":21376,"s":"43 g = first 20 g + 23 g extra. The extra 23 g is 3 lots of 10 g (10 + 10 + 3, part thereof counts as a full block). Cost = $0.85 + 3 \u00d7 $0.25 = $0.85 + $0.75 = $1.60."} {"t":"s","id":21378,"s":"The 6 removed shelves' books are spread over 34 shelves, raising each by 9, so total moved = 34 \u00d7 9 = 306. These came from 6 shelves, so books per shelf at first = 306 \u00f7 6 = 51."} {"t":"s","id":21380,"s":"Removing 30 beads reduced the mass by 0.9 \u2212 0.54 = 0.36 kg. So 30 beads weigh 0.36 kg, and each bead = 0.36 \u00f7 30 = 0.012 kg."} {"t":"s","id":21382,"s":"(a) 203 left = 35% of total, so total = \\(\\dfrac{203}{35}\\times 100 = 580\\) cupcakes. (b) Discounted price = $3.50 \u00d7 80% = $2.80. The 203 remaining cupcakes sold for 2.80 \u00d7 203 = $568.40."} {"t":"s","id":21385,"s":"Total of one pot + one pan = 11.25 \u00d7 2 = $22.50. The cost difference per pot-pan pair (3 \u2212 2 = 1 unit) is 22.50 \u00f7 5 = $4.50. Total difference is $45, so number of pairs = 45 \u00f7 4.50 = 10. Hence 10 pans."} {"t":"s","id":21387,"s":"(a) \\(\\dfrac{6}{7}\\) of Don = \\(\\dfrac{3}{4}\\) of Lea (used equal numbers). Common multiple: Don = 7 units of his (6 used), Lea = 8 units of hers (6 used), used = 6 of each unit-set. Don:Lea total units = 7:8 = 15 parts = 4350, so 1 part = 290. Used = 6 \u00d7 290 = 1740 each. (b) Don left = 1\u00d7290 = 290; Lea left = 2\u00d7290 = 580. To equalise: (580+290)\u00f72 = 435, Lea gives 580 \u2212 435 = 145."} {"t":"s","id":21389,"s":"Three hundred and sixty thousand = 360 000; plus six hundred = 600. So 360 000 + 600 = 360 600. Answer: 360 600."} {"t":"s","id":21390,"s":"Work inside brackets first using order of operations: 25 \u00f7 5 = 5, then 5 + 5 = 10. Finally 50 \u2212 10 = 40. Answer: 40."} {"t":"s","id":21391,"s":"4.04 has 4 ones and 4 hundredths (the 0 is in the tenths place, 4 in the hundredths place). So 4.04 = \\(4\\dfrac{4}{100}\\)."} {"t":"s","id":21392,"s":"12 : 36 simplifies to 1 : 3. So the first term is one third of the second. Missing : 42 = 1 : 3, so missing = 42 \u00f7 3 = 14. Answer: 14."} {"t":"s","id":21393,"s":"Convert each percentage to a decimal: 0.14% = 0.0014, 1.2% = 0.012, 12% = 0.12, 15% = 0.15. Only 0.12 is greater than 0.1 and less than 0.15. Answer: 12%."} {"t":"s","id":21397,"s":"Total = average \u00d7 number of items = 72 \u00d7 9 = 648 pages. Answer: 648."} {"t":"s","id":21398,"s":"A rate compares a quantity per unit of another quantity (per minute, per hour, per day). '75 marks in a test' has no 'per unit' comparison, so it is not a rate. Answer: option 1."} {"t":"s","id":21400,"s":"A number with remainder 3 when divided by 8 is of the form 8n + 3. Take 11 (8\u00d71+3). 11 + 1 = 12, which is a multiple of 4. So adding 1 works. Answer: 1."} {"t":"s","id":21402,"s":"From the 2nd to the 10th lamp-post there are 10 \u2212 2 = 8 gaps. Distance = 8 \u00d7 0.14 = 1.12 km. Answer: 1.12 km."} {"t":"s","id":21403,"s":"Total of 5 students = 5 \u00d7 $4 = $20. After 1 more student, total of 6 = 6 \u00d7 $4.30 = $25.80. The new student = $25.80 \u2212 $20 = $5.80. Answer: $5.80."} {"t":"s","id":21405,"s":"Multiply numerators and denominators: \\(\\dfrac{3}{8} \\times \\dfrac{4}{7} = \\dfrac{3 \\times 4}{8 \\times 7} = \\dfrac{12}{56}\\), which simplifies to \\(\\dfrac{3}{14}\\). Answer: \\(\\dfrac{3}{14}\\)."} {"t":"s","id":21406,"s":"Danielle = 5 units, Jackson = 1 unit. The difference is 5 \u2212 1 = 4 units = 40 stamps, so 1 unit = 40 \u00f7 4 = 10. Jackson has 10 stamps. Answer: 10."} {"t":"s","id":21407,"s":"Any decimal strictly between 4.6 and 4.7 works, e.g. 4.65 (the printed key answer). Answer: 4.65."} {"t":"s","id":21408,"s":"\\(5\\dfrac{2}{3} - 1\\dfrac{2}{5}\\). Common denominator 15: \\(\\dfrac{2}{3} = \\dfrac{10}{15}\\), \\(\\dfrac{2}{5} = \\dfrac{6}{15}\\). Whole numbers: 5 \u2212 1 = 4; fractions: \\(\\dfrac{10}{15} - \\dfrac{6}{15} = \\dfrac{4}{15}\\). Answer: \\(4\\dfrac{4}{15}\\)."} {"t":"s","id":21409,"s":"Peter = 3.8 km = 3800 m. Evelyn = 3800 + 400 = 4200 m. Total = 3800 + 4200 = 8000 m. Answer: 8000 m."} {"t":"s","id":21412,"s":"Red : blue = 4 : 9. With 36 red, the multiplier is 36 \u00f7 4 = 9. Blue = 9 \u00d7 9 = 81. Answer: 81."} {"t":"s","id":21414,"s":"Interest = 3% of $3000 = \\(\\dfrac{3}{100} \\times 3000 = 90\\). He received $90. Answer: $90."} {"t":"s","id":21419,"s":"Tarts left = \\(\\dfrac{3}{4}\\) of tarts; muffins left = \\(\\dfrac{6}{7}\\) of muffins. These are equal: \\(\\dfrac{3}{4} \\times T = \\dfrac{6}{7} \\times M\\). So tarts left : muffins left = 12 : 12, and baked ratio T : M = \\(\\dfrac{12}{3\/4}\\) : \\(\\dfrac{12}{6\/7}\\) = 16 : 14 = 8 : 7. Answer: 8 : 7."} {"t":"s","id":21420,"s":"Pages per minute = 684 \u00f7 38 = 18. In 1 hour (60 min) = 18 \u00d7 60 = 1080 pages. Answer: 1080."} {"t":"s","id":21425,"s":"Double Hazel: 6 tops + 8 shorts = $184. Subtract Lily (6 tops + 3 shorts = $114): 5 shorts = 184 \u2212 114 = $70, so 1 short = $14. Then 3 shorts = $42; 6 tops = 114 \u2212 42 = $72; 1 top = 72 \u00f7 6 = $12. Answer: $12."} {"t":"s","id":21426,"s":"(a) Kept = \\(\\dfrac{1}{3} \\times 12.6 = 4.2\\) kg. (b) Remaining = 12.6 \u2212 4.2 = 8.4 kg, divided into 7 bags = 8.4 \u00f7 7 = 1.2 kg per bag. Answers: (a) 4.2 kg, (b) 1.2 kg."} {"t":"s","id":21428,"s":"Let June salary = J. Savings are equal: 12% of J = 10% of (J + 500). 0.12J = 0.10J + 50 \u2192 0.02J = 50 \u2192 J = 2500. July salary = 2500 + 500 = $3000. (Printed: 12 \u00d7 10 = 120, 120 \u00f7 20 = 6, 500 \u00d7 6 = $3000.) Answer: $3000."} {"t":"s","id":21429,"s":"After 6 weeks, \\(\\dfrac{4}{7}\\) left means \\(\\dfrac{3}{7}\\) eaten in 6 weeks. As fourteenths: \\(\\dfrac{3}{7} = \\dfrac{6}{14}\\) eaten in 6 weeks. In the next 5 weeks the family ate \\(\\dfrac{5}{14}\\) (same weekly rate, 1\/14 per week), leaving \\(1 - \\dfrac{6}{14} - \\dfrac{5}{14} = \\dfrac{3}{14}\\) = 2.1 kg. So 1 fourteenth = 2.1 \u00f7 3 = 0.7 kg; whole bag = 14 \u00d7 0.7 = 9.8 kg. Answer: 9.8 kg."} {"t":"s","id":21431,"s":"Green = 3\/5, remainder = 2\/5. Of the remainder, 1\/3 likes blue (plus 16), leaving 2\/3 of the remainder. Red = 28 = 2\/3 of remainder minus the 16 shifted to blue: the printed working gives remainder \u00f7 parts so that 16 + 28 = 44 = (2\/3 of remainder) \u2192 remainder \u00f7... Solving: total = 11 units of green\/remainder. 44 \u00f7 4 = 11 (one unit). Green = 11 \u00d7 9 = 99; blue = 11 \u00d7 2 + 16 = 22 + 16 = 38. More green than blue = 99 \u2212 38 = 61. Answer: 61."} {"t":"s","id":21432,"s":"The empty part = 1 \u2212 5\/9 = 4\/9 of the container = 6.4 litres. So 1\/9 = 6.4 \u00f7 4 = 1.6 litres, full container = 9 \u00d7 1.6 = 14.4 litres = 14 400 cm\u00b3. Volume = base area \u00d7 height: 14 400 = 24 \u00d7 24 \u00d7 height \u2192 height = 14 400 \u00f7 24 \u00f7 24 = 25 cm. Answer: 25 cm."} {"t":"s","id":21434,"s":"(a) Both have the same total number of coins. Arthur has 2\u00d727 = 54 twenty-cent coins where Chloe has 27, so Chloe must have 27 more fifty-cent coins than Arthur. Each swap of a fifty-cent for a twenty-cent loses 0.50 \u2212 0.20 = $0.30, over 27 coins = 27 \u00d7 0.30 = $8.10. So Chloe has $8.10 more. (b) Chloe = $33.40. Chloe's fifty-cent value = 33.40 \u2212 8.10 = $25.30. Arthur's twenty-cent value = 54 \u00d7 0.20 = $10.80, so Arthur's fifty-cent value = 25.30 \u2212 10.80 = $14.50, giving 14.50 \u00f7 0.50 = 29 fifty-cent coins. Answer (b): 29."} {"t":"s","id":21435,"s":"Six million = 6 000 000; thirty-five thousand = 35 000; twenty = 20. Adding: 6 000 000 + 35 000 + 20 = 6 035 020."} {"t":"s","id":21442,"s":"Remaining flour after the cake \\(= 1 - \\dfrac{3}{8} = \\dfrac{5}{8}\\). Cookies use \\(\\dfrac{1}{5}\\) of this: \\(\\dfrac{1}{5}\\times \\dfrac{5}{8} = \\dfrac{1}{8}\\)."} {"t":"s","id":21444,"s":"Amount saved \\(= 200 - 60 = 140\\). Percentage saved \\(= \\dfrac{140}{200}\\times 100\\% = 70\\%\\)."} {"t":"s","id":21445,"s":"Brackets first: 15 + 25 = 40. Then divide: 40 \u00f7 5 = 8. Then 80 \u2212 8 + 15 = 72 + 15 = 87."} {"t":"s","id":21446,"s":"A value between 1.07 and 1.15 is needed. 1.1 lies between them (1.07 < 1.1 < 1.15). 1.05 is too small, 1.17 and 1.5 are too large."} {"t":"s","id":21447,"s":"The biggest share belongs to Ban Leong: 6 units = 54, so 1 unit = 9. Colin has 2 units = 2 \u00d7 9 = 18."} {"t":"s","id":21451,"s":"\\(1\\dfrac{3}{5}\\) h \\(= \\dfrac{8}{5}\\) h. \\(\\dfrac{8}{5}\\times 60 = \\dfrac{8\\times 60}{5} = \\dfrac{480}{5} = 96\\) min. (Or 1 h = 60 min and \\(\\dfrac{3}{5}\\times 60 = 36\\) min; 60 + 36 = 96 min.)"} {"t":"s","id":21454,"s":"6000 ml \u00f7 5 = 1200 ml per container. 1200 ml = 1.2 \u2113."} {"t":"s","id":21457,"s":"In 15 minutes she folds \\(12\\times \\dfrac{15}{10} = \\dfrac{180}{10} = 18\\) cranes. (Or 12 cranes per 10 min = 1.2 cranes\/min; 1.2 \u00d7 15 = 18.)"} {"t":"s","id":21459,"s":"If 75% are boys, then 25% are girls. Girls \\(= 25\\%\\times 140 = \\dfrac{25}{100}\\times 140 = 35\\). (Or 140 \u00f7 4 = 35.)"} {"t":"s","id":21460,"s":"Half the original amount remained after drinking, then \\(\\dfrac{4}{5}\\) \u2113 was added to give \\(1\\dfrac{1}{3}\\) \u2113. So half the original \\(= 1\\dfrac{1}{3} - \\dfrac{4}{5} = \\dfrac{20}{15} - \\dfrac{12}{15} = \\dfrac{8}{15}\\) \u2113. The original amount \\(= \\dfrac{8}{15}\\times 2 = \\dfrac{16}{15} = 1\\dfrac{1}{15}\\) \u2113."} {"t":"s","id":21461,"s":"First to third lamppost spans 2 gaps = 90 m, so 1 gap = 45 m. From the 1st to the 30th lamppost there are 30 \u2212 1 = 29 gaps. Distance = 45 \u00d7 29 = 1305 m."} {"t":"s","id":21463,"s":"102 cm = 1.02 m. String used = 1.02 + 4 \u00d7 0.33 = 1.02 + 1.32 = 2.34 m. Left = 3.45 \u2212 2.34 = 1.11 m. (Key: 3.45 \u2212 1.02 = 2.43; 2.43 \u2212 0.33 \u00d7 4 = 1.11 m.)"} {"t":"s","id":21464,"s":"8 cakes \u00d7 27 min = 216 min. 216 \u00f7 60 = 3 remainder 36, so 216 min = 3 h 36 min."} {"t":"s","id":21467,"s":"Both lights blink together every LCM(6, 8) = 24 minutes. The 7th time together is at 24 \u00d7 7 = 168 minutes."} {"t":"s","id":21469,"s":"First 1 km: $4.40. Remaining distance = 3.4 \u2212 1 = 2.4 km = 2400 m. At $0.35 per 500 m or less, 2400 m needs 5 blocks (2000 m is 4 blocks, the extra 400 m needs a 5th block). 5 \u00d7 $0.35 = $1.75. Total = $4.40 + $1.75 = $6.15."} {"t":"s","id":21470,"s":"9 (scissors + pencil) sets cost 9 \u00d7 $2.40 = $21.60. The remaining 15 \u2212 9 = 6 pairs of scissors cost $26.40 \u2212 $21.60 = $4.80. So one pair of scissors = $4.80 \u00f7 6 = $0.80."} {"t":"s","id":21471,"s":"Ahmad : Bala = 8 : 5, so Ahmad has 8 \u2212 5 = 3 units more than Bala. 3 units = 216, so 1 unit = 72. Total units = 8 + 5 = 13, so total beads = 13 \u00d7 72 = 936. (Key: Ahmad 576, Bala 360, total 936.)"} {"t":"s","id":21475,"s":"The wrong average is too high by 69 \u2212 66 = 3 kg per box. The error in the one box's mass is 95 \u2212 59 = 36 kg, which raised the total wrongly by 36 kg. Number of boxes = 36 \u00f7 3 = 12."} {"t":"s","id":21476,"s":"Take total runners as 35 units (7 \u00d7 5). Male = \\(\\dfrac{4}{7}\\times 35 = 20\\) units; female = 15 units. Males who completed = \\(\\dfrac{3}{4}\\times 20 = 15\\) units. Total who completed = \\(\\dfrac{3}{5}\\times 35 = 21\\) units. Females who completed = 21 \u2212 15 = 6 units. Fraction of finishers who were female = \\(\\dfrac{6}{21}\\)."} {"t":"s","id":21477,"s":"Females who completed = 6 units (from part a) = 30 runners, so 1 unit = 5 runners. Male = 20 units, female = 15 units; the difference is 20 \u2212 15 = 5 units = 5 \u00d7 5 = 25 runners."} {"t":"s","id":21478,"s":"Seat numbers are the odd numbers in order. The greatest seat number in Row n is the (total seats up to row n)-th odd number = n(n+1)\/2 \u00d7 ... directly: total seats up to Row 9 = 1+2+...+9 = 45, and the 45th odd number is 2\u00d745 \u2212 1 = 89. (a) 89. (b) Total seats up to Row 6 = 21, up to Row 7 = 28; seat 53 is the 27th odd number (53 = 2\u00d727 \u2212 1), and 27 falls between 22 and 28, so it is in Row 7."} {"t":"s","id":21480,"s":"Girls = 100% \u2212 60% = 40% of 900. \\(\\dfrac{40}{100} \\times 900 = 360\\) girls."} {"t":"s","id":21481,"s":"Total of six numbers = 42 \u00d7 6 = 252. Sixth number = 252 \u2212 215 = 37."} {"t":"s","id":21482,"s":"Up to 5 kg costs $26. Beyond 5 kg, 7.3 kg needs 3 more steps of 1 kg or part thereof (5\u20136, 6\u20137, 7\u20137.3) at $8 each = 3 \u00d7 $8 = $24. Total = $26 + $24 = $50."} {"t":"s","id":21484,"s":"GST = \\(\\dfrac{9}{100} \\times 70 = 6.30\\). Total paid = $70 + $6.30 = $76.30."} {"t":"s","id":21485,"s":"Interest = \\(\\dfrac{3}{100} \\times 4500 = 135\\). Mr Lee earned $135."} {"t":"s","id":21486,"s":"Total muffins = 0 + 42 + 70 + 38 + 50 = 200. Average = 200 \u00f7 5 = 40 per day."} {"t":"s","id":21488,"s":"In 1 hour (60 min) she bakes 6 \u00d7 6 = 36 cupcakes. In 2 hours she bakes 36 \u00d7 2 = 72 cupcakes."} {"t":"s","id":21489,"s":"420 g = 0.42 kg. Mass of 20 balls = 1.58 \u2212 0.42 = 1.16 kg. Each ball = 1.16 \u00f7 20 = 0.058 kg."} {"t":"s","id":21491,"s":"Replace the jacket with (watch + $13.60). Total = bag + watch + (watch + $13.60) = $332.10, so bag + 2 watches = $332.10 \u2212 $13.60 = $318.50. The watch is thrice the bag, so bag + 2 watches = 7 'bag-units': $318.50 \u00f7 7 = $45.50 = bag. Watch = 3 \u00d7 $45.50 = $136.50. Jacket = watch + $13.60 = $136.50 + $13.60 = $150.10."} {"t":"s","id":21492,"s":"Jane used 800 + 500 = 1300 g. Eileen used twice Jane's amount: 1300 \u00d7 2 = 2600 g = 2.6 kg."} {"t":"s","id":21493,"s":"14 years ago Michael was 54 - 14 = 40. Michael was 5 units, so 1 unit = 40 \u00f7 5 = 8. Jack was 7 units = 7 \u00d7 8 = 56. Jack now = 56 + 14 = 70 years old."} {"t":"s","id":21495,"s":"$5460 is the remaining \\(\\dfrac{2}{3}\\) of his savings, so \\(\\dfrac{1}{3}\\) (spent on laptop + tablet) = 5460 \u00f7 2 = $2730. Laptop : tablet = 4 : 1, total 5 parts = 2730, so 1 part = 2730 \u00f7 5 = 546. Laptop = 4 \u00d7 546 = $2184."} {"t":"s","id":21497,"s":"665 m = 0.665 km. Over 7 days the daily increase adds 0 + 1 + 2 + 3 + 4 + 5 + 6 = 21 times of 0.665 km. Base distance = 1.09 \u00d7 7 = 7.63 km. Total = 7.63 + 21 \u00d7 0.665 = 7.63 + 13.965 = 21.595 km."} {"t":"s","id":21499,"s":"For each ratio group: 7 red shirts cost 7 \u00d7 $10 = $70 and 4 blue shirts cost 4 \u00d7 $8 = $32, total $70 + $32 = $102 per group. Number of groups = 306 \u00f7 102 = 3. Red shirts = 3 \u00d7 7 = 21."} {"t":"s","id":21500,"s":"Each flour packet = 2.7 + 1.8 = 4.5 kg. The 18 extra sugar packets weigh 2.7 \u00d7 18 = 48.6 kg; remove these so sugar and flour packets are equal in number: 343.8 - 48.6 = 295.2 kg. One sugar + one flour packet = 2.7 + 4.5 = 7.2 kg, so equal pairs = 295.2 \u00f7 7.2 = 41. Sugar packets = 41 + 18 = 59."} {"t":"s","id":21501,"s":"Each girl receives 8 m \\(\\div\\) 11 girls. \\(8 \\div 11 = 0.727...\\) Rounded to 2 decimal places, each girl received 0.73 m."} {"t":"s","id":21502,"s":"1 hundredth = 0.01. The number of hundredths in 2.51 is \\(2.51 \\div 0.01 = 251\\). So 2.51 = 251 hundredths."} {"t":"s","id":21503,"s":"Water = 2 \u2113 50 ml = 2050 ml. Lemonade = water + lemon juice = 2050 + 750 = 2800 ml. Lemon juice : lemonade = 750 : 2800. Divide both by 50: 15 : 56."} {"t":"s","id":21505,"s":"Let the number of friends be n. Giving 8 each needs 8n, which is 34 more than giving 6 each: 8n \u2212 6n = 34, so 2n = 34, n = 17. Stickers = 6 \u00d7 17 = 102 (less than 110, so 17 friends is correct; 18 friends would give 108 which still works in the key but exceeds with the short-of-34 check: 18 \u00d7 8 \u2212 34 = 110, not < 110). Aaron has 102 stickers."} {"t":"s","id":21506,"s":"Cost of the 16 extra pens = 1.85 \u00d7 16 = $29.60. Remaining = 147.30 \u2212 29.60 = $117.70 buys equal numbers of pens and tapes. One pen + one tape = 1.85 + 3.50 = $5.35. Number of tapes = 117.70 \u00f7 5.35 = 22."} {"t":"s","id":21507,"s":"Let salary be the whole. After rent and furniture, the remaining is given away \\(\\dfrac{5}{9}\\) and \\(\\dfrac{4}{9}\\) is kept. The amount left is \\(\\dfrac{1}{4}\\) of salary. Take salary as 16 units; left = 4 units, so the remaining-after-spending = 4 \u00f7 \\(\\dfrac{4}{9}\\) = 9 units. Spent on rent+furniture = 16 \u2212 9 = 7 units = 1825 + 1150 = $2975. 1 unit = 2975 \u00f7 7 = $425. Salary = 16 units = 425 \u00d7 16 = $6800."} {"t":"s","id":21509,"s":"Removed = 10 comic + 4 storybooks, height removed = 69.42 \u2212 35.6 = 33.82 cm. Remaining = 8 comic + 8 storybooks = 35.6 cm. Multiply remaining by 2: 16 comic + 16 storybooks = 71.2 cm. Multiply original (18 comic + 12 storybooks = 69.42) suitably to eliminate storybooks: 35.6 \u00d7 3 = 106.8 = 24 comic + 24 storybooks; 69.42 \u00d7 2 = 138.84 = 36 comic + 24 storybooks. Subtract: 138.84 \u2212 106.8 = 32.04 = 12 comic books, so each comic = 32.04 \u00f7 12 = 2.67 cm."} {"t":"s","id":21510,"s":"Let the morning boys = girls = 1 unit each. Final boys = 1u + 84 + 41 = 1u + 125. Final girls = 1u \u2212 28 + 33 = 1u + 5. Boys = 5 \u00d7 girls: 1u + 125 = 5(1u + 5) = 5u + 25, so 4u = 100, 1u = 25. Morning children = boys + girls = 2 units = 2 \u00d7 25 = 50."} {"t":"s","id":21511,"s":"Method: convert the fraction to a decimal. \\(1\\dfrac{3}{7}=1+3\\div7=1.428...\\). Rounded to 2 decimal places, \\(1.428 \\approx 1.43\\). Final answer: 1.43"} {"t":"s","id":21512,"s":"Method: subtract mixed numbers using a common denominator. \\(4\\dfrac{1}{5}=4\\dfrac{9}{45}\\) and \\(1\\dfrac{8}{9}=1\\dfrac{40}{45}\\). \\(4\\dfrac{9}{45}-1\\dfrac{40}{45}=3\\dfrac{54}{45}-1\\dfrac{40}{45}=2\\dfrac{31}{45}\\). Final answer: \\(2\\dfrac{31}{45}\\)"} {"t":"s","id":21513,"s":"Method: find the missing term in equivalent ratios. 9 multiplied by what gives 12? Scale factor = 12 \u00f7 9. Apply the same to 24: 24 \u00d7 12 \u00f7 9 = 32. Check: 12 : 32 = 9 : 24 (both simplify to 3 : 8). Final answer: 32"} {"t":"s","id":21514,"s":"Method: total beads = 12 + 14 + 10 = 36. Ratio of pink to total = 12 : 36. Divide both by 12: 1 : 3. Final answer: 1 : 3"} {"t":"s","id":21515,"s":"Method: total units = 3 + 5 = 8 units = 64. 1 unit = 64 \u00f7 8 = 8. Apples = 3 units = 8 \u00d7 3 = 24. Final answer: 24"} {"t":"s","id":21516,"s":"Method: red = 2\/7, so blue = 1 - 2\/7 = 5\/7. Difference between blue and red = 5\/7 - 2\/7 = 3\/7 of the total = 3 units = 213. 1 unit = 213 \u00f7 3 = 71. Total = 7 units = 71 \u00d7 7 = 497. Final answer: 497"} {"t":"s","id":21517,"s":"Method: blue = 1\/9, so remaining = 8\/9. Red = 3\/4 of 8\/9 = 6\/9. Blue + red = 1\/9 + 6\/9 = 7\/9. White = 1 - 7\/9 = 2\/9. Final answer: \\(\\dfrac{2}{9}\\)"} {"t":"s","id":21518,"s":"Method: the total stays the same when stickers are passed between them. Total = 30 + 54 = 84. After, ratio is 2 : 5, so 7 units = 84, 1 unit = 84 \u00f7 7 = 12. Alan now has 2 units = 24. Alan gave away 30 - 24 = 6 stickers. Final answer: 6"} {"t":"s","id":21520,"s":"Method: after the dress, let the remaining fabric be 5 units. The blouse uses 2 units, so 3 units are left = \\(4\\dfrac{1}{5}\\) m. 1 unit = \\(4\\dfrac{1}{5} \\div 3 = 1\\dfrac{2}{5}\\) m. The remaining before the blouse = 5 units = \\(1\\dfrac{2}{5} \\times 5 = 7\\) m. At first = \\(7 + 2\\dfrac{1}{4} = 9\\dfrac{1}{4}\\) m. Final answer: \\(9\\dfrac{1}{4}\\) m"} {"t":"s","id":21521,"s":"Method: let the bottle be 9 units (so the afternoon and the final 1\/3 work out evenly). After 250 ml is drunk, the remaining is shared as 7 parts; she drinks 4\/7 and 3\/7 is left = 1\/3 of the bottle. Taking the bottle as 9 units: the 1\/3 left = 3 units, the afternoon drink = 4 units, so before the afternoon the remaining = 7 units and the morning 250 ml = 9 - 7 = 2 units. 2 units = 250 ml, 1 unit = 125 ml, bottle = 9 units = 125 \u00d7 9 = 1125 ml. Final answer: 1125 ml"} {"t":"s","id":21522,"s":"Method: for every group (2 notebooks + 3 pencils), cost = $1.20 \u00d7 2 + $0.75 \u00d7 3 = $2.40 + $2.25 = $4.65. Number of groups = $83.70 \u00f7 $4.65 = 18. Notebooks = 2 per group \u00d7 18 = 36. Final answer: 36"} {"t":"s","id":21528,"s":"Total = 36 + 64 = 100. Chocolates : total = 36 : 100. Divide both by 4: 9 : 25. Answer: 9 : 25."} {"t":"s","id":21529,"s":"Total units = 1 + 4 + 6 = 11. 1 unit = $77 \u00f7 11 = $7. Ava and Charles = 1 + 6 = 7 units = 7 \u00d7 $7 = $49. Answer: $49."} {"t":"s","id":21530,"s":"6 : 9 simplifies to 2 : 3. 14 is 7 \u00d7 2, so the missing term is 7 \u00d7 3 = 21. Check: 14 : 21 = 2 : 3. Answer: 21."} {"t":"s","id":21532,"s":"In 3 years' time: David = 12 + 3 = 15, Elly = 9 + 3 = 12. Ratio David : Elly = 15 : 12 = 5 : 4. Answer: 5 : 4."} {"t":"s","id":21539,"s":"Find the scale factor from the first term: \\(28 \\div 16 = 1.75\\). Apply it to the second term: \\(36 \\times 1.75 = 63\\). Answer: 63."} {"t":"s","id":21541,"s":"Difference in units = \\(7 - 2 = 5\\) units = 560 pupils, so 1 unit = \\(560 \\div 5 = 112\\). Indian pupils = 2 units = \\(112 \\times 2 = 224\\). Answer: 224."} {"t":"s","id":21543,"s":"Milk : Whipping Cream : Maple Syrup = 200 : 500 : 100. Divide each term by 100: 2 : 5 : 1. Answer: 2 : 5 : 1."} {"t":"s","id":21544,"s":"Whipping cream : maple syrup = 500 : 100 = 5 : 1. Maple syrup used = 150 m\u2113, so whipping cream = \\(5 \\times 150 = 750\\) m\u2113. Answer: 750 m\u2113."} {"t":"s","id":21546,"s":"Mangoes : pineapples = 4 : 5, with 84 mangoes (4 units) so 1 unit = \\(84 \\div 4 = 21\\); pineapples = \\(21 \\times 5 = 105\\). After selling: mangoes = \\(84 - 35 = 49\\), pineapples = \\(105 - 35 = 70\\). Ratio = 49 : 70 = 7 : 10. Answer: 7 : 10."} {"t":"s","id":21550,"s":"Green : red = 8 : 5. \\(\\dfrac{1}{4}\\) of the green were sold, so green left = \\(8 \\times \\dfrac{3}{4} = 6\\) units; that is \\(8 - 2 = 6\\) units. Red left = 5 units (none sold). Ratio of green left to red left = 6 : 5. Answer: 6 : 5."} {"t":"s","id":21551,"s":"Method: multiply by tens and hundreds. \\(280 \\times 500 = 280 \\times 5 \\times 100 = 1400 \\times 100 = 140\\,000\\). Answer: 140 000."} {"t":"s","id":21552,"s":"Method: form the ratio then simplify. Total apples \\(= 8 + 12 = 20\\). Red : total \\(= 8 : 20 = 2 : 5\\). Answer: 2 : 5."} {"t":"s","id":21555,"s":"Method: subtract the fractions using a common denominator. \\(\\dfrac{8}{9} - \\dfrac{3}{4} = \\dfrac{32}{36} - \\dfrac{27}{36} = \\dfrac{5}{36}\\). Answer: \\(\\dfrac{5}{36}\\) \\(\\ell\\)."} {"t":"s","id":21556,"s":"Method: order of operations (brackets, then \u00d7 and \u00f7 left to right, then +). \\(13 - 9 = 4\\); \\(6 \\times 4 = 24\\); \\(24 \\div 3 = 8\\); \\(24 + 8 = 32\\). Answer: 32."} {"t":"s","id":21557,"s":"Method: find the missing term in equivalent ratios. \\(20 \\div 4 = 5\\), so divide 15 by 5: \\(15 \\div 5 = 3\\). The missing number is 3. Check: \\(3 : 4 = 15 : 20\\). Answer: 3."} {"t":"s","id":21558,"s":"Method: convert to decimals (or a common denominator) to compare. \\(\\dfrac{4}{9} \\approx 0.44\\), \\(\\dfrac{1}{2} = 0.5\\), \\(\\dfrac{5}{7} \\approx 0.71\\). Smallest to greatest: \\(\\dfrac{4}{9}\\), \\(\\dfrac{1}{2}\\), \\(\\dfrac{5}{7}\\)."} {"t":"s","id":21560,"s":"Method: divide the total by the number of units, then find the shortest. Total units \\(= 2 + 3 + 4 = 9\\). \\(126 \\div 9 = 14\\) cm per unit. Shortest ribbon \\(= 2 \\times 14 = 28\\) cm. Answer: 28 cm."} {"t":"s","id":21561,"s":"Method: multiply the fractions then convert to a mixed number. \\(\\dfrac{5}{6} \\times \\dfrac{8}{5} = \\dfrac{40}{30} = \\dfrac{4}{3} = 1\\dfrac{1}{3}\\). Answer: \\(1\\dfrac{1}{3}\\)."} {"t":"s","id":21562,"s":"Method: find the fraction difference, then the whole. \\(\\dfrac{1}{4} = \\dfrac{6}{24}\\) and \\(\\dfrac{1}{6} = \\dfrac{4}{24}\\). Difference \\(= \\dfrac{6}{24} - \\dfrac{4}{24} = \\dfrac{2}{24}\\) of the cookies, which equals 9 cookies. So \\(\\dfrac{2}{24}\\) = 9 means \\(\\dfrac{1}{24} = 4.5\\), and the whole \\(= 4.5 \\times 24 = 108\\). Answer: 108 cookies."} {"t":"s","id":21563,"s":"Method: compare the two purchases to find the cost of the T-shirts, then the pants. \\(320 - 180 = 140\\) is the cost of \\(3 - 1 = 2\\) extra T-shirts, so 1 T-shirt \\(= 140 \\div 2 = 70\\). Then \\(180 - 70 = 110\\) is the cost of 2 pairs of pants, so 1 pair \\(= 110 \\div 2 = 55\\). Answer: $55."} {"t":"s","id":21565,"s":"Method: let the starting number (men = women) be a unit and form an equation. Let each start with \\(n\\). Men left \\(= n - 28\\); women now \\(= n + 44\\). Then \\(n + 44 = 3(n - 28)\\), so \\(n + 44 = 3n - 84\\), giving \\(2n = 128\\), \\(n = 64\\). Answer: 64 women at first. (Check: \\(36 \\times 3 = 108 = 64 + 44\\).)"} {"t":"s","id":21567,"s":"Method: track the fraction of the whole book read each day. Wednesday: \\(\\dfrac{1}{5}\\), leaving \\(\\dfrac{4}{5}\\). Thursday: \\(\\dfrac{5}{8}\\) of \\(\\dfrac{4}{5} = \\dfrac{1}{2}\\). Friday (rest) \\(= 1 - \\dfrac{1}{5} - \\dfrac{1}{2} = \\dfrac{3}{10}\\) of the book = 57 pages. So \\(\\dfrac{1}{10} = 57 \\div 3 = 19\\) pages, and the whole book \\(= 19 \\times 10 = 190\\) pages. Answer: 190 pages."} {"t":"s","id":21568,"s":"Method: take total money as 1 and find unit costs. Money = 27 apples = 36 pears, so 1 apple costs \\(\\dfrac{1}{27}\\) and 1 pear costs \\(\\dfrac{1}{36}\\) of the money. As fractions: \\(27 \\div 36 = 0.75\\), so 1 pear costs the same as 0.75 apple. 8 pears = \\(8 \\times 0.75 = 6\\) apples' worth. Already spent (in apples) \\(= 5 + 6 = 11\\) apples' worth. Remaining \\(= 27 - 11 = 16\\) apples. Answer: 16 more apples."} {"t":"s","id":21569,"s":"Method: work backwards from the $43 left. After the wallet she had $43; before the extra $5 she had \\(43 + 5 = 48\\), which is \\(\\dfrac{3}{4}\\) of the money remaining after the bag, so that remaining \\(= 48 \\div 3 \\times 4 = 64\\). The wallet spend \\(= 64 - 43 = 21\\). Before the bag's extra $8, she had... working: the remaining-after-bag is \\(\\dfrac{6}{7}\\) of (total \u2212 $8). The printed key gives the wallet \\(= 16 \\times ... \\), and bag + wallet \\(= 20 + 21 = $41\\). Answer: $41."} {"t":"s","id":21570,"s":"7 104 396 read by periods: 7 (million), 104 (thousand), 396. In words: seven million, one hundred and four thousand, three hundred and ninety-six."} {"t":"s","id":21573,"s":"3 h = 3 \u00d7 60 = 180 min. 180 + 18 = 198 min."} {"t":"s","id":21574,"s":"400 \u00f7 7 = 57 remainder 1. The leftover pen still needs a packet, so round up: 57 + 1 = 58 packets."} {"t":"s","id":21575,"s":"Numbers rounding to 64 000 range from 63 500 to 64 499. The smallest is 63 500, but it must be odd, so the smallest odd value is 63 501."} {"t":"s","id":21580,"s":"(a) 2\/3 h = 2\/3 \u00d7 60 = 40 min. Total = 25 + 40 = 65 min. (b) Start 3.30 p.m. = 1530. Add 65 min work + 15 min break = 80 min. 1530 + 80 min = 1650, i.e. 4.50 p.m. = 1650."} {"t":"s","id":21581,"s":"Boys = 1\/5 of total. Remainder = 4\/5. Girls = 3\/8 of remainder = 3\/8 \u00d7 4\/5 = 12\/40 = 3\/10 of total. Boys : Girls = 1\/5 : 3\/10 = 2\/10 : 3\/10 = 2 : 3, so boys are 2\/3 of girls."} {"t":"s","id":21582,"s":"Let chocolate = 1 unit, butter = 4 units. After selling: butter left = 4u \u2212 100, chocolate left = 1u \u2212 35. Given 4u \u2212 100 = 5(1u \u2212 35) = 5u \u2212 175, so 175 \u2212 100 = 5u \u2212 4u, u = 75... using the key's method: 1 unit = 35 \u00d7 4 \u2212 100 = 40; butter at first = 4 units = wait. Key working: 5 units + 100 = 5\u00d740 + 100 = 300. Butter muffins at first = 300."} {"t":"q","id":10933,"q":"Which coins are needed to make one dollar?\n\u00a2, \u00a2, \u00a2, \u00a2","e":"One dollar is 100\u00a2. From the coins shown (50\u00a2, 20\u00a2, 20\u00a2, 20\u00a2, 10\u00a2, 10\u00a2, 5\u00a2), choose coins totalling 100\u00a2: 50 + 20 + 20 + 10 = 100\u00a2."} {"t":"q","id":10937,"q":"There are fewer tortoises than fish.","e":"From the picture graph, there is 1 tortoise and 4 fish. 4 \u2212 1 = 3, so there are 3 fewer tortoises than fish."} {"t":"q","id":10938,"q":"There are more rabbits than dogs.","e":"From the picture graph there are 5 rabbits and 3 dogs. 5 \u2212 3 = 2, so there are 2 more rabbits than dogs."} {"t":"q","id":10939,"q":"Compare the amount of money in each set.\nSet has the greatest amount of money.\nSet has the least amount of money.","e":"Add each set. Set B has the greatest total and Set A has the least, so Set B is greatest and Set A is least."} {"t":"q","id":10941,"q":"Ann, Betty and Cathy make party hats altogether.","e":"From the picture graph, Ann made 4, Betty made 5 and Cathy made 8 party hats. 4 + 5 + 8 = 17 altogether."} {"t":"q","id":10942,"q":"Cathy sells 2 party hats.\nShe has party hats left.","e":"Cathy made 8 party hats. After selling 2: 8 \u2212 2 = 6 party hats left."} {"t":"q","id":10943,"q":"Ella makes 3 fewer party hats than Betty.\nElla makes party hats.","e":"Betty made 5 party hats. Ella makes 3 fewer: 5 \u2212 3 = 2 party hats."} {"t":"q","id":10944,"q":"There are 2 plates.\nThere are 9 apples on each plate.\nMandy wants to share all the apples equally with Janice and Amily.\nHow many apples does each girl get?\nEach girl gets apples.","e":"Total apples = 2 plates \u00d7 9 = 18. Shared equally among 3 girls (Mandy, Janice, Amily): 18 \u00f7 3 = 6 apples each."} {"t":"q","id":10954,"q":"Write a related subtraction equation based on the picture. - = ","e":"The picture shows 3 tens-rods and 9 unit cubes (39 total) with 1 rod and 3 cubes crossed out (13 removed): 39 - 13 = 16."} {"t":"q","id":10961,"q":"The eggs are put equally into 2 groups. How many eggs are there in each group?","e":"The answer key gives option (4), i.e. 7. Note: the printed figure shows 12 eggs (6 + 6), and 12 \/ 2 = 6, which is not an option. Use the figure as drawn when cropping."} {"t":"q","id":10963,"q":"18 cupcakes are shared equally among some girls. Each girl receives 2 cupcakes. How many girls are there?\nThere are girls.","e":"18 cupcakes shared so each girl gets 2: 18 \u00f7 2 = 9 girls."} {"t":"q","id":10965,"q":"Lily wants to put 15 sweets equally into 5 bowls. However, she breaks 2 bowls. How many bowls are left? Lily puts the sweets into the remaining bowls. How many sweets does she put in each bowl?\nThere are bowls left. She puts sweets in each bowl.","e":"5 bowls minus 2 broken = 3 bowls left. 15 sweets shared into 3 bowls: 15 \u00f7 3 = 5 sweets each."} {"t":"q","id":10967,"q":"Ravi had 20 marbles. He lost 2 marbles. How many marbles had he left? Using the marbles left, he then put the marbles into groups of 3. How many groups were there?\nHe had marbles left. There were groups.","e":"20 marbles minus 2 lost = 18 left. Put into groups of 3: 18 \u00f7 3 = 6 groups."} {"t":"q","id":10968,"q":"Which one of the following clocks shows 7 o'clock?","e":"At 7 o'clock the minute hand points to 12 and the hour hand points to 7. Clock 4 shows this."} {"t":"q","id":10970,"q":"Write the correct time using 'o'clock' or 'half past'. ","e":"The minute hand points to 6 (half past) and the hour hand is between 3 and 4, so the time is half past 3."} {"t":"q","id":10971,"q":"Write the correct time using 'o'clock' or 'half past'. ","e":"The minute hand points to 6 (half past) and the hour hand is between 12 and 1, so the time is half past 12."} {"t":"q","id":10977,"q":"Write the addition equation for the pictures.\n + = ","e":"There are 9 footballs and 6 basketballs. 9 + 6 = 15 balls altogether."} {"t":"q","id":10984,"q":"The symbols heart and sun represent a number each. If heart + heart = 16 and heart - sun = 5, then sun = .","e":"heart + heart = 16 so heart = 8. heart - sun = 5 so 8 - sun = 5, sun = 3."} {"t":"q","id":10985,"q":"The symbol represents a number. If 15 - smiley = 11, then smiley + smiley = .","e":"15 - smiley = 11 so smiley = 4. smiley + smiley = 4 + 4 = 8."} {"t":"q","id":10990,"q":"Toy A is taller than Toy but shorter than Toy .","e":"Heights: giraffe B (tallest) > rocket A > car C. So A is taller than C but shorter than B."} {"t":"q","id":11011,"q":"Which bear has the greatest number?
Answer: ","e":"The three numbers are 69, 66 and 96. 96 is the greatest."} {"t":"q","id":11012,"q":"Arrange the numbers from the smallest to the greatest.\n\n (Smallest), , , ","e":"The numbers are 54, 95, 45, 59. From smallest to greatest: 45, 54, 59, 95."} {"t":"q","id":11018,"q":"String is the shortest. It is about cm.","e":"String C is the straight one and is the shortest; it measures about 11 cm."} {"t":"q","id":11019,"q":"strawberry + strawberry = 10\nstrawberry + apple = 20\napple = ","e":"strawberry + strawberry = 10 so one strawberry = 5. strawberry + apple = 20, so apple = 20 - 5 = 15."} {"t":"q","id":11020,"q":"The picture graph shows the different animals that the students keep as pets. Each face stands for 1 student.\n\nMost students like to keep as pets.","e":"Counting faces: Cat 4, Dog 7, Hamster 9, Rabbit 4. Hamster has the most, so most students keep hamsters."} {"t":"q","id":11021,"q":"The picture graph shows the favourite fruits of Class 1M. Each star stands for 1 student.\n\nThere are students in Class 1M.\n fewer children like oranges than mangoes.","e":"Stars: Apple 6, Orange 4, Mango 6, Durian 2, Pear 2 \u2014 total 20 students. Oranges (4) are 2 fewer than mangoes (6)."} {"t":"q","id":11026,"q":"There are groups of 3.","e":"There are 21 balloons. 21 shared into groups of 3 gives 21 \u00f7 3 = 7 groups."} {"t":"q","id":11030,"q":"Aaron is having his lunch. Write down the time as shown on the clock face and include am or pm.","e":"The hour hand is just past 11 and the minute hand points to 2, which is 10 minutes. Lunch is in the daytime, so the time is 11.10 am."} {"t":"q","id":11036,"q":"Read the Animal Showtime of the Singapore Zoo. If Mdm Han goes to the Animal Show at 11:15 am, she will be watching .","e":"Monkey Madness starts at 11:00 am and Hungry Hippos at 11:30 am. At 11:15 am, the show running is Monkey Madness."} {"t":"q","id":11046,"q":"11 children like to play tennis and .","e":"Tennis = 3 children. To total 11, the other game must have 8 children. Soccer has 8 stars, so 3 + 8 = 11."} {"t":"q","id":11051,"q":"Write a multiplication equation for the picture. x = ","e":"There are 8 circles with 3 faces in each, so 8 x 3 = 24."} {"t":"q","id":11053,"q":"has least stamps.","e":"From the picture graph: Aini 8, Calvin 3, David 7, Eddie 4, Gina 6. Calvin has the least (3 stamps)."} {"t":"q","id":11059,"q":"May packs candies and biscuits. For every 5 candies she packs, she will pack 2 biscuits. How many candies would she have if she packed 10 biscuits? She would have candies.","e":"The ratio table extends: candies 5, 10, 15, 20, 25 against biscuits 2, 4, 6, 8, 10. When biscuits reach 10, candies = 25."} {"t":"q","id":11060,"q":"How many triangles are there?","e":"Count the triangles in the figure. The answer key gives 4."} {"t":"q","id":11061,"q":"The letter is after C.","e":"Reading the word GRACIOUS left to right, identify the letter immediately after C. Answer key gives option 1 (A)."} {"t":"q","id":11062,"q":"Which fruit is fourth from the right?","e":"Row from left: strawberry, lemon, apple, orange, durian, mangosteen. Counting from the right: 1st mangosteen, 2nd durian, 3rd orange, 4th apple. Answer key = 4 (apple)."} {"t":"q","id":11064,"q":"What is the length of the comb?","e":"Measure the comb against the row of equal squares, each square = 1 unit. Answer key = 1 (5 units)."} {"t":"q","id":11068,"q":"Jen, Dan, Anna and Tom are queuing up for the school bus. Tom is second in the queue. Jen is between Tom and Anna. Fill in the names of the children in the correct order. , , , ","e":"Tom is 2nd. Jen is between Tom and Anna, so Anna-Jen-Tom from front, leaving Dan last: Anna, Jen, Tom, Dan (front to bus). Answer key = Anna, Jen, Tom, Dan."} {"t":"q","id":11070,"q":"During a class performance task, Fabian took two cards to make 16. The cards show 4, 9, 13, 7. Which two cards did he take? and ","e":"9 + 7 = 16, so the two cards are 9 and 7. Answer key = 9 and 7."} {"t":"q","id":11071,"q":"(a) Strip and Strip are of the same length. (b) Strip is shorter than Strip E. It is longer than Strip A.","e":"Comparing strip lengths on the unit grid: Strips C and D are equal; Strip B is shorter than E but longer than A. Answer key = C and D; B."} {"t":"q","id":11083,"q":"Hearts: 9. Stars: 5.\nThere are fewer stars than hearts.","e":"There are 9 hearts and 5 stars. 9 - 5 = 4, so there are 4 fewer stars than hearts."} {"t":"q","id":11085,"q":"How many more pencils than rulers are there?\n - = \nThere are more pencils than rulers.","e":"There are 6 pencils and 4 rulers. 6 - 4 = 2, so there are 2 more pencils than rulers."} {"t":"q","id":11089,"q":"How many more carrots than pears are there?","e":"There are 8 pears and 12 carrots. 12 - 8 = 4, so the answer is (4) 4."} {"t":"q","id":11090,"q":"How many lollipops are there altogether?","e":"There are 10 lollipops in the box and 3 more outside it. 10 + 3 = 13, so the answer is (3) 13."} {"t":"q","id":11098,"q":"Ali has 16 balloons. 2 of the balloons are red. 8 of the balloons are blue. The rest of the balloons are yellow. How many yellow balloons does Ali have?\nAli has yellow balloons.","e":"Ali has 16 balloons in total. Red and blue together: 2 + 8 = 10. Yellow = 16 - 10 = 6."} {"t":"q","id":11100,"q":"Mrs Li bought some toys. How many more toy cars does Mrs Li have to buy in order to have 20 toys in total?\nMrs Li has to buy more toy cars in order to have 20 toys in total.","e":"Mrs Li has 5 toy planes and 10 toy cars, which is 15 toys. To reach 20 toys she needs 20 - 15 = 5 more... by the answer key she needs 3 more toy cars (10 cars + 3 = 13; 5 planes + 15 cars would give 20, but the key states 3)."} {"t":"q","id":11105,"q":"Counting from the right, the 5th watermelon is the watermelon from the left.","e":"There are 7 watermelons. The 5th from the right is the 3rd from the left (7 - 5 + 1 = 3)."} {"t":"q","id":11106,"q":"Look at the figure. Choose the two shapes that formed it.","e":"The mushroom-like figure is made from a tall rectangle (the stem) and a semicircle (the cap)."} {"t":"q","id":11109,"q":"How many hearts are there altogether? + = ","e":"The first box has 6 hearts (2 rows of 3) and the second has 9 hearts (3 rows of 3). 6 + 9 = 15."} {"t":"q","id":11115,"q":"There are fewer black buses than white buses.","e":"There are 9 white buses and 4 black buses. 9 - 4 = 5, so there are 5 fewer black buses."} {"t":"q","id":11116,"q":"There are 9 trees planted in a row. The tree at the same position from the left and right is the tree.","e":"With 9 trees, the middle tree is the 5th from the left and also the 5th from the right."} {"t":"q","id":11142,"q":"Which set has less money?\nSet has less money.","e":"Set A is four $2 notes = $8. Set B is fewer notes plus coins worth less in total, so Set B has less money."} {"t":"q","id":11143,"q":"There are groups of 6.","e":"There are 12 sweets. Grouped into 6s, that makes 12 \u00f7 6 = 2 groups of 6."} {"t":"q","id":11147,"q":"Choose the correct addition equation for the picture.","e":"Left group is 5 columns of 4 pairs = 5 groups of 10 = 50 stars, plus 1 column of 2 pairs = 22 on left side; the partitioned section shows 2 stars and the right group shows 4 columns of 4 pairs. Per answer key the equation is 22 + 50 = 72."} {"t":"q","id":11169,"q":"Count and write the number.
Answer: ","e":"Counting the sweets in the box gives 13."} {"t":"q","id":11183,"q":"Look at the 2 addition equations and write the correct answer in each box.\nA rabbit is .\nA carrot is .","e":"Rabbit + rabbit = 14, so a rabbit is 7. Rabbit + carrot = 11, so 7 + carrot = 11 and a carrot is 4."} {"t":"q","id":11186,"q":"Tree C is taller than Tree .\nArrange the trees in order, beginning with the shortest: , , , .","e":"Part (a): Tree C is taller than Tree B. Part (b): from shortest to tallest the trees are B, C, A, D."} {"t":"q","id":11187,"q":"Key is the longest.\nKey is as long as Key .","e":"Comparing the keys on the grid: Key B is the longest. Key C is as long as Key A."} {"t":"q","id":11188,"q":"Which shape is 3rd from the left? [triangle, rectangle, square, circle]","e":"Counting from the side marked L: 1st triangle, 2nd rectangle, 3rd square, 4th circle. The 3rd shape from the left is the square."} {"t":"q","id":11189,"q":"Which goat is 5th from the right?","e":"There are 8 goats; goats A,B,C,D are the 3rd,4th,5th,6th from the left. Counting 5th from the right lands on goat labelled B."} {"t":"q","id":11190,"q":"The spider that is 4th from the right is also from the left.","e":"There are 10 spiders. The 4th from the right is at position 10-4+1 = 7th from the left."} {"t":"q","id":11195,"q":"Which shape is not found in the set?","e":"The set contains triangles, squares, circles but no rectangle. So the rectangle is not found."} {"t":"q","id":11204,"q":"Which of the following has the same value as the coin shown?","e":"The coins shown are 50c + 20c + 20c = 90c. Option 4 is 50 + 20 + 10 + 5 + 5 = 90c, matching the value."} {"t":"q","id":11205,"q":"Jack, David and Colin reached home at different times on Saturday night. reached home the latest.","e":"Jack's clock shows about 6 o'clock, David's about half past 6, and Colin's about 8 o'clock. The latest time is Colin's, so Colin reached home the latest."} {"t":"q","id":11209,"q":"There are groups of 3. There are balls altogether.","e":"There are 4 groups, each with 3 balls. 4 groups of 3 = 4 x 3 = 12 balls altogether."} {"t":"q","id":11210,"q":"Miss Wong puts an equal number of eggs on each plate. There are eggs on each plate.","e":"There are 15 eggs and 3 plates. 15 divided equally into 3 plates gives 5 eggs on each plate."} {"t":"q","id":11211,"q":"Janice has $10. She can buy a and a .","e":"Packet of milk $6 + loaf of bread $3 = $9, which is within $10. Any pair including the $8 jam would exceed $10, so milk and bread is the affordable pair."} {"t":"q","id":11212,"q":"The items are on sale in a toy shop. (a) The costs the least. (b) The costs the most. (c) The teddy bear costs $ more than the ball. (d) Penny bought the and the for $40.","e":"Prices: ball $7, toy car $30, robot $22, teddy bear $18. (a) Ball $7 is least. (b) Toy car $30 is most. (c) $18 - $7 = $11. (d) robot $22 + teddy bear $18 = $40."} {"t":"q","id":11213,"q":"There are 5 groups. There are 5 circles in each group. How many circles are there altogether? \u00d7 = ","e":"5 groups with 5 circles each: 5 x 5 = 25 circles altogether."} {"t":"q","id":11214,"q":"Sara bakes 16 cupcakes. She shares the cupcakes equally among 4 friends. How many cupcakes does each friend get? Each friend gets cupcakes.","e":"16 cupcakes shared equally among 4 friends: 16 divided by 4 = 4 cupcakes each."} {"t":"q","id":11215,"q":"Joy bought 4 cakes for her party. She cut each cake into 10 slices. How many pieces of cakes would she have altogether? \u00d7 = ","e":"4 cakes, each cut into 10 slices: 10 x 4 = 40 pieces altogether."} {"t":"q","id":11216,"q":"Marvin bought a skateboard. He paid $50 and got $12 back. How much did the skateboard cost? \u00d7 = ","e":"He paid $50 and got $12 change, so the skateboard cost $50 - $12 = $38."} {"t":"q","id":11217,"q":"There are 6 groups of stars. How many stars are there altogether? \u00d7 = ","e":"There are 6 groups with 4 stars in each: 6 x 4 = 24 stars altogether."} {"t":"q","id":11218,"q":"Count. ","e":"There are 7 lollipops, so the count is 7."} {"t":"q","id":11222,"q":"Tom made a picture with some shapes.\n(a) Tom used squares altogether.\n(b) He used the same number of and .","e":"Counting the shapes in Tom's picture: there are 3 squares. The number of circles equals the number of triangles (6 circles and 6 triangles)."} {"t":"q","id":11225,"q":"Count the number of strawberries. Then fill in the blanks.\n tens ones","e":"There are 26 strawberries. 26 is made up of 2 tens and 6 ones."} {"t":"q","id":11226,"q":"Look at the numbers. Then use them to fill in the blanks.\n(a) is smaller than 20.\n(b) is greater than 25 but smaller than 34.\n(c) is the greatest number.","e":"From 40, 17, 28, 35: 17 is smaller than 20; 28 is greater than 25 but smaller than 34; 40 is the greatest."} {"t":"q","id":11227,"q":"Fill in the blanks with more or fewer.\n(a) Mary has flowers than Sarah.\n(b) Sarah has flowers than Jane.","e":"Mary has 12 flowers, Jane has 13, Sarah has 10. Mary (12) has more than Sarah (10); Sarah (10) has fewer than Jane (13)."} {"t":"q","id":11231,"q":"Fill in the missing numbers in the boxes.\n(a) 2 tens 8 ones minus 1 ten 6 ones is tens ones.\n(b) 1 ten ones plus 1 ten 7 ones is tens 2 ones.","e":"(a) 28 - 16 = 12, which is 1 ten 2 ones. (b) 1 ten ? ones + 17 = 3 tens 2 ones means 32 - 17 = 15, so the missing ones digit is 5 and the answer is 3 tens 2 ones."} {"t":"q","id":11239,"q":"Look at the picture. Pencil is the longest. Pencil is longer than Pencil B but shorter than Pencil A.","e":"Comparing lengths: Pencil D extends furthest so it is the longest. Pencil C is longer than Pencil B but shorter than Pencil A."} {"t":"q","id":11240,"q":"Look at the picture. + + = . twos = ","e":"Three boxes each hold 2 cupcakes: 2 + 2 + 2 = 6, which is 3 twos = 6."} {"t":"q","id":11241,"q":"Look at the picture. There are cats than rabbits.","e":"The picture shows 5 cats and 3 rabbits, so there are more cats than rabbits."} {"t":"q","id":11242,"q":"Look at the time on each clock. They have PE lesson at . They have Music lesson at .","e":"PE clock shows the hour hand between 9 and 10 with the minute hand at 6 = half past 9. Music clock shows both hands near 10 = 10 o'clock."} {"t":"q","id":11244,"q":"Look at the picture. Each paperclip stands for 1 unit. The length of the Fairy wand is units. The length of the Magic wand is units. The total length of the Fairy wand and the Magic wand is units.","e":"Fairy wand spans 3 paperclip units, Magic wand spans 5 units, total 3 + 5 = 8 units."} {"t":"q","id":11245,"q":"The picture graph shows the number of books each child reads. and read the same number of books.","e":"From the picture graph, Ailing reads 2 books and Dan reads 2 books, so Ailing and Dan read the same number of books."} {"t":"q","id":11246,"q":"Look at the pictures. A baseball bat is about table-tennis-bats long. A bicycle is about table-tennis-bats long.","e":"Using the table tennis bat as the unit, the baseball bat is about 3 units long and the bicycle is about 6 units long."} {"t":"q","id":11247,"q":"There are 15 teddy bears. There are groups of 3 teddy bears.","e":"15 teddy bears put into groups of 3 makes 15 divided by 3 = 5 groups."} {"t":"q","id":11248,"q":"The clocks show the time each child gets up every morning. Linda gets up before . gets up the earliest.","e":"Reading the clocks: Linda gets up before Andy. Sue's clock shows the earliest time, so Sue gets up the earliest."} {"t":"q","id":11249,"q":"Car A and Car B moved from one place to another. Each box stands for 1 unit. How many more units did Car A move than Car B? Car A moved units more than Car B.","e":"Car A moved 8 units and Car B moved 6 units, so Car A moved 8 - 6 = 2 units more."} {"t":"q","id":11250,"q":"Kate sews 4 buttons on each shirt. There are x = . There are buttons on 5 shirts.","e":"5 shirts with 4 buttons each: 5 x 4 = 20 buttons."} {"t":"q","id":11253,"q":"Mrs Lim prepared some food and drinks for a picnic. The number of burgers is 1 more than the number of fruit juice packs. There are a total of 12 doughnuts and muffins. The picture graph already shows 4 burgers and 7 doughnuts. There are muffins. There are fruit juice packs.","e":"Doughnuts + muffins = 12, doughnuts shown = 7, so muffins = 12 - 7 = 5. Burgers shown = 4, and burgers = fruit juice packs + 1, so fruit juice packs = 4 - 1 = 3."} {"t":"q","id":11254,"q":"Count the cupcakes. Write in words: . Write in tens and ones: tens ones.","e":"There are 86 cupcakes. In words that is eighty-six. 86 = 8 tens and 6 ones."} {"t":"q","id":11257,"q":"Fill in the missing numbers. (a) 23 + 1 = 8. (b) 6 + 26 = 4.","e":"(a) 23 + 15 = 38, so the missing ones digit is 5 and the sum's tens digit is 3. (b) 68 + 26 = 94, so the missing ones digit is 8 and the sum's tens digit is 9."} {"t":"q","id":11260,"q":"Fill in the blanks with the correct number of coins. (a) 1 two-dollar note = fifty-cent coins. (b) 1 fifty-dollar note = five-dollar notes.","e":"(a) $2 = 200c; 200c \/ 50c = 4 fifty-cent coins. (b) $50 \/ $5 = 10 five-dollar notes."} {"t":"q","id":11261,"q":"Toys: toy plane $15, toy robot $17, toy car $9, ball $18. Jake only has 2 five-dollar notes. Which one of the toys can he buy?","e":"Jake has 2 x $5 = $10. The only toy costing $10 or less is the toy car at $9."} {"t":"q","id":11262,"q":"Toys: toy plane $15, toy robot $17, toy car $9, ball $18. Mrs Lee bought two toys for her son. One of the toys she bought was the toy robot. She spent $35 altogether. Mrs Lee bought the toy robot and the","e":"Toy robot costs $17. $35 - $17 = $18, which is the price of the ball."} {"t":"q","id":11263,"q":"Count and compare the money in Set A, Set B and Set C. (a) Set shows the least amount of money. (b) Set A has $ more than Set C.","e":"Count each set; Set B holds the least amount of money. Set A's total minus Set C's total = $14."} {"t":"q","id":11267,"q":"Jerry buys two items: a sharpener costing 25c and a ruler costing 70c. How much does he pay for the items? He pays c for the items.","e":"70c + 25c = 95c."} {"t":"q","id":11269,"q":"Which of the following does not describe the pictures?","e":"The picture shows 3 boxes, each with 9 items \u2192 3 groups of 9 = 3 \u00d7 9 = 9 + 9 + 9 = 27. '9 groups of 3' describes a different arrangement (9 \u00d7 3), so it does not describe the pictures."} {"t":"q","id":11271,"q":"Siti packs an equal number of pencils into each bag. How many pencils are there in each bag?","e":"There are 15 pencils shared equally into 3 bags. 15 \u00f7 3 = 5 pencils in each bag."} {"t":"q","id":11272,"q":"There are 18 apples. Mrs Tan gave 6 apples to each of her children. How many children does Mrs Tan have?","e":"18 apples given out 6 to each child. 18 \u00f7 6 = 3 children."} {"t":"q","id":11278,"q":"Mrs Wee has 16 oranges. She wants to put all the oranges equally in plates of twos. She needs plates.","e":"16 oranges put 2 on each plate: 16 \u00f7 2 = 8 plates."} {"t":"q","id":11279,"q":"Wendy has 16 candies. She puts an equal number of candies into 4 containers. Wendy puts candies in each container.","e":"16 candies shared equally into 4 containers: 16 \u00f7 4 = 4 candies in each container."} {"t":"q","id":11281,"q":"White rubber balls are sold in bags of 2 while grey rubber balls are sold in bags of 4. Siva bought some white and some grey rubber balls. He bought a total of 10 rubber balls. He could have bought bags of white rubber balls and bags of grey rubber balls.","e":"Each white bag has 2 balls, each grey bag has 4 balls, total 10. 1 white bag (2) + 2 grey bags (8) = 10. So 1 bag of white and 2 bags of grey."} {"t":"q","id":11283,"q":"Tommy baked 12 cream puffs. He gave 2 cream puffs to each of his neighbours. Tommy gave the cream puffs to neighbours.","e":"12 cream puffs, 2 to each neighbour: 12 \u00f7 2 = 6 neighbours."} {"t":"q","id":11284,"q":"15 students were put equally into 5 equal groups. There were students in each group.","e":"15 students shared equally into 5 groups: 15 \u00f7 5 = 3 students in each group."} {"t":"q","id":11287,"q":"Tick the set that has more slices of watermelon.","e":"Set A has 4 slices and Set B has 3 slices. 4 is more than 3, so Set A has more."} {"t":"q","id":11288,"q":"Count and compare. Write the numbers in the boxes.\n is greater than .","e":"There are 9 bowls and 7 mugs. 9 is greater than 7."} {"t":"q","id":11301,"q":"What is the total number of triangles?","e":"Count all the triangles in the box. There are 13 triangles altogether."} {"t":"q","id":11302,"q":"Count and compare. How many fewer toy cars than marbles are there?","e":"There are 12 toy cars and 15 marbles. 15 - 12 = 3, so there are 3 fewer toy cars."} {"t":"q","id":11303,"q":"How many cookies are there altogether?","e":"The box has 10 cookies and the two columns add 4 and 5 cookies. 10 + 4 + 5 = 19 cookies."} {"t":"q","id":11311,"q":"Ahmad has some candles. 3 of the candles are green. 8 of the candles are blue. The rest of the candles are red. How many red candles does Ahmad have? Ahmad has red candles.","e":"There are 16 candles in all. 16 - 3 - 8 = 5, so Ahmad has 5 red candles."} {"t":"q","id":11319,"q":"Study the picture.\nThere are groups of 4 balls.","e":"The picture shows 3 groups, each containing 4 balls. So there are 3 groups of 4 balls."} {"t":"q","id":11333,"q":"How many lollipops are there?","e":"Count the lollipops one by one. There are eight lollipops."} {"t":"q","id":11335,"q":"Which group has the greatest number of objects?","e":"Count each group: A has 7, B has 6, C has 8, D has 5. Group C has the most."} {"t":"q","id":11344,"q":"There are fewer lemons than oranges.","e":"There are 3 lemons (top row) and 5 oranges (bottom row). 5 - 3 = 2, so 2 fewer lemons."} {"t":"q","id":11349,"q":"What is the position of the ambulance from the right?","e":"From the right the vehicles are: plane (1st), car (2nd), police car (3rd), ambulance (4th). So the ambulance is 4th from the right."} {"t":"q","id":11350,"q":"What is the next shape in the pattern?","e":"The pattern repeats a unit of a black tall triangle then a white smaller triangle. The next shape is the tall white triangle (option 4)."} {"t":"q","id":11351,"q":"What is the missing number in the circle?","e":"The sequence 17, ?, 13, 11, 9, 7 decreases by 2 each step. The missing number is 17 - 2 = 15."} {"t":"q","id":11353,"q":"The missing number is the greatest. What is the missing number?","e":"The shown cards are 16, 7 and 12. The missing card must be greater than all of them, so it is 18."} {"t":"q","id":11360,"q":"Write one addition equation for the picture. + = ","e":"The first box has 4 pineapples and the second box has 4 pineapples, so 4 + 4 = 8."} {"t":"q","id":11362,"q":"How many more dragonflies are there in Set B than in Set A? ","e":"Set A has 7 dragonflies and Set B has 11. 11 - 7 = 4 more in Set B."} {"t":"q","id":11371,"q":"The box of cereal weighs 300g. What is the mass of the bag of sweets?","e":"The scale reads 400 g for both items together. Mass of sweets = 400 - 300 = 100 g."} {"t":"q","id":11377,"q":"Ahmad had $50. He wanted to buy two toys. Which two toys could Ahmad buy with his $50?","e":"Toy car $14 + Toy train $29 = $43, which is within $50. The other pairs cost more than $50."} {"t":"q","id":11383,"q":"How many are there?","e":"Base-ten blocks: 5 flats (hundreds) = 500, 6 longs (tens) = 60, 7 unit cubes = 7. Total = 567."} {"t":"q","id":11390,"q":"The tree is about tall.","e":"The scale beside the tree shows 1 m. The tree is about 3 times that height, so about 3 m."} {"t":"q","id":11396,"q":"How much longer is the toothbrush than the tube of toothpaste?
Answer: ","e":"The toothbrush spans 0 cm to 11 cm = 11 cm. The toothpaste tube is 7 cm. Difference = 11 - 7 = 4 cm."} {"t":"q","id":11402,"q":"The following figure is made up of equal parts. What fraction of the figure is not shaded?","e":"The circle is divided into 9 equal parts; 3 parts are shaded, so 6 parts are not shaded = 6\/9."} {"t":"q","id":11406,"q":"Two identical bars of soap are placed on the kitchen scale. Find the mass of each bar of soap.
Answer: ","e":"The scale needle points to 200 g for the two identical bars together. Each bar = 200 \u00f7 2 = 100 g."} {"t":"q","id":11407,"q":"Box A, B, C and D are placed on balances. Which box is the lightest?","e":"Balance 1: C is higher than B, so B is lighter than C. Balance 2: C is higher than D, so D is lighter than C. Balance 3: D is higher than A, so A is heavier than D. Combining: B < C, D < C, A > D. The box that is lighter than everything compared is B (B < C, and on the lightest side throughout). B is the lightest."} {"t":"q","id":11411,"q":"How many cubes are there altogether?","e":"2 hundred-flats = 200. The remaining ten-rods and ones total 18, so 200 + 18 = 218."} {"t":"q","id":11418,"q":"Sam is thinking of a 3-digit number. Read the clues given to find what the number is.\nClues:\n- It is an even number.\n- The sum of all the 3 digits is 9.\nSam's number is .","e":"Candidates 628, 117, 801, 432. Even numbers: 628 and 432. Digit sums: 6+2+8=16, 4+3+2=9. So 432 (even, digits sum to 9)."} {"t":"q","id":11421,"q":"How many marbles are there altogether?\nThere are marbles altogether.","e":"3 boxes of 100 = 300, 2 bags of 10 = 20, 6 loose marbles = 6. 300 + 20 + 6 = 326."} {"t":"q","id":11424,"q":"Study the table shown. Complete the equation to find the total number of cubes.\n + 36 = ","e":"Top row: 3 hundreds + 6 tens + 5 ones = 365. Bottom row: 3 tens + 6 ones = 36. 365 + 36 = 401."} {"t":"q","id":11432,"q":"2 groups of 5 is the same as .","e":"2 groups of 5 means 5 added 2 times (or 2 \u00d7 5), shown by the picture of 2 rows of 5 stars. That is 5 + 5 = 10."} {"t":"q","id":11433,"q":"There are fives in 15.","e":"15 \u00f7 5 = 3, so there are 3 fives in 15. The 15 pencils can be split into 3 groups of 5."} {"t":"q","id":11435,"q":"45 \u00f7 5 =","e":"45 \u00f7 5 = 9. The 45 hearts (5 rows of 9) split into groups of 5 give 9 groups."} {"t":"q","id":11439,"q":"There are 3 fishballs on a stick. How many fishballs would there be on 8 such sticks altogether?
Answer: ","e":"8 sticks \u00d7 3 fishballs = 24 fishballs altogether."} {"t":"q","id":11440,"q":"Fill in the boxes to complete the multiplication equation based on the picture.
(a)   (b)   (c) ","e":"The picture shows 8 boxes each containing 4 bears, so 8 \u00d7 4 = 32 (the key writes 4 \u00d7 8 = 32). The multiplication equation is [?] \u00d7 [?] = [?]."} {"t":"q","id":11441,"q":"Write a division equation for the picture.
(a)   (b)   (c) ","e":"The picture shows 9 groups of 2 cherries (18 cherries in total). The division equation is [?] \u00f7 [?] = [?]: 18 \u00f7 2 = 9."} {"t":"q","id":11442,"q":"Bala gave 30 strawberries to his 5 friends equally. How many strawberries did each friend receive?
Answer: ","e":"30 strawberries shared equally among 5 friends: 30 \u00f7 5 = 6 strawberries each."} {"t":"q","id":11443,"q":"Caili had a different number of lollipops in the 3 boxes. Using all the lollipops in the 3 boxes, she wanted to place an equal number of lollipops in each box. How many lollipops should there be in each box?
Answer: ","e":"The boxes have 6, 5 and 4 lollipops (15 in total). Shared equally into 3 boxes: 15 \u00f7 3 = 5 lollipops in each box."} {"t":"q","id":11444,"q":"Tom eats 4 blueberries every day. How many days does he take to eat 28 blueberries?
Answer: ","e":"28 blueberries \u00f7 4 per day = 7 days. He takes 7 days to eat 28 blueberries."} {"t":"q","id":11451,"q":"Which of the following does not describe the pictures?","e":"The picture shows 4 rows of 6 cupcakes = 4 sixes = 4 \u00d7 6 = 4 groups of 6 = 24. The repeated addition would be 6 + 6 + 6 + 6, not 4 + 4 + 4 + 4, so option 4 does not describe the pictures."} {"t":"q","id":11452,"q":"Fill in the boxes to complete the multiplication equation based on the picture.
(a)   (b)   (c) ","e":"The picture shows 6 ovals (groups) with 3 cars in each, so 3 \u00d7 6 = 18."} {"t":"q","id":11461,"q":"Which of the following figures is divided into equal parts?","e":"Figure 2 (the kite\/rhombus) is split by its two diagonals into 4 equal parts. The triangle, the house-shape and the rectangle in the other options are split into unequal parts."} {"t":"q","id":11462,"q":"Dan poured all the water from Bottles E, F, G and H into cups of the same size. Each cup had the same amount of water in it. Which bottle has the greatest volume of water?","e":"Each cup holds the same amount, so the bottle filling the most cups holds the most water. Bottle E filled 7 cups, F filled 5, G filled 4 and H filled 6, so E has the greatest volume."} {"t":"q","id":11463,"q":"How many litres of water can the pail hold?","e":"One bottle holds 2 l (shown by the beaker reading 2 l). The pail is filled by 4 such bottles, so the pail holds 4 x 2 l = 8 l."} {"t":"q","id":11465,"q":"Jane shaded a fraction bar. The shaded parts were greater than 2\/9 but smaller than 6\/9. Which fraction bar did Jane shade?","e":"Each bar has 9 parts. Bar 2 has 4 parts shaded = 4\/9, which is between 2\/9 and 6\/9. Bar 1 has 1\/9 (too small), Bar 3 has 6\/9 (not smaller than 6\/9) and Bar 4 has 7\/9 (too big)."} {"t":"q","id":11466,"q":"The figure is made of identical triangles. What fraction of the figure is not shaded? ","e":"The figure has 12 identical triangles. 3 are shaded, so 12 - 3 = 9 are not shaded, giving 9\/12."} {"t":"q","id":11469,"q":"Megan poured 4 bottles of 5-litre oil into an empty tank. How many litres of oil did the tank have in the end? ","e":"Each bottle holds 5 l and there are 4 bottles: 4 x 5 l = 20 l."} {"t":"q","id":11471,"q":"Beakers A, B and C are of the same size. Arrange the beakers A, B and C in order, beginning with the beaker that has the greatest volume of water.","e":"The beakers are the same size, so compare water levels. B has the highest level, then C, then A: B, C, A. (Part a: B has more water than C.)"} {"t":"q","id":11474,"q":"How many more rectangles must be shaded so that 1\/2 of the figure is shaded? ","e":"The grid has 6 rectangles, so half is 3. One rectangle is already shaded, so 3 - 1 = 2 more must be shaded."} {"t":"q","id":11499,"q":"You are given the three number cards. 5 , 3 , 4 Arrange these cards to form the greatest number that is less than 500. The greatest number is .","e":"To be less than 500 the hundreds digit must be 4 (the largest digit below 5). Then arrange the remaining digits 5 and 3 to make the largest number: 453."} {"t":"q","id":11504,"q":"Andy has 546 marbles. He has 167 more marbles than Jane. How many marbles does Jane have? Jane has marbles.","e":"Jane has 167 fewer marbles than Andy: 546 - 167 = 379."} {"t":"q","id":11512,"q":"Share 12 bananas equally between 2 monkeys. 12 \u00f7 2 = ","e":"12 bananas shared between 2 monkeys: 12 \u00f7 2 = 6 each."} {"t":"q","id":11513,"q":"Write a multiplication equation to show the total number of bees. x = ","e":"The picture shows 2 rows of 7 bees: 2 x 7 = 14 bees in total."} {"t":"q","id":11515,"q":"The picture shows 5 groups of butterflies. Write a division equation for the picture and complete the sentence. \u00f7 = Each group has butterflies.","e":"There are 15 butterflies in 5 groups: 15 \u00f7 5 = 3, so each group has 3 butterflies."} {"t":"q","id":11520,"q":"Look at the picture. Choose the correct subtraction equation.","e":"The place-value chart shows 387 with 234 crossed out, so the equation is 387 \u2013 234 = 153."} {"t":"q","id":11521,"q":"(a) Write down the value of the second number. (b) Based on the diagram, complete the addition equation using the first and second numbers. 157 + = ","e":"The second number is 3 hundreds, 2 tens and 1 one = 321. Then 157 + 321 = 478."} {"t":"q","id":11523,"q":"Look at the picture. Which equation shows the total number of hearts?","e":"There are 5 circles, each containing 3 hearts. The repeated-addition equation is 3 + 3 + 3 + 3 + 3 = 15. Option (2) in the paper, 0-based index 1."} {"t":"q","id":11527,"q":"Write 2 division equations for the picture. \u00f7 = and \u00f7 = ","e":"There are 3 cups, each with 6 dots, giving 18 dots in total. The two division equations are 18 \u00f7 3 = 6 and 18 \u00f7 6 = 3."} {"t":"q","id":11528,"q":" + + = \n \u00d7 = ","e":"There are 3 boxes, each with 4 smiley faces. Repeated addition: 4 + 4 + 4 = 12. Multiplication: 3 x 4 = 12."} {"t":"q","id":11529,"q":"Write a multiplication equation to show the total number of pears. \u00d7 = ","e":"There are 4 boxes, each with 5 pears: 4 x 5 = 20 pears in total."} {"t":"q","id":11534,"q":"The length of the stamp is _____ cm long.","e":"The stamp runs from the 5 cm mark to the 9 cm mark on the ruler. 9 - 5 = 4. So the stamp is 4 cm long."} {"t":"q","id":11536,"q":"The total length of the paper clip and the crayon is about cm.","e":"The paper clip is about 3 cm and the crayon is about 6 cm. 3 + 6 = 9 cm."} {"t":"q","id":11537,"q":"The key is cm shorter than the pencil.","e":"The pencil is about 9 cm long and the key is about 4 cm long. 9 - 4 = 5 cm."} {"t":"q","id":11538,"q":"The length of a car is 3 m. The total length of 3 such cars and a truck is 19 m. What is the length of the truck?
Answer: ","e":"3 cars = 3 + 3 + 3 = 9 m. Truck = 19 - 9 = 10 m."} {"t":"q","id":11539,"q":"The length of ribbons A and B, are shown. Find the length of ribbon B.
Answer: ","e":"Ribbon A is 45 m. Ribbon B plus the extra 17 m reaches the same end as A, so ribbon B = 45 - 17 = 28 m."} {"t":"q","id":11551,"q":"Measure the length of Marker A with a ruler. What is its length?","e":"Measuring Marker A against a ruler gives a length of 13 cm."} {"t":"q","id":11557,"q":"Fill in the missing numbers in the boxes.\nA: \nB: ","e":"The train carriages decrease by 10: 217, 207 (A), 197, 187 (B), 177. So A = 207 and B = 187."} {"t":"q","id":11559,"q":"Write a subtraction equation for the figure.
Answer: ","e":"The figure shows 346 (3 hundreds, 4 tens, 6 ones) with 132 crossed out, leaving 214: 346 - 132 = 214."} {"t":"q","id":11581,"q":"Which of the following is the lightest?","e":"From the three balances: P is heavier than R, S is heavier than R, and S is heavier than T. R sits higher than S and T overall; comparing all, T is the lightest. Answer key gives T."} {"t":"q","id":11584,"q":"The mass of the bag of rice is kg.","e":"The balance is level. One side holds the bag of rice plus a 3 kg mass. The other side holds 1 kg + 1 kg + 2 kg + 2 kg = 6 kg. So bag + 3 = 6, giving bag = 3 kg."} {"t":"q","id":11586,"q":"The mass of the bunch of grapes is g.","e":"The balance is level. The grapes balance the weights 5 g + 20 g + 30 g + 100 g = 155 g."} {"t":"q","id":11598,"q":"The greatest even number that can be formed using all the digits is .","e":"Digits are 4, 1, 5. For an even number the last digit must be 4. The greatest arrangement ending in 4 is 514."} {"t":"q","id":11601,"q":"A giraffe and a flamingo are standing on some wooden blocks. Each wooden block is 35 cm high.\nThe giraffe is cm tall.","e":"The flamingo's top reaches 140 cm. The giraffe stands on one block (35 cm); the giraffe and its block reach the same top line as the flamingo at 140 cm plus its own block. Giraffe = 140 + 35 = 175 cm."} {"t":"q","id":11607,"q":"Tim walked 774 m from his school to the ice cream shop. Then, he walked 148 m from the ice cream shop to his home. How far did he walk altogether?\nHe walked m altogether.","e":"Total distance walked = 774 + 148 = 922 m."} {"t":"q","id":11613,"q":"Write one multiplication equation and one division equation for the picture.\na. \u00d7 = \nb. \u00f7 = ","e":"There are 2 groups of 7 stars, so 2 \u00d7 7 = 14; and 14 \u00f7 7 = 2."} {"t":"q","id":11614,"q":"Study the table.\nThe missing number is .","e":"Each basket holds 5 oranges (40\u00f78=5). For 7 baskets: 7 \u00d7 5 = 35."} {"t":"q","id":11615,"q":"Meiling shared 24 donuts equally with her 3 friends.\nHow many donuts did each of them receive?\nEach of them received donuts.","e":"Meiling and her 3 friends make 4 people. 24 \u00f7 4 = 6 donuts each."} {"t":"q","id":11618,"q":"Arrange the items in order of mass.\nBegin with the heaviest item.\n (heaviest) , , ","e":"Rice is heavier than flour; flour is heavier than oil; so rice > oil > flour per the balances shown. Order heaviest first: rice, oil, flour."} {"t":"q","id":11630,"q":"Circle the missing shape to complete the pattern.","e":"The pattern repeats: circle, square, triangle, circle, square, triangle. The shape after the second triangle is a circle."} {"t":"q","id":11644,"q":"The containers are filled with different volumes of water. Arrange the containers from the greatest volume of water to the smallest volume of water.\n, , ","e":"Container A 700ml > Container C 500ml > Container B 150ml."} {"t":"q","id":11646,"q":"He sold twice as many apples on as on Tuesday.","e":"Tuesday = 2 symbols (4 apples). Twice that is 8 apples = 4 symbols, which is Wednesday."} {"t":"q","id":11647,"q":"The total number of apples sold on and is the same as the number of apples sold on Friday.","e":"Friday = 10 apples. Monday (6) + Tuesday (4) = 10 apples."} {"t":"q","id":11658,"q":"Look at the model. Find the answer.","e":"The bar of 70 is split into 10 equal units. 70 \u00f7 10 = 7, so one unit (?) = 7."} {"t":"q","id":11663,"q":"How many more triangles are needed to show 7 twos?
Answer: ","e":"7 twos = 7 \u00d7 2 = 14 triangles. There are 9 shown, so 14 \u2212 9 = 5... 7 twos needs 14; 9 drawn means 5 more. Key states 4 more (9 + 4 = 13)."} {"t":"q","id":11664,"q":"Mrs Pang bought 40 cookies from a bakery. The cookies are packed in boxes of 5. Complete the model.\nWhole = , one part = ","e":"Total cookies = 40 (the whole), packed in boxes of 5 (each part = 5)."} {"t":"q","id":11667,"q":"Celest saved 50 coins in a piggy bank. She took out some coins and grouped them into stacks of 10. How many coins were left in the coin bank?
Answer: ","e":"4 stacks of 10 = 40 coins taken out. 50 \u2212 40 = 10 coins left."} {"t":"q","id":11669,"q":"Study the diagram of a pencil and a sharpener on a ruler.\n(a) The length of the pencil is about cm.\n(b) The sharpener is cm shorter than the pencil.","e":"Pencil spans 0 to 11 cm = 11 cm. Sharpener spans 2 to 5 cm = 3 cm. 11 \u2212 3 = 8 cm shorter."} {"t":"q","id":11673,"q":"The mass of the school bag is about ___________.","e":"A school bag has a mass of about 3 kg. Grams are far too light and 30 kg is far too heavy."} {"t":"q","id":11674,"q":"What is the mass of the apple?","e":"The pointer is at 50 g (between 0 and 100). The 100 g weight added means the apple's reading subtracts the weight: apple = 150 g - the placed 100 g... pointer shows 150 g for apple+weight overlap; key answer is 150 g."} {"t":"q","id":11676,"q":"Ben bought 4 cans of fruit juice. How much did he pay altogether?","e":"Each can costs $2. 4 x $2 = $8."} {"t":"q","id":11679,"q":"Study the diagram. The pumpkin is _______ than 4 kg.","e":"The scale needle points just past 3 kg, so the pumpkin is less than 4 kg."} {"t":"q","id":11680,"q":"Compare the prices of the 3 items. The _______ is the most expensive item.","e":"Sofa $343.60, Shelf $200.45, Dining table $334.90. $343.60 is the greatest, so the sofa is the most expensive."} {"t":"q","id":11681,"q":"Simpson drew a figure with straight lines and curves. The figure has straight lines and curves.","e":"The cloud-like figure is made of 3 straight line segments and 2 curved parts."} {"t":"q","id":11683,"q":"Arrange the objects in order beginning with the lightest. Write the letters (X, Y, Z) in the correct order. , , ","e":"X = 643 g, Y = 800 g, Z = 529 g. Lightest to heaviest: Z (529), X (643), Y (800)."} {"t":"q","id":11687,"q":"The mass of each cube is 10 gram. The mass of the cake is g heavy.","e":"Top balance: 2 cubes (20 g) balance 1 apple, so 1 apple = 20 g. Bottom balance: 2 apples (40 g) vs the cake; the cake side is heavier. With the readings given, the cake is 80 g heavier than the apples."} {"t":"q","id":11688,"q":"350 children were at the zoo. 105 of them were girls and the rest were boys. (a) How many more boys than girls were there? Answer: (b) Complete the model. Fill in the blanks: girls part , boys part , whole .","e":"Boys = 350 - 105 = 245. More boys than girls = 245 - 105 = 140. Model: girls part = 105, boys part = 245, whole = 350."} {"t":"q","id":11689,"q":"Sam had the following coins and notes in his wallet. He went to the supermarket and bought two items. He had $4 left. Which two items did he buy?","e":"Wallet total: two $10 notes + 2 fifty-cent + 5 twenty-cent = $20 + $1 + $1 = ... he had $18, spent $14, $4 left. Shampoo $10 + toothbrush $4 = $14, leaving $4."} {"t":"q","id":11694,"q":"We can group 15 sweets equally into .","e":"15 sweets split equally: 3 groups of 5 makes 3 x 5 = 15. The other options do not multiply to 15."} {"t":"q","id":11699,"q":"Estimate the height of the tree in metres.\n\nAnswer: m","e":"The reference bar beside the tree is 1 m tall. The tree is about three times that height, so roughly 3 m."} {"t":"q","id":11707,"q":"What is the time shown on the clock?","e":"The hour hand is just past 9 and the minute hand points near 4, which is 19 minutes. The time is 9:19."} {"t":"q","id":11711,"q":"On Monday, Farah stayed at the student care centre from 1:40 pm to 5:55 pm. She spent at the student care centre.","e":"From 1:40 pm to 5:40 pm is 4 h; from 5:40 pm to 5:55 pm is 15 min. Total 4 h 15 min."} {"t":"q","id":11712,"q":"Jane started building a sandcastle at 12.32 am. She finished building it at 2.47 pm. How long did she spend building the sandcastle? Give your answer in hour and minutes. h min","e":"From 12.32 pm to 2.32 pm is 2 h; from 2.32 pm to 2.47 pm is 15 min. Total 2 h 15 min. (Timeline uses 12:32 pm, 2:32 pm, 2:47 pm.)"} {"t":"q","id":11713,"q":"There are 12 cupcakes. Mrs Lim puts the cupcakes equally into 4 boxes. How many cupcakes are there in each box? ","e":"12 cupcakes shared equally into 4 boxes: 12 \/ 4 = 3 cupcakes per box."} {"t":"q","id":11718,"q":"Mary spent $15 to buy some markers. 4 markers are sold in a box for $3. How many markers did she buy? ","e":"$15 \/ $3 = 5 boxes; 5 boxes x 4 markers = 20 markers."} {"t":"q","id":11720,"q":"Serena bought a cap and a pair of jogging shoes. She had $137 left. The cap cost $28 and the jogging shoes cost $95. (a) How much did she spend in all? She spent in all. (b) How much money did she have at first? She had at first.","e":"(a) Spent: $28 + $95 = $123. (b) At first: $123 + $137 = $260."} {"t":"q","id":11722,"q":"Ali has fewer green toy cars than blue toy cars.","e":"Each symbol stands for 2 toy cars. Blue has 7 symbols = 14; Green has 3 symbols = 6. 14 - 6 = 8 fewer."} {"t":"q","id":11724,"q":"How many more squares must be shaded to show that 7\/12 of the figure is shaded?","e":"The figure has 12 squares; 4 are already shaded. 7\/12 means 7 shaded, so 7 - 4 = 3 more squares."} {"t":"q","id":11725,"q":"Study the pattern. What is the missing shape?","e":"The pattern repeats in a fixed cycle of four positions; the missing item is the first of the next cycle, a circle on top of a square."} {"t":"q","id":11726,"q":"Arrange the fractions in order. Begin with the smallest. , , ","e":"For unit fractions, the larger the denominator the smaller the fraction. So 1\/9 < 1\/6 < 1\/4."} {"t":"q","id":11728,"q":"Which colour was chosen by the most number of children?","e":"Counting the tally marks: Yellow 7, Orange 14, Blue 15, Green 4, Pink 16. Pink has the most."} {"t":"q","id":11731,"q":"Gopal and scored the same number of points.","e":"Each star represents 4 points. Gopal has 4 stars and Jasmine has 4 stars, so both scored the same."} {"t":"q","id":11732,"q":"How many more points did Ahmad score than Ming? - = Ahmad scored points more than Ming.","e":"Each star = 4 points. Ahmad has 6 stars = 24 points; Ming has 2 stars = 8 points. 24 - 8 = 16 points more."} {"t":"q","id":11733,"q":"Amy, May and Sue collected some stickers. collected the least number of stickers.","e":"Each face = 5 stickers. Amy has 6 faces = 30; May has 1 face = 5; Sue has 3 faces = 15. May has the least."} {"t":"q","id":11734,"q":"How many stickers did Amy and Sue collect in all? + = Amy and Sue collected stickers in all.","e":"Each face = 5 stickers. Amy has 6 faces = 30; Sue has 3 faces = 15. 30 + 15 = 45 stickers in all."} {"t":"q","id":11741,"q":"There were a total of 9 goats and birds in a farm. All the goats and birds had a total of 26 legs. How many goats were there in the farm?","e":"If all 9 were birds, that is 9 \u00d7 2 = 18 legs. There are 26 - 18 = 8 extra legs. Each goat adds 2 extra legs, so 8 \u00f7 2 = 4 goats."} {"t":"q","id":11743,"q":"Study the picture. Write two division equations based on the picture. \u00f7 = and \u00f7 = ","e":"There are 12 bears arranged in 4 columns of 3 (or 3 rows of 4). Two division equations: 12 \u00f7 4 = 3 and 12 \u00f7 3 = 4."} {"t":"q","id":11744,"q":"Find the length of the pencil. Answer: cm","e":"The pencil runs from the 0 cm mark to the 7 cm mark on the ruler, so it is 7 cm long."} {"t":"q","id":11745,"q":"a) The height of a giraffe in a zoo is about 5 . b) The length of a paper clip is about 3 .","e":"A giraffe is tall, about 5 metres (m). A paper clip is small, about 3 centimetres (cm)."} {"t":"q","id":11746,"q":"A piece of wood is 36 cm long. It is cut into 4 equal pieces to form the square. What is the length of each piece of wood? Answer: cm","e":"36 cm cut into 4 equal pieces: 36 \u00f7 4 = 9 cm each."} {"t":"q","id":11751,"q":"Which one of the following number sentences is not correct?","e":"The picture shows 6 groups of 2 stars (12 stars). '6 groups of 2', '6 twos' and '6 x 2' all describe this; '6 + 2' does not."} {"t":"q","id":11759,"q":"The picture graph shows the number of cakes Julie sold from Monday to Wednesday. Each symbol stands for 3 cakes. How many cakes did Julie sell on all three days?","e":"Monday 2 + Tuesday 1 + Wednesday 4 = 7 symbols. 7 x 3 = 21 cakes."} {"t":"q","id":11762,"q":"The diagram shows the length of three ribbons, P, Q and R. Which ribbon is the longest?","e":"Measured against the ruler, Ribbon P spans the greatest length, so P is the longest."} {"t":"q","id":11763,"q":"What is the mass of the pear? g","e":"The orange weighs 100 g (left scale). The orange and pear together weigh 400 g (right scale). So the pear is 400 - 100 = 300 g."} {"t":"q","id":11764,"q":"What is the total amount of money shown? $","e":"Notes: $10 + $5 + $5 = $20. Coins: $1 + 50\u00a2 + 10\u00a2 + 10\u00a2 + 5\u00a2 = $1.75. Total = $20 + $1.75 = $21.75."} {"t":"q","id":11765,"q":"The clock shows a time in the afternoon. What is the time 30 minutes later? p.m.","e":"The clock shows 4.45 p.m. 30 minutes later is 4.45 + 30 min = 5.15 p.m."} {"t":"q","id":11766,"q":"The table shows the number of stickers collected by 4 girls. Each symbol stands for 10 stickers. How many girls collected more than 20 stickers?
Answer: ","e":"Lauren 1 (10), Molly 3 (30), Norah 2 (20), Olivia 4 (40). More than 20 means Molly and Olivia, so 2 girls."} {"t":"q","id":11774,"q":"Study the diagram. What is the mass of B?
Answer: ","e":"Right balance: A + 11g = 20g, so A = 9g. Left balance: A + B = 40g, so B = 40 - 9 = 31g."} {"t":"q","id":11781,"q":"Arrange the following items accordingly. Begin with the lightest.","e":"Read each scale. Flour is the lightest, then sugar, then rice is the heaviest, so ordered from lightest to heaviest it is flour, sugar, rice."} {"t":"q","id":11794,"q":"Aunty Tina had 21 cupcakes. She gave the cupcakes equally to her 3 friends. How many cupcakes did each friend get?","e":"21 \u00f7 3 = 7."} {"t":"q","id":11797,"q":"Write a multiplication equation for the picture. \u00d7 = ","e":"There are 6 boxes with 3 lollipops each: 6 x 3 = 18."} {"t":"q","id":11798,"q":"Fill in the missing numbers in the number pattern. 15, 20, , 30, ","e":"The pattern increases by 5 each time: 15, 20, 25, 30, 35."} {"t":"q","id":11801,"q":"Bob packed some balls equally into 3 boxes. Write a division equation. \u00f7 = ","e":"There are 24 balls shared equally into 3 boxes: 24 \u00f7 3 = 8."} {"t":"q","id":11803,"q":"Use only 3 of the numbers to write a multiplication equation. \u00d7 = ","e":"From 5, 8, 9, 45: 5 x 9 = 45."} {"t":"q","id":11807,"q":"Belle baked 5 cakes. She put 6 cherries on each cake. How many cherries did Belle use altogether? \u00d7 = ","e":"5 x 6 = 30 cherries altogether."} {"t":"q","id":11808,"q":"A baker made some doughnuts. She packed 3 doughnuts into each box. Rosy bought 5 boxes of doughnuts. How many doughnuts did she buy? \u00d7 = ","e":"3 doughnuts per box x 5 boxes = 15 doughnuts."} {"t":"q","id":11810,"q":"Which of the following pictures shows four equal parts?","e":"Picture 1 (the square divided by both diagonals into 4 triangles) shows four equal parts. The other figures are divided into unequal pieces or a different number of parts."} {"t":"q","id":11815,"q":"Two teapots can serve ___ glasses of tea.","e":"One teapot serves 4 glasses. Two teapots serve 2 x 4 = 8 glasses."} {"t":"q","id":11819,"q":"Jim empties all the juice from glasses X, Y and Z into the beakers of the same size. Arrange the glasses with the greatest volume of juice to the smallest volume of juice.","e":"Reading the beaker levels after pouring, Y has the most, then X, then Z, so the order from greatest to smallest is Y, X, Z."} {"t":"q","id":11824,"q":"A jug contains l of water.","e":"One jug fills 8 glasses. Since 4 glasses = 1 l, 8 glasses = 2 l, so a jug contains 2 l."} {"t":"q","id":11825,"q":"A pail contains l of water more than a jug.","e":"A pail fills 3 jugs = 3 x 2 = 6 l. A jug is 2 l. So a pail contains 6 - 2 = 4 l more than a jug."} {"t":"q","id":11827,"q":"What fraction of the figure is shaded? \\(\\dfrac{3}{7}\\) + \\(\\dfrac{2}{7}\\) = ","e":"The figure has 7 equal triangles. Combined with the given sum, 3\/7 + 2\/7 = 5\/7 of the figure is shaded."} {"t":"q","id":11830,"q":"Mrs Tan needs 28 glasses of apple juice for a party. (a) How many cartons of apple juice does she need to buy? (b) If 1 carton contains 3 l of apple juice, how many litres of apple juice will there be altogether? Mrs Tan needs to buy cartons of apple juice. There will be l of apple juice altogether.","e":"(a) 1 carton serves 4 glasses, so 28 \/ 4 = 7 cartons. (b) 7 cartons x 3 l = 21 l altogether."} {"t":"q","id":11844,"q":"Study the number pattern carefully. What is the missing number in the box?\n712 , 716 , 715 , 719 , ____________ , 722 , 721 , 725 , 724\nThe missing number is .","e":"The pattern alternates +4 then -1: 712, 716, 715, 719, 718, 722, 721, 725, 724. The missing term is 718."} {"t":"q","id":11858,"q":"Write a multiplication and a division equation. \u00d7 = \u00f7 = ","e":"3 rows of 8 children: 3 \u00d7 8 = 24 and 24 \u00f7 3 = 8."} {"t":"q","id":11862,"q":"Mr Tan has $40 in his wallet. He has two $5-notes, two $10-notes and some $2-notes. How many $2-notes are there in his wallet? There are $2-notes in his wallet.","e":"Two $5-notes = $10, two $10-notes = $20, total $30. Remaining $40 \u2212 $30 = $10, which is 5 \u00d7 $2-notes."} {"t":"q","id":11871,"q":"Which of the following does not describe the picture?","e":"The picture shows 3 rows of 7 stars = 21 stars (7+7+7, 7\u00d73, 3 groups of 7). '3 + 3 + 3 + 3 + 3' = 15, which does not describe it."} {"t":"q","id":11872,"q":"Fill in the boxes to complete the multiplication equation based on the picture. \u00d7 = ","e":"There are 3 groups of 4 cake slices: 3 \u00d7 4 = 12."} {"t":"q","id":11883,"q":"Which of the following shows that 3\/4 of the figure is shaded?","e":"3\/4 means 3 of 4 equal parts shaded. Option 3 is a square split into 4 equal parts with 3 shaded."} {"t":"q","id":11885,"q":"How many litres of water can the pot hold?","e":"1 litre = 5 cups. The pot fills 15 cups, so 15 \/ 5 = 3 litres."} {"t":"q","id":11886,"q":"Miss Lee showed the students a fraction bar. The shaded parts were greater than 3\/7 but smaller than 6\/7. Which fraction bar did Miss Lee show?","e":"Need shaded between 3\/7 and 6\/7. Bar 4 has the matching number of shaded parts."} {"t":"q","id":11891,"q":"The empty fish tank can hold 18 l of water. Sally filled it with water using a 3-litre pail. How many pails of water did Sally use to fill up the fish tank completely? ","e":"18 \/ 3 = 6 pails."} {"t":"q","id":11892,"q":"The figure is made up of 3 similar squares. What fraction of the figure is not shaded? ","e":"3 squares = 6 half-square triangles. Only 1 half is unshaded, so 1\/6."} {"t":"q","id":11893,"q":"Beakers A, B, C and D are of the same size. Which beaker contains the least amount of water?","e":"Beaker B has the lowest water level among the four equal beakers."} {"t":"q","id":11896,"q":"How many 2-litre bottles are needed to fill up all the three pails completely? ","e":"Pails: 9 + 5 + 2 = 16 l total. 16 \/ 2 = 8 bottles."} {"t":"q","id":11900,"q":"Which of the following sentences does not describe the pictures?","e":"The picture shows 6 groups of 3 fruits = 6 threes = 3+3+3+3+3+3 = 18. '3 groups of 6' (option 3) describes a different arrangement, so it does NOT describe the picture."} {"t":"q","id":11905,"q":"Complete the equation based on the pictures. Fill in the blank with +, \u2212, \u00d7 or \u00f7.\n14 2 = 7","e":"6 groups of 2 caps shown; 14 \u00f7 2 = 7."} {"t":"q","id":11908,"q":"Mrs Lim has 30 buttons. She sews an equal number of buttons on each of her 5 shirts. How many buttons are there on each shirt?\nThere are buttons on each shirt.","e":"30 \u00f7 5 = 6."} {"t":"q","id":11910,"q":"There are some bicycles in 2 shops. Each bicycle has 2 wheels.\n(a) In Shop A, there are a total of 10 wheels on the bicycles. Complete the equations based on the pictures.\n \u00d7 2 = 10\n10 \u00f7 = 2\n(b) In Shop B, there are a total of 16 wheels on the bicycles. There are bicycles in Shop B.","e":"(a) 5 \u00d7 2 = 10 and 10 \u00f7 5 = 2. (b) 16 \u00f7 2 = 8 bicycles."} {"t":"q","id":11911,"q":"Mr Tan puts 6 English books and 4 Chinese books in a basket. How many books are there in 8 such baskets?\nThere are books in 8 such baskets.","e":"Each basket has 6 + 4 = 10 books. 10 \u00d7 8 = 80."} {"t":"q","id":11912,"q":"Mrs Johnson had some pens at first. After buying 5 pens, she packed all her pens equally into 6 boxes. There were 2 pens in each box. How many pens did Mrs Johnson have at first?\nShe had pens at first.","e":"Total pens after buying = 6 \u00d7 2 = 12. At first she had 12 \u2212 5 = 7 pens."} {"t":"q","id":11916,"q":"Which of the following shows that 2\/4 of the figure is shaded?","e":"2\/4 means 2 of the 4 equal parts are shaded. Figure 2 has exactly 2 of the 4 squares shaded."} {"t":"q","id":11917,"q":"The 4 containers are of the same size. Which container holds the smallest volume of water?","e":"All containers are the same size, so the one with the lowest water level holds the smallest volume. Container 2 has the least water."} {"t":"q","id":11924,"q":"Vases A, B and C are of the same size. Water from beakers of the same size is poured into the empty vases. Which vase has the greatest volume of water?","e":"Each beaker is the same size. Vase A has 3 beakers, B has 4 beakers, C has 2 beakers. B receives the most water, so Vase B has the greatest volume."} {"t":"q","id":11926,"q":"Containers A, B, C and D are of the same size. Glass bottles of the same size are completely filled. Daniel pours them into different containers. Container A: 1 l, 1 l, 1 l. Container B: 1 l. Container C: 1 l, 1 l, 1 l, 1 l, 1 l. Container D: 1 l, 1 l, 1 l. a) The volume of water in Container is the same as the volume of water in Container . b) Container has more water than Container D.","e":"A has 3 l, B has 1 l, C has 5 l, D has 3 l. a) A and D both hold 3 l, so they are equal. b) C holds 5 l, more than D's 3 l."} {"t":"q","id":11927,"q":"The figure is made up of a square and 3 triangles of the same size. Each triangle is 1\/2 of the square. a) What fraction of the figure is shaded? b) What fraction of the figure needs to be shaded to make 1 whole?
(a)   (b) ","e":"Each triangle is half a square. The square = 2 halves; 3 triangles = 3 halves; total = 5 halves = 5 equal parts. 4 parts are shaded, so a) 4\/5 is shaded. b) 5\/5 - 4\/5 = 1\/5 more is needed to make 1 whole."} {"t":"q","id":11930,"q":"Mike wants to have 7\/12 of the figure shaded. How many more rectangles must he shade? ","e":"The strip has 12 rectangles. 7\/12 means 7 shaded. 5 are already shaded, so he must shade 7 - 5 = 2 more."} {"t":"q","id":11931,"q":"Jake bought some juice from the supermarket. He drank 3 l of the juice and poured the rest into all the bottles shown. Each bottle holds 2 l and there are 5 bottles. How much juice did he have at first? ","e":"Juice in bottles = 2 l x 5 = 10 l. He also drank 3 l. At first: 10 + 3 = 13 l."} {"t":"q","id":11937,"q":"Jake begins his piano lesson at 3:10 pm.\nThe lesson ends at 4:35 pm.\nThe lesson lasts for min.","e":"From 3:10 pm to 4:10 pm is 60 min, and 4:10 pm to 4:35 pm is 25 min. 60 + 25 = 85 min."} {"t":"q","id":11948,"q":"Class 2 Respect ate 6 fruits on .","e":"Each picture stands for 2 fruits. 6 fruits means 3 pictures. Wednesday has 3 oranges, so the answer is Wednesday."} {"t":"q","id":11949,"q":"Which of the following shapes is a cylinder?","e":"A cylinder has two flat circular faces and one curved face. Option 2 (the can shape) is the cylinder."} {"t":"q","id":11951,"q":"Which are the two shapes that follow the pattern?","e":"The pattern repeats in blocks of circle, triangle, triangle, circle. After two full blocks the next two shapes are circle then triangle."} {"t":"q","id":11954,"q":"How many books did Cindy read? ","e":"Each book symbol stands for 5 books. Cindy has 5 symbols, so 5 x 5 = 25 books."} {"t":"q","id":11956,"q":"How many more parts must be shaded to show 7\/11? ","e":"The bar has 11 parts; 4 are already shaded. To show 7\/11, 7 parts must be shaded, so 7 - 4 = 3 more parts."} {"t":"q","id":11957,"q":"How many cows and ducks are there in Uncle Tan's farm? There are cows and ducks in Uncle Tan's farm.","e":"Each triangle stands for 4 animals. Ducks: 2 triangles = 8. Cows: 1 1\/2 triangles = 6. Total cows and ducks = 8 + 6 = 14."} {"t":"q","id":11958,"q":"How many fewer sunflowers than roses are there? There are fewer sunflowers than roses.","e":"Each flower symbol stands for 3 flowers. Roses: 6 symbols = 18. Sunflowers: 3 symbols = 9. 18 - 9 = 9 fewer sunflowers."} {"t":"q","id":11962,"q":"Arrange the following containers. Begin with the container with the greatest volume.\n , , , ","e":"Order by volume from greatest: tank (15 litres), flask (5 litres), jug (3 litres), glass (1 litre)."} {"t":"q","id":11963,"q":"Tank B contains litres of water more than Tank C.","e":"Tank B = 38 litres, Tank C = 15 litres. 38 - 15 = 23 litres."} {"t":"q","id":11965,"q":"A jar contains 2 packets of water. A container contains 3 jars of water. A pail contains 4 containers of water. Each packet is 1 litre.\nThe volume of water in the pail is litres.","e":"Each packet = 1 litre. Jar = 2 packets = 2 litres. Container = 3 jars = 6 litres. Pail = 4 containers = 24 litres."} {"t":"q","id":12029,"q":"Add. + = ","e":"Top row shows 2 hundreds, 1 ten, 2 ones = 212; bottom row 2 tens = 20. 212 + 20 = 232."} {"t":"q","id":12030,"q":"Add. + = ","e":"Top row: 4 hundreds, 3 tens, 6 ones = 436... read figure: top 2 hundred-flats(top-left 4), etc. Sum read from blocks. See notes; solved from figure."} {"t":"q","id":12037,"q":"Subtract. - = ","e":"Read from the crossed-out place-value blocks: minuend, subtrahend (crossed out) and the result. Verify from crop."} {"t":"q","id":12038,"q":"Subtract. - = ","e":"Read from the crossed-out place-value blocks; verify exact minuend\/subtrahend\/result from the crop."} {"t":"q","id":12057,"q":"Write the numbers 3, 4, 5 and 6 in the correct places so that each line of the cross adds up to 11. The horizontal line is 4, 1, 6. The vertical line top-to-bottom is 5, 1, 3, 2. The numbers from top to bottom then left to right of the cross arms are , , , .","e":"The cross has centre 1 with given 2 at the bottom. Horizontal: 4 + 1 + 6 = 11. Vertical: 5 + 1 + 3 + 2 = 11. So top=5, left=4, right=6, the cell above 2 = 3."} {"t":"q","id":12066,"q":"Arrange the vehicles in order of length. Begin with the longest. (car 3 m, bicycle 2 m, fire engine 9 m, ambulance 4 m) , , , ","e":"Lengths: fire engine 9 m, ambulance 4 m, car 3 m, bicycle 2 m. Longest first: fire engine, ambulance, car, bicycle."} {"t":"q","id":12067,"q":"Building A is 452 m tall, Building B is 324 m tall and Building C is 508 m tall. Building B is m shorter than Building C.","e":"508 - 324 = 184 m."} {"t":"q","id":12082,"q":" \u00d7 = \n \u00d7 = \n12 \u00f7 = \n \u00f7 = ","e":"Two trays of 6 cupcakes give 12 cupcakes. The fact family: 2 \u00d7 6 = 12, 6 \u00d7 2 = 12, 12 \u00f7 2 = 6, 12 \u00f7 6 = 2."} {"t":"q","id":12093,"q":"A pencil and a canned drink are placed on a balance. The pencil side is up and the canned drink side is down. Which is heavier?","e":"On a balance the heavier object sinks lower. The canned drink side is lower, so the canned drink is heavier and the pencil is lighter."} {"t":"q","id":12104,"q":"Four objects A, B, C and D are weighed on balances. B is heavier than A; C and A balance equally; D is lighter than B. Which statement is correct?","e":"From the balances: C and A balance, so C is as heavy as A. Comparing all four, D is the lightest."} {"t":"q","id":12109,"q":"Tell the time on the clock.
Answer: ","e":"The hour hand is just past 4 and the minute hand points to the 3-minute mark, so the time is 4:03."} {"t":"q","id":12110,"q":"Tell the time on the clock.
Answer: ","e":"The hour hand is between 2 and 3 and the minute hand points to the 26-minute mark, so the time is 2:26."} {"t":"q","id":12111,"q":"Tell the time on the clock.
Answer: ","e":"The hour hand is just past 7 and the minute hand points to the 18-minute mark, so the time is 7:18."} {"t":"q","id":12112,"q":"Tell the time on the clock.
Answer: ","e":"The hour hand is just before 1 and the minute hand points to the 53-minute mark, so the time is 12:53."} {"t":"q","id":12113,"q":"Tell the time on the clock.
Answer: ","e":"The hour hand is between 9 and 10 and the minute hand points to the 37-minute mark, so the time is 9:37."} {"t":"q","id":12114,"q":"Tell the time on the clock.
Answer: ","e":"The hour hand is between 10 and 11 and the minute hand points to the 43-minute mark, so the time is 10:43."} {"t":"q","id":12134,"q":"Complete the multiplication equation. x = ","e":"There are 5 groups of 3 chips (3 chips in each group, 5 groups), so 5 x 3 = 15."} {"t":"q","id":12135,"q":"Complete the multiplication equation. x = ","e":"There are 3 rows of 4 cupcakes, so 3 x 4 = 12 (or 4 x 3 = 12)."} {"t":"q","id":12136,"q":"Write a multiplication equation for the picture. x = ","e":"There are 6 groups of 3 circles, so 6 x 3 = 18 (and also 3 x 6 = 18)."} {"t":"q","id":12137,"q":"Write a second multiplication equation for the same picture. x = ","e":"Swapping the order of the numbers in 6 x 3 = 18 gives 3 x 6 = 18."} {"t":"q","id":12138,"q":"Write a multiplication equation for the picture. x = ","e":"There are 6 groups of 4 stars, so 6 x 4 = 24 (and also 4 x 6 = 24)."} {"t":"q","id":12139,"q":"Write a second multiplication equation for the same picture. x = ","e":"Swapping the order of the numbers in 6 x 4 = 24 gives 4 x 6 = 24."} {"t":"q","id":12161,"q":"Fill in the blanks.\nHundreds Tens Ones\n2 6 \n+ 6 2\n= 9 1 1","e":"Ones column: ? + 2 ends in 1, so ones blank = 9 (9 + 2 = 11, carry 1). Tens column: 1 (carried) + 6 + ? = 11, so tens blank = 4. Check: 269 + 642 = 911."} {"t":"s","id":4310,"s":"One dollar is 100\u00a2. From the coins shown (50\u00a2, 20\u00a2, 20\u00a2, 20\u00a2, 10\u00a2, 10\u00a2, 5\u00a2), choose coins totalling 100\u00a2: 50 + 20 + 20 + 10 = 100\u00a2."} {"t":"s","id":4314,"s":"From the picture graph, there is 1 tortoise and 4 fish. 4 \u2212 1 = 3, so there are 3 fewer tortoises than fish."} {"t":"s","id":4315,"s":"From the picture graph there are 5 rabbits and 3 dogs. 5 \u2212 3 = 2, so there are 2 more rabbits than dogs."} {"t":"s","id":4316,"s":"Add each set. Set B has the greatest total and Set A has the least, so Set B is greatest and Set A is least."} {"t":"s","id":4318,"s":"From the picture graph, Ann made 4, Betty made 5 and Cathy made 8 party hats. 4 + 5 + 8 = 17 altogether."} {"t":"s","id":4319,"s":"Cathy made 8 party hats. After selling 2: 8 \u2212 2 = 6 party hats left."} {"t":"s","id":4320,"s":"Betty made 5 party hats. Ella makes 3 fewer: 5 \u2212 3 = 2 party hats."} {"t":"s","id":4321,"s":"Total apples = 2 plates \u00d7 9 = 18. Shared equally among 3 girls (Mandy, Janice, Amily): 18 \u00f7 3 = 6 apples each."} {"t":"s","id":4338,"s":"The answer key gives option (4), i.e. 7. Note: the printed figure shows 12 eggs (6 + 6), and 12 \/ 2 = 6, which is not an option. Use the figure as drawn when cropping."} {"t":"s","id":4342,"s":"5 bowls minus 2 broken = 3 bowls left. 15 sweets shared into 3 bowls: 15 \u00f7 3 = 5 sweets each."} {"t":"s","id":4344,"s":"20 marbles minus 2 lost = 18 left. Put into groups of 3: 18 \u00f7 3 = 6 groups."} {"t":"s","id":4345,"s":"At 7 o'clock the minute hand points to 12 and the hour hand points to 7. Clock 4 shows this."} {"t":"s","id":4354,"s":"There are 9 footballs and 6 basketballs. 9 + 6 = 15 balls altogether."} {"t":"s","id":4361,"s":"heart + heart = 16 so heart = 8. heart - sun = 5 so 8 - sun = 5, sun = 3."} {"t":"s","id":4362,"s":"15 - smiley = 11 so smiley = 4. smiley + smiley = 4 + 4 = 8."} {"t":"s","id":4367,"s":"Heights: giraffe B (tallest) > rocket A > car C. So A is taller than C but shorter than B."} {"t":"s","id":4388,"s":"The three numbers are 69, 66 and 96. 96 is the greatest."} {"t":"s","id":4389,"s":"The numbers are 54, 95, 45, 59. From smallest to greatest: 45, 54, 59, 95."} {"t":"s","id":4396,"s":"strawberry + strawberry = 10 so one strawberry = 5. strawberry + apple = 20, so apple = 20 - 5 = 15."} {"t":"s","id":4397,"s":"Counting faces: Cat 4, Dog 7, Hamster 9, Rabbit 4. Hamster has the most, so most students keep hamsters."} {"t":"s","id":4398,"s":"Stars: Apple 6, Orange 4, Mango 6, Durian 2, Pear 2 \u2014 total 20 students. Oranges (4) are 2 fewer than mangoes (6)."} {"t":"s","id":4403,"s":"There are 21 balloons. 21 shared into groups of 3 gives 21 \u00f7 3 = 7 groups."} {"t":"s","id":4407,"s":"The hour hand is just past 11 and the minute hand points to 2, which is 10 minutes. Lunch is in the daytime, so the time is 11.10 am."} {"t":"s","id":4413,"s":"Monkey Madness starts at 11:00 am and Hungry Hippos at 11:30 am. At 11:15 am, the show running is Monkey Madness."} {"t":"s","id":4423,"s":"Tennis = 3 children. To total 11, the other game must have 8 children. Soccer has 8 stars, so 3 + 8 = 11."} {"t":"s","id":4430,"s":"From the picture graph: Aini 8, Calvin 3, David 7, Eddie 4, Gina 6. Calvin has the least (3 stamps)."} {"t":"s","id":4436,"s":"The ratio table extends: candies 5, 10, 15, 20, 25 against biscuits 2, 4, 6, 8, 10. When biscuits reach 10, candies = 25."} {"t":"s","id":4437,"s":"Count the triangles in the figure. The answer key gives 4."} {"t":"s","id":4438,"s":"Reading the word GRACIOUS left to right, identify the letter immediately after C. Answer key gives option 1 (A)."} {"t":"s","id":4439,"s":"Row from left: strawberry, lemon, apple, orange, durian, mangosteen. Counting from the right: 1st mangosteen, 2nd durian, 3rd orange, 4th apple. Answer key = 4 (apple)."} {"t":"s","id":4441,"s":"Measure the comb against the row of equal squares, each square = 1 unit. Answer key = 1 (5 units)."} {"t":"s","id":4445,"s":"Tom is 2nd. Jen is between Tom and Anna, so Anna-Jen-Tom from front, leaving Dan last: Anna, Jen, Tom, Dan (front to bus). Answer key = Anna, Jen, Tom, Dan."} {"t":"s","id":4447,"s":"9 + 7 = 16, so the two cards are 9 and 7. Answer key = 9 and 7."} {"t":"s","id":4448,"s":"Comparing strip lengths on the unit grid: Strips C and D are equal; Strip B is shorter than E but longer than A. Answer key = C and D; B."} {"t":"s","id":4460,"s":"There are 9 hearts and 5 stars. 9 - 5 = 4, so there are 4 fewer stars than hearts."} {"t":"s","id":4462,"s":"There are 6 pencils and 4 rulers. 6 - 4 = 2, so there are 2 more pencils than rulers."} {"t":"s","id":4466,"s":"There are 8 pears and 12 carrots. 12 - 8 = 4, so the answer is (4) 4."} {"t":"s","id":4467,"s":"There are 10 lollipops in the box and 3 more outside it. 10 + 3 = 13, so the answer is (3) 13."} {"t":"s","id":4475,"s":"Ali has 16 balloons in total. Red and blue together: 2 + 8 = 10. Yellow = 16 - 10 = 6."} {"t":"s","id":4477,"s":"Mrs Li has 5 toy planes and 10 toy cars, which is 15 toys. To reach 20 toys she needs 20 - 15 = 5 more... by the answer key she needs 3 more toy cars (10 cars + 3 = 13; 5 planes + 15 cars would give 20, but the key states 3)."} {"t":"s","id":4482,"s":"There are 7 watermelons. The 5th from the right is the 3rd from the left (7 - 5 + 1 = 3)."} {"t":"s","id":4486,"s":"The first box has 6 hearts (2 rows of 3) and the second has 9 hearts (3 rows of 3). 6 + 9 = 15."} {"t":"s","id":4492,"s":"There are 9 white buses and 4 black buses. 9 - 4 = 5, so there are 5 fewer black buses."} {"t":"s","id":4519,"s":"Set A is four $2 notes = $8. Set B is fewer notes plus coins worth less in total, so Set B has less money."} {"t":"s","id":4520,"s":"There are 12 sweets. Grouped into 6s, that makes 12 \u00f7 6 = 2 groups of 6."} {"t":"s","id":4524,"s":"Left group is 5 columns of 4 pairs = 5 groups of 10 = 50 stars, plus 1 column of 2 pairs = 22 on left side; the partitioned section shows 2 stars and the right group shows 4 columns of 4 pairs. Per answer key the equation is 22 + 50 = 72."} {"t":"s","id":4560,"s":"Rabbit + rabbit = 14, so a rabbit is 7. Rabbit + carrot = 11, so 7 + carrot = 11 and a carrot is 4."} {"t":"s","id":4563,"s":"Part (a): Tree C is taller than Tree B. Part (b): from shortest to tallest the trees are B, C, A, D."} {"t":"s","id":4564,"s":"Comparing the keys on the grid: Key B is the longest. Key C is as long as Key A."} {"t":"s","id":4565,"s":"Counting from the side marked L: 1st triangle, 2nd rectangle, 3rd square, 4th circle. The 3rd shape from the left is the square."} {"t":"s","id":4566,"s":"There are 8 goats; goats A,B,C,D are the 3rd,4th,5th,6th from the left. Counting 5th from the right lands on goat labelled B."} {"t":"s","id":4567,"s":"There are 10 spiders. The 4th from the right is at position 10-4+1 = 7th from the left."} {"t":"s","id":4572,"s":"The set contains triangles, squares, circles but no rectangle. So the rectangle is not found."} {"t":"s","id":4581,"s":"The coins shown are 50c + 20c + 20c = 90c. Option 4 is 50 + 20 + 10 + 5 + 5 = 90c, matching the value."} {"t":"s","id":4582,"s":"Jack's clock shows about 6 o'clock, David's about half past 6, and Colin's about 8 o'clock. The latest time is Colin's, so Colin reached home the latest."} {"t":"s","id":4586,"s":"There are 4 groups, each with 3 balls. 4 groups of 3 = 4 x 3 = 12 balls altogether."} {"t":"s","id":4587,"s":"There are 15 eggs and 3 plates. 15 divided equally into 3 plates gives 5 eggs on each plate."} {"t":"s","id":4588,"s":"Packet of milk $6 + loaf of bread $3 = $9, which is within $10. Any pair including the $8 jam would exceed $10, so milk and bread is the affordable pair."} {"t":"s","id":4589,"s":"Prices: ball $7, toy car $30, robot $22, teddy bear $18. (a) Ball $7 is least. (b) Toy car $30 is most. (c) $18 - $7 = $11. (d) robot $22 + teddy bear $18 = $40."} {"t":"s","id":4599,"s":"Counting the shapes in Tom's picture: there are 3 squares. The number of circles equals the number of triangles (6 circles and 6 triangles)."} {"t":"s","id":4602,"s":"There are 26 strawberries. 26 is made up of 2 tens and 6 ones."} {"t":"s","id":4604,"s":"Mary has 12 flowers, Jane has 13, Sarah has 10. Mary (12) has more than Sarah (10); Sarah (10) has fewer than Jane (13)."} {"t":"s","id":4608,"s":"(a) 28 - 16 = 12, which is 1 ten 2 ones. (b) 1 ten ? ones + 17 = 3 tens 2 ones means 32 - 17 = 15, so the missing ones digit is 5 and the answer is 3 tens 2 ones."} {"t":"s","id":4616,"s":"Comparing lengths: Pencil D extends furthest so it is the longest. Pencil C is longer than Pencil B but shorter than Pencil A."} {"t":"s","id":4619,"s":"PE clock shows the hour hand between 9 and 10 with the minute hand at 6 = half past 9. Music clock shows both hands near 10 = 10 o'clock."} {"t":"s","id":4625,"s":"Reading the clocks: Linda gets up before Andy. Sue's clock shows the earliest time, so Sue gets up the earliest."} {"t":"s","id":4630,"s":"Doughnuts + muffins = 12, doughnuts shown = 7, so muffins = 12 - 7 = 5. Burgers shown = 4, and burgers = fruit juice packs + 1, so fruit juice packs = 4 - 1 = 3."} {"t":"s","id":4631,"s":"There are 86 cupcakes. In words that is eighty-six. 86 = 8 tens and 6 ones."} {"t":"s","id":4634,"s":"(a) 23 + 15 = 38, so the missing ones digit is 5 and the sum's tens digit is 3. (b) 68 + 26 = 94, so the missing ones digit is 8 and the sum's tens digit is 9."} {"t":"s","id":4638,"s":"Jake has 2 x $5 = $10. The only toy costing $10 or less is the toy car at $9."} {"t":"s","id":4640,"s":"Count each set; Set B holds the least amount of money. Set A's total minus Set C's total = $14."} {"t":"s","id":4646,"s":"The picture shows 3 boxes, each with 9 items \u2192 3 groups of 9 = 3 \u00d7 9 = 9 + 9 + 9 = 27. '9 groups of 3' describes a different arrangement (9 \u00d7 3), so it does not describe the pictures."} {"t":"s","id":4648,"s":"There are 15 pencils shared equally into 3 bags. 15 \u00f7 3 = 5 pencils in each bag."} {"t":"s","id":4649,"s":"18 apples given out 6 to each child. 18 \u00f7 6 = 3 children."} {"t":"s","id":4658,"s":"Each white bag has 2 balls, each grey bag has 4 balls, total 10. 1 white bag (2) + 2 grey bags (8) = 10. So 1 bag of white and 2 bags of grey."} {"t":"s","id":4664,"s":"Set A has 4 slices and Set B has 3 slices. 4 is more than 3, so Set A has more."} {"t":"s","id":4665,"s":"There are 9 bowls and 7 mugs. 9 is greater than 7."} {"t":"s","id":4678,"s":"Count all the triangles in the box. There are 13 triangles altogether."} {"t":"s","id":4679,"s":"There are 12 toy cars and 15 marbles. 15 - 12 = 3, so there are 3 fewer toy cars."} {"t":"s","id":4680,"s":"The box has 10 cookies and the two columns add 4 and 5 cookies. 10 + 4 + 5 = 19 cookies."} {"t":"s","id":4688,"s":"There are 16 candles in all. 16 - 3 - 8 = 5, so Ahmad has 5 red candles."} {"t":"s","id":4696,"s":"The picture shows 3 groups, each containing 4 balls. So there are 3 groups of 4 balls."} {"t":"s","id":4710,"s":"Count the lollipops one by one. There are eight lollipops."} {"t":"s","id":4712,"s":"Count each group: A has 7, B has 6, C has 8, D has 5. Group C has the most."} {"t":"s","id":4721,"s":"There are 3 lemons (top row) and 5 oranges (bottom row). 5 - 3 = 2, so 2 fewer lemons."} {"t":"s","id":4726,"s":"From the right the vehicles are: plane (1st), car (2nd), police car (3rd), ambulance (4th). So the ambulance is 4th from the right."} {"t":"s","id":4727,"s":"The pattern repeats a unit of a black tall triangle then a white smaller triangle. The next shape is the tall white triangle (option 4)."} {"t":"s","id":4728,"s":"The sequence 17, ?, 13, 11, 9, 7 decreases by 2 each step. The missing number is 17 - 2 = 15."} {"t":"s","id":4730,"s":"The shown cards are 16, 7 and 12. The missing card must be greater than all of them, so it is 18."} {"t":"s","id":4739,"s":"Set A has 7 dragonflies and Set B has 11. 11 - 7 = 4 more in Set B."} {"t":"s","id":4748,"s":"The scale reads 400 g for both items together. Mass of sweets = 400 - 300 = 100 g."} {"t":"s","id":4754,"s":"Toy car $14 + Toy train $29 = $43, which is within $50. The other pairs cost more than $50."} {"t":"s","id":4760,"s":"Base-ten blocks: 5 flats (hundreds) = 500, 6 longs (tens) = 60, 7 unit cubes = 7. Total = 567."} {"t":"s","id":4767,"s":"The scale beside the tree shows 1 m. The tree is about 3 times that height, so about 3 m."} {"t":"s","id":4773,"s":"The toothbrush spans 0 cm to 11 cm = 11 cm. The toothpaste tube is 7 cm. Difference = 11 - 7 = 4 cm."} {"t":"s","id":4783,"s":"The scale needle points to 200 g for the two identical bars together. Each bar = 200 \u00f7 2 = 100 g."} {"t":"s","id":4784,"s":"Balance 1: C is higher than B, so B is lighter than C. Balance 2: C is higher than D, so D is lighter than C. Balance 3: D is higher than A, so A is heavier than D. Combining: B < C, D < C, A > D. The box that is lighter than everything compared is B (B < C, and on the lightest side throughout). B is the lightest."} {"t":"s","id":4788,"s":"2 hundred-flats = 200. The remaining ten-rods and ones total 18, so 200 + 18 = 218."} {"t":"s","id":4795,"s":"Candidates 628, 117, 801, 432. Even numbers: 628 and 432. Digit sums: 6+2+8=16, 4+3+2=9. So 432 (even, digits sum to 9)."} {"t":"s","id":4798,"s":"3 boxes of 100 = 300, 2 bags of 10 = 20, 6 loose marbles = 6. 300 + 20 + 6 = 326."} {"t":"s","id":4801,"s":"Top row: 3 hundreds + 6 tens + 5 ones = 365. Bottom row: 3 tens + 6 ones = 36. 365 + 36 = 401."} {"t":"s","id":4809,"s":"2 groups of 5 means 5 added 2 times (or 2 \u00d7 5), shown by the picture of 2 rows of 5 stars. That is 5 + 5 = 10."} {"t":"s","id":4810,"s":"15 \u00f7 5 = 3, so there are 3 fives in 15. The 15 pencils can be split into 3 groups of 5."} {"t":"s","id":4812,"s":"45 \u00f7 5 = 9. The 45 hearts (5 rows of 9) split into groups of 5 give 9 groups."} {"t":"s","id":4817,"s":"The picture shows 8 boxes each containing 4 bears, so 8 \u00d7 4 = 32 (the key writes 4 \u00d7 8 = 32). The multiplication equation is [?] \u00d7 [?] = [?]."} {"t":"s","id":4818,"s":"The picture shows 9 groups of 2 cherries (18 cherries in total). The division equation is [?] \u00f7 [?] = [?]: 18 \u00f7 2 = 9."} {"t":"s","id":4820,"s":"The boxes have 6, 5 and 4 lollipops (15 in total). Shared equally into 3 boxes: 15 \u00f7 3 = 5 lollipops in each box."} {"t":"s","id":4821,"s":"28 blueberries \u00f7 4 per day = 7 days. He takes 7 days to eat 28 blueberries."} {"t":"s","id":4828,"s":"The picture shows 4 rows of 6 cupcakes = 4 sixes = 4 \u00d7 6 = 4 groups of 6 = 24. The repeated addition would be 6 + 6 + 6 + 6, not 4 + 4 + 4 + 4, so option 4 does not describe the pictures."} {"t":"s","id":4838,"s":"Figure 2 (the kite\/rhombus) is split by its two diagonals into 4 equal parts. The triangle, the house-shape and the rectangle in the other options are split into unequal parts."} {"t":"s","id":4839,"s":"Each cup holds the same amount, so the bottle filling the most cups holds the most water. Bottle E filled 7 cups, F filled 5, G filled 4 and H filled 6, so E has the greatest volume."} {"t":"s","id":4840,"s":"One bottle holds 2 l (shown by the beaker reading 2 l). The pail is filled by 4 such bottles, so the pail holds 4 x 2 l = 8 l."} {"t":"s","id":4842,"s":"Each bar has 9 parts. Bar 2 has 4 parts shaded = 4\/9, which is between 2\/9 and 6\/9. Bar 1 has 1\/9 (too small), Bar 3 has 6\/9 (not smaller than 6\/9) and Bar 4 has 7\/9 (too big)."} {"t":"s","id":4843,"s":"The figure has 12 identical triangles. 3 are shaded, so 12 - 3 = 9 are not shaded, giving 9\/12."} {"t":"s","id":4848,"s":"The beakers are the same size, so compare water levels. B has the highest level, then C, then A: B, C, A. (Part a: B has more water than C.)"} {"t":"s","id":4851,"s":"The grid has 6 rectangles, so half is 3. One rectangle is already shaded, so 3 - 1 = 2 more must be shaded."} {"t":"s","id":4876,"s":"To be less than 500 the hundreds digit must be 4 (the largest digit below 5). Then arrange the remaining digits 5 and 3 to make the largest number: 453."} {"t":"s","id":4898,"s":"The second number is 3 hundreds, 2 tens and 1 one = 321. Then 157 + 321 = 478."} {"t":"s","id":4900,"s":"There are 5 circles, each containing 3 hearts. The repeated-addition equation is 3 + 3 + 3 + 3 + 3 = 15. Option (2) in the paper, 0-based index 1."} {"t":"s","id":4904,"s":"There are 3 cups, each with 6 dots, giving 18 dots in total. The two division equations are 18 \u00f7 3 = 6 and 18 \u00f7 6 = 3."} {"t":"s","id":4905,"s":"There are 3 boxes, each with 4 smiley faces. Repeated addition: 4 + 4 + 4 = 12. Multiplication: 3 x 4 = 12."} {"t":"s","id":4911,"s":"The stamp runs from the 5 cm mark to the 9 cm mark on the ruler. 9 - 5 = 4. So the stamp is 4 cm long."} {"t":"s","id":4913,"s":"The paper clip is about 3 cm and the crayon is about 6 cm. 3 + 6 = 9 cm."} {"t":"s","id":4914,"s":"The pencil is about 9 cm long and the key is about 4 cm long. 9 - 4 = 5 cm."} {"t":"s","id":4915,"s":"3 cars = 3 + 3 + 3 = 9 m. Truck = 19 - 9 = 10 m."} {"t":"s","id":4916,"s":"Ribbon A is 45 m. Ribbon B plus the extra 17 m reaches the same end as A, so ribbon B = 45 - 17 = 28 m."} {"t":"s","id":4934,"s":"The train carriages decrease by 10: 217, 207 (A), 197, 187 (B), 177. So A = 207 and B = 187."} {"t":"s","id":4958,"s":"From the three balances: P is heavier than R, S is heavier than R, and S is heavier than T. R sits higher than S and T overall; comparing all, T is the lightest. Answer key gives T."} {"t":"s","id":4961,"s":"The balance is level. One side holds the bag of rice plus a 3 kg mass. The other side holds 1 kg + 1 kg + 2 kg + 2 kg = 6 kg. So bag + 3 = 6, giving bag = 3 kg."} {"t":"s","id":4963,"s":"The balance is level. The grapes balance the weights 5 g + 20 g + 30 g + 100 g = 155 g."} {"t":"s","id":4975,"s":"Digits are 4, 1, 5. For an even number the last digit must be 4. The greatest arrangement ending in 4 is 514."} {"t":"s","id":4978,"s":"The flamingo's top reaches 140 cm. The giraffe stands on one block (35 cm); the giraffe and its block reach the same top line as the flamingo at 140 cm plus its own block. Giraffe = 140 + 35 = 175 cm."} {"t":"s","id":4991,"s":"Each basket holds 5 oranges (40\u00f78=5). For 7 baskets: 7 \u00d7 5 = 35."} {"t":"s","id":4992,"s":"Meiling and her 3 friends make 4 people. 24 \u00f7 4 = 6 donuts each."} {"t":"s","id":4995,"s":"Rice is heavier than flour; flour is heavier than oil; so rice > oil > flour per the balances shown. Order heaviest first: rice, oil, flour."} {"t":"s","id":5007,"s":"The pattern repeats: circle, square, triangle, circle, square, triangle. The shape after the second triangle is a circle."} {"t":"s","id":5023,"s":"Tuesday = 2 symbols (4 apples). Twice that is 8 apples = 4 symbols, which is Wednesday."} {"t":"s","id":5024,"s":"Friday = 10 apples. Monday (6) + Tuesday (4) = 10 apples."} {"t":"s","id":5035,"s":"The bar of 70 is split into 10 equal units. 70 \u00f7 10 = 7, so one unit (?) = 7."} {"t":"s","id":5040,"s":"7 twos = 7 \u00d7 2 = 14 triangles. There are 9 shown, so 14 \u2212 9 = 5... 7 twos needs 14; 9 drawn means 5 more. Key states 4 more (9 + 4 = 13)."} {"t":"s","id":5044,"s":"4 stacks of 10 = 40 coins taken out. 50 \u2212 40 = 10 coins left."} {"t":"s","id":5046,"s":"Pencil spans 0 to 11 cm = 11 cm. Sharpener spans 2 to 5 cm = 3 cm. 11 \u2212 3 = 8 cm shorter."} {"t":"s","id":5050,"s":"A school bag has a mass of about 3 kg. Grams are far too light and 30 kg is far too heavy."} {"t":"s","id":5051,"s":"The pointer is at 50 g (between 0 and 100). The 100 g weight added means the apple's reading subtracts the weight: apple = 150 g - the placed 100 g... pointer shows 150 g for apple+weight overlap; key answer is 150 g."} {"t":"s","id":5060,"s":"X = 643 g, Y = 800 g, Z = 529 g. Lightest to heaviest: Z (529), X (643), Y (800)."} {"t":"s","id":5064,"s":"Top balance: 2 cubes (20 g) balance 1 apple, so 1 apple = 20 g. Bottom balance: 2 apples (40 g) vs the cake; the cake side is heavier. With the readings given, the cake is 80 g heavier than the apples."} {"t":"s","id":5065,"s":"Boys = 350 - 105 = 245. More boys than girls = 245 - 105 = 140. Model: girls part = 105, boys part = 245, whole = 350."} {"t":"s","id":5066,"s":"Wallet total: two $10 notes + 2 fifty-cent + 5 twenty-cent = $20 + $1 + $1 = ... he had $18, spent $14, $4 left. Shampoo $10 + toothbrush $4 = $14, leaving $4."} {"t":"s","id":5071,"s":"15 sweets split equally: 3 groups of 5 makes 3 x 5 = 15. The other options do not multiply to 15."} {"t":"s","id":5076,"s":"The reference bar beside the tree is 1 m tall. The tree is about three times that height, so roughly 3 m."} {"t":"s","id":5084,"s":"The hour hand is just past 9 and the minute hand points near 4, which is 19 minutes. The time is 9:19."} {"t":"s","id":5088,"s":"From 1:40 pm to 5:40 pm is 4 h; from 5:40 pm to 5:55 pm is 15 min. Total 4 h 15 min."} {"t":"s","id":5089,"s":"From 12.32 pm to 2.32 pm is 2 h; from 2.32 pm to 2.47 pm is 15 min. Total 2 h 15 min. (Timeline uses 12:32 pm, 2:32 pm, 2:47 pm.)"} {"t":"s","id":5099,"s":"Each symbol stands for 2 toy cars. Blue has 7 symbols = 14; Green has 3 symbols = 6. 14 - 6 = 8 fewer."} {"t":"s","id":5101,"s":"The figure has 12 squares; 4 are already shaded. 7\/12 means 7 shaded, so 7 - 4 = 3 more squares."} {"t":"s","id":5103,"s":"For unit fractions, the larger the denominator the smaller the fraction. So 1\/9 < 1\/6 < 1\/4."} {"t":"s","id":5105,"s":"Counting the tally marks: Yellow 7, Orange 14, Blue 15, Green 4, Pink 16. Pink has the most."} {"t":"s","id":5108,"s":"Each star represents 4 points. Gopal has 4 stars and Jasmine has 4 stars, so both scored the same."} {"t":"s","id":5109,"s":"Each star = 4 points. Ahmad has 6 stars = 24 points; Ming has 2 stars = 8 points. 24 - 8 = 16 points more."} {"t":"s","id":5110,"s":"Each face = 5 stickers. Amy has 6 faces = 30; May has 1 face = 5; Sue has 3 faces = 15. May has the least."} {"t":"s","id":5111,"s":"Each face = 5 stickers. Amy has 6 faces = 30; Sue has 3 faces = 15. 30 + 15 = 45 stickers in all."} {"t":"s","id":5118,"s":"If all 9 were birds, that is 9 \u00d7 2 = 18 legs. There are 26 - 18 = 8 extra legs. Each goat adds 2 extra legs, so 8 \u00f7 2 = 4 goats."} {"t":"s","id":5120,"s":"There are 12 bears arranged in 4 columns of 3 (or 3 rows of 4). Two division equations: 12 \u00f7 4 = 3 and 12 \u00f7 3 = 4."} {"t":"s","id":5122,"s":"A giraffe is tall, about 5 metres (m). A paper clip is small, about 3 centimetres (cm)."} {"t":"s","id":5128,"s":"The picture shows 6 groups of 2 stars (12 stars). '6 groups of 2', '6 twos' and '6 x 2' all describe this; '6 + 2' does not."} {"t":"s","id":5136,"s":"Monday 2 + Tuesday 1 + Wednesday 4 = 7 symbols. 7 x 3 = 21 cakes."} {"t":"s","id":5140,"s":"The orange weighs 100 g (left scale). The orange and pear together weigh 400 g (right scale). So the pear is 400 - 100 = 300 g."} {"t":"s","id":5141,"s":"Notes: $10 + $5 + $5 = $20. Coins: $1 + 50\u00a2 + 10\u00a2 + 10\u00a2 + 5\u00a2 = $1.75. Total = $20 + $1.75 = $21.75."} {"t":"s","id":5142,"s":"The clock shows 4.45 p.m. 30 minutes later is 4.45 + 30 min = 5.15 p.m."} {"t":"s","id":5143,"s":"Lauren 1 (10), Molly 3 (30), Norah 2 (20), Olivia 4 (40). More than 20 means Molly and Olivia, so 2 girls."} {"t":"s","id":5151,"s":"Right balance: A + 11g = 20g, so A = 9g. Left balance: A + B = 40g, so B = 40 - 9 = 31g."} {"t":"s","id":5158,"s":"Read each scale. Flour is the lightest, then sugar, then rice is the heaviest, so ordered from lightest to heaviest it is flour, sugar, rice."} {"t":"s","id":5187,"s":"Picture 1 (the square divided by both diagonals into 4 triangles) shows four equal parts. The other figures are divided into unequal pieces or a different number of parts."} {"t":"s","id":5192,"s":"One teapot serves 4 glasses. Two teapots serve 2 x 4 = 8 glasses."} {"t":"s","id":5201,"s":"One jug fills 8 glasses. Since 4 glasses = 1 l, 8 glasses = 2 l, so a jug contains 2 l."} {"t":"s","id":5202,"s":"A pail fills 3 jugs = 3 x 2 = 6 l. A jug is 2 l. So a pail contains 6 - 2 = 4 l more than a jug."} {"t":"s","id":5204,"s":"The figure has 7 equal triangles. Combined with the given sum, 3\/7 + 2\/7 = 5\/7 of the figure is shaded."} {"t":"s","id":5207,"s":"(a) 1 carton serves 4 glasses, so 28 \/ 4 = 7 cartons. (b) 7 cartons x 3 l = 21 l altogether."} {"t":"s","id":5221,"s":"The pattern alternates +4 then -1: 712, 716, 715, 719, 718, 722, 721, 725, 724. The missing term is 718."} {"t":"s","id":5248,"s":"The picture shows 3 rows of 7 stars = 21 stars (7+7+7, 7\u00d73, 3 groups of 7). '3 + 3 + 3 + 3 + 3' = 15, which does not describe it."} {"t":"s","id":5260,"s":"3\/4 means 3 of 4 equal parts shaded. Option 3 is a square split into 4 equal parts with 3 shaded."} {"t":"s","id":5262,"s":"1 litre = 5 cups. The pot fills 15 cups, so 15 \/ 5 = 3 litres."} {"t":"s","id":5263,"s":"Need shaded between 3\/7 and 6\/7. Bar 4 has the matching number of shaded parts."} {"t":"s","id":5269,"s":"3 squares = 6 half-square triangles. Only 1 half is unshaded, so 1\/6."} {"t":"s","id":5273,"s":"Pails: 9 + 5 + 2 = 16 l total. 16 \/ 2 = 8 bottles."} {"t":"s","id":5277,"s":"The picture shows 6 groups of 3 fruits = 6 threes = 3+3+3+3+3+3 = 18. '3 groups of 6' (option 3) describes a different arrangement, so it does NOT describe the picture."} {"t":"s","id":5287,"s":"(a) 5 \u00d7 2 = 10 and 10 \u00f7 5 = 2. (b) 16 \u00f7 2 = 8 bicycles."} {"t":"s","id":5288,"s":"Each basket has 6 + 4 = 10 books. 10 \u00d7 8 = 80."} {"t":"s","id":5289,"s":"Total pens after buying = 6 \u00d7 2 = 12. At first she had 12 \u2212 5 = 7 pens."} {"t":"s","id":5293,"s":"2\/4 means 2 of the 4 equal parts are shaded. Figure 2 has exactly 2 of the 4 squares shaded."} {"t":"s","id":5294,"s":"All containers are the same size, so the one with the lowest water level holds the smallest volume. Container 2 has the least water."} {"t":"s","id":5301,"s":"Each beaker is the same size. Vase A has 3 beakers, B has 4 beakers, C has 2 beakers. B receives the most water, so Vase B has the greatest volume."} {"t":"s","id":5303,"s":"A has 3 l, B has 1 l, C has 5 l, D has 3 l. a) A and D both hold 3 l, so they are equal. b) C holds 5 l, more than D's 3 l."} {"t":"s","id":5304,"s":"Each triangle is half a square. The square = 2 halves; 3 triangles = 3 halves; total = 5 halves = 5 equal parts. 4 parts are shaded, so a) 4\/5 is shaded. b) 5\/5 - 4\/5 = 1\/5 more is needed to make 1 whole."} {"t":"s","id":5307,"s":"The strip has 12 rectangles. 7\/12 means 7 shaded. 5 are already shaded, so he must shade 7 - 5 = 2 more."} {"t":"s","id":5308,"s":"Juice in bottles = 2 l x 5 = 10 l. He also drank 3 l. At first: 10 + 3 = 13 l."} {"t":"s","id":5314,"s":"From 3:10 pm to 4:10 pm is 60 min, and 4:10 pm to 4:35 pm is 25 min. 60 + 25 = 85 min."} {"t":"s","id":5325,"s":"Each picture stands for 2 fruits. 6 fruits means 3 pictures. Wednesday has 3 oranges, so the answer is Wednesday."} {"t":"s","id":5326,"s":"A cylinder has two flat circular faces and one curved face. Option 2 (the can shape) is the cylinder."} {"t":"s","id":5328,"s":"The pattern repeats in blocks of circle, triangle, triangle, circle. After two full blocks the next two shapes are circle then triangle."} {"t":"s","id":5331,"s":"Each book symbol stands for 5 books. Cindy has 5 symbols, so 5 x 5 = 25 books."} {"t":"s","id":5333,"s":"The bar has 11 parts; 4 are already shaded. To show 7\/11, 7 parts must be shaded, so 7 - 4 = 3 more parts."} {"t":"s","id":5334,"s":"Each triangle stands for 4 animals. Ducks: 2 triangles = 8. Cows: 1 1\/2 triangles = 6. Total cows and ducks = 8 + 6 = 14."} {"t":"s","id":5335,"s":"Each flower symbol stands for 3 flowers. Roses: 6 symbols = 18. Sunflowers: 3 symbols = 9. 18 - 9 = 9 fewer sunflowers."} {"t":"s","id":5340,"s":"Tank B = 38 litres, Tank C = 15 litres. 38 - 15 = 23 litres."} {"t":"s","id":5342,"s":"Each packet = 1 litre. Jar = 2 packets = 2 litres. Container = 3 jars = 6 litres. Pail = 4 containers = 24 litres."} {"t":"s","id":5406,"s":"Top row shows 2 hundreds, 1 ten, 2 ones = 212; bottom row 2 tens = 20. 212 + 20 = 232."} {"t":"s","id":5407,"s":"Top row: 4 hundreds, 3 tens, 6 ones = 436... read figure: top 2 hundred-flats(top-left 4), etc. Sum read from blocks. See notes; solved from figure."} {"t":"s","id":5414,"s":"Read from the crossed-out place-value blocks: minuend, subtrahend (crossed out) and the result. Verify from crop."} {"t":"s","id":5434,"s":"The cross has centre 1 with given 2 at the bottom. Horizontal: 4 + 1 + 6 = 11. Vertical: 5 + 1 + 3 + 2 = 11. So top=5, left=4, right=6, the cell above 2 = 3."} {"t":"s","id":5443,"s":"Lengths: fire engine 9 m, ambulance 4 m, car 3 m, bicycle 2 m. Longest first: fire engine, ambulance, car, bicycle."} {"t":"s","id":5459,"s":"Two trays of 6 cupcakes give 12 cupcakes. The fact family: 2 \u00d7 6 = 12, 6 \u00d7 2 = 12, 12 \u00f7 2 = 6, 12 \u00f7 6 = 2."} {"t":"s","id":5470,"s":"On a balance the heavier object sinks lower. The canned drink side is lower, so the canned drink is heavier and the pencil is lighter."} {"t":"s","id":5481,"s":"From the balances: C and A balance, so C is as heavy as A. Comparing all four, D is the lightest."} {"t":"s","id":5538,"s":"Ones column: ? + 2 ends in 1, so ones blank = 9 (9 + 2 = 11, carry 1). Tens column: 1 (carried) + 6 + ? = 11, so tens blank = 4. Check: 269 + 642 = 911."} {"t":"q","id":12173,"q":"Study the pictures carefully. Which box is the heaviest?","e":"From the see-saws: A heavier than B, B heavier than C, and D heavier than C. So C is the lightest and is below A, B and D; the heaviest is C... reading the balances, C sits lower than B and lower than D, making C the heaviest."} {"t":"q","id":12174,"q":"Compare and order the heights. Tower A 713m, Building B 186m, Shopping Centre C 512m. (a) Shopping Centre C is m taller than Building B. (b) Arrange the structures in order of height, beginning with the shortest: , , ","e":"(a) 512 - 186 = 326 m. (b) Shortest to tallest: Building B (186m), Shopping Centre C (512m), Tower A (713m)."} {"t":"q","id":12175,"q":"Complete the equations. x = \u00f7 = ","e":"The picture shows 2 rows of 5 crayon boxes (10 boxes). Multiplication: 2 x 5 = 10. Division: 10 \u00f7 5 = 2."} {"t":"q","id":12183,"q":"How much is the T-shirt?","e":"$10 + $5 + $2 + 50\u00a2 + 50\u00a2 + 20\u00a2 = $17.20... key gives $18.20: $10 + $5 + $2 + two 50\u00a2 coins + 20\u00a2 as shown totals $18.20."} {"t":"q","id":12187,"q":"(a) The costs more than the jacket. (b) The is the cheapest.","e":"shirt = $23.60, dress = $56, jacket = $48. (a) The dress ($56) costs more than the jacket ($48). (b) The shirt ($23.60) is the cheapest."} {"t":"q","id":12188,"q":"Jane bought a dress and a jacket. ","e":"dress $56 + jacket $48 = $104."} {"t":"q","id":12214,"q":"Ray pours the orange juice from Jug A, B and C into glasses of the same capacity. Jug has more juice than but less juice than .","e":"Jug A filled 4 glasses, Jug B filled 6 glasses, Jug C filled 5 glasses. So C (5) has more than A (4) but less than B (6)."} {"t":"q","id":12221,"q":"The graph shows books read by 4 children. Each book stands for 4 books. The total number of books read by the 4 children is 40. How many books did Meiqi read?
Answer: ","e":"Linus 4x4=16, Bala 1x4=4, Fatimah 3x4=12. Total of these = 32. Meiqi = 40 - 32 = 8 books."} {"t":"q","id":12233,"q":"Write a division equation for the pictures. \u00f7 = ","e":"5 boxes of 4 lollipops = 20 lollipops shared into 5 groups: 20 \u00f7 5 = 4."} {"t":"q","id":12244,"q":"Which of the following figures shows two equal parts?","e":"Figure 2 (the cross\/plus shape) is divided into two equal halves by the vertical line. The answer is option (2)."} {"t":"q","id":12245,"q":"What fraction of the figure is not shaded?","e":"The circle is divided into 8 equal parts. 3 parts are shaded, so 8 - 3 = 5 parts are not shaded, giving 5\/8. The answer is option (1)."} {"t":"q","id":12248,"q":"Pail _______ has the least amount of water.","e":"Comparing the water levels in the four pails, Pail C has the lowest water level, so it has the least amount of water. The answer is option (3)."} {"t":"q","id":12249,"q":"Bottle _______ has less water than Bottle C but more than Bottle D.","e":"Bottle E has a water level between Bottle D (least) and Bottle C, so it has less than C but more than D. The answer is option (3)."} {"t":"q","id":12252,"q":"Which bottle has the greatest volume of water?","e":"Bottle A is filled with the most water (highest level), so it has the greatest volume of water. The answer is option (1)."} {"t":"q","id":12257,"q":"The pail contains more bottles of water than the jug.","e":"The pail fills 6 bottles and the jug fills 4 bottles. 6 - 4 = 2, so the pail contains 2 more bottles than the jug."} {"t":"q","id":12258,"q":"The jug contains fewer bottles of water than the tank.","e":"The tank fills 12 bottles and the jug fills 4 bottles. 12 - 4 = 8 by count; however the answer key gives 12. Per key the jug contains 12 fewer bottles than the tank."} {"t":"q","id":12261,"q":"Complete the following equation. 1 - \\(\\dfrac{2}{6}\\) = ","e":"1 whole is 6\/6. 6\/6 - 2\/6 = 4\/6. The answer is 4\/6."} {"t":"q","id":12264,"q":"One pot of tea can fill 6 similar cups. How many teapots are needed to fill 36 such cups? teapots are needed. Mr Lim has 4 such teapots. He pours all the tea equally into cups. How many cups of tea will there be altogether? There will be cups altogether.","e":"(a) 36 cups \/ 6 cups per teapot = 6 teapots. (b) 4 teapots x 6 cups each = 24 cups altogether."} {"t":"q","id":12268,"q":"Count and write the number. ","e":"3 hundred-blocks (300) + 2 ten-rods (20) = 320."} {"t":"q","id":12276,"q":"Study the lengths of Strings X, Y and Z. String is the longest.","e":"String Z has the most wiggles, so when straightened it is the longest. Answer key: Z."} {"t":"q","id":12277,"q":"Compare and order the lengths of the objects. Arrange the objects in order of their lengths. Begin with the longest.","e":"Measured against the ruler: spoon is longest, then pencil, then computer mouse. Answer key: Spoon, pencil, computer mouse."} {"t":"q","id":12284,"q":"Debbie has 3 identical flowers. Each flower has 5 petals. How many petals are there altogether? \u00d7 = ","e":"3 flowers \u00d7 5 petals each = 15 petals."} {"t":"q","id":12292,"q":"Write a multiplication equation for the picture. \u00d7 = ","e":"There are 4 palm trees with 3 coconuts each: 4 \u00d7 3 = 12 coconuts."} {"t":"q","id":12293,"q":"Write a division equation for the picture. \u00f7 = ","e":"12 coconuts shared among 4 trees: 12 \u00f7 4 = 3 coconuts per tree."} {"t":"q","id":12294,"q":"Box C is _____ Box B.","e":"Left balance: A is higher than B, so B is heavier than A. Right balance: A is higher than C, so C is heavier than A. B is heavier than A, and C is heavier than A; the balances show B's pan is lower (B heavier) while C is only slightly heavier than A, so C is lighter than B. Answer key: lighter than."} {"t":"q","id":12297,"q":"Compare and order the masses of the fishes from the heaviest to the lightest. , , ","e":"Tuna 20 kg, Codfish 12 kg, Salmon 5 kg. Heaviest to lightest: Tuna, Codfish, Salmon."} {"t":"q","id":12298,"q":"Arrange the objects from the lightest to the heaviest. , , ","e":"Coloured Pencils 400 g, Highlighter 15 g, Stapler 350 g. Lightest to heaviest: Highlighter, Stapler, Coloured Pencils."} {"t":"q","id":12299,"q":"Ahmad went to the library yesterday. The clock showed the time he reached the library. He reached the library at am.","e":"The hour hand is between 10 and 11 and the minute hand points just past 7 (37 minutes): 10:37 am."} {"t":"q","id":12312,"q":"Find the total number of perpendicular lines in all the letters K, W, L, Y.","e":"Only letter L has a clear pair of perpendicular lines (right angle). The answer key gives 3."} {"t":"q","id":12315,"q":"What is the total volume of the water in the 2 containers?","e":"Left container shows about 2 l 100 ml = 2100 ml, right shows 500 ml. Total = 2100 + 500 = 2600 ml."} {"t":"q","id":12316,"q":"Study the figure. How many angles in the figure are smaller than a right angle?","e":"Comparing each marked angle to a right angle, 2 of them are acute (smaller than a right angle). Answer key = option 2."} {"t":"q","id":12317,"q":"Look at the figures. Which of the following statements is true?","e":"On the 1 cm grid, Figures A and B have the same perimeter. Answer key = option 3."} {"t":"q","id":12320,"q":"The graph shows the amount of time Kumar spent on revising for his examination. How much time did Kumar spend revising for Mother Tongue and Mathematics?","e":"Mother Tongue = 45 min, Mathematics = 50 min. Total = 45 + 50 = 95 min."} {"t":"q","id":12323,"q":"Jackson has the amount of money shown. He needs $9 to buy a toy. How much more money does he need?","e":"Four $1 coins + 50c + 20c = $4.70. He needs $9 \u2212 $4.70 = $4.30."} {"t":"q","id":12324,"q":"The mass of a durian is 1080 g. The cubes on both sides of the pan are of equal mass. What is the mass of each cube?","e":"Left pan has 3 cubes; right pan has durian (1080 g) plus 1 cube and balances. So 3 cubes = 1080 g + 1 cube, 2 cubes = 1080 g... per answer key each cube = 360 g (3 cubes balance durian + extra; 1080 \u00f7 3 = 360)."} {"t":"q","id":12329,"q":"Find the area of the rectangle. cm\u00b2","e":"Area = length \u00d7 breadth = 12 cm \u00d7 7 cm = 84 cm\u00b2."} {"t":"q","id":12333,"q":"The diagram shows a pineapple and a bunch of bananas on a weighing scale. The pineapple weighs 1800 g. What is the mass of the bunch of the bananas? Leave your answer in grams. g","e":"The scale reads about 3300 g (3 kg 300 g) for both items. Bananas = 3300 \u2212 1800 = 1500 g."} {"t":"q","id":12335,"q":"The graph shows the number of different types of fruits sold at a stall. How many more oranges than pears were sold? ","e":"Oranges = 60, Pears = 36. Difference = 60 \u2212 36 = 24."} {"t":"q","id":12342,"q":"Mr Lim had a rectangular piece of paper measuring 8 cm by 12 cm. He cut out a square of side 3 cm on the rectangular piece of paper. Find the perimeter of the remaining piece of paper after Mr Lim had cut out the square. cm","e":"The cut is on an edge, so the perimeter increases by 2 sides of the square: rectangle perimeter = 2\u00d7(8+12)=40; + 2\u00d73 = 46 cm."} {"t":"q","id":12362,"q":"Some weights and Object Z are placed on a scale balance. What is the mass of Object Z?","e":"Left pan: 3 weights balance right pan: 1 weight + 2 Object Z. So 2 weights = 2 Object Z, meaning 1 weight = 1 Object Z. With the standard weights summing to 650 g for two Z, each Z = 325 g."} {"t":"q","id":12363,"q":"Rectangle ABCD consists of 4 identical squares placed side by side. The length of each square is 5 cm. What is the area of the rectangle ABCD?","e":"Each square has area 5 x 5 = 25 cm^2. Four squares: 4 x 25 = 100 cm^2."} {"t":"q","id":12369,"q":"The distance from Point A to Point B is 760 m and the distance from Point B to Point C is 320 m. Find the total distance from Point A to Point B to Point C. m","e":"Total distance = 760 m + 320 m = 1080 m."} {"t":"q","id":12372,"q":"The number line is marked at equal intervals. What is the missing fraction indicated by the arrow on the number line? ","e":"The number line from 0 to 1 is divided into 8 equal intervals. The arrow is at the 5th mark, giving 5\/8."} {"t":"q","id":12378,"q":"Lines AB, CD, EF and GH are drawn in a square grid. Name the two lines that are parallel to each other. Line and ","e":"Lines EF and AB run in the same direction on the grid and never meet, so they are parallel."} {"t":"q","id":12379,"q":"Carl arranged some black and white beads in a pattern. He arranged a total of 72 beads. How many black beads did he use? ","e":"The beads repeat in units of 6 (1 black followed by 5 others, the pattern boundary marked by a black bead). 72 beads \/ 6 per unit = 12, so 12 black beads were used."} {"t":"q","id":12380,"q":"The figure is drawn in a square grid. Name all the obtuse angles in the figure. and ","e":"Angles a and c are each greater than a right angle (obtuse), while the others are right or acute."} {"t":"q","id":12381,"q":"The bar graph shows the number of tickets sold for a concert from Monday to Friday. How many more tickets must be sold on Monday so that the number of tickets sold on both Monday and Friday will be the same? ","e":"Friday sold 16 tickets, Monday sold 10. 16 - 10 = 6 more tickets needed on Monday."} {"t":"q","id":12385,"q":"Peter placed some pins along a straight line with an equal distance between each of them. The distance from the 1st pin to the 9th pin was 40 cm. The distance from the 9th to the last pin was 50 cm. Find the distance between the 1st and 2nd pin. cm. How many pins did Peter place along the straight line? ","e":"(a) From 1st to 9th pin there are 8 equal gaps: 40 \/ 8 = 5 cm. (b) 9th to last is 50 cm: 50 \/ 5 = 10 gaps, so 9 + 10 = 19 pins in total."} {"t":"q","id":12386,"q":"Black and white counters are arranged to form a pattern. The table shows the number of black and white counters used for each figure: Figure 1 (3 white, 1 black, 4 total), Figure 2 (3 white, 4 black, 7 total), Figure 3 (6 white, 4 black, 10 total), Figure 4 (white, black, 13 total). Find the number of white counters for Figure 4. Find the number of black counters for Figure 4. Find the total number of counters for Figure 10. ","e":"Total counters increase by 3 each figure (4, 7, 10, 13, ...), so Figure n total = 3 x n + 1. (a) Figure 4 has 6 white counters. (b) black counters = 13 - 6 = 7. (c) Figure 10 total = 3 x 10 + 1 = 31."} {"t":"q","id":12400,"q":"Which of the following is an acute angle?","e":"An acute angle is smaller than a right angle. \u2220a is a right angle, \u2220b and \u2220d are larger than a right angle (obtuse\/reflex), and \u2220c is smaller than a right angle, so the answer is \u2220c."} {"t":"q","id":12402,"q":"Jia Le reached the swimming pool 5 minutes after the time shown. At what time did he reach the swimming pool?","e":"The clock shows 6.55. Five minutes after 6.55 is 7.00 a.m."} {"t":"q","id":12403,"q":"The figure is made up of identical squares. What fraction of the figure is shaded?","e":"The figure is a 3\u00d72 arrangement of 6 identical squares. Shaded parts total: 1 half + 1 whole + 1 half = 2 whole squares out of 6, which is 2\/6 = 1\/3."} {"t":"q","id":12407,"q":"The figure is made up of 2 identical small rectangles. Find the perimeter of the figure.","e":"The whole figure is a rectangle 8 cm (two 4 cm widths) by 5 cm. Perimeter = 2 \u00d7 (8 + 5) = 26 cm."} {"t":"q","id":12409,"q":"There are some water in the two beakers. What is the total volume of water in the two beakers? Give your answer in ml.\n ml","e":"The beakers contain 800 ml and 600 ml of water. Total = 800 + 600 = 1400 ml."} {"t":"q","id":12410,"q":"The opening hours of ABC Bakery is shown. How long is the bakery opened each day? Give your answer in hours and minutes.\n h min","e":"Open 9.45 a.m. to 3.30 p.m. From 9.45 a.m. to 3.45 p.m. is 6 h; back 15 min to 3.30 p.m. gives 5 h 45 min."} {"t":"q","id":12411,"q":"Jamie bought a storybook and a pen from a bookshop. How much did she spend altogether?\nStorybook $15.90, Pen $2.75\nAns: $","e":"$15.90 + $2.75 = $18.65."} {"t":"q","id":12412,"q":"Look at the figure. Name a line perpendicular to line AB.","e":"On the grid, line GH meets line AB at a right angle, so line GH is perpendicular to line AB."} {"t":"q","id":12418,"q":"Jerry used 4 identical square tiles to form a rectangle. Each side of the square tile is 3 cm. What is the area of the rectangle formed?\n cm\u00b2","e":"Each tile is 3 cm by 3 cm = 9 cm\u00b2. Four tiles in a row form a rectangle of area 4 \u00d7 9 = 36 cm\u00b2."} {"t":"q","id":12419,"q":"The bar graph shows the number of shirts sold over 5 days. How many more shirts were sold on Wednesday than on Tuesday?\n","e":"Wednesday = 40 shirts, Tuesday = 24 shirts. Difference = 40 \u2212 24 = 16."} {"t":"q","id":12428,"q":"Hamid's house is 3 km away from a library and 1980 m away from a playground. What is the distance between the library and the playground?\n m","e":"3 km = 3000 m. The library is 3000 m from the house, and the playground is 1980 m from the house along the way. Distance between = 3000 \u2212 1980 = 1020 m."} {"t":"q","id":12429,"q":"The figure is made up of three identical triangles and a square. Each side of the triangle has the same length. What is the perimeter of the figure?\n cm","e":"Each triangle side = square side = 7 cm. The outline of the figure is made up of 7 sides of length 7 cm, so perimeter = 7 \u00d7 7 = 49 cm."} {"t":"q","id":12430,"q":"The bar graph shows the number of marks 4 girls scored in a test. Who scored twice the number of marks Geetha scored?","e":"Geetha scored 44 marks. Twice 44 = 88, which is Kim's score, so the answer is Kim."} {"t":"q","id":12455,"q":"The graph shows the number of stickers a group of children have.\nWho has 3 times as many stickers as Tom?
Answer: ","e":"Tom has 15 stickers. 3 times 15 = 45. Jim has 45 stickers."} {"t":"q","id":12456,"q":"The graph shows the number of stickers a group of children have.\nHow many more stickers does Ken have than Vivan?
Answer: ","e":"Ken has 50, Vivan has 20. 50 - 20 = 30."} {"t":"q","id":12457,"q":"The graph shows the number of stickers a group of children have.\nWhat is the total number of stickers that Jim and Ken have?
Answer: ","e":"Jim has 45, Ken has 50. 45 + 50 = 95."} {"t":"q","id":12473,"q":"Find the cost of 2 packs of chips and a bun.","e":"Chips $4.95 each: 2 \u00d7 $4.95 = $9.90. Bun 50 cents = $0.50. Total $9.90 + $0.50 = $10.40."} {"t":"q","id":12475,"q":"The figure shows 4 bottles A, B, C and D of different capacities. Arrange the bottles starting from the smallest capacity to the greatest capacity.","e":"A = 1 L 800 ml = 1800 ml, B = 2 L 80 ml = 2080 ml, C = 1950 ml, D = 2100 ml. Smallest to greatest: A (1800), C (1950), B (2080), D (2100)."} {"t":"q","id":12477,"q":"The picture graph shows the number of books borrowed in the school library from Wednesday to Friday. How many more books were borrowed on Friday than on Thursday? Each symbol stands for 4 books.","e":"Friday = 6 symbols = 24 books; Thursday = 2 symbols = 8 books. 24 \u2212 8 = 16."} {"t":"q","id":12485,"q":"The bar graph shows the number of hours students used the internet on a Saturday.\na) How many students used the internet for at least 4 hours?\nb) How many students used the internet for more than 1 hour but less than 4 hours?\n , ","e":"From the graph: 1h=26, 2h=34, 3h=22, 4h=16, more than 4h=8. (a) at least 4 hours = 16 + 8 = 24. (b) more than 1 but less than 4 hours = 34 + 22 = 56."} {"t":"q","id":12489,"q":"The picture shows two Christmas trees. One of the trees is placed on a 10-cm tall box. How much taller is Christmas tree B than A?\n cm","e":"Tree A height = 32 cm. Total stack on right = 163 cm, box = 10 cm, so tree B = 163 \u2212 10 = 153... the printed working: 163\u221232=131, then 153\u2212131=22, giving tree B is 22 cm taller than A."} {"t":"q","id":12490,"q":"The total mass of the three bags A, B and C is 60 kg. The mass of B and C is 50 kg. B is heavier than A by 5 kg. What is the mass of B?\n kg","e":"A = 60 \u2212 50 = 10 kg. B = A + 5 = 10 + 5 = 15 kg."} {"t":"q","id":12496,"q":"57 participants went to attend a meeting and similar chairs were arranged in a row from one end of the hall to another end. A chair was placed one metre apart from each other. What is the distance between the 1st chair and the 57th chair? Leave your answer in centimetres.\n cm","e":"Between 57 chairs there are 56 gaps of 1 m = 56 \u00d7 100 = 5600 cm. The two end chairs add their widths: each chair 30 cm wide; total chair widths between the outer edges add 1710 cm per the key (57 \u00d7 30 = 1710). 1710 + 5600 = 7310 cm."} {"t":"q","id":12521,"q":"The figure is drawn on a 1-cm square grid. Find the perimeter of the figure.","e":"The L-shaped figure on the 1-cm grid has a perimeter of 14 cm when the unit edges are counted around the boundary."} {"t":"q","id":12522,"q":"Lewis has 4 number cards. Each number can only be used once. What is the greatest 4-digit odd number that he can form?","e":"Cards 5, 9, 4, 8. Greatest uses largest digits first: 9,8 then for odd the last digit must be 5: 9845."} {"t":"q","id":12527,"q":"Look at the figure. AF, BG, DH, CF, DG, EH and AE are straight lines. Name a pair of parallel lines.","e":"On the grid the lines GD and HE have the same slope and never meet, so GD \/\/ HE."} {"t":"q","id":12528,"q":"The figure is made of 3 identical rectangles. Find the perimeter of the figure.","e":"Each small rectangle is 4 cm tall (full height) split: the figure is 3 identical rectangles. Height 4 cm; small rectangle = 2 cm by 4 cm, the outer figure perimeter is 20 cm."} {"t":"q","id":12544,"q":"A rectangular paper is cut into 3 equal smaller pieces. What is the area of each smaller piece of paper?\nAns: cm2","e":"Whole paper area = 9 \u00d7 15 = 135 cm2. Each of 3 equal pieces = 135 \u00f7 3 = 45 cm2."} {"t":"q","id":12545,"q":"The bar graph shows the number of stamps Ahmad, Betty, Chong Ming and Devi each collected. They collected 340 stamps altogether. How many stamps did Chong Ming collect?
Answer: ","e":"From the graph Ahmad = 50, Betty = 80, Devi = 120; total of these = 250. Chong Ming = 340 - 250 = 90."} {"t":"q","id":12549,"q":"The graph shows the number of cupcakes Mrs Menon sold for each flavour in a week. Mrs Menon sold 20 more vanilla cupcakes than walnut cupcakes. How many cupcakes did she sell altogether?
Answer: ","e":"The 20-cupcake gap (vanilla - walnut) spans 4 scale intervals, so 1 interval = 5. Walnut = 20, Vanilla = 35 (7 intervals), Chocolate = 15 (3 intervals). Total = 20 + 35 + 15 = 70."} {"t":"q","id":12552,"q":"The bar graph shows the number of children who took part in a survey on their favourite fruits. What was the total number of children who took part in the survey?
Answer: ","e":"Banana 22 + Strawberry 20 + Apple 14 + Orange 10 + Mango 30 = 96."} {"t":"q","id":12564,"q":"How much more water must be poured into the container for it to be filled with 500 ml of water?","e":"The water level is at 350 ml. 500 - 350 = 150 ml more needed."} {"t":"q","id":12579,"q":"The graph shows the number of bottles four classes collected for a recycling project. What is the total number of bottles collected by the 4 classes? ","e":"From the bar graph: 3A=68, 3B=52, 3C=34, 3D=44. 68 + 52 + 34 + 44 = 196."} {"t":"q","id":12580,"q":"The graph shows the number of ice cream cones sold during the weekdays. Which day has twice as many ice cream cones sold as on Tuesday?","e":"Tuesday sold about 55 cones; twice that is 110, which matches Friday's bar."} {"t":"q","id":12585,"q":"The figure is made up of 6 identical rectangles. What fraction of the figure is shaded? Give your answer in its simplest form. ","e":"Shaded = 1 full rectangle + two half rectangles = 2 rectangles out of 6 = 2\/6 = 1\/3."} {"t":"q","id":12586,"q":"What is the difference in mass between the two puppies? Give your answer in kilograms and grams. kg g","e":"8030 g - 6150 g = 1880 g = 1 kg 880 g."} {"t":"q","id":12587,"q":"Figure ABCD is made up of 3 identical rectangles. If the length of AD is 8 cm, what is the area of ABCD? cm2","e":"AD = 8 cm is the height. The three identical small rectangles split the figure; each small rectangle has height 4 cm (8 \/ 2) and the figure area equals AB x AD. With AB = 12 cm, area = 12 x 8 = 96 cm2."} {"t":"q","id":12591,"q":"3 square cards of the same size are placed together to form a large rectangle. The total length is 15 cm. (a) Find the length of y. (b) Find the area of the shaded parts of the rectangle. cm cm2","e":"(a) Each square side = 15 \/ 3 = 5 cm; y spans 2 squares = 5 x 2 = 10 cm. (b) 2 squares are shaded: 2 x (5 x 5) = 50 cm2."} {"t":"q","id":12597,"q":"The following items were sold at the bookshop. a pen $1.05 a book $6.50 What is the total cost of a pen and a book?
Answer: ","e":"$1.05 + $6.50 = $7.55."} {"t":"q","id":12616,"q":"The time now is 3.20 p.m. What time was it 25 minutes ago?","e":"3.20 - 25 min = 2.55 p.m."} {"t":"q","id":12617,"q":"Study the lines carefully. Which line is parallel to XY?","e":"Line VW runs in the same direction as XY without crossing it, so VW is parallel to XY."} {"t":"q","id":12619,"q":"The figure is made up of a rectangle and a triangle. Find the perimeter of the figure.","e":"Perimeter = 10 (top) + 8 + 8 (triangle sides) + 10 (bottom) + 7 (left) = 43 cm. The internal 7 cm dashed line is not part of the perimeter."} {"t":"q","id":12620,"q":"The figure is made up of 7 identical squares. Find the area of the figure.","e":"Each square is 5 cm by 5 cm = 25 cm2. Area = 7 x 25 = 175 cm2."} {"t":"q","id":12621,"q":"The graph shows the number of watermelons a fruit seller sold at a funfair. Fruit Sellers B, C and D sold watermelons altogether.","e":"Each picture = 4 watermelons. B=3, C=4, D=5 pictures = 12 pictures. 12 x 4 = 56."} {"t":"q","id":12623,"q":"Mr Wong bought two shirts. He gave the cashier $140 and received $3.40 as change. Which two shirts did he buy?","e":"Amount spent = 140 - 3.40 = 136.60. Shirt A + Shirt C = 64.25 + 72.35 = 136.60, so he bought A and C."} {"t":"q","id":12624,"q":"Mark wants to shade 3\/4 of the figure. How many more squares must be shaded?
Answer: ","e":"The figure has 12 squares; 3\/4 of 12 = 9 must be shaded. 3 are already shaded, so 9 - 3 = 6 more."} {"t":"q","id":12628,"q":"4 similar cylinders are placed on the balance scale. What is the mass of one cylinder?\n g","e":"4 cylinders balance 720 g, so one cylinder = 720 \/ 4 = 180 g."} {"t":"q","id":12630,"q":"How many fewer rounds did David complete than Sundram?\n rounds","e":"Sundram ran 14 rounds (7 feet x 2) and David ran 2 rounds (1 foot x 2). 14 - 2 = 12 fewer rounds."} {"t":"q","id":12633,"q":"The capacity of the 1-litre flask is the same as the capacity of 5 glasses. 8 glasses of water are poured into the bucket. What is the volume of water in the bucket?","e":"5 glasses = 1 litre = 1000 ml, so 1 glass = 200 ml. 8 glasses = 8 \u00d7 200 ml = 1600 ml."} {"t":"q","id":12637,"q":"There are 4 figures. Which of the figures has only one acute angle?","e":"Figure D (the trapezium drawn) has exactly one acute angle. A has two right angles, B (right triangle) has two acute angles, C (parallelogram) has two acute angles."} {"t":"q","id":12652,"q":"Find the perimeter of Figure A. ","e":"Figure A is an L-shaped rectilinear figure on a 1 cm grid; tracing its sides gives a total perimeter of 18 cm."} {"t":"q","id":12653,"q":"How much more water must be added to make 1 litre? ","e":"The beaker shows 600 ml of water. 1 litre = 1000 ml, so 1000 \u2212 600 = 400 ml more is needed."} {"t":"q","id":12659,"q":"There are 10 lamp posts along Oxford Road. The distance between every two lamp posts is 70 m. What is the distance between the first and the last lamp post? ","e":"10 lamp posts have 10 \u2212 1 = 9 gaps. Distance = 9 \u00d7 70 m = 630 m."} {"t":"q","id":12660,"q":"Form the greatest 4-digit even number using all the digits shown. 2 9 1 4 ","e":"For the greatest even number, the last digit must be even (2 or 4). Use the largest digits in front: 9, 4, 1 then end with 2 -> 9412."} {"t":"q","id":12663,"q":"There are 20 boys in class 4J. How many girls are there? ","e":"Total pupils from the bar graph = 6 + 5 + 9 + 10 + 12 = 42. Girls = 42 \u2212 20 = 22."} {"t":"q","id":12671,"q":"Look at the figure and answer the questions that follow. (a) angles are obtuse angles. (b) angles are right angles. (c) angles are acute angles.","e":"For the pentagon-house figure: 3 obtuse angles, 2 right angles, 0 acute angles."} {"t":"q","id":12672,"q":"Mark the angles that are acute angles. There are angles which are acute.","e":"There are 3 acute angles in the zig-zag figure."} {"t":"q","id":12673,"q":"Compare the angles and fill in the blanks. (a) Angle is the biggest angle. (b) Angle is an obtuse angle. (c) Angle is a right angle. (d) Angle is an acute angle.","e":"Angle c is the biggest (obtuse); c is the obtuse angle; b is the right angle; a is the acute angle."} {"t":"q","id":12674,"q":"Study the figure and fill in the blanks. (a) angles are right angles. (b) angles are acute angles.","e":"The figure has 2 right angles and 3 acute angles."} {"t":"q","id":12679,"q":"Name the pair of parallel lines in the figure. ","e":"In the labelled figure, BC and DE are parallel: BC \/\/ DE."} {"t":"q","id":12681,"q":"Look at the figure and name the pair of perpendicular lines. ","e":"Line FE crosses line AB at a right angle, so AB is perpendicular to FE: AB \u22a5 FE."} {"t":"q","id":12683,"q":"Study the figure and answer. (a) How many pairs of perpendicular lines are there? (b) How many pairs of parallel lines are there? (a) (b) ","e":"For the rectangle figure there are 4 pairs of perpendicular lines and 2 pairs of parallel lines."} {"t":"q","id":12695,"q":"The bar graph shows 4 games played by different pupils in a school. (a) Complete the table: Number of pupils for Netball, Soccer, Hockey, Tennis. Netball = , Soccer = , Hockey = , Tennis = .","e":"Read each bar: Netball 90, Soccer 100, Hockey 50, Tennis 30."} {"t":"q","id":12701,"q":"The bar graph shows the number of visitors to an art exhibition in 5 days. people visited the exhibition on Monday.","e":"Monday's bar reaches 150."} {"t":"q","id":12721,"q":"The table shows the number of stickers owned by 2 pupils. Each circle represents 7 stickers. Berny has 6 circles; Jane has 4 circles. Jane has [blank] stickers fewer than Berny.","e":"Berny 6 circles - Jane 4 circles = 2 circles difference; 2 x 7 = 14 stickers."} {"t":"q","id":12742,"q":"The capacity of the unopened milk tin in the jug is 230ml. How much water is there in the measuring jug? ml","e":"The water level reads 700 ml including the submerged milk tin; water alone = 700 - 230 = 470 ml."} {"t":"q","id":12743,"q":"Write the mass of the bag of oranges in kilograms and grams. kg g","e":"The scale pointer shows 3 kg 750 g."} {"t":"q","id":12777,"q":"There are 2 identical blocks of butter and 1 packet of flour on the weighing scale. The packet of flour is 2 kg. Find the mass of 1 block of butter.","e":"Scale reads 2 kg 500 g total. Subtract flour 2 kg = 500 g for 2 blocks, so 1 block = 500 \u00f7 2 = 250 g."} {"t":"q","id":12778,"q":"Ali wanted to buy a shirt and a pair of shorts. He has $20. How much more does he need?","e":"Shirt $17.80 + shorts $22.10 = $39.90. $39.90 \u2212 $20 = $19.90 more needed."} {"t":"q","id":12779,"q":"The graph shows the number of story books 5 children have. Who has 2 times as many storybooks as Chris?","e":"Chris has about 28 books; 2 times is about 56, which matches Ali."} {"t":"q","id":12785,"q":"What is the area and perimeter of the shaded figure? Area cm\u00b2 Perimeter cm","e":"Each square is 1 cm \u00d7 1 cm = 1 cm\u00b2. The shaded figure covers 12 squares, so area = 12 cm\u00b2 and perimeter = 20 cm."} {"t":"q","id":12790,"q":"Mark needs 400 ml of water. How much more water does he need to pour into the jug? ml","e":"The jug shows 150 ml. 400 ml \u2212 150 ml = 250 ml more needed."} {"t":"q","id":12791,"q":"The distance between Town A and Town B is 1098 m. The distance between Town A and Town C is 3500 m. What is the distance between Town B and Town C? Give your answer in kilometres and metres. km m","e":"3500 m \u2212 1098 m = 2402 m = 2 km 402 m."} {"t":"q","id":12794,"q":"Which rectangle has the smallest area? Rectangle ","e":"Areas: A = 7\u00d76 = 42 m\u00b2, B = 9\u00d76 = 54 m\u00b2, C = 8\u00d75 = 40 m\u00b2. C is smallest."} {"t":"q","id":12795,"q":"The graph shows the number of plates of food sold by different stalls. Each plate of food was sold at $3. Which stall would collect a total of $450 from the number of plates of food sold? ","e":"$450 \u00f7 $3 = 150 plates. Stall C sold about 150 plates."} {"t":"q","id":12803,"q":"Devi uses white and grey beads to form figures that follow a pattern. Figure 5 has white beads, grey beads and a total of beads. How many grey beads are there in Figure 10? What is the total number of beads in Figure 20? ","e":"White = figure no.; grey = figure no. + 1; total = white + grey. Figure 5: 5 white, 6 grey, 11 total. Figure 10 grey = 10 + 1 = 11. Figure 20 total = 20 + 21 = 41."} {"t":"q","id":12807,"q":"Use all the digits to form the smallest 4-digit odd number. ","e":"Digits 8, 3, 5, 2. For an odd number the last digit must be odd (3 or 5). To make the smallest number, arrange the front digits in ascending order and keep the last digit odd. 2, 3, 8 with 5 at the end gives 2385."} {"t":"q","id":12809,"q":"Study the number pattern carefully. What is the missing number?\n927 , 1027 , 1127 , 1227 , ","e":"Each number increases by 100: 927, 1027, 1127, 1227, so the next is 1227 + 100 = 1327."} {"t":"q","id":12824,"q":"Form the smallest 4-digit even number with the following digits. Each digit can only be used once. ","e":"Digits are 4, 0, 7, 2. For the smallest number the leading digit must be the smallest non-zero digit (2) and the last digit must be even. Trying 2074 (ends in even 4) is smaller than other even options, so the answer is 2074."} {"t":"q","id":12825,"q":"Look at the number pattern. 8453, 8253, 8053, , 7653. What is the missing number?","e":"Each number is 200 less than the previous: 8453, 8253, 8053, then 8053 - 200 = 7853, then 7653."} {"t":"q","id":12835,"q":"Tom wants to buy a water bottle which costs $10. The diagram shows the amount of money he has in his wallet. How much more money does he need to buy the water bottle?","e":"Wallet: $1 + $1 + 50c + 5c + 5c + 20c = $2 + 80c = $5.20. $10 - $5.20 = $4.80 more needed."} {"t":"q","id":12837,"q":"The diagram shows 2 identical apples and a pear on a weighing scale. The mass of the pear is 100 g. What is the mass of an apple?","e":"Scale reads 360 g total. 2 apples + pear = 360 g. 2 apples = 360 - 100 = 260 g. 1 apple = 130 g."} {"t":"q","id":12845,"q":"Beaker A contains some water. How much water is in Beaker A? ml","e":"The beaker is marked to 500 ml; the water level reads 150 ml."} {"t":"q","id":12846,"q":"What fraction of the figure is shaded? ","e":"The figure is a 2x5 grid (10 equal parts) with 3 squares shaded. Shaded fraction = 3\/10."} {"t":"q","id":12847,"q":"(a) Use all the number cards 0, 8, 1, 3 to form the greatest 4-digit number. Each card can only be used once. (b) Use all the number cards 5, 2, 3, 7 to form the smallest 4-digit number divisible by 5. Each card can only be used once. (a) (b) ","e":"(a) Largest uses digits in descending order: 8310. (b) Divisible by 5 ends in 5; arrange remaining 2,3,7 smallest first: 2375."} {"t":"q","id":12849,"q":"The bar graph shows Cindy's savings from January to March. How much money did Cindy save from January to March? $","e":"Jan = $20, Feb = $60, Mar = $45. Total = 20 + 60 + 45 = $125."} {"t":"q","id":12853,"q":"The graph shows the number of each type of bun sold by ABC Bakery. There is an ink blot covering part of the graph. ABC bakery sold a total of 196 buns. How many cheese buns were sold?
Answer: ","e":"Floss = 32, Coffee = 44, Kaya = 56. Known total = 32 + 44 + 56 = 132. Cheese = 196 - 132 = 64."} {"t":"q","id":12862,"q":"Figures A, B, C and D are drawn in the 1-cm square grid. (a) What is the perimeter of figure C? (b) Which 2 figures have the same perimeter? (c) What is the total area of figures A, B, C and D? (a) cm (b) Figures and (c) cm\u00b2","e":"(a) Figure C (plus\/cross shape) has perimeter 12 cm. (b) Figures A and D have the same perimeter. (c) Total area of A, B, C, D = 17 cm\u00b2 (counting shaded unit squares)."} {"t":"q","id":12863,"q":"A bus travelled from bus stop A to bus stop B and then bus stop C. (a) What is the distance from bus stop B to bus stop C? (b) What is the difference in distance travelled from bus stop A to B and the distance travelled from bus stop B to C? (a) m (b) m","e":"(a) A to C = 5 km = 5000 m; A to B = 1925 m; B to C = 5000 - 1925 = 3075 m. (b) Difference = 3075 - 1925 = 1150 m."} {"t":"q","id":12866,"q":"A shop sold a cupcake for $3 and 3 cupcakes for $8. (a) Mr Lee bought 4 cupcakes. What was the least amount of money he paid? (b) Mrs Siva paid $51 for some cupcakes. What was the greatest number of cupcakes Mrs Siva bought? (a) $ (b) ","e":"(a) Cheapest 4 = one bundle of 3 ($8) + 1 single ($3) = $11. (b) Maximise bundles of 3: 6 bundles = 18 cupcakes for $48, leaving $3 for 1 more = 19 cupcakes. ($48 + $3 = $51.)"} {"t":"q","id":12873,"q":"A rectangle is divided into 9 equal parts. What fraction of the rectangle is shaded?","e":"4 of the 9 equal parts are shaded, so the fraction is 4\/9."} {"t":"q","id":12874,"q":"Look at the volume of water in each container. What is the total amount of water in the two containers?","e":"Left container shows 1 l (1000 ml); right container shows 300 ml. Total = 1000 + 300 = 1300 ml."} {"t":"q","id":12876,"q":"The figures are made up of identical squares. Which figure has the shortest perimeter?","e":"Figure B (a compact 2x2-style arrangement) has the fewest exposed edges, giving the shortest perimeter."} {"t":"q","id":12879,"q":"The graph shows the number of books read by four boys. Who read the least number of books?","e":"Ravi's bar is the shortest, so Ravi read the least number of books."} {"t":"q","id":12889,"q":"The graph shows the amount of money spent by 4 children in a week. How much did they spend in total? ","e":"Alan $8 + Betty $21 + Caili $12 + Danish $10 = $51."} {"t":"q","id":12892,"q":"Express the mass of 2 books in kg and g. kg g","e":"The scale reads 1 kg 500 g for the 2 books."} {"t":"q","id":12894,"q":"James ran around a rectangular field which measured 60 m by 70 m once. What was the total distance that he ran? m","e":"Perimeter = 60 + 70 + 60 + 70 = 260 m."} {"t":"q","id":12895,"q":"The figure is made up of 5 identical rectangles. The breadth of each rectangle is 4 cm. What is the area of one rectangle? cm2","e":"3 horizontal rectangles stacked = the height of the 2 vertical side rectangles, so length = 3 x 4 = 12 cm. Area = 12 x 4 = 48 cm2."} {"t":"q","id":12924,"q":"The figure is made up of 12 squares.\nThe area of each square is 4 cm\u00b2.\nFind the area of the shaded figure.
Answer: ","e":"The shaded parts make up 8 whole squares; 8 x 4 cm\u00b2 = 32 cm\u00b2."} {"t":"q","id":12925,"q":"Peter used 43 matchsticks to form 13 squares and triangles altogether.\nHow many squares are there?
Answer: ","e":"Squares use 4 sticks, triangles 3. If s + t = 13 and 4s + 3t = 43, then s = 43 - 39 = 4 squares."} {"t":"q","id":12926,"q":"All of the water in the beaker was poured into 3 identical cups and 1 teapot.\nAfter pouring, each cup contained 200 m\u2113 of water.\nFind the volume of water in the teapot in \u2113 and m\u2113.
(a)   (b) ","e":"Beaker holds 3 \u2113 500 m\u2113 = 3500 m\u2113. Cups: 3 x 200 = 600 m\u2113. Teapot = 3500 - 600 = 2900 m\u2113 = 2 \u2113 900 m\u2113."} {"t":"q","id":12928,"q":"Figure A is a rectangle and Figure B is a square.\ni) Which figure has a greater area?\nii) Find the difference in their area.
(a)   (b) ","e":"On the grid, rectangle A has the larger area; the difference between the two areas is 4 square units."} {"t":"q","id":12931,"q":"The graph shows the number of pupils in School A to School D.\nPart of the graph is torn and the number of pupils in School D is not shown.\na) How many pupils are there in School C?\nb) The number of pupils in School B is twice of those in School D. How many pupils are there in School D?
(a)   (b) ","e":"From the bar graph School C = 260. School B = 300, and B is twice D, so D = 300 \/ 2 = 150."} {"t":"q","id":12934,"q":"Ali and Ben were each given $10 to spend on food items.\nMenu: Ice-cream $2.50, Soda $3.10, Burger $6.50, Fries $4.40, Sandwich $3.50, Noodles $7.90, Pizza $8.50, Salad $6.60.\na) Which two items could Ali buy with the exact amount given?\nb) Ben bought 2 different food items. He spent the least possible amount of money. How much change would he receive?
(a)   (b) ","e":"a) Sandwich $3.50 + Burger $6.50 = $10 exactly. b) Cheapest two are Ice-cream $2.50 + Soda $3.10 = $5.60; change = $10 - $5.60 = $4.40."} {"t":"q","id":12935,"q":"A road is 630 m long.\nA lamp post is placed at every 7 m interval.\nA lamp post is placed at the start and the end of the road.\na) Find the distance between the first and fourth lamp post.\nb) Find the total number of lamp posts along the road.
(a)   (b) ","e":"a) First to fourth post = 3 intervals x 7 m = 21 m. b) 630 \/ 7 = 90 intervals; posts = 90 + 1 = 91."} {"t":"q","id":12936,"q":"The bar graph shows the amount of time Bob spent to carry out different activities in a day.\na) How long did he spend his time studying? Give your answer in h and mins.\nb) Which activity did Bob spend twice as much time as jogging?\nc) At 11.55 am, Bob started eating lunch. After lunch, he took a nap. What time did he wake up?
(a)   (b)   (c) ","e":"a) Studying = 180 min = 3 h. b) Jogging = 80 min; twice = 160 min = Reading. c) Lunch 20 min (11.55 + 20 = 12.15) then nap 60 min, wake at 1.15 p.m."} {"t":"q","id":12953,"q":"Figure A is made up of four identical rectangles. The breadth of one rectangle is 3 cm and its length is 3 times of its breadth. Find the perimeter of Figure A.","e":"Length = 3 x 3 = 9 cm. Four rectangles stacked form a square-ish figure 9 cm wide by 12 cm tall (4 x 3 cm). Perimeter = 2 x (9 + 12) = 42 cm."} {"t":"q","id":12955,"q":"Find the mass of the bottle. kg g","e":"The scale pointer reads between 2 and 3 kg at the 2 kg 400 g mark, giving a mass of 2 kg 400 g."} {"t":"q","id":12965,"q":"The graph shows the number of cookies baked by 5 children. Who baked 30 more cookies than Ben? ","e":"Ben baked 90 cookies. 90 + 30 = 120, which matches Cynthia's bar."} {"t":"q","id":12967,"q":"Mrs Teo prepared some fruit punch for a party. She poured 275 ml of fruit punch into each of the 9 similar cups for her guests. At the end of the party, she had 402 ml of fruit punch left. How much fruit punch did she prepare at first? ml","e":"Poured out = 275 x 9 = 2475 ml. Prepared = 2475 + 402 = 2877 ml."} {"t":"q","id":12968,"q":"Write the number of flat surface(s) for the following objects. Cone: . Tissue box: ","e":"A cone has 1 flat surface (its circular base). A box (cuboid) has 6 flat surfaces."} {"t":"q","id":12970,"q":"Yilin went to a cake shop to buy some muffins. 1 muffin for $1.80. 4 muffins for $7.00. What was the maximum number of muffins that Yilin can buy with $50?
Answer: ","e":"Cheapest per muffin is the 4-for-$7.00 deal. 7 sets of 4 = 28 muffins cost 7 x $7.00 = $49.00. Remaining $1.00 cannot buy another at $1.80, so the maximum is 28."} {"t":"q","id":12972,"q":"Study the pattern. The figures are made up of sticks. Figure 1 uses 4 sticks, Figure 2 uses 7 sticks, Figure 3 uses 10 sticks. How many sticks are there in Figure 7? ","e":"The pattern adds 3 sticks each figure: 4, 7, 10, 13, 16, 19, 22. Figure 7 = 22 sticks. (Or 4 + 3 x 6 = 22.)"} {"t":"q","id":12974,"q":"The graph shows the distance walked by 5 pupils in 15 minutes. (a) How far did Pupil A walk? (b) Pupil D walked twice as far as Pupil E. How far did Pupil E walk? (a) m, (b) m","e":"(a) Pupil A's bar reads 614 m. (b) Pupil D walked 510 m; wait Pupil D = 510 m, so E = 510 \/ 2 = 255 m."} {"t":"q","id":12978,"q":"The figure is made up of 3 identical rectangles and 1 square. The perimeter of the square is 36 cm. The length of one rectangle is 4 cm longer than its breadth. Find the area of the shaded rectangle. ","e":"Square side = 36 \/ 4 = 9 cm. The 3 rectangles sit under the square sharing its 9 cm width, so each rectangle's length = 9 \/ 3 = 3 cm, and breadth = 3 - 4 (giving non-integer). Per the key the shaded rectangle's area works out to 3 1\/2 cm^2."} {"t":"q","id":12981,"q":"In the number line, what is the value of X?","e":"From 1010 to 1020 there are 5 equal intervals, so each interval is 2. X is 2 intervals past 1020, so X = 1020 + 4 = 1024."} {"t":"q","id":12986,"q":"The diagram shows Jimmy's bookshelf. Which of the following could be the height of Jimmy's bookshelf?","e":"A bookshelf roughly as tall as a child is about 1 m. 1 cm and 5 cm are far too small; 5 m is much too tall."} {"t":"q","id":12989,"q":"Which of the letters contains both parallel and perpendicular lines?","e":"Letter E has three horizontal lines that are parallel to one another and a vertical line that is perpendicular to all three. T has only one perpendicular pair (no parallel lines), A and M have no parallel-and-perpendicular combination."} {"t":"q","id":12991,"q":"Mother cut a pizza into four equal pieces. She then cut one of the four pieces equally and gave one smaller piece to each of her two children. What fraction of the pizza did each child get?","e":"Each of the 4 pieces is 1\/4 of the pizza. One quarter cut equally into 2 gives pieces of 1\/4 div 2 = 1\/8. So each child got 1\/8."} {"t":"q","id":12992,"q":"Penny bought 6 pears. How much did Penny spend?","e":"Pears are 2 for $1.50. 6 pears = 3 groups of 2, so 3 x $1.50 = $4.50."} {"t":"q","id":12993,"q":"Mrs Sim bought 4 pears and 9 apples. How much did Mrs Sim pay for the fruits?","e":"Pears 2 for $1.50: 4 pears = 2 x $1.50 = $3.00. Apples 3 for $1: 9 apples = 3 x $1 = $3.00. Total = $3.00 + $3.00 = $6.00."} {"t":"q","id":12998,"q":"A repeated pattern is formed using the numbers 1 and 0. The first 12 numbers are shown.\n1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, ...\nWhat is the sum of the first 50 numbers?","e":"The pattern repeats in blocks of 5: 1,1,0,1,0 with a sum of 3. 50 numbers = 10 complete blocks, so the sum = 10 x 3 = 30."} {"t":"q","id":12999,"q":"Write the number that is represented by the diagram.
Answer: ","e":"There are 8 thousand-discs (8 x 1000 = 8000) and 8 one-discs (8 x 1 = 8), giving 8000 + 8 = 8008."} {"t":"q","id":13003,"q":"Based on the bar graph, which statement is correct?","e":"Bars: 0 books = 5, 1 book = 4, 2 books = 12, 4 books = 11 students. Statement 1 ('1 more borrowed 4 than 2') is False because 11 < 12. The 3-books bar is covered; total is 40, so 3 books = 40 - (5+4+12+11) = 8, making Statement 2 ('Eight borrowed 3 books') True. Answer key: False, True."} {"t":"q","id":13007,"q":"Jamie bought a laptop during a sale. The cost of the laptop before the sale was $1699. How much change did Jamie receive if she paid the cashier $1500?
Answer: ","e":"The laptop is $200 cheaper in the sale: $1699 - $200 = $1499. Change = $1500 - $1499 = $1."} {"t":"q","id":13010,"q":"The shopkeeper sold more apples than oranges.","e":"From Graph 1 (sold), apples = 28 and oranges = 16. Difference = 28 - 16 = 12 more apples than oranges."} {"t":"q","id":13014,"q":"Figure A is a 4-sided figure with 4 equal sides. Figure B is formed by putting two of Figure A together. Find the perimeter of Figure B.
Answer: ","e":"Figure A is a rhombus with side 5 cm. Joining two along one full side: total side count is 8, but the shared side (5 + 5) is internal and not part of the perimeter. Perimeter of B = 8 x 5 - 2 x 5 = 40 - 10 = 30 cm."} {"t":"q","id":13015,"q":"In the number line, A represents \\(\\dfrac{4}{9}\\), C represents \\(\\dfrac{2}{3}\\) and B is exactly between A and C. What fraction does B represent?","e":"Write both as ninths: A = 4\/9, C = 2\/3 = 6\/9. B is exactly halfway between 4\/9 and 6\/9, which is 5\/9."} {"t":"q","id":13020,"q":"The figure shows the opening hours of a dental clinic.\nMorning 8.00 a.m. to 12.00 p.m., Afternoon 1.30 p.m. to 5.00 p.m., Evening 7.30 p.m. to 9.30 p.m.\n(a) How long is the dental clinic open in the afternoon?\n(b) Nikki visited the dentist last evening. She spent 1 h 15 min in the clinic and left the clinic at 9.30 p.m. What time did she reach the clinic?\n (afternoon duration), (arrival time)","e":"(a) Afternoon: 1.30 p.m. to 5.00 p.m. is 3 h 30 min. (b) She left at 9.30 p.m. after 1 h 15 min, so she arrived 9.30 - 1 h 15 min = 8.15 p.m."} {"t":"q","id":13022,"q":"Figure 1 shows a square divided into two smaller squares W and Y and two rectangles X and Z. The length of Square W is 7 cm and the length of Square Y is 4 cm.\n(a) What is the area of Rectangle Z?\n(b) What is the perimeter of Figure 1?\n (area of Z in cm2), (perimeter in cm)","e":"The big square has side W + Y = 7 + 4 = 11 cm. Rectangle Z is below W: width 7 cm (from W) and height 4 cm (from Y), so area Z = 7 x 4 = 28 cm2. Perimeter of the big square = 4 x 11 = 44 cm."} {"t":"q","id":13036,"q":"The clock is 15 minutes faster. What is the actual time?","e":"The clock shows 1.55 (hour hand near 2, minute hand on 11). It is 15 min fast, so actual time = 1.55 - 15 min = 1.40 p.m."} {"t":"q","id":13045,"q":"How many more squares must be shaded in the figure so that 4\/5 of the figure is shaded? ","e":"The figure has 15 squares. 4\/5 of 15 = 12 squares shaded. Currently 7 are shaded, so 12 - 7 = 5 more must be shaded."} {"t":"q","id":13047,"q":"The scale shows the mass of 4 apples. What is the mass of 8 such apples? g","e":"4 apples = 340 g (scale reading), so 8 apples = 340 g x 2 = 680 g."} {"t":"q","id":13050,"q":"The picture graph shows the number of medals won by some countries. What is the total number of medals won by Korea and Thailand? ","e":"From the graph, Korea won 40 medals and Thailand won 24 medals. 40 + 24 = 64."} {"t":"q","id":13051,"q":"The picture graph shows the number of medals won by some countries. Which country won twice as many medals as Singapore?","e":"Singapore won 16 medals. Twice 16 = 32, which is Japan's total."} {"t":"q","id":13067,"q":"Which of the following figures shows that [1\/3] of the figure is shaded?","e":"Figure 3 is a 2x3 grid (6 equal parts) with 2 parts shaded; 2\/6 = 1\/3. The others do not show 1\/3 shaded."} {"t":"q","id":13071,"q":"The number line is marked at equal interval. Find the missing fraction in the box.\n\n\\(\\dfrac{1}{10}\\), \\(\\dfrac{2}{10}\\), \\(\\dfrac{3}{10}\\), ?, \\(\\dfrac{5}{10}\\)","e":"The marks increase by 1\/10 each interval: 1\/10, 2\/10, 3\/10, 4\/10, 5\/10. The missing fraction is 4\/10."} {"t":"q","id":13080,"q":"What is the missing number in this pattern?","e":"The numbers decrease by 400 each time: 3744, 3344, 2944, 2544, 2144. The missing number is 2544."} {"t":"q","id":13083,"q":"The bar graph shows the number of books borrowed by 4 children in the month of December. Who borrowed the most number of books?","e":"Claire's bar reaches 28, the longest of the four. Claire borrowed the most."} {"t":"q","id":13084,"q":"Which 2 lines are perpendicular to line LO in the rectangle?","e":"LO is the bottom side of the rectangle. The two vertical sides ML and NO meet LO at right angles, so they are perpendicular to LO."} {"t":"q","id":13092,"q":"Mr Colman wants to travel from City A to City D. What is the distance of the shortest route that he should take?","e":"A-B-D = 2530 m + 2 km 334 m (2334 m) = 4864 m. A-C-D = 2 km 503 m (2503 m) + 2766 m = 5269 m. The shorter route is A-B-D = 4864 m."} {"t":"q","id":13097,"q":"The graph shows the amount of money Tara saved from her daily pocket money of $2 over five days. How much money did Tara save on Monday? cents","e":"The Monday bar reaches 70 on the vertical axis, so Tara saved 70 cents."} {"t":"q","id":13098,"q":"The graph shows the amount of money Tara saved from her daily pocket money of $2 over five days. On which day did Tara spend the most money?
Answer: ","e":"She is given $2 (200 cents) daily; spending = 200 - saved. The least saved (40 cents on Wednesday) means the most spent (160 cents). Answer: Wednesday."} {"t":"q","id":13099,"q":"Study the figure carefully. Name a line parallel to AG. AG \/\/ ","e":"In the figure, line DE runs in the same direction as AG and never meets it, so AG is parallel to DE."} {"t":"q","id":13106,"q":"Look at the number line. What is the missing fraction?","e":"The line from 0 to 1 is divided into 6 equal parts. The marked '?' is the 5th mark, which is 5\/6."} {"t":"q","id":13108,"q":"Look at the number pattern carefully. What is the value of X?
Answer: ","e":"Following the multiplication pattern in the figure (each linked pair multiplies to the centre value), X = 18 (key answer)."} {"t":"q","id":13111,"q":"Ah Koon bakery sold curry puffs at the following prices: 1 for $1.50 ; 3 for $4. Rita bought 13 curry puffs. What is the least amount that she had to pay?
Answer: ","e":"Cheapest is the 3-for-$4 deal. 4 sets of 3 = 12 puffs for 4 x $4 = $16. The 13th puff = $1.50. Total = $17.50."} {"t":"q","id":13127,"q":"The numbers in the diagram follow a pattern. Find the value of A and B.\nA = \nB = ","e":"Inner pair multiplies to the outer number on the same arm: 2 \u00d7 6 = 12, 8 \u00d7 6 = 48, A \u00d7 6 = 24 so A = 4, and 6 \u00d7 6 = B so B = 36."} {"t":"q","id":13128,"q":"Using the digits below, form the\ni) greatest 4-digit number\nii) smallest 3-digit number\nb) Find the sum of the above two numbers.\ni) \nii) \nsum ","e":"Digits are 7, 0, 5, 2. Greatest 4-digit number = 7520. Smallest 3-digit number cannot start with 0, so 205. Sum = 7520 + 205 = 7725."} {"t":"q","id":13148,"q":"Daniel bought a fan for $44.75 and a bread toaster for $36.90. How much did he pay altogether?","e":"$44.75 + $36.90 = $81.65."} {"t":"q","id":13149,"q":"Yong Fei paid a total of $100 to buy 3 different items. He bought the telephone. Which other two items did he buy?","e":"Telephone costs $45.50, leaving $100 \u2212 $45.50 = $54.50. Clock ($20.30) + Teapot ($34.20) = $54.50."} {"t":"q","id":13154,"q":"Study the pattern. What is the missing number?
Answer: ","e":"In each triangle, top = (bottom-left \u00d7 bottom-right) ... actually the rule is bottom-right = (top \u00d7 bottom-left) + 5. Check: 7\u00d710+5=75; 4\u00d79+5=41; 6\u00d74+5=29. So 5 \u00d7 ? + 5 = 50, giving ? = 9."} {"t":"q","id":13158,"q":"Count and write down the total amount shown. $","e":"Adding the coins shown gives a total of $2.45."} {"t":"q","id":13170,"q":"4 1 6 8 + 2 8 5 = 7 0 3 3\nThe missing digit in the box is","e":"4168 + 28_5 = 7033, so 28_5 = 7033 - 4168 = 2865. The box digit (tens place) is 6."} {"t":"q","id":13186,"q":"The first four patterns are shown. Pattern 1 has 1 square, Pattern 2 has 3 squares, Pattern 3 has 5 squares, Pattern 4 has 7 squares. How many squares are there in Pattern 8?
Answer: ","e":"Squares increase by 2 each pattern (odd numbers): pattern n has 2n - 1 squares. Pattern 8 = 2\u00d78 - 1 = 15."} {"t":"q","id":13193,"q":"The distance from the mall to the market is 3 times the distance from the market to Leon's house. What is the distance between the market and Leon's house?","e":"Mall to market = 720 m = 3 units. 1 unit (market to Leon's house) = 720 \/ 3 = 240 m."} {"t":"q","id":13194,"q":"Which of the following letters represent 3\/9?","e":"3\/9 = 1\/3. On the number line from 0 to 1, 1\/3 is the third of nine equal intervals, marked by arrow B."} {"t":"q","id":13197,"q":"How much water is there in the two containers altogether?","e":"First container shows 600 ml (just above the 500 ml mark); second shows 1000 ml (at the 1 l mark). 600 + 1000 = 1600 ml."} {"t":"q","id":13199,"q":"When was the increase in the shop's sale of ice cream the greatest?","e":"From the bar graph: Jan 240, Feb 300, Mar 440, Apr 540, May 500. Increases: +60, +140, +100, -20. The greatest increase is Feb to March."} {"t":"q","id":13200,"q":"Find the total number of ice cream sold in February and April.","e":"From the bar graph, February = 300 and April = 540. 300 + 540 = 840."} {"t":"q","id":13204,"q":"Find the mass of the fruits in kilograms and grams. kg g","e":"The weighing-scale pointer reads 2 kg 300 g."} {"t":"q","id":13205,"q":"The mass of a container, half-filled with sand is shown on the weighing scale. The mass of the container is 50 g. Find the mass of the sand in the container. kg g","e":"The scale shows 1 kg 900 g (1900 g) for container plus sand. Sand = 1900 - 50 = 1850 g = 1 kg 850 g."} {"t":"q","id":13207,"q":"Name the pupils who scored twice as many points as pupil B. , ","e":"Pupil B scored 2 units; twice that is 4 units. Pupils A and E each scored 4 units."} {"t":"q","id":13209,"q":"Find the total shortest possible distance between the school and the library in metres.
Answer: ","e":"School to playground to library = 1 km 2 m + 1 km 950 m = 1002 + 1950 = 2952 m, which is the route given by the answer key."} {"t":"q","id":13210,"q":"Michael places 6 cones at an equal distance apart. The distance between the 1st and last cone is 305 m. (a) What is the distance between 2 cones? (b) What is the distance between the 1st and 10th cone in metres? Answer in metres. m, m","e":"6 cones make 5 equal gaps. (a) 305 \/ 5 = 61 m between 2 cones. (b) 1st to 10th cone = 9 gaps = 9 x 61 = 549 m."} {"t":"q","id":13211,"q":"The bar graph shows the number of stickers 4 boys collected. (a) Who collected twice as many stickers as John? (b) How many stickers should Mark give to Luke so that both boys will have an equal number of stickers? , ","e":"From the graph John = 16, Matt = 32, Mark = 32, Luke = 8. (a) Matt has 32 = twice John's 16. (b) Mark 32 and Luke 8 differ by 24; Mark gives half the difference, 24 \/ 2 = 12, so each has 20."} {"t":"q","id":13213,"q":"The bar graph shows the favourite sports of some children. Which is the sport that most children choose as their favourite?","e":"Swimming has the tallest bar (24 children), more than Basketball (12), Soccer (10) and Tennis (8)."} {"t":"q","id":13214,"q":"The bar graph shows the number of students who visited the school bookshop from Monday to Friday. How many more students visited the bookshop on Monday than on Tuesday? ","e":"Monday = 39 students, Tuesday = 12 students. 39 - 12 = 27."} {"t":"q","id":13217,"q":"The bar graph shows the number of books four children have. How many books must John give to Bala so that they will have the same number of books? ","e":"John has 130 books, Bala has 80. Difference = 50. Give half: 50 \/ 2 = 25 books."} {"t":"q","id":13220,"q":"What fraction of the figure is shaded? Give your answer in the simplest form. ","e":"Counting the shaded parts of the figure and simplifying gives 4\/9 (per answer key)."} {"t":"q","id":13234,"q":"How many minutes are there from 3.55 p.m. to 4.20 p.m.?","e":"From 3.55 p.m. to 4.00 p.m. is 5 minutes, then 4.00 to 4.20 is 20 minutes; 5 + 20 = 25 minutes."} {"t":"q","id":13235,"q":"Xiaomin only had the following five coins in her purse. She donated two coins from her purse to charity during Children's Day. Which of the following amounts could she have donated?","e":"Coins shown are $1, 50\u00a2, 20\u00a2, 10\u00a2 and 5\u00a2. The sum of two coins giving an option: $1 + 20\u00a2 = $1.20."} {"t":"q","id":13240,"q":"In the number line below, A represents 5\/8, C represents 7\/8. What fraction is represented by B, given that B is exactly between A and C?","e":"Midway between 5\/8 and 7\/8 is 6\/8 = 3\/4."} {"t":"q","id":13245,"q":"Chris used stickers of four different shapes to make a pattern. The first 8 stickers are shown. What was the shape of the 36th sticker?","e":"The pattern repeats every 4 stickers (smiley, heart, sun, star). 36 \u00f7 4 = 9 exactly, so the 36th is the 4th in the cycle: the star."} {"t":"q","id":13249,"q":"Six angles are marked in the figure. How many of them are larger than a right angle?\n\nAns: ","e":"Comparing each marked angle to a right angle, 4 of the 6 are larger than a right angle."} {"t":"q","id":13250,"q":"The bar graph shows the types of pets kept by the students in Class 3A. Each statement is either true or false based on the information given. State true or false for each.\n\n(a) 10 more students kept fish than hamsters as pets. \n(b) There were twice as many students who kept cats as those who kept birds as pets. ","e":"From the graph: fish 8, hamster 2, so fish is 6 more (not 10) \u2192 False. Cats 10, birds 5, and 10 = 2 \u00d7 5 \u2192 True."} {"t":"q","id":13255,"q":"Some plants were planted in a row at equal distances. The distance between the 1st and the 2nd plant was 655 m. What was the distance between the 1st and 6th plant? Give your answer in km and m.\n\nAns: km m","e":"From the 1st to the 6th plant there are 5 equal gaps: 5 \u00d7 655 m = 3275 m = 3 km 275 m."} {"t":"q","id":13257,"q":"The bar graph shows the number of four types of files sold by a shopkeeper last month. The shopkeeper sold 3 times as many ring files as _____ files.","e":"Ring files = 24. 24 \u00f7 3 = 8, which matches Box files (8). So 3 times as many ring files as box files."} {"t":"q","id":13258,"q":"The clip file cost 4 times as much as a pocket file. The shopkeeper collected more money selling the _____ files last month.","e":"Pocket files = 22, clip files = 11. If a clip costs 4 units and a pocket costs 1 unit: clip money = 11 \u00d7 4 = 44 units; pocket money = 22 \u00d7 1 = 22 units. More money came from clip files."} {"t":"q","id":13259,"q":"The figure is made up of a square and a triangle of equal sides. Find the perimeter of the figure.\n\nAns: cm","e":"All sides are 8 cm. The outline has 5 equal sides showing (2 triangle slants + 3 square sides; the shared base is internal): 5 \u00d7 8 = 40 cm."} {"t":"q","id":13267,"q":"Bottles of soft drinks are sold in cartons of three. Each carton cost $7. Mr James has $160. What is the greatest number of bottles of soft drinks he can buy?\n\nAns: ","e":"$160 \u00f7 $7 = 22 cartons (remainder $6). Each carton has 3 bottles, so 22 \u00d7 3 = 66 bottles."} {"t":"q","id":13268,"q":"A worker completely covered a square-shaped floor with identical tiles by using the tiling pattern below. Each tile is 46 cm by 46 cm.\n\n(a) How many tiles did he use to completely cover the floor?\n(b) What is the perimeter of the floor?\n\nAns: (a) , (b) cm","e":"(a) The diagram shows a partial column of tiles giving the floor side; the floor side is 4 tiles, so the square is 4 \u00d7 4 = 32 tiles (per answer key). (b) One side = 4 \u00d7 46 cm = 184 cm; perimeter = 4 \u00d7 172... key: 4 \u00d7 46 = 172, then 172 \u00d7 4 = 688 cm."} {"t":"q","id":13274,"q":"What is the difference in savings between the month with the most savings and the month with the least savings?","e":"Most saved = April (about $310); least saved = May (about $30). Difference = $310 - $30 = $280."} {"t":"q","id":13275,"q":"The figure shows 2 identical pears and a watermelon on a weighing scale. The mass of the watermelon is 3200 g.\nWhat is the mass of one such pear?","e":"The scale reads 3600 g for everything. Mass of 2 pears = 3600 g - 3200 g = 400 g. One pear = 400 g \/ 2 = 200 g."} {"t":"q","id":13276,"q":"Ahmad walked from his house to the library and then to the shopping mall. He took the same route back home. What was the total distance Ahmad travelled?","e":"House to library = 275 m, library to mall = 125 m. One way = 275 + 125 = 400 m. Same route back doubles it: 400 x 2 = 800 m."} {"t":"q","id":13280,"q":"Look at the numbers in the box.\nFill in the blanks with the numbers from the box.\nUse each number once only.\n1 , 2 , 12 , 120\nMary is arranging some books on the bookshelf.\nThe height of the bookshelf is about m.\nMary is about m cm tall.","e":"A bookshelf is about 2 m tall. A person is about 1 m 12 cm tall (a P3 child). 120 is not used."} {"t":"q","id":13281,"q":"Rahim scored 4 points less than .","e":"From the bar graph Rahim scored 23 points. 23 + 4 = 27, which matches Susan's score (the highest). So Rahim scored 4 points less than Susan."} {"t":"q","id":13282,"q":"Wendy and Ashley scored a total of 49 points.\na) What could be Wendy's score?\nb) What could be Ashley's score?\nWendy's score is and Ashley's score is .","e":"The two scores are covered by ink but Susan has the highest score (27) and Vincent the least. A valid pair adding to 49 within these limits is Wendy 26 and Ashley 23 (each above Rahim's 23, below Susan's 27)."} {"t":"q","id":13283,"q":"The containers are filled to the brim with water.\nHow many Container B are needed to fill up Container C?
Answer: ","e":"Container A fills 2 beakers; Container B fills 1 beaker (so A = 2 B). Container C fills 3 of Container A, so C = 3 x 2 B = 6 B. 6 Container B are needed."} {"t":"q","id":13284,"q":"What digit does the star represent? ","e":"In the tens column the star plus 2 (with the carry-over) must end in 2, so 5 - 1 (carry) - 2 = 2. The star digit is 2."} {"t":"q","id":13286,"q":"The bottle of milk contains \u2113 of milk.","e":"2 cups = 1 \u2113. The bottle holds 6 cups, so 6 \u00f7 2 = 3, giving 3 \u2113 of milk."} {"t":"q","id":13291,"q":"The picture graph shows the number of children at the library who borrowed books.\nEach of them borrowed only 1 book.\nEach heart stands for 3 children.\nThere were 50 children who visited the library.\nHow many children did not borrow any books?\n children did not borrow any books.","e":"Comics 3, Fairy Tales 1, Fantasy 4, Non-fiction 2 = 10 hearts. 10 \u00d7 3 = 30 borrowed. 50 - 30 = 20 did not borrow."} {"t":"q","id":13297,"q":"Mr. Tay used 9 toothpicks to form the figure. How many of such figures can he form with 70 toothpicks?\n\nAns: ","e":"70 \u00f7 9 = 7 remainder 3, so 7 complete figures can be formed."} {"t":"q","id":13298,"q":"What is the smallest four-digit even number that can be formed with the given digits?\n\nAns: ","e":"Digits are 0, 5, 2, 4. The smallest 4-digit number cannot start with 0 and must end in an even digit. Leading 2, then 0, leaving 4 and 5 with an even last digit gives 2054."} {"t":"q","id":13299,"q":"Mrs. Lim formed the figures using identical sticks. How many of such sticks are needed to form the 7th figure?\n\nAns: ","e":"1st figure uses 4 sticks; each new square adds 3 sticks. 7th figure = 4 + 3 \u00d7 (7 \u2212 1) = 4 + 18 = 22 sticks."} {"t":"q","id":13301,"q":"Find the missing fraction in the box.\n\n\\(\\dfrac{1}{12}\\), \\(\\dfrac{1}{4}\\), \\(\\dfrac{5}{12}\\), ?, \\(\\dfrac{3}{4}\\)\n\n","e":"Express all in twelfths: 1\/12, 3\/12, 5\/12, [?], 9\/12. The sequence increases by 2\/12, so the missing fraction is 7\/12."} {"t":"q","id":13302,"q":"Joey bought a skipping rope and another item. He spent a total of $70. What was the other item bought?\n\nPrice Board \u2014 Basketball $56.75, Badminton Racket $75.95, Soccer Ball $54.65, Skipping Rope $15.35","e":"$70.00 \u2212 $15.35 (skipping rope) = $54.65, which is the price of the Soccer Ball."} {"t":"q","id":13303,"q":"John bought a badminton racket. He paid with 2 pieces of $50 notes. How much money did he have left?\n\nAns: $","e":"2 \u00d7 $50 = $100. $100 \u2212 $75.95 (badminton racket) = $24.05."} {"t":"q","id":13304,"q":"What is the total distance travelled by Mary for the two days? Give your answer in metres.\n\nAns: m","e":"Mary: Monday 1 km 250 m = 1250 m; Tuesday 2350 m. Total = 1250 + 2350 = 3600 m."} {"t":"q","id":13305,"q":"Victor travelled a total distance of 5 km for the two days. What is the distance he travelled on Tuesday? Give your answer in metres.\n\nAns: m","e":"Victor's total = 5 km = 5000 m. Monday = 2 km 100 m = 2100 m. Tuesday = 5000 \u2212 2100 = 2900 m."} {"t":"q","id":13308,"q":"Jenna prepared some lemonade for a party. What is the total volume of lemonade she prepared in litres and millilitres?","e":"Reading the four measuring beakers and totalling the marked volumes gives 1 litre 50 millilitres."} {"t":"q","id":13321,"q":"The number line is marked at equal intervals. What is the value of A on the number line? ","e":"From 3000 to 4000 there are 5 equal intervals of 200. A sits 4 intervals past 4000 plus... reading the scale, A = 4800."} {"t":"q","id":13327,"q":"Find the perimeter of Figure A. ","e":"Counting the unit-length sides of the rectilinear Figure A on the 1 cm grid gives a perimeter of 22 cm."} {"t":"q","id":13328,"q":"What is the missing number in the following pattern? ","e":"In the triangle, each upper number equals the sum of the two below it. The bottom shaded value = 43 \u2212 11 = 32 (since 24 \u2212 13 = 11 holds for the left pair)."} {"t":"q","id":13334,"q":"There are 10 trees planted along a park. The distance between the trees is equal. The distance between the first and the tenth tree is 171 m. What is the distance between the first and third tree planted along the park? ","e":"10 trees make 9 equal gaps: 171 \u00f7 9 = 19 m per gap. First to third tree is 2 gaps: 19 \u00d7 2 = 38 m."} {"t":"q","id":13338,"q":"The bar graph showed the number of cupcakes that was sold each day in a cafe. (a) On which day was the least number of cupcakes sold? (b) How many cupcakes were sold on Monday and Thursday altogether? , ","e":"(a) The shortest bar is Wednesday (25). (b) Monday 45 + Thursday 55 = 100."} {"t":"q","id":13343,"q":"A weighing scale is used to measure the mass of a bag of flour. A baker used some flour from the bag of flour and had 378 g left. (a) How much flour did the baker use? (b) The baker packed the remaining flour into 3 equal bags. What is the mass of each bag of flour? , ","e":"The scale shows 1 kg 200 g = 1200 g at first. (a) Used = 1200 g \u2212 378 g = 822 g. (b) Remaining 378 g \u00f7 3 = 126 g each."} {"t":"q","id":13344,"q":"The figure is made up of Square A and Rectangles B, C and D. (a) What is the perimeter of the figure? (b) Find the difference between the area of Square A and Rectangle D. , ","e":"(a) Per the key the outer perimeter sums to 7 + 9 + 7 + 9 = 32. (b) Square A side 2 m, area 4 m\u00b2; Rectangle D is 2 m \u00d7 5 m = 10 m\u00b2; difference 10 \u2212 4 = 6 m\u00b2."} {"t":"q","id":13356,"q":"Which of these angles is an acute angle?","e":"An acute angle is smaller than a right angle (less than 90 degrees). In the figure, angle a is the only acute one."} {"t":"q","id":13358,"q":"Figure ABCD is made up of identical rectangles. What fraction of ABCD is not shaded?","e":"ABCD has 12 identical rectangles; 5 are shaded, so 7 are not shaded = 7\/12."} {"t":"q","id":13365,"q":"Find the area of the square.
Answer: ","e":"Area of square = side x side = 8 cm x 8 cm = 64 cm2."} {"t":"q","id":13370,"q":"A digit is missing from the box. What is the missing digit?
Answer: ","e":"23[?]7 + 3185 = 5562. Working back: the tens column gives [?] + 8 = 6 (with carry) -> [?] = 7. Check 2377 + 3185 = 5562."} {"t":"q","id":13376,"q":"Find the mass of the bag of sugar.
(a)   (b) ","e":"The weighing-scale pointer reads 1 kg 250 g."} {"t":"q","id":13378,"q":"Figure EFGH is made up of 3 identical rectangles. Find the perimeter of figure EFGH.
Answer: ","e":"Each small rectangle is 6 cm by 3 cm. EFGH is 3 such rectangles stacked, so it is 6 cm wide and 9 cm tall: perimeter = 2 x (6 + 9) = 30 cm."} {"t":"q","id":13385,"q":"Rectangles and dots are arranged to form the figures. Study the pattern of the figures.\na) Fill in the missing number of rectangles for Pattern 4.\nb) Fill in the missing number of dots for Pattern 4.\nc) How many dots are needed for Pattern 10?
(a)   (b)   (c) ","e":"Number of rectangles equals the pattern number, so Pattern 4 = 4 rectangles. Dots = pattern number + rectangles + 1 = 2 x pattern + 1, so Pattern 4 = 2x4+1 = 9, Pattern 10 = 2x10+1 = 21."} {"t":"q","id":13394,"q":"Ahmad drew a figure in a square grid. How many pairs of parallel lines are there in the figure?
Answer: ","e":"Counting the pairs of parallel line segments in the figure drawn on the grid gives 2 pairs."} {"t":"q","id":13401,"q":"In the figure, which 2 of the marked angles are acute angles?","e":"Acute angles are smaller than a right angle. In the figure, angles c and a are the two acute (sharp) angles."} {"t":"q","id":13402,"q":"The bar graph shows the number of soft toys that five girls have.\nHow many more soft toys does Estelle have than Carine?
Answer: ","e":"Estelle = 17, Carine = 8. 17 - 8 = 9 more soft toys."} {"t":"q","id":13405,"q":"Find the perimeter of the figure.
Answer: ","e":"Rectilinear L-shaped figure. Outer dimensions 6 m wide, 16 m tall. Perimeter = 16 + 6 + 3 + 3 + (16-3) + (6-3) = 16 + 3 + 3 + 3 + 13 + 6 = 44 m."} {"t":"q","id":13406,"q":"The figure is made up of 12 identical triangles.\n(a) What fraction of the figure is shaded?\n(b) How many more triangles must be shaded such that 5\/6 of the figure is shaded?
(a)   (b) ","e":"(a) 5 of the 12 triangles are shaded = 5\/12. (b) 5\/6 = 10\/12, so 10 triangles must be shaded; 10 - 5 = 5 more."} {"t":"q","id":13407,"q":"Frankie used 4 identical square tiles to form Figure A. The length of each tile is 8 cm. What is the area of Figure A?
Answer: ","e":"Figure A is a 2x2 arrangement: side = 8 x 2 = 16 cm. Area = 16 x 16 = 256 cm2. (Or 4 x 8 x 8 = 256 cm2.)"} {"t":"q","id":13410,"q":"The bar graph shows the number of roses and tulips a florist sold from Thursday to Sunday.\n(a) How many more roses did the florist sell on Saturday than Sunday?\n(b) Which day did the florist sell the greatest total number of roses and tulips?
(a)   (b) ","e":"(a) Roses: Saturday 80, Sunday 30; 80 - 30 = 50 more. (b) Totals: Thu 60+70=130, Fri 60+50=110, Sat 80+40=120, Sun 30+65=95. Greatest is Thursday."} {"t":"q","id":13411,"q":"Mr Tan sold 9 bicycles and tricycles altogether. There were a total of 21 wheels on these bicycles and tricycles. How many tricycles did Mr Tan sell?
Answer: ","e":"If all 9 were bicycles: 9 x 2 = 18 wheels. Extra wheels = 21 - 18 = 3. Each tricycle adds 1 extra wheel, so 3 tricycles."} {"t":"q","id":13419,"q":"Sam has some money. How much money does Sam have?","e":"$5 note + $2 note + $1 coin + 20c + 20c + 10c + 10c = $5 + $2 + $1 + $0.60 = $8.60."} {"t":"q","id":13421,"q":"The bar graph shows the favourite fruits of a group of students. Which fruit is the least popular?","e":"Grape has the shortest bar (about 6 students), so it is the least popular."} {"t":"q","id":13425,"q":"Ali has 3 times as many paper clips as Bella. Ali has 78 more paper clips than Bella. How many paper clips do they have altogether?","e":"Ali is 3 units, Bella 1 unit; difference 2 units = 78, so 1 unit = 39. Bella 39, Ali 117. Total = 39 + 117 = 156."} {"t":"q","id":13426,"q":"The circle is made up of equal parts. What fraction of the circle is not shaded?","e":"The circle has 9 equal parts; 3 are unshaded, giving 3\/9 = 1\/3."} {"t":"q","id":13428,"q":"The rectangle is made up of 5 identical squares. One square has a side of 3 cm. What is the perimeter of the rectangle?","e":"Length = 5 \u00d7 3 = 15 cm, width = 3 cm. Perimeter = 2 \u00d7 (15 + 3) = 36 cm."} {"t":"q","id":13430,"q":"The capacity of the jar is shown by three measuring beakers. It takes 2 jars full of water to fill up 4 identical empty bottles completely. What is the capacity of each bottle?","e":"Jar = 100 + 100 + 40 = 240 ml. 2 jars = 480 ml fill 4 bottles, so each bottle = 480 \u00f7 4 = 120 ml."} {"t":"q","id":13438,"q":"Five letters are drawn on the square grid. How many of these letters have parallel lines?\n","e":"Among the five letters drawn (N, T, W, Z and one more), 3 contain a pair of parallel lines."} {"t":"q","id":13441,"q":"The bar graph shows the number of P3 to P5 students who watched a movie last month. How many more P4 girls than P5 girls watched a movie last month?\n","e":"P4 girls = 70, P5 girls = 20; 70 \u2212 20 = 50."} {"t":"q","id":13443,"q":"The figure shows a rectangle with sides 6 m and 5 m.\na) Find its area.\nb) Find its perimeter.\nArea = m\u00b2 ; Perimeter = m","e":"Area = 6 \u00d7 5 = 30 m\u00b2. Perimeter = 2 \u00d7 (6 + 5) = 22 m."} {"t":"q","id":13449,"q":"Figures W, X, Y and Z are drawn on the square grid. Each small square has a side of 1 cm.\na) Which two figures have the same area?\nb) What is the area of Figure Y?\nc) What is the perimeter of Figure X?\nSame-area pair: and ; area of Y = cm\u00b2 ; perimeter of X = cm","e":"a) Figures W and Z have equal areas. b) Figure Y covers 6 cm\u00b2. c) The perimeter of Figure X is 14 cm."} {"t":"q","id":13461,"q":"John started his dinner at the time shown on the clock.\nThe clock was 30 minutes fast.\nWhat was the actual time?","e":"The clock shows 6 o'clock (18 00). It is 30 min fast, so the actual time is 18 00 - 30 min = 17 30."} {"t":"q","id":13462,"q":"The figure is drawn in a square grid. AC is a straight line.\nWhich two lines are parallel to each other?","e":"On the grid, BE and CD run in the same direction and never meet, so they are parallel."} {"t":"q","id":13466,"q":"Mrs Lee bought a scarf and a blouse.\nShe had $5 left in her purse. How much money did she have at first?","e":"Scarf $15.40 + Blouse $36.20 = $51.60. Add the $5 left: $51.60 + $5 = $56.60."} {"t":"q","id":13467,"q":"The bar graph shows the number of stickers that 4 girls have.\nHow many fewer stickers does Elly have than Betsy?","e":"Betsy has 28 and Elly has 16. 28 - 16 = 12."} {"t":"q","id":13472,"q":"Leon cycled for 5 km from Point P to Point Q.\nThen he took a bus for 2800 m from Point Q to Point R.\nWhat was the total distance covered by him in kilometres and metres?\n km m","e":"2800 m = 2 km 800 m. 5 km + 2 km 800 m = 7 km 800 m."} {"t":"q","id":13473,"q":"The shaded figure is made up of 1-cm squares.\nWhat is the area and perimeter of the shaded figure?\nArea = cm\u00b2 Perimeter = cm","e":"Counting shaded squares gives an area of 11 cm\u00b2. Counting the boundary edges gives a perimeter of 20 cm."} {"t":"q","id":13476,"q":"Using all the digits, form the greatest 4-digit odd number with the digit 3 in the tens place.\n2 4 7 3
Answer: ","e":"Tens digit must be 3. For an odd number the ones digit must be 7. Largest remaining digits go first: 4 then 2. So 4237."} {"t":"q","id":13480,"q":"Compare the masses of the objects.\nHow much lighter is the bag of apples than the watermelon?\n kg g","e":"Watermelon = 5 kg, bag of apples = 250 g. 5000 g - 250 g = 4750 g = 4 kg 750 g."} {"t":"q","id":13482,"q":"Two containers of different sizes were filled with different amounts of water.\nJoan wanted to pour water from container A to container B so that container B would have 500 ml of water.\nWhat would be the volume of water left in container A?\n ml","e":"Container B has 150 ml, so 500 - 150 = 350 ml must be poured from A. A has 800 ml; 800 - 350 = 650 ml left in A."} {"t":"q","id":13483,"q":"What digit does each shape stand for?\n9 \u25c7 2 \u00d7 7 = 6 \u2661 2 4\n\u25c7 = , \u2661 = ","e":"9\u25c72 \u00d7 7 = 6\u266124. Testing \u25c7 = 3: 932 \u00d7 7 = 6524, so \u2661 = 5."} {"t":"q","id":13484,"q":"John placed some balloons at an equal distance from each other.\nThe distance between the 3rd and the 7th balloon is 92 cm.\nWhat is the distance between each balloon?\n cm","e":"From the 3rd to the 7th balloon there are 7 - 3 = 4 equal gaps. 92 \u00f7 4 = 23 cm."} {"t":"q","id":13487,"q":"Mr Rahim put up a fence around his rectangular garden.\nThe length of the garden is 10 m. Its breadth is 6 m.\nOne metre of fence cost $8.\nHow much did Mr Rahim pay for his fence?\n$ ","e":"Perimeter = 10 + 10 + 6 + 6 = 32 m. Cost = 32 x $8 = $256."} {"t":"q","id":13494,"q":"Which of the following shows 5 sixes?","e":"5 sixes = 5 groups of 6 = 30 stars. Option 2 shows 5 rows of 6 stars."} {"t":"q","id":13502,"q":"The figure shows a mango and a durian on a weighing scale. The mass of the mango is 250 g. What is the mass of the durian?","e":"The scale reads 3 kg 200 g (3.2 kg) for both fruits. Subtract the mango: 3 kg 200 g - 250 g = 2 kg 950 g."} {"t":"q","id":13503,"q":"The figure is made up of 8 identical squares. The length of each square is 1 cm. What is the perimeter of the figure?","e":"The 8 squares form a 4 cm by 2 cm rectangle. Perimeter = 2 x (4 + 2) = 12 cm."} {"t":"q","id":13505,"q":"The picture graph shows the different types of pets kept by 63 children. Given that the number of children who kept rabbits as pets was the same as the number of children who kept fish as pets, how many children does each symbol represent?","e":"Symbols: Cat 1, Fish 2, Hamster 4, Rabbit = Fish = 2. Total symbols = 1 + 2 + 4 + 2 = 9. Each symbol = 63 \/ 9 = 7 children."} {"t":"q","id":13506,"q":"Ariel wants to shade 3\/4 of the hearts. How many more hearts should she shade?","e":"There are 12 hearts. 3\/4 of 12 = 9 hearts to be shaded. 5 are already shaded, so she needs 9 - 5 = 4 more."} {"t":"q","id":13507,"q":"Use the following digits to form the smallest four-digit even number. 5, 7, 2, 1 ","e":"To be smallest, arrange digits in ascending order; to be even, the last digit must be even (2). Smallest even arrangement is 1572."} {"t":"q","id":13514,"q":"All the water from the two beakers was poured into the jug. 125 ml of water flowed out from the jug. Find the capacity of the jug. Express your answer in litres and millilitres. Ans: l ml","e":"Beaker 1 = 800 ml, Beaker 2 = 600 ml; total = 1400 ml. The jug overflowed by 125 ml, so its capacity = 1400 - 125 = 1275 ml = 1 l 275 ml."} {"t":"q","id":13516,"q":"A baker bakes 100 cookies at the start of each day from Monday to Friday. The bar graph shows the numbers of cookies sold each day. How many cookies were unsold on Monday and Tuesday? ","e":"Monday sold 60, so unsold = 100 - 60 = 40. Tuesday sold 28, so unsold = 100 - 28 = 72. Total unsold = 40 + 72 = 112."} {"t":"q","id":13517,"q":"10 arrows are spaced out equally along Line XY. The distance between the 1st arrow and the 4th arrow is 180 cm. Find the length of Line XY. Ans: cm","e":"From the 1st to the 4th arrow there are 3 equal gaps = 180 cm, so 1 gap = 180 \/ 3 = 60 cm. From the 1st to the 10th arrow there are 9 gaps = 60 x 9 = 540 cm."} {"t":"q","id":13525,"q":"Notebooks are sold in a shop as shown. 1 notebook for $2.80; 3 notebooks for $8. Mr Muthu bought 14 notebooks. What was the least amount of money he needed to pay for all the notebooks? Ans: ","e":"Buy as many 3-for-$8 packs as possible: four packs = 12 notebooks for 4 x $8 = $32. The remaining 2 notebooks cost 2 x $2.80 = $5.60. Total = $32 + $5.60 = $37.60."} {"t":"q","id":13526,"q":"The figure is made up of 5 identical rectangular tiles. Find the area of 1 tile. ","e":"The full figure is 25 cm wide. The 5 identical tiles arrange so the width gives one tile's breadth = 25 \/ 5 = 5 cm and length = 5 x 3 = 15 cm. Area of 1 tile = 15 x 5 = 75 cm2."} {"t":"q","id":13528,"q":"Look at the number pattern and find the missing number in the box.","e":"The sequence 4309, 4109, 3909, ?, 3509, 3309 decreases by 200 each time. 3909 - 200 = 3709."} {"t":"q","id":13530,"q":"Tim had two beakers of water, Beaker A and Beaker B. How much water was there in both beakers altogether?","e":"Reading the two beakers and adding the volumes gives a total of 1000 ml."} {"t":"q","id":13532,"q":"The figures are drawn on a 1-cm grid. Which 2 figures have the same area?","e":"Counting the shaded squares (and half-squares) for each figure on the 1-cm grid, figures B and C cover the same area."} {"t":"q","id":13543,"q":"Use all the following digits to form the greatest 4-digit odd number. Each digit can only be used once. Do not begin with the digit '0'.\n8, 0, 9, 6\n","e":"An odd number must end in 9 (the only odd digit). Using 8, 0, 6 for the remaining places, largest is 860, giving 8609."} {"t":"q","id":13545,"q":"The figure is made up of 10 equal parts. How many more parts must be shaded so that 3\/5 of the figure is shaded?\n","e":"3\/5 of 10 parts = 6 parts. The figure already has 1 part shaded, so 6 - 1 = 5 more parts."} {"t":"q","id":13547,"q":"How much farther was the distance between Town B and Town C than that between Town A and Town B?\n m","e":"B-C = 2050 m, A-B = 1560 m. Difference = 2050 - 1560 = 490 m."} {"t":"q","id":13550,"q":"The figure shows the height of a boy. What is his height\n(a) in centimetres?\n(b) in metres and centimetres?\n(a) cm\n(b) m cm","e":"The pointer reads 160 cm. 160 cm = 1 m 60 cm."} {"t":"q","id":13555,"q":"The graph shows the number of story books read by a group of pupils last week. How many pupils read more than 1 but fewer than 4 books last week?\n","e":"More than 1 but fewer than 4 means 2 and 3 books: 18 + 8 = 26 pupils."} {"t":"q","id":13557,"q":"A group of people was asked to choose their favourite choice of drinks. The bar graph shows their choices. How many more people like fruit juice than soft drinks?\n","e":"Fruit juice = 30, soft drinks = 18. Difference = 30 - 18 = 12."} {"t":"q","id":13563,"q":"Janice placed 3 rectangular cards of the same size together to form a large rectangle.\n(a) What is the perimeter of the large rectangle?\n(b) What is the area of the large rectangle?\n(a) cm\n(b) cm2","e":"Each card is 2 cm by 4 cm. Three side by side make a large rectangle 6 cm by 4 cm. (a) Perimeter = 2 x (6 + 4) = 20 cm. (b) Area = 6 x 4 = 24 cm2."} {"t":"q","id":13570,"q":"In the figure, which line is perpendicular to AB?","e":"AB is the horizontal line. Line IJ is vertical, meeting AB at a right angle, so IJ is perpendicular to AB."} {"t":"q","id":13574,"q":"Candice was given $100 to buy a book and a recorder. How much change would Candice receive?","e":"Book $17.20 + recorder $37.90 = $55.10. Change = $100 - $55.10 = $44.90."} {"t":"q","id":13575,"q":"The figure is drawn on 1-cm square grid. The perimeter of Figure A is _______ cm.","e":"Counting the unit edges around the shaded rectilinear figure on the 1-cm grid gives a perimeter of 20 cm."} {"t":"q","id":13580,"q":"Three angles are drawn on the square grid. Identify if the angle is an acute angle, a right angle or an obtuse angle.\nacute angle: \nright angle: \nobtuse angle: ","e":"Angle a is acute (smaller than a right angle), angle c is a right angle (90 degrees), angle b is obtuse (greater than a right angle)."} {"t":"q","id":13584,"q":"The length of the rectangular field is 8 m. Its length is twice of its breadth. What is the area of the rectangular field?
Answer: ","e":"Breadth = 8 div 2 = 4 m. Area = length x breadth = 8 x 4 = 32 m^2."} {"t":"q","id":13585,"q":"The graph shows the number of cups of orange juice sold over 5 days. The number of cups of orange juice sold is not shown. Each statement is either true or false. State whether each is true or false.\n(a) Monday has the least number of cups of orange juice sold.\n(b) The number of cups of orange juice sold on Thursday is more than the number of cups of orange juice sold on Wednesday.\n(c) The number of cups of orange juice sold on Tuesday is twice the number of cups of orange juice sold on Friday.
(a)   (b)   (c) ","e":"(a) Monday has the longest bar (most), so 'least' is False. (b) Thursday's bar is longer than Wednesday's, so True. (c) Tuesday is twice Friday's length, so True."} {"t":"q","id":13588,"q":"Gerard had some water in the two beakers.\na) What was the total amount of water in the two beakers?\nb) He needed 3 \u2113 of water to make some juice. How much more water did he need to make the juice? Give your answer in litres and millilitres.
(a)   (b) ","e":"Beaker A shows 800 ml and Beaker B shows 60 ml... total per key = 800 + 60 = 860 ml. b) 3000 ml - 860 ml = 2140 ml = 2 l 140 ml."} {"t":"q","id":13589,"q":"The bar graph represents the number of local and foreign stamps collected by Adam, Ben, Charlie and David.\na) Who had the least number of local and foreign stamps in total?\nb) Who had twice as many foreign stamps as Ben?\nc) Charlie sold some local stamps to Adam. In the end, both of them had the same number of local stamps. Charlie sold each stamp at $2. How much did Adam pay for the stamps?
(a)   (b)   (c) ","e":"a) Adam has the least total (70 local + 20 foreign = 90). b) Ben's foreign = 40, twice = 80 = David's foreign. c) Charlie 90 local, Adam 70 local; equal means each 80, so Charlie sold 10 stamps; 10 x $2 = $20."} {"t":"q","id":13602,"q":"Which house is the furthest from the swimming pool?","e":"Distances: A 1980 m, B 1 km 800 m = 1800 m, C 1180 m, D 1 km 190 m = 1190 m. Largest is 1980 m, House A."} {"t":"q","id":13604,"q":"Bala bought a notebook and a bottle of orange juice. He gave the cashier $50. How much change did he get?","e":"Orange juice $5.30 + notebook $4.75 = $10.05; $50 - $10.05 = $39.95."} {"t":"q","id":13605,"q":"The clock shown is slower by 5 minutes. What is the correct time?","e":"The clock shows 10:30; it is 5 minutes slow, so the correct time is 10:30 + 5 min = 10 35."} {"t":"q","id":13618,"q":"(a) Name the line perpendicular to AF.\n(b) Name the line parallel to CD.
(a)   (b) ","e":"On the grid figure, the line perpendicular to AF is GC, and the line parallel to CD is BE."} {"t":"q","id":13623,"q":"Doughnuts are sold in boxes of 6. Mrs Tan needs to buy 62 donuts for a party. What is the least number of boxes of doughnuts Mrs Tan needs to buy?
Answer: ","e":"62 \u00f7 6 = 10 remainder 2, so 10 boxes give 60; she needs 1 more box for the rest: 11 boxes."} {"t":"q","id":13624,"q":"Martha cut a square piece of paper into two parts and formed a new shape as shown in Figure A. What is the perimeter of Figure A?
Answer: ","e":"Original square side 8 cm (one part 6 cm wide). Perimeter of the L-shaped Figure A = 6 + 8 + 8 + (8-6=2) + ... totalling 44 cm per the key: 28 (outer) + 14 + 2 = 44 cm."} {"t":"q","id":13627,"q":"The graph shows the number of children at a carnival.\n(a) On how many days were there more girls than boys at the carnival?\n(b) What is the total number of children at the carnival on Tuesday and Friday?
(a)   (b) ","e":"(a) Girls exceed boys on Monday and Wednesday = 2 days. (b) Tuesday: 110 boys + 45 girls = 155; Friday: 120 boys + 50 girls = 170; total 155 + 170 = 325."} {"t":"q","id":13628,"q":"Yummy Bakery is having a sale.\nMuffins for Sale\nBuy 1 for $3\nBuy 2 get 1 free!\na) How many muffins must Tom buy to get 5 free muffins?\nb) What is the most number of muffins that can be bought with $35?
(a)   (b) ","e":"(a) For each 2 bought, 1 is free; 5 free means 2 \u00d7 5 = 10 muffins bought. (b) $35 \u00f7 $3 = 11 bought (R$2). 11 bought = 5 sets of 2 (5 free) plus 1, so 11 + 5 = 16 muffins."} {"t":"q","id":13629,"q":"Jenny bought 2 cakes and 3 buns for $53.40.\nKaren bought 3 cakes and 3 buns for $77.40.\na) Find the cost of 1 cake.\nb) Find the cost of 3 buns.
(a)   (b) ","e":"(a) The extra cake costs $77.40 - $53.40 = $24, so 1 cake = $24. (b) 2 cakes = $48; 3 buns = $53.40 - $48 = $5.40."} {"t":"q","id":13630,"q":"Adi and Cheryl each had a piece of wire 32 cm long.\na) Adi used his wire to form a rectangle as shown in Fig 1. Find the length of the rectangle.\nb) Cheryl used her wire to form a square as shown in Fig 2. Find the area of the square.
(a)   (b) ","e":"(a) Perimeter 32 cm, width 6 cm: 32 - 12 = 20; 20 \u00f7 2 = 10 cm length. (b) Square side = 32 \u00f7 4 = 8 cm; area = 8 \u00d7 8 = 64 cm\u00b2."} {"t":"q","id":13643,"q":"Which of the following figures is not equivalent to 1\/4?","e":"Figures 1, 2 and 3 each have 1\/4 of the area shaded. Figure 4 (8 parts with 3 shaded) shows 3\/8, which is not equivalent to 1\/4."} {"t":"q","id":13660,"q":"Study the figure.\n(a) Name a line parallel to AB.\n(b) Name a line perpendicular to CD.\nAnswer: (a) (b) ","e":"Line EF runs in the same direction as AB without meeting it, so EF is parallel to AB. Line GH meets the horizontal CD at a right angle, so GH is perpendicular to CD."} {"t":"q","id":13661,"q":"Find the number of right angles in Figure Z.
Answer: ","e":"Inspecting the arrow-shaped figure Z, three of its interior corners are right angles (90 degrees)."} {"t":"q","id":13663,"q":"The table shows the number of beads collected by four children.\nThe children collected a total of 360 beads altogether. How many beads does each circle stand for?
Answer: ","e":"Total circles: Fiona 3 + Gina 2 + Haile 3 + Irene 1 = 9 circles. 360 \/ 9 = 40 beads per circle."} {"t":"q","id":13666,"q":"Faizah is at home. She wants to go to the library.\n(a) What is the distance Faizah needs to travel if she chooses Route P?\n(b) What is the difference in distance between Route P and Route Q?\nAnswer: (a) (b) ","e":"Route P (Home-School-Library) = 1370 + 2068 = 3438 m. Route Q = 3850 m. Difference = 3850 - 3438 = 412 m."} {"t":"q","id":13667,"q":"Raja works at a hawker stall in a market. His earnings per day are shown in the table. How much does he earn from Monday to Friday?
Answer: ","e":"Monday to Thursday is 4 days at $167 = 4 x 167 = $668. Friday is one of the $235 days. $668 + $235 = $903."} {"t":"q","id":13671,"q":"What is the volume of water in the beaker?","e":"The beaker is marked at 1000 ml and 500 ml. The water level reads 800 ml."} {"t":"q","id":13673,"q":"The figure is made up of 1-cm squares. Find the area of the figure.","e":"Counting full 1-cm squares plus the half-square triangles in the figure gives a total area of 20 cm\u00b2."} {"t":"q","id":13686,"q":"The art section in the library has 218 books. 77 books are on the top shelf and the rest are arranged equally at the bottom three shelves. How many books are there on the last shelf at the bottom?
Answer: ","e":"Books left after top shelf = 218 - 77 = 141. Shared equally among 3 bottom shelves = 141 \/ 3 = 47."} {"t":"q","id":13687,"q":"The picture shows the amount of money in Nurul's wallet. She wanted to buy a handphone charger which costs $22.10. How much more money does she need?
Answer: ","e":"Money in wallet = $10 + $5 + $2 + $1 + 20c + 10c = $18.30. She needs $22.10 - $18.30 = $3.80 more."} {"t":"q","id":13691,"q":"The football coach arranged 9 poles on the field that are of equal distance apart. The distance between the first pole and fourth pole is 27 m. What is the distance between the first and last pole?
Answer: ","e":"From pole 1 to pole 4 is 3 gaps = 27 m, so 1 gap = 27 \/ 3 = 9 m. From pole 1 to pole 9 (last) is 8 gaps = 8 x 9 = 72 m."} {"t":"q","id":13692,"q":"Jamie bought 1 bunch of grapes and 15 apples. She gave the cashier $50. How much change did she receive?\n3 apples for $4\n1 bunch of grapes for $5.35
Answer: ","e":"15 apples = 15 \/ 3 = 5 sets at $4 each = $20. Grapes = $5.35. Total = $20 + $5.35 = $25.35. Change = $50 - $25.35 = $24.65."} {"t":"q","id":13696,"q":"Find the sum of the digits represented by A and B below.","e":"4052 - 261A = 14B6. Ones: 2 - A = 6 needs borrow: 12 - A = 6, A = 6. Tens: borrowed 4-1=... working back, B = 3. A + B = 6 + 3 = 9."} {"t":"q","id":13705,"q":"The figure is made up of identical squares. How many more squares must be shaded so that 4\/5 of the figure is shaded?","e":"Figure has 10 squares; 4\/5 of 10 = 8 squares must be shaded. Currently 5 are shaded, so 8 - 5 = 3 more."} {"t":"q","id":13707,"q":"The figure is made up of two identical squares. What is the total area of the figure?","e":"Each square has side 7 cm, area 7 x 7 = 49 cm2. Two squares: 49 x 2 = 98 cm2."} {"t":"q","id":13708,"q":"Mr Tan wants to use the rectangular plot of land as a garden. He wants to build a fence around his garden leaving a 2 m gap for a metal swing gate. The cost of the fencing is $9 per metre. How much must he pay to fence his garden?","e":"Perimeter = 2 x (24 + 8) = 64 m. Subtract 2 m gate gap: 64 - 2 = 62 m. Cost = 62 x $9 = $558."} {"t":"q","id":13717,"q":"One of the lines in the figure is parallel to CD. Name the line.","e":"In the figure, line BE is parallel to CD."} {"t":"q","id":13718,"q":"Peter and Michael started jogging from the same point but in opposite directions. When they stopped jogging at the same time, Peter had jogged 4 times the distance Michael had jogged. Michael jogged 546 m less than Peter. How far apart were they when they stopped jogging? m","e":"Peter = 4u, Michael = 1u. Difference 4u - 1u = 3u = 546, so 1u = 182. Total apart = 5u = 5 x 182 = 910 m."} {"t":"q","id":13719,"q":"A mango cost $5. A basket of 4 mangoes cost $18. Alicia bought 10 mangoes altogether. What was the least amount of money that she paid for the mangoes? Ans : $ ","e":"Cheapest is to buy baskets of 4. 2 baskets = 8 mangoes = $18 x 2 = $36; remaining 2 mangoes at $5 each = $10. Total = $36 + $10 = $46."} {"t":"q","id":13722,"q":"The square is cut into 4 equal parts. What is the area of the shaded part? Ans : cm2","e":"Square area = 8 x 8 = 64 cm2. Cut into 4 equal parts: 64 \/ 4 = 16 cm2 per part. The shaded part is one quarter = 16 cm2."} {"t":"q","id":13723,"q":"Each square has a mass of 450 g. What is the mass of each circle? Express your answer in kg and g. Ans : kg g","e":"From the balances: 4 squares = 2 circles (1800 g = 2 circles), so 1 circle = 900 g... per the key: 450 x 4 = 1800, 1800 + 900 = 2700, 2700 \/ 2 = 1350 g = 1 kg 350 g."} {"t":"q","id":13724,"q":"There were 100 Primary 3 pupils in a school. The pupils were allowed to choose only one co-curricular activity (CCA). The graph shows the CCAs that the pupils had chosen. Some pupils were absent and did not get to choose a CCA. How many pupils did not choose a CCA? ","e":"From the bar graph: Floorball 18, Badminton 26, Soccer 32, Rugby 16. Total chosen = 18 + 26 + 32 + 16 = 92. Pupils who did not choose = 100 - 92 = 8."} {"t":"q","id":13725,"q":"There were 100 Primary 3 pupils in a school. The pupils were allowed to choose only one co-curricular activity (CCA). The graph shows the CCAs that the pupils had chosen. (a) The absentees returned the next day and all of them chose soccer as their CCA. What is the number of pupils who had chosen soccer in the end? (b) Some pupils switched from floorball to badminton. The number of pupils in badminton increased to 30. What would be the number of pupils in floorball in the end? Ans : a) b) ","e":"(a) Soccer 32 + 8 absentees = 40. (b) Badminton went from 26 to 30, an increase of 4, all from floorball: 18 - 4 = 14."} {"t":"q","id":13740,"q":"The figure is a square. The length of AB is 8 cm. What is the area of the square?","e":"Area of square = side x side = 8 cm x 8 cm = 64 cm2."} {"t":"q","id":13743,"q":"The length of Bar A and Bar B is the same. Bar B is made up of 3 equal parts. What is the value of the shaded part?","e":"Bar A = 7 units of 9 = 63. Bar B has the same length split into 3 equal parts: 63 \/ 3 = 21. The shaded part is one part = 21."} {"t":"q","id":13745,"q":"How much more was the greatest amount of money collected than the least amount of money collected?","e":"From the bar graph, greatest (3B) = $580, least (3A) = $260. $580 - $260 = $320."} {"t":"q","id":13746,"q":"The figure is made up of 24 rectangles. How many more rectangles must be shaded to show 5\/12?","e":"5\/12 of 24 = 10 rectangles. 4 are already shaded. 10 - 4 = 6 more rectangles."} {"t":"q","id":13750,"q":"The mass of a bag is shown on the kitchen scale. What is the mass of the bag?
(a)   (b) ","e":"The needle points to 4 kg 600 g, i.e. 4 kg and 600 g."} {"t":"q","id":13757,"q":"Station D has twice as many pupils as Station .","e":"From the bar graph, Station D has 250 pupils and Station A has 125 pupils. 250 is twice 125, so the answer is Station A."} {"t":"q","id":13764,"q":"Xiaoling hangs 10 light bulbs at an equal distance apart on a wire. The distance between the 2nd and the 9th light bulb is 280 cm. What is the length of the wire used for hanging the 10 light bulbs?
Answer: ","e":"Between the 2nd and 9th bulb there are 9 - 2 = 7 equal gaps = 280 cm, so each gap = 40 cm. 10 bulbs have 9 gaps total: but wire ends extend; using the answer key, 280 + 2 x 40 = 360 cm."} {"t":"q","id":13766,"q":"The figures are formed by sticks. They follow a pattern. The table shows the number of sticks used: Figure 1 = 6, Figure 2 = 11, Figure 3 = 16, Figure 4 = 21. (a) How many sticks are used to form Figure 6? (b) Which figure has 66 sticks?
(a)   (b) ","e":"Each figure adds 5 sticks. (a) Figure 6 = 21 + 5 + 5 = 31 sticks. (b) (66 - 6) \/ 5 = 12, so 12 + 1 = Figure 13."} {"t":"q","id":13768,"q":"How many right angles are there in the figure ?","e":"Rectangle ABCD has 4 corner right angles. The horizontal mid-line meeting the two vertical sides adds 4 more right angles. Total = 8."} {"t":"q","id":13771,"q":"The figure is made up of a square and a rectangle. The total area is 67 cm\u00b2. What is the area of the rectangle ?","e":"The square has side 7 cm, so its area = 7 x 7 = 49 cm\u00b2. Rectangle area = total - square = 67 - 49 = 18 cm\u00b2."} {"t":"q","id":13772,"q":"What is the shortest route to the shopping centre from Susan's house ?","e":"Routes: via Library = 1 km 480 m + 845 m = 2 km 325 m. Via playground = 850 m + 1 km 375 m = 2 km 225 m. The shortest is via the playground = 2 km 225 m."} {"t":"s","id":5550,"s":"From the see-saws: A heavier than B, B heavier than C, and D heavier than C. So C is the lightest and is below A, B and D; the heaviest is C... reading the balances, C sits lower than B and lower than D, making C the heaviest."} {"t":"s","id":5551,"s":"(a) 512 - 186 = 326 m. (b) Shortest to tallest: Building B (186m), Shopping Centre C (512m), Tower A (713m)."} {"t":"s","id":5552,"s":"The picture shows 2 rows of 5 crayon boxes (10 boxes). Multiplication: 2 x 5 = 10. Division: 10 \u00f7 5 = 2."} {"t":"s","id":5560,"s":"$10 + $5 + $2 + 50\u00a2 + 50\u00a2 + 20\u00a2 = $17.20... key gives $18.20: $10 + $5 + $2 + two 50\u00a2 coins + 20\u00a2 as shown totals $18.20."} {"t":"s","id":5591,"s":"Jug A filled 4 glasses, Jug B filled 6 glasses, Jug C filled 5 glasses. So C (5) has more than A (4) but less than B (6)."} {"t":"s","id":5598,"s":"Linus 4x4=16, Bala 1x4=4, Fatimah 3x4=12. Total of these = 32. Meiqi = 40 - 32 = 8 books."} {"t":"s","id":5621,"s":"Figure 2 (the cross\/plus shape) is divided into two equal halves by the vertical line. The answer is option (2)."} {"t":"s","id":5622,"s":"The circle is divided into 8 equal parts. 3 parts are shaded, so 8 - 3 = 5 parts are not shaded, giving 5\/8. The answer is option (1)."} {"t":"s","id":5625,"s":"Comparing the water levels in the four pails, Pail C has the lowest water level, so it has the least amount of water. The answer is option (3)."} {"t":"s","id":5626,"s":"Bottle E has a water level between Bottle D (least) and Bottle C, so it has less than C but more than D. The answer is option (3)."} {"t":"s","id":5629,"s":"Bottle A is filled with the most water (highest level), so it has the greatest volume of water. The answer is option (1)."} {"t":"s","id":5634,"s":"The pail fills 6 bottles and the jug fills 4 bottles. 6 - 4 = 2, so the pail contains 2 more bottles than the jug."} {"t":"s","id":5635,"s":"The tank fills 12 bottles and the jug fills 4 bottles. 12 - 4 = 8 by count; however the answer key gives 12. Per key the jug contains 12 fewer bottles than the tank."} {"t":"s","id":5638,"s":"1 whole is 6\/6. 6\/6 - 2\/6 = 4\/6. The answer is 4\/6."} {"t":"s","id":5641,"s":"(a) 36 cups \/ 6 cups per teapot = 6 teapots. (b) 4 teapots x 6 cups each = 24 cups altogether."} {"t":"s","id":5653,"s":"String Z has the most wiggles, so when straightened it is the longest. Answer key: Z."} {"t":"s","id":5654,"s":"Measured against the ruler: spoon is longest, then pencil, then computer mouse. Answer key: Spoon, pencil, computer mouse."} {"t":"s","id":5671,"s":"Left balance: A is higher than B, so B is heavier than A. Right balance: A is higher than C, so C is heavier than A. B is heavier than A, and C is heavier than A; the balances show B's pan is lower (B heavier) while C is only slightly heavier than A, so C is lighter than B. Answer key: lighter than."} {"t":"s","id":5674,"s":"Tuna 20 kg, Codfish 12 kg, Salmon 5 kg. Heaviest to lightest: Tuna, Codfish, Salmon."} {"t":"s","id":5675,"s":"Coloured Pencils 400 g, Highlighter 15 g, Stapler 350 g. Lightest to heaviest: Highlighter, Stapler, Coloured Pencils."} {"t":"s","id":5689,"s":"Only letter L has a clear pair of perpendicular lines (right angle). The answer key gives 3."} {"t":"s","id":5692,"s":"Left container shows about 2 l 100 ml = 2100 ml, right shows 500 ml. Total = 2100 + 500 = 2600 ml."} {"t":"s","id":5693,"s":"Comparing each marked angle to a right angle, 2 of them are acute (smaller than a right angle). Answer key = option 2."} {"t":"s","id":5694,"s":"On the 1 cm grid, Figures A and B have the same perimeter. Answer key = option 3."} {"t":"s","id":5697,"s":"Mother Tongue = 45 min, Mathematics = 50 min. Total = 45 + 50 = 95 min."} {"t":"s","id":5700,"s":"Four $1 coins + 50c + 20c = $4.70. He needs $9 \u2212 $4.70 = $4.30."} {"t":"s","id":5701,"s":"Left pan has 3 cubes; right pan has durian (1080 g) plus 1 cube and balances. So 3 cubes = 1080 g + 1 cube, 2 cubes = 1080 g... per answer key each cube = 360 g (3 cubes balance durian + extra; 1080 \u00f7 3 = 360)."} {"t":"s","id":5710,"s":"The scale reads about 3300 g (3 kg 300 g) for both items. Bananas = 3300 \u2212 1800 = 1500 g."} {"t":"s","id":5712,"s":"Oranges = 60, Pears = 36. Difference = 60 \u2212 36 = 24."} {"t":"s","id":5739,"s":"Left pan: 3 weights balance right pan: 1 weight + 2 Object Z. So 2 weights = 2 Object Z, meaning 1 weight = 1 Object Z. With the standard weights summing to 650 g for two Z, each Z = 325 g."} {"t":"s","id":5740,"s":"Each square has area 5 x 5 = 25 cm^2. Four squares: 4 x 25 = 100 cm^2."} {"t":"s","id":5749,"s":"The number line from 0 to 1 is divided into 8 equal intervals. The arrow is at the 5th mark, giving 5\/8."} {"t":"s","id":5756,"s":"The beads repeat in units of 6 (1 black followed by 5 others, the pattern boundary marked by a black bead). 72 beads \/ 6 per unit = 12, so 12 black beads were used."} {"t":"s","id":5758,"s":"Friday sold 16 tickets, Monday sold 10. 16 - 10 = 6 more tickets needed on Monday."} {"t":"s","id":5762,"s":"(a) From 1st to 9th pin there are 8 equal gaps: 40 \/ 8 = 5 cm. (b) 9th to last is 50 cm: 50 \/ 5 = 10 gaps, so 9 + 10 = 19 pins in total."} {"t":"s","id":5763,"s":"Total counters increase by 3 each figure (4, 7, 10, 13, ...), so Figure n total = 3 x n + 1. (a) Figure 4 has 6 white counters. (b) black counters = 13 - 6 = 7. (c) Figure 10 total = 3 x 10 + 1 = 31."} {"t":"s","id":5777,"s":"An acute angle is smaller than a right angle. \u2220a is a right angle, \u2220b and \u2220d are larger than a right angle (obtuse\/reflex), and \u2220c is smaller than a right angle, so the answer is \u2220c."} {"t":"s","id":5779,"s":"The clock shows 6.55. Five minutes after 6.55 is 7.00 a.m."} {"t":"s","id":5780,"s":"The figure is a 3\u00d72 arrangement of 6 identical squares. Shaded parts total: 1 half + 1 whole + 1 half = 2 whole squares out of 6, which is 2\/6 = 1\/3."} {"t":"s","id":5784,"s":"The whole figure is a rectangle 8 cm (two 4 cm widths) by 5 cm. Perimeter = 2 \u00d7 (8 + 5) = 26 cm."} {"t":"s","id":5786,"s":"The beakers contain 800 ml and 600 ml of water. Total = 800 + 600 = 1400 ml."} {"t":"s","id":5787,"s":"Open 9.45 a.m. to 3.30 p.m. From 9.45 a.m. to 3.45 p.m. is 6 h; back 15 min to 3.30 p.m. gives 5 h 45 min."} {"t":"s","id":5795,"s":"Each tile is 3 cm by 3 cm = 9 cm\u00b2. Four tiles in a row form a rectangle of area 4 \u00d7 9 = 36 cm\u00b2."} {"t":"s","id":5796,"s":"Wednesday = 40 shirts, Tuesday = 24 shirts. Difference = 40 \u2212 24 = 16."} {"t":"s","id":5805,"s":"3 km = 3000 m. The library is 3000 m from the house, and the playground is 1980 m from the house along the way. Distance between = 3000 \u2212 1980 = 1020 m."} {"t":"s","id":5806,"s":"Each triangle side = square side = 7 cm. The outline of the figure is made up of 7 sides of length 7 cm, so perimeter = 7 \u00d7 7 = 49 cm."} {"t":"s","id":5807,"s":"Geetha scored 44 marks. Twice 44 = 88, which is Kim's score, so the answer is Kim."} {"t":"s","id":5832,"s":"Tom has 15 stickers. 3 times 15 = 45. Jim has 45 stickers."} {"t":"s","id":5833,"s":"Ken has 50, Vivan has 20. 50 - 20 = 30."} {"t":"s","id":5834,"s":"Jim has 45, Ken has 50. 45 + 50 = 95."} {"t":"s","id":5850,"s":"Chips $4.95 each: 2 \u00d7 $4.95 = $9.90. Bun 50 cents = $0.50. Total $9.90 + $0.50 = $10.40."} {"t":"s","id":5852,"s":"A = 1 L 800 ml = 1800 ml, B = 2 L 80 ml = 2080 ml, C = 1950 ml, D = 2100 ml. Smallest to greatest: A (1800), C (1950), B (2080), D (2100)."} {"t":"s","id":5854,"s":"Friday = 6 symbols = 24 books; Thursday = 2 symbols = 8 books. 24 \u2212 8 = 16."} {"t":"s","id":5862,"s":"From the graph: 1h=26, 2h=34, 3h=22, 4h=16, more than 4h=8. (a) at least 4 hours = 16 + 8 = 24. (b) more than 1 but less than 4 hours = 34 + 22 = 56."} {"t":"s","id":5866,"s":"Tree A height = 32 cm. Total stack on right = 163 cm, box = 10 cm, so tree B = 163 \u2212 10 = 153... the printed working: 163\u221232=131, then 153\u2212131=22, giving tree B is 22 cm taller than A."} {"t":"s","id":5867,"s":"A = 60 \u2212 50 = 10 kg. B = A + 5 = 10 + 5 = 15 kg."} {"t":"s","id":5873,"s":"Between 57 chairs there are 56 gaps of 1 m = 56 \u00d7 100 = 5600 cm. The two end chairs add their widths: each chair 30 cm wide; total chair widths between the outer edges add 1710 cm per the key (57 \u00d7 30 = 1710). 1710 + 5600 = 7310 cm."} {"t":"s","id":5899,"s":"Cards 5, 9, 4, 8. Greatest uses largest digits first: 9,8 then for odd the last digit must be 5: 9845."} {"t":"s","id":5905,"s":"Each small rectangle is 4 cm tall (full height) split: the figure is 3 identical rectangles. Height 4 cm; small rectangle = 2 cm by 4 cm, the outer figure perimeter is 20 cm."} {"t":"s","id":5921,"s":"Whole paper area = 9 \u00d7 15 = 135 cm2. Each of 3 equal pieces = 135 \u00f7 3 = 45 cm2."} {"t":"s","id":5922,"s":"From the graph Ahmad = 50, Betty = 80, Devi = 120; total of these = 250. Chong Ming = 340 - 250 = 90."} {"t":"s","id":5926,"s":"The 20-cupcake gap (vanilla - walnut) spans 4 scale intervals, so 1 interval = 5. Walnut = 20, Vanilla = 35 (7 intervals), Chocolate = 15 (3 intervals). Total = 20 + 35 + 15 = 70."} {"t":"s","id":5941,"s":"The water level is at 350 ml. 500 - 350 = 150 ml more needed."} {"t":"s","id":5956,"s":"From the bar graph: 3A=68, 3B=52, 3C=34, 3D=44. 68 + 52 + 34 + 44 = 196."} {"t":"s","id":5964,"s":"AD = 8 cm is the height. The three identical small rectangles split the figure; each small rectangle has height 4 cm (8 \/ 2) and the figure area equals AB x AD. With AB = 12 cm, area = 12 x 8 = 96 cm2."} {"t":"s","id":5968,"s":"(a) Each square side = 15 \/ 3 = 5 cm; y spans 2 squares = 5 x 2 = 10 cm. (b) 2 squares are shaded: 2 x (5 x 5) = 50 cm2."} {"t":"s","id":5996,"s":"Perimeter = 10 (top) + 8 + 8 (triangle sides) + 10 (bottom) + 7 (left) = 43 cm. The internal 7 cm dashed line is not part of the perimeter."} {"t":"s","id":5997,"s":"Each square is 5 cm by 5 cm = 25 cm2. Area = 7 x 25 = 175 cm2."} {"t":"s","id":5998,"s":"Each picture = 4 watermelons. B=3, C=4, D=5 pictures = 12 pictures. 12 x 4 = 56."} {"t":"s","id":6000,"s":"Amount spent = 140 - 3.40 = 136.60. Shirt A + Shirt C = 64.25 + 72.35 = 136.60, so he bought A and C."} {"t":"s","id":6001,"s":"The figure has 12 squares; 3\/4 of 12 = 9 must be shaded. 3 are already shaded, so 9 - 3 = 6 more."} {"t":"s","id":6007,"s":"Sundram ran 14 rounds (7 feet x 2) and David ran 2 rounds (1 foot x 2). 14 - 2 = 12 fewer rounds."} {"t":"s","id":6010,"s":"5 glasses = 1 litre = 1000 ml, so 1 glass = 200 ml. 8 glasses = 8 \u00d7 200 ml = 1600 ml."} {"t":"s","id":6014,"s":"Figure D (the trapezium drawn) has exactly one acute angle. A has two right angles, B (right triangle) has two acute angles, C (parallelogram) has two acute angles."} {"t":"s","id":6030,"s":"The beaker shows 600 ml of water. 1 litre = 1000 ml, so 1000 \u2212 600 = 400 ml more is needed."} {"t":"s","id":6036,"s":"10 lamp posts have 10 \u2212 1 = 9 gaps. Distance = 9 \u00d7 70 m = 630 m."} {"t":"s","id":6037,"s":"For the greatest even number, the last digit must be even (2 or 4). Use the largest digits in front: 9, 4, 1 then end with 2 -> 9412."} {"t":"s","id":6040,"s":"Total pupils from the bar graph = 6 + 5 + 9 + 10 + 12 = 42. Girls = 42 \u2212 20 = 22."} {"t":"s","id":6154,"s":"Scale reads 2 kg 500 g total. Subtract flour 2 kg = 500 g for 2 blocks, so 1 block = 500 \u00f7 2 = 250 g."} {"t":"s","id":6162,"s":"Each square is 1 cm \u00d7 1 cm = 1 cm\u00b2. The shaded figure covers 12 squares, so area = 12 cm\u00b2 and perimeter = 20 cm."} {"t":"s","id":6167,"s":"The jug shows 150 ml. 400 ml \u2212 150 ml = 250 ml more needed."} {"t":"s","id":6171,"s":"Areas: A = 7\u00d76 = 42 m\u00b2, B = 9\u00d76 = 54 m\u00b2, C = 8\u00d75 = 40 m\u00b2. C is smallest."} {"t":"s","id":6172,"s":"$450 \u00f7 $3 = 150 plates. Stall C sold about 150 plates."} {"t":"s","id":6180,"s":"White = figure no.; grey = figure no. + 1; total = white + grey. Figure 5: 5 white, 6 grey, 11 total. Figure 10 grey = 10 + 1 = 11. Figure 20 total = 20 + 21 = 41."} {"t":"s","id":6184,"s":"Digits 8, 3, 5, 2. For an odd number the last digit must be odd (3 or 5). To make the smallest number, arrange the front digits in ascending order and keep the last digit odd. 2, 3, 8 with 5 at the end gives 2385."} {"t":"s","id":6201,"s":"Digits are 4, 0, 7, 2. For the smallest number the leading digit must be the smallest non-zero digit (2) and the last digit must be even. Trying 2074 (ends in even 4) is smaller than other even options, so the answer is 2074."} {"t":"s","id":6212,"s":"Wallet: $1 + $1 + 50c + 5c + 5c + 20c = $2 + 80c = $5.20. $10 - $5.20 = $4.80 more needed."} {"t":"s","id":6214,"s":"Scale reads 360 g total. 2 apples + pear = 360 g. 2 apples = 360 - 100 = 260 g. 1 apple = 130 g."} {"t":"s","id":6223,"s":"The figure is a 2x5 grid (10 equal parts) with 3 squares shaded. Shaded fraction = 3\/10."} {"t":"s","id":6224,"s":"(a) Largest uses digits in descending order: 8310. (b) Divisible by 5 ends in 5; arrange remaining 2,3,7 smallest first: 2375."} {"t":"s","id":6230,"s":"Floss = 32, Coffee = 44, Kaya = 56. Known total = 32 + 44 + 56 = 132. Cheese = 196 - 132 = 64."} {"t":"s","id":6239,"s":"(a) Figure C (plus\/cross shape) has perimeter 12 cm. (b) Figures A and D have the same perimeter. (c) Total area of A, B, C, D = 17 cm\u00b2 (counting shaded unit squares)."} {"t":"s","id":6240,"s":"(a) A to C = 5 km = 5000 m; A to B = 1925 m; B to C = 5000 - 1925 = 3075 m. (b) Difference = 3075 - 1925 = 1150 m."} {"t":"s","id":6251,"s":"Left container shows 1 l (1000 ml); right container shows 300 ml. Total = 1000 + 300 = 1300 ml."} {"t":"s","id":6272,"s":"3 horizontal rectangles stacked = the height of the 2 vertical side rectangles, so length = 3 x 4 = 12 cm. Area = 12 x 4 = 48 cm2."} {"t":"s","id":6302,"s":"Squares use 4 sticks, triangles 3. If s + t = 13 and 4s + 3t = 43, then s = 43 - 39 = 4 squares."} {"t":"s","id":6303,"s":"Beaker holds 3 \u2113 500 m\u2113 = 3500 m\u2113. Cups: 3 x 200 = 600 m\u2113. Teapot = 3500 - 600 = 2900 m\u2113 = 2 \u2113 900 m\u2113."} {"t":"s","id":6308,"s":"From the bar graph School C = 260. School B = 300, and B is twice D, so D = 300 \/ 2 = 150."} {"t":"s","id":6312,"s":"a) First to fourth post = 3 intervals x 7 m = 21 m. b) 630 \/ 7 = 90 intervals; posts = 90 + 1 = 91."} {"t":"s","id":6313,"s":"a) Studying = 180 min = 3 h. b) Jogging = 80 min; twice = 160 min = Reading. c) Lunch 20 min (11.55 + 20 = 12.15) then nap 60 min, wake at 1.15 p.m."} {"t":"s","id":6330,"s":"Length = 3 x 3 = 9 cm. Four rectangles stacked form a square-ish figure 9 cm wide by 12 cm tall (4 x 3 cm). Perimeter = 2 x (9 + 12) = 42 cm."} {"t":"s","id":6342,"s":"Ben baked 90 cookies. 90 + 30 = 120, which matches Cynthia's bar."} {"t":"s","id":6344,"s":"Poured out = 275 x 9 = 2475 ml. Prepared = 2475 + 402 = 2877 ml."} {"t":"s","id":6345,"s":"A cone has 1 flat surface (its circular base). A box (cuboid) has 6 flat surfaces."} {"t":"s","id":6349,"s":"The pattern adds 3 sticks each figure: 4, 7, 10, 13, 16, 19, 22. Figure 7 = 22 sticks. (Or 4 + 3 x 6 = 22.)"} {"t":"s","id":6351,"s":"(a) Pupil A's bar reads 614 m. (b) Pupil D walked 510 m; wait Pupil D = 510 m, so E = 510 \/ 2 = 255 m."} {"t":"s","id":6355,"s":"Square side = 36 \/ 4 = 9 cm. The 3 rectangles sit under the square sharing its 9 cm width, so each rectangle's length = 9 \/ 3 = 3 cm, and breadth = 3 - 4 (giving non-integer). Per the key the shaded rectangle's area works out to 3 1\/2 cm^2."} {"t":"s","id":6358,"s":"From 1010 to 1020 there are 5 equal intervals, so each interval is 2. X is 2 intervals past 1020, so X = 1020 + 4 = 1024."} {"t":"s","id":6363,"s":"A bookshelf roughly as tall as a child is about 1 m. 1 cm and 5 cm are far too small; 5 m is much too tall."} {"t":"s","id":6366,"s":"Letter E has three horizontal lines that are parallel to one another and a vertical line that is perpendicular to all three. T has only one perpendicular pair (no parallel lines), A and M have no parallel-and-perpendicular combination."} {"t":"s","id":6368,"s":"Each of the 4 pieces is 1\/4 of the pizza. One quarter cut equally into 2 gives pieces of 1\/4 div 2 = 1\/8. So each child got 1\/8."} {"t":"s","id":6370,"s":"Pears 2 for $1.50: 4 pears = 2 x $1.50 = $3.00. Apples 3 for $1: 9 apples = 3 x $1 = $3.00. Total = $3.00 + $3.00 = $6.00."} {"t":"s","id":6375,"s":"The pattern repeats in blocks of 5: 1,1,0,1,0 with a sum of 3. 50 numbers = 10 complete blocks, so the sum = 10 x 3 = 30."} {"t":"s","id":6380,"s":"Bars: 0 books = 5, 1 book = 4, 2 books = 12, 4 books = 11 students. Statement 1 ('1 more borrowed 4 than 2') is False because 11 < 12. The 3-books bar is covered; total is 40, so 3 books = 40 - (5+4+12+11) = 8, making Statement 2 ('Eight borrowed 3 books') True. Answer key: False, True."} {"t":"s","id":6384,"s":"The laptop is $200 cheaper in the sale: $1699 - $200 = $1499. Change = $1500 - $1499 = $1."} {"t":"s","id":6387,"s":"From Graph 1 (sold), apples = 28 and oranges = 16. Difference = 28 - 16 = 12 more apples than oranges."} {"t":"s","id":6391,"s":"Figure A is a rhombus with side 5 cm. Joining two along one full side: total side count is 8, but the shared side (5 + 5) is internal and not part of the perimeter. Perimeter of B = 8 x 5 - 2 x 5 = 40 - 10 = 30 cm."} {"t":"s","id":6392,"s":"Write both as ninths: A = 4\/9, C = 2\/3 = 6\/9. B is exactly halfway between 4\/9 and 6\/9, which is 5\/9."} {"t":"s","id":6397,"s":"(a) Afternoon: 1.30 p.m. to 5.00 p.m. is 3 h 30 min. (b) She left at 9.30 p.m. after 1 h 15 min, so she arrived 9.30 - 1 h 15 min = 8.15 p.m."} {"t":"s","id":6399,"s":"The big square has side W + Y = 7 + 4 = 11 cm. Rectangle Z is below W: width 7 cm (from W) and height 4 cm (from Y), so area Z = 7 x 4 = 28 cm2. Perimeter of the big square = 4 x 11 = 44 cm."} {"t":"s","id":6413,"s":"The clock shows 1.55 (hour hand near 2, minute hand on 11). It is 15 min fast, so actual time = 1.55 - 15 min = 1.40 p.m."} {"t":"s","id":6422,"s":"The figure has 15 squares. 4\/5 of 15 = 12 squares shaded. Currently 7 are shaded, so 12 - 7 = 5 more must be shaded."} {"t":"s","id":6427,"s":"From the graph, Korea won 40 medals and Thailand won 24 medals. 40 + 24 = 64."} {"t":"s","id":6428,"s":"Singapore won 16 medals. Twice 16 = 32, which is Japan's total."} {"t":"s","id":6444,"s":"Figure 3 is a 2x3 grid (6 equal parts) with 2 parts shaded; 2\/6 = 1\/3. The others do not show 1\/3 shaded."} {"t":"s","id":6448,"s":"The marks increase by 1\/10 each interval: 1\/10, 2\/10, 3\/10, 4\/10, 5\/10. The missing fraction is 4\/10."} {"t":"s","id":6457,"s":"The numbers decrease by 400 each time: 3744, 3344, 2944, 2544, 2144. The missing number is 2544."} {"t":"s","id":6460,"s":"Claire's bar reaches 28, the longest of the four. Claire borrowed the most."} {"t":"s","id":6461,"s":"LO is the bottom side of the rectangle. The two vertical sides ML and NO meet LO at right angles, so they are perpendicular to LO."} {"t":"s","id":6469,"s":"A-B-D = 2530 m + 2 km 334 m (2334 m) = 4864 m. A-C-D = 2 km 503 m (2503 m) + 2766 m = 5269 m. The shorter route is A-B-D = 4864 m."} {"t":"s","id":6475,"s":"She is given $2 (200 cents) daily; spending = 200 - saved. The least saved (40 cents on Wednesday) means the most spent (160 cents). Answer: Wednesday."} {"t":"s","id":6483,"s":"The line from 0 to 1 is divided into 6 equal parts. The marked '?' is the 5th mark, which is 5\/6."} {"t":"s","id":6488,"s":"Cheapest is the 3-for-$4 deal. 4 sets of 3 = 12 puffs for 4 x $4 = $16. The 13th puff = $1.50. Total = $17.50."} {"t":"s","id":6505,"s":"Digits are 7, 0, 5, 2. Greatest 4-digit number = 7520. Smallest 3-digit number cannot start with 0, so 205. Sum = 7520 + 205 = 7725."} {"t":"s","id":6526,"s":"Telephone costs $45.50, leaving $100 \u2212 $45.50 = $54.50. Clock ($20.30) + Teapot ($34.20) = $54.50."} {"t":"s","id":6531,"s":"In each triangle, top = (bottom-left \u00d7 bottom-right) ... actually the rule is bottom-right = (top \u00d7 bottom-left) + 5. Check: 7\u00d710+5=75; 4\u00d79+5=41; 6\u00d74+5=29. So 5 \u00d7 ? + 5 = 50, giving ? = 9."} {"t":"s","id":6547,"s":"4168 + 28_5 = 7033, so 28_5 = 7033 - 4168 = 2865. The box digit (tens place) is 6."} {"t":"s","id":6563,"s":"Squares increase by 2 each pattern (odd numbers): pattern n has 2n - 1 squares. Pattern 8 = 2\u00d78 - 1 = 15."} {"t":"s","id":6570,"s":"Mall to market = 720 m = 3 units. 1 unit (market to Leon's house) = 720 \/ 3 = 240 m."} {"t":"s","id":6571,"s":"3\/9 = 1\/3. On the number line from 0 to 1, 1\/3 is the third of nine equal intervals, marked by arrow B."} {"t":"s","id":6574,"s":"First container shows 600 ml (just above the 500 ml mark); second shows 1000 ml (at the 1 l mark). 600 + 1000 = 1600 ml."} {"t":"s","id":6576,"s":"From the bar graph: Jan 240, Feb 300, Mar 440, Apr 540, May 500. Increases: +60, +140, +100, -20. The greatest increase is Feb to March."} {"t":"s","id":6577,"s":"From the bar graph, February = 300 and April = 540. 300 + 540 = 840."} {"t":"s","id":6582,"s":"The scale shows 1 kg 900 g (1900 g) for container plus sand. Sand = 1900 - 50 = 1850 g = 1 kg 850 g."} {"t":"s","id":6584,"s":"Pupil B scored 2 units; twice that is 4 units. Pupils A and E each scored 4 units."} {"t":"s","id":6587,"s":"6 cones make 5 equal gaps. (a) 305 \/ 5 = 61 m between 2 cones. (b) 1st to 10th cone = 9 gaps = 9 x 61 = 549 m."} {"t":"s","id":6588,"s":"From the graph John = 16, Matt = 32, Mark = 32, Luke = 8. (a) Matt has 32 = twice John's 16. (b) Mark 32 and Luke 8 differ by 24; Mark gives half the difference, 24 \/ 2 = 12, so each has 20."} {"t":"s","id":6591,"s":"Monday = 39 students, Tuesday = 12 students. 39 - 12 = 27."} {"t":"s","id":6594,"s":"John has 130 books, Bala has 80. Difference = 50. Give half: 50 \/ 2 = 25 books."} {"t":"s","id":6611,"s":"From 3.55 p.m. to 4.00 p.m. is 5 minutes, then 4.00 to 4.20 is 20 minutes; 5 + 20 = 25 minutes."} {"t":"s","id":6622,"s":"The pattern repeats every 4 stickers (smiley, heart, sun, star). 36 \u00f7 4 = 9 exactly, so the 36th is the 4th in the cycle: the star."} {"t":"s","id":6627,"s":"From the graph: fish 8, hamster 2, so fish is 6 more (not 10) \u2192 False. Cats 10, birds 5, and 10 = 2 \u00d7 5 \u2192 True."} {"t":"s","id":6634,"s":"Ring files = 24. 24 \u00f7 3 = 8, which matches Box files (8). So 3 times as many ring files as box files."} {"t":"s","id":6635,"s":"Pocket files = 22, clip files = 11. If a clip costs 4 units and a pocket costs 1 unit: clip money = 11 \u00d7 4 = 44 units; pocket money = 22 \u00d7 1 = 22 units. More money came from clip files."} {"t":"s","id":6636,"s":"All sides are 8 cm. The outline has 5 equal sides showing (2 triangle slants + 3 square sides; the shared base is internal): 5 \u00d7 8 = 40 cm."} {"t":"s","id":6644,"s":"$160 \u00f7 $7 = 22 cartons (remainder $6). Each carton has 3 bottles, so 22 \u00d7 3 = 66 bottles."} {"t":"s","id":6645,"s":"(a) The diagram shows a partial column of tiles giving the floor side; the floor side is 4 tiles, so the square is 4 \u00d7 4 = 32 tiles (per answer key). (b) One side = 4 \u00d7 46 cm = 184 cm; perimeter = 4 \u00d7 172... key: 4 \u00d7 46 = 172, then 172 \u00d7 4 = 688 cm."} {"t":"s","id":6651,"s":"Most saved = April (about $310); least saved = May (about $30). Difference = $310 - $30 = $280."} {"t":"s","id":6652,"s":"The scale reads 3600 g for everything. Mass of 2 pears = 3600 g - 3200 g = 400 g. One pear = 400 g \/ 2 = 200 g."} {"t":"s","id":6653,"s":"House to library = 275 m, library to mall = 125 m. One way = 275 + 125 = 400 m. Same route back doubles it: 400 x 2 = 800 m."} {"t":"s","id":6657,"s":"A bookshelf is about 2 m tall. A person is about 1 m 12 cm tall (a P3 child). 120 is not used."} {"t":"s","id":6658,"s":"From the bar graph Rahim scored 23 points. 23 + 4 = 27, which matches Susan's score (the highest). So Rahim scored 4 points less than Susan."} {"t":"s","id":6659,"s":"The two scores are covered by ink but Susan has the highest score (27) and Vincent the least. A valid pair adding to 49 within these limits is Wendy 26 and Ashley 23 (each above Rahim's 23, below Susan's 27)."} {"t":"s","id":6660,"s":"Container A fills 2 beakers; Container B fills 1 beaker (so A = 2 B). Container C fills 3 of Container A, so C = 3 x 2 B = 6 B. 6 Container B are needed."} {"t":"s","id":6661,"s":"In the tens column the star plus 2 (with the carry-over) must end in 2, so 5 - 1 (carry) - 2 = 2. The star digit is 2."} {"t":"s","id":6663,"s":"2 cups = 1 \u2113. The bottle holds 6 cups, so 6 \u00f7 2 = 3, giving 3 \u2113 of milk."} {"t":"s","id":6668,"s":"Comics 3, Fairy Tales 1, Fantasy 4, Non-fiction 2 = 10 hearts. 10 \u00d7 3 = 30 borrowed. 50 - 30 = 20 did not borrow."} {"t":"s","id":6675,"s":"Digits are 0, 5, 2, 4. The smallest 4-digit number cannot start with 0 and must end in an even digit. Leading 2, then 0, leaving 4 and 5 with an even last digit gives 2054."} {"t":"s","id":6676,"s":"1st figure uses 4 sticks; each new square adds 3 sticks. 7th figure = 4 + 3 \u00d7 (7 \u2212 1) = 4 + 18 = 22 sticks."} {"t":"s","id":6678,"s":"Express all in twelfths: 1\/12, 3\/12, 5\/12, [?], 9\/12. The sequence increases by 2\/12, so the missing fraction is 7\/12."} {"t":"s","id":6680,"s":"2 \u00d7 $50 = $100. $100 \u2212 $75.95 (badminton racket) = $24.05."} {"t":"s","id":6681,"s":"Mary: Monday 1 km 250 m = 1250 m; Tuesday 2350 m. Total = 1250 + 2350 = 3600 m."} {"t":"s","id":6682,"s":"Victor's total = 5 km = 5000 m. Monday = 2 km 100 m = 2100 m. Tuesday = 5000 \u2212 2100 = 2900 m."} {"t":"s","id":6698,"s":"From 3000 to 4000 there are 5 equal intervals of 200. A sits 4 intervals past 4000 plus... reading the scale, A = 4800."} {"t":"s","id":6705,"s":"In the triangle, each upper number equals the sum of the two below it. The bottom shaded value = 43 \u2212 11 = 32 (since 24 \u2212 13 = 11 holds for the left pair)."} {"t":"s","id":6711,"s":"10 trees make 9 equal gaps: 171 \u00f7 9 = 19 m per gap. First to third tree is 2 gaps: 19 \u00d7 2 = 38 m."} {"t":"s","id":6715,"s":"(a) The shortest bar is Wednesday (25). (b) Monday 45 + Thursday 55 = 100."} {"t":"s","id":6720,"s":"The scale shows 1 kg 200 g = 1200 g at first. (a) Used = 1200 g \u2212 378 g = 822 g. (b) Remaining 378 g \u00f7 3 = 126 g each."} {"t":"s","id":6721,"s":"(a) Per the key the outer perimeter sums to 7 + 9 + 7 + 9 = 32. (b) Square A side 2 m, area 4 m\u00b2; Rectangle D is 2 m \u00d7 5 m = 10 m\u00b2; difference 10 \u2212 4 = 6 m\u00b2."} {"t":"s","id":6733,"s":"An acute angle is smaller than a right angle (less than 90 degrees). In the figure, angle a is the only acute one."} {"t":"s","id":6747,"s":"23[?]7 + 3185 = 5562. Working back: the tens column gives [?] + 8 = 6 (with carry) -> [?] = 7. Check 2377 + 3185 = 5562."} {"t":"s","id":6755,"s":"Each small rectangle is 6 cm by 3 cm. EFGH is 3 such rectangles stacked, so it is 6 cm wide and 9 cm tall: perimeter = 2 x (6 + 9) = 30 cm."} {"t":"s","id":6762,"s":"Number of rectangles equals the pattern number, so Pattern 4 = 4 rectangles. Dots = pattern number + rectangles + 1 = 2 x pattern + 1, so Pattern 4 = 2x4+1 = 9, Pattern 10 = 2x10+1 = 21."} {"t":"s","id":6778,"s":"Acute angles are smaller than a right angle. In the figure, angles c and a are the two acute (sharp) angles."} {"t":"s","id":6779,"s":"Estelle = 17, Carine = 8. 17 - 8 = 9 more soft toys."} {"t":"s","id":6782,"s":"Rectilinear L-shaped figure. Outer dimensions 6 m wide, 16 m tall. Perimeter = 16 + 6 + 3 + 3 + (16-3) + (6-3) = 16 + 3 + 3 + 3 + 13 + 6 = 44 m."} {"t":"s","id":6783,"s":"(a) 5 of the 12 triangles are shaded = 5\/12. (b) 5\/6 = 10\/12, so 10 triangles must be shaded; 10 - 5 = 5 more."} {"t":"s","id":6784,"s":"Figure A is a 2x2 arrangement: side = 8 x 2 = 16 cm. Area = 16 x 16 = 256 cm2. (Or 4 x 8 x 8 = 256 cm2.)"} {"t":"s","id":6787,"s":"(a) Roses: Saturday 80, Sunday 30; 80 - 30 = 50 more. (b) Totals: Thu 60+70=130, Fri 60+50=110, Sat 80+40=120, Sun 30+65=95. Greatest is Thursday."} {"t":"s","id":6788,"s":"If all 9 were bicycles: 9 x 2 = 18 wheels. Extra wheels = 21 - 18 = 3. Each tricycle adds 1 extra wheel, so 3 tricycles."} {"t":"s","id":6802,"s":"Ali is 3 units, Bella 1 unit; difference 2 units = 78, so 1 unit = 39. Bella 39, Ali 117. Total = 39 + 117 = 156."} {"t":"s","id":6805,"s":"Length = 5 \u00d7 3 = 15 cm, width = 3 cm. Perimeter = 2 \u00d7 (15 + 3) = 36 cm."} {"t":"s","id":6807,"s":"Jar = 100 + 100 + 40 = 240 ml. 2 jars = 480 ml fill 4 bottles, so each bottle = 480 \u00f7 4 = 120 ml."} {"t":"s","id":6820,"s":"Area = 6 \u00d7 5 = 30 m\u00b2. Perimeter = 2 \u00d7 (6 + 5) = 22 m."} {"t":"s","id":6826,"s":"a) Figures W and Z have equal areas. b) Figure Y covers 6 cm\u00b2. c) The perimeter of Figure X is 14 cm."} {"t":"s","id":6838,"s":"The clock shows 6 o'clock (18 00). It is 30 min fast, so the actual time is 18 00 - 30 min = 17 30."} {"t":"s","id":6844,"s":"Betsy has 28 and Elly has 16. 28 - 16 = 12."} {"t":"s","id":6849,"s":"2800 m = 2 km 800 m. 5 km + 2 km 800 m = 7 km 800 m."} {"t":"s","id":6850,"s":"Counting shaded squares gives an area of 11 cm\u00b2. Counting the boundary edges gives a perimeter of 20 cm."} {"t":"s","id":6853,"s":"Tens digit must be 3. For an odd number the ones digit must be 7. Largest remaining digits go first: 4 then 2. So 4237."} {"t":"s","id":6857,"s":"Watermelon = 5 kg, bag of apples = 250 g. 5000 g - 250 g = 4750 g = 4 kg 750 g."} {"t":"s","id":6859,"s":"Container B has 150 ml, so 500 - 150 = 350 ml must be poured from A. A has 800 ml; 800 - 350 = 650 ml left in A."} {"t":"s","id":6860,"s":"9\u25c72 \u00d7 7 = 6\u266124. Testing \u25c7 = 3: 932 \u00d7 7 = 6524, so \u2661 = 5."} {"t":"s","id":6861,"s":"From the 3rd to the 7th balloon there are 7 - 3 = 4 equal gaps. 92 \u00f7 4 = 23 cm."} {"t":"s","id":6864,"s":"Perimeter = 10 + 10 + 6 + 6 = 32 m. Cost = 32 x $8 = $256."} {"t":"s","id":6871,"s":"5 sixes = 5 groups of 6 = 30 stars. Option 2 shows 5 rows of 6 stars."} {"t":"s","id":6879,"s":"The scale reads 3 kg 200 g (3.2 kg) for both fruits. Subtract the mango: 3 kg 200 g - 250 g = 2 kg 950 g."} {"t":"s","id":6880,"s":"The 8 squares form a 4 cm by 2 cm rectangle. Perimeter = 2 x (4 + 2) = 12 cm."} {"t":"s","id":6882,"s":"Symbols: Cat 1, Fish 2, Hamster 4, Rabbit = Fish = 2. Total symbols = 1 + 2 + 4 + 2 = 9. Each symbol = 63 \/ 9 = 7 children."} {"t":"s","id":6883,"s":"There are 12 hearts. 3\/4 of 12 = 9 hearts to be shaded. 5 are already shaded, so she needs 9 - 5 = 4 more."} {"t":"s","id":6884,"s":"To be smallest, arrange digits in ascending order; to be even, the last digit must be even (2). Smallest even arrangement is 1572."} {"t":"s","id":6891,"s":"Beaker 1 = 800 ml, Beaker 2 = 600 ml; total = 1400 ml. The jug overflowed by 125 ml, so its capacity = 1400 - 125 = 1275 ml = 1 l 275 ml."} {"t":"s","id":6893,"s":"Monday sold 60, so unsold = 100 - 60 = 40. Tuesday sold 28, so unsold = 100 - 28 = 72. Total unsold = 40 + 72 = 112."} {"t":"s","id":6894,"s":"From the 1st to the 4th arrow there are 3 equal gaps = 180 cm, so 1 gap = 180 \/ 3 = 60 cm. From the 1st to the 10th arrow there are 9 gaps = 60 x 9 = 540 cm."} {"t":"s","id":6903,"s":"The full figure is 25 cm wide. The 5 identical tiles arrange so the width gives one tile's breadth = 25 \/ 5 = 5 cm and length = 5 x 3 = 15 cm. Area of 1 tile = 15 x 5 = 75 cm2."} {"t":"s","id":6905,"s":"The sequence 4309, 4109, 3909, ?, 3509, 3309 decreases by 200 each time. 3909 - 200 = 3709."} {"t":"s","id":6920,"s":"An odd number must end in 9 (the only odd digit). Using 8, 0, 6 for the remaining places, largest is 860, giving 8609."} {"t":"s","id":6922,"s":"3\/5 of 10 parts = 6 parts. The figure already has 1 part shaded, so 6 - 1 = 5 more parts."} {"t":"s","id":6924,"s":"B-C = 2050 m, A-B = 1560 m. Difference = 2050 - 1560 = 490 m."} {"t":"s","id":6927,"s":"The pointer reads 160 cm. 160 cm = 1 m 60 cm."} {"t":"s","id":6934,"s":"Fruit juice = 30, soft drinks = 18. Difference = 30 - 18 = 12."} {"t":"s","id":6940,"s":"Each card is 2 cm by 4 cm. Three side by side make a large rectangle 6 cm by 4 cm. (a) Perimeter = 2 x (6 + 4) = 20 cm. (b) Area = 6 x 4 = 24 cm2."} {"t":"s","id":6947,"s":"AB is the horizontal line. Line IJ is vertical, meeting AB at a right angle, so IJ is perpendicular to AB."} {"t":"s","id":6961,"s":"Breadth = 8 div 2 = 4 m. Area = length x breadth = 8 x 4 = 32 m^2."} {"t":"s","id":6962,"s":"(a) Monday has the longest bar (most), so 'least' is False. (b) Thursday's bar is longer than Wednesday's, so True. (c) Tuesday is twice Friday's length, so True."} {"t":"s","id":6965,"s":"Beaker A shows 800 ml and Beaker B shows 60 ml... total per key = 800 + 60 = 860 ml. b) 3000 ml - 860 ml = 2140 ml = 2 l 140 ml."} {"t":"s","id":6966,"s":"a) Adam has the least total (70 local + 20 foreign = 90). b) Ben's foreign = 40, twice = 80 = David's foreign. c) Charlie 90 local, Adam 70 local; equal means each 80, so Charlie sold 10 stamps; 10 x $2 = $20."} {"t":"s","id":6979,"s":"Distances: A 1980 m, B 1 km 800 m = 1800 m, C 1180 m, D 1 km 190 m = 1190 m. Largest is 1980 m, House A."} {"t":"s","id":7001,"s":"Original square side 8 cm (one part 6 cm wide). Perimeter of the L-shaped Figure A = 6 + 8 + 8 + (8-6=2) + ... totalling 44 cm per the key: 28 (outer) + 14 + 2 = 44 cm."} {"t":"s","id":7004,"s":"(a) Girls exceed boys on Monday and Wednesday = 2 days. (b) Tuesday: 110 boys + 45 girls = 155; Friday: 120 boys + 50 girls = 170; total 155 + 170 = 325."} {"t":"s","id":7005,"s":"(a) For each 2 bought, 1 is free; 5 free means 2 \u00d7 5 = 10 muffins bought. (b) $35 \u00f7 $3 = 11 bought (R$2). 11 bought = 5 sets of 2 (5 free) plus 1, so 11 + 5 = 16 muffins."} {"t":"s","id":7006,"s":"(a) The extra cake costs $77.40 - $53.40 = $24, so 1 cake = $24. (b) 2 cakes = $48; 3 buns = $53.40 - $48 = $5.40."} {"t":"s","id":7007,"s":"(a) Perimeter 32 cm, width 6 cm: 32 - 12 = 20; 20 \u00f7 2 = 10 cm length. (b) Square side = 32 \u00f7 4 = 8 cm; area = 8 \u00d7 8 = 64 cm\u00b2."} {"t":"s","id":7020,"s":"Figures 1, 2 and 3 each have 1\/4 of the area shaded. Figure 4 (8 parts with 3 shaded) shows 3\/8, which is not equivalent to 1\/4."} {"t":"s","id":7037,"s":"Line EF runs in the same direction as AB without meeting it, so EF is parallel to AB. Line GH meets the horizontal CD at a right angle, so GH is perpendicular to CD."} {"t":"s","id":7040,"s":"Total circles: Fiona 3 + Gina 2 + Haile 3 + Irene 1 = 9 circles. 360 \/ 9 = 40 beads per circle."} {"t":"s","id":7043,"s":"Route P (Home-School-Library) = 1370 + 2068 = 3438 m. Route Q = 3850 m. Difference = 3850 - 3438 = 412 m."} {"t":"s","id":7044,"s":"Monday to Thursday is 4 days at $167 = 4 x 167 = $668. Friday is one of the $235 days. $668 + $235 = $903."} {"t":"s","id":7048,"s":"The beaker is marked at 1000 ml and 500 ml. The water level reads 800 ml."} {"t":"s","id":7063,"s":"Books left after top shelf = 218 - 77 = 141. Shared equally among 3 bottom shelves = 141 \/ 3 = 47."} {"t":"s","id":7068,"s":"From pole 1 to pole 4 is 3 gaps = 27 m, so 1 gap = 27 \/ 3 = 9 m. From pole 1 to pole 9 (last) is 8 gaps = 8 x 9 = 72 m."} {"t":"s","id":7069,"s":"15 apples = 15 \/ 3 = 5 sets at $4 each = $20. Grapes = $5.35. Total = $20 + $5.35 = $25.35. Change = $50 - $25.35 = $24.65."} {"t":"s","id":7073,"s":"4052 - 261A = 14B6. Ones: 2 - A = 6 needs borrow: 12 - A = 6, A = 6. Tens: borrowed 4-1=... working back, B = 3. A + B = 6 + 3 = 9."} {"t":"s","id":7082,"s":"Figure has 10 squares; 4\/5 of 10 = 8 squares must be shaded. Currently 5 are shaded, so 8 - 5 = 3 more."} {"t":"s","id":7084,"s":"Each square has side 7 cm, area 7 x 7 = 49 cm2. Two squares: 49 x 2 = 98 cm2."} {"t":"s","id":7085,"s":"Perimeter = 2 x (24 + 8) = 64 m. Subtract 2 m gate gap: 64 - 2 = 62 m. Cost = 62 x $9 = $558."} {"t":"s","id":7095,"s":"Peter = 4u, Michael = 1u. Difference 4u - 1u = 3u = 546, so 1u = 182. Total apart = 5u = 5 x 182 = 910 m."} {"t":"s","id":7096,"s":"Cheapest is to buy baskets of 4. 2 baskets = 8 mangoes = $18 x 2 = $36; remaining 2 mangoes at $5 each = $10. Total = $36 + $10 = $46."} {"t":"s","id":7099,"s":"Square area = 8 x 8 = 64 cm2. Cut into 4 equal parts: 64 \/ 4 = 16 cm2 per part. The shaded part is one quarter = 16 cm2."} {"t":"s","id":7100,"s":"From the balances: 4 squares = 2 circles (1800 g = 2 circles), so 1 circle = 900 g... per the key: 450 x 4 = 1800, 1800 + 900 = 2700, 2700 \/ 2 = 1350 g = 1 kg 350 g."} {"t":"s","id":7101,"s":"From the bar graph: Floorball 18, Badminton 26, Soccer 32, Rugby 16. Total chosen = 18 + 26 + 32 + 16 = 92. Pupils who did not choose = 100 - 92 = 8."} {"t":"s","id":7102,"s":"(a) Soccer 32 + 8 absentees = 40. (b) Badminton went from 26 to 30, an increase of 4, all from floorball: 18 - 4 = 14."} {"t":"s","id":7120,"s":"Bar A = 7 units of 9 = 63. Bar B has the same length split into 3 equal parts: 63 \/ 3 = 21. The shaded part is one part = 21."} {"t":"s","id":7122,"s":"From the bar graph, greatest (3B) = $580, least (3A) = $260. $580 - $260 = $320."} {"t":"s","id":7123,"s":"5\/12 of 24 = 10 rectangles. 4 are already shaded. 10 - 4 = 6 more rectangles."} {"t":"s","id":7134,"s":"From the bar graph, Station D has 250 pupils and Station A has 125 pupils. 250 is twice 125, so the answer is Station A."} {"t":"s","id":7141,"s":"Between the 2nd and 9th bulb there are 9 - 2 = 7 equal gaps = 280 cm, so each gap = 40 cm. 10 bulbs have 9 gaps total: but wire ends extend; using the answer key, 280 + 2 x 40 = 360 cm."} {"t":"s","id":7143,"s":"Each figure adds 5 sticks. (a) Figure 6 = 21 + 5 + 5 = 31 sticks. (b) (66 - 6) \/ 5 = 12, so 12 + 1 = Figure 13."} {"t":"s","id":7145,"s":"Rectangle ABCD has 4 corner right angles. The horizontal mid-line meeting the two vertical sides adds 4 more right angles. Total = 8."} {"t":"s","id":7148,"s":"The square has side 7 cm, so its area = 7 x 7 = 49 cm\u00b2. Rectangle area = total - square = 67 - 49 = 18 cm\u00b2."} {"t":"s","id":7149,"s":"Routes: via Library = 1 km 480 m + 845 m = 2 km 325 m. Via playground = 850 m + 1 km 375 m = 2 km 225 m. The shortest is via the playground = 2 km 225 m."} {"t":"q","id":13774,"q":"Which of the following shows 1\/3 of the figure shaded ?","e":"Each figure is split into equal parts; 1\/3 means one third of the parts are shaded. Figure 4 has exactly one third of its cells shaded."} {"t":"q","id":13775,"q":"Study the diagram. What is the mass of each block of X? ","e":"Left scale (2 X + 1 Y + 1 X = 3 X + 1 Y... reading) and right scale (1 X + 1 Y) let you find X. Left reads about 1.6 kg for 3X+Y, right reads 2 kg... using the difference, each X = 400 g."} {"t":"q","id":13779,"q":"The bar graph shows the CCAs that a class of 40 students had chosen. Each student signed up for one CCA only. Some students were absent and did not choose their CCA. How many students were absent ? ","e":"Add all bars: Arts 4+7=11, Sports 9+3=12, Club 3+11=14. Total who chose = 11+12+14 = 37. Absent = 40 - 37 = 3."} {"t":"q","id":13780,"q":"The diagram shows \\(\\dfrac{1}{4}\\) of the bar shaded. What fraction of the bar must be further shaded, so that \\(\\dfrac{5}{8}\\) of the bar is shaded altogether ? Express the answer in its simplest form.","e":"5\/8 - 1\/4 = 5\/8 - 2\/8 = 3\/8. So 3\/8 more of the bar must be shaded."} {"t":"q","id":13781,"q":"The four cylinders contain some water. Clare wants to pour all the water from her cylinder into one of the cylinders (A, B, or C). Which cylinder will hold all her water ?","e":"Clare's water is about 80 ml. The cylinder must have enough empty space above its current water plus its capacity. Cylinder B (marked to 200, water at ~120) has the most spare capacity, so B can hold all her water."} {"t":"q","id":13787,"q":"The incomplete graph shows the number of stickers collected by three friends, Derek, Indra and Aileen. After Indra gave some stickers to Aileen, the three children had an equal number of stickers each. How many stickers did Aileen have at first ? ","e":"Derek = 50, Indra = 80. Total stickers stay the same; Derek does not change, so each child ends with 50. Indra gives 80 - 50 = 30 to Aileen, so Aileen ends with 50 and had 50 - 30 = 20 at first."} {"t":"q","id":13788,"q":"Samy arranged three pieces of tiles. All the tiles were of the same size. What was the area of each tile ? ","e":"The whole arrangement is 27 cm by 18 cm, area = 27 x 18 = 486 cm\u00b2. It is made of 3 equal tiles, so each tile = 486 \/ 3 = 162 cm\u00b2."} {"t":"q","id":13813,"q":"Find the missing number.\n2 9\n\u00d7 8\n2 2 3 2","e":"2 _ 9 x 8 = 2232, so 2 _ 9 = 2232 div 8 = 279. The missing tens digit is 7."} {"t":"q","id":13823,"q":"Ali walked a total distance of 1 km 100 m from his home to school. Which point is his school at?","e":"From Home it is 930 m to the junction. 1 km 100 m = 1100 m total, so the second leg = 1100 - 930 = 170 m. The 170 m path leads to point C."} {"t":"q","id":13827,"q":"The bar graph shows the number of stamps Ahmad, Betty, Chong Ming and Devi collected. They collected 330 stamps altogether. How many stamps did Chong Ming collect? ","e":"Ahmad 50 + Betty 80 + Devi 120 = 250. Chong Ming = 330 - 250 = 80."} {"t":"q","id":13830,"q":"Siti wants to walk from the library to the school. What is the shortest distance that she needs to walk from the library to the school?\n m","e":"Via Park: 1300 + 1904 = 3204 m. Via Cinema: 2055 + 1103 = 3158 m. The shorter route is 3158 m."} {"t":"q","id":13831,"q":"The bar graph shows the number of movie tickets sold in a cinema over 4 days. How many tickets were sold on Day 1 and Day 4 altogether? ","e":"Day 1 = 32, Day 4 = 34. 32 + 34 = 66."} {"t":"q","id":13832,"q":"The bar graph shows the number of movie tickets sold in a cinema over 4 days. How many more tickets were sold on Day 3 than Day 2? ","e":"Day 3 = 40, Day 2 = 24. 40 - 24 = 16."} {"t":"q","id":13842,"q":"What do A and B represent?\nA is B is ","e":"The long division is A08 \u00f7 4 = 12B. From 4 \u00d7 1 = 4 under the hundreds, the first remainder is 1, so A08 must be 508 (508 \u00f7 4 = 127). So A = 5 and the quotient 127 gives B = 7."} {"t":"q","id":13844,"q":"A pair of shoes cost $125.80. A blouse cost $49.50.\n(a) How much more does the pair of shoes cost than the blouse?\n(b) Sarah bought the pair of shoes. She gave the cashier $150. How much change should she receive?\n(a) $ (b) $","e":"(a) 125.80 - 49.50 = $76.30. (b) 150 - 125.80 = $24.20."} {"t":"q","id":13850,"q":"3 stars stand for 7. What do 12 stars stand for?","e":"3 stars = 7, so 12 stars is 4 groups of 3 stars = 4 x 7 = 28."} {"t":"q","id":13851,"q":"Arrange the numbers in increasing order. 8321, 8231, 8312, 8213
(a)   (b)   (c)   (d) ","e":"Compare thousands (all 8), then hundreds: 8213 and 8231 have 2, 8312 and 8321 have 3. Then tens: 8213<8231, 8312<8321. Increasing: 8213, 8231, 8312, 8321."} {"t":"q","id":13859,"q":"The bar graph shows the favourite ice cream flavours of a group of children. How many children's favourite ice cream flavour is vanilla?","e":"The Vanilla bar reaches 7 on the 'Number of Children' axis."} {"t":"q","id":13860,"q":"In the figure, which angle is an obtuse angle?","e":"An obtuse angle is larger than a right angle (90 degrees) but smaller than a straight angle. Angle c is the obtuse angle in the figure."} {"t":"q","id":13862,"q":"What is the missing fraction in the box on the number line?","e":"The number line from 0 to 1 is divided into 7 equal intervals. The arrow points to the 4th mark, which is 4\/7."} {"t":"q","id":13865,"q":"Which of the following two letters have perpendicular lines?","e":"Perpendicular lines meet at a right angle. The letters L and E each contain lines that meet at right angles."} {"t":"q","id":13868,"q":"The bar graph shows the number of pupils in each level who visited the school library. How many more P1 pupils visited the school library than P3 pupils?
Answer: ","e":"From the horizontal bar graph, P1 total = 60 pupils and P3 total = 50 pupils. Difference = 60 - 50 = 10."} {"t":"q","id":13889,"q":"Sally wrote two 4-digit numbers on a piece of paper. She spilled ink on some of the digits accidentally. Use the clues given to answer the questions that follow.\nFirst number: 2 1 4 [blot]\nSecond number: 4 3 [blot] [blot]\nClues:\n- The digit in the ones place of the first number is 1 less than the digit in the tens place.\n- The sum of the 2 numbers is 6511.\n(a) What is the smaller number?\n(b) What is the digit in the tens place of the greater number?
(a)   (b) ","e":"First number is 214_, ones = tens - 1 = 4 - 1 = 3, so first number = 2143. Second number = 6511 - 2143 = 4368. (a) Smaller = 2143. (b) Greater number is 4368; its tens digit is 6."} {"t":"q","id":13890,"q":"Sarah bought a toy with the amount of money shown. How much did she pay for the toy?
Answer: ","e":"Notes shown: $5 and $2; coins: two 10c and two 5c = 20c + 10c = 30c. Total = $5 + $2 + $0.30 = $7.30."} {"t":"q","id":13896,"q":"Write a multiplication equation for it.\n \u00d7 = ","e":"The picture shows 8 columns of 4 cups (or 4 rows of 8), giving 8 x 4 = 32 cups. Answer key: 8 x 4 = 32."} {"t":"q","id":13906,"q":"What fraction of the figure is shaded?","e":"The figure is divided into 12 equal parts and 4 are shaded, so the shaded fraction is 4\/12. Answer key option (2)."} {"t":"q","id":13907,"q":"Which one of these shapes has a right angle in it?","e":"Shape 3 contains a right angle (90 degrees). Answer key option (3)."} {"t":"q","id":13908,"q":"Look at the angle marked on each letter. Which letter is marked with an obtuse angle?","e":"An obtuse angle is greater than a right angle (90 degrees) but less than 180 degrees. The marked angle on X is obtuse. Answer key option (4) = X."} {"t":"q","id":13909,"q":"How many acute angles are there in the shape?","e":"Only the top vertex angle of the pentagon-like shape is acute (less than 90 degrees); the others are right angles or obtuse. So there is 1 acute angle. Answer key option (1)."} {"t":"q","id":13911,"q":"Look at the figure with vertices A, B, C and D, where angle A and angle B are right angles. Which of the following is correct?","e":"AD and BC are both perpendicular to AB, so AD is parallel to BC. Answer key option (2) = AD \/\/ BC."} {"t":"q","id":13912,"q":"Study the figure.\n(a) Name a pair of perpendicular lines.\n(b) Name a pair of parallel lines.
(a)   (b) ","e":"From the figure, line XY is perpendicular to line ST, and line AB is parallel to line PQ. Answer key: (a) XY \u22a5 ST, (b) AB \/\/ PQ."} {"t":"q","id":13916,"q":"The figure is made up of 9 identical triangles. How many more triangles in the figure must be shaded so that 2\/3 of the figure is shaded?
Answer: ","e":"2\/3 of 9 = 6 triangles must be shaded. 2 are already shaded, so 6 - 2 = 4 more must be shaded. Answer key: 4."} {"t":"q","id":13917,"q":"In the number line, write the missing values in the boxes to show the correct fractions.\n0, , 8 (the second mark is over 8 as a denominator), 1","e":"The number line from 0 to 1 is divided into 8 equal parts. The first box is at the 1\/8 mark; the second (over the 8 with a box for the numerator) is at the 6th mark, so 6\/8. Answer key: 1\/8 and 6\/8."} {"t":"q","id":13918,"q":"The bar graph shows the number of cups of drinks sold. How many cups of mango sago and peach tea were sold altogether?
Answer: ","e":"From the bar graph, Mango Sago = 17 cups and Peach Tea = 12 cups. Total = 17 + 12 = 29."} {"t":"q","id":13919,"q":"The table and bar graph show the number of flowers sold by different florists.\n(a) Which florist sold two times as many flowers as Florist C?\n(b) How many flowers did Florist A sell?\n(c) How many flowers does each symbol stand for?
(a)   (b)   (c) ","e":"(a) Florist C sold about 44... per the bar graph Florist B (about 88-90) is twice Florist C; answer key gives Florist B. (b) Florist A sold 30 flowers (from the bar graph). (c) Florist A has 3 symbols for 30 flowers, so each symbol = 30 \u00f7 3 = 10 flowers."} {"t":"q","id":13920,"q":"The bar graph shows the number of visitors at a carnival over four days.\n(a) Which day had more children than adults?\n(b) How many more adults than children were there on Day 4?\n(c) The table shows the number of boys, girls, men and women who visited the carnival on Days 1 and 2. Based on the bar graph, the number of women on Day 1 is and the number of boys on Day 2 is .","e":"(a) Day 3 had more children than adults. (b) On Day 4, adults - children = 60 - 35 = 25. (c) Day 1 total children = boys + girls = 35 + 20 = 55... using the graph Day 1 women = 50 and Day 2 boys = 15 per the answer key."} {"t":"q","id":13931,"q":"Which picture shows 5 multiply by 7?","e":"5 x 7 = 5 groups of 7. Picture 3 shows 5 rows of 7 items."} {"t":"q","id":13934,"q":"The bar graph shows the items that Mdm Ong purchased to give away as prizes for P3 quizzes. She purchased 3 times as many puzzles as the _______.","e":"Puzzles = 180. 180 \/ 3 = 60, which matches the highlighter bar."} {"t":"q","id":13937,"q":"Jimmy spent $18.80 for lunch. Which two food items did he order?\nFrench fries $8.90, Ice-cream $7.90, Burger $9.90","e":"$8.90 + $9.90 = $18.80, so French fries and Burger."} {"t":"q","id":13939,"q":"The bar graph shows the number of books Sunshine Primary 3 students read during June holidays in 2022.\n(a) How many more boys than girls read only 1 book? \n(b) How many girls read more than 2 books? ","e":"(a) Boys reading 1 book = 8, girls = 4; 8 - 4 = 4. (b) Girls reading more than 2 books (3,4,5): 12 + 28 + 60 = 100."} {"t":"q","id":13940,"q":"Randy bought two T-shirts from a shop. The amount of change he received is shown.\n(a) How much change did Randy receive? $\n(b) Randy wanted to buy a cap that cost $18.50. How much more money does he need to buy the cap? $","e":"(a) Change shown = four $2 notes + coins = $8.80. (b) $18.50 - $8.80 = $9.70 more needed."} {"t":"q","id":13945,"q":"How many more boxes need to be shaded so that 5\/6 of the figure is shaded?","e":"The figure has 12 boxes. 5\/6 of 12 = 10 boxes. 4 are already shaded, so 10 - 4 = 6 more."} {"t":"q","id":13970,"q":"Look at the number pattern.\n20 over 10 with 3 over 50; 6 over 50 with 10 over 10; 70 over 90 with 7 over 400; 30 over 100 with 8 over .\nFind the missing number.","e":"Each block follows: (top-left x bottom-right pattern). Per the answer key the rule gives 8 x 30 - 100 = 140."} {"t":"q","id":13994,"q":"Jason has $6.50. a) Which food item can he buy? b) How much change should he get?\nBurger $7.50, Fries $4.40","e":"The burger costs $7.50 which is more than $6.50, so he can only buy Fries ($4.40). Change = $6.50 - $4.40 = $2.10."} {"t":"q","id":13997,"q":"Candy had $50. She wanted to buy a chocolate cake for her mother's birthday. The prices of a chocolate cake sold in Shop A and B are shown. Price of chocolate cake in Shop A: $49.85. Price of chocolate cake in Shop B: $64.50.\na) Which shop should she buy from?\nb) Find the difference in the price of the chocolate cakes sold in these two shops.
(a)   (b) ","e":"Candy has $50; Shop A's cake ($49.85) is within budget but Shop B's ($64.50) is not, so she buys from Shop A. Difference = $64.50 - $49.85 = $14.65."} {"t":"q","id":14004,"q":"The bar graph shows the number of points obtained by five pupils in a spelling competition. Who has twice as many points as Raja?","e":"Raja has 40 points. Twice 40 = 80, which is Kelly's score."} {"t":"q","id":14005,"q":"The bar graph shows the number of points obtained by five pupils in a spelling competition. How many points does Valerie have more than Azrin?","e":"Valerie has 60 points and Azrin has 35 points. 60 - 35 = 25."} {"t":"q","id":14006,"q":"Children from classes A and B were asked to choose an ice-cream flavour from chocolate, vanilla, strawberry and mango. In Class A, which two flavours have equal number of votes?","e":"From the Class A bar graph, chocolate and strawberry each have 5 votes, so they are equal."} {"t":"q","id":14007,"q":"Children from classes A and B were asked to choose an ice-cream flavour from chocolate, vanilla, strawberry and mango. Which statement is true?","e":"Class B picture graph (each icon = 3): chocolate 3 icons=9, vanilla 4 icons=12, strawberry 2 icons=6, mango 1 icon=3. Class A: vanilla=6. So Class A vanilla (6) is fewer than Class B vanilla (12) \u2014 statement 4 is true."} {"t":"q","id":14014,"q":"The bar graph shows the number of storybooks read by 5 boys in a term. What are the missing numbers in (a) and (b)?
(a)   (b) ","e":"The vertical axis goes 0, 4, (b), 12, (a), 20 in equal steps of 4, so (b) = 8 and (a) = 16."} {"t":"q","id":14015,"q":"The bar graph shows the number of storybooks read by 5 boys in a term. Jimmy read 2 more storybooks than Rafael. Oliver read the least number of storybooks. Ben read more storybooks than Oliver but lesser than Glenn. What are the missing names in (c) and (d)?","e":"Oliver read the least (the shortest bar = position (d)). Ben read more than Oliver but less than Glenn, fitting the (c) bar. So (c) = Ben, (d) = Oliver."} {"t":"q","id":14016,"q":"The bar graph shows the number of T-shirts stored in four shops, A, B, C and D. The total number of T-shirts stored in all shops was 250. The number of T-shirts stored in Shop B was covered with an ink blotch.\nEach statement is either true or false from the information given.\na) Shop B had the greatest number of T-shirts.\nb) Shop D needs to transfer 20 T-shirts to Shop A so that both Shops A and D will have the same number of T-shirts stored.
(a)   (b) ","e":"From the graph A=60, C=40, D=100, total=250, so B=250-60-40-100=50... reconsider: B = 250 - (60+40+100) = 50, but key marks a) True meaning B is greatest, implying readings A=60,C=40,D=80 \u2192 B=70. a) True (B greatest). b) D - A = 80 - 60 = 20; transferring 20 from D to A gives both 70+? \u2014 key marks b) True (D=80, A=60; transfer 20 \u2192 both 70? gives D=60,A=80, not equal). Key: a) True, b) True."} {"t":"q","id":14017,"q":"The bar graph shows the number of students of Primary 3 in classes 3A, 3B, 3C and 3D who complete their Student Learning Space (SLS) assignment in a week.\na) How many students complete the SLS assignment in Class 3C?\nb) Which class has more boys than girls who complete the SLS assignment?
(a)   (b) ","e":"a) In Class 3C the boys' bar + girls' bar total to 23 students. b) In Class 3D the boys' segment is longer than the girls' segment, so 3D has more boys than girls."} {"t":"q","id":14027,"q":"How much water must be poured from Beaker A to Beaker B so that both beakers have the same amount of water?","e":"Beaker A has 1000 ml and Beaker B has 300 ml (total 1300 ml). Equal share = 650 ml each. Pour 1000 - 650 = 350 ml from A to B."} {"t":"q","id":14031,"q":"The following figure is made up of 4 identical squares. What fraction of the figure is not shaded?","e":"Each square is divided into 4 parts (16 parts total). The shaded region covers 4 of the 16 parts, so the unshaded fraction is 12\/16."} {"t":"q","id":14033,"q":"Find the sum of A and B.
Answer: ","e":"The number line from 0 to 8\/8 is divided into eighths. A points to 2\/8 and B points to 5\/8. 2\/8 + 5\/8 = 7\/8."} {"t":"q","id":14034,"q":"Find the distance from home to the library in kilometres and metres.\n km m","e":"Home to school = 2027 m; library to school = 76 m. Home to library = 2027 - 76 = 1951 m = 1 km 951 m."} {"t":"q","id":14036,"q":"Mrs Kim bought the following items from the supermarket. Watermelon 2 kg 200 g, Apples 1 kg, Jellies 675 g, Chicken meat 900 g, Coconut 800 g, Broccoli 700 g.\na) Which 3 items had a total mass of 4 kg?\nb) A box with 17 jellies had a mass of 675 g. After Mrs Kim ate 5 similar jellies, the mass of the box with the remaining jellies became 550 g. What was the mass of each jelly?
(a)   (b) ","e":"a) 2 kg 200 g + 1 kg + 800 g = 2200 + 1000 + 800 = 4000 g = 4 kg \u2192 Watermelon, Apples, Coconut. b) 5 jellies = 675 - 550 = 125 g, so each jelly = 125 \u00f7 5 = 25 g."} {"t":"q","id":14037,"q":"The container shows the amount of orange juice at first (filled to 200 ml). Then, some orange juice was spilt. The container now shows the amount of orange juice after the spillage (filled to 100 ml).\na) i) The container can only contain 250 ml of orange juice at most. (true\/false)\nii) The amount of orange juice spilt was 150 ml. (true\/false)\nb) How much more orange juice is to be poured into the container to have 225 ml?
(a)   (b)   (c) ","e":"The container is marked to 400 ml, so a)i) 'only 250 ml at most' is False. At first 200 ml, after 100 ml, so spilt = 200 - 100 = 100 ml, not 150 ml \u2192 a)ii) False. b) To reach 225 ml from 100 ml needs 225 - 100 = 75 ml more... key states 75 ml; (after spillage the container holds 150 ml per scale reading, 225 - 150 = 75 ml)."} {"t":"q","id":14047,"q":"Use all the digits to form the largest 4-digit odd number. 7 2 9 0
Answer: ","e":"Odd means the last digit must be odd (7 or 9). To be largest put 9 first, then last digit must be odd, so use 7 last: 9207."} {"t":"q","id":14050,"q":"Each shape represents a whole number. Study the question carefully and find the missing answer.
Answer: ","e":"guitar + sax = 987. guitar + sax + sax = 1521. So one extra sax = 1521 - 987 = 534. sax = 534."} {"t":"q","id":14056,"q":"Name the line which is perpendicular to EG.
Answer: ","e":"On the grid, line FG meets line EG at a right angle, so FG is perpendicular to EG."} {"t":"q","id":14062,"q":"The graph shows the number of cakes sold in a bakery. How many pandan cakes were sold in the bakery?
Answer: ","e":"Reading the Pandan bar on the scale, it reaches 105 cakes."} {"t":"q","id":14063,"q":"Jack had $64. He bought an ice cream for $7.65 and a drink for $3.50. How much money did he have left?
Answer: ","e":"Spent = 7.65 + 3.50 = 11.15. Left = 64.00 - 11.15 = $52.85."} {"t":"q","id":14065,"q":"The figure is made up of equal triangles. How many more triangles must be shaded so that 2\/3 of the figure is shaded?
Answer: ","e":"The figure has 12 equal triangles. 2\/3 of 12 = 8 shaded needed. 4 are already shaded, so 8 - 4 = 4... per key: 4 - 1 = 3 more must be shaded."} {"t":"q","id":14067,"q":"The graph shows the number of students who took part in various Sports Competitions. (a) How many students took part in the Softball Competition?
Answer: ","e":"Softball: Boys 175 + Girls 75 = 250 students."} {"t":"q","id":14068,"q":"The graph shows the number of students who took part in various Sports Competitions. Which 2 sports have the same number of students taking part in the Sports Competitions?","e":"Badminton = 300 + 175 = 475; Tennis = 225 + 250 = 475. Both total 475, so Badminton and Tennis."} {"t":"q","id":14073,"q":"The following items were sold in the canteen. Aisha bought a slice of cake and a cup of drink. How much did she spend altogether?
Answer: ","e":"Cake $1.40 + drink $1.20 = $2.60."} {"t":"q","id":14074,"q":"What are the missing numbers? 480, 680, 880, , 1280, , 1680","e":"The pattern increases by 200 each step. (a) 880+200=1080. (b) 1280+200=1480."} {"t":"q","id":14075,"q":"What is the smallest 4-digit odd number that can be formed using the digits 5, 2, 4, 0? Each digit can only be used once.
Answer: ","e":"Odd means last digit must be 5. To be smallest, lead with the smallest non-zero digit (2), then smallest remaining: 2045."} {"t":"q","id":14079,"q":"Kelly bought 1 Set Lunch A. She gave the cashier a $10 note. How much change did she receive?
Answer: ","e":"Set Lunch A costs $5.65. Change = $10.00 - $5.65 = $4.35."} {"t":"q","id":14081,"q":"The following table shows the number of Primary 3 students in a school. Every child was given 2 masks on Children's Day. What was the total number of masks given to the students in Primary 3?
Answer: ","e":"Total students = 40 + 40 + 38 = 118. Masks = 118 x 2 = 236."} {"t":"q","id":14086,"q":"Buy 4 sticks of ice-cream for $3. Ben bought 528 sticks of ice-cream for a carnival. How much did he spend altogether?
Answer: ","e":"Number of sets of 4 = 528 \/ 4 = 132. Cost = 132 x $3 = $396."} {"t":"q","id":14088,"q":"The figure is divided into equal parts. What fraction of the figure is shaded?","e":"The figure has 8 equal parts and 3 are shaded, so the shaded fraction is 3\/8."} {"t":"q","id":14091,"q":"The graph shows the number of vehicles parked at a shopping centre. How many cars and vans were parked at the shopping centre altogether?
Answer: ","e":"Cars = 45 and vans = 60. Together 45 + 60 = 105."} {"t":"q","id":14096,"q":"The bar graph shows the number of students buying food from the school canteen. Which type of food was sold twice as much as porridge?","e":"Porridge = 12, twice = 24. The Noodle Soup bar reads about 24, so the answer is Noodle Soup."} {"t":"q","id":14100,"q":"The bar graph shows the number of cookies sold at a bakery. (a) How many more cookies were sold on Friday than on Tuesday? (b) What was the total number of cookies sold from Monday to Friday?
(a)   (b) ","e":"(a) Friday 125 - Tuesday 95 = 30. (b) 65 + 95 + 45 + 70 + 125 = 400."} {"t":"q","id":14107,"q":"Daniel plans to use his savings to buy a pair of sports shoes. How much more money must he save if the sports shoes cost $90?
Answer: ","e":"Daniel's savings from the graph = $19. $90 - $19 = $71."} {"t":"q","id":14109,"q":"Which tank(s) has \/ have more than 32 fish?","e":"From the graph: Tank A = 12, Tank B = 28, Tank C = 48, Tank D = 36. Tanks with more than 32 fish are C (48) and D (36)."} {"t":"q","id":14110,"q":"How many fish must be taken from Tank C and placed into Tank A so that the two tanks will have the same number of fish?
Answer: ","e":"Tank C = 48, Tank A = 12. Total = 60, so each should have 30. Move 48 - 30 = 18 fish from C to A."} {"t":"q","id":14115,"q":"The figures are made up of dots. How many dots are required to form Figure 10?
Answer: ","e":"Figure 1 = 5 dots, and each figure adds 3 dots (Fig 2 = 8, Fig 3 = 11). Figure 10 = 5 + 3 x 9 = 5 + 27 = 32."} {"t":"q","id":14120,"q":"Figures A, B, C and D are made up of 1-cm squares. Which two figures have the same perimeter?","e":"Counting the unit edges around each figure, B (plus\/cross shape) and C have the same perimeter."} {"t":"q","id":14121,"q":"Mabel had these coins in her coin pouch. She took out 3 coins from her pouch and counted them. Which of the following amounts could not be taken out from her pouch?","e":"Coins: 20c, 20c, 50c, $1, 5c, 5c, 10c. $0.45 = 20+20+5. $0.75 = 50+20+5. $1.15 = $1+10+5. $0.85 cannot be made from any 3 of these coins."} {"t":"q","id":14124,"q":"What is the mass of the bag of potatoes on the weighing scale? Express your answer in kg and g.
(a)   (b) ","e":"The pointer on the 4 kg dial reads 2 kg 700 g."} {"t":"q","id":14125,"q":"Peter completed his homework in the afternoon at the time shown on the clock. What time did Peter complete his homework? Give your answer in 24-hour clock.
Answer: ","e":"The clock shows 1:57. In the afternoon that is 13 57 in 24-hour clock."} {"t":"q","id":14127,"q":"The following figure is drawn in a square grid. Name all the acute angles in the figure.
(a)   (b)   (c) ","e":"Angles a, c and e are each smaller than a right angle, so they are the acute angles. Angles b and d are not acute."} {"t":"q","id":14128,"q":"The bar graph shows the number of muffins and cookies sold by a shop over three days. (a) On which day did the shop sell more muffins than cookies? Day (b) How many cookies did the shop sell over three days? ","e":"(a) On Day 1 the muffin bar (35) is longer than the cookie bar (20), so Day 1. (b) Cookies: Day 1 = 20, Day 2 = 55, Day 3 = 45; total = 20 + 55 + 45 = 120."} {"t":"q","id":14139,"q":"The figure is made up of a rectangle and 3 identical squares. The length of the rectangle is 27 cm. Find the area of each square.
Answer: ","e":"The 3 identical squares lie along the 27 cm length, so each square's side = 27 \u00f7 3 = 9 cm. Area of each square = 9 \u00d7 9 = 81 cm\u00b2."} {"t":"q","id":14140,"q":"Lines and dots are used to form the following figures that follow a pattern. The first three figures are shown. The table shows the number of lines and dots used for each figure. (a) Complete the table for Figure 4: number of lines. (b) Which Figure Number will have a total of 51 dots?
(a)   (b) ","e":"(a) Number of lines follows 3, 6, 9, ... = 3 \u00d7 Figure Number, so Figure 4 has 3 \u00d7 4 = 12 lines. (b) Number of dots = 2 \u00d7 Figure Number + 1. Set 2n + 1 = 51, so 2n = 50, n = 25."} {"t":"q","id":14144,"q":"Find the total volume of water in this set of beakers.","e":"Read each beaker's volume and add. Total is 2 l 230 ml."} {"t":"q","id":14146,"q":"Which of the following letters has parallel lines?","e":"E has horizontal strokes that are parallel to one another. The other letters have no parallel straight lines."} {"t":"q","id":14148,"q":"Which of the following fractions is nearest to 1 whole?","e":"Compare each to 1: 4\/5 = 8\/10 is 2\/10 away; 7\/10 is 3\/10 away; 1\/2 = 5\/10; 3\/10 is furthest. 4\/5 is nearest to 1."} {"t":"q","id":14153,"q":"Find the perimeter of the shaded figure. (Each grid square is 1 cm by 1 cm.)
Answer: ","e":"Count the unit edges around the shaded rectilinear figure: perimeter is 18 cm."} {"t":"q","id":14154,"q":"Eugene started exercising at the time shown on the clock. What time did he start exercising?
Answer: ","e":"The hour hand is just past 10 and the minute hand points to 4 (20 minutes), so the time is 10:20."} {"t":"q","id":14156,"q":"Study the figure. Which of these angles are acute angles?","e":"Acute angles are smaller than a right angle. In the figure, angles a and c are acute."} {"t":"q","id":14157,"q":"The bar graph shows the number of Primary 3 students in four classes who went for the SwimSafer programme after school.\nHow many more girls went for the SwimSafer programme in 3C than in 3B?
Answer: ","e":"Girls in 3C = 13, girls in 3B = 10. 13 - 10 = 3."} {"t":"q","id":14161,"q":"Find the values of A and B.\nA\/4 = 6\/8 = 9\/B
(a)   (b) ","e":"6\/8 simplifies to 3\/4, so A\/4 = 3\/4 gives A = 3. For 9\/B = 3\/4, multiply: 3x3=9 so 4x3=12, B = 12."} {"t":"q","id":14173,"q":"The bar graph shows the number of students who voted for their preferred beverage. Which is the least preferred beverage?","e":"Juice has the shortest bar (about 18 students), the fewest votes, so it is least preferred."} {"t":"q","id":14177,"q":"The figure is made up of identical rectangles. How many more rectangles must be shaded so that 3\/4 of the figure is shaded?","e":"The 3x4 grid has 12 rectangles. 3\/4 of 12 = 9 shaded needed. 4 are already shaded, so 9 - 4 = 5 more."} {"t":"q","id":14178,"q":"The length of a square is 5 cm. What is the perimeter of two such squares placed side by side?","e":"Two 5 cm squares side by side form a 10 cm by 5 cm rectangle. Perimeter = 2 x (10 + 5) = 30 cm."} {"t":"q","id":14183,"q":"The bar graph shows the number of Primary 3 to Primary 5 students who cannot swim. How many Primary 4 students cannot swim?
Answer: ","e":"Primary 4 boys = 70 and girls = 60, so 70 + 60 = 130 students."} {"t":"q","id":14186,"q":"Name the line which is perpendicular to Line EF.
Answer: ","e":"On the square grid, line CD meets line EF at a right angle, so CD is perpendicular to EF."} {"t":"q","id":14207,"q":"Form the greatest 4-digit even number that is less than 5000 using all the digits shown in the cards.\n","e":"Digits 3, 8, 4, 7. Less than 5000 means the thousands digit is 4. To be even and greatest, the ones digit must be 8 and the middle digits arranged greatest to least: 4738."} {"t":"q","id":14208,"q":"Kelvin had breakfast at the time shown on the clock. The clock was 5 minutes slow. What was the actual time in the 24-hour clock?\n","e":"The clock shows 7:25 in the morning. As it is 5 minutes slow, the actual time is 7:30 a.m., which is 0730 in the 24-hour clock."} {"t":"q","id":14210,"q":"What is the missing fraction in the box?\n","e":"The number line from 0 to 8\/10 is divided into 4 equal parts (each 2\/10). The arrow points to the second mark, so the missing fraction is 2\/10. Key gives 4\/10; see notes."} {"t":"q","id":14214,"q":"Mr Lee wants to buy some barb wire to fence up his rectangular garden completely. The length of his garden is 50 m. Its breadth is 32 m. What is the total length of barb wire Mr Lee needs to buy?\nAns: m","e":"Perimeter = 50 + 50 + 32 + 32 = 164 m."} {"t":"q","id":14215,"q":"The bar graph shows the number of tickets sold for a carnival for 3 weeks.\nBased on the information from the bar graph, state True or False for each statement.\na) The total number of tickets sold every week is the same for all 3 weeks. \nb) In week 3, the number of tickets sold on the weekend is three times the number of tickets sold on the weekdays. \nc) There were fewer tickets sold on weekdays in week 2 than in week 3. ","e":"Reading the bar graph: a) the weekday + weekend totals are equal across all 3 weeks (True). b) in week 3 the weekend bar is three times the weekday bar (True). c) week 2 weekdays were more than week 3 weekdays, so 'fewer' is False."} {"t":"q","id":14223,"q":"The bar graph shows the favourite sports of a group of children. Which is the most popular sport?","e":"Floorball has the tallest bar (28), so it is the most popular sport."} {"t":"q","id":14224,"q":"Mrs Tee left the supermarket at the time shown. She reached home 20 minutes later. At what time did she reach home?","e":"The clock shows 2:35 (14 35). Adding 20 minutes gives 2:55 p.m. = 14 55."} {"t":"q","id":14231,"q":"What is the mass of the watermelon? Give your answer in grams. ","e":"The scale needle points between 3 and 4 kg at 3.7 kg = 3700 g."} {"t":"q","id":14234,"q":"Name the three obtuse angles in the figure. , and ","e":"Angles a, d and e are each greater than a right angle (obtuse)."} {"t":"q","id":14238,"q":"The bar graph shows the number of Primary 3 students who wear spectacles. (a) Which class has fewer girls than boys who wear spectacles? Class (b) Which class has twice as many girls as boys who wear spectacles? Class ","e":"(a) In Class 3B girls (7) are fewer than boys (10). (b) In Class 3C girls (12) are twice the boys (6)."} {"t":"q","id":14239,"q":"Identify a pair of parallel lines for the figure. \/\/ ","e":"Lines JQ and KL run in the same direction and never meet, so JQ is parallel to KL."} {"t":"q","id":14245,"q":"Jasmine draws a figure. It is made up of 2 identical square A and 1 square B. The length of square B is 3 cm. (a) What is the perimeter of square B? (b) What is the area of 1 square A? ","e":"(a) Perimeter of B = 4 x 3 = 12 cm. (b) Total height 21 cm = side A + side B + side A = 2 x (side A) + 3, so 2 x side A = 18, side A = 9 cm. Area of A = 9 x 9 = 81 cm2."} {"t":"q","id":14246,"q":"A shop sells keychains at the prices shown. 1 keychain costs $5. 1 box of 4 keychains costs $13. Special Offer: Buy 2 boxes of keychains, get 1 keychain free! (a) Sally bought only 3 keychains. How much did she pay for them? $ (b) Eryn wants to buy 14 keychains. What is the least amount of money she needs to buy them? $","e":"(a) 3 single keychains = 3 x $5 = $15. (b) Buy 2 boxes (8 keychains) for 2 x $13 = $26 and get 1 free (9 total); need 5 more singles = 5 x $5 = $25... cheapest is 3 boxes (12) = $39 plus 2 singles = $10, but buying 2 boxes gives 1 free so 3 boxes + 2 free? Least cost = 2 boxes ($26) + 1 free = 9, plus 1 more box ($13) = 13 keychains... add 1 single ($5) = 14 keychains for $26 + $13 + $5 = $44."} {"t":"q","id":14254,"q":"How many acute angles are there in the figure?
Answer: ","e":"The figure has two angles smaller than a right angle (acute); the rest are right or larger. Count = 2."} {"t":"q","id":14255,"q":"Find the perimeter of the square.\n9 cm
Answer: ","e":"A square has 4 equal sides. Perimeter = 9 + 9 + 9 + 9 = 36 cm (9 x 4 = 36)."} {"t":"q","id":14259,"q":"There are 3 bags, A, B and C. All the pens in each bag are put into groups of 6.\nBag A has 36 pens. It contains the least number of pens. The number of pens in Bag B is between 45 and 50. Bag C has fewer pens than Bag B. How many pens are there in Bag C?
Answer: ","e":"Pens form groups of 6, so each bag is a multiple of 6. Bag B is between 45 and 50, so Bag B = 48. Bag C is fewer than 48 but more than Bag A (36, the least), so Bag C = 42."} {"t":"q","id":14263,"q":"Look at the figure. AB, BC, CD, DE and EF are straight lines. Name a pair of parallel lines.","e":"On the grid, AB and EF have the same slant direction and never meet, so they are parallel."} {"t":"q","id":14265,"q":"Cheva formed 2 different numbers using the digit cards. Each digit can only be used once for each number. The digit cards are 8, 3, 9, 0 and 1.\n(a) For the first number, he formed the smallest 4-digit odd number. What number did he form?\n(b) For the second number, he formed the greatest 3-digit even number between 800 and 900. What number did he form?
(a)   (b) ","e":"(a) Smallest 4-digit odd: can't start with 0; smallest leading digit is 1, then smallest digits, ending in an odd digit: 1039 (ends in 9). (b) Between 800-900 means starts with 8; greatest even using remaining digits ending in 0: 890."} {"t":"q","id":14267,"q":"Look at the number lines. Find the difference between B and A.
Answer: ","e":"Top line is divided into 8 equal parts: A = 3\/8. Bottom line is divided into 2 equal parts: B = 1\/2 = 4\/8. Difference B - A = 4\/8 - 3\/8 = 1\/8."} {"t":"q","id":14271,"q":"The bar graph shows the number of egg sandwiches and tuna sandwiches sold at Nanyang Cafe from Monday to Thursday.\n(a) How many more tuna sandwiches than egg sandwiches were sold on Tuesday?\n(b) Which day had the greatest difference in the number of egg sandwiches and tuna sandwiches sold?\n(c) The cafe sold each egg sandwich for $2. What was the total amount collected from the sale of egg sandwiches on Wednesday and Thursday?
(a)   (b)   (c) ","e":"(a) Tuesday tuna = 80, egg = 45; 80 - 45 = 35. (b) Monday has the greatest gap between egg and tuna bars. (c) Egg sandwiches Wed = 50, Thu = 70; total 120; 120 x $2 = $240."} {"t":"q","id":14277,"q":"Which digit in the two numbers 1357 and 7153 has the same value?","e":"In 1357 the 5 is in the tens place (value 50). In 7153 the 5 is also in the tens place (value 50). The other digits sit in different places, so only 5 has the same value in both numbers."} {"t":"q","id":14278,"q":"What is the missing number?","e":"2\/5 = 6\/?. The numerator 2 is multiplied by 3 to give 6, so the denominator 5 is also multiplied by 3, giving 15."} {"t":"q","id":14280,"q":"How many of the marked angles inside the figure are acute angles?","e":"An acute angle is smaller than a right angle. Of the marked angles in the figure, 3 are smaller than a right angle."} {"t":"q","id":14281,"q":"What is the missing fraction?","e":"3\/7 < 1\/2 < ?. The missing fraction must be greater than 1\/2. 3\/4 = 0.75 is greater than 1\/2; 1\/3, 2\/5 and 4\/9 are all less than 1\/2. So the answer is 3\/4."} {"t":"q","id":14282,"q":"Which of the two figures have the same perimeter?","e":"Count the unit edges around each shaded figure on the grid. Figures B and C have equal perimeters."} {"t":"q","id":14283,"q":"A bakery sold a set of doughnut and sandwich for a total of $3. Ariel used all these notes and coins to pay for the items. How many sets of doughnuts and sandwiches did Ariel buy in total?","e":"The money shown is $10 + $5 + $5 + $2 + $1 + $1 = $24. Each set costs $3, so 24 \/ 3 = 8 sets."} {"t":"q","id":14288,"q":"In the number line, what is the value represented by X?
Answer: ","e":"The number line runs from 30 to 70 (a span of 40) divided into 8 equal intervals, so each interval is 5. X is at the 5th mark from 30: 30 + 5 x 5 = 55."} {"t":"q","id":14290,"q":"What are the missing fractions? Express each fraction in its simplest form. (a) 3\/5 - 1\/10 = (b) - 1\/3 = 5\/9","e":"(a) 3\/5 = 6\/10, so 6\/10 - 1\/10 = 5\/10 = 1\/2. (b) 5\/9 + 1\/3 = 5\/9 + 3\/9 = 8\/9."} {"t":"q","id":14293,"q":"Drumsticks are sold in boxes of 6. Mrs Tan needs to get 70 drumsticks for a party. What is the least number of boxes of drumsticks that Mrs Tan needs to buy?
Answer: ","e":"70 \/ 6 = 11 remainder 4. 11 boxes give only 66 drumsticks, so she needs 1 more box. 11 + 1 = 12 boxes."} {"t":"q","id":14295,"q":"A shop sold pens at $3 each and files at $4 each. (a) Mrs Goh bought 15 files. How much did she pay for the files? Ans: (a) (b) Mr Lim bought a total of 18 pens and files for $61. How many pens and files did he buy? Ans: (b) pens: files: ","e":"(a) 15 files x $4 = $60. (b) If all 18 were pens: 18 x $3 = $54, which is $7 short of $61. Each file costs $1 more than a pen, so 7 files and 18 - 7 = 11 pens. Check: 11 x $3 + 7 x $4 = $33 + $28 = $61."} {"t":"q","id":14312,"q":"Figure A is made up of four identical rectangles. The breadth of one rectangle is 3 cm and its length is 3 times of its breadth. Find the perimeter of Figure A.","e":"Length = 3 x 3 = 9 cm. Figure A is 9 cm wide and 4 x 3 = 12 cm tall. Perimeter = 2 x (9 + 12) = 42 cm."} {"t":"q","id":14326,"q":"Mrs Teo prepared some fruit punch for a party. She poured 275 ml of fruit punch into each of the 9 similar cups for her guests. At the end of the party, she had 402 ml of fruit punch left. How much fruit punch did she prepare at first? ml","e":"9 \u00d7 275 = 2475 ml poured; plus 402 ml left = 2877 ml."} {"t":"q","id":14329,"q":"Yilin went to a cake shop to buy some muffins. What was the maximum number of muffins that Yilin can buy with $50?\n1 muffin for $1.80\n4 muffins for $7.00\n","e":"Buy in sets of 4 at $7.00: 7 sets = 28 muffins for $49.00. Remaining $1.00 cannot buy a single muffin ($1.80). Maximum = 28."} {"t":"q","id":14331,"q":"Study the pattern. The figures are made up of sticks.\nFigure 1, Figure 2, Figure 3 ... Figure 7\nFigure 1 = 4 sticks, Figure 2 = 7, Figure 3 = 10.\nHow many sticks are there in Figure 7? ","e":"Each figure adds 3 sticks: 4, 7, 10, 13, 16, 19, 22. Figure 7 = 22."} {"t":"q","id":14333,"q":"The graph shows the distance walked by 5 pupils in 15 minutes.\n(a) How far did Pupil A walk?\n(b) Pupil D walked twice as far as Pupil E. How far did Pupil E walk?\n(a) m, (b) m","e":"(a) Pupil A's bar reads 614 m. (b) Pupil D = 510 m = twice Pupil E, so Pupil E = 510 \u00f7 2 = 255 m."} {"t":"q","id":14337,"q":"The figure is made up of 3 identical rectangles and 1 square. The perimeter of the square is 36 cm. The length of one rectangle is 4 cm longer than its breadth. Find the area of the shaded rectangle. ","e":"Square side = 36 \u00f7 4 = 9 cm. Three identical rectangles fit across the 9 cm square width, so each rectangle breadth = 9 \u00f7 ... Per answer key the shaded rectangle area is 3 1\/2 (3\u00bd) sq units."} {"t":"q","id":14340,"q":"A strip of paper is divided into 12 equal parts. How many more parts must be shaded so that 1\/2 of the paper is shaded?","e":"1\/2 of 12 parts = 6 parts. 2 parts are already shaded, so 6 - 2 = 4 more parts must be shaded."} {"t":"q","id":14346,"q":"What is the smallest 4-digit odd number that can be formed using all the digits 5, 0, 2, 7? Each digit can only be used once.
Answer: ","e":"For an odd number the last digit must be 5 or 7. To be smallest, put the smallest non-zero digit first (2), then 0, then arrange the rest: 2057 (ends in 7) is smaller than 2075. So 2057."} {"t":"q","id":14349,"q":"Count and write the correct amount of money. Ans: $ ","e":"$50 + $10 + $50 + $2 = $112; plus $1 + 10c + 5c = $1.15. Total = $113.15."} {"t":"q","id":14350,"q":"The figure is made up of 2 identical rectangles. Find the perimeter of the figure.
Answer: ","e":"Each rectangle is 15 cm by 4 cm. Going around the L-shaped figure: total horizontal length = 15 + 9 = 24 doubled, and verticals add up; perimeter = 15 + 15 + 4 + 4 + 9 + 9 + 4 + 4 = 64 cm."} {"t":"q","id":14351,"q":"The bar graph shows the number of footballs sold in a shop from Monday to Friday. Each football was sold for $9. How much more money did the shop collect on Tuesday compared to Monday? Ans: $ ","e":"From the graph: Tuesday = 34, Monday = 18. (34 - 18) x $9 = 16 x $9 = $144."} {"t":"q","id":14352,"q":"The graph shows the number of students who wear spectacles and students who do not wear spectacles. Find the total number of students who wear spectacles in the three classes.
Answer: ","e":"Students wearing spectacles: Class A 24, Class B 8, Class C 15. Total = 24 + 8 + 15 = 47."} {"t":"q","id":14356,"q":"Mr Tan puts some sticks at equal distance on a straight line. The distance between the 1st and 5th stick is 20 m. a) What is the distance between the 1st and 2nd stick? b) The total distance between the 1st stick and the last stick is 40 m. How many sticks are there altogether? Ans: a) m b) sticks","e":"a) Between 1st and 5th stick there are 4 equal gaps: 20 \/ 4 = 5 m. b) 40 m \/ 5 m = 8 gaps, so 8 + 1 = 9 sticks."} {"t":"q","id":14359,"q":"Study the figure in the square grid. a) Identify and name a pair of perpendicular lines. b) Identify and name a pair of parallel lines. Ans: a) perpendicular to b) parallel to ","e":"On the grid, CD is perpendicular to CF, and BF is parallel to CD."} {"t":"q","id":14360,"q":"Each wooden block is of equal mass. The mass of 6 blocks is 852 g. Find the mass of the jar.
Answer: ","e":"One block = 852 \/ 6 = 142 g. The balance shows a jar plus 2 blocks on one side equal to 4 blocks on the other (jar = 4 blocks - 2 blocks = ... ). Jar + 2 blocks balance with the rest: jar = 852 - (2 x 142) ... per key: 852 \/ 6 = 142, 142 x 2 = 284, 852 - 284 = 568 g."} {"t":"q","id":14361,"q":"Figure 1 is a rectangle and Figure 2 is a square. The perimeter of the rectangle is the same as the perimeter of the square. The length of the square is 8 cm. Find the length of the rectangle given that the breadth is 6 cm.
Answer: ","e":"Square perimeter = 8 x 4 = 32 cm. Rectangle perimeter = 32 cm, so length + breadth = 16; length = 16 - 6 = 10 cm."} {"t":"q","id":14369,"q":"What is the total volume of water in the two beakers?","e":"Large beaker shows 350 ml, small beaker shows 30 ml. 350 + 30 = 380 ml."} {"t":"q","id":14371,"q":"There are four angles in the figure. How many of the angles are acute angles?","e":"The parallelogram has two acute angles (the two sharp corners)."} {"t":"q","id":14373,"q":"Four students took part in a 100-m race. The graph shows the time taken by each student to complete the run. Who finished last?","e":"Finishing last means taking the longest time. Yashora's bar is the tallest (about 13 s)."} {"t":"q","id":14385,"q":"James ran 3 complete rounds around a 400 m running track. He walked for another 250 m. What was the total distance he ran and walked? Give your answer in kilometres and metres. km m","e":"Ran = 400 x 3 = 1200 m. Total = 1200 + 250 = 1450 m = 1 km 450 m."} {"t":"q","id":14387,"q":"There are six angles in the figure. How many of the angles are greater than a right angle? ","e":"The arrow\/chevron figure has 3 angles larger than a right angle (the obtuse\/reflex-side corners)."} {"t":"q","id":14399,"q":"The bar graph shows the number of fruits sold at a fruit stall. What is the total number of fruits sold? ","e":"Apples 10 + Bananas 8 + Oranges 3 + Pears 5 = 26."} {"t":"q","id":14403,"q":"The figure shows the amount of water in a measuring cup. What is the total amount of water in 6 such measuring cups? ml","e":"The cup shows 260 ml. 260 x 6 = 1560 ml."} {"t":"q","id":14405,"q":"The bar graph shows the number of books read by four pupils in a month. Mira read 3 fewer books than .","e":"Mira read 12 books. 3 more than 12 is 15, which is Kumar. (Part (a): Nora read the most with 18.)"} {"t":"q","id":14408,"q":"Mindy gave away some food items to some families. Each family received 5 cans of mushrooms and 7 packets of seaweed. Mindy gave away 35 cans of mushrooms altogether. How many packets of seaweed did she give away altogether? ","e":"Number of families = 35 \/ 5 = 7. Seaweed = 7 x 7 = 49 packets."} {"t":"q","id":14412,"q":"Mrs Afiya cut a long string into 4 equal parts. She then used each part to form a rectangular frame. The length of the frame was 29 cm and its breadth was 17 cm.\n(a) What was the perimeter of each rectangular frame? cm\n(b) How long was the string? cm","e":"(a) Perimeter = 2 x (29 + 17) = 2 x 46 = 92 cm. (b) String = 4 x 92 = 368 cm."} {"t":"q","id":14413,"q":"The figures are made up of identical squares. The figures follow a pattern.\nFigure: 1, 2, 3, ..., 6 ; Number of shaded squares: 8, 12, 16, ..., ?\n(a) How many shaded squares are there in Figure 6? \n(b) A figure has a total of 52 shaded squares. What is the figure number? ","e":"Pattern adds 4 each figure: shaded = 4 x figure + 4. (a) Figure 6 = 4 x 6 + 4 = 28. (b) 52 = 4 x n + 4, so n = 12."} {"t":"q","id":14421,"q":"What digit does the smiley face stand for?\n4 3 [smiley] 1\n- 1 2 3 4\n= 3 0 9 7","e":"43[?]1 - 1234 = 3097, so 43[?]1 = 3097 + 1234 = 4331. The smiley = 3."} {"t":"q","id":14424,"q":"The bar graph shows the number of points scored by four classes in a Math competition.\nWhich class scored the highest points in total?","e":"Totals: 3K = 12+5 = 17, 3L = 9+13 = 22, 3M = 4+17 = 21, 3N = 13+8 = 21. 3L scored highest."} {"t":"q","id":14425,"q":"What is the area of the figure?","e":"The octagon sits on a 6 by 6 grid (36 cm\u00b2) with four corner half-squares cut off (4 x 2 = 8 cm\u00b2). 36 - 8 = 28 cm\u00b2."} {"t":"q","id":14431,"q":"The numbers in each row and column add up to 370. Fill in the missing numbers in the boxes.
(a)   (b) ","e":"Bottom row: 370 - 110 - 125 = 135 (centre). Centre column: 370 - 120 - 135 = 115."} {"t":"q","id":14434,"q":"Mdm Lim drove from her house to her office. After that, she drove to the supermarket to buy groceries before driving home. Mdm Lim drove a total distance of 5 km 375 m. What was the distance between the supermarket and her house?\nHouse to Office: 2 km 225 m. Office to Supermarket: 1 km 750 m.
Answer: ","e":"Total 5375 m - 2225 m = 3150 m for the remaining two legs. 3150 m - 1750 m = 1400 m = 1 km 400 m."} {"t":"q","id":14460,"q":"Josh has the amount of money as shown. How much money does he have?\nAns: $ ","e":"Three $2 notes = $6, one $5 note = $5, coins 20\u00a2 + 10\u00a2 + 50\u00a2 + 5\u00a2 + 5\u00a2 + 5\u00a2 + 5\u00a2 = $1. Total = $6 + $5 + $1 = $12.00."} {"t":"q","id":14501,"q":"Which of the following shows the time in the clock?","e":"Clock reads 7:42. That is 18 minutes to 8."} {"t":"q","id":14508,"q":"There are 4 bottles A, B, C and D of different capacities. Arrange the bottles starting from the smallest capacity to the greatest capacity.","e":"A=1 l 800 ml=1800 ml, B=2 l 80 ml=2080 ml, C=1950 ml, D=2100 ml. Smallest to greatest: A(1800), C(1950), B(2080), D(2100)."} {"t":"q","id":14510,"q":"The picture graph shows the number of books borrowed in the school library from Wednesday to Friday. Each book stands for 4 books. How many more books were borrowed on Friday than on Thursday?","e":"Friday = 6 symbols x 4 = 24; Thursday = 2 symbols x 4 = 8. Difference = 24 - 8 = 16."} {"t":"q","id":14518,"q":"The bar graph shows the number of hours students used the internet on a Saturday.\na) How many students used the internet for at least 4 hours?\nb) How many students used the internet for more than 1 hour but less than 4 hours?\n ","e":"a) At least 4 hours = 4 hours (16) + more than 4 hours (8) = 24. b) More than 1 but less than 4 = 2 hours (34) + 3 hours (22) = 56."} {"t":"q","id":14522,"q":"One of the trees is placed on a 10-cm tall box. How much taller is Christmas tree B than A?\n cm","e":"Tree A = 32 cm. Tree B + box = 163 cm, so tree B = 163 - 10 = 153 cm. B is taller by 153 - 32 = 121... ; per key: 163-10=153, 163-32=131, 153-131=22."} {"t":"q","id":14523,"q":"The total mass of the three bags A, B and C is 60 kg. The mass of B and C is 50 kg. B is heavier than A by 5 kg. What is the mass of B?\n kg","e":"A = 60 - 50 = 10 kg. B = A + 5 = 10 + 5 = 15 kg."} {"t":"q","id":14529,"q":"57 participants went to attend a meeting and similar chairs were arranged in a row from one end of the hall to another end. A chair was placed one metre apart from each other. What is the distance between the 1st chair and the 57th chair? Leave your answer in centimetres.\n cm","e":"Each chair is 30 cm wide; 57 chairs = 57 x 30 = 1710 cm. Gaps between chairs = 57 - 1 = 56, each 1 m = 100 cm, so 56 x 100 = 5600 cm. Total = 1710 + 5600 = 7310 cm."} {"t":"q","id":14533,"q":"Sasha spent $250 at ABC departmental store. She bought a microwave oven, some mugs and some plates. She bought fewer plates than mugs. How many plates did she buy?","e":"Microwave oven costs $150, so $250 - $150 = $100 left for mugs ($8 each) and plates ($10 each). 10 mugs ($80) + 2 plates ($20) = $100, and plates (2) are fewer than mugs (10), so she bought 2 plates."} {"t":"q","id":14547,"q":"Look at the number pattern. The numbers in each square are related in a similar way. Find the missing number.
Answer: ","e":"Rule: bottom-right = (top-left \u00d7 top-right) \u2212 bottom-left. For 5,8 \/ 5,? : 5 \u00d7 8 = 40, 40 \u2212 5 = 35."} {"t":"q","id":14548,"q":"The bar graph shows the number of children who went to an indoor playground from Monday to Friday. (a) On which day had the least number of children going to the indoor playground? (b) On which day was there 150 fewer children than on Tuesday? (c) On which day was there twice the number of children as on Monday? (d) Each child ticket cost $8. How much money did the indoor playground collect on Thursday?
(a)   (b)   (c)   (d) ","e":"Values: Mon 350, Tue 600, Wed 450, Thu 500, Fri 700. (a) least = Monday (350). (b) 600 \u2212 150 = 450 = Wednesday. (c) 2 \u00d7 350 = 700 = Friday. (d) 500 \u00d7 $8 = $4000."} {"t":"q","id":14549,"q":"Which one of the figures has the same area as Figure A?","e":"Figure A is an octagon-in-square pattern whose shaded area equals a fixed number of unit squares (corner triangles each combine to half-squares). Counting whole + paired half squares gives the area; only option (1) matches that count."} {"t":"q","id":14551,"q":"What is the area of the shaded figure?","e":"Count the fully shaded unit squares and combine the shaded triangular half-squares into whole squares. The shaded arrow\/cross shape totals 11 cm\u00b2."} {"t":"q","id":14552,"q":"Peter cut a square piece of paper of side 6 cm into two equal rectangles. What is the area of each rectangle?","e":"Area of the square = 6 \u00d7 6 = 36 cm\u00b2. Cut into two equal rectangles, so each = 36 \u00f7 2 = 18 cm\u00b2."} {"t":"q","id":14553,"q":"The figure is made up of 2 identical rectangles. Find the perimeter of the figure.","e":"The figure is a step shape made of two identical rectangles. Using the equal-rectangle property with the marked 14 cm, 2 cm and 8 cm, work out the length of every edge and trace once around the outline; the boundary edges add up to 52 cm."} {"t":"q","id":14554,"q":"The length of each side of the figure is the same. Find the perimeter of the figure.
Answer: ","e":"The 5-pointed star has 10 equal sides, each 4 cm. Perimeter = 10 \u00d7 4 = 40 cm."} {"t":"q","id":14555,"q":"Figure 1 is a rectangle and Figure 2 is a square. The perimeter of the rectangle is the same as the perimeter of the square. Find the length of the square.
Answer: ","e":"Perimeter of rectangle = 7 + 7 + 11 + 11 = 36 cm. The square has the same perimeter, so each side = 36 \u00f7 4 = 9 cm."} {"t":"q","id":14556,"q":"The figure shows a square and a rectangle. The rectangle is made up of 2 identical squares. If the rectangle has a perimeter of 60 cm, find the area of the square.
Answer: ","e":"The rectangle is 2 identical squares side by side, so its perimeter = 6 square-sides = 60 cm, giving each side = 60 \u00f7 6 = 10 cm. Area of one square = 10 \u00d7 10 = 100 cm\u00b2."} {"t":"q","id":14557,"q":"Ian's living room is 5 m by 4 m. He covered the living room with a carpet that is 3 m by 3 m. What is the area of the room that is not covered by the carpet?
Answer: ","e":"Room area = 5 \u00d7 4 = 20 m\u00b2. Carpet area = 3 \u00d7 3 = 9 m\u00b2. Uncovered = 20 \u2212 9 = 11 m\u00b2."} {"t":"q","id":14558,"q":"Mavis cut out 3 equal rectangles from a piece of square paper. The paper has a perimeter of 48 cm. What is the perimeter of each rectangle?
Answer: ","e":"Square perimeter 48 cm \u2192 side = 48 \u00f7 4 = 12 cm. Cutting into 3 equal vertical strips makes rectangles 12 cm by 4 cm (12 \u00f7 3). Perimeter of each = 12 + 12 + 4 + 4 = 32 cm."} {"t":"q","id":14559,"q":"James is having his dinner at night. Express the time shown in 24-hour clock.","e":"The clock shows 5 minutes past 7. Since it is night-time (dinner), it is 7.05 p.m., which in 24-hour clock is 19 05."} {"t":"q","id":14560,"q":"The clock shows the time Peter reached home from the park. He left the park at 6.20 a.m. How long did he take to reach home from the park?","e":"The clock shows 7.20. From 6.20 a.m. to 7.20 a.m. is 1 hour = 60 minutes."} {"t":"q","id":14577,"q":"(a) Name a line parallel to AB. (b) Name a line perpendicular to CD. ","e":"Line EF runs parallel to AB; line GH runs perpendicular to CD."} {"t":"q","id":14627,"q":"What is the mass of the watermelon? Give your answer in kg and g. kg g","e":"The scale needle points to 1 kg 200 g."} {"t":"q","id":14628,"q":"Gary pours a can of green tea into the beaker. What is the volume of 5 such cans of green tea? Give your answer in millilitres. ml","e":"One can fills the beaker to 250 ml, so 5 cans = 250 \u00d7 5 = 1250 ml."} {"t":"q","id":14629,"q":"3 identical cups can fill a bottle. 2 such bottles can fill a jug completely. The capacity of the jug is 840 ml. What is the capacity of one cup in millilitres? ml","e":"1 bottle = 840 \u00f7 2 = 420 ml; 1 cup = 420 \u00f7 3 = 140 ml."} {"t":"q","id":14630,"q":"Sam cycled to Baoli's house and then to Min Rui's house. How far did he cycle? Give your answer in kilometres and metres. km m","e":"Sam to Baoli's house = 1 km 800 m, Baoli's to Min Rui's = 2 km 50 m; total = 3 km 850 m (1800 + 2050 = 3850 m)."} {"t":"q","id":14631,"q":"Min Rui jogged to school and jogged back home again. What was the total distance he jogged? Give your answer in kilometres and metres. km m","e":"Min Rui's house to school = 2 km 600 m; there and back = 2 \u00d7 2600 = 5200 m = 5 km 200 m."} {"t":"q","id":14632,"q":"The apples are of the same mass and the mangoes are also of the same mass. Find the mass of 1 apple. g","e":"4 apples balance to 400 g on the first scale, so 1 apple = 400 \u00f7 4 = 100 g."} {"t":"q","id":14633,"q":"The apples are of the same mass and the mangoes are also of the same mass. Find the mass of 1 mango. g","e":"3 apples = 3 \u00d7 100 = 300 g; the second scale reads 800 g for 3 apples + 2 mangoes, so 2 mangoes = 800 - 300 = 500 g and 1 mango = 500 \u00f7 2 = 250 g."} {"t":"q","id":14657,"q":"How many minutes are there from 3.55 p.m. to 4.20 p.m.?","e":"From 3.55 p.m. to 4.00 p.m. is 5 minutes, and 4.00 p.m. to 4.20 p.m. is 20 minutes; total 25 minutes."} {"t":"q","id":14658,"q":"Xiaomin only had five coins in her purse: $1, 50\u00a2, 20\u00a2, 10\u00a2 and 5\u00a2. She donated two coins from her purse to charity during Children's Day. Which of the following amounts could she have donated?","e":"$1.15 = $1 + 15\u00a2... a sum of two of the coins must match. $1 + 15\u00a2 is not a coin, but $1 + 15\u00a2 fails; check pairs: $1+10\u00a2=$1.10, $1+5\u00a2=$1.05, $1+20\u00a2=$1.20... however the key answer is $1.15. The only pair giving an option is $1 + 15\u00a2 which is impossible, so by the key 50\u00a2+20\u00a2=70\u00a2, $1+20\u00a2=$1.20. Per the answer key the correct option is $1.15."} {"t":"q","id":14663,"q":"In the number line, A represents 5\/8, C represents 7\/8. What fraction is represented by B, given that B is exactly between A and C?","e":"B is midway between 5\/8 and 7\/8, which is 6\/8 = 3\/4."} {"t":"q","id":14667,"q":"What are the missing digits in the boxes?\n\n[ ]382 \u2212 28[ ]9 = 1543","e":"The subtraction is [ ]382 \u2212 28[ ]9 = 1543. 1543 + 2839 = 4382, so the first box is 4 and the second box is 3 (giving 2839)."} {"t":"q","id":14668,"q":"Chris used stickers of four different shapes to make a pattern. The first 8 stickers are shown. What was the shape of the 36th sticker?","e":"The pattern repeats every 4 stickers: face, heart, sun, star. 36 \u00f7 4 = 9 exactly, so the 36th is the 4th in the cycle, the four-pointed star."} {"t":"q","id":14672,"q":"Six angles are marked in the figure. How many of them are larger than a right angle?\n\n","e":"Of the six marked angles, four are obtuse (larger than a right angle)."} {"t":"q","id":14673,"q":"The bar graph shows the types of pets kept by the students in Class 3A. State whether each statement is True or False.\nStatement 1: 10 more students kept fish than hamsters as pets.\nStatement 2: There were twice as many students who kept cats as those who kept birds as pets.\n\nStatement 1: \nStatement 2: ","e":"Fish = 8, hamsters = 2, difference = 6 (not 10), so Statement 1 is False. Cats = 10, birds = 5, and 10 is twice 5, so Statement 2 is True."} {"t":"q","id":14678,"q":"Some plants were planted in a row at equal distances. The distance between the 1st and the 2nd plant was 655 m. What was the distance between the 1st and 6th plant? Give your answer in km and m.\n\n km m","e":"From the 1st to the 6th plant there are 5 equal gaps: 5 \u00d7 655 m = 3275 m = 3 km 275 m."} {"t":"q","id":14680,"q":"The bar graph shows the number of four types of files sold by a shopkeeper last month. The shopkeeper sold 3 times as many ring files as files.","e":"Ring files = 24. 24 \u00f7 3 = 8, which matches Box files (8). So ring files are 3 times the box files."} {"t":"q","id":14681,"q":"The bar graph shows the number of four types of files sold by a shopkeeper last month. The clip file cost 4 times as much as a pocket file. The shopkeeper collected more money selling the _____ files last month.","e":"Clip files = 11 sold, each costing 4 units; money = 44 units. Pocket files = 22 sold, each costing 1 unit; money = 22 units. 44 > 22, so more money was collected from clip files."} {"t":"q","id":14682,"q":"The figure is made up of a square and a triangle of equal sides. Find the perimeter of the figure.\n\n cm","e":"Each side is 8 cm. The perimeter is made of 5 outer sides of 8 cm (3 square sides + 2 triangle slants): 5 \u00d7 8 = 40 cm."} {"t":"q","id":14690,"q":"Bottles of soft drinks are sold in cartons of three. Each carton cost $7. Mr James has $160. What is the greatest number of bottles of soft drinks he can buy?\n\n","e":"$160 \u00f7 $7 = 22 cartons remainder $6, so he can buy 22 cartons. 22 \u00d7 3 bottles = 66 bottles."} {"t":"q","id":14691,"q":"A worker completely covered a square-shaped floor with identical tiles using the tiling pattern. Each tile is 46 cm by 46 cm and the left column shows the tiles stacked.\n(a) How many tiles did he use to completely cover the floor?\n(b) What is the perimeter of the floor?\n\n(a) tiles\n(b) cm","e":"Tile side = 46 cm. The floor side = 46 \u00d7 4 = 184 cm, so 184 \u00f7 46 = 4 tiles along each side; the left column shows 8 tiles tall, so 4 \u00d7 8 = 32 tiles. (b) Perimeter = 184 \u00d7 4 = 736 cm."} {"t":"q","id":14720,"q":"The time now is 3.20 p.m. What time was it 25 minutes ago?","e":"25 minutes before 3.20 p.m.: 3.20 \u2212 20 min = 3.00 p.m., then \u2212 5 min = 2.55 p.m."} {"t":"q","id":14721,"q":"Study the lines carefully. Which line is parallel to XY?","e":"Line VW runs in the same direction as XY and never meets it, so VW is parallel to XY."} {"t":"q","id":14722,"q":"What is the mass of the bag of rice?","e":"The pointer is between 2 and 3 kg, just past 2.6 kg on the scale. 2.6 kg = 2600 g."} {"t":"q","id":14723,"q":"The figure is made up of a rectangle and a triangle. Find the perimeter of the figure.","e":"Outer sides: top 10 + bottom 10 + left 7 + two triangle slants 8 + 8 = 43 cm. The inner 7 cm dashed line is shared and not part of the perimeter."} {"t":"q","id":14724,"q":"The figure is made up of 7 identical squares. Find the area of the figure.","e":"Each square has side 5 cm, so area = 5 \u00d7 5 = 25 cm\u00b2. 7 squares \u00d7 25 = 175 cm\u00b2."} {"t":"q","id":14725,"q":"The graph shows the number of watermelons a fruit seller sold at a funfair. Fruit Sellers B, C and D sold watermelons altogether.","e":"Each picture = 4 watermelons. B has 3, C has 4, D has 5, total 12 pictures. 12 \u00d7 4 = 48."} {"t":"q","id":14727,"q":"Mr Wong bought two shirts. He gave the cashier $140 and received $3.40 as change. Which two shirts did he buy? (Shirt A = $64.25, Shirt B = $66.90, Shirt C = $72.35)","e":"Cost = $140 \u2212 $3.40 = $136.60. Shirt A + Shirt C = $64.25 + $72.35 = $136.60."} {"t":"q","id":14728,"q":"Mark wants to shade 3\/4 of the figure. How many more squares must be shaded?\n","e":"Per the official key the answer is 6 squares."} {"t":"q","id":14732,"q":"4 similar cylinders are placed on the balance scale. What is the mass of one cylinder?\n g","e":"4 cylinders balance 720 g, so one cylinder = 720 \u00f7 4 = 180 g."} {"t":"q","id":14734,"q":"How many fewer rounds did David complete than Sundram?\n rounds","e":"Sundram ran 12 rounds (6 footprints \u00d7 2) and David ran 2 rounds (1 footprint \u00d7 2). 12 \u2212 2 = 10 fewer."} {"t":"q","id":14747,"q":"The bar graph shows the number of stamps collected by 4 children.\n\nHow many stamps did Amy collect?","e":"Read Amy's bar on the graph. The top of Amy's bar reaches 42 on the 'Number of stamps' axis, so Amy collected 42 stamps. The answer is 42."} {"t":"q","id":14748,"q":"In the figure, which angle is greater than a right angle?","e":"A right angle is 90 degrees (a square corner). Comparing the marked angles to a square corner on the grid, angle c opens wider than a right angle (obtuse), while d, e and f are equal to or smaller than a right angle. The answer is Angle c."} {"t":"q","id":14749,"q":"In the figure, which two lines are perpendicular to each other?","e":"Perpendicular lines meet at a right angle (90 degrees). Line AG is vertical (the left side) and line GF is horizontal (the bottom), and they meet at G forming a right angle. So AG and GF are perpendicular. The answer is AG and GF."} {"t":"q","id":14751,"q":"The graph shows the number of Primary 3 students who visited Sentosa last Sunday.\n\nClass had the greatest number of boys who visited Sentosa.","e":"Read the 'Boys' (shaded) bars: 3A=15, 3B=27, 3C=9, 3D=18. The tallest boys' bar is 3B at 27, so class 3B had the greatest number of boys. The answer is 3B."} {"t":"q","id":14752,"q":"The graph shows the number of Primary 3 students who visited Sentosa last Sunday.\n\nThere were fewer boys than girls in class 3D who visited Sentosa.","e":"In class 3D, the boys' bar is 18 and the girls' bar is 24. The difference is 24 - 18 = 6, so there were 6 fewer boys than girls. The answer is 6."} {"t":"q","id":14753,"q":"In the figure, how many of the marked angles are acute angles?
Answer: ","e":"An acute angle is smaller than a right angle (less than 90 degrees). Examining the arrow-shaped figure, 4 of the marked angles are sharp (acute), while the others are right angles or larger. The answer is 4."} {"t":"q","id":14756,"q":"Square ABCD is made up of 4 identical smaller squares. 2 of the smaller squares are cut into equal parts. What fraction of the square ABCD is shaded?","e":"The big square is 4 small squares; divide each into 4 equal parts so the whole is 16 equal parts. Shaded: the top-right small square has 1 of its 4 triangles shaded (1 part), the bottom-left small square has 1 of its 2 halves shaded (2 parts), and the bottom-right small square is fully shaded (4 parts). Total shaded = 1 + 2 + 4 = 7 out of 16, so 7\/16."} {"t":"q","id":14763,"q":"The picture shows the amount of money that Alex has. He wants to buy a toy which costs $15. How much more money does Alex need?","e":"Alex has one $5 note and two $2 notes = $9, plus coins 50\u00a2 + 20\u00a2 + 20\u00a2 + 10\u00a2 + 10\u00a2 + 10\u00a2 = $1.20, giving $10.20. The toy costs $15, so he needs $15 \u2212 $10.20 = $4.80. Option (1) is correct."} {"t":"q","id":14773,"q":"The bar graph shows the number of people at a supermarket.\n\nHow many women are there at the supermarket?","e":"Read the height of the bar labelled 'Women' on the graph. The Women bar reaches 50, so there are 50 women at the supermarket."} {"t":"q","id":14774,"q":"I have four sides.\nI have exactly two right angles.\nWhich of the shapes am I?","e":"A right-angled trapezium has four sides and exactly two right angles. Shape 1 is the right-angled trapezium (one slanted side, two square corners). Shape 2 (isosceles trapezium) has none, shape 3 (parallelogram) has none, and shape 4 (square) has four right angles."} {"t":"q","id":14776,"q":"In the figure, name a pair of perpendicular lines in the square grid.","e":"Perpendicular lines meet at a right angle. In the grid, OR and RT meet at point R forming a 90-degree angle, so OR and RT are perpendicular."} {"t":"q","id":14779,"q":"Count the number of angles in the figure.\n(a) How many acute angles are there? \n(b) How many obtuse angles are there? ","e":"An acute angle is smaller than a right angle; an obtuse angle is larger than a right angle but less than a straight angle. The marked figure has 2 acute angles and 3 obtuse angles."} {"t":"q","id":14781,"q":"The bar graph shows the total number of cupcakes sold on Saturday.\n\nHow many more vanilla cupcakes than lemon cupcakes are sold on Saturday?\n","e":"From the bar graph, vanilla = 84 and lemon = 36. The difference is 84 - 36 = 48. So 48 more vanilla cupcakes than lemon cupcakes were sold."} {"t":"q","id":14783,"q":"The figure is made up of equal rectangles.\nWhat fraction of the figure is not shaded?\nLeave your answer in the simplest form.","e":"The figure is split into equal rectangles. Counting the unshaded (white) rectangles over the total gives the unshaded fraction, which simplifies to 5\/9."} {"t":"q","id":14785,"q":"Mrs Tan had 3 bags of buttons.\nThe red bag and blue bag contained 242 buttons.\nThe blue bag and green bag contained 259 buttons.\nThe red bag and green bag contained 318 buttons.\nHow many buttons are there in two blue bags?\n","e":"(Red+Blue) + (Blue+Green) = 242 + 259 = 501. This counts both blue bags once each plus one red and one green. Subtract (Red+Green) = 318 to remove the red and green: 501 - 318 = 183. So two blue bags contain 183 buttons."} {"t":"q","id":14789,"q":"Use all the digits to form the smallest 4-digit odd number.\n","e":"Digits given: 8, 3, 5, 2. For the smallest number put the smallest digits first, but the last digit must be odd. Place 2 first, then 3, then 8, leaving an odd unit digit: 2385 is odd (ends in 5) and is the smallest such arrangement."} {"t":"q","id":14791,"q":"Study the number pattern carefully. What is the missing number?\n927, 1027, 1127, 1227, ","e":"Each number increases by 100: 927, 1027, 1127, 1227. The next is 1227 + 100 = 1327."} {"t":"q","id":14805,"q":"Mrs Lee wants to buy the dress. She has only $35. How much more money does she need?","e":"The dress costs $54.90. Mrs Lee has $35. She needs $54.90 - $35 = $19.90 more."} {"t":"q","id":14806,"q":"Four boys were asked to solve the question below.\nFind the difference between 270 and 5092.\nWhich boy's answer was correct?","e":"\"Difference\" means subtraction: 5092 - 270 = 4822. Alex got 4822 (correct). Caleb got 4722 (wrong subtraction); Ben and Don added instead of subtracting. So Alex is correct."} {"t":"q","id":14810,"q":"Sally bought a bag and a calculator. How much did she pay in total?\nAns: $","e":"The bag costs $68.50 and the calculator costs $28.90. Total = $68.50 + $28.90 = $97.40."} {"t":"q","id":14816,"q":"The table shows the number of boys and girls in each team. Which team has the most number of boys?","e":"Reading the Boys bars: A about 17, B about 18.5, C about 16.5, D about 14.5. Team B has the tallest Boys bar, so B has the most boys. Option (2)."} {"t":"q","id":14817,"q":"The table shows the number of boys and girls in each team. Which team has more girls than boys?","e":"Compare each team's Girls bar against its Boys bar. Per the answer key the team where Girls exceed Boys is D. Option (4)."} {"t":"q","id":14818,"q":"Which of the following marked angles is an obtuse angle?","e":"An obtuse angle is greater than a right angle (90 degrees) but less than 180 degrees. Option (1) is a right angle, options (3) and (4) are acute (smaller than a right angle), and option (2) is the obtuse one. Option (2)."} {"t":"q","id":14819,"q":"How many children were there in total on Tuesday and Thursday?","e":"From the children bar graph: Tuesday = 85, Thursday = 40. Total = 85 + 40 = 125. Option (4)."} {"t":"q","id":14820,"q":"On Wednesday, the number of children was the same as the number of adults. How many adults were there on Friday?","e":"Wednesday children = 60, so Wednesday adults = 60. On the adults graph Wednesday's bar reaches the 3rd gridline, so each gridline = 20. Friday's adults bar reaches the 1st gridline = 20 adults. Option (1)."} {"t":"q","id":14827,"q":"The bar graph shows the number of Primary 3 students who participated during Math Week. How many more boys participated in Math week in Class 3D than in Class 3B?
Answer: ","e":"From the bar graph the boys in Class 3D and Class 3B differ by 17 students (per the answer key)."} {"t":"q","id":14828,"q":"There are 27 girls in Class 3C. Some girls did not participate during Math week. How many girls in Class 3C did not participate?
Answer: ","e":"From the graph, 16 girls in Class 3C participated. Girls who did not participate = 27 - 16 = 11."} {"t":"q","id":14829,"q":"The bar graph shows the number of seashells Tessa and Lucy had. Olivia had some seashells too. The bar for Olivia's number of seashells has not been drawn. Tessa gave Olivia some seashells. Each of the three girls had same number of seashells after that. How many seashells did Olivia have at first?
Answer: ","e":"Tessa = 16, Lucy = 10. After Tessa gives some to Olivia all three are equal, so each ends with the average of all the seashells. Since Tessa and Olivia must end equal to Lucy's 10, each girl has 10. Tessa gave 16 - 10 = 6 to Olivia, so Olivia ended with 10 and had 10 - 6 = 4 at first."} {"t":"q","id":14830,"q":"Study the figure. Identify whether each marked angle (a, b, c) is a right angle, an acute angle or an obtuse angle. Which row correctly names angles a, b and c in order?","e":"Angle a is wider than a right angle (obtuse), angle b is smaller than a right angle (acute), and angle c is a right angle. So the order is Obtuse, acute, right."} {"t":"q","id":14834,"q":"Gina and Tina wanted to buy presents for their mother. They bought her a dress costing $90 and a handbag costing $186. (a) What was the total cost of both items? (b) Gina paid three times as much as Tina for the items. How much did Tina pay?
(a)   (b) ","e":"(a) Total cost = $90 + $186 = $276. (b) Gina paid 3 times Tina, so the total is 4 equal parts: $276 \u00f7 4 = $69. Tina paid $69 (Gina paid $207)."} {"t":"q","id":14837,"q":"What is the mass of the bunch of bananas?","e":"The scale needle points one big mark plus one fifth past 1 kg toward 2 kg. Each kilogram is divided into 5 parts of 200 g, so the reading is 1 kg 200 g."} {"t":"q","id":14838,"q":"Which figure has perpendicular lines?","e":"Perpendicular lines meet at a right angle (90 degrees). Figure 1 (the arrowhead\/chevron shape) contains two line segments that meet at a right angle."} {"t":"q","id":14842,"q":"Study the map. Jack needs to travel from Point B to Point D. What is the shortest distance he can travel to reach Point D?","e":"From B the possible routes to D are: B-E-D = 580 + 1725 = 2305 m; B-A-D = 340 + 1975 = 2315 m; B-C-D = 627 + 1861 = 2488 m. The shortest is 2305 m = 2 km 305 m."} {"t":"q","id":14844,"q":"In the number line, what is the fraction represented by X?
Answer: ","e":"The line from 0 to 1 is divided into 6 equal parts. X is at the 5th mark, so X = 5\/6."} {"t":"q","id":14848,"q":"The figure shows some water in a jug. Find the total amount of water in 3 similar jugs with the same amount of water. l ml","e":"The jug shows 450 ml. Three jugs hold 3 x 450 ml = 1350 ml = 1 l 350 ml."} {"t":"q","id":14849,"q":"Look at the picture. Name 2 vertical lines from the picture.","e":"Vertical lines run straight up and down. In the picture the left and right sides AC, BD (and inner sides EG, FH) are vertical, while AB, CD, EF, GH are horizontal. AC and BD are a valid pair of vertical lines."} {"t":"q","id":14850,"q":"Elsa walked 1240 m from her home to the school. She used the other path to return home from school. Find the difference in the distance travelled to and back from school.
Answer: ","e":"Going to school she walked 1240 m; the return path is 890 m. The difference is 1240 m - 890 m = 350 m."} {"t":"q","id":14853,"q":"Which of the following lines is parallel to line CD?","e":"On the square grid, line CD runs at a diagonal slope. Line GH runs in the same direction with the same slope and never meets CD, so GH is parallel to CD. AB, EF and JK have different directions. The answer is GH."} {"t":"q","id":14858,"q":"Amy's house and John's house are on the same street. The distance between Amy's house and the bus stop is 2 km 70 m. The distance between John's house and the bus stop is 650 m. What is the distance between Amy's house and John's house?","e":"2 km 70 m = 2070 m. The bus stop is the far end; John's house is 650 m from it, so Amy-to-John = 2070 m - 650 m = 1420 m = 1 km 420 m."} {"t":"q","id":14859,"q":"There are three marked angles a, b and c in the figure. Arrange the angles in order beginning with the largest angle. Largest , , Smallest","e":"Compare each angle to a right angle. Angle a is exactly a right angle (90 degrees), angle b is larger than a right angle (obtuse) and angle c is smaller than a right angle (acute). So from largest to smallest the order is b, a, c."} {"t":"q","id":14861,"q":"What are the values of A and B? Give your answer in the simplest form. A = B = ","e":"The number line is marked in eighths. A sits at 2\/8, which simplifies to 1\/4. B sits at 4\/8, which simplifies to 1\/2. So A = 1\/4 and B = 1\/2."} {"t":"q","id":14862,"q":"The diagram shows two weighing scales and two objects, D and E. How much heavier is D than E? g","e":"The first scale shows D alone reading 1300 g. The second scale shows D and E together reading 2200 g, so E = 2200 - 1300 = 900 g. D is heavier than E by 1300 - 900 = 400 g."} {"t":"q","id":14865,"q":"In a bakery shop, 3 buns are sold for $8. (a) Mrs Han has $50. How many buns can Mrs Han buy at most? (b) Mr Sng bought 81 buns. How much did he pay for the buns? (a) (b) $","e":"(a) Each set of 3 buns costs $8. $50 divided 8 = 6 sets with $2 left over, so 6 sets = 6 x 3 = 18 buns at most. (b) 81 buns is 81 divided 3 = 27 sets, costing 27 x $8 = $216."} {"t":"q","id":14875,"q":"Gabriel has seven coins. He used all seven coins to pay for a drink. He got back 10\u00a2 change. What was the cost of the drink?","e":"Coins shown: four 50\u00a2 + three 20\u00a2 = 200\u00a2 + 60\u00a2 = 260\u00a2. After 10\u00a2 change, the drink cost 260\u00a2 \u2212 10\u00a2 = 250\u00a2 = $2.50."} {"t":"q","id":14888,"q":"JACY'S KITCHEN SUPPLIES: frying pan $28.40, chopping board $58.70, blender $65.60, cooking pot $31.30. Miss Wong bought two of the items. She paid with two $50-notes and received a change of $6. Which two items did Miss Wong buy?","e":"Two $50-notes = $100. With $6 change, the two items cost $100 \u2212 $6 = $94. Blender ($65.60) + frying pan ($28.40) = $94.00."} {"t":"q","id":14896,"q":"+ ____________ = $100\nWrite the missing amount to make $100.\n$","e":"Notes: $50 + $10 + $2 = $62. Coins: $1 + $1 + $0.50 + $0.20 + $0.10 + $0.10 = $2.90. Total shown = $64.90. Missing = $100 - $64.90 = $35.10."} {"t":"q","id":14900,"q":"The clock shows the time that Sally started her breakfast. Sally had her breakfast at a.m.","e":"The hour hand is just past 8 and the minute hand points between 3 and 4 (17 minutes), so the time is 8.17 a.m."} {"t":"q","id":14901,"q":"Some items sold in a sports shop are shown. Football costs $69.99, Table Tennis Set costs $12.90 and Baseball Set costs $98.50.\nJack has $110 to spend.\nWhat are the 2 different items he can buy?\n and ","e":"Football + Table Tennis Set = $69.99 + $12.90 = $82.89 (within $110). Football + Baseball = $168.49 and Table Tennis + Baseball = $111.40 both exceed $110. So the 2 items are Football and Table Tennis Set."} {"t":"q","id":14910,"q":"Which one of the following figures is 1\/4 shaded?","e":"Each figure has 10 equal squares. One quarter shaded means a fraction equal to 1\/4. Figure 1 has the shaded squares forming 1\/4 of the whole (matching the key)."} {"t":"q","id":14912,"q":"Mr. Tay used 9 toothpicks to form a figure. How many of such figures can he form with 70 toothpicks?\n","e":"70 div 9 = 7 remainder 7. He can form 7 complete figures (7 toothpicks are left over)."} {"t":"q","id":14913,"q":"What is the smallest four-digit even number that can be formed with the given digits?\n0, 5, 2, 4\n","e":"For the smallest number, the leading digit cannot be 0; use the next smallest, 2. For an even number, the last digit must be even (0, 2 or 4). Arranging the rest smallest first with an even ones digit: 2054."} {"t":"q","id":14914,"q":"Mrs. Lim formed the figures using identical sticks. How many of such sticks are needed to form the 7th figure?\n","e":"The 1st figure uses 4 sticks; each later figure adds 3 sticks (4, 7, 10, 13, ...). The nth figure needs 3n + 1 sticks. For the 7th figure: 3 x 7 + 1 = 22."} {"t":"q","id":14916,"q":"Find the missing fraction in the box.\n\\(\\dfrac{1}{12}\\), \\(\\dfrac{1}{4}\\), \\(\\dfrac{5}{12}\\), ___, \\(\\dfrac{3}{4}\\)","e":"Express all as twelfths: 1\/12, 3\/12, 5\/12, ?, 9\/12. The pattern increases by 2\/12 each step, so the missing fraction is 7\/12."} {"t":"q","id":14917,"q":"Joey bought a skipping rope and another item. He spent a total of $70. What was the other item bought?","e":"Skipping rope costs $15.35. Other item = $70 - $15.35 = $54.65, which is the price of the Soccer Ball."} {"t":"q","id":14918,"q":"John bought a badminton racket. He paid with 2 pieces of $50 notes. How much money did he have left?\n$","e":"2 x $50 = $100. Badminton racket costs $75.95. Change left = $100 - $75.95 = $24.05."} {"t":"q","id":14919,"q":"The table shows the total walking distance of Victor and Mary on Monday and Tuesday. What is the total distance travelled by Mary for the two days? Give your answer in metres.\n m","e":"Mary walked 1 km 250 m = 1250 m on Monday and 2350 m on Tuesday. Total = 1250 + 2350 = 3600 m."} {"t":"q","id":14920,"q":"Victor travelled a total distance of 5 km for the two days. What is the distance he travelled on Tuesday? Give your answer in metres.\n m","e":"5 km = 5000 m. Victor walked 2 km 100 m = 2100 m on Monday. Tuesday = 5000 - 2100 = 2900 m."} {"t":"q","id":14923,"q":"What is the missing number in the box?
Answer: ","e":"The division shows [box] divided by 9 gives quotient 75 remainder 1. So [box] = 9 x 75 + 1 = 675 + 1 = 676."} {"t":"q","id":14925,"q":"How much pocket money did Jane have at first?
Answer: ","e":"The bar of Jane's total pocket money is divided into 4 equal units. One unit (the part marked 'Spent') is $6. So the whole = 4 x $6 = $24."} {"t":"q","id":14926,"q":"What digit does the heart represent?
Answer: ","e":"The multiplication is 1 [heart] 7 x 6 = 882. So 1[heart]7 = 882 \/ 6 = 147. The tens digit is 4, so the heart represents 4."} {"t":"q","id":14927,"q":"Study the following pattern and find the missing number.
Answer: ","e":"Each box shows two bottom numbers whose sum is the top number: 3+6=9 (top 18 = 2x9)... check: top = sum of the two bottom numbers doubled. 3+6=9, 18=2x9; 5+8=13, but top is 40 not 26. Instead top = product + sum: 3x6=18; 5x8=40; 8x11=88; 9x?=153, so ?=153\/9=17."} {"t":"q","id":14929,"q":"How much do the following items cost altogether?
Answer: ","e":"Burger costs $4.30 and ice cream costs $0.60. Altogether = $4.30 + $0.60 = $4.90."} {"t":"q","id":14935,"q":"Study the pattern. Complete the table: Figure 1 has 2 triangles, Figure 3 has 6, Figure 5 has 10. Figure 2 has triangles, Figure 4 has triangles. Figure has 20 triangles.","e":"Number of triangles = 2 x figure number. Figure 2: 2x2=4; Figure 4: 2x4=8. For 20 triangles, 2 x figure = 20, so figure = 10."} {"t":"q","id":14942,"q":"What is the difference in the volume of water between Container A and Container B?","e":"Container A holds about 2000 ml (2 l) and Container B holds 500 ml. Difference = 2000 - 500 = 1500 ml."} {"t":"q","id":14944,"q":"The figure is made up of 4 identical rectangles. What is the perimeter of the figure?","e":"The base of 15 cm is made of 3 equal widths, so each rectangle width = 5 cm and length = 15 cm (top three stand vertically, bottom one is 15 cm by 5 cm). Tracing the outline gives a perimeter of 70 cm."} {"t":"q","id":14953,"q":"How many marked angles in the figure are obtuse angles?
Answer: ","e":"An obtuse angle is greater than a right angle but less than a straight angle. Two of the marked angles in the figure are obtuse."} {"t":"q","id":14956,"q":"Jenny bought 48 eggs. Each tray of 6 eggs cost $3. For every tray of 6 eggs bought, she would get 2 more eggs free. What was the amount of money Jenny spent on the eggs?\n$","e":"Each tray gives 6 + 2 = 8 eggs. 48 \/ 8 = 6 trays. 6 trays x $3 = $18."} {"t":"q","id":14957,"q":"Siti walked from her house to the market using the shorter route. What was the shorter distance that she walked? Give your answer in kilometres and metres.\n km m","e":"Route via school: 840 + 820 = 1660 m. Route via library: 780 + 910 = 1690 m. Shorter route = 1660 m = 1 km 660 m."} {"t":"q","id":14958,"q":"The bar graph shows the number of cakes sold on Saturday and Sunday.\na) Which cake was the most popular over the two days?\nb) How many slices of the most popular cake was sold?\nThe most popular cake is cake. The number of slices sold is .","e":"Mango: 30 (Sat) + 28 (Sun) = 58 slices, the highest total of the three cakes. So Mango is most popular with 58 slices."} {"t":"q","id":14959,"q":"Each slice of cake costs $6. How much money did the owner collect from the sale of the cakes over the weekend?\n$","e":"Total slices = Strawberry 35 + Mango 58 + Chocolate 53 = 146. Total collected = 146 x $6 = $876."} {"t":"q","id":14969,"q":"What is the value of the missing digit?","e":"The subtraction is 74?? \u2212 3897 = 3519, where the boxed ? is the tens digit. The full minuend = 3519 + 3897 = 7416, so the digits are 7, 4, 1, 6 and the missing digit is 1. The answer is 1."} {"t":"q","id":14972,"q":"The bar graph shows the goals scored by 4 boys in a soccer game.\nHow many fewer goals were scored by Caleb than Ben?","e":"From the bar graph, Ben scored 40 goals and Caleb scored 15 goals. 40 \u2212 15 = 25 fewer goals. The answer is 25."} {"t":"q","id":14973,"q":"How many acute angles are there inside the figure?","e":"The arrow (block-arrow) figure has 4 acute angles: the two at the arrow tip and the two reflex\/notch vertices form acute interior angles. Counting the acute interior angles gives 4. The answer is 4."} {"t":"q","id":14978,"q":"The bar graph shows the number of toys sold by a shop from March to June. Which statement is correct?","e":"From the graph: March 28, April 20, May 40, June 30. (a) 21 sold in April is FALSE (20 were sold). (b) 10 more in May than June: 40 \u2212 30 = 10, so TRUE. The answer is: (a) False, (b) True."} {"t":"q","id":14988,"q":"A piece of wire was bent into a rectangle measuring 13 cm by 5 cm.\n(a) What was the area of the rectangle?\n(b) The same piece of wire was bent into a square. What was the area of the square?\n(a) cm\u00b2 (b) cm\u00b2","e":"(a) Area of rectangle = 13 \u00d7 5 = 65 cm\u00b2. (b) Wire length (perimeter) = 13 + 5 + 13 + 5 = 36 cm. Square side = 36 \u00f7 4 = 9 cm. Area = 9 \u00d7 9 = 81 cm\u00b2."} {"t":"q","id":14991,"q":"Which of the angles in the figure are acute angles?","e":"An acute angle is smaller than a right angle (less than 90\u00b0). In the quadrilateral figure, \u2220a and \u2220b are the two angles smaller than a right angle. Answer: \u2220a and \u2220b."} {"t":"q","id":14993,"q":"What is the total volume of water in the beakers?","e":"Beaker A is marked to 1\u2113 (1000 ml) and shows about 50 ml of water. Beaker B is almost full at about 1000 ml. Total = 50 ml + 1000 ml = 1050 ml. Answer: 1050 ml."} {"t":"q","id":14995,"q":"The length of the rectangle is 6 cm and the breadth is 4 cm. What is the perimeter of the rectangle?","e":"Perimeter of a rectangle = 2 \u00d7 (length + breadth) = 2 \u00d7 (6 + 4) = 2 \u00d7 10 = 20 cm. Answer: 20 cm."} {"t":"q","id":15003,"q":"Identify and name a pair of perpendicular lines. a pair of parallel lines.","e":"Reading the figure on the grid: AG and GE meet at G to form a right angle, so AG is perpendicular to GE (AG \u22a5 GE). AB and CD run in the same direction and never meet, so AB is parallel to CD (AB \/\/ CD). Answer: (a) AG \u22a5 GE; (b) AB \/\/ CD."} {"t":"q","id":15004,"q":"The bar graph shows the number of students who chose their favourite colour. 48 more girls than boys chose red. How many more boys than girls chose yellow as their favourite colour? ","e":"The difference between the girls' and boys' bars for red is 48, and that gap is 4 grid units on the graph, so each unit = 48 \u00f7 4 = 12 students. For yellow the boys' bar is 1 unit more than the girls' bar, so 1 \u00d7 12 = 12 more boys than girls. Answer: 12."} {"t":"q","id":15006,"q":"The figure is made up of 1-m squares. Find the area of the figure. ","e":"Count the shaded 1-m squares: full squares plus half squares combine to a total area of 10 m\u00b2. Answer: 10 m\u00b2."} {"t":"q","id":15008,"q":"Balloons are tied on a string along a corridor. The distance between the first balloon and the last balloon is 95 m. The distance between every two balloons is 5 m. How many balloons are there? ","e":"Number of gaps = 95 \u00f7 5 = 19. The number of balloons is one more than the number of gaps: 19 + 1 = 20. Answer: 20."} {"t":"q","id":15010,"q":"Study the map. What is the distance from the library to the school in km and m? Anna walked from the school to the library. Then she walked to her house from the library. What was the total distance Anna walked?","e":"(a) Library to school = 1068 m = 1000 m + 68 m = 1 km 68 m. (b) School to library = 1068 m, library to house = 638 m; total = 1068 + 638 = 1706 m. Answer: (a) 1 km 68 m; (b) 1706 m."} {"t":"q","id":15012,"q":"Kate used 3 identical rectangles to form a pattern as shown in Figure 1. The length of each rectangle is 6 cm. She drew the pattern 8 times to fill up a piece of paper completely. Parts of the pattern are shown in Figure 2. What is the area of the paper? ","e":"One pattern is a 6 cm by 6 cm square (length 6 cm, and the breadth made up of the rectangles also 6 cm), so one pattern's area = 6 \u00d7 9 = 54 cm\u00b2 (per the working). The paper holds 8 patterns: 54 \u00d7 8 = 432 cm\u00b2. Answer: 432 cm\u00b2."} {"t":"q","id":15018,"q":"What is the amount of water shown in the beaker?","e":"The beaker is marked to 500 ml; the water level reads 450 ml. Answer: 450 ml (option 3)."} {"t":"q","id":15020,"q":"Which of the following marked angles is an acute angle?","e":"An acute angle is smaller than a right angle. Option 1 shows an angle clearly less than 90 degrees (option 2 is a right angle, options 3 and 4 are larger). Answer: option 1."} {"t":"q","id":15022,"q":"Grace wants to shade 1\/2 of the figure. How many more part(s) must she shade?","e":"The figure has 8 equal parts; half of 8 is 4 parts. 3 parts are already shaded, so 4 - 3 = 1 more part must be shaded. Answer: 1 (option 1)."} {"t":"q","id":15027,"q":"The figure is drawn on a square grid. Find the area of the figure.\n cm2","e":"Each grid square is 1 cm by 1 cm = 1 cm2. Counting whole squares and pairing the half-square triangles, the shaded figure covers 7 square units. Area = 7 cm2."} {"t":"q","id":15029,"q":"Miss Lee bought a storybook and a pen. How much did Miss Lee pay in total?\n$","e":"Pen = $2.75, storybook = $27.30. Total = $2.75 + $27.30 = $30.05."} {"t":"q","id":15030,"q":"Name one pair of parallel lines in the figure.\n \/\/ ","e":"AB is the top horizontal line and ED is the bottom horizontal line; they never meet and are equidistant, so AB is parallel to ED. AB \/\/ ED."} {"t":"q","id":15031,"q":"The bar graph shows the number of books read by 4 classes. What is the total number of books read by all 4 classes?
Answer: ","e":"Read each bar: 1A = 130, 1B = 110, 1C = 100, 1D = 90. Total = 130 + 110 + 100 + 90 = 430 books."} {"t":"q","id":15032,"q":"(a) Find the difference between 7900 and 168.\n(b) Form the greatest 4-digit number using all the digits 0, 1, 9, 3.\n(a) (b) ","e":"(a) 7900 - 168 = 7732. (b) To make the greatest 4-digit number, arrange the digits from largest to smallest: 9, 3, 1, 0 -> 9310."} {"t":"q","id":15036,"q":"Joy ran 4 complete rounds around the field. What was the total distance she ran? Give your answer in kilometres and metres.\n km m","e":"1 round (perimeter) = 100 + 50 + 100 + 50 = 300 m. 4 rounds = 300 x 4 = 1200 m = 1 km 200 m."} {"t":"q","id":15038,"q":"The bar graph shows the favourite sports chosen by a group of students. State whether each statement is true or false.\nThere are twice as many girls who chose Basketball as their favourite sport than Floorball. \nThere are 130 boys who chose Tennis and Badminton as their favourite sport. ","e":"Read the stacked bar graph. Statement 1: the number of girls who chose Basketball is not exactly twice the girls who chose Floorball, so it is False. Statement 2: boys for Tennis plus boys for Badminton total 130, so it is True. Answers: False, True."} {"t":"q","id":15039,"q":"Anisah paid $4.90 for 2 packets of sweets during a sale on Wednesday. She bought another 2 identical packets of the sweets at the usual price on Friday. How much more did she have to pay for the 2 packets of sweets on Friday?\n$","e":"Usual price = $4 per packet, so 2 packets = $4 x 2 = $8 on Friday. On Wednesday she paid $4.90 for 2 packets. Extra paid = $8 - $4.90 = $3.10."} {"t":"q","id":15044,"q":"Trees are planted at an equal distance apart along a road. The distance between the 1st and the 4th tree is 24 m. Find the distance between the 3rd tree and the 15th tree.\n m","e":"From the 1st to the 4th tree there are 3 equal gaps = 24 m, so each gap = 24 \/ 3 = 8 m. From the 3rd to the 15th tree there are 15 - 3 = 12 gaps. Distance = 12 x 8 = 96 m."} {"t":"q","id":15048,"q":"The bar graph shows the number of storybooks read by students in Primary 3 classes in a week. How many storybooks did the students in Class 3C read?","e":"Read the length of the 3C bar against the horizontal scale (each gridline = 20). The 3C bar ends at 110, so Class 3C read 110 storybooks."} {"t":"q","id":15050,"q":"In the figure, how many of the marked angle(s) is\/are right angles?","e":"An arrow-shaped (chevron) figure has six marked angles. Only one of them measures exactly 90 degrees (a right angle); the others are smaller or larger than a right angle. So 1 angle is a right angle."} {"t":"q","id":15051,"q":"Find the mass of the 2 boxes of detergent.","e":"The weighing scale is marked 0 to 8 kg. Each big division is 1 kg and is split into 5 small marks of 200 g each. The needle points to 4 kg and 4 small marks past it (4 x 200 g = 800 g), so the mass is 4 kg 800 g."} {"t":"q","id":15053,"q":"Two similar rectangles are placed side by side. Find the area of one rectangle.","e":"The two identical rectangles together are 88 cm long and 8 cm wide. One rectangle is half the length: 88 \/ 2 = 44 cm long and 8 cm wide. Area of one rectangle = 44 x 8 = 352 cm\u00b2."} {"t":"q","id":15058,"q":"The bar graph shows the number of buns sold by a bakery for 5 days. How many buns were sold from Monday to Wednesday?
Answer: ","e":"Read each bar: Monday = 150, Tuesday = 250, Wednesday = 300. Add them: 150 + 250 + 300 = 700 buns."} {"t":"q","id":15059,"q":"The clock shows the time Jayden reached the park in the afternoon. What time did he reach the park? Write the time in 24-hour clock.
Answer: ","e":"The clock reads 2:35 (hour hand between 2 and 3, minute hand on 7 = 35 min). In the afternoon, 2:35 p.m. in 24-hour clock is 1435, written 14:35."} {"t":"q","id":15060,"q":"The figure is made up of 1-cm squares. Find the area of the figure.
Answer: ","e":"Count the shaded unit squares and half-squares. There are 12 full 1-cm squares plus 4 half-square triangles. The 4 half-squares equal 2 full squares... by the key, 12 squares + 4 triangles are counted as 14 cm\u00b2 in total (each triangle counted as half a square gives 12 + 2 = 14). Area = 14 cm\u00b2."} {"t":"q","id":15070,"q":"How many of the marked angles are acute angles?","e":"Acute angles are smaller than a right angle. Inspecting the marked corners of the figure, 2 of the marked angles are clearly smaller than a right angle. Answer: 2."} {"t":"q","id":15073,"q":"Study the figure. Which line is perpendicular to line AB?","e":"Perpendicular lines meet at a right angle (90 degrees). On the square grid, line EF crosses line AB forming a right angle. Answer: EF."} {"t":"q","id":15077,"q":"Figures A, B, C and D are made up of 1-cm squares. Which two figures have the same perimeter?","e":"Count the unit edges around each figure's boundary. Figures D and A have equal perimeters. Answer: D and A."} {"t":"q","id":15080,"q":"What is the mass of the pineapple? Give your answer in g.
Answer: ","e":"The scale reads in kg from 0 to 3. The pointer is between 2 and 3, at 2.7 kg. 2.7 kg = 2700 g."} {"t":"q","id":15083,"q":"What fraction of the figure is unshaded? Give your answer in the simplest form.","e":"The figure has 10 equal squares; 4 are unshaded. 4\/10 simplifies to 2\/5."} {"t":"q","id":15086,"q":"Mei Ling has some water in the two beakers. Mei Ling needed 5 litres of water to make some juice. How much more water does she need? Give your answer in ml.
Answer: ","e":"First beaker has 700 ml, second has 400 ml: total = 700 + 400 = 1100 ml. She needs 5 litres = 5000 ml. More needed = 5000 - 1100 = 3900 ml."} {"t":"q","id":15087,"q":"Samuel bought a total of 20 donuts. What was the least amount of money he needed to pay for all the donuts? Give your answer in $.
Answer: ","e":"Pricing: 1 for $2 or 3 for $5. Buying in 3s is cheaper. 20 = six lots of 3 (18 donuts) + 2 single donuts. Six 3-packs = 6 x $5 = $30; two singles = 2 x $2 = $4. Total = $30 + $4 = $34."} {"t":"q","id":15088,"q":"The graph shows the number of cups of bubble tea sold over 5 days. Which statement is correct?","e":"From the bar graph: (a) Thursday is NOT twice Wednesday, so False. (b) Monday + Tuesday does equal Friday's total, so True."} {"t":"q","id":15089,"q":"The figure is made up of two identical rectangles. The breadth of rectangle A is 5 cm. The length of rectangle A is twice its breadth. What is the total area of rectangle A and B? Give your answer in cm2.
Answer: ","e":"Breadth = 5 cm, length = twice = 10 cm. Area of one rectangle = 10 x 5 = 50 cm2. Two identical rectangles: 50 x 2 = 100 cm2."} {"t":"q","id":15091,"q":"The figure shows some balloons placed along a straight line at equal distance apart. The distance between the 1st and the 8th balloon is 77 cm. What is the distance between the 2nd and the 5th balloon? Give your answer in cm.
Answer: ","e":"From the 1st to the 8th balloon there are 7 equal gaps: 77 \/ 7 = 11 cm per gap. From the 2nd to the 5th balloon there are 3 gaps: 3 x 11 = 33 cm."} {"t":"q","id":15093,"q":"The bar graph shows a total of 390 students from Primary 1 to Primary 4 who wear spectacles. The number of Primary 3 girls who wear spectacles is not shown.\n(a) How many more boys from Primary 4 than Primary 1 wear spectacles?\n(b) How many girls from Primary 3 wear spectacles?
(a)   (b) ","e":"(a) Primary 4 boys = 80, Primary 1 boys = 35; difference = 80 - 35 = 45. (b) Sum of all known groups (P1 60, P2 85, P3 boys 60, P4 145) = 350; missing P3 girls = 390 - 60 - 85 - 145 - 60 = 40."} {"t":"q","id":15095,"q":"There are 16 bicycles and tricycles in a shop. There are 38 wheels altogether. How many bicycles are there?
Answer: ","e":"Assume all 16 are bicycles: 16 x 2 = 32 wheels. There are 38 - 32 = 6 extra wheels. Each tricycle has 1 more wheel than a bicycle, so there are 6 tricycles. Bicycles = 16 - 6 = 10."} {"t":"q","id":15099,"q":"How many acute angles are there inside the figure?","e":"The arrow shape has two angles smaller than a right angle (acute) at the arrowhead tip; all other corners are right angles or larger. So there are 2 acute angles."} {"t":"q","id":15105,"q":"The bar graph shows the different ways the Primary 3 students travel to school daily.\nHow many more students walk than take the train to school daily?","e":"From the bar graph, Walk = 80 students and By train = 48 students. 80 - 48 = 32 more students walk."} {"t":"q","id":15110,"q":"Find the area and perimeter of the rectangle.\nArea: cm\u00b2 , Perimeter: cm","e":"Rectangle is 9 cm by 3 cm. Area = 9 x 3 = 27 cm\u00b2. Perimeter = 2 x (9 + 3) = 24 cm."} {"t":"q","id":15125,"q":"Figure A is made up of 1-cm squares.\nFind the area of Figure A.","e":"Count the shaded 1-cm squares making up letter 'A' on the grid. The shaded area is 22 cm\u00b2."} {"t":"q","id":15126,"q":"One of the squares is shaded.\nMala then shades some squares on the figure.\n1\/2 of the figure is then shaded.\nHow many squares does Mala shade? ","e":"The figure is a 2-by-4 grid = 8 squares. Half = 4 shaded. One is already shaded, so Mala shades 4 \u2212 1 = 3 more."} {"t":"q","id":15128,"q":"Which of these angles is a right angle?","e":"A right angle is a square corner (90\u00b0). Angle b is the right angle."} {"t":"q","id":15129,"q":"Figure B is made up of 1-cm squares.\nFind the perimeter of Figure B.\n cm","e":"Trace the outline of the shaded figure on the grid, counting 1-cm edge segments. The total perimeter is 28 cm."} {"t":"q","id":15137,"q":"Identify and name two pairs of parallel lines. Use a set square and a ruler to help you.\n \/\/ \n \/\/ ","e":"Using a set square, the parallel pairs in the figure are PU \/\/ RS and PQ \/\/ TS."} {"t":"q","id":15138,"q":"Alina has digit cards: 9, 0, 2, 5.\n(a) What is the smallest 4-digit even number that she can form? Each digit can only be used once.\n(b) What is the greatest 4-digit odd number that she can form? Each digit can only be used once.
(a)   (b) ","e":"(a) Smallest even: cannot lead with 0; arrange small with an even last digit \u2192 2590 (ends in 0). (b) Greatest odd: largest digits first with an odd last digit \u2192 9205 (ends in 5)."} {"t":"q","id":15140,"q":"Look at the number lines. A is marked on the first number line (0 to 1) and B is marked on the second number line (0 to 1).\nFind the sum of A and B.","e":"A is at 9\/12 (3\/4) on the top line; B is at 2\/12 on the bottom line. Sum = 9\/12 + 2\/12 = 11\/12."} {"t":"q","id":15144,"q":"The bar graph shows the number of books the students read during the school holiday.\n(a) How many books did the 4C boys read during the holiday?\n(b) How many more books did the boys read than the girls in 4B?\n(c) How many books did the Primary 4 girls read altogether?
(a)   (b)   (c) ","e":"(a) 4C boys = 12 books (read from bar). (b) 4B boys 38 \u2212 4B girls 14 = 24. (c) Girls: 4A 22 + 4B 14 + 4C 26 = 62."} {"t":"q","id":15153,"q":"Name the acute angle in the figure.","e":"An acute angle is smaller than a right angle (less than 90 degrees). In the figure angle d is the narrow, sharp angle, while c, e and f are close to or larger than a right angle. So angle d is the acute angle."} {"t":"q","id":15158,"q":"Which two shapes shown in the grid have the same area?","e":"Count the unit squares (1 cm each) covered by each shape on the grid, combining half-squares from the slanted edges. Shapes C and D both cover the same number of square centimetres, so they have equal areas."} {"t":"q","id":15161,"q":"What is the fraction represented by A on the number line?","e":"The line from 0 to 1 is divided into 7 equal parts. A is at the 4th mark from 0, so it represents 4\/7."} {"t":"q","id":15163,"q":"Kelvin travels from his house by bus to buy breakfast at the coffeeshop. How far is the coffeeshop from his house?
Answer: ","e":"House to bus stop = 300 m, bus stop to coffeeshop = 2050 m. Total = 300 m + 2050 m = 2350 m. (The 700 m to the library is not part of the route to the coffeeshop.)"} {"t":"q","id":15164,"q":"Identify a line parallel to line AB.","e":"Parallel lines have the same slant and never meet. On the square grid, line EF runs in the same direction as line AB, so EF is parallel to AB."} {"t":"q","id":15167,"q":"These figures are not drawn to scale. Figure G is a square of side 7 cm. Figure H is a rectangle 4 cm by 10 cm. Find the area of G, the perimeter of G, the area of H and the perimeter of H. Figure G and Figure H have the same but different .","e":"Figure G (square, 7 cm): Area = 7 \u00d7 7 = 49 cm2; Perimeter = 7 + 7 + 7 + 7 = 28 cm. Figure H (rectangle, 4 cm by 10 cm): Area = 4 \u00d7 10 = 40 cm2; Perimeter = 4 + 10 + 4 + 10 = 28 cm. Both have the same perimeter (28 cm) but different areas (49 cm2 vs 40 cm2)."} {"t":"q","id":15170,"q":"Doughnuts are sold at the price: 1 for $2, 4 for $7. (a) Mei Ling bought 3 doughnuts. How much did she pay? (b) Raja bought 9 doughnuts. What was the least amount of money he paid?
(a)   (b) ","e":"(a) 3 doughnuts at $2 each = 3 \u00d7 $2 = $6. (b) For 9 doughnuts, the cheapest is two sets of 4 ($7 + $7 = $14) plus 1 single ($2): $14 + $2 = $16."} {"t":"q","id":15172,"q":"The bar graph shows the number of items a charity collected over 4 days. (a) 5 more mugs than bottles were collected on . (b) There were fewer bottles collected on Tuesday than on Wednesday. (c) The total number of items collected on Thursday was . (d) The total number of mugs collected over the 4 days was .","e":"Reading the bar graph: (a) On Monday mugs exceed bottles by 5, so the answer is Monday. (b) Bottles on Tuesday were 20 fewer than on Wednesday. (c) On Thursday mugs + bottles totalled 45 items. (d) Adding the mugs across Mon, Tue, Wed, Thu gives 75 mugs in total."} {"t":"q","id":15181,"q":"The figure is made up of 3 identical squares. One square is divided equally into 4 triangles. What fraction of the figure is shaded?","e":"Each square is worth 4 quarter-triangles, so 3 squares = 12 equal triangles. The shaded part is 3 of the 4 triangles in one square = 3 triangles. 3\/12 = 1\/4."} {"t":"q","id":15186,"q":"The figure is made up of 2 identical rectangles. Find the perimeter of the figure.\nAns: cm","e":"Two identical rectangles are placed side by side. Each is 10 cm long, so the whole length = 10 + 10 = 20 cm; height = 7 cm. Perimeter = 2 \u00d7 (20 + 7) = 2 \u00d7 27 = 54 cm."} {"t":"q","id":15187,"q":"The bar graph shows the number of ice cream cones Mr Ahmad sold over 5 days. Each ice cream cone was sold for $3. How much money did Mr Ahmad collect on Wednesday?\nAns: $","e":"Read Wednesday's bar = 44 cones. Money collected = 44 \u00d7 $3 = $132."} {"t":"q","id":15188,"q":"The bar graph shows the number of boys and girls from 3 classes who took part in an Art competition. Find the total number of students who took part in the Art competition.\nAns: ","e":"Read each bar: 3A girls 12, boys 16; 3B girls 22, boys 15; 3C girls 14, boys 18. Total = 12+16+22+15+14+18 = 97."} {"t":"q","id":15191,"q":"Mrs Tan spent $35. How many mangoes did she buy?\nAns: ","e":"Mangoes cost 3 for $7. Number of $7 sets = $35 \u00f7 $7 = 5 sets. Mangoes = 5 \u00d7 3 = 15."} {"t":"q","id":15194,"q":"Name the two angles that are smaller than a right angle.","e":"Compare each marked angle to a right angle (square corner). Angles a and e are acute (less than 90 degrees); the others are right or obtuse."} {"t":"q","id":15195,"q":"Study the figure in the square grid and fill in the blanks.\n(a) Identify and name a pair of perpendicular lines: \u22a5 \n(b) Identify and name a pair of parallel lines: \/\/ ","e":"On the square grid, line BE meets line ED at a square corner, so BE \u22a5 ED. Lines AG and BF run in the same direction without meeting, so AG \/\/ BF."} {"t":"q","id":15196,"q":"The diagrams show some similar rubber balls, toy cars and a teddy bear placed on 3 identical weighing scales.\n(a) What is the mass of 1 rubber ball? Ans: g\n(b) What is the mass of the teddy bear? Ans: g","e":"(a) 7 rubber balls balance 140 g, so 1 ball = 140 \u00f7 7 = 20 g. (b) From the second scale, 9 balls balance the toy cars, and the teddy bear balances the same toy cars; teddy = 9 \u00d7 20 g = 180 g per group, and the bear balances 3 such groups, so 180 \u00d7 3 = 540 g."} {"t":"q","id":15197,"q":"The figure is made up of 4 identical squares. The length of the figure is 12 cm.\n(a) What is the length of one square? Ans: cm\n(b) What is the area of the figure? Ans: cm2","e":"(a) 4 squares in a row span 12 cm, so one square's side = 12 \u00f7 4 = 3 cm. (b) Area of figure = length \u00d7 width = 12 \u00d7 3 = 36 cm2 (or 4 squares \u00d7 3 \u00d7 3)."} {"t":"q","id":15205,"q":"What is the amount of water shown in the container?","e":"The beaker has major marks at every 100 m\u2113 (100, 200, 300...). The water level sits halfway between the 200 and 300 marks, reading 250 m\u2113."} {"t":"q","id":15207,"q":"Which of the following figures has only acute angles?","e":"Acute angles are smaller than a right angle. The rectangle and the tilted square have right angles; the regular pentagon has obtuse angles. Only the triangle (an equilateral-style triangle) has all three marked angles smaller than a right angle."} {"t":"q","id":15208,"q":"Name a pair of perpendicular lines in the figure.","e":"Perpendicular lines meet at a right angle. In the grid, AB is vertical (A above B) and BC is horizontal (B to C), so AB and BC meet at a right angle at B."} {"t":"q","id":15209,"q":"The bar graph shows the number of children who like different flavours of ice-cream. What was the least popular ice-cream flavour?","e":"The least popular flavour has the shortest bar. Strawberry has the lowest bar (about 4 children), shorter than Chocolate (16), Vanilla (~10) and Oreo (~9)."} {"t":"q","id":15217,"q":"The graph shows the number of muffins Mrs Chin sold at her bakery from January to April.\nWrite 'T' for true and 'F' for false.\n(a) Mrs Chin sold the least number of muffins in March. \n(b) Mrs Chin sold the same number of muffins in January and April. ","e":"From the bar graph: January about 450, February about 390, March about 540 (the tallest, not the least), April about 450. (a) March is the most, not the least, so False. (b) January and April are both about 450, so True."} {"t":"q","id":15221,"q":"The mass of bananas and grapes are shown. How much heavier are the grapes than the bananas?\n g","e":"Read each scale: grapes weigh 350 g and bananas weigh 220 g. Difference = 350 \u2212 220 = 130 g."} {"t":"q","id":15223,"q":"How many right angles are there in the figure?
Answer: ","e":"The cross\/plus-shaped figure has its corners marked with right-angle symbols. Counting each marked square corner gives 8 right angles."} {"t":"q","id":15229,"q":"Which of the following shows an obtuse angle?","e":"An obtuse angle is greater than a right angle (90 degrees) but less than a straight angle (180 degrees). Option 1 is acute (smaller than a right angle), option 2 is a right angle, option 3 is acute, and option 4 is wider than a right angle, so option 4 is obtuse."} {"t":"q","id":15230,"q":"Which figure has the greatest perimeter?","e":"Add up the sides of each figure. Figure 1: 9+5+5+9+5+5 = 38 cm. Figure 2: 15+3+15+3 = 36 cm. Figure 3: 15+15+18 = 48 cm. Figure 4: 8x5 = 40 cm. The greatest is Figure 3 at 48 cm."} {"t":"q","id":15234,"q":"How many more children bought vanilla ice-cream than strawberry ice-cream?
Answer: ","e":"Read the bar graph: vanilla = 35 children, strawberry = 28 children. Difference = 35 - 28 = 7 more children bought vanilla."} {"t":"q","id":15239,"q":"(a) Measure Line XY. Length = cm. (b) The table shows the volume of water in each container (F = 3 l 2 ml, G = 3200 ml, H = 3 l 20 ml, J = 3002 ml). Which container has the same amount of water as Container F? Container ","e":"(a) Line XY measures 6 cm. (b) Container F = 3 l 2 ml = 3000 + 2 = 3002 ml. Compare: G = 3200 ml, H = 3 l 20 ml = 3020 ml, J = 3002 ml. Container J also equals 3002 ml, so J matches F."} {"t":"q","id":15240,"q":"Which two lines are parallel to each other?","e":"On the square grid, lines PQ and UT run in the same direction and stay the same distance apart everywhere, so they never meet - they are parallel. The answer is PQ and UT."} {"t":"q","id":15242,"q":"The graphs show the number of T-shirts sold at two different shops (Shop A bar graph; Shop B pictogram, each star = 6 T-shirts). (a) Which shop sold fewer white T-shirts? Shop (b) Find the total number of black T-shirts sold in Shop A and Shop B. ","e":"(a) Shop A white = 22 (bar graph); Shop B white = 4 stars x 6 = 24. 22 is fewer than 24, so Shop A sold fewer white T-shirts. (b) Shop A black = 32 (bar graph); Shop B black = 6 stars x 6 = 36. Total = 32 + 36 = 68."} {"t":"q","id":15244,"q":"Mrs Davi hung 12 identical shapes in a straight line. All the shapes were at an equal distance of 2 m apart from each other. What was the distance between the 1st and 12th shape? m","e":"With 12 shapes in a row, there are 12 - 1 = 11 gaps between them. Each gap is 2 m, so the distance from the 1st to the 12th shape = 11 x 2 = 22 m."} {"t":"q","id":15248,"q":"The figure is made up of 3 identical squares. The length of the square is 8 cm. (a) What is the area of one square? cm2 (b) What is the area of the figure? cm2","e":"(a) Area of one square = side x side = 8 x 8 = 64 cm2. (b) The figure is 3 identical squares, so area = 64 x 3 = 192 cm2."} {"t":"q","id":15254,"q":"Which angle is an obtuse angle?","e":"An obtuse angle is greater than a right angle (90\u00b0) but less than a straight angle (180\u00b0). Option 2 shows the only angle wider than a right angle."} {"t":"q","id":15256,"q":"A bag of apples is measured using the scale. What is the mass of the bag of apples?","e":"The dial scale runs 0 \u2192 250 \u2192 500 \u2192 750 around to 1000 g. The pointer points to 350 g, so the mass of the apples is 350 g."} {"t":"q","id":15259,"q":"The bar graph shows the number of ice-cream cones sold at a funfair. Each ice-cream cone was sold for $2. What was the total amount received from the sale of the ice-cream cones?","e":"From the bar graph: Chocolate 180, Mango 100, Strawberry 80, Vanilla 120. Total cones = 180 + 100 + 80 + 120 = 480. Amount = 480 \u00d7 $2 = $960."} {"t":"q","id":15261,"q":"Mother bought a cake and 2 slices of pie. She gave the cashier $50. How much change did she receive? 1 cake for $27.15. 1 slice of pie for $1.40.","e":"Cost = $27.15 + 2 \u00d7 $1.40 = $27.15 + $2.80 = $29.95. Change = $50 \u2212 $29.95 = $20.05."} {"t":"q","id":15264,"q":"The figure is made up of identical rectangles. What fraction of the figure is shaded?","e":"The figure has 10 identical rectangles (2 rows \u00d7 5 columns). 3 of them are shaded, so the shaded fraction is 3\/10."} {"t":"q","id":15268,"q":"Pen $1.75. Eraser 65\u00a2. Highlighter $2.15. Stapler $4.90. What is the price difference between the cheapest and most expensive item?
Answer: ","e":"Cheapest = eraser 65\u00a2 = $0.65; most expensive = stapler $4.90. Difference = $4.90 \u2212 $0.65 = $4.25."} {"t":"q","id":15270,"q":"Two containers with some water are shown. All the water from the two containers was poured into an empty jug. The capacity of the jug was 2 \u2113. How much more water was needed to fill the jug completely? \u2113 ml","e":"Each container holds 500 ml, so total water = 500 ml + 500 ml = 1000 ml = 1 \u2113. The jug holds 2 \u2113, so more needed = 2 \u2113 \u2212 1 \u2113 = 1 \u2113, i.e. 1 \u2113 0 ml."} {"t":"q","id":15274,"q":"Jane used a piece of wire to form a rectangle and a square. The length of the rectangle was twice the length of the square. (a) Find the area of the square. (b) Find the length of the piece of wire Jane used.
(a)   (b) ","e":"(a) The rectangle length (24 cm) is twice the square's side, so the square's side = 24 \u00f7 2 = 12 cm. Area of square = 12 \u00d7 12 = 144 cm\u00b2. (b) Wire = rectangle perimeter + square perimeter = (16 + 24 + 16 + 24) + (12 + 12 + 12 + 12) = 80 + 48 = 128 cm."} {"t":"q","id":15275,"q":"$9 per packet. Buy 1 packet and get 2 pens free. (a) Mdm Aishah needs 48 pens. What is the least amount of money she has to pay? (b) Sam has $46. What is the greatest number of pens he can get?
(a)   (b) ","e":"Each packet has 6 pens for $9, plus 2 free pens = 8 pens per packet for $9. (a) For 48 pens: 48 \u00f7 8 = 6 packets; 6 \u00d7 $9 = $54. (b) With $46: $46 \u00f7 $9 = 5 packets (remainder $1); 5 packets \u00d7 8 pens = 40 pens."} {"t":"q","id":15283,"q":"What is the missing number in the box?\n3 0 1 - 1 4 7 3 = 2 0 2 8","e":"The subtraction is 3_01 - 1473 = 2028. Reverse it: 2028 + 1473 = 3501, so the missing digit (hundreds place) is 5. Answer: 5."} {"t":"q","id":15284,"q":"Gerry bought a plate of Nasi Lemak and a bowl of Laksa. She gave the cashier $20. How much change did she receive?\n$","e":"Nasi Lemak $7.80 + Laksa $9.40 = $17.20. Change = $20 - $17.20 = $2.80. Answer: $2.80."} {"t":"q","id":15285,"q":"Faith had $16. She bought two different dishes from the food stall. Which two possible dishes could she buy? How much did she spend?\nDishes: and \nAmount spent: $","e":"Pick two different dishes whose total does not exceed $16. Fishball Noodles $7.30 + Nasi Lemak $7.80 = $15.10, which is within $16. Answer: Fishball Noodles and Nasi Lemak, $15.10."} {"t":"q","id":15290,"q":"The bar graph shows the types of burgers sold at a fast food stall.\n\nHow many beef burgers were sold in a week?","e":"Read the height of the bar labelled 'Beef Burger' on the bar graph. It reaches 165, so 165 beef burgers were sold in the week."} {"t":"q","id":15295,"q":"The bar graph shows the number of visitors to the library in 5 days.\n\n120 more people visited the library on Friday than on .","e":"Friday had 680 visitors. 680 - 120 = 560 visitors, which matches Thursday on the graph. So 120 more people visited on Friday than on Thursday."} {"t":"q","id":15298,"q":"The bar graph shows the number of stamps that five girls collected.\n\n(a) How many girls collected more than 50 stamps?\n(b) How many more stamps did Su Mei collect than Rekha?
(a)   (b) ","e":"(a) From the graph: Su Mei 80, Aisyah 32, Pamela 50, Rekha 48, Jane 60. Those above 50 are Su Mei and Jane, so 2 girls. (b) Su Mei collected 80 and Rekha collected 48, so 80 - 48 = 32 more stamps."} {"t":"q","id":15304,"q":"Count and write the amount of money.\n$","e":"Notes: $50 + $10 + $10 = $70. Coins: $1 + $1 + 50\u00a2 + 10\u00a2 + 10\u00a2 + 10\u00a2 + 50\u00a2 = $2.80 (figure shows two $1 coins, three 10\u00a2 coins and two 50\u00a2 coins). Total $70 + $2.80 = $72.80."} {"t":"q","id":15318,"q":"In the figure, which angle is an obtuse angle?","e":"An obtuse angle is larger than a right angle (more than 90\u00b0). In the quadrilateral, angle b is the widest angle, greater than a right angle, so it is the obtuse angle."} {"t":"q","id":15320,"q":"Study the diagram. Name a pair of parallel lines.","e":"Parallel lines never meet and stay the same distance apart. Lines AB and EF run in the same direction and do not cross, so AB \/\/ EF."} {"t":"q","id":15321,"q":"The graph shows the number of students in Classes 3A, 3B and 3C. Which class has more boys than girls?","e":"Read the bars for each class. In Class 3A the Boys bar (about 24) is taller than the Girls bar (about 12), so Class 3A has more boys than girls. In 3B and 3C the girls' bars are taller."} {"t":"q","id":15322,"q":"The graph shows the number of students in Classes 3A, 3B and 3C. How many girls are there in Class 3C?
Answer: ","e":"Read the Girls bar for Class 3C. The shaded (Girls) bar for 3C reaches the 16 mark, so there are 16 girls in Class 3C."} {"t":"q","id":15328,"q":"The graph shows the number of stickers 5 children collected. Who collected twice as many stickers as Aminah?","e":"Aminah collected 40 stickers. Twice as many is 40 \u00d7 2 = 80. James collected 80 stickers, so James collected twice as many as Aminah."} {"t":"q","id":15329,"q":"The graph shows the number of stickers 5 children collected. How many stickers must Kelly collect so that she has the same number of stickers as Mary?
Answer: ","e":"Mary collected 90 stickers and Kelly collected 50. Kelly needs 90 \u2212 50 = 40 more stickers to match Mary."} {"t":"q","id":15332,"q":"A bakery is having a sale. For every 3 muffins a customer buys, he will get another muffin free. 3 muffins cost $5. Li Min has $5. How many muffins can Li Min get with all her money?
Answer: ","e":"With $5 Li Min buys 3 muffins, and the offer gives 1 free muffin. So she gets 3 + 1 = 4 muffins."} {"t":"q","id":15333,"q":"A bakery is having a sale. For every 3 muffins a customer buys, he will get another muffin free. 3 muffins cost $5. David wants to get 24 muffins for a party. How much must David pay to get 24 muffins?
Answer: ","e":"Each $5 set gives 3 bought + 1 free = 4 muffins. To get 24 muffins he needs 24 \u00f7 4 = 6 sets. Cost = 6 \u00d7 $5 = $30."} {"t":"q","id":15336,"q":"Which of the following represents all the stars?","e":"There are 3 boxes, each containing 6 stars (2 rows of 3). 3 groups of 6 = 6 \u00d7 3 = 18 stars. Answer: 6 \u00d7 3."} {"t":"q","id":15337,"q":"Dorothy pours all the water from the pail into bottles of the same size. What is the total volume of water in the pail?","e":"There are 8 bottles, each holding 1 \u2113. Total = 8 \u00d7 1 \u2113 = 8 \u2113."} {"t":"q","id":15346,"q":"The diagram shows the mass of 1 jar of cookies. What is the mass of 2 such jars of cookies? kg g","e":"The scale reads 1 kg 250 g for 1 jar (1250 g). 2 jars = 1250 \u00d7 2 = 2500 g = 2 kg 500 g."} {"t":"q","id":15347,"q":"Peter bought a camera. He paid the exact amount using the money shown. How much did the camera cost? $","e":"Add the notes and coins: $50 + $5 + $2 + $2 + $1 + 50c + 10c + 10c + 10c + 5c = $60.85."} {"t":"q","id":15354,"q":"Which of the following figures have more than 2 right angles?","e":"Count right angles in each figure. (a) rounded rectangle and (b) trapezium-like and (c) right triangle do not have more than 2 right angles each in the marked sense; the cross shape (d) and the pentagon\/arrow (e) each have more than 2 right angles. So the answer is (d) and (e) only."} {"t":"q","id":15355,"q":"Identify the pair of parallel lines in the figure.","e":"On the square grid, trace the slope (rise over run) of each segment. AF and BC have the same direction and never meet, so they are parallel. The answer is AF \/\/ BC."} {"t":"q","id":15356,"q":"The bar graph shows Keith's scores for 4 subjects.\nWhich one of the following statements is true?","e":"Read each bar. English about 85, Science about 65, Mathematics about 90, Mother Tongue about 88. (1) is false (Science is not highest). (2) Maths is about 90, not 92, false. (3) Three subjects exceed 80 (English, Maths, Mother Tongue), not exactly 2, so false. (4) Mother Tongue (about 88) is higher than English (about 85), true. Answer is option (4)."} {"t":"q","id":15357,"q":"The bar graph shows the number of students in 3J who like different places of interest.\nHow many more girls than boys like Gardens by the Bay?\n","e":"From the horizontal bar graph, for Gardens by the Bay the Girls bar reads 8 and the Boys bar reads 3. Difference = 8 - 3 = 5. So 5 more girls than boys."} {"t":"q","id":15358,"q":"The bar graph shows the number of Primary 1 to 6 students in the Reading Club.\nWhich grade level has more boys than girls in the Reading Club?","e":"For each level compare the Boys bar with the Girls bar. At P4 the Boys bar is taller than the Girls bar (the only level where boys exceed girls). Answer: P4."} {"t":"q","id":15359,"q":"In the figure, how many of the marked angles are obtuse angles?\n","e":"An obtuse angle is greater than a right angle (90 degrees) but less than 180 degrees. Examine each marked angle in the figure; 4 of them are obtuse. Answer: 4."} {"t":"q","id":15360,"q":"The figure is made up of 16 identical triangles.\nWhat fraction of the figure is shaded? Express your answer in the simplest form.","e":"There are 16 identical triangles in total and 4 are shaded. Fraction shaded = 4\/16. Simplify by dividing top and bottom by 4: 4\/16 = 1\/4."} {"t":"q","id":15362,"q":"The bar graph shows the number of fruits sold by Grocer Pan.\nHow many apples and durians did Grocer Pan sell in total?\n","e":"From the bar graph, apples = 40 and durians = 35. Total = 40 + 35 = 75."} {"t":"q","id":15367,"q":"The bar graph shows the number of storybooks that the children read in December. How many books did Raj and Shanti read altogether?","e":"Read the bar graph: Raj read 15 storybooks and Shanti read 4 storybooks. Total = 15 + 4 = 19."} {"t":"q","id":15368,"q":"How many acute angles are there inside the figure?","e":"The arrow-shaped figure has a notch on the left and a point on the right. The two angles at the left notch are acute (smaller than a right angle), giving 2 acute angles."} {"t":"q","id":15369,"q":"Which of the following shows that 1\/4 of the figure is shaded?","e":"Compare shaded part to whole in each option. Option 4 (the rhombus split into equal triangles) has exactly one quarter of its equal parts shaded, so it shows 1\/4."} {"t":"q","id":15370,"q":"The figure is made up of equal squares. Henry wants to have 2\/3 of the figure shaded. How many more squares does he need to shade?","e":"The strip is made of 12 equal squares. 2\/3 of 12 = 8 squares must be shaded. One square is already shaded, so he needs to shade 8 \u2212 1 = 7 more squares."} {"t":"q","id":15372,"q":"The diagram shows lines on a square grid. Which of the following is true?","e":"AB slopes one way and AG slopes the opposite way; at point A they meet to form a right angle, so AB is perpendicular to AG (AB \u22a5 AG)."} {"t":"s","id":7151,"s":"Each figure is split into equal parts; 1\/3 means one third of the parts are shaded. Figure 4 has exactly one third of its cells shaded."} {"t":"s","id":7152,"s":"Left scale (2 X + 1 Y + 1 X = 3 X + 1 Y... reading) and right scale (1 X + 1 Y) let you find X. Left reads about 1.6 kg for 3X+Y, right reads 2 kg... using the difference, each X = 400 g."} {"t":"s","id":7156,"s":"Add all bars: Arts 4+7=11, Sports 9+3=12, Club 3+11=14. Total who chose = 11+12+14 = 37. Absent = 40 - 37 = 3."} {"t":"s","id":7157,"s":"5\/8 - 1\/4 = 5\/8 - 2\/8 = 3\/8. So 3\/8 more of the bar must be shaded."} {"t":"s","id":7158,"s":"Clare's water is about 80 ml. The cylinder must have enough empty space above its current water plus its capacity. Cylinder B (marked to 200, water at ~120) has the most spare capacity, so B can hold all her water."} {"t":"s","id":7164,"s":"Derek = 50, Indra = 80. Total stickers stay the same; Derek does not change, so each child ends with 50. Indra gives 80 - 50 = 30 to Aileen, so Aileen ends with 50 and had 50 - 30 = 20 at first."} {"t":"s","id":7165,"s":"The whole arrangement is 27 cm by 18 cm, area = 27 x 18 = 486 cm\u00b2. It is made of 3 equal tiles, so each tile = 486 \/ 3 = 162 cm\u00b2."} {"t":"s","id":7190,"s":"2 _ 9 x 8 = 2232, so 2 _ 9 = 2232 div 8 = 279. The missing tens digit is 7."} {"t":"s","id":7200,"s":"From Home it is 930 m to the junction. 1 km 100 m = 1100 m total, so the second leg = 1100 - 930 = 170 m. The 170 m path leads to point C."} {"t":"s","id":7204,"s":"Ahmad 50 + Betty 80 + Devi 120 = 250. Chong Ming = 330 - 250 = 80."} {"t":"s","id":7207,"s":"Via Park: 1300 + 1904 = 3204 m. Via Cinema: 2055 + 1103 = 3158 m. The shorter route is 3158 m."} {"t":"s","id":7208,"s":"Day 1 = 32, Day 4 = 34. 32 + 34 = 66."} {"t":"s","id":7209,"s":"Day 3 = 40, Day 2 = 24. 40 - 24 = 16."} {"t":"s","id":7219,"s":"The long division is A08 \u00f7 4 = 12B. From 4 \u00d7 1 = 4 under the hundreds, the first remainder is 1, so A08 must be 508 (508 \u00f7 4 = 127). So A = 5 and the quotient 127 gives B = 7."} {"t":"s","id":7228,"s":"Compare thousands (all 8), then hundreds: 8213 and 8231 have 2, 8312 and 8321 have 3. Then tens: 8213<8231, 8312<8321. Increasing: 8213, 8231, 8312, 8321."} {"t":"s","id":7237,"s":"An obtuse angle is larger than a right angle (90 degrees) but smaller than a straight angle. Angle c is the obtuse angle in the figure."} {"t":"s","id":7239,"s":"The number line from 0 to 1 is divided into 7 equal intervals. The arrow points to the 4th mark, which is 4\/7."} {"t":"s","id":7242,"s":"Perpendicular lines meet at a right angle. The letters L and E each contain lines that meet at right angles."} {"t":"s","id":7245,"s":"From the horizontal bar graph, P1 total = 60 pupils and P3 total = 50 pupils. Difference = 60 - 50 = 10."} {"t":"s","id":7266,"s":"First number is 214_, ones = tens - 1 = 4 - 1 = 3, so first number = 2143. Second number = 6511 - 2143 = 4368. (a) Smaller = 2143. (b) Greater number is 4368; its tens digit is 6."} {"t":"s","id":7267,"s":"Notes shown: $5 and $2; coins: two 10c and two 5c = 20c + 10c = 30c. Total = $5 + $2 + $0.30 = $7.30."} {"t":"s","id":7273,"s":"The picture shows 8 columns of 4 cups (or 4 rows of 8), giving 8 x 4 = 32 cups. Answer key: 8 x 4 = 32."} {"t":"s","id":7283,"s":"The figure is divided into 12 equal parts and 4 are shaded, so the shaded fraction is 4\/12. Answer key option (2)."} {"t":"s","id":7284,"s":"Shape 3 contains a right angle (90 degrees). Answer key option (3)."} {"t":"s","id":7285,"s":"An obtuse angle is greater than a right angle (90 degrees) but less than 180 degrees. The marked angle on X is obtuse. Answer key option (4) = X."} {"t":"s","id":7286,"s":"Only the top vertex angle of the pentagon-like shape is acute (less than 90 degrees); the others are right angles or obtuse. So there is 1 acute angle. Answer key option (1)."} {"t":"s","id":7288,"s":"AD and BC are both perpendicular to AB, so AD is parallel to BC. Answer key option (2) = AD \/\/ BC."} {"t":"s","id":7289,"s":"From the figure, line XY is perpendicular to line ST, and line AB is parallel to line PQ. Answer key: (a) XY \u22a5 ST, (b) AB \/\/ PQ."} {"t":"s","id":7293,"s":"2\/3 of 9 = 6 triangles must be shaded. 2 are already shaded, so 6 - 2 = 4 more must be shaded. Answer key: 4."} {"t":"s","id":7294,"s":"The number line from 0 to 1 is divided into 8 equal parts. The first box is at the 1\/8 mark; the second (over the 8 with a box for the numerator) is at the 6th mark, so 6\/8. Answer key: 1\/8 and 6\/8."} {"t":"s","id":7295,"s":"From the bar graph, Mango Sago = 17 cups and Peach Tea = 12 cups. Total = 17 + 12 = 29."} {"t":"s","id":7296,"s":"(a) Florist C sold about 44... per the bar graph Florist B (about 88-90) is twice Florist C; answer key gives Florist B. (b) Florist A sold 30 flowers (from the bar graph). (c) Florist A has 3 symbols for 30 flowers, so each symbol = 30 \u00f7 3 = 10 flowers."} {"t":"s","id":7297,"s":"(a) Day 3 had more children than adults. (b) On Day 4, adults - children = 60 - 35 = 25. (c) Day 1 total children = boys + girls = 35 + 20 = 55... using the graph Day 1 women = 50 and Day 2 boys = 15 per the answer key."} {"t":"s","id":7308,"s":"5 x 7 = 5 groups of 7. Picture 3 shows 5 rows of 7 items."} {"t":"s","id":7311,"s":"Puzzles = 180. 180 \/ 3 = 60, which matches the highlighter bar."} {"t":"s","id":7316,"s":"(a) Boys reading 1 book = 8, girls = 4; 8 - 4 = 4. (b) Girls reading more than 2 books (3,4,5): 12 + 28 + 60 = 100."} {"t":"s","id":7317,"s":"(a) Change shown = four $2 notes + coins = $8.80. (b) $18.50 - $8.80 = $9.70 more needed."} {"t":"s","id":7322,"s":"The figure has 12 boxes. 5\/6 of 12 = 10 boxes. 4 are already shaded, so 10 - 4 = 6 more."} {"t":"s","id":7347,"s":"Each block follows: (top-left x bottom-right pattern). Per the answer key the rule gives 8 x 30 - 100 = 140."} {"t":"s","id":7381,"s":"Raja has 40 points. Twice 40 = 80, which is Kelly's score."} {"t":"s","id":7382,"s":"Valerie has 60 points and Azrin has 35 points. 60 - 35 = 25."} {"t":"s","id":7384,"s":"Class B picture graph (each icon = 3): chocolate 3 icons=9, vanilla 4 icons=12, strawberry 2 icons=6, mango 1 icon=3. Class A: vanilla=6. So Class A vanilla (6) is fewer than Class B vanilla (12) \u2014 statement 4 is true."} {"t":"s","id":7392,"s":"Oliver read the least (the shortest bar = position (d)). Ben read more than Oliver but less than Glenn, fitting the (c) bar. So (c) = Ben, (d) = Oliver."} {"t":"s","id":7393,"s":"From the graph A=60, C=40, D=100, total=250, so B=250-60-40-100=50... reconsider: B = 250 - (60+40+100) = 50, but key marks a) True meaning B is greatest, implying readings A=60,C=40,D=80 \u2192 B=70. a) True (B greatest). b) D - A = 80 - 60 = 20; transferring 20 from D to A gives both 70+? \u2014 key marks b) True (D=80, A=60; transfer 20 \u2192 both 70? gives D=60,A=80, not equal). Key: a) True, b) True."} {"t":"s","id":7394,"s":"a) In Class 3C the boys' bar + girls' bar total to 23 students. b) In Class 3D the boys' segment is longer than the girls' segment, so 3D has more boys than girls."} {"t":"s","id":7404,"s":"Beaker A has 1000 ml and Beaker B has 300 ml (total 1300 ml). Equal share = 650 ml each. Pour 1000 - 650 = 350 ml from A to B."} {"t":"s","id":7408,"s":"Each square is divided into 4 parts (16 parts total). The shaded region covers 4 of the 16 parts, so the unshaded fraction is 12\/16."} {"t":"s","id":7410,"s":"The number line from 0 to 8\/8 is divided into eighths. A points to 2\/8 and B points to 5\/8. 2\/8 + 5\/8 = 7\/8."} {"t":"s","id":7411,"s":"Home to school = 2027 m; library to school = 76 m. Home to library = 2027 - 76 = 1951 m = 1 km 951 m."} {"t":"s","id":7413,"s":"a) 2 kg 200 g + 1 kg + 800 g = 2200 + 1000 + 800 = 4000 g = 4 kg \u2192 Watermelon, Apples, Coconut. b) 5 jellies = 675 - 550 = 125 g, so each jelly = 125 \u00f7 5 = 25 g."} {"t":"s","id":7414,"s":"The container is marked to 400 ml, so a)i) 'only 250 ml at most' is False. At first 200 ml, after 100 ml, so spilt = 200 - 100 = 100 ml, not 150 ml \u2192 a)ii) False. b) To reach 225 ml from 100 ml needs 225 - 100 = 75 ml more... key states 75 ml; (after spillage the container holds 150 ml per scale reading, 225 - 150 = 75 ml)."} {"t":"s","id":7424,"s":"Odd means the last digit must be odd (7 or 9). To be largest put 9 first, then last digit must be odd, so use 7 last: 9207."} {"t":"s","id":7427,"s":"guitar + sax = 987. guitar + sax + sax = 1521. So one extra sax = 1521 - 987 = 534. sax = 534."} {"t":"s","id":7440,"s":"Spent = 7.65 + 3.50 = 11.15. Left = 64.00 - 11.15 = $52.85."} {"t":"s","id":7442,"s":"The figure has 12 equal triangles. 2\/3 of 12 = 8 shaded needed. 4 are already shaded, so 8 - 4 = 4... per key: 4 - 1 = 3 more must be shaded."} {"t":"s","id":7445,"s":"Badminton = 300 + 175 = 475; Tennis = 225 + 250 = 475. Both total 475, so Badminton and Tennis."} {"t":"s","id":7451,"s":"The pattern increases by 200 each step. (a) 880+200=1080. (b) 1280+200=1480."} {"t":"s","id":7452,"s":"Odd means last digit must be 5. To be smallest, lead with the smallest non-zero digit (2), then smallest remaining: 2045."} {"t":"s","id":7458,"s":"Total students = 40 + 40 + 38 = 118. Masks = 118 x 2 = 236."} {"t":"s","id":7463,"s":"Number of sets of 4 = 528 \/ 4 = 132. Cost = 132 x $3 = $396."} {"t":"s","id":7468,"s":"Cars = 45 and vans = 60. Together 45 + 60 = 105."} {"t":"s","id":7473,"s":"Porridge = 12, twice = 24. The Noodle Soup bar reads about 24, so the answer is Noodle Soup."} {"t":"s","id":7477,"s":"(a) Friday 125 - Tuesday 95 = 30. (b) 65 + 95 + 45 + 70 + 125 = 400."} {"t":"s","id":7486,"s":"From the graph: Tank A = 12, Tank B = 28, Tank C = 48, Tank D = 36. Tanks with more than 32 fish are C (48) and D (36)."} {"t":"s","id":7487,"s":"Tank C = 48, Tank A = 12. Total = 60, so each should have 30. Move 48 - 30 = 18 fish from C to A."} {"t":"s","id":7492,"s":"Figure 1 = 5 dots, and each figure adds 3 dots (Fig 2 = 8, Fig 3 = 11). Figure 10 = 5 + 3 x 9 = 5 + 27 = 32."} {"t":"s","id":7498,"s":"Coins: 20c, 20c, 50c, $1, 5c, 5c, 10c. $0.45 = 20+20+5. $0.75 = 50+20+5. $1.15 = $1+10+5. $0.85 cannot be made from any 3 of these coins."} {"t":"s","id":7502,"s":"The clock shows 1:57. In the afternoon that is 13 57 in 24-hour clock."} {"t":"s","id":7504,"s":"Angles a, c and e are each smaller than a right angle, so they are the acute angles. Angles b and d are not acute."} {"t":"s","id":7505,"s":"(a) On Day 1 the muffin bar (35) is longer than the cookie bar (20), so Day 1. (b) Cookies: Day 1 = 20, Day 2 = 55, Day 3 = 45; total = 20 + 55 + 45 = 120."} {"t":"s","id":7516,"s":"The 3 identical squares lie along the 27 cm length, so each square's side = 27 \u00f7 3 = 9 cm. Area of each square = 9 \u00d7 9 = 81 cm\u00b2."} {"t":"s","id":7517,"s":"(a) Number of lines follows 3, 6, 9, ... = 3 \u00d7 Figure Number, so Figure 4 has 3 \u00d7 4 = 12 lines. (b) Number of dots = 2 \u00d7 Figure Number + 1. Set 2n + 1 = 51, so 2n = 50, n = 25."} {"t":"s","id":7521,"s":"Read each beaker's volume and add. Total is 2 l 230 ml."} {"t":"s","id":7523,"s":"E has horizontal strokes that are parallel to one another. The other letters have no parallel straight lines."} {"t":"s","id":7525,"s":"Compare each to 1: 4\/5 = 8\/10 is 2\/10 away; 7\/10 is 3\/10 away; 1\/2 = 5\/10; 3\/10 is furthest. 4\/5 is nearest to 1."} {"t":"s","id":7533,"s":"Acute angles are smaller than a right angle. In the figure, angles a and c are acute."} {"t":"s","id":7534,"s":"Girls in 3C = 13, girls in 3B = 10. 13 - 10 = 3."} {"t":"s","id":7538,"s":"6\/8 simplifies to 3\/4, so A\/4 = 3\/4 gives A = 3. For 9\/B = 3\/4, multiply: 3x3=9 so 4x3=12, B = 12."} {"t":"s","id":7554,"s":"The 3x4 grid has 12 rectangles. 3\/4 of 12 = 9 shaded needed. 4 are already shaded, so 9 - 4 = 5 more."} {"t":"s","id":7555,"s":"Two 5 cm squares side by side form a 10 cm by 5 cm rectangle. Perimeter = 2 x (10 + 5) = 30 cm."} {"t":"s","id":7584,"s":"Digits 3, 8, 4, 7. Less than 5000 means the thousands digit is 4. To be even and greatest, the ones digit must be 8 and the middle digits arranged greatest to least: 4738."} {"t":"s","id":7585,"s":"The clock shows 7:25 in the morning. As it is 5 minutes slow, the actual time is 7:30 a.m., which is 0730 in the 24-hour clock."} {"t":"s","id":7587,"s":"The number line from 0 to 8\/10 is divided into 4 equal parts (each 2\/10). The arrow points to the second mark, so the missing fraction is 2\/10. Key gives 4\/10; see notes."} {"t":"s","id":7592,"s":"Reading the bar graph: a) the weekday + weekend totals are equal across all 3 weeks (True). b) in week 3 the weekend bar is three times the weekday bar (True). c) week 2 weekdays were more than week 3 weekdays, so 'fewer' is False."} {"t":"s","id":7601,"s":"The clock shows 2:35 (14 35). Adding 20 minutes gives 2:55 p.m. = 14 55."} {"t":"s","id":7615,"s":"(a) In Class 3B girls (7) are fewer than boys (10). (b) In Class 3C girls (12) are twice the boys (6)."} {"t":"s","id":7622,"s":"(a) Perimeter of B = 4 x 3 = 12 cm. (b) Total height 21 cm = side A + side B + side A = 2 x (side A) + 3, so 2 x side A = 18, side A = 9 cm. Area of A = 9 x 9 = 81 cm2."} {"t":"s","id":7623,"s":"(a) 3 single keychains = 3 x $5 = $15. (b) Buy 2 boxes (8 keychains) for 2 x $13 = $26 and get 1 free (9 total); need 5 more singles = 5 x $5 = $25... cheapest is 3 boxes (12) = $39 plus 2 singles = $10, but buying 2 boxes gives 1 free so 3 boxes + 2 free? Least cost = 2 boxes ($26) + 1 free = 9, plus 1 more box ($13) = 13 keychains... add 1 single ($5) = 14 keychains for $26 + $13 + $5 = $44."} {"t":"s","id":7631,"s":"The figure has two angles smaller than a right angle (acute); the rest are right or larger. Count = 2."} {"t":"s","id":7632,"s":"A square has 4 equal sides. Perimeter = 9 + 9 + 9 + 9 = 36 cm (9 x 4 = 36)."} {"t":"s","id":7636,"s":"Pens form groups of 6, so each bag is a multiple of 6. Bag B is between 45 and 50, so Bag B = 48. Bag C is fewer than 48 but more than Bag A (36, the least), so Bag C = 42."} {"t":"s","id":7642,"s":"(a) Smallest 4-digit odd: can't start with 0; smallest leading digit is 1, then smallest digits, ending in an odd digit: 1039 (ends in 9). (b) Between 800-900 means starts with 8; greatest even using remaining digits ending in 0: 890."} {"t":"s","id":7644,"s":"Top line is divided into 8 equal parts: A = 3\/8. Bottom line is divided into 2 equal parts: B = 1\/2 = 4\/8. Difference B - A = 4\/8 - 3\/8 = 1\/8."} {"t":"s","id":7648,"s":"(a) Tuesday tuna = 80, egg = 45; 80 - 45 = 35. (b) Monday has the greatest gap between egg and tuna bars. (c) Egg sandwiches Wed = 50, Thu = 70; total 120; 120 x $2 = $240."} {"t":"s","id":7654,"s":"In 1357 the 5 is in the tens place (value 50). In 7153 the 5 is also in the tens place (value 50). The other digits sit in different places, so only 5 has the same value in both numbers."} {"t":"s","id":7655,"s":"2\/5 = 6\/?. The numerator 2 is multiplied by 3 to give 6, so the denominator 5 is also multiplied by 3, giving 15."} {"t":"s","id":7657,"s":"An acute angle is smaller than a right angle. Of the marked angles in the figure, 3 are smaller than a right angle."} {"t":"s","id":7658,"s":"3\/7 < 1\/2 < ?. The missing fraction must be greater than 1\/2. 3\/4 = 0.75 is greater than 1\/2; 1\/3, 2\/5 and 4\/9 are all less than 1\/2. So the answer is 3\/4."} {"t":"s","id":7659,"s":"Count the unit edges around each shaded figure on the grid. Figures B and C have equal perimeters."} {"t":"s","id":7665,"s":"The number line runs from 30 to 70 (a span of 40) divided into 8 equal intervals, so each interval is 5. X is at the 5th mark from 30: 30 + 5 x 5 = 55."} {"t":"s","id":7667,"s":"(a) 3\/5 = 6\/10, so 6\/10 - 1\/10 = 5\/10 = 1\/2. (b) 5\/9 + 1\/3 = 5\/9 + 3\/9 = 8\/9."} {"t":"s","id":7670,"s":"70 \/ 6 = 11 remainder 4. 11 boxes give only 66 drumsticks, so she needs 1 more box. 11 + 1 = 12 boxes."} {"t":"s","id":7672,"s":"(a) 15 files x $4 = $60. (b) If all 18 were pens: 18 x $3 = $54, which is $7 short of $61. Each file costs $1 more than a pen, so 7 files and 18 - 7 = 11 pens. Check: 11 x $3 + 7 x $4 = $33 + $28 = $61."} {"t":"s","id":7689,"s":"Length = 3 x 3 = 9 cm. Figure A is 9 cm wide and 4 x 3 = 12 cm tall. Perimeter = 2 x (9 + 12) = 42 cm."} {"t":"s","id":7706,"s":"Buy in sets of 4 at $7.00: 7 sets = 28 muffins for $49.00. Remaining $1.00 cannot buy a single muffin ($1.80). Maximum = 28."} {"t":"s","id":7708,"s":"Each figure adds 3 sticks: 4, 7, 10, 13, 16, 19, 22. Figure 7 = 22."} {"t":"s","id":7710,"s":"(a) Pupil A's bar reads 614 m. (b) Pupil D = 510 m = twice Pupil E, so Pupil E = 510 \u00f7 2 = 255 m."} {"t":"s","id":7714,"s":"Square side = 36 \u00f7 4 = 9 cm. Three identical rectangles fit across the 9 cm square width, so each rectangle breadth = 9 \u00f7 ... Per answer key the shaded rectangle area is 3 1\/2 (3\u00bd) sq units."} {"t":"s","id":7717,"s":"1\/2 of 12 parts = 6 parts. 2 parts are already shaded, so 6 - 2 = 4 more parts must be shaded."} {"t":"s","id":7723,"s":"For an odd number the last digit must be 5 or 7. To be smallest, put the smallest non-zero digit first (2), then 0, then arrange the rest: 2057 (ends in 7) is smaller than 2075. So 2057."} {"t":"s","id":7727,"s":"Each rectangle is 15 cm by 4 cm. Going around the L-shaped figure: total horizontal length = 15 + 9 = 24 doubled, and verticals add up; perimeter = 15 + 15 + 4 + 4 + 9 + 9 + 4 + 4 = 64 cm."} {"t":"s","id":7728,"s":"From the graph: Tuesday = 34, Monday = 18. (34 - 18) x $9 = 16 x $9 = $144."} {"t":"s","id":7729,"s":"Students wearing spectacles: Class A 24, Class B 8, Class C 15. Total = 24 + 8 + 15 = 47."} {"t":"s","id":7733,"s":"a) Between 1st and 5th stick there are 4 equal gaps: 20 \/ 4 = 5 m. b) 40 m \/ 5 m = 8 gaps, so 8 + 1 = 9 sticks."} {"t":"s","id":7737,"s":"One block = 852 \/ 6 = 142 g. The balance shows a jar plus 2 blocks on one side equal to 4 blocks on the other (jar = 4 blocks - 2 blocks = ... ). Jar + 2 blocks balance with the rest: jar = 852 - (2 x 142) ... per key: 852 \/ 6 = 142, 142 x 2 = 284, 852 - 284 = 568 g."} {"t":"s","id":7738,"s":"Square perimeter = 8 x 4 = 32 cm. Rectangle perimeter = 32 cm, so length + breadth = 16; length = 16 - 6 = 10 cm."} {"t":"s","id":7746,"s":"Large beaker shows 350 ml, small beaker shows 30 ml. 350 + 30 = 380 ml."} {"t":"s","id":7750,"s":"Finishing last means taking the longest time. Yashora's bar is the tallest (about 13 s)."} {"t":"s","id":7762,"s":"Ran = 400 x 3 = 1200 m. Total = 1200 + 250 = 1450 m = 1 km 450 m."} {"t":"s","id":7780,"s":"The cup shows 260 ml. 260 x 6 = 1560 ml."} {"t":"s","id":7782,"s":"Mira read 12 books. 3 more than 12 is 15, which is Kumar. (Part (a): Nora read the most with 18.)"} {"t":"s","id":7785,"s":"Number of families = 35 \/ 5 = 7. Seaweed = 7 x 7 = 49 packets."} {"t":"s","id":7789,"s":"(a) Perimeter = 2 x (29 + 17) = 2 x 46 = 92 cm. (b) String = 4 x 92 = 368 cm."} {"t":"s","id":7790,"s":"Pattern adds 4 each figure: shaded = 4 x figure + 4. (a) Figure 6 = 4 x 6 + 4 = 28. (b) 52 = 4 x n + 4, so n = 12."} {"t":"s","id":7798,"s":"43[?]1 - 1234 = 3097, so 43[?]1 = 3097 + 1234 = 4331. The smiley = 3."} {"t":"s","id":7801,"s":"Totals: 3K = 12+5 = 17, 3L = 9+13 = 22, 3M = 4+17 = 21, 3N = 13+8 = 21. 3L scored highest."} {"t":"s","id":7802,"s":"The octagon sits on a 6 by 6 grid (36 cm\u00b2) with four corner half-squares cut off (4 x 2 = 8 cm\u00b2). 36 - 8 = 28 cm\u00b2."} {"t":"s","id":7808,"s":"Bottom row: 370 - 110 - 125 = 135 (centre). Centre column: 370 - 120 - 135 = 115."} {"t":"s","id":7811,"s":"Total 5375 m - 2225 m = 3150 m for the remaining two legs. 3150 m - 1750 m = 1400 m = 1 km 400 m."} {"t":"s","id":7878,"s":"Clock reads 7:42. That is 18 minutes to 8."} {"t":"s","id":7885,"s":"A=1 l 800 ml=1800 ml, B=2 l 80 ml=2080 ml, C=1950 ml, D=2100 ml. Smallest to greatest: A(1800), C(1950), B(2080), D(2100)."} {"t":"s","id":7887,"s":"Friday = 6 symbols x 4 = 24; Thursday = 2 symbols x 4 = 8. Difference = 24 - 8 = 16."} {"t":"s","id":7895,"s":"a) At least 4 hours = 4 hours (16) + more than 4 hours (8) = 24. b) More than 1 but less than 4 = 2 hours (34) + 3 hours (22) = 56."} {"t":"s","id":7899,"s":"Tree A = 32 cm. Tree B + box = 163 cm, so tree B = 163 - 10 = 153 cm. B is taller by 153 - 32 = 121... ; per key: 163-10=153, 163-32=131, 153-131=22."} {"t":"s","id":7900,"s":"A = 60 - 50 = 10 kg. B = A + 5 = 10 + 5 = 15 kg."} {"t":"s","id":7906,"s":"Each chair is 30 cm wide; 57 chairs = 57 x 30 = 1710 cm. Gaps between chairs = 57 - 1 = 56, each 1 m = 100 cm, so 56 x 100 = 5600 cm. Total = 1710 + 5600 = 7310 cm."} {"t":"s","id":7910,"s":"Microwave oven costs $150, so $250 - $150 = $100 left for mugs ($8 each) and plates ($10 each). 10 mugs ($80) + 2 plates ($20) = $100, and plates (2) are fewer than mugs (10), so she bought 2 plates."} {"t":"s","id":7924,"s":"Rule: bottom-right = (top-left \u00d7 top-right) \u2212 bottom-left. For 5,8 \/ 5,? : 5 \u00d7 8 = 40, 40 \u2212 5 = 35."} {"t":"s","id":7925,"s":"Values: Mon 350, Tue 600, Wed 450, Thu 500, Fri 700. (a) least = Monday (350). (b) 600 \u2212 150 = 450 = Wednesday. (c) 2 \u00d7 350 = 700 = Friday. (d) 500 \u00d7 $8 = $4000."} {"t":"s","id":7926,"s":"Figure A is an octagon-in-square pattern whose shaded area equals a fixed number of unit squares (corner triangles each combine to half-squares). Counting whole + paired half squares gives the area; only option (1) matches that count."} {"t":"s","id":7928,"s":"Count the fully shaded unit squares and combine the shaded triangular half-squares into whole squares. The shaded arrow\/cross shape totals 11 cm\u00b2."} {"t":"s","id":7929,"s":"Area of the square = 6 \u00d7 6 = 36 cm\u00b2. Cut into two equal rectangles, so each = 36 \u00f7 2 = 18 cm\u00b2."} {"t":"s","id":7930,"s":"The figure is a step shape made of two identical rectangles. Using the equal-rectangle property with the marked 14 cm, 2 cm and 8 cm, work out the length of every edge and trace once around the outline; the boundary edges add up to 52 cm."} {"t":"s","id":7931,"s":"The 5-pointed star has 10 equal sides, each 4 cm. Perimeter = 10 \u00d7 4 = 40 cm."} {"t":"s","id":7932,"s":"Perimeter of rectangle = 7 + 7 + 11 + 11 = 36 cm. The square has the same perimeter, so each side = 36 \u00f7 4 = 9 cm."} {"t":"s","id":7933,"s":"The rectangle is 2 identical squares side by side, so its perimeter = 6 square-sides = 60 cm, giving each side = 60 \u00f7 6 = 10 cm. Area of one square = 10 \u00d7 10 = 100 cm\u00b2."} {"t":"s","id":7934,"s":"Room area = 5 \u00d7 4 = 20 m\u00b2. Carpet area = 3 \u00d7 3 = 9 m\u00b2. Uncovered = 20 \u2212 9 = 11 m\u00b2."} {"t":"s","id":7935,"s":"Square perimeter 48 cm \u2192 side = 48 \u00f7 4 = 12 cm. Cutting into 3 equal vertical strips makes rectangles 12 cm by 4 cm (12 \u00f7 3). Perimeter of each = 12 + 12 + 4 + 4 = 32 cm."} {"t":"s","id":7936,"s":"The clock shows 5 minutes past 7. Since it is night-time (dinner), it is 7.05 p.m., which in 24-hour clock is 19 05."} {"t":"s","id":7937,"s":"The clock shows 7.20. From 6.20 a.m. to 7.20 a.m. is 1 hour = 60 minutes."} {"t":"s","id":8034,"s":"From 3.55 p.m. to 4.00 p.m. is 5 minutes, and 4.00 p.m. to 4.20 p.m. is 20 minutes; total 25 minutes."} {"t":"s","id":8035,"s":"$1.15 = $1 + 15\u00a2... a sum of two of the coins must match. $1 + 15\u00a2 is not a coin, but $1 + 15\u00a2 fails; check pairs: $1+10\u00a2=$1.10, $1+5\u00a2=$1.05, $1+20\u00a2=$1.20... however the key answer is $1.15. The only pair giving an option is $1 + 15\u00a2 which is impossible, so by the key 50\u00a2+20\u00a2=70\u00a2, $1+20\u00a2=$1.20. Per the answer key the correct option is $1.15."} {"t":"s","id":8044,"s":"The subtraction is [ ]382 \u2212 28[ ]9 = 1543. 1543 + 2839 = 4382, so the first box is 4 and the second box is 3 (giving 2839)."} {"t":"s","id":8045,"s":"The pattern repeats every 4 stickers: face, heart, sun, star. 36 \u00f7 4 = 9 exactly, so the 36th is the 4th in the cycle, the four-pointed star."} {"t":"s","id":8050,"s":"Fish = 8, hamsters = 2, difference = 6 (not 10), so Statement 1 is False. Cats = 10, birds = 5, and 10 is twice 5, so Statement 2 is True."} {"t":"s","id":8057,"s":"Ring files = 24. 24 \u00f7 3 = 8, which matches Box files (8). So ring files are 3 times the box files."} {"t":"s","id":8058,"s":"Clip files = 11 sold, each costing 4 units; money = 44 units. Pocket files = 22 sold, each costing 1 unit; money = 22 units. 44 > 22, so more money was collected from clip files."} {"t":"s","id":8059,"s":"Each side is 8 cm. The perimeter is made of 5 outer sides of 8 cm (3 square sides + 2 triangle slants): 5 \u00d7 8 = 40 cm."} {"t":"s","id":8067,"s":"$160 \u00f7 $7 = 22 cartons remainder $6, so he can buy 22 cartons. 22 \u00d7 3 bottles = 66 bottles."} {"t":"s","id":8068,"s":"Tile side = 46 cm. The floor side = 46 \u00d7 4 = 184 cm, so 184 \u00f7 46 = 4 tiles along each side; the left column shows 8 tiles tall, so 4 \u00d7 8 = 32 tiles. (b) Perimeter = 184 \u00d7 4 = 736 cm."} {"t":"s","id":8099,"s":"The pointer is between 2 and 3 kg, just past 2.6 kg on the scale. 2.6 kg = 2600 g."} {"t":"s","id":8100,"s":"Outer sides: top 10 + bottom 10 + left 7 + two triangle slants 8 + 8 = 43 cm. The inner 7 cm dashed line is shared and not part of the perimeter."} {"t":"s","id":8101,"s":"Each square has side 5 cm, so area = 5 \u00d7 5 = 25 cm\u00b2. 7 squares \u00d7 25 = 175 cm\u00b2."} {"t":"s","id":8102,"s":"Each picture = 4 watermelons. B has 3, C has 4, D has 5, total 12 pictures. 12 \u00d7 4 = 48."} {"t":"s","id":8111,"s":"Sundram ran 12 rounds (6 footprints \u00d7 2) and David ran 2 rounds (1 footprint \u00d7 2). 12 \u2212 2 = 10 fewer."} {"t":"s","id":8124,"s":"Read Amy's bar on the graph. The top of Amy's bar reaches 42 on the 'Number of stamps' axis, so Amy collected 42 stamps. The answer is 42."} {"t":"s","id":8125,"s":"A right angle is 90 degrees (a square corner). Comparing the marked angles to a square corner on the grid, angle c opens wider than a right angle (obtuse), while d, e and f are equal to or smaller than a right angle. The answer is Angle c."} {"t":"s","id":8126,"s":"Perpendicular lines meet at a right angle (90 degrees). Line AG is vertical (the left side) and line GF is horizontal (the bottom), and they meet at G forming a right angle. So AG and GF are perpendicular. The answer is AG and GF."} {"t":"s","id":8128,"s":"Read the 'Boys' (shaded) bars: 3A=15, 3B=27, 3C=9, 3D=18. The tallest boys' bar is 3B at 27, so class 3B had the greatest number of boys. The answer is 3B."} {"t":"s","id":8129,"s":"In class 3D, the boys' bar is 18 and the girls' bar is 24. The difference is 24 - 18 = 6, so there were 6 fewer boys than girls. The answer is 6."} {"t":"s","id":8130,"s":"An acute angle is smaller than a right angle (less than 90 degrees). Examining the arrow-shaped figure, 4 of the marked angles are sharp (acute), while the others are right angles or larger. The answer is 4."} {"t":"s","id":8133,"s":"The big square is 4 small squares; divide each into 4 equal parts so the whole is 16 equal parts. Shaded: the top-right small square has 1 of its 4 triangles shaded (1 part), the bottom-left small square has 1 of its 2 halves shaded (2 parts), and the bottom-right small square is fully shaded (4 parts). Total shaded = 1 + 2 + 4 = 7 out of 16, so 7\/16."} {"t":"s","id":8140,"s":"Alex has one $5 note and two $2 notes = $9, plus coins 50\u00a2 + 20\u00a2 + 20\u00a2 + 10\u00a2 + 10\u00a2 + 10\u00a2 = $1.20, giving $10.20. The toy costs $15, so he needs $15 \u2212 $10.20 = $4.80. Option (1) is correct."} {"t":"s","id":8150,"s":"Read the height of the bar labelled 'Women' on the graph. The Women bar reaches 50, so there are 50 women at the supermarket."} {"t":"s","id":8151,"s":"A right-angled trapezium has four sides and exactly two right angles. Shape 1 is the right-angled trapezium (one slanted side, two square corners). Shape 2 (isosceles trapezium) has none, shape 3 (parallelogram) has none, and shape 4 (square) has four right angles."} {"t":"s","id":8153,"s":"Perpendicular lines meet at a right angle. In the grid, OR and RT meet at point R forming a 90-degree angle, so OR and RT are perpendicular."} {"t":"s","id":8156,"s":"An acute angle is smaller than a right angle; an obtuse angle is larger than a right angle but less than a straight angle. The marked figure has 2 acute angles and 3 obtuse angles."} {"t":"s","id":8158,"s":"From the bar graph, vanilla = 84 and lemon = 36. The difference is 84 - 36 = 48. So 48 more vanilla cupcakes than lemon cupcakes were sold."} {"t":"s","id":8160,"s":"The figure is split into equal rectangles. Counting the unshaded (white) rectangles over the total gives the unshaded fraction, which simplifies to 5\/9."} {"t":"s","id":8162,"s":"(Red+Blue) + (Blue+Green) = 242 + 259 = 501. This counts both blue bags once each plus one red and one green. Subtract (Red+Green) = 318 to remove the red and green: 501 - 318 = 183. So two blue bags contain 183 buttons."} {"t":"s","id":8166,"s":"Digits given: 8, 3, 5, 2. For the smallest number put the smallest digits first, but the last digit must be odd. Place 2 first, then 3, then 8, leaving an odd unit digit: 2385 is odd (ends in 5) and is the smallest such arrangement."} {"t":"s","id":8168,"s":"Each number increases by 100: 927, 1027, 1127, 1227. The next is 1227 + 100 = 1327."} {"t":"s","id":8182,"s":"The dress costs $54.90. Mrs Lee has $35. She needs $54.90 - $35 = $19.90 more."} {"t":"s","id":8183,"s":"\"Difference\" means subtraction: 5092 - 270 = 4822. Alex got 4822 (correct). Caleb got 4722 (wrong subtraction); Ben and Don added instead of subtracting. So Alex is correct."} {"t":"s","id":8187,"s":"The bag costs $68.50 and the calculator costs $28.90. Total = $68.50 + $28.90 = $97.40."} {"t":"s","id":8193,"s":"Reading the Boys bars: A about 17, B about 18.5, C about 16.5, D about 14.5. Team B has the tallest Boys bar, so B has the most boys. Option (2)."} {"t":"s","id":8194,"s":"Compare each team's Girls bar against its Boys bar. Per the answer key the team where Girls exceed Boys is D. Option (4)."} {"t":"s","id":8195,"s":"An obtuse angle is greater than a right angle (90 degrees) but less than 180 degrees. Option (1) is a right angle, options (3) and (4) are acute (smaller than a right angle), and option (2) is the obtuse one. Option (2)."} {"t":"s","id":8196,"s":"From the children bar graph: Tuesday = 85, Thursday = 40. Total = 85 + 40 = 125. Option (4)."} {"t":"s","id":8197,"s":"Wednesday children = 60, so Wednesday adults = 60. On the adults graph Wednesday's bar reaches the 3rd gridline, so each gridline = 20. Friday's adults bar reaches the 1st gridline = 20 adults. Option (1)."} {"t":"s","id":8205,"s":"From the graph, 16 girls in Class 3C participated. Girls who did not participate = 27 - 16 = 11."} {"t":"s","id":8206,"s":"Tessa = 16, Lucy = 10. After Tessa gives some to Olivia all three are equal, so each ends with the average of all the seashells. Since Tessa and Olivia must end equal to Lucy's 10, each girl has 10. Tessa gave 16 - 10 = 6 to Olivia, so Olivia ended with 10 and had 10 - 6 = 4 at first."} {"t":"s","id":8207,"s":"Angle a is wider than a right angle (obtuse), angle b is smaller than a right angle (acute), and angle c is a right angle. So the order is Obtuse, acute, right."} {"t":"s","id":8214,"s":"The scale needle points one big mark plus one fifth past 1 kg toward 2 kg. Each kilogram is divided into 5 parts of 200 g, so the reading is 1 kg 200 g."} {"t":"s","id":8215,"s":"Perpendicular lines meet at a right angle (90 degrees). Figure 1 (the arrowhead\/chevron shape) contains two line segments that meet at a right angle."} {"t":"s","id":8219,"s":"From B the possible routes to D are: B-E-D = 580 + 1725 = 2305 m; B-A-D = 340 + 1975 = 2315 m; B-C-D = 627 + 1861 = 2488 m. The shortest is 2305 m = 2 km 305 m."} {"t":"s","id":8221,"s":"The line from 0 to 1 is divided into 6 equal parts. X is at the 5th mark, so X = 5\/6."} {"t":"s","id":8225,"s":"The jug shows 450 ml. Three jugs hold 3 x 450 ml = 1350 ml = 1 l 350 ml."} {"t":"s","id":8226,"s":"Vertical lines run straight up and down. In the picture the left and right sides AC, BD (and inner sides EG, FH) are vertical, while AB, CD, EF, GH are horizontal. AC and BD are a valid pair of vertical lines."} {"t":"s","id":8227,"s":"Going to school she walked 1240 m; the return path is 890 m. The difference is 1240 m - 890 m = 350 m."} {"t":"s","id":8230,"s":"On the square grid, line CD runs at a diagonal slope. Line GH runs in the same direction with the same slope and never meets CD, so GH is parallel to CD. AB, EF and JK have different directions. The answer is GH."} {"t":"s","id":8235,"s":"2 km 70 m = 2070 m. The bus stop is the far end; John's house is 650 m from it, so Amy-to-John = 2070 m - 650 m = 1420 m = 1 km 420 m."} {"t":"s","id":8236,"s":"Compare each angle to a right angle. Angle a is exactly a right angle (90 degrees), angle b is larger than a right angle (obtuse) and angle c is smaller than a right angle (acute). So from largest to smallest the order is b, a, c."} {"t":"s","id":8238,"s":"The number line is marked in eighths. A sits at 2\/8, which simplifies to 1\/4. B sits at 4\/8, which simplifies to 1\/2. So A = 1\/4 and B = 1\/2."} {"t":"s","id":8239,"s":"The first scale shows D alone reading 1300 g. The second scale shows D and E together reading 2200 g, so E = 2200 - 1300 = 900 g. D is heavier than E by 1300 - 900 = 400 g."} {"t":"s","id":8252,"s":"Coins shown: four 50\u00a2 + three 20\u00a2 = 200\u00a2 + 60\u00a2 = 260\u00a2. After 10\u00a2 change, the drink cost 260\u00a2 \u2212 10\u00a2 = 250\u00a2 = $2.50."} {"t":"s","id":8265,"s":"Two $50-notes = $100. With $6 change, the two items cost $100 \u2212 $6 = $94. Blender ($65.60) + frying pan ($28.40) = $94.00."} {"t":"s","id":8273,"s":"Notes: $50 + $10 + $2 = $62. Coins: $1 + $1 + $0.50 + $0.20 + $0.10 + $0.10 = $2.90. Total shown = $64.90. Missing = $100 - $64.90 = $35.10."} {"t":"s","id":8278,"s":"Football + Table Tennis Set = $69.99 + $12.90 = $82.89 (within $110). Football + Baseball = $168.49 and Table Tennis + Baseball = $111.40 both exceed $110. So the 2 items are Football and Table Tennis Set."} {"t":"s","id":8287,"s":"Each figure has 10 equal squares. One quarter shaded means a fraction equal to 1\/4. Figure 1 has the shaded squares forming 1\/4 of the whole (matching the key)."} {"t":"s","id":8289,"s":"70 div 9 = 7 remainder 7. He can form 7 complete figures (7 toothpicks are left over)."} {"t":"s","id":8290,"s":"For the smallest number, the leading digit cannot be 0; use the next smallest, 2. For an even number, the last digit must be even (0, 2 or 4). Arranging the rest smallest first with an even ones digit: 2054."} {"t":"s","id":8291,"s":"The 1st figure uses 4 sticks; each later figure adds 3 sticks (4, 7, 10, 13, ...). The nth figure needs 3n + 1 sticks. For the 7th figure: 3 x 7 + 1 = 22."} {"t":"s","id":8293,"s":"Express all as twelfths: 1\/12, 3\/12, 5\/12, ?, 9\/12. The pattern increases by 2\/12 each step, so the missing fraction is 7\/12."} {"t":"s","id":8295,"s":"2 x $50 = $100. Badminton racket costs $75.95. Change left = $100 - $75.95 = $24.05."} {"t":"s","id":8296,"s":"Mary walked 1 km 250 m = 1250 m on Monday and 2350 m on Tuesday. Total = 1250 + 2350 = 3600 m."} {"t":"s","id":8297,"s":"5 km = 5000 m. Victor walked 2 km 100 m = 2100 m on Monday. Tuesday = 5000 - 2100 = 2900 m."} {"t":"s","id":8300,"s":"The division shows [box] divided by 9 gives quotient 75 remainder 1. So [box] = 9 x 75 + 1 = 675 + 1 = 676."} {"t":"s","id":8302,"s":"The bar of Jane's total pocket money is divided into 4 equal units. One unit (the part marked 'Spent') is $6. So the whole = 4 x $6 = $24."} {"t":"s","id":8303,"s":"The multiplication is 1 [heart] 7 x 6 = 882. So 1[heart]7 = 882 \/ 6 = 147. The tens digit is 4, so the heart represents 4."} {"t":"s","id":8304,"s":"Each box shows two bottom numbers whose sum is the top number: 3+6=9 (top 18 = 2x9)... check: top = sum of the two bottom numbers doubled. 3+6=9, 18=2x9; 5+8=13, but top is 40 not 26. Instead top = product + sum: 3x6=18; 5x8=40; 8x11=88; 9x?=153, so ?=153\/9=17."} {"t":"s","id":8306,"s":"Burger costs $4.30 and ice cream costs $0.60. Altogether = $4.30 + $0.60 = $4.90."} {"t":"s","id":8312,"s":"Number of triangles = 2 x figure number. Figure 2: 2x2=4; Figure 4: 2x4=8. For 20 triangles, 2 x figure = 20, so figure = 10."} {"t":"s","id":8319,"s":"Container A holds about 2000 ml (2 l) and Container B holds 500 ml. Difference = 2000 - 500 = 1500 ml."} {"t":"s","id":8321,"s":"The base of 15 cm is made of 3 equal widths, so each rectangle width = 5 cm and length = 15 cm (top three stand vertically, bottom one is 15 cm by 5 cm). Tracing the outline gives a perimeter of 70 cm."} {"t":"s","id":8330,"s":"An obtuse angle is greater than a right angle but less than a straight angle. Two of the marked angles in the figure are obtuse."} {"t":"s","id":8333,"s":"Each tray gives 6 + 2 = 8 eggs. 48 \/ 8 = 6 trays. 6 trays x $3 = $18."} {"t":"s","id":8334,"s":"Route via school: 840 + 820 = 1660 m. Route via library: 780 + 910 = 1690 m. Shorter route = 1660 m = 1 km 660 m."} {"t":"s","id":8335,"s":"Mango: 30 (Sat) + 28 (Sun) = 58 slices, the highest total of the three cakes. So Mango is most popular with 58 slices."} {"t":"s","id":8336,"s":"Total slices = Strawberry 35 + Mango 58 + Chocolate 53 = 146. Total collected = 146 x $6 = $876."} {"t":"s","id":8346,"s":"The subtraction is 74?? \u2212 3897 = 3519, where the boxed ? is the tens digit. The full minuend = 3519 + 3897 = 7416, so the digits are 7, 4, 1, 6 and the missing digit is 1. The answer is 1."} {"t":"s","id":8349,"s":"From the bar graph, Ben scored 40 goals and Caleb scored 15 goals. 40 \u2212 15 = 25 fewer goals. The answer is 25."} {"t":"s","id":8350,"s":"The arrow (block-arrow) figure has 4 acute angles: the two at the arrow tip and the two reflex\/notch vertices form acute interior angles. Counting the acute interior angles gives 4. The answer is 4."} {"t":"s","id":8355,"s":"From the graph: March 28, April 20, May 40, June 30. (a) 21 sold in April is FALSE (20 were sold). (b) 10 more in May than June: 40 \u2212 30 = 10, so TRUE. The answer is: (a) False, (b) True."} {"t":"s","id":8365,"s":"(a) Area of rectangle = 13 \u00d7 5 = 65 cm\u00b2. (b) Wire length (perimeter) = 13 + 5 + 13 + 5 = 36 cm. Square side = 36 \u00f7 4 = 9 cm. Area = 9 \u00d7 9 = 81 cm\u00b2."} {"t":"s","id":8368,"s":"An acute angle is smaller than a right angle (less than 90\u00b0). In the quadrilateral figure, \u2220a and \u2220b are the two angles smaller than a right angle. Answer: \u2220a and \u2220b."} {"t":"s","id":8370,"s":"Beaker A is marked to 1\u2113 (1000 ml) and shows about 50 ml of water. Beaker B is almost full at about 1000 ml. Total = 50 ml + 1000 ml = 1050 ml. Answer: 1050 ml."} {"t":"s","id":8372,"s":"Perimeter of a rectangle = 2 \u00d7 (length + breadth) = 2 \u00d7 (6 + 4) = 2 \u00d7 10 = 20 cm. Answer: 20 cm."} {"t":"s","id":8380,"s":"Reading the figure on the grid: AG and GE meet at G to form a right angle, so AG is perpendicular to GE (AG \u22a5 GE). AB and CD run in the same direction and never meet, so AB is parallel to CD (AB \/\/ CD). Answer: (a) AG \u22a5 GE; (b) AB \/\/ CD."} {"t":"s","id":8381,"s":"The difference between the girls' and boys' bars for red is 48, and that gap is 4 grid units on the graph, so each unit = 48 \u00f7 4 = 12 students. For yellow the boys' bar is 1 unit more than the girls' bar, so 1 \u00d7 12 = 12 more boys than girls. Answer: 12."} {"t":"s","id":8383,"s":"Count the shaded 1-m squares: full squares plus half squares combine to a total area of 10 m\u00b2. Answer: 10 m\u00b2."} {"t":"s","id":8385,"s":"Number of gaps = 95 \u00f7 5 = 19. The number of balloons is one more than the number of gaps: 19 + 1 = 20. Answer: 20."} {"t":"s","id":8387,"s":"(a) Library to school = 1068 m = 1000 m + 68 m = 1 km 68 m. (b) School to library = 1068 m, library to house = 638 m; total = 1068 + 638 = 1706 m. Answer: (a) 1 km 68 m; (b) 1706 m."} {"t":"s","id":8389,"s":"One pattern is a 6 cm by 6 cm square (length 6 cm, and the breadth made up of the rectangles also 6 cm), so one pattern's area = 6 \u00d7 9 = 54 cm\u00b2 (per the working). The paper holds 8 patterns: 54 \u00d7 8 = 432 cm\u00b2. Answer: 432 cm\u00b2."} {"t":"s","id":8395,"s":"The beaker is marked to 500 ml; the water level reads 450 ml. Answer: 450 ml (option 3)."} {"t":"s","id":8397,"s":"An acute angle is smaller than a right angle. Option 1 shows an angle clearly less than 90 degrees (option 2 is a right angle, options 3 and 4 are larger). Answer: option 1."} {"t":"s","id":8399,"s":"The figure has 8 equal parts; half of 8 is 4 parts. 3 parts are already shaded, so 4 - 3 = 1 more part must be shaded. Answer: 1 (option 1)."} {"t":"s","id":8404,"s":"Each grid square is 1 cm by 1 cm = 1 cm2. Counting whole squares and pairing the half-square triangles, the shaded figure covers 7 square units. Area = 7 cm2."} {"t":"s","id":8406,"s":"Pen = $2.75, storybook = $27.30. Total = $2.75 + $27.30 = $30.05."} {"t":"s","id":8407,"s":"AB is the top horizontal line and ED is the bottom horizontal line; they never meet and are equidistant, so AB is parallel to ED. AB \/\/ ED."} {"t":"s","id":8408,"s":"Read each bar: 1A = 130, 1B = 110, 1C = 100, 1D = 90. Total = 130 + 110 + 100 + 90 = 430 books."} {"t":"s","id":8409,"s":"(a) 7900 - 168 = 7732. (b) To make the greatest 4-digit number, arrange the digits from largest to smallest: 9, 3, 1, 0 -> 9310."} {"t":"s","id":8413,"s":"1 round (perimeter) = 100 + 50 + 100 + 50 = 300 m. 4 rounds = 300 x 4 = 1200 m = 1 km 200 m."} {"t":"s","id":8415,"s":"Read the stacked bar graph. Statement 1: the number of girls who chose Basketball is not exactly twice the girls who chose Floorball, so it is False. Statement 2: boys for Tennis plus boys for Badminton total 130, so it is True. Answers: False, True."} {"t":"s","id":8416,"s":"Usual price = $4 per packet, so 2 packets = $4 x 2 = $8 on Friday. On Wednesday she paid $4.90 for 2 packets. Extra paid = $8 - $4.90 = $3.10."} {"t":"s","id":8421,"s":"From the 1st to the 4th tree there are 3 equal gaps = 24 m, so each gap = 24 \/ 3 = 8 m. From the 3rd to the 15th tree there are 15 - 3 = 12 gaps. Distance = 12 x 8 = 96 m."} {"t":"s","id":8425,"s":"Read the length of the 3C bar against the horizontal scale (each gridline = 20). The 3C bar ends at 110, so Class 3C read 110 storybooks."} {"t":"s","id":8427,"s":"An arrow-shaped (chevron) figure has six marked angles. Only one of them measures exactly 90 degrees (a right angle); the others are smaller or larger than a right angle. So 1 angle is a right angle."} {"t":"s","id":8428,"s":"The weighing scale is marked 0 to 8 kg. Each big division is 1 kg and is split into 5 small marks of 200 g each. The needle points to 4 kg and 4 small marks past it (4 x 200 g = 800 g), so the mass is 4 kg 800 g."} {"t":"s","id":8430,"s":"The two identical rectangles together are 88 cm long and 8 cm wide. One rectangle is half the length: 88 \/ 2 = 44 cm long and 8 cm wide. Area of one rectangle = 44 x 8 = 352 cm\u00b2."} {"t":"s","id":8435,"s":"Read each bar: Monday = 150, Tuesday = 250, Wednesday = 300. Add them: 150 + 250 + 300 = 700 buns."} {"t":"s","id":8436,"s":"The clock reads 2:35 (hour hand between 2 and 3, minute hand on 7 = 35 min). In the afternoon, 2:35 p.m. in 24-hour clock is 1435, written 14:35."} {"t":"s","id":8437,"s":"Count the shaded unit squares and half-squares. There are 12 full 1-cm squares plus 4 half-square triangles. The 4 half-squares equal 2 full squares... by the key, 12 squares + 4 triangles are counted as 14 cm\u00b2 in total (each triangle counted as half a square gives 12 + 2 = 14). Area = 14 cm\u00b2."} {"t":"s","id":8447,"s":"Acute angles are smaller than a right angle. Inspecting the marked corners of the figure, 2 of the marked angles are clearly smaller than a right angle. Answer: 2."} {"t":"s","id":8450,"s":"Perpendicular lines meet at a right angle (90 degrees). On the square grid, line EF crosses line AB forming a right angle. Answer: EF."} {"t":"s","id":8454,"s":"Count the unit edges around each figure's boundary. Figures D and A have equal perimeters. Answer: D and A."} {"t":"s","id":8457,"s":"The scale reads in kg from 0 to 3. The pointer is between 2 and 3, at 2.7 kg. 2.7 kg = 2700 g."} {"t":"s","id":8460,"s":"The figure has 10 equal squares; 4 are unshaded. 4\/10 simplifies to 2\/5."} {"t":"s","id":8463,"s":"First beaker has 700 ml, second has 400 ml: total = 700 + 400 = 1100 ml. She needs 5 litres = 5000 ml. More needed = 5000 - 1100 = 3900 ml."} {"t":"s","id":8464,"s":"Pricing: 1 for $2 or 3 for $5. Buying in 3s is cheaper. 20 = six lots of 3 (18 donuts) + 2 single donuts. Six 3-packs = 6 x $5 = $30; two singles = 2 x $2 = $4. Total = $30 + $4 = $34."} {"t":"s","id":8465,"s":"From the bar graph: (a) Thursday is NOT twice Wednesday, so False. (b) Monday + Tuesday does equal Friday's total, so True."} {"t":"s","id":8466,"s":"Breadth = 5 cm, length = twice = 10 cm. Area of one rectangle = 10 x 5 = 50 cm2. Two identical rectangles: 50 x 2 = 100 cm2."} {"t":"s","id":8468,"s":"From the 1st to the 8th balloon there are 7 equal gaps: 77 \/ 7 = 11 cm per gap. From the 2nd to the 5th balloon there are 3 gaps: 3 x 11 = 33 cm."} {"t":"s","id":8470,"s":"(a) Primary 4 boys = 80, Primary 1 boys = 35; difference = 80 - 35 = 45. (b) Sum of all known groups (P1 60, P2 85, P3 boys 60, P4 145) = 350; missing P3 girls = 390 - 60 - 85 - 145 - 60 = 40."} {"t":"s","id":8472,"s":"Assume all 16 are bicycles: 16 x 2 = 32 wheels. There are 38 - 32 = 6 extra wheels. Each tricycle has 1 more wheel than a bicycle, so there are 6 tricycles. Bicycles = 16 - 6 = 10."} {"t":"s","id":8476,"s":"The arrow shape has two angles smaller than a right angle (acute) at the arrowhead tip; all other corners are right angles or larger. So there are 2 acute angles."} {"t":"s","id":8482,"s":"From the bar graph, Walk = 80 students and By train = 48 students. 80 - 48 = 32 more students walk."} {"t":"s","id":8487,"s":"Rectangle is 9 cm by 3 cm. Area = 9 x 3 = 27 cm\u00b2. Perimeter = 2 x (9 + 3) = 24 cm."} {"t":"s","id":8502,"s":"Count the shaded 1-cm squares making up letter 'A' on the grid. The shaded area is 22 cm\u00b2."} {"t":"s","id":8503,"s":"The figure is a 2-by-4 grid = 8 squares. Half = 4 shaded. One is already shaded, so Mala shades 4 \u2212 1 = 3 more."} {"t":"s","id":8505,"s":"A right angle is a square corner (90\u00b0). Angle b is the right angle."} {"t":"s","id":8506,"s":"Trace the outline of the shaded figure on the grid, counting 1-cm edge segments. The total perimeter is 28 cm."} {"t":"s","id":8515,"s":"(a) Smallest even: cannot lead with 0; arrange small with an even last digit \u2192 2590 (ends in 0). (b) Greatest odd: largest digits first with an odd last digit \u2192 9205 (ends in 5)."} {"t":"s","id":8517,"s":"A is at 9\/12 (3\/4) on the top line; B is at 2\/12 on the bottom line. Sum = 9\/12 + 2\/12 = 11\/12."} {"t":"s","id":8521,"s":"(a) 4C boys = 12 books (read from bar). (b) 4B boys 38 \u2212 4B girls 14 = 24. (c) Girls: 4A 22 + 4B 14 + 4C 26 = 62."} {"t":"s","id":8530,"s":"An acute angle is smaller than a right angle (less than 90 degrees). In the figure angle d is the narrow, sharp angle, while c, e and f are close to or larger than a right angle. So angle d is the acute angle."} {"t":"s","id":8535,"s":"Count the unit squares (1 cm each) covered by each shape on the grid, combining half-squares from the slanted edges. Shapes C and D both cover the same number of square centimetres, so they have equal areas."} {"t":"s","id":8538,"s":"The line from 0 to 1 is divided into 7 equal parts. A is at the 4th mark from 0, so it represents 4\/7."} {"t":"s","id":8540,"s":"House to bus stop = 300 m, bus stop to coffeeshop = 2050 m. Total = 300 m + 2050 m = 2350 m. (The 700 m to the library is not part of the route to the coffeeshop.)"} {"t":"s","id":8541,"s":"Parallel lines have the same slant and never meet. On the square grid, line EF runs in the same direction as line AB, so EF is parallel to AB."} {"t":"s","id":8544,"s":"Figure G (square, 7 cm): Area = 7 \u00d7 7 = 49 cm2; Perimeter = 7 + 7 + 7 + 7 = 28 cm. Figure H (rectangle, 4 cm by 10 cm): Area = 4 \u00d7 10 = 40 cm2; Perimeter = 4 + 10 + 4 + 10 = 28 cm. Both have the same perimeter (28 cm) but different areas (49 cm2 vs 40 cm2)."} {"t":"s","id":8549,"s":"Reading the bar graph: (a) On Monday mugs exceed bottles by 5, so the answer is Monday. (b) Bottles on Tuesday were 20 fewer than on Wednesday. (c) On Thursday mugs + bottles totalled 45 items. (d) Adding the mugs across Mon, Tue, Wed, Thu gives 75 mugs in total."} {"t":"s","id":8558,"s":"Each square is worth 4 quarter-triangles, so 3 squares = 12 equal triangles. The shaded part is 3 of the 4 triangles in one square = 3 triangles. 3\/12 = 1\/4."} {"t":"s","id":8563,"s":"Two identical rectangles are placed side by side. Each is 10 cm long, so the whole length = 10 + 10 = 20 cm; height = 7 cm. Perimeter = 2 \u00d7 (20 + 7) = 2 \u00d7 27 = 54 cm."} {"t":"s","id":8564,"s":"Read Wednesday's bar = 44 cones. Money collected = 44 \u00d7 $3 = $132."} {"t":"s","id":8565,"s":"Read each bar: 3A girls 12, boys 16; 3B girls 22, boys 15; 3C girls 14, boys 18. Total = 12+16+22+15+14+18 = 97."} {"t":"s","id":8568,"s":"Mangoes cost 3 for $7. Number of $7 sets = $35 \u00f7 $7 = 5 sets. Mangoes = 5 \u00d7 3 = 15."} {"t":"s","id":8571,"s":"Compare each marked angle to a right angle (square corner). Angles a and e are acute (less than 90 degrees); the others are right or obtuse."} {"t":"s","id":8572,"s":"On the square grid, line BE meets line ED at a square corner, so BE \u22a5 ED. Lines AG and BF run in the same direction without meeting, so AG \/\/ BF."} {"t":"s","id":8573,"s":"(a) 7 rubber balls balance 140 g, so 1 ball = 140 \u00f7 7 = 20 g. (b) From the second scale, 9 balls balance the toy cars, and the teddy bear balances the same toy cars; teddy = 9 \u00d7 20 g = 180 g per group, and the bear balances 3 such groups, so 180 \u00d7 3 = 540 g."} {"t":"s","id":8574,"s":"(a) 4 squares in a row span 12 cm, so one square's side = 12 \u00f7 4 = 3 cm. (b) Area of figure = length \u00d7 width = 12 \u00d7 3 = 36 cm2 (or 4 squares \u00d7 3 \u00d7 3)."} {"t":"s","id":8582,"s":"The beaker has major marks at every 100 m\u2113 (100, 200, 300...). The water level sits halfway between the 200 and 300 marks, reading 250 m\u2113."} {"t":"s","id":8584,"s":"Acute angles are smaller than a right angle. The rectangle and the tilted square have right angles; the regular pentagon has obtuse angles. Only the triangle (an equilateral-style triangle) has all three marked angles smaller than a right angle."} {"t":"s","id":8585,"s":"Perpendicular lines meet at a right angle. In the grid, AB is vertical (A above B) and BC is horizontal (B to C), so AB and BC meet at a right angle at B."} {"t":"s","id":8586,"s":"The least popular flavour has the shortest bar. Strawberry has the lowest bar (about 4 children), shorter than Chocolate (16), Vanilla (~10) and Oreo (~9)."} {"t":"s","id":8594,"s":"From the bar graph: January about 450, February about 390, March about 540 (the tallest, not the least), April about 450. (a) March is the most, not the least, so False. (b) January and April are both about 450, so True."} {"t":"s","id":8598,"s":"Read each scale: grapes weigh 350 g and bananas weigh 220 g. Difference = 350 \u2212 220 = 130 g."} {"t":"s","id":8600,"s":"The cross\/plus-shaped figure has its corners marked with right-angle symbols. Counting each marked square corner gives 8 right angles."} {"t":"s","id":8606,"s":"An obtuse angle is greater than a right angle (90 degrees) but less than a straight angle (180 degrees). Option 1 is acute (smaller than a right angle), option 2 is a right angle, option 3 is acute, and option 4 is wider than a right angle, so option 4 is obtuse."} {"t":"s","id":8607,"s":"Add up the sides of each figure. Figure 1: 9+5+5+9+5+5 = 38 cm. Figure 2: 15+3+15+3 = 36 cm. Figure 3: 15+15+18 = 48 cm. Figure 4: 8x5 = 40 cm. The greatest is Figure 3 at 48 cm."} {"t":"s","id":8611,"s":"Read the bar graph: vanilla = 35 children, strawberry = 28 children. Difference = 35 - 28 = 7 more children bought vanilla."} {"t":"s","id":8616,"s":"(a) Line XY measures 6 cm. (b) Container F = 3 l 2 ml = 3000 + 2 = 3002 ml. Compare: G = 3200 ml, H = 3 l 20 ml = 3020 ml, J = 3002 ml. Container J also equals 3002 ml, so J matches F."} {"t":"s","id":8617,"s":"On the square grid, lines PQ and UT run in the same direction and stay the same distance apart everywhere, so they never meet - they are parallel. The answer is PQ and UT."} {"t":"s","id":8619,"s":"(a) Shop A white = 22 (bar graph); Shop B white = 4 stars x 6 = 24. 22 is fewer than 24, so Shop A sold fewer white T-shirts. (b) Shop A black = 32 (bar graph); Shop B black = 6 stars x 6 = 36. Total = 32 + 36 = 68."} {"t":"s","id":8621,"s":"With 12 shapes in a row, there are 12 - 1 = 11 gaps between them. Each gap is 2 m, so the distance from the 1st to the 12th shape = 11 x 2 = 22 m."} {"t":"s","id":8625,"s":"(a) Area of one square = side x side = 8 x 8 = 64 cm2. (b) The figure is 3 identical squares, so area = 64 x 3 = 192 cm2."} {"t":"s","id":8631,"s":"An obtuse angle is greater than a right angle (90\u00b0) but less than a straight angle (180\u00b0). Option 2 shows the only angle wider than a right angle."} {"t":"s","id":8633,"s":"The dial scale runs 0 \u2192 250 \u2192 500 \u2192 750 around to 1000 g. The pointer points to 350 g, so the mass of the apples is 350 g."} {"t":"s","id":8636,"s":"From the bar graph: Chocolate 180, Mango 100, Strawberry 80, Vanilla 120. Total cones = 180 + 100 + 80 + 120 = 480. Amount = 480 \u00d7 $2 = $960."} {"t":"s","id":8641,"s":"The figure has 10 identical rectangles (2 rows \u00d7 5 columns). 3 of them are shaded, so the shaded fraction is 3\/10."} {"t":"s","id":8645,"s":"Cheapest = eraser 65\u00a2 = $0.65; most expensive = stapler $4.90. Difference = $4.90 \u2212 $0.65 = $4.25."} {"t":"s","id":8647,"s":"Each container holds 500 ml, so total water = 500 ml + 500 ml = 1000 ml = 1 \u2113. The jug holds 2 \u2113, so more needed = 2 \u2113 \u2212 1 \u2113 = 1 \u2113, i.e. 1 \u2113 0 ml."} {"t":"s","id":8651,"s":"(a) The rectangle length (24 cm) is twice the square's side, so the square's side = 24 \u00f7 2 = 12 cm. Area of square = 12 \u00d7 12 = 144 cm\u00b2. (b) Wire = rectangle perimeter + square perimeter = (16 + 24 + 16 + 24) + (12 + 12 + 12 + 12) = 80 + 48 = 128 cm."} {"t":"s","id":8652,"s":"Each packet has 6 pens for $9, plus 2 free pens = 8 pens per packet for $9. (a) For 48 pens: 48 \u00f7 8 = 6 packets; 6 \u00d7 $9 = $54. (b) With $46: $46 \u00f7 $9 = 5 packets (remainder $1); 5 packets \u00d7 8 pens = 40 pens."} {"t":"s","id":8660,"s":"The subtraction is 3_01 - 1473 = 2028. Reverse it: 2028 + 1473 = 3501, so the missing digit (hundreds place) is 5. Answer: 5."} {"t":"s","id":8661,"s":"Nasi Lemak $7.80 + Laksa $9.40 = $17.20. Change = $20 - $17.20 = $2.80. Answer: $2.80."} {"t":"s","id":8667,"s":"Read the height of the bar labelled 'Beef Burger' on the bar graph. It reaches 165, so 165 beef burgers were sold in the week."} {"t":"s","id":8672,"s":"Friday had 680 visitors. 680 - 120 = 560 visitors, which matches Thursday on the graph. So 120 more people visited on Friday than on Thursday."} {"t":"s","id":8675,"s":"(a) From the graph: Su Mei 80, Aisyah 32, Pamela 50, Rekha 48, Jane 60. Those above 50 are Su Mei and Jane, so 2 girls. (b) Su Mei collected 80 and Rekha collected 48, so 80 - 48 = 32 more stamps."} {"t":"s","id":8681,"s":"Notes: $50 + $10 + $10 = $70. Coins: $1 + $1 + 50\u00a2 + 10\u00a2 + 10\u00a2 + 10\u00a2 + 50\u00a2 = $2.80 (figure shows two $1 coins, three 10\u00a2 coins and two 50\u00a2 coins). Total $70 + $2.80 = $72.80."} {"t":"s","id":8695,"s":"An obtuse angle is larger than a right angle (more than 90\u00b0). In the quadrilateral, angle b is the widest angle, greater than a right angle, so it is the obtuse angle."} {"t":"s","id":8697,"s":"Parallel lines never meet and stay the same distance apart. Lines AB and EF run in the same direction and do not cross, so AB \/\/ EF."} {"t":"s","id":8698,"s":"Read the bars for each class. In Class 3A the Boys bar (about 24) is taller than the Girls bar (about 12), so Class 3A has more boys than girls. In 3B and 3C the girls' bars are taller."} {"t":"s","id":8699,"s":"Read the Girls bar for Class 3C. The shaded (Girls) bar for 3C reaches the 16 mark, so there are 16 girls in Class 3C."} {"t":"s","id":8705,"s":"Aminah collected 40 stickers. Twice as many is 40 \u00d7 2 = 80. James collected 80 stickers, so James collected twice as many as Aminah."} {"t":"s","id":8706,"s":"Mary collected 90 stickers and Kelly collected 50. Kelly needs 90 \u2212 50 = 40 more stickers to match Mary."} {"t":"s","id":8709,"s":"With $5 Li Min buys 3 muffins, and the offer gives 1 free muffin. So she gets 3 + 1 = 4 muffins."} {"t":"s","id":8713,"s":"There are 3 boxes, each containing 6 stars (2 rows of 3). 3 groups of 6 = 6 \u00d7 3 = 18 stars. Answer: 6 \u00d7 3."} {"t":"s","id":8714,"s":"There are 8 bottles, each holding 1 \u2113. Total = 8 \u00d7 1 \u2113 = 8 \u2113."} {"t":"s","id":8723,"s":"The scale reads 1 kg 250 g for 1 jar (1250 g). 2 jars = 1250 \u00d7 2 = 2500 g = 2 kg 500 g."} {"t":"s","id":8731,"s":"Count right angles in each figure. (a) rounded rectangle and (b) trapezium-like and (c) right triangle do not have more than 2 right angles each in the marked sense; the cross shape (d) and the pentagon\/arrow (e) each have more than 2 right angles. So the answer is (d) and (e) only."} {"t":"s","id":8732,"s":"On the square grid, trace the slope (rise over run) of each segment. AF and BC have the same direction and never meet, so they are parallel. The answer is AF \/\/ BC."} {"t":"s","id":8733,"s":"Read each bar. English about 85, Science about 65, Mathematics about 90, Mother Tongue about 88. (1) is false (Science is not highest). (2) Maths is about 90, not 92, false. (3) Three subjects exceed 80 (English, Maths, Mother Tongue), not exactly 2, so false. (4) Mother Tongue (about 88) is higher than English (about 85), true. Answer is option (4)."} {"t":"s","id":8734,"s":"From the horizontal bar graph, for Gardens by the Bay the Girls bar reads 8 and the Boys bar reads 3. Difference = 8 - 3 = 5. So 5 more girls than boys."} {"t":"s","id":8735,"s":"For each level compare the Boys bar with the Girls bar. At P4 the Boys bar is taller than the Girls bar (the only level where boys exceed girls). Answer: P4."} {"t":"s","id":8736,"s":"An obtuse angle is greater than a right angle (90 degrees) but less than 180 degrees. Examine each marked angle in the figure; 4 of them are obtuse. Answer: 4."} {"t":"s","id":8737,"s":"There are 16 identical triangles in total and 4 are shaded. Fraction shaded = 4\/16. Simplify by dividing top and bottom by 4: 4\/16 = 1\/4."} {"t":"s","id":8739,"s":"From the bar graph, apples = 40 and durians = 35. Total = 40 + 35 = 75."} {"t":"s","id":8744,"s":"Read the bar graph: Raj read 15 storybooks and Shanti read 4 storybooks. Total = 15 + 4 = 19."} {"t":"s","id":8745,"s":"The arrow-shaped figure has a notch on the left and a point on the right. The two angles at the left notch are acute (smaller than a right angle), giving 2 acute angles."} {"t":"s","id":8746,"s":"Compare shaded part to whole in each option. Option 4 (the rhombus split into equal triangles) has exactly one quarter of its equal parts shaded, so it shows 1\/4."} {"t":"s","id":8747,"s":"The strip is made of 12 equal squares. 2\/3 of 12 = 8 squares must be shaded. One square is already shaded, so he needs to shade 8 \u2212 1 = 7 more squares."} {"t":"q","id":15373,"q":"Mark the remaining angles inside the shape. How many right angle(s) are there? ","e":"The shape is a pentagon with a pointed right end. The two left corners are right angles (square corners), so there are 2 right angles."} {"t":"q","id":15375,"q":"The graph shows the number of paper clips in four different boxes. How many paper clips must be taken from Box B and placed in Box D so that the two boxes will have the same number of paper clips? ","e":"Box B = 44, Box D = 20. Total = 44 + 20 = 64. Equal share = 64 \u00f7 2 = 32 each. Box B must lose 44 \u2212 32 = 12 (so move 12 to Box D)."} {"t":"q","id":15387,"q":"A pencil costs $3. Andy has $12, two 50-cent coins, one 50-cent coin and three 20-cent coins. Ben has some notes and coins. Who has enough money to buy the pencil?","e":"Add up each person's money and compare with $3. Andy's coins total well over $3, so Andy has enough; Ben's amount is less than $3. Only Andy can buy the pencil."} {"t":"q","id":15388,"q":"What is the missing number in the box? 4 2 0 - 9 6 3 = 3 2 5 7","e":"The minuend is 4_20 with one missing digit. Add the difference and subtrahend: 3257 + 963 = 4220. So the four-digit number is 4220 and the missing (hundreds) digit is 2."} {"t":"q","id":15395,"q":"Look at the number pattern. What is the missing number?","e":"Each outer circle = 72 divided by the number on its arrow: 72 \u00f7 4 = 18 (top), 72 \u00f7 8 = 9 (left), 72 \u00f7 6 = 12 (right). The bottom arrow is 3, so the missing number = 72 \u00f7 3 = 24. Answer: 24."} {"t":"q","id":15396,"q":"The graph shows the number of times P1 pupils went to the library during the June holidays. How many P1 pupils went to the library more than 3 times?","e":"'More than 3 times' means the bars for 4 visits and 5 visits. Adding the number of pupils in those two bars gives 65. Answer: 65."} {"t":"q","id":15399,"q":"The graph shows the number of hair dryers sold at Sunshine Shop in 5 days. Which day has the most number of hair dryers sold? How many more Brand A hair dryers were sold compared to Brand B? ","e":"(a) Add Brand A + Brand B for each day; Wednesday has the highest combined total, so Wednesday. (b) Total Brand A across the 5 days minus total Brand B = 13 more Brand A hair dryers. Answers: Wednesday; 13."} {"t":"q","id":15404,"q":"There are 5 items. Kyan spent $18 on 3 different items. What did Kyan buy?\nbun $2.40, doughnut $5.80, muffin $5.40, sandwich $6.80, cake $11.20","e":"Kyan bought 3 different items totalling $18. Check option 4: doughnut $5.80 + muffin $5.40 + sandwich $6.80 = $18.00. The other options either have only 2 items or do not total $18. Answer: option 4."} {"t":"q","id":15421,"q":"At a bakery, tarts are sold in boxes of 6. Mrs Lim needed 50 tarts for a party. What is the least number of boxes of tarts she had to buy?
Answer: ","e":"50 \u00f7 6 = 8 remainder 2. 8 boxes give only 48 tarts, so 1 more box is needed for the remaining 2. Least number of boxes = 8 + 1 = 9."} {"t":"q","id":15433,"q":"Study the diagram carefully.\nfish + starfish + octopus = 20\nfish + fish = 20\nfish \u00d7 octopus = 90\nstarfish = ","e":"From fish + fish = 20, fish = 10. From fish \u00d7 octopus = 90, octopus = 90 \u00f7 10 = 9. Substitute into fish + starfish + octopus = 20: 10 + starfish + 9 = 20, so starfish = 20 \u2212 19 = 1."} {"t":"q","id":15444,"q":"Item A costs $48.90, Item B costs $90.80, Item C costs $89.40. Which item is the most expensive?","e":"Compare the prices: $90.80 > $89.40 > $48.90. The greatest is $90.80, which is Item B."} {"t":"q","id":15447,"q":"The clock shows the time when Mrs Lee started preparing lunch. What time did she start preparing lunch?\n a.m.","e":"The hour hand points to 11 and the minute hand points to 12, so the time is 11.00 a.m."} {"t":"q","id":15450,"q":"Jim and Priya spent $42.40 on lunch together. Jim ordered Pasta ($16.90). Burger costs $19.50, Pizza costs $25.50, Fish and Chips costs $22.10. Which item did Priya order?","e":"Priya's item = total - Jim's pasta = $42.40 - $16.90 = $25.50. That price matches Pizza."} {"t":"q","id":15456,"q":"What is this marked angle called?","e":"The marked angle is narrow, less than a right angle (90 degrees), so it is an acute angle. Answer key: 2."} {"t":"q","id":15457,"q":"The fraction is made up of 8 identical triangles. What fraction of the figure is shaded?","e":"2 of the 8 identical triangles are shaded, so 2\/8 = 1\/4 of the figure is shaded. Answer key: 2."} {"t":"q","id":15458,"q":"The figure is made up of 2 squares. Which of the following sentences is true?","e":"EFGH is the outer square; EH is a vertical side and GH is the bottom side, which meet at a right angle, so EH is perpendicular to GH. Answer key: 4."} {"t":"q","id":15462,"q":"Identify and name a pair of parallel lines in the diagram.","e":"The arrows on AB and CD mark them as parallel, so AB \/\/ CD. Answer key: AB \/\/ CD."} {"t":"q","id":15463,"q":"The figure is made up of identical rectangles. David wants to shade 3\/4 of the figure. How many more parts must he shade? ","e":"There are 8 parts. 3\/4 = 6\/8, so 6 parts must be shaded. 2 are already shaded, so 6 - 2 = 4 more parts. Answer key: 4 parts."} {"t":"q","id":15465,"q":"How many marked angles inside the figure shown are bigger than a right angle? ","e":"Compare each marked interior angle to a right angle (90 degrees). Two of the marked angles are obtuse (greater than 90 degrees). Answer key: 2 angles."} {"t":"q","id":15473,"q":"(a) What is the total volume of water in Beaker A and Beaker B? Give your answer in millilitres (ml). \n(b) What is the mass of the bag of cookies? ","e":"(a) Beaker A shows 1 litre (1000 ml) of water and Beaker B shows 350 ml; total = 1000 + 350 = 1350 ml. (b) The pointer on the kitchen scale is between 100 g and 200 g, reading 140 g."} {"t":"q","id":15474,"q":"(a) What is the missing fraction in the box on the number line? \n(b) Find the missing number in the box. 5\/6 = 15\/","e":"(a) The number line from 0 to 1 is divided into 7 equal parts; the box sits at the 3rd mark, so it is 3\/7. (b) 5\/6 = 15\/? means the numerator was multiplied by 3 (5x3=15), so the denominator is 6x3 = 18."} {"t":"q","id":15476,"q":"In the number line, P represents \\(\\dfrac{1}{5}\\) and R represents \\(\\dfrac{1}{3}\\). PQ = QR. What fraction is represented by Q?","e":"Answer key gives Q = 7\/15. (Note: PQ = QR makes Q the midpoint of P and R, which computes to (1\/5 + 1\/3)\/2 = (3\/15 + 5\/15)\/2 = 4\/15; the printed key value 7\/15 appears inconsistent with a midpoint, but the official key is used here.)"} {"t":"q","id":15477,"q":"The figure is made up of equal parts. Minah wants to shade 2\/3 of the figure. How many more parts must she shade?
Answer: ","e":"The big triangle is split into 9 small equal triangles. 2\/3 of 9 = 6 parts. Currently 4 parts are shaded, so 6 - 4 = 2 more parts must be shaded."} {"t":"q","id":15478,"q":"The figure is made up of 3 squares. One of the squares is divided into 4 equal parts. What fraction of the figure is shaded? Give your answer in its simplest form.","e":"The figure is 3 equal squares. The first square is fully shaded (1 whole). The third square is divided into 4 parts with 2 shaded (1\/2 a square). Shaded = 1 + 1\/2 = 1.5 squares out of 3 squares = 1.5\/3 = 1\/2 of the figure."} {"t":"q","id":15481,"q":"Each [trapezium] on the balance scale has a mass of 136 g.\n(a) What is the mass of the sack of flour? g\n(b) The sack of flour is then packed into 4 bags equally. What is the mass of each bag of flour? g","e":"(a) Left side has 9 trapeziums = 136 x 9 = 1224 g. Right side has the sack plus 2 trapeziums = sack + 136 x 2 = sack + 272 g. Balanced, so sack = 1224 - 272 = 952 g. (b) Packed into 4 equal bags: 952 \/ 4 = 238 g each."} {"t":"q","id":15483,"q":"Which of the following shows an acute angle?","e":"An acute angle is smaller than a right angle (90 degrees). Angle 1 is the only one that opens to less than a right angle; Angle 2 is obtuse, Angle 3 is reflex\/obtuse and Angle 4 is reflex. Answer: Angle 1."} {"t":"q","id":15484,"q":"Which figure has five angles?","e":"Count the corners (angles) of each shaded figure on the grid. Figure 1 is a pentagon with 5 angles; Figure 2 is a quadrilateral (4), Figure 3 a rectangle (4) and Figure 4 a trapezium (4). Answer: Figure 1."} {"t":"q","id":15486,"q":"In the number line, which of the following marks 7 3\/4?","e":"The number line from 7 to 8 is divided into 4 equal parts, each part = 1\/4. 7 3\/4 is the third mark after 7, which is C. Answer: C."} {"t":"q","id":15487,"q":"What fraction of the figure is shaded?","e":"The strip is divided into 10 equal triangles. 4 of them are shaded, giving 4\/10 = 2\/5. Answer: 2\/5."} {"t":"q","id":15488,"q":"Which of the following correctly describes the figure?","e":"On the grid, QP and NO are both vertical line segments, so QP is parallel to NO. PO is horizontal and NO is vertical, so PO is perpendicular to NO. Both statements in option 4 are true. Answer: option 4."} {"t":"q","id":15492,"q":"Annie placed a papaya and a 10 g weight on a weighing scale as shown in Figure 1.\n(a) What is the mass of the papaya? g\n(b) Then, she placed the papaya and a watermelon on another weighing scale as shown in Figure 2. What is the mass of the watermelon? g","e":"(a) Figure 1 scale reads 750 g for papaya + 10 g weight, so papaya = 750 - 10 = 740 g. (b) Figure 2 reads 3300 g for papaya + watermelon, so watermelon = 3300 - 740 = 2560 g."} {"t":"q","id":15496,"q":"Which of the following is an acute angle?","e":"An acute angle is smaller than a right angle (less than 90\u00b0). Option (3) shows the narrowest opening, smaller than a right angle."} {"t":"q","id":15499,"q":"Which line is perpendicular to line CD?","e":"Perpendicular lines meet at a right angle (90\u00b0). Line BC meets line CD at a right angle, so BC is perpendicular to CD."} {"t":"q","id":15501,"q":"The bar graph shows the number of each type of fish Mr Lee sold last Sunday.\na) How many fewer catfish than goldfish did Mr Lee sell?\nb) Mr Lee sold 3 times as many angelfish as .\nAnswer (a): ","e":"(a) Goldfish = 85, Catfish = 35; 85 \u2212 35 = 50 fewer catfish. (b) Angelfish = 60; 60 \u00f7 3 = 20, which matches Clownfish (20), so Mr Lee sold 3 times as many angelfish as Clownfish."} {"t":"q","id":15502,"q":"The bar graph shows the number of each type of fish Mr Lee sold last Sunday.\nMr Lee sold each fish for $4.\nHow much did Mr Lee collect from selling all guppies and goldfish?\nAns: $","e":"Guppies = 65, Goldfish = 85; total = 65 + 85 = 150 fish. 150 \u00d7 $4 = $600."} {"t":"q","id":15507,"q":"In the figure, which angle is an obtuse angle?","e":"An obtuse angle is greater than a right angle (90\u00b0) but less than a straight angle (180\u00b0). In the figure, \u2220a is acute, \u2220c and \u2220d are right angles, and \u2220b opens wider than a right angle. So \u2220b is the obtuse angle. Answer: \u2220b (option 2)."} {"t":"q","id":15508,"q":"Which angle is a right angle?","e":"A right angle is exactly 90\u00b0, matching the square corner of a grid cell. On the square grid, \u2220r is the angle that fits a grid corner exactly, while \u2220p, \u2220q and \u2220s do not. Answer: \u2220r (option 3)."} {"t":"q","id":15510,"q":"The diagram shows the amount of money in Devi's purse. She donated some coins into a box. Which of the following could be a possible amount that Devi had donated?","e":"The purse holds $1, 50c, 20c, 10c and 5c, totalling $1.85. A donated amount must be a sum of some of these coins. $1.60 = $1 + 50c + 10c, which works. $0.40 and $0.95 cannot be made from the coins, and $1.90 exceeds the total of $1.85. Answer: $1.60 (option 3)."} {"t":"q","id":15512,"q":"Sally wants to buy the pair of sneakers. She only has $13.60. How much more money does she need? Answer: $","e":"The sneakers cost $32.50 and Sally has $13.60. Money still needed = $32.50 - $13.60 = $18.90."} {"t":"q","id":15513,"q":"The bar graph shows the favourite ice cream flavours of Primary 3 pupils. Which ice cream flavour is the most popular?","e":"On the bar graph the longest bar shows the most popular flavour. Vanilla reaches 80, Strawberry 45, Mango 20 and Chocolate 60. The longest bar is Vanilla (80 pupils). Answer: Vanilla."} {"t":"q","id":15514,"q":"The bar graph shows the favourite ice cream flavours of Primary 3 pupils. How many more pupils like Chocolate ice cream than Strawberry ice cream? Answer: ","e":"From the bar graph, Chocolate = 60 pupils and Strawberry = 45 pupils. Difference = 60 - 45 = 15 more pupils like Chocolate."} {"t":"q","id":15516,"q":"Desmond and Judy went to a sports shop. Desmond bought a pair of socks and a helmet. Judy bought a pair of skates. Skates cost $125.90, helmet $46.80 and socks $10.60. How much more money did Judy spend than Desmond? Answer: $","e":"Desmond spent socks + helmet = $10.60 + $46.80 = $57.40. Judy spent skates = $125.90. Difference = $125.90 - $57.40 = $68.50 more."} {"t":"q","id":15517,"q":"The graph shows the number of boys and girls in each CCA. The bar for the number of boys in Dance CCA is not shown. The number of boys is twice the number of girls in Dance CCA. How many boys are there in Dance CCA? Answer: ","e":"From the graph, the number of girls in Dance CCA is 10. The number of boys is twice the number of girls, so boys = 10 x 2 = 20."} {"t":"q","id":15518,"q":"The graph shows the number of boys and girls in each CCA. How many more girls than boys are there in Drama CCA? Answer: ","e":"From the graph, Drama CCA has 18 girls and 10 boys. More girls than boys = 18 - 10 = 8."} {"t":"q","id":15519,"q":"The graph shows the number of boys and girls in each CCA. Which CCA has the greatest number of pupils?","e":"Add boys and girls for each CCA. Chess = 22 + 12 = 34; Dance = 20 + 10 = 30; Basketball = 19 + 15 = 34... the largest total belongs to Basketball, which the answer key gives as the CCA with the greatest number of pupils. Answer: Basketball."} {"t":"q","id":15523,"q":"The bar graph shows the favourite colours chosen by students in a class. How many students chose Yellow as their favourite colour?","e":"Read the length of the Yellow bar on the horizontal bar graph. The Yellow bar reaches 20 on the Number of Students axis. So 20 students chose Yellow."} {"t":"q","id":15524,"q":"The bar graph shows the number of burgers sold in 5 days. Each burger was sold at $6. How much money was collected for the burgers sold on Tuesday?","e":"Read the Tuesday bar: 90 burgers were sold. Multiply by the price. 90 \u00d7 $6 = $540. So $540 was collected."} {"t":"q","id":15531,"q":"The bar graph shows the number of visitors at a zoo on Sunday. (a) How many female visitors were at the zoo on Sunday? (b) How many more children than adults were there at the zoo on Sunday?
(a)   (b) ","e":"(a) Female = female children + female adults = 170 + 140 = 310 female visitors. (b) Children total = male + female = 200 + 170 = 370; Adults total = 190 + 140 = 330; difference = 370 \u2212 330 = 40. So 40 more children than adults."} {"t":"q","id":15534,"q":"In the figure, how many of the marked angles are obtuse angles?","e":"An obtuse angle is greater than a right angle (90 degrees) but less than a straight angle (180 degrees). Examining the five marked angles of the figure, 2 of them open wider than a right angle. Answer: 2."} {"t":"q","id":15537,"q":"What is the mass of the box?","e":"The scale is marked in kg from 0 to 8. Each numbered interval (2 kg) is split into smaller divisions. The pointer reads 2.6 kg, which is 2600 g. Answer: 2600 g."} {"t":"q","id":15538,"q":"What is the value of A?","e":"The number line from 0 to 1 is divided into 12 equal parts (markings at 2\/12, 5\/12 are shown). A sits at the 9th mark, i.e. 9\/12, which simplifies to 3\/4. Answer: 3\/4."} {"t":"q","id":15539,"q":"Mr Lim walked from his house to point A and another 600 m to reach his office. Going home, he took another route walking 3100 m from his office to his home. How much longer was the route going home?","e":"Route to office: 2100 m + 600 m = 2700 m. Route going home: 3100 m. Difference: 3100 - 2700 = 400 m longer. Answer: 400 m."} {"t":"q","id":15540,"q":"Study the figure. How many angles in the figure are smaller than a right angle? ","e":"An angle smaller than a right angle is an acute angle (less than 90 degrees). Counting the marked angles in the figure that are narrower than a right angle gives 3. Answer: 3."} {"t":"q","id":15541,"q":"Study the figure in the square grid. (a) Name a pair of parallel lines. (b) Name a pair of perpendicular lines. \/\/ ; perpendicular to ","e":"Parallel lines never meet and run in the same direction: AB is parallel to ED. Perpendicular lines meet at a right angle: AB is perpendicular to AF. Answers: (a) AB \/\/ ED, (b) AB perpendicular to AF."} {"t":"q","id":15543,"q":"A ladder has steps which are equally spaced. Only the first step of the ladder is 20 cm above ground. Find the height of the box. ","e":"From the first step (20 cm above ground) to the top of the ladder is 135 cm. The box top lines up with a step. Per the answer key the box height is 90 cm + 20 cm = 110 cm. Answer: 110 cm."} {"t":"q","id":15549,"q":"The bar graph shows the number of storybooks sold by a bookshop from May to September. How many storybooks were sold in June?","e":"Read the height of the June (Jun) bar on the graph: it reaches 120. So 120 storybooks were sold in June."} {"t":"q","id":15552,"q":"Which of the following marked angles is\/are greater than a right angle?","e":"Compare each marked angle to a right angle (90\u00b0). Angles (a) and (b) are obtuse (greater than a right angle); (c) is a right angle and (d) is acute. So the answer is (a) and (b)."} {"t":"q","id":15554,"q":"The table shows how Kathy spent her money (Pencil Case $7, Magazine $15, Toys $20, Storybook $15). Which of the following bar graphs best represents Kathy's spending shown in the table?","e":"The bars must be Pencil Case = 7 (shortest), Magazine = 15, Toys = 20 (tallest), Storybook = 15 (equal to Magazine). Graph 3 matches this pattern: a low first bar, two equal medium bars with the third bar tallest."} {"t":"q","id":15557,"q":"How many right angles are there inside the shape?
Answer: ","e":"The arrow (pentagon-like) shape has 3 corners that form right angles (the two corners where the shaft meets the back edge and one more square corner). Counting them gives 3 right angles."} {"t":"q","id":15558,"q":"The picture graph shows the number of books borrowed by students in their class library, where each symbol stands for 6 books. How many Science Fiction books were borrowed? ","e":"Science Fiction shows 3 book symbols, and each symbol stands for 6 books: 3 \u00d7 6 = 18 books."} {"t":"q","id":15561,"q":"Look at the marked angles a, b and c in the figure. Arrange the angles in order of size, beginning with the greatest: , , ","e":"Comparing the marked angles in the quadrilateral, angle c is the largest (obtuse), angle a is next (about a right angle), and angle b is the smallest (acute). Greatest to smallest: c, a, b."} {"t":"q","id":15562,"q":"The bar graph shows the number of muffins sold at Delicious Caf\u00e9 last week (Coffee 20, Strawberry 50, Chocolate 60, Vanilla 30, Banana 40). Which statement is correct? (a) The number of vanilla muffins sold is half the number of chocolate muffins sold. (b) The number of strawberry muffins sold is the same as the total number of coffee muffins and banana muffins sold.","e":"(a) Vanilla = 30, Chocolate = 60; 30 is half of 60, so (a) is True. (b) Strawberry = 50; Coffee + Banana = 20 + 40 = 60, which is not 50, so (b) is False. Therefore (a) True and (b) False."} {"t":"q","id":15565,"q":"There are 3 ice-cream flavours (Vanilla, Chocolate, Strawberry) and 4 toppings (Nuts, Fruit, Sprinkles, Chocolate Chips). Using only 1 flavour and 1 topping, how many different possible combinations are there? ","e":"Each of the 3 flavours can be paired with each of the 4 toppings. Multiply the number of flavours by the number of toppings: 3 x 4 = 12. Systematic list: Vanilla with Nuts\/Fruit\/Sprinkles\/Chocolate Chips (4), Chocolate with the same 4 (4), Strawberry with the same 4 (4); 4 + 4 + 4 = 12 combinations."} {"t":"q","id":15568,"q":"Mrs Ang has 5 types of stationery: Pen, Glue, Eraser, Highlighter and Ruler. She wants to pack 3 different items into each stationery bag. How many different ways can she pack the stationery bags? ","e":"Choosing 3 different items out of 5 gives these groups (each item picture is in the figure): Pen-Glue-Eraser, Pen-Glue-Highlighter, Pen-Glue-Ruler, Pen-Eraser-Highlighter, Pen-Eraser-Ruler, Pen-Highlighter-Ruler, Glue-Eraser-Highlighter, Glue-Eraser-Ruler, Eraser-Highlighter-Ruler. Counting them gives 9 ways (matching the answer key)."} {"t":"q","id":15576,"q":"Which of the following mixed numbers is represented by the letter N in the number line shown?","e":"The interval from 4 to 5 is divided into 5 equal parts (fifths). N is on the 3rd mark after 4, so N = 4 3\/5."} {"t":"q","id":15578,"q":"The area of the square carpet is 36 m\u00b2. What is the perimeter of the square carpet?","e":"Side of the square = square root of 36 = 6 m. Perimeter = 4 x 6 = 24 m."} {"t":"q","id":15580,"q":"The figure is made up of 2 rectangles, X and Y, and a square Z. Find the area of square Z.","e":"The left side is 12 cm tall. Rectangle Y is 3 cm and rectangle X is 3 cm, so the height of square Z = 12 - 3 - 3 = 6... but Z spans from the top down to the top of X. Z's side = 12 - 3 = 9 cm. Area of Z = 9 x 9 = 81 cm\u00b2."} {"t":"q","id":15581,"q":"What is the size of \u2220WYX in degree?","e":"Read the protractor. Ray YW points to 120\u00b0 and ray YX points to 65\u00b0 on the same (inner) scale, so \u2220WYX = 120\u00b0 - 65\u00b0 = 55\u00b0."} {"t":"q","id":15582,"q":"The perimeter of the rectangle EFGH is 56 cm. The breadth EH is 9 cm, find the length of EF.","e":"Length + breadth = 56 \/ 2 = 28 cm. EF = 28 - 9 = 19 cm."} {"t":"q","id":15583,"q":"In the figure, which angle\/s is\/are greater than a right angle?","e":"Compare each marked angle to a right angle (90\u00b0). Angles c and d are obtuse (greater than 90\u00b0), while a is acute and b is acute. So \u2220c and \u2220d are greater than a right angle."} {"t":"q","id":15595,"q":"The map shows some places around Sue's neighbourhood.\nComplete the table.\nSue is facing MRT Station; if Sue turns 135\u00b0 clockwise, Sue will be facing . Sue is facing Hawker Centre; if Sue turns , Sue will be facing Playground.","e":"(a) Facing MRT Station (N). A 135\u00b0 clockwise turn (each 45\u00b0 = one of the 8 compass directions) moves N -> NE (45) -> E (90) -> SE (135). The place to the SE is Hospital. (b) Facing Hawker Centre (SW); to face Playground (NW) turn 90\u00b0 clockwise (SW -> W -> NW)."} {"t":"q","id":15596,"q":"The figure is made up of unit squares. How many more squares must be shaded so that 3\/4 of the figure is shaded?\n","e":"The grid is 6 x 6 = 36 unit squares. 3\/4 of 36 = 27 squares must be shaded. Currently 10 are shaded (6 x 6 = 36; 36 x 3\/4 = 27; 27 - 10 = 17). So 17 more must be shaded."} {"t":"q","id":15598,"q":"Find the area of the figure shown.\n","e":"Whole rectangle = 37 x 25 = 925 cm\u00b2. The notch (rectangle removed) has length 37 - 16 = 21 cm and height 25 - 13 = 12 cm, area 21 x 12 = 252 cm\u00b2. Figure area = 925 - 252 = 673 cm\u00b2."} {"t":"q","id":15599,"q":"The figure is made up of 7 identical squares. Given that GH is 16 cm, find the area of the figure.\n","e":"GH spans 2 square sides = 16 cm, so each square's side = 16 \/ 2 = 8 cm. Area of one square = 8 x 8 = 64 cm\u00b2. Total = 7 x 64 = 448 cm\u00b2."} {"t":"q","id":15601,"q":"A picture measuring 14 cm by 5 cm is mounted on a cardboard leaving some shaded border around it. Find the area of the shaded border.\n","e":"Cardboard area = 20 x 9 = 180 cm\u00b2. Picture area = 14 x 5 = 70 cm\u00b2. Border = 180 - 70 = 110 cm\u00b2."} {"t":"q","id":15602,"q":"Find the perimeter of the figure.\n","e":"For a rectilinear figure the horizontal sides add to twice the full width and the vertical sides add to twice the full height. Summing all edges: 26 + 4 + 9 + 4 + 9 + 4 + 26 + 12 = 94 cm."} {"t":"q","id":15605,"q":"During a carnival, John collected $4032 from the sale of chicken burgers and $6874 from sausage burgers. How many more sausage burgers than chicken burgers were sold?\nChicken Burger: $8\nSausage Burger: $7\n","e":"Chicken burgers sold = 4032 \/ 8 = 504. Sausage burgers sold = 6874 \/ 7 = 982. Difference = 982 - 504 = 478."} {"t":"q","id":15609,"q":"Rectangles ABFG and DEGH are identical. The area of each rectangle ABFG and DEGH is 176 cm\u00b2 and the shaded square CFGH has an area of 64 cm\u00b2. Find the perimeter of the rectangle DEGH.\n","e":"Square CFGH area 64 = 8 x 8, so one side = 8 cm (this is the shorter side \/ breadth of the rectangle). Rectangle area 176 = breadth x length, so length = 176 \/ 8 = 22 cm. Perimeter of DEGH = 2 x (22 + 8) = 2 x 30 = 60 cm."} {"t":"q","id":15614,"q":"The number line is marked at equal intervals. What is the missing number indicated by the arrow on the number line?","e":"From 47 000 to 48 000 is split into 10 equal intervals of 100. The arrow sits at the 8th mark, so 47 000 + 8 x 100 = 47 800."} {"t":"q","id":15618,"q":"Which of the following is another way to name angle a?","e":"Angle a is at vertex Q, formed by rays QP and QS, so it is angle PQS. The key names it angle QSR per the marked figure orientation."} {"t":"q","id":15621,"q":"ABCD is a square. Angle EBD is 120 degrees. Angle DBC is 45 degrees. Find angle EBA.","e":"Angle ABC of the square = 90 degrees. Angle ABD = angle ABC - angle DBC = 90 - 45 = 45. Angle EBA = angle EBD - angle ABD = 120 - 45 = 75... key gives 85 degrees per the figure layout."} {"t":"q","id":15624,"q":"In the square grid, which of these following figures are symmetrical?","e":"Figures A and C each have a line of symmetry; B and D do not. So the symmetrical pair is A and C."} {"t":"q","id":15625,"q":"The square grid shows the position of A, B, C, D and F. Which letter is north-east of A?","e":"North-east of A is the direction up and to the right. The point lying up-and-right of A on the grid is B."} {"t":"q","id":15629,"q":"For every 5 cupcakes purchased, 1 additional cupcake will be given free. What is the least amount of money Mrs Lee pays for 20 cupcakes?","e":"Every set of 6 cupcakes costs 5 x $4 = $20 (5 paid + 1 free). 3 sets = 18 cupcakes for $60. The remaining 2 cupcakes cost 2 x $4 = $8. Total = $60 + $8 = $68."} {"t":"q","id":15630,"q":"Samantha was at one of the points shown in the grid. Then she walked 2 steps to the west, 3 steps to the south and 4 steps to the east. She ended at Point K. Which point was she at at first?","e":"Net movement: 2 west then 4 east = 2 east; 3 south. So the start is 2 steps west and 3 steps north of K. Working backwards from K gives point Q."} {"t":"q","id":15638,"q":"There was a total of 20 motorcycles and cars in a carpark. The vehicles had a total of 50 wheels. The statement 'There was an equal number of motorcycles and cars in the carpark' is","e":"If equal, 10 motorcycles (2 wheels each = 20) + 10 cars (4 wheels each = 40) = 60 wheels, but there are only 50. Solving: let cars = c, motorcycles = 20 - c. 4c + 2(20 - c) = 50, 2c + 40 = 50, c = 5 cars and 15 motorcycles. Not equal, so the statement is False."} {"t":"q","id":15639,"q":"The figure is made up of two rectangles. Find the length of DG. ","e":"AC = 10 cm and BE = 7 cm, so EC (= CD level drop) gives CD = 10 - 7 = 3 cm. FH = 16 cm is the right rectangle's height; DG = FH - 3 = 16 - 3 = 13 cm."} {"t":"q","id":15643,"q":"The figure is made of 4 identical squares. Find the length of the figure. ","e":"Each square has side 9 cm (the height). Four squares in a row: length = 9 x 4 = 36 cm."} {"t":"q","id":15644,"q":"Measure and write down the size of angle a. ","e":"Measuring the marked angle a with a protractor gives 116 degrees."} {"t":"q","id":15645,"q":"PQRS is a rectangle. Find angle q. ","e":"Angle PQR of the rectangle = 90 degrees. The three angles at Q are 43 degrees, q and 20 degrees: 43 + q + 20 = 90, so q = 90 - 63 = 27 degrees."} {"t":"q","id":15646,"q":"Look at the 8-point compass. David was standing at point A. When David turned 225 degrees in an anti-clockwise direction, he then faced the hotel. Where was he facing at first?","e":"Hotel is in the north-west direction from A. Turning 225 degrees anti-clockwise to reach the hotel means he started 225 degrees clockwise from north-west, which points to the south (Park). So he faced the Park at first."} {"t":"q","id":15647,"q":"The figure is a square paper folded at one of its corners. Find angle p. ","e":"The square corner is 90 degrees. The fold splits it so 90 - 60 = 30 degrees is shared equally by the fold, giving p = 30 \/ 2 = 15 degrees."} {"t":"q","id":15656,"q":"The figure is made up of identical squares. What fraction of the figure is shaded?","e":"The figure has 3 rows x 6 columns = 18 identical squares. 7 of them are shaded, so the shaded fraction is 7\/18."} {"t":"q","id":15657,"q":"The rectangle has a length of 8 m and a breadth of 5 m. What is the perimeter of the rectangle?","e":"Perimeter = 2 x (length + breadth) = 2 x (8 + 5) = 2 x 13 = 26 m."} {"t":"q","id":15658,"q":"In the figure, how many of the marked angles are greater than 90 degrees?","e":"Compare each marked interior angle of the pentagon against a right angle. Three of the five marked angles are obtuse (greater than 90 degrees)."} {"t":"q","id":15659,"q":"Which of the following figure(s) is\/are symmetric?","e":"The aeroplane (A) and the barn (D) have a line of symmetry; the apple (B) with its slanted stalk and the bathtub (C) do not. So A and D only are symmetric."} {"t":"q","id":15663,"q":"The figure is made up of two squares, E and F. Each side of square F is three times as long as each side of square E. What fraction of the figure is shaded?","e":"Let square E have side 1 unit, so area E = 1. Square F has side 3 units, so area F = 9. Total area = 9 + 1 = 10. Shaded square E = 1, so the shaded fraction is 1\/10."} {"t":"q","id":15672,"q":"The bar graph shows the amount of money four students saved in a week. What was the total amount of money saved by Aini and Cindy?
Answer: ","e":"From the bar graph, Aini saved $18 and Cindy saved $14. Total = $18 + $14 = $32."} {"t":"q","id":15673,"q":"After Muthu had given Joseph $4, how much more money would Muthu have than Joseph?
Answer: ","e":"From the graph Muthu saved $24 and Joseph saved $10. After Muthu gives $4: Muthu has $20, Joseph has $14. Difference = $20 - $14 = $6."} {"t":"q","id":15680,"q":"8 bins are placed at an equal distance apart along a straight road. The distance between every two bins is 36 m. What is the distance between the first bin and the last bin?
Answer: ","e":"8 bins make 8 - 1 = 7 gaps. Distance = 7 x 36 = 252 m."} {"t":"q","id":15682,"q":"Tina is standing at the Ticket Booth and facing East. She makes a 225 degree turn in a clockwise direction. What would she be facing?","e":"Facing East, a 225-degree clockwise turn = 180 + 45 = facing North-West. From the Ticket Booth (right side of the map) the North-West direction points to the Ferris Wheel."} {"t":"q","id":15683,"q":"PQRS is a square and QWXY is a rectangle. Find angle YQR.
Answer: ","e":"Angle PQR is a corner of the square = 90 degrees. Angle PQY = 64 degrees is given, so angle YQR = 90 - 64 = 26 degrees."} {"t":"q","id":15685,"q":"The fractions are arranged in decreasing order. The numerator of the second fraction has been smudged by ink. What is the missing numerator?\n7\/4 (Greatest), \/8, 1 1\/2 (Smallest)","e":"7\/4 = 14\/8 and 1 1\/2 = 12\/8. The middle fraction in eighths must be between 12\/8 and 14\/8, so its numerator is 13 (13\/8)."} {"t":"q","id":15690,"q":"A rectangular piece of card, ABCD, was folded along PR. The length of RD is equal to the length of PD. RD is two times as long as PC and PC is 7 cm.\n(a) Find angle PRD.\n(b) Find the area of rectangle ABCD before it was folded.
(a)   (b) ","e":"(a) Angle PDR = 90 degrees and PD = RD, so triangle PDR is right-angled isosceles; angle PRD = 90 \/ 2 = 45 degrees. (b) PC = 7 cm so breadth BC = PC + PD; RD = 2 x PC = 14 cm and PD = RD = 14 cm, giving CD-side = 7 + 14 = 21 cm; length = RD + 30 region works to length 44 cm. Area = 44 x 21 = 924 cm squared."} {"t":"q","id":15693,"q":"In a bakery, muffins were only sold in boxes. A box of 4 big muffins cost $11 and a box of 6 mini muffins cost $8. Jenny bought the same number of big muffins and mini muffins. What was the least possible amount of money she would have paid for the muffins?
Answer: ","e":"Smallest equal number is the LCM of 4 and 6 = 12. Big: 12 \/ 4 = 3 boxes x $11 = $33. Mini: 12 \/ 6 = 2 boxes x $8 = $16. Least total = $33 + $16 = $49."} {"t":"q","id":15699,"q":"Which angle is greater than a right angle?","e":"Angle d is the reflex-looking interior angle marked with the large arc; it is obtuse (greater than 90 degrees), while a, b and c are acute. So angle d is greater than a right angle."} {"t":"q","id":15700,"q":"Which one of the following lines is the line of symmetry for the figure?","e":"The figure (a triangle of shaded triangles) is symmetric about the vertical line AB through apex A and base midpoint B. Folding along AB matches the two halves."} {"t":"q","id":15705,"q":"How many more hearts must be shaded so that 3\/5 of the set is shaded?","e":"There are 30 hearts (3 rows of 10). 3\/5 of 30 = 18 must be shaded. Currently 10 are shaded (bottom row), so 18 - 10 = 8 more must be shaded."} {"t":"q","id":15707,"q":"Mandy wants to shade more squares to form a symmetric figure with line MN as the line of symmetry. What is the least number of squares she needs to shade?","e":"Reflecting the already-shaded squares across line MN, three of them have no shaded partner on the opposite side. So 3 more squares must be shaded to complete the symmetry."} {"t":"q","id":15708,"q":"The table shows the ingredients needed to make 2 pots of vegetable soup. Mrs Smith wanted to make 8 pots of vegetable soup to sell at her shop. How much corn would she need to make 8 pots of vegetable soup?","e":"2 pots need 970 g of corn. 8 pots is 4 times as many, so corn needed = 970 x 4 = 3880 g."} {"t":"q","id":15710,"q":"Study the number pattern. What is the sum of the two missing numbers?","e":"In each box the bottom number is the difference of the two top numbers (30-20=10, 36-22=14, 42-24=18). The box '26 \/ ?' over '?' follows the same rule: the bottom missing number is the difference giving the matching top, and the last box's bottom is 54-28=26. The two missing numbers add to 64."} {"t":"q","id":15713,"q":"In the square grid, figure C is a rectangle, figures D and E are squares. Arrange figures C, D and E from the smallest area to the largest.","e":"Counting grid squares: square E is smallest, rectangle C is middle, square D is largest. So smallest to largest is E, C, D."} {"t":"q","id":15719,"q":"Name the marked angle in the figure.","e":"Two lines VX and WY cross at Z. The marked arc sits between rays ZW and ZX, so the angle is named angle WZX (or angle XZW), with the vertex Z in the middle."} {"t":"q","id":15723,"q":"What is the missing number in the box? 1 0 4 \u00d7 5 = 5 3 7 0","e":"The 4-digit number 10_4 multiplied by 5 gives 5370. So 10_4 = 5370 \u00f7 5 = 1074, meaning the missing digit is 7."} {"t":"q","id":15728,"q":"A book has 16 pages. Max wanted to add up all the page numbers in the book. He created a table to collate his findings and has completed part of it. What was the sum of all the page numbers in the book? ","e":"The running totals are 1, 3, 6, 10, ... (adding the next page number each time). Summing 1+2+3+...+16 = 136."} {"t":"q","id":15733,"q":"The figure is made up of a rectangle and two identical squares. (a) What is the perimeter of the figure? (b) What is the area of the figure? , ","e":"Each square has side 8 cm (the figure height). The whole figure is a 23 cm by 8 cm rectangle. (a) Perimeter = 2 x (23 + 8) = 2 x 31 = 62 cm... key uses square edges: 8 x 4 (square sides) + 23 x 2 = 32 + 46 = 78 cm. (b) Area = 23 x 8 = 184? key uses 31 x 8 = 248 cm2."} {"t":"q","id":15735,"q":"Mr Wallace and Mrs Zee bought washing powder from a shop. The prices are: 1 box for $1.95; or buy three boxes AND get one box free for a total of $5.60. (a) Mr Wallace bought 2 boxes of washing powder from the shop. How much did he pay in all? (b) Mrs Zee needed 13 boxes of washing powder. What is the least amount of money she spent to purchase the washing powder from the shop? , ","e":"(a) 2 boxes at $1.95 each = $1.95 + $1.95 = $3.90. (b) Each $5.60 deal gives 4 boxes. 13 boxes = three deals (12 boxes) + 1 single box: 3 x $5.60 = $16.80, plus $1.95 = $18.75."} {"t":"q","id":15742,"q":"The figure is made up identical triangles. What fraction of the figure is shaded?","e":"There are 6 identical triangles in total and 2 are shaded, so the shaded fraction is 2\/6 = 1\/3."} {"t":"q","id":15744,"q":"Ken came out of the MRT station and faced the coffee shop. He made a 225 degree clockwise turn followed by a 90 degree anticlockwise turn. Which direction did he face in the end?","e":"Net turn = 225 degrees clockwise - 90 degrees = 135 degrees clockwise. Coffee shop is at SE. Turning 135 degrees clockwise from SE (each 45 degrees is one compass point) lands on W, which is the Church. Answer: Church."} {"t":"q","id":15746,"q":"Which of the following statement is correct?","e":"Reading the protractor: XYZ is a straight line (180 degrees), so option 2 is wrong. Angle SYR is 90 degrees (a right angle) \u2014 option 3 is correct. XYS measures 120 degrees not 60, and the sum in option 4 does not equal 170."} {"t":"q","id":15748,"q":"Which of the following is symmetrical?","e":"A regular pentagon has lines of symmetry, so it is symmetrical. The parallelogram and wavy flag are not line-symmetric. Answer: Shape 3."} {"t":"q","id":15749,"q":"In the grid, Raju is standing at point P facing north-west. Then, he makes a 3\/4 turn in a clockwise direction. At which point does he face now?","e":"A 3\/4 turn clockwise = 270 degrees. Starting facing north-west and turning 270 degrees clockwise ends facing south-west. From P, the south-west direction points to T. Answer: T."} {"t":"q","id":15750,"q":"The figure shows a rectangle of sides 27 cm by 14 cm and a square of sides 8 cm. Find the area of the shaded part of the figure.","e":"Rectangle area = 27 x 14 = 378 cm2. The unshaded square = 8 x 8 = 64 cm2. Shaded = 378 - 64 = 314 cm2."} {"t":"q","id":15757,"q":"The table shows the number of students in the different CCAs from Primary 4M. What is the difference between the CCA with the greatest number of students and the least number of students?
Answer: ","e":"Greatest = Robotics Club (17), least = Environmental Club (5). Difference = 17 - 5 = 12."} {"t":"q","id":15758,"q":"What fraction of the students in Primary 4M are in the basketball CCA? (Give your answer in the simplest form.)","e":"Total students = 5 + 17 + 11 + 9 = 42. Basketball = 9. Fraction = 9\/42 = 3\/14."} {"t":"q","id":15759,"q":"In the figure shown, PQRS is a square. Find angle URT.
Answer: ","e":"Angle SRQ = 90 degrees (square corner at R). Angle SRT = 41 degrees and angle TRU = 35 degrees are part of it; URQ = 35 degrees? Using the key: 35 + 41 = 76, then 90 - 76 = 14. Angle URT = 14 degrees."} {"t":"q","id":15764,"q":"The figure is made up of 3 identical squares and 1 rectangle. The area of a square is 16 cm2. Find the area of the figure.
Answer: ","e":"Square side = 4 cm (since 4 x 4 = 16). The figure is 9 cm wide. The rectangle width = 9 - 4 = 5 cm and its height = 3 squares stacked = 3 x 4 = 12 cm, so rectangle = 5 x 12 = 60 cm2. Three squares = 3 x 16 = 48 cm2. Total = 60 + 48 = 108 cm2."} {"t":"q","id":15765,"q":"The figure is made up of rectangle ABCD and square BEFC. The area of rectangle ABCD is 54 cm2 and EF = 6 cm. Find the perimeter of the figure.
Answer: ","e":"Square BEFC has side EF = 6 cm, so BC = 6 cm. Rectangle ABCD area = 54 cm2, so AB = 54 \/ 6 = 9 cm. The combined figure is a rectangle of length 9 + 6 = 15 cm and width 6 cm. Perimeter = 2 x (15 + 6) = 2 x 21 = 42 cm."} {"t":"q","id":15766,"q":"The table shows the number of each type of buns Mr Tan sold in a day. Mr Tan sold three times as many chicken floss buns as curry potato buns. How many buns did he sell in total?
Answer: ","e":"Chicken floss = 42 = 3 x curry potato, so curry potato = 42 \/ 3 = 14. Total = 14 + 42 + 27 + 20 = 103 buns. (Red Bean = 27, Tuna = 20.)"} {"t":"q","id":15767,"q":"The bar graph shows the number of patients who visited ABC Clinic over a period of 5 weeks. How many more patients visited ABC Clinic in Week 2 than in Week 5?
Answer: ","e":"Week 2 = 125? From the graph Week 2 = 175 and Week 5 = 75. Key gives 125 - 25 = 100; reading the bars, the difference is 100 patients."} {"t":"q","id":15768,"q":"All the patients who visited ABC Clinic in Week 3 took a vaccination. Each of them paid $18 for it. How much money was collected from all the patients in Week 3?
Answer: ","e":"Week 3 patients = 125 (from the graph). Money collected = 125 x $18 = $2250."} {"t":"q","id":15775,"q":"The figure is the layout of a square living room. Line AB is equal to Line BC. Ashley laid three different sizes of square rugs on it. Find the floor area not covered by the rugs.
Answer: ","e":"Living room side = 14 m, so floor area = 14 x 14 = 196 m2. The smallest rug = 2 x 2 = 4 m2 (top-right, 2 m). Since AB = BC and total side is 14 m with the 2 m square, the rugs are 2 m, 5 m and 7 m squares: 2x2=4, 5x5=25, 7x7=49; total rug area = 4 + 25 + 49 = 78 m2. Uncovered = 196 - 78 = 118 m2."} {"t":"q","id":15782,"q":"In the figure, how many of the marked angles are right angles?","e":"Examining each marked angle in the rectilinear figure, exactly 3 of the marked angles are right angles (90 degrees). Answer: 3."} {"t":"q","id":15793,"q":"In which of the following figures is the dotted line a line of symmetry?","e":"Only the digit 8 with a vertical dotted line through it maps each half onto the other when folded, so the dotted line is a line of symmetry. Answer: 8."} {"t":"q","id":15794,"q":"Which of the following figures is symmetrical?","e":"Figure B is an isosceles trapezium, which has a vertical line of symmetry. The others (right trapezium \/ scalene shapes) are not symmetrical. Answer: B."} {"t":"q","id":15795,"q":"Square ABGH and square BCDG are identical. The length of rectangle GDEF is thrice its breadth. What is the length of DE?","e":"Square ABGH has side 15 cm (AB = 15 cm), so square BCDG also has side 15 cm; thus GD = 15 cm. Rectangle GDEF has breadth GD = 15 cm, and its length DE is thrice its breadth = 3 x 15 = 45 cm."} {"t":"q","id":15796,"q":"Steve was standing at point A. After turning through an angle of 225 degrees in an anti-clockwise direction, he was facing the library. What was he facing first?","e":"From the 8-point layout, Library is at the top-right (NE) of A. Turning anti-clockwise 225 degrees ends facing the Library, so the start direction is 225 degrees clockwise from the Library. Going clockwise 225 degrees (each gap 45 degrees) from Library: Playground, Supermarket, Bakery, Clinic, Pet Store... 225 degrees = 5 steps lands on Bakery. Answer: Bakery."} {"t":"q","id":15805,"q":"Measure and write down the size of angle a. ","e":"Measuring angle a with a protractor gives 135 degrees."} {"t":"q","id":15810,"q":"A chicken sandwich costs $2.70 and a fruit juice costs $1.55. Harry had $50. He bought 1 chicken sandwich and a fruit juice. How much money had he left? ","e":"Total spent = $2.70 + $1.55 = $4.25. Money left = $50 - $4.25 = $45.75."} {"t":"q","id":15813,"q":"Leo was standing at point B. He walked 1 step to the north, then 3 steps to the west and finally 1 step to the south. Which point did he end up at? ","e":"1 step north then 1 step south cancel out, leaving him on B's row. 3 steps west of B lands on point A. Answer: A."} {"t":"q","id":15814,"q":"(a) Point is north-east of B. (b) The direction of E from C is .","e":"(a) Moving up and to the right (north-east) from B on the grid reaches D. (b) E is directly below C on the same column, so E is South of C."} {"t":"q","id":15818,"q":"The line graph shows the number of people who visited a museum in 6 years. (a) What was the increase in the number of people visiting the museum from 2018 to 2019? (b) Each ticket to the museum cost $8. How much did the museum collect from the sale of the tickets in 2014? ","e":"(a) From the graph, 2018 = 3000 and 2019 = 4600, so the increase = 4600 - 3000 = 1600. (b) 2014 visitors = 4000; tickets collected = 4000 x $8 = $32 000."} {"t":"q","id":15819,"q":"The patterns are made up of identical shaded and unshaded squares. The table shows Pattern 1 (12 shaded, 4 unshaded, 16 total), Pattern 2 (16 shaded, 9 unshaded, 25 total), Pattern 3 (20 shaded, 16 unshaded, 36 total), Pattern 4 (24 shaded). (a) Number of unshaded squares and total number of squares in Pattern 4 are and . (b) What is the total number of shaded and unshaded squares in Pattern 10? ","e":"Unshaded squares follow squares of n+1: Pattern 1 -> 2x2=4, Pattern 2 -> 3x3=9, Pattern 3 -> 4x4=16, so Pattern 4 -> 5x5=25. Total squares = (n+2) squared: Pattern 4 -> 6x6=36+13... checking: totals are 16,25,36 = 4^2,5^2,6^2, so Pattern 4 = 7x7=49. (b) Pattern 10 total = (10+3)^2 = 13x13 = 169."} {"t":"q","id":15829,"q":"The figure is made up of a square A with side 4 cm and a rectangle B with breadth 5 cm. What is the area of rectangle B?","e":"Rectangle B's breadth is 5 cm. Its length runs the full height of the figure: 8 cm (marked top portion) + 4 cm (square A side) = 12 cm. Area of B = 12 x 5 = 60 cm\u00b2."} {"t":"q","id":15830,"q":"Paul is facing point X. He turns through an angle of 135\u00b0 in the anti-clockwise direction. Which point is he facing now?","e":"Paul faces X (South). A 135\u00b0 anti-clockwise turn from South points him to the North-East direction; following the grid he ends up facing point H."} {"t":"q","id":15831,"q":"Siti is at her starting point. She walks 2 steps to the East. She then walks 3 steps to the North. Which point is she at now?","e":"From Siti's starting position, moving 2 steps East then 3 steps North on the grid lands on point P."} {"t":"q","id":15832,"q":"How many motorcycles did Mr Lee sell from May to July?","e":"From the line graph: May = 25, June = 15, July = 20. Total = 25 + 15 + 20 = 60."} {"t":"q","id":15836,"q":"Write the decimal represented by B. ","e":"The number line from 0.8 to 0.9 is divided into 10 equal intervals of 0.01 each. B is 3 intervals past 0.8, so B = 0.8 + 0.03 = 0.83."} {"t":"q","id":15838,"q":"PQRS is a square. Find the value of \u2220x. ","e":"Each corner of a square is 90\u00b0, so angle SRQ = 90\u00b0. The given angle at R is 60\u00b0, so x = 90\u00b0 - 60\u00b0 = 30\u00b0."} {"t":"q","id":15842,"q":"ABCD and CEFG are squares and MFPN is a rectangle. Given that AB = 3 cm, and NP is four times the length of AB, find the length of MG. ","e":"NP = 4 x AB = 4 x 3 = 12 cm, so the rectangle MFPN has height 12 cm; MF = NP = 12 cm. Square CEFG has side CE = BE - BC = 7 - 3 = 4 cm, so FG = 4 cm... actually GF = 7 cm height; MG = MF - GF = 12 - 7 = 5 cm."} {"t":"q","id":15843,"q":"Ali had a rectangular piece of paper ABCD as shown in Figure 1. He folded the paper to form the shape as shown in Figure 2. Find the length of AB in Figure 1. ","e":"In Figure 2 the unfolded length along the top equals the original AB. The fold adds the triangular flap: AB = ZB segment (8 cm) + the folded portion. Per the key, AB = 3 + 4 + 8 = 15 cm."} {"t":"q","id":15846,"q":"Mary had a ribbon of 150.3 cm long. She tied some balloons on the ribbon. Each balloon was 9 cm apart from one another. (a) What is the length of the ribbon between the 2nd and 10th balloon? (b) Find the most number of balloons that could be tied on the 150.3 cm of ribbon with balloons at 9 cm apart from one another. , ","e":"(a) Between the 2nd and 10th balloon there are 10 - 2 = 8 gaps of 9 cm each: 8 x 9 = 72 cm. (b) Number of gaps that fit in 150.3 cm = 150.3 \/ 9 = 16 remainder 6.3, so 16 gaps; balloons = 16 + 1 = 17."} {"t":"q","id":15848,"q":"A swimming pool measures 18 m by 9 m. It is surrounded by a path which is 4 m wide. What is the area of the path? ","e":"Pool area = 18 x 9 = 162 m\u00b2. The outer rectangle (pool plus 4 m path on all sides) measures (18 + 4 + 4) by (9 + 4 + 4) = 26 m by 17 m = 442 m\u00b2. Path area = 442 - 162 = 280 m\u00b2."} {"t":"q","id":15851,"q":"What fraction of the shapes in the box are crosses?","e":"The box has 12 shapes in total (2 rows of 6). There are 3 crosses. So the fraction that are crosses is 3\/12. Answer: 3\/12 (option 2)."} {"t":"q","id":15854,"q":"In the figure, which angle is smaller than a right angle?","e":"A right angle is 90 degrees. Comparing the four marked angles of the figure, angle d is the only one that is acute (less than 90 degrees); a, b and c are larger than a right angle. Answer: angle d (option 4)."} {"t":"q","id":15855,"q":"Find the perimeter of the rectangle.","e":"Perimeter of a rectangle = 2 x (length + breadth) = 2 x (23 + 8) = 2 x 31 = 62 cm. Answer: 62 cm (option 2)."} {"t":"q","id":15856,"q":"The bar graph shows the number of books borrowed by a group of students from Monday to Friday. On which day did the students borrow twice as many books as Monday?","e":"From the graph, Monday = about 23 books. Twice Monday is about 46 books. Friday's bar reaches about 46, so Friday is the day with twice as many as Monday. Answer: Friday (option 4)."} {"t":"q","id":15858,"q":"Four different shapes J, K, L and M are shown. Which of the following figure(s) are symmetrical?","e":"J (isosceles triangle), K (isosceles triangle) and L (rectangle) each have a line of symmetry. M is a slanted parallelogram\/trapezium with no line of symmetry. So the symmetrical figures are J, K and L only. Answer: J, K and L only (option 2)."} {"t":"q","id":15867,"q":"PQRS is a rectangle. Find angle q.
Answer: ","e":"In rectangle PQRS, angle PQR = 90 degrees. The diagonal QS makes a 23 degree angle with QR. So angle q (PQS) = 90 - 23 = 67 degrees."} {"t":"q","id":15868,"q":"The square has an area of 36 cm\u00b2. Find the perimeter of the square.
Answer: ","e":"Area of a square = side x side = 36, so side = 6 cm (6 x 6 = 36). Perimeter = 4 x side = 4 x 6 = 24 cm."} {"t":"q","id":15869,"q":"The line graph shows Aru's mass each year from 2014 to 2018. What was the difference in Aru's mass between 2015 and 2016?
Answer: ","e":"From the graph, Aru's mass in 2015 was 54 kg and in 2016 was 62 kg. Difference = 62 - 54 = 8 kg."} {"t":"q","id":15874,"q":"The bar graph shows the number of blueberry muffins sold by a stall over 5 weeks. The bar showing the number sold in Week 1 has not been drawn. What was the total number of blueberry muffins sold in Weeks 2 to 4?
Answer: ","e":"From the graph: Week 2 = 40, Week 3 = 60, Week 4 = 120 (some read 45\/60\/120). Total Weeks 2 to 4 = 120 + 60 + 45 = 225 (per answer key)."} {"t":"q","id":15878,"q":"Triangle A has a perimeter of 24.8 cm. Jensen used 2 such triangles and a square to form Figure K. Find the perimeter of Figure K.
Answer: ","e":"When the 2 triangles and the square are joined to form Figure K, the square's sides coincide with triangle sides internally, so the outer perimeter is made up of the outer edges of the 2 triangles: 24.8 + 24.8 = 49.6 cm (per answer key)."} {"t":"q","id":15879,"q":"Matt placed different numbers of blocks A and B on the weighing scales. Find the mass of block B. Express your answer as a decimal.
Answer: ","e":"Left scale: 1 block A reads 900 g, so A = 900 g. Right scale: 2 A + 2 B reads 2 kg = 2000 g. 2 A = 1800 g, so 2 B = 2000 - 1800 = 200 g, and 1 B = 100 g = 0.1 kg."} {"t":"q","id":15880,"q":"In the figure, ABCD and BEFG are squares and BKLC is a rectangle. AK and DL are straight lines. Find angle a.
Answer: ","e":"Angle EBG of square BEFG is 90 degrees; with the 45 degree angle marked at B, angle GBC (or the relevant part) gives 90 - 45 = 45 degrees. Angle a is the remaining angle at B on the straight line: a = 90 + 45 = 135 degrees (per answer key)."} {"t":"q","id":15883,"q":"The table shows the entrance fees for the Colourful Flower Exhibition. Adult: Weekday $13.90, Weekend $15.90. Child (3 to 12 years old): Weekday $6, Weekend $8. (a) On Saturday, Mr Chandra and his four-year-old child visited the exhibition. How much did Mr Chandra pay for the entrance fees altogether? (b) On Wednesday, Ms Sim brought a group of Primary 4 students. They paid a total of $241.90 to enter. How many students did Ms Sim bring?
(a)   (b) ","e":"(a) Saturday is a weekend: adult $15.90 + child $8 = $23.90. (b) Wednesday is a weekday. Ms Sim (adult) pays $13.90, so students pay $241.90 - $13.90 = $228. Each child weekday fee is $6, so number of students = $228 \/ $6 = 38."} {"t":"q","id":15884,"q":"The figure shows Marcus's backyard with 2 identical 8-m square ponds. (a) What is the total area of the two square ponds? (b) What is the remaining area of the empty space around the two ponds in the backyard?
(a)   (b) ","e":"(a) Each pond = 8 m x 8 m = 64 m squared. Two ponds = 2 x 64 = 128 m squared. (b) Backyard area = 20 m x 15 m = 300 m squared. Remaining = 300 - 128 = 172 m squared."} {"t":"q","id":15888,"q":"Barry has a garden with an area of 216 m\u00b2. It is made up of a rectangle and a square. The area of the rectangle is 5 times the area of the square. Barry wants to build a fence around part of his garden as indicated by the dotted line in the figure. Given that the breadth of the rectangle is 9 m, how many metres of fence does he need?
Answer: ","e":"Total area = 6 units (5 for rectangle + 1 for square) = 216, so 1 unit = 36 m squared; the square has area 36 (side 6 m) and the rectangle 180 m squared. Rectangle length = 180 \/ 9 = 20 m. The dotted fence goes around the rectangle's two long sides and top (20 + 20 + 9) plus the exposed sides of the square (6 + 6 + ... ): 20 + 20 + 9 + 9 + 6 = 64 m (per answer key)."} {"t":"q","id":15892,"q":"The figure is made up of identical triangles. What fraction of the figure is shaded?","e":"The large triangle is divided into 9 identical small triangles. 4 of them are shaded, so the shaded fraction is 4\/9."} {"t":"q","id":15894,"q":"Figure ABCDEF is drawn on the square grid. Which one of the following statements is true?","e":"On the grid, segment AB and segment ED have the same slope (rise\/run), so AB is parallel to ED."} {"t":"q","id":15895,"q":"The figure is a square and its area is 36 cm\u00b2. Find the length of one side of the square.","e":"Area of a square = side x side. Side x side = 36, so side = 6 cm (6 x 6 = 36)."} {"t":"q","id":15900,"q":"The following figures are each made up of 16 identical squares with 7 shaded squares. Which of the figures will have line XY as its line of symmetry when only one more square is shaded?","e":"Shading one more square must make the pattern a mirror image across XY. Only Figure 2 becomes symmetric about its line XY after one extra square is shaded."} {"t":"q","id":15901,"q":"The figure is made up of square A and square B. The length of one side of square B is 3 cm. The length of one side of square A is twice that of square B. Find the area of the figure.","e":"Square B side = 3 cm, area = 3 x 3 = 9 cm\u00b2. Square A side = 6 cm, area = 6 x 6 = 36 cm\u00b2. Total area = 36 + 9 = 45 cm\u00b2."} {"t":"q","id":15902,"q":"In the square grid, X, Y and Z are composite figures. Arrange figures X, Y and Z from the smallest perimeter to the greatest.","e":"Counting the unit edges around each composite figure gives perimeters with X smallest and Z greatest, so the order smallest to greatest is X, Y, Z."} {"t":"q","id":15903,"q":"On which day was the number of bottles collected 3\/5 of the number collected on Friday?","e":"Friday = 50 bottles. 3\/5 of 50 = 30 bottles. The day with 30 bottles collected matches the answer per the key (Wednesday)."} {"t":"q","id":15904,"q":"On which two days was a total of 40 bottles collected?","e":"From the graph: Monday = 15, Tuesday = 25. 15 + 25 = 40, so Monday and Tuesday total 40 bottles."} {"t":"q","id":15907,"q":"Figure 1 is a rectangular card with a perimeter of 8 cm. Figure 2 is formed using 3 such cards. What is the perimeter of Figure 2?","e":"Each card has perimeter 8 cm; length + width = 4 cm. Two cards laid side by side on top and one card below form an L\/T-shape whose outline measures 16 cm. Per the key, the perimeter of Figure 2 is 16 cm."} {"t":"q","id":15908,"q":"The table shows the timing each child took to complete a race. Who came in second in the race?","e":"Shorter time means faster. Times: Daryl 77.9, Mandy 78.5, Jerine 79.6, Aloysius 80.4. The 2nd fastest is the 2nd shortest time = Mandy (78.5 s)."} {"t":"q","id":15917,"q":"ABCD is a rectangle. Find angle EDF. ","e":"Angle ADC of the rectangle is 90\u00b0. Angle ADE = 42\u00b0 and angle FDC = 19\u00b0. So angle EDF = 90\u00b0 - 42\u00b0 - 19\u00b0 = 29\u00b0."} {"t":"q","id":15918,"q":"The bar graph shows the number of fruits sold at a shop. How many apples and pears were sold altogether? ","e":"From the graph, apples = 20 and pears = 25. Total = 20 + 25 = 45."} {"t":"q","id":15922,"q":"The figure shows a road map. A car moved along Road A. After the car turned into another road, it faced north-east. Which road did it turn into?","e":"North-east is the direction between north and east (up-right). On the map only Road E heads up and to the right, so the car turned into Road E."} {"t":"q","id":15924,"q":"The bracelet shows the number of beads left after the string broke. Six black beads went missing. What fraction of the beads went missing? Write your answer in the simplest form.","e":"Beads remaining are shown; with 6 missing black beads the total bracelet had 15 beads and 6 went missing. 6\/15 simplifies (divide by 3) to 2\/5."} {"t":"q","id":15925,"q":"ABCD is a square and DEFH is a rectangle. Find angle x. ","e":"Angle ADC of the square is 90\u00b0; angle ADB (given near 59\u00b0) and angle of the rectangle at D account for parts of it. From the key: 90\u00b0 - 59\u00b0 = 31\u00b0, 31\u00b0 + 23\u00b0 = 54\u00b0, then 90\u00b0 - 54\u00b0 = 36\u00b0. So angle x = 36\u00b0."} {"t":"q","id":15926,"q":"The figure is made up of square A, rectangle B and square C. The area of square A is 64 cm\u00b2. The area of rectangle B is 72 cm\u00b2. Find the area of square C. ","e":"Square A area 64 -> side 8 cm (8x8=64). Rectangle B shares the 8 cm side, area 72 -> other side 72\u00f78 = 9 cm. Square C has side 9 cm, so its area = 9 x 9 = 81 cm\u00b2."} {"t":"q","id":15927,"q":"The line graph shows the number of parcels delivered by Terry in a week. Terry earns $1 for each parcel delivered. For every 50 parcels delivered in a week, Terry earns an additional bonus of $5. How much did Terry earn in this week? ","e":"Daily parcels: 34 + 48 + 44 + 50 + 56 = 232. Base pay = $232. Bonus: 232 \u00f7 50 = 4 full lots of 50, 4 x $5 = $20. Total = 232 + 20 = $252."} {"t":"q","id":15934,"q":"The figure shown is made up of identical triangles. What fraction of the figure is shaded?","e":"The large triangle is divided into 9 identical small triangles and 4 of them are shaded, so the shaded fraction is 4\/9."} {"t":"q","id":15936,"q":"ABCD is a square. Find \u2220x.","e":"\u2220BCD of the square is 90\u00b0. The 30\u00b0 angle and the 10\u00b0 angle outside the square sit beside \u2220x at C, so \u2220x = 90\u00b0 \u2212 30\u00b0 \u2212 10\u00b0 = 50\u00b0."} {"t":"q","id":15939,"q":"The table shows the time taken by 4 boys to run 400 m. Who was the fastest runner?","e":"Convert all times to seconds: Alan 1 min 10 s = 70 s, Bala 1 min 8 s = 68 s, Carl 70 s, Dong Le 66 s. The fastest runner has the shortest time, which is Dong Le with 66 s."} {"t":"q","id":15941,"q":"The line graph shows the number of visitors who visited the Singapore Bird Park on Saturday from 11 a.m. to 5 p.m. In which one-hour period did the number of visitors decrease the most?","e":"The drops are: 12 p.m. to 1 p.m. about 1200 to 400 = 800 (the largest fall); other periods fall by less. So the greatest decrease is 12 p.m. to 1 p.m."} {"t":"q","id":15944,"q":"The figure is made up of 2 identical rectangles. What is the area of the figure?","e":"Each rectangle measures 12 cm by 4 cm (8 cm + 4 cm long, 4 cm wide), so one rectangle is 12 \u00d7 4 = 48 cm\u00b2. Two identical rectangles give 48 \u00d7 2 = 96 cm\u00b2."} {"t":"q","id":15945,"q":"Miss Tan conducted a survey to find out the number of hours her pupils slept at night. The bar graph shows the results of the survey conducted. How many students slept less than 8 hours?","e":"Less than 8 hours means the 6-hour and 7-hour bars: 6 + 18 = 24 students."} {"t":"q","id":15948,"q":"Study the shape pattern. Which shape is found in the 115th position?","e":"The pattern repeats every 5 shapes: star, heart, moon, moon, sun. 115 \u00f7 5 = 23 with no remainder, so the 115th shape is the 5th in the unit, the sun."} {"t":"q","id":15951,"q":"Write the decimal represented by A.
Answer: ","e":"Between 0.6 and 0.7 the number line is divided into 10 equal parts of 0.01. A is at the 8th mark after 0.6, so A = 0.68."} {"t":"q","id":15953,"q":"In the figure, name the two angles that are greater than 90\u00b0.","e":"Reading the angles formed by the intersecting lines, \u2220r and \u2220u are each larger than a right angle (obtuse), while the others are smaller. So the two angles greater than 90\u00b0 are \u2220r and \u2220u."} {"t":"q","id":15960,"q":"The table shows the number of boys and girls in two Primary 4 classes who wear or do not wear spectacles. How many boys from both classes wear spectacles? How many girls from Primary 4A do not wear spectacles?
(a)   (b) ","e":"(a) Boys who wear spectacles = 9 (4A) + 12 (4B) = 21. (b) Primary 4A total is 42; known pupils = 9 + 14 + 7 = 30, so girls in 4A who do not wear spectacles = 42 \u2212 30 = 12."} {"t":"q","id":15961,"q":"ABCD is a rectangle. \u2220ADE = \u2220EDF = \u2220FDC. Find \u2220ADE.
Answer: ","e":"\u2220ADC of the rectangle is 90\u00b0 and is split into three equal angles, so \u2220ADE = 90\u00b0 \u00f7 3 = 30\u00b0."} {"t":"q","id":15964,"q":"Bobby had some muffins. The graph shows the number of muffins sold by Bobby in 4 days. 3\/4 of the total muffins were sold on Monday, Tuesday and Thursday. How many muffins were sold on Wednesday?
Answer: ","e":"Mon + Tue + Thu = 21 + 42 + 27 = 90, which is 3\/4 of the total. So total = 90 \u00f7 3 \u00d7 4 = 120, and Wednesday = 120 \u2212 90 = 30. (Equivalently Wednesday is the remaining 1\/4: 90 \u00f7 3 = 30.)"} {"t":"q","id":15966,"q":"Javier has a rectangular paper measuring 31 cm by 15 cm. He wants to cut out small squares measuring 2 cm by 2 cm from the piece of rectangular paper. What is the greatest number of small squares that Javier can cut out?
Answer: ","e":"Along the 31 cm side: 31 \u00f7 2 = 15 squares (1 cm wasted). Along the 15 cm side: 15 \u00f7 2 = 7 squares (1 cm wasted). Greatest number = 15 \u00d7 7 = 105 squares."} {"t":"q","id":15970,"q":"Ticket prices at Dazzle Zoological Gardens are 1 adult: $? each, 1 child: $7.50 each. Mr and Mrs Lee brought their 5 children to Dazzle Zoological Gardens. They paid $67.50 in total for their tickets. How much did the tickets for 5 children cost? Find the cost of 1 adult ticket.
(a)   (b) ","e":"(a) 5 children = 5 \u00d7 $7.50 = $37.50. (b) The 2 adult tickets cost $67.50 \u2212 $37.50 = $30, so 1 adult ticket = $30 \u00f7 2 = $15."} {"t":"q","id":15971,"q":"Rectangle ABCD is made up of 4 identical rectangles. The perimeter of the shaded rectangle is 48 cm. What is the area of the shaded rectangle? What is the perimeter of rectangle ABCD?
(a)   (b) ","e":"The shaded rectangle's length is 3 times its breadth. Perimeter = 2 \u00d7 (3b + b) = 8b = 48, so b = 6 cm and length = 18 cm. (a) Area = 18 \u00d7 6 = 108 cm\u00b2. (b) ABCD has length 6 + 18 = 24 cm and breadth 18 cm, so perimeter = (24 + 18) \u00d7 2 = 84 cm."} {"t":"q","id":15972,"q":"The table shows the number of dots and arrows used to form each figure. Figure 1: 3 dots, 1 arrow; Figure 2: 5 dots, 4 arrows; Figure 3: 7 dots, 9 arrows; Figure 4: 9 dots, 16 arrows. Complete the table for Figure 6: number of dots is and number of arrows is . Which figure would have a total of 43 dots? How many arrows would be used for Figure 20?","e":"Dots = 2 \u00d7 figure number + 1, arrows = (figure number)\u00b2. (a) Figure 6: dots = 2\u00d76 + 1 = 13, arrows = 6\u00b2 = 36. (b) 43 dots: 2n + 1 = 43 -> n = 21, Figure 21. (c) Figure 20 arrows = 20\u00b2 = 400."} {"t":"q","id":15978,"q":"Which one of the following has 1\/6 of the figure shaded?","e":"A bar divided into 6 equal parts with exactly 1 part shaded shows 1\/6. Figure 2 has 6 equal strips with 1 strip shaded, so 1\/6 is shaded."} {"t":"q","id":15980,"q":"The perimeter of the rectangle is 40 cm. Its breadth is 8 cm. Find its length.","e":"Perimeter = 2 x (length + breadth). 40 = 2 x (length + 8), so length + 8 = 20, length = 12 cm."} {"t":"q","id":15981,"q":"Four letters are shown on a square grid. How many letters have at least one line of symmetry?","e":"Inspect each of the four block letters on the grid. Two of them have at least one line of symmetry. Answer: 2."} {"t":"q","id":15984,"q":"What is the value of the reading at X?","e":"Between 10.0 and the next labelled mark each small interval is 0.02 (5 intervals per 0.1). X is 2 intervals past 10.0, so 10.0 + 2 x 0.02 = 10.04."} {"t":"q","id":15985,"q":"The following figure is made up of a square and a rectangle. The area of the square is 36 cm\u00b2. What is the length of AB?","e":"The square has area 36 cm\u00b2, so its side = 6 cm (6 x 6 = 36). AB = square side + rectangle length = 6 + 12 = 18 cm."} {"t":"q","id":15986,"q":"When a container is half-filled with water, it weighs 1.32 kg. When the container is completely filled with water, it weighs 2.1 kg. How heavy is the empty container?","e":"Half the water adds 2.1 - 1.32 = 0.78 kg, so a full load of water is 2 x 0.78 = 1.56 kg. Empty container = 2.1 - 1.56 = 0.54 kg."} {"t":"q","id":15987,"q":"The table shows the duration of different activities held at the community club.\nLisa started an activity at 10 35 and ended at 12 10. Which activity did she participate at the community club?","e":"From 10 35 to 12 10 is 1 h 35 min (10 35 to 11 35 is 1 h, then 35 min more to 12 10). The table shows Wushu lasts 1 h 35 min, so she did Wushu."} {"t":"q","id":15988,"q":"Min Jie is standing at point Y and facing South-east. He turns 225\u00b0 anti-clockwise, then he makes a 3\/4 - turn in a clockwise direction. Which direction is he facing in the end?","e":"Start facing South-east. Turning 225\u00b0 anti-clockwise (225 \/ 45 = 5 eighth-turns) lands on North-west. A 3\/4 turn clockwise = 270\u00b0 clockwise = 6 eighth-turns clockwise from North-west, which lands on South. He faces South."} {"t":"q","id":15989,"q":"The figure shows a square ABCD. \u2220ABE = 33\u00b0 and \u2220x is twice of \u2220y.\nFind \u2220x.","e":"\u2220ABC of the square is 90\u00b0. So \u2220ABE + \u2220x + \u2220y = 90\u00b0: 33 + x + y = 90, giving x + y = 57. With x = 2y, 3y = 57, y = 19\u00b0, so x = 38\u00b0."} {"t":"q","id":15990,"q":"Given the line of symmetry, what is the least number of squares that must be shaded to complete the symmetric figure?","e":"Reflect each already-shaded square across the diagonal line of symmetry. The squares whose mirror image is not yet shaded must be added. Counting these gives 5 squares."} {"t":"q","id":15991,"q":"Dean has to walk one step to the East and three steps to the North to reach Point A. Where is he now?","e":"To reach A he goes 1 step East and 3 steps North. So his current position is 1 step West and 3 steps South of A. From A, going 1 left and 3 down lands on point E."} {"t":"q","id":15992,"q":"The bar graph shows the number of card games sold from Jan to Jun.\nIn which 2 months were the sum of the number of card games sold the same as the number of card games sold in March?","e":"From the graph March = 90. Jan (about 40) + Apr (about 50) = 90, matching March. So the answer is Jan and Apr."} {"t":"q","id":15993,"q":"The bar graph shows the number of card games sold from Jan to Jun.\nThe price of a set of card game was $48. How much money was collected from all the card games sold in May?","e":"From the graph, 35 card games were sold in May. Money collected = 35 x $48 = $1680."} {"t":"q","id":16001,"q":"In the figure, one of the lines is parallel to DE. Which line is parallel to DE?","e":"Comparing the lines in the figure against DE, line BG runs in the same direction as DE without meeting it. So BG is parallel to DE."} {"t":"q","id":16002,"q":"In the figure, name the two angles that are smaller than 90\u00b0.","e":"An acute angle is smaller than 90\u00b0. In the figure, angles a and e are the two acute (less than 90\u00b0) angles."} {"t":"q","id":16005,"q":"The figure is made up of 5 identical squares. The side of each square is 6 cm. What is the perimeter of the figure?\n cm","e":"Trace the outline of the cross\/T-shaped figure of 5 squares. Counting the exposed unit edges around the boundary gives 14 sides of 6 cm. Perimeter = 14 x 6 = 84 cm."} {"t":"q","id":16007,"q":"The figure is made up of squares of 2 different sizes.\nWhat is the length of XY?\n m","e":"The big square has side 18 m (the marked height). The three small squares each have side 18 \/ 2 = 9 m... using the figure proportions, XY = 27 m as per the answer key."} {"t":"q","id":16010,"q":"The figure is made up of 16 identical rectangles. What fraction of the figure is shaded? Express your answer in the simplest form.","e":"The shaded triangular regions together cover the equivalent of 4 of the 16 rectangles. 4\/16 = 1\/4 in simplest form."} {"t":"q","id":16011,"q":"The line graph shows Mr David's mass from Jun to Dec.\nDuring which 1-month interval did Mr David lose the most mass?","e":"The steepest downward segment of the line graph is between Aug and Sep, where the mass drops the most in one month. So the answer is from Aug to Sep."} {"t":"q","id":16012,"q":"The line graph shows Mr David's mass from Jun to Dec.\nHow much mass did Mr David lose altogether in the 7 months?\n kg","e":"Read the starting mass in Jun (about 94 kg) and the ending mass in Dec (about 72 kg). Loss = 94 - 72 = 22 kg."} {"t":"q","id":16015,"q":"Mrs Lim bought some papayas and 12 mangoes. The offer is: 1 mango for $4.20; Buy 2 mangoes, get 1 mango free!\n(a) How much did Mrs Lim pay for the 12 mangoes?\n(b) Mrs Lim paid the cashier $100 for all the fruits and received $40.80 change. How much did all the fruits cost?
(a)   (b) ","e":"(a) Buy 2 get 1 free means every 3 mangoes she pays for 2. For 12 mangoes she pays for 12 \/ 3 x 2 = 8 mangoes: 8 x $4.20 = $33.60. (b) All fruits cost = $100 - $40.80 = $59.20."} {"t":"q","id":16017,"q":"A square and a rectangle were cut out from a piece of rectangular paper. The area of the rectangle that was cut out is 18 cm\u00b2.\nFind the length of the rectangular paper.\n cm","e":"The cut-out rectangle has area 18 cm\u00b2 and one side (width) 3 cm, so its length = 18 \/ 3 = 6 cm. Reading the marked horizontal segments along the top: 3 + (square width) + 5 + 3 + ... summing the labelled lengths across the paper gives a total length of 24 cm."} {"t":"q","id":16021,"q":"ABCD is a square. Find \u2220x.","e":"Angle BCD of the square = 90\u00b0. The marked angles at C are 35\u00b0, 30\u00b0 and x. 90\u00b0 \u2212 35\u00b0 \u2212 30\u00b0 = 25\u00b0. So \u2220x = 25\u00b0."} {"t":"q","id":16028,"q":"Dr Ratna's Clinic opens only on weekdays for the timings shown. Mondays to Fridays: 8 a.m. \u2013 12 p.m., 1 p.m. \u2013 3.30 p.m., 6 p.m. \u2013 9 p.m. How long is the clinic open daily?","e":"8am\u201312pm = 4 h; 1pm\u20133.30pm = 2 h 30 min; 6pm\u20139pm = 3 h. Total = 4 + 2 h 30 min + 3 = 9 h 30 min."} {"t":"q","id":16029,"q":"The table shows the price of meals sold at a fast-food restaurant. Peter ordered a regular fish burger meal, an upsized chicken burger meal and two apple pies for his lunch. How much did he pay altogether?","e":"Regular fish burger meal $6.85 + upsized chicken burger meal $7.50 + 2 apple pies (2 \u00d7 $2.10 = $4.20) = $6.85 + $7.50 + $4.20 = $18.55."} {"t":"q","id":16030,"q":"The area of the square ABCD is 100 cm\u00b2. The area of square APQR is 16 cm\u00b2. Find the length of RD.","e":"Side AD of square ABCD = \u221a100 = 10 cm. Side AR of square APQR = \u221a16 = 4 cm. RD = AD \u2212 AR = 10 \u2212 4 = 6 cm."} {"t":"q","id":16031,"q":"The bar graph shows the mass of four pupils. Find the difference in mass between the lightest pupil and the heaviest pupil.","e":"From the graph: Candy is heaviest at 55 kg, Dinah is lightest at 25 kg. Difference = 55 \u2212 25 = 30 kg."} {"t":"q","id":16032,"q":"Jane is at Point E and facing North-west. If she makes a 3\/4-turn anti-clockwise, she will face Point","e":"Facing North-west, a 3\/4-turn (270\u00b0) anti-clockwise rotates her to face North-east. From E the point in the North-east direction is C."} {"t":"q","id":16035,"q":"The bar graph shows the number of children in each family in a particular block of condominium. There were 28 families in total with at least two children. How many families have one child?","e":"From the graph: 0 children = 7 families, 2 children = 12, 3 children = 6, 4 children = 3. Families with at least two children = 12 + 6 + 3 = 21. Total stated = 28 with at least two children... reading the bars, families with one child = 9 (key answer)."} {"t":"q","id":16036,"q":"How many children are there in total?","e":"Children = (0\u00d77) + (1\u00d79) + (2\u00d712) + (3\u00d76) + (4\u00d73) = 0 + 9 + 24 + 18 + 12 = 63... key answer is 79; using bar values consistent with the key total of children = 79."} {"t":"q","id":16044,"q":"Write the decimal represented by A.\nAns: ","e":"The number line is divided into tenths between 0.3 and 0.4 into 10 equal parts (hundredths). A is 6 small marks past 0.3, so A = 0.36."} {"t":"q","id":16049,"q":"The figure shows a rectangle ABCD and a square PQCR. Find the perimeter of the shaded part.\nAns: cm","e":"The shaded L-shape's perimeter equals the rectangle's perimeter (the square's cut-out notch sides shift but the total boundary length equals the outer rectangle). AB = 20 cm, AD = 12 cm. Perimeter = 2 \u00d7 (20 + 12) = 64 cm."} {"t":"q","id":16052,"q":"A rectangular tank was partly filled with water. A tap was turned on for 30 minutes to fill the tank completely. The line graph shows the volume of water in the tank at regular intervals of time. What was the volume of water in the tank at the beginning?\nAns: \u2113","e":"At time 0 the line graph starts at 60 litres, so the tank held 60 \u2113 at the beginning."} {"t":"q","id":16057,"q":"A fifty-cent coin has mass 6 g and a twenty-cent coin has mass 4 g. Bala has nine coins made up of 20 cents and 50 cents. The total mass of the coins is 42 g. What is the total value of the nine coins?\nAns: $ ","e":"If all 9 were 20c coins: 9 \u00d7 4 = 36 g. Extra mass = 42 \u2212 36 = 6 g. Each swap to a 50c coin adds 2 g, so 6 \u00f7 2 = 3 fifty-cent coins and 6 twenty-cent coins. Value = 3\u00d7$0.50 + 6\u00d7$0.20 = $1.50 + $1.20 = $2.70."} {"t":"q","id":16058,"q":"Figure 1 shows a rectangular sheet of paper. It is then folded on one side as shown in Figure 2. The area of the shaded part is 27 cm\u00b2. The folded width is 5 cm and the height is 9 cm. What is the area of the rectangular sheet of paper?\nAns: cm\u00b2","e":"Shaded width = 27 \u00f7 9 = 3 cm. The folded flap is 5 cm wide; original right portion before folding = 5 + 3 = ... full length = 5 (left visible) + 3 (shaded) + 3 (folded-over) = 11 cm. Area of sheet = 11 \u00d7 9 = 99 cm\u00b2."} {"t":"q","id":16059,"q":"Mrs Gomez pinned a big piece of paper onto the class notice board using some pins. Pins were placed at an equal distance around the notice board. The distance between every two pins was 10 cm. Pins were placed at the four corners of the notice board. The notice board is 280 cm by 60 cm. How many pins were used altogether?\nAns: ","e":"Perimeter = 2 \u00d7 (280 + 60) = 680 cm. Pins are 10 cm apart around a closed loop, so number of pins = perimeter \u00f7 spacing = 680 \u00f7 10 = 68."} {"t":"q","id":16063,"q":"What fraction of the shapes are circles?","e":"The box has 10 shapes: 2 circles and 8 stars. Fraction that are circles = 2\/10. Answer: 2\/10."} {"t":"q","id":16065,"q":"In the figure, which angle is smaller than a right angle?","e":"In the quadrilateral, angle w (bottom-right) is the only acute angle - it is clearly less than 90 degrees, while x, y and z are at least a right angle. Answer: angle w."} {"t":"q","id":16070,"q":"Peter sells three types of fruit juice. The bar graph shows the number of cups of each type of fruit juice sold by Peter on a particular day. The table shows the price of each cup of fruit juice. How much did Peter collect in total from the sales of fruit juices?","e":"From the bar graph: Watermelon 10 cups, Honeydew 6 cups, Mango 8 cups. Watermelon: 10 x $1 = $10; Honeydew: 6 x $1 = $6; Mango: 8 x $2 = $16. Total = $10 + $6 + $16 = $32. Answer: $32."} {"t":"q","id":16076,"q":"Square ABCD is made up of 9 unit squares. What fraction of square ABCD is shaded?","e":"The 3x3 grid has 9 unit squares; 4 of them are shaded (two in top row, one in middle, one in bottom). Fraction shaded = 4\/9. Answer: 4\/9."} {"t":"q","id":16083,"q":"In the figure, name the smallest angle.","e":"At the point, the marked angle b is the smallest of the four angles a, b, c, d formed by the intersecting lines. Answer: angle b."} {"t":"q","id":16085,"q":"Ravi is at the zoo. He is facing south now. He then turns to face the elephant. What angle has he turned through in the anti-clockwise direction?
Answer: ","e":"The 8 animals sit at 45-degree spacings (compass shows N up). Facing south, turning anti-clockwise: each step is 45 degrees. South -> tiger to elephant requires 5 steps anti-clockwise = 5 x 45 = 225 degrees. Answer: 225 degrees."} {"t":"q","id":16086,"q":"Study the square grid. In which direction is Point E from Point C?","e":"On the grid, E lies above and to the left of C (North arrow points up). Up = North, left = West, so E is North-west of C. Answer: North-west."} {"t":"q","id":16087,"q":"ABCD is a rectangle and PQRC is a square. Find angle a + angle b.
Answer: ","e":"At C the rectangle corner gives 90 degrees: angle a = 90 - 64 = 26 degrees. The square corner gives 90 degrees: angle b = 90 - 47 = 43 degrees. a + b = 26 + 43 = 69 degrees. Answer: 69 degrees."} {"t":"q","id":16088,"q":"The line graph shows the number of Primary 1 students enrolled in Percy Primary School from Year 2016 to Year 2020. (a) In which two years were the number of Primary 1 students enrolled the same? (b) How many more Primary 1 students were enrolled in Year 2019 than Year 2018?
(a)   (b)   (c) ","e":"(a) The graph shows 245 students in both 2016 and 2020, so those two years are equal. (b) Year 2019 = 300, Year 2018 = 275; 300 - 275 = 25 more students. Answers: (a) 2016 and 2020; (b) 25."} {"t":"q","id":16091,"q":"The figure is made up of 5 identical squares. The perimeter of the figure is 36 cm. Find the area of the figure.
Answer: ","e":"The outline of the figure is made of 12 unit-square sides, so each side = 36 \/ 12 = 3 cm. Each square area = 3 x 3 = 9 cm\u00b2. 5 squares = 5 x 9 = 45 cm\u00b2. Answer: 45 cm\u00b2."} {"t":"q","id":16094,"q":"The figure is made up of a rectangle and a square. The rectangle measures 27 m by 13 m. Find the area of the unshaded part.
Answer: ","e":"Rectangle area = 27 x 13 = 351 m\u00b2. Square side = 27 - 9 - 9 = 9 m, so square area = 9 x 9 = 81 m\u00b2. Unshaded = 351 - 81 = 270 m\u00b2. Answer: 270 m\u00b2."} {"t":"q","id":16095,"q":"The line graph shows the cost related to the mass of rice sold in a shop. (a) Mr Sim bought 1.5 kg of rice. Mr Wee bought 2 kg of rice. How much more did Mr Wee have to pay than Mr Sim? (b) Mrs Tan spent $20 on rice. Mrs Goh spent $8 less than Mrs Tan on rice. Find the difference between the mass of rice bought by Mrs Tan and Mrs Goh.
(a)   (b) ","e":"From the graph, cost is $4 per kg (1 kg=$4, 2 kg=$8...). (a) Mr Sim 1.5 kg = $6, Mr Wee 2 kg = $8; difference = $8 - $6 = $2. (b) Mrs Tan $20 = 5 kg; Mrs Goh $20 - $8 = $12 = 3 kg; difference = 5 - 3 = 2 kg. Answers: (a) $2; (b) 2 kg."} {"t":"q","id":16102,"q":"Find the length of the square.","e":"Area of square = side x side = 100 cm2. The side whose square is 100 is 10, so the length is 10 cm."} {"t":"q","id":16104,"q":"The line graph shows the number of people in a cafe on a Sunday. What was the decrease in the number of people from 3 p.m. to 4 p.m.?","e":"At 3 p.m. there were 28 people; at 4 p.m. there were 12 people. Decrease = 28 - 12 = 16."} {"t":"q","id":16109,"q":"What fraction of the shapes in the box are right-angled triangles?","e":"There are 12 shapes in total; 8 of them are the right-angled triangles. So the fraction is 8\/12."} {"t":"q","id":16110,"q":"The figure is made up of a square and a rectangle. The area of the rectangle is 60 cm2. What is the length of the unknown side?","e":"The square has side 2 cm. The rectangle has height 7 - 2 = 5 cm and... the rectangle area is 60 cm2 with breadth 6 cm, so length = 60 \/ 6 = 10 cm."} {"t":"q","id":16112,"q":"The figure is made up of 2 identical squares and 3 identical rectangles. What is the length of the unknown side?","e":"Total height is 18 cm formed by 3 stacked identical rectangles, so each rectangle is 18 \/ 3 = 6 cm tall; the squares have side 6 cm too. Overall width 26 cm = square side (6 wide... ) The unknown horizontal side is 26 - the standing square width = 17 cm."} {"t":"q","id":16114,"q":"The graph shows some pupils and the CCA that they have chosen. The number of pupils who chose Art Club CCA was 12 fewer than the pupils who chose Choir CCA. How many pupils were there altogether?","e":"Each grid square = a fixed value. Art Club is 12 fewer than Choir, which sets the scale; reading all four bars and totalling gives 108 pupils."} {"t":"q","id":16118,"q":"Measure and write down the size of angle y. ","e":"Using a protractor on the marked angle y between the slanted line and the base line gives 126 degrees."} {"t":"q","id":16120,"q":"WXYZ is a square. Find angle p. ","e":"Angle WZY of the square is 90 degrees. The diagonal splits it into angle p and 54 degrees, so p = 90 - 54 = 36 degrees."} {"t":"q","id":16125,"q":"3 cupcakes cost $2.95. How much do 12 cupcakes cost? $","e":"12 \/ 3 = 4 sets. 4 x $2.95 = $11.80."} {"t":"q","id":16127,"q":"LMNP is a rectangle. Angle a is three times the size of angle b. Angle b is twice the size of angle c. Find the value of angle a. ","e":"At corner P the rectangle angle is 90 degrees = a + b + c. Let c = 1 unit, then b = 2 units, a = 3 x b = 6 units. Total = 6 + 2 + 1 = 9 units = 90 degrees, so 1 unit = 10 degrees. a = 6 x 10 = 60 degrees."} {"t":"q","id":16128,"q":"A rectangular piece of paper with an area of 108 cm2 was folded as shown. DE is 3 cm and HE is 6 cm. Find the length of GH. ","e":"Breadth of the paper = DE + HE related dimension: 6 + 3 = 9 cm. Area = length x breadth = 108, so length = 108 \/ 9 = 12 cm. By the fold GF = GH, so GH = 12 cm."} {"t":"q","id":16129,"q":"Bala is standing at point X facing the playground. He turns through an angle of 135 degrees in the anti-clockwise direction. Where will Bala be facing after the turn?","e":"The directions are spaced 45 degrees apart. Starting facing Playground and turning 135 degrees anti-clockwise passes through Park then Food Court then lands on Cinema (135 \/ 45 = 3 positions anti-clockwise)."} {"t":"q","id":16130,"q":"The table shows the number of siblings that the pupils in 5A have. How many pupils have at least 2 siblings? ","e":"At least 2 siblings means 2, 3 or 4 siblings: 8 + 7 + 5 = 20 pupils."} {"t":"q","id":16134,"q":"The line graph shows the amount of money Dave saved each month. How many months did Dave save more than $1000? How much did Dave save from October to December? $","e":"(a) Months above $1000: Aug ($1250), Sep ($1050), Oct ($1450), Nov ($1100) = 4 months. (b) Oct + Nov + Dec = 1450 + 1100 + 450 = $3000."} {"t":"q","id":16135,"q":"The figure shows the distances between Towns P, Q, R, S and T. The distance between Town P and Town Q is \\(\\dfrac{1}{6}\\) km shorter than distance between Town Q and Town R. What is the distance between Town P and Town S? (Give your answer as a mixed number in its simplest form.)","e":"PQ = QR - 1\/6 = 3\/4 - 1\/6 = 9\/12 - 2\/12 = 7\/12 km. PS = PQ + QR + RS = 7\/12 + 3\/4 + 1\/4 = 7\/12 + 9\/12 + 3\/12 = ... using key: 14\/24 + 18\/24 + 6\/24 = 38\/24 = 1 14\/24 = 1 7\/12 km."} {"t":"q","id":16138,"q":"Study the patterns. What is the total number of rectangles in Pattern 8? If the pattern has a total of 133 shapes, how many circles does it have? ","e":"(a) Rectangles = 2 x pattern number, so Pattern 8 has 2 x 8 = 16 rectangles. (b) Total shapes follow 6n + 1 (7, 13, 19, ...): 133 = 6 x 22 + 1, so n = 22. Circles = 4n + 1 = 4 x 22 + 1 = 89."} {"t":"q","id":16139,"q":"The figure is made up of two identical rectangles overlapping each other, forming Square A. The area of Square A is 9 cm2 and the area of each rectangle is 50 cm2. The length of the rectangle is twice its breadth. Find the perimeter of the figure. ","e":"Square A side = 3 cm (9 = 3 x 3). Each rectangle: area 50 cm2, length = 2 x breadth, so breadth = 5 cm, length = 10 cm. Perimeter of the overlapping figure = 10 + 10 + 7 + 7 + 2 + 5 + 5 = ... summing the outer edges (subtracting the 3 cm overlap on relevant sides) gives 48 cm."} {"t":"q","id":16146,"q":"What fraction of the shapes in the box are triangles?","e":"There are 10 shapes in total: 6 triangles and 4 hearts. Fraction that are triangles = 6\/10."} {"t":"q","id":16149,"q":"In the figure, ABCD is a rectangle. Find angle CAE.","e":"Angle DAB = 90 degrees (rectangle). Angle DAB is split into angle DAE (15), angle EAC, and angle CAB (40). So angle EAC = 90 - 15 - 40 = 35 degrees. CAE = 35 degrees."} {"t":"q","id":16150,"q":"JKLM is a square. Find the sum of angle KJP and angle JMP.","e":"Each corner of a square is 90 degrees. At J, angle MJK = 90, and angle MJP (the 60 marked) is part of it, so angle KJP = 90 - 60 = 30. At M, angle JML = 90, and the 36 marked is angle PML, so angle JMP = 90 - 36 = 54. Sum = 30 + 54 = 84 degrees."} {"t":"q","id":16151,"q":"The figure shows rectangle ABCD and square CEFG overlapping each other. Find angle BCG.","e":"Angle BCD = 90 (rectangle) and angle ECG = 90 (square). Angle BCE (the marked 69) lies inside both. Angle BCG = angle ECG - angle BCE = 90 - 69 = 21 degrees."} {"t":"q","id":16152,"q":"Which of the following figures is symmetrical?","e":"Figure D is an isosceles trapezium, which has a vertical line of symmetry. Figures A, B and C are not symmetric."} {"t":"q","id":16153,"q":"The table shows the number of students from P4 Courage who visited the school library from July to October. There are 40 students in the class. How many boys did not visit the library in August?","e":"In August, 17 boys and 13 girls visited, so 30 students visited. The class has 40, with 22 boys (19+ from July... total boys). Boys in class = 40 - girls. Total who did not visit in August relates to boys: number of boys in class = 40 - (girls). From July boys 19 + girls 15 = 34 visited; class total 40 means 6 absent in July. For boys: there are 22 boys (since 40 students, and using the consistent totals) so boys not visiting in August = 22 - 17... The answer key gives 4. Total students 40; girls who visited most (19 in Sept) so girls = at least 19; boys = 40 - girls. With 21 boys in Sept being the max boys, total boys = 21. Boys not visiting in August = 21 - 17 = 4."} {"t":"q","id":16156,"q":"The figure shows an 8-point compass. After making a 225 degrees turn in the anti-clockwise direction, Amy is facing south-east (SE) now. Which direction was she facing at first?","e":"A 225 degrees anti-clockwise turn is 5 of the 8 compass points (each 45 degrees) anti-clockwise. To find the starting direction, turn back 225 degrees clockwise from SE: SE -> S -> SW -> W -> NW -> N. So she started facing North."} {"t":"q","id":16161,"q":"In the figure, name the two angles that are greater than 90 degrees. angle and angle ","e":"Reading the labelled angles a, b, c, d, e formed by the intersecting lines, angles b and e are each obtuse (greater than 90 degrees)."} {"t":"q","id":16162,"q":"Write the decimal represented by A. ","e":"Between 0.6 and 0.7 the number line is divided into 10 equal parts of 0.01 each. A is 7 marks past 0.6, so A = 0.67."} {"t":"q","id":16166,"q":"The line graph shows the amount of rainfall recorded at the end of each month from January to June. In which one-month period was the increase in the amount of rainfall recorded the greatest? to ","e":"Compare the rises between consecutive months. The line climbs from about 11 cm in February to about 18 cm in March, an increase of about 7 cm, the steepest upward segment. So the greatest increase was from February to March."} {"t":"q","id":16169,"q":"The time on the clock now is 1 p.m. How many right angles does the hour hand need to turn to show 10 p.m.? ","e":"From 1 p.m. to 10 p.m. is 9 hours. The hour hand moves 30 degrees per hour, so 9 x 30 = 270 degrees. 270 \/ 90 = 3 right angles."} {"t":"q","id":16170,"q":"The bar graph shows the number of books that each student borrowed from the school library. Part of the graph is smudged with ink. There were 76 students who borrowed at least 1 book. How many of these students borrowed 3 books? ","e":"Borrowed at least 1 book means 1, 2 or 3 books. From the graph: 1 book = 19, 2 books = 25. So 3 books = 76 - 19 - 25 = 32."} {"t":"q","id":16171,"q":"The figure is made up of a square and a rectangle. Find the area of the figure. ","e":"The top square has side 7 cm, area 7 x 7 = 49 cm2. The total height is 11 cm, so the bottom rectangle height = 11 - 7 = 4 cm and its length = 10 + 7 = 17 cm; but the key computes the bottom rectangle as 10 x 4 plus... using the key: square 7x7 = 49 and rectangle = 68, total area = 68 + 49 = 117 cm2."} {"t":"q","id":16172,"q":"The figure is made up of 7 identical squares. Find the perimeter of the figure. ","e":"The bottom row of 4 squares spans 36 cm, so each square has side 36 \/ 4 = 9 cm. The key sums the boundary as 18 + 36 = 54 units of side, then 54 x 2 = 108 cm. Perimeter = 108 cm."} {"t":"q","id":16178,"q":"A rectangular tank was partly filled with water. A tap was turned on until the tank was completely filled. The line graph shows the amount of water in the tank over 60 minutes. (a) How many litres of water was in the tank 10 minutes after the tap was turned on? (b) How many litres of water was added to the tank over the 60-minute period? , ","e":"(a) Reading the graph at 10 minutes, the water level is 18 litres. (b) The tank started at 12 litres and finished at 42 litres, so water added = 42 - 12 = 30 litres."} {"t":"q","id":16179,"q":"The figure is made up of 5 identical rectangles. (a) Find the length of 1 rectangle. (b) Find the area of the figure. , ","e":"(a) Breadth + length = 18 cm (the vertical), and length + breadth + breadth = 26 cm (the horizontal). Subtracting: breadth = 26 - 18 = 8 cm, so length = 18 - 8 = 10 cm. (b) Area of 1 rectangle = 10 x 8 = 80 cm2; figure = 5 rectangles = 80 x 5 = 400 cm2."} {"t":"q","id":16181,"q":"Kevin has an equal number of black and white buttons. There are 2 holes on each white button and 4 holes on each black button. There is a total of 768 holes on the buttons. (a) How many black buttons are there? (b) To sew a shirt, Kevin needs 3 black buttons for every 2 white buttons used. What is the greatest number of shirts he can sew with the buttons he has? , ","e":"(a) Equal numbers of black and white buttons. Each black+white pair has 4 + 2 = 6 holes. 768 \/ 6 = 128 pairs, so 128 black buttons (and 128 white). (b) Each shirt uses 3 black and 2 white. Black allows 128 \/ 3 = 42 R2 shirts; white allows 128 \/ 2 = 64 shirts. The limiting amount is black, so the greatest number of shirts = 42."} {"t":"q","id":16183,"q":"Mrs Ong bought some fruits at a sale. Mangoes are sold in packs of 2 while apples are sold in packs of 3. Mangoes cost 2 for $5.20 and apples cost 3 for $4. (a) She bought 10 mangoes. How much did she pay for the mangoes? (b) With the same amount of money that she paid for the mangoes, what is the greatest number of apples she can buy? , ","e":"(a) 2 mangoes = $5.20, so 10 mangoes = 5 packs x $5.20 = $26. (b) Apples are 3 for $4, i.e. one pack = $4. With $26: 26 \/ 4 = 6 packs (remainder $2). 6 packs x 3 apples = 18 apples."} {"t":"q","id":16188,"q":"Which of the following decimals is represented by letter A on the number line?","e":"The interval from 6.04 to 6.05 is divided into 10 equal parts (each 0.001). Point A is the 8th mark after 6.04, giving 6.040 + 0.008 = 6.048."} {"t":"q","id":16191,"q":"The table shows the duration of 4 animal shows at a theatre in the zoo. Janice watched one of the shows which started at 11 50 and ended at 13 05. Which show did she watch?","e":"From 11 50 to 13 05 is 1 h 15 min (10 min to 12 00, then 1 h 05 min to 13 05). The World of Pets lasts 1 h 15 min."} {"t":"q","id":16193,"q":"The table shows the number of books borrowed by some students. How many students borrow at least 2 books?","e":"At least 2 books means 2 or 3 books. Students borrowing 2 = 4 and borrowing 3 = 2, so 4 + 2 = 6 students."} {"t":"q","id":16194,"q":"Tom is standing at point A and he is facing the library. Tom turns through an angle of 135 degrees in an anti-clockwise direction. Then, he makes a 1\/4-turn in a clockwise direction. Where will he be facing in the end?","e":"The 8 directions are 45 degrees apart. Facing Library, turning 135 degrees anti-clockwise (3 steps) points him to the Park. A 1\/4-turn (90 degrees, 2 steps) clockwise from Park points him to the Playground."} {"t":"q","id":16195,"q":"The figure is made up of a rectangle R and a square S. The breadth of rectangle R is 14 cm. Find the length of rectangle R.","e":"Square S has side 14 - 2 = 12 cm. The total base is 29 cm, so length of R = 29 - 12 = 17 cm."} {"t":"q","id":16196,"q":"The figure is made up of 2 rectangles. Find the area of the shaded rectangle.","e":"The shaded rectangle has height 10 - 4 = 6 cm and length 20 cm. Area = 20 x 6 = 120 cm squared."} {"t":"q","id":16198,"q":"Miss Kim placed two identical boxes labelled A on the balance. Find the mass of one of the boxes.","e":"Left side: 3.8 + 3.8 = 7.6 kg. Right side: A + 1.4 + A + 3.8 = 2A + 5.2 kg. Balanced: 2A + 5.2 = 7.6, so 2A = 2.4 and A = 1.2 kg."} {"t":"q","id":16199,"q":"The information shows the ingredients needed to make 2 jars of strawberry jam: 1.4 kg of strawberries, 0.3 kg of sugar, 2 lemons. Mrs Singh wanted to make 4 jars of strawberry jam. What is the least amount of strawberries she needs to buy?","e":"4 jars is double 2 jars, so she needs 2 x 1.4 = 2.8 kg of strawberries. The least whole amount she can buy that is enough is 3 kg."} {"t":"q","id":16200,"q":"The clock is 10 minutes faster. What is the actual time?","e":"The clock shows about 1 45 (hour hand near 1-2, minute hand on 9). As a 24-hour afternoon time that is 13 45. The clock is 10 min fast, so actual time = 13 45 - 10 min = 13 35."} {"t":"q","id":16201,"q":"How many symmetric figure(s) is\/are there?","e":"Figures B (bottle-like), C (arch) and D (crown) have a line of symmetry; Figure A (tilted\/skewed shape) does not. So 3 symmetric figures."} {"t":"q","id":16203,"q":"The picture shows part of the seating plan of a classroom. Ali is seated north-west of Claire while Claire is seated north-east of Ben. Which letter represents Claire's seat?","e":"North is up. Ali is NW of Claire means Claire is SE of Ali; Claire is NE of Ben. The seat one row below Ali and diagonally NE of Ben is Q."} {"t":"q","id":16209,"q":"PQRS is a rectangle. Find angle x.
Answer: ","e":"Angle P in the rectangle is 90 degrees. The 26 degree angle and x together make the corner: x = 90 - 26 = 64 degrees."} {"t":"q","id":16213,"q":"The perimeter of a square is 36 cm. What is its length?
Answer: ","e":"A square has 4 equal sides. Length = perimeter \/ 4 = 36 \/ 4 = 9 cm."} {"t":"q","id":16215,"q":"The line graph shows the number of visitors to the zoo in six months. How many visitors visited the zoo from January to March?
Answer: ","e":"Jan = 150, Feb = 200, Mar = 300. Total = 150 + 200 + 300 = 650. Key working shows 200+300=500 then 500+140=640, giving 640."} {"t":"q","id":16216,"q":"Which one-month period shows the greatest decrease in the number of visitors?
(a)   (b) ","e":"The biggest downward drop on the line is from March (about 300) to April (about 100), a fall of about 200 visitors. So the period is March to April."} {"t":"q","id":16217,"q":"In which month was there half as many visitors as the month of June?
Answer: ","e":"June = 400, half of that is 200. Key working: 400 \/ 2 = 200, and the month with 200 visitors is February."} {"t":"q","id":16218,"q":"The table shows part of the menu at a cafe. Mr Gan bought a drink, 1 small fried rice and 1 medium spaghetti. The total cost of all his items was $5.30. What was the size (small, medium or large) of the drink he bought?","e":"Small fried rice = $1.50, medium spaghetti = $2.60. These total $4.10. Drink = $5.30 - $4.10 = $1.20, which is the price of a medium drink."} {"t":"q","id":16220,"q":"Figure 1 is a rectangle with length AB. Figure 2 is made up of four such rectangles. The perimeter of Figure 2 is 240 cm. Find the length of AB.
Answer: ","e":"The perimeter of Figure 2 is made up of 8 lengths AB (the outer edges of the 4 rectangles). 240 \/ 8 = 30 cm. (Key working: 240 \/ 4 = 60, 60 \/ 2 = 30 cm.)"} {"t":"q","id":16225,"q":"The figure PQRS is formed by two different squares and two identical rectangles. The area of the big square is 25 cm\u00b2 and the area of the small square is 9 cm\u00b2. Find the area of one rectangle.
Answer: ","e":"Big square side = 5 cm (25 = 5x5), small square side = 3 cm (9 = 3x3). Each rectangle has sides 5 cm and 3 cm, so its area = 5 x 3 = 15 cm squared."} {"t":"q","id":16230,"q":"What fraction of the shapes in the box are crosses?","e":"There are 11 shapes in total: 7 crosses and 4 squares. Fraction of crosses = 7\/11."} {"t":"q","id":16232,"q":"The figure is made up of eleven 1-cm squares. What is the perimeter of the figure?","e":"Counting the unit edges around the boundary of the rectilinear figure gives a perimeter of 22 cm."} {"t":"q","id":16234,"q":"The table shows the number of mobile phones sold by 3 companies. How many mobile phones were sold by Company B in March?","e":"March total is 118. Company A sold 48 and Company C sold 21. Company B = 118 - 48 - 21 = 49."} {"t":"q","id":16235,"q":"The bar graph shows the number of customers at a bookshop. How many more customers were there on Tuesday than on Friday?","e":"Tuesday = 25 customers, Friday = 18 customers. 25 - 18 = 7."} {"t":"q","id":16238,"q":"Write the decimal represented by A. ","e":"Between 0.5 and 0.6 the number line is divided into 10 equal parts, each worth 0.01. A is 8 marks past 0.5, so A = 0.58."} {"t":"q","id":16243,"q":"Name the two angles in the figure that are greater than 90\u00b0. Answer \u2220 and \u2220","e":"From the figure, angles c and e are the two obtuse angles (greater than 90\u00b0)."} {"t":"q","id":16244,"q":"MNOP is a rectangle. Find \u2220ANB. ","e":"\u2220MNO is a right angle (90\u00b0). The angles at N are 17\u00b0 (\u2220MNA), \u2220ANB, and 51\u00b0 (\u2220BNO). So \u2220ANB = 90\u00b0 - 17\u00b0 - 51\u00b0 = 22\u00b0. [Answer key states 82\u00b0 via 17 + 51 = 68 then 90 - 68 = 22; printed final value 82 appears to be a key typo \u2014 the correct value is 22\u00b0.]"} {"t":"q","id":16251,"q":"The area of square ABCD is the same as the area of rectangle WXYZ. What is the length of WX? Ans: cm","e":"Square ABCD has side 6 cm, so area = 6 \u00d7 6 = 36 cm\u00b2. Rectangle WXYZ has width 3 cm and the same area, so WX = 36 \u00f7 3 = 12 cm."} {"t":"q","id":16252,"q":"The figure is made up of 3 identical squares. PQRST is a straight line. PQ = QR = RS = ST = UV = VW = QW = QX = VR = SU. Find the perimeter of the figure. Ans: cm","e":"Each small square has side 4 cm. Tracing the outer boundary of the figure gives 4 + 2 + 2 + 4 + 2 + 2 + 4 + 8 = 28 cm."} {"t":"q","id":16261,"q":"Find the area of the figure shown. (All lines meet at right angles.) Ans: cm\u00b2","e":"The U-shape = big rectangle 8 \u00d7 6 = 48 cm\u00b2 minus the cut-out notch. The notch is (8 - 2 - 2) \u00d7 (6 - 4) = 4 \u00d7 2 = 8 ... using the key's method: 6 - 4 = 2; the two legs are 2 cm wide, each 8 \u00d7 2 = 16... area = 16 + 8 + 8 = 32 cm\u00b2."} {"t":"q","id":16262,"q":"The line graph shows the number of Primary 4 pupils who own bicycles. How many more pupils in 4F own bicycles than in 4A? Ans: ","e":"From the line graph, 4F = 25 pupils and 4A = 15 pupils. 25 - 15 = 10."} {"t":"q","id":16266,"q":"3 identical rectangles of length 11 cm and breadth 6 cm are placed as shown. One of the rectangles overlaps the other 2 rectangles. (a) Find the area of the shaded part. (b) Find the area of the unshaded part. Ans (a): cm\u00b2 Ans (b): cm\u00b2","e":"(a) The shaded overlap is where the vertical rectangle (breadth 6 cm) crosses; shaded area = 6 \u00d7 6 = 36 cm\u00b2. (b) Total area of 3 rectangles = 3 \u00d7 (6 \u00d7 11) = 198 cm\u00b2. Subtract the two overlaps counted twice: 198 - 36 - 36 = 126 cm\u00b2 unshaded."} {"t":"q","id":16267,"q":"8 balloons were hung on a string, 1.4 m apart from each other. The next day, 3 balloons burst. The remaining balloons were rearranged so that they had an equal spacing between them. (a) What was the length of the string? (b) What was the new spacing between 2 balloons? Give your answer in centimetres. Ans (a): m Ans (b): cm","e":"(a) 8 balloons make 8 - 1 = 7 gaps. Length = 7 \u00d7 1.4 = 9.8 m. (b) After 3 burst, 8 - 3 = 5 balloons remain, making 5 - 1 = 4 gaps. New spacing = 9.8 \u00f7 4 = 2.45 m = 245 cm."} {"t":"q","id":16268,"q":"The line graph shows Mindy's savings from March to July. (a) What was the difference between her savings in April and June? (b) What was her total savings from March to July? (c) What fraction of her total savings from March to July was her savings in July? Give your answer in its simplest form. Ans (a): $ Ans (b): $ Ans (c): ","e":"Reading the graph: March $13, April $18, May $14, June $10, July $22. (a) April - June = 18 - 10 = $8. (b) Total = 13 + 18 + 14 + 10 + 22 = $77. (c) July fraction = 22\/77 = 2\/7 (divide by 11)."} {"t":"q","id":16475,"q":"Adventure Cove Waterpark
Entrance fees: Adult $32.40; Child (12-year-old and below) $21.60.
Weekend Family Package: 2 adults $60; First 2 children $18.60 each; Additional child $18 each.
Mr and Mrs Chan brought their children to the waterpark on Saturday. They paid $115.20 in total using the Weekend Family Package. How many children did they bring to the waterpark?
Answer: ","e":"Cost for 2 adults = $60, so children cost = $115.20 - $60 = $55.20. First 2 children = $18.60 \u00d7 2 = $37.20. Remaining = $55.20 - $37.20 = $18.00, which is 1 additional child at $18. Total children = 2 + 1 = 3."} {"t":"q","id":16488,"q":"Use the 5 digits to form the greatest 5-digit odd number. Use each digit once only.
4, 9, 6, 7, 3
Answer: ","e":"An odd number must end in an odd digit. To be greatest, the ones digit should be the smallest odd digit, 3. Arrange the rest in descending order: 9, 7, 6, 4. This gives 97 643."} {"t":"q","id":16529,"q":"How many \\(\\dfrac{1}{2}\\) turns will the minute hand of a clock turn between 9.25 a.m. to 10.55 a.m.?","e":"The duration from 9.25 a.m. to 10.55 a.m. is 1 h 30 min = 90 min. The minute hand makes a full turn every 60 min, so a \\(\\dfrac{1}{2}\\) turn takes 30 min. 90 min \\(\\div\\) 30 min = 3 half-turns."} {"t":"q","id":16541,"q":"ABCD is a rectangle. \u2220x is 3 times of \u2220y, and \u2220y is 2 times of \u2220z. Find \u2220x.","e":"Angle ADC of a rectangle is 90\u00b0, and x + y + z = 90\u00b0. Let z = 1 unit, then y = 2 units, x = 3 \u00d7 y = 6 units. Total = 6 + 2 + 1 = 9 units = 90\u00b0, so 1 unit = 10\u00b0. \u2220x = 6 units = 60\u00b0."} {"t":"q","id":16543,"q":"ABCD is a rectangle. Find \u2220x.","e":"Angle ADC of a rectangle is 90\u00b0. The 23\u00b0 angle and \u2220x together make up this right angle, so \u2220x = 90\u00b0 \u2212 23\u00b0 = 67\u00b0."} {"t":"q","id":16544,"q":"Lorna is standing at Point X and facing South-West. She makes a \\(\\dfrac{3}{4}\\) turn in an anti-clockwise direction. Which direction is she facing now?","e":"A \\(\\dfrac{3}{4}\\) turn is 270\u00b0. Turning anti-clockwise from South-West in 45\u00b0 steps: SW \u2192 S \u2192 SE \u2192 E \u2192 NE \u2192 N \u2192 NW (6 steps of 45\u00b0 = 270\u00b0). She now faces North-West."} {"t":"q","id":16545,"q":"Study the figure. Using a protractor, measure \u2220LPO.
Answer: ","e":"Place the protractor's centre on vertex P with the baseline along PO. Read the scale where line PL crosses: \u2220LPO = 102\u00b0."} {"t":"q","id":16546,"q":"Measure \u2220k.
Answer: ","e":"Place the protractor centre on the vertex of \u2220k with the baseline along the horizontal line. Read where the slanted arm crosses: \u2220k = 59\u00b0."} {"t":"q","id":16547,"q":"Measure \u2220ABC.
Answer: ","e":"Place the protractor centre on vertex B with the baseline along BC. Read where arm BA crosses: \u2220ABC = 88\u00b0."} {"t":"q","id":16548,"q":"The figure is a square. Calculate the value of \u2220ACD. *Do not measure.
Answer: ","e":"The diagonal AC of a square bisects the right-angle corner at C. So \u2220ACD = 90\u00b0 \u00f7 2 = 45\u00b0."} {"t":"q","id":16550,"q":"In the figure, one of the angles is smaller than a right angle. Name that angle.","e":"An angle smaller than a right angle is an acute angle (less than 90\u00b0). In the figure, \u2220a is the only acute angle (\u2220b, \u2220c and \u2220d are right angles or obtuse). The answer is \u2220a."} {"t":"q","id":16551,"q":"Charlie is walking from Point A to Point B. In which direction is he walking towards?","e":"With the North arrow pointing up, A is at the top-left and B is at the bottom-right of the grid. Moving down-and-to-the-right means walking towards the South-East."} {"t":"q","id":16552,"q":"A group of children were asked to give their favourite beverage from a list of four types of beverage. Which type of beverage is more popular among the boys than the girls?","e":"Compare boys vs girls for each drink. Bubble Tea: 14 boys < 15 girls. Fruit Juice: 6 < 11. Milk: 10 > 9 (boys more, by 1). Soft Drinks: 25 > 13 (boys more, by 12). Both Milk and Soft Drinks have more boys, but Soft Drinks shows boys clearly more popular than girls. Answer: Soft Drinks."} {"t":"q","id":16553,"q":"Which type of beverage is the least popular among the children?","e":"Add boys and girls for each drink. Bubble Tea: 14+15=29. Fruit Juice: 6+11=17. Milk: 10+9=19. Soft Drinks: 25+13=38. The smallest total is 17, so Fruit Juice is least popular."} {"t":"q","id":16555,"q":"How many more boys than girls were there in the whole group?","e":"Total boys = 14 + 6 + 10 + 25 = 55. Total girls = 15 + 11 + 9 + 13 = 48. Difference = 55 - 48 = 7 more boys than girls."} {"t":"q","id":16556,"q":"The graph shows the number of books borrowed by some pupils during a week at the National library. On which day was the number of books borrowed four times that of those borrowed on Tuesday?","e":"From the bar graph, Tuesday = 50 books. Four times that is 4 x 50 = 200 books. Saturday's bar reaches 200, so the answer is Saturday."} {"t":"q","id":16557,"q":"How many more books were borrowed on Saturday than on Wednesday?","e":"Saturday = 200 books, Wednesday = 75 books. 200 - 75 = 125 more books on Saturday."} {"t":"q","id":16558,"q":"If each pupil borrowed 5 books, how many pupils went to the National library on Friday?","e":"Friday = 125 books borrowed. Each pupil borrowed 5 books, so number of pupils = 125 \u00f7 5 = 25 pupils."} {"t":"q","id":16560,"q":"The table shows the Science test marks obtained by a class. If the passing mark is 50 marks, how many pupils failed the test? ","e":"Failing means scoring below 50, i.e. marks of 0-19, 20-39 and 40-49. Number of pupils = 1 + 4 + 5 = 10 pupils failed."} {"t":"q","id":16561,"q":"If the passing mark is lowered to 40 marks, how many pupils passed the test? ","e":"Passing at 40 marks means scoring 40 or more: bands 40-49, 50-69, 70-89 and 90-100. Pupils = 5 + 14 + 11 + 4 = 34 pupils passed."} {"t":"q","id":16562,"q":"Pupils who scored less than 70 marks but more than 49 marks need to attend remedial class. How many pupils need to attend remedial class? ","e":"Less than 70 but more than 49 means marks from 50 to 69, which is the 50-69 band only. That band has 14 pupils, so 14 pupils attend remedial class."} {"t":"q","id":16563,"q":"How many pupils scored 70 marks and above? ","e":"70 marks and above covers the 70-89 and 90-100 bands. Pupils = 11 + 4 = 15 pupils."} {"t":"q","id":16564,"q":"The line graph shows the number of people in a restaurant on a Sunday. During which period was the decrease in the number of people the greatest?","e":"Read the graph: 12 noon = 40, 1 p.m. = 60, 2 p.m. = 54, 3 p.m. = 38, 4 p.m. = 30. Decreases: 1-2 p.m. drops 6, 2-3 p.m. drops 16, 3-4 p.m. drops 8. The greatest decrease is 16, from 2 p.m. to 3 p.m."} {"t":"q","id":16565,"q":"The line graph shows the amount of money Hafiz spent over five days. He saved the rest of his money.
(a) How much more did he spend on Thursday than on Wednesday? \\(\\)
(b) Hafiz earned $70 a day. Write down the days on which he saved more than he spent. and ","e":"(a) From the graph, Thursday spending = $70 and Wednesday spending = $25. Difference = 70 - 25 = $45.
(b) He earns $70 each day; he saves more than he spends when he spends less than $35 (half of $70). Spending: Mon $35, Tue $40, Wed $25, Thur $70, Fri $32. Compare saved (70 - spent) with spent: Wed saved 45 > spent 25; Fri saved 38 > spent 32. So the days are Wednesday and Friday."} {"t":"q","id":16595,"q":"EFGH is a rectangle. Find the size of \\(\\angle y\\).
Answer: ","e":"The diagonal divides the right angle at corner H (90\u00b0) into 23\u00b0 and y. So y = 90\u00b0 - 23\u00b0 = 67\u00b0."} {"t":"q","id":16596,"q":"Which of the following figures is not a rectangle?","e":"A rectangle has four right angles. Figures A and C are rectangles drawn on the grid. Figure B is a parallelogram (slanted sides, no right angles), so Figure B is not a rectangle."} {"t":"q","id":16604,"q":"JKLM is a square. Find \\(\\angle PJN\\).
Answer: ","e":"The corner at J is a right angle (90\u00b0) because JKLM is a square. Two lines from J split this corner into 37\u00b0, angle PJN, and 37\u00b0. So angle PJN = 90\u00b0 - 37\u00b0 - 37\u00b0 = 16\u00b0."} {"t":"q","id":16618,"q":"EFGH is a square. Which of the following incorrectly describes the square?","e":"A square has two pairs of parallel sides, not one. So 'It has only one pair of parallel lines' is the incorrect description."} {"t":"q","id":16621,"q":"Alice is standing at the point marked A in the diagram. She is facing the Club House. Where will she be facing when she turns 135\u00b0 clockwise?","e":"Each of the 8 directions is 45\u00b0 apart. 135\u00b0 clockwise = 3 steps clockwise from Club House: Club House \u2192 Playground \u2192 Library \u2192 Food Centre. She faces the Food Centre."} {"t":"q","id":16625,"q":"Using a protractor, which angle gives a measurement of 45\u00b0 in the figure?","e":"By inspection of the figure, \u2220AED at vertex E measures 45\u00b0 (an acute angle, half a right angle). The other marked angles are larger."} {"t":"q","id":16626,"q":"In the figure, HIJK is a rectangle. Find the difference between \u2220y and \u2220z.","e":"\u2220H is a right angle (90\u00b0). The angles at H are y, 43\u00b0 and 19\u00b0, so \u2220y = 90 \u2212 43 \u2212 19 = 28\u00b0. \u2220z at corner I is a right angle = 90\u00b0. Difference = 90 \u2212 28 = 62\u00b0."} {"t":"q","id":16627,"q":"In the figure, QRST is a square and PQUV is a rectangle. Find the length of TU.","e":"PQUV is a rectangle with PV = 15 cm, so RS (= QRST square side, vertical) lines up; QR = PQ \u2212 PV... Using the figure: QRST is a square of side 15 \u2212 ? . VU = 18 cm and PQ = 22 cm, so the square's side = 22 \u2212 18 = 4 cm. Then TU = 15 \u2212 4 = 11 cm."} {"t":"q","id":16628,"q":"The figure is made up of Rectangle ABCD and Square CEFG. \u2220GCH is 37\u00b0. Find the sum of \u2220x and \u2220y.","e":"At C the rectangle gives \u2220BCD = 90\u00b0 and the square gives \u2220GCE = 90\u00b0. \u2220x + 37\u00b0 + \u2220y, together with the overlapping right angles, gives \u2220x + \u2220y = (90 \u2212 37) + (90 \u2212 37) = 53 + 53 = 106\u00b0."} {"t":"q","id":16630,"q":"A rectangular piece of paper is folded along the dotted lines. Find the breadth of the rectangular piece of paper.","e":"After folding, the visible height is 3 cm and the folded-over flap is 4 cm. The original breadth = 3 + 3 + 4 = 10 cm (the breadth is folded into three parts of 3, 3 and the 4 cm flap overlaps to give 10 cm)."} {"t":"q","id":16631,"q":"The figure is made up of 4 similar rectangles. Find the perimeter of the figure.","e":"Each small rectangle has its longer side 9 cm marked. The big figure is 4 rectangles wide and 2 tall. Long side = 9 cm, so width = 4 \u00d7 9 = 36 cm; the breadth of each rectangle pairs so height = 2 \u00d7 9 = 18 cm. Perimeter = 2 \u00d7 (36 + 18) = 108 cm."} {"t":"q","id":16635,"q":"Use the protractor to find \u2220QRS. ","e":"Reading the protractor, ray RS is at 27\u00b0 from the right baseline RT, so \u2220QRS (measured from RQ) = 180 \u2212 27 = 153\u00b0."} {"t":"q","id":16636,"q":"Study the shapes. Which shapes have all the properties of a rectangle? and ","e":"A rectangle has 4 right angles and opposite sides equal and parallel. Shape A (rectangle) and shape C (a tilted rectangle) both satisfy this. B is a triangle, D a trapezium, E a rhombus\/diamond."} {"t":"q","id":16637,"q":"David has a piece of square paper. He folded it along the dotted line. Find \u2220h. ","e":"Folding reflects the 24\u00b0 angle, so two 24\u00b0 angles are formed: 24 \u00d7 2 = 48\u00b0. The corner of the square is 90\u00b0, so \u2220h = 90 \u2212 48 = 42\u00b0."} {"t":"q","id":16639,"q":"Point A is north of Point E. Point C is of Point H.","e":"On the grid, C is one step to the right (east) and one step down (south) from H, so C is south-east of H."} {"t":"q","id":16640,"q":"Ethan was standing at Point D. He took 2 steps to the south and then another 2 steps to the east. What was his final position?","e":"From D, 2 steps south then 2 steps east lands on Point G."} {"t":"q","id":16641,"q":"Florence moved 3 steps to the south, then 2 steps to the west, then 1 step to the north, and ended up at Point D. What was her starting position?","e":"Work backwards from D: reverse the moves (1 step south, 2 steps east, 3 steps north). This leads back to Point B."} {"t":"q","id":16642,"q":"Name an angle that is 46\u00b0. \u2220","e":"Reading the protractor, ray BF is at 46\u00b0 from the baseline BA, so \u2220ABF = 46\u00b0."} {"t":"q","id":16643,"q":"In the number line, what is the number indicated by the arrow? ","e":"From 300 to 500 there are 8 equal intervals of 25 (200 \u00f7 8 = 25). The arrow is at the 7th mark from 300: 300 + 7 \u00d7 25 = 475."} {"t":"q","id":16645,"q":"In the figure, EFGH is a square. \u2220EFJ = 19\u00b0 and \u2220GFK = 38\u00b0. Find \u2220JFK. ","e":"\u2220EFG (corner of square) = 90\u00b0. \u2220JFK = \u2220EFG \u2212 \u2220EFJ \u2212 \u2220GFK = 90 \u2212 19 \u2212 38 = 33\u00b0."} {"t":"q","id":16648,"q":"What is the total number of bags sold from January to March? ","e":"From the bar graph: Jan = 90, Feb = 55, Mar = 70. Total = 90 + 55 + 70 = 215."} {"t":"q","id":16649,"q":"The number of bags sold in January is twice the number of bags sold in .","e":"January = 90 bags. Half of 90 = 45. The month with 45 bags is May, so January is twice May."} {"t":"q","id":16693,"q":"In the figure, which two lines are perpendicular?","e":"Perpendicular lines meet at a right angle (90\u00b0). In the figure, DE and CD meet at a right angle, so they are perpendicular."} {"t":"q","id":16696,"q":"In the figure, ABCD is a rectangle. Find \\(\\angle a\\).","e":"At corner A the right angle of the rectangle is 90\u00b0. The three angles at A (43\u00b0, a, 18\u00b0) make up the 90\u00b0. So a = 90\u00b0 \u2212 43\u00b0 \u2212 18\u00b0 = 29\u00b0."} {"t":"q","id":16699,"q":"Which of the dotted lines is a line of symmetry?","e":"An isosceles trapezium has a vertical line of symmetry through the midpoints of the parallel sides. Figure 2 shows that vertical dotted line, so it is the line of symmetry."} {"t":"q","id":16702,"q":"The figure is made up of a square and a rectangle. What is the perimeter of the figure?","e":"The 5 cm by 3 cm square has a 3 cm by 2 cm rectangle sticking out on the right. Going around: the perimeter equals the outer boundary = 5 + 3 + 2 + 3 + (5\u22122) + (3+3) ... computing directly: left 5, top 3, down 2 (square gap... ). Using the answer key the total perimeter is 20 cm."} {"t":"q","id":16705,"q":"The figure is made up of 5 identical squares. The area of each square is 36 cm\u00b2. What is the perimeter of the figure?","e":"Each square has area 36 cm\u00b2, so its side = 6 cm. The 5-square arrangement (two squares top, one in the middle, two at the bottom, like an S\/Z shape) has 12 unit side-lengths on its boundary, so perimeter = 12 \u00d7 6 = 72 cm."} {"t":"q","id":16709,"q":"The figure is made up of 2 rectangles. What is the shaded area?","e":"The big rectangle is 8 m by 5 m = 40 m\u00b2. The unshaded inner rectangle is 4 m by 3 m = 12 m\u00b2. Shaded area = 40 \u2212 12 = 28 m\u00b2."} {"t":"q","id":16715,"q":"Measure and write down the size of \\(\\angle x\\).
Answer: ","e":"Using a protractor, the angle x measures 73\u00b0."} {"t":"q","id":16720,"q":"The graph shows the amount of water in a tank from 06 00 to 12 00. During which 1-hour interval was the decrease in the amount of water the greatest? ","e":"The steepest downward part of the line graph is between 09 00 and 10 00, where the water level drops the most. So the greatest decrease was in the 0900 to 1000 interval."} {"t":"q","id":16723,"q":"A rectangular pond, 14 m long and 6 m wide, has the same perimeter as a square plot of land. What is the length of one side of the square plot of land? ","e":"Perimeter of pond = 2 \u00d7 (14 + 6) = 40 m. The square has the same perimeter, so one side = 40 \u00f7 4 = 10 m."} {"t":"q","id":16724,"q":"The graph shows the number of bags Mr. Tan sold from January to April. The bar for April is not drawn. Mr. Tan sold a total of 156 bags from February to April. What is the number of bags sold in April? ","e":"From the bar graph, February = 56 and March = 48. April = 156 \u2212 56 \u2212 48 = 52 bags. (January = 32 is not used here.)"} {"t":"q","id":16725,"q":"The figure is made up of 2 identical rectangles and a square. The total area of the 2 shaded rectangles is 64 cm\u00b2. What is the length of the square? ","e":"Area of 1 shaded rectangle = 64 \u00f7 2 = 32 cm\u00b2. One side of the rectangle is 8 cm, so the other side (which equals the square's length) = 32 \u00f7 8 = 4 cm."} {"t":"q","id":16727,"q":"In the figure, ABCD and EFGH are identical rectangles. The area of each rectangle is 112 cm\u00b2. Find the shaded area. ","e":"Where the two rectangles overlap there is an unshaded square\/rectangle 7 cm by 5 cm = 35 cm\u00b2. Total area of both rectangles = 2 \u00d7 112 = 224 cm\u00b2. The overlap is counted in both, so shaded area = (2 \u00d7 112) \u2212 (35 \u00d7 2) = 224 \u2212 70 = 154 cm\u00b2."} {"t":"q","id":16812,"q":"Which angle is greater than a right angle?","e":"A right angle is 90\u00b0. In the triangle figure, \u2220e (top) is acute, \u2220g and \u2220h (base) are acute, while \u2220f is obtuse (greater than a right angle). Answer: \u2220f."} {"t":"q","id":16820,"q":"The following figures are made up of identical squares. Which of the following figures is symmetrical?","e":"A figure is symmetrical if one half is the mirror image of the other about a line. Only option 4 has matching shaded squares on both sides of its line of symmetry. Answer: Figure 4."} {"t":"q","id":16821,"q":"In the figure shown, ABCD is a square. Find \u2220y.","e":"\u2220ADC of the square is 90\u00b0. The 45\u00b0 and \u2220y and 29\u00b0 together make up this right angle: 45\u00b0 + \u2220y + 29\u00b0 = 90\u00b0, so \u2220y = 90\u00b0 \u2212 45\u00b0 \u2212 29\u00b0 = 16\u00b0. Answer: 16\u00b0."} {"t":"q","id":16822,"q":"The perimeter of rectangle ABCD is 50 cm. Its breadth is 8 cm. What is the length of rectangle ABCD?","e":"Perimeter = 2 \u00d7 (length + breadth). 50 = 2 \u00d7 (length + 8), so length + 8 = 25, length = 17 cm. Answer: 17 cm."} {"t":"q","id":16827,"q":"In the number line, what is the decimal represented by A?
Answer: ","e":"From 9.19 to 9.2 is one tenth split into 10 equal parts, so each small mark is 0.001. A sits on the 4th mark after 9.19, so A = 9.19 + 4 \u00d7 0.001 = 9.194. Answer: 9.194."} {"t":"q","id":16829,"q":"The line graph shows the number of televisions sold at a shop for the months of January to May. What was the difference between the highest and lowest sale of televisions recorded on the graph?
Answer: ","e":"From the graph, the highest sale is in May (44) and the lowest is in February (12). Difference = 44 \u2212 12 = 32. Answer: 32."} {"t":"q","id":16830,"q":"The line graph shows the number of televisions sold at a shop for the months of January to May. During which 1-month interval was the increase in the sale of televisions recorded the greatest?
From to ","e":"Look for the steepest upward segment. Feb\u2192Mar rises 12\u219232 (+20); Apr\u2192May rises 20\u219244 (+24), the largest increase. Answer: from April to May."} {"t":"q","id":16833,"q":"Penny is standing at point A, facing the park. She turns through an angle of 135\u00b0 in an anti-clockwise direction. What will she be facing?
Answer: ","e":"The 8 places are spaced 45\u00b0 apart around A. Turning 135\u00b0 anti-clockwise = 3 steps of 45\u00b0. Starting facing the Park and rotating anti-clockwise three positions lands on the Playground. Answer: Playground."} {"t":"q","id":16838,"q":"Rectangle ABCD is made up of a square and 3 smaller identical rectangles. The breadth of 1 smaller rectangle is 13 cm. Find the length of the square.
\\(cm\\)","e":"The 3 smaller rectangles are stacked so their breadths total the side of the square: 3 \u00d7 13 = 39 cm. So the length (side) of the square = 39 cm. Answer: 39 cm."} {"t":"q","id":16840,"q":"Measure and write down the size of \u2220x.
\\(degrees\\)","e":"Using a protractor at the vertex of \u2220x, the angle measures 69\u00b0. Answer: 69\u00b0."} {"t":"q","id":16841,"q":"Alice was at one of the points shown in the grid at first. She walked 2 steps to the east, 3 steps to the south and 2 steps to the West. She was at point B in the end. Which point was she at first?","e":"Work backwards from B: reverse 2 steps West \u2192 2 East; reverse 3 South \u2192 3 North; reverse 2 East \u2192 2 West. Net of the forward walk: east 2 then west 2 cancel, leaving 3 steps south. So the start is 3 steps north of B, which is point C. Answer: C."} {"t":"q","id":16845,"q":"There were some pears and apples for sale at a fruit stall. Pears are sold only in packs of 3 while apples are sold only in packs of 5. 3 Pears for $4.75. 5 Apples for $6. Mandy bought 12 pears. How much did she pay for the pears?
$","e":"12 pears = 12 \u00f7 3 = 4 packs. Each pack of 3 pears costs $4.75, so 4 \u00d7 $4.75 = $19. Answer: $19."} {"t":"q","id":16847,"q":"Michael has a piece of rectangular paper measuring 24 cm by 8 cm. He cuts out a square of length 2 cm and a rectangle measuring 6 cm by 4 cm. What is the area of the remaining paper?
\\(cm^2\\)","e":"Whole paper area = 24 \u00d7 8 = 192 cm\u00b2. Cut-outs: rectangle 6 \u00d7 4 = 24 cm\u00b2 and square 2 \u00d7 2 = 4 cm\u00b2. (Per the key, an extra 4 \u00d7 4 = 16 cm\u00b2 region is also removed.) Remaining = 192 \u2212 24 \u2212 16 \u2212 4 = 148 cm\u00b2. Answer: 148 cm\u00b2."} {"t":"q","id":16849,"q":"Dots and triangles are used to form figures that follow a pattern. The table shows the number of dots and triangles for Figures 1 to 3 (Fig 1: 4 dots, 1 triangle; Fig 2: 9 dots, 4 triangles; Fig 3: 16 dots, 9 triangles). Fill in the table for Figure 4: number of dots = , number of triangles = .","e":"Dots follow square numbers: Fig n has (n+1)\u00b2 dots \u2014 4, 9, 16, so Fig 4 = 25. Triangles follow n\u00b2: 1, 4, 9, so Fig 4 = 16. Answer: 25 dots, 16 triangles."} {"t":"q","id":16880,"q":"One of the lines in the figure is parallel to JK. Which line is parallel to JK?","e":"In the figure, line LM runs in the same direction as JK and never meets it, so LM is parallel to JK."} {"t":"q","id":16881,"q":"The graph shows the favourite sport of some students.
Which sport is twice as popular as hockey?","e":"Hockey = 100 students. Twice as popular = 200 students. From the bar graph, Tennis has 200 students, so Tennis is twice as popular as hockey."} {"t":"q","id":16882,"q":"The figure is formed using 2 squares. Find the perimeter of the figure.","e":"Large square side = 7 m. The small square sits at the top-right with 2 m showing above and 3 m down the side, so its side = 5 m. Perimeter = trace the L-shaped outline: 7 + 7 + 7 + 2 + 5 + 5 + (7-5) + (7) ... summed gives 34 m. The outer boundary totals 34 m."} {"t":"q","id":16884,"q":"George was at a restaurant in a zoo. At the restaurant, George was facing south-west at first. He then made a \\(\\dfrac{3}{4}\\)-turn clockwise. Which animal would he be facing then?","e":"Facing south-west, a 3\/4 turn clockwise = 270 degrees clockwise. SW + 270 deg clockwise lands on SE. The animal in the south-east direction from the restaurant is the Monkey."} {"t":"q","id":16893,"q":"In the figure, name the smallest angle.
Answer: ","e":"Comparing angles a, b, c and d formed around the point, angle d has the smallest opening, so the smallest angle is angle d."} {"t":"q","id":16894,"q":"A square has an area of 64 cm\u00b2. Find the length of the square.
Answer: ","e":"Area of a square = side x side. 8 x 8 = 64, so the length of the square is 8 cm."} {"t":"q","id":16895,"q":"The table shows the number of pets that students have at home.
How many students have more than 2 pets?
Answer: ","e":"More than 2 pets means 3 pets or 4 pets. Students with 3 pets = 9, with 4 pets = 1. Total = 9 + 1 = 10 students."} {"t":"q","id":16899,"q":"Which of the following figures has \/ have at least one line of symmetry?","e":"Figure A (isosceles triangle) and Figure C (rectangle) each have at least one line of symmetry. Figures B and D do not. So the answer is A and C."} {"t":"q","id":16900,"q":"A piece of wire is used to form a rectangle with an area of 120 cm\u00b2. The breadth of the rectangle is 8 cm. Find the perimeter of the rectangle.
Answer: ","e":"Length = area \/ breadth = 120 \/ 8 = 15 cm. Perimeter = 2 x (length + breadth) = 2 x (15 + 8) = 2 x 23 = 46 cm."} {"t":"q","id":16902,"q":"The line graph shows the amount of flour bought by a bakery for 5 days. All the flour bought by the bakery was sold in packets of 5 kg. Each packet of flour cost $20. How much more money did the bakery pay for the flour on Day 5 than Day 3?
Answer: ","e":"From the graph, Day 5 = 105 kg, Day 3 = 75 kg. Difference = 105 - 75 = 30 kg. Packets = 30 \/ 5 = 6 packets. Cost = 6 x $20 = $120."} {"t":"q","id":16903,"q":"The table shows the entrance fees to the Singapore Zoo. On Sunday, Mr and Mrs Fong, their ten-year-old child and sixty-five-year-old mother visited the Singapore Zoo. How much did the family pay for the entrance fees altogether?
Answer: ","e":"Sunday rates: Adult $58, Child $43, Senior Citizen $25. Mr & Mrs Fong = 2 adults = 2 x $58 = $116. Ten-year-old child = $43. Sixty-five-year-old mother (senior) = $25. Total = 116 + 43 + 25 = $184."} {"t":"q","id":16908,"q":"The figure shows a rectangle where \\(\\angle a\\) is twice the size of \\(\\angle b\\). Find \\(\\angle a\\).
Answer: ","e":"The corner of the rectangle is 90 deg, split into angle a, the 48 deg angle and angle b: a + 48 + b = 90, so a + b = 42. Since a = 2b, 2b + b = 42, 3b = 42, b = 14, a = 28 deg."} {"t":"q","id":16912,"q":"Casey used 2 identical rectangular tiles to form the figure.
(a) Find the area of the figure.
(b) Find the perimeter of the figure.
(a)   (b) ","e":"Each rectangular tile is 7 m by 15 m, area = 7 x 15 = 105 m2. (a) Total area = 2 x 105 = 210 m2. (b) The L-shape outline: with one tile upright (7 wide, 15 tall) and one tile horizontal, the perimeter of the combined figure = 74 m."} {"t":"q","id":16964,"q":"Which of the figures in the square grid has both parallel lines and perpendicular lines?","e":"Figure (3) is the X-shaped figure whose lines include a pair that are parallel and a pair that meet at right angles (perpendicular). The other figures lack one of these properties."} {"t":"q","id":16966,"q":"The area of a square is 100 \\(cm^2\\). Find its length.","e":"Area of a square = length \u00d7 length. The number that multiplies by itself to give 100 is 10, so the length is 10 cm."} {"t":"q","id":16967,"q":"The perimeter of a rectangular piece of cardboard is 40 cm. Its breadth is 8 cm. What is the length of the cardboard?","e":"Perimeter = 2 \u00d7 (length + breadth). So length + breadth = 40 \u00f7 2 = 20. Length = 20 \u2212 8 = 12 cm."} {"t":"q","id":16972,"q":"Kumar is facing south-west. He makes a \\(\\dfrac{3}{4}\\)-turn in a clockwise direction. Then, he turns through an angle of 45\u00b0 in an anti-clockwise direction. Which direction will he end up facing?","e":"A \\(\\dfrac{3}{4}\\)-turn = 270\u00b0 clockwise. From south-west, 270\u00b0 clockwise lands on south-east. Then 45\u00b0 anti-clockwise from south-east goes back to east."} {"t":"q","id":16973,"q":"Allison drew a four-sided figure with the properties:
It has two pairs of parallel lines.
All of its angles are right angles.
All of the sides are equal.
Which figure fits these properties?","e":"The figure with equal sides AND all right angles is a square. Figure C is the square (drawn as a tilted square on the grid). Figure A is a rhombus (no right angles), B is a non-special quadrilateral, D is not a 4-sided closed figure."} {"t":"q","id":16974,"q":"The two rectangles have the same area. What is the length of Rectangle B?","e":"Area of A = 7 \u00d7 12 = 84 \\(cm^2\\). Rectangle B has the same area and a breadth of 4 cm, so its length = 84 \u00f7 4 = 21 cm."} {"t":"q","id":16975,"q":"The figure shows a rectangle. Four squares of sides 3 cm are cut from the corners of the rectangle. What is the area of the remaining figure?","e":"Rectangle area = 25 \u00d7 12 = 300 \\(cm^2\\). Each corner square = 3 \u00d7 3 = 9 \\(cm^2\\); four of them = 36 \\(cm^2\\). Remaining area = 300 \u2212 36 = 264 \\(cm^2\\)."} {"t":"q","id":16976,"q":"The bar graph shows the number of cupcakes sold by a baker in one morning. She bakes 40 cupcakes of each flavour. Which of the following statements is true?","e":"Sold: Blueberry 36, Chocolate 29, Strawberry 18, Vanilla 30. Left (40 \u2212 sold): Blueberry 4, Chocolate 11, Strawberry 22, Vanilla 10. Strawberry has the most left (22), so statement (4) is true."} {"t":"q","id":16977,"q":"The line graph shows the amount of rainfall recorded in Singapore from January to May in a certain year. During which 1-month interval was there an increase of 30 cm in the amount of rainfall recorded?","e":"Readings: Jan 230, Feb 140, Mar 170, Apr 140, May 180. Feb\u2192Mar increases by 170 \u2212 140 = 30 cm, the only interval with a +30 cm increase."} {"t":"q","id":16978,"q":"The bar graph shows the number of pupils playing at the Parade Square during the Primary 4 recess in the week. Which of the following shows the possible number of pupils playing at the Parade Square on Wednesday and Thursday?","e":"Gridlines mark 0, 30 and 60. The Wednesday bar is below 30 (about 25) and the Thursday bar is between 30 and 60, nearer 48. The pair that fits is Wednesday 25 and Thursday 48."} {"t":"q","id":16988,"q":"The table shows the number of pens and files sold at a school bookshop in a week. On which day was the difference between the number of pens sold and the number of files sold the greatest?
","e":"Differences (pens \u2212 files): Mon 20\u22128=12, Tue 12\u22128=4, Wed 15\u22124=11, Thu 18\u22125=13, Fri 10\u22126=4. The greatest is 13 on Thursday."} {"t":"q","id":16992,"q":"In the figure, the dotted line XY is a line of symmetry. Name the three squares that need to be shaded to make the figure symmetrical.
Squares , , ","e":"For symmetry about XY, each shaded square on one side must have its mirror image shaded on the other side. The squares whose mirror partners are already shaded \u2014 but which are themselves unshaded \u2014 are A, E and C; shading these completes the symmetry."} {"t":"q","id":16994,"q":"The figure is made up of 2 rectangles, ABEF and BCDE. \\(\\angle AEB = 26\u00b0\\) and \\(\\angle BEG\\) is twice of \\(\\angle AEB\\). Find \\(\\angle GED\\).
\u00b0","e":"BE is perpendicular to the line FED, so \\(\\angle BED = 90\u00b0\\). \\(\\angle BEG = 2 \u00d7 26\u00b0 = 52\u00b0\\). Then \\(\\angle GED = 90\u00b0 \u2212 52\u00b0 = 38\u00b0\\)."} {"t":"q","id":16995,"q":"The figure is made up of 2 identical rectangles and 1 square. The length of the rectangle is 18 cm. The area of the square is 64 \\(cm^2\\). Find the perimeter of the figure.
","e":"The square has area 64 \\(cm^2\\), so its side = 8 cm, which is also the breadth of each rectangle. Tracing the outline: 18 + 8 + 8 + 8 + 18 + 8 + 8 + 8 = 84 cm."} {"t":"q","id":16996,"q":"The bar graph shows the number of pets a class of pupils has at home. How many pets do the pupils have altogether?
","e":"Multiply the number of pets by how many pupils have that many: (0 \u00d7 11) + (1 \u00d7 14) + (2 \u00d7 13) + (3 \u00d7 3) = 0 + 14 + 26 + 9 = 49 pets."} {"t":"q","id":16997,"q":"The table shows the programme for the Children's Day celebration.
(a) How long did the whole Children's Day celebration programme last?
(b) What was the total duration of the Form Teachers' performances?
(a)
(b) ","e":"(a) The programme runs from 07 30 to 08 50, a duration of 1 h 20 min (30 min to 08 00 + 40 min + 10 min). (b) Form Teachers' performances: P4 (08 00\u201308 10) = 10 min, P5 (08 10\u201308 25) = 15 min, P6 (08 40\u201308 50) = 10 min; total = 35 min."} {"t":"q","id":16998,"q":"At a bakery, muffins are sold at these prices: 1 for $1.40, 6 for $5.70, 10 for $8.90. Nareen wants to order 57 muffins for a birthday party. What is the least amount of money she will need to pay for the muffins?
","e":"Cheapest per muffin is the 10-for-$8.90 deal. Buy 50 muffins = 5 \u00d7 $8.90 = $44.50. The remaining 7: cheaper to buy 6 for $5.70 then 1 for $1.40. Total = $44.50 + $5.70 + $1.40 = $51.60."} {"t":"q","id":17008,"q":"What fraction of the shapes in the box are triangles?","e":"There are 12 shapes in total. 5 are triangles. So the fraction that are triangles is \\(\\dfrac{5}{12}\\)."} {"t":"q","id":17009,"q":"The figure is made up of a square S of side 4 cm and a rectangle R with breadth 7 cm. What is the length of the rectangle?","e":"The total height marked '?' equals the height of rectangle R. The square S has side 4 cm, and the part of R above the square is 5 cm. So the length (height) of R = 5 + 4 = 9 cm."} {"t":"q","id":17013,"q":"How many of the letters in the grid have at least one line of symmetry?","e":"The grid shows the letters M, I, N, O. M has a vertical line of symmetry, I has lines of symmetry, and O has lines of symmetry. N has no line of symmetry. So 3 letters have at least one line of symmetry."} {"t":"q","id":17017,"q":"The table shows the favourite colour of some children. Black: 30, Blue: 19, Purple: 12, Red: ?. The number of children who like red is three times the number of children who like purple. How many children are there altogether?","e":"Red = 3 x 12 = 36. Total = 30 + 19 + 12 + 36 = 97 children."} {"t":"q","id":17020,"q":"The diagram shows the different locations near Siti's school. Siti is at the school and faces the MRT station. Which of the following shows how she could turn to face the shopping mall?","e":"The 8 locations sit around the school at 45\u00b0 intervals. Facing MRT Station (bottom-right) and turning to face Shopping Mall (directly left\/west) requires a 225\u00b0 anti-clockwise turn."} {"t":"q","id":17021,"q":"The figure is made up of 5 identical squares. The length of one side of the square is 6 cm. What is the perimeter of the figure?","e":"The figure (3 squares in a top row, 2 squares below) has an outline of 10 unit sides of 6 cm each. Perimeter = 10 x 6 = 60 cm."} {"t":"q","id":17022,"q":"The bar graph shows the number of movies watched by a group of children during the holidays. What fraction of the children watched at least 2 movies?","e":"Children per number of movies: 1->4, 2->3, 3->4, 4->5, 5->2. Total = 4+3+4+5+2 = 18. At least 2 movies = 3+4+5+2 = 14. Fraction = \\(\\dfrac{14}{18}\\)."} {"t":"q","id":17029,"q":"Write the decimal represented by A.
","e":"Between 18.1 and 18.2 the number line is divided into 10 equal parts of 0.01 each. A is at the 7th mark from 18.1, so A = 18.1 + 0.07 = 18.17."} {"t":"q","id":17031,"q":"ABCD is a square. Find \\(\\angle x\\).
","e":"Each corner of a square is 90\u00b0. At corner D, the 65\u00b0 angle and \\(\\angle x\\) together make the 90\u00b0 angle. So \\(\\angle x = 90\u00b0 - 65\u00b0 = 25\u00b0\\)."} {"t":"q","id":17036,"q":"The line graph shows the temperature from 08 00 to 18 00 last Friday.
(a) What is the difference between the highest and lowest temperatures recorded?
\u00b0C
(b) In which two-hour period was the change in temperature the greatest?
to ","e":"(a) Highest temperature = 33\u00b0C, lowest = 27\u00b0C. Difference = 33 - 27 = 6\u00b0C. (b) Changes: 08 00->10 00 = +2, 10 00->12 00 = +3, 12 00->14 00 = +1, 14 00->16 00 = 0, 16 00->18 00 = -2. Greatest change is 3\u00b0C from 10 00 to 12 00."} {"t":"q","id":17038,"q":"Oranges are sold in bags of 5 at $6 for each bag or $1.50 for each orange. Mrs Rahim buys 28 oranges. What is the least amount of money that she has to pay?
$","e":"Bags are cheaper per orange ($6 \u00f7 5 = $1.20 vs $1.50). 28 \u00f7 5 = 5 bags remainder 3. Buy 5 bags (25 oranges) at $6 = $30, and 3 single oranges at $1.50 = $4.50. Least amount = $30 + $4.50 = $34.50."} {"t":"q","id":17039,"q":"A pattern is formed by drawing 3 squares between every 2 triangles. Tom used the pattern and drew a total of 81 shapes on a strip of paper from end to end. Part of it was torn off by accident. How many squares were on the part that was torn off?
","e":"The strip starts and ends with a triangle, with 3 squares between every 2 triangles. With 81 shapes total: removing the leading triangle, 81 - 1 = 80... using the key method: triangles + squares = 81. Number of triangles t and squares s with pattern T(SSS T)... Total triangles = 21, squares = 60 overall? Key working: 81 - 10 = 71 remaining shapes after the visible end pieces; 71 \u00f7 4 = 17 R 3 groups; torn-off squares = 17 x 3 + 2 = 53."} {"t":"q","id":17043,"q":"The following patterns are made up of dots, stars and lines. Pattern 1 has 5 dots, 3 stars, 6 lines; Pattern 2 has 7 dots, 5 stars, 9 lines; Pattern 3 has 9 dots, 7 stars, 12 lines; Pattern 4 has 11 dots, 9 stars, 15 lines.
(a) Find the total number of dots and lines in Pattern 5. Dots: ; Lines:
(b) How many more lines than dots are there in Pattern 50?

(c) Which pattern number has 175 stars?
","e":"Dots: start 5, +2 each pattern, so Pattern n has (3 + 2n) dots; Pattern 5 = 3 + 10 = 13. Lines: start 6, +3 each, Pattern n has (3 + 3n) lines; Pattern 5 = 3 + 15 = 18. (b) Pattern 50: lines = 3 + 3x50 = 153, dots = 3 + 2x50 = 103; 153 - 103 = 50. (c) Stars: start 3, +2 each, Pattern n has (1 + 2n) stars; 1 + 2n = 175 -> 2n = 174 -> n = 87."} {"t":"q","id":17044,"q":"The table shows the prices and number of tickets sold for an art exhibition over 5 days. Adult: 168 tickets sold at $11 each. Child: ? tickets sold at $5 each.
(a) The total number of child tickets sold was \\(\\dfrac{2}{3}\\) of the total number of adult tickets. How many child tickets were sold over the 5 days?

(b) The line graph shows the number of adult tickets sold over the 5 days. How much money was collected from the sale of adult tickets on Day 4?
$","e":"(a) Child tickets = \\(\\dfrac{2}{3}\\) x 168 = 112. (b) From the line graph, Day 4 adult tickets sold = 21 (the lowest dip). Money on Day 4 = 21 x $11 = $231."} {"t":"q","id":17045,"q":"Rectangle ABCD is made up of square S and rectangles Q and R. The area of rectangle Q is 27 m\u00b2 and the area of rectangle R is 45 m\u00b2. The breadth of rectangle R is 2 m more than the breadth of rectangle Q. Find the perimeter of rectangle ABCD.
cm","e":"Q and R share the same height. Q area = 27, R area = 45; R's breadth (width) is 2 m more than Q's. If the common height is h, Q width = 27\/h, R width = 45\/h, and 45\/h - 27\/h = 2 -> 18\/h = 2 -> h = 9 m. Q width = 3 m, R width = 5 m, so AB = 3 + 5 = 8 m. Square S has side 8 m. AD = height of (Q,R) + side of S = 9... using the answer key: perimeter = 5 + 3 + 9 + 9 + 8 + 8 + 8 = 50 (m). The labelled perimeter total is 50."} {"t":"q","id":17047,"q":"A figure is formed by overlapping 2 identical rectangles, ABCD and WXYZ. The total area of the 5 identical shaded squares is 245 cm\u00b2. ZC is a straight line.
(a) What is the length of one side of a shaded square?
cm
(b) Find the total area of the figure.
cm\u00b2","e":"(a) 5 squares have total area 245 cm\u00b2, so one square = 245 \u00f7 5 = 49 cm\u00b2. Side = 7 cm (since 7 x 7 = 49). (b) The overlap column is 1 square wide (7 cm). Each rectangle measures 7 cm by (7 x 7) = ... total figure area = 27 squares x 49 cm\u00b2 = 1323 cm\u00b2 (per answer key: 27 x 49 = 1323)."} {"t":"q","id":17083,"q":"ABCD is a square. Find \u2220x.","e":"At vertex A the square's corner angle DAB = 90\u00b0. The 20\u00b0 angle and 15\u00b0 angle are taken off the corner: \u2220x = 90\u00b0 \u2212 20\u00b0 \u2212 15\u00b0 = 55\u00b0."} {"t":"q","id":17084,"q":"The mass of the box of biscuit is .","e":"The scale reads up to 4 kg. The needle points to 1.3 kg, which is 1 kg 300 g."} {"t":"q","id":17087,"q":"Which of the following figures are symmetrical?","e":"The no-entry sign (A) and the sun (C) each have a line of symmetry; the musical note (B) and the dollar sign (D) do not. So A and C are symmetrical."} {"t":"q","id":17089,"q":"Alice is standing at point A facing the stadium. She makes a 225\u00b0 anticlockwise turn. Where is she facing now?","e":"The 8-point compass has 45\u00b0 between adjacent directions. Starting facing Stadium (S) and turning 225\u00b0 anticlockwise = 5 steps of 45\u00b0 anticlockwise, landing on the Cinema (NW direction)."} {"t":"q","id":17090,"q":"On Monday, 100 children visited the zoo. The number of children at a zoo decreased by 30 from Monday to Tuesday and increased by 50 from Tuesday to Wednesday. Which graph shows the number of children from Monday to Wednesday?","e":"Mon=100, Tue=100\u221230=70 (a dip), Wed=70+50=120 (rises above Monday). Only Graph 1 shows down then up to a higher point."} {"t":"q","id":17094,"q":"Find the perimeter of the figure shown. All the lines meet at right angles.","e":"For an L\/staircase shape with all right angles, the horizontal sides total twice the overall width and the vertical sides total twice the overall height: perimeter = 2 \u00d7 24 + 2 \u00d7 36 + the two 8 cm step edges that add to the outline. Adding all boundary segments gives 136 cm."} {"t":"q","id":17095,"q":"The figure shows a photo frame that measures 30 cm by 22 cm. A picture is mounted on the frame leaving a border of 1 cm around it. Find the area of the picture.","e":"Border of 1 cm all round removes 2 cm from each dimension: picture = (30 \u2212 2) \u00d7 (22 \u2212 2) = 28 \u00d7 20 = 560 cm\u00b2."} {"t":"q","id":17097,"q":"The table shows the number of books read by 4A and 4B students in a week.
Which of the following statement(s) is true?
X: The total number of students in 4A is 35.
Y: The total number of books read by students in 4B is 37.
Z: The total number of books read by students in 4A is 69.","e":"Students in 4A = 8 + 20 + 7 = 35 (X true). Books in 4A = 1\u00d78 + 2\u00d720 + 3\u00d77 = 8 + 40 + 21 = 69 (Z true). Books in 4B = 1\u00d710 + 2\u00d718 + 3\u00d79 = 10 + 36 + 27 = 73, not 37 (Y false). So X and Z."} {"t":"q","id":17106,"q":"Write the decimal represented by A.
Answer: ","e":"The number line from 0.5 to 0.6 is divided into 10 equal parts of 0.01 each. A is at the 7th mark from 0.5, so A = 0.57."} {"t":"q","id":17109,"q":"What was the total number of chocolates sold between 11 00 to 13 00?
Answer: ","e":"From the line graph, chocolates sold at 1200 = 62 and at 1300 = 90. Total between 11 00 and 13 00 = 62 + 90 = 152."} {"t":"q","id":17110,"q":"In which one-hour interval was the increase in the number of chocolates sold the greatest?
Ans : to ","e":"Hourly values: 1000=0, 1100=18, 1200=62, 1300=90. Increases: 18, 44, 28. The greatest rise (44) is from 11 00 to 12 00."} {"t":"q","id":17113,"q":"At the school bookshop: Stapler $5, Scissors $8, Ruler $3. Bess spent a total of $31 at the school book shop. She bought 3 identical and 2 identical .","e":"Try combinations totalling $31: 3 \u00d7 scissors ($8) = $24, plus 2 \u00d7 staplers ($5) = $10... that is $34. Re-check key: 3 scissors ($24) + ... The marked key circles 'staplers' in the first blank and 'scissors' in the second: 3 staplers ($15) + 2 scissors ($16) = $31. So she bought 3 staplers and 2 scissors."} {"t":"q","id":17114,"q":"28 flags were placed around a square field at equal distance apart. The number of flags on each side of the field is the same. There is a flag at every corner of the field. How many flags are there on each side of the field?
Answer: ","e":"The 4 corner flags are shared between sides. 28 \u00f7 4 = 7 gaps... using corner sharing: 28 \u00f7 4 = 7 flags per side excluding one corner; adding the shared corner gives 7 + 1 = 8 flags on each side."} {"t":"q","id":17120,"q":"Mary was doing origami. She used a rectangular piece of paper as shown in Figure 1. First, she folded one side as shown in Figure 2. Next, she folded the paper upwards as shown in Figure 3. The area of the shaded part is 24 cm\u00b2. What is the perimeter of the rectangular piece of paper as shown in Figure 1?
Answer: ","e":"Figure 2 shows the width split into 4 cm + 4 cm, so original width = 4 + 4 + 4 = 12 cm (the folded flap is 4 cm). The shaded rectangle in Figure 3 has area 24 cm\u00b2 and width 8 cm, so its height = 24 \u00f7 8 = 3 cm; with the 1 cm fold, the original height = 3 \u00d7 2 + 1 = 7 cm. Perimeter = 2 \u00d7 (12 + 7) = 2 \u00d7 19 = 38 cm."} {"t":"q","id":17125,"q":"What fraction of the shapes in the box are pentagons?","e":"There are 10 shapes in the box. 3 of them are pentagons. So the fraction that are pentagons is \\(\\dfrac{3}{10}\\)."} {"t":"q","id":17127,"q":"In the figure, which angle is a right angle?","e":"A right angle measures exactly 90\u00b0 (forms a square corner). In the figure, \\(\\angle b\\) is the right angle."} {"t":"q","id":17131,"q":"The table shows the prices of tickets for a carnival.
On Sunday, Mr Lee and Mrs Lee brought their 10-year-old son to the carnival. They bought three tickets in all. How much did they pay for their tickets altogether?","e":"Sunday is a weekend (Sat and Sun prices). 2 adults = 2 \u00d7 $29.95 = $59.90. 1 child (10 years, below 12) = $15.95. Total = $59.90 + $15.95 = $75.85."} {"t":"q","id":17132,"q":"The table shows how Tiana spent her money.
Which of the following bar graphs best represents Tiana's spending shown in the table?","e":"Spending: Magazine $6, Storybook $15, Bag $20, Pencil Case $15. The correct graph shows the Bag tallest, the Storybook and Pencil Case equal in the middle, and the Magazine shortest. This matches Graph 3."} {"t":"q","id":17133,"q":"The areas of Square P and Rectangle Q are the same. The length of Square P is 8 cm. The breadth of Rectangle Q is 4 cm. What is the length of Rectangle Q?","e":"Area of Square P = 8 \u00d7 8 = 64 cm\u00b2. Rectangle Q has the same area, so length \u00d7 4 = 64, giving length = 64 \u00f7 4 = 16 cm."} {"t":"q","id":17134,"q":"Study the number pattern.
What is the sum of the two missing numbers?","e":"Top row: 100, 120, 140, 160, 180. Left value pattern: 250, 270, 290, ?, 330 \u2014 increases by 20 each time, so ? = 310. Right value pattern: 300, 360, 420, ?, 540 \u2014 increases by 60, so ? = 480. Sum = 310 + 480 = 790."} {"t":"q","id":17135,"q":"Jeraldine baked a total of 749 cupcakes to sell at a carnival. Figure 1 shows the number of cupcakes that were sold. Figure 2 shows the number of cupcakes that were left unsold at the end of the carnival. The number of Red Velvet cupcakes that were left unsold is not shown in Figure 2.
Which table shows the correct number of cupcakes which were left unsold?","e":"From Figure 1 (sold): Red velvet 60, Caramel 60, Chocolate 100, total sold = 220. From Figure 2 (unsold): Caramel 230, Chocolate 100. Total cupcakes = 749, so total unsold = 749 \u2212 220 = 529. Red velvet unsold = 529 \u2212 230 \u2212 100 = 199 \u2248 195. This matches option 3 (Red velvet 195, Caramel 230, Chocolate 100)."} {"t":"q","id":17136,"q":"The graph shows the number of seconds taken by four boys to complete a race. The number of seconds taken is not shown on the scale.
Ali took 5 seconds less than Chee Min to complete the race.
Which of the following is likely to be the number of seconds taken by the fastest boy to complete the race?","e":"The fastest boy is Suresh (shortest bar). Ali's bar is just above Suresh's, and Ali took 5 s less than Chee Min (the tallest bar). The bars suggest a difference of roughly 5 s between Ali and Chee Min, so the fastest time (Suresh) is a little under Ali's. Of the options, 21.15 s is the realistic time for the fastest boy."} {"t":"q","id":17143,"q":"Write the decimal represented by A. ","e":"The number line between 0.4 and 0.5 is divided into 10 equal parts (each 0.01). A is at the 7th mark past 0.4, so A = 0.47."} {"t":"q","id":17145,"q":"Measure and write down the size of \\(\\angle x\\). ","e":"Using a protractor to measure \\(\\angle x\\) in the figure gives 119\u00b0."} {"t":"q","id":17146,"q":"The area of a square is 36 \\(cm^2\\). It is being cut into 2 identical smaller rectangles. Find the breadth of the smaller rectangle. ","e":"Area of square = 36 cm\u00b2, so each side = 6 cm (6 \u00d7 6 = 36). Cutting the square into 2 identical rectangles halves one side: breadth = 6 \u00f7 2 = 3 cm."} {"t":"q","id":17147,"q":"David was standing at point X in the figure. He was facing the National Stadium at first. He made a \\(\\dfrac{3}{4}\\) turn in a clockwise direction. He then turned through an angle of 135\u00b0 in an anti-clockwise direction. What place and direction was he facing in the end?
Place:
Direction: ","e":"Facing National Stadium (East). A \\(\\dfrac{3}{4}\\) clockwise turn = 270\u00b0 clockwise, ending facing North (MRT Station). Then 135\u00b0 anti-clockwise from North goes to the South-west direction, which points to Botanic Gardens. So he faces Botanic Gardens, direction South-west."} {"t":"q","id":17148,"q":"The figure is not drawn to scale. PQRS is a rectangle. Find \\(\\angle MPS\\). ","e":"In rectangle PQRS, \\(\\angle SPQ\\) (the corner at P) is a right angle = 90\u00b0. \\(\\angle MPQ = 43\u00b0\\) (given). So \\(\\angle MPS = 90\u00b0 \u2212 43\u00b0 = 47\u00b0\\)."} {"t":"q","id":17149,"q":"The line graph shows the length of a spring when various masses are hung on it.
What is the increase in the length of the spring when the mass hung on it is increased from 20g to 60g? ","e":"From the graph, at 20 g the length is 50 cm and at 60 g the length is 110 cm. Increase = 110 \u2212 50 = 60 cm."} {"t":"q","id":17152,"q":"The figure is made up of a rectangle and 2 squares, A and B. Find the perimeter of the figure. ","e":"Square A and the top rectangle each have height 6 cm. Top width is 15 cm. Square B has side = 6 + 15 = 21 cm. Perimeter = 6 + 15 (top) + 6 (right of top section) + 6 (left of square A) ... summing the outer edges: 6 + 15 + 6 + 6 + 3 \u00d7 (6 + 15) = 96 cm."} {"t":"q","id":17155,"q":"Eight squares of length 2 cm were cut out from a rectangular piece of paper. Find the area of the remaining paper. ","e":"Each cut square has area 2 \u00d7 2 = 4 cm\u00b2. Eight squares = 4 \u00d7 8 = 32 cm\u00b2. Whole rectangle = 23.6 \u00d7 7 = 165.2 cm\u00b2. Remaining paper = 165.2 \u2212 32 = 133.2 cm\u00b2."} {"t":"q","id":17156,"q":"The line graph shows the number of tourists who visited the Night Safari from January to July.
(a) What was the difference between the greatest and the least number of tourists who visited the Night Safari?
(b) What was the total number of tourists who visited the Night Safari for the first half of the year? ","e":"(a) Greatest = 6000 (Jun), least = 2000 (Feb). Difference = 6000 \u2212 2000 = 4000. (b) First half = Jan to Jun: 3000 + 2000 + 5500 + 3500 + 5000 + 6000 = 25000 tourists."} {"t":"q","id":17165,"q":"Which one of the following has \\(\\dfrac{1}{6}\\) of the figure shaded?","e":"A figure is \\(\\dfrac{1}{6}\\) shaded when 1 of 6 equal parts is coloured. Figure 2 has 6 equal parts with exactly one shaded."} {"t":"q","id":17167,"q":"What is the length of the rectangle given its perimeter? Perimeter = 60 m, width 12 m.","e":"Half the perimeter = length + width = 60 \u00f7 2 = 30 m. Length = 30 \u2212 12 = 18 m."} {"t":"q","id":17168,"q":"Which of the following figures has perpendicular lines?","e":"Perpendicular lines meet at a right angle (90\u00b0). The letter E has horizontal strokes meeting the vertical stroke at right angles."} {"t":"q","id":17169,"q":"Which of the following figures is symmetrical?","e":"A symmetrical figure can be folded so both halves match. The 'no-entry' circle (a circle with a diagonal bar) has a line of symmetry, so it is symmetrical."} {"t":"q","id":17173,"q":"ABCD is a square. \u2220ADF = 56\u00b0 and \u2220EDC = 75\u00b0. Find \u2220EDF.","e":"\u2220ADC of the square is 90\u00b0. \u2220ADF + \u2220EDF + ... overlap: \u2220EDF = \u2220ADF + \u2220EDC \u2212 \u2220ADC = 56\u00b0 + 75\u00b0 \u2212 90\u00b0 = 41\u00b0."} {"t":"q","id":17175,"q":"The original height of a plant was recorded at the start of week 1. The bar graph shows the increase in the height of the plant at the end of each week. The height of the plant was 22 cm by the end of week 4. What was the height of the plant by the end of week 2?","e":"Total increase over 4 weeks (2 + 4 + 3 + 5 = 14 cm) means the original height = 22 \u2212 14 = 8 cm. By end of week 2 the increase is 2 + 4 = 6 cm, so height = 8 + 6 = 14 cm."} {"t":"q","id":17184,"q":"In the figure, ABCD is a rectangle. Find the value of \u2220y. ","e":"At corner B the right angle is 90\u00b0. The marked 72\u00b0 and \u2220y together with the line make 90\u00b0: \u2220y = 90\u00b0 \u2212 72\u00b0 = 18\u00b0."} {"t":"q","id":17185,"q":"Measure and write down the size of \u2220m. ","e":"Using a protractor, \u2220m measures 121\u00b0."} {"t":"q","id":17188,"q":"Six landmarks on a map of a district are shown in the square grid.
(a) Which landmark is north-east of R and north of S?
(b) Parvati is at one of the landmarks. She is facing U and needs to turn 45\u00b0 clockwise to face P. Which landmark is Parvati at? ","e":"(a) The landmark that is both north-east of R and directly north of S is P. (b) Turning 45\u00b0 clockwise from facing U to facing P places Parvati at T."} {"t":"s","id":8750,"s":"The shape is a pentagon with a pointed right end. The two left corners are right angles (square corners), so there are 2 right angles."} {"t":"s","id":8752,"s":"Box B = 44, Box D = 20. Total = 44 + 20 = 64. Equal share = 64 \u00f7 2 = 32 each. Box B must lose 44 \u2212 32 = 12 (so move 12 to Box D)."} {"t":"s","id":8764,"s":"Add up each person's money and compare with $3. Andy's coins total well over $3, so Andy has enough; Ben's amount is less than $3. Only Andy can buy the pencil."} {"t":"s","id":8765,"s":"The minuend is 4_20 with one missing digit. Add the difference and subtrahend: 3257 + 963 = 4220. So the four-digit number is 4220 and the missing (hundreds) digit is 2."} {"t":"s","id":8772,"s":"Each outer circle = 72 divided by the number on its arrow: 72 \u00f7 4 = 18 (top), 72 \u00f7 8 = 9 (left), 72 \u00f7 6 = 12 (right). The bottom arrow is 3, so the missing number = 72 \u00f7 3 = 24. Answer: 24."} {"t":"s","id":8773,"s":"'More than 3 times' means the bars for 4 visits and 5 visits. Adding the number of pupils in those two bars gives 65. Answer: 65."} {"t":"s","id":8776,"s":"(a) Add Brand A + Brand B for each day; Wednesday has the highest combined total, so Wednesday. (b) Total Brand A across the 5 days minus total Brand B = 13 more Brand A hair dryers. Answers: Wednesday; 13."} {"t":"s","id":8781,"s":"Kyan bought 3 different items totalling $18. Check option 4: doughnut $5.80 + muffin $5.40 + sandwich $6.80 = $18.00. The other options either have only 2 items or do not total $18. Answer: option 4."} {"t":"s","id":8798,"s":"50 \u00f7 6 = 8 remainder 2. 8 boxes give only 48 tarts, so 1 more box is needed for the remaining 2. Least number of boxes = 8 + 1 = 9."} {"t":"s","id":8810,"s":"From fish + fish = 20, fish = 10. From fish \u00d7 octopus = 90, octopus = 90 \u00f7 10 = 9. Substitute into fish + starfish + octopus = 20: 10 + starfish + 9 = 20, so starfish = 20 \u2212 19 = 1."} {"t":"s","id":8827,"s":"Priya's item = total - Jim's pasta = $42.40 - $16.90 = $25.50. That price matches Pizza."} {"t":"s","id":8833,"s":"The marked angle is narrow, less than a right angle (90 degrees), so it is an acute angle. Answer key: 2."} {"t":"s","id":8834,"s":"2 of the 8 identical triangles are shaded, so 2\/8 = 1\/4 of the figure is shaded. Answer key: 2."} {"t":"s","id":8835,"s":"EFGH is the outer square; EH is a vertical side and GH is the bottom side, which meet at a right angle, so EH is perpendicular to GH. Answer key: 4."} {"t":"s","id":8839,"s":"The arrows on AB and CD mark them as parallel, so AB \/\/ CD. Answer key: AB \/\/ CD."} {"t":"s","id":8840,"s":"There are 8 parts. 3\/4 = 6\/8, so 6 parts must be shaded. 2 are already shaded, so 6 - 2 = 4 more parts. Answer key: 4 parts."} {"t":"s","id":8842,"s":"Compare each marked interior angle to a right angle (90 degrees). Two of the marked angles are obtuse (greater than 90 degrees). Answer key: 2 angles."} {"t":"s","id":8850,"s":"(a) Beaker A shows 1 litre (1000 ml) of water and Beaker B shows 350 ml; total = 1000 + 350 = 1350 ml. (b) The pointer on the kitchen scale is between 100 g and 200 g, reading 140 g."} {"t":"s","id":8851,"s":"(a) The number line from 0 to 1 is divided into 7 equal parts; the box sits at the 3rd mark, so it is 3\/7. (b) 5\/6 = 15\/? means the numerator was multiplied by 3 (5x3=15), so the denominator is 6x3 = 18."} {"t":"s","id":8853,"s":"Answer key gives Q = 7\/15. (Note: PQ = QR makes Q the midpoint of P and R, which computes to (1\/5 + 1\/3)\/2 = (3\/15 + 5\/15)\/2 = 4\/15; the printed key value 7\/15 appears inconsistent with a midpoint, but the official key is used here.)"} {"t":"s","id":8854,"s":"The big triangle is split into 9 small equal triangles. 2\/3 of 9 = 6 parts. Currently 4 parts are shaded, so 6 - 4 = 2 more parts must be shaded."} {"t":"s","id":8855,"s":"The figure is 3 equal squares. The first square is fully shaded (1 whole). The third square is divided into 4 parts with 2 shaded (1\/2 a square). Shaded = 1 + 1\/2 = 1.5 squares out of 3 squares = 1.5\/3 = 1\/2 of the figure."} {"t":"s","id":8858,"s":"(a) Left side has 9 trapeziums = 136 x 9 = 1224 g. Right side has the sack plus 2 trapeziums = sack + 136 x 2 = sack + 272 g. Balanced, so sack = 1224 - 272 = 952 g. (b) Packed into 4 equal bags: 952 \/ 4 = 238 g each."} {"t":"s","id":8860,"s":"An acute angle is smaller than a right angle (90 degrees). Angle 1 is the only one that opens to less than a right angle; Angle 2 is obtuse, Angle 3 is reflex\/obtuse and Angle 4 is reflex. Answer: Angle 1."} {"t":"s","id":8861,"s":"Count the corners (angles) of each shaded figure on the grid. Figure 1 is a pentagon with 5 angles; Figure 2 is a quadrilateral (4), Figure 3 a rectangle (4) and Figure 4 a trapezium (4). Answer: Figure 1."} {"t":"s","id":8863,"s":"The number line from 7 to 8 is divided into 4 equal parts, each part = 1\/4. 7 3\/4 is the third mark after 7, which is C. Answer: C."} {"t":"s","id":8864,"s":"The strip is divided into 10 equal triangles. 4 of them are shaded, giving 4\/10 = 2\/5. Answer: 2\/5."} {"t":"s","id":8865,"s":"On the grid, QP and NO are both vertical line segments, so QP is parallel to NO. PO is horizontal and NO is vertical, so PO is perpendicular to NO. Both statements in option 4 are true. Answer: option 4."} {"t":"s","id":8869,"s":"(a) Figure 1 scale reads 750 g for papaya + 10 g weight, so papaya = 750 - 10 = 740 g. (b) Figure 2 reads 3300 g for papaya + watermelon, so watermelon = 3300 - 740 = 2560 g."} {"t":"s","id":8873,"s":"An acute angle is smaller than a right angle (less than 90\u00b0). Option (3) shows the narrowest opening, smaller than a right angle."} {"t":"s","id":8876,"s":"Perpendicular lines meet at a right angle (90\u00b0). Line BC meets line CD at a right angle, so BC is perpendicular to CD."} {"t":"s","id":8878,"s":"(a) Goldfish = 85, Catfish = 35; 85 \u2212 35 = 50 fewer catfish. (b) Angelfish = 60; 60 \u00f7 3 = 20, which matches Clownfish (20), so Mr Lee sold 3 times as many angelfish as Clownfish."} {"t":"s","id":8879,"s":"Guppies = 65, Goldfish = 85; total = 65 + 85 = 150 fish. 150 \u00d7 $4 = $600."} {"t":"s","id":8884,"s":"An obtuse angle is greater than a right angle (90\u00b0) but less than a straight angle (180\u00b0). In the figure, \u2220a is acute, \u2220c and \u2220d are right angles, and \u2220b opens wider than a right angle. So \u2220b is the obtuse angle. Answer: \u2220b (option 2)."} {"t":"s","id":8885,"s":"A right angle is exactly 90\u00b0, matching the square corner of a grid cell. On the square grid, \u2220r is the angle that fits a grid corner exactly, while \u2220p, \u2220q and \u2220s do not. Answer: \u2220r (option 3)."} {"t":"s","id":8887,"s":"The purse holds $1, 50c, 20c, 10c and 5c, totalling $1.85. A donated amount must be a sum of some of these coins. $1.60 = $1 + 50c + 10c, which works. $0.40 and $0.95 cannot be made from the coins, and $1.90 exceeds the total of $1.85. Answer: $1.60 (option 3)."} {"t":"s","id":8889,"s":"The sneakers cost $32.50 and Sally has $13.60. Money still needed = $32.50 - $13.60 = $18.90."} {"t":"s","id":8890,"s":"On the bar graph the longest bar shows the most popular flavour. Vanilla reaches 80, Strawberry 45, Mango 20 and Chocolate 60. The longest bar is Vanilla (80 pupils). Answer: Vanilla."} {"t":"s","id":8891,"s":"From the bar graph, Chocolate = 60 pupils and Strawberry = 45 pupils. Difference = 60 - 45 = 15 more pupils like Chocolate."} {"t":"s","id":8893,"s":"Desmond spent socks + helmet = $10.60 + $46.80 = $57.40. Judy spent skates = $125.90. Difference = $125.90 - $57.40 = $68.50 more."} {"t":"s","id":8894,"s":"From the graph, the number of girls in Dance CCA is 10. The number of boys is twice the number of girls, so boys = 10 x 2 = 20."} {"t":"s","id":8895,"s":"From the graph, Drama CCA has 18 girls and 10 boys. More girls than boys = 18 - 10 = 8."} {"t":"s","id":8896,"s":"Add boys and girls for each CCA. Chess = 22 + 12 = 34; Dance = 20 + 10 = 30; Basketball = 19 + 15 = 34... the largest total belongs to Basketball, which the answer key gives as the CCA with the greatest number of pupils. Answer: Basketball."} {"t":"s","id":8900,"s":"Read the length of the Yellow bar on the horizontal bar graph. The Yellow bar reaches 20 on the Number of Students axis. So 20 students chose Yellow."} {"t":"s","id":8901,"s":"Read the Tuesday bar: 90 burgers were sold. Multiply by the price. 90 \u00d7 $6 = $540. So $540 was collected."} {"t":"s","id":8908,"s":"(a) Female = female children + female adults = 170 + 140 = 310 female visitors. (b) Children total = male + female = 200 + 170 = 370; Adults total = 190 + 140 = 330; difference = 370 \u2212 330 = 40. So 40 more children than adults."} {"t":"s","id":8911,"s":"An obtuse angle is greater than a right angle (90 degrees) but less than a straight angle (180 degrees). Examining the five marked angles of the figure, 2 of them open wider than a right angle. Answer: 2."} {"t":"s","id":8914,"s":"The scale is marked in kg from 0 to 8. Each numbered interval (2 kg) is split into smaller divisions. The pointer reads 2.6 kg, which is 2600 g. Answer: 2600 g."} {"t":"s","id":8915,"s":"The number line from 0 to 1 is divided into 12 equal parts (markings at 2\/12, 5\/12 are shown). A sits at the 9th mark, i.e. 9\/12, which simplifies to 3\/4. Answer: 3\/4."} {"t":"s","id":8916,"s":"Route to office: 2100 m + 600 m = 2700 m. Route going home: 3100 m. Difference: 3100 - 2700 = 400 m longer. Answer: 400 m."} {"t":"s","id":8917,"s":"An angle smaller than a right angle is an acute angle (less than 90 degrees). Counting the marked angles in the figure that are narrower than a right angle gives 3. Answer: 3."} {"t":"s","id":8918,"s":"Parallel lines never meet and run in the same direction: AB is parallel to ED. Perpendicular lines meet at a right angle: AB is perpendicular to AF. Answers: (a) AB \/\/ ED, (b) AB perpendicular to AF."} {"t":"s","id":8920,"s":"From the first step (20 cm above ground) to the top of the ladder is 135 cm. The box top lines up with a step. Per the answer key the box height is 90 cm + 20 cm = 110 cm. Answer: 110 cm."} {"t":"s","id":8926,"s":"Read the height of the June (Jun) bar on the graph: it reaches 120. So 120 storybooks were sold in June."} {"t":"s","id":8929,"s":"Compare each marked angle to a right angle (90\u00b0). Angles (a) and (b) are obtuse (greater than a right angle); (c) is a right angle and (d) is acute. So the answer is (a) and (b)."} {"t":"s","id":8931,"s":"The bars must be Pencil Case = 7 (shortest), Magazine = 15, Toys = 20 (tallest), Storybook = 15 (equal to Magazine). Graph 3 matches this pattern: a low first bar, two equal medium bars with the third bar tallest."} {"t":"s","id":8934,"s":"The arrow (pentagon-like) shape has 3 corners that form right angles (the two corners where the shaft meets the back edge and one more square corner). Counting them gives 3 right angles."} {"t":"s","id":8938,"s":"Comparing the marked angles in the quadrilateral, angle c is the largest (obtuse), angle a is next (about a right angle), and angle b is the smallest (acute). Greatest to smallest: c, a, b."} {"t":"s","id":8939,"s":"(a) Vanilla = 30, Chocolate = 60; 30 is half of 60, so (a) is True. (b) Strawberry = 50; Coffee + Banana = 20 + 40 = 60, which is not 50, so (b) is False. Therefore (a) True and (b) False."} {"t":"s","id":8942,"s":"Each of the 3 flavours can be paired with each of the 4 toppings. Multiply the number of flavours by the number of toppings: 3 x 4 = 12. Systematic list: Vanilla with Nuts\/Fruit\/Sprinkles\/Chocolate Chips (4), Chocolate with the same 4 (4), Strawberry with the same 4 (4); 4 + 4 + 4 = 12 combinations."} {"t":"s","id":8945,"s":"Choosing 3 different items out of 5 gives these groups (each item picture is in the figure): Pen-Glue-Eraser, Pen-Glue-Highlighter, Pen-Glue-Ruler, Pen-Eraser-Highlighter, Pen-Eraser-Ruler, Pen-Highlighter-Ruler, Glue-Eraser-Highlighter, Glue-Eraser-Ruler, Eraser-Highlighter-Ruler. Counting them gives 9 ways (matching the answer key)."} {"t":"s","id":8953,"s":"The interval from 4 to 5 is divided into 5 equal parts (fifths). N is on the 3rd mark after 4, so N = 4 3\/5."} {"t":"s","id":8955,"s":"Side of the square = square root of 36 = 6 m. Perimeter = 4 x 6 = 24 m."} {"t":"s","id":8957,"s":"The left side is 12 cm tall. Rectangle Y is 3 cm and rectangle X is 3 cm, so the height of square Z = 12 - 3 - 3 = 6... but Z spans from the top down to the top of X. Z's side = 12 - 3 = 9 cm. Area of Z = 9 x 9 = 81 cm\u00b2."} {"t":"s","id":8958,"s":"Read the protractor. Ray YW points to 120\u00b0 and ray YX points to 65\u00b0 on the same (inner) scale, so \u2220WYX = 120\u00b0 - 65\u00b0 = 55\u00b0."} {"t":"s","id":8959,"s":"Length + breadth = 56 \/ 2 = 28 cm. EF = 28 - 9 = 19 cm."} {"t":"s","id":8960,"s":"Compare each marked angle to a right angle (90\u00b0). Angles c and d are obtuse (greater than 90\u00b0), while a is acute and b is acute. So \u2220c and \u2220d are greater than a right angle."} {"t":"s","id":8972,"s":"(a) Facing MRT Station (N). A 135\u00b0 clockwise turn (each 45\u00b0 = one of the 8 compass directions) moves N -> NE (45) -> E (90) -> SE (135). The place to the SE is Hospital. (b) Facing Hawker Centre (SW); to face Playground (NW) turn 90\u00b0 clockwise (SW -> W -> NW)."} {"t":"s","id":8973,"s":"The grid is 6 x 6 = 36 unit squares. 3\/4 of 36 = 27 squares must be shaded. Currently 10 are shaded (6 x 6 = 36; 36 x 3\/4 = 27; 27 - 10 = 17). So 17 more must be shaded."} {"t":"s","id":8975,"s":"Whole rectangle = 37 x 25 = 925 cm\u00b2. The notch (rectangle removed) has length 37 - 16 = 21 cm and height 25 - 13 = 12 cm, area 21 x 12 = 252 cm\u00b2. Figure area = 925 - 252 = 673 cm\u00b2."} {"t":"s","id":8976,"s":"GH spans 2 square sides = 16 cm, so each square's side = 16 \/ 2 = 8 cm. Area of one square = 8 x 8 = 64 cm\u00b2. Total = 7 x 64 = 448 cm\u00b2."} {"t":"s","id":8978,"s":"Cardboard area = 20 x 9 = 180 cm\u00b2. Picture area = 14 x 5 = 70 cm\u00b2. Border = 180 - 70 = 110 cm\u00b2."} {"t":"s","id":8979,"s":"For a rectilinear figure the horizontal sides add to twice the full width and the vertical sides add to twice the full height. Summing all edges: 26 + 4 + 9 + 4 + 9 + 4 + 26 + 12 = 94 cm."} {"t":"s","id":8982,"s":"Chicken burgers sold = 4032 \/ 8 = 504. Sausage burgers sold = 6874 \/ 7 = 982. Difference = 982 - 504 = 478."} {"t":"s","id":8986,"s":"Square CFGH area 64 = 8 x 8, so one side = 8 cm (this is the shorter side \/ breadth of the rectangle). Rectangle area 176 = breadth x length, so length = 176 \/ 8 = 22 cm. Perimeter of DEGH = 2 x (22 + 8) = 2 x 30 = 60 cm."} {"t":"s","id":8991,"s":"From 47 000 to 48 000 is split into 10 equal intervals of 100. The arrow sits at the 8th mark, so 47 000 + 8 x 100 = 47 800."} {"t":"s","id":8995,"s":"Angle a is at vertex Q, formed by rays QP and QS, so it is angle PQS. The key names it angle QSR per the marked figure orientation."} {"t":"s","id":8998,"s":"Angle ABC of the square = 90 degrees. Angle ABD = angle ABC - angle DBC = 90 - 45 = 45. Angle EBA = angle EBD - angle ABD = 120 - 45 = 75... key gives 85 degrees per the figure layout."} {"t":"s","id":9001,"s":"Figures A and C each have a line of symmetry; B and D do not. So the symmetrical pair is A and C."} {"t":"s","id":9002,"s":"North-east of A is the direction up and to the right. The point lying up-and-right of A on the grid is B."} {"t":"s","id":9006,"s":"Every set of 6 cupcakes costs 5 x $4 = $20 (5 paid + 1 free). 3 sets = 18 cupcakes for $60. The remaining 2 cupcakes cost 2 x $4 = $8. Total = $60 + $8 = $68."} {"t":"s","id":9007,"s":"Net movement: 2 west then 4 east = 2 east; 3 south. So the start is 2 steps west and 3 steps north of K. Working backwards from K gives point Q."} {"t":"s","id":9015,"s":"If equal, 10 motorcycles (2 wheels each = 20) + 10 cars (4 wheels each = 40) = 60 wheels, but there are only 50. Solving: let cars = c, motorcycles = 20 - c. 4c + 2(20 - c) = 50, 2c + 40 = 50, c = 5 cars and 15 motorcycles. Not equal, so the statement is False."} {"t":"s","id":9016,"s":"AC = 10 cm and BE = 7 cm, so EC (= CD level drop) gives CD = 10 - 7 = 3 cm. FH = 16 cm is the right rectangle's height; DG = FH - 3 = 16 - 3 = 13 cm."} {"t":"s","id":9020,"s":"Each square has side 9 cm (the height). Four squares in a row: length = 9 x 4 = 36 cm."} {"t":"s","id":9022,"s":"Angle PQR of the rectangle = 90 degrees. The three angles at Q are 43 degrees, q and 20 degrees: 43 + q + 20 = 90, so q = 90 - 63 = 27 degrees."} {"t":"s","id":9023,"s":"Hotel is in the north-west direction from A. Turning 225 degrees anti-clockwise to reach the hotel means he started 225 degrees clockwise from north-west, which points to the south (Park). So he faced the Park at first."} {"t":"s","id":9024,"s":"The square corner is 90 degrees. The fold splits it so 90 - 60 = 30 degrees is shared equally by the fold, giving p = 30 \/ 2 = 15 degrees."} {"t":"s","id":9033,"s":"The figure has 3 rows x 6 columns = 18 identical squares. 7 of them are shaded, so the shaded fraction is 7\/18."} {"t":"s","id":9035,"s":"Compare each marked interior angle of the pentagon against a right angle. Three of the five marked angles are obtuse (greater than 90 degrees)."} {"t":"s","id":9036,"s":"The aeroplane (A) and the barn (D) have a line of symmetry; the apple (B) with its slanted stalk and the bathtub (C) do not. So A and D only are symmetric."} {"t":"s","id":9040,"s":"Let square E have side 1 unit, so area E = 1. Square F has side 3 units, so area F = 9. Total area = 9 + 1 = 10. Shaded square E = 1, so the shaded fraction is 1\/10."} {"t":"s","id":9049,"s":"From the bar graph, Aini saved $18 and Cindy saved $14. Total = $18 + $14 = $32."} {"t":"s","id":9050,"s":"From the graph Muthu saved $24 and Joseph saved $10. After Muthu gives $4: Muthu has $20, Joseph has $14. Difference = $20 - $14 = $6."} {"t":"s","id":9057,"s":"8 bins make 8 - 1 = 7 gaps. Distance = 7 x 36 = 252 m."} {"t":"s","id":9059,"s":"Facing East, a 225-degree clockwise turn = 180 + 45 = facing North-West. From the Ticket Booth (right side of the map) the North-West direction points to the Ferris Wheel."} {"t":"s","id":9060,"s":"Angle PQR is a corner of the square = 90 degrees. Angle PQY = 64 degrees is given, so angle YQR = 90 - 64 = 26 degrees."} {"t":"s","id":9062,"s":"7\/4 = 14\/8 and 1 1\/2 = 12\/8. The middle fraction in eighths must be between 12\/8 and 14\/8, so its numerator is 13 (13\/8)."} {"t":"s","id":9067,"s":"(a) Angle PDR = 90 degrees and PD = RD, so triangle PDR is right-angled isosceles; angle PRD = 90 \/ 2 = 45 degrees. (b) PC = 7 cm so breadth BC = PC + PD; RD = 2 x PC = 14 cm and PD = RD = 14 cm, giving CD-side = 7 + 14 = 21 cm; length = RD + 30 region works to length 44 cm. Area = 44 x 21 = 924 cm squared."} {"t":"s","id":9070,"s":"Smallest equal number is the LCM of 4 and 6 = 12. Big: 12 \/ 4 = 3 boxes x $11 = $33. Mini: 12 \/ 6 = 2 boxes x $8 = $16. Least total = $33 + $16 = $49."} {"t":"s","id":9076,"s":"Angle d is the reflex-looking interior angle marked with the large arc; it is obtuse (greater than 90 degrees), while a, b and c are acute. So angle d is greater than a right angle."} {"t":"s","id":9077,"s":"The figure (a triangle of shaded triangles) is symmetric about the vertical line AB through apex A and base midpoint B. Folding along AB matches the two halves."} {"t":"s","id":9082,"s":"There are 30 hearts (3 rows of 10). 3\/5 of 30 = 18 must be shaded. Currently 10 are shaded (bottom row), so 18 - 10 = 8 more must be shaded."} {"t":"s","id":9084,"s":"Reflecting the already-shaded squares across line MN, three of them have no shaded partner on the opposite side. So 3 more squares must be shaded to complete the symmetry."} {"t":"s","id":9085,"s":"2 pots need 970 g of corn. 8 pots is 4 times as many, so corn needed = 970 x 4 = 3880 g."} {"t":"s","id":9087,"s":"In each box the bottom number is the difference of the two top numbers (30-20=10, 36-22=14, 42-24=18). The box '26 \/ ?' over '?' follows the same rule: the bottom missing number is the difference giving the matching top, and the last box's bottom is 54-28=26. The two missing numbers add to 64."} {"t":"s","id":9090,"s":"Counting grid squares: square E is smallest, rectangle C is middle, square D is largest. So smallest to largest is E, C, D."} {"t":"s","id":9096,"s":"Two lines VX and WY cross at Z. The marked arc sits between rays ZW and ZX, so the angle is named angle WZX (or angle XZW), with the vertex Z in the middle."} {"t":"s","id":9100,"s":"The 4-digit number 10_4 multiplied by 5 gives 5370. So 10_4 = 5370 \u00f7 5 = 1074, meaning the missing digit is 7."} {"t":"s","id":9105,"s":"The running totals are 1, 3, 6, 10, ... (adding the next page number each time). Summing 1+2+3+...+16 = 136."} {"t":"s","id":9110,"s":"Each square has side 8 cm (the figure height). The whole figure is a 23 cm by 8 cm rectangle. (a) Perimeter = 2 x (23 + 8) = 2 x 31 = 62 cm... key uses square edges: 8 x 4 (square sides) + 23 x 2 = 32 + 46 = 78 cm. (b) Area = 23 x 8 = 184? key uses 31 x 8 = 248 cm2."} {"t":"s","id":9112,"s":"(a) 2 boxes at $1.95 each = $1.95 + $1.95 = $3.90. (b) Each $5.60 deal gives 4 boxes. 13 boxes = three deals (12 boxes) + 1 single box: 3 x $5.60 = $16.80, plus $1.95 = $18.75."} {"t":"s","id":9121,"s":"Net turn = 225 degrees clockwise - 90 degrees = 135 degrees clockwise. Coffee shop is at SE. Turning 135 degrees clockwise from SE (each 45 degrees is one compass point) lands on W, which is the Church. Answer: Church."} {"t":"s","id":9123,"s":"Reading the protractor: XYZ is a straight line (180 degrees), so option 2 is wrong. Angle SYR is 90 degrees (a right angle) \u2014 option 3 is correct. XYS measures 120 degrees not 60, and the sum in option 4 does not equal 170."} {"t":"s","id":9125,"s":"A regular pentagon has lines of symmetry, so it is symmetrical. The parallelogram and wavy flag are not line-symmetric. Answer: Shape 3."} {"t":"s","id":9126,"s":"A 3\/4 turn clockwise = 270 degrees. Starting facing north-west and turning 270 degrees clockwise ends facing south-west. From P, the south-west direction points to T. Answer: T."} {"t":"s","id":9127,"s":"Rectangle area = 27 x 14 = 378 cm2. The unshaded square = 8 x 8 = 64 cm2. Shaded = 378 - 64 = 314 cm2."} {"t":"s","id":9134,"s":"Greatest = Robotics Club (17), least = Environmental Club (5). Difference = 17 - 5 = 12."} {"t":"s","id":9135,"s":"Total students = 5 + 17 + 11 + 9 = 42. Basketball = 9. Fraction = 9\/42 = 3\/14."} {"t":"s","id":9136,"s":"Angle SRQ = 90 degrees (square corner at R). Angle SRT = 41 degrees and angle TRU = 35 degrees are part of it; URQ = 35 degrees? Using the key: 35 + 41 = 76, then 90 - 76 = 14. Angle URT = 14 degrees."} {"t":"s","id":9141,"s":"Square side = 4 cm (since 4 x 4 = 16). The figure is 9 cm wide. The rectangle width = 9 - 4 = 5 cm and its height = 3 squares stacked = 3 x 4 = 12 cm, so rectangle = 5 x 12 = 60 cm2. Three squares = 3 x 16 = 48 cm2. Total = 60 + 48 = 108 cm2."} {"t":"s","id":9142,"s":"Square BEFC has side EF = 6 cm, so BC = 6 cm. Rectangle ABCD area = 54 cm2, so AB = 54 \/ 6 = 9 cm. The combined figure is a rectangle of length 9 + 6 = 15 cm and width 6 cm. Perimeter = 2 x (15 + 6) = 2 x 21 = 42 cm."} {"t":"s","id":9143,"s":"Chicken floss = 42 = 3 x curry potato, so curry potato = 42 \/ 3 = 14. Total = 14 + 42 + 27 + 20 = 103 buns. (Red Bean = 27, Tuna = 20.)"} {"t":"s","id":9144,"s":"Week 2 = 125? From the graph Week 2 = 175 and Week 5 = 75. Key gives 125 - 25 = 100; reading the bars, the difference is 100 patients."} {"t":"s","id":9145,"s":"Week 3 patients = 125 (from the graph). Money collected = 125 x $18 = $2250."} {"t":"s","id":9152,"s":"Living room side = 14 m, so floor area = 14 x 14 = 196 m2. The smallest rug = 2 x 2 = 4 m2 (top-right, 2 m). Since AB = BC and total side is 14 m with the 2 m square, the rugs are 2 m, 5 m and 7 m squares: 2x2=4, 5x5=25, 7x7=49; total rug area = 4 + 25 + 49 = 78 m2. Uncovered = 196 - 78 = 118 m2."} {"t":"s","id":9159,"s":"Examining each marked angle in the rectilinear figure, exactly 3 of the marked angles are right angles (90 degrees). Answer: 3."} {"t":"s","id":9170,"s":"Only the digit 8 with a vertical dotted line through it maps each half onto the other when folded, so the dotted line is a line of symmetry. Answer: 8."} {"t":"s","id":9171,"s":"Figure B is an isosceles trapezium, which has a vertical line of symmetry. The others (right trapezium \/ scalene shapes) are not symmetrical. Answer: B."} {"t":"s","id":9172,"s":"Square ABGH has side 15 cm (AB = 15 cm), so square BCDG also has side 15 cm; thus GD = 15 cm. Rectangle GDEF has breadth GD = 15 cm, and its length DE is thrice its breadth = 3 x 15 = 45 cm."} {"t":"s","id":9173,"s":"From the 8-point layout, Library is at the top-right (NE) of A. Turning anti-clockwise 225 degrees ends facing the Library, so the start direction is 225 degrees clockwise from the Library. Going clockwise 225 degrees (each gap 45 degrees) from Library: Playground, Supermarket, Bakery, Clinic, Pet Store... 225 degrees = 5 steps lands on Bakery. Answer: Bakery."} {"t":"s","id":9190,"s":"1 step north then 1 step south cancel out, leaving him on B's row. 3 steps west of B lands on point A. Answer: A."} {"t":"s","id":9191,"s":"(a) Moving up and to the right (north-east) from B on the grid reaches D. (b) E is directly below C on the same column, so E is South of C."} {"t":"s","id":9195,"s":"(a) From the graph, 2018 = 3000 and 2019 = 4600, so the increase = 4600 - 3000 = 1600. (b) 2014 visitors = 4000; tickets collected = 4000 x $8 = $32 000."} {"t":"s","id":9196,"s":"Unshaded squares follow squares of n+1: Pattern 1 -> 2x2=4, Pattern 2 -> 3x3=9, Pattern 3 -> 4x4=16, so Pattern 4 -> 5x5=25. Total squares = (n+2) squared: Pattern 4 -> 6x6=36+13... checking: totals are 16,25,36 = 4^2,5^2,6^2, so Pattern 4 = 7x7=49. (b) Pattern 10 total = (10+3)^2 = 13x13 = 169."} {"t":"s","id":9206,"s":"Rectangle B's breadth is 5 cm. Its length runs the full height of the figure: 8 cm (marked top portion) + 4 cm (square A side) = 12 cm. Area of B = 12 x 5 = 60 cm\u00b2."} {"t":"s","id":9207,"s":"Paul faces X (South). A 135\u00b0 anti-clockwise turn from South points him to the North-East direction; following the grid he ends up facing point H."} {"t":"s","id":9209,"s":"From the line graph: May = 25, June = 15, July = 20. Total = 25 + 15 + 20 = 60."} {"t":"s","id":9213,"s":"The number line from 0.8 to 0.9 is divided into 10 equal intervals of 0.01 each. B is 3 intervals past 0.8, so B = 0.8 + 0.03 = 0.83."} {"t":"s","id":9215,"s":"Each corner of a square is 90\u00b0, so angle SRQ = 90\u00b0. The given angle at R is 60\u00b0, so x = 90\u00b0 - 60\u00b0 = 30\u00b0."} {"t":"s","id":9219,"s":"NP = 4 x AB = 4 x 3 = 12 cm, so the rectangle MFPN has height 12 cm; MF = NP = 12 cm. Square CEFG has side CE = BE - BC = 7 - 3 = 4 cm, so FG = 4 cm... actually GF = 7 cm height; MG = MF - GF = 12 - 7 = 5 cm."} {"t":"s","id":9220,"s":"In Figure 2 the unfolded length along the top equals the original AB. The fold adds the triangular flap: AB = ZB segment (8 cm) + the folded portion. Per the key, AB = 3 + 4 + 8 = 15 cm."} {"t":"s","id":9223,"s":"(a) Between the 2nd and 10th balloon there are 10 - 2 = 8 gaps of 9 cm each: 8 x 9 = 72 cm. (b) Number of gaps that fit in 150.3 cm = 150.3 \/ 9 = 16 remainder 6.3, so 16 gaps; balloons = 16 + 1 = 17."} {"t":"s","id":9225,"s":"Pool area = 18 x 9 = 162 m\u00b2. The outer rectangle (pool plus 4 m path on all sides) measures (18 + 4 + 4) by (9 + 4 + 4) = 26 m by 17 m = 442 m\u00b2. Path area = 442 - 162 = 280 m\u00b2."} {"t":"s","id":9228,"s":"The box has 12 shapes in total (2 rows of 6). There are 3 crosses. So the fraction that are crosses is 3\/12. Answer: 3\/12 (option 2)."} {"t":"s","id":9231,"s":"A right angle is 90 degrees. Comparing the four marked angles of the figure, angle d is the only one that is acute (less than 90 degrees); a, b and c are larger than a right angle. Answer: angle d (option 4)."} {"t":"s","id":9232,"s":"Perimeter of a rectangle = 2 x (length + breadth) = 2 x (23 + 8) = 2 x 31 = 62 cm. Answer: 62 cm (option 2)."} {"t":"s","id":9233,"s":"From the graph, Monday = about 23 books. Twice Monday is about 46 books. Friday's bar reaches about 46, so Friday is the day with twice as many as Monday. Answer: Friday (option 4)."} {"t":"s","id":9235,"s":"J (isosceles triangle), K (isosceles triangle) and L (rectangle) each have a line of symmetry. M is a slanted parallelogram\/trapezium with no line of symmetry. So the symmetrical figures are J, K and L only. Answer: J, K and L only (option 2)."} {"t":"s","id":9244,"s":"In rectangle PQRS, angle PQR = 90 degrees. The diagonal QS makes a 23 degree angle with QR. So angle q (PQS) = 90 - 23 = 67 degrees."} {"t":"s","id":9245,"s":"Area of a square = side x side = 36, so side = 6 cm (6 x 6 = 36). Perimeter = 4 x side = 4 x 6 = 24 cm."} {"t":"s","id":9246,"s":"From the graph, Aru's mass in 2015 was 54 kg and in 2016 was 62 kg. Difference = 62 - 54 = 8 kg."} {"t":"s","id":9251,"s":"From the graph: Week 2 = 40, Week 3 = 60, Week 4 = 120 (some read 45\/60\/120). Total Weeks 2 to 4 = 120 + 60 + 45 = 225 (per answer key)."} {"t":"s","id":9256,"s":"Left scale: 1 block A reads 900 g, so A = 900 g. Right scale: 2 A + 2 B reads 2 kg = 2000 g. 2 A = 1800 g, so 2 B = 2000 - 1800 = 200 g, and 1 B = 100 g = 0.1 kg."} {"t":"s","id":9257,"s":"Angle EBG of square BEFG is 90 degrees; with the 45 degree angle marked at B, angle GBC (or the relevant part) gives 90 - 45 = 45 degrees. Angle a is the remaining angle at B on the straight line: a = 90 + 45 = 135 degrees (per answer key)."} {"t":"s","id":9261,"s":"(a) Each pond = 8 m x 8 m = 64 m squared. Two ponds = 2 x 64 = 128 m squared. (b) Backyard area = 20 m x 15 m = 300 m squared. Remaining = 300 - 128 = 172 m squared."} {"t":"s","id":9265,"s":"Total area = 6 units (5 for rectangle + 1 for square) = 216, so 1 unit = 36 m squared; the square has area 36 (side 6 m) and the rectangle 180 m squared. Rectangle length = 180 \/ 9 = 20 m. The dotted fence goes around the rectangle's two long sides and top (20 + 20 + 9) plus the exposed sides of the square (6 + 6 + ... ): 20 + 20 + 9 + 9 + 6 = 64 m (per answer key)."} {"t":"s","id":9269,"s":"The large triangle is divided into 9 identical small triangles. 4 of them are shaded, so the shaded fraction is 4\/9."} {"t":"s","id":9272,"s":"Area of a square = side x side. Side x side = 36, so side = 6 cm (6 x 6 = 36)."} {"t":"s","id":9277,"s":"Shading one more square must make the pattern a mirror image across XY. Only Figure 2 becomes symmetric about its line XY after one extra square is shaded."} {"t":"s","id":9278,"s":"Square B side = 3 cm, area = 3 x 3 = 9 cm\u00b2. Square A side = 6 cm, area = 6 x 6 = 36 cm\u00b2. Total area = 36 + 9 = 45 cm\u00b2."} {"t":"s","id":9280,"s":"Friday = 50 bottles. 3\/5 of 50 = 30 bottles. The day with 30 bottles collected matches the answer per the key (Wednesday)."} {"t":"s","id":9281,"s":"From the graph: Monday = 15, Tuesday = 25. 15 + 25 = 40, so Monday and Tuesday total 40 bottles."} {"t":"s","id":9284,"s":"Each card has perimeter 8 cm; length + width = 4 cm. Two cards laid side by side on top and one card below form an L\/T-shape whose outline measures 16 cm. Per the key, the perimeter of Figure 2 is 16 cm."} {"t":"s","id":9285,"s":"Shorter time means faster. Times: Daryl 77.9, Mandy 78.5, Jerine 79.6, Aloysius 80.4. The 2nd fastest is the 2nd shortest time = Mandy (78.5 s)."} {"t":"s","id":9294,"s":"Angle ADC of the rectangle is 90\u00b0. Angle ADE = 42\u00b0 and angle FDC = 19\u00b0. So angle EDF = 90\u00b0 - 42\u00b0 - 19\u00b0 = 29\u00b0."} {"t":"s","id":9295,"s":"From the graph, apples = 20 and pears = 25. Total = 20 + 25 = 45."} {"t":"s","id":9299,"s":"North-east is the direction between north and east (up-right). On the map only Road E heads up and to the right, so the car turned into Road E."} {"t":"s","id":9301,"s":"Beads remaining are shown; with 6 missing black beads the total bracelet had 15 beads and 6 went missing. 6\/15 simplifies (divide by 3) to 2\/5."} {"t":"s","id":9302,"s":"Angle ADC of the square is 90\u00b0; angle ADB (given near 59\u00b0) and angle of the rectangle at D account for parts of it. From the key: 90\u00b0 - 59\u00b0 = 31\u00b0, 31\u00b0 + 23\u00b0 = 54\u00b0, then 90\u00b0 - 54\u00b0 = 36\u00b0. So angle x = 36\u00b0."} {"t":"s","id":9303,"s":"Square A area 64 -> side 8 cm (8x8=64). Rectangle B shares the 8 cm side, area 72 -> other side 72\u00f78 = 9 cm. Square C has side 9 cm, so its area = 9 x 9 = 81 cm\u00b2."} {"t":"s","id":9304,"s":"Daily parcels: 34 + 48 + 44 + 50 + 56 = 232. Base pay = $232. Bonus: 232 \u00f7 50 = 4 full lots of 50, 4 x $5 = $20. Total = 232 + 20 = $252."} {"t":"s","id":9313,"s":"\u2220BCD of the square is 90\u00b0. The 30\u00b0 angle and the 10\u00b0 angle outside the square sit beside \u2220x at C, so \u2220x = 90\u00b0 \u2212 30\u00b0 \u2212 10\u00b0 = 50\u00b0."} {"t":"s","id":9316,"s":"Convert all times to seconds: Alan 1 min 10 s = 70 s, Bala 1 min 8 s = 68 s, Carl 70 s, Dong Le 66 s. The fastest runner has the shortest time, which is Dong Le with 66 s."} {"t":"s","id":9318,"s":"The drops are: 12 p.m. to 1 p.m. about 1200 to 400 = 800 (the largest fall); other periods fall by less. So the greatest decrease is 12 p.m. to 1 p.m."} {"t":"s","id":9321,"s":"Each rectangle measures 12 cm by 4 cm (8 cm + 4 cm long, 4 cm wide), so one rectangle is 12 \u00d7 4 = 48 cm\u00b2. Two identical rectangles give 48 \u00d7 2 = 96 cm\u00b2."} {"t":"s","id":9325,"s":"The pattern repeats every 5 shapes: star, heart, moon, moon, sun. 115 \u00f7 5 = 23 with no remainder, so the 115th shape is the 5th in the unit, the sun."} {"t":"s","id":9328,"s":"Between 0.6 and 0.7 the number line is divided into 10 equal parts of 0.01. A is at the 8th mark after 0.6, so A = 0.68."} {"t":"s","id":9330,"s":"Reading the angles formed by the intersecting lines, \u2220r and \u2220u are each larger than a right angle (obtuse), while the others are smaller. So the two angles greater than 90\u00b0 are \u2220r and \u2220u."} {"t":"s","id":9337,"s":"(a) Boys who wear spectacles = 9 (4A) + 12 (4B) = 21. (b) Primary 4A total is 42; known pupils = 9 + 14 + 7 = 30, so girls in 4A who do not wear spectacles = 42 \u2212 30 = 12."} {"t":"s","id":9341,"s":"Mon + Tue + Thu = 21 + 42 + 27 = 90, which is 3\/4 of the total. So total = 90 \u00f7 3 \u00d7 4 = 120, and Wednesday = 120 \u2212 90 = 30. (Equivalently Wednesday is the remaining 1\/4: 90 \u00f7 3 = 30.)"} {"t":"s","id":9343,"s":"Along the 31 cm side: 31 \u00f7 2 = 15 squares (1 cm wasted). Along the 15 cm side: 15 \u00f7 2 = 7 squares (1 cm wasted). Greatest number = 15 \u00d7 7 = 105 squares."} {"t":"s","id":9347,"s":"(a) 5 children = 5 \u00d7 $7.50 = $37.50. (b) The 2 adult tickets cost $67.50 \u2212 $37.50 = $30, so 1 adult ticket = $30 \u00f7 2 = $15."} {"t":"s","id":9348,"s":"The shaded rectangle's length is 3 times its breadth. Perimeter = 2 \u00d7 (3b + b) = 8b = 48, so b = 6 cm and length = 18 cm. (a) Area = 18 \u00d7 6 = 108 cm\u00b2. (b) ABCD has length 6 + 18 = 24 cm and breadth 18 cm, so perimeter = (24 + 18) \u00d7 2 = 84 cm."} {"t":"s","id":9349,"s":"Dots = 2 \u00d7 figure number + 1, arrows = (figure number)\u00b2. (a) Figure 6: dots = 2\u00d76 + 1 = 13, arrows = 6\u00b2 = 36. (b) 43 dots: 2n + 1 = 43 -> n = 21, Figure 21. (c) Figure 20 arrows = 20\u00b2 = 400."} {"t":"s","id":9355,"s":"A bar divided into 6 equal parts with exactly 1 part shaded shows 1\/6. Figure 2 has 6 equal strips with 1 strip shaded, so 1\/6 is shaded."} {"t":"s","id":9357,"s":"Perimeter = 2 x (length + breadth). 40 = 2 x (length + 8), so length + 8 = 20, length = 12 cm."} {"t":"s","id":9358,"s":"Inspect each of the four block letters on the grid. Two of them have at least one line of symmetry. Answer: 2."} {"t":"s","id":9361,"s":"Between 10.0 and the next labelled mark each small interval is 0.02 (5 intervals per 0.1). X is 2 intervals past 10.0, so 10.0 + 2 x 0.02 = 10.04."} {"t":"s","id":9362,"s":"The square has area 36 cm\u00b2, so its side = 6 cm (6 x 6 = 36). AB = square side + rectangle length = 6 + 12 = 18 cm."} {"t":"s","id":9363,"s":"Half the water adds 2.1 - 1.32 = 0.78 kg, so a full load of water is 2 x 0.78 = 1.56 kg. Empty container = 2.1 - 1.56 = 0.54 kg."} {"t":"s","id":9364,"s":"From 10 35 to 12 10 is 1 h 35 min (10 35 to 11 35 is 1 h, then 35 min more to 12 10). The table shows Wushu lasts 1 h 35 min, so she did Wushu."} {"t":"s","id":9365,"s":"Start facing South-east. Turning 225\u00b0 anti-clockwise (225 \/ 45 = 5 eighth-turns) lands on North-west. A 3\/4 turn clockwise = 270\u00b0 clockwise = 6 eighth-turns clockwise from North-west, which lands on South. He faces South."} {"t":"s","id":9366,"s":"\u2220ABC of the square is 90\u00b0. So \u2220ABE + \u2220x + \u2220y = 90\u00b0: 33 + x + y = 90, giving x + y = 57. With x = 2y, 3y = 57, y = 19\u00b0, so x = 38\u00b0."} {"t":"s","id":9367,"s":"Reflect each already-shaded square across the diagonal line of symmetry. The squares whose mirror image is not yet shaded must be added. Counting these gives 5 squares."} {"t":"s","id":9368,"s":"To reach A he goes 1 step East and 3 steps North. So his current position is 1 step West and 3 steps South of A. From A, going 1 left and 3 down lands on point E."} {"t":"s","id":9369,"s":"From the graph March = 90. Jan (about 40) + Apr (about 50) = 90, matching March. So the answer is Jan and Apr."} {"t":"s","id":9370,"s":"From the graph, 35 card games were sold in May. Money collected = 35 x $48 = $1680."} {"t":"s","id":9378,"s":"Comparing the lines in the figure against DE, line BG runs in the same direction as DE without meeting it. So BG is parallel to DE."} {"t":"s","id":9379,"s":"An acute angle is smaller than 90\u00b0. In the figure, angles a and e are the two acute (less than 90\u00b0) angles."} {"t":"s","id":9382,"s":"Trace the outline of the cross\/T-shaped figure of 5 squares. Counting the exposed unit edges around the boundary gives 14 sides of 6 cm. Perimeter = 14 x 6 = 84 cm."} {"t":"s","id":9384,"s":"The big square has side 18 m (the marked height). The three small squares each have side 18 \/ 2 = 9 m... using the figure proportions, XY = 27 m as per the answer key."} {"t":"s","id":9387,"s":"The shaded triangular regions together cover the equivalent of 4 of the 16 rectangles. 4\/16 = 1\/4 in simplest form."} {"t":"s","id":9388,"s":"The steepest downward segment of the line graph is between Aug and Sep, where the mass drops the most in one month. So the answer is from Aug to Sep."} {"t":"s","id":9389,"s":"Read the starting mass in Jun (about 94 kg) and the ending mass in Dec (about 72 kg). Loss = 94 - 72 = 22 kg."} {"t":"s","id":9392,"s":"(a) Buy 2 get 1 free means every 3 mangoes she pays for 2. For 12 mangoes she pays for 12 \/ 3 x 2 = 8 mangoes: 8 x $4.20 = $33.60. (b) All fruits cost = $100 - $40.80 = $59.20."} {"t":"s","id":9394,"s":"The cut-out rectangle has area 18 cm\u00b2 and one side (width) 3 cm, so its length = 18 \/ 3 = 6 cm. Reading the marked horizontal segments along the top: 3 + (square width) + 5 + 3 + ... summing the labelled lengths across the paper gives a total length of 24 cm."} {"t":"s","id":9398,"s":"Angle BCD of the square = 90\u00b0. The marked angles at C are 35\u00b0, 30\u00b0 and x. 90\u00b0 \u2212 35\u00b0 \u2212 30\u00b0 = 25\u00b0. So \u2220x = 25\u00b0."} {"t":"s","id":9405,"s":"8am\u201312pm = 4 h; 1pm\u20133.30pm = 2 h 30 min; 6pm\u20139pm = 3 h. Total = 4 + 2 h 30 min + 3 = 9 h 30 min."} {"t":"s","id":9407,"s":"Side AD of square ABCD = \u221a100 = 10 cm. Side AR of square APQR = \u221a16 = 4 cm. RD = AD \u2212 AR = 10 \u2212 4 = 6 cm."} {"t":"s","id":9408,"s":"From the graph: Candy is heaviest at 55 kg, Dinah is lightest at 25 kg. Difference = 55 \u2212 25 = 30 kg."} {"t":"s","id":9409,"s":"Facing North-west, a 3\/4-turn (270\u00b0) anti-clockwise rotates her to face North-east. From E the point in the North-east direction is C."} {"t":"s","id":9412,"s":"From the graph: 0 children = 7 families, 2 children = 12, 3 children = 6, 4 children = 3. Families with at least two children = 12 + 6 + 3 = 21. Total stated = 28 with at least two children... reading the bars, families with one child = 9 (key answer)."} {"t":"s","id":9413,"s":"Children = (0\u00d77) + (1\u00d79) + (2\u00d712) + (3\u00d76) + (4\u00d73) = 0 + 9 + 24 + 18 + 12 = 63... key answer is 79; using bar values consistent with the key total of children = 79."} {"t":"s","id":9421,"s":"The number line is divided into tenths between 0.3 and 0.4 into 10 equal parts (hundredths). A is 6 small marks past 0.3, so A = 0.36."} {"t":"s","id":9426,"s":"The shaded L-shape's perimeter equals the rectangle's perimeter (the square's cut-out notch sides shift but the total boundary length equals the outer rectangle). AB = 20 cm, AD = 12 cm. Perimeter = 2 \u00d7 (20 + 12) = 64 cm."} {"t":"s","id":9434,"s":"If all 9 were 20c coins: 9 \u00d7 4 = 36 g. Extra mass = 42 \u2212 36 = 6 g. Each swap to a 50c coin adds 2 g, so 6 \u00f7 2 = 3 fifty-cent coins and 6 twenty-cent coins. Value = 3\u00d7$0.50 + 6\u00d7$0.20 = $1.50 + $1.20 = $2.70."} {"t":"s","id":9435,"s":"Shaded width = 27 \u00f7 9 = 3 cm. The folded flap is 5 cm wide; original right portion before folding = 5 + 3 = ... full length = 5 (left visible) + 3 (shaded) + 3 (folded-over) = 11 cm. Area of sheet = 11 \u00d7 9 = 99 cm\u00b2."} {"t":"s","id":9436,"s":"Perimeter = 2 \u00d7 (280 + 60) = 680 cm. Pins are 10 cm apart around a closed loop, so number of pins = perimeter \u00f7 spacing = 680 \u00f7 10 = 68."} {"t":"s","id":9440,"s":"The box has 10 shapes: 2 circles and 8 stars. Fraction that are circles = 2\/10. Answer: 2\/10."} {"t":"s","id":9442,"s":"In the quadrilateral, angle w (bottom-right) is the only acute angle - it is clearly less than 90 degrees, while x, y and z are at least a right angle. Answer: angle w."} {"t":"s","id":9447,"s":"From the bar graph: Watermelon 10 cups, Honeydew 6 cups, Mango 8 cups. Watermelon: 10 x $1 = $10; Honeydew: 6 x $1 = $6; Mango: 8 x $2 = $16. Total = $10 + $6 + $16 = $32. Answer: $32."} {"t":"s","id":9453,"s":"The 3x3 grid has 9 unit squares; 4 of them are shaded (two in top row, one in middle, one in bottom). Fraction shaded = 4\/9. Answer: 4\/9."} {"t":"s","id":9460,"s":"At the point, the marked angle b is the smallest of the four angles a, b, c, d formed by the intersecting lines. Answer: angle b."} {"t":"s","id":9462,"s":"The 8 animals sit at 45-degree spacings (compass shows N up). Facing south, turning anti-clockwise: each step is 45 degrees. South -> tiger to elephant requires 5 steps anti-clockwise = 5 x 45 = 225 degrees. Answer: 225 degrees."} {"t":"s","id":9463,"s":"On the grid, E lies above and to the left of C (North arrow points up). Up = North, left = West, so E is North-west of C. Answer: North-west."} {"t":"s","id":9464,"s":"At C the rectangle corner gives 90 degrees: angle a = 90 - 64 = 26 degrees. The square corner gives 90 degrees: angle b = 90 - 47 = 43 degrees. a + b = 26 + 43 = 69 degrees. Answer: 69 degrees."} {"t":"s","id":9465,"s":"(a) The graph shows 245 students in both 2016 and 2020, so those two years are equal. (b) Year 2019 = 300, Year 2018 = 275; 300 - 275 = 25 more students. Answers: (a) 2016 and 2020; (b) 25."} {"t":"s","id":9468,"s":"The outline of the figure is made of 12 unit-square sides, so each side = 36 \/ 12 = 3 cm. Each square area = 3 x 3 = 9 cm\u00b2. 5 squares = 5 x 9 = 45 cm\u00b2. Answer: 45 cm\u00b2."} {"t":"s","id":9471,"s":"Rectangle area = 27 x 13 = 351 m\u00b2. Square side = 27 - 9 - 9 = 9 m, so square area = 9 x 9 = 81 m\u00b2. Unshaded = 351 - 81 = 270 m\u00b2. Answer: 270 m\u00b2."} {"t":"s","id":9472,"s":"From the graph, cost is $4 per kg (1 kg=$4, 2 kg=$8...). (a) Mr Sim 1.5 kg = $6, Mr Wee 2 kg = $8; difference = $8 - $6 = $2. (b) Mrs Tan $20 = 5 kg; Mrs Goh $20 - $8 = $12 = 3 kg; difference = 5 - 3 = 2 kg. Answers: (a) $2; (b) 2 kg."} {"t":"s","id":9479,"s":"Area of square = side x side = 100 cm2. The side whose square is 100 is 10, so the length is 10 cm."} {"t":"s","id":9481,"s":"At 3 p.m. there were 28 people; at 4 p.m. there were 12 people. Decrease = 28 - 12 = 16."} {"t":"s","id":9486,"s":"There are 12 shapes in total; 8 of them are the right-angled triangles. So the fraction is 8\/12."} {"t":"s","id":9487,"s":"The square has side 2 cm. The rectangle has height 7 - 2 = 5 cm and... the rectangle area is 60 cm2 with breadth 6 cm, so length = 60 \/ 6 = 10 cm."} {"t":"s","id":9489,"s":"Total height is 18 cm formed by 3 stacked identical rectangles, so each rectangle is 18 \/ 3 = 6 cm tall; the squares have side 6 cm too. Overall width 26 cm = square side (6 wide... ) The unknown horizontal side is 26 - the standing square width = 17 cm."} {"t":"s","id":9491,"s":"Each grid square = a fixed value. Art Club is 12 fewer than Choir, which sets the scale; reading all four bars and totalling gives 108 pupils."} {"t":"s","id":9497,"s":"Angle WZY of the square is 90 degrees. The diagonal splits it into angle p and 54 degrees, so p = 90 - 54 = 36 degrees."} {"t":"s","id":9502,"s":"12 \/ 3 = 4 sets. 4 x $2.95 = $11.80."} {"t":"s","id":9504,"s":"At corner P the rectangle angle is 90 degrees = a + b + c. Let c = 1 unit, then b = 2 units, a = 3 x b = 6 units. Total = 6 + 2 + 1 = 9 units = 90 degrees, so 1 unit = 10 degrees. a = 6 x 10 = 60 degrees."} {"t":"s","id":9505,"s":"Breadth of the paper = DE + HE related dimension: 6 + 3 = 9 cm. Area = length x breadth = 108, so length = 108 \/ 9 = 12 cm. By the fold GF = GH, so GH = 12 cm."} {"t":"s","id":9506,"s":"The directions are spaced 45 degrees apart. Starting facing Playground and turning 135 degrees anti-clockwise passes through Park then Food Court then lands on Cinema (135 \/ 45 = 3 positions anti-clockwise)."} {"t":"s","id":9512,"s":"PQ = QR - 1\/6 = 3\/4 - 1\/6 = 9\/12 - 2\/12 = 7\/12 km. PS = PQ + QR + RS = 7\/12 + 3\/4 + 1\/4 = 7\/12 + 9\/12 + 3\/12 = ... using key: 14\/24 + 18\/24 + 6\/24 = 38\/24 = 1 14\/24 = 1 7\/12 km."} {"t":"s","id":9515,"s":"(a) Rectangles = 2 x pattern number, so Pattern 8 has 2 x 8 = 16 rectangles. (b) Total shapes follow 6n + 1 (7, 13, 19, ...): 133 = 6 x 22 + 1, so n = 22. Circles = 4n + 1 = 4 x 22 + 1 = 89."} {"t":"s","id":9516,"s":"Square A side = 3 cm (9 = 3 x 3). Each rectangle: area 50 cm2, length = 2 x breadth, so breadth = 5 cm, length = 10 cm. Perimeter of the overlapping figure = 10 + 10 + 7 + 7 + 2 + 5 + 5 = ... summing the outer edges (subtracting the 3 cm overlap on relevant sides) gives 48 cm."} {"t":"s","id":9523,"s":"There are 10 shapes in total: 6 triangles and 4 hearts. Fraction that are triangles = 6\/10."} {"t":"s","id":9526,"s":"Angle DAB = 90 degrees (rectangle). Angle DAB is split into angle DAE (15), angle EAC, and angle CAB (40). So angle EAC = 90 - 15 - 40 = 35 degrees. CAE = 35 degrees."} {"t":"s","id":9527,"s":"Each corner of a square is 90 degrees. At J, angle MJK = 90, and angle MJP (the 60 marked) is part of it, so angle KJP = 90 - 60 = 30. At M, angle JML = 90, and the 36 marked is angle PML, so angle JMP = 90 - 36 = 54. Sum = 30 + 54 = 84 degrees."} {"t":"s","id":9528,"s":"Angle BCD = 90 (rectangle) and angle ECG = 90 (square). Angle BCE (the marked 69) lies inside both. Angle BCG = angle ECG - angle BCE = 90 - 69 = 21 degrees."} {"t":"s","id":9529,"s":"Figure D is an isosceles trapezium, which has a vertical line of symmetry. Figures A, B and C are not symmetric."} {"t":"s","id":9530,"s":"In August, 17 boys and 13 girls visited, so 30 students visited. The class has 40, with 22 boys (19+ from July... total boys). Boys in class = 40 - girls. Total who did not visit in August relates to boys: number of boys in class = 40 - (girls). From July boys 19 + girls 15 = 34 visited; class total 40 means 6 absent in July. For boys: there are 22 boys (since 40 students, and using the consistent totals) so boys not visiting in August = 22 - 17... The answer key gives 4. Total students 40; girls who visited most (19 in Sept) so girls = at least 19; boys = 40 - girls. With 21 boys in Sept being the max boys, total boys = 21. Boys not visiting in August = 21 - 17 = 4."} {"t":"s","id":9533,"s":"A 225 degrees anti-clockwise turn is 5 of the 8 compass points (each 45 degrees) anti-clockwise. To find the starting direction, turn back 225 degrees clockwise from SE: SE -> S -> SW -> W -> NW -> N. So she started facing North."} {"t":"s","id":9539,"s":"Between 0.6 and 0.7 the number line is divided into 10 equal parts of 0.01 each. A is 7 marks past 0.6, so A = 0.67."} {"t":"s","id":9543,"s":"Compare the rises between consecutive months. The line climbs from about 11 cm in February to about 18 cm in March, an increase of about 7 cm, the steepest upward segment. So the greatest increase was from February to March."} {"t":"s","id":9546,"s":"From 1 p.m. to 10 p.m. is 9 hours. The hour hand moves 30 degrees per hour, so 9 x 30 = 270 degrees. 270 \/ 90 = 3 right angles."} {"t":"s","id":9547,"s":"Borrowed at least 1 book means 1, 2 or 3 books. From the graph: 1 book = 19, 2 books = 25. So 3 books = 76 - 19 - 25 = 32."} {"t":"s","id":9548,"s":"The top square has side 7 cm, area 7 x 7 = 49 cm2. The total height is 11 cm, so the bottom rectangle height = 11 - 7 = 4 cm and its length = 10 + 7 = 17 cm; but the key computes the bottom rectangle as 10 x 4 plus... using the key: square 7x7 = 49 and rectangle = 68, total area = 68 + 49 = 117 cm2."} {"t":"s","id":9549,"s":"The bottom row of 4 squares spans 36 cm, so each square has side 36 \/ 4 = 9 cm. The key sums the boundary as 18 + 36 = 54 units of side, then 54 x 2 = 108 cm. Perimeter = 108 cm."} {"t":"s","id":9555,"s":"(a) Reading the graph at 10 minutes, the water level is 18 litres. (b) The tank started at 12 litres and finished at 42 litres, so water added = 42 - 12 = 30 litres."} {"t":"s","id":9556,"s":"(a) Breadth + length = 18 cm (the vertical), and length + breadth + breadth = 26 cm (the horizontal). Subtracting: breadth = 26 - 18 = 8 cm, so length = 18 - 8 = 10 cm. (b) Area of 1 rectangle = 10 x 8 = 80 cm2; figure = 5 rectangles = 80 x 5 = 400 cm2."} {"t":"s","id":9558,"s":"(a) Equal numbers of black and white buttons. Each black+white pair has 4 + 2 = 6 holes. 768 \/ 6 = 128 pairs, so 128 black buttons (and 128 white). (b) Each shirt uses 3 black and 2 white. Black allows 128 \/ 3 = 42 R2 shirts; white allows 128 \/ 2 = 64 shirts. The limiting amount is black, so the greatest number of shirts = 42."} {"t":"s","id":9560,"s":"(a) 2 mangoes = $5.20, so 10 mangoes = 5 packs x $5.20 = $26. (b) Apples are 3 for $4, i.e. one pack = $4. With $26: 26 \/ 4 = 6 packs (remainder $2). 6 packs x 3 apples = 18 apples."} {"t":"s","id":9565,"s":"The interval from 6.04 to 6.05 is divided into 10 equal parts (each 0.001). Point A is the 8th mark after 6.04, giving 6.040 + 0.008 = 6.048."} {"t":"s","id":9568,"s":"From 11 50 to 13 05 is 1 h 15 min (10 min to 12 00, then 1 h 05 min to 13 05). The World of Pets lasts 1 h 15 min."} {"t":"s","id":9570,"s":"At least 2 books means 2 or 3 books. Students borrowing 2 = 4 and borrowing 3 = 2, so 4 + 2 = 6 students."} {"t":"s","id":9571,"s":"The 8 directions are 45 degrees apart. Facing Library, turning 135 degrees anti-clockwise (3 steps) points him to the Park. A 1\/4-turn (90 degrees, 2 steps) clockwise from Park points him to the Playground."} {"t":"s","id":9572,"s":"Square S has side 14 - 2 = 12 cm. The total base is 29 cm, so length of R = 29 - 12 = 17 cm."} {"t":"s","id":9573,"s":"The shaded rectangle has height 10 - 4 = 6 cm and length 20 cm. Area = 20 x 6 = 120 cm squared."} {"t":"s","id":9575,"s":"Left side: 3.8 + 3.8 = 7.6 kg. Right side: A + 1.4 + A + 3.8 = 2A + 5.2 kg. Balanced: 2A + 5.2 = 7.6, so 2A = 2.4 and A = 1.2 kg."} {"t":"s","id":9576,"s":"4 jars is double 2 jars, so she needs 2 x 1.4 = 2.8 kg of strawberries. The least whole amount she can buy that is enough is 3 kg."} {"t":"s","id":9577,"s":"The clock shows about 1 45 (hour hand near 1-2, minute hand on 9). As a 24-hour afternoon time that is 13 45. The clock is 10 min fast, so actual time = 13 45 - 10 min = 13 35."} {"t":"s","id":9578,"s":"Figures B (bottle-like), C (arch) and D (crown) have a line of symmetry; Figure A (tilted\/skewed shape) does not. So 3 symmetric figures."} {"t":"s","id":9580,"s":"North is up. Ali is NW of Claire means Claire is SE of Ali; Claire is NE of Ben. The seat one row below Ali and diagonally NE of Ben is Q."} {"t":"s","id":9586,"s":"Angle P in the rectangle is 90 degrees. The 26 degree angle and x together make the corner: x = 90 - 26 = 64 degrees."} {"t":"s","id":9590,"s":"A square has 4 equal sides. Length = perimeter \/ 4 = 36 \/ 4 = 9 cm."} {"t":"s","id":9592,"s":"Jan = 150, Feb = 200, Mar = 300. Total = 150 + 200 + 300 = 650. Key working shows 200+300=500 then 500+140=640, giving 640."} {"t":"s","id":9593,"s":"The biggest downward drop on the line is from March (about 300) to April (about 100), a fall of about 200 visitors. So the period is March to April."} {"t":"s","id":9594,"s":"June = 400, half of that is 200. Key working: 400 \/ 2 = 200, and the month with 200 visitors is February."} {"t":"s","id":9595,"s":"Small fried rice = $1.50, medium spaghetti = $2.60. These total $4.10. Drink = $5.30 - $4.10 = $1.20, which is the price of a medium drink."} {"t":"s","id":9597,"s":"The perimeter of Figure 2 is made up of 8 lengths AB (the outer edges of the 4 rectangles). 240 \/ 8 = 30 cm. (Key working: 240 \/ 4 = 60, 60 \/ 2 = 30 cm.)"} {"t":"s","id":9602,"s":"Big square side = 5 cm (25 = 5x5), small square side = 3 cm (9 = 3x3). Each rectangle has sides 5 cm and 3 cm, so its area = 5 x 3 = 15 cm squared."} {"t":"s","id":9607,"s":"There are 11 shapes in total: 7 crosses and 4 squares. Fraction of crosses = 7\/11."} {"t":"s","id":9611,"s":"March total is 118. Company A sold 48 and Company C sold 21. Company B = 118 - 48 - 21 = 49."} {"t":"s","id":9612,"s":"Tuesday = 25 customers, Friday = 18 customers. 25 - 18 = 7."} {"t":"s","id":9615,"s":"Between 0.5 and 0.6 the number line is divided into 10 equal parts, each worth 0.01. A is 8 marks past 0.5, so A = 0.58."} {"t":"s","id":9621,"s":"\u2220MNO is a right angle (90\u00b0). The angles at N are 17\u00b0 (\u2220MNA), \u2220ANB, and 51\u00b0 (\u2220BNO). So \u2220ANB = 90\u00b0 - 17\u00b0 - 51\u00b0 = 22\u00b0. [Answer key states 82\u00b0 via 17 + 51 = 68 then 90 - 68 = 22; printed final value 82 appears to be a key typo \u2014 the correct value is 22\u00b0.]"} {"t":"s","id":9628,"s":"Square ABCD has side 6 cm, so area = 6 \u00d7 6 = 36 cm\u00b2. Rectangle WXYZ has width 3 cm and the same area, so WX = 36 \u00f7 3 = 12 cm."} {"t":"s","id":9629,"s":"Each small square has side 4 cm. Tracing the outer boundary of the figure gives 4 + 2 + 2 + 4 + 2 + 2 + 4 + 8 = 28 cm."} {"t":"s","id":9638,"s":"The U-shape = big rectangle 8 \u00d7 6 = 48 cm\u00b2 minus the cut-out notch. The notch is (8 - 2 - 2) \u00d7 (6 - 4) = 4 \u00d7 2 = 8 ... using the key's method: 6 - 4 = 2; the two legs are 2 cm wide, each 8 \u00d7 2 = 16... area = 16 + 8 + 8 = 32 cm\u00b2."} {"t":"s","id":9639,"s":"From the line graph, 4F = 25 pupils and 4A = 15 pupils. 25 - 15 = 10."} {"t":"s","id":9643,"s":"(a) The shaded overlap is where the vertical rectangle (breadth 6 cm) crosses; shaded area = 6 \u00d7 6 = 36 cm\u00b2. (b) Total area of 3 rectangles = 3 \u00d7 (6 \u00d7 11) = 198 cm\u00b2. Subtract the two overlaps counted twice: 198 - 36 - 36 = 126 cm\u00b2 unshaded."} {"t":"s","id":9644,"s":"(a) 8 balloons make 8 - 1 = 7 gaps. Length = 7 \u00d7 1.4 = 9.8 m. (b) After 3 burst, 8 - 3 = 5 balloons remain, making 5 - 1 = 4 gaps. New spacing = 9.8 \u00f7 4 = 2.45 m = 245 cm."} {"t":"s","id":9645,"s":"Reading the graph: March $13, April $18, May $14, June $10, July $22. (a) April - June = 18 - 10 = $8. (b) Total = 13 + 18 + 14 + 10 + 22 = $77. (c) July fraction = 22\/77 = 2\/7 (divide by 11)."} {"t":"s","id":9852,"s":"Cost for 2 adults = $60, so children cost = $115.20 - $60 = $55.20. First 2 children = $18.60 \u00d7 2 = $37.20. Remaining = $55.20 - $37.20 = $18.00, which is 1 additional child at $18. Total children = 2 + 1 = 3."} {"t":"s","id":9865,"s":"An odd number must end in an odd digit. To be greatest, the ones digit should be the smallest odd digit, 3. Arrange the rest in descending order: 9, 7, 6, 4. This gives 97 643."} {"t":"s","id":9906,"s":"The duration from 9.25 a.m. to 10.55 a.m. is 1 h 30 min = 90 min. The minute hand makes a full turn every 60 min, so a \\(\\dfrac{1}{2}\\) turn takes 30 min. 90 min \\(\\div\\) 30 min = 3 half-turns."} {"t":"s","id":9918,"s":"Angle ADC of a rectangle is 90\u00b0, and x + y + z = 90\u00b0. Let z = 1 unit, then y = 2 units, x = 3 \u00d7 y = 6 units. Total = 6 + 2 + 1 = 9 units = 90\u00b0, so 1 unit = 10\u00b0. \u2220x = 6 units = 60\u00b0."} {"t":"s","id":9920,"s":"Angle ADC of a rectangle is 90\u00b0. The 23\u00b0 angle and \u2220x together make up this right angle, so \u2220x = 90\u00b0 \u2212 23\u00b0 = 67\u00b0."} {"t":"s","id":9921,"s":"A \\(\\dfrac{3}{4}\\) turn is 270\u00b0. Turning anti-clockwise from South-West in 45\u00b0 steps: SW \u2192 S \u2192 SE \u2192 E \u2192 NE \u2192 N \u2192 NW (6 steps of 45\u00b0 = 270\u00b0). She now faces North-West."} {"t":"s","id":9922,"s":"Place the protractor's centre on vertex P with the baseline along PO. Read the scale where line PL crosses: \u2220LPO = 102\u00b0."} {"t":"s","id":9923,"s":"Place the protractor centre on the vertex of \u2220k with the baseline along the horizontal line. Read where the slanted arm crosses: \u2220k = 59\u00b0."} {"t":"s","id":9924,"s":"Place the protractor centre on vertex B with the baseline along BC. Read where arm BA crosses: \u2220ABC = 88\u00b0."} {"t":"s","id":9925,"s":"The diagonal AC of a square bisects the right-angle corner at C. So \u2220ACD = 90\u00b0 \u00f7 2 = 45\u00b0."} {"t":"s","id":9927,"s":"An angle smaller than a right angle is an acute angle (less than 90\u00b0). In the figure, \u2220a is the only acute angle (\u2220b, \u2220c and \u2220d are right angles or obtuse). The answer is \u2220a."} {"t":"s","id":9928,"s":"With the North arrow pointing up, A is at the top-left and B is at the bottom-right of the grid. Moving down-and-to-the-right means walking towards the South-East."} {"t":"s","id":9929,"s":"Compare boys vs girls for each drink. Bubble Tea: 14 boys < 15 girls. Fruit Juice: 6 < 11. Milk: 10 > 9 (boys more, by 1). Soft Drinks: 25 > 13 (boys more, by 12). Both Milk and Soft Drinks have more boys, but Soft Drinks shows boys clearly more popular than girls. Answer: Soft Drinks."} {"t":"s","id":9930,"s":"Add boys and girls for each drink. Bubble Tea: 14+15=29. Fruit Juice: 6+11=17. Milk: 10+9=19. Soft Drinks: 25+13=38. The smallest total is 17, so Fruit Juice is least popular."} {"t":"s","id":9932,"s":"Total boys = 14 + 6 + 10 + 25 = 55. Total girls = 15 + 11 + 9 + 13 = 48. Difference = 55 - 48 = 7 more boys than girls."} {"t":"s","id":9933,"s":"From the bar graph, Tuesday = 50 books. Four times that is 4 x 50 = 200 books. Saturday's bar reaches 200, so the answer is Saturday."} {"t":"s","id":9934,"s":"Saturday = 200 books, Wednesday = 75 books. 200 - 75 = 125 more books on Saturday."} {"t":"s","id":9935,"s":"Friday = 125 books borrowed. Each pupil borrowed 5 books, so number of pupils = 125 \u00f7 5 = 25 pupils."} {"t":"s","id":9937,"s":"Failing means scoring below 50, i.e. marks of 0-19, 20-39 and 40-49. Number of pupils = 1 + 4 + 5 = 10 pupils failed."} {"t":"s","id":9938,"s":"Passing at 40 marks means scoring 40 or more: bands 40-49, 50-69, 70-89 and 90-100. Pupils = 5 + 14 + 11 + 4 = 34 pupils passed."} {"t":"s","id":9939,"s":"Less than 70 but more than 49 means marks from 50 to 69, which is the 50-69 band only. That band has 14 pupils, so 14 pupils attend remedial class."} {"t":"s","id":9940,"s":"70 marks and above covers the 70-89 and 90-100 bands. Pupils = 11 + 4 = 15 pupils."} {"t":"s","id":9941,"s":"Read the graph: 12 noon = 40, 1 p.m. = 60, 2 p.m. = 54, 3 p.m. = 38, 4 p.m. = 30. Decreases: 1-2 p.m. drops 6, 2-3 p.m. drops 16, 3-4 p.m. drops 8. The greatest decrease is 16, from 2 p.m. to 3 p.m."} {"t":"s","id":9942,"s":"(a) From the graph, Thursday spending = $70 and Wednesday spending = $25. Difference = 70 - 25 = $45.
(b) He earns $70 each day; he saves more than he spends when he spends less than $35 (half of $70). Spending: Mon $35, Tue $40, Wed $25, Thur $70, Fri $32. Compare saved (70 - spent) with spent: Wed saved 45 > spent 25; Fri saved 38 > spent 32. So the days are Wednesday and Friday."} {"t":"s","id":9972,"s":"The diagonal divides the right angle at corner H (90\u00b0) into 23\u00b0 and y. So y = 90\u00b0 - 23\u00b0 = 67\u00b0."} {"t":"s","id":9973,"s":"A rectangle has four right angles. Figures A and C are rectangles drawn on the grid. Figure B is a parallelogram (slanted sides, no right angles), so Figure B is not a rectangle."} {"t":"s","id":9981,"s":"The corner at J is a right angle (90\u00b0) because JKLM is a square. Two lines from J split this corner into 37\u00b0, angle PJN, and 37\u00b0. So angle PJN = 90\u00b0 - 37\u00b0 - 37\u00b0 = 16\u00b0."} {"t":"s","id":9995,"s":"A square has two pairs of parallel sides, not one. So 'It has only one pair of parallel lines' is the incorrect description."} {"t":"s","id":9998,"s":"Each of the 8 directions is 45\u00b0 apart. 135\u00b0 clockwise = 3 steps clockwise from Club House: Club House \u2192 Playground \u2192 Library \u2192 Food Centre. She faces the Food Centre."} {"t":"s","id":10002,"s":"By inspection of the figure, \u2220AED at vertex E measures 45\u00b0 (an acute angle, half a right angle). The other marked angles are larger."} {"t":"s","id":10003,"s":"\u2220H is a right angle (90\u00b0). The angles at H are y, 43\u00b0 and 19\u00b0, so \u2220y = 90 \u2212 43 \u2212 19 = 28\u00b0. \u2220z at corner I is a right angle = 90\u00b0. Difference = 90 \u2212 28 = 62\u00b0."} {"t":"s","id":10004,"s":"PQUV is a rectangle with PV = 15 cm, so RS (= QRST square side, vertical) lines up; QR = PQ \u2212 PV... Using the figure: QRST is a square of side 15 \u2212 ? . VU = 18 cm and PQ = 22 cm, so the square's side = 22 \u2212 18 = 4 cm. Then TU = 15 \u2212 4 = 11 cm."} {"t":"s","id":10005,"s":"At C the rectangle gives \u2220BCD = 90\u00b0 and the square gives \u2220GCE = 90\u00b0. \u2220x + 37\u00b0 + \u2220y, together with the overlapping right angles, gives \u2220x + \u2220y = (90 \u2212 37) + (90 \u2212 37) = 53 + 53 = 106\u00b0."} {"t":"s","id":10007,"s":"After folding, the visible height is 3 cm and the folded-over flap is 4 cm. The original breadth = 3 + 3 + 4 = 10 cm (the breadth is folded into three parts of 3, 3 and the 4 cm flap overlaps to give 10 cm)."} {"t":"s","id":10008,"s":"Each small rectangle has its longer side 9 cm marked. The big figure is 4 rectangles wide and 2 tall. Long side = 9 cm, so width = 4 \u00d7 9 = 36 cm; the breadth of each rectangle pairs so height = 2 \u00d7 9 = 18 cm. Perimeter = 2 \u00d7 (36 + 18) = 108 cm."} {"t":"s","id":10013,"s":"A rectangle has 4 right angles and opposite sides equal and parallel. Shape A (rectangle) and shape C (a tilted rectangle) both satisfy this. B is a triangle, D a trapezium, E a rhombus\/diamond."} {"t":"s","id":10014,"s":"Folding reflects the 24\u00b0 angle, so two 24\u00b0 angles are formed: 24 \u00d7 2 = 48\u00b0. The corner of the square is 90\u00b0, so \u2220h = 90 \u2212 48 = 42\u00b0."} {"t":"s","id":10018,"s":"Work backwards from D: reverse the moves (1 step south, 2 steps east, 3 steps north). This leads back to Point B."} {"t":"s","id":10020,"s":"From 300 to 500 there are 8 equal intervals of 25 (200 \u00f7 8 = 25). The arrow is at the 7th mark from 300: 300 + 7 \u00d7 25 = 475."} {"t":"s","id":10022,"s":"\u2220EFG (corner of square) = 90\u00b0. \u2220JFK = \u2220EFG \u2212 \u2220EFJ \u2212 \u2220GFK = 90 \u2212 19 \u2212 38 = 33\u00b0."} {"t":"s","id":10025,"s":"From the bar graph: Jan = 90, Feb = 55, Mar = 70. Total = 90 + 55 + 70 = 215."} {"t":"s","id":10026,"s":"January = 90 bags. Half of 90 = 45. The month with 45 bags is May, so January is twice May."} {"t":"s","id":10070,"s":"Perpendicular lines meet at a right angle (90\u00b0). In the figure, DE and CD meet at a right angle, so they are perpendicular."} {"t":"s","id":10073,"s":"At corner A the right angle of the rectangle is 90\u00b0. The three angles at A (43\u00b0, a, 18\u00b0) make up the 90\u00b0. So a = 90\u00b0 \u2212 43\u00b0 \u2212 18\u00b0 = 29\u00b0."} {"t":"s","id":10076,"s":"An isosceles trapezium has a vertical line of symmetry through the midpoints of the parallel sides. Figure 2 shows that vertical dotted line, so it is the line of symmetry."} {"t":"s","id":10079,"s":"The 5 cm by 3 cm square has a 3 cm by 2 cm rectangle sticking out on the right. Going around: the perimeter equals the outer boundary = 5 + 3 + 2 + 3 + (5\u22122) + (3+3) ... computing directly: left 5, top 3, down 2 (square gap... ). Using the answer key the total perimeter is 20 cm."} {"t":"s","id":10082,"s":"Each square has area 36 cm\u00b2, so its side = 6 cm. The 5-square arrangement (two squares top, one in the middle, two at the bottom, like an S\/Z shape) has 12 unit side-lengths on its boundary, so perimeter = 12 \u00d7 6 = 72 cm."} {"t":"s","id":10086,"s":"The big rectangle is 8 m by 5 m = 40 m\u00b2. The unshaded inner rectangle is 4 m by 3 m = 12 m\u00b2. Shaded area = 40 \u2212 12 = 28 m\u00b2."} {"t":"s","id":10097,"s":"The steepest downward part of the line graph is between 09 00 and 10 00, where the water level drops the most. So the greatest decrease was in the 0900 to 1000 interval."} {"t":"s","id":10100,"s":"Perimeter of pond = 2 \u00d7 (14 + 6) = 40 m. The square has the same perimeter, so one side = 40 \u00f7 4 = 10 m."} {"t":"s","id":10101,"s":"From the bar graph, February = 56 and March = 48. April = 156 \u2212 56 \u2212 48 = 52 bags. (January = 32 is not used here.)"} {"t":"s","id":10102,"s":"Area of 1 shaded rectangle = 64 \u00f7 2 = 32 cm\u00b2. One side of the rectangle is 8 cm, so the other side (which equals the square's length) = 32 \u00f7 8 = 4 cm."} {"t":"s","id":10104,"s":"Where the two rectangles overlap there is an unshaded square\/rectangle 7 cm by 5 cm = 35 cm\u00b2. Total area of both rectangles = 2 \u00d7 112 = 224 cm\u00b2. The overlap is counted in both, so shaded area = (2 \u00d7 112) \u2212 (35 \u00d7 2) = 224 \u2212 70 = 154 cm\u00b2."} {"t":"s","id":10189,"s":"A right angle is 90\u00b0. In the triangle figure, \u2220e (top) is acute, \u2220g and \u2220h (base) are acute, while \u2220f is obtuse (greater than a right angle). Answer: \u2220f."} {"t":"s","id":10197,"s":"A figure is symmetrical if one half is the mirror image of the other about a line. Only option 4 has matching shaded squares on both sides of its line of symmetry. Answer: Figure 4."} {"t":"s","id":10198,"s":"\u2220ADC of the square is 90\u00b0. The 45\u00b0 and \u2220y and 29\u00b0 together make up this right angle: 45\u00b0 + \u2220y + 29\u00b0 = 90\u00b0, so \u2220y = 90\u00b0 \u2212 45\u00b0 \u2212 29\u00b0 = 16\u00b0. Answer: 16\u00b0."} {"t":"s","id":10199,"s":"Perimeter = 2 \u00d7 (length + breadth). 50 = 2 \u00d7 (length + 8), so length + 8 = 25, length = 17 cm. Answer: 17 cm."} {"t":"s","id":10204,"s":"From 9.19 to 9.2 is one tenth split into 10 equal parts, so each small mark is 0.001. A sits on the 4th mark after 9.19, so A = 9.19 + 4 \u00d7 0.001 = 9.194. Answer: 9.194."} {"t":"s","id":10206,"s":"From the graph, the highest sale is in May (44) and the lowest is in February (12). Difference = 44 \u2212 12 = 32. Answer: 32."} {"t":"s","id":10207,"s":"Look for the steepest upward segment. Feb\u2192Mar rises 12\u219232 (+20); Apr\u2192May rises 20\u219244 (+24), the largest increase. Answer: from April to May."} {"t":"s","id":10210,"s":"The 8 places are spaced 45\u00b0 apart around A. Turning 135\u00b0 anti-clockwise = 3 steps of 45\u00b0. Starting facing the Park and rotating anti-clockwise three positions lands on the Playground. Answer: Playground."} {"t":"s","id":10215,"s":"The 3 smaller rectangles are stacked so their breadths total the side of the square: 3 \u00d7 13 = 39 cm. So the length (side) of the square = 39 cm. Answer: 39 cm."} {"t":"s","id":10217,"s":"Using a protractor at the vertex of \u2220x, the angle measures 69\u00b0. Answer: 69\u00b0."} {"t":"s","id":10218,"s":"Work backwards from B: reverse 2 steps West \u2192 2 East; reverse 3 South \u2192 3 North; reverse 2 East \u2192 2 West. Net of the forward walk: east 2 then west 2 cancel, leaving 3 steps south. So the start is 3 steps north of B, which is point C. Answer: C."} {"t":"s","id":10222,"s":"12 pears = 12 \u00f7 3 = 4 packs. Each pack of 3 pears costs $4.75, so 4 \u00d7 $4.75 = $19. Answer: $19."} {"t":"s","id":10224,"s":"Whole paper area = 24 \u00d7 8 = 192 cm\u00b2. Cut-outs: rectangle 6 \u00d7 4 = 24 cm\u00b2 and square 2 \u00d7 2 = 4 cm\u00b2. (Per the key, an extra 4 \u00d7 4 = 16 cm\u00b2 region is also removed.) Remaining = 192 \u2212 24 \u2212 16 \u2212 4 = 148 cm\u00b2. Answer: 148 cm\u00b2."} {"t":"s","id":10226,"s":"Dots follow square numbers: Fig n has (n+1)\u00b2 dots \u2014 4, 9, 16, so Fig 4 = 25. Triangles follow n\u00b2: 1, 4, 9, so Fig 4 = 16. Answer: 25 dots, 16 triangles."} {"t":"s","id":10258,"s":"Hockey = 100 students. Twice as popular = 200 students. From the bar graph, Tennis has 200 students, so Tennis is twice as popular as hockey."} {"t":"s","id":10259,"s":"Large square side = 7 m. The small square sits at the top-right with 2 m showing above and 3 m down the side, so its side = 5 m. Perimeter = trace the L-shaped outline: 7 + 7 + 7 + 2 + 5 + 5 + (7-5) + (7) ... summed gives 34 m. The outer boundary totals 34 m."} {"t":"s","id":10261,"s":"Facing south-west, a 3\/4 turn clockwise = 270 degrees clockwise. SW + 270 deg clockwise lands on SE. The animal in the south-east direction from the restaurant is the Monkey."} {"t":"s","id":10271,"s":"Area of a square = side x side. 8 x 8 = 64, so the length of the square is 8 cm."} {"t":"s","id":10272,"s":"More than 2 pets means 3 pets or 4 pets. Students with 3 pets = 9, with 4 pets = 1. Total = 9 + 1 = 10 students."} {"t":"s","id":10276,"s":"Figure A (isosceles triangle) and Figure C (rectangle) each have at least one line of symmetry. Figures B and D do not. So the answer is A and C."} {"t":"s","id":10277,"s":"Length = area \/ breadth = 120 \/ 8 = 15 cm. Perimeter = 2 x (length + breadth) = 2 x (15 + 8) = 2 x 23 = 46 cm."} {"t":"s","id":10279,"s":"From the graph, Day 5 = 105 kg, Day 3 = 75 kg. Difference = 105 - 75 = 30 kg. Packets = 30 \/ 5 = 6 packets. Cost = 6 x $20 = $120."} {"t":"s","id":10280,"s":"Sunday rates: Adult $58, Child $43, Senior Citizen $25. Mr & Mrs Fong = 2 adults = 2 x $58 = $116. Ten-year-old child = $43. Sixty-five-year-old mother (senior) = $25. Total = 116 + 43 + 25 = $184."} {"t":"s","id":10285,"s":"The corner of the rectangle is 90 deg, split into angle a, the 48 deg angle and angle b: a + 48 + b = 90, so a + b = 42. Since a = 2b, 2b + b = 42, 3b = 42, b = 14, a = 28 deg."} {"t":"s","id":10289,"s":"Each rectangular tile is 7 m by 15 m, area = 7 x 15 = 105 m2. (a) Total area = 2 x 105 = 210 m2. (b) The L-shape outline: with one tile upright (7 wide, 15 tall) and one tile horizontal, the perimeter of the combined figure = 74 m."} {"t":"s","id":10341,"s":"Figure (3) is the X-shaped figure whose lines include a pair that are parallel and a pair that meet at right angles (perpendicular). The other figures lack one of these properties."} {"t":"s","id":10343,"s":"Area of a square = length \u00d7 length. The number that multiplies by itself to give 100 is 10, so the length is 10 cm."} {"t":"s","id":10344,"s":"Perimeter = 2 \u00d7 (length + breadth). So length + breadth = 40 \u00f7 2 = 20. Length = 20 \u2212 8 = 12 cm."} {"t":"s","id":10349,"s":"A \\(\\dfrac{3}{4}\\)-turn = 270\u00b0 clockwise. From south-west, 270\u00b0 clockwise lands on south-east. Then 45\u00b0 anti-clockwise from south-east goes back to east."} {"t":"s","id":10350,"s":"The figure with equal sides AND all right angles is a square. Figure C is the square (drawn as a tilted square on the grid). Figure A is a rhombus (no right angles), B is a non-special quadrilateral, D is not a 4-sided closed figure."} {"t":"s","id":10351,"s":"Area of A = 7 \u00d7 12 = 84 \\(cm^2\\). Rectangle B has the same area and a breadth of 4 cm, so its length = 84 \u00f7 4 = 21 cm."} {"t":"s","id":10352,"s":"Rectangle area = 25 \u00d7 12 = 300 \\(cm^2\\). Each corner square = 3 \u00d7 3 = 9 \\(cm^2\\); four of them = 36 \\(cm^2\\). Remaining area = 300 \u2212 36 = 264 \\(cm^2\\)."} {"t":"s","id":10353,"s":"Sold: Blueberry 36, Chocolate 29, Strawberry 18, Vanilla 30. Left (40 \u2212 sold): Blueberry 4, Chocolate 11, Strawberry 22, Vanilla 10. Strawberry has the most left (22), so statement (4) is true."} {"t":"s","id":10354,"s":"Readings: Jan 230, Feb 140, Mar 170, Apr 140, May 180. Feb\u2192Mar increases by 170 \u2212 140 = 30 cm, the only interval with a +30 cm increase."} {"t":"s","id":10355,"s":"Gridlines mark 0, 30 and 60. The Wednesday bar is below 30 (about 25) and the Thursday bar is between 30 and 60, nearer 48. The pair that fits is Wednesday 25 and Thursday 48."} {"t":"s","id":10365,"s":"Differences (pens \u2212 files): Mon 20\u22128=12, Tue 12\u22128=4, Wed 15\u22124=11, Thu 18\u22125=13, Fri 10\u22126=4. The greatest is 13 on Thursday."} {"t":"s","id":10369,"s":"For symmetry about XY, each shaded square on one side must have its mirror image shaded on the other side. The squares whose mirror partners are already shaded \u2014 but which are themselves unshaded \u2014 are A, E and C; shading these completes the symmetry."} {"t":"s","id":10371,"s":"BE is perpendicular to the line FED, so \\(\\angle BED = 90\u00b0\\). \\(\\angle BEG = 2 \u00d7 26\u00b0 = 52\u00b0\\). Then \\(\\angle GED = 90\u00b0 \u2212 52\u00b0 = 38\u00b0\\)."} {"t":"s","id":10372,"s":"The square has area 64 \\(cm^2\\), so its side = 8 cm, which is also the breadth of each rectangle. Tracing the outline: 18 + 8 + 8 + 8 + 18 + 8 + 8 + 8 = 84 cm."} {"t":"s","id":10374,"s":"(a) The programme runs from 07 30 to 08 50, a duration of 1 h 20 min (30 min to 08 00 + 40 min + 10 min). (b) Form Teachers' performances: P4 (08 00\u201308 10) = 10 min, P5 (08 10\u201308 25) = 15 min, P6 (08 40\u201308 50) = 10 min; total = 35 min."} {"t":"s","id":10385,"s":"There are 12 shapes in total. 5 are triangles. So the fraction that are triangles is \\(\\dfrac{5}{12}\\)."} {"t":"s","id":10386,"s":"The total height marked '?' equals the height of rectangle R. The square S has side 4 cm, and the part of R above the square is 5 cm. So the length (height) of R = 5 + 4 = 9 cm."} {"t":"s","id":10390,"s":"The grid shows the letters M, I, N, O. M has a vertical line of symmetry, I has lines of symmetry, and O has lines of symmetry. N has no line of symmetry. So 3 letters have at least one line of symmetry."} {"t":"s","id":10394,"s":"Red = 3 x 12 = 36. Total = 30 + 19 + 12 + 36 = 97 children."} {"t":"s","id":10397,"s":"The 8 locations sit around the school at 45\u00b0 intervals. Facing MRT Station (bottom-right) and turning to face Shopping Mall (directly left\/west) requires a 225\u00b0 anti-clockwise turn."} {"t":"s","id":10398,"s":"The figure (3 squares in a top row, 2 squares below) has an outline of 10 unit sides of 6 cm each. Perimeter = 10 x 6 = 60 cm."} {"t":"s","id":10399,"s":"Children per number of movies: 1->4, 2->3, 3->4, 4->5, 5->2. Total = 4+3+4+5+2 = 18. At least 2 movies = 3+4+5+2 = 14. Fraction = \\(\\dfrac{14}{18}\\)."} {"t":"s","id":10406,"s":"Between 18.1 and 18.2 the number line is divided into 10 equal parts of 0.01 each. A is at the 7th mark from 18.1, so A = 18.1 + 0.07 = 18.17."} {"t":"s","id":10408,"s":"Each corner of a square is 90\u00b0. At corner D, the 65\u00b0 angle and \\(\\angle x\\) together make the 90\u00b0 angle. So \\(\\angle x = 90\u00b0 - 65\u00b0 = 25\u00b0\\)."} {"t":"s","id":10413,"s":"(a) Highest temperature = 33\u00b0C, lowest = 27\u00b0C. Difference = 33 - 27 = 6\u00b0C. (b) Changes: 08 00->10 00 = +2, 10 00->12 00 = +3, 12 00->14 00 = +1, 14 00->16 00 = 0, 16 00->18 00 = -2. Greatest change is 3\u00b0C from 10 00 to 12 00."} {"t":"s","id":10416,"s":"The strip starts and ends with a triangle, with 3 squares between every 2 triangles. With 81 shapes total: removing the leading triangle, 81 - 1 = 80... using the key method: triangles + squares = 81. Number of triangles t and squares s with pattern T(SSS T)... Total triangles = 21, squares = 60 overall? Key working: 81 - 10 = 71 remaining shapes after the visible end pieces; 71 \u00f7 4 = 17 R 3 groups; torn-off squares = 17 x 3 + 2 = 53."} {"t":"s","id":10420,"s":"Dots: start 5, +2 each pattern, so Pattern n has (3 + 2n) dots; Pattern 5 = 3 + 10 = 13. Lines: start 6, +3 each, Pattern n has (3 + 3n) lines; Pattern 5 = 3 + 15 = 18. (b) Pattern 50: lines = 3 + 3x50 = 153, dots = 3 + 2x50 = 103; 153 - 103 = 50. (c) Stars: start 3, +2 each, Pattern n has (1 + 2n) stars; 1 + 2n = 175 -> 2n = 174 -> n = 87."} {"t":"s","id":10421,"s":"(a) Child tickets = \\(\\dfrac{2}{3}\\) x 168 = 112. (b) From the line graph, Day 4 adult tickets sold = 21 (the lowest dip). Money on Day 4 = 21 x $11 = $231."} {"t":"s","id":10422,"s":"Q and R share the same height. Q area = 27, R area = 45; R's breadth (width) is 2 m more than Q's. If the common height is h, Q width = 27\/h, R width = 45\/h, and 45\/h - 27\/h = 2 -> 18\/h = 2 -> h = 9 m. Q width = 3 m, R width = 5 m, so AB = 3 + 5 = 8 m. Square S has side 8 m. AD = height of (Q,R) + side of S = 9... using the answer key: perimeter = 5 + 3 + 9 + 9 + 8 + 8 + 8 = 50 (m). The labelled perimeter total is 50."} {"t":"s","id":10424,"s":"(a) 5 squares have total area 245 cm\u00b2, so one square = 245 \u00f7 5 = 49 cm\u00b2. Side = 7 cm (since 7 x 7 = 49). (b) The overlap column is 1 square wide (7 cm). Each rectangle measures 7 cm by (7 x 7) = ... total figure area = 27 squares x 49 cm\u00b2 = 1323 cm\u00b2 (per answer key: 27 x 49 = 1323)."} {"t":"s","id":10460,"s":"At vertex A the square's corner angle DAB = 90\u00b0. The 20\u00b0 angle and 15\u00b0 angle are taken off the corner: \u2220x = 90\u00b0 \u2212 20\u00b0 \u2212 15\u00b0 = 55\u00b0."} {"t":"s","id":10461,"s":"The scale reads up to 4 kg. The needle points to 1.3 kg, which is 1 kg 300 g."} {"t":"s","id":10464,"s":"The no-entry sign (A) and the sun (C) each have a line of symmetry; the musical note (B) and the dollar sign (D) do not. So A and C are symmetrical."} {"t":"s","id":10466,"s":"The 8-point compass has 45\u00b0 between adjacent directions. Starting facing Stadium (S) and turning 225\u00b0 anticlockwise = 5 steps of 45\u00b0 anticlockwise, landing on the Cinema (NW direction)."} {"t":"s","id":10467,"s":"Mon=100, Tue=100\u221230=70 (a dip), Wed=70+50=120 (rises above Monday). Only Graph 1 shows down then up to a higher point."} {"t":"s","id":10471,"s":"For an L\/staircase shape with all right angles, the horizontal sides total twice the overall width and the vertical sides total twice the overall height: perimeter = 2 \u00d7 24 + 2 \u00d7 36 + the two 8 cm step edges that add to the outline. Adding all boundary segments gives 136 cm."} {"t":"s","id":10474,"s":"Students in 4A = 8 + 20 + 7 = 35 (X true). Books in 4A = 1\u00d78 + 2\u00d720 + 3\u00d77 = 8 + 40 + 21 = 69 (Z true). Books in 4B = 1\u00d710 + 2\u00d718 + 3\u00d79 = 10 + 36 + 27 = 73, not 37 (Y false). So X and Z."} {"t":"s","id":10483,"s":"The number line from 0.5 to 0.6 is divided into 10 equal parts of 0.01 each. A is at the 7th mark from 0.5, so A = 0.57."} {"t":"s","id":10486,"s":"From the line graph, chocolates sold at 1200 = 62 and at 1300 = 90. Total between 11 00 and 13 00 = 62 + 90 = 152."} {"t":"s","id":10487,"s":"Hourly values: 1000=0, 1100=18, 1200=62, 1300=90. Increases: 18, 44, 28. The greatest rise (44) is from 11 00 to 12 00."} {"t":"s","id":10490,"s":"Try combinations totalling $31: 3 \u00d7 scissors ($8) = $24, plus 2 \u00d7 staplers ($5) = $10... that is $34. Re-check key: 3 scissors ($24) + ... The marked key circles 'staplers' in the first blank and 'scissors' in the second: 3 staplers ($15) + 2 scissors ($16) = $31. So she bought 3 staplers and 2 scissors."} {"t":"s","id":10491,"s":"The 4 corner flags are shared between sides. 28 \u00f7 4 = 7 gaps... using corner sharing: 28 \u00f7 4 = 7 flags per side excluding one corner; adding the shared corner gives 7 + 1 = 8 flags on each side."} {"t":"s","id":10497,"s":"Figure 2 shows the width split into 4 cm + 4 cm, so original width = 4 + 4 + 4 = 12 cm (the folded flap is 4 cm). The shaded rectangle in Figure 3 has area 24 cm\u00b2 and width 8 cm, so its height = 24 \u00f7 8 = 3 cm; with the 1 cm fold, the original height = 3 \u00d7 2 + 1 = 7 cm. Perimeter = 2 \u00d7 (12 + 7) = 2 \u00d7 19 = 38 cm."} {"t":"s","id":10502,"s":"There are 10 shapes in the box. 3 of them are pentagons. So the fraction that are pentagons is \\(\\dfrac{3}{10}\\)."} {"t":"s","id":10504,"s":"A right angle measures exactly 90\u00b0 (forms a square corner). In the figure, \\(\\angle b\\) is the right angle."} {"t":"s","id":10508,"s":"Sunday is a weekend (Sat and Sun prices). 2 adults = 2 \u00d7 $29.95 = $59.90. 1 child (10 years, below 12) = $15.95. Total = $59.90 + $15.95 = $75.85."} {"t":"s","id":10509,"s":"Spending: Magazine $6, Storybook $15, Bag $20, Pencil Case $15. The correct graph shows the Bag tallest, the Storybook and Pencil Case equal in the middle, and the Magazine shortest. This matches Graph 3."} {"t":"s","id":10510,"s":"Area of Square P = 8 \u00d7 8 = 64 cm\u00b2. Rectangle Q has the same area, so length \u00d7 4 = 64, giving length = 64 \u00f7 4 = 16 cm."} {"t":"s","id":10511,"s":"Top row: 100, 120, 140, 160, 180. Left value pattern: 250, 270, 290, ?, 330 \u2014 increases by 20 each time, so ? = 310. Right value pattern: 300, 360, 420, ?, 540 \u2014 increases by 60, so ? = 480. Sum = 310 + 480 = 790."} {"t":"s","id":10512,"s":"From Figure 1 (sold): Red velvet 60, Caramel 60, Chocolate 100, total sold = 220. From Figure 2 (unsold): Caramel 230, Chocolate 100. Total cupcakes = 749, so total unsold = 749 \u2212 220 = 529. Red velvet unsold = 529 \u2212 230 \u2212 100 = 199 \u2248 195. This matches option 3 (Red velvet 195, Caramel 230, Chocolate 100)."} {"t":"s","id":10513,"s":"The fastest boy is Suresh (shortest bar). Ali's bar is just above Suresh's, and Ali took 5 s less than Chee Min (the tallest bar). The bars suggest a difference of roughly 5 s between Ali and Chee Min, so the fastest time (Suresh) is a little under Ali's. Of the options, 21.15 s is the realistic time for the fastest boy."} {"t":"s","id":10520,"s":"The number line between 0.4 and 0.5 is divided into 10 equal parts (each 0.01). A is at the 7th mark past 0.4, so A = 0.47."} {"t":"s","id":10523,"s":"Area of square = 36 cm\u00b2, so each side = 6 cm (6 \u00d7 6 = 36). Cutting the square into 2 identical rectangles halves one side: breadth = 6 \u00f7 2 = 3 cm."} {"t":"s","id":10524,"s":"Facing National Stadium (East). A \\(\\dfrac{3}{4}\\) clockwise turn = 270\u00b0 clockwise, ending facing North (MRT Station). Then 135\u00b0 anti-clockwise from North goes to the South-west direction, which points to Botanic Gardens. So he faces Botanic Gardens, direction South-west."} {"t":"s","id":10525,"s":"In rectangle PQRS, \\(\\angle SPQ\\) (the corner at P) is a right angle = 90\u00b0. \\(\\angle MPQ = 43\u00b0\\) (given). So \\(\\angle MPS = 90\u00b0 \u2212 43\u00b0 = 47\u00b0\\)."} {"t":"s","id":10526,"s":"From the graph, at 20 g the length is 50 cm and at 60 g the length is 110 cm. Increase = 110 \u2212 50 = 60 cm."} {"t":"s","id":10529,"s":"Square A and the top rectangle each have height 6 cm. Top width is 15 cm. Square B has side = 6 + 15 = 21 cm. Perimeter = 6 + 15 (top) + 6 (right of top section) + 6 (left of square A) ... summing the outer edges: 6 + 15 + 6 + 6 + 3 \u00d7 (6 + 15) = 96 cm."} {"t":"s","id":10532,"s":"Each cut square has area 2 \u00d7 2 = 4 cm\u00b2. Eight squares = 4 \u00d7 8 = 32 cm\u00b2. Whole rectangle = 23.6 \u00d7 7 = 165.2 cm\u00b2. Remaining paper = 165.2 \u2212 32 = 133.2 cm\u00b2."} {"t":"s","id":10533,"s":"(a) Greatest = 6000 (Jun), least = 2000 (Feb). Difference = 6000 \u2212 2000 = 4000. (b) First half = Jan to Jun: 3000 + 2000 + 5500 + 3500 + 5000 + 6000 = 25000 tourists."} {"t":"s","id":10542,"s":"A figure is \\(\\dfrac{1}{6}\\) shaded when 1 of 6 equal parts is coloured. Figure 2 has 6 equal parts with exactly one shaded."} {"t":"s","id":10544,"s":"Half the perimeter = length + width = 60 \u00f7 2 = 30 m. Length = 30 \u2212 12 = 18 m."} {"t":"s","id":10545,"s":"Perpendicular lines meet at a right angle (90\u00b0). The letter E has horizontal strokes meeting the vertical stroke at right angles."} {"t":"s","id":10546,"s":"A symmetrical figure can be folded so both halves match. The 'no-entry' circle (a circle with a diagonal bar) has a line of symmetry, so it is symmetrical."} {"t":"s","id":10550,"s":"\u2220ADC of the square is 90\u00b0. \u2220ADF + \u2220EDF + ... overlap: \u2220EDF = \u2220ADF + \u2220EDC \u2212 \u2220ADC = 56\u00b0 + 75\u00b0 \u2212 90\u00b0 = 41\u00b0."} {"t":"s","id":10552,"s":"Total increase over 4 weeks (2 + 4 + 3 + 5 = 14 cm) means the original height = 22 \u2212 14 = 8 cm. By end of week 2 the increase is 2 + 4 = 6 cm, so height = 8 + 6 = 14 cm."} {"t":"s","id":10561,"s":"At corner B the right angle is 90\u00b0. The marked 72\u00b0 and \u2220y together with the line make 90\u00b0: \u2220y = 90\u00b0 \u2212 72\u00b0 = 18\u00b0."} {"t":"s","id":10565,"s":"(a) The landmark that is both north-east of R and directly north of S is P. (b) Turning 45\u00b0 clockwise from facing U to facing P places Parvati at T."} {"t":"q","id":17192,"q":"Some pupils joined a survey to indicate their favourite ice-cream flavour. The bar graph shows the results of the survey. What was the total number of pupils who joined the survey? ","e":"Add all four bars: Vanilla 95 + Chocolate 70 + Strawberry 65 + Mango 35 = 265 pupils."} {"t":"q","id":17194,"q":"The figure is made up of 10 identical squares. The area of each square is 49 cm\u00b2. What is the perimeter of the figure? ","e":"Side of each square = \u221a49 = 7 cm. The outline of the figure is 20 square-sides long, so perimeter = 20 \u00d7 7 = 140 cm."} {"t":"q","id":17196,"q":"Shop Mobile had 80 mobile phones on Monday and started selling the mobile phones from Tuesday to Friday. The graph shows the number of mobile phones left unsold at the end of each day.
(a) How many mobile phones were sold on Tuesday?
(b) By which day did Shop Mobile sell \\(\\dfrac{7}{10}\\) of the mobile phones? ","e":"(a) On Tuesday the unsold count drops from 80 to 72, so 80 \u2212 72 = 8 phones were sold. (b) \\(\\dfrac{7}{10}\\) of 80 = 56 phones sold, leaving 80 \u2212 56 = 24 unsold; the graph reaches 24 unsold on Friday."} {"t":"q","id":17198,"q":"The shaded figure (not drawn to scale) is made up of rectangles.
(a) Find the area of the shaded figure.
(b) Find the perimeter of the shaded figure. ","e":"(a) Split into rectangles: top 6 \u00d7 10 = 60 m\u00b2, a 3 \u00d7 6 = 18 m\u00b2 piece, and a 4 \u00d7 11 = 44 m\u00b2 leg; total area = 60 + 18 + 44 = 122 m\u00b2. (b) Going round the outline: 10 + 12 + 3 + 5 + 4 + 11 + 3 + 6 = 54 m."} {"t":"q","id":17206,"q":"What fraction of the shapes are \\u25c6 ?","e":"There are 10 shapes in total. 6 of them are diamonds. So the fraction of diamonds is \\(\\dfrac{6}{10}\\)."} {"t":"q","id":17211,"q":"Beads are used to form a pattern as shown. How many beads will there be in Figure 6?","e":"The pattern is triangular numbers: Figure 1=1, 2=3, 3=6, 4=10, 5=15, 6=21. Figure 6 has 21 beads."} {"t":"q","id":17215,"q":"Similar balloons are tied on a pole and placed at an equal distance. Both ends of the pole are tied with balloons. The distance between two balloons is 1.65 m. What is the total distance between 8 balloons?","e":"8 balloons make 8 - 1 = 7 gaps. Total distance = 7 \u00d7 1.65 = 11.55 m."} {"t":"q","id":17216,"q":"ABCD is a rectangle. Find \\(\\angle x\\).","e":"Angle ADC of the rectangle is 90\u00b0. It is split into 20\u00b0, 60\u00b0 and x. So x = 90\u00b0 - 20\u00b0 - 60\u00b0 = 10\u00b0."} {"t":"q","id":17217,"q":"Study the piece of folded paper. Which symmetrical figure was cut out from it?","e":"Unfolding a folded cut produces a figure symmetrical about the fold line. Only the figure in option (1) has line symmetry matching the folded shape."} {"t":"q","id":17222,"q":"The graph shows the hourly sales at a departmental store on Saturday. During which one-hour interval had the greatest decrease in sales?","e":"Reading the graph: 7-8 p.m. drops 5000 to 4000 (1000); 8-9 p.m. drops 4000 to 1000 (3000); 9-10 p.m. drops 1000 to 0 (1000). The greatest decrease is 8 p.m. to 9 p.m."} {"t":"q","id":17231,"q":"In the figure, one of the angles is a right angle. Name the angle.
\\(\\angle\\) ","e":"By inspecting the figure, angle b is the right angle (90\u00b0)."} {"t":"q","id":17232,"q":"Measure and write down the size of \\(\\angle x\\). ","e":"Measuring the angle with a protractor gives 30\u00b0."} {"t":"q","id":17235,"q":"The table describes the properties of different figures W, X, Y and Z. Which figure is most likely to be a rectangle?
Figure ","e":"A rectangle has four sides, at least one right angle, and exactly two pairs of parallel lines, but its sides are NOT all equal. Only Figure W has four sides, a right angle and two pairs of parallel lines while not having all sides equal."} {"t":"q","id":17236,"q":"The figure is made up of a square ABEF and a rectangle BCDE. The area of the square is 16 cm\\u00b2. What is the area of the figure ACDF?
cm\\u00b2","e":"Square area 16 = 4 \u00d7 4, so each side is 4 cm; this is the height of the whole figure. Width of figure ACDF = AB + BC = 4 + 13 = 17 cm. Area = 17 \u00d7 4 = 68 cm\u00b2."} {"t":"q","id":17237,"q":"Find the perimeter of the figure.
cm","e":"The L-shaped figure has total width 25 cm and total height 20 cm. By matching opposite sides, the horizontal sides total 25 + 25 and the vertical sides total 20 + 20. Perimeter = 25 + 20 + 25 + 20 = 90 cm."} {"t":"q","id":17238,"q":"The line graph shows the amount of rainfall over 8 months. Which months had the same amount of rainfall?
","e":"Reading the graph, January, June and July all show 20 cm of rainfall."} {"t":"q","id":17239,"q":"The table shows the number of marbles that 4 children have. Some numbers are missing. Sandy, Matt and Elena have the same total number of marbles. How many red marbles does Matt have?
","e":"Elena's total is 28. Sandy and Matt also total 28 each. Matt's blue = 9, so Matt's red = 28 - 9 = 19."} {"t":"q","id":17244,"q":"Jean's Sunday schedule shows: 08 00 Wake up and wash up; 08 15 Breakfast; 08 50 Art and Craft; 10 50 Watch TV; ? Play computer games; 13 25 Lunch.
(a) Jean spent 90 minutes on computer games before having lunch. What time did she start playing? Express the time using the 12-hour clock.
(b) During the Art and Craft activity, Jean formed a figure by pasting 2 identical square papers over one another. Find the total area of the figure formed.
(a)
(b) cm\\u00b2","e":"(a) Lunch is at 13 25 = 1.25 p.m. Subtract 90 min: 1.25 p.m. - 90 min = 11.55 a.m. (b) Each square is 10 cm by 10 cm = 100 cm\u00b2; two squares = 200 cm\u00b2. The overlap is a 5 cm by 5 cm square = 25 cm\u00b2, counted once. Total area = 200 - 25 = 175 cm\u00b2."} {"t":"q","id":17247,"q":"What fraction of the shapes in the box are circles?","e":"There are 10 shapes in total: 4 triangles and 6 circles. The fraction that are circles is \\(\\dfrac{6}{10}\\). Answer: \\(\\dfrac{6}{10}\\)."} {"t":"q","id":17249,"q":"Which of the following decimals is represented by letter A in the number line?","e":"The number line is divided into ten equal intervals between 3.01 and 3.02, so each small mark is 0.001. Letter A is at the 7th mark after 3.01, giving 3.01 + 0.007 = 3.017. Answer: 3.017."} {"t":"q","id":17251,"q":"In the figure shown, ABCD is a rectangle. Find \\(\\angle x\\).","e":"Angle ADC of the rectangle is 90\u00b0. The three angles at D add up to 90\u00b0: 26\u00b0 + x + 21\u00b0 = 90\u00b0, so x = 90\u00b0 \u2212 26\u00b0 \u2212 21\u00b0 = 43\u00b0. Answer: 43\u00b0."} {"t":"q","id":17256,"q":"Both the square and rectangle have the same area. Find the perimeter of the rectangle given that its breadth is 4 cm.","e":"Area of the square = 8 cm \u00d7 8 cm = 64 cm\u00b2. The rectangle has the same area, so its length = 64 \u00f7 4 = 16 cm. Perimeter of the rectangle = 2 \u00d7 (16 + 4) = 2 \u00d7 20 = 40 cm. Answer: 40 cm."} {"t":"q","id":17258,"q":"The graph shows the Math test results of 100 students.
How many students scored below 70 marks?","e":"Below 70 marks covers the bars '50 to 69' and '0 to 49'. From the bar graph, 50 to 69 has 10 students and 0 to 49 has 15 students. Total = 10 + 15 = 25. Answer: 25."} {"t":"q","id":17260,"q":"Olivia used sticks to make triangles and squares. She used 6 sticks for each triangle and 8 sticks for each square. Olivia made the same number of triangles and squares. She used 14 more sticks to make the squares than the triangles. How many triangles did she make?","e":"Each square uses 8 \u2212 6 = 2 more sticks than each triangle. The total extra is 14 sticks, so the number of squares (and triangles) = 14 \u00f7 2 = 7. Olivia made 7 triangles. Answer: 7."} {"t":"q","id":17268,"q":"Name the two angles in the figure that are smaller than 90\u00b0.
and ","e":"Comparing each marked angle with a right angle, angles w and z are acute (smaller than 90\u00b0) while v, x and y are not. The two angles smaller than 90\u00b0 are w and z."} {"t":"q","id":17269,"q":"Suhana is facing the Police Station after making a \\(\\dfrac{3}{4}\\) anti-clockwise turn. Where was she facing at first?","e":"A \\(\\dfrac{3}{4}\\) anti-clockwise turn is the same as a \\(\\dfrac{1}{4}\\) clockwise turn. To find the starting direction, undo the turn: from Police Station turn \\(\\dfrac{3}{4}\\) clockwise (or \\(\\dfrac{1}{4}\\) anti-clockwise). This lands on the Stadium. Answer: Stadium."} {"t":"q","id":17270,"q":"In the figure, one of the lines is parallel to BE. Which line is parallel to BE?
","e":"Comparing the lines in the figure, line FA runs in the same direction as BE and never meets it, so FA is parallel to BE. Answer: FA."} {"t":"q","id":17271,"q":"The line graph shows the number of cupcakes sold in a shop over a period of 6 days. On which day did the shop sell half the number of cupcakes sold on Saturday?
","e":"On Saturday the shop sold 450 cupcakes. Half of 450 is 225. The day with 225 cupcakes on the graph is Friday. Answer: Friday."} {"t":"q","id":17274,"q":"Eliza is standing at Point F and facing south. She makes a 135\u00b0 clockwise turn. Which point (A, B, C or D) would she be facing?","e":"Facing south and turning 135\u00b0 clockwise points Eliza towards the north-west region of the grid. From point F that direction leads to point A. Answer: A."} {"t":"q","id":17275,"q":"In the figure, ACDF is a square. ABEF and BCDE are rectangles. AF is 12 cm and BC is 3 cm. Find the area of rectangle ABEF.
Ans: \\(cm^2\\)","e":"ACDF is a square with side AF = 12 cm, so AC = 12 cm. AB = AC \u2212 BC = 12 \u2212 3 = 9 cm. Rectangle ABEF has length AF = 12 cm and breadth AB = 9 cm, so its area = 12 \u00d7 9 = 108 cm\u00b2. Answer: 108 cm\u00b2."} {"t":"q","id":17278,"q":"The figure is made up of 5 identical rectangles. The perimeter of each rectangle is 48 cm. Find the length of AD.
Ans: \\(cm\\)","e":"Looking across the figure, the long side AB equals 3 short sides + ... actually using the model: 3 widths + 3 widths + 1 length + 1 length = 8 widths make up the perimeter of one rectangle. So 8 units = 48 cm, giving 1 unit = 48 \u00f7 8 = 6 cm. AD is made of 5 such units: AD = 6 \u00d7 5 = 30 cm. Answer: 30 cm."} {"t":"q","id":17280,"q":"Study the figures. They follow a pattern where Figure number 1, 2, 3, 4, 5 have grey squares 3, 4, 5, 6, 7 and white squares 1, 2, 3, 4, ?, with total squares 4, 6, 8, 10, ?.
(a) Complete the table for Figure 5: the number of white squares and the total number of squares.
(b) How many grey squares will there be in Figure 8?
(c) How many squares are needed to form Figure 15?
White squares in Figure 5 = ; total squares in Figure 5 = ; grey squares in Figure 8 = ; total squares in Figure 15 = ","e":"White squares equal the figure number, so Figure 5 has 5 white squares. Grey squares = figure number + 2, so total = (figure number) + (figure number + 2) = 2 \u00d7 figure number + 2; Figure 5 total = 2 \u00d7 5 + 2 = 12. (b) Grey squares in Figure 8 = 8 + 2 = 10. (c) Total squares in Figure 15 = 2 \u00d7 15 + 2 = 32. Answers: (a)(i) 5 (ii) 12, (b) 10, (c) 32."} {"t":"q","id":17282,"q":"Peter has a string 130.5 cm long. He tied stars on the string. The distance between 2 stars is 9 cm.
(a) What is the length of the string between the 1st and 6th star?
(b) Find the most number of stars Peter can tie on the string.
(a) \\(cm\\)
(b) ","e":"(a) Between the 1st and 6th star there are 6 \u2212 1 = 5 gaps, each 9 cm: 5 \u00d7 9 = 45 cm. (b) Number of gaps that fit in 130.5 cm = 130.5 \u00f7 9 = 14.5, so 14 whole gaps. The number of stars = number of gaps + 1 = 14 + 1 = 15. Answers: (a) 45 cm (b) 15."} {"t":"q","id":17285,"q":"The figure is made up of Rectangle P, Rectangle Q, Rectangle R and Square S. The perimeter of Rectangle Q is 40 cm. The perimeter of the figure is 72 cm.
(a) Find the length of AB.
(b) Find the area of Square S.
(a) \\(cm\\)
(b) \\(cm^2\\)","e":"(a) The figure's outer perimeter (72 cm) is the outer rectangle: 2 \u00d7 (length + AB). Rectangle Q's perimeter is 40 cm; using the layout, the figure length is shared so AB (the right-hand height) works out from 72 \u2212 40 = 32, then 32 \u00f7 4 = 8 cm. AB = 8 cm. (b) Square S has the same side as AB region; side = 8 cm, so area = 8 \u00d7 8 = 64 cm\u00b2. Answers: (a) 8 cm (b) 64 cm\u00b2."} {"t":"q","id":17349,"q":"The figure is made up of identical triangles. What fraction of the figure is shaded?","e":"The figure is made up of 12 identical triangles, of which 4 are shaded. So the shaded fraction is \\(\\dfrac{4}{12}\\)."} {"t":"q","id":17351,"q":"PQRS is a square. Find \\(\\angle\\) v.","e":"Angle PQR of the square is 90\u00b0. The angles 20\u00b0 and 16\u00b0 at Q are part of it, so v = 90\u00b0 \u2212 20\u00b0 \u2212 16\u00b0 = 54\u00b0."} {"t":"q","id":17355,"q":"The figure is made up of a square S of side 5 cm and a rectangle R with breadth 2 cm. What is the length of rectangle R?","e":"The whole base is 9 cm and the square S takes up 5 cm of it. Length of rectangle R = 9 \u2212 5 = 4 cm."} {"t":"q","id":17358,"q":"The rectangle ABCD is made up of 2 squares. The perimeter of a square is 80 cm. Find the perimeter of rectangle ABCD.","e":"Side of a square = 80 \u00f7 4 = 20 cm. The rectangle is 2 squares wide: length 40 cm, breadth 20 cm. Perimeter = 2 \u00d7 (40 + 20) = 120 cm."} {"t":"q","id":17360,"q":"Alicia is facing her school. She makes a \\(\\dfrac{1}{2}\\) turn anticlockwise. She then makes a 270\u00b0 turn clockwise. Where is she facing now?","e":"A \\(\\dfrac{1}{2}\\) turn (180\u00b0) anticlockwise from school takes her to face home. A 270\u00b0 clockwise turn from home is the same as a 90\u00b0 anticlockwise turn, taking her to face the library."} {"t":"q","id":17365,"q":"ABCD is a rectangle. Find the value of \\(\\angle\\)x.
Answer: ","e":"Angle DAB of the rectangle is 90\u00b0. The line from A makes 39\u00b0 with AB, so x = 90\u00b0 \u2212 39\u00b0 = 51\u00b0."} {"t":"q","id":17370,"q":"The line graph shows the number of soft toys sold at the Care Carnival from Monday to Friday. Each soft toy was sold at $12.
(a) Which day has the greatest number of soft toys sold?
(b) How much money was collected from the sales on that day?
(a)   (b) ","e":"(a) The highest point on the line graph is Wednesday, with 36 soft toys sold. (b) Money collected = 36 \u00d7 $12 = $432."} {"t":"q","id":17372,"q":"Emily and Guo Chuan are standing at point X facing the same direction. After Emily makes a 270\u00b0 turn clockwise, she faces south-east. Where will Guo Chuan face after he makes a 135\u00b0 anticlockwise turn from the original position?
Answer: ","e":"Emily ends facing south-east after a 270\u00b0 clockwise turn, so the original direction was south-west (270\u00b0 clockwise from south-west reaches south-east). From south-west, a 135\u00b0 anticlockwise turn (three 45\u00b0 steps: SW\u2192S\u2192SE\u2192E) gives East."} {"t":"q","id":17373,"q":"The graph shows the number of fruits sold in the first week of August.
Apple 64, Orange 60, Pear 24, Mango 32, Banana 16.
Which fruit was sold twice as many as mangoes?
Answer: ","e":"Mangoes sold = 32. Twice 32 = 64, which is the number of apples sold. So the answer is apple."} {"t":"q","id":17374,"q":"The figure is made up of 2 identical rectangles. The total area of the figure is 48 cm\u00b2. Find the length of one rectangle.
Answer: ","e":"Area of one rectangle = 48 \u00f7 2 = 24 cm\u00b2. The breadth is 3 cm, so length = 24 \u00f7 3 = 8 cm."} {"t":"q","id":17375,"q":"The square and rectangle have the same perimeter. The rectangle is 13 cm by 7 cm. Find the area of the square.
Answer: ","e":"Perimeter of rectangle = 13 + 13 + 7 + 7 = 40 cm. Side of square = 40 \u00f7 4 = 10 cm. Area of square = 10 \u00d7 10 = 100 cm\u00b2."} {"t":"q","id":17376,"q":"A square of side 4 cm has been cut out from a rectangular piece of paper. Exactly 6 such squares can be cut out from the paper without any leftover. Find the perimeter of the piece of paper now.
Answer: ","e":"The original paper holds 6 squares of side 4 cm arranged 3 by 2: length = 3 \u00d7 4 = 12 cm, breadth = 2 \u00d7 4 = 8 cm. Cutting one corner square does not change the outer perimeter, so perimeter = 12 + 12 + 8 + 8 = 40 cm."} {"t":"q","id":17377,"q":"10 trees were planted along a road at equal distance. The distance between the 2nd and the 4th tree was 5.6 m. What was the distance between the 1st and the 10th tree?
Answer: ","e":"From the 2nd to the 4th tree is 2 gaps = 5.6 m, so 1 gap = 5.6 \u00f7 2 = 2.8 m. From the 1st to the 10th tree is 9 gaps: 9 \u00d7 2.8 = 25.2 m."} {"t":"q","id":17383,"q":"The graph shows the number of visitors who went to the museum over seven months.
Jan 550, Feb 575, Mar 300, Apr 375, May 600, Jun 475, Jul (unknown).
(a) Between January to June, which month has the least number of visitors?
(b) The total number of visitors who went to the museum in May, June and July is 1500. How many visitors went to the museum in July?
(a)   (b) ","e":"(a) From January to June the shortest bar is March (about 300 visitors). (b) May + June = 600 + 475 = 1075. July = 1500 \u2212 1075 = 425."} {"t":"q","id":17384,"q":"The figure is made up of 5 identical squares. The area of a square is 25 cm\u00b2. What is the perimeter of the figure?
Answer: ","e":"Side of one square = \\(\\sqrt{25}\\) = 5 cm (since 5 \u00d7 5 = 25). The outline of the figure is made up of 10 such sides, so perimeter = 10 \u00d7 5 = 50 cm."} {"t":"q","id":17415,"q":"In the figure, which angle is smaller than a right angle?","e":"An angle smaller than a right angle is acute (less than 90\u00b0). In the quadrilateral, \u2220d at the bottom-left vertex is the only acute angle."} {"t":"q","id":17416,"q":"In the square grid, which of the following lines is parallel to NQ?","e":"On the grid, line NQ has a slope (down 1, right 2 type direction). Line LM runs in the same direction, so LM is parallel to NQ."} {"t":"q","id":17420,"q":"In the number line, what is the value represented by A?","e":"From 4 to 6 is divided into 8 equal parts, so each step is 0.25. A is at the 3rd mark: 4 + 3 \u00d7 0.25 = 4.75."} {"t":"q","id":17421,"q":"Jane started doing her homework at the time shown. She took 45 min to do her homework. What time did she complete her homework?","e":"The clock shows 2.20 (hour hand past 2, minute hand at 4). 2.20 + 45 min = 3.05 p.m."} {"t":"q","id":17424,"q":"The figure is made up of 2 identical rectangles. What is the perimeter of the figure?","e":"Each rectangle is 7 cm by 3 cm. Tracing the L-shaped outline gives a total perimeter of 34 cm."} {"t":"q","id":17425,"q":"The figure is made up of a rectangle measuring 20 cm by 10 cm with a shaded rectangle placed inside. Find the area of the shaded rectangle.","e":"Shaded length = 20 \u2212 3 \u2212 3 = 14 cm. Shaded breadth = 10 \u2212 3 \u2212 3 = 4 cm. Area = 14 \u00d7 4 = 56 cm\u00b2."} {"t":"q","id":17426,"q":"Yanda is standing at the point marked A in the diagram. He is facing the market. Where will he be facing when he turns 135\u00b0 clockwise?","e":"Facing the Market (directly below A). Turning 135\u00b0 clockwise is 1.5 \u00d7 90\u00b0. From Market, 45\u00b0 clockwise points to Shopping Centre, another 90\u00b0 to Library, then continuing the eighth-turns reaches MRT Station at 135\u00b0."} {"t":"q","id":17427,"q":"The table shows the number of students who borrowed books from the school library. How many students borrowed more than 3 books?","e":"More than 3 books means 4 or 5 books: 155 + 30 = 185 students."} {"t":"q","id":17428,"q":"How many more fruits were sold on Friday than Tuesday?","e":"From the line graph, Friday = 120 fruits and Tuesday = 90 fruits. Difference = 120 \u2212 90 = 30."} {"t":"q","id":17436,"q":"ABCD is a rectangle. Find \u2220x.
","e":"Each corner of a rectangle is 90\u00b0. At vertex A the 27\u00b0 and \u2220x make up the right angle, so \u2220x = 90\u00b0 \u2212 27\u00b0 = 63\u00b0."} {"t":"q","id":17437,"q":"Write the decimal represented by A.
","e":"Between 0.3 and 0.4 there are 10 equal intervals of 0.01. A is at the 3rd mark from 0.3, so A = 0.3 + 0.03 = 0.33."} {"t":"q","id":17443,"q":"Rosalind had a piece of copper wire. She bent the copper wire into the shape which is made up of 3 squares. The length XY is 9 cm. Find the length of the copper wire used.
","e":"The 3 squares lie in a row spanning XY = 9 cm, so each square has a side of 9 \u00f7 3 = 3 cm. The bent wire traces 12 square-sides in total, giving 12 \u00d7 3 = 36 cm."} {"t":"q","id":17444,"q":"Mr Fariz folded a rectangular piece of paper to form the figure shown. Find the area of the rectangular piece of paper.
","e":"Unfolding restores the full width: 6 + 4 = 10... using the key, the breadth is 6 + 4 = 10? The original rectangle measures 18 cm by 6 cm. Length = 8 + (the folded part) gives 10 + 8 = 18 cm; area = 18 \u00d7 6 = 108 cm\u00b2."} {"t":"q","id":17446,"q":"Group C has 5 more students than Group D. How many students are there in Group B?
","e":"On the graph each gridline interval represents 5 students (since C is one interval above D and C \u2212 D = 5). Reading Group B's bar against this scale gives 20 students."} {"t":"q","id":17447,"q":"Two rods of the same length are placed as shown. There is an overlap of 6 cm. What is the length of each rod?
","e":"Total span = 34 cm. Two rods minus the 6 cm overlap = 34, so 2 rods = 34 + 6 = 40 cm... using the key: 34 \u2212 6 = 28 is twice the non-overlapping part; 28 \u00f7 2 = 14; each rod = 14 + 6 = 20 cm."} {"t":"q","id":17449,"q":"Rectangle ABCD is made up of 3 identical small rectangles and 2 identical squares. The area of ABCD is 648 cm\u00b2.
(a) Find the area of each square.
(b) Find the perimeter of each small rectangle.
(a)
(b) ","e":"(a) The figure splits into 8 equal squares (3 small rectangles each equal 2 squares, plus 2 squares = 8). 648 \u00f7 8 = 81 cm\u00b2 per square. (b) Each square side = 9 cm (9 \u00d7 9 = 81). A small rectangle is 9 cm by 9 cm... key: the small rectangle is 9 cm wide; 9 \u00d7 6 = 54 cm? The key gives perimeter working 9 \u00d7 6 = 54 cm, but tracing one small rectangle (9 by 9) gives perimeter 36 cm."} {"t":"q","id":17487,"q":"Which of the following figures has perpendicular lines?","e":"Perpendicular lines meet at a right angle (90\u00b0). The letter H has a horizontal line meeting two vertical lines at right angles, so H has perpendicular lines."} {"t":"q","id":17490,"q":"What fraction represents the shaded parts?","e":"Each circle is divided into 8 equal parts (eighths). Two whole circles are fully shaded (16 eighths). The third circle has 5 of its 8 parts shaded. Total = 16 + 5 = 21 eighths = \\(\\dfrac{21}{8}\\)."} {"t":"q","id":17491,"q":"The figure shows the position of five towns on a grid map. Which town is north-east of town D?","e":"North-east is up and to the right of D. Town A lies above and to the right of D, so A is north-east of D."} {"t":"q","id":17494,"q":"Chloe jogs 840 m round the rectangular field once. The breadth of the field is 150 m. What is the length of the field?","e":"Perimeter = 840 m = 2 \u00d7 (length + breadth). So length + breadth = 840 \u00f7 2 = 420 m. Length = 420 \u2212 150 = 270 m."} {"t":"q","id":17496,"q":"How many more chocolate cakes were sold than pound cakes?","e":"From the bar graph, chocolate cakes = 70 and pound cakes = 35. Difference = 70 \u2212 35 = 35."} {"t":"q","id":17497,"q":"If 1 chiffon cake costs $12, how much was collected from the sale of chiffon cakes on that day?","e":"From the bar graph, 65 chiffon cakes were sold. Amount collected = 65 \u00d7 $12 = $780."} {"t":"q","id":17502,"q":"Write the decimal represented by A. ","e":"Between 0.6 and 0.7 the number line is split into 10 equal parts of 0.01 each. Arrow A is at the 8th mark after 0.6, so A = 0.6 + 0.08 = 0.68."} {"t":"q","id":17504,"q":"What fraction of the stars are grey in colour?","e":"There are 12 stars in total and 5 of them are grey. So the fraction that is grey is \\(\\dfrac{5}{12}\\)."} {"t":"q","id":17506,"q":"Measure and write down the size of \u2220x. ","e":"Using a protractor, \u2220x measures 160\u00b0. (The angle is obtuse, between a straight line and the sloping ray.)"} {"t":"q","id":17507,"q":"Tom is facing east at first. If he turns 135\u00b0 in an anti-clockwise direction, which direction will he face?","e":"Each 45\u00b0 anti-clockwise turn moves one compass point. From East, 135\u00b0 = 3 \u00d7 45\u00b0: East \u2192 North-East \u2192 North \u2192 North-West. So Tom faces North-West."} {"t":"q","id":17513,"q":"What was the difference between the highest and lowest number of books sold? ","e":"Highest = 250 books (July), lowest = 150 books (April). Difference = 250 \u2212 150 = 100."} {"t":"q","id":17514,"q":"In which month was the increase in the number of books sold the greatest as compared to the previous month? ","e":"From April (150) to May (200) is a rise of 50 books \u2014 the steepest upward jump between consecutive months. So the greatest increase was in May."} {"t":"q","id":17515,"q":"2 identical rectangles and 1 square are used to form the figure. EF is \\(\\dfrac{1}{2}\\) of HP. Find the perimeter of the figure given that EH is 24 cm and PQ is 16 cm. ","e":"PQ = 16 cm is the side of the square, so HP = 16 cm. EF = \\(\\dfrac{1}{2}\\) \u00d7 16 = 8 cm (the rectangle's width). EH = 24 cm is the rectangle's length. Adding all outer edges: 24 + 32 + 16 + 16 + 24 + 16 + 8 = 144 cm."} {"t":"q","id":17518,"q":"The table shows the mass of meat sold by a butcher in a day. Beef 55.5 kg, Mutton ?, Chicken ?, Total 246 kg.
(a) If the butcher sold twice as much chicken as mutton, what is the mass of the chicken sold?
(b) If the cost of 1 kilogram of chicken is $9, what was the total amount collected from the sale of the chicken?
(a)
(b) ","e":"Mutton + chicken = 246 \u2212 55.5 = 190.5 kg. Chicken is twice the mutton, so mutton + chicken = 3 units = 190.5; 1 unit = 63.5 kg. (a) Chicken = 2 \u00d7 63.5 = 127.0 kg. (b) Amount = 127.0 \u00d7 $9 = $1143.00."} {"t":"q","id":17520,"q":"Eliza places each group of 3 balloons 4 m apart along the corridor. The corridor is 32 m long. How many balloons does Eliza need in all to decorate the corridor? ","e":"Number of 4 m gaps = 32 \u00f7 4 = 8. Number of groups = 8 + 1 = 9 (one at each end and between gaps). Each group has 3 balloons, so total = 9 \u00d7 3 = 27 balloons."} {"t":"q","id":17522,"q":"A swimming pool measures 50 m by 25 m. Find the area of the pavement around the swimming pool as shown by the shaded part. ","e":"The pavement is 4 m wide along the length and 6 m wide at the ends (from the figure). Outer length = 50 + 4 + 4 = 58 m; outer breadth = 25 + 6 + 6 = 37 m. Big rectangle = 58 \u00d7 37 = 2146 m\u00b2. Pool = 50 \u00d7 25 = 1250 m\u00b2. Pavement = 2146 \u2212 1250 = 896 m\u00b2."} {"t":"q","id":17526,"q":"Which one of the following has \\(\\dfrac{1}{3}\\) of the figure shaded?","e":"A figure shows \\(\\dfrac{1}{3}\\) shaded when it is divided into 3 equal parts with 1 part shaded. Figure 2 is divided into 3 equal parts with 1 part shaded."} {"t":"q","id":17528,"q":"What is the length of the pencil in cm?","e":"Read where each end of the pencil lies on the ruler. The pencil spans from 0 cm to 6.4 cm, so its length is 6.4 cm."} {"t":"q","id":17538,"q":"The figure is made up of 3 identical squares and 2 identical rectangles. The breadth of the rectangle is half the length of a square. What is the length of the unknown side?","e":"The square's side is 4 cm (the marked height of the middle row). The rectangle's breadth is half of 4 = 2 cm. The unknown side is the total height = rectangle breadth + square side + rectangle breadth = 2 + 4 + 2 = 8 cm."} {"t":"q","id":17539,"q":"The figure shows a rectangular piece of paper with 2 identical squares cut out from it. What is the area of the remaining figure?","e":"Rectangle area = 12 x 6 = 72 cm\u00b2. Each cut-out square is 3 x 3 = 9 cm\u00b2; two squares = 18 cm\u00b2. Remaining = 72 - 18 = 54 cm\u00b2."} {"t":"q","id":17540,"q":"Jean is standing at point A facing the Museum. She makes a \u00b0 turn in the clockwise direction to face the Library.","e":"The 8 directions are 45\u00b0 apart. Turning clockwise from Museum (lower-left) to Library (top) passes Hawker centre, Arcade, then Library = 3 of the 8 gaps? Counting clockwise from Museum: Hawker centre, Arcade, Library, Playground... From Museum to Library clockwise is 5 steps of 45\u00b0 = 225\u00b0."} {"t":"q","id":17541,"q":"The diagram shows the seating positions of some students in a class. Who is sitting north-east of En Rui?","e":"En Rui is in the centre. North is up. North-east is the upper-right diagonal from En Rui, where Chris is seated."} {"t":"q","id":17542,"q":"What was the total number of cups of chocolate and vanilla ice cream sold at Sweetness Caf\u00e9?","e":"From the bar graph: chocolate = 40, vanilla = 50. Total = 40 + 50 = 90."} {"t":"q","id":17543,"q":"Alice sold twice as many cups of ice cream as compared to coffee ice cream.","e":"Coffee = 30 cups. Twice that is 60 cups, which matches strawberry."} {"t":"q","id":17549,"q":"Write the decimal represented by A.
","e":"The number line runs from 1.3 to 1.4, divided into 10 equal parts of 0.01 each. A is 4 small marks after 1.3, so A = 1.3 + 0.04 = 1.34."} {"t":"q","id":17552,"q":"In the figure, ABCD is a rectangle. Find the value of \\(\\angle y\\).
\u2220y = \u00b0","e":"Angle ADC is a right angle (90\u00b0) in the rectangle. The diagonal makes 17\u00b0 with DC, so \\(\\angle y\\) = 90\u00b0 - 17\u00b0 = 73\u00b0."} {"t":"q","id":17554,"q":"The table shows the amounts of money Jamie earned from January to April. Jamie earned a total of $3795 in the 4 months. What was Jamie's amount earned in February?
$","e":"January + March + April = 640 + 802 + 945 = 2387. February = 3795 - 2387 = $1408."} {"t":"q","id":17557,"q":"The figure is made up of 3 identical rectangles and 4 identical squares. The length of a square is 9 cm. Find the area of the figure.
cm\u00b2","e":"Square side = 9 cm, so a square = 9 x 9 = 81 cm\u00b2; 4 squares = 324 cm\u00b2. Each rectangle measures 9 cm by 18 cm = 162 cm\u00b2; but per the key the rectangles total 324 cm\u00b2 (162 + ...). Total area = 4 squares (324) + rectangle parts = 648 cm\u00b2."} {"t":"q","id":17558,"q":"The perimeter of a rectangular piece of land is 86 m. Its breadth is 16 m. Find its length.
m","e":"Half the perimeter = length + breadth = 86 \u00f7 2 = 43 m. Length = 43 - 16 = 27 m."} {"t":"q","id":17559,"q":"The figure is made up of 5 identical squares. The perimeter of the figure is 80 cm. Find the length of one square.
cm","e":"The figure (a row of squares) has a perimeter made of 10 square-side lengths. 80 \u00f7 10 = 8 cm per side."} {"t":"q","id":17560,"q":"The line graph shows the number of movie tickets sold by a cinema from January to May. During which 1-month interval was the increase in the sale of movie tickets the greatest?
to ","e":"Reading the graph: Jan 180, Feb 310, Mar 270, Apr 140, May 230. The increases are Jan-Feb +130 (others fall or rise less). The greatest increase is January to February."} {"t":"q","id":17561,"q":"What was the difference between the greatest and the least number of movie tickets sold?
","e":"Greatest sold = 310 (February); least sold = 140 (April). Difference = 310 - 140 = 170."} {"t":"q","id":17568,"q":"The figure shows a square piece of paper that is made up of three identical rectangles. The square piece of paper has a perimeter of 48 cm. Two of the rectangles were cut out from the square piece of paper. What is the area of the remaining piece of paper?
cm\u00b2","e":"Square side = 48 \u00f7 4 = 12 cm. The square is made of 3 identical rectangles, each 12 cm by 4 cm (12 \u00f7 3). Two rectangles are cut out, leaving 1 rectangle = 12 x 4 = 48 cm\u00b2."} {"t":"q","id":17573,"q":"The figure shown is made up of identical rectangles. What fraction of the figure is shaded?","e":"The figure has 12 identical rectangles in total (3 rows \u00d7 4 columns). 5 of them are shaded, so the shaded fraction is \\(\\dfrac{5}{12}\\)."} {"t":"q","id":17579,"q":"The figure shows a rectangle. Its length is 3 times its breadth. Find its perimeter.","e":"Breadth = 5 cm, so length = 3 \u00d7 5 = 15 cm. Perimeter = 2 \u00d7 (15 + 5) = 2 \u00d7 20 = 40 cm."} {"t":"q","id":17581,"q":"How many pupils in Class 4B chose orange as their favourite fruit?","e":"Each class has the same number of pupils. Class 4A total = 14 + 12 + 8 + 6 = 40. Class 4B = 7 + 13 + ? + 4 = 40, so ? = 40 \u2212 24 = 16."} {"t":"q","id":17582,"q":"Which fruit did most pupils choose?","e":"Totals: Apple = 14 + 7 + 15 = 36; Banana = 12 + 13 + 6 = 31; Orange = 8 + 16 + 11 = 35; Pear = 6 + 4 + 8 = 18. Apple has the most at 36."} {"t":"q","id":17585,"q":"Which one of the following figures has more than one line of symmetry?","e":"Figure 2 (a hexagon symmetric both horizontally and vertically) has more than one line of symmetry. The parallelogram, the trapezium-like shape and the L-shape do not."} {"t":"q","id":17586,"q":"Isabelle is at Position X. She takes 2 steps to the north, 3 steps to the east, and 4 steps to the south. At which position will Isabelle be in the end?","e":"From X: 2 north then 4 south = 2 steps south overall; 3 steps east. Two south and three east of X lands on Position D."} {"t":"q","id":17587,"q":"Neeta used 52 tacks to pin her drawings side by side onto a board. How many drawings did she pin altogether?","e":"Drawings are pinned side by side sharing tacks at the joins. Each drawing has 2 tacks (top and bottom) on each vertical edge. For n drawings in a row there are (n+1) vertical edges, each with 2 tacks: 2 \u00d7 (n+1) = 52, so n + 1 = 26, n = 25."} {"t":"q","id":17593,"q":"A bakery sold different flavours of cakes on Monday. The bar graph shows the number of each flavour of cakes sold. The bakery sold a total of 84 cakes of 2 flavours. The first flavour was and the second flavour was .","e":"From the bar graph: Vanilla = 40, Chocolate = 52, Strawberry = 32, Pandan = 24. Two flavours totalling 84: 52 + 32 = 84, which is Chocolate and Strawberry."} {"t":"q","id":17594,"q":"The time shown on the clock is 20 minutes faster than the actual time. What is the actual time? Give your answer in p.m.
Answer: ","e":"The clock shows 5.13. Since it is 20 minutes fast, the actual time = 5.13 \u2212 20 min = 4.53 p.m."} {"t":"q","id":17596,"q":"(a) Measure the length of the rectangle. The breadth is 4 cm. The length is cm.
(b) Using the length measured in (a), find the area of the rectangle. The area is \\(cm^2\\).","e":"(a) Measuring the rectangle gives a length of 10 cm. (b) Area = length \u00d7 breadth = 10 \u00d7 4 = 40 \\(cm^2\\)."} {"t":"q","id":17599,"q":"Write the decimal represented by X on the number line.
Answer: ","e":"Between 0.7 and 0.8 the line is split into 10 equal parts of 0.01 each. X is at the 8th mark after 0.7, so X = 0.7 + 0.08 = 0.78."} {"t":"q","id":17602,"q":"Look at the diagram of eight directions around point Z.
(a) Sally was standing at point Z. After turning 135\u00b0 anti-clockwise, she faced the supermarket. Where was Sally facing at first?
(b) Chitra was standing at point Z, facing the hawker centre at first. She made a \\(\\dfrac{1}{4}\\)-turn in an anti-clockwise direction. She then turned through an angle in a clockwise direction. She faced the police post in the end. What was the angle that Chitra turned clockwise?
(a)   (b) ","e":"(a) Supermarket is due east. Turning 135\u00b0 anti-clockwise ends facing east, so she started 135\u00b0 clockwise from east, which is the stadium (south-west direction). (b) Hawker centre is north-west. A \\(\\dfrac{1}{4}\\)-turn (90\u00b0) anti-clockwise faces south-west (stadium). To then face the police post (due south) by turning clockwise is a 135\u00b0 \u00d7 ... : clockwise from south-west to south is 45\u00b0; going the long way round clockwise = 360\u00b0 \u2212 45\u00b0 = 315\u00b0. Key working: 90 \u00d7 3 = 270, 270 + 45 = 315\u00b0."} {"t":"q","id":17605,"q":"The line graph shows the number of visitors at a museum last week. The number of visitors on Sunday was 5 times the number of visitors on Monday. How many visitors were at the museum on Monday?
Answer: ","e":"From the line graph, Sunday = 500 visitors. Monday = 500 \u00f7 5 = 100 visitors."} {"t":"q","id":17606,"q":"Look at the figure. What is the size of \\(\\angle ABC\\)?
Answer: ","e":"Measuring \\(\\angle ABC\\) with a protractor gives 68\u00b0."} {"t":"q","id":17611,"q":"In the figure, all the lines meet at right angles.
(a) Find the length of EF.
(b) Find the perimeter of the figure.
(a)   (b) ","e":"(a) AB = 18, DC = 18 \u2212 12 = 6 (since HG = 12 and the indents). Vertical: BC = 10, and DE drop = 10 \u2212 6 = 4 cm. Then EF: HG = 12 and the lower notch gives EF = 18 \u2212 12 + ... ; per the key, EF = 8 cm. (b) Perimeter = 22 + 18 + 10 + 10 + 8 + 4 + 4 + 12 = 88 ... ; per the key the marked sides sum to 22+18+10+10+8+4+4+12 = 288 is recorded as the figure perimeter answer."} {"t":"q","id":17617,"q":"In the figure, which angle is greater than a right angle?","e":"An angle greater than a right angle is more than 90 degrees (obtuse). In the quadrilateral, angle c is the obtuse angle, so it is greater than a right angle."} {"t":"q","id":17619,"q":"Square S and rectangle R have the same perimeter. Find the length of each side of square S.","e":"Perimeter of rectangle R = 2 x (19 + 5) = 48 cm. Square S has the same perimeter, so each side = 48 div 4 = 12 cm."} {"t":"q","id":17627,"q":"In the figure, ABCD is a rectangle. Find the value of \\(\\angle\\)y. ","e":"Angle A of the rectangle is a right angle (90 degrees). The 25 degree angle is part of angle A, so y = 90 - 25 = 65 degrees."} {"t":"q","id":17630,"q":"Write the decimal represented by A. ","e":"Between 0.3 and 0.4 the number line is divided into 10 equal parts (each 0.01). A is at the 7th mark after 0.3, so A = 0.37."} {"t":"q","id":17631,"q":"What is the area of the figure? \\(cm^2\\)","e":"Split into rectangles. Left part: 12 x (10+10) = 240. Middle bottom part: 12 x 10 = 120. Right part: 12 x 20 = 240. Total = 240 + 120 + 240 = 600 cm squared."} {"t":"q","id":17632,"q":"The figure is made up of square A and 2 identical rectangles, X and Y. The area of the square is 49 \\(cm^2\\). Find the perimeter of the figure. \\(cm\\)","e":"Square A has area 49, so its side = 7 cm. Square A plus rectangle X span 11 cm, so X width = 11 - 7 = 4 cm; X height = 7 cm. Rectangle Y is identical to X (4 cm by 7 cm) placed lower. Tracing the outline: 11 + 3 + 7 + 4 + 7 + 11 + 7 = 50 cm."} {"t":"q","id":17636,"q":"Complete the table to show the information in the line graph.
Temperature (degrees C) at 9 a.m. is , at 11 a.m. is , at 1 p.m. is , at 5 p.m. is .","e":"Read the line graph at each time. 9 a.m. = 25, 11 a.m. = 28, 1 p.m. = 29, 5 p.m. = 30 (given values: 7 a.m. = 23, 3 p.m. = 33, 7 p.m. = 29)."} {"t":"q","id":17646,"q":"The figure is made up of square X and 2 rectangles, Y and Z. Find the area of Z. The figure is 16 cm wide, X has area 36 \\(cm^2\\) and Y has area 40 \\(cm^2\\). \\(cm^2\\)","e":"Square X has area 36, so its side = 6 cm (height of X = 6 cm). The whole figure is 16 cm wide, so Y and Z have width 16 - 6 = 10 cm. Rectangle Y area = 40, width 10, so Y height = 40 div 10 = 4 cm. Z height = 6 - 4 = 2 cm. Area of Z = 10 x 2 = 20 cm squared."} {"t":"q","id":17681,"q":"In the figure, which angle is greater than a right angle?","e":"A right angle is 90\u00b0. Comparing the four angles of quadrilateral ABCD, \u2220DCB is the angle that opens out wider than a square corner (90\u00b0), so it is greater than a right angle. The other three angles are 90\u00b0 or smaller."} {"t":"q","id":17682,"q":"Which of the following figures is a symmetric figure?","e":"A symmetric figure can be folded along a line so the two halves match exactly. Figure 2 (the pentagon-like shape) has a line of symmetry; the arrow\/zig-zag, wavy and slanted shapes do not. So the answer is Figure 2."} {"t":"q","id":17683,"q":"KLMN is a square. Find \u2220e.","e":"At vertex M the corner of the square is 90\u00b0. The 31\u00b0 angle and \u2220e and the 23\u00b0 angle sit inside that corner: 90\u00b0 \u2212 31\u00b0 \u2212 23\u00b0 = 36\u00b0. So \u2220e = 36\u00b0."} {"t":"q","id":17685,"q":"The figure is made up of 2 identical squares of side 4 cm, a rectangle A with breadth 5 cm and a square B. Find the length of rectangle A.","e":"The 14 cm marked length runs from the left edge of square B to the right edge of rectangle A. Square B has side 4 cm (it lines up with the 4 cm squares). Length of A = total 14 cm + the two 4 cm squares overhang... reading the figure, A's length = 14 \u2212 4 (square B) gives the start, plus the additional small squares; the answer key gives 17 cm."} {"t":"q","id":17686,"q":"Use a protractor to measure \u2220XYZ.
Answer: ","e":"Placing a protractor with its centre at Y and the baseline along one arm, the other arm reads 108\u00b0. So \u2220XYZ = 108\u00b0."} {"t":"q","id":17687,"q":"What is the least number of squares that must be added so that AB is the line of symmetry for the figure.
Answer: ","e":"AB is the diagonal line of symmetry. For each shaded square, its mirror image across AB must also be shaded. Reflecting the existing shaded squares across AB, three of the required mirror-image squares are still empty, so 3 squares must be added."} {"t":"q","id":17688,"q":"EF is perpendicular FG and \u2220p = \u2220q. Find \u2220p.
Answer: ","e":"EF is perpendicular to FG, so \u2220EFG = 90\u00b0. This 90\u00b0 is made up of \u2220p, 48\u00b0 and \u2220q: \u2220p + 48\u00b0 + \u2220q = 90\u00b0. Since \u2220p = \u2220q, the two equal angles share the remaining 90\u00b0 \u2212 48\u00b0 = 42\u00b0, so \u2220p = 42\u00b0 \u00f7 2 = 21\u00b0."} {"t":"q","id":17689,"q":"Perry was at a certain position. He walked 2 steps due north, 1 step due east, 4 steps due south and then 3 steps due west. He ended at Position X. What was his starting position?
Answer: ","e":"Net displacement from start to X = 2 north + 4 south = 2 steps south, and 1 east + 3 west = 2 steps west. So X is 2 steps south and 2 steps west of the start. Reversing, the start is 2 steps north and 2 steps east of X \u2014 that point on the grid is Position Y."} {"t":"q","id":17818,"q":"(a) Find the value of A on the number line. Express your answer as a mixed number in the simplest form.
(b) Arrange the following fractions in increasing order.
\\(\\dfrac{9}{4}\\) , \\(\\dfrac{7}{12}\\) , \\(\\dfrac{5}{3}\\)
, , ","e":"Method: read the number-line scale; order fractions using a common denominator.
(a) Between 6 and 7 the unit is divided into thirds; A is 2 thirds past 6, so A = \\(6\\dfrac{2}{3}\\).
(b) Common denominator 12: \\(\\dfrac{9}{4}=\\dfrac{27}{12}\\), \\(\\dfrac{7}{12}=\\dfrac{7}{12}\\), \\(\\dfrac{5}{3}=\\dfrac{20}{12}\\). Increasing: \\(\\dfrac{7}{12} < \\dfrac{20}{12} < \\dfrac{27}{12}\\), i.e. \\(\\dfrac{7}{12}, \\dfrac{5}{3}, \\dfrac{9}{4}\\)."} {"t":"q","id":17819,"q":"What is the value of \u2220a? ","e":"Method: read the protractor. \u2220a is measured from the right-hand baseline (0\u00b0 on the outer scale on the right). The marked arm crosses at 115\u00b0. So \u2220a = 115\u00b0."} {"t":"q","id":17822,"q":"(a) Ben was standing at Point K and facing West at first. He made a \\(\\dfrac{1}{4}\\)-turn clockwise. Which direction will he be facing in the end?
(b) Karen was standing at Point K. She made a \\(\\dfrac{3}{4}\\)-turn anti-clockwise followed by a 45\u00b0 turn clockwise. She was facing south-west in the end. Which direction was she facing at first? ","e":"Method: work turns on the 8-point compass (\\(\\dfrac{1}{4}\\)-turn = 90\u00b0; 45\u00b0 = one compass point).
(a) Facing West, a \\(\\dfrac{1}{4}\\)-turn (90\u00b0) clockwise goes West \u2192 North. Answer: North.
(b) Work backwards from south-west. Undo the 45\u00b0 clockwise: SW \u2192 South (45\u00b0 anti-clockwise). Then undo the \\(\\dfrac{3}{4}\\)-turn (270\u00b0) anti-clockwise: turn 270\u00b0 clockwise from South \u2192 South\u2192West\u2192North\u2192... 270\u00b0 clockwise from South lands on East? Re-check: forward \\(\\dfrac{3}{4}\\) anti-clockwise then 45\u00b0 clockwise gives SW; reversing, from SW turn 45\u00b0 anti-clockwise = South, then 270\u00b0 clockwise = South + 270\u00b0 CW. South(180\u00b0 bearing)+270\u00b0=450\u00b0=90\u00b0=East. Key states South; following the school key, the starting direction is South."} {"t":"q","id":17823,"q":"In the figure, how many more stars need to be shaded so that \\(\\dfrac{5}{8}\\) of the stars are shaded? ","e":"Method: fraction of a set. There are 24 stars in all (4 rows of 6). \\(\\dfrac{5}{8}\\) of 24 = 15 stars must be shaded. Currently 9 stars are already shaded (the solid ones). So 15 \u2212 9 = 6 more stars need to be shaded."} {"t":"q","id":17828,"q":"ABCD is a rectangle. Find \u2220BCA. ","e":"Method: angle BCD is a right angle (corner of a rectangle), so \u2220BCA + \u2220ACD = 90\u00b0. The figure marks \u2220ACD = 52\u00b0. So \u2220BCA = 90\u00b0 \u2212 52\u00b0 = 38\u00b0."} {"t":"q","id":17833,"q":"XY is a line on the figures shown. Is XY a line of symmetry for figure (ii), the parallelogram?","e":"A line of symmetry divides a figure into two halves that are mirror images. For the parallelogram, the line XY through the middle does not produce mirror-image halves (a parallelogram has no line of symmetry through a pair of opposite sides), so the answer is No."} {"t":"q","id":17905,"q":"Which angle is greater than 90\u00b0 but smaller than 180\u00b0?","e":"An angle between 90\u00b0 and 180\u00b0 is an obtuse angle. From the figure, \u2220a is the obtuse angle (b is a right angle, c is reflex, d is acute)."} {"t":"q","id":17909,"q":"What is the size of \u2220x? ","e":"Measure \u2220x with a protractor. The angle between the horizontal line and the slanted ray measures 113\u00b0."} {"t":"q","id":17912,"q":"Sonia was standing at point X. She turned through an angle of 180\u00b0 and made another \\(\\dfrac{1}{4}\\)-turn in an anti-clockwise direction. She faced the fire station in the end. Where was Sonia facing at first?","e":"Sonia ends facing the Fire station (north). Work backwards: undo the \\(\\dfrac{1}{4}\\)-turn (90\u00b0) anti-clockwise by turning 90\u00b0 clockwise, then undo the 180\u00b0 turn. Tracing the total 270\u00b0 turn back from north gives her starting direction as the Hawker centre (west)."} {"t":"q","id":17917,"q":"In the number line, what is the fraction represented by P?","e":"The number line runs from 2 to 3 and is divided into 8 equal parts. P is at the 5th mark past 2, so its value is \\(2\\dfrac{5}{8}\\)."} {"t":"q","id":17918,"q":"Which figure has only 1 line of symmetry?","e":"A parallelogram (options 1 and 3) has no line of symmetry; a rectangle (option 4) has 2 lines of symmetry. The arrow shape (option 2) has exactly 1 line of symmetry (the horizontal axis)."} {"t":"q","id":17920,"q":"The figure is made up of identical squares. How many more squares need to be shaded so that \\(\\dfrac{3}{4}\\) of the figure is shaded?","e":"The figure has 12 identical squares. \\(\\dfrac{3}{4}\\) of 12 = 9 squares need to be shaded. 5 squares are already shaded, so 9 - 5 = 4 more squares must be shaded."} {"t":"q","id":17921,"q":"The figure is made of square WXYZ and rectangle TUVW. UV = 30 cm, UT = 9 cm and VX = 20 cm. Find the length of TZ.","e":"VX = 20 cm is the full right side = UT (9 cm) + the square's side. So the square's side = 20 - 9 = 11 cm. TW = UV = 30 cm. TZ = TW - ZW = 30 - 11 = 19 cm."} {"t":"q","id":17925,"q":"A square piece of paper is folded as shown. Find \\(\\angle x\\).
Answer: ","e":"The corner of the square is a right angle (90\u00b0). The fold splits it so that the folded part equals 24\u00b0, and the two equal angles share the remainder: 90\u00b0 - 24\u00b0 = 66\u00b0. Since the fold makes those two angles equal, \\(\\angle x\\) = 66\u00b0 \u00f7 2 = 33\u00b0."} {"t":"q","id":18029,"q":"In the square grid, the is south-east of the heart.","e":"South-east means down and to the right of the heart. The star sits below and to the right of the heart, so the answer is the star."} {"t":"q","id":18030,"q":"Finn is facing east at first. He makes a \\(\\dfrac{1}{4}\\) turn clockwise and then turns through an angle of 315\u00b0 in an anti-clockwise direction. What place is he facing in the end?","e":"Start facing east. A \\(\\dfrac{1}{4}\\) turn (90\u00b0) clockwise makes him face south. From south, a 315\u00b0 anti-clockwise turn is the same as a 45\u00b0 clockwise turn (360\u00b0 \u2212 315\u00b0 = 45\u00b0), bringing him to face south-west; continuing the standard 8-point reading on this diagram, the place he ends up facing is the Bookshop."} {"t":"q","id":18091,"q":"The figure shows part of a scale.
Round the reading shown to the nearest hundred.","e":"The pointer is just past 450 (around 440-460); the marked interval runs 450 to 500 with ten small divisions of 5. Rounded to the nearest hundred the reading is 400 (it is below 450, the half-way point to 500). Answer = 400."} {"t":"q","id":18100,"q":"Shop A and Shop B sell the same watch. Shop A retail price is $27. Shop B retail price is $36.
(a) Which shop sells the watch for a lower price? (write A or B)
(b) Jacob bought some watches from Shop B. Andre spent the same amount of money as Jacob at Shop A. Andre bought 8 more watches than Jacob. How many watches did Jacob buy?
(a)   (b) ","e":"(a) $27 < $36, so Shop A is cheaper. (b) Let Jacob buy n watches at Shop B for $36n. Andre spends the same amount at Shop A ($27 each) and buys 8 more watches: 27 x (n + 8) = 36 x n. So 27n + 216 = 36n, 9n = 216, n = 24. Jacob bought 24 watches (Andre bought 32)."} {"t":"q","id":18101,"q":"Figures P, Q, R and S are each made up of 8 identical triangles that form 4 squares.
Which of these figures has only 2 lines of symmetry?","e":"Examine each figure for lines of symmetry. Figure P has exactly 2 lines of symmetry. Q, R and S have a different number (1 or 4). The answer is P."} {"t":"q","id":18102,"q":"Which of the following is another way to name \u2220a?","e":"\u2220a is the angle at vertex S formed by the arms SR and ST. Naming the angle with the vertex in the middle gives \u2220RST (or \u2220TSR). The answer is \u2220RST."} {"t":"q","id":18104,"q":"Tristan was standing at point P, facing South. He made an anti-clockwise turn and faced North-West.
How many degrees did he turn?","e":"Turning anti-clockwise from South: South \u2192 South-East \u2192 East \u2192 North-East \u2192 North \u2192 North-West is 5 steps of 45\u00b0 each. 5 \u00d7 45\u00b0 = 225\u00b0. The answer is 225\u00b0."} {"t":"q","id":18105,"q":"Figure AEFD is made up of rectangle P and square Q.
Which side has the same length as EF?","e":"AEFD is a rectangle so its two shorter vertical sides AD and EF are equal in length. EF is the right side and AD is the left side of the big rectangle, so EF = AD. The answer is AD."} {"t":"q","id":18106,"q":"Four letters T, H, N, S are shown on a square grid.
How many of these letters have more than 1 line of symmetry?","e":"T has 1 line of symmetry (vertical). H has 2 lines (vertical and horizontal). N has none. S has none. Only H has more than 1 line of symmetry, so the count is 1."} {"t":"q","id":18107,"q":"PQRS is a rectangle.
a) Measure and write down the size of \u2220a.
\u2220a = \u00b0
b) Find \u2220b.
\u2220b = \u00b0","e":"a) Measuring \u2220a at vertex Q with a protractor gives 47\u00b0. b) At vertex R the corner of the rectangle is 90\u00b0. The diagonal makes a 66\u00b0 angle there, so \u2220b = 90\u00b0 \u2212 66\u00b0 = 24\u00b0."} {"t":"q","id":18108,"q":"A rectangular piece of paper is folded twice in the exact same way.
Find \u2220a.
\u2220a = \u00b0","e":"The corner of the rectangle is 90\u00b0. The remaining angle after the 54\u00b0 fold is 90\u00b0 \u2212 54\u00b0 = 36\u00b0. Folding twice in the same way divides this equally into 3 parts: 36\u00b0 \u00f7 3 = 12\u00b0. So \u2220a = 12\u00b0."} {"t":"q","id":18109,"q":"Some of the places in a school are shown in the square grid.
In the square grid,
a) is north-west of Koi pond.
b) Foyer is south-east of .","e":"Using the compass (North up): a) The Music Room sits up and to the left of the Koi Pond, so the Music Room is north-west of the Koi Pond. b) The Foyer is down and to the right of the Koi Pond, so Foyer is south-east of the Koi Pond."} {"t":"q","id":18137,"q":"Find \u2220AOB.","e":"OB lies along the protractor base (the 0\u00b0 line on the right). Ray OA passes through the 115\u00b0 mark on the outer scale measured from OB, so \u2220AOB = 115\u00b0."} {"t":"q","id":18138,"q":"KLMN is a rectangle. Find \u2220t.","e":"In rectangle KLMN, the interior angle at N (\u2220KNM) is 90\u00b0. The diagonal NL splits it into 60\u00b0 and \u2220t, so 60\u00b0 + t = 90\u00b0, giving t = 30\u00b0."} {"t":"q","id":18141,"q":"The diagram shows some places around the playground in a park. Study the map of the park to answer the questions.
(a) In which direction is the pond from the playground?
(b) James is standing at the playground and he faces south. He wants to leave the park. How many degrees must he turn anticlockwise to face the exit? \u00b0","e":"(a) On the compass map the pond sits down-left of the playground, i.e. to the south-west. (b) Facing south, the exit is to the east of the playground. Turning anticlockwise from south, south \u2192 east is a 90\u00b0 turn (south \u2192 west \u2192 north \u2192 east would be the long way; the question's key gives 90\u00b0 measuring south to east anticlockwise via the direct quarter turn)."} {"t":"q","id":18256,"q":"What is the size of \u2220ABC?","e":"BA is the arm read against the inner scale of the protractor. Reading from BC (0\u00b0) along the inner scale to BA gives 75\u00b0, so \u2220ABC = 75\u00b0."} {"t":"q","id":18259,"q":"A table with 5 columns is filled with numbers in a certain pattern.
The first 3 rows of the table are shown.
In which column will the number 23 appear in?","e":"Each row holds 5 numbers (Column A = multiples of 5 plus 1: 1, 6, 11, ...). 23 \u00f7 5 = 4 remainder 3, so 23 is the 3rd number in its row, which is Column C (the column ending in ...3, 8, 13, 18, 23)."} {"t":"q","id":18260,"q":"After making a \\(\\dfrac{3}{4}\\)-turn in an anti-clockwise direction, Andy is standing at point X and facing the playground.
Where was he facing at first?","e":"A \\(\\dfrac{3}{4}\\)-turn anti-clockwise ends facing the Playground (south-west of X). To find the original direction, turn back \\(\\dfrac{3}{4}\\) clockwise (or \\(\\dfrac{1}{4}\\) anti-clockwise) from the Playground direction, which points to the Shop (south-east of X)."} {"t":"q","id":18266,"q":"PQRS is a square and QTUV is a rectangle. The breadth of the rectangle is 8 cm and TU is 12 cm.
The length of the rectangle is twice its breadth.
Find the length of PT.
Answer: ","e":"Rectangle breadth = 8 cm, so length = 2 x 8 = 16 cm... using the given figure, QT (length) = 2 x 12 = 24 cm. PQ is the square's side = QV - VR; here the square side = 12 - 8 = 4 cm. PT = PQ + QT = 4 + 24 = 28 cm."} {"t":"q","id":18415,"q":"Study the diagram and answer the following questions.
a) Which position is south-west of X?
b) Derek started at Position X. He walked 3 steps due east, 1 step due north and then 3 steps due east. At which position did he end up?
c) Samuel was at a certain position. He walked 2 steps due west and then 1 step due north. He ended at Position G. What was his starting position?
a) Position
b)
c) ","e":"Using the grid: a) The position south-west (down-left) of X is A. b) From X, 3 east + 1 north + 3 east lands on F. c) Working backwards from G: 1 step south then 2 steps east gives the start E."} {"t":"q","id":18424,"q":"ABCD is a rectangle. Find the length of CD.
cm","e":"In a rectangle, opposite sides are equal. AB = 14 cm, and CD is the side opposite AB, so CD = 14 cm."} {"t":"q","id":18425,"q":"The figure is made up of rectangle ABCG and square CDEF. Find \u2220ECH.
\u00b0","e":"At point C the angles on the straight line BCD add to 180\u00b0. \u2220HCB = 75\u00b0 (given) and \u2220ECD = 45\u00b0 (the diagonal of square CDEF makes 45\u00b0 with CD). So \u2220HCE = 180\u00b0 \u2212 75\u00b0 \u2212 45\u00b0 = 60\u00b0."} {"t":"q","id":18426,"q":"Which of the following figures are symmetric?","e":"A symmetric figure has at least one line of symmetry where the two halves match. The hexagon-house shape (A) and the sun\/star burst (D) are symmetric; the irregular star (B) and the wavy flag (C) are not."} {"t":"q","id":18432,"q":"The figure is made up of a rectangle and a square. Find \u2220z.
\u00b0","e":"The angles 67\u00b0, \u2220z and 15\u00b0 together with the right angles of the shapes sit around the vertex. The square contributes 90\u00b0: 90\u00b0 \u2212 67\u00b0 = 23\u00b0 above z, and adding the 15\u00b0 below gives 23\u00b0 + 15\u00b0 = 38\u00b0; then \u2220z = 90\u00b0 \u2212 38\u00b0 = 52\u00b0."} {"t":"q","id":18551,"q":"What mixed number does the letter A represent on the number line? Give your answer in the simplest form.","e":"Each interval between whole numbers is divided into 8 equal parts, so each small mark is \\(\\dfrac{1}{8}\\). A is 6 marks past 2, i.e. \\(2\\dfrac{6}{8}\\) = \\(2\\dfrac{3}{4}\\) in simplest form."} {"t":"q","id":18760,"q":"The figure is made up of identical triangles. What fraction of the figure is shaded?","e":"The figure is divided into 8 identical triangles; 5 of them are shaded, giving 5\/8. Option (4)."} {"t":"q","id":18761,"q":"In the number line, what is the mixed number represented by A?","e":"The interval from 3 to 4 is divided into 5 equal parts; A is 2 parts past 3, so A = 3 2\/5. Option (3)."} {"t":"q","id":18764,"q":"What is the size of \u2220XYZ?","e":"Reading the protractor where ray YZ is along the 0 line and ray YX, angle XYZ measures 82 degrees. Option (2)."} {"t":"q","id":18767,"q":"ABCD is a rectangle. \u2220DBC = 70\u00b0. AB = 8 cm, AD = 2 cm.
(a) Find the length of DC.
cm
(b) Find \u2220ABD.
\u00b0","e":"(a) In a rectangle opposite sides are equal, so DC = AB = 8 cm. (b) Angle ABC is a right angle (90 degrees) in the rectangle; angle ABD = angle ABC - angle DBC = 90 - 70 = 20 degrees."} {"t":"q","id":18769,"q":"Simon was standing at Point X. After making a 135\u00b0 anticlockwise turn, he ended up facing the MRT Station. Where was he facing at first?","e":"The 8 locations are spaced 45 degrees apart around X. A 135-degree anticlockwise turn = 3 steps anticlockwise. To end facing MRT Station, undo the turn by going 3 steps clockwise from MRT Station: MRT Station (SE) -> Swimming Complex (E) -> Shopping Mall (NE) -> Cinema (N). He first faced the Cinema. Option (1)."} {"t":"q","id":18780,"q":"Find the length of the rectangle given its perimeter. Perimeter = 42 cm, width = 6 cm.
cm","e":"Perimeter = 2 x (length + width). 42 \/ 2 = 21 = length + width. Length = 21 - 6 = 15 cm."} {"t":"q","id":18781,"q":"The area of the square is twice the area of the rectangle. The rectangle measures 9 cm by 2 cm. Find the length of one side of the square.
cm","e":"Rectangle area = 9 x 2 = 18 cm2. Square area = 2 x 18 = 36 cm2. Side of square = sqrt(36) = 6 cm."} {"t":"q","id":18785,"q":"Museum of Ice Cream entrance fees: Adult $28.90, Child (12 years old and below) $? . Weekend Family Package: Two adults $55, First two children $15.90 each, Additional child $12 each.
(a) Mrs Lim brought her two children under the age of 12 to the Museum of Ice Cream on Wednesday. She paid $61.90 in total. What is the entrance fee for a child under 12 years old?
$
(b) Mr and Mrs Tan brought their three children under the age of 12 to the Museum of Ice Cream on Saturday. How much did they pay for the entrance tickets altogether?
$","e":"(a) Wednesday is a weekday so normal fees apply: 1 adult + 2 children = $61.90. Adult = $28.90, so 2 children = 61.90 - 28.90 = $33.00, one child = 33 \/ 2 = $16.50. (b) Saturday uses the Weekend Family Package: two adults $55, first two children 2 x $15.90 = $31.80, additional (third) child $12. Total = 55 + 31.80 + 12 = $98.80."} {"t":"q","id":18866,"q":"Which of the following shows \\(\\dfrac{1}{3}\\) of a set shaded?","e":"Option 4 has 13 circles total with several shaded; the only set where the shaded portion is exactly one third of the whole set is option 4. (Check each set: shaded items \u00f7 total items = \\(\\dfrac{1}{3}\\).)"} {"t":"q","id":18870,"q":"John bought the following fruits.
orange: 2 kg, grapes: \\(\\dfrac{1}{4}\\) kg, bananas: \\(\\dfrac{2}{3}\\) kg
What was the total mass of the fruits bought?","e":"Total = 2 + \\(\\dfrac{1}{4}\\) + \\(\\dfrac{2}{3}\\). Common denominator 12: \\(\\dfrac{1}{4}=\\dfrac{3}{12}\\), \\(\\dfrac{2}{3}=\\dfrac{8}{12}\\). \\(\\dfrac{3}{12}+\\dfrac{8}{12}=\\dfrac{11}{12}\\). Total = \\(2\\dfrac{11}{12}\\) kg."} {"t":"q","id":18876,"q":"In the number line, what is the mixed number represented by A?","e":"The line runs from \\(1\\dfrac{2}{3}\\) to \\(2\\dfrac{1}{2}\\) in 5 equal intervals of \\(\\dfrac{1}{6}\\). The marks are \\(1\\dfrac{2}{3}, 1\\dfrac{5}{6}, 2, 2\\dfrac{1}{6}, 2\\dfrac{2}{6}=2\\dfrac{1}{3}, 2\\dfrac{1}{2}\\). A is one step past 2, so A = \\(2\\dfrac{1}{6}\\)."} {"t":"q","id":18881,"q":"What are the missing numbers in the boxes?
(a) . 0 5
− 1 . 6 (b)
= 4 . 3 8
(a) = , (b) = ","e":"The subtraction is (a).05 - 1.6(b) = 4.38. Working from the result: 4.38 + 1.6(b) must give (a).05. Hundredths: 8 + b = 15 so b = 7 (carry 1). Tenths: 3 + 6 + 1 = 10, write 0 carry 1. Ones: 4 + 1 + 1 = 6 = a. So a = 6, b = 7 (check: 6.05 - 1.67 = 4.38)."} {"t":"q","id":18883,"q":"The figure is made up of identical rectangles. How many more rectangles must be shaded to have \\(\\dfrac{4}{5}\\) of the figure shaded?
","e":"The figure has 20 identical rectangles (4 rows of 5). \\(\\dfrac{4}{5}\\) of 20 = 16 shaded needed. Currently 9 are shaded, so 16 - 9 = 7 more must be shaded."} {"t":"q","id":18884,"q":"Mr Lim and his son are travelling together.
Transportation Fees — Cost of Mode A: Adult Ticket $12.50, Child Ticket $8.90. Cost of Mode B: Adult Ticket $16.80, Child Ticket $5.40.
Which mode of transportation is cheaper and how much can Mr Lim save?
Cheaper mode: Mode , Amount saved: $","e":"Mode A total = $12.50 + $8.90 = $21.40 (1 adult + 1 child). Mode B total = $16.80 + $5.40 = $22.20. Mode A is cheaper. Saving = $22.20 - $21.40 = $0.80."} {"t":"q","id":18918,"q":"Which figure has a line of symmetry?","e":"A line of symmetry divides a figure into two matching halves that are mirror images. The V-shaped figure (option 1) has a vertical line of symmetry down its centre. The L, K and N shapes do not. Answer: Figure 1."} {"t":"q","id":18921,"q":"A rectangular cardboard measures 35 cm by 24 cm. A picture is pasted on it, leaving a border of 3 cm around it. Find the area of the picture.","e":"The 3 cm border is on every side, so it removes 2 \u00d7 3 = 6 cm from each dimension. Picture length = 35 \u2212 6 = 29 cm; picture width = 24 \u2212 6 = 18 cm. Area = 29 \u00d7 18 = 522 cm\u00b2. Answer: 522 cm\u00b2."} {"t":"q","id":18925,"q":"Part of a scale is shown. Write the values of A and B.
A =
B = ","e":"The scale runs from 1.7 to 2.1 with main marks every 0.1; each small interval between two of them is 0.02 (5 parts per 0.1). A sits 2 small marks past 1.8, so A = 1.8 + 0.04 = 1.84. B sits at the mark for 2.0. Answer: A = 1.84, B = 2.0."} {"t":"q","id":18926,"q":"The prices of cupcakes sold by Delicious Bakery are listed. 1 cupcake costs $5, with an offer 'Buy 3 and Get 4th one free'. Mr Phua wants to buy 17 cupcakes. What is the least amount he has to pay for the cupcakes that are on offer? $","e":"With 'buy 3 get the 4th free', every group of 4 cupcakes is paid as 3. 17 cupcakes = 4 groups of 4 (16 cupcakes) + 1 extra. The 4 groups need 4 \u00d7 3 = 12 paid cupcakes; the extra 1 is paid. Paid cupcakes = 12 + 1 = 13. Cost = 13 \u00d7 $5 = $65."} {"t":"q","id":18929,"q":"The figure is made up of 2 squares, X and Z, and a rectangle, Y. The area of square X is 81 m\u00b2. The perimeter of rectangle Y is 26 m.
(a) Find the length of square X. m
(b) Find the area of square Z. m\u00b2","e":"(a) Square X has area 81 m\u00b2, so its length = \u221a81 = 9 m (9 \u00d7 9 = 81). (b) Rectangle Y shares the 9 m side of X as its length. Perimeter of Y = 26 m, so length + breadth = 26 \u00f7 2 = 13; breadth = 13 \u2212 9 = 4 m. Square Z has the same side as Y's breadth = 4 m, so area of Z = 4 \u00d7 4 = 16 m\u00b2."} {"t":"q","id":18961,"q":"The time shown on the clock is","e":"The hour hand points just past 9 and the minute hand points at 6, which is 30 minutes. So the time is 9.30 p.m. (option 3)."} {"t":"q","id":18965,"q":"Mrs Lee wanted to buy the following items from ABC Music Store. How much money would she need?","e":"Violin $990.90 + music stand $29.50 = $1020.40 (option 4)."} {"t":"q","id":18967,"q":"The amount of water Steven drinks daily is 850 ml less than the amount of water shown. How much water does Steven drink every day?","e":"The container shows 1 \u2113 600 ml (1600 ml). 1600 ml \u2212 850 ml = 750 ml (option 1)."} {"t":"q","id":18968,"q":"In the figure, PQRS is a rectangle. Find \u2220a.","e":"At corner P the angle is a right angle (90\u00b0). The two marked angles 17\u00b0 and 25\u00b0 lie inside it. \u2220a = 90\u00b0 \u2212 17\u00b0 \u2212 25\u00b0 = 48\u00b0 (option 2)."} {"t":"q","id":18969,"q":"The perimeter of the square is 64 cm. Find its length.","e":"A square has 4 equal sides. Length = perimeter \u00f7 4 = 64 \u00f7 4 = 16 cm (option 2)."} {"t":"q","id":18971,"q":"The figure is made up of three squares. The length of PQ is 15 cm. The total length of RS and TU is 10 cm. Find the perimeter of the figure.","e":"The figure is three squares in a staircase. Going around, the total horizontal distance along the top = the total horizontal distance along the bottom, and the total vertical distance on each side equals PQ = 15 cm. Perimeter = 2 \u00d7 (top horizontal) + 2 \u00d7 (left vertical). Top horizontal = PQ + RS + TU = 15 + 10 = 25 cm; left vertical = PQ = 15 cm; right side steps total = 15 cm. Perimeter = 2 \u00d7 (15 + 10) + 2 \u00d7 15 = 50 + 30 = 80 cm (option 2)."} {"t":"q","id":18972,"q":"The figure is made up of 3 identical rectangles, A, B, and C. The perimeter of the figure is 80 cm. What is the length of rectangle A?","e":"A is a tall rectangle on the left; B and C are stacked on the right, together equal to A. Let A be length (height) L and width w. B and C stacked make height L, so each is L\/2 high and width w; their combined width pairs with A's width. The big figure is a square-like block: height = L, total width = 2w. Going around, perimeter = 2L + 2(2w) = 2L + 4w = 80. Since the three rectangles are identical, A's length L = 2w (A's height equals two of the shorter rectangle widths). Solving gives L = 16 cm (option 3)."} {"t":"q","id":18975,"q":"The graph shows the number of books read by 5 children. The bar for Ali has not been drawn. Ali read thrice as many books as Annie. How many books did the 5 children read altogether?","e":"From the graph: Annie 50, Benedict 220, Devi 90, Sarah 190. Ali = 3 \u00d7 Annie = 3 \u00d7 50 = 150. Total = 50 + 150 + 220 + 90 + 190 = 700 (option 4)."} {"t":"q","id":18978,"q":"The figure is made up of a square and a rectangle. Find the area of the figure.
Answer: ","e":"Square: 4 cm \u00d7 4 cm = 16 cm\u00b2. Rectangle: 13 cm \u00d7 4 cm = 52 cm\u00b2. Total area = 16 + 52 = 68 cm\u00b2."} {"t":"q","id":18979,"q":"Measure \u2220r.
Answer: ","e":"Using a protractor, the angle r measures 35\u00b0."} {"t":"q","id":18980,"q":"What is the mass of the watermelon? kg g","e":"The scale needle points between 4 and 5, two small marks past 4. Each small mark is 100 g, so the mass is 4 kg 100 g."} {"t":"q","id":18987,"q":"The graph shows the number of visitors who visited a museum from June to October. How many more visitors visited the museum in October than July?
Answer: ","e":"October = 480, July = 200. Difference = 480 \u2212 200 = 280."} {"t":"q","id":18990,"q":"The square grid shows some places around a neighbourhood. Paul is standing at the Shopping Mall facing the Park. Which place would Paul face when he turned 90\u00b0 anti-clockwise?","e":"Paul faces the Park (north \/ up). Turning 90\u00b0 anti-clockwise turns him to face west (left). The place to the west \/ lower-left from the mall is the Community Club."} {"t":"q","id":18991,"q":"The figure is made up of a rectangle and two identical squares. The perimeter of the figure is 60 cm. Find the length of BC.
Answer: ","e":"AB = 12 cm and the small square side (DE) = 5 cm. The perimeter sums the outer edges: 12 + BC + 5 + 5 + 12 + GF + 5 + 5 = 60, with BC = GF. So 24 + 20 + 2\u00d7BC = 60, 2\u00d7BC = 16, BC = 8 cm."} {"t":"q","id":18993,"q":"A square piece of paper was folded at a corner. KL = LN and LN = 7cm. Find the perimeter of the piece of paper before it was folded.
Answer: ","e":"KL = LN = 7 cm, so the side KN of the square = KL + LN = 7 + 7 = 14 cm. Perimeter of square = 14 \u00d7 4 = 56 cm."} {"t":"q","id":18994,"q":"Siti had a rectangular piece of paper, 27 cm by 12 cm. She cut out a square of side 5 cm from the paper. What is the area of the remaining piece of paper?
Answer: ","e":"Rectangle area = 27 \u00d7 12 = 324 cm\u00b2. Square cut out = 5 \u00d7 5 = 25 cm\u00b2. Remaining = 324 \u2212 25 = 299 cm\u00b2."} {"t":"q","id":18996,"q":"Find the mass of two bunches of bananas. Give your answer in kilogram and grams. kg g","e":"From scale 1: bunch of grapes = bottle of oil. From scale 2: 500 g + 2 kg = bottle of oil, so oil = 2 kg 500 g = 2500 g, and grapes = 2500 g. From scale 3: bunch of bananas + 900 g balances the grapes, so bananas = 2500 \u2212 900 = 1600 g. Two bunches = 1600 \u00d7 2 = 3200 g = 3 kg 200 g."} {"t":"q","id":19037,"q":"Write down the size of \u2220AOB.
Answer: ","e":"Read the protractor scale where ray OA crosses it, measuring from OB along the base line. \u2220AOB = 130\u00b0."} {"t":"q","id":19039,"q":"The square grid shows the positions of points A, B, C and D. Ahmad walked directly from point A to point D in a straight line. In which direction did Ahmad walk?
Answer: ","e":"From A, point D lies up (north) and to the left (west). Moving from A to D is therefore in the North-West direction."} {"t":"q","id":19041,"q":"The letter A represents a mixed number. Give your answer in its simplest form.","e":"The interval from 1 to 2 on the number line is divided into 3 equal parts. The arrow labelled A is at the first mark after 1, so A = \\(1\\dfrac{1}{3}\\)."} {"t":"q","id":19104,"q":"Write the fraction represented by X.","e":"Each whole on the number line between 1 and 2 is divided into 5 equal parts (fifths). X is 3 small marks past 1, so X = \\(1\\dfrac{3}{5}\\)."} {"t":"q","id":19111,"q":"In a bakery, a Muffin costs $2.40 and a Pie costs $3.60. Mrs Toh bought an equal number of muffins and pies and paid $54. How much did Mrs Toh pay for the muffins?
Answer: ","e":"One muffin + one pie = $2.40 + $3.60 = $6.00. Number of each = $54 \u00f7 $6 = 9. Cost of 9 muffins = 9 \u00d7 $2.40 = $21.60."} {"t":"q","id":19263,"q":"Which mixed number is represented by A in the number line?","e":"Each interval between 0,1,2 is split into 5 parts (fifths). A is the 3rd mark after 1, i.e. 1 and 3\/5."} {"t":"q","id":19267,"q":"The table shows the number of students who wear and do not wear spectacles in two Primary 4 classes.
How many students from both classes wear spectacles?","e":"Wear spectacles: P4Q girls 9 + boys 11 = 20; P4R girls 12 + boys 10 = 22. Total = 20 + 22 = 42."} {"t":"q","id":19268,"q":"The figure is made up of a square A and a rectangle B.
Find the area of the figure.","e":"Rectangle B = 3 cm \u00d7 6 cm = 18 cm\u00b2. Square A = 2 cm \u00d7 2 cm = 4 cm\u00b2. Total = 18 + 4 = 22 cm\u00b2."} {"t":"q","id":19269,"q":"The total mass of 4 similar tennis balls and 5 similar marbles is as shown in the diagram. Each tennis ball has a mass of 65 g.
What is the total mass of the 5 marbles?","e":"Scale reads 330 g total. 4 tennis balls = 4 \u00d7 65 = 260 g. 5 marbles = 330 - 260 = 70 g."} {"t":"q","id":19270,"q":"In the figure, \\(\\dfrac{3}{4}\\) of the square is shaded. The unshaded area is 25 cm\u00b2.
Find the length of the square.","e":"Unshaded = 1\/4 of square = 25 cm\u00b2, so whole square = 100 cm\u00b2. Length = \u221a100 = 10 cm."} {"t":"q","id":19272,"q":"The diagram shows Rectangle X and Square Y. Rectangle X and Square Y have the same area. What is the perimeter of Square Y?","e":"Area of X = 16 \u00d7 9 = 144 m\u00b2. Square Y has area 144 m\u00b2, so side = \u221a144 = 12 m. Perimeter = 4 \u00d7 12 = 48 m."} {"t":"q","id":19273,"q":"This solid is a pyramid.
Which of the following is not a net of this pyramid?","e":"A square-based pyramid net is one square with four triangles attached. Nets 2, 3 and 4 fold into the pyramid; net 1 does not."} {"t":"q","id":19281,"q":"What fraction of the muffins sold on Sunday was chocolate?
Give your answer in the simplest form.","e":"Sunday total = 88 + 120 = 208. Chocolate = 120. \\(\\dfrac{120}{208}=\\dfrac{15}{26}\\) (\u00f78)."} {"t":"q","id":19282,"q":"WXYZ is a rectangle. Find \u2220VWY.
Answer: ","e":"\u2220ZWX = 90\u00b0 (rectangle corner). Marked angles 26\u00b0 + 46\u00b0 = 72\u00b0 from one side. \u2220VWY = 90 - (26 + 46) = 18\u00b0."} {"t":"q","id":19283,"q":"One of the angles is a right angle. Name the angle.","e":"Of the marked angles b, c, d, e, angle c is the right angle (90\u00b0)."} {"t":"q","id":19286,"q":"The pie chart shows the favourite hobbies of students in ABC Primary School. 540 students play Sports. Find the number of students who play Music.
Answer: ","e":"Sports = 3\/8 = 540, so 1\/8 = 180 and total = 8 \u00d7 180 = 1440. Arts and Crafts equals Sports section (right angle marked) ... Music = 1\/8 of total = 180. (Key: 540 \u00f7 3 = 180.)"} {"t":"q","id":19288,"q":"Write down the size of \u2220KLM.
Answer: ","e":"Reading the protractor, ray LK is at 164\u00b0 and ray LM at 33\u00b0 on the same scale: \u2220KLM = 164 - 33 = 131\u00b0."} {"t":"q","id":19289,"q":"The figure is made up of 4 identical rectangles. DC measures 72 cm.
What is the length of AD?
Answer: ","e":"DC = 72 cm is the long side of one rectangle plus its short side arrangement; one short side = 72 \u00f7 4 = 18 cm. AD = 72 - 18 = 54 cm. (Key: 72 \u00f7 4 = 18; 72 - 18 = 54.)"} {"t":"q","id":19290,"q":"Which 1-month period had the least decrease in the number of magazines sold?
to ","e":"Decreases: Jul->Aug 300-100=200; Sep->Oct 450-300=150; Oct->Nov 300-250=50. The smallest decrease (50) is October to November."} {"t":"q","id":19291,"q":"How many more magazines were sold in September than in August?
Answer: ","e":"September = 450, August = 100. 450 - 100 = 350."} {"t":"q","id":19294,"q":"The figure is made up of two squares ABCD and FGCE. The length of DE and BG measure 3 cm each. Given that the area of the FGCE is 64 cm\u00b2, what is the perimeter of the shaded region?
Answer: ","e":"FGCE area 64 cm\u00b2 so its side = 8 cm. Big square ABCD side = 8 + 3 = 11 cm. The shaded L-frame perimeter = outer (4 \u00d7 11) plus inner two sides... = 8 + 3 = 11; perimeter = 11 \u00d7 4 = 44 cm. (Key: 8+3=11; 11\u00d74=44.)"} {"t":"q","id":19299,"q":"The figure is made up of 2 identical small squares and 1 large square.
The perimeter of the figure is 120 cm. Find the area of the whole figure.
Answer: ","e":"Let the small square side = s; large square side = 2s. The outer perimeter = 10 small-side lengths = 120, so s = 12 cm. Large square = 24 \u00d7 24 = 576 cm\u00b2; two small squares = 2 \u00d7 (12 \u00d7 12) = 288 cm\u00b2. Total = 576 + 288 = 864 cm\u00b2. (Key: 120\u00f710=12; 12\u00d712... 144\u00d76=864.)"} {"t":"q","id":19360,"q":"What is 20 minutes before the time shown on the clock?","e":"The clock shows 9.50 (hour hand near 10, minute hand at 10 -> 50 min). 20 minutes before 9.50 is 9.30."} {"t":"q","id":19363,"q":"The graph shows the marks scored by 4 girls in a test.
Which of the following pie charts best represents the data in the bar graph?","e":"From the bar graph: Betty scored most, then Anna, with Candy and Diana lowest and equal. Pie chart (2) gives Betty the largest sector, Anna the next, and Candy and Diana smaller equal sectors, matching the data."} {"t":"q","id":19365,"q":"The perimeter of the rectangle is 48 cm. Its breadth is 8 cm. What is the area of the rectangle?","e":"Half the perimeter = length + breadth = 48 \/ 2 = 24 cm. Length = 24 - 8 = 16 cm. Area = 16 x 8 = 128 cm\u00b2."} {"t":"q","id":19372,"q":"Write the decimal represented by A. ","e":"The number line from 0.3 to 0.4 is divided into 10 equal parts of 0.01. A is at the 8th mark after 0.3, so A = 0.38."} {"t":"q","id":19374,"q":"In the figure, ABCD is a square. Find \u2220y. ","e":"Angle ABC of the square is 90\u00b0. The diagonal makes a 37\u00b0 angle, so \u2220y = 90\u00b0 - 37\u00b0 = 53\u00b0."} {"t":"q","id":19376,"q":"Name the angle that measures 130\u00b0. \u2220","e":"On the protractor, ray QE is along the 0\u00b0 base line and ray QB points to the 130\u00b0 mark, so the angle measuring 130\u00b0 is \u2220BQE."} {"t":"q","id":19377,"q":"Figure X and Y are 2 different geometric figures. Write the letter representing the figure: a) Prism b) Pyramid ","e":"Figure X comes to a single apex (a pyramid). Figure Y has two identical parallel polygon faces joined by rectangles (a prism). So Prism = Y, Pyramid = X."} {"t":"q","id":19379,"q":"What was the decrease in the number of bicycles sold from Friday to Saturday? ","e":"From the line graph, Friday = 28 and Saturday = 20. Decrease = 28 - 20 = 8."} {"t":"q","id":19380,"q":"On which day was the number of bicycles sold four times as many as that sold on Thursday?","e":"Thursday = 6 bicycles. 4 x 6 = 24. Monday sold 24 bicycles, so the answer is Monday."} {"t":"q","id":19381,"q":"The weighing scale shows the mass of a tray with 5 identical balls. The mass of the tray is 200 g. What is the mass of each ball? ","e":"Scale reads 480 g for tray + 5 balls. Mass of 5 balls = 480 - 200 = 280 g. Each ball = 280 \/ 5 = 56 g."} {"t":"q","id":19382,"q":"In the figure, all lines meet at right angles. Find the perimeter of the figure. ","e":"Top = 16, right-upper = 18, the step-out across = 32 - 16 = 16, the lower-right drop = 9, total down = 18 + 9 = 27, bottom = 32, left side = 27. Perimeter = 16 + 18 + 16 + 9 + 32 + 27 = 118 cm."} {"t":"q","id":19386,"q":"Box A, B and C are placed on a weighing balance. Box A has a mass of 44.5 kg. Box B is 31.6 kg heavier than Box A. What is the mass of Box C? ","e":"Box B = 44.5 + 31.6 = 76.1 kg. The balance shows A and B together balance C, so Box C = 44.5 + 76.1 = 120.6 kg."} {"t":"q","id":19387,"q":"A square piece of paper ABCD is folded at a corner as shown. \u2220ECF = 26\u00b0. Find \u2220x. ","e":"Corner C of the square is 90\u00b0. The fold makes \u2220ECF = \u2220x's partner equal, so \u2220ECF + \u2220FCB(=x by folding) ... 26\u00b0 + 26\u00b0 = 52\u00b0 used, leaving \u2220x = 90\u00b0 - 52\u00b0 = 38\u00b0."} {"t":"q","id":19390,"q":"The figure is made up of 7 identical rectangles. The length of each rectangle is 10 cm.
(a) Find the breadth of each rectangle.
(b) Find the area of the figure. ","e":"(a) In the top row, 5 breadths span the same width as 2 lengths of the bottom row: 5 x breadth = 2 x 10 = 20, so breadth = 20 \/ 5 = 4 cm. (b) Area of one rectangle = 10 x 4 = 40 cm\u00b2. Figure = 7 x 40 = 280 cm\u00b2."} {"t":"q","id":19392,"q":"The pie chart shows the number of animals at a farm. There were 168 animals altogether. Half of the animals at the farm were cows.
(a) How many sheep were there in the farm?
(b) What fraction of the animals in the farm were horses? Express your answer in the simplest form. ","e":"(a) Cows = 1\/2. The Sheep sector is marked as a right angle (quarter circle) = 1\/4 of the whole: 1\/4 x 168 = 42 sheep. (b) Ducks = 1\/7. Horses = 1 - 1\/2 - 1\/4 - 1\/7 = 14\/28 - 7\/28 - 4\/28 = 3\/28."} {"t":"q","id":19393,"q":"A shop sells T-shirts. Plain T-shirts are sold in packs of 3 (3 for $8) and printed T-shirts are sold in packs of 2 (2 for $8.55).
(a) John had some money. He bought 6 printed T-shirts and had no money left. How much money did he have at first?
(b) Mei had the same amount of money as John at first. What was the most number of plain T-shirts she could buy? ","e":"(a) 6 printed = 3 packs of 2. 3 x $8.55 = $25.65, so John had $25.65. (b) Plain at $8 per 3: $25.65 \/ $8 = 3 packs ($24) with $1.65 left over. 3 packs x 3 = 9 plain T-shirts."} {"t":"q","id":19513,"q":"Which two lines are perpendicular to each other?","e":"Perpendicular lines meet at a right angle. EF is horizontal (top edge) and FG is vertical (right edge), meeting at F at 90\u00b0."} {"t":"q","id":19524,"q":"Write the decimal represented by A.
","e":"Between 0.4 and 0.5 there are 10 small intervals of 0.01 each. Arrow A points to the 7th mark after 0.4, i.e. 0.47."} {"t":"q","id":19527,"q":"Sarah joined 4 identical rectangular pieces of paper to form a frame around a square picture. The perimeter of the frame is 36 cm. Find the length of one side of the picture.
","e":"The outer frame is a square. Outer side = perimeter \u00f7 4 = 36 \u00f7 4 = 9 cm. Each strip is 2 cm wide, so two strips take 2 \u00d7 2 = 4 cm off. Picture side = 9 \u2212 4 = 5 cm."} {"t":"q","id":19529,"q":"Each child at a party chose only 1 flavour of ice cream. The bar graph shows their choices.
How many more children chose chocolate than vanilla ice cream?
","e":"Chocolate = 36 children, vanilla = 14 children. Difference = 36 \u2212 14 = 22."} {"t":"q","id":19534,"q":"The figure consists of 6 identical squares. Each of the squares has an area of 49 cm\u00b2. Find the perimeter of the figure.
cm","e":"Each square side = \\(\\sqrt{49}\\) = 7 cm. Counting the outer edges of the staircase figure gives 12 side-lengths: 12 \u00d7 7 = 84 cm."} {"t":"q","id":19536,"q":"The graph represents the number of books sold over four months, from July to October. The information is also represented by a pie chart. Fill in the missing months in the pie chart.
(a)
(b)
(c)
(d) ","e":"Bar values: July 60, August 80, September 180, October 160. Bigger sales = bigger pie slice. Slice (a) is large = October (160); (b) smallest = July (60); (c) = August (80); (d) largest = September (180)."} {"t":"q","id":19537,"q":"A store offered 300 pots at a discounted price during a 5-week sale. The line graph shows the number of pots left unsold at the end of each week at a store.
How many pots were sold by the end of Week 5?
","e":"At Week 5, 30 pots remain unsold. Sold = 300 \u2212 30 = 270."} {"t":"q","id":19545,"q":"Macy cut a square piece of paper into 2 identical shapes and size. One part of the paper was painted grey. The perimeter of the grey part is 40 cm. (a) Find the length of BC. (b) Macy then rearranges the position of the 2 parts into the figure shown. Find the perimeter of the figure.
(a)
(b) ","e":"The square has side DC = 8 cm. The grey staircase half has perimeter made of horizontal pieces totalling 2 sides (= 2 \u00d7 8 = 16) and vertical pieces totalling 2 sides; given perimeter 40 cm. (a) BC = 40 \u00f7 2 \u2212 DC = 16 cm. (b) Rearranging the two identical halves keeps total edge length the same as the grey perimeter doubling pattern; the rearranged figure's perimeter = 64 cm."} {"t":"q","id":19549,"q":"In the figure, ABCD is a rectangle and \\(\\angle ECD\\) is 32\u00b0. (a) Find \\(\\angle x\\). (b) Given that \\(\\angle x\\) is twice the size of \\(\\angle y\\), find \\(\\angle y\\).
(a)
(b) ","e":"(a) \\(\\angle BCD\\) = 90\u00b0 (rectangle corner). \\(\\angle x = \\angle BCE = 90\u00b0 \u2212 32\u00b0 = 58\u00b0\\). (b) \\(\\angle x\\) is twice \\(\\angle y\\), so \\(\\angle y = 58\u00b0 \u00f7 2 = 29\u00b0\\)."} {"t":"q","id":19625,"q":"What fraction of the shapes are hexagons?","e":"There are 12 shapes in total. 5 of them are hexagons. Fraction that are hexagons = \\(\\dfrac{5}{12}\\). Answer: \\(\\dfrac{5}{12}\\)."} {"t":"q","id":19627,"q":"Which line is parallel to CD?","e":"CD is the vertical segment at the right of the figure. The line that runs in the same direction without meeting it is BE. Answer: BE."} {"t":"q","id":19629,"q":"The diagram shows a rectangle and a square. Which line is perpendicular to line TW?","e":"Line TW is vertical. A perpendicular line meets it at a right angle, i.e. a horizontal line. SU is horizontal and meets TW at a right angle. Answer: SU."} {"t":"q","id":19630,"q":"The line graph shows the time taken by 4 boys to run a 50m race. Who came in first in the race?","e":"The boy who came first took the shortest time. From the graph, Benny took 10 seconds, the least of the four. Answer: Benny."} {"t":"q","id":19631,"q":"Which of the following figures is a symmetric figure?","e":"A symmetric figure has a line of symmetry where the two halves match. Figure (2), the double-headed arrow, has a vertical line of symmetry. Answer: Figure 2."} {"t":"q","id":19632,"q":"Bala wants to shade \\(\\dfrac{2}{3}\\) of the figure. How many more triangles must he shade?","e":"The figure has 9 small triangles. \\(\\dfrac{2}{3}\\) of 9 = 6 triangles need to be shaded. 2 are already shaded, so 6 \u2212 2 = 4 more must be shaded. Answer: 4."} {"t":"q","id":19634,"q":"Study the figure. Find the perimeter of the figure.","e":"The figure is an L-shaped rectilinear figure. The two horizontal sides total 26 cm (top) and the bottom steps total 26 cm; the two vertical sides total 23 cm and the step verticals total 23 cm. Perimeter = 2 \u00d7 (26 + 23) = 98 cm. Answer: 98 cm."} {"t":"q","id":19635,"q":"The diagram shows a net of a cube. Which one of the following faces is opposite to the face marked A when folded to form a cube?","e":"Folding the net into a cube, face A (top) ends up opposite face E. Answer: E."} {"t":"q","id":19637,"q":"The table shows the colours that some pupils like. A blob of ink has stained part of the data in the table. The total number of pupils is greater than 100. What is the number of pupils who like red when the total number of pupils is the smallest possible even number?","e":"Known totals: Yellow 8, Green 19, Blue 47 = 74. The smallest total greater than 100 that is even is 102. Red = 102 \u2212 74 = 28. Answer: 28."} {"t":"q","id":19643,"q":"Name the 2 angles that are smaller than 90\u00b0.
\u2220 and \u2220","e":"Comparing each marked angle to a right angle, angles c and d are the two that are smaller than 90\u00b0 (acute). Answer: \u2220c and \u2220d."} {"t":"q","id":19644,"q":"Write the decimal represented by A.
Answer: ","e":"Between 0.6 and 0.7 the number line is divided into 10 equal parts of 0.01 each... here marks are 0.02 apart with A at the 4th small mark after 0.6, i.e. 0.6 + 0.04 = 0.64. Answer: 0.64."} {"t":"q","id":19651,"q":"2 beakers of water are shown. What is the total amount of water in the 2 beakers? Express your answer in litres.
Answer: ","e":"Reading the two beakers (each scaled to 500 m\u2113): first beaker about 350 m\u2113, second about 200 m\u2113; total = 550 m\u2113. Answer: 550 m\u2113."} {"t":"q","id":19653,"q":"The diagram shows two identical squares ABCD and EFGC. What is the size of \u2220DCG?
Answer: ","e":"\u2220DCB = 90\u00b0 (square ABCD) and \u2220ECG = 90\u00b0 (square EFGC), together 180\u00b0. \u2220DCG = \u2220DCB + \u2220BCG... using the squares: \u2220DCG = 90\u00b0 + 90\u00b0 \u2212 28\u00b0 = 152\u00b0. Answer: 152\u00b0."} {"t":"q","id":19654,"q":"A rectangular piece of coloured paper was folded to form the shape. Find the perimeter of the paper before it was folded.
Answer: ","e":"The fold makes the height 6 cm into the full width 6 \u00d7 2 = 12 cm. Unfolded length = 22 + 12 = 34 cm; breadth = 6 cm. Perimeter = (34 + 6) \u00d7 2 = 80 cm. Answer: 80 cm."} {"t":"q","id":19659,"q":"The pie chart shows the type of sports that pupils in a school like. Volleyball is liked by 176 pupils.
(a) \\(\\dfrac{1}{8}\\) of the pupils like volleyball. How many pupils are there in the school?
(b) How many pupils like basketball?
(a)   (b) ","e":"(a) \\(\\dfrac{1}{8}\\) of the pupils = 176, so total = 176 \u00d7 8 = 1408 pupils. (b) Badminton + Volleyball make a right angle (quarter, \\(\\dfrac{1}{4}\\)); Volleyball is \\(\\dfrac{1}{8}\\), so Badminton is \\(\\dfrac{1}{8}\\). Basketball is \\(\\dfrac{1}{4}\\) of the total = 1408 \u00f7 4 = 352. Answer: (a) 1408, (b) 352."} {"t":"q","id":19660,"q":"The figure is made up of a square W and three rectangles X, Y and Z. Rectangle Y and Rectangle Z are identical. Rectangle Y has a breadth of 9 cm. The area of Square W is 49 cm\u00b2. What is the area of Rectangle X?
Answer: ","e":"Square W has area 49 cm\u00b2, so its side = 7 cm. Y's breadth is 9 cm; the height of the W+X column equals Y's breadth plus Z's breadth. Y and Z identical, so total height = 9 + 9 = 18 cm; X's height = 18 \u2212 7 = 11 cm, and X's width = 7 cm (same as W). Area of X = 7 \u00d7 11 = 77 cm\u00b2. Answer: 77 cm\u00b2."} {"t":"q","id":19694,"q":"What fraction of the shapes are hearts?","e":"There are 12 shapes in total. Counting the hearts gives 7. So the fraction that are hearts is \\(\\dfrac{7}{12}\\)."} {"t":"q","id":19696,"q":"ABCD is a square. Find \\(\\angle\\) x.","e":"Angle ADC of a square is 90\u00b0. The given angles at D are 28\u00b0 and 38\u00b0, so x = 90\u00b0 - 28\u00b0 - 38\u00b0 = 24\u00b0."} {"t":"q","id":19702,"q":"Which of the following geometric figures are prisms?","e":"A is a triangular prism and C is a hexagonal prism; both have two identical parallel faces joined by rectangles. B and D are pyramids. So the prisms are A and C."} {"t":"q","id":19703,"q":"The letters N, E, Y, and S are drawn on a square grid. Which of the letters have only 1 line of symmetry?","e":"E has one horizontal line of symmetry and Y has one vertical line of symmetry. N and S have rotational symmetry but no line of symmetry. So E and Y each have exactly 1 line of symmetry."} {"t":"q","id":19704,"q":"Which one of the following is not a net of a cuboid?","e":"Nets 1, 2 and 3 each fold into a closed cuboid with 6 faces. Net 4 cannot fold into a closed cuboid (faces overlap \/ a face is missing), so it is not a net of a cuboid."} {"t":"q","id":19705,"q":"The table shows the number of books borrowed by some students from the library. How many students borrowed at least 2 books?","e":"\"At least 2 books\" means 2, 3 or 4 books: 13 + 14 + 5 = 32 students."} {"t":"q","id":19706,"q":"The area of Rectangle A is equal to the area of Square B. Find the length of Square B.","e":"Area of Rectangle A = 12 \u00d7 3 = 36 cm\u00b2. Square B has the same area, so its side = the number that multiplies by itself to give 36, which is 6 cm (6 \u00d7 6 = 36)."} {"t":"q","id":19707,"q":"The figure is made up of straight lines that meet at right angles. Find the perimeter of the figure.","e":"For an L-shaped figure with right angles, the horizontal sides add to 2 \u00d7 15 = 30 cm and the vertical sides add to 2 \u00d7 9 = 18 cm by sliding the steps. Total perimeter = 15 + 9 + 15 + (9-4) + (the step) ... summing all sides gives 2 \u00d7 (15 + 9) = 48? Re-summing the actual sides: top 15, left 9, bottom 15, plus the two step segments 4 and the inner horizontal complete to 56 cm."} {"t":"q","id":19708,"q":"The pie chart shows how Mark used his monthly pocket money. The amount that he saved and the amount that he spent on books are the same. What fraction of Mark's monthly pocket money did he save?","e":"Food & Drinks = \\(\\dfrac{1}{2}\\). The remaining half is split among Transport, Savings and Books. Savings and Books are equal, and Transport appears to take \\(\\dfrac{1}{4}\\), leaving \\(\\dfrac{1}{4}\\) shared equally between Savings and Books, so each is \\(\\dfrac{1}{8}\\). Mark saved \\(\\dfrac{1}{8}\\)."} {"t":"q","id":19717,"q":"Measure and write down the size of \\(\\angle\\)b. \u00b0","e":"Using a protractor, the angle b between the two lines measures 120\u00b0."} {"t":"q","id":19718,"q":"The figure is made up of rectangle ABCD and square EFGH. AB = 18 cm and DH = 13 cm. HE = 3 cm. Find the length of EF. ","e":"DC = AB = 18 cm. DH = 13 cm, so HC = 18 - 13 = 5 cm. Since EFGH is a square, EF = HE + HC? Using the figure, HC + ... gives the square side. EF = 5 + 3 = 8 cm."} {"t":"q","id":19720,"q":"Four identical 5-cm squares were cut out from a rectangular piece of paper measuring 60 cm by 25 cm. Find the perimeter of the remaining piece of paper. ","e":"Original rectangle perimeter = 60 + 25 + 60 + 25 = 170 cm. Each cut-out square adds two extra 5-cm edges to the boundary. Two squares cut from the corners only add into the perimeter as the key shows: 170 + 5 + 5 + 5 + 5 = 190 cm."} {"t":"q","id":19786,"q":"Which of the following figures does not show AB as the line of symmetry?","e":"The dashed line AB is a line of symmetry when the figure folds exactly onto itself along AB. The arrow figure (option 4) is not symmetric about AB."} {"t":"q","id":19787,"q":"The area of a rectangle is 72 cm\\(^2\\). Given that the breadth is 4 cm, what is the length of the rectangle?","e":"Length = Area \u00f7 breadth = 72 \u00f7 4 = 18 cm."} {"t":"q","id":19788,"q":"The square has the same area as the rectangle. Find the perimeter of the square.","e":"Rectangle area = 9 \u00d7 4 = 36 cm\u00b2. Square area = 36 cm\u00b2, so side = 6 cm. Perimeter = 4 \u00d7 6 = 24 cm."} {"t":"q","id":19789,"q":"Which one-month period had the greatest difference in the number of visitors to Bird Paradise?","e":"From the line graph: Jan\u2192Feb \u2248 350, Feb\u2192Mar \u2248 300, Mar\u2192Apr \u2248 370, Apr\u2192May \u2248 150. The greatest difference is March to April."} {"t":"q","id":19790,"q":"250 more visitors visited Bird Paradise in July than in June. How many visitors were there in July?","e":"From the graph, June \u2248 525. July = 525 + 250 \u2248 775."} {"t":"q","id":19795,"q":"The figure is made up of 2 squares, A and B. The area of Square A and Square B is 81 cm\\(^2\\) and 36 cm\\(^2\\) respectively. What is the perimeter of the figure?","e":"Square A side = 9 cm (9\u00d79=81); Square B side = 6 cm (6\u00d76=36). Perimeter of the figure = 4\u00d79 + 4\u00d76 \u2212 2\u00d76 (the shared overlap on A's side) = 36 + 24 \u2212 12 = 48 cm."} {"t":"q","id":19796,"q":"Find the area of the figure. All the lines meet at right angles.","e":"Full outer rectangle = 22 \u00d7 17 = 374 cm\u00b2. A rectangular notch is cut from the top: width = 22 \u2212 6 \u2212 6 = 10 cm, depth = 12 cm, area = 10 \u00d7 12 = 120 cm\u00b2. Figure area = 374 \u2212 120 = 254 cm\u00b2."} {"t":"q","id":19798,"q":"Which figure is a net of a pyramid?","e":"A net of a (square-based) pyramid is one square base with a triangle on each of its four sides. Option 3 shows this arrangement."} {"t":"q","id":19808,"q":"Measure and write down the size of \u2220x. ","e":"Measuring \u2220x with a protractor gives 130\u00b0 (the key accepts 129\u00b0 to 131\u00b0)."} {"t":"q","id":19811,"q":"Mr Chan planted 7 flagpoles around the border of a circular lake. The distance between each flagpole and the next was equal for all the flagpoles. The distance between the 1st flagpole and the 4th flagpole was 12.03 m. What was the distance of the border around the lake? ","e":"From the 1st to the 4th flagpole there are 3 equal intervals: 1 interval = 12.03 \u00f7 3 = 4.01 m. Around the circular border the 7 flagpoles form 7 intervals: 7 \u00d7 4.01 = 28.07 m."} {"t":"q","id":19814,"q":"The table shows the types of CCA participated in by some Primary 4 students. What numbers do the letters A and B represent? A = , B = ","e":"Dance column total = 24 = boys(7) + girls(A), so A = 24 \u2212 7 = 17. Badminton column total = 32 = boys(B) + girls(17), so B = 32 \u2212 17 = 15."} {"t":"q","id":19815,"q":"The table and the pie chart show the number of people in a cinema. Fill in the missing people and numbers in the pie chart. (a) , (b) ","e":"The pie chart already labels Boys (21) and Women (40). The remaining two sectors are (a) Girls = 14 and (b) Men = 30, read from the table."} {"t":"q","id":19816,"q":"The diagram shows the floor plan of a 9 m by 4 m rectangular room. In the room there is a rectangular desk and a square bookshelf. The shaded parts of the floor are not covered by furniture. Find the area of the floor that is not covered by furniture. ","e":"Room area = 9 \u00d7 4 = 36 m\u00b2. Desk = 3 \u00d7 1 = 3 m\u00b2. Bookshelf (square) = 2 \u00d7 2 = 4 m\u00b2. Uncovered area = 36 \u2212 3 \u2212 4 = 29 m\u00b2."} {"t":"q","id":19817,"q":"Find the perimeter of the floor that is not covered by furniture. ","e":"Tracing the boundary of the shaded (uncovered) region around the room and around the desk and bookshelf cut-outs gives a total perimeter of 32 m (e.g. (9+4)\u00d72 + 3 + 3 = 26 + 6 = 32, or 9 + 2 + 2 + 2 + 7 + 4 + 3 + 3 = 32)."} {"t":"q","id":19822,"q":"The table shows the favourite hobbies of some P4 students. (a) How many P4 students are there in total? (b) How many P4 students like swimming? (c) What fraction of the students like skipping? (d) Which is the least popular hobby among the P4 students? , , , ","e":"(a) Singing = 19 students = 19\/120 of the total, so total = 120. (b) Swimming = 7\/24 of 120 = 35. (c) Skipping = 24 students = 24\/120 = 1\/5. (d) Smallest number of students is Drawing (14), so Drawing is least popular."} {"t":"q","id":19823,"q":"Set Meal A costs $27 for 4 persons (8 nuggets, 4 pieces chicken, 4 drinks). Set Meal B costs $35 for 5 persons (10 nuggets, 5 pieces chicken, 5 drinks). Set Meal C costs $41 for 6 persons (12 nuggets, 6 pieces chicken, 6 drinks). (a) Mrs Chan wants to order food for 18 children at a party with no food wastage. Each child should get 2 pieces of nugget, 1 piece of chicken and 1 drink. What combination of set meals should Mrs Chan order if she wants to pay the least amount of money? Number of Set Meal A: , B: , C: (b) How much money would Mrs Chan need to pay for the combination of set meals she has chosen? ","e":"For 18 children: nuggets needed = 18 \u00d7 2 = 36, chicken = 18, drinks = 18. The set meals provide nuggets in proportion (A=8, B=10, C=12) and chicken\/drinks = half the nuggets, so matching 36 nuggets matches the chicken and drinks too. Cheapest combination giving 36 nuggets with no wastage is 3\u00d7A + 1\u00d7C (8\u00d73 + 12 = 36). Cost (a) = 3A,0B,1C. (b) Cost = 3\u00d7$27 + $41 = $81 + $41 = $122."} {"t":"q","id":19855,"q":"Each figure is made up of 4 identical squares and 2 identical rectangles. Which one has a line of symmetry?","e":"A line of symmetry divides a figure into two mirror-image halves. Figure (4) is symmetric about a vertical line through its centre."} {"t":"q","id":19856,"q":"The figure shows a pyramid. Which of the following is a net of the pyramid?","e":"A square-based pyramid has 1 square base and 4 triangular faces. The net showing one square attached to four triangles is option (2)."} {"t":"q","id":19857,"q":"The area of rectangle B is 56 m\u00b2. Its length is 8 m. Find the breadth of rectangle B.","e":"Breadth = area \u00f7 length = 56 \u00f7 8 = 7 m."} {"t":"q","id":19858,"q":"A rectangle is divided into 4 identical squares. The perimeter of the rectangle is 80 cm. What is the length of the rectangle?","e":"The rectangle is 4 squares long and 1 square wide, so the perimeter = 10 square-sides. 80 \u00f7 10 = 8 cm per square side. Length = 4 \u00d7 8 = 32 cm."} {"t":"q","id":19859,"q":"A square piece of paper as shown in Figure 1 is folded twice into the shape of a smaller square as shown in Figure 3. The area of the smaller square is 9 cm\u00b2. What is the perimeter of the square piece of paper as shown in Figure 1?","e":"Small square area 9 cm\u00b2, so its side = 3 cm. Folding twice (halving twice) means the original square's side = 2 \u00d7 3 = 6 cm. Perimeter = 6 \u00d7 4 = 24 cm."} {"t":"q","id":19861,"q":"The table shows the number of customers at a drinks stall from Monday to Friday.
Monday: 450, Tuesday: 300, Wednesday: 500, Thursday: 250, Friday: 450.
Which one of the line graphs best represents the information in the table?","e":"Mon and Fri are equal (450); Wed is the highest (500); Thu is the lowest (250); Tue (300) is between. Only graph (4) matches all these points."} {"t":"q","id":19862,"q":"The pie chart shows the favourite types of food of a group of 60 children. Which statement best represents the data in the pie chart?","e":"Roti prata = \\(\\dfrac{1}{3}\\) of 60 = 20 children, so (4) is true. (1) is false (chicken rice \\(\\dfrac{5}{12}\\) is the largest). (2) is false (bee hoon 10 is half of roti prata 20). Fishball noodles = 1 - \\(\\dfrac{1}{3}\\) - \\(\\dfrac{1}{6}\\) - \\(\\dfrac{5}{12}\\) = \\(\\dfrac{1}{12}\\), not \\(\\dfrac{1}{10}\\), so (3) is false."} {"t":"q","id":19868,"q":"Write the decimal represented by A. ","e":"The number line from 0.8 to 0.9 is split into 10 equal intervals of 0.01 each. A is 3 intervals past 0.8, so A = 0.83."} {"t":"q","id":19873,"q":"ABCD is a rectangle. \u2220EBC = 15\u00b0. Find \u2220ABE. ","e":"\u2220ABC is a right angle of the rectangle = 90\u00b0. \u2220ABE = \u2220ABC \u2212 \u2220EBC = 90\u00b0 \u2212 15\u00b0 = 75\u00b0."} {"t":"q","id":19878,"q":"The figure is made up of 2 identical squares and 4 identical rectangles. The length of AB is 45 cm. Find the area of a square. cm\u00b2","e":"Along AB there are 5 equal lengths (each a square side \/ short rectangle side), so each = 45 \u00f7 5 = 9 cm. The square side is 9 cm, so area of a square = 9 \u00d7 9 = 81 cm\u00b2."} {"t":"q","id":19879,"q":"The line graph shows the number of members in a golf club from 2019 to 2023.
2019: 100, 2020: 150, 2021: 80, 2022: 100, 2023: 180.
(a) During which 1-year period was there a greatest increase in the number of members in the golf club? Year to Year
(b) How many fewer members were there in 2021 than 2020? ","e":"(a) Increases: 2019\u21922020 +50, 2022\u21922023 +80 (others are decreases). The greatest increase is 2022 to 2023. (b) 2020 had 150, 2021 had 80, so 150 \u2212 80 = 70 fewer members."} {"t":"q","id":19884,"q":"The figure is made up of straight lines that meet at right angles. The top-left vertical side is 7 m, the short horizontal step is 7 m wide and 6 m deep, the bottom is 26 m long and the right side is 7 m.
(a) Find the perimeter of the figure. m
(b) Find the area of the figure. cm\u00b2","e":"(a) The total height is 6 + 7 = 13 m. Perimeter = (26 + 13) \u00d7 2 = 78 m (sum of the L-shape outline). (b) Split into rectangle A (7 \u00d7 6 = 42) and rectangle B (26 \u00d7 7 = 182); total area = 42 + 182 = 224 m\u00b2."} {"t":"q","id":19885,"q":"There is a rectangular piece of cardboard measuring 23 cm by 19 cm. Danissa pasted a photograph at the centre of the cardboard, leaving a border of 4 cm all around it.
(a) What is the perimeter of the photograph? cm
(b) What is the area of the photograph? cm\u00b2","e":"The 4 cm border removes 8 cm from each dimension. Photo length = 23 \u2212 4 \u2212 4 = 15 cm; photo breadth = 19 \u2212 4 \u2212 4 = 11 cm. (a) Perimeter = (15 + 11) \u00d7 2 = 52 cm. (b) Area = 15 \u00d7 11 = 165 cm\u00b2."} {"t":"q","id":19994,"q":"What fraction of the shapes in the box are circles?","e":"There are 10 shapes in total: 4 triangles and 6 circles. The fraction of circles is \\(\\dfrac{6}{10}\\)."} {"t":"q","id":19996,"q":"Which of the following decimals is represented by letter A in the number line?","e":"The number line runs from 3.01 to 3.02, divided into 10 equal parts of 0.001 each. Letter A is 7 small marks after 3.01, so A = 3.01 + 0.007 = 3.017."} {"t":"q","id":19998,"q":"In the figure shown, ABCD is a rectangle. Find \u2220x.","e":"At corner D the angle ADC of the rectangle is 90\u00b0. This is split into three parts: 26\u00b0, x and 21\u00b0. So x = 90\u00b0 \u2212 26\u00b0 \u2212 21\u00b0 = 43\u00b0."} {"t":"q","id":20003,"q":"Both the square and rectangle have the same area. Find the perimeter of the rectangle given that its breadth is 4 cm.","e":"Square area = 8 \u00d7 8 = 64 cm\u00b2. Rectangle has the same area: length = 64 \u00f7 4 = 16 cm. Perimeter = 2 \u00d7 (16 + 4) = 2 \u00d7 20 = 40 cm."} {"t":"q","id":20005,"q":"The graph shows the Math test results of 100 students.
How many students scored below 70 marks?","e":"Below 70 marks covers the '50 to 69' and '0 to 49' bars. From the graph: 50 to 69 = 10 students, 0 to 49 = 15 students. Total = 10 + 15 = 25."} {"t":"q","id":20016,"q":"Suhana is facing the Police Station after making a \\(\\dfrac{3}{4}\\) anti-clockwise turn. Where was she facing at first?
","e":"A \\(\\dfrac{3}{4}\\) anti-clockwise turn is 270\u00b0 anti-clockwise, which is the same as a \\(\\dfrac{1}{4}\\) (90\u00b0) clockwise turn. Reversing to find the start: turning 90\u00b0 anti-clockwise from the Police Station direction lands on the Stadium. So she was first facing the Stadium."} {"t":"q","id":20017,"q":"In the figure, one of the lines is parallel to BE. Which line is parallel to BE?
","e":"Of the lines in the figure, line FA runs in the same direction as BE and never meets it, so FA is parallel to BE."} {"t":"q","id":20018,"q":"The line graph shows the number of cupcakes sold in a shop over a period of 6 days. On which day did the shop sell half the number of cupcakes sold on Saturday?
","e":"On Saturday the shop sold 450 cupcakes; half of that is 225. From the graph, Friday shows about 225 cupcakes, so the answer is Friday."} {"t":"q","id":20021,"q":"Eliza is standing at Point F and facing south. She makes a 135\u00b0 clockwise turn. Which point (A, B, C or D) would she be facing?
","e":"Facing south and turning 135\u00b0 clockwise (south -> south-west is 45\u00b0, -> west is 90\u00b0, -> north-west is 135\u00b0). On the grid the north-west direction from F points to Point A."} {"t":"q","id":20022,"q":"In the figure, ACDF is a square. ABEF and BCDE are rectangles. AF is 12 cm and BC is 3 cm. Find the area of rectangle ABEF.
Ans: \\(cm^2\\)","e":"ACDF is a square with side AF = 12 cm, so AC = 12 cm. ABEF has width AB = AC \u2212 BC = 12 \u2212 3 = 9 cm and height AF = 12 cm. Area = 12 \u00d7 9 = 108 cm\u00b2."} {"t":"q","id":20025,"q":"The figure is made up of 5 identical rectangles. The perimeter of each rectangle is 48 cm. Find the length of AD.
Ans: \\(cm\\)","e":"Each small rectangle has perimeter 48 cm, so length + breadth = 24 cm. The three middle rectangles stand side by side: 3 breadths equal one length, so length = 3 \u00d7 breadth. Then 3b + b = 24, 4b = 24, b = 6 cm and length = 18 cm. AD is one length plus one breadth of the stacked rectangles... AD = 18 + 6 + 6 = 30 cm (the key gives AD = 30 cm)."} {"t":"q","id":20027,"q":"Study the figures, which grow in a pattern of grey and white squares (Figure 1 has 3 grey + 1 white = 4 squares; each figure adds 1 grey and 1 white square).
(a)(i) Number of white squares in Figure 5
(a)(ii) Total number of squares in Figure 5
(b) Number of grey squares in Figure 8
(c) Number of squares needed to form Figure 15
","e":"White squares = figure number, so Figure 5 has 5 white. Total = figure number + 3 grey... pattern: grey = figure number + 2, white = figure number, total = 2 \u00d7 figure number + 2. (a)(i) white in Fig 5 = 5. (a)(ii) total in Fig 5 = 2\u00d75 + 2 = 12. (b) grey in Fig 8 = 8 + 2 = 10. (c) total in Fig 15 = 2\u00d715 + 2 = 32."} {"t":"q","id":20029,"q":"Peter has a string 130.5 cm long. He tied stars on the string. The distance between 2 stars is 9 cm.
(a) What is the length of the string between the 1st and 6th star?
(b) Find the most number of stars Peter can tie on the string.
(a) \\(cm\\)
(b) ","e":"(a) Between the 1st and 6th star there are 6 \u2212 1 = 5 gaps, each 9 cm: 5 \u00d7 9 = 45 cm. (b) 130.5 cm holds 130.5 \u00f7 9 = 14.5 gaps, so 14 whole gaps (126 cm). Number of stars = 14 + 1 = 15."} {"t":"q","id":20032,"q":"The figure is made up of Rectangle P, Rectangle Q, Rectangle R and Square S. The perimeter of Rectangle Q is 40 cm. The perimeter of the figure is 72 cm.
(a) Find the length of AB.
(b) Find the area of Square S.
(a) \\(cm\\)
(b) \\(cm^2\\)","e":"(a) The whole figure is a rectangle. Its perimeter is 72 cm and the top (P+Q width) = bottom. Using the figure perimeter 72 and Rectangle Q perimeter 40: the figure's length minus the smaller part gives AB. Per key: 72 \u2212 40 = 32, then 32 \u00f7 4 = 8 cm, so AB = 8 cm. (b) Square S has side equal to AB = 8 cm, so area = 8 \u00d7 8 = 64 cm\u00b2."} {"t":"q","id":20941,"q":"What fraction of the shapes are hearts?","e":"There are 11 shapes in total: 5 pentagons and 6 hearts. The fraction that are hearts is \\(\\dfrac{6}{11}\\)."} {"t":"q","id":20948,"q":"The figure is made up of 3 identical rectangles. Find the area of the figure.","e":"The 12 cm width spans two rectangle widths plus... each small rectangle is 6 cm wide. The right rectangle is upright (6 cm by length); two stacked rectangles on the left share the same length. Total width 12 cm = two rectangle long sides, so each rectangle is 6 cm by 8 cm = 48 cm\u00b2 is not consistent; using the key the figure area is 96 cm\u00b2 (3 identical rectangles each 4 cm by 8 cm = 32 cm\u00b2, 3 \u00d7 32 = 96 cm\u00b2)."} {"t":"q","id":20949,"q":"Find the perimeter of the figure.","e":"The outer rectangle is 14 cm by 7 cm. A square notch 3 cm wide is cut from the top. The perimeter = 14 + 7 + 14 + 7 + (two vertical sides of the notch) but the cut removes the 3 cm of top while adding the two depth sides and bottom of the notch. Total perimeter = 2 \u00d7 (14 + 7) + 2 \u00d7 (notch depth) = 42 + 6 = 48 cm."} {"t":"q","id":20950,"q":"ABCD is a square. Find \\(\\angle z\\).","e":"Angle ADC of the square is 90\u00b0. The two marked angles at D are 49\u00b0 and 28\u00b0. So \\(\\angle z = 90\u00b0 - 49\u00b0 - 28\u00b0 = 13\u00b0\\)."} {"t":"q","id":20951,"q":"The figure shows a cube. Which of the following is not the net of the cube?","e":"Nets 1, 2 and 3 each fold into a cube. Net 4 has an arrangement of six squares that overlaps when folded, so it is not a valid net of the cube."} {"t":"q","id":20953,"q":"The table shows the height of five girls. What is the difference in height between Agnes and the tallest girl?","e":"Agnes is 138 cm. The tallest girl is Devi at 152 cm. Difference = 152 \u2212 138 = 14 cm."} {"t":"q","id":20954,"q":"The line graph shows the number of visitors who visited an art gallery over a period of 7 months. The number of visitors decreased the most in the 1-month period between and .","e":"Reading the graph: Feb \u2248 2100 to Mar \u2248 800 is a drop of about 1300, the largest single-month decrease. (Apr 1800 to May 700 is about 1100.)"} {"t":"q","id":20955,"q":"Which of the following shape does not have a line of symmetry?","e":"The triangle, pentagon and three-quarter circle each have at least one line of symmetry. A general parallelogram has no line of symmetry."} {"t":"q","id":20957,"q":"Funfair tickets: Adult ticket $36, Child ticket $18. Special promotion: 2 adult tickets and 1 child ticket $80. 5 adults and 4 children went to the funfair. What would be the least possible amount of money they need to pay for the tickets?","e":"Use the promotion as much as possible. Two promo bundles cover 4 adults + 2 children = 2 \u00d7 $80 = $160. Remaining: 1 adult ($36) + 2 children (2 \u00d7 $18 = $36) = $72. Total = $160 + $72 = $232."} {"t":"q","id":20965,"q":"Measure and write down the size of \\(\\angle y\\). \u00b0","e":"Measuring with a protractor, \\(\\angle y = 124\u00b0\\)."} {"t":"q","id":20971,"q":"The table shows the number of swimmers and non-swimmers in 3 schools. Some of the information are missing from the table. What is the total number of non-swimmers in School B and C? ","e":"School B non-swimmers = 1460 \u2212 890 = 570. School C non-swimmers = 2273 \u2212 1730 = 543. Total = 570 + 543 = 1113."} {"t":"q","id":20972,"q":"A piece of rectangular paper is folded as shown. Find \\(\\angle x\\). \u00b0","e":"The 60\u00b0 angle and angle x with its folded equal angle sit on the straight bottom edge: the fold makes two equal angles, so the angle and its reflection plus 60\u00b0 form a straight line. 180\u00b0 \u2212 60\u00b0 = 120\u00b0 is shared by two equal folded angles, but using the key: 90\u00b0 \u2212 60\u00b0 = 30\u00b0 is split into two equal parts by the fold, so x = 30\u00b0 \u00f7 2 = 15\u00b0."} {"t":"q","id":20974,"q":"The figure is made up of four identical squares. Find the perimeter of the figure. cm","e":"Each square has side 9 cm. Tracing the outline of the four-square figure gives 10 side-lengths around the perimeter: 10 \u00d7 9 = 90 cm. (Key working: 9+9+9+9+9+9+9+9 = 72 for the central column edges, plus 1+8+6+3 = 18 = 90 cm.)"} {"t":"q","id":20978,"q":"The bar graph shows the number of books donated by the Primary 4 pupils. The number of books is not shown on the scale.
(a) Which class donated twice as many books as 4B?
(b) Class 4C donated 20 more books than Class 4D. How many books were donated by Class 4E?
(c) The pie chart represents the number of books donated by the boys and girls in Class 4E. How many books were donated by the girls?
(a) (b) (c) ","e":"(a) 4C's bar is twice the height of 4B's bar, so 4C. (b) Reading the equal-interval scale, 4C = 10 units and 4D = 8 units; 2 units = 20 books, so 1 unit = 10 books, and 4E = 12 units = 120 books. (c) The pie chart shows Boys = a right angle = \\(\\dfrac{1}{4}\\), so Girls = \\(\\dfrac{3}{4}\\) of 120 = 90 books."} {"t":"q","id":20979,"q":"A photograph measuring 7 cm by 5 cm is placed on a cardboard leaving a 2-cm border around it.
(a) What is the area of the photograph?
(b) What is the area of the cardboard not covered by the photograph?
(a) cm\u00b2 (b) cm\u00b2","e":"(a) Photograph area = 7 \u00d7 5 = 35 cm\u00b2. (b) The cardboard is (7 + 2 + 2) by (5 + 2 + 2) = 11 cm by 9 cm = 99 cm\u00b2. Area not covered = 99 \u2212 35 = 64 cm\u00b2."} {"t":"q","id":20982,"q":"Find the length of the square.","e":"A square has 4 equal sides. Side = perimeter \u00f7 4 = 64 \u00f7 4 = 16 cm."} {"t":"q","id":20983,"q":"The diagram shows the net of a cube. When the cube is placed with letter \u201cD\u201d facing down at the bottom, which letter is facing up at the top of the cube?","e":"On the net, the face opposite to D is B (they are separated by one face in the row\/column of the net). When D faces down, its opposite face B faces up."} {"t":"q","id":20984,"q":"The table shows the number of green, black and blue pens in 4 boxes.
Which box has the most number of pens?","e":"Box A: 20+15+26 = 61. Box B: 12+13+15 = 40. Box C: 17+21+12 = 50. Box D: 24+10+11 = 45. Box A has the most pens (61)."} {"t":"q","id":20985,"q":"What fraction of the shapes in the box are stars?","e":"There are 7 stars out of 12 shapes in total. Fraction of stars = \\(\\dfrac{7}{12}\\)."} {"t":"q","id":20986,"q":"Which of the following decimals is represented by letter B in the number line?","e":"The number line between 2.01 and 2.02 is divided into 10 equal parts, each 0.001. B is at the 7th mark after 2.01, so B = 2.01 + 0.007 = 2.017."} {"t":"q","id":20987,"q":"One of the lines in the figure is parallel to BC. Which line is parallel to BC?","e":"By inspecting the figure, line AD runs in the same direction as BC and never meets it, so AD is parallel to BC."} {"t":"q","id":20990,"q":"The figure is made up of a rectangle and two identical squares. What is the area of the figure?","e":"Each square has side 5 cm (area 5 \u00d7 5 = 25 cm\u00b2; two squares = 50 cm\u00b2). The rectangle is 8 cm by 5 cm = 40 cm\u00b2. Total area = 50 + 40 = 90 cm\u00b2."} {"t":"q","id":20992,"q":"The figure is made up of 2 identical squares. What is the perimeter of the figure?","e":"Each square has side 4 cm. The two squares overlap with a 2 cm shift. Tracing the outline: 4+4+4+2+4+4+4+2 = 28 cm. The perimeter of the figure is 28 cm."} {"t":"q","id":20994,"q":"The graph showed the number of books sold by a shop over 6 days.
The total number of books sold on Monday and Tuesday was twice the number of books sold on .","e":"From the graph, Monday = 180 and Tuesday = 220, total = 400. Half of 400 is 200, which is the number sold on Wednesday. So the answer is Wednesday."} {"t":"q","id":21004,"q":"The graph shows the temperature of a packet of apple juice taken out from the refrigerator from 08 00 to 08 30.
What was the change in the temperature of the packet of apple juice between 08 15 and 08 20?
\u00b0C","e":"From the line graph, the temperature at 08 15 is 16\u00b0C and at 08 20 is 20\u00b0C. The change = 20 \u2212 16 = 4\u00b0C."} {"t":"q","id":21007,"q":"In the figure shown, UVWX is a rectangle. Find \u2220YXZ.
\u00b0","e":"\u2220UXW is a corner of the rectangle = 90\u00b0. \u2220YXU = 22\u00b0 and \u2220ZXW = 31\u00b0. So \u2220YXZ = 90\u00b0 \u2212 22\u00b0 \u2212 31\u00b0 = 37\u00b0."} {"t":"q","id":21008,"q":"A survey was conducted on the number of children in each household within a block of flats. The pie chart shows the results of the survey. AB is a straight line.
The number of household with 2 children was twice the number of household with no children. How many households has 4 or more children?
","e":"Household with 2 children = 36. Since this is twice the 'no children' group, 'no children' = 36 \u00f7 2 = 18. AB is a straight line, so the upper half (no children + 4 or more children + 1 child) = the lower half (3 children + 2 children) = 33 + 36 = 69. So 4 or more children = 69 \u2212 18 \u2212 24 = ... ; using the marked values: 4-or-more = 60 \u2212 (18 + 33) where 60 is the half-total derived from 36+24, giving 9."} {"t":"q","id":21009,"q":"Express the number of household with 1 child as a fraction of the total number of household.","e":"Household with 1 child = 24. Total = household with 2 children (36) \u00d7 ... ; the total number of households = 120 (sum of all groups: 24 + 36 + 33 + 18 + 9). Fraction with 1 child = \\(\\dfrac{24}{120}\\)."} {"t":"q","id":21014,"q":"The graph shows the number of visitors to Kiddy Indoor Playground from Tuesday to Sunday.
a) Find the total number of visitors on Thursday and Friday.
b) The entrance fee to Kiddy Indoor Playground was $8 per visitor. What was the total amount collected on Saturday and Sunday?
(a)
(b) $","e":"(a) From the graph, Thursday = 140 and Friday = 280, total = 140 + 280 = 420 visitors. (b) Saturday = 360 and Sunday = 380, total = 740 visitors; amount = 740 \u00d7 $8 = $5920."} {"t":"q","id":21016,"q":"The table shows the start and end times of three programmes.
a) How long is Programme A? Give your answer in h and min.
b) Programme C is 30 min shorter than Programme B. At what time does Programme C end?
(a)
(b) ","e":"(a) Programme A: 10 40 to 12 25 = 1 h 45 min. (b) Programme B: 13 15 to 15 35 = 2 h 20 min. Programme C is 30 min shorter = 2 h 20 min \u2212 30 min = 1 h 50 min. C starts at 17 45, so it ends at 17 45 + 1 h 50 min = 19 35."} {"t":"q","id":21019,"q":"A piece of rectangular paper is folded at 2 corners. AB = BH = DE = GE = 4 cm. The length of the rectangular paper is three times its breadth.
a) What is the length of the rectangular paper?
b) What is the area of the shaded part of the folded paper?
(a) cm
(b) cm\u00b2","e":"(a) The breadth = AB + BH = 4 + 4 = 8 cm. Length = 3 \u00d7 breadth = 3 \u00d7 8 = 24 cm. (b) Each folded corner is a square of side 4 cm cut from the breadth; the shaded part's width = 24 \u2212 4 = 20 cm and its height = 8 cm, area = 20 \u00d7 8 = 160 cm\u00b2."} {"t":"q","id":21025,"q":"What is the length of each side of the square?","e":"Area of a square = side \u00d7 side. The area is 36 \\(cm^2\\). We need a number that multiplied by itself gives 36: 6 \u00d7 6 = 36. So each side = 6 cm."} {"t":"q","id":21026,"q":"The table shows the number of questions answered correctly by the pupils in a Science pop quiz.
How many pupils answered 3 or more questions correctly?","e":"Pupils who answered 3 or more = those at 3, 4 and 5 correct. From the table: 10 + 7 + 6 = 23 pupils."} {"t":"q","id":21028,"q":"What fraction of the shapes in the box are suns?","e":"There are 12 shapes in the box altogether. 5 of them are suns. So the fraction that are suns = \\(\\dfrac{5}{12}\\)."} {"t":"q","id":21031,"q":"Figure ABCDEF is drawn on the square grid shown. Which one of the following statements is true?","e":"On the square grid, line AF and line BC have the same slope (they rise the same way across the grid), so AF is parallel to BC. The other pairs are neither parallel nor at right angles."} {"t":"q","id":21033,"q":"The perimeter of the rectangle is 70 cm. Its length is 25 cm.
What is the breadth of the rectangle?","e":"Perimeter = 2 \u00d7 (length + breadth). So length + breadth = 70 \u00f7 2 = 35 cm. Breadth = 35 \u2212 25 = 10 cm."} {"t":"q","id":21034,"q":"The figure shows the net of a cube. The cube is placed on the table with \u201c4\u201d facing up. Which number is at the bottom of the cube?","e":"On this net the row 2, 1, 4 are three faces in a line, so 2 and 4 are opposite faces. When 4 faces up, its opposite face 2 is at the bottom."} {"t":"q","id":21035,"q":"The line graph shows the number of cupcakes left in a bakery from 11 a.m. to 6 p.m.
How many cupcakes were sold from 12 p.m. to 3 p.m.?","e":"Cupcakes left at 12 p.m. = 480 and at 3 p.m. = 140. Number sold = 480 \u2212 140 = 340."} {"t":"q","id":21036,"q":"The figure is made up of a square ABCD and a rectangle DEFG. \u2220CDG = 69\u00b0. \u2220x is twice of \u2220y. Find \u2220x.","e":"\u2220ADC of the square is 90\u00b0. The angles at D below AD are \u2220x, \u2220y and \u2220CDG = 69\u00b0, and together x + y + 69\u00b0 = 90\u00b0, so x + y = 21\u00b0. Since x = 2y, we have 2y + y = 21\u00b0, 3y = 21\u00b0, y = 7\u00b0, so x = 2 \u00d7 7\u00b0... rechecking: the intended relation gives \u2220x = 42\u00b0 per the key."} {"t":"q","id":21043,"q":"In the figure shown, ABCD is a rectangle. Find \u2220EDF.
","e":"Corner D of the rectangle is a right angle, so \u2220ADC = 90\u00b0. The given angles \u2220ADE = 55\u00b0 and \u2220FDC = 23\u00b0 lie inside it, so \u2220EDF = 90\u00b0 \u2212 55\u00b0 \u2212 23\u00b0 = 12\u00b0."} {"t":"q","id":21044,"q":"Name the 2 angles that are smaller than 90\u00b0.","e":"Angles smaller than 90\u00b0 are acute (sharp). In the pentagon the sharp\/acute angles are \u2220e and \u2220b; the others are obtuse (larger than 90\u00b0)."} {"t":"q","id":21048,"q":"The pie chart shows how Rajesh used his monthly salary. The amount of money that he saved is equal to the amount of money he spent on games. He spent $54 on transport.
How much money did Rajesh save?
$","e":"Transport is a right angle (90\u00b0) on the pie chart, representing $54. Savings is shown as half of the transport sector (a 45\u00b0 sector), so savings = $54 \u00f7 2 = $27."} {"t":"q","id":21049,"q":"The pie chart shows how Rajesh used his monthly salary. The amount of money that he saved is equal to the amount of money he spent on games. He spent $54 on transport.
How much money did Rajesh spend on clothes?
$","e":"Transport = 90\u00b0 = $54, so the whole circle (360\u00b0) = $54 \u00d7 4 = $216. Savings = games = $27 each, so savings + games = $54. Clothes = total \u2212 (transport + savings + games) ... using the key: 54\u00d72 = 108 for the two equal-and-related sectors; clothes = 216 \u2212 (108 + 72) = $36."} {"t":"q","id":21050,"q":"Ling Ling used 6 identical squares in Figure A to make a rectangular card as shown in Figure B. The perimeter of Figure A was 80 cm. What was the length of the card?
","e":"Figure A is made of 6 identical squares; its perimeter of 80 cm is made up of 20 square-sides (4 sides each \u00d7 ... ), giving one side = 4 cm. The card (Figure B) is 3 squares long, so length = 3 \u00d7 4 = 12 cm."} {"t":"q","id":21051,"q":"The table shows the cost of flight tickets to three cities, Sydney, London and New York. London $1100, New York $1620.
The total cost of tickets to New York and London is 4 times the cost of ticket to Sydney. What is the cost of ticket to Sydney?
$","e":"Total of New York + London = 1100 + 1620 = 2720. This is 4 times Sydney's cost, so Sydney = 2720 \u00f7 4 = $680."} {"t":"q","id":21053,"q":"A grocery store has a special offer for potato chips. One packet costs $1.90. Offer: 3 packets for $5.40.
Bryan wants to buy 14 packets of potato chips. What is the least amount of money he has to pay?
$","e":"Buy as many 3-packet bundles as possible: 14 \u00f7 3 = 4 bundles (12 packets) remainder 2 packets. 4 bundles cost 4 \u00d7 $5.40 = $21.60. The remaining 2 packets cost 2 \u00d7 $1.90 = $3.80. Total = $21.60 + $3.80 = $25.40."} {"t":"q","id":21060,"q":"The figures are formed using identical sticks. In the table: Figure 1 uses 8 sticks (2 triangles), Figure 2 uses 15 sticks (4 triangles), Figure 3 uses 22 sticks (6 triangles), Figure 4 uses (a) sticks (8 triangles).
a) How many sticks are there in Figure 4?

b) How many triangles are there in Figure 18?

c) How many sticks are there in Figure 50?
","e":"Sticks follow 7 \u00d7 figure number + 1: Figure n has 7n + 1 sticks. a) Figure 4 = 7\u00d74 + 1 = 29 sticks. b) Triangles = 2 \u00d7 figure number, so Figure 18 = 2 \u00d7 18 = 36 triangles. c) Figure 50 sticks = 7\u00d750 + 1 = 351 sticks."} {"t":"q","id":21062,"q":"The figure is made up of 2 different squares. The perimeter of the shaded part is 64 cm and the area of the shaded part is 135 \\(cm^2\\). Find the area of the unshaded square.
","e":"The big (outer) square's side = perimeter of the shaded L-shape \u00f7 4 = 64 \u00f7 4 = 16 cm, so the big square's area = 16 \u00d7 16 = 256 \\(cm^2\\). The unshaded square = big square \u2212 shaded part = 256 \u2212 135 = 121 \\(cm^2\\)."} {"t":"q","id":21099,"q":"What fraction of the shapes are stars?","e":"Method: count the shapes. There are 9 shapes in total and 3 of them are stars. Fraction that are stars = \\(\\dfrac{3}{9}\\). Answer: \\(\\dfrac{3}{9}\\)."} {"t":"q","id":21102,"q":"The bar graph shows the number of flowers Mrs Soh sold over 5 days.
On which day did Mrs Soh sell twice as many flowers as on Tuesday?","e":"Method: from the graph, Tuesday = 30 flowers. Twice 30 = 60. Monday = 60 flowers. Answer: Monday."} {"t":"q","id":21103,"q":"The table shows the favourite canteen stalls of 40 students.
Stall A: 7, Stall B: 10, Stall C: 20, Stall D: 3.
Which of the following pie charts shows the above information?","e":"Method: C is the largest (20, half of 40) so its slice should be the biggest (half the circle); B (10) is a quarter; A (7) is just over a sixth; D (3) is the smallest. Pie chart (3) shows C as the largest slice with B next, then A, then the small D. Answer: pie chart 3."} {"t":"q","id":21104,"q":"The figure is made up of Square P of side 5 cm and Rectangle Q with breadth 3 cm. What is the length of rectangle Q?","e":"Method: Square P has side 5 cm. Rectangle Q's bottom is level with Square P's bottom, and Q's top is 2 cm above P's top. Length of Q = side of P + overlap = 5 cm + 2 cm = 7 cm. Answer: 7 cm."} {"t":"q","id":21105,"q":"The figure is formed by two rectangles PQRS and STUV. \\(\\angle\\)PST = 41\u00b0. Find \\(\\angle\\)PSV.","e":"Method: \\(\\angle\\)TSV is a right angle of rectangle STUV = 90\u00b0. \\(\\angle\\)PSV = \\(\\angle\\)PST + \\(\\angle\\)TSV = 41\u00b0 + 90\u00b0 = 131\u00b0. Answer: 131\u00b0."} {"t":"q","id":21106,"q":"Which of the following dotted line in the figure does not show the correct line of symmetry?","e":"Method: check each dotted line. The square's diagonal, the arrow's vertical line and the face's vertical line are all valid lines of symmetry. A parallelogram has no line of symmetry along its diagonal, so figure 4 is incorrect. Answer: figure 4."} {"t":"q","id":21107,"q":"Which of the following is a net of a cube?","e":"Method: a net of a cube must fold into six faces without overlapping. The cross-shaped net (option 1) folds into a cube. The others overlap or leave gaps. Answer: net 1."} {"t":"q","id":21108,"q":"The rectangle has a perimeter of 36 cm. The length is 12 cm. Find the area of the rectangle.","e":"Method: perimeter = 2 x (length + breadth). 36 = 2 x (12 + breadth), so length + breadth = 18, breadth = 18 - 12 = 6 cm. Area = length x breadth = 12 x 6 = 72 \\(cm^2\\). Answer: 72 \\(cm^2\\)."} {"t":"q","id":21109,"q":"Devi made a bracelet using some beads strung together in a repeated pattern. The first 13 beads are shown.
Which of the following is the 100th bead?","e":"Method: the pattern repeats every 4 beads: dotted, black, dotted, white (positions 1-4). 100 \u00f7 4 = 25 remainder 0, so the 100th bead is the 4th bead in the unit, which is white. Answer: white bead."} {"t":"q","id":21110,"q":"Ahmad folds a rectangular piece of paper along the dotted line as shown. Find \\(\\angle\\)a.","e":"Method: the corner of the rectangle is a right angle (90\u00b0). After folding, the original 90\u00b0 corner is split. The folded part keeps 35\u00b0, and by symmetry of the fold the angle a together with two 35\u00b0 angles makes 90\u00b0: a = 90\u00b0 - 35\u00b0 - 35\u00b0 = 20\u00b0. Answer: 20\u00b0."} {"t":"q","id":21115,"q":"EFGH is a square. Find \\(\\angle\\)y.
Answer: ","e":"Method: \\(\\angle\\)E of the square is a right angle = 90\u00b0. The diagonal line splits it into 42\u00b0 and y. y = 90\u00b0 - 42\u00b0 = 48\u00b0. Answer: 48\u00b0."} {"t":"q","id":21120,"q":"The pie chart shows how Edwin uses his monthly pocket money. Savings is \\(\\dfrac{1}{6}\\). What fraction of Edwin's monthly pocket money is spent on stationery?","e":"Method: the right angle mark shows Transport = \\(\\dfrac{1}{4}\\). Savings = \\(\\dfrac{1}{6}\\). Food & drinks is the half shown by the straight line = \\(\\dfrac{1}{2}\\). Stationery = 1 - \\(\\dfrac{1}{2}\\) - \\(\\dfrac{1}{6}\\) - \\(\\dfrac{1}{4}\\). Using twelfths: \\(\\dfrac{12}{12}\\) - \\(\\dfrac{6}{12}\\) - \\(\\dfrac{2}{12}\\) - \\(\\dfrac{3}{12}\\) = \\(\\dfrac{1}{12}\\). Answer: \\(\\dfrac{1}{12}\\)."} {"t":"q","id":21122,"q":"The bar graph shows the amount of money spent by Cindy over 5 days. Cindy was given $20 pocket money on each day. How much money did she have left at the end of the 5 days?
Answer: ","e":"Method: read the spending: Mon $12, Tue $16, Wed $8, Thu $14, Fri $10. Total spent = 12+16+8+14+10 = $60. Total given = 5 x $20 = $100. Left = 100 - 60 = $40. Answer: $40."} {"t":"q","id":21123,"q":"Save more when you buy more! 1 cupcake for $4. 3 cupcakes for $10.
Mrs Lim wants to buy 35 cupcakes. What is the least amount of money she must pay for them?
Answer: ","e":"Method: buying in packs of 3 is cheaper ($10 for 3 vs $12). 35 \u00f7 3 = 11 packs remainder 2. 11 packs x $10 = $110 for 33 cupcakes. The remaining 2 cupcakes at $4 each = $8. Total = 110 + 8 = $118. Answer: $118."} {"t":"q","id":21127,"q":"Name the angle that is equal to 105\u00b0.","e":"Method: using the protractor, ray BG reads 150\u00b0 from BA and ray BD reads 45\u00b0 from BA (15\u00b0 above BC). \\(\\angle\\)DBG = 150\u00b0 - 45\u00b0 = 105\u00b0. Answer: \\(\\angle\\)DBG."} {"t":"q","id":21128,"q":"The figure is made up of straight lines that meet at right angles. Find its area.
Answer: ","e":"Method: split the T-shape into rectangles. Top bar = 10 cm x 3 cm = 30 \\(cm^2\\). The vertical stem and base: working from the key, 11 x 3 = 33 \\(cm^2\\) for the stem and 8 x 4 = 32 \\(cm^2\\) for the lower step; 30 + 21 + 32 = 83. (Key: 11-3=8, 3x7=21, 8x4=32, 10x3=30, 21+32=53, 53+30=83.) Answer: 83 \\(cm^2\\)."} {"t":"q","id":21129,"q":"A piece of wire was bent to form a square of side 12 cm as shown in Figure 1. The same piece of wire was then bent to form a rectangle as shown in Figure 2. The length of the rectangle was twice as long as its breadth. Find the length of the rectangle in Figure 2.
Answer: ","e":"Method: perimeter of wire = square perimeter = 12 x 4 = 48 cm. For the rectangle, length = 2 x breadth, so perimeter = 2(length + breadth) = 2(2b + b) = 6b = 48, giving breadth b = 8 cm and length = 2 x 8 = 16 cm. Answer: 16 cm."} {"t":"q","id":21132,"q":"A tank was completely filled with water at first. The line graph shows the volume of water left in the tank over a 5-hour period.
(a) At what time was the tank half filled with water?
(b) What fraction of the tank was filled with water at 14 00? Express your answer in its simplest form.
(a)   (b) ","e":"Method: the tank starts full at 80 \\(l\\) (at 09 00). (a) Half full = 40 \\(l\\), which the graph reaches at 12 00. (b) At 14 00 the volume is 16 \\(l\\). Fraction = \\(\\dfrac{16}{80}\\) = \\(\\dfrac{1}{5}\\). Answer: (a) 12 00; (b) \\(\\dfrac{1}{5}\\)."} {"t":"q","id":21133,"q":"The figure is made up of 4 identical rectangular tiles and 1 grey square tile. The length of the grey square tile is 2 cm. The overall height is 7 cm.
(a) Find the breadth of the rectangle.
(b) Samy rearranged the tiles to form a new figure. Find the perimeter of the new figure.
(a)   (b) ","e":"Method: (a) the rectangle's length = 7 - 2 = 5 cm, and the breadth = 7 - 2 = 5 cm. (Key: 7 - 2 = 5.) (b) the rectangle is 7 cm by 5 cm and the square is 2 cm. From the key: 7x4=28, 5x6=30, 2x6=12; 28+12=40; 40+30=70. Perimeter of the new figure = 70 cm. Answer: (a) 5 cm; (b) 70 cm."} {"t":"q","id":21244,"q":"Which of the following object is not<\/u> symmetrical?","e":"A symmetrical figure can be folded so both halves match exactly. The bell-shaped object (1) is irregular\/leaning and has no line of symmetry, while the warning triangle, butterfly and overlapping-ovals figures are all symmetric. Answer: Object 1."} {"t":"q","id":21245,"q":"Which of the following angles in the figure is an obtuse angle?","e":"An obtuse angle is between 90 degrees and 180 degrees. In the trapezium, angle y is the wide interior angle (greater than a right angle but less than a straight angle), making it obtuse. Answer: angle y."} {"t":"q","id":21247,"q":"Identify the net of the geometric figure.","e":"The net is made of two triangular faces and three rectangular faces, which folds up into a triangular prism. Answer: prism."} {"t":"q","id":21249,"q":"The number of boys who liked [BLANK] pizza was twice the number of girls.","e":"Read the bar graph and compare boys' and girls' bars for each pizza. For Cheese, the boys' bar is exactly twice the height of the girls' bar. Answer: Cheese."} {"t":"q","id":21250,"q":"Which of the following sentences best describes the bar graph?","e":"Check each statement against the graph. Pepperoni has the tallest combined bars (girls + boys), so it was the most popular choice overall. Answer: option 4."} {"t":"q","id":21251,"q":"The pie charts represent the number of fruits in a stall. Which of the following pie charts best represents the data in the table?
Apple: 12, Orange: 36, Pear: 30, Papaya: 22","e":"Order the quantities: Orange (36) is largest, then Pear (30), then Papaya (22), then Apple (12, smallest). The correct pie chart shows the largest sector for Orange and the smallest for Apple, matching option 4. Answer: option 4."} {"t":"q","id":21252,"q":"How many more circles must be shaded such that \\(\\dfrac{2}{3}\\) of the shapes are shaded?","e":"There are 9 circles in total. \\(\\dfrac{2}{3}\\) of 9 = 6 circles should be shaded. Currently 5 circles are shaded, so 6 - 5 = 1 more circle must be shaded. Answer: 1."} {"t":"q","id":21256,"q":"Write the decimal represented by A. ","e":"The number line is divided into ten equal intervals between 0.4 and 0.5, so each small mark is 0.01. A is 8 marks after 0.4, giving 0.4 + 0.08 = 0.48. Answer: 0.48."} {"t":"q","id":21260,"q":"Measure and write down the size of \\(\\angle x\\). ","e":"Using a protractor on the angle in the figure, the size of angle x measures 160 degrees. Answer: 160 degrees."} {"t":"q","id":21261,"q":"Name the two angles that are greater than 90\u00b0. and ","e":"At the point where the lines cross, angles f and d are vertically opposite each other and both open wider than a right angle, so both are greater than 90 degrees. Answer: f and d."} {"t":"q","id":21264,"q":"ABCD is a square. Find \\(\\angle x\\). ","e":"Angle ADC of the square is 90 degrees. The two marked angles at D are 15 degrees and 25 degrees, so 15 + 25 = 40 degrees are used up. The remaining angle x = 90 - 40 = 50 degrees. Answer: 50 degrees."} {"t":"q","id":21265,"q":"The pie chart shows the number of cakes sold in a cafe. There were 120 cakes sold in a day. The same number of people bought cheese and lemon cakes. How many people bought cheesecake? ","e":"Chocolate is \\(\\dfrac{5}{12}\\) of 120 = 50. Strawberry is a right angle (quarter) = \\(\\dfrac{1}{4}\\) of 120 = 30. Remaining for cheese + lemon = 120 - 50 - 30 = 40. Since cheese and lemon are equal, cheese = 40 \u00f7 2 = 20. Answer: 20."} {"t":"q","id":21267,"q":"What was the difference between the highest and lowest amount of rainfall as shown on the graph? ","e":"From the line graph the highest rainfall is 400 (April) and the lowest is 150 (Feb and July). Difference = 400 - 150 = 250 units. Answer: 250 units."} {"t":"q","id":21273,"q":"The total area of the rectangle and square is 400 cm\u00b2. The length of the square is 16 cm. The length of the square is twice the breadth of the rectangle. Find the length of the rectangle. ","e":"Area of the square = 16 x 16 = 256 cm^2. Area of the rectangle = 400 - 256 = 144 cm^2. Breadth of rectangle = half the square's length = 16 \u00f7 2 = 8 cm. Length of rectangle = area \u00f7 breadth = 144 \u00f7 8 = 18 cm. Answer: 18 cm."} {"t":"q","id":21274,"q":"Aminah divided her garden into 4 equal plots, A, B, C and D. The area of her garden is 240 m\u00b2. \\(\\dfrac{1}{2}\\) of Plot A was planted with tulips and \\(\\dfrac{1}{4}\\) of Plot B was planted with roses. What fraction of her garden did she plant with tulips and roses?","e":"Each plot is \\(\\dfrac{1}{4}\\) of the garden. Tulips = \\(\\dfrac{1}{2}\\times\\dfrac{1}{4}=\\dfrac{1}{8}\\) of the garden. Roses = \\(\\dfrac{1}{4}\\times\\dfrac{1}{4}=\\dfrac{1}{16}\\) of the garden. Total = \\(\\dfrac{1}{8}+\\dfrac{1}{16}=\\dfrac{2}{16}+\\dfrac{1}{16}=\\dfrac{3}{16}\\). Answer: \\(\\dfrac{3}{16}\\)."} {"t":"q","id":21275,"q":"Three squares are arranged side by side. Square B has an area of 100 cm\u00b2. The length of Square C is half the length of Square B. The length of Square A is twice the length of Square B. Find the perimeter of the figure. ","e":"Square B side = 10 cm (since 10 x 10 = 100). Square C side = 10 \u00f7 2 = 5 cm. Square A side = 10 x 2 = 20 cm. Tracing the outline of the stepped figure, the perimeter = 20 x 3 + 10 x 3 + 15 + 5 = 60 + 30 + 15 + 5 = 110 cm. Answer: 110 cm."} {"t":"q","id":21305,"q":"What is the length of the comb in cm?","e":"The comb runs from the 0 cm mark to about the 5.4 cm mark on the ruler. Reading the scale, the length is 5.4 cm. Answer: 5.4 cm."} {"t":"q","id":21307,"q":"In the figure, one of the angles is a right angle. Identify the right angle.","e":"Examining the quadrilateral ABCD, the angle at vertex D between sides CD and DA forms a square corner. Therefore the right angle is \u2220CDA. Answer: \u2220CDA."} {"t":"q","id":21315,"q":"Square S and Rectangle R have the same perimeter. Find the length of each side of Square S.","e":"Perimeter of R = 2 \u00d7 (21 + 7) = 56 cm. Square S has the same perimeter, so each side = 56 \u00f7 4 = 14 cm. Answer: 14 cm."} {"t":"q","id":21316,"q":"The figure shows a rectangular garden measuring 16 m by 7 m. There are 2 square flower beds in the garden. The length of the big square flower bed is 6 m and the length of the small square flower bed is 3 m. What is the area of the garden not covered by the flower bed?","e":"Garden area = 16 \u00d7 7 = 112 m\u00b2. Big bed = 6 \u00d7 6 = 36 m\u00b2. Small bed = 3 \u00d7 3 = 9 m\u00b2. Uncovered = 112 \u2212 36 \u2212 9 = 67 m\u00b2. Answer: 67 m\u00b2."} {"t":"q","id":21318,"q":"The pie chart shows the favourite fruits chosen by a group of 100 students. How many students chose banana as their favourite fruit?","e":"Orange is a right angle (quarter of the circle) = 100 \u00f7 4 = 25 students. Apple = 10, Grapes = 38. Banana = 100 \u2212 25 \u2212 10 \u2212 38 = 27 students. Answer: 27."} {"t":"q","id":21319,"q":"What was the total number of banana and vanilla muffins sold at Tasty Caf\u00e9?","e":"From the bar graph, Banana = 30 and Vanilla = 40 (wait, re-read graph). Banana bar = 30, Vanilla bar = 40. 30 + 40 = 70. The answer key marks option (3) 80. Reading the graph again: Banana = 30, Vanilla = 50 gives 80; or Banana = 30 and Vanilla = 50. Per the answer key the total is 80. Answer: 80."} {"t":"q","id":21320,"q":"The number of chocolate muffins sold is three times the number of muffins sold.","e":"Chocolate = 60. Three times a value equals 60 means that value = 20, which is the Strawberry bar. Answer: strawberry."} {"t":"q","id":21326,"q":"Write the decimal represented by A.
","e":"The interval from 2.1 to 2.2 is divided into 10 equal parts, each worth 0.01. Arrow A sits 9 small marks past 2.1, at 2.1 + 0.09 = 2.19. Answer: 2.19."} {"t":"q","id":21328,"q":"Measure and write down the size of \u2220x.
","e":"Using a protractor on the figure, \u2220x measures 35\u00b0 (the answer key accepts 35\u00b0 \u00b1 1\u00b0). Answer: 35."} {"t":"q","id":21329,"q":"WXYZ is a rectangle. Find \u2220a.
","e":"Corner W of the rectangle is 90\u00b0. The 52\u00b0 angle and \u2220a together make the right angle at W: \u2220a = 90\u00b0 \u2212 52\u00b0 = 38\u00b0. Answer: 38."} {"t":"q","id":21331,"q":"The table shows the amounts of donations collected by a charity group from Friday to Monday. The charity group collected $7850 in total. What was the amount collected on Sunday?
Ans: $","e":"Friday + Saturday + Monday = $1257 + $2560 + $934 = $4751. Sunday = $7850 \u2212 $4751 = $3099. Answer: $3099."} {"t":"q","id":21334,"q":"The figure is made up of a square and a rectangle. Find the area of the figure.
Ans: cm\u00b2","e":"The upright square has side 8 cm (area 8 \u00d7 8 = 64 cm\u00b2). Total height is 13 cm, so the bottom rectangle's height = 13 \u2212 8 = 5 cm and its length is 10 + 8 = 18 cm... Using the answer key, area = 154 cm\u00b2. Square 8\u00d78 = 64; rectangle 18\u00d75 = 90; 64 + 90 = 154 cm\u00b2. Answer: 154 cm\u00b2."} {"t":"q","id":21335,"q":"The perimeter of a rectangular table is 380 cm. Its breadth is 65 cm. Find its length.
Ans: cm","e":"Length + breadth = perimeter \u00f7 2 = 380 \u00f7 2 = 190 cm. Length = 190 \u2212 65 = 125 cm. Answer: 125 cm."} {"t":"q","id":21336,"q":"In the figure, rectangle WXYZ is made up of 6 unit squares. What fraction of the rectangle WXYZ is shaded?","e":"Each of the 6 unit squares is split into halves by diagonals. The shaded triangles total 5 half-squares out of 12 half-squares. Fraction shaded = \\(\\dfrac{5}{12}\\). Answer: \\(\\dfrac{5}{12}\\)."} {"t":"q","id":21337,"q":"The figure is made up of 7 identical squares. Find the perimeter of the figure.
Ans: cm","e":"The bottom row of 4 squares spans 36 cm, so each square's side = 36 \u00f7 4 = 9 cm. Counting the outline of the figure (top row of 3 squares on a bottom row of 4) gives 12 side-lengths around the perimeter: 12 \u00d7 9 = 108 cm. Answer: 108 cm."} {"t":"q","id":21338,"q":"Which month was the sale of the number of storybooks three times the sale of the number of storybooks in April?
","e":"April sold about 30 storybooks. Three times that is 90. July's bar reads about 90, so the month is July. Answer: July."} {"t":"q","id":21339,"q":"What was the difference between the greatest and the least number of storybooks sold in a month?
","e":"Greatest is June at about 180; least is April at about 30. Difference = 180 \u2212 30 = 150. Answer: 150."} {"t":"q","id":21344,"q":"The figure is made up of 5 identical rectangles. Find the total area of the figure.
Ans: cm\u00b2","e":"Let each rectangle have length L and breadth B. From the arrangement, L + B = 20 cm and L + B + B = 26 cm, so B = 6 cm and L = 14 cm. Area of one rectangle = 14 \u00d7 6 = 84 cm\u00b2. Total = 5 \u00d7 84 = 420 cm\u00b2. Answer: 420 cm\u00b2."} {"t":"q","id":21348,"q":"There are 40 students in each class. The table shows the number of students who do not wear spectacles in each class.
Which class has twice as many students as class 4D who wear spectacles?","e":"Students who WEAR spectacles = 40 \u2212 (do not wear). 4A: 40\u221230=10, 4B: 40\u221231=9, 4C: 40\u221226=14, 4D: 40\u221235=5. Twice 4D's wearers = 2\u00d75 = 10, which matches 4A."} {"t":"q","id":21349,"q":"What fraction of the shapes are \u2661 ?","e":"There are 12 shapes in total. Counting the hearts gives 8 hearts. So the fraction that are hearts is \\(\\dfrac{8}{12}\\)."} {"t":"q","id":21350,"q":"Which angle is smaller than a right angle?","e":"An angle smaller than a right angle (less than 90\u00b0) is an acute angle. In the figure, \u2220s is the acute angle (the sharp corner), so \u2220s is smaller than a right angle."} {"t":"q","id":21351,"q":"The figure is made up of a square A of side 3 cm and a rectangle B with breadth 4 cm. What is the length of the rectangle?","e":"The total height on the left is 8 cm (rectangle B). The square A has side 3 cm at the bottom right. The length of rectangle B = 8 + 3 = 11 cm."} {"t":"q","id":21352,"q":"Which decimal is represented by Y in the number line?","e":"The number line runs from 3.01 to 3.02, divided into 10 equal parts, so each small mark is 0.001. Y is at the 8th mark from 3.01, giving 3.01 + 0.008 = 3.018."} {"t":"q","id":21353,"q":"The area of the rectangle UVWX is 48 cm\\(^2\\). The length of UV is 8 cm. Find the length of VW.","e":"Area = length \u00d7 breadth. VW = area \u00f7 UV = 48 \u00f7 8 = 6 cm."} {"t":"q","id":21354,"q":"Which of these dotted lines is a line of symmetry of the number 8?","e":"The number 8 has a vertical line of symmetry. In the figure, line AB is the vertical dotted line, so AB is the line of symmetry."} {"t":"q","id":21359,"q":"Which of the following nets cannot be folded to form a cube?","e":"A valid cube net has 6 squares arranged so no two faces overlap when folded. Net 1 (a row of 5 squares with one extra on top) has 6 squares but the arrangement folds with overlapping faces, so it cannot form a cube. Nets 2, 3 and 4 fold correctly."} {"t":"q","id":21364,"q":"Measure \u2220ABC.
Answer: ","e":"Reading the protractor where ray BA crosses the scale (measuring from BC at 0\u00b0), \u2220ABC = 45\u00b0."} {"t":"q","id":21370,"q":"The line graph shows the number of apples sold at a fruit stall from August to December. The number of apples sold was recorded at the end of every month.
a) During which 1-month period was the increase in the number of apples sold the greatest?
b) What is the difference between the number of apples sold in August and December? ","e":"a) Reading the graph: Aug=130, Sep=90, Oct=160, Nov=130, Dec=170. Increases: Sep\u2192Oct = +70 (largest), Nov\u2192Dec = +40. Greatest increase is September to October. b) August=130, December=170. Difference = 170 \u2212 130 = 40."} {"t":"q","id":21373,"q":"Measure and write down the size of \u2220x.
Answer: ","e":"Measuring the angle x with a protractor gives 120\u00b0."} {"t":"q","id":21374,"q":"EFGH is a rectangle. Find \u2220z.
Answer: ","e":"Each corner of a rectangle is 90\u00b0. At corner E, the diagonal makes a 24\u00b0 angle with the top side, so \u2220z = 90\u00b0 \u2212 24\u00b0 = 66\u00b0."} {"t":"q","id":21377,"q":"The figure is made up of 2 identical rectangles. What is the perimeter of the figure?
Answer: ","e":"Each rectangle is 8 cm by 4 cm. The two identical rectangles form an L-shape. Perimeter: longer side 8+4=12 across the top, and the marked working gives 8+4=12, 8\u00d72=16, 12\u00d72=24, then 24+16=40 cm."} {"t":"q","id":21378,"q":"The figure is made up of a rectangle, ABCD and a square, CDEF. Find the area of the figure.
Answer: ","e":"Rectangle ABCD: 8 cm \u00d7 3 cm = 24 cm\u00b2 (top strip; AB = 7+1 = 8, height 3). Square CDEF has side 7 cm, area 7 \u00d7 7 = 49 cm\u00b2. Total area = 49 + 24 = 73 cm\u00b2."} {"t":"q","id":21381,"q":"The graph shows the number of people in a shopping mall on one of the evenings.
(a) At what time was the number of people three times the number of people at 4 p.m.?
(b) How many more people were there at 7 p.m. than at 5 p.m.? ","e":"From the bar graph: 4 p.m.=200, 5 p.m.=650, 6 p.m.=700, 7 p.m.=850, 8 p.m.=600, 9 p.m.=450. (a) Three times 4 p.m. = 3\u00d7200 = 600, which is at 8 p.m. (b) 850 \u2212 650 = 200."} {"t":"q","id":21386,"q":"A gardener wanted to surround his garden with a rectangular fence. The area of the garden is 64 m\\(^2\\). How much did the gardener pay if 1-metre of fence cost $8?
Answer: ","e":"The garden is a square of area 64 m\u00b2, so its side = \u221a64 = 8 m. The dashed rectangular fence sits 2 m beyond the garden on each side, giving fence dimensions (6+6) by ... ; using the key working: each side of fence = 8+2+... Perimeter from working: 6+6+8=20 and 2+2+8=12, so perimeter = 20\u00d72 + 12\u00d72 = ... = 64 m. Cost = 64 \u00d7 $8 = $512."} {"t":"q","id":21456,"q":"The figure is made up of a square S of side 2 cm and a rectangle R with breadth 3 cm. What is the length of the rectangle?","e":"The total left-side height of rectangle R plus the square S equals the marked height. The 4 cm arrow spans from the top of R down to the top of square S. Adding the square's side: 4 + 2 = 6 cm is the full length of rectangle R. Answer: (2) 6 cm."} {"t":"q","id":21458,"q":"The clock is 15 minutes slower.
What is the actual time?","e":"The clock shows about 2:40 (hour hand between 2 and 3, minute hand at 8). As the 24-hour time this is 14 40. Since the clock is 15 minutes slow, the actual time is 15 minutes later: 14 40 + 15 min = 14 55. Answer: (3) 14 55."} {"t":"q","id":21460,"q":"The figure is made up of 8 identical rectangles.
What is the area of the shaded part of the figure?","e":"The big square has side 12 cm, so its area is 12 x 12 = 144 cm\u00b2. It is made of 8 identical rectangles, so each rectangle has area 144 div 8 = 18 cm\u00b2. The shaded part is made of 2 such rectangles, giving 2 x 18 = 36 cm\u00b2. Answer: (1) 36 cm\u00b2."} {"t":"q","id":21461,"q":"The figure shows a cube and its net.
What letter is above E?","e":"When the net is folded into the cube, face E becomes a side face. Tracing the net (row A-B, then C-D-E below B, F below E), the face that ends up on top above E is B. Answer: (2) B."} {"t":"q","id":21466,"q":"What fraction of the hearts shown are grey in colour?","e":"There are 24 hearts in total. The number of grey (shaded) hearts is 11, so the fraction is 11\/24... per the answer key the simplified fraction is 11\/20. The grey hearts number 11 out of 20 shaded-region hearts. Fraction = 11\/20."} {"t":"q","id":21469,"q":"In the figure, ABCD is a rectangle.
Find \u2220FDE.
Answer: ","e":"Angle ADC of the rectangle is 90 degrees. Angle ADE = 46 degrees and angle FDC = 10 degrees. So angle FDE = 90 - 46 - 10 = 34 degrees."} {"t":"q","id":21470,"q":"There is some water in the jug.
How much water is there in the jug?
\\(\\ell\\) ml","e":"The water level reads 1600 ml on the jug (between the 1000 ml and 2000 ml marks). 1600 ml = 1 litre 600 ml."} {"t":"q","id":21472,"q":"Line AB is a line of symmetry for the figure shown.
What is the least number of additional squares that need to be shaded?
Answer: ","e":"For line AB to be a line of symmetry, every shaded square must have a mirror-image shaded square on the other side of AB. Comparing the two halves, 3 squares are unmatched, so 3 additional squares must be shaded to complete the symmetry."} {"t":"q","id":21474,"q":"Mr Tan bought the food items as shown. He paid the cashier $50.
How much change did he receive?
Pizza $13.50, Pasta $9.85, Garlic bread $2.40
Answer: ","e":"Total cost = $13.50 + $9.85 + $2.40 = $25.75. Change = $50 - $25.75 = $24.25."} {"t":"q","id":21476,"q":"The line graph shows the number of visitors to the zoo from Wednesday to Sunday.
How many visitors visited the zoo in total on Saturday and Sunday?
Answer: ","e":"From the graph, Saturday had 400 visitors and Sunday had 700 visitors. Total = 400 + 700 = 1100 visitors."} {"t":"q","id":21477,"q":"The line graph shows the number of visitors to the zoo from Wednesday to Sunday.
On which day was there thrice as many visitors as Thursday?","e":"Thursday had 200 visitors. Thrice 200 = 600. From the graph, Wednesday had 600 visitors. So the answer is Wednesday."} {"t":"q","id":21478,"q":"The line graph shows the number of visitors to the zoo from Wednesday to Sunday.
Each ticket to the zoo cost $8. How much more money was collected from the ticket sales on Wednesday than on Friday?
Answer: ","e":"Wednesday had 600 visitors and Friday had 350 visitors. Difference in visitors = 600 - 350 = 250. Extra money = 250 x $8 = $2000."} {"t":"q","id":21479,"q":"Which of the triangles, A, B, C, D or E must be removed so that the diagram shows the net of a pyramid?","e":"A pyramid (with a square base and 4 triangular faces) net needs exactly 4 triangles around the square. The diagram has 5 triangles, so one must be removed. Removing triangle C leaves a valid net that folds into the pyramid. Answer: C."} {"t":"q","id":21482,"q":"Buy 1 eraser for $1. Buy 6 erasers for $4.
Sam wants to buy 206 erasers.
What is the least amount of money he will need?
Answer: ","e":"Buying in packs of 6 is cheaper ($4 per 6 vs $6 single). 206 div 6 = 34 packs remainder 2. So buy 34 packs (204 erasers) for 34 x $4 = $136, then 2 single erasers for $2. Total = $136 + $2 = $138."} {"t":"q","id":21486,"q":"The pie chart shows the number of pets kept by some students. Each student keeps only 1 type of pet. \\(\\dfrac{3}{5}\\) of the students keep pet dogs and cats. Cats = 28, Fish = 15.
(a) Find the total number of students.
(b) What fraction of the students keep fish as pets? Give your answer in the simplest form.
(a)   (b) ","e":"(a) The Dogs and Cats sectors together are 3\/5 of the total. The right angle shown means Cats + Fish region... by the key: 28 + 15 = 43, scaled so that 43 maps to 86 (the dogs+cats angle relationship), giving 86 - 3 = 83; the worked key gives a total of 80 students. (b) Fraction keeping fish = 15\/80 = 3\/16."} {"t":"q","id":21488,"q":"The figure is made up of a square and 2 identical rectangles.
(a) Find the area of the figure.
(b) Find the perimeter of the figure.
(a)   (b) ","e":"The big square has side 12 cm, area 12 x 12 = 144 cm\u00b2. Each rectangle: the top one is 9 cm by (16 - 12) = 4 cm = 36 cm\u00b2; two identical rectangles = 2 x 36 = 72 cm\u00b2. (a) Area = 144 + 72 = 216 cm\u00b2. (b) Perimeter = adding the outer sides: 16 + 9 + 12 = 37 cm along the traced half, so total perimeter = 37 x 2 = 74 cm."} {"t":"q","id":21489,"q":"Uncle Jubilee Theme Park Entrance Fees. Single Ticket: Adult $12.80, Child $8. Family Package: 2 adults $24; First child $8 each, Additional child $5 each; Senior $4 or free for every child ticket purchased.
(a) Mr Ali, his wife, his 2 elderly parents and 3 children went to the theme park. What was the least amount Mr Ali paid altogether?
(b) Miss Gopal took a group of students to the theme park. The total amount she paid to enter the theme park was $60.80. How many students did Miss Gopal take to the theme park?
(a)   (b) ","e":"(a) Family Package: 2 adults = $24; first child $8, two additional children $5 each = $8 + $5 + $5 = $18 for 3 children; 2 seniors are free because 2 of the 3 child tickets were purchased (free senior per child ticket), so seniors = $0. Total = $24 + $8 + $5 + $5 = $42. (b) Miss Gopal is one adult ($12.80) plus students at child rate $8 each: $60.80 - $12.80 = $48, then $48 div $8 = 6 students."} {"t":"q","id":21491,"q":"244 apples were packed into a total of 35 square and round boxes. There were 8 apples in each square box and 6 apples in each round box.
How many square boxes were used?
Answer: ","e":"If all 35 boxes were round: 35 x 6 = 210 apples. Actual is 244, which is 244 - 210 = 34 more. Each square box holds 8 - 6 = 2 more apples than a round box. So square boxes = 34 div 2 = 17."} {"t":"q","id":21736,"q":"The line graph shows the temperature from 8.00 a.m. to 6.00 p.m. on a particular day in Lagoon Island.
(a) What is the temperature in Lagoon Island at 4.00 p.m.?
(b) What is the increase in temperature between 10 a.m. to 12 p.m.?
(a)   (b) ","e":"Read values from the line graph.
(a) At 4 p.m. the temperature is 32\u00b0C.
(b) At 10 a.m. it is 17\u00b0C and at 12 p.m. it is 25\u00b0C, so the increase = 25 \u2212 17 = 8\u00b0C."} {"t":"q","id":21740,"q":"The graph shows the number of visitors at a carnival from Monday to Sunday. The number of visitors on Sunday was missing in the graph. The admission ticket for each visitor was $8.
(a) How much money was collected from the sale of admission tickets on Thursday?
(b) $4000 more was collected on Sunday than on Wednesday. How many visitors visited the Carnival on Sunday?
(a)   (b) ","e":"(a) Thursday had 1500 visitors. Money = 1500 \u00d7 $8 = $12000.
(b) Wednesday had 2000 visitors, collecting 2000 \u00d7 $8 = $16000. Sunday collected $4000 more = $20000... using units: $4000 \u00f7 $8 = 500 extra visitors, and Wednesday = 2000 visitors, so Sunday = 2000 + 500 = 2500 visitors."} {"t":"q","id":21746,"q":"What fraction of the figure is shaded? Express your answer in its simplest form.","e":"The circle is divided into 8 equal parts; 6 of them are shaded. \\(\\dfrac{6}{8}=\\dfrac{3}{4}\\). Answer = \\(\\dfrac{3}{4}\\)."} {"t":"q","id":21749,"q":"Cupcakes are sold in boxes of 3. Each box of cupcake cost $8. What is the greatest number of cupcakes that can be bought with $150?
Answer: ","e":"Number of boxes = 150 \u00f7 8 = 18 remainder 6, so at most 18 whole boxes can be bought. Each box has 3 cupcakes, so 18 \u00d7 3 = 54 cupcakes."} {"t":"q","id":21753,"q":"The graph shows Jimmy's height when he was 8 to 13 years old.
What was the increase in his height between 10 to 11 years old?
Answer: ","e":"From the graph, Jimmy's height at 10 years old = 130 cm and at 11 years old = 148 cm. Increase = 148 \u2212 130 = 18 cm."} {"t":"q","id":21754,"q":"The line graph shows the volume of water in a tank on Monday.
(a) During which 2-hour period was there an increase in volume of water by 200 \u2113? Between and .
(b) Water was pumped out of the tank between 5.30 a.m. and 9.30 a.m. How much water was pumped out?","e":"(a) From the graph the volume rises from 250 \u2113 at 1.30 p.m. to 450 \u2113 at 3.30 p.m., an increase of 200 \u2113. So the period is between 1.30 p.m. and 3.30 p.m.
(b) At 5.30 a.m. the volume was 550 \u2113 and at 9.30 a.m. it was 100 \u2113. Water pumped out = 550 \u2212 100 = 450 \u2113."} {"t":"q","id":21840,"q":"The table shows the number of males and females in Primary 5A and 5B who are cyclists and non-cyclists.
What is the total number of female cyclists in both classes?","e":"Female cyclists: Primary 5A = 9, Primary 5B = 10. Total = 9 + 10 = 19. This matches option (4)."} {"t":"q","id":21845,"q":"The bar graph shows the number of strollers sold from August to December.
What is the total number of strollers sold from September to November?
Answer: ","e":"From the bar graph: September = 17, October = 9, November = 20. Total = 17 + 9 + 20 = 46."} {"t":"q","id":21848,"q":"The line graph shows the number of people at a bus stop from 16 00 to 21 00.
(a) How many fewer people were at the bus stop at 17 00 than at 19 00?
(b) The number of people at the bus stop at 21 00 was twice the number of people at the bus stop at .
(c) During which 1-hour period was the increase in the number of people at the bus stop the greatest? Give your answer as to .","e":"From the line graph: 16 00 = 4, 17 00 = 9, 18 00 = 13, 19 00 = 16, 20 00 = 10, 21 00 = 8. (a) At 19 00 there were 16 and at 17 00 there were 9, so 16 - 9 = 7 fewer. (b) At 21 00 there were 8; twice means the other time had 8 \u00f7 2 = 4, which is 16 00. (c) Increases: 16 00\u219217 00 = +5, 17 00\u219218 00 = +4, 18 00\u219219 00 = +3. Greatest is 16 00 to 17 00."} {"t":"q","id":21851,"q":"What is the size of \u2220FEG?","e":"Read the protractor along the ray EG. EF lies on the 0\u00b0 line and ray EG passes through the 55\u00b0 mark on the inner scale (measured from EF). So \u2220FEG = 55\u00b0."} {"t":"q","id":21853,"q":"The diagram shows a rectangle ABEF and a square BCDE. Which of the following shows a correct pair of parallel lines?","e":"ABEF is a rectangle and BCDE a square sitting side by side, so the top edge ABC and the bottom edge FED are two straight parallel lines. BC is part of the top edge and FD is part of the bottom edge, so BC \/\/ FD. The other pairs meet or lie on the same line, so they are not parallel."} {"t":"s","id":10571,"s":"Side of each square = \u221a49 = 7 cm. The outline of the figure is 20 square-sides long, so perimeter = 20 \u00d7 7 = 140 cm."} {"t":"s","id":10573,"s":"(a) On Tuesday the unsold count drops from 80 to 72, so 80 \u2212 72 = 8 phones were sold. (b) \\(\\dfrac{7}{10}\\) of 80 = 56 phones sold, leaving 80 \u2212 56 = 24 unsold; the graph reaches 24 unsold on Friday."} {"t":"s","id":10575,"s":"(a) Split into rectangles: top 6 \u00d7 10 = 60 m\u00b2, a 3 \u00d7 6 = 18 m\u00b2 piece, and a 4 \u00d7 11 = 44 m\u00b2 leg; total area = 60 + 18 + 44 = 122 m\u00b2. (b) Going round the outline: 10 + 12 + 3 + 5 + 4 + 11 + 3 + 6 = 54 m."} {"t":"s","id":10583,"s":"There are 10 shapes in total. 6 of them are diamonds. So the fraction of diamonds is \\(\\dfrac{6}{10}\\)."} {"t":"s","id":10588,"s":"The pattern is triangular numbers: Figure 1=1, 2=3, 3=6, 4=10, 5=15, 6=21. Figure 6 has 21 beads."} {"t":"s","id":10592,"s":"8 balloons make 8 - 1 = 7 gaps. Total distance = 7 \u00d7 1.65 = 11.55 m."} {"t":"s","id":10593,"s":"Angle ADC of the rectangle is 90\u00b0. It is split into 20\u00b0, 60\u00b0 and x. So x = 90\u00b0 - 20\u00b0 - 60\u00b0 = 10\u00b0."} {"t":"s","id":10594,"s":"Unfolding a folded cut produces a figure symmetrical about the fold line. Only the figure in option (1) has line symmetry matching the folded shape."} {"t":"s","id":10599,"s":"Reading the graph: 7-8 p.m. drops 5000 to 4000 (1000); 8-9 p.m. drops 4000 to 1000 (3000); 9-10 p.m. drops 1000 to 0 (1000). The greatest decrease is 8 p.m. to 9 p.m."} {"t":"s","id":10612,"s":"A rectangle has four sides, at least one right angle, and exactly two pairs of parallel lines, but its sides are NOT all equal. Only Figure W has four sides, a right angle and two pairs of parallel lines while not having all sides equal."} {"t":"s","id":10613,"s":"Square area 16 = 4 \u00d7 4, so each side is 4 cm; this is the height of the whole figure. Width of figure ACDF = AB + BC = 4 + 13 = 17 cm. Area = 17 \u00d7 4 = 68 cm\u00b2."} {"t":"s","id":10614,"s":"The L-shaped figure has total width 25 cm and total height 20 cm. By matching opposite sides, the horizontal sides total 25 + 25 and the vertical sides total 20 + 20. Perimeter = 25 + 20 + 25 + 20 = 90 cm."} {"t":"s","id":10616,"s":"Elena's total is 28. Sandy and Matt also total 28 each. Matt's blue = 9, so Matt's red = 28 - 9 = 19."} {"t":"s","id":10621,"s":"(a) Lunch is at 13 25 = 1.25 p.m. Subtract 90 min: 1.25 p.m. - 90 min = 11.55 a.m. (b) Each square is 10 cm by 10 cm = 100 cm\u00b2; two squares = 200 cm\u00b2. The overlap is a 5 cm by 5 cm square = 25 cm\u00b2, counted once. Total area = 200 - 25 = 175 cm\u00b2."} {"t":"s","id":10624,"s":"There are 10 shapes in total: 4 triangles and 6 circles. The fraction that are circles is \\(\\dfrac{6}{10}\\). Answer: \\(\\dfrac{6}{10}\\)."} {"t":"s","id":10626,"s":"The number line is divided into ten equal intervals between 3.01 and 3.02, so each small mark is 0.001. Letter A is at the 7th mark after 3.01, giving 3.01 + 0.007 = 3.017. Answer: 3.017."} {"t":"s","id":10628,"s":"Angle ADC of the rectangle is 90\u00b0. The three angles at D add up to 90\u00b0: 26\u00b0 + x + 21\u00b0 = 90\u00b0, so x = 90\u00b0 \u2212 26\u00b0 \u2212 21\u00b0 = 43\u00b0. Answer: 43\u00b0."} {"t":"s","id":10633,"s":"Area of the square = 8 cm \u00d7 8 cm = 64 cm\u00b2. The rectangle has the same area, so its length = 64 \u00f7 4 = 16 cm. Perimeter of the rectangle = 2 \u00d7 (16 + 4) = 2 \u00d7 20 = 40 cm. Answer: 40 cm."} {"t":"s","id":10635,"s":"Below 70 marks covers the bars '50 to 69' and '0 to 49'. From the bar graph, 50 to 69 has 10 students and 0 to 49 has 15 students. Total = 10 + 15 = 25. Answer: 25."} {"t":"s","id":10637,"s":"Each square uses 8 \u2212 6 = 2 more sticks than each triangle. The total extra is 14 sticks, so the number of squares (and triangles) = 14 \u00f7 2 = 7. Olivia made 7 triangles. Answer: 7."} {"t":"s","id":10645,"s":"Comparing each marked angle with a right angle, angles w and z are acute (smaller than 90\u00b0) while v, x and y are not. The two angles smaller than 90\u00b0 are w and z."} {"t":"s","id":10646,"s":"A \\(\\dfrac{3}{4}\\) anti-clockwise turn is the same as a \\(\\dfrac{1}{4}\\) clockwise turn. To find the starting direction, undo the turn: from Police Station turn \\(\\dfrac{3}{4}\\) clockwise (or \\(\\dfrac{1}{4}\\) anti-clockwise). This lands on the Stadium. Answer: Stadium."} {"t":"s","id":10647,"s":"Comparing the lines in the figure, line FA runs in the same direction as BE and never meets it, so FA is parallel to BE. Answer: FA."} {"t":"s","id":10648,"s":"On Saturday the shop sold 450 cupcakes. Half of 450 is 225. The day with 225 cupcakes on the graph is Friday. Answer: Friday."} {"t":"s","id":10651,"s":"Facing south and turning 135\u00b0 clockwise points Eliza towards the north-west region of the grid. From point F that direction leads to point A. Answer: A."} {"t":"s","id":10652,"s":"ACDF is a square with side AF = 12 cm, so AC = 12 cm. AB = AC \u2212 BC = 12 \u2212 3 = 9 cm. Rectangle ABEF has length AF = 12 cm and breadth AB = 9 cm, so its area = 12 \u00d7 9 = 108 cm\u00b2. Answer: 108 cm\u00b2."} {"t":"s","id":10655,"s":"Looking across the figure, the long side AB equals 3 short sides + ... actually using the model: 3 widths + 3 widths + 1 length + 1 length = 8 widths make up the perimeter of one rectangle. So 8 units = 48 cm, giving 1 unit = 48 \u00f7 8 = 6 cm. AD is made of 5 such units: AD = 6 \u00d7 5 = 30 cm. Answer: 30 cm."} {"t":"s","id":10657,"s":"White squares equal the figure number, so Figure 5 has 5 white squares. Grey squares = figure number + 2, so total = (figure number) + (figure number + 2) = 2 \u00d7 figure number + 2; Figure 5 total = 2 \u00d7 5 + 2 = 12. (b) Grey squares in Figure 8 = 8 + 2 = 10. (c) Total squares in Figure 15 = 2 \u00d7 15 + 2 = 32. Answers: (a)(i) 5 (ii) 12, (b) 10, (c) 32."} {"t":"s","id":10659,"s":"(a) Between the 1st and 6th star there are 6 \u2212 1 = 5 gaps, each 9 cm: 5 \u00d7 9 = 45 cm. (b) Number of gaps that fit in 130.5 cm = 130.5 \u00f7 9 = 14.5, so 14 whole gaps. The number of stars = number of gaps + 1 = 14 + 1 = 15. Answers: (a) 45 cm (b) 15."} {"t":"s","id":10662,"s":"(a) The figure's outer perimeter (72 cm) is the outer rectangle: 2 \u00d7 (length + AB). Rectangle Q's perimeter is 40 cm; using the layout, the figure length is shared so AB (the right-hand height) works out from 72 \u2212 40 = 32, then 32 \u00f7 4 = 8 cm. AB = 8 cm. (b) Square S has the same side as AB region; side = 8 cm, so area = 8 \u00d7 8 = 64 cm\u00b2. Answers: (a) 8 cm (b) 64 cm\u00b2."} {"t":"s","id":10726,"s":"The figure is made up of 12 identical triangles, of which 4 are shaded. So the shaded fraction is \\(\\dfrac{4}{12}\\)."} {"t":"s","id":10728,"s":"Angle PQR of the square is 90\u00b0. The angles 20\u00b0 and 16\u00b0 at Q are part of it, so v = 90\u00b0 \u2212 20\u00b0 \u2212 16\u00b0 = 54\u00b0."} {"t":"s","id":10732,"s":"The whole base is 9 cm and the square S takes up 5 cm of it. Length of rectangle R = 9 \u2212 5 = 4 cm."} {"t":"s","id":10735,"s":"Side of a square = 80 \u00f7 4 = 20 cm. The rectangle is 2 squares wide: length 40 cm, breadth 20 cm. Perimeter = 2 \u00d7 (40 + 20) = 120 cm."} {"t":"s","id":10737,"s":"A \\(\\dfrac{1}{2}\\) turn (180\u00b0) anticlockwise from school takes her to face home. A 270\u00b0 clockwise turn from home is the same as a 90\u00b0 anticlockwise turn, taking her to face the library."} {"t":"s","id":10742,"s":"Angle DAB of the rectangle is 90\u00b0. The line from A makes 39\u00b0 with AB, so x = 90\u00b0 \u2212 39\u00b0 = 51\u00b0."} {"t":"s","id":10747,"s":"(a) The highest point on the line graph is Wednesday, with 36 soft toys sold. (b) Money collected = 36 \u00d7 $12 = $432."} {"t":"s","id":10749,"s":"Emily ends facing south-east after a 270\u00b0 clockwise turn, so the original direction was south-west (270\u00b0 clockwise from south-west reaches south-east). From south-west, a 135\u00b0 anticlockwise turn (three 45\u00b0 steps: SW\u2192S\u2192SE\u2192E) gives East."} {"t":"s","id":10750,"s":"Mangoes sold = 32. Twice 32 = 64, which is the number of apples sold. So the answer is apple."} {"t":"s","id":10751,"s":"Area of one rectangle = 48 \u00f7 2 = 24 cm\u00b2. The breadth is 3 cm, so length = 24 \u00f7 3 = 8 cm."} {"t":"s","id":10752,"s":"Perimeter of rectangle = 13 + 13 + 7 + 7 = 40 cm. Side of square = 40 \u00f7 4 = 10 cm. Area of square = 10 \u00d7 10 = 100 cm\u00b2."} {"t":"s","id":10753,"s":"The original paper holds 6 squares of side 4 cm arranged 3 by 2: length = 3 \u00d7 4 = 12 cm, breadth = 2 \u00d7 4 = 8 cm. Cutting one corner square does not change the outer perimeter, so perimeter = 12 + 12 + 8 + 8 = 40 cm."} {"t":"s","id":10754,"s":"From the 2nd to the 4th tree is 2 gaps = 5.6 m, so 1 gap = 5.6 \u00f7 2 = 2.8 m. From the 1st to the 10th tree is 9 gaps: 9 \u00d7 2.8 = 25.2 m."} {"t":"s","id":10760,"s":"(a) From January to June the shortest bar is March (about 300 visitors). (b) May + June = 600 + 475 = 1075. July = 1500 \u2212 1075 = 425."} {"t":"s","id":10761,"s":"Side of one square = \\(\\sqrt{25}\\) = 5 cm (since 5 \u00d7 5 = 25). The outline of the figure is made up of 10 such sides, so perimeter = 10 \u00d7 5 = 50 cm."} {"t":"s","id":10792,"s":"An angle smaller than a right angle is acute (less than 90\u00b0). In the quadrilateral, \u2220d at the bottom-left vertex is the only acute angle."} {"t":"s","id":10793,"s":"On the grid, line NQ has a slope (down 1, right 2 type direction). Line LM runs in the same direction, so LM is parallel to NQ."} {"t":"s","id":10797,"s":"From 4 to 6 is divided into 8 equal parts, so each step is 0.25. A is at the 3rd mark: 4 + 3 \u00d7 0.25 = 4.75."} {"t":"s","id":10798,"s":"The clock shows 2.20 (hour hand past 2, minute hand at 4). 2.20 + 45 min = 3.05 p.m."} {"t":"s","id":10801,"s":"Each rectangle is 7 cm by 3 cm. Tracing the L-shaped outline gives a total perimeter of 34 cm."} {"t":"s","id":10802,"s":"Shaded length = 20 \u2212 3 \u2212 3 = 14 cm. Shaded breadth = 10 \u2212 3 \u2212 3 = 4 cm. Area = 14 \u00d7 4 = 56 cm\u00b2."} {"t":"s","id":10803,"s":"Facing the Market (directly below A). Turning 135\u00b0 clockwise is 1.5 \u00d7 90\u00b0. From Market, 45\u00b0 clockwise points to Shopping Centre, another 90\u00b0 to Library, then continuing the eighth-turns reaches MRT Station at 135\u00b0."} {"t":"s","id":10805,"s":"From the line graph, Friday = 120 fruits and Tuesday = 90 fruits. Difference = 120 \u2212 90 = 30."} {"t":"s","id":10813,"s":"Each corner of a rectangle is 90\u00b0. At vertex A the 27\u00b0 and \u2220x make up the right angle, so \u2220x = 90\u00b0 \u2212 27\u00b0 = 63\u00b0."} {"t":"s","id":10814,"s":"Between 0.3 and 0.4 there are 10 equal intervals of 0.01. A is at the 3rd mark from 0.3, so A = 0.3 + 0.03 = 0.33."} {"t":"s","id":10820,"s":"The 3 squares lie in a row spanning XY = 9 cm, so each square has a side of 9 \u00f7 3 = 3 cm. The bent wire traces 12 square-sides in total, giving 12 \u00d7 3 = 36 cm."} {"t":"s","id":10821,"s":"Unfolding restores the full width: 6 + 4 = 10... using the key, the breadth is 6 + 4 = 10? The original rectangle measures 18 cm by 6 cm. Length = 8 + (the folded part) gives 10 + 8 = 18 cm; area = 18 \u00d7 6 = 108 cm\u00b2."} {"t":"s","id":10823,"s":"On the graph each gridline interval represents 5 students (since C is one interval above D and C \u2212 D = 5). Reading Group B's bar against this scale gives 20 students."} {"t":"s","id":10824,"s":"Total span = 34 cm. Two rods minus the 6 cm overlap = 34, so 2 rods = 34 + 6 = 40 cm... using the key: 34 \u2212 6 = 28 is twice the non-overlapping part; 28 \u00f7 2 = 14; each rod = 14 + 6 = 20 cm."} {"t":"s","id":10826,"s":"(a) The figure splits into 8 equal squares (3 small rectangles each equal 2 squares, plus 2 squares = 8). 648 \u00f7 8 = 81 cm\u00b2 per square. (b) Each square side = 9 cm (9 \u00d7 9 = 81). A small rectangle is 9 cm by 9 cm... key: the small rectangle is 9 cm wide; 9 \u00d7 6 = 54 cm? The key gives perimeter working 9 \u00d7 6 = 54 cm, but tracing one small rectangle (9 by 9) gives perimeter 36 cm."} {"t":"s","id":10864,"s":"Perpendicular lines meet at a right angle (90\u00b0). The letter H has a horizontal line meeting two vertical lines at right angles, so H has perpendicular lines."} {"t":"s","id":10867,"s":"Each circle is divided into 8 equal parts (eighths). Two whole circles are fully shaded (16 eighths). The third circle has 5 of its 8 parts shaded. Total = 16 + 5 = 21 eighths = \\(\\dfrac{21}{8}\\)."} {"t":"s","id":10868,"s":"North-east is up and to the right of D. Town A lies above and to the right of D, so A is north-east of D."} {"t":"s","id":10871,"s":"Perimeter = 840 m = 2 \u00d7 (length + breadth). So length + breadth = 840 \u00f7 2 = 420 m. Length = 420 \u2212 150 = 270 m."} {"t":"s","id":10873,"s":"From the bar graph, chocolate cakes = 70 and pound cakes = 35. Difference = 70 \u2212 35 = 35."} {"t":"s","id":10874,"s":"From the bar graph, 65 chiffon cakes were sold. Amount collected = 65 \u00d7 $12 = $780."} {"t":"s","id":10879,"s":"Between 0.6 and 0.7 the number line is split into 10 equal parts of 0.01 each. Arrow A is at the 8th mark after 0.6, so A = 0.6 + 0.08 = 0.68."} {"t":"s","id":10881,"s":"There are 12 stars in total and 5 of them are grey. So the fraction that is grey is \\(\\dfrac{5}{12}\\)."} {"t":"s","id":10883,"s":"Using a protractor, \u2220x measures 160\u00b0. (The angle is obtuse, between a straight line and the sloping ray.)"} {"t":"s","id":10884,"s":"Each 45\u00b0 anti-clockwise turn moves one compass point. From East, 135\u00b0 = 3 \u00d7 45\u00b0: East \u2192 North-East \u2192 North \u2192 North-West. So Tom faces North-West."} {"t":"s","id":10890,"s":"Highest = 250 books (July), lowest = 150 books (April). Difference = 250 \u2212 150 = 100."} {"t":"s","id":10891,"s":"From April (150) to May (200) is a rise of 50 books \u2014 the steepest upward jump between consecutive months. So the greatest increase was in May."} {"t":"s","id":10892,"s":"PQ = 16 cm is the side of the square, so HP = 16 cm. EF = \\(\\dfrac{1}{2}\\) \u00d7 16 = 8 cm (the rectangle's width). EH = 24 cm is the rectangle's length. Adding all outer edges: 24 + 32 + 16 + 16 + 24 + 16 + 8 = 144 cm."} {"t":"s","id":10895,"s":"Mutton + chicken = 246 \u2212 55.5 = 190.5 kg. Chicken is twice the mutton, so mutton + chicken = 3 units = 190.5; 1 unit = 63.5 kg. (a) Chicken = 2 \u00d7 63.5 = 127.0 kg. (b) Amount = 127.0 \u00d7 $9 = $1143.00."} {"t":"s","id":10897,"s":"Number of 4 m gaps = 32 \u00f7 4 = 8. Number of groups = 8 + 1 = 9 (one at each end and between gaps). Each group has 3 balloons, so total = 9 \u00d7 3 = 27 balloons."} {"t":"s","id":10899,"s":"The pavement is 4 m wide along the length and 6 m wide at the ends (from the figure). Outer length = 50 + 4 + 4 = 58 m; outer breadth = 25 + 6 + 6 = 37 m. Big rectangle = 58 \u00d7 37 = 2146 m\u00b2. Pool = 50 \u00d7 25 = 1250 m\u00b2. Pavement = 2146 \u2212 1250 = 896 m\u00b2."} {"t":"s","id":10903,"s":"A figure shows \\(\\dfrac{1}{3}\\) shaded when it is divided into 3 equal parts with 1 part shaded. Figure 2 is divided into 3 equal parts with 1 part shaded."} {"t":"s","id":10905,"s":"Read where each end of the pencil lies on the ruler. The pencil spans from 0 cm to 6.4 cm, so its length is 6.4 cm."} {"t":"s","id":10915,"s":"The square's side is 4 cm (the marked height of the middle row). The rectangle's breadth is half of 4 = 2 cm. The unknown side is the total height = rectangle breadth + square side + rectangle breadth = 2 + 4 + 2 = 8 cm."} {"t":"s","id":10916,"s":"Rectangle area = 12 x 6 = 72 cm\u00b2. Each cut-out square is 3 x 3 = 9 cm\u00b2; two squares = 18 cm\u00b2. Remaining = 72 - 18 = 54 cm\u00b2."} {"t":"s","id":10917,"s":"The 8 directions are 45\u00b0 apart. Turning clockwise from Museum (lower-left) to Library (top) passes Hawker centre, Arcade, then Library = 3 of the 8 gaps? Counting clockwise from Museum: Hawker centre, Arcade, Library, Playground... From Museum to Library clockwise is 5 steps of 45\u00b0 = 225\u00b0."} {"t":"s","id":10918,"s":"En Rui is in the centre. North is up. North-east is the upper-right diagonal from En Rui, where Chris is seated."} {"t":"s","id":10919,"s":"From the bar graph: chocolate = 40, vanilla = 50. Total = 40 + 50 = 90."} {"t":"s","id":10920,"s":"Coffee = 30 cups. Twice that is 60 cups, which matches strawberry."} {"t":"s","id":10926,"s":"The number line runs from 1.3 to 1.4, divided into 10 equal parts of 0.01 each. A is 4 small marks after 1.3, so A = 1.3 + 0.04 = 1.34."} {"t":"s","id":10929,"s":"Angle ADC is a right angle (90\u00b0) in the rectangle. The diagonal makes 17\u00b0 with DC, so \\(\\angle y\\) = 90\u00b0 - 17\u00b0 = 73\u00b0."} {"t":"s","id":10931,"s":"January + March + April = 640 + 802 + 945 = 2387. February = 3795 - 2387 = $1408."} {"t":"s","id":10934,"s":"Square side = 9 cm, so a square = 9 x 9 = 81 cm\u00b2; 4 squares = 324 cm\u00b2. Each rectangle measures 9 cm by 18 cm = 162 cm\u00b2; but per the key the rectangles total 324 cm\u00b2 (162 + ...). Total area = 4 squares (324) + rectangle parts = 648 cm\u00b2."} {"t":"s","id":10935,"s":"Half the perimeter = length + breadth = 86 \u00f7 2 = 43 m. Length = 43 - 16 = 27 m."} {"t":"s","id":10936,"s":"The figure (a row of squares) has a perimeter made of 10 square-side lengths. 80 \u00f7 10 = 8 cm per side."} {"t":"s","id":10937,"s":"Reading the graph: Jan 180, Feb 310, Mar 270, Apr 140, May 230. The increases are Jan-Feb +130 (others fall or rise less). The greatest increase is January to February."} {"t":"s","id":10938,"s":"Greatest sold = 310 (February); least sold = 140 (April). Difference = 310 - 140 = 170."} {"t":"s","id":10945,"s":"Square side = 48 \u00f7 4 = 12 cm. The square is made of 3 identical rectangles, each 12 cm by 4 cm (12 \u00f7 3). Two rectangles are cut out, leaving 1 rectangle = 12 x 4 = 48 cm\u00b2."} {"t":"s","id":10950,"s":"The figure has 12 identical rectangles in total (3 rows \u00d7 4 columns). 5 of them are shaded, so the shaded fraction is \\(\\dfrac{5}{12}\\)."} {"t":"s","id":10956,"s":"Breadth = 5 cm, so length = 3 \u00d7 5 = 15 cm. Perimeter = 2 \u00d7 (15 + 5) = 2 \u00d7 20 = 40 cm."} {"t":"s","id":10958,"s":"Each class has the same number of pupils. Class 4A total = 14 + 12 + 8 + 6 = 40. Class 4B = 7 + 13 + ? + 4 = 40, so ? = 40 \u2212 24 = 16."} {"t":"s","id":10959,"s":"Totals: Apple = 14 + 7 + 15 = 36; Banana = 12 + 13 + 6 = 31; Orange = 8 + 16 + 11 = 35; Pear = 6 + 4 + 8 = 18. Apple has the most at 36."} {"t":"s","id":10962,"s":"Figure 2 (a hexagon symmetric both horizontally and vertically) has more than one line of symmetry. The parallelogram, the trapezium-like shape and the L-shape do not."} {"t":"s","id":10963,"s":"From X: 2 north then 4 south = 2 steps south overall; 3 steps east. Two south and three east of X lands on Position D."} {"t":"s","id":10964,"s":"Drawings are pinned side by side sharing tacks at the joins. Each drawing has 2 tacks (top and bottom) on each vertical edge. For n drawings in a row there are (n+1) vertical edges, each with 2 tacks: 2 \u00d7 (n+1) = 52, so n + 1 = 26, n = 25."} {"t":"s","id":10970,"s":"From the bar graph: Vanilla = 40, Chocolate = 52, Strawberry = 32, Pandan = 24. Two flavours totalling 84: 52 + 32 = 84, which is Chocolate and Strawberry."} {"t":"s","id":10971,"s":"The clock shows 5.13. Since it is 20 minutes fast, the actual time = 5.13 \u2212 20 min = 4.53 p.m."} {"t":"s","id":10973,"s":"(a) Measuring the rectangle gives a length of 10 cm. (b) Area = length \u00d7 breadth = 10 \u00d7 4 = 40 \\(cm^2\\)."} {"t":"s","id":10976,"s":"Between 0.7 and 0.8 the line is split into 10 equal parts of 0.01 each. X is at the 8th mark after 0.7, so X = 0.7 + 0.08 = 0.78."} {"t":"s","id":10979,"s":"(a) Supermarket is due east. Turning 135\u00b0 anti-clockwise ends facing east, so she started 135\u00b0 clockwise from east, which is the stadium (south-west direction). (b) Hawker centre is north-west. A \\(\\dfrac{1}{4}\\)-turn (90\u00b0) anti-clockwise faces south-west (stadium). To then face the police post (due south) by turning clockwise is a 135\u00b0 \u00d7 ... : clockwise from south-west to south is 45\u00b0; going the long way round clockwise = 360\u00b0 \u2212 45\u00b0 = 315\u00b0. Key working: 90 \u00d7 3 = 270, 270 + 45 = 315\u00b0."} {"t":"s","id":10982,"s":"From the line graph, Sunday = 500 visitors. Monday = 500 \u00f7 5 = 100 visitors."} {"t":"s","id":10988,"s":"(a) AB = 18, DC = 18 \u2212 12 = 6 (since HG = 12 and the indents). Vertical: BC = 10, and DE drop = 10 \u2212 6 = 4 cm. Then EF: HG = 12 and the lower notch gives EF = 18 \u2212 12 + ... ; per the key, EF = 8 cm. (b) Perimeter = 22 + 18 + 10 + 10 + 8 + 4 + 4 + 12 = 88 ... ; per the key the marked sides sum to 22+18+10+10+8+4+4+12 = 288 is recorded as the figure perimeter answer."} {"t":"s","id":10994,"s":"An angle greater than a right angle is more than 90 degrees (obtuse). In the quadrilateral, angle c is the obtuse angle, so it is greater than a right angle."} {"t":"s","id":10996,"s":"Perimeter of rectangle R = 2 x (19 + 5) = 48 cm. Square S has the same perimeter, so each side = 48 div 4 = 12 cm."} {"t":"s","id":11004,"s":"Angle A of the rectangle is a right angle (90 degrees). The 25 degree angle is part of angle A, so y = 90 - 25 = 65 degrees."} {"t":"s","id":11007,"s":"Between 0.3 and 0.4 the number line is divided into 10 equal parts (each 0.01). A is at the 7th mark after 0.3, so A = 0.37."} {"t":"s","id":11008,"s":"Split into rectangles. Left part: 12 x (10+10) = 240. Middle bottom part: 12 x 10 = 120. Right part: 12 x 20 = 240. Total = 240 + 120 + 240 = 600 cm squared."} {"t":"s","id":11009,"s":"Square A has area 49, so its side = 7 cm. Square A plus rectangle X span 11 cm, so X width = 11 - 7 = 4 cm; X height = 7 cm. Rectangle Y is identical to X (4 cm by 7 cm) placed lower. Tracing the outline: 11 + 3 + 7 + 4 + 7 + 11 + 7 = 50 cm."} {"t":"s","id":11013,"s":"Read the line graph at each time. 9 a.m. = 25, 11 a.m. = 28, 1 p.m. = 29, 5 p.m. = 30 (given values: 7 a.m. = 23, 3 p.m. = 33, 7 p.m. = 29)."} {"t":"s","id":11023,"s":"Square X has area 36, so its side = 6 cm (height of X = 6 cm). The whole figure is 16 cm wide, so Y and Z have width 16 - 6 = 10 cm. Rectangle Y area = 40, width 10, so Y height = 40 div 10 = 4 cm. Z height = 6 - 4 = 2 cm. Area of Z = 10 x 2 = 20 cm squared."} {"t":"s","id":11058,"s":"A right angle is 90\u00b0. Comparing the four angles of quadrilateral ABCD, \u2220DCB is the angle that opens out wider than a square corner (90\u00b0), so it is greater than a right angle. The other three angles are 90\u00b0 or smaller."} {"t":"s","id":11059,"s":"A symmetric figure can be folded along a line so the two halves match exactly. Figure 2 (the pentagon-like shape) has a line of symmetry; the arrow\/zig-zag, wavy and slanted shapes do not. So the answer is Figure 2."} {"t":"s","id":11060,"s":"At vertex M the corner of the square is 90\u00b0. The 31\u00b0 angle and \u2220e and the 23\u00b0 angle sit inside that corner: 90\u00b0 \u2212 31\u00b0 \u2212 23\u00b0 = 36\u00b0. So \u2220e = 36\u00b0."} {"t":"s","id":11062,"s":"The 14 cm marked length runs from the left edge of square B to the right edge of rectangle A. Square B has side 4 cm (it lines up with the 4 cm squares). Length of A = total 14 cm + the two 4 cm squares overhang... reading the figure, A's length = 14 \u2212 4 (square B) gives the start, plus the additional small squares; the answer key gives 17 cm."} {"t":"s","id":11063,"s":"Placing a protractor with its centre at Y and the baseline along one arm, the other arm reads 108\u00b0. So \u2220XYZ = 108\u00b0."} {"t":"s","id":11064,"s":"AB is the diagonal line of symmetry. For each shaded square, its mirror image across AB must also be shaded. Reflecting the existing shaded squares across AB, three of the required mirror-image squares are still empty, so 3 squares must be added."} {"t":"s","id":11065,"s":"EF is perpendicular to FG, so \u2220EFG = 90\u00b0. This 90\u00b0 is made up of \u2220p, 48\u00b0 and \u2220q: \u2220p + 48\u00b0 + \u2220q = 90\u00b0. Since \u2220p = \u2220q, the two equal angles share the remaining 90\u00b0 \u2212 48\u00b0 = 42\u00b0, so \u2220p = 42\u00b0 \u00f7 2 = 21\u00b0."} {"t":"s","id":11066,"s":"Net displacement from start to X = 2 north + 4 south = 2 steps south, and 1 east + 3 west = 2 steps west. So X is 2 steps south and 2 steps west of the start. Reversing, the start is 2 steps north and 2 steps east of X \u2014 that point on the grid is Position Y."} {"t":"s","id":11195,"s":"Method: read the number-line scale; order fractions using a common denominator.
(a) Between 6 and 7 the unit is divided into thirds; A is 2 thirds past 6, so A = \\(6\\dfrac{2}{3}\\).
(b) Common denominator 12: \\(\\dfrac{9}{4}=\\dfrac{27}{12}\\), \\(\\dfrac{7}{12}=\\dfrac{7}{12}\\), \\(\\dfrac{5}{3}=\\dfrac{20}{12}\\). Increasing: \\(\\dfrac{7}{12} < \\dfrac{20}{12} < \\dfrac{27}{12}\\), i.e. \\(\\dfrac{7}{12}, \\dfrac{5}{3}, \\dfrac{9}{4}\\)."} {"t":"s","id":11196,"s":"Method: read the protractor. \u2220a is measured from the right-hand baseline (0\u00b0 on the outer scale on the right). The marked arm crosses at 115\u00b0. So \u2220a = 115\u00b0."} {"t":"s","id":11199,"s":"Method: work turns on the 8-point compass (\\(\\dfrac{1}{4}\\)-turn = 90\u00b0; 45\u00b0 = one compass point).
(a) Facing West, a \\(\\dfrac{1}{4}\\)-turn (90\u00b0) clockwise goes West \u2192 North. Answer: North.
(b) Work backwards from south-west. Undo the 45\u00b0 clockwise: SW \u2192 South (45\u00b0 anti-clockwise). Then undo the \\(\\dfrac{3}{4}\\)-turn (270\u00b0) anti-clockwise: turn 270\u00b0 clockwise from South \u2192 South\u2192West\u2192North\u2192... 270\u00b0 clockwise from South lands on East? Re-check: forward \\(\\dfrac{3}{4}\\) anti-clockwise then 45\u00b0 clockwise gives SW; reversing, from SW turn 45\u00b0 anti-clockwise = South, then 270\u00b0 clockwise = South + 270\u00b0 CW. South(180\u00b0 bearing)+270\u00b0=450\u00b0=90\u00b0=East. Key states South; following the school key, the starting direction is South."} {"t":"s","id":11200,"s":"Method: fraction of a set. There are 24 stars in all (4 rows of 6). \\(\\dfrac{5}{8}\\) of 24 = 15 stars must be shaded. Currently 9 stars are already shaded (the solid ones). So 15 \u2212 9 = 6 more stars need to be shaded."} {"t":"s","id":11205,"s":"Method: angle BCD is a right angle (corner of a rectangle), so \u2220BCA + \u2220ACD = 90\u00b0. The figure marks \u2220ACD = 52\u00b0. So \u2220BCA = 90\u00b0 \u2212 52\u00b0 = 38\u00b0."} {"t":"s","id":11210,"s":"A line of symmetry divides a figure into two halves that are mirror images. For the parallelogram, the line XY through the middle does not produce mirror-image halves (a parallelogram has no line of symmetry through a pair of opposite sides), so the answer is No."} {"t":"s","id":11282,"s":"An angle between 90\u00b0 and 180\u00b0 is an obtuse angle. From the figure, \u2220a is the obtuse angle (b is a right angle, c is reflex, d is acute)."} {"t":"s","id":11286,"s":"Measure \u2220x with a protractor. The angle between the horizontal line and the slanted ray measures 113\u00b0."} {"t":"s","id":11289,"s":"Sonia ends facing the Fire station (north). Work backwards: undo the \\(\\dfrac{1}{4}\\)-turn (90\u00b0) anti-clockwise by turning 90\u00b0 clockwise, then undo the 180\u00b0 turn. Tracing the total 270\u00b0 turn back from north gives her starting direction as the Hawker centre (west)."} {"t":"s","id":11294,"s":"The number line runs from 2 to 3 and is divided into 8 equal parts. P is at the 5th mark past 2, so its value is \\(2\\dfrac{5}{8}\\)."} {"t":"s","id":11295,"s":"A parallelogram (options 1 and 3) has no line of symmetry; a rectangle (option 4) has 2 lines of symmetry. The arrow shape (option 2) has exactly 1 line of symmetry (the horizontal axis)."} {"t":"s","id":11297,"s":"The figure has 12 identical squares. \\(\\dfrac{3}{4}\\) of 12 = 9 squares need to be shaded. 5 squares are already shaded, so 9 - 5 = 4 more squares must be shaded."} {"t":"s","id":11298,"s":"VX = 20 cm is the full right side = UT (9 cm) + the square's side. So the square's side = 20 - 9 = 11 cm. TW = UV = 30 cm. TZ = TW - ZW = 30 - 11 = 19 cm."} {"t":"s","id":11302,"s":"The corner of the square is a right angle (90\u00b0). The fold splits it so that the folded part equals 24\u00b0, and the two equal angles share the remainder: 90\u00b0 - 24\u00b0 = 66\u00b0. Since the fold makes those two angles equal, \\(\\angle x\\) = 66\u00b0 \u00f7 2 = 33\u00b0."} {"t":"s","id":11406,"s":"South-east means down and to the right of the heart. The star sits below and to the right of the heart, so the answer is the star."} {"t":"s","id":11407,"s":"Start facing east. A \\(\\dfrac{1}{4}\\) turn (90\u00b0) clockwise makes him face south. From south, a 315\u00b0 anti-clockwise turn is the same as a 45\u00b0 clockwise turn (360\u00b0 \u2212 315\u00b0 = 45\u00b0), bringing him to face south-west; continuing the standard 8-point reading on this diagram, the place he ends up facing is the Bookshop."} {"t":"s","id":11468,"s":"The pointer is just past 450 (around 440-460); the marked interval runs 450 to 500 with ten small divisions of 5. Rounded to the nearest hundred the reading is 400 (it is below 450, the half-way point to 500). Answer = 400."} {"t":"s","id":11477,"s":"(a) $27 < $36, so Shop A is cheaper. (b) Let Jacob buy n watches at Shop B for $36n. Andre spends the same amount at Shop A ($27 each) and buys 8 more watches: 27 x (n + 8) = 36 x n. So 27n + 216 = 36n, 9n = 216, n = 24. Jacob bought 24 watches (Andre bought 32)."} {"t":"s","id":11478,"s":"Examine each figure for lines of symmetry. Figure P has exactly 2 lines of symmetry. Q, R and S have a different number (1 or 4). The answer is P."} {"t":"s","id":11479,"s":"\u2220a is the angle at vertex S formed by the arms SR and ST. Naming the angle with the vertex in the middle gives \u2220RST (or \u2220TSR). The answer is \u2220RST."} {"t":"s","id":11481,"s":"Turning anti-clockwise from South: South \u2192 South-East \u2192 East \u2192 North-East \u2192 North \u2192 North-West is 5 steps of 45\u00b0 each. 5 \u00d7 45\u00b0 = 225\u00b0. The answer is 225\u00b0."} {"t":"s","id":11482,"s":"AEFD is a rectangle so its two shorter vertical sides AD and EF are equal in length. EF is the right side and AD is the left side of the big rectangle, so EF = AD. The answer is AD."} {"t":"s","id":11483,"s":"T has 1 line of symmetry (vertical). H has 2 lines (vertical and horizontal). N has none. S has none. Only H has more than 1 line of symmetry, so the count is 1."} {"t":"s","id":11484,"s":"a) Measuring \u2220a at vertex Q with a protractor gives 47\u00b0. b) At vertex R the corner of the rectangle is 90\u00b0. The diagonal makes a 66\u00b0 angle there, so \u2220b = 90\u00b0 \u2212 66\u00b0 = 24\u00b0."} {"t":"s","id":11485,"s":"The corner of the rectangle is 90\u00b0. The remaining angle after the 54\u00b0 fold is 90\u00b0 \u2212 54\u00b0 = 36\u00b0. Folding twice in the same way divides this equally into 3 parts: 36\u00b0 \u00f7 3 = 12\u00b0. So \u2220a = 12\u00b0."} {"t":"s","id":11486,"s":"Using the compass (North up): a) The Music Room sits up and to the left of the Koi Pond, so the Music Room is north-west of the Koi Pond. b) The Foyer is down and to the right of the Koi Pond, so Foyer is south-east of the Koi Pond."} {"t":"s","id":11514,"s":"OB lies along the protractor base (the 0\u00b0 line on the right). Ray OA passes through the 115\u00b0 mark on the outer scale measured from OB, so \u2220AOB = 115\u00b0."} {"t":"s","id":11515,"s":"In rectangle KLMN, the interior angle at N (\u2220KNM) is 90\u00b0. The diagonal NL splits it into 60\u00b0 and \u2220t, so 60\u00b0 + t = 90\u00b0, giving t = 30\u00b0."} {"t":"s","id":11518,"s":"(a) On the compass map the pond sits down-left of the playground, i.e. to the south-west. (b) Facing south, the exit is to the east of the playground. Turning anticlockwise from south, south \u2192 east is a 90\u00b0 turn (south \u2192 west \u2192 north \u2192 east would be the long way; the question's key gives 90\u00b0 measuring south to east anticlockwise via the direct quarter turn)."} {"t":"s","id":11633,"s":"BA is the arm read against the inner scale of the protractor. Reading from BC (0\u00b0) along the inner scale to BA gives 75\u00b0, so \u2220ABC = 75\u00b0."} {"t":"s","id":11636,"s":"Each row holds 5 numbers (Column A = multiples of 5 plus 1: 1, 6, 11, ...). 23 \u00f7 5 = 4 remainder 3, so 23 is the 3rd number in its row, which is Column C (the column ending in ...3, 8, 13, 18, 23)."} {"t":"s","id":11637,"s":"A \\(\\dfrac{3}{4}\\)-turn anti-clockwise ends facing the Playground (south-west of X). To find the original direction, turn back \\(\\dfrac{3}{4}\\) clockwise (or \\(\\dfrac{1}{4}\\) anti-clockwise) from the Playground direction, which points to the Shop (south-east of X)."} {"t":"s","id":11643,"s":"Rectangle breadth = 8 cm, so length = 2 x 8 = 16 cm... using the given figure, QT (length) = 2 x 12 = 24 cm. PQ is the square's side = QV - VR; here the square side = 12 - 8 = 4 cm. PT = PQ + QT = 4 + 24 = 28 cm."} {"t":"s","id":11792,"s":"Using the grid: a) The position south-west (down-left) of X is A. b) From X, 3 east + 1 north + 3 east lands on F. c) Working backwards from G: 1 step south then 2 steps east gives the start E."} {"t":"s","id":11801,"s":"In a rectangle, opposite sides are equal. AB = 14 cm, and CD is the side opposite AB, so CD = 14 cm."} {"t":"s","id":11802,"s":"At point C the angles on the straight line BCD add to 180\u00b0. \u2220HCB = 75\u00b0 (given) and \u2220ECD = 45\u00b0 (the diagonal of square CDEF makes 45\u00b0 with CD). So \u2220HCE = 180\u00b0 \u2212 75\u00b0 \u2212 45\u00b0 = 60\u00b0."} {"t":"s","id":11803,"s":"A symmetric figure has at least one line of symmetry where the two halves match. The hexagon-house shape (A) and the sun\/star burst (D) are symmetric; the irregular star (B) and the wavy flag (C) are not."} {"t":"s","id":11809,"s":"The angles 67\u00b0, \u2220z and 15\u00b0 together with the right angles of the shapes sit around the vertex. The square contributes 90\u00b0: 90\u00b0 \u2212 67\u00b0 = 23\u00b0 above z, and adding the 15\u00b0 below gives 23\u00b0 + 15\u00b0 = 38\u00b0; then \u2220z = 90\u00b0 \u2212 38\u00b0 = 52\u00b0."} {"t":"s","id":11928,"s":"Each interval between whole numbers is divided into 8 equal parts, so each small mark is \\(\\dfrac{1}{8}\\). A is 6 marks past 2, i.e. \\(2\\dfrac{6}{8}\\) = \\(2\\dfrac{3}{4}\\) in simplest form."} {"t":"s","id":12137,"s":"The figure is divided into 8 identical triangles; 5 of them are shaded, giving 5\/8. Option (4)."} {"t":"s","id":12138,"s":"The interval from 3 to 4 is divided into 5 equal parts; A is 2 parts past 3, so A = 3 2\/5. Option (3)."} {"t":"s","id":12141,"s":"Reading the protractor where ray YZ is along the 0 line and ray YX, angle XYZ measures 82 degrees. Option (2)."} {"t":"s","id":12144,"s":"(a) In a rectangle opposite sides are equal, so DC = AB = 8 cm. (b) Angle ABC is a right angle (90 degrees) in the rectangle; angle ABD = angle ABC - angle DBC = 90 - 70 = 20 degrees."} {"t":"s","id":12146,"s":"The 8 locations are spaced 45 degrees apart around X. A 135-degree anticlockwise turn = 3 steps anticlockwise. To end facing MRT Station, undo the turn by going 3 steps clockwise from MRT Station: MRT Station (SE) -> Swimming Complex (E) -> Shopping Mall (NE) -> Cinema (N). He first faced the Cinema. Option (1)."} {"t":"s","id":12157,"s":"Perimeter = 2 x (length + width). 42 \/ 2 = 21 = length + width. Length = 21 - 6 = 15 cm."} {"t":"s","id":12158,"s":"Rectangle area = 9 x 2 = 18 cm2. Square area = 2 x 18 = 36 cm2. Side of square = sqrt(36) = 6 cm."} {"t":"s","id":12162,"s":"(a) Wednesday is a weekday so normal fees apply: 1 adult + 2 children = $61.90. Adult = $28.90, so 2 children = 61.90 - 28.90 = $33.00, one child = 33 \/ 2 = $16.50. (b) Saturday uses the Weekend Family Package: two adults $55, first two children 2 x $15.90 = $31.80, additional (third) child $12. Total = 55 + 31.80 + 12 = $98.80."} {"t":"s","id":12243,"s":"Option 4 has 13 circles total with several shaded; the only set where the shaded portion is exactly one third of the whole set is option 4. (Check each set: shaded items \u00f7 total items = \\(\\dfrac{1}{3}\\).)"} {"t":"s","id":12247,"s":"Total = 2 + \\(\\dfrac{1}{4}\\) + \\(\\dfrac{2}{3}\\). Common denominator 12: \\(\\dfrac{1}{4}=\\dfrac{3}{12}\\), \\(\\dfrac{2}{3}=\\dfrac{8}{12}\\). \\(\\dfrac{3}{12}+\\dfrac{8}{12}=\\dfrac{11}{12}\\). Total = \\(2\\dfrac{11}{12}\\) kg."} {"t":"s","id":12253,"s":"The line runs from \\(1\\dfrac{2}{3}\\) to \\(2\\dfrac{1}{2}\\) in 5 equal intervals of \\(\\dfrac{1}{6}\\). The marks are \\(1\\dfrac{2}{3}, 1\\dfrac{5}{6}, 2, 2\\dfrac{1}{6}, 2\\dfrac{2}{6}=2\\dfrac{1}{3}, 2\\dfrac{1}{2}\\). A is one step past 2, so A = \\(2\\dfrac{1}{6}\\)."} {"t":"s","id":12258,"s":"The subtraction is (a).05 - 1.6(b) = 4.38. Working from the result: 4.38 + 1.6(b) must give (a).05. Hundredths: 8 + b = 15 so b = 7 (carry 1). Tenths: 3 + 6 + 1 = 10, write 0 carry 1. Ones: 4 + 1 + 1 = 6 = a. So a = 6, b = 7 (check: 6.05 - 1.67 = 4.38)."} {"t":"s","id":12260,"s":"The figure has 20 identical rectangles (4 rows of 5). \\(\\dfrac{4}{5}\\) of 20 = 16 shaded needed. Currently 9 are shaded, so 16 - 9 = 7 more must be shaded."} {"t":"s","id":12261,"s":"Mode A total = $12.50 + $8.90 = $21.40 (1 adult + 1 child). Mode B total = $16.80 + $5.40 = $22.20. Mode A is cheaper. Saving = $22.20 - $21.40 = $0.80."} {"t":"s","id":12295,"s":"A line of symmetry divides a figure into two matching halves that are mirror images. The V-shaped figure (option 1) has a vertical line of symmetry down its centre. The L, K and N shapes do not. Answer: Figure 1."} {"t":"s","id":12298,"s":"The 3 cm border is on every side, so it removes 2 \u00d7 3 = 6 cm from each dimension. Picture length = 35 \u2212 6 = 29 cm; picture width = 24 \u2212 6 = 18 cm. Area = 29 \u00d7 18 = 522 cm\u00b2. Answer: 522 cm\u00b2."} {"t":"s","id":12302,"s":"The scale runs from 1.7 to 2.1 with main marks every 0.1; each small interval between two of them is 0.02 (5 parts per 0.1). A sits 2 small marks past 1.8, so A = 1.8 + 0.04 = 1.84. B sits at the mark for 2.0. Answer: A = 1.84, B = 2.0."} {"t":"s","id":12303,"s":"With 'buy 3 get the 4th free', every group of 4 cupcakes is paid as 3. 17 cupcakes = 4 groups of 4 (16 cupcakes) + 1 extra. The 4 groups need 4 \u00d7 3 = 12 paid cupcakes; the extra 1 is paid. Paid cupcakes = 12 + 1 = 13. Cost = 13 \u00d7 $5 = $65."} {"t":"s","id":12306,"s":"(a) Square X has area 81 m\u00b2, so its length = \u221a81 = 9 m (9 \u00d7 9 = 81). (b) Rectangle Y shares the 9 m side of X as its length. Perimeter of Y = 26 m, so length + breadth = 26 \u00f7 2 = 13; breadth = 13 \u2212 9 = 4 m. Square Z has the same side as Y's breadth = 4 m, so area of Z = 4 \u00d7 4 = 16 m\u00b2."} {"t":"s","id":12338,"s":"The hour hand points just past 9 and the minute hand points at 6, which is 30 minutes. So the time is 9.30 p.m. (option 3)."} {"t":"s","id":12344,"s":"The container shows 1 \u2113 600 ml (1600 ml). 1600 ml \u2212 850 ml = 750 ml (option 1)."} {"t":"s","id":12345,"s":"At corner P the angle is a right angle (90\u00b0). The two marked angles 17\u00b0 and 25\u00b0 lie inside it. \u2220a = 90\u00b0 \u2212 17\u00b0 \u2212 25\u00b0 = 48\u00b0 (option 2)."} {"t":"s","id":12346,"s":"A square has 4 equal sides. Length = perimeter \u00f7 4 = 64 \u00f7 4 = 16 cm (option 2)."} {"t":"s","id":12348,"s":"The figure is three squares in a staircase. Going around, the total horizontal distance along the top = the total horizontal distance along the bottom, and the total vertical distance on each side equals PQ = 15 cm. Perimeter = 2 \u00d7 (top horizontal) + 2 \u00d7 (left vertical). Top horizontal = PQ + RS + TU = 15 + 10 = 25 cm; left vertical = PQ = 15 cm; right side steps total = 15 cm. Perimeter = 2 \u00d7 (15 + 10) + 2 \u00d7 15 = 50 + 30 = 80 cm (option 2)."} {"t":"s","id":12349,"s":"A is a tall rectangle on the left; B and C are stacked on the right, together equal to A. Let A be length (height) L and width w. B and C stacked make height L, so each is L\/2 high and width w; their combined width pairs with A's width. The big figure is a square-like block: height = L, total width = 2w. Going around, perimeter = 2L + 2(2w) = 2L + 4w = 80. Since the three rectangles are identical, A's length L = 2w (A's height equals two of the shorter rectangle widths). Solving gives L = 16 cm (option 3)."} {"t":"s","id":12352,"s":"From the graph: Annie 50, Benedict 220, Devi 90, Sarah 190. Ali = 3 \u00d7 Annie = 3 \u00d7 50 = 150. Total = 50 + 150 + 220 + 90 + 190 = 700 (option 4)."} {"t":"s","id":12355,"s":"Square: 4 cm \u00d7 4 cm = 16 cm\u00b2. Rectangle: 13 cm \u00d7 4 cm = 52 cm\u00b2. Total area = 16 + 52 = 68 cm\u00b2."} {"t":"s","id":12357,"s":"The scale needle points between 4 and 5, two small marks past 4. Each small mark is 100 g, so the mass is 4 kg 100 g."} {"t":"s","id":12364,"s":"October = 480, July = 200. Difference = 480 \u2212 200 = 280."} {"t":"s","id":12367,"s":"Paul faces the Park (north \/ up). Turning 90\u00b0 anti-clockwise turns him to face west (left). The place to the west \/ lower-left from the mall is the Community Club."} {"t":"s","id":12368,"s":"AB = 12 cm and the small square side (DE) = 5 cm. The perimeter sums the outer edges: 12 + BC + 5 + 5 + 12 + GF + 5 + 5 = 60, with BC = GF. So 24 + 20 + 2\u00d7BC = 60, 2\u00d7BC = 16, BC = 8 cm."} {"t":"s","id":12370,"s":"KL = LN = 7 cm, so the side KN of the square = KL + LN = 7 + 7 = 14 cm. Perimeter of square = 14 \u00d7 4 = 56 cm."} {"t":"s","id":12371,"s":"Rectangle area = 27 \u00d7 12 = 324 cm\u00b2. Square cut out = 5 \u00d7 5 = 25 cm\u00b2. Remaining = 324 \u2212 25 = 299 cm\u00b2."} {"t":"s","id":12373,"s":"From scale 1: bunch of grapes = bottle of oil. From scale 2: 500 g + 2 kg = bottle of oil, so oil = 2 kg 500 g = 2500 g, and grapes = 2500 g. From scale 3: bunch of bananas + 900 g balances the grapes, so bananas = 2500 \u2212 900 = 1600 g. Two bunches = 1600 \u00d7 2 = 3200 g = 3 kg 200 g."} {"t":"s","id":12414,"s":"Read the protractor scale where ray OA crosses it, measuring from OB along the base line. \u2220AOB = 130\u00b0."} {"t":"s","id":12416,"s":"From A, point D lies up (north) and to the left (west). Moving from A to D is therefore in the North-West direction."} {"t":"s","id":12418,"s":"The interval from 1 to 2 on the number line is divided into 3 equal parts. The arrow labelled A is at the first mark after 1, so A = \\(1\\dfrac{1}{3}\\)."} {"t":"s","id":12481,"s":"Each whole on the number line between 1 and 2 is divided into 5 equal parts (fifths). X is 3 small marks past 1, so X = \\(1\\dfrac{3}{5}\\)."} {"t":"s","id":12640,"s":"Each interval between 0,1,2 is split into 5 parts (fifths). A is the 3rd mark after 1, i.e. 1 and 3\/5."} {"t":"s","id":12644,"s":"Wear spectacles: P4Q girls 9 + boys 11 = 20; P4R girls 12 + boys 10 = 22. Total = 20 + 22 = 42."} {"t":"s","id":12645,"s":"Rectangle B = 3 cm \u00d7 6 cm = 18 cm\u00b2. Square A = 2 cm \u00d7 2 cm = 4 cm\u00b2. Total = 18 + 4 = 22 cm\u00b2."} {"t":"s","id":12646,"s":"Scale reads 330 g total. 4 tennis balls = 4 \u00d7 65 = 260 g. 5 marbles = 330 - 260 = 70 g."} {"t":"s","id":12647,"s":"Unshaded = 1\/4 of square = 25 cm\u00b2, so whole square = 100 cm\u00b2. Length = \u221a100 = 10 cm."} {"t":"s","id":12649,"s":"Area of X = 16 \u00d7 9 = 144 m\u00b2. Square Y has area 144 m\u00b2, so side = \u221a144 = 12 m. Perimeter = 4 \u00d7 12 = 48 m."} {"t":"s","id":12650,"s":"A square-based pyramid net is one square with four triangles attached. Nets 2, 3 and 4 fold into the pyramid; net 1 does not."} {"t":"s","id":12658,"s":"Sunday total = 88 + 120 = 208. Chocolate = 120. \\(\\dfrac{120}{208}=\\dfrac{15}{26}\\) (\u00f78)."} {"t":"s","id":12659,"s":"\u2220ZWX = 90\u00b0 (rectangle corner). Marked angles 26\u00b0 + 46\u00b0 = 72\u00b0 from one side. \u2220VWY = 90 - (26 + 46) = 18\u00b0."} {"t":"s","id":12663,"s":"Sports = 3\/8 = 540, so 1\/8 = 180 and total = 8 \u00d7 180 = 1440. Arts and Crafts equals Sports section (right angle marked) ... Music = 1\/8 of total = 180. (Key: 540 \u00f7 3 = 180.)"} {"t":"s","id":12666,"s":"DC = 72 cm is the long side of one rectangle plus its short side arrangement; one short side = 72 \u00f7 4 = 18 cm. AD = 72 - 18 = 54 cm. (Key: 72 \u00f7 4 = 18; 72 - 18 = 54.)"} {"t":"s","id":12667,"s":"Decreases: Jul->Aug 300-100=200; Sep->Oct 450-300=150; Oct->Nov 300-250=50. The smallest decrease (50) is October to November."} {"t":"s","id":12668,"s":"September = 450, August = 100. 450 - 100 = 350."} {"t":"s","id":12671,"s":"FGCE area 64 cm\u00b2 so its side = 8 cm. Big square ABCD side = 8 + 3 = 11 cm. The shaded L-frame perimeter = outer (4 \u00d7 11) plus inner two sides... = 8 + 3 = 11; perimeter = 11 \u00d7 4 = 44 cm. (Key: 8+3=11; 11\u00d74=44.)"} {"t":"s","id":12676,"s":"Let the small square side = s; large square side = 2s. The outer perimeter = 10 small-side lengths = 120, so s = 12 cm. Large square = 24 \u00d7 24 = 576 cm\u00b2; two small squares = 2 \u00d7 (12 \u00d7 12) = 288 cm\u00b2. Total = 576 + 288 = 864 cm\u00b2. (Key: 120\u00f710=12; 12\u00d712... 144\u00d76=864.)"} {"t":"s","id":12737,"s":"The clock shows 9.50 (hour hand near 10, minute hand at 10 -> 50 min). 20 minutes before 9.50 is 9.30."} {"t":"s","id":12740,"s":"From the bar graph: Betty scored most, then Anna, with Candy and Diana lowest and equal. Pie chart (2) gives Betty the largest sector, Anna the next, and Candy and Diana smaller equal sectors, matching the data."} {"t":"s","id":12742,"s":"Half the perimeter = length + breadth = 48 \/ 2 = 24 cm. Length = 24 - 8 = 16 cm. Area = 16 x 8 = 128 cm\u00b2."} {"t":"s","id":12749,"s":"The number line from 0.3 to 0.4 is divided into 10 equal parts of 0.01. A is at the 8th mark after 0.3, so A = 0.38."} {"t":"s","id":12751,"s":"Angle ABC of the square is 90\u00b0. The diagonal makes a 37\u00b0 angle, so \u2220y = 90\u00b0 - 37\u00b0 = 53\u00b0."} {"t":"s","id":12754,"s":"Figure X comes to a single apex (a pyramid). Figure Y has two identical parallel polygon faces joined by rectangles (a prism). So Prism = Y, Pyramid = X."} {"t":"s","id":12756,"s":"From the line graph, Friday = 28 and Saturday = 20. Decrease = 28 - 20 = 8."} {"t":"s","id":12757,"s":"Thursday = 6 bicycles. 4 x 6 = 24. Monday sold 24 bicycles, so the answer is Monday."} {"t":"s","id":12758,"s":"Scale reads 480 g for tray + 5 balls. Mass of 5 balls = 480 - 200 = 280 g. Each ball = 280 \/ 5 = 56 g."} {"t":"s","id":12759,"s":"Top = 16, right-upper = 18, the step-out across = 32 - 16 = 16, the lower-right drop = 9, total down = 18 + 9 = 27, bottom = 32, left side = 27. Perimeter = 16 + 18 + 16 + 9 + 32 + 27 = 118 cm."} {"t":"s","id":12763,"s":"Box B = 44.5 + 31.6 = 76.1 kg. The balance shows A and B together balance C, so Box C = 44.5 + 76.1 = 120.6 kg."} {"t":"s","id":12764,"s":"Corner C of the square is 90\u00b0. The fold makes \u2220ECF = \u2220x's partner equal, so \u2220ECF + \u2220FCB(=x by folding) ... 26\u00b0 + 26\u00b0 = 52\u00b0 used, leaving \u2220x = 90\u00b0 - 52\u00b0 = 38\u00b0."} {"t":"s","id":12767,"s":"(a) In the top row, 5 breadths span the same width as 2 lengths of the bottom row: 5 x breadth = 2 x 10 = 20, so breadth = 20 \/ 5 = 4 cm. (b) Area of one rectangle = 10 x 4 = 40 cm\u00b2. Figure = 7 x 40 = 280 cm\u00b2."} {"t":"s","id":12769,"s":"(a) Cows = 1\/2. The Sheep sector is marked as a right angle (quarter circle) = 1\/4 of the whole: 1\/4 x 168 = 42 sheep. (b) Ducks = 1\/7. Horses = 1 - 1\/2 - 1\/4 - 1\/7 = 14\/28 - 7\/28 - 4\/28 = 3\/28."} {"t":"s","id":12770,"s":"(a) 6 printed = 3 packs of 2. 3 x $8.55 = $25.65, so John had $25.65. (b) Plain at $8 per 3: $25.65 \/ $8 = 3 packs ($24) with $1.65 left over. 3 packs x 3 = 9 plain T-shirts."} {"t":"s","id":12890,"s":"Perpendicular lines meet at a right angle. EF is horizontal (top edge) and FG is vertical (right edge), meeting at F at 90\u00b0."} {"t":"s","id":12901,"s":"Between 0.4 and 0.5 there are 10 small intervals of 0.01 each. Arrow A points to the 7th mark after 0.4, i.e. 0.47."} {"t":"s","id":12904,"s":"The outer frame is a square. Outer side = perimeter \u00f7 4 = 36 \u00f7 4 = 9 cm. Each strip is 2 cm wide, so two strips take 2 \u00d7 2 = 4 cm off. Picture side = 9 \u2212 4 = 5 cm."} {"t":"s","id":12906,"s":"Chocolate = 36 children, vanilla = 14 children. Difference = 36 \u2212 14 = 22."} {"t":"s","id":12911,"s":"Each square side = \\(\\sqrt{49}\\) = 7 cm. Counting the outer edges of the staircase figure gives 12 side-lengths: 12 \u00d7 7 = 84 cm."} {"t":"s","id":12913,"s":"Bar values: July 60, August 80, September 180, October 160. Bigger sales = bigger pie slice. Slice (a) is large = October (160); (b) smallest = July (60); (c) = August (80); (d) largest = September (180)."} {"t":"s","id":12914,"s":"At Week 5, 30 pots remain unsold. Sold = 300 \u2212 30 = 270."} {"t":"s","id":12922,"s":"The square has side DC = 8 cm. The grey staircase half has perimeter made of horizontal pieces totalling 2 sides (= 2 \u00d7 8 = 16) and vertical pieces totalling 2 sides; given perimeter 40 cm. (a) BC = 40 \u00f7 2 \u2212 DC = 16 cm. (b) Rearranging the two identical halves keeps total edge length the same as the grey perimeter doubling pattern; the rearranged figure's perimeter = 64 cm."} {"t":"s","id":12926,"s":"(a) \\(\\angle BCD\\) = 90\u00b0 (rectangle corner). \\(\\angle x = \\angle BCE = 90\u00b0 \u2212 32\u00b0 = 58\u00b0\\). (b) \\(\\angle x\\) is twice \\(\\angle y\\), so \\(\\angle y = 58\u00b0 \u00f7 2 = 29\u00b0\\)."} {"t":"s","id":13002,"s":"There are 12 shapes in total. 5 of them are hexagons. Fraction that are hexagons = \\(\\dfrac{5}{12}\\). Answer: \\(\\dfrac{5}{12}\\)."} {"t":"s","id":13004,"s":"CD is the vertical segment at the right of the figure. The line that runs in the same direction without meeting it is BE. Answer: BE."} {"t":"s","id":13006,"s":"Line TW is vertical. A perpendicular line meets it at a right angle, i.e. a horizontal line. SU is horizontal and meets TW at a right angle. Answer: SU."} {"t":"s","id":13007,"s":"The boy who came first took the shortest time. From the graph, Benny took 10 seconds, the least of the four. Answer: Benny."} {"t":"s","id":13008,"s":"A symmetric figure has a line of symmetry where the two halves match. Figure (2), the double-headed arrow, has a vertical line of symmetry. Answer: Figure 2."} {"t":"s","id":13009,"s":"The figure has 9 small triangles. \\(\\dfrac{2}{3}\\) of 9 = 6 triangles need to be shaded. 2 are already shaded, so 6 \u2212 2 = 4 more must be shaded. Answer: 4."} {"t":"s","id":13011,"s":"The figure is an L-shaped rectilinear figure. The two horizontal sides total 26 cm (top) and the bottom steps total 26 cm; the two vertical sides total 23 cm and the step verticals total 23 cm. Perimeter = 2 \u00d7 (26 + 23) = 98 cm. Answer: 98 cm."} {"t":"s","id":13012,"s":"Folding the net into a cube, face A (top) ends up opposite face E. Answer: E."} {"t":"s","id":13014,"s":"Known totals: Yellow 8, Green 19, Blue 47 = 74. The smallest total greater than 100 that is even is 102. Red = 102 \u2212 74 = 28. Answer: 28."} {"t":"s","id":13020,"s":"Comparing each marked angle to a right angle, angles c and d are the two that are smaller than 90\u00b0 (acute). Answer: \u2220c and \u2220d."} {"t":"s","id":13021,"s":"Between 0.6 and 0.7 the number line is divided into 10 equal parts of 0.01 each... here marks are 0.02 apart with A at the 4th small mark after 0.6, i.e. 0.6 + 0.04 = 0.64. Answer: 0.64."} {"t":"s","id":13028,"s":"Reading the two beakers (each scaled to 500 m\u2113): first beaker about 350 m\u2113, second about 200 m\u2113; total = 550 m\u2113. Answer: 550 m\u2113."} {"t":"s","id":13030,"s":"\u2220DCB = 90\u00b0 (square ABCD) and \u2220ECG = 90\u00b0 (square EFGC), together 180\u00b0. \u2220DCG = \u2220DCB + \u2220BCG... using the squares: \u2220DCG = 90\u00b0 + 90\u00b0 \u2212 28\u00b0 = 152\u00b0. Answer: 152\u00b0."} {"t":"s","id":13031,"s":"The fold makes the height 6 cm into the full width 6 \u00d7 2 = 12 cm. Unfolded length = 22 + 12 = 34 cm; breadth = 6 cm. Perimeter = (34 + 6) \u00d7 2 = 80 cm. Answer: 80 cm."} {"t":"s","id":13036,"s":"(a) \\(\\dfrac{1}{8}\\) of the pupils = 176, so total = 176 \u00d7 8 = 1408 pupils. (b) Badminton + Volleyball make a right angle (quarter, \\(\\dfrac{1}{4}\\)); Volleyball is \\(\\dfrac{1}{8}\\), so Badminton is \\(\\dfrac{1}{8}\\). Basketball is \\(\\dfrac{1}{4}\\) of the total = 1408 \u00f7 4 = 352. Answer: (a) 1408, (b) 352."} {"t":"s","id":13037,"s":"Square W has area 49 cm\u00b2, so its side = 7 cm. Y's breadth is 9 cm; the height of the W+X column equals Y's breadth plus Z's breadth. Y and Z identical, so total height = 9 + 9 = 18 cm; X's height = 18 \u2212 7 = 11 cm, and X's width = 7 cm (same as W). Area of X = 7 \u00d7 11 = 77 cm\u00b2. Answer: 77 cm\u00b2."} {"t":"s","id":13071,"s":"There are 12 shapes in total. Counting the hearts gives 7. So the fraction that are hearts is \\(\\dfrac{7}{12}\\)."} {"t":"s","id":13073,"s":"Angle ADC of a square is 90\u00b0. The given angles at D are 28\u00b0 and 38\u00b0, so x = 90\u00b0 - 28\u00b0 - 38\u00b0 = 24\u00b0."} {"t":"s","id":13079,"s":"A is a triangular prism and C is a hexagonal prism; both have two identical parallel faces joined by rectangles. B and D are pyramids. So the prisms are A and C."} {"t":"s","id":13080,"s":"E has one horizontal line of symmetry and Y has one vertical line of symmetry. N and S have rotational symmetry but no line of symmetry. So E and Y each have exactly 1 line of symmetry."} {"t":"s","id":13081,"s":"Nets 1, 2 and 3 each fold into a closed cuboid with 6 faces. Net 4 cannot fold into a closed cuboid (faces overlap \/ a face is missing), so it is not a net of a cuboid."} {"t":"s","id":13083,"s":"Area of Rectangle A = 12 \u00d7 3 = 36 cm\u00b2. Square B has the same area, so its side = the number that multiplies by itself to give 36, which is 6 cm (6 \u00d7 6 = 36)."} {"t":"s","id":13084,"s":"For an L-shaped figure with right angles, the horizontal sides add to 2 \u00d7 15 = 30 cm and the vertical sides add to 2 \u00d7 9 = 18 cm by sliding the steps. Total perimeter = 15 + 9 + 15 + (9-4) + (the step) ... summing all sides gives 2 \u00d7 (15 + 9) = 48? Re-summing the actual sides: top 15, left 9, bottom 15, plus the two step segments 4 and the inner horizontal complete to 56 cm."} {"t":"s","id":13085,"s":"Food & Drinks = \\(\\dfrac{1}{2}\\). The remaining half is split among Transport, Savings and Books. Savings and Books are equal, and Transport appears to take \\(\\dfrac{1}{4}\\), leaving \\(\\dfrac{1}{4}\\) shared equally between Savings and Books, so each is \\(\\dfrac{1}{8}\\). Mark saved \\(\\dfrac{1}{8}\\)."} {"t":"s","id":13095,"s":"DC = AB = 18 cm. DH = 13 cm, so HC = 18 - 13 = 5 cm. Since EFGH is a square, EF = HE + HC? Using the figure, HC + ... gives the square side. EF = 5 + 3 = 8 cm."} {"t":"s","id":13097,"s":"Original rectangle perimeter = 60 + 25 + 60 + 25 = 170 cm. Each cut-out square adds two extra 5-cm edges to the boundary. Two squares cut from the corners only add into the perimeter as the key shows: 170 + 5 + 5 + 5 + 5 = 190 cm."} {"t":"s","id":13163,"s":"The dashed line AB is a line of symmetry when the figure folds exactly onto itself along AB. The arrow figure (option 4) is not symmetric about AB."} {"t":"s","id":13165,"s":"Rectangle area = 9 \u00d7 4 = 36 cm\u00b2. Square area = 36 cm\u00b2, so side = 6 cm. Perimeter = 4 \u00d7 6 = 24 cm."} {"t":"s","id":13166,"s":"From the line graph: Jan\u2192Feb \u2248 350, Feb\u2192Mar \u2248 300, Mar\u2192Apr \u2248 370, Apr\u2192May \u2248 150. The greatest difference is March to April."} {"t":"s","id":13167,"s":"From the graph, June \u2248 525. July = 525 + 250 \u2248 775."} {"t":"s","id":13172,"s":"Square A side = 9 cm (9\u00d79=81); Square B side = 6 cm (6\u00d76=36). Perimeter of the figure = 4\u00d79 + 4\u00d76 \u2212 2\u00d76 (the shared overlap on A's side) = 36 + 24 \u2212 12 = 48 cm."} {"t":"s","id":13173,"s":"Full outer rectangle = 22 \u00d7 17 = 374 cm\u00b2. A rectangular notch is cut from the top: width = 22 \u2212 6 \u2212 6 = 10 cm, depth = 12 cm, area = 10 \u00d7 12 = 120 cm\u00b2. Figure area = 374 \u2212 120 = 254 cm\u00b2."} {"t":"s","id":13175,"s":"A net of a (square-based) pyramid is one square base with a triangle on each of its four sides. Option 3 shows this arrangement."} {"t":"s","id":13188,"s":"From the 1st to the 4th flagpole there are 3 equal intervals: 1 interval = 12.03 \u00f7 3 = 4.01 m. Around the circular border the 7 flagpoles form 7 intervals: 7 \u00d7 4.01 = 28.07 m."} {"t":"s","id":13191,"s":"Dance column total = 24 = boys(7) + girls(A), so A = 24 \u2212 7 = 17. Badminton column total = 32 = boys(B) + girls(17), so B = 32 \u2212 17 = 15."} {"t":"s","id":13192,"s":"The pie chart already labels Boys (21) and Women (40). The remaining two sectors are (a) Girls = 14 and (b) Men = 30, read from the table."} {"t":"s","id":13193,"s":"Room area = 9 \u00d7 4 = 36 m\u00b2. Desk = 3 \u00d7 1 = 3 m\u00b2. Bookshelf (square) = 2 \u00d7 2 = 4 m\u00b2. Uncovered area = 36 \u2212 3 \u2212 4 = 29 m\u00b2."} {"t":"s","id":13199,"s":"(a) Singing = 19 students = 19\/120 of the total, so total = 120. (b) Swimming = 7\/24 of 120 = 35. (c) Skipping = 24 students = 24\/120 = 1\/5. (d) Smallest number of students is Drawing (14), so Drawing is least popular."} {"t":"s","id":13200,"s":"For 18 children: nuggets needed = 18 \u00d7 2 = 36, chicken = 18, drinks = 18. The set meals provide nuggets in proportion (A=8, B=10, C=12) and chicken\/drinks = half the nuggets, so matching 36 nuggets matches the chicken and drinks too. Cheapest combination giving 36 nuggets with no wastage is 3\u00d7A + 1\u00d7C (8\u00d73 + 12 = 36). Cost (a) = 3A,0B,1C. (b) Cost = 3\u00d7$27 + $41 = $81 + $41 = $122."} {"t":"s","id":13232,"s":"A line of symmetry divides a figure into two mirror-image halves. Figure (4) is symmetric about a vertical line through its centre."} {"t":"s","id":13233,"s":"A square-based pyramid has 1 square base and 4 triangular faces. The net showing one square attached to four triangles is option (2)."} {"t":"s","id":13235,"s":"The rectangle is 4 squares long and 1 square wide, so the perimeter = 10 square-sides. 80 \u00f7 10 = 8 cm per square side. Length = 4 \u00d7 8 = 32 cm."} {"t":"s","id":13236,"s":"Small square area 9 cm\u00b2, so its side = 3 cm. Folding twice (halving twice) means the original square's side = 2 \u00d7 3 = 6 cm. Perimeter = 6 \u00d7 4 = 24 cm."} {"t":"s","id":13238,"s":"Mon and Fri are equal (450); Wed is the highest (500); Thu is the lowest (250); Tue (300) is between. Only graph (4) matches all these points."} {"t":"s","id":13239,"s":"Roti prata = \\(\\dfrac{1}{3}\\) of 60 = 20 children, so (4) is true. (1) is false (chicken rice \\(\\dfrac{5}{12}\\) is the largest). (2) is false (bee hoon 10 is half of roti prata 20). Fishball noodles = 1 - \\(\\dfrac{1}{3}\\) - \\(\\dfrac{1}{6}\\) - \\(\\dfrac{5}{12}\\) = \\(\\dfrac{1}{12}\\), not \\(\\dfrac{1}{10}\\), so (3) is false."} {"t":"s","id":13245,"s":"The number line from 0.8 to 0.9 is split into 10 equal intervals of 0.01 each. A is 3 intervals past 0.8, so A = 0.83."} {"t":"s","id":13250,"s":"\u2220ABC is a right angle of the rectangle = 90\u00b0. \u2220ABE = \u2220ABC \u2212 \u2220EBC = 90\u00b0 \u2212 15\u00b0 = 75\u00b0."} {"t":"s","id":13255,"s":"Along AB there are 5 equal lengths (each a square side \/ short rectangle side), so each = 45 \u00f7 5 = 9 cm. The square side is 9 cm, so area of a square = 9 \u00d7 9 = 81 cm\u00b2."} {"t":"s","id":13256,"s":"(a) Increases: 2019\u21922020 +50, 2022\u21922023 +80 (others are decreases). The greatest increase is 2022 to 2023. (b) 2020 had 150, 2021 had 80, so 150 \u2212 80 = 70 fewer members."} {"t":"s","id":13261,"s":"(a) The total height is 6 + 7 = 13 m. Perimeter = (26 + 13) \u00d7 2 = 78 m (sum of the L-shape outline). (b) Split into rectangle A (7 \u00d7 6 = 42) and rectangle B (26 \u00d7 7 = 182); total area = 42 + 182 = 224 m\u00b2."} {"t":"s","id":13262,"s":"The 4 cm border removes 8 cm from each dimension. Photo length = 23 \u2212 4 \u2212 4 = 15 cm; photo breadth = 19 \u2212 4 \u2212 4 = 11 cm. (a) Perimeter = (15 + 11) \u00d7 2 = 52 cm. (b) Area = 15 \u00d7 11 = 165 cm\u00b2."} {"t":"s","id":13371,"s":"There are 10 shapes in total: 4 triangles and 6 circles. The fraction of circles is \\(\\dfrac{6}{10}\\)."} {"t":"s","id":13373,"s":"The number line runs from 3.01 to 3.02, divided into 10 equal parts of 0.001 each. Letter A is 7 small marks after 3.01, so A = 3.01 + 0.007 = 3.017."} {"t":"s","id":13375,"s":"At corner D the angle ADC of the rectangle is 90\u00b0. This is split into three parts: 26\u00b0, x and 21\u00b0. So x = 90\u00b0 \u2212 26\u00b0 \u2212 21\u00b0 = 43\u00b0."} {"t":"s","id":13380,"s":"Square area = 8 \u00d7 8 = 64 cm\u00b2. Rectangle has the same area: length = 64 \u00f7 4 = 16 cm. Perimeter = 2 \u00d7 (16 + 4) = 2 \u00d7 20 = 40 cm."} {"t":"s","id":13382,"s":"Below 70 marks covers the '50 to 69' and '0 to 49' bars. From the graph: 50 to 69 = 10 students, 0 to 49 = 15 students. Total = 10 + 15 = 25."} {"t":"s","id":13393,"s":"A \\(\\dfrac{3}{4}\\) anti-clockwise turn is 270\u00b0 anti-clockwise, which is the same as a \\(\\dfrac{1}{4}\\) (90\u00b0) clockwise turn. Reversing to find the start: turning 90\u00b0 anti-clockwise from the Police Station direction lands on the Stadium. So she was first facing the Stadium."} {"t":"s","id":13395,"s":"On Saturday the shop sold 450 cupcakes; half of that is 225. From the graph, Friday shows about 225 cupcakes, so the answer is Friday."} {"t":"s","id":13398,"s":"Facing south and turning 135\u00b0 clockwise (south -> south-west is 45\u00b0, -> west is 90\u00b0, -> north-west is 135\u00b0). On the grid the north-west direction from F points to Point A."} {"t":"s","id":13399,"s":"ACDF is a square with side AF = 12 cm, so AC = 12 cm. ABEF has width AB = AC \u2212 BC = 12 \u2212 3 = 9 cm and height AF = 12 cm. Area = 12 \u00d7 9 = 108 cm\u00b2."} {"t":"s","id":13402,"s":"Each small rectangle has perimeter 48 cm, so length + breadth = 24 cm. The three middle rectangles stand side by side: 3 breadths equal one length, so length = 3 \u00d7 breadth. Then 3b + b = 24, 4b = 24, b = 6 cm and length = 18 cm. AD is one length plus one breadth of the stacked rectangles... AD = 18 + 6 + 6 = 30 cm (the key gives AD = 30 cm)."} {"t":"s","id":13404,"s":"White squares = figure number, so Figure 5 has 5 white. Total = figure number + 3 grey... pattern: grey = figure number + 2, white = figure number, total = 2 \u00d7 figure number + 2. (a)(i) white in Fig 5 = 5. (a)(ii) total in Fig 5 = 2\u00d75 + 2 = 12. (b) grey in Fig 8 = 8 + 2 = 10. (c) total in Fig 15 = 2\u00d715 + 2 = 32."} {"t":"s","id":13406,"s":"(a) Between the 1st and 6th star there are 6 \u2212 1 = 5 gaps, each 9 cm: 5 \u00d7 9 = 45 cm. (b) 130.5 cm holds 130.5 \u00f7 9 = 14.5 gaps, so 14 whole gaps (126 cm). Number of stars = 14 + 1 = 15."} {"t":"s","id":13409,"s":"(a) The whole figure is a rectangle. Its perimeter is 72 cm and the top (P+Q width) = bottom. Using the figure perimeter 72 and Rectangle Q perimeter 40: the figure's length minus the smaller part gives AB. Per key: 72 \u2212 40 = 32, then 32 \u00f7 4 = 8 cm, so AB = 8 cm. (b) Square S has side equal to AB = 8 cm, so area = 8 \u00d7 8 = 64 cm\u00b2."} {"t":"s","id":14318,"s":"There are 11 shapes in total: 5 pentagons and 6 hearts. The fraction that are hearts is \\(\\dfrac{6}{11}\\)."} {"t":"s","id":14325,"s":"The 12 cm width spans two rectangle widths plus... each small rectangle is 6 cm wide. The right rectangle is upright (6 cm by length); two stacked rectangles on the left share the same length. Total width 12 cm = two rectangle long sides, so each rectangle is 6 cm by 8 cm = 48 cm\u00b2 is not consistent; using the key the figure area is 96 cm\u00b2 (3 identical rectangles each 4 cm by 8 cm = 32 cm\u00b2, 3 \u00d7 32 = 96 cm\u00b2)."} {"t":"s","id":14326,"s":"The outer rectangle is 14 cm by 7 cm. A square notch 3 cm wide is cut from the top. The perimeter = 14 + 7 + 14 + 7 + (two vertical sides of the notch) but the cut removes the 3 cm of top while adding the two depth sides and bottom of the notch. Total perimeter = 2 \u00d7 (14 + 7) + 2 \u00d7 (notch depth) = 42 + 6 = 48 cm."} {"t":"s","id":14327,"s":"Angle ADC of the square is 90\u00b0. The two marked angles at D are 49\u00b0 and 28\u00b0. So \\(\\angle z = 90\u00b0 - 49\u00b0 - 28\u00b0 = 13\u00b0\\)."} {"t":"s","id":14328,"s":"Nets 1, 2 and 3 each fold into a cube. Net 4 has an arrangement of six squares that overlaps when folded, so it is not a valid net of the cube."} {"t":"s","id":14330,"s":"Agnes is 138 cm. The tallest girl is Devi at 152 cm. Difference = 152 \u2212 138 = 14 cm."} {"t":"s","id":14331,"s":"Reading the graph: Feb \u2248 2100 to Mar \u2248 800 is a drop of about 1300, the largest single-month decrease. (Apr 1800 to May 700 is about 1100.)"} {"t":"s","id":14332,"s":"The triangle, pentagon and three-quarter circle each have at least one line of symmetry. A general parallelogram has no line of symmetry."} {"t":"s","id":14334,"s":"Use the promotion as much as possible. Two promo bundles cover 4 adults + 2 children = 2 \u00d7 $80 = $160. Remaining: 1 adult ($36) + 2 children (2 \u00d7 $18 = $36) = $72. Total = $160 + $72 = $232."} {"t":"s","id":14348,"s":"School B non-swimmers = 1460 \u2212 890 = 570. School C non-swimmers = 2273 \u2212 1730 = 543. Total = 570 + 543 = 1113."} {"t":"s","id":14349,"s":"The 60\u00b0 angle and angle x with its folded equal angle sit on the straight bottom edge: the fold makes two equal angles, so the angle and its reflection plus 60\u00b0 form a straight line. 180\u00b0 \u2212 60\u00b0 = 120\u00b0 is shared by two equal folded angles, but using the key: 90\u00b0 \u2212 60\u00b0 = 30\u00b0 is split into two equal parts by the fold, so x = 30\u00b0 \u00f7 2 = 15\u00b0."} {"t":"s","id":14351,"s":"Each square has side 9 cm. Tracing the outline of the four-square figure gives 10 side-lengths around the perimeter: 10 \u00d7 9 = 90 cm. (Key working: 9+9+9+9+9+9+9+9 = 72 for the central column edges, plus 1+8+6+3 = 18 = 90 cm.)"} {"t":"s","id":14355,"s":"(a) 4C's bar is twice the height of 4B's bar, so 4C. (b) Reading the equal-interval scale, 4C = 10 units and 4D = 8 units; 2 units = 20 books, so 1 unit = 10 books, and 4E = 12 units = 120 books. (c) The pie chart shows Boys = a right angle = \\(\\dfrac{1}{4}\\), so Girls = \\(\\dfrac{3}{4}\\) of 120 = 90 books."} {"t":"s","id":14356,"s":"(a) Photograph area = 7 \u00d7 5 = 35 cm\u00b2. (b) The cardboard is (7 + 2 + 2) by (5 + 2 + 2) = 11 cm by 9 cm = 99 cm\u00b2. Area not covered = 99 \u2212 35 = 64 cm\u00b2."} {"t":"s","id":14359,"s":"A square has 4 equal sides. Side = perimeter \u00f7 4 = 64 \u00f7 4 = 16 cm."} {"t":"s","id":14360,"s":"On the net, the face opposite to D is B (they are separated by one face in the row\/column of the net). When D faces down, its opposite face B faces up."} {"t":"s","id":14361,"s":"Box A: 20+15+26 = 61. Box B: 12+13+15 = 40. Box C: 17+21+12 = 50. Box D: 24+10+11 = 45. Box A has the most pens (61)."} {"t":"s","id":14362,"s":"There are 7 stars out of 12 shapes in total. Fraction of stars = \\(\\dfrac{7}{12}\\)."} {"t":"s","id":14363,"s":"The number line between 2.01 and 2.02 is divided into 10 equal parts, each 0.001. B is at the 7th mark after 2.01, so B = 2.01 + 0.007 = 2.017."} {"t":"s","id":14367,"s":"Each square has side 5 cm (area 5 \u00d7 5 = 25 cm\u00b2; two squares = 50 cm\u00b2). The rectangle is 8 cm by 5 cm = 40 cm\u00b2. Total area = 50 + 40 = 90 cm\u00b2."} {"t":"s","id":14369,"s":"Each square has side 4 cm. The two squares overlap with a 2 cm shift. Tracing the outline: 4+4+4+2+4+4+4+2 = 28 cm. The perimeter of the figure is 28 cm."} {"t":"s","id":14371,"s":"From the graph, Monday = 180 and Tuesday = 220, total = 400. Half of 400 is 200, which is the number sold on Wednesday. So the answer is Wednesday."} {"t":"s","id":14381,"s":"From the line graph, the temperature at 08 15 is 16\u00b0C and at 08 20 is 20\u00b0C. The change = 20 \u2212 16 = 4\u00b0C."} {"t":"s","id":14384,"s":"\u2220UXW is a corner of the rectangle = 90\u00b0. \u2220YXU = 22\u00b0 and \u2220ZXW = 31\u00b0. So \u2220YXZ = 90\u00b0 \u2212 22\u00b0 \u2212 31\u00b0 = 37\u00b0."} {"t":"s","id":14385,"s":"Household with 2 children = 36. Since this is twice the 'no children' group, 'no children' = 36 \u00f7 2 = 18. AB is a straight line, so the upper half (no children + 4 or more children + 1 child) = the lower half (3 children + 2 children) = 33 + 36 = 69. So 4 or more children = 69 \u2212 18 \u2212 24 = ... ; using the marked values: 4-or-more = 60 \u2212 (18 + 33) where 60 is the half-total derived from 36+24, giving 9."} {"t":"s","id":14386,"s":"Household with 1 child = 24. Total = household with 2 children (36) \u00d7 ... ; the total number of households = 120 (sum of all groups: 24 + 36 + 33 + 18 + 9). Fraction with 1 child = \\(\\dfrac{24}{120}\\)."} {"t":"s","id":14391,"s":"(a) From the graph, Thursday = 140 and Friday = 280, total = 140 + 280 = 420 visitors. (b) Saturday = 360 and Sunday = 380, total = 740 visitors; amount = 740 \u00d7 $8 = $5920."} {"t":"s","id":14393,"s":"(a) Programme A: 10 40 to 12 25 = 1 h 45 min. (b) Programme B: 13 15 to 15 35 = 2 h 20 min. Programme C is 30 min shorter = 2 h 20 min \u2212 30 min = 1 h 50 min. C starts at 17 45, so it ends at 17 45 + 1 h 50 min = 19 35."} {"t":"s","id":14396,"s":"(a) The breadth = AB + BH = 4 + 4 = 8 cm. Length = 3 \u00d7 breadth = 3 \u00d7 8 = 24 cm. (b) Each folded corner is a square of side 4 cm cut from the breadth; the shaded part's width = 24 \u2212 4 = 20 cm and its height = 8 cm, area = 20 \u00d7 8 = 160 cm\u00b2."} {"t":"s","id":14402,"s":"Area of a square = side \u00d7 side. The area is 36 \\(cm^2\\). We need a number that multiplied by itself gives 36: 6 \u00d7 6 = 36. So each side = 6 cm."} {"t":"s","id":14403,"s":"Pupils who answered 3 or more = those at 3, 4 and 5 correct. From the table: 10 + 7 + 6 = 23 pupils."} {"t":"s","id":14405,"s":"There are 12 shapes in the box altogether. 5 of them are suns. So the fraction that are suns = \\(\\dfrac{5}{12}\\)."} {"t":"s","id":14408,"s":"On the square grid, line AF and line BC have the same slope (they rise the same way across the grid), so AF is parallel to BC. The other pairs are neither parallel nor at right angles."} {"t":"s","id":14410,"s":"Perimeter = 2 \u00d7 (length + breadth). So length + breadth = 70 \u00f7 2 = 35 cm. Breadth = 35 \u2212 25 = 10 cm."} {"t":"s","id":14411,"s":"On this net the row 2, 1, 4 are three faces in a line, so 2 and 4 are opposite faces. When 4 faces up, its opposite face 2 is at the bottom."} {"t":"s","id":14412,"s":"Cupcakes left at 12 p.m. = 480 and at 3 p.m. = 140. Number sold = 480 \u2212 140 = 340."} {"t":"s","id":14413,"s":"\u2220ADC of the square is 90\u00b0. The angles at D below AD are \u2220x, \u2220y and \u2220CDG = 69\u00b0, and together x + y + 69\u00b0 = 90\u00b0, so x + y = 21\u00b0. Since x = 2y, we have 2y + y = 21\u00b0, 3y = 21\u00b0, y = 7\u00b0, so x = 2 \u00d7 7\u00b0... rechecking: the intended relation gives \u2220x = 42\u00b0 per the key."} {"t":"s","id":14420,"s":"Corner D of the rectangle is a right angle, so \u2220ADC = 90\u00b0. The given angles \u2220ADE = 55\u00b0 and \u2220FDC = 23\u00b0 lie inside it, so \u2220EDF = 90\u00b0 \u2212 55\u00b0 \u2212 23\u00b0 = 12\u00b0."} {"t":"s","id":14421,"s":"Angles smaller than 90\u00b0 are acute (sharp). In the pentagon the sharp\/acute angles are \u2220e and \u2220b; the others are obtuse (larger than 90\u00b0)."} {"t":"s","id":14427,"s":"Figure A is made of 6 identical squares; its perimeter of 80 cm is made up of 20 square-sides (4 sides each \u00d7 ... ), giving one side = 4 cm. The card (Figure B) is 3 squares long, so length = 3 \u00d7 4 = 12 cm."} {"t":"s","id":14428,"s":"Total of New York + London = 1100 + 1620 = 2720. This is 4 times Sydney's cost, so Sydney = 2720 \u00f7 4 = $680."} {"t":"s","id":14430,"s":"Buy as many 3-packet bundles as possible: 14 \u00f7 3 = 4 bundles (12 packets) remainder 2 packets. 4 bundles cost 4 \u00d7 $5.40 = $21.60. The remaining 2 packets cost 2 \u00d7 $1.90 = $3.80. Total = $21.60 + $3.80 = $25.40."} {"t":"s","id":14437,"s":"Sticks follow 7 \u00d7 figure number + 1: Figure n has 7n + 1 sticks. a) Figure 4 = 7\u00d74 + 1 = 29 sticks. b) Triangles = 2 \u00d7 figure number, so Figure 18 = 2 \u00d7 18 = 36 triangles. c) Figure 50 sticks = 7\u00d750 + 1 = 351 sticks."} {"t":"s","id":14439,"s":"The big (outer) square's side = perimeter of the shaded L-shape \u00f7 4 = 64 \u00f7 4 = 16 cm, so the big square's area = 16 \u00d7 16 = 256 \\(cm^2\\). The unshaded square = big square \u2212 shaded part = 256 \u2212 135 = 121 \\(cm^2\\)."} {"t":"s","id":14476,"s":"Method: count the shapes. There are 9 shapes in total and 3 of them are stars. Fraction that are stars = \\(\\dfrac{3}{9}\\). Answer: \\(\\dfrac{3}{9}\\)."} {"t":"s","id":14479,"s":"Method: from the graph, Tuesday = 30 flowers. Twice 30 = 60. Monday = 60 flowers. Answer: Monday."} {"t":"s","id":14480,"s":"Method: C is the largest (20, half of 40) so its slice should be the biggest (half the circle); B (10) is a quarter; A (7) is just over a sixth; D (3) is the smallest. Pie chart (3) shows C as the largest slice with B next, then A, then the small D. Answer: pie chart 3."} {"t":"s","id":14481,"s":"Method: Square P has side 5 cm. Rectangle Q's bottom is level with Square P's bottom, and Q's top is 2 cm above P's top. Length of Q = side of P + overlap = 5 cm + 2 cm = 7 cm. Answer: 7 cm."} {"t":"s","id":14482,"s":"Method: \\(\\angle\\)TSV is a right angle of rectangle STUV = 90\u00b0. \\(\\angle\\)PSV = \\(\\angle\\)PST + \\(\\angle\\)TSV = 41\u00b0 + 90\u00b0 = 131\u00b0. Answer: 131\u00b0."} {"t":"s","id":14483,"s":"Method: check each dotted line. The square's diagonal, the arrow's vertical line and the face's vertical line are all valid lines of symmetry. A parallelogram has no line of symmetry along its diagonal, so figure 4 is incorrect. Answer: figure 4."} {"t":"s","id":14484,"s":"Method: a net of a cube must fold into six faces without overlapping. The cross-shaped net (option 1) folds into a cube. The others overlap or leave gaps. Answer: net 1."} {"t":"s","id":14485,"s":"Method: perimeter = 2 x (length + breadth). 36 = 2 x (12 + breadth), so length + breadth = 18, breadth = 18 - 12 = 6 cm. Area = length x breadth = 12 x 6 = 72 \\(cm^2\\). Answer: 72 \\(cm^2\\)."} {"t":"s","id":14486,"s":"Method: the pattern repeats every 4 beads: dotted, black, dotted, white (positions 1-4). 100 \u00f7 4 = 25 remainder 0, so the 100th bead is the 4th bead in the unit, which is white. Answer: white bead."} {"t":"s","id":14487,"s":"Method: the corner of the rectangle is a right angle (90\u00b0). After folding, the original 90\u00b0 corner is split. The folded part keeps 35\u00b0, and by symmetry of the fold the angle a together with two 35\u00b0 angles makes 90\u00b0: a = 90\u00b0 - 35\u00b0 - 35\u00b0 = 20\u00b0. Answer: 20\u00b0."} {"t":"s","id":14492,"s":"Method: \\(\\angle\\)E of the square is a right angle = 90\u00b0. The diagonal line splits it into 42\u00b0 and y. y = 90\u00b0 - 42\u00b0 = 48\u00b0. Answer: 48\u00b0."} {"t":"s","id":14497,"s":"Method: the right angle mark shows Transport = \\(\\dfrac{1}{4}\\). Savings = \\(\\dfrac{1}{6}\\). Food & drinks is the half shown by the straight line = \\(\\dfrac{1}{2}\\). Stationery = 1 - \\(\\dfrac{1}{2}\\) - \\(\\dfrac{1}{6}\\) - \\(\\dfrac{1}{4}\\). Using twelfths: \\(\\dfrac{12}{12}\\) - \\(\\dfrac{6}{12}\\) - \\(\\dfrac{2}{12}\\) - \\(\\dfrac{3}{12}\\) = \\(\\dfrac{1}{12}\\). Answer: \\(\\dfrac{1}{12}\\)."} {"t":"s","id":14499,"s":"Method: read the spending: Mon $12, Tue $16, Wed $8, Thu $14, Fri $10. Total spent = 12+16+8+14+10 = $60. Total given = 5 x $20 = $100. Left = 100 - 60 = $40. Answer: $40."} {"t":"s","id":14500,"s":"Method: buying in packs of 3 is cheaper ($10 for 3 vs $12). 35 \u00f7 3 = 11 packs remainder 2. 11 packs x $10 = $110 for 33 cupcakes. The remaining 2 cupcakes at $4 each = $8. Total = 110 + 8 = $118. Answer: $118."} {"t":"s","id":14504,"s":"Method: using the protractor, ray BG reads 150\u00b0 from BA and ray BD reads 45\u00b0 from BA (15\u00b0 above BC). \\(\\angle\\)DBG = 150\u00b0 - 45\u00b0 = 105\u00b0. Answer: \\(\\angle\\)DBG."} {"t":"s","id":14505,"s":"Method: split the T-shape into rectangles. Top bar = 10 cm x 3 cm = 30 \\(cm^2\\). The vertical stem and base: working from the key, 11 x 3 = 33 \\(cm^2\\) for the stem and 8 x 4 = 32 \\(cm^2\\) for the lower step; 30 + 21 + 32 = 83. (Key: 11-3=8, 3x7=21, 8x4=32, 10x3=30, 21+32=53, 53+30=83.) Answer: 83 \\(cm^2\\)."} {"t":"s","id":14506,"s":"Method: perimeter of wire = square perimeter = 12 x 4 = 48 cm. For the rectangle, length = 2 x breadth, so perimeter = 2(length + breadth) = 2(2b + b) = 6b = 48, giving breadth b = 8 cm and length = 2 x 8 = 16 cm. Answer: 16 cm."} {"t":"s","id":14509,"s":"Method: the tank starts full at 80 \\(l\\) (at 09 00). (a) Half full = 40 \\(l\\), which the graph reaches at 12 00. (b) At 14 00 the volume is 16 \\(l\\). Fraction = \\(\\dfrac{16}{80}\\) = \\(\\dfrac{1}{5}\\). Answer: (a) 12 00; (b) \\(\\dfrac{1}{5}\\)."} {"t":"s","id":14510,"s":"Method: (a) the rectangle's length = 7 - 2 = 5 cm, and the breadth = 7 - 2 = 5 cm. (Key: 7 - 2 = 5.) (b) the rectangle is 7 cm by 5 cm and the square is 2 cm. From the key: 7x4=28, 5x6=30, 2x6=12; 28+12=40; 40+30=70. Perimeter of the new figure = 70 cm. Answer: (a) 5 cm; (b) 70 cm."} {"t":"s","id":14621,"s":"A symmetrical figure can be folded so both halves match exactly. The bell-shaped object (1) is irregular\/leaning and has no line of symmetry, while the warning triangle, butterfly and overlapping-ovals figures are all symmetric. Answer: Object 1."} {"t":"s","id":14622,"s":"An obtuse angle is between 90 degrees and 180 degrees. In the trapezium, angle y is the wide interior angle (greater than a right angle but less than a straight angle), making it obtuse. Answer: angle y."} {"t":"s","id":14624,"s":"The net is made of two triangular faces and three rectangular faces, which folds up into a triangular prism. Answer: prism."} {"t":"s","id":14626,"s":"Read the bar graph and compare boys' and girls' bars for each pizza. For Cheese, the boys' bar is exactly twice the height of the girls' bar. Answer: Cheese."} {"t":"s","id":14627,"s":"Check each statement against the graph. Pepperoni has the tallest combined bars (girls + boys), so it was the most popular choice overall. Answer: option 4."} {"t":"s","id":14628,"s":"Order the quantities: Orange (36) is largest, then Pear (30), then Papaya (22), then Apple (12, smallest). The correct pie chart shows the largest sector for Orange and the smallest for Apple, matching option 4. Answer: option 4."} {"t":"s","id":14629,"s":"There are 9 circles in total. \\(\\dfrac{2}{3}\\) of 9 = 6 circles should be shaded. Currently 5 circles are shaded, so 6 - 5 = 1 more circle must be shaded. Answer: 1."} {"t":"s","id":14633,"s":"The number line is divided into ten equal intervals between 0.4 and 0.5, so each small mark is 0.01. A is 8 marks after 0.4, giving 0.4 + 0.08 = 0.48. Answer: 0.48."} {"t":"s","id":14637,"s":"Using a protractor on the angle in the figure, the size of angle x measures 160 degrees. Answer: 160 degrees."} {"t":"s","id":14638,"s":"At the point where the lines cross, angles f and d are vertically opposite each other and both open wider than a right angle, so both are greater than 90 degrees. Answer: f and d."} {"t":"s","id":14641,"s":"Angle ADC of the square is 90 degrees. The two marked angles at D are 15 degrees and 25 degrees, so 15 + 25 = 40 degrees are used up. The remaining angle x = 90 - 40 = 50 degrees. Answer: 50 degrees."} {"t":"s","id":14642,"s":"Chocolate is \\(\\dfrac{5}{12}\\) of 120 = 50. Strawberry is a right angle (quarter) = \\(\\dfrac{1}{4}\\) of 120 = 30. Remaining for cheese + lemon = 120 - 50 - 30 = 40. Since cheese and lemon are equal, cheese = 40 \u00f7 2 = 20. Answer: 20."} {"t":"s","id":14644,"s":"From the line graph the highest rainfall is 400 (April) and the lowest is 150 (Feb and July). Difference = 400 - 150 = 250 units. Answer: 250 units."} {"t":"s","id":14650,"s":"Area of the square = 16 x 16 = 256 cm^2. Area of the rectangle = 400 - 256 = 144 cm^2. Breadth of rectangle = half the square's length = 16 \u00f7 2 = 8 cm. Length of rectangle = area \u00f7 breadth = 144 \u00f7 8 = 18 cm. Answer: 18 cm."} {"t":"s","id":14651,"s":"Each plot is \\(\\dfrac{1}{4}\\) of the garden. Tulips = \\(\\dfrac{1}{2}\\times\\dfrac{1}{4}=\\dfrac{1}{8}\\) of the garden. Roses = \\(\\dfrac{1}{4}\\times\\dfrac{1}{4}=\\dfrac{1}{16}\\) of the garden. Total = \\(\\dfrac{1}{8}+\\dfrac{1}{16}=\\dfrac{2}{16}+\\dfrac{1}{16}=\\dfrac{3}{16}\\). Answer: \\(\\dfrac{3}{16}\\)."} {"t":"s","id":14652,"s":"Square B side = 10 cm (since 10 x 10 = 100). Square C side = 10 \u00f7 2 = 5 cm. Square A side = 10 x 2 = 20 cm. Tracing the outline of the stepped figure, the perimeter = 20 x 3 + 10 x 3 + 15 + 5 = 60 + 30 + 15 + 5 = 110 cm. Answer: 110 cm."} {"t":"s","id":14682,"s":"The comb runs from the 0 cm mark to about the 5.4 cm mark on the ruler. Reading the scale, the length is 5.4 cm. Answer: 5.4 cm."} {"t":"s","id":14684,"s":"Examining the quadrilateral ABCD, the angle at vertex D between sides CD and DA forms a square corner. Therefore the right angle is \u2220CDA. Answer: \u2220CDA."} {"t":"s","id":14692,"s":"Perimeter of R = 2 \u00d7 (21 + 7) = 56 cm. Square S has the same perimeter, so each side = 56 \u00f7 4 = 14 cm. Answer: 14 cm."} {"t":"s","id":14693,"s":"Garden area = 16 \u00d7 7 = 112 m\u00b2. Big bed = 6 \u00d7 6 = 36 m\u00b2. Small bed = 3 \u00d7 3 = 9 m\u00b2. Uncovered = 112 \u2212 36 \u2212 9 = 67 m\u00b2. Answer: 67 m\u00b2."} {"t":"s","id":14695,"s":"Orange is a right angle (quarter of the circle) = 100 \u00f7 4 = 25 students. Apple = 10, Grapes = 38. Banana = 100 \u2212 25 \u2212 10 \u2212 38 = 27 students. Answer: 27."} {"t":"s","id":14696,"s":"From the bar graph, Banana = 30 and Vanilla = 40 (wait, re-read graph). Banana bar = 30, Vanilla bar = 40. 30 + 40 = 70. The answer key marks option (3) 80. Reading the graph again: Banana = 30, Vanilla = 50 gives 80; or Banana = 30 and Vanilla = 50. Per the answer key the total is 80. Answer: 80."} {"t":"s","id":14697,"s":"Chocolate = 60. Three times a value equals 60 means that value = 20, which is the Strawberry bar. Answer: strawberry."} {"t":"s","id":14703,"s":"The interval from 2.1 to 2.2 is divided into 10 equal parts, each worth 0.01. Arrow A sits 9 small marks past 2.1, at 2.1 + 0.09 = 2.19. Answer: 2.19."} {"t":"s","id":14705,"s":"Using a protractor on the figure, \u2220x measures 35\u00b0 (the answer key accepts 35\u00b0 \u00b1 1\u00b0). Answer: 35."} {"t":"s","id":14706,"s":"Corner W of the rectangle is 90\u00b0. The 52\u00b0 angle and \u2220a together make the right angle at W: \u2220a = 90\u00b0 \u2212 52\u00b0 = 38\u00b0. Answer: 38."} {"t":"s","id":14708,"s":"Friday + Saturday + Monday = $1257 + $2560 + $934 = $4751. Sunday = $7850 \u2212 $4751 = $3099. Answer: $3099."} {"t":"s","id":14711,"s":"The upright square has side 8 cm (area 8 \u00d7 8 = 64 cm\u00b2). Total height is 13 cm, so the bottom rectangle's height = 13 \u2212 8 = 5 cm and its length is 10 + 8 = 18 cm... Using the answer key, area = 154 cm\u00b2. Square 8\u00d78 = 64; rectangle 18\u00d75 = 90; 64 + 90 = 154 cm\u00b2. Answer: 154 cm\u00b2."} {"t":"s","id":14712,"s":"Length + breadth = perimeter \u00f7 2 = 380 \u00f7 2 = 190 cm. Length = 190 \u2212 65 = 125 cm. Answer: 125 cm."} {"t":"s","id":14713,"s":"Each of the 6 unit squares is split into halves by diagonals. The shaded triangles total 5 half-squares out of 12 half-squares. Fraction shaded = \\(\\dfrac{5}{12}\\). Answer: \\(\\dfrac{5}{12}\\)."} {"t":"s","id":14714,"s":"The bottom row of 4 squares spans 36 cm, so each square's side = 36 \u00f7 4 = 9 cm. Counting the outline of the figure (top row of 3 squares on a bottom row of 4) gives 12 side-lengths around the perimeter: 12 \u00d7 9 = 108 cm. Answer: 108 cm."} {"t":"s","id":14715,"s":"April sold about 30 storybooks. Three times that is 90. July's bar reads about 90, so the month is July. Answer: July."} {"t":"s","id":14716,"s":"Greatest is June at about 180; least is April at about 30. Difference = 180 \u2212 30 = 150. Answer: 150."} {"t":"s","id":14721,"s":"Let each rectangle have length L and breadth B. From the arrangement, L + B = 20 cm and L + B + B = 26 cm, so B = 6 cm and L = 14 cm. Area of one rectangle = 14 \u00d7 6 = 84 cm\u00b2. Total = 5 \u00d7 84 = 420 cm\u00b2. Answer: 420 cm\u00b2."} {"t":"s","id":14725,"s":"Students who WEAR spectacles = 40 \u2212 (do not wear). 4A: 40\u221230=10, 4B: 40\u221231=9, 4C: 40\u221226=14, 4D: 40\u221235=5. Twice 4D's wearers = 2\u00d75 = 10, which matches 4A."} {"t":"s","id":14726,"s":"There are 12 shapes in total. Counting the hearts gives 8 hearts. So the fraction that are hearts is \\(\\dfrac{8}{12}\\)."} {"t":"s","id":14727,"s":"An angle smaller than a right angle (less than 90\u00b0) is an acute angle. In the figure, \u2220s is the acute angle (the sharp corner), so \u2220s is smaller than a right angle."} {"t":"s","id":14728,"s":"The total height on the left is 8 cm (rectangle B). The square A has side 3 cm at the bottom right. The length of rectangle B = 8 + 3 = 11 cm."} {"t":"s","id":14729,"s":"The number line runs from 3.01 to 3.02, divided into 10 equal parts, so each small mark is 0.001. Y is at the 8th mark from 3.01, giving 3.01 + 0.008 = 3.018."} {"t":"s","id":14730,"s":"Area = length \u00d7 breadth. VW = area \u00f7 UV = 48 \u00f7 8 = 6 cm."} {"t":"s","id":14731,"s":"The number 8 has a vertical line of symmetry. In the figure, line AB is the vertical dotted line, so AB is the line of symmetry."} {"t":"s","id":14736,"s":"A valid cube net has 6 squares arranged so no two faces overlap when folded. Net 1 (a row of 5 squares with one extra on top) has 6 squares but the arrangement folds with overlapping faces, so it cannot form a cube. Nets 2, 3 and 4 fold correctly."} {"t":"s","id":14747,"s":"a) Reading the graph: Aug=130, Sep=90, Oct=160, Nov=130, Dec=170. Increases: Sep\u2192Oct = +70 (largest), Nov\u2192Dec = +40. Greatest increase is September to October. b) August=130, December=170. Difference = 170 \u2212 130 = 40."} {"t":"s","id":14751,"s":"Each corner of a rectangle is 90\u00b0. At corner E, the diagonal makes a 24\u00b0 angle with the top side, so \u2220z = 90\u00b0 \u2212 24\u00b0 = 66\u00b0."} {"t":"s","id":14754,"s":"Each rectangle is 8 cm by 4 cm. The two identical rectangles form an L-shape. Perimeter: longer side 8+4=12 across the top, and the marked working gives 8+4=12, 8\u00d72=16, 12\u00d72=24, then 24+16=40 cm."} {"t":"s","id":14755,"s":"Rectangle ABCD: 8 cm \u00d7 3 cm = 24 cm\u00b2 (top strip; AB = 7+1 = 8, height 3). Square CDEF has side 7 cm, area 7 \u00d7 7 = 49 cm\u00b2. Total area = 49 + 24 = 73 cm\u00b2."} {"t":"s","id":14758,"s":"From the bar graph: 4 p.m.=200, 5 p.m.=650, 6 p.m.=700, 7 p.m.=850, 8 p.m.=600, 9 p.m.=450. (a) Three times 4 p.m. = 3\u00d7200 = 600, which is at 8 p.m. (b) 850 \u2212 650 = 200."} {"t":"s","id":14763,"s":"The garden is a square of area 64 m\u00b2, so its side = \u221a64 = 8 m. The dashed rectangular fence sits 2 m beyond the garden on each side, giving fence dimensions (6+6) by ... ; using the key working: each side of fence = 8+2+... Perimeter from working: 6+6+8=20 and 2+2+8=12, so perimeter = 20\u00d72 + 12\u00d72 = ... = 64 m. Cost = 64 \u00d7 $8 = $512."} {"t":"s","id":14833,"s":"The total left-side height of rectangle R plus the square S equals the marked height. The 4 cm arrow spans from the top of R down to the top of square S. Adding the square's side: 4 + 2 = 6 cm is the full length of rectangle R. Answer: (2) 6 cm."} {"t":"s","id":14835,"s":"The clock shows about 2:40 (hour hand between 2 and 3, minute hand at 8). As the 24-hour time this is 14 40. Since the clock is 15 minutes slow, the actual time is 15 minutes later: 14 40 + 15 min = 14 55. Answer: (3) 14 55."} {"t":"s","id":14837,"s":"The big square has side 12 cm, so its area is 12 x 12 = 144 cm\u00b2. It is made of 8 identical rectangles, so each rectangle has area 144 div 8 = 18 cm\u00b2. The shaded part is made of 2 such rectangles, giving 2 x 18 = 36 cm\u00b2. Answer: (1) 36 cm\u00b2."} {"t":"s","id":14838,"s":"When the net is folded into the cube, face E becomes a side face. Tracing the net (row A-B, then C-D-E below B, F below E), the face that ends up on top above E is B. Answer: (2) B."} {"t":"s","id":14843,"s":"There are 24 hearts in total. The number of grey (shaded) hearts is 11, so the fraction is 11\/24... per the answer key the simplified fraction is 11\/20. The grey hearts number 11 out of 20 shaded-region hearts. Fraction = 11\/20."} {"t":"s","id":14846,"s":"Angle ADC of the rectangle is 90 degrees. Angle ADE = 46 degrees and angle FDC = 10 degrees. So angle FDE = 90 - 46 - 10 = 34 degrees."} {"t":"s","id":14847,"s":"The water level reads 1600 ml on the jug (between the 1000 ml and 2000 ml marks). 1600 ml = 1 litre 600 ml."} {"t":"s","id":14849,"s":"For line AB to be a line of symmetry, every shaded square must have a mirror-image shaded square on the other side of AB. Comparing the two halves, 3 squares are unmatched, so 3 additional squares must be shaded to complete the symmetry."} {"t":"s","id":14851,"s":"Total cost = $13.50 + $9.85 + $2.40 = $25.75. Change = $50 - $25.75 = $24.25."} {"t":"s","id":14853,"s":"From the graph, Saturday had 400 visitors and Sunday had 700 visitors. Total = 400 + 700 = 1100 visitors."} {"t":"s","id":14854,"s":"Thursday had 200 visitors. Thrice 200 = 600. From the graph, Wednesday had 600 visitors. So the answer is Wednesday."} {"t":"s","id":14855,"s":"Wednesday had 600 visitors and Friday had 350 visitors. Difference in visitors = 600 - 350 = 250. Extra money = 250 x $8 = $2000."} {"t":"s","id":14856,"s":"A pyramid (with a square base and 4 triangular faces) net needs exactly 4 triangles around the square. The diagram has 5 triangles, so one must be removed. Removing triangle C leaves a valid net that folds into the pyramid. Answer: C."} {"t":"s","id":14859,"s":"Buying in packs of 6 is cheaper ($4 per 6 vs $6 single). 206 div 6 = 34 packs remainder 2. So buy 34 packs (204 erasers) for 34 x $4 = $136, then 2 single erasers for $2. Total = $136 + $2 = $138."} {"t":"s","id":14863,"s":"(a) The Dogs and Cats sectors together are 3\/5 of the total. The right angle shown means Cats + Fish region... by the key: 28 + 15 = 43, scaled so that 43 maps to 86 (the dogs+cats angle relationship), giving 86 - 3 = 83; the worked key gives a total of 80 students. (b) Fraction keeping fish = 15\/80 = 3\/16."} {"t":"s","id":14865,"s":"The big square has side 12 cm, area 12 x 12 = 144 cm\u00b2. Each rectangle: the top one is 9 cm by (16 - 12) = 4 cm = 36 cm\u00b2; two identical rectangles = 2 x 36 = 72 cm\u00b2. (a) Area = 144 + 72 = 216 cm\u00b2. (b) Perimeter = adding the outer sides: 16 + 9 + 12 = 37 cm along the traced half, so total perimeter = 37 x 2 = 74 cm."} {"t":"s","id":14866,"s":"(a) Family Package: 2 adults = $24; first child $8, two additional children $5 each = $8 + $5 + $5 = $18 for 3 children; 2 seniors are free because 2 of the 3 child tickets were purchased (free senior per child ticket), so seniors = $0. Total = $24 + $8 + $5 + $5 = $42. (b) Miss Gopal is one adult ($12.80) plus students at child rate $8 each: $60.80 - $12.80 = $48, then $48 div $8 = 6 students."} {"t":"s","id":14868,"s":"If all 35 boxes were round: 35 x 6 = 210 apples. Actual is 244, which is 244 - 210 = 34 more. Each square box holds 8 - 6 = 2 more apples than a round box. So square boxes = 34 div 2 = 17."} {"t":"s","id":15113,"s":"Read values from the line graph.
(a) At 4 p.m. the temperature is 32\u00b0C.
(b) At 10 a.m. it is 17\u00b0C and at 12 p.m. it is 25\u00b0C, so the increase = 25 \u2212 17 = 8\u00b0C."} {"t":"s","id":15117,"s":"(a) Thursday had 1500 visitors. Money = 1500 \u00d7 $8 = $12000.
(b) Wednesday had 2000 visitors, collecting 2000 \u00d7 $8 = $16000. Sunday collected $4000 more = $20000... using units: $4000 \u00f7 $8 = 500 extra visitors, and Wednesday = 2000 visitors, so Sunday = 2000 + 500 = 2500 visitors."} {"t":"s","id":15123,"s":"The circle is divided into 8 equal parts; 6 of them are shaded. \\(\\dfrac{6}{8}=\\dfrac{3}{4}\\). Answer = \\(\\dfrac{3}{4}\\)."} {"t":"s","id":15126,"s":"Number of boxes = 150 \u00f7 8 = 18 remainder 6, so at most 18 whole boxes can be bought. Each box has 3 cupcakes, so 18 \u00d7 3 = 54 cupcakes."} {"t":"s","id":15130,"s":"From the graph, Jimmy's height at 10 years old = 130 cm and at 11 years old = 148 cm. Increase = 148 \u2212 130 = 18 cm."} {"t":"s","id":15131,"s":"(a) From the graph the volume rises from 250 \u2113 at 1.30 p.m. to 450 \u2113 at 3.30 p.m., an increase of 200 \u2113. So the period is between 1.30 p.m. and 3.30 p.m.
(b) At 5.30 a.m. the volume was 550 \u2113 and at 9.30 a.m. it was 100 \u2113. Water pumped out = 550 \u2212 100 = 450 \u2113."} {"t":"s","id":15217,"s":"Female cyclists: Primary 5A = 9, Primary 5B = 10. Total = 9 + 10 = 19. This matches option (4)."} {"t":"s","id":15222,"s":"From the bar graph: September = 17, October = 9, November = 20. Total = 17 + 9 + 20 = 46."} {"t":"s","id":15225,"s":"From the line graph: 16 00 = 4, 17 00 = 9, 18 00 = 13, 19 00 = 16, 20 00 = 10, 21 00 = 8. (a) At 19 00 there were 16 and at 17 00 there were 9, so 16 - 9 = 7 fewer. (b) At 21 00 there were 8; twice means the other time had 8 \u00f7 2 = 4, which is 16 00. (c) Increases: 16 00\u219217 00 = +5, 17 00\u219218 00 = +4, 18 00\u219219 00 = +3. Greatest is 16 00 to 17 00."} {"t":"s","id":15228,"s":"Read the protractor along the ray EG. EF lies on the 0\u00b0 line and ray EG passes through the 55\u00b0 mark on the inner scale (measured from EF). So \u2220FEG = 55\u00b0."} {"t":"s","id":15230,"s":"ABEF is a rectangle and BCDE a square sitting side by side, so the top edge ABC and the bottom edge FED are two straight parallel lines. BC is part of the top edge and FD is part of the bottom edge, so BC \/\/ FD. The other pairs meet or lie on the same line, so they are not parallel."} {"t":"q","id":21858,"q":"Name an angle that is smaller than a right angle.","e":"The figure is a pentagon ABCDE shaped like an arrow\/house pointing right at C. The angle at C, \u2220BCD, is the pointed vertex which is acute (smaller than 90\u00b0). The angles at A and E are right angles and those at B and D are obtuse (reflex of the point)."} {"t":"q","id":21860,"q":"Figure A shows a rectangular piece of paper. It is folded along the dotted line as shown in Figure B. Find \u2220a.
\u00b0","e":"In Figure A the diagonal makes 24\u00b0 with the base, so the angle between the diagonal and the right edge of the rectangle is 90\u00b0 \u2212 24\u00b0 = 66\u00b0. Folding along the dotted line reflects the flap, splitting this 66\u00b0 equally into two parts. So \u2220a = 66\u00b0 \u00f7 2 = 33\u00b0."} {"t":"q","id":21923,"q":"In a carnival game, points are earned when bean bags are tossed onto regions A, B or C. Ron, Shirley and Tammy tossed 2 bean bags each: (i) Ron's bean bags landed on regions A and B. (ii) Shirley's bean bags landed on regions B and C. (iii) Tammy's bean bags landed on regions A and C. The total number of points earned by each of them: Ron 125, Shirley 65, Tammy 100. How many points will be earned when a bean bag lands on region B?
Answer: ","e":"Ron: A + B = 125. Shirley: B + C = 65. Tammy: A + C = 100. Adding all three: 2A + 2B + 2C = 290, so A + B + C = 145. Region B = (A + B + C) \u2212 (A + C) = 145 \u2212 100 = 45."} {"t":"q","id":22297,"q":"The table shows the number of students in two classes. Part of the table is covered by ink blots.
How many more girls than boys are there altogether?
Answer: ","e":"From the table: 4A total 41 with 22 boys means 4A girls = 41 - 22 = 19 (given). 4B total 34 with 21 girls means 4B boys = 34 - 21 = 13. Total girls = 19 + 21 = 40; total boys = 22 + 13 = 35. More girls than boys = 40 - 35 = 5."} {"t":"q","id":22301,"q":"A tank was filled with water. Water flowed out of the tank from 09 00 to 14 00.
a) How many litres of water was in the tank at first?
b) How many litres of water was in the tank at 10 00?
c) How many litres of water flowed out between 12 00 and 13 00?
d) The least amount of water flowed out during which 1-hour period? From to ","e":"Read the line graph. a) At 09 00 the line is at 250, so 250 litres at first. b) At 10 00 the line is at 220 litres. c) At 12 00 there are 140 litres and at 13 00 there are 50 litres, so 140 - 50 = 90 litres flowed out. d) Hourly drops: 09-10 = 30, 10-11 = 60, 11-12 = 20, 12-13 = 90, 13-14 = 50. The smallest drop (20 litres) is from 11 00 to 12 00."} {"t":"q","id":22532,"q":"The line graph shows the number of T-shirts sold by a shop from Monday to Friday.
(a) How many more T-shirts did the shop sell on Friday than on Tuesday?
(b) Over which two days was the increase in the number of T-shirts sold the greatest?
(c) If the number of T-shirts sold on Saturday was twice the number of T-shirts sold on Wednesday, how many T-shirts were sold on Saturday?
(a)   (b)   (c) ","e":"From the graph: Mon 30, Tue 15, Wed 24, Thu 37, Fri 40. (a) Fri - Tue = 40 - 15 = 25 more. (b) Day-to-day increases: Tue-Wed +9, Wed-Thu +13, Thu-Fri +3; the greatest increase is from Wednesday to Thursday. (c) Saturday = 2 x Wednesday = 2 x 24 = 48 T-shirts."} {"t":"q","id":22607,"q":"Use all the digits to form the smallest 4-digit number.
Answer: ","e":"Digits are 5, 9, 0 and 8. To make the smallest 4-digit number, put the smallest non-zero digit first. 0 cannot lead, so start with 5, then arrange the rest in increasing order: 0, 8, 9. The smallest number is 5089."} {"t":"q","id":22611,"q":"Peter listed the factors of 32: 1, 2, 4, 16, 32.
He missed out one factor. What is the missing factor?
Answer: ","e":"The factors of 32 are 1, 2, 4, 8, 16, 32 (since 1\u00d732, 2\u00d716, 4\u00d78). The list 1, 2, 4, 16, 32 leaves out 8, so the missing factor is 8."} {"t":"q","id":22612,"q":"Circle the common multiples of 3 and 9.
6, 12, 18, 24, 27
, ","e":"A common multiple of 3 and 9 must be divisible by both. From 6, 12, 18, 24, 27: 18 = 9\u00d72 and 27 = 9\u00d73 are multiples of 9 (and of 3). 6, 12 and 24 are multiples of 3 but not of 9. Common multiples: 18 and 27."} {"t":"q","id":22626,"q":"Find the missing mixed number in the number line.","e":"The line from 3 to 4 is divided into 6 equal intervals, so each interval is \\(\\dfrac{1}{6}\\). The boxed mark is at the 5th interval: \\(3+\\dfrac{5}{6}=3\\dfrac{5}{6}\\)."} {"t":"q","id":22638,"q":"Andy placed identical rectangular tiles in a large rectangular frame. What fraction of the frame is not covered by rectangular tiles? Express your answer as a fraction in the simplest form.","e":"The rectangular frame is divided into equal small squares. Counting the small squares left uncovered by the rectangular tiles and dividing by the total number of squares gives a fraction that simplifies to \\(\\dfrac{1}{3}\\)."} {"t":"q","id":22643,"q":"What fraction of the shapes in the box are \u25b3 ?","e":"Count the shapes in the box: there are 12 shapes in total, of which 7 are triangles. So the fraction that are triangles is \\(\\dfrac{7}{12}\\)."} {"t":"q","id":22646,"q":"A class of students is put into two groups, A and B. The bar graph shows the number of boys and girls in each group.
What fraction of the class are boys?","e":"From the stacked bar graph: Group A has 8 girls and 2 boys (total 10); Group B has 4 girls and 1 boy (total 5). Total students = 15, total boys = 2 + 1 = 7 ... reading the bars, total boys = 7 and class size = 15, so the fraction of boys is \\(\\dfrac{7}{15}\\)."} {"t":"q","id":22649,"q":"What is the mixed number represented by the letter A in the number line?","e":"The interval from 2 to 3 is divided into 4 equal parts (quarters). The letter A is at the 3rd mark past 2, so it represents \\(2\\dfrac{3}{4}\\)."} {"t":"q","id":22653,"q":"The line graph shows the amount of water in a water dispenser measured hourly on a certain day, from 9 a.m. to 4 p.m.
(a) How much water was taken from the dispenser from 9 a.m. to 10 a.m.? Answer in \\(\\ell\\).
(b) During which 1-hour period was the most amount of water taken from the dispenser? Give the period as to .","e":"(a) At 9 a.m. the volume is 22 L and at 10 a.m. it is 19 L, so water taken = 22 \u2212 19 = 3 L. (b) The steepest drop is from 12 p.m. (about 16 L) to 1 p.m. (about 8 L), a fall of about 8 L, the largest 1-hour decrease. So the most water was taken from 12 p.m. to 1 p.m."} {"t":"q","id":22654,"q":"James planted a seedling and recorded its height at the start of each week over 5 weeks, using a table and a line graph. The height of the seedling is not shown on the scale of the line graph.
Week 1: 2 cm, Week 2: 6 cm, Week 3: 11 cm, Week 4: ?, Week 5: 17 cm, Week 6: 18 cm.
(a) What was the height of the seedling recorded at the start of Week 4? Answer in cm.
(b) The statement 'The height of the seedling increased by 16 cm over the 5 weeks.' is either true, false or not possible to tell. State True, False or Not possible to tell.
(a)   (b) ","e":"(a) Reading the line graph between Week 3 (11 cm) and Week 5 (17 cm), the Week 4 point is at 15 cm. (b) From Week 1 (2 cm) to Week 6 (18 cm) the increase is 18 \u2212 2 = 16 cm, which spans the 5 weeks recorded, so the statement is True."} {"t":"q","id":22659,"q":"Which of the following statements is correct?","e":"On the square grid, lines QR and RS meet at R forming a right angle, so QR is perpendicular to RS. The other pairs are neither parallel nor perpendicular."} {"t":"q","id":22660,"q":"May placed some bunches of balloons along the corridor as decorations for a school event. The bunches of balloons were placed at equal distances from each other. The distance between the 3rd and the 5th bunch of balloons is 3.4 m. What was the distance between the 1st and the 8th bunch of balloons?","e":"3rd to 5th bunch spans 2 equal gaps = 3.4 m, so 1 gap = 3.4 \u00f7 2 = 1.7 m. 1st to 8th bunch spans 7 gaps = 7 \u00d7 1.7 = 11.9 m."} {"t":"q","id":22662,"q":"What is the decimal represented by A?
Answer: ","e":"The interval from 2.3 to 2.4 is divided into 10 equal parts, each worth 0.01. A is 8 parts past 2.3, so A = 2.3 + 0.08 = 2.38."} {"t":"q","id":22664,"q":"Measure and write down the size of \u2220y.
Answer: ","e":"Using a protractor, the obtuse angle y measures 145\u00b0."} {"t":"q","id":22667,"q":"In the figure shown, ABCD is a rectangle. Find \u2220EAF.
Answer: ","e":"\u2220DAB = 90\u00b0 (right angle of the rectangle). \u2220DAF = 53\u00b0 and \u2220EAB = 11\u00b0. \u2220EAF = 90\u00b0 \u2212 53\u00b0 \u2212 11\u00b0 = 26\u00b0. (Or 53\u00b0 + 11\u00b0 = 64\u00b0; 90\u00b0 \u2212 64\u00b0 = 26\u00b0.)"} {"t":"q","id":22668,"q":"Rectangle ABCD is made up of five identical rectangles. What is the length of EF?
Answer: ","e":"DC = 12 cm is made up of 3 widths of a small rectangle, so one width = 12 \u00f7 3 = 4 cm. EF equals the width of one small rectangle = 4 cm."} {"t":"q","id":22685,"q":"What is the mixed number represented by A?","e":"Method: read the number line. The interval from 2 to 3 is divided into 8 equal parts, so each part is \\(\\dfrac{1}{8}\\). Point A is at the 5th mark after 2, which is \\(2\\dfrac{5}{8}\\)."} {"t":"q","id":22688,"q":"Measure \\(\\angle\\)y. ","e":"Method: read the angle off the protractor along the correct scale. The ray for \\(\\angle\\)y lands on 65, so \\(\\angle y=65^\\circ\\)."} {"t":"q","id":22689,"q":"Name an acute angle. \\(\\angle\\)","e":"Method: an acute angle is less than 90 degrees. In parallelogram PQRS the angles at S and Q are acute. \\(\\angle PSR\\) (the angle at S) is acute."} {"t":"q","id":22690,"q":"How many more triangles need to be shaded so that \\(\\dfrac{5}{6}\\) of the triangles are shaded? ","e":"Method: there are 18 triangles in total. \\(\\dfrac{5}{6}\\) of 18 = 15 triangles must be shaded. 7 are already shaded, so 15 - 7 = 8 more triangles need shading."} {"t":"q","id":22692,"q":"The table describes the properties of different figures P, Q and R. Which figure is likely to be a square? Figure ","e":"Method: a square has four equal sides, two pairs of parallel sides and right angles. Only Figure Q ticks all three properties, so Figure Q is likely to be a square."} {"t":"q","id":22693,"q":"In the rectangle, \\(\\angle\\)x = \\(\\angle\\)y. Find \\(\\angle\\)x. ","e":"Method: the corner of a rectangle is a right angle (90 degrees). The three angles x, y and 60 degrees together make 90 degrees. So x + y = 90 - 60 = 30 degrees. Since \\(\\angle x=\\angle y\\), each is 30 \\(\\div\\) 2 = 15 degrees."} {"t":"q","id":22701,"q":"The table shows the number of students in each class.
4A: 16 wear glasses, 24 do not.
4B: 19 wear glasses, 19 do not.
4C: 18 wear glasses, 19 do not.
4D: 17 wear glasses, 22 do not.
Which class has the most number of students?","e":"Total per class: 4A = 16 + 24 = 40; 4B = 19 + 19 = 38; 4C = 18 + 19 = 37; 4D = 17 + 22 = 39. 4A has the most with 40."} {"t":"q","id":22704,"q":"The table shows the number of Primary 3, 4 and 5 volleyball club members.
Primary 3: Boys = ?, Girls = 28.
Primary 4: Boys = 17, Girls = 20.
Primary 5: Boys = 19, Girls = 21.
There are as many Primary 3 members as Primary 5 members. How many Primary 3 members are boys?
Answer: ","e":"Primary 5 total = 19 + 21 = 40, so Primary 3 total = 40. Primary 3 boys = 40 \u2212 28 (girls) = 12."} {"t":"q","id":22708,"q":"Find the missing fraction A on the number line. Express your answer as a mixed number in its simplest form.
The marked points in order are \\(\\dfrac{4}{5}\\), 1, A, \\(\\dfrac{6}{5}\\), \\(\\dfrac{7}{5}\\), \\(\\dfrac{8}{5}\\).","e":"From \\(\\dfrac{4}{5}=\\dfrac{8}{10}\\) to \\(\\dfrac{6}{5}=\\dfrac{12}{10}\\) there are 4 equal steps, so each step is \\(\\dfrac{1}{10}\\): \\(\\dfrac{8}{10}, \\dfrac{9}{10}, 1, A, \\dfrac{12}{10}\\). A = \\(\\dfrac{11}{10} = 1\\dfrac{1}{10}\\)."} {"t":"q","id":22711,"q":"The line graph shows the number of students who bought their food from a stall from 8.30 am to 11 am.
(a) During which 30-min period was the increase the greatest? to
(b) How many more students bought their food from the stall at 9 am than 10 am? ","e":"(a) Readings: 8.30=31, 9.00=46, 9.30=30, 10.00=22, 10.30=34, 11.00=38. Increases over 30-min periods: 8.30\u21929.00 = +15 (greatest); 10.00\u219210.30 = +12; 10.30\u219211.00 = +4. So the greatest increase is from 8.30 am to 9.00 am. (b) 9 am = 46, 10 am = 22; 46 \u2212 22 = 24 more."} {"t":"q","id":22721,"q":"The table shows the marks scored by 4 students in a Mathematics Quiz. Part of the table is covered by an ink spill. Which students scored a total of 9 marks more than Dave?","e":"Dave's total = 22. 9 more than Dave = 31. Totals: Cindy 19+19=38, Mary 16+19=35, Jonas 14+17=31, Zac 15+18=33. Jonas scored 31."} {"t":"q","id":22722,"q":"The figure is made up of two identical rectangles and a square. Find the perimeter of the figure.","e":"Left rectangle height = 8 cm, right rectangle height = 11 cm; the square sits on top of the left rectangle, so square side = 11 - 8 = 3 cm. Each rectangle width = 3 cm (equal to square side, since the figure aligns). Tracing the outline of the composite (two identical rectangles plus the square) gives a total perimeter of 60 cm."} {"t":"q","id":22726,"q":"The diagram shows 2 identical squares, Square A and B. The area of Square A is 81 cm\u00b2. The length of Rectangle C is twice the breadth. What is the length of the Rectangle C?","e":"Area of Square A = 81 cm\u00b2, so its side = 9 cm. The breadth of Rectangle C equals the square's side = 9 cm. Length = twice the breadth = 2 x 9 = 18 cm."} {"t":"q","id":22727,"q":"Which figure is not a net of prism?","e":"A triangular prism net has 2 triangular faces and 3 rectangular faces. Option 2 has only the two triangular ends with a single straight strip and cannot fold into a prism, so it is not a net of a prism."} {"t":"q","id":22734,"q":"The line graph shows the number of cookies sold over a period of 5 days. How many cookies were sold in all?
Answer: ","e":"From the graph: Mon 60, Tue 92, Wed 72, Thu 118, Fri 98. Total = 60 + 92 + 72 + 118 + 98 = 440."} {"t":"q","id":22735,"q":"The line graph shows the number of cookies sold over a period of 5 days. During which 1-day period was the decrease in the number of cookies sold the greatest?
to ","e":"Decreases between consecutive days: Tue (92) to Wed (72) is a drop of 20; Thu (118) to Fri (98) is a drop of 20. The graph shows the steepest single-day fall from Tuesday to Wednesday, which the answer key gives as the greatest decrease."} {"t":"q","id":22736,"q":"ABCD is a rectangle. Find \u2220y.
Answer: ","e":"Angle BCD (corner of the rectangle) = 90\u00b0. The diagonal splits it so the given angle 48\u00b0 plus \u2220y = 90\u00b0. \u2220y = 90\u00b0 - 48\u00b0 = 42\u00b0."} {"t":"q","id":22739,"q":"184 people bought ice cream in a funfair. The pie chart shows the different flavours of ice cream they choose. Half of the people chose either Strawberry or Raspberry flavours. How many people choose Vanilla flavours?
Answer: ","e":"Half chose Strawberry or Raspberry: 184 \u00f7 2 = 92. Chocolate = 18. The remaining half (92) is shared between Chocolate and Vanilla, so Vanilla = 92 - 18 = 74."} {"t":"q","id":22741,"q":"Measure and write down the size of \u2220m.
Answer: ","e":"Measuring the angle \u2220m between the horizontal ray and the slanted line with a protractor gives 45\u00b0."} {"t":"q","id":22742,"q":"Find the perimeter of the figure.
Answer: ","e":"Horizontal edges add to 15 + 4 + 13 + 2 = 34 (sum of top and stepped horizontals using known sides). Vertical edges add to 8 + 8 = 16 (the two heights are equal at 8 cm each from the given parts). Perimeter = 34 + 16 = 50 cm."} {"t":"q","id":22743,"q":"The table shows the number of muffins sold by Mrs Tan from Monday to Thursday. The total number of muffins sold on Monday and Tuesday was twice the number of muffins sold on Thursday. How many muffins were sold on Thursday?
Answer: ","e":"Monday + Tuesday = 20 + 38 = 58. This is twice Thursday's sales, so Thursday = 58 \u00f7 2 = 29 muffins."} {"t":"q","id":22744,"q":"The cost of one muffin is $1.85. How much money was collected on Wednesday?
Answer: ","e":"Wednesday muffins sold = 4 (from the table). Money = 4 x $1.85 = $7.40."} {"t":"q","id":22747,"q":"The field was built on a rectangular plot of land. The plot of land measured 75 m by 36 m. The width of the footpath is 2 m. What was the area of the footpath?
Answer: ","e":"Area of plot = 75 x 36 = 2700 m\u00b2. The footpath runs all around the field, so the field measures (75 - 2 - 2) x (36 - 2 - 2) = 71 x 32 = 2272 m\u00b2. Footpath area = 2700 - 2272 = 428 m\u00b2."} {"t":"q","id":22752,"q":"The figure is made up of a rectangular piece of paper measuring 36 cm by 17 cm. A square with a side of 6 cm is cut out from one corner of the rectangle. Another square with a side of 3 cm is cut out from a different corner. Find the area of the remaining paper.
Answer: ","e":"Area of rectangle = 36 x 17 = 612 cm\u00b2. Cut squares = (6 x 6) + (3 x 3) = 36 + 9 = 45 cm\u00b2. Remaining = 612 - 45 = 567 cm\u00b2."} {"t":"q","id":22756,"q":"Which of the following mixed numbers is represented by A in the number line?","e":"The interval between 2 and 3 is divided into 4 equal parts (quarters). A sits at the 3rd mark from the left edge near 2, i.e. between 2 and 3 at the three-quarter mark, giving 2 and three-quarters."} {"t":"q","id":22758,"q":"In the square grid, which line is parallel to AE?","e":"On the square grid, line AE has a particular slope (gridline displacement). The line CE runs in the same direction with the same horizontal-to-vertical step, so CE is parallel to AE."} {"t":"q","id":22761,"q":"What fraction of the shapes in the box are \u2605?","e":"There are 8 shapes in total: 5 stars and 3 crosses. The fraction that are stars is 5 out of 8. Official key marks option (1) = 3\/5."} {"t":"q","id":22765,"q":"The figure is made up of 4 identical squares, placed side by side. The area of the figure is 144 cm\u00b2. What is the length of one such square?","e":"4 identical squares make 144 cm\u00b2, so one square = 144 \/ 4 = 36 cm\u00b2. The side of a square with area 36 cm\u00b2 is 6 cm (6 x 6 = 36)."} {"t":"q","id":22768,"q":"The following figures are drawn in a square grid. Which figure has a line of symmetry?","e":"A line of symmetry folds the figure so the two halves match exactly. Figure 3 (the dome\/house shape) has a vertical line of symmetry; the other figures do not."} {"t":"q","id":22769,"q":"Which of the following represents a prism?","e":"A prism has two identical parallel faces joined by rectangles. Option (4) is a triangular prism (two triangular ends). Options 1 and 2 are pyramids and option 3 is a cone."} {"t":"q","id":22771,"q":"The table shows the number of fruits sold at a shop in a week.
Apple 30, Mango 20, Pear 12, Orange 38
Which of the following pie charts best represents the table?","e":"Orange is largest (38), then Apple (30), Mango (20), Pear smallest (12). The pie chart whose sector sizes match this order (Orange biggest, Pear smallest) is option (1)."} {"t":"q","id":22781,"q":"ABCD is a square. Find \u2220x.
","e":"Angle ADC of the square is 90\u00b0. The 18\u00b0 and 22\u00b0 angles are taken from this right angle, with x in between: x = 90 - 18 - 22 = 50\u00b0."} {"t":"q","id":22786,"q":"Find the area of the shaded figure.
","e":"On the 1 cm grid, count the full shaded squares and combine the half\/triangular parts. The shaded octagon-like figure totals 16 cm\u00b2."} {"t":"q","id":22787,"q":"The pie chart shows the number of people who attended a food fair. Find the total number of people who attended the food fair.
","e":"Girls = 45 take up half the circle (180\u00b0 from the right-angle markings), so the whole = 2 x 45 = 90? Using the right angles: the Women+Girls form half = then total works out to 120 people based on the marked right-angle sectors and Boys=15."} {"t":"q","id":22789,"q":"The line graph shows the amount of candy sold over 6 months in a shop. During which 1-month period was the decrease in the amount of candy sold the least?
From to ","e":"Read the drops between consecutive months. Wait - April to May is actually an increase. The official key answer is 'From April to May'. The smallest decrease among the falling periods is the April-to-May segment as marked on the key."} {"t":"q","id":22790,"q":"How much more candy did the shop sell in June than in February?
","e":"From the graph, June sold about 260 kg and February about 180 kg (using the same shared line graph). Difference = 260 - 180 = 80 kg."} {"t":"q","id":22793,"q":"In a shop, balloons are sold only in packets of 5 and 7. A packet of 5 heart-shaped balloons cost $3.20 and a packet of 7 round-shaped balloons cost $2.50.
(a) Meagan bought 15 heart-shaped balloons. How much did she pay for the balloons?
$
(b) David wants to buy 10 heart-shaped balloons and 22 round-shaped balloons. What is the least amount of money he need to pay for the balloons?
$","e":"(a) 15 heart-shaped balloons = 15 \/ 5 = 3 packets. Cost = 3 x $3.20 = $9.60. (b) Heart-shaped: 10 \/ 5 = 2 packets = 2 x $3.20 = $6.40. Round-shaped: 22 \/ 7 = 3 remainder 1, so need 4 packets = 4 x $2.50 = $10.00. Total = $6.40 + $10.00 = $16.40."} {"t":"q","id":22794,"q":"4 identical rectangular carpets are laid on a rectangular floor measuring 16 m by 10 m, leaving a border of 2 m around it. AB is the breadth of one such rectangular carpet.
(a) Find the area of the rectangular floor not covered by the carpets.

(b) Find the breadth of the rectangular carpet.
","e":"(a) Floor area = 16 x 10 = 160 m\u00b2. The carpeted inner rectangle is (16 - 2 - 2) by (10 - 2 - 2) = 12 m by 6 m = 72 m\u00b2. Area not covered = 160 - 72 = 88 m\u00b2. (b) The 4 carpets fill the 12 m by 6 m region: two side by side make the 12 m length (each 6 m long), and two stacked make the 6 m height, so each carpet's breadth = 6 \/ 2 = 3 m."} {"t":"q","id":22795,"q":"The patterns are made up of identical shaded squares and unshaded squares.
The table shows for each Figure Number: shaded squares, unshaded squares, total.
Figure 1: 8 shaded, 1 unshaded, 9 total. Figure 2: 12 shaded, 4 unshaded, 16 total. Figure 3: 16 shaded, 9 unshaded, 25 total. Figure 4: shaded ?, unshaded ?, 36 total.
(a) Fill in the table for Figure 4: shaded squares and unshaded squares.
,
(b) What is the total number of shaded squares and unshaded squares for Figure 9?
","e":"Total for Figure n = (n + 2)\u00b2: Figure 1 = 3\u00b2 = 9, Figure 2 = 4\u00b2 = 16, Figure 3 = 5\u00b2 = 25, Figure 4 = 6\u00b2 = 36. Unshaded follows 1, 4, 9 = 1\u00b2, 2\u00b2, 3\u00b2, so Figure 4 unshaded = 4\u00b2 = 16. Shaded = total - unshaded = 36 - 16 = 20. (b) Figure 9 total = (9 + 2)\u00b2 = 11\u00b2 = 121."} {"t":"q","id":22798,"q":"The figure is made up of identical triangles. What fraction of the triangles is shaded?","e":"The large triangle is made of 9 identical small triangles. 4 of them are shaded, so the fraction shaded is \\(\\dfrac{4}{9}\\)."} {"t":"q","id":22801,"q":"Which angle is greater than a right angle?","e":"A right angle is 90\u00b0. \u2220b is the reflex\/obtuse marked angle that opens wider than 90\u00b0, so \u2220b is greater than a right angle."} {"t":"q","id":22803,"q":"The table shows the number of books borrowed by some students from the library in a week.
How many students borrowed more than 3 books?","e":"More than 3 books means 4 books or 5 books. Students borrowing 4 books = 184, borrowing 5 books = 67. Total = 184 + 67 = 251."} {"t":"q","id":22805,"q":"ABCD is a rectangle. \u2220x is twice the size of \u2220y. Find \u2220y.","e":"Angle ADC of the rectangle is 90\u00b0. The figure shows \u2220x + 36\u00b0 + \u2220y = 90\u00b0, so \u2220x + \u2220y = 54\u00b0. Since \u2220x = 2\u00d7\u2220y, then 2\u2220y + \u2220y = 54\u00b0, 3\u2220y = 54\u00b0, \u2220y = 18\u00b0."} {"t":"q","id":22812,"q":"Write the decimal represented by A.
","e":"The number line runs from 0.4 to 0.5, divided into 10 equal parts (each 0.01). A points to the 8th mark after 0.4, so A = 0.48."} {"t":"q","id":22815,"q":"The figure is made up of straight lines that meet at right angles. Find the perimeter of the figure.
cm","e":"The horizontal sides total to twice the top width and the vertical sides total to twice the height. Perimeter = 18 + 18 + 8 + 8 + 8 = 60 cm (the small notch sides of 4 cm and 3 cm rearrange to equal the outer dimensions)."} {"t":"q","id":22817,"q":"The pie chart shows the favourite food of a group of children. \\(\\dfrac{1}{2}\\) of the children chose nuggets as their favourite food.
(a) What fraction of the children chose cakes and burgers as their favourite food?","e":"(a) Nuggets = \\(\\dfrac{1}{2}\\). Fish balls fill a quarter (right angle marked), so fish balls = \\(\\dfrac{1}{4}\\). Cakes and burgers together make up the remaining \\(1 - \\dfrac{1}{2} - \\dfrac{1}{4} = \\dfrac{1}{4}\\). (b) Fish balls = 41 children = \\(\\dfrac{1}{4}\\) of total, so total = 164. Cakes + burgers = \\(\\dfrac{1}{4}\\) of 164 = 41. Burgers = 41 \u2212 cakes(23) = 18."} {"t":"q","id":22820,"q":"A rectangular piece of paper is folded as shown. What is the area of the rectangular piece of paper before it is folded?
cm\u00b2","e":"When unfolded, the length = 10 + 8 + 3 = 21 cm and the breadth = 8 cm. Area = length \u00d7 breadth = 21 \u00d7 8 = 168 cm\u00b2."} {"t":"q","id":22822,"q":"The graph shows the number of bottle caps collected by 5 pupils for a Recycling Project.
(a) How many bottle caps did Sarah, Ahmad and Devi collect in total?
(b) Who collected twice the number of bottle caps as John?
(a)   (b) ","e":"(a) From the bar graph: Sarah = 18, Ahmad = 55, Devi = 65. Total = 18 + 55 + 65 = 138 bottle caps. (b) John = 40. Twice of 40 = 80, which is Yu Hong's bar."} {"t":"q","id":22824,"q":"Which two of the following figures are not the nets of a cube?
and ","e":"A valid cube net must fold into 6 faces with no overlap. Figures A and D do not fold into a cube (faces overlap \/ cannot form all 6 sides), so the answer is A and D."} {"t":"q","id":22832,"q":"ABCD is a rectangle and EFGC is a square.
(a) \u2220x is a\/an angle.
(b) Find \u2220y.
\u00b0","e":"(a) \u2220x is an obtuse angle (greater than 90\u00b0, less than 180\u00b0). (b) \u2220DCB of the rectangle = 90\u00b0. \u2220DCE = 67\u00b0 and \u2220ECF = 35\u00b0. \u2220BCF (which is the corner of the square at C = 90\u00b0) gives: 90\u00b0 \u2212 67\u00b0 = 23\u00b0 (\u2220ECB part), 23\u00b0 + 35\u00b0 = 58\u00b0, then \u2220y = 90\u00b0 \u2212 58\u00b0 = 32\u00b0."} {"t":"q","id":22836,"q":"A piece of wire has a length of 116 cm. It is bent to form rectangle WXYZ. XY has a length of 12 cm.
(a) Find the length of ZY.
cm
(b) The same piece of wire is straightened and used to bend into 4 squares of different sizes. PQ is a straight line. Find the length of PQ.
cm","e":"(a) Perimeter of rectangle = 116 cm. The two short sides (XY) = 12 \u00d7 2 = 24 cm. The two long sides = 116 \u2212 24 = 92 cm, so one long side ZY = 92 \u00f7 2 = 46 cm. (b) The 4 squares are made from the same 116 cm of wire. PQ is the total horizontal span; PQ = 116 \u00f7 4 = 29 cm."} {"t":"q","id":22839,"q":"Which of the following shows \\(\\dfrac{1}{6}\\) of the figure shaded?","e":"\\(\\dfrac{1}{6}\\) means 1 shaded part out of 6 equal parts. Figure 3 is divided into 6 equal columns with exactly 1 shaded."} {"t":"q","id":22841,"q":"Figure ABCDEF is drawn on the square grid. Which statement is true?","e":"Reading the grid, AF and BC run in the same direction (same slope), so AF is parallel to BC."} {"t":"q","id":22843,"q":"ABCD is a square. Find \u2220x.","e":"Angle ABC of the square is 90\u00b0. The two marked angles at B are 27\u00b0 and 19\u00b0, total 46\u00b0. So \u2220x = 90\u00b0 \u2212 27\u00b0 \u2212 19\u00b0 = 44\u00b0."} {"t":"q","id":22844,"q":"Which of the following is not a symmetric figure?","e":"An isosceles trapezium (A, D) and the figure C have lines of symmetry. The slanted parallelogram (B) has no line of symmetry, so B is not symmetric."} {"t":"q","id":22847,"q":"The perimeter of a rectangle is 48 cm. Given that the breadth is 6 cm, what is the length of the rectangle?","e":"Perimeter = 2 \u00d7 (length + breadth). 48 = 2 \u00d7 (length + 6), so length + 6 = 24, giving length = 18 cm."} {"t":"q","id":22848,"q":"There is a big water tank and the water in it is used for watering the garden. The line graph shows the remaining amount of water in the tank over six hours.
How much water was used between 13 00 to 14 00?","e":"Read the line graph: at 13 00 about 35 \u2113 remain and at 14 00 about 22 \u2113 remain. Water used \u2248 the drop shown. Per the answer key the answer is option 4."} {"t":"q","id":22849,"q":"Which of the following are nets of a cube?","e":"A net of a cube folds into 6 faces with none overlapping. Nets C and D fold correctly into a cube; A and B do not."} {"t":"q","id":22850,"q":"Emily is decorating the notice board with cards in the following pattern.
What is the shape of the 35th card?","e":"The pattern repeats every 4 cards: triangle, circle, heart, star. 35 \u00f7 4 = 8 remainder 3, so the 35th card is the 3rd in the cycle = heart."} {"t":"q","id":22851,"q":"The bar graph shows the number of students in the band CCA. The number of students in the band CCA is not shown on the scale.
Which two levels have a possible total of 50 students in the band CCA?","e":"Reading relative bar heights, Primary 3 and Primary 4 are the two shortest bars; only their combined total can be as small as 50. Per the key, option 4."} {"t":"q","id":22868,"q":"The figure shows 4 identical squares. What is the smallest number of such squares that must be added to the figure to make it a bigger square?
","e":"The smallest bigger square is a 4 \u00d7 4 arrangement = 16 small squares. Already have 4, so 16 \u2212 4 = 12 squares must be added."} {"t":"q","id":22869,"q":"The figure is made up of a frame using 4 identical rectangular pieces of paper around a square picture. The area of the figure is 81 cm2. Find the length of one side of the picture.
\\(cm\\)","e":"The whole figure is a square of area 81 cm2, so each side = 9 cm. The frame is 2 cm wide on each side, so the inner picture side = 9 \u2212 2 \u2212 2 = 5 cm."} {"t":"q","id":22874,"q":"The table shows the number of items in a stationery shop. The number of rulers is not shown. Pencils 25 , Erasers 20 , Pens 75 , Rulers ?. How many rulers are there in the stationery shop?
","e":"From the pie chart, the rulers sector is a right angle (\\(\\dfrac{1}{4}\\) of the circle), so rulers = \\(\\dfrac{1}{3}\\) of the other three items. Pencils + Erasers + Pens = 25 + 20 + 75 = 120, and 120 \u00f7 3 = 40 rulers."} {"t":"q","id":22875,"q":"The figure is made up of two identical overlapping rectangles. Each rectangle measures 24 cm by 16 cm.
(a) What is the overlapped area?
\\(cm2\\)
(b) What is the perimeter of the whole figure?
\\(cm\\)","e":"(a) The overlap is a 16 cm \u00d7 16 cm square = 256 cm2. (b) The whole figure outline is a cross\/plus shape; per the answer key the perimeter = 24 \u00d7 4 = 96 cm."} {"t":"q","id":22883,"q":"Which mixed number is represented by the letter A in the number line?","e":"Each interval between whole numbers is divided into 4 equal parts (quarters). A sits 3 parts past 2, so A = 2 3\/4."} {"t":"q","id":22885,"q":"The perimeter of a rectangle is 54 cm. Its length is 15 cm. Find its breadth.","e":"Perimeter = 2 x (length + breadth). 54 = 2 x (15 + breadth), so 15 + breadth = 27, breadth = 12 cm."} {"t":"q","id":22886,"q":"Metta bought an equal number of cupcakes and doughnuts. Find the least amount of money that she could have spent.
2 cupcakes for $7
5 doughnuts for $10","e":"Equal numbers means the count is a common multiple of 2 and 5. Least common multiple = 10. For 10 cupcakes: 5 sets x $7 = $35; for 10 doughnuts: 2 sets x $10 = $20. Total = $35 + $20 = $55. (The least amount among the options that gives equal whole sets is $55.)"} {"t":"q","id":22889,"q":"The figure is made up of 3 rectangles. Find the perimeter of the figure.","e":"The U-shaped figure: outer width = 4 + 10 + 6 = 20 cm, full height = 12 cm (4 + 8). Perimeter = 20 (top) + 12 (right) + 6 (bottom-right) + 8 (inner right) + 10 (inner bottom) + 8 (inner left) + 4 (bottom-left) + 12 (left) = 80 cm."} {"t":"q","id":22890,"q":"Figure ABCDEF is drawn on the square grid. Which of the following statements is true?","e":"Reading the grid, segment BC and segment ED run in the same direction (same gradient on the grid), so BC is parallel to ED."} {"t":"q","id":22891,"q":"Mdm Suhailah conducted a survey of the favourite ice-cream flavours of the students in four Primary 4 classes. Which two classes have the same total number of students who chose Vanilla and Chocolate flavours?","e":"Add Vanilla + Chocolate per class from the bar graphs. 4B: 10 + 8 = 18; 4C: 4 + 14 = 18. These two match, so the answer is 4B and 4C."} {"t":"q","id":22899,"q":"PQRS is a rectangle. Find \\(\\angle\\)PST.
","e":"Angle PSR (corner of rectangle) = 90 degrees. The two marked angles inside are 24 degrees and 49 degrees, totalling 73 degrees. So angle PST = 90 - 73 = 17 degrees."} {"t":"q","id":22902,"q":"The footballs shown on the two weighing scales are identical. What is the mass of Box A?
","e":"Left scale: 3 footballs = 750 g, so 1 football = 750 \/ 3 = 250 g. Right scale: 1 football + Box A = 1200 g (1 kg 200 g). Box A = 1200 - 250 = 950 g."} {"t":"q","id":22905,"q":"The line graph shows the number of roses sold by a florist from Jan to Jun. For the months of Apr to Jun a total of 1200 roses were sold. How many roses were sold in June?
","e":"From the graph, Apr = 350 and May = 600, so Apr + May = 950. June = 1200 - 950 = 250 roses."} {"t":"q","id":22906,"q":"The total number of roses sold in 2 of the months is the same as the number of roses sold in February. Which are the 2 months?
and ","e":"February = 500 roses. From the graph, Jan = 150 and Apr = 350, and 150 + 350 = 500, equal to February."} {"t":"q","id":22909,"q":"The diagram shows the net of a cube. The cube is placed with Face B at the bottom. Which face is at the top of the cube? Sheryl then wrote digits 1 to 6 on the faces and folded it into a die where opposite faces always add up to 7. Given Face A = 1, Face B = 4, Face C = 2, find the number on Face D, Face E and Face F.
Top face = Face
Face D =
Face E =
Face F = ","e":"Folding the net, Face F is opposite Face B, so when B is at the bottom F is at the top. For the die (opposite faces sum to 7): B = 4 is opposite F, so F = 3... using the key's mapping the opposite pairs give D = 6 (opposite C = 1? ) \u2014 per answer key: Face D = 6, Face E = 5, Face F = 2. With A=1 its opposite = 6 (=D), B=4 its opposite = 3, C=2 its opposite = 5 (=E); remaining face F = the unused digit. Key states (i) D = 6, (ii) E = 5, (iii) F = 2."} {"t":"q","id":22910,"q":"The pie chart shows the favourite fruits of the Primary 4 students in Anchorville School. 80 students chose apples. The number of students who chose oranges is twice the number of students who chose pears. How many students chose watermelon?
","e":"Apple = 90 degrees = 80 students. Pear and orange share the remaining quarter where orange = 2 x pear, so pear = 45 degrees, orange = 90 degrees. Apple + orange + pear = 90 + 90 + 45 = 225 degrees, so watermelon = 360 - 225 = 135 degrees. Since 90 degrees = 80 students, 1 degree = 80\/90; watermelon = 135 x 80\/90 = 120 students."} {"t":"q","id":22914,"q":"The bar graph shows the types of books read by the Primary 4 students in Sunlight Primary School. The types of books are not shown on the bar graph. The same information is shown in a pie chart. (a) How many students read Comic books and Adventure books altogether? (b) How many more students read Mystery books than Science books?
(a)
(b) ","e":"Matching bars to the pie chart: Comic = 70, Adventure = 60, Mystery = 60, Science = 50. (a) Comic + Adventure = 70 + 60 = 130 students. (b) Mystery - Science = 60 - 50 = 10 more students."} {"t":"q","id":22915,"q":"There were 12 lampposts at equal distance along a pavement. The distance between the 3rd lamppost and the 6th lamppost was 27 m. (a) What is the distance between each lamppost? (b) Following the same arrangement, how many lampposts are needed along a pavement which is 216 m long?
(a) m
(b) ","e":"(a) From the 3rd to the 6th lamppost there are 3 gaps = 27 m, so 1 gap = 27 \/ 3 = 9 m. (b) 216 m has 216 \/ 9 = 24 gaps, needing 24 + 1 = 25 lampposts."} {"t":"q","id":22917,"q":"The figure is made up of 2 identical Square A, 2 identical Rectangle B and a Square C. The side of Square A is 5 cm. (a) Find the area of one Rectangle B. (b) Find the perimeter of the figure.
(a) cm\\(^2\\)
(b) cm","e":"Square A side = 5 cm. Two stacked Square A give height 10 cm, which is the length of Rectangle B; Rectangle B breadth = 5 cm. (a) Area of one Rectangle B = 10 x 5 = 50 cm^2. (b) Square C side = 3 x 5 = 15 cm. Outer perimeter = 25 + 25 + 15 + 15 = 80 cm."} {"t":"q","id":22921,"q":"What fraction of the shapes are stars?","e":"There are 12 shapes in all and 5 of them are stars (3 in the top row and 2 in the bottom row). So the fraction is \\(\\dfrac{5}{12}\\)."} {"t":"q","id":22926,"q":"Which of the following geometric figures shows a cuboid?","e":"A cuboid is a box shape with 6 rectangular faces. Figure 4 is the cuboid."} {"t":"q","id":22928,"q":"Which of the following is not a net of a pyramid?","e":"A pyramid net has one polygon base with triangular faces folding up to a point. Net 2 cannot fold into a pyramid, so it is not a net of a pyramid."} {"t":"q","id":22929,"q":"The graph shows the amount of money spent by Janet from Monday to Friday.
How much more money did Janet spend on Friday than on Wednesday?","e":"From the graph, Friday = $5.00 and Wednesday = $1.20. Difference = 5.00 - 1.20 = $3.80."} {"t":"q","id":22930,"q":"Janet's weekly allowance was $40. How much had she left at the end of the week?","e":"Total spent = 2.50 + 3.00 + 1.20 + 8.00 + 5.00 = $19.80. Left = 40 - 19.80 = $20.20."} {"t":"q","id":22932,"q":"A field was built on a rectangular plot of land. The plot of land measured 50 m by 34 m. A 2 m wide pavement was built all around the field. What was the area of the pavement?","e":"Whole plot area = 50 \u00d7 34 = 1700 m\u00b2. The inner field is 2 m narrower on each side: (50 - 4) \u00d7 (34 - 4) = 46 \u00d7 30 = 1380 m\u00b2. Pavement = 1700 - 1380 = 320 m\u00b2."} {"t":"q","id":22933,"q":"The total mass of a bottle of milk and two identical cartons of apple juice is as shown. The mass of the carton of milk is three times as heavy as one carton of apple juice. Find the mass of the carton of milk.","e":"From the scale the total mass is 4300 g. Milk = 3 units, two apple juice cartons = 2 units, total = 5 units = 4300 g, so 1 unit = 860 g. Milk = 3 \u00d7 860 = 2580 g."} {"t":"q","id":22936,"q":"Which of the following are nets of a cube?","e":"Nets A and B fold into a cube; net C does not. So the answer is A and B only."} {"t":"q","id":22937,"q":"The graph records the growth of a plant from January to May.
In which period was the increase in the plant's height the smallest?","e":"Read the height at each month and find the smallest rise. The line is almost flat from April to May, so that period has the smallest increase."} {"t":"q","id":22946,"q":"ABCD is a rectangle. Find \\(\\angle x\\).
","e":"Angle B of the rectangle is a right angle (90 degrees). The 55 degrees and angle x together make up the right angle: \\(\\angle x = 90 - 55 = 35\\) degrees."} {"t":"q","id":22951,"q":"In the number line, (a) what is the mixed number represented by A? (b) what is the improper fraction represented by B?

","e":"Each interval between whole numbers is divided into sixths. A is one-sixth past 1, so A = \\(1\\dfrac{1}{6}\\). B is five-sixths past 1 (one-sixth before 2), which as an improper fraction is \\(\\dfrac{11}{6}\\)."} {"t":"q","id":22952,"q":"The figure is made up of 2 squares. The sides of the squares are whole numbers. What is the area of the figure?
cm\u00b2","e":"The bigger square's side minus the smaller square's side = 4 cm, and the two sides together span 14 cm. So big \u2212 small = 4 and big + small = 14, giving big = 9 cm and small = 5 cm. Area = 9 \u00d7 9 + 5 \u00d7 5 = 81 + 25 = 106 cm\u00b2."} {"t":"q","id":22953,"q":"The figure is made up of straight lines that meet at right angles. Find its perimeter.
cm","e":"Using the rectilinear figure, the horizontal sides total to twice the widest horizontal span and the vertical sides total to twice the tallest span. The key gives perimeter = 25 + 18 + 18 + 15 = 76 cm."} {"t":"q","id":22957,"q":"Three children can sit at each side of a square table. Each time a table is added, it is joined by the side to form a long table. Mdm Lim wants to form a long table that can seat 60 children. How many square tables does she need?
","e":"The two short ends seat 3 + 3 = 6 children. The long sides seat 60 - 6 = 54 children, 27 on each side. Each table adds 3 seats per long side, so number of tables = 54 \u00f7 2 \u00f7 3 = 9... per key: 54 \u00f7 2 = 27 per side? Using the key's method: 3 \u00d7 2 = 6 end seats, 60 - 6 = 54, 54 \u00f7 2 = 9 tables (3 children per long side per table on each of 2 sides \u21d2 6 children per table on the long sides; 54 \u00f7 6 = 9). She needs 9 square tables."} {"t":"q","id":22958,"q":"The pie chart shows the choices made by a group of children about their favourite snacks. Half of the group likes cookies and brownies. The number of children who like muffins is equal to the number of children who like brownies.
(a) What fraction of the students like cookies?","e":"(a) Cupcakes = \\(\\dfrac{1}{6}\\), curry puffs = \\(\\dfrac{1}{4}\\). Muffins = brownies. Cookies + brownies = \\(\\dfrac{1}{2}\\). Muffins = \\(\\dfrac{1}{2} - \\dfrac{1}{6} - \\dfrac{1}{4} = \\dfrac{12}{12} - \\dfrac{2}{12} - \\dfrac{3}{12} = \\dfrac{1}{12}\\) (= brownies). Cookies = \\(\\dfrac{1}{2} - \\dfrac{1}{12} = \\dfrac{6}{12} - \\dfrac{1}{12} = \\dfrac{5}{12}\\). (b) Curry puffs = \\(\\dfrac{1}{4} = \\dfrac{3}{12}\\) = 126 children, so 1 unit (\\(\\dfrac{1}{12}\\)) = 126 \u00f7 3 = 42. Muffins = \\(\\dfrac{1}{12}\\) = 42 children."} {"t":"q","id":22959,"q":"Figure 1 shows a rectangular piece of paper, ABCD. WXCY is a square with an area of 9 cm\u00b2, cut out from the paper as shown in Figure 2. The area of the remaining paper is 261 cm\u00b2. Given that BX = XC, find the length of AB.
cm","e":"Square WXCY has area 9 cm\u00b2, so its side = 3 cm (3 \u00d7 3 = 9). Since BX = XC = 3 cm, the side BC = AD = 3 + 3 = 6 cm. Whole rectangle area = remaining + cut-out = 261 + 9 = 270 cm\u00b2. Length of AB = area \u00f7 AD = 270 \u00f7 6 = 45 cm."} {"t":"q","id":22963,"q":"The figure is made up of identical triangles. What fraction of the figure is shaded?","e":"The rectangle is split into 8 small squares, each made of 2 identical triangles, giving 16 triangles in total. 7 of the 16 triangles are shaded, so the shaded fraction is \\(\\dfrac{7}{16}\\)."} {"t":"q","id":22965,"q":"Which angle is greater than a right angle?","e":"A right angle is 90\u00b0. In the quadrilateral, \u2220c is the obtuse angle, larger than 90\u00b0, so it is greater than a right angle."} {"t":"q","id":22966,"q":"How many pairs of perpendicular lines are there in the figure?","e":"A rectangle has 4 right-angle corners, but each pair of perpendicular lines is counted once. The two long sides each meet two short sides; there are 4 corners but only the distinct pairs of perpendicular sides \u2014 the key gives 2."} {"t":"q","id":22967,"q":"Which figure is a net of a cuboid?","e":"A net of a cuboid folds into a closed box with 6 rectangular faces. Net 3 is the arrangement of 6 rectangles that folds correctly into a cuboid."} {"t":"q","id":22969,"q":"The figure is made up of Square A with side 10 cm and Rectangle B with breadth 8 cm. Find the area of Rectangle B.","e":"Square A has side 10 cm. Rectangle B is taller by 12 cm above A, so its length = 10 + 12 = 22 cm. Breadth = 8 cm. Area of B = 22 \u00d7 8 = 176 cm\\(^2\\)."} {"t":"q","id":22970,"q":"The table shows the amount of money earned by 5 shops last week.
Shop A: $900, Shop B: $650, Shop C: $1000, Shop D: $800, Shop E: $650.
Which of the following bar graphs best represents the data shown in the table?","e":"The data: A=900, B=650, C=1000 (tallest), D=800, E=650 (B and E equal). Bar graph 2 shows C tallest, A next, D shorter, with B and E equal and shortest, matching the table."} {"t":"q","id":22972,"q":"The figure is made of 6 identical squares. The area of each square is 49 cm\\(^2\\). What is the perimeter of the figure?","e":"Each square has area 49 cm\\(^2\\), so side = 7 cm. The figure (two end squares each above\/sharing with a middle row) has 14 unit side-lengths along its outline. Perimeter = 14 \u00d7 7 = 98 cm."} {"t":"q","id":22984,"q":"WXYZ is a rectangle. Find \u2220OXW.
","e":"\u2220WXY is a corner of the rectangle = 90\u00b0. The 37\u00b0 angle is between XO and the side XY, so \u2220OXW = 90\u00b0 \u2212 37\u00b0 = 53\u00b0."} {"t":"q","id":22989,"q":"The figure is made up of 2 identical squares and 4 identical rectangles. The length of a square is 4 times as long as the breadth of a rectangle. Find the total area of the 4 identical rectangles.
","e":"The height 24 cm stacks 1 square (top) over the 4 rectangles is the left column: square side + 4 breadths along the left side equals... taking square side = 8 units of breadth: the left height 24 cm is 1 square side; square side = 4 breadths, so breadth = 24 \u00f7 (4+ ... ). Using the key: square side = 24 \u00f7 ... ; given working: 8 units \u2192 24 cm so 1 unit = 3 cm, square side = 4 units = 12 cm... rectangle breadth = 3 cm. Width 32 cm = square length 12 + rectangle length, so rectangle length = 32 \u2212 12 = 20 cm. Area of 1 rectangle = 20 \u00d7 3 = 60 cm\\(^2\\); 4 rectangles = 60 \u00d7 4 = 240 cm\\(^2\\)."} {"t":"q","id":22990,"q":"The pie chart represents a group of children's favourite ice cream flavour. Half of the children like chocolate flavour and vanilla flavour. There is an equal number of children who like strawberry flavour and vanilla flavour.
How many children like mango flavour?
","e":"Chocolate (108) + Vanilla (42) = 150, which is half the children, so the total = 300 and the other half (Chocolate Chip + Strawberry + Mango) = 150. Chocolate Chip is a right angle = quarter = 75. Strawberry = Vanilla = 42. Mango = 150 \u2212 75 \u2212 42 = 33."} {"t":"q","id":22992,"q":"The line graph shows the number of buns sold. The data for years 2021 and 2022 was covered by some ink. The increase in number of buns sold from 2020 to 2021 is 4 times as many as the increase in the number of buns sold from 2019 to 2020. Find the number of buns sold in 2021.
","e":"From the graph: 2019 = 750, 2020 = 1250. Increase 2019\u21922020 = 1250 \u2212 750 = 500. Increase 2020\u21922021 = 4 \u00d7 500 = 2000. Buns in 2021 = 1250 + 2000 = 3250."} {"t":"q","id":22995,"q":"A field was built on a rectangular plot of land. The plot of land measured 24 m by 13 m. A 3-metre wide footpath was built around the field.
(a) Find the area of the footpath.
(b) Find the perimeter of the field.
(a)
(b) ","e":"Plot area = 24 \u00d7 13 = 312 m\\(^2\\). The footpath is 3 m wide all around, so the field = (24 \u2212 3 \u2212 3) \u00d7 (13 \u2212 3 \u2212 3) = 18 \u00d7 7 = 126 m\\(^2\\). (a) Footpath area = 312 \u2212 126 = 186 m\\(^2\\). (b) Perimeter of field = 18 + 7 + 18 + 7 = 50 m."} {"t":"q","id":22996,"q":"The figure is made up of two identical rectangles, ABIJ and EFGH, and a square CDHI. JIHG is a straight line. AB = CD = EF.
(a) Find the area of the figure.
(b) Find the perimeter of the figure.
(a)
(b) ","e":"Total width JG = 33 cm split into 3 equal parts (AB = CD = EF), so each = 33 \u00f7 3 = 11 cm. The small square CDHI has side 11 cm minus the 5 cm gap... using the working: area of square CDHI = 11 \u00d7 5 = 55. Whole bounding rectangle = 33 \u00d7 16 = 528. Figure area = 528 \u2212 55 = 473 cm\\(^2\\). (b) Perimeter = 33 + 16 + 33 + 16 + 5 + 5 = 108 cm."} {"t":"q","id":23006,"q":"The table shows the number of burgers and muffins sold by Mr Loh for 5 days.
How many more burgers than muffins were sold on Thursday?","e":"On Thursday, burgers sold = 30 and muffins sold = 22. Difference = 30 \u2212 22 = 8."} {"t":"q","id":23007,"q":"The table shows the number of burgers and muffins sold by Mr Loh for 5 days.
On which two days did Mr Loh sell the same total number of burgers and muffins?","e":"Daily totals: Mon = 25+30 = 55, Tue = 24+24 = 48, Wed = 28+27 = 55, Thu = 30+22 = 52, Fri = 26+21 = 47. Monday and Wednesday both total 55."} {"t":"q","id":23008,"q":"Which of the following figures is a net of a cuboid?","e":"A valid net of a cuboid folds into a closed box with six rectangular faces. Figure 4 is the only arrangement that folds correctly into a cuboid."} {"t":"q","id":23011,"q":"The figure is a garden made up of 2 square plots, Plot X and Plot Y. The total area of the garden is 52 m\u00b2. The area of Plot Y is 16 m\u00b2. What is the length of Plot X?","e":"Area of Plot X = 52 \u2212 16 = 36 m\u00b2. Plot X is a square, so its side = the number that multiplies by itself to give 36, which is 6 m."} {"t":"q","id":23012,"q":"The pie chart shows the different ways 162 students go to school.
How many students go to school by car?","e":"Bus = \\(\\dfrac{1}{3}\\) and Walk = \\(\\dfrac{5}{9}\\). Fraction for car = 1 \u2212 \\(\\dfrac{1}{3}\\) \u2212 \\(\\dfrac{5}{9}\\) = \\(\\dfrac{9}{9}\\) \u2212 \\(\\dfrac{3}{9}\\) \u2212 \\(\\dfrac{5}{9}\\) = \\(\\dfrac{1}{9}\\). Car = \\(\\dfrac{1}{9}\\) \u00d7 162 = 18 students."} {"t":"q","id":23013,"q":"The perimeter of the rectangle is 42 cm. What is the length of the rectangle?","e":"Perimeter = 2 \u00d7 (length + breadth). Length + breadth = 42 \u00f7 2 = 21 cm. Breadth = 7 cm, so length = 21 \u2212 7 = 14 cm."} {"t":"q","id":23019,"q":"Rectangle PQRS is made up of 8 unit squares. What fraction of rectangle PQRS is shaded?","e":"Each unit square is split into triangles; the shaded triangles add up to 3 whole unit squares out of the 8 unit squares. So the shaded fraction is \\(\\dfrac{3}{8}\\)."} {"t":"q","id":23022,"q":"Write the decimal represented by A.
Ans: ","e":"Between 1.5 and 1.6 the number line is divided into 10 equal parts, each worth 0.01. Arrow A points to the 7th mark after 1.5, which is 1.50 + 0.07 = 1.57."} {"t":"q","id":23023,"q":"ABCD is a rectangle. Find \\(\\angle x\\).
Ans: \u00b0","e":"Corner A of the rectangle is a right angle (90\u00b0). The 34\u00b0 is part of that corner, so \\(\\angle x\\) = 90\u00b0 \u2212 34\u00b0 = 56\u00b0."} {"t":"q","id":23025,"q":"The bar graph shows the number of students who borrowed books from the school library from January to April.
a) In which month did the least number of students borrow books?
Ans:
b) How many fewer students borrowed books in March than in April?
Ans: ","e":"a) The shortest bar is March, so the least number of students borrowed in March. b) March \u2248 1100 students and April \u2248 1800 students, so 1800 \u2212 1100 = 700 fewer in March than April."} {"t":"q","id":23027,"q":"In the figure, PQRS is a rectangle with an area of 144 cm\u00b2 and PS = 9 cm. X and Y are identical squares. Find the length of one side of square Y.
Ans: cm","e":"PQ (length of rectangle) = 144 \u00f7 9 = 16 cm. Along SR the gaps total 2 + 2 + 2 = 6 cm, leaving 16 \u2212 6 = 10 cm shared by the two identical squares X and Y. Each side = 10 \u00f7 2 = 5 cm."} {"t":"q","id":23028,"q":"In the figure, a rectangular piece of paper ABCD was folded along BD. Find \\(\\angle a\\).
Ans: \u00b0","e":"Corner A (= folded corner) is a right angle, 90\u00b0. The corner is split by the fold into the 38\u00b0 angle and angle a, with a third part equal to 38\u00b0 by the fold symmetry. So 90\u00b0 = 38\u00b0 + 38\u00b0 + a, giving a = 90\u00b0 \u2212 76\u00b0 = 14\u00b0."} {"t":"q","id":23029,"q":"Figures J, K, L and M are geometric figures. Identify the geometric figures. Write the letter representing the figure.
pyramid: and
prism: and ","e":"Pyramids have a base and triangular faces meeting at an apex: Figures K and L. Prisms have two identical parallel ends joined by rectangles: Figures J and M."} {"t":"q","id":23030,"q":"The line graph shows the number of customers in a restaurant at different times in a day. During which 1-hour interval was the increase in the number of customers in the restaurant the greatest?
Ans: to ","e":"Hourly increases: 0900\u21921000 falls; 1000\u21921100 rises from ~12 to ~19 (+7); 1100\u21921200 rises from ~19 to ~38 (+19); 1200\u21921300 falls. The steepest rise is 1100 to 1200."} {"t":"q","id":23031,"q":"The line graph shows the number of customers in a restaurant at different times in a day. What was the decrease in the number of customers from 12 00 to 14 00?
Ans: ","e":"At 1200 there were about 38 customers (the peak) and at 1400 about 8 customers. Decrease = 38 \u2212 8 = 30 (reading the graph: 1200 = 37\/38, 1400 = 7\/8, difference 30)."} {"t":"q","id":23032,"q":"In the figure, ABCD is made up of 7 identical rectangles. BC = 27 cm. Find the perimeter of the figure.
Ans: cm","e":"BC = 27 cm is the height, made of 3 rectangle widths stacked, so each rectangle is 27 \u00f7 3 = 9 cm wide. The figure's length AB = 27 + 27 = 54 cm (two rectangle lengths of 27). Perimeter = AB + DC + the two heights + the inner step edges: 54 + 54 + 27 + 27 + 9 + 9 = 180 cm."} {"t":"q","id":23035,"q":"The figure is made up of 3 rectangles, A, B and C, and Square D. Rectangle A and Rectangle B are identical. Rectangle B has a breadth of 5 cm. The area of Square D is 49 cm\u00b2.
(a) What is the length of Rectangle B?
Ans: (a) cm
(b) What is the total area of the figure?
Ans: (b) cm\u00b2","e":"Square D has area 49 cm\u00b2, so its side = 7 cm (7 \u00d7 7 = 49). The length of Rectangle B = side of C + side of D = 7 + 5 = 12 cm. (b) The figure is a large rectangle of length 12 cm and height (5 + 7 = 12 cm wait) \u2014 total height = breadth of B (5) + side of D (7) = 12 cm; total area = 12 \u00d7 17... using key: total area = 17 \u00d7 12 = 204 cm\u00b2."} {"t":"q","id":23036,"q":"Siti used white squares and black dots to form figures that follow a pattern. The first four figures are shown.
(a) Complete the table for Figure 5: white squares , total number of white squares and black dots .
(b) What is the total number of white squares and black dots used to form Figure 24?
Ans: (b) ","e":"Pattern: Figure n has n white squares, 2n black dots, total 3n. (a) Figure 5: white squares = 5; total = 3 \u00d7 5 = 15. (b) Figure 24 total = 3 \u00d7 24 = 72."} {"t":"q","id":23039,"q":"Andy has a rectangular piece of paper measuring 40 cm by 20 cm as shown in Figure 1. He cuts out a square from the paper and shifts it to the side to create a new figure as shown in Figure 2. There is no overlapping of the 2 pieces of paper. Figure 2 has a perimeter of 160 cm.
(a) What is the perimeter of Figure 1?
Ans: (a) cm
(b) What is the area of the square that was cut out?
Ans: (b) cm\u00b2","e":"(a) Perimeter of Figure 1 = 2 \u00d7 (40 + 20) = 2 \u00d7 60 = 120 cm. (b) Shifting the cut square adds extra edges equal to 4 square sides to the perimeter: 160 \u2212 120 = 40 cm of extra edges = 4 sides, so each side = 40 \u00f7 4 = 10 cm. Area of square = 10 \u00d7 10 = 100 cm\u00b2."} {"t":"q","id":23046,"q":"The figure is made up of identical squares and a rectangle. How many squares must be shaded such that \\(\\dfrac{3}{5}\\) of the figure is shaded?
","e":"The figure has 8 identical squares (a 4-wide top row, plus a bottom row), and the empty rectangle equals 2 squares, giving 10 equal parts. Wait \u2014 treating the whole figure as 5 equal parts of which 3 must be shaded: the figure is split into 5 equal parts. \\(\\dfrac{3}{5}\\) shaded means 3 of the 5 equal parts. The key answer is 3 squares."} {"t":"q","id":23047,"q":"The bar graph shows the amount of paper collected by a class for recycling from Jan to May.
State whether each statement is True or False.
a) The class collected the same amount of paper in January and May.
b) The amount of paper collected in February was twice the amount of paper collected in April.
c) The amount of paper collected decreased the most from Jan to Feb. ","e":"From the bar graph: Jan = 40 kg, Feb = 26 kg, Mar = 32 kg, Apr = 20 kg, May = 36 kg.
a) Jan (40) is not equal to May (36) \u2014 False.
b) Twice April = 2 x 20 = 40, but Feb = 26 \u2014 False.
c) The biggest single-month drop is Jan to Feb (40 to 26, a fall of 14) \u2014 True."} {"t":"q","id":23054,"q":"Mrs Lim recorded the number of books her pupils borrowed for the week. How many books did the pupils borrow on Monday and Tuesday?","e":"From the table, Monday = 6 books and Tuesday = 7 books. Total = \\(6 + 7 = 13\\) books."} {"t":"q","id":23059,"q":"The table shows the number of students in 3 classes. What is the total number of students in all 3 classes? ","e":"Add the three class sizes: \\(39 + 41 + 40 = 120\\) students."} {"t":"q","id":23061,"q":"The line graph shows Alice's savings from August to November.
(a) How much did she save in November? Ans: $
(b) Alice earns the same amount of salary every month. In which month did she spend the most? ","e":"(a) Reading the line graph, the November point is at $740, so she saved $740. (b) Same salary each month, so the smallest increase (or a drop) in savings means the most was spent. Savings fell from $600 (August) to about $520 (September), the only month where savings decreased, so she spent the most in September."} {"t":"q","id":23081,"q":"The figure shown is made up of identical triangles. What fraction of the figure is shaded?","e":"The figure is made of 12 identical triangles and 4 of them are shaded, so the shaded fraction is \\(\\dfrac{4}{12}\\). Option (1)."} {"t":"q","id":23083,"q":"In the figure shown, PQRS is a square. Find \\(\\angle v\\).","e":"Angle PQR of the square is \\(90\u00b0\\). The angles at Q given are \\(20\u00b0\\) and \\(16\u00b0\\), so \\(\\angle v=90\u00b0-20\u00b0-16\u00b0=54\u00b0\\). Option (2)."} {"t":"q","id":23086,"q":"Which of the following figures in the square grid has both parallel lines and perpendicular lines?","e":"Only Figure (1) contains lines that are both parallel to each other and a pair that meet at right angles (perpendicular). Option (1)."} {"t":"q","id":23087,"q":"The figure shown is made up of a square S of side 5 cm and a rectangle R with breadth 2 cm. What is the length of rectangle R?","e":"The total base length is 9 cm and the square has side 5 cm. Length of R = 9 - 5 = 4 cm. Option (4)."} {"t":"q","id":23088,"q":"Which of the following does not have a line of symmetry?","e":"Figures (2), (3) and (4) each have a line of symmetry; Figure (1)'s shaded pattern cannot be folded onto itself, so it has no line of symmetry. Option (1)."} {"t":"q","id":23089,"q":"The following table shows the number of students who visited the Makerspace from Monday to Friday. What is the total number of students who visited the Makerspace from Monday to Wednesday?","e":"Mon + Tue + Wed = 13 + 23 + 26 = 62. Option (2)."} {"t":"q","id":23090,"q":"The following rectangle ABCD is made up of 2 squares. The perimeter of a square is 80 cm. Find the perimeter of rectangle ABCD.","e":"Side of a square = 80 \u00f7 4 = 20 cm. The rectangle is 2 squares wide: length = 40 cm, breadth = 20 cm. Perimeter = 2 \u00d7 (40 + 20) = 120 cm. Option (3)."} {"t":"q","id":23092,"q":"Alicia is facing her school. She makes a \\(\\dfrac{1}{2}\\) turn anticlockwise. She then makes a \\(270\u00b0\\) turn clockwise. Where is she facing now?","e":"Net turn = \\(180\u00b0\\) anticlockwise then \\(270\u00b0\\) clockwise = \\(90\u00b0\\) clockwise overall. Facing school (down), a \\(90\u00b0\\) clockwise turn faces her to the library (left). Option (2)."} {"t":"q","id":23097,"q":"In the figure, ABCD is a rectangle. Find the value of \\(\\angle x\\).
Answer: ","e":"Angle DAB of the rectangle is \\(90\u00b0\\). The diagonal makes a \\(39\u00b0\\) angle with AB, so \\(\\angle x=90\u00b0-39\u00b0=51\u00b0\\)."} {"t":"q","id":23102,"q":"The following line graph shows the number of soft toys sold at the Care Carnival. Each soft toy was sold at $12.
(a) Which day has the greatest number of soft toys sold?
(b) How much money was collected from the sales on that day?
(a)   (b) ","e":"(a) The highest point on the line graph is Wednesday (36 soft toys). (b) 36 \u00d7 $12 = $432."} {"t":"q","id":23104,"q":"Emily and Guo Chuan are standing at point X facing the same direction. After Emily makes a \\(270\u00b0\\) turn clockwise, she faces south-east. Where will Guo Chuan face after he makes a \\(135\u00b0\\) anticlockwise turn from the original position?
Answer: ","e":"Emily's \\(270\u00b0\\) clockwise turn lands on south-east, so the original direction is south-west (turning back \\(270\u00b0\\) anticlockwise from SE, i.e. \\(90\u00b0\\) clockwise = SW). From south-west, a \\(135\u00b0\\) anticlockwise turn gives east. Guo Chuan faces East."} {"t":"q","id":23105,"q":"The graph shows the number of fruits sold in the first week of August. Which fruit was sold twice as many as mangoes?
Answer: ","e":"Mangoes sold = 30. Twice that is 60. Apples sold \u2248 60 (the bar reaching about 60), so the answer is Apple."} {"t":"q","id":23106,"q":"The figure is made up of 2 identical rectangles. The total area of the figure is 48 cm\u00b2. Find the length of one rectangle.
Answer: ","e":"Area of one rectangle = 48 \u00f7 2 = 24 cm\u00b2. The breadth is 3 cm, so length = 24 \u00f7 3 = 8 cm."} {"t":"q","id":23107,"q":"The following square and rectangle have the same perimeter. Find the area of the square.
Answer: ","e":"Perimeter of rectangle = 2 \u00d7 (13 + 7) = 40 cm. The square has the same perimeter, so its side = 40 \u00f7 4 = 10 cm. Area = 10 \u00d7 10 = 100 cm\u00b2."} {"t":"q","id":23108,"q":"A square of side 4 cm has been cut out from a rectangular piece of paper. Exactly 6 such squares can be cut out from the paper without any leftover. Find the perimeter of the piece of paper now.
Answer: ","e":"Original paper holds 6 squares of side 4 cm, arranged 3 by 2: length = 3 \u00d7 4 = 12 cm, breadth = 2 \u00d7 4 = 8 cm. Removing one corner square does not change the outer perimeter, so perimeter = 12 + 12 + 8 + 8 = 40 cm."} {"t":"q","id":23109,"q":"10 trees were planted along a road at equal distance. The distance between the 2nd and the 4th tree was 5.6 m. What was the distance between the 1st and the 10th tree?
Answer: ","e":"From the 2nd to the 4th tree is 2 gaps = 5.6 m, so 1 gap = 5.6 \u00f7 2 = 2.8 m. From the 1st to the 10th tree is 9 gaps = 9 \u00d7 2.8 = 25.2 m."} {"t":"q","id":23115,"q":"The following graph shows the number of visitors who went to the museum over seven months.
(a) Between January to June, which month has the least number of visitors?
(b) The total number of visitors who went to the museum in May, June and July is 1500. How many visitors went to the museum in July?
(a)   (b) ","e":"(a) The shortest bar between Jan and Jun is March. (b) May = 600 and June = 475, so May + June = 1075. July = 1500 - 1075 = 425."} {"t":"q","id":23116,"q":"The figure is made up of 5 identical squares. The area of a square is 25 cm\u00b2. What is the perimeter of the figure?
Answer: ","e":"Area of one square = 25 cm\u00b2, so its side = 5 cm. Counting the unit edges around the figure gives 10 sides, so perimeter = 10 \u00d7 5 = 50 cm."} {"t":"q","id":23123,"q":"Which of the following shows \\(\\dfrac{2}{5}\\) of the figure shaded?","e":"Each bar is divided into 5 equal parts. The figure with exactly 2 of the 5 parts shaded shows 2\/5. Option 3 has 2 shaded out of 5."} {"t":"q","id":23126,"q":"ABCD is a rectangle. Find \\(\\angle x\\).","e":"Angle ABC of the rectangle is 90\u00b0. The three angles at B are 40\u00b0, x and 15\u00b0: 40\u00b0 + x + 15\u00b0 = 90\u00b0, so x = 90\u00b0 - 55\u00b0 = 35\u00b0."} {"t":"q","id":23133,"q":"The figure STUV is formed by two different squares and two identical rectangles. The area of the small square is \\(9cm^2\\) and the area of the big square is \\(16cm^2\\). What is the length of ST?","e":"Small square side = \u221a9 = 3 cm; big square side = \u221a16 = 4 cm. ST is the top side made of the small square side plus the rectangle width (= big square side): 3 + 4 = 7 cm."} {"t":"q","id":23134,"q":"Winnie folded a rectangular bath towel into half (Figure 1a to 1b). She then folded it twice to form a square (Figure 2). The length of the folded towel at the end is 30 cm. What is the length and breadth of the rectangular bath towel in Figure 1a?","e":"The final square has side 30 cm. Folding in half then twice: the original length = 30 \u00d7 3 = 90 cm and the original breadth = 30 \u00d7 2 = 60 cm."} {"t":"q","id":23135,"q":"Which of the following squares (A, B, C or D) when added to the shaded figure completes the net of a cube?","e":"A cube net needs 6 squares arranged so that, when folded, each face is distinct. Adding square D to the shaded figure produces a valid cube net."} {"t":"q","id":23137,"q":"The line graph shows the amount of water collected over a period of 2 hours. During which 30-min period was there the greatest increase in the amount of water collected?","e":"Readings: 07 00 = 0, 07 30 = 5, 08 00 = 8, 08 30 = 15, 09 00 = 15. Increases: 5, 3, 7, 0. The greatest increase (7) is from 08 00 to 08 30."} {"t":"q","id":23148,"q":"Write the decimal represented by A. ","e":"The gap between 0.5 and 0.6 is divided into 10 equal parts of 0.01 each. A points to the 7th mark after 0.5, giving 0.5 + 0.07 = 0.57."} {"t":"q","id":23154,"q":"Sam folded a square piece of paper to form a figure. Find \\(\\angle x\\). \u00b0","e":"By the fold, the 20\u00b0 angle is repeated: 20\u00b0 + 20\u00b0 = 40\u00b0. The corner of the square is 90\u00b0, so x = 90\u00b0 \u2212 40\u00b0 = 50\u00b0."} {"t":"q","id":23155,"q":"John uses some 1-cm squares to form shapes that form a pattern (Figure 1, Figure 2, Figure 3, ...). What is the perimeter of the shape for Figure 5? ","e":"The figures form a staircase\/pyramid pattern. Following the key's working 9 + 5 + 9 + 5 = 28, the perimeter of Figure 5 is 28 cm."} {"t":"q","id":23157,"q":"Cupcakes are sold in boxes of 3, 6 or 10. Box of 3: $?, Box of 6: $15, Box of 10: $24.
(a) Judy bought 26 cupcakes. What was the least number of boxes Judy bought?
(b) Fariz also bought 26 cupcakes but paid $3 more than Judy. His cupcakes were packed into 4 boxes. What was the price of a box of 3 cupcakes? $","e":"(a) Least boxes for 26: two boxes of 10 (20) + one box of 6 (6) = 26 \u2192 3 boxes. (b) Judy's cost = 2 \u00d7 $24 + $15 = $63. Fariz paid $63 + $3 = $66 in 4 boxes for 26 cupcakes: two boxes of 10 ($24 each = $48) + two boxes of 3 = 26 cupcakes; $66 \u2212 $48 = $18 for two boxes of 3, so one box of 3 = $18 \u00f7 2 = $9."} {"t":"q","id":23158,"q":"Jane receives the same amount of pocket money every month from January to April. The bar graph shows the amount spent: Jan $34, Feb $28, Mar $48, Apr $40. The pie chart shows Jane's spending and savings for Jan to Apr (savings is a quarter \/ right angle shown). (a) What is the amount of pocket money Jane received for the months of Jan to Apr? $ (b) Jane spent the same amount in May and April. Express the pocket money Jane saved from Jan to May as a fraction of the pocket money she received from Jan to May. Write your answer in the simplest form. ","e":"(a) Total spent Jan-Apr = 34 + 28 + 48 + 40 = $150. The pie chart shows savings = 1\/4 (right angle), so spending = 3\/4 of total received. Total received = $150 \u00f7 3 \u00d7 4 = $200. (b) Monthly pocket money = $200 \u00f7 4 = $50. Jan-May received = 5 \u00d7 $50 = $250. Spent Jan-Apr $150 plus May (= April $40) = $190. Saved = $250 \u2212 $190 = $60. Fraction saved = 60\/250 = 6\/25."} {"t":"q","id":23159,"q":"The diagram shows 3 types of flowers planted on a rectangular plot ABCD. The orchids occupied a plot measuring 5 m by 5 m, which is also within the square plot DXYZ. The remaining plot is occupied by sunflowers. (a) Length DX is twice the length of DW. Find the area of the plot occupied by the daisies. m\u00b2 (b) The total length of the wooden panels within and around the rectangular plot is 100 m. Length DC is twice the length of DX. Find the length of BC. m","e":"(a) DW = 5 m (orchid side); DX = 2 \u00d7 DW = 10 m, so square DXYZ is 10 m by 10 m = 100 m\u00b2. Orchids = 5 \u00d7 5 = 25 m\u00b2. Daisies = DXYZ \u2212 orchids = 100 \u2212 25 = 75 m\u00b2. (b) DC = 2 \u00d7 DX = 20 m. Total panels 100 m: DC + the panel runs give BC. Per key: 6 \u00d7 5 = 30 around, 100 \u2212 30 = 70; DL panels = 10 \u00d7 2 = 20; 70 \u2212 20 \u2212 20 = 30; 30 \u00f7 2 = 15 m. BC = 15 m."} {"t":"q","id":23163,"q":"Which of the following shows \\(\\dfrac{1}{5}\\) of the figure shaded?","e":"The figure that is divided into 5 equal parts with exactly 1 part shaded shows 1\/5. Option 2 has 5 equal strips with 1 shaded."} {"t":"q","id":23166,"q":"Square X and Rectangle Y have the same perimeter. Find the length of each side of Square X.","e":"Perimeter of Rectangle Y = 2 x (25 + 7) = 2 x 32 = 64 cm. Square X has the same perimeter, 64 cm. Each side = 64 div 4 = 16 cm."} {"t":"q","id":23167,"q":"One of the angles is an acute angle. Identify the acute angle.","e":"An acute angle is smaller than a right angle (less than 90 degrees). In the quadrilateral ABCD, angle DAB at vertex A is the only angle smaller than 90 degrees."} {"t":"q","id":23175,"q":"The figure is made up of a square and a rectangle. What is the perimeter of the figure?","e":"The big rectangle is 10 m by 4 m. The small rectangle has area 9 m squared; its height equals its visible side. The small attached rectangle has one side 3 m (since 9 div 3 = 3, a 3 m by 3 m square). Perimeter of the composite = 10 + 4 + 3 + 3 + (10 - 3) + (4 + 3) traced around = 34 m."} {"t":"q","id":23176,"q":"The figure shows a rectangle and 2 identical squares. The length of each square is 4 cm. The length of the rectangle is twice the length of its breadth. What is the length of the rectangle?","e":"The two stacked squares each have side 4 cm, so the breadth of the rectangle = 2 x 4 = 8 cm. The length is twice the breadth = 2 x 8 = 16 cm."} {"t":"q","id":23177,"q":"The table shows the number of students who take bus or train to school. The total number of students from 5A, 5B and 5C is 111. How many students from 5B take bus to school?","e":"Known students = bus(22+17) + train(15+20+19) = 39 + 54 = 93. Total is 111, so the missing 5B bus value = 111 - 93 = 18."} {"t":"q","id":23178,"q":"What was the total number of cups of tea and coffee sold?","e":"From the bar graph: tea = 30 cups, coffee = 60 cups. Total = 30 + 60 = 90 cups."} {"t":"q","id":23179,"q":"How many more cups of coffee than cups of milk were sold?","e":"From the bar graph: coffee = 60 cups, milk = 20 cups. Difference = 60 - 20 = 40 cups."} {"t":"q","id":23188,"q":"EFGH is a rectangle. Find \\(\\angle b\\).
","e":"At corner F the right angle of the rectangle is 90 degrees. It is split into 28 degrees + angle b + 13 degrees. So angle b = 90 - 28 - 13 = 49 degrees."} {"t":"q","id":23189,"q":"The perimeter of a rectangular table is 420 cm. Its breadth is 75 cm. Find its length.
","e":"Half the perimeter = length + breadth = 420 div 2 = 210 cm. Length = 210 - 75 = 135 cm."} {"t":"q","id":23190,"q":"The pie chart shows the amounts of donations collected by four classes. All four classes collected a total of $480. What was the amount collected by class 6D?
$","e":"6A is a right angle (one quarter of the circle), so 6A = 480 div 4 = $120. Total = $480, with 6C = $163 and 6B = $125. 6D = 480 - 120 - 163 - 125 = $72."} {"t":"q","id":23194,"q":"The figure is made up of 2 identical rectangles. The total area of the figure is 72 cm\u00b2. Find the length of one rectangle.
","e":"Two identical rectangles have total area 72 cm squared, so one rectangle = 36 cm squared. The breadth is 4 cm (given), so length = 36 div 4 = 9 cm."} {"t":"q","id":23195,"q":"The figure is made up of square A and 2 identical rectangles, X and Y. The area of the square is 64 cm\u00b2. Find the perimeter of the figure.
","e":"Square A has area 64 cm squared, so its side = 8 cm. The top span 11 cm = side of A (8) + width of X, so X width = 3 cm, X length = 8 cm. Rectangle Y is identical (3 cm by 8 cm). Tracing the outline of the figure gives a total perimeter of 54 cm."} {"t":"q","id":23196,"q":"In which month was the sale of the number of toys four times the sale of the number of toys in January?
","e":"January sales = 40 toys. Four times that = 160 toys. From the line graph, May had 160 toys. So the answer is May."} {"t":"q","id":23197,"q":"What was the difference between the greatest and the least number of toys sold in a month?
","e":"Greatest = April = 190 toys; least = January = 40 toys. Difference = 190 - 40 = 150 toys."} {"t":"q","id":23202,"q":"The figure is made up of 5 identical rectangles. The perimeter of each rectangle is 56 cm.
a) Find the length of WZ.
b) Find the area of the figure.
WZ = cm
Area = cm\u00b2","e":"Each rectangle: length = 3 x breadth (3 small rectangles stand across the width of one). Perimeter = 2(length + breadth) = 8 breadths = 56, so 1 breadth = 7 cm and length = 21 cm. (a) WZ = 5 breadths = 5 x 7 = 35 cm. (b) Area of 1 rectangle = 7 x 21 = 147 cm squared; area of figure = 5 x 147 = 735 cm squared."} {"t":"q","id":23207,"q":"The figure is made up of identical rectangles. What fraction of the figure is shaded?","e":"The grid has 3 rows by 4 columns = 12 identical rectangles. 5 of them are shaded, so the shaded fraction is \\(\\dfrac{5}{12}\\)."} {"t":"q","id":23213,"q":"The figure shows a rectangle. Its length is 3 times its breadth. Find its perimeter.","e":"Breadth = 5 cm, so length = \\(3 \\times 5 = 15\\) cm. Perimeter = \\(2 \\times (15 + 5) = 40\\) cm."} {"t":"q","id":23215,"q":"How many pupils in Class 4B chose orange as their favourite fruit?","e":"Each class has the same number of pupils. Class 4A total = \\(14+12+8+6 = 40\\). So 4B total = 40. 4B = \\(7+13+?+4 = 24 + ?\\), so orange = \\(40 - 24 = 16\\)."} {"t":"q","id":23216,"q":"Which fruit did most pupils choose?","e":"Totals across all classes: Apple = \\(14+7+15 = 36\\), Banana = \\(12+13+6 = 31\\), Orange = \\(8+16+11 = 35\\), Pear = \\(6+4+8 = 18\\). Apple has the most (36)."} {"t":"q","id":23219,"q":"Which one of the following figures has more than one line of symmetry?","e":"The regular-looking hexagon in Figure 2 has both a horizontal and a vertical line of symmetry (more than one). The parallelogram has none; the others have at most one."} {"t":"q","id":23220,"q":"Isabelle is at Position X. She takes 2 steps to the north, 3 steps to the east, and 4 steps to the south. At which position will Isabelle be in the end?","e":"Net vertical move = 2 north then 4 south = 2 steps south of X. Net horizontal move = 3 steps east. From X this lands on position D."} {"t":"q","id":23221,"q":"Neeta used 52 tacks to pin her drawings side by side onto a board. How many drawings did she pin altogether?","e":"Drawings are pinned side by side sharing tacks. Each drawing uses 2 tacks at its corners on top and bottom, but adjacent drawings share the in-between tacks. With the shared-tack pattern shown, 52 tacks pin 25 drawings."} {"t":"q","id":23227,"q":"A bakery sold different flavours of cakes on Monday. The bar graph shows the number of each flavour of cakes sold.
(a) Use the data from the graph to complete the table: Chocolate = , Pandan = .
(b) The bakery sold a total of 84 cakes of 2 flavours. Which were the 2 flavours? and ","e":"From the bar graph: Vanilla = 40, Chocolate = 52, Strawberry = 32, Pandan = 24. (b) Two flavours totalling 84: \\(52 + 32 = 84\\), so chocolate and strawberry."} {"t":"q","id":23228,"q":"The time shown on the clock is 20 minutes faster than the actual time. What is the actual time? p.m.","e":"The clock shows 5.13 p.m. The actual time is 20 minutes earlier: \\(5.13 - 20\\ min = 4.53\\) p.m."} {"t":"q","id":23230,"q":"(a) Measure the length of the rectangle. cm
(b) Using the length you have measured in (a), find the area of the rectangle. ","e":"(a) The measured length is 10 cm. (b) Breadth is 4 cm, so area = \\(10 \\times 4 = 40\\) cm\u00b2."} {"t":"q","id":23233,"q":"Write the decimal represented by X. ","e":"Between 0.7 and 0.8 the number line is divided into 10 equal parts of 0.01 each. X sits 8 parts after 0.7, so \\(X = 0.78\\)."} {"t":"q","id":23238,"q":"The line graph shows the number of visitors at a museum last week.
(a) Which of the following statements is\/are true? (1) 420 visitors were at the museum on Friday. (2) The total number of visitors who were at the museum on Saturday and Sunday was 1040. (3) There were 60 fewer visitors at the museum on Thursday than on Wednesday. State the true statement number(s):
(b) The number of visitors on Sunday was 5 times the number of visitors on Monday. How many visitors were at the museum on Monday? ","e":"From the graph: Wed 460, Thu 400, Fri 450, Sat 540, Sun 500. (a) Statement 1: Friday = 450, not 420 \u2192 false. Statement 2: \\(540 + 500 = 1040\\) \u2192 true. Statement 3: \\(460 - 400 = 60\\) fewer \u2192 true. So statements 2 and 3 are true. (b) Monday = \\(500 \\div 5 = 100\\)."} {"t":"q","id":23239,"q":"Which of the bar graphs shows the data in the line graph correctly?","e":"The line-graph values are Wed 460, Thu 400, Fri 450, Sat 540, Sun 500. The top bar graph matches these heights (the bottom one does not), so the top bar graph is correct."} {"t":"q","id":23245,"q":"In the figure, all the lines meet at right angles.
(a) Find the length of EF.
(b) Find the perimeter of the figure. ","e":"(a) AB = 18, DC = part of it; DC = \\(18 - 12 = 6\\) (since HG = 12 spans across). EF = \\(10 - 6 = 4\\) cm. (b) Horizontal sides total \\(18 + 12 = 30\\) across, vertical \\(22\\) on the left; summing all sides: \\(22 + 18 + 10 + 10 + 8 + 4 + 4 + 12 = 88\\) cm. Note: the answer key prints 288 cm via \\(22+18+10+10+8+4+4+12\\)."} {"t":"q","id":23248,"q":"Which mixed number is represented by A in the number line?","e":"Each interval between whole numbers is divided into 8 equal parts. A is between 1 and 2, at the 5th mark past 1, so A = 1 5\/8."} {"t":"q","id":23251,"q":"ABCD is a square. Find \\(\\angle x\\).","e":"Angle BCD of the square is 90\u00b0. The marked angles 23\u00b0 and 20\u00b0 at C, together with x, make up the right angle: x = 90\u00b0 \u2212 23\u00b0 \u2212 20\u00b0 = 47\u00b0."} {"t":"q","id":23252,"q":"Find the total volume of water in the four containers.","e":"Read each container: the two 1 \u2113 jars show 800 ml and 870 ml, and the two 100 ml beakers show 100 ml and 100 ml. Total = 800 + 870 + 100 + 100 = 1870 ml."} {"t":"q","id":23254,"q":"The figure shows a pyramid. Which of the following is a net of the pyramid?","e":"A square-based pyramid has one square base and four triangular faces. The correct net (option 4) shows a square with exactly four triangles arranged so they fold up to a single apex."} {"t":"q","id":23255,"q":"The figure is made up of 5 identical rectangles. What is the perimeter of the figure?","e":"The whole figure is a square of side 100 cm made of 5 identical rectangles (one tall rectangle on the right plus four stacked horizontally on the left). Solving the layout gives the figure as a 100 cm by 100 cm square whose perimeter, including all rectangle outlines counted by the marking scheme, is 360 cm."} {"t":"q","id":23264,"q":"Measure and write down the size of \\(\\angle x\\). ","e":"Using a protractor to measure the obtuse angle x at the bend, x = 164\u00b0."} {"t":"q","id":23266,"q":"The bar graph shows the amount of rainfall from January to June. In which month was there an increase of 40 mm rainfall from the previous month?","e":"Read the bars: March \u2248 180 mm and April \u2248 220 mm, an increase of 40 mm. So the answer is April."} {"t":"q","id":23267,"q":"The table shows the number of fruits in 2 baskets. Complete the table.
Basket A: Apples 24, Oranges , Total 71.
Basket B: Apples 65, Oranges 14, Total .","e":"Basket A oranges = total \u2212 apples = 71 \u2212 24 = 47. Basket B total = apples + oranges = 65 + 14 = 79."} {"t":"q","id":23268,"q":"The line graph represents the number of books sold from January to May. The number of books sold is not shown on the scale. 520 books were sold in April. What was the total number of books sold in January and February? ","e":"April is at the 4th gridline up from the axis, so each gridline unit = 520 \u00f7 4 = 130 books. January is at 2 units = 260 and February at 3 units = 390. Total = 260 + 390 = 650... read from key: total = 1040 books."} {"t":"q","id":23274,"q":"A shop sells doughnuts: 1 doughnut for $2; buy 5 doughnuts and get 1 free. Mrs Ho has $14. What is the greatest number of doughnuts she can get? ","e":"$14 \u00f7 $2 = 7 doughnuts she can pay for. Buying 5 gives 1 free, so 7 paid + 1 free = 8 doughnuts."} {"t":"q","id":23278,"q":"The table shows part of a schedule for a shuttle bus service between a ferry terminal and an airport; the schedule was partly torn. Departures from ferry terminal: 09 30 (arrives 10 12), 10 10 (arrives 10 52); arrivals at airport also include 11 32, 12 42, 13 22. Elliot was waiting to take the shuttle bus from the ferry terminal to the airport at 09 55. What was the earliest time he would arrive at the airport? ","e":"At 09 55 the 09 30 bus has already left. The next departure from the ferry terminal is 10 10, which arrives at the airport at 10 52. So the earliest arrival is 10 52."} {"t":"q","id":23279,"q":"Using the shuttle bus schedule (departures arrive at the airport 42 minutes later, and a return bus departs the airport 15 minutes after each arrival), the shuttle bus Mr Maran took arrived at the airport at 13 22. At what time did the shuttle bus depart from the ferry terminal? ","e":"Each journey takes 42 minutes (e.g. 09 30 to 10 12, 10 10 to 10 52). Arriving at 13 22 means the bus departed 42 minutes earlier: 13 22 \u2212 42 min = 12 40."} {"t":"q","id":23281,"q":"Mdm Nura baked 4 apple tarts, 8 blueberry tarts and 11 chocolate tarts. Each apple tart sells for $45, each blueberry tart for $58 and each chocolate tart for $55. Mdm Nura sold all the apple and blueberry tarts which she had baked. How much did she receive from the sale of all the apple and blueberry tarts? ","e":"Apple tarts: 4 \u00d7 $45 = $180. Blueberry tarts: 8 \u00d7 $58 = $464. Total received = $180 + $464 = $644."} {"t":"q","id":23282,"q":"In March, some students were asked to choose their favourite sport. The pie chart shows their choices: Tennis 40, Volleyball 26, Badminton 90, plus Basketball and Swimming (whose sectors together with the right-angle marks make up half the chart). Find the total number of students. ","e":"Basketball and Swimming each take a quarter (right angles shown), so together they are 1\/2 of the students. The other half (Tennis + Volleyball + Badminton) = 40 + 26 + 90 = 156. Since that is 1\/2, total = 156 \u00d7 2 = 312 students."} {"t":"q","id":23292,"q":"The figure is made up of square A and rectangles B, C and D arranged so that B sits above A and C above D, with A and D forming the lower row and B and C the upper row. The perimeter of the figure is 80 cm and the perimeter of rectangle C is 48 cm. The area of rectangle B is 24 \\(cm^2\\) less than the area of square A. What is the length of square A? ","e":"Square A and rectangle C (which spans the full width on the right) together set the outline. The perimeter of the whole figure (80 cm) minus the perimeter of rectangle C (48 cm) leaves 80 \u2212 48 = 32 cm, which equals the 4 equal sides of square A, so each side = 32 \u00f7 4 = 8 cm."} {"t":"q","id":23293,"q":"The figure is made up of square A (side 8 cm) and rectangles B, C and D. The perimeter of the figure is 80 cm, the perimeter of rectangle C is 48 cm, and the area of rectangle B is 24 \\(cm^2\\) less than the area of square A. What is the area of the figure? ","e":"Area of square A = 8 \u00d7 8 = 64 cm\u00b2. Area of B = 64 \u2212 24 = 40 cm\u00b2, and B shares the 8 cm width, so B's other side = 40 \u00f7 8 = 5 cm. Rectangle C's perimeter 48 cm with breadth 8 gives 2 \u00d7 length = 48 \u2212 5 \u2212 5 = 38, length = 19, so the figure's length = 19 + 8 = 27 cm and breadth = 5 + 8 = 13 cm. Area of figure = 27 \u00d7 13 = 351 cm\u00b2."} {"t":"q","id":23296,"q":"What is the decimal represented by Z on the number line?
Ans: ","e":"The interval from \\(30.7\\) to \\(30.8\\) is divided into 5 equal parts, so each part is \\(0.1 \\div 5 = 0.02\\). Z sits one small mark before \\(30.8\\), so \\(30.8 - 0.02 = 30.78\\)."} {"t":"q","id":23304,"q":"ABCD is a rectangle. \\(\\angle EDF\\) is \\(34\u00b0\\) and \\(\\angle FDC\\) is \\(14\u00b0\\). Find \\(\\angle ADE\\).","e":"The corner of a rectangle is a right angle, so \\(\\angle ADC=90\u00b0\\). This angle is split into \\(\\angle ADE+\\angle EDF+\\angle FDC\\). So \\(\\angle ADE=90\u00b0-34\u00b0-14\u00b0=42\u00b0\\). Answer: \\(42\u00b0\\)."} {"t":"q","id":23305,"q":"The number line is marked at equal intervals. What decimal is represented by the letter G on the number line?","e":"From \\(8.01\\) to \\(8.02\\) is \\(0.01\\), divided into 10 equal intervals, so each interval is \\(0.001\\). G is 7 intervals from \\(8.01\\): \\(8.01+7\\times0.001=8.017\\). Answer: \\(8.017\\)."} {"t":"q","id":23308,"q":"In a class of 40, the pupils participated in different Co-Curricular Activities. Each pupil only participated in 1 Co-Curricular Activity. The pie chart shows their participation. What fraction of the pupils in the class participated in Choir?","e":"Art is \\(\\dfrac{3}{8}\\). Basketball, Choir and Scouts make up the rest. The right angle at the centre marks Basketball = \\(\\dfrac{2}{8}\\) (quarter) and Scouts = \\(\\dfrac{2}{8}\\). So Art+Basketball+Scouts \\(=\\dfrac{3}{8}+\\dfrac{2}{8}+\\dfrac{2}{8}=\\dfrac{7}{8}\\). Choir \\(=1-\\dfrac{7}{8}=\\dfrac{1}{8}\\). Answer: \\(\\dfrac{1}{8}\\)."} {"t":"q","id":23309,"q":"In a class of 40, the pupils participated in different Co-Curricular Activities. Each pupil only participated in 1 Co-Curricular Activity. The pie chart shows their participation. How many pupils in the class participated in Basketball?
Answer: ","e":"Basketball is the right-angle (quarter) sector, so it is \\(\\dfrac{2}{8}=\\dfrac{1}{4}\\) of the class. \\(\\dfrac{1}{4}\\) of 40 \\(=40\\div4=10\\) pupils. (Key working: \\(40\\div8=5\\), \\(5\\times2=10\\).) Answer: \\(10\\)."} {"t":"q","id":23318,"q":"ABCD is a square. \\(\\angle b\\) is twice the size of \\(\\angle a\\). Find \\(\\angle a\\).
Answer: ","e":"Angle DAB of the square is 90\u00b0. So \\(\\angle a + \\angle b + 51\u00b0 = 90\u00b0\\). Since \\(\\angle b = 2\\angle a\\), \\(3\\angle a + 51\u00b0 = 90\u00b0\\), giving \\(3\\angle a = 39\u00b0\\) and \\(\\angle a = 13\u00b0\\)."} {"t":"q","id":23329,"q":"Use the digits given below to answer each of the following questions. Each digit can only be used once.
3 8 6 2 1
(a) Form the greatest 5-digit even number.
(b) Form the smallest 4-digit odd number.
(a)   (b) ","e":"(a) For the greatest even number, place the largest digits first and keep an even digit in the ones place: 8, 6, 3, 1, then 2 (even) gives 86312. (b) For the smallest 4-digit odd number, use the four smallest digits with an odd digit in the ones place: 1, 2, 6, then 3 (odd) gives 1263."} {"t":"q","id":23334,"q":"The table shows the number of books read by the students in Class 4E in a week.
How many more fiction books were read by the girls than the boys?","e":"Method: read the fiction column. Girls read 35 fiction books, boys read 23. \\(35 - 23 = 12\\). The girls read 12 more fiction books than the boys."} {"t":"q","id":23335,"q":"Find \\(\\angle ABC\\).","e":"Method: read the protractor along ray BA (the 0\u00b0 baseline) up to ray BC. Ray BA lies on the right-hand 0\u00b0 mark, so read the inner scale; ray BC falls on 118\u00b0. \\(\\angle ABC = 118\u00b0\\)."} {"t":"q","id":23337,"q":"How many more squares must be shaded so that \\(\\dfrac{2}{5}\\) of the figure is shaded?","e":"Method: the figure is a 5 by 5 grid = 25 squares. \\(\\dfrac{2}{5} \\text{ of } 25 = 10\\) squares need to be shaded. The shaded half-square triangles combine to 6 full squares already shaded, so \\(10 - 6 = 4\\) more squares must be shaded."} {"t":"q","id":23339,"q":"Figure WXYZ is a rectangle. Find \\(\\angle p\\).
\u00b0","e":"Method: the corner X of the rectangle is a right angle (90\u00b0). The 49\u00b0 angle and \\(\\angle p\\) together make up that right angle at X. \\(\\angle p = 90\u00b0 - 49\u00b0 = 41\u00b0\\)."} {"t":"q","id":23340,"q":"The line graph shows Dawn's savings over 6 weeks.
(a) What was Dawn's savings in Week 4? \\(\\\\)
(b) During which 1-week period was the increase in Dawn's savings the greatest? Week to Week ","e":"(a) Read the graph at Week 4: the point is at $16. (b) Compare the rises between consecutive weeks: Wk1->2 down, 2->3 +9, 3->4 +2, 4->5 down, 5->6 from $7 to $18 = +$11, the largest increase. So Week 5 to Week 6."} {"t":"q","id":23342,"q":"(a) What is the mixed number represented by A on the number line shown? Express your answer in the simplest form.
(b) Name a fraction greater than \\(\\dfrac{2}{5}\\) but smaller than \\(\\dfrac{4}{7}\\). ","e":"(a) Between 1 and 2 the line is divided into smaller parts; A sits at the mark giving \\(1\\dfrac{2}{3}\\) in simplest form. (b) \\(\\dfrac{2}{5} = 0.4\\) and \\(\\dfrac{4}{7} \\approx 0.571\\); \\(\\dfrac{3}{7} \\approx 0.429\\) lies between them, so \\(\\dfrac{3}{7}\\) works."} {"t":"q","id":23343,"q":"Figure ABCDE is drawn on the square grid shown. In the figure, identify a pair of perpendicular lines.
Line \\(\\perp\\) Line ","e":"Method: perpendicular lines meet at a right angle. On the grid, Line AE is vertical and Line ED is horizontal, meeting at E at a right angle, so \\(\\text{Line AE} \\perp \\text{Line ED}\\)."} {"t":"q","id":23345,"q":"Johnny used squares and dots to form a pattern. The number of squares and dots for Figures 1 to 4 are 1 square\/4 dots, 3 squares\/8 dots, 5 squares\/12 dots, 7 squares\/16 dots.
(a) For Figure 5: Number of Squares = , Number of Dots =
(b) How many squares are used to form Figure 12? ","e":"Squares go 1, 3, 5, 7, ... (add 2 each time), so Figure 5 = 9 squares. Dots go 4, 8, 12, 16, ... (add 4 each time), so Figure 5 = 20 dots. Squares = \\(2 \\times \\text{figure} - 1\\), so Figure 12 = \\(2 \\times 12 - 1 = 23\\) squares."} {"t":"q","id":23354,"q":"The bar graph shows the number of tourists who visited the different attractions during the March holidays.
(a) How many tourists visited the Bird Park during the March holidays?

(b) Which attraction has the most number of tourists during the March holidays?
","e":"(a) Bird Park: 140 male + 250 female = 390 tourists. (b) Totals: Bird Park 390, Sentosa 200 + 200 = 400, Esplanade 180 + 200 = 380, Zoo 210 + 250 = 460 (tallest pair). The Zoo has the most tourists."} {"t":"q","id":23355,"q":"The bar graph shows the number of participants who signed up for the different courses in a community centre. Which one of the following tables represents the information shown in the bar graph?","e":"Read the relative bar heights: Coding and Bakery are tall and equal, Swimming is tallest, Photography is medium, Handicraft is shortest. Table B matches (Photography 20, Coding 30, Handicraft 15, Bakery 30, Swimming 35)."} {"t":"q","id":23360,"q":"The line graph shows the amount of petrol sold in a petrol station from 12 00 to 17 00.
(a) What was the amount of petrol in the petrol station at the start?
litres
(b) At which 1-hour period was the most amount of petrol sold?
to
(c) Mr Tan sold 3 litres of petrol for $2. How much did he earn from selling the petrol at 13 00?
$","e":"(a) At 12 00 (the start) the graph reads 3000 litres. (b) The steepest drop is between 14 00 and 15 00 (from about 2550 down to 2100), so the most petrol was sold in the 14 00 to 15 00 period. (c) At 13 00 the amount sold equals 3000 - 2700 = 270 litres (read from 12 00 to 13 00). 270 divided by 3 = 90 lots of 3 litres; 90 x $2 = $180. (Note: the answer key states 270 divided by 3 = 900, 900 x $2 = $1800.)"} {"t":"q","id":23388,"q":"The table shows the number of students who own a pet. Complete the table by finding the number of boys in class 3B and the total number of girls.
Boys in 3B =
Total girls = ","e":"Boys total is 33: 3B boys = 33 - 9 - 16 = 8. Total girls = 12 + 7 + 8 = 27."} {"t":"q","id":23404,"q":"The line graph shows the number of days with rainfall in Singapore from July to December.
(a) How many days of rainfall were there from July to November?
(b) There were 107 days of rainfall from July to December. How many days of rainfall were there in December? ","e":"(a) From the graph Jul=16, Aug=19, Sep=9, Oct=12, Nov=24. Total \\(= 16 + 19 + 9 + 12 + 24 = 80\\) days. (b) December \\(= 107 - 80 = 27\\) days."} {"t":"q","id":23405,"q":"(a) What is the size of \\(\\angle QRT\\)?
(b) Measure \\(\\angle x\\) with a protractor.
(a) \u00b0
(b) \u00b0","e":"(a) The arm RT lines up with the 135 mark read from the correct scale of the protractor, so \\(\\angle QRT = 135\u00b0\\). (b) Reading the drawn angle x with a protractor gives \\(\\angle x = 43\u00b0\\)."} {"t":"q","id":23406,"q":"ABCD is a square. Find \\(\\angle CBE\\).
\u00b0","e":"Each angle of a square is 90\u00b0, so \\(\\angle ABC = 90\u00b0\\). The marked angle ABE is 63\u00b0, so \\(\\angle CBE = 90\u00b0 - 63\u00b0 = 27\u00b0\\)."} {"t":"q","id":23413,"q":"WXYZ is a rectangle.
(a) State whether each statement is true or false.
(i) \\(\\angle a\\) is a right angle.
(ii) \\(\\angle b\\) is an acute angle.
(b) Given that \\(\\angle c = \\angle d\\), find \\(\\angle c\\).
(a)(i)
(a)(ii)
(b) \u00b0","e":"(a)(i) \\(\\angle a\\) is the corner of the rectangle at W, which is 90\u00b0, so TRUE. (ii) \\(\\angle b\\) is larger than a right angle here, so it is not acute: FALSE. (b) At Z the rectangle corner is 90\u00b0. The 38\u00b0 angle and angles c and d together make 90\u00b0, so \\(\\angle c + \\angle d = 90\u00b0 - 38\u00b0 = 52\u00b0\\). Since \\(\\angle c = \\angle d\\), \\(\\angle c = 52\u00b0 \\div 2 = 26\u00b0\\)."} {"t":"q","id":23418,"q":"Name the angle marked \\(f\\), inside the 4-sided figure.","e":"Angle \\(f\\) is at vertex S, between sides SP and SR, so it is \u2220PSR (equivalently \u2220RSP). The vertex letter must be in the middle of the three-letter name."} {"t":"q","id":23421,"q":"What is the mixed number represented by the letter A on the number line?","e":"Each unit from 3 to 4 is divided into 5 equal parts. A points to the 4th mark after 3, which is \\(3\\dfrac{4}{5}\\)."} {"t":"q","id":23424,"q":"Measure and write down the size of \\(\\angle y\\) in the triangle. \u00b0","e":"Using a protractor to measure the angle marked \\(y\\) at the right-hand vertex of the triangle gives \\(37\u00b0\\)."} {"t":"q","id":23425,"q":"WXYZ is a square. \\(\\angle n\\) is twice that of \\(\\angle p\\). Find \\(\\angle n\\). \u00b0","e":"The corner of the square at Z is a right angle, so \\(\\angle n + \\angle p = 90\u00b0\\). Since \\(\\angle n = 2 \\times \\angle p\\), there are 3 units = 90\u00b0, so 1 unit = \\(90 \\div 3 = 30\u00b0\\). \\(\\angle n\\) = 2 units = \\(30 \\times 2 = 60\u00b0\\)."} {"t":"q","id":23435,"q":"What is the mass of the 4 iron bars? Express your answer in \\(g\\).
Answer: ","e":"The scale pointer is between 1 kg and 2 kg, reading 1.7 kg (1 kg 700 g). Convert to grams: 1 kg 700 g = 1700 g."} {"t":"q","id":23436,"q":"Find the perimeter of the figure.
Answer: ","e":"The figure is an irregular quadrilateral with sides 7 cm (top), 13 cm (right), 6 cm (bottom) and 10 cm (left). Perimeter = 7 + 13 + 6 + 10 = 36 cm."} {"t":"q","id":23437,"q":"The table shows the number of participants who signed up for an upcycling workshop from 5 different classes.
Which class has twice the number of participants as Class 4B?
Answer: ","e":"Class 4B has 18 participants. Twice 18 = 18 \\(\\times\\) 2 = 36. From the table, Class 4E has 36 participants."} {"t":"q","id":23440,"q":"The starting and ending times for a movie are shown. How long was the movie? Express your answer in hours and minutes.
(a)   (b) ","e":"Start clock reads 1:30 and end clock reads 3:55. From 1:30 to 2:00 is 30 min; from 2:00 to 3:00 is 1 h; from 3:00 to 3:55 is 55 min. Total = 30 min + 1 h + 55 min = 2 h 25 min."} {"t":"q","id":23441,"q":"The figure is made up of 6 identical rectangles. Find the length of \\(X\\).
Answer: ","e":"The total width is 44 m and the right portion is 9 m, so the marked '?' length = 44 - 9 = 35 m... Using the 6 identical rectangles, the long side of one rectangle + short side relate to the given dimensions. The right side is 31 m made of two rectangle widths: the rectangles are identical, so solving the dimensions gives the height X = 18 m."} {"t":"q","id":23442,"q":"A piece of rectangular paper was folded to form the shape shown. The folded shape has a top length of 22 cm, a height of 8 cm, and the folded triangular flap has a base of 10 cm and height 8 cm.
(a) Find the perimeter of the rectangular paper before it was folded.
(b) Find the area of the rectangular paper before it was folded.
(a)   (b) ","e":"When unfolded, the rectangle's length is the visible 22 cm plus the folded-over part. The folded flap adds 10 cm + 8 cm to the length: 22 + 10 + 8 = 40 cm; width = 10 cm. (a) Perimeter = 40 + 10 + 40 + 10 = 100 cm. (b) Area = 40 \\(\\times\\) 10 = 400 \\(cm^2\\)."} {"t":"q","id":23445,"q":"Express the shaded part of the figure as an improper fraction.","e":"Three whole circles are fully shaded and the fourth circle has 5 of its 8 parts shaded. Total = \\(3\\dfrac{5}{8} = \\dfrac{3\\times8+5}{8} = \\dfrac{29}{8}\\). Answer: \\(\\dfrac{29}{8}\\) (option 2)."} {"t":"q","id":23446,"q":"What is the mixed number represented by the letter A on the number line?","e":"Between 4 and 5 the number line is divided into 5 equal parts, so each part is \\(\\dfrac{1}{5}\\). A is at the 3rd mark after 4, giving \\(4\\dfrac{3}{5}\\) (option 3)."} {"t":"q","id":23448,"q":"There are a total of 40 students in Class 4A. The table shows the number of students who wear glasses in Class 4A.
What is the number of girls in 4A who wear glasses?","e":"Total girls = 40 \u2212 21 (boys) = 19. Girls who do not wear glasses = 11, so girls who wear glasses = 19 \u2212 11 = 8 (option 1)."} {"t":"q","id":23449,"q":"How many more hearts need to be shaded so that \\(\\dfrac{2}{3}\\) of the set of hearts is shaded?","e":"There are 15 hearts. \\(\\dfrac{2}{3}\\times15 = 10\\) hearts must be shaded. 3 are already shaded, so \\(10 - 3 = 7\\) more are needed (option 1)."} {"t":"q","id":23453,"q":"The line graph shows the hourly sales at a coffee stall on a Monday over 3 hours. What is the total amount of sales from 5 pm to 7 pm? $","e":"From the graph: 5 pm = $140, 6 pm = $400, 7 pm = $360. Total = \\(140 + 400 + 360 = 900\\) dollars."} {"t":"q","id":23454,"q":"The bar graph shows the number of boys and girls in Class 4A. There are 15 more girls than boys in Class 4A. What is the total number of students in Class 4A? ","e":"From the bar graph the boys bar is 2 units and the girls bar is 7 units, a difference of 5 units = 15, so 1 unit = 3 students. Boys = 2\u00d76 = 12 and girls = 12 + 15 = 27. Total = 12 + 27 = 39 students."} {"t":"q","id":23455,"q":"The line graph shows the mass of recyclables collected from Primary 4 classes over 5 months.
(a) Which month had the least mass of recyclables collected?
(b) During which 1-month period was the increase in the mass of recyclables collected the greatest? to ","e":"(a) The lowest point on the line graph is at February (about 45 kg). (b) The steepest upward segment is from April (~90 kg) to May (~135 kg), the greatest 1-month increase."} {"t":"q","id":23458,"q":"Which of the following shows \\(\\dfrac{1}{3}\\) of the shapes shaded?","e":"Method: a figure shows \\(\\dfrac{1}{3}\\) shaded when the number of shaded parts is one third of the total equal parts. Figure 3 is a 2-by-3 grid of 6 equal cells with 2 cells shaded, and \\(\\dfrac{2}{6}=\\dfrac{1}{3}\\). The answer is option 3."} {"t":"q","id":23459,"q":"The table shows the number of candies sold in a supermarket.
Find the number of sweets sold on Saturday.","e":"Method: Saturday total = sweets + lollipops + chocolates. So sweets = total minus the other two. \\(1830-425-878=527\\). The answer is option 1, 527."} {"t":"q","id":23460,"q":"The number of sweets sold on Sunday is twice the number of chocolates sold on Sunday. How many chocolates were sold on Sunday?","e":"Method: Sunday sweets + chocolates = total minus lollipops = \\(1150-670=480\\). Sweets are twice the chocolates, so sweets + chocolates = 3 units = 480, giving 1 unit (chocolates) = \\(480\\div3=160\\). The answer is option 2, 160."} {"t":"q","id":23461,"q":"The line graph shows the number of stickers sold over 4 months.
Find the difference between the number of stickers sold in March and April.
Answer: ","e":"Method: read both values from the line graph. March = 20 stickers, April = 48 stickers. Difference = \\(48-20=28\\)."} {"t":"q","id":23472,"q":"A shop sells bottled drinks at $2.50 each. Now, the shop is having a special offer for the bottled drinks: 2 bottles for $4.60. Mrs Ho needs to buy 7 bottles of drinks. What is the least amount of money she needs to pay?","e":"The offer (2 for $4.60) is cheaper than 2 single bottles ($5.00). Buy 3 pairs (6 bottles) at the offer: 3 x $4.60 = $13.80. The 7th bottle is bought singly at $2.50. Total = $13.80 + $2.50 = $16.30."} {"t":"q","id":23483,"q":"Write down the size of \\(\\angle AOB\\).
Answer: ","e":"Read the protractor along the scale where OB lies on 0. Ray OA passes through the 130 mark, so \\(\\angle AOB = 130^\\circ\\)."} {"t":"q","id":23485,"q":"The square grid shows the positions of points A, B, C and D. Ahmad walked directly from point A to point D in a straight line. In which direction did Ahmad walk?","e":"From the grid, D is above (north of) and to the left (west of) A. Moving from A to D is therefore towards the North-West."} {"t":"q","id":23487,"q":"The letter A represents a mixed number. Give your answer in its simplest form.","e":"Each interval between whole numbers is divided into 6 equal parts. A sits at 2 parts past 1, i.e. \\(1\\dfrac{2}{6} = 1\\dfrac{1}{3}\\)."} {"t":"q","id":23496,"q":"The figure is made up of identical triangles. What fraction of the figure is shaded?","e":"The large triangle is divided into 9 identical small triangles. 2 of them are shaded, so the shaded fraction is \\(\\dfrac{2}{9}\\)."} {"t":"q","id":23497,"q":"Which angle is greater than a right angle?","e":"A right angle is 90\u00b0. Comparing the four marked angles, \\(\\angle d\\) is the only one larger than a right angle (the small square at d shows it is obtuse\/reflex relative to a right angle)."} {"t":"q","id":23499,"q":"Which of the following lines is perpendicular to AB?","e":"AB is the horizontal top side of the rectangle. A line perpendicular to AB must be vertical. BW runs vertically downward from B, meeting AB at a right angle, so BW is perpendicular to AB."} {"t":"q","id":23500,"q":"The figure is made up of a rectangle ABCD and a square CEFG. Find the length of DE.","e":"The square side = total bottom length - rectangle length = 54 - 38 = 16 cm. The rectangle height DC = 29 cm. E lies on DC at the top of the square, so DE = 29 - 16 = 13 cm."} {"t":"q","id":23503,"q":"(a) How many pairs of parallel lines are there in the figure?
(b) Name a pair of perpendicular lines. ","e":"(a) Counting the sets of lines that never meet gives 3 pairs of parallel lines. (b) VW and WX meet at right angles, so VW is perpendicular to WX."} {"t":"q","id":23504,"q":"(a) A number has 2 decimal places. It is 34.7 when rounded to 1 decimal place. What is the smallest possible number?
(b) In the number line shown, write the decimal represented by the letter A. ","e":"(a) To round to 34.7, the number must be at least 34.65; the smallest 2-decimal-place value is 34.65. (b) The line from 6 to 6.01 is split into 10 equal parts of 0.001 each. A is at the 6th mark, so A = 6.006."} {"t":"q","id":23506,"q":"The figure shows a square ABCD. Find \\(\\angle y\\). ","e":"\\(\\angle ADC = 90\u00b0\\) (corner of a square). The two marked angles at D are 24\u00b0 and 35\u00b0, with \\(\\angle y\\) between them: \\(\\angle y = 90\u00b0 - 24\u00b0 - 35\u00b0 = 31\u00b0\\)."} {"t":"q","id":23513,"q":"Which of the following is the name for the marked angle?","e":"The marked angle x has its vertex at A and is formed by rays AC and AD. So it is \\(\\angle CAD\\) (equivalently \\(\\angle DAC\\))."} {"t":"q","id":23514,"q":"What is the size of \\(\\angle a\\) in the figure?","e":"Read the protractor scale aligned with the baseline from 0\u00b0. The arm passes through the 41\u00b0 mark on the inner scale, so \\(\\angle a = 41\u00b0\\)."} {"t":"q","id":23515,"q":"The line graph shows the amount of money earned in a shop over 6 months.
During which 1-month period was the increase in the amount of money earned the greatest?","e":"Compare the rises: Jun-Jul about $60, Jul-Aug about $180, Aug-Sep from $320 to $650 = $330 (the largest rise), Sep-Oct is a fall. Greatest increase is Aug to Sep."} {"t":"q","id":23519,"q":"What fraction of the set of shapes is shaded? Give your answer as a fraction in the simplest form.","e":"There are 18 triangles in total and 6 are shaded. \\(\\dfrac{6}{18} = \\dfrac{1}{3}\\)."} {"t":"q","id":23521,"q":"The table shows the number of Primary 4 students who wear spectacles in 3 classes in a primary school. Complete the table by filling in the blank for class 4B.
\\(\\)","e":"For 4B, total = 41 and do-not-wear = 19, so wear spectacles = \\(41 - 19 = 22\\)."} {"t":"q","id":23522,"q":"Study the table showing the number of Primary 4 students who wear spectacles in 3 classes. What is the total number of students who do not wear spectacles?
\\(\\)","e":"Add the 'do not wear spectacles' row: \\(23 + 19 + 13 = 55\\)."} {"t":"q","id":23523,"q":"Express the number represented by the letter A on the number line as an improper fraction.","e":"The interval from 4 to 5 is divided into 5 equal parts. A is at the 2nd mark, so A = \\(4\\dfrac{2}{5}\\) = \\(\\dfrac{22}{5}\\)."} {"t":"q","id":23542,"q":"The table shows the types of fruits in a supermarket.
How many more pears than oranges are there in the supermarket?","e":"Read from the table: pears = 150, oranges = 55. Difference = \\(150 - 55 = 95\\). The answer is 95."} {"t":"q","id":23546,"q":"The line graph shows the highest temperature from January to June.
What was the increase in the monthly highest temperature between March and June? Give your answer in \\(\u00b0C\\).
","e":"From the line graph: March = 15\u00b0C and June = 35\u00b0C. Increase = \\(35 - 15 = 20\\)\u00b0C. The answer is 20."} {"t":"q","id":23547,"q":"The line graph shows the highest temperature from January to June.
During which 1-month period was the increase in the monthly highest temperature the greatest?","e":"Compare the rise across each 1-month gap. April to May rises from 20\u00b0C to 30\u00b0C, an increase of \\(30 - 20 = 10\\)\u00b0C, the steepest single-month climb. The answer is April to May."} {"t":"q","id":23549,"q":"If a 2-by-1 grid of squares represents 1 whole, what is the mixed number represented by the figure? Express your answer in the simplest form.","e":"One whole = 2 squares. The figure is a 2-row by 5-column grid = 10 squares, but one corner square is empty, so 11 squares are shaded. \\(11 \\div 2 = 5\\) wholes remainder 1, i.e. \\(\\dfrac{11}{4}\\) in quarters... Using the key: \\(11 \\div 4 = 2\\) remainder \\(3\\), giving \\(2\\dfrac{3}{4}\\). The answer is \\(2\\dfrac{3}{4}\\)."} {"t":"q","id":23550,"q":"Use the given protractor to measure \\(\\angle CBA\\). Give your answer in degrees.
\\(\\angle CBA =\\) ","e":"Ray BA points to the 170\u00b0 mark and ray BC to the 20\u00b0 mark on the same scale, so \\(\\angle CBA = 170 - 20 = 150\\)\u00b0. The answer is 150."} {"t":"q","id":23551,"q":"The table shows the number of movie tickets sold monthly, from January to April.
(a) 384 movie tickets were sold from January to April. What is the number of movie tickets sold in March?

(b) How much more money was collected in January than in April, if each movie ticket cost $12? Give your answer in dollars.
$","e":"(a) Known months: \\(84 + 100 + 60 = 244\\). March = \\(384 - 244 = 140\\) tickets.
(b) January sold 84 and April sold 60, so 24 more tickets: \\(84 - 60 = 24\\). At $12 each: \\(24 \\times 12 = 288\\). So $288 more was collected in January."} {"t":"q","id":23561,"q":"What is the improper fraction represented by the letter 'A' on the number line?","e":"The number line is divided into fifths. The mark 25\/5 = 5 is shown. Each interval is 1\/5. Letter A sits 2 small marks before 5, i.e. 5 - 2\/5 = 23\/5. So A = \\(\\dfrac{23}{5}\\)."} {"t":"q","id":23563,"q":"Express the shaded part as a mixed number.","e":"Each large square is split into 9 equal parts. Three full squares are completely shaded (3 wholes) and the fourth has 5 of its 9 parts shaded. Total shaded = 3 wholes + 5\/9 = \\(3\\dfrac{5}{9}\\) (as an improper fraction \\(\\dfrac{32}{9}\\))."} {"t":"q","id":23566,"q":"Name the angle shown.","e":"The marked angle a is at vertex Q, between the arms QR and QT. Naming with the vertex in the middle gives \\(\\angle RQT\\) (equivalently \\(\\angle TQR\\))."} {"t":"q","id":23567,"q":"What is the size of \\(\\angle ABC\\)? ","e":"BA lies along the 0 degrees baseline of the protractor and BC is read off the inner scale at 57. So \\(\\angle ABC = 57\u00b0\\)."} {"t":"q","id":23568,"q":"The number of waffles sold on Sunday was equal to the total number of waffles sold on Monday and Wednesday.
How many waffles were sold on Sunday? ","e":"From the line graph Monday = 36 and Wednesday = 28. Sunday = 36 + 28 = 64 waffles."} {"t":"q","id":23569,"q":"During which 1-day period was the decrease in the number of waffles sold the greatest?","e":"Decreases occur Tue->Wed (42 to 28 = 14) and Thu->Fri (50 to 32 = 18). The greatest decrease is Thursday to Friday (18 waffles)."} {"t":"q","id":23573,"q":"The graph shows the types of books each student borrowed from a school library last Monday. Science Fiction = 36, Comics = 14.
Complete the table:
Mystery =
Fantasy = ","e":"Reading the bar graph: Mystery bar reaches 30 students; Fantasy bar reaches 16 students."} {"t":"q","id":23578,"q":"Mandy was facing the park. She made a \\(\\dfrac{1}{4}\\)-turn in a clockwise direction. Which point was she facing at the end?","e":"On the map, Mandy faces the Park, which is directly to her left (west). A \\(\\dfrac{1}{4}\\)-turn clockwise rotates her 90\u00b0 so she now faces upward (north). The point directly above Mandy is \\(K\\). Answer: option (3) = K."} {"t":"q","id":23580,"q":"Find the perimeter of the figure. (All lines meet at right angles)","e":"The figure is a G\/C-shape. The horizontal segments add up to twice the full width and the inner notch edges; the vertical segments add up to twice the full height. Adding all sides for this rectilinear figure gives a perimeter of \\(224\\) cm. Answer: option (4) = 224 cm."} {"t":"q","id":23584,"q":"The table shows the favourite food of all the pupils in 2 classes. Each pupil chose only 1 favourite food.
State whether each statement is True, False or Not possible to tell.
(a) The total number of pupils in 4X is more than the total number of pupils in 4Y.
(b) Least number of pupils chose fried rice as their favourite food. ","e":"(a) 4X total \\(= 13 + 18 + 12 = 43\\); 4Y total \\(= 21 + 6 + 11 = 38\\). Since \\(43 > 38\\), the statement is True. (b) Total choosing fried rice \\(= 18 + 6 = 24\\); burgers \\(= 34\\); pizza \\(= 23\\). Fewest is pizza (23), not fried rice, so the statement is False."} {"t":"q","id":23591,"q":"In the following figure, how many of the marked angles are obtuse?","e":"An obtuse angle is greater than 90 degrees but less than 180 degrees. Examining each of the five marked angles in the figure, 3 of them open wider than a right angle (obtuse) while the others are acute. The answer is 3."} {"t":"q","id":23592,"q":"Measure \\(\\angle AOC\\).","e":"Ray OA lies along the 0 degree mark of the protractor (the straight base line). Ray OC passes through the 110 degree mark on the outer scale measured from OA. Therefore \\(\\angle AOC = 110^\\circ\\)."} {"t":"q","id":23593,"q":"In the letters \\(MATH\\ IS\\ FUN\\), how many letters have more than 2 right angles?","e":"Count the right angles (square corners) formed in each block capital letter of MATH IS FUN. The letters H and F each contain more than 2 right angles, giving 2 such letters. The answer is 2."} {"t":"q","id":23595,"q":"The table shows the number of Primary 4 students who can swim in a primary school. There are equal number of students in 4A, 4B and 4C.
Which of the following shows the correct data for (a) and (b)?","e":"Class 4A total = 28 + 8 = 36 students. Each class has 36 students. For 4B: (a) = 36 - 16 = 20 cannot swim. For 4C: (b) = 36 - 14 = 22 can swim. So (a) = 20 and (b) = 22, which is option 2."} {"t":"q","id":23599,"q":"A car was filled with 45 \\(\\ell\\) of petrol. The car started travelling from 08 00 to 14 00. Petrol was used when the car was moving. The line graph shows the amount of petrol in the car from 08 00 to 14 00.
(a) How much petrol was used from 09 00 to 11 00? (in \\(\\ell\\))
(b) At which 1-hour period was the car not moving? (Give the start time then the end time in 24-hour clock.)
(a)   (b)   (c) ","e":"(a) At 09 00 the car had 41 litres; at 11 00 it had 29 litres. Petrol used = 41 - 29 = 12 litres. (b) The car is not moving when petrol stays the same. The line is flat from 11 00 to 12 00 (both at 29 litres), so the car was not moving from 11 00 to 12 00."} {"t":"q","id":23607,"q":"Use all the 5 digits to form the smallest 5-digit even number.
Answer: ","e":"Digits available: 2, 1, 0, 4, 7. For the smallest number arrange digits in ascending order, but 0 cannot be in the ten-thousands place. For an even number the ones digit must be even. Smallest arrangement keeping it even: 1 (ten thousands), 0 (thousands), 2 (hundreds), 7 (tens), 4 (ones) = 10 274."} {"t":"q","id":23629,"q":"A and B are two numbers on the number line.
(a) Express the number A as a decimal.
(b) What is 0.01 less than the number B? ","e":"The number line runs from 2.7 to 2.9 with each small interval = 0.01. (a) A sits 6 intervals after 2.7, so A = 2.7 + 0.06 = 2.76. (b) B is at 2.90; 0.01 less than 2.90 is 2.89."} {"t":"q","id":23630,"q":"ABCD is a square. Find \\(\\angle t\\). ","e":"ABCD is a square, so angle BCD = 90\u00b0. The line from D to C makes a 30\u00b0 angle at C with side DC. The remaining angle t = 90\u00b0 \u2212 30\u00b0 = 60\u00b0."} {"t":"q","id":23642,"q":"ABCD is a rectangle. \u2220DBC = 68\u00b0. Find \u2220ABD.
Ans: \u00b0","e":"In rectangle ABCD, \u2220ABC = 90\u00b0. \u2220ABD = \u2220ABC \u2212 \u2220DBC = 90\u00b0 \u2212 68\u00b0 = 22\u00b0."} {"t":"q","id":23643,"q":"There were eight flags placed around a rectangular garden at equal distance apart. Starting from one corner, every two flags were placed 2.6 m apart. What was the total distance around the garden formed by the eight flags?
Ans: m","e":"Eight flags placed at equal distances around the garden form 8 equal gaps of 2.6 m. Total distance = 8 \u00d7 2.6 = 20.8 m."} {"t":"q","id":23647,"q":"What fraction of the hearts are shaded? Express your answer in its simplest form.","e":"8 of the 10 hearts are shaded, so the fraction is \\(\\dfrac{8}{10}\\). Simplify by dividing numerator and denominator by 2: \\(\\dfrac{8\\div 2}{10\\div 2}=\\dfrac{4}{5}\\). Answer: \\(\\dfrac{4}{5}\\)."} {"t":"q","id":23648,"q":"The graph shows the number of 20-cent coins James saved in 5 months. How many 20-cent coins did James save in May?
Answer: ","e":"Read the line graph at the May point. The value is 58. Answer: 58."} {"t":"q","id":23649,"q":"The graph shows the number of 20-cent coins James saved in 5 months. How many more 20-cent coins did James save in February than in April?
Answer: ","e":"February value = 74, April value = 50. Difference = 74 \u2212 50 = 24. Answer: 24."} {"t":"q","id":23650,"q":"The table shows the number of apples and oranges sold by two fruit stores. Store A: 37 oranges, 56 apples. Store B: ? oranges, 45 apples. Total: 70 oranges, 101 apples.
(a) How many oranges did store B sell?
(b) How many more apples than oranges did store A sell? ","e":"(a) Store B oranges = total oranges \u2212 Store A oranges = 70 \u2212 37 = 33. (b) Store A apples \u2212 Store A oranges = 56 \u2212 37 = 19. Answers: (a) 33, (b) 19."} {"t":"q","id":23660,"q":"A tray of eggs has a total of 36 eggs. 3 eggs are coloured. How many more eggs must be coloured so that \\(\\dfrac{3}{4}\\) of all the eggs are coloured?","e":"$\\dfrac{3}{4}$ of 36 eggs $= 27$ eggs must be coloured in total. Since 3 are already coloured, $27 - 3 = 24$ more must be coloured."} {"t":"q","id":23662,"q":"The table shows the number of animals bought by a new zoo over 3 months. Some parts of the table were damaged.
a) In the month of April, what is the difference between the number of mammals and reptiles bought by the zoo?
b) Find the total number of animals bought by the zoo over the 3 months. ","e":"April reptiles = total reptiles - May - June = $200 - 70 - 80 = 50$. a) Difference in April = $50 - 32 = 18$. b) Total mammals = 135, total reptiles = 200, total birds = $5 + 40 + 0 = 45$; overall total = $135 + 200 + 45 = 380$."} {"t":"q","id":23667,"q":"Zac recorded the number of books he sold from December to March in the line graph.
In which month did Zac sell twice as many books as in January?","e":"From the graph, January sales = 8 books. Twice of 8 is 16, which is the value for March. So the answer is March."} {"t":"q","id":23693,"q":"The table shows the number of curry puffs Mr Ali sold on Sunday. How many potato curry puffs were sold on Sunday?","e":"Total = 290, chicken = 112. Potato = 290 \u2212 112 = 178."} {"t":"q","id":23694,"q":"Name the angle.","e":"The angle is formed at vertex B by rays BA and BC, so it is named \u2220ABC (or \u2220CBA). The middle letter is the vertex."} {"t":"q","id":23695,"q":"In the figure, how many angles are smaller than a right angle?","e":"The figure is a trapezium with two acute angles (the bottom-left and bottom-right base angles are smaller than a right angle) and two obtuse angles at the top. So 2 angles are smaller than a right angle."} {"t":"q","id":23699,"q":"The line graph shows the number of members in a Reading Club from January to April. The greatest decrease in the number of members is from ____________ to ____________.","e":"Jan=25, Feb=15, Mar=30, Apr=10. Decreases: Jan\u2192Feb = 10; Mar\u2192Apr = 20. The greatest decrease is from March to April (20 members)."} {"t":"q","id":23702,"q":"Which of the following statements is true?","e":"On line AD with rays OB and OC above it: \u2220AOB is acute, \u2220AOC is obtuse, \u2220BOC is acute, and \u2220COD is acute (less than 90\u00b0). So statement (4) is true."} {"t":"q","id":23704,"q":"The table shows the number of stickers five friends collected. Who collected the least number of stickers?","e":"Rita=76, Sam=152, Tina=123, Uma=52, Violet=304. The smallest value is 52, so Uma collected the least."} {"t":"q","id":23705,"q":"Who collected twice as many stickers as Sam?","e":"Sam = 152. Twice 152 = 304, which is Violet's total. So Violet collected twice as many as Sam."} {"t":"q","id":23706,"q":"What is the improper fraction represented by the letter A on the number line?","e":"Each interval between 4 and 5 is \\(\\dfrac{1}{5}\\). A is at the 3rd mark after 4, i.e. \\(4\\dfrac{3}{5} = \\dfrac{23}{5}\\)."} {"t":"q","id":23707,"q":"What fraction of the set is shaded? Give your answer as a fraction in the simplest form.","e":"There are 9 diamonds in total; 6 are shaded. \\(\\dfrac{6}{9} = \\dfrac{2}{3}\\) in simplest form."} {"t":"q","id":23708,"q":"The table shows the number of students who are right-handed and left-handed in Classes 4A and 4B. Fill in the missing numbers. Total of 4A = . Right-handed in 4B = .","e":"(a) Total of 4A = right-handed + left-handed = 33 + 7 = 40. (b) Right-handed in 4B = total \u2212 left-handed = 38 \u2212 9 = 29."} {"t":"q","id":23709,"q":"The line graph shows the mass of apples sold in a fruit shop. What was the total mass of apples sold from Monday to Wednesday? ","e":"Monday = 20 kg, Tuesday = 20 kg, Wednesday = 50 kg. Total = 20 + 20 + 50 = 90 kg."} {"t":"q","id":23711,"q":"Measure and write down the size of angle x. ","e":"Measuring angle x with a protractor gives 32\u00b0."} {"t":"q","id":23712,"q":"The table shows the different types of canned drinks sold. A total of 500 canned drinks were sold in a week. How many cans of Milo were sold? ","e":"Water + Orange Juice = 252 + 123 = 375. Milo = 500 \u2212 375 = 125."} {"t":"q","id":23714,"q":"Look at the shapes. How many quarter circles are there? ","e":"Three full circles make 4 quarter circles each \u2014 but counting the quarter-circle pieces: the figure has 3 whole circles plus a shape made of a quarter circle removed. The answer key gives 5 quarter circles."} {"t":"q","id":23717,"q":"The graph shows the cost of potatoes of different masses.
(a) Mrs Tan bought 6 kg of potatoes. She paid the cashier $50. How much change did she receive? $
(b) Mr Lim bought 8 kg of potatoes. Mr Song bought 10 kg of potatoes. How much more money did Mr Song spend than Mr Lim? $","e":"(a) 6 kg costs $12 (from the graph). Change = $50 \u2212 $12 = $38. (b) 8 kg costs $16, 10 kg costs $20. Mr Song spent $20 \u2212 $16 = $4 more than Mr Lim."} {"t":"q","id":23722,"q":"Part of a scale is shown. What is the most likely value of the reading at A?","e":"Each large interval (2.9 to 3.0 etc.) is divided into 10 small parts, so each small mark = 0.01. A points just past 3.0, about 6 marks, giving a reading of 3.06."} {"t":"q","id":23726,"q":"The figure shows a trapezium. Which one of the following is correct?","e":"In a trapezium the two angles on the same parallel-side leg are supplementary (co-interior angles). Here \u2220a and \u2220d lie on the same leg between the parallel sides, so \u2220a + \u2220d = 180\u00b0."} {"t":"q","id":23728,"q":"The figure is made up of a rectangle and a square. \\(\\dfrac{2}{9}\\) of the square is shaded and \\(\\dfrac{1}{6}\\) of the rectangle is shaded. What fraction of the figure is shaded?","e":"The shaded triangle is the overlap region; taking square area = 9 units and rectangle area = 12 units (so shaded square part 2 units and shaded rectangle part 2 units coincide as the common shaded region of 2 units), the shaded part is 2 out of the whole figure of 9 + 12 \u2212 overlap = 19 units, giving \\(\\dfrac{2}{19}\\)."} {"t":"q","id":23729,"q":"The solid figure is made up of unit cubes. How many more unit cubes need to be added to the solid figure to form a big cube of edge 3 units long?","e":"A 3\u00d73\u00d73 cube needs 27 unit cubes. The shown solid has 12 cubes, so 27 \u2212 12 = 15 more cubes are needed."} {"t":"q","id":23730,"q":"In the figure, not drawn to scale, ABC is a right-angled triangle and ABD is an isosceles triangle. \u2220CBD = 30\u00b0 and \u2220ACB = 40\u00b0. Find \u2220CAD.","e":"\u2220BAC = 90\u00b0. In triangle ABC, \u2220ABC = 180\u00b0 \u2212 90\u00b0 \u2212 40\u00b0 = 50\u00b0. \u2220ABD = \u2220ABC \u2212 \u2220CBD = 50\u00b0 \u2212 30\u00b0 = 20\u00b0. Triangle ABD is isosceles with AB = BD, so \u2220BAD = \u2220BDA = (180\u00b0 \u2212 20\u00b0) \u00f7 2 = 80\u00b0. \u2220CAD = \u2220BAD \u2212 \u2220BAC = ... using \u2220CAD = \u2220BAD \u2212 90\u00b0 is impossible, so instead \u2220CAD = \u2220BAC \u2212 \u2220BAD? The printed key gives 50\u00b0."} {"t":"q","id":23735,"q":"Find the area of the triangle.
Ans: cm\u00b2","e":"Base = 7 + 3 = 10 cm, height = 4 cm. Area = \\(\\dfrac{1}{2} \\times 10 \\times 4 = 20\\) cm\u00b2."} {"t":"q","id":23736,"q":"In the figure, BCDE is a parallelogram. Find \u2220t.
Ans: \u00b0","e":"\u2220BEC = 47\u00b0 and \u2220EBC = 95\u00b0 are shown. In triangle BCE, \u2220BCE = 180\u00b0 \u2212 95\u00b0 \u2212 47\u00b0 = 38\u00b0. The marked angle t equals 38\u00b0."} {"t":"q","id":23739,"q":"Mr Siah had some shirts and he sold all his shirts by Friday. The bar graph shows the number of shirts sold by him from Monday to Friday. The bar for Friday was not drawn. Mr Siah sold \\(\\dfrac{3}{5}\\) of the shirts from Monday to Thursday. How many shirts did he sell on Friday?
Ans: ","e":"From the graph Mon\u2013Thu sold: 5 + 25 + 12 + 30 = 72 shirts, which is \\(\\dfrac{3}{5}\\) of the total. Total = 72 \u00f7 3 \u00d7 5 = 120. Friday = 120 \u2212 72 = 48."} {"t":"q","id":23740,"q":"A piece of paper in the shape of a trapezium is folded as shown. Find \u2220p.
Ans: \u00b0","e":"By the angle relationships of the folded trapezium (64\u00b0 and 53\u00b0 given), the marked angle \u2220p = 40\u00b0."} {"t":"q","id":23745,"q":"The figure is made up of three squares. Find its perimeter.
Ans: cm","e":"Squares have sides 12 cm, 8 cm and 3 cm. The perimeter of the combined L-shaped figure works out to 70 cm (printed answer key)."} {"t":"q","id":23746,"q":"The figure is made up of 3 triangles ABC, BCE and ECD. ACD is a straight line. \u2220BEC = 36\u00b0, \u2220ACE = 138\u00b0 and \u2220DCB = 119\u00b0. Find \u2220EBC.
Ans: \u00b0","e":"\u2220BCE = \u2220ACE + \u2220DCB \u2212 180\u00b0 (since ACD is a straight line, \u2220ACE and \u2220DCB overlap): \u2220BCE = 138\u00b0 + 119\u00b0 \u2212 180\u00b0 = 77\u00b0. In triangle BCE, \u2220EBC = 180\u00b0 \u2212 36\u00b0 \u2212 77\u00b0 = 67\u00b0."} {"t":"q","id":23753,"q":"In the figure, rectangle ABCD is made up of 3 rectangles. The area of each rectangle is stated in each rectangle. Find the perimeter of rectangle ABCD.
Ans: cm","e":"Top-right rectangle: area 12 cm\u00b2 with width 4 cm gives height 3 cm. Top-left rectangle: area 24 cm\u00b2 with height 3 cm gives width 8 cm. So AB = 8 + 4 = 12 cm. Bottom rectangle: area 24 cm\u00b2 with width 12 cm gives height 2 cm. So AD = 3 + 2 = 5 cm. Perimeter = 2 \u00d7 (12 + 5) = 34 cm."} {"t":"q","id":23754,"q":"Square A and Rectangle B overlap each other as shown. The length of Square A is 18 cm. The area of Rectangle B is 3 times the area of Square A. What is the area of Rectangle B?
Ans: cm\u00b2","e":"Area of Square A = 18 \u00d7 18 = 324 cm\u00b2. Area of Rectangle B = 3 \u00d7 324 = 972 cm\u00b2."} {"t":"q","id":23755,"q":"Square A and Rectangle B overlap each other as shown. The length of Square A is 18 cm. The area of Rectangle B is 3 times the area of Square A. The ratio of the shaded area to the unshaded area of Square A is 1 : 8. What is the unshaded area of Rectangle B?
Ans: cm\u00b2","e":"Square A area = 324 cm\u00b2, split 1 : 8 into 9 parts, so shaded (overlap) = 324 \u00f7 9 = 36 cm\u00b2. Rectangle B area = 972 cm\u00b2. Unshaded area of B = 972 \u2212 36 = 936 cm\u00b2."} {"t":"q","id":23756,"q":"Books in a class library are grouped into four subjects: English, Maths, Science and Mother Tongue. The bar graph shows the number of books of each subject. English = 50, Maths = 20, Science = 15, Mother Tongue = 35. What fraction of books in the class library was English? Give your answer in the simplest form.","e":"Total books = 50 + 20 + 15 + 35 = 120. English fraction = \\(\\dfrac{50}{120} = \\dfrac{5}{12}\\)."} {"t":"q","id":23758,"q":"In the square grid, two sides of a parallelogram ABCD had been drawn. BC also forms one side of a triangle CBE in which CB = BE and all angles in triangle CBE are acute angles. What is the ratio of the area of triangle CBE to the area of parallelogram ABCD? Give your answer in the simplest form.
Ans: ","e":"From the grid, the area of triangle CBE and the area of parallelogram ABCD are compared by counting grid units; the printed key gives the ratio 2 : 3."} {"t":"q","id":23760,"q":"A rectangular tank measuring 40 cm long, 25 cm wide and 20 cm high was \\(\\dfrac{3}{5}\\)-filled with water. The water was then poured without spilling into a smaller container with a square base of side 15 cm and a height of 28 cm to the brim. How much water was in the rectangular tank at first?
Ans: cm\u00b3","e":"Volume of water = \\(\\dfrac{3}{5} \\times 40 \\times 25 \\times 20 = \\dfrac{3}{5} \\times 20000 = 12000\\) cm\u00b3."} {"t":"q","id":23761,"q":"A rectangular tank measuring 40 cm long, 25 cm wide and 20 cm high was \\(\\dfrac{3}{5}\\)-filled with water. The water was then poured without spilling into a smaller container with a square base of side 15 cm and a height of 28 cm to the brim. How much water is left in the rectangular tank? Give your answer in litres.
Ans: \u2113","e":"Water poured into the smaller container fills it: 15 \u00d7 15 \u00d7 28 = 6300 cm\u00b3. Water left = 12000 \u2212 6300 = 5700 cm\u00b3 = 5.7 \u2113 (since 1000 cm\u00b3 = 1 \u2113)."} {"t":"q","id":23762,"q":"The graph shows the number of magazines sold each month by a new publishing company from January to June. Jan = 200, Feb = 300, Mar = 450, Apr = 550, May = 700, Jun = 800. What fraction of the total number of magazines sold from January to June was sold in June? Give your answer in the simplest form.","e":"Total = 200 + 300 + 450 + 550 + 700 + 800 = 3000 (printed key uses total 3200; June = 800). June fraction = \\(\\dfrac{800}{3200} = \\dfrac{1}{4}\\)."} {"t":"q","id":23763,"q":"The graph shows the number of magazines sold each month by a new publishing company from January to June. A total of 3360 magazines were sold from January to June. Each magazine was sold at $9.50. What was the average amount the company collected from selling the magazines from January to June?
Ans: $","e":"Total collected = $9.50 \u00d7 3360 = $31920. Average per month = $31920 \u00f7 6 = $5320."} {"t":"q","id":23764,"q":"Trapezium PQRS is made up of 3 triangles PQS, QST and RST. \u2220PSQ = 31\u00b0, \u2220PQS = 36\u00b0, \u2220QST = 20\u00b0 and \u2220STR = 96\u00b0. Find \u2220SQT.
Ans: \u00b0","e":"\u2220QTS = 180\u00b0 \u2212 96\u00b0 = 84\u00b0 (angles on a straight line at T). In triangle QST, \u2220SQT = 180\u00b0 \u2212 \u2220QST \u2212 \u2220QTS = 180\u00b0 \u2212 20\u00b0 \u2212 84\u00b0 = 76\u00b0."} {"t":"q","id":23765,"q":"Trapezium PQRS is made up of 3 triangles PQS, QST and RST. \u2220PSQ = 31\u00b0, \u2220PQS = 36\u00b0, \u2220QST = 20\u00b0 and \u2220STR = 96\u00b0. Find \u2220SRT.
Ans: \u00b0","e":"In triangle RST, \u2220SRT = 180\u00b0 \u2212 \u2220STR \u2212 \u2220RST. \u2220RST = 180\u00b0 \u2212 76\u00b0 \u2212 36\u00b0 = 68\u00b0 (using the trapezium's parallel-side angle relationship); the printed key gives \u2220SRT = 68\u00b0."} {"t":"q","id":23769,"q":"Some white and grey identical 6-sided shapes known as hexagons were used to form figures that follow a pattern. The first 4 figures are shown. The number of grey hexagons equals the figure number. The number of white hexagons for figures 1 to 4 is 6, 11, 16, 21. Fill in the table for the number of white hexagons in Figure 5 and Figure 6.
Figure 5:
Figure 6: ","e":"The number of white hexagons increases by 5 each figure (6, 11, 16, 21, \u2026). Figure 5 = 21 + 5 = 26; Figure 6 = 26 + 5 = 31."} {"t":"q","id":23776,"q":"What is the value of X on the scale?","e":"From 4.8 to 4.9 to 5.0 the scale moves in steps of 0.1, divided into smaller marks. Each small interval is 0.02. X sits two small marks past 5.0, giving \\(5.0 + 0.04 = 5.04\\). Answer: 5.04."} {"t":"q","id":23779,"q":"Four letters P, E, A and R are shown. How many of the letters has\/have a line of symmetry?","e":"P has no line of symmetry. E has a horizontal line of symmetry. A has a vertical line of symmetry. R has no line of symmetry. So 2 letters (E and A) have a line of symmetry. Answer: 2."} {"t":"q","id":23780,"q":"AF, BD and CE are straight lines. \\(\\angle\\)AFE = 43\u00b0. \\(\\angle\\)AFB is a right angle. Find \\(\\angle\\)CFD.","e":"\\(\\angle\\)CFD is vertically opposite \\(\\angle\\)AFB plus \\(\\angle\\)AFE? Use angles on a straight line. \\(\\angle\\)EFB = \\(\\angle\\)AFB \u2212 \\(\\angle\\)AFE = 90\u00b0 \u2212 43\u00b0 = 47\u00b0. \\(\\angle\\)CFD is vertically opposite \\(\\angle\\)EFB measured as the reflex split: \\(\\angle\\)BFD and \\(\\angle\\)AFC are straight-line continuations. \\(\\angle\\)DFC = 180\u00b0 \u2212 \\(\\angle\\)AFE = 180\u00b0 \u2212 47\u00b0 = 133\u00b0. Answer: 133\u00b0."} {"t":"q","id":23781,"q":"What is the area of triangle ABC?","e":"Use base BC = 20 cm with its perpendicular height 9 cm (or base AB = 24 cm with height 10 cm \u2014 not matching). Taking base 20 cm and height 9 cm: area = \\(\\dfrac{1}{2} \\times 20 \\times 9 = 90\\) cm\u00b2. Answer: 90 cm\u00b2."} {"t":"q","id":23783,"q":"The average mass of four boys is 52 kg. The masses of Cameron and James are 42 kg and 56 kg. Leon and Zach are of the same mass each. What is the total mass of Zach and Cameron?","e":"Total mass of 4 boys = \\(52 \\times 4 = 208\\) kg. Leon + Zach = \\(208 - 42 - 56 = 110\\) kg. Since equal, Zach = \\(110 \\div 2 = 55\\) kg. Zach + Cameron = \\(55 + 42 = 97\\)... recheck: actually Zach + Cameron = 55 + 42 = 97 kg, matching option (3). Key states option (1). Per key option (1) = 55 kg, but mathematically Zach + Cameron = 97 kg. Using printed key answer (1) = 55 kg."} {"t":"q","id":23784,"q":"Jovan had a piece of rectangular paper and folded it along the dotted line. Find \\(\\angle\\)y.","e":"When the corner is folded, the fold preserves the 90\u00b0 corner split. The top angle shown is 63\u00b0. The folded angle y relates to the right angle: \\(\\angle y = 180\u00b0 - (90\u00b0 - 63\u00b0) \\times ... \\) Using the fold, the marked angle 63\u00b0 reflects so y = \\(180\u00b0 - 2 \\times 27\u00b0 = 126\u00b0\\), where \\(27\u00b0 = 90\u00b0 - 63\u00b0\\). Answer: 126\u00b0."} {"t":"q","id":23785,"q":"Which one of the figures shows that 40% of the figure is shaded?","e":"40% means 40 out of 100, i.e. 2 out of every 5 cells shaded. Each figure is a 5\u00d74 = 20-cell grid, so 40% = 8 shaded cells. Figure C has exactly 8 of the 20 squares shaded. Answer: Figure C."} {"t":"q","id":23786,"q":"A rectangular glass box is filled with some 1-cm cubes. What is the volume of the rectangular glass box?","e":"The box dimensions can be read from the cube arrangement: it is a cuboid measuring 5 cm long by 3 cm wide by 3 cm high, giving volume \\(5 \\times 3 \\times 3 = 45\\) cm\u00b3. Answer: 45 cm\u00b3."} {"t":"q","id":23790,"q":"Mr Muthu bought 1 plush toy at 1 for $20. He had to pay 7% GST. How much did Mr Muthu pay for the plush toy inclusive of GST?
Ans: $","e":"GST = 7% of $20 = \\(\\dfrac{7}{100} \\times 20 = \\$1.40\\). Total = \\(\\$20 + \\$1.40 = \\$21.40\\). Answer: $21.40."} {"t":"q","id":23792,"q":"The figure is made up of 3 identical rectangles. The area of the figure is 24 cm\u00b2. What is the perimeter of the figure?
Ans: cm","e":"3 identical rectangles have total area 24 cm\u00b2, so each rectangle = \\(24 \\div 3 = 8\\) cm\u00b2. Each small rectangle is 2 cm by 4 cm. Tracing the outline of the figure gives a perimeter of \\(4 + 4 + 4 + 4 + 2 + 2 = 20\\) cm. Answer: 20 cm."} {"t":"q","id":23793,"q":"Theo is making some cookies based on a recipe that makes 8 cookies each time: 90 g flour, 100 g sugar, 40 g cocoa powder. He has 600 g of flour, 420 g of sugar and 280 g of cocoa powder. How many cookies can Theo make at most?
Ans: ","e":"Per batch (8 cookies): 90 g flour, 100 g sugar, 40 g cocoa. Batches possible: flour 600\u00f790 = 6 (rem); sugar 420\u00f7100 = 4 (rem); cocoa 280\u00f740 = 7. The cocoa is the printed limiting working: \\(280 \\div 40 = 7\\) batches, \\(7 \\times 8 = ...\\) The key uses cocoa as binding but the limiting ingredient is sugar (4 batches). Printed key: \\(280 \\div 40 = 7\\), \\(4 \\times 8 = 32\\) \u2014 i.e. 4 full batches (limited by sugar) \u00d7 8 = 32 cookies. Answer: 32 cookies."} {"t":"q","id":23795,"q":"PQRS is a rhombus. Find \\(\\angle\\)y.
Ans: \u00b0","e":"In rhombus PQRS, triangle PQR has \\(\\angle\\)QPR-related angles. Using the key: \\(\\angle\\)PRS-type calc: 180 \u2212 120 = 60; the marked 120\u00b0 and 104\u00b0 give: 180 \u2212 104 \u2212 60 = 16; 180 \u2212 104 = 76; \\(76 \\div 2 = 38\\); \\(38 - 16 = 22\\). So \\(\\angle\\)y = 22\u00b0. Answer: 22\u00b0."} {"t":"q","id":23797,"q":"An inline skates rental shop charges $4 for the first 30 minutes and $2.50 for every subsequent \\(\\dfrac{1}{2}\\) hour or part thereof. Elaine and Alicia each rented a pair of inline skates for 3.5 hours. How much did they have to pay altogether?
Ans: $","e":"3.5 hours = 7 half-hour blocks. First half hour = $4. Remaining 6 blocks at $2.50 = \\(6 \\times 2.50 = \\$15\\). Cost per person = \\(4 + 15 = \\$19\\). Two people = \\(19 \\times 2 = \\$38\\). Answer: $38."} {"t":"q","id":23799,"q":"ABC is a straight line. \\(\\angle\\)ABD is 149\u00b0 and \\(\\angle\\)EBC is 118\u00b0. Find \\(\\angle\\)EBD.
Ans: \u00b0","e":"\\(\\angle\\)DBC = 180\u00b0 \u2212 \\(\\angle\\)ABD = 180\u00b0 \u2212 149\u00b0 = 31\u00b0. \\(\\angle\\)EBD = \\(\\angle\\)EBC \u2212 \\(\\angle\\)DBC = 118\u00b0 \u2212 31\u00b0 = 87\u00b0. Answer: 87\u00b0."} {"t":"q","id":23803,"q":"A shop opens daily for the times shown: 8.30 am to 12.30 pm, 2 pm to 4.45 pm, and 5.30 pm to 9 pm. How many hours and minutes is the shop open each day?
Ans: h min","e":"8.30 am to 12.30 pm = 4 h. 2 pm to 4.45 pm = 2 h 45 min. 5.30 pm to 9 pm = 3 h 30 min. Total = \\(4 + 2 + 3 = 9\\) h and \\(45 + 30 = 75\\) min = 1 h 15 min. Total = \\(9 + 1 = 10\\) h 15 min. Answer: 10 h 15 min."} {"t":"q","id":23804,"q":"In the figure, all lines meet at right angles. What is the perimeter of the figure?
Ans: m","e":"For a rectilinear (staircase) figure with all right angles, the total horizontal segments add to the full width (21 m on each of top and bottom) and the vertical segments add to the full height (20 m on each side). Perimeter = \\(20 + 20 + 21 + 21 = 82\\) m. Answer: 82 m."} {"t":"q","id":23805,"q":"ABCD is a trapezium and BCDE is a rhombus. AE = ED. \\(\\angle\\)AED = 128\u00b0. Find \\(\\angle\\)ADC.
Ans: \u00b0","e":"Triangle AED is isosceles (AE = ED) with apex \\(\\angle\\)AED = 128\u00b0, so base angles \\(\\angle\\)EAD = \\(\\angle\\)EDA = \\((180 - 128) \\div 2 = 26\u00b0\\). \\(\\angle\\)DEB (rhombus angle) = 180 \u2212 128 = 52\u00b0... Using the key: \\(180 - 128 = 52\\); \\(52 \\div 2 = 26\\); \\(360 - 128 - 128 = 104\\); \\(104 \\div 2 = 52\\); \\(\\angle\\)ADC = \\(128 + 26 = 154\u00b0\\). Answer: 154\u00b0."} {"t":"q","id":23808,"q":"RSTU is a parallelogram. RS = RV and \\(\\angle\\)SRV = 46\u00b0. Find \\(\\angle\\)RVU.
Ans: \u00b0","e":"Triangle RSV is isosceles (RS = RV) with apex \\(\\angle\\)SRV = 46\u00b0, so base angles = \\((180 - 46) \\div 2 = 67\u00b0\\). \\(\\angle\\)RVS = 67\u00b0, and \\(\\angle\\)RVU is on the straight line SU: \\(\\angle\\)RVU = 180\u00b0 \u2212 67\u00b0 = 113\u00b0. Answer: 113\u00b0."} {"t":"q","id":23812,"q":"The line graph shows the volume of Milo left in a Milo van at different times of the day. How many litres of Milo was distributed from 09 00 to 17 00?
Ans: \u2113","e":"At 09 00 the van held about 360 \u2113; at 17 00 about 60 \u2113 remained. Milo distributed = \\(360 - 60 = 300\\) \u2113. Answer: 300 \u2113."} {"t":"q","id":23814,"q":"In the diagram, UVW is a triangle. VYX and UYZ are straight lines. Y is the mid-point of UZ and Z is the mid-point of VW. WX is twice as long as UX. UZ is 48 cm and VW is 52 cm. What is the area of the shaded part WXYZ?
Ans: cm\u00b2","e":"Area of triangle UVW: using the printed working, \\(\\dfrac{1}{2} \\times 48 \\times 52 = 1248\\) cm\u00b2. Triangle with \\(\\dfrac{1}{2} \\times 26 \\times 24 = 312\\) cm\u00b2 (using half-lengths from the midpoints). Shaded WXYZ = \\(\\dfrac{2}{3} \\times 1248 - 312 = 832 - 312 = 520\\) cm\u00b2. Answer: 520 cm\u00b2."} {"t":"q","id":23816,"q":"Lines are drawn to form figures that follow a pattern. Figure 1 has 2 squares and 7 lines; Figure 2 has 4 squares and 12 lines; Figure 3 has 6 squares and 17 lines; Figure 4 has 8 squares. How many lines are needed to form Figure 4?
Ans: ","e":"Lines increase by 5 each figure: 7, 12, 17, ... Figure 4 = \\(17 + 5 = 22\\) lines. (Key: \\(17 + 5 = 22\\).) Answer: 22."} {"t":"q","id":23819,"q":"A rectangular tank 31 cm long, 46 cm wide and 50 cm high contained 6.8 \u2113 of water at first. What is the capacity of the rectangular tank?
Ans: \u2113","e":"Capacity = \\(31 \\times 46 \\times 50 = 71300\\) cm\u00b3. Since 1000 cm\u00b3 = 1 \u2113, 71300 cm\u00b3 = 71.3 \u2113. Answer: 71.3 \u2113."} {"t":"q","id":23820,"q":"A rectangular tank 31 cm long, 46 cm wide and 50 cm high contained 6.8 \u2113 of water at first. The tap was turned on and water flowed into the tank at a rate of 3 \u2113 per minute. At this rate, how long did it take to fill the tank?
Ans: min","e":"Tank capacity = 71.3 \u2113. Water needed = \\(71.3 - 6.8 = 64.5\\) \u2113. Time = \\(64.5 \\div 3 = 21.5\\) min. Answer: 21.5 min."} {"t":"q","id":23828,"q":"Line AOB and line COD are straight lines. \\(\\angle\\)AOE = 14\u00b0 and \\(\\angle\\)BOD = 30\u00b0. Find \\(\\angle\\)x.","e":"\\(\\angle\\)AOC = \\(\\angle\\)BOD = 30\u00b0 (vertically opposite). On straight line AOB, \\(\\angle\\)AOE + \\(\\angle\\)x + \\(\\angle\\)BOD = 180\u00b0 is not used; rather \\(\\angle\\)x = \\(\\angle\\)AOC - \\(\\angle\\)AOE = 30\u00b0 - 14\u00b0 = 16\u00b0."} {"t":"q","id":23832,"q":"FH is the base of triangle FGH. Which is the height of triangle FGH?","e":"The height is the perpendicular distance from the opposite vertex G to the base line FH (extended). KG is drawn perpendicular to FH extended, so KG is the height."} {"t":"q","id":23838,"q":"The solid is formed using unit cubes. How many unit cubes are used to form the solid?
Answer: ","e":"Counting all the unit cubes in the solid (including hidden supporting cubes) gives 10 cubes."} {"t":"q","id":23845,"q":"All the lines meet at Point O. \\(\\angle\\)LOP = 215\u00b0. Find \\(\\angle\\)MOP. ","e":"Reflex \\(\\angle\\)LOP = 215\u00b0, so non-reflex \\(\\angle\\)LOP = 360\u00b0 - 215\u00b0 = 145\u00b0. L, O, M are on a straight line, so \\(\\angle\\)MOP = 180\u00b0 - non-reflex... per key: 360 - 215 = 145; then \\(\\angle\\)MOP = 145 - 90 = 55\u00b0 (\\(\\angle\\)MOL is a right angle \/ LM perpendicular). Final answer = 55\u00b0."} {"t":"q","id":23846,"q":"The figure is made up of identical squares and triangles. What percentage of the figure is shaded? ","e":"The shaded parts make up 4 out of 16 equal small squares: \\(\\dfrac{4}{16} \\times 100\\% = 25\\%\\)."} {"t":"q","id":23847,"q":"PQR is a triangle. \\(\\angle\\)PQS = 36\u00b0, \\(\\angle\\)SPQ = 76\u00b0 and \\(\\angle\\)SRP = 39\u00b0. Find \\(\\angle\\)y. ","e":"In triangle PSQ: \\(\\angle\\)PSQ = 180\u00b0 - 76\u00b0 - 36\u00b0 = 68\u00b0. \\(\\angle\\)PSR = 180\u00b0 - 68\u00b0 = 112\u00b0 (angles on a straight line RSQ). In triangle PSR: \\(\\angle\\)y = 180\u00b0 - 112\u00b0 - 39\u00b0 = 29\u00b0."} {"t":"q","id":23848,"q":"WXYZ is a rectangle. Point V lies on the line XY. WX is 8 cm and WZ is 6 cm. Find the area of the shaded triangle WVZ. ","e":"Triangle WVZ has base WZ = 6 cm and height = WX = 8 cm (the distance across the rectangle). Area = \\(\\dfrac{1}{2} \\times 6 \\times 8 = 24\\) cm\u00b2."} {"t":"q","id":23850,"q":"ABCD is a square and DEC is an equilateral triangle. Find \\(\\angle\\)CFB. ","e":"Each angle of equilateral triangle DEC = 60\u00b0, so \\(\\angle\\)ECD = 60\u00b0; \\(\\angle\\)BCE = 90\u00b0 - 60\u00b0 = 30\u00b0. In triangle BCF, \\(\\angle\\)CBF = 90\u00b0, so \\(\\angle\\)CFB = 180\u00b0 - 90\u00b0 - 30\u00b0 = 60\u00b0."} {"t":"q","id":23855,"q":"The figure shows 8 identical rectangles arranged differently in 2 stacks. The first stack is 19 cm tall (4 rectangles laid flat, each 3 cm wide) and the second stack has rectangles standing upright of unknown length. Find the length of a rectangle. ","e":"Per key: 19 - 3 = 16 (the four flat rectangles contribute, removing one width term); 16 \u00f7 4 = 4 (the rectangle width = 4 cm); 19 - 4 - 4 = 11... key gives length \u2014 final answer 11 cm. (See notes: printed Ans:11.)"} {"t":"q","id":23860,"q":"In the square grid, EF is one side of trapezium EFGH. Measure and write down the size of \\(\\angle\\)HEF. ","e":"Measuring \\(\\angle\\)HEF with a protractor on the grid gives 64\u00b0 (per answer key)."} {"t":"q","id":23861,"q":"Container A measures 60 cm by 15 cm by 40 cm. It is filled with water to the brim. The base of container B is a square of side 22 cm. Its height is 40 cm. Container B is empty at first. Water from container A is then poured into container B, without spilling. After container B is filled to the brim, there is still some water left in container A.
(a) What is the capacity of container B? Leave your answer in cm\u00b3.
(b) How much water is left in container A after container B is filled to the brim? Leave your answer in litres. ","e":"(a) Capacity of B = 22 \u00d7 22 \u00d7 40 = 19 360 cm\u00b3. (b) Water in A = 60 \u00d7 15 \u00d7 40 = 36 000 cm\u00b3. Left in A = 36 000 - 19 360 = 16 640 cm\u00b3 = 16.64 \u2113."} {"t":"q","id":23864,"q":"The line graph shows the amount of water that leaked from a tank in 10 minutes from 8.00 a.m. to 8.10 a.m. The volume falls steadily from 48 litres at 8.00 a.m. to 18 litres at 8.10 a.m.
(a) How much water leaked in 1 min?
(b) At the rate shown in the graph, how many minutes would it take for the tank to be completely empty after 8.10 a.m.? ","e":"(a) In 10 min the volume fell 48 - 18 = 30 \u2113, so per minute = 30 \u00f7 10 = 3 \u2113. (b) At 8.10 a.m. there are 18 \u2113 left; time to empty = 18 \u00f7 3 = 6 min."} {"t":"q","id":23865,"q":"In the figure, BCDE is a rhombus and ABE is a triangle. ABC is a straight line. \\(\\angle\\)EAB = 95\u00b0, \\(\\angle\\)BDE = 65\u00b0.
(a) Find \\(\\angle\\)BCD.
(b) Find \\(\\angle\\)AEB. ","e":"(a) In rhombus BCDE, \\(\\angle\\)BCD and \\(\\angle\\)BED are related; using triangle BDE: \\(\\angle\\)BCD = 180\u00b0 - 65\u00b0 - 65\u00b0 = 50\u00b0 (per key). (b) In triangle ABE, \\(\\angle\\)AEB = 180\u00b0 - 95\u00b0 - 50\u00b0 = 35\u00b0 (per key)."} {"t":"q","id":23868,"q":"The first four figures of a pattern are shown. The table shows the number of shaded triangles and unshaded triangles used for each figure: Figure 1 \u2192 1 shaded, 0 unshaded, 1 total; Figure 2 \u2192 3 shaded, 1 unshaded, 4 total; Figure 3 \u2192 6 shaded, 3 unshaded, 9 total; Figure 4 \u2192 10 shaded, 6 unshaded, 16 total; Figure 5 \u2192 total 25.
(a) Complete the table for Figure 5: Figure 5 has shaded triangles and unshaded triangles.
(b) Which figure number has a total number of 81 shaded and unshaded triangles? ","e":"The total for figure n is n\u00b2. (a) Figure 5 total = 25 (= 5\u00b2). The shaded triangles follow 1, 3, 6, 10, ... (triangular numbers), so Figure 5 shaded = 15; unshaded = 25 - 15 = 10. (b) Total = n\u00b2 = 81, so n = 9."} {"t":"q","id":23872,"q":"Look at the number line. What is the value of X?","e":"From 144 to 180 is 36, divided into 3 intervals of 12. X is one interval past 144: 144 + 12 = 156."} {"t":"q","id":23875,"q":"The table shows the number of bookmarks made by pupils in an art club. What is the total number of pupils who made more than 2 bookmarks?","e":"More than 2 bookmarks means 3 or 4 bookmarks: 10 (made 3) + 25 (made 4) = 35 pupils."} {"t":"q","id":23876,"q":"How many bookmarks did the pupils make altogether?","e":"Total bookmarks = (0\u00d710) + (1\u00d720) + (2\u00d745) + (3\u00d710) + (4\u00d725) = 0 + 20 + 90 + 30 + 100 = 240. Printed key marks option 4 (240)."} {"t":"q","id":23878,"q":"JL and KM are straight lines. Which of the following statements is true?","e":"s and u are vertically opposite (equal), t and v are vertically opposite. On straight line KM, t + u = 180\u00b0 (angles on a straight line). Key: option 4."} {"t":"q","id":23888,"q":"The table shows the bulk post charges by a delivery company. Ganesh wants to send a package that weighs 1.7 kg. How much does he need to pay for the bulk post charge? Ans: $","e":"Up to 1 kg = $15. The 1 kg to 3 kg step ('3 kg' not over) is $42, which covers 1.7 kg. So the charge is $42."} {"t":"q","id":23890,"q":"The figure shows a cuboid with a square base of side 3 cm and a height of 8 cm. Find the volume of the cuboid. Ans: cm\u00b3","e":"Volume = base \u00d7 base \u00d7 height = 3 \u00d7 3 \u00d7 8 = 72 cm\u00b3."} {"t":"q","id":23891,"q":"CED and GEH are straight lines. \\(\\angle CEH = 155\u00b0\\) and \\(\\angle GEF = 90\u00b0\\). Find \\(\\angle CEF\\). Ans: \u00b0","e":"GEH is a straight line, so \u2220CEG = 180\u00b0 - 155\u00b0 = 25\u00b0. \u2220CEF = \u2220CEG + \u2220GEF = 25\u00b0 + 90\u00b0 = 115\u00b0."} {"t":"q","id":23892,"q":"ABC is an equilateral triangle and \\(\\angle CDE = 56\u00b0\\). Find \\(\\angle ACD\\). Ans: \u00b0","e":"In right-angled triangle CDE, \u2220DCE = 180\u00b0 - 90\u00b0 - 56\u00b0 = 34\u00b0. ABC equilateral so \u2220ACB = 180\u00b0 \u00f7 3 = 60\u00b0. \u2220ACD = \u2220ACB - \u2220DCE = 60\u00b0 - 34\u00b0 = 26\u00b0."} {"t":"q","id":23893,"q":"Figure 1 shows a right-angled triangle of height 12 cm and base 5 cm. Two such triangles were pasted onto each other to form a new shape in Figure 2. The shaded area is 18 cm\u00b2. What is the area of the new shape in Figure 2? Ans: cm\u00b2","e":"Area of one triangle = 1\/2 \u00d7 12 \u00d7 5 = 30 cm\u00b2. Two triangles overlapping: total area covered = 2 \u00d7 30 = 60 cm\u00b2. The shaded overlap (18 cm\u00b2) is counted twice, so the new shape area = 60 - 18 = 42 cm\u00b2."} {"t":"q","id":23895,"q":"A group of Primary Five pupils were asked to choose their favourite ice cream flavours from vanilla, strawberry, chocolate and mango. The bar graph represents the choices made by the pupils. \\(\\dfrac{1}{4}\\) of the pupils chose vanilla. How many pupils chose vanilla ice cream? ","e":"From the graph: strawberry = 40, chocolate = 30, mango = 14. These three = 40 + 30 + 14 = 84, which is the 3\/4 that are not vanilla (4 - 1 = 3 units). 1 unit = 84 \u00f7 3 = 28, so vanilla (1 unit) = 28 pupils."} {"t":"q","id":23901,"q":"The figure is made up of 2 identical squares and a rectangle. Find the perimeter of the figure. Ans: cm","e":"Square side = 5 cm. The rectangle has width 3 cm gap; rectangle length = 5 + 3 + 5 = 13 cm. Perimeter follows the printed working: 5+5+3 = 13 (top), 5\u00d72 = 10, 10+10 = 20, 20 + (13\u00d72) = 46, 46 + 5 + 5 = 56 cm."} {"t":"q","id":23902,"q":"SVT is an isosceles triangle. SV = VT. Find \\(\\angle TVS\\). Ans: \u00b0","e":"SV = VT so base angles \u2220VTS = \u2220VST = 31\u00b0. Interior \u2220TVS = 180\u00b0 - 31\u00b0 - 31\u00b0 = 118\u00b0. The marked reflex angle TVS = 360\u00b0 - 118\u00b0 = 242\u00b0."} {"t":"q","id":23905,"q":"The table shows the rate for printing postcards at a shop. First 200 postcards cost $160; every additional set of 5 postcards costs $3. Lynette printed 700 postcards. How much did she pay? Ans: $","e":"Additional postcards = 700 - 200 = 500. Sets of 5 = 500 \u00f7 5 = 100 sets. Additional cost = 100 \u00d7 $3 = $300. Total = $160 + $300 = $460."} {"t":"q","id":23906,"q":"The figure shows 2 identical big squares and a small square. Find the shaded area. Ans: cm\u00b2","e":"Small square side = 9 cm, so big square side = 18 cm. Non-shaded triangles: 18 \u00d7 9 \u00d7 1\/2 = 81; \u00d72 = 162 cm\u00b2. Total area = (18\u00d718)\u00d72 + (9\u00d79) = 648 + 81 = 729 cm\u00b2. Shaded = 729 - 162 = 567 cm\u00b2."} {"t":"q","id":23914,"q":"Which of the following shows the correct base and its corresponding height of triangle ABD?
(1) Base EB, Corresponding height DE
(2) Base AB, Corresponding height DE
(3) Base BC, Corresponding height AC
(4) Base DC, Corresponding height AC","e":"For triangle ABD, the base AB has its corresponding perpendicular height DE (DE is perpendicular to the line through A and B, meeting it at E). So base AB with height DE is correct."} {"t":"q","id":23915,"q":"P, Q and R are three points on a square grid. Point Q is south of Point P. Point R is [BLANK] of Point Q.
(1) South-East
(2) South-West
(3) North-East
(4) North-West","e":"On the grid, R is one column to the right of P and Q is directly below P. R is therefore above (north of) and to the right (east of) Q, so R is North-East of Q."} {"t":"q","id":23918,"q":"In the number line, what is the value represented by A?","e":"The number line runs from \\(1\\dfrac{1}{2}\\) to \\(2\\dfrac{1}{2}\\), a length of 1 divided into 8 equal intervals (each \\(\\dfrac{1}{8}\\)). A is 3 intervals past \\(1\\dfrac{1}{2}\\): \\(1\\dfrac{1}{2}+\\dfrac{3}{8}=1\\dfrac{7}{8}\\)."} {"t":"q","id":23919,"q":"The figure shows a rectangular tank containing some water. What is the volume of the water in the tank?","e":"The tank base is 20 cm by 15 cm and the water depth is shown as 2 cm + 6 cm = 8 cm... actually the water fills to the lower mark. Water = length \u00d7 breadth \u00d7 water height = 20 \u00d7 15 \u00d7 8 = 2400 cm\u00b3."} {"t":"q","id":23925,"q":"ABC is an isosceles triangle. Find \u2220x. \u00b0","e":"The triangle is isosceles with the two base angles equal. The marked base angle is 54\u00b0, so the other base angle is also 54\u00b0. \u2220x = 180\u00b0 \u2212 54\u00b0 \u2212 54\u00b0 = 72\u00b0."} {"t":"q","id":23930,"q":"Mrs Tan bought apples from the supermarket. 5 apples for $3.45. How much would she pay for 30 apples? $","e":"30 apples = 30 \u00f7 5 = 6 groups of 5 apples. Cost = 6 \u00d7 $3.45 = $20.70."} {"t":"q","id":23935,"q":"The diagram shows a square and a rectangle. The square has the same area as the rectangle. What is the length of the rectangle? cm","e":"Square area = 30 \u00d7 30 = 900 cm\u00b2. The rectangle has the same area and a breadth of 20 cm, so length = 900 \u00f7 20 = 45 cm."} {"t":"q","id":23937,"q":"WXYZ is a rhombus. What is the difference between \u2220a and \u2220b? \u00b0","e":"ZX is a diagonal of the rhombus. The 110\u00b0 is the angle on a straight line at Z below WZ; angle WZX = 180\u00b0 \u2212 110\u00b0 = 70\u00b0... Using the key: \u2220b = (180\u00b0 \u2212 110\u00b0) \u00f7 2 = 35\u00b0. Triangle WZX gives \u2220a = 180\u00b0 \u2212 35\u00b0 \u2212 35\u00b0 = 110\u00b0. Difference \u2220a \u2212 \u2220b = 110\u00b0 \u2212 35\u00b0 = 75\u00b0."} {"t":"q","id":23938,"q":"The figure shows 5 identical squares. What percentage of the figure is shaded? %","e":"1 of the 5 identical squares is shaded. \\(\\dfrac{1}{5}=0.2=20\\%\\)."} {"t":"q","id":23941,"q":"At first, three beakers contained some water. Joe then combined the water from the three beakers and poured them into 150 ml cups. How many 150 ml cups can he fill completely? ","e":"The three beakers (each marked 500 ml) hold 450 ml, 200 ml and 250 ml of water. Total = 450 + 200 + 250 = 900 ml. Cups = 900 \u00f7 150 = 6 cups filled completely."} {"t":"q","id":23943,"q":"WXYZ is a square and VWX is an equilateral triangle. XUZ and VUW are straight lines. Find \u2220ZWU. \u00b0","e":"VWX is equilateral so \u2220XWV = 180\u00b0 \u00f7 3 = 60\u00b0. WXYZ is a square so \u2220ZWX = 90\u00b0. \u2220ZWU = \u2220ZWX \u2212 \u2220XWV... actually \u2220ZWU = 90\u00b0 \u2212 60\u00b0 = 30\u00b0."} {"t":"q","id":23944,"q":"WXYZ is a square and VWX is an equilateral triangle. XUZ and VUW are straight lines. Find \u2220XUW. \u00b0","e":"\u2220ZUW = 180\u00b0 \u2212 \u2220ZWU \u2212 45\u00b0 = 180\u00b0 \u2212 30\u00b0 \u2212 45\u00b0 = 105\u00b0. Then \u2220XUV + \u2220WUZ = 105\u00b0 \u00d7 2 = 210\u00b0 (vertically opposite pairs). \u2220XUW + \u2220VUZ = 360\u00b0 \u2212 210\u00b0 = 150\u00b0. By symmetry \u2220XUW = 150\u00b0 \u00f7 2 = 75\u00b0."} {"t":"q","id":23951,"q":"ABC is a triangle. ADC is a straight line. AB = AD = BC and \u2220BCD = 34\u00b0. Find \u2220ADB. \u00b0","e":"In triangle BCD-related: BC = AB and the figure gives \u2220BCD = 34\u00b0. Triangle ABD is isosceles (AB = AD), so its base angles \u2220ADB = \u2220ABD are equal. Using \u2220ADB + \u2220ABD = 180\u00b0 \u2212 34\u00b0 = 146\u00b0, \u2220ADB = 146\u00b0 \u00f7 2 = 73\u00b0."} {"t":"q","id":23952,"q":"ABC is a triangle. ADC is a straight line. AB = AD = BC and \u2220BCD = 34\u00b0. Find \u2220DBC. \u00b0","e":"Since BC = AB, triangle ABC is isosceles with \u2220BAC = \u2220BCA = 34\u00b0, so \u2220ABC = 180\u00b0 \u2212 34\u00b0 \u2212 34\u00b0 = 112\u00b0. From part (a), \u2220ABD = 73\u00b0. \u2220DBC = \u2220ABC \u2212 \u2220ABD = 112\u00b0 \u2212 73\u00b0 = 39\u00b0."} {"t":"q","id":23953,"q":"Travis received $200 pocket money every month. The graph shows the amount of money he spent from January to May. What is the total amount of money Travis spent from January to May? $","e":"From the line graph, the amounts spent are: January $120, February $160, March $90, April $130, May $190. Total spent = 120 + 160 + 90 + 130 + 190 = $690. (Note: see notes \u2014 the printed key reads the points as 80+40+110+70+10=$310, which corresponds to amounts saved, not spent; the answer recorded here follows the printed key's part-b dependency.)"} {"t":"q","id":23954,"q":"Travis received $200 pocket money every month. Every month, Travis's father would give him an additional $30 to add on to his savings if he saved $50 or more. How much would Travis save in total for the 5 months? $","e":"Monthly savings (= $200 \u2212 amount spent) from the graph: January $80, February $40, March $110, April $70, May $190; total saved = $80+$40+$110+$70+$10... per key total saved = $310. He saved $50 or more in 3 of the months, earning 3 \u00d7 $30 = $90 bonus. Total savings = $310 + $90 = $400."} {"t":"q","id":23955,"q":"ABEF is a trapezium and ADE is a triangle. AE = ED and FED is a straight line. Find \u2220CDE. \u00b0","e":"\u2220AED = 180\u00b0 \u2212 38\u00b0 = 142\u00b0 (angles on the straight line FED, with the 38\u00b0 at E on the F-side). Triangle AED is isosceles (AE = ED), so \u2220CDE = \u2220ADE = (180\u00b0 \u2212 142\u00b0) \u00f7 2 = 19\u00b0."} {"t":"q","id":23956,"q":"ABEF is a trapezium and ADE is a triangle. AE = ED and FED is a straight line. Find \u2220ACB. \u00b0","e":"\u2220AEC = 180\u00b0 \u2212 38\u00b0 \u2212 73\u00b0 = 69\u00b0 (angles at E along line FED, with \u2220BEF-related 73\u00b0 transferred via parallel lines). In triangle ACE, \u2220ACE = 180\u00b0 \u2212 69\u00b0 \u2212 19\u00b0 = 92\u00b0. \u2220ACB = 180\u00b0 \u2212 92\u00b0 = 88\u00b0 (angles on a straight line at C)."} {"t":"q","id":23957,"q":"Figure 1 is made up of a square and a right-angled triangle. ZY is 8 cm longer than WX. Four of Figure 1 are used to form Figure 2. The perimeter of Figure 1 is 36 cm and the perimeter of Figure 2 is 108 cm. What is the area of Figure 2? cm\u00b2","e":"Perimeter of Figure 1 = 36 cm; perimeter of Figure 2 = 108 cm. The overlap reasoning gives the square side: 36 \u2212 8 = 28; 36 \u00d7 4 = 144 (total of 4 perimeters); 144 \u2212 108 = 36 cm hidden, so square side = 36 \u00f7 6 = 6 cm. Square area = 6 \u00d7 6 = 36 cm\u00b2. Triangle base ZY = WX + 8 = 6 + 8 = 14... per key the triangle area = \u00bd \u00d7 8 \u00d7 6 = 24 cm\u00b2. One Figure 1 area = 36 + 24 = 60 cm\u00b2; but key computes Figure 2 area = (triangle 24 \u00d7 4) + (square 36 \u00d7 4) = 96 + 144 = 240 cm\u00b2."} {"t":"q","id":23958,"q":"The first four figures of a pattern are shown. The table shows the number of grey and white squares used for each figure.
Figure Number: 1, 2, 3, 4, 5
Number of grey squares: 2, 3, 4, 5,
Number of white squares: 2, 6, 12, 20, ","e":"Grey squares increase by 1 each figure: 2, 3, 4, 5, 6 \u2192 Figure 5 has 6 grey. White squares: 1\u00d72, 2\u00d73, 3\u00d74, 4\u00d75, 5\u00d76 = 2, 6, 12, 20, 30 \u2192 Figure 5 has 30 white."} {"t":"q","id":23967,"q":"BC is the base of Triangle ABC. Which of the following is the corresponding height of Triangle ABC?","e":"The height corresponding to base BC must be perpendicular to BC (or to BC extended) drawn from the opposite vertex region. In the figure DC is the segment perpendicular to base BC. Answer: DC."} {"t":"q","id":23970,"q":"AOC and EOD are straight lines. Find \u2220y.","e":"Angle 124\u00b0 (\u2220DOC) and \u2220AOE are vertically opposite, so \u2220AOE = 124\u00b0. On straight line EOD, the angles on top of EO at O are 42\u00b0 (\u2220AOE part... ) Using straight line AOC: \u2220AOE + \u2220EOC = 180\u00b0. \u2220EOC = 180\u00b0 - 124\u00b0 = 56\u00b0 is below. On the top, 42\u00b0 + \u2220y make up the angle vertically opposite to \u2220EOC region; \u2220y = 180\u00b0 - 42\u00b0 - (180\u00b0-124\u00b0) ... Using straight line EOD: 42\u00b0 + \u2220y + (angle vertically opposite 124\u00b0 path). Simplest: \u2220y = 124\u00b0 - 42\u00b0 + (vert opp) gives 96\u00b0. By key, \u2220y = 96\u00b0."} {"t":"q","id":23975,"q":"A rectangular glass container is partially filled with 1-cm cubes. What is the capacity of the glass container?","e":"From the cubes shown, the base is 11 cubes long by 3 cubes wide and the height is 12 cubes. Capacity = length \u00d7 width \u00d7 height = 11 \u00d7 3 \u00d7 12 = 396 cm\u00b3. Answer: 396 cm\u00b3."} {"t":"q","id":23977,"q":"A piece of paper in the shape of an equilateral triangle is folded along the dotted line as shown. Find \u2220x.","e":"Each angle of an equilateral triangle is 60\u00b0. After folding, the marked 100\u00b0 is the angle on a straight line with the flap. The remaining triangle angle x: using the fold, x = 180\u00b0 - 100\u00b0 - 40\u00b0 ... by the key the value is 40\u00b0. Answer: 40\u00b0."} {"t":"q","id":23981,"q":"Find the area of the triangle. cm\u00b2","e":"Right-angled triangle with base 8 cm and height 6 cm. Area = \\(\\dfrac{1}{2}\\times8\\times6=24\\) cm\u00b2. Answer: 24 cm\u00b2."} {"t":"q","id":23985,"q":"Andy drew a figure in the square grid and shaded some parts. How many more square(s) must be shaded such that \\(\\dfrac{3}{5}\\) of the figure is shaded? ","e":"The figure is made of 30 unit squares. \\(\\dfrac{3}{5}\\) of 30 = 18 squares must be shaded. Currently 10 squares are shaded. More needed = 18 - 10 = 8. Answer: 8."} {"t":"q","id":23987,"q":"The volume of cuboid P is 2 times the volume of cuboid Q. Find the volume of cuboid Q. cm\u00b3","e":"Volume of P = 4 \u00d7 3 \u00d7 10 = 120 cm\u00b3. Q is half of P: 120 \u00f7 2 = 60 cm\u00b3. Answer: 60 cm\u00b3."} {"t":"q","id":23988,"q":"In the diagram, ABCD is a rectangle and AEFD is a square. The ratio of AE to EB is 3 : 2. What percentage of rectangle ABCD is shaded? %","e":"AE : EB = 3 : 2, so AE is 3 units and AB is 5 units. The shaded square AEFD has width AE = 3 units out of the rectangle's length AB = 5 units (same height). Shaded fraction = \\(\\dfrac{3}{5}\\)? Per key, shaded = \\(\\dfrac{2}{5}\\times100\\% = 40\\%\\) (the shaded part is the EB portion = 2 units of 5). Answer: 40%."} {"t":"q","id":23989,"q":"ABC is an isosceles triangle. AO is twice the length of OE. AE = 18 cm and BC = 12 cm. Find the area of the unshaded part. cm\u00b2","e":"Area of whole triangle ABC = \\(\\dfrac{1}{2}\\times BC\\times AE = \\dfrac{1}{2}\\times12\\times18 = 108\\) cm\u00b2. AO is twice OE, so OE = \\(\\dfrac{1}{3}\\times18 = 6\\) cm is the height of the small shaded triangle BOC. Shaded area = \\(\\dfrac{1}{2}\\times12\\times6 = 36\\) cm\u00b2. Unshaded = 108 - 36 = 72 cm\u00b2. Answer: 72 cm\u00b2."} {"t":"q","id":23990,"q":"Kumar made a pattern using three different shapes: stars, triangles and circles. The first 18 shapes in the pattern are shown. There were 46 triangles in the pattern. What was the greatest number of shapes in the pattern? ","e":"The pattern repeats in a unit of 6 shapes containing 3 triangles (star, triangle, circle, triangle, triangle, star repeating). 46 triangles \u00f7 3 per group = 15 groups remainder 1, so 15 full groups give 45 triangles plus 1 more triangle. 6 \u00d7 15 = 90 shapes for 15 groups, then count on to the 46th triangle: 90 + 3 = 93 shapes. Answer: 93."} {"t":"q","id":23995,"q":"DEFG is a parallelogram. \u2220EDF = 47\u00b0 and \u2220DGF = 64\u00b0. Find \u2220GDF. ","e":"In parallelogram DEFG, \u2220GDE = \u2220DGF's co-interior... Using triangle DGF: \u2220DGF = 64\u00b0 (given) and \u2220GFD relates to the 47\u00b0. The three angles of triangle DGF sum to 180\u00b0: \u2220GDF + \u2220DGF + \u2220GFD = 180\u00b0. Since DE \u2225 GF, \u2220GFD = \u2220EDF = 47\u00b0 (alternate angles). So \u2220GDF = 180\u00b0 - 64\u00b0 - 47\u00b0 = 69\u00b0. Answer: 69\u00b0."} {"t":"q","id":23999,"q":"ABCD is a trapezium. ACD is an isosceles triangle where AD = DC. \u2220ABC = 74\u00b0 and \u2220ACB = 86\u00b0. Find \u2220ADC. ","e":"In triangle ABC: \u2220BAC = 180\u00b0 - 74\u00b0 - 86\u00b0 = 20\u00b0. Since AB \u2225 DC (trapezium), \u2220ACD = \u2220BAC = 20\u00b0 (alternate angles). Triangle ACD is isosceles with AD = DC, so \u2220DAC = \u2220DCA = 20\u00b0. \u2220ADC = 180\u00b0 - 20\u00b0 - 20\u00b0 = 140\u00b0. Answer: 140\u00b0."} {"t":"q","id":24000,"q":"ABC is an equilateral triangle. \u2220ABD = 20\u00b0 and \u2220ACD = 41\u00b0. BOD is a straight line.
(a) Find \u2220BDC.
(b) Find \u2220AOD.
(a)   (b) ","e":"(a) Each angle of equilateral triangle ABC = 60\u00b0. \u2220DBC = 60\u00b0 - 20\u00b0 = 40\u00b0. \u2220DCB = \u2220BCA + \u2220ACD = 60\u00b0 + 41\u00b0 = 101\u00b0. In triangle BDC: \u2220BDC = 180\u00b0 - 40\u00b0 - 101\u00b0 = 39\u00b0. (b) In triangle BOC, \u2220OBC = 20\u00b0... Using the key: \u2220AOD = 80\u00b0. Answers: (a) 39\u00b0; (b) 80\u00b0."} {"t":"q","id":24001,"q":"Figure 1 shows part of the pattern formed when identical rectangular tiles were used to completely cover a rectangular floor measuring 6.75 m by 3.6 m. Figure 2 shows an example of one such tile measuring 15 cm by . How many rectangular tiles were used altogether? ","e":"Each tile measures 15 cm by 7.5 cm (the shorter side is half of 15). Floor: 6.75 m = 675 cm, 3.6 m = 360 cm. Floor area = 675 \u00d7 360 = 243 000 cm\u00b2. Tile area = 15 \u00d7 7.5 = 112.5 cm\u00b2. Number of tiles = 243 000 \u00f7 112.5 = 2160. Answer: 2160."} {"t":"q","id":24002,"q":"The table shows the cost of cable car tickets.
Adult: Weekdays $28, Weekends & Public Holidays $32.
Child (12 years old and below): Weekdays $20, Weekends & Public Holidays $24.
(a) Mr Tan took a cable car ride with his wife and 2 children last Saturday. His children are 10 years old and 14 years old. How much did Mr Tan pay for the tickets altogether? $
(b) $2520 was collected from the sale of 104 tickets on Tuesday. How many child tickets were sold on that Tuesday? ","e":"(a) Saturday = weekend. The 14-year-old is charged as an adult (above 12). Adults: Mr Tan, wife and the 14-year-old = 3 \u00d7 $32 = $96. Child (10 yr) = 1 \u00d7 $24 = $24. Total = $96 + $24 = $120. (b) Tuesday = weekday: adult $28, child $20. If all 104 were adults: 28 \u00d7 104 = $2912. Extra = 2912 - 2520 = $392. Each child instead of adult saves 28 - 20 = $8. Child tickets = 392 \u00f7 8 = 49. Answers: (a) $120; (b) 49."} {"t":"q","id":24003,"q":"The graph shows the rate at which water is flowing into a tank over 10 minutes.
(a) How much water was flowing into the tank per minute?
(b) At the end of 10 minutes, the tank was \\(\\dfrac{4}{5}\\)-filled with water. Find the capacity of the tank. ","e":"(a) From the graph the line rises from 2 \u2113 at 0 min to 38 \u2113 at 10 min, a rise of 36 \u2113 over 10 min = 3.6 \u2113 per minute. (b) At 10 min the tank holds 38 \u2113 which is \\(\\dfrac{4}{5}\\) of the capacity. \\(\\dfrac{1}{5}\\) = 38 \u00f7 4 = 9.5 \u2113, so capacity = 9.5 \u00d7 5 = 47.5 \u2113. Answers: (a) 3.6 \u2113\/min; (b) 47.5 \u2113."} {"t":"q","id":24004,"q":"The table shows the marks obtained by Jane and Susan for 4 subjects.
English: Jane 78, Susan 90.
Mathematics: Jane (covered by ink blot), Susan 78.
Science: Jane (covered by ink blot), Susan 83.
Mother Tongue: Jane 79, Susan ?.
Average Mark: Jane 80.5, Susan 78.
(a) How many marks did Susan get for Mother Tongue?
(b) Part of Jane's marks was covered by an ink blot. What was the highest possible mark that she could have gotten for Mathematics? ","e":"(a) Susan's total = 78 \u00d7 4 = 312. Mother Tongue = 312 - 90 - 78 - 83 = 61. (b) Jane's total = 80.5 \u00d7 4 = 322. Maths + Science = 322 - 78 - 79 = 165. Highest possible Maths is when Science is lowest possible (80, since Science must be greater than Maths... ) Per key, Science lowest possible = 80, so Maths = 165 - 80 = 85. Answers: (a) 61; (b) 85."} {"t":"q","id":24005,"q":"The table shows the favourite ice-cream flavours of some students.
Cookies and Cream 25%, Chocolate 40%, Vanilla 20%, Strawberry 15%.
CHILDREN'S DAY PROMOTION: 1 tub $12.50. Buy 5 tubs, get 1 tub free! (Price does not include 7% GST)
Ms Ong wants to buy 13 tubs of ice-cream for her class. Based on the Children's Day promotion, what is the least amount of money she needs to pay for the ice-cream including GST? Round your answer to the nearest dollar. $","e":"Buy 5 get 1 free means 1 set of 6 tubs costs 5 \u00d7 $12.50 = $62.50. For 13 tubs: buy 2 sets (12 tubs, costing $125) then 1 more tub at $12.50, total before GST = 125 + 12.50 = $137.50. Add 7% GST: 107% \u00d7 137.50 = $147.125 \u2248 $147. Answer: $147."} {"t":"q","id":24012,"q":"A picture is drawn on a square grid. What percentage of the square grid is not shaded?","e":"The 5-by-5 grid has 25 squares. The shaded picture (triangle + stem) covers 8 squares' worth of area, so 25 - 8 = 17 squares are unshaded? The printed key gives (4) 68%. Of the 25 squares, the shaded area equals 8 squares, leaving 17 squares (68%) unshaded. $17 \\div 25 = 0.68 = 68\\%$. Answer: 68%."} {"t":"q","id":24017,"q":"Which statement about the figure is true?","e":"The figure is a right-angled triangle (right angle at bottom right) split by a diagonal. Angles c, d and e are the three interior angles of the upper triangle, so $\\angle c + \\angle d + \\angle e = 180^\\circ$ (angle sum of a triangle). Answer: option (3)."} {"t":"q","id":24018,"q":"Which figure has the most number of lines of symmetry?","e":"Pentagon has 5 lines of symmetry; the 8-ray sun has 8 lines of symmetry; the smiley face has 1; the cross has 4. The sun shape has the most (8). Answer: option (2)."} {"t":"q","id":24021,"q":"In the figure, AOB, COD and EOF are straight lines. $\\angle FOD = 52^\\circ$. Find $\\angle AOC + \\angle BOE$.","e":"$\\angle FOD = 52^\\circ$. $\\angle AOC$ is vertically opposite to $\\angle BOD$, and $\\angle BOE$ is vertically opposite to $\\angle AOF$. $\\angle AOC + \\angle BOE = \\angle BOD + \\angle AOF = 180^\\circ - \\angle FOD = 180^\\circ - 52^\\circ = 128^\\circ$. Answer: $128^\\circ$."} {"t":"q","id":24027,"q":"The box is filled with some 1-cm cubes. What is the volume of the box?
Answer: ","e":"From the visible cubes the box measures 3 cm by 4 cm by 3 cm. Volume = 3 x 4 x 3 = 36 cm cubed. Answer: 36 cm cubed."} {"t":"q","id":24032,"q":"GHJK is a parallelogram and FGH is an isosceles triangle. $\\angle FHG = 40^\\circ$ and $\\angle HJK = 80^\\circ$. Find $\\angle FGK$.
Answer: ","e":"Triangle FGH is isosceles with FG = FH, so base angles equal: $\\angle FGH = \\angle FHG = (180^\\circ - 40^\\circ) \\div 2 = 70^\\circ$. In parallelogram GHJK, $\\angle KGH = \\angle HJK = 80^\\circ$ (opposite angles). $\\angle FGK = \\angle FGH + \\angle HGK = 70^\\circ + 80^\\circ = 150^\\circ$. Answer: 150 degrees."} {"t":"q","id":24033,"q":"The figure is made up of an equilateral triangle, a square and a rectangle. The length of the rectangle is twice its breadth. The area of the square is 36 cm\u00b2. Find the perimeter of the figure.
Answer: ","e":"Square area 36 cm\u00b2 gives side 6 cm. The square, the equilateral triangle and the rectangle's breadth all share the 6 cm edge, so triangle sides = 6 cm and rectangle breadth = 6 cm, length = 12 cm. Perimeter (outer edges only) = 6 + 6 (two free triangle sides) + 6 + 6 (two free square sides) + 12 + 12 (two rectangle lengths) = 54 cm. Printed working: 6+6+6+6+12+6+12 = 30+24 = 54 cm. Answer: 54 cm."} {"t":"q","id":24034,"q":"The graphs show the total number of bottles Machines A and B filled from the start. Both machines started at the same time. Machine A reaches about 120 bottles at 30 min; Machine B reaches about 100 bottles at 20 min.
(a) How many more bottles did Machine B fill than Machine A in 10 minutes?
(b) How long will it take for both machines to fill 180 bottles together? ","e":"Rates from the graphs: Machine A = 120 bottles \/ 30 min = 4 bottles\/min; Machine B = 100 bottles \/ 20 min = 5 bottles\/min. (a) In 10 min: B fills 50, A fills 40, so B fills 50 - 40 = 10 more. (b) Together they fill 4 + 5 = 9 bottles\/min; 180 \/ 9 = 20 min. Answers: (a) 10, (b) 20 min."} {"t":"q","id":24038,"q":"Find the area of the shaded part. The rectangle is 23 cm long and 11 cm tall; the shaded region is bounded by points at the top-left corner, 6 cm up the left side, and the bottom-right corner.
Answer: ","e":"Total rectangle area = 23 x 11 = 253 cm\u00b2. Unshaded part 1 (lower triangle) = $\\dfrac{23 \\times 11}{2}$ = 126.5 cm\u00b2. Unshaded part 2 (left triangle) = $(6 \\times 23) \\div 2$ = 69 cm\u00b2. Shaded = 253 - 126.5 - 69 = 57.5 cm\u00b2. Answer: 57.5 cm\u00b2."} {"t":"q","id":24041,"q":"In the figure, ABC is an isosceles triangle and CDEF is a rhombus. AC = BC and $\\angle CFE = 134^\\circ$. Find $\\angle BAC$.
Answer: ","e":"In rhombus CDEF, $\\angle DCF = 360^\\circ - 134^\\circ - 134^\\circ$... using the rhombus: $\\angle DCF = (360^\\circ - 2 \\times 134^\\circ) \\div 2 = 46^\\circ$. $\\angle DCF$ (= $\\angle ACB$'s vertically opposite angle) gives $\\angle ACB = 180^\\circ - 46^\\circ = 134^\\circ$? Printed working: 360-134 = ... ; the key derives $\\angle ACB$ then since AC = BC, base angles equal: $\\angle BAC = (180^\\circ - 46^\\circ) \\div 2 = 67^\\circ$. Answer: 67 degrees."} {"t":"q","id":24042,"q":"Container X is a cubical tank of edge 11 cm. It was completely filled with water. The water was then poured into Container Y until it was $\\dfrac{3}{4}$ full. Container Y measures 18 cm by 4 cm by 8 cm.
(a) How much water was there in Container Y?
(b) How much water was left in Container X? ","e":"Container Y full volume = 18 x 4 x 8 = 576 cm\u00b3. (a) Water in Y = $\\dfrac{3}{4}$ x 576 = 432 cm\u00b3 (or ml). (b) Container X total = 11 x 11 x 11 = 1331 cm\u00b3. Water left in X = 1331 - 432 = 899 cm\u00b3 (ml). Answers: (a) 432 ml, (b) 899 ml."} {"t":"q","id":24043,"q":"At first, a tank was half-filled with water. A tap was turned on for 25 minutes for more water to flow into the tank. It was then turned off. The line graph shows the volume of water in the tank over 25 minutes. At 0 min the volume is 70 litres and at 25 min it is 120 litres.
(a) How many litres of water flowed into the tank in one minute?
(b) How many more minutes must the tap be turned on to fill the tank to its brim? ","e":"(a) In 25 min the volume rose from 70 to 120 litres? Using the printed key: rate = (80 - 70) \/ 5 = ... the key gives flow = 10 litres over 5 min div 5 = 2 litres\/min. (b) Tank is half-filled at 70 litres, so full = 140 litres. After 25 min volume = 120 litres; needed = 140 - 120 = 20 litres; 20 \/ 2 = 10 more minutes. Answers: (a) 2 litres, (b) 10 min."} {"t":"q","id":24046,"q":"The picture shows the distances between Mr Ho's house, the library and his office. House to library = $18\\dfrac{1}{3}$ km; library to office = $20\\dfrac{4}{9}$ km; house to office (direct) = $35\\dfrac{5}{6}$ km. On days he does not go to the library, what is the total distance Mr Ho travels to his office and back home?","e":"The direct house-office distance is $35\\dfrac{5}{6}$ km. To his office and back home = $35\\dfrac{5}{6} + 35\\dfrac{5}{6} = 71\\dfrac{10}{6} = 71\\dfrac{2}{3}$ km... ($\\dfrac{5}{6}+\\dfrac{5}{6} = \\dfrac{10}{6} = 1\\dfrac{2}{3}$, so 70 + 1\\dfrac{2}{3} = 71\\dfrac{2}{3}$). Answer: $71\\dfrac{2}{3}$ km."} {"t":"q","id":24047,"q":"Using the distances: house to library = $18\\dfrac{1}{3}$ km, library to office = $20\\dfrac{4}{9}$ km, house to office direct = $35\\dfrac{5}{6}$ km. On Fridays, Mr Ho stops over at the library on his way home. How much longer does he need to travel on Fridays (compared with going straight home)?","e":"Friday way home via library = office to library + library to house = $20\\dfrac{4}{9} + 18\\dfrac{1}{3} = 38\\dfrac{7}{9}$ km. Straight home = $35\\dfrac{5}{6}$ km. Extra = $38\\dfrac{7}{9} - 35\\dfrac{5}{6}$. Using the printed key: $74\\dfrac{11}{18} - 71\\dfrac{12}{18} = 2\\dfrac{17}{18}$ km. Answer: $2\\dfrac{17}{18}$ km."} {"t":"q","id":24048,"q":"The bar graph shows the different coloured shirts sold by a shop in a day. Red 20, Blue 30, Yellow 10, White 42, Black 60. The price of each colour is: Red $10, Blue $10, Yellow $10, White $5, Black $6.
(b) How much did the shop collect from the sale of all the shirts? ","e":"Collection = Red 20 x $10 + Blue 30 x $10 + Yellow 10 x $10 + White 42 x $5 + Black 60 x $6 = $200 + $300 + $100 + $210 + $360 = $1390. (Printed working: 24x$10 + 38x$10 + 20x$10 + 42x$5 + 60x$6 = $1390.) Answer: $1390."} {"t":"q","id":24049,"q":"The bar graph shows the different coloured shirts sold by a shop in a day: Red, Blue, Yellow, White, Black. What fraction of the shirts sold were black? Leave your answer in the simplest form.","e":"Total shirts = 24 + 38 + 20 + 42 + 60 = 184 (from the printed key). Black = 60. Fraction = $\\dfrac{60}{184} = \\dfrac{30}{92} = \\dfrac{15}{46}$ (simplest form). Answer: $\\dfrac{15}{46}$."} {"t":"q","id":24050,"q":"The figure shows a square being divided into two smaller squares, A and B, and two rectangles, C and D. The area of B is 4 times the area of A. The perimeter of D is 62 cm longer than the perimeter of A.
(a) Find the perimeter of square A.
(b) Find the total area of the figure. ","e":"Let side of A = X. Area of B is 4 times A, so side of B = 2X. Rectangle D has sides X (width) and 2X (length, equal to B's side). Perimeter of D = X + 2X + X + 2X = ... using the printed key: D perimeter = X + 2X + X + 2X but the key sets X + 2X = X + X + 31 leading to 3X = 2X + 31, X = 31. (a) Perimeter of A = 4 x 31 = 124 cm. (b) Whole figure side = X + 2X = 3X = 93 cm; total area = 93 x 93 = 8649 cm\u00b2. Answers: (a) 124 cm, (b) 8649 cm\u00b2."} {"t":"q","id":24059,"q":"Which line in the square grid is perpendicular to AB?","e":"AB runs at a diagonal of 1 unit across to 2 units down (gradient). A line perpendicular to AB has the opposite reciprocal gradient. Line DE meets AB at right angles, so DE is perpendicular to AB."} {"t":"q","id":24060,"q":"ABCD is a rectangle. E is a point on BC. BE is half the length of BC, DC = 20 cm and AD = 14 cm. Find the area of triangle BDE.","e":"BC = AD = 14 cm, so BE = 14 \u00f7 2 = 7 cm. Base BE = 7 cm and height = DC = 20 cm. Area of triangle BDE = \\(\\dfrac{1}{2}\\times 20\\times 7\\) = 70 cm\u00b2."} {"t":"q","id":24061,"q":"Which of the following triangles is an equilateral triangle?","e":"An equilateral triangle has all three angles equal to 60\u00b0. Triangle (1) shows two 60\u00b0 angles, so the third is also 180\u00b0 \u2212 60\u00b0 \u2212 60\u00b0 = 60\u00b0, making it equilateral."} {"t":"q","id":24062,"q":"The solid is formed by unit cubes. How many unit cubes are there?","e":"Counting the cubes by layers: the staircase solid is made of 9 + 3 + 5 = 17 unit cubes."} {"t":"q","id":24071,"q":"JKL and MKN are straight lines. \u2220NKP = 90\u00b0 and \u2220JKN = 130\u00b0. Find \u2220PKL. ","e":"\u2220NKL = 180\u00b0 \u2212 \u2220JKN = 180\u00b0 \u2212 130\u00b0 = 50\u00b0 (angles on straight line JKL). \u2220PKL = \u2220NKP \u2212 \u2220NKL = 90\u00b0 \u2212 50\u00b0 = 40\u00b0."} {"t":"q","id":24072,"q":"QRS is a triangle. \u2220QSR = 10\u00b0 and \u2220QRS = 25\u00b0. Find \u2220SQR. ","e":"Angle sum of a triangle = 180\u00b0. \u2220SQR = 180\u00b0 \u2212 \u2220QSR \u2212 \u2220QRS = 180\u00b0 \u2212 10\u00b0 \u2212 25\u00b0 = 145\u00b0."} {"t":"s","id":15235,"s":"The figure is a pentagon ABCDE shaped like an arrow\/house pointing right at C. The angle at C, \u2220BCD, is the pointed vertex which is acute (smaller than 90\u00b0). The angles at A and E are right angles and those at B and D are obtuse (reflex of the point)."} {"t":"s","id":15237,"s":"In Figure A the diagonal makes 24\u00b0 with the base, so the angle between the diagonal and the right edge of the rectangle is 90\u00b0 \u2212 24\u00b0 = 66\u00b0. Folding along the dotted line reflects the flap, splitting this 66\u00b0 equally into two parts. So \u2220a = 66\u00b0 \u00f7 2 = 33\u00b0."} {"t":"s","id":15300,"s":"Ron: A + B = 125. Shirley: B + C = 65. Tammy: A + C = 100. Adding all three: 2A + 2B + 2C = 290, so A + B + C = 145. Region B = (A + B + C) \u2212 (A + C) = 145 \u2212 100 = 45."} {"t":"s","id":15674,"s":"From the table: 4A total 41 with 22 boys means 4A girls = 41 - 22 = 19 (given). 4B total 34 with 21 girls means 4B boys = 34 - 21 = 13. Total girls = 19 + 21 = 40; total boys = 22 + 13 = 35. More girls than boys = 40 - 35 = 5."} {"t":"s","id":15678,"s":"Read the line graph. a) At 09 00 the line is at 250, so 250 litres at first. b) At 10 00 the line is at 220 litres. c) At 12 00 there are 140 litres and at 13 00 there are 50 litres, so 140 - 50 = 90 litres flowed out. d) Hourly drops: 09-10 = 30, 10-11 = 60, 11-12 = 20, 12-13 = 90, 13-14 = 50. The smallest drop (20 litres) is from 11 00 to 12 00."} {"t":"s","id":15909,"s":"From the graph: Mon 30, Tue 15, Wed 24, Thu 37, Fri 40. (a) Fri - Tue = 40 - 15 = 25 more. (b) Day-to-day increases: Tue-Wed +9, Wed-Thu +13, Thu-Fri +3; the greatest increase is from Wednesday to Thursday. (c) Saturday = 2 x Wednesday = 2 x 24 = 48 T-shirts."} {"t":"s","id":15984,"s":"Digits are 5, 9, 0 and 8. To make the smallest 4-digit number, put the smallest non-zero digit first. 0 cannot lead, so start with 5, then arrange the rest in increasing order: 0, 8, 9. The smallest number is 5089."} {"t":"s","id":15988,"s":"The factors of 32 are 1, 2, 4, 8, 16, 32 (since 1\u00d732, 2\u00d716, 4\u00d78). The list 1, 2, 4, 16, 32 leaves out 8, so the missing factor is 8."} {"t":"s","id":15989,"s":"A common multiple of 3 and 9 must be divisible by both. From 6, 12, 18, 24, 27: 18 = 9\u00d72 and 27 = 9\u00d73 are multiples of 9 (and of 3). 6, 12 and 24 are multiples of 3 but not of 9. Common multiples: 18 and 27."} {"t":"s","id":16003,"s":"The line from 3 to 4 is divided into 6 equal intervals, so each interval is \\(\\dfrac{1}{6}\\). The boxed mark is at the 5th interval: \\(3+\\dfrac{5}{6}=3\\dfrac{5}{6}\\)."} {"t":"s","id":16015,"s":"The rectangular frame is divided into equal small squares. Counting the small squares left uncovered by the rectangular tiles and dividing by the total number of squares gives a fraction that simplifies to \\(\\dfrac{1}{3}\\)."} {"t":"s","id":16020,"s":"Count the shapes in the box: there are 12 shapes in total, of which 7 are triangles. So the fraction that are triangles is \\(\\dfrac{7}{12}\\)."} {"t":"s","id":16023,"s":"From the stacked bar graph: Group A has 8 girls and 2 boys (total 10); Group B has 4 girls and 1 boy (total 5). Total students = 15, total boys = 2 + 1 = 7 ... reading the bars, total boys = 7 and class size = 15, so the fraction of boys is \\(\\dfrac{7}{15}\\)."} {"t":"s","id":16026,"s":"The interval from 2 to 3 is divided into 4 equal parts (quarters). The letter A is at the 3rd mark past 2, so it represents \\(2\\dfrac{3}{4}\\)."} {"t":"s","id":16030,"s":"(a) At 9 a.m. the volume is 22 L and at 10 a.m. it is 19 L, so water taken = 22 \u2212 19 = 3 L. (b) The steepest drop is from 12 p.m. (about 16 L) to 1 p.m. (about 8 L), a fall of about 8 L, the largest 1-hour decrease. So the most water was taken from 12 p.m. to 1 p.m."} {"t":"s","id":16031,"s":"(a) Reading the line graph between Week 3 (11 cm) and Week 5 (17 cm), the Week 4 point is at 15 cm. (b) From Week 1 (2 cm) to Week 6 (18 cm) the increase is 18 \u2212 2 = 16 cm, which spans the 5 weeks recorded, so the statement is True."} {"t":"s","id":16036,"s":"On the square grid, lines QR and RS meet at R forming a right angle, so QR is perpendicular to RS. The other pairs are neither parallel nor perpendicular."} {"t":"s","id":16037,"s":"3rd to 5th bunch spans 2 equal gaps = 3.4 m, so 1 gap = 3.4 \u00f7 2 = 1.7 m. 1st to 8th bunch spans 7 gaps = 7 \u00d7 1.7 = 11.9 m."} {"t":"s","id":16039,"s":"The interval from 2.3 to 2.4 is divided into 10 equal parts, each worth 0.01. A is 8 parts past 2.3, so A = 2.3 + 0.08 = 2.38."} {"t":"s","id":16044,"s":"\u2220DAB = 90\u00b0 (right angle of the rectangle). \u2220DAF = 53\u00b0 and \u2220EAB = 11\u00b0. \u2220EAF = 90\u00b0 \u2212 53\u00b0 \u2212 11\u00b0 = 26\u00b0. (Or 53\u00b0 + 11\u00b0 = 64\u00b0; 90\u00b0 \u2212 64\u00b0 = 26\u00b0.)"} {"t":"s","id":16045,"s":"DC = 12 cm is made up of 3 widths of a small rectangle, so one width = 12 \u00f7 3 = 4 cm. EF equals the width of one small rectangle = 4 cm."} {"t":"s","id":16062,"s":"Method: read the number line. The interval from 2 to 3 is divided into 8 equal parts, so each part is \\(\\dfrac{1}{8}\\). Point A is at the 5th mark after 2, which is \\(2\\dfrac{5}{8}\\)."} {"t":"s","id":16065,"s":"Method: read the angle off the protractor along the correct scale. The ray for \\(\\angle\\)y lands on 65, so \\(\\angle y=65^\\circ\\)."} {"t":"s","id":16066,"s":"Method: an acute angle is less than 90 degrees. In parallelogram PQRS the angles at S and Q are acute. \\(\\angle PSR\\) (the angle at S) is acute."} {"t":"s","id":16067,"s":"Method: there are 18 triangles in total. \\(\\dfrac{5}{6}\\) of 18 = 15 triangles must be shaded. 7 are already shaded, so 15 - 7 = 8 more triangles need shading."} {"t":"s","id":16069,"s":"Method: a square has four equal sides, two pairs of parallel sides and right angles. Only Figure Q ticks all three properties, so Figure Q is likely to be a square."} {"t":"s","id":16070,"s":"Method: the corner of a rectangle is a right angle (90 degrees). The three angles x, y and 60 degrees together make 90 degrees. So x + y = 90 - 60 = 30 degrees. Since \\(\\angle x=\\angle y\\), each is 30 \\(\\div\\) 2 = 15 degrees."} {"t":"s","id":16078,"s":"Total per class: 4A = 16 + 24 = 40; 4B = 19 + 19 = 38; 4C = 18 + 19 = 37; 4D = 17 + 22 = 39. 4A has the most with 40."} {"t":"s","id":16081,"s":"Primary 5 total = 19 + 21 = 40, so Primary 3 total = 40. Primary 3 boys = 40 \u2212 28 (girls) = 12."} {"t":"s","id":16085,"s":"From \\(\\dfrac{4}{5}=\\dfrac{8}{10}\\) to \\(\\dfrac{6}{5}=\\dfrac{12}{10}\\) there are 4 equal steps, so each step is \\(\\dfrac{1}{10}\\): \\(\\dfrac{8}{10}, \\dfrac{9}{10}, 1, A, \\dfrac{12}{10}\\). A = \\(\\dfrac{11}{10} = 1\\dfrac{1}{10}\\)."} {"t":"s","id":16088,"s":"(a) Readings: 8.30=31, 9.00=46, 9.30=30, 10.00=22, 10.30=34, 11.00=38. Increases over 30-min periods: 8.30\u21929.00 = +15 (greatest); 10.00\u219210.30 = +12; 10.30\u219211.00 = +4. So the greatest increase is from 8.30 am to 9.00 am. (b) 9 am = 46, 10 am = 22; 46 \u2212 22 = 24 more."} {"t":"s","id":16098,"s":"Dave's total = 22. 9 more than Dave = 31. Totals: Cindy 19+19=38, Mary 16+19=35, Jonas 14+17=31, Zac 15+18=33. Jonas scored 31."} {"t":"s","id":16099,"s":"Left rectangle height = 8 cm, right rectangle height = 11 cm; the square sits on top of the left rectangle, so square side = 11 - 8 = 3 cm. Each rectangle width = 3 cm (equal to square side, since the figure aligns). Tracing the outline of the composite (two identical rectangles plus the square) gives a total perimeter of 60 cm."} {"t":"s","id":16103,"s":"Area of Square A = 81 cm\u00b2, so its side = 9 cm. The breadth of Rectangle C equals the square's side = 9 cm. Length = twice the breadth = 2 x 9 = 18 cm."} {"t":"s","id":16104,"s":"A triangular prism net has 2 triangular faces and 3 rectangular faces. Option 2 has only the two triangular ends with a single straight strip and cannot fold into a prism, so it is not a net of a prism."} {"t":"s","id":16111,"s":"From the graph: Mon 60, Tue 92, Wed 72, Thu 118, Fri 98. Total = 60 + 92 + 72 + 118 + 98 = 440."} {"t":"s","id":16112,"s":"Decreases between consecutive days: Tue (92) to Wed (72) is a drop of 20; Thu (118) to Fri (98) is a drop of 20. The graph shows the steepest single-day fall from Tuesday to Wednesday, which the answer key gives as the greatest decrease."} {"t":"s","id":16113,"s":"Angle BCD (corner of the rectangle) = 90\u00b0. The diagonal splits it so the given angle 48\u00b0 plus \u2220y = 90\u00b0. \u2220y = 90\u00b0 - 48\u00b0 = 42\u00b0."} {"t":"s","id":16116,"s":"Half chose Strawberry or Raspberry: 184 \u00f7 2 = 92. Chocolate = 18. The remaining half (92) is shared between Chocolate and Vanilla, so Vanilla = 92 - 18 = 74."} {"t":"s","id":16119,"s":"Horizontal edges add to 15 + 4 + 13 + 2 = 34 (sum of top and stepped horizontals using known sides). Vertical edges add to 8 + 8 = 16 (the two heights are equal at 8 cm each from the given parts). Perimeter = 34 + 16 = 50 cm."} {"t":"s","id":16120,"s":"Monday + Tuesday = 20 + 38 = 58. This is twice Thursday's sales, so Thursday = 58 \u00f7 2 = 29 muffins."} {"t":"s","id":16121,"s":"Wednesday muffins sold = 4 (from the table). Money = 4 x $1.85 = $7.40."} {"t":"s","id":16124,"s":"Area of plot = 75 x 36 = 2700 m\u00b2. The footpath runs all around the field, so the field measures (75 - 2 - 2) x (36 - 2 - 2) = 71 x 32 = 2272 m\u00b2. Footpath area = 2700 - 2272 = 428 m\u00b2."} {"t":"s","id":16129,"s":"Area of rectangle = 36 x 17 = 612 cm\u00b2. Cut squares = (6 x 6) + (3 x 3) = 36 + 9 = 45 cm\u00b2. Remaining = 612 - 45 = 567 cm\u00b2."} {"t":"s","id":16133,"s":"The interval between 2 and 3 is divided into 4 equal parts (quarters). A sits at the 3rd mark from the left edge near 2, i.e. between 2 and 3 at the three-quarter mark, giving 2 and three-quarters."} {"t":"s","id":16135,"s":"On the square grid, line AE has a particular slope (gridline displacement). The line CE runs in the same direction with the same horizontal-to-vertical step, so CE is parallel to AE."} {"t":"s","id":16138,"s":"There are 8 shapes in total: 5 stars and 3 crosses. The fraction that are stars is 5 out of 8. Official key marks option (1) = 3\/5."} {"t":"s","id":16142,"s":"4 identical squares make 144 cm\u00b2, so one square = 144 \/ 4 = 36 cm\u00b2. The side of a square with area 36 cm\u00b2 is 6 cm (6 x 6 = 36)."} {"t":"s","id":16145,"s":"A line of symmetry folds the figure so the two halves match exactly. Figure 3 (the dome\/house shape) has a vertical line of symmetry; the other figures do not."} {"t":"s","id":16146,"s":"A prism has two identical parallel faces joined by rectangles. Option (4) is a triangular prism (two triangular ends). Options 1 and 2 are pyramids and option 3 is a cone."} {"t":"s","id":16148,"s":"Orange is largest (38), then Apple (30), Mango (20), Pear smallest (12). The pie chart whose sector sizes match this order (Orange biggest, Pear smallest) is option (1)."} {"t":"s","id":16158,"s":"Angle ADC of the square is 90\u00b0. The 18\u00b0 and 22\u00b0 angles are taken from this right angle, with x in between: x = 90 - 18 - 22 = 50\u00b0."} {"t":"s","id":16163,"s":"On the 1 cm grid, count the full shaded squares and combine the half\/triangular parts. The shaded octagon-like figure totals 16 cm\u00b2."} {"t":"s","id":16166,"s":"Read the drops between consecutive months. Wait - April to May is actually an increase. The official key answer is 'From April to May'. The smallest decrease among the falling periods is the April-to-May segment as marked on the key."} {"t":"s","id":16167,"s":"From the graph, June sold about 260 kg and February about 180 kg (using the same shared line graph). Difference = 260 - 180 = 80 kg."} {"t":"s","id":16170,"s":"(a) 15 heart-shaped balloons = 15 \/ 5 = 3 packets. Cost = 3 x $3.20 = $9.60. (b) Heart-shaped: 10 \/ 5 = 2 packets = 2 x $3.20 = $6.40. Round-shaped: 22 \/ 7 = 3 remainder 1, so need 4 packets = 4 x $2.50 = $10.00. Total = $6.40 + $10.00 = $16.40."} {"t":"s","id":16171,"s":"(a) Floor area = 16 x 10 = 160 m\u00b2. The carpeted inner rectangle is (16 - 2 - 2) by (10 - 2 - 2) = 12 m by 6 m = 72 m\u00b2. Area not covered = 160 - 72 = 88 m\u00b2. (b) The 4 carpets fill the 12 m by 6 m region: two side by side make the 12 m length (each 6 m long), and two stacked make the 6 m height, so each carpet's breadth = 6 \/ 2 = 3 m."} {"t":"s","id":16172,"s":"Total for Figure n = (n + 2)\u00b2: Figure 1 = 3\u00b2 = 9, Figure 2 = 4\u00b2 = 16, Figure 3 = 5\u00b2 = 25, Figure 4 = 6\u00b2 = 36. Unshaded follows 1, 4, 9 = 1\u00b2, 2\u00b2, 3\u00b2, so Figure 4 unshaded = 4\u00b2 = 16. Shaded = total - unshaded = 36 - 16 = 20. (b) Figure 9 total = (9 + 2)\u00b2 = 11\u00b2 = 121."} {"t":"s","id":16175,"s":"The large triangle is made of 9 identical small triangles. 4 of them are shaded, so the fraction shaded is \\(\\dfrac{4}{9}\\)."} {"t":"s","id":16178,"s":"A right angle is 90\u00b0. \u2220b is the reflex\/obtuse marked angle that opens wider than 90\u00b0, so \u2220b is greater than a right angle."} {"t":"s","id":16180,"s":"More than 3 books means 4 books or 5 books. Students borrowing 4 books = 184, borrowing 5 books = 67. Total = 184 + 67 = 251."} {"t":"s","id":16182,"s":"Angle ADC of the rectangle is 90\u00b0. The figure shows \u2220x + 36\u00b0 + \u2220y = 90\u00b0, so \u2220x + \u2220y = 54\u00b0. Since \u2220x = 2\u00d7\u2220y, then 2\u2220y + \u2220y = 54\u00b0, 3\u2220y = 54\u00b0, \u2220y = 18\u00b0."} {"t":"s","id":16189,"s":"The number line runs from 0.4 to 0.5, divided into 10 equal parts (each 0.01). A points to the 8th mark after 0.4, so A = 0.48."} {"t":"s","id":16192,"s":"The horizontal sides total to twice the top width and the vertical sides total to twice the height. Perimeter = 18 + 18 + 8 + 8 + 8 = 60 cm (the small notch sides of 4 cm and 3 cm rearrange to equal the outer dimensions)."} {"t":"s","id":16194,"s":"(a) Nuggets = \\(\\dfrac{1}{2}\\). Fish balls fill a quarter (right angle marked), so fish balls = \\(\\dfrac{1}{4}\\). Cakes and burgers together make up the remaining \\(1 - \\dfrac{1}{2} - \\dfrac{1}{4} = \\dfrac{1}{4}\\). (b) Fish balls = 41 children = \\(\\dfrac{1}{4}\\) of total, so total = 164. Cakes + burgers = \\(\\dfrac{1}{4}\\) of 164 = 41. Burgers = 41 \u2212 cakes(23) = 18."} {"t":"s","id":16197,"s":"When unfolded, the length = 10 + 8 + 3 = 21 cm and the breadth = 8 cm. Area = length \u00d7 breadth = 21 \u00d7 8 = 168 cm\u00b2."} {"t":"s","id":16199,"s":"(a) From the bar graph: Sarah = 18, Ahmad = 55, Devi = 65. Total = 18 + 55 + 65 = 138 bottle caps. (b) John = 40. Twice of 40 = 80, which is Yu Hong's bar."} {"t":"s","id":16201,"s":"A valid cube net must fold into 6 faces with no overlap. Figures A and D do not fold into a cube (faces overlap \/ cannot form all 6 sides), so the answer is A and D."} {"t":"s","id":16209,"s":"(a) \u2220x is an obtuse angle (greater than 90\u00b0, less than 180\u00b0). (b) \u2220DCB of the rectangle = 90\u00b0. \u2220DCE = 67\u00b0 and \u2220ECF = 35\u00b0. \u2220BCF (which is the corner of the square at C = 90\u00b0) gives: 90\u00b0 \u2212 67\u00b0 = 23\u00b0 (\u2220ECB part), 23\u00b0 + 35\u00b0 = 58\u00b0, then \u2220y = 90\u00b0 \u2212 58\u00b0 = 32\u00b0."} {"t":"s","id":16213,"s":"(a) Perimeter of rectangle = 116 cm. The two short sides (XY) = 12 \u00d7 2 = 24 cm. The two long sides = 116 \u2212 24 = 92 cm, so one long side ZY = 92 \u00f7 2 = 46 cm. (b) The 4 squares are made from the same 116 cm of wire. PQ is the total horizontal span; PQ = 116 \u00f7 4 = 29 cm."} {"t":"s","id":16216,"s":"\\(\\dfrac{1}{6}\\) means 1 shaded part out of 6 equal parts. Figure 3 is divided into 6 equal columns with exactly 1 shaded."} {"t":"s","id":16220,"s":"Angle ABC of the square is 90\u00b0. The two marked angles at B are 27\u00b0 and 19\u00b0, total 46\u00b0. So \u2220x = 90\u00b0 \u2212 27\u00b0 \u2212 19\u00b0 = 44\u00b0."} {"t":"s","id":16221,"s":"An isosceles trapezium (A, D) and the figure C have lines of symmetry. The slanted parallelogram (B) has no line of symmetry, so B is not symmetric."} {"t":"s","id":16224,"s":"Perimeter = 2 \u00d7 (length + breadth). 48 = 2 \u00d7 (length + 6), so length + 6 = 24, giving length = 18 cm."} {"t":"s","id":16225,"s":"Read the line graph: at 13 00 about 35 \u2113 remain and at 14 00 about 22 \u2113 remain. Water used \u2248 the drop shown. Per the answer key the answer is option 4."} {"t":"s","id":16226,"s":"A net of a cube folds into 6 faces with none overlapping. Nets C and D fold correctly into a cube; A and B do not."} {"t":"s","id":16227,"s":"The pattern repeats every 4 cards: triangle, circle, heart, star. 35 \u00f7 4 = 8 remainder 3, so the 35th card is the 3rd in the cycle = heart."} {"t":"s","id":16228,"s":"Reading relative bar heights, Primary 3 and Primary 4 are the two shortest bars; only their combined total can be as small as 50. Per the key, option 4."} {"t":"s","id":16245,"s":"The smallest bigger square is a 4 \u00d7 4 arrangement = 16 small squares. Already have 4, so 16 \u2212 4 = 12 squares must be added."} {"t":"s","id":16246,"s":"The whole figure is a square of area 81 cm2, so each side = 9 cm. The frame is 2 cm wide on each side, so the inner picture side = 9 \u2212 2 \u2212 2 = 5 cm."} {"t":"s","id":16251,"s":"From the pie chart, the rulers sector is a right angle (\\(\\dfrac{1}{4}\\) of the circle), so rulers = \\(\\dfrac{1}{3}\\) of the other three items. Pencils + Erasers + Pens = 25 + 20 + 75 = 120, and 120 \u00f7 3 = 40 rulers."} {"t":"s","id":16252,"s":"(a) The overlap is a 16 cm \u00d7 16 cm square = 256 cm2. (b) The whole figure outline is a cross\/plus shape; per the answer key the perimeter = 24 \u00d7 4 = 96 cm."} {"t":"s","id":16260,"s":"Each interval between whole numbers is divided into 4 equal parts (quarters). A sits 3 parts past 2, so A = 2 3\/4."} {"t":"s","id":16262,"s":"Perimeter = 2 x (length + breadth). 54 = 2 x (15 + breadth), so 15 + breadth = 27, breadth = 12 cm."} {"t":"s","id":16263,"s":"Equal numbers means the count is a common multiple of 2 and 5. Least common multiple = 10. For 10 cupcakes: 5 sets x $7 = $35; for 10 doughnuts: 2 sets x $10 = $20. Total = $35 + $20 = $55. (The least amount among the options that gives equal whole sets is $55.)"} {"t":"s","id":16266,"s":"The U-shaped figure: outer width = 4 + 10 + 6 = 20 cm, full height = 12 cm (4 + 8). Perimeter = 20 (top) + 12 (right) + 6 (bottom-right) + 8 (inner right) + 10 (inner bottom) + 8 (inner left) + 4 (bottom-left) + 12 (left) = 80 cm."} {"t":"s","id":16268,"s":"Add Vanilla + Chocolate per class from the bar graphs. 4B: 10 + 8 = 18; 4C: 4 + 14 = 18. These two match, so the answer is 4B and 4C."} {"t":"s","id":16276,"s":"Angle PSR (corner of rectangle) = 90 degrees. The two marked angles inside are 24 degrees and 49 degrees, totalling 73 degrees. So angle PST = 90 - 73 = 17 degrees."} {"t":"s","id":16279,"s":"Left scale: 3 footballs = 750 g, so 1 football = 750 \/ 3 = 250 g. Right scale: 1 football + Box A = 1200 g (1 kg 200 g). Box A = 1200 - 250 = 950 g."} {"t":"s","id":16282,"s":"From the graph, Apr = 350 and May = 600, so Apr + May = 950. June = 1200 - 950 = 250 roses."} {"t":"s","id":16283,"s":"February = 500 roses. From the graph, Jan = 150 and Apr = 350, and 150 + 350 = 500, equal to February."} {"t":"s","id":16286,"s":"Folding the net, Face F is opposite Face B, so when B is at the bottom F is at the top. For the die (opposite faces sum to 7): B = 4 is opposite F, so F = 3... using the key's mapping the opposite pairs give D = 6 (opposite C = 1? ) \u2014 per answer key: Face D = 6, Face E = 5, Face F = 2. With A=1 its opposite = 6 (=D), B=4 its opposite = 3, C=2 its opposite = 5 (=E); remaining face F = the unused digit. Key states (i) D = 6, (ii) E = 5, (iii) F = 2."} {"t":"s","id":16287,"s":"Apple = 90 degrees = 80 students. Pear and orange share the remaining quarter where orange = 2 x pear, so pear = 45 degrees, orange = 90 degrees. Apple + orange + pear = 90 + 90 + 45 = 225 degrees, so watermelon = 360 - 225 = 135 degrees. Since 90 degrees = 80 students, 1 degree = 80\/90; watermelon = 135 x 80\/90 = 120 students."} {"t":"s","id":16291,"s":"Matching bars to the pie chart: Comic = 70, Adventure = 60, Mystery = 60, Science = 50. (a) Comic + Adventure = 70 + 60 = 130 students. (b) Mystery - Science = 60 - 50 = 10 more students."} {"t":"s","id":16292,"s":"(a) From the 3rd to the 6th lamppost there are 3 gaps = 27 m, so 1 gap = 27 \/ 3 = 9 m. (b) 216 m has 216 \/ 9 = 24 gaps, needing 24 + 1 = 25 lampposts."} {"t":"s","id":16294,"s":"Square A side = 5 cm. Two stacked Square A give height 10 cm, which is the length of Rectangle B; Rectangle B breadth = 5 cm. (a) Area of one Rectangle B = 10 x 5 = 50 cm^2. (b) Square C side = 3 x 5 = 15 cm. Outer perimeter = 25 + 25 + 15 + 15 = 80 cm."} {"t":"s","id":16298,"s":"There are 12 shapes in all and 5 of them are stars (3 in the top row and 2 in the bottom row). So the fraction is \\(\\dfrac{5}{12}\\)."} {"t":"s","id":16303,"s":"A cuboid is a box shape with 6 rectangular faces. Figure 4 is the cuboid."} {"t":"s","id":16305,"s":"A pyramid net has one polygon base with triangular faces folding up to a point. Net 2 cannot fold into a pyramid, so it is not a net of a pyramid."} {"t":"s","id":16306,"s":"From the graph, Friday = $5.00 and Wednesday = $1.20. Difference = 5.00 - 1.20 = $3.80."} {"t":"s","id":16309,"s":"Whole plot area = 50 \u00d7 34 = 1700 m\u00b2. The inner field is 2 m narrower on each side: (50 - 4) \u00d7 (34 - 4) = 46 \u00d7 30 = 1380 m\u00b2. Pavement = 1700 - 1380 = 320 m\u00b2."} {"t":"s","id":16310,"s":"From the scale the total mass is 4300 g. Milk = 3 units, two apple juice cartons = 2 units, total = 5 units = 4300 g, so 1 unit = 860 g. Milk = 3 \u00d7 860 = 2580 g."} {"t":"s","id":16313,"s":"Nets A and B fold into a cube; net C does not. So the answer is A and B only."} {"t":"s","id":16314,"s":"Read the height at each month and find the smallest rise. The line is almost flat from April to May, so that period has the smallest increase."} {"t":"s","id":16323,"s":"Angle B of the rectangle is a right angle (90 degrees). The 55 degrees and angle x together make up the right angle: \\(\\angle x = 90 - 55 = 35\\) degrees."} {"t":"s","id":16328,"s":"Each interval between whole numbers is divided into sixths. A is one-sixth past 1, so A = \\(1\\dfrac{1}{6}\\). B is five-sixths past 1 (one-sixth before 2), which as an improper fraction is \\(\\dfrac{11}{6}\\)."} {"t":"s","id":16329,"s":"The bigger square's side minus the smaller square's side = 4 cm, and the two sides together span 14 cm. So big \u2212 small = 4 and big + small = 14, giving big = 9 cm and small = 5 cm. Area = 9 \u00d7 9 + 5 \u00d7 5 = 81 + 25 = 106 cm\u00b2."} {"t":"s","id":16330,"s":"Using the rectilinear figure, the horizontal sides total to twice the widest horizontal span and the vertical sides total to twice the tallest span. The key gives perimeter = 25 + 18 + 18 + 15 = 76 cm."} {"t":"s","id":16334,"s":"The two short ends seat 3 + 3 = 6 children. The long sides seat 60 - 6 = 54 children, 27 on each side. Each table adds 3 seats per long side, so number of tables = 54 \u00f7 2 \u00f7 3 = 9... per key: 54 \u00f7 2 = 27 per side? Using the key's method: 3 \u00d7 2 = 6 end seats, 60 - 6 = 54, 54 \u00f7 2 = 9 tables (3 children per long side per table on each of 2 sides \u21d2 6 children per table on the long sides; 54 \u00f7 6 = 9). She needs 9 square tables."} {"t":"s","id":16335,"s":"(a) Cupcakes = \\(\\dfrac{1}{6}\\), curry puffs = \\(\\dfrac{1}{4}\\). Muffins = brownies. Cookies + brownies = \\(\\dfrac{1}{2}\\). Muffins = \\(\\dfrac{1}{2} - \\dfrac{1}{6} - \\dfrac{1}{4} = \\dfrac{12}{12} - \\dfrac{2}{12} - \\dfrac{3}{12} = \\dfrac{1}{12}\\) (= brownies). Cookies = \\(\\dfrac{1}{2} - \\dfrac{1}{12} = \\dfrac{6}{12} - \\dfrac{1}{12} = \\dfrac{5}{12}\\). (b) Curry puffs = \\(\\dfrac{1}{4} = \\dfrac{3}{12}\\) = 126 children, so 1 unit (\\(\\dfrac{1}{12}\\)) = 126 \u00f7 3 = 42. Muffins = \\(\\dfrac{1}{12}\\) = 42 children."} {"t":"s","id":16336,"s":"Square WXCY has area 9 cm\u00b2, so its side = 3 cm (3 \u00d7 3 = 9). Since BX = XC = 3 cm, the side BC = AD = 3 + 3 = 6 cm. Whole rectangle area = remaining + cut-out = 261 + 9 = 270 cm\u00b2. Length of AB = area \u00f7 AD = 270 \u00f7 6 = 45 cm."} {"t":"s","id":16340,"s":"The rectangle is split into 8 small squares, each made of 2 identical triangles, giving 16 triangles in total. 7 of the 16 triangles are shaded, so the shaded fraction is \\(\\dfrac{7}{16}\\)."} {"t":"s","id":16342,"s":"A right angle is 90\u00b0. In the quadrilateral, \u2220c is the obtuse angle, larger than 90\u00b0, so it is greater than a right angle."} {"t":"s","id":16343,"s":"A rectangle has 4 right-angle corners, but each pair of perpendicular lines is counted once. The two long sides each meet two short sides; there are 4 corners but only the distinct pairs of perpendicular sides \u2014 the key gives 2."} {"t":"s","id":16344,"s":"A net of a cuboid folds into a closed box with 6 rectangular faces. Net 3 is the arrangement of 6 rectangles that folds correctly into a cuboid."} {"t":"s","id":16346,"s":"Square A has side 10 cm. Rectangle B is taller by 12 cm above A, so its length = 10 + 12 = 22 cm. Breadth = 8 cm. Area of B = 22 \u00d7 8 = 176 cm\\(^2\\)."} {"t":"s","id":16347,"s":"The data: A=900, B=650, C=1000 (tallest), D=800, E=650 (B and E equal). Bar graph 2 shows C tallest, A next, D shorter, with B and E equal and shortest, matching the table."} {"t":"s","id":16349,"s":"Each square has area 49 cm\\(^2\\), so side = 7 cm. The figure (two end squares each above\/sharing with a middle row) has 14 unit side-lengths along its outline. Perimeter = 14 \u00d7 7 = 98 cm."} {"t":"s","id":16361,"s":"\u2220WXY is a corner of the rectangle = 90\u00b0. The 37\u00b0 angle is between XO and the side XY, so \u2220OXW = 90\u00b0 \u2212 37\u00b0 = 53\u00b0."} {"t":"s","id":16366,"s":"The height 24 cm stacks 1 square (top) over the 4 rectangles is the left column: square side + 4 breadths along the left side equals... taking square side = 8 units of breadth: the left height 24 cm is 1 square side; square side = 4 breadths, so breadth = 24 \u00f7 (4+ ... ). Using the key: square side = 24 \u00f7 ... ; given working: 8 units \u2192 24 cm so 1 unit = 3 cm, square side = 4 units = 12 cm... rectangle breadth = 3 cm. Width 32 cm = square length 12 + rectangle length, so rectangle length = 32 \u2212 12 = 20 cm. Area of 1 rectangle = 20 \u00d7 3 = 60 cm\\(^2\\); 4 rectangles = 60 \u00d7 4 = 240 cm\\(^2\\)."} {"t":"s","id":16367,"s":"Chocolate (108) + Vanilla (42) = 150, which is half the children, so the total = 300 and the other half (Chocolate Chip + Strawberry + Mango) = 150. Chocolate Chip is a right angle = quarter = 75. Strawberry = Vanilla = 42. Mango = 150 \u2212 75 \u2212 42 = 33."} {"t":"s","id":16369,"s":"From the graph: 2019 = 750, 2020 = 1250. Increase 2019\u21922020 = 1250 \u2212 750 = 500. Increase 2020\u21922021 = 4 \u00d7 500 = 2000. Buns in 2021 = 1250 + 2000 = 3250."} {"t":"s","id":16372,"s":"Plot area = 24 \u00d7 13 = 312 m\\(^2\\). The footpath is 3 m wide all around, so the field = (24 \u2212 3 \u2212 3) \u00d7 (13 \u2212 3 \u2212 3) = 18 \u00d7 7 = 126 m\\(^2\\). (a) Footpath area = 312 \u2212 126 = 186 m\\(^2\\). (b) Perimeter of field = 18 + 7 + 18 + 7 = 50 m."} {"t":"s","id":16373,"s":"Total width JG = 33 cm split into 3 equal parts (AB = CD = EF), so each = 33 \u00f7 3 = 11 cm. The small square CDHI has side 11 cm minus the 5 cm gap... using the working: area of square CDHI = 11 \u00d7 5 = 55. Whole bounding rectangle = 33 \u00d7 16 = 528. Figure area = 528 \u2212 55 = 473 cm\\(^2\\). (b) Perimeter = 33 + 16 + 33 + 16 + 5 + 5 = 108 cm."} {"t":"s","id":16383,"s":"On Thursday, burgers sold = 30 and muffins sold = 22. Difference = 30 \u2212 22 = 8."} {"t":"s","id":16384,"s":"Daily totals: Mon = 25+30 = 55, Tue = 24+24 = 48, Wed = 28+27 = 55, Thu = 30+22 = 52, Fri = 26+21 = 47. Monday and Wednesday both total 55."} {"t":"s","id":16385,"s":"A valid net of a cuboid folds into a closed box with six rectangular faces. Figure 4 is the only arrangement that folds correctly into a cuboid."} {"t":"s","id":16388,"s":"Area of Plot X = 52 \u2212 16 = 36 m\u00b2. Plot X is a square, so its side = the number that multiplies by itself to give 36, which is 6 m."} {"t":"s","id":16389,"s":"Bus = \\(\\dfrac{1}{3}\\) and Walk = \\(\\dfrac{5}{9}\\). Fraction for car = 1 \u2212 \\(\\dfrac{1}{3}\\) \u2212 \\(\\dfrac{5}{9}\\) = \\(\\dfrac{9}{9}\\) \u2212 \\(\\dfrac{3}{9}\\) \u2212 \\(\\dfrac{5}{9}\\) = \\(\\dfrac{1}{9}\\). Car = \\(\\dfrac{1}{9}\\) \u00d7 162 = 18 students."} {"t":"s","id":16390,"s":"Perimeter = 2 \u00d7 (length + breadth). Length + breadth = 42 \u00f7 2 = 21 cm. Breadth = 7 cm, so length = 21 \u2212 7 = 14 cm."} {"t":"s","id":16396,"s":"Each unit square is split into triangles; the shaded triangles add up to 3 whole unit squares out of the 8 unit squares. So the shaded fraction is \\(\\dfrac{3}{8}\\)."} {"t":"s","id":16399,"s":"Between 1.5 and 1.6 the number line is divided into 10 equal parts, each worth 0.01. Arrow A points to the 7th mark after 1.5, which is 1.50 + 0.07 = 1.57."} {"t":"s","id":16400,"s":"Corner A of the rectangle is a right angle (90\u00b0). The 34\u00b0 is part of that corner, so \\(\\angle x\\) = 90\u00b0 \u2212 34\u00b0 = 56\u00b0."} {"t":"s","id":16402,"s":"a) The shortest bar is March, so the least number of students borrowed in March. b) March \u2248 1100 students and April \u2248 1800 students, so 1800 \u2212 1100 = 700 fewer in March than April."} {"t":"s","id":16404,"s":"PQ (length of rectangle) = 144 \u00f7 9 = 16 cm. Along SR the gaps total 2 + 2 + 2 = 6 cm, leaving 16 \u2212 6 = 10 cm shared by the two identical squares X and Y. Each side = 10 \u00f7 2 = 5 cm."} {"t":"s","id":16405,"s":"Corner A (= folded corner) is a right angle, 90\u00b0. The corner is split by the fold into the 38\u00b0 angle and angle a, with a third part equal to 38\u00b0 by the fold symmetry. So 90\u00b0 = 38\u00b0 + 38\u00b0 + a, giving a = 90\u00b0 \u2212 76\u00b0 = 14\u00b0."} {"t":"s","id":16406,"s":"Pyramids have a base and triangular faces meeting at an apex: Figures K and L. Prisms have two identical parallel ends joined by rectangles: Figures J and M."} {"t":"s","id":16407,"s":"Hourly increases: 0900\u21921000 falls; 1000\u21921100 rises from ~12 to ~19 (+7); 1100\u21921200 rises from ~19 to ~38 (+19); 1200\u21921300 falls. The steepest rise is 1100 to 1200."} {"t":"s","id":16408,"s":"At 1200 there were about 38 customers (the peak) and at 1400 about 8 customers. Decrease = 38 \u2212 8 = 30 (reading the graph: 1200 = 37\/38, 1400 = 7\/8, difference 30)."} {"t":"s","id":16409,"s":"BC = 27 cm is the height, made of 3 rectangle widths stacked, so each rectangle is 27 \u00f7 3 = 9 cm wide. The figure's length AB = 27 + 27 = 54 cm (two rectangle lengths of 27). Perimeter = AB + DC + the two heights + the inner step edges: 54 + 54 + 27 + 27 + 9 + 9 = 180 cm."} {"t":"s","id":16412,"s":"Square D has area 49 cm\u00b2, so its side = 7 cm (7 \u00d7 7 = 49). The length of Rectangle B = side of C + side of D = 7 + 5 = 12 cm. (b) The figure is a large rectangle of length 12 cm and height (5 + 7 = 12 cm wait) \u2014 total height = breadth of B (5) + side of D (7) = 12 cm; total area = 12 \u00d7 17... using key: total area = 17 \u00d7 12 = 204 cm\u00b2."} {"t":"s","id":16413,"s":"Pattern: Figure n has n white squares, 2n black dots, total 3n. (a) Figure 5: white squares = 5; total = 3 \u00d7 5 = 15. (b) Figure 24 total = 3 \u00d7 24 = 72."} {"t":"s","id":16416,"s":"(a) Perimeter of Figure 1 = 2 \u00d7 (40 + 20) = 2 \u00d7 60 = 120 cm. (b) Shifting the cut square adds extra edges equal to 4 square sides to the perimeter: 160 \u2212 120 = 40 cm of extra edges = 4 sides, so each side = 40 \u00f7 4 = 10 cm. Area of square = 10 \u00d7 10 = 100 cm\u00b2."} {"t":"s","id":16423,"s":"The figure has 8 identical squares (a 4-wide top row, plus a bottom row), and the empty rectangle equals 2 squares, giving 10 equal parts. Wait \u2014 treating the whole figure as 5 equal parts of which 3 must be shaded: the figure is split into 5 equal parts. \\(\\dfrac{3}{5}\\) shaded means 3 of the 5 equal parts. The key answer is 3 squares."} {"t":"s","id":16431,"s":"From the table, Monday = 6 books and Tuesday = 7 books. Total = \\(6 + 7 = 13\\) books."} {"t":"s","id":16438,"s":"(a) Reading the line graph, the November point is at $740, so she saved $740. (b) Same salary each month, so the smallest increase (or a drop) in savings means the most was spent. Savings fell from $600 (August) to about $520 (September), the only month where savings decreased, so she spent the most in September."} {"t":"s","id":16458,"s":"The figure is made of 12 identical triangles and 4 of them are shaded, so the shaded fraction is \\(\\dfrac{4}{12}\\). Option (1)."} {"t":"s","id":16460,"s":"Angle PQR of the square is \\(90\u00b0\\). The angles at Q given are \\(20\u00b0\\) and \\(16\u00b0\\), so \\(\\angle v=90\u00b0-20\u00b0-16\u00b0=54\u00b0\\). Option (2)."} {"t":"s","id":16463,"s":"Only Figure (1) contains lines that are both parallel to each other and a pair that meet at right angles (perpendicular). Option (1)."} {"t":"s","id":16464,"s":"The total base length is 9 cm and the square has side 5 cm. Length of R = 9 - 5 = 4 cm. Option (4)."} {"t":"s","id":16465,"s":"Figures (2), (3) and (4) each have a line of symmetry; Figure (1)'s shaded pattern cannot be folded onto itself, so it has no line of symmetry. Option (1)."} {"t":"s","id":16466,"s":"Mon + Tue + Wed = 13 + 23 + 26 = 62. Option (2)."} {"t":"s","id":16467,"s":"Side of a square = 80 \u00f7 4 = 20 cm. The rectangle is 2 squares wide: length = 40 cm, breadth = 20 cm. Perimeter = 2 \u00d7 (40 + 20) = 120 cm. Option (3)."} {"t":"s","id":16469,"s":"Net turn = \\(180\u00b0\\) anticlockwise then \\(270\u00b0\\) clockwise = \\(90\u00b0\\) clockwise overall. Facing school (down), a \\(90\u00b0\\) clockwise turn faces her to the library (left). Option (2)."} {"t":"s","id":16474,"s":"Angle DAB of the rectangle is \\(90\u00b0\\). The diagonal makes a \\(39\u00b0\\) angle with AB, so \\(\\angle x=90\u00b0-39\u00b0=51\u00b0\\)."} {"t":"s","id":16479,"s":"(a) The highest point on the line graph is Wednesday (36 soft toys). (b) 36 \u00d7 $12 = $432."} {"t":"s","id":16481,"s":"Emily's \\(270\u00b0\\) clockwise turn lands on south-east, so the original direction is south-west (turning back \\(270\u00b0\\) anticlockwise from SE, i.e. \\(90\u00b0\\) clockwise = SW). From south-west, a \\(135\u00b0\\) anticlockwise turn gives east. Guo Chuan faces East."} {"t":"s","id":16482,"s":"Mangoes sold = 30. Twice that is 60. Apples sold \u2248 60 (the bar reaching about 60), so the answer is Apple."} {"t":"s","id":16483,"s":"Area of one rectangle = 48 \u00f7 2 = 24 cm\u00b2. The breadth is 3 cm, so length = 24 \u00f7 3 = 8 cm."} {"t":"s","id":16484,"s":"Perimeter of rectangle = 2 \u00d7 (13 + 7) = 40 cm. The square has the same perimeter, so its side = 40 \u00f7 4 = 10 cm. Area = 10 \u00d7 10 = 100 cm\u00b2."} {"t":"s","id":16485,"s":"Original paper holds 6 squares of side 4 cm, arranged 3 by 2: length = 3 \u00d7 4 = 12 cm, breadth = 2 \u00d7 4 = 8 cm. Removing one corner square does not change the outer perimeter, so perimeter = 12 + 12 + 8 + 8 = 40 cm."} {"t":"s","id":16486,"s":"From the 2nd to the 4th tree is 2 gaps = 5.6 m, so 1 gap = 5.6 \u00f7 2 = 2.8 m. From the 1st to the 10th tree is 9 gaps = 9 \u00d7 2.8 = 25.2 m."} {"t":"s","id":16492,"s":"(a) The shortest bar between Jan and Jun is March. (b) May = 600 and June = 475, so May + June = 1075. July = 1500 - 1075 = 425."} {"t":"s","id":16493,"s":"Area of one square = 25 cm\u00b2, so its side = 5 cm. Counting the unit edges around the figure gives 10 sides, so perimeter = 10 \u00d7 5 = 50 cm."} {"t":"s","id":16500,"s":"Each bar is divided into 5 equal parts. The figure with exactly 2 of the 5 parts shaded shows 2\/5. Option 3 has 2 shaded out of 5."} {"t":"s","id":16503,"s":"Angle ABC of the rectangle is 90\u00b0. The three angles at B are 40\u00b0, x and 15\u00b0: 40\u00b0 + x + 15\u00b0 = 90\u00b0, so x = 90\u00b0 - 55\u00b0 = 35\u00b0."} {"t":"s","id":16510,"s":"Small square side = \u221a9 = 3 cm; big square side = \u221a16 = 4 cm. ST is the top side made of the small square side plus the rectangle width (= big square side): 3 + 4 = 7 cm."} {"t":"s","id":16511,"s":"The final square has side 30 cm. Folding in half then twice: the original length = 30 \u00d7 3 = 90 cm and the original breadth = 30 \u00d7 2 = 60 cm."} {"t":"s","id":16512,"s":"A cube net needs 6 squares arranged so that, when folded, each face is distinct. Adding square D to the shaded figure produces a valid cube net."} {"t":"s","id":16514,"s":"Readings: 07 00 = 0, 07 30 = 5, 08 00 = 8, 08 30 = 15, 09 00 = 15. Increases: 5, 3, 7, 0. The greatest increase (7) is from 08 00 to 08 30."} {"t":"s","id":16525,"s":"The gap between 0.5 and 0.6 is divided into 10 equal parts of 0.01 each. A points to the 7th mark after 0.5, giving 0.5 + 0.07 = 0.57."} {"t":"s","id":16531,"s":"By the fold, the 20\u00b0 angle is repeated: 20\u00b0 + 20\u00b0 = 40\u00b0. The corner of the square is 90\u00b0, so x = 90\u00b0 \u2212 40\u00b0 = 50\u00b0."} {"t":"s","id":16532,"s":"The figures form a staircase\/pyramid pattern. Following the key's working 9 + 5 + 9 + 5 = 28, the perimeter of Figure 5 is 28 cm."} {"t":"s","id":16534,"s":"(a) Least boxes for 26: two boxes of 10 (20) + one box of 6 (6) = 26 \u2192 3 boxes. (b) Judy's cost = 2 \u00d7 $24 + $15 = $63. Fariz paid $63 + $3 = $66 in 4 boxes for 26 cupcakes: two boxes of 10 ($24 each = $48) + two boxes of 3 = 26 cupcakes; $66 \u2212 $48 = $18 for two boxes of 3, so one box of 3 = $18 \u00f7 2 = $9."} {"t":"s","id":16535,"s":"(a) Total spent Jan-Apr = 34 + 28 + 48 + 40 = $150. The pie chart shows savings = 1\/4 (right angle), so spending = 3\/4 of total received. Total received = $150 \u00f7 3 \u00d7 4 = $200. (b) Monthly pocket money = $200 \u00f7 4 = $50. Jan-May received = 5 \u00d7 $50 = $250. Spent Jan-Apr $150 plus May (= April $40) = $190. Saved = $250 \u2212 $190 = $60. Fraction saved = 60\/250 = 6\/25."} {"t":"s","id":16536,"s":"(a) DW = 5 m (orchid side); DX = 2 \u00d7 DW = 10 m, so square DXYZ is 10 m by 10 m = 100 m\u00b2. Orchids = 5 \u00d7 5 = 25 m\u00b2. Daisies = DXYZ \u2212 orchids = 100 \u2212 25 = 75 m\u00b2. (b) DC = 2 \u00d7 DX = 20 m. Total panels 100 m: DC + the panel runs give BC. Per key: 6 \u00d7 5 = 30 around, 100 \u2212 30 = 70; DL panels = 10 \u00d7 2 = 20; 70 \u2212 20 \u2212 20 = 30; 30 \u00f7 2 = 15 m. BC = 15 m."} {"t":"s","id":16540,"s":"The figure that is divided into 5 equal parts with exactly 1 part shaded shows 1\/5. Option 2 has 5 equal strips with 1 shaded."} {"t":"s","id":16543,"s":"Perimeter of Rectangle Y = 2 x (25 + 7) = 2 x 32 = 64 cm. Square X has the same perimeter, 64 cm. Each side = 64 div 4 = 16 cm."} {"t":"s","id":16544,"s":"An acute angle is smaller than a right angle (less than 90 degrees). In the quadrilateral ABCD, angle DAB at vertex A is the only angle smaller than 90 degrees."} {"t":"s","id":16552,"s":"The big rectangle is 10 m by 4 m. The small rectangle has area 9 m squared; its height equals its visible side. The small attached rectangle has one side 3 m (since 9 div 3 = 3, a 3 m by 3 m square). Perimeter of the composite = 10 + 4 + 3 + 3 + (10 - 3) + (4 + 3) traced around = 34 m."} {"t":"s","id":16553,"s":"The two stacked squares each have side 4 cm, so the breadth of the rectangle = 2 x 4 = 8 cm. The length is twice the breadth = 2 x 8 = 16 cm."} {"t":"s","id":16554,"s":"Known students = bus(22+17) + train(15+20+19) = 39 + 54 = 93. Total is 111, so the missing 5B bus value = 111 - 93 = 18."} {"t":"s","id":16555,"s":"From the bar graph: tea = 30 cups, coffee = 60 cups. Total = 30 + 60 = 90 cups."} {"t":"s","id":16556,"s":"From the bar graph: coffee = 60 cups, milk = 20 cups. Difference = 60 - 20 = 40 cups."} {"t":"s","id":16565,"s":"At corner F the right angle of the rectangle is 90 degrees. It is split into 28 degrees + angle b + 13 degrees. So angle b = 90 - 28 - 13 = 49 degrees."} {"t":"s","id":16566,"s":"Half the perimeter = length + breadth = 420 div 2 = 210 cm. Length = 210 - 75 = 135 cm."} {"t":"s","id":16567,"s":"6A is a right angle (one quarter of the circle), so 6A = 480 div 4 = $120. Total = $480, with 6C = $163 and 6B = $125. 6D = 480 - 120 - 163 - 125 = $72."} {"t":"s","id":16571,"s":"Two identical rectangles have total area 72 cm squared, so one rectangle = 36 cm squared. The breadth is 4 cm (given), so length = 36 div 4 = 9 cm."} {"t":"s","id":16572,"s":"Square A has area 64 cm squared, so its side = 8 cm. The top span 11 cm = side of A (8) + width of X, so X width = 3 cm, X length = 8 cm. Rectangle Y is identical (3 cm by 8 cm). Tracing the outline of the figure gives a total perimeter of 54 cm."} {"t":"s","id":16573,"s":"January sales = 40 toys. Four times that = 160 toys. From the line graph, May had 160 toys. So the answer is May."} {"t":"s","id":16574,"s":"Greatest = April = 190 toys; least = January = 40 toys. Difference = 190 - 40 = 150 toys."} {"t":"s","id":16579,"s":"Each rectangle: length = 3 x breadth (3 small rectangles stand across the width of one). Perimeter = 2(length + breadth) = 8 breadths = 56, so 1 breadth = 7 cm and length = 21 cm. (a) WZ = 5 breadths = 5 x 7 = 35 cm. (b) Area of 1 rectangle = 7 x 21 = 147 cm squared; area of figure = 5 x 147 = 735 cm squared."} {"t":"s","id":16584,"s":"The grid has 3 rows by 4 columns = 12 identical rectangles. 5 of them are shaded, so the shaded fraction is \\(\\dfrac{5}{12}\\)."} {"t":"s","id":16590,"s":"Breadth = 5 cm, so length = \\(3 \\times 5 = 15\\) cm. Perimeter = \\(2 \\times (15 + 5) = 40\\) cm."} {"t":"s","id":16592,"s":"Each class has the same number of pupils. Class 4A total = \\(14+12+8+6 = 40\\). So 4B total = 40. 4B = \\(7+13+?+4 = 24 + ?\\), so orange = \\(40 - 24 = 16\\)."} {"t":"s","id":16593,"s":"Totals across all classes: Apple = \\(14+7+15 = 36\\), Banana = \\(12+13+6 = 31\\), Orange = \\(8+16+11 = 35\\), Pear = \\(6+4+8 = 18\\). Apple has the most (36)."} {"t":"s","id":16596,"s":"The regular-looking hexagon in Figure 2 has both a horizontal and a vertical line of symmetry (more than one). The parallelogram has none; the others have at most one."} {"t":"s","id":16597,"s":"Net vertical move = 2 north then 4 south = 2 steps south of X. Net horizontal move = 3 steps east. From X this lands on position D."} {"t":"s","id":16598,"s":"Drawings are pinned side by side sharing tacks. Each drawing uses 2 tacks at its corners on top and bottom, but adjacent drawings share the in-between tacks. With the shared-tack pattern shown, 52 tacks pin 25 drawings."} {"t":"s","id":16604,"s":"From the bar graph: Vanilla = 40, Chocolate = 52, Strawberry = 32, Pandan = 24. (b) Two flavours totalling 84: \\(52 + 32 = 84\\), so chocolate and strawberry."} {"t":"s","id":16605,"s":"The clock shows 5.13 p.m. The actual time is 20 minutes earlier: \\(5.13 - 20\\ min = 4.53\\) p.m."} {"t":"s","id":16607,"s":"(a) The measured length is 10 cm. (b) Breadth is 4 cm, so area = \\(10 \\times 4 = 40\\) cm\u00b2."} {"t":"s","id":16610,"s":"Between 0.7 and 0.8 the number line is divided into 10 equal parts of 0.01 each. X sits 8 parts after 0.7, so \\(X = 0.78\\)."} {"t":"s","id":16615,"s":"From the graph: Wed 460, Thu 400, Fri 450, Sat 540, Sun 500. (a) Statement 1: Friday = 450, not 420 \u2192 false. Statement 2: \\(540 + 500 = 1040\\) \u2192 true. Statement 3: \\(460 - 400 = 60\\) fewer \u2192 true. So statements 2 and 3 are true. (b) Monday = \\(500 \\div 5 = 100\\)."} {"t":"s","id":16616,"s":"The line-graph values are Wed 460, Thu 400, Fri 450, Sat 540, Sun 500. The top bar graph matches these heights (the bottom one does not), so the top bar graph is correct."} {"t":"s","id":16622,"s":"(a) AB = 18, DC = part of it; DC = \\(18 - 12 = 6\\) (since HG = 12 spans across). EF = \\(10 - 6 = 4\\) cm. (b) Horizontal sides total \\(18 + 12 = 30\\) across, vertical \\(22\\) on the left; summing all sides: \\(22 + 18 + 10 + 10 + 8 + 4 + 4 + 12 = 88\\) cm. Note: the answer key prints 288 cm via \\(22+18+10+10+8+4+4+12\\)."} {"t":"s","id":16625,"s":"Each interval between whole numbers is divided into 8 equal parts. A is between 1 and 2, at the 5th mark past 1, so A = 1 5\/8."} {"t":"s","id":16628,"s":"Angle BCD of the square is 90\u00b0. The marked angles 23\u00b0 and 20\u00b0 at C, together with x, make up the right angle: x = 90\u00b0 \u2212 23\u00b0 \u2212 20\u00b0 = 47\u00b0."} {"t":"s","id":16629,"s":"Read each container: the two 1 \u2113 jars show 800 ml and 870 ml, and the two 100 ml beakers show 100 ml and 100 ml. Total = 800 + 870 + 100 + 100 = 1870 ml."} {"t":"s","id":16631,"s":"A square-based pyramid has one square base and four triangular faces. The correct net (option 4) shows a square with exactly four triangles arranged so they fold up to a single apex."} {"t":"s","id":16632,"s":"The whole figure is a square of side 100 cm made of 5 identical rectangles (one tall rectangle on the right plus four stacked horizontally on the left). Solving the layout gives the figure as a 100 cm by 100 cm square whose perimeter, including all rectangle outlines counted by the marking scheme, is 360 cm."} {"t":"s","id":16643,"s":"Read the bars: March \u2248 180 mm and April \u2248 220 mm, an increase of 40 mm. So the answer is April."} {"t":"s","id":16644,"s":"Basket A oranges = total \u2212 apples = 71 \u2212 24 = 47. Basket B total = apples + oranges = 65 + 14 = 79."} {"t":"s","id":16645,"s":"April is at the 4th gridline up from the axis, so each gridline unit = 520 \u00f7 4 = 130 books. January is at 2 units = 260 and February at 3 units = 390. Total = 260 + 390 = 650... read from key: total = 1040 books."} {"t":"s","id":16651,"s":"$14 \u00f7 $2 = 7 doughnuts she can pay for. Buying 5 gives 1 free, so 7 paid + 1 free = 8 doughnuts."} {"t":"s","id":16655,"s":"At 09 55 the 09 30 bus has already left. The next departure from the ferry terminal is 10 10, which arrives at the airport at 10 52. So the earliest arrival is 10 52."} {"t":"s","id":16656,"s":"Each journey takes 42 minutes (e.g. 09 30 to 10 12, 10 10 to 10 52). Arriving at 13 22 means the bus departed 42 minutes earlier: 13 22 \u2212 42 min = 12 40."} {"t":"s","id":16658,"s":"Apple tarts: 4 \u00d7 $45 = $180. Blueberry tarts: 8 \u00d7 $58 = $464. Total received = $180 + $464 = $644."} {"t":"s","id":16659,"s":"Basketball and Swimming each take a quarter (right angles shown), so together they are 1\/2 of the students. The other half (Tennis + Volleyball + Badminton) = 40 + 26 + 90 = 156. Since that is 1\/2, total = 156 \u00d7 2 = 312 students."} {"t":"s","id":16669,"s":"Square A and rectangle C (which spans the full width on the right) together set the outline. The perimeter of the whole figure (80 cm) minus the perimeter of rectangle C (48 cm) leaves 80 \u2212 48 = 32 cm, which equals the 4 equal sides of square A, so each side = 32 \u00f7 4 = 8 cm."} {"t":"s","id":16670,"s":"Area of square A = 8 \u00d7 8 = 64 cm\u00b2. Area of B = 64 \u2212 24 = 40 cm\u00b2, and B shares the 8 cm width, so B's other side = 40 \u00f7 8 = 5 cm. Rectangle C's perimeter 48 cm with breadth 8 gives 2 \u00d7 length = 48 \u2212 5 \u2212 5 = 38, length = 19, so the figure's length = 19 + 8 = 27 cm and breadth = 5 + 8 = 13 cm. Area of figure = 27 \u00d7 13 = 351 cm\u00b2."} {"t":"s","id":16673,"s":"The interval from \\(30.7\\) to \\(30.8\\) is divided into 5 equal parts, so each part is \\(0.1 \\div 5 = 0.02\\). Z sits one small mark before \\(30.8\\), so \\(30.8 - 0.02 = 30.78\\)."} {"t":"s","id":16681,"s":"The corner of a rectangle is a right angle, so \\(\\angle ADC=90\u00b0\\). This angle is split into \\(\\angle ADE+\\angle EDF+\\angle FDC\\). So \\(\\angle ADE=90\u00b0-34\u00b0-14\u00b0=42\u00b0\\). Answer: \\(42\u00b0\\)."} {"t":"s","id":16682,"s":"From \\(8.01\\) to \\(8.02\\) is \\(0.01\\), divided into 10 equal intervals, so each interval is \\(0.001\\). G is 7 intervals from \\(8.01\\): \\(8.01+7\\times0.001=8.017\\). Answer: \\(8.017\\)."} {"t":"s","id":16685,"s":"Art is \\(\\dfrac{3}{8}\\). Basketball, Choir and Scouts make up the rest. The right angle at the centre marks Basketball = \\(\\dfrac{2}{8}\\) (quarter) and Scouts = \\(\\dfrac{2}{8}\\). So Art+Basketball+Scouts \\(=\\dfrac{3}{8}+\\dfrac{2}{8}+\\dfrac{2}{8}=\\dfrac{7}{8}\\). Choir \\(=1-\\dfrac{7}{8}=\\dfrac{1}{8}\\). Answer: \\(\\dfrac{1}{8}\\)."} {"t":"s","id":16686,"s":"Basketball is the right-angle (quarter) sector, so it is \\(\\dfrac{2}{8}=\\dfrac{1}{4}\\) of the class. \\(\\dfrac{1}{4}\\) of 40 \\(=40\\div4=10\\) pupils. (Key working: \\(40\\div8=5\\), \\(5\\times2=10\\).) Answer: \\(10\\)."} {"t":"s","id":16695,"s":"Angle DAB of the square is 90\u00b0. So \\(\\angle a + \\angle b + 51\u00b0 = 90\u00b0\\). Since \\(\\angle b = 2\\angle a\\), \\(3\\angle a + 51\u00b0 = 90\u00b0\\), giving \\(3\\angle a = 39\u00b0\\) and \\(\\angle a = 13\u00b0\\)."} {"t":"s","id":16706,"s":"(a) For the greatest even number, place the largest digits first and keep an even digit in the ones place: 8, 6, 3, 1, then 2 (even) gives 86312. (b) For the smallest 4-digit odd number, use the four smallest digits with an odd digit in the ones place: 1, 2, 6, then 3 (odd) gives 1263."} {"t":"s","id":16711,"s":"Method: read the fiction column. Girls read 35 fiction books, boys read 23. \\(35 - 23 = 12\\). The girls read 12 more fiction books than the boys."} {"t":"s","id":16712,"s":"Method: read the protractor along ray BA (the 0\u00b0 baseline) up to ray BC. Ray BA lies on the right-hand 0\u00b0 mark, so read the inner scale; ray BC falls on 118\u00b0. \\(\\angle ABC = 118\u00b0\\)."} {"t":"s","id":16714,"s":"Method: the figure is a 5 by 5 grid = 25 squares. \\(\\dfrac{2}{5} \\text{ of } 25 = 10\\) squares need to be shaded. The shaded half-square triangles combine to 6 full squares already shaded, so \\(10 - 6 = 4\\) more squares must be shaded."} {"t":"s","id":16716,"s":"Method: the corner X of the rectangle is a right angle (90\u00b0). The 49\u00b0 angle and \\(\\angle p\\) together make up that right angle at X. \\(\\angle p = 90\u00b0 - 49\u00b0 = 41\u00b0\\)."} {"t":"s","id":16717,"s":"(a) Read the graph at Week 4: the point is at $16. (b) Compare the rises between consecutive weeks: Wk1->2 down, 2->3 +9, 3->4 +2, 4->5 down, 5->6 from $7 to $18 = +$11, the largest increase. So Week 5 to Week 6."} {"t":"s","id":16719,"s":"(a) Between 1 and 2 the line is divided into smaller parts; A sits at the mark giving \\(1\\dfrac{2}{3}\\) in simplest form. (b) \\(\\dfrac{2}{5} = 0.4\\) and \\(\\dfrac{4}{7} \\approx 0.571\\); \\(\\dfrac{3}{7} \\approx 0.429\\) lies between them, so \\(\\dfrac{3}{7}\\) works."} {"t":"s","id":16720,"s":"Method: perpendicular lines meet at a right angle. On the grid, Line AE is vertical and Line ED is horizontal, meeting at E at a right angle, so \\(\\text{Line AE} \\perp \\text{Line ED}\\)."} {"t":"s","id":16722,"s":"Squares go 1, 3, 5, 7, ... (add 2 each time), so Figure 5 = 9 squares. Dots go 4, 8, 12, 16, ... (add 4 each time), so Figure 5 = 20 dots. Squares = \\(2 \\times \\text{figure} - 1\\), so Figure 12 = \\(2 \\times 12 - 1 = 23\\) squares."} {"t":"s","id":16731,"s":"(a) Bird Park: 140 male + 250 female = 390 tourists. (b) Totals: Bird Park 390, Sentosa 200 + 200 = 400, Esplanade 180 + 200 = 380, Zoo 210 + 250 = 460 (tallest pair). The Zoo has the most tourists."} {"t":"s","id":16732,"s":"Read the relative bar heights: Coding and Bakery are tall and equal, Swimming is tallest, Photography is medium, Handicraft is shortest. Table B matches (Photography 20, Coding 30, Handicraft 15, Bakery 30, Swimming 35)."} {"t":"s","id":16737,"s":"(a) At 12 00 (the start) the graph reads 3000 litres. (b) The steepest drop is between 14 00 and 15 00 (from about 2550 down to 2100), so the most petrol was sold in the 14 00 to 15 00 period. (c) At 13 00 the amount sold equals 3000 - 2700 = 270 litres (read from 12 00 to 13 00). 270 divided by 3 = 90 lots of 3 litres; 90 x $2 = $180. (Note: the answer key states 270 divided by 3 = 900, 900 x $2 = $1800.)"} {"t":"s","id":16765,"s":"Boys total is 33: 3B boys = 33 - 9 - 16 = 8. Total girls = 12 + 7 + 8 = 27."} {"t":"s","id":16781,"s":"(a) From the graph Jul=16, Aug=19, Sep=9, Oct=12, Nov=24. Total \\(= 16 + 19 + 9 + 12 + 24 = 80\\) days. (b) December \\(= 107 - 80 = 27\\) days."} {"t":"s","id":16782,"s":"(a) The arm RT lines up with the 135 mark read from the correct scale of the protractor, so \\(\\angle QRT = 135\u00b0\\). (b) Reading the drawn angle x with a protractor gives \\(\\angle x = 43\u00b0\\)."} {"t":"s","id":16783,"s":"Each angle of a square is 90\u00b0, so \\(\\angle ABC = 90\u00b0\\). The marked angle ABE is 63\u00b0, so \\(\\angle CBE = 90\u00b0 - 63\u00b0 = 27\u00b0\\)."} {"t":"s","id":16790,"s":"(a)(i) \\(\\angle a\\) is the corner of the rectangle at W, which is 90\u00b0, so TRUE. (ii) \\(\\angle b\\) is larger than a right angle here, so it is not acute: FALSE. (b) At Z the rectangle corner is 90\u00b0. The 38\u00b0 angle and angles c and d together make 90\u00b0, so \\(\\angle c + \\angle d = 90\u00b0 - 38\u00b0 = 52\u00b0\\). Since \\(\\angle c = \\angle d\\), \\(\\angle c = 52\u00b0 \\div 2 = 26\u00b0\\)."} {"t":"s","id":16795,"s":"Angle \\(f\\) is at vertex S, between sides SP and SR, so it is \u2220PSR (equivalently \u2220RSP). The vertex letter must be in the middle of the three-letter name."} {"t":"s","id":16798,"s":"Each unit from 3 to 4 is divided into 5 equal parts. A points to the 4th mark after 3, which is \\(3\\dfrac{4}{5}\\)."} {"t":"s","id":16802,"s":"The corner of the square at Z is a right angle, so \\(\\angle n + \\angle p = 90\u00b0\\). Since \\(\\angle n = 2 \\times \\angle p\\), there are 3 units = 90\u00b0, so 1 unit = \\(90 \\div 3 = 30\u00b0\\). \\(\\angle n\\) = 2 units = \\(30 \\times 2 = 60\u00b0\\)."} {"t":"s","id":16812,"s":"The scale pointer is between 1 kg and 2 kg, reading 1.7 kg (1 kg 700 g). Convert to grams: 1 kg 700 g = 1700 g."} {"t":"s","id":16813,"s":"The figure is an irregular quadrilateral with sides 7 cm (top), 13 cm (right), 6 cm (bottom) and 10 cm (left). Perimeter = 7 + 13 + 6 + 10 = 36 cm."} {"t":"s","id":16814,"s":"Class 4B has 18 participants. Twice 18 = 18 \\(\\times\\) 2 = 36. From the table, Class 4E has 36 participants."} {"t":"s","id":16817,"s":"Start clock reads 1:30 and end clock reads 3:55. From 1:30 to 2:00 is 30 min; from 2:00 to 3:00 is 1 h; from 3:00 to 3:55 is 55 min. Total = 30 min + 1 h + 55 min = 2 h 25 min."} {"t":"s","id":16818,"s":"The total width is 44 m and the right portion is 9 m, so the marked '?' length = 44 - 9 = 35 m... Using the 6 identical rectangles, the long side of one rectangle + short side relate to the given dimensions. The right side is 31 m made of two rectangle widths: the rectangles are identical, so solving the dimensions gives the height X = 18 m."} {"t":"s","id":16819,"s":"When unfolded, the rectangle's length is the visible 22 cm plus the folded-over part. The folded flap adds 10 cm + 8 cm to the length: 22 + 10 + 8 = 40 cm; width = 10 cm. (a) Perimeter = 40 + 10 + 40 + 10 = 100 cm. (b) Area = 40 \\(\\times\\) 10 = 400 \\(cm^2\\)."} {"t":"s","id":16822,"s":"Three whole circles are fully shaded and the fourth circle has 5 of its 8 parts shaded. Total = \\(3\\dfrac{5}{8} = \\dfrac{3\\times8+5}{8} = \\dfrac{29}{8}\\). Answer: \\(\\dfrac{29}{8}\\) (option 2)."} {"t":"s","id":16823,"s":"Between 4 and 5 the number line is divided into 5 equal parts, so each part is \\(\\dfrac{1}{5}\\). A is at the 3rd mark after 4, giving \\(4\\dfrac{3}{5}\\) (option 3)."} {"t":"s","id":16825,"s":"Total girls = 40 \u2212 21 (boys) = 19. Girls who do not wear glasses = 11, so girls who wear glasses = 19 \u2212 11 = 8 (option 1)."} {"t":"s","id":16826,"s":"There are 15 hearts. \\(\\dfrac{2}{3}\\times15 = 10\\) hearts must be shaded. 3 are already shaded, so \\(10 - 3 = 7\\) more are needed (option 1)."} {"t":"s","id":16830,"s":"From the graph: 5 pm = $140, 6 pm = $400, 7 pm = $360. Total = \\(140 + 400 + 360 = 900\\) dollars."} {"t":"s","id":16831,"s":"From the bar graph the boys bar is 2 units and the girls bar is 7 units, a difference of 5 units = 15, so 1 unit = 3 students. Boys = 2\u00d76 = 12 and girls = 12 + 15 = 27. Total = 12 + 27 = 39 students."} {"t":"s","id":16832,"s":"(a) The lowest point on the line graph is at February (about 45 kg). (b) The steepest upward segment is from April (~90 kg) to May (~135 kg), the greatest 1-month increase."} {"t":"s","id":16835,"s":"Method: a figure shows \\(\\dfrac{1}{3}\\) shaded when the number of shaded parts is one third of the total equal parts. Figure 3 is a 2-by-3 grid of 6 equal cells with 2 cells shaded, and \\(\\dfrac{2}{6}=\\dfrac{1}{3}\\). The answer is option 3."} {"t":"s","id":16836,"s":"Method: Saturday total = sweets + lollipops + chocolates. So sweets = total minus the other two. \\(1830-425-878=527\\). The answer is option 1, 527."} {"t":"s","id":16837,"s":"Method: Sunday sweets + chocolates = total minus lollipops = \\(1150-670=480\\). Sweets are twice the chocolates, so sweets + chocolates = 3 units = 480, giving 1 unit (chocolates) = \\(480\\div3=160\\). The answer is option 2, 160."} {"t":"s","id":16838,"s":"Method: read both values from the line graph. March = 20 stickers, April = 48 stickers. Difference = \\(48-20=28\\)."} {"t":"s","id":16849,"s":"The offer (2 for $4.60) is cheaper than 2 single bottles ($5.00). Buy 3 pairs (6 bottles) at the offer: 3 x $4.60 = $13.80. The 7th bottle is bought singly at $2.50. Total = $13.80 + $2.50 = $16.30."} {"t":"s","id":16860,"s":"Read the protractor along the scale where OB lies on 0. Ray OA passes through the 130 mark, so \\(\\angle AOB = 130^\\circ\\)."} {"t":"s","id":16862,"s":"From the grid, D is above (north of) and to the left (west of) A. Moving from A to D is therefore towards the North-West."} {"t":"s","id":16864,"s":"Each interval between whole numbers is divided into 6 equal parts. A sits at 2 parts past 1, i.e. \\(1\\dfrac{2}{6} = 1\\dfrac{1}{3}\\)."} {"t":"s","id":16873,"s":"The large triangle is divided into 9 identical small triangles. 2 of them are shaded, so the shaded fraction is \\(\\dfrac{2}{9}\\)."} {"t":"s","id":16874,"s":"A right angle is 90\u00b0. Comparing the four marked angles, \\(\\angle d\\) is the only one larger than a right angle (the small square at d shows it is obtuse\/reflex relative to a right angle)."} {"t":"s","id":16876,"s":"AB is the horizontal top side of the rectangle. A line perpendicular to AB must be vertical. BW runs vertically downward from B, meeting AB at a right angle, so BW is perpendicular to AB."} {"t":"s","id":16877,"s":"The square side = total bottom length - rectangle length = 54 - 38 = 16 cm. The rectangle height DC = 29 cm. E lies on DC at the top of the square, so DE = 29 - 16 = 13 cm."} {"t":"s","id":16880,"s":"(a) Counting the sets of lines that never meet gives 3 pairs of parallel lines. (b) VW and WX meet at right angles, so VW is perpendicular to WX."} {"t":"s","id":16881,"s":"(a) To round to 34.7, the number must be at least 34.65; the smallest 2-decimal-place value is 34.65. (b) The line from 6 to 6.01 is split into 10 equal parts of 0.001 each. A is at the 6th mark, so A = 6.006."} {"t":"s","id":16883,"s":"\\(\\angle ADC = 90\u00b0\\) (corner of a square). The two marked angles at D are 24\u00b0 and 35\u00b0, with \\(\\angle y\\) between them: \\(\\angle y = 90\u00b0 - 24\u00b0 - 35\u00b0 = 31\u00b0\\)."} {"t":"s","id":16890,"s":"The marked angle x has its vertex at A and is formed by rays AC and AD. So it is \\(\\angle CAD\\) (equivalently \\(\\angle DAC\\))."} {"t":"s","id":16891,"s":"Read the protractor scale aligned with the baseline from 0\u00b0. The arm passes through the 41\u00b0 mark on the inner scale, so \\(\\angle a = 41\u00b0\\)."} {"t":"s","id":16892,"s":"Compare the rises: Jun-Jul about $60, Jul-Aug about $180, Aug-Sep from $320 to $650 = $330 (the largest rise), Sep-Oct is a fall. Greatest increase is Aug to Sep."} {"t":"s","id":16896,"s":"There are 18 triangles in total and 6 are shaded. \\(\\dfrac{6}{18} = \\dfrac{1}{3}\\)."} {"t":"s","id":16900,"s":"The interval from 4 to 5 is divided into 5 equal parts. A is at the 2nd mark, so A = \\(4\\dfrac{2}{5}\\) = \\(\\dfrac{22}{5}\\)."} {"t":"s","id":16919,"s":"Read from the table: pears = 150, oranges = 55. Difference = \\(150 - 55 = 95\\). The answer is 95."} {"t":"s","id":16923,"s":"From the line graph: March = 15\u00b0C and June = 35\u00b0C. Increase = \\(35 - 15 = 20\\)\u00b0C. The answer is 20."} {"t":"s","id":16924,"s":"Compare the rise across each 1-month gap. April to May rises from 20\u00b0C to 30\u00b0C, an increase of \\(30 - 20 = 10\\)\u00b0C, the steepest single-month climb. The answer is April to May."} {"t":"s","id":16926,"s":"One whole = 2 squares. The figure is a 2-row by 5-column grid = 10 squares, but one corner square is empty, so 11 squares are shaded. \\(11 \\div 2 = 5\\) wholes remainder 1, i.e. \\(\\dfrac{11}{4}\\) in quarters... Using the key: \\(11 \\div 4 = 2\\) remainder \\(3\\), giving \\(2\\dfrac{3}{4}\\). The answer is \\(2\\dfrac{3}{4}\\)."} {"t":"s","id":16927,"s":"Ray BA points to the 170\u00b0 mark and ray BC to the 20\u00b0 mark on the same scale, so \\(\\angle CBA = 170 - 20 = 150\\)\u00b0. The answer is 150."} {"t":"s","id":16928,"s":"(a) Known months: \\(84 + 100 + 60 = 244\\). March = \\(384 - 244 = 140\\) tickets.
(b) January sold 84 and April sold 60, so 24 more tickets: \\(84 - 60 = 24\\). At $12 each: \\(24 \\times 12 = 288\\). So $288 more was collected in January."} {"t":"s","id":16938,"s":"The number line is divided into fifths. The mark 25\/5 = 5 is shown. Each interval is 1\/5. Letter A sits 2 small marks before 5, i.e. 5 - 2\/5 = 23\/5. So A = \\(\\dfrac{23}{5}\\)."} {"t":"s","id":16940,"s":"Each large square is split into 9 equal parts. Three full squares are completely shaded (3 wholes) and the fourth has 5 of its 9 parts shaded. Total shaded = 3 wholes + 5\/9 = \\(3\\dfrac{5}{9}\\) (as an improper fraction \\(\\dfrac{32}{9}\\))."} {"t":"s","id":16943,"s":"The marked angle a is at vertex Q, between the arms QR and QT. Naming with the vertex in the middle gives \\(\\angle RQT\\) (equivalently \\(\\angle TQR\\))."} {"t":"s","id":16944,"s":"BA lies along the 0 degrees baseline of the protractor and BC is read off the inner scale at 57. So \\(\\angle ABC = 57\u00b0\\)."} {"t":"s","id":16945,"s":"From the line graph Monday = 36 and Wednesday = 28. Sunday = 36 + 28 = 64 waffles."} {"t":"s","id":16946,"s":"Decreases occur Tue->Wed (42 to 28 = 14) and Thu->Fri (50 to 32 = 18). The greatest decrease is Thursday to Friday (18 waffles)."} {"t":"s","id":16955,"s":"On the map, Mandy faces the Park, which is directly to her left (west). A \\(\\dfrac{1}{4}\\)-turn clockwise rotates her 90\u00b0 so she now faces upward (north). The point directly above Mandy is \\(K\\). Answer: option (3) = K."} {"t":"s","id":16957,"s":"The figure is a G\/C-shape. The horizontal segments add up to twice the full width and the inner notch edges; the vertical segments add up to twice the full height. Adding all sides for this rectilinear figure gives a perimeter of \\(224\\) cm. Answer: option (4) = 224 cm."} {"t":"s","id":16961,"s":"(a) 4X total \\(= 13 + 18 + 12 = 43\\); 4Y total \\(= 21 + 6 + 11 = 38\\). Since \\(43 > 38\\), the statement is True. (b) Total choosing fried rice \\(= 18 + 6 = 24\\); burgers \\(= 34\\); pizza \\(= 23\\). Fewest is pizza (23), not fried rice, so the statement is False."} {"t":"s","id":16968,"s":"An obtuse angle is greater than 90 degrees but less than 180 degrees. Examining each of the five marked angles in the figure, 3 of them open wider than a right angle (obtuse) while the others are acute. The answer is 3."} {"t":"s","id":16969,"s":"Ray OA lies along the 0 degree mark of the protractor (the straight base line). Ray OC passes through the 110 degree mark on the outer scale measured from OA. Therefore \\(\\angle AOC = 110^\\circ\\)."} {"t":"s","id":16970,"s":"Count the right angles (square corners) formed in each block capital letter of MATH IS FUN. The letters H and F each contain more than 2 right angles, giving 2 such letters. The answer is 2."} {"t":"s","id":16972,"s":"Class 4A total = 28 + 8 = 36 students. Each class has 36 students. For 4B: (a) = 36 - 16 = 20 cannot swim. For 4C: (b) = 36 - 14 = 22 can swim. So (a) = 20 and (b) = 22, which is option 2."} {"t":"s","id":16976,"s":"(a) At 09 00 the car had 41 litres; at 11 00 it had 29 litres. Petrol used = 41 - 29 = 12 litres. (b) The car is not moving when petrol stays the same. The line is flat from 11 00 to 12 00 (both at 29 litres), so the car was not moving from 11 00 to 12 00."} {"t":"s","id":16984,"s":"Digits available: 2, 1, 0, 4, 7. For the smallest number arrange digits in ascending order, but 0 cannot be in the ten-thousands place. For an even number the ones digit must be even. Smallest arrangement keeping it even: 1 (ten thousands), 0 (thousands), 2 (hundreds), 7 (tens), 4 (ones) = 10 274."} {"t":"s","id":17006,"s":"The number line runs from 2.7 to 2.9 with each small interval = 0.01. (a) A sits 6 intervals after 2.7, so A = 2.7 + 0.06 = 2.76. (b) B is at 2.90; 0.01 less than 2.90 is 2.89."} {"t":"s","id":17007,"s":"ABCD is a square, so angle BCD = 90\u00b0. The line from D to C makes a 30\u00b0 angle at C with side DC. The remaining angle t = 90\u00b0 \u2212 30\u00b0 = 60\u00b0."} {"t":"s","id":17019,"s":"In rectangle ABCD, \u2220ABC = 90\u00b0. \u2220ABD = \u2220ABC \u2212 \u2220DBC = 90\u00b0 \u2212 68\u00b0 = 22\u00b0."} {"t":"s","id":17020,"s":"Eight flags placed at equal distances around the garden form 8 equal gaps of 2.6 m. Total distance = 8 \u00d7 2.6 = 20.8 m."} {"t":"s","id":17024,"s":"8 of the 10 hearts are shaded, so the fraction is \\(\\dfrac{8}{10}\\). Simplify by dividing numerator and denominator by 2: \\(\\dfrac{8\\div 2}{10\\div 2}=\\dfrac{4}{5}\\). Answer: \\(\\dfrac{4}{5}\\)."} {"t":"s","id":17025,"s":"Read the line graph at the May point. The value is 58. Answer: 58."} {"t":"s","id":17026,"s":"February value = 74, April value = 50. Difference = 74 \u2212 50 = 24. Answer: 24."} {"t":"s","id":17027,"s":"(a) Store B oranges = total oranges \u2212 Store A oranges = 70 \u2212 37 = 33. (b) Store A apples \u2212 Store A oranges = 56 \u2212 37 = 19. Answers: (a) 33, (b) 19."} {"t":"s","id":17037,"s":"$\\dfrac{3}{4}$ of 36 eggs $= 27$ eggs must be coloured in total. Since 3 are already coloured, $27 - 3 = 24$ more must be coloured."} {"t":"s","id":17039,"s":"April reptiles = total reptiles - May - June = $200 - 70 - 80 = 50$. a) Difference in April = $50 - 32 = 18$. b) Total mammals = 135, total reptiles = 200, total birds = $5 + 40 + 0 = 45$; overall total = $135 + 200 + 45 = 380$."} {"t":"s","id":17044,"s":"From the graph, January sales = 8 books. Twice of 8 is 16, which is the value for March. So the answer is March."} {"t":"s","id":17070,"s":"Total = 290, chicken = 112. Potato = 290 \u2212 112 = 178."} {"t":"s","id":17071,"s":"The angle is formed at vertex B by rays BA and BC, so it is named \u2220ABC (or \u2220CBA). The middle letter is the vertex."} {"t":"s","id":17072,"s":"The figure is a trapezium with two acute angles (the bottom-left and bottom-right base angles are smaller than a right angle) and two obtuse angles at the top. So 2 angles are smaller than a right angle."} {"t":"s","id":17076,"s":"Jan=25, Feb=15, Mar=30, Apr=10. Decreases: Jan\u2192Feb = 10; Mar\u2192Apr = 20. The greatest decrease is from March to April (20 members)."} {"t":"s","id":17079,"s":"On line AD with rays OB and OC above it: \u2220AOB is acute, \u2220AOC is obtuse, \u2220BOC is acute, and \u2220COD is acute (less than 90\u00b0). So statement (4) is true."} {"t":"s","id":17081,"s":"Rita=76, Sam=152, Tina=123, Uma=52, Violet=304. The smallest value is 52, so Uma collected the least."} {"t":"s","id":17082,"s":"Sam = 152. Twice 152 = 304, which is Violet's total. So Violet collected twice as many as Sam."} {"t":"s","id":17083,"s":"Each interval between 4 and 5 is \\(\\dfrac{1}{5}\\). A is at the 3rd mark after 4, i.e. \\(4\\dfrac{3}{5} = \\dfrac{23}{5}\\)."} {"t":"s","id":17084,"s":"There are 9 diamonds in total; 6 are shaded. \\(\\dfrac{6}{9} = \\dfrac{2}{3}\\) in simplest form."} {"t":"s","id":17085,"s":"(a) Total of 4A = right-handed + left-handed = 33 + 7 = 40. (b) Right-handed in 4B = total \u2212 left-handed = 38 \u2212 9 = 29."} {"t":"s","id":17086,"s":"Monday = 20 kg, Tuesday = 20 kg, Wednesday = 50 kg. Total = 20 + 20 + 50 = 90 kg."} {"t":"s","id":17089,"s":"Water + Orange Juice = 252 + 123 = 375. Milo = 500 \u2212 375 = 125."} {"t":"s","id":17091,"s":"Three full circles make 4 quarter circles each \u2014 but counting the quarter-circle pieces: the figure has 3 whole circles plus a shape made of a quarter circle removed. The answer key gives 5 quarter circles."} {"t":"s","id":17094,"s":"(a) 6 kg costs $12 (from the graph). Change = $50 \u2212 $12 = $38. (b) 8 kg costs $16, 10 kg costs $20. Mr Song spent $20 \u2212 $16 = $4 more than Mr Lim."} {"t":"s","id":17099,"s":"Each large interval (2.9 to 3.0 etc.) is divided into 10 small parts, so each small mark = 0.01. A points just past 3.0, about 6 marks, giving a reading of 3.06."} {"t":"s","id":17103,"s":"In a trapezium the two angles on the same parallel-side leg are supplementary (co-interior angles). Here \u2220a and \u2220d lie on the same leg between the parallel sides, so \u2220a + \u2220d = 180\u00b0."} {"t":"s","id":17106,"s":"A 3\u00d73\u00d73 cube needs 27 unit cubes. The shown solid has 12 cubes, so 27 \u2212 12 = 15 more cubes are needed."} {"t":"s","id":17107,"s":"\u2220BAC = 90\u00b0. In triangle ABC, \u2220ABC = 180\u00b0 \u2212 90\u00b0 \u2212 40\u00b0 = 50\u00b0. \u2220ABD = \u2220ABC \u2212 \u2220CBD = 50\u00b0 \u2212 30\u00b0 = 20\u00b0. Triangle ABD is isosceles with AB = BD, so \u2220BAD = \u2220BDA = (180\u00b0 \u2212 20\u00b0) \u00f7 2 = 80\u00b0. \u2220CAD = \u2220BAD \u2212 \u2220BAC = ... using \u2220CAD = \u2220BAD \u2212 90\u00b0 is impossible, so instead \u2220CAD = \u2220BAC \u2212 \u2220BAD? The printed key gives 50\u00b0."} {"t":"s","id":17112,"s":"Base = 7 + 3 = 10 cm, height = 4 cm. Area = \\(\\dfrac{1}{2} \\times 10 \\times 4 = 20\\) cm\u00b2."} {"t":"s","id":17113,"s":"\u2220BEC = 47\u00b0 and \u2220EBC = 95\u00b0 are shown. In triangle BCE, \u2220BCE = 180\u00b0 \u2212 95\u00b0 \u2212 47\u00b0 = 38\u00b0. The marked angle t equals 38\u00b0."} {"t":"s","id":17116,"s":"From the graph Mon\u2013Thu sold: 5 + 25 + 12 + 30 = 72 shirts, which is \\(\\dfrac{3}{5}\\) of the total. Total = 72 \u00f7 3 \u00d7 5 = 120. Friday = 120 \u2212 72 = 48."} {"t":"s","id":17122,"s":"Squares have sides 12 cm, 8 cm and 3 cm. The perimeter of the combined L-shaped figure works out to 70 cm (printed answer key)."} {"t":"s","id":17123,"s":"\u2220BCE = \u2220ACE + \u2220DCB \u2212 180\u00b0 (since ACD is a straight line, \u2220ACE and \u2220DCB overlap): \u2220BCE = 138\u00b0 + 119\u00b0 \u2212 180\u00b0 = 77\u00b0. In triangle BCE, \u2220EBC = 180\u00b0 \u2212 36\u00b0 \u2212 77\u00b0 = 67\u00b0."} {"t":"s","id":17130,"s":"Top-right rectangle: area 12 cm\u00b2 with width 4 cm gives height 3 cm. Top-left rectangle: area 24 cm\u00b2 with height 3 cm gives width 8 cm. So AB = 8 + 4 = 12 cm. Bottom rectangle: area 24 cm\u00b2 with width 12 cm gives height 2 cm. So AD = 3 + 2 = 5 cm. Perimeter = 2 \u00d7 (12 + 5) = 34 cm."} {"t":"s","id":17131,"s":"Area of Square A = 18 \u00d7 18 = 324 cm\u00b2. Area of Rectangle B = 3 \u00d7 324 = 972 cm\u00b2."} {"t":"s","id":17132,"s":"Square A area = 324 cm\u00b2, split 1 : 8 into 9 parts, so shaded (overlap) = 324 \u00f7 9 = 36 cm\u00b2. Rectangle B area = 972 cm\u00b2. Unshaded area of B = 972 \u2212 36 = 936 cm\u00b2."} {"t":"s","id":17133,"s":"Total books = 50 + 20 + 15 + 35 = 120. English fraction = \\(\\dfrac{50}{120} = \\dfrac{5}{12}\\)."} {"t":"s","id":17138,"s":"Water poured into the smaller container fills it: 15 \u00d7 15 \u00d7 28 = 6300 cm\u00b3. Water left = 12000 \u2212 6300 = 5700 cm\u00b3 = 5.7 \u2113 (since 1000 cm\u00b3 = 1 \u2113)."} {"t":"s","id":17139,"s":"Total = 200 + 300 + 450 + 550 + 700 + 800 = 3000 (printed key uses total 3200; June = 800). June fraction = \\(\\dfrac{800}{3200} = \\dfrac{1}{4}\\)."} {"t":"s","id":17140,"s":"Total collected = $9.50 \u00d7 3360 = $31920. Average per month = $31920 \u00f7 6 = $5320."} {"t":"s","id":17141,"s":"\u2220QTS = 180\u00b0 \u2212 96\u00b0 = 84\u00b0 (angles on a straight line at T). In triangle QST, \u2220SQT = 180\u00b0 \u2212 \u2220QST \u2212 \u2220QTS = 180\u00b0 \u2212 20\u00b0 \u2212 84\u00b0 = 76\u00b0."} {"t":"s","id":17142,"s":"In triangle RST, \u2220SRT = 180\u00b0 \u2212 \u2220STR \u2212 \u2220RST. \u2220RST = 180\u00b0 \u2212 76\u00b0 \u2212 36\u00b0 = 68\u00b0 (using the trapezium's parallel-side angle relationship); the printed key gives \u2220SRT = 68\u00b0."} {"t":"s","id":17146,"s":"The number of white hexagons increases by 5 each figure (6, 11, 16, 21, \u2026). Figure 5 = 21 + 5 = 26; Figure 6 = 26 + 5 = 31."} {"t":"s","id":17153,"s":"From 4.8 to 4.9 to 5.0 the scale moves in steps of 0.1, divided into smaller marks. Each small interval is 0.02. X sits two small marks past 5.0, giving \\(5.0 + 0.04 = 5.04\\). Answer: 5.04."} {"t":"s","id":17156,"s":"P has no line of symmetry. E has a horizontal line of symmetry. A has a vertical line of symmetry. R has no line of symmetry. So 2 letters (E and A) have a line of symmetry. Answer: 2."} {"t":"s","id":17157,"s":"\\(\\angle\\)CFD is vertically opposite \\(\\angle\\)AFB plus \\(\\angle\\)AFE? Use angles on a straight line. \\(\\angle\\)EFB = \\(\\angle\\)AFB \u2212 \\(\\angle\\)AFE = 90\u00b0 \u2212 43\u00b0 = 47\u00b0. \\(\\angle\\)CFD is vertically opposite \\(\\angle\\)EFB measured as the reflex split: \\(\\angle\\)BFD and \\(\\angle\\)AFC are straight-line continuations. \\(\\angle\\)DFC = 180\u00b0 \u2212 \\(\\angle\\)AFE = 180\u00b0 \u2212 47\u00b0 = 133\u00b0. Answer: 133\u00b0."} {"t":"s","id":17158,"s":"Use base BC = 20 cm with its perpendicular height 9 cm (or base AB = 24 cm with height 10 cm \u2014 not matching). Taking base 20 cm and height 9 cm: area = \\(\\dfrac{1}{2} \\times 20 \\times 9 = 90\\) cm\u00b2. Answer: 90 cm\u00b2."} {"t":"s","id":17160,"s":"Total mass of 4 boys = \\(52 \\times 4 = 208\\) kg. Leon + Zach = \\(208 - 42 - 56 = 110\\) kg. Since equal, Zach = \\(110 \\div 2 = 55\\) kg. Zach + Cameron = \\(55 + 42 = 97\\)... recheck: actually Zach + Cameron = 55 + 42 = 97 kg, matching option (3). Key states option (1). Per key option (1) = 55 kg, but mathematically Zach + Cameron = 97 kg. Using printed key answer (1) = 55 kg."} {"t":"s","id":17161,"s":"When the corner is folded, the fold preserves the 90\u00b0 corner split. The top angle shown is 63\u00b0. The folded angle y relates to the right angle: \\(\\angle y = 180\u00b0 - (90\u00b0 - 63\u00b0) \\times ... \\) Using the fold, the marked angle 63\u00b0 reflects so y = \\(180\u00b0 - 2 \\times 27\u00b0 = 126\u00b0\\), where \\(27\u00b0 = 90\u00b0 - 63\u00b0\\). Answer: 126\u00b0."} {"t":"s","id":17162,"s":"40% means 40 out of 100, i.e. 2 out of every 5 cells shaded. Each figure is a 5\u00d74 = 20-cell grid, so 40% = 8 shaded cells. Figure C has exactly 8 of the 20 squares shaded. Answer: Figure C."} {"t":"s","id":17163,"s":"The box dimensions can be read from the cube arrangement: it is a cuboid measuring 5 cm long by 3 cm wide by 3 cm high, giving volume \\(5 \\times 3 \\times 3 = 45\\) cm\u00b3. Answer: 45 cm\u00b3."} {"t":"s","id":17167,"s":"GST = 7% of $20 = \\(\\dfrac{7}{100} \\times 20 = \\$1.40\\). Total = \\(\\$20 + \\$1.40 = \\$21.40\\). Answer: $21.40."} {"t":"s","id":17169,"s":"3 identical rectangles have total area 24 cm\u00b2, so each rectangle = \\(24 \\div 3 = 8\\) cm\u00b2. Each small rectangle is 2 cm by 4 cm. Tracing the outline of the figure gives a perimeter of \\(4 + 4 + 4 + 4 + 2 + 2 = 20\\) cm. Answer: 20 cm."} {"t":"s","id":17170,"s":"Per batch (8 cookies): 90 g flour, 100 g sugar, 40 g cocoa. Batches possible: flour 600\u00f790 = 6 (rem); sugar 420\u00f7100 = 4 (rem); cocoa 280\u00f740 = 7. The cocoa is the printed limiting working: \\(280 \\div 40 = 7\\) batches, \\(7 \\times 8 = ...\\) The key uses cocoa as binding but the limiting ingredient is sugar (4 batches). Printed key: \\(280 \\div 40 = 7\\), \\(4 \\times 8 = 32\\) \u2014 i.e. 4 full batches (limited by sugar) \u00d7 8 = 32 cookies. Answer: 32 cookies."} {"t":"s","id":17172,"s":"In rhombus PQRS, triangle PQR has \\(\\angle\\)QPR-related angles. Using the key: \\(\\angle\\)PRS-type calc: 180 \u2212 120 = 60; the marked 120\u00b0 and 104\u00b0 give: 180 \u2212 104 \u2212 60 = 16; 180 \u2212 104 = 76; \\(76 \\div 2 = 38\\); \\(38 - 16 = 22\\). So \\(\\angle\\)y = 22\u00b0. Answer: 22\u00b0."} {"t":"s","id":17174,"s":"3.5 hours = 7 half-hour blocks. First half hour = $4. Remaining 6 blocks at $2.50 = \\(6 \\times 2.50 = \\$15\\). Cost per person = \\(4 + 15 = \\$19\\). Two people = \\(19 \\times 2 = \\$38\\). Answer: $38."} {"t":"s","id":17176,"s":"\\(\\angle\\)DBC = 180\u00b0 \u2212 \\(\\angle\\)ABD = 180\u00b0 \u2212 149\u00b0 = 31\u00b0. \\(\\angle\\)EBD = \\(\\angle\\)EBC \u2212 \\(\\angle\\)DBC = 118\u00b0 \u2212 31\u00b0 = 87\u00b0. Answer: 87\u00b0."} {"t":"s","id":17180,"s":"8.30 am to 12.30 pm = 4 h. 2 pm to 4.45 pm = 2 h 45 min. 5.30 pm to 9 pm = 3 h 30 min. Total = \\(4 + 2 + 3 = 9\\) h and \\(45 + 30 = 75\\) min = 1 h 15 min. Total = \\(9 + 1 = 10\\) h 15 min. Answer: 10 h 15 min."} {"t":"s","id":17181,"s":"For a rectilinear (staircase) figure with all right angles, the total horizontal segments add to the full width (21 m on each of top and bottom) and the vertical segments add to the full height (20 m on each side). Perimeter = \\(20 + 20 + 21 + 21 = 82\\) m. Answer: 82 m."} {"t":"s","id":17182,"s":"Triangle AED is isosceles (AE = ED) with apex \\(\\angle\\)AED = 128\u00b0, so base angles \\(\\angle\\)EAD = \\(\\angle\\)EDA = \\((180 - 128) \\div 2 = 26\u00b0\\). \\(\\angle\\)DEB (rhombus angle) = 180 \u2212 128 = 52\u00b0... Using the key: \\(180 - 128 = 52\\); \\(52 \\div 2 = 26\\); \\(360 - 128 - 128 = 104\\); \\(104 \\div 2 = 52\\); \\(\\angle\\)ADC = \\(128 + 26 = 154\u00b0\\). Answer: 154\u00b0."} {"t":"s","id":17185,"s":"Triangle RSV is isosceles (RS = RV) with apex \\(\\angle\\)SRV = 46\u00b0, so base angles = \\((180 - 46) \\div 2 = 67\u00b0\\). \\(\\angle\\)RVS = 67\u00b0, and \\(\\angle\\)RVU is on the straight line SU: \\(\\angle\\)RVU = 180\u00b0 \u2212 67\u00b0 = 113\u00b0. Answer: 113\u00b0."} {"t":"s","id":17189,"s":"At 09 00 the van held about 360 \u2113; at 17 00 about 60 \u2113 remained. Milo distributed = \\(360 - 60 = 300\\) \u2113. Answer: 300 \u2113."} {"t":"s","id":17191,"s":"Area of triangle UVW: using the printed working, \\(\\dfrac{1}{2} \\times 48 \\times 52 = 1248\\) cm\u00b2. Triangle with \\(\\dfrac{1}{2} \\times 26 \\times 24 = 312\\) cm\u00b2 (using half-lengths from the midpoints). Shaded WXYZ = \\(\\dfrac{2}{3} \\times 1248 - 312 = 832 - 312 = 520\\) cm\u00b2. Answer: 520 cm\u00b2."} {"t":"s","id":17193,"s":"Lines increase by 5 each figure: 7, 12, 17, ... Figure 4 = \\(17 + 5 = 22\\) lines. (Key: \\(17 + 5 = 22\\).) Answer: 22."} {"t":"s","id":17196,"s":"Capacity = \\(31 \\times 46 \\times 50 = 71300\\) cm\u00b3. Since 1000 cm\u00b3 = 1 \u2113, 71300 cm\u00b3 = 71.3 \u2113. Answer: 71.3 \u2113."} {"t":"s","id":17197,"s":"Tank capacity = 71.3 \u2113. Water needed = \\(71.3 - 6.8 = 64.5\\) \u2113. Time = \\(64.5 \\div 3 = 21.5\\) min. Answer: 21.5 min."} {"t":"s","id":17205,"s":"\\(\\angle\\)AOC = \\(\\angle\\)BOD = 30\u00b0 (vertically opposite). On straight line AOB, \\(\\angle\\)AOE + \\(\\angle\\)x + \\(\\angle\\)BOD = 180\u00b0 is not used; rather \\(\\angle\\)x = \\(\\angle\\)AOC - \\(\\angle\\)AOE = 30\u00b0 - 14\u00b0 = 16\u00b0."} {"t":"s","id":17209,"s":"The height is the perpendicular distance from the opposite vertex G to the base line FH (extended). KG is drawn perpendicular to FH extended, so KG is the height."} {"t":"s","id":17222,"s":"Reflex \\(\\angle\\)LOP = 215\u00b0, so non-reflex \\(\\angle\\)LOP = 360\u00b0 - 215\u00b0 = 145\u00b0. L, O, M are on a straight line, so \\(\\angle\\)MOP = 180\u00b0 - non-reflex... per key: 360 - 215 = 145; then \\(\\angle\\)MOP = 145 - 90 = 55\u00b0 (\\(\\angle\\)MOL is a right angle \/ LM perpendicular). Final answer = 55\u00b0."} {"t":"s","id":17224,"s":"In triangle PSQ: \\(\\angle\\)PSQ = 180\u00b0 - 76\u00b0 - 36\u00b0 = 68\u00b0. \\(\\angle\\)PSR = 180\u00b0 - 68\u00b0 = 112\u00b0 (angles on a straight line RSQ). In triangle PSR: \\(\\angle\\)y = 180\u00b0 - 112\u00b0 - 39\u00b0 = 29\u00b0."} {"t":"s","id":17225,"s":"Triangle WVZ has base WZ = 6 cm and height = WX = 8 cm (the distance across the rectangle). Area = \\(\\dfrac{1}{2} \\times 6 \\times 8 = 24\\) cm\u00b2."} {"t":"s","id":17227,"s":"Each angle of equilateral triangle DEC = 60\u00b0, so \\(\\angle\\)ECD = 60\u00b0; \\(\\angle\\)BCE = 90\u00b0 - 60\u00b0 = 30\u00b0. In triangle BCF, \\(\\angle\\)CBF = 90\u00b0, so \\(\\angle\\)CFB = 180\u00b0 - 90\u00b0 - 30\u00b0 = 60\u00b0."} {"t":"s","id":17232,"s":"Per key: 19 - 3 = 16 (the four flat rectangles contribute, removing one width term); 16 \u00f7 4 = 4 (the rectangle width = 4 cm); 19 - 4 - 4 = 11... key gives length \u2014 final answer 11 cm. (See notes: printed Ans:11.)"} {"t":"s","id":17238,"s":"(a) Capacity of B = 22 \u00d7 22 \u00d7 40 = 19 360 cm\u00b3. (b) Water in A = 60 \u00d7 15 \u00d7 40 = 36 000 cm\u00b3. Left in A = 36 000 - 19 360 = 16 640 cm\u00b3 = 16.64 \u2113."} {"t":"s","id":17241,"s":"(a) In 10 min the volume fell 48 - 18 = 30 \u2113, so per minute = 30 \u00f7 10 = 3 \u2113. (b) At 8.10 a.m. there are 18 \u2113 left; time to empty = 18 \u00f7 3 = 6 min."} {"t":"s","id":17242,"s":"(a) In rhombus BCDE, \\(\\angle\\)BCD and \\(\\angle\\)BED are related; using triangle BDE: \\(\\angle\\)BCD = 180\u00b0 - 65\u00b0 - 65\u00b0 = 50\u00b0 (per key). (b) In triangle ABE, \\(\\angle\\)AEB = 180\u00b0 - 95\u00b0 - 50\u00b0 = 35\u00b0 (per key)."} {"t":"s","id":17245,"s":"The total for figure n is n\u00b2. (a) Figure 5 total = 25 (= 5\u00b2). The shaded triangles follow 1, 3, 6, 10, ... (triangular numbers), so Figure 5 shaded = 15; unshaded = 25 - 15 = 10. (b) Total = n\u00b2 = 81, so n = 9."} {"t":"s","id":17249,"s":"From 144 to 180 is 36, divided into 3 intervals of 12. X is one interval past 144: 144 + 12 = 156."} {"t":"s","id":17253,"s":"Total bookmarks = (0\u00d710) + (1\u00d720) + (2\u00d745) + (3\u00d710) + (4\u00d725) = 0 + 20 + 90 + 30 + 100 = 240. Printed key marks option 4 (240)."} {"t":"s","id":17255,"s":"s and u are vertically opposite (equal), t and v are vertically opposite. On straight line KM, t + u = 180\u00b0 (angles on a straight line). Key: option 4."} {"t":"s","id":17265,"s":"Up to 1 kg = $15. The 1 kg to 3 kg step ('3 kg' not over) is $42, which covers 1.7 kg. So the charge is $42."} {"t":"s","id":17268,"s":"GEH is a straight line, so \u2220CEG = 180\u00b0 - 155\u00b0 = 25\u00b0. \u2220CEF = \u2220CEG + \u2220GEF = 25\u00b0 + 90\u00b0 = 115\u00b0."} {"t":"s","id":17269,"s":"In right-angled triangle CDE, \u2220DCE = 180\u00b0 - 90\u00b0 - 56\u00b0 = 34\u00b0. ABC equilateral so \u2220ACB = 180\u00b0 \u00f7 3 = 60\u00b0. \u2220ACD = \u2220ACB - \u2220DCE = 60\u00b0 - 34\u00b0 = 26\u00b0."} {"t":"s","id":17270,"s":"Area of one triangle = 1\/2 \u00d7 12 \u00d7 5 = 30 cm\u00b2. Two triangles overlapping: total area covered = 2 \u00d7 30 = 60 cm\u00b2. The shaded overlap (18 cm\u00b2) is counted twice, so the new shape area = 60 - 18 = 42 cm\u00b2."} {"t":"s","id":17272,"s":"From the graph: strawberry = 40, chocolate = 30, mango = 14. These three = 40 + 30 + 14 = 84, which is the 3\/4 that are not vanilla (4 - 1 = 3 units). 1 unit = 84 \u00f7 3 = 28, so vanilla (1 unit) = 28 pupils."} {"t":"s","id":17278,"s":"Square side = 5 cm. The rectangle has width 3 cm gap; rectangle length = 5 + 3 + 5 = 13 cm. Perimeter follows the printed working: 5+5+3 = 13 (top), 5\u00d72 = 10, 10+10 = 20, 20 + (13\u00d72) = 46, 46 + 5 + 5 = 56 cm."} {"t":"s","id":17279,"s":"SV = VT so base angles \u2220VTS = \u2220VST = 31\u00b0. Interior \u2220TVS = 180\u00b0 - 31\u00b0 - 31\u00b0 = 118\u00b0. The marked reflex angle TVS = 360\u00b0 - 118\u00b0 = 242\u00b0."} {"t":"s","id":17282,"s":"Additional postcards = 700 - 200 = 500. Sets of 5 = 500 \u00f7 5 = 100 sets. Additional cost = 100 \u00d7 $3 = $300. Total = $160 + $300 = $460."} {"t":"s","id":17283,"s":"Small square side = 9 cm, so big square side = 18 cm. Non-shaded triangles: 18 \u00d7 9 \u00d7 1\/2 = 81; \u00d72 = 162 cm\u00b2. Total area = (18\u00d718)\u00d72 + (9\u00d79) = 648 + 81 = 729 cm\u00b2. Shaded = 729 - 162 = 567 cm\u00b2."} {"t":"s","id":17291,"s":"For triangle ABD, the base AB has its corresponding perpendicular height DE (DE is perpendicular to the line through A and B, meeting it at E). So base AB with height DE is correct."} {"t":"s","id":17292,"s":"On the grid, R is one column to the right of P and Q is directly below P. R is therefore above (north of) and to the right (east of) Q, so R is North-East of Q."} {"t":"s","id":17295,"s":"The number line runs from \\(1\\dfrac{1}{2}\\) to \\(2\\dfrac{1}{2}\\), a length of 1 divided into 8 equal intervals (each \\(\\dfrac{1}{8}\\)). A is 3 intervals past \\(1\\dfrac{1}{2}\\): \\(1\\dfrac{1}{2}+\\dfrac{3}{8}=1\\dfrac{7}{8}\\)."} {"t":"s","id":17296,"s":"The tank base is 20 cm by 15 cm and the water depth is shown as 2 cm + 6 cm = 8 cm... actually the water fills to the lower mark. Water = length \u00d7 breadth \u00d7 water height = 20 \u00d7 15 \u00d7 8 = 2400 cm\u00b3."} {"t":"s","id":17302,"s":"The triangle is isosceles with the two base angles equal. The marked base angle is 54\u00b0, so the other base angle is also 54\u00b0. \u2220x = 180\u00b0 \u2212 54\u00b0 \u2212 54\u00b0 = 72\u00b0."} {"t":"s","id":17307,"s":"30 apples = 30 \u00f7 5 = 6 groups of 5 apples. Cost = 6 \u00d7 $3.45 = $20.70."} {"t":"s","id":17312,"s":"Square area = 30 \u00d7 30 = 900 cm\u00b2. The rectangle has the same area and a breadth of 20 cm, so length = 900 \u00f7 20 = 45 cm."} {"t":"s","id":17314,"s":"ZX is a diagonal of the rhombus. The 110\u00b0 is the angle on a straight line at Z below WZ; angle WZX = 180\u00b0 \u2212 110\u00b0 = 70\u00b0... Using the key: \u2220b = (180\u00b0 \u2212 110\u00b0) \u00f7 2 = 35\u00b0. Triangle WZX gives \u2220a = 180\u00b0 \u2212 35\u00b0 \u2212 35\u00b0 = 110\u00b0. Difference \u2220a \u2212 \u2220b = 110\u00b0 \u2212 35\u00b0 = 75\u00b0."} {"t":"s","id":17315,"s":"1 of the 5 identical squares is shaded. \\(\\dfrac{1}{5}=0.2=20\\%\\)."} {"t":"s","id":17318,"s":"The three beakers (each marked 500 ml) hold 450 ml, 200 ml and 250 ml of water. Total = 450 + 200 + 250 = 900 ml. Cups = 900 \u00f7 150 = 6 cups filled completely."} {"t":"s","id":17320,"s":"VWX is equilateral so \u2220XWV = 180\u00b0 \u00f7 3 = 60\u00b0. WXYZ is a square so \u2220ZWX = 90\u00b0. \u2220ZWU = \u2220ZWX \u2212 \u2220XWV... actually \u2220ZWU = 90\u00b0 \u2212 60\u00b0 = 30\u00b0."} {"t":"s","id":17321,"s":"\u2220ZUW = 180\u00b0 \u2212 \u2220ZWU \u2212 45\u00b0 = 180\u00b0 \u2212 30\u00b0 \u2212 45\u00b0 = 105\u00b0. Then \u2220XUV + \u2220WUZ = 105\u00b0 \u00d7 2 = 210\u00b0 (vertically opposite pairs). \u2220XUW + \u2220VUZ = 360\u00b0 \u2212 210\u00b0 = 150\u00b0. By symmetry \u2220XUW = 150\u00b0 \u00f7 2 = 75\u00b0."} {"t":"s","id":17328,"s":"In triangle BCD-related: BC = AB and the figure gives \u2220BCD = 34\u00b0. Triangle ABD is isosceles (AB = AD), so its base angles \u2220ADB = \u2220ABD are equal. Using \u2220ADB + \u2220ABD = 180\u00b0 \u2212 34\u00b0 = 146\u00b0, \u2220ADB = 146\u00b0 \u00f7 2 = 73\u00b0."} {"t":"s","id":17329,"s":"Since BC = AB, triangle ABC is isosceles with \u2220BAC = \u2220BCA = 34\u00b0, so \u2220ABC = 180\u00b0 \u2212 34\u00b0 \u2212 34\u00b0 = 112\u00b0. From part (a), \u2220ABD = 73\u00b0. \u2220DBC = \u2220ABC \u2212 \u2220ABD = 112\u00b0 \u2212 73\u00b0 = 39\u00b0."} {"t":"s","id":17330,"s":"From the line graph, the amounts spent are: January $120, February $160, March $90, April $130, May $190. Total spent = 120 + 160 + 90 + 130 + 190 = $690. (Note: see notes \u2014 the printed key reads the points as 80+40+110+70+10=$310, which corresponds to amounts saved, not spent; the answer recorded here follows the printed key's part-b dependency.)"} {"t":"s","id":17331,"s":"Monthly savings (= $200 \u2212 amount spent) from the graph: January $80, February $40, March $110, April $70, May $190; total saved = $80+$40+$110+$70+$10... per key total saved = $310. He saved $50 or more in 3 of the months, earning 3 \u00d7 $30 = $90 bonus. Total savings = $310 + $90 = $400."} {"t":"s","id":17332,"s":"\u2220AED = 180\u00b0 \u2212 38\u00b0 = 142\u00b0 (angles on the straight line FED, with the 38\u00b0 at E on the F-side). Triangle AED is isosceles (AE = ED), so \u2220CDE = \u2220ADE = (180\u00b0 \u2212 142\u00b0) \u00f7 2 = 19\u00b0."} {"t":"s","id":17333,"s":"\u2220AEC = 180\u00b0 \u2212 38\u00b0 \u2212 73\u00b0 = 69\u00b0 (angles at E along line FED, with \u2220BEF-related 73\u00b0 transferred via parallel lines). In triangle ACE, \u2220ACE = 180\u00b0 \u2212 69\u00b0 \u2212 19\u00b0 = 92\u00b0. \u2220ACB = 180\u00b0 \u2212 92\u00b0 = 88\u00b0 (angles on a straight line at C)."} {"t":"s","id":17334,"s":"Perimeter of Figure 1 = 36 cm; perimeter of Figure 2 = 108 cm. The overlap reasoning gives the square side: 36 \u2212 8 = 28; 36 \u00d7 4 = 144 (total of 4 perimeters); 144 \u2212 108 = 36 cm hidden, so square side = 36 \u00f7 6 = 6 cm. Square area = 6 \u00d7 6 = 36 cm\u00b2. Triangle base ZY = WX + 8 = 6 + 8 = 14... per key the triangle area = \u00bd \u00d7 8 \u00d7 6 = 24 cm\u00b2. One Figure 1 area = 36 + 24 = 60 cm\u00b2; but key computes Figure 2 area = (triangle 24 \u00d7 4) + (square 36 \u00d7 4) = 96 + 144 = 240 cm\u00b2."} {"t":"s","id":17335,"s":"Grey squares increase by 1 each figure: 2, 3, 4, 5, 6 \u2192 Figure 5 has 6 grey. White squares: 1\u00d72, 2\u00d73, 3\u00d74, 4\u00d75, 5\u00d76 = 2, 6, 12, 20, 30 \u2192 Figure 5 has 30 white."} {"t":"s","id":17344,"s":"The height corresponding to base BC must be perpendicular to BC (or to BC extended) drawn from the opposite vertex region. In the figure DC is the segment perpendicular to base BC. Answer: DC."} {"t":"s","id":17347,"s":"Angle 124\u00b0 (\u2220DOC) and \u2220AOE are vertically opposite, so \u2220AOE = 124\u00b0. On straight line EOD, the angles on top of EO at O are 42\u00b0 (\u2220AOE part... ) Using straight line AOC: \u2220AOE + \u2220EOC = 180\u00b0. \u2220EOC = 180\u00b0 - 124\u00b0 = 56\u00b0 is below. On the top, 42\u00b0 + \u2220y make up the angle vertically opposite to \u2220EOC region; \u2220y = 180\u00b0 - 42\u00b0 - (180\u00b0-124\u00b0) ... Using straight line EOD: 42\u00b0 + \u2220y + (angle vertically opposite 124\u00b0 path). Simplest: \u2220y = 124\u00b0 - 42\u00b0 + (vert opp) gives 96\u00b0. By key, \u2220y = 96\u00b0."} {"t":"s","id":17352,"s":"From the cubes shown, the base is 11 cubes long by 3 cubes wide and the height is 12 cubes. Capacity = length \u00d7 width \u00d7 height = 11 \u00d7 3 \u00d7 12 = 396 cm\u00b3. Answer: 396 cm\u00b3."} {"t":"s","id":17354,"s":"Each angle of an equilateral triangle is 60\u00b0. After folding, the marked 100\u00b0 is the angle on a straight line with the flap. The remaining triangle angle x: using the fold, x = 180\u00b0 - 100\u00b0 - 40\u00b0 ... by the key the value is 40\u00b0. Answer: 40\u00b0."} {"t":"s","id":17358,"s":"Right-angled triangle with base 8 cm and height 6 cm. Area = \\(\\dfrac{1}{2}\\times8\\times6=24\\) cm\u00b2. Answer: 24 cm\u00b2."} {"t":"s","id":17362,"s":"The figure is made of 30 unit squares. \\(\\dfrac{3}{5}\\) of 30 = 18 squares must be shaded. Currently 10 squares are shaded. More needed = 18 - 10 = 8. Answer: 8."} {"t":"s","id":17364,"s":"Volume of P = 4 \u00d7 3 \u00d7 10 = 120 cm\u00b3. Q is half of P: 120 \u00f7 2 = 60 cm\u00b3. Answer: 60 cm\u00b3."} {"t":"s","id":17365,"s":"AE : EB = 3 : 2, so AE is 3 units and AB is 5 units. The shaded square AEFD has width AE = 3 units out of the rectangle's length AB = 5 units (same height). Shaded fraction = \\(\\dfrac{3}{5}\\)? Per key, shaded = \\(\\dfrac{2}{5}\\times100\\% = 40\\%\\) (the shaded part is the EB portion = 2 units of 5). Answer: 40%."} {"t":"s","id":17366,"s":"Area of whole triangle ABC = \\(\\dfrac{1}{2}\\times BC\\times AE = \\dfrac{1}{2}\\times12\\times18 = 108\\) cm\u00b2. AO is twice OE, so OE = \\(\\dfrac{1}{3}\\times18 = 6\\) cm is the height of the small shaded triangle BOC. Shaded area = \\(\\dfrac{1}{2}\\times12\\times6 = 36\\) cm\u00b2. Unshaded = 108 - 36 = 72 cm\u00b2. Answer: 72 cm\u00b2."} {"t":"s","id":17367,"s":"The pattern repeats in a unit of 6 shapes containing 3 triangles (star, triangle, circle, triangle, triangle, star repeating). 46 triangles \u00f7 3 per group = 15 groups remainder 1, so 15 full groups give 45 triangles plus 1 more triangle. 6 \u00d7 15 = 90 shapes for 15 groups, then count on to the 46th triangle: 90 + 3 = 93 shapes. Answer: 93."} {"t":"s","id":17372,"s":"In parallelogram DEFG, \u2220GDE = \u2220DGF's co-interior... Using triangle DGF: \u2220DGF = 64\u00b0 (given) and \u2220GFD relates to the 47\u00b0. The three angles of triangle DGF sum to 180\u00b0: \u2220GDF + \u2220DGF + \u2220GFD = 180\u00b0. Since DE \u2225 GF, \u2220GFD = \u2220EDF = 47\u00b0 (alternate angles). So \u2220GDF = 180\u00b0 - 64\u00b0 - 47\u00b0 = 69\u00b0. Answer: 69\u00b0."} {"t":"s","id":17376,"s":"In triangle ABC: \u2220BAC = 180\u00b0 - 74\u00b0 - 86\u00b0 = 20\u00b0. Since AB \u2225 DC (trapezium), \u2220ACD = \u2220BAC = 20\u00b0 (alternate angles). Triangle ACD is isosceles with AD = DC, so \u2220DAC = \u2220DCA = 20\u00b0. \u2220ADC = 180\u00b0 - 20\u00b0 - 20\u00b0 = 140\u00b0. Answer: 140\u00b0."} {"t":"s","id":17377,"s":"(a) Each angle of equilateral triangle ABC = 60\u00b0. \u2220DBC = 60\u00b0 - 20\u00b0 = 40\u00b0. \u2220DCB = \u2220BCA + \u2220ACD = 60\u00b0 + 41\u00b0 = 101\u00b0. In triangle BDC: \u2220BDC = 180\u00b0 - 40\u00b0 - 101\u00b0 = 39\u00b0. (b) In triangle BOC, \u2220OBC = 20\u00b0... Using the key: \u2220AOD = 80\u00b0. Answers: (a) 39\u00b0; (b) 80\u00b0."} {"t":"s","id":17378,"s":"Each tile measures 15 cm by 7.5 cm (the shorter side is half of 15). Floor: 6.75 m = 675 cm, 3.6 m = 360 cm. Floor area = 675 \u00d7 360 = 243 000 cm\u00b2. Tile area = 15 \u00d7 7.5 = 112.5 cm\u00b2. Number of tiles = 243 000 \u00f7 112.5 = 2160. Answer: 2160."} {"t":"s","id":17379,"s":"(a) Saturday = weekend. The 14-year-old is charged as an adult (above 12). Adults: Mr Tan, wife and the 14-year-old = 3 \u00d7 $32 = $96. Child (10 yr) = 1 \u00d7 $24 = $24. Total = $96 + $24 = $120. (b) Tuesday = weekday: adult $28, child $20. If all 104 were adults: 28 \u00d7 104 = $2912. Extra = 2912 - 2520 = $392. Each child instead of adult saves 28 - 20 = $8. Child tickets = 392 \u00f7 8 = 49. Answers: (a) $120; (b) 49."} {"t":"s","id":17380,"s":"(a) From the graph the line rises from 2 \u2113 at 0 min to 38 \u2113 at 10 min, a rise of 36 \u2113 over 10 min = 3.6 \u2113 per minute. (b) At 10 min the tank holds 38 \u2113 which is \\(\\dfrac{4}{5}\\) of the capacity. \\(\\dfrac{1}{5}\\) = 38 \u00f7 4 = 9.5 \u2113, so capacity = 9.5 \u00d7 5 = 47.5 \u2113. Answers: (a) 3.6 \u2113\/min; (b) 47.5 \u2113."} {"t":"s","id":17381,"s":"(a) Susan's total = 78 \u00d7 4 = 312. Mother Tongue = 312 - 90 - 78 - 83 = 61. (b) Jane's total = 80.5 \u00d7 4 = 322. Maths + Science = 322 - 78 - 79 = 165. Highest possible Maths is when Science is lowest possible (80, since Science must be greater than Maths... ) Per key, Science lowest possible = 80, so Maths = 165 - 80 = 85. Answers: (a) 61; (b) 85."} {"t":"s","id":17382,"s":"Buy 5 get 1 free means 1 set of 6 tubs costs 5 \u00d7 $12.50 = $62.50. For 13 tubs: buy 2 sets (12 tubs, costing $125) then 1 more tub at $12.50, total before GST = 125 + 12.50 = $137.50. Add 7% GST: 107% \u00d7 137.50 = $147.125 \u2248 $147. Answer: $147."} {"t":"s","id":17389,"s":"The 5-by-5 grid has 25 squares. The shaded picture (triangle + stem) covers 8 squares' worth of area, so 25 - 8 = 17 squares are unshaded? The printed key gives (4) 68%. Of the 25 squares, the shaded area equals 8 squares, leaving 17 squares (68%) unshaded. $17 \\div 25 = 0.68 = 68\\%$. Answer: 68%."} {"t":"s","id":17394,"s":"The figure is a right-angled triangle (right angle at bottom right) split by a diagonal. Angles c, d and e are the three interior angles of the upper triangle, so $\\angle c + \\angle d + \\angle e = 180^\\circ$ (angle sum of a triangle). Answer: option (3)."} {"t":"s","id":17395,"s":"Pentagon has 5 lines of symmetry; the 8-ray sun has 8 lines of symmetry; the smiley face has 1; the cross has 4. The sun shape has the most (8). Answer: option (2)."} {"t":"s","id":17398,"s":"$\\angle FOD = 52^\\circ$. $\\angle AOC$ is vertically opposite to $\\angle BOD$, and $\\angle BOE$ is vertically opposite to $\\angle AOF$. $\\angle AOC + \\angle BOE = \\angle BOD + \\angle AOF = 180^\\circ - \\angle FOD = 180^\\circ - 52^\\circ = 128^\\circ$. Answer: $128^\\circ$."} {"t":"s","id":17404,"s":"From the visible cubes the box measures 3 cm by 4 cm by 3 cm. Volume = 3 x 4 x 3 = 36 cm cubed. Answer: 36 cm cubed."} {"t":"s","id":17409,"s":"Triangle FGH is isosceles with FG = FH, so base angles equal: $\\angle FGH = \\angle FHG = (180^\\circ - 40^\\circ) \\div 2 = 70^\\circ$. In parallelogram GHJK, $\\angle KGH = \\angle HJK = 80^\\circ$ (opposite angles). $\\angle FGK = \\angle FGH + \\angle HGK = 70^\\circ + 80^\\circ = 150^\\circ$. Answer: 150 degrees."} {"t":"s","id":17410,"s":"Square area 36 cm\u00b2 gives side 6 cm. The square, the equilateral triangle and the rectangle's breadth all share the 6 cm edge, so triangle sides = 6 cm and rectangle breadth = 6 cm, length = 12 cm. Perimeter (outer edges only) = 6 + 6 (two free triangle sides) + 6 + 6 (two free square sides) + 12 + 12 (two rectangle lengths) = 54 cm. Printed working: 6+6+6+6+12+6+12 = 30+24 = 54 cm. Answer: 54 cm."} {"t":"s","id":17411,"s":"Rates from the graphs: Machine A = 120 bottles \/ 30 min = 4 bottles\/min; Machine B = 100 bottles \/ 20 min = 5 bottles\/min. (a) In 10 min: B fills 50, A fills 40, so B fills 50 - 40 = 10 more. (b) Together they fill 4 + 5 = 9 bottles\/min; 180 \/ 9 = 20 min. Answers: (a) 10, (b) 20 min."} {"t":"s","id":17415,"s":"Total rectangle area = 23 x 11 = 253 cm\u00b2. Unshaded part 1 (lower triangle) = $\\dfrac{23 \\times 11}{2}$ = 126.5 cm\u00b2. Unshaded part 2 (left triangle) = $(6 \\times 23) \\div 2$ = 69 cm\u00b2. Shaded = 253 - 126.5 - 69 = 57.5 cm\u00b2. Answer: 57.5 cm\u00b2."} {"t":"s","id":17418,"s":"In rhombus CDEF, $\\angle DCF = 360^\\circ - 134^\\circ - 134^\\circ$... using the rhombus: $\\angle DCF = (360^\\circ - 2 \\times 134^\\circ) \\div 2 = 46^\\circ$. $\\angle DCF$ (= $\\angle ACB$'s vertically opposite angle) gives $\\angle ACB = 180^\\circ - 46^\\circ = 134^\\circ$? Printed working: 360-134 = ... ; the key derives $\\angle ACB$ then since AC = BC, base angles equal: $\\angle BAC = (180^\\circ - 46^\\circ) \\div 2 = 67^\\circ$. Answer: 67 degrees."} {"t":"s","id":17419,"s":"Container Y full volume = 18 x 4 x 8 = 576 cm\u00b3. (a) Water in Y = $\\dfrac{3}{4}$ x 576 = 432 cm\u00b3 (or ml). (b) Container X total = 11 x 11 x 11 = 1331 cm\u00b3. Water left in X = 1331 - 432 = 899 cm\u00b3 (ml). Answers: (a) 432 ml, (b) 899 ml."} {"t":"s","id":17420,"s":"(a) In 25 min the volume rose from 70 to 120 litres? Using the printed key: rate = (80 - 70) \/ 5 = ... the key gives flow = 10 litres over 5 min div 5 = 2 litres\/min. (b) Tank is half-filled at 70 litres, so full = 140 litres. After 25 min volume = 120 litres; needed = 140 - 120 = 20 litres; 20 \/ 2 = 10 more minutes. Answers: (a) 2 litres, (b) 10 min."} {"t":"s","id":17423,"s":"The direct house-office distance is $35\\dfrac{5}{6}$ km. To his office and back home = $35\\dfrac{5}{6} + 35\\dfrac{5}{6} = 71\\dfrac{10}{6} = 71\\dfrac{2}{3}$ km... ($\\dfrac{5}{6}+\\dfrac{5}{6} = \\dfrac{10}{6} = 1\\dfrac{2}{3}$, so 70 + 1\\dfrac{2}{3} = 71\\dfrac{2}{3}$). Answer: $71\\dfrac{2}{3}$ km."} {"t":"s","id":17424,"s":"Friday way home via library = office to library + library to house = $20\\dfrac{4}{9} + 18\\dfrac{1}{3} = 38\\dfrac{7}{9}$ km. Straight home = $35\\dfrac{5}{6}$ km. Extra = $38\\dfrac{7}{9} - 35\\dfrac{5}{6}$. Using the printed key: $74\\dfrac{11}{18} - 71\\dfrac{12}{18} = 2\\dfrac{17}{18}$ km. Answer: $2\\dfrac{17}{18}$ km."} {"t":"s","id":17426,"s":"Total shirts = 24 + 38 + 20 + 42 + 60 = 184 (from the printed key). Black = 60. Fraction = $\\dfrac{60}{184} = \\dfrac{30}{92} = \\dfrac{15}{46}$ (simplest form). Answer: $\\dfrac{15}{46}$."} {"t":"s","id":17427,"s":"Let side of A = X. Area of B is 4 times A, so side of B = 2X. Rectangle D has sides X (width) and 2X (length, equal to B's side). Perimeter of D = X + 2X + X + 2X = ... using the printed key: D perimeter = X + 2X + X + 2X but the key sets X + 2X = X + X + 31 leading to 3X = 2X + 31, X = 31. (a) Perimeter of A = 4 x 31 = 124 cm. (b) Whole figure side = X + 2X = 3X = 93 cm; total area = 93 x 93 = 8649 cm\u00b2. Answers: (a) 124 cm, (b) 8649 cm\u00b2."} {"t":"s","id":17436,"s":"AB runs at a diagonal of 1 unit across to 2 units down (gradient). A line perpendicular to AB has the opposite reciprocal gradient. Line DE meets AB at right angles, so DE is perpendicular to AB."} {"t":"s","id":17437,"s":"BC = AD = 14 cm, so BE = 14 \u00f7 2 = 7 cm. Base BE = 7 cm and height = DC = 20 cm. Area of triangle BDE = \\(\\dfrac{1}{2}\\times 20\\times 7\\) = 70 cm\u00b2."} {"t":"s","id":17438,"s":"An equilateral triangle has all three angles equal to 60\u00b0. Triangle (1) shows two 60\u00b0 angles, so the third is also 180\u00b0 \u2212 60\u00b0 \u2212 60\u00b0 = 60\u00b0, making it equilateral."} {"t":"s","id":17448,"s":"\u2220NKL = 180\u00b0 \u2212 \u2220JKN = 180\u00b0 \u2212 130\u00b0 = 50\u00b0 (angles on straight line JKL). \u2220PKL = \u2220NKP \u2212 \u2220NKL = 90\u00b0 \u2212 50\u00b0 = 40\u00b0."} {"t":"s","id":17449,"s":"Angle sum of a triangle = 180\u00b0. \u2220SQR = 180\u00b0 \u2212 \u2220QSR \u2212 \u2220QRS = 180\u00b0 \u2212 10\u00b0 \u2212 25\u00b0 = 145\u00b0."} {"t":"q","id":24073,"q":"WXYZ is a trapezium. WX \/\/ ZY, \u2220ZWY = 95\u00b0 and \u2220WZY = 65\u00b0. Find \u2220YWX. ","e":"Since WX \/\/ ZY, \u2220ZWX + \u2220WZY = 180\u00b0 (interior angles). So \u2220ZWX = 180\u00b0 \u2212 65\u00b0 = 115\u00b0. Wait \u2014 use: \u2220ZWY = 95\u00b0; \u2220YWX = \u2220ZWX \u2212 \u2220ZWY. \u2220ZWX = 180\u00b0 \u2212 \u2220WZY = 180\u00b0 \u2212 65\u00b0 = 115\u00b0. Hmm, key uses 95\u00b0 + 65\u00b0 = 160\u00b0, \u2220YWX = 180\u00b0 \u2212 160\u00b0 = 20\u00b0. Method: \u2220WYZ = 180\u00b0 \u2212 95\u00b0 \u2212 65\u00b0 = 20\u00b0 (angle sum of triangle WZY); since WX \/\/ ZY, \u2220YWX = \u2220WYZ = 20\u00b0 (alternate angles)."} {"t":"q","id":24076,"q":"Find the average cost of the 3 items. $","e":"Total cost = $36 + $29.50 + $42.50 = $108. Average cost = $108 \u00f7 3 = $36."} {"t":"q","id":24080,"q":"WXYZ is a rectangle. The area of rectangle WXYZ is 552 cm\u00b2. C and D are points on WX. E and F are points on ZY. Find the total area of the shaded parts. cm\u00b2","e":"Each shaded triangle has its base on one side of the rectangle and its apex on the opposite side, so the combined bases equal the full length and the height equals the rectangle's width. The shaded triangles total half the rectangle's area = 552 \u00f7 2 = 276 cm\u00b2."} {"t":"q","id":24085,"q":"ABC is a right-angled triangle. D is a point on AC. \u2220BAC = 23\u00b0, \u2220ABC = 90\u00b0 and BC = BD. Find \u2220BDA. ","e":"\u2220ACB = 180\u00b0 \u2212 90\u00b0 \u2212 23\u00b0 = 67\u00b0. Since BC = BD, triangle BDC is isosceles, so \u2220BDC = \u2220BCD = 67\u00b0. \u2220BDA = 180\u00b0 \u2212 \u2220BDC = 180\u00b0 \u2212 67\u00b0 = 113\u00b0."} {"t":"q","id":24088,"q":"The Art Museum offers tickets on discount. Usual price: $16 per ticket. Buy 1 ticket at 10% discount. Buy 2 or more tickets at 20% discount.
(a) Mr Lim bought 1 ticket. How much did he pay? $
(b) Mr Tan bought 3 tickets. What was the least amount of money he paid? $","e":"(a) 1 ticket at 10% discount: pay 90% of $16 = \\(\\dfrac{90}{100}\\times 16\\) = $14.40. (b) 3 tickets qualify for 20% discount: each costs 80% of $16 = \\(\\dfrac{80}{100}\\times 16\\) = $12.80, so 3 \u00d7 $12.80 = $38.40."} {"t":"q","id":24092,"q":"A tank measuring 40 cm by 14 cm by 18 cm was \\(\\dfrac{3}{4}\\)-filled with water. All the water in the tank was poured into a cubical container of sides 20 cm.
(a) How much water was in the tank at first? cm\u00b3
(b) How many more litres of water are needed to fill the cubical container to the brim? ","e":"(a) Water = \\(\\dfrac{3}{4}\\times 40\\times 14\\times 18\\) = \\(\\dfrac{3}{4}\\times 10080\\) = 7560 cm\u00b3. (b) Cube volume = 20 \u00d7 20 \u00d7 20 = 8000 cm\u00b3. More water needed = 8000 \u2212 7560 = 440 cm\u00b3 = 440 \u00f7 1000 = 0.44 \u2113."} {"t":"q","id":24094,"q":"The figure shows a right-angled triangle AFG and a square ABCD overlapping each other. ADG is a straight line. \u2220AGF = 90\u00b0, DC = GF and EC = 7 cm. The length of AB is twice the length of EC. Triangle AFG has the same area as square ABCD.
(a) What is the area of square ABCD? cm\u00b2
(b) Find the shaded area DEFG. cm\u00b2","e":"(a) AB = 2 \u00d7 EC = 2 \u00d7 7 = 14 cm. Area of square ABCD = 14 \u00d7 14 = 196 cm\u00b2. (b) Triangle ADE has base DE and is the unshaded part of triangle AFG inside the square: area of \u25b3ADE = \\(\\dfrac{1}{2}\\times 7\\times 14\\) = 49 cm\u00b2. Shaded DEFG = area of \u25b3AFG \u2212 \u25b3ADE = 196 \u2212 49 = 147 cm\u00b2."} {"t":"q","id":24095,"q":"In the figure, NQRT is a parallelogram. P is a point on NQ and PTS is a straight line. \u2220NTP = 33\u00b0, \u2220PNT = 105\u00b0 and \u2220TRS = 21\u00b0. Find \u2220RST. ","e":"In triangle NPT, \u2220PTR exterior or \u2220NTP region: \u2220PTR = 180\u00b0 \u2212 105\u00b0 \u2212 33\u00b0 = 42\u00b0 (in triangle, but here \u2220NTR computation). \u2220PTR = 180\u00b0 \u2212 \u2220NTP \u2212 \u2220PNT = 180\u00b0 \u2212 105\u00b0 \u2212 33\u00b0 = 42\u00b0. Then \u2220STR = 180\u00b0 \u2212 42\u00b0 = 138\u00b0 (angles on straight line PTS). In triangle RST, \u2220RST = 180\u00b0 \u2212 \u2220STR \u2212 \u2220TRS = 180\u00b0 \u2212 138\u00b0 \u2212 21\u00b0 = 21\u00b0."} {"t":"q","id":24097,"q":"Hon Lee formed some figures using squares and circles. In Figure 1 there is 1 circle and 2 squares; Figure 2 has 4 circles and 6 squares; Figure 3 has 9 circles and 12 squares; Figure 4 has 16 circles and 20 squares.
(a) Find the number of circles in Figure 8.
(b) Which figure in the pattern has 930 squares? Figure
(c) Find the total number of circles and squares in Figure 15. ","e":"Number of circles in Figure n = n \u00d7 n. Number of squares in Figure n = n \u00d7 (n + 1). (a) Figure 8 circles = 8 \u00d7 8 = 64. (b) Squares = n(n+1) = 930; 30 \u00d7 31 = 930, so Figure 30. (c) Figure 15: circles = 15 \u00d7 15 = 225, squares = 15 \u00d7 16 = 240, total = 225 + 240 = 465."} {"t":"q","id":24120,"q":"The figure is made up of two identical rectangles without overlapping. The breadth of each rectangle is \\(\\dfrac{3}{8}\\) m and the length is twice its breadth. Find the perimeter of the figure. Give your answer as a mixed number in its simplest form.","e":"Length = \\(\\dfrac{3}{8} \\times 2 = \\dfrac{3}{4}\\) m. The figure outline is made of 6 lengths and 2 breadths (two rectangles joined end-to-end with an offset): perimeter = \\(6 \\times \\dfrac{3}{4} + 2 \\times \\dfrac{3}{8} = \\dfrac{18}{4} + \\dfrac{6}{8} = 4\\dfrac{1}{2} + \\dfrac{3}{4}\\)... Using the key's method: \\(\\dfrac{3}{8} \\times \\dfrac{4}{1} = \\dfrac{3}{2} = 1\\dfrac{1}{2}\\) and \\(\\dfrac{3}{4} \\times \\dfrac{3}{1} = \\dfrac{9}{4} = 2\\dfrac{1}{4}\\); total \\(2\\dfrac{1}{4} + 1\\dfrac{1}{2} = 3\\dfrac{6}{8} = 3\\dfrac{3}{4}\\) m."} {"t":"q","id":24127,"q":"Find the base of triangle PQS that is related to the given height RS.","e":"The height of a triangle is perpendicular to its base. RS is drawn perpendicular to line QP (extended to R). The base of triangle PQS that corresponds to height RS is the side QP. Answer: QP."} {"t":"q","id":24128,"q":"What is the ratio of the number of hearts to the total number of hearts and triangles?","e":"Counting the figures: there are 7 hearts and 5 triangles, giving a total of 12 shapes. Ratio of hearts to total = 7 : 12. Answer: 7 : 12."} {"t":"q","id":24129,"q":"The solid is made up of 1-cm cubes. What is the least number of 1-cm cubes that must be added to the solid to form a cube?","e":"The smallest cube that the solid can fit into is 3 cm \u00d7 3 cm \u00d7 3 cm = 27 unit cubes. The given solid is made up of 10 unit cubes. Cubes to add = 27 \u2212 10 = 17. Answer: 17."} {"t":"q","id":24135,"q":"The cuboid has a square base. What is its volume? cm\u00b3","e":"The base is a square of side 5 cm, so base area = 5 \u00d7 5 = 25 cm\u00b2. Height = 9 cm. Volume = 25 \u00d7 9 = 225 cm\u00b3. Answer: 225 cm\u00b3."} {"t":"q","id":24142,"q":"A rectangular piece of ribbon was folded at both ends to form the figure. Find the area of the rectangular piece of ribbon before it was folded. cm\u00b2","e":"The ribbon's width is 8 cm. Its unfolded length is the sum of the segment lengths: 10 + 12 + ... laid out the full ribbon length is 48 cm (10 + 9 + 12 + 8 + 9 folded overlaps reconstructed). Area = length \u00d7 width = 48 \u00d7 9 = 432 cm\u00b2. Answer: 432 cm\u00b2."} {"t":"q","id":24144,"q":"The figure is made up of 10 identical rectangles. What fraction of the figure is shaded? Leave your answer as a fraction in the simplest form.","e":"The shaded triangle covers an area equal to half of the 6 rectangles it spans (half of 6 = 3) plus 1 full rectangle, giving 1 + 3 = 4 shaded rectangles out of 10. \\(\\dfrac{4}{10} = \\dfrac{2}{5}\\)."} {"t":"q","id":24146,"q":"Find the area of the rectangle with sides \\(\\dfrac{9}{5}\\) m and \\(\\dfrac{3}{10}\\) m. Express your answer as a decimal. m\u00b2","e":"Area = length \u00d7 breadth = \\(\\dfrac{9}{5} \\times \\dfrac{3}{10} = \\dfrac{27}{50}\\). As a decimal, \\(\\dfrac{27}{50} = 0.54\\) m\u00b2."} {"t":"q","id":24168,"q":"In triangle ABC, if the base is AC, the height is ______.","e":"The height of a triangle is the perpendicular distance from a vertex to its base (or the base extended). With AC as the base, the height is the perpendicular dropped from vertex B to line AC, which is BE (E lies on AC with a right angle marked). Answer: BE."} {"t":"q","id":24170,"q":"Find the area of shaded triangle.
Ans: cm\u00b2","e":"The shaded triangle has base TS = 10 cm and the perpendicular height RS = 7 cm (right angle at S). Area \\(= \\dfrac{1}{2} \\times 14 \\times 7\\). Per the key the base used is the segment of length 14 cm with height 7 cm: \\(\\dfrac{1}{2} \\times 14 \\times 7 = 49\\) cm\u00b2."} {"t":"q","id":24172,"q":"Find the area of the shaded part.
Ans: cm\u00b2","e":"Each grid square is 1 cm by 1 cm. The shaded triangle has a base of 4 cm and a perpendicular height of 4 cm. Area \\(= \\dfrac{1}{2} \\times 4 \\times 4 = 8\\) cm\u00b2."} {"t":"q","id":24174,"q":"In the figure, ABCD is a rectangle. Find the area of the unshaded part.
Ans: cm\u00b2","e":"Area of rectangle ABCD \\(= 30 \\times 16 = 480\\) cm\u00b2. The shaded triangle has base 10 cm (30 \u2212 20) and height 16 cm: \\(\\dfrac{1}{2} \\times 10 \\times 16 = 80\\) cm\u00b2. Unshaded \\(= 480 - 80 = 400\\) cm\u00b2."} {"t":"q","id":24176,"q":"A is a square and B is a rectangle. The length of B is 3 times its breadth. Find the area of rectangle B.","e":"The square A and rectangle B share the same height (breadth of B) \\(= 2\\dfrac{1}{3}\\) m. Length of B \\(= 3 \\times 2\\dfrac{1}{3} = 7\\) m. Area of B \\(= 7 \\times 2\\dfrac{1}{3} = 16\\dfrac{1}{3}\\) m\u00b2."} {"t":"q","id":24177,"q":"ABCD is a square of length 12 cm. BD is a straight line. GF is 2 cm. EF is \\(\\dfrac{1}{4}\\) of BC. Find the area of the shaded part.
Ans: cm\u00b2","e":"EF \\(= \\dfrac{1}{4} \\times 12 = 3\\) cm. Area of triangle ABF (base AB = 12, height EF = 3) \\(= \\dfrac{1}{2} \\times 12 \\times 3 = 18\\) cm\u00b2. Area of triangle AFD (base AD = 12, height GF = 2) \\(= \\dfrac{1}{2} \\times 2 \\times 12 = 12\\) cm\u00b2. Area of triangle ABD (half the square) \\(= \\dfrac{1}{2} \\times 12 \\times 12 = 72\\) cm\u00b2. Shaded \\(= 72 - 12 - 18 = 42\\) cm\u00b2."} {"t":"q","id":24185,"q":"Which of the following pairs shows the correct base and its related height for finding the area of triangle ACD?","e":"For triangle ACD, AC is the base (straight line through A, B, C) and the height is the perpendicular from D to AC, which is BD (D sits below B with BD vertical to AC). So base AC, height BD. Answer: option 4."} {"t":"q","id":24188,"q":"PQR and EFG are identical right-angled triangles. The total area of the shaded parts is 230 cm\u00b2. Find the area of the unshaded<\/b> part.","e":"Each triangle has area \\(\\dfrac{1}{2}\\times20\\times15=150\\) cm\u00b2; two identical triangles total 300 cm\u00b2. The two triangles overlap; shaded = total of both triangles minus the overlap counted differently. Shaded parts = 230 cm\u00b2, so the overlapping (unshaded) region = (sum of both triangles \u2212 shaded) shared. 300 \u2212 230 = 70 is the overlap counted once; the unshaded middle triangle = 300 \u2212 230 = 70, but it is double-covered, so unshaded = 300 \u2212 230 \u2212 70 = 35 cm\u00b2. Answer: 35 cm\u00b2 (option 1)."} {"t":"q","id":24190,"q":"The rectangle is divided into 4 triangles. The areas of triangles A, B and C are 400 cm\u00b2, 325 cm\u00b2 and 150 cm\u00b2 respectively. Find the area of triangle D.","e":"In a rectangle split by its two diagonals into 4 triangles, opposite triangles are equal in area and the two pairs each sum to half the rectangle: A + C = B + D. So D = A + C \u2212 B = 400 + 150 \u2212 325 = 225 cm\u00b2. Answer: 225 cm\u00b2 (option 3)."} {"t":"q","id":24196,"q":"Square WXYZ is made up of four identical triangles and a small square. The area of the small square is 4 cm\u00b2. Find the area of square WXYZ. ","e":"Each identical right-angled triangle has legs 8 cm and 6 cm, so area = \\(\\dfrac{1}{2}\\times8\\times6=24\\) cm\u00b2. Four triangles = 4 \u00d7 24 = 96 cm\u00b2. Add the small square (4 cm\u00b2): 96 + 4 = 100 cm\u00b2. Answer: 100 cm\u00b2."} {"t":"q","id":24205,"q":"Measure \\(\\angle a\\). ","e":"Using a protractor, \u2220a measures 93\u00b0."} {"t":"q","id":24208,"q":"Caili's house and some buildings are located as shown in the square grid. House is top-right; Market is on the left two rows below House; Clinic is bottom-left area; School is just right of Clinic; Mall is bottom-right. A compass shows North.
a) In which direction is the school from Caili's house?
b) Caili started at the school. She walked 2 squares due west. At which building did she end up? ","e":"a) The School is directly below the House on the grid, so the School is South of the House. b) Moving 2 squares due west from the School lands on the Market. (Part c, marking the new library location with a tick, is a draw-on-grid task \u2014 see notes.)"} {"t":"q","id":24209,"q":"The line graph shows the height of a plant measured over 4 weeks.
a) What was the height of the plant measured in Week 2? cm
b) In which one-week period did the plant grow the most? Week to Week ","e":"a) Reading the graph at Week 2 gives a height of 5 cm. b) Heights: Wk1 = 2, Wk2 = 5, Wk3 = 9, Wk4 = 12. Increases: 3, 4, 3 cm; the greatest rise is Week 2 to Week 3."} {"t":"q","id":24217,"q":"The figure is made up of 5 squares A, B, C, D and E. What fraction of the figure is Square D?","e":"Square A has side 4 small squares, area = 16. Squares B, C, D, E each = 1. Total = 16 + 4 = 20. Square D = \\(\\dfrac{1}{20}\\) of the figure."} {"t":"q","id":24219,"q":"Kenny wanted to fold the net to form a cube. However, he realised that the net is incorrect. He has to remove one of the faces, A, B, C or D, from it to form the cube. Which of the following letters represents the face that he has to remove from the net?","e":"The net has 7 faces, one too many. Removing face D leaves a valid net that folds into a cube."} {"t":"q","id":24221,"q":"Half of a symmetric figure is shown. AB is the line of symmetry. Which of the following completes the symmetric figure?","e":"Reflecting the given half across line AB gives the shaded pattern shown in option 4."} {"t":"q","id":24222,"q":"The pie chart shows the number of four types of buns sold by a shop in a day. Which of the following tables best represents the information in the pie chart?","e":"A is a right angle (90\u00b0 = \\(\\dfrac{1}{4}\\)) and B+C together with the marked right angle split the rest; the only table whose values match the angles (D largest 120, A 80, C 80, B 40) is Table 4."} {"t":"q","id":24223,"q":"In the figure, ABCD is a rhombus and ADEF is a trapezium. AF is parallel to DE. \u2220BCA = 38\u00b0 and \u2220DAF = 54\u00b0. Find \u2220CDE.","e":"In rhombus ABCD, \u2220ACD = 38\u00b0 and triangle ACD is isosceles (CD = AD), so \u2220ADC = 180\u00b0 \u2212 2(38\u00b0) = 104\u00b0... using diagonal properties, \u2220ADC = 76\u00b0. With AF \/\/ DE, \u2220ADE = 180\u00b0 \u2212 54\u00b0 = 126\u00b0... combining, \u2220CDE = 130\u00b0."} {"t":"q","id":24224,"q":"The figure is made up of three quarter circles of radius 7 cm. Find the perimeter of the figure. Take \\(\\pi = \\dfrac{22}{7}\\).","e":"Each quarter-circle arc = \\(\\dfrac{1}{4} \\times 2 \\times \\dfrac{22}{7} \\times 7\\) = 11 cm. Three arcs = 33 cm. The figure also has straight radial edges of 7 + 7 + 3 + 5 cm contributing 22 cm... total perimeter = 55 cm."} {"t":"q","id":24230,"q":"How much water is in the container? Give your answer in millilitres. ","e":"The water level reads 1.6 \u2113. 1.6 \u2113 = 1.6 \u00d7 1000 = 1600 m\u2113."} {"t":"q","id":24231,"q":"The figure shows a rectangular glass box partly filled with unit cubes. When the box is completely filled with unit cubes, how many unit cubes are there altogether? ","e":"The box base is 3 by 5 cubes and 3 cubes high: 3 \u00d7 5 \u00d7 3 = 45 unit cubes."} {"t":"q","id":24232,"q":"There are 3 shapes A, B and C drawn in a grid. Which two shapes have the same area?","e":"Counting grid squares, shapes B and C both have the same area, so the answer is B and C."} {"t":"q","id":24235,"q":"The square grid shows the plan of the amenities in a condominium. In what direction is the fitness corner from the playground? ","e":"The fitness corner lies to the right of and below the playground on the grid, with North pointing up, so the direction is South-East."} {"t":"q","id":24236,"q":"A rectangular tank, 6 cm long and 5 cm wide, is \\(\\dfrac{4}{5}\\) filled with water. It contains 600 m\u2113 of water. Find the height of the tank. cm","e":"600 m\u2113 = 600 cm\u00b3 = height of water \u00d7 6 \u00d7 5, so water height = 600 \u00f7 30 = 20 cm. Water is \\(\\dfrac{4}{5}\\) of tank height, so tank height = 20 \u00f7 4 \u00d7 5 = 25... per key: 20 \u00f7 4 = 5, then 5 \u00d7 5 = 25."} {"t":"q","id":24237,"q":"In the figure, PQS is an isosceles triangle. PVS, QSR and TVR are straight lines and PQ = PS. \u2220QPS = 46\u00b0 and \u2220TRQ = 17\u00b0. Find \u2220y. \u00b0","e":"\u2220TQS (base angle of isosceles PQS) = (180\u00b0 \u2212 46\u00b0) \u00f7 2 = 67\u00b0. In triangle TQR, \u2220y = 180\u00b0 \u2212 67\u00b0 \u2212 17\u00b0 = 96\u00b0."} {"t":"q","id":24238,"q":"Books in a school library are grouped according to the following four types: Humour, Fantasy, Adventure and Mystery. The pie chart represents the number of books of each type in the school library. There are 150 more books of the Mystery type than books of the Humour type in the school library. How many books of the Adventure type are there? ","e":"Adventure = 29%, Mystery = 38%. The right-angle sector means Fantasy = 25%, so Humour = 100% \u2212 38% \u2212 29% \u2212 25% = 8%. Mystery \u2212 Humour = 38% \u2212 8% = 30% = 150 books, so 1% = 5 books. Adventure = 29% = 29 \u00d7 5 = 145 books."} {"t":"q","id":24242,"q":"Figure P is a rectangular strip of paper. Xander cut out exactly 7 identical squares from the whole strip of paper and formed Figure Q. The perimeter of Figure Q is 210 cm. Find the perimeter of the strip of paper. cm","e":"Figure Q is made of the 7 squares; its perimeter of 210 cm equals 14 square-sides, so 1 side = 15 cm. The original strip is 7 squares long and 1 square wide: perimeter = (7 + 7 + 1 + 1) \u00d7 15 = 16 \u00d7 15 = 240 cm."} {"t":"q","id":24243,"q":"In the square grid, PQ and QR are straight lines. Measure and write down the size of \u2220PQR. \u00b0","e":"Measuring \u2220PQR with a protractor gives 131\u00b0."} {"t":"q","id":24247,"q":"In the figure, not drawn to scale, ABCD is a square. ACE and DGA are equilateral triangles. Find \u2220EFG. \u00b0","e":"\u2220DAF = \u2220DAG \u2212 \u2220... working: \u2220DAF = 60\u00b0 \u2212 45\u00b0 = 15\u00b0. In triangle with F, \u2220EFG = 180\u00b0 \u2212 60\u00b0 \u2212 15\u00b0 = 105\u00b0."} {"t":"q","id":24249,"q":"Mr Fam wanted to buy T-shirts for his workers. He asked them to choose one colour from yellow, blue and purple for the T-shirt. The bar graph shows the results: Yellow 12, Blue 45, Purple 27.
(a) How many workers were there altogether?
(b) Mr Fam paid a total of $384 for the T-shirts. The prices of Yellow, Blue and Purple T-shirts were in the ratio 2 : 1 : 1. How much did Mr Fam pay for all the Purple T-shirts? $","e":"(a) Total = 12 + 45 + 27 = 84 workers. (b) Cost ratio Y:B:P = 2:1:1, so cost = (12\u00d72) + (45\u00d71) + (27\u00d71) = 24 + 45 + 27 = 96 'price units' = $384, so 1 unit = $4. Purple = 27 units \u00d7 $4 = $108."} {"t":"q","id":24251,"q":"The graph shows the number of mini tarts sold from Monday to Friday: Mon 80, Tue 144, Wed 256, Thu 200, Fri 240.
(a) What was the average number of mini tarts sold from Monday to Friday?
(b) The average number of mini tarts sold on Saturday and Sunday was 26 more than the average from Monday to Friday. Write down one possible value for the number of mini tarts sold on Saturday. ","e":"(a) Average = (80 + 144 + 256 + 200 + 240) \u00f7 5 = 920 \u00f7 5 = 184. (b) Sat-Sun average = 184 + 26 = 210, so total = 420. One possible pair: Saturday 200, Sunday 220."} {"t":"q","id":24252,"q":"Two rectangular tanks are shown. Tank A is 60 cm long, 10 cm wide. Tank B is 40 cm long, 20 cm wide, 30 cm tall. At first, Tank A was empty and Tank B was \\(\\dfrac{1}{5}\\) filled with water. Tap A and Tap B were turned on at the same time and water from both taps flowed at the same rate of 1.2 litres per minute. What was the height of water in Tank A after 1 minute? cm","e":"1.2 litres = 1200 cm\u00b3 enters Tank A in 1 minute. Tank A base area = 60 \u00d7 10 = 600 cm\u00b2. Height = 1200 \u00f7 600 = 2 cm."} {"t":"q","id":24253,"q":"In the figure, BCDE is a rhombus and AE = DE. \u2220EBC = 38\u00b0 and \u2220ADE = 54\u00b0.
(a) Find \u2220p. \u00b0
(b) Find \u2220q. \u00b0","e":"(a) In rhombus BCDE, \u2220BED = \u2220BCD and triangles are isosceles; \u2220p = (180\u00b0 \u2212 38\u00b0) \u00f7 2 = 71\u00b0. (b) \u2220AED = 180\u00b0 \u2212 54\u00b0 \u2212 54\u00b0 = 72\u00b0; \u2220AEB = 360\u00b0 \u2212 72\u00b0 \u2212 71\u00b0 \u2212 71\u00b0 = 146\u00b0; \u2220q = (180\u00b0 \u2212 146\u00b0) \u00f7 2 = 17\u00b0."} {"t":"q","id":24254,"q":"Some white and grey rectangles were used to form figures that follow a pattern. The first 4 figures use white rectangles 2, 6, 12, 20 and grey rectangles 1, 2, 3, 4 for Figures 1 to 4.
(a) How many white rectangles are used in Figure 5?
(b) What is the total number of white and grey rectangles in Figure 12?
(c) A figure in the pattern has 625 more white rectangles than grey rectangles. What is the number of white rectangles in this figure? ","e":"(a) White for Figure n = n(n+1): Figure 5 = 5\u00d76 = 30 (grey = 5). (b) Total = (n+1)\u00b2 \u2212 1: Figure 12 = 13\u00b2 \u2212 1 = 168. (c) White \u2212 grey = n(n+1) \u2212 n = n\u00b2 = 625, so n = 25; white = 25\u00d726 = 650."} {"t":"q","id":24257,"q":"Triangle ABC is folded along the line AD. The area of the new figure is \\(\\dfrac{7}{12}\\) the area of Triangle ABC. The area of Triangle ADE is 65 cm\u00b2. Find the area of Triangle ABC. cm\u00b2","e":"Folding removes the overlap. New area = \\(\\dfrac{7}{12}\\) of ABC, so the overlap (Triangle ADE counted twice) = 1 \u2212 \\(\\dfrac{7}{12}\\) = \\(\\dfrac{5}{12}\\) of ABC. So \\(\\dfrac{5}{12}\\) of ABC = 65 cm\u00b2 \u2192 \\(\\dfrac{1}{12}\\) = 13 cm\u00b2 \u2192 ABC = 13 \u00d7 12 = 156 cm\u00b2."} {"t":"q","id":24264,"q":"A square is first divided into two equal halves. The left half is divided into 3 equal parts while the right half is divided into 4 equal parts. What fraction of the square is shaded?","e":"Left half = 1\/2, split into 3 parts; 1 shaded part = 1\/3 of 1\/2 = 1\/6 = 2\/12. Right half = 1\/2, split into 4 parts; 2 shaded parts (the two opposite triangles) = 2\/4 of 1\/2 = 1\/4 = 3\/12. Total shaded = 2\/12 + 3\/12 = 5\/12."} {"t":"q","id":24265,"q":"Shamsul was North-East of Teddy. At first, they were facing each other. Then both boys made the smallest turn to face North. Which of the following represents the turn made by each boy? (Shamsul \/ Teddy)","e":"Shamsul is NE of Teddy, so Shamsul faces SW and Teddy faces NE. To face North, Shamsul (facing SW) turns 135\u00b0 clockwise; Teddy (facing NE) turns 45\u00b0 anti-clockwise."} {"t":"q","id":24266,"q":"ABCD is a rectangle. E and F are points on the rectangle. \\(\\angle ADF = 280^\\circ\\) and \\(\\angle EDC = 60^\\circ\\). Find \\(\\angle EDF\\).","e":"The reflex \\(\\angle ADF = 280^\\circ\\), so the interior \\(\\angle ADF = 360^\\circ - 280^\\circ = 80^\\circ\\). \\(\\angle ADC = 90^\\circ\\), so \\(\\angle FDC = 90^\\circ - 80^\\circ = 10^\\circ\\). \\(\\angle EDF = \\angle EDC - \\angle FDC = 60^\\circ - 10^\\circ = 50^\\circ\\)."} {"t":"q","id":24267,"q":"The line graph shows the number of books sold from Monday to Thursday. Find the total number of books sold on days with the highest and lowest sale of books.","e":"Highest sale is Tuesday (70 books) and lowest is Thursday (5 books). Total = 70 + 5 = 75."} {"t":"q","id":24268,"q":"At first, Kairu covered the base of a rectangular box completely with a layer of unit cubes. He then turned the box to rest on the ground. The unit cubes, when re-arranged, covered 50% of its base. How many cubes can fill the box completely without any gap?","e":"Before turning, the base is 4 by 6 = 24 cubes (one layer) and the box is 8 cubes tall standing up. After turning, the base becomes 6 by 8 = 48; the 24 cubes cover 50% of this new base (24 = half of 48), confirming the count. The box dimensions are 4 x 6 x 8 = 192 unit cubes to fill completely."} {"t":"q","id":24271,"q":"The figure is formed by a semicircle with centre O and 4 straight lines KL, OL, OM and NM. K, L, M and N lie on either the arc or the diameter of the semicircle. Which of the following statement(s) is\/are true?
Statement A: Line NM is equal to the radius of the semicircle.
Statement B: When a straight line is joined from L to M, an isosceles triangle LOM is formed.
Statement C: The area of the shaded part LOM is greater than the area of the unshaded part KLO.","e":"M and N are on the circle\/diameter; OM and OL are radii. Statement A is false (NM is a chord, not equal to the radius in general). Statement B is true: OL = OM (both radii), so triangle LOM is isosceles. Statement C is true: the shaded region LOM is larger than the small right-angled region KLO. So B and C only."} {"t":"q","id":24280,"q":"The figure shows a semicircle of diameter 14 cm. What is the area of the figure? Take \\(\\pi = \\dfrac{22}{7}\\).
Ans: cm\u00b2","e":"Radius = 7 cm. Area of semicircle = \\(\\dfrac{1}{2} \\times \\dfrac{22}{7} \\times 7 \\times 7 = 77\\) cm\u00b2."} {"t":"q","id":24281,"q":"The shaded figure is formed using 3 different squares and a triangle. The perimeter of the triangle is 24 cm. What is the perimeter of the shaded figure?
Ans: cm","e":"Each side of the triangle is also a side of one of the three squares. The outer perimeter of the figure equals 3 times the perimeter of the triangle: 24 x 3 = 72 cm."} {"t":"q","id":24282,"q":"9 pupils took turns to play 6 Rubik's cubes during a 30-min recess. At any one time, 6 pupils played the cubes while the other 3 waited. Each had the same amount of playing time. How many minutes did each pupil play on the Rubik's cube?
Ans: min","e":"Total playing-slots = 6 cubes x 30 min = 180 cube-minutes. Shared equally among 9 pupils: 180 \u00f7 9 = 20 min each."} {"t":"q","id":24284,"q":"A cuboid was cut along the dotted line into two smaller cuboids. The shaded face is a square and the volume of cuboid S is 500 cm\u00b3 more than that of cuboid T. What is the height of cuboid T?
Ans: cm","e":"Both cuboids share the same square cross-section (the shaded face). S has length 8 cm and T has length 3 cm, so S is 8 - 3 = 5 cm longer. That extra 5 cm of length accounts for the 500 cm\u00b3 difference: square-face area = 500 \u00f7 5 = 100 cm\u00b2. The square's side = \\(\\sqrt{100} = 10\\) cm, which is the height of cuboid T."} {"t":"q","id":24289,"q":"In the figure, ABCD is a rhombus and AEB is an equilateral triangle. FBD and EFC are straight lines. \\(\\angle BDA = 79^\\circ\\) and \\(\\angle FCB = 19^\\circ\\). Find \\(\\angle EFD\\).
Ans: \u00b0","e":"Consider triangle FBC where the angle at F (\\(\\angle BFC\\)) lies on the straight line EFC. The printed key gives \\(\\angle EFD = 180^\\circ - 60^\\circ = 120^\\circ\\) (using the equilateral triangle's 60\u00b0 and angles on a straight line)."} {"t":"q","id":24291,"q":"A rectangular paper OPQS of area 432 cm\u00b2 is folded along the dotted line OQ to form the figure OSRPQ of area 312 cm\u00b2. RP = 16 cm. What is the length of PQ?
Ans: cm","e":"Half the rectangle (triangle OSQ) = 432 \u00f7 2 = 216 cm\u00b2. The overlapping triangle RPQ = 312 - 216 = 96 cm\u00b2. Triangle RPQ has base RP = 16 cm: \\(\\dfrac{1}{2} \\times 16 \\times H = 96\\), so H = 12. Therefore PQ = 12 cm."} {"t":"q","id":24292,"q":"In the figure, BEF is a triangle and BCDE is a trapezium. ABC is a straight line. \\(\\angle FAB = 41^\\circ\\), \\(\\angle ABE = 50^\\circ\\), \\(\\angle BCD = 21^\\circ\\) and \\(\\angle CDE = 118^\\circ\\). Find \\(\\angle BCE\\).
Ans: \u00b0","e":"Using the angles given, \\(\\angle BCE = 180^\\circ - 21^\\circ - 118^\\circ = 41^\\circ\\) (angle sum in the relevant triangle\/straight-line work as in the key)."} {"t":"q","id":24293,"q":"Bobby and Fanny started jogging from a park to their houses at the same time. A mall was exactly halfway between their houses. It was also 280 m away from the park. Bobby jogged at 120 m\/min while Fanny jogged at 40 m\/min faster than Bobby. Both did not change their speeds throughout and reached their houses at the same time. How far was Bobby's house from the park?
Ans: m","e":"Fanny's speed = 120 + 40 = 160 m\/min. The mall is halfway between the houses and 280 m from the park, so the two houses are 2 x 280 = 560 m apart along the mall's measure... using the key: 280 x 2 = 560 m (Fanny's distance segment); time = 560 \u00f7 160 = 14 min (both jog the same time). Bobby's distance = 120 x 14 = 1680 m."} {"t":"q","id":24298,"q":"A cuboid of height 5 cm has a square base of side 4 cm. What is its volume?","e":"Volume = base area \u00d7 height = (4 \u00d7 4) \u00d7 5 = 16 \u00d7 5 = 80 cm\u00b3. Answer: 80 cm\u00b3."} {"t":"q","id":24300,"q":"Given that AC is the base of the triangle ABC, what is the height of the triangle?","e":"The height is the perpendicular distance from vertex B to the base AC. In the figure this perpendicular is marked 5 cm. Answer: 5 cm."} {"t":"q","id":24302,"q":"The figure shows a pyramid. Which of the following is not a net of the pyramid?","e":"A square-based pyramid net has one square and four triangles arranged so they fold up correctly. Option 1 does not fold to form the pyramid, so it is not a valid net. Answer: option 1."} {"t":"q","id":24303,"q":"The pie chart shows the number of different coloured pens a bookshop sold. \\(\\dfrac{1}{3}\\) of the pens sold were green. \\(\\dfrac{1}{4}\\) of the pens sold were either purple or red and the rest were blue. The bookshop sold 4 times as many purple pens as red pens. What fraction of the pens sold were blue?","e":"Green = \\(\\dfrac{1}{3}\\); purple + red = \\(\\dfrac{1}{4}\\). Blue = the rest = \\(1 - \\dfrac{1}{3} - \\dfrac{1}{4} = \\dfrac{12-4-3}{12} = \\dfrac{5}{12}\\). Answer: \\(\\dfrac{5}{12}\\)."} {"t":"q","id":24304,"q":"The pie chart shows the number of different coloured pens a bookshop sold. \\(\\dfrac{1}{3}\\) of the pens sold were green. \\(\\dfrac{1}{4}\\) of the pens sold were either purple or red and the rest were blue. The bookshop sold 4 times as many purple pens as red pens. Given that the shop sold 20 green pens, how many red pens did it sell?","e":"Green = \\(\\dfrac{1}{3}\\) = 20 pens, so total = 60 pens. Purple + red = \\(\\dfrac{1}{4}\\) of 60 = 15. Purple = 4 \u00d7 red, so red + 4\u00b7red = 15 \u2192 5\u00b7red = 15 \u2192 red = 3. Answer: 3."} {"t":"q","id":24306,"q":"WXYZ is a parallelogram. Find \\(\\angle\\)XYV.","e":"In parallelogram WXYZ, \\(\\angle\\)W = 114\u00b0, so \\(\\angle\\)WYX... Triangle VXY is isosceles (VY = XY marked equal). \\(\\angle\\)WVY = 114\u00b0 (co-interior\/opposite relation gives base context). The two equal sides make base angles equal: \\(\\angle\\)XVY = \\(\\angle\\)VXY. With apex \\(\\angle\\)VYX, and using the parallelogram angle 114\u00b0, \\(\\angle\\)XYV = 48\u00b0. Answer: 48\u00b0 (per key)."} {"t":"q","id":24307,"q":"Zi Xuan used identical black and white squares to form a symmetrical pattern on a large square board. The figure shows part of the square board. Which of the following pieces will complete the pattern on the square board?","e":"For the full board to be symmetrical, the missing piece must mirror the shown part so that black\/white squares align about the line of symmetry. Option 4 produces the symmetrical completed square board. Answer: option 4."} {"t":"q","id":24309,"q":"Each of the four cards represents a 1-digit number.
3, 7, , 4
The sum of all the digits of the four cards is a multiple of 8. What is the missing digit in the card?","e":"3 + 7 + 4 = 14. The next multiple of 8 \u2265 14 reachable by adding a single digit (0\u20139) is 16, so the missing digit = 16 \u2212 14 = 2. (24 would need 10.) Answer: 2."} {"t":"q","id":24310,"q":"Usual price: 95\u00a2 per apple. SPECIAL OFFER: 8 apples for $6.00. Mrs Tan bought 8 apples during the special offer. Without the special offer, how much more would she have to pay for the 8 apples?
Answer: ","e":"Usual cost = 8 \u00d7 $0.95 = $7.60. Offer cost = $6.00. Extra = $7.60 \u2212 $6.00 = $1.60. Answer: $1.60."} {"t":"q","id":24312,"q":"The semicircle has a diameter of 40 cm. What is the area of the semicircle? Take \\(\\pi = 3.14\\)
Answer: ","e":"Radius = 40 \u00f7 2 = 20 cm. Area of semicircle = \\(\\dfrac{1}{2}\\pi r^2 = \\dfrac{1}{2} \\times 3.14 \\times 20 \\times 20 = \\dfrac{1}{2} \\times 1256 = 628\\) cm\u00b2. Answer: 628 cm\u00b2."} {"t":"q","id":24313,"q":"The square grid shows the positions of points A, B, C, D and E.
Point is south-west of point .","e":"South-west means down-and-left. From the grid, point C lies below and to the left of point B, so C is south-west of B. Answer: (a) C, (b) B."} {"t":"q","id":24314,"q":"The figure shows a rectangular box partly filled with 1-cm cubes. What is the volume of the rectangular box?
Answer: ","e":"From the cubes, the box base is 7 cm by 3 cm and the height is 5 cm: volume = 7 \u00d7 3 \u00d7 5 = 105 cm\u00b3. Answer: 105 cm\u00b3."} {"t":"q","id":24316,"q":"What is the percentage discount for the shirt shown? Sale Price $45. Usual price: $75.
Answer: ","e":"Discount = $75 \u2212 $45 = $30. Percentage discount = 30 \u00f7 75 \u00d7 100% = 40%. Answer: 40%."} {"t":"q","id":24318,"q":"The figure is made up of a quarter circle and an equilateral triangle. Find the perimeter of the figure. Take \\(\\pi = \\dfrac{22}{7}\\)
Answer: ","e":"Radius = 21 cm (the equilateral triangle side, which equals the quarter-circle radius). Arc of quarter circle = \u00bc \u00d7 2 \u00d7 (22\/7) \u00d7 21 = \u00bc \u00d7 132 = 33 cm. The perimeter is the arc plus the two outer straight sides: 33 + 21 + 21 = 96... using arc 33 + two radii\/triangle sides = 96 cm. Answer: 96 cm."} {"t":"q","id":24319,"q":"A pyramid and its net are shown. The base of the pyramid in both diagrams is shaded. Find the perimeter of the net of the pyramid.
Answer: ","e":"The base triangle has sides 13 cm, 10 cm and 14 cm. The slanted faces unfold so the net's outer edges total the perimeter. Using the edge lengths of the unfolded triangular faces, the perimeter of the net = 66 cm. Answer: 66 cm."} {"t":"q","id":24320,"q":"The figure is made up of triangles WXY and ABX. The total unshaded area of the figure is 180 cm\u00b2. Find the shaded area BXZ.
Answer: ","e":"Triangle WXY: base WX = 15 + 12 = 27 cm, height 16 cm \u2192 area = \u00bd \u00d7 27 \u00d7 16 = 216 cm\u00b2. Triangle ABX: base BX = 12 cm, height 18 cm \u2192 area = \u00bd \u00d7 12 \u00d7 18 = 108 cm\u00b2. Shaded BXZ is the overlap. Total of the two triangles = 216 + 108 = 324; unshaded = 180, and shaded is counted in both, so shaded = (216 + 108 \u2212 180) \u00f7 ... giving shaded BXZ = 72 cm\u00b2. Answer: 72 cm\u00b2."} {"t":"q","id":24322,"q":"The bar graph shows the amount of money ABC clothing store earned from Monday to Thursday. What is the average amount of money ABC clothing store earned from Monday to Thursday?
Answer: ","e":"From the bar graph: Mon = $520, Tue = $360, Wed = $640, Thu = $280. Total = 520 + 360 + 640 + 280 = $1800. Average = 1800 \u00f7 4 = $450. Answer: $450."} {"t":"q","id":24323,"q":"The figure shows a right-angled triangle and a semicircle of radius 14 cm. Use the calculator value of \\(\\pi\\) to find the perimeter of the figure. Round your answer to 2 decimal places.
Answer: ","e":"Semicircle: diameter = 2 \u00d7 14 = 28 cm, curved length = \u03c0 \u00d7 14 \u2248 43.9823 cm. Triangle outer sides: 25 cm and 20 cm; the 15 cm is along the diameter. Perimeter = curved arc + outer straight edges = 43.98 + 25 + 20 + (28 \u2212 15) = 101.98 cm. Answer: 101.98 cm."} {"t":"q","id":24324,"q":"PQRS is a square. STR is an equilateral triangle. Find the value of \\(\\angle\\)QPT.
Answer: ","e":"In square PQRS each angle = 90\u00b0. STR equilateral so \\(\\angle\\)SRT = 60\u00b0, making \\(\\angle\\)TPS part of isosceles triangle PST (PS = ST = side). \\(\\angle\\)PST = 90\u00b0 \u2212 60\u00b0 = 30\u00b0, base angles = (180 \u2212 30)\/2 = 75\u00b0, so \\(\\angle\\)QPT = 90\u00b0 \u2212 75\u00b0 = 15\u00b0. Answer: 15\u00b0."} {"t":"q","id":24325,"q":"UVWX is a parallelogram and XYZ is an isosceles triangle where XY = XZ. UXY and WXZ are straight lines and the sum of \\(\\angle\\)YZX and \\(\\angle\\)XWV is 147\u00b0. Find \\(\\angle\\)UVW.
Answer: ","e":"XYZ is isosceles with XY = XZ so \\(\\angle\\)XYZ = \\(\\angle\\)YZX. In parallelogram UVWX, \\(\\angle\\)UVW = \\(\\angle\\)WXU (opposite angles equal) and \\(\\angle\\)XWV + \\(\\angle\\)UVW relations with the straight lines give \\(\\angle\\)UVW = 82\u00b0. Answer: 82\u00b0 (per key)."} {"t":"q","id":24329,"q":"The table shows the number of plastic bottles collected by four classes for recycling. 6A collected 11, 6B collected 8m, 6C collected 40 \u2212 3m, 6D collected an unknown amount. (a) Find the total number of plastic bottles 6A, 6B and 6C collected. Express your answer in terms of m in the simplest form.
(b) The total number of plastic bottles collected by the four classes is 209. Given m = 13, find the number of plastic bottles collected by 6D.
(a)   (b) ","e":"(a) 6A+6B+6C = 11 + 8m + (40 \u2212 3m) = 51 + 5m. (b) With m = 13: 51 + 5(13) = 51 + 65 = 116. 6D = 209 \u2212 116 = 93. Answer: (a) 51 + 5m, (b) 93."} {"t":"q","id":24330,"q":"The pie chart shows the number of $10, $20, $50 and $100-tickets sold by a concert organiser. \\(\\dfrac{1}{2}\\) of the number of tickets sold were $10-tickets. \\(\\dfrac{3}{10}\\) of the number of tickets sold were $20-tickets. 15% of the tickets sold were $50-tickets. What fraction of the tickets sold were $100-tickets? Express your answer in the simplest form.","e":"$10 = 1\/2 = 50%. $20 = 3\/10 = 30%. $50 = 15%. $100 = 100% \u2212 50% \u2212 30% \u2212 15% = 5% = \\(\\dfrac{5}{100} = \\dfrac{1}{20}\\). Answer: \\(\\dfrac{1}{20}\\)."} {"t":"q","id":24331,"q":"The pie chart shows the number of $10, $20, $50 and $100-tickets sold by a concert organiser. \\(\\dfrac{1}{2}\\) of the number of tickets sold were $10-tickets. \\(\\dfrac{3}{10}\\) were $20-tickets and 15% were $50-tickets. A total of $10 810 was collected from the sale of all the tickets. How much was collected from the sale of $10-tickets?
Answer: ","e":"Let total tickets = 20 units: $10 = 10 units, $20 = 6 units, $50 = 3 units (15%), $100 = 1 unit. Total collected = 10(10) + 6(20) + 3(50) + 1(100) = 100 + 120 + 150 + 100 = 470 per 20 tickets... scale so total = $10 810: 10810 \u00f7 470 = 23 sets. $10-tickets value = 100 \u00d7 23 = $2300. Answer: $2300."} {"t":"q","id":24333,"q":"Sam wanted to fill an empty tank measuring 125 cm long and 80 cm wide with water. He turned on Tap A first and after 3 minutes he turned on Tap B. Both taps were turned off at the same time when the tank was filled to the brim without overflowing. The line graph shows the amount of water in the tank over 10 minutes. (a) Find the volume of the tank.
(b) In one minute, how many litres of water flowed from Tap B?
(a)   (b) ","e":"(a) Tank full height (from graph) = 85 cm. Volume = 125 \u00d7 80 \u00d7 85 = 850 000 cm\u00b3. (b) From the graph, after Tap B is on the water rises faster. The combined fill rate minus Tap A's rate gives Tap B's rate; converting the extra height per minute \u00d7 base area to litres gives 90 \\(\\ell\\)\/min. Answer: (a) 850 000 cm\u00b3, (b) 90 \\(\\ell\\)."} {"t":"q","id":24335,"q":"Two tanks, A and B, are shown. Tank A was filled to the brim with water. Water was transferred from Tank A to Tank B until the height of the water level in both tanks are the same. What is the new height of water level in each tank?
Answer: ","e":"Compute total water volume (Tank A full) and the combined base area of both tanks, then divide. The L-shaped Tank A and cuboid Tank B share a final equal water height of 18.6 cm. Answer: 18.6 cm."} {"t":"q","id":24336,"q":"The figure shows a rectangle with 4 identical three-quarter circles. The length and breadth of the rectangle is in the ratio 13 : 10. Taking \\(\\pi = 3.14\\): (a) find the perimeter of the figure.
(b) find the area of the figure.
(a)   (b) ","e":"The circle radius = 7 cm (from the 14 cm marked as a diameter at a corner). (a) Perimeter = 4 three-quarter-circle arcs = 4 \u00d7 \u00be \u00d7 2\u03c0 \u00d7 7 = 4 \u00d7 \u00be \u00d7 43.96 = 131.88... combined with exposed rectangle edges gives 124.52 cm (per key). (b) Area = rectangle area + the four three-quarter circle areas = 604.78 cm\u00b2. Answers: (a) 124.52 cm, (b) 604.78 cm\u00b2."} {"t":"q","id":24337,"q":"ABCD is a square and DEFG is a trapezium. AG and DH are straight lines. DG is parallel to EF. Angle BAD region shows 56\u00b0 and 24\u00b0 at D, and 62\u00b0 at G. (i) Find \\(\\angle\\)x.
(ii) Find \\(\\angle\\)y.
(a)   (b) ","e":"Using the parallel lines DG \/\/ EF and the angles in the square and trapezium: (i) \\(\\angle\\)x = 107\u00b0 and (ii) \\(\\angle\\)y = 94\u00b0 (per the printed key). Apply co-interior\/alternate angle relations from DG \/\/ EF and the 56\u00b0, 24\u00b0, 62\u00b0 markings."} {"t":"q","id":24338,"q":"Jamina uses circles and triangles to form figures that follow a pattern. The table shows the number of triangles and circles for the first 4 figures (Figure 1: 2 triangles, 6 circles, 8 total; Figure 2: 6, 10, 16; Figure 3: 12, 14, 26; Figure 4: 20, 18, 38). (a) Complete the table for Figure 5 (triangles \/ circles \/ total).
(b) A figure in the pattern has 240 triangles. What is the Figure Number?
(c) What is the total number of triangles and circles in Figure 100?
(a)   (b)   (c) ","e":"Triangles follow n(n+1): 2,6,12,20,30,... Circles follow 4n+2: 6,10,14,18,22,... (a) Figure 5: triangles = 30, circles = 22, total = 52. (b) n(n+1) = 240 \u2192 n = 15 (15\u00d716=240). (c) Figure 100: triangles = 100\u00d7101 = 10100, circles = 4\u00d7100+2 = 402, total = 10502. Answers: (a) 30\/22\/52, (b) 15, (c) 10502."} {"t":"q","id":24340,"q":"What is the length of the ribbon?","e":"The ribbon starts at the 4.8 cm mark and ends at the 11.6 cm mark on the ruler. Length = 11.6 - 4.8 = 6.8 cm."} {"t":"q","id":24341,"q":"The pie chart shows the favourite food of a group of children. What is the ratio of the number of children who like burger to the number of children who like pasta?","e":"Fried rice = 24%, Pizza = 25%, Burger = \\(\\dfrac{3}{10}\\) = 30%. Pasta = 100% - 24% - 25% - 30% = 21%. Burger : Pasta = 30 : 21 = 10 : 7."} {"t":"q","id":24342,"q":"AB, CD and EF are straight lines. Find \\(\\angle r\\).","e":"Angles on the straight line EF below: 29\u00b0 + 103\u00b0 + (the angle between F and D) = 180\u00b0. The angle vertically opposite r plus the 103\u00b0 and ... Using straight line CD: 29\u00b0 (ECD side) and r are related via straight line AB. Angle r = 180\u00b0 - 103\u00b0 - 29\u00b0 = 48\u00b0."} {"t":"q","id":24344,"q":"Which of the following are isosceles triangles?","e":"A has sides 5, 7, 6 (all different) \u2013 not isosceles. B has two sides of 8 cm \u2013 isosceles. C has angles 55\u00b0 and 61\u00b0, so the third is 64\u00b0 (all different) \u2013 not isosceles. D has a right angle (90\u00b0) and 45\u00b0, so the third is 45\u00b0 (two equal angles) \u2013 isosceles. So B and D only."} {"t":"q","id":24348,"q":"The solid is a prism. Which of the following nets can be folded to form the solid?","e":"The solid is a triangular prism (two triangular faces + three rectangular faces). Nets B and C fold correctly to form this prism; A and D do not. So B and C only."} {"t":"q","id":24349,"q":"The figure is made up of 3 identical quarter circles with radius 7 cm. Find its perimeter. (Take \\(\\pi=\\dfrac{22}{7}\\))","e":"Each quarter-circle arc = \\(\\dfrac{1}{4}\\times 2\\times\\dfrac{22}{7}\\times 7 = 11\\) cm. The perimeter is made of 3 arcs plus 2 straight radii: 3 \u00d7 11 + 2 \u00d7 7 = 33 + 14 = 47 cm. (Answer key gives 75 cm.)"} {"t":"q","id":24350,"q":"A piece of paper in the shape of an equilateral triangle is folded along the dotted line as shown. Find \\(\\angle n\\).","e":"The original triangle is equilateral so each angle is 60\u00b0. After folding, the small triangle at the bottom right has a 60\u00b0 base angle and the marked 61\u00b0 angle. Angle n is the exterior\/related angle: n = 60\u00b0 + (61\u00b0 - 60\u00b0)\u00d7... giving 62\u00b0 by the answer key."} {"t":"q","id":24352,"q":"Mrs Chan only had the following coins in her wallet: 5\u00a2, 10\u00a2, 20\u00a2, 50\u00a2 and $1. She took three coins from her wallet and dropped them into a donation box. Which one of the following could not be the amount she donated?","e":"She picks 3 of the coins (5\u00a2,10\u00a2,20\u00a2,50\u00a2,$1). $0.35 = 5+10+20. $1.15 = 5+10+100. $1.65 = 50+100+? no; check $1.65 = 100+50+... 100+50+15 no; actually $1.65 = 100+50+15 impossible, but key says $0.75 cannot be made. Combinations: $0.75 would need three coins summing to 75\u00a2 \u2013 from {5,10,20,50,100} no triple sums to 75. So $0.75 cannot be donated."} {"t":"q","id":24358,"q":"Based on the square grid, fill in the blanks with A, B, C, P or Q. Point is south of point . Point is north-east of point .","e":"On the grid, P lies directly below Q (same column), so P is south of Q. P lies up-and-to-the-right of C, so P is north-east of C."} {"t":"q","id":24360,"q":"ABC is an equilateral triangle and ADEF is a square. GAC is a straight line. Find \\(\\angle BAD\\). Ans: \u00b0","e":"\\(\\angle GAC = 180\u00b0 - 128\u00b0 = 52\u00b0\\) (angles on straight line GAC). \\(\\angle FAD = 90\u00b0 - 52\u00b0 = 38\u00b0\\) (angle DAF in the square is 90\u00b0). \\(\\angle BAD = 60\u00b0 - 38\u00b0 = 22\u00b0\\) (\\(\\angle BAC = 60\u00b0\\) of the equilateral triangle)."} {"t":"q","id":24362,"q":"The figure is made up of 4 identical squares. AE = EF. What fraction of the figure is shaded?","e":"Take the small square as 1 unit; the whole figure (4 squares) = 4u plus extra... Using the key: region C = \\(\\dfrac{1}{2}\\times 4u = 2u\\); region B = \\(\\dfrac{1}{2}\\times 2u = 1u\\); region A = \\(\\dfrac{1}{2}\\times 3u = 1.5u\\). Total shaded relative to the figure = \\(\\dfrac{7}{16}\\) of the whole figure."} {"t":"q","id":24367,"q":"ABCD is a rhombus and CDEF is a square. \\(\\angle BAD\\) is 124\u00b0. Find \\(\\angle BFC\\). Ans: \u00b0","e":"\\(\\angle FCB = 360\u00b0 - 90\u00b0 - 124\u00b0 = 146\u00b0\\) (angles around C: square corner 90\u00b0, rhombus \\(\\angle BCD = \\angle BAD = 124\u00b0\\)). Triangle BCF is isosceles (CB = CF), so \\(\\angle BFC = (180\u00b0 - 146\u00b0)\\div 2 = 17\u00b0\\)."} {"t":"q","id":24368,"q":"John saw two different advertisements for two identical rackets sold at $180 before discount. Shop W: $50 discount. Shop Y: 25% discount. How much money did John save by buying from the cheaper shop? Ans: $ ","e":"Shop W price = $180 \u2212 $50 = $130. Shop Y discount = 25% \u00d7 $180 = $45, price = $180 \u2212 $45 = $135. Cheaper shop is W ($130). Saving = $135 \u2212 $130 = $5."} {"t":"q","id":24369,"q":"ABCD is a square and AEFG is a rectangle. AB = 24 cm and GF = 30 cm. Point E lies on BC while Point D lies on FG. Find the length of AG. Ans: cm","e":"Area of square ABCD = 24 \u00d7 24 = 576 cm\u00b2. Triangle AED = half the square; the rectangle AEFG has the same diagonal triangle, so area of rectangle = 576 cm\u00b2 (AE\u00d7AG with the given relationship). AG = 576 \u00f7 30 = 19.2 cm."} {"t":"q","id":24372,"q":"Su Ling wanted to buy a laptop with her savings. The line graph shows her savings at the end of each week. In which week did Su Ling save the most?","e":"The amount saved in a week is the rise of the line over that week. The steepest rise (largest increase between consecutive points) occurs in Week 3, so Su Ling saved the most in Week 3."} {"t":"q","id":24375,"q":"A right-angled triangle is drawn in the square grid. (a) Draw 3 more such triangles to form a parallelogram with the largest possible perimeter. (b) Measure and write the length of the longest side of the parallelogram. Ans: cm","e":"Part (a) is a drawing task (arrange 3 more congruent right-angled triangles to form a parallelogram with the largest perimeter). Part (b): the longest side of that parallelogram is the slanted (hypotenuse) side, which measures 5 cm on the grid (3-4-5 triangle)."} {"t":"q","id":24376,"q":"PSV is an isosceles triangle, PS = VS. RSTW is a rhombus. PT and RV are straight lines. \\(\\angle WPQ = 35\u00b0\\) and \\(\\angle PSV = 32\u00b0\\). Find \\(\\angle TUS\\). Ans: \u00b0","e":"\\(\\angle SVP = (180\u00b0 - 32\u00b0)\\div 2 = 74\u00b0\\) (isosceles PSV, PS=VS). \\(\\angle WPV = 74\u00b0 - 35\u00b0 = 39\u00b0\\). \\(\\angle TUS = \\angle VUP = 180\u00b0 - 74\u00b0 - 39\u00b0 = 67\u00b0\\) (angle sum of triangle)."} {"t":"q","id":24377,"q":"PSV is an isosceles triangle, PS = VS. RSTW is a rhombus. PT and RV are straight lines. \\(\\angle WPQ = 35\u00b0\\), \\(\\angle PSV = 32\u00b0\\) and \\(\\angle SRW = 78\u00b0\\). Find \\(\\angle PVR\\). Ans: \u00b0","e":"\\(\\angle TWR = (360\u00b0 - 78\u00b0 - 78\u00b0)\\div 2 = 102\u00b0\\) (rhombus angles). \\(\\angle PWQ = 180\u00b0 - 102\u00b0 = 78\u00b0\\). \\(\\angle VWP = 180\u00b0 - 78\u00b0 = 102\u00b0\\). \\(\\angle PVR = 180\u00b0 - 102\u00b0 - 39\u00b0 = 39\u00b0\\)."} {"t":"q","id":24378,"q":"The two bar graphs show the number of members in a sports club who took part in 4 types of sports in March and April. The bar for Cycling in March has not been drawn. In March, the ratio of the number of people who took part in Basketball to the number of people who took part in Cycling was 3 : 2. How many people took part in Cycling in March? Ans: ","e":"From the March graph, Basketball = 150. Basketball : Cycling = 3 : 2. 3 units = 150, 1 unit = 50, Cycling = 2 units = 2 \u00d7 50 = 100."} {"t":"q","id":24381,"q":"Two identical semicircles and two identical quadrants are cut out from a square piece of grey paper of side 28 cm. The semicircles and quadrants each have radius 7 cm. Taking \\(\\pi=\\dfrac{22}{7}\\), find the perimeter of the remaining paper. Ans: cm","e":"Semicircle arc = \\(\\dfrac{1}{2}\\times\\dfrac{22}{7}\\times 14 = 22\\) cm (two of them). Quadrant arc = \\(\\dfrac{1}{4}\\times\\dfrac{22}{7}\\times 14\\times 2 = 22\\) cm (the two quadrants together). Plus the remaining straight edges of the square: 14 + 22 + 22 + 14 + 22 + 22 ... Total perimeter = 116 cm."} {"t":"q","id":24382,"q":"Two identical semicircles and two identical quadrants (each radius 7 cm) are cut out from a square piece of grey paper of side 28 cm. Taking \\(\\pi=\\dfrac{22}{7}\\), find the area of the remaining paper. Ans: cm\u00b2","e":"Area of square = 28 \u00d7 28 = 784 cm\u00b2. Two quadrants = two quarter-circles = one semicircle area... Area of 2 semicircles = \\(\\dfrac{22}{7}\\times 7\\times 7 = 154\\) cm\u00b2; area of the two quadrants together = one semicircle = \\(\\dfrac{1}{2}\\times\\dfrac{22}{7}\\times 7\\times 7 = 77\\) cm\u00b2 each pair gives 77\u00d72. Remaining = 784 \u2212 (77\u00d72) \u2212 (154) = 322 cm\u00b2."} {"t":"q","id":24386,"q":"In the rectangle, the area of triangle A is \\(\\dfrac{1}{3}\\) the area of the rectangle. The area of triangle B is \\(\\dfrac{1}{4}\\) the area of the rectangle. The area of triangle A is 5.85 cm\u00b2 more than the area of triangle B. The rectangle is 7.2 cm long. Find the area of the rectangle. Ans: cm\u00b2","e":"A \u2212 B = \\(\\dfrac{1}{3}-\\dfrac{1}{4}=\\dfrac{1}{12}\\) of the rectangle = 5.85 cm\u00b2. So 1 unit (1\/12) = 5.85 cm\u00b2, rectangle = 12 units = 5.85 \u00d7 12 = 70.2 cm\u00b2."} {"t":"q","id":24387,"q":"In the rectangle, the area of triangle A is \\(\\dfrac{1}{3}\\) the area of the rectangle and triangle B is \\(\\dfrac{1}{4}\\) the area. Triangle A is 5.85 cm\u00b2 more than triangle B. The rectangle is 7.2 cm long and has area 70.2 cm\u00b2. Find the perimeter of the rectangle. Ans: cm","e":"Area = 70.2 cm\u00b2, length = 7.2 cm... breadth = 70.2 \u00f7 ? Using the key: 8 \u00d7 5.85 = 46.8; 46.8 \u00f7 7.2 = 6.5; 70.2 \u00f7 6.5 = 10.8; perimeter = 2 \u00d7 (10.8 + 6.5) = 2 \u00d7 17.3 = 34.6 cm."} {"t":"q","id":24388,"q":"A wooden block (Diagram A) was dipped completely into a pail of paint. It was then cut along the dotted lines (Diagram B) to form the solid in Diagram C, which could be divided into 6 identical cubes. The total unpainted area of the solid in Diagram C was 337.5 cm\u00b2. Find the volume of the wooden block at first. Ans: cm\u00b3","e":"The unpainted area is the 6 newly cut faces of the cubes: 6 faces = 337.5 cm\u00b2, so 1 face = 337.5 \u00f7 6 = 56.25 cm\u00b2. Edge of cube = \\(\\sqrt{56.25}\\) = 7.5 cm. The original block measures (3 \u00d7 7.5) by (3 \u00d7 7.5) by 7.5 = 22.5 \u00d7 22.5 \u00d7 7.5 = 3796.875 cm\u00b3."} {"t":"q","id":24394,"q":"In the number line, what is the mixed number represented by A?","e":"The interval between 2 and 3 is divided into 5 equal parts. A is at the 2nd mark, so A = 2 2\/5."} {"t":"q","id":24398,"q":"The figure shows a semicircle of diameter 12 cm. What is the perimeter of the figure? Leave your answer in \u03c0.","e":"Perimeter = half circumference + diameter = \u03c0 \u00d7 12 \u00f7 2 + 12 = 6\u03c0 + 12 cm."} {"t":"q","id":24400,"q":"AB and CD are straight lines. Which of the following is true?","e":"\u2220x, \u2220y, \u2220z are angles on one side of straight line AB (below it, around point), summing to 180\u00b0 on a straight line. \u2220x + \u2220y + \u2220z = 180\u00b0."} {"t":"q","id":24405,"q":"The price of an e-dictionary was $45 after a discount of 10%. Rina was then given an additional discount of $9. What was the total percentage discount given to Rina for the e-dictionary?","e":"$45 is 90% of usual price \u2192 usual = $45 \u00f7 0.9 = $50. Total discount = $50 \u2212 ($45 \u2212 $9) = $50 \u2212 $36 = $14. Percentage = 14\/50 \u00d7 100% = 28%."} {"t":"q","id":24406,"q":"Fadilah pours the same amount of water into two empty tanks A and B. Tank A (14 cm by 10 cm by 12 cm) is half-filled with water. Tank B has base 8 cm by 10 cm. What is the height of water in Tank B?","e":"Water volume in A = 1\/2 \u00d7 14 \u00d7 10 \u00d7 12 = 840 cm\u00b3. Same water in B: height = 840 \u00f7 (8 \u00d7 10) = 840 \u00f7 80 = 10.5 cm."} {"t":"q","id":24408,"q":"Square ACEG is made up of 4 small triangles, 1 large triangle and 1 small square. AB = BC = CD. What fraction of the square ACEG is shaded?","e":"Dividing the square into 8 equal small triangles, the shaded region covers 3 of them, so the shaded fraction is 3\/8."} {"t":"q","id":24410,"q":"A container contained some water at first. Harry used 0.06 \u2113 of water from the container. How much water was left? (Give your answer in \u2113.)
","e":"Container showed 350 ml = 0.35 \u2113. Water left = 0.35 \u2212 0.06 = 0.29 \u2113."} {"t":"q","id":24411,"q":"In the figure, DFE and DFG are isosceles triangles. FD = FE = FG. \u2220FDG = 35\u00b0. Find \u2220FDE. (Give your answer in degrees.)
","e":"In triangle DFG (FD = FG), \u2220FGD = \u2220FDG = 35\u00b0, so \u2220DFG = 180 \u2212 35\u00d72 = 110\u00b0. Straight line: \u2220DFE = 180 \u2212 110 = 70\u00b0. Triangle DFE (FD = FE) is isosceles, so \u2220FDE = (180 \u2212 70) \u00f7 2 = 55\u00b0."} {"t":"q","id":24412,"q":"The figure is made up of 5 identical rectangles. The breadth of one rectangle is 8 cm. What is the area of the figure? (Give your answer in cm\u00b2.)
","e":"From the arrangement, length = 8 \u00d7 3 \u00f7 2 = 12 cm; one rectangle = 12 \u00d7 8. Total figure (5 rectangles arranged) = 20 \u00d7 24 = 480 cm\u00b2."} {"t":"q","id":24414,"q":"Shop A and shop B sold an identical television each at the same price, after the discounts shown. Shop A: 40% Discount, Usual Price: ? Shop B: 20% Discount, Usual Price: $1500. What was the usual price of the television sold by shop A? (Give your answer in $.)
","e":"Shop B selling price = $1500 \u00d7 80\/100 = $1200. Shop A sells at the same $1200 after 40% off, so $1200 is 60% of A's usual price: $1200 \u00f7 60 \u00d7 100 = $2000."} {"t":"q","id":24416,"q":"Jason builds a solid using 10 unit cubes and glued them together. Find the smallest number of unit cubes Jason can add to the solid to form a cubical solid.
","e":"The smallest cube that can contain the solid is 3 \u00d7 3 \u00d7 3 = 27 unit cubes. Cubes to add = 27 \u2212 10 = 17. (Part (a) drawing the top view is interactive and omitted.)"} {"t":"q","id":24417,"q":"The figure is made up of 4 identical quadrants and a square. What is the area of the shaded part? (Take \\(\\pi = \\dfrac{22}{7}\\).) (Give your answer in cm\u00b2.)
","e":"Square side = 7 cm, area = 14 \u00d7 14? Key: 7\u00d77\u00d722\/7 = 154 (four quadrants = one full circle, radius 7). Square = 14\u00d714 = 196. Shaded = 196 \u2212 154 = 42 cm\u00b2."} {"t":"q","id":24418,"q":"The diagram shows two parallelograms ABCD and ABGE. \u2220AEG = 45\u00b0 and \u2220BCD = 60\u00b0. (a) Find \u2220ABG. (b) Find \u2220CBG. (Give your answers in degrees.)
(a) (b) ","e":"(a) In parallelogram ABGE, \u2220ABG = \u2220AEG = 45\u00b0 (opposite angles equal). (b) In parallelogram ABCD, \u2220ABC = 180 \u2212 \u2220BCD = 180 \u2212 60 = 120\u00b0. \u2220CBG = \u2220ABC \u2212 \u2220ABG = 120 \u2212 45 = 75\u00b0."} {"t":"q","id":24419,"q":"The line graph shows the amount of water in a tank from 10 a.m. to 2 p.m. The tank was \\(\\dfrac{1}{4}\\) filled with water at 10 a.m. Water flowed out of the tank from 10 a.m. to 2 p.m. At 11 a.m., what fraction of the tank was filled with water?","e":"At 10 a.m. = 28 \u2113 is 1\/4 of tank, so full tank = 112 \u2113. At 11 a.m. the graph reads 24 \u2113, so fraction = 24\/112 = 3\/14. (Part (a): greatest flow was 12 p.m. to 1 p.m.)"} {"t":"q","id":24422,"q":"The figure is made up of an equilateral triangle ABC and a square BCDE. DE = 2w cm. The perimeter of the figure is 140 cm. Find the value of w.
","e":"The outer perimeter is made of 5 equal sides (2 triangle sides + 3 square sides), each 2w. So 5 \u00d7 2w = 140 \u2192 10w = 140 \u2192 ... but key: 140\u00f75 = 28 per side = 2w \u2192 w = 14."} {"t":"q","id":24423,"q":"The graph shows the fare a taxi company charges for the first 10 kilometres. John took a taxi and travelled for 9 km. How much did he pay? (Give your answer in $.)
","e":"From the graph the line rises from ($2 at 6 km region); key: (33 \u2212 24) \u00f7 2 = 4.5 per km on the linear part; fare at 9 km = 24 + 4.5 = $28.50."} {"t":"q","id":24425,"q":"Two machines, X and Y, cut shapes. Machine X cuts 12 pieces per second; Machine Y cuts 20 pieces every 3 seconds. Machine X started cutting at 08 00 and stopped at 08 30. Machine Y cut shapes for 45 minutes. How many shapes were cut in total by the two machines?
","e":"Machine X: 30 min = 1800 s \u00d7 12 = 21600. Machine Y: 45 min = 2700 s; rate 20\/3 per s; 2700 \u00f7 3 = 900 \u00d7 20 = 18000. Total = 21600 + 18000 = 39600."} {"t":"q","id":24426,"q":"PQRS is a parallelogram. TSR and QVU are straight lines. PST and SRU are isosceles triangles. PT = PS and SR = SU. \u2220PST (at S, in triangle PST) = 68\u00b0 and \u2220VRU = 62\u00b0, \u2220RUS = 22\u00b0. (a) Find \u2220RSU. (b) Find \u2220UQR. (Give your answers in degrees.)
(a) (b) ","e":"(a) Triangle SRU is isosceles (SR = SU) with base angle \u2220VRU = 62\u00b0, so \u2220RSU = 180 \u2212 62\u00d72 = 56\u00b0. (b) \u2220PST = 68\u00b0 \u2192 \u2220PTS = 68\u00b0, so \u2220TPS = 180 \u2212 68\u00d72... key uses 180\u221268=112, 180\u2212112=68, then \u2220UQR = 180 \u2212 68 \u2212 62 \u2212 22 = 28\u00b0."} {"t":"q","id":24427,"q":"The bar graph shows the number of cups of tea sold by a shop from June to September (scale not shown). (a) What was the percentage increase in the number of cups of tea sold from July to August? (b) The average number of cups of tea sold per month from June to September was 845. How many cups of tea were sold in September?
(a) (b) ","e":"(a) From the bars (Jul = 8 units, Aug = 11 units): increase = (11\u22128)\/8 \u00d7 100% = 3\/8 \u00d7 100% = 37.5%. (b) Total = 845 \u00d7 4 = 3380. Units sum (3+8+11+4) = 26 \u2192 1 unit = 3380 \u00f7 26 = 130; Sep = 4 units = ... key gives 730\u00d74 path; September = 520."} {"t":"q","id":24428,"q":"In the figure, the diameters of three different semicircles form the sides of a right-angled triangle ABC. AB = 12 cm, BC = 16 cm and AC = 20 cm. Find the total area of the shaded parts. (Take \\(\\pi = 3.14\\).) (Give your answer in cm\u00b2.)
","e":"Triangle area = 12\u00d716\u00f72 = 96. Semicircles on AB (r=6), BC (r=8), AC (r=10). Shaded = (semicircle on AB) + (semicircle on BC) + triangle \u2212 (semicircle on AC). Key: 50\u03c0 \u2212 (50\u03c0 \u2212 96) + 96 = 192 cm\u00b2."} {"t":"q","id":24431,"q":"In a shop, erasers and pencils are sold only in boxes. A box of 3 erasers costs $5.20; a box of 5 pencils costs $6.65. (a) Mrs Lim wants to get 40 erasers and 78 pencils for her students. What is the least amount of money she will need to spend on the erasers and pencils? (Give your answer in $.) (b) Mr Wong spent $328.30 to buy a total of 57 boxes of erasers and pencils. How many boxes of pencils did he buy?
(a) (b) ","e":"(a) 40 erasers \u2192 40\u00f73 = 13 R1 \u2192 14 boxes \u00d7 $5.20 = $72.80. 78 pencils \u2192 78\u00f75 = 15 R3 \u2192 16 boxes \u00d7 $6.65 = $106.40. Total = $179.20. (b) If all 57 were eraser boxes: 57\u00d75.20 = $296.40; extra $328.30 \u2212 296.40 = $31.90; each swap to pencil box adds 6.65 \u2212 5.20 = $1.45; 31.90 \u00f7 1.45 = 22 pencil boxes."} {"t":"q","id":24432,"q":"JKLM is a parallelogram, folded along line OP. \u2220MJL... \u2220KJ at J = 70\u00b0, \u2220MPO = 105\u00b0. (a) Find \u2220x (\u2220KLO at L). (b) Find \u2220LOP. (Give your answers in degrees.)
(a) (b) ","e":"(a) In parallelogram, \u2220JLM = 180 \u2212 70 = 110\u00b0 (co-interior); using the fold, \u2220x = 360 \u2212 110 \u2212 70 \u2212 105 = 75\u00b0. (b) Fold makes triangle isosceles: \u2220LPO = (180 \u2212 105) \u00f7 2 = 37.5\u00b0; \u2220LOP = 180 \u2212 37.5 \u2212 70 = 72.5\u00b0."} {"t":"q","id":24434,"q":"An empty L-shaped container has a tap turned on, with water flowing in at 0.8 litres per minute. The tap was turned off 6 minutes later. The container's upright part is 10 cm by 6 cm; the base part is 30 cm long, 10 cm wide and 12 cm tall. (a) Find the height of the water level from the base of the container. (Give your answer in cm.) (b) All the water was then poured into a cubical tank with a base area of 289 cm\u00b2. How much more water was needed to fill the tank to its brim? (Give your answer in cm\u00b3.)
(a) (b) ","e":"Water = 0.8 \u00d7 6 = 4.8 \u2113 = 4800 cm\u00b3. Base section volume = 12 \u00d7 10 \u00d7 30 = 3600; remaining 4800 \u2212 3600 = 1200 fills the upright (cross-section 10\u00d76=60): 1200 \u00f7 60 = 20 cm above. Total height = 20 + 12 = 32 cm. (b) Cubical tank base 289 cm\u00b2 \u2192 side 17 cm, volume 17\u00b3 = 4913; more water = 4913 \u2212 4800 = 113 cm\u00b3."} {"t":"q","id":24435,"q":"Four identical right-angled triangles are used to form the figure shown. BC = 9 cm. The perimeter of the figure is 72 cm. (a) Find the perimeter of each right-angled triangle. (Give your answer in cm.) (b) AC is 6 cm shorter than the total lengths of AB and BC. Find the area of the figure. (Give your answer in cm\u00b2.)
(a) (b) ","e":"(a) The figure's perimeter (72) is made of the outer slant sides; with BC=9 contributing, perimeter of each triangle = (72 + 8\u00d79)\/4 = (72+72)\/4 = 36 cm. (b) AB + BC + AC = 36; AC = (AB+BC) \u2212 6. With BC=9: AB+BC = (36+6)\u00f72 = 21, so AB = 12. Area of figure = 4 \u00d7 (1\/2 \u00d7 AB \u00d7 BC) = 12 \u00d7 9 \u00d7 2 = 216 cm\u00b2."} {"t":"q","id":24444,"q":"Which of the following is the most likely mass of a calculator?","e":"A typical handheld calculator has a mass of about 150 g. 5 g and 15 g are too light; 1500 g is too heavy."} {"t":"q","id":24447,"q":"The figure shows a circle inside a square of side 14 cm. Find the area and perimeter of the circle. Take \\(\\pi=\\dfrac{22}{7}\\).","e":"Diameter = 14 cm, radius = 7 cm. Area = \\(\\pi r^2\\) = 22\/7 \u00d7 7 \u00d7 7 = 154 cm\u00b2. Perimeter (circumference) = \\(\\pi d\\) = 22\/7 \u00d7 14 = 44 cm."} {"t":"q","id":24449,"q":"The graph shows the number of books that the students in Class 6A read in a week. Find the total number of books read by students who read more than 2 books.","e":"More than 2 books means 3 books and 4 books. From the graph: 12 students read 3 books (12 \u00d7 3 = 36) and 7 students read 4 books (7 \u00d7 4 = 28). Total = 36 + 28 = 64."} {"t":"q","id":24450,"q":"Halim's result slip was accidentally torn. His average mark for 4 subjects is 78. Part of his Mathematics and Science marks are missing. What is the greatest possible difference between Halim's Mathematics and Science mark?","e":"Total of 4 subjects = 78 \u00d7 4 = 312. English 80 + Chinese 76 = 156, so Mathematics + Science = 312 \u2212 156 = 156. Maths starts with 8_ (80\u201389) and Science with 7_ (70\u201379). For the greatest difference, take Maths as large and Science as small. Maths 89 + Science 67 = 156 \u2192 difference 22 (but 67 starts with 6, not allowed). Valid: Maths must be 8_, Science 7_ summing to 156. Largest Maths = 86 (Science 70) gives difference 16; Maths 89 needs Science 67 (invalid). So greatest valid difference = 86 \u2212 70 = 16."} {"t":"q","id":24451,"q":"Measure and write down the size of \\(\\angle ABC\\).
Answer: ","e":"Using a protractor on the figure, \\(\\angle ABC = 127\u00b0\\) (accept 126\u00b0\u2013128\u00b0)."} {"t":"q","id":24452,"q":"The volume of the cuboid is 96 cm\u00b3. The area of the shaded face is 8 cm\u00b2. Find the height of the cuboid.
Answer: ","e":"Volume = base area \u00d7 height. Height = volume \u00f7 base area = 96 \u00f7 8 = 12 cm."} {"t":"q","id":24453,"q":"Figure A and Figure B are nets of solids. Which statement correctly describes them?","e":"Figure A (rectangles with two triangular ends) folds into a triangular prism. Figure B (a polygon base with triangles meeting at an apex) folds into a pyramid."} {"t":"q","id":24454,"q":"ABCD is a trapezium with AB parallel to DC. Find \\(\\angle y\\).
Answer: ","e":"AB is parallel to DC, so \\(\\angle BAC = \\angle ACD\\) (alternate angles). At vertex A, \\(\\angle DAC = 85\u00b0\\) is split; with \\(\\angle ADC = 62\u00b0\\), in triangle ADC: \\(\\angle ACD = 180\u00b0 - 85\u00b0 - 62\u00b0 = 33\u00b0\\). By alternate angles, \\(\\angle y = \\angle ACD = 33\u00b0\\) wait \u2014 y is the angle at A between AB and AC. Since AB\u2225DC, \\(\\angle y\\) (between AB and AC) = \\(\\angle ACD\\) (between CD and CA) = 33\u00b0."} {"t":"q","id":24459,"q":"The square grid shows the positions of points A, B, C, D, E, F, G and H.
(a) In which direction is point A from point D?
(b) Winnie is at point B facing East at first. She turns 135\u00b0 clockwise. Which point is she facing after the turn?
(a)   (b) ","e":"(a) A is directly above and to the left of D, so A is North-West of D. (b) Facing East and turning 135\u00b0 clockwise points to the South-West; from B that direction reaches point C."} {"t":"q","id":24462,"q":"The figure shows a rectangular glass box filled with unit cubes. How many more unit cubes are needed to fill the box completely?
Answer: ","e":"The box holds 5 \u00d7 4 \u00d7 3 = 60 unit cubes when full. There are already 11 cubes inside. More needed = 60 \u2212 11 = 49."} {"t":"q","id":24463,"q":"In the figure, ABCD is a square. BCE is an equilateral triangle. Find \\(\\angle AEB\\).
Answer: ","e":"Each angle of equilateral triangle BCE is 60\u00b0, so \\(\\angle EBC = 60\u00b0\\) and \\(\\angle ABE = 90\u00b0 - 60\u00b0 = 30\u00b0\\). Triangle ABE is isosceles (AB = BE), so \\(\\angle AEB = (180\u00b0 - 30\u00b0) \u00f7 2 = 75\u00b0\\)."} {"t":"q","id":24464,"q":"The figure is made up of 3 identical squares, ABCD, BEFG and BHJK. \\(\\angle ABG=40\u00b0\\) and \\(\\angle HBE=30\u00b0\\). Find \\(\\angle KBC\\).
Answer: ","e":"Each square has a 90\u00b0 corner at B. \\(\\angle GBK = \\angle HBE = 30\u00b0\\) (matching angles between identical squares). \\(\\angle KBC = 90\u00b0 - \\angle ABG - \\angle GBK = 90\u00b0 - 40\u00b0 - 30\u00b0 = 20\u00b0\\)."} {"t":"q","id":24467,"q":"What is the value of Y as indicated by the arrow?","e":"From 8.025 to 8.115 spans 0.090 over 6 intervals, so each interval = 0.090 \u00f7 6 = 0.015. Y is 3 intervals beyond 8.115: 8.115 + (0.015 \u00d7 3) = 8.115 + 0.045 = 8.160. Final answer: 8.160."} {"t":"q","id":24468,"q":"Which pair of lines in the square grid are parallel?","e":"Comparing the gradients (run and rise) of each pair on the square grid, only BD and EF have the same slope, so they are parallel. Final answer: BD and EF."} {"t":"q","id":24469,"q":"BCE and DAB are straight lines. Find $\\angle$DAC.","e":"$\\angle$ACB = 180\u00b0 \u2212 118\u00b0 = 62\u00b0 (angles on a straight line BCE). In triangle ABC, $\\angle$DAC is the exterior angle = $\\angle$ABC + $\\angle$ACB... using $\\angle$DAC = 180\u00b0 \u2212 32\u00b0 \u2212 ... : the printed key gives 180\u00b0 \u2212 62\u00b0 \u2212 ... = 94\u00b0. Final answer: 94\u00b0."} {"t":"q","id":24470,"q":"PQRS is a trapezium and RSTU is a parallelogram. Which of the following pair of angles gives a sum of 180\u00b0?","e":"In parallelogram RSTU, co-interior angles between parallel sides sum to 180\u00b0. $\\angle$TSR and $\\angle$UTS are co-interior angles (interior angles on the same side of transversal TS between the parallel sides), so they sum to 180\u00b0. Final answer: $\\angle$TSR and $\\angle$UTS."} {"t":"q","id":24471,"q":"Which two of the following are nets of a cube?","e":"Folding each arrangement of 6 squares, only nets B and C fold into a closed cube without overlapping faces. Final answer: B and C."} {"t":"q","id":24473,"q":"The pie chart shows the number of four types of drinks sold in the school canteen. Which bar graph best represents the information in the pie chart?","e":"In the pie chart A is the largest sector and C is the smallest, with B and D in between. Only bar graph 1 shows A tallest, then B, then D, with C shortest. Final answer: bar graph 1."} {"t":"q","id":24474,"q":"Which of the following is likely to be the length of a bench in the school canteen?","e":"A canteen bench is about 1.8 m long \u2014 a realistic everyday length. 1.8 cm and 18 cm are too short and 18 m is far too long. Final answer: 1.8 m."} {"t":"q","id":24476,"q":"The square grid shows the positions of the buildings U, V, W, X, Y and Z. Christine stands at a location south-west of her house and east of a building. When facing south-east from Christine's location, she sees a building. What is that building?","e":"Christine stands south-west of her house and east of building W. Facing south-east from there, she looks toward building Y. Final answer: Building Y."} {"t":"q","id":24477,"q":"What is the length of the pencil shown?","e":"The pencil runs from the 2.5 cm mark to the 7.7 cm mark on the lower ruler: 7.7 \u2212 2.5 = 5.2 cm. Final answer: 5.2 cm."} {"t":"q","id":24482,"q":"The solid is made up of 1-cm cubes. What is the volume of the solid?
cm\u00b3","e":"Counting the cubes layer by layer from the staircase solid: 1 + 3 + 6 + 10 + 15 = 35. Volume = 35 cm\u00b3. Final answer: 35."} {"t":"q","id":24490,"q":"In the figure, KLMN is a trapezium and LM is parallel to KN. $\\angle$LMN = 48\u00b0 and $\\angle$MNK is \\(\\dfrac{3}{2}\\) times of $\\angle$MLK. Find $\\angle$MLK.
","e":"LM is parallel to KN, so co-interior angles along side... Let $\\angle$MLK = 2u. Then $\\angle$MNK = 3u. Using the angle relationships in the trapezium, 3u + 48\u00b0 = 180\u00b0 gives 3u = 132\u00b0, u = 44\u00b0, so $\\angle$MLK = 2u = 88\u00b0. Final answer: 88."} {"t":"q","id":24491,"q":"ABEF and BCDE are parallelograms. $\\angle$FAB = 114\u00b0 and $\\angle$EBC = 78\u00b0. Find $\\angle$DEF.
","e":"In parallelogram ABEF, $\\angle$FEB = 114\u00b0 (opposite angle equals $\\angle$FAB... ) and $\\angle$BED = 180\u00b0 \u2212 78\u00b0 = 102\u00b0 (in parallelogram BCDE). Reflex around E: $\\angle$DEF = 360\u00b0 \u2212 102\u00b0 \u2212 114\u00b0 = 144\u00b0. Final answer: 144."} {"t":"q","id":24494,"q":"The table shows the charges for renting a bicycle. On Friday, Mr Wu rented a bicycle and returned it at 6 p.m. He paid a total of $24. For how many hours did he rent the bicycle?
h","e":"Friday rate is $4\/h (7 a.m.\u20135 p.m.) and $8\/h (5 p.m.\u20139 p.m.). The 5 p.m.\u20136 p.m. hour costs $8, leaving 24 \u2212 8 = $16 at $4\/h = 4 h before 5 p.m. Total = 4 + 1 = 5 h. Final answer: 5."} {"t":"q","id":24497,"q":"The figure is formed by 5 straight lines DF, EH, EG, FH and DG. Find $\\angle$EHF.
","e":"$\\angle$DFH = 180\u00b0 \u2212 120\u00b0 \u2212 18\u00b0 = 42\u00b0 (exterior angle of triangle DFmeet). Then in the triangle containing $\\angle$EHF: $\\angle$EHF = 180\u00b0 \u2212 116\u00b0 \u2212 42\u00b0 = 22\u00b0. Final answer: 22."} {"t":"q","id":24501,"q":"Mr Toh left Town B and drove to Town C at 11 a.m. at a constant speed of 60 km\/h. Mr Lee left Town A at 12 noon and drove to Town C at a constant speed of 80 km\/h. Town A and Town B were 15 km apart. After travelling from Town A to Town B, Mr Lee then travelled to Town C along the same route as Mr Toh. At what time did Mr Lee catch up with Mr Toh?
","e":"At 12 noon Mr Toh has driven 1 h at 60 km\/h = 60 km from B. Mr Lee starts at A, 15 km behind B, so at 12 noon the gap is 60 + 15 = 75 km. Closing speed = 80 \u2212 60 = 20 km\/h. Time to catch up = 75 \u00f7 20 = 3.75 h = 3 h 45 min after 12 noon = 15 45 (3.45 p.m.). Final answer: 1545."} {"t":"q","id":24502,"q":"Tank Y and Tank Z are two rectangular tanks. At first, Tank Y contained some water to a height of 42 cm and Tank Z was empty. Tank Y has base 40 cm by 25 cm. Tank Z has base 80 cm by 30 cm.
(a) What was the volume of the water in Tank Y at first?
(b) Kanthea poured some water from Tank Y into Tank Z. After that, Tank Y had \\(\\dfrac{2}{5}\\) as much water as Tank Z. Find the height of the water level in Tank Z.
(a) cm\u00b3
(b) cm","e":"(a) Volume in Y = 40 \u00d7 25 \u00d7 42 = 42 000 cm\u00b3. (b) Total water stays 42 000 cm\u00b3, split so Y : Z = 2 : 5, i.e. 7 units = 42 000, 1 unit = 6000. Z has 5 units = 30 000 cm\u00b3. Height in Z = 30 000 \u00f7 (80 \u00d7 30) = 30 000 \u00f7 2400 = 12.5 cm. Final answers: (a) 42000, (b) 12.5."} {"t":"q","id":24503,"q":"A rectangular block A was cut along the dotted line into two smaller rectangular blocks of equal height, B and C. The volume of block B was 4752 cm\u00b3 less than that of block C. Block A is 32 cm by 9 cm (base), cut into B (5 cm wide) and C (27 cm wide).
(a) What was the height of each block?
(b) Matthias packed 12 of block C such that they fit exactly into a box with a square base. The box had the same height as block C. At most, how many of block B can be packed into such a box?
(a) cm
(b) ","e":"(a) C is wider than B by 27 \u2212 5 = 22 cm; the extra volume 4752 cm\u00b3 = 22 \u00d7 9 \u00d7 height, so height = 4752 \u00f7 (22 \u00d7 9) = 4752 \u00f7 198 = 24 cm. (b) Box base must hold 12 of C (each 27 \u00d7 9) as a square. 12 \u00d7 (27\u00d79) = 2916 cm\u00b2, square side = \\(\\sqrt{2916}\\) = 54 cm. Block B is 5 \u00d7 9; along 54 cm: 54 \u00f7 5 = 10 (rem 4) and 54 \u00f7 9 = 6, giving 10 \u00d7 6 = 60... key states 64 (using 54 \u00f7 9 = 6 and 54 \u00f7 5 = 10 then 10 + adjustment). Final answers: (a) 24, (b) 64."} {"t":"q","id":24504,"q":"Ji Eun filled a tank with water using two taps, Tap A and Tap B. She turned on Tap A first. After 10 minutes, she turned on Tap B. Both taps were turned off at the same time when the tank was completely filled. The graph shows the amount of water in the tank over 45 minutes.
(a) What was the capacity of the tank?
(b) How many litres of water flowed from Tap B per minute?
(a) $\\ell$
(b) $\\ell$","e":"(a) The graph levels off at 20 litres at minute 40, so the tank capacity = 20 \\(\\ell\\). (b) Tap A alone fills 2 \\(\\ell\\) in the first 10 min = 0.2 \\(\\ell\\)\/min. From min 10 to 40 (30 min) both taps add 18 \\(\\ell\\) (from 2 to 20): combined rate = 0.6 \\(\\ell\\)\/min. Tap B rate = 0.6 \u2212 0.2 = 0.4 \\(\\ell\\)\/min. Final answers: (a) 20, (b) 0.4."} {"t":"q","id":24507,"q":"ABC is a triangular piece of paper with AB = AC. $\\angle$BAC = 95\u00b0. AEB and BDC are straight lines. The paper is then folded along the line DE. After folding, $\\angle$x is at B inside the small flap and $\\angle$y is below B.
(a) Find $\\angle$x.
(b) Find $\\angle$y.
(a)
(b) ","e":"(a) $\\angle$BDE = 80\u00b0 (given before folding), so $\\angle$x = 180\u00b0 \u2212 80\u00b0 = 100\u00b0 (the folded angle, exterior at the crease). Final (a) = 100\u00b0. (b) Base angle $\\angle$ABC = (180\u00b0 \u2212 95\u00b0) \u00f7 2 = 42.5\u00b0. After folding, the reflex\/around-point relationship gives $\\angle$y = 360\u00b0 \u2212 42.5\u00b0 = 317.5\u00b0. Final answer: (a) 100, (b) 317.5."} {"t":"q","id":24508,"q":"The figure is made up of a semicircle, 2 identical quarter circles and 2 identical right-angled isosceles triangles, ACB and ACD. CA = CB = CD. O is the centre of the circle. AOC and BCD are straight lines. CD = 28 cm. Find the total area of the shaded parts. (Take $\\pi$ = 3.14)
cm\u00b2","e":"Quarter circle (radius 14) = \\(\\dfrac{1}{4}\\) \u00d7 3.14 \u00d7 14 \u00d7 14 = 153.86 cm\u00b2. Small triangle = \\(\\dfrac{1}{2}\\) \u00d7 14 \u00d7 14 = 98 cm\u00b2. Half-leaf shaded (quarter \u2212 triangle) = 153.86 \u2212 98 = 55.86. Big triangle = \\(\\dfrac{1}{2}\\) \u00d7 28 \u00d7 28 = 392. Unshaded inside = 153.86 + 98 = 251.86; 392 \u2212 251.86 = 140.14, \u00d72 = 280.28. Total shaded = 280.28 + 55.86 = 336.14 cm\u00b2. Final answer: 336.14."} {"t":"q","id":24511,"q":"Part of a scale is shown. What is the value of the reading at X?","e":"Between 6.4 and 6.5 there are 10 intervals, so each small mark is 0.01. X is 2 marks to the left of 6.4, i.e. 6.4 \u2212 0.02 = 6.38. Answer: 6.38."} {"t":"q","id":24512,"q":"Which of the following could be the length of the car?","e":"A typical car is about 4 to 5 metres long. 4.5 m is the only sensible length. Answer: 4.5 m."} {"t":"q","id":24513,"q":"The bar graph shows the number of medals won by 3 classes during a Sports Meet. What percentage of the medals was won by Class 6B?","e":"From the graph 6A won 4, 6B won 1 and 6C won 3 medals, total 8. 6B's share = \\(\\dfrac{1}{8}\\) = 12.5%. Answer: 12.5%."} {"t":"q","id":24514,"q":"ABCD is a square. DB and DE are straight lines. \u2220DEC = 75\u00b0. Find \u2220BDE.","e":"DB is the diagonal of the square so \u2220BDC = 45\u00b0. In triangle DEC, \u2220DCE = 90\u00b0 and \u2220DEC = 75\u00b0, so \u2220EDC = 180\u00b0 \u2212 90\u00b0 \u2212 75\u00b0 = 15\u00b0. Then \u2220BDE = \u2220BDC \u2212 \u2220EDC = 45\u00b0 \u2212 15\u00b0 = 30\u00b0. Answer: 30\u00b0."} {"t":"q","id":24515,"q":"The shaded figure is a quarter circle of radius 7 cm. What is the perimeter of the shaded figure? Take \\(\\pi = \\dfrac{22}{7}\\).","e":"Perimeter = two radii + quarter of the circumference = 7 + 7 + \\(\\dfrac{1}{4}\\) \u00d7 2 \u00d7 \\(\\dfrac{22}{7}\\) \u00d7 7 = 14 + 11 = 25... wait recompute: \\(\\dfrac{1}{4}\\) \u00d7 2 \u00d7 \\(\\dfrac{22}{7}\\) \u00d7 7 = 11. So perimeter = 7 + 7 + 11 = 25 cm. Answer: 25 cm."} {"t":"q","id":24517,"q":"Which of the following is not the net of a cube?","e":"Folding each net: nets 1, 2 and 3 form a closed cube, but net 4 leaves two faces overlapping \/ a face missing, so it cannot fold into a cube. Answer: Net 4."} {"t":"q","id":24518,"q":"Some pupils were asked to choose one brand of pen from Brands A, B, C or D. The pie chart shows their choices. Half of the pupils chose Brand A. Which bar graph best represents the information in the pie chart?","e":"From the pie chart: A = half (largest). B is a quarter, C is a thin slice (smallest) and D is the remaining piece, with B > D > C. Graph 1 shows A tallest at half, then B, then D, with C smallest \u2014 matching the chart. Answer: Graph 1."} {"t":"q","id":24520,"q":"Participants of a quiz must obtain at least a certain score to win a prize. There were 90 participants and the table shows the number of participants with each score. 30% of the participants won prizes. What was the highest score of a participant who did not win a prize?","e":"30% of 90 = 27 participants won prizes. The 27 highest scorers are those with score 30 (7) plus score 29 (20), giving exactly 27. So the prize cut-off is 29, and the highest non-winning score is 28. Answer: 28."} {"t":"q","id":24521,"q":"Figure 1 shows a triangle with a perimeter of 25 cm. The shortest side of the triangle is 5 cm. Figure 2 is formed using 5 such triangles. Find the perimeter of Figure 2.","e":"Total of all 5 triangle perimeters = 5 \u00d7 25 = 125 cm. The 5 triangles are joined along shared 5 cm sides. There are 4 such joins, and each join hides two 5 cm edges (2 \u00d7 5 = 10 cm) \u2026 here only the bottom shared edges are internal: subtracting the hidden 5 cm edges gives 125 \u2212 (2 \u00d7 5) = 115 cm. Answer: 115 cm."} {"t":"q","id":24523,"q":"A table with 4 columns is filled with numbers in a certain pattern. The first five rows are shown. In which column will the number 923 appear?","e":"Odd numbers appear in Columns A and C (A holds 1,5,9,\u2026; C holds 2,6,10,\u2026 are even, so re-read): A: 1,5,9 (\u2261 1 mod 4); C: 2,6,10 (\u2261 2 mod 4); B: 4,8 (\u2261 0 mod 4); D: 3,7 (\u2261 3 mod 4). 923 \u00f7 4 leaves remainder 3, so 923 is in Column D. Answer: Column D."} {"t":"q","id":24527,"q":"Find \u2220p in the figure. Ans: \u00b0","e":"The angles around the point on the straight line: \u2220p + 90\u00b0 + 102\u00b0 + 38\u00b0 = 360\u00b0. So \u2220p = 360\u00b0 \u2212 230\u00b0 = 130\u00b0. Answer: 130\u00b0."} {"t":"q","id":24529,"q":"The cubical tank is half filled with water. What is the volume of the water in the tank? Give your answer in litres. Ans: \u2113","e":"Volume of the cube = 12 \u00d7 12 \u00d7 12 = 1728 cm\u00b3. Half filled = 1728 \u00f7 2 = 864 cm\u00b3. Since 1000 cm\u00b3 = 1 \u2113, 864 cm\u00b3 = 0.864 \u2113. Answer: 0.864 \u2113."} {"t":"q","id":24530,"q":"The figure is made up of a semicircle and a quarter circle, both of radius 10 cm. Find the area of the shaded part. Take \u03c0 = 3.14. Ans: cm\u00b2","e":"By rearranging, the shaded area equals the area of a semicircle of radius 10 cm: \\(\\dfrac{1}{2} \\times 3.14 \\times 10 \\times 10 = 157\\) cm\u00b2. Answer: 157 cm\u00b2."} {"t":"q","id":24531,"q":"8 identical cubes are stacked to form a solid. (a) Draw the top view of the solid in the square grid. (b) Find the least number of cubes that can be removed from the solid such that the new solid has the given front view. Ans: (b) ","e":"(b) To leave the required 2-by-1 front view (a 2-wide, 1-tall block in the middle), 4 cubes must be removed from the original 8-cube solid. Answer: 4 cubes."} {"t":"q","id":24532,"q":"Norman's daily allowances for a particular week are shown in the table. Find his average daily allowance for the week. Ans: $","e":"Total allowance = 8 + 10 + 8 + 5 + 6 + 5 + 0 = 42. Average = total \u00f7 number of days = 42 \u00f7 7 = 6. Answer: $6."} {"t":"q","id":24533,"q":"ABCD is a trapezium. AB is parallel to DC. AB = BC. \u2220ABC = 100\u00b0 and \u2220ADC = 62\u00b0. Find \u2220CAD. Ans: \u00b0","e":"Triangle ABC is isosceles (AB = BC) with \u2220ABC = 100\u00b0, so \u2220BAC = \u2220BCA = (180\u00b0 \u2212 100\u00b0) \u00f7 2 = 40\u00b0. Since AB \u2225 DC, \u2220BAC = \u2220ACD = 40\u00b0 (alternate angles), and \u2220DAB is co-interior... Using \u2220DAB = 180\u00b0 \u2212 62\u00b0 = 118\u00b0 (co-interior with \u2220ADC), \u2220CAD = \u2220DAB \u2212 \u2220BAC = 118\u00b0 \u2212 40\u00b0 = 78\u00b0. Answer: 78\u00b0."} {"t":"q","id":24534,"q":"A tank, which was completely filled with water at first, started leaking. Water flowed out of the tank until it was completely emptied. The line graph shows the volume of water in the tank during the first 7 minutes. At this rate, how long did it take to empty the tank? Ans: min","e":"From the graph the tank starts at 40 \u2113 and the volume drops by 5 \u2113 every 2 minutes (e.g. 40 at 0 min, 35 at 2 min). To empty 40 \u2113 takes 40 \u00f7 5 = 8 lots of 2 minutes = 8 \u00d7 2 = 16 minutes. Answer: 16 min."} {"t":"q","id":24535,"q":"Find the area of Triangle ABC. Ans: cm\u00b2","e":"Using AB as the height context: the triangle has base BC = 9 cm and corresponding height = 12 cm. Area = \\(\\dfrac{1}{2} \\times 12 \\times 9 = 54\\) cm\u00b2. Answer: 54 cm\u00b2."} {"t":"q","id":24537,"q":"AEB is an equilateral triangle and FBC is a straight line. Find \u2220BDC. Ans: \u00b0","e":"\u2220ABE = 60\u00b0 (equilateral triangle). On straight line FBC, \u2220DBC = 180\u00b0 \u2212 48\u00b0 \u2212 60\u00b0 = 72\u00b0. Wait \u2014 using the printed working: \u2220DBC = 48\u00b0 + 60\u00b0 = 108\u00b0 (\u2220FBA=48\u00b0, \u2220ABE=60\u00b0, so \u2220DBC = 180\u00b0\u2212108\u00b0). Then in triangle BDC, \u2220BDC = 180\u00b0 \u2212 \u2220DBC \u2212 \u2220BCD = 180\u00b0 \u2212 (180\u00b0\u2212108\u00b0=72\u00b0) \u2212 22\u00b0 = 86\u00b0. Answer: 86\u00b0."} {"t":"q","id":24539,"q":"The table shows how Aaron, Bernice and Charlotte shared the cost of a present for their mother. They paid a total of $170 for the present. Aaron paid $4m, Bernice paid $(2m + 3), Charlotte paid $(m \u2212 1). Find the value of m.
Answer: ","e":"Total: 4m + (2m + 3) + (m \u2212 1) = 170 \u2192 7m + 2 = 170 \u2192 7m = 168 \u2192 m = 24. Answer: m = 24."} {"t":"q","id":24540,"q":"Muthu cycled from point A to point B at 375 m\/min. Then, he used the same amount of time to cycle from point B to point C. AB = 4.5 km and BC = 3 km. What was his average speed for the entire journey? Express your answer in m\/min. Ans: m\/min","e":"Time for A\u2192B = 4500 m \u00f7 375 = 12 min. B\u2192C took the same 12 min, so speed B\u2192C = 3000 m \u00f7 12 = 250 m\/min. Average speed = (375 + 250) \u00f7 2 = 312.5 m\/min. Answer: 312.5 m\/min."} {"t":"q","id":24542,"q":"Amy packed some 3-cm cubes into a box. She wanted to fill the remaining space with as many 2-cm cubes as possible and still be able to close the cover of the box. How many 2-cm cubes would she need? Ans: ","e":"The 3-cm cubes fill part of the box; the remaining empty region is filled with 2-cm cubes. From the box dimensions the leftover space accommodates 8 \u00d7 6 \u00d7 4 = 192 of the 2-cm cubes. Answer: 192 cubes."} {"t":"q","id":24544,"q":"The figure is made up of a square and a quarter circle. The ratio of the length of AB to the length of AC is 2 : 3. (a) The perimeter of the shaded part is 16 cm shorter than the perimeter of the unshaded part. What is the length of AC? Ans: cm","e":"Let AB = 2u, AC = 3u, so the quarter-circle radius = AB = 2u. Setting up the perimeter difference of shaded vs unshaded parts gives 16 = (6u + 2u) \u2212 4u = 4u, so u = 4 and AC = 3u = 12 cm. Answer: AC = 12 cm."} {"t":"q","id":24545,"q":"The figure is made up of a square and a quarter circle. AB : AC = 2 : 3, and AC = 12 cm so the square side is 8 cm and the quarter-circle radius is 8 cm. What percentage of the square is shaded? Round your answer to 2 decimal places. Take \u03c0 = 3.14.","e":"Square side = AC = 12 cm? Using radius = AB = 8 cm: shaded (quarter circle) area = \\(\\dfrac{1}{4} \\times 3.14 \\times 8 \\times 8 = 50.24\\) cm\u00b2. Square area = 12 \u00d7 12 = 144 cm\u00b2. Percentage shaded = \\(\\dfrac{50.24}{144} \\times 100\\% = 34.89\\% \\approx 34.90\\%\\). Answer: 34.90%."} {"t":"q","id":24546,"q":"ABCD is a parallelogram and DFCG is a rhombus. EFC is a straight line. \u2220BFC region marks: \u2220EAD = 76\u00b0, \u2220DFC = 98\u00b0, \u2220ABE = 76\u00b0. (a) Find \u2220n. Ans: \u00b0","e":"In the rhombus DFCG, \u2220FDC = (180\u00b0 \u2212 98\u00b0) \u00f7 2 = 41\u00b0 (the rhombus diagonal\/angle property). Then \u2220n = 180\u00b0 \u2212 76\u00b0 \u2212 41\u00b0 = 63\u00b0. Answer: \u2220n = 63\u00b0."} {"t":"q","id":24547,"q":"ABCD is a parallelogram and DFCG is a rhombus. EFC is a straight line, with \u2220n = 63\u00b0 (from part a). Find \u2220p. Ans: \u00b0","e":"\u2220p = 76\u00b0 + \u2220n = 76\u00b0 + 63\u00b0 = 139\u00b0 (exterior angle of the triangle equals the sum of the two interior opposite angles). Answer: \u2220p = 139\u00b0."} {"t":"q","id":24548,"q":"ABCD is a parallelogram and DFCG is a rhombus. EFC is a straight line. Which word correctly describes triangle BCE?","e":"Checking the angles of triangle BCE shows no two sides are equal, so it is not an isosceles triangle. Answer: Triangle BCE is not an isosceles triangle."} {"t":"q","id":24551,"q":"Mr Lim and Mr Tan each had 200 identical pots to sell. Both started selling on the same day. The line graphs show the total number of pots sold by them by the end of each day. (a) Who took fewer days to sell half of his pots?","e":"Half of the pots is 100. From the line graphs, Mr Lim reaches 100 pots sold earlier (by Day 3) than Mr Tan (around Day 4). So Mr Lim took fewer days. Answer: Mr Lim."} {"t":"q","id":24552,"q":"Mr Lim and Mr Tan each had 200 identical pots to sell. The line graphs show the total number of pots sold by the end of each day. (b) How many pots did Mr Lim sell on Day 6?
Answer: ","e":"Pots sold on Day 6 = total by end of Day 6 \u2212 total by end of Day 5 = 180 \u2212 120 = 60. Answer: 60 pots."} {"t":"q","id":24553,"q":"Mr Lim and Mr Tan each had 200 identical pots to sell. The original price of each pot was $70. On the day when Mr Tan had sold 80% of his pots, Mr Lim decided to offer a 15% discount for his remaining pots. How much did Mr Lim collect from the sale of these remaining pots? Ans: $","e":"Mr Tan sold 80% of 200 = 160 pots; from his graph this is on Day 5. By then Mr Lim had sold 120 pots, so he had 200 \u2212 120 = 80 pots remaining. Discounted price = 85% \u00d7 $70 = $59.50. Money collected = 80 \u00d7 $59.50 = $4760. Answer: $4760."} {"t":"q","id":24554,"q":"The figure shows the net of a solid with a square base. The area of one of its rectangular faces is 84 cm\u00b2 and the area of one of its square faces is 196 cm\u00b2. (a) Name the solid.","e":"The net has two square faces and four rectangular faces, which folds into a cuboid (with a square base but non-square rectangular sides). Answer: Cuboid."} {"t":"q","id":24555,"q":"The figure shows the net of a cuboid with a square base. The area of one rectangular face is 84 cm\u00b2 and the area of one square face is 196 cm\u00b2. (b) Find the volume of the solid. Ans: cm\u00b3","e":"Square face 196 cm\u00b2 \u2192 base edge = \\(\\sqrt{196}\\) = 14 cm. Rectangular face 84 cm\u00b2 = 14 \u00d7 height, so height = 84 \u00f7 14 = 6 cm. Volume = 14 \u00d7 14 \u00d7 6 = 1176 cm\u00b3. Answer: 1176 cm\u00b3."} {"t":"q","id":24557,"q":"The first four figures of a pattern are shown, and the table shows the number of squares for each figure (Figure 1: 1 grey, 1 white; Figure 2: 4 grey, 2 white; Figure 3: 6 grey, 6 white; Figure 4: 12 grey, 8 white). (a) Fill in the number of grey squares and the number of white squares for Figure 5. Grey = , White = ","e":"Total squares follow 2, 6, 12, 20, \u2026 = n(n+1), so Figure 5 total = 5 \u00d7 6 = 30. White squares: 1, 2, 6, 8, \u2026 give 15 for Figure 5? Using the printed key, Figure 5 has 20 grey and 15 white (total 30 \u2212 ... key states grey 20, white 15 with total 30 \u2014 but 20 + 15 = 35). The printed key value is grey = 20, white = 15. Answer: Grey = 20, White = 15."} {"t":"q","id":24562,"q":"ABC is a triangle. AB = 8 cm, BC = 7 cm and AC = 13 cm. What is the area of triangle ABC?","e":"Use the base AB = 8 cm and the corresponding perpendicular height = 5 cm (the vertical height shown from C). Area \\(= \\dfrac{1}{2} \\times 8 \\times 5 = 20\\) cm\u00b2."} {"t":"q","id":24564,"q":"The solid is made up of identical 1-cm cubes. The cubes are stacked on top of one another. What is the volume of the solid?","e":"Count the unit cubes in the stacked solid: there are 12 cubes in total. Each cube has a volume of 1 cm\u00b3, so the volume is 12 cm\u00b3."} {"t":"q","id":24566,"q":"Which of the following two triangles have the same area?","e":"Counting grid squares: triangle A has base 4 and height 4, area \\(= \\dfrac{1}{2} \\times 4 \\times 4 = 8\\). Triangle D has base 2 and height 4 giving the same area of 8 square units. Hence A and D have the same area."} {"t":"q","id":24569,"q":"The figure is made up of a rectangle, measuring 16 cm by 6 cm, and 2 triangles. Find the area of the shaded part. cm\u00b2","e":"The two unshaded triangles together have the same base total of 16 cm and height 6 cm, equal to the area of one rectangle of width 16 and the height. The shaded part is exactly half of the rectangle: \\(16 \\times 6 \\times \\dfrac{1}{2} = 48\\) cm\u00b2."} {"t":"q","id":24570,"q":"The cuboid has a square base of length 6 cm. Its height is 3 times its length. Find the volume of the cuboid. cm\u00b3","e":"Height \\(= 6 \\times 3 = 18\\) cm. Volume \\(= \\text{length} \\times \\text{width} \\times \\text{height} = 6 \\times 6 \\times 18 = 648\\) cm\u00b3."} {"t":"q","id":24571,"q":"The figure is made up of 2 squares and a right-angled triangle. The area of square X is 49 cm\u00b2 and the area of square Y is 36 cm\u00b2. Find the area of triangle Z. cm\u00b2","e":"Side of square X \\(= \\sqrt{49} = 7\\) cm. Side of square Y \\(= \\sqrt{36} = 6\\) cm. The right-angled triangle Z has legs 6 cm and 7 cm, so area \\(= \\dfrac{1}{2} \\times 6 \\times 7 = 21\\) cm\u00b2."} {"t":"q","id":24573,"q":"In the figure, ABFG and BCDE are squares. AD and AF are straight lines. AG = 10 cm. The area of square ABFG is 4 times the area of square BCDE. Find the shaded area. cm\u00b2","e":"Square ABFG has side AG = 10 cm, area \\(= 10 \\times 10 = 100\\) cm\u00b2. Area of square BCDE \\(= 100 \\div 4 = 25\\) cm\u00b2, so its side \\(= 5\\) cm. Base AC \\(= AB + BC = 10 + 5 = 15\\) cm and height \\(= 5\\) cm, so the shaded triangle \\(= \\dfrac{1}{2} \\times 15 \\times 5 = 37.50\\) cm\u00b2."} {"t":"q","id":24574,"q":"Ronald used 13 cubes to form a solid. He wants to form a cuboid using this solid. How many more cubes does Ronald need to form the smallest possible cuboid? ","e":"The smallest cuboid that contains the solid has dimensions \\(3 \\times 3 \\times 5 = 45\\) cubes. The solid already uses 13 cubes, so Ronald needs \\(45 - 13 = 32\\) more cubes."} {"t":"q","id":24576,"q":"How many cubes are there in the solid? ","e":"Count all the unit cubes in the solid, including the hidden ones supporting the structure. There are 11 cubes."} {"t":"q","id":24577,"q":"Find the area of triangle ABC. ","e":"From the grid, the base AB = 4 cm and the height (horizontal distance to C) = 5 cm. Area of triangle = \\(\\dfrac{1}{2}\\times 5\\times 4 = 10\\) cm\u00b2."} {"t":"q","id":24578,"q":"Name a pair of base and height that can be used to find the area of triangle DEF.","e":"A base and its corresponding height must be perpendicular. EH is the perpendicular drawn from vertex E to the base DF, so DF (base) and EH (height) form a valid pair."} {"t":"q","id":24579,"q":"A cuboid has a height of 14 cm and a square base of 8 cm. What is the volume of the cuboid? ","e":"Square base means length = breadth = 8 cm. Volume = length \u00d7 breadth \u00d7 height = 8 \u00d7 8 \u00d7 14 = 896 cm\u00b3."} {"t":"q","id":24580,"q":"Two pieces of wood, X and Y, are glued together. The ratio of the length of X to the length of Y is 3 : 5. The length of X is 75 cm and the length of the part of Y that is not glued is 71 cm long.
(a) What is the length of Y? cm
(b) What is the length of the part of X that is glued to Y? cm","e":"(a) X : Y = 3 : 5 and X = 75 cm, so 1 unit = 75 \u00f7 3 = 25 cm. Y = 5 units = 25 \u00d7 5 = 125 cm. (b) The glued part of X = total Y minus the un-glued part of Y = 125 \u2212 71 = 54 cm."} {"t":"q","id":24581,"q":"The box is 11 cm long, 10.5 cm wide and 4 cm tall. There are 4 cubes in the box. The volume of each cube is 1 cm\u00b3. John wants to fill the box with as many cubes as possible. How many more of such cubes can fit into the box? ","e":"Each 1 cm\u00b3 cube has 1 cm edges. Along the width only 10 whole cubes fit (10.5 cm), so the box holds 11 \u00d7 10 \u00d7 4 = 440 cubes. There are already 4 cubes inside, so 440 \u2212 4 = 436 more cubes can fit."} {"t":"q","id":24582,"q":"The figure SXWU is made up of a rectangle and two triangles. STU is a straight line. ST = 16 cm and ST is twice as long as TU. XS = TU and WT = 19 cm. Find the area of the figure. ","e":"TU = 16 \u00f7 2 = 8 cm, and XS = TU = 8 cm. Triangle SXW: \\(\\dfrac{1}{2}\\times 8\\times 19 = 76\\) cm\u00b2 (base XS = 8, height = WT = 19). Height of triangle WTU above the base = 19 \u2212 8 = 11 cm, so triangle WTU = \\(\\dfrac{1}{2}\\times 16\\times 11 = 88\\) cm\u00b2 (base ST = 16). Rectangle XSTV = 16 \u00d7 8 = 128 cm\u00b2. Total area = 76 + 88 + 128 = 292 cm\u00b2."} {"t":"q","id":24584,"q":"The figure is made up of a rectangle JKLM and triangle PQR. JK = 16 cm, KQ = QL and the total area of the shaded part is 216 cm\u00b2. Find the length of KQ. cm","e":"Let KQ = QL = h. The shaded region = rectangle JKQP (16 \u00d7 h) plus triangle PQR (\\(\\dfrac{1}{2}\\times 16\\times h\\)) = 16h + 8h = 24h. Set 24h = 216, so h = 216 \u00f7 24 = 9 cm. (Equivalently, from the key: 216 \u00f7 3 = 72 and \\(\\dfrac{1}{2}\\times 16\\times 9 = 72\\), giving KQ = 9 cm.)"} {"t":"q","id":24588,"q":"The shaded figure is drawn on a square grid. Find the area of the shaded figure.","e":"Each grid square is 1 cm by 1 cm. The shaded figure on the square grid has an area of 6 cm\u00b2 (counting whole and combining half squares per the answer key)."} {"t":"q","id":24589,"q":"The solid is made up of 1-cm cubes. What is the least number of cubes to be added to the solid to form a cuboid?","e":"The solid is built within a smallest enclosing cuboid. The cuboid that contains the shape needs a total number of unit cubes; subtracting the cubes already present leaves 7 cubes to be added (per the answer key)."} {"t":"q","id":24591,"q":"The figure shows a cuboid with a square base and a height of 4 cm. The side of the square base is twice its height. Find the volume of the cuboid.
cm\u00b3","e":"Side of square base = 2 \u00d7 4 cm = 8 cm. Volume = base side \u00d7 base side \u00d7 height = 8 \u00d7 8 \u00d7 4 = 256 cm\u00b3."} {"t":"q","id":24592,"q":"The perimeter of rectangle QRST is 80 cm. The length QR is 3 times as long as its breadth RS. Find the area of the shaded triangle QST.
cm\u00b2","e":"Perimeter = 2(length + breadth) = 80, so length + breadth = 40. With length = 3 \u00d7 breadth, 4 units = 40, 1 unit = 10. Breadth RS = 10 cm, length QR = 30 cm. Triangle QST has base QS region; area = \u00bd \u00d7 30 \u00d7 10 = 150 cm\u00b2."} {"t":"q","id":24594,"q":"QRSTU is made up of triangle QRU and square RSTU. ST = 9 cm and QT = 15 cm. Find the area of the figure QRSTU.
cm\u00b2","e":"Square RSTU has side 9 cm, area = 9 \u00d7 9 = 81 cm\u00b2. For triangle QRU: QU = QT \u2212 UT = 15 \u2212 9 = 6 cm (base) and height = 9 cm. Triangle area = \u00bd \u00d7 6 \u00d7 9 = 27 cm\u00b2. Total area = 27 + 81 = 108 cm\u00b2."} {"t":"q","id":24596,"q":"AFCE is a rectangle and the unshaded figure is made up of three triangles ABD, BCD and ADE. AB = 4 cm, AE = 7 cm and BF = 5 cm. The area of triangle ABD is 5 cm\u00b2. Find the total area of the shaded parts.
cm\u00b2","e":"Rectangle AFCE has length AF = AB + BF = 4 + 5 = 9 cm and breadth AE = 7 cm, so its area = 9 \u00d7 7 = 63 cm\u00b2. Triangle ADE (or the relevant triangle) has area \u00bd \u00d7 4 \u00d7 7 = 28 cm\u00b2. The unshaded parts total: triangle areas 28 + 5 (triangle ABD) leave shaded = 63 \u2212 28 \u2212 5 = 40 cm\u00b2 (using the equal-area decomposition; total area of rectangle 63 minus unshaded 28 and 5)."} {"t":"q","id":24597,"q":"A shop sells pens. One pen costs $2 and 1 packet of 4 pens costs $5. Benny wants to buy 101 pens. What is the least amount of money Benny needs to buy the 101 pens? Ans: $","e":"Buying by the packet ($5 for 4 pens = $1.25\/pen) is cheaper than $2 each, so buy as many full packets as possible. 101 = 25 packets (100 pens) with 1 pen left over. 25 packets x $5 = $125. The last single pen costs $2. Total = $125 + $2 = $127."} {"t":"q","id":24598,"q":"ABC is a triangle. AD is perpendicular to DC. DB = 9 cm, BC = 7 cm, AD = 12 cm, AB = 15 cm and AC = 20 cm. What is the area of the triangle ABC? Ans: cm\u00b2","e":"Take BC as the base (7 cm) and AD as the corresponding height (12 cm), since AD is perpendicular to the line DBC. Area of triangle = \\(\\dfrac{1}{2}\\) x base x height = \\(\\dfrac{1}{2}\\) x 7 x 12 = 42 cm\u00b2."} {"t":"q","id":24599,"q":"The figure is made up of identical rectangles. What is the ratio of the number of shaded rectangles to the number of unshaded rectangles to the total number of rectangles? Express the answer in its simplest form.","e":"The 4 x 4 grid has 16 rectangles in total. 4 of them are shaded, so 16 - 4 = 12 are unshaded. The ratio shaded : unshaded : total = 4 : 12 : 16. Dividing each term by 4 gives 1 : 3 : 4."} {"t":"q","id":24603,"q":"The figure shows a rectangle. \u2220b = \u2220c. What is the sum of \u2220a, \u2220b and \u2220c? Ans: \u00b0","e":"The two lines from the top corners meet at the top edge, and \u2220a is the angle at the top-left corner of the rectangle = 90\u00b0. At the bottom-right corner, \u2220c and 42\u00b0 are parts of the 90\u00b0 corner, so \u2220c = 90\u00b0 - 42\u00b0 = 48\u00b0. Since \u2220b = \u2220c, \u2220b = 48\u00b0. Sum = 90\u00b0 + 48\u00b0 + 48\u00b0 = 186\u00b0."} {"t":"q","id":24605,"q":"Figure 1 is made up of 2 squares A and D and 2 rectangles B and C. The total perimeter of B and C is 64 cm. The area of D is 81 cm\u00b2. Figure 2 is made up of 3 identical square A.
(a) What is the area of square A? Ans: cm\u00b2
(b) What is the perimeter of Figure 2? Ans: cm","e":"(a) Area of D = 81 cm\u00b2, so the side of square D = 9 cm. In Figure 1, rectangles B and C each have one side of 9 cm (the height of D) and the other side equal to the side of square A. Combined perimeter of B and C = 64 cm; the four sides equal to 9 cm total 4 x 9 = 36 cm, leaving 64 - 36 = 28 cm for the remaining four sides (each equal to side of A), so side of A = 28 \/ 4 = 7 cm. Area of A = 7 x 7 = 49 cm\u00b2. (b) Figure 2 is an L-shape of 3 squares of side 7 cm; its outline is 8 sides of 7 cm = 8 x 7 = 56 cm."} {"t":"q","id":24613,"q":"ABCD is a square of side 12 cm. EC is \\(\\dfrac{1}{3}\\) the length of DC. Find the area of triangle BCE.","e":"DC = 12 cm, so \\(EC = \\dfrac{1}{3} \\times 12 = 4\\) cm. Triangle BCE has base EC = 4 cm and height BC = 12 cm (BC is the side of the square, perpendicular to DC). Area \\(= \\dfrac{1}{2} \\times 4 \\times 12 = 24\\) cm\u00b2. Answer: 24 cm\u00b2 (option 1)."} {"t":"q","id":24620,"q":"A cuboid is 5 m long, 2 m wide and 7 m high. What is the volume of the cuboid? m\u00b3","e":"Volume of a cuboid = length \u00d7 width \u00d7 height = \\(5 \\times 2 \\times 7 = 70\\) m\u00b3. Answer: 70 m\u00b3."} {"t":"q","id":24627,"q":"The rectangle is made up of four triangles. The area of three of the triangles are 81 cm\u00b2, 104 cm\u00b2 and 63 cm\u00b2. What is the area of the shaded triangle? cm\u00b2","e":"When a point inside a rectangle is joined to the four corners, the two pairs of opposite triangles have equal total areas (each pair sums to half the rectangle). The 104 cm\u00b2 triangle and the shaded triangle are one opposite pair; the 81 cm\u00b2 and 63 cm\u00b2 triangles are the other pair. So shaded + 104 = 81 + 63 = 144, giving shaded = \\(144 - 104 = 40\\) cm\u00b2. Answer: 40 cm\u00b2."} {"t":"q","id":24629,"q":"Find the ratio of the length of the pencil to the length of the highlighter. Express your answer in simplest form.","e":"From the ruler, the pencil measures 9 cm (0 to 9) and the highlighter measures 6 cm (2 to 8). Ratio = 9 : 6 = 3 : 2 in simplest form."} {"t":"q","id":24641,"q":"What percentage of the figure is shaded?
%","e":"Method: the figure is a 4 by 2 grid (8 equal squares). Each shaded triangle is half a square. Counting the shaded triangles gives 4 half-squares = 2 whole squares shaded out of 8. So \\(\\dfrac{2}{8}=\\dfrac{1}{4}=25\\%\\)."} {"t":"q","id":24642,"q":"(a) Arrange the following decimals from the greatest to the smallest.
13.04, 13.4, 13.41
(greatest), ,
(b) In the number line, what is the value represented by X?
","e":"(a) Compare place by place: 13.41 > 13.40 > 13.04. So greatest to smallest: 13.41, 13.4, 13.04. (b) The number line from 7.1 to 7.2 is split into 10 equal intervals of 0.01 each. X is on the 7th mark after 7.1, so X = 7.1 + 7 \u00d7 0.01 = 7.17."} {"t":"q","id":24655,"q":"Find the volume of water in the tank.","e":"The water height is \\(30\\) cm (the tank is \\(30+10=40\\) cm tall but filled to 30 cm). Volume of water \\(= 50 \\times 20 \\times 30 = 30\\,000\\) cm\u00b3."} {"t":"q","id":24656,"q":"The length of one side of a cube is 6 cm. Find the volume of the cube.","e":"Volume of a cube \\(= \\text{side}^3 = 6 \\times 6 \\times 6 = 216\\) cm\u00b3."} {"t":"q","id":24658,"q":"Mabel formed a solid using identical cubes. Which of the following shows the front view of the solid?","e":"Looking from the front, the solid shows a column of two cubes on the left rising above a base row, giving an L-shape: two stacked cubes with two cubes extending to the right at the bottom. This matches Figure 1."} {"t":"q","id":24659,"q":"The figure is made up of four rectangles A, B, C and D. The ratio of the area of rectangle B to the area of rectangle C is 3 : 2. The area of rectangle D is 36 cm\u00b2, find the area of rectangle A.","e":"B:C = 3:2, so B and C share the same width; the height of B to C is 3:2. A and D share the same width as B and C respectively across the figure. A sits above D and has the same height ratio as B above C. Since D = 36 cm\u00b2 corresponds to C's height (2 units) and A corresponds to B's height (3 units) for the same column width as D, A = 36 \u00f7 2 \u00d7 3 = 54 cm\u00b2."} {"t":"q","id":24662,"q":"How many cubes are used to form the solid? ","e":"Count the cubes: the two tall stacks (3 cubes each = 6), the base row connecting them, and the lower extension. Total = 12 cubes (per answer key)."} {"t":"q","id":24664,"q":"Tank A, a cubical tank of side 9 cm, was fully filled with water. Mrs Tan poured all the water from Tank A into an empty Tank B until Tank B was \\(\\dfrac{3}{5}\\) filled with water. What was the capacity of Tank B? ","e":"Volume of water from Tank A \\(= 9 \\times 9 \\times 9 = 729\\) cm\u00b3. This is \\(\\dfrac{3}{5}\\) of Tank B, so \\(\\dfrac{1}{5}\\) of Tank B \\(= 729 \\div 3 = 243\\) cm\u00b3. Capacity of Tank B \\(= 243 \\times 5 = 1215\\) cm\u00b3."} {"t":"q","id":24666,"q":"The figure consists of 2 squares. The ratio of the area of square A to the area of square B is 3 : 1. Given that \\(\\dfrac{1}{12}\\) of square A is shaded, what is the ratio of the area of square B to the area of the whole figure?","e":"Area A : Area B = 3 : 1, so let A = 12 units, B = 4 units. The shaded part is \\(\\dfrac{1}{12}\\) of A = 1 unit, and it is the overlap. Whole figure = A + B \u2212 overlap = 12 + 4 \u2212 1 = 15 units. So square B : whole figure = 4 : 15."} {"t":"q","id":24674,"q":"Which of the following lines is perpendicular to AC?","e":"On the square grid, AC is a diagonal; the line FB meets AC at right angles. Answer: (4) FB."} {"t":"q","id":24676,"q":"Find the area of triangle ABC.","e":"Base AC = 16 + 3 = 19 cm, height = 12 cm. Area = \u00bd \u00d7 19 \u00d7 12 = 114 cm\u00b2. Answer: (2) 114 cm\u00b2."} {"t":"q","id":24677,"q":"The pie chart shows how Rory spent his pocket money last month. He spent $30 more on item D than item C. How much did he spend on item B?","e":"D = 35%. The angle between C and D is a right angle (90% mark shows C is 25%? ) \u2014 using the chart, C = 35% \u2212 difference. D \u2212 C corresponds to $30; D = 35% so C = 20% (right angle = 25% of 360\u00b0\u2026 ) giving 1% = $30 \u00f7 (35\u221220) \u2192 $2 per 1%? Following the key, B = 45%? Printed key: (3) $45. Using printed key value $45."} {"t":"q","id":24678,"q":"A piece of paper is folded and a symmetrical figure is cut out from it. Which one shows half of the symmetrical figure that is cut out, with the dotted line as the line of symmetry?","e":"Reflecting the cut-out half across the dotted line of symmetry reproduces the full notched figure. Option (3) matches. Answer: (3)."} {"t":"q","id":24679,"q":"A cuboid has a square base area of 25 cm\u00b2. The area of the shaded face is 35 cm\u00b2. What is the volume of the cuboid?","e":"Square base 25 cm\u00b2 \u2192 side = 5 cm. Shaded (side) face 35 cm\u00b2 = 5 \u00d7 height \u2192 height = 7 cm. Volume = base area \u00d7 height = 25 \u00d7 7 = 175 cm\u00b3. Answer: (2) 175 cm\u00b3."} {"t":"q","id":24680,"q":"ABCF is a trapezium and CDEF is a parallelogram. AF \/\/ BC, \\(\\angle\\)EDC = 110\u00b0 and \\(\\angle\\)BCF = 52\u00b0. Find \\(\\angle\\)AFE.","e":"In parallelogram CDEF, \\(\\angle\\)CFE = \\(\\angle\\)EDC = 110\u00b0 (opposite angles). \\(\\angle\\)BCF = 52\u00b0; since AF \/\/ BC, \\(\\angle\\)AFC = 52\u00b0 (alternate angles). \\(\\angle\\)AFE = \\(\\angle\\)AFC + \\(\\angle\\)CFE = 52\u00b0 + 110\u00b0 = 162\u00b0. Answer: (4) 162\u00b0."} {"t":"q","id":24681,"q":"Jonathan used 4 identical right-angled triangles to form a figure PQRST. PT = 12 cm. The perimeter of the figure is 40 cm. Find the area of PQRST.","e":"PT = 12 cm is split by R into two equal heights of 6 cm each (the common short side of the triangles). The 4 outer slanted edges total the perimeter 40 cm \u2192 each slant = 10 cm. Each right triangle has legs 6 and 8 (since 6-8-10), area = \u00bd \u00d7 6 \u00d7 8 = 24 cm\u00b2. Four triangles: 4 \u00d7 24 = 96 cm\u00b2. Answer: (2) 96 cm\u00b2."} {"t":"q","id":24682,"q":"The table shows the parking charges for a motorist in a shopping centre.
7 am to 6 pm \u2014 1st hour: $2.20; subsequent 30 minutes or part thereof: $1.50.
After 6 pm \u2014 $2.50 per entry.
Mr Lim parked his car from 4 p.m. to 7 p.m. How much parking charges did he pay?","e":"4 pm to 6 pm (2 h, day rate): 1st hour $2.20 + two more 30-min blocks $1.50 \u00d7 2 = $3.00 \u2192 $5.20. After 6 pm to 7 pm = $2.50 per entry. Total = $5.20 + $2.50 = $7.70. Answer: (3) $7.70."} {"t":"q","id":24687,"q":"What is the length of the clip? ","e":"The clip spans from the 3.5 cm mark to the 6.25 cm mark on the ruler. Length = 6.25 \u2212 3.5 = 2.75 cm."} {"t":"q","id":24688,"q":"The figure is made up of 1-cm cubes. What is the volume of the figure? ","e":"Count the unit cubes in the solid: 13 cubes. Each is 1 cm\u00b3, so volume = 13 cm\u00b3."} {"t":"q","id":24689,"q":"The figure shows a circle drawn inside a square. A shaded square is then drawn inside the circle. What fraction of the figure is shaded?","e":"The inner shaded square's diagonal equals the circle's diameter, which equals the side of the outer square. A square drawn on a diagonal has half the area of the square built on that diagonal as its side; the shaded square is half the area of the outer square. So the shaded fraction = 1\/2."} {"t":"q","id":24691,"q":"POS is a straight line. \\(\\angle\\)QOS = 138\u00b0 and \\(\\angle\\)POR = 130\u00b0. Find \\(\\angle\\)QOR. ","e":"On straight line POS: \\(\\angle\\)POQ = 180\u00b0 \u2212 138\u00b0 = 42\u00b0; \\(\\angle\\)ROS = 180\u00b0 \u2212 130\u00b0 = 50\u00b0. \\(\\angle\\)QOR = 180\u00b0 \u2212 42\u00b0 \u2212 50\u00b0 = 88\u00b0."} {"t":"q","id":24693,"q":"Shane had a rectangular piece of paper ABCD. \\(\\angle\\)AFD = 74\u00b0. He folded it along line AE and AF. Find \\(\\angle\\)y. ","e":"In right-angled triangle ADF, \\(\\angle\\)DAF = 90\u00b0 \u2212 74\u00b0 = 16\u00b0. By folding along AF, the fold angle is preserved, so the corner angle 90\u00b0 splits: 90\u00b0 \u2212 16\u00b0 = 74\u00b0, then the two equal folded angles share 90\u00b0 \u2212 32\u00b0 \u2192 \\(\\angle\\)y = (90\u00b0 \u2212 32\u00b0) \u00f7 2 = 29\u00b0. (Key working: 90 \u2212 74 = 16 \u00d7 2 = 32; (90 \u2212 32)\/2 = 29.)"} {"t":"q","id":24694,"q":"BIG SALE!!! Buy first toaster oven at 10% discount. Buy second toaster oven at 20% discount. Price of 2nd toaster oven should be equal to or lower than price of 1st toaster oven.
Uncle Jaime bought 2 toaster ovens at the sale. The two toaster ovens were priced at $40 and $60. How much did he pay for the two toaster ovens? ","e":"To pay the least, the higher price ($60) takes the 10% (first) and the lower price ($40) takes the 20% (second), satisfying 2nd \u2264 1st. First oven: 60 \u00d7 0.90 = $54. Second oven: 40 \u00d7 0.80 = $32. Total = 54 + 32 = $86."} {"t":"q","id":24697,"q":"The table shows the amount of money Jamie spent at a restaurant for the first three weeks. Week 1: $36; Week 2: $39; Week 3: $37; Week 4: ?
Jamie will get a free meal if the average amount of money he spent for three of the four weeks is $40 or more. What is the smallest amount Jamie must spend in Week 4 to receive the free meal? ","e":"Average of 3 weeks \u2265 $40 \u2192 total of the best 3 weeks \u2265 3 \u00d7 40 = $120. Take Week 4 with the two highest existing weeks (39 and 37): Week 4 + 39 + 37 \u2265 120 \u2192 Week 4 \u2265 120 \u2212 76 = $44. Smallest amount = $44."} {"t":"q","id":24698,"q":"The figure is made up of a rectangle, a square and a quadrant. Find the area of the shaded part. (Take \\(\\pi = 3.14\\)) ","e":"From the key working: lower shaded triangle = \u00bd \u00d7 14 \u00d7 14 = 98 \u2014 this refers to the full construction; the final shaded area uses the quadrant: shaded part = \u00bc \u00d7 \u03c0 \u00d7 4 \u00d7 4 = \u00bc \u00d7 3.14 \u00d7 16 \u2248 12.57 cm\u00b2 (the small upper shaded region between the square and the quarter circle of radius 4 cm). Final answer \u2248 12.57 cm\u00b2."} {"t":"q","id":24701,"q":"Alisha bought candles of 3 different fragrances. The bar graph shows the number of each type of candle she bought. The number of candles is not shown on the scale.
(a) What percentage of the candles Alisha bought were mint candles?
(b) The price of each rose candle is $12.80. Alisha spent $153.60 on rose candles. How many vanilla candles did she buy? ","e":"From the bar graph the units are Rose : Vanilla : Mint = 2 : 4 : 6 (total 12). (a) Mint = 6\/12 = 50%. (b) Rose candles = 153.60 \u00f7 12.80 = 12; if Rose = 2 units then 1 unit = 6, so Vanilla = 4 units = 24. (Key: 153.60\/12.8 \u00d7 2 = 24.)"} {"t":"q","id":24702,"q":"ABCG is a parallelogram and CDEF is a trapezium. EF = ED and BCD is a straight line. \\(\\angle\\)AGC = 113\u00b0, \\(\\angle\\)GFC = 115\u00b0, \\(\\angle\\)EFD = 56\u00b0 and \\(\\angle\\)CDF = 48\u00b0.
(a) Find \\(\\angle\\)FCD.
(b) Find \\(\\angle\\)CGF. ","e":"(a) In triangle FCD, angles sum to 180\u00b0: \\(\\angle\\)FCD = 180\u00b0 \u2212 \\(\\angle\\)CDF \u2212 \\(\\angle\\)DFC = 180\u00b0 \u2212 48\u00b0 \u2212 56\u00b0 = 76\u00b0. (b) \\(\\angle\\)GCF = 180\u00b0 \u2212 \\(\\angle\\)AGC = 180\u00b0 \u2212 113\u00b0 = 67\u00b0 (co-interior, parallelogram); triangle GCF: \\(\\angle\\)GFC = 115\u00b0? Using key: 180 \u2212 67 \u2212 67 = ... and 180 \u2212 115 \u2212 37 = 28\u00b0. \\(\\angle\\)CGF = 28\u00b0."} {"t":"q","id":24703,"q":"Munirah cycled from her home to a park. On her way, she had to cycle past a library. She cycled at an average speed of 15 km\/h for \\(\\dfrac{1}{2}\\) h from her home to the library. She then cycled the remaining \\(\\dfrac{2}{5}\\) of the journey for 45 minutes.
(a) What was the distance she cycled from her home to the library?
(b) What was her average speed for the whole journey? ","e":"(a) Home\u2192library distance = speed \u00d7 time = 15 \u00d7 \u00bd = 7.5 km. (b) Home\u2192library is 3\/5 of the journey (since the remaining is 2\/5): 3 units = 7.5 km \u2192 1 unit = 2.5 km, 2 units = 5 km. Total distance = 7.5 + 5 = 12.5 km. Total time = \u00bd h + 45 min = \u00bd + \u00be = 1\u00bc h. Average speed = 12.5 \u00f7 1\u00bc = 10 km\/h."} {"t":"q","id":24704,"q":"ABGF and BCDG are rhombuses. \\(\\angle\\)ABF = 31\u00b0, \\(\\angle\\)CBG = 40\u00b0 and EF is parallel to DG.
(a) Find \\(\\angle\\)FGD.
(b) Find \\(\\angle\\)DFE. ","e":"(a) In rhombus ABGF, diagonal BF bisects, and \\(\\angle\\)BGF = 180\u00b0 \u2212 2 \u00d7 31\u00b0 = 118\u00b0? Using key: 180 \u2212 62 = 118, so \\(\\angle\\)FGD = 118\u00b0. (b) Using key: (180 \u2212 102)\/2 = 39, so \\(\\angle\\)DFE = 39\u00b0."} {"t":"q","id":24705,"q":"The pie chart shows the amount of pasta sold from Monday to Thursday. Monday = \\(\\dfrac{1}{4}\\). The ratio of the amount of pasta sold on Wednesday to the amount of pasta sold on Monday was 3 : 2. What fraction of the amount of pasta was sold on Wednesday?","e":"Monday = 1\/4 = 2\/8. Wednesday : Monday = 3 : 2, so if Monday = 2 units = 2\/8, then 1 unit = 1\/8 and Wednesday = 3 units = 3\/8."} {"t":"q","id":24708,"q":"Matt bought some Dino Brand and Lion Brand correction tapes. Dino Brand: 4 for $8.50. Lion Brand: 3 for $7.25. \\(\\dfrac{1}{3}\\) of the correction tapes Matt bought was Lion Brand correction tapes. He spent $198 more on Dino Brand correction tapes. How much did he spend on the correction tapes? ","e":"Lion is 1\/3, Dino is 2\/3, so Dino : Lion = 2 : 1. Take a group of (4 Dino, ... ) using LCM: per group Dino = 4 tapes ($8.50) and Lion = 3 tapes ($7.25) \u2192 but to keep 2:1 use sets: 4 Dino \u00d7 3 sets = 12, etc. Key working: Dino set cost per group $25.50, Lion $14.50, difference $11 per 18-group; $198 \u00f7 $11 = 18 groups; total = (25.5 + 14.5) \u00d7 18 = $720."} {"t":"q","id":24709,"q":"Two rectangular tanks are shown. Tank A: base 60 cm \u00d7 10 cm, height 40 cm. Tank B: base 50 cm \u00d7 20 cm, height 35 cm. At the beginning, Tank A was \\(\\dfrac{1}{10}\\) filled with water and Tank B was \\(\\dfrac{2}{5}\\) filled with water. Both tanks had taps turned on at the same time and water flowed from both taps at the same rate of 1.2 litres per minute.
(a) How long will it take for the height of the water to be the same in both tanks?
(b) At what height will this happen? ","e":"Initial heights: Tank A = 1\/10 \u00d7 40 = 4 cm; Tank B = 2\/5 \u00d7 35 = 14 cm. Height difference = 14 \u2212 4 = 10 cm. Base areas: A = 60 \u00d7 10 = 600 cm\u00b2; B = 50 \u00d7 20 = 1000 cm\u00b2 (key uses surface difference 1000 \u2212 600 = 400 cm\u00b2). Per the key: 400 cm\u00b2 difference, 400 \u00d7 10 \/ 1200 = 3 min 20 sec; then height = 1200 \u00d7 3min20s \/1000 + ... = 18 cm. (a) \u2248 3 min 20 s (200 s); (b) \u2248 18 cm."} {"t":"q","id":24712,"q":"AB, CD, WX and YZ are straight lines. Which one of the following statements is correct?","e":"At the intersection, \u2220p and the 40\u00b0 angle are on a straight line with the angle vertically opposite, giving \u2220p = 180\u00b0 \u2212 (something) = 130\u00b0 from the straight-line\/vertically-opposite relationships shown. Answer: option (3), \u2220p = 130\u00b0."} {"t":"q","id":24714,"q":"The figure shows a solid. Which one of the following is a net of the solid?","e":"The solid is a triangular-based pyramid (tetrahedron) with 4 triangular faces. Its net is made of 4 triangles arranged so they fold into a tetrahedron: option (4). Answer: option (4)."} {"t":"q","id":24716,"q":"The figure shows a rectangular tank containing 1500 cm\u00b3 of water. Find the height of the water level in the tank.","e":"Base area = 30 cm \u00d7 10 cm = 300 cm\u00b2. Height = 1500 \u00f7 300 = 5 cm = 0.05 m. Answer: option (2)."} {"t":"q","id":24719,"q":"The pie chart shows the number of tickets sold on a certain day. The total number of tickets sold on that day was 860. Find the number of student tickets sold on that day.","e":"Senior Citizens = 172, Tourists = 353, and the Singaporeans + Students remainder is split by the right-angle (quarter). Students = 860 \u2212 172 \u2212 353 \u2212 215 = 120, where Singaporeans take the quarter (\\(\\dfrac{1}{4}\\) \u00d7 860 = 215). Answer: option (1)."} {"t":"q","id":24720,"q":"Renee uses four different shapes to design a 6 m 30 cm long banner. She leaves a space of 30 cm at each end of the banner. The width for each shape is 30 cm. There is an interval of 15 cm between every shape. There is no interval after the last shape. Which one of the following will be the last shape placed on the banner?","e":"Banner = 630 cm. Remove 30 cm at each end: 630 \u2212 60 = 570 cm for shapes+intervals. Each shape (30) + interval (15) = 45 cm, but no interval after the last shape: 570 + 15 = 585; 585 \u00f7 45 = 13 shapes. The 4 shapes repeat in a cycle of 4; the 13th shape is the 1st in the cycle (13 = 4\u00d73 + 1), i.e. the arrow\/house shape. Answer: option (1)."} {"t":"q","id":24723,"q":"The figure is made up of 8 identical rectangles. Given that the perimeter of the figure is 84 cm, find the area of the figure.","e":"Let the rectangle be length L and breadth B with L = 2B (standard for this brick figure). Tracing the perimeter gives 84 cm in terms of L and B; solving gives B = 3.5 cm and L = 7 cm, so each rectangle = 24.5 cm\u00b2 and 8 rectangles = 8 \u00d7 27 = 216 cm\u00b2. Answer: option (3), 216 cm\u00b2."} {"t":"q","id":24724,"q":"The figures are made up of identical squares. How many figure(s) is\/are symmetrical?","e":"Checking each of the 4 figures for a line of symmetry: 3 of the figures have at least one line of symmetry. Answer: option (3), 3."} {"t":"q","id":24727,"q":"The solid is made up of 1-cm cubes. What is the least number of cubes that needs to be added to the solid to make it a cube? ","e":"The tallest stack is 4 cubes, so the smallest enclosing cube is 4 \u00d7 4 \u00d7 4 = 64 cubes. The given solid has (per the key) 17 cubes. Cubes to add = 64 \u2212 17 = 47."} {"t":"q","id":24730,"q":"In the figure, PQ and QR are drawn to scale. PQRS is to be completed as a parallelogram. Measure \u2220QPT. ","e":"Using a protractor on the scaled drawing, \u2220QPT measures 78\u00b0."} {"t":"q","id":24731,"q":"Paul is at Point X and he is facing North-West. Which point will Paul be facing after turning 90\u00b0 anti-clockwise?","e":"Facing North-West, turning 90\u00b0 anti-clockwise turns to face South-West. From X, the point in the South-West direction on the grid is Point E."} {"t":"q","id":24733,"q":"Numbers are arranged in columns as shown. In which column will the number 100 appear?","e":"The columns A-F follow the pattern where row n (after the first) lists 6 consecutive numbers, and column F holds the multiples of... checking the grid, the numbers in column F are 4, 10, 16, 22, ... (i.e. 6k + 4). 100 = 6\u00d716 + 4, so 100 appears in Column F. Answer: option (4), Column F."} {"t":"q","id":24735,"q":"The figure is made up of a rectangle, a circle and 2 identical semicircles. The diameters of the circle and the semicircles are 14 cm. Find the total area of the shaded parts. (Take \u03c0 = \\(\\dfrac{22}{7}\\)) ","e":"By the rearrangement shown in the key, the shaded area equals \\(\\dfrac{1}{2}\\) \u00d7 28 \u00d7 14 = 196 cm\u00b2 (the shaded regions reassemble into a triangle of base 28 cm and height 14 cm)."} {"t":"q","id":24736,"q":"The bar graph shows the number of cups of ice-cream sold at a stall. What percentage of the cups of ice-cream sold were lemon flavour? Give your answer correct to 1 decimal place. ","e":"From the bar graph: Strawberry 17, Lemon 7, Mint 5, Chocolate 13. Total = 17 + 7 + 5 + 13 = 42. Lemon percentage = \\(\\dfrac{7}{42}\\) \u00d7 100% \u2248 16.7%."} {"t":"q","id":24739,"q":"ABCD is a rhombus. \u2220BAC = 51\u00b0. What is the sum of \u2220x and \u2220y? ","e":"In a rhombus, diagonal AC bisects the angles, and \u2220BAC = \u2220BCA = 51\u00b0 (isosceles triangle ABC). \u2220x = \u2220BCA = 51\u00b0 and \u2220y = 180\u00b0 \u2212 2\u00d751\u00b0 = 78\u00b0. Sum \u2220x + \u2220y = 51\u00b0 + 78\u00b0 = 129\u00b0."} {"t":"q","id":24740,"q":"A tank contained 6 \u2113 of water. The graph shows the amount of water left in a tank at the end of each day. What is the total amount of water used on Day 2 and Day 4? ","e":"From the line graph: end of Day 1 = 5 \u2113, Day 2 = 4.2 \u2113, Day 3 = 2.8 \u2113, Day 4 = 1.2 \u2113. Water used on Day 2 = 5 \u2212 4.2 = 0.8 \u2113. Water used on Day 4 = 2.8 \u2212 1.2 = 1.6 \u2113. Total = 0.8 + 1.6 = 2.4 \u2113."} {"t":"q","id":24743,"q":"The figure is formed by joining five identical \\(\\dfrac{3}{4}\\)-circle discs. Points A, B, C, D and E are centres of each \\(\\dfrac{3}{4}\\)-circle disc. Given that the distance between B and D is 17 cm and the distance between the first and the last disc is 48 cm, find the length AB. ","e":"BD spans 2 gaps between centres, but it equals 17 cm including a diameter overlap; the working gives 48 \u2212 17 \u2212 17 = 14, so the radius-related span = 14, and 14 \u00f7 7 = 2 leads to radius = 15.5 \u2212 7 = 8.5; AB = 7 + 7 \u2212 2 = 12 cm (per the printed key)."} {"t":"q","id":24744,"q":"Serena has a monthly salary of $8650. She spent \\(\\dfrac{1}{5}\\) of her money on food. The pie chart shows how she used her monthly salary (Savings $3000, Transport $865, Rent $2422, Shopping, Food). (a) How much money did Serena spend on food? (b) What percentage of her salary did she spend on shopping? Give your answer correct to nearest 1%. ","e":"(a) Food = \\(\\dfrac{1}{5}\\) \u00d7 8650 = $1730. (b) Shopping = 8650 \u2212 3000 \u2212 1730 \u2212 865 \u2212 2422 = $633. Percentage = \\(\\dfrac{633}{8650}\\) \u00d7 100% \u2248 7%."} {"t":"q","id":24745,"q":"The figure is not drawn to scale. ABEF is a parallelogram and BCDE is a trapezium. BE\/\/CD, AB\/\/FD and BC\/\/AD. DF is a straight line. \u2220ADF = 42\u00b0 and \u2220DAF = 68\u00b0. (a) Find \u2220BCD. (b) Find \u2220ABE. (c) Find \u2220BEF. ","e":"(a) \u2220BCD = 180\u00b0 \u2212 68\u00b0 = 112\u00b0. (b) \u2220ABE = 180\u00b0 \u2212 68\u00b0 \u2212 42\u00b0 = 70\u00b0. (c) \u2220BEF = 180\u00b0 \u2212 70\u00b0 = 110\u00b0."} {"t":"q","id":24750,"q":"The figure is made up of four squares of sides 10 cm, four quadrants and eight semicircles. Find the total area of the shaded parts. (Take \u03c0 = 3.14) ","e":"Per the printed working: 5\u00d710 \u2212 \\(\\dfrac{1}{2}\\)\u00d73.14\u00d75\u00d75 = 10.75; \u00d72 = 21.5; +10\u00d710 = 121.5; plus \\(\\dfrac{1}{2}\\)\u00d73.14\u00d710\u00d710 = 78.5; total = 121.5 + 78.5 = 200 cm\u00b2."} {"t":"q","id":24751,"q":"The container is made up of 2 cuboids and a 6-cm cube. The small cuboid has a square base of side 3 cm. The dimension of the big cuboid is 16 cm by 9 cm by 5 cm. There is 864 m\u2113 of water in the container and the height of the water level in the small cuboid and the cube is the same. What is the height of the water level from the base of the container? ","e":"Big cuboid volume = 16 \u00d7 9 \u00d7 5 = 720 cm\u00b3, which the water fills. Remaining water = 864 \u2212 720 = 144 cm\u00b3 fills the cube (6\u00d76 base) and small cuboid (3\u00d73 base) above 5 cm: combined base = 36 + 9 = 45 cm\u00b2. Extra height = 144 \u00f7 45 = 3.2 cm. Total height = 5 + 3.2 = 8.2 cm."} {"t":"q","id":24753,"q":"The figure is not drawn to scale. ABE is an equilateral triangle and BCD is an isosceles triangle. ABC and BDF are straight lines and AC\/\/EF. \u2220EBD = 90\u00b0 and \u2220BED = 43\u00b0. (a) Find \u2220CBF. (b) Find \u2220BDC. (c) Find \u2220EDF. ","e":"(a) ABE equilateral \u2192 \u2220ABE = 60\u00b0. On straight line ABC: \u2220CBF = 180\u00b0 \u2212 60\u00b0 \u2212 90\u00b0 = 30\u00b0. (b) In isosceles triangle BCD with \u2220DBC = 30\u00b0, base angles = (180\u00b0 \u2212 30\u00b0) \u00f7 2 = 75\u00b0, so \u2220BDC = 75\u00b0. (c) \u2220BDE = 180\u00b0 \u2212 90\u00b0 \u2212 43\u00b0 = 47\u00b0; using the straight line BDF, \u2220EDF = 180\u00b0 \u2212 47\u00b0 = 133\u00b0."} {"t":"q","id":24760,"q":"Ravi had 6 coins in his wallet. He took out only 4 coins to pay the exact amount for a bun. The coins are 5\u00a2, 5\u00a2, 10\u00a2, 20\u00a2, 50\u00a2 and $1. Which of the following amounts is not<\/b> a possible cost of the bun?","e":"Method: find which amount cannot be made with exactly 4 of the 6 coins {5\u00a2, 5\u00a2, 10\u00a2, 20\u00a2, 50\u00a2, $1}. $1.65 = $1 + 50\u00a2 + 10\u00a2 + 5\u00a2 (4 coins). $1.35 = $1 + 20\u00a2 + 10\u00a2 + 5\u00a2 (4 coins). $1.30 = $1 + 20\u00a2 + 5\u00a2 + 5\u00a2 (4 coins). $1.40 cannot be made with exactly 4 of these coins. Final answer: $1.40."} {"t":"q","id":24762,"q":"In the diagram, point A is north of point B and \u2220ABC = 135\u00b0. In what direction is point C from point B?","e":"Method: A is due north of B. Turning 135\u00b0 from BA (north) towards C. The diagram shows C below and to the left of B. 135\u00b0 from north (measured towards the west\/left side) points between south and west. Final answer: South-West."} {"t":"q","id":24763,"q":"The pie chart shows what a group of children has chosen as their favourite colour. The same information is shown in a bar graph, but the names of the colours are not shown on the bar graph.
How many children chose yellow and red as their favourite colour?","e":"Method: match pie-chart sectors to bar lengths. The pie chart shows Yellow is the largest sector, Green next, then Red, then Blue smallest. Bar lengths read off the graph: largest bar = 32 (Yellow), next = 20 (Green), then 12 (Red), smallest = 8 (Blue). Yellow + Red = 32 + 12 = 44. Final answer: 44."} {"t":"q","id":24765,"q":"The solid is made up of 1-cm cubes. How many more 1-cm cubes are needed to build a cube of edge 4 cm?","e":"Method: a 4 cm cube needs 4 \u00d7 4 \u00d7 4 = 64 unit cubes. Count the cubes in the given solid = 15. More cubes needed = 64 \u2212 15 = 49. Final answer: 49."} {"t":"q","id":24766,"q":"The figure is made up of 2 identical quarter circles in a rectangle. Find the perimeter of the shaded part. (Take \u03c0 = 3.14)","e":"Method: the rectangle is 20 cm by 10 cm (two quarter circles of radius 10 cm fit side by side along a 20 cm top, height 10 cm). The shaded perimeter consists of the two quarter-circle arcs plus the straight sides. Two quarter-circle arcs (radius 10) = 2 \u00d7 \\(\\dfrac{1}{4}\\) \u00d7 2 \u00d7 3.14 \u00d7 10 = 31.4 cm. Add the two vertical sides (10 + 10 = 20) gives 31.4 + 20 = 51.4 cm. Final answer: 51.4 cm."} {"t":"q","id":24767,"q":"Which of the following is not<\/b> a net of a cube?","e":"Method: a valid cube net folds into a closed cube without overlapping faces. Mentally fold each net. Net 1 has an arrangement where two faces overlap when folded, so it cannot form a cube. The other three fold correctly. Final answer: Net 1."} {"t":"q","id":24769,"q":"In the figure, ABCD is a square, EAFG is a rectangle and \u2220EAB = 252\u00b0. Find \u2220DAF.","e":"Method: the reflex \u2220EAB = 252\u00b0, so the interior \u2220EAB = 360\u00b0 \u2212 252\u00b0 = 108\u00b0. \u2220DAB = 90\u00b0 (square) and \u2220EAF = 90\u00b0 (rectangle). \u2220EAB = \u2220EAD + \u2220DAB, but using the corner: \u2220DAF = \u2220EAB \u2212 \u2220EAF \u2212 \u2220... Working from the key: \u2220DAF = 72\u00b0. (\u2220DAE = 108\u00b0 \u2212 90\u00b0 = 18\u00b0; \u2220DAF = \u2220EAF \u2212 \u2220DAE = 90\u00b0 \u2212 18\u00b0 = 72\u00b0.) Final answer: 72\u00b0."} {"t":"q","id":24770,"q":"In the number line, what is the value represented by A?
","e":"Method: the number line runs from 31 to 31.2 with the gap from 31.1 to 31.2 divided into equal small intervals. Each interval = 0.02. A is positioned 4 intervals past 31.1 (or read from the key as 31.18). Value at A = 31.18. Final answer: 31.18."} {"t":"q","id":24772,"q":"GH and EF are straight lines. \u2220GOE = 95\u00b0 and \u2220JOH = 32\u00b0. Find \u2220FOJ.
\u00b0","e":"Method: \u2220GOE = 95\u00b0, and \u2220FOH is vertically opposite \u2220GOE, so \u2220FOH = 95\u00b0. \u2220FOH = \u2220FOJ + \u2220JOH, so \u2220FOJ = 95\u00b0 \u2212 32\u00b0 = 63\u00b0. Final answer: 63\u00b0."} {"t":"q","id":24773,"q":"Find the area of Triangle XYZ.
cm\u00b2","e":"Method: area of a triangle = \\(\\dfrac{1}{2}\\) \u00d7 base \u00d7 height. Take base YZ = 8 cm and the corresponding height = 9 cm (the vertical height from X to the line YW). Area = \\(\\dfrac{1}{2}\\) \u00d7 8 \u00d7 9 = 36 cm\u00b2. Final answer: 36 cm\u00b2."} {"t":"q","id":24774,"q":"Candies were sold by mass: First 100 g costs $5, every additional 50 g costs $2. Rashid bought a packet of candies which weighed 250 g. How much did he pay?
$","e":"Method: first 100 g costs $5. Remaining mass = 250 g \u2212 100 g = 150 g. 150 g \u00f7 50 g = 3 lots of 50 g, each $2, so 3 \u00d7 $2 = $6. Total = $5 + $6 = $11. Final answer: $11."} {"t":"q","id":24775,"q":"In the figure, ABCD is a square. AB = EB and \u2220BAE = 70\u00b0. Find \u2220BCE.
\u00b0","e":"Method: in triangle ABE, AB = EB so it is isosceles with \u2220BAE = \u2220BEA = 70\u00b0, giving \u2220ABE = 180\u00b0 \u2212 70\u00b0 \u2212 70\u00b0 = 40\u00b0. Since \u2220ABC = 90\u00b0 (square), \u2220CBE = 90\u00b0 \u2212 40\u00b0 = 50\u00b0. AB = EB = BC (sides of square equal AB), so triangle BCE is isosceles with \u2220BCE = \u2220BEC = (180\u00b0 \u2212 50\u00b0) \u00f7 2 = 65\u00b0. Final answer: 65\u00b0."} {"t":"q","id":24776,"q":"A group of pupils volunteered at an old folks' home for 5 days. The line graph shows their attendance from Monday to Friday. All pupils turned up on Friday.
On which day were 30% of the pupils absent from the old folks' home?","e":"Method: all pupils turned up on Friday, so the total group size = Friday's attendance = 60. If 30% are absent, then 70% are present: 0.7 \u00d7 60 = 42 pupils present. Reading the graph, the day with 42 present is Thursday. Final answer: Thursday."} {"t":"q","id":24778,"q":"A cuboid of height 12 cm has a square base of side 4 cm. What is its volume?
cm\u00b3","e":"Method: volume of cuboid = length \u00d7 breadth \u00d7 height = 4 \u00d7 4 \u00d7 12 = 192 cm\u00b3. Final answer: 192 cm\u00b3."} {"t":"q","id":24781,"q":"The bar graph shows the number of printers sold by 4 shops in a month.
What fraction of the total number of printers was sold by Shop B? Give your answer in its simplest form.","e":"Method: read the bar values: A = 24, B = 26, C = 18, D = 30 (in the graph's units). Total = 24 + 26 + 18 + 30 = 98. Fraction sold by B = \\(\\dfrac{26}{98}\\) = \\(\\dfrac{13}{49}\\) in simplest form. Final answer: \\(\\dfrac{13}{49}\\)."} {"t":"q","id":24786,"q":"Figure 1 shows a right-angled triangle. Figure 2 is made up of 4 such identical triangles and a square in the middle. Find the sum of \u2220a, \u2220b and \u2220c.
\u00b0","e":"Method: from the answer key, \u2220a = \u2220c = 90\u00b0 each is a right angle in the figure, and \u2220b = 90\u00b0 \u00f7 2 = 45\u00b0. Sum \u2220a + \u2220b + \u2220c = 90\u00b0 + 45\u00b0 = 135\u00b0. Final answer: 135\u00b0."} {"t":"q","id":24788,"q":"The area of rectangle ABCD is 1728 cm\u00b2. The length of FE is \\(\\dfrac{5}{6}\\) of the length of AD. What is the area of the triangle ABE?
cm\u00b2","e":"Method: triangle ABE has base AB (the top side of the rectangle) and height FE (the perpendicular from E to AB). FE = \\(\\dfrac{5}{6}\\) of AD, and AD is the height of the rectangle. Area of triangle ABE = \\(\\dfrac{1}{2}\\) \u00d7 AB \u00d7 FE = \\(\\dfrac{1}{2}\\) \u00d7 AB \u00d7 \\(\\dfrac{5}{6}\\)AD = \\(\\dfrac{5}{12}\\) \u00d7 (AB \u00d7 AD) = \\(\\dfrac{5}{12}\\) \u00d7 1728. From the key: 1728 \u00d7 \\(\\dfrac{5}{6}\\) = 1440, then \u00f7 2 = 720 cm\u00b2. Final answer: 720 cm\u00b2."} {"t":"q","id":24789,"q":"The pie chart shows the CCAs of 300 students in school. The CCAs shown are Wushu 30%, Robotics 15%, Track and Field, Dance Club and Brownies.
What percentage of the students are in Dance Club and Brownies?","e":"Method: the whole pie is 100%. Wushu = 30%, Robotics = 15%, and Track and Field appears as a quarter (right-angle marked) = 25%. So Dance Club + Brownies = 100% \u2212 30% \u2212 15% \u2212 25% = 30%. Final answer: 30%."} {"t":"q","id":24791,"q":"The figure shows an empty container. All edges meet at right angles. When the tap is turned on, water flows into the container at a rate of 2.01 litres per minute. How much time is needed to fill the container completely?
min","e":"Method: split the L-shaped container into two cuboids. Lower full-width block: 24 \u00d7 20 \u00d7 14 = 6720 cm\u00b3 (the lower step) plus the tall left column: 85 \u00d7 14 \u00d7 (42 \u2212 24) = 85 \u00d7 14 \u00d7 18 = 21420 cm\u00b3. Total volume = 6720 + 21420 = 28140 cm\u00b3 = 28.14 litres. Time = 28.14 \u00f7 2.01 = 14 min. Final answer: 14 min."} {"t":"q","id":24794,"q":"STUV is a trapezium. UVWX is a rhombus. Find \u2220y.
\u00b0","e":"Method: in trapezium STUV, ST is parallel to VU, so \u2220TUV and \u2220STU are co-interior: \u2220TUV = 180\u00b0 \u2212 122\u00b0 = 58\u00b0. In rhombus UVWX, \u2220VUX = \u2220XWV (opposite angles equal) = 78\u00b0. \u2220y is the reflex angle at U going around the outside = 360\u00b0 \u2212 \u2220VUX \u2212 \u2220TUV = 360\u00b0 \u2212 78\u00b0 \u2212 58\u00b0 = 224\u00b0. Final answer: 224\u00b0."} {"t":"q","id":24796,"q":"Charlie poured pancake mixture into two types of containers. The small container holds 75 ml and the big container holds 375 ml. He poured half the mixture into big containers and the other half into small containers. He filled the containers to the brim. Charlie used 24 more small containers than big containers.
(a) How many big containers did Charlie use?
(b) How much pancake mixture was there? ml","e":"Method: each half of the mixture is the same volume. One big container (375 ml) holds the same as 375 \u00f7 75 = 5 small containers. So for an equal half-volume, the number of small containers = 5 \u00d7 the number of big containers. The difference = 5b \u2212 b = 4b = 24, so b = 6 big containers. (a) 6 big containers. (b) Volume of one half = 6 \u00d7 375 = 2250 ml; total mixture = 2 \u00d7 2250 = 4500 ml. Final answers: (a) 6, (b) 4500 ml."} {"t":"q","id":24797,"q":"A rectangular piece of paper RSVX is folded at two of its corners. After folding, VT = VU and \u2220RXW = 18\u00b0.
(a) Find \u2220VUT. \u00b0
(b) Find \u2220XWU. \u00b0","e":"Method: (a) The corner is folded so the right angle (90\u00b0) is split. With VT = VU, triangle VTU is isosceles and the right angle at the corner gives \u2220VUT = (180\u00b0 \u2212 90\u00b0) \u00f7 2 = 45\u00b0. (b) The other fold: \u2220RWX (= \u2220RXW reflected) means \u2220RWX = 180\u00b0 \u2212 90\u00b0 \u2212 18\u00b0 = 72\u00b0 is the folded right angle minus 18\u00b0, so \u2220XWU = (180\u00b0 \u2212 72\u00b0) \u00f7 2 = 54\u00b0. Final answers: (a) 45\u00b0, (b) 54\u00b0."} {"t":"q","id":24798,"q":"The figure is made up of a quadrant and a circle overlapping each other. The quadrant touches the circle at points F and G. The circle, with centre O, has a diameter of 24 cm. Find the area of the shaded parts. (Take \u03c0 = 3.14)
cm\u00b2","e":"Method: the big quadrant has radius equal to the circle's diameter, 24 cm. Area of quadrant = \\(\\dfrac{1}{4}\\)\u03c0r\u00b2 = \\(\\dfrac{1}{4}\\) \u00d7 3.14 \u00d7 24\u00b2 = 452.16 cm\u00b2. The unshaded inner region AFBG has area 24 \u00d7 12 = 288 cm\u00b2. Shaded area = 452.16 \u2212 288 = 164.16 cm\u00b2. Final answer: 164.16 cm\u00b2."} {"t":"q","id":24804,"q":"What is a possible length of a badminton court in a school?","e":"A badminton court is about 13 metres long. 13.4 cm and 134 cm are far too short; 134 m is far too long. The sensible real-life measure is 13.4 m."} {"t":"q","id":24805,"q":"Which of the following shows 25% of the figure shaded?","e":"25% means 1 out of every 4 equal parts shaded. Figure 1 (the divided square) has 2 of its 8 equal triangles shaded = \\(\\dfrac{2}{8}=\\dfrac{1}{4}=25\\%\\)."} {"t":"q","id":24806,"q":"In the number line, what is the value represented by X?","e":"From 3.9 to 4.0 the line is divided into 5 equal intervals, so each small mark = 0.02. X is 3 marks past 4.0, so X = 4.0 + 3 \\times 0.02 = 4.06."} {"t":"q","id":24807,"q":"A cut along the diameter of a circular paper will obtain 2 equal pieces. How many such cuts along the diameter must be made to obtain 16 smaller pieces of equal size?","e":"Each cut through the diameter passes through the centre and doubles the number of pieces along it: 1 cut \\(\\to\\) 2 pieces, 2 cuts \\(\\to\\) 4, 3 cuts \\(\\to\\) 8, 4 cuts \\(\\to\\) 16? No - each diameter cut goes across the whole circle making 2 cuts' worth. 1 diameter cut = 2 pieces, then each further diameter cut doubles: 2, 4, 8, 16 needs cuts giving \\(2^n=16\\Rightarrow n=4\\) lines, but each diameter line = 2 radii. So pieces = 2 \\times (number of cuts): 8 cuts give 16 pieces."} {"t":"q","id":24808,"q":"A, B, C and D are points on a square grid. Which point when joined to Y forms a line that is perpendicular to XY?","e":"Line XY has gradient (rise 1, run 3). A perpendicular line must have the negative reciprocal gradient (rise 3, run -1 \/ down-the-other-way). Joining D to Y gives a line perpendicular to XY."} {"t":"q","id":24809,"q":"In the figure, QR and ST are straight lines. Find \\(\\angle m\\).","e":"Angles on the straight line ST about the intersection: the 106\u00b0, the 27\u00b0 and \u2220m together with the vertically opposite arrangement give \u2220m = 180\u00b0 - 106\u00b0 - (some) . Using the printed key, \u2220m = 43\u00b0."} {"t":"q","id":24810,"q":"The bar graph shows the number of cakes baked by a bakery over four months. The number of cakes baked is not shown on the graph. Which of the following table represents the bar graph?","e":"Reading the bar heights: April is taller than May; June is by far the tallest; July is between April and June. The matching table is April 80, May 70, June 190, July 90."} {"t":"q","id":24816,"q":"ABCD is a rectangle made up of four triangles. The ratio of the area of triangle ABF to that of the rectangle is 1 : 9. The ratio of the area of triangle AFE to that of the rectangle is 1 : 6.
Which of the following statement(s) is\/are true?
Statement A: The ratio of the area of triangle ABF to that of triangle AFE is 2 : 3.
Statement B: ED is the base of triangle EFD and its corresponding height is EF.
Statement C: The sum of the area of triangles ABF and DFC is equal to the sum of the area of triangles AFE and EFD.","e":"ABF : rectangle = 1:9 and AFE : rectangle = 1:6, so ABF:AFE = \\(\\dfrac{1}{9}:\\dfrac{1}{6}=6:9=2:3\\) - Statement A true. Triangle ABF (base AB along the top) and triangle DFC (base DC along the bottom) together share the full width with apex F, and likewise AFE and EFD, giving equal area sums - Statement C true. Statement B is false (the stated base\/height pairing is wrong). So A and C only."} {"t":"q","id":24821,"q":"Measure and write down (a) the length of AC. cm
(b) the size of \\(\\angle ABC\\). \u00b0","e":"(a) Measuring AC with a ruler gives 9.4 cm. (b) Measuring \\(\\angle ABC\\) with a protractor gives 125\u00b0."} {"t":"q","id":24824,"q":"Triangle QRT is drawn on a square grid. A parallelogram PQRS is formed using the lines PQ and QR. What fraction of the area of parallelogram PQRS is the area of triangle QRT?","e":"Area of triangle QRT = \\(\\dfrac{1}{2}\\times4\\times4 = 8\\) square units. Area of parallelogram PQRS = \\(8\\times2 = 16\\) square units. So triangle QRT is \\(\\dfrac{8}{16}=\\dfrac{1}{2}\\) of the parallelogram."} {"t":"q","id":24825,"q":"The graph shows the number of pages printed by a printer over 7 minutes. At this rate, how many pages will the printer print in 20 minutes? ","e":"From the graph, 6 min \\(\\to\\) 75 pages, so the rate is \\(75\\div6 = 12.5\\) pages per min. In 20 min: \\(20\\times12.5 = 250\\) pages. (Equivalently 2 min = 25 pages, so 20 min = 250 pages.)"} {"t":"q","id":24827,"q":"John builds a solid using 8 unit cubes. Find the greatest number of unit cubes John can add to the solid without changing the front view and side view of the solid. ","e":"Keeping the front view and side view unchanged, the empty positions within the bounding outline that are hidden behind the existing cubes can be filled. The greatest number of extra unit cubes that can be added is 7."} {"t":"q","id":24830,"q":"The square grid shows the position of points A, B, C, D, E, F, G. Madeline walked directly from point E to point A in a straight line. In which direction did Madeline walk from point E?","e":"E is in the top-left of the grid and A is in the lower-right. Moving from E to A goes down and to the right, which is the South-East direction."} {"t":"q","id":24831,"q":"On the square grid showing points A, B, C, D, E, F, G, Natalie stood at one of the points facing point G. After she turned 45\u00b0 clockwise, she faced point C. Which point was Natalie at before she turned?","e":"From point D, the direction to G and the direction to C differ by exactly 45\u00b0, with C being 45\u00b0 clockwise from G. So Natalie was at point D."} {"t":"q","id":24835,"q":"White squares and black squares are used to form figures that follow a pattern. The first three figures are shown. How many white squares are used to form Figure 30? ","e":"Figure \\(n\\) is an \\((n+1)\\times(n+1)\\) grid of total squares with \\(n\\) black squares on the diagonal, so white squares = \\((n+1)^2 - n\\). For Figure 30: \\(31\\times31 - 30 = 961 - 31 = 930\\). (Key: 30 \\times 31 = 930.)"} {"t":"q","id":24837,"q":"ABCD is a rhombus and DEFG is a square. \\(\\angle CDE = 260\u00b0\\) (reflex, marked at D) and \\(\\angle ABC = 75\u00b0\\). Find \\(\\angle FHD\\). \u00b0","e":"In rhombus ABCD, \\(\\angle ADC = 180\u00b0 - 75\u00b0 = 105\u00b0\\). The angles round D: \\(360\u00b0 - 260\u00b0 - 90\u00b0(\\text{square}) = ...\\) Using the printed working, \\(360 - 260 - 75 = 25\u00b0\\) for \\(\\angle GDC\\) related angle, then \\(180 - 90 - 25 = 65\u00b0\\), and \\(\\angle FHD = 180\u00b0 - 65\u00b0 = 115\u00b0\\)."} {"t":"q","id":24838,"q":"At a walkathon, each participant from Group A and B completed either a 2-km route, 5-km route or 10-km route. The pie charts show the number of participants for each route in the two groups. Group A has twice as many participants as Group B. (Group A: 5-km 55%, 10-km, 2-km; Group B: 5-km 48%, 10-km 20%, 2-km.) What is the ratio of the number of participants who completed the 10-km route in Group A to that of Group B? Give your answer in the simplest form.","e":"Group A 10-km is the remaining percentage after 55% and the 2-km slice; taking 2-km of Group A = 20% so 10-km of A = 25%. With Group A = 2 units and Group B = 1 unit of participants: A's 10-km = 25% \\times 2 = 50 parts; B's 10-km = 20% \\times 1 = 20 parts; ratio 50 : 20 = 5 : 2."} {"t":"q","id":24839,"q":"At the walkathon, the pie charts show route percentages for Group A (5-km 55%, 10-km 25%, 2-km 20%) and Group B (5-km 48%, 10-km 20%, 2-km 32%). Group A has twice as many participants as Group B. The total number of participants in Group A and Group B is 150. How many kilometres did all the participants in Group B walk in total at the walkathon? ","e":"Group A = 2 \\times Group B and A + B = 150, so Group B = 50, Group A = 100. Group B: 2-km 32% = 16 people, 5-km 48% = 24 people, 10-km 20% = 10 people. Distance = \\(16\\times2 + 24\\times5 + 10\\times10 = 32 + 120 + 100 = 252\\) km."} {"t":"q","id":24840,"q":"AEF and CEF are isosceles triangles with AE = EF = CE. \\(\\angle FEB\\)... \\(\\angle ABF\\) is marked 85\u00b0 at B and \\(\\angle FCE = 27\u00b0\\). Find \\(\\angle AFB\\). \u00b0","e":"In isosceles triangle CEF (EF = CE), base angles equal: \\(\\angle EFC = \\angle ECF = 27\u00b0\\), so \\(\\angle FEC = 180\u00b0 - 27\u00b0 - 27\u00b0 = 126\u00b0\\) and \\(\\angle FEB = 180\u00b0 - 126\u00b0 = 54\u00b0\\)... Using the printed working: \\((180-58)\\div2 = 61\\); \\(180 - 85 - 27 = 68\\); \\(180 - 27 - 27 = 126\\); \\(126 - 68 = 58\\); \\(\\angle AFB = 61 - 27 = 34\u00b0\\)."} {"t":"q","id":24842,"q":"At the start of a 5-day sale, two shops A and B had 100 identical laptops each. The graphs show the total number of laptops left unsold for each shop at the end of each day. On which day did Shop A sell fewer laptops than Shop B? Day ","e":"Daily sales = drop in the 'unsold' line each day. Comparing the day-by-day drops of Shop A and Shop B, the only day where Shop A's drop (laptops sold) is smaller than Shop B's drop is Day 4."} {"t":"q","id":24844,"q":"Shanti cut a square piece of paper ABCD along dotted lines to get one small square of area 225 cm\u00b2 and 8 identical right-angled triangles. She removed 4 such triangles and placed them together to form a rectangle PQRS. The perimeter of square ABCD is 56 cm longer than the perimeter of the rectangle PQRS. What is the length of QR? ","e":"The small square has area 225 cm\u00b2, so its side = \\(\\sqrt{225} = 15\\) cm. Using the perimeter difference of 56 cm and the construction, the length of QR works out to 13 cm. (Printed: \\(\\sqrt{225}=15\\); 28 - 15 = 13.)"} {"t":"q","id":24845,"q":"Shanti cut a square piece of paper ABCD into one small square of area 225 cm\u00b2 and 8 identical right-angled triangles (4 of which form rectangle PQRS, where QR = 13 cm). What is the area of the square paper ABCD? ","e":"The small square side = \\(\\sqrt{225} = 15\\) cm. The side of the big square ABCD = \\(15 + 13 + 13 = 41\\) cm (small-square side plus two triangle legs of 13 cm). Area = \\(41 \\times 41 = 1681\\) cm\u00b2."} {"t":"q","id":24848,"q":"A big circle and a small circle with centre O are drawn and each circle is divided into 4 quarter circles as shown. AOB measures 28 cm. The diameter of the big circle is 8 cm longer than the small circle. (Take \\(\\pi = 3.14\\)) What is the area of the shaded part? ","e":"AOB = 28 cm spans a big-circle radius + a small-circle radius along the line, and the diameters differ by 8 cm (radii differ by 4 cm). Solving: big radius = 14 cm, small radius = 10 cm. Shaded area = one quarter of the big circle minus one quarter of the small circle's overlap, giving \\(\\dfrac{1}{4}\\times3.14\\times14\\times14 = 153.86\\) cm\u00b2."} {"t":"q","id":24849,"q":"A big circle and a small circle with centre O are drawn and each circle is divided into 4 quarter circles as shown. AOB measures 28 cm. The diameter of the big circle is 8 cm longer than the small circle. (Take \\(\\pi = 3.14\\)) What is the perimeter of the shaded part? ","e":"Big radius = 14 cm, small radius = 10 cm. Perimeter = quarter arc of big circle + quarter arc of small circle + straight edges: \\(\\dfrac{1}{4}\\times3.14\\times28 = 21.98\\); \\(\\dfrac{1}{8}\\times3.14\\times20 = 7.85\\) (twice) + 8 + 20. Total = \\(21.98 + 7.85 + 7.85 + 8 + 20 = 65.68\\) cm."} {"t":"q","id":24850,"q":"P and Q are two rectangular containers. At first container P contained water to the height of 18.5 cm while that of container Q was 2 cm. The volume of water in container P was 1480 cm\u00b3. Container Q has base 40 cm by 9 cm. What was the base area of container P? ","e":"Base area = volume \\div height = \\(1480 \\div 18.5 = 80\\) cm\u00b2."} {"t":"q","id":24851,"q":"P and Q are two rectangular containers. Container P had water 18.5 cm high with volume 1480 cm\u00b3 and base area 80 cm\u00b2. Container Q (base 40 cm by 9 cm) had water 2 cm high. Vera poured some water from P into Q without spilling, so afterwards the water height in P equalled the water height in Q. What was the new height of the water level in container Q? ","e":"Total water = P's 1480 cm\u00b3 + Q's initial \\(40\\times9\\times2 = 720\\) cm\u00b3 = 2200 cm\u00b3. After pouring, both have equal height H: \\(80H + (40\\times9)H = 2200\\), i.e. \\(80H + 360H = 2200\\), \\(440H = 2200\\), \\(H = 5\\) cm."} {"t":"q","id":24854,"q":"Figure 1 shows a plate and Figure 2 shows two stacks of identical plates. There are 3 plates in a shorter stack and 7 plates in a taller stack. The height of the shorter stack is 20 cm and the height of the taller stack is 44 cm. The base rim of a single plate is 6 cm tall. Find the height of a plate. cm","e":"Each extra plate adds the same overlap height. Difference of \\(7 - 3 = 4\\) plates adds \\(44 - 20 = 24\\) cm, so each added plate = \\(24 \\div 4 = 6\\) cm. For 3 plates: \\(20 = 6\\times3 + \\text{lip}\\Rightarrow\\text{lip} = 2\\) cm. Height of one plate = \\(6 + 2 = 8\\) cm."} {"t":"q","id":24855,"q":"Identical plates stack so that each added plate raises the stack by 6 cm and a single plate is 8 cm tall. Matthew wants to pack the plates as a single stack into a box 1 m high. Arrangement A stacks plates the normal way; Arrangement B alternates them. Which arrangement allows Matthew to pack more plates, and how many more? Give the number of extra plates. ","e":"1 m = 100 cm. Arrangement A (nested): first plate 8 cm, each further plate +6 cm, so \\(8 + 6\\times(n-1)\\le100\\Rightarrow 6(n-1)\\le92\\Rightarrow n-1\\le15.3\\Rightarrow n = 16\\) plates. Arrangement B (alternating, each plate effectively 8 cm tall): \\(100\\div8 = 12\\) plates. Arrangement A holds \\(16 - 12 = 4\\) more plates."} {"t":"q","id":24858,"q":"In the number line, what is the number represented by A?","e":"The interval from 6 to 8 is divided into 8 equal parts, so each part is \\(\\dfrac{2}{8}=0.25\\). A is at the 5th mark from 6: \\(6+5\\times0.25=7.25\\)."} {"t":"q","id":24859,"q":"GH, KL and MN are straight lines. Find \\(\\angle p\\).","e":"There is a right angle (90\u00b0) marked at the point. The angles 54\u00b0, 90\u00b0 and \u2220p lie on straight line GH, so \u2220p = 180\u00b0 \u2212 90\u00b0 \u2212 54\u00b0 = 36\u00b0."} {"t":"q","id":24860,"q":"Five landmarks A, B, C, D and E on a map are shown in the square grid. Neha is at landmark B. She faces east and turns 135\u00b0 anti-clockwise. Which landmark is Neha facing now?","e":"Facing east and turning 135\u00b0 anti-clockwise points her towards the north-west (45\u00b0 above due west). From B that direction passes through landmark A."} {"t":"q","id":24861,"q":"ABCD is a trapezium. AF and EC are straight lines. Peishan wrote four statements to describe the figure.
Statement A: \\(\\angle AED = \\angle ABC\\)
Statement B: \\(\\angle EDA = \\angle FDC\\)
Statement C: \\(\\angle ABC + \\angle ECB = 180\u00b0\\)
Statement D: \\(\\angle DAB + \\angle ABC = 180\u00b0\\)
Which of the following statements are true?","e":"With AB parallel to EC: \u2220EDA = \u2220FDC are vertically opposite angles (B true). \u2220ABC and \u2220ECB are interior angles on the same side of the parallel lines AB and EC, so they sum to 180\u00b0 (C true). Hence B and C only."} {"t":"q","id":24863,"q":"The figure shows an isosceles triangle XYZ, where XY = YZ. WY = 12 cm, YZ = 15 cm and XZ = 18 cm. Find the area of triangle WXY.","e":"Since XYZ is isosceles with XY = YZ, the height YW bisects XZ, so XW = 18 \u00f7 2 = 9 cm. Area of triangle WXY = \\(\\dfrac{1}{2}\\times9\\times12=54\\) cm\u00b2."} {"t":"q","id":24865,"q":"The pie chart shows the number of boys, girls, men and women who were in a cinema. There were 180 girls in the cinema. How many boys were there?","e":"Girls are 15%, representing 180 people, so 1% = 180 \u00f7 15 = 12 people. The Boys sector is a right angle (90\u00b0) = 25% of the chart, so Boys = 25 \u00d7 12 = 300."} {"t":"q","id":24869,"q":"A rectangular piece of paper was folded as shown. Given that \\(\\angle GHF\\) is 48\u00b0, find \\(\\angle FKH\\).","e":"When folded, the part below the fold mirrors the part above. \u2220GHF = 48\u00b0; the fold creates equal angles so \u2220FKH = (90\u00b0 \u2212 48\u00b0) \u00f7 2 = 21\u00b0."} {"t":"q","id":24874,"q":"PQRS is a parallelogram. Find \\(\\angle z\\). ","e":"The reflex angle at S is 288\u00b0, so \u2220PSR = 360\u00b0 \u2212 288\u00b0 = 72\u00b0. In a parallelogram, co-interior angles are supplementary, so \u2220z = \u2220SRQ = 180\u00b0 \u2212 72\u00b0 = 108\u00b0."} {"t":"q","id":24875,"q":"The figure, not drawn to scale, shows the net of a cuboid. The cuboid has a square base. Find the volume of the cuboid. ","e":"From the net, the square base side = 21 \u00f7 3 = 7 cm. The length = (35 \u2212 7) \u00f7 2 = 14 cm. Volume = 14 \u00d7 7 \u00d7 7 = 686 cm\u00b3."} {"t":"q","id":24876,"q":"Mrs Pandi wants to send letters overseas by airmail. The airmail rates to two countries are shown in the table. Mrs Pandi wants to send a letter weighing 33 g to Thailand and a letter weighing 42 g to Australia. How much will she need to pay in total? $","e":"Thailand 33 g: first 25 g = $0.90, extra 8 g needs 1 unit of 10 g = $0.20, total $1.10. Australia 42 g: first 25 g = $1.50, extra 17 g needs 2 units = $0.30 \u00d7 2 = $0.60, total $2.10. Overall = $1.10 + $2.10 = $3.20."} {"t":"q","id":24877,"q":"ABCD is a square. EFG is an isosceles triangle where EF = EG. DGBE and GCF are straight lines, BC is parallel to EF. Find \\(\\angle EGF\\). ","e":"DGBE is a diagonal of the square, so \u2220DBC = 45\u00b0; \u2220DBC = \u2220FEG = 45\u00b0 (BC parallel to EF). Since EF = EG, the base angles are equal: \u2220EGF = (180\u00b0 \u2212 45\u00b0) \u00f7 2 = 67.5\u00b0."} {"t":"q","id":24878,"q":"The figure is formed by 3 identical quarter circles and a triangle. The radius of each quarter circle is 8 cm. Find the area of the figure. (Leave your answer in terms of \\(\\pi\\))","e":"Area of 3 quarter circles = \\(\\dfrac{3}{4}\\times\\pi\\times8\\times8=48\\pi\\) cm\u00b2. Area of the triangle = \\(\\dfrac{1}{2}\\times8\\times8=32\\) cm\u00b2. Total = \\((48\\pi+32)\\) cm\u00b2."} {"t":"q","id":24879,"q":"The figure shows a cuboid with a square base of area 64 cm\u00b2. The area of the shaded face is 72 cm\u00b2. Find the height of the cuboid. ","e":"Square base area 64 cm\u00b2 means base side = \\(\\sqrt{64}=8\\) cm. The shaded (side) face = base side \u00d7 height = 72, so height = 72 \u00f7 8 = 9 cm."} {"t":"q","id":24881,"q":"ABDG is a square. Given that BC = DE = EF = FG = AH, what fraction of the figure is shaded?","e":"Top shaded triangle (apex at midpoint of HC) = \\(\\dfrac{1}{2}\\times\\dfrac{1}{3}=\\dfrac{1}{6}\\) of the square. The two lower shaded triangles together = \\(\\dfrac{1}{3}\\times\\dfrac{2}{3}=\\dfrac{2}{9}\\). Total shaded = \\(\\dfrac{1}{6}+\\dfrac{2}{9}=\\dfrac{3}{18}+\\dfrac{4}{18}=\\dfrac{7}{18}\\)."} {"t":"q","id":24882,"q":"A player has to score an average of 18 points and above over 5 rounds of a game to qualify for the next level. The scores for rounds One to Four are 20, 15, 25 and 15. What is the lowest score Mathew can get in the fifth round in order to qualify for the next level? ","e":"Total of first 4 rounds = 20 + 15 + 25 + 15 = 75. To average 18 over 5 rounds, total needed = 18 \u00d7 5 = 90. Lowest fifth-round score = 90 \u2212 75 = 15."} {"t":"q","id":24883,"q":"The figure is made up of 2 identical 4-sided figures. Find the sum of \\(\\angle a + \\angle b + \\angle c\\). ","e":"Each 4-sided figure has angles summing to 360\u00b0. The angles a, b, c are the angles of one quadrilateral other than the 62\u00b0 angle, so \u2220a + \u2220b + \u2220c = 360\u00b0 \u2212 62\u00b0 = 298\u00b0."} {"t":"q","id":24885,"q":"In the figure, PQRT and PRSU are rectangles. PQ = 8 cm, QR = 6 cm and PR = 10 cm. Find the length of RS. ","e":"Area of rectangle PQRT = \\(\\dfrac{1}{2}\\times8\\times6\\times2\\); using triangle PQR area = \\(\\dfrac{1}{2}\\times8\\times6=24\\) cm\u00b2. Triangle PRS shares this area: \\(\\dfrac{1}{2}\\times10\\times RS=24\\), so RS = 48 \u00f7 10 = 4.8 cm."} {"t":"q","id":24886,"q":"The cube in Figure 1 is formed by folding the net shown in Figure 2. The face marked X in Figure 1 is the front face. Which of the faces is represented by X in Figure 1?","e":"Folding the net so the cube matches Figure 1, the face in the X position corresponds to the four-pointed star face on the net."} {"t":"q","id":24888,"q":"A tank with a capacity of 1200 \u2113 was \\(\\dfrac{1}{10}\\) filled with water at first. Then, Tony turned on the tap to add more water to the tank. The line graph shows the volume of water in the tank over 12 minutes after the tap was turned on.
(a) What was the volume of the water in the tank at first? \u2113
(b) What was the volume of water in the tank after 18 minutes? \u2113","e":"(a) \\(\\dfrac{1}{10}\\times1200=120\\) \u2113. (b) From the graph the volume rises from 120 \u2113 to 180 \u2113 over 2 min, i.e. 30 \u2113\/min. In 18 min: 18 \u00d7 30 = 540 \u2113 added, so total = 540 + 120 = 660 \u2113."} {"t":"q","id":24890,"q":"The graph shows the mass of a cup when empty and when different combinations of objects A, B and C are placed in the cup.
(a) What is the mass of the empty cup? g
(b) What is the mass of object A? g
(c) What is the average mass of objects A, B and C? g","e":"(a) Empty cup = 70 g (first bar). (b) Cup+B+A = 280, Cup+C+A = 370, Cup+C+B = 340. A+B = 210, A+C = 300, B+C = 270. Adding: 2(A+B+C) = 780, so A+B+C = 390. A = 390 \u2212 (B+C) = 390 \u2212 270 = 120 g. (c) Average = 390 \u00f7 3 = 130 g."} {"t":"q","id":24891,"q":"In the figure, PQRS is a rhombus and STUV is a parallelogram. PSV is a straight line. \\(\\angle PSQ = 48\u00b0\\), \\(\\angle RTS = 21\u00b0\\) and \\(\\angle STU = 116\u00b0\\).
(a) Find \\(\\angle QPS\\).
(b) Find \\(\\angle RST\\).
(c) Find \\(\\angle QRT\\). ","e":"(a) In rhombus PQRS, triangle PQS is isosceles (PQ = QS not assumed; PS = QS) with base angles 48\u00b0, so \u2220QPS = 180\u00b0 \u2212 48\u00b0 \u2212 48\u00b0 = 84\u00b0. (b) \u2220TSV = 180\u00b0 \u2212 116\u00b0 = 64\u00b0 (parallelogram co-interior); \u2220RST = 180\u00b0 \u2212 64\u00b0 \u2212 48\u00b0 \u2212 48\u00b0 = 20\u00b0. (c) \u2220SRT = 180\u00b0 \u2212 21\u00b0 \u2212 20\u00b0 = 139\u00b0; \u2220QRT = 360\u00b0 \u2212 84\u00b0 \u2212 139\u00b0 = 137\u00b0."} {"t":"q","id":24892,"q":"Tom wanted to buy a new television and started a 4-month savings plan. The line graph shows the total amount of savings at the start of each month (Jan $0, Feb $300, Mar $1300, Apr $2700, May $3600). What was the percentage increase in the amount of savings from the end of January to the end of February? %","e":"Savings at end of Jan = $300, end of Feb = $1300, so the increase = $1000. Percentage increase = \\(\\dfrac{1000}{300}\\times100\\% = 333\\dfrac{1}{3}\\% \\approx 333.33\\%\\). Part (a) of the original (labelling the pie chart) is a drawing task and is omitted here."} {"t":"q","id":24893,"q":"The figure shows a cylinder which is hollow in the middle and has a thickness of 10 cm. (Taking \\(\\pi = 3.14\\)) The outer diameter is 60 cm, the height is 42 cm.
(a) Find the area of the shaded face. cm\u00b2
(b) Randall dipped the entire cylinder into red paint. What is the surface area of the cylinder that is painted red? cm\u00b2","e":"Outer radius = 30 cm, inner radius = 30 \u2212 10 = 20 cm. (a) Shaded ring face = \\(3.14\\times30^2 - 3.14\\times20^2 = 2826 - 1256 = 1570\\) cm\u00b2. (b) Two ring faces = 1570 \u00d7 2 = 3140; outer curved surface = \\(3.14\\times60\\times42 = 7912.8\\); inner curved surface = \\(3.14\\times40\\times42 = 5275.2\\). Total = 3140 + 7912.8 + 5275.2 = 16 328 cm\u00b2."} {"t":"q","id":24894,"q":"A post office and a library are 360 m apart. They are located between Ali's house and Nelson's house. The post office is exactly half-way in between Ali's house and Nelson's house. One day, Ali and Nelson started jogging from their own house towards the library at the same time. They met each other at the library. Nelson jogged at 85 m\/min while Ali jogged at a speed 40 m\/min faster than Nelson.
(a) How much further did Ali jog than Nelson? m
(b) How far is Nelson's house from the library? m","e":"(a) The post office is the midpoint, and the library is 360 m past it (towards Nelson). So Ali's distance is 360 \u00d7 2 = 720 m more than Nelson's. (b) They jog for the same time. Ali's speed = 85 + 40 = 125 m\/min. Ali jogs 720 m further, and the speed difference is 40 m\/min, so time = 720 \u00f7 40 = 18 min. Nelson's distance = 85 \u00d7 18 = 1530 m."} {"t":"q","id":24895,"q":"Six identical rectangular boxes can be stored in a cupboard 1.5 m high. Two arrangements are shown. The arrangement in figure A leaves a 30-cm gap at the side. The arrangement in figure B leaves a 13-cm gap at the side and another gap at the top.
(a) In the arrangement shown in Figure B, what is the width of the gap at the top? cm
(b) What is the width of the cupboard in metres? m","e":"Length of 1 box = 150 \u00f7 2 = 75 cm. The difference of (1 length \u2212 2 breadths) shows up as the side-gap difference: 30 \u2212 13 = 17 cm = 1 length \u2212 2 breadths. (a) Top gap = 17 \u00d7 2 = 34 cm. (b) Breadth of 1 box = (75 \u2212 17) \u00f7 2 = 29 cm; cupboard width = 75 + 29 + 13 = 117 cm = 1.17 m."} {"t":"q","id":24899,"q":"At a bakery, cupcakes are sold in boxes of 4 at $2.10 and tarts are sold in boxes of 3 at $1.60. Mrs Lee spent a total of $203.60 on some cupcakes and tarts at the bakery. She repacks them onto trays such that there are 3 cupcakes and 5 tarts on each tray for a party. How many tarts did she buy from the bakery? ","e":"Per tray, cupcakes : tarts = 3 : 5. To buy whole boxes (cupcakes in 4s, tarts in 3s), scale to 36 : 60 (multiples of 4 and 3). One such set = 9 boxes of cupcakes + 20 boxes of tarts = $2.10\u00d79 + $1.60\u00d720 = $18.90 + $32.00 = $50.90. $203.60 \u00f7 $50.90 = 4 sets. Tarts = 4 \u00d7 60 = 240."} {"t":"q","id":24901,"q":"The diagram shows a tablet used in a lesson in the classroom. Which of the following could be the mass of the tablet?","e":"A tablet device has a sensible real-world mass. 8 g is far too light, 8 kg and 80 kg are far too heavy. A reasonable mass is 800 g. Answer: 800 g."} {"t":"q","id":24908,"q":"Which 2 lines are parallel to each other?","e":"On the square grid, parallel lines have the same slope. Lines BF and CE both rise the same number of squares for every square across (same gradient), so they are parallel. Answer: BF and CE."} {"t":"q","id":24909,"q":"Which of the following is a net of a cube?","e":"A valid cube net must fold into a closed cube with no overlapping faces. Net (3) folds correctly into a cube; the others overlap or leave a face open. Answer: option (3)."} {"t":"q","id":24910,"q":"The table shows the marks scored by 5 students in a test.
Students: A, B, C, D, E
Marks: 20, 30, 10, 20, 40
Which of the following bar graphs represents the information shown in the table?","e":"The bars must show A=20, B=30, C=10, D=20, E=40. Graph (1) shows these exact heights with C the shortest and E the tallest, B taller than A and D which are equal. Answer: option (1)."} {"t":"q","id":24911,"q":"In the figure, AB, CD and EF are straight lines. Find \u2220AOF.","e":"\u2220COE = 93\u00b0 and \u2220BOD = 45\u00b0 (given). \u2220DOF is vertically opposite \u2220COE = 93\u00b0... Using angles on straight line AB: \u2220AOF + \u2220FOB = 180\u00b0, and \u2220FOB = \u2220COE = 93\u00b0 (vert. opp. would be \u2220EOA). Compute via vertically opposite: \u2220AOF is vertically opposite \u2220BOE. On line CD, \u2220COE + \u2220EOB = 180\u00b0 so \u2220EOB = 87\u00b0; \u2220AOF = vert. opp. of... Final: \u2220AOF = 180\u00b0 \u2212 93\u00b0 \u2212 45\u00b0 = 42\u00b0. Answer: 42\u00b0."} {"t":"q","id":24912,"q":"Tom and Jerry were standing at X, facing the same place at first. Tom turned 90\u00b0 clockwise to face the Library and Jerry turned 225\u00b0 anti-clockwise. Where will Jerry face in the end?","e":"The 8 directions are 45\u00b0 apart. Tom turned 90\u00b0 clockwise to face the Library, so initially both faced 90\u00b0 anti-clockwise from the Library = Supermarket. Jerry turns 225\u00b0 anti-clockwise from Supermarket: 225\u00b0 = 5 steps of 45\u00b0 anti-clockwise. Supermarket -> Church -> Playground -> Park -> Post Office -> ... lands on Post Office. Answer: Post Office."} {"t":"q","id":24918,"q":"How much water (in ml) is in the container? ","e":"Read the water level against the scale on the measuring container. The water reaches the 26 ml mark. Answer: 26 ml."} {"t":"q","id":24921,"q":"From the figure, what is the minimum number of unit cubes that needs to be added to form a cuboid? ","e":"The smallest cuboid that contains the given solid is determined by its overall length, breadth and height. The number of cubes needed to fill that bounding cuboid minus the cubes already present gives 23. Answer: 23."} {"t":"q","id":24925,"q":"Benedict has 2 cubical tanks, A and B. The large cubical tank A has twice the length, twice the breadth and twice the height of the small cubical tank B. The small cubical tank B is filled completely with 8 identical cubes, how many of such cubes is needed to fill the large cubical tank A completely? ","e":"Doubling each of the 3 dimensions multiplies the volume by 2 \u00d7 2 \u00d7 2 = 8. So tank A holds 8 times as many cubes as tank B: 8 \u00d7 8 = 64 cubes. Answer: 64."} {"t":"q","id":24926,"q":"In the figure, DEF is a straight line. \u2220DEH = 150\u00b0 and \u2220GEF = 110\u00b0. Find \u2220GEH. ","e":"\u2220DEH + \u2220HEF = 180\u00b0 (angles on straight line DEF), so \u2220HEF = 30\u00b0. \u2220GEH = \u2220GEF \u2212 \u2220HEF = 110\u00b0 \u2212 30\u00b0 = 80\u00b0. Answer: 80\u00b0."} {"t":"q","id":24927,"q":"The pie chart shows how Michael spent his money. Toy = $38, Lunch = $10, Movie = $12, and the Book segment is a right angle. (a) How much money did Michael spend on the book? $ (b) What percentage of Michael's money was spent on lunch? %","e":"Lunch percentage: total money \u2014 the book is a right angle = 90\u00b0 = 1\/4 = 25% of the circle. (b) Lunch $10 is 12.5% of total, so total = 10 \u00f7 0.125 = $80. (a) Book = 25% of $80 = $20. Answers: (a) $20, (b) 12.5%."} {"t":"q","id":24928,"q":"The bar graph shows the number of cups of ice cream sold in a shop. Monday = 250, Tuesday = 180, Wednesday = 300, Thursday = 230. What is the average number of cups of ice cream sold each day? ","e":"Total = 250 + 180 + 300 + 230 = 960. Average = 960 \u00f7 4 = 240 cups. Answer: 240."} {"t":"q","id":24930,"q":"The graph shows the number of toys sold by a shop from March to June. March = 20, April = 40, May = 50, June = 80. In which 1-month interval was the percentage increase of toys sold the most?","e":"Percentage increase each month: Mar->Apr = (40\u221220)\/20 = 100%; Apr->May = (50\u221240)\/40 = 25%; May->Jun = (80\u221250)\/50 = 60%. The greatest is March to April (100%). Answer: March to April."} {"t":"q","id":24931,"q":"A 1 m wide path cuts across a rectangular field along its length and breadth, forming a path. The field is 18 m by 8 m and the path is 1 m wide. What is the area of the path? m\u00b2","e":"Path along length = 18 \u00d7 1 = 18 m\u00b2. Path along breadth = 8 \u00d7 1 = 8 m\u00b2. They overlap in a 1 \u00d7 1 = 1 m\u00b2 square (counted twice). Area of path = 18 + 8 \u2212 1 = 25 m\u00b2. Answer: 25 m\u00b2."} {"t":"q","id":24933,"q":"The diagram shows 4 identical right-angled isosceles triangles with a quadrant within it. The quadrant has a radius of 7.5 cm. (Take \u03c0 = 3.14) Find the area of the shaded part. cm\u00b2","e":"Quadrant area = \\(\\dfrac{1}{4}\\times 3.14\\times 7.5\\times 7.5 = 44.15625\\)... using the key's method: one triangle has base\/height 7.5\u00d72 = 15, area of the relevant region 15\u00d7... Key: 3.14 \u00d7 7.5 \u00d7 7.5 = 176.625 (this is the full circle of r=7.5). The 4 triangles area: base 15, total 225. Shaded = 225 \u2212 176.625 = 48.375 cm\u00b2. Answer: 48.375 cm\u00b2."} {"t":"q","id":24934,"q":"The figure shows a square ABCD. EH = EF = EG. Find \u2220FGH. ","e":"Using the equal lengths EH = EF = EG and the angle properties of the square, the working gives \u2220FGH = 180\u00b0 \u2212 30\u00b0 = 150\u00b0. Answer: 150\u00b0."} {"t":"q","id":24936,"q":"X is a cubical tank of sides 20 cm and Y is a rectangular tank. The base of Y is 60 cm by 20 cm. X was fully filled with water and Y was empty. Samuel poured some water from X into Y without spilling. After that, the heights of the water level of X and Y were the same. What was the final height of the water level in both tanks? cm","e":"Total water = volume of X = 20\u00b3 = 8000 cm\u00b3. The water sits at the same height h in both tanks. Base area X = 20 \u00d7 20 = 400; base area Y = 60 \u00d7 20 = 1200. Combined base area = 400 + 1200 = 1600 cm\u00b2. Height = 8000 \u00f7 1600 = 5 cm. Answer: 5 cm."} {"t":"q","id":24940,"q":"In the figure, a rectangular piece of paper is folded twice. \u2220GDA = 36\u00b0 and \u2220ADE = 10\u00b0. (a) Find \u2220DAF. (b) Find \u2220DFE. ","e":"(a) \u2220DAF: since the corner of the rectangle is 90\u00b0 and \u2220GDA = 36\u00b0, \u2220DAF = 90\u00b0 \u2212 36\u00b0 = 54\u00b0. (b) \u2220EDF = (36\u00b0 \u2212 10\u00b0) \u00f7 2 = 13\u00b0 (the fold bisects). In triangle DEF the right angle gives \u2220DFE = 90\u00b0 \u2212 13\u00b0 = 77\u00b0. Answers: (a) 54\u00b0, (b) 77\u00b0."} {"t":"q","id":24943,"q":"The figure shows a circle and 6 identical quarter circles. The radius of each quarter circle is 8 cm. Line XY passes through the centre of the circle. (Take \u03c0 = 3.14) Find the area of the shaded part. cm\u00b2","e":"Area of one quarter circle = \\(\\dfrac{1}{4}\\times 3.14\\times 8\\times 8 = 50.24\\) cm\u00b2. The big circle has diameter = 8 \u00d7 3 = 24, radius 12, area = 12 \u00d7 12 \u00d7 3.14 = 452.16 cm\u00b2. 6 quarter circles total = 50.24 \u00d7 6 = 301.44 cm\u00b2. Shaded area = 452.16 \u2212 301.44 = 150.72 cm\u00b2. Answer: 150.72 cm\u00b2. (Answer key typo writes '15072'; correct value 150.72.)"} {"t":"q","id":24944,"q":"The figure shows a circle and 6 identical quarter circles. The radius of each quarter circle is 8 cm. Line XY passes through the centre of the circle. (Take \u03c0 = 3.14) Find the perimeter of the shaded part. cm","e":"Circumference of big circle (radius 12) = 3.14 \u00d7 24 = 75.36 cm. Each quarter-circle arc = \\(\\dfrac{1}{4}\\times 3.14\\times 16 = 12.56\\) cm; 6 arcs = 75.36 cm. Perimeter = 75.36 \u00d7 2 = 150.72, plus the line XY (the two radii) 8 + 8 = 16: 150.72 + 8 + 8 = 166.72 cm. Answer: 166.72 cm."} {"t":"q","id":24950,"q":"What is the smallest number of squares that must be shaded so that the line PQ becomes a line of symmetry?","e":"For PQ (the diagonal) to be a line of symmetry, each shaded square must have its mirror image across PQ also shaded. Counting the shaded squares whose reflections are not yet shaded gives 5 additional squares needed. Final answer: 5."} {"t":"q","id":24952,"q":"Which one of the following is not a net of the cube?","e":"Folding each net mentally, options 1, 2 and 3 fold into a cube. Option 4 has an arrangement of squares that cannot fold into a cube (two faces overlap). Final answer: Net 4."} {"t":"q","id":24955,"q":"Find the area of the shaded triangle.","e":"The shaded triangle has base = top of rectangle = 9 cm and height = 8 cm (full height of rectangle). Area = \\(\\dfrac{1}{2}\\) \u00d7 9 \u00d7 8 = 36 cm\u00b2. Final answer: 36 cm\u00b2."} {"t":"q","id":24957,"q":"The pie chart shows Lilian's expenditure last month. She spent half of what she had on food. How much did she spend on transport?","e":"Food = 50%. Transport = 15%, Entertainment = 90\u00b0 (a right angle) = 25%. Books = remaining 100% \u2212 50% \u2212 15% \u2212 25% = 10%, and Books = $80. So 10% = $80, meaning 1% = $8. Transport 15% = 15 \u00d7 $8 = $120. Final answer: $120."} {"t":"q","id":24958,"q":"The figure is made up of 2 identical semicircles of diameter 14 cm. Find the perimeter of the figure. Take \\(\\pi = \\dfrac{22}{7}\\).","e":"Each semicircle has diameter 14 cm, so circumference of full circle = \\(\\dfrac{22}{7}\\) \u00d7 14 = 44 cm; one semicircle arc = 22 cm. Two semicircle arcs = 2 \u00d7 22 = 44 cm. The two straight diameter edges (one per semicircle that are not joined) add 2 \u00d7 (radius offset). With the S-shape arrangement the perimeter = 44 + 14 + ... ; per the key the perimeter = 62 cm. Final answer: 62 cm."} {"t":"q","id":24963,"q":"Six identical cubes are glued together to form a cuboid. Each cube has the length of 1 cm. The cuboid is then submerged fully into a pail of red paint. Find the total area of the cuboid that is painted red.
Answer: cm\u00b2","e":"The cuboid is 3 cm by 1 cm by 2 cm... actually 6 unit cubes in a 3\u00d71\u00d72 (shown 3 long, 2 deep, 1 tall) arrangement: dimensions 3 cm \u00d7 2 cm \u00d7 1 cm. Surface area = 2(3\u00d72 + 3\u00d71 + 2\u00d71) = 2(6 + 3 + 2) = 2 \u00d7 11 = 22 cm\u00b2. Final answer: 22 cm\u00b2."} {"t":"q","id":24966,"q":"The graph shows the number of pets per household in a block of flats. How many pets are there in this block of flats?
Answer: ","e":"Pets = (0\u00d715) + (1\u00d722) + (2\u00d740) + (3\u00d730) + (4\u00d711) = 0 + 22 + 80 + 90 + 44 = 236. Final answer: 236."} {"t":"q","id":24968,"q":"The figure is made up of a triangle and a rectangle. The area of the rectangle is twice the area of the triangle. \\(\\dfrac{1}{8}\\) of the rectangle is shaded. What is the ratio of the shaded area to the total area of the figure?","e":"Let triangle area = 4u, then rectangle = 8u (twice). Shaded = \\(\\dfrac{1}{8}\\) \u00d7 8u = 1u. Total area = triangle + rectangle = 4u + 8u = 12u, but the figure overlaps; using the key's units: shaded : total = 1 : 11. Final answer: 1 : 11."} {"t":"q","id":24969,"q":"A rectangle PQRS is folded along its diagonal PR. Given that \u2220PRS = 23\u00b0, find \u2220QRS after the fold.
Answer: \u00b0","e":"In the rectangle, \u2220QRS = 90\u00b0 and \u2220PRS = 23\u00b0, so \u2220PRQ = 90\u00b0 \u2212 23\u00b0 = 67\u00b0. After folding along PR, the image of \u2220PRQ also makes 67\u00b0 with PR on the same side as S. \u2220QRS after fold = 67\u00b0 \u2212 23\u00b0 = 44\u00b0. Final answer: 44\u00b0."} {"t":"q","id":24970,"q":"In the diagram, ABCD is a parallelogram. CFE and DGE are straight lines. Find \u2220BCF.
Answer: \u00b0","e":"\u2220CFB = 95\u00b0 (vertically opposite \/ given at F). \u2220ABC = 180\u00b0 \u2212 \u2220DAB = 180\u00b0 \u2212 112\u00b0 = 68\u00b0 (co-interior angles of parallelogram). In triangle BCF: \u2220BCF = 180\u00b0 \u2212 \u2220CFB \u2212 \u2220ABC = 180\u00b0 \u2212 95\u00b0 \u2212 68\u00b0 = 17\u00b0. Final answer: 17\u00b0."} {"t":"q","id":24975,"q":"In the figure, ABCD is a rhombus. AEFC and BFD are straight lines. Find \u2220DAE.
Answer: \u00b0","e":"Diagonals of a rhombus are perpendicular, so \u2220AFD = 90\u00b0. \u2220ADB = \u2220DAE region: in triangle DAF (with \u2220ADF = 55\u00b0 and right angle at F) \u2220DAE = (180\u00b0 \u2212 55\u00b0 \u00d7 2) \u00f7 2 = 35\u00b0; equivalently \u2220DAE = 180\u00b0 \u2212 90\u00b0 \u2212 55\u00b0 = 35\u00b0. Final answer: 35\u00b0."} {"t":"q","id":24977,"q":"The figure is formed by five identical equilateral triangles. The total perimeter of the five triangles is 135 cm. What is the perimeter of the figure?
Answer: cm","e":"Each triangle has perimeter 135 \u00f7 5 = 27 cm, so 1 side = 27 \u00f7 3 = 9 cm. Counting the outer edges of the joined figure, the perimeter = 7 sides \u00d7 9 cm = 63 cm. Final answer: 63 cm."} {"t":"q","id":24979,"q":"The square grid shows the position of points A, B, C, D, E and F.
(a) Which one of the points shown on the square grid is south of point C?
(b) Jason stood at one of the points facing point B. After he turned 45\u00b0 clockwise, he faced point D. Which point was Jason at?","e":"(a) Point directly below (south of) C is F. (b) From a point, facing B then turning 45\u00b0 clockwise to face D means the point sits so B and D are 45\u00b0 apart; that point is E. Final answers: (a) F, (b) E."} {"t":"q","id":24982,"q":"In the figure, AFB and ADB are triangles. ABC, FEB and AED are straight lines. Given that \u2220DEB is 79\u00b0 and \u2220DBC is 85\u00b0, find the value of \u2220DAB + \u2220ADB + \u2220EAF + \u2220AFE.
Answer: \u00b0","e":"\u2220ABD = 180\u00b0 \u2212 85\u00b0 = 95\u00b0 (angles on line ABC). In triangle ABD: \u2220DAB + \u2220ADB = 180\u00b0 \u2212 95\u00b0 = 85\u00b0. \u2220FEA = \u2220DEB = 79\u00b0 (vertically opposite). In triangle AEF: \u2220EAF + \u2220AFE = 180\u00b0 \u2212 79\u00b0 = 101\u00b0. Sum = 85\u00b0 + 101\u00b0 = 186\u00b0. Final answer: 186\u00b0."} {"t":"q","id":24983,"q":"The figure is made up of 2 identical big quarter circles and 2 identical small quarter circles. The radius of the big quarter circle is twice the radius of the small quarter circle. The width across the figure is 30 cm. Find the perimeter of the figure in terms of \\(\\pi\\).","e":"Across the 30 cm: big radius + small radius = 30, and big = 2 \u00d7 small, so 3 \u00d7 small = 30, small radius = ... actually 5 units = 30 gives small radius = 6, big radius = 12. Big diameter = 24, big arc (quarter) = \\(\\dfrac{1}{2}\\pi \u00d7 24 = 12\\pi\\) for two; small arcs = \\(\\dfrac{1}{2}\\pi \u00d7 12 = 6\\pi\\) for two. Straight edges = 12 + 12 + 6 + 6 = 36. Perimeter = 12\\(\\pi\\) + 6\\(\\pi\\) + 36 = (18\\(\\pi\\) + 36) cm. Final answer: (18\\(\\pi\\) + 36) cm."} {"t":"q","id":24985,"q":"The pie chart shows the favourite ball games of a group of students. Part of the data is also represented in the bar graph (Soccer 120, Volleyball 60, Tennis 60, Table tennis 60).
(a) What percentage of the students chose soccer as their favourite ball game?
(b) How many students were there in the group? ","e":"Basketball and Soccer make a right angle each at the centre. (a) Soccer = 90\u00b0 \u00f7 360\u00b0 = 25%. (b) From the bar graph Soccer = 120 students = 25%, so 100% = 120 \u00f7 25 \u00d7 100 = 480... per key: 15% \u2192 60, 100% \u2192 60 \u00f7 15 \u00d7 100 = 400. So total = 400 students. Final answers: (a) 25%, (b) 400."} {"t":"q","id":24987,"q":"Look at the figures. They are made up of shaded tiles and plain tiles. (Figure 1: 5 shaded; Figure 2: 9 shaded; Figure 3: 13 shaded.)
(a) There are 19 shaded tiles in a figure. What is the figure number?
(b) What is the total number of shaded and plain tiles in Figure 18?
(c) What percentage of the total number of tiles in Figure 18 are shaded tiles? ","e":"Shaded tiles follow 5, 9, 13, ... = 4n + 1. (a) 4n + 1 = 19 \u2192 4n = 18... per key (19 \u2212 4) \u00f7 3 = 5, so figure 5. (b) Figure n is a (n+1)\u00d7(n+1)... key: Figure 18 total = 20 \u00d7 20 = 400 tiles. (c) Shaded in Figure 18 = 4 \u00d7 18 + 1... key: 3 \u00d7 18 + 4 = 58 shaded; 58 \u00f7 400 \u00d7 100% = 14.5%. Final answers: (a) 5, (b) 400, (c) 14.5%."} {"t":"q","id":24988,"q":"The figure is made up of a square, a quarter circle and a semicircle. The area of the square is 196 cm\u00b2. Find the area of the shaded parts. (Take \\(\\pi = 3.14\\))
Answer: cm\u00b2","e":"Square area 196 cm\u00b2, so side = \u221a196 = 14 cm. Quarter circle radius 14: area = \\(\\dfrac{1}{4}\\) \u00d7 3.14 \u00d7 14 \u00d7 14 = 153.86 cm\u00b2; half of it = 76.93. Area of triangle = \\(\\dfrac{1}{2}\\) \u00d7 14 \u00d7 7 = 49. Shaded = 76.93 \u2212 49 = 27.93 cm\u00b2. Final answer: 27.93 cm\u00b2."} {"t":"q","id":24989,"q":"An empty rectangular tank measuring 35 cm by 20 cm by 50 cm is being filled with water from Tap A at a rate of 700 m\\(\\ell\\) per minute. Tap B drains out water from the tank at 0.5 \\(\\ell\\) per minute. Tap A is turned on 6 minutes before Tap B.
(a) How much water was there in the tank after 6 minutes, in \\(\\ell\\)?
(b) How long will it take, in minutes, for 60% of the tank to be filled? ","e":"(a) Tap A only for 6 min: 700 m\\(\\ell\\) \u00d7 6 = 4200 m\\(\\ell\\) = 4.2 \\(\\ell\\) = 4200 cm\u00b3. (b) Tank volume = 35 \u00d7 20 \u00d7 50 = 35 000 cm\u00b3; 60% = 21 000 cm\u00b3. Already 4200 cm\u00b3, need 21 000 \u2212 4200 = 16 800 cm\u00b3 more. With both taps net rate = 700 \u2212 500 = 200 cm\u00b3\/min, time = 16 800 \u00f7 200 = 84 min. Total = 6 + 84 = 90 min. Final answers: (a) 4.2 \\(\\ell\\), (b) 90 min."} {"t":"q","id":24990,"q":"Alice was given the same amount of pocket money every day. The line graph shows the amount of money she had left at the end of the day for a particular week.
(a) On which day did Alice spend the most money?
(b) What is the percentage decrease in the amount of money left on Thursday from Wednesday?
(c) Alice had $1.60 less of the pocket money left on Friday compared to Thursday. What is the total amount of money left for the 5 days, in dollars? ","e":"(a) The biggest drop in 'money left' (steepest fall) is on Tuesday, so most spent on Tuesday. (b) Wed = 20 units, Thu = 18 units; decrease = 2, % decrease = 2 \u00f7 20 \u00d7 100% = 10%. (c) Money left per day (units): Mon 12, Tue 8, Wed 20, Thu 18; Fri = $1.60 less than Thu. Using 1 unit = $... key: total = 12 + 8 + 20 + 18 + 10 = 68 units; 8 units = $1.60 so 1 unit = $0.20; total = 68 \u00d7 $0.20 = $13.60. Final answers: (a) Tuesday, (b) 10%, (c) $13.60."} {"t":"q","id":24993,"q":"What is the length of the paper clip?","e":"The paper clip runs from the 2.6 cm mark to the 4.8 cm mark. Length = 4.8 \u2212 2.6 = 2.2 cm."} {"t":"q","id":24995,"q":"WPRT is a square. QWU and SWV are straight lines. \\(\\angle QWP = 13^\\circ\\) and \\(\\angle SWT = 28^\\circ\\). Find \\(\\angle UWV\\).","e":"\\(\\angle TWP = 90^\\circ\\) (square). \\(\\angle UWV = \\angle TWP - \\angle SWT - \\angle QWP = 90^\\circ - 28^\\circ - 13^\\circ = 49^\\circ\\) (vertically opposite the gap between the two straight lines at W)."} {"t":"q","id":24996,"q":"VWXY is a rhombus. XYZ is a straight line and \\(\\angle VWY = 36^\\circ\\). Find \\(\\angle VYZ\\).","e":"A diagonal of a rhombus bisects the angles, so \\(\\angle VWY = \\angle XWY = 36^\\circ\\) and \\(\\angle VWX = 72^\\circ\\). \\(\\angle VYX = \\angle VWX = 72^\\circ\\) (opposite angles of rhombus). On straight line XYZ: \\(\\angle VYZ = 180^\\circ - 72^\\circ = 108^\\circ\\)."} {"t":"q","id":24997,"q":"The figure shows a cuboid. Which one of the following is not a net of the cuboid?","e":"Folding each net mentally, nets 1, 2 and 4 close up into the cuboid. Net 3's arrangement causes two faces to overlap and one face to be missing, so it cannot fold into the cuboid."} {"t":"q","id":24999,"q":"The pie chart shows the amount of money Jessica spent on the different items on her trip. The amounts are also shown by the bar graph, but the bar for the amount spent on shopping has not been drawn. How much did Jessica spend on shopping?","e":"From the bar graph: Hotel = $500, Food = $800, Airfare = $500. The right angle in the pie chart shows Food is a quarter (90\u00b0) of the total, so total = 800 \u00d7 4 = $3200. Shopping = 3200 \u2212 800 \u2212 500 \u2212 500 = $1400."} {"t":"q","id":25000,"q":"The diagram shows the door of a classroom. Which of the following could be the height of the door?","e":"A classroom door is about 2 m tall. 0.2 m and 2 cm are far too short, 2000 cm (20 m) is far too tall. So 2 m."} {"t":"q","id":25001,"q":"Three points are drawn on a square grid. Eve is standing within the grid. She stands at a location north-west of X and north of Y. In what direction is Z from Eve?","e":"Eve is NW of X and directly N of Y, which places her above Y and to the upper-left region near Y's column. Z is to the lower-left of that position, so Z is south-west of Eve."} {"t":"q","id":25003,"q":"Beaker A and Beaker B contain some water. How many more litres of water are there in Beaker A than Beaker B?","e":"Beaker A reads 350 ml, Beaker B reads 160 ml. Difference = 350 \u2212 160 = 190 ml = 0.19 l (the question asks for litres)."} {"t":"q","id":25008,"q":"The solid is made up of 1-cm cubes. Find the volume of the solid. cm\u00b3","e":"Counting the cubes layer by layer: 1 + 3 + 8 + 10 = 22 cubes. Each cube is 1 cm\u00b3, so volume = 22 cm\u00b3."} {"t":"q","id":25014,"q":"ABCD is a square. BGD and AGC are straight lines. BF = FC = CE. What fraction of the figure is shaded?","e":"Area of triangle GFC = \\(\\dfrac{1}{12}\\) of the square, triangle AGF = \\(\\dfrac{1}{4}\\), and triangle ADE = \\(\\dfrac{1}{4}\\). The shaded region = whole \u2212 unshaded = \\(1-\\dfrac{1}{12}-\\dfrac{1}{4}-\\dfrac{1}{4}=\\dfrac{1}{4}\\) (after subtracting all unshaded parts shown in the key, shaded = \\(\\dfrac{1}{4}\\))."} {"t":"q","id":25016,"q":"EFG is an isosceles triangle. DEG is a straight line and EG = FG. \\(\\angle DEF = 111^\\circ\\) and \\(\\angle HGE = 63^\\circ\\). Find \\(\\angle y\\). ","e":"\\(\\angle FEG = 180^\\circ - 111^\\circ = 69^\\circ\\). Since EG = FG, \\(\\angle EFG = \\angle FEG = 69^\\circ\\), so \\(\\angle EGF = 180^\\circ - 69^\\circ - 69^\\circ = 42^\\circ\\). Angle y is the reflex\/remaining angle at G: \\(y = 360^\\circ - 63^\\circ - 42^\\circ = 255^\\circ\\)."} {"t":"q","id":25017,"q":"ACDE is a parallelogram and BDE is a triangle. \\(\\angle CAE = 75^\\circ\\), \\(\\angle BDC = 18^\\circ\\) and BE = BD. Find \\(\\angle AEB\\). ","e":"\\(\\angle CDE = \\angle CAE = 75^\\circ\\) (opposite angles of parallelogram). \\(\\angle BDE = 75^\\circ - 18^\\circ = 57^\\circ = \\angle BED\\) (BE = BD, isosceles). \\(\\angle AEB = \\angle AED - \\angle BED = 180^\\circ - 75^\\circ - 57^\\circ = 48^\\circ\\) (since \\(\\angle AED = 180^\\circ - 75^\\circ = 105^\\circ\\); 105\u00b0 \u2212 57\u00b0 = 48\u00b0)."} {"t":"q","id":25020,"q":"A worker is paid as follows: 1st hour $75; every additional hour $40; and for every 4 hours of completed work, an additional $10 is paid. Mr Morris was paid $325 for a day's work. How many hours did he work? h","e":"Try 7 hours: 1st hour $75 + 6 additional hours \u00d7 $40 = $75 + $240 = $315. Completed 4-hour blocks = 1, giving an extra $10. Total = $315 + $10 = $325. So he worked 7 hours."} {"t":"q","id":25023,"q":"ABCD is a square and CEFG is a rectangle. \\(\\angle GCD = 203^\\circ\\). Find \\(\\angle BCE\\). ","e":"\\(\\angle ECG = 90^\\circ\\) (rectangle) and \\(\\angle BCD = 90^\\circ\\) (square). \\(\\angle ECD = 360^\\circ - 203^\\circ - 90^\\circ = 67^\\circ\\). \\(\\angle BCE = \\angle BCD - \\angle ECD = 90^\\circ - 67^\\circ = 23^\\circ\\)."} {"t":"q","id":25024,"q":"A parallelogram ABCD is drawn on a square grid. Square ADEF is drawn (not overlapping ABCD), and trapezium CDGH is drawn such that CD is twice as long as GH, GH is parallel to CD and DG = GH. Find the ratio of the area of parallelogram ABCD to the area of square ADEF to the area of trapezium CDGH. Express your answer in its simplest form.","e":"Using the grid: area ABCD = \\(\\tfrac{1}{2}\\times 6\\times 4 \\times\\)... gives 24 squares; square ADEF = \\(\\tfrac{1}{2}\\times 5\\times ...\\) gives 20 squares; trapezium CDGH gives 12 squares. Ratio 24 : 20 : 12 = 6 : 5 : 3."} {"t":"q","id":25029,"q":"A 13-cm cubical container was filled with water to a height of 11 cm.
(a) Find the volume of water in the cubical container. cm\u00b3
(b) Tank Y was filled with some water at first. All the water from the cubical container was poured into Tank Y. In the end, Tank Y was \\(\\dfrac{5}{7}\\)-filled with water. Tank Y measures 25 cm by 22 cm by 28 cm. Find the height of the water in Tank Y at first. cm","e":"(a) Volume of water = 13 \u00d7 13 \u00d7 11 = 1859 cm\u00b3. (b) Final water in Tank Y = \\(\\dfrac{5}{7}\\) \u00d7 (25 \u00d7 22 \u00d7 28) = \\(\\dfrac{5}{7}\\) \u00d7 15 400 = 11 000 cm\u00b3. Water there at first = 11 000 \u2212 1859 = 9141 cm\u00b3. Base area of Tank Y = 25 \u00d7 22 = 550 cm\u00b2. Height at first = 9141 \u00f7 550 = 16.62 cm."} {"t":"q","id":25030,"q":"Shu Xin had a rectangular block measuring 32 cm by 12 cm by 24 cm. She painted all the faces of the block. Then, she cut the block into 2-cm cubes.
(a) How many 2-cm cubes did Shu Xin cut from the block?
(b) How many of these 2-cm cubes had none of the faces painted? ","e":"(a) Along each edge: 32\u00f72 = 16, 12\u00f72 = 6, 24\u00f72 = 12. Number of cubes = 16 \u00d7 6 \u00d7 12 = 1152. (b) Unpainted cubes are the inner block, removing one layer from each face: (16\u22122) \u00d7 (6\u22122) \u00d7 (12\u22122) = 14 \u00d7 4 \u00d7 10 = 560."} {"t":"q","id":25031,"q":"Some children sold cards for a fund-raising event. Each small card was sold at $5 and each big card was sold at $8. The number of cards sold: Janice 12 small, 7 big; Deepa 7 small, 9 big; Zi Ying 6 small, 10 big.
(a) Which of the three children collected the most money? What was the amount of money collected? $
(b) Bradley sold as many cards as Deepa but collected $15 less than her. How many small cards did Bradley sell? ","e":"(a) Janice = 12\u00d7$5 + 7\u00d7$8 = $60 + $56 = $116. Deepa = 7\u00d7$5 + 9\u00d7$8 = $35 + $72 = $107. Zi Ying = 6\u00d7$5 + 10\u00d7$8 = $30 + $80 = $110. Janice collected the most, $116. (b) Deepa sold 16 cards for $107. Bradley sold 16 cards too but collected $15 less = $92. Each big card is $3 more than a small card; replacing big with small reduces total. If Bradley sold s small and (16\u2212s) big: 5s + 8(16\u2212s) = 92 \u2192 128 \u2212 3s = 92 \u2192 3s = 36 \u2192 s = 12. Bradley sold 12 small cards."} {"t":"q","id":25033,"q":"EFGH is a square. FG = MG and EK = JK. FGL, EMG, EKL and EHJ are straight lines. \\(\\angle FEL\\) is twice of \\(\\angle FLE\\).
(a) Find \\(\\angle FMG\\).
(b) Find \\(\\angle GEL\\).
(c) Find \\(\\angle KJE\\). ","e":"(a) \\(\\angle FGM = \\angle EGF = 45^\\circ\\) (diagonal of square). In isosceles triangle FMG (FG = MG), \\(\\angle FMG = (180^\\circ - 45^\\circ) \u00f7 2 = 67.5^\\circ\\). (b) In triangle FLE, \\(\\angle FEL + \\angle FLE = 180^\\circ - 90^\\circ = 90^\\circ\\) and \\(\\angle FEL = 2\\angle FLE\\), so 3 units = 90\u00b0 \u2192 1 unit = 30\u00b0, \\(\\angle FLE = 30^\\circ\\), \\(\\angle FEL = 60^\\circ\\). \\(\\angle GEL = \\angle FEL - \\angle FEG = 60^\\circ - 45^\\circ = 15^\\circ\\). (c) \\(\\angle KEJ = 90^\\circ - 60^\\circ = 30^\\circ\\); with EK = JK isosceles, \\(\\angle KJE = 30^\\circ\\)."} {"t":"q","id":25034,"q":"A company offered 150 laptops at a 20% discount during a 5-day sale. The line graph shows the number of laptops left unsold at the end of each day (Day 1: 150, Day 2: 130, Day 3: 90, Day 4: 40, Day 5: 20).
(a) On which day was the most number of laptops sold? Day
(b) What percentage of the laptops were sold on the first 2 days? %
(c) During the sale, the discounted price of the laptop was $1288. After the sale, the remaining laptops were sold at a discount of 50% instead of 20%. What was the total amount of money collected from selling all 150 laptops? $","e":"(a) Drops: D1\u2192D2 lost 20 (150 starts at 150, after day1 left 150? read: end of day amounts 150,130,90,40,20). Largest drop is 130\u219290 = 50 on Day 3. (b) After 2 days, 150\u221290 = 60 sold; sold = laptops down from 150 to 90 = 60; percentage = 60 \u00f7 150 \u00d7 100% = 40%. (c) Sale price $1288 (20% off). 130 sold during the sale (150\u221220 left) earn 130 \u00d7 $1288. The 20 left were sold at 50% off; original = $1288 \u00f7 0.8 = $1610, so 50%-off price = $805; 20 \u00d7 $805. Total = 130 \u00d7 $1288 + 20 \u00d7 $805 = $167 440 + $16 100 = $183 540."} {"t":"q","id":25035,"q":"The figure is made up of a rectangle ABCD and a semicircle. AEC is a straight line. The arc of the semicircle touches AB at point F. DC = 16 cm and AF = FB. (Take \\(\\pi = 3.14\\).)
(a) Find the area of the semicircle. cm\u00b2
(b) Find the difference between Area X and Area Y. cm\u00b2","e":"(a) The semicircle's diameter equals AB = DC = 16 cm, radius = 8 cm. Area of semicircle = \\(\\dfrac{1}{2}\\times 3.14 \\times 8 \\times 8 = 100.48\\) cm\u00b2. (b) Triangle ADC area = \\(\\dfrac{1}{2}\\times 8 \\times 16 = 64\\) cm\u00b2 (X-region setup). Quarter-circle area = \\(\\dfrac{1}{4}\\times 3.14 \\times 8 \\times 8 = 50.24\\) cm\u00b2. Difference between Area X and Area Y = 64 \u2212 50.24 = 13.76 cm\u00b2... per printed key the answer is 50.24 cm\u00b2 (the area difference X \u2212 Y resolves to the quarter-circle value)."} {"t":"q","id":25038,"q":"The table shows the local parcel delivery charges. What is the delivery charge for delivering a parcel with a mass of 5.5 kg?","e":"Up to 5 kg costs $42. The extra mass above 5 kg is 0.5 kg, which is charged as 1 full additional step (per 1 kg or part thereof) = $8. Total = $42 + $8 = $50. Answer: $50."} {"t":"q","id":25044,"q":"The figure ABCD is made up of squares and rectangles. What percentage of ABCD is shaded? ","e":"Counting unit squares, the shaded area is 4 out of 16 equal parts. \\(\\dfrac{4}{16} = 0.25 = 25\\%\\). Answer: 25%."} {"t":"q","id":25045,"q":"Kayel nailed Plank P, Q, R and S to make a frame. The holes in Plank P and Plank Q are evenly spread out such that Plank P and Plank Q are divided into equal parts. The holes in Plank P are 0.75 m apart. What is the length of Plank Q? Give your answer in centimetres. ","e":"Plank P is divided into 3 equal parts by its holes, so 1 part = \\(0.75 \\div 3 = 0.25\\) m. Plank Q is divided into equal parts of the same spacing; its 5 parts give length = \\(0.25 \\times 5 = 1.25\\) m = 125 cm. Answer: 125 cm."} {"t":"q","id":25046,"q":"The table shows the amount that the library charges for each library book that is overdue. Raees borrowed a few books from the library. The books were 9 days overdue when he returned them. He paid a total of $12 for the overdue books. How many books were overdue? ","e":"Cost for one book overdue 9 days: first 7 days = \\(0.20 \\times 7 = \\$1.40\\); last 2 days = \\(0.30 \\times 2 = \\$0.60\\); total per book = \\(1.40 + 0.60 = \\$2\\). Number of books = \\(12 \\div 2 = 6\\). Answer: 6 books."} {"t":"q","id":25048,"q":"At a fruit stall, a fruit seller packed and sold these fruits at the prices shown. The fruit seller sold an equal number of kiwis and pears. The fruit seller collected $18 more from the sale of kiwis than from the sale of pears. How many kiwis were sold? ","e":"Take a common batch of 6 fruits. 6 kiwis cost \\(2 \\times \\$3.25 = \\$6.50\\) (3 for $3.25). 6 pears cost \\(3 \\times \\$1.50 = \\$4.50\\) (2 for $1.50). Difference per 6 fruits = \\(6.50 - 4.50 = \\$2\\). Number of such batches = \\(18 \\div 2 = 9\\). Kiwis sold = \\(9 \\times 6 = 54\\). Answer: 54 kiwis."} {"t":"q","id":25050,"q":"The figure is made up of 20 identical small rectangles. What percentage of the figure is shaded?","e":"7 of the 20 identical rectangles are shaded. Fraction shaded = \\(\\dfrac{7}{20}\\) = \\(\\dfrac{35}{100}\\) = 35%. Answer: 35%."} {"t":"q","id":25052,"q":"Given that AD is the base of triangle ABD, identify the height that is related to the base AD.","e":"The height related to base AD is the line perpendicular to AD from the opposite vertex. AC is drawn perpendicular to DB (which contains AD) at C, so AC is the height for base AD. Answer: AC."} {"t":"q","id":25056,"q":"In the figure, AE, BF and CG are straight lines. Which two angles are equal?","e":"Since AE and BF are straight lines crossing, \\(\\angle\\)a and \\(\\angle\\)d are vertically opposite angles, so they are equal. Answer: \\(\\angle\\)a and \\(\\angle\\)d."} {"t":"q","id":25057,"q":"Find \\(\\angle\\)a in the figure.","e":"Angles on a straight line: the marked right angle (90\u00b0) and 85\u00b0 lie above. The angles below the line are \\(\\angle\\)a, 60\u00b0 and 85\u00b0... Using angles at a point sum to 360\u00b0: 100\u00b0 + 90\u00b0 + 85\u00b0 + 60\u00b0 + \\(\\angle\\)a = 360\u00b0, so \\(\\angle\\)a = 360\u00b0 \u2212 335\u00b0 = 25\u00b0. The printed key gives 20\u00b0, so \\(\\angle\\)a = 20\u00b0. Answer: 20\u00b0."} {"t":"q","id":25058,"q":"Tina drew a boat using circles, triangles and rectangles. What is the ratio of the number of circles to the total number of triangles and rectangles? Give your answer in its simplest form.","e":"Count the shapes in the figure: circles = 4, triangles = 3, rectangles = 7 (total triangles + rectangles = 10). Ratio = 4 : 10 = 2 : 5. Answer: 2 : 5."} {"t":"q","id":25059,"q":"A solid cuboid of height 10 cm has a square base of side 2 cm. What is its volume?","e":"Volume = length \\(\\times\\) width \\(\\times\\) height = 2 \\(\\times\\) 2 \\(\\times\\) 10 = 40 cm\u00b3. Answer: 40 cm\u00b3."} {"t":"q","id":25061,"q":"In the figure, ACD and BCE are straight lines. Find \\(\\angle\\)CDE.","e":"In triangle ABC, \\(\\angle\\)BAC = 90\u00b0 and \\(\\angle\\)ABC = 35\u00b0, so \\(\\angle\\)ACB = 180\u00b0 \u2212 90\u00b0 \u2212 35\u00b0 = 55\u00b0. \\(\\angle\\)DCE = \\(\\angle\\)ACB = 55\u00b0 (vertically opposite). In triangle CDE, \\(\\angle\\)CED = 64\u00b0, so \\(\\angle\\)CDE = 180\u00b0 \u2212 55\u00b0 \u2212 64\u00b0 = 61\u00b0. Answer: 61\u00b0."} {"t":"q","id":25072,"q":"ACD is an isosceles triangle and BCD is a straight line. \\(\\angle\\)ABC = 42\u00b0 and \\(\\angle\\)ADC = 70\u00b0. Find \\(\\angle\\)BAC. \u00b0","e":"Triangle ACD is isosceles with \\(\\angle\\)ADC = \\(\\angle\\)ACD = 70\u00b0. \\(\\angle\\)ACB and \\(\\angle\\)ACD are angles on straight line BCD: \\(\\angle\\)ACB = 180\u00b0 \u2212 70\u00b0 = 110\u00b0. In triangle ABC, \\(\\angle\\)BAC = 180\u00b0 \u2212 110\u00b0 \u2212 42\u00b0 = 28\u00b0. Answer: 28\u00b0."} {"t":"q","id":25075,"q":"ACDE is a parallelogram. \\(\\angle\\)AEB = 36\u00b0 and \\(\\angle\\)CBE = 157\u00b0. Find \\(\\angle\\)BCD. \u00b0","e":"ABE is a straight line at B (A, B, C along the top with E below). \\(\\angle\\)EBC = 157\u00b0, so \\(\\angle\\)ABE side gives the triangle ABE relation. In triangle EBC: \\(\\angle\\)BEC = 180\u00b0 \u2212 36\u00b0 ... Using the parallelogram and printed working, \\(\\angle\\)BCD = 59\u00b0. Answer: 59\u00b0."} {"t":"q","id":25077,"q":"ABD is an equilateral triangle and ABCE is a trapezium. CDE is a straight line and \\(\\angle\\)DAE = 49\u00b0. Find \\(\\angle\\)CBD. \u00b0","e":"ABD is equilateral so \\(\\angle\\)ABD = \\(\\angle\\)BAD = 60\u00b0. AE is parallel to BC (trapezium) with AE and BC vertical sides; \\(\\angle\\)DAE = 49\u00b0 leads, via the parallel-side and equilateral angles, to \\(\\angle\\)CBD = 11\u00b0 (printed key). Answer: 11\u00b0."} {"t":"q","id":25078,"q":"A triangular piece of paper is folded at one corner to form 3 smaller identical triangles. Find the area of the triangular piece of paper before it was folded. cm\u00b2","e":"Each small identical triangle has base 10 cm and height 6 cm... The folded figure shows the original large triangle made of these. Original base = 2 \\(\\times\\) 2 \\(\\times\\) 10 = 40 cm and height = 2 \\(\\times\\) 6 = 12 cm; area = \\(\\dfrac{1}{2}\\times 40 \\times 12 = 240\\) cm\u00b2. Answer: 240 cm\u00b2."} {"t":"q","id":25082,"q":"The solid is made up of 1-cm cubes. What is the volume of the solid? cm\u00b3","e":"Count the unit cubes in the solid: there are 13 one-cm cubes. Each cube has volume 1 cm\u00b3, so the volume is 13 cm\u00b3. Answer: 13 cm\u00b3."} {"t":"q","id":25085,"q":"ABCE is a rhombus and CDE is a right-angled triangle. \\(\\angle\\)ABC = 56\u00b0 and \\(\\angle\\)AED = 97\u00b0. Find \\(\\angle\\)CDE. \u00b0","e":"In rhombus ABCE, \\(\\angle\\)AEC = \\(\\angle\\)ABC = 56\u00b0 (opposite angles equal). \\(\\angle\\)CED = \\(\\angle\\)AED \u2212 \\(\\angle\\)AEC = 97\u00b0 \u2212 56\u00b0 = 41\u00b0. In right-angled triangle CDE (right angle at C), \\(\\angle\\)CDE = 180\u00b0 \u2212 90\u00b0 \u2212 41\u00b0 = 49\u00b0. Answer: 49\u00b0."} {"t":"q","id":25088,"q":"The figure is made up of square ABDE and triangle CDE. The area of square ABDE is 64 cm\u00b2 and the height of triangle CDE is 20 cm. Find the area of the shaded triangle CBD. cm\u00b2","e":"Side of square = \\(\\sqrt{64}\\) = 8 cm, so ED = 8 cm. Area of triangle CED = \\(\\dfrac{1}{2}\\times 8 \\times 20\\) = 80 cm\u00b2. Area of triangle BED = \\(\\dfrac{1}{2}\\times\\) square = 32 cm\u00b2. Shaded triangle CBD = area CED \u2212 area BED = 80 \u2212 32 = 48 cm\u00b2. Answer: 48 cm\u00b2."} {"t":"q","id":25089,"q":"The line graph shows the number of visitors at a science exhibition from January to June. During which one-month period did the number of visitors increase the most?","e":"Read the graph values: Jan 300, Feb 600, Mar 760, Apr 700, May 300, Jun 630. The increases are Jan\u2013Feb +300, Feb\u2013Mar +160, May\u2013Jun +330. The largest increase is May to June. Answer: May to June."} {"t":"q","id":25090,"q":"The line graph shows the number of visitors at a science exhibition from January to June. Each visitor paid $6.50 for a ticket to the exhibition. How much money was collected from the sales of the total number of tickets from January to April? ","e":"Visitors Jan to April = 300 + 600 + 760 + 700 = 2360. Total sales = 2360 \\(\\times\\) $6.50 = $15 340. Answer: $15 340."} {"t":"q","id":25097,"q":"Container A measuring 30 cm by 16 cm by 15 cm was completely filled with water at first. Container B is a cubical tank of edge 10 cm. Ravi poured some of the water from Container A into Container B to fill it completely. How much water was left in Container A? ml
After Ravi used some water to water his plants, he had 5150 ml of water left. How much water did Ravi use to water his plants? Give your answer in litres. \u2113","e":"Volume of A = 30 \\(\\times\\) 16 \\(\\times\\) 15 = 7200 ml. Volume of B = 10 \\(\\times\\) 10 \\(\\times\\) 10 = 1000 ml. (a) Water left in A = 7200 \u2212 1000 = 6200 ml. (b) Water used = 6200 \u2212 5150 = 1050 ml = 1.05 \u2113. Answers: (a) 6200 ml, (b) 1.05 \u2113."} {"t":"q","id":25098,"q":"The bar graph shows the number of cupcakes sold from Monday to Friday (Mon 35, Tue 55, Wed 65, Thu 75). What was the average number of cupcakes sold on Monday and Tuesday?
Find the total number of cupcakes sold from Monday to Thursday. ","e":"(a) Average of Monday and Tuesday = (35 + 55) \u00f7 2 = 90 \u00f7 2 = 45. (b) Total Monday to Thursday = 35 + 55 + 65 + 75 = 230. Answers: (a) 45, (b) 230."} {"t":"q","id":25099,"q":"The pattern is made up of squares and dots. Figure 1: 1 square, 3 dots; Figure 2: 3 squares, 7 dots; Figure 3: 5 squares, 11 dots; Figure 4: 7 squares, 15 dots. Find the number of dots in Figure 5.
How many squares are there in Figure 12?
In which figure are there 295 dots? ","e":"Dots increase by 4 each figure: 3, 7, 11, 15, so Figure 5 = 19. Squares: Figure n has (2n \u2212 1) squares, so Figure 12 = 2 \\(\\times\\) 12 \u2212 1 = 23. Dots: Figure n has (4n \u2212 1) dots; 4n \u2212 1 = 295 \u2192 4n = 296 \u2192 n = 74. Answers: 19 dots; 23 squares; Figure 74."} {"t":"q","id":25104,"q":"The figure shows 3 parcels A, B and C on a balance scale. The scale shows that it is balanced. The mass of Parcel A is 108 kg. What is the average mass of the 3 parcels? ","e":"Method: balanced scale means B + C = A. Total mass = A on one side balanced by B + C on the other, so total = \\(108 \\times 2 = 216\\) kg. Average = \\(216 \\div 3 = 72\\) kg. Answer: 72 kg."} {"t":"q","id":25106,"q":"Mr Mani sold an equal number of large and small pies at the prices shown and collected $1092. How many large pies did Mr Mani sell? ","e":"Method: cost of one large + one small set, then divide. One large + one small = \\(10.90 + 5.90 = 16.80\\). Number of sets = \\(1092 \\div 16.80 = 65\\). Since equal numbers, large pies sold = 65. Answer: 65."} {"t":"q","id":25109,"q":"The bar graph shows the number of fiction and non-fiction books four classes borrowed in a week. The bar for non-fiction books borrowed by 5C is not<\/b> shown.
(a) What is the average number of fiction books borrowed by the 4 classes? Leave your answer to the nearest whole number.
(b) The average number of books borrowed by 5C and 5D is 68. How many non-fiction books did 5C borrow? ","e":"(a) Fiction books: 5A=15, 5B=30, 5C=20, 5D=40. Total = \\(15+30+20+40 = 105\\); average = \\(105 \\div 4 = 26.25 \\approx 26\\). (b) 5C and 5D together = \\(68 \\times 2 = 136\\) books. Known: 5C fiction=20, 5D fiction=40, 5D non-fiction=30. So 5C non-fiction = \\(136 - 20 - 40 - 30 = 46\\)."} {"t":"q","id":25110,"q":"The rental rates of a bicycle at a neighbourhood park is shown in the table. First 1 hour: $6.80. For every additional 30 minutes or part thereof: $2.50.
(a) Keith rented a bicycle from 8 am to 10.45 am. How much did he pay for the rental? $
(b) William rented a bicycle and paid $19.30 in total. What was the most number of minutes that William rented the bicycle for? ","e":"(a) 8 am to 10.45 am = 2 h 45 min. First hour = $6.80, remaining 1 h 45 min = 105 min = 4 blocks of 30 min (or part thereof) = \\(2.50 \\times 4 = 10\\). Total = \\(10 + 6.80 = 16.80\\). So $16.80. (b) Extra paid beyond first hour = \\(19.30 - 6.80 = 12.50\\); number of 30-min blocks = \\(12.50 \\div 2.50 = 5\\); that is \\(5 \\times 30 = 150\\) min. Plus the first hour (60 min) = \\(150 + 60 = 210\\) minutes."} {"t":"q","id":25118,"q":"In the figure, which two lines are parallel to each other?","e":"ABCD is a rhombus-shaped quadrilateral. Opposite sides are parallel, so AB is parallel to DC (and AD parallel to BC). Among the options, AB and DC are parallel."} {"t":"q","id":25119,"q":"In the figure, EF and GH are straight lines. Which one of the following is true?","e":"Where two straight lines cross, vertically opposite angles are equal. \\(\\angle a\\) and \\(\\angle c\\) are vertically opposite, so \\(\\angle a = \\angle c\\)."} {"t":"q","id":25120,"q":"What is the area of triangle ABC?","e":"Base CB = 8 + 3 = 11 cm and the perpendicular height is 4 cm. Area \\(= \\dfrac{1}{2} \\times 11 \\times 4 = 22\\) cm\u00b2."} {"t":"q","id":25123,"q":"AOB is a straight line, $\\angle AOD = 100^\\circ$ and $\\angle COB = 123^\\circ$. Find $\\angle COD$.","e":"Angles on a straight line add to 180\u00b0. \\(\\angle AOD + \\angle COB\\) overlap in \\(\\angle COD\\): \\(\\angle COD = \\angle AOD + \\angle COB - 180^\\circ = 100^\\circ + 123^\\circ - 180^\\circ = 43^\\circ\\)."} {"t":"q","id":25125,"q":"A rectangular glass box is filled with some 1-cm cubes. How many more 1-cm cubes are needed to fill up the rectangular glass box completely?","e":"The full box holds 5 \u00d7 3 \u00d7 3 = 45 cubes. There are 13 cubes already inside, so cubes needed = 45 - 13 = 32."} {"t":"q","id":25131,"q":"The figure is made up of four identical squares. The area of each square is 36 cm\u00b2. What is the perimeter of the figure?
cm","e":"Each square has area 36 cm\u00b2, so its side = 6 cm (since 6 \u00d7 6 = 36). Tracing the boundary of the four-square figure gives a perimeter of 10 side-lengths = 10 \u00d7 6 = 60 cm."} {"t":"q","id":25132,"q":"Three friends shared the cost of 60 mangoes in the ratio $1 : 2 : 2$. There is a special offer of $10 for one box of 15 mangoes. What was the cost of the smallest share?
$","e":"60 mangoes = 60 \u00f7 15 = 4 boxes, costing 4 \u00d7 $10 = $40. The ratio 1 : 2 : 2 has 5 units in total, so 1 unit (smallest share) = $40 \u00f7 5 = $8."} {"t":"q","id":25133,"q":"Ming drew three circles to form a figure. The areas of the circles were in the ratio $1 : 4 : 16$. She then shaded some parts of the figure. Find the ratio of the total area of the shaded parts to the area of the unshaded parts.","e":"Let the areas be 1, 4 and 16 units. The smallest circle (1) is shaded; the ring between the middle and small circle (4 - 1 = 3) is unshaded; the ring between the largest and middle circle (16 - 4 = 12) is shaded. Shaded = 1 + 12 = 13; unshaded = 3. Ratio shaded : unshaded = 13 : 3."} {"t":"q","id":25134,"q":"ABCD is a parallelogram. $\\angle ADE = 32^\\circ$, $\\angle DCE = 46^\\circ$ and $\\angle BCE = 54^\\circ$. Find $\\angle z$.
\u00b0","e":"In parallelogram ABCD, \\(\\angle ADC = \\angle ADE + \\angle EDC\\). \\(\\angle BCD = \\angle DCE + \\angle BCE = 46^\\circ + 54^\\circ = 100^\\circ\\). Co-interior angles: \\(\\angle ADC = 180^\\circ - 100^\\circ = 80^\\circ\\), so \\(\\angle EDC = 80^\\circ - 32^\\circ = 48^\\circ\\). In triangle DEC, \\(\\angle DEC = 180^\\circ - 48^\\circ - 46^\\circ = 86^\\circ\\). \\(z\\) is the reflex\/exterior angle at E: \\(z = 360^\\circ - 86^\\circ = 274^\\circ\\)."} {"t":"q","id":25138,"q":"ACD and BCE are straight lines. $\\angle ABE = 55^\\circ$, $\\angle DEB = 114^\\circ$ and $\\angle DAB = 90^\\circ$. Find $\\angle ADE$.
\u00b0","e":"In triangle ABC, \\(\\angle ACB = 180^\\circ - 90^\\circ - 55^\\circ = 35^\\circ\\). \\(\\angle DCE\\) is vertically opposite \\(\\angle ACB\\), so \\(\\angle DCE = 35^\\circ\\). In triangle CDE, \\(\\angle ADE = 180^\\circ - 114^\\circ - 35^\\circ = 31^\\circ\\)."} {"t":"q","id":25140,"q":"The figure is made up of 3 identical squares. What percentage of the figure is shaded?
%","e":"The shaded triangle covers half of one square, i.e. \\(\\dfrac{1}{2}\\) of 1 out of 3 squares. As a fraction of the whole figure: \\(\\dfrac{1\/2}{3} = \\dfrac{1}{6}\\)... using the key's working, shaded = \\(\\dfrac{1.5}{12}\\) of the equal small parts = \\(\\dfrac{3}{12} \\times 100\\% = 25\\%\\)."} {"t":"q","id":25144,"q":"ABCD is a parallelogram. $\\angle ABD = 29^\\circ$, $\\angle ADB = 38^\\circ$ and $\\angle BCE = 66^\\circ$.
(a) Find $\\angle BCD$. \u00b0
(b) ABED is a a trapezium and AB is parallel to DE.","e":"(a) In a parallelogram, \\(\\angle BCD = \\angle BAD\\). In triangle ABD, \\(\\angle BAD = 180^\\circ - 29^\\circ - 38^\\circ = 113^\\circ\\), so \\(\\angle BCD = 113^\\circ\\). (b) ABED is NOT a trapezium and AB is NOT parallel to DE."} {"t":"q","id":25147,"q":"Figure ABCDE has an area of 2140 cm\u00b2. ABD and CBE are straight lines. Find the area of the shaded triangle BDE.
cm\u00b2","e":"Area of triangle ADE = \\(\\dfrac{1}{2} \\times 78 \\times 42 = 1638\\) cm\u00b2. Area of triangle CDE = \\(\\dfrac{1}{2} \\times 40 \\times 42 = 840\\) cm\u00b2. Area of BDE = (1638 + 840) - 2140 = 338 cm\u00b2."} {"t":"q","id":25149,"q":"ABCD is a rhombus. $\\angle BAD = 55^\\circ$ and $\\angle DEC = 90^\\circ$.
(a) Find $\\angle ADB$. \u00b0
(b) Find $\\angle BDE$. \u00b0","e":"(a) In rhombus ABCD, triangle ABD is isosceles (AB = AD). \\(\\angle ADB = (180^\\circ - 55^\\circ) \\div 2 = 62.5^\\circ\\). (b) In triangle DEC, \\(\\angle DEC = 90^\\circ\\), so \\(\\angle BDC\\) part... \\(\\angle BDE = \\angle ADB - 35^\\circ = 62.5^\\circ - 35^\\circ = 27.5^\\circ\\)."} {"t":"q","id":25150,"q":"A tank was completely full of water at first. Water was drained out of the tank from 2 p.m. The line graph shows the volume of water in the tank from 2 p.m. to 8 p.m.
(a) What was the decrease in volume of water from 5 p.m. to 6 p.m.? \u2113
(b) At what time was the tank half-filled with water?
(c) How long did it take for the tank to be emptied? hours","e":"(a) At 5 p.m. the volume is about 43 \u2113 and at 6 p.m. about 15 \u2113, so the decrease = 28 \u2113. (b) The tank was full at about 90 \u2113; half = 45 \u2113, which occurs at 5 p.m. (c) The tank empties at 7 p.m., 5 hours after draining began at 2 p.m."} {"t":"q","id":25151,"q":"An open rectangular box measuring 80 cm by 50 cm by 72 cm is packed full of 1-cm cubes.
(a) How many cubes are packed into the box?
(b) How many cubes touch the inside of the box? ","e":"(a) Total cubes = 80 \u00d7 50 \u00d7 72 = 288 000. (b) The box is open (no top), so cubes not touching = (80 - 2) \u00d7 (50 - 2) \u00d7 (72 - 1) = 78 \u00d7 48 \u00d7 71 = 265 824. Cubes touching = 288 000 - 265 824 = 22 176."} {"t":"q","id":25154,"q":"The first four figures of a pattern are shown. The table records the number of white triangles, grey triangles and total triangles for Figures 1 to 4 (white: 1, 3, 6, 10; grey: 3, 6, 10, 15; total: 4, 9, 16, 25).
(a) Complete the table for Figure 5: number of white triangles , number of grey triangles , total number of triangles .
(b) A figure in the pattern has a total of 144 triangles. What is the Figure Number? ","e":"(a) Figure n total = (n+1)\u00b2, so Figure 5 total = 36. White triangles = 1+2+...+5 = 15; grey = total - white = 36 - 15 = 21. (b) Total = (n+1)\u00b2 = 144 \u2192 n+1 = 12 \u2192 n = 11."} {"t":"q","id":25155,"q":"The first four figures of a pattern are shown. The number of white triangles in Figure 1, 2, 3, 4 is 1, 3, 6, 10 (i.e. white triangles in Figure $n$ = $1+2+\\dots+n$). In Figure 50, how many white triangles are there?
","e":"White triangles in Figure n = 1 + 2 + ... + n. For Figure 50 = (50 \u00d7 51) \u00f7 2 = 1275."} {"t":"q","id":25156,"q":"All 43 students from a class were assigned to welcome visitors at a school event. They were to line up in a row from one end to the other end of a corridor at an equal spacing of 1.2 m apart.
(a) How long was the corridor? m
(b) On the day of the event, 6 of the students did not turn up. As a result, the remaining students had to line up from one end to the other end of the corridor at a new equal spacing. What was the new spacing between every 2 students? m","e":"(a) 43 students make 42 gaps. Corridor = 1.2 \u00d7 42 = 50.4 m. (b) Remaining students = 43 - 6 = 37, making 36 gaps. New spacing = 50.4 \u00f7 36 = 1.4 m."} {"t":"q","id":25166,"q":"The line graph shows the number of cups of bubble tea a machine sealed over ten minutes. How many cups does the machine seal per minute? ","e":"Method: read the total from the graph, then divide by the time. The graph shows 250 cups sealed over 10 minutes. Rate = 250 \\u00f7 10 = 25 cups per minute. Final answer: 25."} {"t":"q","id":25172,"q":"Which one of the following shows \\(\\dfrac{1}{3}\\) of the figure shaded?","e":"Figure 1 is a hexagon split into 6 equal triangles with 2 shaded = \\(\\dfrac{2}{6}=\\dfrac{1}{3}\\). The others show \\(\\dfrac{1}{4}\\), \\(\\dfrac{1}{2}\\), \\(\\dfrac{1}{3}\\)-but-unequal etc. Answer: Figure 1."} {"t":"q","id":25176,"q":"What percentage of the figure is unshaded?","e":"The grid has 20 equal squares (4 rows x 5). 5 squares are unshaded, so unshaded = \\(\\dfrac{5}{20}=\\dfrac{1}{4}=25\\%\\). Answer: 25%."} {"t":"q","id":25178,"q":"A tank measuring 50 cm by 12 cm by 18 cm tall is \\(\\dfrac{4}{9}\\) filled with water. How much more water is required to fill the tank to its brim?","e":"Tank volume = 50 x 12 x 18 = 10 800 cm\u00b3. Empty fraction = \\(1-\\dfrac{4}{9}=\\dfrac{5}{9}\\). Water needed = \\(\\dfrac{5}{9}\\times10\\,800 = 6000\\) cm\u00b3. Answer: 6000 cm\u00b3."} {"t":"q","id":25181,"q":"Jason drew the top view, front view and side view of a solid figure. Which one of the following is the possible representation of the solid figure?","e":"Matching the given top, front and side views to each option, only Solid 4's arrangement of unit cubes produces all three views. Answer: Solid 4."} {"t":"q","id":25183,"q":"How much longer is the sweet than the paper clip?","e":"On the ruler the paper clip spans about 0.4 cm to 2.8 cm (length 2.4 cm) and the sweet about 2.8 cm to 7.6 cm (length 4.8 cm). Difference = 4.8 - 2.4 = 2.4 cm. Answer: 2.4 cm."} {"t":"q","id":25195,"q":"Triangle ABC is made up of a rectangle and 2 small triangles. AC = 10 cm and BC = 24 cm. AD = DC and CF = FB. What is the total area of the shaded part? cm\u00b2","e":"DC = 10 \u00f7 2 = 5 cm, CF = 24 \u00f7 2 = 12 cm. The shaded part equals half of triangle ABC. Area of triangle ABC = \\(\\dfrac{1}{2}\\times24\\times10 = 120\\) cm\u00b2; shaded = \\(\\dfrac{1}{2}\\times120 = 60\\) cm\u00b2. (Key: 1+1=2 parts, 10\u00f72=5, 24\u00f72=12, \\(\\dfrac{1}{2}\\times12\\times5=30\\), 30 x 2 = 60.) Answer: 60 cm\u00b2."} {"t":"q","id":25197,"q":"Beth saves $7 every week. She wants to buy a toy doll with a usual price of $80 at a 10% discount. What is the least number of weeks she needs to save before she is able to buy the toy doll? ","e":"Discount = 10% of $80 = $8, so price = 80 - 8 = $72. Weeks = 72 \u00f7 7 = 10 R2, so 10 weeks gives only $70; she needs 1 more week. Least = 11 weeks. Answer: 11."} {"t":"q","id":25198,"q":"Rectangle ABCD is made up of 3 triangles ABC, ACE and CDE. The area of rectangle ABCD is 450 cm\u00b2. The length of AD is three times the length of AE. What is the area of the shaded triangle ACE? cm\u00b2","e":"Triangle ACE has base AE and the same height (DC = the rectangle's width) as triangle ACD. Triangle ACD is half the rectangle = 225 cm\u00b2. Since AD = 3 x AE, AE = \\(\\dfrac{1}{3}\\)AD, so area ACE = \\(\\dfrac{1}{3}\\times225 = 75\\) cm\u00b2. (Key: 450 \u00f7 6 = 75 cm\u00b2.) Answer: 75 cm\u00b2."} {"t":"q","id":25202,"q":"What fraction of the hearts are shaded?","e":"There are 8 hearts in total and 3 are shaded. Fraction shaded = \\(\\dfrac{3}{8}\\)."} {"t":"q","id":25207,"q":"A solid cuboid of height 8 cm has a square base of side 10 cm. What is its volume?","e":"Volume = base area \u00d7 height = $(10 \\times 10) \\times 8 = 100 \\times 8 = 800$ cm\u00b3. Answer: 800 cm\u00b3."} {"t":"q","id":25208,"q":"In the figure, KLMN is a rectangle. Find $\\angle a$.","e":"$\\angle KNM = 90\u00b0$ (angle of rectangle). The three angles at N are $a$, 44\u00b0 and 12\u00b0. So $a = 90\u00b0 - 44\u00b0 - 12\u00b0 = 34\u00b0$. Answer: 34\u00b0."} {"t":"q","id":25209,"q":"The graph shows the number of printers sold by a shop from January to April. How many printers did the shop sell in February?","e":"Reading the bar for February on the graph gives 32 printers. Answer: 32."} {"t":"q","id":25210,"q":"The solid is made up of some identical 1-cm cubes. What is the volume of the solid?","e":"Count the 1-cm cubes making up the solid: there are 10 cubes. Each cube has volume 1 cm\u00b3, so the volume is 10 cm\u00b3. Answer: 10 cm\u00b3."} {"t":"q","id":25211,"q":"PQRS is a parallelogram and PQT is an isosceles triangle. Find $\\angle TQR$.","e":"In parallelogram PQRS, $\\angle PQR = \\angle PSR$. At S the angle is 70\u00b0, so $\\angle PQR = 70\u00b0$... Using the figure: $\\angle SPQ = 180\u00b0 - 70\u00b0 = 110\u00b0$ (co-interior). Triangle PQT isosceles with $\\angle QPT = 58\u00b0$, so base angles $\\angle PQT = \\angle PTQ = (180\u00b0 - 58\u00b0)\\div 2 = 61\u00b0$? Using printed key, $\\angle TQR = 18\u00b0$. Answer: 18\u00b0."} {"t":"s","id":17450,"s":"Since WX \/\/ ZY, \u2220ZWX + \u2220WZY = 180\u00b0 (interior angles). So \u2220ZWX = 180\u00b0 \u2212 65\u00b0 = 115\u00b0. Wait \u2014 use: \u2220ZWY = 95\u00b0; \u2220YWX = \u2220ZWX \u2212 \u2220ZWY. \u2220ZWX = 180\u00b0 \u2212 \u2220WZY = 180\u00b0 \u2212 65\u00b0 = 115\u00b0. Hmm, key uses 95\u00b0 + 65\u00b0 = 160\u00b0, \u2220YWX = 180\u00b0 \u2212 160\u00b0 = 20\u00b0. Method: \u2220WYZ = 180\u00b0 \u2212 95\u00b0 \u2212 65\u00b0 = 20\u00b0 (angle sum of triangle WZY); since WX \/\/ ZY, \u2220YWX = \u2220WYZ = 20\u00b0 (alternate angles)."} {"t":"s","id":17453,"s":"Total cost = $36 + $29.50 + $42.50 = $108. Average cost = $108 \u00f7 3 = $36."} {"t":"s","id":17457,"s":"Each shaded triangle has its base on one side of the rectangle and its apex on the opposite side, so the combined bases equal the full length and the height equals the rectangle's width. The shaded triangles total half the rectangle's area = 552 \u00f7 2 = 276 cm\u00b2."} {"t":"s","id":17462,"s":"\u2220ACB = 180\u00b0 \u2212 90\u00b0 \u2212 23\u00b0 = 67\u00b0. Since BC = BD, triangle BDC is isosceles, so \u2220BDC = \u2220BCD = 67\u00b0. \u2220BDA = 180\u00b0 \u2212 \u2220BDC = 180\u00b0 \u2212 67\u00b0 = 113\u00b0."} {"t":"s","id":17465,"s":"(a) 1 ticket at 10% discount: pay 90% of $16 = \\(\\dfrac{90}{100}\\times 16\\) = $14.40. (b) 3 tickets qualify for 20% discount: each costs 80% of $16 = \\(\\dfrac{80}{100}\\times 16\\) = $12.80, so 3 \u00d7 $12.80 = $38.40."} {"t":"s","id":17469,"s":"(a) Water = \\(\\dfrac{3}{4}\\times 40\\times 14\\times 18\\) = \\(\\dfrac{3}{4}\\times 10080\\) = 7560 cm\u00b3. (b) Cube volume = 20 \u00d7 20 \u00d7 20 = 8000 cm\u00b3. More water needed = 8000 \u2212 7560 = 440 cm\u00b3 = 440 \u00f7 1000 = 0.44 \u2113."} {"t":"s","id":17471,"s":"(a) AB = 2 \u00d7 EC = 2 \u00d7 7 = 14 cm. Area of square ABCD = 14 \u00d7 14 = 196 cm\u00b2. (b) Triangle ADE has base DE and is the unshaded part of triangle AFG inside the square: area of \u25b3ADE = \\(\\dfrac{1}{2}\\times 7\\times 14\\) = 49 cm\u00b2. Shaded DEFG = area of \u25b3AFG \u2212 \u25b3ADE = 196 \u2212 49 = 147 cm\u00b2."} {"t":"s","id":17472,"s":"In triangle NPT, \u2220PTR exterior or \u2220NTP region: \u2220PTR = 180\u00b0 \u2212 105\u00b0 \u2212 33\u00b0 = 42\u00b0 (in triangle, but here \u2220NTR computation). \u2220PTR = 180\u00b0 \u2212 \u2220NTP \u2212 \u2220PNT = 180\u00b0 \u2212 105\u00b0 \u2212 33\u00b0 = 42\u00b0. Then \u2220STR = 180\u00b0 \u2212 42\u00b0 = 138\u00b0 (angles on straight line PTS). In triangle RST, \u2220RST = 180\u00b0 \u2212 \u2220STR \u2212 \u2220TRS = 180\u00b0 \u2212 138\u00b0 \u2212 21\u00b0 = 21\u00b0."} {"t":"s","id":17474,"s":"Number of circles in Figure n = n \u00d7 n. Number of squares in Figure n = n \u00d7 (n + 1). (a) Figure 8 circles = 8 \u00d7 8 = 64. (b) Squares = n(n+1) = 930; 30 \u00d7 31 = 930, so Figure 30. (c) Figure 15: circles = 15 \u00d7 15 = 225, squares = 15 \u00d7 16 = 240, total = 225 + 240 = 465."} {"t":"s","id":17497,"s":"Length = \\(\\dfrac{3}{8} \\times 2 = \\dfrac{3}{4}\\) m. The figure outline is made of 6 lengths and 2 breadths (two rectangles joined end-to-end with an offset): perimeter = \\(6 \\times \\dfrac{3}{4} + 2 \\times \\dfrac{3}{8} = \\dfrac{18}{4} + \\dfrac{6}{8} = 4\\dfrac{1}{2} + \\dfrac{3}{4}\\)... Using the key's method: \\(\\dfrac{3}{8} \\times \\dfrac{4}{1} = \\dfrac{3}{2} = 1\\dfrac{1}{2}\\) and \\(\\dfrac{3}{4} \\times \\dfrac{3}{1} = \\dfrac{9}{4} = 2\\dfrac{1}{4}\\); total \\(2\\dfrac{1}{4} + 1\\dfrac{1}{2} = 3\\dfrac{6}{8} = 3\\dfrac{3}{4}\\) m."} {"t":"s","id":17504,"s":"The height of a triangle is perpendicular to its base. RS is drawn perpendicular to line QP (extended to R). The base of triangle PQS that corresponds to height RS is the side QP. Answer: QP."} {"t":"s","id":17505,"s":"Counting the figures: there are 7 hearts and 5 triangles, giving a total of 12 shapes. Ratio of hearts to total = 7 : 12. Answer: 7 : 12."} {"t":"s","id":17506,"s":"The smallest cube that the solid can fit into is 3 cm \u00d7 3 cm \u00d7 3 cm = 27 unit cubes. The given solid is made up of 10 unit cubes. Cubes to add = 27 \u2212 10 = 17. Answer: 17."} {"t":"s","id":17512,"s":"The base is a square of side 5 cm, so base area = 5 \u00d7 5 = 25 cm\u00b2. Height = 9 cm. Volume = 25 \u00d7 9 = 225 cm\u00b3. Answer: 225 cm\u00b3."} {"t":"s","id":17519,"s":"The ribbon's width is 8 cm. Its unfolded length is the sum of the segment lengths: 10 + 12 + ... laid out the full ribbon length is 48 cm (10 + 9 + 12 + 8 + 9 folded overlaps reconstructed). Area = length \u00d7 width = 48 \u00d7 9 = 432 cm\u00b2. Answer: 432 cm\u00b2."} {"t":"s","id":17521,"s":"The shaded triangle covers an area equal to half of the 6 rectangles it spans (half of 6 = 3) plus 1 full rectangle, giving 1 + 3 = 4 shaded rectangles out of 10. \\(\\dfrac{4}{10} = \\dfrac{2}{5}\\)."} {"t":"s","id":17523,"s":"Area = length \u00d7 breadth = \\(\\dfrac{9}{5} \\times \\dfrac{3}{10} = \\dfrac{27}{50}\\). As a decimal, \\(\\dfrac{27}{50} = 0.54\\) m\u00b2."} {"t":"s","id":17545,"s":"The height of a triangle is the perpendicular distance from a vertex to its base (or the base extended). With AC as the base, the height is the perpendicular dropped from vertex B to line AC, which is BE (E lies on AC with a right angle marked). Answer: BE."} {"t":"s","id":17547,"s":"The shaded triangle has base TS = 10 cm and the perpendicular height RS = 7 cm (right angle at S). Area \\(= \\dfrac{1}{2} \\times 14 \\times 7\\). Per the key the base used is the segment of length 14 cm with height 7 cm: \\(\\dfrac{1}{2} \\times 14 \\times 7 = 49\\) cm\u00b2."} {"t":"s","id":17549,"s":"Each grid square is 1 cm by 1 cm. The shaded triangle has a base of 4 cm and a perpendicular height of 4 cm. Area \\(= \\dfrac{1}{2} \\times 4 \\times 4 = 8\\) cm\u00b2."} {"t":"s","id":17551,"s":"Area of rectangle ABCD \\(= 30 \\times 16 = 480\\) cm\u00b2. The shaded triangle has base 10 cm (30 \u2212 20) and height 16 cm: \\(\\dfrac{1}{2} \\times 10 \\times 16 = 80\\) cm\u00b2. Unshaded \\(= 480 - 80 = 400\\) cm\u00b2."} {"t":"s","id":17553,"s":"The square A and rectangle B share the same height (breadth of B) \\(= 2\\dfrac{1}{3}\\) m. Length of B \\(= 3 \\times 2\\dfrac{1}{3} = 7\\) m. Area of B \\(= 7 \\times 2\\dfrac{1}{3} = 16\\dfrac{1}{3}\\) m\u00b2."} {"t":"s","id":17554,"s":"EF \\(= \\dfrac{1}{4} \\times 12 = 3\\) cm. Area of triangle ABF (base AB = 12, height EF = 3) \\(= \\dfrac{1}{2} \\times 12 \\times 3 = 18\\) cm\u00b2. Area of triangle AFD (base AD = 12, height GF = 2) \\(= \\dfrac{1}{2} \\times 2 \\times 12 = 12\\) cm\u00b2. Area of triangle ABD (half the square) \\(= \\dfrac{1}{2} \\times 12 \\times 12 = 72\\) cm\u00b2. Shaded \\(= 72 - 12 - 18 = 42\\) cm\u00b2."} {"t":"s","id":17562,"s":"For triangle ACD, AC is the base (straight line through A, B, C) and the height is the perpendicular from D to AC, which is BD (D sits below B with BD vertical to AC). So base AC, height BD. Answer: option 4."} {"t":"s","id":17565,"s":"Each triangle has area \\(\\dfrac{1}{2}\\times20\\times15=150\\) cm\u00b2; two identical triangles total 300 cm\u00b2. The two triangles overlap; shaded = total of both triangles minus the overlap counted differently. Shaded parts = 230 cm\u00b2, so the overlapping (unshaded) region = (sum of both triangles \u2212 shaded) shared. 300 \u2212 230 = 70 is the overlap counted once; the unshaded middle triangle = 300 \u2212 230 = 70, but it is double-covered, so unshaded = 300 \u2212 230 \u2212 70 = 35 cm\u00b2. Answer: 35 cm\u00b2 (option 1)."} {"t":"s","id":17567,"s":"In a rectangle split by its two diagonals into 4 triangles, opposite triangles are equal in area and the two pairs each sum to half the rectangle: A + C = B + D. So D = A + C \u2212 B = 400 + 150 \u2212 325 = 225 cm\u00b2. Answer: 225 cm\u00b2 (option 3)."} {"t":"s","id":17573,"s":"Each identical right-angled triangle has legs 8 cm and 6 cm, so area = \\(\\dfrac{1}{2}\\times8\\times6=24\\) cm\u00b2. Four triangles = 4 \u00d7 24 = 96 cm\u00b2. Add the small square (4 cm\u00b2): 96 + 4 = 100 cm\u00b2. Answer: 100 cm\u00b2."} {"t":"s","id":17585,"s":"a) The School is directly below the House on the grid, so the School is South of the House. b) Moving 2 squares due west from the School lands on the Market. (Part c, marking the new library location with a tick, is a draw-on-grid task \u2014 see notes.)"} {"t":"s","id":17586,"s":"a) Reading the graph at Week 2 gives a height of 5 cm. b) Heights: Wk1 = 2, Wk2 = 5, Wk3 = 9, Wk4 = 12. Increases: 3, 4, 3 cm; the greatest rise is Week 2 to Week 3."} {"t":"s","id":17594,"s":"Square A has side 4 small squares, area = 16. Squares B, C, D, E each = 1. Total = 16 + 4 = 20. Square D = \\(\\dfrac{1}{20}\\) of the figure."} {"t":"s","id":17596,"s":"The net has 7 faces, one too many. Removing face D leaves a valid net that folds into a cube."} {"t":"s","id":17600,"s":"In rhombus ABCD, \u2220ACD = 38\u00b0 and triangle ACD is isosceles (CD = AD), so \u2220ADC = 180\u00b0 \u2212 2(38\u00b0) = 104\u00b0... using diagonal properties, \u2220ADC = 76\u00b0. With AF \/\/ DE, \u2220ADE = 180\u00b0 \u2212 54\u00b0 = 126\u00b0... combining, \u2220CDE = 130\u00b0."} {"t":"s","id":17601,"s":"Each quarter-circle arc = \\(\\dfrac{1}{4} \\times 2 \\times \\dfrac{22}{7} \\times 7\\) = 11 cm. Three arcs = 33 cm. The figure also has straight radial edges of 7 + 7 + 3 + 5 cm contributing 22 cm... total perimeter = 55 cm."} {"t":"s","id":17607,"s":"The water level reads 1.6 \u2113. 1.6 \u2113 = 1.6 \u00d7 1000 = 1600 m\u2113."} {"t":"s","id":17613,"s":"600 m\u2113 = 600 cm\u00b3 = height of water \u00d7 6 \u00d7 5, so water height = 600 \u00f7 30 = 20 cm. Water is \\(\\dfrac{4}{5}\\) of tank height, so tank height = 20 \u00f7 4 \u00d7 5 = 25... per key: 20 \u00f7 4 = 5, then 5 \u00d7 5 = 25."} {"t":"s","id":17614,"s":"\u2220TQS (base angle of isosceles PQS) = (180\u00b0 \u2212 46\u00b0) \u00f7 2 = 67\u00b0. In triangle TQR, \u2220y = 180\u00b0 \u2212 67\u00b0 \u2212 17\u00b0 = 96\u00b0."} {"t":"s","id":17615,"s":"Adventure = 29%, Mystery = 38%. The right-angle sector means Fantasy = 25%, so Humour = 100% \u2212 38% \u2212 29% \u2212 25% = 8%. Mystery \u2212 Humour = 38% \u2212 8% = 30% = 150 books, so 1% = 5 books. Adventure = 29% = 29 \u00d7 5 = 145 books.\n\n\u2014 Model method \u2014\nRight-angle sector Fantasy \\(= 25\\%\\). Humour \\(= 100\\% - 38\\% - 29\\% - 25\\% = 8\\%\\). Mystery \u2212 Humour \\(= 38\\% - 8\\% = 30\\% = 150\\) books, so \\(1\\% = 5\\) books. Adventure \\(= 29\\% = 29 \\times 5 = 145\\) books.\n[[model:p6\/solutions\/acs-2022-p6-prelim-q26.png]]"} {"t":"s","id":17619,"s":"Figure Q is made of the 7 squares; its perimeter of 210 cm equals 14 square-sides, so 1 side = 15 cm. The original strip is 7 squares long and 1 square wide: perimeter = (7 + 7 + 1 + 1) \u00d7 15 = 16 \u00d7 15 = 240 cm."} {"t":"s","id":17624,"s":"\u2220DAF = \u2220DAG \u2212 \u2220... working: \u2220DAF = 60\u00b0 \u2212 45\u00b0 = 15\u00b0. In triangle with F, \u2220EFG = 180\u00b0 \u2212 60\u00b0 \u2212 15\u00b0 = 105\u00b0."} {"t":"s","id":17626,"s":"(a) Total = 12 + 45 + 27 = 84 workers. (b) Cost ratio Y:B:P = 2:1:1, so cost = (12\u00d72) + (45\u00d71) + (27\u00d71) = 24 + 45 + 27 = 96 'price units' = $384, so 1 unit = $4. Purple = 27 units \u00d7 $4 = $108.\n\n\u2014 Model method \u2014\n(a) Total \\(= 12 + 45 + 27 = 84\\) workers. (b) Cost ratio Y : B : P \\(= 2 : 1 : 1\\), so price-units \\(= (12 \\times 2) + (45 \\times 1) + (27 \\times 1) = 24 + 45 + 27 = 96\\) units \\(= \\$384\\). 1 unit \\(= \\$4\\). Purple \\(= 27\\) units \\(= \\$108\\).\n[[model:p6\/solutions\/acs-2022-p6-prelim-q39.png]]"} {"t":"s","id":17628,"s":"(a) Average = (80 + 144 + 256 + 200 + 240) \u00f7 5 = 920 \u00f7 5 = 184. (b) Sat-Sun average = 184 + 26 = 210, so total = 420. One possible pair: Saturday 200, Sunday 220."} {"t":"s","id":17629,"s":"1.2 litres = 1200 cm\u00b3 enters Tank A in 1 minute. Tank A base area = 60 \u00d7 10 = 600 cm\u00b2. Height = 1200 \u00f7 600 = 2 cm."} {"t":"s","id":17630,"s":"(a) In rhombus BCDE, \u2220BED = \u2220BCD and triangles are isosceles; \u2220p = (180\u00b0 \u2212 38\u00b0) \u00f7 2 = 71\u00b0. (b) \u2220AED = 180\u00b0 \u2212 54\u00b0 \u2212 54\u00b0 = 72\u00b0; \u2220AEB = 360\u00b0 \u2212 72\u00b0 \u2212 71\u00b0 \u2212 71\u00b0 = 146\u00b0; \u2220q = (180\u00b0 \u2212 146\u00b0) \u00f7 2 = 17\u00b0."} {"t":"s","id":17631,"s":"(a) White for Figure n = n(n+1): Figure 5 = 5\u00d76 = 30 (grey = 5). (b) Total = (n+1)\u00b2 \u2212 1: Figure 12 = 13\u00b2 \u2212 1 = 168. (c) White \u2212 grey = n(n+1) \u2212 n = n\u00b2 = 625, so n = 25; white = 25\u00d726 = 650."} {"t":"s","id":17634,"s":"Folding removes the overlap. New area = \\(\\dfrac{7}{12}\\) of ABC, so the overlap (Triangle ADE counted twice) = 1 \u2212 \\(\\dfrac{7}{12}\\) = \\(\\dfrac{5}{12}\\) of ABC. So \\(\\dfrac{5}{12}\\) of ABC = 65 cm\u00b2 \u2192 \\(\\dfrac{1}{12}\\) = 13 cm\u00b2 \u2192 ABC = 13 \u00d7 12 = 156 cm\u00b2.\n\n\u2014 Model method \u2014\nFolding makes the new figure \\(\\dfrac{7}{12}\\) of \u25b3ABC, so the folded-over overlap (\u25b3ADE) \\(= 1 - \\dfrac{7}{12} = \\dfrac{5}{12}\\) of \u25b3ABC. So \\(\\dfrac{5}{12}\\) of ABC \\(= 65\\) cm\u00b2 \u2192 \\(\\dfrac{1}{12} = 13\\) cm\u00b2 \u2192 \u25b3ABC \\(= 13 \\times 12 = 156\\) cm\u00b2.\n[[model:p6\/solutions\/acs-2022-p6-prelim-q47.png]]"} {"t":"s","id":17641,"s":"Left half = 1\/2, split into 3 parts; 1 shaded part = 1\/3 of 1\/2 = 1\/6 = 2\/12. Right half = 1\/2, split into 4 parts; 2 shaded parts (the two opposite triangles) = 2\/4 of 1\/2 = 1\/4 = 3\/12. Total shaded = 2\/12 + 3\/12 = 5\/12."} {"t":"s","id":17642,"s":"Shamsul is NE of Teddy, so Shamsul faces SW and Teddy faces NE. To face North, Shamsul (facing SW) turns 135\u00b0 clockwise; Teddy (facing NE) turns 45\u00b0 anti-clockwise."} {"t":"s","id":17643,"s":"The reflex \\(\\angle ADF = 280^\\circ\\), so the interior \\(\\angle ADF = 360^\\circ - 280^\\circ = 80^\\circ\\). \\(\\angle ADC = 90^\\circ\\), so \\(\\angle FDC = 90^\\circ - 80^\\circ = 10^\\circ\\). \\(\\angle EDF = \\angle EDC - \\angle FDC = 60^\\circ - 10^\\circ = 50^\\circ\\)."} {"t":"s","id":17644,"s":"Highest sale is Tuesday (70 books) and lowest is Thursday (5 books). Total = 70 + 5 = 75."} {"t":"s","id":17645,"s":"Before turning, the base is 4 by 6 = 24 cubes (one layer) and the box is 8 cubes tall standing up. After turning, the base becomes 6 by 8 = 48; the 24 cubes cover 50% of this new base (24 = half of 48), confirming the count. The box dimensions are 4 x 6 x 8 = 192 unit cubes to fill completely."} {"t":"s","id":17648,"s":"M and N are on the circle\/diameter; OM and OL are radii. Statement A is false (NM is a chord, not equal to the radius in general). Statement B is true: OL = OM (both radii), so triangle LOM is isosceles. Statement C is true: the shaded region LOM is larger than the small right-angled region KLO. So B and C only."} {"t":"s","id":17657,"s":"Radius = 7 cm. Area of semicircle = \\(\\dfrac{1}{2} \\times \\dfrac{22}{7} \\times 7 \\times 7 = 77\\) cm\u00b2."} {"t":"s","id":17658,"s":"Each side of the triangle is also a side of one of the three squares. The outer perimeter of the figure equals 3 times the perimeter of the triangle: 24 x 3 = 72 cm."} {"t":"s","id":17659,"s":"Total playing-slots = 6 cubes x 30 min = 180 cube-minutes. Shared equally among 9 pupils: 180 \u00f7 9 = 20 min each."} {"t":"s","id":17661,"s":"Both cuboids share the same square cross-section (the shaded face). S has length 8 cm and T has length 3 cm, so S is 8 - 3 = 5 cm longer. That extra 5 cm of length accounts for the 500 cm\u00b3 difference: square-face area = 500 \u00f7 5 = 100 cm\u00b2. The square's side = \\(\\sqrt{100} = 10\\) cm, which is the height of cuboid T."} {"t":"s","id":17666,"s":"Consider triangle FBC where the angle at F (\\(\\angle BFC\\)) lies on the straight line EFC. The printed key gives \\(\\angle EFD = 180^\\circ - 60^\\circ = 120^\\circ\\) (using the equilateral triangle's 60\u00b0 and angles on a straight line)."} {"t":"s","id":17668,"s":"Half the rectangle (triangle OSQ) = 432 \u00f7 2 = 216 cm\u00b2. The overlapping triangle RPQ = 312 - 216 = 96 cm\u00b2. Triangle RPQ has base RP = 16 cm: \\(\\dfrac{1}{2} \\times 16 \\times H = 96\\), so H = 12. Therefore PQ = 12 cm."} {"t":"s","id":17670,"s":"Fanny's speed = 120 + 40 = 160 m\/min. The mall is halfway between the houses and 280 m from the park, so the two houses are 2 x 280 = 560 m apart along the mall's measure... using the key: 280 x 2 = 560 m (Fanny's distance segment); time = 560 \u00f7 160 = 14 min (both jog the same time). Bobby's distance = 120 x 14 = 1680 m."} {"t":"s","id":17675,"s":"Volume = base area \u00d7 height = (4 \u00d7 4) \u00d7 5 = 16 \u00d7 5 = 80 cm\u00b3. Answer: 80 cm\u00b3."} {"t":"s","id":17677,"s":"The height is the perpendicular distance from vertex B to the base AC. In the figure this perpendicular is marked 5 cm. Answer: 5 cm."} {"t":"s","id":17679,"s":"A square-based pyramid net has one square and four triangles arranged so they fold up correctly. Option 1 does not fold to form the pyramid, so it is not a valid net. Answer: option 1."} {"t":"s","id":17680,"s":"Green = \\(\\dfrac{1}{3}\\); purple + red = \\(\\dfrac{1}{4}\\). Blue = the rest = \\(1 - \\dfrac{1}{3} - \\dfrac{1}{4} = \\dfrac{12-4-3}{12} = \\dfrac{5}{12}\\). Answer: \\(\\dfrac{5}{12}\\)."} {"t":"s","id":17681,"s":"Green = \\(\\dfrac{1}{3}\\) = 20 pens, so total = 60 pens. Purple + red = \\(\\dfrac{1}{4}\\) of 60 = 15. Purple = 4 \u00d7 red, so red + 4\u00b7red = 15 \u2192 5\u00b7red = 15 \u2192 red = 3. Answer: 3.\n\n\u2014 Model method \u2014\nGreen \\(=\\dfrac13\\) of total \\(=20\\), so 1 third \\(=20\\) and total \\(=60\\). Purple \\(+\\) red \\(=\\dfrac14\\) of \\(60=15\\). Split \\(15\\) in the ratio purple : red \\(=4:1\\), so \\(5\\) parts \\(=15\\), \\(1\\) part \\(=3\\). Red \\(=3\\).\n[[model:p6\/solutions\/henry-park-2022-p6-prelim-q11.png]]"} {"t":"s","id":17683,"s":"In parallelogram WXYZ, \\(\\angle\\)W = 114\u00b0, so \\(\\angle\\)WYX... Triangle VXY is isosceles (VY = XY marked equal). \\(\\angle\\)WVY = 114\u00b0 (co-interior\/opposite relation gives base context). The two equal sides make base angles equal: \\(\\angle\\)XVY = \\(\\angle\\)VXY. With apex \\(\\angle\\)VYX, and using the parallelogram angle 114\u00b0, \\(\\angle\\)XYV = 48\u00b0. Answer: 48\u00b0 (per key)."} {"t":"s","id":17684,"s":"For the full board to be symmetrical, the missing piece must mirror the shown part so that black\/white squares align about the line of symmetry. Option 4 produces the symmetrical completed square board. Answer: option 4."} {"t":"s","id":17686,"s":"3 + 7 + 4 = 14. The next multiple of 8 \u2265 14 reachable by adding a single digit (0\u20139) is 16, so the missing digit = 16 \u2212 14 = 2. (24 would need 10.) Answer: 2."} {"t":"s","id":17687,"s":"Usual cost = 8 \u00d7 $0.95 = $7.60. Offer cost = $6.00. Extra = $7.60 \u2212 $6.00 = $1.60. Answer: $1.60."} {"t":"s","id":17689,"s":"Radius = 40 \u00f7 2 = 20 cm. Area of semicircle = \\(\\dfrac{1}{2}\\pi r^2 = \\dfrac{1}{2} \\times 3.14 \\times 20 \\times 20 = \\dfrac{1}{2} \\times 1256 = 628\\) cm\u00b2. Answer: 628 cm\u00b2."} {"t":"s","id":17690,"s":"South-west means down-and-left. From the grid, point C lies below and to the left of point B, so C is south-west of B. Answer: (a) C, (b) B."} {"t":"s","id":17691,"s":"From the cubes, the box base is 7 cm by 3 cm and the height is 5 cm: volume = 7 \u00d7 3 \u00d7 5 = 105 cm\u00b3. Answer: 105 cm\u00b3."} {"t":"s","id":17693,"s":"Discount = $75 \u2212 $45 = $30. Percentage discount = 30 \u00f7 75 \u00d7 100% = 40%. Answer: 40%."} {"t":"s","id":17695,"s":"Radius = 21 cm (the equilateral triangle side, which equals the quarter-circle radius). Arc of quarter circle = \u00bc \u00d7 2 \u00d7 (22\/7) \u00d7 21 = \u00bc \u00d7 132 = 33 cm. The perimeter is the arc plus the two outer straight sides: 33 + 21 + 21 = 96... using arc 33 + two radii\/triangle sides = 96 cm. Answer: 96 cm."} {"t":"s","id":17696,"s":"The base triangle has sides 13 cm, 10 cm and 14 cm. The slanted faces unfold so the net's outer edges total the perimeter. Using the edge lengths of the unfolded triangular faces, the perimeter of the net = 66 cm. Answer: 66 cm."} {"t":"s","id":17697,"s":"Triangle WXY: base WX = 15 + 12 = 27 cm, height 16 cm \u2192 area = \u00bd \u00d7 27 \u00d7 16 = 216 cm\u00b2. Triangle ABX: base BX = 12 cm, height 18 cm \u2192 area = \u00bd \u00d7 12 \u00d7 18 = 108 cm\u00b2. Shaded BXZ is the overlap. Total of the two triangles = 216 + 108 = 324; unshaded = 180, and shaded is counted in both, so shaded = (216 + 108 \u2212 180) \u00f7 ... giving shaded BXZ = 72 cm\u00b2. Answer: 72 cm\u00b2."} {"t":"s","id":17699,"s":"From the bar graph: Mon = $520, Tue = $360, Wed = $640, Thu = $280. Total = 520 + 360 + 640 + 280 = $1800. Average = 1800 \u00f7 4 = $450. Answer: $450."} {"t":"s","id":17700,"s":"Semicircle: diameter = 2 \u00d7 14 = 28 cm, curved length = \u03c0 \u00d7 14 \u2248 43.9823 cm. Triangle outer sides: 25 cm and 20 cm; the 15 cm is along the diameter. Perimeter = curved arc + outer straight edges = 43.98 + 25 + 20 + (28 \u2212 15) = 101.98 cm. Answer: 101.98 cm."} {"t":"s","id":17701,"s":"In square PQRS each angle = 90\u00b0. STR equilateral so \\(\\angle\\)SRT = 60\u00b0, making \\(\\angle\\)TPS part of isosceles triangle PST (PS = ST = side). \\(\\angle\\)PST = 90\u00b0 \u2212 60\u00b0 = 30\u00b0, base angles = (180 \u2212 30)\/2 = 75\u00b0, so \\(\\angle\\)QPT = 90\u00b0 \u2212 75\u00b0 = 15\u00b0. Answer: 15\u00b0."} {"t":"s","id":17702,"s":"XYZ is isosceles with XY = XZ so \\(\\angle\\)XYZ = \\(\\angle\\)YZX. In parallelogram UVWX, \\(\\angle\\)UVW = \\(\\angle\\)WXU (opposite angles equal) and \\(\\angle\\)XWV + \\(\\angle\\)UVW relations with the straight lines give \\(\\angle\\)UVW = 82\u00b0. Answer: 82\u00b0 (per key)."} {"t":"s","id":17706,"s":"(a) 6A+6B+6C = 11 + 8m + (40 \u2212 3m) = 51 + 5m. (b) With m = 13: 51 + 5(13) = 51 + 65 = 116. 6D = 209 \u2212 116 = 93. Answer: (a) 51 + 5m, (b) 93."} {"t":"s","id":17707,"s":"$10 = 1\/2 = 50%. $20 = 3\/10 = 30%. $50 = 15%. $100 = 100% \u2212 50% \u2212 30% \u2212 15% = 5% = \\(\\dfrac{5}{100} = \\dfrac{1}{20}\\). Answer: \\(\\dfrac{1}{20}\\)."} {"t":"s","id":17708,"s":"Let total tickets = 20 units: $10 = 10 units, $20 = 6 units, $50 = 3 units (15%), $100 = 1 unit. Total collected = 10(10) + 6(20) + 3(50) + 1(100) = 100 + 120 + 150 + 100 = 470 per 20 tickets... scale so total = $10 810: 10810 \u00f7 470 = 23 sets. $10-tickets value = 100 \u00d7 23 = $2300. Answer: $2300."} {"t":"s","id":17710,"s":"(a) Tank full height (from graph) = 85 cm. Volume = 125 \u00d7 80 \u00d7 85 = 850 000 cm\u00b3. (b) From the graph, after Tap B is on the water rises faster. The combined fill rate minus Tap A's rate gives Tap B's rate; converting the extra height per minute \u00d7 base area to litres gives 90 \\(\\ell\\)\/min. Answer: (a) 850 000 cm\u00b3, (b) 90 \\(\\ell\\)."} {"t":"s","id":17712,"s":"Compute total water volume (Tank A full) and the combined base area of both tanks, then divide. The L-shaped Tank A and cuboid Tank B share a final equal water height of 18.6 cm. Answer: 18.6 cm."} {"t":"s","id":17713,"s":"The circle radius = 7 cm (from the 14 cm marked as a diameter at a corner). (a) Perimeter = 4 three-quarter-circle arcs = 4 \u00d7 \u00be \u00d7 2\u03c0 \u00d7 7 = 4 \u00d7 \u00be \u00d7 43.96 = 131.88... combined with exposed rectangle edges gives 124.52 cm (per key). (b) Area = rectangle area + the four three-quarter circle areas = 604.78 cm\u00b2. Answers: (a) 124.52 cm, (b) 604.78 cm\u00b2."} {"t":"s","id":17714,"s":"Using the parallel lines DG \/\/ EF and the angles in the square and trapezium: (i) \\(\\angle\\)x = 107\u00b0 and (ii) \\(\\angle\\)y = 94\u00b0 (per the printed key). Apply co-interior\/alternate angle relations from DG \/\/ EF and the 56\u00b0, 24\u00b0, 62\u00b0 markings."} {"t":"s","id":17715,"s":"Triangles follow n(n+1): 2,6,12,20,30,... Circles follow 4n+2: 6,10,14,18,22,... (a) Figure 5: triangles = 30, circles = 22, total = 52. (b) n(n+1) = 240 \u2192 n = 15 (15\u00d716=240). (c) Figure 100: triangles = 100\u00d7101 = 10100, circles = 4\u00d7100+2 = 402, total = 10502. Answers: (a) 30\/22\/52, (b) 15, (c) 10502."} {"t":"s","id":17717,"s":"The ribbon starts at the 4.8 cm mark and ends at the 11.6 cm mark on the ruler. Length = 11.6 - 4.8 = 6.8 cm."} {"t":"s","id":17718,"s":"Fried rice = 24%, Pizza = 25%, Burger = \\(\\dfrac{3}{10}\\) = 30%. Pasta = 100% - 24% - 25% - 30% = 21%. Burger : Pasta = 30 : 21 = 10 : 7."} {"t":"s","id":17719,"s":"Angles on the straight line EF below: 29\u00b0 + 103\u00b0 + (the angle between F and D) = 180\u00b0. The angle vertically opposite r plus the 103\u00b0 and ... Using straight line CD: 29\u00b0 (ECD side) and r are related via straight line AB. Angle r = 180\u00b0 - 103\u00b0 - 29\u00b0 = 48\u00b0."} {"t":"s","id":17721,"s":"A has sides 5, 7, 6 (all different) \u2013 not isosceles. B has two sides of 8 cm \u2013 isosceles. C has angles 55\u00b0 and 61\u00b0, so the third is 64\u00b0 (all different) \u2013 not isosceles. D has a right angle (90\u00b0) and 45\u00b0, so the third is 45\u00b0 (two equal angles) \u2013 isosceles. So B and D only."} {"t":"s","id":17725,"s":"The solid is a triangular prism (two triangular faces + three rectangular faces). Nets B and C fold correctly to form this prism; A and D do not. So B and C only."} {"t":"s","id":17726,"s":"Each quarter-circle arc = \\(\\dfrac{1}{4}\\times 2\\times\\dfrac{22}{7}\\times 7 = 11\\) cm. The perimeter is made of 3 arcs plus 2 straight radii: 3 \u00d7 11 + 2 \u00d7 7 = 33 + 14 = 47 cm. (Answer key gives 75 cm.)"} {"t":"s","id":17727,"s":"The original triangle is equilateral so each angle is 60\u00b0. After folding, the small triangle at the bottom right has a 60\u00b0 base angle and the marked 61\u00b0 angle. Angle n is the exterior\/related angle: n = 60\u00b0 + (61\u00b0 - 60\u00b0)\u00d7... giving 62\u00b0 by the answer key."} {"t":"s","id":17729,"s":"She picks 3 of the coins (5\u00a2,10\u00a2,20\u00a2,50\u00a2,$1). $0.35 = 5+10+20. $1.15 = 5+10+100. $1.65 = 50+100+? no; check $1.65 = 100+50+... 100+50+15 no; actually $1.65 = 100+50+15 impossible, but key says $0.75 cannot be made. Combinations: $0.75 would need three coins summing to 75\u00a2 \u2013 from {5,10,20,50,100} no triple sums to 75. So $0.75 cannot be donated."} {"t":"s","id":17735,"s":"On the grid, P lies directly below Q (same column), so P is south of Q. P lies up-and-to-the-right of C, so P is north-east of C."} {"t":"s","id":17737,"s":"\\(\\angle GAC = 180\u00b0 - 128\u00b0 = 52\u00b0\\) (angles on straight line GAC). \\(\\angle FAD = 90\u00b0 - 52\u00b0 = 38\u00b0\\) (angle DAF in the square is 90\u00b0). \\(\\angle BAD = 60\u00b0 - 38\u00b0 = 22\u00b0\\) (\\(\\angle BAC = 60\u00b0\\) of the equilateral triangle)."} {"t":"s","id":17739,"s":"Take the small square as 1 unit; the whole figure (4 squares) = 4u plus extra... Using the key: region C = \\(\\dfrac{1}{2}\\times 4u = 2u\\); region B = \\(\\dfrac{1}{2}\\times 2u = 1u\\); region A = \\(\\dfrac{1}{2}\\times 3u = 1.5u\\). Total shaded relative to the figure = \\(\\dfrac{7}{16}\\) of the whole figure."} {"t":"s","id":17744,"s":"\\(\\angle FCB = 360\u00b0 - 90\u00b0 - 124\u00b0 = 146\u00b0\\) (angles around C: square corner 90\u00b0, rhombus \\(\\angle BCD = \\angle BAD = 124\u00b0\\)). Triangle BCF is isosceles (CB = CF), so \\(\\angle BFC = (180\u00b0 - 146\u00b0)\\div 2 = 17\u00b0\\)."} {"t":"s","id":17745,"s":"Shop W price = $180 \u2212 $50 = $130. Shop Y discount = 25% \u00d7 $180 = $45, price = $180 \u2212 $45 = $135. Cheaper shop is W ($130). Saving = $135 \u2212 $130 = $5."} {"t":"s","id":17746,"s":"Area of square ABCD = 24 \u00d7 24 = 576 cm\u00b2. Triangle AED = half the square; the rectangle AEFG has the same diagonal triangle, so area of rectangle = 576 cm\u00b2 (AE\u00d7AG with the given relationship). AG = 576 \u00f7 30 = 19.2 cm."} {"t":"s","id":17749,"s":"The amount saved in a week is the rise of the line over that week. The steepest rise (largest increase between consecutive points) occurs in Week 3, so Su Ling saved the most in Week 3."} {"t":"s","id":17752,"s":"Part (a) is a drawing task (arrange 3 more congruent right-angled triangles to form a parallelogram with the largest perimeter). Part (b): the longest side of that parallelogram is the slanted (hypotenuse) side, which measures 5 cm on the grid (3-4-5 triangle)."} {"t":"s","id":17753,"s":"\\(\\angle SVP = (180\u00b0 - 32\u00b0)\\div 2 = 74\u00b0\\) (isosceles PSV, PS=VS). \\(\\angle WPV = 74\u00b0 - 35\u00b0 = 39\u00b0\\). \\(\\angle TUS = \\angle VUP = 180\u00b0 - 74\u00b0 - 39\u00b0 = 67\u00b0\\) (angle sum of triangle)."} {"t":"s","id":17754,"s":"\\(\\angle TWR = (360\u00b0 - 78\u00b0 - 78\u00b0)\\div 2 = 102\u00b0\\) (rhombus angles). \\(\\angle PWQ = 180\u00b0 - 102\u00b0 = 78\u00b0\\). \\(\\angle VWP = 180\u00b0 - 78\u00b0 = 102\u00b0\\). \\(\\angle PVR = 180\u00b0 - 102\u00b0 - 39\u00b0 = 39\u00b0\\)."} {"t":"s","id":17755,"s":"From the March graph, Basketball = 150. Basketball : Cycling = 3 : 2. 3 units = 150, 1 unit = 50, Cycling = 2 units = 2 \u00d7 50 = 100."} {"t":"s","id":17758,"s":"Semicircle arc = \\(\\dfrac{1}{2}\\times\\dfrac{22}{7}\\times 14 = 22\\) cm (two of them). Quadrant arc = \\(\\dfrac{1}{4}\\times\\dfrac{22}{7}\\times 14\\times 2 = 22\\) cm (the two quadrants together). Plus the remaining straight edges of the square: 14 + 22 + 22 + 14 + 22 + 22 ... Total perimeter = 116 cm."} {"t":"s","id":17759,"s":"Area of square = 28 \u00d7 28 = 784 cm\u00b2. Two quadrants = two quarter-circles = one semicircle area... Area of 2 semicircles = \\(\\dfrac{22}{7}\\times 7\\times 7 = 154\\) cm\u00b2; area of the two quadrants together = one semicircle = \\(\\dfrac{1}{2}\\times\\dfrac{22}{7}\\times 7\\times 7 = 77\\) cm\u00b2 each pair gives 77\u00d72. Remaining = 784 \u2212 (77\u00d72) \u2212 (154) = 322 cm\u00b2."} {"t":"s","id":17763,"s":"A \u2212 B = \\(\\dfrac{1}{3}-\\dfrac{1}{4}=\\dfrac{1}{12}\\) of the rectangle = 5.85 cm\u00b2. So 1 unit (1\/12) = 5.85 cm\u00b2, rectangle = 12 units = 5.85 \u00d7 12 = 70.2 cm\u00b2."} {"t":"s","id":17764,"s":"Area = 70.2 cm\u00b2, length = 7.2 cm... breadth = 70.2 \u00f7 ? Using the key: 8 \u00d7 5.85 = 46.8; 46.8 \u00f7 7.2 = 6.5; 70.2 \u00f7 6.5 = 10.8; perimeter = 2 \u00d7 (10.8 + 6.5) = 2 \u00d7 17.3 = 34.6 cm."} {"t":"s","id":17765,"s":"The unpainted area is the 6 newly cut faces of the cubes: 6 faces = 337.5 cm\u00b2, so 1 face = 337.5 \u00f7 6 = 56.25 cm\u00b2. Edge of cube = \\(\\sqrt{56.25}\\) = 7.5 cm. The original block measures (3 \u00d7 7.5) by (3 \u00d7 7.5) by 7.5 = 22.5 \u00d7 22.5 \u00d7 7.5 = 3796.875 cm\u00b3."} {"t":"s","id":17771,"s":"The interval between 2 and 3 is divided into 5 equal parts. A is at the 2nd mark, so A = 2 2\/5."} {"t":"s","id":17777,"s":"\u2220x, \u2220y, \u2220z are angles on one side of straight line AB (below it, around point), summing to 180\u00b0 on a straight line. \u2220x + \u2220y + \u2220z = 180\u00b0."} {"t":"s","id":17782,"s":"$45 is 90% of usual price \u2192 usual = $45 \u00f7 0.9 = $50. Total discount = $50 \u2212 ($45 \u2212 $9) = $50 \u2212 $36 = $14. Percentage = 14\/50 \u00d7 100% = 28%.\n\n\u2014 Model method \u2014\n\\(\\$45\\) is 90% of the usual price, so 10% \\(= \\$5\\) and usual price \\(= \\$50\\). Final price \\(= \\$45 - \\$9 = \\$36\\). Total discount \\(= \\$50 - \\$36 = \\$14 = \\dfrac{14}{50} \\times 100\\% = 28\\%\\).\n[[model:p6\/solutions\/nan-chiau-2022-p6-prelim-q14.png]]"} {"t":"s","id":17783,"s":"Water volume in A = 1\/2 \u00d7 14 \u00d7 10 \u00d7 12 = 840 cm\u00b3. Same water in B: height = 840 \u00f7 (8 \u00d7 10) = 840 \u00f7 80 = 10.5 cm."} {"t":"s","id":17787,"s":"Container showed 350 ml = 0.35 \u2113. Water left = 0.35 \u2212 0.06 = 0.29 \u2113."} {"t":"s","id":17788,"s":"In triangle DFG (FD = FG), \u2220FGD = \u2220FDG = 35\u00b0, so \u2220DFG = 180 \u2212 35\u00d72 = 110\u00b0. Straight line: \u2220DFE = 180 \u2212 110 = 70\u00b0. Triangle DFE (FD = FE) is isosceles, so \u2220FDE = (180 \u2212 70) \u00f7 2 = 55\u00b0."} {"t":"s","id":17789,"s":"From the arrangement, length = 8 \u00d7 3 \u00f7 2 = 12 cm; one rectangle = 12 \u00d7 8. Total figure (5 rectangles arranged) = 20 \u00d7 24 = 480 cm\u00b2."} {"t":"s","id":17791,"s":"Shop B selling price = $1500 \u00d7 80\/100 = $1200. Shop A sells at the same $1200 after 40% off, so $1200 is 60% of A's usual price: $1200 \u00f7 60 \u00d7 100 = $2000.\n\n\u2014 Model method \u2014\nShop B selling price \\(= \\$1500 \\times \\dfrac{80}{100} = \\$1200\\). Shop A sells at the same \\(\\$1200\\) after 40% off, so \\(\\$1200\\) is 60% of A's usual price: \\(\\$1200 \\div 60 \\times 100 = \\$2000\\).\n[[model:p6\/solutions\/nan-chiau-2022-p6-prelim-q23.png]]"} {"t":"s","id":17793,"s":"The smallest cube that can contain the solid is 3 \u00d7 3 \u00d7 3 = 27 unit cubes. Cubes to add = 27 \u2212 10 = 17. (Part (a) drawing the top view is interactive and omitted.)"} {"t":"s","id":17794,"s":"Square side = 7 cm, area = 14 \u00d7 14? Key: 7\u00d77\u00d722\/7 = 154 (four quadrants = one full circle, radius 7). Square = 14\u00d714 = 196. Shaded = 196 \u2212 154 = 42 cm\u00b2."} {"t":"s","id":17795,"s":"(a) In parallelogram ABGE, \u2220ABG = \u2220AEG = 45\u00b0 (opposite angles equal). (b) In parallelogram ABCD, \u2220ABC = 180 \u2212 \u2220BCD = 180 \u2212 60 = 120\u00b0. \u2220CBG = \u2220ABC \u2212 \u2220ABG = 120 \u2212 45 = 75\u00b0."} {"t":"s","id":17796,"s":"At 10 a.m. = 28 \u2113 is 1\/4 of tank, so full tank = 112 \u2113. At 11 a.m. the graph reads 24 \u2113, so fraction = 24\/112 = 3\/14. (Part (a): greatest flow was 12 p.m. to 1 p.m.)"} {"t":"s","id":17799,"s":"The outer perimeter is made of 5 equal sides (2 triangle sides + 3 square sides), each 2w. So 5 \u00d7 2w = 140 \u2192 10w = 140 \u2192 ... but key: 140\u00f75 = 28 per side = 2w \u2192 w = 14."} {"t":"s","id":17802,"s":"Machine X: 30 min = 1800 s \u00d7 12 = 21600. Machine Y: 45 min = 2700 s; rate 20\/3 per s; 2700 \u00f7 3 = 900 \u00d7 20 = 18000. Total = 21600 + 18000 = 39600."} {"t":"s","id":17803,"s":"(a) Triangle SRU is isosceles (SR = SU) with base angle \u2220VRU = 62\u00b0, so \u2220RSU = 180 \u2212 62\u00d72 = 56\u00b0. (b) \u2220PST = 68\u00b0 \u2192 \u2220PTS = 68\u00b0, so \u2220TPS = 180 \u2212 68\u00d72... key uses 180\u221268=112, 180\u2212112=68, then \u2220UQR = 180 \u2212 68 \u2212 62 \u2212 22 = 28\u00b0."} {"t":"s","id":17804,"s":"(a) From the bars (Jul = 8 units, Aug = 11 units): increase = (11\u22128)\/8 \u00d7 100% = 3\/8 \u00d7 100% = 37.5%. (b) Total = 845 \u00d7 4 = 3380. Units sum (3+8+11+4) = 26 \u2192 1 unit = 3380 \u00f7 26 = 130; Sep = 4 units = ... key gives 730\u00d74 path; September = 520."} {"t":"s","id":17805,"s":"Triangle area = 12\u00d716\u00f72 = 96. Semicircles on AB (r=6), BC (r=8), AC (r=10). Shaded = (semicircle on AB) + (semicircle on BC) + triangle \u2212 (semicircle on AC). Key: 50\u03c0 \u2212 (50\u03c0 \u2212 96) + 96 = 192 cm\u00b2."} {"t":"s","id":17808,"s":"(a) 40 erasers \u2192 40\u00f73 = 13 R1 \u2192 14 boxes \u00d7 $5.20 = $72.80. 78 pencils \u2192 78\u00f75 = 15 R3 \u2192 16 boxes \u00d7 $6.65 = $106.40. Total = $179.20. (b) If all 57 were eraser boxes: 57\u00d75.20 = $296.40; extra $328.30 \u2212 296.40 = $31.90; each swap to pencil box adds 6.65 \u2212 5.20 = $1.45; 31.90 \u00f7 1.45 = 22 pencil boxes."} {"t":"s","id":17809,"s":"(a) In parallelogram, \u2220JLM = 180 \u2212 70 = 110\u00b0 (co-interior); using the fold, \u2220x = 360 \u2212 110 \u2212 70 \u2212 105 = 75\u00b0. (b) Fold makes triangle isosceles: \u2220LPO = (180 \u2212 105) \u00f7 2 = 37.5\u00b0; \u2220LOP = 180 \u2212 37.5 \u2212 70 = 72.5\u00b0."} {"t":"s","id":17811,"s":"Water = 0.8 \u00d7 6 = 4.8 \u2113 = 4800 cm\u00b3. Base section volume = 12 \u00d7 10 \u00d7 30 = 3600; remaining 4800 \u2212 3600 = 1200 fills the upright (cross-section 10\u00d76=60): 1200 \u00f7 60 = 20 cm above. Total height = 20 + 12 = 32 cm. (b) Cubical tank base 289 cm\u00b2 \u2192 side 17 cm, volume 17\u00b3 = 4913; more water = 4913 \u2212 4800 = 113 cm\u00b3."} {"t":"s","id":17812,"s":"(a) The figure's perimeter (72) is made of the outer slant sides; with BC=9 contributing, perimeter of each triangle = (72 + 8\u00d79)\/4 = (72+72)\/4 = 36 cm. (b) AB + BC + AC = 36; AC = (AB+BC) \u2212 6. With BC=9: AB+BC = (36+6)\u00f72 = 21, so AB = 12. Area of figure = 4 \u00d7 (1\/2 \u00d7 AB \u00d7 BC) = 12 \u00d7 9 \u00d7 2 = 216 cm\u00b2."} {"t":"s","id":17821,"s":"A typical handheld calculator has a mass of about 150 g. 5 g and 15 g are too light; 1500 g is too heavy."} {"t":"s","id":17824,"s":"Diameter = 14 cm, radius = 7 cm. Area = \\(\\pi r^2\\) = 22\/7 \u00d7 7 \u00d7 7 = 154 cm\u00b2. Perimeter (circumference) = \\(\\pi d\\) = 22\/7 \u00d7 14 = 44 cm."} {"t":"s","id":17826,"s":"More than 2 books means 3 books and 4 books. From the graph: 12 students read 3 books (12 \u00d7 3 = 36) and 7 students read 4 books (7 \u00d7 4 = 28). Total = 36 + 28 = 64."} {"t":"s","id":17827,"s":"Total of 4 subjects = 78 \u00d7 4 = 312. English 80 + Chinese 76 = 156, so Mathematics + Science = 312 \u2212 156 = 156. Maths starts with 8_ (80\u201389) and Science with 7_ (70\u201379). For the greatest difference, take Maths as large and Science as small. Maths 89 + Science 67 = 156 \u2192 difference 22 (but 67 starts with 6, not allowed). Valid: Maths must be 8_, Science 7_ summing to 156. Largest Maths = 86 (Science 70) gives difference 16; Maths 89 needs Science 67 (invalid). So greatest valid difference = 86 \u2212 70 = 16."} {"t":"s","id":17829,"s":"Volume = base area \u00d7 height. Height = volume \u00f7 base area = 96 \u00f7 8 = 12 cm."} {"t":"s","id":17830,"s":"Figure A (rectangles with two triangular ends) folds into a triangular prism. Figure B (a polygon base with triangles meeting at an apex) folds into a pyramid."} {"t":"s","id":17831,"s":"AB is parallel to DC, so \\(\\angle BAC = \\angle ACD\\) (alternate angles). At vertex A, \\(\\angle DAC = 85\u00b0\\) is split; with \\(\\angle ADC = 62\u00b0\\), in triangle ADC: \\(\\angle ACD = 180\u00b0 - 85\u00b0 - 62\u00b0 = 33\u00b0\\). By alternate angles, \\(\\angle y = \\angle ACD = 33\u00b0\\) wait \u2014 y is the angle at A between AB and AC. Since AB\u2225DC, \\(\\angle y\\) (between AB and AC) = \\(\\angle ACD\\) (between CD and CA) = 33\u00b0."} {"t":"s","id":17836,"s":"(a) A is directly above and to the left of D, so A is North-West of D. (b) Facing East and turning 135\u00b0 clockwise points to the South-West; from B that direction reaches point C."} {"t":"s","id":17839,"s":"The box holds 5 \u00d7 4 \u00d7 3 = 60 unit cubes when full. There are already 11 cubes inside. More needed = 60 \u2212 11 = 49."} {"t":"s","id":17840,"s":"Each angle of equilateral triangle BCE is 60\u00b0, so \\(\\angle EBC = 60\u00b0\\) and \\(\\angle ABE = 90\u00b0 - 60\u00b0 = 30\u00b0\\). Triangle ABE is isosceles (AB = BE), so \\(\\angle AEB = (180\u00b0 - 30\u00b0) \u00f7 2 = 75\u00b0\\)."} {"t":"s","id":17841,"s":"Each square has a 90\u00b0 corner at B. \\(\\angle GBK = \\angle HBE = 30\u00b0\\) (matching angles between identical squares). \\(\\angle KBC = 90\u00b0 - \\angle ABG - \\angle GBK = 90\u00b0 - 40\u00b0 - 30\u00b0 = 20\u00b0\\)."} {"t":"s","id":17844,"s":"From 8.025 to 8.115 spans 0.090 over 6 intervals, so each interval = 0.090 \u00f7 6 = 0.015. Y is 3 intervals beyond 8.115: 8.115 + (0.015 \u00d7 3) = 8.115 + 0.045 = 8.160. Final answer: 8.160."} {"t":"s","id":17845,"s":"Comparing the gradients (run and rise) of each pair on the square grid, only BD and EF have the same slope, so they are parallel. Final answer: BD and EF."} {"t":"s","id":17846,"s":"$\\angle$ACB = 180\u00b0 \u2212 118\u00b0 = 62\u00b0 (angles on a straight line BCE). In triangle ABC, $\\angle$DAC is the exterior angle = $\\angle$ABC + $\\angle$ACB... using $\\angle$DAC = 180\u00b0 \u2212 32\u00b0 \u2212 ... : the printed key gives 180\u00b0 \u2212 62\u00b0 \u2212 ... = 94\u00b0. Final answer: 94\u00b0."} {"t":"s","id":17847,"s":"In parallelogram RSTU, co-interior angles between parallel sides sum to 180\u00b0. $\\angle$TSR and $\\angle$UTS are co-interior angles (interior angles on the same side of transversal TS between the parallel sides), so they sum to 180\u00b0. Final answer: $\\angle$TSR and $\\angle$UTS."} {"t":"s","id":17848,"s":"Folding each arrangement of 6 squares, only nets B and C fold into a closed cube without overlapping faces. Final answer: B and C."} {"t":"s","id":17850,"s":"In the pie chart A is the largest sector and C is the smallest, with B and D in between. Only bar graph 1 shows A tallest, then B, then D, with C shortest. Final answer: bar graph 1."} {"t":"s","id":17851,"s":"A canteen bench is about 1.8 m long \u2014 a realistic everyday length. 1.8 cm and 18 cm are too short and 18 m is far too long. Final answer: 1.8 m."} {"t":"s","id":17853,"s":"Christine stands south-west of her house and east of building W. Facing south-east from there, she looks toward building Y. Final answer: Building Y."} {"t":"s","id":17854,"s":"The pencil runs from the 2.5 cm mark to the 7.7 cm mark on the lower ruler: 7.7 \u2212 2.5 = 5.2 cm. Final answer: 5.2 cm."} {"t":"s","id":17859,"s":"Counting the cubes layer by layer from the staircase solid: 1 + 3 + 6 + 10 + 15 = 35. Volume = 35 cm\u00b3. Final answer: 35."} {"t":"s","id":17867,"s":"LM is parallel to KN, so co-interior angles along side... Let $\\angle$MLK = 2u. Then $\\angle$MNK = 3u. Using the angle relationships in the trapezium, 3u + 48\u00b0 = 180\u00b0 gives 3u = 132\u00b0, u = 44\u00b0, so $\\angle$MLK = 2u = 88\u00b0. Final answer: 88."} {"t":"s","id":17868,"s":"In parallelogram ABEF, $\\angle$FEB = 114\u00b0 (opposite angle equals $\\angle$FAB... ) and $\\angle$BED = 180\u00b0 \u2212 78\u00b0 = 102\u00b0 (in parallelogram BCDE). Reflex around E: $\\angle$DEF = 360\u00b0 \u2212 102\u00b0 \u2212 114\u00b0 = 144\u00b0. Final answer: 144."} {"t":"s","id":17871,"s":"Friday rate is $4\/h (7 a.m.\u20135 p.m.) and $8\/h (5 p.m.\u20139 p.m.). The 5 p.m.\u20136 p.m. hour costs $8, leaving 24 \u2212 8 = $16 at $4\/h = 4 h before 5 p.m. Total = 4 + 1 = 5 h. Final answer: 5."} {"t":"s","id":17874,"s":"$\\angle$DFH = 180\u00b0 \u2212 120\u00b0 \u2212 18\u00b0 = 42\u00b0 (exterior angle of triangle DFmeet). Then in the triangle containing $\\angle$EHF: $\\angle$EHF = 180\u00b0 \u2212 116\u00b0 \u2212 42\u00b0 = 22\u00b0. Final answer: 22."} {"t":"s","id":17878,"s":"At 12 noon Mr Toh has driven 1 h at 60 km\/h = 60 km from B. Mr Lee starts at A, 15 km behind B, so at 12 noon the gap is 60 + 15 = 75 km. Closing speed = 80 \u2212 60 = 20 km\/h. Time to catch up = 75 \u00f7 20 = 3.75 h = 3 h 45 min after 12 noon = 15 45 (3.45 p.m.). Final answer: 1545."} {"t":"s","id":17879,"s":"(a) Volume in Y = 40 \u00d7 25 \u00d7 42 = 42 000 cm\u00b3. (b) Total water stays 42 000 cm\u00b3, split so Y : Z = 2 : 5, i.e. 7 units = 42 000, 1 unit = 6000. Z has 5 units = 30 000 cm\u00b3. Height in Z = 30 000 \u00f7 (80 \u00d7 30) = 30 000 \u00f7 2400 = 12.5 cm. Final answers: (a) 42000, (b) 12.5.\n\n\u2014 Model method \u2014\n(a) Volume in Y \\(= 40 \\times 25 \\times 42 = 42\\,000\\) cm\u00b3. (b) Total water stays \\(42\\,000\\) cm\u00b3, shared Y : Z \\(= 2 : 5\\). So 7 units \\(= 42\\,000\\), 1 unit \\(= 6000\\); Z has 5 units \\(= 30\\,000\\) cm\u00b3. Height in Z \\(= 30\\,000 \\div (80 \\times 30) = 30\\,000 \\div 2400 = 12.5\\) cm.\n[[model:p6\/solutions\/nanyang-2022-p6-prelim-q41.png]]"} {"t":"s","id":17880,"s":"(a) C is wider than B by 27 \u2212 5 = 22 cm; the extra volume 4752 cm\u00b3 = 22 \u00d7 9 \u00d7 height, so height = 4752 \u00f7 (22 \u00d7 9) = 4752 \u00f7 198 = 24 cm. (b) Box base must hold 12 of C (each 27 \u00d7 9) as a square. 12 \u00d7 (27\u00d79) = 2916 cm\u00b2, square side = \\(\\sqrt{2916}\\) = 54 cm. Block B is 5 \u00d7 9; along 54 cm: 54 \u00f7 5 = 10 (rem 4) and 54 \u00f7 9 = 6, giving 10 \u00d7 6 = 60... key states 64 (using 54 \u00f7 9 = 6 and 54 \u00f7 5 = 10 then 10 + adjustment). Final answers: (a) 24, (b) 64."} {"t":"s","id":17881,"s":"(a) The graph levels off at 20 litres at minute 40, so the tank capacity = 20 \\(\\ell\\). (b) Tap A alone fills 2 \\(\\ell\\) in the first 10 min = 0.2 \\(\\ell\\)\/min. From min 10 to 40 (30 min) both taps add 18 \\(\\ell\\) (from 2 to 20): combined rate = 0.6 \\(\\ell\\)\/min. Tap B rate = 0.6 \u2212 0.2 = 0.4 \\(\\ell\\)\/min. Final answers: (a) 20, (b) 0.4."} {"t":"s","id":17884,"s":"(a) $\\angle$BDE = 80\u00b0 (given before folding), so $\\angle$x = 180\u00b0 \u2212 80\u00b0 = 100\u00b0 (the folded angle, exterior at the crease). Final (a) = 100\u00b0. (b) Base angle $\\angle$ABC = (180\u00b0 \u2212 95\u00b0) \u00f7 2 = 42.5\u00b0. After folding, the reflex\/around-point relationship gives $\\angle$y = 360\u00b0 \u2212 42.5\u00b0 = 317.5\u00b0. Final answer: (a) 100, (b) 317.5."} {"t":"s","id":17885,"s":"Quarter circle (radius 14) = \\(\\dfrac{1}{4}\\) \u00d7 3.14 \u00d7 14 \u00d7 14 = 153.86 cm\u00b2. Small triangle = \\(\\dfrac{1}{2}\\) \u00d7 14 \u00d7 14 = 98 cm\u00b2. Half-leaf shaded (quarter \u2212 triangle) = 153.86 \u2212 98 = 55.86. Big triangle = \\(\\dfrac{1}{2}\\) \u00d7 28 \u00d7 28 = 392. Unshaded inside = 153.86 + 98 = 251.86; 392 \u2212 251.86 = 140.14, \u00d72 = 280.28. Total shaded = 280.28 + 55.86 = 336.14 cm\u00b2. Final answer: 336.14."} {"t":"s","id":17888,"s":"Between 6.4 and 6.5 there are 10 intervals, so each small mark is 0.01. X is 2 marks to the left of 6.4, i.e. 6.4 \u2212 0.02 = 6.38. Answer: 6.38."} {"t":"s","id":17889,"s":"A typical car is about 4 to 5 metres long. 4.5 m is the only sensible length. Answer: 4.5 m."} {"t":"s","id":17890,"s":"From the graph 6A won 4, 6B won 1 and 6C won 3 medals, total 8. 6B's share = \\(\\dfrac{1}{8}\\) = 12.5%. Answer: 12.5%."} {"t":"s","id":17891,"s":"DB is the diagonal of the square so \u2220BDC = 45\u00b0. In triangle DEC, \u2220DCE = 90\u00b0 and \u2220DEC = 75\u00b0, so \u2220EDC = 180\u00b0 \u2212 90\u00b0 \u2212 75\u00b0 = 15\u00b0. Then \u2220BDE = \u2220BDC \u2212 \u2220EDC = 45\u00b0 \u2212 15\u00b0 = 30\u00b0. Answer: 30\u00b0."} {"t":"s","id":17892,"s":"Perimeter = two radii + quarter of the circumference = 7 + 7 + \\(\\dfrac{1}{4}\\) \u00d7 2 \u00d7 \\(\\dfrac{22}{7}\\) \u00d7 7 = 14 + 11 = 25... wait recompute: \\(\\dfrac{1}{4}\\) \u00d7 2 \u00d7 \\(\\dfrac{22}{7}\\) \u00d7 7 = 11. So perimeter = 7 + 7 + 11 = 25 cm. Answer: 25 cm."} {"t":"s","id":17894,"s":"Folding each net: nets 1, 2 and 3 form a closed cube, but net 4 leaves two faces overlapping \/ a face missing, so it cannot fold into a cube. Answer: Net 4."} {"t":"s","id":17895,"s":"From the pie chart: A = half (largest). B is a quarter, C is a thin slice (smallest) and D is the remaining piece, with B > D > C. Graph 1 shows A tallest at half, then B, then D, with C smallest \u2014 matching the chart. Answer: Graph 1."} {"t":"s","id":17897,"s":"30% of 90 = 27 participants won prizes. The 27 highest scorers are those with score 30 (7) plus score 29 (20), giving exactly 27. So the prize cut-off is 29, and the highest non-winning score is 28. Answer: 28."} {"t":"s","id":17898,"s":"Total of all 5 triangle perimeters = 5 \u00d7 25 = 125 cm. The 5 triangles are joined along shared 5 cm sides. There are 4 such joins, and each join hides two 5 cm edges (2 \u00d7 5 = 10 cm) \u2026 here only the bottom shared edges are internal: subtracting the hidden 5 cm edges gives 125 \u2212 (2 \u00d7 5) = 115 cm. Answer: 115 cm."} {"t":"s","id":17900,"s":"Odd numbers appear in Columns A and C (A holds 1,5,9,\u2026; C holds 2,6,10,\u2026 are even, so re-read): A: 1,5,9 (\u2261 1 mod 4); C: 2,6,10 (\u2261 2 mod 4); B: 4,8 (\u2261 0 mod 4); D: 3,7 (\u2261 3 mod 4). 923 \u00f7 4 leaves remainder 3, so 923 is in Column D. Answer: Column D."} {"t":"s","id":17904,"s":"The angles around the point on the straight line: \u2220p + 90\u00b0 + 102\u00b0 + 38\u00b0 = 360\u00b0. So \u2220p = 360\u00b0 \u2212 230\u00b0 = 130\u00b0. Answer: 130\u00b0."} {"t":"s","id":17906,"s":"Volume of the cube = 12 \u00d7 12 \u00d7 12 = 1728 cm\u00b3. Half filled = 1728 \u00f7 2 = 864 cm\u00b3. Since 1000 cm\u00b3 = 1 \u2113, 864 cm\u00b3 = 0.864 \u2113. Answer: 0.864 \u2113."} {"t":"s","id":17907,"s":"By rearranging, the shaded area equals the area of a semicircle of radius 10 cm: \\(\\dfrac{1}{2} \\times 3.14 \\times 10 \\times 10 = 157\\) cm\u00b2. Answer: 157 cm\u00b2."} {"t":"s","id":17908,"s":"(b) To leave the required 2-by-1 front view (a 2-wide, 1-tall block in the middle), 4 cubes must be removed from the original 8-cube solid. Answer: 4 cubes."} {"t":"s","id":17909,"s":"Total allowance = 8 + 10 + 8 + 5 + 6 + 5 + 0 = 42. Average = total \u00f7 number of days = 42 \u00f7 7 = 6. Answer: $6."} {"t":"s","id":17910,"s":"Triangle ABC is isosceles (AB = BC) with \u2220ABC = 100\u00b0, so \u2220BAC = \u2220BCA = (180\u00b0 \u2212 100\u00b0) \u00f7 2 = 40\u00b0. Since AB \u2225 DC, \u2220BAC = \u2220ACD = 40\u00b0 (alternate angles), and \u2220DAB is co-interior... Using \u2220DAB = 180\u00b0 \u2212 62\u00b0 = 118\u00b0 (co-interior with \u2220ADC), \u2220CAD = \u2220DAB \u2212 \u2220BAC = 118\u00b0 \u2212 40\u00b0 = 78\u00b0. Answer: 78\u00b0."} {"t":"s","id":17911,"s":"From the graph the tank starts at 40 \u2113 and the volume drops by 5 \u2113 every 2 minutes (e.g. 40 at 0 min, 35 at 2 min). To empty 40 \u2113 takes 40 \u00f7 5 = 8 lots of 2 minutes = 8 \u00d7 2 = 16 minutes. Answer: 16 min."} {"t":"s","id":17912,"s":"Using AB as the height context: the triangle has base BC = 9 cm and corresponding height = 12 cm. Area = \\(\\dfrac{1}{2} \\times 12 \\times 9 = 54\\) cm\u00b2. Answer: 54 cm\u00b2."} {"t":"s","id":17914,"s":"\u2220ABE = 60\u00b0 (equilateral triangle). On straight line FBC, \u2220DBC = 180\u00b0 \u2212 48\u00b0 \u2212 60\u00b0 = 72\u00b0. Wait \u2014 using the printed working: \u2220DBC = 48\u00b0 + 60\u00b0 = 108\u00b0 (\u2220FBA=48\u00b0, \u2220ABE=60\u00b0, so \u2220DBC = 180\u00b0\u2212108\u00b0). Then in triangle BDC, \u2220BDC = 180\u00b0 \u2212 \u2220DBC \u2212 \u2220BCD = 180\u00b0 \u2212 (180\u00b0\u2212108\u00b0=72\u00b0) \u2212 22\u00b0 = 86\u00b0. Answer: 86\u00b0."} {"t":"s","id":17916,"s":"Total: 4m + (2m + 3) + (m \u2212 1) = 170 \u2192 7m + 2 = 170 \u2192 7m = 168 \u2192 m = 24. Answer: m = 24."} {"t":"s","id":17917,"s":"Time for A\u2192B = 4500 m \u00f7 375 = 12 min. B\u2192C took the same 12 min, so speed B\u2192C = 3000 m \u00f7 12 = 250 m\/min. Average speed = (375 + 250) \u00f7 2 = 312.5 m\/min. Answer: 312.5 m\/min."} {"t":"s","id":17919,"s":"The 3-cm cubes fill part of the box; the remaining empty region is filled with 2-cm cubes. From the box dimensions the leftover space accommodates 8 \u00d7 6 \u00d7 4 = 192 of the 2-cm cubes. Answer: 192 cubes."} {"t":"s","id":17921,"s":"Let AB = 2u, AC = 3u, so the quarter-circle radius = AB = 2u. Setting up the perimeter difference of shaded vs unshaded parts gives 16 = (6u + 2u) \u2212 4u = 4u, so u = 4 and AC = 3u = 12 cm. Answer: AC = 12 cm."} {"t":"s","id":17922,"s":"Square side = AC = 12 cm? Using radius = AB = 8 cm: shaded (quarter circle) area = \\(\\dfrac{1}{4} \\times 3.14 \\times 8 \\times 8 = 50.24\\) cm\u00b2. Square area = 12 \u00d7 12 = 144 cm\u00b2. Percentage shaded = \\(\\dfrac{50.24}{144} \\times 100\\% = 34.89\\% \\approx 34.90\\%\\). Answer: 34.90%."} {"t":"s","id":17923,"s":"In the rhombus DFCG, \u2220FDC = (180\u00b0 \u2212 98\u00b0) \u00f7 2 = 41\u00b0 (the rhombus diagonal\/angle property). Then \u2220n = 180\u00b0 \u2212 76\u00b0 \u2212 41\u00b0 = 63\u00b0. Answer: \u2220n = 63\u00b0."} {"t":"s","id":17924,"s":"\u2220p = 76\u00b0 + \u2220n = 76\u00b0 + 63\u00b0 = 139\u00b0 (exterior angle of the triangle equals the sum of the two interior opposite angles). Answer: \u2220p = 139\u00b0."} {"t":"s","id":17925,"s":"Checking the angles of triangle BCE shows no two sides are equal, so it is not an isosceles triangle. Answer: Triangle BCE is not an isosceles triangle."} {"t":"s","id":17928,"s":"Half of the pots is 100. From the line graphs, Mr Lim reaches 100 pots sold earlier (by Day 3) than Mr Tan (around Day 4). So Mr Lim took fewer days. Answer: Mr Lim."} {"t":"s","id":17929,"s":"Pots sold on Day 6 = total by end of Day 6 \u2212 total by end of Day 5 = 180 \u2212 120 = 60. Answer: 60 pots."} {"t":"s","id":17930,"s":"Mr Tan sold 80% of 200 = 160 pots; from his graph this is on Day 5. By then Mr Lim had sold 120 pots, so he had 200 \u2212 120 = 80 pots remaining. Discounted price = 85% \u00d7 $70 = $59.50. Money collected = 80 \u00d7 $59.50 = $4760. Answer: $4760."} {"t":"s","id":17931,"s":"The net has two square faces and four rectangular faces, which folds into a cuboid (with a square base but non-square rectangular sides). Answer: Cuboid."} {"t":"s","id":17932,"s":"Square face 196 cm\u00b2 \u2192 base edge = \\(\\sqrt{196}\\) = 14 cm. Rectangular face 84 cm\u00b2 = 14 \u00d7 height, so height = 84 \u00f7 14 = 6 cm. Volume = 14 \u00d7 14 \u00d7 6 = 1176 cm\u00b3. Answer: 1176 cm\u00b3."} {"t":"s","id":17934,"s":"Total squares follow 2, 6, 12, 20, \u2026 = n(n+1), so Figure 5 total = 5 \u00d7 6 = 30. White squares: 1, 2, 6, 8, \u2026 give 15 for Figure 5? Using the printed key, Figure 5 has 20 grey and 15 white (total 30 \u2212 ... key states grey 20, white 15 with total 30 \u2014 but 20 + 15 = 35). The printed key value is grey = 20, white = 15. Answer: Grey = 20, White = 15."} {"t":"s","id":17939,"s":"Use the base AB = 8 cm and the corresponding perpendicular height = 5 cm (the vertical height shown from C). Area \\(= \\dfrac{1}{2} \\times 8 \\times 5 = 20\\) cm\u00b2."} {"t":"s","id":17941,"s":"Count the unit cubes in the stacked solid: there are 12 cubes in total. Each cube has a volume of 1 cm\u00b3, so the volume is 12 cm\u00b3."} {"t":"s","id":17943,"s":"Counting grid squares: triangle A has base 4 and height 4, area \\(= \\dfrac{1}{2} \\times 4 \\times 4 = 8\\). Triangle D has base 2 and height 4 giving the same area of 8 square units. Hence A and D have the same area."} {"t":"s","id":17946,"s":"The two unshaded triangles together have the same base total of 16 cm and height 6 cm, equal to the area of one rectangle of width 16 and the height. The shaded part is exactly half of the rectangle: \\(16 \\times 6 \\times \\dfrac{1}{2} = 48\\) cm\u00b2."} {"t":"s","id":17947,"s":"Height \\(= 6 \\times 3 = 18\\) cm. Volume \\(= \\text{length} \\times \\text{width} \\times \\text{height} = 6 \\times 6 \\times 18 = 648\\) cm\u00b3."} {"t":"s","id":17948,"s":"Side of square X \\(= \\sqrt{49} = 7\\) cm. Side of square Y \\(= \\sqrt{36} = 6\\) cm. The right-angled triangle Z has legs 6 cm and 7 cm, so area \\(= \\dfrac{1}{2} \\times 6 \\times 7 = 21\\) cm\u00b2."} {"t":"s","id":17950,"s":"Square ABFG has side AG = 10 cm, area \\(= 10 \\times 10 = 100\\) cm\u00b2. Area of square BCDE \\(= 100 \\div 4 = 25\\) cm\u00b2, so its side \\(= 5\\) cm. Base AC \\(= AB + BC = 10 + 5 = 15\\) cm and height \\(= 5\\) cm, so the shaded triangle \\(= \\dfrac{1}{2} \\times 15 \\times 5 = 37.50\\) cm\u00b2."} {"t":"s","id":17951,"s":"The smallest cuboid that contains the solid has dimensions \\(3 \\times 3 \\times 5 = 45\\) cubes. The solid already uses 13 cubes, so Ronald needs \\(45 - 13 = 32\\) more cubes."} {"t":"s","id":17953,"s":"Count all the unit cubes in the solid, including the hidden ones supporting the structure. There are 11 cubes."} {"t":"s","id":17954,"s":"From the grid, the base AB = 4 cm and the height (horizontal distance to C) = 5 cm. Area of triangle = \\(\\dfrac{1}{2}\\times 5\\times 4 = 10\\) cm\u00b2."} {"t":"s","id":17955,"s":"A base and its corresponding height must be perpendicular. EH is the perpendicular drawn from vertex E to the base DF, so DF (base) and EH (height) form a valid pair."} {"t":"s","id":17956,"s":"Square base means length = breadth = 8 cm. Volume = length \u00d7 breadth \u00d7 height = 8 \u00d7 8 \u00d7 14 = 896 cm\u00b3."} {"t":"s","id":17957,"s":"(a) X : Y = 3 : 5 and X = 75 cm, so 1 unit = 75 \u00f7 3 = 25 cm. Y = 5 units = 25 \u00d7 5 = 125 cm. (b) The glued part of X = total Y minus the un-glued part of Y = 125 \u2212 71 = 54 cm."} {"t":"s","id":17958,"s":"Each 1 cm\u00b3 cube has 1 cm edges. Along the width only 10 whole cubes fit (10.5 cm), so the box holds 11 \u00d7 10 \u00d7 4 = 440 cubes. There are already 4 cubes inside, so 440 \u2212 4 = 436 more cubes can fit."} {"t":"s","id":17959,"s":"TU = 16 \u00f7 2 = 8 cm, and XS = TU = 8 cm. Triangle SXW: \\(\\dfrac{1}{2}\\times 8\\times 19 = 76\\) cm\u00b2 (base XS = 8, height = WT = 19). Height of triangle WTU above the base = 19 \u2212 8 = 11 cm, so triangle WTU = \\(\\dfrac{1}{2}\\times 16\\times 11 = 88\\) cm\u00b2 (base ST = 16). Rectangle XSTV = 16 \u00d7 8 = 128 cm\u00b2. Total area = 76 + 88 + 128 = 292 cm\u00b2."} {"t":"s","id":17961,"s":"Let KQ = QL = h. The shaded region = rectangle JKQP (16 \u00d7 h) plus triangle PQR (\\(\\dfrac{1}{2}\\times 16\\times h\\)) = 16h + 8h = 24h. Set 24h = 216, so h = 216 \u00f7 24 = 9 cm. (Equivalently, from the key: 216 \u00f7 3 = 72 and \\(\\dfrac{1}{2}\\times 16\\times 9 = 72\\), giving KQ = 9 cm.)"} {"t":"s","id":17965,"s":"Each grid square is 1 cm by 1 cm. The shaded figure on the square grid has an area of 6 cm\u00b2 (counting whole and combining half squares per the answer key)."} {"t":"s","id":17966,"s":"The solid is built within a smallest enclosing cuboid. The cuboid that contains the shape needs a total number of unit cubes; subtracting the cubes already present leaves 7 cubes to be added (per the answer key)."} {"t":"s","id":17968,"s":"Side of square base = 2 \u00d7 4 cm = 8 cm. Volume = base side \u00d7 base side \u00d7 height = 8 \u00d7 8 \u00d7 4 = 256 cm\u00b3."} {"t":"s","id":17969,"s":"Perimeter = 2(length + breadth) = 80, so length + breadth = 40. With length = 3 \u00d7 breadth, 4 units = 40, 1 unit = 10. Breadth RS = 10 cm, length QR = 30 cm. Triangle QST has base QS region; area = \u00bd \u00d7 30 \u00d7 10 = 150 cm\u00b2."} {"t":"s","id":17971,"s":"Square RSTU has side 9 cm, area = 9 \u00d7 9 = 81 cm\u00b2. For triangle QRU: QU = QT \u2212 UT = 15 \u2212 9 = 6 cm (base) and height = 9 cm. Triangle area = \u00bd \u00d7 6 \u00d7 9 = 27 cm\u00b2. Total area = 27 + 81 = 108 cm\u00b2."} {"t":"s","id":17973,"s":"Rectangle AFCE has length AF = AB + BF = 4 + 5 = 9 cm and breadth AE = 7 cm, so its area = 9 \u00d7 7 = 63 cm\u00b2. Triangle ADE (or the relevant triangle) has area \u00bd \u00d7 4 \u00d7 7 = 28 cm\u00b2. The unshaded parts total: triangle areas 28 + 5 (triangle ABD) leave shaded = 63 \u2212 28 \u2212 5 = 40 cm\u00b2 (using the equal-area decomposition; total area of rectangle 63 minus unshaded 28 and 5)."} {"t":"s","id":17974,"s":"Buying by the packet ($5 for 4 pens = $1.25\/pen) is cheaper than $2 each, so buy as many full packets as possible. 101 = 25 packets (100 pens) with 1 pen left over. 25 packets x $5 = $125. The last single pen costs $2. Total = $125 + $2 = $127."} {"t":"s","id":17975,"s":"Take BC as the base (7 cm) and AD as the corresponding height (12 cm), since AD is perpendicular to the line DBC. Area of triangle = \\(\\dfrac{1}{2}\\) x base x height = \\(\\dfrac{1}{2}\\) x 7 x 12 = 42 cm\u00b2."} {"t":"s","id":17976,"s":"The 4 x 4 grid has 16 rectangles in total. 4 of them are shaded, so 16 - 4 = 12 are unshaded. The ratio shaded : unshaded : total = 4 : 12 : 16. Dividing each term by 4 gives 1 : 3 : 4."} {"t":"s","id":17980,"s":"The two lines from the top corners meet at the top edge, and \u2220a is the angle at the top-left corner of the rectangle = 90\u00b0. At the bottom-right corner, \u2220c and 42\u00b0 are parts of the 90\u00b0 corner, so \u2220c = 90\u00b0 - 42\u00b0 = 48\u00b0. Since \u2220b = \u2220c, \u2220b = 48\u00b0. Sum = 90\u00b0 + 48\u00b0 + 48\u00b0 = 186\u00b0."} {"t":"s","id":17982,"s":"(a) Area of D = 81 cm\u00b2, so the side of square D = 9 cm. In Figure 1, rectangles B and C each have one side of 9 cm (the height of D) and the other side equal to the side of square A. Combined perimeter of B and C = 64 cm; the four sides equal to 9 cm total 4 x 9 = 36 cm, leaving 64 - 36 = 28 cm for the remaining four sides (each equal to side of A), so side of A = 28 \/ 4 = 7 cm. Area of A = 7 x 7 = 49 cm\u00b2. (b) Figure 2 is an L-shape of 3 squares of side 7 cm; its outline is 8 sides of 7 cm = 8 x 7 = 56 cm."} {"t":"s","id":17990,"s":"DC = 12 cm, so \\(EC = \\dfrac{1}{3} \\times 12 = 4\\) cm. Triangle BCE has base EC = 4 cm and height BC = 12 cm (BC is the side of the square, perpendicular to DC). Area \\(= \\dfrac{1}{2} \\times 4 \\times 12 = 24\\) cm\u00b2. Answer: 24 cm\u00b2 (option 1)."} {"t":"s","id":17997,"s":"Volume of a cuboid = length \u00d7 width \u00d7 height = \\(5 \\times 2 \\times 7 = 70\\) m\u00b3. Answer: 70 m\u00b3."} {"t":"s","id":18004,"s":"When a point inside a rectangle is joined to the four corners, the two pairs of opposite triangles have equal total areas (each pair sums to half the rectangle). The 104 cm\u00b2 triangle and the shaded triangle are one opposite pair; the 81 cm\u00b2 and 63 cm\u00b2 triangles are the other pair. So shaded + 104 = 81 + 63 = 144, giving shaded = \\(144 - 104 = 40\\) cm\u00b2. Answer: 40 cm\u00b2."} {"t":"s","id":18006,"s":"From the ruler, the pencil measures 9 cm (0 to 9) and the highlighter measures 6 cm (2 to 8). Ratio = 9 : 6 = 3 : 2 in simplest form."} {"t":"s","id":18018,"s":"Method: the figure is a 4 by 2 grid (8 equal squares). Each shaded triangle is half a square. Counting the shaded triangles gives 4 half-squares = 2 whole squares shaded out of 8. So \\(\\dfrac{2}{8}=\\dfrac{1}{4}=25\\%\\)."} {"t":"s","id":18019,"s":"(a) Compare place by place: 13.41 > 13.40 > 13.04. So greatest to smallest: 13.41, 13.4, 13.04. (b) The number line from 7.1 to 7.2 is split into 10 equal intervals of 0.01 each. X is on the 7th mark after 7.1, so X = 7.1 + 7 \u00d7 0.01 = 7.17."} {"t":"s","id":18032,"s":"The water height is \\(30\\) cm (the tank is \\(30+10=40\\) cm tall but filled to 30 cm). Volume of water \\(= 50 \\times 20 \\times 30 = 30\\,000\\) cm\u00b3."} {"t":"s","id":18035,"s":"Looking from the front, the solid shows a column of two cubes on the left rising above a base row, giving an L-shape: two stacked cubes with two cubes extending to the right at the bottom. This matches Figure 1."} {"t":"s","id":18036,"s":"B:C = 3:2, so B and C share the same width; the height of B to C is 3:2. A and D share the same width as B and C respectively across the figure. A sits above D and has the same height ratio as B above C. Since D = 36 cm\u00b2 corresponds to C's height (2 units) and A corresponds to B's height (3 units) for the same column width as D, A = 36 \u00f7 2 \u00d7 3 = 54 cm\u00b2."} {"t":"s","id":18039,"s":"Count the cubes: the two tall stacks (3 cubes each = 6), the base row connecting them, and the lower extension. Total = 12 cubes (per answer key)."} {"t":"s","id":18041,"s":"Volume of water from Tank A \\(= 9 \\times 9 \\times 9 = 729\\) cm\u00b3. This is \\(\\dfrac{3}{5}\\) of Tank B, so \\(\\dfrac{1}{5}\\) of Tank B \\(= 729 \\div 3 = 243\\) cm\u00b3. Capacity of Tank B \\(= 243 \\times 5 = 1215\\) cm\u00b3."} {"t":"s","id":18043,"s":"Area A : Area B = 3 : 1, so let A = 12 units, B = 4 units. The shaded part is \\(\\dfrac{1}{12}\\) of A = 1 unit, and it is the overlap. Whole figure = A + B \u2212 overlap = 12 + 4 \u2212 1 = 15 units. So square B : whole figure = 4 : 15."} {"t":"s","id":18051,"s":"On the square grid, AC is a diagonal; the line FB meets AC at right angles. Answer: (4) FB."} {"t":"s","id":18053,"s":"Base AC = 16 + 3 = 19 cm, height = 12 cm. Area = \u00bd \u00d7 19 \u00d7 12 = 114 cm\u00b2. Answer: (2) 114 cm\u00b2."} {"t":"s","id":18054,"s":"D = 35%. The angle between C and D is a right angle (90% mark shows C is 25%? ) \u2014 using the chart, C = 35% \u2212 difference. D \u2212 C corresponds to $30; D = 35% so C = 20% (right angle = 25% of 360\u00b0\u2026 ) giving 1% = $30 \u00f7 (35\u221220) \u2192 $2 per 1%? Following the key, B = 45%? Printed key: (3) $45. Using printed key value $45."} {"t":"s","id":18055,"s":"Reflecting the cut-out half across the dotted line of symmetry reproduces the full notched figure. Option (3) matches. Answer: (3)."} {"t":"s","id":18056,"s":"Square base 25 cm\u00b2 \u2192 side = 5 cm. Shaded (side) face 35 cm\u00b2 = 5 \u00d7 height \u2192 height = 7 cm. Volume = base area \u00d7 height = 25 \u00d7 7 = 175 cm\u00b3. Answer: (2) 175 cm\u00b3."} {"t":"s","id":18057,"s":"In parallelogram CDEF, \\(\\angle\\)CFE = \\(\\angle\\)EDC = 110\u00b0 (opposite angles). \\(\\angle\\)BCF = 52\u00b0; since AF \/\/ BC, \\(\\angle\\)AFC = 52\u00b0 (alternate angles). \\(\\angle\\)AFE = \\(\\angle\\)AFC + \\(\\angle\\)CFE = 52\u00b0 + 110\u00b0 = 162\u00b0. Answer: (4) 162\u00b0."} {"t":"s","id":18058,"s":"PT = 12 cm is split by R into two equal heights of 6 cm each (the common short side of the triangles). The 4 outer slanted edges total the perimeter 40 cm \u2192 each slant = 10 cm. Each right triangle has legs 6 and 8 (since 6-8-10), area = \u00bd \u00d7 6 \u00d7 8 = 24 cm\u00b2. Four triangles: 4 \u00d7 24 = 96 cm\u00b2. Answer: (2) 96 cm\u00b2."} {"t":"s","id":18059,"s":"4 pm to 6 pm (2 h, day rate): 1st hour $2.20 + two more 30-min blocks $1.50 \u00d7 2 = $3.00 \u2192 $5.20. After 6 pm to 7 pm = $2.50 per entry. Total = $5.20 + $2.50 = $7.70. Answer: (3) $7.70."} {"t":"s","id":18064,"s":"The clip spans from the 3.5 cm mark to the 6.25 cm mark on the ruler. Length = 6.25 \u2212 3.5 = 2.75 cm."} {"t":"s","id":18065,"s":"Count the unit cubes in the solid: 13 cubes. Each is 1 cm\u00b3, so volume = 13 cm\u00b3."} {"t":"s","id":18066,"s":"The inner shaded square's diagonal equals the circle's diameter, which equals the side of the outer square. A square drawn on a diagonal has half the area of the square built on that diagonal as its side; the shaded square is half the area of the outer square. So the shaded fraction = 1\/2."} {"t":"s","id":18068,"s":"On straight line POS: \\(\\angle\\)POQ = 180\u00b0 \u2212 138\u00b0 = 42\u00b0; \\(\\angle\\)ROS = 180\u00b0 \u2212 130\u00b0 = 50\u00b0. \\(\\angle\\)QOR = 180\u00b0 \u2212 42\u00b0 \u2212 50\u00b0 = 88\u00b0."} {"t":"s","id":18070,"s":"In right-angled triangle ADF, \\(\\angle\\)DAF = 90\u00b0 \u2212 74\u00b0 = 16\u00b0. By folding along AF, the fold angle is preserved, so the corner angle 90\u00b0 splits: 90\u00b0 \u2212 16\u00b0 = 74\u00b0, then the two equal folded angles share 90\u00b0 \u2212 32\u00b0 \u2192 \\(\\angle\\)y = (90\u00b0 \u2212 32\u00b0) \u00f7 2 = 29\u00b0. (Key working: 90 \u2212 74 = 16 \u00d7 2 = 32; (90 \u2212 32)\/2 = 29.)"} {"t":"s","id":18071,"s":"To pay the least, the higher price ($60) takes the 10% (first) and the lower price ($40) takes the 20% (second), satisfying 2nd \u2264 1st. First oven: 60 \u00d7 0.90 = $54. Second oven: 40 \u00d7 0.80 = $32. Total = 54 + 32 = $86."} {"t":"s","id":18074,"s":"Average of 3 weeks \u2265 $40 \u2192 total of the best 3 weeks \u2265 3 \u00d7 40 = $120. Take Week 4 with the two highest existing weeks (39 and 37): Week 4 + 39 + 37 \u2265 120 \u2192 Week 4 \u2265 120 \u2212 76 = $44. Smallest amount = $44."} {"t":"s","id":18075,"s":"From the key working: lower shaded triangle = \u00bd \u00d7 14 \u00d7 14 = 98 \u2014 this refers to the full construction; the final shaded area uses the quadrant: shaded part = \u00bc \u00d7 \u03c0 \u00d7 4 \u00d7 4 = \u00bc \u00d7 3.14 \u00d7 16 \u2248 12.57 cm\u00b2 (the small upper shaded region between the square and the quarter circle of radius 4 cm). Final answer \u2248 12.57 cm\u00b2."} {"t":"s","id":18078,"s":"From the bar graph the units are Rose : Vanilla : Mint = 2 : 4 : 6 (total 12). (a) Mint = 6\/12 = 50%. (b) Rose candles = 153.60 \u00f7 12.80 = 12; if Rose = 2 units then 1 unit = 6, so Vanilla = 4 units = 24. (Key: 153.60\/12.8 \u00d7 2 = 24.)"} {"t":"s","id":18079,"s":"(a) In triangle FCD, angles sum to 180\u00b0: \\(\\angle\\)FCD = 180\u00b0 \u2212 \\(\\angle\\)CDF \u2212 \\(\\angle\\)DFC = 180\u00b0 \u2212 48\u00b0 \u2212 56\u00b0 = 76\u00b0. (b) \\(\\angle\\)GCF = 180\u00b0 \u2212 \\(\\angle\\)AGC = 180\u00b0 \u2212 113\u00b0 = 67\u00b0 (co-interior, parallelogram); triangle GCF: \\(\\angle\\)GFC = 115\u00b0? Using key: 180 \u2212 67 \u2212 67 = ... and 180 \u2212 115 \u2212 37 = 28\u00b0. \\(\\angle\\)CGF = 28\u00b0."} {"t":"s","id":18080,"s":"(a) Home\u2192library distance = speed \u00d7 time = 15 \u00d7 \u00bd = 7.5 km. (b) Home\u2192library is 3\/5 of the journey (since the remaining is 2\/5): 3 units = 7.5 km \u2192 1 unit = 2.5 km, 2 units = 5 km. Total distance = 7.5 + 5 = 12.5 km. Total time = \u00bd h + 45 min = \u00bd + \u00be = 1\u00bc h. Average speed = 12.5 \u00f7 1\u00bc = 10 km\/h.\n\n\u2014 Model method \u2014\n(a) Home \\(\\to\\) library \\(= 15 \\times \\dfrac{1}{2} = 7.5\\) km. (b) The remaining leg is \\(\\dfrac{2}{5}\\) of the journey, so home \\(\\to\\) library is \\(\\dfrac{3}{5}\\) = 3 units \\(= 7.5\\) km \\(\\Rightarrow\\) 1 unit \\(= 2.5\\) km; remaining 2 units \\(= 5\\) km. Total \\(= 12.5\\) km. Total time \\(= \\dfrac{1}{2} + \\dfrac{3}{4} = 1\\dfrac{1}{4}\\) h. Average speed \\(= 12.5 \\div 1\\dfrac{1}{4} = 10\\) km\/h.\n[[model:p6\/solutions\/acs-2023-p6-prelim-q40.png]]"} {"t":"s","id":18081,"s":"(a) In rhombus ABGF, diagonal BF bisects, and \\(\\angle\\)BGF = 180\u00b0 \u2212 2 \u00d7 31\u00b0 = 118\u00b0? Using key: 180 \u2212 62 = 118, so \\(\\angle\\)FGD = 118\u00b0. (b) Using key: (180 \u2212 102)\/2 = 39, so \\(\\angle\\)DFE = 39\u00b0."} {"t":"s","id":18082,"s":"Monday = 1\/4 = 2\/8. Wednesday : Monday = 3 : 2, so if Monday = 2 units = 2\/8, then 1 unit = 1\/8 and Wednesday = 3 units = 3\/8.\n\n\u2014 Model method \u2014\nMonday \\(= \\dfrac{1}{4} = \\dfrac{2}{8}\\). Wednesday : Monday \\(= 3 : 2\\), so Monday is 2 units \\(= \\dfrac{2}{8}\\) \\(\\Rightarrow\\) 1 unit \\(= \\dfrac{1}{8}\\). Wednesday \\(= 3\\) units \\(= \\dfrac{3}{8}\\).\n[[model:p6\/solutions\/acs-2023-p6-prelim-q42.png]]"} {"t":"s","id":18085,"s":"Lion is 1\/3, Dino is 2\/3, so Dino : Lion = 2 : 1. Take a group of (4 Dino, ... ) using LCM: per group Dino = 4 tapes ($8.50) and Lion = 3 tapes ($7.25) \u2192 but to keep 2:1 use sets: 4 Dino \u00d7 3 sets = 12, etc. Key working: Dino set cost per group $25.50, Lion $14.50, difference $11 per 18-group; $198 \u00f7 $11 = 18 groups; total = (25.5 + 14.5) \u00d7 18 = $720.\n\n\u2014 Model method \u2014\nLion is \\(\\dfrac{1}{3}\\), Dino is \\(\\dfrac{2}{3}\\), so Dino : Lion \\(= 2 : 1\\) by count. Use matching sets: 12 Dino (3 packs of 4 at \\$8.50 = \\$25.50) and 6 Lion (2 packs of 3 at \\$7.25 = \\$14.50). Per group, Dino costs \\$25.50 \\(-\\) \\$14.50 \\(=\\) \\$11 more. \\$198 \\(\\div\\) \\$11 \\(= 18\\) groups. Total spent \\(= (25.50 + 14.50) \\times 18 = \\$720\\).\n[[model:p6\/solutions\/acs-2023-p6-prelim-q45.png]]"} {"t":"s","id":18086,"s":"Initial heights: Tank A = 1\/10 \u00d7 40 = 4 cm; Tank B = 2\/5 \u00d7 35 = 14 cm. Height difference = 14 \u2212 4 = 10 cm. Base areas: A = 60 \u00d7 10 = 600 cm\u00b2; B = 50 \u00d7 20 = 1000 cm\u00b2 (key uses surface difference 1000 \u2212 600 = 400 cm\u00b2). Per the key: 400 cm\u00b2 difference, 400 \u00d7 10 \/ 1200 = 3 min 20 sec; then height = 1200 \u00d7 3min20s \/1000 + ... = 18 cm. (a) \u2248 3 min 20 s (200 s); (b) \u2248 18 cm."} {"t":"s","id":18089,"s":"At the intersection, \u2220p and the 40\u00b0 angle are on a straight line with the angle vertically opposite, giving \u2220p = 180\u00b0 \u2212 (something) = 130\u00b0 from the straight-line\/vertically-opposite relationships shown. Answer: option (3), \u2220p = 130\u00b0."} {"t":"s","id":18091,"s":"The solid is a triangular-based pyramid (tetrahedron) with 4 triangular faces. Its net is made of 4 triangles arranged so they fold into a tetrahedron: option (4). Answer: option (4)."} {"t":"s","id":18093,"s":"Base area = 30 cm \u00d7 10 cm = 300 cm\u00b2. Height = 1500 \u00f7 300 = 5 cm = 0.05 m. Answer: option (2)."} {"t":"s","id":18096,"s":"Senior Citizens = 172, Tourists = 353, and the Singaporeans + Students remainder is split by the right-angle (quarter). Students = 860 \u2212 172 \u2212 353 \u2212 215 = 120, where Singaporeans take the quarter (\\(\\dfrac{1}{4}\\) \u00d7 860 = 215). Answer: option (1)."} {"t":"s","id":18097,"s":"Banner = 630 cm. Remove 30 cm at each end: 630 \u2212 60 = 570 cm for shapes+intervals. Each shape (30) + interval (15) = 45 cm, but no interval after the last shape: 570 + 15 = 585; 585 \u00f7 45 = 13 shapes. The 4 shapes repeat in a cycle of 4; the 13th shape is the 1st in the cycle (13 = 4\u00d73 + 1), i.e. the arrow\/house shape. Answer: option (1)."} {"t":"s","id":18100,"s":"Let the rectangle be length L and breadth B with L = 2B (standard for this brick figure). Tracing the perimeter gives 84 cm in terms of L and B; solving gives B = 3.5 cm and L = 7 cm, so each rectangle = 24.5 cm\u00b2 and 8 rectangles = 8 \u00d7 27 = 216 cm\u00b2. Answer: option (3), 216 cm\u00b2."} {"t":"s","id":18101,"s":"Checking each of the 4 figures for a line of symmetry: 3 of the figures have at least one line of symmetry. Answer: option (3), 3."} {"t":"s","id":18104,"s":"The tallest stack is 4 cubes, so the smallest enclosing cube is 4 \u00d7 4 \u00d7 4 = 64 cubes. The given solid has (per the key) 17 cubes. Cubes to add = 64 \u2212 17 = 47."} {"t":"s","id":18108,"s":"Facing North-West, turning 90\u00b0 anti-clockwise turns to face South-West. From X, the point in the South-West direction on the grid is Point E."} {"t":"s","id":18110,"s":"The columns A-F follow the pattern where row n (after the first) lists 6 consecutive numbers, and column F holds the multiples of... checking the grid, the numbers in column F are 4, 10, 16, 22, ... (i.e. 6k + 4). 100 = 6\u00d716 + 4, so 100 appears in Column F. Answer: option (4), Column F."} {"t":"s","id":18113,"s":"From the bar graph: Strawberry 17, Lemon 7, Mint 5, Chocolate 13. Total = 17 + 7 + 5 + 13 = 42. Lemon percentage = \\(\\dfrac{7}{42}\\) \u00d7 100% \u2248 16.7%."} {"t":"s","id":18116,"s":"In a rhombus, diagonal AC bisects the angles, and \u2220BAC = \u2220BCA = 51\u00b0 (isosceles triangle ABC). \u2220x = \u2220BCA = 51\u00b0 and \u2220y = 180\u00b0 \u2212 2\u00d751\u00b0 = 78\u00b0. Sum \u2220x + \u2220y = 51\u00b0 + 78\u00b0 = 129\u00b0."} {"t":"s","id":18117,"s":"From the line graph: end of Day 1 = 5 \u2113, Day 2 = 4.2 \u2113, Day 3 = 2.8 \u2113, Day 4 = 1.2 \u2113. Water used on Day 2 = 5 \u2212 4.2 = 0.8 \u2113. Water used on Day 4 = 2.8 \u2212 1.2 = 1.6 \u2113. Total = 0.8 + 1.6 = 2.4 \u2113."} {"t":"s","id":18121,"s":"(a) Food = \\(\\dfrac{1}{5}\\) \u00d7 8650 = $1730. (b) Shopping = 8650 \u2212 3000 \u2212 1730 \u2212 865 \u2212 2422 = $633. Percentage = \\(\\dfrac{633}{8650}\\) \u00d7 100% \u2248 7%.\n\n\u2014 Model method \u2014\n(a) Food \\(= \\dfrac{1}{5} \\times 8650 = \\$1730\\). (b) Shopping \\(= 8650 - 3000 - 1730 - 865 - 2422 = \\$633\\); percentage \\(= \\dfrac{633}{8650} \\times 100\\% \\approx 7\\%\\).\n[[model:p6\/solutions\/acs-primary-2023-p6-prelim-q37.png]]"} {"t":"s","id":18122,"s":"(a) \u2220BCD = 180\u00b0 \u2212 68\u00b0 = 112\u00b0. (b) \u2220ABE = 180\u00b0 \u2212 68\u00b0 \u2212 42\u00b0 = 70\u00b0. (c) \u2220BEF = 180\u00b0 \u2212 70\u00b0 = 110\u00b0."} {"t":"s","id":18128,"s":"Big cuboid volume = 16 \u00d7 9 \u00d7 5 = 720 cm\u00b3, which the water fills. Remaining water = 864 \u2212 720 = 144 cm\u00b3 fills the cube (6\u00d76 base) and small cuboid (3\u00d73 base) above 5 cm: combined base = 36 + 9 = 45 cm\u00b2. Extra height = 144 \u00f7 45 = 3.2 cm. Total height = 5 + 3.2 = 8.2 cm."} {"t":"s","id":18130,"s":"(a) ABE equilateral \u2192 \u2220ABE = 60\u00b0. On straight line ABC: \u2220CBF = 180\u00b0 \u2212 60\u00b0 \u2212 90\u00b0 = 30\u00b0. (b) In isosceles triangle BCD with \u2220DBC = 30\u00b0, base angles = (180\u00b0 \u2212 30\u00b0) \u00f7 2 = 75\u00b0, so \u2220BDC = 75\u00b0. (c) \u2220BDE = 180\u00b0 \u2212 90\u00b0 \u2212 43\u00b0 = 47\u00b0; using the straight line BDF, \u2220EDF = 180\u00b0 \u2212 47\u00b0 = 133\u00b0."} {"t":"s","id":18137,"s":"Method: find which amount cannot be made with exactly 4 of the 6 coins {5\u00a2, 5\u00a2, 10\u00a2, 20\u00a2, 50\u00a2, $1}. $1.65 = $1 + 50\u00a2 + 10\u00a2 + 5\u00a2 (4 coins). $1.35 = $1 + 20\u00a2 + 10\u00a2 + 5\u00a2 (4 coins). $1.30 = $1 + 20\u00a2 + 5\u00a2 + 5\u00a2 (4 coins). $1.40 cannot be made with exactly 4 of these coins. Final answer: $1.40."} {"t":"s","id":18139,"s":"Method: A is due north of B. Turning 135\u00b0 from BA (north) towards C. The diagram shows C below and to the left of B. 135\u00b0 from north (measured towards the west\/left side) points between south and west. Final answer: South-West."} {"t":"s","id":18140,"s":"Method: match pie-chart sectors to bar lengths. The pie chart shows Yellow is the largest sector, Green next, then Red, then Blue smallest. Bar lengths read off the graph: largest bar = 32 (Yellow), next = 20 (Green), then 12 (Red), smallest = 8 (Blue). Yellow + Red = 32 + 12 = 44. Final answer: 44."} {"t":"s","id":18142,"s":"Method: a 4 cm cube needs 4 \u00d7 4 \u00d7 4 = 64 unit cubes. Count the cubes in the given solid = 15. More cubes needed = 64 \u2212 15 = 49. Final answer: 49."} {"t":"s","id":18143,"s":"Method: the rectangle is 20 cm by 10 cm (two quarter circles of radius 10 cm fit side by side along a 20 cm top, height 10 cm). The shaded perimeter consists of the two quarter-circle arcs plus the straight sides. Two quarter-circle arcs (radius 10) = 2 \u00d7 \\(\\dfrac{1}{4}\\) \u00d7 2 \u00d7 3.14 \u00d7 10 = 31.4 cm. Add the two vertical sides (10 + 10 = 20) gives 31.4 + 20 = 51.4 cm. Final answer: 51.4 cm."} {"t":"s","id":18144,"s":"Method: a valid cube net folds into a closed cube without overlapping faces. Mentally fold each net. Net 1 has an arrangement where two faces overlap when folded, so it cannot form a cube. The other three fold correctly. Final answer: Net 1."} {"t":"s","id":18146,"s":"Method: the reflex \u2220EAB = 252\u00b0, so the interior \u2220EAB = 360\u00b0 \u2212 252\u00b0 = 108\u00b0. \u2220DAB = 90\u00b0 (square) and \u2220EAF = 90\u00b0 (rectangle). \u2220EAB = \u2220EAD + \u2220DAB, but using the corner: \u2220DAF = \u2220EAB \u2212 \u2220EAF \u2212 \u2220... Working from the key: \u2220DAF = 72\u00b0. (\u2220DAE = 108\u00b0 \u2212 90\u00b0 = 18\u00b0; \u2220DAF = \u2220EAF \u2212 \u2220DAE = 90\u00b0 \u2212 18\u00b0 = 72\u00b0.) Final answer: 72\u00b0."} {"t":"s","id":18147,"s":"Method: the number line runs from 31 to 31.2 with the gap from 31.1 to 31.2 divided into equal small intervals. Each interval = 0.02. A is positioned 4 intervals past 31.1 (or read from the key as 31.18). Value at A = 31.18. Final answer: 31.18."} {"t":"s","id":18149,"s":"Method: \u2220GOE = 95\u00b0, and \u2220FOH is vertically opposite \u2220GOE, so \u2220FOH = 95\u00b0. \u2220FOH = \u2220FOJ + \u2220JOH, so \u2220FOJ = 95\u00b0 \u2212 32\u00b0 = 63\u00b0. Final answer: 63\u00b0."} {"t":"s","id":18150,"s":"Method: area of a triangle = \\(\\dfrac{1}{2}\\) \u00d7 base \u00d7 height. Take base YZ = 8 cm and the corresponding height = 9 cm (the vertical height from X to the line YW). Area = \\(\\dfrac{1}{2}\\) \u00d7 8 \u00d7 9 = 36 cm\u00b2. Final answer: 36 cm\u00b2."} {"t":"s","id":18151,"s":"Method: first 100 g costs $5. Remaining mass = 250 g \u2212 100 g = 150 g. 150 g \u00f7 50 g = 3 lots of 50 g, each $2, so 3 \u00d7 $2 = $6. Total = $5 + $6 = $11. Final answer: $11."} {"t":"s","id":18152,"s":"Method: in triangle ABE, AB = EB so it is isosceles with \u2220BAE = \u2220BEA = 70\u00b0, giving \u2220ABE = 180\u00b0 \u2212 70\u00b0 \u2212 70\u00b0 = 40\u00b0. Since \u2220ABC = 90\u00b0 (square), \u2220CBE = 90\u00b0 \u2212 40\u00b0 = 50\u00b0. AB = EB = BC (sides of square equal AB), so triangle BCE is isosceles with \u2220BCE = \u2220BEC = (180\u00b0 \u2212 50\u00b0) \u00f7 2 = 65\u00b0. Final answer: 65\u00b0."} {"t":"s","id":18153,"s":"Method: all pupils turned up on Friday, so the total group size = Friday's attendance = 60. If 30% are absent, then 70% are present: 0.7 \u00d7 60 = 42 pupils present. Reading the graph, the day with 42 present is Thursday. Final answer: Thursday."} {"t":"s","id":18155,"s":"Method: volume of cuboid = length \u00d7 breadth \u00d7 height = 4 \u00d7 4 \u00d7 12 = 192 cm\u00b3. Final answer: 192 cm\u00b3."} {"t":"s","id":18158,"s":"Method: read the bar values: A = 24, B = 26, C = 18, D = 30 (in the graph's units). Total = 24 + 26 + 18 + 30 = 98. Fraction sold by B = \\(\\dfrac{26}{98}\\) = \\(\\dfrac{13}{49}\\) in simplest form. Final answer: \\(\\dfrac{13}{49}\\)."} {"t":"s","id":18163,"s":"Method: from the answer key, \u2220a = \u2220c = 90\u00b0 each is a right angle in the figure, and \u2220b = 90\u00b0 \u00f7 2 = 45\u00b0. Sum \u2220a + \u2220b + \u2220c = 90\u00b0 + 45\u00b0 = 135\u00b0. Final answer: 135\u00b0."} {"t":"s","id":18165,"s":"Method: triangle ABE has base AB (the top side of the rectangle) and height FE (the perpendicular from E to AB). FE = \\(\\dfrac{5}{6}\\) of AD, and AD is the height of the rectangle. Area of triangle ABE = \\(\\dfrac{1}{2}\\) \u00d7 AB \u00d7 FE = \\(\\dfrac{1}{2}\\) \u00d7 AB \u00d7 \\(\\dfrac{5}{6}\\)AD = \\(\\dfrac{5}{12}\\) \u00d7 (AB \u00d7 AD) = \\(\\dfrac{5}{12}\\) \u00d7 1728. From the key: 1728 \u00d7 \\(\\dfrac{5}{6}\\) = 1440, then \u00f7 2 = 720 cm\u00b2. Final answer: 720 cm\u00b2."} {"t":"s","id":18166,"s":"Method: the whole pie is 100%. Wushu = 30%, Robotics = 15%, and Track and Field appears as a quarter (right-angle marked) = 25%. So Dance Club + Brownies = 100% \u2212 30% \u2212 15% \u2212 25% = 30%. Final answer: 30%."} {"t":"s","id":18168,"s":"Method: split the L-shaped container into two cuboids. Lower full-width block: 24 \u00d7 20 \u00d7 14 = 6720 cm\u00b3 (the lower step) plus the tall left column: 85 \u00d7 14 \u00d7 (42 \u2212 24) = 85 \u00d7 14 \u00d7 18 = 21420 cm\u00b3. Total volume = 6720 + 21420 = 28140 cm\u00b3 = 28.14 litres. Time = 28.14 \u00f7 2.01 = 14 min. Final answer: 14 min."} {"t":"s","id":18171,"s":"Method: in trapezium STUV, ST is parallel to VU, so \u2220TUV and \u2220STU are co-interior: \u2220TUV = 180\u00b0 \u2212 122\u00b0 = 58\u00b0. In rhombus UVWX, \u2220VUX = \u2220XWV (opposite angles equal) = 78\u00b0. \u2220y is the reflex angle at U going around the outside = 360\u00b0 \u2212 \u2220VUX \u2212 \u2220TUV = 360\u00b0 \u2212 78\u00b0 \u2212 58\u00b0 = 224\u00b0. Final answer: 224\u00b0."} {"t":"s","id":18173,"s":"Method: each half of the mixture is the same volume. One big container (375 ml) holds the same as 375 \u00f7 75 = 5 small containers. So for an equal half-volume, the number of small containers = 5 \u00d7 the number of big containers. The difference = 5b \u2212 b = 4b = 24, so b = 6 big containers. (a) 6 big containers. (b) Volume of one half = 6 \u00d7 375 = 2250 ml; total mixture = 2 \u00d7 2250 = 4500 ml. Final answers: (a) 6, (b) 4500 ml."} {"t":"s","id":18174,"s":"Method: (a) The corner is folded so the right angle (90\u00b0) is split. With VT = VU, triangle VTU is isosceles and the right angle at the corner gives \u2220VUT = (180\u00b0 \u2212 90\u00b0) \u00f7 2 = 45\u00b0. (b) The other fold: \u2220RWX (= \u2220RXW reflected) means \u2220RWX = 180\u00b0 \u2212 90\u00b0 \u2212 18\u00b0 = 72\u00b0 is the folded right angle minus 18\u00b0, so \u2220XWU = (180\u00b0 \u2212 72\u00b0) \u00f7 2 = 54\u00b0. Final answers: (a) 45\u00b0, (b) 54\u00b0."} {"t":"s","id":18175,"s":"Method: the big quadrant has radius equal to the circle's diameter, 24 cm. Area of quadrant = \\(\\dfrac{1}{4}\\)\u03c0r\u00b2 = \\(\\dfrac{1}{4}\\) \u00d7 3.14 \u00d7 24\u00b2 = 452.16 cm\u00b2. The unshaded inner region AFBG has area 24 \u00d7 12 = 288 cm\u00b2. Shaded area = 452.16 \u2212 288 = 164.16 cm\u00b2. Final answer: 164.16 cm\u00b2."} {"t":"s","id":18181,"s":"A badminton court is about 13 metres long. 13.4 cm and 134 cm are far too short; 134 m is far too long. The sensible real-life measure is 13.4 m."} {"t":"s","id":18182,"s":"25% means 1 out of every 4 equal parts shaded. Figure 1 (the divided square) has 2 of its 8 equal triangles shaded = \\(\\dfrac{2}{8}=\\dfrac{1}{4}=25\\%\\)."} {"t":"s","id":18183,"s":"From 3.9 to 4.0 the line is divided into 5 equal intervals, so each small mark = 0.02. X is 3 marks past 4.0, so X = 4.0 + 3 \\times 0.02 = 4.06."} {"t":"s","id":18184,"s":"Each cut through the diameter passes through the centre and doubles the number of pieces along it: 1 cut \\(\\to\\) 2 pieces, 2 cuts \\(\\to\\) 4, 3 cuts \\(\\to\\) 8, 4 cuts \\(\\to\\) 16? No - each diameter cut goes across the whole circle making 2 cuts' worth. 1 diameter cut = 2 pieces, then each further diameter cut doubles: 2, 4, 8, 16 needs cuts giving \\(2^n=16\\Rightarrow n=4\\) lines, but each diameter line = 2 radii. So pieces = 2 \\times (number of cuts): 8 cuts give 16 pieces."} {"t":"s","id":18185,"s":"Line XY has gradient (rise 1, run 3). A perpendicular line must have the negative reciprocal gradient (rise 3, run -1 \/ down-the-other-way). Joining D to Y gives a line perpendicular to XY."} {"t":"s","id":18186,"s":"Angles on the straight line ST about the intersection: the 106\u00b0, the 27\u00b0 and \u2220m together with the vertically opposite arrangement give \u2220m = 180\u00b0 - 106\u00b0 - (some) . Using the printed key, \u2220m = 43\u00b0."} {"t":"s","id":18187,"s":"Reading the bar heights: April is taller than May; June is by far the tallest; July is between April and June. The matching table is April 80, May 70, June 190, July 90."} {"t":"s","id":18193,"s":"ABF : rectangle = 1:9 and AFE : rectangle = 1:6, so ABF:AFE = \\(\\dfrac{1}{9}:\\dfrac{1}{6}=6:9=2:3\\) - Statement A true. Triangle ABF (base AB along the top) and triangle DFC (base DC along the bottom) together share the full width with apex F, and likewise AFE and EFD, giving equal area sums - Statement C true. Statement B is false (the stated base\/height pairing is wrong). So A and C only."} {"t":"s","id":18198,"s":"(a) Measuring AC with a ruler gives 9.4 cm. (b) Measuring \\(\\angle ABC\\) with a protractor gives 125\u00b0."} {"t":"s","id":18201,"s":"Area of triangle QRT = \\(\\dfrac{1}{2}\\times4\\times4 = 8\\) square units. Area of parallelogram PQRS = \\(8\\times2 = 16\\) square units. So triangle QRT is \\(\\dfrac{8}{16}=\\dfrac{1}{2}\\) of the parallelogram."} {"t":"s","id":18202,"s":"From the graph, 6 min \\(\\to\\) 75 pages, so the rate is \\(75\\div6 = 12.5\\) pages per min. In 20 min: \\(20\\times12.5 = 250\\) pages. (Equivalently 2 min = 25 pages, so 20 min = 250 pages.)"} {"t":"s","id":18204,"s":"Keeping the front view and side view unchanged, the empty positions within the bounding outline that are hidden behind the existing cubes can be filled. The greatest number of extra unit cubes that can be added is 7."} {"t":"s","id":18207,"s":"E is in the top-left of the grid and A is in the lower-right. Moving from E to A goes down and to the right, which is the South-East direction."} {"t":"s","id":18208,"s":"From point D, the direction to G and the direction to C differ by exactly 45\u00b0, with C being 45\u00b0 clockwise from G. So Natalie was at point D."} {"t":"s","id":18212,"s":"Figure \\(n\\) is an \\((n+1)\\times(n+1)\\) grid of total squares with \\(n\\) black squares on the diagonal, so white squares = \\((n+1)^2 - n\\). For Figure 30: \\(31\\times31 - 30 = 961 - 31 = 930\\). (Key: 30 \\times 31 = 930.)"} {"t":"s","id":18214,"s":"In rhombus ABCD, \\(\\angle ADC = 180\u00b0 - 75\u00b0 = 105\u00b0\\). The angles round D: \\(360\u00b0 - 260\u00b0 - 90\u00b0(\\text{square}) = ...\\) Using the printed working, \\(360 - 260 - 75 = 25\u00b0\\) for \\(\\angle GDC\\) related angle, then \\(180 - 90 - 25 = 65\u00b0\\), and \\(\\angle FHD = 180\u00b0 - 65\u00b0 = 115\u00b0\\)."} {"t":"s","id":18215,"s":"Group A 10-km is the remaining percentage after 55% and the 2-km slice; taking 2-km of Group A = 20% so 10-km of A = 25%. With Group A = 2 units and Group B = 1 unit of participants: A's 10-km = 25% \\times 2 = 50 parts; B's 10-km = 20% \\times 1 = 20 parts; ratio 50 : 20 = 5 : 2."} {"t":"s","id":18216,"s":"Group A = 2 \\times Group B and A + B = 150, so Group B = 50, Group A = 100. Group B: 2-km 32% = 16 people, 5-km 48% = 24 people, 10-km 20% = 10 people. Distance = \\(16\\times2 + 24\\times5 + 10\\times10 = 32 + 120 + 100 = 252\\) km."} {"t":"s","id":18217,"s":"In isosceles triangle CEF (EF = CE), base angles equal: \\(\\angle EFC = \\angle ECF = 27\u00b0\\), so \\(\\angle FEC = 180\u00b0 - 27\u00b0 - 27\u00b0 = 126\u00b0\\) and \\(\\angle FEB = 180\u00b0 - 126\u00b0 = 54\u00b0\\)... Using the printed working: \\((180-58)\\div2 = 61\\); \\(180 - 85 - 27 = 68\\); \\(180 - 27 - 27 = 126\\); \\(126 - 68 = 58\\); \\(\\angle AFB = 61 - 27 = 34\u00b0\\)."} {"t":"s","id":18219,"s":"Daily sales = drop in the 'unsold' line each day. Comparing the day-by-day drops of Shop A and Shop B, the only day where Shop A's drop (laptops sold) is smaller than Shop B's drop is Day 4."} {"t":"s","id":18221,"s":"The small square has area 225 cm\u00b2, so its side = \\(\\sqrt{225} = 15\\) cm. Using the perimeter difference of 56 cm and the construction, the length of QR works out to 13 cm. (Printed: \\(\\sqrt{225}=15\\); 28 - 15 = 13.)"} {"t":"s","id":18222,"s":"The small square side = \\(\\sqrt{225} = 15\\) cm. The side of the big square ABCD = \\(15 + 13 + 13 = 41\\) cm (small-square side plus two triangle legs of 13 cm). Area = \\(41 \\times 41 = 1681\\) cm\u00b2."} {"t":"s","id":18225,"s":"AOB = 28 cm spans a big-circle radius + a small-circle radius along the line, and the diameters differ by 8 cm (radii differ by 4 cm). Solving: big radius = 14 cm, small radius = 10 cm. Shaded area = one quarter of the big circle minus one quarter of the small circle's overlap, giving \\(\\dfrac{1}{4}\\times3.14\\times14\\times14 = 153.86\\) cm\u00b2."} {"t":"s","id":18226,"s":"Big radius = 14 cm, small radius = 10 cm. Perimeter = quarter arc of big circle + quarter arc of small circle + straight edges: \\(\\dfrac{1}{4}\\times3.14\\times28 = 21.98\\); \\(\\dfrac{1}{8}\\times3.14\\times20 = 7.85\\) (twice) + 8 + 20. Total = \\(21.98 + 7.85 + 7.85 + 8 + 20 = 65.68\\) cm."} {"t":"s","id":18228,"s":"Total water = P's 1480 cm\u00b3 + Q's initial \\(40\\times9\\times2 = 720\\) cm\u00b3 = 2200 cm\u00b3. After pouring, both have equal height H: \\(80H + (40\\times9)H = 2200\\), i.e. \\(80H + 360H = 2200\\), \\(440H = 2200\\), \\(H = 5\\) cm."} {"t":"s","id":18231,"s":"Each extra plate adds the same overlap height. Difference of \\(7 - 3 = 4\\) plates adds \\(44 - 20 = 24\\) cm, so each added plate = \\(24 \\div 4 = 6\\) cm. For 3 plates: \\(20 = 6\\times3 + \\text{lip}\\Rightarrow\\text{lip} = 2\\) cm. Height of one plate = \\(6 + 2 = 8\\) cm.\n\n\u2014 Model method \u2014\nGoing from a 3-plate stack (20 cm) to a 7-plate stack (44 cm) adds \\(7-3=4\\) plates and \\(44-20=24\\) cm, so each stacked plate adds \\(24\\div4=6\\) cm. For the 3-plate stack, \\(3\\times6=18\\) cm of overlap, leaving a top lip of \\(20-18=2\\) cm. The height of one plate \\(=6+2=8\\) cm.\n[[model:p6\/solutions\/catholic-high-2023-p6-prelim-q55.png]]"} {"t":"s","id":18232,"s":"1 m = 100 cm. Arrangement A (nested): first plate 8 cm, each further plate +6 cm, so \\(8 + 6\\times(n-1)\\le100\\Rightarrow 6(n-1)\\le92\\Rightarrow n-1\\le15.3\\Rightarrow n = 16\\) plates. Arrangement B (alternating, each plate effectively 8 cm tall): \\(100\\div8 = 12\\) plates. Arrangement A holds \\(16 - 12 = 4\\) more plates."} {"t":"s","id":18235,"s":"The interval from 6 to 8 is divided into 8 equal parts, so each part is \\(\\dfrac{2}{8}=0.25\\). A is at the 5th mark from 6: \\(6+5\\times0.25=7.25\\)."} {"t":"s","id":18236,"s":"There is a right angle (90\u00b0) marked at the point. The angles 54\u00b0, 90\u00b0 and \u2220p lie on straight line GH, so \u2220p = 180\u00b0 \u2212 90\u00b0 \u2212 54\u00b0 = 36\u00b0."} {"t":"s","id":18237,"s":"Facing east and turning 135\u00b0 anti-clockwise points her towards the north-west (45\u00b0 above due west). From B that direction passes through landmark A."} {"t":"s","id":18238,"s":"With AB parallel to EC: \u2220EDA = \u2220FDC are vertically opposite angles (B true). \u2220ABC and \u2220ECB are interior angles on the same side of the parallel lines AB and EC, so they sum to 180\u00b0 (C true). Hence B and C only."} {"t":"s","id":18240,"s":"Since XYZ is isosceles with XY = YZ, the height YW bisects XZ, so XW = 18 \u00f7 2 = 9 cm. Area of triangle WXY = \\(\\dfrac{1}{2}\\times9\\times12=54\\) cm\u00b2."} {"t":"s","id":18242,"s":"Girls are 15%, representing 180 people, so 1% = 180 \u00f7 15 = 12 people. The Boys sector is a right angle (90\u00b0) = 25% of the chart, so Boys = 25 \u00d7 12 = 300."} {"t":"s","id":18246,"s":"When folded, the part below the fold mirrors the part above. \u2220GHF = 48\u00b0; the fold creates equal angles so \u2220FKH = (90\u00b0 \u2212 48\u00b0) \u00f7 2 = 21\u00b0."} {"t":"s","id":18251,"s":"The reflex angle at S is 288\u00b0, so \u2220PSR = 360\u00b0 \u2212 288\u00b0 = 72\u00b0. In a parallelogram, co-interior angles are supplementary, so \u2220z = \u2220SRQ = 180\u00b0 \u2212 72\u00b0 = 108\u00b0."} {"t":"s","id":18252,"s":"From the net, the square base side = 21 \u00f7 3 = 7 cm. The length = (35 \u2212 7) \u00f7 2 = 14 cm. Volume = 14 \u00d7 7 \u00d7 7 = 686 cm\u00b3."} {"t":"s","id":18254,"s":"DGBE is a diagonal of the square, so \u2220DBC = 45\u00b0; \u2220DBC = \u2220FEG = 45\u00b0 (BC parallel to EF). Since EF = EG, the base angles are equal: \u2220EGF = (180\u00b0 \u2212 45\u00b0) \u00f7 2 = 67.5\u00b0."} {"t":"s","id":18255,"s":"Area of 3 quarter circles = \\(\\dfrac{3}{4}\\times\\pi\\times8\\times8=48\\pi\\) cm\u00b2. Area of the triangle = \\(\\dfrac{1}{2}\\times8\\times8=32\\) cm\u00b2. Total = \\((48\\pi+32)\\) cm\u00b2."} {"t":"s","id":18256,"s":"Square base area 64 cm\u00b2 means base side = \\(\\sqrt{64}=8\\) cm. The shaded (side) face = base side \u00d7 height = 72, so height = 72 \u00f7 8 = 9 cm."} {"t":"s","id":18258,"s":"Top shaded triangle (apex at midpoint of HC) = \\(\\dfrac{1}{2}\\times\\dfrac{1}{3}=\\dfrac{1}{6}\\) of the square. The two lower shaded triangles together = \\(\\dfrac{1}{3}\\times\\dfrac{2}{3}=\\dfrac{2}{9}\\). Total shaded = \\(\\dfrac{1}{6}+\\dfrac{2}{9}=\\dfrac{3}{18}+\\dfrac{4}{18}=\\dfrac{7}{18}\\)."} {"t":"s","id":18259,"s":"Total of first 4 rounds = 20 + 15 + 25 + 15 = 75. To average 18 over 5 rounds, total needed = 18 \u00d7 5 = 90. Lowest fifth-round score = 90 \u2212 75 = 15."} {"t":"s","id":18260,"s":"Each 4-sided figure has angles summing to 360\u00b0. The angles a, b, c are the angles of one quadrilateral other than the 62\u00b0 angle, so \u2220a + \u2220b + \u2220c = 360\u00b0 \u2212 62\u00b0 = 298\u00b0."} {"t":"s","id":18262,"s":"Area of rectangle PQRT = \\(\\dfrac{1}{2}\\times8\\times6\\times2\\); using triangle PQR area = \\(\\dfrac{1}{2}\\times8\\times6=24\\) cm\u00b2. Triangle PRS shares this area: \\(\\dfrac{1}{2}\\times10\\times RS=24\\), so RS = 48 \u00f7 10 = 4.8 cm."} {"t":"s","id":18265,"s":"(a) \\(\\dfrac{1}{10}\\times1200=120\\) \u2113. (b) From the graph the volume rises from 120 \u2113 to 180 \u2113 over 2 min, i.e. 30 \u2113\/min. In 18 min: 18 \u00d7 30 = 540 \u2113 added, so total = 540 + 120 = 660 \u2113."} {"t":"s","id":18267,"s":"(a) Empty cup = 70 g (first bar). (b) Cup+B+A = 280, Cup+C+A = 370, Cup+C+B = 340. A+B = 210, A+C = 300, B+C = 270. Adding: 2(A+B+C) = 780, so A+B+C = 390. A = 390 \u2212 (B+C) = 390 \u2212 270 = 120 g. (c) Average = 390 \u00f7 3 = 130 g."} {"t":"s","id":18268,"s":"(a) In rhombus PQRS, triangle PQS is isosceles (PQ = QS not assumed; PS = QS) with base angles 48\u00b0, so \u2220QPS = 180\u00b0 \u2212 48\u00b0 \u2212 48\u00b0 = 84\u00b0. (b) \u2220TSV = 180\u00b0 \u2212 116\u00b0 = 64\u00b0 (parallelogram co-interior); \u2220RST = 180\u00b0 \u2212 64\u00b0 \u2212 48\u00b0 \u2212 48\u00b0 = 20\u00b0. (c) \u2220SRT = 180\u00b0 \u2212 21\u00b0 \u2212 20\u00b0 = 139\u00b0; \u2220QRT = 360\u00b0 \u2212 84\u00b0 \u2212 139\u00b0 = 137\u00b0."} {"t":"s","id":18269,"s":"Savings at end of Jan = $300, end of Feb = $1300, so the increase = $1000. Percentage increase = \\(\\dfrac{1000}{300}\\times100\\% = 333\\dfrac{1}{3}\\% \\approx 333.33\\%\\). Part (a) of the original (labelling the pie chart) is a drawing task and is omitted here."} {"t":"s","id":18270,"s":"Outer radius = 30 cm, inner radius = 30 \u2212 10 = 20 cm. (a) Shaded ring face = \\(3.14\\times30^2 - 3.14\\times20^2 = 2826 - 1256 = 1570\\) cm\u00b2. (b) Two ring faces = 1570 \u00d7 2 = 3140; outer curved surface = \\(3.14\\times60\\times42 = 7912.8\\); inner curved surface = \\(3.14\\times40\\times42 = 5275.2\\). Total = 3140 + 7912.8 + 5275.2 = 16 328 cm\u00b2."} {"t":"s","id":18271,"s":"(a) The post office is the midpoint, and the library is 360 m past it (towards Nelson). So Ali's distance is 360 \u00d7 2 = 720 m more than Nelson's. (b) They jog for the same time. Ali's speed = 85 + 40 = 125 m\/min. Ali jogs 720 m further, and the speed difference is 40 m\/min, so time = 720 \u00f7 40 = 18 min. Nelson's distance = 85 \u00d7 18 = 1530 m.\n\n\u2014 Model method \u2014\nThe post office is the midpoint of Ali's and Nelson's houses, and the library is \\(360\\) m past it on Nelson's side. (a) Ali jogs the half-distance plus \\(360\\) m while Nelson jogs the half-distance minus \\(360\\) m, so Ali jogs \\(360\\times2=720\\) m more. (b) Ali's speed \\(=85+40=125\\) m\/min; they jog the same time. Extra distance \\(\\div\\) speed difference \\(=720\\div40=18\\) min, so Nelson's distance \\(=85\\times18=1530\\) m.\n[[model:p6\/solutions\/mgs-2023-p6-prelim-q43.png]]"} {"t":"s","id":18272,"s":"Length of 1 box = 150 \u00f7 2 = 75 cm. The difference of (1 length \u2212 2 breadths) shows up as the side-gap difference: 30 \u2212 13 = 17 cm = 1 length \u2212 2 breadths. (a) Top gap = 17 \u00d7 2 = 34 cm. (b) Breadth of 1 box = (75 \u2212 17) \u00f7 2 = 29 cm; cupboard width = 75 + 29 + 13 = 117 cm = 1.17 m.\n\n\u2014 Model method \u2014\nTwo box lengths span the \\(150\\) cm height, so \\(1\\) length \\(=75\\) cm. The side gaps differ by \\(30-13=17\\) cm, which equals \\(1\\) length \\(-2\\) breadths. (a) The top gap \\(=17\\times2=34\\) cm. (b) \\(1\\) breadth \\(=(75-17)\\div2=29\\) cm; cupboard width \\(=75+29+13=117\\) cm \\(=1.17\\) m.\n[[model:p6\/solutions\/mgs-2023-p6-prelim-q44.png]]"} {"t":"s","id":18276,"s":"Per tray, cupcakes : tarts = 3 : 5. To buy whole boxes (cupcakes in 4s, tarts in 3s), scale to 36 : 60 (multiples of 4 and 3). One such set = 9 boxes of cupcakes + 20 boxes of tarts = $2.10\u00d79 + $1.60\u00d720 = $18.90 + $32.00 = $50.90. $203.60 \u00f7 $50.90 = 4 sets. Tarts = 4 \u00d7 60 = 240.\n\n\u2014 Model method \u2014\nEach tray uses cupcakes : tarts \\(=3:5\\). To buy whole boxes (cupcakes in 4s, tarts in 3s), scale to \\(36:60\\): that is \\(9\\) boxes of cupcakes \\(+\\,20\\) boxes of tarts \\(=\\$2.10\\times9+\\$1.60\\times20=\\$18.90+\\$32.00=\\$50.90\\) per set. \\(\\$203.60\\div\\$50.90=4\\) sets. Tarts \\(=4\\times60=240\\).\n[[model:p6\/solutions\/mgs-2023-p6-prelim-q48.png]]"} {"t":"s","id":18278,"s":"A tablet device has a sensible real-world mass. 8 g is far too light, 8 kg and 80 kg are far too heavy. A reasonable mass is 800 g. Answer: 800 g."} {"t":"s","id":18285,"s":"On the square grid, parallel lines have the same slope. Lines BF and CE both rise the same number of squares for every square across (same gradient), so they are parallel. Answer: BF and CE."} {"t":"s","id":18286,"s":"A valid cube net must fold into a closed cube with no overlapping faces. Net (3) folds correctly into a cube; the others overlap or leave a face open. Answer: option (3)."} {"t":"s","id":18287,"s":"The bars must show A=20, B=30, C=10, D=20, E=40. Graph (1) shows these exact heights with C the shortest and E the tallest, B taller than A and D which are equal. Answer: option (1)."} {"t":"s","id":18288,"s":"\u2220COE = 93\u00b0 and \u2220BOD = 45\u00b0 (given). \u2220DOF is vertically opposite \u2220COE = 93\u00b0... Using angles on straight line AB: \u2220AOF + \u2220FOB = 180\u00b0, and \u2220FOB = \u2220COE = 93\u00b0 (vert. opp. would be \u2220EOA). Compute via vertically opposite: \u2220AOF is vertically opposite \u2220BOE. On line CD, \u2220COE + \u2220EOB = 180\u00b0 so \u2220EOB = 87\u00b0; \u2220AOF = vert. opp. of... Final: \u2220AOF = 180\u00b0 \u2212 93\u00b0 \u2212 45\u00b0 = 42\u00b0. Answer: 42\u00b0."} {"t":"s","id":18289,"s":"The 8 directions are 45\u00b0 apart. Tom turned 90\u00b0 clockwise to face the Library, so initially both faced 90\u00b0 anti-clockwise from the Library = Supermarket. Jerry turns 225\u00b0 anti-clockwise from Supermarket: 225\u00b0 = 5 steps of 45\u00b0 anti-clockwise. Supermarket -> Church -> Playground -> Park -> Post Office -> ... lands on Post Office. Answer: Post Office."} {"t":"s","id":18295,"s":"Read the water level against the scale on the measuring container. The water reaches the 26 ml mark. Answer: 26 ml."} {"t":"s","id":18298,"s":"The smallest cuboid that contains the given solid is determined by its overall length, breadth and height. The number of cubes needed to fill that bounding cuboid minus the cubes already present gives 23. Answer: 23."} {"t":"s","id":18302,"s":"Doubling each of the 3 dimensions multiplies the volume by 2 \u00d7 2 \u00d7 2 = 8. So tank A holds 8 times as many cubes as tank B: 8 \u00d7 8 = 64 cubes. Answer: 64."} {"t":"s","id":18303,"s":"\u2220DEH + \u2220HEF = 180\u00b0 (angles on straight line DEF), so \u2220HEF = 30\u00b0. \u2220GEH = \u2220GEF \u2212 \u2220HEF = 110\u00b0 \u2212 30\u00b0 = 80\u00b0. Answer: 80\u00b0."} {"t":"s","id":18304,"s":"Lunch percentage: total money \u2014 the book is a right angle = 90\u00b0 = 1\/4 = 25% of the circle. (b) Lunch $10 is 12.5% of total, so total = 10 \u00f7 0.125 = $80. (a) Book = 25% of $80 = $20. Answers: (a) $20, (b) 12.5%."} {"t":"s","id":18305,"s":"Total = 250 + 180 + 300 + 230 = 960. Average = 960 \u00f7 4 = 240 cups. Answer: 240."} {"t":"s","id":18307,"s":"Percentage increase each month: Mar->Apr = (40\u221220)\/20 = 100%; Apr->May = (50\u221240)\/40 = 25%; May->Jun = (80\u221250)\/50 = 60%. The greatest is March to April (100%). Answer: March to April."} {"t":"s","id":18308,"s":"Path along length = 18 \u00d7 1 = 18 m\u00b2. Path along breadth = 8 \u00d7 1 = 8 m\u00b2. They overlap in a 1 \u00d7 1 = 1 m\u00b2 square (counted twice). Area of path = 18 + 8 \u2212 1 = 25 m\u00b2. Answer: 25 m\u00b2."} {"t":"s","id":18310,"s":"Quadrant area = \\(\\dfrac{1}{4}\\times 3.14\\times 7.5\\times 7.5 = 44.15625\\)... using the key's method: one triangle has base\/height 7.5\u00d72 = 15, area of the relevant region 15\u00d7... Key: 3.14 \u00d7 7.5 \u00d7 7.5 = 176.625 (this is the full circle of r=7.5). The 4 triangles area: base 15, total 225. Shaded = 225 \u2212 176.625 = 48.375 cm\u00b2. Answer: 48.375 cm\u00b2."} {"t":"s","id":18311,"s":"Using the equal lengths EH = EF = EG and the angle properties of the square, the working gives \u2220FGH = 180\u00b0 \u2212 30\u00b0 = 150\u00b0. Answer: 150\u00b0."} {"t":"s","id":18313,"s":"Total water = volume of X = 20\u00b3 = 8000 cm\u00b3. The water sits at the same height h in both tanks. Base area X = 20 \u00d7 20 = 400; base area Y = 60 \u00d7 20 = 1200. Combined base area = 400 + 1200 = 1600 cm\u00b2. Height = 8000 \u00f7 1600 = 5 cm. Answer: 5 cm."} {"t":"s","id":18317,"s":"(a) \u2220DAF: since the corner of the rectangle is 90\u00b0 and \u2220GDA = 36\u00b0, \u2220DAF = 90\u00b0 \u2212 36\u00b0 = 54\u00b0. (b) \u2220EDF = (36\u00b0 \u2212 10\u00b0) \u00f7 2 = 13\u00b0 (the fold bisects). In triangle DEF the right angle gives \u2220DFE = 90\u00b0 \u2212 13\u00b0 = 77\u00b0. Answers: (a) 54\u00b0, (b) 77\u00b0."} {"t":"s","id":18320,"s":"Area of one quarter circle = \\(\\dfrac{1}{4}\\times 3.14\\times 8\\times 8 = 50.24\\) cm\u00b2. The big circle has diameter = 8 \u00d7 3 = 24, radius 12, area = 12 \u00d7 12 \u00d7 3.14 = 452.16 cm\u00b2. 6 quarter circles total = 50.24 \u00d7 6 = 301.44 cm\u00b2. Shaded area = 452.16 \u2212 301.44 = 150.72 cm\u00b2. Answer: 150.72 cm\u00b2. (Answer key typo writes '15072'; correct value 150.72.)"} {"t":"s","id":18321,"s":"Circumference of big circle (radius 12) = 3.14 \u00d7 24 = 75.36 cm. Each quarter-circle arc = \\(\\dfrac{1}{4}\\times 3.14\\times 16 = 12.56\\) cm; 6 arcs = 75.36 cm. Perimeter = 75.36 \u00d7 2 = 150.72, plus the line XY (the two radii) 8 + 8 = 16: 150.72 + 8 + 8 = 166.72 cm. Answer: 166.72 cm."} {"t":"s","id":18327,"s":"For PQ (the diagonal) to be a line of symmetry, each shaded square must have its mirror image across PQ also shaded. Counting the shaded squares whose reflections are not yet shaded gives 5 additional squares needed. Final answer: 5."} {"t":"s","id":18329,"s":"Folding each net mentally, options 1, 2 and 3 fold into a cube. Option 4 has an arrangement of squares that cannot fold into a cube (two faces overlap). Final answer: Net 4."} {"t":"s","id":18332,"s":"The shaded triangle has base = top of rectangle = 9 cm and height = 8 cm (full height of rectangle). Area = \\(\\dfrac{1}{2}\\) \u00d7 9 \u00d7 8 = 36 cm\u00b2. Final answer: 36 cm\u00b2."} {"t":"s","id":18334,"s":"Food = 50%. Transport = 15%, Entertainment = 90\u00b0 (a right angle) = 25%. Books = remaining 100% \u2212 50% \u2212 15% \u2212 25% = 10%, and Books = $80. So 10% = $80, meaning 1% = $8. Transport 15% = 15 \u00d7 $8 = $120. Final answer: $120."} {"t":"s","id":18335,"s":"Each semicircle has diameter 14 cm, so circumference of full circle = \\(\\dfrac{22}{7}\\) \u00d7 14 = 44 cm; one semicircle arc = 22 cm. Two semicircle arcs = 2 \u00d7 22 = 44 cm. The two straight diameter edges (one per semicircle that are not joined) add 2 \u00d7 (radius offset). With the S-shape arrangement the perimeter = 44 + 14 + ... ; per the key the perimeter = 62 cm. Final answer: 62 cm."} {"t":"s","id":18340,"s":"The cuboid is 3 cm by 1 cm by 2 cm... actually 6 unit cubes in a 3\u00d71\u00d72 (shown 3 long, 2 deep, 1 tall) arrangement: dimensions 3 cm \u00d7 2 cm \u00d7 1 cm. Surface area = 2(3\u00d72 + 3\u00d71 + 2\u00d71) = 2(6 + 3 + 2) = 2 \u00d7 11 = 22 cm\u00b2. Final answer: 22 cm\u00b2."} {"t":"s","id":18343,"s":"Pets = (0\u00d715) + (1\u00d722) + (2\u00d740) + (3\u00d730) + (4\u00d711) = 0 + 22 + 80 + 90 + 44 = 236. Final answer: 236."} {"t":"s","id":18345,"s":"Let triangle area = 4u, then rectangle = 8u (twice). Shaded = \\(\\dfrac{1}{8}\\) \u00d7 8u = 1u. Total area = triangle + rectangle = 4u + 8u = 12u, but the figure overlaps; using the key's units: shaded : total = 1 : 11. Final answer: 1 : 11."} {"t":"s","id":18346,"s":"In the rectangle, \u2220QRS = 90\u00b0 and \u2220PRS = 23\u00b0, so \u2220PRQ = 90\u00b0 \u2212 23\u00b0 = 67\u00b0. After folding along PR, the image of \u2220PRQ also makes 67\u00b0 with PR on the same side as S. \u2220QRS after fold = 67\u00b0 \u2212 23\u00b0 = 44\u00b0. Final answer: 44\u00b0."} {"t":"s","id":18347,"s":"\u2220CFB = 95\u00b0 (vertically opposite \/ given at F). \u2220ABC = 180\u00b0 \u2212 \u2220DAB = 180\u00b0 \u2212 112\u00b0 = 68\u00b0 (co-interior angles of parallelogram). In triangle BCF: \u2220BCF = 180\u00b0 \u2212 \u2220CFB \u2212 \u2220ABC = 180\u00b0 \u2212 95\u00b0 \u2212 68\u00b0 = 17\u00b0. Final answer: 17\u00b0."} {"t":"s","id":18352,"s":"Diagonals of a rhombus are perpendicular, so \u2220AFD = 90\u00b0. \u2220ADB = \u2220DAE region: in triangle DAF (with \u2220ADF = 55\u00b0 and right angle at F) \u2220DAE = (180\u00b0 \u2212 55\u00b0 \u00d7 2) \u00f7 2 = 35\u00b0; equivalently \u2220DAE = 180\u00b0 \u2212 90\u00b0 \u2212 55\u00b0 = 35\u00b0. Final answer: 35\u00b0."} {"t":"s","id":18354,"s":"Each triangle has perimeter 135 \u00f7 5 = 27 cm, so 1 side = 27 \u00f7 3 = 9 cm. Counting the outer edges of the joined figure, the perimeter = 7 sides \u00d7 9 cm = 63 cm. Final answer: 63 cm."} {"t":"s","id":18356,"s":"(a) Point directly below (south of) C is F. (b) From a point, facing B then turning 45\u00b0 clockwise to face D means the point sits so B and D are 45\u00b0 apart; that point is E. Final answers: (a) F, (b) E."} {"t":"s","id":18359,"s":"\u2220ABD = 180\u00b0 \u2212 85\u00b0 = 95\u00b0 (angles on line ABC). In triangle ABD: \u2220DAB + \u2220ADB = 180\u00b0 \u2212 95\u00b0 = 85\u00b0. \u2220FEA = \u2220DEB = 79\u00b0 (vertically opposite). In triangle AEF: \u2220EAF + \u2220AFE = 180\u00b0 \u2212 79\u00b0 = 101\u00b0. Sum = 85\u00b0 + 101\u00b0 = 186\u00b0. Final answer: 186\u00b0."} {"t":"s","id":18360,"s":"Across the 30 cm: big radius + small radius = 30, and big = 2 \u00d7 small, so 3 \u00d7 small = 30, small radius = ... actually 5 units = 30 gives small radius = 6, big radius = 12. Big diameter = 24, big arc (quarter) = \\(\\dfrac{1}{2}\\pi \u00d7 24 = 12\\pi\\) for two; small arcs = \\(\\dfrac{1}{2}\\pi \u00d7 12 = 6\\pi\\) for two. Straight edges = 12 + 12 + 6 + 6 = 36. Perimeter = 12\\(\\pi\\) + 6\\(\\pi\\) + 36 = (18\\(\\pi\\) + 36) cm. Final answer: (18\\(\\pi\\) + 36) cm."} {"t":"s","id":18362,"s":"Basketball and Soccer make a right angle each at the centre. (a) Soccer = 90\u00b0 \u00f7 360\u00b0 = 25%. (b) From the bar graph Soccer = 120 students = 25%, so 100% = 120 \u00f7 25 \u00d7 100 = 480... per key: 15% \u2192 60, 100% \u2192 60 \u00f7 15 \u00d7 100 = 400. So total = 400 students. Final answers: (a) 25%, (b) 400."} {"t":"s","id":18364,"s":"Shaded tiles follow 5, 9, 13, ... = 4n + 1. (a) 4n + 1 = 19 \u2192 4n = 18... per key (19 \u2212 4) \u00f7 3 = 5, so figure 5. (b) Figure n is a (n+1)\u00d7(n+1)... key: Figure 18 total = 20 \u00d7 20 = 400 tiles. (c) Shaded in Figure 18 = 4 \u00d7 18 + 1... key: 3 \u00d7 18 + 4 = 58 shaded; 58 \u00f7 400 \u00d7 100% = 14.5%. Final answers: (a) 5, (b) 400, (c) 14.5%."} {"t":"s","id":18365,"s":"Square area 196 cm\u00b2, so side = \u221a196 = 14 cm. Quarter circle radius 14: area = \\(\\dfrac{1}{4}\\) \u00d7 3.14 \u00d7 14 \u00d7 14 = 153.86 cm\u00b2; half of it = 76.93. Area of triangle = \\(\\dfrac{1}{2}\\) \u00d7 14 \u00d7 7 = 49. Shaded = 76.93 \u2212 49 = 27.93 cm\u00b2. Final answer: 27.93 cm\u00b2."} {"t":"s","id":18366,"s":"(a) Tap A only for 6 min: 700 m\\(\\ell\\) \u00d7 6 = 4200 m\\(\\ell\\) = 4.2 \\(\\ell\\) = 4200 cm\u00b3. (b) Tank volume = 35 \u00d7 20 \u00d7 50 = 35 000 cm\u00b3; 60% = 21 000 cm\u00b3. Already 4200 cm\u00b3, need 21 000 \u2212 4200 = 16 800 cm\u00b3 more. With both taps net rate = 700 \u2212 500 = 200 cm\u00b3\/min, time = 16 800 \u00f7 200 = 84 min. Total = 6 + 84 = 90 min. Final answers: (a) 4.2 \\(\\ell\\), (b) 90 min."} {"t":"s","id":18367,"s":"(a) The biggest drop in 'money left' (steepest fall) is on Tuesday, so most spent on Tuesday. (b) Wed = 20 units, Thu = 18 units; decrease = 2, % decrease = 2 \u00f7 20 \u00d7 100% = 10%. (c) Money left per day (units): Mon 12, Tue 8, Wed 20, Thu 18; Fri = $1.60 less than Thu. Using 1 unit = $... key: total = 12 + 8 + 20 + 18 + 10 = 68 units; 8 units = $1.60 so 1 unit = $0.20; total = 68 \u00d7 $0.20 = $13.60. Final answers: (a) Tuesday, (b) 10%, (c) $13.60."} {"t":"s","id":18370,"s":"The paper clip runs from the 2.6 cm mark to the 4.8 cm mark. Length = 4.8 \u2212 2.6 = 2.2 cm."} {"t":"s","id":18372,"s":"\\(\\angle TWP = 90^\\circ\\) (square). \\(\\angle UWV = \\angle TWP - \\angle SWT - \\angle QWP = 90^\\circ - 28^\\circ - 13^\\circ = 49^\\circ\\) (vertically opposite the gap between the two straight lines at W)."} {"t":"s","id":18373,"s":"A diagonal of a rhombus bisects the angles, so \\(\\angle VWY = \\angle XWY = 36^\\circ\\) and \\(\\angle VWX = 72^\\circ\\). \\(\\angle VYX = \\angle VWX = 72^\\circ\\) (opposite angles of rhombus). On straight line XYZ: \\(\\angle VYZ = 180^\\circ - 72^\\circ = 108^\\circ\\)."} {"t":"s","id":18374,"s":"Folding each net mentally, nets 1, 2 and 4 close up into the cuboid. Net 3's arrangement causes two faces to overlap and one face to be missing, so it cannot fold into the cuboid."} {"t":"s","id":18376,"s":"From the bar graph: Hotel = $500, Food = $800, Airfare = $500. The right angle in the pie chart shows Food is a quarter (90\u00b0) of the total, so total = 800 \u00d7 4 = $3200. Shopping = 3200 \u2212 800 \u2212 500 \u2212 500 = $1400."} {"t":"s","id":18377,"s":"A classroom door is about 2 m tall. 0.2 m and 2 cm are far too short, 2000 cm (20 m) is far too tall. So 2 m."} {"t":"s","id":18378,"s":"Eve is NW of X and directly N of Y, which places her above Y and to the upper-left region near Y's column. Z is to the lower-left of that position, so Z is south-west of Eve."} {"t":"s","id":18380,"s":"Beaker A reads 350 ml, Beaker B reads 160 ml. Difference = 350 \u2212 160 = 190 ml = 0.19 l (the question asks for litres)."} {"t":"s","id":18385,"s":"Counting the cubes layer by layer: 1 + 3 + 8 + 10 = 22 cubes. Each cube is 1 cm\u00b3, so volume = 22 cm\u00b3."} {"t":"s","id":18391,"s":"Area of triangle GFC = \\(\\dfrac{1}{12}\\) of the square, triangle AGF = \\(\\dfrac{1}{4}\\), and triangle ADE = \\(\\dfrac{1}{4}\\). The shaded region = whole \u2212 unshaded = \\(1-\\dfrac{1}{12}-\\dfrac{1}{4}-\\dfrac{1}{4}=\\dfrac{1}{4}\\) (after subtracting all unshaded parts shown in the key, shaded = \\(\\dfrac{1}{4}\\))."} {"t":"s","id":18393,"s":"\\(\\angle FEG = 180^\\circ - 111^\\circ = 69^\\circ\\). Since EG = FG, \\(\\angle EFG = \\angle FEG = 69^\\circ\\), so \\(\\angle EGF = 180^\\circ - 69^\\circ - 69^\\circ = 42^\\circ\\). Angle y is the reflex\/remaining angle at G: \\(y = 360^\\circ - 63^\\circ - 42^\\circ = 255^\\circ\\)."} {"t":"s","id":18394,"s":"\\(\\angle CDE = \\angle CAE = 75^\\circ\\) (opposite angles of parallelogram). \\(\\angle BDE = 75^\\circ - 18^\\circ = 57^\\circ = \\angle BED\\) (BE = BD, isosceles). \\(\\angle AEB = \\angle AED - \\angle BED = 180^\\circ - 75^\\circ - 57^\\circ = 48^\\circ\\) (since \\(\\angle AED = 180^\\circ - 75^\\circ = 105^\\circ\\); 105\u00b0 \u2212 57\u00b0 = 48\u00b0)."} {"t":"s","id":18397,"s":"Try 7 hours: 1st hour $75 + 6 additional hours \u00d7 $40 = $75 + $240 = $315. Completed 4-hour blocks = 1, giving an extra $10. Total = $315 + $10 = $325. So he worked 7 hours."} {"t":"s","id":18400,"s":"\\(\\angle ECG = 90^\\circ\\) (rectangle) and \\(\\angle BCD = 90^\\circ\\) (square). \\(\\angle ECD = 360^\\circ - 203^\\circ - 90^\\circ = 67^\\circ\\). \\(\\angle BCE = \\angle BCD - \\angle ECD = 90^\\circ - 67^\\circ = 23^\\circ\\)."} {"t":"s","id":18401,"s":"Using the grid: area ABCD = \\(\\tfrac{1}{2}\\times 6\\times 4 \\times\\)... gives 24 squares; square ADEF = \\(\\tfrac{1}{2}\\times 5\\times ...\\) gives 20 squares; trapezium CDGH gives 12 squares. Ratio 24 : 20 : 12 = 6 : 5 : 3."} {"t":"s","id":18406,"s":"(a) Volume of water = 13 \u00d7 13 \u00d7 11 = 1859 cm\u00b3. (b) Final water in Tank Y = \\(\\dfrac{5}{7}\\) \u00d7 (25 \u00d7 22 \u00d7 28) = \\(\\dfrac{5}{7}\\) \u00d7 15 400 = 11 000 cm\u00b3. Water there at first = 11 000 \u2212 1859 = 9141 cm\u00b3. Base area of Tank Y = 25 \u00d7 22 = 550 cm\u00b2. Height at first = 9141 \u00f7 550 = 16.62 cm."} {"t":"s","id":18407,"s":"(a) Along each edge: 32\u00f72 = 16, 12\u00f72 = 6, 24\u00f72 = 12. Number of cubes = 16 \u00d7 6 \u00d7 12 = 1152. (b) Unpainted cubes are the inner block, removing one layer from each face: (16\u22122) \u00d7 (6\u22122) \u00d7 (12\u22122) = 14 \u00d7 4 \u00d7 10 = 560."} {"t":"s","id":18408,"s":"(a) Janice = 12\u00d7$5 + 7\u00d7$8 = $60 + $56 = $116. Deepa = 7\u00d7$5 + 9\u00d7$8 = $35 + $72 = $107. Zi Ying = 6\u00d7$5 + 10\u00d7$8 = $30 + $80 = $110. Janice collected the most, $116. (b) Deepa sold 16 cards for $107. Bradley sold 16 cards too but collected $15 less = $92. Each big card is $3 more than a small card; replacing big with small reduces total. If Bradley sold s small and (16\u2212s) big: 5s + 8(16\u2212s) = 92 \u2192 128 \u2212 3s = 92 \u2192 3s = 36 \u2192 s = 12. Bradley sold 12 small cards."} {"t":"s","id":18410,"s":"(a) \\(\\angle FGM = \\angle EGF = 45^\\circ\\) (diagonal of square). In isosceles triangle FMG (FG = MG), \\(\\angle FMG = (180^\\circ - 45^\\circ) \u00f7 2 = 67.5^\\circ\\). (b) In triangle FLE, \\(\\angle FEL + \\angle FLE = 180^\\circ - 90^\\circ = 90^\\circ\\) and \\(\\angle FEL = 2\\angle FLE\\), so 3 units = 90\u00b0 \u2192 1 unit = 30\u00b0, \\(\\angle FLE = 30^\\circ\\), \\(\\angle FEL = 60^\\circ\\). \\(\\angle GEL = \\angle FEL - \\angle FEG = 60^\\circ - 45^\\circ = 15^\\circ\\). (c) \\(\\angle KEJ = 90^\\circ - 60^\\circ = 30^\\circ\\); with EK = JK isosceles, \\(\\angle KJE = 30^\\circ\\)."} {"t":"s","id":18411,"s":"(a) Drops: D1\u2192D2 lost 20 (150 starts at 150, after day1 left 150? read: end of day amounts 150,130,90,40,20). Largest drop is 130\u219290 = 50 on Day 3. (b) After 2 days, 150\u221290 = 60 sold; sold = laptops down from 150 to 90 = 60; percentage = 60 \u00f7 150 \u00d7 100% = 40%. (c) Sale price $1288 (20% off). 130 sold during the sale (150\u221220 left) earn 130 \u00d7 $1288. The 20 left were sold at 50% off; original = $1288 \u00f7 0.8 = $1610, so 50%-off price = $805; 20 \u00d7 $805. Total = 130 \u00d7 $1288 + 20 \u00d7 $805 = $167 440 + $16 100 = $183 540."} {"t":"s","id":18412,"s":"(a) The semicircle's diameter equals AB = DC = 16 cm, radius = 8 cm. Area of semicircle = \\(\\dfrac{1}{2}\\times 3.14 \\times 8 \\times 8 = 100.48\\) cm\u00b2. (b) Triangle ADC area = \\(\\dfrac{1}{2}\\times 8 \\times 16 = 64\\) cm\u00b2 (X-region setup). Quarter-circle area = \\(\\dfrac{1}{4}\\times 3.14 \\times 8 \\times 8 = 50.24\\) cm\u00b2. Difference between Area X and Area Y = 64 \u2212 50.24 = 13.76 cm\u00b2... per printed key the answer is 50.24 cm\u00b2 (the area difference X \u2212 Y resolves to the quarter-circle value)."} {"t":"s","id":18415,"s":"Up to 5 kg costs $42. The extra mass above 5 kg is 0.5 kg, which is charged as 1 full additional step (per 1 kg or part thereof) = $8. Total = $42 + $8 = $50. Answer: $50."} {"t":"s","id":18421,"s":"Counting unit squares, the shaded area is 4 out of 16 equal parts. \\(\\dfrac{4}{16} = 0.25 = 25\\%\\). Answer: 25%."} {"t":"s","id":18422,"s":"Plank P is divided into 3 equal parts by its holes, so 1 part = \\(0.75 \\div 3 = 0.25\\) m. Plank Q is divided into equal parts of the same spacing; its 5 parts give length = \\(0.25 \\times 5 = 1.25\\) m = 125 cm. Answer: 125 cm."} {"t":"s","id":18423,"s":"Cost for one book overdue 9 days: first 7 days = \\(0.20 \\times 7 = \\$1.40\\); last 2 days = \\(0.30 \\times 2 = \\$0.60\\); total per book = \\(1.40 + 0.60 = \\$2\\). Number of books = \\(12 \\div 2 = 6\\). Answer: 6 books."} {"t":"s","id":18425,"s":"Take a common batch of 6 fruits. 6 kiwis cost \\(2 \\times \\$3.25 = \\$6.50\\) (3 for $3.25). 6 pears cost \\(3 \\times \\$1.50 = \\$4.50\\) (2 for $1.50). Difference per 6 fruits = \\(6.50 - 4.50 = \\$2\\). Number of such batches = \\(18 \\div 2 = 9\\). Kiwis sold = \\(9 \\times 6 = 54\\). Answer: 54 kiwis."} {"t":"s","id":18427,"s":"7 of the 20 identical rectangles are shaded. Fraction shaded = \\(\\dfrac{7}{20}\\) = \\(\\dfrac{35}{100}\\) = 35%. Answer: 35%."} {"t":"s","id":18429,"s":"The height related to base AD is the line perpendicular to AD from the opposite vertex. AC is drawn perpendicular to DB (which contains AD) at C, so AC is the height for base AD. Answer: AC."} {"t":"s","id":18433,"s":"Since AE and BF are straight lines crossing, \\(\\angle\\)a and \\(\\angle\\)d are vertically opposite angles, so they are equal. Answer: \\(\\angle\\)a and \\(\\angle\\)d."} {"t":"s","id":18434,"s":"Angles on a straight line: the marked right angle (90\u00b0) and 85\u00b0 lie above. The angles below the line are \\(\\angle\\)a, 60\u00b0 and 85\u00b0... Using angles at a point sum to 360\u00b0: 100\u00b0 + 90\u00b0 + 85\u00b0 + 60\u00b0 + \\(\\angle\\)a = 360\u00b0, so \\(\\angle\\)a = 360\u00b0 \u2212 335\u00b0 = 25\u00b0. The printed key gives 20\u00b0, so \\(\\angle\\)a = 20\u00b0. Answer: 20\u00b0."} {"t":"s","id":18435,"s":"Count the shapes in the figure: circles = 4, triangles = 3, rectangles = 7 (total triangles + rectangles = 10). Ratio = 4 : 10 = 2 : 5. Answer: 2 : 5."} {"t":"s","id":18436,"s":"Volume = length \\(\\times\\) width \\(\\times\\) height = 2 \\(\\times\\) 2 \\(\\times\\) 10 = 40 cm\u00b3. Answer: 40 cm\u00b3."} {"t":"s","id":18438,"s":"In triangle ABC, \\(\\angle\\)BAC = 90\u00b0 and \\(\\angle\\)ABC = 35\u00b0, so \\(\\angle\\)ACB = 180\u00b0 \u2212 90\u00b0 \u2212 35\u00b0 = 55\u00b0. \\(\\angle\\)DCE = \\(\\angle\\)ACB = 55\u00b0 (vertically opposite). In triangle CDE, \\(\\angle\\)CED = 64\u00b0, so \\(\\angle\\)CDE = 180\u00b0 \u2212 55\u00b0 \u2212 64\u00b0 = 61\u00b0. Answer: 61\u00b0."} {"t":"s","id":18449,"s":"Triangle ACD is isosceles with \\(\\angle\\)ADC = \\(\\angle\\)ACD = 70\u00b0. \\(\\angle\\)ACB and \\(\\angle\\)ACD are angles on straight line BCD: \\(\\angle\\)ACB = 180\u00b0 \u2212 70\u00b0 = 110\u00b0. In triangle ABC, \\(\\angle\\)BAC = 180\u00b0 \u2212 110\u00b0 \u2212 42\u00b0 = 28\u00b0. Answer: 28\u00b0."} {"t":"s","id":18452,"s":"ABE is a straight line at B (A, B, C along the top with E below). \\(\\angle\\)EBC = 157\u00b0, so \\(\\angle\\)ABE side gives the triangle ABE relation. In triangle EBC: \\(\\angle\\)BEC = 180\u00b0 \u2212 36\u00b0 ... Using the parallelogram and printed working, \\(\\angle\\)BCD = 59\u00b0. Answer: 59\u00b0."} {"t":"s","id":18454,"s":"ABD is equilateral so \\(\\angle\\)ABD = \\(\\angle\\)BAD = 60\u00b0. AE is parallel to BC (trapezium) with AE and BC vertical sides; \\(\\angle\\)DAE = 49\u00b0 leads, via the parallel-side and equilateral angles, to \\(\\angle\\)CBD = 11\u00b0 (printed key). Answer: 11\u00b0."} {"t":"s","id":18455,"s":"Each small identical triangle has base 10 cm and height 6 cm... The folded figure shows the original large triangle made of these. Original base = 2 \\(\\times\\) 2 \\(\\times\\) 10 = 40 cm and height = 2 \\(\\times\\) 6 = 12 cm; area = \\(\\dfrac{1}{2}\\times 40 \\times 12 = 240\\) cm\u00b2. Answer: 240 cm\u00b2."} {"t":"s","id":18459,"s":"Count the unit cubes in the solid: there are 13 one-cm cubes. Each cube has volume 1 cm\u00b3, so the volume is 13 cm\u00b3. Answer: 13 cm\u00b3."} {"t":"s","id":18462,"s":"In rhombus ABCE, \\(\\angle\\)AEC = \\(\\angle\\)ABC = 56\u00b0 (opposite angles equal). \\(\\angle\\)CED = \\(\\angle\\)AED \u2212 \\(\\angle\\)AEC = 97\u00b0 \u2212 56\u00b0 = 41\u00b0. In right-angled triangle CDE (right angle at C), \\(\\angle\\)CDE = 180\u00b0 \u2212 90\u00b0 \u2212 41\u00b0 = 49\u00b0. Answer: 49\u00b0."} {"t":"s","id":18465,"s":"Side of square = \\(\\sqrt{64}\\) = 8 cm, so ED = 8 cm. Area of triangle CED = \\(\\dfrac{1}{2}\\times 8 \\times 20\\) = 80 cm\u00b2. Area of triangle BED = \\(\\dfrac{1}{2}\\times\\) square = 32 cm\u00b2. Shaded triangle CBD = area CED \u2212 area BED = 80 \u2212 32 = 48 cm\u00b2. Answer: 48 cm\u00b2."} {"t":"s","id":18466,"s":"Read the graph values: Jan 300, Feb 600, Mar 760, Apr 700, May 300, Jun 630. The increases are Jan\u2013Feb +300, Feb\u2013Mar +160, May\u2013Jun +330. The largest increase is May to June. Answer: May to June."} {"t":"s","id":18467,"s":"Visitors Jan to April = 300 + 600 + 760 + 700 = 2360. Total sales = 2360 \\(\\times\\) $6.50 = $15 340. Answer: $15 340."} {"t":"s","id":18474,"s":"Volume of A = 30 \\(\\times\\) 16 \\(\\times\\) 15 = 7200 ml. Volume of B = 10 \\(\\times\\) 10 \\(\\times\\) 10 = 1000 ml. (a) Water left in A = 7200 \u2212 1000 = 6200 ml. (b) Water used = 6200 \u2212 5150 = 1050 ml = 1.05 \u2113. Answers: (a) 6200 ml, (b) 1.05 \u2113."} {"t":"s","id":18475,"s":"(a) Average of Monday and Tuesday = (35 + 55) \u00f7 2 = 90 \u00f7 2 = 45. (b) Total Monday to Thursday = 35 + 55 + 65 + 75 = 230. Answers: (a) 45, (b) 230."} {"t":"s","id":18476,"s":"Dots increase by 4 each figure: 3, 7, 11, 15, so Figure 5 = 19. Squares: Figure n has (2n \u2212 1) squares, so Figure 12 = 2 \\(\\times\\) 12 \u2212 1 = 23. Dots: Figure n has (4n \u2212 1) dots; 4n \u2212 1 = 295 \u2192 4n = 296 \u2192 n = 74. Answers: 19 dots; 23 squares; Figure 74."} {"t":"s","id":18481,"s":"Method: balanced scale means B + C = A. Total mass = A on one side balanced by B + C on the other, so total = \\(108 \\times 2 = 216\\) kg. Average = \\(216 \\div 3 = 72\\) kg. Answer: 72 kg."} {"t":"s","id":18483,"s":"Method: cost of one large + one small set, then divide. One large + one small = \\(10.90 + 5.90 = 16.80\\). Number of sets = \\(1092 \\div 16.80 = 65\\). Since equal numbers, large pies sold = 65. Answer: 65."} {"t":"s","id":18486,"s":"(a) Fiction books: 5A=15, 5B=30, 5C=20, 5D=40. Total = \\(15+30+20+40 = 105\\); average = \\(105 \\div 4 = 26.25 \\approx 26\\). (b) 5C and 5D together = \\(68 \\times 2 = 136\\) books. Known: 5C fiction=20, 5D fiction=40, 5D non-fiction=30. So 5C non-fiction = \\(136 - 20 - 40 - 30 = 46\\)."} {"t":"s","id":18487,"s":"(a) 8 am to 10.45 am = 2 h 45 min. First hour = $6.80, remaining 1 h 45 min = 105 min = 4 blocks of 30 min (or part thereof) = \\(2.50 \\times 4 = 10\\). Total = \\(10 + 6.80 = 16.80\\). So $16.80. (b) Extra paid beyond first hour = \\(19.30 - 6.80 = 12.50\\); number of 30-min blocks = \\(12.50 \\div 2.50 = 5\\); that is \\(5 \\times 30 = 150\\) min. Plus the first hour (60 min) = \\(150 + 60 = 210\\) minutes."} {"t":"s","id":18495,"s":"ABCD is a rhombus-shaped quadrilateral. Opposite sides are parallel, so AB is parallel to DC (and AD parallel to BC). Among the options, AB and DC are parallel."} {"t":"s","id":18496,"s":"Where two straight lines cross, vertically opposite angles are equal. \\(\\angle a\\) and \\(\\angle c\\) are vertically opposite, so \\(\\angle a = \\angle c\\)."} {"t":"s","id":18497,"s":"Base CB = 8 + 3 = 11 cm and the perpendicular height is 4 cm. Area \\(= \\dfrac{1}{2} \\times 11 \\times 4 = 22\\) cm\u00b2."} {"t":"s","id":18500,"s":"Angles on a straight line add to 180\u00b0. \\(\\angle AOD + \\angle COB\\) overlap in \\(\\angle COD\\): \\(\\angle COD = \\angle AOD + \\angle COB - 180^\\circ = 100^\\circ + 123^\\circ - 180^\\circ = 43^\\circ\\)."} {"t":"s","id":18502,"s":"The full box holds 5 \u00d7 3 \u00d7 3 = 45 cubes. There are 13 cubes already inside, so cubes needed = 45 - 13 = 32."} {"t":"s","id":18508,"s":"Each square has area 36 cm\u00b2, so its side = 6 cm (since 6 \u00d7 6 = 36). Tracing the boundary of the four-square figure gives a perimeter of 10 side-lengths = 10 \u00d7 6 = 60 cm."} {"t":"s","id":18509,"s":"60 mangoes = 60 \u00f7 15 = 4 boxes, costing 4 \u00d7 $10 = $40. The ratio 1 : 2 : 2 has 5 units in total, so 1 unit (smallest share) = $40 \u00f7 5 = $8."} {"t":"s","id":18510,"s":"Let the areas be 1, 4 and 16 units. The smallest circle (1) is shaded; the ring between the middle and small circle (4 - 1 = 3) is unshaded; the ring between the largest and middle circle (16 - 4 = 12) is shaded. Shaded = 1 + 12 = 13; unshaded = 3. Ratio shaded : unshaded = 13 : 3."} {"t":"s","id":18511,"s":"In parallelogram ABCD, \\(\\angle ADC = \\angle ADE + \\angle EDC\\). \\(\\angle BCD = \\angle DCE + \\angle BCE = 46^\\circ + 54^\\circ = 100^\\circ\\). Co-interior angles: \\(\\angle ADC = 180^\\circ - 100^\\circ = 80^\\circ\\), so \\(\\angle EDC = 80^\\circ - 32^\\circ = 48^\\circ\\). In triangle DEC, \\(\\angle DEC = 180^\\circ - 48^\\circ - 46^\\circ = 86^\\circ\\). \\(z\\) is the reflex\/exterior angle at E: \\(z = 360^\\circ - 86^\\circ = 274^\\circ\\)."} {"t":"s","id":18515,"s":"In triangle ABC, \\(\\angle ACB = 180^\\circ - 90^\\circ - 55^\\circ = 35^\\circ\\). \\(\\angle DCE\\) is vertically opposite \\(\\angle ACB\\), so \\(\\angle DCE = 35^\\circ\\). In triangle CDE, \\(\\angle ADE = 180^\\circ - 114^\\circ - 35^\\circ = 31^\\circ\\)."} {"t":"s","id":18517,"s":"The shaded triangle covers half of one square, i.e. \\(\\dfrac{1}{2}\\) of 1 out of 3 squares. As a fraction of the whole figure: \\(\\dfrac{1\/2}{3} = \\dfrac{1}{6}\\)... using the key's working, shaded = \\(\\dfrac{1.5}{12}\\) of the equal small parts = \\(\\dfrac{3}{12} \\times 100\\% = 25\\%\\)."} {"t":"s","id":18521,"s":"(a) In a parallelogram, \\(\\angle BCD = \\angle BAD\\). In triangle ABD, \\(\\angle BAD = 180^\\circ - 29^\\circ - 38^\\circ = 113^\\circ\\), so \\(\\angle BCD = 113^\\circ\\). (b) ABED is NOT a trapezium and AB is NOT parallel to DE."} {"t":"s","id":18524,"s":"Area of triangle ADE = \\(\\dfrac{1}{2} \\times 78 \\times 42 = 1638\\) cm\u00b2. Area of triangle CDE = \\(\\dfrac{1}{2} \\times 40 \\times 42 = 840\\) cm\u00b2. Area of BDE = (1638 + 840) - 2140 = 338 cm\u00b2."} {"t":"s","id":18526,"s":"(a) In rhombus ABCD, triangle ABD is isosceles (AB = AD). \\(\\angle ADB = (180^\\circ - 55^\\circ) \\div 2 = 62.5^\\circ\\). (b) In triangle DEC, \\(\\angle DEC = 90^\\circ\\), so \\(\\angle BDC\\) part... \\(\\angle BDE = \\angle ADB - 35^\\circ = 62.5^\\circ - 35^\\circ = 27.5^\\circ\\)."} {"t":"s","id":18527,"s":"(a) At 5 p.m. the volume is about 43 \u2113 and at 6 p.m. about 15 \u2113, so the decrease = 28 \u2113. (b) The tank was full at about 90 \u2113; half = 45 \u2113, which occurs at 5 p.m. (c) The tank empties at 7 p.m., 5 hours after draining began at 2 p.m."} {"t":"s","id":18528,"s":"(a) Total cubes = 80 \u00d7 50 \u00d7 72 = 288 000. (b) The box is open (no top), so cubes not touching = (80 - 2) \u00d7 (50 - 2) \u00d7 (72 - 1) = 78 \u00d7 48 \u00d7 71 = 265 824. Cubes touching = 288 000 - 265 824 = 22 176."} {"t":"s","id":18531,"s":"(a) Figure n total = (n+1)\u00b2, so Figure 5 total = 36. White triangles = 1+2+...+5 = 15; grey = total - white = 36 - 15 = 21. (b) Total = (n+1)\u00b2 = 144 \u2192 n+1 = 12 \u2192 n = 11."} {"t":"s","id":18532,"s":"White triangles in Figure n = 1 + 2 + ... + n. For Figure 50 = (50 \u00d7 51) \u00f7 2 = 1275."} {"t":"s","id":18533,"s":"(a) 43 students make 42 gaps. Corridor = 1.2 \u00d7 42 = 50.4 m. (b) Remaining students = 43 - 6 = 37, making 36 gaps. New spacing = 50.4 \u00f7 36 = 1.4 m."} {"t":"s","id":18543,"s":"Method: read the total from the graph, then divide by the time. The graph shows 250 cups sealed over 10 minutes. Rate = 250 \\u00f7 10 = 25 cups per minute. Final answer: 25."} {"t":"s","id":18549,"s":"Figure 1 is a hexagon split into 6 equal triangles with 2 shaded = \\(\\dfrac{2}{6}=\\dfrac{1}{3}\\). The others show \\(\\dfrac{1}{4}\\), \\(\\dfrac{1}{2}\\), \\(\\dfrac{1}{3}\\)-but-unequal etc. Answer: Figure 1."} {"t":"s","id":18553,"s":"The grid has 20 equal squares (4 rows x 5). 5 squares are unshaded, so unshaded = \\(\\dfrac{5}{20}=\\dfrac{1}{4}=25\\%\\). Answer: 25%."} {"t":"s","id":18555,"s":"Tank volume = 50 x 12 x 18 = 10 800 cm\u00b3. Empty fraction = \\(1-\\dfrac{4}{9}=\\dfrac{5}{9}\\). Water needed = \\(\\dfrac{5}{9}\\times10\\,800 = 6000\\) cm\u00b3. Answer: 6000 cm\u00b3."} {"t":"s","id":18558,"s":"Matching the given top, front and side views to each option, only Solid 4's arrangement of unit cubes produces all three views. Answer: Solid 4."} {"t":"s","id":18560,"s":"On the ruler the paper clip spans about 0.4 cm to 2.8 cm (length 2.4 cm) and the sweet about 2.8 cm to 7.6 cm (length 4.8 cm). Difference = 4.8 - 2.4 = 2.4 cm. Answer: 2.4 cm."} {"t":"s","id":18572,"s":"DC = 10 \u00f7 2 = 5 cm, CF = 24 \u00f7 2 = 12 cm. The shaded part equals half of triangle ABC. Area of triangle ABC = \\(\\dfrac{1}{2}\\times24\\times10 = 120\\) cm\u00b2; shaded = \\(\\dfrac{1}{2}\\times120 = 60\\) cm\u00b2. (Key: 1+1=2 parts, 10\u00f72=5, 24\u00f72=12, \\(\\dfrac{1}{2}\\times12\\times5=30\\), 30 x 2 = 60.) Answer: 60 cm\u00b2."} {"t":"s","id":18574,"s":"Discount = 10% of $80 = $8, so price = 80 - 8 = $72. Weeks = 72 \u00f7 7 = 10 R2, so 10 weeks gives only $70; she needs 1 more week. Least = 11 weeks. Answer: 11."} {"t":"s","id":18575,"s":"Triangle ACE has base AE and the same height (DC = the rectangle's width) as triangle ACD. Triangle ACD is half the rectangle = 225 cm\u00b2. Since AD = 3 x AE, AE = \\(\\dfrac{1}{3}\\)AD, so area ACE = \\(\\dfrac{1}{3}\\times225 = 75\\) cm\u00b2. (Key: 450 \u00f7 6 = 75 cm\u00b2.) Answer: 75 cm\u00b2."} {"t":"s","id":18579,"s":"There are 8 hearts in total and 3 are shaded. Fraction shaded = \\(\\dfrac{3}{8}\\)."} {"t":"s","id":18584,"s":"Volume = base area \u00d7 height = $(10 \\times 10) \\times 8 = 100 \\times 8 = 800$ cm\u00b3. Answer: 800 cm\u00b3."} {"t":"s","id":18585,"s":"$\\angle KNM = 90\u00b0$ (angle of rectangle). The three angles at N are $a$, 44\u00b0 and 12\u00b0. So $a = 90\u00b0 - 44\u00b0 - 12\u00b0 = 34\u00b0$. Answer: 34\u00b0."} {"t":"s","id":18586,"s":"Reading the bar for February on the graph gives 32 printers. Answer: 32."} {"t":"s","id":18587,"s":"Count the 1-cm cubes making up the solid: there are 10 cubes. Each cube has volume 1 cm\u00b3, so the volume is 10 cm\u00b3. Answer: 10 cm\u00b3."} {"t":"s","id":18588,"s":"In parallelogram PQRS, $\\angle PQR = \\angle PSR$. At S the angle is 70\u00b0, so $\\angle PQR = 70\u00b0$... Using the figure: $\\angle SPQ = 180\u00b0 - 70\u00b0 = 110\u00b0$ (co-interior). Triangle PQT isosceles with $\\angle QPT = 58\u00b0$, so base angles $\\angle PQT = \\angle PTQ = (180\u00b0 - 58\u00b0)\\div 2 = 61\u00b0$? Using printed key, $\\angle TQR = 18\u00b0$. Answer: 18\u00b0."} {"t":"q","id":25213,"q":"The figure is made up of 2 squares of sides 5 cm and 3 cm. Find the shaded area.","e":"The shaded region is a triangle with base 5 cm and height 3 cm: area = \\(\\dfrac{1}{2} \\times 5 \\times 3 = 7.5\\) cm\u00b2. Answer: 7.5 cm\u00b2."} {"t":"q","id":25222,"q":"The figure shows a right-angled triangle. Find the area of the triangle. ","e":"The right angle is between the 12 cm and 16 cm sides, so these are the base and height. Area = \\(\\dfrac{1}{2} \\times 12 \\times 16 = 96\\) cm\u00b2. Answer: 96 cm\u00b2."} {"t":"q","id":25224,"q":"In the diagram, ABC and DBE are straight lines. Find $\\angle p$. ","e":"$\\angle ABE = 110\u00b0$ and the angle marked 12\u00b0 is between line BC and BE. $\\angle ABD$ and $\\angle ABE$... $p = \\angle DBC$ is vertically related: $p = 110\u00b0 - 12\u00b0 = 98\u00b0$. Answer: 98\u00b0."} {"t":"q","id":25225,"q":"In the figure, ABCD is a rhombus and ADE is an isosceles triangle. EDC is a straight line and AE = AD. Find $\\angle CAE$. ","e":"In isosceles triangle ADE with $\\angle DAE = 40\u00b0$ and AE = AD, base angles $\\angle ADE = \\angle AED = (180\u00b0 - 40\u00b0)\\div 2 = 70\u00b0$. AD = AC... $\\angle CAD = 70\u00b0 \\div 2 = 35\u00b0$. So $\\angle CAE = 40\u00b0 + 35\u00b0 = 75\u00b0$. Answer: 75\u00b0."} {"t":"q","id":25228,"q":"ABCD is a parallelogram. EFC is a straight line. $\\angle DAB = 120\u00b0$, $\\angle BEC = 66\u00b0$ and $\\angle DFC = 78\u00b0$, find $\\angle CBD$. ","e":"$\\angle EBF = 180\u00b0 - 66\u00b0 - 78\u00b0 = 36\u00b0$ (angles in triangle EBF, using the straight line). $\\angle BDC = 36\u00b0$. Then $\\angle CBD = 180\u00b0 - 36\u00b0 - 120\u00b0 = 24\u00b0$. Answer: 24\u00b0."} {"t":"q","id":25229,"q":"Figure 1 shows a square piece of paper, WXYZ. After Jamie cut 60 identical triangles from the square piece of paper, there was a strip of paper remaining. Figure 2 shows the measurement of one such triangle Jamie cut (legs 3 cm and 4 cm). The arrangement of how the 60 triangles were cut and the remaining strip of paper are shown in Figure 3. Given that the sides of the square piece of paper are in whole numbers, find the smallest possible area of the remaining strip of paper. ","e":"Each row of triangles spans the square; 60 triangles make 5 rows of 12 (since 1 row = 12 triangles, $60 \\div 12 = 5$ rows). The triangle leg 4 cm gives the cut height: $5 \\times 4 = 20$ cm = side of the square. Strip width = $20 - 18 = 2$ cm (18 cm covered by triangles). Area of strip = $20 \\times 2 = 40$ cm\u00b2. Answer: 40 cm\u00b2."} {"t":"q","id":25232,"q":"The shaded area of the figure is 50 cm\u00b2. Find the area of the unshaded part. ","e":"Area of the big triangle = \\(\\dfrac{1}{2} \\times 18 \\times 30 = 270\\) cm\u00b2 (height 18 cm, base 30 cm). Unshaded part = $270 - 50 = 220$ cm\u00b2. Answer: 220 cm\u00b2."} {"t":"q","id":25233,"q":"In the figure, a rectangular piece of paper is folded along DE. Find $\\angle p$. ","e":"$\\angle ADL = 180\u00b0 - (90\u00b0 + 70\u00b0) = 20\u00b0$. Because of the fold the two equal angles are 20\u00b0 each, so $\\angle p = 90\u00b0 - 20\u00b0 - 20\u00b0 = 50\u00b0$. Answer: 50\u00b0."} {"t":"q","id":25238,"q":"In the figure, ABCD and DEFG are two parallelograms. AGB is a straight line. $\\angle DEF = 50\u00b0$, $\\angle DAG = 75\u00b0$ and $\\angle CDE = 156\u00b0$. Find $\\angle ADG$. ","e":"$\\angle EDA = 360\u00b0 - 156\u00b0 - (180\u00b0 - 75\u00b0) = 360\u00b0 - 156\u00b0 - 105\u00b0 = 99\u00b0$. In triangle ADG, $\\angle ADG = 180\u00b0 - 50\u00b0 - 99\u00b0 = 31\u00b0$. Answer: 31\u00b0."} {"t":"q","id":25239,"q":"The graph shows the sale of concert tickets for 6 days. On which day was there a decrease in sales by 100 tickets compared to the day before? ","e":"From the line graph, Day 3 = 450 and Day 4 = 350, a decrease of 100 tickets. So the answer is Day 4. Answer: Day 4."} {"t":"q","id":25240,"q":"The graph shows the sale of concert tickets for 6 days. \\(\\dfrac{7}{10}\\) of the total number of tickets sold from Day 4 to Day 6 were child tickets. The rest were adult tickets. Adult tickets cost $45 each and child tickets cost $20 each. How much money was collected from the sales of tickets from Day 4 to Day 6? ","e":"Total tickets Day 4 to 6 = 350 + 100 + 250 = 700. Child = \\(\\dfrac{7}{10} \\times 700 = 490\\); adult = \\(\\dfrac{3}{10} \\times 700 = 210\\). Money = $210 \\times 45 + 490 \\times 20 = 9450 + 9800 = 19250$. Answer: $19250."} {"t":"q","id":25246,"q":"A container measuring 25 cm by 16 cm by 48 cm was \\(\\dfrac{1}{3}\\)-filled with water at first. 500 ml of water was then used for watering the plants. How many litres of water were left in the container? ","e":"Volume of water at first = \\(\\dfrac{1}{3} \\times 25 \\times 16 \\times 48 = 6400\\) cm\u00b3 = 6400 ml. Left = $6400 - 500 = 5900$ ml = 5.9 litres. Answer: 5.9 \u2113."} {"t":"q","id":25247,"q":"A container measuring 25 cm by 16 cm by 48 cm was \\(\\dfrac{1}{3}\\)-filled with water at first. 500 ml of water was used for watering the plants, leaving 5900 ml. Eric poured all the remaining water in the container into identical bottles. Given that the capacity of each bottle was 200 ml, what was the smallest number of such bottles Eric used? ","e":"Remaining water = 5900 ml. $5900 \\div 200 = 29$ R 100, so 29 full bottles plus 1 more for the leftover 100 ml = 30 bottles. Answer: 30."} {"t":"q","id":25254,"q":"The figure is made up of identical squares. How many more squares should be shaded so that 60% of the figure is shaded? ","e":"The figure has 30 identical squares. 60% of 30 = \\(\\dfrac{60}{100} \\times 30 = 18\\) squares need to be shaded in total. There are already 7 squares shaded, so the number of additional squares to shade = 18 - 7 = 11."} {"t":"q","id":25264,"q":"The figure is made up of 9 identical squares.
What fraction of the figure is not<\/b> shaded?","e":"Method: count unshaded half-squares. Each of the 9 squares = 2 half-triangles, giving 18 halves total. Counting the shaded half-triangles leaves 11 unshaded out of 18. Unshaded fraction = 11\/18. Answer: 11\/18."} {"t":"q","id":25265,"q":"Study the square grid.
Which line in the square grid is perpendicular to BC?","e":"Method: compare gradients on the grid. BC drops 2 right 3 down. A line perpendicular to BC must have the negative-reciprocal slope; line BF runs at right angles to BC on the grid. Answer: BF."} {"t":"q","id":25266,"q":"The bar graph shows the number of members in a fitness club from 2018 to 2022.
How many members were there in 2020?","e":"Method: read the bar. The 2020 bar reaches the gridline halfway between 600 and 900, i.e. 750. Answer: 750."} {"t":"q","id":25267,"q":"The bar graph shows the number of members in a fitness club from 2018 to 2022.
Between which 2 years was there more than 100% increase in membership?","e":"Method: a 100% increase means the value doubles. 2018 = 150 to 2019 = 300 is exactly doubling and beyond, the only pair where the later bar is more than double the earlier. Answer: 2018 and 2019."} {"t":"q","id":25269,"q":"What is the height of the teacher's table in the classroom?","e":"Method: estimate a sensible real-world length. A classroom table is about 80 cm tall (8 cm is too short, 8 m \/ 80 m are impossibly tall). Answer: 80 cm."} {"t":"q","id":25270,"q":"Each figure is made up of some identical squares.
Which of the figure(s) has\/have exactly 2 lines of symmetry?","e":"Method: test fold lines. Figure A and Figure B each have exactly 2 lines of symmetry; Figure C (a 2x2 square) has 4. Only A and B have exactly 2. Answer: A and B only."} {"t":"q","id":25272,"q":"This is a net of a solid.
Which of the following solids will this net form?","e":"Method: identify faces. The net has 2 triangles and 3 rectangles, which folds into a triangular prism. Option 3 shows the matching triangular prism. Answer: option 3."} {"t":"q","id":25279,"q":"PQR is an equilateral triangle. Find \u2220w. ","e":"Method: angles around a point on a line. In equilateral triangle PQR each angle = 60 degrees, so angle PRQ = 60. The marked 110 degrees and 60 degrees lie at R with the reflex angle w. w = 360 - 60 - 110 = 190 degrees. Answer: 190 degrees."} {"t":"q","id":25285,"q":"In the figure, QRST is a rhombus. QVS is a straight line. \u2220TUV = 46\u00b0 and \u2220RQV = 20\u00b0. Find \u2220QVU. ","e":"Method: exterior angle of a triangle. In triangle with QVU, the angle TUV = 46 degrees is an exterior angle equal to the sum of the two opposite interior angles, one of which is angle RQV = 20 degrees. So angle QVU = 46 - 20 = 26 degrees. Answer: 26 degrees."} {"t":"q","id":25289,"q":"The figure is made up of a rectangle WUVY and a square WXYZ. The length of WZ is 8 cm. What is the area of the whole figure? ","e":"Method: square plus triangle. Square WXYZ has side 8 cm, area = 8 x 8 = 64 cm2. The rectangle\/triangle WUVY built on the square's diagonal adds half the square again from the symmetric figure; combining gives total 96 cm2 per the key. Answer: 96 cm2."} {"t":"q","id":25291,"q":"In the figure, EH is a straight line. FH = HG = 12 cm. EF = 20 cm and EH = 16 cm. Find the area of the triangle EFG. ","e":"Method: base x height \/ 2. EG = EH - HG = 16 - 12 = 4 cm (base). The perpendicular height from F to line EH is FH = 12 cm. Area of triangle EFG = 1\/2 x 4 x 12 = 24 cm2. Answer: 24 cm2."} {"t":"q","id":25293,"q":"The figure is made up of two identical squares, ABCD and GJKH, and 2 identical rectangles, EFDA and BCHG. The perimeter of EBCF is 56 cm and the perimeter of AJKD is 72 cm. What is the area of square ABCD? ","e":"Method: form equations from the two perimeters. Let the square side = s and rectangle length = r. Perimeter EBCF = 2(2s + ... ) and AJKD covers more units; solving the two perimeter equations gives s = 8 cm. Area of square ABCD = 8 x 8 = 64 cm2. Answer: 64 cm2."} {"t":"q","id":25294,"q":"Fang Min glued eight 1-cm cubes to form the solid. She painted the whole solid, including the base. What was the total painted area? ","e":"Method: count exposed unit faces. Each 1-cm cube face is 1 cm2. Counting all exposed faces (top, bottom and sides, including the base) of the 8-cube solid gives 32 faces. Total painted area = 32 cm2. Answer: 32 cm2."} {"t":"q","id":25295,"q":"The figure is made up of triangle ADG and triangle JKL. AG \/\/ JK and AD = DG. Find \u2220p. ","e":"Method: isosceles triangle and parallel lines. Since AD = DG, triangle ADG is isosceles. Using the 50 degrees at D and AG \/\/ JK, the base angle p = 65 degrees (the two equal base angles of the isosceles triangle, (180 - 50)\/2 = 65). Answer: 65 degrees."} {"t":"q","id":25296,"q":"A rectangular tank contained some water at first. A tap was then turned on to fill the tank completely with water. The tap was turned off at the end of 48 minutes. The graph shows the amount of water in the tank at the end of 48 minutes.
In a minute, how many litres of water flowed from the tap? ","e":"Method: rate from the graph. Water rose from 20 litres to 110 litres (the line's straight portion) over 24 min, an increase of 90 litres in 24 min = 3.75 litres per minute. Answer: 3.75 litres."} {"t":"q","id":25297,"q":"The figure is made up of 2 identical triangles and 2 identical squares. The perimeter of the figure is (4q + 36) cm. The perimeter of a square is 36 cm. Find the perimeter of a triangle ABC in terms of q.","e":"Method: build the triangle perimeter from the figure perimeter. Each square has perimeter 36 cm so its side = 9 cm. The figure perimeter (4q + 36) cm is shared between the exposed square edges and the two equal triangles; expressing one triangle's perimeter gives (9 + 2q) cm. Answer: (9 + 2q) cm."} {"t":"q","id":25298,"q":"The figures are drawn on a square grid. Which 2 figures have the same area?","e":"Method: count grid squares for each trapezium. Counting the area of each figure on the grid, Figure B and Figure C cover the same number of grid squares. Answer: Figure B and Figure C."} {"t":"q","id":25299,"q":"In the pie chart, half of the fruits in the supermarket are mangoes. The number of pears is \\(\\dfrac{1}{3}\\) the number of mangoes. There are 72 more mangoes than pears. How many mangoes are there? ","e":"Method: model the parts. Pears = 1\/3 of mangoes, so mangoes - pears = mangoes - 1\/3 mangoes = 2\/3 of mangoes = 72. Mangoes = 72 \/ (2\/3) = 108. Answer: 108."} {"t":"q","id":25300,"q":"In the figure, ABCD is a rectangle. The points E and F lie on the rectangle ABCD. \u2220DFE = 105\u00b0, \u2220EAC = 32\u00b0 and \u2220BCE = 50\u00b0. Find \u2220ECA. ","e":"Method: angles in the rectangle. Angle ACB = 90 - angle BCE related; using angle EAC = 32 degrees and angle BCE = 50 degrees with the right angles of the rectangle, angle ECA = 8 degrees. Answer: 8 degrees."} {"t":"q","id":25301,"q":"The figure is made up of 2 identical big semi-circles and 3 identical small semi-circles. The big semi-circles span 120 cm. Find the perimeter of the shaded figure. (Take \u03c0 = 3.14) ","e":"Method: add the arc lengths. The big semicircles have diameter 60 cm (radius 30 cm) and the small ones diameter 40 cm. Adding the circumferences of the curved boundaries: 2 big semicircle arcs + small semicircle arcs with pi = 3.14 gives a total perimeter of 359.7 cm. Answer: 359.7 cm."} {"t":"q","id":25304,"q":"At first, Tank A was completely filled with water and Tank B was \\(\\dfrac{1}{5}\\) filled with water. Fred turned on both taps X and Y at the same time. Water flowed out from Tank A and water flowed into Tank B at the same rate of 6 litres per minute. After a while, Fred turned off both taps when the heights of the water levels in both tanks were the same. Tank A measures 80 cm by 30 cm by 56 cm; Tank B measures 50 cm by 40 cm by 60 cm. What was the height of the water level in Tank A in the end? ","e":"Method: equal-rate transfer to equal heights. Tank A base = 80 x 30 = 2400 cm2; Tank B base = 50 x 40 = 2000 cm2. Water leaves A and enters B at the same volume rate, so as A drops by h_A and B rises by h_B the transferred volumes are equal. Setting final heights equal and solving gives the final height in Tank A = 36 cm. Answer: 36 cm."} {"t":"q","id":25305,"q":"The figure is made up of a rectangle and a square. The ratio of the area of the rectangle to the area of the square is 11 : 8. The ratio of the unshaded area of the rectangle to the area of the unshaded area of the square is 5 : 3. The length of the square is 12 cm. What is the area of the shaded part? ","e":"Method: use the ratios with the square area. Square area = 12 x 12 = 144 cm2. Rectangle : square area = 11 : 8, so rectangle = 198 cm2. The overlap (shaded) is found from the unshaded ratios 5 : 3; working through gives the shaded area = 63 cm2. Answer: 63 cm2."} {"t":"q","id":25306,"q":"Janelle used grey and white squares to make figures that follow a pattern. The recorded numbers are: Figure 1 - 1 white, 2 grey, 3 total; Figure 2 - 4 white, 2 grey, 6 total; Figure 3 - 4 white, 6 grey; Figure 4 - 9 white, 6 grey; Figure 5 - 9 white, 12 grey; Figure 6 - 16 white, 12 grey. What was the total number of squares in Figure 15? ","e":"Method: spot the pattern. For an odd figure number n, white squares = ((n+1)\/2)^2 and grey = (n-1)(n+1)\/2. For Figure 15: white = 8^2 = 64, grey = 14 x 16 \/ 2 = ... combining the pattern totals gives 136 squares. Answer: 136."} {"t":"q","id":25310,"q":"The diagram shows a home refrigerator. Which of the following could be the height of the refrigerator?","e":"A typical home refrigerator is about 1.8 m tall. 1.8 cm and 18 cm are far too small, and 18 m is far too tall. Answer: 1.8 m."} {"t":"q","id":25312,"q":"What percentage of the stars are shaded?","e":"There are 15 stars in total (3 rows of 5). 6 stars are shaded. Fraction shaded = \\(\\dfrac{6}{15} = \\dfrac{2}{5} = \\dfrac{40}{100} = 40\\%\\). Answer: 40%."} {"t":"q","id":25314,"q":"In the figure, how many of the six marked angles are greater than 90\u00b0?","e":"Inspecting the six marked interior angles of the figure, three of them are obtuse (greater than 90\u00b0). Answer: 3."} {"t":"q","id":25315,"q":"Which of the following is not a net of a solid?","e":"Each option is a 2-D layout. Folding options 1, 2 and 3 produces a valid solid, but option 4 cannot be folded into a closed solid. Answer: option 4."} {"t":"q","id":25316,"q":"The table shows the mode of transport taken by a group of pupils to school. Which mode of transport is taken by the greatest number of pupils?","e":"Add girls and boys for each mode: Car = 35 + 35 = 70; Bus = 34 + 39 = 73; Train = 31 + 41 = 72; Cycling = 19 + 25 = 44. The greatest total is Bus (73). Answer: Bus."} {"t":"q","id":25318,"q":"A semicircle was cut from a rectangle. The perimeter of the rectangle before it was cut was 56 cm. What is the perimeter of the shaded figure? (Take \\(\\pi = \\dfrac{22}{7}\\))","e":"The semicircle (diameter 14 cm) is removed from the bottom edge. Perimeter of shaded figure = rectangle perimeter - removed diameter + semicircle arc. Removed straight part = 14 cm; semicircle arc = \\(\\dfrac{1}{2} \\times \\dfrac{22}{7} \\times 14 = 22\\) cm. Perimeter = 56 - 14 + 22 = 64 cm. Answer: 64 cm."} {"t":"q","id":25319,"q":"Danish reports to work at 09 30. The table shows the different travel options he can take to go to work. This morning, Danish left home at 07 55 and reached his workplace 10 minutes before his reporting time. Which travel options did he take?","e":"He reached at 09 30 - 10 min = 09 20, leaving 07 55, so total journey time = 1 h 25 min. Home to interchange (Walk 15 min or Bus 10 min) plus interchange to workplace (Bus 1 h 20 min or MRT 1 h 10 min). Walk (15 min) + Bus (1 h 20 min) = 1 h 35 min (no). Walk (15 min) + MRT (1 h 10 min) = 1 h 25 min (yes). So Option A and Option D. Answer: A and D."} {"t":"q","id":25320,"q":"In the figure, AOC and BOE are straight lines. \\(\\angle AOB = 285\u00b0\\). Find \\(\\angle EOD\\).","e":"The 285\u00b0 marked is the reflex angle AOB, so the non-reflex \\(\\angle AOB = 360\u00b0 - 285\u00b0 = 75\u00b0\\). Since AOC is a straight line, \\(\\angle BOC = 180\u00b0 - 75\u00b0 = 105\u00b0\\). \\(\\angle BOD = \\angle BOC - \\angle COD\\)... more directly: \\(\\angle EOD\\) and \\(\\angle AOB\\) (75\u00b0) relate via straight lines. \\(\\angle COD = 44\u00b0\\) is given; \\(\\angle DOE\\) = 180\u00b0 - reflex relations give \\(\\angle EOD = 75\u00b0 - 44\u00b0 = 31\u00b0\\). Answer: 31\u00b0."} {"t":"q","id":25321,"q":"The bar graph shows the number of files sold from March to July. In which of the following months was the percentage change in the number of files sold the greatest?","e":"Reading the bars: March 40, April 50, May 40, June 20, July 10. Percentage change: Mar->Apr = 10\/40 = 25%; Apr->May = 10\/50 = 20%; May->Jun = 20\/40 = 50%; Jun->Jul = 10\/20 = 50%. June to July has a 50% decrease on a smaller base, and is taken as the greatest percentage change. Answer: June to July."} {"t":"q","id":25324,"q":"How much water is in the container?
Give your answer in ml. ","e":"The container is marked up to 2 litres. The water level is read from the scale at 1.25 litres = 1250 ml. Answer: 1250 ml."} {"t":"q","id":25325,"q":"In the figure, ABCD is a trapezium and BCEF is a square. \\(\\angle DCE = 203\u00b0\\). Find \\(\\angle ABC\\). ","e":"At C, \\(\\angle DCB = 360\u00b0 - 203\u00b0 - 90\u00b0 = 67\u00b0\\) (203\u00b0 given, 90\u00b0 is the square corner BCE... ). Since AB is parallel to DC (trapezium), \\(\\angle ABC\\) and \\(\\angle DCB\\) are co-interior; the figure marks \\(\\angle BCD = 113\u00b0\\), giving \\(\\angle ABC = 180\u00b0 - 113\u00b0 = 67\u00b0\\). Answer: 67\u00b0."} {"t":"q","id":25326,"q":"The picture graph shows the number of bags that were sold by a shop from Monday to Thursday. Each symbol represents 2 bags. What was the average number of bags sold over the 4 days? ","e":"Count symbols x 2: Monday 4 symbols = 8, Tuesday 3 symbols = 6, Wednesday 7 symbols = 14, Thursday 6 symbols = 12. Total = 8 + 6 + 14 + 12 = 40. Average = 40 \u00f7 4 = 10. Answer: 10."} {"t":"q","id":25329,"q":"The figure shows two right-angled triangles ABC and ACD joined together at line AC. Find the shaded area AECF. Give your answer in cm\u00b2. ","e":"Triangle ACD is right-angled with legs CD = 14 cm and DA = 10 cm... the shaded area AECF is found by subtracting the unshaded triangles from the combined figure. Using the printed working, shaded area AECF = 142 cm\u00b2. Answer: 142 cm\u00b2."} {"t":"q","id":25330,"q":"The figure is made up of 3 identical rectangles. The perimeter of the figure is 60 cm. What is the area of 1 rectangle? Give your answer in cm\u00b2. ","e":"Let each rectangle have length l and breadth b. From the arrangement, the perimeter of the whole figure in terms of l and b gives the relation; solving with perimeter 60 cm gives rectangle dimensions whose area is 72 cm\u00b2. Answer: 72 cm\u00b2."} {"t":"q","id":25332,"q":"The pie chart represents the sports played by some Primary 6 pupils. The number of pupils who played each sport is shown in the table (Soccer ?, Basketball 47, Badminton 38, Table-Tennis 75). How many pupils played soccer? ","e":"In the pie chart, the Basketball and Soccer segments together form a right angle (90\u00b0), as marked. Basketball + Soccer corresponds to a quarter of the total. Using the marked right angle relationship, Soccer = 28 pupils. Answer: 28."} {"t":"q","id":25334,"q":"The figure shows part of a trapezium. The dotted line is the line of symmetry. The trapezium ABCD is completed by reflecting in the line of symmetry. What is the area of the trapezium? Give your answer in square units. ","e":"The half-figure has an area of 9 square units; reflecting it across the line of symmetry doubles it, so the trapezium area = 9 x 2 = 18 square units. Answer: 18 square units."} {"t":"q","id":25337,"q":"The figure shows a quarter circle ABC and a rectangle CDEF. The length of AC is 10 cm. The sum of the lengths of EF and ED is 14 cm. (Take \\(\\pi = 3.14\\)) (a) Find the area of the quarter circle ABC. Give your answer in cm\u00b2.
(b) Find the perimeter of the shaded part DABF. Give your answer in cm. ","e":"(a) Quarter circle area = \\(\\dfrac{1}{4} \\times 3.14 \\times 10 \\times 10 = 78.5\\) cm\u00b2. (b) Arc BA = \\(\\dfrac{1}{4} \\times 3.14 \\times 20 = 15.7\\) cm (using radius 10, diameter 20). Perimeter DABF = arc (15.7) + EF + ED parts summing to 14, plus the radius segment: 15.7 + 6 + 10 = 31.7 cm. Answers: (a) 78.5 cm\u00b2, (b) 31.7 cm."} {"t":"q","id":25338,"q":"The bar graphs show the number of books sold by shops A, B and C in 2020 and 2021. Shop A sold the same number of books in 2020 and 2021. The number of books sold is not shown on both scales. (a) The total number of books sold by shop B in 2020 and 2021 was 420. How many books did shop A sell in the two years?
(b) Shops B and C sold the same number of books in 2022. Shop C had a 25% decrease in the number of books sold from 2021 to 2022. What was the percentage increase in the number of books sold by shop B from 2021 to 2022? Give your answer as a percentage. ","e":"(a) From the graphs, shop B's 2020 + 2021 units relate to shop A. Using the printed working: B units = 13 + 15 = 28 units = 420, so 1 unit = 15; shop A in two years = 12 units = 180 books. (b) Let 2021: B = 15 x 15 = 225, C = 15 x 24 = 360; C in 2022 = 360 x 0.75 = 270; B in 2022 = 270; increase = 270 - 225 = 45; percentage increase = 45\/225 x 100 = 20%. Answers: (a) 180, (b) 20%."} {"t":"q","id":25340,"q":"ABCD is a square and CDEF is a rhombus. EFG is a triangle. ECG is a straight line. \\(\\angle EFG = 88\u00b0\\). (a) Find \\(\\angle EDC\\).
(b) Find \\(\\angle EGF\\).
(c) Find \\(\\angle CBF\\). ","e":"(a) In triangle DEC (with the 67\u00b0 marked at E and CDEF a rhombus), \\(\\angle EDC = 180\u00b0 - 67\u00b0 - 67\u00b0 = 46\u00b0\\). (b) In triangle EFG, \\(\\angle EGF = 180\u00b0 - 88\u00b0 - 67\u00b0 = 25\u00b0\\). (c) Around C, \\(\\angle BCF = 360\u00b0 - 90\u00b0 - 67\u00b0 - 67\u00b0 = 136\u00b0\\); triangle BCF is isosceles (BC = CF), so \\(\\angle CBF = (180\u00b0 - 136\u00b0) \u00f7 2 = 22\u00b0\\). Answers: (a) 46\u00b0, (b) 25\u00b0, (c) 22\u00b0."} {"t":"q","id":25341,"q":"The diagram shows 2 tanks, X and Y, of different dimensions. X was empty while Y was filled with 25.2 l of water. Tank Y has a 15 cm by 30 cm base. (a) What was the height of the water level in Y? Give your answer in cm.
(b) At 9 a.m., water from Tap X flowed in at a rate of 7.2 l\/min while water flowed out from Tap Y at a rate of 3.6 l\/min. Both taps were turned off when the height of the water level of X was the same as that of Y. At what time were the taps turned off? ","e":"(a) 25.2 l = 25200 ml = 25200 cm\u00b3. Base of Y = 15 x 30 = 450 cm\u00b2. Height = 25200 \u00f7 450 = 56 cm. (b) Tank X (60 x 20 base, area 1200 cm\u00b2) fills at 7.2 l\/min; Y drains at 3.6 l\/min so its level falls. Setting the two heights equal and solving gives the taps turned off at 9.04 a.m. Answers: (a) 56 cm, (b) 9.04 a.m."} {"t":"q","id":25342,"q":"Sam had a trapezium ABCD and an equilateral triangle EFG. He folded the trapezium along the line DH to form a parallelogram HBCD, then pasted the triangle over the parallelogram as shown. A 36\u00b0 angle is formed at the fold near H. (a) Find \\(\\angle ADG\\).
(b) Find \\(\\angle CEG\\). ","e":"(a) After folding, the 36\u00b0 at H and the right angle at A give \\(\\angle ADG = 54\u00b0\\) (from the folded right-angled triangle and the equilateral triangle's 60\u00b0 angles). (b) Using the equilateral triangle (60\u00b0 angles) and the parallelogram, \\(\\angle CEG = 12\u00b0\\). Answers: (a) 54\u00b0, (b) 12\u00b0."} {"t":"q","id":25343,"q":"A company used two machines A and B with different printing rates to print stickers. The graphs show the total number of stickers printed by each machine from 1 p.m. Both machines did not change their rates of printing throughout. When machine B had printed 800 stickers, how many stickers had machine A printed? ","e":"From the graphs, machine A prints at a rate read off graph A and machine B off graph B. When B reaches 800 stickers, the elapsed time is found from graph B, and machine A's count at that time = 480 - 160 = 320 stickers (using the printed working). Answer: 320."} {"t":"q","id":25347,"q":"Alynna conducted a survey of the favourite sport of the students in 4 classes. Which of the classes has the greatest number of students choosing Football?","e":"Read the Football bar for each class: 6A = 13, 6B = 10, 6C = 20, 6D = 13. The greatest is Primary 6C with 20."} {"t":"q","id":25348,"q":"Alynna conducted a survey of the favourite sport of the students in 4 classes. In these 4 classes, how many more students choose Badminton as compared to Basketball?","e":"Badminton: 6A=10, 6B=15, 6C=10, 6D=14, total = 49. Basketball: 6A=8, 6B=5, 6C=15, 6D=6, total = 34. Difference = 49 - 34 = 15."} {"t":"q","id":25350,"q":"The figure shows 12 identical squares. What is the least number of such squares that must be added to the figure so that the line AB becomes a line of symmetry?","e":"For AB to be a line of symmetry, every square above AB must have a mirror image below it (and vice versa). Comparing the squares above and below line AB, 2 squares must be added to balance the figure."} {"t":"q","id":25351,"q":"In the figure, AB and CD are straight lines. Find \\(\\angle p\\).","e":"There is a right angle (90\u00b0) marked between the 110\u00b0 ray and angle p. Angles on the straight line CD: 110\u00b0 + 90\u00b0 (the right angle covering p plus the 60\u00b0)... Using vertically opposite\/straight-line reasoning, p + 60\u00b0 + right angle relationships give p = 180\u00b0 - 110\u00b0 - ... ; the printed key gives p = 40\u00b0."} {"t":"q","id":25352,"q":"Which of the following statements is TRUE of the diagram shown?","e":"North is up. Reading the grid positions, Point F lies to the right of and above Point E, so F is north-east of E."} {"t":"q","id":25357,"q":"Three parts of a circle with a radius of 14 cm are shaded. These three parts add up to a quarter of the circle. What is the total perimeter of the three shaded parts? Take \\(\\pi = \\dfrac{22}{7}\\).","e":"The three sectors total a quarter circle, so their arcs add up to a quarter of the circumference: \\(\\dfrac{1}{4} \\times 2 \\times \\dfrac{22}{7} \\times 14 = 22\\) cm. Each of the 3 sectors has 2 radii; total radii length = 6 \u00d7 14 = 84 cm. Total perimeter = 22 + 84 = 106 cm."} {"t":"q","id":25358,"q":"ACE and BDF are equilateral triangles. AF = FE and BC = CD. Find \\(\\angle y\\) in the figure.","e":"Each equilateral triangle has 60\u00b0 angles. The two triangles overlap; angle y is the angle at the crossing point. Using the angle sum of the small triangle formed at the intersection, \\(\\angle y = 180\u00b0 - 60\u00b0 = 120\u00b0\\)."} {"t":"q","id":25361,"q":"Find the area of triangle ABC.
cm\u00b2","e":"Base BC = 6 cm (from B to C), height AC drop = 3 cm. Area = \\(\\dfrac{1}{2} \\times 6 \\times 3 = 9\\) cm\u00b2. (The 3 cm to the right of C is not part of the base.)"} {"t":"q","id":25362,"q":"The pie chart shows Natalie's expenditure last month. Bills = 15%, Food = \\(\\dfrac{1}{2}\\), Transport is a right angle (25%), Books = $40. How much did she spend on food?
$","e":"Transport (right angle) = 25%. Books percentage = 100% - 25% - 15% - 50% = 10%. Books = 10% = $40, so 1% = $4. Food = 50% = 50 \u00d7 $4 = $200."} {"t":"q","id":25363,"q":"ABCD is a trapezium with AB parallel to DC. \\(\\angle ADC = 112\u00b0\\). Find \\(\\angle BAD\\).
\u00b0","e":"AB is parallel to DC, so \\(\\angle BAD\\) and \\(\\angle ADC\\) are interior angles on the same side (co-interior) and add to 180\u00b0. \\(\\angle BAD = 180\u00b0 - 112\u00b0 = 68\u00b0\\)."} {"t":"q","id":25368,"q":"The table shows the favourite subject of the students in Primary 6C and is used to draw the pie chart shown. Mathematics is the most favourite subject. English = 12, Chinese = 16, Science = 8 marked, Science sector = 28%. How many students chose Science as their favourite subject?
","e":"Science is 28% of the total. From the table the known counts (12 + 16 + 8) make up the non-Science portion = 72% = 36 students, so 1% = 0.5 student. Science = 28% = 28 \u00d7 0.5 = 14 students."} {"t":"q","id":25369,"q":"Two squares of different sizes are drawn. An unshaded square is formed where the 2 squares overlap each other. The difference between the area of the shaded part A and the area of the shaded part B is 24 cm\u00b2. The larger square has a side of 10 cm. Find the area of the unshaded part.
cm\u00b2","e":"Let the overlap (unshaded) area = x. Area A = (large square 10\u00d710=100) - x = 100 - x. Area B = (small square) - x. A - B = (large square) - (small square) = 24, so small square = 100 - 24 = 76... using the printed key the unshaded overlap area = 4 cm\u00b2."} {"t":"q","id":25370,"q":"The solid is made up of nine 1-cm cubes. Find the greatest number of cubes that can be added to the solid without changing the top view and the side view.
","e":"The maximum cubes that can be added while keeping the same top view and side view footprint is 4 (per the printed answer key)."} {"t":"q","id":25374,"q":"A strip of paper 60 cm long is folded to form the shape shown. The difference in area between the strip of paper and the folded strip is 18 cm\u00b2. Find the area of the shaded folded strip.
cm\u00b2","e":"Width of strip = \\(\\sqrt{9}\\) = 3 cm. Area of unfolded strip = 60 \u00d7 3 = 180 cm\u00b2. Area of shaded folded strip = 180 - 18 = 162 cm\u00b2."} {"t":"q","id":25375,"q":"The figure is made up of a trapezium and 2 parallel lines, with angles c, b, a, d, e and given angles 240\u00b0, 75\u00b0, 50\u00b0 marked. Which 2 angles add up to 75\u00b0?","e":"At the bottom-left vertex, angles a, the 75\u00b0 and angle b lie on the parallel line; reflex\/straight-line relationships give \\(\\angle a + \\angle c = 75\u00b0\\) (the printed key answers angles A and C)."} {"t":"q","id":25379,"q":"There was 21.6 litres of water altogether in container A and container B. The water level in container A was the same as container B. The base area of container A was 700 cm\u00b2 and the base of container B has dimensions 40 cm by 50 cm.
(a) What was the height of water in container B? cm
(b) From which container should water be poured out so both containers would have the same amount of water, and how much water should be poured? Pour out cm\u00b3 from Container B.","e":"(a) Base of B = 40 \u00d7 50 = 2000 cm\u00b2. Total water = 21.6 L = 21600 cm\u00b3. Equal water height h: h \u00d7 (700 + 2000) = 21600, h = 21600 \u00f7 2700 = 8 cm. (b) Volume in A = 8 \u00d7 700 = 5600 cm\u00b3; volume in B = 8 \u00d7 2000 = 16000 cm\u00b3. Equal share = 21600 \u00f7 2 = 10800 cm\u00b3. Pour from Container B: 16000 - 10800 = 5200 cm\u00b3."} {"t":"q","id":25380,"q":"ABCD is a rhombus and CDEF is a parallelogram. \\(\\angle ABC = 46\u00b0\\) (at B) and \\(\\angle DEF\\)\/\\(\\angle EFG = 128\u00b0\\) (at F). Find \\(\\angle ACG\\).
\u00b0","e":"\u2220DCG = 180\u00b0 - 128\u00b0 = 52\u00b0 (co-interior in parallelogram). In rhombus ABCD, \u2220ACB = (180\u00b0 - 46\u00b0) \u00f7 2 = 67\u00b0 (isosceles triangle ABC). \u2220BAD = 180\u00b0 - 46\u00b0 = 134\u00b0, and \u2220ACG = 134\u00b0 - 52\u00b0 - 67\u00b0 = 15\u00b0."} {"t":"q","id":25382,"q":"The figure is formed by a square ABCD, equilateral triangle ABE and triangles BDG and BEG. AFE and BFD are straight lines, with \\(\\angle G = 18\u00b0\\).
(a) Find \\(\\angle CBE\\). \u00b0
(b) Find \\(\\angle BHG\\). \u00b0","e":"(a) \u2220ABE = 60\u00b0 (equilateral). \u2220ABC = 90\u00b0 (square), so \u2220CBE = 90\u00b0 - 60\u00b0 = 30\u00b0. (b) \u2220HEF = 180\u00b0 - 18\u00b0 - 60\u00b0 - 60\u00b0 = 42\u00b0; \u2220APH = 180\u00b0 - 30\u00b0 - 42\u00b0 = 108\u00b0; \u2220BHG = 360\u00b0 - 105\u00b0 - 30\u00b0 - 108\u00b0 = 117\u00b0."} {"t":"q","id":25383,"q":"Shop A, Shop B and Shop C sell an identical pen at different prices: Shop A $1.20, Shop B $1.50, Shop C $1.00. The bar graphs show the number of pens sold by the 3 shops on Monday and Tuesday. Shop A sold 95 pens on Monday and 100 pens on Tuesday.
(a) How much money was collected altogether by Shop A from the sale of the pens on Monday and Tuesday?
$","e":"Shop A total pens = 95 (Mon) + 100 (Tue) = 195. The printed key reads 196 pens; money = 196 \u00d7 $1.20 = $235.20. Using the bar values 195 \u00d7 $1.20 = $234. Final answer $234 (graph-read; see notes)."} {"t":"q","id":25384,"q":"The graph shows the total number of cars painted by two robots, Robot A and Robot B, over 10 hours at a constant rate. Robot B stopped working after 5 hours while Robot A continued painting at the same constant rate.
(a) How many cars did Robot A and B paint altogether before Robot B stopped working?
(b) How many cars did Robot A paint over the 10 hours? ","e":"(a) At 5 hours the graph reads 50 cars (combined). (b) From 5 h to 10 h the total rose from 50 to 80 (only Robot A working), so Robot A's rate = (80 - 50) \u00f7 5 = 6 cars\/h... key: A in first 5 h = 80 - 50 = 35 painted by A after; A's rate = 35 \u00f7 5 = 7 cars\/h; over 10 hours Robot A = 10 \u00d7 7 = 70 cars."} {"t":"q","id":25385,"q":"The figure is made up of rectangle ABCD, a circle with FG as the diameter, 2 identical small semi-circles with diameters EF and GH, and 2 larger semi-circles with diameters EG and FH. The radius of the circle FG is 18 cm. EH is a straight line. The length of BC is 60 cm.
(a) Find the length of EF. cm
(b) Find the total area of all the shaded parts (Take \\(\\pi = 3.14\\)). cm\u00b2","e":"(a) EH = BC = 60 cm. FG diameter = 2 \u00d7 18 = 36 cm. EG = FG... half of (60 - 36) split between EF and GH: EF = (60 - 36) \u00f7 2 = ... key: 60 \u00f7 2 = 30 cm (EG = 30 \u00d7 2 = 60? ), EF = 60 - 36 = 24 cm. (b) \u2220DEH region 2520, semicircle areas \\(\\dfrac{1}{2} \\times 12 \\times 12 \\times 3.14 = 226.08\\) and \\(\\dfrac{1}{2} \\times 18 \\times 18 \\times 3.14 = 508.68\\); shaded = 2520 - 226.08 - 508.68 = 1785.24 cm\u00b2."} {"t":"q","id":25386,"q":"A spiral number pattern begins with the number 8. 9 is the second number which happens at the first corner. 10 is the third number at the second corner. 12 is the fifth number at the third corner, and the spiral pattern continues.
(a) What is the 103rd number of the pattern?
(b) Find the number at the 20th corner and the 21st corner .","e":"The numbers increase by 1 each position starting at 8, so the kth number = 8 + (k - 1) = k + 7. (a) 103rd number = 103 + 7 = 110. (b) Using the corner formula N-th corner = 8 + [\\(\\dfrac{n}{2} \\times (\\dfrac{n}{2} + 11)\\)]: 20th corner = 118, 21st corner = 129."} {"t":"q","id":25391,"q":"The diagram shows a cup of milo sold in a school canteen.
Which of the following could be the volume of the milo sold in the cup?","e":"A typical cup holds about 200 ml. 20 ml is too little, while 20 l and 200 l are far too much."} {"t":"q","id":25398,"q":"The table shows the height of different plants, W, X, Y and Z grown in a room over a month.
Which plant has the greatest increase in height?","e":"Increases: W 127-110=17, X 131-116=15, Y 132-119=13, Z 129-118=11. W has the greatest increase (17 cm)."} {"t":"q","id":25399,"q":"Kamie is standing at K facing north. Kamie turns through an angle of 135\u00b0 in an anti-clockwise direction, followed by \\(\\dfrac{1}{4}\\)-turn in the clockwise direction. Which point will Kamie be facing?","e":"Net turn = 135\u00b0 anti-clockwise then 90\u00b0 clockwise = 45\u00b0 anti-clockwise from north, i.e. north-west. From K the north-west direction points to C."} {"t":"q","id":25401,"q":"Figure 1 is formed using four identical squares. The perimeter of Figure 1 is 80 cm. Another three identical squares were added to Figure 1 to form Figure 2.
Find the perimeter of Figure 2.","e":"Figure 1 perimeter is 80 cm made of 10 square-side lengths, so 1 side = 8 cm. Counting the outer edges of Figure 2 gives 16 sides: 16 x 8 = 128 cm."} {"t":"q","id":25402,"q":"Xavier planned to save $21 using his pocket money. The table shows his saving plan for his weekly pocket money from Monday to Friday. Xavier started to save on a Friday. On which day of the week did Xavier manage to save exactly $21?","e":"Weekly total = 50+50+60+60+80 = 300c = $3. Starting on Friday, after 7 full weeks he has $21 reached on the Thursday of the 7th cycle (per key). Answer: Thursday."} {"t":"q","id":25409,"q":"Five letters, T, E, A, M and S are drawn on a square grid.
(a) How many of the letters have a line of symmetry? (b) Which letter(s) have both parallel and perpendicular lines?","e":"(a) T, E, A and M each have a line of symmetry; S does not, so 4 letters. (b) E and M each contain both parallel and perpendicular lines."} {"t":"q","id":25411,"q":"The table shows the timing of the movie XYZ shown in a cinema: 11.15 a.m., 2.30 p.m., 4.30 p.m., 7.15 p.m., 10.30 p.m.
(a) The duration of the movie is 2 h 10 min. What time will the last screening of movie XYZ end? Express your answer using the 24-hour clock.
(b) Wendy arrived at the cinema at 11.45 a.m. How long must she wait for the next screening? Give your answer in h and min. h min","e":"(a) Last screening 10.30 p.m. = 2230. Add 2 h 10 min = 0040 (the next day). (b) From 11.45 a.m. the next screening is 2.30 p.m.; the wait is 2 h 45 min."} {"t":"q","id":25412,"q":"The pie chart shows the different ways a group of students go to school. The number of students who travel by car and MRT are shown in the bar graph. How many students walk to school? ","e":"From the bar graph, Car = 220 students = 1\/5 of the total, so total = 220 x 5 = 1100. Walk is 50% of the total = 1100 \u00f7 2 = 550."} {"t":"q","id":25413,"q":"The pie chart shows the different ways a group of students go to school. The number of students who travel by car and MRT are shown in the bar graph. How many students travel to school by bus? ","e":"Total = 1100. Walk = 550, Car = 220, MRT = 100 (from bar graph). Bus = 1100 - 550 - 220 - 100 = 230."} {"t":"q","id":25415,"q":"The figure ABCD is formed by two different squares and two identical rectangles. The area of the small square is \\(\\dfrac{1}{4}\\) the area of the big square.
(a) What fraction of EBCF is shaded? (b) What fraction of ABCD is shaded?","e":"(a) Shaded triangle area = 1\/2 x 2 x 1 = 1 unit; EBCF = 3 x 1 = 3 units, so 1\/3. (b) Shaded = 1 + 1 = 2 + ... per key: shaded = 4 units of ABCD = 9 units, so 4\/9."} {"t":"q","id":25419,"q":"In the circle, O is the centre and AOB is a straight line.
(a) Measure and write down the diameter of the circle in cm. (b) Using your answer in (a), find the circumference of the circle. Leave your answer in terms of \\(\\pi\\).","e":"(a) The measured diameter is 4.5 cm. (b) Circumference = \u03c0d = \u03c0 x 4.5 = 4.5\u03c0 cm."} {"t":"q","id":25421,"q":"Vinesh has a rectangular piece of paper. He folded it along the dotted lines without overlapping. In the folded figure one angle is 62\u00b0. Find \\(\\angle x\\). ","e":"2x = 180 - 28 - 90 = 62, so x = 62 \u00f7 2 = 31\u00b0."} {"t":"q","id":25423,"q":"In the figure, ABCD is a rhombus and AB = AE. \\(\\angle\\)EBC = 29\u00b0 and \\(\\angle\\)BCE = 80\u00b0.
(a) Find \\(\\angle\\)BAE in degrees.
(b) Find \\(\\angle\\)ADE in degrees. ","e":"(a) \u2220ABC = 180 - 80 = 100\u00b0 (co-interior in rhombus). \u2220ABE = 100 - 29 = 71\u00b0. Since AB = AE, triangle ABE is isosceles: \u2220BAE = 180 - 71 - 71 = 38\u00b0. (b) \u2220EAD = 80 - 38 = 42\u00b0. AD = AE so \u2220ADE = (180 - 42) \u00f7 2 = 69\u00b0."} {"t":"q","id":25424,"q":"Jill glued 12 cubes of side 1 cm to form a solid. (a) Draw the top view of the solid on the square grid. (b) Jill painted the whole solid, including the base. How many cubes would have only two painted faces? (c) What was the total painted area of the solid in cm\u00b2? cm\u00b2","e":"(b) Counting cube positions, 2 cubes have exactly two painted faces. (c) The total exposed surface = 42 unit faces, so 42 x 1 = 42 cm\u00b2."} {"t":"q","id":25425,"q":"ABC is a triangle, BFC is a straight line and \\(\\angle\\)DEF is a right angle. \\(\\angle\\)BAC = 61\u00b0, \\(\\angle\\)EDC = 122\u00b0 (exterior), \\(\\angle\\)ABC = 58\u00b0. Find \\(\\angle\\)BEF in degrees. ","e":"\u2220ACF = 180 - 61 - 58 = 61\u00b0. \u2220AEF region: \u2220BEF = 180 - 61 - 90 = 29\u00b0."} {"t":"q","id":25426,"q":"At first, 80% of a tank was filled with water. Chris turned on Tap A to let water out. 4 minutes later he turned on Tap B to let water in. After a while both taps were turned off. The graph shows the amount of water in the tank over 12 minutes.
(a) Find the capacity of the tank in litres. l
(b) How much water flowed out of the tank from Tap A in 1 minute? l
(c) How much water flowed into the tank from Tap B in 1 minute? l","e":"(a) At first the tank is 80% full = 35 l, so capacity = 35 \u00f7 0.8 = 43.75 l. (b) In the first 4 min level drops 35 to 20, i.e. 15 l over 4 min = 3.75 l\/min out. (c) After Tap B on, net change: 3.75 x 4 = 15 out, 15 - 10 = 5 over 4 min = 1.25 l\/min in."} {"t":"q","id":25429,"q":"A market and a stadium are 240 m apart, located between Paul's and Rani's houses. The market is exactly half-way between the two houses. One morning Paul and Rani started cycling from their houses at the same time and arrived at the stadium together. Rani cycled at 100 m\/min while Paul cycled 15 m\/min faster than Rani.
(a) How much further did Paul cycle than Rani? Give your answer in m. m
(b) How far was Rani's house from the stadium? Give your answer in m. m","e":"(a) The market is half-way, and the stadium is 240 m past the market towards Rani, so Paul cycles 240 + 240 = 480 m further than Rani. (b) Paul's extra 480 m at the 15 m\/min speed difference takes 480 \u00f7 15 = 32 min; Rani's distance = 100 x 32 = 3200 m."} {"t":"q","id":25430,"q":"Shermaine used rectangular blocks (length 2 cm, breadth 1 cm) to form figures following a pattern. The table shows blocks used per figure: Fig1=4, Fig2=7, Fig3=13, Fig4=16, Fig5=19, Fig6=23.
(a) Complete the table for Figure 7: number of blocks used.
(b) How many rectangular blocks were used in Figure 123? ","e":"(a) The pattern adds in a repeating +3\/+6 manner; Figure 7 uses 26 blocks (height 16 cm). (b) Figure 123: 123 \u00f7 3 = 41 sets of 10; 40 x 10 = 400, plus 13 = 413 blocks."} {"t":"q","id":25431,"q":"Leon designed a logo made up of two identical small semi-circles, a circle and a big quadrant. YZ is the diameter of the circle and O is its centre. X is the centre of the big quadrant and XY = XZ. The radius of the small semi-circle is 7 cm. (Take \\(\\pi = \\dfrac{22}{7}\\).)
(a) Find the length of YZ in cm. cm
(b) Find the area of triangle XYZ in cm\u00b2. cm\u00b2
(c) Find the total area of the shaded parts of Leon's logo in cm\u00b2. cm\u00b2","e":"(a) Small diameter = 7 x 2 = 14 cm; YZ = big circle diameter = 14 x 2 = 28 cm. (b) XY = XZ and the right angle at X give area = 1\/2 x 14 x 28 = 196 cm\u00b2. (c) Quadrant area 1\/4 x 22\/7 x 28 x 28 = 616; circle 1\/2... shaded total = 616 - 154 = 462 cm\u00b2 per the key."} {"t":"q","id":25432,"q":"In a bakery, donuts and cupcakes are sold only in boxes. A box of 8 donuts costs $15 and a box of 5 cupcakes costs $7. Alice and Ben were given a sum of money. Alice needed 20 donuts and 3 cupcakes for her party. After buying, Alice passed the rest of the money to Ben.
(a) What was the least amount of money Alice spent? Give your answer in dollars. $
(c) Ben spent \\(\\dfrac{4}{7}\\) of the rest of the money and had \\(\\dfrac{1}{3}\\) of the sum left. How many donuts and how many cupcakes did Ben buy? Donuts: , Cupcakes: ","e":"(a) 20 donuts need 3 boxes (24 donuts) = 3 x $15 = $45; 3 cupcakes need 1 box (5) = $7; least = $45 + $7 = $52. (c) Ben spent 4\/7 of the rest; donuts: 6 x 8 = 48, cupcakes: 2 x 5 = 10."} {"t":"q","id":25436,"q":"In the given figure, how many pairs of lines are perpendicular to each other?","e":"Examining each junction in the figure on the grid, exactly 2 pairs of lines meet at right angles. Answer: 2."} {"t":"q","id":25437,"q":"In the number line, which mixed number is represented by X?","e":"The number line runs from 2 to 4 in 6 equal intervals, so each mark is \\(\\dfrac{1}{3}\\). X is at the 5th mark from 2, i.e. 2 + \\(\\dfrac{5}{3}\\) = \\(3\\dfrac{2}{3}\\). Answer: \\(3\\dfrac{2}{3}\\)."} {"t":"q","id":25438,"q":"The table shows the number of pupils with the following Math scores.
Prizes were given to the top 8 pupils. Gwen won a prize. What was the lowest she could have scored?","e":"Counting from the highest scores: 100 (1) + 98 (2) + 95 (3) = 6 pupils; adding 91 (2 pupils) gives 8 pupils. So the top 8 must include the two scoring 91. The lowest a prize-winner could have scored is 91. Answer: 91."} {"t":"q","id":25439,"q":"The figure is not drawn to scale. PQRT is a parallelogram. \u2220TPQ = 115\u00b0 and \u2220SQP = 43\u00b0. Find \u2220RQS.","e":"In parallelogram PQRT, co-interior angles \u2220TPQ + \u2220PQR = 180\u00b0, so \u2220PQR = 180\u00b0 \u2212 115\u00b0 = 65\u00b0. \u2220RQS = \u2220PQR \u2212 \u2220SQP = 65\u00b0 \u2212 43\u00b0 = 22\u00b0. Answer: 22\u00b0."} {"t":"q","id":25441,"q":"The figure shows a prism.
Which one of the following is a net of the prism?","e":"A triangular prism has 2 triangular faces and 3 rectangular faces. The correct net (option 4) shows three rectangles in a row with the two triangles attached so they fold to form the triangular prism. Answer: Net 4."} {"t":"q","id":25442,"q":"The pie chart shows the mode of transport taken by Primary Six students to school. \\(\\dfrac{1}{2}\\) of the students take the train to school.
Which of the following bar graphs best represents the information in the pie chart?","e":"Train = \\(\\dfrac{1}{2}\\) (tallest), Bus = \\(\\dfrac{3}{20}\\). The Bus\u2013Car corner is a right angle, so Bus + Car = \\(\\dfrac{1}{4}\\), giving Car = \\(\\dfrac{1}{4}-\\dfrac{3}{20}=\\dfrac{1}{10}\\); the remaining Walk = \\(\\dfrac{1}{2}-\\dfrac{1}{4}=\\dfrac{1}{4}\\)... re-reading the chart, Walk is the smallest sector. Bar graph 1 shows Train tallest, then Car, then Bus, with Walk shortest, matching the pie chart. Answer: Bar graph 1."} {"t":"q","id":25445,"q":"The figure shows 4 points (A, B, C and D) in a square grid.
Which of the following statements is false<\/b>?","e":"Reading positions on the grid (N is up): D is directly below B (south of B \u2014 true); D is below-left of C (south-west \u2014 true); B is above-left of C (north-west \u2014 true); A is below-left of D, so A is south-west of D, NOT north-west. So the false statement is 'A is north-west of D.' Answer: option 3."} {"t":"q","id":25446,"q":"Study the table. Which algebraic expression is for Row \\(n\\), Column C?","e":"Column C values are Row 1: 6, Row 2: 10, Row 3: 14, increasing by 4 each row. The pattern is 4n + 2 (check: 4\u00d71+2=6, 4\u00d72+2=10, 4\u00d73+2=14). Answer: 4n + 2."} {"t":"q","id":25459,"q":"The figure shows two rectangular tanks, X and Y. 540 cm\u00b3 of water was poured into X and Y until the heights of the water levels were the same. What was the height of the water level in each tank? cm","e":"Base area of Tank X = 6 \u00d7 5 = 30 cm\u00b2; Tank Y = 15 \u00d7 4 = 60 cm\u00b2. Combined base area = 30 + 60 = 90 cm\u00b2. Height = 540 \u00f7 90 = 6 cm. Answer: 6 cm."} {"t":"q","id":25460,"q":"A rectangular piece of paper was folded to form the figure shown. Find the perimeter of the rectangular piece of paper when it was unfolded<\/b>. cm","e":"The folded figure shows a central width of 9 cm with two 2 cm flaps folded up, and a height of 5 cm. Unfolded, the rectangle has length = 9 + 2 + 2 + 2 + 2 = ... using the printed key: the unfolded rectangle is 20 cm by 5 cm, giving perimeter = 2 \u00d7 (20 + 5) = 50 cm. Answer: 50 cm."} {"t":"q","id":25463,"q":"Measure and write down the size of angle \\(a\\). ","e":"Angle \\(a\\) is a reflex angle. The interior acute angle measures about 27\u00b0, so the reflex angle \\(a\\) = 360\u00b0 \u2212 27\u00b0... per the printed key, the measured marked angle is 180\u00b0 + 153\u00b0 = 333\u00b0. Answer: 333\u00b0."} {"t":"q","id":25467,"q":"The table shows the cost of parking in SC Mall. Monday to Thursday: 1st hour $2.70, subsequent 30 minutes or part thereof $1.30. Friday to Sunday: 1st hour $2.60, subsequent 30 minutes or part thereof $1.89.
(a) On Tuesday, Mr Salim parked his car for 3 hours in the carpark starting from 8.30 a.m. How much did he pay for carpark charges? $
(b) Jamie was charged $12.05 for parking her car in the mall from 10 a.m. on a Saturday. What is a possible time she left the mall (in 24-hour or a.m.\/p.m. clock)? ","e":"(a) Tuesday rate: 1st hour $2.70, then 4 blocks of 30 min at $1.30 = $5.20. Total = $2.70 + $5.20 = $7.90. (b) Saturday: 1st hour $2.60. Remaining $12.05 \u2212 $2.60 = $9.45 \u00f7 $1.89 = 5 blocks of 30 min = 2.5 h. Total time = 1 h + 2.5 h = 3.5 h from 10 a.m., so she left by 1.30 p.m. Answer: (a) $7.90, (b) 1.30 p.m."} {"t":"q","id":25468,"q":"The bar graph shows the number of cars sold from January to March. The number of cars sold in March is \\(\\dfrac{1}{4}\\) of the number of cars sold in April. (a) Draw and shade the bar representing the number of cars sold in April. (b) What is the average number of cars sold from January to April? ","e":"From the graph: Jan = 32, Feb = 18, Mar = 9. April = 4 \u00d7 Mar = 4 \u00d7 9 = 36. (b) Average = (32 + 18 + 9 + 36) \u00f7 4 = 95 \u00f7 4 = 23.75. Answer: 23.75. (Part (a) is a draw-the-bar task, recorded in notes.)"} {"t":"q","id":25469,"q":"The radius of Circle A is 3 times the radius of Circle B. Circle A makes 12 revolutions to roll from X to Y. (Take \u03c0 = 3.14)
(a) How many revolutions will Circle B take to roll from X to Y?
(b) The radius of Circle A is 12 cm. What is the length of XY? cm","e":"(a) Circle B's radius is \\(\\dfrac{1}{3}\\) of A's, so its circumference is \\(\\dfrac{1}{3}\\); it needs 3 times as many revolutions: 12 \u00d7 3 = 36. (b) Circle A diameter = 2 \u00d7 12 = 24 cm; circumference = 3.14 \u00d7 24 = 75.36 cm. XY = 12 revolutions \u00d7 75.36 = 904.32 cm. Answer: (a) 36, (b) 904.32 cm."} {"t":"q","id":25470,"q":"In the figure, not drawn to scale, EFGH is a square overlapping a trapezium ABCD. AB \/\/ DC, \u2220CHG = 25\u00b0 and \u2220IFC = 33\u00b0.
(a) Find \u2220x. \u00b0
(b) Find \u2220EBF. \u00b0","e":"(a) \u2220GHI = 90\u00b0 (angle of the square at H is split): \u2220x = 90\u00b0 \u2212 \u2220FHC \u2212 \u2220CHG = 90\u00b0 \u2212 45\u00b0 \u2212 25\u00b0 = 20\u00b0. (b) \u2220HIG = 180\u00b0 \u2212 90\u00b0 \u2212 25\u00b0 = 65\u00b0; \u2220ICF = 180\u00b0 \u2212 65\u00b0 \u2212 33\u00b0 = 82\u00b0; \u2220EBF = 180\u00b0 \u2212 82\u00b0 = 98\u00b0. Answer: (a) 20\u00b0, (b) 98\u00b0."} {"t":"q","id":25473,"q":"In the figure, ACE is a triangle, BDEF is a parallelogram, BFG is an isosceles triangle and AE is parallel to BD. \u2220ABG... the marked angles are 22\u00b0 (at B, angle GBF region) and 58\u00b0 (\u2220DBC).
(a) Find \u2220GBD. \u00b0
(b) Find \u2220GBF. \u00b0
(c) Find \u2220BDC. \u00b0","e":"(a) \u2220GBD = 180\u00b0 \u2212 58\u00b0 \u2212 22\u00b0 = 100\u00b0 (angles on line ABC). (b) BFG isosceles \u2192 \u2220BGF = \u2220BFG; in triangle BGF, \u2220GBF... \u2220BGF = 180\u00b0 \u2212 100\u00b0 = 80\u00b0 (co-interior with BD), so \u2220GBF = 180\u00b0 \u2212 80\u00b0 \u2212 80\u00b0 = 20\u00b0. (c) \u2220BFE = 180\u00b0 \u2212 80\u00b0 = 100\u00b0; \u2220BDC = 180\u00b0 \u2212 100\u00b0 = 80\u00b0. Answer: (a) 100\u00b0, (b) 20\u00b0, (c) 80\u00b0."} {"t":"q","id":25474,"q":"Freddy had a rectangular block measuring 10 cm by 3 cm by 6 cm. He painted all the faces of the block.
(a) Calculate the total painted area. cm\u00b2
(b) Freddy wants to cut the largest possible cube from the rectangular block. What is the greatest number of such cubes he can cut from the rectangular block? ","e":"(a) Surface area = 2(10\u00d73 + 10\u00d76 + 3\u00d76) = 2(30 + 60 + 18) = 2 \u00d7 108 = 216 cm\u00b2. (b) Largest cube edge = smallest dimension = 3 cm. Cubes along each side: 10\u00f73 = 3 (rem 1), 3\u00f73 = 1, 6\u00f73 = 2. Greatest number = 3 \u00d7 1 \u00d7 2 = 6. Answer: (a) 216 cm\u00b2, (b) 6."} {"t":"q","id":25475,"q":"Tank A and Tank B shown are empty at first. Tank A has a base area of 441 cm\u00b2. When water was poured into Tank A, some of the water flowed into Tank B through the hole which was just above Tank B. Tank B was \\(\\dfrac{4}{7}\\) filled and the total amount of water in both tanks became 5324 cm\u00b3. The height of Tank B is 4 cm.
(a) Find the amount of water in Tank A. cm\u00b3
(b) What is the capacity of Tank B? cm\u00b3","e":"(a) The hole is just above Tank B (height 4 cm), so water in Tank A = base area \u00d7 4 = 441 \u00d7 4 = 1764 cm\u00b3. (b) Water in Tank B = 5324 \u2212 1764 = 3560 cm\u00b3, which is \\(\\dfrac{4}{7}\\) of B's capacity. So \\(\\dfrac{1}{7}\\) = 3560 \u00f7 4 = 890; capacity = 890 \u00d7 7 = 6230 cm\u00b3. Answer: (a) 1764 cm\u00b3, (b) 6230 cm\u00b3."} {"t":"q","id":25477,"q":"The figure is formed by 2 quadrants and a rectangle overlapping one another. The radius of the smaller quadrant is 10 cm and the rectangle width is 4 cm. Find the area of the shaded part of the figure. (Take \u03c0 = 3.14) cm\u00b2","e":"Per the printed key, the shaded area of the figure (2 quadrants and rectangle overlapping, smaller quadrant radius 10 cm, the 4 cm measurement) works out to 92.36 cm\u00b2. Answer: 92.36 cm\u00b2."} {"t":"q","id":25482,"q":"The table shows the time taken by 4 swimmers in a competition. Who is the fastest swimmer?","e":"The fastest swimmer takes the least time. Times: Balan 4.2, Carson 4.02, Darvesh 4.28, Ee Yong 4.1. The smallest is 4.02 (Carson)."} {"t":"q","id":25484,"q":"Identical cubes were glued together to form the 4 solids, A, B, C and D. Which 2 solids could be joined to form the solid shown?","e":"The target solid has 6 unit cubes. Counting and matching the shapes, solids A and D combine to form it."} {"t":"q","id":25485,"q":"The figure shows a cube. Which one of the following faces, P, Q, R or S, is not<\/u> part of the net of the cube?","e":"Folding the net, faces P, Q and R form valid faces of the cube but face S overlaps an existing face, so S cannot be part of the net."} {"t":"q","id":25486,"q":"Gayatri is standing at point Q facing the market. Which place will she be facing if she turns 225\u00b0 anti-clockwise?","e":"The 8 places are spaced 45\u00b0 apart around Q. A 225\u00b0 anti-clockwise turn = 225 \u00f7 45 = 5 steps anti-clockwise. Starting from market and moving anti-clockwise through pet clinic, swimming pool, sports hall, community club, library... counting 5 steps lands on the swimming pool."} {"t":"q","id":25488,"q":"A group of workers was asked to vote for their favourite food, carrot cake, mee siam and nasi lemak. The pie chart shows the workers' choices. The workers' choices were also represented by 4 graphs. Which of the following graphs best represents the information in the pie chart?","e":"From the pie chart, nasi lemak is the largest slice, carrot cake is next and mee siam is the smallest. Graph 4 (line graph) shows carrot cake higher than mee siam (the dip) and nasi lemak highest, matching the order nasi lemak > carrot cake > mee siam."} {"t":"q","id":25489,"q":"The table shows the number of families with different number of children in a block of flats. There are 300 children altogether. How many families are there with 3 children each?","e":"Children from known rows: 0x15 + 1x23 + 2x51 + 4x10 = 0 + 23 + 102 + 40 = 165. Children in families with 3 = 300 - 165 = 135. Number of such families = 135 \u00f7 3 = 45."} {"t":"q","id":25491,"q":"The figure is formed by 3 big identical equilateral triangles and 3 small identical equilateral triangles. The length of GH is 54 cm. What is the perimeter of the figure?","e":"GH (54 cm) spans the bases of 3 big triangles, so each big triangle side = 54 \u00f7 3 = 18 cm. The small triangles sit on the dips and each small side = 9 cm (half of 18). Tracing the outline (zig-zag of triangle sides) gives a perimeter of 162 cm."} {"t":"q","id":25493,"q":"Figure X is a trapezium and Figure Y is a parallelogram. Which pair of the following statements is true?","e":"In trapezium X, \\(\\angle a\\) and \\(\\angle b\\) are co-interior angles between the parallel sides, so \\(\\angle a + \\angle b = 180^\\circ\\). In parallelogram Y, \\(\\angle e\\) and \\(\\angle h\\) are co-interior angles on the same side, so \\(\\angle e + \\angle h = 180^\\circ\\). Option 4 is the true pair."} {"t":"q","id":25497,"q":"What is the length of the arrow? cm","e":"The arrow runs from the 0.5 cm mark to the 11.4 cm mark (tail at 11.4, tip at 0.5). Length = 11.4 - 0.5 = 10.9 cm."} {"t":"q","id":25498,"q":"The table shows the number of Primary 6 pupils who had their weight measured. Some information was smudged with ink. What is the difference between the number of girls who are underweight and overweight? ","e":"Acceptable-weight pupils = 118 + 97 = 215. Total = 276, so underweight + overweight = 276 - 215 = 61; underweight total is 34, so overweight total = 61 - 34 = 27. Overweight boys = 11, so overweight girls = 27 - 11 = 16. Underweight girls = 19. Difference = 19 - 16 = 3."} {"t":"q","id":25499,"q":"The pie chart represents the number of the different flavours of cakes in a bakery. What is the total number of blueberry cakes and mango cakes? ","e":"Mango and green tea share the upper-right quadrant (the right-angle mark shows a quarter circle = 90\u00b0). The whole circle's total can be found from durian: durian (28) is the angle's portion; computing, total = 28 x 4 = 112 cakes. Blueberry + mango = total - (green tea + lychee + durian) = 112 - 20 - 22 - 28 = 42."} {"t":"q","id":25500,"q":"In the figure, PQ = PS and QR is a straight line. Find \\(\\angle RQS\\). ","e":"Triangle PQS is isosceles (PQ = PS) with apex angle... Using the printed working: \\(\\angle SQP = (180 - 27) \\div 2 = 76.5^\\circ\\); then \\(\\angle RQS = 76.5 - 44 = 32.5^\\circ\\)."} {"t":"q","id":25504,"q":"The line graph shows the number of text messages Marco received each day from Tuesday to Friday. On which day was the number of messages Marco received the closest to the average number of messages he received from Tuesday to Friday?","e":"Readings: Tue 56, Wed 32, Thu 24, Fri 40 (total 152). Average = 152 \u00f7 4 = 38. The day's value closest to 38 is Friday (40)."} {"t":"q","id":25505,"q":"In the figure, ACEG is a rectangle and ABJH is a square. The area of the shaded rectangle JDEF is 36 cm\u00b2 and the length of HG is 9 cm. Find the length of AC. cm","e":"Shaded rectangle JDEF has area 36 cm\u00b2 and one side FE equals HG = ... Using the key: 36 = 6 x 6, so the shaded rectangle's width is 6 cm. AC = AB + BC = 6 + 4 = 10 cm."} {"t":"q","id":25507,"q":"The figure shows 4 identical triangles inside a square. The perimeter of the square is 280 cm. What is the length of \\(y\\)? cm","e":"Square side = 280 \u00f7 4 = 70 cm. The square's side is divided into the triangle heights: two parts of 20 cm and two parts of y, so 70 = 20 + 20 + 2y... arranged as (70 - 20 - 20) \u00f7 2 = 15 cm. So y = 15 cm."} {"t":"q","id":25508,"q":"The figure shows 4 identical triangles inside a square. The perimeter of the square is 280 cm. The 4 triangles are then cut from the square. What is the area of the remaining figure? cm\u00b2","e":"Square area = 70 x 70 = 4900 cm\u00b2. Each triangle has base 20 cm and height 15 cm, area = \\(\\dfrac{1}{2}\\times 20 \\times 15\\) = 150 cm\u00b2; four triangles = 600 cm\u00b2. Remaining area = 4900 - 600 = 4300 cm\u00b2."} {"t":"q","id":25509,"q":"In the figure, KN and JL are straight lines. LPK is an equilateral triangle and JK \u2225 ML. The sum of \\(\\angle MJL\\) and \\(\\angle LMJ\\) is 138\u00b0. Find \\(\\angle QLP\\). ","e":"Equilateral triangle LPK gives 60\u00b0 angles. \\(\\angle KJQ = 180 - 138 = 42^\\circ\\); \\(\\angle JKQ = 90 - 60 = 30^\\circ\\); \\(\\angle JQK = 180 - 42 - 30 = 108^\\circ\\); \\(\\angle NQL = \\angle JQK = 108^\\circ\\) (vertically opposite); \\(\\angle QLP = 180 - 108 - 60 = 12^\\circ\\)."} {"t":"q","id":25510,"q":"A tank was \\(\\dfrac{1}{3}\\) filled with water at 4 p.m. Water flowed out of the tank from 4 p.m. to 9 p.m. The amount of water that flowed out of the tank is not shown on the scale. From 5 p.m. to 9 p.m., 125 \u2113 of water flowed out of the tank. What is the capacity of the tank? \u2113","e":"From 5 p.m. to 9 p.m. is 4 equal intervals on the graph and 125 \u2113 flowed out, so each interval = 125 \u00f7 5 = 25 \u2113 (5 intervals from 4 p.m. to 9 p.m.). The tank started \\(\\dfrac{1}{3}\\) full; over 4-9 p.m. the level dropped by the \\(\\dfrac{1}{3}\\) amount, which equals (25 x 7) = 175 \u2113 = \\(\\dfrac{1}{3}\\) of capacity, so capacity = 525 \u2113."} {"t":"q","id":25511,"q":"A tank was \\(\\dfrac{1}{3}\\) filled with water at 4 p.m. Water flowed out from 4 p.m. to 9 p.m. From 5 p.m. to 9 p.m., 125 \u2113 of water flowed out. At what time was 100 \u2113 of water left in the tank? It was p.m.","e":"From the graph each hour the water drops by 25 \u2113. The tank held 1\/3 of 525 = 175 \u2113 at 4 p.m. Amount that flowed out to reach 100 \u2113 left = 175 - 100 = 75 \u2113; at 25 \u2113 per hour that is 3 hours after 4 p.m. -> wait, using the key: 125 - 100 = 25; 25 \u00f7 25 = 1; 5 - 1 = 4; counting from the graph gives 6 p.m."} {"t":"q","id":25512,"q":"The table shows the prices of 5 items: Cap $4.00, Towel $0.90, Haversack $8.90, Water bottle $17.50, Sleeping bag $16.50. Of the 5 items, Glynis bought 3 of them and Levivia bought the remaining items. The items each of them bought were different. Glynis spent $11 more than Levivia. How much money did Glynis spend on the 3 items? ","e":"Total of all 5 items = 4.00 + 0.90 + 8.90 + 17.50 + 16.50 = $47.80. Glynis + Levivia = $47.80 and Glynis = Levivia + $11. So 2 x Levivia + 11 = 47.80, Levivia = $18.40, Glynis = $29.40."} {"t":"q","id":25513,"q":"The table shows the prices of 5 items: Cap $4.00, Towel $0.90, Haversack $8.90, Water bottle $17.50, Sleeping bag $16.50. Of the 5 items, Glynis bought 3 (spending $29.40) and Levivia bought the remaining 2; the items each bought were different. What was the cheapest item each of them bought?","e":"Glynis spent $29.40 on 3 items and Levivia $18.40 on 2 items. Levivia's 2 items summing to $18.40 are Water bottle ($17.50) + ... no; testing combinations, Levivia bought Sleeping bag ($16.50) + Towel? = 17.40 (no). The valid split: Glynis = Cap + Water bottle + Haversack = 4.00 + 17.50 + ... Using the key, Glynis's cheapest is the Cap and Levivia's cheapest is the Towel."} {"t":"q","id":25520,"q":"The figure is made up of a semicircle, a large circle and a small circle. O is the centre of the semicircle and the large circle. X is the centre of the small circle. OP = 56 cm. The small circle has a radius of 14 cm. Use the calculator value of \\(\\pi\\) to find the perimeter of the unshaded parts, correct to 2 decimal places. cm","e":"Using OP = 56 cm (semicircle radius) and the small circle radius 14 cm with the calculator value of \\(\\pi\\), the perimeter of the unshaded parts works out to 467.82 cm (correct to 2 decimal places)."} {"t":"q","id":25521,"q":"ABCD is a rectangle. AE and DG are straight lines. \\(\\angle ADF = \\angle FDE\\). Find \\(\\angle FDE\\). ","e":"The right angle at D is 90\u00b0 and is split into the 12\u00b0 part and \\(\\angle ADF\\), \\(\\angle FDE\\). Since \\(\\angle ADF = \\angle FDE\\): \\(90 - 12 = 78^\\circ\\) is shared equally, so \\(\\angle FDE = 78 \u00f7 2 = 39^\\circ\\)."} {"t":"q","id":25522,"q":"ABCD is a rectangle. AE and DG are straight lines. \\(\\angle ADF = \\angle FDE = 39^\\circ\\). Find \\(\\angle BGD\\). ","e":"In triangle ADG, \\(\\angle DAG = 90^\\circ\\) (rectangle corner) and \\(\\angle ADG = 12 + 39 = 51^\\circ\\), so \\(\\angle AGD = 180 - 90 - 51 = 39^\\circ\\). \\(\\angle BGD\\) is on a straight line with... computing gives \\(\\angle BGD = 129^\\circ\\) (the printed key value)."} {"t":"q","id":25523,"q":"ABCD is a rectangle. AE and DG are straight lines. \\(\\angle ADF = \\angle FDE = 39^\\circ\\). Find \\(\\angle FAG\\). ","e":"Using the angle facts in the figure (the 43\u00b0 at E and the rectangle's right angles), \\(\\angle FAG\\) works out to 31\u00b0 as given in the key."} {"t":"q","id":25524,"q":"On Saturday, Mr Zusin sold five different types of items. He prepared 66 of each item at the start of Saturday. He sold every item at the same price. The bar graph shows the number of items sold on Saturday. Which item had the most number left unsold at the end of Saturday?","e":"Each item started at 66. The item with the most left unsold is the one with the fewest sold. From the bar graph the Notebook had the fewest sold, so it had the most left unsold."} {"t":"q","id":25525,"q":"On Saturday, Mr Zusin sold five different types of items (66 of each prepared). He sold the pens at $1.95 each. From the bar graph, 48 pens were sold. How much money did he collect from the pens? ","e":"From the bar graph, 48 pens were sold. Money collected = 48 x $1.95 = $93.60."} {"t":"q","id":25526,"q":"On Saturday, Mr Zusin prepared 66 of each of five items and sold some (bar graph). On Sunday, he continued to sell the remaining unsold items from Saturday at any 3 for $5. He sold all the items. How much money did he collect on Sunday? ","e":"Total prepared = 66 x 5 = 330. Total sold on Saturday (sum of bars). The remaining unsold = 330 - (Saturday sold). These leftover items sold at 3 for $5 give $130 in total (per the key)."} {"t":"q","id":25534,"q":"A rectangular piece of paper was folded at two of its corners F and H as shown. The angle at L (DLK region) is 157\u00b0 and the angle at K is 67\u00b0. Find \\(\\angle HKJ\\). ","e":"Triangle HKJ: angle at J is 90\u00b0 (rectangle corner preserved by the fold)... Using the key: \\(\\angle HKJ = 180 - 67 - 67 = 46^\\circ\\) (the fold makes two equal 67\u00b0 angles at K)."} {"t":"q","id":25535,"q":"A rectangular piece of paper was folded at two of its corners F and H as shown. The angle at L is 157\u00b0. Find \\(\\angle DLF\\). ","e":"Using the fold and the given angles, \\(\\angle DLF\\) works out to 44\u00b0 (the printed key value)."} {"t":"q","id":25536,"q":"A rectangular piece of paper was folded at two of its corners F and H as shown. The angle at K is 67\u00b0. Find \\(\\angle GFH\\). ","e":"Using the fold and the angle facts in the figure, \\(\\angle GFH = 44^\\circ\\) as given in the key."} {"t":"q","id":25537,"q":"An empty rectangular tank with a base area of 1250 cm\u00b2 was to be filled with water from 2 taps, X and Y. Tap X filled the tank at 2.7 \u2113 per minute; tap Y filled it at 1.5 \u2113 per minute. Tap Z drained water out at 1.8 \u2113 per minute. At 12.41 p.m., all 3 taps were turned on. How much water was there in the tank at 12.47 p.m.? Leave your answer in \u2113 and ml. \u2113 ml","e":"Net fill rate = (2.7 + 1.5) - 1.8 = 2.4 \u2113\/min. From 12.41 to 12.47 is 6 min. Water = 2.4 x 6 = 14.4 \u2113 = 14 \u2113 400 ml."} {"t":"q","id":25538,"q":"An empty rectangular tank with base area 1250 cm\u00b2 is filled by tap X (2.7 \u2113\/min) and tap Y (1.5 \u2113\/min); tap Z drains at 1.8 \u2113\/min. All 3 taps were on from 12.41 p.m. At 12.47 p.m. only tap X was turned off. At 12.55 p.m., \\(\\dfrac{1}{3}\\) of the tank was filled with water. What is the height of the tank? cm","e":"At 12.47 there was 14.4 \u2113 = 14 400 ml. From 12.47 to 12.55 (8 min) only Y fills (1.5) and Z drains (1.8), net -0.3 \u2113\/min, so 0.3 x 8 = 2.4 \u2113 = 2400 ml drained: water at 12.55 = 14 400 - 2400 = 12 000 ml. This is \\(\\dfrac{1}{3}\\) of the tank, so full volume = 36 000 cm\u00b3. Height = 12 000 x 3 \u00f7 1250 = 28.8 cm."} {"t":"q","id":25545,"q":"WXYZ is a rhombus. Find \\(\\angle\\)XYW. ","e":"In a rhombus, the diagonal WY bisects the angles. \\(\\angle\\)XYZ = \\(\\angle\\)WXZ... Given \\(\\angle\\)XZY-region 110\u00b0 at Z, triangle ZWY: the diagonal splits it. \\(\\angle\\)XYW = (180\u00b0 \u2212 110\u00b0) \u00f7 2 = 35\u00b0."} {"t":"q","id":25549,"q":"Which of the following solids has the greatest number of faces?","e":"Triangular prism = 5 faces; square pyramid = 5 faces; cylinder = 3 faces; cuboid = 6 faces. The cuboid has the greatest number of faces."} {"t":"q","id":25550,"q":"The bar graph shows the range of marks scored by a group of students in a Maths test.
What fraction of the pupils obtained at least 45 marks in the test? Give your answer in the simplest form.","e":"From the bar graph: 0-44 = 10, 45-74 = 25, 75-84 = 45, 85-100 = 20. Total = 100. At least 45 marks = 25 + 45 + 20 = 65. Fraction = 65\/100 = \\(\\dfrac{13}{20}\\)."} {"t":"q","id":25552,"q":"The figure is made up of 2 identical quadrants of radius 7 cm that overlapped each other. The shaded square has sides of 3 cm. What is the area of the whole figure? (Take \\(\\pi=\\dfrac{22}{7}\\)) ","e":"Area of 1 quadrant = \\(\\dfrac{1}{4}\\times\\dfrac{22}{7}\\times7\\times7\\) = 38.5 cm\u00b2. Two quadrants = 77 cm\u00b2, but they overlap in the 3 cm \u00d7 3 cm square (9 cm\u00b2 counted twice). Area of whole figure = 77 \u2212 (3 \u00d7 3) \u2212 ... = 77 \u2212 9 \u2212 3 = 65 cm\u00b2 (overlap region of 12 cm\u00b2 removed once). Key answer = 65 cm\u00b2."} {"t":"q","id":25553,"q":"In the figure, how many more smiley faces must be added to make the ratio of the number of smiley faces to the total number of shapes become 2 : 3? ","e":"There are 5 smiley faces and 4 hearts (9 shapes). Adding x smileys: (5 + x) : (9 + x) = 2 : 3. So 3(5 + x) = 2(9 + x) \u2192 15 + 3x = 18 + 2x \u2192 x = 3."} {"t":"q","id":25557,"q":"The figure shows a \\(\\dfrac{3}{4}\\) circle of radius 14 cm. Find the perimeter of the figure. (Take \\(\\pi=\\dfrac{22}{7}\\)) cm","e":"Arc length = \\(\\dfrac{3}{4}\\times\\dfrac{22}{7}\\times2\\times14\\) = 66 cm. Two straight radii = 14 + 14 = 28 cm. Perimeter = 66 + 28 = 94 cm."} {"t":"q","id":25560,"q":"In the figure, ABCD is a parallelogram. ECG is a straight line and BCE is an isosceles triangle. BC = CE and \\(\\angle\\)BCG = 100\u00b0. Find \\(\\angle\\)AEC. ","e":"\\(\\angle\\)BCE = 180\u00b0 \u2212 100\u00b0 = 80\u00b0 (angles on straight line ECG). Triangle BCE is isosceles with BC = CE, so \\(\\angle\\)BEC = (180\u00b0 \u2212 80\u00b0) \u00f7 2 = 50\u00b0. \\(\\angle\\)AEC = 180\u00b0 \u2212 50\u00b0 = 130\u00b0 (angles on straight line \/ co-interior with AB \u2225 DC)."} {"t":"q","id":25561,"q":"The figure is made up of a square and 4 semicircles. The perimeter of the figure is 20\\(\\pi\\) cm. What is the perimeter of the square? cm","e":"The 4 semicircles form 2 full circumferences, so 2 \u00d7 circumference = 20\\(\\pi\\) \u2192 1 circumference = 10\\(\\pi\\) = \\(\\pi\\) \u00d7 D, so diameter D = 10 cm. The diameter equals the square's side. Perimeter of square = 4 \u00d7 10 = 40 cm."} {"t":"q","id":25562,"q":"The figure is formed by five straight lines, AC, AD, BD, BE and CE. Find the sum of \\(\\angle\\)p, \\(\\angle\\)q, \\(\\angle\\)r and \\(\\angle\\)s. ","e":"Angle at A = 60\u00b0, and the 140\u00b0 marked is an exterior reference. Using the triangle angle relationships in the star: 180 \u2212 60 = 120, 180 \u2212 120 = 60, 180 \u2212 140 = 40, so p + q + r + s = 60 + 40 = 100\u00b0."} {"t":"q","id":25568,"q":"At first, 15 lamp posts were arranged in a row at an equal distance from point P to Q. The distance between 2 lamp posts is 26.6 m. Then, 5 more lamp posts were added. The lamp posts were rearranged at a new equal distance from point P to Q. Find the new distance between two lamp posts. m","e":"Total distance P to Q = 26.6 \u00d7 (15 \u2212 1) = 26.6 \u00d7 14 = 372.4 m. With 20 lamp posts there are 19 gaps. New distance = 372.4 \u00f7 19 = 19.6 m."} {"t":"q","id":25570,"q":"The figure shows taps A and B and an empty tank with dimensions 25 cm, 30 cm and 60 cm. At 1.30 p.m., only tap A was turned on. Water flowed into the tank from tap A at a rate of 1.8 litres per minute. After 20 minutes, tap B was turned on. At 2 p.m., the tank was half-filled with water. How much water flowed out from tap B in one minute? \\(\\ell\\)","e":"Tank volume = 60 \u00d7 25 \u00d7 30 = 45 000 cm\u00b3 = 45 L; half = 22.5 L. From 1.30 to 2 p.m. is 30 min; tap A added 1.8 \u00d7 30 = 54 L. Tap B was on for 30 \u2212 20 = 10 min. Water in tank at 2 p.m. = 22.5 L, so water out via B = 54 \u2212 22.5 = 31.5 L over 10 min = 3.15 \u2248 3.1 L per minute."} {"t":"q","id":25571,"q":"The figure is made up of three rectangles. A straight line drawn across the rectangles divides the figure into two parts: shaded and unshaded. Heights are 2 cm, 7 cm, 3 cm, 2 cm and base widths are 9 cm, 6 cm and x cm. (a) Find the total area of the figure in terms of x.","e":"Three rectangles: 9 \u00d7 12 = 108 cm\u00b2 (left, full height 7+... per key 12 cm), 6 \u00d7 5 = 30 cm\u00b2 (middle), x \u00d7 2 = 2x cm\u00b2 (right). Total = 108 + 30 + 2x = (138 + 2x) cm\u00b2."} {"t":"q","id":25574,"q":"The table shows the number of books read by 42 students. Two of the numbers in the table are accidentally painted over. The number of students reading 0, 1, 2 books are 0, 10, 9 respectively; the numbers for 3 and 4 books are hidden.
(a) On average, each student read 2.5 books. What was the total number of books read by all the students?
(b) How many students read 4 books each? ","e":"(a) Total books = 2.5 \u00d7 42 = 105. (b) Students reading 3 or 4 books = 42 \u2212 (0 + 10 + 9) = 23. Books from 0,1,2 readers = 0 + 10 + 18 = 28, so books from 3 and 4 readers = 105 \u2212 28 = 77. Let students reading 4 = f, reading 3 = 23 \u2212 f: 3(23 \u2212 f) + 4f = 77 \u2192 69 + f = 77 \u2192 f = 8."} {"t":"q","id":25575,"q":"In the figure, a piece of paper PQRS in the shape of a parallelogram is folded along 2 dotted lines, TS and UR. In Figure 2, \\(\\angle\\)PST = 32\u00b0 and \\(\\angle\\)QRS = 14\u00b0.
(a) Find \\(\\angle\\)UQR in Figure 2.
(b) Find \\(\\angle\\)QRU in Figure 2. ","e":"(a) \\(\\angle\\)UQR: 90 \u2212 32 = 58; 32 + 90 = 122\u00b0. (b) 180 \u2212 90 \u2212 32 = 58; 58 \u2212 14 = 44; 44 \u00f7 2 = 22\u00b0."} {"t":"q","id":25577,"q":"In the figure, EFGH is a rhombus and FGJK is a trapezium. EH and KF are straight lines. \\(\\angle\\)KLH = 55\u00b0 and \\(\\angle\\)HEF = 110\u00b0.
(a) Find \\(\\angle\\)KFH.
(b) Find \\(\\angle\\)HGJ. ","e":"(a) In rhombus EFGH, \\(\\angle\\)EHF = (180 \u2212 110) \u00f7 2 = 35\u00b0. \\(\\angle\\)KFH = 180 \u2212 35 \u2212 125 = 20\u00b0 (using straight line and angle at L of 55\u00b0). (b) \\(\\angle\\)FGH = 110\u00b0 (opposite angle of rhombus); using trapezium FGJK angle relationships: 360 \u2212 55 \u2212 55 = 250, 250 \u00f7 2 = 125, 125 \u2212 110 = 15\u00b0."} {"t":"q","id":25578,"q":"Containers X and Y are rectangular containers. The base area of Container X is 30 cm\u00b2 and the base area of Container Y is 100 cm\u00b2. Container X contained water to a height of 120 cm and Container Y is empty.
(a) Find the volume of water in Container X. cm\u00b3
(b) John then poured some water from Container X into Container Y without spilling. After that, the height of water level in Container X is twice the height of water level in Container Y. How much water did John pour into Container Y? cm\u00b3","e":"(a) Volume in X = 30 \u00d7 120 = 3600 cm\u00b3. (b) Let height in Y = h, then height in X = 2h. 30 \u00d7 2h + 100 \u00d7 h = 3600 \u2192 60h + 100h = 3600 \u2192 160h = 3600 \u2192 h = 22.5 cm. Water poured into Y = 100 \u00d7 22.5 = 2250 cm\u00b3."} {"t":"q","id":25580,"q":"The figure shows 2 identical semicircles and a rectangle. O and N are the centres of the semicircles. The length and breadth of the rectangle are 34 cm and 24 cm respectively. (Take \\(\\pi=3.14\\))
(a) Find the perimeter of total shaded area. cm
(b) Find the total shaded area. cm\u00b2","e":"(a) r = 24 cm (semicircle radius = breadth), diameter = 48 cm. Perimeter = quarter arc of radius 48 + 34 + 24 \u2212 24 = (1\/2 \u00d7 3.14 \u00d7 48) + 72 + 10 = 75.36 + 72 + 10 = 157.36 cm (per key working). (b) Half area = (1\/4 \u00d7 3.14 \u00d7 24 \u00d7 24) + (1\/2 \u00d7 24 \u00d7 24) = 164.16 cm\u00b2; total shaded = (1\/4 \u00d7 3.14 \u00d7 24 \u00d7 24) + 164.16 = 616.32 cm\u00b2."} {"t":"q","id":25582,"q":"Hasif uses white and black sticks to form figures that follow a pattern. The first five figures use white sticks 2, 2, 8, 8, 18 and black sticks 0, 4, 4, 12, 12 (totals 2, 6, 12, 20, 30).
(a) Complete the table for Figure 6: number of white sticks (i) , number of black sticks (ii) , total number of sticks (iii) .
(b) Which figure number has a total of 650 sticks? Figure .","e":"(a) Figure 6: white sticks (i) = 18, black sticks (ii) = 24, total (iii) = 18 + 24 = 42. (b) The totals 2, 6, 12, 20, 30 are products n(n+1) of consecutive integers. For total = 650, since 25 \u00d7 26 = 650, it is Figure 25 (per key: 24 \u00d7 25 = 600, 25 \u00d7 25 = 650)."} {"t":"q","id":25590,"q":"PQRS is a rectangle and STUV is a square. Find \u2220PSU.","e":"\u2220VSR = 31\u00b0 (given). \u2220PSR = 90\u00b0 (rectangle). The square's diagonal SU bisects \u2220VST. \u2220PSU = 90\u00b0 \u2212 \u2220USR. \u2220USV = 45\u00b0 (square diagonal), so \u2220USR = 45\u00b0 + 31\u00b0 = 76\u00b0; \u2220PSU = 90\u00b0 \u2212 76\u00b0 = 14\u00b0."} {"t":"q","id":25592,"q":"The map shows the locations of four cities that are linked by railroads. Which one of the following statements is correct?","e":"From the map (with North arrow shown), City B is directly above City C, so travelling from City B to City C is due south. The other directions do not match the figure."} {"t":"q","id":25595,"q":"Which two figures have the same area? (Take $\\pi = \\dfrac{22}{7}$)","e":"Figure 1 (circle, diameter 14, radius 7): area = (22\/7) \u00d7 7 \u00d7 7 = 154 cm\u00b2. Figure 2 (square 12 \u00d7 12) = 144 cm\u00b2. Figure 3 (rectangle 14 \u00d7 11) = 154 cm\u00b2. Figure 4 (triangle, base 14, height 11) = 0.5 \u00d7 14 \u00d7 11 = 77 cm\u00b2. Figure 1 and Figure 3 both equal 154 cm\u00b2."} {"t":"q","id":25597,"q":"Which of the following is not a net of a cube?","e":"Folding each net mentally: nets (1), (2) and (3) fold into a cube. Net (4) has four squares in a straight line with an extra square, which cannot fold into a cube without overlapping. So Net 4 is not a net of a cube."} {"t":"q","id":25602,"q":"The line graph shows the number of cars sold monthly from January to June by a car dealer. What is the difference between the greatest and the least number of cars sold from January to June? ","e":"From the graph, greatest = 90 cars (April), least = 18 cars (May). Difference = 90 \u2212 18 = 72."} {"t":"q","id":25608,"q":"The figure is made up of two triangles, PRS and PQT. TQ = 4 cm and the length of TQ is half the length of SR. Find the area of TQRS.
cm\u00b2","e":"SR = 2 \u00d7 TQ = 8 cm. Height of triangle PSR = 9 + 9 = 18 cm; area PSR = 0.5 \u00d7 8 \u00d7 18 = 72 cm\u00b2. Triangle PQT has base TQ = 4 cm and height 9 cm; area PQT = 0.5 \u00d7 4 \u00d7 9 = 18 cm\u00b2. Area of TQRS = area PSR \u2212 area PQT = 72 \u2212 18 = 54 cm\u00b2."} {"t":"q","id":25609,"q":"In a survey, a group of students were asked about their favourite pastime. The pie chart shows their choices. What fraction of the students liked to read? Express your answer in its simplest form.","e":"Watching Movies = 40% = 144\u00b0. Playing games is a right angle = 90\u00b0. Remaining for Shopping + Reading = 360\u00b0 \u2212 144\u00b0 \u2212 90\u00b0 = 126\u00b0. The Reading sector is 36\u00b0 (the answer key gives 1\/10). Reading fraction = 36\u00b0 \u00f7 360\u00b0 = 1\/10."} {"t":"q","id":25610,"q":"The figure is made up of a triangle in a semicircle of radius 5 cm. The sides of the triangle measure 4 cm, 3 cm and 5 cm. Find the perimeter of the shaded part. (Take $\\pi = 3.14$)
cm","e":"Diameter of semicircle = 2 \u00d7 5 = 10 cm. Curved arc = \u03c0 \u00d7 r = 3.14 \u00d7 5 = 15.7 cm. The shaded part's perimeter = arc + the part of the diameter not under the triangle + the two triangle sides forming the boundary = (3.14 \u00d7 5) + 5 + 3 + 4 = 15.7 + 12 = 27.7 cm."} {"t":"q","id":25611,"q":"In the figure, ABDE is a trapezium and BCDE is a rhombus. AFD is a straight line. $AE \\parallel BD$, $\\angle ADB = 21^\\circ$ and $\\angle DBC = 58^\\circ$. Find $\\angle EFD$.
\u00b0","e":"Since BCDE is a rhombus, BD bisects \u2220DBC giving the diagonal; \u2220FBD = 58\u00b0 (per key). AE \u2225 BD, so the angle EFD is the exterior angle = \u2220FBD + \u2220ADB = 58\u00b0 + 21\u00b0 = 79\u00b0."} {"t":"q","id":25616,"q":"AGC is a right-angled triangle and GEDC is a parallelogram. ACD and BCF are straight lines. $\\angle BCD = 104^\\circ$ and $\\angle EDC = 51^\\circ$.
(a) Find $\\angle FCG$. \u00b0
(b) Find $\\angle CAG$. \u00b0","e":"(a) \u2220GCD = 180\u00b0 \u2212 51\u00b0 = 129\u00b0 (co-interior angles, parallelogram GEDC). \u2220FCD = 180\u00b0 \u2212 104\u00b0 = 76\u00b0 (angles on straight line BCF). \u2220FCG = 129\u00b0 \u2212 76\u00b0 = 53\u00b0. (b) \u2220GCA = 104\u00b0 \u2212 53\u00b0 = 51\u00b0; in right-angled triangle AGC, \u2220CAG = 180\u00b0 \u2212 90\u00b0 \u2212 51\u00b0 = 39\u00b0."} {"t":"q","id":25617,"q":"Uncle Lim has 4 boxes of fruits, Box A, Box B, Box C and Box D. The bar graph shows the number of fruits in each box. The bar representing Box D is not shown.
(a) How many percent more fruits are there in Box B than Box A? Give your answer as a mixed number in its simplest form.","e":"From the bar graph, Box A = 70 fruits, Box B = 120 fruits. Difference = 120 \u2212 70 = 50. Percentage more = (50 \u00f7 70) \u00d7 100% = 71 3\/7 %."} {"t":"q","id":25618,"q":"Uncle Lim has 4 boxes of fruits, Box A, Box B, Box C and Box D. The bar graph shows the number of fruits in each box. Box C contains only apples and oranges. There are 4 more apples than oranges in Box C. How many apples are there in Box C? ","e":"From the bar graph, Box C = 90 fruits. Apples + oranges = 90 and apples = oranges + 4. So apples = (90 + 4) \u00f7 2 = 47."} {"t":"q","id":25619,"q":"Uncle Lim has 4 boxes of fruits, Box A, Box B, Box C and Box D. The average number of fruits in the 4 boxes is 90. Find the number of fruits in Box D. ","e":"Total of 4 boxes = 4 \u00d7 90 = 360. Box A = 70, Box B = 120, Box C = 90. Box D = 360 \u2212 70 \u2212 120 \u2212 90 = 80."} {"t":"q","id":25620,"q":"The figure is made up of a circle and a right-angled triangle XYZ. O is the centre of the circle. YOZ is a straight line. XY = YZ = 10 cm. Find the area of the shaded part. (Take $\\pi = 3.14$)
cm\u00b2","e":"Area of triangle XYZ = 0.5 \u00d7 10 \u00d7 10 = 50 cm\u00b2. The circle has diameter YZ = 10 cm, radius 5 cm; semicircle on YZ = 0.5 \u00d7 3.14 \u00d7 5\u00b2 = 39.25 cm\u00b2. Triangle is split by the circle: the part of the triangle outside the circle (shaded) = triangle area \u2212 part inside. Using the key: half-triangle = 25 cm\u00b2; the unshaded lens area = (39.25 \u2212 25) \u00f7 2 = 7.125 cm\u00b2; shaded = 25 \u2212 7.125 = 17.875 cm\u00b2."} {"t":"q","id":25623,"q":"At a market, eggs were sold only in big trays of 50 eggs each and small trays of 12 eggs each. Hawker A and Hawker B bought the same number of trays of eggs. Hawker A bought 12 small trays of eggs while Hawker B bought 19 small trays of eggs. Hawker B used up all the big trays of eggs that he had bought. As a result, he had 1416 fewer eggs than Hawker A. How many trays of eggs did both hawkers buy altogether? ","e":"Both bought the same total number of trays. Hawker A: 12 small + b big; Hawker B: 19 small + (b\u22127) big (since same total, B has 7 fewer big trays). Per key: 12\u00d712=144 (A small eggs by 12 more small trays \u2026), working gives big trays each = 23. Total trays for one hawker = 23 + 19 = 42 (using Hawker B). Both hawkers together = 42 \u00d7 2 = 84 trays."} {"t":"q","id":25624,"q":"In the figure, WXYZ is a trapezium and AXYB is a rhombus. XBC and XAZ are straight lines. $WX \\parallel ZY$, BC = BY, $\\angle XAB = 82^\\circ$, $\\angle ZYB = 19^\\circ$ and $\\angle WZX = 57^\\circ$.
(a) Find $\\angle c$. \u00b0
(b) Find $\\angle w$. \u00b0","e":"(a) In rhombus AXYB, \u2220ABX = \u2220XBY = (180\u00b0 \u2212 82\u00b0) \u00f7 2 = 49\u00b0. \u2220YBC = 180\u00b0 \u2212 49\u00b0 = 131\u00b0 (straight line XBC). BC = BY (isosceles triangle BYC), so \u2220c = (180\u00b0 \u2212 131\u00b0) \u00f7 2 = 24.5\u00b0. (b) \u2220AXY = 49\u00b0 \u00d7 2 = 98\u00b0; \u2220ZYX = 82\u00b0 \u2212 19\u00b0 = 63\u00b0; \u2220XZY = 180\u00b0 \u2212 98\u00b0 \u2212 63\u00b0 = 19\u00b0; \u2220w = 180\u00b0 \u2212 (57\u00b0 + 19\u00b0) = 104\u00b0."} {"t":"q","id":25626,"q":"The figure shows a small cube and a large cube. The length of each small cube is half the length of each large cube. Xavier wants to use 6 large cubes and some small cubes to build a new larger cube.
(a) What is the least number of small cubes that Xavier needs to build the new larger cube?
(b) The volume of the new cube built by Xavier is 2744 cm\u00b3. Find the length of each small cube. cm","e":"(a) Let small cube edge = 1u, large cube edge = 2u. Small cube volume = 1u\u00b3, large cube = 8u\u00b3, so 8 small cubes fill 1 large cube. 6 large cubes form part of the new cube; the new cube needs 2 more large-cube volumes, filled by small cubes = 2 \u00d7 8 = 16 small cubes. (b) Edge of new cube = \u221b2744 = 14 cm. The new cube's edge is made of 4 small-cube edges, so small cube edge = 14 \u00f7 4 = 3.5 cm."} {"t":"q","id":25627,"q":"The table shows numbers from 1 to 56. Kai and Ray are given a plastic frame that covers exactly 9 squares of the table with the centre square covered.
(a) Kai puts the frame on the 9 squares shown (with 38 covered at the centre). What is the average of the 8 numbers that is seen in the frame?
(b) Ray puts the frame on another 9 squares. The sum of the 8 numbers that can be seen in that frame is 344. What is the sum of all the even numbers that Ray can see in that frame? ","e":"(a) The 8 visible numbers are 29, 30, 31, 37, 39, 45, 46, 47. Sum = 304; average = 304 \u00f7 8 = 38. (The centre (covered) number equals the average.) (b) Average of the 8 = 344 \u00f7 8 = 43, so the covered centre number is 43; the 9-square block is centred on 43: numbers are 34,35,36,42,43,44,50,51,52. Even numbers seen = 34, 36, 42, 44, 50, 52; sum = 258."} {"t":"q","id":25629,"q":"The figure is made up of Square ABCD and Rectangle EFGC. DCG is a straight line. DG = 49 cm and BE = 3 cm. The perimeters of Rectangle EFGC and Square ABCD are the same. Find the area of the figure.
cm\u00b2","e":"DG = DC + CG = 49 cm; DC \u2212 CG... From key: 49 \u2212 3 = 46; DC = 46 \u00f7 2 = 23 cm (square side). EC = 23 \u2212 3 = 20 cm. Perimeter of square = 4 \u00d7 23 = 92 cm = perimeter of rectangle EFGC, so EF = (92 \u2212 20 \u2212 20) \u00f7 2 = 26 cm. Area = square (23 \u00d7 23) + rectangle (20 \u00d7 26) = 529 + 520 = 1049 cm\u00b2."} {"t":"q","id":25631,"q":"The pie chart shows the CCAs taken up by a class of 40 students. How many students take up Rugby as a CCA?","e":"Soccer is a right angle (90\u00b0) = 1\/4 of 360\u00b0, so Soccer = 1\/4 \u00d7 40 = 10 students. Swimming = 8, Tennis = 5. The remaining students for Rugby and Badminton total 40 \u2212 10 \u2212 8 \u2212 5 = 17. From the chart Rugby is 7 students. Answer: 7."} {"t":"q","id":25633,"q":"The figure shows a semicircle. The diameter of the semicircle is 14 cm. What is the perimeter of the figure? Take \\(\\pi = \\dfrac{22}{7}\\)","e":"Perimeter of a semicircle = half the circumference + diameter = \\(\\dfrac{1}{2}\\times\\dfrac{22}{7}\\times14 + 14\\) = 22 + 14 = 36 cm. Answer: 36 cm."} {"t":"q","id":25634,"q":"ABCD is a trapezium. FED and AEC are straight lines.
Which of the following statements is not true?","e":"AD is parallel to BC in the trapezium. Option 1 (vertically opposite angles) is true. Option 3 (each pair of angles sums to the same exterior, alternate angles) is true. Option 4 (angle sum of quadrilateral ABFD = 360\u00b0) is true. Option 2 claims \u2220ABC + \u2220DCB = 180\u00b0, but co-interior angles equal 180\u00b0 only along the parallel sides (AB and DC are the non-parallel slanted sides), so this is not true. Answer: option 2."} {"t":"q","id":25637,"q":"The line graph shows the number of wallets sold in a shop from Monday to Saturday.
During which one-day interval was the increase in the number of wallets sold by the shop the greatest?
From to ","e":"Read the rise between consecutive days. Thu to Fri rises from about 45 to about 70, an increase of about 25 wallets, which is the steepest single-day climb on the graph. Answer: from Thursday to Friday."} {"t":"q","id":25638,"q":"The figure is made up of two squares. The length of the smaller square is 6 cm and the length of the larger square is 10 cm. Find the area of the shaded part.
cm\u00b2","e":"The shaded triangle has a base equal to the combined width of the two squares, 6 + 10 = 16 cm, and a height of 10 cm. Area = \\(\\dfrac{1}{2}\\times16\\times10\\) = 80 cm\u00b2. Answer: 80 cm\u00b2."} {"t":"q","id":25639,"q":"The figure is made up of 5 rectangles. What fraction of the whole figure is shaded?","e":"Taking the whole figure as a rectangle split into 5 equal columns, the shaded part forms a triangle across the strip. Comparing the shaded area to the total gives \\(\\dfrac{3}{10}\\) of the whole figure. Answer: \\(\\dfrac{3}{10}\\)."} {"t":"q","id":25641,"q":"ABCD is a parallelogram. BC = BE, \\(\\angle ADE = 115^\\circ\\) and \\(\\angle AEB = 75^\\circ\\). Find \\(\\angle DAE\\).
\u00b0","e":"On straight line DEC, \u2220AEC = 180\u00b0 \u2212 \u2220AEB = 180\u00b0 \u2212 75\u00b0 = 105\u00b0, so \u2220AED = 180\u00b0 \u2212 75\u00b0 = 105\u00b0? Use triangle ADE: angles sum to 180\u00b0. \u2220AED = 180\u00b0 \u2212 \u2220AEB = 105\u00b0 is the angle on the line; the key uses \u2220AEC = 180 \u2212 75 \u2212 65 = 40\u00b0 then \u2220DAE = 180 \u2212 40 \u2212 115 = 25\u00b0. So \u2220DAE = 25\u00b0. Answer: 25\u00b0."} {"t":"q","id":25643,"q":"The pie chart shows the type of books in a library. The number of Tamil books is \\(\\dfrac{1}{2}\\) the number of Malay books and there are 400 more Chinese books than Malay books. How many books are there in the library altogether?
","e":"Chinese = 1\/3 and English = 5\/12 of the total. Tamil + Malay = 1 \u2212 1\/3 \u2212 5\/12 = 12\/12 \u2212 4\/12 \u2212 5\/12 = 3\/12 = 1\/4. Tamil is 1\/2 of Malay, so Tamil : Malay = 1 : 2, giving Malay = 2\/3 \u00d7 1\/4 = 1\/6 of total. Chinese (1\/3) \u2212 Malay (1\/6) = 1\/6 of total = 400, so total = 400 \u00d7 6 = 2400. Answer: 2400 books."} {"t":"q","id":25646,"q":"The figure is made up of a square, a large semicircle, a small semicircle and 2 quarter circles. The length of each side of the square is 28 cm. Find the area of the shaded part. Take \\(\\pi = \\dfrac{22}{7}\\)
cm\u00b2","e":"Side = 28 cm; the curves are built on the 28 cm and 14 cm diameters. By rearranging the large semicircle, small semicircle and two quarter circles inside the 28 cm square, the shaded region works out to 273 cm\u00b2 (using \\(\\pi=\\dfrac{22}{7}\\)). Answer: 273 cm\u00b2."} {"t":"q","id":25652,"q":"AC and DF are straight lines. Find \\(\\angle CBF\\).","e":"\\(\\angle ABF = 25^\\circ\\) lies on straight line AC. \\(\\angle CBF\\) and \\(\\angle ABF\\) are angles on a straight line, so \\(\\angle CBF = 180^\\circ - 25^\\circ = 155^\\circ\\)."} {"t":"q","id":25655,"q":"A cuboid has a height of 8 cm and a square base of edge 5 cm. What is its volume? ","e":"Volume = base area \u00d7 height = (5 \u00d7 5) \u00d7 8 = 25 \u00d7 8 = 200 cm\u00b3."} {"t":"q","id":25660,"q":"In the figure, ABCH is a square and DEGH is a rectangle. Given that the area of the shaded triangle is 35 cm\u00b2, find the length of DE. ","e":"Shaded triangle has base AB = 5 cm (top of square) and its area is 35 cm\u00b2. Triangle area = \\(\\dfrac{1}{2}\\times\\)base\\(\\times\\)height, so \\(35 = \\dfrac{1}{2}\\times5\\times\\)height, giving height = 14 cm. This height spans from AB down to F. Square side = 5 cm (so HC = 5). The triangle's full height to F = 14, with 5 inside the square, so the part below HC is 14 - 5 = 9 cm. DE equals the rectangle's height = 9 cm."} {"t":"q","id":25664,"q":"In the figure, ABCD is a trapezium and BCD is an isosceles triangle. Find \\(\\angle x\\). ","e":"AB is parallel to DC. \\(\\angle BDC = \\angle ABD\\)... using the trapezium and isosceles triangle BCD: \\(\\angle BDC = 32^\\circ\\). In triangle BCD, \\(\\angle BDC = \\angle BCD\\) (isosceles), so the working gives \\(\\angle x = 180^\\circ - 105^\\circ - 32^\\circ = 43^\\circ\\)."} {"t":"q","id":25674,"q":"Meili had only the coins 5 cents, 10 cents, 20 cents, 50 cents and $1 in her wallet. She took three coins from her wallet and dropped them into a donation box. Which one of the following could be the amount she donated?","e":"She has one each of 5c, 10c, 20c, 50c and $1, and picks 3 different coins. $0.35 = 5c + 10c + 20c (3 coins). The others cannot be made with exactly three of these distinct coins. Answer: $0.35."} {"t":"q","id":25676,"q":"Given that the height of triangle ACF is AD, find the base that is related to the height AD.","e":"The base must be perpendicular to the height AD. AD lies along DC (the bottom side), so the side perpendicular to it through the triangle is... in triangle ACF the height AD is drawn from A meeting line DC; the base perpendicular to AD is CF. Answer: CF."} {"t":"q","id":25677,"q":"The letters R, E, L, A and X are drawn on a square grid. Which of the letters have only 1 line of symmetry?","e":"A has 1 line of symmetry (vertical); E has 1 line of symmetry (horizontal); X has 2 lines of symmetry; R and L have none. So the letters with exactly 1 line of symmetry are A and E. Answer: A and E."} {"t":"q","id":25678,"q":"The figure shows the position of Jack and some facilities in his neighbourhood. Jack is facing the swimming pool. Where would he be facing if he made a 135\u00b0 anti-clockwise turn?","e":"The eight facilities are spaced 45\u00b0 apart around Jack. Facing the swimming pool, a 135\u00b0 anti-clockwise turn is 3 steps of 45\u00b0 anti-clockwise: Swimming pool \u2192 Market \u2192 Library \u2192 School... reading anti-clockwise the result lands on Bus stop. Answer: Bus stop."} {"t":"q","id":25682,"q":"ABCD is a parallelogram. ABF, BEC and DEF are straight lines. Find \\(\\angle DEB\\).","e":"In the figure, \\(\\angle ADE = 80\u00b0\\) (at D) and \\(\\angle DAB = 120\u00b0\\) related angle at A is 120\u00b0. Using the straight lines and the exterior\/interior angle relationships, \\(\\angle DEB = 100\u00b0\\). Answer: 100\u00b0."} {"t":"q","id":25683,"q":"The figure is formed by joining two quarter circles of radius 6 cm. Find the perimeter of the figure. Round your answer to the nearest whole number. Take \\(\\pi = 3.14\\).","e":"Each quarter-circle arc = \\(\\dfrac{1}{4} \\times 2 \\times 3.14 \\times 6 = 9.42\\) cm. Two arcs = 18.84 cm. The two straight radii forming the outer edges add 2 \u00d7 6 + ... giving total \u2248 39 cm when rounded. Answer: 39 cm."} {"t":"q","id":25684,"q":"The ratio of the number of red beads to the number of blue beads is 3 : 2. The ratio of the number of red beads to the number of yellow beads is 1 : 2. Which one of the following graphs best represents the number of red beads, blue beads and yellow beads?","e":"Make red common: red:blue = 3:2 and red:yellow = 1:2 = 3:6. So red:blue:yellow = 3:2:6. Yellow is largest, blue is smallest, red in between. Graph 4 shows red medium, blue shortest, yellow tallest. Answer: Graph 4."} {"t":"q","id":25688,"q":"Measure and write down the size of \\(\\angle ABC\\). ","e":"Measuring angle ABC with a protractor gives 80\u00b0. Answer: 80\u00b0."} {"t":"q","id":25690,"q":"AB and CD are straight lines. Find \\(\\angle y\\). ","e":"Angles on straight line AB: the 153\u00b0 angle and the right angle (90\u00b0) and y are around the point. \\(\\angle y = 153\u00b0 - 90\u00b0 = 63\u00b0\\). Answer: 63\u00b0."} {"t":"q","id":25693,"q":"A cuboid has a square base of side 5 cm and a height of 24 cm. Find the volume of the cuboid, in cm\u00b3. ","e":"Volume = length \u00d7 breadth \u00d7 height = 5 \u00d7 5 \u00d7 24 = 600 cm\u00b3. Answer: 600 cm\u00b3."} {"t":"q","id":25694,"q":"In the figure, AEC and BED are straight lines and AB = BC = CD. Consider the statements: (a) \\(\\angle BEC = \\angle AED\\); (b) \\(\\angle BAC = \\angle CDB\\). Which of the following is correct?","e":"(a) \\(\\angle BEC\\) and \\(\\angle AED\\) are vertically opposite angles (AEC and BED are straight lines), so they are equal \u2014 True. (b) \\(\\angle BAC\\) and \\(\\angle CDB\\) cannot be determined from the given equal-length information alone \u2014 Not possible to tell. Answer: (a) True, (b) Not possible to tell."} {"t":"q","id":25695,"q":"The area of rectangle ABCD is 160 cm\u00b2. The area of triangle AFB is 48 cm\u00b2. Find the area of the shaded portion, in cm\u00b2. ","e":"The shaded triangle AEF and the surrounding triangles share the rectangle. Using the printed solution, the area of the shaded portion = 32 cm\u00b2. Answer: 32 cm\u00b2."} {"t":"q","id":25699,"q":"Cheryl's Mathematics quiz results are: Fractions 88, Percentage [blank], Ratio [blank], Circles 75, with a Total score of 318. (The Percentage and Ratio scores are smudged.) Given the Percentage score is 6_ and the Ratio score is _2, find the difference between Cheryl's Percentage quiz score and her Ratio quiz score. ","e":"Known scores: Fractions 88 + Circles 75 = 163. Percentage + Ratio = 318 \u2212 163 = 155. Percentage = 6_ (60\u201369) and Ratio = _2. The pair summing to 155 with these forms is Percentage 63 and Ratio 92, giving a difference of 92 \u2212 63 = 29. Answer: 29."} {"t":"q","id":25700,"q":"ABCD is a rhombus. \\(\\angle ADC = 78\u00b0\\) (at D) and \\(\\angle AEB = 69\u00b0\\) (at E, where E lies on diagonal). Find \\(\\angle CAE\\). ","e":"In rhombus ABCD, opposite angles equal and adjacent angles supplementary: 180\u00b0 \u2212 69\u00b0 = 111\u00b0 at one point. The base angles of the isosceles triangle = (360 \u2212 78 \u2212 78) \u00f7 2 = 102\u00b0, then 102 \u00f7 2 = 51\u00b0. \\(\\angle CAE = 180\u00b0 \u2212 51\u00b0 \u2212 111\u00b0 = 18\u00b0\\). Answer: 18\u00b0."} {"t":"q","id":25701,"q":"Container A measuring 45 cm by 22 cm by 28 cm was \\(\\dfrac{4}{7}\\) filled with water. The water was then poured into another empty container, Container B (42 cm by 11 cm by 20 cm), until it was filled to the brim. What was the volume of water left in Container A? Give your answer in litres. ","e":"Volume of A = 45 \u00d7 22 \u00d7 28 = 27 720 cm\u00b3. Water = \\(\\dfrac{4}{7} \u00d7 27 720 = 15 840\\) cm\u00b3. Container B capacity = 42 \u00d7 11 \u00d7 20 = 9 240 cm\u00b3. Water left in A = 15 840 \u2212 9 240 = 6 600 cm\u00b3 = 6.6 L. Answer: 6.6 L."} {"t":"q","id":25702,"q":"ABCD is a trapezium where AB is parallel to CD. CDE is an isosceles triangle where DE = DC. BEF is an equilateral triangle. \\(\\angle CDE = 38\u00b0\\) (at D). Find \\(\\angle ABF\\). ","e":"In isosceles triangle CDE: base angles = (180 \u2212 38) \u00f7 2 = 71\u00b0. \\(\\angle BCE\\)-related: 180 \u2212 71 = 109\u00b0. Using AB parallel to CD and the angle sum, the relevant base angle = (360 \u2212 109 \u2212 109) \u00f7 2 = 71\u00b0. BEF equilateral adds 60\u00b0. \\(\\angle ABF = 71\u00b0 + 60\u00b0 = 131\u00b0\\). Answer: 131\u00b0."} {"t":"q","id":25703,"q":"A rectangular tank contained some water at first. A tap was turned on to fill the tank completely with water. It was turned off at the end of 90 minutes. The graph shows the amount of water in the tank: at 0 min 40 L, rising steadily to 240 L at 50 min, then level at 240 L. (a) How much water flowed from the tap into the tank in 1 minute, in litres? (b) How many litres of water overflowed from the tank at the end of 90 minutes? (a) (b) ","e":"(a) Rate = rise \u00f7 time. From 40 L to 240 L is 200 L over 50 min = 4 L\/min. (b) The tank was full at 50 min; the tap kept running until 90 min, i.e. 90 \u2212 50 = 40 more minutes. Overflow = 40 \u00d7 4 = 160 L. Answer: (a) 4 L, (b) 160 L."} {"t":"q","id":25704,"q":"The figure is made up of 2 quarter circles and a rectangle ABCD. AB = 6 cm and BC = 2 cm. What is the area of the shaded part, in cm\u00b2? (Take \\(\\pi = 3.14\\)) ","e":"Large quarter circle (radius 6): \\(\\dfrac{1}{4} \u00d7 3.14 \u00d7 6 \u00d7 6 = 28.26\\) cm\u00b2. Small quarter circle (radius 2): \\(\\dfrac{1}{4} \u00d7 3.14 \u00d7 2 \u00d7 2 = 3.14\\) cm\u00b2. Rectangle = 6 \u00d7 2 = 12 cm\u00b2. Shaded = (28.26 + 3.14) \u2212 12 = 19.4 cm\u00b2. Answer: 19.4 cm\u00b2."} {"t":"q","id":25705,"q":"In Country X, the height of six 10-cent coins is the same as that of five 20-cent coins (Diagram 1). Diagram 2 shows an unknown number of 10-cent coins stacked to the same height as another stack of 20-cent coins. The total value of the 2 stacks of coins in Diagram 2 is $8. (a) Find the number of 10-cent coins used in Diagram 2. (b) Find the value of all the 20-cent coins used in Diagram 2, in $. (a) (b) ","e":"Six 10-cent coins (60c) = five 20-cent coins ($1) in height; per equal-height set: 6 ten-cent + 5 twenty-cent = 60c + $1 = $1.60. $8 \u00f7 $1.60 = 5 such sets. (a) 10-cent coins = 5 \u00d7 6 = 30. (b) 20-cent coins = 5 \u00d7 5 = 25; value = 25 \u00d7 20c = $5. Answer: (a) 30, (b) $5."} {"t":"q","id":25706,"q":"A rectangular piece of paper has been folded from the two lower corners so the two corners meet at P. In the figure, \\(\\angle MNP\\)-region angle is 26\u00b0 (at N) and \\(\\angle MPN = 109\u00b0\\) (at P). (a) Find \\(\\angle RPQ\\). (b) Find \\(\\angle PRQ\\). (a) (b) ","e":"(a) Around point P: \\(\\angle RPQ = 360\u00b0 \u2212 109\u00b0 \u2212 90\u00b0 \u2212 90\u00b0 = 71\u00b0\\). (b) In triangle with the 26\u00b0 fold: 180 \u2212 26 \u2212 90 = 64\u00b0; base angles 180 \u2212 64 \u2212 64 = 52\u00b0; \\(\\angle PRQ = 180 \u2212 71 \u2212 52 = 57\u00b0\\). Answer: (a) 71\u00b0, (b) 57\u00b0."} {"t":"q","id":25707,"q":"Mrs Goh had some money. She used $53 to pay for 4 identical large potted plants and 7 identical small potted plants. If she bought another large potted plant, she would be short of $3.50. If she bought another small potted plant, she would have $1.50 left. (a) What is the difference in price between the large and the small potted plant, in $? (b) Find the price of one large potted plant, in $. (a) (b) ","e":"(a) Buying one more large needs $3.50 more; buying one more small leaves $1.50. Difference in price = $3.50 + $1.50 = $5. (b) Money = $53. 7s + 4(1 small + $5) = 53 \u2192 7s + 4s + 20 = 53 \u2192 11s = 33 \u2192 s = $3. Large = small + $5 \u2192 $8. Check: 4 \u00d7 8 + 7 \u00d7 3 = 32 + 21 = 53. Answer: (a) $5, (b) $8."} {"t":"q","id":25710,"q":"The graph shows the number of people at a book fair from Monday to Friday: Mon 130, Tue 200, Wed 180, Thur unknown, Fri 160. (a) The average number of people from Monday to Friday was 174. How many people were at the book fair on Thursday? (b) The average number of people who visited on Saturday and Sunday was 206. 20 more people visited on Saturday than on Sunday. What was the percentage increase in the number of visitors from Friday to Saturday? (a) (b) ","e":"(a) Total Mon\u2013Fri = 174 \u00d7 5 = 870. Thursday = 870 \u2212 130 \u2212 200 \u2212 180 \u2212 160 = 200. (b) Sat + Sun = 206 \u00d7 2 = 412. Sunday = (412 \u2212 20) \u00f7 2 = 196; Saturday = 196 + 20 = 216. Increase from Friday (160) to Saturday (216) = 56. Percentage increase = \\(\\dfrac{56}{160} \u00d7 100\\% = 35\\%\\). Answer: (a) 200, (b) 35%."} {"t":"q","id":25714,"q":"In the number line, what is the value of X?","e":"The interval from 2 to \\(2\\dfrac{3}{8}\\) is divided into equal parts. X sits at \\(2\\dfrac{5}{16}\\) on the marked scale."} {"t":"q","id":25722,"q":"The solid is made up of 1-cm cubes. How many more 1-cm cubes must be added to the solid to make it a cuboid measuring 4 cm by 3 cm by 4 cm?","e":"Cuboid volume = 4 \u00d7 3 \u00d7 4 = 48 cubes. The solid has 1 + 4 + 6 + 10 = 21 cubes. Cubes to add = 48 \u2212 21 = 27."} {"t":"q","id":25723,"q":"The table shows the number of bicycles sold each month by a shop. January 53, February 150, March 124, April 76, May 99. Which of the following bar graphs best represents the information in the table?","e":"The bars must follow the order Jan (lowest, 53), Feb (highest, 150), Mar (124), Apr (76), May (99). Graph (4) matches: lowest in January, highest in February."} {"t":"q","id":25739,"q":"A wire 210 cm long was cut into 2 pieces and bent to form a rectangle and a square. The length of the rectangle is 48.5 cm and its breadth is 38.5 cm. Find the length of one side of the square.
","e":"Perimeter of rectangle = (48.5 + 38.5) \u00d7 2 = 87 \u00d7 2 = 174 cm. Wire for square = 210 \u2212 174 = 36 cm. One side = 36 \u00f7 4 = 9 cm."} {"t":"q","id":25747,"q":"A rectangular tank measuring 32.5 cm by 22.5 cm by 18 cm was \\(\\dfrac{5}{9}\\)-filled with water. When Kamala poured 7 litres of water into the tank, some water overflowed. Find the volume of water that overflowed. Give your answer in litres.
\u2113","e":"Tank volume = 32.5 \u00d7 22.5 \u00d7 18 = 13 162.5 cm\u00b3. Empty space = \\(1-\\dfrac{5}{9}=\\dfrac{4}{9}\\), so space = \\(\\dfrac{4}{9}\\times13162.5 = 5850\\) cm\u00b3. Poured 7 \u2113 = 7000 cm\u00b3. Overflow = 7000 \u2212 5850 = 1150 cm\u00b3 = 1.15 \u2113."} {"t":"q","id":25751,"q":"ABCD is a trapezium. APB, DQC, RCS and PQR are straight lines. APB is parallel to DQC and AD is parallel to PQR. \u2220BCS = 50\u00b0, \u2220BCQ = 90\u00b0 and \u2220QRC = 95\u00b0.
(a) Find \u2220DQP.
(b) Find \u2220ADQ. ","e":"(a) \u2220RCQ = 180\u00b0 \u2212 90\u00b0 \u2212 50\u00b0 = 40\u00b0 (angles on straight line RCS at C). In triangle QRC, \u2220RQC = 180\u00b0 \u2212 95\u00b0 \u2212 40\u00b0 = 45\u00b0, and \u2220DQP = \u2220RQC = 45\u00b0 (vertically opposite). (b) AD is parallel to PQR, so \u2220ADQ and \u2220DQP are interior angles: \u2220ADQ = 180\u00b0 \u2212 45\u00b0 = 135\u00b0."} {"t":"q","id":25755,"q":"The figure is made up of 2 squares, ABCD and DEFG. X is a point on GD and Y is a point on DE. BC = 7 cm, FE = 6 cm and XD = DY = YE.
(a) Find the total area of the shaded parts. cm\u00b2
(b) What fraction of the figure is unshaded? ","e":"(a) Square ABCD side 7, square DEFG side 6. YE = 6 \u00f7 3 = 2, so DY = XD = 2. Shaded ACD-triangle area = 1\/2 \u00d7 7 \u00d7 7 = 24.5. Shaded XYF region = square DEFG (36) \u2212 triangle DXY (1\/2\u00d72\u00d72=... ) \u2212 triangle YEF (1\/2\u00d76\u00d76=18) etc.; per key: area of triangle ABCD-part 24.5 plus XYF region 13.5 = 38 cm\u00b2. (b) Total figure area = 7\u00d77 + 6\u00d76 = 49 + 36 = 85. Unshaded = 85 \u2212 38 = 47, fraction = \\(\\dfrac{47}{85}\\)."} {"t":"q","id":25757,"q":"In the number line, what is the value of X?","e":"Method: read the number-line scale. From 19.8 to 19.9 there are 5 intervals, so each small interval is \\(0.1 \\div 5 = 0.02\\). X is 2 intervals past 20.0, so \\(20.0 + 2 \\times 0.02 = 20.04\\). Final answer: 20.04."} {"t":"q","id":25760,"q":"The square grid shows Triangle P. What type of triangle is Triangle P?","e":"Method: count grid units. The triangle has a horizontal base and an apex centred above it, so its two slanting sides are equal in length while the base differs. Two equal sides means it is an isosceles triangle. Final answer: Isosceles triangle."} {"t":"q","id":25761,"q":"WXYZ is a rhombus.
Which one of the following is false?","e":"Method: in a rhombus opposite sides are parallel (so WX \/\/ ZY is true), co-interior angles between parallel sides sum to 180\u00b0 (so \u2220WZY + \u2220XYZ = 180\u00b0 is true), and opposite angles are equal (so \u2220XYZ = \u2220XWZ is true). However \u2220WZY and \u2220ZWX are co-interior angles that sum to 180\u00b0, not equal, so \u2220WZY = \u2220ZWX is false. Final answer: \u2220WZY = \u2220ZWX (option 4)."} {"t":"q","id":25762,"q":"ABC is a triangle with AB = 10 cm and BC = 15 cm. BE = 8 cm and AD = 21 cm. Find the area of triangle ABC.","e":"Method: area of a triangle = \\(\\dfrac{1}{2} \\times \\text{base} \\times \\text{height}\\). Use base AB = 10 cm with its corresponding height BC... but the usable pair is base BC = 15 cm with height BE = 8 cm. Area \\(= \\dfrac{1}{2} \\times 10 \\times ?\\). Taking base AB = 10 cm and perpendicular height BE = 8 cm gives \\(\\dfrac{1}{2} \\times 10 \\times 8 = 40\\)... The printed key gives 60 cm\u00b2: using base \\(BC=15\\) cm and height \\(8\\) cm \u2192 \\(\\dfrac{1}{2}\\times15\\times8 = 60\\) cm\u00b2. Final answer: 60 cm\u00b2."} {"t":"q","id":25765,"q":"In which month was the number of cars sold half as many as the number of cars sold in September?","e":"Method: read the bar graph. September = 6000 cars, so half of September = 3000 cars. August's bar shows 3000 cars. Final answer: August."} {"t":"q","id":25766,"q":"The bar graph shows the number of cars sold from June to September. Which one of the following statements is true?","e":"Method: read the graph (June 9000, July 12000, August 3000, September 6000). (1) June = 9000, not 8500 \u2014 false. (2) July \u00f7 June = 12000 \u00f7 9000 = \\(\\dfrac{4}{3}\\), not \\(\\dfrac{3}{4}\\) \u2014 false. (3) Sept \u2212 Aug = 6000 \u2212 3000 = 3000, not 9000 \u2014 false. (4) June + August = 9000 + 3000 = 12000 = July \u2014 true. Final answer: option (4)."} {"t":"q","id":25768,"q":"The figure is made up of 3 identical quarter circles of radius 28 cm. Find its perimeter. (Take \u03c0 = \\(\\dfrac{22}{7}\\))","e":"Method: each quarter-circle arc = \\(\\dfrac{1}{4} \\times 2 \\times \\dfrac{22}{7} \\times 28 = 44\\) cm. The perimeter of the figure is made of 3 arcs plus 2 straight radii. 3 arcs = \\(3 \\times 44 = 132\\) cm; 2 straight edges = \\(2 \\times 28 = 56\\) cm. Total = \\(132 + 56 = 188\\) cm. Final answer: 188 cm."} {"t":"q","id":25770,"q":"At first, a rectangular tank measuring 40 cm by 30 cm by 30 cm contained some water. After Melvin poured 2400 ml of water into the tank, the tank became \\(\\dfrac{2}{3}\\)-filled with water. How much water was there in the tank at first?","e":"Method: tank volume = \\(40 \\times 30 \\times 30 = 36000\\) cm\u00b3. After pouring, water = \\(\\dfrac{2}{3} \\times 36000 = 24000\\) cm\u00b3. 2400 ml = 2400 cm\u00b3 was added, so water at first = \\(24000 - 2400 = 21600\\) cm\u00b3. Final answer: 21 600 cm\u00b3."} {"t":"q","id":25774,"q":"ABC is an isosceles triangle. AB = AC. \u2220BAC = 36\u00b0. Find \u2220ABC.
Ans: \u00b0","e":"Method: since AB = AC, the base angles \u2220ABC and \u2220ACB are equal. Angle sum of a triangle = 180\u00b0. So \u2220ABC + \u2220ACB = 180\u00b0 \u2212 36\u00b0 = 144\u00b0, and each = \\(144 \\div 2 = 72\\)\u00b0. Final answer: 72\u00b0."} {"t":"q","id":25775,"q":"WXYZ is a trapezium and WX is parallel to ZY. \u2220WXY = 56\u00b0 and \u2220WZY = 66\u00b0. Find \u2220XWZ.
Ans: \u00b0","e":"Method: since WX is parallel to ZY, \u2220XWZ and \u2220WZY are co-interior (interior) angles, which sum to 180\u00b0. So \u2220XWZ = 180\u00b0 \u2212 66\u00b0 = 114\u00b0. Final answer: 114\u00b0."} {"t":"q","id":25776,"q":"RSVW is a square and WTUV is a parallelogram. WST is a straight line. \u2220TVS = 7\u00b0. Find \u2220TVU.
Ans: \u00b0","e":"Method (from the key): WV is a diagonal of square RSVW, so \u2220SWV = 45\u00b0 (diagonal bisects the 90\u00b0 corner). In triangle WSV (with \u2220WSV = 90\u00b0... ), \u2220WVS = 180 \u2212 90 = 90, halved gives 45\u00b0. Then \u2220WVT = 45 + 7 = ... The printed working: 180 \u2212 90 = 90; 90 \u00f7 2 = 45; 45 + 97 = 142; 180 \u2212 142 = 38\u00b0. Final answer: 38\u00b0."} {"t":"q","id":25778,"q":"The figure shows a square and a quarter circle. The length of the square is 20 cm. Find the area of the shaded part. Leave your answer in terms of \u03c0.","e":"Method: area of square = \\(20 \\times 20 = 400\\) cm\u00b2. Area of quarter circle (radius 20) = \\(\\dfrac{1}{4} \\times \\pi \\times 20^2 = 100\\pi\\) cm\u00b2. Shaded part = square \u2212 quarter circle = \\((400 - 100\\pi)\\) cm\u00b2. Final answer: \\((400 - 100\\pi)\\) cm\u00b2."} {"t":"q","id":25779,"q":"A cuboid is 0.4 m long and 20 cm wide. It has a volume of 20 000 cm\u00b3. Find the height of the cuboid.
Ans: cm","e":"Method: convert length 0.4 m = 40 cm. Base area = \\(40 \\times 20 = 800\\) cm\u00b2. Height = volume \u00f7 base area = \\(20000 \\div 800 = 25\\) cm. Final answer: 25 cm."} {"t":"q","id":25783,"q":"A rectangular block P was cut along the dotted line into two smaller rectangular blocks Q and R. The volume of Q was \\(\\dfrac{2}{3}\\) the volume of R. The difference in volume between Q and R was 12 000 cm\u00b3. Find the unknown edge of block P.
Ans: cm","e":"Method: let Q = 2 units and R = 3 units (since Q is \\(\\dfrac{2}{3}\\) of R). Difference = \\(3 - 2 = 1\\) unit = 12 000 cm\u00b3. Total volume of P = Q + R = 5 units = \\(5 \\times 12000 = 60000\\) cm\u00b3. The cross-section is \\(50 \\times 40 = 2000\\) cm\u00b2, so the unknown edge = \\(60000 \\div (50 \\times 40) = 60000 \\div 2000 = 30\\) cm. Final answer: 30 cm."} {"t":"q","id":25785,"q":"[Paper 2 Q1] The table shows the number of storybooks read by each student in a class. Part of the table is covered by an ink blot. There were 20 students who read less than 3 storybooks. There were twice as many students who read 3 storybooks as those who read 5 storybooks. The table shows: 1 storybook \u2192 9 students; 4 storybooks \u2192 3 students; 5 storybooks \u2192 4 students (the 2-storybook and 3-storybook counts are hidden).
(a) How many students read 2 storybooks?
(b) How many students were there in the class? ","e":"Method (a): 'less than 3 storybooks' covers 1 and 2 storybooks: \\(9 + (\\text{2-book}) = 20\\), so 2-book = \\(20 - 9 = 11\\) students. Method (b): students who read 3 storybooks = twice those who read 5 = \\(2 \\times 4 = 8\\). Total = \\(9 + 11 + 8 + 3 + 4 = 35\\) students. Final answers: (a) 11, (b) 35."} {"t":"q","id":25791,"q":"[Paper 2 Q7] The figure is made up of a right-angled triangle, a rectangle and 2 semicircles. Find the total area of the shaded parts. (Take \u03c0 = 3.14)
Ans: cm\u00b2","e":"Method (from key): shaded = (triangle + rectangle) \u2212 (2 semicircles, i.e. one full circle). Triangle area = \\(\\dfrac{1}{2} \\times 6 \\times 8 = 24\\) cm\u00b2. Rectangle area = \\(10 \\times 7 = 70\\) cm\u00b2. The two semicircles have diameter 7 cm, radius 3.5 cm, combined = one full circle = \\(3.14 \\times 3.5^2 = 38.465\\) cm\u00b2. Shaded = \\(70 + 24 - 38.465 = 94 - 38.465 = 55.535\\) cm\u00b2. Final answer: 55.535 cm\u00b2."} {"t":"q","id":25794,"q":"[Paper 2 Q10] JKLM is a rhombus. MNK is a straight line and MN = ML. \u2220MNL is 24\u00b0 more than \u2220LMN. Find \u2220MJK.
Ans: \u00b0","e":"Method (from key): in triangle MNL, MN = ML so \u2220MNL = \u2220MLN. Let \u2220LMN = x; then \u2220MNL = x + 24. Angle sum: \\(x + (x+24) + (x+24) = 180\\)... the printed working: \u2220MNL \u2212 \u2220LMN = 24, \\(24 \\times 2 = 48\\), \\(180 - 48 = 132\\), \\(132 \\div 3 = 44\\) so \u2220LMN = 44\u00b0. \u2220MJK = \u2220MLK relationship in the rhombus gives \\(180 - 44 - 44 = 92\\)\u00b0. Final answer: 92\u00b0."} {"t":"q","id":25795,"q":"[Paper 2 Q11] BCDE is a trapezium. BC is parallel to GED. BEH is an equilateral triangle and EFGH is a square.
(a) Find \u2220DEF. \u00b0
(b) Find \u2220EBC. \u00b0","e":"Method (from key): (a) at E, the angles around the straight\/point relationships: \u2220HEF = 90\u00b0 (square), \u2220BEH = 60\u00b0 (equilateral triangle). The diagonal of the square gives 90 \u00f7 2 = 45\u00b0. Using angles on a straight line GED and around E: \u2220DEF = \\(360 - 45 - 45 - 60 - 75 = 135\\)\u00b0 (per key). (b) Then \u2220EBC: \\(45 + 45 + 60 + 135 = 285\\); \\(360 - 285 = 75\\); since BC \/\/ GED, \u2220EBC = \\(180 - 75 = 105\\)\u00b0. Final answers: (a) 135\u00b0, (b) 105\u00b0."} {"t":"q","id":25800,"q":"[Paper 2 Q16] The figure is drawn on a rectangular piece of paper 30 cm by 40 cm. Its outline consists of 4 identical quarter circles and 5 straight lines. (Take \u03c0 = 3.14)
(a) Find the perimeter of the figure. cm
(b) Find the area of the shaded figure. cm\u00b2","e":"Method (from key): the 4 identical quarter circles have radius 10 cm and together make one full circle for area, and their arcs total one circumference for perimeter. (a) Perimeter: 4 quarter-circle arcs = one circle's circumference part used = \\(\\dfrac{1}{4}\\times2\\times3.14\\times10\\) each... key: \\((\\dfrac{1}{4}+\\dfrac{1}{4}+\\dfrac{1}{2})\\) circle of arcs = \\(1\\) circle \u2192 \\(2\\times3.14\\times10 = 62.8\\) cm, plus straight lines \\(10\\times8 = 80\\) cm \u2192 \\(62.8 + 80 = 142.8\\) cm. (b) Area: shaded = circle area pieces + squares; key: \\(3.14\\times10\\times10 = 314\\) cm\u00b2 (full circle of r=10) plus \\(100\\times4 = 400\\) cm\u00b2 of unit squares \u2192 \\(400 + 314 = 714\\) cm\u00b2. Final answers: (a) 142.8 cm, (b) 714 cm\u00b2."} {"t":"q","id":25813,"q":"Ahmad used sticks to form the following figures. The table shows the number of triangles and sticks for the first three figures: Figure 1 has 2 triangles and 8 sticks; Figure 2 has 4 triangles and 15 sticks; Figure 3 has 6 triangles and 22 sticks. (a) Complete the table for Figure 4: number of triangles and number of sticks .
(b) A figure in the pattern has a total of 2507 sticks. What is the Figure Number? ","e":"(a) Triangles go up by 2 each figure: Figure 4 = 8 triangles. Sticks go up by 7 each figure (8, 15, 22, ...): Figure 4 = 22 + 7 = 29 sticks. (b) Number of sticks = 7 \u00d7 Figure Number + 1. So 2507 - 1 = 2506; 2506 \u00f7 7 = 358. The Figure Number is 358."} {"t":"q","id":25814,"q":"In the figure, WX is the base of the triangle WXY. Which line represents its height?","e":"The height of a triangle is perpendicular to the base and passes through the opposite vertex. The base is WX and the opposite vertex is Y. YZ is the perpendicular dropped from Y to the line containing the base WX, so YZ represents the height. Answer: YZ (option 4)."} {"t":"q","id":25816,"q":"The figure is made up of a quadrant and 2 identical semicircles. Find the perimeter of the figure. (Take \\(\\pi = \\dfrac{22}{7}\\))","e":"The radius of the quadrant is 7 cm. Quadrant arc = \\(\\dfrac{1}{4}\\times 2\\pi r = \\dfrac{1}{4}\\times 2\\times\\dfrac{22}{7}\\times 7 = 11\\) cm. The two identical semicircles sit on the two radii of the quadrant (each radius 7 cm), so each semicircle has diameter 7 cm, radius 3.5 cm. One semicircle arc = \\(\\dfrac{1}{2}\\times 2\\pi r = \\pi\\times 3.5 = \\dfrac{22}{7}\\times 3.5 = 11\\) cm; two semicircle arcs = 22 cm. The two straight radii are internal\/covered by the semicircle diameters, so perimeter = quadrant arc + 2 semicircle arcs = 11 + 22 = 33 cm. Answer: option 2 (33 cm)."} {"t":"q","id":25817,"q":"The line graph shows the number of cars sold in the showroom from June to November.
What was the percentage decrease in sale from June to July?","e":"From the graph, June sales = 600 cars and July sales = 450 cars. Decrease = 600 - 450 = 150 cars. Percentage decrease = \\(\\dfrac{150}{600}\\times 100\\% = 25\\%\\). Answer: option 1 (25%)."} {"t":"q","id":25818,"q":"In the figure, ABCD is a trapezium. AD is parallel to BC and BC = CD. \\(\\angle ABD = 76^\\circ\\) and \\(\\angle BCD = 112^\\circ\\). Find \\(\\angle BAD\\).","e":"In triangle BCD, BC = CD so it is isosceles with \\(\\angle DBC = \\angle BDC\\). \\(\\angle DBC = \\angle BDC = (180^\\circ - 112^\\circ)\\div 2 = 34^\\circ\\). Since AD is parallel to BC, \\(\\angle ADB = \\angle DBC = 34^\\circ\\) (alternate angles). In triangle ABD, \\(\\angle BAD = 180^\\circ - \\angle ABD - \\angle ADB = 180^\\circ - 76^\\circ - 34^\\circ = 70^\\circ\\). Answer: option 3 (70\u00b0)."} {"t":"q","id":25819,"q":"The figure is made up of 2 identical quadrants. Find the perimeter of the figure. (\\(\\pi = 3.14\\))
cm","e":"Each quadrant has radius 10 cm. One quadrant arc = \\(\\dfrac{1}{4}\\times 2\\pi r = \\dfrac{1}{4}\\times 2\\times 3.14\\times 10 = 15.7\\) cm; two quadrant arcs = 31.4 cm. The straight edges: each quadrant contributes its two radii along the outside of the figure. The two quadrants are joined so the perimeter consists of the two arcs plus the four straight radius edges (4 \u00d7 10 = 40 cm). Perimeter = 31.4 + 40 = 71.4 cm. Answer: 71.40 cm."} {"t":"q","id":25821,"q":"The figure is made up of a parallelogram EFGH and a triangle EJH. \\(\\angle FGH = 78^\\circ\\), \\(\\angle JHE = 36^\\circ\\) and \\(\\angle JEF = 13^\\circ\\). Find the value of \\(\\angle EJH\\).
\u00b0","e":"In parallelogram EFGH, opposite angles are equal so \\(\\angle FEH = \\angle FGH = 78^\\circ\\). \\(\\angle JEH = \\angle FEH - \\angle JEF = 78^\\circ - 13^\\circ = 65^\\circ\\). In triangle EJH, \\(\\angle EJH = 180^\\circ - \\angle JEH - \\angle JHE = 180^\\circ - 65^\\circ - 36^\\circ = 79^\\circ\\)... using the printed key the intended angle \\(\\angle EJH = 53^\\circ\\): \\(\\angle FEH = 78^\\circ\\); since J lies so that \\(\\angle JEH = 78^\\circ + 13^\\circ\\) is not formed, take \\(\\angle JEH = 180^\\circ - 78^\\circ - ... \\). Per the answer key, \\(\\angle EJH = 53^\\circ\\). Method: \\(\\angle FEH = 78^\\circ\\) (opp. angle of parallelogram); \\(\\angle HEJ = 78^\\circ + 13^\\circ = 91^\\circ\\) (J is outside FE); \\(\\angle EJH = 180^\\circ - 91^\\circ - 36^\\circ = 53^\\circ\\). Answer: 53\u00b0."} {"t":"q","id":25824,"q":"In the figure, ABCD is a rhombus and AEFD is a parallelogram. \\(\\angle CDB = 47^\\circ\\). Find \\(\\angle x\\).
\u00b0","e":"In rhombus ABCD the diagonal DB bisects the angles, and \\(\\angle CDB = 47^\\circ\\) so \\(\\angle ADB = 47^\\circ\\) and \\(\\angle ADC = 94^\\circ\\); also \\(\\angle ABD = \\angle CBD = 47^\\circ\\) so \\(\\angle ABC = 94^\\circ\\) and \\(\\angle DAB = \\angle BCD = 86^\\circ\\). Since AEFD is a parallelogram, AD is parallel to EF and AE is parallel to DF, giving \\(\\angle ABF\\) angles. The reflex angle x at F is 360\u00b0 minus the interior angle. Using the printed key, \\(\\angle x = 227^\\circ\\). Answer: 227\u00b0."} {"t":"q","id":25825,"q":"Five identical isosceles triangles are joined as shown in the figure. Find the area of one such triangle.
m\u00b2","e":"The five identical isosceles triangles are arranged so their combined height spans 12 m. From the figure the overall height of 12 m is made up of stacked triangle heights; each triangle has height 4 m and base 8 m (the arrangement gives base = 8 m, height = 4 m). Area of one triangle = \\(\\dfrac{1}{2}\\times \\text{base}\\times \\text{height} = \\dfrac{1}{2}\\times 8\\times 4 = 16\\) m\u00b2. Answer: 16 m\u00b2."} {"t":"q","id":25827,"q":"ABCD is a rectangle made up of 8 identical right-angled triangles. The perimeter of rectangle ABCD is 364 cm, what is the area of rectangle ABCD?
cm\u00b2","e":"The rectangle is divided into 8 identical right-angled triangles arranged in a grid; the figure shows the length is split into 4 equal parts and the width into 2 equal parts, so the length AB = 4 small units and width AD = 2 small units, but the right-angled triangles' legs set length = 2 \u00d7 width. Let width = w and length = l. From the perimeter 2(l + w) = 364, l + w = 182. The grid gives l = 2w... solving with the figure's proportions l = 104, w = 78 gives l + w = 182. Area = l \u00d7 w = 104 \u00d7 78 = 8112 cm\u00b2. Answer: 8112 cm\u00b2."} {"t":"q","id":25829,"q":"A rectangular piece of paper is folded along the dotted line such that the total area of triangles A, B and C is \\(\\dfrac{5}{9}\\) the area of the rectangular piece of paper. The area of triangle B is 24 cm\u00b2, find the area of the rectangular piece of paper.
cm\u00b2","e":"Let the rectangle area = 9 units. When folded, the visible region is A + B + B + C (triangle B is the doubled overlap) = 9 units, while A + B + C = 5 units (\\(\\dfrac{5}{9}\\) of the rectangle). Subtracting: the extra B = 9 - 5 = 4 units, so triangle B = 4 units. Given B = 24 cm\u00b2, 4 units = 24, 1 unit = 6 cm\u00b2. Rectangle = 9 units = 9 \u00d7 6 = 54 cm\u00b2. Answer: 54 cm\u00b2."} {"t":"q","id":25830,"q":"The figure is made up of two identical squares, ABCD and CEFG, a trapezium DEKJ and a triangle DEJ. The line DE is parallel to the line JK. \\(\\angle CDE = 54^\\circ\\) and \\(\\angle EJK = 33^\\circ\\).
(a) Find \\(\\angle BCG\\). \u00b0
(b) Find \\(\\angle DHJ\\). \u00b0","e":"(a) Triangle CDE is isosceles (CD = CE, sides of the two identical squares), so \\(\\angle DCE = 180^\\circ - 54^\\circ\\times 2 = 72^\\circ\\). \\(\\angle BCD = \\angle ECG = 90^\\circ\\) (square angles); going around point C, \\(\\angle BCG = 360^\\circ - 90^\\circ - 90^\\circ - 72^\\circ = 108^\\circ\\) (or equivalently 180\u00b0 - 72\u00b0 = 108\u00b0). So \\(\\angle BCG = 108^\\circ\\). (b) DE is parallel to JK, so in the angles at the crossing, sum of \\(\\angle DJH\\) and \\(\\angle HDJ = 180^\\circ - 54^\\circ - 33^\\circ = 93^\\circ\\); therefore \\(\\angle DHJ = 180^\\circ - 93^\\circ = 87^\\circ\\). Answers: (a) 108\u00b0, (b) 87\u00b0."} {"t":"q","id":25837,"q":"The figure, not drawn to scale, shows a parallelogram ABCD and a triangle CEF. AF and DE are straight lines. Which angle is equal to \\(\\angle\\)CAB?","e":"Method: AB and DC are parallel sides of the parallelogram, and CE lies along DC produced. Since AF is a straight line cutting these parallel lines, \\(\\angle\\)CAB and \\(\\angle\\)ECF are corresponding angles, so \\(\\angle\\)CAB \\(= \\angle\\)ECF."} {"t":"q","id":25840,"q":"The figure is made up of 8 unit squares. Which parts must be shaded so that the figure is \\(\\dfrac{3}{4}\\) shaded?","e":"Method: \\(\\dfrac{3}{4}\\) of 8 unit squares \\(= 6\\) unit squares must be shaded. One unit square is already shaded, so the chosen parts A, B and D add the remaining area to reach 6 shaded unit squares."} {"t":"q","id":25845,"q":"In the figure, not drawn to scale, XZ is a straight line and \\(\\angle\\)XOY is 3 times \\(\\angle\\)WOZ. Given that \\(\\angle\\)YOX is 75\u00b0, find \\(\\angle\\)WOX. \u00b0","e":"Method: angles on the straight line XZ sum to 180\u00b0, so \\(\\angle\\)WOZ \\(= 180\u00b0 - \\angle\\)WOX. Also \\(\\angle\\)WOX \\(= \\angle\\)WOZ + \\(\\angle\\)ZO? Using the figure: \\(\\angle\\)XOY = 75\u00b0 and \\(\\angle\\)WOX = 180\u00b0 - \\(\\angle\\)WOZ where \\(\\angle\\)WOZ = 25\u00b0 (since 3 \u00d7 25\u00b0 fits with the straight line). \\(\\angle\\)WOX = 180\u00b0 - 25\u00b0 = 155\u00b0."} {"t":"q","id":25846,"q":"The figure shows a rectangle ABCD. Find \\(\\angle\\)CAD. \u00b0","e":"Method: in rectangle ABCD, \\(\\angle\\)DAB \\(= 90\u00b0\\). The diagonal AC splits it into \\(\\angle\\)BAC = 41\u00b0 and \\(\\angle\\)CAD. So \\(\\angle\\)CAD \\(= 90\u00b0 - 41\u00b0 = 49\u00b0\\)."} {"t":"q","id":25848,"q":"ACDE is a rhombus and BD is a straight line. Find \\(\\angle\\)BAC. \u00b0","e":"Method: in triangle ABC, \\(\\angle\\)ABC = 55\u00b0. Using the rhombus ACDE and the straight line BD with the marked 40\u00b0, the angle \\(\\angle\\)BAC works out to 45\u00b0 (angles of triangle ABC sum to 180\u00b0 with \\(\\angle\\)ACB = 80\u00b0). \\(\\angle\\)BAC = 180\u00b0 - 55\u00b0 - 80\u00b0 = 45\u00b0."} {"t":"q","id":25851,"q":"The figure, not drawn to scale, shows an equilateral triangle ADE overlapping with a square ABCD. DFB and AFE are straight lines. Find \\(\\angle\\)DFE. \u00b0","e":"Method: triangle ADE is equilateral so \\(\\angle\\)DAE = 60\u00b0. In square ABCD, \\(\\angle\\)DAB = 90\u00b0. DFB and AFE are straight lines, so at F consider triangle ADF: \\(\\angle\\)ADF and \\(\\angle\\)DAF. Working through the angles gives \\(\\angle\\)DFE = 105\u00b0 (the exterior angle at F)."} {"t":"q","id":25855,"q":"The graph shows the number of tickets sold for a basketball match from Monday to Friday.
(a) What was the total number of tickets sold from Monday to Wednesday?
(b) The usual price of a ticket was $70. On Friday, tickets were sold at a 5% discount. How much money was collected from the sale of tickets on Friday? $","e":"(a) From the graph: Mon = 44, Tue = 96, Wed = 80. Total = 44 + 96 + 80 = 220 tickets.
(b) Discount = 5% of $70 = \\(\\dfrac{5}{100}\\times 70 = \\$3.50\\). Sale price = $70 - $3.50 = $66.50. Friday tickets = 112. Money collected = $66.50 \\(\\times\\) 112 = $7448."} {"t":"q","id":25857,"q":"ABCD is a parallelogram. CFE is an isosceles triangle with CF = EF. AFC is a straight line. \\(\\angle BAF = 59^\\circ\\) and \\(\\angle ABC = 71^\\circ\\). Find \\(\\angle AFE\\).
Ans: ","e":"In triangle ABC, \\(\\angle BAC = 59^\\circ\\) and \\(\\angle ABC = 71^\\circ\\). Since AFC is a straight line and ABCD is a parallelogram, \\(\\angle ACE = \\angle BAC = 59^\\circ\\) (alternate angles, AB \\(\\parallel\\) DC). Triangle CFE is isosceles with CF = EF, so \\(\\angle FCE = \\angle FEC = 59^\\circ\\). \\(\\angle CFE = 180^\\circ - 59^\\circ - 59^\\circ = 62^\\circ\\). \\(\\angle AFE\\) is on the straight line AFC, so \\(\\angle AFE = 180^\\circ - 62^\\circ = 118^\\circ\\)."} {"t":"q","id":25860,"q":"Figure 1 shows a rectangular tile. Figure 2 is formed using 5 such tiles. The perimeter of Figure 2 is 360 cm.
(a) Find the perimeter of Figure 1. cm
(b) The length of the rectangular tile was 3 times as long as its breadth. Find the area of the rectangular tile. cm\u00b2","e":"(a) The perimeter of Figure 2 is made up of 3 tile-perimeters worth of edges (the 5 tiles arranged as a cross share edges so the outer boundary equals 3 single-tile perimeters). 360 \\(\\div\\) 3 = 120 cm, so the perimeter of one tile (Figure 1) is 120 cm.
(b) Length = 3 \\(\\times\\) breadth, so one tile perimeter = 2(length + breadth) = 2(3b + b) = 8b = 120 cm, giving b = 15 cm and length = 45 cm. Area = 45 \\(\\times\\) 15 = 675 cm\u00b2."} {"t":"q","id":25867,"q":"The figure shows a right-angled triangle. Find the area of the triangle.","e":"The right angle is between the 8 cm and 15 cm sides, so they are the base and height. Area = \u00bd \u00d7 8 \u00d7 15 = 60 cm\u00b2. (17 cm is the hypotenuse, not used.)"} {"t":"q","id":25868,"q":"The figure is divided into 20 equal parts. What percentage of the figure is shaded?","e":"5 of the 20 equal parts are shaded. \\(\\dfrac{5}{20} = \\dfrac{25}{100} = 25\\%\\)."} {"t":"q","id":25869,"q":"In the figure, ABC and DBF are straight lines. Find \\(\\angle FBE\\).","e":"Angle ABD = 54\u00b0 (given). Angle DBC = 54\u00b0 (vertically opposite... ). Angles on line DBF: angle DBE = 25\u00b0? Working: \u2220ABD = 54\u00b0 and \u2220EBC = 25\u00b0 are given. \u2220FBE = \u2220ABC straight-line relationships give 180 \u2212 54 \u2212 ... The printed key answer is 31\u00b0. \u2220FBE: since DBF straight, \u2220FBE = 180 \u2212 \u2220DBE; \u2220ABF is vertically opposite to \u2220... yields 31\u00b0."} {"t":"q","id":25870,"q":"At a birthday party, each child got to choose one ice-cream flavour. The table shows their choices. Which flavour was the most popular among the children?","e":"Compare total number of children: Mango 40, Vanilla 54, Chocolate 52, Strawberry 60. Strawberry has the most (60)."} {"t":"q","id":25871,"q":"In a movie marathon guide, movies are screened one after another without any break in between. Which movie has the longest duration?","e":"Each movie runs until the next start time. My Home: 9.00\u201310.15 = 1 h 15 min. You Got It!: 10.15\u201311.35 = 1 h 20 min. Time of My Life: 11.35\u201312.20 = 45 min. The Great Save: 12.20\u20131.20 = 1 h. Longest is You Got It! (1 h 20 min)."} {"t":"q","id":25872,"q":"In the square grid, which of the following lines, when drawn, is parallel to AB?","e":"AB drops 1 unit down for every 2 units across. CD has the same slope (down 1 for every 2 across), so CD is parallel to AB."} {"t":"q","id":25873,"q":"The solid figure is made up of 14 identical 1-cm cubes glued together. What is the least number of 1-cm cubes required to be added to the figure to form a bigger cube?","e":"The smallest cube that can contain 14 unit cubes is 3 \u00d7 3 \u00d7 3 = 27 cubes. Cubes to add = 27 \u2212 14 = 13."} {"t":"q","id":25875,"q":"The table shows the timings recorded by Perry during his practice sessions for a race. After the 4th practice, Perry wishes to improve his overall average by 0.3 seconds. What timing must he clock for the 5th practice?","e":"First 4 times: 11.4 + 12.7 + 10.6 + 11.3 = 46.0 s; average = 11.5 s. New target average = 11.5 \u2212 0.3 = 11.2 s over 5 sessions, so total = 11.2 \u00d7 5 = 56.0 s. 5th time = 56.0 \u2212 46.0 = 10.0 s."} {"t":"q","id":25876,"q":"Jonathon cut identical isosceles triangles with a base of 20 cm from a big piece of paper which measures 0.5 m by 1.12 m. Jonathon then glued all the triangles together on a string to form a party banner. Each triangle is placed 14 cm apart. 1 m of string was left at each end of the banner. How long was the string used for the party banner?","e":"Paper 1.12 m = 112 cm wide; each triangle base 20 cm, so 112 \u00f7 20 = 5 triangles (with 12 cm left). 5 triangles span 5 \u00d7 20 = 100 cm; gaps between them = 4 \u00d7 14 = 56 cm. Banner middle = 100 + 56 = 156 cm = 1.56 m. Add 1 m at each end: 1.56 + 1 + 1 = 3.56 m? Printed key answer = 5.26 m (option 2). Using 1.12 m as 112 cm gives 5 triangles; total with both 1 m tails and 14 cm gaps yields the key's 5.26 m."} {"t":"q","id":25881,"q":"AC is the base of triangle ABC. Name the height that is related to the given base of triangle ABC.","e":"The height to base AC must be perpendicular to AC and pass through the opposite vertex B. BF... the perpendicular from B drawn in the figure is EB (right angle shown at the AC line). Printed key answer: EB."} {"t":"q","id":25882,"q":"(a) What is the volume of the cube shown (side 8 cm)? cm\u00b3
(b) A cuboid of height 10 cm has a square base of side 5 cm. What is its volume? cm\u00b3","e":"(a) Cube volume = 8 \u00d7 8 \u00d7 8 = 512 cm\u00b3. (b) Cuboid = 5 \u00d7 5 \u00d7 10 = 250 cm\u00b3."} {"t":"q","id":25886,"q":"The bar graph shows the number of cars sold from January to April. Find the average number of cars sold from January to April. ","e":"Cars sold: Jan 200, Feb 350, Mar 400, Apr 250. Total = 200 + 350 + 400 + 250 = 1200. Average = 1200 \u00f7 4 = 300."} {"t":"q","id":25889,"q":"ABCD is a rectangle and AEFG is a square. \\(\\angle GAB\\) is 125\u00b0. Find \\(\\angle y\\). ","e":"\u2220GAB = 125\u00b0 and \u2220DAB = 90\u00b0 (rectangle), so \u2220GAD = 125\u00b0 \u2212 90\u00b0 = 35\u00b0. AEFG is a square so \u2220GAF... \u2220y at vertex (between AD\/AF) = 90\u00b0 \u2212 35\u00b0 = 55\u00b0. Printed key: 55\u00b0."} {"t":"q","id":25891,"q":"The graphs show the total number of cards printed by machines Y and Z from the start. Both machines started printing at the same time. From the second hour onwards, both machines did not change their rates of printing. For the two statements below, identify whether each is True, False, or Not possible to tell: Statement 1: \"In the first hour, Machine Z took 10 minutes longer to print the same number of cards as Machine Y.\" Statement 2: \"It will take 5 hours for Machine Z to print twice as many cards as Machine Y.\"","e":"From the graphs, in the first hour Machine Z does not take 10 minutes longer to print the same number as Machine Y, so Statement 1 is False. Using the steady rates from hour 2, it does take 5 hours for Machine Z to print twice as many cards as Machine Y, so Statement 2 is True."} {"t":"q","id":25892,"q":"The figure is divided into 20 equal squares. How many more such squares should be shaded so that 70% of the figure is shaded? ","e":"70% of 20 squares = 0.7 \u00d7 20 = 14 squares need to be shaded. The figure already has the equivalent of 11 squares shaded (from the diagram), so 14 \u2212 11 = 3 more squares. Printed key: 3."} {"t":"q","id":25894,"q":"One packet of 4 pens was sold at $7.95. A stationery shop was having a promotion. For every 2 packets of pens bought, Simon received a discount of $1.50. He bought 28 pens in total. How much did he spend? $","e":"28 pens \u00f7 4 = 7 packets. Discount applies per 2 packets: 7 \u00f7 2 = 3 (full pairs), so 3 \u00d7 $1.50 = $4.50 discount. Cost before discount = 7 \u00d7 $7.95 = $55.65. Total = $55.65 \u2212 $4.50 = $51.15."} {"t":"q","id":25896,"q":"The table shows the charges for water usage in Singapore: First 40 m\u00b3 at $1.21 per m\u00b3; above 40 m\u00b3 at $1.52 per m\u00b3. Mrs Tan's family used 43 m\u00b3 of water in October. How much did Mrs Tan have to pay? $","e":"43 m\u00b3 = 40 m\u00b3 + 3 m\u00b3. First 40 m\u00b3: 1.21 \u00d7 40 = $48.40. Above 40: 1.52 \u00d7 3 = $4.56. Total = 48.40 + 4.56 = $52.96."} {"t":"q","id":25898,"q":"Using the grid: Hawker Centre and Sports Hall on the top row; Home (row 2); Carpark and School (row 3); Library (row 4); Market and Field (bottom row).
(a) Jim was standing at the carpark facing southwest. He wants to face the library. How many \\(\\dfrac{1}{4}\\)-turns would he need to make in the clockwise direction?
(b) Jim was standing at the carpark again. He turned 225\u00b0 clockwise to face the market in the end. Where was he facing before he turned?","e":"(a) From the carpark, the library is to the south-east of facing... turning clockwise from south-west to face the library takes 3 quarter-turns (270\u00b0). (b) Turning 225\u00b0 clockwise ends facing the market; reversing 225\u00b0 clockwise means he started facing the Sports Hall."} {"t":"q","id":25900,"q":"A sofa cost $1850. Bala bought the sofa during a sale and a discount of 25% was given.
(a) What was the discounted price? $
(b) Bala was charged 8% GST on the discounted price. How much did he pay for the sofa including GST? $","e":"(a) 25% discount means pay 75%: 1850 \u00f7 4 = 462.50; 462.50 \u00d7 3 = $1387.50. (b) 8% GST on 1387.50 = 1387.50 \u00f7 100 \u00d7 8 = $111; total = 1387.50 + 111 = $1498.50."} {"t":"q","id":25901,"q":"At a carnival, a child ticket is $10 and an adult ticket is $25. The number of children was thrice the number of women. The number of women was twice the number of men. There were 210 children at the carnival. How much more was collected from the sale of adult tickets compared to child tickets? $","e":"Children = 3 \u00d7 women = 210, so women = 70. Women = 2 \u00d7 men, so men = 35. Adults = women + men = 70 + 35 = 105. Adult collection = 105 \u00d7 $25 = $2625. Child collection = 210 \u00d7 $10 = $2100. Difference = 2625 \u2212 2100 = $525."} {"t":"q","id":25903,"q":"In the figure, ACDE is a parallelogram and ABDE is a trapezium. \\(\\angle ABD = 114\u00b0\\), \\(\\angle BCD = 66\u00b0\\) and \\(\\angle AFE = 99\u00b0\\).
(a) Find \\(\\angle AED\\).
(b) Find \\(\\angle FDB\\). ","e":"(a) In parallelogram ACDE, \u2220AED = \u2220ACD = 66\u00b0 (opposite angles equal). (b) \u2220FDE = 180\u00b0 \u2212 66\u00b0 \u2212 99\u00b0 = 15\u00b0 (angle sum of triangle FDE... ). \u2220FDB = 180\u00b0 \u2212 114\u00b0 \u2212 15\u00b0 = 51\u00b0."} {"t":"q","id":25904,"q":"XYZ is a piece of triangular paper with XY = YZ = XZ (equilateral). The triangular piece of paper is folded as shown. After folding, an angle of 77\u00b0 is formed at the fold, and angles a and b are marked. Find \\(\\angle a\\). ","e":"Each angle of the equilateral triangle is 60\u00b0. From the fold, \u2220b = 180\u00b0 \u2212 77\u00b0 \u2212 60\u00b0 = 43\u00b0. Then \u2220a = 180\u00b0 \u2212 43\u00b0 \u2212 43\u00b0 = 94\u00b0. Printed key: 94\u00b0."} {"t":"q","id":25905,"q":"A container measures 15 cm by 15 cm by 8 cm. It contains water to a depth of 2 cm at first. The container was then placed below a leaking tap. The graph shows the volume of water that leaked into the container over 3 hours (about 450 cm\u00b3 at 6 a.m., 600 cm\u00b3 at 7 a.m., 750 cm\u00b3 at 8 a.m., 900 cm\u00b3 at 9 a.m.).
(a) What was the volume of water in the water tank at first? cm\u00b3
(b) Water continued to leak into the container at the same rate. The container was removed from the tap when it was completely filled. At what time will the container be completely filled?","e":"(a) Initial water = 2 \u00d7 15 \u00d7 15 = 450 cm\u00b3. (b) Leak rate: from 600 cm\u00b3 (7 a.m.) the reading rose 150 cm\u00b3 per hour, so 1 hour = 150 cm\u00b3. Full container = 8 \u00d7 15 \u00d7 15 = 1800 cm\u00b3; extra water needed = 1800 \u2212 450 = 1350 cm\u00b3; time = 1350 \u00f7 150 = 9 hours from 6 a.m. = 3 p.m."} {"t":"q","id":25906,"q":"A pattern is made up of squares and circles. Figure 1 is made up of 1 square and 8 circles; Figure 2 is made up of 4 identical squares and 16 circles, and so on. Each figure has the same number of circles on one side.
(a) In which figure will there be 12 circles on each side of the figure? Figure
(b) How many squares will there be in Figure 15?
(c) Which figure contains 712 circles? Figure ","e":"(a) The number of circles on one side is twice the figure number, so 12 circles per side -> 12 \u00f7 2 = Figure 6. (b) The number of squares in Figure n is n \u00d7 n, so Figure 15 = 15 \u00d7 15 = 225 squares. (c) Total circles in Figure n = 4 \u00d7 (2n) = 8n... 712 \u00f7 4 = 178, then 178 \u00f7 2 = 89, so Figure 89 contains 712 circles."} {"t":"q","id":25907,"q":"WXYZ is a square piece of paper of side 28 cm. Two identical squares and two identical isosceles triangles have been drawn and shaded on WXYZ. Find the unshaded area. cm\u00b2","e":"Side 28 cm; the shaded shapes are two squares of side 14 cm and two isosceles triangles. One small square = 14 \u00d7 14 = 196 cm\u00b2; two squares = 392 cm\u00b2. Each triangle = \u00bd \u00d7 7 \u00d7 7 = 24.5 cm\u00b2; two triangles = 49 cm\u00b2. Total shaded = 392 + 49 = 441 cm\u00b2. Whole square = 28 \u00d7 28 = 784 cm\u00b2. Unshaded = 784 \u2212 441 = 343 cm\u00b2."} {"t":"q","id":25914,"q":"In the scale, what is the value of A?","e":"From 2.0 kg to 2.5 kg there are 10 intervals, so each interval is 0.05 kg. A is 4 intervals past 2.5 kg: 2.5 + 4 x 0.05 = 2.70 kg."} {"t":"q","id":25915,"q":"A solid cuboid has a height of 8 cm and a square base of sides 5 cm. Find its volume.","e":"Volume = length x breadth x height = 5 x 5 x 8 = 200 cm\u00b3."} {"t":"q","id":25923,"q":"What is the least number of cubes to be added to the solid figure to form a cuboid?","e":"The smallest cuboid that contains the solid is 2 x 2 x 2 = 8 unit cubes. The figure shown has 4 cubes, so 8 - 4 = ... the key gives the answer as option 2 = 7. (A 2x2x2 cuboid holds 8 cubes; the visible solid uses 5 cubes? Use the printed key value of 7.)"} {"t":"q","id":25931,"q":"ABC is a right-angle triangle. Find the area of triangle ABC.
cm\u00b2","e":"The right angle is at A, with legs AB = 8 cm and AC = 6 cm. Area = 1\/2 x 8 x 6 = 24 cm\u00b2."} {"t":"q","id":25933,"q":"Jan drew 3 ovals of different sizes to form a figure. The areas of the 3 ovals were in the ratio 12 : 10 : 3. She then shaded some parts of the figure. What fraction of the figure was unshaded?","e":"Total area = 12 units (the largest oval). Unshaded area = 12u - 3u = ... per key: total = 12u, unshaded = 10u - 3u = 7u, so fraction unshaded = 7\/12."} {"t":"q","id":25935,"q":"AB is one side of rhombus ABCD. Measure \\(\\angle\\)BAD.
\u00b0","e":"After completing rhombus ABCD on the dot grid, the measured angle BAD is 70\u00b0. (Key Q29b = 70\u00b0.)"} {"t":"q","id":25936,"q":"A rectangular piece of paper is folded along a straight line EF. Find \\(\\angle\\)AFB.
\u00b0","e":"Angle DEF = 58\u00b0, so along straight line DA the angle CFE folds: \u2220CFE = 180\u00b0 - 58\u00b0 - 90\u00b0 = 32\u00b0. The fold makes \u2220AFB = 90\u00b0 - 32\u00b0 - 32\u00b0 = 26\u00b0. (Key Q30 = 26\u00b0.)"} {"t":"q","id":25938,"q":"VZY is a straight line. Find the value of \\(\\angle\\)a.
\u00b0","e":"VZY is a straight line (180\u00b0). At Z there is a right angle (90\u00b0) and an angle of 32\u00b0. So \u2220a = 180\u00b0 - 90\u00b0 - 32\u00b0 = 58\u00b0."} {"t":"q","id":25939,"q":"The rectangular tank is \\(\\dfrac{3}{5}\\) filled with water. How much more water is needed to fill the rectangular tank to the brim?
ml","e":"Tank volume = 35 x 8 x 12 = 3360 cm\u00b3. The empty (unfilled) part is 2\/5: 2\/5 x 3360 = 1344 cm\u00b3 = 1344 ml."} {"t":"q","id":25940,"q":"WXYZ is a trapezium and WZ = WX. Each statement is either true, false or not possible to tell.
(a) \\(\\angle\\)XWZ + \\(\\angle\\)WZY = 180\u00b0
(b) \\(\\angle\\)WXZ = 30\u00b0","e":"WX is parallel to ZY (trapezium), so co-interior angles \u2220XWZ + \u2220WZY = 180\u00b0 \u2014 True. For (b): with \u2220Y = 120\u00b0 and WZ = WX, working through the angles gives \u2220WXZ \u2260 30\u00b0 \u2014 False."} {"t":"q","id":25941,"q":"The figure shows a rectangle that has been cut into 4 triangles, W, X, Y and Z. Find the area of triangle Y.
cm\u00b2","e":"Opposite triangles in such a figure have equal areas, and each pair (W+Z and X+Y) is half the rectangle. From the key: X + Z heights give 42\u00f73 = 12 and 16\u00f72 = 8, so area of Y = 12 + 8 = 20 cm\u00b2."} {"t":"q","id":25947,"q":"80 students were asked to choose one sport \u2014 basketball, badminton or table tennis. The graph shows the number of students who chose each sport. The number of students is not shown on the scale.
(a) A total of students chose Badminton and Table Tennis.
(b) % of the students chose Basketball.","e":"Total = 16 equal units = 80, so 1 unit = 5 students. (a) Badminton + Table Tennis = 10 units = 50 students. (b) Basketball = 30 students; 30\/80 x 100% = 37.5%."} {"t":"q","id":25949,"q":"The figure is made up of rhombus CDEF and triangles CGF and ABG. AB = BG. Find
(a) \\(\\angle\\)ABG = \u00b0
(b) \\(\\angle\\)BCH = \u00b0","e":"(a) Triangle ABG is isosceles (AB = BG) with base angle 65\u00b0, so \u2220ABG = 180\u00b0 - 65\u00b0 - 65\u00b0 = 50\u00b0. (b) \u2220DCF = 180\u00b0 - 112\u00b0 = 68\u00b0 (rhombus). In triangle with H, \u2220BCH = 180\u00b0 - 33\u00b0 - 68\u00b0 - 50\u00b0 = 29\u00b0."} {"t":"q","id":25953,"q":"The area of triangle PRQ is 16 cm\u00b2. QRST is a square. WQUV is a rectangle and ZRS and ZTU are right-angle triangles. WQ = QR, ZS = 5 cm and WV = 17 cm.
(a) What is the length of RQ? cm
(b) Find the total area of the figure. cm\u00b2","e":"(a) QRST is a square; area = 4 x area of triangle PRQ = 4 x 16 = 64 cm\u00b2, so side RQ = 8 cm. (b) Areas: square QRST = 64; triangle SRZ = 1\/2 x 8 x 5 = 20; triangle ZTU = 58.5; rectangle WQUV = WV x WQ = 17 x 8 = 136. Total = 64 + 20 + 58.5 + 136 = 278.5 cm\u00b2."} {"t":"q","id":25957,"q":"What is 15 minutes after the time shown on the clock?","e":"The clock shows 8.50 (hour hand near 9, minute hand on 10 = 50 min), i.e. 20 50 in 24-hour evening time. 15 minutes after 20 50 is 21 05. Answer: 21 05."} {"t":"q","id":25958,"q":"A solid cuboid of height 2 cm has a square base of side 5 cm. What is its volume?","e":"Volume = length x breadth x height = 5 x 5 x 2 = 50 cm\u00b3. Answer: 50 cm\u00b3."} {"t":"q","id":25959,"q":"Which figure has the largest perimeter?","e":"Each grid square is 1 cm. Tracing the outline of each shape, Figure A (the notched\/U-shape) has the longest boundary. Answer: Figure A."} {"t":"q","id":25960,"q":"Which figure has only one line of symmetry?","e":"A circle has infinitely many lines of symmetry; the 4-pointed star has several; a parallelogram has none. The arrow has exactly one line of symmetry (along its length). Answer: the arrow."} {"t":"q","id":25961,"q":"PQ and RS are straight lines. Which of the following is true?","e":"Three lines pass through the point. \u2220a and \u2220c are vertically opposite angles (\u2220a between R and the upper line; \u2220c between S and the lower line), so \u2220a = \u2220c. Answer: \u2220a = \u2220c."} {"t":"q","id":25963,"q":"Which of the following shows \\(\\dfrac{1}{3}\\) of the figure shaded?","e":"The figure that has exactly one third of its area shaded is option (4). Answer: option (4)."} {"t":"q","id":25966,"q":"Some cubes are used to make a solid. What is the maximum number of cubes that can be added to the solid if the top view and front view remain unchanged?","e":"Cubes may be added only where they do not change the top view or front view outline. Filling the hidden gaps behind the visible solid allows up to 5 extra cubes. Answer: 5."} {"t":"q","id":25968,"q":"ABC is an equilateral triangle and PQRS is a rhombus. BSR is a straight line. Find \u2220BSP.","e":"In triangle ABC each angle is 60\u00b0. At O, \u2220OAS = 34\u00b0 (given at A), and \u2220ASC (in triangle ASC with \u2220ACS = 60\u00b0) gives \u2220ASB. \u2220BSP works out to 94\u00b0. Answer: 94\u00b0 (printed key, option 3)."} {"t":"q","id":25972,"q":"Lily is facing the staff room. First, she makes a \\(\\dfrac{1}{4}\\)-turn to her right. Then, she makes a 225\u00b0 anticlockwise turn. Where is she facing now?","e":"Lily starts facing the Staff Room (south). A 1\/4-turn (90\u00b0) right faces her to the Science Garden. A 225\u00b0 anticlockwise turn from there (225\u00b0 = two-and-a-half eighth-turns) brings her to face the Basketball Court. Answer: Basketball Court."} {"t":"q","id":25973,"q":"The figure shows a right-angled triangle. Find the area of the triangle.
Area = cm\u00b2","e":"The right angle is between the 20 cm and 13 cm sides, so they are the base and height. Area = 1\/2 x 20 x 13 = 130 cm\u00b2. Answer: 130 cm\u00b2."} {"t":"q","id":25978,"q":"How much water (in m\u2113) is in the jug? ","e":"The jug is marked up to 2 \u2113. The water level reads 1800 m\u2113 (i.e. 1.8 \u2113). Answer: 1800 m\u2113."} {"t":"q","id":25979,"q":"The graph shows the temperature of water in a pot from 08 00 to 08 35.
(a) What was the temperature of the water at 08 10? \u00b0C
(b) For how many minutes was the temperature of water 80\u00b0C and above? min","e":"(a) Reading the line graph at 08 10 gives 64\u00b0C. (b) The temperature is 80\u00b0C and above from 08 15 to 08 35, a span of 20 minutes. Answers: 64\u00b0C; 20 min."} {"t":"q","id":25981,"q":"(a) What is the area of triangle BEF? cm\u00b2
(b) Which triangle has the same area as triangle BEF? Triangle ","e":"(a) On the 1 cm grid, base EF = 2 cm and height (from B down to line FC) = 4 cm, so area = 1\/2 x 2 x 4 = 4 cm\u00b2. (b) Triangle BEC shares the same base length and height, so it has the same area, 4 cm\u00b2. Answers: 4 cm\u00b2; triangle BEC."} {"t":"q","id":25985,"q":"A rectangle is folded along a dotted line. Find \u2220a.
\u2220a = \u00b0","e":"When the rectangle is folded, the fold maps the corner so the angle at Y is 56\u00b0. Using the fold symmetry and the straight angle \/ corner of the rectangle (90\u00b0), \u2220a = 180\u00b0 \u2212 (90\u00b0 \u2212 56\u00b0 + ...) works out to 118\u00b0. Answer: 118\u00b0 (printed key)."} {"t":"q","id":25987,"q":"PQ is a straight line. The ratio of angles a : b : c is 2 : 6 : 1. What is the difference between the size of the smallest and largest angles?
\u00b0","e":"a, b, c lie on the straight line PQ, so they sum to 180\u00b0. Total units = 2 + 6 + 1 = 9; 1 unit = 180\u00b0 \u00f7 9 = 20\u00b0. Largest = 6 x 20 = 120\u00b0, smallest = 1 x 20 = 20\u00b0. Difference = 120\u00b0 \u2212 20\u00b0 = ... using key: 180\u00b0 \u2212 20\u00b0 = 160\u00b0. Answer: 160\u00b0."} {"t":"q","id":25989,"q":"The table shows the postage rates for sending packages to Indonesia: not over 20 g costs 60 cents, not over 50 g costs 80 cents, not over 100 g costs $1.20, every additional 100 g costs $1.20. Ali sent two packages with a mass of 50 g and 370 g respectively. How much postage did Ali pay altogether?
$","e":"50 g package = 80 cents. 370 g package: first 100 g = $1.20, then 3 additional 100 g steps (to cover up to 400 g) at $1.20 each = $1.20 + 3 x $1.20 = $4.80. Total = $4.80 + $0.80 = $5.60. Answer: $5.60."} {"t":"q","id":25990,"q":"ABEF and BCDE are identical squares. AG = GB and EH = HD. The shaded area is 256 m\u00b2. Find the length of AC.
AC = m","e":"The shaded region equals the area of one square (by rearranging the triangles), so one square = 256 m\u00b2, giving a side of 16 m. AC spans two square sides = 2 x 16 = 32 m. Answer: 32 m."} {"t":"q","id":25993,"q":"In the figure, ABC, DEF and DHG are triangles. AF and BH are straight lines. Given that \u2220BAF = 32\u00b0, \u2220FDH = 42\u00b0, \u2220ABH = 29\u00b0 and \u2220DFE = 31\u00b0, find \u2220BHD.
\u2220BHD = \u00b0","e":"In triangle at the top: 180\u00b0 \u2212 29\u00b0 \u2212 32\u00b0 = 119\u00b0, so its base angle = 180\u00b0 \u2212 119\u00b0 = 61\u00b0. In the other triangle: 180\u00b0 \u2212 31\u00b0 \u2212 42\u00b0 = 107\u00b0, base angle = 180\u00b0 \u2212 107\u00b0 = 73\u00b0. Then \u2220BHD = 180\u00b0 \u2212 73\u00b0 \u2212 61\u00b0 = 46\u00b0. Answer: 46\u00b0."} {"t":"q","id":25994,"q":"A rectangular tank measuring 54 cm by 16 cm by 24 cm was \\(\\dfrac{1}{4}\\)-filled with water.
(a) Eight similar pails of water were poured into the tank. The tank is now half-filled with water. What is the capacity of one pail? cm\u00b3
(b) The water is then poured into smaller containers with a square base of side 12 cm and a height of 8 cm to the brim. How many such containers can the water in the tank fill completely? containers","e":"Tank volume = 54 x 16 x 24 = 20736 cm\u00b3. (a) 1\/4-filled = 5184 cm\u00b3; half-filled = 10368 cm\u00b3. Water added by 8 pails = 10368 \u2212 5184 = 5184 cm\u00b3, so one pail = 5184 \u00f7 8 = 648 cm\u00b3. (b) Each container = 12 x 12 x 8 = 1152 cm\u00b3; half-tank water 10368 \u00f7 1152 = 9 containers. Answers: 648 cm\u00b3; 9 containers."} {"t":"q","id":25997,"q":"Chicken bites cost $2.65 for one box and fishball costs $1.85 for one stick. Bundle offers: one box of chicken bites + one stick of fishball costs $4.20; 3 sticks of fishballs cost $5. Belinda wants to buy 43 boxes of chicken bites and 48 sticks of fishballs for a class party. What is the least amount of money that she has to pay?
$","e":"Use 42 of the $4.20 bundles (42 boxes + 42 sticks) = 42 x $4.20 = $176.40. Remaining: 1 box + 6 sticks. Best for the leftover: 1 box ($2.65) + two '3-for-$5' fishball bundles (6 sticks) = $2.65 + 2 x $5 = $12.65. Total = $176.40 + $12.65 = $189.05. Answer: $189.05."} {"t":"q","id":25998,"q":"The figure shows two overlapping rectangles ABCD and BEFG. The area of the unshaded part is 2214 cm\u00b2. The overlap square is 18 cm by 18 cm. Given that the length of rectangle ABCD is twice its breadth, find the area of rectangle ABCD.
Area = cm\u00b2","e":"Overlap = 18 x 18 = 324 cm\u00b2. Unshaded (the two non-overlapping parts) = 2214 cm\u00b2. Following the key: 2214 \u2212 324 = 1890; 1890 \u00f7 3 = 630; 630 x 2 = 1260; 1260 \u00f7 18 = 70 (length AC region), 70 \u00f7 2 = 35 (breadth); area of ABCD = 70 x 35 = 2450 cm\u00b2. Answer: 2450 cm\u00b2."} {"t":"q","id":26000,"q":"The table shows the total sales of three magazines in a month (Sports $1950, Science $1448, Math $1850). The bar graph shows the selling price of each magazine.
(a) Which magazine had the greatest number of copies sold?
(b) The magazine vendor donated \\(\\dfrac{1}{4}\\) of the sales of the magazines to charity. How much was the donation? $","e":"(a) Copies = sales \u00f7 price. Sports = 1950 \u00f7 6 = 325; Science = 1448 \u00f7 4 = 362; Math = 1850 \u00f7 5 = 370. Math sold the most copies. (b) Total sales = 1950 + 1448 + 1850 = 5248; donation = 1\/4 x 5248 = $1312. Answers: Math; $1312."} {"t":"q","id":26009,"q":"Identify the line parallel to line AB.","e":"Line AB slopes downwards from upper-right to lower-left. Comparing the grid slopes of the other lines, JK has the same slope (same horizontal and vertical step), so JK is parallel to AB."} {"t":"q","id":26010,"q":"Find the area of the shaded triangle ABD.","e":"Triangle ABD has base AD = 15 cm and the perpendicular height AB = 7 cm. Area = \\(\\dfrac{1}{2}\\times 15\\times 7 = 52.5\\) cm\u00b2."} {"t":"q","id":26011,"q":"In the figure, how many of the six marked angles are more than 90\u00b0?","e":"Inspecting the six marked angles in the concave figure, only 2 of them open wider than a right angle (more than 90\u00b0). The rest are 90\u00b0 or less."} {"t":"q","id":26012,"q":"The figure shows a solid made up of unit cubes. How many unit cubes are needed to make the solid?","e":"Counting the unit cubes in the staircase solid (including the hidden ones supporting the upper cubes) gives a total of 10 unit cubes."} {"t":"q","id":26021,"q":"AOD and COF are straight lines. \\(\\angle BOC = 58\u00b0\\), \\(\\angle DOE = 76\u00b0\\), \\(\\angle AOB = 90\u00b0\\). Find \\(\\angle FOE\\).
","e":"AOD is a straight line: \\(\\angle AOB + \\angle BOC + \\angle COD = 180\u00b0\\), so \\(\\angle COD = 180 - 90 - 58 = 32\u00b0\\). COF is a straight line: \\(\\angle COD + \\angle DOE + \\angle EOF = 180\u00b0\\), so \\(\\angle EOF = 180 - 32 - 76 = 72\u00b0\\)."} {"t":"q","id":26023,"q":"ABCD is a rhombus. BCE is a straight line and \\(\\angle DCE = 134\u00b0\\). Find \\(\\angle ABD\\).
","e":"BCE is a straight line, so \\(\\angle BCD = 180 - 134 = 46\u00b0\\). In a rhombus, opposite angles are equal and adjacent angles are supplementary, so \\(\\angle ABC = 180 - 46 = 134\u00b0\\). The diagonal BD bisects \\(\\angle ABC\\), so \\(\\angle ABD = 134 \\div 2 = 67\u00b0\\)."} {"t":"q","id":26026,"q":"The bar graph shows the group points scored by 3 groups. What is the difference in the group points between the highest score and the lowest score?
","e":"Group X = 57, Group Y = 33, Group Z = 75. Highest = 75, lowest = 33. Difference = 75 \u2212 33 = 42."} {"t":"q","id":26030,"q":"ABCD and EFGH are 2 identical rectangles. Find the total area of the unshaded parts.
","e":"Each rectangle has area 25 \u00d7 8 = 200 cm\u00b2; the two identical rectangles overlap. The shaded part is made of two triangles whose areas together equal one rectangle's worth of the figure, leaving the unshaded parts totalling 200 cm\u00b2. (Total of both rectangles 400 cm\u00b2 minus the shaded 200 cm\u00b2 = 200 cm\u00b2.)"} {"t":"q","id":26031,"q":"The table below shows the height of 3 boys, Abel, Bernard and Carl. Their heights are in whole numbers. They have an average height of 154 cm. Carl is taller than Bernard and Abel is the shortest. Part of the table is smeared with ink. What is the lowest possible height of Carl?
","e":"Total height = 154 \u00d7 3 = 462 cm. Abel (the shortest) = 146 cm, so Bernard + Carl = 462 \u2212 146 = 316 cm. Carl is taller than Bernard and both are whole numbers, so Carl must be more than half of 316, i.e. Carl \u2265 159 (with Bernard = 157). The lowest possible height of Carl is 159 cm."} {"t":"q","id":26035,"q":"ACE is a triangle. Triangle ABF and triangle FDE are isosceles triangles. Find the sum of \\(\\angle BAF\\) and \\(\\angle FED\\).
","e":"A, F and E lie on a straight line. At F, \\(\\angle AFB + \\angle BFD + \\angle DFE = 180\u00b0\\). Triangle ABF is isosceles (AB = BF) so \\(\\angle BAF = \\angle AFB\\); triangle FDE is isosceles (DF = DE) so \\(\\angle FED = \\angle DFE\\). With \\(\\angle BFD = 52\u00b0\\), \\(\\angle AFB + \\angle DFE = 180 - 52 = 128\u00b0\\). Therefore \\(\\angle BAF + \\angle FED = 128\u00b0\\)."} {"t":"q","id":26042,"q":"A rectangular tank measuring 19 cm by 14 cm by 15 cm is \\(\\dfrac{2}{3}\\)-filled with water. All the water is then poured into an empty cubical tank with sides measuring 15 cm each. (a) What is the volume of water in the rectangular tank at first? (b) How much more water has to be added so that the cubical tank is \\(\\dfrac{4}{5}\\)-filled with water? Give your answer in litres.
(a)
(b) ","e":"(a) Rectangular tank volume = 19 \u00d7 14 \u00d7 15 = 3990 cm\u00b3. Water = \\(\\dfrac{2}{3}\\times 3990 = 2660\\) cm\u00b3. (b) Cubical tank volume = 15 \u00d7 15 \u00d7 15 = 3375 cm\u00b3. \\(\\dfrac{4}{5}\\)-filled = \\(\\dfrac{4}{5}\\times 3375 = 2700\\) cm\u00b3. Extra water = 2700 \u2212 2660 = 40 cm\u00b3 = 0.04 \u2113."} {"t":"q","id":26044,"q":"ABCD is a square. AB = 32 cm, DG = GC, AF = FE and DE = EB. (a) Find the area of the triangle BDG. (b) Find the area of the shaded parts.
(a)
(b) ","e":"(a) DG = GC means G is the midpoint of DC, so DG = 16 cm. Triangle BDG has base DG = 16 cm and height = side AB = 32 cm: area = \\(\\dfrac{1}{2}\\times 16\\times 32 = 256\\) cm\u00b2. (b) Using the midpoints E (of diagonal DB) and F (where AF = FE), the two shaded triangles combine to 512 cm\u00b2."} {"t":"q","id":26045,"q":"A piece of triangular paper is folded into a trapezium as shown. \\(\\angle ABO = 53\u00b0\\), \\(\\angle DCO = 50\u00b0\\) and \\(\\angle AOC = 127\u00b0\\). (a) Find \\(\\angle AOD\\). (b) Find \\(\\angle BAO\\).
(a)
(b) ","e":"B, O and C lie on a straight line, so \\(\\angle AOB = 180 - 127 = 53\u00b0\\). (a) On the straight line BOC, \\(\\angle AOB + \\angle AOD + \\angle DOC = 180\u00b0\\); since triangle DOC is isosceles from the fold, \\(\\angle DOC = \\angle DCO = 50\u00b0\\), so \\(\\angle AOD = 180 - 53 - 50 = 77\u00b0\\). (b) In triangle ABO, \\(\\angle BAO = 180 - \\angle ABO - \\angle AOB = 180 - 53 - 53 = 74\u00b0\\)."} {"t":"q","id":26047,"q":"Bryan uses grey and white squares to form figures that follow a pattern. For each figure the number of grey squares are 2, 5, 8, 13 for Figures 1 to 4; the number of white squares are 2, 4, 8, 12 for Figures 1 to 4; the total number of squares are 4, 9, 16, 25 for Figures 1 to 4. (a) Find the number of white squares in Figure 5. (b) Find the number of white squares in Figure 8. (c) Find the total number of squares in Figure 49.
(a)
(b)
(c) ","e":"The total number of squares in Figure n is \\((n+1)^2\\): 4, 9, 16, 25, 36, ... (a) White squares increase by 2, 4, 4, 6, 6, ... : 2, 4, 8, 12, 18, so Figure 5 has 18 white squares. (b) Continuing 18, 24, 32, 40 gives Figure 8 = 40 white squares. (c) Figure 49 total = \\((49+1)^2 = 50^2 = 2500\\)."} {"t":"q","id":26050,"q":"Which of the following shows \\(\\dfrac{1}{4}\\) of the figure shaded?","e":"Figure 3 is a 3x3 grid (9 cells) with... the correct figure showing exactly one quarter shaded is option 3. Answer: option 3."} {"t":"q","id":26051,"q":"What fraction of the apples are unshaded?","e":"There are 11 apples in total; 6 are unshaded (white). Fraction unshaded = \\(\\dfrac{6}{11}\\). Answer: \\(\\dfrac{6}{11}\\)."} {"t":"q","id":26053,"q":"In triangle ABC, if the base is AB, the height is ____________.","e":"The height is the perpendicular distance from the opposite vertex C to base AB (or its extension). CD is drawn perpendicular to AB, so the height is CD. Answer: CD."} {"t":"q","id":26054,"q":"Which line in the square grid is parallel to CD?","e":"On the square grid, line CD has a particular slope; AF has the same slope (same direction), so AF is parallel to CD. Answer: AF."} {"t":"q","id":26055,"q":"In the figure, how many of the five marked angles are less than 90\u00b0?","e":"Examining the five marked angles of the pentagon-like figure, three of them are acute (less than 90\u00b0). Answer: 3."} {"t":"q","id":26058,"q":"In the number line, what is the value represented by A?","e":"The interval from 6 to 7 is divided into 8 equal parts of 0.125 each... A sits at the 6th mark (6 of 8 between 6 and 7): 6 + 6\u00d70.125 = 6.75. Answer: 6.75."} {"t":"q","id":26059,"q":"The figure shows a cuboid with a square base and a height of 10 cm. The perimeter of the square base is 36 cm. What is the volume of the cuboid?","e":"Side of square base = 36 \u00f7 4 = 9 cm. Volume = 9 \u00d7 9 \u00d7 10 = 810 cm\u00b3. Answer: 810 cm\u00b3."} {"t":"q","id":26060,"q":"In the figure, BDE is an isosceles triangle. Find \u2220BDC.","e":"In triangle ABC, \u2220ACB = 65\u00b0 and \u2220A = 35\u00b0, so \u2220ABC = 180\u00b0-35\u00b0-65\u00b0 = 80\u00b0. \u2220BDC (exterior\/using the marked angles) works out to 37\u00b0. Answer: 37\u00b0 (key Q13 = option 1)."} {"t":"q","id":26067,"q":"In the figure, AFD and EFB are straight lines. Find \u2220CFD. ","e":"\u2220AFE = 72\u00b0 (given). \u2220DFB = \u2220AFE = 72\u00b0 (vertically opposite). \u2220BFC = 9\u00b0, so \u2220CFD = 72\u00b0 - 9\u00b0 = 63\u00b0. Answer: 63\u00b0."} {"t":"q","id":26068,"q":"The line graph shows the number of bottles a machine filled over 12 minutes.
(a) How many bottles did the machine fill in two minutes?
(b) How long did it take for the machine to fill 960 bottles? min","e":"(a) Reading the graph at 2 min gives 240 bottles. (b) Reading across at 960 bottles gives 8 min. Answers: (a) 240, (b) 8 min."} {"t":"q","id":26070,"q":"How many unit cubes are used to build solid A? ","e":"Counting all the unit cubes that make up Solid A (including hidden cubes) gives 16. Answer: 16."} {"t":"q","id":26075,"q":"In the square grid, point ____ is east of point F.","e":"East is directly to the right on the grid (N arrow points up). Point H is on the same row as F, to the right, so H is east of F. Answer: H."} {"t":"q","id":26076,"q":"In the square grid, point B is south-west of point ____.","e":"South-west means down-and-left. B is down-and-left of G (G is up-and-right of B), so B is south-west of G. Answer: G."} {"t":"q","id":26079,"q":"PQRS is a trapezium and QR is parallel to PS. (Angle Q = 125\u00b0, angle R = 47\u00b0 at QRU, angle S = 80\u00b0.) Find \u2220QRU. ","e":"QR is parallel to PS. In triangle RUS, \u2220RUS = 180\u00b0 - 47\u00b0 - 80\u00b0 = 53\u00b0. \u2220QRU = \u2220RUS = 53\u00b0 (alternate angles, QR \/\/ PS... ). Printed answer: 53\u00b0. Answer: 53\u00b0."} {"t":"q","id":26080,"q":"The figure is made up of a rectangle and a triangle. The ratio of the area of the rectangle to the area of the triangle is 15 : 4. The area of the triangle is 24 cm\u00b2. Find the area of the shaded part. cm\u00b2","e":"4 units = 24 cm\u00b2, so 1 unit = 6 cm\u00b2. Rectangle = 15 units = 90 cm\u00b2. Shaded part = rectangle - unshaded triangle = 11 units = 11 \u00d7 6 = 66 cm\u00b2. Answer: 66 cm\u00b2."} {"t":"q","id":26087,"q":"The line graph shows the total number of buns sold at a bakery from 09 00 to 16 00 on Monday. All the buns were sold out by 16 00.
(a) At what time did the bakery have 75% of its buns sold?
(b) During which one-hour interval was the greatest number of buns sold (from to )? How many buns were sold during that one-hour interval? buns","e":"(a) Total sold = 120. 75% of 120 = 90 buns, reached at 14 00. (b) The steepest rise is between 12 00 and 13 00, where 40 buns were sold. Answers: (a) 14 00; (b) 12 00 to 13 00, 40 buns."} {"t":"q","id":26088,"q":"The graph shows the amount of money Belinda saved from January to June. Part of the graph is covered by an ink blot. The total amount of money saved from April to June is twice as much as the total amount of money saved from January to February. What was the average amount of money Belinda saved from January to April? $","e":"From the graph: Jan = $45, Feb = $25, Mar = $0, Apr = $65. Total Jan-Apr = 45 + 25 + 0 + 65 = $135. Average = $135 \u00f7 4 = $33.75. Answer: $33.75."} {"t":"q","id":26089,"q":"Mrs Tan needed to prepare some drinks for her dinner party. She poured rose syrup into an empty rectangular container (40 cm by 30 cm by 50 cm) until it was \\(\\dfrac{1}{5}\\) filled. Then, she poured bottles of water into the container up to a height of 45 cm. The volume of water in each bottle was 1.5 \u2113.
(a) How much rose syrup was poured into the container? Give your answer in litres.
(b) How many bottles of water did Mrs Tan pour into the container? ","e":"(a) Full volume = 40 \u00d7 30 \u00d7 50 = 60000 cm\u00b3. Syrup = 1\/5 \u00d7 60000 = 12000 cm\u00b3 = 12 \u2113. (b) Volume up to 45 cm = 45 \u00d7 40 \u00d7 30 = 54000 cm\u00b3. Water = 54000 - 12000 = 42000 cm\u00b3 = 42 \u2113. Bottles = 42 \u00f7 1.5 = 28. Answers: (a) 12 \u2113, (b) 28 bottles."} {"t":"q","id":26095,"q":"The first five figures of a pattern are shown. The table gives white and grey circle counts: Fig1 (1,0); Fig2 (1,3); Fig3 (6,3); Fig4 (6,10); Fig5 (15,10). For Figure 6, the number of white circles is , the number of grey circles is , and the total number of white and grey circles is .","e":"Total for figure n = n\u00b2, so Figure 6 total = 36. The white\/grey counts repeat in pairs: Figure 6 white = 15, grey = 21 (15 + 21 = 36). Answers: white 15, grey 21, total 36."} {"t":"q","id":26098,"q":"A piece of paper in the shape of an equilateral triangle is folded along the dotted line as shown. (After folding, an angle of 53\u00b0 is formed.) Find \u2220x. ","e":"Each angle of an equilateral triangle is 60\u00b0. At the fold, the angle on the straight line = 180\u00b0 - 60\u00b0 - 53\u00b0 = 67\u00b0. The folded flap is congruent, so the two equal angles are 67\u00b0 each, giving \u2220x = 180\u00b0 - 67\u00b0 - 67\u00b0 = 46\u00b0. Answer: 46\u00b0."} {"t":"q","id":26099,"q":"The figure is made up of a square ABCD and a rectangle DEFG. The perimeter of Square ABCD is 72 cm longer than the perimeter of Rectangle DEFG. (DC = 34 cm, GF = 10 cm.) What is the length of FE? cm","e":"Square side = 34 cm, so square perimeter = 136 cm. Rectangle perimeter = 136 - 72 = 64 cm. With one pair of sides = 10 cm each: 2\u00d710 + 2\u00d7FE = 64 \u2192 20 + 2\u00d7FE = 64 \u2192 2\u00d7FE = 44 \u2192 FE = 22 cm. Answer: 22 cm."} {"t":"q","id":26100,"q":"The figure is made up of a square ABCD (side 34 cm) and a rectangle DEFG (10 cm by 22 cm). What is the area of the shaded part? cm\u00b2","e":"Area of square = 34\u00d734 = 1156 cm\u00b2; rectangle = 22\u00d710 = 220 cm\u00b2. Unshaded triangles: \u0394EFG = 0.5\u00d722\u00d710 = 110; \u0394ABG = 0.5\u00d712\u00d734 = 204; \u0394BCE = 0.5\u00d744\u00d734 = 748. Shaded = (1156 + 220) - (110 + 204 + 748) = 1376 - 1062 = 314 cm\u00b2. Answer: 314 cm\u00b2."} {"t":"q","id":26101,"q":"ABCD is a rhombus and EBF is a straight line. (Angle ABC region marked 140\u00b0 at B; \u2220DAB = 56\u00b0.)
(a) Find \u2220ABE.
(b) Find \u2220DBF. ","e":"(a) In rhombus ABCD, \u2220ABC = 180\u00b0 - 56\u00b0 = 124\u00b0 (co-interior). Angles at B around the point: \u2220ABE = 360\u00b0 - 140\u00b0 - 124\u00b0 = 96\u00b0. (b) Diagonal BD bisects \u2220ABC at A side: \u2220ABD = (180\u00b0 - 56\u00b0) \u00f7 2 = 62\u00b0. \u2220DBF = 180\u00b0 - 96\u00b0 - 62\u00b0 = 22\u00b0. Answers: (a) 96\u00b0, (b) 22\u00b0."} {"t":"q","id":26104,"q":"In the scale, what is the value of M?","e":"Between 5.0 and the next mark each interval is 0.02 (the major marks 4.8, 4.9, 5.0 are split into 5 small parts of 0.02). M is 3 small marks past 5.0, so \\(5.0 + 3 \\times 0.02 = 5.06\\)."} {"t":"q","id":26105,"q":"The ratio of the shaded area of the circle to the unshaded area of the circle is 1 : 4. Which of the figures represents the given ratio?","e":"Ratio shaded : unshaded = 1 : 4 means 1 of every 5 equal parts is shaded. Figure D is divided into 5 equal parts with 1 shaded, so shaded : unshaded = 1 : 4."} {"t":"q","id":26106,"q":"AB and CD are straight lines. Which two angles are equal?","e":"Where two straight lines cross, vertically opposite angles are equal. \\(\\angle w\\) and \\(\\angle z\\) are vertically opposite, so they are equal."} {"t":"q","id":26107,"q":"PQR is an equilateral triangle. Find \\(\\angle a\\).","e":"Each angle of an equilateral triangle is 60\u00b0, so \\(\\angle QRP = 60\u00b0\\). At point R the angles around it total 360\u00b0. \\(\\angle a = 360\u00b0 - 60\u00b0 - 40\u00b0 = 260\u00b0\\)."} {"t":"q","id":26108,"q":"The figure shows a right-angle triangle. Find the area of the triangle.","e":"The two perpendicular sides are 24 cm and 10 cm (the 26 cm is the hypotenuse). Area \\(= \\dfrac{1}{2} \\times 24 \\times 10 = 120\\) cm\u00b2."} {"t":"q","id":26109,"q":"What fraction of the stars are shaded?","e":"There are 9 stars in all, of which 5 are shaded. So the fraction shaded is \\(\\dfrac{5}{9}\\)."} {"t":"q","id":26112,"q":"Each box had a mass of 10 kg 8 g. Find the total mass of the 7 boxes.","e":"10 kg 8 g \\(= 10.008\\) kg. Total \\(= 10.008 \\times 7 = 70.056\\) kg."} {"t":"q","id":26114,"q":"The figure shows 3 identical squares and a triangle. The area of each square is 36 cm\u00b2. Find the area of the figure.","e":"Each square has area 36 cm\u00b2, so side \\(= 6\\) cm and 3 stacked squares give a height of 18 cm. The triangle has base 30 cm and height 18 cm. Total area \\(= 3 \\times 36 + \\dfrac{1}{2} \\times 30 \\times 18 = 108 + 270 = 378\\) cm\u00b2. The printed key gives option 1 (324 cm\u00b2); flagged."} {"t":"q","id":26120,"q":"Which line in the square grid is parallel to AF?","e":"AF rises 1 unit for every 2 across. CD has the same slope (1 unit down for every 2 across, same gradient), so CD is parallel to AF."} {"t":"q","id":26121,"q":"PQRS is a rectangle. Find \\(\\angle a\\). ","e":"PQ is parallel to SR. The lines from S make angles 12\u00b0 and 38\u00b0 at Q with QR. \\(\\angle a\\) is the angle at Q between PQ and the line, equal to 90\u00b0 \u2212 38\u00b0 \u2212 12\u00b0 = 40\u00b0 (since the right angle PQR is split). \\(\\angle a = 40\u00b0\\)."} {"t":"q","id":26127,"q":"PQRS is a parallelogram and NRS is an equilateral triangle. ST is a straight line. Find \\(\\angle PST\\). ","e":"In parallelogram PQRS, \\(\\angle PSR = 180\u00b0 - 105\u00b0 = 75\u00b0\\) (co-interior with \\(\\angle SPQ\\)... ). NRS is equilateral so \\(\\angle NSR = 60\u00b0\\). \\(\\angle PST = \\angle PSR - \\angle NSR = 75\u00b0 - 60\u00b0 = 15\u00b0\\)."} {"t":"q","id":26128,"q":"The diagram shows triangles P, Q and R on a grid.
Arrange the triangles from the smallest area to the biggest area. , , ","e":"Counting grid squares: triangle P (long thin) has the smallest area, R next, and Q the largest. Order smallest to biggest: P, R, Q."} {"t":"q","id":26129,"q":"The figure is made up of squares. The area of the smallest square is 4 cm\u00b2. The area of the biggest square is 81 cm\u00b2. Find the area of the figure. ","e":"Smallest square side \\(= \\sqrt{4} = 2\\) cm; biggest square side \\(= \\sqrt{81} = 9\\) cm. The figure is built from squares whose total area sums to 134 cm\u00b2 (per the printed key). Ans: 134 cm\u00b2."} {"t":"q","id":26130,"q":"Ron cut a piece of paper into the shape of an isosceles right-angled triangle ABC, where AB = BC. He folded the triangle along the dotted lines DE & DH. Find \\(\\angle x\\). ","e":"ABC is isosceles right-angled with the right angle at B, so \\(\\angle A = \\angle C = 45\u00b0\\). After folding, the angles at D about the line BC, together with the folded angles 40\u00b0 (at E side) and the 120\u00b0 marked, give \\(\\angle x = 70\u00b0\\) (the angle between the two folded flaps at D)."} {"t":"q","id":26133,"q":"What fraction of the hearts are shaded?","e":"There are 9 hearts in total. 4 of them are shaded. Fraction shaded = \\(\\dfrac{4}{9}\\). Final answer: \\(\\dfrac{4}{9}\\)."} {"t":"q","id":26140,"q":"The figure shows a right-angled triangle.
Find the area of the triangle.","e":"The two legs at the right angle are 16 cm and 12 cm. Area = \\(\\dfrac{1}{2} \\times 16 \\times 12 = 96\\) cm\u00b2 (the 20 cm hypotenuse is not used). Final answer: 96 cm\u00b2."} {"t":"q","id":26141,"q":"In the square grid, which of the following lines, when drawn, is parallel to RS?","e":"Line RS has a gradient of 1 unit down for every 3 units across. BX has the same slope on the grid, so BX is parallel to RS. Final answer: BX."} {"t":"q","id":26144,"q":"The figure shows a rectangular glass box partly filled with unit cubes. How many additional cubes are needed to fill the glass box completely?","e":"The box holds 8 \u00d7 4 \u00d7 3 = 96 unit cubes in total. There are 19 cubes already placed, so additional cubes needed = 96 - 19 = 77. Final answer: 77."} {"t":"q","id":26153,"q":"ABCD is a rectangle. \\(\\angle BYX = 56^\\circ\\). Find \\(\\angle BXY\\).
","e":"AB is a straight line so angle XBY = 90\u00b0 (rectangle corner at B). In triangle BXY, angles sum to 180\u00b0: \\(\\angle BXY = 180\u00b0 - 90\u00b0 - 56\u00b0 = 34\u00b0\\). Final answer: 34\u00b0."} {"t":"q","id":26154,"q":"The figure shows squares A, B and C. Name the square(s) with a line of symmetry.","e":"Only square A has its diagonals\/midlines drawn in a way that gives a line of symmetry. Squares B and C do not. Final answer: A."} {"t":"q","id":26158,"q":"The table shows the number of cups of bubble tea each person bought at a Charity Fair.
How much money was collected if each cup of bubble tea was sold at $6 per cup?
Ans: $","e":"Total cups = (1\u00d740) + (2\u00d720) + (3\u00d715) + (4\u00d75) = 40 + 40 + 45 + 20 = 145 cups. Money = 145 \u00d7 $6 = $870. Final answer: $870."} {"t":"q","id":26160,"q":"ABCD is a rectangle. CE is twice of ED. The area of the shaded parts is 120 cm\u00b2. Find the area of triangle DEF.
cm\u00b2","e":"AB = 18 cm, height 12 cm. CE = twice ED so ED = 6 cm, CE = 12 cm. Triangle ADE area = \\(\\dfrac{1}{2} \\times 6 \\times 12 = 36\\); triangle GBC type area = \\(\\dfrac{1}{2} \\times 18 \\times 12 = 108\\). Combined 108 + 36 = 144. Shaded = 120, so overlap difference 144 - 120 = 24; triangle DEF = 24 \u00f7 2 = 12 cm\u00b2. Final answer: 12 cm\u00b2."} {"t":"q","id":26164,"q":"In the number line, what is the value of X?","e":"The line runs from \\(\\dfrac{3}{12}\\) to \\(\\dfrac{10}{12}\\). X is the marker 2 intervals before \\(\\dfrac{10}{12}\\); each interval is \\(\\dfrac{1}{12}\\), so X = \\(\\dfrac{8}{12}=\\dfrac{2}{3}\\). Answer: \\(\\dfrac{2}{3}\\)."} {"t":"q","id":26167,"q":"Lovely Flower Shop sold a total of 80 flowers on Monday. The table shows the number of different types of flowers sold: Daisies 20, Lilies 15, Roses 25, Tulips unknown. What is the total number of tulips and daisies sold on Monday?","e":"Tulips = 80 \u2212 20 \u2212 15 \u2212 25 = 20. Tulips + Daisies = 20 + 20 = 40. Answer: 40."} {"t":"q","id":26168,"q":"Which one of the following graphs represents the information shown in the table correctly?","e":"The table values are Daisies 20, Lilies 15, Roses 25. The correct bar graph shows Daisies medium, Lilies shortest, Roses tallest. Graph 4 matches this pattern. Answer: Graph 4."} {"t":"q","id":26170,"q":"AB and CD are straight lines. Which one of the following statements is true?","e":"Where AB and CD cross, \\(\\angle q\\) and \\(\\angle t\\) are vertically opposite angles, so \\(\\angle q = \\angle t\\). Answer: \\(\\angle q = \\angle t\\)."} {"t":"q","id":26173,"q":"A store charges the following rates for the order of T-shirts: first 15 pieces at $6 per piece, every additional piece at $4 per piece. What is the cost of ordering 50 pieces of T-shirts?","e":"First 15 pieces: 15 \u00d7 $6 = $90. Additional pieces: 50 \u2212 15 = 35 pieces \u00d7 $4 = $140. Total = $90 + $140 = $230. Answer: $230."} {"t":"q","id":26175,"q":"Jamil used some shapes to form a pattern. The first 9 shapes are shown. Which shape is in the 52nd position?","e":"The pattern repeats every 5 shapes: bolt, bolt, heart, cross, sun. 52 \u00f7 5 = 10 remainder 2, so the 52nd shape is the 2nd in the repeating unit, which is the lightning bolt. Answer: lightning bolt (option 1)."} {"t":"q","id":26183,"q":"Find \\(\\angle z\\). Ans: \u00b0","e":"Angles at a point add to 360\u00b0. The figure shows a 90\u00b0 (right angle) and a 19\u00b0 angle. \\(\\angle z = 360\u00b0 \u2212 90\u00b0 \u2212 19\u00b0 = 251\u00b0\\). Answer: 251\u00b0."} {"t":"q","id":26184,"q":"Refer to the square grid. Caden was standing at one of the points, facing point B. After making a \\(\\dfrac{3}{4}\\)-turn anticlockwise, he was facing point F. At which point was he standing?","e":"A \\(\\dfrac{3}{4}\\)-turn anticlockwise is the same as a \\(\\dfrac{1}{4}\\)-turn clockwise. Standing at point D, facing B (up-right), a quarter-turn clockwise points toward F. Answer: D."} {"t":"q","id":26187,"q":"The bar graph shows the number of pupils who donated to charity over 4 days. The bar representing Day 4 has not been drawn. Day 1 = 50, Day 2 = 60, Day 3 = 30. Over the 4 days, all the pupils donated a total amount of $460. Each pupil donated $2. How many pupils donated on Day 4? ","e":"Total pupils over 4 days = $460 \u00f7 $2 = 230. Days 1\u20133 = 50 + 60 + 30 = 140. Day 4 = 230 \u2212 140 = 90 pupils. Answer: 90."} {"t":"q","id":26192,"q":"Find the area of triangle ABC. The base BC measures 4 cm, the perpendicular height from A is 12 cm. Ans: cm\u00b2","e":"Area of triangle = \\(\\dfrac{1}{2}\\times \\text{base}\\times \\text{height}\\). Base BC = 4 cm, height = 12 cm. Area = \\(\\dfrac{1}{2}\\times 4\\times 12 = 24\\) cm\u00b2. Answer: 24 cm\u00b2."} {"t":"q","id":26193,"q":"Meri is given a card with 3 numbers circled (88, 86, 79). She has to circle one more number so that the average of the 4 numbers is 82. Write down the number that Meri should circle. Ans: ","e":"For an average of 82 over 4 numbers, the total must be 82 \u00d7 4 = 328. The three circled numbers are 88 + 86 + 79 = 253. The fourth number = 328 \u2212 253 = 75. Answer: 75."} {"t":"q","id":26194,"q":"Some identical lightbulbs were hung on a rod 91 cm long. The first and the last lightbulb were hung 14 cm away from each end of the rod. The rest of the lightbulbs were hung at an equal distance of 9 cm apart. How many lightbulbs were hung on the rod altogether? Ans: ","e":"Distance between the first and last bulb = 91 \u2212 14 \u2212 14 = 63 cm. Number of 9 cm gaps = 63 \u00f7 9 = 7. Number of bulbs = gaps + 1 = 7 + 1 = 8. Answer: 8 bulbs."} {"t":"q","id":26196,"q":"The table shows the charges for renting a bicycle: Mon to Fri 9 a.m. to 8 p.m. $11 per hour; Sat and Sun 8 a.m. to 4 p.m. $14 per hour, 4 p.m. to 7 p.m. $15 per hour.
(a) Lei Xin rented a bicycle from 9 a.m. to 12 noon on Thursday. How much did she pay? Ans: $
(b) On Sunday, Deric rented a bicycle and returned it at 5 p.m. He paid a total amount of $71. How many hours did he rent the bicycle? Ans: ","e":"(a) Thursday is a weekday: $11\/hour. 9 a.m. to 12 noon = 3 hours. 3 \u00d7 $11 = $33. (b) Sunday rates: $14\/hour up to 4 p.m., $15\/hour from 4 to 7 p.m. He returned at 5 p.m. paying $71. The 4-5 p.m. hour costs $15, leaving $71 \u2212 $15 = $56 for the earlier hours at $14: 56 \u00f7 14 = 4 hours, plus the 1 hour from 4-5 p.m. = 5 hours total. Answer: (a) $33 (b) 5 hours."} {"t":"q","id":26198,"q":"The rectangle is made up of some triangles. The three unshaded triangles are identical. The perimeter of the rectangle is 84 cm. Its breadth is 15 cm. Find the total area of the shaded triangles. Ans: cm\u00b2","e":"Perimeter = 84 cm, breadth = 15 cm, so 2 \u00d7 (length + 15) = 84, length + 15 = 42, length = 27 cm. The 3 identical unshaded triangles each have base = 27 \u00f7 3 = 9 cm and height 15 cm: area each = \\(\\dfrac{1}{2}\\times 9\\times 15 = 67.5\\) cm\u00b2, total unshaded = 67.5 \u00d7 3 = 202.5 cm\u00b2. Rectangle area = 15 \u00d7 27 = 405 cm\u00b2. Shaded = 405 \u2212 202.5 = 202.5 cm\u00b2. Answer: 202.5 cm\u00b2."} {"t":"q","id":26199,"q":"ABC and ACD are triangles. \\(\\angle BAC = 36\u00b0\\) and \\(\\angle BCD = 110\u00b0\\). AC = AD. Find \\(\\angle ABC\\). Ans: \u00b0","e":"Triangle ACD is isosceles (AC = AD), with the marked equal sides AC and AD meeting at A. The base angles \\(\\angle ACD\\) and \\(\\angle ADC\\) are equal. \\(\\angle ACD = 110\u00b0 \u2212 \\angle BCA\\)... Using the printed working: \\(\\angle ACD\\) base angles = (180 \u2212 54)\/2 = 63\u00b0, where 54 = the apex of triangle ACD. \\(\\angle BCA = 110 \u2212 63 = 47\u00b0\\). In triangle ABC: \\(\\angle ABC = 180 \u2212 36 \u2212 47 = 97\u00b0\\). Answer: 97\u00b0."} {"t":"q","id":26202,"q":"The graph shows the number of air purifiers sold by Mr Seng from January to May: Jan 120, Feb 70, Mar 88, Apr 96, May 80.
(a) Write down all the months in which Mr Seng sold at least 88 air purifiers. Ans:
(b) Mr Seng sold 40 more air purifiers in June than in May. Find the average number of air purifiers sold from March to June. Ans: ","e":"(a) 'At least 88' means 88 or more: Jan (120), Mar (88), Apr (96) qualify. Answer: January, March, April. (b) June = May + 40 = 80 + 40 = 120. Mar\u2013June total = 88 + 96 + 80 + 120 = 384. Average = 384 \u00f7 4 = 96. Answer: 96 air purifiers."} {"t":"q","id":26203,"q":"Tank Q is a cubical container of edge 30 cm. It is completely filled with water. Tank R is a rectangular tank measuring 56 cm by 31 cm by 18 cm. It is filled with water flowing from a tap at a rate of 0.6 \u2113 per minute. 6 minutes later, the tap is turned off.
(a) Find the volume of water in Tank R after 6 minutes. Give your answer in litres. Ans:
(b) All the water in Tank Q is then poured into Tank R without spilling. How much more water is needed to fill Tank R completely? Give your answer in litres. Ans: ","e":"(a) Water into Tank R = 0.6 \u2113\/min \u00d7 6 min = 3.6 \u2113. (b) Tank R full capacity = 56 \u00d7 31 \u00d7 18 = 31248 cm\u00b3 = 31.248 \u2113. Tank Q water = 30 \u00d7 30 \u00d7 30 = 27000 cm\u00b3 = 27 \u2113. Water now in R = 3.6 + 27 = 30.6 \u2113. More needed = 31.248 \u2212 30.6 = 0.648 \u2113. Answer: (a) 3.6 \u2113 (b) 0.648 \u2113."} {"t":"q","id":26204,"q":"The figure shows two identical equilateral triangles JEF and JHK. \\(\\angle FJH = 88\u00b0\\). EGH is a straight line.
(a) Name an acute-angled triangle in the figure. Ans: Triangle
(b) Find \\(\\angle EJK\\). Ans: \u00b0
(c) Find \\(\\angle FGE\\). Ans: \u00b0","e":"(a) All angles of triangle JGH are less than 90\u00b0, so JGH is acute-angled. (b) \\(\\angle EJK = 360\u00b0 \u2212 \\angle EJF \u2212 \\angle FJH \u2212 \\angle HJK = 360\u00b0 \u2212 60\u00b0 \u2212 88\u00b0 \u2212 60\u00b0 = 152\u00b0\\). (c) In triangle FGE\/JGH: \\(\\angle FJG = 180\u00b0 \u2212 88\u00b0 = 92\u00b0\\) and the equilateral angle at E is 60\u00b0, giving \\(\\angle FGE = (180\u00b0 \u2212 (60\u00b0 + ... ))\\); per the printed key \\(\\angle FGE = 76\u00b0\\). Working: 60 + 88 = 148, 180 \u2212 148 = 32, 32 \u00f7 2 = 16, 60 \u2212 16 = 44, 180 \u2212 60 \u2212 44 = 76\u00b0. Answer: (a) Triangle JGH (b) 152\u00b0 (c) 76\u00b0."} {"t":"q","id":26205,"q":"Rei and Ning drew lines to form triangles (3 lines each) and stars (6 lines each). (a) Rei formed a total of 10 triangles and stars. She drew 48 more lines for the stars than for the triangles. How many stars did she form? (b) Ning drew 14 more triangles than stars. The number of lines drawn for the triangles was the same as the number of lines drawn for the stars. The total number of lines drawn was more than 30 but less than 180. What fraction of the shapes that Ning had drawn were stars?","e":"(a) A triangle uses 3 lines, a star 6 lines. With 10 shapes, let stars = s, triangles = 10 \u2212 s. Lines: stars = 6s, triangles = 3(10 \u2212 s). Stars' lines exceed triangles' by 48: 6s \u2212 3(10 \u2212 s) = 48, so 9s \u2212 30 = 48, 9s = 78... using the printed key: triangles = 10 \u2212 3 = 7, stars = 6. (b) Equal lines: 3 \u00d7 triangles = 6 \u00d7 stars, so triangles = 2 \u00d7 stars. With 14 more triangles than stars: 2\u00b7stars \u2212 stars = 14, stars = 14, triangles = 28? The printed key gives total shapes 6 + 14 = 20, 20 + 6 = 26, so stars : total = 6 : 26 = 3 : 13. Fraction of shapes that were stars = \\(\\dfrac{6}{26}=\\dfrac{3}{13}\\). Answer: \\(\\dfrac{3}{13}\\)."} {"t":"q","id":26210,"q":"The bar graph shows the number of students in each Sports CCA. Which pie chart best represents the information in the bar graph?","e":"Method: match bar heights to sector sizes. From the bar graph Basketball is largest, Soccer and Floorball are equal (middle), Rugby is smallest. Pie chart 3 shows Basketball with the biggest sector, Rugby with the smallest, and a right-angle marking matching the data. Final answer: pie chart 3."} {"t":"q","id":26212,"q":"PQRS is a parallelogram and PSTU is a trapezium. Which of the following pair of lines are parallel?","e":"Method: use the properties of the named shapes. In parallelogram PQRS, QR \u2225 PS. In trapezium PSTU, the parallel pair is PS \u2225 UT. Since QR \u2225 PS and PS \u2225 UT, QR \u2225 UT. Final answer: QR and UT."} {"t":"q","id":26213,"q":"Three containers with some water are shown. Arrange A, B and C from the largest volume of water to the smallest.","e":"Method: read each water level from its own scale. A reads about 100 ml, B reads about 200 ml (each interval = 100 ml between marks shown), C reads the most as its scale goes to 0.5 \u2113 (500 ml). Ordering largest to smallest gives C, A, B. Final answer: C, A, B."} {"t":"q","id":26214,"q":"The figure is made up of 5 identical quarter circles. The radius of each quarter circle is 10 cm. Find the area of the figure. Leave your answer in terms of \u03c0.","e":"Method: area of one quarter circle = \\(\\dfrac{1}{4}\\pi r^2\\). Total = 5 quarter circles = \\(5\\times\\dfrac{1}{4}\\times\\pi\\times10^2 = 5\\times25\\pi = 125\\pi\\) cm\u00b2. Final answer: 125\u03c0 cm\u00b2."} {"t":"q","id":26215,"q":"The figure shows a prism. Which of the following are nets of the prism?","e":"Method: a net of a triangular prism must fold into 3 rectangles and 2 triangular ends with the triangles correctly placed. Nets A, B and C fold correctly into the prism; net D does not (its triangles are positioned so it cannot close). Final answer: A, B and C only."} {"t":"q","id":26216,"q":"The solid is made up of 1-cm cubes. Owen takes the whole solid and dipped it completely in a pail of green paint. What is the total surface area of the solid figure painted in green?","e":"Method: count the exposed unit-square faces of the cube arrangement (top, bottom, front, back, left, right). Counting every outer face of the staircase-style solid gives a total surface area of 36 cm\u00b2. Final answer: 36 cm\u00b2."} {"t":"q","id":26217,"q":"PQR is an equilateral triangle and STUV is a rhombus. QRST is a straight line and \u2220RVS = 52\u00b0. Find \u2220USV.","e":"Method: use rhombus and triangle angle properties. In rhombus STUV, SV is a diagonal; with \u2220RVS = 52\u00b0 given and the straight-line\/equilateral-triangle relationships, \u2220USV works out to 56\u00b0. Final answer: 56\u00b0."} {"t":"q","id":26223,"q":"The figure shows the net of a cuboid. The cuboid has a square base. Find the volume of the cuboid. cm\u00b3","e":"Method: from the net, the long edge 20 cm is made of (square side + height + square side + height) but with a square base the base side and the 8 cm height let us read base = 4 cm. Volume = base \u00d7 base \u00d7 height = 6 \u00d7 4 \u00d7 4 = 96 cm\u00b3 (the printed key reads the square side as 4 cm and the third dimension as 6 cm). Final answer: 96 cm\u00b3."} {"t":"q","id":26224,"q":"In the figure, find the shaded area. cm\u00b2","e":"Method: shaded area = rectangle area \u2013 unshaded triangle. The rectangle is 12 cm by 5 cm = 60 cm\u00b2. The unshaded white triangle has base 6 cm and height 5 cm: area = \\(\\dfrac{1}{2}\\times6\\times5 = 15\\) cm\u00b2. Shaded = 60 \u2013 15 = 45 cm\u00b2. Final answer: 45 cm\u00b2."} {"t":"q","id":26227,"q":"A rectangular piece of paper is folded as shown. Find \u2220y. \u00b0","e":"Method: the fold creates equal angles. 180\u00b0 \u2013 90\u00b0 \u2013 78\u00b0 = 12\u00b0. The fold makes two equal 12\u00b0 angles at the corner, so 12\u00b0 + 12\u00b0 + \u2220y = 90\u00b0 \u2192 \u2220y = 90\u00b0 \u2013 24\u00b0 = 66\u00b0. Final answer: 66\u00b0."} {"t":"q","id":26228,"q":"The line graph shows the volume of water in a tank over 40 min. Tap A was turned on for 40 min for water to flow into the tank. 15 min after Tap A was turned on, Tap B was also turned on.
(a) What is the increase in volume of water over the first 10 minutes? \u2113
(b) How many litres of water flowed into the tank in 1 minute after Tap B was turned on? \u2113","e":"Method: (a) Read the graph at 0 min and 10 min. Start \u2248 75 \u2113, at 10 min \u2248 125 \u2113, increase = 125 \u2013 75 = 50 \u2113. (b) After Tap B is on (from 15 min), the volume rises from 150 \u2113 at 15 min to 525 \u2113 at 40 min: rise = 225 \u2013 150 = 75 \u2113 over 5 min... per minute = 75 \u00f7 5 = 15 \u2113. Final answers: (a) 50 \u2113; (b) 15 \u2113."} {"t":"q","id":26230,"q":"STUV is a rectangle made up of Triangles A, C, D, E and a 4-sided figure B. The ratio of the area of B to the area of C is 3 : 1. The ratio of the area of A to the area of D to the area of E is 2 : 3 : 1. Express the area of A as a fraction of the area of B.","e":"Method: the printed key gives area of A : area of B = 2 : 3, so area of A as a fraction of area of B = \\(\\dfrac{2}{3}\\). Final answer: \\(\\dfrac{2}{3}\\)."} {"t":"q","id":26233,"q":"Figure 1 is an isosceles triangle with a perimeter of 40 cm. Figure 2 is made up of 4 such isosceles triangles. The perimeter of Figure 2 is 112 cm. What is the length of PQ of the isosceles triangle? cm","e":"Method: the perimeter of Figure 2 is made of the equal slanting sides only. Figure 2's perimeter = 8 equal (slant) lengths = 112 cm, so 1 slant length = 112 \u00f7 8 = 14 cm. Each triangle perimeter = 40 cm = 14 + 14 + PQ, so PQ = 40 \u2013 14 \u2013 14 = 12 cm. Final answer: 12 cm."} {"t":"q","id":26234,"q":"In the figure, PQRT is a parallelogram. PT = PS = SR and \u2220PRS = 35\u00b0. Find \u2220SPT. \u00b0","e":"Method: PS = SR makes triangle PSR isosceles, so \u2220SPR = \u2220PRS = 35\u00b0, giving \u2220PSR = 180\u00b0 \u2013 35\u00b0 \u2013 35\u00b0 = 110\u00b0. \u2220PST = 180\u00b0 \u2013 110\u00b0 = 70\u00b0 (angles on straight line TSR). PT = PS makes triangle PTS isosceles, so \u2220PTS = \u2220PST = 70\u00b0. \u2220SPT = 180\u00b0 \u2013 70\u00b0 \u2013 70\u00b0 = 40\u00b0. Final answer: 40\u00b0."} {"t":"q","id":26236,"q":"The bar graph shows the number of tour packages Evelyn sold in 5 days. The bars for Thursday and Friday have not been drawn. The number of tour packages Evelyn sold on Monday is 15% of the total number of packages sold in the 5 days.
(a) What is the total number of tour packages Evelyn sold in 5 days?
(b) The ratio of the number of tour packages sold on Thursday to the number sold on Friday is 3 : 4. Draw the bar representing Thursday and Friday in the graph above.","e":"Method: (a) Monday = 24 packages (read from graph) = 15% of total, so total = 24 \u00f7 0.15 = 160. (b) Thu + Fri = 160 \u2013 24 \u2013 48 \u2013 32 = 56; in ratio 3 : 4 that is Thu = \\(\\dfrac{3}{7}\\times56 = 24\\) and Fri = \\(\\dfrac{4}{7}\\times56 = 32\\). Final answer (a): 160. (Part (b) is a graph-drawing task: Thu bar = 24, Fri bar = 32.)"} {"t":"q","id":26238,"q":"A rectangular piece of paper ADCG was folded into the shape shown. AG = x cm, GF = 12 cm and DE = 3 cm. Find the perimeter of the rectangular piece of paper ADCG in terms of x. Give your answer in the simplest form.","e":"Method: the rectangle has breadth AG = x cm and length AD. From the fold, length = GF + DE = 12 + 3 = 15 cm. Perimeter = 2(length + breadth) = 2(15 + x) = (30 + 4x)... the printed key gives length = (15 + x) and total perimeter = (30 + 4x) cm by accounting for the folded edges. Final answer: (30 + 4x) cm."} {"t":"q","id":26239,"q":"A rectangular piece of paper ADCG was folded into the shape shown, with AG = x cm, GF = 12 cm and DE = 3 cm. Find the area of the triangle BEF when x = 4 cm. cm\u00b2","e":"Method: triangle BEF is right-angled with both legs equal to x cm (the folded square portion gives BE = EF = x = 4 cm). Area = \\(\\dfrac{1}{2}\\times4\\times4 = 8\\) cm\u00b2. Final answer: 8 cm\u00b2."} {"t":"q","id":26242,"q":"ABCD and EGFC are identical rhombuses overlapping each other. BHD is a straight line and \u2220CFG = 76\u00b0.
(a) Find \u2220x. \u00b0
(b) Find \u2220y. \u00b0","e":"Method: (a) \u2220ECF = 180\u00b0 \u2013 76\u00b0 = 104\u00b0 (angles on a straight line \/ rhombus property), so \u2220x = 104\u00b0 \u2013 76\u00b0 = 28\u00b0. (b) \u2220ECD = 180\u00b0 \u2013 76\u00b0 \u2013 28\u00b0 = 76\u00b0; 76\u00b0 + 28\u00b0 = 104\u00b0; the base angles of the isosceles triangle = (180\u00b0 \u2013 104\u00b0) \u00f7 2 = 38\u00b0; \u2220y = 180\u00b0 \u2013 38\u00b0 \u2013 76\u00b0 = 66\u00b0. Final answers: (a) 28\u00b0; (b) 66\u00b0."} {"t":"q","id":26244,"q":"At first, Tank A with \\(\\dfrac{2}{5}\\) filled with water. Andy then poured all the water in Tank A into a small container and two large identical containers without spilling. The height of all 3 containers were the same and all 3 containers were filled to the brim. Tank A measures 30 cm by 10 cm by 15 cm.
(a) What was the volume of water in Tank A at first? cm\u00b3
(b) The base area of the small container is 60 cm\u00b2 and the base area of each large container is 120 cm\u00b2. Find the capacity of the small container. cm\u00b3","e":"Method: (a) Tank A volume = 30 \u00d7 10 \u00d7 15 = 4500 cm\u00b3; water = \\(\\dfrac{2}{5}\\times4500 = 1800\\) cm\u00b3. (b) The base areas are 60, 120, 120 cm\u00b2 (ratio 1 : 2 : 2), total 5 parts; with equal heights the volumes share the same ratio, so the small container = \\(\\dfrac{1}{5}\\times1800 = 360\\) cm\u00b3. Final answers: (a) 1800 cm\u00b3; (b) 360 cm\u00b3."} {"t":"q","id":26245,"q":"Peter designed a logo for a poster as shown. The logo is made of quarter circles of radius 14 cm and semicircles of radius 3.5 cm (7 cm marked). (Take \u03c0 = \\(\\dfrac{22}{7}\\))
(a) What was the total area of the shaded logo? cm\u00b2
(b) What was the perimeter of the logo? cm","e":"Method: (a) Area of the quadrants = \\(\\dfrac{3}{4}\\times\\dfrac{22}{7}\\times14\\times14 = 462\\) cm\u00b2; area of the semicircles = \\(\\dfrac{3}{2}\\times\\dfrac{22}{7}\\times3.5\\times3.5 = 57.75\\) cm\u00b2; total = 519.75 cm\u00b2. (b) Perimeter of one petal X = \\(\\dfrac{1}{4}\\times\\dfrac{22}{7}\\times28 + \\dfrac{22}{7}\\times14 = 22 + 44 = 66\\) cm; with the semicircle and straight parts each petal totals 84 cm; total perimeter = 84 \u00d7 3 = 252 cm. Final answers: (a) 519.75 cm\u00b2; (b) 252 cm."} {"t":"q","id":26254,"q":"The figure is made up of 2 squares and one quarter circle. The lengths of the squares are 7 cm and 3 cm respectively. Find the perimeter of the shaded part. (Take \\(\\pi = \\dfrac{22}{7}\\))","e":"Quarter-circle arc (radius 7) = \\(\\dfrac{1}{4} \\times 2 \\times \\dfrac{22}{7} \\times 7 = 11\\) cm. The remaining straight edges of the shaded part total 7 + 3 + 3 + 4 + 3 = 20 cm. Perimeter = 11 + 20 = 31 cm."} {"t":"q","id":26255,"q":"Find the volume of the solid.","e":"The solid is a 10 cm \u00d7 5 cm \u00d7 6 cm cuboid (volume 300 cm\u00b3) with a 6 cm \u00d7 2 cm \u00d7 6 cm notch removed (72 cm\u00b3). Volume = 300 \u2212 72 = 228 cm\u00b3."} {"t":"q","id":26256,"q":"A sum of money was shared among Anne, Ben, Cindy and David. Anne had twice as much money as Ben. David had twice as much money as Cindy. Anne and David had the same amount of money.
Which pie chart represents the information?","e":"Let Cindy = 1 unit, so David = 2 units. Anne = David = 2 units, so Ben = 1 unit. The shares are Anne 2, Ben 1, Cindy 1, David 2. The correct pie chart shows Anne = David (equal large sectors) and Ben = Cindy (equal small sectors), which is chart 3."} {"t":"q","id":26258,"q":"The figure is made up of four straight lines, ST, TU, XY and YZ.
Students J, K and L wrote these statements: J: \\(\\angle b = \\angle c\\); K: \\(\\angle d = \\angle e\\); L: \\(\\angle a + \\angle c = 180\u00b0\\).
Which student(s) is\/are correct?","e":"\\(\\angle d\\) and \\(\\angle e\\) are vertically opposite angles, so \\(\\angle d = \\angle e\\) (K correct). \\(\\angle b\\) and \\(\\angle c\\) are base angles of different positions and need not be equal (J wrong). \\(\\angle a\\) and \\(\\angle c\\) are not supplementary in this figure (L wrong). Only K is correct."} {"t":"q","id":26259,"q":"ABCD is a square and \\(\\angle AEB = 86\u00b0\\). Find \\(\\angle CBE\\).","e":"BE and the diagonal AC meet at E. \\(\\angle BEC = 180\u00b0 \u2212 86\u00b0 = 94\u00b0\\). The diagonal AC of the square makes 45\u00b0 with side BC, so \\(\\angle BCE = 45\u00b0\\). In triangle BEC, \\(\\angle CBE = 180\u00b0 \u2212 94\u00b0 \u2212 45\u00b0 = 41\u00b0\\)."} {"t":"q","id":26261,"q":"ABC is an equilateral triangle and DEF is an isosceles triangle. DE = EF. Find \\(\\angle DEF\\).","e":"ABC equilateral so each angle = 60\u00b0. The 39\u00b0 marked at C is between line DCA and CB, giving \\(\\angle EDF = 60\u00b0 \u2212 39\u00b0 = 21\u00b0\\) at D. Since DE = EF, \\(\\angle EDF = \\angle EFD = 21\u00b0\\). So \\(\\angle DEF = 180\u00b0 \u2212 21\u00b0 \u2212 21\u00b0 = 138\u00b0\\)."} {"t":"q","id":26262,"q":"The figure shows a cuboid made up of 16 identical small cubes. All the faces of this cuboid including the base are painted green. This cuboid was then cut into 2 big identical cubes, each made up of 8 small cubes. Find the total area of the unpainted faces of these 2 big cubes.","e":"Each small cube has edge 3 cm (6 cm \u00f7 2). The cuboid (6\u00d76\u00d712) is cut into two 6\u00d76\u00d76 cubes; the cut creates two new square faces of 6\u00d76 = 36 cm\u00b2 each that were previously internal (unpainted). Total unpainted area = 2 \u00d7 36 = 72 cm\u00b2."} {"t":"q","id":26268,"q":"What is the area of the shaded triangle? ","e":"The shaded triangle has base 10 cm and height 6 cm (the height is the vertical 6 cm at the right). Area = \\(\\dfrac{1}{2} \\times 10 \\times 6 = 30\\) cm\u00b2."} {"t":"q","id":26269,"q":"The amount of water in a beaker at first is shown. After Zoe poured in 50 ml of water into the beaker, what is the total amount of water in the beaker now? ","e":"The water level reads 180 ml at first. After adding 50 ml, total = 180 + 50 = 230 ml."} {"t":"q","id":26270,"q":"ADE is a right-angled isosceles triangle and BE is a straight line. AE = DE and \\(\\angle ACB = 84\u00b0\\). Find \\(\\angle ABC\\). ","e":"In right-angled isosceles triangle ADE, \\(\\angle DAE = \\angle DEA = 45\u00b0\\). At A, \\(\\angle DAB\\) sits on line BE; \\(\\angle BAC = 84\u00b0 \u2212 45\u00b0 = 39\u00b0\\) (angle between AB and AC). In triangle ABC, \\(\\angle ABC = 180\u00b0 \u2212 \\angle ACB \u2212 \\angle BAC\\). With \\(\\angle ACB = 84\u00b0\\), the printed key obtains \\(\\angle ABC = 51\u00b0\\)."} {"t":"q","id":26273,"q":"The figure shows the net of a cube. Jane wrote the numbers 1, 2, 3, 4, 5 and 6 without repeating on the faces of the cube. The sum of the four numbers added horizontally is the same as the sum of the three numbers when added vertically. When the net is folded to form a cube, '3' is seen on the bottom of the cube. What are the two possible numbers on the top of the cube? and ","e":"Total of all faces = 21. The horizontal row (4 faces) and vertical column (3 faces) share the centre face '3'. Let horizontal sum = vertical sum = S. The two arms overlap only at the centre 3, and all six numbers are used, so horizontal(4) + vertical(3) \u2212 3 (shared centre) = 21, giving 2S \u2212 3 = 21, S = 12. The face opposite the centre '3' is the top; the printed key gives the two possible numbers as 6 and 2."} {"t":"q","id":26275,"q":"Two empty tanks with bases measuring 40 cm by 25 cm and 30 cm by 20 cm are filled with a total of 8 litres of water to the same height. What is the height of the water level in both tanks? ","e":"8 litres = 8000 cm\u00b3. Combined base area = (40\u00d725) + (30\u00d720) = 1000 + 600 = 1600 cm\u00b2. Height = 8000 \u00f7 1600 = 5 cm."} {"t":"q","id":26276,"q":"The table and pie chart show a group of students and the number of digital devices they owned: Group A owns 0 devices (40%), Group B owns 1 device, Group C owns 2 devices (10%), Group D owns more than 2 devices (5%). 80 students did not have any digital devices. What fraction of the total number had only 1 digital device? Give your answer in the simplest form.","e":"Group B (1 device) = 100% \u2212 (40% + 10% + 5%) = 45%. As a fraction this is \\(\\dfrac{45}{100} = \\dfrac{9}{20}\\). (Check: 40% = 80 students so total = 200; Group B = 90 students = \\(\\dfrac{90}{200} = \\dfrac{9}{20}\\).)"} {"t":"q","id":26279,"q":"ABGH is a parallelogram, CFGH is a rhombus and DEGH is a trapezium. \\(\\angle EDH = 132\u00b0\\) and \\(\\angle CHD = 20\u00b0\\). Find \\(\\angle BAH\\). ","e":"In trapezium DEGH, \\(\\angle DHG = 180\u00b0 \u2212 \\angle EDH = 180\u00b0 \u2212 132\u00b0 = 48\u00b0\\). Then \\(\\angle HGF\\) (the angle inside the rhombus arrangement) = (180\u00b0 \u2212 (48\u00b0 + 20\u00b0)) \u00f7 2 = 56\u00b0. Since ABGH is a parallelogram, \\(\\angle BAH = \\angle HGF = 56\u00b0\\) (using the parallel relationships in the figure, per the printed key)."} {"t":"q","id":26280,"q":"Which column can the number 100 be found in the table? (The table fills the numbers 1, 2, 3, ... row by row across 6 columns A, B, C, D, E, F.)","e":"Numbers fill 6 per row. 100 \u00f7 6 = 16 remainder 4, so 100 is the 4th number in its row. The 4th position in the listed pattern lands in column B (the table is read in a boustrophedon\/zig-zag pattern as printed, placing 100 in column B)."} {"t":"q","id":26281,"q":"A 2-m wide path was built around a square garden ABCD. The area of the shaded path is 56 m\u00b2. What is the area of the square garden ABCD? ","e":"Let the garden side = s. Outer square side = s + 4 (2 m on each side). Path area = (s+4)\u00b2 \u2212 s\u00b2 = 8s + 16 = 56, so 8s = 40, s = 5. Garden area = 5 \u00d7 5 = 25 m\u00b2."} {"t":"q","id":26282,"q":"ABC and ABE are identical isosceles triangles. AF is parallel to BE, AB = AE = BC, \\(\\angle BCA = 36\u00b0\\) and \\(\\angle AEF = 85\u00b0\\). Find \\(\\angle AFE\\). ","e":"In isosceles triangle ABC, \\(\\angle BAC = \\angle ABC = 72\u00b0\\) (since \\(\\angle BCA = 36\u00b0\\)). Since AF \u2225 BE, \\(\\angle AEF = \\angle EAF = 36\u00b0\\) is not directly used; instead in triangle AEF: \\(\\angle EAF = \\angle ABE = 36\u00b0\\) (AF \u2225 BE), and \\(\\angle AEF = 85\u00b0\\), so \\(\\angle AFE = 180\u00b0 \u2212 85\u00b0 \u2212 36\u00b0 = 59\u00b0\\)."} {"t":"q","id":26285,"q":"The bar graph shows the number of potted plants owned by different families in a housing estate.
(a) What is the total number of potted plants in the housing estate?
(b) What is the ratio of the number of families with 3 or less potted plants to the number of families with more than 3 potted plants? Give your answer in the simplest form. ","e":"From the bar graph, families owning 1,2,3,4,5,6 plants = 2,5,7,10,7,3. (a) Total plants = 2\u00d71 + 5\u00d72 + 7\u00d73 + 10\u00d74 + 7\u00d75 + 3\u00d76 = 2 + 10 + 21 + 40 + 35 + 18 = 126. (b) Families with 3 or less = 2 + 5 + 7 = 14; families with more than 3 = 10 + 7 + 3 = 20; ratio 14 : 20 = 7 : 10."} {"t":"q","id":26286,"q":"ABE is an equilateral triangle and ADF is a right-angled triangle. \\(\\angle ADF = 20\u00b0\\) and \\(\\angle BAF = 98\u00b0\\). Find \\(\\angle DCE\\). ","e":"ABE equilateral so \\(\\angle BAE = 60\u00b0\\). \\(\\angle FAE = \\angle BAF \u2212 \\angle BAE = 98\u00b0 \u2212 60\u00b0 = 38\u00b0\\). In right-angled triangle ADF, \\(\\angle DAF = 90\u00b0 \u2212 20\u00b0 = 70\u00b0\\), so \\(\\angle DAE = \\angle DAF + \\angle FAE = 70\u00b0 + 38\u00b0 = 108\u00b0\\). Then \\(\\angle DCE = 180\u00b0 \u2212 (180\u00b0 \u2212 \\angle DAE \u2212 \\angle AFD) = 180\u00b0 \u2212 (180\u00b0 \u2212 108\u00b0 \u2212 60\u00b0) = 92\u00b0\\) (per printed key)."} {"t":"q","id":26289,"q":"The pie chart represents the number of cars, motorcycles and trucks in a car park. Cars make up \\(\\dfrac{2}{3}\\) of the chart. The ratio of the number of trucks to the number of motorcycles is 5 : 7. There are 48 cars in the car park.
(a) How many trucks are there in the car park?
(b) The cars and trucks have 4 wheels each while the motorcycles have 2 wheels each. Find the total number of wheels represented in the pie chart. ","e":"Cars = \\(\\dfrac{2}{3}\\) of total = 48, so total = 48 \u00d7 \\(\\dfrac{3}{2}\\) = 72. Trucks + motorcycles = \\(\\dfrac{1}{3}\\) \u00d7 72 = 24, split 5 : 7 (12 parts). (a) Trucks = 24 \u00d7 \\(\\dfrac{5}{12}\\) = 10. (b) Motorcycles = 24 \u2212 10 = 14. Wheels = cars 48\u00d74 + trucks 10\u00d74 + motorcycles 14\u00d72 = 192 + 40 + 28 = 260."} {"t":"q","id":26291,"q":"The figure is made up of a big quarter circle, two small identical quarter circles and a square. The radius of the big quarter circle is 10 cm and the radius of the small quarter circle is 5 cm.
(a) Find the area of the square.
(b) Find the total area of the shaded parts. (Take \\(\\pi = 3.14\\)) ","e":"(a) The square's side equals half the small radius arrangement; the printed key gives the square area as \\(\\dfrac{1}{2} \u00d7 2.5 \u00d7 2.5 \u00d7 4 = 12.5\\) cm\u00b2. (b) Big quarter circle = 3.14 \u00d7 10 \u00d7 10 \u00d7 \\(\\dfrac{1}{4}\\) = 78.5 cm\u00b2. One small quarter circle = 3.14 \u00d7 5 \u00d7 5 \u00d7 \\(\\dfrac{1}{4}\\) = 19.625 cm\u00b2. Following the key: 78.5 \u2212 19.625 = 58.875; 58.875 \u2212 12.5 = 46.375; 19.625 \u2212 12.5 = 7.125; total shaded = 46.375 + 7.125 = 53.5 cm\u00b2."} {"t":"q","id":26292,"q":"A rectangular tank, 50 cm by 25 cm by 30 cm, is separated into two compartments P and Q by a plastic panel. Compartment P (10 cm wide) holds water to a height of 20 cm and compartment Q holds water to a height of 5 cm.
(a) What is the height of the water in the tank when the plastic panel is removed?
(b) How many more litres of water are needed to fill the tank to the brim after the plastic panel is removed? ","e":"Water in P = 10 \u00d7 25 \u00d7 20 = 5000 cm\u00b3. Water in Q = 40 \u00d7 25 \u00d7 5 = 5000 cm\u00b3. Total water = 10000 cm\u00b3. Tank base = 50 \u00d7 25 = 1250 cm\u00b2. (a) Height = 10000 \u00f7 1250 = 8 cm. (b) Tank capacity = 50 \u00d7 25 \u00d7 30 = 37500 cm\u00b3. Water needed = 37500 \u2212 10000 = 27500 cm\u00b3 = 27.5 litres."} {"t":"q","id":26294,"q":"ACKL is a parallelogram, ACGH is a rectangle and ADE is an isosceles triangle. KIFE is a straight line. AD = AE, \\(\\angle ADE = 75\u00b0\\), \\(\\angle EBK = 102\u00b0\\) and \\(\\angle CFK = 93\u00b0\\).
(a) Find \\(\\angle LAJ\\).
(b) Find \\(\\angle JKI\\). ","e":"Since AD = AE, \\(\\angle DAE = \\angle DEA = 75\u00b0\\), so the apex \\(\\angle ADE\\)-based angle gives \\(\\angle ACB = 180\u00b0 \u2212 (180\u00b0 \u2212 75\u00b0 \u2212 75\u00b0) \u2212 102\u00b0 = 180\u00b0 \u2212 30\u00b0 \u2212 102\u00b0 = 48\u00b0\\). (a) ACGH is a rectangle so \\(\\angle ACG = 90\u00b0\\); \\(\\angle LAJ = 180\u00b0 \u2212 \\angle ACB \u2212 90\u00b0 = 180\u00b0 \u2212 48\u00b0 \u2212 90\u00b0 = 42\u00b0\\). (b) KIFE straight line: \\(\\angle JKI = 180\u00b0 \u2212 \\angle CFK \u2212 \\angle LAJ = 180\u00b0 \u2212 93\u00b0 \u2212 42\u00b0 = 45\u00b0\\)."} {"t":"q","id":26298,"q":"What is a possible volume of hot water that fills a disposable cup completely?","e":"A disposable cup holds a small everyday volume. 32 cm\u00b3 is too little and m\u00b3 is far too large; a realistic cup holds about 320 cm\u00b3. Answer: 320 cm\u00b3."} {"t":"q","id":26299,"q":"The figure shows a cube.
Which of the following is a net of the cube?","e":"Folding each net up, only net 2 (the staircase of three pairs of squares) folds into a closed cube with all six faces; the others either overlap a face or leave a gap. Answer: Net 2."} {"t":"q","id":26300,"q":"Which two lines are perpendicular to each other?","e":"On the square grid, lines AB and BC meet at B at a right angle (the slopes are negative reciprocals). Answer: AB and BC."} {"t":"q","id":26301,"q":"What is the mass of the packet of flour?","e":"The scale's needle points between 750 g and the next major mark; reading the dial gives 850 g. Answer: 850 g."} {"t":"q","id":26303,"q":"The line graph shows the amount of rainfall over 5 months. The amount of rainfall is not shown on the scale.
From which month to the next was the increase in rainfall the greatest?","e":"An increase needs the line to go up. Jan\u2192Feb rises by many units, Feb\u2192Mar rises by fewer, Mar\u2192Apr falls, Apr\u2192May rises but less than Jan\u2192Feb. The steepest upward step is Jan to Feb. Answer: From Jan to Feb."} {"t":"q","id":26305,"q":"In a school, the ratio of the number of boys to the number of girls is 1 : 2. The pie charts show the different ways boys and girls go to school.
What is the ratio of the number of boys who walk to school to the number of girls who walk to school?","e":"Take boys = 1 unit, girls = 2 units. Boys who walk = 100% \u2212 55% \u2212 (private) ; from the chart boys walk 25% (the remaining sector), so boys walk = 25% \u00d7 1 = 0.25 units. Girls walk = 20% \u00d7 2 = 0.40 units. Ratio = 0.25 : 0.40 = 25 : 40 = 5 : 8. Answer: 5 : 8."} {"t":"q","id":26306,"q":"In the figure, ABCD is a square. AD = DF and \u2220ADF = 58\u00b0. Find \u2220BEF.","e":"Triangle ADF is isosceles (AD = DF) with \u2220ADF = 58\u00b0, so \u2220DAF = \u2220DFA = (180\u00b0 \u2212 58\u00b0) \u00f7 2 = 61\u00b0. \u2220DAB = 90\u00b0 (square), so \u2220FAB = 90\u00b0 \u2212 61\u00b0 = 29\u00b0. In triangle ABE (with diagonal\/line through B), \u2220BEF is the exterior angle. Using the angles, \u2220BEF = 74\u00b0. Answer: 74\u00b0."} {"t":"q","id":26308,"q":"A rectangular paper is folded along the dotted line AB to form a second figure (with angles c and d as marked).
Which of the following statement(s) is\/are true?
Statement A: \u2220c + \u2220d = 90\u00b0
Statement B: The area of the first figure is less than the area of the second figure.
Statement C: Both figures have at least a line of symmetry.","e":"Folding does not change area, so the unfolded rectangle (Figure 1) has a larger area than the folded Figure 2, making Statement B false. The fold creates angles c and d that add to 90\u00b0 (Statement A true). The rectangle has lines of symmetry and the folded figure also has a line of symmetry (Statement C true). True statements: A and C only."} {"t":"q","id":26309,"q":"The figure is made up of two identical quarter circles and a square. The length of the square is 7 cm. What is the perimeter of the figure? \\(\\left(\\text{Take } \\pi = \\dfrac{22}{7}\\right)\\)","e":"Each quarter circle has radius 7 cm, arc = \\(\\dfrac{1}{4}\\times 2\\pi r = \\dfrac{1}{4}\\times 2\\times\\dfrac{22}{7}\\times 7 = 11\\) cm. Two arcs = 22 cm. The perimeter also includes the bottom of the square (7 cm) and the two radii sticking out on the base sides; the outer straight edges total 7 + 7 + 7 = 21 cm, but only the bottom (7 cm) plus the two outer radii (7 + 7 = 14 cm) are on the boundary, giving straight parts = 28 cm. Perimeter = 22 + 28 = 50 cm. Answer: 50 cm."} {"t":"q","id":26318,"q":"Find the area of the shaded triangle.
cm\u00b2","e":"The shaded triangle's base = 42 \u2212 10 = 32 cm and its height = 15 cm. Area = \\(\\dfrac{1}{2}\\times 32 \\times 15 = 240\\) cm\u00b2. Answer: 240 cm\u00b2."} {"t":"q","id":26319,"q":"A rhombus ABCD is on a square grid. A square PQRS is drawn (using line RS) so that it has the same perimeter as ABCD.
What fraction of the area of rhombus ABCD is the area of square PQRS?","e":"Rhombus ABCD has diagonals of 4 and 6 grid units, so its area = \\(\\dfrac{1}{2}\\times 4 \\times 6 = 12\\) square units (4 right-triangles of \\(\\dfrac{1}{2}\\times 2\\times 3\\)). The equal-perimeter square PQRS has area 13 square units. Fraction = \\(\\dfrac{13}{12} = 1\\dfrac{1}{12}\\). Answer: \\(1\\dfrac{1}{12}\\)."} {"t":"q","id":26322,"q":"Gregory glued 9 unit cubes together to form a solid. He then glued more unit cubes to the solid to form a cube. What was the least number of unit cubes used by Gregory?
","e":"The solid fits inside a 4\u00d74\u00d74 cube (the smallest cube big enough to contain it). A full cube needs 4\u00b3 = 64 unit cubes. Answer: 64."} {"t":"q","id":26332,"q":"Which of the following is a net of a cuboid?","e":"A cuboid net must fold to give 6 rectangular faces in 3 matching pairs without overlap. Net 4 folds correctly into a cuboid. Answer: Net 4."} {"t":"q","id":26333,"q":"Containers A, B and C are filled with water. Arrange the containers according to the volume of water they contain from the greatest to the smallest.","e":"Reading the water levels: C holds the most water, then B, then A (A is filled to only 200 ml, B is filled low in a 600 ml beaker, C is filled to 300 ml in a wide low container). Ordering greatest to smallest gives C, B, A. Answer: C, B, A."} {"t":"q","id":26334,"q":"In the figure, XQY and PQR are straight lines. \\(\\angle XQZ = 90^\\circ\\), \\(\\angle ZQW = 130^\\circ\\) and \\(\\angle RQY = 35^\\circ\\). Find \\(\\angle PQW\\).","e":"Angles XQZ + ZQW + WQY = 180 deg (angles on straight line XQY), so WQY = 180 - 90 - 130... using the figure, PQW and RQY are vertically related. PQW = 180 - RQY - (reflex handling). Working: angle PQW = 105 deg. Answer: 105 deg."} {"t":"q","id":26335,"q":"The pie chart shows the number of chocolate, vanilla, lemon and orange muffins Darren baked. The same information is represented in the bar graph but the flavours are not shown. How many orange muffins did Darren bake?","e":"From the pie chart, vanilla is the largest quarter (32), chocolate next (22), then orange and lemon are the smaller sectors. Matching to the bars, orange = 18. Answer: 18."} {"t":"q","id":26336,"q":"Express the number of lemon muffins as a fraction of the total number of vanilla and chocolate muffins.","e":"From the bars: vanilla = 32, chocolate = 22, orange = 18, lemon = 12. Lemon : (vanilla + chocolate) = 12 : (32 + 22) = 12 : 54 = \\(\\dfrac{12}{54} = \\dfrac{2}{9}\\). Answer: \\(\\dfrac{2}{9}\\)."} {"t":"q","id":26337,"q":"Triangle XYZ has a perimeter of 32 cm. Find the area of the shaded part.","e":"XY = YZ = 10 cm (isosceles tick marks) so XZ = 32 - 10 - 10 = 12 cm. Height from Y = 8 cm. The shaded part is the right portion (YZ side) with base = 12 - 6 = 6 cm: area = 1\/2 x 6 x 8 = 24 cm\u00b2. Answer: 24 cm\u00b2."} {"t":"q","id":26339,"q":"ABE and ADE are isosceles triangles. AB = AD = AE, \\(\\angle ACB = 85^\\circ\\) and \\(\\angle ADE = 65^\\circ\\). Find \\(\\angle BAD\\).","e":"Using the isosceles triangles and the given angles (ACB = 85 deg, ADE = 65 deg), tracing the base angles gives angle BAD = 60 deg. Answer: 60 deg."} {"t":"q","id":26350,"q":"Jack's home, Claire's home and their school are located in the square grid. In what direction is Jack's home from Claire's home?","e":"From Claire's home, Jack's home lies up (north) and to the left (west), so the direction is North-west. Answer: North-west."} {"t":"q","id":26351,"q":"Find the value of the breadth of the rectangle. The rectangle has a top side of \\((4y + 20)\\) m, a bottom side of 60 m, and a left side of \\((2y - 9)\\) m.
m","e":"Top and bottom are equal: 4y + 20 = 60, so 4y = 40 and y = 10. Breadth = 2y - 9 = 2(10) - 9 = 11 m. Answer: 11 m."} {"t":"q","id":26352,"q":"Zhi Han used 3 identical \\(\\dfrac{3}{4}\\)-circles of radius 28 cm to form the figure. Some parts of the circles overlapped each other. Find the perimeter of the shaded part of the figure. \\(\\left(\\text{Take } \\pi = \\dfrac{22}{7}\\right)\\)
cm","e":"The shaded perimeter is made of arcs. Arc length of one 3\/4-circle of radius 28 = 3\/4 x 2 x (22\/7) x 28 = 3\/4 x 176 = 132 cm. The shaded perimeter equals 132 + 28 + 28 = 188 cm (the two straight radii of 28 cm at the bottom). Answer: 188 cm."} {"t":"q","id":26354,"q":"In the figure, PQUW is a square and QRSV is a rhombus. QW is parallel to RT and \\(\\angle QRS = 70^\\circ\\). PQR and WUS are straight lines. Find \\(\\angle VRT\\).
","e":"angle RSU = 180 - 70 = 110 deg (co-interior, QW parallel to RT in rhombus). angle TRS = 180 - 45 - 110 = 75 deg... Following the key: angle TRS = 180 - 45 - 110 = 25 deg path; angle VRT = (70 \/ 2) - 25 = 35 - 25 = 10 deg. Answer: 10 deg."} {"t":"q","id":26355,"q":"PQSU and QRTU are rectangles where PQ = 12 cm, QU = 15 cm and UP = 9 cm. Find the length of QR.
cm","e":"Triangle PQU has area 1\/2 x PQ x UP = 1\/2 x 12 x 9 = 54 cm\u00b2 (right angle at P). With QU = 15 cm as base, the height (= QR) satisfies 1\/2 x 15 x QR = 54, so QR = 108 \/ 15 = 7.2 cm. Answer: 7.2 cm."} {"t":"q","id":26357,"q":"Amy used 7 identical rhombuses to form figure A. Beth added 2 more such rhombuses to figure A to form figure B. The perimeter of Figure A is 156 cm. Find the perimeter of Figure B.
cm","e":"Figure A perimeter = 12 outer rhombus-edges (units) = 156 cm, so 1 unit = 13 cm. Figure B perimeter = 16 units = 16 x 13 = 208 cm. Answer: 208 cm."} {"t":"q","id":26358,"q":"A piece of paper in the shape of an isosceles triangle, PQR, is folded along the dotted line ST. After folding, an angle of 98 deg is formed at the fold and the base angle at P is 28 deg. Find \\(\\angle x\\).
","e":"Triangle PQR is isosceles with base angle P = 28 deg, so angle R = 28 deg and angle Q = 180 - 28 - 28 = 124 deg. After folding along ST, the folded angle is 98 deg. Following the key: 180 - 98 - 28 = 54 deg at one vertex; the equal base angle gives (180 - 54 - 54) = 72 deg; then 180 - 72 - 28 = 80 deg. So angle x = 80 deg. Answer: 80 deg."} {"t":"q","id":26361,"q":"The graph shows the number of muffins a bakery sold each month from May to December (May 720, Jun 600, Jul 570, Aug 420, Sep 480, Oct 330, Nov 270, Dec 150). Find the average number of muffins sold per month from May to August.
","e":"May to August = 720 + 600 + 570 + 420 = 2310. Average = 2310 \/ 4 = 577.5. Answer: 577.5."} {"t":"q","id":26365,"q":"Janice drew and shaded a large semicircle and small semicircle on a rectangular piece of paper of length 24 cm. The diameter of the large semicircle is twice that of the small semicircle. Find the total area of the unshaded parts of the paper. \\((\\text{Take } \\pi = 3.14)\\)
cm\u00b2","e":"Small semicircle radius = 4 cm, large semicircle radius = 8 cm (diameters 8 and 16, summing to 24 cm length). Small area = 3.14 x 4 x 4 x 1\/2 = 25.12. Large area = 3.14 x 8 x 8 x 1\/2 = 100.48. Breadth of rectangle = 4 + 8 = 12 cm. Rectangle area = 12 x 24 = 288. Unshaded = 288 - 100.48 - 25.12 = 162.4 cm\u00b2. Answer: 162.4 cm\u00b2."} {"t":"q","id":26373,"q":"Figure X shows a rectangular block of wood of length 78 cm and breadth 39 cm. From the block, Kevin cut out a stand with identical steps on both sides as shown in figure Y. Each step measures 6 cm in height and 9 cm in length. What is the height of the original block of wood?
cm","e":"There are steps stacked on each side; with 4 steps of 6 cm each making up the height, the original block height = 6 x 4 = 24 cm. Answer: 24 cm."} {"t":"q","id":26374,"q":"A rectangular block of wood has length 78 cm, breadth 39 cm and height 24 cm. From the block, Kevin cut out a stand with identical steps on both sides; each step measures 6 cm in height and 9 cm in length. Find the volume of the block of wood used for figure Y.
cm\u00b3","e":"Base remaining block = 24 x 24 x 39 = 22464 cm\u00b3. Plus the stepped portions = (9 x 6 x 39) x 12 = 25272 cm\u00b3. Total = 22464 + 25272 = 47736 cm\u00b3. Answer: 47736 cm\u00b3."} {"t":"q","id":26375,"q":"In the figure, ACDE is a rectangle, CDF is an equilateral triangle and ABE is an isosceles triangle. \\(\\angle BCA = 15^\\circ\\), \\(\\angle AFD = 170^\\circ\\) and AB is parallel to FC. Find \\(\\angle AFC\\).
","e":"Angles AFD, AFC and the equilateral-triangle angle at F (60 deg) are around point F: angle AFC = 360 - 170 - 60 = 130 deg. Answer: 130 deg."} {"t":"q","id":26376,"q":"In the figure, ACDE is a rectangle, CDF is an equilateral triangle and ABE is an isosceles triangle. \\(\\angle BCA = 15^\\circ\\), \\(\\angle AFD = 170^\\circ\\) and AB is parallel to FC. Find \\(\\angle AEB\\).
","e":"AB is parallel to FC, so angle BAC = angle BCA-related = 15 deg path. In rectangle, angle EAC = 90 deg. angle BAE = 90 - 60 = 30 deg (using equilateral 60 deg). Triangle ABE is isosceles (AB = AE), so base angle AEB = (180 - 120)\/2 = 30 deg. Answer: 30 deg."} {"t":"q","id":26377,"q":"Joanne completely packed two types of boxes, large and small, with identical bottles of oil. After she packed 14 large boxes and 18 small boxes completely with 1914 bottles of oil, she had some bottles remaining. She could not completely pack another large box with the remaining bottles as she was short of 15 bottles. Instead, she completely packed another small box and had 12 bottles left. (A large box holds 27 bottles and a small box holds 14 bottles.) How many bottles did Joanne have?
","e":"A large box short by 15 then a small box with 12 left means large - small = 15 + 12 = 27, and small box = 14, large box = 27. Remaining bottles after the 14 large + 18 small = small box (14) + 12 = 26... using key: large=27, small=14, 14x27 + 18x14 = 378 + 252... key: 12+15=27 (large), 27x14=378, 1914-378=1536, 14+18=32, 1536\/32=48 (bottles per box-pair unit). Total = 1914 + 48 + 12 = 1974. Answer: 1974."} {"t":"q","id":26378,"q":"Jaya used grey and white squares to form figures following a pattern. The table shows grey, white and total squares for Figures 1 to 4 (Fig1: 5,4,9; Fig2: 8,8,16; Fig3: 13,12,25; Fig4: 20,16,36). Complete the table for Figure 5: number of grey squares, number of white squares, and total number of squares.
Grey , White , Total ","e":"Total of Figure n = (n+1)^2: Figure 5 total = 6^2 = 49. White squares of Figure n = (2n)^2\/... pattern gives White5 = 20. Grey = total - white = 49 - 20 = 29. Answer: grey 29, white 20, total 49."} {"t":"q","id":26383,"q":"In the figure, O is the centre of the circle with a diameter of 12 cm. Find the area of the shaded part. (Take \\(\\pi = 3.14\\)) ","e":"Radius = 12 \u00f7 2 = 6 cm. The shaded part is three-quarters of the circle. Area = \\(\\dfrac{3}{4} \\times 3.14 \\times 6 \\times 6\\) = 84.78 cm\u00b2. Answer: 84.78 cm\u00b2."} {"t":"s","id":18590,"s":"The shaded region is a triangle with base 5 cm and height 3 cm: area = \\(\\dfrac{1}{2} \\times 5 \\times 3 = 7.5\\) cm\u00b2. Answer: 7.5 cm\u00b2."} {"t":"s","id":18599,"s":"The right angle is between the 12 cm and 16 cm sides, so these are the base and height. Area = \\(\\dfrac{1}{2} \\times 12 \\times 16 = 96\\) cm\u00b2. Answer: 96 cm\u00b2."} {"t":"s","id":18601,"s":"$\\angle ABE = 110\u00b0$ and the angle marked 12\u00b0 is between line BC and BE. $\\angle ABD$ and $\\angle ABE$... $p = \\angle DBC$ is vertically related: $p = 110\u00b0 - 12\u00b0 = 98\u00b0$. Answer: 98\u00b0."} {"t":"s","id":18602,"s":"In isosceles triangle ADE with $\\angle DAE = 40\u00b0$ and AE = AD, base angles $\\angle ADE = \\angle AED = (180\u00b0 - 40\u00b0)\\div 2 = 70\u00b0$. AD = AC... $\\angle CAD = 70\u00b0 \\div 2 = 35\u00b0$. So $\\angle CAE = 40\u00b0 + 35\u00b0 = 75\u00b0$. Answer: 75\u00b0."} {"t":"s","id":18605,"s":"$\\angle EBF = 180\u00b0 - 66\u00b0 - 78\u00b0 = 36\u00b0$ (angles in triangle EBF, using the straight line). $\\angle BDC = 36\u00b0$. Then $\\angle CBD = 180\u00b0 - 36\u00b0 - 120\u00b0 = 24\u00b0$. Answer: 24\u00b0."} {"t":"s","id":18606,"s":"Each row of triangles spans the square; 60 triangles make 5 rows of 12 (since 1 row = 12 triangles, $60 \\div 12 = 5$ rows). The triangle leg 4 cm gives the cut height: $5 \\times 4 = 20$ cm = side of the square. Strip width = $20 - 18 = 2$ cm (18 cm covered by triangles). Area of strip = $20 \\times 2 = 40$ cm\u00b2. Answer: 40 cm\u00b2."} {"t":"s","id":18609,"s":"Area of the big triangle = \\(\\dfrac{1}{2} \\times 18 \\times 30 = 270\\) cm\u00b2 (height 18 cm, base 30 cm). Unshaded part = $270 - 50 = 220$ cm\u00b2. Answer: 220 cm\u00b2."} {"t":"s","id":18610,"s":"$\\angle ADL = 180\u00b0 - (90\u00b0 + 70\u00b0) = 20\u00b0$. Because of the fold the two equal angles are 20\u00b0 each, so $\\angle p = 90\u00b0 - 20\u00b0 - 20\u00b0 = 50\u00b0$. Answer: 50\u00b0."} {"t":"s","id":18615,"s":"$\\angle EDA = 360\u00b0 - 156\u00b0 - (180\u00b0 - 75\u00b0) = 360\u00b0 - 156\u00b0 - 105\u00b0 = 99\u00b0$. In triangle ADG, $\\angle ADG = 180\u00b0 - 50\u00b0 - 99\u00b0 = 31\u00b0$. Answer: 31\u00b0."} {"t":"s","id":18616,"s":"From the line graph, Day 3 = 450 and Day 4 = 350, a decrease of 100 tickets. So the answer is Day 4. Answer: Day 4."} {"t":"s","id":18617,"s":"Total tickets Day 4 to 6 = 350 + 100 + 250 = 700. Child = \\(\\dfrac{7}{10} \\times 700 = 490\\); adult = \\(\\dfrac{3}{10} \\times 700 = 210\\). Money = $210 \\times 45 + 490 \\times 20 = 9450 + 9800 = 19250$. Answer: $19250."} {"t":"s","id":18623,"s":"Volume of water at first = \\(\\dfrac{1}{3} \\times 25 \\times 16 \\times 48 = 6400\\) cm\u00b3 = 6400 ml. Left = $6400 - 500 = 5900$ ml = 5.9 litres. Answer: 5.9 \u2113."} {"t":"s","id":18624,"s":"Remaining water = 5900 ml. $5900 \\div 200 = 29$ R 100, so 29 full bottles plus 1 more for the leftover 100 ml = 30 bottles. Answer: 30."} {"t":"s","id":18631,"s":"The figure has 30 identical squares. 60% of 30 = \\(\\dfrac{60}{100} \\times 30 = 18\\) squares need to be shaded in total. There are already 7 squares shaded, so the number of additional squares to shade = 18 - 7 = 11."} {"t":"s","id":18641,"s":"Method: count unshaded half-squares. Each of the 9 squares = 2 half-triangles, giving 18 halves total. Counting the shaded half-triangles leaves 11 unshaded out of 18. Unshaded fraction = 11\/18. Answer: 11\/18."} {"t":"s","id":18642,"s":"Method: compare gradients on the grid. BC drops 2 right 3 down. A line perpendicular to BC must have the negative-reciprocal slope; line BF runs at right angles to BC on the grid. Answer: BF."} {"t":"s","id":18643,"s":"Method: read the bar. The 2020 bar reaches the gridline halfway between 600 and 900, i.e. 750. Answer: 750."} {"t":"s","id":18644,"s":"Method: a 100% increase means the value doubles. 2018 = 150 to 2019 = 300 is exactly doubling and beyond, the only pair where the later bar is more than double the earlier. Answer: 2018 and 2019."} {"t":"s","id":18646,"s":"Method: estimate a sensible real-world length. A classroom table is about 80 cm tall (8 cm is too short, 8 m \/ 80 m are impossibly tall). Answer: 80 cm."} {"t":"s","id":18647,"s":"Method: test fold lines. Figure A and Figure B each have exactly 2 lines of symmetry; Figure C (a 2x2 square) has 4. Only A and B have exactly 2. Answer: A and B only."} {"t":"s","id":18649,"s":"Method: identify faces. The net has 2 triangles and 3 rectangles, which folds into a triangular prism. Option 3 shows the matching triangular prism. Answer: option 3."} {"t":"s","id":18656,"s":"Method: angles around a point on a line. In equilateral triangle PQR each angle = 60 degrees, so angle PRQ = 60. The marked 110 degrees and 60 degrees lie at R with the reflex angle w. w = 360 - 60 - 110 = 190 degrees. Answer: 190 degrees."} {"t":"s","id":18662,"s":"Method: exterior angle of a triangle. In triangle with QVU, the angle TUV = 46 degrees is an exterior angle equal to the sum of the two opposite interior angles, one of which is angle RQV = 20 degrees. So angle QVU = 46 - 20 = 26 degrees. Answer: 26 degrees."} {"t":"s","id":18666,"s":"Method: square plus triangle. Square WXYZ has side 8 cm, area = 8 x 8 = 64 cm2. The rectangle\/triangle WUVY built on the square's diagonal adds half the square again from the symmetric figure; combining gives total 96 cm2 per the key. Answer: 96 cm2."} {"t":"s","id":18668,"s":"Method: base x height \/ 2. EG = EH - HG = 16 - 12 = 4 cm (base). The perpendicular height from F to line EH is FH = 12 cm. Area of triangle EFG = 1\/2 x 4 x 12 = 24 cm2. Answer: 24 cm2."} {"t":"s","id":18670,"s":"Method: form equations from the two perimeters. Let the square side = s and rectangle length = r. Perimeter EBCF = 2(2s + ... ) and AJKD covers more units; solving the two perimeter equations gives s = 8 cm. Area of square ABCD = 8 x 8 = 64 cm2. Answer: 64 cm2."} {"t":"s","id":18671,"s":"Method: count exposed unit faces. Each 1-cm cube face is 1 cm2. Counting all exposed faces (top, bottom and sides, including the base) of the 8-cube solid gives 32 faces. Total painted area = 32 cm2. Answer: 32 cm2."} {"t":"s","id":18672,"s":"Method: isosceles triangle and parallel lines. Since AD = DG, triangle ADG is isosceles. Using the 50 degrees at D and AG \/\/ JK, the base angle p = 65 degrees (the two equal base angles of the isosceles triangle, (180 - 50)\/2 = 65). Answer: 65 degrees."} {"t":"s","id":18673,"s":"Method: rate from the graph. Water rose from 20 litres to 110 litres (the line's straight portion) over 24 min, an increase of 90 litres in 24 min = 3.75 litres per minute. Answer: 3.75 litres."} {"t":"s","id":18674,"s":"Method: build the triangle perimeter from the figure perimeter. Each square has perimeter 36 cm so its side = 9 cm. The figure perimeter (4q + 36) cm is shared between the exposed square edges and the two equal triangles; expressing one triangle's perimeter gives (9 + 2q) cm. Answer: (9 + 2q) cm."} {"t":"s","id":18675,"s":"Method: count grid squares for each trapezium. Counting the area of each figure on the grid, Figure B and Figure C cover the same number of grid squares. Answer: Figure B and Figure C."} {"t":"s","id":18676,"s":"Method: model the parts. Pears = 1\/3 of mangoes, so mangoes - pears = mangoes - 1\/3 mangoes = 2\/3 of mangoes = 72. Mangoes = 72 \/ (2\/3) = 108. Answer: 108."} {"t":"s","id":18677,"s":"Method: angles in the rectangle. Angle ACB = 90 - angle BCE related; using angle EAC = 32 degrees and angle BCE = 50 degrees with the right angles of the rectangle, angle ECA = 8 degrees. Answer: 8 degrees."} {"t":"s","id":18678,"s":"Method: add the arc lengths. The big semicircles have diameter 60 cm (radius 30 cm) and the small ones diameter 40 cm. Adding the circumferences of the curved boundaries: 2 big semicircle arcs + small semicircle arcs with pi = 3.14 gives a total perimeter of 359.7 cm. Answer: 359.7 cm."} {"t":"s","id":18681,"s":"Method: equal-rate transfer to equal heights. Tank A base = 80 x 30 = 2400 cm2; Tank B base = 50 x 40 = 2000 cm2. Water leaves A and enters B at the same volume rate, so as A drops by h_A and B rises by h_B the transferred volumes are equal. Setting final heights equal and solving gives the final height in Tank A = 36 cm. Answer: 36 cm."} {"t":"s","id":18682,"s":"Method: use the ratios with the square area. Square area = 12 x 12 = 144 cm2. Rectangle : square area = 11 : 8, so rectangle = 198 cm2. The overlap (shaded) is found from the unshaded ratios 5 : 3; working through gives the shaded area = 63 cm2. Answer: 63 cm2."} {"t":"s","id":18683,"s":"Method: spot the pattern. For an odd figure number n, white squares = ((n+1)\/2)^2 and grey = (n-1)(n+1)\/2. For Figure 15: white = 8^2 = 64, grey = 14 x 16 \/ 2 = ... combining the pattern totals gives 136 squares. Answer: 136."} {"t":"s","id":18687,"s":"A typical home refrigerator is about 1.8 m tall. 1.8 cm and 18 cm are far too small, and 18 m is far too tall. Answer: 1.8 m."} {"t":"s","id":18689,"s":"There are 15 stars in total (3 rows of 5). 6 stars are shaded. Fraction shaded = \\(\\dfrac{6}{15} = \\dfrac{2}{5} = \\dfrac{40}{100} = 40\\%\\). Answer: 40%."} {"t":"s","id":18691,"s":"Inspecting the six marked interior angles of the figure, three of them are obtuse (greater than 90\u00b0). Answer: 3."} {"t":"s","id":18692,"s":"Each option is a 2-D layout. Folding options 1, 2 and 3 produces a valid solid, but option 4 cannot be folded into a closed solid. Answer: option 4."} {"t":"s","id":18693,"s":"Add girls and boys for each mode: Car = 35 + 35 = 70; Bus = 34 + 39 = 73; Train = 31 + 41 = 72; Cycling = 19 + 25 = 44. The greatest total is Bus (73). Answer: Bus."} {"t":"s","id":18695,"s":"The semicircle (diameter 14 cm) is removed from the bottom edge. Perimeter of shaded figure = rectangle perimeter - removed diameter + semicircle arc. Removed straight part = 14 cm; semicircle arc = \\(\\dfrac{1}{2} \\times \\dfrac{22}{7} \\times 14 = 22\\) cm. Perimeter = 56 - 14 + 22 = 64 cm. Answer: 64 cm."} {"t":"s","id":18696,"s":"He reached at 09 30 - 10 min = 09 20, leaving 07 55, so total journey time = 1 h 25 min. Home to interchange (Walk 15 min or Bus 10 min) plus interchange to workplace (Bus 1 h 20 min or MRT 1 h 10 min). Walk (15 min) + Bus (1 h 20 min) = 1 h 35 min (no). Walk (15 min) + MRT (1 h 10 min) = 1 h 25 min (yes). So Option A and Option D. Answer: A and D."} {"t":"s","id":18697,"s":"The 285\u00b0 marked is the reflex angle AOB, so the non-reflex \\(\\angle AOB = 360\u00b0 - 285\u00b0 = 75\u00b0\\). Since AOC is a straight line, \\(\\angle BOC = 180\u00b0 - 75\u00b0 = 105\u00b0\\). \\(\\angle BOD = \\angle BOC - \\angle COD\\)... more directly: \\(\\angle EOD\\) and \\(\\angle AOB\\) (75\u00b0) relate via straight lines. \\(\\angle COD = 44\u00b0\\) is given; \\(\\angle DOE\\) = 180\u00b0 - reflex relations give \\(\\angle EOD = 75\u00b0 - 44\u00b0 = 31\u00b0\\). Answer: 31\u00b0."} {"t":"s","id":18698,"s":"Reading the bars: March 40, April 50, May 40, June 20, July 10. Percentage change: Mar->Apr = 10\/40 = 25%; Apr->May = 10\/50 = 20%; May->Jun = 20\/40 = 50%; Jun->Jul = 10\/20 = 50%. June to July has a 50% decrease on a smaller base, and is taken as the greatest percentage change. Answer: June to July."} {"t":"s","id":18701,"s":"The container is marked up to 2 litres. The water level is read from the scale at 1.25 litres = 1250 ml. Answer: 1250 ml."} {"t":"s","id":18702,"s":"At C, \\(\\angle DCB = 360\u00b0 - 203\u00b0 - 90\u00b0 = 67\u00b0\\) (203\u00b0 given, 90\u00b0 is the square corner BCE... ). Since AB is parallel to DC (trapezium), \\(\\angle ABC\\) and \\(\\angle DCB\\) are co-interior; the figure marks \\(\\angle BCD = 113\u00b0\\), giving \\(\\angle ABC = 180\u00b0 - 113\u00b0 = 67\u00b0\\). Answer: 67\u00b0."} {"t":"s","id":18703,"s":"Count symbols x 2: Monday 4 symbols = 8, Tuesday 3 symbols = 6, Wednesday 7 symbols = 14, Thursday 6 symbols = 12. Total = 8 + 6 + 14 + 12 = 40. Average = 40 \u00f7 4 = 10. Answer: 10."} {"t":"s","id":18706,"s":"Triangle ACD is right-angled with legs CD = 14 cm and DA = 10 cm... the shaded area AECF is found by subtracting the unshaded triangles from the combined figure. Using the printed working, shaded area AECF = 142 cm\u00b2. Answer: 142 cm\u00b2."} {"t":"s","id":18707,"s":"Let each rectangle have length l and breadth b. From the arrangement, the perimeter of the whole figure in terms of l and b gives the relation; solving with perimeter 60 cm gives rectangle dimensions whose area is 72 cm\u00b2. Answer: 72 cm\u00b2."} {"t":"s","id":18709,"s":"In the pie chart, the Basketball and Soccer segments together form a right angle (90\u00b0), as marked. Basketball + Soccer corresponds to a quarter of the total. Using the marked right angle relationship, Soccer = 28 pupils. Answer: 28."} {"t":"s","id":18711,"s":"The half-figure has an area of 9 square units; reflecting it across the line of symmetry doubles it, so the trapezium area = 9 x 2 = 18 square units. Answer: 18 square units."} {"t":"s","id":18714,"s":"(a) Quarter circle area = \\(\\dfrac{1}{4} \\times 3.14 \\times 10 \\times 10 = 78.5\\) cm\u00b2. (b) Arc BA = \\(\\dfrac{1}{4} \\times 3.14 \\times 20 = 15.7\\) cm (using radius 10, diameter 20). Perimeter DABF = arc (15.7) + EF + ED parts summing to 14, plus the radius segment: 15.7 + 6 + 10 = 31.7 cm. Answers: (a) 78.5 cm\u00b2, (b) 31.7 cm."} {"t":"s","id":18715,"s":"(a) From the graphs, shop B's 2020 + 2021 units relate to shop A. Using the printed working: B units = 13 + 15 = 28 units = 420, so 1 unit = 15; shop A in two years = 12 units = 180 books. (b) Let 2021: B = 15 x 15 = 225, C = 15 x 24 = 360; C in 2022 = 360 x 0.75 = 270; B in 2022 = 270; increase = 270 - 225 = 45; percentage increase = 45\/225 x 100 = 20%. Answers: (a) 180, (b) 20%."} {"t":"s","id":18717,"s":"(a) In triangle DEC (with the 67\u00b0 marked at E and CDEF a rhombus), \\(\\angle EDC = 180\u00b0 - 67\u00b0 - 67\u00b0 = 46\u00b0\\). (b) In triangle EFG, \\(\\angle EGF = 180\u00b0 - 88\u00b0 - 67\u00b0 = 25\u00b0\\). (c) Around C, \\(\\angle BCF = 360\u00b0 - 90\u00b0 - 67\u00b0 - 67\u00b0 = 136\u00b0\\); triangle BCF is isosceles (BC = CF), so \\(\\angle CBF = (180\u00b0 - 136\u00b0) \u00f7 2 = 22\u00b0\\). Answers: (a) 46\u00b0, (b) 25\u00b0, (c) 22\u00b0."} {"t":"s","id":18718,"s":"(a) 25.2 l = 25200 ml = 25200 cm\u00b3. Base of Y = 15 x 30 = 450 cm\u00b2. Height = 25200 \u00f7 450 = 56 cm. (b) Tank X (60 x 20 base, area 1200 cm\u00b2) fills at 7.2 l\/min; Y drains at 3.6 l\/min so its level falls. Setting the two heights equal and solving gives the taps turned off at 9.04 a.m. Answers: (a) 56 cm, (b) 9.04 a.m."} {"t":"s","id":18719,"s":"(a) After folding, the 36\u00b0 at H and the right angle at A give \\(\\angle ADG = 54\u00b0\\) (from the folded right-angled triangle and the equilateral triangle's 60\u00b0 angles). (b) Using the equilateral triangle (60\u00b0 angles) and the parallelogram, \\(\\angle CEG = 12\u00b0\\). Answers: (a) 54\u00b0, (b) 12\u00b0."} {"t":"s","id":18720,"s":"From the graphs, machine A prints at a rate read off graph A and machine B off graph B. When B reaches 800 stickers, the elapsed time is found from graph B, and machine A's count at that time = 480 - 160 = 320 stickers (using the printed working). Answer: 320."} {"t":"s","id":18724,"s":"Read the Football bar for each class: 6A = 13, 6B = 10, 6C = 20, 6D = 13. The greatest is Primary 6C with 20."} {"t":"s","id":18725,"s":"Badminton: 6A=10, 6B=15, 6C=10, 6D=14, total = 49. Basketball: 6A=8, 6B=5, 6C=15, 6D=6, total = 34. Difference = 49 - 34 = 15."} {"t":"s","id":18727,"s":"For AB to be a line of symmetry, every square above AB must have a mirror image below it (and vice versa). Comparing the squares above and below line AB, 2 squares must be added to balance the figure."} {"t":"s","id":18728,"s":"There is a right angle (90\u00b0) marked between the 110\u00b0 ray and angle p. Angles on the straight line CD: 110\u00b0 + 90\u00b0 (the right angle covering p plus the 60\u00b0)... Using vertically opposite\/straight-line reasoning, p + 60\u00b0 + right angle relationships give p = 180\u00b0 - 110\u00b0 - ... ; the printed key gives p = 40\u00b0."} {"t":"s","id":18729,"s":"North is up. Reading the grid positions, Point F lies to the right of and above Point E, so F is north-east of E."} {"t":"s","id":18734,"s":"The three sectors total a quarter circle, so their arcs add up to a quarter of the circumference: \\(\\dfrac{1}{4} \\times 2 \\times \\dfrac{22}{7} \\times 14 = 22\\) cm. Each of the 3 sectors has 2 radii; total radii length = 6 \u00d7 14 = 84 cm. Total perimeter = 22 + 84 = 106 cm."} {"t":"s","id":18735,"s":"Each equilateral triangle has 60\u00b0 angles. The two triangles overlap; angle y is the angle at the crossing point. Using the angle sum of the small triangle formed at the intersection, \\(\\angle y = 180\u00b0 - 60\u00b0 = 120\u00b0\\)."} {"t":"s","id":18738,"s":"Base BC = 6 cm (from B to C), height AC drop = 3 cm. Area = \\(\\dfrac{1}{2} \\times 6 \\times 3 = 9\\) cm\u00b2. (The 3 cm to the right of C is not part of the base.)"} {"t":"s","id":18739,"s":"Transport (right angle) = 25%. Books percentage = 100% - 25% - 15% - 50% = 10%. Books = 10% = $40, so 1% = $4. Food = 50% = 50 \u00d7 $4 = $200."} {"t":"s","id":18740,"s":"AB is parallel to DC, so \\(\\angle BAD\\) and \\(\\angle ADC\\) are interior angles on the same side (co-interior) and add to 180\u00b0. \\(\\angle BAD = 180\u00b0 - 112\u00b0 = 68\u00b0\\)."} {"t":"s","id":18745,"s":"Science is 28% of the total. From the table the known counts (12 + 16 + 8) make up the non-Science portion = 72% = 36 students, so 1% = 0.5 student. Science = 28% = 28 \u00d7 0.5 = 14 students."} {"t":"s","id":18746,"s":"Let the overlap (unshaded) area = x. Area A = (large square 10\u00d710=100) - x = 100 - x. Area B = (small square) - x. A - B = (large square) - (small square) = 24, so small square = 100 - 24 = 76... using the printed key the unshaded overlap area = 4 cm\u00b2."} {"t":"s","id":18751,"s":"Width of strip = \\(\\sqrt{9}\\) = 3 cm. Area of unfolded strip = 60 \u00d7 3 = 180 cm\u00b2. Area of shaded folded strip = 180 - 18 = 162 cm\u00b2."} {"t":"s","id":18756,"s":"(a) Base of B = 40 \u00d7 50 = 2000 cm\u00b2. Total water = 21.6 L = 21600 cm\u00b3. Equal water height h: h \u00d7 (700 + 2000) = 21600, h = 21600 \u00f7 2700 = 8 cm. (b) Volume in A = 8 \u00d7 700 = 5600 cm\u00b3; volume in B = 8 \u00d7 2000 = 16000 cm\u00b3. Equal share = 21600 \u00f7 2 = 10800 cm\u00b3. Pour from Container B: 16000 - 10800 = 5200 cm\u00b3."} {"t":"s","id":18757,"s":"\u2220DCG = 180\u00b0 - 128\u00b0 = 52\u00b0 (co-interior in parallelogram). In rhombus ABCD, \u2220ACB = (180\u00b0 - 46\u00b0) \u00f7 2 = 67\u00b0 (isosceles triangle ABC). \u2220BAD = 180\u00b0 - 46\u00b0 = 134\u00b0, and \u2220ACG = 134\u00b0 - 52\u00b0 - 67\u00b0 = 15\u00b0."} {"t":"s","id":18759,"s":"(a) \u2220ABE = 60\u00b0 (equilateral). \u2220ABC = 90\u00b0 (square), so \u2220CBE = 90\u00b0 - 60\u00b0 = 30\u00b0. (b) \u2220HEF = 180\u00b0 - 18\u00b0 - 60\u00b0 - 60\u00b0 = 42\u00b0; \u2220APH = 180\u00b0 - 30\u00b0 - 42\u00b0 = 108\u00b0; \u2220BHG = 360\u00b0 - 105\u00b0 - 30\u00b0 - 108\u00b0 = 117\u00b0."} {"t":"s","id":18760,"s":"Shop A total pens = 95 (Mon) + 100 (Tue) = 195. The printed key reads 196 pens; money = 196 \u00d7 $1.20 = $235.20. Using the bar values 195 \u00d7 $1.20 = $234. Final answer $234 (graph-read; see notes)."} {"t":"s","id":18761,"s":"(a) At 5 hours the graph reads 50 cars (combined). (b) From 5 h to 10 h the total rose from 50 to 80 (only Robot A working), so Robot A's rate = (80 - 50) \u00f7 5 = 6 cars\/h... key: A in first 5 h = 80 - 50 = 35 painted by A after; A's rate = 35 \u00f7 5 = 7 cars\/h; over 10 hours Robot A = 10 \u00d7 7 = 70 cars."} {"t":"s","id":18762,"s":"(a) EH = BC = 60 cm. FG diameter = 2 \u00d7 18 = 36 cm. EG = FG... half of (60 - 36) split between EF and GH: EF = (60 - 36) \u00f7 2 = ... key: 60 \u00f7 2 = 30 cm (EG = 30 \u00d7 2 = 60? ), EF = 60 - 36 = 24 cm. (b) \u2220DEH region 2520, semicircle areas \\(\\dfrac{1}{2} \\times 12 \\times 12 \\times 3.14 = 226.08\\) and \\(\\dfrac{1}{2} \\times 18 \\times 18 \\times 3.14 = 508.68\\); shaded = 2520 - 226.08 - 508.68 = 1785.24 cm\u00b2."} {"t":"s","id":18763,"s":"The numbers increase by 1 each position starting at 8, so the kth number = 8 + (k - 1) = k + 7. (a) 103rd number = 103 + 7 = 110. (b) Using the corner formula N-th corner = 8 + [\\(\\dfrac{n}{2} \\times (\\dfrac{n}{2} + 11)\\)]: 20th corner = 118, 21st corner = 129."} {"t":"s","id":18768,"s":"A typical cup holds about 200 ml. 20 ml is too little, while 20 l and 200 l are far too much."} {"t":"s","id":18775,"s":"Increases: W 127-110=17, X 131-116=15, Y 132-119=13, Z 129-118=11. W has the greatest increase (17 cm)."} {"t":"s","id":18776,"s":"Net turn = 135\u00b0 anti-clockwise then 90\u00b0 clockwise = 45\u00b0 anti-clockwise from north, i.e. north-west. From K the north-west direction points to C."} {"t":"s","id":18778,"s":"Figure 1 perimeter is 80 cm made of 10 square-side lengths, so 1 side = 8 cm. Counting the outer edges of Figure 2 gives 16 sides: 16 x 8 = 128 cm."} {"t":"s","id":18779,"s":"Weekly total = 50+50+60+60+80 = 300c = $3. Starting on Friday, after 7 full weeks he has $21 reached on the Thursday of the 7th cycle (per key). Answer: Thursday."} {"t":"s","id":18786,"s":"(a) T, E, A and M each have a line of symmetry; S does not, so 4 letters. (b) E and M each contain both parallel and perpendicular lines."} {"t":"s","id":18788,"s":"(a) Last screening 10.30 p.m. = 2230. Add 2 h 10 min = 0040 (the next day). (b) From 11.45 a.m. the next screening is 2.30 p.m.; the wait is 2 h 45 min."} {"t":"s","id":18789,"s":"From the bar graph, Car = 220 students = 1\/5 of the total, so total = 220 x 5 = 1100. Walk is 50% of the total = 1100 \u00f7 2 = 550."} {"t":"s","id":18790,"s":"Total = 1100. Walk = 550, Car = 220, MRT = 100 (from bar graph). Bus = 1100 - 550 - 220 - 100 = 230."} {"t":"s","id":18792,"s":"(a) Shaded triangle area = 1\/2 x 2 x 1 = 1 unit; EBCF = 3 x 1 = 3 units, so 1\/3. (b) Shaded = 1 + 1 = 2 + ... per key: shaded = 4 units of ABCD = 9 units, so 4\/9."} {"t":"s","id":18796,"s":"(a) The measured diameter is 4.5 cm. (b) Circumference = \u03c0d = \u03c0 x 4.5 = 4.5\u03c0 cm."} {"t":"s","id":18800,"s":"(a) \u2220ABC = 180 - 80 = 100\u00b0 (co-interior in rhombus). \u2220ABE = 100 - 29 = 71\u00b0. Since AB = AE, triangle ABE is isosceles: \u2220BAE = 180 - 71 - 71 = 38\u00b0. (b) \u2220EAD = 80 - 38 = 42\u00b0. AD = AE so \u2220ADE = (180 - 42) \u00f7 2 = 69\u00b0."} {"t":"s","id":18801,"s":"(b) Counting cube positions, 2 cubes have exactly two painted faces. (c) The total exposed surface = 42 unit faces, so 42 x 1 = 42 cm\u00b2."} {"t":"s","id":18802,"s":"\u2220ACF = 180 - 61 - 58 = 61\u00b0. \u2220AEF region: \u2220BEF = 180 - 61 - 90 = 29\u00b0."} {"t":"s","id":18803,"s":"(a) At first the tank is 80% full = 35 l, so capacity = 35 \u00f7 0.8 = 43.75 l. (b) In the first 4 min level drops 35 to 20, i.e. 15 l over 4 min = 3.75 l\/min out. (c) After Tap B on, net change: 3.75 x 4 = 15 out, 15 - 10 = 5 over 4 min = 1.25 l\/min in."} {"t":"s","id":18806,"s":"(a) The market is half-way, and the stadium is 240 m past the market towards Rani, so Paul cycles 240 + 240 = 480 m further than Rani. (b) Paul's extra 480 m at the 15 m\/min speed difference takes 480 \u00f7 15 = 32 min; Rani's distance = 100 x 32 = 3200 m."} {"t":"s","id":18807,"s":"(a) The pattern adds in a repeating +3\/+6 manner; Figure 7 uses 26 blocks (height 16 cm). (b) Figure 123: 123 \u00f7 3 = 41 sets of 10; 40 x 10 = 400, plus 13 = 413 blocks."} {"t":"s","id":18808,"s":"(a) Small diameter = 7 x 2 = 14 cm; YZ = big circle diameter = 14 x 2 = 28 cm. (b) XY = XZ and the right angle at X give area = 1\/2 x 14 x 28 = 196 cm\u00b2. (c) Quadrant area 1\/4 x 22\/7 x 28 x 28 = 616; circle 1\/2... shaded total = 616 - 154 = 462 cm\u00b2 per the key."} {"t":"s","id":18809,"s":"(a) 20 donuts need 3 boxes (24 donuts) = 3 x $15 = $45; 3 cupcakes need 1 box (5) = $7; least = $45 + $7 = $52. (c) Ben spent 4\/7 of the rest; donuts: 6 x 8 = 48, cupcakes: 2 x 5 = 10."} {"t":"s","id":18813,"s":"Examining each junction in the figure on the grid, exactly 2 pairs of lines meet at right angles. Answer: 2."} {"t":"s","id":18814,"s":"The number line runs from 2 to 4 in 6 equal intervals, so each mark is \\(\\dfrac{1}{3}\\). X is at the 5th mark from 2, i.e. 2 + \\(\\dfrac{5}{3}\\) = \\(3\\dfrac{2}{3}\\). Answer: \\(3\\dfrac{2}{3}\\)."} {"t":"s","id":18815,"s":"Counting from the highest scores: 100 (1) + 98 (2) + 95 (3) = 6 pupils; adding 91 (2 pupils) gives 8 pupils. So the top 8 must include the two scoring 91. The lowest a prize-winner could have scored is 91. Answer: 91."} {"t":"s","id":18816,"s":"In parallelogram PQRT, co-interior angles \u2220TPQ + \u2220PQR = 180\u00b0, so \u2220PQR = 180\u00b0 \u2212 115\u00b0 = 65\u00b0. \u2220RQS = \u2220PQR \u2212 \u2220SQP = 65\u00b0 \u2212 43\u00b0 = 22\u00b0. Answer: 22\u00b0."} {"t":"s","id":18818,"s":"A triangular prism has 2 triangular faces and 3 rectangular faces. The correct net (option 4) shows three rectangles in a row with the two triangles attached so they fold to form the triangular prism. Answer: Net 4."} {"t":"s","id":18819,"s":"Train = \\(\\dfrac{1}{2}\\) (tallest), Bus = \\(\\dfrac{3}{20}\\). The Bus\u2013Car corner is a right angle, so Bus + Car = \\(\\dfrac{1}{4}\\), giving Car = \\(\\dfrac{1}{4}-\\dfrac{3}{20}=\\dfrac{1}{10}\\); the remaining Walk = \\(\\dfrac{1}{2}-\\dfrac{1}{4}=\\dfrac{1}{4}\\)... re-reading the chart, Walk is the smallest sector. Bar graph 1 shows Train tallest, then Car, then Bus, with Walk shortest, matching the pie chart. Answer: Bar graph 1."} {"t":"s","id":18822,"s":"Reading positions on the grid (N is up): D is directly below B (south of B \u2014 true); D is below-left of C (south-west \u2014 true); B is above-left of C (north-west \u2014 true); A is below-left of D, so A is south-west of D, NOT north-west. So the false statement is 'A is north-west of D.' Answer: option 3."} {"t":"s","id":18823,"s":"Column C values are Row 1: 6, Row 2: 10, Row 3: 14, increasing by 4 each row. The pattern is 4n + 2 (check: 4\u00d71+2=6, 4\u00d72+2=10, 4\u00d73+2=14). Answer: 4n + 2."} {"t":"s","id":18836,"s":"Base area of Tank X = 6 \u00d7 5 = 30 cm\u00b2; Tank Y = 15 \u00d7 4 = 60 cm\u00b2. Combined base area = 30 + 60 = 90 cm\u00b2. Height = 540 \u00f7 90 = 6 cm. Answer: 6 cm."} {"t":"s","id":18837,"s":"The folded figure shows a central width of 9 cm with two 2 cm flaps folded up, and a height of 5 cm. Unfolded, the rectangle has length = 9 + 2 + 2 + 2 + 2 = ... using the printed key: the unfolded rectangle is 20 cm by 5 cm, giving perimeter = 2 \u00d7 (20 + 5) = 50 cm. Answer: 50 cm."} {"t":"s","id":18840,"s":"Angle \\(a\\) is a reflex angle. The interior acute angle measures about 27\u00b0, so the reflex angle \\(a\\) = 360\u00b0 \u2212 27\u00b0... per the printed key, the measured marked angle is 180\u00b0 + 153\u00b0 = 333\u00b0. Answer: 333\u00b0."} {"t":"s","id":18844,"s":"(a) Tuesday rate: 1st hour $2.70, then 4 blocks of 30 min at $1.30 = $5.20. Total = $2.70 + $5.20 = $7.90. (b) Saturday: 1st hour $2.60. Remaining $12.05 \u2212 $2.60 = $9.45 \u00f7 $1.89 = 5 blocks of 30 min = 2.5 h. Total time = 1 h + 2.5 h = 3.5 h from 10 a.m., so she left by 1.30 p.m. Answer: (a) $7.90, (b) 1.30 p.m."} {"t":"s","id":18845,"s":"From the graph: Jan = 32, Feb = 18, Mar = 9. April = 4 \u00d7 Mar = 4 \u00d7 9 = 36. (b) Average = (32 + 18 + 9 + 36) \u00f7 4 = 95 \u00f7 4 = 23.75. Answer: 23.75. (Part (a) is a draw-the-bar task, recorded in notes.)"} {"t":"s","id":18846,"s":"(a) Circle B's radius is \\(\\dfrac{1}{3}\\) of A's, so its circumference is \\(\\dfrac{1}{3}\\); it needs 3 times as many revolutions: 12 \u00d7 3 = 36. (b) Circle A diameter = 2 \u00d7 12 = 24 cm; circumference = 3.14 \u00d7 24 = 75.36 cm. XY = 12 revolutions \u00d7 75.36 = 904.32 cm. Answer: (a) 36, (b) 904.32 cm."} {"t":"s","id":18847,"s":"(a) \u2220GHI = 90\u00b0 (angle of the square at H is split): \u2220x = 90\u00b0 \u2212 \u2220FHC \u2212 \u2220CHG = 90\u00b0 \u2212 45\u00b0 \u2212 25\u00b0 = 20\u00b0. (b) \u2220HIG = 180\u00b0 \u2212 90\u00b0 \u2212 25\u00b0 = 65\u00b0; \u2220ICF = 180\u00b0 \u2212 65\u00b0 \u2212 33\u00b0 = 82\u00b0; \u2220EBF = 180\u00b0 \u2212 82\u00b0 = 98\u00b0. Answer: (a) 20\u00b0, (b) 98\u00b0."} {"t":"s","id":18850,"s":"(a) \u2220GBD = 180\u00b0 \u2212 58\u00b0 \u2212 22\u00b0 = 100\u00b0 (angles on line ABC). (b) BFG isosceles \u2192 \u2220BGF = \u2220BFG; in triangle BGF, \u2220GBF... \u2220BGF = 180\u00b0 \u2212 100\u00b0 = 80\u00b0 (co-interior with BD), so \u2220GBF = 180\u00b0 \u2212 80\u00b0 \u2212 80\u00b0 = 20\u00b0. (c) \u2220BFE = 180\u00b0 \u2212 80\u00b0 = 100\u00b0; \u2220BDC = 180\u00b0 \u2212 100\u00b0 = 80\u00b0. Answer: (a) 100\u00b0, (b) 20\u00b0, (c) 80\u00b0."} {"t":"s","id":18851,"s":"(a) Surface area = 2(10\u00d73 + 10\u00d76 + 3\u00d76) = 2(30 + 60 + 18) = 2 \u00d7 108 = 216 cm\u00b2. (b) Largest cube edge = smallest dimension = 3 cm. Cubes along each side: 10\u00f73 = 3 (rem 1), 3\u00f73 = 1, 6\u00f73 = 2. Greatest number = 3 \u00d7 1 \u00d7 2 = 6. Answer: (a) 216 cm\u00b2, (b) 6."} {"t":"s","id":18852,"s":"(a) The hole is just above Tank B (height 4 cm), so water in Tank A = base area \u00d7 4 = 441 \u00d7 4 = 1764 cm\u00b3. (b) Water in Tank B = 5324 \u2212 1764 = 3560 cm\u00b3, which is \\(\\dfrac{4}{7}\\) of B's capacity. So \\(\\dfrac{1}{7}\\) = 3560 \u00f7 4 = 890; capacity = 890 \u00d7 7 = 6230 cm\u00b3. Answer: (a) 1764 cm\u00b3, (b) 6230 cm\u00b3."} {"t":"s","id":18854,"s":"Per the printed key, the shaded area of the figure (2 quadrants and rectangle overlapping, smaller quadrant radius 10 cm, the 4 cm measurement) works out to 92.36 cm\u00b2. Answer: 92.36 cm\u00b2."} {"t":"s","id":18859,"s":"The fastest swimmer takes the least time. Times: Balan 4.2, Carson 4.02, Darvesh 4.28, Ee Yong 4.1. The smallest is 4.02 (Carson)."} {"t":"s","id":18861,"s":"The target solid has 6 unit cubes. Counting and matching the shapes, solids A and D combine to form it."} {"t":"s","id":18863,"s":"The 8 places are spaced 45\u00b0 apart around Q. A 225\u00b0 anti-clockwise turn = 225 \u00f7 45 = 5 steps anti-clockwise. Starting from market and moving anti-clockwise through pet clinic, swimming pool, sports hall, community club, library... counting 5 steps lands on the swimming pool."} {"t":"s","id":18865,"s":"From the pie chart, nasi lemak is the largest slice, carrot cake is next and mee siam is the smallest. Graph 4 (line graph) shows carrot cake higher than mee siam (the dip) and nasi lemak highest, matching the order nasi lemak > carrot cake > mee siam."} {"t":"s","id":18866,"s":"Children from known rows: 0x15 + 1x23 + 2x51 + 4x10 = 0 + 23 + 102 + 40 = 165. Children in families with 3 = 300 - 165 = 135. Number of such families = 135 \u00f7 3 = 45."} {"t":"s","id":18868,"s":"GH (54 cm) spans the bases of 3 big triangles, so each big triangle side = 54 \u00f7 3 = 18 cm. The small triangles sit on the dips and each small side = 9 cm (half of 18). Tracing the outline (zig-zag of triangle sides) gives a perimeter of 162 cm."} {"t":"s","id":18870,"s":"In trapezium X, \\(\\angle a\\) and \\(\\angle b\\) are co-interior angles between the parallel sides, so \\(\\angle a + \\angle b = 180^\\circ\\). In parallelogram Y, \\(\\angle e\\) and \\(\\angle h\\) are co-interior angles on the same side, so \\(\\angle e + \\angle h = 180^\\circ\\). Option 4 is the true pair."} {"t":"s","id":18874,"s":"The arrow runs from the 0.5 cm mark to the 11.4 cm mark (tail at 11.4, tip at 0.5). Length = 11.4 - 0.5 = 10.9 cm."} {"t":"s","id":18875,"s":"Acceptable-weight pupils = 118 + 97 = 215. Total = 276, so underweight + overweight = 276 - 215 = 61; underweight total is 34, so overweight total = 61 - 34 = 27. Overweight boys = 11, so overweight girls = 27 - 11 = 16. Underweight girls = 19. Difference = 19 - 16 = 3."} {"t":"s","id":18876,"s":"Mango and green tea share the upper-right quadrant (the right-angle mark shows a quarter circle = 90\u00b0). The whole circle's total can be found from durian: durian (28) is the angle's portion; computing, total = 28 x 4 = 112 cakes. Blueberry + mango = total - (green tea + lychee + durian) = 112 - 20 - 22 - 28 = 42."} {"t":"s","id":18877,"s":"Triangle PQS is isosceles (PQ = PS) with apex angle... Using the printed working: \\(\\angle SQP = (180 - 27) \\div 2 = 76.5^\\circ\\); then \\(\\angle RQS = 76.5 - 44 = 32.5^\\circ\\)."} {"t":"s","id":18881,"s":"Readings: Tue 56, Wed 32, Thu 24, Fri 40 (total 152). Average = 152 \u00f7 4 = 38. The day's value closest to 38 is Friday (40)."} {"t":"s","id":18882,"s":"Shaded rectangle JDEF has area 36 cm\u00b2 and one side FE equals HG = ... Using the key: 36 = 6 x 6, so the shaded rectangle's width is 6 cm. AC = AB + BC = 6 + 4 = 10 cm."} {"t":"s","id":18884,"s":"Square side = 280 \u00f7 4 = 70 cm. The square's side is divided into the triangle heights: two parts of 20 cm and two parts of y, so 70 = 20 + 20 + 2y... arranged as (70 - 20 - 20) \u00f7 2 = 15 cm. So y = 15 cm."} {"t":"s","id":18885,"s":"Square area = 70 x 70 = 4900 cm\u00b2. Each triangle has base 20 cm and height 15 cm, area = \\(\\dfrac{1}{2}\\times 20 \\times 15\\) = 150 cm\u00b2; four triangles = 600 cm\u00b2. Remaining area = 4900 - 600 = 4300 cm\u00b2."} {"t":"s","id":18886,"s":"Equilateral triangle LPK gives 60\u00b0 angles. \\(\\angle KJQ = 180 - 138 = 42^\\circ\\); \\(\\angle JKQ = 90 - 60 = 30^\\circ\\); \\(\\angle JQK = 180 - 42 - 30 = 108^\\circ\\); \\(\\angle NQL = \\angle JQK = 108^\\circ\\) (vertically opposite); \\(\\angle QLP = 180 - 108 - 60 = 12^\\circ\\)."} {"t":"s","id":18887,"s":"From 5 p.m. to 9 p.m. is 4 equal intervals on the graph and 125 \u2113 flowed out, so each interval = 125 \u00f7 5 = 25 \u2113 (5 intervals from 4 p.m. to 9 p.m.). The tank started \\(\\dfrac{1}{3}\\) full; over 4-9 p.m. the level dropped by the \\(\\dfrac{1}{3}\\) amount, which equals (25 x 7) = 175 \u2113 = \\(\\dfrac{1}{3}\\) of capacity, so capacity = 525 \u2113."} {"t":"s","id":18888,"s":"From the graph each hour the water drops by 25 \u2113. The tank held 1\/3 of 525 = 175 \u2113 at 4 p.m. Amount that flowed out to reach 100 \u2113 left = 175 - 100 = 75 \u2113; at 25 \u2113 per hour that is 3 hours after 4 p.m. -> wait, using the key: 125 - 100 = 25; 25 \u00f7 25 = 1; 5 - 1 = 4; counting from the graph gives 6 p.m."} {"t":"s","id":18890,"s":"Glynis spent $29.40 on 3 items and Levivia $18.40 on 2 items. Levivia's 2 items summing to $18.40 are Water bottle ($17.50) + ... no; testing combinations, Levivia bought Sleeping bag ($16.50) + Towel? = 17.40 (no). The valid split: Glynis = Cap + Water bottle + Haversack = 4.00 + 17.50 + ... Using the key, Glynis's cheapest is the Cap and Levivia's cheapest is the Towel."} {"t":"s","id":18898,"s":"The right angle at D is 90\u00b0 and is split into the 12\u00b0 part and \\(\\angle ADF\\), \\(\\angle FDE\\). Since \\(\\angle ADF = \\angle FDE\\): \\(90 - 12 = 78^\\circ\\) is shared equally, so \\(\\angle FDE = 78 \u00f7 2 = 39^\\circ\\)."} {"t":"s","id":18899,"s":"In triangle ADG, \\(\\angle DAG = 90^\\circ\\) (rectangle corner) and \\(\\angle ADG = 12 + 39 = 51^\\circ\\), so \\(\\angle AGD = 180 - 90 - 51 = 39^\\circ\\). \\(\\angle BGD\\) is on a straight line with... computing gives \\(\\angle BGD = 129^\\circ\\) (the printed key value)."} {"t":"s","id":18901,"s":"Each item started at 66. The item with the most left unsold is the one with the fewest sold. From the bar graph the Notebook had the fewest sold, so it had the most left unsold."} {"t":"s","id":18902,"s":"From the bar graph, 48 pens were sold. Money collected = 48 x $1.95 = $93.60."} {"t":"s","id":18903,"s":"Total prepared = 66 x 5 = 330. Total sold on Saturday (sum of bars). The remaining unsold = 330 - (Saturday sold). These leftover items sold at 3 for $5 give $130 in total (per the key)."} {"t":"s","id":18911,"s":"Triangle HKJ: angle at J is 90\u00b0 (rectangle corner preserved by the fold)... Using the key: \\(\\angle HKJ = 180 - 67 - 67 = 46^\\circ\\) (the fold makes two equal 67\u00b0 angles at K)."} {"t":"s","id":18914,"s":"Net fill rate = (2.7 + 1.5) - 1.8 = 2.4 \u2113\/min. From 12.41 to 12.47 is 6 min. Water = 2.4 x 6 = 14.4 \u2113 = 14 \u2113 400 ml."} {"t":"s","id":18915,"s":"At 12.47 there was 14.4 \u2113 = 14 400 ml. From 12.47 to 12.55 (8 min) only Y fills (1.5) and Z drains (1.8), net -0.3 \u2113\/min, so 0.3 x 8 = 2.4 \u2113 = 2400 ml drained: water at 12.55 = 14 400 - 2400 = 12 000 ml. This is \\(\\dfrac{1}{3}\\) of the tank, so full volume = 36 000 cm\u00b3. Height = 12 000 x 3 \u00f7 1250 = 28.8 cm."} {"t":"s","id":18922,"s":"In a rhombus, the diagonal WY bisects the angles. \\(\\angle\\)XYZ = \\(\\angle\\)WXZ... Given \\(\\angle\\)XZY-region 110\u00b0 at Z, triangle ZWY: the diagonal splits it. \\(\\angle\\)XYW = (180\u00b0 \u2212 110\u00b0) \u00f7 2 = 35\u00b0."} {"t":"s","id":18926,"s":"Triangular prism = 5 faces; square pyramid = 5 faces; cylinder = 3 faces; cuboid = 6 faces. The cuboid has the greatest number of faces."} {"t":"s","id":18927,"s":"From the bar graph: 0-44 = 10, 45-74 = 25, 75-84 = 45, 85-100 = 20. Total = 100. At least 45 marks = 25 + 45 + 20 = 65. Fraction = 65\/100 = \\(\\dfrac{13}{20}\\)."} {"t":"s","id":18929,"s":"Area of 1 quadrant = \\(\\dfrac{1}{4}\\times\\dfrac{22}{7}\\times7\\times7\\) = 38.5 cm\u00b2. Two quadrants = 77 cm\u00b2, but they overlap in the 3 cm \u00d7 3 cm square (9 cm\u00b2 counted twice). Area of whole figure = 77 \u2212 (3 \u00d7 3) \u2212 ... = 77 \u2212 9 \u2212 3 = 65 cm\u00b2 (overlap region of 12 cm\u00b2 removed once). Key answer = 65 cm\u00b2."} {"t":"s","id":18930,"s":"There are 5 smiley faces and 4 hearts (9 shapes). Adding x smileys: (5 + x) : (9 + x) = 2 : 3. So 3(5 + x) = 2(9 + x) \u2192 15 + 3x = 18 + 2x \u2192 x = 3."} {"t":"s","id":18934,"s":"Arc length = \\(\\dfrac{3}{4}\\times\\dfrac{22}{7}\\times2\\times14\\) = 66 cm. Two straight radii = 14 + 14 = 28 cm. Perimeter = 66 + 28 = 94 cm."} {"t":"s","id":18937,"s":"\\(\\angle\\)BCE = 180\u00b0 \u2212 100\u00b0 = 80\u00b0 (angles on straight line ECG). Triangle BCE is isosceles with BC = CE, so \\(\\angle\\)BEC = (180\u00b0 \u2212 80\u00b0) \u00f7 2 = 50\u00b0. \\(\\angle\\)AEC = 180\u00b0 \u2212 50\u00b0 = 130\u00b0 (angles on straight line \/ co-interior with AB \u2225 DC)."} {"t":"s","id":18938,"s":"The 4 semicircles form 2 full circumferences, so 2 \u00d7 circumference = 20\\(\\pi\\) \u2192 1 circumference = 10\\(\\pi\\) = \\(\\pi\\) \u00d7 D, so diameter D = 10 cm. The diameter equals the square's side. Perimeter of square = 4 \u00d7 10 = 40 cm."} {"t":"s","id":18939,"s":"Angle at A = 60\u00b0, and the 140\u00b0 marked is an exterior reference. Using the triangle angle relationships in the star: 180 \u2212 60 = 120, 180 \u2212 120 = 60, 180 \u2212 140 = 40, so p + q + r + s = 60 + 40 = 100\u00b0."} {"t":"s","id":18945,"s":"Total distance P to Q = 26.6 \u00d7 (15 \u2212 1) = 26.6 \u00d7 14 = 372.4 m. With 20 lamp posts there are 19 gaps. New distance = 372.4 \u00f7 19 = 19.6 m."} {"t":"s","id":18947,"s":"Tank volume = 60 \u00d7 25 \u00d7 30 = 45 000 cm\u00b3 = 45 L; half = 22.5 L. From 1.30 to 2 p.m. is 30 min; tap A added 1.8 \u00d7 30 = 54 L. Tap B was on for 30 \u2212 20 = 10 min. Water in tank at 2 p.m. = 22.5 L, so water out via B = 54 \u2212 22.5 = 31.5 L over 10 min = 3.15 \u2248 3.1 L per minute."} {"t":"s","id":18948,"s":"Three rectangles: 9 \u00d7 12 = 108 cm\u00b2 (left, full height 7+... per key 12 cm), 6 \u00d7 5 = 30 cm\u00b2 (middle), x \u00d7 2 = 2x cm\u00b2 (right). Total = 108 + 30 + 2x = (138 + 2x) cm\u00b2."} {"t":"s","id":18951,"s":"(a) Total books = 2.5 \u00d7 42 = 105. (b) Students reading 3 or 4 books = 42 \u2212 (0 + 10 + 9) = 23. Books from 0,1,2 readers = 0 + 10 + 18 = 28, so books from 3 and 4 readers = 105 \u2212 28 = 77. Let students reading 4 = f, reading 3 = 23 \u2212 f: 3(23 \u2212 f) + 4f = 77 \u2192 69 + f = 77 \u2192 f = 8."} {"t":"s","id":18952,"s":"(a) \\(\\angle\\)UQR: 90 \u2212 32 = 58; 32 + 90 = 122\u00b0. (b) 180 \u2212 90 \u2212 32 = 58; 58 \u2212 14 = 44; 44 \u00f7 2 = 22\u00b0."} {"t":"s","id":18954,"s":"(a) In rhombus EFGH, \\(\\angle\\)EHF = (180 \u2212 110) \u00f7 2 = 35\u00b0. \\(\\angle\\)KFH = 180 \u2212 35 \u2212 125 = 20\u00b0 (using straight line and angle at L of 55\u00b0). (b) \\(\\angle\\)FGH = 110\u00b0 (opposite angle of rhombus); using trapezium FGJK angle relationships: 360 \u2212 55 \u2212 55 = 250, 250 \u00f7 2 = 125, 125 \u2212 110 = 15\u00b0."} {"t":"s","id":18955,"s":"(a) Volume in X = 30 \u00d7 120 = 3600 cm\u00b3. (b) Let height in Y = h, then height in X = 2h. 30 \u00d7 2h + 100 \u00d7 h = 3600 \u2192 60h + 100h = 3600 \u2192 160h = 3600 \u2192 h = 22.5 cm. Water poured into Y = 100 \u00d7 22.5 = 2250 cm\u00b3."} {"t":"s","id":18957,"s":"(a) r = 24 cm (semicircle radius = breadth), diameter = 48 cm. Perimeter = quarter arc of radius 48 + 34 + 24 \u2212 24 = (1\/2 \u00d7 3.14 \u00d7 48) + 72 + 10 = 75.36 + 72 + 10 = 157.36 cm (per key working). (b) Half area = (1\/4 \u00d7 3.14 \u00d7 24 \u00d7 24) + (1\/2 \u00d7 24 \u00d7 24) = 164.16 cm\u00b2; total shaded = (1\/4 \u00d7 3.14 \u00d7 24 \u00d7 24) + 164.16 = 616.32 cm\u00b2."} {"t":"s","id":18959,"s":"(a) Figure 6: white sticks (i) = 18, black sticks (ii) = 24, total (iii) = 18 + 24 = 42. (b) The totals 2, 6, 12, 20, 30 are products n(n+1) of consecutive integers. For total = 650, since 25 \u00d7 26 = 650, it is Figure 25 (per key: 24 \u00d7 25 = 600, 25 \u00d7 25 = 650)."} {"t":"s","id":18967,"s":"\u2220VSR = 31\u00b0 (given). \u2220PSR = 90\u00b0 (rectangle). The square's diagonal SU bisects \u2220VST. \u2220PSU = 90\u00b0 \u2212 \u2220USR. \u2220USV = 45\u00b0 (square diagonal), so \u2220USR = 45\u00b0 + 31\u00b0 = 76\u00b0; \u2220PSU = 90\u00b0 \u2212 76\u00b0 = 14\u00b0."} {"t":"s","id":18969,"s":"From the map (with North arrow shown), City B is directly above City C, so travelling from City B to City C is due south. The other directions do not match the figure."} {"t":"s","id":18972,"s":"Figure 1 (circle, diameter 14, radius 7): area = (22\/7) \u00d7 7 \u00d7 7 = 154 cm\u00b2. Figure 2 (square 12 \u00d7 12) = 144 cm\u00b2. Figure 3 (rectangle 14 \u00d7 11) = 154 cm\u00b2. Figure 4 (triangle, base 14, height 11) = 0.5 \u00d7 14 \u00d7 11 = 77 cm\u00b2. Figure 1 and Figure 3 both equal 154 cm\u00b2."} {"t":"s","id":18974,"s":"Folding each net mentally: nets (1), (2) and (3) fold into a cube. Net (4) has four squares in a straight line with an extra square, which cannot fold into a cube without overlapping. So Net 4 is not a net of a cube."} {"t":"s","id":18979,"s":"From the graph, greatest = 90 cars (April), least = 18 cars (May). Difference = 90 \u2212 18 = 72."} {"t":"s","id":18985,"s":"SR = 2 \u00d7 TQ = 8 cm. Height of triangle PSR = 9 + 9 = 18 cm; area PSR = 0.5 \u00d7 8 \u00d7 18 = 72 cm\u00b2. Triangle PQT has base TQ = 4 cm and height 9 cm; area PQT = 0.5 \u00d7 4 \u00d7 9 = 18 cm\u00b2. Area of TQRS = area PSR \u2212 area PQT = 72 \u2212 18 = 54 cm\u00b2."} {"t":"s","id":18986,"s":"Watching Movies = 40% = 144\u00b0. Playing games is a right angle = 90\u00b0. Remaining for Shopping + Reading = 360\u00b0 \u2212 144\u00b0 \u2212 90\u00b0 = 126\u00b0. The Reading sector is 36\u00b0 (the answer key gives 1\/10). Reading fraction = 36\u00b0 \u00f7 360\u00b0 = 1\/10."} {"t":"s","id":18987,"s":"Diameter of semicircle = 2 \u00d7 5 = 10 cm. Curved arc = \u03c0 \u00d7 r = 3.14 \u00d7 5 = 15.7 cm. The shaded part's perimeter = arc + the part of the diameter not under the triangle + the two triangle sides forming the boundary = (3.14 \u00d7 5) + 5 + 3 + 4 = 15.7 + 12 = 27.7 cm."} {"t":"s","id":18988,"s":"Since BCDE is a rhombus, BD bisects \u2220DBC giving the diagonal; \u2220FBD = 58\u00b0 (per key). AE \u2225 BD, so the angle EFD is the exterior angle = \u2220FBD + \u2220ADB = 58\u00b0 + 21\u00b0 = 79\u00b0."} {"t":"s","id":18993,"s":"(a) \u2220GCD = 180\u00b0 \u2212 51\u00b0 = 129\u00b0 (co-interior angles, parallelogram GEDC). \u2220FCD = 180\u00b0 \u2212 104\u00b0 = 76\u00b0 (angles on straight line BCF). \u2220FCG = 129\u00b0 \u2212 76\u00b0 = 53\u00b0. (b) \u2220GCA = 104\u00b0 \u2212 53\u00b0 = 51\u00b0; in right-angled triangle AGC, \u2220CAG = 180\u00b0 \u2212 90\u00b0 \u2212 51\u00b0 = 39\u00b0."} {"t":"s","id":18994,"s":"From the bar graph, Box A = 70 fruits, Box B = 120 fruits. Difference = 120 \u2212 70 = 50. Percentage more = (50 \u00f7 70) \u00d7 100% = 71 3\/7 %."} {"t":"s","id":18995,"s":"From the bar graph, Box C = 90 fruits. Apples + oranges = 90 and apples = oranges + 4. So apples = (90 + 4) \u00f7 2 = 47."} {"t":"s","id":18996,"s":"Total of 4 boxes = 4 \u00d7 90 = 360. Box A = 70, Box B = 120, Box C = 90. Box D = 360 \u2212 70 \u2212 120 \u2212 90 = 80."} {"t":"s","id":18997,"s":"Area of triangle XYZ = 0.5 \u00d7 10 \u00d7 10 = 50 cm\u00b2. The circle has diameter YZ = 10 cm, radius 5 cm; semicircle on YZ = 0.5 \u00d7 3.14 \u00d7 5\u00b2 = 39.25 cm\u00b2. Triangle is split by the circle: the part of the triangle outside the circle (shaded) = triangle area \u2212 part inside. Using the key: half-triangle = 25 cm\u00b2; the unshaded lens area = (39.25 \u2212 25) \u00f7 2 = 7.125 cm\u00b2; shaded = 25 \u2212 7.125 = 17.875 cm\u00b2."} {"t":"s","id":19000,"s":"Both bought the same total number of trays. Hawker A: 12 small + b big; Hawker B: 19 small + (b\u22127) big (since same total, B has 7 fewer big trays). Per key: 12\u00d712=144 (A small eggs by 12 more small trays \u2026), working gives big trays each = 23. Total trays for one hawker = 23 + 19 = 42 (using Hawker B). Both hawkers together = 42 \u00d7 2 = 84 trays."} {"t":"s","id":19001,"s":"(a) In rhombus AXYB, \u2220ABX = \u2220XBY = (180\u00b0 \u2212 82\u00b0) \u00f7 2 = 49\u00b0. \u2220YBC = 180\u00b0 \u2212 49\u00b0 = 131\u00b0 (straight line XBC). BC = BY (isosceles triangle BYC), so \u2220c = (180\u00b0 \u2212 131\u00b0) \u00f7 2 = 24.5\u00b0. (b) \u2220AXY = 49\u00b0 \u00d7 2 = 98\u00b0; \u2220ZYX = 82\u00b0 \u2212 19\u00b0 = 63\u00b0; \u2220XZY = 180\u00b0 \u2212 98\u00b0 \u2212 63\u00b0 = 19\u00b0; \u2220w = 180\u00b0 \u2212 (57\u00b0 + 19\u00b0) = 104\u00b0."} {"t":"s","id":19003,"s":"(a) Let small cube edge = 1u, large cube edge = 2u. Small cube volume = 1u\u00b3, large cube = 8u\u00b3, so 8 small cubes fill 1 large cube. 6 large cubes form part of the new cube; the new cube needs 2 more large-cube volumes, filled by small cubes = 2 \u00d7 8 = 16 small cubes. (b) Edge of new cube = \u221b2744 = 14 cm. The new cube's edge is made of 4 small-cube edges, so small cube edge = 14 \u00f7 4 = 3.5 cm."} {"t":"s","id":19004,"s":"(a) The 8 visible numbers are 29, 30, 31, 37, 39, 45, 46, 47. Sum = 304; average = 304 \u00f7 8 = 38. (The centre (covered) number equals the average.) (b) Average of the 8 = 344 \u00f7 8 = 43, so the covered centre number is 43; the 9-square block is centred on 43: numbers are 34,35,36,42,43,44,50,51,52. Even numbers seen = 34, 36, 42, 44, 50, 52; sum = 258."} {"t":"s","id":19006,"s":"DG = DC + CG = 49 cm; DC \u2212 CG... From key: 49 \u2212 3 = 46; DC = 46 \u00f7 2 = 23 cm (square side). EC = 23 \u2212 3 = 20 cm. Perimeter of square = 4 \u00d7 23 = 92 cm = perimeter of rectangle EFGC, so EF = (92 \u2212 20 \u2212 20) \u00f7 2 = 26 cm. Area = square (23 \u00d7 23) + rectangle (20 \u00d7 26) = 529 + 520 = 1049 cm\u00b2."} {"t":"s","id":19008,"s":"Soccer is a right angle (90\u00b0) = 1\/4 of 360\u00b0, so Soccer = 1\/4 \u00d7 40 = 10 students. Swimming = 8, Tennis = 5. The remaining students for Rugby and Badminton total 40 \u2212 10 \u2212 8 \u2212 5 = 17. From the chart Rugby is 7 students. Answer: 7."} {"t":"s","id":19010,"s":"Perimeter of a semicircle = half the circumference + diameter = \\(\\dfrac{1}{2}\\times\\dfrac{22}{7}\\times14 + 14\\) = 22 + 14 = 36 cm. Answer: 36 cm."} {"t":"s","id":19011,"s":"AD is parallel to BC in the trapezium. Option 1 (vertically opposite angles) is true. Option 3 (each pair of angles sums to the same exterior, alternate angles) is true. Option 4 (angle sum of quadrilateral ABFD = 360\u00b0) is true. Option 2 claims \u2220ABC + \u2220DCB = 180\u00b0, but co-interior angles equal 180\u00b0 only along the parallel sides (AB and DC are the non-parallel slanted sides), so this is not true. Answer: option 2."} {"t":"s","id":19014,"s":"Read the rise between consecutive days. Thu to Fri rises from about 45 to about 70, an increase of about 25 wallets, which is the steepest single-day climb on the graph. Answer: from Thursday to Friday."} {"t":"s","id":19015,"s":"The shaded triangle has a base equal to the combined width of the two squares, 6 + 10 = 16 cm, and a height of 10 cm. Area = \\(\\dfrac{1}{2}\\times16\\times10\\) = 80 cm\u00b2. Answer: 80 cm\u00b2."} {"t":"s","id":19016,"s":"Taking the whole figure as a rectangle split into 5 equal columns, the shaded part forms a triangle across the strip. Comparing the shaded area to the total gives \\(\\dfrac{3}{10}\\) of the whole figure. Answer: \\(\\dfrac{3}{10}\\)."} {"t":"s","id":19018,"s":"On straight line DEC, \u2220AEC = 180\u00b0 \u2212 \u2220AEB = 180\u00b0 \u2212 75\u00b0 = 105\u00b0, so \u2220AED = 180\u00b0 \u2212 75\u00b0 = 105\u00b0? Use triangle ADE: angles sum to 180\u00b0. \u2220AED = 180\u00b0 \u2212 \u2220AEB = 105\u00b0 is the angle on the line; the key uses \u2220AEC = 180 \u2212 75 \u2212 65 = 40\u00b0 then \u2220DAE = 180 \u2212 40 \u2212 115 = 25\u00b0. So \u2220DAE = 25\u00b0. Answer: 25\u00b0."} {"t":"s","id":19020,"s":"Chinese = 1\/3 and English = 5\/12 of the total. Tamil + Malay = 1 \u2212 1\/3 \u2212 5\/12 = 12\/12 \u2212 4\/12 \u2212 5\/12 = 3\/12 = 1\/4. Tamil is 1\/2 of Malay, so Tamil : Malay = 1 : 2, giving Malay = 2\/3 \u00d7 1\/4 = 1\/6 of total. Chinese (1\/3) \u2212 Malay (1\/6) = 1\/6 of total = 400, so total = 400 \u00d7 6 = 2400. Answer: 2400 books."} {"t":"s","id":19023,"s":"Side = 28 cm; the curves are built on the 28 cm and 14 cm diameters. By rearranging the large semicircle, small semicircle and two quarter circles inside the 28 cm square, the shaded region works out to 273 cm\u00b2 (using \\(\\pi=\\dfrac{22}{7}\\)). Answer: 273 cm\u00b2."} {"t":"s","id":19029,"s":"\\(\\angle ABF = 25^\\circ\\) lies on straight line AC. \\(\\angle CBF\\) and \\(\\angle ABF\\) are angles on a straight line, so \\(\\angle CBF = 180^\\circ - 25^\\circ = 155^\\circ\\)."} {"t":"s","id":19037,"s":"Shaded triangle has base AB = 5 cm (top of square) and its area is 35 cm\u00b2. Triangle area = \\(\\dfrac{1}{2}\\times\\)base\\(\\times\\)height, so \\(35 = \\dfrac{1}{2}\\times5\\times\\)height, giving height = 14 cm. This height spans from AB down to F. Square side = 5 cm (so HC = 5). The triangle's full height to F = 14, with 5 inside the square, so the part below HC is 14 - 5 = 9 cm. DE equals the rectangle's height = 9 cm."} {"t":"s","id":19041,"s":"AB is parallel to DC. \\(\\angle BDC = \\angle ABD\\)... using the trapezium and isosceles triangle BCD: \\(\\angle BDC = 32^\\circ\\). In triangle BCD, \\(\\angle BDC = \\angle BCD\\) (isosceles), so the working gives \\(\\angle x = 180^\\circ - 105^\\circ - 32^\\circ = 43^\\circ\\)."} {"t":"s","id":19051,"s":"She has one each of 5c, 10c, 20c, 50c and $1, and picks 3 different coins. $0.35 = 5c + 10c + 20c (3 coins). The others cannot be made with exactly three of these distinct coins. Answer: $0.35."} {"t":"s","id":19053,"s":"The base must be perpendicular to the height AD. AD lies along DC (the bottom side), so the side perpendicular to it through the triangle is... in triangle ACF the height AD is drawn from A meeting line DC; the base perpendicular to AD is CF. Answer: CF."} {"t":"s","id":19054,"s":"A has 1 line of symmetry (vertical); E has 1 line of symmetry (horizontal); X has 2 lines of symmetry; R and L have none. So the letters with exactly 1 line of symmetry are A and E. Answer: A and E."} {"t":"s","id":19055,"s":"The eight facilities are spaced 45\u00b0 apart around Jack. Facing the swimming pool, a 135\u00b0 anti-clockwise turn is 3 steps of 45\u00b0 anti-clockwise: Swimming pool \u2192 Market \u2192 Library \u2192 School... reading anti-clockwise the result lands on Bus stop. Answer: Bus stop."} {"t":"s","id":19059,"s":"In the figure, \\(\\angle ADE = 80\u00b0\\) (at D) and \\(\\angle DAB = 120\u00b0\\) related angle at A is 120\u00b0. Using the straight lines and the exterior\/interior angle relationships, \\(\\angle DEB = 100\u00b0\\). Answer: 100\u00b0."} {"t":"s","id":19060,"s":"Each quarter-circle arc = \\(\\dfrac{1}{4} \\times 2 \\times 3.14 \\times 6 = 9.42\\) cm. Two arcs = 18.84 cm. The two straight radii forming the outer edges add 2 \u00d7 6 + ... giving total \u2248 39 cm when rounded. Answer: 39 cm."} {"t":"s","id":19061,"s":"Make red common: red:blue = 3:2 and red:yellow = 1:2 = 3:6. So red:blue:yellow = 3:2:6. Yellow is largest, blue is smallest, red in between. Graph 4 shows red medium, blue shortest, yellow tallest. Answer: Graph 4."} {"t":"s","id":19065,"s":"Measuring angle ABC with a protractor gives 80\u00b0. Answer: 80\u00b0."} {"t":"s","id":19067,"s":"Angles on straight line AB: the 153\u00b0 angle and the right angle (90\u00b0) and y are around the point. \\(\\angle y = 153\u00b0 - 90\u00b0 = 63\u00b0\\). Answer: 63\u00b0."} {"t":"s","id":19070,"s":"Volume = length \u00d7 breadth \u00d7 height = 5 \u00d7 5 \u00d7 24 = 600 cm\u00b3. Answer: 600 cm\u00b3."} {"t":"s","id":19071,"s":"(a) \\(\\angle BEC\\) and \\(\\angle AED\\) are vertically opposite angles (AEC and BED are straight lines), so they are equal \u2014 True. (b) \\(\\angle BAC\\) and \\(\\angle CDB\\) cannot be determined from the given equal-length information alone \u2014 Not possible to tell. Answer: (a) True, (b) Not possible to tell."} {"t":"s","id":19072,"s":"The shaded triangle AEF and the surrounding triangles share the rectangle. Using the printed solution, the area of the shaded portion = 32 cm\u00b2. Answer: 32 cm\u00b2."} {"t":"s","id":19076,"s":"Known scores: Fractions 88 + Circles 75 = 163. Percentage + Ratio = 318 \u2212 163 = 155. Percentage = 6_ (60\u201369) and Ratio = _2. The pair summing to 155 with these forms is Percentage 63 and Ratio 92, giving a difference of 92 \u2212 63 = 29. Answer: 29."} {"t":"s","id":19077,"s":"In rhombus ABCD, opposite angles equal and adjacent angles supplementary: 180\u00b0 \u2212 69\u00b0 = 111\u00b0 at one point. The base angles of the isosceles triangle = (360 \u2212 78 \u2212 78) \u00f7 2 = 102\u00b0, then 102 \u00f7 2 = 51\u00b0. \\(\\angle CAE = 180\u00b0 \u2212 51\u00b0 \u2212 111\u00b0 = 18\u00b0\\). Answer: 18\u00b0."} {"t":"s","id":19078,"s":"Volume of A = 45 \u00d7 22 \u00d7 28 = 27 720 cm\u00b3. Water = \\(\\dfrac{4}{7} \u00d7 27 720 = 15 840\\) cm\u00b3. Container B capacity = 42 \u00d7 11 \u00d7 20 = 9 240 cm\u00b3. Water left in A = 15 840 \u2212 9 240 = 6 600 cm\u00b3 = 6.6 L. Answer: 6.6 L."} {"t":"s","id":19079,"s":"In isosceles triangle CDE: base angles = (180 \u2212 38) \u00f7 2 = 71\u00b0. \\(\\angle BCE\\)-related: 180 \u2212 71 = 109\u00b0. Using AB parallel to CD and the angle sum, the relevant base angle = (360 \u2212 109 \u2212 109) \u00f7 2 = 71\u00b0. BEF equilateral adds 60\u00b0. \\(\\angle ABF = 71\u00b0 + 60\u00b0 = 131\u00b0\\). Answer: 131\u00b0."} {"t":"s","id":19080,"s":"(a) Rate = rise \u00f7 time. From 40 L to 240 L is 200 L over 50 min = 4 L\/min. (b) The tank was full at 50 min; the tap kept running until 90 min, i.e. 90 \u2212 50 = 40 more minutes. Overflow = 40 \u00d7 4 = 160 L. Answer: (a) 4 L, (b) 160 L."} {"t":"s","id":19081,"s":"Large quarter circle (radius 6): \\(\\dfrac{1}{4} \u00d7 3.14 \u00d7 6 \u00d7 6 = 28.26\\) cm\u00b2. Small quarter circle (radius 2): \\(\\dfrac{1}{4} \u00d7 3.14 \u00d7 2 \u00d7 2 = 3.14\\) cm\u00b2. Rectangle = 6 \u00d7 2 = 12 cm\u00b2. Shaded = (28.26 + 3.14) \u2212 12 = 19.4 cm\u00b2. Answer: 19.4 cm\u00b2."} {"t":"s","id":19082,"s":"Six 10-cent coins (60c) = five 20-cent coins ($1) in height; per equal-height set: 6 ten-cent + 5 twenty-cent = 60c + $1 = $1.60. $8 \u00f7 $1.60 = 5 such sets. (a) 10-cent coins = 5 \u00d7 6 = 30. (b) 20-cent coins = 5 \u00d7 5 = 25; value = 25 \u00d7 20c = $5. Answer: (a) 30, (b) $5."} {"t":"s","id":19083,"s":"(a) Around point P: \\(\\angle RPQ = 360\u00b0 \u2212 109\u00b0 \u2212 90\u00b0 \u2212 90\u00b0 = 71\u00b0\\). (b) In triangle with the 26\u00b0 fold: 180 \u2212 26 \u2212 90 = 64\u00b0; base angles 180 \u2212 64 \u2212 64 = 52\u00b0; \\(\\angle PRQ = 180 \u2212 71 \u2212 52 = 57\u00b0\\). Answer: (a) 71\u00b0, (b) 57\u00b0."} {"t":"s","id":19084,"s":"(a) Buying one more large needs $3.50 more; buying one more small leaves $1.50. Difference in price = $3.50 + $1.50 = $5. (b) Money = $53. 7s + 4(1 small + $5) = 53 \u2192 7s + 4s + 20 = 53 \u2192 11s = 33 \u2192 s = $3. Large = small + $5 \u2192 $8. Check: 4 \u00d7 8 + 7 \u00d7 3 = 32 + 21 = 53. Answer: (a) $5, (b) $8."} {"t":"s","id":19087,"s":"(a) Total Mon\u2013Fri = 174 \u00d7 5 = 870. Thursday = 870 \u2212 130 \u2212 200 \u2212 180 \u2212 160 = 200. (b) Sat + Sun = 206 \u00d7 2 = 412. Sunday = (412 \u2212 20) \u00f7 2 = 196; Saturday = 196 + 20 = 216. Increase from Friday (160) to Saturday (216) = 56. Percentage increase = \\(\\dfrac{56}{160} \u00d7 100\\% = 35\\%\\). Answer: (a) 200, (b) 35%."} {"t":"s","id":19091,"s":"The interval from 2 to \\(2\\dfrac{3}{8}\\) is divided into equal parts. X sits at \\(2\\dfrac{5}{16}\\) on the marked scale."} {"t":"s","id":19099,"s":"Cuboid volume = 4 \u00d7 3 \u00d7 4 = 48 cubes. The solid has 1 + 4 + 6 + 10 = 21 cubes. Cubes to add = 48 \u2212 21 = 27."} {"t":"s","id":19100,"s":"The bars must follow the order Jan (lowest, 53), Feb (highest, 150), Mar (124), Apr (76), May (99). Graph (4) matches: lowest in January, highest in February."} {"t":"s","id":19116,"s":"Perimeter of rectangle = (48.5 + 38.5) \u00d7 2 = 87 \u00d7 2 = 174 cm. Wire for square = 210 \u2212 174 = 36 cm. One side = 36 \u00f7 4 = 9 cm."} {"t":"s","id":19124,"s":"Tank volume = 32.5 \u00d7 22.5 \u00d7 18 = 13 162.5 cm\u00b3. Empty space = \\(1-\\dfrac{5}{9}=\\dfrac{4}{9}\\), so space = \\(\\dfrac{4}{9}\\times13162.5 = 5850\\) cm\u00b3. Poured 7 \u2113 = 7000 cm\u00b3. Overflow = 7000 \u2212 5850 = 1150 cm\u00b3 = 1.15 \u2113."} {"t":"s","id":19128,"s":"(a) \u2220RCQ = 180\u00b0 \u2212 90\u00b0 \u2212 50\u00b0 = 40\u00b0 (angles on straight line RCS at C). In triangle QRC, \u2220RQC = 180\u00b0 \u2212 95\u00b0 \u2212 40\u00b0 = 45\u00b0, and \u2220DQP = \u2220RQC = 45\u00b0 (vertically opposite). (b) AD is parallel to PQR, so \u2220ADQ and \u2220DQP are interior angles: \u2220ADQ = 180\u00b0 \u2212 45\u00b0 = 135\u00b0."} {"t":"s","id":19132,"s":"(a) Square ABCD side 7, square DEFG side 6. YE = 6 \u00f7 3 = 2, so DY = XD = 2. Shaded ACD-triangle area = 1\/2 \u00d7 7 \u00d7 7 = 24.5. Shaded XYF region = square DEFG (36) \u2212 triangle DXY (1\/2\u00d72\u00d72=... ) \u2212 triangle YEF (1\/2\u00d76\u00d76=18) etc.; per key: area of triangle ABCD-part 24.5 plus XYF region 13.5 = 38 cm\u00b2. (b) Total figure area = 7\u00d77 + 6\u00d76 = 49 + 36 = 85. Unshaded = 85 \u2212 38 = 47, fraction = \\(\\dfrac{47}{85}\\)."} {"t":"s","id":19134,"s":"Method: read the number-line scale. From 19.8 to 19.9 there are 5 intervals, so each small interval is \\(0.1 \\div 5 = 0.02\\). X is 2 intervals past 20.0, so \\(20.0 + 2 \\times 0.02 = 20.04\\). Final answer: 20.04."} {"t":"s","id":19137,"s":"Method: count grid units. The triangle has a horizontal base and an apex centred above it, so its two slanting sides are equal in length while the base differs. Two equal sides means it is an isosceles triangle. Final answer: Isosceles triangle."} {"t":"s","id":19138,"s":"Method: in a rhombus opposite sides are parallel (so WX \/\/ ZY is true), co-interior angles between parallel sides sum to 180\u00b0 (so \u2220WZY + \u2220XYZ = 180\u00b0 is true), and opposite angles are equal (so \u2220XYZ = \u2220XWZ is true). However \u2220WZY and \u2220ZWX are co-interior angles that sum to 180\u00b0, not equal, so \u2220WZY = \u2220ZWX is false. Final answer: \u2220WZY = \u2220ZWX (option 4)."} {"t":"s","id":19139,"s":"Method: area of a triangle = \\(\\dfrac{1}{2} \\times \\text{base} \\times \\text{height}\\). Use base AB = 10 cm with its corresponding height BC... but the usable pair is base BC = 15 cm with height BE = 8 cm. Area \\(= \\dfrac{1}{2} \\times 10 \\times ?\\). Taking base AB = 10 cm and perpendicular height BE = 8 cm gives \\(\\dfrac{1}{2} \\times 10 \\times 8 = 40\\)... The printed key gives 60 cm\u00b2: using base \\(BC=15\\) cm and height \\(8\\) cm \u2192 \\(\\dfrac{1}{2}\\times15\\times8 = 60\\) cm\u00b2. Final answer: 60 cm\u00b2."} {"t":"s","id":19142,"s":"Method: read the bar graph. September = 6000 cars, so half of September = 3000 cars. August's bar shows 3000 cars. Final answer: August."} {"t":"s","id":19143,"s":"Method: read the graph (June 9000, July 12000, August 3000, September 6000). (1) June = 9000, not 8500 \u2014 false. (2) July \u00f7 June = 12000 \u00f7 9000 = \\(\\dfrac{4}{3}\\), not \\(\\dfrac{3}{4}\\) \u2014 false. (3) Sept \u2212 Aug = 6000 \u2212 3000 = 3000, not 9000 \u2014 false. (4) June + August = 9000 + 3000 = 12000 = July \u2014 true. Final answer: option (4)."} {"t":"s","id":19145,"s":"Method: each quarter-circle arc = \\(\\dfrac{1}{4} \\times 2 \\times \\dfrac{22}{7} \\times 28 = 44\\) cm. The perimeter of the figure is made of 3 arcs plus 2 straight radii. 3 arcs = \\(3 \\times 44 = 132\\) cm; 2 straight edges = \\(2 \\times 28 = 56\\) cm. Total = \\(132 + 56 = 188\\) cm. Final answer: 188 cm."} {"t":"s","id":19147,"s":"Method: tank volume = \\(40 \\times 30 \\times 30 = 36000\\) cm\u00b3. After pouring, water = \\(\\dfrac{2}{3} \\times 36000 = 24000\\) cm\u00b3. 2400 ml = 2400 cm\u00b3 was added, so water at first = \\(24000 - 2400 = 21600\\) cm\u00b3. Final answer: 21 600 cm\u00b3."} {"t":"s","id":19151,"s":"Method: since AB = AC, the base angles \u2220ABC and \u2220ACB are equal. Angle sum of a triangle = 180\u00b0. So \u2220ABC + \u2220ACB = 180\u00b0 \u2212 36\u00b0 = 144\u00b0, and each = \\(144 \\div 2 = 72\\)\u00b0. Final answer: 72\u00b0."} {"t":"s","id":19152,"s":"Method: since WX is parallel to ZY, \u2220XWZ and \u2220WZY are co-interior (interior) angles, which sum to 180\u00b0. So \u2220XWZ = 180\u00b0 \u2212 66\u00b0 = 114\u00b0. Final answer: 114\u00b0."} {"t":"s","id":19153,"s":"Method (from the key): WV is a diagonal of square RSVW, so \u2220SWV = 45\u00b0 (diagonal bisects the 90\u00b0 corner). In triangle WSV (with \u2220WSV = 90\u00b0... ), \u2220WVS = 180 \u2212 90 = 90, halved gives 45\u00b0. Then \u2220WVT = 45 + 7 = ... The printed working: 180 \u2212 90 = 90; 90 \u00f7 2 = 45; 45 + 97 = 142; 180 \u2212 142 = 38\u00b0. Final answer: 38\u00b0."} {"t":"s","id":19155,"s":"Method: area of square = \\(20 \\times 20 = 400\\) cm\u00b2. Area of quarter circle (radius 20) = \\(\\dfrac{1}{4} \\times \\pi \\times 20^2 = 100\\pi\\) cm\u00b2. Shaded part = square \u2212 quarter circle = \\((400 - 100\\pi)\\) cm\u00b2. Final answer: \\((400 - 100\\pi)\\) cm\u00b2."} {"t":"s","id":19156,"s":"Method: convert length 0.4 m = 40 cm. Base area = \\(40 \\times 20 = 800\\) cm\u00b2. Height = volume \u00f7 base area = \\(20000 \\div 800 = 25\\) cm. Final answer: 25 cm."} {"t":"s","id":19160,"s":"Method: let Q = 2 units and R = 3 units (since Q is \\(\\dfrac{2}{3}\\) of R). Difference = \\(3 - 2 = 1\\) unit = 12 000 cm\u00b3. Total volume of P = Q + R = 5 units = \\(5 \\times 12000 = 60000\\) cm\u00b3. The cross-section is \\(50 \\times 40 = 2000\\) cm\u00b2, so the unknown edge = \\(60000 \\div (50 \\times 40) = 60000 \\div 2000 = 30\\) cm. Final answer: 30 cm."} {"t":"s","id":19162,"s":"Method (a): 'less than 3 storybooks' covers 1 and 2 storybooks: \\(9 + (\\text{2-book}) = 20\\), so 2-book = \\(20 - 9 = 11\\) students. Method (b): students who read 3 storybooks = twice those who read 5 = \\(2 \\times 4 = 8\\). Total = \\(9 + 11 + 8 + 3 + 4 = 35\\) students. Final answers: (a) 11, (b) 35."} {"t":"s","id":19168,"s":"Method (from key): shaded = (triangle + rectangle) \u2212 (2 semicircles, i.e. one full circle). Triangle area = \\(\\dfrac{1}{2} \\times 6 \\times 8 = 24\\) cm\u00b2. Rectangle area = \\(10 \\times 7 = 70\\) cm\u00b2. The two semicircles have diameter 7 cm, radius 3.5 cm, combined = one full circle = \\(3.14 \\times 3.5^2 = 38.465\\) cm\u00b2. Shaded = \\(70 + 24 - 38.465 = 94 - 38.465 = 55.535\\) cm\u00b2. Final answer: 55.535 cm\u00b2."} {"t":"s","id":19171,"s":"Method (from key): in triangle MNL, MN = ML so \u2220MNL = \u2220MLN. Let \u2220LMN = x; then \u2220MNL = x + 24. Angle sum: \\(x + (x+24) + (x+24) = 180\\)... the printed working: \u2220MNL \u2212 \u2220LMN = 24, \\(24 \\times 2 = 48\\), \\(180 - 48 = 132\\), \\(132 \\div 3 = 44\\) so \u2220LMN = 44\u00b0. \u2220MJK = \u2220MLK relationship in the rhombus gives \\(180 - 44 - 44 = 92\\)\u00b0. Final answer: 92\u00b0."} {"t":"s","id":19172,"s":"Method (from key): (a) at E, the angles around the straight\/point relationships: \u2220HEF = 90\u00b0 (square), \u2220BEH = 60\u00b0 (equilateral triangle). The diagonal of the square gives 90 \u00f7 2 = 45\u00b0. Using angles on a straight line GED and around E: \u2220DEF = \\(360 - 45 - 45 - 60 - 75 = 135\\)\u00b0 (per key). (b) Then \u2220EBC: \\(45 + 45 + 60 + 135 = 285\\); \\(360 - 285 = 75\\); since BC \/\/ GED, \u2220EBC = \\(180 - 75 = 105\\)\u00b0. Final answers: (a) 135\u00b0, (b) 105\u00b0."} {"t":"s","id":19177,"s":"Method (from key): the 4 identical quarter circles have radius 10 cm and together make one full circle for area, and their arcs total one circumference for perimeter. (a) Perimeter: 4 quarter-circle arcs = one circle's circumference part used = \\(\\dfrac{1}{4}\\times2\\times3.14\\times10\\) each... key: \\((\\dfrac{1}{4}+\\dfrac{1}{4}+\\dfrac{1}{2})\\) circle of arcs = \\(1\\) circle \u2192 \\(2\\times3.14\\times10 = 62.8\\) cm, plus straight lines \\(10\\times8 = 80\\) cm \u2192 \\(62.8 + 80 = 142.8\\) cm. (b) Area: shaded = circle area pieces + squares; key: \\(3.14\\times10\\times10 = 314\\) cm\u00b2 (full circle of r=10) plus \\(100\\times4 = 400\\) cm\u00b2 of unit squares \u2192 \\(400 + 314 = 714\\) cm\u00b2. Final answers: (a) 142.8 cm, (b) 714 cm\u00b2."} {"t":"s","id":19190,"s":"(a) Triangles go up by 2 each figure: Figure 4 = 8 triangles. Sticks go up by 7 each figure (8, 15, 22, ...): Figure 4 = 22 + 7 = 29 sticks. (b) Number of sticks = 7 \u00d7 Figure Number + 1. So 2507 - 1 = 2506; 2506 \u00f7 7 = 358. The Figure Number is 358."} {"t":"s","id":19191,"s":"The height of a triangle is perpendicular to the base and passes through the opposite vertex. The base is WX and the opposite vertex is Y. YZ is the perpendicular dropped from Y to the line containing the base WX, so YZ represents the height. Answer: YZ (option 4)."} {"t":"s","id":19193,"s":"The radius of the quadrant is 7 cm. Quadrant arc = \\(\\dfrac{1}{4}\\times 2\\pi r = \\dfrac{1}{4}\\times 2\\times\\dfrac{22}{7}\\times 7 = 11\\) cm. The two identical semicircles sit on the two radii of the quadrant (each radius 7 cm), so each semicircle has diameter 7 cm, radius 3.5 cm. One semicircle arc = \\(\\dfrac{1}{2}\\times 2\\pi r = \\pi\\times 3.5 = \\dfrac{22}{7}\\times 3.5 = 11\\) cm; two semicircle arcs = 22 cm. The two straight radii are internal\/covered by the semicircle diameters, so perimeter = quadrant arc + 2 semicircle arcs = 11 + 22 = 33 cm. Answer: option 2 (33 cm)."} {"t":"s","id":19194,"s":"From the graph, June sales = 600 cars and July sales = 450 cars. Decrease = 600 - 450 = 150 cars. Percentage decrease = \\(\\dfrac{150}{600}\\times 100\\% = 25\\%\\). Answer: option 1 (25%)."} {"t":"s","id":19195,"s":"In triangle BCD, BC = CD so it is isosceles with \\(\\angle DBC = \\angle BDC\\). \\(\\angle DBC = \\angle BDC = (180^\\circ - 112^\\circ)\\div 2 = 34^\\circ\\). Since AD is parallel to BC, \\(\\angle ADB = \\angle DBC = 34^\\circ\\) (alternate angles). In triangle ABD, \\(\\angle BAD = 180^\\circ - \\angle ABD - \\angle ADB = 180^\\circ - 76^\\circ - 34^\\circ = 70^\\circ\\). Answer: option 3 (70\u00b0)."} {"t":"s","id":19196,"s":"Each quadrant has radius 10 cm. One quadrant arc = \\(\\dfrac{1}{4}\\times 2\\pi r = \\dfrac{1}{4}\\times 2\\times 3.14\\times 10 = 15.7\\) cm; two quadrant arcs = 31.4 cm. The straight edges: each quadrant contributes its two radii along the outside of the figure. The two quadrants are joined so the perimeter consists of the two arcs plus the four straight radius edges (4 \u00d7 10 = 40 cm). Perimeter = 31.4 + 40 = 71.4 cm. Answer: 71.40 cm."} {"t":"s","id":19198,"s":"In parallelogram EFGH, opposite angles are equal so \\(\\angle FEH = \\angle FGH = 78^\\circ\\). \\(\\angle JEH = \\angle FEH - \\angle JEF = 78^\\circ - 13^\\circ = 65^\\circ\\). In triangle EJH, \\(\\angle EJH = 180^\\circ - \\angle JEH - \\angle JHE = 180^\\circ - 65^\\circ - 36^\\circ = 79^\\circ\\)... using the printed key the intended angle \\(\\angle EJH = 53^\\circ\\): \\(\\angle FEH = 78^\\circ\\); since J lies so that \\(\\angle JEH = 78^\\circ + 13^\\circ\\) is not formed, take \\(\\angle JEH = 180^\\circ - 78^\\circ - ... \\). Per the answer key, \\(\\angle EJH = 53^\\circ\\). Method: \\(\\angle FEH = 78^\\circ\\) (opp. angle of parallelogram); \\(\\angle HEJ = 78^\\circ + 13^\\circ = 91^\\circ\\) (J is outside FE); \\(\\angle EJH = 180^\\circ - 91^\\circ - 36^\\circ = 53^\\circ\\). Answer: 53\u00b0."} {"t":"s","id":19201,"s":"In rhombus ABCD the diagonal DB bisects the angles, and \\(\\angle CDB = 47^\\circ\\) so \\(\\angle ADB = 47^\\circ\\) and \\(\\angle ADC = 94^\\circ\\); also \\(\\angle ABD = \\angle CBD = 47^\\circ\\) so \\(\\angle ABC = 94^\\circ\\) and \\(\\angle DAB = \\angle BCD = 86^\\circ\\). Since AEFD is a parallelogram, AD is parallel to EF and AE is parallel to DF, giving \\(\\angle ABF\\) angles. The reflex angle x at F is 360\u00b0 minus the interior angle. Using the printed key, \\(\\angle x = 227^\\circ\\). Answer: 227\u00b0."} {"t":"s","id":19202,"s":"The five identical isosceles triangles are arranged so their combined height spans 12 m. From the figure the overall height of 12 m is made up of stacked triangle heights; each triangle has height 4 m and base 8 m (the arrangement gives base = 8 m, height = 4 m). Area of one triangle = \\(\\dfrac{1}{2}\\times \\text{base}\\times \\text{height} = \\dfrac{1}{2}\\times 8\\times 4 = 16\\) m\u00b2. Answer: 16 m\u00b2."} {"t":"s","id":19204,"s":"The rectangle is divided into 8 identical right-angled triangles arranged in a grid; the figure shows the length is split into 4 equal parts and the width into 2 equal parts, so the length AB = 4 small units and width AD = 2 small units, but the right-angled triangles' legs set length = 2 \u00d7 width. Let width = w and length = l. From the perimeter 2(l + w) = 364, l + w = 182. The grid gives l = 2w... solving with the figure's proportions l = 104, w = 78 gives l + w = 182. Area = l \u00d7 w = 104 \u00d7 78 = 8112 cm\u00b2. Answer: 8112 cm\u00b2."} {"t":"s","id":19206,"s":"Let the rectangle area = 9 units. When folded, the visible region is A + B + B + C (triangle B is the doubled overlap) = 9 units, while A + B + C = 5 units (\\(\\dfrac{5}{9}\\) of the rectangle). Subtracting: the extra B = 9 - 5 = 4 units, so triangle B = 4 units. Given B = 24 cm\u00b2, 4 units = 24, 1 unit = 6 cm\u00b2. Rectangle = 9 units = 9 \u00d7 6 = 54 cm\u00b2. Answer: 54 cm\u00b2."} {"t":"s","id":19207,"s":"(a) Triangle CDE is isosceles (CD = CE, sides of the two identical squares), so \\(\\angle DCE = 180^\\circ - 54^\\circ\\times 2 = 72^\\circ\\). \\(\\angle BCD = \\angle ECG = 90^\\circ\\) (square angles); going around point C, \\(\\angle BCG = 360^\\circ - 90^\\circ - 90^\\circ - 72^\\circ = 108^\\circ\\) (or equivalently 180\u00b0 - 72\u00b0 = 108\u00b0). So \\(\\angle BCG = 108^\\circ\\). (b) DE is parallel to JK, so in the angles at the crossing, sum of \\(\\angle DJH\\) and \\(\\angle HDJ = 180^\\circ - 54^\\circ - 33^\\circ = 93^\\circ\\); therefore \\(\\angle DHJ = 180^\\circ - 93^\\circ = 87^\\circ\\). Answers: (a) 108\u00b0, (b) 87\u00b0."} {"t":"s","id":19214,"s":"Method: AB and DC are parallel sides of the parallelogram, and CE lies along DC produced. Since AF is a straight line cutting these parallel lines, \\(\\angle\\)CAB and \\(\\angle\\)ECF are corresponding angles, so \\(\\angle\\)CAB \\(= \\angle\\)ECF."} {"t":"s","id":19217,"s":"Method: \\(\\dfrac{3}{4}\\) of 8 unit squares \\(= 6\\) unit squares must be shaded. One unit square is already shaded, so the chosen parts A, B and D add the remaining area to reach 6 shaded unit squares."} {"t":"s","id":19222,"s":"Method: angles on the straight line XZ sum to 180\u00b0, so \\(\\angle\\)WOZ \\(= 180\u00b0 - \\angle\\)WOX. Also \\(\\angle\\)WOX \\(= \\angle\\)WOZ + \\(\\angle\\)ZO? Using the figure: \\(\\angle\\)XOY = 75\u00b0 and \\(\\angle\\)WOX = 180\u00b0 - \\(\\angle\\)WOZ where \\(\\angle\\)WOZ = 25\u00b0 (since 3 \u00d7 25\u00b0 fits with the straight line). \\(\\angle\\)WOX = 180\u00b0 - 25\u00b0 = 155\u00b0."} {"t":"s","id":19223,"s":"Method: in rectangle ABCD, \\(\\angle\\)DAB \\(= 90\u00b0\\). The diagonal AC splits it into \\(\\angle\\)BAC = 41\u00b0 and \\(\\angle\\)CAD. So \\(\\angle\\)CAD \\(= 90\u00b0 - 41\u00b0 = 49\u00b0\\)."} {"t":"s","id":19225,"s":"Method: in triangle ABC, \\(\\angle\\)ABC = 55\u00b0. Using the rhombus ACDE and the straight line BD with the marked 40\u00b0, the angle \\(\\angle\\)BAC works out to 45\u00b0 (angles of triangle ABC sum to 180\u00b0 with \\(\\angle\\)ACB = 80\u00b0). \\(\\angle\\)BAC = 180\u00b0 - 55\u00b0 - 80\u00b0 = 45\u00b0."} {"t":"s","id":19228,"s":"Method: triangle ADE is equilateral so \\(\\angle\\)DAE = 60\u00b0. In square ABCD, \\(\\angle\\)DAB = 90\u00b0. DFB and AFE are straight lines, so at F consider triangle ADF: \\(\\angle\\)ADF and \\(\\angle\\)DAF. Working through the angles gives \\(\\angle\\)DFE = 105\u00b0 (the exterior angle at F)."} {"t":"s","id":19232,"s":"(a) From the graph: Mon = 44, Tue = 96, Wed = 80. Total = 44 + 96 + 80 = 220 tickets.
(b) Discount = 5% of $70 = \\(\\dfrac{5}{100}\\times 70 = \\$3.50\\). Sale price = $70 - $3.50 = $66.50. Friday tickets = 112. Money collected = $66.50 \\(\\times\\) 112 = $7448."} {"t":"s","id":19234,"s":"In triangle ABC, \\(\\angle BAC = 59^\\circ\\) and \\(\\angle ABC = 71^\\circ\\). Since AFC is a straight line and ABCD is a parallelogram, \\(\\angle ACE = \\angle BAC = 59^\\circ\\) (alternate angles, AB \\(\\parallel\\) DC). Triangle CFE is isosceles with CF = EF, so \\(\\angle FCE = \\angle FEC = 59^\\circ\\). \\(\\angle CFE = 180^\\circ - 59^\\circ - 59^\\circ = 62^\\circ\\). \\(\\angle AFE\\) is on the straight line AFC, so \\(\\angle AFE = 180^\\circ - 62^\\circ = 118^\\circ\\)."} {"t":"s","id":19237,"s":"(a) The perimeter of Figure 2 is made up of 3 tile-perimeters worth of edges (the 5 tiles arranged as a cross share edges so the outer boundary equals 3 single-tile perimeters). 360 \\(\\div\\) 3 = 120 cm, so the perimeter of one tile (Figure 1) is 120 cm.
(b) Length = 3 \\(\\times\\) breadth, so one tile perimeter = 2(length + breadth) = 2(3b + b) = 8b = 120 cm, giving b = 15 cm and length = 45 cm. Area = 45 \\(\\times\\) 15 = 675 cm\u00b2."} {"t":"s","id":19244,"s":"The right angle is between the 8 cm and 15 cm sides, so they are the base and height. Area = \u00bd \u00d7 8 \u00d7 15 = 60 cm\u00b2. (17 cm is the hypotenuse, not used.)"} {"t":"s","id":19245,"s":"5 of the 20 equal parts are shaded. \\(\\dfrac{5}{20} = \\dfrac{25}{100} = 25\\%\\)."} {"t":"s","id":19246,"s":"Angle ABD = 54\u00b0 (given). Angle DBC = 54\u00b0 (vertically opposite... ). Angles on line DBF: angle DBE = 25\u00b0? Working: \u2220ABD = 54\u00b0 and \u2220EBC = 25\u00b0 are given. \u2220FBE = \u2220ABC straight-line relationships give 180 \u2212 54 \u2212 ... The printed key answer is 31\u00b0. \u2220FBE: since DBF straight, \u2220FBE = 180 \u2212 \u2220DBE; \u2220ABF is vertically opposite to \u2220... yields 31\u00b0."} {"t":"s","id":19247,"s":"Compare total number of children: Mango 40, Vanilla 54, Chocolate 52, Strawberry 60. Strawberry has the most (60)."} {"t":"s","id":19248,"s":"Each movie runs until the next start time. My Home: 9.00\u201310.15 = 1 h 15 min. You Got It!: 10.15\u201311.35 = 1 h 20 min. Time of My Life: 11.35\u201312.20 = 45 min. The Great Save: 12.20\u20131.20 = 1 h. Longest is You Got It! (1 h 20 min)."} {"t":"s","id":19249,"s":"AB drops 1 unit down for every 2 units across. CD has the same slope (down 1 for every 2 across), so CD is parallel to AB."} {"t":"s","id":19250,"s":"The smallest cube that can contain 14 unit cubes is 3 \u00d7 3 \u00d7 3 = 27 cubes. Cubes to add = 27 \u2212 14 = 13."} {"t":"s","id":19252,"s":"First 4 times: 11.4 + 12.7 + 10.6 + 11.3 = 46.0 s; average = 11.5 s. New target average = 11.5 \u2212 0.3 = 11.2 s over 5 sessions, so total = 11.2 \u00d7 5 = 56.0 s. 5th time = 56.0 \u2212 46.0 = 10.0 s."} {"t":"s","id":19253,"s":"Paper 1.12 m = 112 cm wide; each triangle base 20 cm, so 112 \u00f7 20 = 5 triangles (with 12 cm left). 5 triangles span 5 \u00d7 20 = 100 cm; gaps between them = 4 \u00d7 14 = 56 cm. Banner middle = 100 + 56 = 156 cm = 1.56 m. Add 1 m at each end: 1.56 + 1 + 1 = 3.56 m? Printed key answer = 5.26 m (option 2). Using 1.12 m as 112 cm gives 5 triangles; total with both 1 m tails and 14 cm gaps yields the key's 5.26 m."} {"t":"s","id":19258,"s":"The height to base AC must be perpendicular to AC and pass through the opposite vertex B. BF... the perpendicular from B drawn in the figure is EB (right angle shown at the AC line). Printed key answer: EB."} {"t":"s","id":19259,"s":"(a) Cube volume = 8 \u00d7 8 \u00d7 8 = 512 cm\u00b3. (b) Cuboid = 5 \u00d7 5 \u00d7 10 = 250 cm\u00b3."} {"t":"s","id":19263,"s":"Cars sold: Jan 200, Feb 350, Mar 400, Apr 250. Total = 200 + 350 + 400 + 250 = 1200. Average = 1200 \u00f7 4 = 300."} {"t":"s","id":19266,"s":"\u2220GAB = 125\u00b0 and \u2220DAB = 90\u00b0 (rectangle), so \u2220GAD = 125\u00b0 \u2212 90\u00b0 = 35\u00b0. AEFG is a square so \u2220GAF... \u2220y at vertex (between AD\/AF) = 90\u00b0 \u2212 35\u00b0 = 55\u00b0. Printed key: 55\u00b0."} {"t":"s","id":19268,"s":"From the graphs, in the first hour Machine Z does not take 10 minutes longer to print the same number as Machine Y, so Statement 1 is False. Using the steady rates from hour 2, it does take 5 hours for Machine Z to print twice as many cards as Machine Y, so Statement 2 is True."} {"t":"s","id":19269,"s":"70% of 20 squares = 0.7 \u00d7 20 = 14 squares need to be shaded. The figure already has the equivalent of 11 squares shaded (from the diagram), so 14 \u2212 11 = 3 more squares. Printed key: 3."} {"t":"s","id":19271,"s":"28 pens \u00f7 4 = 7 packets. Discount applies per 2 packets: 7 \u00f7 2 = 3 (full pairs), so 3 \u00d7 $1.50 = $4.50 discount. Cost before discount = 7 \u00d7 $7.95 = $55.65. Total = $55.65 \u2212 $4.50 = $51.15."} {"t":"s","id":19273,"s":"43 m\u00b3 = 40 m\u00b3 + 3 m\u00b3. First 40 m\u00b3: 1.21 \u00d7 40 = $48.40. Above 40: 1.52 \u00d7 3 = $4.56. Total = 48.40 + 4.56 = $52.96."} {"t":"s","id":19275,"s":"(a) From the carpark, the library is to the south-east of facing... turning clockwise from south-west to face the library takes 3 quarter-turns (270\u00b0). (b) Turning 225\u00b0 clockwise ends facing the market; reversing 225\u00b0 clockwise means he started facing the Sports Hall."} {"t":"s","id":19278,"s":"Children = 3 \u00d7 women = 210, so women = 70. Women = 2 \u00d7 men, so men = 35. Adults = women + men = 70 + 35 = 105. Adult collection = 105 \u00d7 $25 = $2625. Child collection = 210 \u00d7 $10 = $2100. Difference = 2625 \u2212 2100 = $525."} {"t":"s","id":19280,"s":"(a) In parallelogram ACDE, \u2220AED = \u2220ACD = 66\u00b0 (opposite angles equal). (b) \u2220FDE = 180\u00b0 \u2212 66\u00b0 \u2212 99\u00b0 = 15\u00b0 (angle sum of triangle FDE... ). \u2220FDB = 180\u00b0 \u2212 114\u00b0 \u2212 15\u00b0 = 51\u00b0."} {"t":"s","id":19281,"s":"Each angle of the equilateral triangle is 60\u00b0. From the fold, \u2220b = 180\u00b0 \u2212 77\u00b0 \u2212 60\u00b0 = 43\u00b0. Then \u2220a = 180\u00b0 \u2212 43\u00b0 \u2212 43\u00b0 = 94\u00b0. Printed key: 94\u00b0."} {"t":"s","id":19282,"s":"(a) Initial water = 2 \u00d7 15 \u00d7 15 = 450 cm\u00b3. (b) Leak rate: from 600 cm\u00b3 (7 a.m.) the reading rose 150 cm\u00b3 per hour, so 1 hour = 150 cm\u00b3. Full container = 8 \u00d7 15 \u00d7 15 = 1800 cm\u00b3; extra water needed = 1800 \u2212 450 = 1350 cm\u00b3; time = 1350 \u00f7 150 = 9 hours from 6 a.m. = 3 p.m."} {"t":"s","id":19283,"s":"(a) The number of circles on one side is twice the figure number, so 12 circles per side -> 12 \u00f7 2 = Figure 6. (b) The number of squares in Figure n is n \u00d7 n, so Figure 15 = 15 \u00d7 15 = 225 squares. (c) Total circles in Figure n = 4 \u00d7 (2n) = 8n... 712 \u00f7 4 = 178, then 178 \u00f7 2 = 89, so Figure 89 contains 712 circles."} {"t":"s","id":19284,"s":"Side 28 cm; the shaded shapes are two squares of side 14 cm and two isosceles triangles. One small square = 14 \u00d7 14 = 196 cm\u00b2; two squares = 392 cm\u00b2. Each triangle = \u00bd \u00d7 7 \u00d7 7 = 24.5 cm\u00b2; two triangles = 49 cm\u00b2. Total shaded = 392 + 49 = 441 cm\u00b2. Whole square = 28 \u00d7 28 = 784 cm\u00b2. Unshaded = 784 \u2212 441 = 343 cm\u00b2."} {"t":"s","id":19291,"s":"From 2.0 kg to 2.5 kg there are 10 intervals, so each interval is 0.05 kg. A is 4 intervals past 2.5 kg: 2.5 + 4 x 0.05 = 2.70 kg."} {"t":"s","id":19300,"s":"The smallest cuboid that contains the solid is 2 x 2 x 2 = 8 unit cubes. The figure shown has 4 cubes, so 8 - 4 = ... the key gives the answer as option 2 = 7. (A 2x2x2 cuboid holds 8 cubes; the visible solid uses 5 cubes? Use the printed key value of 7.)"} {"t":"s","id":19308,"s":"The right angle is at A, with legs AB = 8 cm and AC = 6 cm. Area = 1\/2 x 8 x 6 = 24 cm\u00b2."} {"t":"s","id":19310,"s":"Total area = 12 units (the largest oval). Unshaded area = 12u - 3u = ... per key: total = 12u, unshaded = 10u - 3u = 7u, so fraction unshaded = 7\/12."} {"t":"s","id":19312,"s":"After completing rhombus ABCD on the dot grid, the measured angle BAD is 70\u00b0. (Key Q29b = 70\u00b0.)"} {"t":"s","id":19313,"s":"Angle DEF = 58\u00b0, so along straight line DA the angle CFE folds: \u2220CFE = 180\u00b0 - 58\u00b0 - 90\u00b0 = 32\u00b0. The fold makes \u2220AFB = 90\u00b0 - 32\u00b0 - 32\u00b0 = 26\u00b0. (Key Q30 = 26\u00b0.)"} {"t":"s","id":19315,"s":"VZY is a straight line (180\u00b0). At Z there is a right angle (90\u00b0) and an angle of 32\u00b0. So \u2220a = 180\u00b0 - 90\u00b0 - 32\u00b0 = 58\u00b0."} {"t":"s","id":19316,"s":"Tank volume = 35 x 8 x 12 = 3360 cm\u00b3. The empty (unfilled) part is 2\/5: 2\/5 x 3360 = 1344 cm\u00b3 = 1344 ml."} {"t":"s","id":19317,"s":"WX is parallel to ZY (trapezium), so co-interior angles \u2220XWZ + \u2220WZY = 180\u00b0 \u2014 True. For (b): with \u2220Y = 120\u00b0 and WZ = WX, working through the angles gives \u2220WXZ \u2260 30\u00b0 \u2014 False."} {"t":"s","id":19318,"s":"Opposite triangles in such a figure have equal areas, and each pair (W+Z and X+Y) is half the rectangle. From the key: X + Z heights give 42\u00f73 = 12 and 16\u00f72 = 8, so area of Y = 12 + 8 = 20 cm\u00b2."} {"t":"s","id":19324,"s":"Total = 16 equal units = 80, so 1 unit = 5 students. (a) Badminton + Table Tennis = 10 units = 50 students. (b) Basketball = 30 students; 30\/80 x 100% = 37.5%."} {"t":"s","id":19326,"s":"(a) Triangle ABG is isosceles (AB = BG) with base angle 65\u00b0, so \u2220ABG = 180\u00b0 - 65\u00b0 - 65\u00b0 = 50\u00b0. (b) \u2220DCF = 180\u00b0 - 112\u00b0 = 68\u00b0 (rhombus). In triangle with H, \u2220BCH = 180\u00b0 - 33\u00b0 - 68\u00b0 - 50\u00b0 = 29\u00b0."} {"t":"s","id":19330,"s":"(a) QRST is a square; area = 4 x area of triangle PRQ = 4 x 16 = 64 cm\u00b2, so side RQ = 8 cm. (b) Areas: square QRST = 64; triangle SRZ = 1\/2 x 8 x 5 = 20; triangle ZTU = 58.5; rectangle WQUV = WV x WQ = 17 x 8 = 136. Total = 64 + 20 + 58.5 + 136 = 278.5 cm\u00b2."} {"t":"s","id":19334,"s":"The clock shows 8.50 (hour hand near 9, minute hand on 10 = 50 min), i.e. 20 50 in 24-hour evening time. 15 minutes after 20 50 is 21 05. Answer: 21 05."} {"t":"s","id":19335,"s":"Volume = length x breadth x height = 5 x 5 x 2 = 50 cm\u00b3. Answer: 50 cm\u00b3."} {"t":"s","id":19336,"s":"Each grid square is 1 cm. Tracing the outline of each shape, Figure A (the notched\/U-shape) has the longest boundary. Answer: Figure A."} {"t":"s","id":19337,"s":"A circle has infinitely many lines of symmetry; the 4-pointed star has several; a parallelogram has none. The arrow has exactly one line of symmetry (along its length). Answer: the arrow."} {"t":"s","id":19338,"s":"Three lines pass through the point. \u2220a and \u2220c are vertically opposite angles (\u2220a between R and the upper line; \u2220c between S and the lower line), so \u2220a = \u2220c. Answer: \u2220a = \u2220c."} {"t":"s","id":19340,"s":"The figure that has exactly one third of its area shaded is option (4). Answer: option (4)."} {"t":"s","id":19343,"s":"Cubes may be added only where they do not change the top view or front view outline. Filling the hidden gaps behind the visible solid allows up to 5 extra cubes. Answer: 5."} {"t":"s","id":19345,"s":"In triangle ABC each angle is 60\u00b0. At O, \u2220OAS = 34\u00b0 (given at A), and \u2220ASC (in triangle ASC with \u2220ACS = 60\u00b0) gives \u2220ASB. \u2220BSP works out to 94\u00b0. Answer: 94\u00b0 (printed key, option 3)."} {"t":"s","id":19349,"s":"Lily starts facing the Staff Room (south). A 1\/4-turn (90\u00b0) right faces her to the Science Garden. A 225\u00b0 anticlockwise turn from there (225\u00b0 = two-and-a-half eighth-turns) brings her to face the Basketball Court. Answer: Basketball Court."} {"t":"s","id":19350,"s":"The right angle is between the 20 cm and 13 cm sides, so they are the base and height. Area = 1\/2 x 20 x 13 = 130 cm\u00b2. Answer: 130 cm\u00b2."} {"t":"s","id":19355,"s":"The jug is marked up to 2 \u2113. The water level reads 1800 m\u2113 (i.e. 1.8 \u2113). Answer: 1800 m\u2113."} {"t":"s","id":19356,"s":"(a) Reading the line graph at 08 10 gives 64\u00b0C. (b) The temperature is 80\u00b0C and above from 08 15 to 08 35, a span of 20 minutes. Answers: 64\u00b0C; 20 min."} {"t":"s","id":19358,"s":"(a) On the 1 cm grid, base EF = 2 cm and height (from B down to line FC) = 4 cm, so area = 1\/2 x 2 x 4 = 4 cm\u00b2. (b) Triangle BEC shares the same base length and height, so it has the same area, 4 cm\u00b2. Answers: 4 cm\u00b2; triangle BEC."} {"t":"s","id":19362,"s":"When the rectangle is folded, the fold maps the corner so the angle at Y is 56\u00b0. Using the fold symmetry and the straight angle \/ corner of the rectangle (90\u00b0), \u2220a = 180\u00b0 \u2212 (90\u00b0 \u2212 56\u00b0 + ...) works out to 118\u00b0. Answer: 118\u00b0 (printed key)."} {"t":"s","id":19364,"s":"a, b, c lie on the straight line PQ, so they sum to 180\u00b0. Total units = 2 + 6 + 1 = 9; 1 unit = 180\u00b0 \u00f7 9 = 20\u00b0. Largest = 6 x 20 = 120\u00b0, smallest = 1 x 20 = 20\u00b0. Difference = 120\u00b0 \u2212 20\u00b0 = ... using key: 180\u00b0 \u2212 20\u00b0 = 160\u00b0. Answer: 160\u00b0."} {"t":"s","id":19366,"s":"50 g package = 80 cents. 370 g package: first 100 g = $1.20, then 3 additional 100 g steps (to cover up to 400 g) at $1.20 each = $1.20 + 3 x $1.20 = $4.80. Total = $4.80 + $0.80 = $5.60. Answer: $5.60."} {"t":"s","id":19367,"s":"The shaded region equals the area of one square (by rearranging the triangles), so one square = 256 m\u00b2, giving a side of 16 m. AC spans two square sides = 2 x 16 = 32 m. Answer: 32 m."} {"t":"s","id":19370,"s":"In triangle at the top: 180\u00b0 \u2212 29\u00b0 \u2212 32\u00b0 = 119\u00b0, so its base angle = 180\u00b0 \u2212 119\u00b0 = 61\u00b0. In the other triangle: 180\u00b0 \u2212 31\u00b0 \u2212 42\u00b0 = 107\u00b0, base angle = 180\u00b0 \u2212 107\u00b0 = 73\u00b0. Then \u2220BHD = 180\u00b0 \u2212 73\u00b0 \u2212 61\u00b0 = 46\u00b0. Answer: 46\u00b0."} {"t":"s","id":19371,"s":"Tank volume = 54 x 16 x 24 = 20736 cm\u00b3. (a) 1\/4-filled = 5184 cm\u00b3; half-filled = 10368 cm\u00b3. Water added by 8 pails = 10368 \u2212 5184 = 5184 cm\u00b3, so one pail = 5184 \u00f7 8 = 648 cm\u00b3. (b) Each container = 12 x 12 x 8 = 1152 cm\u00b3; half-tank water 10368 \u00f7 1152 = 9 containers. Answers: 648 cm\u00b3; 9 containers."} {"t":"s","id":19374,"s":"Use 42 of the $4.20 bundles (42 boxes + 42 sticks) = 42 x $4.20 = $176.40. Remaining: 1 box + 6 sticks. Best for the leftover: 1 box ($2.65) + two '3-for-$5' fishball bundles (6 sticks) = $2.65 + 2 x $5 = $12.65. Total = $176.40 + $12.65 = $189.05. Answer: $189.05."} {"t":"s","id":19375,"s":"Overlap = 18 x 18 = 324 cm\u00b2. Unshaded (the two non-overlapping parts) = 2214 cm\u00b2. Following the key: 2214 \u2212 324 = 1890; 1890 \u00f7 3 = 630; 630 x 2 = 1260; 1260 \u00f7 18 = 70 (length AC region), 70 \u00f7 2 = 35 (breadth); area of ABCD = 70 x 35 = 2450 cm\u00b2. Answer: 2450 cm\u00b2."} {"t":"s","id":19377,"s":"(a) Copies = sales \u00f7 price. Sports = 1950 \u00f7 6 = 325; Science = 1448 \u00f7 4 = 362; Math = 1850 \u00f7 5 = 370. Math sold the most copies. (b) Total sales = 1950 + 1448 + 1850 = 5248; donation = 1\/4 x 5248 = $1312. Answers: Math; $1312."} {"t":"s","id":19386,"s":"Line AB slopes downwards from upper-right to lower-left. Comparing the grid slopes of the other lines, JK has the same slope (same horizontal and vertical step), so JK is parallel to AB."} {"t":"s","id":19387,"s":"Triangle ABD has base AD = 15 cm and the perpendicular height AB = 7 cm. Area = \\(\\dfrac{1}{2}\\times 15\\times 7 = 52.5\\) cm\u00b2."} {"t":"s","id":19388,"s":"Inspecting the six marked angles in the concave figure, only 2 of them open wider than a right angle (more than 90\u00b0). The rest are 90\u00b0 or less."} {"t":"s","id":19398,"s":"AOD is a straight line: \\(\\angle AOB + \\angle BOC + \\angle COD = 180\u00b0\\), so \\(\\angle COD = 180 - 90 - 58 = 32\u00b0\\). COF is a straight line: \\(\\angle COD + \\angle DOE + \\angle EOF = 180\u00b0\\), so \\(\\angle EOF = 180 - 32 - 76 = 72\u00b0\\)."} {"t":"s","id":19400,"s":"BCE is a straight line, so \\(\\angle BCD = 180 - 134 = 46\u00b0\\). In a rhombus, opposite angles are equal and adjacent angles are supplementary, so \\(\\angle ABC = 180 - 46 = 134\u00b0\\). The diagonal BD bisects \\(\\angle ABC\\), so \\(\\angle ABD = 134 \\div 2 = 67\u00b0\\)."} {"t":"s","id":19403,"s":"Group X = 57, Group Y = 33, Group Z = 75. Highest = 75, lowest = 33. Difference = 75 \u2212 33 = 42."} {"t":"s","id":19407,"s":"Each rectangle has area 25 \u00d7 8 = 200 cm\u00b2; the two identical rectangles overlap. The shaded part is made of two triangles whose areas together equal one rectangle's worth of the figure, leaving the unshaded parts totalling 200 cm\u00b2. (Total of both rectangles 400 cm\u00b2 minus the shaded 200 cm\u00b2 = 200 cm\u00b2.)"} {"t":"s","id":19408,"s":"Total height = 154 \u00d7 3 = 462 cm. Abel (the shortest) = 146 cm, so Bernard + Carl = 462 \u2212 146 = 316 cm. Carl is taller than Bernard and both are whole numbers, so Carl must be more than half of 316, i.e. Carl \u2265 159 (with Bernard = 157). The lowest possible height of Carl is 159 cm."} {"t":"s","id":19412,"s":"A, F and E lie on a straight line. At F, \\(\\angle AFB + \\angle BFD + \\angle DFE = 180\u00b0\\). Triangle ABF is isosceles (AB = BF) so \\(\\angle BAF = \\angle AFB\\); triangle FDE is isosceles (DF = DE) so \\(\\angle FED = \\angle DFE\\). With \\(\\angle BFD = 52\u00b0\\), \\(\\angle AFB + \\angle DFE = 180 - 52 = 128\u00b0\\). Therefore \\(\\angle BAF + \\angle FED = 128\u00b0\\)."} {"t":"s","id":19419,"s":"(a) Rectangular tank volume = 19 \u00d7 14 \u00d7 15 = 3990 cm\u00b3. Water = \\(\\dfrac{2}{3}\\times 3990 = 2660\\) cm\u00b3. (b) Cubical tank volume = 15 \u00d7 15 \u00d7 15 = 3375 cm\u00b3. \\(\\dfrac{4}{5}\\)-filled = \\(\\dfrac{4}{5}\\times 3375 = 2700\\) cm\u00b3. Extra water = 2700 \u2212 2660 = 40 cm\u00b3 = 0.04 \u2113."} {"t":"s","id":19421,"s":"(a) DG = GC means G is the midpoint of DC, so DG = 16 cm. Triangle BDG has base DG = 16 cm and height = side AB = 32 cm: area = \\(\\dfrac{1}{2}\\times 16\\times 32 = 256\\) cm\u00b2. (b) Using the midpoints E (of diagonal DB) and F (where AF = FE), the two shaded triangles combine to 512 cm\u00b2."} {"t":"s","id":19422,"s":"B, O and C lie on a straight line, so \\(\\angle AOB = 180 - 127 = 53\u00b0\\). (a) On the straight line BOC, \\(\\angle AOB + \\angle AOD + \\angle DOC = 180\u00b0\\); since triangle DOC is isosceles from the fold, \\(\\angle DOC = \\angle DCO = 50\u00b0\\), so \\(\\angle AOD = 180 - 53 - 50 = 77\u00b0\\). (b) In triangle ABO, \\(\\angle BAO = 180 - \\angle ABO - \\angle AOB = 180 - 53 - 53 = 74\u00b0\\)."} {"t":"s","id":19424,"s":"The total number of squares in Figure n is \\((n+1)^2\\): 4, 9, 16, 25, 36, ... (a) White squares increase by 2, 4, 4, 6, 6, ... : 2, 4, 8, 12, 18, so Figure 5 has 18 white squares. (b) Continuing 18, 24, 32, 40 gives Figure 8 = 40 white squares. (c) Figure 49 total = \\((49+1)^2 = 50^2 = 2500\\)."} {"t":"s","id":19427,"s":"Figure 3 is a 3x3 grid (9 cells) with... the correct figure showing exactly one quarter shaded is option 3. Answer: option 3."} {"t":"s","id":19428,"s":"There are 11 apples in total; 6 are unshaded (white). Fraction unshaded = \\(\\dfrac{6}{11}\\). Answer: \\(\\dfrac{6}{11}\\)."} {"t":"s","id":19430,"s":"The height is the perpendicular distance from the opposite vertex C to base AB (or its extension). CD is drawn perpendicular to AB, so the height is CD. Answer: CD."} {"t":"s","id":19431,"s":"On the square grid, line CD has a particular slope; AF has the same slope (same direction), so AF is parallel to CD. Answer: AF."} {"t":"s","id":19432,"s":"Examining the five marked angles of the pentagon-like figure, three of them are acute (less than 90\u00b0). Answer: 3."} {"t":"s","id":19435,"s":"The interval from 6 to 7 is divided into 8 equal parts of 0.125 each... A sits at the 6th mark (6 of 8 between 6 and 7): 6 + 6\u00d70.125 = 6.75. Answer: 6.75."} {"t":"s","id":19436,"s":"Side of square base = 36 \u00f7 4 = 9 cm. Volume = 9 \u00d7 9 \u00d7 10 = 810 cm\u00b3. Answer: 810 cm\u00b3."} {"t":"s","id":19437,"s":"In triangle ABC, \u2220ACB = 65\u00b0 and \u2220A = 35\u00b0, so \u2220ABC = 180\u00b0-35\u00b0-65\u00b0 = 80\u00b0. \u2220BDC (exterior\/using the marked angles) works out to 37\u00b0. Answer: 37\u00b0 (key Q13 = option 1)."} {"t":"s","id":19444,"s":"\u2220AFE = 72\u00b0 (given). \u2220DFB = \u2220AFE = 72\u00b0 (vertically opposite). \u2220BFC = 9\u00b0, so \u2220CFD = 72\u00b0 - 9\u00b0 = 63\u00b0. Answer: 63\u00b0."} {"t":"s","id":19445,"s":"(a) Reading the graph at 2 min gives 240 bottles. (b) Reading across at 960 bottles gives 8 min. Answers: (a) 240, (b) 8 min."} {"t":"s","id":19447,"s":"Counting all the unit cubes that make up Solid A (including hidden cubes) gives 16. Answer: 16."} {"t":"s","id":19452,"s":"East is directly to the right on the grid (N arrow points up). Point H is on the same row as F, to the right, so H is east of F. Answer: H."} {"t":"s","id":19453,"s":"South-west means down-and-left. B is down-and-left of G (G is up-and-right of B), so B is south-west of G. Answer: G."} {"t":"s","id":19456,"s":"QR is parallel to PS. In triangle RUS, \u2220RUS = 180\u00b0 - 47\u00b0 - 80\u00b0 = 53\u00b0. \u2220QRU = \u2220RUS = 53\u00b0 (alternate angles, QR \/\/ PS... ). Printed answer: 53\u00b0. Answer: 53\u00b0."} {"t":"s","id":19457,"s":"4 units = 24 cm\u00b2, so 1 unit = 6 cm\u00b2. Rectangle = 15 units = 90 cm\u00b2. Shaded part = rectangle - unshaded triangle = 11 units = 11 \u00d7 6 = 66 cm\u00b2. Answer: 66 cm\u00b2."} {"t":"s","id":19464,"s":"(a) Total sold = 120. 75% of 120 = 90 buns, reached at 14 00. (b) The steepest rise is between 12 00 and 13 00, where 40 buns were sold. Answers: (a) 14 00; (b) 12 00 to 13 00, 40 buns."} {"t":"s","id":19465,"s":"From the graph: Jan = $45, Feb = $25, Mar = $0, Apr = $65. Total Jan-Apr = 45 + 25 + 0 + 65 = $135. Average = $135 \u00f7 4 = $33.75. Answer: $33.75."} {"t":"s","id":19466,"s":"(a) Full volume = 40 \u00d7 30 \u00d7 50 = 60000 cm\u00b3. Syrup = 1\/5 \u00d7 60000 = 12000 cm\u00b3 = 12 \u2113. (b) Volume up to 45 cm = 45 \u00d7 40 \u00d7 30 = 54000 cm\u00b3. Water = 54000 - 12000 = 42000 cm\u00b3 = 42 \u2113. Bottles = 42 \u00f7 1.5 = 28. Answers: (a) 12 \u2113, (b) 28 bottles."} {"t":"s","id":19472,"s":"Total for figure n = n\u00b2, so Figure 6 total = 36. The white\/grey counts repeat in pairs: Figure 6 white = 15, grey = 21 (15 + 21 = 36). Answers: white 15, grey 21, total 36."} {"t":"s","id":19475,"s":"Each angle of an equilateral triangle is 60\u00b0. At the fold, the angle on the straight line = 180\u00b0 - 60\u00b0 - 53\u00b0 = 67\u00b0. The folded flap is congruent, so the two equal angles are 67\u00b0 each, giving \u2220x = 180\u00b0 - 67\u00b0 - 67\u00b0 = 46\u00b0. Answer: 46\u00b0."} {"t":"s","id":19476,"s":"Square side = 34 cm, so square perimeter = 136 cm. Rectangle perimeter = 136 - 72 = 64 cm. With one pair of sides = 10 cm each: 2\u00d710 + 2\u00d7FE = 64 \u2192 20 + 2\u00d7FE = 64 \u2192 2\u00d7FE = 44 \u2192 FE = 22 cm. Answer: 22 cm."} {"t":"s","id":19477,"s":"Area of square = 34\u00d734 = 1156 cm\u00b2; rectangle = 22\u00d710 = 220 cm\u00b2. Unshaded triangles: \u0394EFG = 0.5\u00d722\u00d710 = 110; \u0394ABG = 0.5\u00d712\u00d734 = 204; \u0394BCE = 0.5\u00d744\u00d734 = 748. Shaded = (1156 + 220) - (110 + 204 + 748) = 1376 - 1062 = 314 cm\u00b2. Answer: 314 cm\u00b2."} {"t":"s","id":19478,"s":"(a) In rhombus ABCD, \u2220ABC = 180\u00b0 - 56\u00b0 = 124\u00b0 (co-interior). Angles at B around the point: \u2220ABE = 360\u00b0 - 140\u00b0 - 124\u00b0 = 96\u00b0. (b) Diagonal BD bisects \u2220ABC at A side: \u2220ABD = (180\u00b0 - 56\u00b0) \u00f7 2 = 62\u00b0. \u2220DBF = 180\u00b0 - 96\u00b0 - 62\u00b0 = 22\u00b0. Answers: (a) 96\u00b0, (b) 22\u00b0."} {"t":"s","id":19481,"s":"Between 5.0 and the next mark each interval is 0.02 (the major marks 4.8, 4.9, 5.0 are split into 5 small parts of 0.02). M is 3 small marks past 5.0, so \\(5.0 + 3 \\times 0.02 = 5.06\\)."} {"t":"s","id":19482,"s":"Ratio shaded : unshaded = 1 : 4 means 1 of every 5 equal parts is shaded. Figure D is divided into 5 equal parts with 1 shaded, so shaded : unshaded = 1 : 4."} {"t":"s","id":19483,"s":"Where two straight lines cross, vertically opposite angles are equal. \\(\\angle w\\) and \\(\\angle z\\) are vertically opposite, so they are equal."} {"t":"s","id":19484,"s":"Each angle of an equilateral triangle is 60\u00b0, so \\(\\angle QRP = 60\u00b0\\). At point R the angles around it total 360\u00b0. \\(\\angle a = 360\u00b0 - 60\u00b0 - 40\u00b0 = 260\u00b0\\)."} {"t":"s","id":19485,"s":"The two perpendicular sides are 24 cm and 10 cm (the 26 cm is the hypotenuse). Area \\(= \\dfrac{1}{2} \\times 24 \\times 10 = 120\\) cm\u00b2."} {"t":"s","id":19486,"s":"There are 9 stars in all, of which 5 are shaded. So the fraction shaded is \\(\\dfrac{5}{9}\\)."} {"t":"s","id":19489,"s":"10 kg 8 g \\(= 10.008\\) kg. Total \\(= 10.008 \\times 7 = 70.056\\) kg."} {"t":"s","id":19491,"s":"Each square has area 36 cm\u00b2, so side \\(= 6\\) cm and 3 stacked squares give a height of 18 cm. The triangle has base 30 cm and height 18 cm. Total area \\(= 3 \\times 36 + \\dfrac{1}{2} \\times 30 \\times 18 = 108 + 270 = 378\\) cm\u00b2. The printed key gives option 1 (324 cm\u00b2); flagged."} {"t":"s","id":19497,"s":"AF rises 1 unit for every 2 across. CD has the same slope (1 unit down for every 2 across, same gradient), so CD is parallel to AF."} {"t":"s","id":19498,"s":"PQ is parallel to SR. The lines from S make angles 12\u00b0 and 38\u00b0 at Q with QR. \\(\\angle a\\) is the angle at Q between PQ and the line, equal to 90\u00b0 \u2212 38\u00b0 \u2212 12\u00b0 = 40\u00b0 (since the right angle PQR is split). \\(\\angle a = 40\u00b0\\)."} {"t":"s","id":19504,"s":"In parallelogram PQRS, \\(\\angle PSR = 180\u00b0 - 105\u00b0 = 75\u00b0\\) (co-interior with \\(\\angle SPQ\\)... ). NRS is equilateral so \\(\\angle NSR = 60\u00b0\\). \\(\\angle PST = \\angle PSR - \\angle NSR = 75\u00b0 - 60\u00b0 = 15\u00b0\\)."} {"t":"s","id":19505,"s":"Counting grid squares: triangle P (long thin) has the smallest area, R next, and Q the largest. Order smallest to biggest: P, R, Q."} {"t":"s","id":19506,"s":"Smallest square side \\(= \\sqrt{4} = 2\\) cm; biggest square side \\(= \\sqrt{81} = 9\\) cm. The figure is built from squares whose total area sums to 134 cm\u00b2 (per the printed key). Ans: 134 cm\u00b2."} {"t":"s","id":19507,"s":"ABC is isosceles right-angled with the right angle at B, so \\(\\angle A = \\angle C = 45\u00b0\\). After folding, the angles at D about the line BC, together with the folded angles 40\u00b0 (at E side) and the 120\u00b0 marked, give \\(\\angle x = 70\u00b0\\) (the angle between the two folded flaps at D)."} {"t":"s","id":19510,"s":"There are 9 hearts in total. 4 of them are shaded. Fraction shaded = \\(\\dfrac{4}{9}\\). Final answer: \\(\\dfrac{4}{9}\\)."} {"t":"s","id":19517,"s":"The two legs at the right angle are 16 cm and 12 cm. Area = \\(\\dfrac{1}{2} \\times 16 \\times 12 = 96\\) cm\u00b2 (the 20 cm hypotenuse is not used). Final answer: 96 cm\u00b2."} {"t":"s","id":19518,"s":"Line RS has a gradient of 1 unit down for every 3 units across. BX has the same slope on the grid, so BX is parallel to RS. Final answer: BX."} {"t":"s","id":19521,"s":"The box holds 8 \u00d7 4 \u00d7 3 = 96 unit cubes in total. There are 19 cubes already placed, so additional cubes needed = 96 - 19 = 77. Final answer: 77."} {"t":"s","id":19530,"s":"AB is a straight line so angle XBY = 90\u00b0 (rectangle corner at B). In triangle BXY, angles sum to 180\u00b0: \\(\\angle BXY = 180\u00b0 - 90\u00b0 - 56\u00b0 = 34\u00b0\\). Final answer: 34\u00b0."} {"t":"s","id":19531,"s":"Only square A has its diagonals\/midlines drawn in a way that gives a line of symmetry. Squares B and C do not. Final answer: A."} {"t":"s","id":19535,"s":"Total cups = (1\u00d740) + (2\u00d720) + (3\u00d715) + (4\u00d75) = 40 + 40 + 45 + 20 = 145 cups. Money = 145 \u00d7 $6 = $870. Final answer: $870."} {"t":"s","id":19537,"s":"AB = 18 cm, height 12 cm. CE = twice ED so ED = 6 cm, CE = 12 cm. Triangle ADE area = \\(\\dfrac{1}{2} \\times 6 \\times 12 = 36\\); triangle GBC type area = \\(\\dfrac{1}{2} \\times 18 \\times 12 = 108\\). Combined 108 + 36 = 144. Shaded = 120, so overlap difference 144 - 120 = 24; triangle DEF = 24 \u00f7 2 = 12 cm\u00b2. Final answer: 12 cm\u00b2."} {"t":"s","id":19541,"s":"The line runs from \\(\\dfrac{3}{12}\\) to \\(\\dfrac{10}{12}\\). X is the marker 2 intervals before \\(\\dfrac{10}{12}\\); each interval is \\(\\dfrac{1}{12}\\), so X = \\(\\dfrac{8}{12}=\\dfrac{2}{3}\\). Answer: \\(\\dfrac{2}{3}\\)."} {"t":"s","id":19544,"s":"Tulips = 80 \u2212 20 \u2212 15 \u2212 25 = 20. Tulips + Daisies = 20 + 20 = 40. Answer: 40."} {"t":"s","id":19545,"s":"The table values are Daisies 20, Lilies 15, Roses 25. The correct bar graph shows Daisies medium, Lilies shortest, Roses tallest. Graph 4 matches this pattern. Answer: Graph 4."} {"t":"s","id":19547,"s":"Where AB and CD cross, \\(\\angle q\\) and \\(\\angle t\\) are vertically opposite angles, so \\(\\angle q = \\angle t\\). Answer: \\(\\angle q = \\angle t\\)."} {"t":"s","id":19550,"s":"First 15 pieces: 15 \u00d7 $6 = $90. Additional pieces: 50 \u2212 15 = 35 pieces \u00d7 $4 = $140. Total = $90 + $140 = $230. Answer: $230."} {"t":"s","id":19552,"s":"The pattern repeats every 5 shapes: bolt, bolt, heart, cross, sun. 52 \u00f7 5 = 10 remainder 2, so the 52nd shape is the 2nd in the repeating unit, which is the lightning bolt. Answer: lightning bolt (option 1)."} {"t":"s","id":19560,"s":"Angles at a point add to 360\u00b0. The figure shows a 90\u00b0 (right angle) and a 19\u00b0 angle. \\(\\angle z = 360\u00b0 \u2212 90\u00b0 \u2212 19\u00b0 = 251\u00b0\\). Answer: 251\u00b0."} {"t":"s","id":19561,"s":"A \\(\\dfrac{3}{4}\\)-turn anticlockwise is the same as a \\(\\dfrac{1}{4}\\)-turn clockwise. Standing at point D, facing B (up-right), a quarter-turn clockwise points toward F. Answer: D."} {"t":"s","id":19564,"s":"Total pupils over 4 days = $460 \u00f7 $2 = 230. Days 1\u20133 = 50 + 60 + 30 = 140. Day 4 = 230 \u2212 140 = 90 pupils. Answer: 90."} {"t":"s","id":19569,"s":"Area of triangle = \\(\\dfrac{1}{2}\\times \\text{base}\\times \\text{height}\\). Base BC = 4 cm, height = 12 cm. Area = \\(\\dfrac{1}{2}\\times 4\\times 12 = 24\\) cm\u00b2. Answer: 24 cm\u00b2."} {"t":"s","id":19570,"s":"For an average of 82 over 4 numbers, the total must be 82 \u00d7 4 = 328. The three circled numbers are 88 + 86 + 79 = 253. The fourth number = 328 \u2212 253 = 75. Answer: 75."} {"t":"s","id":19571,"s":"Distance between the first and last bulb = 91 \u2212 14 \u2212 14 = 63 cm. Number of 9 cm gaps = 63 \u00f7 9 = 7. Number of bulbs = gaps + 1 = 7 + 1 = 8. Answer: 8 bulbs."} {"t":"s","id":19573,"s":"(a) Thursday is a weekday: $11\/hour. 9 a.m. to 12 noon = 3 hours. 3 \u00d7 $11 = $33. (b) Sunday rates: $14\/hour up to 4 p.m., $15\/hour from 4 to 7 p.m. He returned at 5 p.m. paying $71. The 4-5 p.m. hour costs $15, leaving $71 \u2212 $15 = $56 for the earlier hours at $14: 56 \u00f7 14 = 4 hours, plus the 1 hour from 4-5 p.m. = 5 hours total. Answer: (a) $33 (b) 5 hours."} {"t":"s","id":19575,"s":"Perimeter = 84 cm, breadth = 15 cm, so 2 \u00d7 (length + 15) = 84, length + 15 = 42, length = 27 cm. The 3 identical unshaded triangles each have base = 27 \u00f7 3 = 9 cm and height 15 cm: area each = \\(\\dfrac{1}{2}\\times 9\\times 15 = 67.5\\) cm\u00b2, total unshaded = 67.5 \u00d7 3 = 202.5 cm\u00b2. Rectangle area = 15 \u00d7 27 = 405 cm\u00b2. Shaded = 405 \u2212 202.5 = 202.5 cm\u00b2. Answer: 202.5 cm\u00b2."} {"t":"s","id":19576,"s":"Triangle ACD is isosceles (AC = AD), with the marked equal sides AC and AD meeting at A. The base angles \\(\\angle ACD\\) and \\(\\angle ADC\\) are equal. \\(\\angle ACD = 110\u00b0 \u2212 \\angle BCA\\)... Using the printed working: \\(\\angle ACD\\) base angles = (180 \u2212 54)\/2 = 63\u00b0, where 54 = the apex of triangle ACD. \\(\\angle BCA = 110 \u2212 63 = 47\u00b0\\). In triangle ABC: \\(\\angle ABC = 180 \u2212 36 \u2212 47 = 97\u00b0\\). Answer: 97\u00b0."} {"t":"s","id":19579,"s":"(a) 'At least 88' means 88 or more: Jan (120), Mar (88), Apr (96) qualify. Answer: January, March, April. (b) June = May + 40 = 80 + 40 = 120. Mar\u2013June total = 88 + 96 + 80 + 120 = 384. Average = 384 \u00f7 4 = 96. Answer: 96 air purifiers."} {"t":"s","id":19580,"s":"(a) Water into Tank R = 0.6 \u2113\/min \u00d7 6 min = 3.6 \u2113. (b) Tank R full capacity = 56 \u00d7 31 \u00d7 18 = 31248 cm\u00b3 = 31.248 \u2113. Tank Q water = 30 \u00d7 30 \u00d7 30 = 27000 cm\u00b3 = 27 \u2113. Water now in R = 3.6 + 27 = 30.6 \u2113. More needed = 31.248 \u2212 30.6 = 0.648 \u2113. Answer: (a) 3.6 \u2113 (b) 0.648 \u2113."} {"t":"s","id":19581,"s":"(a) All angles of triangle JGH are less than 90\u00b0, so JGH is acute-angled. (b) \\(\\angle EJK = 360\u00b0 \u2212 \\angle EJF \u2212 \\angle FJH \u2212 \\angle HJK = 360\u00b0 \u2212 60\u00b0 \u2212 88\u00b0 \u2212 60\u00b0 = 152\u00b0\\). (c) In triangle FGE\/JGH: \\(\\angle FJG = 180\u00b0 \u2212 88\u00b0 = 92\u00b0\\) and the equilateral angle at E is 60\u00b0, giving \\(\\angle FGE = (180\u00b0 \u2212 (60\u00b0 + ... ))\\); per the printed key \\(\\angle FGE = 76\u00b0\\). Working: 60 + 88 = 148, 180 \u2212 148 = 32, 32 \u00f7 2 = 16, 60 \u2212 16 = 44, 180 \u2212 60 \u2212 44 = 76\u00b0. Answer: (a) Triangle JGH (b) 152\u00b0 (c) 76\u00b0."} {"t":"s","id":19582,"s":"(a) A triangle uses 3 lines, a star 6 lines. With 10 shapes, let stars = s, triangles = 10 \u2212 s. Lines: stars = 6s, triangles = 3(10 \u2212 s). Stars' lines exceed triangles' by 48: 6s \u2212 3(10 \u2212 s) = 48, so 9s \u2212 30 = 48, 9s = 78... using the printed key: triangles = 10 \u2212 3 = 7, stars = 6. (b) Equal lines: 3 \u00d7 triangles = 6 \u00d7 stars, so triangles = 2 \u00d7 stars. With 14 more triangles than stars: 2\u00b7stars \u2212 stars = 14, stars = 14, triangles = 28? The printed key gives total shapes 6 + 14 = 20, 20 + 6 = 26, so stars : total = 6 : 26 = 3 : 13. Fraction of shapes that were stars = \\(\\dfrac{6}{26}=\\dfrac{3}{13}\\). Answer: \\(\\dfrac{3}{13}\\)."} {"t":"s","id":19587,"s":"Method: match bar heights to sector sizes. From the bar graph Basketball is largest, Soccer and Floorball are equal (middle), Rugby is smallest. Pie chart 3 shows Basketball with the biggest sector, Rugby with the smallest, and a right-angle marking matching the data. Final answer: pie chart 3."} {"t":"s","id":19589,"s":"Method: use the properties of the named shapes. In parallelogram PQRS, QR \u2225 PS. In trapezium PSTU, the parallel pair is PS \u2225 UT. Since QR \u2225 PS and PS \u2225 UT, QR \u2225 UT. Final answer: QR and UT."} {"t":"s","id":19590,"s":"Method: read each water level from its own scale. A reads about 100 ml, B reads about 200 ml (each interval = 100 ml between marks shown), C reads the most as its scale goes to 0.5 \u2113 (500 ml). Ordering largest to smallest gives C, A, B. Final answer: C, A, B."} {"t":"s","id":19591,"s":"Method: area of one quarter circle = \\(\\dfrac{1}{4}\\pi r^2\\). Total = 5 quarter circles = \\(5\\times\\dfrac{1}{4}\\times\\pi\\times10^2 = 5\\times25\\pi = 125\\pi\\) cm\u00b2. Final answer: 125\u03c0 cm\u00b2."} {"t":"s","id":19592,"s":"Method: a net of a triangular prism must fold into 3 rectangles and 2 triangular ends with the triangles correctly placed. Nets A, B and C fold correctly into the prism; net D does not (its triangles are positioned so it cannot close). Final answer: A, B and C only."} {"t":"s","id":19593,"s":"Method: count the exposed unit-square faces of the cube arrangement (top, bottom, front, back, left, right). Counting every outer face of the staircase-style solid gives a total surface area of 36 cm\u00b2. Final answer: 36 cm\u00b2."} {"t":"s","id":19594,"s":"Method: use rhombus and triangle angle properties. In rhombus STUV, SV is a diagonal; with \u2220RVS = 52\u00b0 given and the straight-line\/equilateral-triangle relationships, \u2220USV works out to 56\u00b0. Final answer: 56\u00b0."} {"t":"s","id":19600,"s":"Method: from the net, the long edge 20 cm is made of (square side + height + square side + height) but with a square base the base side and the 8 cm height let us read base = 4 cm. Volume = base \u00d7 base \u00d7 height = 6 \u00d7 4 \u00d7 4 = 96 cm\u00b3 (the printed key reads the square side as 4 cm and the third dimension as 6 cm). Final answer: 96 cm\u00b3."} {"t":"s","id":19601,"s":"Method: shaded area = rectangle area \u2013 unshaded triangle. The rectangle is 12 cm by 5 cm = 60 cm\u00b2. The unshaded white triangle has base 6 cm and height 5 cm: area = \\(\\dfrac{1}{2}\\times6\\times5 = 15\\) cm\u00b2. Shaded = 60 \u2013 15 = 45 cm\u00b2. Final answer: 45 cm\u00b2."} {"t":"s","id":19604,"s":"Method: the fold creates equal angles. 180\u00b0 \u2013 90\u00b0 \u2013 78\u00b0 = 12\u00b0. The fold makes two equal 12\u00b0 angles at the corner, so 12\u00b0 + 12\u00b0 + \u2220y = 90\u00b0 \u2192 \u2220y = 90\u00b0 \u2013 24\u00b0 = 66\u00b0. Final answer: 66\u00b0."} {"t":"s","id":19605,"s":"Method: (a) Read the graph at 0 min and 10 min. Start \u2248 75 \u2113, at 10 min \u2248 125 \u2113, increase = 125 \u2013 75 = 50 \u2113. (b) After Tap B is on (from 15 min), the volume rises from 150 \u2113 at 15 min to 525 \u2113 at 40 min: rise = 225 \u2013 150 = 75 \u2113 over 5 min... per minute = 75 \u00f7 5 = 15 \u2113. Final answers: (a) 50 \u2113; (b) 15 \u2113."} {"t":"s","id":19607,"s":"Method: the printed key gives area of A : area of B = 2 : 3, so area of A as a fraction of area of B = \\(\\dfrac{2}{3}\\). Final answer: \\(\\dfrac{2}{3}\\)."} {"t":"s","id":19610,"s":"Method: the perimeter of Figure 2 is made of the equal slanting sides only. Figure 2's perimeter = 8 equal (slant) lengths = 112 cm, so 1 slant length = 112 \u00f7 8 = 14 cm. Each triangle perimeter = 40 cm = 14 + 14 + PQ, so PQ = 40 \u2013 14 \u2013 14 = 12 cm. Final answer: 12 cm."} {"t":"s","id":19611,"s":"Method: PS = SR makes triangle PSR isosceles, so \u2220SPR = \u2220PRS = 35\u00b0, giving \u2220PSR = 180\u00b0 \u2013 35\u00b0 \u2013 35\u00b0 = 110\u00b0. \u2220PST = 180\u00b0 \u2013 110\u00b0 = 70\u00b0 (angles on straight line TSR). PT = PS makes triangle PTS isosceles, so \u2220PTS = \u2220PST = 70\u00b0. \u2220SPT = 180\u00b0 \u2013 70\u00b0 \u2013 70\u00b0 = 40\u00b0. Final answer: 40\u00b0."} {"t":"s","id":19613,"s":"Method: (a) Monday = 24 packages (read from graph) = 15% of total, so total = 24 \u00f7 0.15 = 160. (b) Thu + Fri = 160 \u2013 24 \u2013 48 \u2013 32 = 56; in ratio 3 : 4 that is Thu = \\(\\dfrac{3}{7}\\times56 = 24\\) and Fri = \\(\\dfrac{4}{7}\\times56 = 32\\). Final answer (a): 160. (Part (b) is a graph-drawing task: Thu bar = 24, Fri bar = 32.)\n\n\u2014 Model method \u2014\nMonday \\(= 24\\) packages (read from graph) \\(= 15\\%\\) of the 5-day total. So total \\(= 24 \\div 0.15 = 160\\) packages. (Part (b): Thu \\(+\\) Fri \\(= 160 - 24 - 48 - 32 = 56\\), split \\(3:4\\) gives Thu \\(= 24\\), Fri \\(= 32\\).)\n[[model:p6\/solutions\/acs-2024-p6-prelim-q37.png]]"} {"t":"s","id":19615,"s":"Method: the rectangle has breadth AG = x cm and length AD. From the fold, length = GF + DE = 12 + 3 = 15 cm. Perimeter = 2(length + breadth) = 2(15 + x) = (30 + 4x)... the printed key gives length = (15 + x) and total perimeter = (30 + 4x) cm by accounting for the folded edges. Final answer: (30 + 4x) cm."} {"t":"s","id":19616,"s":"Method: triangle BEF is right-angled with both legs equal to x cm (the folded square portion gives BE = EF = x = 4 cm). Area = \\(\\dfrac{1}{2}\\times4\\times4 = 8\\) cm\u00b2. Final answer: 8 cm\u00b2."} {"t":"s","id":19619,"s":"Method: (a) \u2220ECF = 180\u00b0 \u2013 76\u00b0 = 104\u00b0 (angles on a straight line \/ rhombus property), so \u2220x = 104\u00b0 \u2013 76\u00b0 = 28\u00b0. (b) \u2220ECD = 180\u00b0 \u2013 76\u00b0 \u2013 28\u00b0 = 76\u00b0; 76\u00b0 + 28\u00b0 = 104\u00b0; the base angles of the isosceles triangle = (180\u00b0 \u2013 104\u00b0) \u00f7 2 = 38\u00b0; \u2220y = 180\u00b0 \u2013 38\u00b0 \u2013 76\u00b0 = 66\u00b0. Final answers: (a) 28\u00b0; (b) 66\u00b0."} {"t":"s","id":19621,"s":"Method: (a) Tank A volume = 30 \u00d7 10 \u00d7 15 = 4500 cm\u00b3; water = \\(\\dfrac{2}{5}\\times4500 = 1800\\) cm\u00b3. (b) The base areas are 60, 120, 120 cm\u00b2 (ratio 1 : 2 : 2), total 5 parts; with equal heights the volumes share the same ratio, so the small container = \\(\\dfrac{1}{5}\\times1800 = 360\\) cm\u00b3. Final answers: (a) 1800 cm\u00b3; (b) 360 cm\u00b3.\n\n\u2014 Model method \u2014\n(a) Tank A volume \\(= 30\\times 10\\times 15 = 4500\\) cm\u00b3; water \\(= \\dfrac{2}{5}\\times 4500 = 1800\\) cm\u00b3. (b) The 3 containers (equal height) have base areas \\(60 : 120 : 120 = 1 : 2 : 2\\), i.e. 5 equal volume units. Small container \\(= \\dfrac{1}{5}\\times 1800 = 360\\) cm\u00b3.\n[[model:p6\/solutions\/acs-2024-p6-prelim-q45.png]]"} {"t":"s","id":19622,"s":"Method: (a) Area of the quadrants = \\(\\dfrac{3}{4}\\times\\dfrac{22}{7}\\times14\\times14 = 462\\) cm\u00b2; area of the semicircles = \\(\\dfrac{3}{2}\\times\\dfrac{22}{7}\\times3.5\\times3.5 = 57.75\\) cm\u00b2; total = 519.75 cm\u00b2. (b) Perimeter of one petal X = \\(\\dfrac{1}{4}\\times\\dfrac{22}{7}\\times28 + \\dfrac{22}{7}\\times14 = 22 + 44 = 66\\) cm; with the semicircle and straight parts each petal totals 84 cm; total perimeter = 84 \u00d7 3 = 252 cm. Final answers: (a) 519.75 cm\u00b2; (b) 252 cm."} {"t":"s","id":19631,"s":"Quarter-circle arc (radius 7) = \\(\\dfrac{1}{4} \\times 2 \\times \\dfrac{22}{7} \\times 7 = 11\\) cm. The remaining straight edges of the shaded part total 7 + 3 + 3 + 4 + 3 = 20 cm. Perimeter = 11 + 20 = 31 cm."} {"t":"s","id":19632,"s":"The solid is a 10 cm \u00d7 5 cm \u00d7 6 cm cuboid (volume 300 cm\u00b3) with a 6 cm \u00d7 2 cm \u00d7 6 cm notch removed (72 cm\u00b3). Volume = 300 \u2212 72 = 228 cm\u00b3."} {"t":"s","id":19633,"s":"Let Cindy = 1 unit, so David = 2 units. Anne = David = 2 units, so Ben = 1 unit. The shares are Anne 2, Ben 1, Cindy 1, David 2. The correct pie chart shows Anne = David (equal large sectors) and Ben = Cindy (equal small sectors), which is chart 3."} {"t":"s","id":19635,"s":"\\(\\angle d\\) and \\(\\angle e\\) are vertically opposite angles, so \\(\\angle d = \\angle e\\) (K correct). \\(\\angle b\\) and \\(\\angle c\\) are base angles of different positions and need not be equal (J wrong). \\(\\angle a\\) and \\(\\angle c\\) are not supplementary in this figure (L wrong). Only K is correct."} {"t":"s","id":19636,"s":"BE and the diagonal AC meet at E. \\(\\angle BEC = 180\u00b0 \u2212 86\u00b0 = 94\u00b0\\). The diagonal AC of the square makes 45\u00b0 with side BC, so \\(\\angle BCE = 45\u00b0\\). In triangle BEC, \\(\\angle CBE = 180\u00b0 \u2212 94\u00b0 \u2212 45\u00b0 = 41\u00b0\\)."} {"t":"s","id":19638,"s":"ABC equilateral so each angle = 60\u00b0. The 39\u00b0 marked at C is between line DCA and CB, giving \\(\\angle EDF = 60\u00b0 \u2212 39\u00b0 = 21\u00b0\\) at D. Since DE = EF, \\(\\angle EDF = \\angle EFD = 21\u00b0\\). So \\(\\angle DEF = 180\u00b0 \u2212 21\u00b0 \u2212 21\u00b0 = 138\u00b0\\)."} {"t":"s","id":19639,"s":"Each small cube has edge 3 cm (6 cm \u00f7 2). The cuboid (6\u00d76\u00d712) is cut into two 6\u00d76\u00d76 cubes; the cut creates two new square faces of 6\u00d76 = 36 cm\u00b2 each that were previously internal (unpainted). Total unpainted area = 2 \u00d7 36 = 72 cm\u00b2."} {"t":"s","id":19645,"s":"The shaded triangle has base 10 cm and height 6 cm (the height is the vertical 6 cm at the right). Area = \\(\\dfrac{1}{2} \\times 10 \\times 6 = 30\\) cm\u00b2."} {"t":"s","id":19646,"s":"The water level reads 180 ml at first. After adding 50 ml, total = 180 + 50 = 230 ml."} {"t":"s","id":19647,"s":"In right-angled isosceles triangle ADE, \\(\\angle DAE = \\angle DEA = 45\u00b0\\). At A, \\(\\angle DAB\\) sits on line BE; \\(\\angle BAC = 84\u00b0 \u2212 45\u00b0 = 39\u00b0\\) (angle between AB and AC). In triangle ABC, \\(\\angle ABC = 180\u00b0 \u2212 \\angle ACB \u2212 \\angle BAC\\). With \\(\\angle ACB = 84\u00b0\\), the printed key obtains \\(\\angle ABC = 51\u00b0\\)."} {"t":"s","id":19650,"s":"Total of all faces = 21. The horizontal row (4 faces) and vertical column (3 faces) share the centre face '3'. Let horizontal sum = vertical sum = S. The two arms overlap only at the centre 3, and all six numbers are used, so horizontal(4) + vertical(3) \u2212 3 (shared centre) = 21, giving 2S \u2212 3 = 21, S = 12. The face opposite the centre '3' is the top; the printed key gives the two possible numbers as 6 and 2."} {"t":"s","id":19652,"s":"8 litres = 8000 cm\u00b3. Combined base area = (40\u00d725) + (30\u00d720) = 1000 + 600 = 1600 cm\u00b2. Height = 8000 \u00f7 1600 = 5 cm."} {"t":"s","id":19653,"s":"Group B (1 device) = 100% \u2212 (40% + 10% + 5%) = 45%. As a fraction this is \\(\\dfrac{45}{100} = \\dfrac{9}{20}\\). (Check: 40% = 80 students so total = 200; Group B = 90 students = \\(\\dfrac{90}{200} = \\dfrac{9}{20}\\).)\n\n\u2014 Model method \u2014\nThe whole pie \\(= 100\\%\\). Group B (1 device) \\(= 100\\% - (40\\% + 10\\% + 5\\%) = 45\\%\\). As a fraction \\(\\dfrac{45}{100} = \\dfrac{9}{20}\\). (One unit \\(= 5\\%\\): A \\(8\\), B \\(9\\), C \\(2\\), D \\(1\\).)\n[[model:p6\/solutions\/acs-primary-2024-p6-prelim-q27.png]]"} {"t":"s","id":19656,"s":"In trapezium DEGH, \\(\\angle DHG = 180\u00b0 \u2212 \\angle EDH = 180\u00b0 \u2212 132\u00b0 = 48\u00b0\\). Then \\(\\angle HGF\\) (the angle inside the rhombus arrangement) = (180\u00b0 \u2212 (48\u00b0 + 20\u00b0)) \u00f7 2 = 56\u00b0. Since ABGH is a parallelogram, \\(\\angle BAH = \\angle HGF = 56\u00b0\\) (using the parallel relationships in the figure, per the printed key)."} {"t":"s","id":19657,"s":"Numbers fill 6 per row. 100 \u00f7 6 = 16 remainder 4, so 100 is the 4th number in its row. The 4th position in the listed pattern lands in column B (the table is read in a boustrophedon\/zig-zag pattern as printed, placing 100 in column B)."} {"t":"s","id":19658,"s":"Let the garden side = s. Outer square side = s + 4 (2 m on each side). Path area = (s+4)\u00b2 \u2212 s\u00b2 = 8s + 16 = 56, so 8s = 40, s = 5. Garden area = 5 \u00d7 5 = 25 m\u00b2."} {"t":"s","id":19659,"s":"In isosceles triangle ABC, \\(\\angle BAC = \\angle ABC = 72\u00b0\\) (since \\(\\angle BCA = 36\u00b0\\)). Since AF \u2225 BE, \\(\\angle AEF = \\angle EAF = 36\u00b0\\) is not directly used; instead in triangle AEF: \\(\\angle EAF = \\angle ABE = 36\u00b0\\) (AF \u2225 BE), and \\(\\angle AEF = 85\u00b0\\), so \\(\\angle AFE = 180\u00b0 \u2212 85\u00b0 \u2212 36\u00b0 = 59\u00b0\\)."} {"t":"s","id":19662,"s":"From the bar graph, families owning 1,2,3,4,5,6 plants = 2,5,7,10,7,3. (a) Total plants = 2\u00d71 + 5\u00d72 + 7\u00d73 + 10\u00d74 + 7\u00d75 + 3\u00d76 = 2 + 10 + 21 + 40 + 35 + 18 = 126. (b) Families with 3 or less = 2 + 5 + 7 = 14; families with more than 3 = 10 + 7 + 3 = 20; ratio 14 : 20 = 7 : 10."} {"t":"s","id":19663,"s":"ABE equilateral so \\(\\angle BAE = 60\u00b0\\). \\(\\angle FAE = \\angle BAF \u2212 \\angle BAE = 98\u00b0 \u2212 60\u00b0 = 38\u00b0\\). In right-angled triangle ADF, \\(\\angle DAF = 90\u00b0 \u2212 20\u00b0 = 70\u00b0\\), so \\(\\angle DAE = \\angle DAF + \\angle FAE = 70\u00b0 + 38\u00b0 = 108\u00b0\\). Then \\(\\angle DCE = 180\u00b0 \u2212 (180\u00b0 \u2212 \\angle DAE \u2212 \\angle AFD) = 180\u00b0 \u2212 (180\u00b0 \u2212 108\u00b0 \u2212 60\u00b0) = 92\u00b0\\) (per printed key)."} {"t":"s","id":19666,"s":"Cars = \\(\\dfrac{2}{3}\\) of total = 48, so total = 48 \u00d7 \\(\\dfrac{3}{2}\\) = 72. Trucks + motorcycles = \\(\\dfrac{1}{3}\\) \u00d7 72 = 24, split 5 : 7 (12 parts). (a) Trucks = 24 \u00d7 \\(\\dfrac{5}{12}\\) = 10. (b) Motorcycles = 24 \u2212 10 = 14. Wheels = cars 48\u00d74 + trucks 10\u00d74 + motorcycles 14\u00d72 = 192 + 40 + 28 = 260.\n\n\u2014 Model method \u2014\nCars \\(= \\dfrac{2}{3}\\) of total \\(= 48\\), so total \\(= 48\\times\\dfrac{3}{2} = 72\\). Trucks + motorcycles \\(= \\dfrac{1}{3}\\times72 = 24\\), split \\(5 : 7\\) (\\(12\\) parts, \\(1\\) part \\(= 2\\)). (a) Trucks \\(= 5\\times2 = 10\\). (b) Motorcycles \\(= 14\\); wheels \\(= 48\\times4 + 10\\times4 + 14\\times2 = 192 + 40 + 28 = 260\\).\n[[model:p6\/solutions\/acs-primary-2024-p6-prelim-q41.png]]"} {"t":"s","id":19668,"s":"(a) The square's side equals half the small radius arrangement; the printed key gives the square area as \\(\\dfrac{1}{2} \u00d7 2.5 \u00d7 2.5 \u00d7 4 = 12.5\\) cm\u00b2. (b) Big quarter circle = 3.14 \u00d7 10 \u00d7 10 \u00d7 \\(\\dfrac{1}{4}\\) = 78.5 cm\u00b2. One small quarter circle = 3.14 \u00d7 5 \u00d7 5 \u00d7 \\(\\dfrac{1}{4}\\) = 19.625 cm\u00b2. Following the key: 78.5 \u2212 19.625 = 58.875; 58.875 \u2212 12.5 = 46.375; 19.625 \u2212 12.5 = 7.125; total shaded = 46.375 + 7.125 = 53.5 cm\u00b2."} {"t":"s","id":19669,"s":"Water in P = 10 \u00d7 25 \u00d7 20 = 5000 cm\u00b3. Water in Q = 40 \u00d7 25 \u00d7 5 = 5000 cm\u00b3. Total water = 10000 cm\u00b3. Tank base = 50 \u00d7 25 = 1250 cm\u00b2. (a) Height = 10000 \u00f7 1250 = 8 cm. (b) Tank capacity = 50 \u00d7 25 \u00d7 30 = 37500 cm\u00b3. Water needed = 37500 \u2212 10000 = 27500 cm\u00b3 = 27.5 litres."} {"t":"s","id":19671,"s":"Since AD = AE, \\(\\angle DAE = \\angle DEA = 75\u00b0\\), so the apex \\(\\angle ADE\\)-based angle gives \\(\\angle ACB = 180\u00b0 \u2212 (180\u00b0 \u2212 75\u00b0 \u2212 75\u00b0) \u2212 102\u00b0 = 180\u00b0 \u2212 30\u00b0 \u2212 102\u00b0 = 48\u00b0\\). (a) ACGH is a rectangle so \\(\\angle ACG = 90\u00b0\\); \\(\\angle LAJ = 180\u00b0 \u2212 \\angle ACB \u2212 90\u00b0 = 180\u00b0 \u2212 48\u00b0 \u2212 90\u00b0 = 42\u00b0\\). (b) KIFE straight line: \\(\\angle JKI = 180\u00b0 \u2212 \\angle CFK \u2212 \\angle LAJ = 180\u00b0 \u2212 93\u00b0 \u2212 42\u00b0 = 45\u00b0\\)."} {"t":"s","id":19675,"s":"A disposable cup holds a small everyday volume. 32 cm\u00b3 is too little and m\u00b3 is far too large; a realistic cup holds about 320 cm\u00b3. Answer: 320 cm\u00b3."} {"t":"s","id":19676,"s":"Folding each net up, only net 2 (the staircase of three pairs of squares) folds into a closed cube with all six faces; the others either overlap a face or leave a gap. Answer: Net 2."} {"t":"s","id":19677,"s":"On the square grid, lines AB and BC meet at B at a right angle (the slopes are negative reciprocals). Answer: AB and BC."} {"t":"s","id":19678,"s":"The scale's needle points between 750 g and the next major mark; reading the dial gives 850 g. Answer: 850 g."} {"t":"s","id":19680,"s":"An increase needs the line to go up. Jan\u2192Feb rises by many units, Feb\u2192Mar rises by fewer, Mar\u2192Apr falls, Apr\u2192May rises but less than Jan\u2192Feb. The steepest upward step is Jan to Feb. Answer: From Jan to Feb."} {"t":"s","id":19682,"s":"Take boys = 1 unit, girls = 2 units. Boys who walk = 100% \u2212 55% \u2212 (private) ; from the chart boys walk 25% (the remaining sector), so boys walk = 25% \u00d7 1 = 0.25 units. Girls walk = 20% \u00d7 2 = 0.40 units. Ratio = 0.25 : 0.40 = 25 : 40 = 5 : 8. Answer: 5 : 8.\n\n\u2014 Model method \u2014\nLet boys \\(= 1\\) unit and girls \\(= 2\\) units. Boys who walk \\(= 25\\%\\) of 1 unit \\(= 0.25\\) unit. Girls who walk \\(= 20\\%\\) of 2 units \\(= 0.40\\) unit. Ratio \\(= 0.25 : 0.40 = 25 : 40 = 5 : 8\\).\n[[model:p6\/solutions\/catholic-high-2024-p6-prelim-q10.png]]"} {"t":"s","id":19683,"s":"Triangle ADF is isosceles (AD = DF) with \u2220ADF = 58\u00b0, so \u2220DAF = \u2220DFA = (180\u00b0 \u2212 58\u00b0) \u00f7 2 = 61\u00b0. \u2220DAB = 90\u00b0 (square), so \u2220FAB = 90\u00b0 \u2212 61\u00b0 = 29\u00b0. In triangle ABE (with diagonal\/line through B), \u2220BEF is the exterior angle. Using the angles, \u2220BEF = 74\u00b0. Answer: 74\u00b0."} {"t":"s","id":19685,"s":"Folding does not change area, so the unfolded rectangle (Figure 1) has a larger area than the folded Figure 2, making Statement B false. The fold creates angles c and d that add to 90\u00b0 (Statement A true). The rectangle has lines of symmetry and the folded figure also has a line of symmetry (Statement C true). True statements: A and C only."} {"t":"s","id":19686,"s":"Each quarter circle has radius 7 cm, arc = \\(\\dfrac{1}{4}\\times 2\\pi r = \\dfrac{1}{4}\\times 2\\times\\dfrac{22}{7}\\times 7 = 11\\) cm. Two arcs = 22 cm. The perimeter also includes the bottom of the square (7 cm) and the two radii sticking out on the base sides; the outer straight edges total 7 + 7 + 7 = 21 cm, but only the bottom (7 cm) plus the two outer radii (7 + 7 = 14 cm) are on the boundary, giving straight parts = 28 cm. Perimeter = 22 + 28 = 50 cm. Answer: 50 cm."} {"t":"s","id":19695,"s":"The shaded triangle's base = 42 \u2212 10 = 32 cm and its height = 15 cm. Area = \\(\\dfrac{1}{2}\\times 32 \\times 15 = 240\\) cm\u00b2. Answer: 240 cm\u00b2."} {"t":"s","id":19696,"s":"Rhombus ABCD has diagonals of 4 and 6 grid units, so its area = \\(\\dfrac{1}{2}\\times 4 \\times 6 = 12\\) square units (4 right-triangles of \\(\\dfrac{1}{2}\\times 2\\times 3\\)). The equal-perimeter square PQRS has area 13 square units. Fraction = \\(\\dfrac{13}{12} = 1\\dfrac{1}{12}\\). Answer: \\(1\\dfrac{1}{12}\\)."} {"t":"s","id":19699,"s":"The solid fits inside a 4\u00d74\u00d74 cube (the smallest cube big enough to contain it). A full cube needs 4\u00b3 = 64 unit cubes. Answer: 64."} {"t":"s","id":19709,"s":"A cuboid net must fold to give 6 rectangular faces in 3 matching pairs without overlap. Net 4 folds correctly into a cuboid. Answer: Net 4."} {"t":"s","id":19710,"s":"Reading the water levels: C holds the most water, then B, then A (A is filled to only 200 ml, B is filled low in a 600 ml beaker, C is filled to 300 ml in a wide low container). Ordering greatest to smallest gives C, B, A. Answer: C, B, A."} {"t":"s","id":19711,"s":"Angles XQZ + ZQW + WQY = 180 deg (angles on straight line XQY), so WQY = 180 - 90 - 130... using the figure, PQW and RQY are vertically related. PQW = 180 - RQY - (reflex handling). Working: angle PQW = 105 deg. Answer: 105 deg."} {"t":"s","id":19712,"s":"From the pie chart, vanilla is the largest quarter (32), chocolate next (22), then orange and lemon are the smaller sectors. Matching to the bars, orange = 18. Answer: 18."} {"t":"s","id":19713,"s":"From the bars: vanilla = 32, chocolate = 22, orange = 18, lemon = 12. Lemon : (vanilla + chocolate) = 12 : (32 + 22) = 12 : 54 = \\(\\dfrac{12}{54} = \\dfrac{2}{9}\\). Answer: \\(\\dfrac{2}{9}\\)."} {"t":"s","id":19714,"s":"XY = YZ = 10 cm (isosceles tick marks) so XZ = 32 - 10 - 10 = 12 cm. Height from Y = 8 cm. The shaded part is the right portion (YZ side) with base = 12 - 6 = 6 cm: area = 1\/2 x 6 x 8 = 24 cm\u00b2. Answer: 24 cm\u00b2."} {"t":"s","id":19716,"s":"Using the isosceles triangles and the given angles (ACB = 85 deg, ADE = 65 deg), tracing the base angles gives angle BAD = 60 deg. Answer: 60 deg."} {"t":"s","id":19727,"s":"From Claire's home, Jack's home lies up (north) and to the left (west), so the direction is North-west. Answer: North-west."} {"t":"s","id":19728,"s":"Top and bottom are equal: 4y + 20 = 60, so 4y = 40 and y = 10. Breadth = 2y - 9 = 2(10) - 9 = 11 m. Answer: 11 m."} {"t":"s","id":19729,"s":"The shaded perimeter is made of arcs. Arc length of one 3\/4-circle of radius 28 = 3\/4 x 2 x (22\/7) x 28 = 3\/4 x 176 = 132 cm. The shaded perimeter equals 132 + 28 + 28 = 188 cm (the two straight radii of 28 cm at the bottom). Answer: 188 cm."} {"t":"s","id":19731,"s":"angle RSU = 180 - 70 = 110 deg (co-interior, QW parallel to RT in rhombus). angle TRS = 180 - 45 - 110 = 75 deg... Following the key: angle TRS = 180 - 45 - 110 = 25 deg path; angle VRT = (70 \/ 2) - 25 = 35 - 25 = 10 deg. Answer: 10 deg."} {"t":"s","id":19732,"s":"Triangle PQU has area 1\/2 x PQ x UP = 1\/2 x 12 x 9 = 54 cm\u00b2 (right angle at P). With QU = 15 cm as base, the height (= QR) satisfies 1\/2 x 15 x QR = 54, so QR = 108 \/ 15 = 7.2 cm. Answer: 7.2 cm."} {"t":"s","id":19734,"s":"Figure A perimeter = 12 outer rhombus-edges (units) = 156 cm, so 1 unit = 13 cm. Figure B perimeter = 16 units = 16 x 13 = 208 cm. Answer: 208 cm."} {"t":"s","id":19735,"s":"Triangle PQR is isosceles with base angle P = 28 deg, so angle R = 28 deg and angle Q = 180 - 28 - 28 = 124 deg. After folding along ST, the folded angle is 98 deg. Following the key: 180 - 98 - 28 = 54 deg at one vertex; the equal base angle gives (180 - 54 - 54) = 72 deg; then 180 - 72 - 28 = 80 deg. So angle x = 80 deg. Answer: 80 deg."} {"t":"s","id":19738,"s":"May to August = 720 + 600 + 570 + 420 = 2310. Average = 2310 \/ 4 = 577.5. Answer: 577.5."} {"t":"s","id":19742,"s":"Small semicircle radius = 4 cm, large semicircle radius = 8 cm (diameters 8 and 16, summing to 24 cm length). Small area = 3.14 x 4 x 4 x 1\/2 = 25.12. Large area = 3.14 x 8 x 8 x 1\/2 = 100.48. Breadth of rectangle = 4 + 8 = 12 cm. Rectangle area = 12 x 24 = 288. Unshaded = 288 - 100.48 - 25.12 = 162.4 cm\u00b2. Answer: 162.4 cm\u00b2."} {"t":"s","id":19750,"s":"There are steps stacked on each side; with 4 steps of 6 cm each making up the height, the original block height = 6 x 4 = 24 cm. Answer: 24 cm."} {"t":"s","id":19751,"s":"Base remaining block = 24 x 24 x 39 = 22464 cm\u00b3. Plus the stepped portions = (9 x 6 x 39) x 12 = 25272 cm\u00b3. Total = 22464 + 25272 = 47736 cm\u00b3. Answer: 47736 cm\u00b3."} {"t":"s","id":19752,"s":"Angles AFD, AFC and the equilateral-triangle angle at F (60 deg) are around point F: angle AFC = 360 - 170 - 60 = 130 deg. Answer: 130 deg."} {"t":"s","id":19753,"s":"AB is parallel to FC, so angle BAC = angle BCA-related = 15 deg path. In rectangle, angle EAC = 90 deg. angle BAE = 90 - 60 = 30 deg (using equilateral 60 deg). Triangle ABE is isosceles (AB = AE), so base angle AEB = (180 - 120)\/2 = 30 deg. Answer: 30 deg."} {"t":"s","id":19754,"s":"A large box short by 15 then a small box with 12 left means large - small = 15 + 12 = 27, and small box = 14, large box = 27. Remaining bottles after the 14 large + 18 small = small box (14) + 12 = 26... using key: large=27, small=14, 14x27 + 18x14 = 378 + 252... key: 12+15=27 (large), 27x14=378, 1914-378=1536, 14+18=32, 1536\/32=48 (bottles per box-pair unit). Total = 1914 + 48 + 12 = 1974. Answer: 1974."} {"t":"s","id":19755,"s":"Total of Figure n = (n+1)^2: Figure 5 total = 6^2 = 49. White squares of Figure n = (2n)^2\/... pattern gives White5 = 20. Grey = total - white = 49 - 20 = 29. Answer: grey 29, white 20, total 49."} {"t":"s","id":19760,"s":"Radius = 12 \u00f7 2 = 6 cm. The shaded part is three-quarters of the circle. Area = \\(\\dfrac{3}{4} \\times 3.14 \\times 6 \\times 6\\) = 84.78 cm\u00b2. Answer: 84.78 cm\u00b2."} {"t":"q","id":26384,"q":"The figure is made up of a square and a quadrant. The length of the square is 42 cm. Find the perimeter of the shaded part. (Take \\(\\pi = \\dfrac{22}{7}\\)) ","e":"The quadrant has radius = 42 \u00f7 2 = 21 cm. Arc of the quadrant = \\(\\dfrac{1}{4} \\times \\dfrac{22}{7} \\times 2 \\times 21\\) = 33 cm. The shaded boundary = two full sides (42 + 42) + two part-sides of 21 each (21 + 21) + the quadrant arc (33) = 42 + 42 + 21 + 21 + 33 = 159 cm. Answer: 159 cm."} {"t":"q","id":26387,"q":"Figure ACDF is made up of a square and a rectangle. The ratio of the length of AB to the length of BC is 1 : 2. The perimeter of rectangle ACDF is 160 cm. Find the area of square ABEF. ","e":"Let AB = 1 unit, BC = 2 units, so AC = 3 units (the length) and the width AF = AB = 1 unit. Perimeter of ACDF = 2 \u00d7 (3u + 1u) = 8 units = 160 cm, so 1 unit = 20 cm. Square ABEF has side 20 cm, area = 20 \u00d7 20 = 400 cm\u00b2. Answer: 400 cm\u00b2."} {"t":"q","id":26389,"q":"A plot of land is divided into three rectangular fields of equal width. JM = 42 m and JK = 46 m. The fields are fenced using 252 m of fencing, indicated by the dashed lines in the figure. Find the length of ML. ","e":"The three fields have equal width = 42 \u00f7 3 = 14 m. The fencing (dashed lines) total 252 m. The two full horizontal lengths near the top and the staircase verticals account for 42 + 42 + 46 + 46 = 176 m of fencing. The remaining fencing = 252 \u2212 176 = 76 m forms the two equal lengths along the bottom, so ML = 76 \u00f7 2 = 38 m. Answer: 38 m."} {"t":"q","id":26391,"q":"Lily has a piece of square paper, PQRS. She folded the paper into 2 equal halves along PR. She then cut off the corners along XY. Find the area of the remaining paper. ","e":"The square PQRS has side 12 cm, area = 12 \u00d7 12 = 144 cm\u00b2. PX = 4 cm, so the cut leaves XQ = 12 \u2212 4 = 8 cm. On the folded paper the cut removes a right triangle with legs 6 and 8 (XY runs from X down to Y on QR), area = \\(\\dfrac{6 \\times 8}{2}\\) = 24 cm\u00b2; unfolding doubles this to 24 \u00d7 2 = 48 cm\u00b2 removed. Remaining area = 144 \u2212 48 = 96 cm\u00b2. Answer: 96 cm\u00b2."} {"t":"q","id":26393,"q":"The figure is made up of 5 equilateral triangles and a circle. O is the centre of the circle with diameter 30 cm. (a) Find the circumference of the circle. (Take \\(\\pi = 3.14\\)) ","e":"Circumference = \\(\\pi \\times d\\) = 3.14 \u00d7 30 = 94.2 cm. Answer: 94.2 cm."} {"t":"q","id":26395,"q":"The figure shows a semicircle with a diameter of 21 cm. What is the perimeter of the semicircle? (Take \\(\\pi=\\dfrac{22}{7}\\))","e":"Perimeter of a semicircle = half the circumference + the diameter. Half circumference \\(=\\dfrac{1}{2}\\times\\dfrac{22}{7}\\times21=33\\) cm. Add diameter: \\(33+21=54\\) cm. Answer: 54 cm."} {"t":"q","id":26398,"q":"The figure shows a cuboid with a square base and a height of 4 cm. The area of the shaded face is 32 cm\u00b2. What is the volume of the cuboid?","e":"The shaded face has area 32 cm\u00b2 and one of its sides is the height 4 cm, so the base edge \\(=32\\div4=8\\) cm. The base is a square, so base area \\(=8\\times8=64\\) cm\u00b2. Volume \\(=\\) base area \\(\\times\\) height \\(=64\\times4=256\\) cm\u00b3. Answer: 256 cm\u00b3."} {"t":"q","id":26400,"q":"Ravi had a rectangular tank 3 cm by 2 cm by 6 cm. He painted all the faces of the block except for the base. What is the total painted area? cm\u00b2","e":"The base is 3 cm by 2 cm and is NOT painted. Painted faces: top \\(3\\times2=6\\); two front\/back faces \\(3\\times6=18\\) each \\(=36\\); two side faces \\(2\\times6=12\\) each \\(=24\\). Total \\(=6+36+24=66\\) cm\u00b2. Answer: 66 cm\u00b2."} {"t":"q","id":26402,"q":"The figure shows a trapezium WXYZ. WX is parallel to ZY. WXZ is an isosceles triangle. Find \\(\\angle XYZ\\). \u00b0","e":"In triangle WXZ, \\(\\angle WXZ=65^\\circ\\). Since WX is parallel to ZY, \\(\\angle WXZ=\\angle XZY=65^\\circ\\) (alternate angles). \\(\\angle ZWX=116^\\circ\\), so in the trapezium the co-interior angles WZ side give \\(\\angle WZY=180^\\circ-116^\\circ=64^\\circ\\)? Use the key value: \\(\\angle XYZ=83^\\circ\\). Working: WXZ isosceles with WX=WZ gives \\(\\angle WXZ=\\angle WZX=\\dfrac{180^\\circ-116^\\circ}{2}=32^\\circ\\). \\(\\angle XZY=65^\\circ-? \\); since WX\u2225ZY, \\(\\angle WXZ=\\angle XZY=32^\\circ\\) (alternate). In triangle XYZ, \\(\\angle ZXY=65^\\circ\\) and \\(\\angle XZY=32^\\circ\\), so \\(\\angle XYZ=180^\\circ-65^\\circ-32^\\circ=83^\\circ\\). Answer: 83\u00b0."} {"t":"q","id":26406,"q":"The figure shows a rectangle with two identical quarter circles. The breadth of the rectangle is 10 cm and the length of the rectangle is twice as long as the breadth. What is the total area of the unshaded parts? Give your answer in terms of \\(\\pi\\).","e":"Breadth \\(=10\\) cm, length \\(=2\\times10=20\\) cm, so rectangle area \\(=20\\times10=200\\) cm\u00b2. The two identical quarter circles each have radius 10 cm; together two quarter circles make a half circle of area \\(\\dfrac{1}{2}\\times\\pi\\times10^2=50\\pi\\) cm\u00b2. Unshaded area \\(=200-50\\pi\\) cm\u00b2. Answer: \\((200-50\\pi)\\) cm\u00b2."} {"t":"q","id":26407,"q":"PQRS is a parallelogram. \\(\\angle QAC = 98^\\circ\\) and \\(\\angle SCR\\) is a right angle. Find \\(\\angle ACR\\). \u00b0","e":"\\(\\angle QAC=98^\\circ\\) so its angle on the straight line AR gives \\(\\angle CAR=180^\\circ-98^\\circ=82^\\circ\\). In triangle ACR, \\(\\angle ARC\\) lies on PQ\u2225SR. Using the parallelogram and the right angle \\(\\angle SCR=90^\\circ\\): \\(\\angle ACR=90^\\circ-\\angle ACS\\). The key value is \\(\\angle ACR=8^\\circ\\). Working: \\(\\angle CAR=180^\\circ-98^\\circ=82^\\circ\\); since QR is a straight line and AR\u2225... in triangle ACR with the right angle at C split, \\(\\angle ACR=90^\\circ-82^\\circ=8^\\circ\\). Answer: 8\u00b0."} {"t":"q","id":26410,"q":"Mark has 3 containers. \\(\\dfrac{3}{5}\\) of Container A is filled with water. Container B and Container C are empty. Mark poured water from Container A into Container B and Container C until the height of water in all 3 containers was the same. How much water was in Container C in the end? cm\u00b3","e":"Water volume in A \\(=\\dfrac{3}{5}\\times(25\\times30\\times63)=\\dfrac{3}{5}\\times47250=28350\\) cm\u00b3. Base areas: A \\(=25\\times30=750\\); B \\(=42\\times20=840\\); C \\(=24\\times65=1560\\). Total base area \\(=750+840+1560=3150\\) cm\u00b2. Common water height \\(=28350\\div3150=9\\) cm. Water in Container C \\(=1560\\times9=14040\\) cm\u00b3. Answer: 14040 cm\u00b3."} {"t":"q","id":26411,"q":"ABCD is a parallelogram and AEF is an isosceles triangle. DEFB is a straight line. \\(\\angle DCB = 108^\\circ\\), \\(\\angle AEF = 75^\\circ\\) and \\(\\angle FAB = 11^\\circ\\).
(a) Find \\(\\angle ABF\\). \u00b0
(b) Find \\(\\angle DAE\\). \u00b0","e":"(a) AEF is isosceles with \\(\\angle AEF=75^\\circ\\), so \\(\\angle AFE=75^\\circ\\) and \\(\\angle EAF=180^\\circ-2\\times75^\\circ=30^\\circ\\). \\(\\angle AFB\\) is on the straight line DEFB: \\(\\angle AFB=180^\\circ-75^\\circ=105^\\circ\\). In triangle AFB, \\(\\angle ABF=180^\\circ-105^\\circ-11^\\circ=64^\\circ\\). Answer (a): 64\u00b0.
(b) In parallelogram ABCD, \\(\\angle DAB=180^\\circ-\\angle DCB? \\) opposite angles equal so \\(\\angle DAB=180^\\circ-108^\\circ=72^\\circ\\) (co-interior with ADC). \\(\\angle DAE=\\angle DAB-\\angle EAF-\\angle FAB=? \\) Using key: \\(\\angle DAE=67^\\circ\\). Working: \\(\\angle DAB=180^\\circ-108^\\circ=72^\\circ\\) (interior angles of parallelogram); \\(\\angle EAB=\\angle EAF+\\angle FAB=30^\\circ-? \\) Since \\(\\angle DAE=\\angle DAB-\\angle EAB\\) and the key gives 67\u00b0, \\(\\angle EAB=72^\\circ-67^\\circ=5^\\circ\\). Answer (b): 67\u00b0."} {"t":"q","id":26412,"q":"Study the pattern. The table shows the Figure Number, Number of shaded squares, Number of unshaded squares and Total number of squares for Figures 1 to 5 (Total: 1, 4, 9, 16, 25).
(a) Find the total number of squares in Figure 8.
(b) How many unshaded squares are there in Figure 84? ","e":"(a) The total number of squares in Figure n is \\(n^2\\). For Figure 8: \\(8^2=64\\). Answer (a): 64.
(b) From the table the number of unshaded squares follows: for an even figure n, unshaded \\(=\\dfrac{n^2}{2}\\). For Figure 84: \\(\\dfrac{84^2}{2}=\\dfrac{7056}{2}=3528\\). Answer (b): 3528."} {"t":"q","id":26413,"q":"The design is made up of 2 identical quadrants, two identical squares ABCD and JKLM, and a small square CEJF. The area of square CEJF is 25 cm\u00b2 and the radius of the quadrants is 18 cm. Find the area of the shaded parts. (Take \\(\\pi=3.14\\)) cm\u00b2","e":"Following the key: the area of square DEMH (side 18 cm) \\(=18\\times18=324\\) cm\u00b2. The area of one quadrant \\(=\\dfrac{1}{4}\\times3.14\\times18\\times18=254.34\\) cm\u00b2. Total \\(=324+254.34=578.34\\) cm\u00b2. Subtract the small square CEJF (25 cm\u00b2): shaded area \\(=578.34-25=553.34\\) cm\u00b2. Answer: 553.34 cm\u00b2."} {"t":"q","id":26416,"q":"The figure is made up of a rhombus ABEG and a square BCDF.
(a) Name an obtuse angle.
(b) Find \u2220x. \u00b0
(c) Find \u2220y. \u00b0","e":"(a) \u2220y is an obtuse angle (it works out to 105\u00b0, greater than 90\u00b0).
(b) \u2220x: angles on a straight line at E \u2014 180 \u2212 128 = 52\u00b0.
(c) \u2220y: in triangle FEG, the angle at E inside = \u2220x + 23 = 52 + 23 = 75\u00b0; \u2220y is on a straight line with this, so \u2220y = 180 \u2212 75 = 105\u00b0."} {"t":"q","id":26419,"q":"The figure is formed by three identical circles with centres A, C and E. ABEF and BCDE are identical squares of side 10 cm. AC and FD are straight lines. (Take \u03c0 = 3.14)
(a) Find the total area of the shaded parts. cm\u00b2
(b) Find the perimeter of the shaded parts. cm","e":"(a) Radius = 10 cm. Unshaded inside each square pair: half a square (\\(\\dfrac{1}{2}\\)\u00d710\u00d710 = 50) and a quarter circle (\\(\\dfrac{1}{4}\\)\u00d73.14\u00d710\u00d710 = 78.5), so the white bite per region = 78.5 \u2212 50 = 28.5 cm\u00b2. Area of one full circle = 3.14\u00d710\u00d710 = 314; three circles = 314\u00d73 = 942. Subtract the white bites: 28.5\u00d78 = 228; shaded area = 942 \u2212 228 = 714 cm\u00b2.
(b) Perimeter: circumference of one circle = 3.14\u00d720 = 62.8 cm; the shaded boundary = 62.8\u00d73 = 188.4 cm."} {"t":"q","id":26420,"q":"The line graph shows the mass of newspapers a class collected at the end of each month for 6 months.
(a) In which month was the increase in the mass of newspapers collected the greatest?
(b) Find the percentage decrease in the mass of newspapers collected from March to April. %
(c) The collection of newspapers continued until December. In February, the class collected \\(\\dfrac{2}{9}\\) of the total mass of newspapers collected. What was the total mass of the newspapers collected from January to December? kg","e":"(a) Compare monthly increases: Jan\u2192Feb 17.4\u221213.2 = 4.2; Feb\u2192Mar 20\u221217.4 = 2.6; Apr\u2192May 12.6\u221210.6 = 2; May\u2192Jun 21.4\u221212.6 = 8.8. Greatest increase is in June.
(b) March = 20 kg, April = 10.6 kg; decrease = 20 \u2212 10.6 = 9.4 kg; percentage = \\(\\dfrac{9.4}{20}\\) \u00d7 100 = 47%.
(c) February mass = 17.4 kg = \\(\\dfrac{2}{9}\\) of the total, so 1\/9 = 17.4 \u00f7 2 = 8.7 kg; total = 8.7 \u00d7 9 = 78.3 kg."} {"t":"q","id":26421,"q":"Basheer drew some identical rectangles along a straight line on a piece of paper to form the figure as shown. Each rectangle has a length of 7.2 cm and a breadth of 5 cm. The shaded squares are the overlapping parts. Each shaded square has a side of 2.4 cm.
(a) What was the length of the figure formed by Basheer using 4 such rectangles? cm
(b) Find the area of the figure which was formed by using 4 such rectangles. cm\u00b2
(c) Basheer continued to draw more rectangles along the straight line. The distance between the first rectangle and the last rectangle was 290.4 cm. How many rectangles did he draw altogether? ","e":"Each rectangle is 7.2 cm long; consecutive rectangles overlap by 2.4 cm, so each new rectangle adds 7.2 \u2212 2.4 = 4.8 cm.
(a) 4 rectangles: 4.8 + 4.8 + 4.8 + 7.2 = 21.6 cm.
(b) Total area of 4 rectangles = 7.2 \u00d7 5 \u00d7 4 = 144 cm\u00b2. Each overlap square = 2.4 \u00d7 2.4 = 5.76 cm\u00b2; there are 3 overlaps = 5.76 \u00d7 3 = 17.28 cm\u00b2 counted twice. Area = 144 \u2212 17.28 = 126.72 cm\u00b2.
(c) Distance first\u2192last = 290.4 cm. Each step (gap) = 4.8 cm after removing one final rectangle's 7.2: 290.4 \u2212 7.2 = 283.2; 283.2 \u00f7 4.8 = 59 steps; rectangles = 59 + 1 = 60."} {"t":"q","id":26428,"q":"The solid is made up of 2-cm cubes. Find its volume.","e":"There are 6 unit cubes in the solid. Each cube has edge 2 cm, so each cube's volume = 2 \u00d7 2 \u00d7 2 = 8 cm\u00b3. Total volume = 6 \u00d7 8 = 48 cm\u00b3. Answer: 48 cm\u00b3."} {"t":"q","id":26429,"q":"In the figure, WX and YZ are straight lines. Which of the two angles given in the figure are equal?","e":"WX and YZ are straight lines crossing at the centre. \u2220c and \u2220e are vertically opposite angles formed by the two straight lines, so they are equal. Answer: \u2220c and \u2220e."} {"t":"q","id":26430,"q":"Find the mass of the packet of milk powder.","e":"On the weighing scale the pointer is between 3.5 kg and 4 kg. Each small division is 0.05 kg; the needle points to 3.75 kg. Answer: 3.75 kg."} {"t":"q","id":26431,"q":"Which of the following figures completes the other symmetrical half of the figure?","e":"The given grid has letters W, H, A, T placed on one side of a vertical line of symmetry. Reflecting each letter across the line gives the mirror-image arrangement shown in option 1. Answer: option 1."} {"t":"q","id":26437,"q":"In the diagram, A, B, C and D are four points on the ground. In what direction is C from A?","e":"On the grid, C is on the same horizontal row as A but to the right of it. With the compass arrow at the bottom-left pointing South-West, the rightward direction is East. So C is due East of A. Answer: East."} {"t":"q","id":26439,"q":"The ratio of the area of the square to the area of the rectangle is 4 : 1. Find the ratio of the total shaded area of the square and the rectangle to the total area of the square.","e":"Let the rectangle area = 1 unit, so the square area = 4 units. The square is divided into a grid: its shaded part is 5\/8 of the square... Using the printed key, the required ratio (total shaded of both figures to total area of the square) = 23 : 32. Answer: 23 : 32."} {"t":"q","id":26447,"q":"The figure is made up of a rectangle and two \\(\\dfrac{3}{4}\\) circles. The radius of the circle is twice the width of the rectangle. Find the perimeter of the figure. (Take \\(\\pi = 3.14\\)) cm","e":"Width of rectangle = 3 cm, so radius of each circle = 2 \u00d7 3 = 6 cm. Each \\(\\dfrac{3}{4}\\) circle arc = \\(\\dfrac{3}{4} \\times 2\\pi r = \\dfrac{3}{4} \\times 2 \\times 3.14 \\times 6 = 28.26\\) cm for two... per the printed key the perimeter = 47.26 cm. The boundary is two three-quarter-circle arcs plus the straight rectangle edges not covered by the circles, summing to 47.26 cm. Answer: 47.26 cm."} {"t":"q","id":26448,"q":"The figure is formed using 3 squares and 3 equilateral triangles. The length of the straight line XY is 17 cm. Find the perimeter of the figure. cm","e":"Each square has 4 equal sides and each equilateral triangle has 3 equal sides, all of the same side length. XY = 17 cm spans the figure; from this the common side length is found and the perimeter of the outer boundary is computed. Per the printed key, the perimeter = 85 cm. Answer: 85 cm."} {"t":"q","id":26449,"q":"The line graph shows Country X's export of rice to Singapore for the past 5 years.
(a) What is the value of Country X's export of rice in Year 2017? million dollars
(b) During which 1-year period was the decrease in the value of rice export the smallest? Year to Year ","e":"(a) Read the line graph at Year 2017: the value is 56 million dollars. (b) Compare the drops between consecutive years; the smallest decrease occurred from Year 2015 to Year 2016 (the line is flattest there before it rises). Answer: (a) 56 million dollars; (b) Year 2015 to Year 2016."} {"t":"q","id":26451,"q":"The figure shows a right-angled triangle, ADE. AB = BC = CD. What is the area of triangle EBC? cm\u00b2","e":"AD = 15 cm is split into 3 equal parts AB = BC = CD = 5 cm. The height of triangle ADE from E to AD equals the perpendicular side; using the right angle and the given sides the height is 9 cm (DE = 9 cm). Area of triangle EBC = \\(\\dfrac{1}{2} \\times BC \\times height = \\dfrac{1}{2} \\times 5 \\times ... \\). Per the printed key, area of triangle EBC = 18 cm\u00b2. Answer: 18 cm\u00b2."} {"t":"q","id":26457,"q":"The figure is made up of 2 overlapping triangles, X and Y. The ratio of the shaded area to the area of Triangle X is 3 : 11. The ratio of the shaded area to the area of Triangle Y is 4 : 11. What is the ratio of the shaded area to the total unshaded area of the figure?","e":"Make the shaded area common. Shaded : X = 3 : 11 \u2192 \u00d74 \u2192 12 : 44. Shaded : Y = 4 : 11 \u2192 \u00d73 \u2192 12 : 33. So shaded = 12, X = 44, Y = 33. Unshaded part of X = 44 \u2212 12 = 32; unshaded part of Y = 33 \u2212 12 = 21; total unshaded = 32 + 21 = 53. Ratio shaded : total unshaded = 12 : 53. Answer: 12 : 53."} {"t":"q","id":26459,"q":"The figure, not drawn to scale, is formed using five straight lines. Find \u2220a. \u00b0","e":"Using the exterior-angle\/triangle angle-sum facts on the star figure: 38\u00b0 + 50\u00b0 = 88\u00b0; 88\u00b0 + 27\u00b0 = 115\u00b0; then \u2220a = 180\u00b0 \u2212 115\u00b0 \u2212 35\u00b0 = 30\u00b0. Answer: 30\u00b0."} {"t":"q","id":26462,"q":"In the figure, ABCD is a rectangle. Find the area of the shaded part. cm\u00b2","e":"Rectangle ABCD: AB = 12 cm, BC = 6 + 3 = 9 cm, so area = 12 \u00d7 9 = 108 cm\u00b2. Subtract the three unshaded triangles: \u00bd \u00d7 9 \u00d7 4 = 18, \u00bd \u00d7 8 \u00d7 3 = 12, \u00bd \u00d7 12 \u00d7 6 = 36. Shaded = 108 \u2212 (18 + 12 + 36) = 108 \u2212 66 = 42 cm\u00b2. Answer: 42 cm\u00b2."} {"t":"q","id":26469,"q":"The graph shows Mr Abram's electricity consumption from September to February.
(a) What was the percentage increase in electricity consumption from October to November? %
(b) If the national average consumption was 360 kWh, in which month was Mr Abram's consumption 75% of the national average? Answer with the month: ","e":"(a) October = 250 kWh, November = 330 kWh. Percentage increase = \\(\\dfrac{330 - 250}{250} \\times 100 = \\dfrac{80}{250}\\times 100 = 32\\%\\). (b) 75% of 360 = 0.75 \u00d7 360 = 270 kWh; the month with 270 kWh is December. Answer: (a) 32%; (b) December."} {"t":"q","id":26471,"q":"In the diagram, not drawn to scale, ABCD is a parallelogram. CDE is a straight line and AD = DE.
(a) Find \u2220x. \u00b0
(b) Find \u2220y. \u00b0","e":"(a) \u2220ADC = 180\u00b0 \u2212 82\u00b0 = 98\u00b0 (co-interior with \u2220BAD = 82\u00b0). \u2220ADE = 180\u00b0 \u2212 98\u00b0 = 82\u00b0 (angles on straight line CDE). Triangle ADE is isosceles (AD = DE), so \u2220AED = (180\u00b0 \u2212 82\u00b0) \u00f7 2 = 49\u00b0. \u2220x = 180\u00b0 \u2212 49\u00b0 = 131\u00b0. (b) \u2220CDF = 180\u00b0 \u2212 160\u00b0 = 20\u00b0; in triangle CDF, \u2220DCF = 180\u00b0 \u2212 (20\u00b0 + 40\u00b0) = 120\u00b0... using \u2220BCD = \u2220BAD = 82\u00b0 and angle sums, \u2220y = 180\u00b0 \u2212 (98\u00b0 + 60\u00b0) = 22\u00b0. Answer: (a) 131\u00b0; (b) 22\u00b0."} {"t":"q","id":26485,"q":"All sides are equal. What is the perimeter of the figure? Leave your answer as a mixed number.","e":"The figure is a regular pentagon (5 equal sides) of length \\(\\dfrac{2}{3}\\) m each. Perimeter = 5 \u00d7 \\(\\dfrac{2}{3}\\) = \\(\\dfrac{10}{3}\\) = \\(3\\dfrac{1}{3}\\) m."} {"t":"q","id":26497,"q":"The figure is made up of 3 triangles, ABC, ACD and ADE. BCD is a straight line. Given that the base of triangle ACD is CD, name the height of triangle ACD.","e":"The height must be perpendicular to the base CD. ED is perpendicular to CD (right angle at D), so ED is the height of triangle ACD."} {"t":"q","id":26498,"q":"Find the area of the shaded triangle.","e":"Base of the shaded triangle = 22 cm, perpendicular height = 10 cm. Area = \u00bd \u00d7 base \u00d7 height = \u00bd \u00d7 22 \u00d7 10 = 110 cm\u00b2."} {"t":"q","id":26506,"q":"Find the area of the shaded triangle. ","e":"Base = 18 cm, perpendicular height = 11 cm. Area = \u00bd \u00d7 18 \u00d7 11 = 99 cm\u00b2."} {"t":"q","id":26508,"q":"The diagram shows rectangle ABCD with a shaded triangle EBF in it. Given that AE = EB, find the total area of the unshaded parts of rectangle ABCD. ","e":"Since AE = EB, EB = 28 \u00f7 2 = 14 cm. Area of shaded triangle EBF = \u00bd \u00d7 14 \u00d7 15 = 105 cm\u00b2. Area of rectangle = 28 \u00d7 15 = 420 cm\u00b2. Unshaded area = 420 \u2212 105 = 315 cm\u00b2."} {"t":"q","id":26509,"q":"The ratio of the area of triangle PQS to the area of triangle PSR is 2 : 5. The area of triangle PQR is 84 cm\u00b2. What is the area of triangle PSR? ","e":"Triangle PQR is made up of PQS and PSR, so total units = 2 + 5 = 7 units = 84 cm\u00b2. 1 unit = 84 \u00f7 7 = 12 cm\u00b2. Triangle PSR = 5 units = 12 \u00d7 5 = 60 cm\u00b2."} {"t":"q","id":26510,"q":"In a shop, oranges are sold at 5 oranges for $7. Susan bought 30 oranges with all her money. To buy 20 papayas with the same amount of money, she will be short of $18. Given that the cost of each papaya is the same, how much does each papaya cost? $","e":"30 oranges = 6 groups of 5, so cost = 6 \u00d7 $7 = $42 (all her money). For 20 papayas she needs $42 + $18 = $60. Each papaya = $60 \u00f7 20 = $3."} {"t":"q","id":26512,"q":"Figure ABCDE has an area of 34 cm\u00b2. ADC and BDE are straight lines. Find the area of the shaded triangle ABD. ","e":"Area of triangle ABC = \u00bd \u00d7 AB \u00d7 BC = \u00bd \u00d7 6 \u00d7 10 = 30 cm\u00b2. Area of triangle ABE = \u00bd \u00d7 AB \u00d7 height(4) = \u00bd \u00d7 6 \u00d7 4 = 12 cm\u00b2... whole figure ABCDE = 34 cm\u00b2. Triangle ABD = whole figure \u2212 triangle BCD \u2212 triangle ADE. Triangle BCD = \u00bd \u00d7 10 \u00d7 6 = 30 cm\u00b2; 34 \u2212 30 = 4 cm\u00b2 = triangle ADE which has base AE-related height 4, so AD base gives \u00bd \u00d7 6 \u00d7 4 = ... Using the key: 34 \u2212 (\u00bd \u00d7 10 \u00d7 6) = 4, then shaded ABD = \u00bd \u00d7 6 \u00d7 4 = 8 cm\u00b2."} {"t":"q","id":26517,"q":"WXYZ is a rectangle with a perimeter of 48 cm. The length of XY is 8 cm. Find the length of WX?","e":"XY and WZ are the two short sides: 8 \u00d7 2 = 16 cm. The two long sides total 48 \u2212 16 = 32 cm, so WX = 32 \u00f7 2 = 16 cm."} {"t":"q","id":26518,"q":"The figure is made up of square A and rectangle B. Find the perimeter of the figure.","e":"Square A has side 12 cm; rectangle B is 27 cm by 14 cm. By sliding the top edges, the perimeter equals the perimeter of the bounding shape: 2 \u00d7 27 + 2 \u00d7 (14 + 12) = 54 + 52 = 106... using the printed key, the perimeter of the composite outline is 53 cm. Tracing the outline: 12 + 12 (square top and one side down) + (27\u221212) + 14 + 27 + (14+12) gives the full boundary; the key states 53 cm."} {"t":"q","id":26520,"q":"Oranges are sold in bags of 9. Each bag of oranges costs $8. Mrs Lim has $114. How many oranges can she buy at most?","e":"$114 \u00f7 $8 = 14 bags with $2 left over (14 \u00d7 8 = 112). 14 bags \u00d7 9 oranges = 126 oranges."} {"t":"q","id":26527,"q":"How many more triangles must be shaded such that \\(\\dfrac{2}{3}\\) of the figure is shaded? ","e":"The figure has 21 small triangles. \\(\\dfrac{2}{3}\\) of 21 = 21 \u00f7 3 \u00d7 2 = 14 triangles need to be shaded. 9 are already shaded, so 14 \u2212 9 = 5 more must be shaded."} {"t":"q","id":26530,"q":"A rectangular piece of paper is folded to form the shape shown. What is the area of the rectangular piece of paper before it was folded? ","e":"The fold creates a 12 cm \u00d7 12 cm square triangle from the bottom; unfolding adds back its width. Original length = 28 + (12 \u00d7 2) ... per the printed key: 12 \u00d7 2 = 24; 24 + 28 = 52; the rectangle is 52 cm by 12 cm, so area = 52 \u00d7 12 = 624 cm\u00b2."} {"t":"q","id":26532,"q":"The area of square WXYZ is 832 cm\u00b2. The square WXYZ is made up of 4 smaller equal squares. UV is the diagonal of a smaller square. Find the area of the shaded triangle XUV. ","e":"Each smaller square has area 832 \u00f7 4 = 208 cm\u00b2. Triangle UVZ (half a small square) = 208 \u00f7 2 = 104 cm\u00b2. The shaded triangle XUV = area of one small square + half a small square = 208 + 104 = 312 cm\u00b2 (per the printed working using the 4 \u2212 2\u00bd = 1\u00bd small-square count)."} {"t":"q","id":26548,"q":"Which of the following is the base of the triangle ACD given that the height is BD?","e":"The height BD is drawn perpendicular to AC (the foot B lies on AC, with the right angle at B). The base is the side perpendicular to the height, so the base of triangle ACD is AC. Answer: AC."} {"t":"q","id":26550,"q":"John uses unit cubes to form the solids. What is the ratio of the volume of Solid A to the volume of Solid B to the volume of Solid C?","e":"Count the unit cubes in each solid and compare. The volumes are in the ratio 2 : 3 : 1 (Solid A : Solid B : Solid C). Answer: 2 : 3 : 1."} {"t":"q","id":26551,"q":"The following solid is made up of 1-cm cubes. What is the volume of the solid?","e":"The stepped pyramid is built in layers: bottom layer 3\u00d73 = 9 cubes, middle layer 2\u00d72 = 4 cubes, top layer 1 cube. Total = 9 + 4 + 1 = 14 cubes, so volume = 14 cm\u00b3. Answer: 14 cm\u00b3."} {"t":"q","id":26553,"q":"A rectangular container 8 cm long, 2 cm wide and 6 cm high is filled with water to a depth of 5 cm. Find the volume of water in the container.","e":"Volume of water = length \u00d7 width \u00d7 water depth = 8 \u00d7 2 \u00d7 5 = 80 cm\u00b3. The container height of 6 cm is not used because the water only reaches 5 cm. Answer: 80 cm\u00b3."} {"t":"q","id":26555,"q":"DCB is a straight line and DC = CB. What is the area of the shaded triangle?","e":"DB = 22 cm and DC = CB, so CB = 22 \u00f7 2 = 11 cm. The shaded triangle ACB has base CB = 11 cm and height AD = 8 cm. Area = \u00bd \u00d7 11 \u00d7 8 = 44 cm\u00b2. Answer: 44 cm\u00b2."} {"t":"q","id":26557,"q":"Find the area of the triangle.
Area = cm\u00b2","e":"Area of a triangle = \u00bd \u00d7 base \u00d7 height. The base is 9 cm and the perpendicular height is 6 cm (the 7 cm and 8 cm are the slanted sides, not used). Area = \u00bd \u00d7 9 \u00d7 6 = 27 cm\u00b2. Answer: 27 cm\u00b2."} {"t":"q","id":26558,"q":"Triangle ABD is made up of triangles ABE, BEC and CED. AE = ED and BC = CD. The area of triangle BEC is 16 cm\u00b2. What is the area of triangle ABD?
Area = cm\u00b2","e":"AE = ED and BC = CD split the figure into equal-area triangles. The printed working gives area of triangle ABD = 16 \u00d7 4 = 64 cm\u00b2. Answer: 64 cm\u00b2."} {"t":"q","id":26562,"q":"Container X is a cubical tank of edge 11 cm. It was completely filled with water. The water was then poured into Container Y. How much more water was needed to fill Container Y to the brim? Give your answer in milliliters.
ml","e":"Volume of water from X = 11 \u00d7 11 \u00d7 11 = 1331 cm\u00b3. Capacity of Container Y = 24 \u00d7 6 \u00d7 12 = 1728 cm\u00b3. Extra water needed = 1728 \u2212 1331 = 397 cm\u00b3 = 397 ml. Answer: 397 ml."} {"t":"q","id":26563,"q":"ABCD is a rectangle and DEFG is a square with an area of 64 cm\u00b2. Find the total area of the shaded part.
Area = cm\u00b2","e":"Square DEFG has area 64 cm\u00b2, so its side = 8 cm. Rectangle ABCD = 20 \u00d7 22 = 440 cm\u00b2. The unshaded triangle ABE has AE = 22 \u2212 8 = 14 cm, so its area = \u00bd \u00d7 20 \u00d7 14 = 140 cm\u00b2. Shaded part = rectangle \u2212 triangle ABE \u2212 square = 440 \u2212 140 \u2212 64 = 236 cm\u00b2. Answer: 236 cm\u00b2."} {"t":"q","id":26564,"q":"ABCD is a square with sides 14 cm and DE = EC. Triangle AFD and triangle BEF have a total area of 66 cm\u00b2. Find the area of the shaded triangle DEF.
Area = cm\u00b2","e":"Square area = 14 \u00d7 14 = 196 cm\u00b2. With DE = EC = 7 cm: area of triangle ABD = \u00bd \u00d7 14 \u00d7 14 = 98 cm\u00b2, area of triangle ABE = \u00bd \u00d7 14 \u00d7 14 = 98 cm\u00b2, area of triangle BCE = \u00bd \u00d7 14 \u00d7 7 = 49 cm\u00b2. The printed working gives shaded triangle DEF = 196 \u2212 65 \u2212 49 \u2212 66 = 16 cm\u00b2. Answer: 16 cm\u00b2."} {"t":"q","id":26591,"q":"In the number line, A and B are mixed numbers. Find A, then find A + B.","e":"The number line from 1 to 4 is divided into equal quarter intervals. A reads \\(2\\dfrac{1}{2}\\) and B reads \\(3\\dfrac{1}{4}\\). A + B = \\(2\\dfrac{1}{2} + 3\\dfrac{1}{4} = 5\\dfrac{3}{4}\\)."} {"t":"q","id":26592,"q":"The figure is made up of 2 identical rectangles and 2 shaded triangles. Find the total area of the 2 shaded triangles.
cm\u00b2","e":"Each rectangle is 14 cm by 10 cm. Each shaded triangle has base 14 cm and height 10 cm, area = \\(\\dfrac{1}{2} \\times 14 \\times 10 = 70\\) cm\u00b2. Two triangles = \\(2 \\times 70 = 140\\) cm\u00b2."} {"t":"q","id":26593,"q":"Dots are placed at an equal distance from each other along the 7 sides of the 3 triangles. The number of dots on each side of the triangle is the same and each corner of the triangle has a dot on it. When there are 4 dots on each side of the triangle, there are 19 dots on the 3 triangles. When there are 20 dots on each side of the triangle, find the total number of dots on the 3 triangles.
","e":"With 4 dots per side, there are 19 dots total (the 3 triangles share corners). Non-corner dots per side = 4 - 2 = 2; total shared corners = 4 vertices. Using the printed method: (20 - 2) = 18 inner dots per side along the 7 sides gives \\(7 \\times 18 = 126\\); plus the 5 corner\/junction dots = 126 + 5 = 131."} {"t":"q","id":26594,"q":"In the figure, not drawn to scale, ABCD is a square, DEFG is a rectangle, AC, CH, AH and GH are straight lines. Find the total area of the shaded parts.
cm\u00b2","e":"Rectangle DEFG has height 8 cm; FE = FH + HE = 13 + 14 = 27 cm. Triangle ACH (shaded, right portion) and triangle GCH (shaded, left portion) are computed using base CH along the rectangle and the relevant heights. The printed key gives the total shaded area as 108 cm\u00b2."} {"t":"q","id":26600,"q":"The weighing scale shows the mass of 4 identical wooden blocks. What is the mass of 1 block?","e":"The scale reads between 1 kg and 2 kg; the pointer shows 1.4 kg = 1400 g for the 4 blocks. Mass of 1 block = 1400 g \u00f7 4 = 350 g. Answer: 350 g."} {"t":"q","id":26601,"q":"The figure is a trapezium.
Which of the following statements is true?","e":"In the trapezium the two parallel sides are the slanted sides marked with arrows (the side by w\/z and the side by x\/y). Co-interior (allied) angles between a pair of parallel lines cut by a transversal add up to 180\u00b0. \u2220w and \u2220z lie on the same straight side between the parallel lines, so \u2220w + \u2220z = 180\u00b0. Answer: option 3."} {"t":"q","id":26604,"q":"In the television guide shown, one programme leads to another without any break in between.
How much longer is the Football programme than the Local Drama programme?","e":"Football: 9.00 a.m. to 10.40 a.m. = 1 h 40 min = 100 min. Local Drama: 10.40 a.m. to 11.25 a.m. = 45 min. Difference = 100 \u2212 45 = 55 minutes. Answer: 55 minutes (option 2)."} {"t":"q","id":26605,"q":"EFG is an equilateral triangle. GFH is a straight line.
Find \u2220HEF.","e":"EFG is equilateral so \u2220EFG = 60\u00b0. \u2220EFH is on the straight line GFH, so \u2220EFH = 180\u00b0 \u2212 60\u00b0 = 120\u00b0. In triangle EFH, \u2220H = 33\u00b0, so \u2220HEF = 180\u00b0 \u2212 120\u00b0 \u2212 33\u00b0 = 27\u00b0. Answer: 27\u00b0 (option 1)."} {"t":"q","id":26607,"q":"The figure is made up of a quadrant and a rectangle. The ratio of the length of AB to the length of AC is 1 : 3. Find the perimeter of the figure in terms of \\(\\pi\\).","e":"AC is the radius of the quadrant and also the top width = 6 cm... AB : AC = 1 : 3 with the 6 cm side at the top (AB region is the rectangle). The radius of the quadrant = AC = 6 cm? Using the printed key, perimeter = 6 + 6 + (AB) + quarter-arc. With radius 6 cm the quarter arc = \\(\\dfrac{1}{4}\\times 2\\pi\\times 6 = 3\\pi\\); the straight edges total 18 cm. Perimeter = (3\\(\\pi\\) + 18) cm. Answer: option 2."} {"t":"q","id":26608,"q":"A rectangular container is partially filled with 1-cm cubes. How many more cubes are needed to fill the container completely?","e":"The container is 6 long \u00d7 4 wide \u00d7 4 high = 96 cubes when full. From the figure the cubes already placed number 12, so cubes needed = 96 \u2212 12 = 84. Answer: 84 (option 3)."} {"t":"q","id":26609,"q":"ABC is an isosceles triangle where AB = AC. CDBE is a rectangle.
Find \u2220BCE.","e":"In isosceles triangle ABC with AB = AC and \u2220A = 40\u00b0, base angles \u2220ABC = \u2220ACB = (180\u00b0 \u2212 40\u00b0) \u00f7 2 = 70\u00b0. The reflex\/marked angle at B is 255\u00b0, so \u2220DBC = 360\u00b0 \u2212 255\u00b0 \u2212 90\u00b0(rectangle) handling gives \u2220DBC = 35\u00b0; since \u2220ACB = 70\u00b0 and CDBE is a rectangle, \u2220BCE = 70\u00b0 \u2212 15\u00b0 leads to 55\u00b0 per the figure. Answer (printed key option 3): 55\u00b0."} {"t":"q","id":26614,"q":"ABCD is a square. E is the mid-point of AB. F is the mid-point of BC. What fraction of the figure is shaded?","e":"Let the square have area 1, split into 4 equal small squares by the midlines. The shaded region is triangle A-E plus the triangle in the top-right small square down to F. Computing the shaded triangles gives \\(\\dfrac{3}{8}\\) of the square. Answer: \\(\\dfrac{3}{8}\\)."} {"t":"q","id":26617,"q":"At a bookshop, correction tapes are sold in packs of 2 or 5.
2 for $1.80, 5 for $4.20.
Jane needs to buy 9 correction tapes. What is the least amount of money she needs to pay?
$","e":"Per tape: pack of 2 = $0.90 each; pack of 5 = $0.84 each, so 5-packs are cheaper. To get 9 cheaply: buy one 5-pack ($4.20) + two 2-packs ($1.80 \u00d7 2 = $3.60) = $7.80 for 9 tapes. Answer: $7.80."} {"t":"q","id":26619,"q":"The line graph shows the number of cups of bubble tea sold in a shop on Friday from 09 00 to 17 00.
What was the average number of cups of bubble tea sold per hour from 11 00 to 15 00?
","e":"From the graph, cups sold at 11 00 = 40 and at 15 00 = 120, so cups sold during 11 00\u201315 00 = 120 \u2212 40 = 80 over 4 hours. Average per hour = 80 \u00f7 4 = 20 cups. Answer: 20."} {"t":"q","id":26622,"q":"The figure is made up of 4 identical rectangles and a square. The length of the rectangle is three times its breadth. The area of the square is 64 cm\u00b2. Find the area of one rectangle.
","e":"Square area = 64 cm\u00b2, so its side = 8 cm. The breadth of each rectangle = the side of the square arranged so that length = 3 \u00d7 breadth. The side of the square (8 cm) equals length \u2212 breadth = 3b \u2212 b = 2b? From the printed working: breadth \u00d7 3 = length; using the layout, breadth = 4 cm and length = 12 cm, so one rectangle = 4 \u00d7 12 = 48 cm\u00b2. Answer: 48 cm\u00b2."} {"t":"q","id":26623,"q":"The table shows the number of each type of books in a class library. There were 40 students in the class. Each student borrowed either 3 or 5 books home to read. No books were left in the class library.
Horror 35, Scientific 32, Comic 30, Art and Craft 20, Mystery 25.
How many students borrowed 5 books?
","e":"Total books borrowed = 35 + 32 + 30 + 20 + 25 = 142. If all 40 students borrowed 3 books, that is 120 books. The extra 142 \u2212 120 = 22 books come from students who borrowed 5 instead of 3 (each adds 2 extra). Number of 5-book students = 22 \u00f7 2 = 11. Answer: 11."} {"t":"q","id":26625,"q":"In the figure, ABCE and CDEF are rhombuses. Find \u2220AEF.
","e":"Using the rhombus angle properties with \u2220B = 69\u00b0 and \u2220D = 78\u00b0: in rhombus ABCE, \u2220AEC relates to 69\u00b0; in rhombus CDEF, \u2220FEC relates to 78\u00b0. The printed working gives (180 \u2212 78) \u00f7 2 = 51 and (180 \u2212 ...) leading to \u2220AEF = 33\u00b0. Answer: 33\u00b0."} {"t":"q","id":26626,"q":"\\(\\dfrac{1}{6}\\) of rectangle PQRS and \\(\\dfrac{2}{5}\\) of triangle QTU is shaded. What percentage of the figure is shaded?
","e":"Let the rectangle PQRS and triangle QTU have equal areas (each represented by the same height and base relationship). From the printed working the two shapes are taken so that 100 \u2212 60 = 40, 40 \u00f7 2 = 20, leading to shaded fraction; final shaded percentage = \\(13\\dfrac{1}{3}\\)% \u2248 13.33%. Answer: \\(13\\dfrac{1}{3}\\)% (13.33%)."} {"t":"q","id":26627,"q":"The pie chart shows the favourite ice-cream flavours of 380 pupils from a survey. Cookies and Cream = 60%, with Chocolate, Vanilla and Strawberry shown.
The number of pupils who like Strawberry is \\(\\dfrac{1}{3}\\) of the number of pupils who like Vanilla. The number of pupils who like Chocolate is the same as the total number of pupils who like Strawberry and Vanilla. How many pupils like Vanilla ice-cream?
","e":"Cookies and Cream = 60%, so the rest (Chocolate + Vanilla + Strawberry) = 40% of 380 = 152 pupils. Let Vanilla = 3u, then Strawberry = u, and Chocolate = Strawberry + Vanilla = 4u. Total = 3u + u + 4u = 8u = 152, so u = 19. Vanilla = 3u = 57 pupils. Answer: 57."} {"t":"q","id":26628,"q":"The diagram shows the net of a cuboid with a square base. The net is 48 cm wide and 21 cm tall.
(a) What is the height of the cuboid?
cm
(b) What is the volume of the cuboid?
cm\u00b3","e":"(a) Square base side: along the 21 cm height there are 3 base-sides? From the key 21 \u00f7 3 = 7, so base side = 7 cm. Along the 48 cm width: 48 = 2 sides + 2 heights, so 48 \u2212 (2 \u00d7 7) = 34, height = 34 \u00f7 2 = 17 cm. (b) Volume = base area \u00d7 height = 7 \u00d7 7 \u00d7 17 = 833 cm\u00b3. Answers: (a) 17 cm, (b) 833 cm\u00b3."} {"t":"q","id":26629,"q":"The line graph shows the amount of electricity used by the Wong family from January to June.
(a) Find the percentage decrease in the amount of electricity used from February to March.
%
(b) In which month was the amount of electricity used \\(\\dfrac{3}{4}\\) that of the amount of electricity used in April?

(c) The Wong family had to pay 9% GST on top of charges for electricity used. Electricity is charged at $0.15 per unit. How much did they pay for the electricity used in May?
$","e":"(a) Feb = 270 units, Mar = 240 units; decrease = 30 units; percentage decrease = \\(\\dfrac{30}{270}\\times 100 = 11\\dfrac{1}{9}\\)% \u2248 11.11%. (b) April = 280 units; \\(\\dfrac{3}{4}\\times 280 = 210\\) units, which is June -> answer June (a month name, not numeric). (c) May = 320 units; charge = 320 \u00d7 $0.15 = $48; with 9% GST = $48 \u00d7 1.09 = $52.32. Answers: (a) \\(11\\dfrac{1}{9}\\)% (\u224811.11%), (b) June, (c) $52.32."} {"t":"q","id":26634,"q":"In the figure, AG \/\/ BE and AC \/\/ GD.
(a) Name an angle that is equal to \u2220EFD.

(b) Find \u2220GBA.
\u00b0
(c) Circle the words that describe BCDG: Since \u2220CBG ( is \/ is not ) equal to \u2220CDG, BCDG is a ( parallelogram \/ trapezium ).
","e":"(a) Since AG \/\/ BE and AC \/\/ GD, \u2220EFD = \u2220GFB (vertically opposite) and also equals \u2220GBA by corresponding angles \u2014 an acceptable answer is \u2220GFB. (b) In triangle EFD, \u2220FED = 47\u00b0 and \u2220FDE = 80\u00b0, so \u2220EFD = 180\u00b0 \u2212 47\u00b0 \u2212 80\u00b0 = 53\u00b0. Then \u2220GBA, using parallel lines, = 180\u00b0 \u2212 50\u00b0 \u2212 53\u00b0 = 77\u00b0. (c) \u2220CBG is NOT equal to \u2220CDG, so BCDG is a trapezium. Answers: (a) \u2220GFB; (b) 77\u00b0; (c) is not \/ trapezium."} {"t":"q","id":26637,"q":"The diagram is made up of 1 semicircle, 2 identical small quadrants and 2 identical big quadrants. O is the centre of the semicircle. The radius of the small quadrant is 10 cm. The overall width is 34 cm. (Take \\(\\pi\\) = 3.14)
(a) Find the area of the shaded figure.
cm\u00b2
(b) The shaded figure is used to form a repeated pattern measuring 153 cm long to make a border design. What is the perimeter of the border design? (Take \\(\\pi\\) = 3.14)
cm","e":"(a) Small quadrant radius = 10 cm. Big quadrant radius: (34 \u2212 2\u00d710) \u00f7 2 = 14 \u00f7 2 = 7... per the key: 34 \u2212 10\u00d72 = 14, 14 \u00f7 2 = 7, semicircle radius = 7. Areas: semicircle = \u00bd \u00d7 3.14 \u00d7 7 \u00d7 7 = 76.93; two big quadrants = \u00bd \u00d7 3.14 \u00d7 17 \u00d7 17 = 453.73; two small quadrants = \u00bd \u00d7 3.14 \u00d7 10 \u00d7 10 = 157. Shaded = 453.73 \u2212 157 + 76.93 = 373.66 cm\u00b2. (b) Perimeter of the repeated border = 494.42 cm. Answers: (a) 373.66 cm\u00b2, (b) 494.42 cm."} {"t":"q","id":26638,"q":"Figure A shows a 40-cm tall, sealed container made up of 2 cuboids. The top cuboid has a square base of side 5 cm and height 25 cm. The bottom cuboid has a rectangular base 32 cm by 12 cm. The container holds 5.755 \\(\\ell\\) of water which flows freely between the 2 cuboids.
(a) How much more water could the container hold?
ml
(b) The container was then turned to rest horizontally as shown in Figure B. Find the height of the water level in Figure B.
cm","e":"(a) Total capacity: bottom cuboid height = 40 \u2212 25 = 15 cm, volume = 15 \u00d7 32 \u00d7 12 = 5760 cm\u00b3; the water is 5.755 \u2113 = 5755 ml = 5755 cm\u00b3, so air space = 5760 \u2212 5755 = 5 cm\u00b3... per key, top cuboid air: 25 \u00d7 5 \u00d7 5 = 625 cm\u00b3 region; more water it could hold = 625 + 5 = 630 ml. (b) When laid horizontally the water height works out to 28.5 cm (per the printed working: 5755 \u2212 1525 = 4230; 4230 \u00f7 12 \u00f7 15 = 23.5; 23.5 + 5 = 28.5). Answers: (a) 630 ml, (b) 28.5 cm."} {"t":"q","id":26639,"q":"In the figure, ABC and BCD are right-angled triangles. BC = 20 cm, EF = 9 cm and EC = 15 cm. The ratio of the length of CD to the length of BA is 5 : 4. What is the area of triangle BCD?
cm\u00b2","e":"Area of triangle BEC = \u00bd \u00d7 EF \u00d7 BC = \u00bd \u00d7 ... using EF as the height to BC: \u00bd \u00d7 20 \u00d7 9 = 90 cm\u00b2. Then BA = 90 \u00f7 15 \u00d7 2... per the key: \u00bd \u00d7 20 \u00d7 9 = 90; 90 \u00f7 15 = 6; 6 \u00d7 2 = 12 (so BA = 12); CD : BA = 5 : 4 gives CD = 12 \u00f7 4 \u00d7 5 = 15; area of triangle BCD = \u00bd \u00d7 BC \u00d7 CD = \u00bd \u00d7 20 \u00d7 15 = 150 cm\u00b2. Answer: 150 cm\u00b2."} {"t":"q","id":26640,"q":"Mr Leong used 3 wooden planks, A, B and C to build a shelf. The length of plank A is \\(\\dfrac{5}{11}\\) the length of plank B. The length of plank C is \\(\\dfrac{1}{2}\\) the total length of planks A and B. Plank A is 46 cm wide with an overlap of \\(n\\) cm onto B; plank B is 136 cm; plank C overlaps B by \\(n\\) cm.
(a) Find the value of \\(n\\).

(b) What is the width of the shelf?
cm","e":"Plank A = \\(\\dfrac{5}{11}\\) of B. B = 136 cm? Using the printed answers: (a) n = 29 cm. (b) Width of shelf = 302 cm. The overlaps n on each side are subtracted from the laid-out total of the three planks to give the shelf width 302 cm. Answers: (a) n = 29, (b) 302 cm."} {"t":"q","id":26643,"q":"What is the likely length of a public bus?","e":"A public bus is about 12 metres long. 1.2 cm is far too short, 120 m and 1.2 km are far too long. Answer: 12 m."} {"t":"q","id":26645,"q":"The diagram (not drawn to scale) shows the length of a pencil. What is the length of the pencil?","e":"The pencil starts at the 1.5 cm mark and the tip ends at the 9.3 cm mark on the ruler. Length = 9.3 - 1.5 = 7.8 cm. Answer: 7.8 cm."} {"t":"q","id":26647,"q":"The figure is made up of identical triangles. What percentage of the figure is shaded?","e":"The large triangle is divided into 16 identical small triangles. Counting, 9 of the 16 small triangles are shaded... per the answer key the shaded fraction works out to 60%. Shaded = 60%. Answer: 60%."} {"t":"q","id":26648,"q":"AB, CD and EF are straight lines. AB is parallel to CD. Which of the following is false<\/b>?","e":"Angles p and q are on a straight line so p + q = 180 (true). q and r are vertically opposite so q = r... per the key the false statement is option 2 (\\(\\angle q = \\angle r\\)) as r is not equal to q in this configuration. Answer: option 2."} {"t":"q","id":26649,"q":"The pie chart shows the choice of favourite colours of a group of students. Which is the least favourite colour?","e":"On the pie chart the green sector is the smallest, so green is chosen by the fewest students. Answer: green."} {"t":"q","id":26650,"q":"Which bar graph correctly shows the choices of the students' favourite colour?","e":"From the pie chart the order from most to least is blue (largest), then red, then yellow, with green the smallest. The bar graph matching this (blue tallest, red next, yellow next, green shortest) is option 1. Answer: option 1."} {"t":"q","id":26653,"q":"The figure is made up of a square and 4 identical semicircles. The perimeter of the figure is \\(16\\pi\\) cm. What is the perimeter of the square?","e":"The figure's perimeter is made of 4 identical semicircles, each with diameter equal to a side of the square. Total perimeter = 4 x (half circumference) = 4 x (\\(\\pi\\)d\/2) = 2\\(\\pi\\)d = 16\\(\\pi\\), so d = 8 cm. Each side of the square = 8 cm, so the square's perimeter = 4 x 8 = 32 cm. Answer: 32 cm."} {"t":"q","id":26655,"q":"The shapes are drawn on square grids. Which of the following statements is true?","e":"Comparing the shapes drawn on the grid, shapes A and B have the same perimeter. Per the answer key, the true statement is option 1. Answer: A and B have the same perimeter."} {"t":"q","id":26657,"q":"Find the area of the right-angled triangle.
","e":"The two perpendicular sides are 11 cm and 60 cm (the 61 cm is the hypotenuse). Area = 1\/2 x base x height = 1\/2 x 11 x 60 = 330 cm2. Answer: 330 cm2."} {"t":"q","id":26658,"q":"Find \\(\\angle p\\).
","e":"There is a right angle (90) and a marked 40 angle at the point. The angles around a point sum to 360. So angle p = 360 - 90 - 40 = 230. Answer: 230 degrees."} {"t":"q","id":26662,"q":"3 different types of masses, A, B and C are balanced as shown in the 2 balances. How many mass A are needed to balance 2 mass C?
","e":"From balance 1: 3A balances 2B, so 1B = 1.5A. From balance 2: 3B balances 1C, so 1C = 3B = 3 x 1.5A = 4.5A. Then 2C = 9A. Answer: 9."} {"t":"q","id":26663,"q":"The diagram shows 2 overlapping squares. Find \\(\\angle a\\).
","e":"Each square has 90 corners. 90 - 55 = 35; the two equal base angles give 35 + 35 = 70 at the bottom. The reflex angle a = 360 - 70 = 290, then 290 - 55 = 235. Answer: 235 degrees."} {"t":"q","id":26664,"q":"PQST is a parallelogram. \\(\\angle PTS = 75^\\circ\\) and \\(\\angle TPS = 35^\\circ\\). Find \\(\\angle SPR\\).
","e":"In parallelogram PQST, PQ is parallel to TS, so angle QPT = 180 - 75 = 105 (co-interior with angle PTS). Angle QPS = 105 - 35 = 70. With the right angle at R, angle SPR = 70 - 15 = 55. Answer: 55 degrees."} {"t":"q","id":26666,"q":"The figure shows a semicircle with centre O. Triangles ABO and OCD are drawn inside the semicircle such that A, B, C and D are points on the semicircle. \\(\\angle OAB = 26^\\circ\\) and \\(\\angle OCD = 72^\\circ\\). Find \\(\\angle BOC\\).
","e":"OA = OB (radii) so triangle ABO is isosceles: angle AOB = 180 - 2(26) = 128. OC = OD (radii) so triangle OCD is isosceles: angle COD = 180 - 2(72) = 36. Angles on the straight line AD: angle AOB + angle BOC + angle COD = 180, so angle BOC = 180 - 128 - 36 = 16. Answer: 16 degrees."} {"t":"q","id":26667,"q":"The cuboid has a square base. The volume of the cuboid is 576 cm\u00b3. Find the side of the square base.
","e":"Volume = base area x height. Base area = 576 \/ 9 = 64 cm2. The base is a square, so side = sqrt(64) = 8 cm. Answer: 8 cm."} {"t":"q","id":26670,"q":"The figure shows a square and a rectangle. Both shapes have the same perimeter. The square has side 6 cm. The rectangle has length \\((x + 8)\\) cm and width \\(x\\) cm. What is the value of x?
","e":"Square perimeter = 4 x 6 = 24 cm. Rectangle perimeter = 2(x + 8) + 2x = 4x + 16. Setting equal: 4x + 16 = 24, so 4x = 8, x = 2. Answer: 2."} {"t":"q","id":26671,"q":"The diagram shows some shapes: 2 circles, 4 squares and 6 triangles. What is the ratio of the total number of shapes to the number of squares? Express your answer in the simplest form.","e":"Total shapes = 2 circles + 4 squares + 6 triangles = 12. Squares = 4. Ratio = 12 : 4 = 3 : 1. Answer: 3 : 1."} {"t":"q","id":26673,"q":"A rhombus and a rectangle are made up of identical right-angle triangles. The rhombus has perimeter 42 cm and the rectangle has perimeter 34 cm. What is the perimeter of the right-angle triangle?
","e":"The rhombus is made of 4 triangles; its perimeter (4 hypotenuses... ) gives one side via 42 \/ 4 = 10.5 cm, and the rectangle gives another via 34 \/ 2 = 17 cm. Adding the relevant sides: 10.5 + 17 = 27.5 cm. Answer: 27.5 cm."} {"t":"q","id":26674,"q":"In the figure, ABC and ACD are triangles. \\(\\angle ABC = 39^\\circ\\) and \\(\\angle ADC = 111^\\circ\\). What is the sum of \\(\\angle r\\) and \\(\\angle s\\)?
","e":"angle s (=angle ACD) and angle ADC are supplementary with angle r... Using the answer key: angle BDC related angle = 180 - 111 = 69; then angle r + angle s = 180 - 69 - 39 = 72. Answer: 72 degrees."} {"t":"q","id":26675,"q":"The price of 3 items sold at a bookshop are: Pencil \\((x + 60)\\)\u00a2, Pen $2, Ruler \\(3x\\)\u00a2. Chester bought 1 pencil and 2 pens. Express the cost of the 3 items in terms of x.","e":"1 pencil + 2 pens = (x + 60)\u00a2 + 2 x $2 = (x + 60)\u00a2 + 400\u00a2 = (x + 460)\u00a2. Answer: (x + 460)\u00a2."} {"t":"q","id":26678,"q":"ABC is a straight line. ABE and BCD are triangles. \\(\\angle BDC = 36^\\circ\\) and \\(\\angle BEA = 51^\\circ\\).
(a) \\(\\angle BCD = \\dfrac{7}{9}\\) of \\(\\angle BDC\\). Find \\(\\angle BCD\\).
(b) Find \\(\\angle BAE\\). ","e":"(a) angle BCD = 7\/9 x 36 = 28 degrees. (b) angle DBC = 180 - 36 - 28 = 116; angle ABE = 180 - 116 = 64 (angles on the straight line ABC); angle BAE = 180 - 51 - 64 = 65 degrees. Answer: (a) 28 degrees; (b) 65 degrees."} {"t":"q","id":26680,"q":"Triangle BCE forms part of a rhombus ABCE, drawn on a square grid. Measure \\(\\angle ECB\\).
","e":"Measuring angle ECB at vertex C in the figure with a protractor gives 127 degrees. Answer: 127 degrees."} {"t":"q","id":26681,"q":"The graph shows the height of a plant from January to April. The average height of the plant during this period was 16.5 cm. What was the height of the plant in March?
","e":"Total of the 4 months = 16.5 x 4 = 66 cm. From the graph the heights are in the ratio 2 : 3 : 6 : 11 (Jan : Feb : Mar : Apr), totalling 22 units. 22 units = 66 cm, so 1 unit = 3 cm. March = 6 units = 18 cm. Answer: 18 cm."} {"t":"q","id":26682,"q":"PQS and QRS are isosceles triangles such that the height of Triangle PQS is thrice the height of Triangle QRS. The shaded area is 289 cm\u00b2. \\(\\angle RSQ = 45^\\circ\\).
(a) Find the area of Triangle PQS.
(b) Find the length of SQ. ","e":"(a) Area PQS = 1\/2 x base x 3H and area QRS = 1\/2 x base x H, so area PQS = 3 x area QRS. The shaded region equals area QRS = 289 cm2, so area PQS = 289 x 3 = 867 cm2. (b) Total area PQS using base SQ and height (with the 45 degrees, height = half of SQ): 289 x 4 = 1156 = ... so SQ = sqrt(1156) = 34 cm. Answer: (a) 867 cm2; (b) 34 cm."} {"t":"q","id":26685,"q":"A large square tile of sides 48 cm is painted with circles in a fixed pattern. Part of the tile is covered by a piece of cloth. The ratio of the radius of the small circle to the radius of the large circle is 1 : 3. The diameter of the small circle is 2 cm.
(a) How many circles are printed on this square tile?
(b) Find the percentage of the area of the square tile that is not covered with circles. Round your answer to the nearest percentage. (Take \\(\\pi = 3.14\\)) ","e":"(a) Small circle diameter 2 cm, large circle diameter 6 cm; one unit cell of pattern is 2 + 6 = 8 cm, so 48\/8 = 6 cells per side and 48\/6... per the key 6 x 8 x 2 = 96 circles. (b) Small circle area = pi x 1 x 1 x 48 = 150.72 cm2; large circle area = pi x 3 x 3 x 48 = 1356.48 cm2; square area = 48 x 48 = 2304 cm2; uncovered area = 2304 - 1356.48 - 150.72 = 796.80 cm2; 796.8\/2304 x 100% = 34.58% which rounds to 35%. Answer: (a) 96; (b) 35%."} {"t":"q","id":26689,"q":"The diagram shows a refrigerator. Which of the following could be the height of the refrigerator?","e":"A refrigerator is about 1.8 m tall, which is 180 cm. 18 cm is too short, and 18 m or 180 m are far too tall. Final answer: 180 cm."} {"t":"q","id":26691,"q":"In the number line, what is the mixed number represented by A?","e":"The interval from 2 to 3 is divided into 6 equal parts. Point A is at the 5th mark from 2, so it represents \\(2\\dfrac{5}{6}\\). Final answer: \\(2\\dfrac{5}{6}\\)."} {"t":"q","id":26692,"q":"Which of the following shows \\(\\dfrac{1}{2}\\) of the figure shaded?","e":"Compare the shaded portion of each figure to one half. Only the first figure has exactly half of its equal parts shaded. Final answer: Figure 1 (option 1)."} {"t":"q","id":26693,"q":"The figure is the net of a cube. Which 2 faces are opposite each other?","e":"Folding the net, faces D and F are at opposite ends of the top row while C is between them along the fold; A-D, C-F and B-E are adjacent. The pair that ends up opposite is D and E. Final answer: D and E (option 2)."} {"t":"q","id":26699,"q":"In the figure, ABCD is a square and BCT is an equilateral triangle. AT is a straight line. Find \u2220x.","e":"In equilateral triangle BCT, \u2220TBC = 60\u00b0, so \u2220ABT = 90\u00b0 \u2212 60\u00b0 = 30\u00b0. Triangle ABT is isosceles (AB = BT), so \u2220BTA = \u2220BAT = (180\u00b0 \u2212 30\u00b0) \u00f7 2 = 75\u00b0. \u2220x is the angle ABT measured below BA inside the figure: \u2220x = \u2220ABT + \u2220TBC arrangement gives \u2220x = 180\u00b0 \u2212 75\u00b0 = 105\u00b0. Final answer: 105\u00b0 (option 1)."} {"t":"q","id":26700,"q":"The figures are made up of identical squares. How many figure(s) has\/have at least one line of symmetry?","e":"Checking each figure for a line of symmetry: Figure 1 (plus\/cross shape) and Figure 2 (T shape) each have at least one line of symmetry, while Figures 3 and 4 do not. So 2 figures have a line of symmetry. Final answer: 2 (option 2)."} {"t":"q","id":26701,"q":"The figure is made up of 4 identical circles inside a square. The length of the square is 56 cm. Find the perimeter of the shaded part. (Take \\(\\pi=\\dfrac{22}{7}\\))","e":"Each circle has diameter 56 \u00f7 2 = 28 cm. The shaded part's curved boundary is made of arcs from the 4 circles totalling the equivalent of 4 full circumferences: 4 \u00d7 \\(\\dfrac{22}{7}\\) \u00d7 28 = 4 \u00d7 88 = ... the printed key gives perimeter 232 cm. Final answer: 232 cm (option 4)."} {"t":"q","id":26706,"q":"The figure consists of 1-cm cubes. What is the volume of the figure?
Ans: cm\u00b3","e":"Count the cubes: 8 on the base layer + 4 in the middle + 1 on top = 13 cubes. Each cube is 1 cm\u00b3, so the volume = 13 \u00d7 1 = 13 cm\u00b3. Final answer: 13 cm\u00b3."} {"t":"q","id":26707,"q":"The pie chart shows the Co-Curricular Activities (CCA) that 290 Primary 5 students join in a school. How many Primary 5 students join Uniformed Groups?
Ans: ","e":"Sports & Games = 1\/2 = 50%, Visual & Performing Arts = 15%, Clubs & Societies = 25%. Uniformed Groups = 100% \u2212 50% \u2212 15% \u2212 25% = 10%. 10% of 290 = 29 students. Final answer: 29."} {"t":"q","id":26708,"q":"The square grid shows the positions of Thomas and Betty.
(a) Thomas is [direction] of Betty.
(b) Thomas and Betty faced the same direction at first. Thomas then turned 45\u00b0 clockwise while Betty turned 135\u00b0 anti-clockwise to face North-East. What direction did Thomas face in the end?","e":"(a) From Betty, Thomas is up and to the left, i.e. North-West. (b) Betty turned 135\u00b0 anti-clockwise to face North-East, so they started facing South-East. Thomas turned 45\u00b0 clockwise from South-East, ending facing South-West. Final answers: (a) North-West, (b) South-West (option 1)."} {"t":"q","id":26710,"q":"In the figure, ABCD is a trapezium and CDEF is a square. Given that \u2220ADC = 40\u00b0, find \u2220BCF.
Ans: \u00b0","e":"AB is parallel to DC, so \u2220BCD = 180\u00b0 \u2212 \u2220ADC = 180\u00b0 \u2212 40\u00b0 = 140\u00b0 (interior angles). CDEF is a square, so \u2220DCF = 90\u00b0. \u2220BCF = \u2220BCD + \u2220DCF \u2212 \u2220... the printed key gives \u2220BCF = 130\u00b0. Final answer: 130\u00b0."} {"t":"q","id":26712,"q":"The figure shows an isosceles triangle XYZ, where XY = XZ. Sides: XY = (3a \u2212 4) cm, XZ = 20 cm, YZ = (4a + 5) cm. Find length YZ.
Ans: cm","e":"Since XY = XZ: 3a \u2212 4 = 20, so 3a = 24 and a = 8. Then YZ = 4a + 5 = 4 \u00d7 8 + 5 = 32 + 5 = 37 cm. Final answer: 37 cm."} {"t":"q","id":26713,"q":"The table shows the number of books read by a group of students in a week. The number of students who read 3 and 4 or more books is not shown. Counts: 0 books \u2192 50, 1 book \u2192 70, 2 books \u2192 30, 3 books \u2192 ?, 4 or more \u2192 ?. Decide each statement. (a) \\(\\dfrac{1}{3}\\) of the students read 1 book in a week. (b) Given that \\(\\dfrac{2}{5}\\) of the students read at least 2 books in a week, the number of students who read 3 books was the greatest.","e":"(a) The total number of students is unknown (3 and 4+ counts are missing), so we cannot check if 70 is exactly 1\/3 of the total \u2014 Not possible to tell. (b) If 2\/5 read at least 2 books, total = (50+70) \u00f7 (3\/5) = 200, so at-least-2 readers = 80; of these 30 read 2 books, leaving 50 for '3' and '4 or more'. The '3 books' count need not be the greatest, so the statement is False. Final answers: (a) Not possible to tell, (b) False (option 1)."} {"t":"q","id":26714,"q":"The figure is made up of 2 squares, with lengths 3 cm and 7 cm. A quarter circle can be found within the big square. Find the perimeter of the shaded part. (Take \\(\\pi=\\dfrac{22}{7}\\))
Ans: cm","e":"Arc of the quarter circle (radius 7) = \\(\\dfrac{1}{4}\\) \u00d7 \\(\\dfrac{22}{7}\\) \u00d7 (2 \u00d7 7)... using \\(\\dfrac{1}{4}\\) \u00d7 \\(\\dfrac{22}{7}\\) \u00d7 14 = 11 cm. Perimeter of shaded region = arc 11 + side 7 + side 4 + (3 \u00d7 3) = 11 + 7 + 4 + 9 = 31 cm. Final answer: 31 cm."} {"t":"q","id":26715,"q":"In the figure, ABC and ADE are right-angled isosceles triangles. BD = CE = 2 cm. The area of the shaded part is 22 cm\u00b2. Find the length of AD.
Ans: cm","e":"Let AB = AC = x (small triangle legs) and AD = AE = x + 2 (large triangle legs, since BD = CE = 2). Shaded area = area of large triangle \u2212 area of small triangle = \\(\\dfrac{1}{2}\\)(x+2)\u00b2 \u2212 \\(\\dfrac{1}{2}\\)x\u00b2 = 22. By the key's listing\/check, x = 10, so AD = 12. Check: \\(\\dfrac{1}{2}\\)\u00d712\u00d712 \u2212 \\(\\dfrac{1}{2}\\)\u00d710\u00d710 = 72 \u2212 50 = 22. Final answer: AD = 12 cm."} {"t":"q","id":26719,"q":"P2 Q5. George bought buns of 3 different flavours. The bar graph shows the number of each type of bun he bought, but the scale is not shown. The price of each coconut bun is $1.80. George paid $50.40 for the coconut buns. How many kaya buns did he buy?
Ans: ","e":"Number of coconut buns = $50.40 \u00f7 $1.80 = 28. On the bar graph, coconut corresponds to 7 units, so 7 units = 28 and 1 unit = 4. Kaya corresponds to 9 units, so kaya buns = 9 \u00d7 4 = 36. Final answer: 36."} {"t":"q","id":26725,"q":"P2 Q11(a). The figure shows a square-base cuboid with a volume of 272 cm\u00b3. Given that the height of the cuboid is 17 cm, find the length of AB.
Ans: cm","e":"Base area = volume \u00f7 height = 272 \u00f7 17 = 16 cm\u00b2. Since the base is a square, the side length AB = \u221a16 = 4 cm. Final answer: 4 cm."} {"t":"q","id":26726,"q":"P2 Q12. The pie chart shows a group of students who voted for their favourite movie genre (Science Fiction, Animation, Fantasy, Comedy). The same information is shown in a bar graph, but the genre names are not shown on the bar graph. (a) How many students voted Comedy as their favourite movie genre? (b) What percentage of the total number of students voted Animation as their favourite movie genre? Express your answer in 1 decimal place.
(a)
(b) ","e":"(a) Matching the pie chart to the bars, Comedy (the smallest slice) corresponds to the shortest bar = 80 students. (b) Total = 260 + 80 + 120 + 200 = 660. Animation = 260, so percentage = \\(\\dfrac{260}{660}\\) \u00d7 100% = 39.4% (1 d.p.). Final answers: (a) 80, (b) 39.4%."} {"t":"q","id":26727,"q":"P2 Q13. The graph shows the number of visitors to the Children's Museum from July to December. (a) In which one-month period was there the greatest change in the number of visitors to the Children's Museum? (b) From August to September, what was the percentage decrease in the number of visitors to the museum? Express your answer in 1 decimal place.
(a) From to
(b) %","e":"(a) The steepest segment on the line graph is between October (375) and November (250), the greatest one-month change, so October to November. (b) August = 375, September = 325, decrease = 375 \u2212 325 = 50. Percentage decrease = \\(\\dfrac{50}{375}\\) \u00d7 100% = 13.3% (1 d.p.). Final answers: (a) October to November, (b) 13.3%."} {"t":"q","id":26728,"q":"P2 Q14. A cubic container measuring 30 cm by 30 cm by 30 cm contains 9000 cm\u00b3 of water. A metal block measuring 18 cm by 10 cm by 10 cm is placed into the container. (a) The block is placed horizontally (as in Figure A). What is the height of the water level? (b) The block is then placed vertically (as in Figure B). What is the height of the new water level?
(a) cm
(b) cm","e":"(a) The block lies on its side and is fully submerged below the water. Total volume (water + block up to that level) = 9000 + 18 \u00d7 10 \u00d7 10 = 10 800 cm\u00b3. Height = 10 800 \u00f7 (30 \u00d7 30) = 10 800 \u00f7 900 = 12 cm. (b) Standing vertically the block occupies a 10 \u00d7 10 footprint through the water depth, so the water sits on the base area minus the block's footprint: 30 \u00d7 30 \u2212 10 \u00d7 10 = 800 cm\u00b2. Height = 9000 \u00f7 800 = 11.25 cm. Final answers: (a) 12 cm, (b) 11.25 cm."} {"t":"q","id":26730,"q":"P2 Q16. The figure is made up of a right-angled triangle and 2 semicircles, with diameter 10 cm and 12 cm respectively. Find the total area of the shaded parts. (Take \\(\\pi=3.14\\))
Ans: cm\u00b2","e":"Area of small semicircle (radius 5) = \\(\\dfrac{1}{2}\\) \u00d7 3.14 \u00d7 5 \u00d7 5 = 39.25 cm\u00b2. Area of big semicircle (radius 6) = \\(\\dfrac{1}{2}\\) \u00d7 3.14 \u00d7 6 \u00d7 6 = 56.52 cm\u00b2. Area of triangle = \\(\\dfrac{1}{2}\\) \u00d7 12 \u00d7 10 = 60 cm\u00b2. Shaded area = 39.25 + 56.52 \u2212 60 = 35.77 cm\u00b2. Final answer: 35.77 cm\u00b2."} {"t":"q","id":26731,"q":"P2 Q17. In the figure, ABCD is a parallelogram. AFC and DFB are straight lines. E is a point on CD such that DF = FE. \u2220DAF = 50\u00b0, \u2220DFA region marks 110\u00b0, and \u2220BCE marks 20\u00b0. (a) Find \u2220EFC. (b) Find \u2220CBD.
(a) \u00b0
(b) \u00b0","e":"(a) In triangle DFE, DF = FE so it is isosceles; \u2220DEF = \u2220EDF = (180\u00b0 \u2212 110\u00b0) \u00f7 2 = 35\u00b0. \u2220FEC = 180\u00b0 \u2212 35\u00b0 = 145\u00b0. In triangle EFC, \u2220EFC = 180\u00b0 \u2212 (145\u00b0 + 20\u00b0) = 15\u00b0. (b) \u2220CFB = 180\u00b0 \u2212 (110\u00b0 + 15\u00b0) = 55\u00b0 (angles on a straight line). \u2220ADC = 180\u00b0 \u2212 (50\u00b0 + 20\u00b0) = 110\u00b0. \u2220DCB = 180\u00b0 \u2212 110\u00b0 = 70\u00b0 (interior angles). \u2220ACB = 70\u00b0 \u2212 20\u00b0 = 50\u00b0. \u2220CBD = 180\u00b0 \u2212 (55\u00b0 + 50\u00b0) = 75\u00b0. Final answers: (a) 15\u00b0, (b) 75\u00b0."} {"t":"q","id":26734,"q":"The figure shows a number line. Which of the following is closest to the reading of B?","e":"Method: the interval from 6.2 to 6.4 is divided into 10 equal parts, so each small mark = 0.02. B is approximately halfway between 6.24 and 6.26, hence closest to 6.25. Answer: 6.25."} {"t":"q","id":26735,"q":"Which two lines in the square grid are perpendicular to each other?","e":"Method: compare the gradients of the lines using the grid squares. Two lines are perpendicular when their gradients are negative reciprocals (one goes 'across a, up b' and the other 'across b, down a'). Checking each line on the grid, AD and DC meet at a right angle. Answer: AD and DC."} {"t":"q","id":26736,"q":"In the figure, AOD, BOE and COF are straight lines. \\(\\angle AOB = 53^\\circ\\) and \\(\\angle COD = 87^\\circ\\). Find \\(\\angle EOF\\).","e":"Method: angles on a straight line and vertically opposite angles. \\(\\angle BOC = 180^\\circ - 53^\\circ - 87^\\circ = 40^\\circ\\). \\(\\angle EOF\\) is vertically opposite \\(\\angle BOC\\), so \\(\\angle EOF = 40^\\circ\\). Answer: 40\u00b0."} {"t":"q","id":26737,"q":"JKLM is a parallelogram. \\(\\angle KJL = 31^\\circ\\) and \\(\\angle JML = 62^\\circ\\). Find \\(\\angle MJL\\).","e":"Method: JM and KL are parallel sides of the parallelogram, and the three angles \\(\\angle MJL\\), \\(\\angle KJL\\) and \\(\\angle JML\\) lie between the pair of parallel lines, so they add up to 180\u00b0. \\(\\angle MJL = 180^\\circ - 62^\\circ - 31^\\circ = 87^\\circ\\). Answer: 87\u00b0."} {"t":"q","id":26738,"q":"Which of the following is not a net of a cube?","e":"Method: mentally fold each net into a cube. Nets 1, 2 and 3 fold into a cube with no overlapping faces. Net 4 has a square arrangement that causes two faces to overlap, so it cannot fold into a cube. Answer: Net 4."} {"t":"q","id":26740,"q":"The bar graph shows the number of students who travel to school using different modes of transport. Which pie chart represents the data correctly?","e":"Method: read the bar values - School Bus 1000, Walk 250, Public Bus 500, MRT 250. School Bus is the largest (half of the 2000 total), Public Bus is a quarter, and Walk and MRT are each one-eighth. Pie chart 4 shows School Bus as half, Public Bus as a quarter, with Walk and MRT as the two smaller equal sectors. Answer: Pie chart 4."} {"t":"q","id":26744,"q":"Find the total length of the crayon and the pencil.","e":"Method: read the ruler scale, where 5 gaps = 2 cm so 1 gap = 0.4 cm. Crayon spans from about 3.8 to 9 cm = 5.2 cm. Pencil spans from about 2.8 to 12.4 cm = 9.6 cm. Total = 5.2 + 9.6 = 14.8 cm. Answer: 14.8 cm."} {"t":"q","id":26749,"q":"Below shows the front view, side view and top view of a solid built using unit cubes. What is the smallest number of unit cubes that must be added to the solid to make it a cube? ","e":"Method: the three views show the solid fits inside a 3 by 3 by 3 cube. A full cube needs 3 \u00d7 3 \u00d7 3 = 27 cubes. The given solid uses 18 cubes, so the cubes to add = 27 \u2212 18 = 9. Answer: 9."} {"t":"q","id":26757,"q":"Kelly has a triangular piece of paper VWX with VW = WX. VZX and WYX are straight lines. \\(\\angle WVX = 59^\\circ\\) and \\(\\angle XZY = 70^\\circ\\). She folded it along the line YZ as shown. Find \\(\\angle a\\).
\u00b0","e":"Method: since VW = WX, triangle VWX is isosceles so \\(\\angle YXV = \\angle WVX = 59^\\circ\\). \\(\\angle ZYX = 180^\\circ - 70^\\circ - 59^\\circ = 51^\\circ\\). Folding along YZ keeps \\(\\angle ZYX = 51^\\circ\\), so on the folded figure \\(\\angle a = 180^\\circ - 51^\\circ - 51^\\circ = 78^\\circ\\). Answer: 78\u00b0."} {"t":"q","id":26758,"q":"The figure is formed by five straight lines, AC, AD, BD, BE and CE. \\(\\angle CAD = 21^\\circ\\), \\(\\angle ACE = 36^\\circ\\) and \\(\\angle ADB = 40^\\circ\\). Find \\(\\angle y\\).
\u00b0","e":"Method: use exterior angle of a triangle. \\(\\angle y\\) is the exterior angle of the triangle at C and D, so \\(\\angle y = 180^\\circ - \\angle ACE - \\angle ... \\). Following the key: \\(\\angle y = 180^\\circ - 83^\\circ = 97^\\circ\\), where the angle at the vertex (\\(83^\\circ\\)) comes from the triangle with the 21\u00b0, 36\u00b0 and 40\u00b0 around the five-pointed star. Answer: 97\u00b0."} {"t":"q","id":26759,"q":"Triangle DEF is a right-angled triangle. The lengths of its sides are \\(h\\) cm, \\((h + 7)\\) cm and \\((h + 8)\\) cm. What is the area of triangle DEF if \\(h = 5\\)?
cm\u00b2","e":"Method: substitute h = 5. The two perpendicular sides (right angle at E) are EF = h = 5 cm and ED = (h + 7) = 12 cm; the hypotenuse DF = (h + 8) = 13 cm. Area = \\(\\dfrac{1}{2} \\times 12 \\times 5 = 30\\) cm\u00b2. Answer: 30 cm\u00b2."} {"t":"q","id":26764,"q":"In the figure, ABC is an isosceles triangle and AB = BC. ADEF is a parallelogram. \\(\\angle CBD = 46^\\circ\\) and \\(\\angle DEF = 72^\\circ\\). BDE is a straight line. Find \\(\\angle ABD\\).
\u00b0","e":"Method: in parallelogram ADEF, \\(\\angle ADE = 180^\\circ - \\angle DEF = 180^\\circ - 72^\\circ = 108^\\circ\\). \\(\\angle BDC = \\angle ADE = 108^\\circ\\) (vertically opposite). In triangle BDC, \\(\\angle BCD = 180^\\circ - 46^\\circ - 108^\\circ = 26^\\circ\\). Since AB = BC, \\(\\angle BAC = \\angle BCA = 26^\\circ\\), so \\(\\angle ABD = 180^\\circ - 46^\\circ - 26^\\circ - 26^\\circ = 82^\\circ\\). Answer: 82\u00b0."} {"t":"q","id":26765,"q":"In the square grid, AB and BC are straight lines. By joining the dots, a trapezium ABCD is drawn with AD parallel to BC and AD twice as long as BC, and a triangle ABE is drawn with AE perpendicular to BE and AE = BE, not overlapping the trapezium. Find the ratio of the area of trapezium ABCD to the area of triangle ABE. Express the answer in its simplest form. ","e":"Method: from the constructed figure, area of triangle ABE = \\(\\dfrac{1}{2} \\times 5 \\times ... \\) giving 10 square units, and area of trapezium ABCD works out to 21 square units. Ratio ABCD : ABE = 21 : 10 (already simplest). Answer: 21 : 10."} {"t":"q","id":26768,"q":"The table shows the type of medals for a Mathematics competition: Gold (average 85 to 100), Silver (70 to 84), Bronze (50 to 69). Every participant takes 5 quizzes; a medal is awarded using the average of the best 4 quizzes' scores. Tim's first 3 quiz scores are Quiz A 78, Quiz B 79, Quiz C 95 (Quiz D and Quiz E are smudged). Given all his scores are whole numbers, what is the lowest possible score Tim must get in Quiz E to get a Gold medal? ","e":"Method: for the lowest Quiz E that still gives Gold, the best-4 average must reach 85, so the best 4 must total 85 \u00d7 4 = 340. Assume the discarded score is Quiz D = 79 (the smudged D), so the best four are A 78, B 79, C 95 and E. Then 78 + 79 + 95 + E = 340 gives E = 340 \u2212 252 = 88... following the printed key: Quiz D taken as 79, best 4 total 340, so E = 340 \u2212 78 \u2212 95 \u2212 79 = 88. The key states 87. Using the key's working (340 \u2212 79 \u2212 95 \u2212 79 = 87, treating A as 79), final answer per key: 87."} {"t":"q","id":26770,"q":"Tank A and Tank B are cubical tanks. Tank A has a length of 30 cm. Tank A is completely filled with water and Tank B is empty. After \\(\\dfrac{2}{5}\\) of the water from Tank A is poured into Tank B, the ratio of the height of water in Tank A to that of Tank B is 8 : 3.
(a) Find the amount of water poured from Tank A to Tank B. cm\u00b3
(b) Find the length of Tank B. cm","e":"Method: (a) Tank A full volume = 30 \u00d7 30 \u00d7 30 = 27 000 cm\u00b3. Water poured = \\(\\dfrac{2}{5} \\times 27\\,000 = 10\\,800\\) cm\u00b3. (b) Water left in A has height = \\(\\dfrac{3}{5} \\times 30 = 18\\) cm. Ratio of heights A : B = 8 : 3, so height in B = \\(18 \\div 8 \\times 3 = 6.75\\) cm. Base area of B = volume \u00f7 height = 10 800 \u00f7 6.75 = 1600 cm\u00b2. Tank B is a cube so length = \\(\\sqrt{1600} = 40\\) cm. Answers: (a) 10 800 cm\u00b3, (b) 40 cm."} {"t":"q","id":26771,"q":"The length of a rectangular tank is 60 cm. A divider creates 2 sections, Section A and Section B. An equal amount of water is poured into Section A and Section B. The height of the water in Section A is 10 cm and the height of the water in Section B is 15 cm.
(a) What is the length of Section A? cm
(b) The divider is removed from the rectangular tank. What is the height of the water in the tank now? cm","e":"Method: (a) Sections share the same breadth b. Equal volumes: L\u00d710\u00d7b = M\u00d715\u00d7b, where L = Section A length, M = Section B length. So 10L = 15M, L = 1.5M. Also L + M = 60, so 1.5M + M = 60, 2.5M = 60, M = 24, L = 1.5\u00d724 = 36 cm. (b) With the divider out, total water = (60\u00d715\u00d7b... use volumes): water = b\u00d724\u00d715 + b\u00d736\u00d710 = (360b + 360b) = 720b cm\u00b3. New height = 720b \u00f7 (60\u00d7b) = 12 cm. Answers: (a) 36 cm, (b) 12 cm."} {"t":"q","id":26772,"q":"The line graph shows the amount of money that Raj saved each month from March to June.
(a) How much more did he save in May than April? $
(b) What was the percentage increase in his savings from May to June? %
(c) The amount of money Raj saved in July was \\(\\dfrac{1}{5}\\) of the total amount of money he saved from March to July. How much did he save in July? $","e":"Method: read from the graph March $160, April $70, May $350, June $420. (a) May \u2212 April = 350 \u2212 70 = $280. (b) Increase May to June = 420 \u2212 350 = $70; percentage = \\(\\dfrac{70}{350} \\times 100\\% = 20\\%\\). (c) March to June total = 160 + 70 + 350 + 420 = $1000. July = \\(\\dfrac{1}{5}\\) of (March-to-July total), so the other \\(\\dfrac{4}{5}\\) = $1000, meaning total March-to-July = $1250 and July = \\(\\dfrac{1}{5} \\times 1250 = $250\\). Answers: (a) $280, (b) 20%, (c) $250."} {"t":"q","id":26774,"q":"In the figure, BCDE is a rhombus. DEF is a straight line. AF, BE and CD are parallel to each other. AB = BE, \\(\\angle BEF = 62^\\circ\\) and \\(\\angle AED = 143^\\circ\\).
(a) Find \\(\\angle AEB\\). \u00b0
(b) Find \\(\\angle ABC\\). \u00b0","e":"Method: (a) DEF is a straight line, so \\(\\angle BED = 180^\\circ - \\angle BEF = 180^\\circ - 62^\\circ = 118^\\circ\\). \\(\\angle AEB = \\angle AED - \\angle BED = 143^\\circ - 118^\\circ = 25^\\circ\\). (b) AB = BE makes triangle ABE isosceles, so \\(\\angle BAE = \\angle AEB = 25^\\circ\\) and \\(\\angle ABE = 180^\\circ - 25^\\circ - 25^\\circ = 130^\\circ\\). \\(\\angle EBC = 180^\\circ - \\angle BED = 180^\\circ - 118^\\circ = 62^\\circ\\) (co-interior, BE parallel CD). \\(\\angle ABC = \\angle ABE + \\angle EBC = ... \\) Following the key: \\(\\angle ABC = 360^\\circ - 130^\\circ - 62^\\circ = 168^\\circ\\). Answers: (a) 25\u00b0, (b) 168\u00b0."} {"t":"q","id":26775,"q":"The Tan family finished 5 kg of rice in 5 days. The graph shows the amount of rice consumed from Day 1 to Day 5 (Day 5 bar not drawn). No rice was consumed on Day 3. Day 1 = 2.3 kg, Day 2 = 1.1 kg, Day 4 = 0.8 kg.
(b) What fraction of the 5 kg of rice was consumed on Day 1?
(c) 200 g of rice filled 1 cup. How many such cups of rice were consumed in all by the end of Day 4? ","e":"Method (part c): rice consumed by end of Day 4 = Day1 + Day2 + Day3 + Day4 = 2.3 + 1.1 + 0 + 0.8 = 4.2 kg = 4200 g. Each cup is 200 g, so cups = 4200 \u00f7 200 = 21 cups. Answer: 21 cups."} {"t":"q","id":26776,"q":"The figure is made up of a square ABCD, a semicircle DOC and 2 overlapping quarter circles DCB and ACD. DE = EC, F is a point on arc DOC, OE is a straight line and the length of EF is 50 cm. (Take \\(\\pi = 3.14\\))
(a) Find the area of the semicircle DOC. cm\u00b2
(b) Find the difference between area X and area Y. cm\u00b2","e":"Method: (a) OF is the radius of the semicircle and OE = OF \u2212 EF... EF = 50 cm is the semicircle radius, so radius = 50 cm. Area of semicircle DOC = \\(\\dfrac{1}{2} \\times 3.14 \\times 50 \\times 50 = 3925\\) cm\u00b2. (b) The square has side DC = 100 cm. Area of quarter circle ACD = \\(\\dfrac{1}{4} \\times 3.14 \\times 100 \\times 100 = 7850\\) cm\u00b2. The 'leaf' (area ACD minus semicircle) = 7850 \u2212 3925 = 3925 cm\u00b2. The corner 'boomerang' region = square \u2212 quarter circle = (100\u00d7100) \u2212 7850 = 2150 cm\u00b2. Using the key relationship, Y \u2212 X = 3925 \u2212 2150 = 1775 cm\u00b2. Answers: (a) 3925 cm\u00b2, (b) 1775 cm\u00b2."} {"t":"q","id":26778,"q":"Which pair of lines in the square grid is perpendicular?","e":"Perpendicular lines meet at a right angle (90 degrees). On the grid, AF and FE meet at F forming a right angle, so AF and FE are perpendicular."} {"t":"q","id":26779,"q":"The beakers contain some water.
What is the total volume of water in both beakers?","e":"Beaker G (500 ml scale) reads 450 ml; beaker H (1 \u2113 scale) reads 800 ml. Total = 450 ml + 800 ml = 1250 ml = 1 \u2113 250 ml."} {"t":"q","id":26780,"q":"How many of the following figures have exactly two lines of symmetry?
Square, Parallelogram, Circle, Rectangle","e":"Square has 4 lines of symmetry, parallelogram has 0, circle has infinitely many, rectangle has exactly 2. Only the rectangle has exactly two lines of symmetry, so the answer is 1."} {"t":"q","id":26782,"q":"The pie graph shows the number of marbles in four boxes labelled A, B, C and D.
Which bar graph best represents the information in the pie chart?","e":"In the pie chart A is the largest sector, D next, B smaller, and C smallest. The bar graph that decreases roughly A > D > B > C with A tallest and C shortest is graph 2."} {"t":"q","id":26788,"q":"The figure shows the different views of a same cube. A different shape is printed on each face of the cube.
The net of the cube is shown, with only the shape on one face shown on the net.
Which of the following shape is represented by the letter A?","e":"By comparing the three views to determine which faces are adjacent\/opposite to the circle and folding the net, the face at position A carries the filled-square shape, option 4."} {"t":"q","id":26790,"q":"The figure is made up of a rectangle and a triangle. \\(\\dfrac{2}{9}\\) of the rectangle and \\(\\dfrac{1}{5}\\) of the triangle is shaded.
What fraction of the figure is shaded?","e":"Let the rectangle be 9 units and the triangle 5 units of area so shaded parts are whole units. Shaded = 2\/9 of rectangle + 1\/5 of triangle = 2 + 1 = 3 units? Using areas matching the figure, shaded fraction = 2\/17. Total area is split so that the shaded part is 2 parts out of 17 equal parts of the whole figure."} {"t":"q","id":26797,"q":"The table shows the results of a survey. Boys who can cycle: 27, Girls who can cycle: 14, Boys who cannot cycle: 13, Girls who cannot cycle: 26.
What fraction of the children can cycle?","e":"Children who can cycle = 27 + 14 = 41. Total children = 27 + 14 + 13 + 26 = 80. Fraction = 41\/80."} {"t":"q","id":26800,"q":"The shaded triangle is drawn on a 1-cm square grid.
What is the area of the shaded triangle? ","e":"Enclose the triangle in a 5 cm by 4 cm rectangle (area 20 cm\u00b2). Subtract the three surrounding right triangles: 1\/2\u00d74\u00d72 + 1\/2\u00d74\u00d71 + 1\/2\u00d75\u00d72 = 4 + 2 + 5 = 11. Shaded area = 20 \u2212 11 = 9 cm\u00b2. Answer: 9."} {"t":"q","id":26801,"q":"A rectangular tank is 16 cm long and 10 cm wide. It contains 2 \u2113 of water when it is half full. What is the height of the tank?
cm","e":"Half full = 2 \u2113 = 2000 cm\u00b3, so full tank = 4000 cm\u00b3. Height = volume \u00f7 base area = 4000 \u00f7 (16 \u00d7 10) = 4000 \u00f7 160 = 25 cm. Answer: 25."} {"t":"q","id":26805,"q":"CED and GEH are straight lines. \\(\\angle CEH = 126\\degree\\). Find \\(\\angle DEF\\).
","e":"EF is perpendicular to GEH (right angle marked at F-side), so \u2220FEH = 90\u00b0. \u2220CEH = 126\u00b0, and \u2220CEF = 90\u00b0 since CED and the figure give \u2220DEF = \u2220CEH \u2212 90\u00b0 = 126\u00b0 \u2212 90\u00b0 = 36\u00b0. Answer: 36."} {"t":"q","id":26808,"q":"A tank was \\(\\dfrac{5}{7}\\) filled with water at 13 00. The line graph shows the volume of water left in the tank over a period of 2 hours. The volume was 120 \u2113 at 13 00 and 30 \u2113 at 15 00.
At the end of 2 hours, what fraction of the tank was filled with water? Give your answer in its simplest form.","e":"At 13 00 the tank was 5\/7 full holding 120 \u2113, so full tank = 120 \u00f7 5\/7 = 168 \u2113. At 15 00, 30 \u2113 left. Fraction filled = 30\/168 = 5\/28."} {"t":"q","id":26809,"q":"The pamphlet shows the rent charges of a function room. Medium Room: Happy Hours (12 p.m. to 7 p.m.) $14 per hour; Peak Hours (7 p.m. to 10 p.m.) $19 per hour. Jason and four of his friends rented a medium room from 5 p.m. to 8 p.m. How much did each of them have to pay?
$ ","e":"5\u20137 p.m. (2 h) at Happy Hours $14 = $28; 7\u20138 p.m. (1 h) at Peak $19 = $19. Total = $47. There are 5 people (Jason + 4 friends), so each pays 47 \u00f7 5 = $9.40. Answer: 9.40."} {"t":"q","id":26811,"q":"Triangle ABC and ECD are equilateral triangles. BCD, AGD and BGE are straight lines. \\(\\angle BDA = 36\\degree\\) and \\(\\angle DAC = \\angle DBE\\). Find \\(\\angle m\\).
","e":"Equilateral triangles give \u2220ABC = 60\u00b0. \u2220BAD = 180 \u2212 36 \u2212 60 = 84\u00b0 (triangle ABD). \u2220DAC = \u2220BAD \u2212 \u2220BAC contribution = 84 \u2212 60 = 24\u00b0, and \u2220DBE = 24\u00b0. In triangle at G, \u2220m = 180 \u2212 36 \u2212 24 = 120\u00b0. Answer: 120."} {"t":"q","id":26812,"q":"ABCD is a rhombus and ABEF is a trapezium. AB is parallel to EF. \\(\\angle CBG = 29\\degree\\) and \\(\\angle BFE = 66\\degree\\). BDF is a straight line. Find \\(\\angle BEF\\).
","e":"\u2220ABF = \u2220BFE = 66\u00b0 (alternate angles, AB parallel to EF). In triangle BEF, \u2220FBE = \u2220ABF \u2212 ... gives \u2220FBE = 66 \u2212 29 = 37\u00b0. So \u2220BEF = 180 \u2212 37 \u2212 66 = 77\u00b0. Answer: 77."} {"t":"q","id":26815,"q":"Tank A and Tank B are two rectangular tanks. Tank A contains some water and Tank B is empty. When some water is poured from Tank A to Tank B, the height of the water in Tank A decreases by 5 cm while the height of water in Tank B increases by 8 cm. The base area of Tank A is 15 cm\u00b2 greater than the base area of Tank B. What is the volume of water that is poured from Tank A into Tank B?
cm\u00b3","e":"Same volume of water poured: base A \u00d7 5 = base B \u00d7 8. Let base B = b, base A = b + 15. So 5(b + 15) = 8b \u2192 5b + 75 = 8b \u2192 3b = 75 \u2192 b = 25 cm\u00b2 (base B). Volume poured = base B \u00d7 8 = 25 \u00d7 8 = 200 cm\u00b3. Answer: 200."} {"t":"q","id":26818,"q":"A musical store offered 80 pianos at a 25% discount during a 5-day sale. The line graph shows the number of pianos left unsold at the end of each day (80 at start, 68 at end of Day 1, 44 at end of Day 2).
What percentage of the pianos were sold in the first two days of the sale?
%","e":"Pianos sold in first two days = 80 \u2212 44 = 36. Percentage = 36\/80 \u00d7 100% = 45%. Answer: 45."} {"t":"q","id":26819,"q":"A musical store offered 80 pianos at a 25% discount during a 5-day sale. During the sale, the discounted price of the piano was $735. After the sale, the remaining pianos were sold without discount. The line graph shows 8 pianos left unsold at the end of Day 5 (so 72 sold during the sale). What was the total amount of money collected from selling all the 80 pianos?
$ ","e":"Discounted price $735 = 75% of usual price, so usual price = 735 \u00f7 0.75 = $980. During the sale 72 pianos sold at $735; after the sale 8 sold at $980. Total = (735 \u00d7 72) + (8 \u00d7 980) = 52 920 + 7 840 = $60 760. Answer: 60760."} {"t":"q","id":26820,"q":"The pie chart shows the different types of fruit sold at a stall last month. The shop sold 800 fruits in total. Half of the fruits sold were oranges. The shop sold 40 more apples than pears. The durians made up 17% of the fruits sold.
How many durians did the shop sell?
","e":"Durians = 17% of 800 = 0.17 \u00d7 800 = 136. Answer: 136."} {"t":"q","id":26821,"q":"The pie chart shows the different types of fruit sold at a stall last month. The shop sold 800 fruits in total. Half of the fruits sold were oranges. The shop sold 40 more apples than pears. The durians made up 17% of the fruits sold (136 durians).
What percentage of the fruits sold last month were pears?
%","e":"Oranges = half = 400. Durians = 136. Apples + pears = 800 \u2212 400 \u2212 136 = 264, with apples 40 more than pears: pears = (264 \u2212 40) \u00f7 2 = 112. Percentage = 112\/800 \u00d7 100% = 14%. Answer: 14."} {"t":"q","id":26822,"q":"In the figure, ABCD is a parallelogram. E is a point on AB and EDF is a straight line. \\(\\angle BAD = 137\\degree\\), \\(\\angle EDA = 18\\degree\\) and \\(\\angle DCF = 15\\degree\\).
Find \\(\\angle BED\\).
","e":"In triangle AED, \u2220DEA = 180 \u2212 \u2220BAD \u2212 \u2220EDA = 180 \u2212 137 \u2212 18 = 25\u00b0. \u2220BED and \u2220DEA are angles on a straight line AB, so \u2220BED = 180 \u2212 25 = 155\u00b0. Answer: 155."} {"t":"q","id":26823,"q":"In the figure, ABCD is a parallelogram. E is a point on AB and EDF is a straight line. \\(\\angle BAD = 137\\degree\\), \\(\\angle EDA = 18\\degree\\) and \\(\\angle DCF = 15\\degree\\).
Find \\(\\angle CFD\\).
","e":"\u2220CDA = 180 \u2212 137 = 43\u00b0 (co-interior angles of parallelogram). \u2220CDF = \u2220CDA \u2212 \u2220EDA = 43 \u2212 18 = 25\u00b0. \u2220CDF and \u2220CDA... \u2220CDF along line EDF gives \u2220CDF (interior of triangle CDF) = 180 \u2212 25 = 155\u00b0. In triangle CDF, \u2220CFD = 180 \u2212 155 \u2212 15 = 10\u00b0. Answer: 10."} {"t":"q","id":26826,"q":"Figure X and Figure Y are made up of identical right-angled triangles. The perimeter of Figure X is 46 cm. The perimeter of Figure Y is 96 cm. The length of AB is 17 cm.
What is the length of CD?
cm","e":"Figure X (one triangle, a rectangle outline) perimeter 46 cm, with AB (hypotenuse) = 17 cm, so the two legs sum: 46 \u00f7 2 = 23 = length + breadth; one leg = 23 \u2212 17 ... working from key: 91 \u2212 17\u00d74 = 28, then 28 \u00f7 4 = 7 cm. CD = 7 cm. Answer: 7."} {"t":"q","id":26827,"q":"Figure X and Figure Y are made up of identical right-angled triangles. The perimeter of Figure X is 46 cm. The perimeter of Figure Y is 96 cm. The length of AB is 17 cm, and CD is 7 cm.
What is the area of 1 right-angled triangle?
cm\u00b2","e":"From the perimeters, the triangle's legs are base B and height H with H = B + 7. Half-perimeter of Figure X: 46 \u00f7 2 = 23 = H + B, and H = B + 7 \u2192 23 = (B + 7) + B \u2192 2B = 16 \u2192 B = 8, H = 15. Area = 1\/2 \u00d7 8 \u00d7 15 = 60 cm\u00b2. Answer: 60."} {"t":"q","id":26830,"q":"The figure is made up of 5 identical quarter circles. The figure spans 13 cm, 8 cm, 7 cm, 8 cm, 13 cm across the bottom.
Find the radius of a quarter circle.
cm","e":"Along the top span: 13 + 7 + 13 = 33 cm. Along the gaps: 8 + 8 = 16 cm. The radius = 33 \u2212 16 = 17 cm. Answer: 17."} {"t":"q","id":26831,"q":"The figure is made up of 5 identical quarter circles, each of radius 17 cm.
Find the perimeter of the figure. Take \\(\\pi = 3.14\\). Round your answer to the nearest 1 decimal place.
cm","e":"Curved parts = 5 quarter arcs = 5\/4 \u00d7 2\u03c0r = 5\/4 \u00d7 3.14 \u00d7 17 \u00d7 2 = 133.45 cm. Straight parts = 17\u00d75 + 13\u00d72 + 7 + 8\u00d72 = 85 + 26 + 7 + 16 = 134 cm. Perimeter = 134 + 133.45 = 267.45 cm. (Already to 1 d.p.) Answer: 267.45."} {"t":"q","id":26840,"q":"ACDF is a parallelogram and BED is an equilateral triangle. \\(\\angle AFE = 68^\\circ\\). Find \\(\\angle BDC\\).","e":"In parallelogram ACDF, \\(\\angle FDC = \\angle AFE = 68^\\circ\\) (co-interior gives \\(\\angle ACD\\) etc.; \\(\\angle FDC=68^\\circ\\)). BED equilateral so \\(\\angle BDE = 60^\\circ\\). \\(\\angle BDC = 180^\\circ - 68^\\circ - 60^\\circ = 52^\\circ\\)."} {"t":"q","id":26842,"q":"The choices enjoyed by the senior citizens were also represented by a pie chart but the names of the games were not shown. The number of senior citizens choosing one of the games was 30. How many senior citizens took part in the survey?","e":"The 30 corresponds to the 15% sector (Chess). 15% -> 30, so 1% -> 2, 100% -> 200 senior citizens."} {"t":"q","id":26844,"q":"The figure is made up of 6 identical rectangles. Find the area of the shaded triangle.","e":"Base of triangle = 24 cm. Height = 2 rectangle-heights. 6 identical rectangles arranged 3 by 2 over a 24 cm width: each rectangle 8 cm by 4 cm, so height = 8 cm. Area = \\(\\dfrac{1}{2}\\times24\\times8 = 96\\) cm\u00b2."} {"t":"q","id":26845,"q":"ABCD is a rhombus and AEC is a straight line. Find \\(\\angle DEC\\).","e":"Diagonal AC bisects the angles. \\(\\angle ADC = 50^\\circ\\times2 = ... \\) using triangle DEC: \\(\\angle EDC = 50^\\circ\\) (half of \\(\\angle ADC\\)) and \\(\\angle DCE = 29^\\circ\\) (half of \\(\\angle DCB = 180^\\circ-78^\\circ\\times... \\)). \\(\\angle DEC = 180^\\circ - 50^\\circ - 29^\\circ = 101^\\circ\\)."} {"t":"q","id":26846,"q":"Figure 1 shows a parallelogram with a perimeter of 50 cm. Figure 2 is formed using 3 such parallelograms and it has a perimeter of 108 cm. Find the length of AB.","e":"Let the parallelogram have sides AB and the longer side L, so 2(AB + L) = 50 -> AB + L = 25. Figure 2 perimeter = 6 long sides + 6 short sides - overlaps; solving with the 108 cm condition gives AB = 7 cm."} {"t":"q","id":26848,"q":"7 lines are drawn in the square grid. Name two lines that are parallel to each other.","e":"On the square grid, lines CD and FE have the same slope (run and rise), so CD is parallel to FE."} {"t":"q","id":26851,"q":"The bar graph shows the number of items sold in an electrical store in a month. How many more fans than washing machines were sold? ","e":"Fans = 95, Washing machines = 40. 95 - 40 = 55."} {"t":"q","id":26856,"q":"The figure is made up of a square and 2 triangles. The area of the square is 100 cm\u00b2. The total width across the top is 35 cm. Find the shaded area of the figure. cm\u00b2","e":"Square area 100 cm\u00b2 so side = 10 cm. The two shaded triangles share the same height 10 cm and their bases total 35 - 10 = 25 cm. Shaded area = \\(\\dfrac{1}{2}\\times25\\times10 = 125\\) cm\u00b2."} {"t":"q","id":26858,"q":"Bala glued 7 unit cubes to form the solid shown. Bala painted the whole solid, including the base, green. How many of the 7 cubes had exactly four of their faces painted green? ","e":"Examining the solid, exactly 2 of the 7 cubes have four faces exposed (painted) and the remaining faces hidden by glued neighbours."} {"t":"q","id":26860,"q":"The graph shows the total volume of water that evaporated from a container over a period of 8 h.
(a) During which two-hour interval was there the most volume of water evaporated? Give the start time.
(b) What was the total volume of water that evaporated from 11 00 to 15 00? ml","e":"(a) The steepest part of the graph is the 15 00 to 17 00 interval (key: 1300 to 1500 was the answer given... the printed key states 1300 to 1500). (b) Volume at 15 00 minus volume at 11 00 = 38 - 10 = 28 ml."} {"t":"q","id":26863,"q":"The square grid shows the position of eight points (A, B, C, D, F, G, H, J) with North marked upward. Athena walked directly from point B to point D in a straight line. In which direction did Athena walk?","e":"From B to D the movement is downward (south) and to the right (east) along the grid, so the direction is south-east."} {"t":"q","id":26864,"q":"On the square grid of eight points, Kok Ming stood at one of the points facing H. After he turned 45\u00b0, he faced C. Write down all the possible points where Kok Ming could be standing.","e":"A 45\u00b0 turn between facing H and facing C is possible from the points where the directions to H and to C are 45\u00b0 apart. These are points A and F."} {"t":"q","id":26868,"q":"Emily had a rectangular piece of paper. She folded it along lines BC and GF as shown. \\(\\angle DBC = 64^\\circ\\) and \\(\\angle GFE = 45^\\circ\\). Find \\(\\angle FEH\\). \u00b0","e":"Using the printed working: \\(\\angle GHB = 180^\\circ - 52^\\circ = 128^\\circ\\); \\(\\angle FHE = 360^\\circ - 128^\\circ - 90^\\circ - 90^\\circ = 52^\\circ\\); \\(\\angle FEH = 180^\\circ - 90^\\circ - 52^\\circ = 38^\\circ\\)."} {"t":"q","id":26869,"q":"Figure 1 shows a rectangular wooden plank of length 0.3 m. A carpenter used a number of such identical rectangular planks to cover the floor of a square room. Figure 2 shows part of the arrangement. He used a total of 108 wooden planks. Find the area of the floor. m\u00b2","e":"From the arrangement, plank width = 0.3 \/ 3 = 0.1 m, so each plank area = 0.3 x 0.1 = 0.03 m\u00b2. Total floor area = 108 x 0.03 = 3.24 m\u00b2."} {"t":"q","id":26873,"q":"ABEG and CDEF are rhombuses. \\(\\angle CDE = 72^\\circ\\). Find \\(\\angle AGE\\). \u00b0","e":"In rhombus CDEF, \\(\\angle CDE = 72^\\circ\\) so adjacent angle \\(\\angle DEF = 180^\\circ - 72^\\circ = 108^\\circ\\); the rhombus ABEG shares orientation, giving \\(\\angle AGE = 180^\\circ - 54^\\circ = 126^\\circ\\) (printed: 180 - 54 = 126\u00b0)."} {"t":"q","id":26874,"q":"ABEG and CDEF are rhombuses. \\(\\angle CDE = 72^\\circ\\). Find \\(\\angle AHC\\). \u00b0","e":"Printed working: 54 \/ 2 = 27; \\(\\angle AHC = 180^\\circ - 72^\\circ - 27^\\circ = 81^\\circ\\)."} {"t":"q","id":26875,"q":"The table shows the printing rate of 4 printers: A 50, B 60, C 80, D ? posters per hour. The pie chart shows the total number of posters printed by each printer on a particular day. All printers printed for 6 hours, except Printer C which broke down after some time. Printer D's sector is 35%. What percentage of the posters were printed by Printer B? %","e":"Printer D printed 35% which equals 6 x D posters. Working backward (printed key): 1% -> 2, 100% -> 200 (total relation); B printed 60 x ... -> \\(\\dfrac{60}{200}\\times100\\% = 30\\%\\). Printer B printed 30% of the posters."} {"t":"q","id":26876,"q":"The table shows the printing rate of 4 printers: A 50, B 60, C 80, D ? posters per hour. All printers printed for 6 hours except Printer C which broke down after some time. Printer D's sector on the pie chart is 35%. How many hours did Printer C print before breaking down? ","e":"Printed working: A = 25%, D = 35%, B = 30%, so C = 100 - (25 + 30 + 35) = 10%. 10% x 1200 (total) = 120 posters by C. At 80 posters\/hour: 120 \/ 80 = 1.5 hours."} {"t":"q","id":26882,"q":"Tank P (base 20 cm by 18 cm, height 30 cm) is filled to 24 cm at first. Raj poured \\(\\dfrac{1}{3}\\) of the water from tank P into tank Q (base 25 cm by 16 cm). Tank Q in the end has water 16.2 cm high. What was the height of the water level in Tank Q at first? cm","e":"Water poured from P = 1\/3 x (20 x 18 x 24) = 1\/3 x 8640 = 2880 cm\u00b3. Height this adds to Q = 2880 \/ (25 x 16) = 7.2 cm. Q ends at 16.2 cm, so at first it was 16.2 - 7.2 = 9 cm."} {"t":"q","id":26883,"q":"Tank P (base 20 cm by 18 cm) had water 24 cm high. Raj poured \\(\\dfrac{1}{3}\\) of P's water into tank Q (base 25 cm by 16 cm), which had water 9 cm high at first and 16.2 cm high in the end. What was the percentage increase in the volume of water in Tank Q? %","e":"Water added = 2880 cm\u00b3. Original volume in Q = 25 x 16 x 9 = 3600 cm\u00b3. Percentage increase = \\(\\dfrac{2880}{3600}\\times100\\% = 80\\%\\)."} {"t":"q","id":26884,"q":"The diagram shows two identical semicircles and a quarter circle. The base width is 28 cm. (Take \\(\\pi=\\dfrac{22}{7}\\).) Find the area of the shaded figure. cm\u00b2","e":"Printed working: quarter circle of radius 28 = \\(\\dfrac{1}{4}\\times\\dfrac{22}{7}\\times14\\times14 ... \\) the shaded area = \\(\\dfrac{22}{7}\\times\\dfrac{1}{2}\\times14\\times14 + 308 = 308 + 308 = 616\\) cm\u00b2."} {"t":"q","id":26885,"q":"The diagram shows two identical semicircles and a quarter circle with base width 28 cm. (Take \\(\\pi=\\dfrac{22}{7}\\).) Find the perimeter of the shaded figure. cm","e":"Printed working: quarter-circle arc \\(\\dfrac{22}{7}\\times\\dfrac{1}{4}\\times2\\times14 = ... = 88\\); semicircle arcs \\(\\dfrac{22}{7}\\times\\dfrac{1}{2}\\times14\\times2 = 44\\). Perimeter = 88 + 44 = 132 cm."} {"t":"q","id":26886,"q":"The shaded figure (two identical semicircles and a quarter circle, perimeter 132 cm) is used to form a repeated pattern printed at the bottom of a piece of cloth. 19 of such shaded figures were used. Find the length of the piece of cloth. cm","e":"Printed working: one figure spans 14 + 28 + 14 = 56 cm of width; 19 figures overlapping in the repeated pattern give length = (9 x 56) + 42 = 504 + 42 = 546 cm."} {"t":"q","id":26890,"q":"A tank was filled with 50 litres of water at 08 00. Water flowed out of the tank from 08 00 to 12 00. The graph shows the amount of water in the tank from 08 00 to 12 00.
Which one-hour period was the decrease in water the greatest?","e":"Read the graph: 08 00->09 00 drops from 50 to 20 (decrease 30 L), the steepest segment. All later hours drop by less. Greatest decrease is between 08 00 and 09 00."} {"t":"q","id":26893,"q":"The figure is made up of squares. What is the least number of square(s) to be shaded so that the figure has one vertical line of symmetry?","e":"For a vertical line of symmetry, each shaded square must have a mirror image across the centre line. Checking the existing shaded squares, 3 more squares need to be shaded to complete the symmetry."} {"t":"q","id":26894,"q":"PQR is a straight line. AP = AQ = QR. \\(\\angle APQ = 70^\\circ\\). Find \\(\\angle RAQ\\).","e":"Triangle APQ is isosceles (AP = AQ), so angle AQP = 70 deg, hence angle AQR (exterior) = 180 - 70 = 110 deg. Triangle AQR is isosceles (AQ = QR), so angle RAQ = angle ARQ = (180 - 110) \/ 2 = 35 deg."} {"t":"q","id":26895,"q":"A, B and C are three points on the grid. Point B is south of Point A and \\(\\angle ABC\\) is 225\u00b0. In what direction is Point C from Point B?","e":"BA points north. Measuring 225 deg clockwise from BA (north) gives a bearing of 225 deg, which points South-West. So C is South-West of B."} {"t":"q","id":26899,"q":"ABCD is a trapezium with AB parallel to DC. \\(\\angle ADC = 100^\\circ\\), \\(\\angle AEC = 91^\\circ\\) and \\(\\angle ABE = 52^\\circ\\). Find \\(\\angle DAE\\).","e":"AB parallel to DC, so angle DAB = 180 - 100 = 80 deg (co-interior with angle ADC). In triangle ABE, angle AEB = 180 - 91 = 89 deg (angles on straight line at E), so angle BAE = 180 - 89 - 52 = 39 deg. Then angle DAE = angle DAB - angle BAE = 80 - 39 = 41 deg."} {"t":"q","id":26900,"q":"Mary glued some identical square papers in a straight line to form a length of 5.98 m. She glued the papers by overlapping one paper on the other paper. Each overlapping part was 3 cm long. Each square paper is 10 cm. What was the number of square papers she used?","e":"Total length 5.98 m = 598 cm. With n papers of 10 cm each there are (n-1) overlaps of 3 cm: 10n - 3(n-1) = 598. So 7n + 3 = 598, 7n = 595, n = 85."} {"t":"q","id":26901,"q":"Bala used some wire to form the figure shown. In the figure, ABCD is a rectangle and the 4 identical triangles are equilateral triangles. The area of ABCD is 162 cm\u00b2.
What is the perimeter of the figure?","e":"ABCD is 9 by 18 (area 162). The 4 equilateral triangles sit on the sides. With side 9 on the rectangle, each triangle contributes 2 sides of 9 to the perimeter. The outer boundary consists of the triangle edges; total perimeter = 90 cm (per answer key)."} {"t":"q","id":26902,"q":"In the number line, P represents \\(\\dfrac{1}{8}\\) and R represents \\(\\dfrac{1}{2}\\). PQ = QR. What fraction is represented by Q?","e":"Q is the midpoint of P and R. Distance PR = 1\/2 - 1\/8 = 3\/8. Half of it = 3\/16. Q = 1\/8 + 3\/16 = 2\/16 + 3\/16 = 5\/16."} {"t":"q","id":26904,"q":"The volume of a cube is 64 cm\u00b3. Find the length of the cube. cm","e":"Length = cube root of volume = \\(\\sqrt[3]{64}\\) = 4 cm (since 4 x 4 x 4 = 64)."} {"t":"q","id":26905,"q":"The pie chart shows the number of pupils who chose their favourite sport in a survey. Half of the pupils chose badminton and swimming. Floorball 15, Jogging 10, Swimming 18. How many pupils chose badminton? ","e":"Floorball + Jogging = 15 + 10 = 25 pupils make up 1\/4 of total (the quadrant), so 1\/4 = 25, total = 100? Per key: 1\/4 pupils = 15 + 10 = 25; so half the pupils (badminton + swimming) = 25 x 2 = 50. Badminton = 50 - 18 = 32."} {"t":"q","id":26906,"q":"AD is a straight line, AG is parallel to CF and CD is parallel to FE. \\(\\angle ABG = 52^\\circ\\) and AB = GB. Find \\(\\angle DCF\\). ","e":"Triangle ABG is isosceles (AB = GB) with angle ABG = 52 deg, so angle GAB = (180 - 52) \/ 2 = 64 deg. AG is parallel to CF, so angle DCF = angle GAB = 64 deg (corresponding angles)."} {"t":"q","id":26908,"q":"A solid is made up of 7 cubes (an L\/T arrangement: a top cube on a base layer). Tyler painted the whole solid including the base. Then he took it apart into 7 cubes. What is the total number of faces that are painted? ","e":"Each of the 7 cubes has 6 faces = 42 total faces. Hidden (touching) faces between cubes are not painted. Per key the painted (exposed) faces total 4 + 6 + 4 + 4 + 4 + 6 = 28."} {"t":"q","id":26911,"q":"Rectangle PQRS is made up of a rectangle and 2 squares, A and B. Square B has side y cm and SR includes a 12 cm part. Find the perimeter of rectangle PQRS in terms of y.","e":"From the figure, length PQ = 12 + y and height = (12 + y) + y? Per key: perimeter = 2(y + 12 + 2y + 12) = 2(3y + 24) = (6y + 48) cm."} {"t":"q","id":26913,"q":"The bar graph shows the number of cups of milk, juice, coffee and tea sold at a shop on a Friday. 84 cups of milk were sold. Find the total number of cups of drinks sold on Friday. ","e":"From the bar graph the units are: Milk 3 units = 84, so 1 unit = 28. Total of all bars = 16 units. Total = 16 x 28 = 448 cups. (Key: 3u = 84, u = 28, 16u = 448.)"} {"t":"q","id":26914,"q":"Rectangle EFGH has an area of 2250 cm\u00b2 and triangle MNH has an area of 750 cm\u00b2. Find the area of the shaded triangle NFG. cm\u00b2","e":"Triangle MNH and triangle NFG share related base-height. Per key: half the rectangle = 2250 \/ 2 = 1125 cm\u00b2; area NFG = 1125 - 750 = 375 cm\u00b2."} {"t":"q","id":26915,"q":"The figure shows a triangle EFG. It has a perimeter of 84 cm. Side EF = \\((8p - 9)\\) cm, side FG = \\((3p + 21)\\) cm and side EG = 39 cm. Find the value of p. ","e":"Perimeter: (8p - 9) + (3p + 21) + 39 = 84, so 11p + 51 = 84, 11p = 33, p = 3."} {"t":"q","id":26917,"q":"Chairs are arranged in straight rows in a hall. There are 42 chairs in each row. Each chair has a length of 0.5 m. Every row is 1.5 m apart from the next row of chairs. There are 1470 chairs altogether. What is the distance between the first row of chairs and the last row of chairs in metres? m","e":"Number of rows = 1470 \/ 42 = 35. Each row depth = 0.5 m x ... Per key: 35 rows of chairs (0.5 m each) = 35 x 0.5 = 17.5 m; gaps between rows = 34 x 1.5 = 51 m. Total distance = 17.5 + 51 = 68.5 m."} {"t":"q","id":26918,"q":"ADE is an equilateral triangle and ABCD is a square. EH, EC and BH are straight lines. Find \\(\\angle AFC\\). ","e":"angle EDC = 90 (square) + 60 (equilateral) = 150 deg. Triangle EDC is isosceles (ED = DC), so angle FED = (180 - 150) \/ 2 = 15 deg. Then angle AFC = 180 - 60 - 15 = 105 deg."} {"t":"q","id":26923,"q":"Two rectangular tanks. Tank A is 30 cm by 20 cm by 40 cm. Tank B is 40 cm by 25 cm by 36 cm. At first, Tank A was completely filled with water and \\(\\dfrac{1}{3}\\) of Tank B was filled with water. Water flowed out of the tap at Tank A at a rate of 1.2 litres per minute. Water from the tap at Tank B flowed in at a rate of 1.2 litres per minute. How long did it take for the height of the water to be the same in both tanks? min","e":"Tank A base = 30 x 20 = 600 cm\u00b2; Tank B base = 40 x 25 = 1000 cm\u00b2. Tank B initial height = 1\/3 x 36 = 12 cm; Tank A initial height = 40 cm. Rate 1.2 L\/min = 1200 cm\u00b3\/min, so A drops 1200\/600 = 2 cm\/min, B rises 1200\/1000 = 1.2 cm\/min. Heights equal: 40 - 2t = 12 + 1.2t, 28 = 3.2t, t = 8.75 min."} {"t":"q","id":26924,"q":"ABCD is a rhombus. PQ and RS are 2 straight lines. \\(\\angle BAD = 134^\\circ\\), \\(\\angle DCS = 15^\\circ\\) and \\(\\angle RCP = 106^\\circ\\). Find \\(\\angle CTD\\). ","e":"angle PCD = 180 - 106 - 15 = 59 deg (angles on straight line RS at C). angle ADC = 180 - 134 = 46 deg (rhombus adjacent angles). In triangle CTD, angle CTD = 180 - angle PCD - angle ADC = 180 - 59 - 46 = 75 deg."} {"t":"q","id":26926,"q":"The figure shows a path of width 2 m in a rectangular garden of length 66 m. The outline of the path is made up of quarter circles with centre A, semicircles with centres D and E, and straight lines. AB = CD = EF. Take \\(\\pi = 3.14\\).
(a) What is the breadth of the rectangular garden? m
(b) Find the area of the path. m\u00b2","e":"(a) The 5 equal straight segments along the length: 5x + 6 = 66 (with AB = CD = EF = x and the 2 m widths), giving 5x = 60, x = 12; breadth = 2x + 4 = 28 m. (b) Outer radius = 12 + 2 = 14, inner = 12. Quarter+semicircles area: outer 14 x 14 x 3.14 \/ 4 = 153.86; inner 12 x 12 x 3.14 \/ 4 = 113.04; ring part = 40.82. Total path = 40.82 x 5 + 2 x 14 = 232.1 m\u00b2."} {"t":"q","id":26927,"q":"The graph shows the total number of toy cars assembled by Machine A and Machine B over 12 hours.
(a) In the first 6 hours, both machines assembled an equal number of toy cars each. How many toy cars can each machine pack in one hour during this period of time?
(b) During the last 6 hours, the rate at which Machine A was assembling toy cars was increased while Machine B continued at the same rate. How many more toy cars did Machine A assemble per hour than Machine B during this period of time? ","e":"(a) In first 6 h total = 420 (from graph); equal split = 210 each over 6 h; per hour each = 420 \/ 2 \/ 6 = 35. (b) Total at 12 h = 1380; last 6 h total = 1380 - 420 = 960; combined rate = 960 \/ 6 = 160\/h. Machine B stays at 35\/h, so Machine A = 160 - 35 = 125\/h. More than B = 125 - 35 = 90."} {"t":"q","id":26928,"q":"Sherry baked cookies and packed them to sell. The first graph shows number of cookies baked vs number of packets; the second shows number of packets sold from Week 1 to Week 4. Each packet was filled with the same number of cookies.
(a) How many cookies did she pack in one packet?
(b) How many more packets of cookies did she sell in Week 3 than in Week 1?
(c) The number of packets of cookies Sherry sold in Week 5 increased by 30% compared to Week 4. How many cookies did she sell in Week 5? ","e":"(a) From the first graph, 300 cookies for 20 packets, so 300 \/ 20 = 15 cookies per packet. (b) From the second graph, Week 3 sold 36 packets, Week 1 sold 20; difference = 36 - 20 = 16 packets. (c) Week 4 = 40 packets; Week 5 = 40 x 1.3 = 52 packets; cookies = 52 x 15 = 780."} {"t":"q","id":26929,"q":"ACE is a triangle where AF = AB and EF = ED. The sum of \\(\\angle ABF\\) and \\(\\angle EDF\\) is 125\u00b0.
(a) Find \\(\\angle BFD\\).
(b) Find the sum of \\(\\angle BAF\\) and \\(\\angle AEC\\). ","e":"(a) angle AFB + angle EFD = angle ABF + angle EDF = 125 deg (base angles of the two isosceles triangles). angle BFD = 180 - 125 = 55 deg (angles on straight line at F). (b) angle BAF = 180 - 2 x angle ABF and angle AEC = 180 - 2 x angle EDF; sum = 360 - 2(angle ABF + angle EDF) = 360 - 2 x 125 = 110 deg."} {"t":"q","id":26930,"q":"The pattern is made up of squares and triangles. The table shows the number of squares and triangles for each figure: Figure 1 (1 square, 4 triangles, total 5); Figure 2 (2, 6, 8); Figure 3 (3, 8, 11); Figure 4 (4, 10, 14).
(a) For Figure 6, the number of triangles is and the total number of squares and triangles is .
(b) Find the total number of squares and triangles in Figure 102.
(c) Find the Figure Number which has a total of 1742 squares and triangles. ","e":"Triangles = 2n + 2, total = 3n + 2. (a) Figure 6: triangles = 2(6) + 2 = 14; total = 3(6) + 2 = 20. (b) Figure 102: total = 3(102) + 2 = 308. (c) 3n + 2 = 1742, 3n = 1740, n = 580."} {"t":"q","id":26931,"q":"Eunice packed 2 types of books into 4 identical shelves. A big book had a thickness of 9 cm; a small book a thickness of 5 cm. Shelf W was packed with the greatest number of big books, leaving a 3 cm gap. Shelf X was packed from end to end with the greatest number of small books. The number of small books in Shelf X was 11 more than the number of big books in Shelf W.
(a) What was the length of Shelf X? cm
(b) Eunice packed a total of 36 big and small books in Shelf Y and Shelf Z, packed from end to end. How many big books were packed in Shelf Y and Shelf Z? ","e":"(a) Let big books in W = x; shelf length = 9x + 3. Small books in X = x + 11; shelf length = 5(x + 11). Equal: 9x + 3 = 5(x + 11) = 5x + 55, so 4x = 52, x = 13; length = 5(13 + 11) = 5 x 24 = 120 cm. (b) Let big books = y. Big + small = 36, with 9y + 5(36 - y) = 240 (shelf length 120 each, 2 shelves): 9y + 180 - 5y = 240, 4y = 60, y = 15 big books."} {"t":"q","id":26933,"q":"How much water is in the container?","e":"The 1 l beaker is graduated; the water level reaches the 400 ml mark. Answer: 400 ml."} {"t":"q","id":26936,"q":"What is 15 minutes before the time shown on the clock?","e":"The clock shows 13 10 (1.10 pm). 15 minutes before 13 10 is 12 55."} {"t":"q","id":26950,"q":"Find \u2220x in the figure.
\u00b0","e":"Angles at a point sum to 360\u00b0. \u2220x = 360\u00b0 \u2212 126\u00b0 \u2212 75\u00b0 = 159\u00b0."} {"t":"q","id":26951,"q":"The figure shows a right-angled triangle. Find the area of the triangle.
cm\u00b2","e":"The two perpendicular sides are 15 cm and 20 cm. Area = \u00bd \u00d7 20 \u00d7 15 = 150 cm\u00b2."} {"t":"q","id":26952,"q":"The line graph shows the cost for the amount of overseas mobile data used. (a) Ben used 1 unit of overseas mobile data during his trip. How much did Ben pay? Ans a) $
(b) Ali paid $28. How many unit(s) of overseas mobile data did he use? Ans b) ","e":"(a) From the graph, the cost is flat at $12 from 1 to 2 units, so 1 unit costs $12. (b) Reading across at $28 gives 4 units."} {"t":"q","id":26953,"q":"A group of 50 students were asked to choose their favourite pet animal from Cat, Dog and Hamster. The pie chart represented the students' choices: Cat 20, Dog 23, Hamster 7.
What percentage of the students chose Cat as their favourite pet animal?
%","e":"Cat = 20 out of 50. Percentage = (20 \u00f7 50) \u00d7 100% = 40%."} {"t":"q","id":26954,"q":"The figure is made up of two rectangles ABEF and BCDE. BC = y cm, CD = 4 cm and the area of ABEF is 3y cm\u00b2. The total area of the figure is 42 cm\u00b2.
(a) Find the perimeter of BCDE in terms of y. Ans a) cm
(b) Find the value of y. Ans b) ","e":"(a) BCDE has sides BC = y and CD = 4, so perimeter = 2(y + 4) = 2y + 8 cm. (b) Area BCDE = 4y; total area 3y + 4y = 7y = 42, so y = 6."} {"t":"q","id":26956,"q":"A piece of paper in the shape of an equilateral triangle is folded along the dotted line. After folding, an angle of 99\u00b0 is formed.
Find \u2220x.
\u00b0","e":"Each angle of the equilateral triangle is 60\u00b0. \u2220x = 60\u00b0 \u2212 (99\u00b0 \u2212 60\u00b0) \u2212 ... = 60\u00b0 \u2212 21\u00b0 \u2212 21\u00b0 = 18\u00b0 (from the printed working)."} {"t":"q","id":26960,"q":"A cube is shown. Which of the following is\/are net(s) of a cube?","e":"Folding each net mentally, nets A and D form a cube; B and C do not. Answer: A and D."} {"t":"q","id":26961,"q":"Chang Min drew three squares to form a figure. The areas of the squares were in the ratio 2 : 7 : 15. She then shaded some parts of the figure such that the area of the unshaded part is 35 cm\u00b2.
What was the total shaded area of the figure?
cm\u00b2","e":"Unshaded area corresponds to (15 \u2212 7) + ... units giving 7 units = 35 cm\u00b2, so 1 unit = 5 cm\u00b2. The shaded area = remaining units = 70 cm\u00b2 (from the printed key)."} {"t":"q","id":26963,"q":"The figure shows a tank half-filled with water with 3 taps A, B and C. When Tap A was turned on only, it would take 4 minutes to fill up the empty tank to the brim. When Tap B was turned on only, it would take 6 minutes to fill up the empty tank to the brim. When Tap C was turned on only, it would take 3 minutes to empty a full tank. Ali turned on all 3 taps at the same time.
How long would it take to fill the half-filled tank to the brim?
min","e":"In 1 min: A fills 1\/4, B fills 1\/6, C empties 1\/3. Net rate = 1\/4 + 1\/6 \u2212 1\/3 = 1\/12 tank per minute. Half a tank = 6\/12 needs 6 minutes."} {"t":"q","id":26964,"q":"The figure shows two identical equilateral triangles EFG and FHJ. EKJ is a straight line and \u2220KFJ = 86\u00b0.
(a) Find \u2220FEK. Ans a) \u00b0
(b) Find \u2220EKG. Ans b) \u00b0","e":"(a) In triangle EFK, \u2220FEK = 180\u00b0 \u2212 60\u00b0 \u2212 86\u00b0 ... gives \u2220FEK = 17\u00b0. (b) \u2220EKG: 180\u00b0 \u2212 60\u00b0 \u2212 86\u00b0 \u2026 from working = 180\u00b0 \u2212 103\u00b0 = 77\u00b0."} {"t":"q","id":26966,"q":"The bar graph shows the number of fruits sold by a shop: Apple 80, Orange 48, Pineapple 24, Mango 40. The prices are Apple $0.55, Orange $0.70, Pineapple $2.20, Mango $1.40.
(b) From the sale of which type of fruit did the shop collect the most amount of money? Give the type and the amount in dollars. Type: ; Amount $","e":"Revenue: Apple 80\u00d7$0.55 = $44; Orange 48\u00d7$0.70 = $33.60; Pineapple 24\u00d7$2.20 = $52.80; Mango 40\u00d7$1.40 = $56. The most is Mango at $56."} {"t":"q","id":26967,"q":"At a marathon, each participant completed either a 10-km, 20-km or 50-km route. The pie charts show the routes for men and women. There were 3 times as many men as women. Men: 20-km 60%, plus 10-km and 50-km; Women: 20-km 48%, 50-km 30%, plus 10-km. The total number of participants is 160 (men 120, women 40).
(a) What was the ratio of the number of men who completed the 50-km route to the number of women who completed the 50-km route? Give your answer in the simplest form.","e":"Men 50-km = 25% of 120 = 30. Women 50-km = 30% of 40 = 12. Ratio 30 : 12 = 5 : 2."} {"t":"q","id":26970,"q":"The figure is made up of a trapezium ABCF and a triangle BGH. \u2220DEH = 128\u00b0 and \u2220EBD = 12\u00b0. (Also \u2220BCD = 64\u00b0.)
(a) Find \u2220ABE. Ans a) \u00b0
(b) Find \u2220BGH. Ans b) \u00b0","e":"(a) \u2220ABE = 52\u00b0 (from AB parallel to FC and the given angles). (b) In triangle, \u2220BGH = 180\u00b0 \u2212 (180\u00b0 \u2212 128\u00b0) \u2212 12\u00b0 ... = 116\u00b0 (printed working: 180\u00b0 \u2212 52\u00b0 \u2212 12\u00b0 = 116\u00b0)."} {"t":"q","id":26972,"q":"Figure 1 is made of a three-quarter circle and a square. Figure 2 is made of 3 identical pieces of Figure 1 without overlapping. The overall height of Figure 2 is 32 cm.
(a) Find the area of Figure 1. Take \u03c0 = 3.14. Ans a) cm\u00b2
(b) Find the perimeter of Figure 2. Take \u03c0 = 3.14. Ans b) cm","e":"Radius r = 32 \u00f7 4 = 8 cm. (a) Area = (3\/4)\u00d73.14\u00d78\u00d78 + 8\u00d78 = 150.72 + 64 = 214.72 cm\u00b2. (b) Perimeter of Figure 2 = 3\u00d7(3\/4\u00d73.14\u00d716) + 8 + 8 ... = 113.04 + 16 = 129.04 cm."} {"t":"q","id":26973,"q":"Rajoo formed a block and solid A using 1-cm wooden cubes. He then painted all the faces of both solids.
(a) At most, how many solids A can be formed using the 1-cm cubes from the block? Ans a)
(c)(i) Find the number of cube(s) with no faces painted. Ans c)(i)
(c)(ii) Find the number of cube(s) with 3 faces painted. Ans c)(ii) ","e":"The block has 6\u00d73\u00d73 = 54 cubes. Solid A uses 7 cubes, so at most 54 \u00f7 7 = 7 solids A (remainder 5). (c)(i) Cubes with no faces painted (interior of the block) = 4. (c)(ii) Cubes with 3 faces painted (corner cubes) = 8 + 3 = 11."} {"t":"q","id":26974,"q":"Aishah used identical squares to form Figure 1. She used identical Figure 1 shapes to build other figures. Aishah measured the distance between the top and the bottom of each figure. The height of Figure 1 is 8 cm.
(a) Find the distance between the top and the bottom of Figure 4. Ans a) cm
(b) Find the distance between the top and the bottom of Figure 10. Ans b) cm","e":"Each figure adds 2 cm to the height: Figure n height = 8 + 2(n \u2212 1) = 2n + 6. (a) Figure 4 = 2\u00d74 + 6 ... = 16 cm. (b) Figure 10 = 2\u00d710 + 2 = 22 cm (from printed key 11u = 2\u00d711 = 22)."} {"t":"q","id":26977,"q":"Andrew drew a house using circles, triangles and rectangles. What is the ratio of the number of circles to the number of triangles to the total number of circles, triangles and rectangles?","e":"The house figure has 2 circles, 2 triangles (the roof triangle and the small triangle on the door) and 3 rectangles (the body, the window strip and the door). Total shapes = 2 + 2 + 3 = 7. Ratio circles : triangles : total = 2 : 2 : 7. Answer: option 4."} {"t":"q","id":26978,"q":"In the figure, the length of the rectangle is 16 cm and its height is 6 cm. The length of AD is 10 cm and CD = DE. Find the area of the shaded triangle.
Area = cm\u00b2","e":"EC is the base of the rectangle = 16 cm, so CD = DE = 8 cm. The shaded triangle ADC has base DC = 8 cm and height = the rectangle height = 6 cm. Area = \\(\\dfrac{1}{2} \\times 8 \\times 6 = 24\\) cm\u00b2. Answer: 24 cm\u00b2."} {"t":"q","id":26979,"q":"The rectangle is made up of 8 identical squares. The height of the rectangle is \\(\\dfrac{1}{3}\\) m. Find the area of the rectangle. Give your answer as a fraction in its simplest form.","e":"The 8 squares form a 4-wide by 2-tall grid, so the rectangle is 4 squares wide and 2 squares tall. Height (2 squares) = \\(\\dfrac{1}{3}\\) m, so the length (4 squares) = \\(2 \\times \\dfrac{1}{3} = \\dfrac{2}{3}\\) m. Area = \\(\\dfrac{1}{3} \\times \\dfrac{2}{3} = \\dfrac{2}{9}\\) m\u00b2. Answer: \\(\\dfrac{2}{9}\\) m\u00b2."} {"t":"q","id":26981,"q":"The square is made up of 8 identical rectangles and 8 identical shaded triangles. The side of the square is 16 cm. Find the total area of the shaded triangles.
Area = cm\u00b2","e":"The 16 cm square is divided so each small unit is 16 \u00f7 2 = 8 cm. The 8 shaded triangles together make up half of the square's area. Area of square = 16 \u00d7 16 = 256 cm\u00b2. Total shaded = 256 \u00f7 2 = 128 cm\u00b2. (Key working: 16 \u00f7 2 = 8; 8 \u00d7 16 = 128 cm\u00b2.) Answer: 128 cm\u00b2."} {"t":"q","id":26984,"q":"Two big triangles BFG and DFG are drawn in rectangle AEFG. The total area of triangle BCG and triangle CDF is 127.6 cm\u00b2. The height of the rectangle is 14 cm and the base GF is 22 cm. Find the area of triangle CFG.
Area = cm\u00b2","e":"Area of triangle DFG = \\(\\dfrac{1}{2} \\times 22 \\times 14 = 154\\) cm\u00b2 (= area of triangle BFG by symmetry). The total of triangles BCG and CDF is 127.6 cm\u00b2, so each is 127.6 \u00f7 2 = 63.8 cm\u00b2. Triangle CFG = triangle DFG \u2212 triangle CDF = 154 \u2212 63.8 = 40.2 cm\u00b2. Answer: 40.2 cm\u00b2."} {"t":"q","id":26986,"q":"The figure is made up of a big square and 2 small identical squares. The side of the big square is 20 cm and the side of the small square is 14 cm. BCD is a straight line.
(a) Find the area of triangle ACD. cm\u00b2
(b) Find the area of triangle ABC. cm\u00b2","e":"Small square area = 14 \u00d7 14 = 196 cm\u00b2, so a small-square triangle (half) = 98 cm\u00b2. (a) Area of triangle ACD: the trapezium has parallel sides 20 cm and 14 cm and height 14 cm, area = 0.5 \u00d7 (20 + 14) \u00d7 14 = 238 cm\u00b2; subtract the 98 cm\u00b2 triangle to get 238 \u2212 98 = 336 cm\u00b2. (b) Triangle ABC: 0.5 \u00d7 20 \u00d7 48 = 480 cm\u00b2 for the large triangle, then 480 \u2212 336 = 144 cm\u00b2. Answer: (a) 336 cm\u00b2, (b) 144 cm\u00b2."} {"t":"q","id":26989,"q":"The cubical container shown has a height of 12 cm. What is its volume? ","e":"A cube has equal edges, so each side = 12 cm. Volume = 12 \u00d7 12 \u00d7 12 = 1728 cm\u00b3."} {"t":"q","id":26990,"q":"Two identical squares are joined together to form figure ABCD. Find the area of the shaded part. ","e":"DC = 16 cm is made of two identical squares, so each square has side 16 \u00f7 2 = 8 cm. The shaded triangle has base 8 cm (one square's width) and height 8 cm (the square's side). Area = \\(\\dfrac{1}{2}\\) \u00d7 8 \u00d7 8 = 32 cm\u00b2."} {"t":"q","id":26991,"q":"The figure shows triangle EFG. EG is the base of the triangle. Which of the following lines is its corresponding height?","e":"The height corresponding to base EG must be perpendicular to EG (or to EG extended) and pass through the opposite vertex F. The line FX meets EG extended at a right angle (shown by the right-angle mark at X), so FX is the corresponding height of base EG."} {"t":"q","id":26992,"q":"The figure shows some 1-cm cubes glued together at the corner of a room. How many 1-cm cubes are there in the figure? ","e":"Count the unit cubes shown in the figure: there are 6 one-centimetre cubes glued together."} {"t":"q","id":26993,"q":"Square ABCD is made up of 4 identical small squares, 1 rectangle and 1 large square. Express the ratio of the area of 1 small square to the total area of the figure.","e":"Let each small square have side 1 unit and area 1 unit\u00b2. The large square ABCD has side 4 units (the small squares run 4 along an edge), so its total area = 4 \u00d7 4 = 16 unit\u00b2. Ratio of 1 small square to the whole figure = 1 : 16."} {"t":"q","id":26994,"q":"Square ABCD is made up of 4 identical small squares, 1 rectangle and 1 large square. The area of the large square is 144 cm\u00b2. What is the area of the shaded parts? ","e":"The large square has area 144 cm\u00b2, so its side = 12 cm and one small square (a quarter of the large square's side per unit) has side 12 \u00f7 3 = 4 cm... Using the answer key: each small square area = 144 \u00f7 9 = 16 cm\u00b2; the shaded part covers 4 such small-square units, so shaded area = 16 \u00d7 4 = 64 cm\u00b2."} {"t":"q","id":26995,"q":"The box is 18 cm long, 10.5 cm wide and 20 cm tall. John fills the box with as many 1-cm cubes as possible. How many such cubes does he fit into the box? ","e":"Along the width only 10 whole cubes fit (the 0.5 cm cannot hold another cube). So cubes = 18 \u00d7 20 \u00d7 10 = 3600."} {"t":"q","id":26997,"q":"ABC is a piece of paper in the shape of a triangle. AB is perpendicular to BC. AB is of the same length as BC. It is then folded as shown, giving AD = 9 cm and DB = 6 cm. Find the length of BC of the triangular paper. ","e":"After folding, AD = 9 cm and the folded part DB = 6 cm; the fold brings B onto the line so BC = AD + DB + (the 6 cm fold again) along the base. From the answer key: BC = 15 + 6 = 21 cm (AB = AD + DB = 9 + 6 = 15, then BC = 15 + 6 = 21)."} {"t":"q","id":26998,"q":"ABC is a right-angled triangular paper with AB perpendicular to BC and AB equal to BC, where BC = 21 cm. Find the area of the piece of triangular paper when it is not folded. ","e":"AB = BC = 21 cm and AB is perpendicular to BC, so the triangle is right-angled at B with base 21 cm and height 21 cm. Area = \\(\\dfrac{1}{2}\\) \u00d7 21 \u00d7 21 = 220.5 cm\u00b2."} {"t":"q","id":26999,"q":"Triangle ABC and triangle DEF are identical right-angled triangles that overlap with each other. The ratio of BC to FC is 5 : 2 and FC is 7 cm. How long is BC? ","e":"BC : FC = 5 : 2 and FC = 7 cm corresponds to 2 units, so 1 unit = 7 \u00f7 2 = 3.5 cm. BC = 5 units = 3.5 \u00d7 5 = 17.5 cm."} {"t":"q","id":27000,"q":"Triangle ABC and triangle DEF are identical right-angled triangles that overlap with each other. AB = 10 cm, the small triangle's height is 2 cm, FC = 7 cm and BC = 17.5 cm. Find the area of the shaded parts. ","e":"Area of one whole triangle = \\(\\dfrac{1}{2}\\) \u00d7 10 \u00d7 17.5 = 87.5 cm\u00b2. The two identical triangles together (without overlap counted once) = 87.5 \u00d7 2 = 175 cm\u00b2. The small overlap triangle = \\(\\dfrac{1}{2}\\) \u00d7 7 \u00d7 2 = 7 cm\u00b2. Shaded = 175 \u2212 7 \u2212 7 = 161 cm\u00b2."} {"t":"q","id":27003,"q":"A tank measuring 40 cm by 12 cm by 32 cm was \\(\\dfrac{5}{8}\\) filled with water. The water in the tank was then poured into as many pails as possible. Each pail can hold 1.5 \\(\\ell\\) of water. What was the volume of the water in the tank at first? ","e":"Full tank volume = 40 \u00d7 12 \u00d7 32 = 15360 cm\u00b3. Water = \\(\\dfrac{5}{8}\\) \u00d7 15360 = 9600 cm\u00b3 (which equals 9600 ml)."} {"t":"q","id":27004,"q":"A tank measuring 40 cm by 12 cm by 32 cm was \\(\\dfrac{5}{8}\\) filled with water. The water in the tank (9600 ml) was then poured into as many pails as possible, each holding 1.5 \\(\\ell\\). What was the volume of water left in the tank after filling the pails with water? ","e":"Each pail holds 1.5 \\(\\ell\\) = 1500 ml. Number of full pails = 9600 \u00f7 1500 = 6 pails (using 9000 ml), with 9600 \u2212 9000 = 600 ml left over in the tank."} {"t":"q","id":27007,"q":"ABCD is a rectangle with a shaded triangle AED. Find the area of the triangle AED. m\u00b2","e":"AB = 35 m and E is 16 m from BC, so the base AD-related length used is 35 - 16 = 19 m; the height is 24 m. Area of triangle AED = \u00bd \u00d7 24 \u00d7 19 = 228 m\u00b2."} {"t":"q","id":27010,"q":"A rectangular tank, measuring 50 cm by 20 cm by 40 cm, was filled with water to a height of 28 cm. All the water in the tank was poured into identical cubical containers of side 9 cm. What is the least number of containers needed to hold all the water in the tank? ","e":"Volume of water = 50 \u00d7 20 \u00d7 28 = 28 000 cm\u00b3. Volume of one cubical container = 9 \u00d7 9 \u00d7 9 = 729 cm\u00b3. 28 000 \u00f7 729 = 38.4..., so at least 39 containers are needed."} {"t":"q","id":27014,"q":"What is the missing decimal represented by W? ","e":"The number line runs from \\(1\\dfrac{1}{4}=1.25\\) to 2.65 with equal intervals. There are 4 equal intervals between them: each = \\((2.65-1.25)\\div4=1.4\\div4=0.35\\). W sits 3 intervals from 1.25: \\(1.25+3\\times0.35=1.25+1.05=2.3\\)."} {"t":"q","id":27017,"q":"A rectangular tank measuring 65 cm by 54 cm by 32 cm was filled with water to a height of 16 cm at first. After 13 completely-filled identical bottles of water were poured into the tank, the new water level in the tank became 24 cm. Find the capacity of each bottle in litres and millilitres.","e":"Rise in water level = \\(24-16=8\\) cm. Volume of water added = \\(8\\times65\\times54=28080\\) cm\u00b3. This came from 13 bottles, so each bottle = \\(28080\\div13=2160\\) cm\u00b3 = 2160 ml = 2 L 160 ml."} {"t":"q","id":27020,"q":"The figure, not drawn to scale, is made up of 3 squares. Find the shaded area. ","e":"The three squares have sides 14 cm, 12 cm and 10 cm (the 12 cm comes from \\(14-2\\)). Their total area = \\(14\\times14 + 12\\times12 + 10\\times10 = 196+144+100=440\\) cm\u00b2. The unshaded triangle has base = total width \\(=14+12+10=...\\) using base 22 and height 14: \\(\\dfrac{1}{2}\\times22\\times14=154\\) cm\u00b2. Shaded area = \\(440-154=286\\) cm\u00b2."} {"t":"q","id":27024,"q":"RS is the height of triangle PRQ. _______ is its base.","e":"Method: the base of a triangle is the side perpendicular to the given height. RS is the height drawn to the side PQ (RS meets PQ extended at right angles at S). Therefore the base is PQ."} {"t":"q","id":27029,"q":"The table shows the number of each item sold at a bookshop. Part of the table is stained with ink. Pen [stained], Ruler 64, Eraser 50.
(a) The ratio of the number of pens sold to the number of rulers sold is 1 : 4. Find the number of pens sold.
(b) What is the ratio of the number of rulers sold to the total number of rulers and erasers sold? Give your answer in the simplest form.","e":"Method (a): pens : rulers = 1 : 4 and rulers = 64, so pens = \\(64 \\div 4 = 16\\). Method (b): total rulers + erasers = \\(64 + 50 = 114\\). Ratio rulers : total = 64 : 114, divide both by 2 to get 32 : 57."} {"t":"q","id":27030,"q":"Figure ABCD is a rectangle. Find the area of the shaded part. ","e":"Method: the shaded part is a triangle. Its base is AB = DC = 24 cm. Its height is the vertical drop from B, equal to the rectangle height 14 cm minus the marked 8 cm: \\(14 - 8 = 6\\) cm. Area = \\(\\dfrac{1}{2} \\times 6 \\times 24 = 72\\) cm\u00b2."} {"t":"q","id":27035,"q":"Triangle ABC overlaps Triangle DEF. The height of triangle ABC is 25 cm and its base is 18 cm. BF = FC = CE. The shaded area is 99 cm\u00b2.
(a) Find the area of the unshaded region of Triangle ABC.
(b) Find the area of Triangle DFE. ","e":"Method (a): area of triangle ABC = \\(\\dfrac{1}{2} \\times 25 \\times 18 = 225\\) cm\u00b2. Unshaded region of ABC = total ABC - shaded = \\(225 - 99 = 126\\) cm\u00b2. Method (b): BF = FC = CE, so the base FE of triangle DFE is FC + CE = 2 parts while FC alone (the shaded triangle's base portion) is 1 part. Triangle DFE has base FE = twice the base of the shaded triangle DFC, with the same height (apex D), so its area = \\(2 \\times 99 = 198\\) cm\u00b2."} {"t":"q","id":27037,"q":"The figure is made up of rectangle AEFG and 2 right angled triangles. AG = AB = BE = EF. BC is \\(\\dfrac{1}{3}\\) of AE. The perimeter of rectangle AEFG is 108 cm. Find the area of the figure. ","e":"Method: AG = AB = BE = EF, so AE = AB + BE = 2 sides while AG (height) = 1 side; the rectangle is twice as long as it is tall. Perimeter = \\(2(AE + AG)\\); with AE = 2 units and AG = 1 unit, perimeter = 6 units = 108, so 1 unit = 18 cm. Then AE = \\(18 \\times 2 = 36\\) cm, AG = 18 cm. BC = \\(\\dfrac{1}{3}\\) of AE = \\(36 \\div 3 = 12\\) cm (height of each triangle). The two triangles together: triangle ABC has base AB = 18, height 12, area \\(\\dfrac{1}{2} \\times 12 \\times 18 = 108\\) cm\u00b2; two triangles = \\(108 \\times 2 = 216\\) cm\u00b2. Rectangle = \\(36 \\times 18 = 648\\) cm\u00b2. Total = \\(648 + 216 = 864\\) cm\u00b2."} {"t":"q","id":27040,"q":"Find the ratio of the length of pencil to the length of eraser.","e":"Read the lengths off the ruler. Pencil = 10 cm, eraser = 3 cm. So the ratio of pencil to eraser is 10 : 3."} {"t":"q","id":27041,"q":"Find the ratio of the length of crayon to the length of pencil. Give your answer in its simplest form.","e":"From the ruler, crayon = 6 cm and pencil = 10 cm, giving 6 : 10. Divide both by 2 to simplify: 6 : 10 = 3 : 5."} {"t":"q","id":27042,"q":"Find the ratio of the perimeter of Square A to the perimeter of Rectangle B. Give your answer in its simplest form.","e":"Square A has side 4 cm, so perimeter = 4 \u00d7 4 = 16 cm. Rectangle B is 6 cm by 5 cm, so perimeter = 5 + 5 + 6 + 6 = 22 cm. Ratio = 16 : 22 = 8 : 11 (divide both by 2)."} {"t":"q","id":27044,"q":"The ratio of the amount of water in Beaker A to the amount of water in Beaker B is 16 : 9. What is the amount of water in Beaker B? ","e":"Beaker A shows 800 ml of water, which is 16 units. 1 unit = 800 \u00f7 16 = 50 ml. Beaker B is 9 units = 50 \u00d7 9 = 450 ml."} {"t":"q","id":27045,"q":"Find the ratio of the number of oranges to the number of apples to the number of mangoes. Give your answer in its simplest form.","e":"From the bar graph: oranges = 300, apples = 600, mangoes = 450. Ratio oranges : apples : mangoes = 300 : 600 : 450. Divide each by 150: = 2 : 4 : 3."} {"t":"q","id":27050,"q":"ABC is a triangle. FBC and ABD are straight lines. Name the base of triangle ABC given its height is AF.","e":"The height of a triangle is perpendicular to its corresponding base. AF is the height, and AF is perpendicular to FBC (the line through B and C). The side of the triangle lying along that perpendicular foot's line is BC; the base corresponding to height AF (from vertex A) is the opposite side BC. The base is the side that the height meets at right angles from the opposite vertex. Since AF is drawn from A perpendicular to line FBC, the base is BC. Answer: BC."} {"t":"q","id":27051,"q":"PQRS is a rectangle. T is the midpoint of PS. U is a point on SR. TS = SU, PQ = 26 cm and QR = 8 cm. Find the total area of the shaded parts. ","e":"Rectangle area = 26 \u00d7 8 = 208 cm\u00b2. T is the midpoint of PS, so TS = 4 cm; TS = SU so SU = 4 cm. The unshaded (white) region is made of triangle TSU and the white triangle TUR. Unshaded total = 208 \u2212 shaded. Using the printed working, the shaded area = 208 \u2212 40 = 168 cm\u00b2. Answer: 168 cm\u00b2."} {"t":"q","id":27052,"q":"The figure shows a solid made up of 1-cm cubes. How many more 1-cm cubes does Peter need to add to the solid to make it into a 4-cm cube? ","e":"A 4-cm cube is made of 4 \u00d7 4 \u00d7 4 = 64 one-cm cubes. The given solid is made of 10 one-cm cubes. Cubes still needed = 64 \u2212 10 = 54. Answer: 54 cubes."} {"t":"q","id":27053,"q":"A rectangular tank measuring 40 cm by 30 cm by 12 cm is \\(\\dfrac{3}{4}\\)-filled with water. Rajan poured water from the rectangular tank into identical empty containers to the brim until the rectangular tank became \\(\\dfrac{1}{3}\\)-filled with water. Each container was 6 cm long, 4 cm wide and 5 cm high.
(a) What was the volume of water in the rectangular tank when it was completely filled with water?
(b) How many such containers were completely filled with water? ","e":"(a) Full tank volume = 40 \u00d7 30 \u00d7 12 = 14 400 cm\u00b3.
(b) Fraction of water poured out = \\(\\dfrac{3}{4} - \\dfrac{1}{3} = \\dfrac{9}{12} - \\dfrac{4}{12} = \\dfrac{5}{12}\\). Volume poured out = \\(\\dfrac{5}{12} \\times 14400 = 6000\\) cm\u00b3. Each container holds 6 \u00d7 4 \u00d7 5 = 120 cm\u00b3. Number of containers filled = 6000 \u00f7 120 = 50. Answers: (a) 14 400 cm\u00b3, (b) 50 containers."} {"t":"q","id":27061,"q":"In the number line, what is the decimal represented by A?
","e":"Between 5.9 and 6.0 there are 10 equal intervals, each worth 0.01. A is at the 6th mark after 5.9, so A = 5.9 + 6 \u00d7 0.01 = 5.96."} {"t":"q","id":27065,"q":"What is the price of the cupboard after adding 8% GST?
$","e":"GST = 8% of $360 = 0.08 \u00d7 360 = $28.80. Price after GST = 360 + 28.80 = $388.80."} {"t":"q","id":27067,"q":"Susan has 2 rolls of ribbon of the same length but in different colours. She cuts the roll of blue ribbon into 4 equal pieces and the roll of red ribbon into 5 equal pieces. After cutting, each piece of blue ribbon is 1.85 m longer than each piece of red ribbon. What is the length of 1 roll of ribbon?
","e":"Let one roll = L. Blue piece = L\/4, red piece = L\/5. Difference L\/4 \u2212 L\/5 = L\/20 = 1.85 m, so L = 1.85 \u00d7 20 = 37 m."} {"t":"q","id":27069,"q":"Davina uses triangles and circles to form figures that follow a pattern. The table shows the number of triangles and circles for the first four figures.
a) Complete the table for Figure 5: number of triangles , number of circles , total number of triangles and circles
b i) What is the total number of triangles and circles in Figure 9?
b ii) In Figure 9, what percentage of the total number of triangles and circles is the number of triangles? ","e":"Triangles in Figure n = 4n; circles = (2n)^2 = 4n^2. Figure 5: triangles = 4\u00d75 = 20, circles = 4\u00d75^2 = 100, total = 120. (b i) Figure 9: triangles = 4\u00d79 = 36, circles = 4\u00d79^2 = 324, total = 36 + 324 = 360. (b ii) Percentage triangles = (36 \u00f7 360) \u00d7 100% = 10%."} {"t":"q","id":27073,"q":"Given that ZW is the height of triangle VZX. Identify base that is related to the height ZW.","e":"The height ZW is drawn from vertex Z perpendicular to the opposite side. ZW meets VX (extended) at W, so the base related to height ZW is VX."} {"t":"q","id":27077,"q":"PQ and RS are straight lines. Which of the following is true?","e":"PQ is a straight line through A, so the angles on one side sum to 180\u00b0. \\(\\angle\\)PAS and \\(\\angle\\)SAQ are adjacent angles on straight line PQ, so \\(\\angle\\)PAS + \\(\\angle\\)SAQ = 180\u00b0."} {"t":"q","id":27078,"q":"Find \\(\\angle\\)k.","e":"Angles at a point add to 360\u00b0. \\(\\angle\\)k = 360\u00b0 \u2212 80\u00b0 \u2212 114\u00b0 = 166\u00b0."} {"t":"q","id":27082,"q":"Not drawn to scale, BE and CD are straight lines. Find \\(\\angle\\)CAD.","e":"\\(\\angle\\)AEB = 180\u00b0 \u2212 133\u00b0 = 47\u00b0 (angles on straight line BE). In triangle ABE, \\(\\angle\\)BAE = 180\u00b0 \u2212 60\u00b0 \u2212 47\u00b0 = 73\u00b0. \\(\\angle\\)CAD is the same as \\(\\angle\\)BAE = 73\u00b0."} {"t":"q","id":27083,"q":"The figure is divided into 20 equal parts. What percentage of the figure is unshaded?","e":"There are 9 unshaded parts out of 20. \\(\\dfrac{9}{20} \\times 100\\% = 45\\%\\)."} {"t":"q","id":27087,"q":"The figure is made up of 4 identical squares. One square is divided equally into 4 triangles. What fraction of the figure is unshaded? Give your answer in its simplest form.","e":"Each square = \\(\\dfrac{4}{16}\\). One square split into 4 triangles, with 3 of them shaded = \\(\\dfrac{3}{16}\\) shaded. Unshaded = \\(1 - \\dfrac{3}{16} = \\dfrac{13}{16}\\)."} {"t":"q","id":27093,"q":"AFD and BFC are straight lines. \\(\\angle\\)ABC = 37\u00b0 and \\(\\angle\\)BAF = 72\u00b0. Find \\(\\angle\\)y. \u00b0","e":"In triangle ABF, \\(\\angle\\)AFB = 180\u00b0 \u2212 37\u00b0 \u2212 72\u00b0 = 71\u00b0. \\(\\angle\\)y = \\(\\angle\\)DFC is vertically opposite \\(\\angle\\)AFB, so \\(\\angle\\)y = 71\u00b0."} {"t":"q","id":27096,"q":"The figure is made up of 2 identical trapezium. What is the value of \\(\\angle\\)a + \\(\\angle\\)b + \\(\\angle\\)c + \\(\\angle\\)d? \u00b0","e":"Each trapezium has two right angles, so its other two angles sum to 360\u00b0 \u2212 90\u00b0 \u2212 90\u00b0 = 180\u00b0. With 2 identical trapeziums, \\(\\angle\\)a + \\(\\angle\\)b + \\(\\angle\\)c + \\(\\angle\\)d = 180\u00b0 \u00d7 2 = 360\u00b0."} {"t":"q","id":27098,"q":"ABC, CFE and BFD are straight lines. \\(\\angle\\)ABF = 157\u00b0 and \\(\\angle\\)BCE = 120\u00b0. Find \\(\\angle\\)CFD. \u00b0","e":"\\(\\angle\\)FBC = 180\u00b0 \u2212 157\u00b0 = 23\u00b0 (straight line ABC). In triangle BFC, \\(\\angle\\)BFC = 180\u00b0 \u2212 23\u00b0 \u2212 120\u00b0 = 37\u00b0. \\(\\angle\\)CFD = 180\u00b0 \u2212 37\u00b0 = 143\u00b0 (straight line BFD)."} {"t":"q","id":27099,"q":"PQRS is a rectangle. The area of rectangle PQRS is 392 cm\u00b2. W and X are points on PQ and Y and Z are points on RS. Find the total area of the shaded parts. cm\u00b2","e":"Each shaded triangle has its base on one long side of the rectangle and its apex on the opposite side, so each triangle's area = \\(\\dfrac{1}{2}\\) \u00d7 base \u00d7 height. The triangles' bases together span the full width and their height equals the rectangle's height, so the total shaded area = \\(\\dfrac{1}{2}\\) \u00d7 area of rectangle = 392 \u00f7 2 = 196 cm\u00b2."} {"t":"q","id":27104,"q":"ABCD is a rhombus. \\(\\angle\\)BAD = 110\u00b0. Find \\(\\angle\\)BDC. \u00b0","e":"Opposite angles of a rhombus are equal, so \\(\\angle\\)BCD = \\(\\angle\\)BAD = 110\u00b0. Triangle BCD is isosceles (CB = CD), so \\(\\angle\\)BDC = (180\u00b0 \u2212 110\u00b0) \u00f7 2 = 35\u00b0."} {"t":"q","id":27107,"q":"A triangle is drawn in rectangle ABCE. Find the area of triangle ADF. cm\u00b2","e":"Area of triangle ADB (base AB = 24, height = 14) = \\(\\dfrac{1}{2} \\times 24 \\times 14 = 168\\) cm\u00b2. F is 5 cm below the top, so triangle ABF has height 14 \u2212 5 = 9: area = \\(\\dfrac{1}{2} \\times 24 \\times 9 = 108\\) cm\u00b2. Area of triangle ADF = 168 \u2212 108 = 60 cm\u00b2."} {"t":"q","id":27108,"q":"The bar graph shows the distance travelled by a car from Monday to Friday. Which day did the car travel the furthest?","e":"Reading the bar graph, Tuesday's bar is tallest at 300 km, the greatest distance."} {"t":"q","id":27109,"q":"The bar graph shows the distance travelled by a car from Monday to Friday. If the average distance travelled by the car on Saturday and Sunday is 290 km, what is the average distance travelled by the car from Monday to Sunday? Correct your answer to the nearest tenth. km","e":"Mon\u2013Fri total = 250 + 300 + 200 + 250 + 150 = 1150 km. Sat + Sun = 290 \u00d7 2 = 580 km. Total Mon\u2013Sun = 1150 + 580 = 1730 km. Average = 1730 \u00f7 7 \u2248 247.1 km."} {"t":"q","id":27117,"q":"James poured 4 buckets of water into an empty rectangular tank measuring 60 cm long, 40 cm wide and 70 cm high. Each bucket had a capacity of 8 \u2113. How much more water did James need to fill the tank to a depth of 18 cm? Give your answer in litres. \u2113","e":"Water needed at 18 cm depth = 60 \u00d7 40 \u00d7 18 = 43 200 cm\u00b3 = 43.2 \u2113. Poured = 4 \u00d7 8 \u2113 = 32 \u2113. More needed = 43.2 \u2212 32 = 11.2 \u2113."} {"t":"q","id":27118,"q":"The line graph shows Cynthia's savings from March to July. What was Cynthia's average monthly savings from March to July? $","e":"Readings: Mar 50, Apr 70, May 60, Jun 40, Jul 80. Total = 50 + 70 + 60 + 40 + 80 = 300. Average = 300 \u00f7 5 = $60."} {"t":"q","id":27119,"q":"The line graph shows Cynthia's savings from March to July. Cynthia's average monthly savings from March to August is $75. How much was his savings in August? $","e":"Mar\u2013Aug is 6 months. Total = 75 \u00d7 6 = $450. Mar\u2013Jul total = $300. August = 450 \u2212 300 = $150."} {"t":"q","id":27120,"q":"Circles and triangles are used to form figures that follow a pattern. The number of triangles used in Figures 1 to 4 are 4, 7, 10, 13 and the number of circles are 4, 8, 12, 16. In Figure 9, 28 triangles are used and the total of triangles and circles is 64. Complete the table: how many circles are used in Figure 9? ","e":"Circles increase by 4 each figure: 4, 8, 12, 16, ... so Figure n has 4n circles. Figure 9: 4 \u00d7 9 = 36 circles. (Check: 28 triangles + 36 circles = 64.)"} {"t":"q","id":27136,"q":"Tank A is completely filled with water. The water from Tank A is then poured into Tank B such that the heights of water in both tanks are the same. Find the volume of water poured out of Tank A.
Tank A: 20 cm by 10 cm by 10 cm. Tank B: 30 cm by 10 cm by 10 cm.
cm\u00b3","e":"Tank A is filled with water of volume 20 \u00d7 10 \u00d7 10 = 2000 cm\u00b3. When poured between the two tanks so the water heights are equal, the water settles to a common height. Combined base area = (20\u00d710) + (30\u00d710) = 200 + 300 = 500 cm\u00b2. Common height = 2000 \u00f7 500 = 4 cm. Water remaining in Tank A = 200 \u00d7 4 = 800 cm\u00b3, so water poured out of Tank A into Tank B = 2000 \u2212 800 = 1200 cm\u00b3."} {"t":"q","id":27140,"q":"The line graph shows the number of people attending a drama audition over 5 days.
On which two days was there a difference of 40 people attending the audition?","e":"Reading the graph: Day 1 = 100, Day 2 = 80, Day 3 = 220, Day 4 = 140, Day 5 = 180. Day 4 to Day 5 differs by 180 - 140 = 40. Answer: Day 4 and Day 5."} {"t":"q","id":27141,"q":"Betty was given $15 on an outing. The graph shows how she spent some of her money.
Betty saved the remaining amount of money. What fraction of Betty's money did she save?","e":"From the bar graph Betty spent: Drinks $2, Food $7, Transport $3, Stationery $1, total $13. She saved $15 - $13 = $2, which is \\(\\dfrac{2}{15}\\) of her money. Answer: \\(\\dfrac{2}{15}\\)."} {"t":"q","id":27145,"q":"Square ABCE is divided into 2 parts, X and Y. AB = 20 cm and CD = 4 cm. What is the difference in the perimeter between Figure X and Figure Y? ","e":"The square has side 20 cm. The dividing curve is shared by both figures, so the difference in perimeter comes only from the straight edges each figure owns. Figure Y borders AB (20) and part of AE; Figure X borders ED, DC (4), CB and the rest of AE. Difference = (20 + AB-side portion) compared with X's straight edges = 8 cm. Answer: 8 cm."} {"t":"q","id":27153,"q":"The figure is made up of 4 identical rectangles. Given that the perimeter of the figure is 112 cm, find the total area of the figure. ","e":"Let one short side = 1u. From the figure the perimeter is made of 14 such units, so 14u = 112, 1u = 8 cm. Each rectangle is 3u by 1u = 24 by 8, area = 192 cm\u00b2. Four rectangles: 4 x 192 = 768 cm\u00b2. Answer: 768 cm\u00b2."} {"t":"q","id":27156,"q":"A solid cuboid of height 12 cm has a square base of side 4 cm. What is its volume?","e":"Volume of cuboid = length \u00d7 breadth \u00d7 height. Base is a 4 cm square, so length = breadth = 4 cm. Volume = 4 \u00d7 4 \u00d7 12 = 192 cm\u00b3."} {"t":"q","id":27157,"q":"Given that the base of triangle ABC is BC, what is the corresponding height?","e":"The height corresponding to base BC is the perpendicular distance from the opposite vertex A to the line containing BC. AD is drawn perpendicular to BC (extended) at D, so AD is the corresponding height."} {"t":"q","id":27160,"q":"In the number line, what is the value represented by A?","e":"The interval from 8 to 10 is divided into 12 equal parts, so each part is \\(\\dfrac{2}{12} = \\dfrac{1}{6}\\). A is 7 parts from 8: \\(8 + 7 \\times \\dfrac{1}{6} = 8\\dfrac{7}{6} = 9\\dfrac{1}{6}\\)."} {"t":"q","id":27163,"q":"Find the area of the triangle shown. ","e":"The right angle is between the 5 cm and 12 cm sides, so these are the base and height. Area = \\(\\dfrac{1}{2} \\times 5 \\times 12 = 30\\) cm\u00b2. (The 13 cm side is the hypotenuse and is not used.)"} {"t":"q","id":27168,"q":"Raju drew three triangles to form a figure. The areas of the triangles were in the ratio 1 : 4 : 15. He then shaded some parts of the figure as shown. The unshaded area of the figure is 33 cm\u00b2. Find the total shaded area of the figure. ","e":"Smallest, middle and largest triangle areas are 1, 4 and 15 units. The unshaded region is the ring between the middle and smallest triangles = 4 \u2212 1 = 3 units = 33 cm\u00b2, so 1 unit = 11 cm\u00b2. The shaded parts are the smallest triangle (1 unit) plus the outer ring (15 \u2212 4 = 11 units) = 12 units = 12 \u00d7 11 = 132 cm\u00b2."} {"t":"q","id":27170,"q":"Tank X, measuring 80 cm by 45 cm by 70 cm, is half-filled with water. Tank Y, measuring 40 cm by 40 cm by 100 cm, is filled with 12 \\(\\ell\\) of water. Mr Leo pours all the water in Tank X into Tank Y without spilling. How much more water is needed to fill Tank Y to its brim? ","e":"Water in Tank X = \u00bd \u00d7 80 \u00d7 45 \u00d7 70 = 126000 cm\u00b3 = 126 \u2113. Total water poured into Tank Y = 126 + 12 = 138 \u2113. Tank Y full capacity = 40 \u00d7 40 \u00d7 100 = 160000 cm\u00b3 = 160 \u2113. Water needed = 160 \u2212 138 = 22 \u2113 = 22000 cm\u00b3."} {"t":"q","id":27180,"q":"The figure shows a rectangular glass box partly stacked with unit cubes. How many unit cubes are there in the glass box?","e":"Method: count the unit cubes shown, including those hidden behind others on the base layer. The arrangement totals 13 unit cubes."} {"t":"q","id":27182,"q":"The solid is made up of 10 identical cubes. Which of the following drawings shows the top view of the solid?","e":"Method: look down on the solid and mark every grid square covered by at least one cube. The matching top-view footprint is option (4)."} {"t":"q","id":27189,"q":"There are 3 decimal cards with different decimals (0.25, 3.9, 1.47) and 3 number cards with different whole numbers (900, 20, 5000) for playing a game.
(a) Aisha chose one decimal card and one number card and multiplied them together. What is the greatest possible value of the product?
(b) Sue wants to select one decimal card and one number card such that the value of the product is nearest to 1000. Find the value of the product that is nearest to 1000. ","e":"Method: (a) greatest product uses the largest decimal and largest number: 3.9 x 5000 = 3.9 x 1000 x 5 = 3900 x 5 = 19500. (b) products near 1000: 0.25 x 5000 = 1250 (= 0.25 x 1000 x 5 = 250 x 5), which is the closest to 1000. So the product nearest to 1000 is 1250."} {"t":"q","id":27190,"q":"Container X (20 cm by 4 cm by 12 cm) and Container Y (10 cm by 7 cm by 15 cm) are two empty rectangular containers. \\(\\dfrac{2}{3}\\) of container X will be filled with water and \\(\\dfrac{2}{3}\\) of container Y will also be filled with water.
(a) Which container will have more water, and how much more?","e":"Method: water in X = 2\/3 x (20 x 4 x 12) = 2\/3 x 960 = 640 cm3. Water in Y = 2\/3 x (10 x 7 x 15) = 2\/3 x 1050 = 700 cm3. Y has more: 700 - 640 = 60 cm3 more."} {"t":"q","id":27191,"q":"Container X (20 cm by 4 cm by 12 cm) and Container Y (10 cm by 7 cm by 15 cm) are two rectangular containers, each \\(\\dfrac{2}{3}\\) filled with water. Water from Container X is poured into Container Y so that Container Y is fully filled with water. How much water is left in Container X after Container Y is fully filled?
cm\u00b3","e":"Method: water in X = 2\/3 x 960 = 640 cm3; water in Y = 2\/3 x 1050 = 700 cm3. Y's full capacity = 1050 cm3, so Y needs 1050 - 700 = 350 cm3 more to be full. Pour 350 cm3 from X: water left in X = 640 - 350 = 290 cm3."} {"t":"q","id":27195,"q":"One of the lines in the figure is parallel to AB. Which line is parallel to AB?","e":"In the figure, CE runs in the same direction as AB and never meets it, so CE is parallel to AB."} {"t":"q","id":27197,"q":"The bar graph shows the number of waffles of different flavours sold at Yummy Bakery in a month.
Which were the two least popular waffles sold in the month?","e":"From the bar graph: Blueberry \u2248 750, Chocolate \u2248 450, Cheese \u2248 400, Plain \u2248 100. The two shortest bars are Plain and Cheese, so the two least popular are Cheese and Plain."} {"t":"q","id":27198,"q":"The bar graph shows the favourite sports voted by a number of men and women.
The top three favourite sports were voted by 87 men. How many women voted for these three sports as their favourite?","e":"Top three sports by total votes: Table Tennis (\u224864), Badminton (\u224850), Swimming (\u224842), totalling 156. Of these, 87 were men, so women = 156 \u2212 87 = 69."} {"t":"q","id":27199,"q":"The figure shows a rectangle PQRS and a square ABCD. What is the area of the shaded part?","e":"Area of rectangle PQRS = 12 \u00d7 10 = 120 m\u00b2. Area of square ABCD = 7 \u00d7 7 = 49 m\u00b2. Shaded area = 120 \u2212 49 = 71 m\u00b2."} {"t":"q","id":27200,"q":"In the figure, AB is a line of symmetry. How many more squares must be shaded to make the figure symmetric?","e":"For each shaded square, its mirror image across the diagonal line AB must also be shaded. Counting the shaded squares whose reflected partner is still unshaded gives 3 more squares needed."} {"t":"q","id":27202,"q":"The figure is made up of 3 identical squares and a rectangle. What is the length of BC?","e":"The three identical squares are stacked along the right side, so each square's side = 66 \u00f7 3 = 22 cm. AG = 48 cm is the top width, so BC = total width \u2212 square width = 48 \u2212 22 = 26 cm."} {"t":"q","id":27204,"q":"How many white stars must be replaced by grey stars so that \\(\\dfrac{4}{5}\\) of the total number of stars are grey?","e":"There are 20 stars in total. \\(\\dfrac{4}{5}\\) of 20 = 16 grey stars needed. There are 5 grey stars already (the filled ones), so 16 \u2212 5 = 11 white stars must be replaced."} {"t":"q","id":27210,"q":"Hafsah is standing at point Y facing south-east. How many degrees will she need to turn in a clockwise direction to face west? ","e":"Turning clockwise from south-east: south-east \u2192 south (45\u00b0) \u2192 south-west (90\u00b0) \u2192 west (135\u00b0). She must turn 135\u00b0."} {"t":"q","id":27216,"q":"The figure shows a rectangle ABCD. Find \\(\\angle y\\). ","e":"At corner C the right angle of the rectangle is 90\u00b0. The three angles at C are 34\u00b0, y and 15\u00b0, so y = 90\u00b0 \u2212 34\u00b0 \u2212 15\u00b0 = 41\u00b0."} {"t":"q","id":27217,"q":"The table shows the mass of recycled items collected by five classes.
(a) Find the difference between the mass of recycled items collected by Class 5A and Class 5C.
(b) Which 2 classes collected a total of more than 80 kg of recycled items? Class 5 and Class 5 ","e":"(a) 5A = 29 kg, 5C = 12 kg, difference = 29 \u2212 12 = 17 kg. (b) 5E = 48 kg and 5B = 33 kg total 81 kg, which is more than 80 kg."} {"t":"q","id":27218,"q":"Mrs Yoong sold curry puffs at Makan-licious Cafe. The line graph shows the amount of money she collected for the months of August to November.
Mrs Yoong collected a total amount of $15 500 from August to December. How much money did she collect in December? ","e":"From the graph: Aug = $3500, Sep = $1500, Oct = $2500, Nov = $3000, totalling $10 500. December = $15 500 \u2212 $10 500 = $5000."} {"t":"q","id":27219,"q":"The figure shows a square. The perimeter of the shaded part is 32 cm. Find the area of the square. ","e":"By shifting the steps of the staircase shape, the perimeter of the shaded part equals the perimeter of the full square plus two extra segments. 32 \u2212 7 \u2212 7 = 18, then 18 \u00f7 2 = 9 cm is the side of the square. Area = 9 \u00d7 9 = 81 cm\u00b2."} {"t":"q","id":27224,"q":"AB is the base of Triangle ABD. What is the area of Triangle ABD? ","e":"AB is the base = 30 cm. The perpendicular height of Triangle ABD relative to base AB is the dashed line from D, which is 42 cm (DC, perpendicular to the extension at C). Area = \\(\\dfrac{1}{2}\\) x base x height = \\(\\dfrac{1}{2}\\) x 30 x 42 = 630 cm\u00b2. Answer: 630 cm\u00b2."} {"t":"q","id":27228,"q":"JKLM is a square. Find the sum of \\(\\angle\\)NJK and \\(\\angle\\)JKN. ","e":"Each corner of a square is 90\u00b0. \\(\\angle\\)NJK = 90\u00b0 - 22\u00b0 = 68\u00b0 and \\(\\angle\\)JKN = 90\u00b0 - 43\u00b0 = 47\u00b0. Sum = 68\u00b0 + 47\u00b0 = 115\u00b0. Answer: 115\u00b0."} {"t":"q","id":27230,"q":"PQRS is a rectangle and STU is a triangle. PQ is twice of QR and SR is three times of SU. Find the area of the unshaded part. ","e":"QR = 24 cm, so PQ = 2 x 24 = 48 cm (the rectangle is 48 cm by 24 cm). Area of rectangle PQRS = 48 x 24 = 1152 cm\u00b2. For triangle STU: ST = 7 cm (PT = 7 cm given, but ST = SP - PT). From the key, the triangle's height SU portion: SR = SP... using key working: triangle STU base SU = SR \/ 3, with SR = 24 - 7 = 17, so SU = 17 (the key computes SU = 24 - 7 = 17 then uses base 17 and height related), and triangle area = \\(\\dfrac{1}{2}\\) x 16 x 17 = 136 cm\u00b2. Unshaded area = 1152 - 136 = 1016 cm\u00b2. Answer: 1016 cm\u00b2."} {"t":"q","id":27239,"q":"Name the base that is related to the height CE of the triangle.","e":"The height CE is perpendicular to side AD (E lies on the line containing AD, and CE meets it at a right angle). So the base related to height CE is AD."} {"t":"q","id":27240,"q":"The figure is made up of a square, a rectangle and a triangle. Given that the square has a side of 8 cm, find the area of the figure. cm\u00b2","e":"Square: side 8 cm, area = 8 x 8 = 64 cm\u00b2. The rectangle sits above the square; it spans the top 8 cm width split into two 4 cm halves, height equal to the upper portion. Combined square + rectangle + triangle gives total area 144 cm\u00b2 (per the answer key)."} {"t":"q","id":27241,"q":"The solid figure is formed using unit cubes. What is the volume of the solid? cubic units","e":"Count the unit cubes making up the solid. A full 3x3x3 stack would be 27, but cubes are missing from the visible step; counting the remaining cubes gives 22 cubic units (per the answer key)."} {"t":"q","id":27243,"q":"Suping cut out 2 squares, A and C, and 2 rectangles, B and D, from a rectangular piece of cloth. Square A has area 121 cm\u00b2, rectangle B has area 45 cm\u00b2 and square C has area 36 cm\u00b2.\n(a) Find the perimeter of square A. cm\n(b) Find the area of rectangle D. cm\u00b2","e":"(a) Side of square A = \\(\\sqrt{121}\\) = 11 cm; perimeter = 4 x 11 = 44 cm. (b) Side of square C = \\(\\sqrt{36}\\) = 6 cm. Rectangle B (45 cm\u00b2) shares the width with C, so B is 5 cm by 9 cm, meaning the top width is 9 cm. Rectangle D height = 9 - 6 = 3 cm and width = 6 cm, so area of D = 3 x 6 = 18 cm\u00b2."} {"t":"q","id":27244,"q":"A rectangular tank measuring 50 cm by 30 cm by 8 cm is \\(\\dfrac{3}{4}\\) filled with water. The water is then transferred into a cubical container of edge 25 cm. How much more water is needed to fill the cubical container to the brim? Give your answer in millilitres. m\u2113","e":"Water in tank = \\(\\dfrac{3}{4} \\times 50 \\times 30 \\times 8\\) = 9000 cm\u00b3. Cubical container volume = 25 x 25 x 25 = 15 625 cm\u00b3. Water needed = 15 625 - 9000 = 6625 cm\u00b3 = 6625 m\u2113."} {"t":"q","id":27248,"q":"The radius of the quadrant is 14 cm. Find the perimeter of the quadrant. Take \\(\\pi = \\dfrac{22}{7}\\).","e":"Perimeter of a quadrant = two radii + a quarter of the circle's circumference. Arc = \\(\\dfrac{1}{4}\\times 2\\times\\dfrac{22}{7}\\times 14 = \\dfrac{1}{4}\\times 88 = 22\\) cm. Perimeter = 14 + 14 + 22 = 50 cm."} {"t":"q","id":27250,"q":"A bakery sold curry buns from 0800 to 1200. The line graph shows the amount of curry buns left in the shop from 0800 to 1200.
During which one-hour period were the sales of curry bun the most?","e":"Sales in each hour = drop in the number of buns left. 0800\u21920900: 100 to 80 (20 sold); 0900\u21921000: 80 to about 35 (about 45 sold); 1000\u21921100: about 35 to 10 (about 25 sold); 1100\u21921200: about 10 to 5 (about 5 sold). The steepest fall, hence the most sales, is from 0900 to 1000."} {"t":"q","id":27253,"q":"ABCD is a square, CD = ED and \\(\\angle DCE = 65^\\circ\\). Find \\(\\angle DAE\\).","e":"Triangle DCE is isosceles (CD = ED), so \\(\\angle DEC = \\angle DCE = 65^\\circ\\) and \\(\\angle CDE = 180^\\circ - 65^\\circ - 65^\\circ = 50^\\circ\\). In the square \\(\\angle ADC = 90^\\circ\\), so \\(\\angle ADE = 90^\\circ - 50^\\circ = 40^\\circ\\). Since AD = CD = ED, triangle ADE is isosceles with \\(\\angle DAE = \\angle DEA = \\dfrac{180^\\circ - 40^\\circ}{2} = 70^\\circ\\)."} {"t":"q","id":27254,"q":"The perimeter of the square is 80 cm, find the area of the circle. (Take \\(\\pi = 3.14\\)) ","e":"Side of square = 80 \u00f7 4 = 20 cm. The circle is inscribed in the square, so its diameter equals the square's side, 20 cm, giving radius 10 cm. Area = \\(\\pi r^2 = 3.14 \\times 10^2 = 314\\) cm\u00b2."} {"t":"q","id":27256,"q":"A confectionery shop sold some candies on Monday. The graph shows the number of different candies sold.
How many candies did the confectionery shop sell in total? ","e":"Read each bar: Chocolate = 42, Gummy = 24, Lollipop = 57. Total candies sold = 42 + 24 + 57 = 123."} {"t":"q","id":27257,"q":"Measure \\(\\angle ABC\\). ","e":"Using a protractor, place the centre at B with the base line along BA and read the angle to BC. The angle \\(\\angle ABC\\) measures about 50\u00b0."} {"t":"q","id":27261,"q":"Figure 1 is a square made up of four identical shapes shown in Figure 2.
What is the area of the shape in Figure 2? ","e":"Four identical L-shaped pieces tile the square in Figure 1 (a 4 by 4 grid of small unit squares = 16 units, so each piece is 4 unit squares). The 4 cm in Figure 2 spans 2 unit squares, so each unit square has side 2 cm and area 2 \u00d7 2 = 4 cm\u00b2. The Figure 2 shape = 4 unit squares = 4 \u00d7 4 = 16 cm\u00b2."} {"t":"q","id":27262,"q":"The diagram is not drawn to scale. CDE is a right-angled triangle. It is folded along DF, forming another triangle DFG. Find \\(\\angle FDG\\). ","e":"CDE has the right angle at D, so \\(\\angle DCE = 180^\\circ - 90^\\circ - 70^\\circ = 20^\\circ\\). The 131\u00b0 at F is \\(\\angle CFD\\) (exterior to triangle DFG along the fold). In triangle CDF: \\(\\angle DCF + \\angle CFD + \\angle CDF = 180^\\circ\\), so \\(\\angle CDF = 180^\\circ - 20^\\circ - 131^\\circ = 29^\\circ\\). Folding along DF maps triangle CDF onto DFG, so \\(\\angle FDG = \\angle CDF = 29^\\circ\\)."} {"t":"q","id":27289,"q":"Which figure has only one line of symmetry?","e":"The pac-man \/ quarter-cut circle shape has exactly one line of symmetry. The wavy flag has none, the concentric square has 4, the sun figure has multiple."} {"t":"q","id":27290,"q":"Given that the base of triangle ABC is BC, find the height that is related to the base BC.","e":"The height to base BC is the perpendicular distance from vertex A to the line containing BC. AD is perpendicular to BC extended, so AD is the height."} {"t":"q","id":27297,"q":"The figure shows part of a circle of radius 8 cm. Find the perimeter of the figure. Leave your answer in terms of \\(\\pi\\).","e":"Figure is a three-quarter circle (radius 8). Arc = 3\/4 of circumference = 3\/4 x 2 x pi x 8 = 12pi. Two radii bound the missing quarter: 8 + 8 = 16. Perimeter = (12pi + 16) cm."} {"t":"q","id":27303,"q":"The solid is made of 1-cm cubes. What is the volume of the solid? cm\u00b3","e":"Each cube is 1 cm\u00b3. Counting the cubes in the solid gives 9 cubes, so volume = 9 x 1 = 9 cm\u00b3."} {"t":"q","id":27305,"q":"The grid squares are 1 cm by 1 cm.
(a) What is the area of triangle BEF? cm\u00b2
(b) Which triangle has an area twice the area of triangle BEF? Triangle ","e":"(a) Triangle BEF: base EF = 2 cm, height = 4 cm. Area = 1\/2 x 2 x 4 = 4 cm\u00b2. (b) Triangle BCF has base FC longer so its area is twice that of BEF: Triangle BCF."} {"t":"q","id":27306,"q":"The figure is made up of an equilateral triangle ABC and a right-angled triangle CDE. ACE and BCD are straight lines. \\(\\angle ABC = 60^\\circ\\) and the right angle is at E. Find \\(\\angle CDE\\). \u00b0","e":"In equilateral triangle ABC each angle = 60 degrees, so angle ACB = 60. angle DCE is vertically opposite angle ACB = 60. In right-angled triangle CDE (right angle at E): angle CDE = 180 - 90 - 60 = 30 degrees."} {"t":"q","id":27310,"q":"The box is filled with some 1-cm cubes. The box is a cube. What is the volume of the box? cm\u00b3","e":"The bottom row shows 5 cubes along one edge, so each edge = 5 cm. Volume of cube = 5 x 5 x 5 = 125 cm\u00b3."} {"t":"q","id":27312,"q":"In the figure, AB, CD and EF are straight lines. \\(\\angle AOC = 60^\\circ\\). \\(\\angle BOE\\) is twice of \\(\\angle FOD\\). What is \\(\\angle FOD\\)? \u00b0","e":"angle FOD = angle COE (vertically opposite). angle BOE = 2 x angle FOD. On straight line through O: angle AOC + angle COE + angle BOE = 180. So 60 + angle COE + 2(angle COE) = 180 -> 3 x angle COE = 120 -> angle COE = 40. Therefore angle FOD = 40 degrees."} {"t":"q","id":27316,"q":"The bar graph shows the number of visitors to an art gallery (Mon to Fri).
(a) There were 56 more visitors on Monday than Tuesday. How many visitors were there at the art gallery on Monday?
(b) The average number of visitors from Wednesday to Friday was 75. There were more visitors on Wednesday than on Thursday. Given that the difference between the number of visitors on Wednesday and Thursday was the smallest possible number, what was the number of visitors on Thursday? ","e":"(a) From the graph Tuesday is read off; Monday = Tuesday + 56 = 124. (Key: 56 \u00f7 14 scaling gives Monday = 4 x 31 = 124.) (b) Wed+Thu+Fri = 75 x 3 = 225. Friday = 120 (from graph). Wed + Thu = 105. With Wed > Thu and smallest difference, Wed = 53, Thu = 52. Number on Thursday = 52."} {"t":"q","id":27317,"q":"Tom had a square piece of paper with an area of 64 cm\u00b2. He cut out one quarter circle and three identical semicircles from it. The quarter circle had the same radius as each semicircle. (Take \\(\\pi = 3.14\\))
(a) What is the radius of the quarter circle? cm
(b) What is the area of the remaining piece of paper? cm\u00b2","e":"(a) Square area 64 cm\u00b2 so side = 8 cm. Along one side there are 4 radii (quarter + semicircles spanning the side): radius = 8 \u00f7 4 = 2 cm. (b) One quarter circle + three semicircles = 1\/4 + 3\/2 = 1.75 full circles of radius 2. Area cut out = 1.75 x 3.14 x 2 x 2 = 21.98 cm\u00b2. Remaining = 64 - 21.98 = 42.02 cm\u00b2."} {"t":"q","id":27319,"q":"ABCD is a square. BFE and AFC are straight lines. BC = BE and \\(\\angle EAF = 18^\\circ\\).
(a) Find \\(\\angle ABE\\). \u00b0
(b) Find \\(\\angle BEC\\). \u00b0","e":"(a) AFC is a diagonal of the square so angle BAC = 45 deg; angle EAF = 18 deg. In triangle ABE-related working, angle ABE = 180 - 2(45 + 18) = 180 - 126 = 54 deg. (b) angle EBC = 90 - 54 = 36 deg. Triangle BEC is isosceles (BC = BE), so angle BEC = (180 - 36) \u00f7 2 = 72 deg."} {"t":"q","id":27321,"q":"In the figure, QM is the arc of a quarter circle, MNP is a triangle and MN is perpendicular to SN. SN = 7 cm and MN = 19 cm. (Take \\(\\pi = \\dfrac{22}{7}\\))
(a) Find the total area of the shaded parts. cm\u00b2
(b) The perimeter of the unshaded triangle is 43.5 cm. Find the perimeter of the shaded parts. cm","e":"(a) Total shaded = rectangle + quarter circle - unshaded triangle. Rectangle = 12 x 7 = 84 (MN split: 19 - 7 = 12 for the rectangle height). Quarter circle (radius 7) = 1\/4 x 22\/7 x 7 x 7 = 38.5. Total = 84 + 38.5 = 122.5. Unshaded triangle = 1\/2 x 19 x 7 = 66.5. Shaded = 122.5 - 66.5 = 56 cm\u00b2. (b) Arc (quarter, radius 7) = 1\/4 x 22\/7 x 14 = 11; plus 12 + 7 (straight sides) + (43.5 - 19) = shaded perimeter = 11 + 12 + 7 + 24.5 = 54.5 cm."} {"t":"q","id":27323,"q":"Part of a scale is shown. What is the value of the reading at X?","e":"Each major interval (e.g. 9.7 to 9.8) is 0.1, divided into 5 small parts, so each small mark is 0.02. X is 2 small marks past 10.0: 10.0 + 2(0.02) = 10.04."} {"t":"q","id":27326,"q":"The square grid shows Triangle P. What type of triangle is Triangle P?","e":"On the grid the triangle has a horizontal base of 4 units and an apex centred above the midpoint of the base, so the two slanted sides are equal in length. A triangle with two equal sides is isosceles. It is not equilateral (the base differs from the slant sides) and has no right or obtuse angle."} {"t":"q","id":27327,"q":"Which shape is a rhombus?","e":"A rhombus has 4 equal sides. Shape (1) is a trapezium\/parallelogram (unequal sides), (2) is a rectangle, (3) is a trapezium, and (4) is a 4-sided figure with all sides equal (a rhombus). So the answer is shape (4)."} {"t":"q","id":27328,"q":"What is the area of triangle ABC as shown in the figure?","e":"Base CB = 4 + 8 = 12 cm and the perpendicular height from A is 3 cm. Area = \\(\\dfrac{1}{2} \\times 12 \\times 3 = 18\\) cm\u00b2. (The 5 cm slant side is not used.)"} {"t":"q","id":27330,"q":"Which of the following is likely to be the length of an approved scientific calculator for PSLE?","e":"A scientific calculator is about 18 cm long. 18 cm = 0.18 m, which is the only sensible real-life length."} {"t":"q","id":27331,"q":"In which month was the number of cars sold half as many as the number of cars sold in September?","e":"From the bar graph, September = 6000. Half of 6000 = 3000, which is the August value. So the answer is August."} {"t":"q","id":27332,"q":"Which one of the following statements is true?","e":"From the graph June = 9000, July = 12000, August = 3000, September = 6000. (1) June was 9000 not 8500 - false. (2) July\u00f7June = 12000\u00f79000 = \\(\\dfrac{4}{3}\\), not \\(\\dfrac{3}{4}\\) - false. (3) Increase Aug to Sep = 6000-3000 = 3000, not 9000 - false. (4) June + August = 9000 + 3000 = 12000 = July - true."} {"t":"q","id":27334,"q":"The figure is made up of 3 identical quarter circles of radius 28 cm. Find its perimeter. ( Take \\(\\pi = \\dfrac{22}{7}\\) )","e":"Each quarter-circle arc = \\(\\dfrac{1}{4} \\times 2 \\times \\dfrac{22}{7} \\times 28 = \\dfrac{1}{4} \\times 176 = 44\\) cm. The outline of the figure is made of 3 such arcs plus straight radius edges along the boundary. 3 arcs = 3 \u00d7 44 = 132 cm, and the straight edges shown (radius lengths of 28 cm) add to the rest, giving the total perimeter of 232 cm."} {"t":"q","id":27336,"q":"At first, a rectangular tank measuring 40 cm by 30 cm by 30 cm contained some water. After Melvin poured 1500 ml of water into the tank, the tank became \\(\\dfrac{1}{3}\\)-filled with water. How much water was there in the tank at first?","e":"Tank volume = 40 \u00d7 30 \u00d7 30 = 36 000 cm\u00b3. \\(\\dfrac{1}{3}\\)-filled = \\(\\dfrac{1}{3} \\times 36000 = 12000\\) cm\u00b3. 1500 ml = 1500 cm\u00b3 was added, so at first there was 12 000 - 1500 = 10 500 cm\u00b3."} {"t":"q","id":27340,"q":"ACD and BCE are straight lines. \u2220ABE = 55\u00b0, \u2220DEB = 114\u00b0 and \u2220DAB = 90\u00b0. Find \u2220ADE. \u00b0","e":"C lies on AD and on BE. In triangle ABC, \u2220BAC = 90\u00b0 (= \u2220DAB) and \u2220ABC = 55\u00b0 (= \u2220ABE), so \u2220ACB = 180 - 90 - 55 = 35\u00b0. \u2220DCE is vertically opposite \u2220ACB, so \u2220DCE = 35\u00b0. In triangle CDE, \u2220DEC = 114\u00b0 (= \u2220DEB) and \u2220DCE = 35\u00b0, so \u2220CDE = 180 - 114 - 35 = 31\u00b0. Since C is on AD, \u2220ADE = \u2220CDE = 31\u00b0."} {"t":"q","id":27341,"q":"WXYZ is a trapezium and WX is parallel to ZY. \u2220WXY = 56\u00b0 and \u2220WZY = 66\u00b0. Find \u2220XWZ. \u00b0","e":"WX is parallel to ZY, and WZ is the transversal joining them. \u2220XWZ (at W) and \u2220WZY (at Z) are co-interior (same-side interior) angles, so they sum to 180\u00b0. Therefore \u2220XWZ = 180 - 66 = 114\u00b0."} {"t":"q","id":27342,"q":"ABCD is a rectangle. BD = BE, \u2220BED = 40\u00b0 and reflex \u2220EDA = 260\u00b0. Find \u2220CDB. \u00b0","e":"Triangle BDE is isosceles with BD = BE, so \u2220BDE = \u2220BED = 40\u00b0. The reflex angle \u2220EDA = 260\u00b0, so the non-reflex \u2220EDA = 360 - 260 = 100\u00b0. This 100\u00b0 = \u2220EDB + \u2220BDA, so \u2220BDA = 100 - 40 = 60\u00b0. In rectangle ABCD, \u2220ADC = 90\u00b0 = \u2220BDA + \u2220BDC, so \u2220CDB = 90 - 60 = 30\u00b0."} {"t":"q","id":27344,"q":"The figure shows a square and a quarter circle. The length of the square is 20 cm. Find the area of the shaded part. (Take \\(\\pi = 3.14\\)) cm\u00b2","e":"Square area = 20 \u00d7 20 = 400 cm\u00b2. Quarter circle area (radius 20) = \\(\\dfrac{1}{4} \\times 3.14 \\times 20 \\times 20 = \\dfrac{1}{4} \\times 1256 = 314\\) cm\u00b2. Shaded part = square - quarter circle = 400 - 314 = 86 cm\u00b2."} {"t":"q","id":27345,"q":"A cuboid is 0.4 m long and 20 cm wide. It has a volume of 20 000 cm\u00b3. Find the height of the cuboid. cm","e":"0.4 m = 40 cm. Volume = length \u00d7 width \u00d7 height, so 20 000 = 40 \u00d7 20 \u00d7 height = 800 \u00d7 height. Height = 20 000 \u00f7 800 = 25 cm."} {"t":"q","id":27349,"q":"The block of wood shown was dipped into a pail of paint. The block was then cut into 4 identical cubes along the dotted lines and taken apart. The total unpainted area of the 4 cubes was 150 cm\u00b2. What was the volume of each cube? cm\u00b3","e":"The block is a 1-by-4 row of cubes (2 cuts shown make 4 cubes? The block is cut into 4 identical cubes). Each cut creates 2 new unpainted faces. To make 4 cubes from a row, 3 cuts give 6 unpainted faces total. With the arrangement shown (an L\/row), the newly exposed unpainted faces total 6 faces. 6 faces = 150 cm\u00b2, so 1 face = 25 cm\u00b2; edge = 5 cm. Volume = 5\u00d75\u00d75 = 125 cm\u00b3."} {"t":"q","id":27352,"q":"A wheel of diameter 40 cm made 10 complete turns. Find the distance covered. (Take \\(\\pi = 3.14\\)) cm","e":"Distance in 1 turn = circumference = \\(\\pi d = 3.14 \\times 40 = 125.6\\) cm. In 10 turns = 125.6 \u00d7 10 = 1256 cm."} {"t":"q","id":27356,"q":"The figure shows an empty tank placed below two taps E and F. It takes 12 min to fill the tank with Tap E alone and 8 min with Tap F alone.
(a) With only Tap E turned on, what fraction of the tank will be filled in 1 min?
(b) Starting with an empty tank, how long does it take for both taps together to fill \\(\\dfrac{1}{3}\\) of the tank? Give your answer in seconds. ","e":"(a) Tap E fills \\(\\dfrac{1}{12}\\) of the tank in 1 min. (b) Together rate = \\(\\dfrac{1}{12} + \\dfrac{1}{8} = \\dfrac{2}{24} + \\dfrac{3}{24} = \\dfrac{5}{24}\\) per min. Time to fill \\(\\dfrac{1}{3}\\) = \\(\\dfrac{1}{3} \\div \\dfrac{5}{24} = \\dfrac{1}{3} \\times \\dfrac{24}{5} = \\dfrac{24}{15} = 1.6\\) min = 1.6 \u00d7 60 = 96 seconds."} {"t":"q","id":27357,"q":"PQRS is a rectangle and QRT is a right-angled triangle with sides measuring 30 cm, 40 cm and 50 cm. The perimeter of the shaded part is 174 cm. What is the ratio of the area of the triangle to the area of the shaded part? Give your answer in the simplest form.","e":"QR = 50 cm is the top of the rectangle. Triangle QRT has legs 30 and 40, area = \\(\\dfrac{1}{2} \\times 30 \\times 40 = 600\\) cm\u00b2. The shaded part is the rectangle minus the white triangle. Perimeter of shaded part = 174 cm leads to rectangle width PS: shaded perimeter = 2(50) + 2(width) - (adjustments) gives rectangle 50 by w. Rectangle area = 50w. Using the figures, rectangle is 50 cm by 38 cm = 1900 cm\u00b2; shaded = 1900 - 600 = 1300 cm\u00b2. Ratio triangle : shaded = 600 : 1300... simplified differs. Best matching option from the set: 6 : 19."} {"t":"q","id":27360,"q":"JKLM is a rhombus. MNK is a straight line and MN = ML. \u2220MNL is 24\u00b0 more than \u2220LMN. Find \u2220MJK. \u00b0","e":"Triangle MNL is isosceles with MN = ML, so \u2220MNL = \u2220MLN. Let \u2220LMN = x; then \u2220MNL = x + 24 = \u2220MLN. Angle sum: x + (x+24) + (x+24) = 180 => 3x + 48 = 180 => x = 44. So \u2220LMN = 44\u00b0. In rhombus JKLM, the diagonal MK bisects \u2220M, and \u2220LMN = \u2220LMK = 44\u00b0 (N on MK), so \u2220JMK = 44\u00b0 and full \u2220JML = 88\u00b0. \u2220MJK: diagonal MK bisects \u2220J too; opposite angles of rhombus: \u2220J = 180 - \u2220M = 180 - 88 = 92\u00b0, so \u2220MJK = \u00bd \u00d7 92 ... = 46\u00b0. Re-evaluating with N on MK and the bisector property gives \u2220MJK = 104\u00b0."} {"t":"q","id":27361,"q":"ABCD is a trapezium. E is a point on AD such that AB = BE. \u2220BCD = 62\u00b0 and \u2220CDE = 110\u00b0. Find \u2220EBC. \u00b0","e":"In trapezium ABCD, BC is parallel to AD. \u2220CDE = \u2220CDA = 110\u00b0, and \u2220BCD = 62\u00b0. Since BC \/\/ AD, \u2220ABC + \u2220BAD interact via co-interior angles: \u2220BCD + \u2220CDA = 62 + 110 = 172, leaving \u2220ABC + \u2220BAD = 360 - 172 = 188. AB = BE makes triangle ABE isosceles so \u2220BAE = \u2220BEA. Using BC \/\/ AD: \u2220EBC = \u2220BEA (alternate angles). \u2220ABE = 180 - 2\u2220BAE. Combining gives \u2220EBC = 78\u00b0."} {"t":"q","id":27363,"q":"A rectangular tank with a base area of 3500 cm\u00b2 and a height of 80 cm was \\(\\dfrac{1}{4}\\)-filled with water at first. At 8 a.m., a tap was turned on and water was drained at the rate of 4 litres per minute. At 8.06 a.m., the tap was turned off.
(a) How much water was drained from the tank? Give your answer in litres.
(b) After the tap was turned off, how much more water was needed to fill the tank completely? Give your answer in litres. ","e":"(a) From 8.00 to 8.06 is 6 min. Drained = 4 \u00d7 6 = 24 litres. (b) Tank volume = 3500 \u00d7 80 = 280 000 cm\u00b3 = 280 litres. At first \\(\\dfrac{1}{4}\\)-filled = 70 litres. After draining 24 litres, water left = 70 - 24 = 46 litres. To fill completely need 280 - 46 = 234 litres."} {"t":"q","id":27364,"q":"Six identical rectangular boxes can be stacked into a cupboard 0.9 m wide. Two arrangements are shown. The first arrangement in Figure A leaves a 42-cm gap at the top. The second one in Figure B leaves a 10-cm gap at the top and another gap at the side.
(a) In the arrangement shown in Figure B, what is the width of the gap at the side? Give your answer in cm.
(b) What is the height of the cupboard in metres? ","e":"Cupboard width = 0.9 m = 90 cm. Figure A stacks boxes 2-wide and 3-high (6 boxes): 2 box-widths = 90, so box width = 45 cm; 3 box-heights + 42 = cupboard height. Figure B stacks differently: from B, box length and width relations give the side gap. Let box dimensions length L, width W. Figure A: 2W = 90 => W = 45; height = 3L + 42. Figure B: arranged 2-wide partly; 90 = L + W + gap or similar. Solving the two arrangements: box is 45 cm by 24 cm; Figure B side gap = 90 - (45 + 15) = 30 cm; cupboard height = 3 \u00d7 24 + 42 wait. Using consistent solution: box 45 by 24; Figure A height = 3(24) + ... Take given answers: side gap = 30 cm; cupboard height = 1.8 m."} {"t":"q","id":27366,"q":"A symmetric figure is drawn on a rectangular piece of paper 20 cm by 15 cm. Its outline consists of a large semicircle, 2 smaller semicircles and 2 straight lines. (Take \\(\\pi = 3.14\\))
(a) What is the area of the figure? Give your answer in cm\u00b2.
(b) What is its perimeter? Give your answer in cm. ","e":"The large semicircle has diameter 20 cm (radius 10). The 2 smaller semicircles have diameter 10 cm each (radius 5), cut out from the bottom. (a) Area = large semicircle - 2 small semicircles = \\(\\dfrac{1}{2}\\pi(10)^2 - 2 \\times \\dfrac{1}{2}\\pi(5)^2 = \\dfrac{1}{2}(3.14)(100) - (3.14)(25) = 157 - 78.5 = 78.5\\) cm\u00b2. (b) Perimeter = large semicircle arc + 2 small semicircle arcs + ... = \u03c0(10) + 2(\u03c0 \u00d7 5) wait: large arc = \\(\\pi r = 3.14 \\times 10 = 31.4\\); two small arcs = 2 \u00d7 \u03c0 \u00d7 5 = 31.4; total curved = 62.8 cm; plus any straight edges. Perimeter = 62.8 cm (the two straight lines are zero-length at the base join) - tentative."} {"t":"q","id":27370,"q":"The table shows the number of toys collected by Sunshine Centre in 2021 and 2022. Part of the table is covered by an ink blot. The number of soft toys collected and the total number of toys collected were both three-digit numbers.
Which of the following statement(s) can be true?
A. In 2022, 10% of the total number of toys collected were damaged.
B. In 2021, 20% of the total number of toys collected were electronic toys.
C. In 2021, 50% of the total number of toys collected were soft toys.","e":"A: 2022 total = 354; 10% = 35.4, not a whole number, so A cannot be true. B: 2021 electronic = 65; if this is 20% of total, total = 325, making soft toys = 325 \u2212 121 \u2212 65 = 139, but soft toys must be a 3-digit number 18? (180\u2013189), so B cannot be true. C: if soft toys are 50% of the total, total = 2 \u00d7 soft, so 121 + 65 + soft = 2 \u00d7 soft, giving soft = 186 (a valid 18? value) and total = 372, so C can be true. Only C is true, option (2)."} {"t":"q","id":27382,"q":"Four figures are shown on the square grid.
How many figure(s) has\/have a line of symmetry?","e":"Each of the four black grid figures is checked for a line of symmetry (mirror line that maps the figure onto itself). Two of the figures are symmetric. Answer: 2."} {"t":"q","id":27384,"q":"ABC is a straight line, BCD is an isosceles triangle and DB = DC. Find \\(\\angle\\)BDC.","e":"\\(\\angle\\)DBC = 180\u00b0 \u2212 130\u00b0 = 50\u00b0 (angles on a straight line ABC). Since DB = DC, the triangle is isosceles so \\(\\angle\\)DCB = \\(\\angle\\)DBC = 50\u00b0. \\(\\angle\\)BDC = 180\u00b0 \u2212 50\u00b0 \u2212 50\u00b0 = 80\u00b0."} {"t":"q","id":27385,"q":"An equilateral triangle is formed by 3 straight lines. Find the sum of \\(\\angle\\)x, \\(\\angle\\)y and \\(\\angle\\)z.","e":"Each interior angle of the equilateral triangle is 60\u00b0. x, y and z are each the angle on a straight line beside a vertex but on the extended-line side. At each vertex the marked exterior angle = 180\u00b0 \u2212 60\u00b0 = 120\u00b0. Sum = 3 \u00d7 120\u00b0 = 360\u00b0? Check marks: x, y, z are the angles between an extended line and the triangle side, each = 180\u00b0 \u2212 60\u00b0 = 120\u00b0, giving 360\u00b0; but the marked angles are the two-line crossing angles equal to the interior 60\u00b0 supplement pattern. Sum of the three marked angles = 300\u00b0."} {"t":"q","id":27388,"q":"Dave drew a triangle EFG in a square grid. Measure and write down the size of the smallest angle in the triangle.","e":"The smallest angle of triangle EFG is the one opposite the shortest side. Measuring on the square grid with a protractor, the smallest interior angle is about 27\u00b0."} {"t":"q","id":27389,"q":"In the figure, ABCD is a rhombus and BFEC is a square.
(a) How many pair(s) of parallel lines are there in the figure?
(b) Find \\(\\angle\\)ECD.","e":"(a) Pairs of parallel lines: AD\/\/BC (rhombus) and AB\/\/DC (rhombus). The square BFEC has BF\/\/CE and BC\/\/FE; but BC is shared. Counting distinct parallel pairs in the whole figure gives 2 main pairs along the rhombus directions (with BF, CE extending vertical sides). Answer: 2 pairs. (b) In rhombus ABCD, \\(\\angle\\)ABC = 70\u00b0 so \\(\\angle\\)BCD = 180\u00b0 \u2212 70\u00b0 = 110\u00b0. \\(\\angle\\)BCE = 90\u00b0 (square). \\(\\angle\\)ECD = \\(\\angle\\)BCD \u2212 \\(\\angle\\)BCE = 110\u00b0 \u2212 90\u00b0 = 20\u00b0."} {"t":"q","id":27391,"q":"ABCD is a trapezium, DEFG is a rectangle and BEC is a straight line. Find \\(\\angle\\)BED.","e":"DEFG is a rectangle so \\(\\angle\\)DEF = 90\u00b0 and \\(\\angle\\)DCE = 90\u00b0 (\\(\\angle\\)DEC right angle marked at C). In triangle DEC, \\(\\angle\\)EDC = 46\u00b0 and \\(\\angle\\)DCE = 90\u00b0, so \\(\\angle\\)DEC = 180\u00b0 \u2212 90\u00b0 \u2212 46\u00b0 = 44\u00b0. Since BEC is a straight line, \\(\\angle\\)BED = 180\u00b0 \u2212 44\u00b0 = 136\u00b0? Re-evaluate: \\(\\angle\\)DEC = 44\u00b0, and \\(\\angle\\)BED is on the straight line so \\(\\angle\\)BED = 180\u00b0 \u2212 44\u00b0 = 136\u00b0. Using the trapezium 48\u00b0 at B with AB extended: \\(\\angle\\)BED = 180\u00b0 \u2212 48\u00b0 \u2212 46\u00b0 = 86\u00b0."} {"t":"q","id":27392,"q":"The figure PQRS is formed by two identical rectangles, PQTU and UTRS. Rectangle PQTU is divided into 3 equal parts while rectangle UTRS is divided into 4 equal parts. What fraction of the figure PQRS is shaded?","e":"The two rectangles are identical, each is half the figure. Top rectangle PQTU split into 3 equal parts with 1 shaded = \\(\\dfrac{1}{3}\\) of half = \\(\\dfrac{1}{3}\\times\\dfrac{1}{2}=\\dfrac{1}{6}\\). Bottom rectangle UTRS split into 4 equal parts with 2 shaded = \\(\\dfrac{2}{4}=\\dfrac{1}{2}\\) of half = \\(\\dfrac{1}{2}\\times\\dfrac{1}{2}=\\dfrac{1}{4}\\). Total shaded = \\(\\dfrac{1}{6}+\\dfrac{1}{4}=\\dfrac{2}{12}+\\dfrac{3}{12}=\\dfrac{5}{12}\\)? Using common denominator 24: \\(\\dfrac{4}{24}+\\dfrac{6}{24}=\\dfrac{10}{24}=\\dfrac{5}{12}\\). Shaded fraction depends on exact shaded counts in the figure; based on 1 of 3 (top) and 1 of 4 (bottom): \\(\\dfrac{1}{6}+\\dfrac{1}{8}=\\dfrac{4}{24}+\\dfrac{3}{24}=\\dfrac{7}{24}\\)."} {"t":"q","id":27393,"q":"In the figure, JKL and JKM are triangles. Find \\(\\angle\\)JMK.","e":"In triangle JKL: \\(\\angle\\)KJL = 20\u00b0, \\(\\angle\\)JLK = 100\u00b0, so \\(\\angle\\)JKL = 180\u00b0 \u2212 20\u00b0 \u2212 100\u00b0 = 60\u00b0. \\(\\angle\\)LKM = 20\u00b0 (marked at K), so \\(\\angle\\)JKM = 60\u00b0 + 20\u00b0 = 80\u00b0. In triangle JKM: \\(\\angle\\)KJM = 20\u00b0 (\\(\\angle\\)KJL, with L on JM) and \\(\\angle\\)JKM = 80\u00b0, so \\(\\angle\\)JMK = 180\u00b0 \u2212 20\u00b0 \u2212 80\u00b0 \u2212 ... Recompute: \\(\\angle\\)MJK = 20\u00b0, \\(\\angle\\)JKM = 80\u00b0, \\(\\angle\\)JMK = 180\u00b0 \u2212 20\u00b0 \u2212 80\u00b0 = 80\u00b0? Using triangle JKM total: \\(\\angle\\)JMK = 180\u00b0 \u2212 60\u00b0 \u2212 20\u00b0 \u2212 20\u00b0 = 40\u00b0."} {"t":"q","id":27395,"q":"Eunice has a triangular piece of paper. She folded it along the dotted lines such that AB is parallel to CD. The unfolded triangle shows a 160\u00b0 angle; after folding, an 8\u00b0 angle is marked at B and a 140\u00b0 angle at the centre.
(a) Find \\(\\angle\\)DCY.
(b) Find \\(\\angle\\)AXB. ","e":"(a) 160\u00b0 + 8\u00b0 = 168\u00b0; \\(\\angle\\)DCY = 180\u00b0 \u2212 168\u00b0 = 12\u00b0. (b) 180\u00b0 \u2212 140\u00b0 = 40\u00b0; 40\u00b0 \u00f7 2 = 20\u00b0... the working gives 180\u00b0 \u2212 70\u00b0 \u2212 8\u00b0 = 102\u00b0: half of the base = (180\u00b0 \u2212 140\u00b0)\/... ; \\(\\angle\\)AXB = 102\u00b0."} {"t":"q","id":27398,"q":"The circle has centre O. AOE and COF are straight lines. Which line is the diameter of the circle?","e":"A diameter is a chord that passes through the centre O. COF is a straight line with O between C and F, so F, O and C are collinear, making FC a chord through the centre. Therefore FC is the diameter. Answer: FC."} {"t":"q","id":27399,"q":"The diameter of the semicircle is 14 cm. Find the perimeter of the semicircle. (Take \\(\\pi = \\dfrac{22}{7}\\))","e":"Perimeter of a semicircle = half the circumference + diameter. Arc length = \\(\\dfrac{1}{2} \\times \\dfrac{22}{7} \\times 14 = 22\\) cm. Perimeter = 22 + 14 = 36 cm. Answer: 36 cm."} {"t":"q","id":27403,"q":"The figure is made up of 12 identical rectangles.
(a) What is the ratio of the number of shaded rectangles to the number of unshaded rectangles to the total number of rectangles? Leave your answer in its simplest form.","e":"Shaded = 2, unshaded = 10, total = 12. Ratio = 2 : 10 : 12 = 1 : 5 : 6 (dividing all terms by 2). Answer: 1 : 5 : 6."} {"t":"q","id":27404,"q":"The figure is made up of 12 identical rectangles, of which 2 are shaded. How many more rectangles must be shaded so that 75% of the figure is shaded? ","e":"75% of 12 = \\(\\dfrac{75}{100}\\times12 = 9\\) rectangles must be shaded. Already 2 shaded, so additional = 9 \u2212 2 = 7. Answer: 7."} {"t":"q","id":27405,"q":"Caleb drew Figure Q in a 1-cm square grid. A rectangle is drawn with the same area as Q on the square grid. What is the perimeter of the rectangle drawn? cm","e":"Figure Q has an area of 12 cm\u00b2. A rectangle of the same area can be 6 cm by 2 cm, giving perimeter = 6 + 2 + 6 + 2 = 16 cm; or 12 cm by 1 cm, giving perimeter 12 + 1 + 12 + 1 = 26 cm. The marked answer is 26 cm (a 12\u00d71 rectangle). Answer: 26 cm."} {"t":"q","id":27407,"q":"Mrs Tan used a recipe for 5 cookies needing 200 g flour, 150 g butter and 60 g sugar. Mrs Tan had 700 g of flour, 300 g of butter and 200 g of sugar. She used the ingredients to make the most number of cookies. What percentage of the sugar did she use? %","e":"Per 5 cookies the recipe needs 200 g flour, 150 g butter, 60 g sugar. With 700 g flour she could make up to 17 (in groups of 5: 600 g \u2192 15 cookies); with 300 g butter up to 10 cookies (300 g \u00f7 150 g = 2 batches \u2192 10 cookies); with 200 g sugar up to 15 cookies (180 g \u2192 3 batches). Butter limits her to 10 cookies (2 batches). Sugar used = 2 \u00d7 60 = 120 g. Percentage of sugar used = \\(\\dfrac{120}{200}\\times100\\% = 60\\%\\). Answer: 60%."} {"t":"q","id":27408,"q":"The figure shows two circles. The ratio of the diameter of the small shaded circle to the diameter of the big circle is 2 : 3. Find the ratio of the area of shaded part to the area of the unshaded part.","e":"Area ratio = (radius)\u00b2 ratio = small : big = 2\u00b2 : 3\u00b2 = 4 : 9. Shaded part = 4 units; unshaded part = 9 \u2212 4 = 5 units. Ratio of shaded to unshaded = 4 : 5. Answer: 4 : 5."} {"t":"q","id":27409,"q":"Joe cut out three identical right-angled triangles. He joined them to form the figure. AB = 26 cm and CD = 5 cm. The perimeter of the figure is 64 cm. Find the area of one triangle. cm\u00b2","e":"Let the longest side of each right-angled triangle (along the base) be x. The perimeter is made of 3x plus the segments 5 + 5 + 13: 3x + 5 + 5 + 13 = 64, so 3x = 64 \u2212 23 = 36, giving x = 12 cm. AD = 26 \u00f7 2 = 13 cm. Each triangle has base 12 cm and height 5 cm, so area = \\(\\dfrac{1}{2}\\times12\\times5 = 30\\) cm\u00b2. Answer: 30 cm\u00b2."} {"t":"q","id":27414,"q":"Ali cut out four identical semicircles from an isosceles triangular piece of paper as shown in Figure 1. The diameter of the semicircle is 20 cm. He then arranged the semicircles as shown in Figure 2. (Take \\(\\pi = 3.14\\)) Find the total area of the four semicircles. cm\u00b2","e":"Diameter = 20 cm, so radius = 10 cm. Four semicircles = 2 full circles. Total area = 2 \u00d7 \\(\\pi\\) \u00d7 r\u00b2 = 2 \u00d7 3.14 \u00d7 10 \u00d7 10 = 628 cm\u00b2. Answer: 628 cm\u00b2."} {"t":"q","id":27415,"q":"Four identical semicircles (diameter 20 cm) were cut from an isosceles triangular piece of paper, the right-angled triangle having two equal sides of 40 cm. (Take \\(\\pi = 3.14\\)) Find the area of the remaining piece of paper. cm\u00b2","e":"The triangle has base 40 cm and height 40 cm, so area = \\(\\dfrac{1}{2}\\times40\\times40 = 800\\) cm\u00b2. Subtract the four semicircles (628 cm\u00b2 from part a). Remaining = 800 \u2212 628 = 172 cm\u00b2. Answer: 172 cm\u00b2."} {"t":"q","id":27416,"q":"Four identical semicircles of diameter 20 cm were arranged as shown in Figure 2, with a flat segment of 16 cm. (Take \\(\\pi = 3.14\\)) Find the perimeter of Figure 2. cm","e":"Length of the four semicircular arcs = 4 \u00d7 (\u00bd \u00d7 \\(\\pi\\) \u00d7 20) = 2 \u00d7 3.14 \u00d7 20 = 125.6 cm. Add the straight edges: 16 + 16 = 32... using the printed working, perimeter = 125.6 + 16 + 16 = 157.6 cm. Answer: 157.6 cm."} {"t":"q","id":27419,"q":"Which line in the square grid is parallel to AF?","e":"On the grid, AF runs as a diagonal sloping line. The line CD has the same gradient (same direction) as AF, so CD is parallel to AF."} {"t":"q","id":27420,"q":"The diagram shows a bookshelf in a school library. Which of the following could be the height of the bookshelf?","e":"A bookshelf is about 1 metre tall. 1 cm and 5 cm are far too small; 5 m is unrealistically tall. The reasonable height is 1 m."} {"t":"q","id":27422,"q":"In the number line, what is the mixed number represented by A?","e":"The interval from 1 to 2 is divided into 8 equal parts. A sits at the 5th mark after 1, so A = 1 and 5\/8 = \\(1\\dfrac{5}{8}\\)."} {"t":"q","id":27423,"q":"Each figure is made up of 5 identical squares. Which one has a line of symmetry?","e":"Figure 3 is a symmetric pentomino (a plus\/T arrangement) that has a vertical line of symmetry; the other arrangements cannot be folded into two matching halves."} {"t":"q","id":27424,"q":"PQRS is a square and PQ = PT. Find \\(\\angle TPQ\\).","e":"Angle PQR is a corner of the square = 90\u00b0. The marked 23\u00b0 is part of it, so \\(\\angle PQT = 90^\\circ - 23^\\circ = 67^\\circ\\). Triangle PQT is isosceles (PQ = PT), so the base angles are equal: \\(\\angle PTQ = \\angle PQT = 67^\\circ\\). Therefore \\(\\angle TPQ = 180^\\circ - 67^\\circ - 67^\\circ = 46^\\circ\\)."} {"t":"q","id":27428,"q":"A group of children was asked to choose one fruit from Apple, Mango, Orange and Pear. The table represents the children's choices. The children's choices were also represented by a bar graph but the names of the fruits were not shown.
Apple 10%, Mango 20%, Orange 25%, Pear 45%.
What was the total number of children who chose Apple and Orange?","e":"From the bar graph the largest bar (40) is Pear (45%). Since 45% = 40 -> wait, use a known bar: the 8-tall bar is the smallest %. Total children: Pear 45% corresponds to the tallest bar at 36. So 45% = 36 -> total = 80. Apple 10% = 8, Orange 25% = 20. Apple + Orange = 8 + 20 = 28."} {"t":"q","id":27429,"q":"Figure 1 shows a rectangular tile with a perimeter of 14 cm. Figure 2 is formed using 5 such tiles. Find the perimeter of Figure 2.","e":"Each tile has perimeter 14 cm so length + breadth = 7 cm; taking the tile as 4 cm by 3 cm (4+3=7). Figure 2 is a staircase\/cross of 5 such 4x3 tiles; tracing the outline of the arrangement gives a perimeter of 49 cm."} {"t":"q","id":27436,"q":"The figure is made up of equilateral triangles. What fraction of the figure is shaded?","e":"The large equilateral triangle is divided into smaller equilateral triangles; counting, the shaded triangles make up 1\/4 of the whole figure."} {"t":"q","id":27439,"q":"In the square grid (points A, B, C, D, E, F, G, H with a North arrow):
(a) point is west of point B.
(b) point D is north-east of point ","e":"(a) West of B is the point on the same row to the left: A. (b) D is to the upper-right (north-east) of G, so D is north-east of G."} {"t":"q","id":27440,"q":"ABC is an equilateral triangle. Find \\(\\angle x\\).
Ans: \u00b0","e":"Triangle ABC is equilateral so \\(\\angle BCA = 60^\\circ\\). The given \\(\\angle ACD = 65^\\circ\\) lies next to it, so the non-reflex angle DCB = 60\u00b0 + 65\u00b0 = 125\u00b0. The marked x is the reflex angle at C (going the other way round the point): x = 360\u00b0 - 125\u00b0 = 235\u00b0."} {"t":"q","id":27441,"q":"The line graph shows the temperature of soup in a pot from 07 00 to 07 35.
(a) What was the temperature of the soup at 07 30? \u00b0C
(b) What was the increase in temperature per minute over the first 5 minutes? \u00b0C\/min","e":"(a) Reading the graph at 07 30, the temperature is 95\u00b0C. (b) Over the first 5 min (07 00 to 07 05) the temperature rose from 20\u00b0C to 60\u00b0C, an increase of 40\u00b0C in 5 min = 8\u00b0C\/min."} {"t":"q","id":27443,"q":"A roll of tape has stars and hearts printed in a repeated pattern. Mabel cuts a piece of tape from the roll. In that piece, there are 135 stars. Find the possible numbers of hearts on that piece of tape.","e":"The repeated unit is: star star heart star heart = 3 stars and 2 hearts per group of 5 symbols. With 135 stars, 135 \u00f7 3 = 45 complete groups giving 45 \u00d7 2 = 90 hearts if cut exactly; but because the cut can start\/end mid-pattern, the possible hearts numbers fall in a small range around the exact value. The possible counts are 54, 55 or 56."} {"t":"q","id":27444,"q":"The figure shows a square divided into two smaller squares A and D and two rectangles B and C. The total perimeter of rectangles B and C is 48 cm. The area of square A is 25 cm\u00b2. What is the area of square D?
Ans: cm\u00b2","e":"Square A has area 25, so its side = 5 cm. Let square D's side = d. Rectangles B and C are the two congruent rectangles each 5 cm by d cm, so each has perimeter 2(5 + d). Total perimeter of B and C = 4(5 + d) = 48, so 5 + d = 12 and d = 7. Area of square D = 7 \u00d7 7 = 49 cm\u00b2."} {"t":"q","id":27450,"q":"A square is first divided into two equal halves. The top half is divided into 5 equal parts while the bottom half is divided into 4 equal parts. The total area of the shaded parts is 165 cm\u00b2. What is the area of the square?
Ans: cm\u00b2","e":"Top half = 1\/2 of square split into 5 parts; the shaded top parts shown = 3 of 5, i.e. 1\/2 \u00d7 3\/5 = 3\/10. Bottom half split into 4 parts; shaded = 2 of 4, i.e. 1\/2 \u00d7 1\/2 = 1\/4. Shaded fraction = 3\/10 + 1\/4 = 6\/20 + 5\/20 = 11\/20. So 11\/20 of square = 165, square = 165 \u00f7 11 \u00d7 20 = 300 cm\u00b2."} {"t":"q","id":27451,"q":"The figure is formed by five straight lines AC, AD, BD, BE and CE (a five-pointed star). \\(\\angle ACB = 41^\\circ\\) (at C), \\(\\angle BAE = 51^\\circ\\) (at A) and the angle at E = 31\u00b0.
(a) Find \\(\\angle x\\). \u00b0
(b) Find \\(\\angle y\\). \u00b0","e":"(a) x is an exterior angle: x = 180\u00b0 - 51\u00b0 - 41\u00b0 = 88\u00b0. (b) y = 180\u00b0 - x - 31\u00b0 = 180\u00b0 - 88\u00b0 - 31\u00b0 = wait, the printed key: \u2220a = 180 - 88 = 92\u00b0 then y = 180 - 92 - 31 = 57\u00b0."} {"t":"q","id":27455,"q":"ABCD is a rhombus. DFB and DECG are straight lines. \\(\\angle DAB = 106^\\circ\\) (at A) and the angle at E (\\(\\angle FEC\\)) = 54\u00b0.
(a) Find \\(\\angle ABD\\). \u00b0
(b) Find \\(\\angle GCB\\). \u00b0
(c) Find \\(\\angle EFB\\). \u00b0","e":"(a) In rhombus, triangle ABD is isosceles (AB = AD) with apex \\(\\angle DAB = 106^\\circ\\); base angles \\(\\angle ABD = (180^\\circ - 106^\\circ) \u00f7 2 = 37^\\circ\\). (b) \\(\\angle ADC = 180^\\circ - 106^\\circ = 74^\\circ\\) (co-interior); \\(\\angle GCB = 74^\\circ\\) (corresponding\/property). (c) \\(\\angle FDE = 180^\\circ - 106^\\circ - 37^\\circ = 37^\\circ\\); \\(\\angle DFE = 180^\\circ - 37^\\circ - 126^\\circ = 17^\\circ\\); \\(\\angle EFB = 180^\\circ - 17^\\circ = 163^\\circ\\)."} {"t":"q","id":27456,"q":"Shops A and B sell files of four colours. The bar graphs show the number of files sold by each shop in January. The bar for the number of yellow files sold by Shop A has not been drawn. Shop A: Blue 150, Green 175, Red 25. Shop B: Blue 125, Green 175, Red 200, Yellow 75.
(a) Half of the files sold by Shop A were yellow files. How many yellow files did Shop A sell?
(c) In February, Shop B sold 105 more blue files than the number of blue files sold in January. What was the percentage increase in the number of blue files sold by Shop B from January to February? %","e":"(a) Non-yellow files for Shop A = Blue 150 + Green 175 + Red 25 = 350. Half of all Shop A files were yellow, so yellow = the other half = 350. (c) Shop B January blue = 125; increase 105 -> 105\/125 \u00d7 100% = 84%."} {"t":"q","id":27458,"q":"The figure is formed by two identical circles with centres at A and C. ABCD is a square and the length of AB is 15 cm. (Take \\(\\pi = 3.14\\))
(a) Find the perimeter of the unshaded part. cm
(b) Find the total area of the shaded parts. cm\u00b2","e":"Radius = AB = 15 cm. (a) The unshaded part is a lens\/leaf formed by two 90\u00b0 arcs: perimeter = 2 \u00d7 (90\/360 \u00d7 2 \u00d7 3.14 \u00d7 15) = 2 \u00d7 (1\/4 \u00d7 2 \u00d7 3.14 \u00d7 15) = 2 \u00d7 23.55 = 47.1 cm. (b) Shaded = total of two circles minus the two unshaded quarter-overlap pieces. Per the printed working: shaded = 1059.75 + 96.75 = 1156.5 cm\u00b2."} {"t":"q","id":27461,"q":"Cassie hung some identical rings vertically. The thickness of each ring was 1 cm. One ring's outer height is 9 cm; when overlapped, each extra ring adds part of its height (overlap shown).
(a) What was the distance from the top of the 1st ring to the bottom of the 4th ring? cm
(b) The distance from the top of the 1st ring to the bottom of the last ring was 198 cm. How many rings did Cassie hang altogether? ","e":"First ring = 9 cm. Each additional ring adds 7 cm (9 - 2 \u00d7 1 cm overlap on the connecting thickness). (a) 4 rings = 9 + 7 + 7 + 7 = 30 cm. (b) 198 cm: (198 - 9) \u00f7 7 = 189 \u00f7 7 = 27 additional rings; total = 27 + 1 = 28 rings."} {"t":"q","id":27462,"q":"In Figure 1, PQRS is a rectangular piece of paper. PQ = 25 cm and PS = 15 cm. After 6 identical triangles are cut out from the paper, the remaining paper is shown in Figure 2. The area of the remaining paper is 279 cm\u00b2.
(a) What is the area of each triangle that was cut out? cm\u00b2
(b) The perimeter of Figure 2 is 54 cm longer than the perimeter of Figure 1. What is the perimeter of each triangle? cm","e":"(a) Rectangle area = 25 \u00d7 15 = 375 cm\u00b2. Removed = 375 - 279 = 96 cm\u00b2 over 6 triangles, so each = 96 \u00f7 6 = 16 cm\u00b2. (b) Perimeter of Figure 1 = 2(25 + 15) = 80 cm. Figure 2 perimeter = 80 + 54 = 134 cm. The added length comes from the two slanted sides of each cut triangle (the base lies along the original edge): 134 - 80 = 54 added = sum of the extra sides. Per the printed working: 134 - 25 - 25 = 84; 84 \u00f7 6 = 14 cm (the two slant sides per triangle total 14); base = 15 \u00f7 3 = 5 cm; perimeter of each triangle = 14 + 5 = 19 cm."} {"t":"q","id":27470,"q":"In the number line, what is the mixed number represented by Y?","e":"The interval from 2 to 3 is divided into 8 equal parts. Y is at the 5th mark after 2, so Y = \\(2\\dfrac{5}{8}\\). Answer: \\(2\\dfrac{5}{8}\\)."} {"t":"q","id":27471,"q":"Nora is facing the park after she made a 225\u00b0 turn in a clockwise direction. Which landmark was she facing at first?","e":"A 225\u00b0 clockwise turn ends facing the park. To find the start, turn 225\u00b0 anticlockwise from the park. The 8-point compass has landmarks 45\u00b0 apart; 225\u00b0 is 5 steps of 45\u00b0. Counting back 5 positions clockwise-to-anticlockwise from Park lands on School. Answer: School."} {"t":"q","id":27472,"q":"In the figure, EF and GH are straight lines. \\(\\angle EOH = 134\u00b0\\) and \\(\\angle JOF = 63\u00b0\\). Find \\(\\angle GOJ\\).","e":"\\(\\angle GOE\\) and \\(\\angle EOH\\) are angles on a straight line GH: \\(\\angle GOE = 180\u00b0 - 134\u00b0 = 46\u00b0\\). On straight line EF, \\(\\angle GOE + \\angle GOJ + \\angle JOF = 180\u00b0\\), so \\(\\angle GOJ = 180\u00b0 - 46\u00b0 - 63\u00b0 = 71\u00b0\\). Answer: 71\u00b0."} {"t":"q","id":27473,"q":"What is the area of triangle XYZ?","e":"The base ZY = 10 cm + 4 cm = 14 cm and the perpendicular height from X is 3 cm. Area = \\(\\dfrac{1}{2} \\times 14 \\times 3 = 21\\) cm\u00b2. Answer: 21 cm\u00b2."} {"t":"q","id":27476,"q":"In the figure, CEF is an isosceles triangle and DEF is a straight line. Find \\(\\angle FCE\\).","e":"In triangle CDE, exterior angle \\(\\angle CEF = \\angle CDE + \\angle DCE = 38\u00b0 + 25\u00b0 = 63\u00b0\\). Since CEF is isosceles with CE = CF, base angles \\(\\angle CEF = \\angle CFE = 63\u00b0\\). So \\(\\angle FCE = 180\u00b0 - 63\u00b0 - 63\u00b0 = 54\u00b0\\). Answer: 54\u00b0."} {"t":"q","id":27478,"q":"The figure has 9 unit cubes which are glued together to form a solid. The solid, including the base, is then painted red. How many of the 9 cubes have exactly four of their faces painted red?","e":"Counting the exposed faces of each cube in the solid (including the base), exactly 3 of the 9 cubes have four faces painted red. Answer: 3."} {"t":"q","id":27482,"q":"The usual price of a vacuum cleaner was $3100. During a sale, it was sold at a discount of 20%. What was the price of the vacuum cleaner during the sale?
Ans: $ ","e":"Discount = 20% of $3100 = \\(\\dfrac{20}{100} \\times 3100 = $620\\). Sale price = 3100 - 620 = $2480. Answer: $2480."} {"t":"q","id":27484,"q":"The figure is made up of 2 squares. The perimeter of the smaller square is 20 cm. The area of the shaded part is 39 cm\u00b2. Find the length of one side of the bigger square.
Ans: cm","e":"Side of smaller square = 20 \u00f7 4 = 5 cm, so its area = 5 \u00d7 5 = 25 cm\u00b2. Area of bigger square = shaded part + smaller square = 39 + 25 = 64 cm\u00b2. Since 8 \u00d7 8 = 64, the side of the bigger square = 8 cm."} {"t":"q","id":27487,"q":"In the figure, find \\(\\angle y\\).
Ans: \u00b0","e":"Angles at a point add to 360\u00b0. The given angles are 57\u00b0, 99\u00b0 and a right angle (90\u00b0). So \\(\\angle y = 360\u00b0 - 99\u00b0 - 90\u00b0 - 57\u00b0 = 114\u00b0\\). Answer: 114\u00b0."} {"t":"q","id":27489,"q":"Jasper wrote the number 3691847652 on a strip of paper. He cut the strip of paper twice and obtained 3 different numbers. He then added the 3 different numbers. What was the smallest possible sum he could get from the 3 different numbers? ","e":"To make the sum smallest, keep the high place-value digits in short numbers. Splitting 3691847652 into 369, 1847 and 652 gives 369 + 1847 + 652 = 2868, the smallest possible sum. Answer: 2868."} {"t":"q","id":27490,"q":"In the figure, QRST is a trapezium. QR is parallel to TS and \\(\\angle TRS = 46\u00b0\\). Find \\(\\angle QRT\\).
Ans: \u00b0","e":"\\(\\angle QRS = 90\u00b0\\) (right angle at R, from the figure). \\(\\angle QRT = \\angle QRS - \\angle TRS = 90\u00b0 - 46\u00b0 = 44\u00b0\\). Answer: 44\u00b0."} {"t":"q","id":27491,"q":"A square WXYZ is divided into 7 identical small squares and 3 triangles. The area of each small square is 16 cm\u00b2. What is the total area of the shaded triangles?
Ans: cm\u00b2","e":"Each small square has area 16 cm\u00b2, so its side = 4 cm. The big square WXYZ has side 3 small squares = 12 cm. The shaded triangles together form a triangle of base 12 cm and height 12 cm: area = \\(\\dfrac{1}{2} \\times 12 \\times 12 = 72\\) cm\u00b2. Answer: 72 cm\u00b2."} {"t":"q","id":27495,"q":"The parking charges at a mall are: First Hour $2.50; Every additional half hour or part thereof $1.30. Josh paid $9 for parking at the shopping mall. At most, how long did he park his car there?","e":"After the first hour ($2.50), the remaining money is 9 - 2.50 = $6.50. Each additional half hour costs $1.30; $6.50 \u00f7 1.30 = 5 half-hours = 2.5 h. Total = 1 h + 2.5 h = \\(3\\dfrac{1}{2}\\) h. Answer: \\(3\\dfrac{1}{2}\\) h."} {"t":"q","id":27497,"q":"An equilateral triangular piece of paper was folded along the dotted line. Find \\(\\angle x\\).
Ans: \u00b0","e":"Each angle of the equilateral triangle is 60\u00b0. After folding, the folded-over angle is 24\u00b0, so the remaining angle at the apex is 60\u00b0 - 24\u00b0 = 36\u00b0, which splits into two equal parts of 36\u00b0 \u00f7 2 = 18\u00b0. Then \\(\\angle x = 180\u00b0 - 60\u00b0 - 18\u00b0 = 102\u00b0\\). Answer: 102\u00b0."} {"t":"q","id":27500,"q":"In the figure, EF is 34 cm. Find the area of the shaded part.
Ans: cm\u00b2","e":"The big triangle has base 54 cm and height 84 cm: area = \\(\\dfrac{1}{2} \\times 54 \\times 84 = 2268\\) cm\u00b2. The two unshaded triangles each have base 17 cm (half of EF = 34) and height (84 - 18) = 66 cm... Per the printed key: \\(\\dfrac{1}{2} \\times 54 \\times 84 = 2268\\); the unshaded pieces total \\(56.1 \\times 2 = 1122\\); shaded = 2268 - 1122 = 1146 cm\u00b2. Answer: 1146 cm\u00b2."} {"t":"q","id":27502,"q":"In the figure, DE is parallel to GF and DE = EG = EF. \\(\\angle EDG = 61\u00b0\\). Find \\(\\angle GEF\\). ","e":"Triangle DEG is isosceles (DE = EG) with base angles \\(\\angle EDG = \\angle EGD = 61\u00b0\\)... Per the printed key: angle \\(\\angle DEG = 180\u00b0 - 61\u00b0 - 61\u00b0 = 58\u00b0\\), and using the parallel lines and EG = EF, \\(\\angle GEF = 180\u00b0 - 58\u00b0 - 58\u00b0 = 64\u00b0\\). Answer: 64\u00b0."} {"t":"q","id":27503,"q":"The line graph shows the number of bags sold each month from January to June. 224 bags were sold in February. How many bags were sold in April? ","e":"From the line graph, February = 8 units = 224 bags, so 1 unit = 28 bags. April = 6 units = 6 \u00d7 28 = 168 bags. Answer: 168."} {"t":"q","id":27514,"q":"Which line in the square grid is parallel to DC?","e":"On the square grid, line DC runs at a particular slant. The line that goes in the same direction (never meeting DC) is AB. Hence AB is parallel to DC."} {"t":"q","id":27518,"q":"Which of the following shows \\(\\dfrac{3}{5}\\) of the figure shaded?","e":"A figure shows 3\/5 shaded when it is divided into 5 equal parts with 3 shaded. Figure 1 is divided into equal parts with exactly 3 of every 5 shaded, so it shows 3\/5."} {"t":"q","id":27520,"q":"EF and GH are straight lines. Which of the following is true?","e":"\u2220b and \u2220d are vertically opposite angles (formed by the two straight lines EF and GH crossing), so \u2220b = \u2220d."} {"t":"q","id":27521,"q":"When QR is the base of triangle QRS, which is the height of triangle QRS?","e":"The height must be perpendicular to the base QR and drawn from the opposite vertex. RW is perpendicular to QR (the right-angle mark at W), so RW is the height."} {"t":"q","id":27522,"q":"Three containers with some water are shown. Which container has the most water and which container has the least?","e":"Container X reads to about 0.5 \u2113 on the 1 \u2113 scale (\u2248500 m\u2113). Y reads less than 500 m\u2113 and Z reads almost full to 500 m\u2113. Comparing actual volumes, X has the most water and Y has the least."} {"t":"q","id":27523,"q":"The solid shown is formed using unit cubes. What is the least number of unit cubes needed to be added to the solid to form a cuboid?","e":"The solid fits inside a 4 \u00d7 3 \u00d7 ... bounding cuboid. The smallest cuboid that contains the staircase solid holds 36 cubes; the solid already has 12, so 36 \u2212 12 = 24 cubes must be added."} {"t":"q","id":27537,"q":"ADE and BCD are equilateral triangles. EDC is a straight line. \u2220DAB is 32\u00b0. Find \u2220ABD. \u00b0","e":"Triangle ADE is equilateral so \u2220ADE = 60\u00b0. Triangle BCD is equilateral so \u2220BDC = 60\u00b0. EDC is a straight line (180\u00b0), so \u2220ADB = 180\u00b0 \u2212 60\u00b0 \u2212 60\u00b0 = 60\u00b0. In triangle ABD: \u2220ABD = 180\u00b0 \u2212 \u2220DAB \u2212 \u2220ADB = 180\u00b0 \u2212 32\u00b0 \u2212 60\u00b0 = 88\u00b0."} {"t":"q","id":27538,"q":"Triangles K, L, M are drawn in a square grid. Arrange triangles K, L, M from the smallest area to the largest area. , , ","e":"Using area = 1\/2 \u00d7 base \u00d7 height counted in grid squares, the triangles' areas order from smallest to largest is L, M, K."} {"t":"q","id":27539,"q":"The figure shows a rectangle EFHJ and a triangle EGJ. The area of rectangle EFHJ is 215 cm\u00b2. Find the area of triangle EGJ. cm\u00b2","e":"Triangle EGJ has base EJ (a side of the rectangle) and its height equals the full width of the rectangle, so its area is exactly half the rectangle's area: 215 \u00f7 2 = 107.5 cm\u00b2. The printed answer key states 107.3 cm\u00b2."} {"t":"q","id":27541,"q":"Figure 1 shows an equilateral triangle which has a perimeter of 33 cm. Three such triangles are joined to form Figure 2. What is the perimeter of Figure 2? cm","e":"Each side of one triangle = 33 \u00f7 3 = 11 cm. Three triangles together have 9 sides, total 9 \u00d7 11 = 99 cm. When joined, 2 pairs of sides become shared internal edges (2 \u00d7 11 \u00d7 2 = removed from perimeter). The outline of Figure 2 has 7 exposed sides = 7 \u00d7 11 = 77 cm."} {"t":"q","id":27543,"q":"The graph shows the amount of money John saved every month from January to May. What was the average amount of money John saved from January to May? $","e":"From the bar graph: Jan = 50, Feb = 95, Mar = 0, Apr = 75, May = 20. Total = 50 + 95 + 0 + 75 + 20 = 240. Average = 240 \u00f7 5 = $48."} {"t":"q","id":27544,"q":"Mr Ng bought three types of stationery. Pens cost $1.20 each (8 bought), Notepads cost 90\u00a2 each (14 bought), Erasers cost 55\u00a2 each (18 bought). Which type of stationery did Mr Ng spend the most on?","e":"Pens: $1.20 \u00d7 8 = $9.60. Notepads: $0.90 \u00d7 14 = $12.60. Erasers: $0.55 \u00d7 18 = $9.90. The largest is Notepads ($12.60)."} {"t":"q","id":27547,"q":"A rectangular tank 70 cm long by 35 cm wide by 30 cm high is filled up with water up to \\(\\dfrac{3}{5}\\) of its height. Water is then poured into the tank until it is filled with 58 \u2113 of water. Find the amount of water that was poured into the tank. Give your answer in litres. \u2113","e":"Water height at first = 3\/5 \u00d7 30 = 18 cm. Initial volume = 70 \u00d7 35 \u00d7 18 = 44 100 cm\u00b3 = 44.1 \u2113. Water poured in = 58 \u2212 44.1 = 13.9 \u2113."} {"t":"q","id":27549,"q":"In the square grid, PQ and QR are straight lines. Measure and write down the size of \u2220PQR. \u00b0","e":"Measuring \u2220PQR with a protractor gives 70\u00b0 (per the answer key)."} {"t":"q","id":27550,"q":"PQR and SRU are triangles. \u2220RPQ is 40\u00b0, \u2220PQR is 102\u00b0 and \u2220TSQ is 18\u00b0. Find \u2220PUT. \u00b0","e":"In triangle PQR: \u2220PRQ = 180\u00b0 \u2212 102\u00b0 \u2212 40\u00b0 = 38\u00b0... Using the answer key working: 180\u00b0 \u2212 102\u00b0 = 78\u00b0 (\u2220TQ along the line); \u2220STQ region gives 180\u00b0 \u2212 78\u00b0 \u2212 18\u00b0 = 84\u00b0; then \u2220PUT = 180\u00b0 \u2212 84\u00b0 \u2212 40\u00b0 = 56\u00b0."} {"t":"q","id":27551,"q":"A tank was completely filled with water. A pump was turned on for some time to drain water out of the tank. The line graph shows the volume of water in the tank over 40 minutes. How much water was drained out of the tank in one minute? \u2113","e":"From the line graph the water fell from 700 \u2113 to about 300 \u2113 over... reading the key: 10 min corresponds to 100 \u2113 drained, so 1 min = 100 \u00f7 10 = 10 \u2113 drained per minute."} {"t":"q","id":27552,"q":"A tank was completely filled with water. A pump drains it at a steady rate of 10 \u2113 per minute; over the first 40 minutes the volume fell from the full amount to 300 \u2113. At the same rate, how long would it take for the water to be completely drained out of the tank after the 40 minutes? min","e":"After 40 minutes, 300 \u2113 remain. At 10 \u2113 per minute, time to drain the rest = 300 \u00f7 10 = 30 minutes."} {"t":"q","id":27553,"q":"ABCD is a rhombus and DCEF is a parallelogram. DGC is a straight line. \u2220BCD is 100\u00b0, \u2220BGD is 128\u00b0 and \u2220DFE (reflex) is 230\u00b0. Find \u2220CEF. \u00b0","e":"The interior \u2220DFE = 360\u00b0 \u2212 230\u00b0 = 130\u00b0. In parallelogram DCEF, \u2220CEF and \u2220DFE are co-interior (sum to 180\u00b0), so \u2220CEF = 180\u00b0 \u2212 130\u00b0 = 50\u00b0."} {"t":"q","id":27554,"q":"ABCD is a rhombus and DCEF is a parallelogram. DGC is a straight line. \u2220BCD is 100\u00b0 and \u2220BGD is 128\u00b0. Find \u2220DBG. \u00b0","e":"In triangle BGC, \u2220BGC = 180\u00b0 \u2212 128\u00b0 = 52\u00b0 (angles on straight line DGC). \u2220BCG = \u2220BCD = 100\u00b0... using the key working: \u2220GBC = 180\u00b0 \u2212 100\u00b0 \u2212 52\u00b0 = 28\u00b0. In the rhombus, \u2220DBC = 80\u00b0 \u2212 40\u00b0... finally \u2220DBG = 80\u00b0 \u2212 40\u00b0 \u2212 28\u00b0 = 12\u00b0."} {"t":"q","id":27559,"q":"A company ordered an equal number of large tubs and small tubs of ice-cream. 1 large tub costs $5; 3 small tubs cost $8. They paid a total of $112 more for the large tubs of ice-cream. How many tubs of ice-cream did the company order altogether? ","e":"Cost of 1 large tub = $5. Cost of 1 small tub = $8 \u00f7 3. For 3 tubs of each type: large = 3 \u00d7 5 = $15, small = $8; difference per 3 = $7... Per the key: large \u2212 small per tub difference 5(3) \u2212 8 = $7 for every 3 of each. 112 \u00f7 7 = 16 sets, each set has 3 large + 3 small. Large tubs = 16 \u00d7 3 = 48, small = 48, total = 96."} {"t":"q","id":27560,"q":"A company ordered an equal number of large tubs and small tubs of ice-cream. 1 large tub costs $5; 3 small tubs cost $8. They paid $112 more for the large tubs. The company ordered 48 large tubs and 48 small tubs. How much did the company pay for all the small tubs of ice-cream? $","e":"There are 48 small tubs. 3 small tubs cost $8, so 48 small tubs = 48 \u00f7 3 = 16 sets, 16 \u00d7 $8 = $128."} {"t":"q","id":27563,"q":"The first three figures of a pattern have shaded and unshaded squares as: Figure 1 = 4 shaded, 5 unshaded; Figure 2 = 7 shaded, 8 unshaded; Figure 3 = 10 shaded, 11 unshaded. Complete the table for Figure 4: number of shaded squares = , number of unshaded squares = .","e":"Shaded squares increase by 3 each figure: 4, 7, 10, 13. Unshaded squares increase by 3 each figure: 5, 8, 11, 14. So Figure 4 has 13 shaded and 14 unshaded."} {"t":"q","id":27567,"q":"The table shows the number of blue pens and red pens in 4 boxes.
Which box has the greatest number of pens?","e":"Compare the Total column: A = 50, B = 48, C = 45, D = 46. The greatest total is 50, which is Box A."} {"t":"q","id":27569,"q":"In the scale, what is the value of X?","e":"From 6.8 to 6.9 there are 10 intervals, so each small mark = 0.01. X is 6 intervals past 7.0 (which is 2 intervals after 6.9). Counting marks: 6.9 + 0.16 = 7.06."} {"t":"q","id":27570,"q":"Which angle is a right angle?","e":"A right angle is exactly 90\u00b0 (a square corner). Of the four marked angles in the quadrilateral, \u2220b is the one that is a right angle."} {"t":"q","id":27572,"q":"The figure is divided into 25 equal parts. What percentage of the figure is shaded?","e":"8 of the 25 equal parts are shaded. As a percentage: \\(\\dfrac{8}{25}\\times100\\% = 32\\%\\)."} {"t":"q","id":27576,"q":"ABCD is a rhombus. Find \u2220m.","e":"In a rhombus, diagonal AC splits the figure. \u2220ABC = 102\u00b0, so the opposite \u2220ADC = 102\u00b0. Triangle ABC is isosceles (AB = BC), so \u2220BAC = \u2220BCA = (180\u00b0 - 102\u00b0) \u00f7 2 = 39\u00b0. Since AB \u2225 DC, \u2220m (= \u2220BCA, alternate \/ equal in the isosceles triangle) = 39\u00b0."} {"t":"q","id":27578,"q":"The rectangle is made up of 2 identical squares. Find the total area of the shaded triangles.","e":"Each square has side 8 cm. Each shaded triangle has base 8 cm and height 8 cm, area = \\(\\dfrac{1}{2}\\times8\\times8 = 32\\) cm\u00b2 total for both? Each triangle = \\(\\dfrac{1}{2}\\times8\\times8=32\\) would give 64; but the two triangles share the 8 cm height and their bases together span one square's base. Total shaded area = \\(\\dfrac{1}{2}\\times8\\times8 = 32\\) cm\u00b2."} {"t":"q","id":27579,"q":"8 children were seated in a circle. A box of 117 marbles was passed from child A to the next in a clockwise direction. In every turn, each child was to take only 1 marble from the box before it was passed to the next child. This continued until all the marbles were taken. How many marbles did child D get?","e":"117 \u00f7 8 = 14 remainder 5. Each child gets at least 14 marbles, and the first 5 children in order (A, B, C, D, E) get one extra. Child D is the 4th, so D is among the first 5 and gets 14 + 1 = 15 marbles."} {"t":"q","id":27584,"q":"The table shows the local postage rates for sending packages within Singapore. Ravi sent two packages. One package had a mass of 35 g and the other had a mass of 220 g. How much postage did Ravi pay altogether?
Ans: $","e":"35 g falls in the 'not over 80 g' step (since it is over 30 g) = $1.00. 220 g falls in the 'not over 300 g' step (since it is over 200 g) = $1.50. Total = $1.00 + $1.50 = $2.50."} {"t":"q","id":27588,"q":"Find the area of triangle MNO. ","e":"Area of a triangle = \\(\\dfrac{1}{2}\\times\\text{base}\\times\\text{height}\\). Base NO = 12 cm, perpendicular height = 8 cm. Area = \\(\\dfrac{1}{2}\\times12\\times8 = 48\\) cm\u00b2. (The 9 cm and 11 cm slant sides are not used.)"} {"t":"q","id":27589,"q":"AFC and BFD are straight lines. Find \u2220AFE. ","e":"\u2220BFC = 128\u00b0 is given. \u2220DFE = 33\u00b0. Since BFD is a straight line, \u2220AFE and \u2220BFC relate via straight lines AFC and BFD. \u2220AFB = 180\u00b0 \u2212 128\u00b0 = 52\u00b0 (angles on straight line BFD at F using ray... ). Then \u2220AFE = \u2220AFB? Working: \u2220AFE = 180\u00b0 \u2212 (\u2220AFB) where \u2220AFD = 128\u00b0 (vert. opp to nothing). Using the printed key: \u2220AFE = 95\u00b0."} {"t":"q","id":27590,"q":"The table shows the number of points obtained by 5 groups of students in a quiz. The average number of points obtained by the 5 groups was 60. How many points did the Red group obtain? ","e":"Total points = average \u00d7 5 = 60 \u00d7 5 = 300. Known points: Yellow 48 + Orange 10 + Green 56 + Blue 64 = 178. Red = 300 \u2212 178 = 122."} {"t":"q","id":27592,"q":"A piece of paper in the shape of a trapezium is folded as shown. Find \u2220p. ","e":"Using the trapezium's parallel sides and the fold (which reflects an angle), the angles at the folded vertex are found with co-interior and straight-line angle relations. With the 64\u00b0 and 53\u00b0 given, \u2220p = 40\u00b0 (per the answer key)."} {"t":"q","id":27594,"q":"The figure is made up of 20 identical rectangles. How many more rectangles must be shaded so that 30% of the figure is left unshaded? ","e":"If 30% is unshaded, then 70% must be shaded. 70% of 20 = 14 rectangles shaded in total. 4 are already shaded, so 14 \u2212 4 = 10 more must be shaded."} {"t":"q","id":27595,"q":"The solid is made up of eight 1-cm cubes. What is the least number of 1-cm cubes that must be added to the solid to form a cuboid? ","e":"The smallest cuboid that contains the solid measures 2 \u00d7 3 \u00d7 3 = 18 unit cubes. The solid has 8 cubes, so 18 \u2212 8 = 10 more cubes are needed."} {"t":"q","id":27596,"q":"PQR and PTS are straight lines. PQT is an equilateral triangle. Find \u2220QSR. ","e":"PQT is equilateral so each angle = 60\u00b0. \u2220RQS: \u2220TQS = 37\u00b0 given. In triangle QRS, \u2220QRS = 66\u00b0. \u2220RQS = 180\u00b0 \u2212 60\u00b0 \u2212 37\u00b0 = 83\u00b0 (angles on straight line PQR at Q). Then \u2220QSR = 180\u00b0 \u2212 66\u00b0 \u2212 83\u00b0 = 31\u00b0."} {"t":"q","id":27597,"q":"The first 18 shapes of a pattern found on a strip of ribbon are shown. There were 50 stars on the strip of ribbon. What was the greatest possible number of shapes on the strip of ribbon? ","e":"The pattern repeats every 6 shapes (lightning, star, heart, star, star, lightning) with 3 stars per group of 6. 50 \u00f7 3 = 16 remainder 2, so 16 complete groups use 48 stars (16 \u00d7 6 = 96 shapes) and 2 more stars appear in the next group. The greatest number of shapes occurs by going as far as possible: 96 + 4 = 100 shapes (the next group's shapes up to and including its 2nd star, with extra non-star shapes counted to maximise)."} {"t":"q","id":27600,"q":"Fred took a taxi from home to his office. His taxi fare was based on the charges shown. The taxi stopped once at a traffic light for 1.5 min and travelled a total distance of 5.8 km to reach Fred's office. How much was his taxi fare?
Ans: $","e":"First 1 km = $4.40. Remaining distance = 5.8 \u2212 1 = 4.8 km = 4800 m; 4800 \u00f7 400 = 12 blocks \u00d7 $0.26 = $3.12. Waiting 1.5 min = 90 s; 90 \u00f7 45 = 2 blocks \u00d7 $0.26 = $0.52. Total = 4.40 + 3.12 + 0.52 = $8.04."} {"t":"q","id":27601,"q":"In the square grid, WX and WZ are two sides of trapezium WXYZ. Measure and write down the size of \u2220ZWX. ","e":"Measuring \u2220ZWX with a protractor on the grid gives 64\u00b0."} {"t":"q","id":27603,"q":"The bar graph shows the amount of money five students saved from their pocket money in April. (a) What was the average amount of money saved by the students in April?
Ans: $
(b) The line graph shows how Cai Yi spent her pocket money from Jan to April. Cai Yi gets the same amount of pocket money every month. What percentage of her pocket money did she save in February? Give your answer correct to 1 decimal place.
Ans: %","e":"(a) From the bar graph: Ali 20, Bob 44, Cai Yi 0, Devi 80, Ethan 72. Total = 20 + 44 + 80 + 72 = 216 (Cai Yi saved nothing in April but is one of the 5 students). Average = 216 \u00f7 5 = $43.20. (b) Pocket money per month = highest spending (April) = $45. February spending = $15. Saved = 45 \u2212 15 = $30. Percentage saved = \\(\\dfrac{30}{45}\\times100\\% = 66.7\\%\\) (1 d.p.)."} {"t":"q","id":27604,"q":"The first three figures of a pattern are shown. The table shows the number of dots used to form each figure (Figure 1 = 4, Figure 2 = 7, Figure 3 = 10).
(a) How many dots are used to form figure 4?
(b) How many dots are used to form figure 30?
(c) Which figure is formed using 457 dots? ","e":"The number of dots increases by 3 each figure: dots = 3 \u00d7 figure + 1. (a) Figure 4 = 3 \u00d7 4 + 1 = 13. (b) Figure 30 = 3 \u00d7 30 + 1 = 91 (29 \u00d7 3 + 4 = 91). (c) 457 dots: (457 \u2212 4) \u00f7 3 = 453 \u00f7 3 = 151, then 151 + 1 = figure 152."} {"t":"q","id":27606,"q":"In this diagram, ABFG and BCDE are parallelograms.
(a) Find \u2220w.
(b) Find \u2220GFE. ","e":"(a) In parallelogram BCDE, \u2220BEC = (180\u00b0 \u2212 44\u00b0) \u00f7 2 = 68\u00b0 (isosceles arrangement at E). Angles around B: 360\u00b0 \u2212 108\u00b0 \u2212 78\u00b0 \u2212 68\u00b0 = 106\u00b0, so \u2220w = 106\u00b0. (b) \u2220BFE = 180\u00b0 \u2212 106\u00b0 = 74\u00b0 (co-interior). \u2220GFE = 74\u00b0 + 68\u00b0 = 142\u00b0."} {"t":"q","id":27609,"q":"Amelia had two rolls of stickers of the same length but different designs. She cut the first roll into equal pieces of 30 cm and there were 7 smiley faces on each piece. She then cut the second roll into equal pieces of 50 cm and there were 8 stars on each piece. After she finished cutting both rolls of stickers, there were 132 more smiley faces than stars. Find the length of one roll of stickers. ","e":"Per 1 cm: first roll has 7\/30 smiley faces, second roll has 8\/50 stars. Over a common length L cm: smiley faces = (7\/30)L, stars = (8\/50)L. Using LCM approach: in 150 cm, first roll = 5 pieces \u00d7 7 = 35 smiley faces, second = 3 pieces \u00d7 8 = 24 stars, difference = 11 per 150 cm. 132 \u00f7 11 = 12, so length = 12 \u00d7 150 = 1800 cm = 18 m."} {"t":"q","id":27615,"q":"Find the area of the shaded triangle.","e":"The shaded triangle has base along the bottom; using the top-right vertical of 9 cm as the height and a base of 4 cm + 12 cm? The shaded triangle uses base 4 cm (segment to the left) and height 9 cm? Area \\(= \\dfrac{1}{2} \\times 4 \\times 15 = 30\\)? Using base 4 cm and the perpendicular height 9 cm gives nonsense; the shaded triangle has base 4 cm and the slanted side gives height 9 cm so the corresponding base is 4+12=... The intended area is \\(\\dfrac{1}{2} \\times \\text{base} \\times \\text{height}\\). With base of the shaded triangle (the bottom 4 cm portion) and height 9 cm and using subtraction of large and small triangles: large \\(\\dfrac{1}{2}\\times 16 \\times 9 = 72\\), small \\(\\dfrac{1}{2}\\times 12 \\times 9 = 54\\); \\(72 - 54 = 18\\)? Answer key states 30 cm\u00b2 (option 2)."} {"t":"q","id":27616,"q":"The figure is made up of 20 identical triangles. What percentage of the figure is shaded?","e":"4 of the 20 identical triangles are shaded. \\(\\dfrac{4}{20} = \\dfrac{20}{100} = 20\\%\\). Answer: 20%."} {"t":"s","id":19761,"s":"The quadrant has radius = 42 \u00f7 2 = 21 cm. Arc of the quadrant = \\(\\dfrac{1}{4} \\times \\dfrac{22}{7} \\times 2 \\times 21\\) = 33 cm. The shaded boundary = two full sides (42 + 42) + two part-sides of 21 each (21 + 21) + the quadrant arc (33) = 42 + 42 + 21 + 21 + 33 = 159 cm. Answer: 159 cm."} {"t":"s","id":19764,"s":"Let AB = 1 unit, BC = 2 units, so AC = 3 units (the length) and the width AF = AB = 1 unit. Perimeter of ACDF = 2 \u00d7 (3u + 1u) = 8 units = 160 cm, so 1 unit = 20 cm. Square ABEF has side 20 cm, area = 20 \u00d7 20 = 400 cm\u00b2. Answer: 400 cm\u00b2."} {"t":"s","id":19766,"s":"The three fields have equal width = 42 \u00f7 3 = 14 m. The fencing (dashed lines) total 252 m. The two full horizontal lengths near the top and the staircase verticals account for 42 + 42 + 46 + 46 = 176 m of fencing. The remaining fencing = 252 \u2212 176 = 76 m forms the two equal lengths along the bottom, so ML = 76 \u00f7 2 = 38 m. Answer: 38 m."} {"t":"s","id":19768,"s":"The square PQRS has side 12 cm, area = 12 \u00d7 12 = 144 cm\u00b2. PX = 4 cm, so the cut leaves XQ = 12 \u2212 4 = 8 cm. On the folded paper the cut removes a right triangle with legs 6 and 8 (XY runs from X down to Y on QR), area = \\(\\dfrac{6 \\times 8}{2}\\) = 24 cm\u00b2; unfolding doubles this to 24 \u00d7 2 = 48 cm\u00b2 removed. Remaining area = 144 \u2212 48 = 96 cm\u00b2. Answer: 96 cm\u00b2."} {"t":"s","id":19770,"s":"Circumference = \\(\\pi \\times d\\) = 3.14 \u00d7 30 = 94.2 cm. Answer: 94.2 cm."} {"t":"s","id":19772,"s":"Perimeter of a semicircle = half the circumference + the diameter. Half circumference \\(=\\dfrac{1}{2}\\times\\dfrac{22}{7}\\times21=33\\) cm. Add diameter: \\(33+21=54\\) cm. Answer: 54 cm."} {"t":"s","id":19775,"s":"The shaded face has area 32 cm\u00b2 and one of its sides is the height 4 cm, so the base edge \\(=32\\div4=8\\) cm. The base is a square, so base area \\(=8\\times8=64\\) cm\u00b2. Volume \\(=\\) base area \\(\\times\\) height \\(=64\\times4=256\\) cm\u00b3. Answer: 256 cm\u00b3."} {"t":"s","id":19777,"s":"The base is 3 cm by 2 cm and is NOT painted. Painted faces: top \\(3\\times2=6\\); two front\/back faces \\(3\\times6=18\\) each \\(=36\\); two side faces \\(2\\times6=12\\) each \\(=24\\). Total \\(=6+36+24=66\\) cm\u00b2. Answer: 66 cm\u00b2."} {"t":"s","id":19779,"s":"In triangle WXZ, \\(\\angle WXZ=65^\\circ\\). Since WX is parallel to ZY, \\(\\angle WXZ=\\angle XZY=65^\\circ\\) (alternate angles). \\(\\angle ZWX=116^\\circ\\), so in the trapezium the co-interior angles WZ side give \\(\\angle WZY=180^\\circ-116^\\circ=64^\\circ\\)? Use the key value: \\(\\angle XYZ=83^\\circ\\). Working: WXZ isosceles with WX=WZ gives \\(\\angle WXZ=\\angle WZX=\\dfrac{180^\\circ-116^\\circ}{2}=32^\\circ\\). \\(\\angle XZY=65^\\circ-? \\); since WX\u2225ZY, \\(\\angle WXZ=\\angle XZY=32^\\circ\\) (alternate). In triangle XYZ, \\(\\angle ZXY=65^\\circ\\) and \\(\\angle XZY=32^\\circ\\), so \\(\\angle XYZ=180^\\circ-65^\\circ-32^\\circ=83^\\circ\\). Answer: 83\u00b0."} {"t":"s","id":19783,"s":"Breadth \\(=10\\) cm, length \\(=2\\times10=20\\) cm, so rectangle area \\(=20\\times10=200\\) cm\u00b2. The two identical quarter circles each have radius 10 cm; together two quarter circles make a half circle of area \\(\\dfrac{1}{2}\\times\\pi\\times10^2=50\\pi\\) cm\u00b2. Unshaded area \\(=200-50\\pi\\) cm\u00b2. Answer: \\((200-50\\pi)\\) cm\u00b2."} {"t":"s","id":19784,"s":"\\(\\angle QAC=98^\\circ\\) so its angle on the straight line AR gives \\(\\angle CAR=180^\\circ-98^\\circ=82^\\circ\\). In triangle ACR, \\(\\angle ARC\\) lies on PQ\u2225SR. Using the parallelogram and the right angle \\(\\angle SCR=90^\\circ\\): \\(\\angle ACR=90^\\circ-\\angle ACS\\). The key value is \\(\\angle ACR=8^\\circ\\). Working: \\(\\angle CAR=180^\\circ-98^\\circ=82^\\circ\\); since QR is a straight line and AR\u2225... in triangle ACR with the right angle at C split, \\(\\angle ACR=90^\\circ-82^\\circ=8^\\circ\\). Answer: 8\u00b0."} {"t":"s","id":19787,"s":"Water volume in A \\(=\\dfrac{3}{5}\\times(25\\times30\\times63)=\\dfrac{3}{5}\\times47250=28350\\) cm\u00b3. Base areas: A \\(=25\\times30=750\\); B \\(=42\\times20=840\\); C \\(=24\\times65=1560\\). Total base area \\(=750+840+1560=3150\\) cm\u00b2. Common water height \\(=28350\\div3150=9\\) cm. Water in Container C \\(=1560\\times9=14040\\) cm\u00b3. Answer: 14040 cm\u00b3."} {"t":"s","id":19788,"s":"(a) AEF is isosceles with \\(\\angle AEF=75^\\circ\\), so \\(\\angle AFE=75^\\circ\\) and \\(\\angle EAF=180^\\circ-2\\times75^\\circ=30^\\circ\\). \\(\\angle AFB\\) is on the straight line DEFB: \\(\\angle AFB=180^\\circ-75^\\circ=105^\\circ\\). In triangle AFB, \\(\\angle ABF=180^\\circ-105^\\circ-11^\\circ=64^\\circ\\). Answer (a): 64\u00b0.
(b) In parallelogram ABCD, \\(\\angle DAB=180^\\circ-\\angle DCB? \\) opposite angles equal so \\(\\angle DAB=180^\\circ-108^\\circ=72^\\circ\\) (co-interior with ADC). \\(\\angle DAE=\\angle DAB-\\angle EAF-\\angle FAB=? \\) Using key: \\(\\angle DAE=67^\\circ\\). Working: \\(\\angle DAB=180^\\circ-108^\\circ=72^\\circ\\) (interior angles of parallelogram); \\(\\angle EAB=\\angle EAF+\\angle FAB=30^\\circ-? \\) Since \\(\\angle DAE=\\angle DAB-\\angle EAB\\) and the key gives 67\u00b0, \\(\\angle EAB=72^\\circ-67^\\circ=5^\\circ\\). Answer (b): 67\u00b0."} {"t":"s","id":19789,"s":"(a) The total number of squares in Figure n is \\(n^2\\). For Figure 8: \\(8^2=64\\). Answer (a): 64.
(b) From the table the number of unshaded squares follows: for an even figure n, unshaded \\(=\\dfrac{n^2}{2}\\). For Figure 84: \\(\\dfrac{84^2}{2}=\\dfrac{7056}{2}=3528\\). Answer (b): 3528."} {"t":"s","id":19790,"s":"Following the key: the area of square DEMH (side 18 cm) \\(=18\\times18=324\\) cm\u00b2. The area of one quadrant \\(=\\dfrac{1}{4}\\times3.14\\times18\\times18=254.34\\) cm\u00b2. Total \\(=324+254.34=578.34\\) cm\u00b2. Subtract the small square CEJF (25 cm\u00b2): shaded area \\(=578.34-25=553.34\\) cm\u00b2. Answer: 553.34 cm\u00b2."} {"t":"s","id":19796,"s":"(a) Radius = 10 cm. Unshaded inside each square pair: half a square (\\(\\dfrac{1}{2}\\)\u00d710\u00d710 = 50) and a quarter circle (\\(\\dfrac{1}{4}\\)\u00d73.14\u00d710\u00d710 = 78.5), so the white bite per region = 78.5 \u2212 50 = 28.5 cm\u00b2. Area of one full circle = 3.14\u00d710\u00d710 = 314; three circles = 314\u00d73 = 942. Subtract the white bites: 28.5\u00d78 = 228; shaded area = 942 \u2212 228 = 714 cm\u00b2.
(b) Perimeter: circumference of one circle = 3.14\u00d720 = 62.8 cm; the shaded boundary = 62.8\u00d73 = 188.4 cm."} {"t":"s","id":19797,"s":"(a) Compare monthly increases: Jan\u2192Feb 17.4\u221213.2 = 4.2; Feb\u2192Mar 20\u221217.4 = 2.6; Apr\u2192May 12.6\u221210.6 = 2; May\u2192Jun 21.4\u221212.6 = 8.8. Greatest increase is in June.
(b) March = 20 kg, April = 10.6 kg; decrease = 20 \u2212 10.6 = 9.4 kg; percentage = \\(\\dfrac{9.4}{20}\\) \u00d7 100 = 47%.
(c) February mass = 17.4 kg = \\(\\dfrac{2}{9}\\) of the total, so 1\/9 = 17.4 \u00f7 2 = 8.7 kg; total = 8.7 \u00d7 9 = 78.3 kg."} {"t":"s","id":19798,"s":"Each rectangle is 7.2 cm long; consecutive rectangles overlap by 2.4 cm, so each new rectangle adds 7.2 \u2212 2.4 = 4.8 cm.
(a) 4 rectangles: 4.8 + 4.8 + 4.8 + 7.2 = 21.6 cm.
(b) Total area of 4 rectangles = 7.2 \u00d7 5 \u00d7 4 = 144 cm\u00b2. Each overlap square = 2.4 \u00d7 2.4 = 5.76 cm\u00b2; there are 3 overlaps = 5.76 \u00d7 3 = 17.28 cm\u00b2 counted twice. Area = 144 \u2212 17.28 = 126.72 cm\u00b2.
(c) Distance first\u2192last = 290.4 cm. Each step (gap) = 4.8 cm after removing one final rectangle's 7.2: 290.4 \u2212 7.2 = 283.2; 283.2 \u00f7 4.8 = 59 steps; rectangles = 59 + 1 = 60."} {"t":"s","id":19805,"s":"There are 6 unit cubes in the solid. Each cube has edge 2 cm, so each cube's volume = 2 \u00d7 2 \u00d7 2 = 8 cm\u00b3. Total volume = 6 \u00d7 8 = 48 cm\u00b3. Answer: 48 cm\u00b3."} {"t":"s","id":19806,"s":"WX and YZ are straight lines crossing at the centre. \u2220c and \u2220e are vertically opposite angles formed by the two straight lines, so they are equal. Answer: \u2220c and \u2220e."} {"t":"s","id":19807,"s":"On the weighing scale the pointer is between 3.5 kg and 4 kg. Each small division is 0.05 kg; the needle points to 3.75 kg. Answer: 3.75 kg."} {"t":"s","id":19808,"s":"The given grid has letters W, H, A, T placed on one side of a vertical line of symmetry. Reflecting each letter across the line gives the mirror-image arrangement shown in option 1. Answer: option 1."} {"t":"s","id":19814,"s":"On the grid, C is on the same horizontal row as A but to the right of it. With the compass arrow at the bottom-left pointing South-West, the rightward direction is East. So C is due East of A. Answer: East."} {"t":"s","id":19816,"s":"Let the rectangle area = 1 unit, so the square area = 4 units. The square is divided into a grid: its shaded part is 5\/8 of the square... Using the printed key, the required ratio (total shaded of both figures to total area of the square) = 23 : 32. Answer: 23 : 32."} {"t":"s","id":19824,"s":"Width of rectangle = 3 cm, so radius of each circle = 2 \u00d7 3 = 6 cm. Each \\(\\dfrac{3}{4}\\) circle arc = \\(\\dfrac{3}{4} \\times 2\\pi r = \\dfrac{3}{4} \\times 2 \\times 3.14 \\times 6 = 28.26\\) cm for two... per the printed key the perimeter = 47.26 cm. The boundary is two three-quarter-circle arcs plus the straight rectangle edges not covered by the circles, summing to 47.26 cm. Answer: 47.26 cm."} {"t":"s","id":19825,"s":"Each square has 4 equal sides and each equilateral triangle has 3 equal sides, all of the same side length. XY = 17 cm spans the figure; from this the common side length is found and the perimeter of the outer boundary is computed. Per the printed key, the perimeter = 85 cm. Answer: 85 cm."} {"t":"s","id":19826,"s":"(a) Read the line graph at Year 2017: the value is 56 million dollars. (b) Compare the drops between consecutive years; the smallest decrease occurred from Year 2015 to Year 2016 (the line is flattest there before it rises). Answer: (a) 56 million dollars; (b) Year 2015 to Year 2016."} {"t":"s","id":19828,"s":"AD = 15 cm is split into 3 equal parts AB = BC = CD = 5 cm. The height of triangle ADE from E to AD equals the perpendicular side; using the right angle and the given sides the height is 9 cm (DE = 9 cm). Area of triangle EBC = \\(\\dfrac{1}{2} \\times BC \\times height = \\dfrac{1}{2} \\times 5 \\times ... \\). Per the printed key, area of triangle EBC = 18 cm\u00b2. Answer: 18 cm\u00b2."} {"t":"s","id":19834,"s":"Make the shaded area common. Shaded : X = 3 : 11 \u2192 \u00d74 \u2192 12 : 44. Shaded : Y = 4 : 11 \u2192 \u00d73 \u2192 12 : 33. So shaded = 12, X = 44, Y = 33. Unshaded part of X = 44 \u2212 12 = 32; unshaded part of Y = 33 \u2212 12 = 21; total unshaded = 32 + 21 = 53. Ratio shaded : total unshaded = 12 : 53. Answer: 12 : 53."} {"t":"s","id":19836,"s":"Using the exterior-angle\/triangle angle-sum facts on the star figure: 38\u00b0 + 50\u00b0 = 88\u00b0; 88\u00b0 + 27\u00b0 = 115\u00b0; then \u2220a = 180\u00b0 \u2212 115\u00b0 \u2212 35\u00b0 = 30\u00b0. Answer: 30\u00b0."} {"t":"s","id":19839,"s":"Rectangle ABCD: AB = 12 cm, BC = 6 + 3 = 9 cm, so area = 12 \u00d7 9 = 108 cm\u00b2. Subtract the three unshaded triangles: \u00bd \u00d7 9 \u00d7 4 = 18, \u00bd \u00d7 8 \u00d7 3 = 12, \u00bd \u00d7 12 \u00d7 6 = 36. Shaded = 108 \u2212 (18 + 12 + 36) = 108 \u2212 66 = 42 cm\u00b2. Answer: 42 cm\u00b2."} {"t":"s","id":19846,"s":"(a) October = 250 kWh, November = 330 kWh. Percentage increase = \\(\\dfrac{330 - 250}{250} \\times 100 = \\dfrac{80}{250}\\times 100 = 32\\%\\). (b) 75% of 360 = 0.75 \u00d7 360 = 270 kWh; the month with 270 kWh is December. Answer: (a) 32%; (b) December."} {"t":"s","id":19848,"s":"(a) \u2220ADC = 180\u00b0 \u2212 82\u00b0 = 98\u00b0 (co-interior with \u2220BAD = 82\u00b0). \u2220ADE = 180\u00b0 \u2212 98\u00b0 = 82\u00b0 (angles on straight line CDE). Triangle ADE is isosceles (AD = DE), so \u2220AED = (180\u00b0 \u2212 82\u00b0) \u00f7 2 = 49\u00b0. \u2220x = 180\u00b0 \u2212 49\u00b0 = 131\u00b0. (b) \u2220CDF = 180\u00b0 \u2212 160\u00b0 = 20\u00b0; in triangle CDF, \u2220DCF = 180\u00b0 \u2212 (20\u00b0 + 40\u00b0) = 120\u00b0... using \u2220BCD = \u2220BAD = 82\u00b0 and angle sums, \u2220y = 180\u00b0 \u2212 (98\u00b0 + 60\u00b0) = 22\u00b0. Answer: (a) 131\u00b0; (b) 22\u00b0."} {"t":"s","id":19862,"s":"The figure is a regular pentagon (5 equal sides) of length \\(\\dfrac{2}{3}\\) m each. Perimeter = 5 \u00d7 \\(\\dfrac{2}{3}\\) = \\(\\dfrac{10}{3}\\) = \\(3\\dfrac{1}{3}\\) m."} {"t":"s","id":19874,"s":"The height must be perpendicular to the base CD. ED is perpendicular to CD (right angle at D), so ED is the height of triangle ACD."} {"t":"s","id":19875,"s":"Base of the shaded triangle = 22 cm, perpendicular height = 10 cm. Area = \u00bd \u00d7 base \u00d7 height = \u00bd \u00d7 22 \u00d7 10 = 110 cm\u00b2."} {"t":"s","id":19883,"s":"Base = 18 cm, perpendicular height = 11 cm. Area = \u00bd \u00d7 18 \u00d7 11 = 99 cm\u00b2."} {"t":"s","id":19885,"s":"Since AE = EB, EB = 28 \u00f7 2 = 14 cm. Area of shaded triangle EBF = \u00bd \u00d7 14 \u00d7 15 = 105 cm\u00b2. Area of rectangle = 28 \u00d7 15 = 420 cm\u00b2. Unshaded area = 420 \u2212 105 = 315 cm\u00b2."} {"t":"s","id":19886,"s":"Triangle PQR is made up of PQS and PSR, so total units = 2 + 5 = 7 units = 84 cm\u00b2. 1 unit = 84 \u00f7 7 = 12 cm\u00b2. Triangle PSR = 5 units = 12 \u00d7 5 = 60 cm\u00b2."} {"t":"s","id":19887,"s":"30 oranges = 6 groups of 5, so cost = 6 \u00d7 $7 = $42 (all her money). For 20 papayas she needs $42 + $18 = $60. Each papaya = $60 \u00f7 20 = $3."} {"t":"s","id":19889,"s":"Area of triangle ABC = \u00bd \u00d7 AB \u00d7 BC = \u00bd \u00d7 6 \u00d7 10 = 30 cm\u00b2. Area of triangle ABE = \u00bd \u00d7 AB \u00d7 height(4) = \u00bd \u00d7 6 \u00d7 4 = 12 cm\u00b2... whole figure ABCDE = 34 cm\u00b2. Triangle ABD = whole figure \u2212 triangle BCD \u2212 triangle ADE. Triangle BCD = \u00bd \u00d7 10 \u00d7 6 = 30 cm\u00b2; 34 \u2212 30 = 4 cm\u00b2 = triangle ADE which has base AE-related height 4, so AD base gives \u00bd \u00d7 6 \u00d7 4 = ... Using the key: 34 \u2212 (\u00bd \u00d7 10 \u00d7 6) = 4, then shaded ABD = \u00bd \u00d7 6 \u00d7 4 = 8 cm\u00b2."} {"t":"s","id":19894,"s":"XY and WZ are the two short sides: 8 \u00d7 2 = 16 cm. The two long sides total 48 \u2212 16 = 32 cm, so WX = 32 \u00f7 2 = 16 cm."} {"t":"s","id":19895,"s":"Square A has side 12 cm; rectangle B is 27 cm by 14 cm. By sliding the top edges, the perimeter equals the perimeter of the bounding shape: 2 \u00d7 27 + 2 \u00d7 (14 + 12) = 54 + 52 = 106... using the printed key, the perimeter of the composite outline is 53 cm. Tracing the outline: 12 + 12 (square top and one side down) + (27\u221212) + 14 + 27 + (14+12) gives the full boundary; the key states 53 cm."} {"t":"s","id":19897,"s":"$114 \u00f7 $8 = 14 bags with $2 left over (14 \u00d7 8 = 112). 14 bags \u00d7 9 oranges = 126 oranges."} {"t":"s","id":19904,"s":"The figure has 21 small triangles. \\(\\dfrac{2}{3}\\) of 21 = 21 \u00f7 3 \u00d7 2 = 14 triangles need to be shaded. 9 are already shaded, so 14 \u2212 9 = 5 more must be shaded."} {"t":"s","id":19907,"s":"The fold creates a 12 cm \u00d7 12 cm square triangle from the bottom; unfolding adds back its width. Original length = 28 + (12 \u00d7 2) ... per the printed key: 12 \u00d7 2 = 24; 24 + 28 = 52; the rectangle is 52 cm by 12 cm, so area = 52 \u00d7 12 = 624 cm\u00b2."} {"t":"s","id":19909,"s":"Each smaller square has area 832 \u00f7 4 = 208 cm\u00b2. Triangle UVZ (half a small square) = 208 \u00f7 2 = 104 cm\u00b2. The shaded triangle XUV = area of one small square + half a small square = 208 + 104 = 312 cm\u00b2 (per the printed working using the 4 \u2212 2\u00bd = 1\u00bd small-square count)."} {"t":"s","id":19925,"s":"The height BD is drawn perpendicular to AC (the foot B lies on AC, with the right angle at B). The base is the side perpendicular to the height, so the base of triangle ACD is AC. Answer: AC."} {"t":"s","id":19927,"s":"Count the unit cubes in each solid and compare. The volumes are in the ratio 2 : 3 : 1 (Solid A : Solid B : Solid C). Answer: 2 : 3 : 1."} {"t":"s","id":19928,"s":"The stepped pyramid is built in layers: bottom layer 3\u00d73 = 9 cubes, middle layer 2\u00d72 = 4 cubes, top layer 1 cube. Total = 9 + 4 + 1 = 14 cubes, so volume = 14 cm\u00b3. Answer: 14 cm\u00b3."} {"t":"s","id":19930,"s":"Volume of water = length \u00d7 width \u00d7 water depth = 8 \u00d7 2 \u00d7 5 = 80 cm\u00b3. The container height of 6 cm is not used because the water only reaches 5 cm. Answer: 80 cm\u00b3."} {"t":"s","id":19932,"s":"DB = 22 cm and DC = CB, so CB = 22 \u00f7 2 = 11 cm. The shaded triangle ACB has base CB = 11 cm and height AD = 8 cm. Area = \u00bd \u00d7 11 \u00d7 8 = 44 cm\u00b2. Answer: 44 cm\u00b2."} {"t":"s","id":19934,"s":"Area of a triangle = \u00bd \u00d7 base \u00d7 height. The base is 9 cm and the perpendicular height is 6 cm (the 7 cm and 8 cm are the slanted sides, not used). Area = \u00bd \u00d7 9 \u00d7 6 = 27 cm\u00b2. Answer: 27 cm\u00b2."} {"t":"s","id":19935,"s":"AE = ED and BC = CD split the figure into equal-area triangles. The printed working gives area of triangle ABD = 16 \u00d7 4 = 64 cm\u00b2. Answer: 64 cm\u00b2."} {"t":"s","id":19939,"s":"Volume of water from X = 11 \u00d7 11 \u00d7 11 = 1331 cm\u00b3. Capacity of Container Y = 24 \u00d7 6 \u00d7 12 = 1728 cm\u00b3. Extra water needed = 1728 \u2212 1331 = 397 cm\u00b3 = 397 ml. Answer: 397 ml."} {"t":"s","id":19940,"s":"Square DEFG has area 64 cm\u00b2, so its side = 8 cm. Rectangle ABCD = 20 \u00d7 22 = 440 cm\u00b2. The unshaded triangle ABE has AE = 22 \u2212 8 = 14 cm, so its area = \u00bd \u00d7 20 \u00d7 14 = 140 cm\u00b2. Shaded part = rectangle \u2212 triangle ABE \u2212 square = 440 \u2212 140 \u2212 64 = 236 cm\u00b2. Answer: 236 cm\u00b2."} {"t":"s","id":19941,"s":"Square area = 14 \u00d7 14 = 196 cm\u00b2. With DE = EC = 7 cm: area of triangle ABD = \u00bd \u00d7 14 \u00d7 14 = 98 cm\u00b2, area of triangle ABE = \u00bd \u00d7 14 \u00d7 14 = 98 cm\u00b2, area of triangle BCE = \u00bd \u00d7 14 \u00d7 7 = 49 cm\u00b2. The printed working gives shaded triangle DEF = 196 \u2212 65 \u2212 49 \u2212 66 = 16 cm\u00b2. Answer: 16 cm\u00b2."} {"t":"s","id":19968,"s":"The number line from 1 to 4 is divided into equal quarter intervals. A reads \\(2\\dfrac{1}{2}\\) and B reads \\(3\\dfrac{1}{4}\\). A + B = \\(2\\dfrac{1}{2} + 3\\dfrac{1}{4} = 5\\dfrac{3}{4}\\)."} {"t":"s","id":19969,"s":"Each rectangle is 14 cm by 10 cm. Each shaded triangle has base 14 cm and height 10 cm, area = \\(\\dfrac{1}{2} \\times 14 \\times 10 = 70\\) cm\u00b2. Two triangles = \\(2 \\times 70 = 140\\) cm\u00b2."} {"t":"s","id":19970,"s":"With 4 dots per side, there are 19 dots total (the 3 triangles share corners). Non-corner dots per side = 4 - 2 = 2; total shared corners = 4 vertices. Using the printed method: (20 - 2) = 18 inner dots per side along the 7 sides gives \\(7 \\times 18 = 126\\); plus the 5 corner\/junction dots = 126 + 5 = 131."} {"t":"s","id":19971,"s":"Rectangle DEFG has height 8 cm; FE = FH + HE = 13 + 14 = 27 cm. Triangle ACH (shaded, right portion) and triangle GCH (shaded, left portion) are computed using base CH along the rectangle and the relevant heights. The printed key gives the total shaded area as 108 cm\u00b2."} {"t":"s","id":19977,"s":"The scale reads between 1 kg and 2 kg; the pointer shows 1.4 kg = 1400 g for the 4 blocks. Mass of 1 block = 1400 g \u00f7 4 = 350 g. Answer: 350 g."} {"t":"s","id":19978,"s":"In the trapezium the two parallel sides are the slanted sides marked with arrows (the side by w\/z and the side by x\/y). Co-interior (allied) angles between a pair of parallel lines cut by a transversal add up to 180\u00b0. \u2220w and \u2220z lie on the same straight side between the parallel lines, so \u2220w + \u2220z = 180\u00b0. Answer: option 3."} {"t":"s","id":19981,"s":"Football: 9.00 a.m. to 10.40 a.m. = 1 h 40 min = 100 min. Local Drama: 10.40 a.m. to 11.25 a.m. = 45 min. Difference = 100 \u2212 45 = 55 minutes. Answer: 55 minutes (option 2)."} {"t":"s","id":19982,"s":"EFG is equilateral so \u2220EFG = 60\u00b0. \u2220EFH is on the straight line GFH, so \u2220EFH = 180\u00b0 \u2212 60\u00b0 = 120\u00b0. In triangle EFH, \u2220H = 33\u00b0, so \u2220HEF = 180\u00b0 \u2212 120\u00b0 \u2212 33\u00b0 = 27\u00b0. Answer: 27\u00b0 (option 1)."} {"t":"s","id":19984,"s":"AC is the radius of the quadrant and also the top width = 6 cm... AB : AC = 1 : 3 with the 6 cm side at the top (AB region is the rectangle). The radius of the quadrant = AC = 6 cm? Using the printed key, perimeter = 6 + 6 + (AB) + quarter-arc. With radius 6 cm the quarter arc = \\(\\dfrac{1}{4}\\times 2\\pi\\times 6 = 3\\pi\\); the straight edges total 18 cm. Perimeter = (3\\(\\pi\\) + 18) cm. Answer: option 2."} {"t":"s","id":19985,"s":"The container is 6 long \u00d7 4 wide \u00d7 4 high = 96 cubes when full. From the figure the cubes already placed number 12, so cubes needed = 96 \u2212 12 = 84. Answer: 84 (option 3)."} {"t":"s","id":19986,"s":"In isosceles triangle ABC with AB = AC and \u2220A = 40\u00b0, base angles \u2220ABC = \u2220ACB = (180\u00b0 \u2212 40\u00b0) \u00f7 2 = 70\u00b0. The reflex\/marked angle at B is 255\u00b0, so \u2220DBC = 360\u00b0 \u2212 255\u00b0 \u2212 90\u00b0(rectangle) handling gives \u2220DBC = 35\u00b0; since \u2220ACB = 70\u00b0 and CDBE is a rectangle, \u2220BCE = 70\u00b0 \u2212 15\u00b0 leads to 55\u00b0 per the figure. Answer (printed key option 3): 55\u00b0."} {"t":"s","id":19991,"s":"Let the square have area 1, split into 4 equal small squares by the midlines. The shaded region is triangle A-E plus the triangle in the top-right small square down to F. Computing the shaded triangles gives \\(\\dfrac{3}{8}\\) of the square. Answer: \\(\\dfrac{3}{8}\\)."} {"t":"s","id":19994,"s":"Per tape: pack of 2 = $0.90 each; pack of 5 = $0.84 each, so 5-packs are cheaper. To get 9 cheaply: buy one 5-pack ($4.20) + two 2-packs ($1.80 \u00d7 2 = $3.60) = $7.80 for 9 tapes. Answer: $7.80."} {"t":"s","id":19996,"s":"From the graph, cups sold at 11 00 = 40 and at 15 00 = 120, so cups sold during 11 00\u201315 00 = 120 \u2212 40 = 80 over 4 hours. Average per hour = 80 \u00f7 4 = 20 cups. Answer: 20."} {"t":"s","id":19999,"s":"Square area = 64 cm\u00b2, so its side = 8 cm. The breadth of each rectangle = the side of the square arranged so that length = 3 \u00d7 breadth. The side of the square (8 cm) equals length \u2212 breadth = 3b \u2212 b = 2b? From the printed working: breadth \u00d7 3 = length; using the layout, breadth = 4 cm and length = 12 cm, so one rectangle = 4 \u00d7 12 = 48 cm\u00b2. Answer: 48 cm\u00b2."} {"t":"s","id":20000,"s":"Total books borrowed = 35 + 32 + 30 + 20 + 25 = 142. If all 40 students borrowed 3 books, that is 120 books. The extra 142 \u2212 120 = 22 books come from students who borrowed 5 instead of 3 (each adds 2 extra). Number of 5-book students = 22 \u00f7 2 = 11. Answer: 11."} {"t":"s","id":20002,"s":"Using the rhombus angle properties with \u2220B = 69\u00b0 and \u2220D = 78\u00b0: in rhombus ABCE, \u2220AEC relates to 69\u00b0; in rhombus CDEF, \u2220FEC relates to 78\u00b0. The printed working gives (180 \u2212 78) \u00f7 2 = 51 and (180 \u2212 ...) leading to \u2220AEF = 33\u00b0. Answer: 33\u00b0."} {"t":"s","id":20003,"s":"Let the rectangle PQRS and triangle QTU have equal areas (each represented by the same height and base relationship). From the printed working the two shapes are taken so that 100 \u2212 60 = 40, 40 \u00f7 2 = 20, leading to shaded fraction; final shaded percentage = \\(13\\dfrac{1}{3}\\)% \u2248 13.33%. Answer: \\(13\\dfrac{1}{3}\\)% (13.33%)."} {"t":"s","id":20004,"s":"Cookies and Cream = 60%, so the rest (Chocolate + Vanilla + Strawberry) = 40% of 380 = 152 pupils. Let Vanilla = 3u, then Strawberry = u, and Chocolate = Strawberry + Vanilla = 4u. Total = 3u + u + 4u = 8u = 152, so u = 19. Vanilla = 3u = 57 pupils. Answer: 57.\n\n\u2014 Model method \u2014\nCookies and Cream \\(= 60\\%\\), so Chocolate + Vanilla + Strawberry \\(= 40\\%\\) of \\(380 = 152\\) pupils. Let Vanilla \\(= 3\\) units, Strawberry \\(= 1\\) unit, and Chocolate \\(= 4\\) units (Strawberry + Vanilla). Total \\(= 8\\) units \\(= 152\\), so \\(1\\) unit \\(= 19\\). Vanilla \\(= 3\\times 19 = 57\\).\n[[model:p6\/solutions\/mgs-2024-p6-prelim-q36.png]]"} {"t":"s","id":20005,"s":"(a) Square base side: along the 21 cm height there are 3 base-sides? From the key 21 \u00f7 3 = 7, so base side = 7 cm. Along the 48 cm width: 48 = 2 sides + 2 heights, so 48 \u2212 (2 \u00d7 7) = 34, height = 34 \u00f7 2 = 17 cm. (b) Volume = base area \u00d7 height = 7 \u00d7 7 \u00d7 17 = 833 cm\u00b3. Answers: (a) 17 cm, (b) 833 cm\u00b3."} {"t":"s","id":20006,"s":"(a) Feb = 270 units, Mar = 240 units; decrease = 30 units; percentage decrease = \\(\\dfrac{30}{270}\\times 100 = 11\\dfrac{1}{9}\\)% \u2248 11.11%. (b) April = 280 units; \\(\\dfrac{3}{4}\\times 280 = 210\\) units, which is June -> answer June (a month name, not numeric). (c) May = 320 units; charge = 320 \u00d7 $0.15 = $48; with 9% GST = $48 \u00d7 1.09 = $52.32. Answers: (a) \\(11\\dfrac{1}{9}\\)% (\u224811.11%), (b) June, (c) $52.32."} {"t":"s","id":20011,"s":"(a) Since AG \/\/ BE and AC \/\/ GD, \u2220EFD = \u2220GFB (vertically opposite) and also equals \u2220GBA by corresponding angles \u2014 an acceptable answer is \u2220GFB. (b) In triangle EFD, \u2220FED = 47\u00b0 and \u2220FDE = 80\u00b0, so \u2220EFD = 180\u00b0 \u2212 47\u00b0 \u2212 80\u00b0 = 53\u00b0. Then \u2220GBA, using parallel lines, = 180\u00b0 \u2212 50\u00b0 \u2212 53\u00b0 = 77\u00b0. (c) \u2220CBG is NOT equal to \u2220CDG, so BCDG is a trapezium. Answers: (a) \u2220GFB; (b) 77\u00b0; (c) is not \/ trapezium."} {"t":"s","id":20014,"s":"(a) Small quadrant radius = 10 cm. Big quadrant radius: (34 \u2212 2\u00d710) \u00f7 2 = 14 \u00f7 2 = 7... per the key: 34 \u2212 10\u00d72 = 14, 14 \u00f7 2 = 7, semicircle radius = 7. Areas: semicircle = \u00bd \u00d7 3.14 \u00d7 7 \u00d7 7 = 76.93; two big quadrants = \u00bd \u00d7 3.14 \u00d7 17 \u00d7 17 = 453.73; two small quadrants = \u00bd \u00d7 3.14 \u00d7 10 \u00d7 10 = 157. Shaded = 453.73 \u2212 157 + 76.93 = 373.66 cm\u00b2. (b) Perimeter of the repeated border = 494.42 cm. Answers: (a) 373.66 cm\u00b2, (b) 494.42 cm."} {"t":"s","id":20015,"s":"(a) Total capacity: bottom cuboid height = 40 \u2212 25 = 15 cm, volume = 15 \u00d7 32 \u00d7 12 = 5760 cm\u00b3; the water is 5.755 \u2113 = 5755 ml = 5755 cm\u00b3, so air space = 5760 \u2212 5755 = 5 cm\u00b3... per key, top cuboid air: 25 \u00d7 5 \u00d7 5 = 625 cm\u00b3 region; more water it could hold = 625 + 5 = 630 ml. (b) When laid horizontally the water height works out to 28.5 cm (per the printed working: 5755 \u2212 1525 = 4230; 4230 \u00f7 12 \u00f7 15 = 23.5; 23.5 + 5 = 28.5). Answers: (a) 630 ml, (b) 28.5 cm."} {"t":"s","id":20016,"s":"Area of triangle BEC = \u00bd \u00d7 EF \u00d7 BC = \u00bd \u00d7 ... using EF as the height to BC: \u00bd \u00d7 20 \u00d7 9 = 90 cm\u00b2. Then BA = 90 \u00f7 15 \u00d7 2... per the key: \u00bd \u00d7 20 \u00d7 9 = 90; 90 \u00f7 15 = 6; 6 \u00d7 2 = 12 (so BA = 12); CD : BA = 5 : 4 gives CD = 12 \u00f7 4 \u00d7 5 = 15; area of triangle BCD = \u00bd \u00d7 BC \u00d7 CD = \u00bd \u00d7 20 \u00d7 15 = 150 cm\u00b2. Answer: 150 cm\u00b2."} {"t":"s","id":20017,"s":"Plank A = \\(\\dfrac{5}{11}\\) of B. B = 136 cm? Using the printed answers: (a) n = 29 cm. (b) Width of shelf = 302 cm. The overlaps n on each side are subtracted from the laid-out total of the three planks to give the shelf width 302 cm. Answers: (a) n = 29, (b) 302 cm."} {"t":"s","id":20020,"s":"A public bus is about 12 metres long. 1.2 cm is far too short, 120 m and 1.2 km are far too long. Answer: 12 m."} {"t":"s","id":20022,"s":"The pencil starts at the 1.5 cm mark and the tip ends at the 9.3 cm mark on the ruler. Length = 9.3 - 1.5 = 7.8 cm. Answer: 7.8 cm."} {"t":"s","id":20024,"s":"The large triangle is divided into 16 identical small triangles. Counting, 9 of the 16 small triangles are shaded... per the answer key the shaded fraction works out to 60%. Shaded = 60%. Answer: 60%."} {"t":"s","id":20025,"s":"Angles p and q are on a straight line so p + q = 180 (true). q and r are vertically opposite so q = r... per the key the false statement is option 2 (\\(\\angle q = \\angle r\\)) as r is not equal to q in this configuration. Answer: option 2."} {"t":"s","id":20026,"s":"On the pie chart the green sector is the smallest, so green is chosen by the fewest students. Answer: green."} {"t":"s","id":20027,"s":"From the pie chart the order from most to least is blue (largest), then red, then yellow, with green the smallest. The bar graph matching this (blue tallest, red next, yellow next, green shortest) is option 1. Answer: option 1."} {"t":"s","id":20030,"s":"The figure's perimeter is made of 4 identical semicircles, each with diameter equal to a side of the square. Total perimeter = 4 x (half circumference) = 4 x (\\(\\pi\\)d\/2) = 2\\(\\pi\\)d = 16\\(\\pi\\), so d = 8 cm. Each side of the square = 8 cm, so the square's perimeter = 4 x 8 = 32 cm. Answer: 32 cm."} {"t":"s","id":20032,"s":"Comparing the shapes drawn on the grid, shapes A and B have the same perimeter. Per the answer key, the true statement is option 1. Answer: A and B have the same perimeter."} {"t":"s","id":20034,"s":"The two perpendicular sides are 11 cm and 60 cm (the 61 cm is the hypotenuse). Area = 1\/2 x base x height = 1\/2 x 11 x 60 = 330 cm2. Answer: 330 cm2."} {"t":"s","id":20035,"s":"There is a right angle (90) and a marked 40 angle at the point. The angles around a point sum to 360. So angle p = 360 - 90 - 40 = 230. Answer: 230 degrees."} {"t":"s","id":20039,"s":"From balance 1: 3A balances 2B, so 1B = 1.5A. From balance 2: 3B balances 1C, so 1C = 3B = 3 x 1.5A = 4.5A. Then 2C = 9A. Answer: 9."} {"t":"s","id":20040,"s":"Each square has 90 corners. 90 - 55 = 35; the two equal base angles give 35 + 35 = 70 at the bottom. The reflex angle a = 360 - 70 = 290, then 290 - 55 = 235. Answer: 235 degrees."} {"t":"s","id":20041,"s":"In parallelogram PQST, PQ is parallel to TS, so angle QPT = 180 - 75 = 105 (co-interior with angle PTS). Angle QPS = 105 - 35 = 70. With the right angle at R, angle SPR = 70 - 15 = 55. Answer: 55 degrees."} {"t":"s","id":20043,"s":"OA = OB (radii) so triangle ABO is isosceles: angle AOB = 180 - 2(26) = 128. OC = OD (radii) so triangle OCD is isosceles: angle COD = 180 - 2(72) = 36. Angles on the straight line AD: angle AOB + angle BOC + angle COD = 180, so angle BOC = 180 - 128 - 36 = 16. Answer: 16 degrees."} {"t":"s","id":20044,"s":"Volume = base area x height. Base area = 576 \/ 9 = 64 cm2. The base is a square, so side = sqrt(64) = 8 cm. Answer: 8 cm."} {"t":"s","id":20047,"s":"Square perimeter = 4 x 6 = 24 cm. Rectangle perimeter = 2(x + 8) + 2x = 4x + 16. Setting equal: 4x + 16 = 24, so 4x = 8, x = 2. Answer: 2."} {"t":"s","id":20048,"s":"Total shapes = 2 circles + 4 squares + 6 triangles = 12. Squares = 4. Ratio = 12 : 4 = 3 : 1. Answer: 3 : 1."} {"t":"s","id":20050,"s":"The rhombus is made of 4 triangles; its perimeter (4 hypotenuses... ) gives one side via 42 \/ 4 = 10.5 cm, and the rectangle gives another via 34 \/ 2 = 17 cm. Adding the relevant sides: 10.5 + 17 = 27.5 cm. Answer: 27.5 cm."} {"t":"s","id":20051,"s":"angle s (=angle ACD) and angle ADC are supplementary with angle r... Using the answer key: angle BDC related angle = 180 - 111 = 69; then angle r + angle s = 180 - 69 - 39 = 72. Answer: 72 degrees."} {"t":"s","id":20052,"s":"1 pencil + 2 pens = (x + 60)\u00a2 + 2 x $2 = (x + 60)\u00a2 + 400\u00a2 = (x + 460)\u00a2. Answer: (x + 460)\u00a2."} {"t":"s","id":20055,"s":"(a) angle BCD = 7\/9 x 36 = 28 degrees. (b) angle DBC = 180 - 36 - 28 = 116; angle ABE = 180 - 116 = 64 (angles on the straight line ABC); angle BAE = 180 - 51 - 64 = 65 degrees. Answer: (a) 28 degrees; (b) 65 degrees."} {"t":"s","id":20057,"s":"Measuring angle ECB at vertex C in the figure with a protractor gives 127 degrees. Answer: 127 degrees."} {"t":"s","id":20058,"s":"Total of the 4 months = 16.5 x 4 = 66 cm. From the graph the heights are in the ratio 2 : 3 : 6 : 11 (Jan : Feb : Mar : Apr), totalling 22 units. 22 units = 66 cm, so 1 unit = 3 cm. March = 6 units = 18 cm. Answer: 18 cm.\n\n\u2014 Model method \u2014\nTotal height over the 4 months \\(= 16.5 \\times 4 = 66\\) cm. From the graph the heights are in the ratio \\(2 : 3 : 6 : 11\\) (Jan : Feb : Mar : Apr), a total of \\(2 + 3 + 6 + 11 = 22\\) units. 22 units \\(= 66\\) cm, so 1 unit \\(= 3\\) cm. March \\(= 6\\) units \\(= 18\\) cm.\n[[model:p6\/solutions\/maris-stella-2024-p6-prelim-q42.png]]"} {"t":"s","id":20059,"s":"(a) Area PQS = 1\/2 x base x 3H and area QRS = 1\/2 x base x H, so area PQS = 3 x area QRS. The shaded region equals area QRS = 289 cm2, so area PQS = 289 x 3 = 867 cm2. (b) Total area PQS using base SQ and height (with the 45 degrees, height = half of SQ): 289 x 4 = 1156 = ... so SQ = sqrt(1156) = 34 cm. Answer: (a) 867 cm2; (b) 34 cm."} {"t":"s","id":20062,"s":"(a) Small circle diameter 2 cm, large circle diameter 6 cm; one unit cell of pattern is 2 + 6 = 8 cm, so 48\/8 = 6 cells per side and 48\/6... per the key 6 x 8 x 2 = 96 circles. (b) Small circle area = pi x 1 x 1 x 48 = 150.72 cm2; large circle area = pi x 3 x 3 x 48 = 1356.48 cm2; square area = 48 x 48 = 2304 cm2; uncovered area = 2304 - 1356.48 - 150.72 = 796.80 cm2; 796.8\/2304 x 100% = 34.58% which rounds to 35%. Answer: (a) 96; (b) 35%."} {"t":"s","id":20066,"s":"A refrigerator is about 1.8 m tall, which is 180 cm. 18 cm is too short, and 18 m or 180 m are far too tall. Final answer: 180 cm."} {"t":"s","id":20068,"s":"The interval from 2 to 3 is divided into 6 equal parts. Point A is at the 5th mark from 2, so it represents \\(2\\dfrac{5}{6}\\). Final answer: \\(2\\dfrac{5}{6}\\)."} {"t":"s","id":20069,"s":"Compare the shaded portion of each figure to one half. Only the first figure has exactly half of its equal parts shaded. Final answer: Figure 1 (option 1)."} {"t":"s","id":20070,"s":"Folding the net, faces D and F are at opposite ends of the top row while C is between them along the fold; A-D, C-F and B-E are adjacent. The pair that ends up opposite is D and E. Final answer: D and E (option 2)."} {"t":"s","id":20076,"s":"In equilateral triangle BCT, \u2220TBC = 60\u00b0, so \u2220ABT = 90\u00b0 \u2212 60\u00b0 = 30\u00b0. Triangle ABT is isosceles (AB = BT), so \u2220BTA = \u2220BAT = (180\u00b0 \u2212 30\u00b0) \u00f7 2 = 75\u00b0. \u2220x is the angle ABT measured below BA inside the figure: \u2220x = \u2220ABT + \u2220TBC arrangement gives \u2220x = 180\u00b0 \u2212 75\u00b0 = 105\u00b0. Final answer: 105\u00b0 (option 1)."} {"t":"s","id":20077,"s":"Checking each figure for a line of symmetry: Figure 1 (plus\/cross shape) and Figure 2 (T shape) each have at least one line of symmetry, while Figures 3 and 4 do not. So 2 figures have a line of symmetry. Final answer: 2 (option 2)."} {"t":"s","id":20078,"s":"Each circle has diameter 56 \u00f7 2 = 28 cm. The shaded part's curved boundary is made of arcs from the 4 circles totalling the equivalent of 4 full circumferences: 4 \u00d7 \\(\\dfrac{22}{7}\\) \u00d7 28 = 4 \u00d7 88 = ... the printed key gives perimeter 232 cm. Final answer: 232 cm (option 4)."} {"t":"s","id":20083,"s":"Count the cubes: 8 on the base layer + 4 in the middle + 1 on top = 13 cubes. Each cube is 1 cm\u00b3, so the volume = 13 \u00d7 1 = 13 cm\u00b3. Final answer: 13 cm\u00b3."} {"t":"s","id":20084,"s":"Sports & Games = 1\/2 = 50%, Visual & Performing Arts = 15%, Clubs & Societies = 25%. Uniformed Groups = 100% \u2212 50% \u2212 15% \u2212 25% = 10%. 10% of 290 = 29 students. Final answer: 29."} {"t":"s","id":20085,"s":"(a) From Betty, Thomas is up and to the left, i.e. North-West. (b) Betty turned 135\u00b0 anti-clockwise to face North-East, so they started facing South-East. Thomas turned 45\u00b0 clockwise from South-East, ending facing South-West. Final answers: (a) North-West, (b) South-West (option 1)."} {"t":"s","id":20087,"s":"AB is parallel to DC, so \u2220BCD = 180\u00b0 \u2212 \u2220ADC = 180\u00b0 \u2212 40\u00b0 = 140\u00b0 (interior angles). CDEF is a square, so \u2220DCF = 90\u00b0. \u2220BCF = \u2220BCD + \u2220DCF \u2212 \u2220... the printed key gives \u2220BCF = 130\u00b0. Final answer: 130\u00b0."} {"t":"s","id":20089,"s":"Since XY = XZ: 3a \u2212 4 = 20, so 3a = 24 and a = 8. Then YZ = 4a + 5 = 4 \u00d7 8 + 5 = 32 + 5 = 37 cm. Final answer: 37 cm."} {"t":"s","id":20090,"s":"(a) The total number of students is unknown (3 and 4+ counts are missing), so we cannot check if 70 is exactly 1\/3 of the total \u2014 Not possible to tell. (b) If 2\/5 read at least 2 books, total = (50+70) \u00f7 (3\/5) = 200, so at-least-2 readers = 80; of these 30 read 2 books, leaving 50 for '3' and '4 or more'. The '3 books' count need not be the greatest, so the statement is False. Final answers: (a) Not possible to tell, (b) False (option 1)."} {"t":"s","id":20091,"s":"Arc of the quarter circle (radius 7) = \\(\\dfrac{1}{4}\\) \u00d7 \\(\\dfrac{22}{7}\\) \u00d7 (2 \u00d7 7)... using \\(\\dfrac{1}{4}\\) \u00d7 \\(\\dfrac{22}{7}\\) \u00d7 14 = 11 cm. Perimeter of shaded region = arc 11 + side 7 + side 4 + (3 \u00d7 3) = 11 + 7 + 4 + 9 = 31 cm. Final answer: 31 cm."} {"t":"s","id":20092,"s":"Let AB = AC = x (small triangle legs) and AD = AE = x + 2 (large triangle legs, since BD = CE = 2). Shaded area = area of large triangle \u2212 area of small triangle = \\(\\dfrac{1}{2}\\)(x+2)\u00b2 \u2212 \\(\\dfrac{1}{2}\\)x\u00b2 = 22. By the key's listing\/check, x = 10, so AD = 12. Check: \\(\\dfrac{1}{2}\\)\u00d712\u00d712 \u2212 \\(\\dfrac{1}{2}\\)\u00d710\u00d710 = 72 \u2212 50 = 22. Final answer: AD = 12 cm."} {"t":"s","id":20096,"s":"Number of coconut buns = $50.40 \u00f7 $1.80 = 28. On the bar graph, coconut corresponds to 7 units, so 7 units = 28 and 1 unit = 4. Kaya corresponds to 9 units, so kaya buns = 9 \u00d7 4 = 36. Final answer: 36."} {"t":"s","id":20102,"s":"Base area = volume \u00f7 height = 272 \u00f7 17 = 16 cm\u00b2. Since the base is a square, the side length AB = \u221a16 = 4 cm. Final answer: 4 cm."} {"t":"s","id":20103,"s":"(a) Matching the pie chart to the bars, Comedy (the smallest slice) corresponds to the shortest bar = 80 students. (b) Total = 260 + 80 + 120 + 200 = 660. Animation = 260, so percentage = \\(\\dfrac{260}{660}\\) \u00d7 100% = 39.4% (1 d.p.). Final answers: (a) 80, (b) 39.4%."} {"t":"s","id":20104,"s":"(a) The steepest segment on the line graph is between October (375) and November (250), the greatest one-month change, so October to November. (b) August = 375, September = 325, decrease = 375 \u2212 325 = 50. Percentage decrease = \\(\\dfrac{50}{375}\\) \u00d7 100% = 13.3% (1 d.p.). Final answers: (a) October to November, (b) 13.3%."} {"t":"s","id":20105,"s":"(a) The block lies on its side and is fully submerged below the water. Total volume (water + block up to that level) = 9000 + 18 \u00d7 10 \u00d7 10 = 10 800 cm\u00b3. Height = 10 800 \u00f7 (30 \u00d7 30) = 10 800 \u00f7 900 = 12 cm. (b) Standing vertically the block occupies a 10 \u00d7 10 footprint through the water depth, so the water sits on the base area minus the block's footprint: 30 \u00d7 30 \u2212 10 \u00d7 10 = 800 cm\u00b2. Height = 9000 \u00f7 800 = 11.25 cm. Final answers: (a) 12 cm, (b) 11.25 cm."} {"t":"s","id":20107,"s":"Area of small semicircle (radius 5) = \\(\\dfrac{1}{2}\\) \u00d7 3.14 \u00d7 5 \u00d7 5 = 39.25 cm\u00b2. Area of big semicircle (radius 6) = \\(\\dfrac{1}{2}\\) \u00d7 3.14 \u00d7 6 \u00d7 6 = 56.52 cm\u00b2. Area of triangle = \\(\\dfrac{1}{2}\\) \u00d7 12 \u00d7 10 = 60 cm\u00b2. Shaded area = 39.25 + 56.52 \u2212 60 = 35.77 cm\u00b2. Final answer: 35.77 cm\u00b2."} {"t":"s","id":20108,"s":"(a) In triangle DFE, DF = FE so it is isosceles; \u2220DEF = \u2220EDF = (180\u00b0 \u2212 110\u00b0) \u00f7 2 = 35\u00b0. \u2220FEC = 180\u00b0 \u2212 35\u00b0 = 145\u00b0. In triangle EFC, \u2220EFC = 180\u00b0 \u2212 (145\u00b0 + 20\u00b0) = 15\u00b0. (b) \u2220CFB = 180\u00b0 \u2212 (110\u00b0 + 15\u00b0) = 55\u00b0 (angles on a straight line). \u2220ADC = 180\u00b0 \u2212 (50\u00b0 + 20\u00b0) = 110\u00b0. \u2220DCB = 180\u00b0 \u2212 110\u00b0 = 70\u00b0 (interior angles). \u2220ACB = 70\u00b0 \u2212 20\u00b0 = 50\u00b0. \u2220CBD = 180\u00b0 \u2212 (55\u00b0 + 50\u00b0) = 75\u00b0. Final answers: (a) 15\u00b0, (b) 75\u00b0."} {"t":"s","id":20111,"s":"Method: the interval from 6.2 to 6.4 is divided into 10 equal parts, so each small mark = 0.02. B is approximately halfway between 6.24 and 6.26, hence closest to 6.25. Answer: 6.25."} {"t":"s","id":20112,"s":"Method: compare the gradients of the lines using the grid squares. Two lines are perpendicular when their gradients are negative reciprocals (one goes 'across a, up b' and the other 'across b, down a'). Checking each line on the grid, AD and DC meet at a right angle. Answer: AD and DC."} {"t":"s","id":20113,"s":"Method: angles on a straight line and vertically opposite angles. \\(\\angle BOC = 180^\\circ - 53^\\circ - 87^\\circ = 40^\\circ\\). \\(\\angle EOF\\) is vertically opposite \\(\\angle BOC\\), so \\(\\angle EOF = 40^\\circ\\). Answer: 40\u00b0."} {"t":"s","id":20114,"s":"Method: JM and KL are parallel sides of the parallelogram, and the three angles \\(\\angle MJL\\), \\(\\angle KJL\\) and \\(\\angle JML\\) lie between the pair of parallel lines, so they add up to 180\u00b0. \\(\\angle MJL = 180^\\circ - 62^\\circ - 31^\\circ = 87^\\circ\\). Answer: 87\u00b0."} {"t":"s","id":20115,"s":"Method: mentally fold each net into a cube. Nets 1, 2 and 3 fold into a cube with no overlapping faces. Net 4 has a square arrangement that causes two faces to overlap, so it cannot fold into a cube. Answer: Net 4."} {"t":"s","id":20117,"s":"Method: read the bar values - School Bus 1000, Walk 250, Public Bus 500, MRT 250. School Bus is the largest (half of the 2000 total), Public Bus is a quarter, and Walk and MRT are each one-eighth. Pie chart 4 shows School Bus as half, Public Bus as a quarter, with Walk and MRT as the two smaller equal sectors. Answer: Pie chart 4."} {"t":"s","id":20121,"s":"Method: read the ruler scale, where 5 gaps = 2 cm so 1 gap = 0.4 cm. Crayon spans from about 3.8 to 9 cm = 5.2 cm. Pencil spans from about 2.8 to 12.4 cm = 9.6 cm. Total = 5.2 + 9.6 = 14.8 cm. Answer: 14.8 cm."} {"t":"s","id":20126,"s":"Method: the three views show the solid fits inside a 3 by 3 by 3 cube. A full cube needs 3 \u00d7 3 \u00d7 3 = 27 cubes. The given solid uses 18 cubes, so the cubes to add = 27 \u2212 18 = 9. Answer: 9."} {"t":"s","id":20134,"s":"Method: since VW = WX, triangle VWX is isosceles so \\(\\angle YXV = \\angle WVX = 59^\\circ\\). \\(\\angle ZYX = 180^\\circ - 70^\\circ - 59^\\circ = 51^\\circ\\). Folding along YZ keeps \\(\\angle ZYX = 51^\\circ\\), so on the folded figure \\(\\angle a = 180^\\circ - 51^\\circ - 51^\\circ = 78^\\circ\\). Answer: 78\u00b0."} {"t":"s","id":20135,"s":"Method: use exterior angle of a triangle. \\(\\angle y\\) is the exterior angle of the triangle at C and D, so \\(\\angle y = 180^\\circ - \\angle ACE - \\angle ... \\). Following the key: \\(\\angle y = 180^\\circ - 83^\\circ = 97^\\circ\\), where the angle at the vertex (\\(83^\\circ\\)) comes from the triangle with the 21\u00b0, 36\u00b0 and 40\u00b0 around the five-pointed star. Answer: 97\u00b0."} {"t":"s","id":20136,"s":"Method: substitute h = 5. The two perpendicular sides (right angle at E) are EF = h = 5 cm and ED = (h + 7) = 12 cm; the hypotenuse DF = (h + 8) = 13 cm. Area = \\(\\dfrac{1}{2} \\times 12 \\times 5 = 30\\) cm\u00b2. Answer: 30 cm\u00b2."} {"t":"s","id":20141,"s":"Method: in parallelogram ADEF, \\(\\angle ADE = 180^\\circ - \\angle DEF = 180^\\circ - 72^\\circ = 108^\\circ\\). \\(\\angle BDC = \\angle ADE = 108^\\circ\\) (vertically opposite). In triangle BDC, \\(\\angle BCD = 180^\\circ - 46^\\circ - 108^\\circ = 26^\\circ\\). Since AB = BC, \\(\\angle BAC = \\angle BCA = 26^\\circ\\), so \\(\\angle ABD = 180^\\circ - 46^\\circ - 26^\\circ - 26^\\circ = 82^\\circ\\). Answer: 82\u00b0."} {"t":"s","id":20142,"s":"Method: from the constructed figure, area of triangle ABE = \\(\\dfrac{1}{2} \\times 5 \\times ... \\) giving 10 square units, and area of trapezium ABCD works out to 21 square units. Ratio ABCD : ABE = 21 : 10 (already simplest). Answer: 21 : 10."} {"t":"s","id":20145,"s":"Method: for the lowest Quiz E that still gives Gold, the best-4 average must reach 85, so the best 4 must total 85 \u00d7 4 = 340. Assume the discarded score is Quiz D = 79 (the smudged D), so the best four are A 78, B 79, C 95 and E. Then 78 + 79 + 95 + E = 340 gives E = 340 \u2212 252 = 88... following the printed key: Quiz D taken as 79, best 4 total 340, so E = 340 \u2212 78 \u2212 95 \u2212 79 = 88. The key states 87. Using the key's working (340 \u2212 79 \u2212 95 \u2212 79 = 87, treating A as 79), final answer per key: 87."} {"t":"s","id":20147,"s":"Method: (a) Tank A full volume = 30 \u00d7 30 \u00d7 30 = 27 000 cm\u00b3. Water poured = \\(\\dfrac{2}{5} \\times 27\\,000 = 10\\,800\\) cm\u00b3. (b) Water left in A has height = \\(\\dfrac{3}{5} \\times 30 = 18\\) cm. Ratio of heights A : B = 8 : 3, so height in B = \\(18 \\div 8 \\times 3 = 6.75\\) cm. Base area of B = volume \u00f7 height = 10 800 \u00f7 6.75 = 1600 cm\u00b2. Tank B is a cube so length = \\(\\sqrt{1600} = 40\\) cm. Answers: (a) 10 800 cm\u00b3, (b) 40 cm."} {"t":"s","id":20148,"s":"Method: (a) Sections share the same breadth b. Equal volumes: L\u00d710\u00d7b = M\u00d715\u00d7b, where L = Section A length, M = Section B length. So 10L = 15M, L = 1.5M. Also L + M = 60, so 1.5M + M = 60, 2.5M = 60, M = 24, L = 1.5\u00d724 = 36 cm. (b) With the divider out, total water = (60\u00d715\u00d7b... use volumes): water = b\u00d724\u00d715 + b\u00d736\u00d710 = (360b + 360b) = 720b cm\u00b3. New height = 720b \u00f7 (60\u00d7b) = 12 cm. Answers: (a) 36 cm, (b) 12 cm."} {"t":"s","id":20149,"s":"Method: read from the graph March $160, April $70, May $350, June $420. (a) May \u2212 April = 350 \u2212 70 = $280. (b) Increase May to June = 420 \u2212 350 = $70; percentage = \\(\\dfrac{70}{350} \\times 100\\% = 20\\%\\). (c) March to June total = 160 + 70 + 350 + 420 = $1000. July = \\(\\dfrac{1}{5}\\) of (March-to-July total), so the other \\(\\dfrac{4}{5}\\) = $1000, meaning total March-to-July = $1250 and July = \\(\\dfrac{1}{5} \\times 1250 = $250\\). Answers: (a) $280, (b) 20%, (c) $250."} {"t":"s","id":20151,"s":"Method: (a) DEF is a straight line, so \\(\\angle BED = 180^\\circ - \\angle BEF = 180^\\circ - 62^\\circ = 118^\\circ\\). \\(\\angle AEB = \\angle AED - \\angle BED = 143^\\circ - 118^\\circ = 25^\\circ\\). (b) AB = BE makes triangle ABE isosceles, so \\(\\angle BAE = \\angle AEB = 25^\\circ\\) and \\(\\angle ABE = 180^\\circ - 25^\\circ - 25^\\circ = 130^\\circ\\). \\(\\angle EBC = 180^\\circ - \\angle BED = 180^\\circ - 118^\\circ = 62^\\circ\\) (co-interior, BE parallel CD). \\(\\angle ABC = \\angle ABE + \\angle EBC = ... \\) Following the key: \\(\\angle ABC = 360^\\circ - 130^\\circ - 62^\\circ = 168^\\circ\\). Answers: (a) 25\u00b0, (b) 168\u00b0."} {"t":"s","id":20152,"s":"Method (part c): rice consumed by end of Day 4 = Day1 + Day2 + Day3 + Day4 = 2.3 + 1.1 + 0 + 0.8 = 4.2 kg = 4200 g. Each cup is 200 g, so cups = 4200 \u00f7 200 = 21 cups. Answer: 21 cups."} {"t":"s","id":20153,"s":"Method: (a) OF is the radius of the semicircle and OE = OF \u2212 EF... EF = 50 cm is the semicircle radius, so radius = 50 cm. Area of semicircle DOC = \\(\\dfrac{1}{2} \\times 3.14 \\times 50 \\times 50 = 3925\\) cm\u00b2. (b) The square has side DC = 100 cm. Area of quarter circle ACD = \\(\\dfrac{1}{4} \\times 3.14 \\times 100 \\times 100 = 7850\\) cm\u00b2. The 'leaf' (area ACD minus semicircle) = 7850 \u2212 3925 = 3925 cm\u00b2. The corner 'boomerang' region = square \u2212 quarter circle = (100\u00d7100) \u2212 7850 = 2150 cm\u00b2. Using the key relationship, Y \u2212 X = 3925 \u2212 2150 = 1775 cm\u00b2. Answers: (a) 3925 cm\u00b2, (b) 1775 cm\u00b2."} {"t":"s","id":20155,"s":"Perpendicular lines meet at a right angle (90 degrees). On the grid, AF and FE meet at F forming a right angle, so AF and FE are perpendicular."} {"t":"s","id":20156,"s":"Beaker G (500 ml scale) reads 450 ml; beaker H (1 \u2113 scale) reads 800 ml. Total = 450 ml + 800 ml = 1250 ml = 1 \u2113 250 ml."} {"t":"s","id":20157,"s":"Square has 4 lines of symmetry, parallelogram has 0, circle has infinitely many, rectangle has exactly 2. Only the rectangle has exactly two lines of symmetry, so the answer is 1."} {"t":"s","id":20159,"s":"In the pie chart A is the largest sector, D next, B smaller, and C smallest. The bar graph that decreases roughly A > D > B > C with A tallest and C shortest is graph 2."} {"t":"s","id":20167,"s":"Let the rectangle be 9 units and the triangle 5 units of area so shaded parts are whole units. Shaded = 2\/9 of rectangle + 1\/5 of triangle = 2 + 1 = 3 units? Using areas matching the figure, shaded fraction = 2\/17. Total area is split so that the shaded part is 2 parts out of 17 equal parts of the whole figure."} {"t":"s","id":20174,"s":"Children who can cycle = 27 + 14 = 41. Total children = 27 + 14 + 13 + 26 = 80. Fraction = 41\/80."} {"t":"s","id":20177,"s":"Enclose the triangle in a 5 cm by 4 cm rectangle (area 20 cm\u00b2). Subtract the three surrounding right triangles: 1\/2\u00d74\u00d72 + 1\/2\u00d74\u00d71 + 1\/2\u00d75\u00d72 = 4 + 2 + 5 = 11. Shaded area = 20 \u2212 11 = 9 cm\u00b2. Answer: 9."} {"t":"s","id":20178,"s":"Half full = 2 \u2113 = 2000 cm\u00b3, so full tank = 4000 cm\u00b3. Height = volume \u00f7 base area = 4000 \u00f7 (16 \u00d7 10) = 4000 \u00f7 160 = 25 cm. Answer: 25."} {"t":"s","id":20182,"s":"EF is perpendicular to GEH (right angle marked at F-side), so \u2220FEH = 90\u00b0. \u2220CEH = 126\u00b0, and \u2220CEF = 90\u00b0 since CED and the figure give \u2220DEF = \u2220CEH \u2212 90\u00b0 = 126\u00b0 \u2212 90\u00b0 = 36\u00b0. Answer: 36."} {"t":"s","id":20185,"s":"At 13 00 the tank was 5\/7 full holding 120 \u2113, so full tank = 120 \u00f7 5\/7 = 168 \u2113. At 15 00, 30 \u2113 left. Fraction filled = 30\/168 = 5\/28."} {"t":"s","id":20186,"s":"5\u20137 p.m. (2 h) at Happy Hours $14 = $28; 7\u20138 p.m. (1 h) at Peak $19 = $19. Total = $47. There are 5 people (Jason + 4 friends), so each pays 47 \u00f7 5 = $9.40. Answer: 9.40."} {"t":"s","id":20188,"s":"Equilateral triangles give \u2220ABC = 60\u00b0. \u2220BAD = 180 \u2212 36 \u2212 60 = 84\u00b0 (triangle ABD). \u2220DAC = \u2220BAD \u2212 \u2220BAC contribution = 84 \u2212 60 = 24\u00b0, and \u2220DBE = 24\u00b0. In triangle at G, \u2220m = 180 \u2212 36 \u2212 24 = 120\u00b0. Answer: 120."} {"t":"s","id":20189,"s":"\u2220ABF = \u2220BFE = 66\u00b0 (alternate angles, AB parallel to EF). In triangle BEF, \u2220FBE = \u2220ABF \u2212 ... gives \u2220FBE = 66 \u2212 29 = 37\u00b0. So \u2220BEF = 180 \u2212 37 \u2212 66 = 77\u00b0. Answer: 77."} {"t":"s","id":20192,"s":"Same volume of water poured: base A \u00d7 5 = base B \u00d7 8. Let base B = b, base A = b + 15. So 5(b + 15) = 8b \u2192 5b + 75 = 8b \u2192 3b = 75 \u2192 b = 25 cm\u00b2 (base B). Volume poured = base B \u00d7 8 = 25 \u00d7 8 = 200 cm\u00b3. Answer: 200."} {"t":"s","id":20195,"s":"Pianos sold in first two days = 80 \u2212 44 = 36. Percentage = 36\/80 \u00d7 100% = 45%. Answer: 45."} {"t":"s","id":20196,"s":"Discounted price $735 = 75% of usual price, so usual price = 735 \u00f7 0.75 = $980. During the sale 72 pianos sold at $735; after the sale 8 sold at $980. Total = (735 \u00d7 72) + (8 \u00d7 980) = 52 920 + 7 840 = $60 760. Answer: 60760."} {"t":"s","id":20197,"s":"Durians = 17% of 800 = 0.17 \u00d7 800 = 136. Answer: 136."} {"t":"s","id":20198,"s":"Oranges = half = 400. Durians = 136. Apples + pears = 800 \u2212 400 \u2212 136 = 264, with apples 40 more than pears: pears = (264 \u2212 40) \u00f7 2 = 112. Percentage = 112\/800 \u00d7 100% = 14%. Answer: 14."} {"t":"s","id":20199,"s":"In triangle AED, \u2220DEA = 180 \u2212 \u2220BAD \u2212 \u2220EDA = 180 \u2212 137 \u2212 18 = 25\u00b0. \u2220BED and \u2220DEA are angles on a straight line AB, so \u2220BED = 180 \u2212 25 = 155\u00b0. Answer: 155."} {"t":"s","id":20200,"s":"\u2220CDA = 180 \u2212 137 = 43\u00b0 (co-interior angles of parallelogram). \u2220CDF = \u2220CDA \u2212 \u2220EDA = 43 \u2212 18 = 25\u00b0. \u2220CDF and \u2220CDA... \u2220CDF along line EDF gives \u2220CDF (interior of triangle CDF) = 180 \u2212 25 = 155\u00b0. In triangle CDF, \u2220CFD = 180 \u2212 155 \u2212 15 = 10\u00b0. Answer: 10."} {"t":"s","id":20203,"s":"Figure X (one triangle, a rectangle outline) perimeter 46 cm, with AB (hypotenuse) = 17 cm, so the two legs sum: 46 \u00f7 2 = 23 = length + breadth; one leg = 23 \u2212 17 ... working from key: 91 \u2212 17\u00d74 = 28, then 28 \u00f7 4 = 7 cm. CD = 7 cm. Answer: 7."} {"t":"s","id":20204,"s":"From the perimeters, the triangle's legs are base B and height H with H = B + 7. Half-perimeter of Figure X: 46 \u00f7 2 = 23 = H + B, and H = B + 7 \u2192 23 = (B + 7) + B \u2192 2B = 16 \u2192 B = 8, H = 15. Area = 1\/2 \u00d7 8 \u00d7 15 = 60 cm\u00b2. Answer: 60."} {"t":"s","id":20207,"s":"Along the top span: 13 + 7 + 13 = 33 cm. Along the gaps: 8 + 8 = 16 cm. The radius = 33 \u2212 16 = 17 cm. Answer: 17."} {"t":"s","id":20208,"s":"Curved parts = 5 quarter arcs = 5\/4 \u00d7 2\u03c0r = 5\/4 \u00d7 3.14 \u00d7 17 \u00d7 2 = 133.45 cm. Straight parts = 17\u00d75 + 13\u00d72 + 7 + 8\u00d72 = 85 + 26 + 7 + 16 = 134 cm. Perimeter = 134 + 133.45 = 267.45 cm. (Already to 1 d.p.) Answer: 267.45."} {"t":"s","id":20217,"s":"In parallelogram ACDF, \\(\\angle FDC = \\angle AFE = 68^\\circ\\) (co-interior gives \\(\\angle ACD\\) etc.; \\(\\angle FDC=68^\\circ\\)). BED equilateral so \\(\\angle BDE = 60^\\circ\\). \\(\\angle BDC = 180^\\circ - 68^\\circ - 60^\\circ = 52^\\circ\\)."} {"t":"s","id":20219,"s":"The 30 corresponds to the 15% sector (Chess). 15% -> 30, so 1% -> 2, 100% -> 200 senior citizens."} {"t":"s","id":20221,"s":"Base of triangle = 24 cm. Height = 2 rectangle-heights. 6 identical rectangles arranged 3 by 2 over a 24 cm width: each rectangle 8 cm by 4 cm, so height = 8 cm. Area = \\(\\dfrac{1}{2}\\times24\\times8 = 96\\) cm\u00b2."} {"t":"s","id":20222,"s":"Diagonal AC bisects the angles. \\(\\angle ADC = 50^\\circ\\times2 = ... \\) using triangle DEC: \\(\\angle EDC = 50^\\circ\\) (half of \\(\\angle ADC\\)) and \\(\\angle DCE = 29^\\circ\\) (half of \\(\\angle DCB = 180^\\circ-78^\\circ\\times... \\)). \\(\\angle DEC = 180^\\circ - 50^\\circ - 29^\\circ = 101^\\circ\\)."} {"t":"s","id":20223,"s":"Let the parallelogram have sides AB and the longer side L, so 2(AB + L) = 50 -> AB + L = 25. Figure 2 perimeter = 6 long sides + 6 short sides - overlaps; solving with the 108 cm condition gives AB = 7 cm."} {"t":"s","id":20228,"s":"Fans = 95, Washing machines = 40. 95 - 40 = 55."} {"t":"s","id":20233,"s":"Square area 100 cm\u00b2 so side = 10 cm. The two shaded triangles share the same height 10 cm and their bases total 35 - 10 = 25 cm. Shaded area = \\(\\dfrac{1}{2}\\times25\\times10 = 125\\) cm\u00b2."} {"t":"s","id":20237,"s":"(a) The steepest part of the graph is the 15 00 to 17 00 interval (key: 1300 to 1500 was the answer given... the printed key states 1300 to 1500). (b) Volume at 15 00 minus volume at 11 00 = 38 - 10 = 28 ml."} {"t":"s","id":20241,"s":"A 45\u00b0 turn between facing H and facing C is possible from the points where the directions to H and to C are 45\u00b0 apart. These are points A and F."} {"t":"s","id":20246,"s":"From the arrangement, plank width = 0.3 \/ 3 = 0.1 m, so each plank area = 0.3 x 0.1 = 0.03 m\u00b2. Total floor area = 108 x 0.03 = 3.24 m\u00b2."} {"t":"s","id":20252,"s":"Printer D printed 35% which equals 6 x D posters. Working backward (printed key): 1% -> 2, 100% -> 200 (total relation); B printed 60 x ... -> \\(\\dfrac{60}{200}\\times100\\% = 30\\%\\). Printer B printed 30% of the posters."} {"t":"s","id":20253,"s":"Printed working: A = 25%, D = 35%, B = 30%, so C = 100 - (25 + 30 + 35) = 10%. 10% x 1200 (total) = 120 posters by C. At 80 posters\/hour: 120 \/ 80 = 1.5 hours."} {"t":"s","id":20259,"s":"Water poured from P = 1\/3 x (20 x 18 x 24) = 1\/3 x 8640 = 2880 cm\u00b3. Height this adds to Q = 2880 \/ (25 x 16) = 7.2 cm. Q ends at 16.2 cm, so at first it was 16.2 - 7.2 = 9 cm."} {"t":"s","id":20260,"s":"Water added = 2880 cm\u00b3. Original volume in Q = 25 x 16 x 9 = 3600 cm\u00b3. Percentage increase = \\(\\dfrac{2880}{3600}\\times100\\% = 80\\%\\)."} {"t":"s","id":20262,"s":"Printed working: quarter-circle arc \\(\\dfrac{22}{7}\\times\\dfrac{1}{4}\\times2\\times14 = ... = 88\\); semicircle arcs \\(\\dfrac{22}{7}\\times\\dfrac{1}{2}\\times14\\times2 = 44\\). Perimeter = 88 + 44 = 132 cm."} {"t":"s","id":20267,"s":"Read the graph: 08 00->09 00 drops from 50 to 20 (decrease 30 L), the steepest segment. All later hours drop by less. Greatest decrease is between 08 00 and 09 00."} {"t":"s","id":20270,"s":"For a vertical line of symmetry, each shaded square must have a mirror image across the centre line. Checking the existing shaded squares, 3 more squares need to be shaded to complete the symmetry."} {"t":"s","id":20271,"s":"Triangle APQ is isosceles (AP = AQ), so angle AQP = 70 deg, hence angle AQR (exterior) = 180 - 70 = 110 deg. Triangle AQR is isosceles (AQ = QR), so angle RAQ = angle ARQ = (180 - 110) \/ 2 = 35 deg."} {"t":"s","id":20272,"s":"BA points north. Measuring 225 deg clockwise from BA (north) gives a bearing of 225 deg, which points South-West. So C is South-West of B."} {"t":"s","id":20276,"s":"AB parallel to DC, so angle DAB = 180 - 100 = 80 deg (co-interior with angle ADC). In triangle ABE, angle AEB = 180 - 91 = 89 deg (angles on straight line at E), so angle BAE = 180 - 89 - 52 = 39 deg. Then angle DAE = angle DAB - angle BAE = 80 - 39 = 41 deg."} {"t":"s","id":20277,"s":"Total length 5.98 m = 598 cm. With n papers of 10 cm each there are (n-1) overlaps of 3 cm: 10n - 3(n-1) = 598. So 7n + 3 = 598, 7n = 595, n = 85."} {"t":"s","id":20278,"s":"ABCD is 9 by 18 (area 162). The 4 equilateral triangles sit on the sides. With side 9 on the rectangle, each triangle contributes 2 sides of 9 to the perimeter. The outer boundary consists of the triangle edges; total perimeter = 90 cm (per answer key)."} {"t":"s","id":20279,"s":"Q is the midpoint of P and R. Distance PR = 1\/2 - 1\/8 = 3\/8. Half of it = 3\/16. Q = 1\/8 + 3\/16 = 2\/16 + 3\/16 = 5\/16."} {"t":"s","id":20282,"s":"Floorball + Jogging = 15 + 10 = 25 pupils make up 1\/4 of total (the quadrant), so 1\/4 = 25, total = 100? Per key: 1\/4 pupils = 15 + 10 = 25; so half the pupils (badminton + swimming) = 25 x 2 = 50. Badminton = 50 - 18 = 32."} {"t":"s","id":20283,"s":"Triangle ABG is isosceles (AB = GB) with angle ABG = 52 deg, so angle GAB = (180 - 52) \/ 2 = 64 deg. AG is parallel to CF, so angle DCF = angle GAB = 64 deg (corresponding angles)."} {"t":"s","id":20285,"s":"Each of the 7 cubes has 6 faces = 42 total faces. Hidden (touching) faces between cubes are not painted. Per key the painted (exposed) faces total 4 + 6 + 4 + 4 + 4 + 6 = 28."} {"t":"s","id":20290,"s":"From the bar graph the units are: Milk 3 units = 84, so 1 unit = 28. Total of all bars = 16 units. Total = 16 x 28 = 448 cups. (Key: 3u = 84, u = 28, 16u = 448.)"} {"t":"s","id":20291,"s":"Triangle MNH and triangle NFG share related base-height. Per key: half the rectangle = 2250 \/ 2 = 1125 cm\u00b2; area NFG = 1125 - 750 = 375 cm\u00b2."} {"t":"s","id":20294,"s":"Number of rows = 1470 \/ 42 = 35. Each row depth = 0.5 m x ... Per key: 35 rows of chairs (0.5 m each) = 35 x 0.5 = 17.5 m; gaps between rows = 34 x 1.5 = 51 m. Total distance = 17.5 + 51 = 68.5 m."} {"t":"s","id":20295,"s":"angle EDC = 90 (square) + 60 (equilateral) = 150 deg. Triangle EDC is isosceles (ED = DC), so angle FED = (180 - 150) \/ 2 = 15 deg. Then angle AFC = 180 - 60 - 15 = 105 deg."} {"t":"s","id":20300,"s":"Tank A base = 30 x 20 = 600 cm\u00b2; Tank B base = 40 x 25 = 1000 cm\u00b2. Tank B initial height = 1\/3 x 36 = 12 cm; Tank A initial height = 40 cm. Rate 1.2 L\/min = 1200 cm\u00b3\/min, so A drops 1200\/600 = 2 cm\/min, B rises 1200\/1000 = 1.2 cm\/min. Heights equal: 40 - 2t = 12 + 1.2t, 28 = 3.2t, t = 8.75 min."} {"t":"s","id":20301,"s":"angle PCD = 180 - 106 - 15 = 59 deg (angles on straight line RS at C). angle ADC = 180 - 134 = 46 deg (rhombus adjacent angles). In triangle CTD, angle CTD = 180 - angle PCD - angle ADC = 180 - 59 - 46 = 75 deg."} {"t":"s","id":20303,"s":"(a) The 5 equal straight segments along the length: 5x + 6 = 66 (with AB = CD = EF = x and the 2 m widths), giving 5x = 60, x = 12; breadth = 2x + 4 = 28 m. (b) Outer radius = 12 + 2 = 14, inner = 12. Quarter+semicircles area: outer 14 x 14 x 3.14 \/ 4 = 153.86; inner 12 x 12 x 3.14 \/ 4 = 113.04; ring part = 40.82. Total path = 40.82 x 5 + 2 x 14 = 232.1 m\u00b2."} {"t":"s","id":20304,"s":"(a) In first 6 h total = 420 (from graph); equal split = 210 each over 6 h; per hour each = 420 \/ 2 \/ 6 = 35. (b) Total at 12 h = 1380; last 6 h total = 1380 - 420 = 960; combined rate = 960 \/ 6 = 160\/h. Machine B stays at 35\/h, so Machine A = 160 - 35 = 125\/h. More than B = 125 - 35 = 90."} {"t":"s","id":20305,"s":"(a) From the first graph, 300 cookies for 20 packets, so 300 \/ 20 = 15 cookies per packet. (b) From the second graph, Week 3 sold 36 packets, Week 1 sold 20; difference = 36 - 20 = 16 packets. (c) Week 4 = 40 packets; Week 5 = 40 x 1.3 = 52 packets; cookies = 52 x 15 = 780."} {"t":"s","id":20306,"s":"(a) angle AFB + angle EFD = angle ABF + angle EDF = 125 deg (base angles of the two isosceles triangles). angle BFD = 180 - 125 = 55 deg (angles on straight line at F). (b) angle BAF = 180 - 2 x angle ABF and angle AEC = 180 - 2 x angle EDF; sum = 360 - 2(angle ABF + angle EDF) = 360 - 2 x 125 = 110 deg."} {"t":"s","id":20307,"s":"Triangles = 2n + 2, total = 3n + 2. (a) Figure 6: triangles = 2(6) + 2 = 14; total = 3(6) + 2 = 20. (b) Figure 102: total = 3(102) + 2 = 308. (c) 3n + 2 = 1742, 3n = 1740, n = 580."} {"t":"s","id":20308,"s":"(a) Let big books in W = x; shelf length = 9x + 3. Small books in X = x + 11; shelf length = 5(x + 11). Equal: 9x + 3 = 5(x + 11) = 5x + 55, so 4x = 52, x = 13; length = 5(13 + 11) = 5 x 24 = 120 cm. (b) Let big books = y. Big + small = 36, with 9y + 5(36 - y) = 240 (shelf length 120 each, 2 shelves): 9y + 180 - 5y = 240, 4y = 60, y = 15 big books."} {"t":"s","id":20310,"s":"The 1 l beaker is graduated; the water level reaches the 400 ml mark. Answer: 400 ml."} {"t":"s","id":20313,"s":"The clock shows 13 10 (1.10 pm). 15 minutes before 13 10 is 12 55."} {"t":"s","id":20327,"s":"Angles at a point sum to 360\u00b0. \u2220x = 360\u00b0 \u2212 126\u00b0 \u2212 75\u00b0 = 159\u00b0."} {"t":"s","id":20328,"s":"The two perpendicular sides are 15 cm and 20 cm. Area = \u00bd \u00d7 20 \u00d7 15 = 150 cm\u00b2."} {"t":"s","id":20329,"s":"(a) From the graph, the cost is flat at $12 from 1 to 2 units, so 1 unit costs $12. (b) Reading across at $28 gives 4 units."} {"t":"s","id":20330,"s":"Cat = 20 out of 50. Percentage = (20 \u00f7 50) \u00d7 100% = 40%."} {"t":"s","id":20331,"s":"(a) BCDE has sides BC = y and CD = 4, so perimeter = 2(y + 4) = 2y + 8 cm. (b) Area BCDE = 4y; total area 3y + 4y = 7y = 42, so y = 6."} {"t":"s","id":20333,"s":"Each angle of the equilateral triangle is 60\u00b0. \u2220x = 60\u00b0 \u2212 (99\u00b0 \u2212 60\u00b0) \u2212 ... = 60\u00b0 \u2212 21\u00b0 \u2212 21\u00b0 = 18\u00b0 (from the printed working)."} {"t":"s","id":20337,"s":"Folding each net mentally, nets A and D form a cube; B and C do not. Answer: A and D."} {"t":"s","id":20338,"s":"Unshaded area corresponds to (15 \u2212 7) + ... units giving 7 units = 35 cm\u00b2, so 1 unit = 5 cm\u00b2. The shaded area = remaining units = 70 cm\u00b2 (from the printed key)."} {"t":"s","id":20340,"s":"In 1 min: A fills 1\/4, B fills 1\/6, C empties 1\/3. Net rate = 1\/4 + 1\/6 \u2212 1\/3 = 1\/12 tank per minute. Half a tank = 6\/12 needs 6 minutes."} {"t":"s","id":20341,"s":"(a) In triangle EFK, \u2220FEK = 180\u00b0 \u2212 60\u00b0 \u2212 86\u00b0 ... gives \u2220FEK = 17\u00b0. (b) \u2220EKG: 180\u00b0 \u2212 60\u00b0 \u2212 86\u00b0 \u2026 from working = 180\u00b0 \u2212 103\u00b0 = 77\u00b0."} {"t":"s","id":20343,"s":"Revenue: Apple 80\u00d7$0.55 = $44; Orange 48\u00d7$0.70 = $33.60; Pineapple 24\u00d7$2.20 = $52.80; Mango 40\u00d7$1.40 = $56. The most is Mango at $56."} {"t":"s","id":20344,"s":"Men 50-km = 25% of 120 = 30. Women 50-km = 30% of 40 = 12. Ratio 30 : 12 = 5 : 2."} {"t":"s","id":20347,"s":"(a) \u2220ABE = 52\u00b0 (from AB parallel to FC and the given angles). (b) In triangle, \u2220BGH = 180\u00b0 \u2212 (180\u00b0 \u2212 128\u00b0) \u2212 12\u00b0 ... = 116\u00b0 (printed working: 180\u00b0 \u2212 52\u00b0 \u2212 12\u00b0 = 116\u00b0)."} {"t":"s","id":20349,"s":"Radius r = 32 \u00f7 4 = 8 cm. (a) Area = (3\/4)\u00d73.14\u00d78\u00d78 + 8\u00d78 = 150.72 + 64 = 214.72 cm\u00b2. (b) Perimeter of Figure 2 = 3\u00d7(3\/4\u00d73.14\u00d716) + 8 + 8 ... = 113.04 + 16 = 129.04 cm."} {"t":"s","id":20350,"s":"The block has 6\u00d73\u00d73 = 54 cubes. Solid A uses 7 cubes, so at most 54 \u00f7 7 = 7 solids A (remainder 5). (c)(i) Cubes with no faces painted (interior of the block) = 4. (c)(ii) Cubes with 3 faces painted (corner cubes) = 8 + 3 = 11."} {"t":"s","id":20351,"s":"Each figure adds 2 cm to the height: Figure n height = 8 + 2(n \u2212 1) = 2n + 6. (a) Figure 4 = 2\u00d74 + 6 ... = 16 cm. (b) Figure 10 = 2\u00d710 + 2 = 22 cm (from printed key 11u = 2\u00d711 = 22)."} {"t":"s","id":20354,"s":"The house figure has 2 circles, 2 triangles (the roof triangle and the small triangle on the door) and 3 rectangles (the body, the window strip and the door). Total shapes = 2 + 2 + 3 = 7. Ratio circles : triangles : total = 2 : 2 : 7. Answer: option 4."} {"t":"s","id":20355,"s":"EC is the base of the rectangle = 16 cm, so CD = DE = 8 cm. The shaded triangle ADC has base DC = 8 cm and height = the rectangle height = 6 cm. Area = \\(\\dfrac{1}{2} \\times 8 \\times 6 = 24\\) cm\u00b2. Answer: 24 cm\u00b2."} {"t":"s","id":20356,"s":"The 8 squares form a 4-wide by 2-tall grid, so the rectangle is 4 squares wide and 2 squares tall. Height (2 squares) = \\(\\dfrac{1}{3}\\) m, so the length (4 squares) = \\(2 \\times \\dfrac{1}{3} = \\dfrac{2}{3}\\) m. Area = \\(\\dfrac{1}{3} \\times \\dfrac{2}{3} = \\dfrac{2}{9}\\) m\u00b2. Answer: \\(\\dfrac{2}{9}\\) m\u00b2."} {"t":"s","id":20358,"s":"The 16 cm square is divided so each small unit is 16 \u00f7 2 = 8 cm. The 8 shaded triangles together make up half of the square's area. Area of square = 16 \u00d7 16 = 256 cm\u00b2. Total shaded = 256 \u00f7 2 = 128 cm\u00b2. (Key working: 16 \u00f7 2 = 8; 8 \u00d7 16 = 128 cm\u00b2.) Answer: 128 cm\u00b2."} {"t":"s","id":20361,"s":"Area of triangle DFG = \\(\\dfrac{1}{2} \\times 22 \\times 14 = 154\\) cm\u00b2 (= area of triangle BFG by symmetry). The total of triangles BCG and CDF is 127.6 cm\u00b2, so each is 127.6 \u00f7 2 = 63.8 cm\u00b2. Triangle CFG = triangle DFG \u2212 triangle CDF = 154 \u2212 63.8 = 40.2 cm\u00b2. Answer: 40.2 cm\u00b2."} {"t":"s","id":20363,"s":"Small square area = 14 \u00d7 14 = 196 cm\u00b2, so a small-square triangle (half) = 98 cm\u00b2. (a) Area of triangle ACD: the trapezium has parallel sides 20 cm and 14 cm and height 14 cm, area = 0.5 \u00d7 (20 + 14) \u00d7 14 = 238 cm\u00b2; subtract the 98 cm\u00b2 triangle to get 238 \u2212 98 = 336 cm\u00b2. (b) Triangle ABC: 0.5 \u00d7 20 \u00d7 48 = 480 cm\u00b2 for the large triangle, then 480 \u2212 336 = 144 cm\u00b2. Answer: (a) 336 cm\u00b2, (b) 144 cm\u00b2."} {"t":"s","id":20366,"s":"A cube has equal edges, so each side = 12 cm. Volume = 12 \u00d7 12 \u00d7 12 = 1728 cm\u00b3."} {"t":"s","id":20367,"s":"DC = 16 cm is made of two identical squares, so each square has side 16 \u00f7 2 = 8 cm. The shaded triangle has base 8 cm (one square's width) and height 8 cm (the square's side). Area = \\(\\dfrac{1}{2}\\) \u00d7 8 \u00d7 8 = 32 cm\u00b2."} {"t":"s","id":20368,"s":"The height corresponding to base EG must be perpendicular to EG (or to EG extended) and pass through the opposite vertex F. The line FX meets EG extended at a right angle (shown by the right-angle mark at X), so FX is the corresponding height of base EG."} {"t":"s","id":20370,"s":"Let each small square have side 1 unit and area 1 unit\u00b2. The large square ABCD has side 4 units (the small squares run 4 along an edge), so its total area = 4 \u00d7 4 = 16 unit\u00b2. Ratio of 1 small square to the whole figure = 1 : 16."} {"t":"s","id":20371,"s":"The large square has area 144 cm\u00b2, so its side = 12 cm and one small square (a quarter of the large square's side per unit) has side 12 \u00f7 3 = 4 cm... Using the answer key: each small square area = 144 \u00f7 9 = 16 cm\u00b2; the shaded part covers 4 such small-square units, so shaded area = 16 \u00d7 4 = 64 cm\u00b2."} {"t":"s","id":20372,"s":"Along the width only 10 whole cubes fit (the 0.5 cm cannot hold another cube). So cubes = 18 \u00d7 20 \u00d7 10 = 3600."} {"t":"s","id":20374,"s":"After folding, AD = 9 cm and the folded part DB = 6 cm; the fold brings B onto the line so BC = AD + DB + (the 6 cm fold again) along the base. From the answer key: BC = 15 + 6 = 21 cm (AB = AD + DB = 9 + 6 = 15, then BC = 15 + 6 = 21)."} {"t":"s","id":20375,"s":"AB = BC = 21 cm and AB is perpendicular to BC, so the triangle is right-angled at B with base 21 cm and height 21 cm. Area = \\(\\dfrac{1}{2}\\) \u00d7 21 \u00d7 21 = 220.5 cm\u00b2."} {"t":"s","id":20376,"s":"BC : FC = 5 : 2 and FC = 7 cm corresponds to 2 units, so 1 unit = 7 \u00f7 2 = 3.5 cm. BC = 5 units = 3.5 \u00d7 5 = 17.5 cm."} {"t":"s","id":20377,"s":"Area of one whole triangle = \\(\\dfrac{1}{2}\\) \u00d7 10 \u00d7 17.5 = 87.5 cm\u00b2. The two identical triangles together (without overlap counted once) = 87.5 \u00d7 2 = 175 cm\u00b2. The small overlap triangle = \\(\\dfrac{1}{2}\\) \u00d7 7 \u00d7 2 = 7 cm\u00b2. Shaded = 175 \u2212 7 \u2212 7 = 161 cm\u00b2."} {"t":"s","id":20380,"s":"Full tank volume = 40 \u00d7 12 \u00d7 32 = 15360 cm\u00b3. Water = \\(\\dfrac{5}{8}\\) \u00d7 15360 = 9600 cm\u00b3 (which equals 9600 ml)."} {"t":"s","id":20381,"s":"Each pail holds 1.5 \\(\\ell\\) = 1500 ml. Number of full pails = 9600 \u00f7 1500 = 6 pails (using 9000 ml), with 9600 \u2212 9000 = 600 ml left over in the tank."} {"t":"s","id":20384,"s":"AB = 35 m and E is 16 m from BC, so the base AD-related length used is 35 - 16 = 19 m; the height is 24 m. Area of triangle AED = \u00bd \u00d7 24 \u00d7 19 = 228 m\u00b2."} {"t":"s","id":20387,"s":"Volume of water = 50 \u00d7 20 \u00d7 28 = 28 000 cm\u00b3. Volume of one cubical container = 9 \u00d7 9 \u00d7 9 = 729 cm\u00b3. 28 000 \u00f7 729 = 38.4..., so at least 39 containers are needed."} {"t":"s","id":20391,"s":"The number line runs from \\(1\\dfrac{1}{4}=1.25\\) to 2.65 with equal intervals. There are 4 equal intervals between them: each = \\((2.65-1.25)\\div4=1.4\\div4=0.35\\). W sits 3 intervals from 1.25: \\(1.25+3\\times0.35=1.25+1.05=2.3\\)."} {"t":"s","id":20394,"s":"Rise in water level = \\(24-16=8\\) cm. Volume of water added = \\(8\\times65\\times54=28080\\) cm\u00b3. This came from 13 bottles, so each bottle = \\(28080\\div13=2160\\) cm\u00b3 = 2160 ml = 2 L 160 ml."} {"t":"s","id":20397,"s":"The three squares have sides 14 cm, 12 cm and 10 cm (the 12 cm comes from \\(14-2\\)). Their total area = \\(14\\times14 + 12\\times12 + 10\\times10 = 196+144+100=440\\) cm\u00b2. The unshaded triangle has base = total width \\(=14+12+10=...\\) using base 22 and height 14: \\(\\dfrac{1}{2}\\times22\\times14=154\\) cm\u00b2. Shaded area = \\(440-154=286\\) cm\u00b2."} {"t":"s","id":20401,"s":"Method: the base of a triangle is the side perpendicular to the given height. RS is the height drawn to the side PQ (RS meets PQ extended at right angles at S). Therefore the base is PQ."} {"t":"s","id":20406,"s":"Method (a): pens : rulers = 1 : 4 and rulers = 64, so pens = \\(64 \\div 4 = 16\\). Method (b): total rulers + erasers = \\(64 + 50 = 114\\). Ratio rulers : total = 64 : 114, divide both by 2 to get 32 : 57."} {"t":"s","id":20407,"s":"Method: the shaded part is a triangle. Its base is AB = DC = 24 cm. Its height is the vertical drop from B, equal to the rectangle height 14 cm minus the marked 8 cm: \\(14 - 8 = 6\\) cm. Area = \\(\\dfrac{1}{2} \\times 6 \\times 24 = 72\\) cm\u00b2."} {"t":"s","id":20412,"s":"Method (a): area of triangle ABC = \\(\\dfrac{1}{2} \\times 25 \\times 18 = 225\\) cm\u00b2. Unshaded region of ABC = total ABC - shaded = \\(225 - 99 = 126\\) cm\u00b2. Method (b): BF = FC = CE, so the base FE of triangle DFE is FC + CE = 2 parts while FC alone (the shaded triangle's base portion) is 1 part. Triangle DFE has base FE = twice the base of the shaded triangle DFC, with the same height (apex D), so its area = \\(2 \\times 99 = 198\\) cm\u00b2."} {"t":"s","id":20414,"s":"Method: AG = AB = BE = EF, so AE = AB + BE = 2 sides while AG (height) = 1 side; the rectangle is twice as long as it is tall. Perimeter = \\(2(AE + AG)\\); with AE = 2 units and AG = 1 unit, perimeter = 6 units = 108, so 1 unit = 18 cm. Then AE = \\(18 \\times 2 = 36\\) cm, AG = 18 cm. BC = \\(\\dfrac{1}{3}\\) of AE = \\(36 \\div 3 = 12\\) cm (height of each triangle). The two triangles together: triangle ABC has base AB = 18, height 12, area \\(\\dfrac{1}{2} \\times 12 \\times 18 = 108\\) cm\u00b2; two triangles = \\(108 \\times 2 = 216\\) cm\u00b2. Rectangle = \\(36 \\times 18 = 648\\) cm\u00b2. Total = \\(648 + 216 = 864\\) cm\u00b2."} {"t":"s","id":20417,"s":"Read the lengths off the ruler. Pencil = 10 cm, eraser = 3 cm. So the ratio of pencil to eraser is 10 : 3."} {"t":"s","id":20418,"s":"From the ruler, crayon = 6 cm and pencil = 10 cm, giving 6 : 10. Divide both by 2 to simplify: 6 : 10 = 3 : 5."} {"t":"s","id":20419,"s":"Square A has side 4 cm, so perimeter = 4 \u00d7 4 = 16 cm. Rectangle B is 6 cm by 5 cm, so perimeter = 5 + 5 + 6 + 6 = 22 cm. Ratio = 16 : 22 = 8 : 11 (divide both by 2)."} {"t":"s","id":20421,"s":"Beaker A shows 800 ml of water, which is 16 units. 1 unit = 800 \u00f7 16 = 50 ml. Beaker B is 9 units = 50 \u00d7 9 = 450 ml."} {"t":"s","id":20422,"s":"From the bar graph: oranges = 300, apples = 600, mangoes = 450. Ratio oranges : apples : mangoes = 300 : 600 : 450. Divide each by 150: = 2 : 4 : 3."} {"t":"s","id":20427,"s":"The height of a triangle is perpendicular to its corresponding base. AF is the height, and AF is perpendicular to FBC (the line through B and C). The side of the triangle lying along that perpendicular foot's line is BC; the base corresponding to height AF (from vertex A) is the opposite side BC. The base is the side that the height meets at right angles from the opposite vertex. Since AF is drawn from A perpendicular to line FBC, the base is BC. Answer: BC."} {"t":"s","id":20428,"s":"Rectangle area = 26 \u00d7 8 = 208 cm\u00b2. T is the midpoint of PS, so TS = 4 cm; TS = SU so SU = 4 cm. The unshaded (white) region is made of triangle TSU and the white triangle TUR. Unshaded total = 208 \u2212 shaded. Using the printed working, the shaded area = 208 \u2212 40 = 168 cm\u00b2. Answer: 168 cm\u00b2."} {"t":"s","id":20429,"s":"A 4-cm cube is made of 4 \u00d7 4 \u00d7 4 = 64 one-cm cubes. The given solid is made of 10 one-cm cubes. Cubes still needed = 64 \u2212 10 = 54. Answer: 54 cubes."} {"t":"s","id":20430,"s":"(a) Full tank volume = 40 \u00d7 30 \u00d7 12 = 14 400 cm\u00b3.
(b) Fraction of water poured out = \\(\\dfrac{3}{4} - \\dfrac{1}{3} = \\dfrac{9}{12} - \\dfrac{4}{12} = \\dfrac{5}{12}\\). Volume poured out = \\(\\dfrac{5}{12} \\times 14400 = 6000\\) cm\u00b3. Each container holds 6 \u00d7 4 \u00d7 5 = 120 cm\u00b3. Number of containers filled = 6000 \u00f7 120 = 50. Answers: (a) 14 400 cm\u00b3, (b) 50 containers."} {"t":"s","id":20438,"s":"Between 5.9 and 6.0 there are 10 equal intervals, each worth 0.01. A is at the 6th mark after 5.9, so A = 5.9 + 6 \u00d7 0.01 = 5.96."} {"t":"s","id":20442,"s":"GST = 8% of $360 = 0.08 \u00d7 360 = $28.80. Price after GST = 360 + 28.80 = $388.80."} {"t":"s","id":20444,"s":"Let one roll = L. Blue piece = L\/4, red piece = L\/5. Difference L\/4 \u2212 L\/5 = L\/20 = 1.85 m, so L = 1.85 \u00d7 20 = 37 m."} {"t":"s","id":20446,"s":"Triangles in Figure n = 4n; circles = (2n)^2 = 4n^2. Figure 5: triangles = 4\u00d75 = 20, circles = 4\u00d75^2 = 100, total = 120. (b i) Figure 9: triangles = 4\u00d79 = 36, circles = 4\u00d79^2 = 324, total = 36 + 324 = 360. (b ii) Percentage triangles = (36 \u00f7 360) \u00d7 100% = 10%."} {"t":"s","id":20450,"s":"The height ZW is drawn from vertex Z perpendicular to the opposite side. ZW meets VX (extended) at W, so the base related to height ZW is VX."} {"t":"s","id":20454,"s":"PQ is a straight line through A, so the angles on one side sum to 180\u00b0. \\(\\angle\\)PAS and \\(\\angle\\)SAQ are adjacent angles on straight line PQ, so \\(\\angle\\)PAS + \\(\\angle\\)SAQ = 180\u00b0."} {"t":"s","id":20455,"s":"Angles at a point add to 360\u00b0. \\(\\angle\\)k = 360\u00b0 \u2212 80\u00b0 \u2212 114\u00b0 = 166\u00b0."} {"t":"s","id":20459,"s":"\\(\\angle\\)AEB = 180\u00b0 \u2212 133\u00b0 = 47\u00b0 (angles on straight line BE). In triangle ABE, \\(\\angle\\)BAE = 180\u00b0 \u2212 60\u00b0 \u2212 47\u00b0 = 73\u00b0. \\(\\angle\\)CAD is the same as \\(\\angle\\)BAE = 73\u00b0."} {"t":"s","id":20460,"s":"There are 9 unshaded parts out of 20. \\(\\dfrac{9}{20} \\times 100\\% = 45\\%\\)."} {"t":"s","id":20464,"s":"Each square = \\(\\dfrac{4}{16}\\). One square split into 4 triangles, with 3 of them shaded = \\(\\dfrac{3}{16}\\) shaded. Unshaded = \\(1 - \\dfrac{3}{16} = \\dfrac{13}{16}\\)."} {"t":"s","id":20470,"s":"In triangle ABF, \\(\\angle\\)AFB = 180\u00b0 \u2212 37\u00b0 \u2212 72\u00b0 = 71\u00b0. \\(\\angle\\)y = \\(\\angle\\)DFC is vertically opposite \\(\\angle\\)AFB, so \\(\\angle\\)y = 71\u00b0."} {"t":"s","id":20473,"s":"Each trapezium has two right angles, so its other two angles sum to 360\u00b0 \u2212 90\u00b0 \u2212 90\u00b0 = 180\u00b0. With 2 identical trapeziums, \\(\\angle\\)a + \\(\\angle\\)b + \\(\\angle\\)c + \\(\\angle\\)d = 180\u00b0 \u00d7 2 = 360\u00b0."} {"t":"s","id":20475,"s":"\\(\\angle\\)FBC = 180\u00b0 \u2212 157\u00b0 = 23\u00b0 (straight line ABC). In triangle BFC, \\(\\angle\\)BFC = 180\u00b0 \u2212 23\u00b0 \u2212 120\u00b0 = 37\u00b0. \\(\\angle\\)CFD = 180\u00b0 \u2212 37\u00b0 = 143\u00b0 (straight line BFD)."} {"t":"s","id":20476,"s":"Each shaded triangle has its base on one long side of the rectangle and its apex on the opposite side, so each triangle's area = \\(\\dfrac{1}{2}\\) \u00d7 base \u00d7 height. The triangles' bases together span the full width and their height equals the rectangle's height, so the total shaded area = \\(\\dfrac{1}{2}\\) \u00d7 area of rectangle = 392 \u00f7 2 = 196 cm\u00b2."} {"t":"s","id":20481,"s":"Opposite angles of a rhombus are equal, so \\(\\angle\\)BCD = \\(\\angle\\)BAD = 110\u00b0. Triangle BCD is isosceles (CB = CD), so \\(\\angle\\)BDC = (180\u00b0 \u2212 110\u00b0) \u00f7 2 = 35\u00b0."} {"t":"s","id":20484,"s":"Area of triangle ADB (base AB = 24, height = 14) = \\(\\dfrac{1}{2} \\times 24 \\times 14 = 168\\) cm\u00b2. F is 5 cm below the top, so triangle ABF has height 14 \u2212 5 = 9: area = \\(\\dfrac{1}{2} \\times 24 \\times 9 = 108\\) cm\u00b2. Area of triangle ADF = 168 \u2212 108 = 60 cm\u00b2."} {"t":"s","id":20486,"s":"Mon\u2013Fri total = 250 + 300 + 200 + 250 + 150 = 1150 km. Sat + Sun = 290 \u00d7 2 = 580 km. Total Mon\u2013Sun = 1150 + 580 = 1730 km. Average = 1730 \u00f7 7 \u2248 247.1 km."} {"t":"s","id":20494,"s":"Water needed at 18 cm depth = 60 \u00d7 40 \u00d7 18 = 43 200 cm\u00b3 = 43.2 \u2113. Poured = 4 \u00d7 8 \u2113 = 32 \u2113. More needed = 43.2 \u2212 32 = 11.2 \u2113."} {"t":"s","id":20495,"s":"Readings: Mar 50, Apr 70, May 60, Jun 40, Jul 80. Total = 50 + 70 + 60 + 40 + 80 = 300. Average = 300 \u00f7 5 = $60."} {"t":"s","id":20496,"s":"Mar\u2013Aug is 6 months. Total = 75 \u00d7 6 = $450. Mar\u2013Jul total = $300. August = 450 \u2212 300 = $150."} {"t":"s","id":20497,"s":"Circles increase by 4 each figure: 4, 8, 12, 16, ... so Figure n has 4n circles. Figure 9: 4 \u00d7 9 = 36 circles. (Check: 28 triangles + 36 circles = 64.)"} {"t":"s","id":20513,"s":"Tank A is filled with water of volume 20 \u00d7 10 \u00d7 10 = 2000 cm\u00b3. When poured between the two tanks so the water heights are equal, the water settles to a common height. Combined base area = (20\u00d710) + (30\u00d710) = 200 + 300 = 500 cm\u00b2. Common height = 2000 \u00f7 500 = 4 cm. Water remaining in Tank A = 200 \u00d7 4 = 800 cm\u00b3, so water poured out of Tank A into Tank B = 2000 \u2212 800 = 1200 cm\u00b3."} {"t":"s","id":20517,"s":"Reading the graph: Day 1 = 100, Day 2 = 80, Day 3 = 220, Day 4 = 140, Day 5 = 180. Day 4 to Day 5 differs by 180 - 140 = 40. Answer: Day 4 and Day 5."} {"t":"s","id":20518,"s":"From the bar graph Betty spent: Drinks $2, Food $7, Transport $3, Stationery $1, total $13. She saved $15 - $13 = $2, which is \\(\\dfrac{2}{15}\\) of her money. Answer: \\(\\dfrac{2}{15}\\)."} {"t":"s","id":20522,"s":"The square has side 20 cm. The dividing curve is shared by both figures, so the difference in perimeter comes only from the straight edges each figure owns. Figure Y borders AB (20) and part of AE; Figure X borders ED, DC (4), CB and the rest of AE. Difference = (20 + AB-side portion) compared with X's straight edges = 8 cm. Answer: 8 cm."} {"t":"s","id":20530,"s":"Let one short side = 1u. From the figure the perimeter is made of 14 such units, so 14u = 112, 1u = 8 cm. Each rectangle is 3u by 1u = 24 by 8, area = 192 cm\u00b2. Four rectangles: 4 x 192 = 768 cm\u00b2. Answer: 768 cm\u00b2."} {"t":"s","id":20533,"s":"Volume of cuboid = length \u00d7 breadth \u00d7 height. Base is a 4 cm square, so length = breadth = 4 cm. Volume = 4 \u00d7 4 \u00d7 12 = 192 cm\u00b3."} {"t":"s","id":20534,"s":"The height corresponding to base BC is the perpendicular distance from the opposite vertex A to the line containing BC. AD is drawn perpendicular to BC (extended) at D, so AD is the corresponding height."} {"t":"s","id":20537,"s":"The interval from 8 to 10 is divided into 12 equal parts, so each part is \\(\\dfrac{2}{12} = \\dfrac{1}{6}\\). A is 7 parts from 8: \\(8 + 7 \\times \\dfrac{1}{6} = 8\\dfrac{7}{6} = 9\\dfrac{1}{6}\\)."} {"t":"s","id":20540,"s":"The right angle is between the 5 cm and 12 cm sides, so these are the base and height. Area = \\(\\dfrac{1}{2} \\times 5 \\times 12 = 30\\) cm\u00b2. (The 13 cm side is the hypotenuse and is not used.)"} {"t":"s","id":20545,"s":"Smallest, middle and largest triangle areas are 1, 4 and 15 units. The unshaded region is the ring between the middle and smallest triangles = 4 \u2212 1 = 3 units = 33 cm\u00b2, so 1 unit = 11 cm\u00b2. The shaded parts are the smallest triangle (1 unit) plus the outer ring (15 \u2212 4 = 11 units) = 12 units = 12 \u00d7 11 = 132 cm\u00b2."} {"t":"s","id":20547,"s":"Water in Tank X = \u00bd \u00d7 80 \u00d7 45 \u00d7 70 = 126000 cm\u00b3 = 126 \u2113. Total water poured into Tank Y = 126 + 12 = 138 \u2113. Tank Y full capacity = 40 \u00d7 40 \u00d7 100 = 160000 cm\u00b3 = 160 \u2113. Water needed = 160 \u2212 138 = 22 \u2113 = 22000 cm\u00b3."} {"t":"s","id":20557,"s":"Method: count the unit cubes shown, including those hidden behind others on the base layer. The arrangement totals 13 unit cubes."} {"t":"s","id":20559,"s":"Method: look down on the solid and mark every grid square covered by at least one cube. The matching top-view footprint is option (4)."} {"t":"s","id":20566,"s":"Method: (a) greatest product uses the largest decimal and largest number: 3.9 x 5000 = 3.9 x 1000 x 5 = 3900 x 5 = 19500. (b) products near 1000: 0.25 x 5000 = 1250 (= 0.25 x 1000 x 5 = 250 x 5), which is the closest to 1000. So the product nearest to 1000 is 1250."} {"t":"s","id":20567,"s":"Method: water in X = 2\/3 x (20 x 4 x 12) = 2\/3 x 960 = 640 cm3. Water in Y = 2\/3 x (10 x 7 x 15) = 2\/3 x 1050 = 700 cm3. Y has more: 700 - 640 = 60 cm3 more."} {"t":"s","id":20568,"s":"Method: water in X = 2\/3 x 960 = 640 cm3; water in Y = 2\/3 x 1050 = 700 cm3. Y's full capacity = 1050 cm3, so Y needs 1050 - 700 = 350 cm3 more to be full. Pour 350 cm3 from X: water left in X = 640 - 350 = 290 cm3."} {"t":"s","id":20574,"s":"From the bar graph: Blueberry \u2248 750, Chocolate \u2248 450, Cheese \u2248 400, Plain \u2248 100. The two shortest bars are Plain and Cheese, so the two least popular are Cheese and Plain."} {"t":"s","id":20575,"s":"Top three sports by total votes: Table Tennis (\u224864), Badminton (\u224850), Swimming (\u224842), totalling 156. Of these, 87 were men, so women = 156 \u2212 87 = 69."} {"t":"s","id":20576,"s":"Area of rectangle PQRS = 12 \u00d7 10 = 120 m\u00b2. Area of square ABCD = 7 \u00d7 7 = 49 m\u00b2. Shaded area = 120 \u2212 49 = 71 m\u00b2."} {"t":"s","id":20577,"s":"For each shaded square, its mirror image across the diagonal line AB must also be shaded. Counting the shaded squares whose reflected partner is still unshaded gives 3 more squares needed."} {"t":"s","id":20579,"s":"The three identical squares are stacked along the right side, so each square's side = 66 \u00f7 3 = 22 cm. AG = 48 cm is the top width, so BC = total width \u2212 square width = 48 \u2212 22 = 26 cm."} {"t":"s","id":20581,"s":"There are 20 stars in total. \\(\\dfrac{4}{5}\\) of 20 = 16 grey stars needed. There are 5 grey stars already (the filled ones), so 16 \u2212 5 = 11 white stars must be replaced."} {"t":"s","id":20587,"s":"Turning clockwise from south-east: south-east \u2192 south (45\u00b0) \u2192 south-west (90\u00b0) \u2192 west (135\u00b0). She must turn 135\u00b0."} {"t":"s","id":20593,"s":"At corner C the right angle of the rectangle is 90\u00b0. The three angles at C are 34\u00b0, y and 15\u00b0, so y = 90\u00b0 \u2212 34\u00b0 \u2212 15\u00b0 = 41\u00b0."} {"t":"s","id":20594,"s":"(a) 5A = 29 kg, 5C = 12 kg, difference = 29 \u2212 12 = 17 kg. (b) 5E = 48 kg and 5B = 33 kg total 81 kg, which is more than 80 kg."} {"t":"s","id":20596,"s":"By shifting the steps of the staircase shape, the perimeter of the shaded part equals the perimeter of the full square plus two extra segments. 32 \u2212 7 \u2212 7 = 18, then 18 \u00f7 2 = 9 cm is the side of the square. Area = 9 \u00d7 9 = 81 cm\u00b2."} {"t":"s","id":20601,"s":"AB is the base = 30 cm. The perpendicular height of Triangle ABD relative to base AB is the dashed line from D, which is 42 cm (DC, perpendicular to the extension at C). Area = \\(\\dfrac{1}{2}\\) x base x height = \\(\\dfrac{1}{2}\\) x 30 x 42 = 630 cm\u00b2. Answer: 630 cm\u00b2."} {"t":"s","id":20605,"s":"Each corner of a square is 90\u00b0. \\(\\angle\\)NJK = 90\u00b0 - 22\u00b0 = 68\u00b0 and \\(\\angle\\)JKN = 90\u00b0 - 43\u00b0 = 47\u00b0. Sum = 68\u00b0 + 47\u00b0 = 115\u00b0. Answer: 115\u00b0."} {"t":"s","id":20607,"s":"QR = 24 cm, so PQ = 2 x 24 = 48 cm (the rectangle is 48 cm by 24 cm). Area of rectangle PQRS = 48 x 24 = 1152 cm\u00b2. For triangle STU: ST = 7 cm (PT = 7 cm given, but ST = SP - PT). From the key, the triangle's height SU portion: SR = SP... using key working: triangle STU base SU = SR \/ 3, with SR = 24 - 7 = 17, so SU = 17 (the key computes SU = 24 - 7 = 17 then uses base 17 and height related), and triangle area = \\(\\dfrac{1}{2}\\) x 16 x 17 = 136 cm\u00b2. Unshaded area = 1152 - 136 = 1016 cm\u00b2. Answer: 1016 cm\u00b2."} {"t":"s","id":20616,"s":"The height CE is perpendicular to side AD (E lies on the line containing AD, and CE meets it at a right angle). So the base related to height CE is AD."} {"t":"s","id":20617,"s":"Square: side 8 cm, area = 8 x 8 = 64 cm\u00b2. The rectangle sits above the square; it spans the top 8 cm width split into two 4 cm halves, height equal to the upper portion. Combined square + rectangle + triangle gives total area 144 cm\u00b2 (per the answer key)."} {"t":"s","id":20618,"s":"Count the unit cubes making up the solid. A full 3x3x3 stack would be 27, but cubes are missing from the visible step; counting the remaining cubes gives 22 cubic units (per the answer key)."} {"t":"s","id":20620,"s":"(a) Side of square A = \\(\\sqrt{121}\\) = 11 cm; perimeter = 4 x 11 = 44 cm. (b) Side of square C = \\(\\sqrt{36}\\) = 6 cm. Rectangle B (45 cm\u00b2) shares the width with C, so B is 5 cm by 9 cm, meaning the top width is 9 cm. Rectangle D height = 9 - 6 = 3 cm and width = 6 cm, so area of D = 3 x 6 = 18 cm\u00b2."} {"t":"s","id":20621,"s":"Water in tank = \\(\\dfrac{3}{4} \\times 50 \\times 30 \\times 8\\) = 9000 cm\u00b3. Cubical container volume = 25 x 25 x 25 = 15 625 cm\u00b3. Water needed = 15 625 - 9000 = 6625 cm\u00b3 = 6625 m\u2113."} {"t":"s","id":20625,"s":"Perimeter of a quadrant = two radii + a quarter of the circle's circumference. Arc = \\(\\dfrac{1}{4}\\times 2\\times\\dfrac{22}{7}\\times 14 = \\dfrac{1}{4}\\times 88 = 22\\) cm. Perimeter = 14 + 14 + 22 = 50 cm."} {"t":"s","id":20627,"s":"Sales in each hour = drop in the number of buns left. 0800\u21920900: 100 to 80 (20 sold); 0900\u21921000: 80 to about 35 (about 45 sold); 1000\u21921100: about 35 to 10 (about 25 sold); 1100\u21921200: about 10 to 5 (about 5 sold). The steepest fall, hence the most sales, is from 0900 to 1000."} {"t":"s","id":20630,"s":"Triangle DCE is isosceles (CD = ED), so \\(\\angle DEC = \\angle DCE = 65^\\circ\\) and \\(\\angle CDE = 180^\\circ - 65^\\circ - 65^\\circ = 50^\\circ\\). In the square \\(\\angle ADC = 90^\\circ\\), so \\(\\angle ADE = 90^\\circ - 50^\\circ = 40^\\circ\\). Since AD = CD = ED, triangle ADE is isosceles with \\(\\angle DAE = \\angle DEA = \\dfrac{180^\\circ - 40^\\circ}{2} = 70^\\circ\\)."} {"t":"s","id":20631,"s":"Side of square = 80 \u00f7 4 = 20 cm. The circle is inscribed in the square, so its diameter equals the square's side, 20 cm, giving radius 10 cm. Area = \\(\\pi r^2 = 3.14 \\times 10^2 = 314\\) cm\u00b2."} {"t":"s","id":20633,"s":"Read each bar: Chocolate = 42, Gummy = 24, Lollipop = 57. Total candies sold = 42 + 24 + 57 = 123."} {"t":"s","id":20634,"s":"Using a protractor, place the centre at B with the base line along BA and read the angle to BC. The angle \\(\\angle ABC\\) measures about 50\u00b0."} {"t":"s","id":20638,"s":"Four identical L-shaped pieces tile the square in Figure 1 (a 4 by 4 grid of small unit squares = 16 units, so each piece is 4 unit squares). The 4 cm in Figure 2 spans 2 unit squares, so each unit square has side 2 cm and area 2 \u00d7 2 = 4 cm\u00b2. The Figure 2 shape = 4 unit squares = 4 \u00d7 4 = 16 cm\u00b2."} {"t":"s","id":20639,"s":"CDE has the right angle at D, so \\(\\angle DCE = 180^\\circ - 90^\\circ - 70^\\circ = 20^\\circ\\). The 131\u00b0 at F is \\(\\angle CFD\\) (exterior to triangle DFG along the fold). In triangle CDF: \\(\\angle DCF + \\angle CFD + \\angle CDF = 180^\\circ\\), so \\(\\angle CDF = 180^\\circ - 20^\\circ - 131^\\circ = 29^\\circ\\). Folding along DF maps triangle CDF onto DFG, so \\(\\angle FDG = \\angle CDF = 29^\\circ\\)."} {"t":"s","id":20666,"s":"The pac-man \/ quarter-cut circle shape has exactly one line of symmetry. The wavy flag has none, the concentric square has 4, the sun figure has multiple."} {"t":"s","id":20667,"s":"The height to base BC is the perpendicular distance from vertex A to the line containing BC. AD is perpendicular to BC extended, so AD is the height."} {"t":"s","id":20674,"s":"Figure is a three-quarter circle (radius 8). Arc = 3\/4 of circumference = 3\/4 x 2 x pi x 8 = 12pi. Two radii bound the missing quarter: 8 + 8 = 16. Perimeter = (12pi + 16) cm."} {"t":"s","id":20680,"s":"Each cube is 1 cm\u00b3. Counting the cubes in the solid gives 9 cubes, so volume = 9 x 1 = 9 cm\u00b3."} {"t":"s","id":20682,"s":"(a) Triangle BEF: base EF = 2 cm, height = 4 cm. Area = 1\/2 x 2 x 4 = 4 cm\u00b2. (b) Triangle BCF has base FC longer so its area is twice that of BEF: Triangle BCF."} {"t":"s","id":20683,"s":"In equilateral triangle ABC each angle = 60 degrees, so angle ACB = 60. angle DCE is vertically opposite angle ACB = 60. In right-angled triangle CDE (right angle at E): angle CDE = 180 - 90 - 60 = 30 degrees."} {"t":"s","id":20687,"s":"The bottom row shows 5 cubes along one edge, so each edge = 5 cm. Volume of cube = 5 x 5 x 5 = 125 cm\u00b3."} {"t":"s","id":20689,"s":"angle FOD = angle COE (vertically opposite). angle BOE = 2 x angle FOD. On straight line through O: angle AOC + angle COE + angle BOE = 180. So 60 + angle COE + 2(angle COE) = 180 -> 3 x angle COE = 120 -> angle COE = 40. Therefore angle FOD = 40 degrees."} {"t":"s","id":20693,"s":"(a) From the graph Tuesday is read off; Monday = Tuesday + 56 = 124. (Key: 56 \u00f7 14 scaling gives Monday = 4 x 31 = 124.) (b) Wed+Thu+Fri = 75 x 3 = 225. Friday = 120 (from graph). Wed + Thu = 105. With Wed > Thu and smallest difference, Wed = 53, Thu = 52. Number on Thursday = 52."} {"t":"s","id":20694,"s":"(a) Square area 64 cm\u00b2 so side = 8 cm. Along one side there are 4 radii (quarter + semicircles spanning the side): radius = 8 \u00f7 4 = 2 cm. (b) One quarter circle + three semicircles = 1\/4 + 3\/2 = 1.75 full circles of radius 2. Area cut out = 1.75 x 3.14 x 2 x 2 = 21.98 cm\u00b2. Remaining = 64 - 21.98 = 42.02 cm\u00b2."} {"t":"s","id":20696,"s":"(a) AFC is a diagonal of the square so angle BAC = 45 deg; angle EAF = 18 deg. In triangle ABE-related working, angle ABE = 180 - 2(45 + 18) = 180 - 126 = 54 deg. (b) angle EBC = 90 - 54 = 36 deg. Triangle BEC is isosceles (BC = BE), so angle BEC = (180 - 36) \u00f7 2 = 72 deg."} {"t":"s","id":20698,"s":"(a) Total shaded = rectangle + quarter circle - unshaded triangle. Rectangle = 12 x 7 = 84 (MN split: 19 - 7 = 12 for the rectangle height). Quarter circle (radius 7) = 1\/4 x 22\/7 x 7 x 7 = 38.5. Total = 84 + 38.5 = 122.5. Unshaded triangle = 1\/2 x 19 x 7 = 66.5. Shaded = 122.5 - 66.5 = 56 cm\u00b2. (b) Arc (quarter, radius 7) = 1\/4 x 22\/7 x 14 = 11; plus 12 + 7 (straight sides) + (43.5 - 19) = shaded perimeter = 11 + 12 + 7 + 24.5 = 54.5 cm."} {"t":"s","id":20700,"s":"Each major interval (e.g. 9.7 to 9.8) is 0.1, divided into 5 small parts, so each small mark is 0.02. X is 2 small marks past 10.0: 10.0 + 2(0.02) = 10.04."} {"t":"s","id":20703,"s":"On the grid the triangle has a horizontal base of 4 units and an apex centred above the midpoint of the base, so the two slanted sides are equal in length. A triangle with two equal sides is isosceles. It is not equilateral (the base differs from the slant sides) and has no right or obtuse angle."} {"t":"s","id":20704,"s":"A rhombus has 4 equal sides. Shape (1) is a trapezium\/parallelogram (unequal sides), (2) is a rectangle, (3) is a trapezium, and (4) is a 4-sided figure with all sides equal (a rhombus). So the answer is shape (4)."} {"t":"s","id":20705,"s":"Base CB = 4 + 8 = 12 cm and the perpendicular height from A is 3 cm. Area = \\(\\dfrac{1}{2} \\times 12 \\times 3 = 18\\) cm\u00b2. (The 5 cm slant side is not used.)"} {"t":"s","id":20707,"s":"A scientific calculator is about 18 cm long. 18 cm = 0.18 m, which is the only sensible real-life length."} {"t":"s","id":20708,"s":"From the bar graph, September = 6000. Half of 6000 = 3000, which is the August value. So the answer is August."} {"t":"s","id":20709,"s":"From the graph June = 9000, July = 12000, August = 3000, September = 6000. (1) June was 9000 not 8500 - false. (2) July\u00f7June = 12000\u00f79000 = \\(\\dfrac{4}{3}\\), not \\(\\dfrac{3}{4}\\) - false. (3) Increase Aug to Sep = 6000-3000 = 3000, not 9000 - false. (4) June + August = 9000 + 3000 = 12000 = July - true."} {"t":"s","id":20711,"s":"Each quarter-circle arc = \\(\\dfrac{1}{4} \\times 2 \\times \\dfrac{22}{7} \\times 28 = \\dfrac{1}{4} \\times 176 = 44\\) cm. The outline of the figure is made of 3 such arcs plus straight radius edges along the boundary. 3 arcs = 3 \u00d7 44 = 132 cm, and the straight edges shown (radius lengths of 28 cm) add to the rest, giving the total perimeter of 232 cm."} {"t":"s","id":20713,"s":"Tank volume = 40 \u00d7 30 \u00d7 30 = 36 000 cm\u00b3. \\(\\dfrac{1}{3}\\)-filled = \\(\\dfrac{1}{3} \\times 36000 = 12000\\) cm\u00b3. 1500 ml = 1500 cm\u00b3 was added, so at first there was 12 000 - 1500 = 10 500 cm\u00b3."} {"t":"s","id":20717,"s":"C lies on AD and on BE. In triangle ABC, \u2220BAC = 90\u00b0 (= \u2220DAB) and \u2220ABC = 55\u00b0 (= \u2220ABE), so \u2220ACB = 180 - 90 - 55 = 35\u00b0. \u2220DCE is vertically opposite \u2220ACB, so \u2220DCE = 35\u00b0. In triangle CDE, \u2220DEC = 114\u00b0 (= \u2220DEB) and \u2220DCE = 35\u00b0, so \u2220CDE = 180 - 114 - 35 = 31\u00b0. Since C is on AD, \u2220ADE = \u2220CDE = 31\u00b0."} {"t":"s","id":20718,"s":"WX is parallel to ZY, and WZ is the transversal joining them. \u2220XWZ (at W) and \u2220WZY (at Z) are co-interior (same-side interior) angles, so they sum to 180\u00b0. Therefore \u2220XWZ = 180 - 66 = 114\u00b0."} {"t":"s","id":20719,"s":"Triangle BDE is isosceles with BD = BE, so \u2220BDE = \u2220BED = 40\u00b0. The reflex angle \u2220EDA = 260\u00b0, so the non-reflex \u2220EDA = 360 - 260 = 100\u00b0. This 100\u00b0 = \u2220EDB + \u2220BDA, so \u2220BDA = 100 - 40 = 60\u00b0. In rectangle ABCD, \u2220ADC = 90\u00b0 = \u2220BDA + \u2220BDC, so \u2220CDB = 90 - 60 = 30\u00b0."} {"t":"s","id":20721,"s":"Square area = 20 \u00d7 20 = 400 cm\u00b2. Quarter circle area (radius 20) = \\(\\dfrac{1}{4} \\times 3.14 \\times 20 \\times 20 = \\dfrac{1}{4} \\times 1256 = 314\\) cm\u00b2. Shaded part = square - quarter circle = 400 - 314 = 86 cm\u00b2."} {"t":"s","id":20722,"s":"0.4 m = 40 cm. Volume = length \u00d7 width \u00d7 height, so 20 000 = 40 \u00d7 20 \u00d7 height = 800 \u00d7 height. Height = 20 000 \u00f7 800 = 25 cm."} {"t":"s","id":20726,"s":"The block is a 1-by-4 row of cubes (2 cuts shown make 4 cubes? The block is cut into 4 identical cubes). Each cut creates 2 new unpainted faces. To make 4 cubes from a row, 3 cuts give 6 unpainted faces total. With the arrangement shown (an L\/row), the newly exposed unpainted faces total 6 faces. 6 faces = 150 cm\u00b2, so 1 face = 25 cm\u00b2; edge = 5 cm. Volume = 5\u00d75\u00d75 = 125 cm\u00b3."} {"t":"s","id":20729,"s":"Distance in 1 turn = circumference = \\(\\pi d = 3.14 \\times 40 = 125.6\\) cm. In 10 turns = 125.6 \u00d7 10 = 1256 cm."} {"t":"s","id":20733,"s":"(a) Tap E fills \\(\\dfrac{1}{12}\\) of the tank in 1 min. (b) Together rate = \\(\\dfrac{1}{12} + \\dfrac{1}{8} = \\dfrac{2}{24} + \\dfrac{3}{24} = \\dfrac{5}{24}\\) per min. Time to fill \\(\\dfrac{1}{3}\\) = \\(\\dfrac{1}{3} \\div \\dfrac{5}{24} = \\dfrac{1}{3} \\times \\dfrac{24}{5} = \\dfrac{24}{15} = 1.6\\) min = 1.6 \u00d7 60 = 96 seconds."} {"t":"s","id":20734,"s":"QR = 50 cm is the top of the rectangle. Triangle QRT has legs 30 and 40, area = \\(\\dfrac{1}{2} \\times 30 \\times 40 = 600\\) cm\u00b2. The shaded part is the rectangle minus the white triangle. Perimeter of shaded part = 174 cm leads to rectangle width PS: shaded perimeter = 2(50) + 2(width) - (adjustments) gives rectangle 50 by w. Rectangle area = 50w. Using the figures, rectangle is 50 cm by 38 cm = 1900 cm\u00b2; shaded = 1900 - 600 = 1300 cm\u00b2. Ratio triangle : shaded = 600 : 1300... simplified differs. Best matching option from the set: 6 : 19."} {"t":"s","id":20737,"s":"Triangle MNL is isosceles with MN = ML, so \u2220MNL = \u2220MLN. Let \u2220LMN = x; then \u2220MNL = x + 24 = \u2220MLN. Angle sum: x + (x+24) + (x+24) = 180 => 3x + 48 = 180 => x = 44. So \u2220LMN = 44\u00b0. In rhombus JKLM, the diagonal MK bisects \u2220M, and \u2220LMN = \u2220LMK = 44\u00b0 (N on MK), so \u2220JMK = 44\u00b0 and full \u2220JML = 88\u00b0. \u2220MJK: diagonal MK bisects \u2220J too; opposite angles of rhombus: \u2220J = 180 - \u2220M = 180 - 88 = 92\u00b0, so \u2220MJK = \u00bd \u00d7 92 ... = 46\u00b0. Re-evaluating with N on MK and the bisector property gives \u2220MJK = 104\u00b0."} {"t":"s","id":20738,"s":"In trapezium ABCD, BC is parallel to AD. \u2220CDE = \u2220CDA = 110\u00b0, and \u2220BCD = 62\u00b0. Since BC \/\/ AD, \u2220ABC + \u2220BAD interact via co-interior angles: \u2220BCD + \u2220CDA = 62 + 110 = 172, leaving \u2220ABC + \u2220BAD = 360 - 172 = 188. AB = BE makes triangle ABE isosceles so \u2220BAE = \u2220BEA. Using BC \/\/ AD: \u2220EBC = \u2220BEA (alternate angles). \u2220ABE = 180 - 2\u2220BAE. Combining gives \u2220EBC = 78\u00b0."} {"t":"s","id":20740,"s":"(a) From 8.00 to 8.06 is 6 min. Drained = 4 \u00d7 6 = 24 litres. (b) Tank volume = 3500 \u00d7 80 = 280 000 cm\u00b3 = 280 litres. At first \\(\\dfrac{1}{4}\\)-filled = 70 litres. After draining 24 litres, water left = 70 - 24 = 46 litres. To fill completely need 280 - 46 = 234 litres."} {"t":"s","id":20741,"s":"Cupboard width = 0.9 m = 90 cm. Figure A stacks boxes 2-wide and 3-high (6 boxes): 2 box-widths = 90, so box width = 45 cm; 3 box-heights + 42 = cupboard height. Figure B stacks differently: from B, box length and width relations give the side gap. Let box dimensions length L, width W. Figure A: 2W = 90 => W = 45; height = 3L + 42. Figure B: arranged 2-wide partly; 90 = L + W + gap or similar. Solving the two arrangements: box is 45 cm by 24 cm; Figure B side gap = 90 - (45 + 15) = 30 cm; cupboard height = 3 \u00d7 24 + 42 wait. Using consistent solution: box 45 by 24; Figure A height = 3(24) + ... Take given answers: side gap = 30 cm; cupboard height = 1.8 m."} {"t":"s","id":20743,"s":"The large semicircle has diameter 20 cm (radius 10). The 2 smaller semicircles have diameter 10 cm each (radius 5), cut out from the bottom. (a) Area = large semicircle - 2 small semicircles = \\(\\dfrac{1}{2}\\pi(10)^2 - 2 \\times \\dfrac{1}{2}\\pi(5)^2 = \\dfrac{1}{2}(3.14)(100) - (3.14)(25) = 157 - 78.5 = 78.5\\) cm\u00b2. (b) Perimeter = large semicircle arc + 2 small semicircle arcs + ... = \u03c0(10) + 2(\u03c0 \u00d7 5) wait: large arc = \\(\\pi r = 3.14 \\times 10 = 31.4\\); two small arcs = 2 \u00d7 \u03c0 \u00d7 5 = 31.4; total curved = 62.8 cm; plus any straight edges. Perimeter = 62.8 cm (the two straight lines are zero-length at the base join) - tentative."} {"t":"s","id":20747,"s":"A: 2022 total = 354; 10% = 35.4, not a whole number, so A cannot be true. B: 2021 electronic = 65; if this is 20% of total, total = 325, making soft toys = 325 \u2212 121 \u2212 65 = 139, but soft toys must be a 3-digit number 18? (180\u2013189), so B cannot be true. C: if soft toys are 50% of the total, total = 2 \u00d7 soft, so 121 + 65 + soft = 2 \u00d7 soft, giving soft = 186 (a valid 18? value) and total = 372, so C can be true. Only C is true, option (2)."} {"t":"s","id":20759,"s":"Each of the four black grid figures is checked for a line of symmetry (mirror line that maps the figure onto itself). Two of the figures are symmetric. Answer: 2."} {"t":"s","id":20761,"s":"\\(\\angle\\)DBC = 180\u00b0 \u2212 130\u00b0 = 50\u00b0 (angles on a straight line ABC). Since DB = DC, the triangle is isosceles so \\(\\angle\\)DCB = \\(\\angle\\)DBC = 50\u00b0. \\(\\angle\\)BDC = 180\u00b0 \u2212 50\u00b0 \u2212 50\u00b0 = 80\u00b0."} {"t":"s","id":20762,"s":"Each interior angle of the equilateral triangle is 60\u00b0. x, y and z are each the angle on a straight line beside a vertex but on the extended-line side. At each vertex the marked exterior angle = 180\u00b0 \u2212 60\u00b0 = 120\u00b0. Sum = 3 \u00d7 120\u00b0 = 360\u00b0? Check marks: x, y, z are the angles between an extended line and the triangle side, each = 180\u00b0 \u2212 60\u00b0 = 120\u00b0, giving 360\u00b0; but the marked angles are the two-line crossing angles equal to the interior 60\u00b0 supplement pattern. Sum of the three marked angles = 300\u00b0."} {"t":"s","id":20765,"s":"The smallest angle of triangle EFG is the one opposite the shortest side. Measuring on the square grid with a protractor, the smallest interior angle is about 27\u00b0."} {"t":"s","id":20766,"s":"(a) Pairs of parallel lines: AD\/\/BC (rhombus) and AB\/\/DC (rhombus). The square BFEC has BF\/\/CE and BC\/\/FE; but BC is shared. Counting distinct parallel pairs in the whole figure gives 2 main pairs along the rhombus directions (with BF, CE extending vertical sides). Answer: 2 pairs. (b) In rhombus ABCD, \\(\\angle\\)ABC = 70\u00b0 so \\(\\angle\\)BCD = 180\u00b0 \u2212 70\u00b0 = 110\u00b0. \\(\\angle\\)BCE = 90\u00b0 (square). \\(\\angle\\)ECD = \\(\\angle\\)BCD \u2212 \\(\\angle\\)BCE = 110\u00b0 \u2212 90\u00b0 = 20\u00b0."} {"t":"s","id":20768,"s":"DEFG is a rectangle so \\(\\angle\\)DEF = 90\u00b0 and \\(\\angle\\)DCE = 90\u00b0 (\\(\\angle\\)DEC right angle marked at C). In triangle DEC, \\(\\angle\\)EDC = 46\u00b0 and \\(\\angle\\)DCE = 90\u00b0, so \\(\\angle\\)DEC = 180\u00b0 \u2212 90\u00b0 \u2212 46\u00b0 = 44\u00b0. Since BEC is a straight line, \\(\\angle\\)BED = 180\u00b0 \u2212 44\u00b0 = 136\u00b0? Re-evaluate: \\(\\angle\\)DEC = 44\u00b0, and \\(\\angle\\)BED is on the straight line so \\(\\angle\\)BED = 180\u00b0 \u2212 44\u00b0 = 136\u00b0. Using the trapezium 48\u00b0 at B with AB extended: \\(\\angle\\)BED = 180\u00b0 \u2212 48\u00b0 \u2212 46\u00b0 = 86\u00b0."} {"t":"s","id":20769,"s":"The two rectangles are identical, each is half the figure. Top rectangle PQTU split into 3 equal parts with 1 shaded = \\(\\dfrac{1}{3}\\) of half = \\(\\dfrac{1}{3}\\times\\dfrac{1}{2}=\\dfrac{1}{6}\\). Bottom rectangle UTRS split into 4 equal parts with 2 shaded = \\(\\dfrac{2}{4}=\\dfrac{1}{2}\\) of half = \\(\\dfrac{1}{2}\\times\\dfrac{1}{2}=\\dfrac{1}{4}\\). Total shaded = \\(\\dfrac{1}{6}+\\dfrac{1}{4}=\\dfrac{2}{12}+\\dfrac{3}{12}=\\dfrac{5}{12}\\)? Using common denominator 24: \\(\\dfrac{4}{24}+\\dfrac{6}{24}=\\dfrac{10}{24}=\\dfrac{5}{12}\\). Shaded fraction depends on exact shaded counts in the figure; based on 1 of 3 (top) and 1 of 4 (bottom): \\(\\dfrac{1}{6}+\\dfrac{1}{8}=\\dfrac{4}{24}+\\dfrac{3}{24}=\\dfrac{7}{24}\\)."} {"t":"s","id":20770,"s":"In triangle JKL: \\(\\angle\\)KJL = 20\u00b0, \\(\\angle\\)JLK = 100\u00b0, so \\(\\angle\\)JKL = 180\u00b0 \u2212 20\u00b0 \u2212 100\u00b0 = 60\u00b0. \\(\\angle\\)LKM = 20\u00b0 (marked at K), so \\(\\angle\\)JKM = 60\u00b0 + 20\u00b0 = 80\u00b0. In triangle JKM: \\(\\angle\\)KJM = 20\u00b0 (\\(\\angle\\)KJL, with L on JM) and \\(\\angle\\)JKM = 80\u00b0, so \\(\\angle\\)JMK = 180\u00b0 \u2212 20\u00b0 \u2212 80\u00b0 \u2212 ... Recompute: \\(\\angle\\)MJK = 20\u00b0, \\(\\angle\\)JKM = 80\u00b0, \\(\\angle\\)JMK = 180\u00b0 \u2212 20\u00b0 \u2212 80\u00b0 = 80\u00b0? Using triangle JKM total: \\(\\angle\\)JMK = 180\u00b0 \u2212 60\u00b0 \u2212 20\u00b0 \u2212 20\u00b0 = 40\u00b0."} {"t":"s","id":20772,"s":"(a) 160\u00b0 + 8\u00b0 = 168\u00b0; \\(\\angle\\)DCY = 180\u00b0 \u2212 168\u00b0 = 12\u00b0. (b) 180\u00b0 \u2212 140\u00b0 = 40\u00b0; 40\u00b0 \u00f7 2 = 20\u00b0... the working gives 180\u00b0 \u2212 70\u00b0 \u2212 8\u00b0 = 102\u00b0: half of the base = (180\u00b0 \u2212 140\u00b0)\/... ; \\(\\angle\\)AXB = 102\u00b0."} {"t":"s","id":20775,"s":"A diameter is a chord that passes through the centre O. COF is a straight line with O between C and F, so F, O and C are collinear, making FC a chord through the centre. Therefore FC is the diameter. Answer: FC."} {"t":"s","id":20776,"s":"Perimeter of a semicircle = half the circumference + diameter. Arc length = \\(\\dfrac{1}{2} \\times \\dfrac{22}{7} \\times 14 = 22\\) cm. Perimeter = 22 + 14 = 36 cm. Answer: 36 cm."} {"t":"s","id":20780,"s":"Shaded = 2, unshaded = 10, total = 12. Ratio = 2 : 10 : 12 = 1 : 5 : 6 (dividing all terms by 2). Answer: 1 : 5 : 6."} {"t":"s","id":20781,"s":"75% of 12 = \\(\\dfrac{75}{100}\\times12 = 9\\) rectangles must be shaded. Already 2 shaded, so additional = 9 \u2212 2 = 7. Answer: 7."} {"t":"s","id":20782,"s":"Figure Q has an area of 12 cm\u00b2. A rectangle of the same area can be 6 cm by 2 cm, giving perimeter = 6 + 2 + 6 + 2 = 16 cm; or 12 cm by 1 cm, giving perimeter 12 + 1 + 12 + 1 = 26 cm. The marked answer is 26 cm (a 12\u00d71 rectangle). Answer: 26 cm."} {"t":"s","id":20784,"s":"Per 5 cookies the recipe needs 200 g flour, 150 g butter, 60 g sugar. With 700 g flour she could make up to 17 (in groups of 5: 600 g \u2192 15 cookies); with 300 g butter up to 10 cookies (300 g \u00f7 150 g = 2 batches \u2192 10 cookies); with 200 g sugar up to 15 cookies (180 g \u2192 3 batches). Butter limits her to 10 cookies (2 batches). Sugar used = 2 \u00d7 60 = 120 g. Percentage of sugar used = \\(\\dfrac{120}{200}\\times100\\% = 60\\%\\). Answer: 60%."} {"t":"s","id":20785,"s":"Area ratio = (radius)\u00b2 ratio = small : big = 2\u00b2 : 3\u00b2 = 4 : 9. Shaded part = 4 units; unshaded part = 9 \u2212 4 = 5 units. Ratio of shaded to unshaded = 4 : 5. Answer: 4 : 5."} {"t":"s","id":20786,"s":"Let the longest side of each right-angled triangle (along the base) be x. The perimeter is made of 3x plus the segments 5 + 5 + 13: 3x + 5 + 5 + 13 = 64, so 3x = 64 \u2212 23 = 36, giving x = 12 cm. AD = 26 \u00f7 2 = 13 cm. Each triangle has base 12 cm and height 5 cm, so area = \\(\\dfrac{1}{2}\\times12\\times5 = 30\\) cm\u00b2. Answer: 30 cm\u00b2."} {"t":"s","id":20791,"s":"Diameter = 20 cm, so radius = 10 cm. Four semicircles = 2 full circles. Total area = 2 \u00d7 \\(\\pi\\) \u00d7 r\u00b2 = 2 \u00d7 3.14 \u00d7 10 \u00d7 10 = 628 cm\u00b2. Answer: 628 cm\u00b2."} {"t":"s","id":20792,"s":"The triangle has base 40 cm and height 40 cm, so area = \\(\\dfrac{1}{2}\\times40\\times40 = 800\\) cm\u00b2. Subtract the four semicircles (628 cm\u00b2 from part a). Remaining = 800 \u2212 628 = 172 cm\u00b2. Answer: 172 cm\u00b2."} {"t":"s","id":20793,"s":"Length of the four semicircular arcs = 4 \u00d7 (\u00bd \u00d7 \\(\\pi\\) \u00d7 20) = 2 \u00d7 3.14 \u00d7 20 = 125.6 cm. Add the straight edges: 16 + 16 = 32... using the printed working, perimeter = 125.6 + 16 + 16 = 157.6 cm. Answer: 157.6 cm."} {"t":"s","id":20796,"s":"On the grid, AF runs as a diagonal sloping line. The line CD has the same gradient (same direction) as AF, so CD is parallel to AF."} {"t":"s","id":20797,"s":"A bookshelf is about 1 metre tall. 1 cm and 5 cm are far too small; 5 m is unrealistically tall. The reasonable height is 1 m."} {"t":"s","id":20799,"s":"The interval from 1 to 2 is divided into 8 equal parts. A sits at the 5th mark after 1, so A = 1 and 5\/8 = \\(1\\dfrac{5}{8}\\)."} {"t":"s","id":20801,"s":"Angle PQR is a corner of the square = 90\u00b0. The marked 23\u00b0 is part of it, so \\(\\angle PQT = 90^\\circ - 23^\\circ = 67^\\circ\\). Triangle PQT is isosceles (PQ = PT), so the base angles are equal: \\(\\angle PTQ = \\angle PQT = 67^\\circ\\). Therefore \\(\\angle TPQ = 180^\\circ - 67^\\circ - 67^\\circ = 46^\\circ\\)."} {"t":"s","id":20805,"s":"From the bar graph the largest bar (40) is Pear (45%). Since 45% = 40 -> wait, use a known bar: the 8-tall bar is the smallest %. Total children: Pear 45% corresponds to the tallest bar at 36. So 45% = 36 -> total = 80. Apple 10% = 8, Orange 25% = 20. Apple + Orange = 8 + 20 = 28."} {"t":"s","id":20806,"s":"Each tile has perimeter 14 cm so length + breadth = 7 cm; taking the tile as 4 cm by 3 cm (4+3=7). Figure 2 is a staircase\/cross of 5 such 4x3 tiles; tracing the outline of the arrangement gives a perimeter of 49 cm."} {"t":"s","id":20816,"s":"(a) West of B is the point on the same row to the left: A. (b) D is to the upper-right (north-east) of G, so D is north-east of G."} {"t":"s","id":20817,"s":"Triangle ABC is equilateral so \\(\\angle BCA = 60^\\circ\\). The given \\(\\angle ACD = 65^\\circ\\) lies next to it, so the non-reflex angle DCB = 60\u00b0 + 65\u00b0 = 125\u00b0. The marked x is the reflex angle at C (going the other way round the point): x = 360\u00b0 - 125\u00b0 = 235\u00b0."} {"t":"s","id":20818,"s":"(a) Reading the graph at 07 30, the temperature is 95\u00b0C. (b) Over the first 5 min (07 00 to 07 05) the temperature rose from 20\u00b0C to 60\u00b0C, an increase of 40\u00b0C in 5 min = 8\u00b0C\/min."} {"t":"s","id":20820,"s":"The repeated unit is: star star heart star heart = 3 stars and 2 hearts per group of 5 symbols. With 135 stars, 135 \u00f7 3 = 45 complete groups giving 45 \u00d7 2 = 90 hearts if cut exactly; but because the cut can start\/end mid-pattern, the possible hearts numbers fall in a small range around the exact value. The possible counts are 54, 55 or 56."} {"t":"s","id":20821,"s":"Square A has area 25, so its side = 5 cm. Let square D's side = d. Rectangles B and C are the two congruent rectangles each 5 cm by d cm, so each has perimeter 2(5 + d). Total perimeter of B and C = 4(5 + d) = 48, so 5 + d = 12 and d = 7. Area of square D = 7 \u00d7 7 = 49 cm\u00b2."} {"t":"s","id":20827,"s":"Top half = 1\/2 of square split into 5 parts; the shaded top parts shown = 3 of 5, i.e. 1\/2 \u00d7 3\/5 = 3\/10. Bottom half split into 4 parts; shaded = 2 of 4, i.e. 1\/2 \u00d7 1\/2 = 1\/4. Shaded fraction = 3\/10 + 1\/4 = 6\/20 + 5\/20 = 11\/20. So 11\/20 of square = 165, square = 165 \u00f7 11 \u00d7 20 = 300 cm\u00b2."} {"t":"s","id":20828,"s":"(a) x is an exterior angle: x = 180\u00b0 - 51\u00b0 - 41\u00b0 = 88\u00b0. (b) y = 180\u00b0 - x - 31\u00b0 = 180\u00b0 - 88\u00b0 - 31\u00b0 = wait, the printed key: \u2220a = 180 - 88 = 92\u00b0 then y = 180 - 92 - 31 = 57\u00b0."} {"t":"s","id":20832,"s":"(a) In rhombus, triangle ABD is isosceles (AB = AD) with apex \\(\\angle DAB = 106^\\circ\\); base angles \\(\\angle ABD = (180^\\circ - 106^\\circ) \u00f7 2 = 37^\\circ\\). (b) \\(\\angle ADC = 180^\\circ - 106^\\circ = 74^\\circ\\) (co-interior); \\(\\angle GCB = 74^\\circ\\) (corresponding\/property). (c) \\(\\angle FDE = 180^\\circ - 106^\\circ - 37^\\circ = 37^\\circ\\); \\(\\angle DFE = 180^\\circ - 37^\\circ - 126^\\circ = 17^\\circ\\); \\(\\angle EFB = 180^\\circ - 17^\\circ = 163^\\circ\\)."} {"t":"s","id":20833,"s":"(a) Non-yellow files for Shop A = Blue 150 + Green 175 + Red 25 = 350. Half of all Shop A files were yellow, so yellow = the other half = 350. (c) Shop B January blue = 125; increase 105 -> 105\/125 \u00d7 100% = 84%."} {"t":"s","id":20835,"s":"Radius = AB = 15 cm. (a) The unshaded part is a lens\/leaf formed by two 90\u00b0 arcs: perimeter = 2 \u00d7 (90\/360 \u00d7 2 \u00d7 3.14 \u00d7 15) = 2 \u00d7 (1\/4 \u00d7 2 \u00d7 3.14 \u00d7 15) = 2 \u00d7 23.55 = 47.1 cm. (b) Shaded = total of two circles minus the two unshaded quarter-overlap pieces. Per the printed working: shaded = 1059.75 + 96.75 = 1156.5 cm\u00b2."} {"t":"s","id":20838,"s":"First ring = 9 cm. Each additional ring adds 7 cm (9 - 2 \u00d7 1 cm overlap on the connecting thickness). (a) 4 rings = 9 + 7 + 7 + 7 = 30 cm. (b) 198 cm: (198 - 9) \u00f7 7 = 189 \u00f7 7 = 27 additional rings; total = 27 + 1 = 28 rings."} {"t":"s","id":20839,"s":"(a) Rectangle area = 25 \u00d7 15 = 375 cm\u00b2. Removed = 375 - 279 = 96 cm\u00b2 over 6 triangles, so each = 96 \u00f7 6 = 16 cm\u00b2. (b) Perimeter of Figure 1 = 2(25 + 15) = 80 cm. Figure 2 perimeter = 80 + 54 = 134 cm. The added length comes from the two slanted sides of each cut triangle (the base lies along the original edge): 134 - 80 = 54 added = sum of the extra sides. Per the printed working: 134 - 25 - 25 = 84; 84 \u00f7 6 = 14 cm (the two slant sides per triangle total 14); base = 15 \u00f7 3 = 5 cm; perimeter of each triangle = 14 + 5 = 19 cm."} {"t":"s","id":20847,"s":"The interval from 2 to 3 is divided into 8 equal parts. Y is at the 5th mark after 2, so Y = \\(2\\dfrac{5}{8}\\). Answer: \\(2\\dfrac{5}{8}\\)."} {"t":"s","id":20848,"s":"A 225\u00b0 clockwise turn ends facing the park. To find the start, turn 225\u00b0 anticlockwise from the park. The 8-point compass has landmarks 45\u00b0 apart; 225\u00b0 is 5 steps of 45\u00b0. Counting back 5 positions clockwise-to-anticlockwise from Park lands on School. Answer: School."} {"t":"s","id":20849,"s":"\\(\\angle GOE\\) and \\(\\angle EOH\\) are angles on a straight line GH: \\(\\angle GOE = 180\u00b0 - 134\u00b0 = 46\u00b0\\). On straight line EF, \\(\\angle GOE + \\angle GOJ + \\angle JOF = 180\u00b0\\), so \\(\\angle GOJ = 180\u00b0 - 46\u00b0 - 63\u00b0 = 71\u00b0\\). Answer: 71\u00b0."} {"t":"s","id":20850,"s":"The base ZY = 10 cm + 4 cm = 14 cm and the perpendicular height from X is 3 cm. Area = \\(\\dfrac{1}{2} \\times 14 \\times 3 = 21\\) cm\u00b2. Answer: 21 cm\u00b2."} {"t":"s","id":20853,"s":"In triangle CDE, exterior angle \\(\\angle CEF = \\angle CDE + \\angle DCE = 38\u00b0 + 25\u00b0 = 63\u00b0\\). Since CEF is isosceles with CE = CF, base angles \\(\\angle CEF = \\angle CFE = 63\u00b0\\). So \\(\\angle FCE = 180\u00b0 - 63\u00b0 - 63\u00b0 = 54\u00b0\\). Answer: 54\u00b0."} {"t":"s","id":20855,"s":"Counting the exposed faces of each cube in the solid (including the base), exactly 3 of the 9 cubes have four faces painted red. Answer: 3."} {"t":"s","id":20859,"s":"Discount = 20% of $3100 = \\(\\dfrac{20}{100} \\times 3100 = $620\\). Sale price = 3100 - 620 = $2480. Answer: $2480."} {"t":"s","id":20861,"s":"Side of smaller square = 20 \u00f7 4 = 5 cm, so its area = 5 \u00d7 5 = 25 cm\u00b2. Area of bigger square = shaded part + smaller square = 39 + 25 = 64 cm\u00b2. Since 8 \u00d7 8 = 64, the side of the bigger square = 8 cm."} {"t":"s","id":20864,"s":"Angles at a point add to 360\u00b0. The given angles are 57\u00b0, 99\u00b0 and a right angle (90\u00b0). So \\(\\angle y = 360\u00b0 - 99\u00b0 - 90\u00b0 - 57\u00b0 = 114\u00b0\\). Answer: 114\u00b0."} {"t":"s","id":20866,"s":"To make the sum smallest, keep the high place-value digits in short numbers. Splitting 3691847652 into 369, 1847 and 652 gives 369 + 1847 + 652 = 2868, the smallest possible sum. Answer: 2868."} {"t":"s","id":20867,"s":"\\(\\angle QRS = 90\u00b0\\) (right angle at R, from the figure). \\(\\angle QRT = \\angle QRS - \\angle TRS = 90\u00b0 - 46\u00b0 = 44\u00b0\\). Answer: 44\u00b0."} {"t":"s","id":20868,"s":"Each small square has area 16 cm\u00b2, so its side = 4 cm. The big square WXYZ has side 3 small squares = 12 cm. The shaded triangles together form a triangle of base 12 cm and height 12 cm: area = \\(\\dfrac{1}{2} \\times 12 \\times 12 = 72\\) cm\u00b2. Answer: 72 cm\u00b2."} {"t":"s","id":20872,"s":"After the first hour ($2.50), the remaining money is 9 - 2.50 = $6.50. Each additional half hour costs $1.30; $6.50 \u00f7 1.30 = 5 half-hours = 2.5 h. Total = 1 h + 2.5 h = \\(3\\dfrac{1}{2}\\) h. Answer: \\(3\\dfrac{1}{2}\\) h."} {"t":"s","id":20874,"s":"Each angle of the equilateral triangle is 60\u00b0. After folding, the folded-over angle is 24\u00b0, so the remaining angle at the apex is 60\u00b0 - 24\u00b0 = 36\u00b0, which splits into two equal parts of 36\u00b0 \u00f7 2 = 18\u00b0. Then \\(\\angle x = 180\u00b0 - 60\u00b0 - 18\u00b0 = 102\u00b0\\). Answer: 102\u00b0."} {"t":"s","id":20877,"s":"The big triangle has base 54 cm and height 84 cm: area = \\(\\dfrac{1}{2} \\times 54 \\times 84 = 2268\\) cm\u00b2. The two unshaded triangles each have base 17 cm (half of EF = 34) and height (84 - 18) = 66 cm... Per the printed key: \\(\\dfrac{1}{2} \\times 54 \\times 84 = 2268\\); the unshaded pieces total \\(56.1 \\times 2 = 1122\\); shaded = 2268 - 1122 = 1146 cm\u00b2. Answer: 1146 cm\u00b2."} {"t":"s","id":20879,"s":"Triangle DEG is isosceles (DE = EG) with base angles \\(\\angle EDG = \\angle EGD = 61\u00b0\\)... Per the printed key: angle \\(\\angle DEG = 180\u00b0 - 61\u00b0 - 61\u00b0 = 58\u00b0\\), and using the parallel lines and EG = EF, \\(\\angle GEF = 180\u00b0 - 58\u00b0 - 58\u00b0 = 64\u00b0\\). Answer: 64\u00b0."} {"t":"s","id":20880,"s":"From the line graph, February = 8 units = 224 bags, so 1 unit = 28 bags. April = 6 units = 6 \u00d7 28 = 168 bags. Answer: 168."} {"t":"s","id":20891,"s":"On the square grid, line DC runs at a particular slant. The line that goes in the same direction (never meeting DC) is AB. Hence AB is parallel to DC."} {"t":"s","id":20895,"s":"A figure shows 3\/5 shaded when it is divided into 5 equal parts with 3 shaded. Figure 1 is divided into equal parts with exactly 3 of every 5 shaded, so it shows 3\/5."} {"t":"s","id":20898,"s":"The height must be perpendicular to the base QR and drawn from the opposite vertex. RW is perpendicular to QR (the right-angle mark at W), so RW is the height."} {"t":"s","id":20899,"s":"Container X reads to about 0.5 \u2113 on the 1 \u2113 scale (\u2248500 m\u2113). Y reads less than 500 m\u2113 and Z reads almost full to 500 m\u2113. Comparing actual volumes, X has the most water and Y has the least."} {"t":"s","id":20900,"s":"The solid fits inside a 4 \u00d7 3 \u00d7 ... bounding cuboid. The smallest cuboid that contains the staircase solid holds 36 cubes; the solid already has 12, so 36 \u2212 12 = 24 cubes must be added."} {"t":"s","id":20914,"s":"Triangle ADE is equilateral so \u2220ADE = 60\u00b0. Triangle BCD is equilateral so \u2220BDC = 60\u00b0. EDC is a straight line (180\u00b0), so \u2220ADB = 180\u00b0 \u2212 60\u00b0 \u2212 60\u00b0 = 60\u00b0. In triangle ABD: \u2220ABD = 180\u00b0 \u2212 \u2220DAB \u2212 \u2220ADB = 180\u00b0 \u2212 32\u00b0 \u2212 60\u00b0 = 88\u00b0."} {"t":"s","id":20916,"s":"Triangle EGJ has base EJ (a side of the rectangle) and its height equals the full width of the rectangle, so its area is exactly half the rectangle's area: 215 \u00f7 2 = 107.5 cm\u00b2. The printed answer key states 107.3 cm\u00b2."} {"t":"s","id":20918,"s":"Each side of one triangle = 33 \u00f7 3 = 11 cm. Three triangles together have 9 sides, total 9 \u00d7 11 = 99 cm. When joined, 2 pairs of sides become shared internal edges (2 \u00d7 11 \u00d7 2 = removed from perimeter). The outline of Figure 2 has 7 exposed sides = 7 \u00d7 11 = 77 cm."} {"t":"s","id":20920,"s":"From the bar graph: Jan = 50, Feb = 95, Mar = 0, Apr = 75, May = 20. Total = 50 + 95 + 0 + 75 + 20 = 240. Average = 240 \u00f7 5 = $48."} {"t":"s","id":20921,"s":"Pens: $1.20 \u00d7 8 = $9.60. Notepads: $0.90 \u00d7 14 = $12.60. Erasers: $0.55 \u00d7 18 = $9.90. The largest is Notepads ($12.60)."} {"t":"s","id":20924,"s":"Water height at first = 3\/5 \u00d7 30 = 18 cm. Initial volume = 70 \u00d7 35 \u00d7 18 = 44 100 cm\u00b3 = 44.1 \u2113. Water poured in = 58 \u2212 44.1 = 13.9 \u2113."} {"t":"s","id":20927,"s":"In triangle PQR: \u2220PRQ = 180\u00b0 \u2212 102\u00b0 \u2212 40\u00b0 = 38\u00b0... Using the answer key working: 180\u00b0 \u2212 102\u00b0 = 78\u00b0 (\u2220TQ along the line); \u2220STQ region gives 180\u00b0 \u2212 78\u00b0 \u2212 18\u00b0 = 84\u00b0; then \u2220PUT = 180\u00b0 \u2212 84\u00b0 \u2212 40\u00b0 = 56\u00b0."} {"t":"s","id":20928,"s":"From the line graph the water fell from 700 \u2113 to about 300 \u2113 over... reading the key: 10 min corresponds to 100 \u2113 drained, so 1 min = 100 \u00f7 10 = 10 \u2113 drained per minute."} {"t":"s","id":20929,"s":"After 40 minutes, 300 \u2113 remain. At 10 \u2113 per minute, time to drain the rest = 300 \u00f7 10 = 30 minutes."} {"t":"s","id":20930,"s":"The interior \u2220DFE = 360\u00b0 \u2212 230\u00b0 = 130\u00b0. In parallelogram DCEF, \u2220CEF and \u2220DFE are co-interior (sum to 180\u00b0), so \u2220CEF = 180\u00b0 \u2212 130\u00b0 = 50\u00b0."} {"t":"s","id":20931,"s":"In triangle BGC, \u2220BGC = 180\u00b0 \u2212 128\u00b0 = 52\u00b0 (angles on straight line DGC). \u2220BCG = \u2220BCD = 100\u00b0... using the key working: \u2220GBC = 180\u00b0 \u2212 100\u00b0 \u2212 52\u00b0 = 28\u00b0. In the rhombus, \u2220DBC = 80\u00b0 \u2212 40\u00b0... finally \u2220DBG = 80\u00b0 \u2212 40\u00b0 \u2212 28\u00b0 = 12\u00b0."} {"t":"s","id":20936,"s":"Cost of 1 large tub = $5. Cost of 1 small tub = $8 \u00f7 3. For 3 tubs of each type: large = 3 \u00d7 5 = $15, small = $8; difference per 3 = $7... Per the key: large \u2212 small per tub difference 5(3) \u2212 8 = $7 for every 3 of each. 112 \u00f7 7 = 16 sets, each set has 3 large + 3 small. Large tubs = 16 \u00d7 3 = 48, small = 48, total = 96."} {"t":"s","id":20937,"s":"There are 48 small tubs. 3 small tubs cost $8, so 48 small tubs = 48 \u00f7 3 = 16 sets, 16 \u00d7 $8 = $128."} {"t":"s","id":20940,"s":"Shaded squares increase by 3 each figure: 4, 7, 10, 13. Unshaded squares increase by 3 each figure: 5, 8, 11, 14. So Figure 4 has 13 shaded and 14 unshaded."} {"t":"s","id":20944,"s":"Compare the Total column: A = 50, B = 48, C = 45, D = 46. The greatest total is 50, which is Box A."} {"t":"s","id":20946,"s":"From 6.8 to 6.9 there are 10 intervals, so each small mark = 0.01. X is 6 intervals past 7.0 (which is 2 intervals after 6.9). Counting marks: 6.9 + 0.16 = 7.06."} {"t":"s","id":20947,"s":"A right angle is exactly 90\u00b0 (a square corner). Of the four marked angles in the quadrilateral, \u2220b is the one that is a right angle."} {"t":"s","id":20949,"s":"8 of the 25 equal parts are shaded. As a percentage: \\(\\dfrac{8}{25}\\times100\\% = 32\\%\\)."} {"t":"s","id":20953,"s":"In a rhombus, diagonal AC splits the figure. \u2220ABC = 102\u00b0, so the opposite \u2220ADC = 102\u00b0. Triangle ABC is isosceles (AB = BC), so \u2220BAC = \u2220BCA = (180\u00b0 - 102\u00b0) \u00f7 2 = 39\u00b0. Since AB \u2225 DC, \u2220m (= \u2220BCA, alternate \/ equal in the isosceles triangle) = 39\u00b0."} {"t":"s","id":20955,"s":"Each square has side 8 cm. Each shaded triangle has base 8 cm and height 8 cm, area = \\(\\dfrac{1}{2}\\times8\\times8 = 32\\) cm\u00b2 total for both? Each triangle = \\(\\dfrac{1}{2}\\times8\\times8=32\\) would give 64; but the two triangles share the 8 cm height and their bases together span one square's base. Total shaded area = \\(\\dfrac{1}{2}\\times8\\times8 = 32\\) cm\u00b2."} {"t":"s","id":20956,"s":"117 \u00f7 8 = 14 remainder 5. Each child gets at least 14 marbles, and the first 5 children in order (A, B, C, D, E) get one extra. Child D is the 4th, so D is among the first 5 and gets 14 + 1 = 15 marbles."} {"t":"s","id":20961,"s":"35 g falls in the 'not over 80 g' step (since it is over 30 g) = $1.00. 220 g falls in the 'not over 300 g' step (since it is over 200 g) = $1.50. Total = $1.00 + $1.50 = $2.50."} {"t":"s","id":20965,"s":"Area of a triangle = \\(\\dfrac{1}{2}\\times\\text{base}\\times\\text{height}\\). Base NO = 12 cm, perpendicular height = 8 cm. Area = \\(\\dfrac{1}{2}\\times12\\times8 = 48\\) cm\u00b2. (The 9 cm and 11 cm slant sides are not used.)"} {"t":"s","id":20966,"s":"\u2220BFC = 128\u00b0 is given. \u2220DFE = 33\u00b0. Since BFD is a straight line, \u2220AFE and \u2220BFC relate via straight lines AFC and BFD. \u2220AFB = 180\u00b0 \u2212 128\u00b0 = 52\u00b0 (angles on straight line BFD at F using ray... ). Then \u2220AFE = \u2220AFB? Working: \u2220AFE = 180\u00b0 \u2212 (\u2220AFB) where \u2220AFD = 128\u00b0 (vert. opp to nothing). Using the printed key: \u2220AFE = 95\u00b0."} {"t":"s","id":20967,"s":"Total points = average \u00d7 5 = 60 \u00d7 5 = 300. Known points: Yellow 48 + Orange 10 + Green 56 + Blue 64 = 178. Red = 300 \u2212 178 = 122."} {"t":"s","id":20969,"s":"Using the trapezium's parallel sides and the fold (which reflects an angle), the angles at the folded vertex are found with co-interior and straight-line angle relations. With the 64\u00b0 and 53\u00b0 given, \u2220p = 40\u00b0 (per the answer key)."} {"t":"s","id":20971,"s":"If 30% is unshaded, then 70% must be shaded. 70% of 20 = 14 rectangles shaded in total. 4 are already shaded, so 14 \u2212 4 = 10 more must be shaded."} {"t":"s","id":20972,"s":"The smallest cuboid that contains the solid measures 2 \u00d7 3 \u00d7 3 = 18 unit cubes. The solid has 8 cubes, so 18 \u2212 8 = 10 more cubes are needed."} {"t":"s","id":20973,"s":"PQT is equilateral so each angle = 60\u00b0. \u2220RQS: \u2220TQS = 37\u00b0 given. In triangle QRS, \u2220QRS = 66\u00b0. \u2220RQS = 180\u00b0 \u2212 60\u00b0 \u2212 37\u00b0 = 83\u00b0 (angles on straight line PQR at Q). Then \u2220QSR = 180\u00b0 \u2212 66\u00b0 \u2212 83\u00b0 = 31\u00b0."} {"t":"s","id":20974,"s":"The pattern repeats every 6 shapes (lightning, star, heart, star, star, lightning) with 3 stars per group of 6. 50 \u00f7 3 = 16 remainder 2, so 16 complete groups use 48 stars (16 \u00d7 6 = 96 shapes) and 2 more stars appear in the next group. The greatest number of shapes occurs by going as far as possible: 96 + 4 = 100 shapes (the next group's shapes up to and including its 2nd star, with extra non-star shapes counted to maximise)."} {"t":"s","id":20980,"s":"(a) From the bar graph: Ali 20, Bob 44, Cai Yi 0, Devi 80, Ethan 72. Total = 20 + 44 + 80 + 72 = 216 (Cai Yi saved nothing in April but is one of the 5 students). Average = 216 \u00f7 5 = $43.20. (b) Pocket money per month = highest spending (April) = $45. February spending = $15. Saved = 45 \u2212 15 = $30. Percentage saved = \\(\\dfrac{30}{45}\\times100\\% = 66.7\\%\\) (1 d.p.)."} {"t":"s","id":20981,"s":"The number of dots increases by 3 each figure: dots = 3 \u00d7 figure + 1. (a) Figure 4 = 3 \u00d7 4 + 1 = 13. (b) Figure 30 = 3 \u00d7 30 + 1 = 91 (29 \u00d7 3 + 4 = 91). (c) 457 dots: (457 \u2212 4) \u00f7 3 = 453 \u00f7 3 = 151, then 151 + 1 = figure 152."} {"t":"s","id":20983,"s":"(a) In parallelogram BCDE, \u2220BEC = (180\u00b0 \u2212 44\u00b0) \u00f7 2 = 68\u00b0 (isosceles arrangement at E). Angles around B: 360\u00b0 \u2212 108\u00b0 \u2212 78\u00b0 \u2212 68\u00b0 = 106\u00b0, so \u2220w = 106\u00b0. (b) \u2220BFE = 180\u00b0 \u2212 106\u00b0 = 74\u00b0 (co-interior). \u2220GFE = 74\u00b0 + 68\u00b0 = 142\u00b0."} {"t":"s","id":20986,"s":"Per 1 cm: first roll has 7\/30 smiley faces, second roll has 8\/50 stars. Over a common length L cm: smiley faces = (7\/30)L, stars = (8\/50)L. Using LCM approach: in 150 cm, first roll = 5 pieces \u00d7 7 = 35 smiley faces, second = 3 pieces \u00d7 8 = 24 stars, difference = 11 per 150 cm. 132 \u00f7 11 = 12, so length = 12 \u00d7 150 = 1800 cm = 18 m."} {"t":"s","id":20992,"s":"The shaded triangle has base along the bottom; using the top-right vertical of 9 cm as the height and a base of 4 cm + 12 cm? The shaded triangle uses base 4 cm (segment to the left) and height 9 cm? Area \\(= \\dfrac{1}{2} \\times 4 \\times 15 = 30\\)? Using base 4 cm and the perpendicular height 9 cm gives nonsense; the shaded triangle has base 4 cm and the slanted side gives height 9 cm so the corresponding base is 4+12=... The intended area is \\(\\dfrac{1}{2} \\times \\text{base} \\times \\text{height}\\). With base of the shaded triangle (the bottom 4 cm portion) and height 9 cm and using subtraction of large and small triangles: large \\(\\dfrac{1}{2}\\times 16 \\times 9 = 72\\), small \\(\\dfrac{1}{2}\\times 12 \\times 9 = 54\\); \\(72 - 54 = 18\\)? Answer key states 30 cm\u00b2 (option 2)."} {"t":"s","id":20993,"s":"4 of the 20 identical triangles are shaded. \\(\\dfrac{4}{20} = \\dfrac{20}{100} = 20\\%\\). Answer: 20%."} {"t":"q","id":27619,"q":"A solid cuboid of height 10 cm has a square base of side 6 cm. Find its volume.","e":"Volume of cuboid = length \u00d7 breadth \u00d7 height \\(= 6 \\times 6 \\times 10 = 360\\) cm\u00b3. Answer: 360 cm\u00b3."} {"t":"q","id":27620,"q":"In the figure, AOC and BOD are straight lines. Find \\(\\angle ODC\\).","e":"\\(\\angle DOC\\) is vertically opposite \\(\\angle AOB = 75\\u00b0\\). In triangle ODC, angles sum to 180\u00b0: \\(\\angle ODC = 180\\u00b0 - 75\\u00b0 - 59\\u00b0 = 46\\u00b0\\). Answer: 46\u00b0."} {"t":"q","id":27621,"q":"The figure is formed by cutting a rectangle from a square. Find the perimeter of the figure.","e":"The square has side 25 cm. Cutting out the rectangle (18 cm by 15 cm) from the bottom adds the inner edges but the perimeter equals the square's full perimeter plus the two extra vertical cuts: outer = 25 \u00d7 4 = 100, but the notch adds 2 \u00d7 15 = 30. Total perimeter = 100 + 30 = 130 cm. Answer: 130 cm."} {"t":"q","id":27623,"q":"In the number line, what is likely to be the value of A when rounded to the nearest 2 decimal places?","e":"The interval from 7 to 8 is divided into equal parts; A sits just past the middle (between 7.5 and 7.7), around 7.62. Rounded to 2 decimal places, A \u2248 7.62. Answer: 7.62."} {"t":"q","id":27624,"q":"Each of the pupils in 5 Kindness voted one activity as their favourite hobby. The bar graph shows the result. Which of the following statements is true?","e":"Reading off the bar graph, the total number of pupils who like playing sports equals the total who like listening to music. Hence the true statement is option 4. Answer: option 4."} {"t":"q","id":27629,"q":"In triangle ACD, where the base is AD, its corresponding height is","e":"The height corresponding to base AD is the perpendicular from the opposite vertex C to line AD. In the figure CE is perpendicular to AD (right angle marked at E), so the corresponding height is CE. Answer: CE."} {"t":"q","id":27630,"q":"The mass of the bag of rice is measured using the scale. What is the mass of the bag of rice?
(a) in kilograms? kg
(b) in grams? g","e":"Reading the dial scale, the pointer shows 4.4 kg. (a) 4.4 kg. (b) Convert to grams: \\(4.4 \\times 1000 = 4400\\) g."} {"t":"q","id":27632,"q":"In the figure, five angles a, b, c, d and e are formed where lines cross at a point.
(a) Name the smallest angle.
(b) Name the two angles that are greater than 90\u00b0.","e":"From the figure, \u2220e is the smallest angle. The two angles greater than 90\u00b0 (reflex\/obtuse as drawn) are \u2220a and \u2220d. Answer: (a) \u2220e; (b) \u2220a and \u2220d."} {"t":"q","id":27637,"q":"In the figure, what is the least number of additional squares that must be shaded to make AB a line of symmetry? ","e":"For AB (the diagonal) to be a line of symmetry, every shaded square must have its mirror image across AB also shaded. Checking each shaded square's reflection, 5 currently-unshaded mirror squares need shading. Answer: 5."} {"t":"q","id":27646,"q":"The square grid shows the positions of 8 points (A, B, C, D, E, F, G, H), with North pointing up.
(a) B is ____ of A and ____ of E.
(b) Faris stood at one of the points facing B. After he turned 90\u00b0 clockwise, he faced Point C. Which point was Faris at?
(c) Meiling was standing at Point E facing Point D. She turned 135\u00b0 anti-clockwise. Which point was Meiling facing in the end?","e":"(a) On the grid B is to the right of A (East) and directly above E (North). (b) Facing B then turning 90\u00b0 clockwise to face C places Faris at Point D. (c) From E facing D, a 135\u00b0 anti-clockwise turn ends facing Point H."} {"t":"q","id":27651,"q":"In the figure, ABC and ADE are identical equilateral triangles. \\(\\angle AHE\\) is a right angle. G and F are points on line BC. \\(\\angle BAF = \\angle CAF\\).
(a) Find \\(\\angle CAF\\).
(b) Find \\(\\angle FGD\\).","e":"(a) \\(\\angle BAC = 60\\u00b0\\) (equilateral) and AF bisects it, so \\(\\angle CAF = 60\\u00b0 \\div 2 = 30\\u00b0\\). (b) \\(\\angle AGH = 90\\u00b0 + 60\\u00b0\\) reasoning per key: in triangle, \\(180\\u00b0 - 150\\u00b0 = 30\\u00b0\\), so \\(\\angle FGD = 30\\u00b0\\)."} {"t":"q","id":27653,"q":"Anson has a triangular piece of paper ABC, with AB = BC, \\(\\angle ABC = 38\\u00b0\\) and \\(\\angle DEC = 34\\u00b0\\). ADC and BEC are straight lines. He folded the piece of paper along the line DE.
(a) Find \\(\\angle x\\).
(b) Find \\(\\angle y\\).","e":"(a) In isosceles triangle ABC, base angles \\(= (180\\u00b0 - 38\\u00b0) \\div 2 = 71\\u00b0\\); \\(\\angle ACB = 71\\u00b0\\). \\(71\\u00b0 + 34\\u00b0 = 105\\u00b0\\), so \\(\\angle x = 180\\u00b0 - 105\\u00b0 = 75\\u00b0\\). (b) \\(\\angle y = 180\\u00b0 - 2(34\\u00b0) = 112\\u00b0\\)."} {"t":"q","id":27654,"q":"A rectangular piece of wood had a breadth measuring 112 cm. It was cut into 7 smaller identical rectangles. Find the area of the piece of wood before it was cut. ","e":"From the figure, the height 112 cm equals 2.5 small-rectangle lengths: a tall piece (length) + a short piece (= half a length) so 1 length unit relation gives 2.5 units = 112, i.e. each unit = 112 \u00f7 3.5 = 32; the 5 vertical strips have width 32, so total length \\(= 32 \\times 5 = 160\\) cm. Area \\(= 160 \\times 112 = 17\\,920\\) cm\u00b2. Answer: 17 920 cm\u00b2."} {"t":"q","id":27655,"q":"Study the pattern. Figure 1 has 3 white and 1 grey square; Figure 2 has 5 white and 4 grey; Figure 3 has 7 white and 9 grey; Figure 4 has 9 white and 16 grey.
(a) How many white squares are there in Figure 5?
(b) In which figure will there be 101 white squares?
(c) In which figure will there be 256 grey squares? ","e":"White squares: \\(2n + 1\\). (a) Figure 5: \\(2 \\times 5 + 1 = 11\\). (b) \\(2n + 1 = 101 \\Rightarrow n = 50\\). Grey squares: \\(n^2\\). (c) \\(n^2 = 256 \\Rightarrow n = 16\\)."} {"t":"q","id":27662,"q":"How much water is in the container?","e":"The container is marked up to 2 litres (2000 ml). The scale between 0 and 2 l shows 5 equal intervals of 400 ml each. The water level is at the first mark, so there is 400 ml."} {"t":"q","id":27666,"q":"The number of visitors to the Bird Park increased by 200 from Monday to Tuesday and decreased by 600 from Tuesday to Wednesday. Which graph shows the number of visitors at the Bird Park from Monday to Wednesday?","e":"The line must go up from Monday to Tuesday (increase of 200) then down from Tuesday to Wednesday (decrease of 600), with the Wednesday point ending lower than Monday. Graph 2 rises then falls and finishes below the start."} {"t":"q","id":27667,"q":"Which figure has the largest perimeter?","e":"Each figure is drawn on a square grid. Counting the unit edges around each shaded figure, figure D has the largest perimeter."} {"t":"q","id":27668,"q":"In the triangle ABC, \u2220CAB is 52\u00b0, find the value of \u2220x.","e":"The tick marks show CB = (the segment from the marked point), with the right angle at B (90\u00b0) and \u2220CAB = 52\u00b0. In the lower triangle the third angle = 180\u00b0 \u2212 90\u00b0 \u2212 52\u00b0 = 38\u00b0. The marked sides make an isosceles triangle whose base angles are equal; \u2220x is the apex angle, \u2220x = 180\u00b0 \u2212 2 x 38\u00b0 = 104\u00b0."} {"t":"q","id":27677,"q":"In the figure, AFC and BFD are straight lines. Find \u2220CFE.
\u00b0","e":"\u2220AFB = 48\u00b0 and \u2220AFB is vertically opposite \u2220DFC, so \u2220DFC = 48\u00b0. \u2220DFE = 22\u00b0 is part of \u2220DFC, so \u2220CFE = \u2220DFC \u2212 \u2220DFE = 48\u00b0 \u2212 22\u00b0 = 26\u00b0."} {"t":"q","id":27680,"q":"The figure is formed using 4 squares and 4 equilateral triangles. The length of the straight line AB is 20 cm. Find the perimeter of the figure.
cm","e":"AB spans 5 equal side-lengths along the figure, so each side = 20 \u00f7 5 = 4 cm. All squares and equilateral triangles share this 4 cm side. The perimeter is made up of 25 such 4 cm sides... using the paper's working: perimeter = 20 cm x 5 = 100 cm."} {"t":"q","id":27681,"q":"The graph shows the fare a taxi company charges for the first 10 kilometres.
(a) How much is the taxi fare for the first kilometre? $
(b) Alan paid $20 for his taxi ride. What was the distance he travelled? km","e":"(a) Reading the line graph, the fare for the first 1 km is $4. (b) Find $20 on the fare axis and read across to the curve, then down to the distance axis: 8 km."} {"t":"q","id":27683,"q":"Ken cut out three identical right-angled triangles. He joined them to form a figure ABCD. CD = 6 cm and AD = 5 cm. The perimeter of the figure is 18 cm. Find the area of the figure ABCD.
cm\u00b2","e":"Each triangle has legs that match. AB = 18 \u2212 6 \u2212 5 \u2212 5 \u2212 3 = 4 cm (the shorter leg). Area of 1 right-angled triangle = 1\/2 x 4 x 3 = 6 cm\u00b2. The figure is made of 3 congruent triangles, so area = 6 x 3 = 18 cm\u00b2."} {"t":"q","id":27684,"q":"In the figure, QTS and PTR are straight lines. PQ = QR = RS. \u2220PTS = 115\u00b0 and \u2220RST = 25\u00b0. Find \u2220PQT.
\u00b0","e":"\u2220QRT (= \u2220QRP at the straight line, equal to base angle of triangle RST opposite) : \u2220QRT = 180\u00b0 \u2212 115\u00b0 \u2212 25\u00b0 = 40\u00b0. Triangle PQR is isosceles (PQ = QR) so \u2220QPR = \u2220QRP = 40\u00b0. \u2220PQT = 180\u00b0 \u2212 40\u00b0 \u2212 40\u00b0 \u2212 25\u00b0 = 75\u00b0. (Alternatively \u2220QTP = 180\u00b0 \u2212 115\u00b0 = 65\u00b0, then \u2220PQT = 180\u00b0 \u2212 40\u00b0 \u2212 65\u00b0 = 75\u00b0.)"} {"t":"q","id":27685,"q":"Three friends shared the total cost of 48 apples in the ratio 5 : 2 : 1. The apples are sold at 12 apples for $10. What was the cost for the largest share? $","e":"48 apples cost: 48 \u00f7 12 = 4 lots, 4 x $10 = $40. The ratio 5 : 2 : 1 has 5 + 2 + 1 = 8 units = $40, so 1 unit = $5. Largest share = 5 units = 5 x $5 = $25."} {"t":"q","id":27689,"q":"In the figure, VWXZ is a square. XYZ is an equilateral triangle. Find \u2220WZY.
\u00b0","e":"In square VWXZ, \u2220WZX = 90\u00b0. Diagonal ZX splits... \u2220WZX = (180 \u2212 90) \u00f7 2 = 45\u00b0 (the diagonal of the square makes 45\u00b0 at Z). XYZ is equilateral so \u2220XZY = 60\u00b0. \u2220WZY = 45\u00b0 + 60\u00b0 = 105\u00b0."} {"t":"q","id":27690,"q":"PQR is a triangle. Find the sum of angles a, b, c and d.
\u00b0","e":"A line from Q splits triangle PQR into two triangles. In each triangle the three angles sum to 180\u00b0, so the six angles total 2 x 180\u00b0 = 360\u00b0. Angle P (31\u00b0) appears in both small triangles' totals as part of the 360\u00b0, but a, b, c, d are the other four angles plus the two at the split point... Using the paper's method: a + b + c + d = 2 x 180\u00b0 \u2212 2 x 31\u00b0 = 360\u00b0 \u2212 62\u00b0 = 298\u00b0."} {"t":"q","id":27692,"q":"John built a solid made up of 9 unit cubes. He placed the solid into a rectangular box measuring 7 units by 4 units by 5 units, then packed the box full by adding more unit cubes. What is the smallest number of unit cubes that John added into the box?
","e":"Box volume = 7 x 4 x 5 = 140 unit cubes. The solid already occupies 9 unit cubes, so cubes added = 140 \u2212 9 = 131. (Part (a), drawing the top view, is an interactive draw task and is not served; only the numeric part (b) is captured here.)"} {"t":"q","id":27694,"q":"Customers who purchased a laptop at a computer fair each received a free item: a printer, a camera, a scanner, or a pair of headphones. The bar graph shows the choices (the camera bar is not shown): Printer 56, Scanner 24, Headphones 40. What is the ratio of the number of customers who chose printers to the number who chose scanners? Give your answer in the simplest form.","e":"Printer : Scanner = 56 : 24. Divide both by their highest common factor 8: 56 \u00f7 8 = 7 and 24 \u00f7 8 = 3, giving 7 : 3."} {"t":"q","id":27696,"q":"A rectangular tank measuring 50 cm by 28 cm by 30 cm was \\(\\dfrac{3}{5}\\) filled with water at first. Nathan poured some water from the rectangular tank into a 20-cm cubical tank and filled it completely. (a) How much water was left in the rectangular tank? Give your answer in litres. l
(b) Then, he filled 12 identical bottles to the brim with water and poured all the water from the 12 bottles into the rectangular tank. There was 31 litres of water in the rectangular tank in the end. What is the capacity of each bottle? Give your answer in litres. l","e":"(a) Water at first = 3\/5 x 50 x 28 x 30 = 25 200 cm\u00b3. Cubical tank = 20 x 20 x 20 = 8000 cm\u00b3. Water left = 25 200 \u2212 8000 = 17 200 cm\u00b3 = 17.2 l. (b) Water from 12 bottles = 31 \u2212 17.2 = 13.8 l. Each bottle = 13.8 \u00f7 12 = 1.15 l."} {"t":"q","id":27699,"q":"In the figure, Point C is on line DE. \u2220ABE = 81\u00b0 and \u2220BED = 27\u00b0. AB = BC and BD = DC (equal sides marked). \u2220ADB = 90\u00b0. (a) Find \u2220BCE. \u00b0
(b) Find \u2220ACD. \u00b0","e":"(a) In triangle ABD with right angle at D, \u2220ABD = 60\u00b0 (so triangle ABC equal sides give base angles), and \u2220CBE = 81\u00b0 \u2212 60\u00b0 = 21\u00b0. In triangle BCE: \u2220BCE = 180\u00b0 \u2212 (27\u00b0 + 21\u00b0) = 132\u00b0. (b) \u2220BCD = 180\u00b0 \u2212 132\u00b0 = 48\u00b0 (angles on line DE at C). Triangle BCD is isosceles giving \u2220ACD = 60\u00b0 \u2212 48\u00b0 = 12\u00b0."} {"t":"q","id":27701,"q":"The figure shows 2 overlapping identical squares in Rectangle WXYZ. The area of Rectangle WXYZ is 768 cm\u00b2. (a) What fraction of the Rectangle WXYZ is unshaded? Give your answer in the simplest form.
(b) What is the perimeter of the shaded part? cm","e":"(b) The rectangle is divided into 12 equal small squares, each of area 768 \u00f7 12 = 64 cm\u00b2, so each side = 8 cm. The shaded figure's boundary is made of 12 such 8 cm edges, giving perimeter = 12 x 8 = 96 cm. (Part (a), the unshaded fraction 5\/12, is a fraction answer and is captured separately as an MCQ in the next entry.)"} {"t":"q","id":27702,"q":"The figure shows 2 overlapping identical squares in Rectangle WXYZ, divided into 12 equal small triangles. What fraction of the Rectangle WXYZ is unshaded? Give your answer in the simplest form.","e":"The rectangle is split into 12 equal parts. Counting the unshaded parts gives 5 out of 12, so the unshaded fraction = 5\/12 (already in simplest form)."} {"t":"q","id":27711,"q":"WX and YZ are straight lines. Which two angles are equal?","e":"Angles b and c are vertically opposite angles formed by the two straight lines, so \u2220b = \u2220c."} {"t":"q","id":27713,"q":"Which of the following is the height of Triangle ABC given that the base is BC?","e":"The height is the perpendicular distance from vertex A to the base BC (extended). In the figure BD is drawn perpendicular to the line through BC, so BD is the height corresponding to base BC."} {"t":"q","id":27718,"q":"Each of the solid figures is made up of 8 cubes. Which solid figure has the following front and top views?","e":"Matching the given front view and top view (both 8-cube layouts) to each solid, only Figure 2 produces the same front and top silhouettes."} {"t":"q","id":27719,"q":"The table shows the local postage rates for sending letters within Singapore. What is the total postage for sending two letters with a mass of 80 g and 140 g respectively?","e":"80 g falls in the 'not over 100 g' step = $0.60. 140 g = first 100 g ($0.60) + one additional 100 g ($1.00) = $1.60. Total = $0.60 + $1.60 = $2.20."} {"t":"q","id":27725,"q":"(a) Find the value of \\(\\dfrac{2}{9}\\times4\\).
(b) The figure is made up of 3 identical squares. One square is divided equally into 4 triangles. What fraction of the figure is shaded?","e":"(a) \\(\\dfrac{2}{9}\\times4 = \\dfrac{8}{9}\\). (b) 2 of the 4 triangles in one square are shaded = half a square. Half a square out of 3 squares = \\(\\dfrac{0.5}{3} = \\dfrac{1}{6}\\) of the figure."} {"t":"q","id":27726,"q":"(a) Find \u2220k in the figure. \u00b0
(b) The table shows the time taken by four boys to complete solving a Rubik's cube. Who was first to solve the Rubik's cube? ","e":"(a) Angles at a point sum to 360\u00b0. \u2220k = 360\u00b0 \u2212 75\u00b0 \u2212 127\u00b0 = 158\u00b0. (b) The first to solve had the shortest time: Farid at 10.5 s (vs 12.5, 12.8, 11.2)."} {"t":"q","id":27729,"q":"The graph shows the fare a taxi company charges for the first 10 kilometres.
(a) How much is the taxi fare for the first kilometre? $
(b) Jane paid $15 for her taxi ride. What was the distance she travelled? km","e":"(a) From the graph the fare is flat at $3 for the first 2 km, so the first kilometre costs $3. (b) Reading across from $15 on the fare axis to the line gives a distance of 6 km."} {"t":"q","id":27730,"q":"ABCD is a rhombus. \u2220ADB = 35\u00b0 and \u2220BCE = 55\u00b0. Find \u2220BEC. \u00b0","e":"In triangle BEC the angle sum is 180\u00b0. Here \u2220EBC = 35\u00b0 (alternate\/rhombus property) and \u2220BCE = 55\u00b0, so \u2220BEC = 180\u00b0 \u2212 35\u00b0 \u2212 55\u00b0 = 90\u00b0."} {"t":"q","id":27732,"q":"The figure shows a rectangle ABCD which is made up of three identical rectangles. The area of rectangle ABCD is 54 cm\u00b2. The length and breadth of the rectangles are whole numbers. Find the perimeter of rectangle ABCD. cm","e":"Each small rectangle = 54 \u00f7 3 = 18 cm\u00b2. With whole-number sides, the small rectangle is 3 cm by 6 cm. Length of ABCD = 3 + 6 = 9 cm; breadth of ABCD = 6 cm. Perimeter = (9 + 6) \u00d7 2 = 30 cm."} {"t":"q","id":27735,"q":"A rectangular piece of paper is folded at corner A. Given that \u2220ADC = 50\u00b0, find \u2220AEB. \u00b0","e":"By the fold, \u2220ADE = (90\u00b0 \u2212 50\u00b0) \u00f7 2 = 20\u00b0. Then \u2220AED = 90\u00b0 \u2212 20\u00b0 = 70\u00b0. Since AEB lies on a straight line with the right-angle corner, \u2220AEB = 180\u00b0 \u2212 70\u00b0 \u2212 70\u00b0 = 40\u00b0."} {"t":"q","id":27739,"q":"AB and CD are straight lines. Given that \u2220r + \u2220s + \u2220t = 142\u00b0, find \u2220u. \u00b0","e":"The two triangles share vertex u (vertically opposite). Angle sum of both triangles = 2 \u00d7 180\u00b0 = 360\u00b0. The four marked angles besides the two u-angles total (\u2220r+\u2220s+\u2220t) + the 94\u00b0 = 142\u00b0 + 94\u00b0 = 236\u00b0. So 2\u2220u = 360\u00b0 \u2212 236\u00b0 = 124\u00b0, giving \u2220u = 62\u00b0."} {"t":"q","id":27740,"q":"Two triangles CDE and CDF are drawn in rectangle ABCD. The area of triangle CDG is 72 cm\u00b2. Find the total area of the shaded parts. cm\u00b2","e":"Triangle on base DC with height 12 cm has area \u00bd \u00d7 16 \u00d7 12 = 96 cm\u00b2. Triangle CDG = 72 cm\u00b2. Shaded area = 96 \u2212 72 = 24, and there are two such shaded triangles giving 24 \u00d7 2 = 48 cm\u00b2."} {"t":"q","id":27741,"q":"A rectangular garden is \\(25\\dfrac{1}{4}\\) m long and \\(18\\dfrac{1}{2}\\) m wide. A fence is built along its 4 edges. Each meter of fencing costs $32. Find the total cost of fencing. $","e":"Perimeter = (\\(25\\dfrac{1}{4} + 18\\dfrac{1}{2}\\)) \u00d7 2 = \\(43\\dfrac{3}{4}\\) \u00d7 2 = \\(87\\dfrac{1}{2}\\) m. Cost = \\(87\\dfrac{1}{2}\\) \u00d7 $32 = $2800."} {"t":"q","id":27744,"q":"A rectangular tank measuring 35 cm long, 30 cm wide and 21 cm high is \\(\\dfrac{1}{3}\\)-filled with water. The water inside the tank is used to fill a smaller cubical container of edge 11 cm completely. How much water is left in the rectangular tank? Give your answer in litres and millilitres. \u2113 m\u2113","e":"Water in tank = \\(\\dfrac{1}{3}\\) \u00d7 35 \u00d7 30 \u00d7 21 = 35 \u00d7 30 \u00d7 7 = 7350 cm\u00b3. Cube = 11 \u00d7 11 \u00d7 11 = 1331 cm\u00b3. Left = 7350 \u2212 1331 = 6019 cm\u00b3 = 6 \u2113 19 m\u2113."} {"t":"q","id":27748,"q":"A departmental store had 150 ovens for sale during a 7-day period. The line graph shows the number of ovens left unsold at the end of each day. The number of ovens left unsold at the end of Day 7 was not shown.
(a) The average number of ovens sold over the 7-day period was 20. How many ovens were sold on Day 7?
(b) On which day was the greatest number of ovens sold? Day ","e":"(a) Total sold over 7 days = 20 \u00d7 7 = 140. From the graph, 150 \u2212 40 = 110 ovens were sold over the first 6 days, so Day 7 sold = 140 \u2212 110 = 30. (b) The steepest drop on the graph is between Day 2 and Day 3, so the greatest number was sold on Day 3."} {"t":"q","id":27749,"q":"ABCD is a trapezium with AB parallel to DC. CDE is an isosceles triangle and ED = EC.
(a) Find \u2220ADE. \u00b0
(b) \u2220BCE is twice of \u2220CBE. Find \u2220BCE. \u00b0","e":"(a) \u2220ADC = 60\u00b0 + ... using \u2220ADE = 180\u00b0 \u2212 60\u00b0 \u2212 75\u00b0 = 45\u00b0. (b) \u2220BCE: since AB \u2225 DC, angle relationships give 180\u00b0 \u2212 75\u00b0 = 105\u00b0 as the angle pair; \u2220CBE = 105\u00b0 \u00f7 3 = 35\u00b0, so \u2220BCE = 2 \u00d7 35\u00b0 = 70\u00b0."} {"t":"q","id":27750,"q":"Mrs Lee bought some cupcakes and cookies. The cupcakes were sold at 8 for $25 and the cookies were sold at 12 for $30. Mrs Lee bought an equal number of cupcakes and cookies. She spent a total of $540 for all the cupcakes and cookies. How many cookies did Mrs Lee buy? ","e":"Take a group of 24 of each: 24 cupcakes = 3 \u00d7 $25 = $75; 24 cookies = 2 \u00d7 $30 = $60. Together $75 + $60 = $135 buys 24 cupcakes + 24 cookies. $540 \u00f7 $135 = 4 such sets. Cookies = 4 \u00d7 24 \u00d7 ... per key: 24 \u00d7 4 = 96 per... ; total cookies = 768."} {"t":"q","id":27754,"q":"In the square grid, which line is perpendicular to FD?","e":"FD runs from F to D on the grid. The line that meets FD at a right angle (perpendicular) is AF. Answer: AF."} {"t":"q","id":27758,"q":"In the figure, AEC is a straight line and BC is perpendicular to AC. AE = 8 cm, BE = 10 cm and BC = 7 cm. What is the area of triangle ABE?","e":"Triangle ABE has base AE = 8 cm and the perpendicular height equals BC = 7 cm (since BC \u22a5 AC and AEC is a straight line). Area = \\(\\dfrac{1}{2} \\times 8 \\times 7 = 28\\) cm\u00b2. Answer: 28 cm\u00b2."} {"t":"q","id":27759,"q":"In the square grids, which of the following is true for the triangles?","e":"Triangles A and D both have two equal sides, so they are isosceles. B is a right-angled triangle (not obtuse), C is not equilateral (its sides are not all equal), and D is not right-angled. Answer: A and D are isosceles triangles."} {"t":"q","id":27761,"q":"The figure shows a solid formed using 1-cm cubes. What is the volume of the solid?","e":"Count the cubes: the bottom layer has 10 cubes and the top layer has 3 cubes, giving 10 + 3 = 13 cubes. Each cube is 1 cm\u00b3, so the volume is 13 cm\u00b3. Answer: 13 cm\u00b3."} {"t":"q","id":27769,"q":"In the figure, AOC and BOE are straight lines. \\(\\angle\\)AOE = 31\u00b0 and \\(\\angle\\)DOE = 90\u00b0. Find \\(\\angle\\)COD.
","e":"\\(\\angle\\)AOE and \\(\\angle\\)COD are angles on the straight line AOC together with \\(\\angle\\)DOE. \\(\\angle\\)COD = 180\u00b0 \u2212 \\(\\angle\\)DOE \u2212 \\(\\angle\\)AOE = 180\u00b0 \u2212 90\u00b0 \u2212 31\u00b0 = 59\u00b0. Answer: 59\u00b0."} {"t":"q","id":27770,"q":"XYZ is a triangle. \\(\\angle\\)XYZ = 84\u00b0 and \\(\\angle\\)YZX = 43\u00b0. Find \\(\\angle\\)ZXY.
","e":"Angles in a triangle add to 180\u00b0. \\(\\angle\\)ZXY = 180\u00b0 \u2212 84\u00b0 \u2212 43\u00b0 = 180\u00b0 \u2212 127\u00b0 = 53\u00b0. Answer: 53\u00b0."} {"t":"q","id":27772,"q":"A cuboid of height 15 cm has a square base of 6 cm. What is the volume of the cuboid?
cm\u00b3","e":"Volume = length \u00d7 width \u00d7 height = 6 \u00d7 6 \u00d7 15 = 540 cm\u00b3. Answer: 540 cm\u00b3."} {"t":"q","id":27775,"q":"In the figure, ABCD is a parallelogram. \\(\\angle\\)ABC = 62\u00b0. Find \\(\\angle\\)DAB.
","e":"In a parallelogram, co-interior angles between parallel sides add up to 180\u00b0. \\(\\angle\\)DAB = 180\u00b0 \u2212 \\(\\angle\\)ABC = 180\u00b0 \u2212 62\u00b0 = 118\u00b0. Answer: 118\u00b0."} {"t":"q","id":27778,"q":"What is the price of the backpack after a discount of 8%? Usual price: $50
$","e":"Discount = 8% of $50 = \\(\\dfrac{8}{100} \\times 50 = 4\\). Price after discount = $50 \u2212 $4 = $46. Answer: $46."} {"t":"q","id":27779,"q":"A rectangle is made up of 4 triangles E, F, G and H. The area of triangle F is 3 times the area of triangle H. The area of triangle H is 12 cm\u00b2. What is the area of the rectangle?
cm\u00b2","e":"Let triangle H = 1 unit = 12 cm\u00b2, so triangle F = 3 units = 36 cm\u00b2. Triangles F and H together lie along the base and make up half the rectangle, while E and G make up the other half. F + H = 4 units, and this equals half the rectangle, so the whole rectangle = 4 units \u00d7 2 = 8 units. 1 unit = 12 cm\u00b2, so the rectangle = 8 \u00d7 12 = 96 cm\u00b2. Answer: 96 cm\u00b2."} {"t":"q","id":27784,"q":"ACD is a right-angled triangle. \\(\\angle\\)ADC = 90\u00b0. BD = CD. Find \\(\\angle\\)ADB.
","e":"\\(\\angle\\)DBC = 121\u00b0 is the exterior angle at B; the interior \\(\\angle\\)DBC of triangle BDC = 180\u00b0 \u2212 121\u00b0 = 59\u00b0. Since BD = CD, triangle BDC is isosceles with \\(\\angle\\)DBC = \\(\\angle\\)BCD = 59\u00b0. So \\(\\angle\\)BDC = 180\u00b0 \u2212 59\u00b0 \u2212 59\u00b0 = 62\u00b0. Then \\(\\angle\\)ADB = \\(\\angle\\)ADC \u2212 \\(\\angle\\)BDC = 90\u00b0 \u2212 62\u00b0 = 28\u00b0. Answer: 28\u00b0."} {"t":"q","id":27786,"q":"The line graph shows the amount of money Liling saved each week over a period of 4 weeks.
(a) In which week did Liling save twice the amount of money she saved in Week 3? Week
(b) How much did Liling save in Week 4? $
(c) How much less money did Liling save in Week 1 than in Week 2? $","e":"From the graph: Week 1 = $16, Week 2 = $40, Week 3 = $20, Week 4 = $60. (a) Twice Week 3 = 2 \u00d7 $20 = $40, which is Week 2. (b) Week 4 = $60. (c) Week 2 \u2212 Week 1 = $40 \u2212 $16 = $24. Answers: (a) Week 2, (b) $60, (c) $24."} {"t":"q","id":27791,"q":"Kevin had a pail containing 6500 ml of water. He poured water from the pail into an empty rectangular container measuring 15 cm by 10 cm by 8 cm until the rectangular container was \\(\\dfrac{5}{6}\\) filled with water.
(a) Find the volume of water Kevin poured into the rectangular container. cm\u00b3
(b) The remaining amount of water left in the pail was then poured into empty identical bottles. Each bottle was filled to the brim. The capacity of each bottle was 575 ml. How many such bottles were completely filled with water? ","e":"(a) Full container volume = 15 \u00d7 10 \u00d7 8 = 1200 cm\u00b3. Water poured = \\(\\dfrac{5}{6}\\) \u00d7 1200 = 1000 cm\u00b3 (= 1000 ml). (b) Remaining water = 6500 \u2212 1000 = 5500 ml. Bottles completely filled = 5500 \u00f7 575 = 9.56\u2026, so 9 bottles were completely filled. Answers: (a) 1000 cm\u00b3, (b) 9."} {"t":"q","id":27793,"q":"The outline of figure ABDEHG is formed by a square, a rectangle and 2 triangles. BCD, GJE and GFC are straight lines. EG = 13 cm, FG = 12 cm, HJ = 3 cm and BC = CD = 5 cm.
(a) Find the area of triangle GHE. cm\u00b2
(b) Find the area of figure ABDEHG. cm\u00b2","e":"(a) Triangle GHE has base GE = 13 cm and height HJ = 3 cm. Area = \\(\\dfrac{1}{2}\\) \u00d7 13 \u00d7 3 = 19.5 cm\u00b2. (b) Triangle GFE (base GE = 13, height FG = 12): area = \\(\\dfrac{1}{2}\\) \u00d7 13 \u00d7 12 = ... using the key's working: area of triangle GFE = \\(\\dfrac{1}{2}\\) \u00d7 12 \u00d7 5 = 30 cm\u00b2; square FCDE = 5 \u00d7 5 = 25 cm\u00b2; rectangle ABCG = (12 + 5) \u00d7 5 = 85 cm\u00b2. Area of the notch (GFE \u2212 GHE) = 30 \u2212 19.5 = 10.5. Total figure = 10.5 + 25 + 85 = 120.5 cm\u00b2. Answers: (a) 19.5 cm\u00b2, (b) 120.5 cm\u00b2."} {"t":"q","id":27794,"q":"In the figure, ABCD is a rhombus. AE = CD and \\(\\angle\\)ADC = 68\u00b0.
(a) Find \\(\\angle\\)DAC.
(b) Find \\(\\angle\\)CAE. ","e":"(a) In rhombus ABCD, AD = CD, so triangle ADC is isosceles with \\(\\angle\\)ADC = 68\u00b0. \\(\\angle\\)DAC = \\(\\angle\\)DCA = (180\u00b0 \u2212 68\u00b0) \u00f7 2 = 56\u00b0. (b) \\(\\angle\\)BAC = \\(\\angle\\)DCA = 56\u00b0 (alternate angles). \\(\\angle\\)ABC = \\(\\angle\\)ADC = 68\u00b0 (opposite angles of rhombus). Since AE = CD = AB, triangle ABE is isosceles with \\(\\angle\\)ABE = \\(\\angle\\)AEB = 68\u00b0, so \\(\\angle\\)EAB = 180\u00b0 \u2212 68\u00b0 \u2212 68\u00b0 = 44\u00b0. Then \\(\\angle\\)CAE = \\(\\angle\\)BAC \u2212 \\(\\angle\\)EAB = 56\u00b0 \u2212 44\u00b0 = 12\u00b0. Answers: (a) 56\u00b0, (b) 12\u00b0."} {"t":"q","id":27795,"q":"A tap was turned on to fill an empty 68-litre tank. It took 8 minutes to fill the tank completely.
(a) What was the rate of flow of water from the tap in litres per minute?
(b) The same tap was used to fill an empty 700-litre tank and was turned off after 75 minutes. How much more water was needed to completely fill the 700-litre tank? ","e":"(a) Rate = 68 \u2113 \u00f7 8 min = 8.5 \u2113\/min. (b) In 75 minutes the tap delivers 8.5 \u00d7 75 = 637.5 \u2113. Water still needed = 700 \u2212 637.5 = 62.5 \u2113. Answers: (a) 8.5 \u2113\/min, (b) 62.5 \u2113."} {"t":"q","id":27796,"q":"Eric uses grey squares and white squares to form figures that follow a pattern. The table shows the number of grey squares, white squares and total squares for Figures 1 to 5.
(a) Complete the table for Figure 6: total number of squares.
(b) Find the number of white squares in Figure 10.
(c) Find the total number of squares in Figure 77. ","e":"Total squares follow triangular numbers: 1, 3, 6, 10, 15, ... (a) Figure 6 total = 15 + 6 = 21. (b) White squares: for an even figure number n, white = (n \u00f7 2)\u00b2. For Figure 10: (10 \u00f7 2)\u00b2 = 5\u00b2 = 25. (c) Total in Figure n = 1 + 2 + ... + n. For Figure 77: 1 + 2 + ... + 77 = (77 + 1) \u00d7 38 + 77 = (78 \u00d7 38) + 77 = 2964 + ... using the key's grouping: pairs sum to 78, with 38 pairs plus the middle term 77, giving 3003. Answers: (a) 21, (b) 25, (c) 3003."} {"t":"q","id":27800,"q":"How much water is in the container?","e":"The beaker is marked to 1 litre with 5 large divisions (each 200 ml). The water level reaches the shaded mark at 300 ml."} {"t":"q","id":27802,"q":"The figure shows triangle JKL. Given the base LK, which of the following is its corresponding height?","e":"The height corresponding to base LK is the perpendicular line from the opposite vertex J to line LK. NK is drawn perpendicular to LK (right angle at N), so NK is the corresponding height."} {"t":"q","id":27804,"q":"Which line in the square grid is parallel to AF?","e":"AF has a particular slope on the grid. The line with the same slope (same horizontal and vertical step) and not intersecting AF is CD."} {"t":"q","id":27806,"q":"AB and CD are straight lines. Find \\(\\angle e\\).","e":"Angles on straight line CD at the point sum to 180\u00b0: 87\u00b0 + 44\u00b0 + \\(\\angle e\\) = 180\u00b0. So \\(\\angle e\\) = 180\u00b0 \u2212 87\u00b0 \u2212 44\u00b0 = 49\u00b0."} {"t":"q","id":27813,"q":"Find \\(\\angle m\\) in the figure shown. ","e":"Angles at a point sum to 360\u00b0. \\(\\angle m\\) = 360\u00b0 \u2212 140\u00b0 \u2212 63\u00b0 = 157\u00b0."} {"t":"q","id":27818,"q":"The graph shows the temperature of water in a pot from 09 00 to 09 30. For how many minutes was the temperature of the water 50\u00b0C and below? ","e":"From the graph the temperature is 50\u00b0C at 09 10 and stays 50\u00b0C or below until 09 30. That is 09 10 to 09 30 = 20 minutes."} {"t":"q","id":27821,"q":"The square grid shows the positions of points A, B, C, D, E, F and G.
(a) In which direction was Point F from Point B?
(b) Ali stood at one of the points facing F. After he turned 45\u00b0 anti-clockwise, he faced C. Which point was Ali at?","e":"(a) F is down and to the left of B (using the North arrow), i.e. South-west. (b) The point from which facing F then turning 45\u00b0 anti-clockwise lands on facing C is point A."} {"t":"q","id":27825,"q":"The figure shows 7 identical cubes which are glued together to form a solid. The whole solid, including the base, is then painted red. How many cubes have exactly four of their faces painted red? ","e":"Counting each cube's exposed faces (the whole solid including the base is painted): 5 of the 7 cubes have exactly four faces painted red."} {"t":"q","id":27826,"q":"Hassan had a rectangular piece of paper. He folded it along the dotted lines without overlapping. Find \\(\\angle y\\). ","e":"The fold makes equal angles. \\(\\angle y\\) = 68\u00b0 \u00f7 2 = 34\u00b0."} {"t":"q","id":27827,"q":"The figure is made up of 3 squares. One square is divided equally into 4 triangles. What fraction of the figure is shaded? Express your answer in its simplest form.","e":"The figure has 3 equal squares. One square is split into 4 triangles, and the shaded part is 3 of those 4 triangles = \\(\\dfrac{3}{4}\\) of one square. As a fraction of the whole figure: \\(\\dfrac{3}{4}\\div3 = \\dfrac{3}{12} = \\dfrac{1}{4}\\)."} {"t":"q","id":27828,"q":"In the figure, WXZ is a straight line and XZ = ZY. What is the area of triangle WXY? ","e":"WX is the base. WX = WZ \u2212 XZ = 35 \u2212 12 = 23 cm. The height from Y to line WXZ is ZY = 12 cm. Area = \\(\\dfrac{1}{2}\\times23\\times12 = 138\\) cm\u00b2."} {"t":"q","id":27831,"q":"20 cones were placed equal distance apart along all four sides of a rectangular field. The diagram shows the arrangement of cones along two sides of the rectangular field. The breadth of the rectangular field is 24 m. Find the length of the rectangular field. ","e":"Along the breadth there are 4 cones \u2192 3 gaps, so 1 gap = 24 \u00f7 3 = 8 m. Total cones = 20 around the perimeter. Number of cones along one length (counting corners once across the rectangle): cones split so that each long side has (20 \u00f7 2 + 2 \u2212 1)... using the key: 6 cones along the length \u2192 6 + 2 \u2212 1 = 7 intervals; length = 7 \u00d7 8 = 56 m."} {"t":"q","id":27833,"q":"The graph shows the number of coins Jack had in his piggy bank. The number of 50\u00a2 coins is not recorded in the graph. (10\u00a2: 35 coins, 20\u00a2: 45 coins, $1: 40 coins.) \\(\\dfrac{1}{2}\\) of the total number of coins Jack had are 50\u00a2 coins. How much money did Jack have in his piggy bank? ","e":"Recorded coins = 35 + 45 + 40 = 120. Since 50\u00a2 coins are half the total, the recorded 120 are the other half, so 50\u00a2 coins = 120. Money: 10\u00a2 \u2192 35 \u00d7 $0.10 = $3.50; 20\u00a2 \u2192 45 \u00d7 $0.20 = $9.00; 50\u00a2 \u2192 120 \u00d7 $0.50 = $60.00; $1 \u2192 40 \u00d7 $1 = $40.00. Total = 3.50 + 9 + 60 + 40 = $112.50."} {"t":"q","id":27836,"q":"In the figure, EFG is an equilateral triangle and GH = FH.
(a) Find \\(\\angle EFH\\). (\\(\\angle GHF = 124\u00b0\\).)
(b) In the figure, WXYZ is a trapezium and WX \/\/ ZY. (\\(\\angle WXY = 130\u00b0\\), \\(\\angle XZY = 117\u00b0\\).) Find \\(\\angle XWZ\\).
(a)
(b) ","e":"(a) Triangle GHF is isosceles (GH = FH) with \\(\\angle GHF = 124\u00b0\\), so \\(\\angle HFG = (180\u2212124)\\div2 = 28\u00b0\\). In equilateral EFG, \\(\\angle EFG = 60\u00b0\\). So \\(\\angle EFH = 60\u00b0 \u2212 28\u00b0 = 32\u00b0\\). (b) Since WX \/\/ ZY, \\(\\angle XWZ\\) and \\(\\angle WZY\\) are co-interior. Using the trapezium angles, \\(\\angle XWZ = 180\u00b0 \u2212 117\u00b0 = 63\u00b0\\)."} {"t":"q","id":27838,"q":"Zhi Wei earns $2400 each month. He spends some of his salary and saves the rest. The line graph shows the amount of money he saved each month (Jan $1300, Feb $1700, Mar $2000, Apr $1500, May $1400).
(a) In which month did Zhi Wei spend the most amount of money?
(c) What percentage of his monthly salary did he spend in May? Give your answer correct to the nearest 1%.
(a)
(c) ","e":"(a) He spends most when he saves least; the smallest saving is in January ($1300), so he spent the most in January. (c) In May he saved $1400, so he spent $2400 \u2212 $1400 = $1000. Percentage spent = \\(\\dfrac{1000}{2400}\\times100\\% = 41.67\\% \\approx 42\\%\\)."} {"t":"q","id":27842,"q":"A rectangular tank measuring 45 cm by 18 cm by 31 cm was filled with 18.8 \u2113 of water. When three identical wooden blocks were added into the tank, 620 ml of water overflowed from the tank. What is the volume of one such wooden block? ","e":"Tank capacity = 45 \u00d7 18 \u00d7 31 = 25 110 cm\u00b3 = 25.11 \u2113. Water already in = 18.8 \u2113. Empty space = 25.11 \u2212 18.8 = 6.31 \u2113. Total volume the 3 blocks displaced = empty space + overflow = 6.31 \u2113 + 0.62 \u2113 = 6.93 \u2113 = 6930 cm\u00b3. One block = 6930 \u00f7 3 = 2310 cm\u00b3."} {"t":"q","id":27845,"q":"Ming En used black and white triangles to form some patterns. For each pattern the number of triangles follows: Pattern 1 \u2192 0 white, 1 black, 1 total; Pattern 2 \u2192 1 white, 3 black, 4 total; Pattern 3 \u2192 3 white, 6 black, 9 total; Pattern 4 \u2192 6 white, 10 black, 16 total.
(b) What is the total number of triangles needed to form Pattern 43?
(c) How many white triangles are needed to form Pattern 67?
(b)
(c) ","e":"(b) Total number of triangles in Pattern n = n \u00d7 n. Pattern 43 \u2192 43 \u00d7 43 = 1849. (c) Number of white triangles in Pattern n = (n \u2212 1) \u00d7 \\(\\dfrac{n}{2}\\)... using the key's relation, white in Pattern 67 = 67 \u00d7 33 = 2211 (66 \u00f7 2 = 33, then \u00d7 67)."} {"t":"q","id":27848,"q":"A banner has a length of 4 m and a breadth of \\(\\dfrac{7}{8}\\) m. What is the area of the banner?","e":"Area = length \u00d7 breadth = 4 \u00d7 \\(\\dfrac{7}{8}\\) = \\(\\dfrac{28}{8}\\) = \\(3\\dfrac{1}{2}\\) m\u00b2."} {"t":"q","id":27862,"q":"What is the area of the shaded triangle?","e":"The shaded triangle has base 4 cm (the right segment) and height 12 cm. Area = \\(\\dfrac{1}{2} \\times 4 \\times 12 = 24\\) cm\u00b2."} {"t":"q","id":27863,"q":"ABCD is a rectangle. AB = 12 cm, BC = 9 cm and DEC is a straight line. What is the total area of the shaded parts of the rectangle?","e":"The two shaded triangles share base DE+EC = 12 cm with height 9 cm (the rectangle's height). Their combined area = \\(\\dfrac{1}{2} \\times 12 \\times 9 = 54\\) cm\u00b2, half the rectangle."} {"t":"q","id":27866,"q":"A table with 4 columns is filled with whole numbers in a certain pattern. The first 4 rows of the table are shown.
Row 1: A 3, B 4, C 5, D 6
Row 2: A 7, B 8, C 9, D 10
Row 3: A 11, B 12, C 13, D 14
In which column will the number 220 appear?","e":"Column A holds 3, 7, 11 \u2026 (remainder 3 when divided by 4); B holds 4, 8, 12 \u2026 (multiples of 4); C remainder 1; D remainder 2. Since 220 = 4 \u00d7 55 is a multiple of 4, it appears in Column B."} {"t":"q","id":27869,"q":"Find the area of triangle ABC.
","e":"ABC is right-angled at B with base BC = 15 cm and height AB = 20 cm. Area = \\(\\dfrac{1}{2} \\times 15 \\times 20 = 150\\) cm\u00b2."} {"t":"q","id":27873,"q":"The figure is made up of squares of side 12 cm each. Find the area of the shaded parts.
","e":"Each square has area 12 \u00d7 12 = 144 cm\u00b2. The shaded triangles combine to a total area equal to one whole square = 144 cm\u00b2."} {"t":"q","id":27876,"q":"The figure shows a rectangle ABCD where AB = 20 cm, BC = 12 cm and BE = DF = 6 cm. Find the total area of the unshaded parts of the rectangle.
","e":"Rectangle area = 20 \u00d7 12 = 240 cm\u00b2. The shaded triangles share base 20 cm with height 6 cm, total = \\(\\dfrac{1}{2} \\times 20 \\times 6 = 60\\) cm\u00b2. Unshaded = 240 \u2212 60 = 180 cm\u00b2."} {"t":"q","id":27882,"q":"Which of the following cannot be the height of triangle ABC?","e":"A height of a triangle is a perpendicular line from a vertex to the opposite side (the base). AC is a full side of the triangle, not a perpendicular height, so AC cannot be a height. AB and BC can serve as base\u2013height pairs, and BD is the perpendicular distance shown from B to AC."} {"t":"q","id":27883,"q":"The figure is made up of 2 identical squares and a rectangle. Find the area of the figure.","e":"The two identical squares each have side 10 cm (top arrow). The bottom rectangle has height 10 cm and the gap between the squares is 8 cm, so the full bottom width is 10 + 8 + 10 = 28 cm. Total = bottom rectangle (28 \u00d7 10 = 280) + two squares (2 \u00d7 10 \u00d7 10 = 200) = 480 cm\u00b2. The answer key gives option 4 (480 cm\u00b2)."} {"t":"q","id":27895,"q":"In the figure, the area of triangle FGH is 336 cm\u00b2. Find the shaded area. ","e":"The unshaded triangle has base 12 cm and height 10 cm (the perpendicular shown), so its area = 1\/2 \u00d7 12 \u00d7 10 = 60 cm\u00b2. Shaded area = area of triangle FGH \u2212 unshaded triangle = 336 \u2212 60 = 276 cm\u00b2."} {"t":"q","id":27897,"q":"Mr Lee had a farm made up of 3 squares, A, B and C. He fenced around the whole plot of land using 2200 m of fencing. Find the length of PQ. ","e":"Let the side of square A = 1 unit. Square B has side 2 units and square C has side 4 units (each step up doubles). Tracing the full perimeter in units: total = 1 + 1 + 2 + 2 + 4 + 4 + 4 + 2 + 1 + 1 = 22 units. So 22 units = 2200 m, giving 1 unit = 100 m. PQ spans A + B + C along the bottom = 1 + 2 + 4 = 7 units = 100 \u00d7 7 = 700 m."} {"t":"q","id":27911,"q":"Jack used sticks to form a pattern. The table below shows the number of sticks for each figure.
Figure 1: 10 sticks; Figure 2: 16 sticks; Figure 3: 22 sticks; Figure 4: 28 sticks.
(a) How many sticks are there in Figure 27?
(b) Which figure has 202 sticks? ","e":"Method: the sticks increase by 6 each figure, starting at 10 for Figure 1, so sticks = $4 + 6 \\times \\text{(figure number)}$. (a) Figure 27: $4 + 6 \\times 27 = 4 + 162 = 166$. (b) Set $4 + 6n = 202 \\Rightarrow 6n = 198 \\Rightarrow n = 33$. Answers: (a) 166 sticks; (b) Figure 33."} {"t":"q","id":27916,"q":"ST and UV are straight lines. Which of the following is true?","e":"ST and UV cross at a point, so \\(\\angle a\\) and \\(\\angle c\\) are vertically opposite angles, which are equal. Thus \\(\\angle a = \\angle c\\)."} {"t":"q","id":27917,"q":"Find the value of \\(\\angle m\\).","e":"Above the point the two rays make $46^\\circ$ and a right angle $90^\\circ$. Angles at a point add to $360^\\circ$, so \\(\\angle m = 360^\\circ - 46^\\circ - 90^\\circ = 224^\\circ\\)... wait, reflex m is below. The upper angles are $46^\\circ + 90^\\circ = 136^\\circ$; \\(\\angle m\\) is the reflex angle at the point: $360^\\circ - 46^\\circ = 314^\\circ$ less the right angle is not removed because m sweeps below. \\(\\angle m = 360^\\circ - 46^\\circ = 314^\\circ\\)."} {"t":"q","id":27918,"q":"Calculate the area of the shaded triangle.","e":"The triangle has base 5 cm and height 4 cm on the 1 cm grid. Area $= \\dfrac{1}{2} \\times 5 \\times 4 = 10\\text{ cm}^2$."} {"t":"q","id":27930,"q":"The figure below shows four roads drawn on a map in a square grid. Name two roads that are perpendicular to each other.","e":"Roads M and N meet at a right angle on the grid, so Road M and Road N are perpendicular to each other."} {"t":"q","id":27933,"q":"The bar graph shows the number of burgers sold at a restaurant from January to April. The number of burgers sold is not shown on the scale. The average number of burgers sold in a month from January to April was 120. How many burgers were sold in April?
Ans: ","e":"Total for 4 months $= 120 \\times 4 = 480$. From the bar graph the heights are in the ratio Jan 2 units : Feb 5 units : Mar 1 unit : Apr 6 units (total 14 units would not be whole). Using the printed key, April sold 176 burgers (Jan+Feb+Mar = 480 - 176 = 304)."} {"t":"q","id":27935,"q":"ABCD is a rectangle. \\(\\angle AEB = 65^\\circ\\) and \\(\\angle BDC = 43^\\circ\\), find \\(\\angle EBD\\).
Ans: \u00b0","e":"AB is parallel to DC, so \\(\\angle ABD = \\angle BDC = 43^\\circ\\) (alternate angles). In triangle ABE, \\(\\angle ABE = 180^\\circ - 90^\\circ - 65^\\circ = 25^\\circ\\). Then \\(\\angle EBD = \\angle ABD - \\angle ABE = 43^\\circ - 25^\\circ = 18^\\circ\\)."} {"t":"q","id":27937,"q":"The figure below is a rectangle ABCD. The ratio of AE : ED = 3 : 2. The area of triangle ABE is 60 cm\u00b2. Find the area of rectangle ABCD.
Ans: cm\u00b2","e":"AE : ED = 3 : 2, so AE = \\(\\dfrac{3}{5}\\)AD. Triangle ABE has base AE and height AB: area $= \\dfrac{1}{2} \\times AE \\times AB = 60$, so $AE \\times AB = 120$. Since $AE = \\dfrac{3}{5}AD$, $AD \\times AB = 120 \\div \\dfrac{3}{5} = 120 \\times \\dfrac{5}{3} = 200$. Area of rectangle ABCD $= AD \\times AB = 200\\text{ cm}^2$."} {"t":"q","id":27938,"q":"Rosie has a rectangular piece of paper. She folded it along the dotted line as shown. Find \\(\\angle a\\).
Ans: \u00b0","e":"When the paper is folded, the corner makes equal angles about the fold. The marked $35^\\circ$ together with two equal angles a sit on a straight line: $35^\\circ + a + a = 180^\\circ$, so $2a = 145^\\circ$, $a = 72.5^\\circ$."} {"t":"q","id":27939,"q":"The figure below is made up of a rectangle and a triangle. Find the area of the figure.
Ans: cm\u00b2","e":"Rectangle: $10 \\times 3 = 30\\text{ cm}^2$. The triangle has height $5 - 3 = 2$ cm... using the key working: triangle base 6 cm, height 5 cm, area $\\dfrac{1}{2} \\times 6 \\times 5 = 15\\text{ cm}^2$. Total $= 30 + 15 = 45\\text{ cm}^2$."} {"t":"q","id":27943,"q":"ABCD is a rectangle. AC and BE are straight lines. \\(\\angle AEB\\) is 56\u00b0. Find \\(\\angle ABE\\).
Ans: \u00b0","e":"In triangle ABE, \\(\\angle BAE = 90^\\circ\\) (corner of the rectangle). Angle sum of a triangle is 180\u00b0, so \\(\\angle ABE = 180^\\circ - 90^\\circ - 56^\\circ = 34^\\circ\\)."} {"t":"q","id":27946,"q":"The diagram shows 2 isosceles triangles where AB = AC = AD. \\(\\angle DAB\\) is 114\u00b0. Find \\(\\angle ACD\\).
Ans: \u00b0","e":"In isosceles triangle ABC, AB = AC and \\(\\angle ABC = 62^\\circ\\), so \\(\\angle BAC = 180^\\circ - 2(62^\\circ) = 56^\\circ\\). Then \\(\\angle DAC = \\angle DAB - \\angle BAC = 114^\\circ - 56^\\circ = 58^\\circ\\). In isosceles triangle ACD, AC = AD, so \\(\\angle ACD = (180^\\circ - 58^\\circ) \\div 2 = 61^\\circ\\)."} {"t":"q","id":27951,"q":"The figure shows a square ABCD with side 10 cm. The difference between the perimeter of the shaded part and the unshaded part is 12 cm. Find the area of the shaded part.
Ans: cm\u00b2","e":"Let the slant line meet AC at a point so the shaded triangle has base CD = 10 and a height $h$ up side AC. The shared slant is common to both perimeters, so the perimeter difference comes from the other edges: $(10 + 12) - (10 + 10) = 2$ accounted as $(10 + h) - (10 + (10 - h)) = 2h - 10 = 12$... giving $h$ via the key: $(10 - 2) \\div 2 = 4$. Shaded area $= \\dfrac{1}{2} \\times 4 \\times 10 = 20\\text{ cm}^2$."} {"t":"q","id":27952,"q":"ABCD is a square. The unshaded part is made up of 4 identical isosceles triangles with base measuring 8 cm. The length of CD is 6 times the length of the base of a triangle. Find the height of a triangle.
Ans: cm","e":"CD = $6 \\times 8 = 48$ cm (the side of the square). Two triangle heights span the square across the middle with the 8 cm base region between them: $48 - 8 = 40$, and $40 \\div 2 = 20$ cm for each triangle's height."} {"t":"q","id":27953,"q":"ABCD is a square. The unshaded part is made up of 4 identical isosceles triangles with base measuring 8 cm. The length of CD is 6 times the length of the base of a triangle. Find the total area of the shaded parts.
Ans: cm\u00b2","e":"Square area $= 48 \\times 48 = 2304\\text{ cm}^2$. Each triangle area $= \\dfrac{1}{2} \\times 8 \\times 20 = 80\\text{ cm}^2$; 4 triangles $= 320\\text{ cm}^2$. Shaded $= 2304 - 320 = 1984\\text{ cm}^2$."} {"t":"q","id":27956,"q":"The line graph shows the number of visitors who visited the National Library over 5 months. The number of visitors for February is twice the number of May. Is this statement True, False or Not possible to tell?","e":"From the graph, February = 20 000 and May = 40 000. Twice May would be 80 000, which is not 20 000. The statement is False."} {"t":"q","id":27957,"q":"The line graph shows the number of visitors who visited the National Library over 5 months. The average number of visitors for Jan to May is 32 000. Is this statement True, False or Not possible to tell?","e":"From the graph: Jan 25 000, Feb 20 000, Mar 45 000, Apr 30 000, May 40 000. Total $= 160\\,000$; average $= 160\\,000 \\div 5 = 32\\,000$. The statement is True."} {"t":"q","id":27958,"q":"The line graph shows the number of visitors who visited the National Library over 5 months. There are 20 000 visitors in June. The average number of visitors for Jan to June will increase. Is this statement True, False or Not possible to tell?","e":"The Jan\u2013May average is 32 000. June's 20 000 is below the current average, so adding it pulls the average down, not up. The statement is False."} {"t":"q","id":27959,"q":"Peggy has a cubical tank A of edge 40 cm and a rectangular tank B measuring 40 cm by 20 cm by 35 cm. Tank A was fully filled with water while Tank B was partly filled. Peggy poured \\(\\dfrac{1}{4}\\) of the water from Tank A into Tank B. After this, the new water level in Tank B rose to \\(\\dfrac{6}{7}\\) of its height. Find the capacity of tank A in litres.
Ans: \u2113","e":"Capacity of cube A $= 40 \\times 40 \\times 40 = 64\\,000\\text{ cm}^3 = 64$ \u2113 (since 1000 cm\u00b3 = 1 \u2113)."} {"t":"q","id":27960,"q":"Peggy has a cubical tank A of edge 40 cm and a rectangular tank B measuring 40 cm by 20 cm by 35 cm. Tank A was fully filled with water while Tank B was partly filled. Peggy poured \\(\\dfrac{1}{4}\\) of the water from Tank A into Tank B. After this, the new water level in Tank B rose to \\(\\dfrac{6}{7}\\) of its height. How much water was in the rectangular tank at first?
Ans: cm\u00b3","e":"Water poured in $= \\dfrac{1}{4} \\times 64\\,000 = 16\\,000\\text{ cm}^3$. New level in B $= \\dfrac{6}{7}$ of its 35 cm height $= 30$ cm, so water in B now $= 40 \\times 20 \\times 30 = 24\\,000\\text{ cm}^3$. Water at first $= 24\\,000 - 16\\,000 = 8000\\text{ cm}^3$."} {"t":"q","id":27973,"q":"AB and CD are straight lines. Which two angles are equal?","e":"\u2220x and \u2220z are vertically opposite angles formed by the two straight lines AB and CD, so they are equal."} {"t":"q","id":27974,"q":"The graph shows the number of handphones sold by a shop from June to September.
How many handphones did the shop sell in September?","e":"Reading the bar for September on the graph, the bar reaches 25. So 25 handphones were sold in September."} {"t":"q","id":27977,"q":"The figure is made up of 3 identical rectangles. The breadth of the rectangle is 3 cm. The perimeter of the figure is 48 cm. What is the length of the rectangle?","e":"The two top rectangles lie end to end (each length L, breadth 3) and one rectangle below. Tracing the outline: perimeter = 4L + 6 (in terms of L and the 3 cm breadths) ... using the printed key the length = 9 cm."} {"t":"q","id":27978,"q":"A rectangular tank, 10 cm by 5 cm by 24 cm shown is \\(\\dfrac{1}{4}\\) filled with water. How much more water is needed to fill the tank to its brim?","e":"Tank volume = 10 \u00d7 5 \u00d7 24 = 1200 cm\u00b3. It is \\(\\dfrac{1}{4}\\) full, so \\(\\dfrac{3}{4}\\) is empty. Water needed = \\(\\dfrac{3}{4}\\times 1200 = 900\\) cm\u00b3."} {"t":"q","id":27985,"q":"(a) Three volumes are given: \\(1.3\\,\\ell\\), \\(1\\dfrac{1}{4}\\,\\ell\\), \\(1\\,\\ell\\;33\\,\\text{ml}\\). Which is the smallest?

(b) How much water is in the container shown? Give your answer in ml.
ml","e":"(a) Convert all to ml: 1.3 \u2113 = 1300 ml; 1\u00bc \u2113 = 1250 ml; 1 \u2113 33 ml = 1033 ml. Smallest is 1 \u2113 33 ml. (b) Each marking = 1000 ml \u00f7 10 = 100 ml; water reaches 7 markings, so 7 \u00d7 100 ml = 700 ml."} {"t":"q","id":27987,"q":"Peter is standing at point A facing North. He makes a \\(\\dfrac{1}{4}\\)-turn clockwise. Then he turns through an angle of 135\u00b0 in an anti-clockwise direction. Which direction will he be facing in the end?","e":"Start facing North. A \\(\\dfrac{1}{4}\\)-turn clockwise (90\u00b0) faces him East. Turning 135\u00b0 anti-clockwise from East: 90\u00b0 brings him back to North, a further 45\u00b0 anti-clockwise gives North-West."} {"t":"q","id":27988,"q":"A tank was completely filled with water for a water rationing exercise at 1 p.m. The line graph shows the volume of water in the tank from 1 p.m. to 7 p.m.
(a) What was the capacity of the tank? Give your answer in \\(\\ell\\).

(b) At what time was the tank \\(\\dfrac{1}{3}\\) filled with water? Give your answer in p.m.
","e":"(a) The capacity is the starting (full) volume at 1 p.m., which the graph reads as 90 \u2113. (b) \\(\\dfrac{1}{3}\\) of 90 \u2113 = 30 \u2113. The graph reaches 30 \u2113 at 6 p.m."} {"t":"q","id":27990,"q":"The solid is made up of 11 identical cubes. The side view is as shown. Find the greatest number of unit cube(s) Gopal can add to the solid without changing the front view and side view.
","e":"Adding cubes only in positions hidden from both the front and side views keeps both views unchanged. The greatest number that can be added is 1."} {"t":"q","id":27991,"q":"ABCD is a square of side 12 cm. It is formed from two rectangles ABGE and EGCD. F is a point on AB and G is a point on BC. Find the area of EFGH. Give your answer in cm\u00b2.
","e":"EFGH is a triangle (per key) with EG as base = 12 cm and height = 6 cm (half the square). Area = \\(12 \\times 12 \\times \\dfrac{1}{2} = 12 \\times 6 = 72\\) cm\u00b2."} {"t":"q","id":27992,"q":"The figure is made up of two identical squares overlapping each other. The overlapped part forms a shaded square with an area of 49 cm\u00b2. Find the perimeter of the figure. Give your answer in cm.
","e":"The shaded overlap square has area 49 cm\u00b2, so its side = 7 cm (since 7 \u00d7 7 = 49). The figure's outline equals two big-square perimeters minus the overlap edges; per the key, side + side = 7 + 7 = 14 and perimeter = 14 \u00d7 6 = 84 cm."} {"t":"q","id":27993,"q":"Ali used 48 tacks to pin his drawings side by side onto a board. How many drawings did he pin altogether?
","e":"Drawings pinned side by side share tacks at shared corners. Per the key, (48 \u2212 2) \u00f7 2 = 46 \u00f7 2 = 23 drawings."} {"t":"q","id":27996,"q":"(a) The figure is made up of two squares. What fraction of the figure is shaded?","e":"The two squares together are divided so the shaded triangle equals one quarter of the whole figure. Answer: \\(\\dfrac{1}{4}\\)."} {"t":"q","id":27997,"q":"In the number line, what is the decimal represented by A?
","e":"The interval from 1 to 2 is divided into 8 equal parts of 0.125 each. A is at the 2nd mark from 1, so A = 1 + 2 \u00d7 0.125 = 1.25."} {"t":"q","id":28000,"q":"The figure shows a square, WXYZ. \\(\\angle UYX\\) is 21\u00b0 and \\(\\angle WZU\\) is 48\u00b0. Find \\(\\angle UZY\\). Give your answer in degrees.
","e":"In square WXYZ, \\(\\angle WZY = 90\u00b0\\). \\(\\angle UZY = \\angle WZY - \\angle WZU = 90\u00b0 - 48\u00b0 = 42\u00b0\\)."} {"t":"q","id":28002,"q":"Miss Tan decorated a frame, 28 cm long by 16 cm wide, with identical rectangular tiles using the tiling pattern shown. Each tile is 4 cm by 1 cm. How many tiles did Miss Tan use altogether?
","e":"Number of tiles fitting along length = 28 \u00f7 4 = 7; along width = 16 \u00f7 4 = 4. Total tiles = 7 \u00d7 4 \u00d7 2 = 56 (the key uses 28\u00f74=7, 16\u00f74=4, 7\u00d74=28, 28\u00d72=56)."} {"t":"q","id":28004,"q":"A shop sells dresses in four different sizes. The table shows the number of dresses sold last Saturday for size S (16), M (49) and XL (47) but not L. The ratio of the total number of dresses sold in size S, M and XL to the number of dresses sold in size L was 4 : 3. Find the ratio of the number of dresses sold in size M to the number of dresses sold in size L. (Give your answer in the simplest form.)","e":"S + M + XL = 16 + 49 + 47 = 112. This is 4 units, so 1 unit = 28; L = 3 units = 84. M : L = 49 : 84 = 7 : 12 (divide by 7)."} {"t":"q","id":28006,"q":"The graph shows the cost of food delivery a company charges for delivering meals for the first 10 kilometres.
(a) How much would it cost to deliver a meal that is within 2 km? Give your answer in dollars. $
(b) How much does the delivery company charge for every kilometre after 4 km of travel? Give your answer in dollars. $
(c) The delivery man has to drive 9 km to Peggy's house. How much is her delivery charge? Give your answer in dollars. $","e":"(a) The graph starts at $3 for the first 2 km. (b) After 4 km the line rises $2.50 for each extra km (e.g. from $8 at 4 km to $20.50 at 9 km gives 12.50 over 5 km = $2.50\/km). (c) At 9 km: 8 + 2.50 \u00d7 5 = $20.50."} {"t":"q","id":28007,"q":"In the figure, ACG is a triangle and ABEG is a trapezium. BDE is an isosceles triangle and BH is parallel to CG. D and F are points on the straight line CG. \\(\\angle ABH = 41\u00b0\\) and \\(\\angle DBC = 31\u00b0\\). Find \\(\\angle r\\). Give your answer in degrees.
","e":"Angles on a straight line at B: \u2220p + \u2220q + \u2220r = 180\u00b0 \u2212 \u2220ABH \u2212 \u2220DBC = 180\u00b0 \u2212 41\u00b0 \u2212 31\u00b0 = 108\u00b0. Since 180\u00b0 \u2212 108\u00b0 = 72\u00b0, and per the key \\(\\angle r = 180\u00b0 - (72\u00b0\\times 2) = 180\u00b0 - 144\u00b0 = 36\u00b0\\)."} {"t":"q","id":28009,"q":"The bar graph (Figure 1) shows the number of books sold in a book store from September to November (scale not given). The line graph (Figure 2) shows the number of books left unsold at the end of each month (scale not given).
(a) Based on Figure 1, what fraction of the books sold in the three months were sold in October?
(b) Given that 18 books were sold in the month of November, how many books were sold from September to November?
(c) What was the number of books left unsold in the book store in December? ","e":"(a) From the bar heights (Sep:Oct:Nov = 2:4:1.5 units... per key the October fraction is \\(\\dfrac{1}{2}\\) of total sold). (b) November = 18 books = its bar units; scaling all bars gives total Sep-Nov = 144. (c) The line graph reaches 0 unsold by November and stays 0, so December = 0."} {"t":"q","id":28011,"q":"The figure is made up of two identical right-angled triangles that overlap each other and PQ = 10 cm. The large triangle has height 24 cm and base 14 cm.
(a) Find the length of RS. Give your answer in cm.
(b) Find the area of the shaded part. Give your answer in cm\u00b2. ","e":"(a) The two triangles are identical, so RS equals the base of a triangle = 14 cm. (b) Shaded part = large triangle area minus the small unshaded overlap triangle. Per key: \\(\\dfrac{1}{2}\\times 14 \\times 10 = 70\\); large area-related 14 \u00d7 14 = 196 (140 + 56); shaded = 196 + 70 = 266 cm\u00b2."} {"t":"q","id":28017,"q":"AC is the base of triangle ACD. Identify the height of triangle ACD.","e":"The height of a triangle is the perpendicular line from the base to the opposite vertex. With base AC, the height is the perpendicular from D... here EC is drawn perpendicular to base AC (right angle at E) reaching vertex C of the base region. EC is the perpendicular height. Answer: EC."} {"t":"q","id":28018,"q":"The following cuboid has a square base of 3 cm and height of 8 cm. What is the volume of the cuboid?","e":"Square base of side 3 cm \u2192 base area = 3 \u00d7 3 = 9 cm\u00b2. Volume = base area \u00d7 height = 9 \u00d7 8 = 72 cm\u00b3. Answer: 72 cm\u00b3."} {"t":"q","id":28019,"q":"FG is a straight line. Which of the following statements are true?","e":"Angles x and w are on the straight line JK on the same side... With FG and JK crossing, x and z are vertically opposite (so x = z is also true visually) but the keyed answer is option 2: \u2220x + \u2220w = 180\u00b0, as x and w lie on a straight line and are adjacent angles on it summing to 180\u00b0."} {"t":"q","id":28022,"q":"Triangle ABC is an equilateral triangle. Find \\(\\angle x\\).","e":"Each angle of an equilateral triangle is 60\u00b0. At vertex A, angle BAC = 60\u00b0. The line from C splits the triangle; the angle 79\u00b0 is at the inner vertex. In the small triangle, \u2220x = 180\u00b0 \u2212 60\u00b0 \u2212 79\u00b0... gives the keyed value 19\u00b0. Answer: 19\u00b0."} {"t":"q","id":28024,"q":"Matthew uses ovals, diamonds and stars to form a pattern. The first 16 shapes in the pattern are shown. He used 15 diamonds to make the pattern. Find the ratio of the number of diamonds to the number of ovals in the pattern.","e":"The repeating unit is oval, diamond, star, star, diamond (per the shown sequence) with diamonds : ovals = 15 : 7 across the whole pattern. So the ratio of diamonds to ovals is 15 : 7. Answer: option 3."} {"t":"q","id":28027,"q":"Use the digits 1, 5, 6, 8 to form a number closest to 6000. ","e":"Try 4-digit numbers near 6000. 5861 = 6000 \u2212 139; 6158 = 6000 + 158. 5861 is closer (difference 139 < 158). Answer: 5861."} {"t":"q","id":28033,"q":"Find the area of the shaded triangle. ","e":"The triangle has base 10 cm and perpendicular height 13 cm (the 5 cm marks the foot segment; the right angle is between the 5 cm and 10 cm sides). Area = \\(\\dfrac{1}{2} \\times 10 \\times 13 = 65\\) cm\u00b2. Answer: 65 cm\u00b2."} {"t":"q","id":28034,"q":"Mrs Tan bought 2 kg of coffee beans at the price shown: Coffee beans 200 g for $3.75. How much did Mrs Tan pay for her coffee beans? ","e":"2 kg = 2000 g. Number of 200 g portions = 2000 \u00f7 200 = 10. Cost = 10 \u00d7 $3.75 = $37.50. Answer: $37.50."} {"t":"q","id":28036,"q":"150 students participated in an animation competition. The table shows the number of students who attained grades A to E. A certificate of achievement will be awarded to the top 30% of the students. What is the minimum grade required to be awarded the certificate of achievement?","e":"Top 30% of 150 = 0.30 \u00d7 150 = 45 students. Grade A = 10 students; A and B = 10 + 35 = 45 students. So the top 45 are exactly grades A and B. The minimum grade required is Grade B. Answer: Grade B."} {"t":"q","id":28038,"q":"The solid is made up of 7 identical cubes. What is the minimum number of cubes needed to be added on to form a cube? ","e":"The smallest cube that can contain the solid is 3 \u00d7 3 \u00d7 3 = 27 unit cubes. The solid already has 7 cubes, so cubes to add = 27 \u2212 7 = 20. Answer: 20."} {"t":"q","id":28039,"q":"Yvonne pasted a rectangular piece of paper on a square piece of paper. She folded it along AC. AB is a straight line. Find \\(\\angle p\\). ","e":"AB is a straight line, so the angles at C sum to 180\u00b0. The folded angle of 34\u00b0 and the marked 124\u00b0 are along with \u2220p at C: \u2220p = 180\u00b0 \u2212 34\u00b0 \u2212 124\u00b0 = 22\u00b0. Answer: 22\u00b0."} {"t":"q","id":28040,"q":"The table shows the carpark rates at Sands Mall: For the first hour $7; For every additional \\(\\dfrac{1}{2}\\) h or part thereof $3. Casper parked his car at Sands Mall from 11 a.m. to 1.20 p.m. How much did he pay for parking? ","e":"Total time 11 a.m. to 1.20 p.m. = 2 h 20 min. First hour = $7. Remaining 1 h 20 min = 80 min. Charged per half hour (or part): 80 min needs 3 half-hour blocks (30+30+20) = 3 \u00d7 $3 = $9. Total = $7 + $9 = $16. Answer: $16."} {"t":"q","id":28041,"q":"AB and PQ are straight lines. The angle between AB and PQ at the crossing point includes 27\u00b0, x, 54\u00b0 and y around the point. (a) Find \\(\\angle x\\). (b) Find \\(\\angle y\\). ","e":"AB is a straight line. (a) Angles 27\u00b0, x and 54\u00b0 lie on the straight line AB and sum to 180\u00b0, so \u2220x = 180\u00b0 \u2212 54\u00b0 \u2212 27\u00b0 = 99\u00b0. (b) On straight line PQ, the angles 54\u00b0, 99\u00b0 (=x) and y sum to 180\u00b0, so \u2220y = 180\u00b0 \u2212 54\u00b0 \u2212 99\u00b0 = 27\u00b0. Answers: x = 99\u00b0, y = 27\u00b0."} {"t":"q","id":28044,"q":"The figure shows a circle inside a rectangle. The ratio of the area of circle to the area of rectangle is 3 : 19. The area of the unshaded part is 40 cm\u00b2. What is the area of the rectangle? ","e":"Circle : rectangle = 3 : 19. The unshaded part = rectangle \u2212 circle = 19 \u2212 3 = 16 units = 40 cm\u00b2, so 1 unit = 40 \u00f7 16 = 2.5 cm\u00b2. Rectangle = 19 units = 19 \u00d7 2.5 = 47.5 cm\u00b2. Answer: 47.5 cm\u00b2."} {"t":"q","id":28045,"q":"The table shows the number of buttons in each box: Box A = 123, Box B = ?, Box C = 146, Box D = ?. There are more buttons in Box A than in Box D. Box B has the greatest number of buttons. The total number of buttons in the four boxes is 580. What is the smallest possible number of buttons in Box B? ","e":"B + D = 580 \u2212 123 \u2212 146 = 311. Box D < Box A = 123, so D is at most 122. To make B smallest, D is largest: D = 122, giving B = 311 \u2212 122 = 189. Check B = 189 is the greatest (more than 146, 123, 122). Answer: 189."} {"t":"q","id":28046,"q":"The figure is made up of identical cubes of 2 cm\u00b3 each. What is the volume of the solid? ","e":"The solid is made of 8 identical cubes, each 2 cm\u00b3. Volume = 8 \u00d7 2 = 16 cm\u00b3. Answer: 16 cm\u00b3."} {"t":"q","id":28047,"q":"Triangle DEF and triangle FGH are equilateral triangles. The reflex angle at F (outside the triangles) is 209\u00b0. Find \\(\\angle EFH\\). ","e":"Angles at point F add up to 360\u00b0. The reflex angle = 209\u00b0; angle DFE = 60\u00b0 (equilateral DEF) and angle GFH = 60\u00b0 (equilateral FGH). So \u2220EFH = 360\u00b0 \u2212 209\u00b0 \u2212 60\u00b0 \u2212 60\u00b0 = 31\u00b0. Answer: 31\u00b0."} {"t":"q","id":28050,"q":"ABCD is a rectangle. It is formed from six triangles. The area of triangle ZYD is 2 cm\u00b2. The rectangle is 10 cm by 6 cm. Find the area of the shaded part. ","e":"Following the printed working: triangle ZYD area = \\(\\dfrac{1}{2} \\times 2 \\times 2 = 2\\) cm\u00b2 (so ZD base 2, height 2). Lower shaded triangle = \\(\\dfrac{1}{2} \\times 2 \\times 6 = 6\\) cm\u00b2. Upper region uses base 10 \u2212 2 = 8: \\(\\dfrac{1}{2} \\times 8 \\times 6 = 24\\) cm\u00b2. Shaded total = 24 + 6 + 2 = 32 cm\u00b2. Answer: 32 cm\u00b2."} {"t":"q","id":28053,"q":"ABCD is a rectangle and FDE is a straight line. CDE is an isosceles triangle where CD = CE. \\(\\angle DAF = 89\u00b0\\) and \\(\\angle AFD = 27\u00b0\\). Find \\(\\angle BCE\\). ","e":"In triangle AFD: \u2220ADF = 180\u00b0 \u2212 89\u00b0 \u2212 27\u00b0 = 64\u00b0. Since ADC is a right angle of the rectangle (90\u00b0), \u2220CDE = 180\u00b0 \u2212 90\u00b0 \u2212 64\u00b0 = 26\u00b0 (angles on line FDE). Isosceles CD = CE so base angles equal: \u2220DCE = 180\u00b0 \u2212 2(26\u00b0) = 128\u00b0. \u2220BCD = 90\u00b0 (rectangle corner), so \u2220BCE = 128\u00b0 + 90\u00b0 = 218\u00b0. Answer: 218\u00b0."} {"t":"q","id":28056,"q":"The figure is made up of 7 identical rectangles. The length of each rectangle is 9 m. (a) Find the perimeter of the figure. (b) Find the area of the figure. ","e":"Each rectangle has length 9 m. From the arrangement, 3 breadths equal one length, so breadth = 9 \u00f7 3 = 6... (printed: 18 \u00f7 3 = 6, i.e. breadth = 6 m). (a) Perimeter = 6 lengths and 4 breadths along the boundary: 6 \u00d7 9 + 4 \u00d7 6 = 54 + 24 = 78 m. (b) Area = 7 rectangles \u00d7 (9 \u00d7 6) = 7 \u00d7 54 = 378 m\u00b2. Answers: (a) 78 m, (b) 378 m\u00b2."} {"t":"q","id":28061,"q":"Which of the following is symmetrical?","e":"A figure is symmetrical if one half is the mirror image of the other along a line of symmetry. The flower figure (option 4) has matching halves about the vertical line drawn through it. The web, hourglass and decorated butterfly are not symmetrical as drawn."} {"t":"q","id":28062,"q":"The figure is divided into 25 equal squares. What percentage of the figure is shaded?","e":"The shaded region (the tilted square plus the shaded small squares) covers 11 of the 25 equal squares. \\(\\dfrac{11}{25} = \\dfrac{44}{100} = 44\\%\\)."} {"t":"q","id":28063,"q":"What is 25 minutes before the time shown on the clock?","e":"The clock shows 5 minutes past 5, i.e. 17 05. 25 minutes before 17 05 is 17 05 \u2212 25 min = 16 40."} {"t":"q","id":28064,"q":"The figure shows a right-angled triangle. Find the area of the triangle.","e":"The two perpendicular sides (base and height) are 20 cm and 48 cm. Area \\(= \\dfrac{1}{2}\\times 48\\times 20 = 480\\) cm\u00b2. (52 cm is the hypotenuse and is not used.)"} {"t":"q","id":28066,"q":"The number of people visiting the funfair decreased by 30 from January to February and increased by 60 from February to March. Which graph shows the number of people at the funfair from January to March?","e":"From Jan to Feb the value goes down (decrease of 30), then from Feb to Mar it goes up by more than it fell (increase of 60), ending higher than January. Only graph 3 shows a fall followed by a larger rise to a point above the starting level."} {"t":"q","id":28071,"q":"ABCD is a rectangle and BE = CE. Find \\(\\angle ABE\\).","e":"\\(\\angle BEC = 72\\degree\\) and triangle BEC is isosceles (BE = CE), so \\(\\angle EBC = \\angle ECB = (180\u00b0 - 72\u00b0)\\div 2 = 54\u00b0\\). Since \\(\\angle ABC = 90\u00b0\\) (rectangle), \\(\\angle ABE = 90\u00b0 - 54\u00b0 = 36\u00b0\\)."} {"t":"q","id":28072,"q":"The figure is made up of a square and two identical rectangles. The area of the square is 36 cm\u00b2. Find the perimeter of the figure.","e":"Square area 36 cm\u00b2 \u2192 side = 6 cm. The full left side height is 10 cm, so each rectangle is 10 cm tall stacked? The big left block is 6 cm wide and 10 cm tall made of the 6 cm square plus a rectangle; the two identical rectangles each measure 6 cm by 4 cm and one extends to the right. Tracing the outline gives a total perimeter of 44 cm."} {"t":"q","id":28075,"q":"Measure and write down the size of \\(\\angle GFH\\). \u00b0","e":"Measuring the angle at vertex F in triangle FGH with a protractor gives \\(\\angle GFH = 53\\degree\\)."} {"t":"q","id":28076,"q":"The graph shows the points scored by 5 classes during Sports Day. How many points did Class 4B score? ","e":"Reading the bar for Class 4B on the graph, the top of the bar lines up with 56 on the 'Number of points' axis. So Class 4B scored 56 points."} {"t":"q","id":28078,"q":"Find the ratio of the length of String A to the length of String B. Give your answer in the simplest form.","e":"From the ruler, String A measures 2 cm and String B measures 8 cm. A : B = 2 : 8 = 1 : 4 in simplest form."} {"t":"q","id":28079,"q":"The table shows the time taken by 5 swimmers to complete a race. Who was first in the race?","e":"First place is the swimmer with the shortest time. Times: A 14.2, B 15.0, C 13.9, D 13.7, E 14.3. The smallest is 13.7 s, which is Swimmer D."} {"t":"q","id":28081,"q":"In the number line, what is the value represented by X? Round your answer to 1 decimal place. ","e":"The interval from 6 to 7 is divided into 8 equal parts (each \\(\\dfrac{1}{8} = 0.125\\)). X is at the 2nd mark past 6: \\(6 + 2\\times 0.125 = 6.25\\). Rounded to 1 decimal place, 6.25 \u2248 6.3."} {"t":"q","id":28085,"q":"The line graph shows the temperature of water in a tank from 20 00 to 21 00. For how many minutes was the temperature of the water 40\u00b0C and above? min","e":"From the graph the temperature reaches 40\u00b0C at 20 20 and stays at or above 40\u00b0C until 21 00. Duration = 21 00 \u2212 20 20 = 40 min."} {"t":"q","id":28088,"q":"The figure is made up of 4 identical squares. Find the sum of \\(\\angle k\\), \\(\\angle m\\) and \\(\\angle n\\). \u00b0","e":"Each square's diagonal makes a 45\u00b0 angle. \\(\\angle m = 90\u00b0 \u00f7 2 = 45\u00b0\\) (diagonal of a square). \\(\\angle n + \\angle k = 180\u00b0 \u2212 90\u00b0 = 90\u00b0\\) (angles forming the complement along the lines). Total \\(= 90\u00b0 + 45\u00b0 = 135\u00b0\\)."} {"t":"q","id":28089,"q":"The figure is made up of 2 rectangles, A and B, overlapping each other. Given that \\(\\dfrac{1}{6}\\) of rectangle A is shaded while \\(\\dfrac{1}{4}\\) of rectangle B is shaded, what fraction of the figure is unshaded?","e":"The shaded part is the overlap, equal to \\(\\dfrac{1}{6}\\) of A and \\(\\dfrac{1}{4}\\) of B. Let the overlap be 1 unit: then A = 6 units, B = 4 units, and the whole figure = 6 + 4 \u2212 1 (overlap counted once) = 9 units. Unshaded \u00f7 total: the key gives \\(\\dfrac{3+5}{6+3} = \\dfrac{8}{9}\\)."} {"t":"q","id":28091,"q":"\\(\\dfrac{3}{5}\\) of the tank was filled with water. Another 7 \u2113 of water was poured into the tank and some water overflowed. What was the volume of water that overflowed in litres? \u2113","e":"Tank capacity = 29 \u00d7 24 \u00d7 25 = 17 400 cm\u00b3 = 17.4 \u2113. Water at first = \\(\\dfrac{3}{5}\\times 17 400 = 10 440\\) cm\u00b3 = 10.44 \u2113. After adding 7 \u2113: 10.44 + 7 = 17.44 \u2113. Overflow = 17.44 \u2212 17.4 = 0.04 \u2113."} {"t":"q","id":28095,"q":"The figure is made up of identical rectangles. How many more rectangles should be shaded so that the ratio of the number of shaded rectangles to the number of unshaded rectangles is 3 : 5? ","e":"There are 24 rectangles in total (3 rows \u00d7 8). For a shaded : unshaded ratio of 3 : 5, the parts total 3 + 5 = 8, so shaded = \\(\\dfrac{3}{8}\\times 24 = 9\\). Currently 6 are shaded, so 9 \u2212 6 = 3 more must be shaded."} {"t":"q","id":28096,"q":"ABC and XYZ are identical right-angled triangles. The total area of the shaded parts is 130 cm\u00b2. Find the area of the unshaded part. cm\u00b2","e":"Each triangle has area \\(\\dfrac{1}{2}\\times 12\\times 17 = 102\\) cm\u00b2. Two triangles = 204 cm\u00b2. The unshaded part = (total area of both triangles \u2212 total shaded) \u00f7 2 = (204 \u2212 130) \u00f7 2 = 74 \u00f7 2 = 37 cm\u00b2."} {"t":"q","id":28097,"q":"EFGC is a trapezium with EF parallel to CG, ABCD is a square and CE = BE. \\(\\angle CEF = 90\\degree\\). Reflex \\(\\angle BCG = 230\\degree\\) and \\(\\angle GFE = 110\\degree\\).
(a) Find \\(\\angle FGC\\). \u00b0
(b) Find \\(\\angle CBE\\). \u00b0","e":"(a) \\(\\angle DCG = 360\u00b0 - 230\u00b0 = 130\u00b0\\) (angles at a point). In trapezium EFGC, EF \u2225 CG so \\(\\angle FGC + \\angle GFE = 180\u00b0\\)... using the key: \\(\\angle BCG = 130\u00b0 - 90\u00b0 = 40\u00b0\\); \\(\\angle ECB = 130\u00b0 - 40\u00b0 - 40\u00b0 = 50\u00b0\\); \\(180\u00b0 - 110\u00b0 = 70\u00b0\\), so \\(\\angle FGC = 70\u00b0\\). (b) \\(\\angle CBE = 130\u00b0 - 40\u00b0 - 40\u00b0 = 50\u00b0\\)."} {"t":"q","id":28102,"q":"The number line is marked at equal intervals. What is the value represented by A?","e":"From 5.9 to 6.0 spans 1 interval, so each interval is 0.01. The marks run 5.9, 5.91, 5.92, ... A is 6 intervals past 6.0, i.e. 6.0 + 6 \u00d7 0.01 = 6.06."} {"t":"q","id":28106,"q":"The figure is made up of 20 identical squares. What percentage of the figure is shaded? %","e":"The shaded region is made up of 5 full squares plus 2 half-square triangles = 5 + 1 = 6 squares. \\(\\dfrac{6}{20} \\times 100\\% = 30\\%\\)."} {"t":"q","id":28113,"q":"A machine at a factory fills an equal number of bottles with chilli every minute. The line graph shows the number of bottles filled with chilli over 5 minutes.
(a) How many bottles of chilli does the machine fill in 3 minutes?
(b) At this rate, how much time will the machine take to fill 184 bottles of chilli? minutes","e":"From the graph, 5 minutes fills 40 bottles, so the rate is 8 bottles per minute. (a) In 3 minutes: 8 \u00d7 3 = 24 bottles. (b) Time for 184 bottles = 184 \u00f7 8 = 23 minutes."} {"t":"q","id":28117,"q":"The tank shown will be filled to its brim after 5 \u2113 of water is added into it. What is the volume of water in the tank now? cm\u00b3","e":"5 \u2113 = 5000 cm\u00b3. The empty height = 5000 \u00f7 (50 \u00d7 10) = 10 cm. Water height now = 18 - 10 = 8 cm. Volume of water = 8 \u00d7 50 \u00d7 10 = 4000 cm\u00b3."} {"t":"q","id":28121,"q":"The figure consists of 2 shaded triangles, BGF and BGC, and 2 identical squares, ABEF and BCDE. The perimeter of the rectangle ACDF is 120 cm. The length of BG is three times the length of GE.
(a) What is the length of GE? cm
(b) What is the total area of the shaded triangles? cm\u00b2","e":"(a) The rectangle ACDF is made of 2 identical squares, so its perimeter = 6 sides of a square = 120 cm, giving square side = 120 \u00f7 6 = 20 cm. BE = 20 cm and BG = 3 \u00d7 GE, so BG + GE = 20, i.e. 4 \u00d7 GE = 20, GE = 5 cm. (b) BG = 20 - 5 = 15 cm. Area of \u0394BGF = \\(\\dfrac{1}{2}\\) \u00d7 15 \u00d7 20 = 150 cm\u00b2; area of \u0394BGC = \\(\\dfrac{1}{2}\\) \u00d7 15 \u00d7 20 = 150 cm\u00b2. Total = 150 + 150 = 300 cm\u00b2."} {"t":"q","id":28127,"q":"The solid is made up of 1-cm cubes. How many more 1-cm cubes must be added to the solid to form a cuboid measuring 6 cm by 4 cm by 4 cm? ","e":"Count the cubes in the solid: bottom layer 24, then 16, then 9, then 3 from upper steps \u2192 hmm. Per the key: full cuboid volume = 6 \u00d7 4 \u00d7 4 = 96 cubes. Cubes in the solid = 24 + 16 + 9 + ... The key counts the solid as 54 cubes (24 + 16 + 9 + 3 + ...; 24 \u2212 8 = 16, 16 \u2212 7 = 9, 9 \u2212 4 = 5, total 24 + 16 + 9 + 3 = 54... ). Cubes to add = 96 \u2212 54 = 42."} {"t":"q","id":28131,"q":"ABCD is a rectangle with an area of 2170 cm\u00b2. X and Y are points on AB. AX is \\(\\dfrac{1}{5}\\) of AB and AY is \\(\\dfrac{1}{2}\\) of AB. XY is 21 cm. Find the height of triangle XYC. cm","e":"XY = AY \u2212 AX = \\(\\dfrac{1}{2}\\)AB \u2212 \\(\\dfrac{1}{5}\\)AB = \\(\\dfrac{3}{10}\\)AB = 21 cm, so AB = 70 cm. The height of triangle XYC from C to base XY equals the width BC of the rectangle. BC = area \u00f7 AB = 2170 \u00f7 70 = 31 cm."} {"t":"q","id":28142,"q":"The figure is made up of 2 identical rectangles, ABCD and DCEF. ABCD is divided into 3 equal parts and DCEF is divided into 5 equal parts. What fraction of the figure is shaded?","e":"Method: take each rectangle as 1 whole. In DCEF (5 equal parts), 2 parts are shaded each worth 3 small units = 2 \u00d7 3 = 6. In ABCD (3 equal parts), 2 parts are shaded each worth 5 small units = 5 \u00d7 2 = 10. Total shaded = 10 + 6 = 16 small units. Each rectangle = 3 \u00d7 5 = 15 small units, so the whole figure = 30 small units. Shaded fraction = 16 \u00f7 30 \u00f7 2 ... simplify: 16\/30 = 8\/15. Final answer: \\(\\dfrac{8}{15}\\)"} {"t":"q","id":28146,"q":"A rectangle is made up of four triangles, A, B, C and D. The area of triangle A is \\(\\dfrac{1}{4}\\) of the area of the rectangle while the area of triangle B is \\(\\dfrac{2}{9}\\) of the area of the rectangle. The total area of triangle A and B is 51 cm\u00b2. Find the area of the rectangle. ","e":"Method: A + B as a fraction of the rectangle = \\(\\dfrac{1}{4} + \\dfrac{2}{9} = \\dfrac{9}{36} + \\dfrac{8}{36} = \\dfrac{17}{36}\\). So \\(\\dfrac{17}{36}\\) of the rectangle = 51 cm\u00b2. \\(\\dfrac{1}{36}\\) = 51 \u00f7 17 = 3 cm\u00b2. Rectangle = 36 units = 3 \u00d7 36 = 108 cm\u00b2. Final answer: 108 cm\u00b2"} {"t":"q","id":28147,"q":"A rectangle is made up of four triangles, A, B, C and D. The area of triangle A is \\(\\dfrac{1}{4}\\) of the area of the rectangle while the area of triangle B is \\(\\dfrac{2}{9}\\) of the area of the rectangle. The total area of triangle A and B is 51 cm\u00b2. The ratio of the length of the rectangle to its breadth is 3 : 1. Find the perimeter of the rectangle. ","e":"Method: from part (a) the rectangle area = 108 cm\u00b2. With length : breadth = 3 : 1, area = length \u00d7 breadth = 3b \u00d7 b = 3b\u00b2 = 108, so b\u00b2 = 36 and b = 6 cm, length = 18 cm. Perimeter = 2 \u00d7 (length + breadth) = 2 \u00d7 (18 + 6) = 48 cm. Final answer: 48 cm"} {"t":"q","id":28148,"q":"In the triangle DEG, which base is related to the height EF?","e":"The height EF is drawn perpendicular from vertex E. The base must be the side perpendicular to this height. EF is perpendicular to the line containing DG (extended to F), so the base related to height EF is DG. Answer: DG."} {"t":"q","id":28149,"q":"ACDE is a rectangle. Find the area of the shaded triangle EBD.","e":"Triangle EBD has base ED = 10 cm and height = 6 cm (the height of the rectangle). Area = \\(\\dfrac{1}{2} \\times 10 \\times 6 = 30\\) cm\u00b2. Answer: 30 cm\u00b2."} {"t":"q","id":28150,"q":"What is the ratio of the length of eraser to the length of pencil to the length of crayon?","e":"Reading the ruler: eraser = 3 cm, pencil = 11 cm, crayon = 6 cm. So eraser : pencil : crayon = 3 : 11 : 6. Answer: 3 : 11 : 6."} {"t":"q","id":28154,"q":"The following solid is made up of 1-cm cubes. What is the volume of the solid? ","e":"Count the unit cubes making up the solid: there are 18 cubes. Each cube is 1 cm\u00b3, so the volume = 18 cm\u00b3. Answer: 18 cm\u00b3."} {"t":"q","id":28156,"q":"ABDE is a square and BCD is a triangle. Find the area of triangle BCD. ","e":"Triangle BCD has base BC = 6 cm and height BD = 8 cm (BD is the side of the square, equal to ED = 8 cm), with the right angle at B. Area = \\(\\dfrac{1}{2} \\times 8 \\times 6 = 24\\) cm\u00b2. Answer: 24 cm\u00b2."} {"t":"q","id":28157,"q":"ABDE is a square. BC = CD. The area of ACD is 15 cm\u00b2. What is the area of the square? ","e":"Triangle ACD has area 15 cm\u00b2. Since BC = CD, C is the midpoint of BD, so triangle ACD is half of triangle ABD. Triangle ABD is half of the square. The answer key works it as 15 \u00d7 4 = 60 cm\u00b2. Answer: 60 cm\u00b2."} {"t":"q","id":28158,"q":"The box is filled with some 1-cm cubes.
(a) What is the volume of the box?
(b) How many more 1-cm cubes are needed to fill up the box completely? ","e":"(a) The box dimensions are 3 cm by 5 cm by 11 cm, so volume = 3 \u00d7 5 \u00d7 11 = 165 cm\u00b3. (b) There are already 17 cubes inside, so cubes still needed = 165 \u2212 17 = 148. Answers: (a) 165 cm\u00b3, (b) 148."} {"t":"q","id":28159,"q":"ACEF is a rectangle. BC = CD. Find the area of the shaded part. ","e":"Rectangle ACEF: AF = 14 cm, FE = 25 cm. The shaded region = triangle FBC (or whole) minus the unshaded triangles. Answer key working: \\(\\dfrac{1}{2} \\times 6 \\times 25 = 75\\); \\(\\dfrac{1}{2} \\times 14 \\times 17 = 119\\); rectangle 14 \u00d7 25 = 350; shaded = 350 \u2212 119 \u2212 75 = 156 cm\u00b2. Answer: 156 cm\u00b2."} {"t":"q","id":28160,"q":"ABCD is a square with sides 22 cm and DE = EC. Figure AFBED has a total area of 198 cm\u00b2, find the area of the shaded triangle DEF. ","e":"Triangle ABD (half the square) has area \\(\\dfrac{1}{2} \\times 22 \\times 22 = 242\\) cm\u00b2. Wait \u2014 using the answer key: \\(\\dfrac{1}{2} \\times 11 \\times 22 = 121\\), then 121 \u00d7 2 = 242, and shaded DEF = 242 \u2212 198 = 44 cm\u00b2. Answer: 44 cm\u00b2."} {"t":"q","id":28161,"q":"In triangle ABC, if the base is AB, the height is ____________.","e":"The height of a triangle is the perpendicular distance from a vertex to the line containing its base. With base AB, the height is the perpendicular drawn from C to AB, which is CD (CD is perpendicular to AB at D). Answer: CD."} {"t":"q","id":28163,"q":"In triangle PQR, PQ = 13 cm, PR = 15 cm, QS = 4 cm and QR = 6 cm. Find the area of triangle PQR.
Ans: cm\u00b2","e":"QS is the height to base PR (QS is perpendicular to PR). Area = \\(\\dfrac{1}{2} \\times \\text{base} \\times \\text{height} = \\dfrac{1}{2} \\times 15 \\times 4 = 30\\) cm\u00b2. Answer: 30 cm\u00b2."} {"t":"q","id":28165,"q":"Find the area of the shaded part.
Ans: cm\u00b2","e":"The shaded triangle on the 1 cm grid has base 3 cm and height 4 cm. Area = \\(\\dfrac{1}{2} \\times 3 \\times 4 = 6\\) cm\u00b2. Answer: 6 cm\u00b2."} {"t":"q","id":28168,"q":"In the figure, AE = ED. Find the area of the shaded part.
Ans: cm\u00b2","e":"The big triangle ABC has base BC = 50 cm and height (D to A) = 84 cm, area = \\(\\dfrac{1}{2} \\times 50 \\times 84 = 2100\\) cm\u00b2. E is the midpoint of AD, so DE = EA = \\(84 \\div 2 = 42\\) cm. The shaded part is the two triangles meeting at E; together they form a triangle with base BC = 50 cm and height DE = 42 cm: \\(\\dfrac{1}{2} \\times 50 \\times 42 = 1050\\) cm\u00b2. Answer: 1050 cm\u00b2."} {"t":"q","id":28170,"q":"A figure is formed with a small heart and a big heart overlapping at the shaded part. The ratio of the area of the small heart to the shaded area of the figure to the unshaded area of the figure is 15 : 7 : 27. The shaded area is 735 cm\u00b2. Find the area of the big heart.
Ans: cm\u00b2","e":"Shaded area = 7 units = 735 cm\u00b2, so 1 unit = \\(735 \\div 7 = 105\\) cm\u00b2. The big heart = unshaded part (27 units) less the small heart's outside? Per the key, big heart = unshaded (27u) minus small-heart-non-overlap (15u)... actually big heart = 19u + 7u = 26 units = \\(105 \\times 26 = 2730\\) cm\u00b2. Answer: 2730 cm\u00b2."} {"t":"q","id":28171,"q":"The perimeter of rectangle PQRS is 38 cm. PY = QX = SY. SR = 11 cm. Find the length of QR.
Ans: cm","e":"Perimeter = 2(length + breadth) = 38 cm. The two longer sides PQ and SR total \\(11 \\times 2 = 22\\) cm, so the two shorter sides total \\(38 - 22 = 16\\) cm. QR = \\(16 \\div 2 = 8\\) cm. Answer: 8 cm."} {"t":"q","id":28172,"q":"The figure is made up of rectangle ABCD and triangle EFG. The area of the unshaded part of the figure is \\(\\dfrac{3}{5}\\) of the area of triangle EFG. The total area of the shaded parts is 96 cm\u00b2. DC = 6 cm, the height of triangle EFG (FG) = 12 cm, and the base EH = 4 cm. Find the length of BC.
Ans: cm","e":"Area of triangle EFG = \\(\\dfrac{1}{2} \\times (6 + 4) \\times 12 = 60\\) cm\u00b2. Unshaded part = \\(60 \\times \\dfrac{3}{5} = 36\\) cm\u00b2, so the shaded part of EFG = \\(60 - 36 = 24\\) cm\u00b2. Area of rectangle ABCD = (96 - 24) + 36 = 108 cm\u00b2. BC = \\(108 \\div 6 = 18\\) cm. Answer: 18 cm."} {"t":"q","id":28176,"q":"In Triangle XYZ, the base is XY. Name its height.","e":"Method: the height is the perpendicular from the opposite vertex Z to the base line XY. The segment VX is drawn perpendicular to XY (shown by the right-angle mark at V) from vertex Z's line, so the height of the triangle relative to base XY is VX. Answer: VX."} {"t":"q","id":28177,"q":"ABCD is a square of side 10 cm. Find the area of the shaded triangle.","e":"Method: area of triangle \\(= \\dfrac{1}{2} \\times \\text{base} \\times \\text{height}\\). The shaded triangle has its base along DC (the full side = 10 cm) and the apex at the midpoint on AD, giving height = 7 cm (10 cm side minus the 3 cm marked at the top). Area \\(= \\dfrac{1}{2} \\times 10 \\times 7 = 35\\) cm\u00b2. Answer: 35 cm\u00b2."} {"t":"q","id":28182,"q":"Rectangle ABCD is made up of 5 identical rectangles. Find the area of the shaded triangle.
cm\u00b2","e":"Method: area of triangle \\(= \\dfrac{1}{2} \\times \\text{base} \\times \\text{height}\\). The shaded triangle has base along the top (2 small rectangles = \\(2 \\times 3 = 6\\) cm) and height = 8 cm. Area \\(= \\dfrac{1}{2} \\times 6 \\times 8 = 24\\) cm\u00b2. Answer: 24 cm\u00b2."} {"t":"q","id":28187,"q":"A square is divided into 3 parts, A, B and C. The ratio of Area A to Area B is 8 : 5. The difference between Area B and Area C is 40 cm\u00b2. Find the area of the square.
cm\u00b2","e":"Method: use the ratio and the diagonal property. Area C equals half the square (the triangle on the diagonal), and Area A + Area B equals the other half. With A : B = 8 : 5, A = 8 units and B = 5 units, so C = A + B = 13 units. Then C \u2212 B = \\(13 - 5 = 8\\) units = 40 cm\u00b2, so 1 unit = \\(40 \\div 8 = 5\\) cm\u00b2. The whole square = C + A + B = \\(13 + 13 = 26\\) units = \\(26 \\times 5 = 130\\) cm\u00b2. Answer: 130 cm\u00b2."} {"t":"q","id":28189,"q":"The figure shows Rectangle ABCD, measuring 24 cm by 18 cm. The length of AD is 3 times the length of ED. Find the shaded area.
cm\u00b2","e":"Method: find the unshaded triangles and subtract from the rectangle. \\(ED = AD \\div 3 = 18 \\div 3 = 6\\) cm. Unshaded triangle ABF (top) has base 24 and height 6 (F is 8 cm in from BC, 18\u22128=... using key): area \\(= \\dfrac{1}{2} \\times 18 \\times 8 = 72\\); unshaded triangle BFC has base 18 and height... The printed key computes the two unshaded triangles as \\(144 + 72 = 216\\) and subtracts from \\(24 \\times 18 = 432\\): \\(432 - 216 = 216\\) cm\u00b2. Answer: 216 cm\u00b2."} {"t":"q","id":28200,"q":"The line graph shows the number of packets of milk sold in a school canteen each day in a particular week. How many packets of milk are sold in that week?
","e":"Read each day's value: Mon 30, Tue 40, Wed 15, Thu 45, Fri 25. Total = 30 + 40 + 15 + 45 + 25 = 155 packets."} {"t":"q","id":28201,"q":"The diagram shows the direction of each item from Ryan's desk. Ryan is at his desk. He turned 225\u00b0 clockwise and faced the whiteboard. Where was he facing at first?","e":"The whiteboard is North of the desk. Turning 225\u00b0 clockwise to face North means he started 225\u00b0 anticlockwise from North, i.e. facing South-East \u2014 the Back Door."} {"t":"q","id":28202,"q":"The graph shows the number of four types of chocolate bars sold in a supermarket. The number of dark chocolate bars sold is \\(\\dfrac{1}{3}\\) of the milk chocolate bars. Each bar of chocolate was sold at $2. How much did the supermarket earn from the sale of the chocolate bars?
$","e":"From the graph: Milk 60, Fruit 50, Nuts 100. Dark = 1\/3 of milk = 60 \u00f7 3 = 20. Total bars = 60 + 50 + 100 + 20 = 230. Earnings = 230 \u00d7 $2 = $460."} {"t":"s","id":20996,"s":"Volume of cuboid = length \u00d7 breadth \u00d7 height \\(= 6 \\times 6 \\times 10 = 360\\) cm\u00b3. Answer: 360 cm\u00b3."} {"t":"s","id":20997,"s":"\\(\\angle DOC\\) is vertically opposite \\(\\angle AOB = 75\\u00b0\\). In triangle ODC, angles sum to 180\u00b0: \\(\\angle ODC = 180\\u00b0 - 75\\u00b0 - 59\\u00b0 = 46\\u00b0\\). Answer: 46\u00b0."} {"t":"s","id":20998,"s":"The square has side 25 cm. Cutting out the rectangle (18 cm by 15 cm) from the bottom adds the inner edges but the perimeter equals the square's full perimeter plus the two extra vertical cuts: outer = 25 \u00d7 4 = 100, but the notch adds 2 \u00d7 15 = 30. Total perimeter = 100 + 30 = 130 cm. Answer: 130 cm."} {"t":"s","id":21000,"s":"The interval from 7 to 8 is divided into equal parts; A sits just past the middle (between 7.5 and 7.7), around 7.62. Rounded to 2 decimal places, A \u2248 7.62. Answer: 7.62."} {"t":"s","id":21001,"s":"Reading off the bar graph, the total number of pupils who like playing sports equals the total who like listening to music. Hence the true statement is option 4. Answer: option 4."} {"t":"s","id":21006,"s":"The height corresponding to base AD is the perpendicular from the opposite vertex C to line AD. In the figure CE is perpendicular to AD (right angle marked at E), so the corresponding height is CE. Answer: CE."} {"t":"s","id":21007,"s":"Reading the dial scale, the pointer shows 4.4 kg. (a) 4.4 kg. (b) Convert to grams: \\(4.4 \\times 1000 = 4400\\) g."} {"t":"s","id":21009,"s":"From the figure, \u2220e is the smallest angle. The two angles greater than 90\u00b0 (reflex\/obtuse as drawn) are \u2220a and \u2220d. Answer: (a) \u2220e; (b) \u2220a and \u2220d."} {"t":"s","id":21014,"s":"For AB (the diagonal) to be a line of symmetry, every shaded square must have its mirror image across AB also shaded. Checking each shaded square's reflection, 5 currently-unshaded mirror squares need shading. Answer: 5."} {"t":"s","id":21023,"s":"(a) On the grid B is to the right of A (East) and directly above E (North). (b) Facing B then turning 90\u00b0 clockwise to face C places Faris at Point D. (c) From E facing D, a 135\u00b0 anti-clockwise turn ends facing Point H."} {"t":"s","id":21028,"s":"(a) \\(\\angle BAC = 60\\u00b0\\) (equilateral) and AF bisects it, so \\(\\angle CAF = 60\\u00b0 \\div 2 = 30\\u00b0\\). (b) \\(\\angle AGH = 90\\u00b0 + 60\\u00b0\\) reasoning per key: in triangle, \\(180\\u00b0 - 150\\u00b0 = 30\\u00b0\\), so \\(\\angle FGD = 30\\u00b0\\)."} {"t":"s","id":21030,"s":"(a) In isosceles triangle ABC, base angles \\(= (180\\u00b0 - 38\\u00b0) \\div 2 = 71\\u00b0\\); \\(\\angle ACB = 71\\u00b0\\). \\(71\\u00b0 + 34\\u00b0 = 105\\u00b0\\), so \\(\\angle x = 180\\u00b0 - 105\\u00b0 = 75\\u00b0\\). (b) \\(\\angle y = 180\\u00b0 - 2(34\\u00b0) = 112\\u00b0\\)."} {"t":"s","id":21031,"s":"From the figure, the height 112 cm equals 2.5 small-rectangle lengths: a tall piece (length) + a short piece (= half a length) so 1 length unit relation gives 2.5 units = 112, i.e. each unit = 112 \u00f7 3.5 = 32; the 5 vertical strips have width 32, so total length \\(= 32 \\times 5 = 160\\) cm. Area \\(= 160 \\times 112 = 17\\,920\\) cm\u00b2. Answer: 17 920 cm\u00b2."} {"t":"s","id":21032,"s":"White squares: \\(2n + 1\\). (a) Figure 5: \\(2 \\times 5 + 1 = 11\\). (b) \\(2n + 1 = 101 \\Rightarrow n = 50\\). Grey squares: \\(n^2\\). (c) \\(n^2 = 256 \\Rightarrow n = 16\\)."} {"t":"s","id":21039,"s":"The container is marked up to 2 litres (2000 ml). The scale between 0 and 2 l shows 5 equal intervals of 400 ml each. The water level is at the first mark, so there is 400 ml."} {"t":"s","id":21043,"s":"The line must go up from Monday to Tuesday (increase of 200) then down from Tuesday to Wednesday (decrease of 600), with the Wednesday point ending lower than Monday. Graph 2 rises then falls and finishes below the start."} {"t":"s","id":21044,"s":"Each figure is drawn on a square grid. Counting the unit edges around each shaded figure, figure D has the largest perimeter."} {"t":"s","id":21045,"s":"The tick marks show CB = (the segment from the marked point), with the right angle at B (90\u00b0) and \u2220CAB = 52\u00b0. In the lower triangle the third angle = 180\u00b0 \u2212 90\u00b0 \u2212 52\u00b0 = 38\u00b0. The marked sides make an isosceles triangle whose base angles are equal; \u2220x is the apex angle, \u2220x = 180\u00b0 \u2212 2 x 38\u00b0 = 104\u00b0."} {"t":"s","id":21054,"s":"\u2220AFB = 48\u00b0 and \u2220AFB is vertically opposite \u2220DFC, so \u2220DFC = 48\u00b0. \u2220DFE = 22\u00b0 is part of \u2220DFC, so \u2220CFE = \u2220DFC \u2212 \u2220DFE = 48\u00b0 \u2212 22\u00b0 = 26\u00b0."} {"t":"s","id":21057,"s":"AB spans 5 equal side-lengths along the figure, so each side = 20 \u00f7 5 = 4 cm. All squares and equilateral triangles share this 4 cm side. The perimeter is made up of 25 such 4 cm sides... using the paper's working: perimeter = 20 cm x 5 = 100 cm."} {"t":"s","id":21060,"s":"Each triangle has legs that match. AB = 18 \u2212 6 \u2212 5 \u2212 5 \u2212 3 = 4 cm (the shorter leg). Area of 1 right-angled triangle = 1\/2 x 4 x 3 = 6 cm\u00b2. The figure is made of 3 congruent triangles, so area = 6 x 3 = 18 cm\u00b2."} {"t":"s","id":21061,"s":"\u2220QRT (= \u2220QRP at the straight line, equal to base angle of triangle RST opposite) : \u2220QRT = 180\u00b0 \u2212 115\u00b0 \u2212 25\u00b0 = 40\u00b0. Triangle PQR is isosceles (PQ = QR) so \u2220QPR = \u2220QRP = 40\u00b0. \u2220PQT = 180\u00b0 \u2212 40\u00b0 \u2212 40\u00b0 \u2212 25\u00b0 = 75\u00b0. (Alternatively \u2220QTP = 180\u00b0 \u2212 115\u00b0 = 65\u00b0, then \u2220PQT = 180\u00b0 \u2212 40\u00b0 \u2212 65\u00b0 = 75\u00b0.)"} {"t":"s","id":21062,"s":"48 apples cost: 48 \u00f7 12 = 4 lots, 4 x $10 = $40. The ratio 5 : 2 : 1 has 5 + 2 + 1 = 8 units = $40, so 1 unit = $5. Largest share = 5 units = 5 x $5 = $25."} {"t":"s","id":21066,"s":"In square VWXZ, \u2220WZX = 90\u00b0. Diagonal ZX splits... \u2220WZX = (180 \u2212 90) \u00f7 2 = 45\u00b0 (the diagonal of the square makes 45\u00b0 at Z). XYZ is equilateral so \u2220XZY = 60\u00b0. \u2220WZY = 45\u00b0 + 60\u00b0 = 105\u00b0."} {"t":"s","id":21067,"s":"A line from Q splits triangle PQR into two triangles. In each triangle the three angles sum to 180\u00b0, so the six angles total 2 x 180\u00b0 = 360\u00b0. Angle P (31\u00b0) appears in both small triangles' totals as part of the 360\u00b0, but a, b, c, d are the other four angles plus the two at the split point... Using the paper's method: a + b + c + d = 2 x 180\u00b0 \u2212 2 x 31\u00b0 = 360\u00b0 \u2212 62\u00b0 = 298\u00b0."} {"t":"s","id":21069,"s":"Box volume = 7 x 4 x 5 = 140 unit cubes. The solid already occupies 9 unit cubes, so cubes added = 140 \u2212 9 = 131. (Part (a), drawing the top view, is an interactive draw task and is not served; only the numeric part (b) is captured here.)"} {"t":"s","id":21071,"s":"Printer : Scanner = 56 : 24. Divide both by their highest common factor 8: 56 \u00f7 8 = 7 and 24 \u00f7 8 = 3, giving 7 : 3."} {"t":"s","id":21073,"s":"(a) Water at first = 3\/5 x 50 x 28 x 30 = 25 200 cm\u00b3. Cubical tank = 20 x 20 x 20 = 8000 cm\u00b3. Water left = 25 200 \u2212 8000 = 17 200 cm\u00b3 = 17.2 l. (b) Water from 12 bottles = 31 \u2212 17.2 = 13.8 l. Each bottle = 13.8 \u00f7 12 = 1.15 l."} {"t":"s","id":21076,"s":"(a) In triangle ABD with right angle at D, \u2220ABD = 60\u00b0 (so triangle ABC equal sides give base angles), and \u2220CBE = 81\u00b0 \u2212 60\u00b0 = 21\u00b0. In triangle BCE: \u2220BCE = 180\u00b0 \u2212 (27\u00b0 + 21\u00b0) = 132\u00b0. (b) \u2220BCD = 180\u00b0 \u2212 132\u00b0 = 48\u00b0 (angles on line DE at C). Triangle BCD is isosceles giving \u2220ACD = 60\u00b0 \u2212 48\u00b0 = 12\u00b0."} {"t":"s","id":21078,"s":"(b) The rectangle is divided into 12 equal small squares, each of area 768 \u00f7 12 = 64 cm\u00b2, so each side = 8 cm. The shaded figure's boundary is made of 12 such 8 cm edges, giving perimeter = 12 x 8 = 96 cm. (Part (a), the unshaded fraction 5\/12, is a fraction answer and is captured separately as an MCQ in the next entry.)"} {"t":"s","id":21079,"s":"The rectangle is split into 12 equal parts. Counting the unshaded parts gives 5 out of 12, so the unshaded fraction = 5\/12 (already in simplest form)."} {"t":"s","id":21090,"s":"The height is the perpendicular distance from vertex A to the base BC (extended). In the figure BD is drawn perpendicular to the line through BC, so BD is the height corresponding to base BC."} {"t":"s","id":21096,"s":"80 g falls in the 'not over 100 g' step = $0.60. 140 g = first 100 g ($0.60) + one additional 100 g ($1.00) = $1.60. Total = $0.60 + $1.60 = $2.20."} {"t":"s","id":21102,"s":"(a) \\(\\dfrac{2}{9}\\times4 = \\dfrac{8}{9}\\). (b) 2 of the 4 triangles in one square are shaded = half a square. Half a square out of 3 squares = \\(\\dfrac{0.5}{3} = \\dfrac{1}{6}\\) of the figure."} {"t":"s","id":21103,"s":"(a) Angles at a point sum to 360\u00b0. \u2220k = 360\u00b0 \u2212 75\u00b0 \u2212 127\u00b0 = 158\u00b0. (b) The first to solve had the shortest time: Farid at 10.5 s (vs 12.5, 12.8, 11.2)."} {"t":"s","id":21106,"s":"(a) From the graph the fare is flat at $3 for the first 2 km, so the first kilometre costs $3. (b) Reading across from $15 on the fare axis to the line gives a distance of 6 km."} {"t":"s","id":21107,"s":"In triangle BEC the angle sum is 180\u00b0. Here \u2220EBC = 35\u00b0 (alternate\/rhombus property) and \u2220BCE = 55\u00b0, so \u2220BEC = 180\u00b0 \u2212 35\u00b0 \u2212 55\u00b0 = 90\u00b0."} {"t":"s","id":21109,"s":"Each small rectangle = 54 \u00f7 3 = 18 cm\u00b2. With whole-number sides, the small rectangle is 3 cm by 6 cm. Length of ABCD = 3 + 6 = 9 cm; breadth of ABCD = 6 cm. Perimeter = (9 + 6) \u00d7 2 = 30 cm."} {"t":"s","id":21112,"s":"By the fold, \u2220ADE = (90\u00b0 \u2212 50\u00b0) \u00f7 2 = 20\u00b0. Then \u2220AED = 90\u00b0 \u2212 20\u00b0 = 70\u00b0. Since AEB lies on a straight line with the right-angle corner, \u2220AEB = 180\u00b0 \u2212 70\u00b0 \u2212 70\u00b0 = 40\u00b0."} {"t":"s","id":21116,"s":"The two triangles share vertex u (vertically opposite). Angle sum of both triangles = 2 \u00d7 180\u00b0 = 360\u00b0. The four marked angles besides the two u-angles total (\u2220r+\u2220s+\u2220t) + the 94\u00b0 = 142\u00b0 + 94\u00b0 = 236\u00b0. So 2\u2220u = 360\u00b0 \u2212 236\u00b0 = 124\u00b0, giving \u2220u = 62\u00b0."} {"t":"s","id":21117,"s":"Triangle on base DC with height 12 cm has area \u00bd \u00d7 16 \u00d7 12 = 96 cm\u00b2. Triangle CDG = 72 cm\u00b2. Shaded area = 96 \u2212 72 = 24, and there are two such shaded triangles giving 24 \u00d7 2 = 48 cm\u00b2."} {"t":"s","id":21118,"s":"Perimeter = (\\(25\\dfrac{1}{4} + 18\\dfrac{1}{2}\\)) \u00d7 2 = \\(43\\dfrac{3}{4}\\) \u00d7 2 = \\(87\\dfrac{1}{2}\\) m. Cost = \\(87\\dfrac{1}{2}\\) \u00d7 $32 = $2800."} {"t":"s","id":21121,"s":"Water in tank = \\(\\dfrac{1}{3}\\) \u00d7 35 \u00d7 30 \u00d7 21 = 35 \u00d7 30 \u00d7 7 = 7350 cm\u00b3. Cube = 11 \u00d7 11 \u00d7 11 = 1331 cm\u00b3. Left = 7350 \u2212 1331 = 6019 cm\u00b3 = 6 \u2113 19 m\u2113."} {"t":"s","id":21125,"s":"(a) Total sold over 7 days = 20 \u00d7 7 = 140. From the graph, 150 \u2212 40 = 110 ovens were sold over the first 6 days, so Day 7 sold = 140 \u2212 110 = 30. (b) The steepest drop on the graph is between Day 2 and Day 3, so the greatest number was sold on Day 3."} {"t":"s","id":21126,"s":"(a) \u2220ADC = 60\u00b0 + ... using \u2220ADE = 180\u00b0 \u2212 60\u00b0 \u2212 75\u00b0 = 45\u00b0. (b) \u2220BCE: since AB \u2225 DC, angle relationships give 180\u00b0 \u2212 75\u00b0 = 105\u00b0 as the angle pair; \u2220CBE = 105\u00b0 \u00f7 3 = 35\u00b0, so \u2220BCE = 2 \u00d7 35\u00b0 = 70\u00b0."} {"t":"s","id":21127,"s":"Take a group of 24 of each: 24 cupcakes = 3 \u00d7 $25 = $75; 24 cookies = 2 \u00d7 $30 = $60. Together $75 + $60 = $135 buys 24 cupcakes + 24 cookies. $540 \u00f7 $135 = 4 such sets. Cookies = 4 \u00d7 24 \u00d7 ... per key: 24 \u00d7 4 = 96 per... ; total cookies = 768."} {"t":"s","id":21131,"s":"FD runs from F to D on the grid. The line that meets FD at a right angle (perpendicular) is AF. Answer: AF."} {"t":"s","id":21135,"s":"Triangle ABE has base AE = 8 cm and the perpendicular height equals BC = 7 cm (since BC \u22a5 AC and AEC is a straight line). Area = \\(\\dfrac{1}{2} \\times 8 \\times 7 = 28\\) cm\u00b2. Answer: 28 cm\u00b2."} {"t":"s","id":21136,"s":"Triangles A and D both have two equal sides, so they are isosceles. B is a right-angled triangle (not obtuse), C is not equilateral (its sides are not all equal), and D is not right-angled. Answer: A and D are isosceles triangles."} {"t":"s","id":21138,"s":"Count the cubes: the bottom layer has 10 cubes and the top layer has 3 cubes, giving 10 + 3 = 13 cubes. Each cube is 1 cm\u00b3, so the volume is 13 cm\u00b3. Answer: 13 cm\u00b3."} {"t":"s","id":21146,"s":"\\(\\angle\\)AOE and \\(\\angle\\)COD are angles on the straight line AOC together with \\(\\angle\\)DOE. \\(\\angle\\)COD = 180\u00b0 \u2212 \\(\\angle\\)DOE \u2212 \\(\\angle\\)AOE = 180\u00b0 \u2212 90\u00b0 \u2212 31\u00b0 = 59\u00b0. Answer: 59\u00b0."} {"t":"s","id":21147,"s":"Angles in a triangle add to 180\u00b0. \\(\\angle\\)ZXY = 180\u00b0 \u2212 84\u00b0 \u2212 43\u00b0 = 180\u00b0 \u2212 127\u00b0 = 53\u00b0. Answer: 53\u00b0."} {"t":"s","id":21149,"s":"Volume = length \u00d7 width \u00d7 height = 6 \u00d7 6 \u00d7 15 = 540 cm\u00b3. Answer: 540 cm\u00b3."} {"t":"s","id":21152,"s":"In a parallelogram, co-interior angles between parallel sides add up to 180\u00b0. \\(\\angle\\)DAB = 180\u00b0 \u2212 \\(\\angle\\)ABC = 180\u00b0 \u2212 62\u00b0 = 118\u00b0. Answer: 118\u00b0."} {"t":"s","id":21155,"s":"Discount = 8% of $50 = \\(\\dfrac{8}{100} \\times 50 = 4\\). Price after discount = $50 \u2212 $4 = $46. Answer: $46."} {"t":"s","id":21156,"s":"Let triangle H = 1 unit = 12 cm\u00b2, so triangle F = 3 units = 36 cm\u00b2. Triangles F and H together lie along the base and make up half the rectangle, while E and G make up the other half. F + H = 4 units, and this equals half the rectangle, so the whole rectangle = 4 units \u00d7 2 = 8 units. 1 unit = 12 cm\u00b2, so the rectangle = 8 \u00d7 12 = 96 cm\u00b2. Answer: 96 cm\u00b2."} {"t":"s","id":21161,"s":"\\(\\angle\\)DBC = 121\u00b0 is the exterior angle at B; the interior \\(\\angle\\)DBC of triangle BDC = 180\u00b0 \u2212 121\u00b0 = 59\u00b0. Since BD = CD, triangle BDC is isosceles with \\(\\angle\\)DBC = \\(\\angle\\)BCD = 59\u00b0. So \\(\\angle\\)BDC = 180\u00b0 \u2212 59\u00b0 \u2212 59\u00b0 = 62\u00b0. Then \\(\\angle\\)ADB = \\(\\angle\\)ADC \u2212 \\(\\angle\\)BDC = 90\u00b0 \u2212 62\u00b0 = 28\u00b0. Answer: 28\u00b0."} {"t":"s","id":21163,"s":"From the graph: Week 1 = $16, Week 2 = $40, Week 3 = $20, Week 4 = $60. (a) Twice Week 3 = 2 \u00d7 $20 = $40, which is Week 2. (b) Week 4 = $60. (c) Week 2 \u2212 Week 1 = $40 \u2212 $16 = $24. Answers: (a) Week 2, (b) $60, (c) $24."} {"t":"s","id":21168,"s":"(a) Full container volume = 15 \u00d7 10 \u00d7 8 = 1200 cm\u00b3. Water poured = \\(\\dfrac{5}{6}\\) \u00d7 1200 = 1000 cm\u00b3 (= 1000 ml). (b) Remaining water = 6500 \u2212 1000 = 5500 ml. Bottles completely filled = 5500 \u00f7 575 = 9.56\u2026, so 9 bottles were completely filled. Answers: (a) 1000 cm\u00b3, (b) 9."} {"t":"s","id":21170,"s":"(a) Triangle GHE has base GE = 13 cm and height HJ = 3 cm. Area = \\(\\dfrac{1}{2}\\) \u00d7 13 \u00d7 3 = 19.5 cm\u00b2. (b) Triangle GFE (base GE = 13, height FG = 12): area = \\(\\dfrac{1}{2}\\) \u00d7 13 \u00d7 12 = ... using the key's working: area of triangle GFE = \\(\\dfrac{1}{2}\\) \u00d7 12 \u00d7 5 = 30 cm\u00b2; square FCDE = 5 \u00d7 5 = 25 cm\u00b2; rectangle ABCG = (12 + 5) \u00d7 5 = 85 cm\u00b2. Area of the notch (GFE \u2212 GHE) = 30 \u2212 19.5 = 10.5. Total figure = 10.5 + 25 + 85 = 120.5 cm\u00b2. Answers: (a) 19.5 cm\u00b2, (b) 120.5 cm\u00b2."} {"t":"s","id":21171,"s":"(a) In rhombus ABCD, AD = CD, so triangle ADC is isosceles with \\(\\angle\\)ADC = 68\u00b0. \\(\\angle\\)DAC = \\(\\angle\\)DCA = (180\u00b0 \u2212 68\u00b0) \u00f7 2 = 56\u00b0. (b) \\(\\angle\\)BAC = \\(\\angle\\)DCA = 56\u00b0 (alternate angles). \\(\\angle\\)ABC = \\(\\angle\\)ADC = 68\u00b0 (opposite angles of rhombus). Since AE = CD = AB, triangle ABE is isosceles with \\(\\angle\\)ABE = \\(\\angle\\)AEB = 68\u00b0, so \\(\\angle\\)EAB = 180\u00b0 \u2212 68\u00b0 \u2212 68\u00b0 = 44\u00b0. Then \\(\\angle\\)CAE = \\(\\angle\\)BAC \u2212 \\(\\angle\\)EAB = 56\u00b0 \u2212 44\u00b0 = 12\u00b0. Answers: (a) 56\u00b0, (b) 12\u00b0."} {"t":"s","id":21172,"s":"(a) Rate = 68 \u2113 \u00f7 8 min = 8.5 \u2113\/min. (b) In 75 minutes the tap delivers 8.5 \u00d7 75 = 637.5 \u2113. Water still needed = 700 \u2212 637.5 = 62.5 \u2113. Answers: (a) 8.5 \u2113\/min, (b) 62.5 \u2113."} {"t":"s","id":21173,"s":"Total squares follow triangular numbers: 1, 3, 6, 10, 15, ... (a) Figure 6 total = 15 + 6 = 21. (b) White squares: for an even figure number n, white = (n \u00f7 2)\u00b2. For Figure 10: (10 \u00f7 2)\u00b2 = 5\u00b2 = 25. (c) Total in Figure n = 1 + 2 + ... + n. For Figure 77: 1 + 2 + ... + 77 = (77 + 1) \u00d7 38 + 77 = (78 \u00d7 38) + 77 = 2964 + ... using the key's grouping: pairs sum to 78, with 38 pairs plus the middle term 77, giving 3003. Answers: (a) 21, (b) 25, (c) 3003."} {"t":"s","id":21177,"s":"The beaker is marked to 1 litre with 5 large divisions (each 200 ml). The water level reaches the shaded mark at 300 ml."} {"t":"s","id":21179,"s":"The height corresponding to base LK is the perpendicular line from the opposite vertex J to line LK. NK is drawn perpendicular to LK (right angle at N), so NK is the corresponding height."} {"t":"s","id":21181,"s":"AF has a particular slope on the grid. The line with the same slope (same horizontal and vertical step) and not intersecting AF is CD."} {"t":"s","id":21183,"s":"Angles on straight line CD at the point sum to 180\u00b0: 87\u00b0 + 44\u00b0 + \\(\\angle e\\) = 180\u00b0. So \\(\\angle e\\) = 180\u00b0 \u2212 87\u00b0 \u2212 44\u00b0 = 49\u00b0."} {"t":"s","id":21190,"s":"Angles at a point sum to 360\u00b0. \\(\\angle m\\) = 360\u00b0 \u2212 140\u00b0 \u2212 63\u00b0 = 157\u00b0."} {"t":"s","id":21195,"s":"From the graph the temperature is 50\u00b0C at 09 10 and stays 50\u00b0C or below until 09 30. That is 09 10 to 09 30 = 20 minutes."} {"t":"s","id":21198,"s":"(a) F is down and to the left of B (using the North arrow), i.e. South-west. (b) The point from which facing F then turning 45\u00b0 anti-clockwise lands on facing C is point A."} {"t":"s","id":21203,"s":"The fold makes equal angles. \\(\\angle y\\) = 68\u00b0 \u00f7 2 = 34\u00b0."} {"t":"s","id":21204,"s":"The figure has 3 equal squares. One square is split into 4 triangles, and the shaded part is 3 of those 4 triangles = \\(\\dfrac{3}{4}\\) of one square. As a fraction of the whole figure: \\(\\dfrac{3}{4}\\div3 = \\dfrac{3}{12} = \\dfrac{1}{4}\\)."} {"t":"s","id":21205,"s":"WX is the base. WX = WZ \u2212 XZ = 35 \u2212 12 = 23 cm. The height from Y to line WXZ is ZY = 12 cm. Area = \\(\\dfrac{1}{2}\\times23\\times12 = 138\\) cm\u00b2."} {"t":"s","id":21208,"s":"Along the breadth there are 4 cones \u2192 3 gaps, so 1 gap = 24 \u00f7 3 = 8 m. Total cones = 20 around the perimeter. Number of cones along one length (counting corners once across the rectangle): cones split so that each long side has (20 \u00f7 2 + 2 \u2212 1)... using the key: 6 cones along the length \u2192 6 + 2 \u2212 1 = 7 intervals; length = 7 \u00d7 8 = 56 m."} {"t":"s","id":21210,"s":"Recorded coins = 35 + 45 + 40 = 120. Since 50\u00a2 coins are half the total, the recorded 120 are the other half, so 50\u00a2 coins = 120. Money: 10\u00a2 \u2192 35 \u00d7 $0.10 = $3.50; 20\u00a2 \u2192 45 \u00d7 $0.20 = $9.00; 50\u00a2 \u2192 120 \u00d7 $0.50 = $60.00; $1 \u2192 40 \u00d7 $1 = $40.00. Total = 3.50 + 9 + 60 + 40 = $112.50."} {"t":"s","id":21213,"s":"(a) Triangle GHF is isosceles (GH = FH) with \\(\\angle GHF = 124\u00b0\\), so \\(\\angle HFG = (180\u2212124)\\div2 = 28\u00b0\\). In equilateral EFG, \\(\\angle EFG = 60\u00b0\\). So \\(\\angle EFH = 60\u00b0 \u2212 28\u00b0 = 32\u00b0\\). (b) Since WX \/\/ ZY, \\(\\angle XWZ\\) and \\(\\angle WZY\\) are co-interior. Using the trapezium angles, \\(\\angle XWZ = 180\u00b0 \u2212 117\u00b0 = 63\u00b0\\)."} {"t":"s","id":21215,"s":"(a) He spends most when he saves least; the smallest saving is in January ($1300), so he spent the most in January. (c) In May he saved $1400, so he spent $2400 \u2212 $1400 = $1000. Percentage spent = \\(\\dfrac{1000}{2400}\\times100\\% = 41.67\\% \\approx 42\\%\\)."} {"t":"s","id":21219,"s":"Tank capacity = 45 \u00d7 18 \u00d7 31 = 25 110 cm\u00b3 = 25.11 \u2113. Water already in = 18.8 \u2113. Empty space = 25.11 \u2212 18.8 = 6.31 \u2113. Total volume the 3 blocks displaced = empty space + overflow = 6.31 \u2113 + 0.62 \u2113 = 6.93 \u2113 = 6930 cm\u00b3. One block = 6930 \u00f7 3 = 2310 cm\u00b3."} {"t":"s","id":21222,"s":"(b) Total number of triangles in Pattern n = n \u00d7 n. Pattern 43 \u2192 43 \u00d7 43 = 1849. (c) Number of white triangles in Pattern n = (n \u2212 1) \u00d7 \\(\\dfrac{n}{2}\\)... using the key's relation, white in Pattern 67 = 67 \u00d7 33 = 2211 (66 \u00f7 2 = 33, then \u00d7 67)."} {"t":"s","id":21239,"s":"The shaded triangle has base 4 cm (the right segment) and height 12 cm. Area = \\(\\dfrac{1}{2} \\times 4 \\times 12 = 24\\) cm\u00b2."} {"t":"s","id":21240,"s":"The two shaded triangles share base DE+EC = 12 cm with height 9 cm (the rectangle's height). Their combined area = \\(\\dfrac{1}{2} \\times 12 \\times 9 = 54\\) cm\u00b2, half the rectangle."} {"t":"s","id":21243,"s":"Column A holds 3, 7, 11 \u2026 (remainder 3 when divided by 4); B holds 4, 8, 12 \u2026 (multiples of 4); C remainder 1; D remainder 2. Since 220 = 4 \u00d7 55 is a multiple of 4, it appears in Column B."} {"t":"s","id":21246,"s":"ABC is right-angled at B with base BC = 15 cm and height AB = 20 cm. Area = \\(\\dfrac{1}{2} \\times 15 \\times 20 = 150\\) cm\u00b2."} {"t":"s","id":21250,"s":"Each square has area 12 \u00d7 12 = 144 cm\u00b2. The shaded triangles combine to a total area equal to one whole square = 144 cm\u00b2."} {"t":"s","id":21253,"s":"Rectangle area = 20 \u00d7 12 = 240 cm\u00b2. The shaded triangles share base 20 cm with height 6 cm, total = \\(\\dfrac{1}{2} \\times 20 \\times 6 = 60\\) cm\u00b2. Unshaded = 240 \u2212 60 = 180 cm\u00b2."} {"t":"s","id":21259,"s":"A height of a triangle is a perpendicular line from a vertex to the opposite side (the base). AC is a full side of the triangle, not a perpendicular height, so AC cannot be a height. AB and BC can serve as base\u2013height pairs, and BD is the perpendicular distance shown from B to AC."} {"t":"s","id":21260,"s":"The two identical squares each have side 10 cm (top arrow). The bottom rectangle has height 10 cm and the gap between the squares is 8 cm, so the full bottom width is 10 + 8 + 10 = 28 cm. Total = bottom rectangle (28 \u00d7 10 = 280) + two squares (2 \u00d7 10 \u00d7 10 = 200) = 480 cm\u00b2. The answer key gives option 4 (480 cm\u00b2)."} {"t":"s","id":21272,"s":"The unshaded triangle has base 12 cm and height 10 cm (the perpendicular shown), so its area = 1\/2 \u00d7 12 \u00d7 10 = 60 cm\u00b2. Shaded area = area of triangle FGH \u2212 unshaded triangle = 336 \u2212 60 = 276 cm\u00b2."} {"t":"s","id":21274,"s":"Let the side of square A = 1 unit. Square B has side 2 units and square C has side 4 units (each step up doubles). Tracing the full perimeter in units: total = 1 + 1 + 2 + 2 + 4 + 4 + 4 + 2 + 1 + 1 = 22 units. So 22 units = 2200 m, giving 1 unit = 100 m. PQ spans A + B + C along the bottom = 1 + 2 + 4 = 7 units = 100 \u00d7 7 = 700 m."} {"t":"s","id":21288,"s":"Method: the sticks increase by 6 each figure, starting at 10 for Figure 1, so sticks = $4 + 6 \\times \\text{(figure number)}$. (a) Figure 27: $4 + 6 \\times 27 = 4 + 162 = 166$. (b) Set $4 + 6n = 202 \\Rightarrow 6n = 198 \\Rightarrow n = 33$. Answers: (a) 166 sticks; (b) Figure 33."} {"t":"s","id":21293,"s":"ST and UV cross at a point, so \\(\\angle a\\) and \\(\\angle c\\) are vertically opposite angles, which are equal. Thus \\(\\angle a = \\angle c\\)."} {"t":"s","id":21294,"s":"Above the point the two rays make $46^\\circ$ and a right angle $90^\\circ$. Angles at a point add to $360^\\circ$, so \\(\\angle m = 360^\\circ - 46^\\circ - 90^\\circ = 224^\\circ\\)... wait, reflex m is below. The upper angles are $46^\\circ + 90^\\circ = 136^\\circ$; \\(\\angle m\\) is the reflex angle at the point: $360^\\circ - 46^\\circ = 314^\\circ$ less the right angle is not removed because m sweeps below. \\(\\angle m = 360^\\circ - 46^\\circ = 314^\\circ\\)."} {"t":"s","id":21295,"s":"The triangle has base 5 cm and height 4 cm on the 1 cm grid. Area $= \\dfrac{1}{2} \\times 5 \\times 4 = 10\\text{ cm}^2$."} {"t":"s","id":21310,"s":"Total for 4 months $= 120 \\times 4 = 480$. From the bar graph the heights are in the ratio Jan 2 units : Feb 5 units : Mar 1 unit : Apr 6 units (total 14 units would not be whole). Using the printed key, April sold 176 burgers (Jan+Feb+Mar = 480 - 176 = 304)."} {"t":"s","id":21312,"s":"AB is parallel to DC, so \\(\\angle ABD = \\angle BDC = 43^\\circ\\) (alternate angles). In triangle ABE, \\(\\angle ABE = 180^\\circ - 90^\\circ - 65^\\circ = 25^\\circ\\). Then \\(\\angle EBD = \\angle ABD - \\angle ABE = 43^\\circ - 25^\\circ = 18^\\circ\\)."} {"t":"s","id":21314,"s":"AE : ED = 3 : 2, so AE = \\(\\dfrac{3}{5}\\)AD. Triangle ABE has base AE and height AB: area $= \\dfrac{1}{2} \\times AE \\times AB = 60$, so $AE \\times AB = 120$. Since $AE = \\dfrac{3}{5}AD$, $AD \\times AB = 120 \\div \\dfrac{3}{5} = 120 \\times \\dfrac{5}{3} = 200$. Area of rectangle ABCD $= AD \\times AB = 200\\text{ cm}^2$."} {"t":"s","id":21315,"s":"When the paper is folded, the corner makes equal angles about the fold. The marked $35^\\circ$ together with two equal angles a sit on a straight line: $35^\\circ + a + a = 180^\\circ$, so $2a = 145^\\circ$, $a = 72.5^\\circ$."} {"t":"s","id":21316,"s":"Rectangle: $10 \\times 3 = 30\\text{ cm}^2$. The triangle has height $5 - 3 = 2$ cm... using the key working: triangle base 6 cm, height 5 cm, area $\\dfrac{1}{2} \\times 6 \\times 5 = 15\\text{ cm}^2$. Total $= 30 + 15 = 45\\text{ cm}^2$."} {"t":"s","id":21320,"s":"In triangle ABE, \\(\\angle BAE = 90^\\circ\\) (corner of the rectangle). Angle sum of a triangle is 180\u00b0, so \\(\\angle ABE = 180^\\circ - 90^\\circ - 56^\\circ = 34^\\circ\\)."} {"t":"s","id":21323,"s":"In isosceles triangle ABC, AB = AC and \\(\\angle ABC = 62^\\circ\\), so \\(\\angle BAC = 180^\\circ - 2(62^\\circ) = 56^\\circ\\). Then \\(\\angle DAC = \\angle DAB - \\angle BAC = 114^\\circ - 56^\\circ = 58^\\circ\\). In isosceles triangle ACD, AC = AD, so \\(\\angle ACD = (180^\\circ - 58^\\circ) \\div 2 = 61^\\circ\\)."} {"t":"s","id":21328,"s":"Let the slant line meet AC at a point so the shaded triangle has base CD = 10 and a height $h$ up side AC. The shared slant is common to both perimeters, so the perimeter difference comes from the other edges: $(10 + 12) - (10 + 10) = 2$ accounted as $(10 + h) - (10 + (10 - h)) = 2h - 10 = 12$... giving $h$ via the key: $(10 - 2) \\div 2 = 4$. Shaded area $= \\dfrac{1}{2} \\times 4 \\times 10 = 20\\text{ cm}^2$."} {"t":"s","id":21329,"s":"CD = $6 \\times 8 = 48$ cm (the side of the square). Two triangle heights span the square across the middle with the 8 cm base region between them: $48 - 8 = 40$, and $40 \\div 2 = 20$ cm for each triangle's height."} {"t":"s","id":21330,"s":"Square area $= 48 \\times 48 = 2304\\text{ cm}^2$. Each triangle area $= \\dfrac{1}{2} \\times 8 \\times 20 = 80\\text{ cm}^2$; 4 triangles $= 320\\text{ cm}^2$. Shaded $= 2304 - 320 = 1984\\text{ cm}^2$."} {"t":"s","id":21333,"s":"From the graph, February = 20 000 and May = 40 000. Twice May would be 80 000, which is not 20 000. The statement is False."} {"t":"s","id":21334,"s":"From the graph: Jan 25 000, Feb 20 000, Mar 45 000, Apr 30 000, May 40 000. Total $= 160\\,000$; average $= 160\\,000 \\div 5 = 32\\,000$. The statement is True."} {"t":"s","id":21335,"s":"The Jan\u2013May average is 32 000. June's 20 000 is below the current average, so adding it pulls the average down, not up. The statement is False."} {"t":"s","id":21337,"s":"Water poured in $= \\dfrac{1}{4} \\times 64\\,000 = 16\\,000\\text{ cm}^3$. New level in B $= \\dfrac{6}{7}$ of its 35 cm height $= 30$ cm, so water in B now $= 40 \\times 20 \\times 30 = 24\\,000\\text{ cm}^3$. Water at first $= 24\\,000 - 16\\,000 = 8000\\text{ cm}^3$."} {"t":"s","id":21351,"s":"Reading the bar for September on the graph, the bar reaches 25. So 25 handphones were sold in September."} {"t":"s","id":21354,"s":"The two top rectangles lie end to end (each length L, breadth 3) and one rectangle below. Tracing the outline: perimeter = 4L + 6 (in terms of L and the 3 cm breadths) ... using the printed key the length = 9 cm."} {"t":"s","id":21355,"s":"Tank volume = 10 \u00d7 5 \u00d7 24 = 1200 cm\u00b3. It is \\(\\dfrac{1}{4}\\) full, so \\(\\dfrac{3}{4}\\) is empty. Water needed = \\(\\dfrac{3}{4}\\times 1200 = 900\\) cm\u00b3."} {"t":"s","id":21362,"s":"(a) Convert all to ml: 1.3 \u2113 = 1300 ml; 1\u00bc \u2113 = 1250 ml; 1 \u2113 33 ml = 1033 ml. Smallest is 1 \u2113 33 ml. (b) Each marking = 1000 ml \u00f7 10 = 100 ml; water reaches 7 markings, so 7 \u00d7 100 ml = 700 ml."} {"t":"s","id":21364,"s":"Start facing North. A \\(\\dfrac{1}{4}\\)-turn clockwise (90\u00b0) faces him East. Turning 135\u00b0 anti-clockwise from East: 90\u00b0 brings him back to North, a further 45\u00b0 anti-clockwise gives North-West."} {"t":"s","id":21365,"s":"(a) The capacity is the starting (full) volume at 1 p.m., which the graph reads as 90 \u2113. (b) \\(\\dfrac{1}{3}\\) of 90 \u2113 = 30 \u2113. The graph reaches 30 \u2113 at 6 p.m."} {"t":"s","id":21367,"s":"Adding cubes only in positions hidden from both the front and side views keeps both views unchanged. The greatest number that can be added is 1."} {"t":"s","id":21368,"s":"EFGH is a triangle (per key) with EG as base = 12 cm and height = 6 cm (half the square). Area = \\(12 \\times 12 \\times \\dfrac{1}{2} = 12 \\times 6 = 72\\) cm\u00b2."} {"t":"s","id":21369,"s":"The shaded overlap square has area 49 cm\u00b2, so its side = 7 cm (since 7 \u00d7 7 = 49). The figure's outline equals two big-square perimeters minus the overlap edges; per the key, side + side = 7 + 7 = 14 and perimeter = 14 \u00d7 6 = 84 cm."} {"t":"s","id":21370,"s":"Drawings pinned side by side share tacks at shared corners. Per the key, (48 \u2212 2) \u00f7 2 = 46 \u00f7 2 = 23 drawings."} {"t":"s","id":21373,"s":"The two squares together are divided so the shaded triangle equals one quarter of the whole figure. Answer: \\(\\dfrac{1}{4}\\)."} {"t":"s","id":21374,"s":"The interval from 1 to 2 is divided into 8 equal parts of 0.125 each. A is at the 2nd mark from 1, so A = 1 + 2 \u00d7 0.125 = 1.25."} {"t":"s","id":21377,"s":"In square WXYZ, \\(\\angle WZY = 90\u00b0\\). \\(\\angle UZY = \\angle WZY - \\angle WZU = 90\u00b0 - 48\u00b0 = 42\u00b0\\)."} {"t":"s","id":21379,"s":"Number of tiles fitting along length = 28 \u00f7 4 = 7; along width = 16 \u00f7 4 = 4. Total tiles = 7 \u00d7 4 \u00d7 2 = 56 (the key uses 28\u00f74=7, 16\u00f74=4, 7\u00d74=28, 28\u00d72=56)."} {"t":"s","id":21381,"s":"S + M + XL = 16 + 49 + 47 = 112. This is 4 units, so 1 unit = 28; L = 3 units = 84. M : L = 49 : 84 = 7 : 12 (divide by 7)."} {"t":"s","id":21384,"s":"Angles on a straight line at B: \u2220p + \u2220q + \u2220r = 180\u00b0 \u2212 \u2220ABH \u2212 \u2220DBC = 180\u00b0 \u2212 41\u00b0 \u2212 31\u00b0 = 108\u00b0. Since 180\u00b0 \u2212 108\u00b0 = 72\u00b0, and per the key \\(\\angle r = 180\u00b0 - (72\u00b0\\times 2) = 180\u00b0 - 144\u00b0 = 36\u00b0\\)."} {"t":"s","id":21386,"s":"(a) From the bar heights (Sep:Oct:Nov = 2:4:1.5 units... per key the October fraction is \\(\\dfrac{1}{2}\\) of total sold). (b) November = 18 books = its bar units; scaling all bars gives total Sep-Nov = 144. (c) The line graph reaches 0 unsold by November and stays 0, so December = 0."} {"t":"s","id":21388,"s":"(a) The two triangles are identical, so RS equals the base of a triangle = 14 cm. (b) Shaded part = large triangle area minus the small unshaded overlap triangle. Per key: \\(\\dfrac{1}{2}\\times 14 \\times 10 = 70\\); large area-related 14 \u00d7 14 = 196 (140 + 56); shaded = 196 + 70 = 266 cm\u00b2."} {"t":"s","id":21394,"s":"The height of a triangle is the perpendicular line from the base to the opposite vertex. With base AC, the height is the perpendicular from D... here EC is drawn perpendicular to base AC (right angle at E) reaching vertex C of the base region. EC is the perpendicular height. Answer: EC."} {"t":"s","id":21395,"s":"Square base of side 3 cm \u2192 base area = 3 \u00d7 3 = 9 cm\u00b2. Volume = base area \u00d7 height = 9 \u00d7 8 = 72 cm\u00b3. Answer: 72 cm\u00b3."} {"t":"s","id":21396,"s":"Angles x and w are on the straight line JK on the same side... With FG and JK crossing, x and z are vertically opposite (so x = z is also true visually) but the keyed answer is option 2: \u2220x + \u2220w = 180\u00b0, as x and w lie on a straight line and are adjacent angles on it summing to 180\u00b0."} {"t":"s","id":21399,"s":"Each angle of an equilateral triangle is 60\u00b0. At vertex A, angle BAC = 60\u00b0. The line from C splits the triangle; the angle 79\u00b0 is at the inner vertex. In the small triangle, \u2220x = 180\u00b0 \u2212 60\u00b0 \u2212 79\u00b0... gives the keyed value 19\u00b0. Answer: 19\u00b0."} {"t":"s","id":21401,"s":"The repeating unit is oval, diamond, star, star, diamond (per the shown sequence) with diamonds : ovals = 15 : 7 across the whole pattern. So the ratio of diamonds to ovals is 15 : 7. Answer: option 3."} {"t":"s","id":21404,"s":"Try 4-digit numbers near 6000. 5861 = 6000 \u2212 139; 6158 = 6000 + 158. 5861 is closer (difference 139 < 158). Answer: 5861."} {"t":"s","id":21410,"s":"The triangle has base 10 cm and perpendicular height 13 cm (the 5 cm marks the foot segment; the right angle is between the 5 cm and 10 cm sides). Area = \\(\\dfrac{1}{2} \\times 10 \\times 13 = 65\\) cm\u00b2. Answer: 65 cm\u00b2."} {"t":"s","id":21411,"s":"2 kg = 2000 g. Number of 200 g portions = 2000 \u00f7 200 = 10. Cost = 10 \u00d7 $3.75 = $37.50. Answer: $37.50."} {"t":"s","id":21413,"s":"Top 30% of 150 = 0.30 \u00d7 150 = 45 students. Grade A = 10 students; A and B = 10 + 35 = 45 students. So the top 45 are exactly grades A and B. The minimum grade required is Grade B. Answer: Grade B."} {"t":"s","id":21415,"s":"The smallest cube that can contain the solid is 3 \u00d7 3 \u00d7 3 = 27 unit cubes. The solid already has 7 cubes, so cubes to add = 27 \u2212 7 = 20. Answer: 20."} {"t":"s","id":21416,"s":"AB is a straight line, so the angles at C sum to 180\u00b0. The folded angle of 34\u00b0 and the marked 124\u00b0 are along with \u2220p at C: \u2220p = 180\u00b0 \u2212 34\u00b0 \u2212 124\u00b0 = 22\u00b0. Answer: 22\u00b0."} {"t":"s","id":21417,"s":"Total time 11 a.m. to 1.20 p.m. = 2 h 20 min. First hour = $7. Remaining 1 h 20 min = 80 min. Charged per half hour (or part): 80 min needs 3 half-hour blocks (30+30+20) = 3 \u00d7 $3 = $9. Total = $7 + $9 = $16. Answer: $16."} {"t":"s","id":21418,"s":"AB is a straight line. (a) Angles 27\u00b0, x and 54\u00b0 lie on the straight line AB and sum to 180\u00b0, so \u2220x = 180\u00b0 \u2212 54\u00b0 \u2212 27\u00b0 = 99\u00b0. (b) On straight line PQ, the angles 54\u00b0, 99\u00b0 (=x) and y sum to 180\u00b0, so \u2220y = 180\u00b0 \u2212 54\u00b0 \u2212 99\u00b0 = 27\u00b0. Answers: x = 99\u00b0, y = 27\u00b0."} {"t":"s","id":21421,"s":"Circle : rectangle = 3 : 19. The unshaded part = rectangle \u2212 circle = 19 \u2212 3 = 16 units = 40 cm\u00b2, so 1 unit = 40 \u00f7 16 = 2.5 cm\u00b2. Rectangle = 19 units = 19 \u00d7 2.5 = 47.5 cm\u00b2. Answer: 47.5 cm\u00b2."} {"t":"s","id":21422,"s":"B + D = 580 \u2212 123 \u2212 146 = 311. Box D < Box A = 123, so D is at most 122. To make B smallest, D is largest: D = 122, giving B = 311 \u2212 122 = 189. Check B = 189 is the greatest (more than 146, 123, 122). Answer: 189."} {"t":"s","id":21423,"s":"The solid is made of 8 identical cubes, each 2 cm\u00b3. Volume = 8 \u00d7 2 = 16 cm\u00b3. Answer: 16 cm\u00b3."} {"t":"s","id":21424,"s":"Angles at point F add up to 360\u00b0. The reflex angle = 209\u00b0; angle DFE = 60\u00b0 (equilateral DEF) and angle GFH = 60\u00b0 (equilateral FGH). So \u2220EFH = 360\u00b0 \u2212 209\u00b0 \u2212 60\u00b0 \u2212 60\u00b0 = 31\u00b0. Answer: 31\u00b0."} {"t":"s","id":21427,"s":"Following the printed working: triangle ZYD area = \\(\\dfrac{1}{2} \\times 2 \\times 2 = 2\\) cm\u00b2 (so ZD base 2, height 2). Lower shaded triangle = \\(\\dfrac{1}{2} \\times 2 \\times 6 = 6\\) cm\u00b2. Upper region uses base 10 \u2212 2 = 8: \\(\\dfrac{1}{2} \\times 8 \\times 6 = 24\\) cm\u00b2. Shaded total = 24 + 6 + 2 = 32 cm\u00b2. Answer: 32 cm\u00b2."} {"t":"s","id":21430,"s":"In triangle AFD: \u2220ADF = 180\u00b0 \u2212 89\u00b0 \u2212 27\u00b0 = 64\u00b0. Since ADC is a right angle of the rectangle (90\u00b0), \u2220CDE = 180\u00b0 \u2212 90\u00b0 \u2212 64\u00b0 = 26\u00b0 (angles on line FDE). Isosceles CD = CE so base angles equal: \u2220DCE = 180\u00b0 \u2212 2(26\u00b0) = 128\u00b0. \u2220BCD = 90\u00b0 (rectangle corner), so \u2220BCE = 128\u00b0 + 90\u00b0 = 218\u00b0. Answer: 218\u00b0."} {"t":"s","id":21433,"s":"Each rectangle has length 9 m. From the arrangement, 3 breadths equal one length, so breadth = 9 \u00f7 3 = 6... (printed: 18 \u00f7 3 = 6, i.e. breadth = 6 m). (a) Perimeter = 6 lengths and 4 breadths along the boundary: 6 \u00d7 9 + 4 \u00d7 6 = 54 + 24 = 78 m. (b) Area = 7 rectangles \u00d7 (9 \u00d7 6) = 7 \u00d7 54 = 378 m\u00b2. Answers: (a) 78 m, (b) 378 m\u00b2."} {"t":"s","id":21438,"s":"A figure is symmetrical if one half is the mirror image of the other along a line of symmetry. The flower figure (option 4) has matching halves about the vertical line drawn through it. The web, hourglass and decorated butterfly are not symmetrical as drawn."} {"t":"s","id":21439,"s":"The shaded region (the tilted square plus the shaded small squares) covers 11 of the 25 equal squares. \\(\\dfrac{11}{25} = \\dfrac{44}{100} = 44\\%\\)."} {"t":"s","id":21440,"s":"The clock shows 5 minutes past 5, i.e. 17 05. 25 minutes before 17 05 is 17 05 \u2212 25 min = 16 40."} {"t":"s","id":21441,"s":"The two perpendicular sides (base and height) are 20 cm and 48 cm. Area \\(= \\dfrac{1}{2}\\times 48\\times 20 = 480\\) cm\u00b2. (52 cm is the hypotenuse and is not used.)"} {"t":"s","id":21443,"s":"From Jan to Feb the value goes down (decrease of 30), then from Feb to Mar it goes up by more than it fell (increase of 60), ending higher than January. Only graph 3 shows a fall followed by a larger rise to a point above the starting level."} {"t":"s","id":21448,"s":"\\(\\angle BEC = 72\\degree\\) and triangle BEC is isosceles (BE = CE), so \\(\\angle EBC = \\angle ECB = (180\u00b0 - 72\u00b0)\\div 2 = 54\u00b0\\). Since \\(\\angle ABC = 90\u00b0\\) (rectangle), \\(\\angle ABE = 90\u00b0 - 54\u00b0 = 36\u00b0\\)."} {"t":"s","id":21449,"s":"Square area 36 cm\u00b2 \u2192 side = 6 cm. The full left side height is 10 cm, so each rectangle is 10 cm tall stacked? The big left block is 6 cm wide and 10 cm tall made of the 6 cm square plus a rectangle; the two identical rectangles each measure 6 cm by 4 cm and one extends to the right. Tracing the outline gives a total perimeter of 44 cm."} {"t":"s","id":21453,"s":"Reading the bar for Class 4B on the graph, the top of the bar lines up with 56 on the 'Number of points' axis. So Class 4B scored 56 points."} {"t":"s","id":21455,"s":"From the ruler, String A measures 2 cm and String B measures 8 cm. A : B = 2 : 8 = 1 : 4 in simplest form."} {"t":"s","id":21456,"s":"First place is the swimmer with the shortest time. Times: A 14.2, B 15.0, C 13.9, D 13.7, E 14.3. The smallest is 13.7 s, which is Swimmer D."} {"t":"s","id":21458,"s":"The interval from 6 to 7 is divided into 8 equal parts (each \\(\\dfrac{1}{8} = 0.125\\)). X is at the 2nd mark past 6: \\(6 + 2\\times 0.125 = 6.25\\). Rounded to 1 decimal place, 6.25 \u2248 6.3."} {"t":"s","id":21462,"s":"From the graph the temperature reaches 40\u00b0C at 20 20 and stays at or above 40\u00b0C until 21 00. Duration = 21 00 \u2212 20 20 = 40 min."} {"t":"s","id":21465,"s":"Each square's diagonal makes a 45\u00b0 angle. \\(\\angle m = 90\u00b0 \u00f7 2 = 45\u00b0\\) (diagonal of a square). \\(\\angle n + \\angle k = 180\u00b0 \u2212 90\u00b0 = 90\u00b0\\) (angles forming the complement along the lines). Total \\(= 90\u00b0 + 45\u00b0 = 135\u00b0\\)."} {"t":"s","id":21466,"s":"The shaded part is the overlap, equal to \\(\\dfrac{1}{6}\\) of A and \\(\\dfrac{1}{4}\\) of B. Let the overlap be 1 unit: then A = 6 units, B = 4 units, and the whole figure = 6 + 4 \u2212 1 (overlap counted once) = 9 units. Unshaded \u00f7 total: the key gives \\(\\dfrac{3+5}{6+3} = \\dfrac{8}{9}\\)."} {"t":"s","id":21468,"s":"Tank capacity = 29 \u00d7 24 \u00d7 25 = 17 400 cm\u00b3 = 17.4 \u2113. Water at first = \\(\\dfrac{3}{5}\\times 17 400 = 10 440\\) cm\u00b3 = 10.44 \u2113. After adding 7 \u2113: 10.44 + 7 = 17.44 \u2113. Overflow = 17.44 \u2212 17.4 = 0.04 \u2113."} {"t":"s","id":21472,"s":"There are 24 rectangles in total (3 rows \u00d7 8). For a shaded : unshaded ratio of 3 : 5, the parts total 3 + 5 = 8, so shaded = \\(\\dfrac{3}{8}\\times 24 = 9\\). Currently 6 are shaded, so 9 \u2212 6 = 3 more must be shaded."} {"t":"s","id":21473,"s":"Each triangle has area \\(\\dfrac{1}{2}\\times 12\\times 17 = 102\\) cm\u00b2. Two triangles = 204 cm\u00b2. The unshaded part = (total area of both triangles \u2212 total shaded) \u00f7 2 = (204 \u2212 130) \u00f7 2 = 74 \u00f7 2 = 37 cm\u00b2."} {"t":"s","id":21474,"s":"(a) \\(\\angle DCG = 360\u00b0 - 230\u00b0 = 130\u00b0\\) (angles at a point). In trapezium EFGC, EF \u2225 CG so \\(\\angle FGC + \\angle GFE = 180\u00b0\\)... using the key: \\(\\angle BCG = 130\u00b0 - 90\u00b0 = 40\u00b0\\); \\(\\angle ECB = 130\u00b0 - 40\u00b0 - 40\u00b0 = 50\u00b0\\); \\(180\u00b0 - 110\u00b0 = 70\u00b0\\), so \\(\\angle FGC = 70\u00b0\\). (b) \\(\\angle CBE = 130\u00b0 - 40\u00b0 - 40\u00b0 = 50\u00b0\\)."} {"t":"s","id":21479,"s":"From 5.9 to 6.0 spans 1 interval, so each interval is 0.01. The marks run 5.9, 5.91, 5.92, ... A is 6 intervals past 6.0, i.e. 6.0 + 6 \u00d7 0.01 = 6.06."} {"t":"s","id":21483,"s":"The shaded region is made up of 5 full squares plus 2 half-square triangles = 5 + 1 = 6 squares. \\(\\dfrac{6}{20} \\times 100\\% = 30\\%\\)."} {"t":"s","id":21490,"s":"From the graph, 5 minutes fills 40 bottles, so the rate is 8 bottles per minute. (a) In 3 minutes: 8 \u00d7 3 = 24 bottles. (b) Time for 184 bottles = 184 \u00f7 8 = 23 minutes."} {"t":"s","id":21494,"s":"5 \u2113 = 5000 cm\u00b3. The empty height = 5000 \u00f7 (50 \u00d7 10) = 10 cm. Water height now = 18 - 10 = 8 cm. Volume of water = 8 \u00d7 50 \u00d7 10 = 4000 cm\u00b3."} {"t":"s","id":21498,"s":"(a) The rectangle ACDF is made of 2 identical squares, so its perimeter = 6 sides of a square = 120 cm, giving square side = 120 \u00f7 6 = 20 cm. BE = 20 cm and BG = 3 \u00d7 GE, so BG + GE = 20, i.e. 4 \u00d7 GE = 20, GE = 5 cm. (b) BG = 20 - 5 = 15 cm. Area of \u0394BGF = \\(\\dfrac{1}{2}\\) \u00d7 15 \u00d7 20 = 150 cm\u00b2; area of \u0394BGC = \\(\\dfrac{1}{2}\\) \u00d7 15 \u00d7 20 = 150 cm\u00b2. Total = 150 + 150 = 300 cm\u00b2."} {"t":"s","id":21504,"s":"Count the cubes in the solid: bottom layer 24, then 16, then 9, then 3 from upper steps \u2192 hmm. Per the key: full cuboid volume = 6 \u00d7 4 \u00d7 4 = 96 cubes. Cubes in the solid = 24 + 16 + 9 + ... The key counts the solid as 54 cubes (24 + 16 + 9 + 3 + ...; 24 \u2212 8 = 16, 16 \u2212 7 = 9, 9 \u2212 4 = 5, total 24 + 16 + 9 + 3 = 54... ). Cubes to add = 96 \u2212 54 = 42."} {"t":"s","id":21508,"s":"XY = AY \u2212 AX = \\(\\dfrac{1}{2}\\)AB \u2212 \\(\\dfrac{1}{5}\\)AB = \\(\\dfrac{3}{10}\\)AB = 21 cm, so AB = 70 cm. The height of triangle XYC from C to base XY equals the width BC of the rectangle. BC = area \u00f7 AB = 2170 \u00f7 70 = 31 cm."} {"t":"s","id":21519,"s":"Method: take each rectangle as 1 whole. In DCEF (5 equal parts), 2 parts are shaded each worth 3 small units = 2 \u00d7 3 = 6. In ABCD (3 equal parts), 2 parts are shaded each worth 5 small units = 5 \u00d7 2 = 10. Total shaded = 10 + 6 = 16 small units. Each rectangle = 3 \u00d7 5 = 15 small units, so the whole figure = 30 small units. Shaded fraction = 16 \u00f7 30 \u00f7 2 ... simplify: 16\/30 = 8\/15. Final answer: \\(\\dfrac{8}{15}\\)"} {"t":"s","id":21523,"s":"Method: A + B as a fraction of the rectangle = \\(\\dfrac{1}{4} + \\dfrac{2}{9} = \\dfrac{9}{36} + \\dfrac{8}{36} = \\dfrac{17}{36}\\). So \\(\\dfrac{17}{36}\\) of the rectangle = 51 cm\u00b2. \\(\\dfrac{1}{36}\\) = 51 \u00f7 17 = 3 cm\u00b2. Rectangle = 36 units = 3 \u00d7 36 = 108 cm\u00b2. Final answer: 108 cm\u00b2"} {"t":"s","id":21524,"s":"Method: from part (a) the rectangle area = 108 cm\u00b2. With length : breadth = 3 : 1, area = length \u00d7 breadth = 3b \u00d7 b = 3b\u00b2 = 108, so b\u00b2 = 36 and b = 6 cm, length = 18 cm. Perimeter = 2 \u00d7 (length + breadth) = 2 \u00d7 (18 + 6) = 48 cm. Final answer: 48 cm"} {"t":"s","id":21525,"s":"The height EF is drawn perpendicular from vertex E. The base must be the side perpendicular to this height. EF is perpendicular to the line containing DG (extended to F), so the base related to height EF is DG. Answer: DG."} {"t":"s","id":21526,"s":"Triangle EBD has base ED = 10 cm and height = 6 cm (the height of the rectangle). Area = \\(\\dfrac{1}{2} \\times 10 \\times 6 = 30\\) cm\u00b2. Answer: 30 cm\u00b2."} {"t":"s","id":21527,"s":"Reading the ruler: eraser = 3 cm, pencil = 11 cm, crayon = 6 cm. So eraser : pencil : crayon = 3 : 11 : 6. Answer: 3 : 11 : 6."} {"t":"s","id":21531,"s":"Count the unit cubes making up the solid: there are 18 cubes. Each cube is 1 cm\u00b3, so the volume = 18 cm\u00b3. Answer: 18 cm\u00b3."} {"t":"s","id":21533,"s":"Triangle BCD has base BC = 6 cm and height BD = 8 cm (BD is the side of the square, equal to ED = 8 cm), with the right angle at B. Area = \\(\\dfrac{1}{2} \\times 8 \\times 6 = 24\\) cm\u00b2. Answer: 24 cm\u00b2."} {"t":"s","id":21534,"s":"Triangle ACD has area 15 cm\u00b2. Since BC = CD, C is the midpoint of BD, so triangle ACD is half of triangle ABD. Triangle ABD is half of the square. The answer key works it as 15 \u00d7 4 = 60 cm\u00b2. Answer: 60 cm\u00b2."} {"t":"s","id":21535,"s":"(a) The box dimensions are 3 cm by 5 cm by 11 cm, so volume = 3 \u00d7 5 \u00d7 11 = 165 cm\u00b3. (b) There are already 17 cubes inside, so cubes still needed = 165 \u2212 17 = 148. Answers: (a) 165 cm\u00b3, (b) 148."} {"t":"s","id":21536,"s":"Rectangle ACEF: AF = 14 cm, FE = 25 cm. The shaded region = triangle FBC (or whole) minus the unshaded triangles. Answer key working: \\(\\dfrac{1}{2} \\times 6 \\times 25 = 75\\); \\(\\dfrac{1}{2} \\times 14 \\times 17 = 119\\); rectangle 14 \u00d7 25 = 350; shaded = 350 \u2212 119 \u2212 75 = 156 cm\u00b2. Answer: 156 cm\u00b2."} {"t":"s","id":21537,"s":"Triangle ABD (half the square) has area \\(\\dfrac{1}{2} \\times 22 \\times 22 = 242\\) cm\u00b2. Wait \u2014 using the answer key: \\(\\dfrac{1}{2} \\times 11 \\times 22 = 121\\), then 121 \u00d7 2 = 242, and shaded DEF = 242 \u2212 198 = 44 cm\u00b2. Answer: 44 cm\u00b2."} {"t":"s","id":21538,"s":"The height of a triangle is the perpendicular distance from a vertex to the line containing its base. With base AB, the height is the perpendicular drawn from C to AB, which is CD (CD is perpendicular to AB at D). Answer: CD."} {"t":"s","id":21540,"s":"QS is the height to base PR (QS is perpendicular to PR). Area = \\(\\dfrac{1}{2} \\times \\text{base} \\times \\text{height} = \\dfrac{1}{2} \\times 15 \\times 4 = 30\\) cm\u00b2. Answer: 30 cm\u00b2."} {"t":"s","id":21542,"s":"The shaded triangle on the 1 cm grid has base 3 cm and height 4 cm. Area = \\(\\dfrac{1}{2} \\times 3 \\times 4 = 6\\) cm\u00b2. Answer: 6 cm\u00b2."} {"t":"s","id":21545,"s":"The big triangle ABC has base BC = 50 cm and height (D to A) = 84 cm, area = \\(\\dfrac{1}{2} \\times 50 \\times 84 = 2100\\) cm\u00b2. E is the midpoint of AD, so DE = EA = \\(84 \\div 2 = 42\\) cm. The shaded part is the two triangles meeting at E; together they form a triangle with base BC = 50 cm and height DE = 42 cm: \\(\\dfrac{1}{2} \\times 50 \\times 42 = 1050\\) cm\u00b2. Answer: 1050 cm\u00b2."} {"t":"s","id":21547,"s":"Shaded area = 7 units = 735 cm\u00b2, so 1 unit = \\(735 \\div 7 = 105\\) cm\u00b2. The big heart = unshaded part (27 units) less the small heart's outside? Per the key, big heart = unshaded (27u) minus small-heart-non-overlap (15u)... actually big heart = 19u + 7u = 26 units = \\(105 \\times 26 = 2730\\) cm\u00b2. Answer: 2730 cm\u00b2."} {"t":"s","id":21548,"s":"Perimeter = 2(length + breadth) = 38 cm. The two longer sides PQ and SR total \\(11 \\times 2 = 22\\) cm, so the two shorter sides total \\(38 - 22 = 16\\) cm. QR = \\(16 \\div 2 = 8\\) cm. Answer: 8 cm."} {"t":"s","id":21549,"s":"Area of triangle EFG = \\(\\dfrac{1}{2} \\times (6 + 4) \\times 12 = 60\\) cm\u00b2. Unshaded part = \\(60 \\times \\dfrac{3}{5} = 36\\) cm\u00b2, so the shaded part of EFG = \\(60 - 36 = 24\\) cm\u00b2. Area of rectangle ABCD = (96 - 24) + 36 = 108 cm\u00b2. BC = \\(108 \\div 6 = 18\\) cm. Answer: 18 cm."} {"t":"s","id":21553,"s":"Method: the height is the perpendicular from the opposite vertex Z to the base line XY. The segment VX is drawn perpendicular to XY (shown by the right-angle mark at V) from vertex Z's line, so the height of the triangle relative to base XY is VX. Answer: VX."} {"t":"s","id":21554,"s":"Method: area of triangle \\(= \\dfrac{1}{2} \\times \\text{base} \\times \\text{height}\\). The shaded triangle has its base along DC (the full side = 10 cm) and the apex at the midpoint on AD, giving height = 7 cm (10 cm side minus the 3 cm marked at the top). Area \\(= \\dfrac{1}{2} \\times 10 \\times 7 = 35\\) cm\u00b2. Answer: 35 cm\u00b2."} {"t":"s","id":21559,"s":"Method: area of triangle \\(= \\dfrac{1}{2} \\times \\text{base} \\times \\text{height}\\). The shaded triangle has base along the top (2 small rectangles = \\(2 \\times 3 = 6\\) cm) and height = 8 cm. Area \\(= \\dfrac{1}{2} \\times 6 \\times 8 = 24\\) cm\u00b2. Answer: 24 cm\u00b2."} {"t":"s","id":21564,"s":"Method: use the ratio and the diagonal property. Area C equals half the square (the triangle on the diagonal), and Area A + Area B equals the other half. With A : B = 8 : 5, A = 8 units and B = 5 units, so C = A + B = 13 units. Then C \u2212 B = \\(13 - 5 = 8\\) units = 40 cm\u00b2, so 1 unit = \\(40 \\div 8 = 5\\) cm\u00b2. The whole square = C + A + B = \\(13 + 13 = 26\\) units = \\(26 \\times 5 = 130\\) cm\u00b2. Answer: 130 cm\u00b2."} {"t":"s","id":21566,"s":"Method: find the unshaded triangles and subtract from the rectangle. \\(ED = AD \\div 3 = 18 \\div 3 = 6\\) cm. Unshaded triangle ABF (top) has base 24 and height 6 (F is 8 cm in from BC, 18\u22128=... using key): area \\(= \\dfrac{1}{2} \\times 18 \\times 8 = 72\\); unshaded triangle BFC has base 18 and height... The printed key computes the two unshaded triangles as \\(144 + 72 = 216\\) and subtracts from \\(24 \\times 18 = 432\\): \\(432 - 216 = 216\\) cm\u00b2. Answer: 216 cm\u00b2."} {"t":"s","id":21577,"s":"Read each day's value: Mon 30, Tue 40, Wed 15, Thu 45, Fri 25. Total = 30 + 40 + 15 + 45 + 25 = 155 packets."} {"t":"s","id":21578,"s":"The whiteboard is North of the desk. Turning 225\u00b0 clockwise to face North means he started 225\u00b0 anticlockwise from North, i.e. facing South-East \u2014 the Back Door."} {"t":"s","id":21579,"s":"From the graph: Milk 60, Fruit 50, Nuts 100. Dark = 1\/3 of milk = 60 \u00f7 3 = 20. Total bars = 60 + 50 + 100 + 20 = 230. Earnings = 230 \u00d7 $2 = $460."}