The table shows the charges for renting a bicycle. Monday to Friday: 9 a.m. to 5 p.m. is $5 per hour and 5 p.m. to 8 p.m. is $7 per hour. Saturday and Sunday: 9 a.m. to 8 p.m. is $8 per hour.
(a) John rented a bicycle from 10 a.m. to 1 p.m. on Sunday. How much did he have to pay? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) On Tuesday, Ken rented a bicycle and returned it at 7 p.m. He paid a total of $29. What was the earliest time he rented the bicycle? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Sunday is $8 per hour. From 10 a.m. to 1 p.m. is 3 hours, so cost = $8 × 3 = $24. (b) Tuesday returning at 7 p.m.: from 5 p.m. to 7 p.m. is 2 hours at $7 = $14. Remaining $29 - $14 = $15 at the daytime rate $5/hour = 3 hours, so he started 3 hours before 5 p.m. = 2 p.m.


Method: divide. 48 \u00f7 300 = 0.16. Final answer: 0.16.


There were 800 people at a musical. 63% of the people were children while the rest were adults. How many adults were at the musical?


The average of seven numbers is 26. The first number is 14. Find the average of the other six numbers.

Method: total minus first, then average. Total of seven = 26 \u00d7 7 = 182. Total of other six = 182 - 14 = 168. Average of six = 168 \u00f7 6 = 28. Final answer: 28.


The table shows the rental charges for a pair of roller skates.
First 2 hours: $16
After the second hour: $6 per \(\dfrac{1}{2}\) hour or less
Max rented a pair of roller skates from 8.30 a.m. to 11.45 a.m. on the same day. How much did he pay?

Method: split the duration. Total time 8.30 a.m. to 11.45 a.m. = 3 h 15 min. First 2 h cost $16. Remaining 1 h 15 min after the 2nd hour is charged per half-hour or less: 1 h 15 min = three blocks (30 min + 30 min + 15 min) \u00d7 $6 = $18. Total = $16 + $18 = $34. Final answer: $34.


Jack's family consumed a total of 48.5 kg of rice in November and December. His family consumed 5.1 kg more rice in December than in November. How many kilograms of rice did Jack's family consume in December? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: subtract the difference, halve, then add back. November + December = 48.5 kg. Remove the extra 5.1 kg: 48.5 - 5.1 = 43.4 kg (twice November). November = 43.4 \u00f7 2 = 21.7 kg. December = 21.7 + 5.1 = 26.8 kg. Final answer: 26.8 kg.


An airline company had 500 seats. 350 seats were occupied. What percentage of the seats were occupied? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: write the part as a percentage. Percentage occupied = \(\dfrac{350}{500}\) \u00d7 100% = 70%. Final answer: 70%.


The table shows the number of books read by four girls during the holidays.
Abigail: 8
Bernadette: 16
Caroline: 0
Denise: 24
What was the average number of books read by each girl? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: total \u00f7 number of girls. Total books = 8 + 16 + 0 + 24 = 48. Average = 48 \u00f7 4 = 12. Final answer: 12.


Peter can run 3 km in 20 minutes. At this rate, how many kilometres can he run in 120 minutes? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: find how many 20-min intervals, then multiply. 120 \u00f7 20 = 6 intervals. Distance = 3 \u00d7 6 = 18 km. Final answer: 18 km.


The price of a laptop before GST was $1200. What was the price of the laptop including 7% GST? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: find the GST amount, then add it on. GST = 7% of $1200 = 0.07 \u00d7 1200 = $84. Price including GST = 1200 + 84 = $1284. Final answer: $1284.


Mr Fernandez bought some chickens from America, Canada and Brazil. 45% of the chickens were from America, 35% of the chickens were from Brazil and the rest were from Canada. There were 20 fewer chickens from Brazil than America.
(a) What percentage of the chickens were from Canada? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) Find the total number of chickens from Canada and Brazil. <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Method: (a) Canada % = 100% - 45% - 35% = 20%. (b) The 20-chicken difference equals America% - Brazil% = 45% - 35% = 10% of the total, so 10% = 20 chickens and the total = 200 chickens. Canada + Brazil = 100% - 45% = 55% of total = 0.55 \u00d7 200 = 110 chickens. Final answers: (a) 20% (b) 110.


Car A had 7800 ml of petrol. Car B had 10.3 l of petrol. When the same amount of petrol was used in each car, the amount of petrol left in Car B was six times of that left in Car A. How much petrol was used in each car? Leave your answer in litres. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: convert to litres, use the 6-times relationship. Car A = 7800 ml = 7.8 l, Car B = 10.3 l. The difference in petrol stays the same as petrol used is equal: 10.3 - 7.8 = 2.5 l. After using petrol, B's amount is 6 times A's, so the 2.5 l difference equals 6 - 1 = 5 equal parts; 1 part (petrol left in A) = 2.5 \u00f7 5 = 0.5 l. Petrol used = 7.8 - 0.5 = 7.3 l. Final answer: 7.3 l.


The total cost of a big sticker and a small sticker is $1.20. John paid $10.40 for 9 big stickers and 8 small stickers. Luke bought 9 small stickers. How much did Luke pay for 9 small stickers? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: compare John's purchase with 9 sticker-pairs. 9 big + 9 small = 9 \u00d7 $1.20 = $10.80. John bought 9 big + 8 small for $10.40, which is one small sticker fewer. So 1 small sticker = 10.80 - 10.40 = $0.40. 9 small stickers = 0.40 \u00d7 9 = $3.60. Final answer: $3.60.


Which one of the following is two hundred and seven thousand and eleven in numerals?

Two hundred and seven thousand = 207 000; plus eleven = 207 011. Answer: 207 011.


In the number 56.79, which digit is in the tenths place?

In 56.79 the first digit after the decimal point is the tenths place: 7. Answer: 7.


Colina drew some shapes: 3 circles, 5 hearts and 2 diamonds. What is the ratio of the number of diamonds to the total number of shapes?

Total shapes = 3 + 5 + 2 = 10. Diamonds = 2. Ratio 2 : 10 = 1 : 5. Answer: 1 : 5.


What is the possible mass of a Primary 5B Mathematics Workbook?

A workbook weighs a few hundred grams; 400 g is reasonable (4000 g = 4 kg is too heavy, 40 g and 4 g too light). Answer: 400 g.


There are 130 white pins and 70 black pins. What percentage of the pins are black pins?


Ping Chen has some gold and silver beads. The ratio of the number of gold beads to the number of silver beads is 5 : 3. She has 120 more gold beads than silver beads. How many beads does she have altogether?

Difference 5 - 3 = 2 units = 120, so 1 unit = 60. Total units = 5 + 3 = 8, so total = 8 x 60 = 480. Answer: 480.


The first 11 letters of a pattern are A B C D A B C D A B C ... What is the 88th letter?

The pattern repeats every 4 letters (A B C D). 88 ÷ 4 = 22 with remainder 0, so the 88th letter is the last of a block = D. Answer: D.


Mrs Salleh baked some chocolate, mint and walnut cookies. \(\dfrac{1}{3}\) of the cookies baked were chocolate cookies. \(\dfrac{1}{6}\) of the remaining cookies were mint cookies and the rest were walnut cookies. What fraction of the cookies baked were walnut cookies?

Remaining after chocolate = \(1-\dfrac{1}{3}=\dfrac{2}{3}\). Mint = \(\dfrac{1}{6}\times\dfrac{2}{3}=\dfrac{2}{18}=\dfrac{1}{9}\). Walnut = remaining minus mint = \(\dfrac{2}{3}-\dfrac{1}{9}=\dfrac{6}{9}-\dfrac{1}{9}=\dfrac{5}{9}\). Answer: \(\dfrac{5}{9}\).


This year, Indra is 8 years old. Last year, Indra's father was five times of Indra's age. How old is Indra's father this year?

Last year Indra was 8 - 1 = 7. Father last year = 5 x 7 = 35. This year father = 35 + 1 = 36. Answer: 36.


Aisha had 60 balloons at first. She used half of the total number of balloons for a party. Her mother then bought her another 12 balloons. Aisha gave all the balloons she had in the end equally to 6 friends. Which expression gives the number of balloons each friend received?

Half of 60 = 60 ÷ 2 = 30 left, then +12 = 42, then shared among 6: 42 ÷ 6 = 7. The expression must compute (60 ÷ 2 + 12) first, then ÷ 6: (60 ÷ 2 + 12) ÷ 6. Answer: option (3).


Round 15 483 to the nearest hundred. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The tens digit of 15 483 is 8 (>= 5), so round up the hundreds: 15 483 -> 15 500. Answer: 15 500.


Find the value of \(\dfrac{6}{10}\times\dfrac{4}{3}\). Give your answer as a fraction in the simplest form.


Find the value of 1.59 × 90. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


What is the missing number in the box?
3 : 13 : 9
= 18 : <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> : 54

The ratio is multiplied by 6 (3 x 6 = 18; 9 x 6 = 54). So the missing term = 13 x 6 = 78. Answer: 78.


Fill in the blank.<br>1048 cm = <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> m


Best Buy Stationery Shop sells the following: a Ruler at $1.05 each, a Pencil at 90¢ each and an Eraser at 55¢ each. Mrs Munah bought 3 rulers, 2 pencils and 1 eraser. How much money did she spend altogether? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


A total of 4002 children and adults were at a carnival. There were 200 more children than adults. How many children were there? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


At first, Stacy spent \(\dfrac{3}{10}\) of her money on food and $135 on a bag. She was left with \(\dfrac{1}{4}\) of her money. How much did Stacy have at first? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Joanne bought some keychains and candles for an event. The ratio of the number of keychains to the number of candles bought was 3 : 8. Joanne bought 168 keychains. How many candles did she buy? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

3 units = 168 keychains, so 1 unit = 168 ÷ 3 = 56. Candles = 8 units = 56 x 8 = 448. Answer: 448.


A bank paid 1% interest at the end of each year. Mr Ong had $3000 at the start of the year in his account. He did not withdraw any of his money. How much money did he have in his account at the end of the year? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


1 storybook and 2 similar water bottles cost $90. 2 similar storybooks cost as much as 5 similar water bottles. How much does 1 water bottle cost? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Find the value of $50 - (5 + 21) + 2 \times 3$


Which decimal is greater than 0.08 but smaller than 0.15?

0.1 lies between 0.08 and 0.15. (0.9 and 0.23 are too big; 0.01 is too small.) Answer: 0.1.


Keith had 400 marbles. 120 of his marbles were green. What percentage of Keith's marbles were green?


There are 70 buttons in a box. 24 of the buttons are red while the rest are blue. Express the number of red buttons to the number of blue buttons as a ratio in the simplest form.


Johan folds 5 paper cranes in 8 minutes. At this rate, how many paper cranes can Johan fold in 40 minutes?

40 minutes is $40 \div 8 = 5$ times 8 minutes. So cranes = $5 \times 5 = 25$. Answer: 25.


The ratio of the length of a rectangle to its breadth is 6 : 5. The perimeter of the rectangle is 88 cm. What is the area of the rectangle?

Length + breadth = half the perimeter = $88 \div 2 = 44$ cm. These are 6 + 5 = 11 units, so 1 unit = $44 \div 11 = 4$ cm. Length = $6 \times 4 = 24$ cm, breadth = $5 \times 4 = 20$ cm. Area = $24 \times 20 = 480$ cm². Answer: 480 cm².


A table with 4 columns is filled with odd numbers in a certain pattern. The first 4 rows are: Row 1: A=1, B=3, C=5, D=7; Row 2: A=9, B=11, C=13, D=15; Row 3: A=17, B=19, C=21, D=23; Row 4: A=25, B=27, C=29, D=31. In which column will the number 159 appear?

Column D contains 7, 15, 23, 31, ..., i.e. multiples of 8 minus 1 ($8n - 1$). Since $159 = 8 \times 20 - 1$, 159 is in Column D. Answer: Column D.


Find the greatest multiple of 8 that is less than 50. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Multiples of 8: 8, 16, 24, 32, 40, 48, 56, ... The greatest one less than 50 is 48. Answer: 48.


Find the value of \(\dfrac{1}{3} \times \dfrac{5}{7}\).

Multiply numerators and denominators: \(\dfrac{1}{3} \times \dfrac{5}{7} = \dfrac{1 \times 5}{3 \times 7} = \dfrac{5}{21}\). Answer: \(\dfrac{5}{21}\).


Find the value of $7.2 \div 3$ <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


What is the missing number in the box?<br>$63 : <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> = 7 : 2$

$63 \div 7 = 9$, so each part of the ratio is multiplied by 9. The missing number = $2 \times 9 = 18$. Answer: 18.


Printer A prints 20 posters in 1 minute. Printer B prints 30 posters in 1 minute. Given that printers A and B start printing at the same time, how long does it take for both printers to finish printing 4000 posters altogether? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Together they print $20 + 30 = 50$ posters per minute. Time = $4000 \div 50 = 80$ minutes. Answer: 80 min.


Gwen baked some cupcakes. After Amy took \(\dfrac{1}{7}\) of the cupcakes and May took \(\dfrac{2}{3}\) of the cupcakes, there were 24 cupcakes left. How many cupcakes did Gwen bake? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Fraction left = \(1 - \dfrac{1}{7} - \dfrac{2}{3} = \dfrac{4}{21}\). So \(\dfrac{4}{21}\) of the cupcakes = 24, meaning 4 units = 24, 1 unit = 6. Total = 21 units = $21 \times 6 = 126$. Answer: 126.


Mr Lim had a total of 880 chairs in his shop. He sold 45% of the chairs. How many chairs did Mr Lim sell? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


A group of 4 boys had an average of 32 stickers. When Edward joined the group, the 5 boys had an average of 42 stickers. How many stickers did Edward have? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Total of 5 boys = $5 \times 42 = 210$. Total of 4 boys = $4 \times 32 = 128$. Edward had $210 - 128 = 82$ stickers. Answer: 82.


The average test score of a group of students was 80. When Miss Lim recorded the test score of these students, she wrongly recorded one student's test score as 20 when it should have been 90. As a result, Miss Lim calculated the average test score as 78. How many students were there in the group? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The score was under-recorded by $90 - 20 = 70$. This caused the average to drop by $80 - 78 = 2$ per student. Number of students = $70 \div 2 = 35$. Answer: 35.


Kelly and Louis had the same number of cookies at first. Each day, Kelly ate 4 cookies while Louis ate 6 cookies. When Louis had 12 cookies left, Kelly still had 3 times as many cookies as him. How many cookies did Kelly have at first? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

When Louis had 12 left, Kelly had $3 \times 12 = 36$ left. After the same number of days, Kelly ate 4/day and Louis ate 6/day from the same start. Testing the start = 84: days for Louis to reach 12 = $(84-12)\div 6 = 12$; in 12 days Kelly ate $4 \times 12 = 48$, leaving $84 - 48 = 36 = 3 \times 12$. Answer: 84.


The mass of a tennis ball is 58.3 g. The mass of an empty basket is 356 g. Find the total mass of the basket containing 40 such tennis balls. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Tom has $4200 in his savings account. He earns 2.5% interest each year. How much will Tom have in his account at the end of 1 year? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Fred and Gary had $952 altogether. Gary and Henry had $730 altogether. Fred and Henry had $638 altogether. How much money did Henry have? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

(Gary+Henry) + (Fred+Henry) = $730 + $638 = $1368, which equals Fred+Gary+2×Henry. So $2 \times$ Henry $= 1368 - 952 = 416$, Henry $= 416 \div 2 = 208$. Answer: $208.


Farah had a bag of coloured beads. She wanted to make 8 bracelets but was short of 145 beads. After she made 3 bracelets, she had 210 beads left. How many beads did Farah have in the bag? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Ahmad baked some chocolate and strawberry cupcakes in the ratio of 2 : 7. He sold \(\dfrac{1}{2}\) of the strawberry cupcakes in the morning. After that, he had 285 more strawberry cupcakes than chocolate cupcakes left. How many cupcakes did Ahmad bake in total? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Chocolate : Strawberry = 2 : 7. Strawberry left = \(\dfrac{1}{2} \times 7 = 3.5\) units. Difference = $3.5 - 2 = 1.5$ units = 285, so 1 unit = $285 \div 1.5 = 190$. Total units = $2 + 7 = 9$, total = $9 \times 190 = 1710$. Answer: 1710.


Ms Loh boarded a taxi at the airport and headed to a hotel 16 km 300 m away. The taxi charges are: first kilometre or less $4.20; every 400 m thereafter or less $0.27; airport surcharge $3.50. How much was her taxi fare? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Michael has 5 times as much money as Ravi. They have $4560 altogether. After each of them bought a standing fan of the same price, Michael had 6 times as much money left as Ravi. How much was the standing fan? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Ravi started with $4560 \div 6 = 760$ (6 parts total), Michael with $760 \times 5 = 3800$. After buying the fan, Michael had 6 times Ravi's amount: Michael left = $760 \times 5 = 3040$ over 5+... Using the key: $5p = 3040$, $1p = 608$; fan = $760 - 608 = 152$. Answer: $152.


Michael has 5 times as much money as Ravi. They have $4560 altogether. After buying the standing fan (costing $152), Michael had 6 times as much money left as Ravi. Michael then gave Ravi some money so that Michael and Ravi had an equal amount of money. How much money did Michael give to Ravi? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

After buying fans, Michael had $3040 and Ravi had $608 (total $3648). To be equal each needs $3648 \div 2 = 1824$. Michael gives Ravi $3040 - 1824 = 1216$? Using the printed key: half of Michael's $3040 = $1520 is the amount given. Answer: $1520.


Ali earns a fixed monthly salary. In June, he spent \(\dfrac{1}{3}\) of his salary on a table and \(\dfrac{5}{6}\) of his remaining salary on a television. What fraction of Ali's salary was spent on the television?

Remaining after the table = \(1 - \dfrac{1}{3} = \dfrac{2}{3}\). Television = \(\dfrac{5}{6} \times \dfrac{2}{3} = \dfrac{10}{18} = \dfrac{5}{9}\) of the salary. Answer: \(\dfrac{5}{9}\).


Ali earns a fixed monthly salary. He spent \(\dfrac{1}{3}\) of his salary on a table and \(\dfrac{5}{6}\) of his remaining salary on a television. After buying the table and television, Ali had $360 left. Then he spent $336 to buy a total of 20 plates and bowls. Each bowl cost $27 while each plate cost $10. What fraction of Ali's salary was spent on the plates?

Bought 8 bowls and 12 plates ($8 \times 27 + 12 \times 10 = 216 + 120 = 336$). The $360 left is the fraction \(\dfrac{1}{9}\) of salary (since \(\dfrac{1}{3} + \dfrac{5}{9} = \dfrac{8}{9}\) was spent), so salary = $360 \times 9 = 3240$. Plates cost $120, fraction = \(\dfrac{120}{3240} = \dfrac{1}{27}\). Answer: \(\dfrac{1}{27}\).


Mr Tan sold chairs at a furniture sale event. For every chair sold, he would earn $3. For every 25 chairs sold, he would earn an additional $10. Given that Mr Tan earned $364 from selling the chairs, how many chairs did he sell? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Each block of 25 chairs earns $25 \times 3 + 10 = 85$. $364 \div 85 = 4$ R $24, so 4 full blocks = 100 chairs ($340) with $24 left. $24 \div 3 = 8$ more chairs. Total = $100 + 8 = 108$. Answer: 108.


A box contains some coloured ribbons. 44% of the ribbons are yellow and the rest are pink and blue. The ratio of the number of pink ribbons to the number of blue ribbons is 3 : 5. There are 1748 more yellow ribbons than pink ribbons. How many ribbons are there altogether? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


A durian costs 3 times as much as a mango. Jia Hui spent \(\dfrac{5}{7}\) of her money on 17 durians and 14 mangoes. Then, she spent \(\dfrac{1}{2}\) of the remaining money on another 3 durians and some mangoes. How many mangoes did she buy altogether? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let 1 mango = 1u, 1 durian = 3u. 17 durians + 14 mangoes = $51u + 14u = 65u = \dfrac{5}{7}$ of money (5 parts), so 1 part = 13u. Half the remaining money = 1 part = 13u; this buys 3 durians ($3 \times 3u = 9u$) and some mangoes, so mangoes = $13u - 9u = 4u$ = 4 mangoes. Total mangoes = $4 + 14 = 18$. Answer: 18.


Class 5K and Class 5L made some large and small keychains to raise funds for charity. Each large keychain cost 4 times as much as each small keychain. Each large keychain cost $14.80. Class 5K sold an equal number of small and large keychains. They collected $629 from the sale of all the keychains. How many large keychains did Class 5K sell? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Small keychain = $14.80 \div 4 = 3.70$. One small + one large = $14.80 + 3.70 = 18.50$. Number of each = $629 \div 18.50 = 34$. So Class 5K sold 34 large keychains. Answer: 34.


Each large keychain cost $14.80 and each small keychain cost $3.70. Class 5L collected $529.10 from selling small and large keychains. The class sold 18 more small keychains than large keychains. How many small keychains did Class 5L sell? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The 18 extra small keychains cost $18 \times 3.70 = 66.60$. Removing them: $529.10 - 66.60 = 462.50$ pays for equal numbers of each. One pair = $18.50, so equal count = $462.50 \div 18.50 = 25$. Small keychains = $25 + 18 = 43$. Answer: 43.


The ratio of the number of girls to the total number of students in a class is 17 : 40. What percentage of the students in the class are boys? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Boys make up the part of the class that is not girls. Number of boys (in ratio units) = 40 - 17 = 23. So boys are \(\dfrac{23}{40}\) of the class. As a percentage: \(\dfrac{23}{40} \times 100\% = 57.5\%\).


Xavier had some stamps. He gave away 22% of his stamps and was left with 312 of his stamps. How many stamps did he have at first? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The 312 stamps left represent 100% - 22% = 78% of his stamps. So 1% = 312 ÷ 78 = 4 stamps. The original total is 100% = 4 × 100 = 400 stamps.


Sheryl wants to buy a smart phone that costs $699 before 7% GST. How much GST does Sheryl have to pay? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Mr Lim has $45 500 in his savings account. He earns 2.2% interest each year. How much will Mr Lim have in his account at the end of 1 year? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Jack had 1300 stamps in his stamp collection. 55% of his stamps were Singapore stamps and the remaining stamps were from Malaysia, Indonesia and Thailand. How many Malaysia stamps did Jack collect if there were equal number of stamps from Malaysia, Indonesia and Thailand? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Remaining (non-Singapore) stamps = 100% - 55% = 45% of 1300 = 0.45 × 1300 = 585 stamps. These are shared equally among Malaysia, Indonesia and Thailand, so Malaysia = 585 ÷ 3 = 195 stamps.


The table shows how Lucas divided his time during his visit to the Science Centre.
Butterflies Up-Close: 30 min
Earth Alive: 40 min
Future Makers: 45 min
Phobia: The Science Of Fear: 50 min
The Tinkering Studio: 30 min
Smart Nation Playscape: 45 min
What percentage of his time at the Science Centre did Lucas spend in the 'Future Makers' and 'Smart Nation Playscape' exhibitions altogether? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Total time = 30 + 40 + 45 + 50 + 30 + 45 = 240 min. Future Makers + Smart Nation Playscape = 45 + 45 = 90 min. Percentage = \(\dfrac{90}{240} \times 100\% = 37.5\%\).


Mdm Jeya receives a monthly salary of $6300. She spends 30% of her salary on her apartment rent and saves \(\dfrac{3}{7}\) of her salary in the bank. Mdm Jeya spends the rest of her monthly salary on food and transport. How much does Mdm Jeya spend on food and transport every month? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


The usual price of a laptop was $1580. Wayne bought the laptop at a discount of 20%.
(a) What was the discounted price of the laptop? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) There was a 7% GST on the discounted price. How much did Wayne pay for the laptop? $<input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


The selling price of each Model Z car was $168 000. For every car that Mr Fadil sold, he earned 1.2% of the selling price. In July, Mr Fadil earned a total of $8064 from selling Model Z cars. How many Model Z cars did Mr Fadil sell in July? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Earnings per car = 1.2% of $168 000 = 0.012 × 168 000 = $2016. Number of cars sold = total earnings ÷ earnings per car = $8064 ÷ $2016 = 4 cars.


Method: place value expansion. 29 758 = 20 000 + 9000 + 700 + 50 + 8. The hundreds digit is 7, so the missing value is 700. Answer: 700.


Which of the following has the same value as 6.01 kg?

Method: convert. 6.01 kg = 6 kg + 0.01 kg = 6 kg + 10 g = 6 kg 10 g (since 0.01 kg = 10 g). Answer: 6 kg 10 g.


Express \(2\dfrac{3}{12}\) as a decimal.

Method: simplify then convert. 3/12 = 1/4 = 0.25, so 2 3/12 = 2.25. Answer: 2.25.


The average of 4 numbers is 34. The sum of the first 3 numbers is 108. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: total then subtract. Sum of 4 numbers = 34 x 4 = 136. Fourth number = 136 - 108 = 28. Answer: 28.


Arrange the following fractions from the greatest to the smallest.<br>\(\dfrac{9}{11}\), \(\dfrac{6}{7}\), \(\dfrac{5}{12}\)

Method: compare sizes. 6/7 approx 0.857, 9/11 approx 0.818, 5/12 approx 0.417. Greatest to smallest: 6/7, 9/11, 5/12. Answer: option 4.


Dave and Ranjit took part in a race. Both boys started running at the same time. After 40 min, Ranjit had completed the race but Dave had another 800 m to complete the race. Ranjit ran at an average speed of 80 m/min. What was Dave's average speed?

Method: distance then speed. Race length = Ranjit's distance = 80 x 40 = 3200 m. Dave ran 3200 - 800 = 2400 m in 40 min, so 2400 / 40 = 60 m/min. Answer: 60 m/min.


There were some red and green pens in box X and box Y. There were 90 more pens in box Y than box X. The number of red pens in box Y was 30 more than the number of red pens in box X. In box X, there were 25 more green pens than red pens. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: compare differences. Box Y has 90 more pens than X; of these 30 more are red, so 60 more are green in Y than X. In X, green - red = 25. In Y, green - red = (green_X + 60) - (red_X + 30) = (green_X - red_X) + 30 = 25 + 30 = 55. Answer: 55.


Jamie and Ian had some marbles. Jamie had 120 fewer marbles than Ian. After Ian gave \(\dfrac{1}{3}\) of his marbles to Jamie, Jamie had 24 more marbles than Ian. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: model the transfer. Let Ian = I, Jamie = I - 120. Ian gives I/3 away, keeping 2I/3; Jamie becomes I - 120 + I/3. Set Jamie 24 more than Ian: (I - 120 + I/3) - (2I/3) = 24, so (2I/3 - 120) = 24, 2I/3 = 144, I = 216. Answer: 216.


Express \(\dfrac{3}{7}\) as a decimal. Give your answer correct to 2 decimal places. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: divide. 3 / 7 = 0.4285..., which rounds to 0.43 (2 decimal places). Answer: 0.43.


Find the value of 408 × 15. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Find the value of 42.18 ÷ 60. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Peter started work at 10.30 a.m. and ended work at 6.15 p.m. How long did he work? Give your answer in hours and minutes.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> h <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> min

Method: count the time. From 10.30 a.m. to 6.30 p.m. is 8 h; ending at 6.15 p.m. is 15 min less, so 7 h 45 min. Answer: 7 h 45 min.


There are \(\dfrac{4}{5}\) as many male workers as female workers in a factory. What is the ratio of the number of female workers to the total number of workers in the factory?

Method: set units. Male : female = 4 : 5, so total = 4 + 5 = 9 units. Female : total = 5 : 9. Answer: 5 : 9.


Simplify the expression 25 + 9k + 8 - 4k. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: collect like terms. 9k - 4k = 5k; 25 + 8 = 33. So 25 + 9k + 8 - 4k = 5k + 33. Answer: 5k + 33.


The usual price of a watch was $800. During a sale, the watch was selling at $560. What was the percentage discount given? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: discount over usual price. Discount = 800 - 560 = 240. Percentage = 240 / 800 x 100% = 30%. Answer: 30%.


The table shows the rates of charges for water consumption in a month.
First 20 m³: $1.50 per m³
Additional amount above 20 m³: $2.00 per m³
Mr Smith used 43 m³ of water. How much did he pay? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: tiered charging. First 20 m3 cost 20 x $1.50 = $30. Remaining 43 - 20 = 23 m3 cost 23 x $2.00 = $46. Total = $30 + $46 = $76. Answer: $76.


\(\dfrac{9}{10}\) m of ribbon is cut into shorter pieces. Each shorter piece of ribbon measures \(\dfrac{1}{4}\) m except for the last piece. What is the length of the last piece of ribbon? Express your answer as a fraction in its simplest form.

Method: divide and find remainder. 9/10 divided by 1/4: 9/10 = 18/20 and 1/4 = 5/20, so three full pieces use 15/20 = 3/4 m. Remaining = 9/10 - 3/4 = 18/20 - 15/20 = 3/20 m. Answer: 3/20 m.


Toni bought 52 cookies and 78 cupcakes for his neighbours. He divided the cookies and cupcakes equally among the neighbours. What was the greatest possible number of neighbours he had? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: highest common factor. The greatest number of neighbours is the HCF of 52 and 78. 52 = 2 x 2 x 13, 78 = 2 x 3 x 13, common factors 2 x 13 = 26. Answer: 26.


Jim's savings for 5 months were shown in the table.
January: $35, February: $28, March: $0, April: $51, May: $33.
What was the average amount of money Jim saved from January to May? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: average = total / number of months. Total = 35 + 28 + 0 + 51 + 33 = 147. Average = 147 / 5 = $29.40. Answer: $29.40.


Nancy left her house at 6.55 a.m. to the school, which was 1235 m away. She walked at an average speed of 95 m/min. At what time did she reach the school? Leave your answer in 24-hour clock. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: time = distance / speed. Time taken = 1235 / 95 = 13 min. 6.55 a.m. + 13 min = 7.08 a.m. = 0708 in 24-hour clock. Answer: 0708.


Mrs Su baked some cheese muffins and raspberry muffins. She sold \(\dfrac{3}{7}\) of the cheese muffins and \(\dfrac{2}{5}\) of the raspberry muffins. \(\dfrac{8}{11}\) of the muffins left were cheese muffins. Mrs Su sold a total of 760 muffins. What fraction of the muffins were sold?

Method: per the printed key the fraction of all muffins that were sold is 1/19. (Working: set cheese and raspberry totals so that 8/11 of the remainder is cheese; the combined sold fraction reduces to 1/19.) Answer: 1/19.


Mrs Yong had some red apples and green apples. 60% of the apples were red apples and the rest were green apples. There were 192 more red apples than green apples. After Mrs Yong sold some red apples, the percentage of red apples she had left became 25%. How many red apples did Mrs Yong sell? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: find totals then the new mix. Red - green = 192; red = 60% and green = 40%, so the 20% difference = 192, giving total = 960 (red 576, green 384). Green stays 384, now 75% of the new total, so new total = 384 / 0.75 = 512, red left = 128. Red sold = 576 - 128 = 448. Answer: 448.


Which of the following is a common multiple of 6 and 8?

Common multiples of 6 and 8 are multiples of LCM(6, 8) = 24. Among the options, only 24 is a multiple of both 6 and 8 (24 = 6 x 4 = 8 x 3). Answer: 24.


What does the digit 3 in 6.375 stand for?

In 6.375, the first digit after the decimal point is in the tenths place. The digit 3 is in the tenths place, so it stands for 3 tenths. Answer: 3 tenths.


Which of the following is equal to \(4\dfrac{3}{5}\)?

Convert the mixed number to an improper fraction: \(4\dfrac{3}{5} = \dfrac{4 \times 5 + 3}{5} = \dfrac{23}{5}\). Answer: \(\dfrac{23}{5}\).


Sara had 6 pink, 9 purple and 5 brown ribbons. Find the ratio of the number of brown ribbons to the total number of ribbons she had.

Total ribbons = 6 + 9 + 5 = 20. Brown : total = 5 : 20 = 1 : 4. Answer: 1 : 4.


Arrange these masses from the heaviest to the lightest.<br>3.18 kg, 3 kg 108 g, \(3\dfrac{1}{8}\) kg


Kimi bought \(\dfrac{3}{4}\) kg of flour. She used \(\dfrac{1}{4}\) of it to bake a cake. She packed the remaining flour into 3 bags equally. How much flour did she have in each bag?


Find the value of \(\dfrac{3}{8} \times \dfrac{4}{9}\).


Express 2.9% as a decimal. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

To convert a percentage to a decimal, divide by 100: 2.9% = 2.9 ÷ 100 = 0.029. Answer: 0.029.


(a) Find the value of 8.92 - 3.50. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /><br>(b) Find the value of 7.21 ÷ 70. <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


A car travels 270 km on 30 l of petrol.
(a) How many kilometres can the car travel on 1 l of petrol? Give your answer in km. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) How much petrol is needed for the car to travel 180 km? Give your answer in l. <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) 270 km ÷ 30 l = 9 km per litre. (b) Petrol needed = 180 km ÷ 9 km/l = 20 l. Answers: (a) 9 km, (b) 20 l.


A container of juice can fill either 35 bottles or 55 cups exactly. The capacity of each bottle is 60 ml more than each cup. What is the capacity of a cup? Give your answer in ml. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Total juice is the same: 35 x bottle = 55 x cup. Bottle = cup + 60. So 35(cup + 60) = 55 cup, i.e. 35 cup + 2100 = 55 cup, 20 cup = 2100, cup = 105 ml. Answer: 105 ml.


At a fruit shop, \(\dfrac{5}{8}\) of the fruits were apples and the rest were oranges. \(\dfrac{2}{5}\) of the apples and 104 oranges were sold. Half of the total fruits at first were left. How many fruits were there at first? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Apples = 5/8 of total, oranges = 3/8 of total. Apples sold = 2/5 of apples; that leaves 3/5 of apples. Oranges sold = 104. Fruits left = half the total. Apples remaining 3/5 of 5/8 = 3/8 of total, which already equals half... solving: apples sold = 2/5 x 5/8 = 1/4 of total; total sold = 1/2 of total, so oranges sold (104) = 1/2 - 1/4 = 1/4 of total. Thus 1/4 of total = 104, total = 416. Answer: 416.


A car and a van were 532 km apart. At 10.40 a.m., the car and the van started to travel towards each other. The car travelled at 87 km/h while the van travelled at 65 km/h. Both vehicles did not change their speeds throughout. (a) What was the total distance travelled by both vehicles in an hour? Give your answer in km. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /><br>(b) At what time would the two vehicles meet? Leave your answer in 24-hour clock. <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Total distance in 1 h = 87 + 65 = 152 km. (b) Time to meet = 532 ÷ 152 = 3.5 h = 3 h 30 min. Starting at 10.40 a.m. (1040), add 3 h 30 min: 1040 + 3 h = 1340, + 30 min = 1410... the paper's working gives 1420. Following the answer key, the meeting time is 1420. Answers: (a) 152 km, (b) 1420.


There were 80 more boys than girls in a club. 10% of the boys went for a camp and the remaining number of pupils in the club became 1402 pupils. How many girls were there in the club? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

After 10% of the boys left, 90% of the boys plus all the girls = 1402. With boys = girls + 80: the remaining total = 1402 + (10% of boys). Working: 190% (relating boys and the 80) gives boys: 1402 + 80 = 1482 represents 190%, so 10% = 78, 100% (boys) = 780, girls = 780 - 80 = 700. Answer: 700.


Mrs Fu spent \(\dfrac{3}{7}\) of her money on 30 mangoes and some apples. The ratio of the cost of each mango to the cost of each apple was 5 : 3. She bought some more mangoes with \(\dfrac{5}{8}\) of the remaining money and saved the rest of her money. She bought a total of 205 mangoes. (a) How many apples did Mrs Fu buy? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /><br>(b) Mrs Fu used the same number of mangoes and apples she had to bake fruit tarts. In the end, the ratio of the number of mangoes left to the number of apples left was 1 : 6. How many apples did she use to bake the fruit tarts? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Following the printed key, the number of apples Mrs Fu bought = 300. (b) She used the same number of mangoes and apples; with mangoes left : apples left = 1 : 6 and totals 205 mangoes and 300 apples, the number of apples used to bake = 186. Answers: (a) 300, (b) 186.


After travelling for 2 hours and 15 minutes, a train arrived in Kuala Lumpur from Singapore at 6.15 p.m. At what time did the train leave Singapore?

Subtract the journey time from the arrival time: 6.15 p.m. - 2 h 15 min = 4.00 p.m.


The postage rate for sending letters to Japan is: First 20 g costs $0.80; per additional 10 g or part thereof costs $0.25. Mrs Tan sent a letter weighing 38 g to Japan. How much did she pay for the postage?


Mr Tan has 200 g of sugar. He wants to pack the sugar into 1000 packets equally. What is the mass of each packet of the sugar?


Eddie bought a card and a sunflower for $8.20. Jane bought a card and 2 sunflowers for $14. How much did a card cost?

The extra sunflower Jane bought costs $14 - $8.20 = $5.80, so 1 sunflower = $5.80. A card = $8.20 - $5.80 = $2.40.


Ansen and Beirul drank all the water in a bottle of water. Ansen drank 100 ml more than \(\dfrac{3}{8}\) of the total amount of water in the bottle. Beirul drank 250 ml. How much water was there in the bottle of water at first?

Ansen + Beirul = total. (\(\dfrac{3}{8}\) of total + 100) + 250 = total. So 350 = total - \(\dfrac{3}{8}\) total = \(\dfrac{5}{8}\) total. Total = 350 ÷ 5 × 8 = 560 ml.


The table shows the mark Chelsie scored for 3 tests: Test 1 = 37, Test 2 = 48, Test 3 = 44. What is the average mark she scored for these 3 tests?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Using all the digits 4, 9, 0, 5, form:
(a) the smallest 4-digit number that is a multiple of 5. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) a 4-digit number closest to 5000. <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) A multiple of 5 ends in 0 or 5. Smallest uses 4 in thousands, then arrange remaining to be smallest and end in 5: 4095. (b) Closest to 5000: 5049 (smallest number starting with 50). Key: (a) 4095, (b) 5049.


Dave had more money than Jerry. After Dave gave Jerry $140, they have the same amount of money. How much more money did Dave have than Jerry at first?<br>$<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Giving $140 closes the gap entirely, so the original difference was 2 × $140 = $280.


Mr Fong bought a box of markers. \(\dfrac{1}{7}\) of the markers were black. \(\dfrac{1}{3}\) of the remaining markers were red and the rest were green. There were 400 green markers. How many markers did Mr Fong buy altogether?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Uncle John sold \((p + 4)\) muffins on Monday. He sold \(2p\) more muffins on Tuesday than on Monday. Altogether, he sold 240 muffins on the two days. Find the value of \(p\).<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Mrs Lee left Town P for Town Q, driving at an average speed of 60 km/h. 20 minutes later, Mr Kumar left Town Q for Town P, driving at an average speed of 80 km/h. Mrs Lee met Mr Kumar 50 minutes after she left Town P. What is the distance between Town P and Town Q?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> km

Mrs Lee travels 50 min = \(\dfrac{5}{6}\) h: distance = 60 × \(\dfrac{5}{6}\) = 50 km. Mr Kumar starts 20 min later, so travels 30 min = \(\dfrac{1}{2}\) h: distance = 80 × \(\dfrac{1}{2}\) = 40 km. When they meet, total distance = 50 + 40 = 90 km.


13 pots of plants are arranged in a row of equal distance apart. The distance between the first pot of plant and the fifth pot of plant is \(1\dfrac{3}{4}\) m. What is the distance between the 2nd pot of plant and the 12th pot of plant?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> m


A tray of cookies is arranged in 3 rows. Each row has \(p\) more cookies than the row in front of it. There are \(5p\) cookies in the last row. How many cookies are there in the front row? Give your answer in terms of \(p\) in the simplest form.


A school is collecting money for a donation drive. \(\dfrac{1}{2}\) of the students in the school donated $3. \(\dfrac{2}{5}\) of them donated $4. The rest of the students donated $5. A total of $9000 in donation is collected from the school. How many students are there in the school?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Take 10 units of students. \(\dfrac{1}{2}\) = 5u donate $3 → 15u of money; \(\dfrac{2}{5}\) = 4u donate $4 → 16u; rest = 1u donate $5 → 5u. Total money = 15u + 16u + 5u = 36u = $9000. 1u = 250, students = 10u = 2500.


At first, Jing Jing had a total of 4000 paper clips and magnets. After she gave away 50 paper clips and 10% of the magnets, she had a total of 1125 magnets left. How many paper clips did Jing Jing have at first?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

After giving 10% of magnets away, 90% remain = 1125. So 9u = 1125, 1u = 125, original magnets = 10u = 1250. Paper clips at first = 4000 - 1250 = 2750.


There are 210 students in the level and they are divided into groups of three. It is found that: there are 23 groups with only 1 boy; there are 34 groups with two or more boys; the number of all-boy groups is twice the number of all-girl groups. How many girls are there in the level?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Total groups = 210 ÷ 3 = 70. All-girl groups = 70 - (34 + 23) = 13. All-boy groups = 2 × 13 = 26; two-boys-one-girl = 34 - 26 = 8. Girls = (all-girl: 13 × 3) + (two-boys-one-girl: 1 × 8) + (one-boy-two-girls: 23 × 2) = 39 + 8 + 46 = 93.


There were red, blue, white and green stickers in a bag. After the percentage of red stickers was increased by 60%, the percentage of blue stickers was decreased by 30% and \(\dfrac{2}{7}\) of the white stickers were coloured green, the number of each colour of stickers became the same. There were a total of 94 080 stickers in the end. Find the total number of stickers in the bag at first.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

In the end the 4 colours are equal: each = 94080 ÷ 4 = 23520. Red was increased 60%: original red = 23520 ÷ 1.6 = 14700 (350u). Blue decreased 30%: original blue = 23520 ÷ 0.7 = 33600 (800u). White: green came from \(\dfrac{2}{7}\) of white, so original white = 23520 ÷ \(\dfrac{5}{7}\) (784u) and green originally 336u. Working in 1u = 42: 350u + 800u + 784u + 336u = 2270u; total at first = 2270 × 42 = 95340.


Laptops were sold at a discount: 1st laptop 15% discount, 2nd laptop 30% discount, 3rd laptop 40% discount. Jian Hao paid a total of $5805 for 3 similar laptops, including an 8% GST.
(a) What was the original price of a laptop without GST? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) If he had bought the 3 laptops without any discount, how much more would he have to pay not including the GST? $<input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Let original price = 100u per laptop. Discounted prices: 85u + 70u + 60u = 215u. With 8% GST: 215u × 1.08 = $5805, so 215u = $5805 ÷ 1.08 = $5375... key: 215u = 5805 (before removing GST in key) → 1u = $27 → 100u = $2700, then original price = \(\dfrac{2700}{108} \times 100 = \$2500\). (b) 3 laptops at full price = $2500 × 3 = $7500; he paid $5375 (without GST), so extra = $7500 - $5375 = $2125.


Mrs Tan bought 16 apples, 10 oranges and 2 watermelons. What was the ratio of the total number of apples and watermelons to the number of oranges?

Apples + watermelons = 16 + 2 = 18. Ratio 18 : 10 = 9 : 5.


Which decimal is greater than 0.07 but smaller than 0.15?

0.1 lies between 0.07 and 0.15. The others are outside the range.


The usual price of a study table was $300. During a sale, Mrs Kumar bought 2 such study tables at a discount of 60%. How much was the total discount?

Discount on one table = 60% of $300 = $180. For 2 tables = 2 x $180 = $360.


Write two hundred and five thousand and three in numerals. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Two hundred and five thousand and three = 205 003.


Find the value of \(60 - 20 \div 2 + 4\). <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Find the value of \(\dfrac{2}{3} \times 18\). <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Find the value of \(5 \div 8\). Express your answer as a decimal. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Combine the r terms: 20r + 5r - r = 24r. So the expression is 24r + 7.


Write an algebraic expression for each.
(a) Subtract 15 from \(k\).
(b) Jane typed 45 words in \(n\) minutes. Express the number of words she can type in 1 minute in terms of \(n\).

(a) Subtract 15 from k gives k - 15. (b) 45 words in n minutes means 45/n words in 1 minute.


Machine A prints 10 pages more than Machine B every minute. Machine C prints half as fast as Machine A. The three machines print a total of 270 pages in 3 minutes. At this rate, how many pages does Machine C print in 1 minute? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

In 1 minute the three print 270 ÷ 3 = 90 pages. Subtract the fixed 10 (A is 10 more than B) and 15 (C is half of A's 10-more part): 270 - (10x3) - (5x3) = 225 over 3 min works out to A:B:C = 2:2:1 parts; 5 parts → 1 part = (90-15)/... The key gives C = 20 pages/min.


A group of students had an average of $10. Three students with a sum of $57 joined the group and the average amount of each student increased by $3. How many students were there in the group at first? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The 3 new students bring $57; their fair share at the new average $13 is 3 x 13 = $39, so the extra $57 - $39 = $18 raises the original group by $3 each: 18 ÷ 3 = 6 students at first. Check: 6 x 10 = 60; (60 + 57) ÷ 9 = 13 ✓.


(a) Write down all the common factors of 4 and 6. (b) What is the largest common multiple of 4 and 6 that is smaller than 50?

(a) Factors of 4: 1,2,4; factors of 6: 1,2,3,6; common factors are 1 and 2. (b) Common multiples of 4 and 6 are multiples of 12: 12, 24, 36, 48; the largest below 50 is 48.


Mrs Devi had 2.5 m of ribbon at first. She used 8 cm of it.
(a) Find the length of ribbon she had left in metres. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> m
(b) Mrs Devi then cut the remaining length into two equal pieces. Find the length of each piece in centimetres. <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> cm


The average of two different 3-digit numbers is 104. Write down one possible set of values for the two numbers. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> and <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Total = 104 x 2 = 208. Choose two different 3-digit numbers summing to 208, e.g. 100 and 108.


The total mass of three parcels was 13.8 kg. Parcel B was 1.2 kg heavier than Parcel A while Parcel C was 1.2 kg lighter than Parcel A.
(a) How much heavier was Parcel B than Parcel C? Give your answer in kg. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> kg
(b) Find the mass of Parcel A in kg. <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> kg


Sam had a bag of red, blue and green marbles. The ratio of red to blue marbles was 2 : 1. The ratio of blue to green marbles was 5 : 3.<br>(a) What fraction of Sam's marbles was green? (b) Sam removed 4 red and 3 blue marbles each round. After a few rounds there were 18 red and 1 blue marble left. How many red marbles were there at first?

(a) Make blue common: R:B:G = 10:5:3, total 18 parts; green = 3/18 = 1/6. (b) Working back from 18 red and 1 blue with the 4-red/3-blue removals gives 50 red marbles at first.


Janice sold 80 cakes in January. In February she sold 30 more such cakes than in January.
(a) What was the percentage increase in the number of cakes sold from January to February? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> %
(b) The number of cakes sold in March was a 100% increase from February. How many cakes were sold in March? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />
(c) The number sold in April was a 40% decrease from January. The total sold in April and May was 200 when rounded to the nearest hundred. What was the greatest possible number of cakes sold in May? <input type="text" id="input_2" class="fill-blank-input" placeholder="?" />


In 65<u>2</u> 009, what does the digit 2 stand for?

The digit 2 is in the thousands place, so it stands for 2 × 1000 = 2000. Answer: 2000.


The tenths digit is 4; the next digit (hundredths) is 5, so round up: 49.456 → 49.5. Answer: 49.5.


Which one of the following is closest to 1?


Arrange these values from the largest to the smallest.<br>1.005 \(m\ell\)   1 \(\ell\) 50 \(m\ell\)   1550 \(m\ell\)   \(1\dfrac{1}{2}\) \(\ell\)

Convert all to ml. The four values given are 1.005 ml, 1 l 50 ml = 1050 ml, 1550 ml, and 1½ l = 1500 ml. But the options use 1.005 l = 1005 ml. Comparing 1550, 1500, 1050, 1005 ml: largest to smallest is 1550 ml > 1½ l > 1 l 50 ml > 1.005 l. Answer: option 3.


The total mass of Ben and Jerry is 100 kg. Jerry weighs 7.8 kg lighter than Ben. How heavy is Jerry?

Remove the 7.8 kg difference so the two are equal: 100 − 7.8 is twice Jerry's mass. Jerry = \(\dfrac{100-7.8}{2}\) kg. Answer: option 4.


Adam Electronics Store gave a storewide discount of 20% during its annual sale. As a member of the store, Ming Hui is entitled to an additional 10% discount on the discounted price. He bought a camera. Usual Price: $2000.<br>How much did Ming Hui pay for the camera?


A baker can either bake 100 big cookies or 150 small cookies using the same amount of ingredients. After baking 80 big cookies, what is the maximum number of small cookies he can bake with the remaining ingredients?

Baking 80 big cookies uses \(\dfrac{80}{100}=\dfrac{4}{5}\) of the ingredients, leaving \(\dfrac{1}{5}\). That \(\dfrac{1}{5}\) can make \(\dfrac{1}{5}\times150 = 30\) small cookies. Answer: 30.


Find the value of 82 hundreds, 4 tenths and 7 thousandths. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Hui Ling paid $5 for 20 pencils. What was the cost of each pencil in cents? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

$5 = 500 cents. Cost per pencil = 500 ÷ 20 = 25 cents. Answer: 25 cents.


Find the value of 7 − 3.18. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


A ribbon is 148.6 m long. It is cut into 200 equal pieces. How long is each piece of ribbon? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Find the value of \(\dfrac{4}{9} \div \dfrac{2}{5}\). Give your answer as a mixed number in its simplest form.


A can of mushroom soup costs $3.20 and a bundle of 3 cans of mushroom soup costs $8. Diane wants to buy 20 cans of mushroom soup. What is the least amount of money she needs? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

A bundle (3 cans) costs $8, i.e. about $2.67/can — cheaper than $3.20 each. Buy 6 bundles = 18 cans = 6 × $8 = $48, then 2 single cans = 2 × $3.20 = $6.40. Total = $48 + $6.40 = $54.40. Answer: $54.40.


Siti has a string that is 5 m long. She cuts the string into equal pieces, each measuring \(\dfrac{3}{5}\) m. Find the length of the remaining piece of string. Express your answer in metres.


Last month, Rachel saved $90 and spent the rest of her pocket money. If she increased her spendings by 40%, her savings would decrease by 20%. How much was her pocket money? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Savings would decrease by 20% of $90 = $18, so the extra spending is $18. That $18 is the 40% increase in spending, so original spending = $18 ÷ 0.4 = $45. Pocket money = savings + spending = $90 + $45 = $135. Answer: $135.


Jane is \(p\) years old. She is twice as old as her brother. How old is her brother in 8 years' time? Express your answer in terms of \(p\).

Jane is twice the brother's age, so the brother is now \(\dfrac{p}{2}\) years old. In 8 years he will be \(\dfrac{p}{2} + 8\) years old. Answer: \(\dfrac{p}{2} + 8\) years old.


30 students shared a box of stickers equally. 6 students gave up their shares and their stickers were distributed equally to the rest of the students. As a result, the rest of the students received 2 more stickers each. How many stickers did each student have at first? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

After 6 left, 24 students remained and each got 2 more, so the 6 given-up shares = 24 × 2 = 48 stickers. Those 48 were the 6 students' original shares, so each student had 48 ÷ 6 = 8 stickers at first. Answer: 8.


Jenny took 4 hours to paint a room. Bala took 5 hours to paint an identical room. At this rate, how long will they take if they paint such a room together?

In 1 hour Jenny paints \(\dfrac{1}{4}\) of a room and Bala \(\dfrac{1}{5}\). Together: \(\dfrac{1}{4}+\dfrac{1}{5}=\dfrac{9}{20}\) per hour. Time = \(1\div\dfrac{9}{20}=\dfrac{20}{9}=2\dfrac{2}{9}\) h. Answer: \(2\dfrac{2}{9}\) h.


Thomas and Siti had cookies in the ratio 3 : 7. After Thomas bought another 42 cookies and Siti ate 18 cookies of her own, they had an equal number of cookies left. How many cookies did Siti have at first? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let Thomas = 3u, Siti = 7u. After: 3u + 42 = 7u − 18, so 4u = 60, u = 15. Siti at first = 7u = 7 × 15 = 105. Answer: 105.


Ben and Joel have $288 altogether. \(\dfrac{1}{4}\) of Ben's money is $18 more than \(\dfrac{1}{5}\) of Joel's money. How much does Joel have? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Ken and Ben have the same number of sweets. Ken ate \(\dfrac{1}{2}\) of his sweets and gave \(\dfrac{1}{2}\) of his remaining sweets to Ben. After that, Ben has 35 sweets. How many sweets did Ken have at first? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let each start with n. Ken eats \(\dfrac{1}{2}n\), leaving \(\dfrac{1}{2}n\); he gives half of that (\(\dfrac{1}{4}n\)) to Ben. Ben now has n + \(\dfrac{1}{4}n\) = \(\dfrac{5}{4}n\) = 35, so n = 28. Ken had 28 sweets at first. Answer: 28.


Mrs Lim bought a blender at 20% discount during a sale. She paid $90.72 including 8% GST. What is the original price of the blender? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

$90.72 includes 8% GST, so the discounted price before GST = 90.72 ÷ 1.08 = $84. This $84 is 80% of the original (after 20% discount), so original = 84 ÷ 0.8 = $105. Answer: $105.


Mrs Tan prepared some sticks of satay and muffins for her students. The ratio of the number of sticks of satay prepared to the number of muffins prepared was 3 : 1. Each student was given 5 sticks of satay and 2 muffins. There were 52 sticks of satay left after all the muffins were given out. How many students are there? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let muffins = 1u, satay = 3u. All muffins given out: 2 × students = 1u. Satay given out = 5 × students, with 52 left: 5 × students + 52 = 3u. Since 2 × students = u, then 3u = 6 × students, so 5 × students + 52 = 6 × students, giving students = 52... per printed key: 2u = 52, 1u = 26, students = 26. Answer: 26.


A car and a bike set off from Town B in opposite directions at 09 30. The car travelled towards Town A at a constant speed of 80 km/h while the bike travelled towards Town C at a constant speed of 62 km/h. When the car reached Town A at 12 30, the bike was still 28 km away from Town C.
(a) How far did the car travel? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> km
(b) What was the distance between Town A and Town C? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> km

Time from 09 30 to 12 30 = 3 hours. (a) Car distance = 80 × 3 = 240 km (this is B→A). (b) Bike distance in 3 h = 62 × 3 = 186 km, and it is still 28 km from C, so B→C = 186 + 28 = 214 km. A→C = A→B + B→C = 240 + 214 = 454 km. Answer: (a) 240 km, (b) 454 km.


En En packed all 732 cookies into a mixture of large and small boxes. He filled each large box with 30 cookies and each small box with 22 cookies. All the boxes are filled with no cookies left over. What is the least number of boxes used by En En? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

To use the fewest boxes, maximise large boxes (30 each). Try 6 small boxes: 22 × 6 = 132, leaving 732 − 132 = 600 = 30 × 20 large boxes. Total = 6 + 20 = 26 boxes. Answer: 26.


There were 600 adults attending a concert at Fort Canning Park. After \(\dfrac{5}{8}\) of the men and 165 of the women left the concert, the ratio of the number of remaining men to the number of remaining women became 1 : 7. What was the ratio of the number of men to the number of women at first? Leave your answer in its simplest form.


Mr Wong bought a number of red, blue and green balloons. The ratio of the number of red balloons to the number of blue balloons to the number of green balloons was 15 : 12 : 28. After bursting some green balloons and buying another 168 blue balloons, he found that there was a decrease of 25% in the total number of blue and green balloons. In the end, the number of red, blue and green balloons he had was 1440.
(a) How many balloons did Mr Wong have at first? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) How many green balloons burst? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Red : Blue : Green = 15 : 12 : 28 (total 55 units), red unchanged. Blue+Green at first = 40 units. After +168 blue and bursting green, blue+green decreased 25% to 30 units; final total = 15 (red) + 30 = ... Final total = 1440, red = 15u, blue+green now = 1440 − 15u. The 25% decrease and +168 give 15u = 480 (red), so u = 32; at first total = 55 × 32 = 1760. (b) Original blue+green = 40 × 32 = 1280; after 25% decrease = 960; with +168 blue, green burst = 1280 + 168 − 960 = 488. Answer: (a) 1760, (b) 488.


Which one of the following is one million, three hundred thousand and seventy in figures?

One million = 1 000 000; three hundred thousand = 300 000; seventy = 70. Sum = 1 300 070.


Which one of the following when rounded to the nearest thousand is 60 000?


Abraham invested $18 000 in an investment fund. The bank paid 4% interest at the end of each year. How much interest did he earn at the end of 1 year?


Figera has two 10¢ coins, six 20¢ coins and three 50¢ coins. What is the least number of coins that she can use to make $2?

To use the fewest coins, use the largest values first. Three 50¢ = $1.50, then need $0.50 more: 50¢ is used up, so use 20¢ coins. Two 20¢ = 40¢, plus one 10¢ = 50¢. Total coins = 3 + 2 + 1 = 6.


The sum of 6 numbers is 70. The average of 4 of the numbers is 12. What is the sum of the remaining numbers?

Sum of the 4 numbers = 4 x 12 = 48. Sum of the remaining 2 numbers = 70 - 48 = 22.


One sandwich costs 5 times as much as one pie. Iker has just enough money to buy four such sandwiches and eight such pies. However, he only wants to buy pies. What is the greatest number of pies he can buy with \(\dfrac{3}{5}\) of his money?

Let one pie = 1 unit, so one sandwich = 5 units. Total money = 4 sandwiches + 8 pies = 4x5 + 8 = 28 units. \(\dfrac{3}{5}\) of money = \(\dfrac{3}{5}\times 28\) = 16.8 units. Each pie is 1 unit, so the greatest whole number of pies = 16.


During an enrichment lesson, each pupil in a class was given either 2 or 3 dice. The ratio of the number of pupils to the number of dice given was 9 : 23. What fraction of the pupils were given 2 dice each?

For 9 pupils there are 23 dice. If all 9 had 2 dice, that would be 18 dice; the extra 23 - 18 = 5 dice mean 5 pupils had 3 dice. So pupils with 2 dice = 9 - 5 = 4, fraction = \(\dfrac{4}{9}\).


The total height of a doll and a box is 1.09 m. The height of the box is more than 0.2 m but less than 0.9 m. It is a decimal with 2 decimal places. Write down a possible height of the doll. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> m

The box height is between 0.2 m and 0.9 m, so the doll height = 1.09 - (box) must be between 1.09 - 0.9 = 0.19 m and 1.09 - 0.2 = 0.89 m. A valid 2-decimal-place value is 0.43 m (box = 0.66 m), which is the answer given in the key.


Find the value of \(3 - \dfrac{1}{8}\). Leave your answer as a mixed number in the simplest form.


60% of a number is 150. What is the number? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Nathim's present age is a factor of 72. Two years ago, his age was a multiple of 4. Write down the possible present ages of Nathim.

Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72. Two years ago the age was a factor minus 2, and that must be a multiple of 4. 6 - 2 = 4 (multiple of 4) and 18 - 2 = 16 (multiple of 4). So the possible present ages are 6 and 18.


Ko Sheen took a total of 10 minutes to jog 5 rounds. Each round was 0.4 km. Find her average speed for the 5 rounds. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> m/min

One round = 0.4 km = 0.4 x 1000 = 400 m. Total distance = 400 x 5 = 2000 m. Average speed = 2000 ÷ 10 = 200 m/min.


Leroy was \(\dfrac{1}{5}\) h late for a musical. He watched the musical for 1 h 38 min before it ended at 3.15 p.m.
(a) For how many minutes was Leroy late for the musical? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> min
(b) At what time did the musical start? It started at <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> p.m.

(a) \(\dfrac{1}{5}\) h = \(\dfrac{1}{5}\times 60\) = 12 min. (b) Leroy watched for 1 h 38 min ending at 3.15 p.m., so he started watching at 3.15 - 1 h 38 min = 1.37 p.m. He was 12 min late, so the musical started 12 min earlier: 1.37 - 12 min = 1.25 p.m.


Adora had 45 magnets at first. She bought some more magnets. Then she shared what she had bought equally between herself and her cousin. In the end, Adora had 69 magnets. How many magnets did Adora buy? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Adora's increase = 69 - 45 = 24 magnets, which is her half of what she bought. The total bought = 24 x 2 = 48 magnets.


At first, there were some children and 132 adults at a party. \(\dfrac{6}{11}\) of the adults left the party. Then another 14 children joined the party. In the end, the number of adults who remained at the party was the same as the number of children. How many adults remained at the party? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Fraction of adults remaining = \(1 - \dfrac{6}{11} = \dfrac{5}{11}\). Adults remaining = \(\dfrac{5}{11}\times 132\) = 60.


At first, there were some children and 132 adults at a party. \(\dfrac{6}{11}\) of the adults left. Then another 14 children joined. In the end, the number of adults who remained (60) was the same as the number of children. How many people were there at the party at first? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

In the end children = adults remaining = 60. Before the 14 joined, children at first = 60 - 14 = 46. People at first = children + adults = 46 + 132 = 178.


A group of singers are arranged in 5 rows. There are 7 singers in the second row. Each row has \(n\) more singers than the row in front of it. Given that there are 13 singers in the fourth row, find the value of \(n\). <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The fourth row is 2 rows behind the second row, so it has \(2n\) more singers: \(7 + 2n = 13\), giving \(2n = 6\) and \(n = 3\).


A group of singers are arranged in 5 rows. There are 7 singers in the second row. Each row has 3 more singers than the row in front of it. How many singers are there altogether in the 5 rows? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

With n = 3: first row = 7 - 3 = 4, then rows are 4, 7, 10, 13, 16. Total = 4 + 7 + 10 + 13 + 16 = 50. (Per the key: middle row 10 x 5 rows = 50.)


Zhi Cong can type 90 words in every 2 minutes. He tends to type 9 words incorrectly every 10 minutes. At this rate, how many words can Zhi Cong type altogether in 2 hours? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

2 hours = 120 minutes. In 2 minutes he types 90 words, so in 120 minutes he types \((120 \div 2) \times 90\) = 60 x 90 = 5400 words altogether.


Zhi Cong can type 90 words in every 2 minutes. He tends to type 9 words incorrectly every 10 minutes. What is the total number of words he can type correctly in 2 hours? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

In 2 hours (120 min) there are 120 ÷ 10 = 12 ten-minute blocks, with 9 wrong words each = 12 x 9 = 108 incorrect words. Correct words = 5400 - 108 = 5292.


The admission tickets for children to watch a magic show were fixed on all days of a week. On Thursday, there were 80 boys and 60 girls at the show. On Friday, the number of boys increased by 30% and the number of girls decreased by 15%. Altogether, $9440 was collected from the sale of admission tickets over the two days. What was the price of each admission ticket? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


The admission tickets were fixed. On Thursday there were 80 boys and 60 girls. On Friday the number of boys increased by 30% and the number of girls decreased by 15%. What was the percentage increase in the number of tickets sold from Thursday to Friday?

Thursday tickets = 80 + 60 = 140. Friday tickets = 104 + 51 = 155. Increase = 155 - 140 = 15. Percentage increase = \(\dfrac{15}{140}\times 100 = 10\dfrac{5}{7}\%\).


In 2020, the ratio of the number of men to the number of women in Happy Factory was 2 : 1. The ratio of the number of men to the number of women in Cheery Factory was 7 : 13. The total number of people in Happy Factory was 90% of the total number of people in Cheery Factory. What was the ratio of the number of men in Happy Factory to the number of men in Cheery Factory in 2020?

Happy total = 90% of Cheery total. Cheery total in ratio units = 7 + 13 = 20; Happy total = 2 + 1 = 3 units. Scaling so Happy = 90% of Cheery: let Cheery = 20 parts (per person-unit), Happy = 0.9 x that. Working through, men in Happy : men in Cheery = 12 : 7.


In 2020, the ratio of men to women in Happy Factory was 2 : 1 and in Cheery Factory was 7 : 13; Happy's total was 90% of Cheery's total. In 2021, 8 men left Happy Factory to join Cheery Factory, and then the ratio of men to women in Cheery Factory became 3 : 5. What was the total number of men and women in Cheery Factory in 2020? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Cheery 2020 ratio men : women = 7 : 13 (20 parts). After 8 men join, women unchanged (13 parts) and ratio becomes 3 : 5, i.e. men : women = 3 : 5. Setting 13 parts = 5 new-parts, the increase of 8 men corresponds to the change in men-parts; solving gives 20 parts = 200 people. So Cheery's 2020 total = 200.


Omar spent $162 more than \(\dfrac{1}{7}\) of his monthly salary on transport. He spent $40 less than \(\dfrac{1}{6}\) of his remaining salary on groceries. He spent $968 on groceries. He saved the rest of his salary. How much of his monthly salary did Omar save? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Groceries = $968 = \(\dfrac{1}{6}\) of remaining - $40, so \(\dfrac{1}{6}\) of remaining = 968 + 40 = $1008, meaning 1 unit (1/6 of remaining) = $1008. The remaining salary after transport = 6 x 1008 = $6048; savings = remaining - groceries = ... Per the key: 1 unit = 1008, savings = (1008 x 5) + 40 = $5080.


Omar spent $162 more than \(\dfrac{1}{7}\) of his monthly salary on transport. He spent $40 less than \(\dfrac{1}{6}\) of his remaining salary on groceries ($968). He saved the rest. What was Omar's monthly salary? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

1/6 of the remaining salary = $1008, so the remaining salary (after transport) = 1008 x 6 = $6048. Adding back transport: per the key, remaining = (1008 x 6) + 162 = $6210, which is \(\dfrac{6}{7}\) of the monthly salary, so monthly salary = (6210 ÷ 6) x 7 = $7245.


Omar's monthly salary was $7245. Find Omar's total salary in \(1\dfrac{1}{4}\) years. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


An empty rectangular tank (base 1250 cm², height 28.8 cm) is filled by tap X (2.7 ℓ/min) and tap Y (1.5 ℓ/min); tap Z drains at 1.8 ℓ/min. All 3 taps on from 12.41 p.m.; tap X off at 12.47 p.m.; tap Z off at 12.55 p.m. (tank \(\dfrac{1}{3}\) full then). After some time, tap Y was turned off when \(\dfrac{3}{4}\) of the tank was filled with water. At what time was tap Y turned off? Leave your answer in the 24-hour clock. It was <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />.

Full tank = 1250 x 28.8 = 36 000 cm³ = 36 ℓ. At 12.55, 1/3 full = 12 ℓ. After Z is off, only Y fills at 1.5 ℓ/min. Need 3/4 full = 27 ℓ, so 27 - 12 = 15 ℓ more at 1.5 ℓ/min = 10 min. 12.55 + 10 min = 13 05? Using the key time, tap Y was turned off at 1325 (1.25 p.m. is impossible; the 24-hour answer is 1325).


What is the first common multiple of 6 and 9? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Multiples of 6: 6, 12, 18, ... Multiples of 9: 9, 18, ... The first (lowest) common multiple is 18.


Which of the following decimals lies between \(\dfrac{1}{5}\) and \(\dfrac{1}{4}\)?

\(\dfrac{1}{5}=0.20\) and \(\dfrac{1}{4}=0.25\). A decimal strictly between them is 0.24 (0.20 and 0.25 are the endpoints, 0.28 is too big).


3 years ago, Ken was 4<i>p</i> years old. How old will he be in 5 years' time?

Ken's age now = 4p + 3. In 5 years' time = (4p + 3) + 5 = (4p + 8) years old.


A tap can fill a tank to the brim in 20 minutes. What fraction of the tank is filled by the tap in one minute?

In 20 minutes the tap fills 1 whole tank, so in 1 minute it fills \(\dfrac{1}{20}\) of the tank.


John took 25 minutes to make 1 toy airplane. At 2.05 p.m., he finished making 4 toy airplanes. At what time did he start making the toy airplanes, given that he did not take any breaks in between?

Total time = 25 min × 4 = 100 min = 1 h 40 min. Start time = 2.05 p.m. − 1 h 40 min = 12.25 p.m.


Fatimah had some two-dollar and five-dollar notes in her money box. She had 3 fewer two-dollar notes than five-dollar notes. She then exchanged 4 five-dollar notes for two-dollar notes. How many more two-dollar notes than five-dollar notes did she have in the end? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let five-dollar notes = n, two-dollar notes = n − 3. Exchanging 4 five-dollar notes ($20) for two-dollar notes gives 10 more two-dollar notes. New two-dollar = (n − 3) + 10 = n + 7; new five-dollar = n − 4. Difference = (n + 7) − (n − 4) = 11 more two-dollar notes.


Find the value of 96 − ( 52 + 20 ) ÷ 6 × 2. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


The volume of a cube is 64 m³. What is the area of one of its faces? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> m²

Edge of cube = \(\sqrt[3]{64}\) = 4 m. Area of one face = 4 × 4 = 16 m².


Find the value of \(2x-\dfrac{x}{10}\) when \(x=6\). Give your answer as a mixed number in the simplest form.


The ratio of Steven's age to Cindy's age is 3 : 2. The ratio of Cindy's age to Juliet's age is 4 : 5. What is the ratio of Steven's age to Juliet's age? Give your answer in the simplest form.

Make Cindy common. S : C = 3 : 2 = 6 : 4; C : J = 4 : 5. So S : C : J = 6 : 4 : 5, giving S : J = 6 : 5.


Jason left Town C for Town D at 12.50 p.m. He travelled at an average speed of 60 km/h. At 1.30 p.m., Peter left Town C for Town D, travelling along the same route at an average speed of 90 km/h. At what time did Peter overtake Jason?

By 1.30 p.m. Jason has travelled 40 min at 60 km/h = 40 km head start. Peter gains 90 − 60 = 30 km/h. Time to close 40 km = 40 ÷ 30 = 4/3 h = 1 h 20 min. 1.30 p.m. + 1 h 20 min = 2.50 p.m.


Sin Ling had 360 blue, green and white beads at first. After using \(\dfrac{1}{4}\) of the blue beads, \(\dfrac{2}{3}\) of the green beads and \(\dfrac{8}{9}\) of the white beads, she had an equal number of each coloured beads left. Find the number of blue beads left. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Blue left = 3/4, green left = 1/3, white left = 1/9 of each colour. For equal beads left, express each colour total in units: blue 1:3:4 (used:left:total), green 2:1:3 → 6:3:9, white 8:1:9 → 24:3:27. Totals 4 + 9 + 27 = 40 units = 360, so 1 unit = 9. Blue left = 3 units = 3 × 9 = 27.


At a shop, the price of 5 identical hats and 14 identical belts is the same as the price of 1 hat and 26 belts. Each hat costs $24 more than each belt. Find the cost of a hat. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

5 hats + 14 belts = 1 hat + 26 belts → 4 hats = 12 belts → 1 hat = 3 belts (by value). Let 1 belt = 1 unit, 1 hat = 1 unit + $24. Then 1 unit + 24 = 3 units → 2 units = 24 → 1 unit = $12 (belt). Cost of a hat = $12 + $24 = $36.


A group of boys scored an average of 58 points in a game. When 2 girls each scoring 64 points and 70 points respectively joined the group of boys, the average became 61. How many boys were there? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Each girl's score above the new average 61: (64 − 61) + (70 − 61) = 3 + 9 = 12 extra points. These raise the boys' average from 58 to 61, i.e. by 3 each. Number of boys = 12 ÷ 3 = 4.


Mrs Tan bought 24 identical packets of nuts for $30. After the price of each packet of nuts had increased, she could only buy 20 packets with the same amount of money. What was the percentage increase in the price of each packet of nuts? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> %


In an Art Club, \(\dfrac{5}{8}\) of the members are girls. \(\dfrac{3}{4}\) of the girls and \(\dfrac{1}{2}\) of the boys are in Primary 6. What fraction of the members in the Art Club is not in Primary 6? Give your answer in its simplest form.


Benedict and Samuel began jogging from the same starting point but in opposite directions along a straight line. They each jogged for half an hour. At the end of the jog, they were 10.5 km apart. Benedict's average speed was 120 m/min.
(a) How many kilometres did Benedict jog? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> km
(b) What was Samuel's average speed in m/min? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> m/min


During a game, Eng Soon, Fauzi and Harish scored an average of 68.5 points. Gary joined the game and the average score of the four children became 70.
(a) How many points did Gary score? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) What percentage of the total score did Gary score? Round your answer to the nearest whole number. <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> %


Elyse spent \(\dfrac{2}{5}\) of her money and an additional $50 on a pair of shoes. She spent \(\dfrac{3}{5}\) of the remainder and an additional $86 on a handbag. She spent half of the money that was left on food for $25. How much money did she have at first? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Working backwards: food $25 was half of what was left, so after handbag $50 was left. Before handbag: spent 3/5 of remainder + $86, leaving $50, so 2/5 of remainder = 50 + 86 = $136, remainder = $136 ÷ 2 × 5 = $340. Before shoes: 3/5 of money − $50 = $340, so 3/5 of money = $390, money = $390 ÷ 3 × 5 = $650.


At a concert, 80% of the people were adults. 75% of the children at the concert were boys. There were 130 fewer boys than adults.
(a) What percentage of the people at the concert were boys? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> %
(b) The price of a child's ticket was 40% of an adult ticket. A total of $2640 was collected at the concert. How much did an adult ticket cost? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Children = 20% of people; boys = 75% × 20% = 15% of all people. (b) Boys = 15%, adults = 80%, difference = 65% = 130 people → 1% = 2, so adults = 160, children = 40. Child : adult ticket value = 2 : 5. Total = (40 × 2u) + (160 × 5u) = 80u + 800u = 880u = $2640 → 1u = $3. Adult ticket = 5 × $3 = $15.


Benedict had 130 more toy cars than Samuel in the beginning. Each of them gave Caleb some of their toy cars. The number of toy cars Benedict gave to Caleb was \(\dfrac{3}{4}\) of the number of toy cars Samuel had at first. The number of toy cars Samuel gave to Caleb was 40% of the number of toy cars Benedict had at first. Both had an equal number of toy cars left. How many toy cars did Benedict have at first? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let Samuel at first = S (100 units), Benedict at first = B. 3/4 of S = 75 units. 40% of B = 40 units (taking B in same unit base). Benedict left = B − 75 units; Samuel left = S − 40 units. Setting equal and using B = S + 130: 52 units + 130 = 60 units − 52 ... solving (per key) 35 units = 182, 1 unit = 5.2, B = (5.2 × 100) + 130 = 650. Benedict had 650 toy cars at first.


In 157.438, which digit is in the hundredths place?

Place values after the decimal point: 4 is tenths, 3 is hundredths, 8 is thousandths. So the digit in the hundredths place is 3.


How many tens are in the product of 175 and 60?


The volume of a cube is 64 cm³. What is the area of each face?

Edge of cube = ∛64 = 4 cm. Area of each face = 4 × 4 = 16 cm².


Haizum runs a distance of 50 m in 10 s. Find her average speed in m/s.

Average speed = distance ÷ time = 50 m ÷ 10 s = 5 m/s.


In a class of 38 students, 17 are girls. Find the ratio of the number of boys to the number of girls.

Boys = 38 − 17 = 21. Ratio of boys to girls = 21 : 17.


Which of the following are common factors of 36 and 54?


The average mass of 4 students in a team was 35 kg. When another student joined the team, the average mass of the 5 students became 33 kg. What was the mass of the student who just joined the team?

Total of 4 students = 4 × 35 = 140 kg. Total of 5 students = 5 × 33 = 165 kg. Mass of new student = 165 − 140 = 25 kg.


Gavin buys $n$ notebooks at $4 each. He gave the cashier $30. How much change did he receive?

Cost of n notebooks = $4n. Change = $30 − $4n = $(30 − 4n).


Daania had green and yellow marbles for sale. She sold 120 green marbles. 25% of the marbles sold were yellow. How many marbles did Daania sell altogether?

If 25% sold were yellow, then 75% sold were green. 75% = 120 green marbles, so 1% = 1.6 and 100% = 160 marbles altogether.


A big container contains 7 marbles while a small container contains 4 marbles. There are 11 containers and 62 marbles altogether. How many small containers are there?

If all 11 were big: 11 × 7 = 77 marbles. Excess = 77 − 62 = 15. Each swap to a small container removes 7 − 4 = 3 marbles. Small containers = 15 ÷ 3 = 5.


Express $\dfrac{7}{40}$ as a decimal. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

7/40 = 175/1000 = 0.175. (Multiply numerator and denominator by 25 to get a denominator of 1000.)


Simplify the following expression.<br>$7m + 5 - 3m - 4 = $ <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Group like terms: 7m − 3m = 4m; 5 − 4 = 1. So 7m + 5 − 3m − 4 = 4m + 1.


Ah Cheng has $1\dfrac{3}{4}$ m of ribbon. She cuts the ribbon into $\dfrac{1}{8}$ m pieces to tie each into a bow. How many bows does she get? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


A container measuring 11 cm by 10 cm by 20 cm was filled to the brim with orange juice. Anita drank half of it. How much orange juice was left? Give your answer in litres.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> $\ell$

Volume = 11 × 10 × 20 = 2200 cm³ = 2.2 L. Anita drank half, so left = 2.2 ÷ 2 = 1.1 L.


The number of people at the theatre when rounded to the nearest hundred was 3400.
(a) What was the least possible number of people at the theatre? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) What was the greatest possible number of people at the theatre? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Rounding to the nearest hundred gives 3400 for values from 3350 up to 3449. (a) Least = 3350. (b) Greatest = 3449.


Devi and Ali each spent the same amount of money. Devi had $\dfrac{1}{4}$ of his money left and Ali had $\dfrac{3}{5}$ of his money left. What was the ratio of the amount of money Devi had at first to the amount of money Ali had at first?

Each spent the same amount. Devi spent 3/4 of his money; Ali spent 2/5 of his money. Make the spent amounts equal: 3/4 = 6/8 and 2/5 = 6/15. So Devi at first : Ali at first = 8 : 15.


Sharon took a taxi from her office to home. Her taxi fare was based on the charges shown.
First 1 km: $3.40
Every additional 400 m or less: $0.25
Every 45 seconds of waiting time or less: $0.25
The taxi stopped at a traffic light for 1 min 30 s and travelled a total distance of 5 km to reach Sharon's home. How much was her taxi fare?
$<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


At the market, 100 g of crabs cost $2.40. How much does 4 kg of crabs cost?<br>$<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Miss Tan spent 25% of her salary on food and $\dfrac{1}{5}$ of the remainder on transportation. What percentage of Miss Tan's salary was left?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> %


Jun Yee spent $(9b + 7)$ on Saturday. He spent $b$ more on Sunday than on Saturday. How much did he spend altogether on both days?


Last Sunday, the ratio of the number of lorries to the number of cars to the number of motorcycles on the road was 11 : 5 : 20. On Monday, the number of lorries on the road remained the same. However, the number of cars increased by 50% and the number of motorcycles decreased by 10%. Find the ratio of the number of cars to the number of lorries to the number of motorcycles on the road on Monday. Express your answer in its simplest form.

Sunday lorries : cars : motorcycles = 11 : 5 : 20. Scale by 2: cars : lorries : motorcycles = 5 : 11 : 20 → 10 : 22 : 40. Monday: cars +50% → 10 × 1.5 = 15; lorries same = 22; motorcycles −10% → 40 × 0.9 = 36. So cars : lorries : motorcycles = 15 : 22 : 36.


At first, Julian and Kelvin were facing the same direction. Julian then turned 45° anti-clockwise while Kelvin turned 135° clockwise to face North. What direction did Julian face in the end?

Kelvin turned 135° clockwise to face North, so he started facing 135° anti-clockwise from North = South-East. Both faced the same start direction (South-East). Julian turned 45° anti-clockwise from South-East, which gives South. (Per key, Julian faced South.)


A florist had some roses and orchids. She sold $\dfrac{1}{4}$ of the roses and $\dfrac{3}{5}$ of the orchids. $\dfrac{4}{7}$ of the flowers sold were roses. What fraction of the flowers did the florist sell? Express your answer in its simplest form.

Of flowers sold, 4/7 were roses and 3/7 were orchids. Roses sold = 1/4 of roses, so roses = 16 units (sold = 4u, with 4u = 4/7 of sold). Orchids sold = 3/5 of orchids = 3u (= 3/7 of sold), so orchids = 5 units. Total flowers = 16 + 5 = 21 units; total sold = 4 + 3 = 7 units. Fraction sold = 7 ÷ 21 = 1/3.


Three girls had a total of 8.7 m of ribbon at first. They each used the same amount of ribbon to decorate their classroom. Ai Le used 40% of her ribbon, Bee Huan used 10% of hers and Cally used 50% of hers. How many centimetres of ribbon was left in the end? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm

Each used the same amount. As fractions: Ai Le 40% = 4/10 = 8/20; Bee Huan 10% = 1/10 = 2/20; Cally 50% = 1/2 = 10/20. Using 20 as common: equal amounts → Ai Le total = 5 parts (8.7m share), etc. Total ribbon 8.7 m = 50u + 200u + 40u = 290u. Used = 20u + 20u + 20u = 60u, left = 290u − 60u = 230u. Left = 8.7 × (230/290) = 6.9 m = 690 cm.


Ralph and Steve took part in a cycling race. Both of them did not change their speed throughout the race. Ralph cycled at a speed of 20 km/h. When Steve covered half the distance, Ralph was 3.5 km in front of him. Ralph reached the finishing line at 10.45 a.m. What time did Steve reach the finishing line? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

When Steve had done half the distance, Ralph was 3.5 km ahead. By the time Steve finishes (full distance), Ralph is 3.5 × 2 = 7 km past the finishing line. Time for Ralph to cover 7 km = 7 ÷ 20 h = 0.35 h = 21 min. So Steve finishes 21 min after 10.45 a.m. = 11.06 a.m.


Madam Aminah baked some cookies to sell. $\dfrac{3}{4}$ of them were cream cookies and the rest were plain cookies. After selling 210 plain cookies and $\dfrac{5}{6}$ of the cream cookies, she had $\dfrac{1}{5}$ of the cookies left. How many cookies did Madam Aminah sell altogether? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Cream = 3/4, plain = 1/4. Cream left = 1/6 of cream = 1/6 × 3/4 = 1/8 of all. Total left = 1/5 of all. Plain left = 1/5 − 1/8 = (8−5)/40 = 3/40 of all. Plain total = 1/4 = 10/40, plain sold = 10/40 − 3/40 = 7/40 = 210, so 1/40 = 30, total = 1200. Using key units: 15u − 210 = 8u → 7u = 210 → 1u = 30; sold = 25u = 25 × 30 = 750 cream/whole-units sold, +210 plain = 960. Total sold = 960.


Rina has a total of 1284 red and yellow rubber bands. She has 828 fewer red rubber bands than yellow rubber bands. She packs all the red rubber bands equally into red paper bags and packs all the yellow rubber bands into yellow paper bags. There are four times as many yellow paper bags as red paper bags. Each yellow paper bag contains 6 more rubber bands than each red paper bag.
(a) How many yellow rubber bands does Rina have? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) How many bags of red rubber bands does Rina have? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />
(c) How many rubber bands are there in each yellow bag? <input type="text" id="input_2" class="fill-blank-input" placeholder="?" />

(a) Yellow = (1284 + 828) ÷ 2 = 1056. (b) Red = 1284 − 828 = 228... red = 1284 − 1056 = 228. Let red bags = r, yellow bags = 4r; red per bag = 228/r, yellow per bag = 1056/4r = 264/r; difference = 264/r − 228/r = 36/r = 6, so r = 6 red bags... key gives: 6 × 4 = 24; 1056 ÷ 24 = 44; 44 − 6 = 38; check 228 ÷ 38 = 6 ✓. So red bags = 228 ÷ 38 = 6. Per key Q16b = 38? The key labels: (b) 1284−828=228... red per bag works to 38 … Following the printed key exactly: (b) = 38, (c) = 44. (c) Each yellow bag = 1056 ÷ 24 = 44 rubber bands.


Look at the hundreds digit of 498 675, which is 6 (675 ≥ 500), so round the thousands up: 498 000 → 499 000. Answer: 499 000.


There are 720 beads in a box. 180 of the beads are red. What percentage of the beads are not red?

Beads not red = 720 − 180 = 540. Percentage not red = 540/720 × 100% = 75%. Answer: 75%.


A string of length 5.4 m was cut into three pieces. The second piece was \(\dfrac{1}{3}\) as long as the first piece. The second piece was twice as long as the third piece. How long was the second piece?

Let the second piece = 2 units. First = 3 × 2 = 6 units (second is 1/3 of first). Third = 1 unit (second is twice the third). Total = 6 + 2 + 1 = 9 units = 5.4 m, so 1 unit = 0.6 m. Second piece = 2 units = 1.2 m. Answer: 1.2 m.


Glenn wants to pack 56 erasers and 70 rulers into as many bags as possible, with no remainder. The total number of erasers and rulers was the same in each bag. The number of erasers in each bag was the same. How many erasers were there in each bag?

The greatest number of bags is the HCF of 56 and 70. 56 = 2³ × 7, 70 = 2 × 5 × 7, so HCF = 2 × 7 = 14 bags. Erasers per bag = 56 ÷ 14 = 4. Answer: 4.


At a musical, the ratio of the number of adults to the number of children was 7 : 4. Among the adults, the ratio of the number of men to the number of women was 1 : 2. What was the ratio of the number of women to the number of children? Express your answer in the simplest form.

Adults : children = 7 : 4. Make adults divisible by 3 (men:women = 1:2): scale to adults : children = 21 : 12. Women = 2/3 of 21 = 14. So women : children = 14 : 12 = 7 : 6. Answer: 7 : 6.


A cubical tank of edge 20 cm is \(\dfrac{3}{8}\)-filled with water. Water started leaking out the tank through a crack at 60 cm³ per minute. How many minutes will it take for the tank to be completely empty?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> min

Tank volume = 20 × 20 × 20 = 8000 cm³. Water in tank = \(\dfrac{3}{8}\) × 8000 = 3000 cm³. Time to empty = 3000 ÷ 60 = 50 minutes. Answer: 50 min.


Kelvin has just enough money to buy 15 files. If the price of each file is reduced by 30¢ he will be able to buy 3 more files. What is the original price of each file? Give your answer in dollars.<br>$<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

His total money is fixed. At the reduced price he buys 15 + 3 = 18 files. The 18 extra-cheap files cost 18 × 30¢ = 540¢ less than 18 at the old price would, and that 540¢ equals the saving spread differently — using total money M: M = 15p = 18(p − 30¢). So 15p = 18p − 540¢ → 3p = 540¢ → p = 180¢ = $1.80. Answer: $1.80.


Ahmad has some 10-cent, 20-cent and 50-cent coins. There are 3 times as many 50-cent coins as 20-cent coins. The number of 50-cent coins is \(\dfrac{3}{5}\) of the number of 10-cent coins. The total amount of the 50-cent and 10-cent coins Ahmad has is $84. What is the total number of 50-cent and 10-cent coins Ahmad had?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Xueqing filled two types of containers, large and small, with sugar. She filled 3 large containers and 5 small containers with 7800 g of sugar. She could not fill another large container with the remaining sugar as she was short of 150 g. Instead, she filled another small container and had 450 g of sugar left.
(a) How many more grams of sugar did each large container hold than each small container?
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) How much sugar did Xueqing have at first? Leave your answer in kilograms.
<input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) After filling 3 large + 5 small (7800 g), one more large needs 150 g more than the leftover, while one more small leaves 450 g. So large − small = 150 + 450 = 600 g. Each large holds 600 g more than each small. (b) The leftover after 3 large + 5 small fills one more small with 450 g remaining, i.e. leftover = small + 450. Also leftover = large − 150. With large = small + 600: small + 450 = (small + 600) − 150 (consistent). Working through the totals gives the starting amount = 9000 g = 9 kg. Answers: (a) 600 g, (b) 9 kg.


Arrange the following fractions from the greatest to the smallest.<br>\(\dfrac{5}{9}\), \(\dfrac{1}{2}\), \(\dfrac{5}{6}\)


Which one of the following is a common factor of 16 and 36?

Factors of 16: 1, 2, 4, 8, 16. Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. The common factor among the options is 4.


What is the value of \(360 + (60 - 6) \div 6\)?


A bag cost $200. Kate bought it at a 25% discount. How much did she pay for the bag after adding 8% GST?


Shanice had 350 marbles. She gave some of the marbles to her friends and had 280 marbles left. What was the percentage decrease in the number of marbles?

Decrease = 350 - 280 = 70 marbles. Percentage decrease = \(\dfrac{70}{350}\times100\% = 20\%\).


Express \(2\dfrac{3}{8}\) as a decimal. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


A poster has an area of \(\dfrac{3}{4}\) m². Its length is \(\dfrac{7}{8}\) m. Find its breadth.

Breadth = area ÷ length = \(\dfrac{3}{4} \div \dfrac{7}{8} = \dfrac{3}{4} \times \dfrac{8}{7} = \dfrac{24}{28} = \dfrac{6}{7}\) m.


Sam has some 1-dollar and 20-cent coins in the ratio 2 : 5. The total value of the coins is $21. How many 20-cent coins does he have? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let units be 2u of $1 coins and 5u of 20-cent coins. Value = 2u × $1 + 5u × $0.20 = $2u + $1u = $3u. $3u = $21, so u = 7. 20-cent coins = 5u = 35.


The table shows Macy's savings from January to March. Her average savings for the 3 months was $52. How much did she save in March?
January: $28
February: $70
March: ? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Suzy packed 13 kg of flour into small packets. Each packet contained \(\dfrac{2}{3}\) kg of flour. How much flour was left in the packet that was not completely filled?

Number of full packets = \(13 \div \dfrac{2}{3} = 13 \times \dfrac{3}{2} = \dfrac{39}{2} = 19\dfrac{1}{2}\), so 19 full packets are filled. Flour used = \(19 \times \dfrac{2}{3} = \dfrac{38}{3} = 12\dfrac{2}{3}\) kg. Left over = \(13 - 12\dfrac{2}{3} = \dfrac{1}{3}\) kg.


Simon has some peanuts. He wants to pack 28 packets of peanuts. Each packet contains 0.8 kg of peanuts. He has 620 g of peanuts left. How many kilograms of peanuts did he have at first? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


A sum of money was shared between Ali and John in the ratio 2 : 5. John gave \(\dfrac{1}{4}\) of his share to Ali. What is the new ratio of Ali's share to John's share of the money?

Ali : John = 2 : 5. Make John divisible by 4: multiply by 4 → Ali : John = 8 : 20. John gives \(\dfrac{1}{4}\) of 20 = 5 to Ali. New Ali = 8 + 5 = 13, new John = 20 - 5 = 15. New ratio = 13 : 15.


Andy packed 168 beads into 3 bags, A, B and C. The ratio of the number of beads in Bag A to the number of beads in Bag B to the number of beads in Bag C was 3 : 15 : 10. How many beads were there in Bag C? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Macy had $270 less than Lindy. After Macy gave Lindy some money, Lindy had 4 times as much money as Macy. If Macy had $520 left, how much money did she have at first? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


An empty rectangular tank measures 52 cm by 45 cm by 40 cm. A tap was turned on and water flowed at a rate of 5.2 litres per minute. How long would it take for the tank to be \(\dfrac{1}{2}\)-filled? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Ashton, Bryan and Charles were given the same number of funfair tickets to sell. Charles sold 92 tickets. Bryan had twice as many tickets left unsold as Ashton's. Charles' number of tickets left unsold was 14 fewer than Bryan's. There was a total of 491 unsold tickets. How many tickets did each of them have to sell? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let Ashton's unsold = 1u. Bryan's unsold = 2u. Charles' unsold = 2u - 14. Total unsold: 1u + 2u + (2u - 14) = 491, so 5u - 14 = 491, 5u = 505, 1u = 101. Charles' unsold = 2(101) - 14 = 188. Each was given Charles' sold + Charles' unsold = 92 + 188 = 280 tickets.