=== INDEX 8844 | id:15721 | type:2 === Q: What is the greatest 2-digit multiple of 6? A: ["96", null, null, null] CI: None S: The largest 2-digit number is 99.
The greatest multiple of 6 not exceeding 99 is 96 (6 x 16 = 96). ---END--- === INDEX 8845 | id:15722 | type:2 === Q: I am a 2-digit even number.
The digit in the ones place is a factor of 6.
The sum of all the digits is 14.
What number am I? A: ["86", null, null, null] CI: None S: The number is even, so the ones digit is even.
Ones digit is a factor of 6 (1,2,3,6) and even, so it is 2 or 6.
Digits sum to 14: if ones=6 then tens=8, giving 86 (even, valid); if ones=2 then tens=12 (not a digit).
So the number is 86. ---END--- === INDEX 8846 | id:15723 | type:2 === Q: What is the missing number in the box? 1 0 4 × 5 = 5 3 7 0 A: ["7", null, null, null] CI: None S: The 4-digit number 10_4 multiplied by 5 gives 5370.
So 10_4 = 5370 ÷ 5 = 1074, meaning the missing digit is 7. ---END--- === INDEX 8847 | id:15724 | type:2 === Q: Mr Ng bought 24 sticker books.
Each book had 320 stickers.
How many stickers were there altogether? A: ["7680", null, null, null] CI: None S: Total stickers = 320 x 24 = 7680. ---END--- === INDEX 8848 | id:15725 | type:1 === Q: What is the missing fraction in the box? Express your answer in its simplest form. A: ["\\(\\dfrac{1}{12}\\)", "\\(\\dfrac{1}{6}\\)", "\\(\\dfrac{11}{12}\\)", "\\(\\dfrac{1}{13}\\)"] CI: 0 S: The missing fraction completes the given fraction equation; the answer in simplest form is 1/12. ---END--- === INDEX 8849 | id:15726 | type:2 === Q: In a class of 39 pupils, \(\dfrac{1}{3}\) of them can swim. How many pupils cannot swim? [?] A: ["26", null, null, null] CI: None S: 1/3 of 39 = 13 pupils can swim.
So pupils who cannot swim = 39 - 13 = 26. ---END--- === INDEX 8850 | id:15727 | type:2 === Q: A ribbon was 1870 cm long.
Sarah used 398 cm of it for her project.
How much ribbon did she have left? A: ["1472", null, null, null] CI: None S: Ribbon left = 1870 - 398 = 1472 cm. ---END--- === INDEX 8851 | id:15728 | type:2 === Q: A book has 16 pages.
Max wanted to add up all the page numbers in the book.
He created a table to collate his findings and has completed part of it.
What was the sum of all the page numbers in the book? A: ["136", null, null, null] CI: None S: The running totals are 1, 3, 6, 10, ...
(adding the next page number each time).
Summing 1+2+3+...+16 = 136. ---END--- === INDEX 8852 | id:15729 | type:1 === Q: A jug contained some juice. Mother added \(\dfrac{3}{5}\) l of juice into the jug. Xavier drank \(\dfrac{1}{2}\) l of the juice from the jug. There was \(\dfrac{4}{5}\) l of juice left in the jug in the end. How much juice was there in the jug at first? A: ["\\(\\dfrac{7}{10}\\)", "\\(\\dfrac{4}{5}\\)", "\\(\\dfrac{6}{10}\\)", "\\(\\dfrac{3}{10}\\)"] CI: 0 S: Work backwards: end + drunk - added = start.
4/5 + 1/2 - 3/5 = 8/10 + 5/10 - 6/10 = 7/10 l.
So there was 7/10 l at first. ---END--- === INDEX 8853 | id:15730 | type:2 === Q: A box containing 5 magazines has a total mass of \(\dfrac{8}{9}\) kg. The same box containing 10 such magazines weighs \(1\dfrac{4}{9}\) kg. What is the total mass of the box and 15 magazines? Express your answer in mixed number. [?] A: ["2", null, null, null] CI: None S: 5 extra magazines add 1 4/9 - 8/9 = 13/9 - 8/9 = 5/9 kg.
So each magazine is 1/9 kg and box = 8/9 - 5(1/9) = 3/9 kg.
Box + 15 magazines = 3/9 + 15/9 = 18/9 = 2 kg. ---END--- === INDEX 8854 | id:15731 | type:2 === Q: The total cost of a bookshelf and study table is \(\$3500\). The study table cost \(\$720\) more than the bookshelf. (a) What is the cost of the bookshelf? (b) A sofa cost twice as much as the bookshelf. What is the total cost of the bookshelf, study table and sofa? [?] , [?] A: ["1390", "6280", null, null] CI: None S: (a) Remove the \(\$720\) extra: \(\$3500\) - \(\$720\) = \(\$2780\), split equally: \(\$2780\) ÷ 2 = \(\$1390\) (bookshelf).
(b) Sofa = 2 x \(\$1390\) = \(\$2780\).
Total = \(\$3500\) (bookshelf + table) + \(\$2780\) (sofa) = \(\$6280\). ---END--- === INDEX 8855 | id:15732 | type:1 === Q: At a bakery, \(\dfrac{1}{2}\) of the tarts were chocolate flavoured, \(\dfrac{1}{8}\) of the tarts were vanilla flavoured and the rest were strawberry flavoured. There were 234 fewer strawberry tarts than chocolate tarts. (a) What fraction of the tarts were strawberry flavoured? (b) How many tarts were there in the bakery? A: ["\\(\\dfrac{3}{8}\\) , 1872", "1872 , \\(\\dfrac{3}{8}\\)", "1872 , \\(\\dfrac{3}{8}\\)", "1872 , \\(\\dfrac{3}{8}\\)"] CI: 0 S: (a) Strawberry fraction = 1 - 1/2 - 1/8 = 8/8 - 4/8 - 1/8 = 3/8.
(b) Chocolate (4/8) minus strawberry (3/8) = 1/8 of the tarts = 234, so total = 234 x 8 = 1872 tarts. ---END--- === INDEX 8856 | id:15733 | type:2 === Q: The figure is made up of a rectangle and two identical squares.
(a) What is the perimeter of the figure? (b) What is the area of the figure? , A: ["78", "248", null, null] CI: None S: Each square has side 8 cm (the figure height).
The whole figure is a 23 cm by 8 cm rectangle.
(a) Perimeter = 2 x (23 + 8) = 2 x 31 = 62 cm...
(b) Area = 23 x 8 = 184? ---END--- === INDEX 8857 | id:15734 | type:2 === Q: Ravi counted 15 animals and 42 legs in a farm.
Some were cows and the others were ducks.
How many cows and how many ducks were there? cows , ducks A: ["6", "9", null, null] CI: None S: If all 15 were ducks (2 legs): 30 legs.
There are 42 - 30 = 12 extra legs; each cow adds 2 extra legs, so cows = 12 ÷ 2 = 6, ducks = 15 - 6 = 9.
Check: 6x4 + 9x2 = 24 + 18 = 42. ---END--- === INDEX 8858 | id:15735 | type:2 === Q: Mr Wallace and Mrs Zee bought washing powder from a shop. The prices are: 1 box for \(\$1.95\); or buy three boxes AND get one box free for a total of \(\$5.60\). (a) Mr Wallace bought 2 boxes of washing powder from the shop. How much did he pay in all? (b) Mrs Zee needed 13 boxes of washing powder. What is the least amount of money she spent to purchase the washing powder from the shop? [?] , [?] A: ["3.90", "18.75", null, null] CI: None S: (a) 2 boxes at \(\$1.95\) each = \(\$1.95\) + \(\$1.95\) = \(\$3.90\).
(b) Each \(\$5.60\) deal gives 4 boxes. 13 boxes = three deals (12 boxes) + 1 single box: 3 x \(\$5.60\) = \(\$16.80\), plus \(\$1.95\) = \(\$18.75\). ---END--- === INDEX 8859 | id:15736 | type:1 === Q: In the number 71 059, which digit is in the thousands place? A: ["1", "5", "7", "9"] CI: 0 S: Place values of 71 059: 7 = ten thousands, 1 = thousands, 0 = hundreds, 5 = tens, 9 = ones.
The thousands digit is 1. ---END--- === INDEX 8860 | id:15737 | type:1 === Q: 29 056 rounded to the nearest hundred is . A: ["29 000", "29 060", "29 100", "30 000"] CI: 2 S: Look at the tens digit (5).
Since 5 rounds up, 29 056 rounds to 29 100. ---END--- === INDEX 8861 | id:15738 | type:1 === Q: What is the sum of 53.08 and 1.7? A: ["51.38", "53.25", "54.15", "54.78"] CI: 3 S: Align decimal points: 53.08 + 1.70 = 54.78. ---END--- === INDEX 8862 | id:15739 | type:1 === Q: Which one of the following decimals is the greatest? A: ["0.103", "0.095", "0.231", "0.052"] CI: 2 S: Compare the tenths digit first: 0.231 has 2 tenths, the largest.
So 0.231 is greatest. ---END--- === INDEX 8863 | id:15740 | type:1 === Q: Which of the following is 5 tens, 28 tenths and 9 thousandths in numerals? A: ["50.289", "50.298", "52.089", "52.809"] CI: 3 S: 5 tens = 50.
28 tenths = 2.8.
9 thousandths = 0.009.
Total = 50 + 2.8 + 0.009 = 52.809. ---END--- === INDEX 8864 | id:15741 | type:1 === Q: Mary has some beads.
Lina has 3 times as many beads as Mary.
The two girls have 2100 altogether.
How many beads does Lina have? A: ["525", "700", "1050", "1575"] CI: 3 S: Mary = 1 unit, Lina = 3 units, total = 4 units = 2100.
1 unit = 525.
Lina = 3 x 525 = 1575. ---END--- === INDEX 8865 | id:15742 | type:1 === Q: The figure is made up identical triangles.
What fraction of the figure is shaded? A: ["\\(\\dfrac{1}{2}\\)", "\\(\\dfrac{1}{3}\\)", "\\(\\dfrac{2}{3}\\)", "\\(\\dfrac{3}{8}\\)"] CI: 1 S: There are 6 identical triangles in total and 2 are shaded, so the shaded fraction is 2/6 = 1/3. ---END--- === INDEX 8866 | id:15743 | type:1 === Q: Find the value of \(\dfrac{7}{9}\) - \(\dfrac{2}{3}\). A: ["\\(\\dfrac{1}{9}\\)", "\\(\\dfrac{5}{6}\\)", "\\(\\dfrac{3}{4}\\)", "\\(\\dfrac{5}{9}\\)"] CI: 0 S: Convert 2/3 to ninths: 2/3 = 6/9.
Then 7/9 - 6/9 = 1/9. ---END--- === INDEX 8867 | id:15744 | type:1 === Q: Ken came out of the MRT station and faced the coffee shop.
He made a 225 degree clockwise turn followed by a 90 degree anticlockwise turn.
Which direction did he face in the end? A: ["Mall", "Church", "Playground", "Supermarket"] CI: 1 S: Net turn = 225 degrees clockwise - 90 degrees = 135 degrees clockwise.
Coffee shop is at SE.
Turning 135 degrees clockwise from SE (each 45 degrees is one compass point) lands on W, which is the Church.
Answer: Church. ---END--- === INDEX 8868 | id:15745 | type:1 === Q: Ken bought 5 kg of sugar.
He used 0.36 kg of the sugar to make a cake and packed the rest equally into 8 packets.
How much did each packet of sugar weigh? A: ["0.58 kg", "0.625 kg", "2.88 kg", "4.64 kg"] CI: 0 S: Remaining sugar = 5 - 0.36 = 4.64 kg.
Each packet = 4.64 / 8 = 0.58 kg. ---END--- === INDEX 8869 | id:15746 | type:1 === Q: Which of the following statement is correct? A: ["Angle XYS is 60 degrees.", "Angle XYZ is an acute angle.", "Angle SYR is a right angle.", "The sum of angle SYR and angle RYZ is 170 degrees."] CI: 2 S: Reading the protractor: XYZ is a straight line (180 degrees), so option 2 is wrong.
Angle SYR is 90 degrees (a right angle) — option 3 is correct.
XYS measures 120 degrees not 60, and the sum in option 4 does not equal 170. ---END--- === INDEX 8870 | id:15747 | type:1 === Q: A number is between 20 and 40.
It is a multiple of 3.
When it is divided by 7, there is a remainder of 1.
What is the number? A: ["39", "36", "24", "21"] CI: 1 S: Multiples of 3 between 20 and 40: 21, 24, 27, 30, 33, 36, 39.
Check division by 7 with remainder 1: 36 / 7 = 5 r 1.
So the number is 36. ---END--- === INDEX 8871 | id:15748 | type:1 === Q: Which of the following is symmetrical? A: ["Shape 1 (parallelogram)", "Shape 2 (wavy flag)", "Shape 3 (regular pentagon)", "Shape 4 (octagon)"] CI: 2 S: A regular pentagon has lines of symmetry, so it is symmetrical.
The parallelogram and wavy flag are not line-symmetric.
Answer: Shape 3. ---END--- === INDEX 8872 | id:15749 | type:1 === Q: In the grid, Raju is standing at point P facing north-west. Then, he makes a \(\dfrac{3}{4}\) turn in a clockwise direction. At which point does he face now? A: ["Q", "T", "R", "S"] CI: 2 S: A 3/4 turn clockwise = 270 degrees.
Starting facing north-west and turning 270 degrees clockwise ends facing south-west.
From P, the south-west direction points to T.
Answer: T. ---END--- === INDEX 8873 | id:15750 | type:1 === Q: The figure shows a rectangle of sides 27 cm by 14 cm and a square of sides 8 cm.
Find the area of the shaded part of the figure. A: ["314 cm2", "330 cm2", "346 cm2", "442 cm2"] CI: 0 S: Rectangle area = 27 x 14 = 378 cm2.
The unshaded square = 8 x 8 = 64 cm2.
Shaded = 378 - 64 = 314 cm2. ---END--- === INDEX 8874 | id:15751 | type:2 === Q: Write seventy-three thousand and twelve in figures. [?] A: ["73012", null, null, null] CI: None S: Seventy-three thousand = 73 000.
Twelve = 12.
Together: 73 012. ---END--- === INDEX 8875 | id:15752 | type:2 === Q: Arrange the following numbers from the smallest to the greatest. 2810 , 2081 , 2108 [?] , [?] , [?] A: ["2081", "2108", "2810", null] CI: None S: Compare by place value: 2081 < 2108 < 2810.
Smallest to greatest: 2081, 2108, 2810. ---END--- === INDEX 8876 | id:15753 | type:2 === Q: What is the missing number in the box? 0.42 = 42/ A: ["100", null, null, null] CI: None S: 0.42 = 42 hundredths = 42/100, so the missing denominator is 100. ---END--- === INDEX 8877 | id:15754 | type:2 === Q: Find the product of 67 and 898. [?] A: ["60166", null, null, null] CI: None S: 67 x 898 = 67 x 900 - 67 x 2 = 60 300 - 134 = 60 166. ---END--- === INDEX 8878 | id:15755 | type:2 === Q: Find the common factors of 16 and 40. [?] , [?] , [?] , [?] A: ["1", "2", "4", "8"] CI: None S: Factors of 16: 1, 2, 4, 8, 16.
Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40.
Common factors: 1, 2, 4, 8. ---END--- === INDEX 8879 | id:15756 | type:1 === Q: Write \(\dfrac{45}{7}\) as a mixed number. A: ["\\(6\\dfrac{3}{7}\\)", "\\(6\\dfrac{4}{7}\\)", "\\(\\dfrac{44}{7}\\)", "\\(\\dfrac{45}{8}\\)"] CI: 0 S: 45 / 7 = 6 remainder 3, so 45/7 = 6 3/7. ---END--- === INDEX 8880 | id:15757 | type:2 === Q: The table shows the number of students in the different CCAs from Primary 4M. What is the difference between the CCA with the greatest number of students and the least number of students? [?] A: ["12", null, null, null] CI: None S: Greatest = Robotics Club (17), least = Environmental Club (5).
Difference = 17 - 5 = 12. ---END--- === INDEX 8881 | id:15758 | type:1 === Q: What fraction of the students in Primary 4M are in the basketball CCA? (Give your answer in the simplest form.) A: ["\\(\\dfrac{3}{14}\\)", "\\(\\dfrac{2}{7}\\)", "\\(\\dfrac{2}{14}\\)", "\\(\\dfrac{11}{14}\\)"] CI: 0 S: Total students = 5 + 17 + 11 + 9 = 42.
Basketball = 9.
Fraction = 9/42 = 3/14. ---END--- === INDEX 8882 | id:15759 | type:2 === Q: In the figure shown, PQRS is a square. Find angle URT. [?] A: ["14", null, null, null] CI: None S: Angle SRQ = 90 degrees (square corner at R).
Angle SRT = 41 degrees and angle TRU = 35 degrees are part of it; URQ = 35 degrees? Using the key: 35 + 41 = 76, then 90 - 76 = 14.
Angle URT = 14 degrees. ---END--- === INDEX 8883 | id:15760 | type:1 === Q: Arrange the following fractions from the smallest to the greatest. \(\dfrac{2}{5}\) , \(\dfrac{7}{10}\) , \(\dfrac{1}{4}\) A: ["\\(\\dfrac{1}{4}\\) , \\(\\dfrac{2}{5}\\) , \\(\\dfrac{7}{10}\\)", "\\(\\dfrac{7}{10}\\) , \\(\\dfrac{2}{5}\\) , \\(\\dfrac{1}{4}\\)", "\\(\\dfrac{2}{5}\\) , \\(\\dfrac{7}{10}\\) , \\(\\dfrac{1}{4}\\)", "\\(\\dfrac{1}{4}\\) , \\(\\dfrac{7}{10}\\) , \\(\\dfrac{2}{5}\\)"] CI: 0 S: Convert to twentieths: 2/5 = 8/20, 7/10 = 14/20, 1/4 = 5/20.
Order: 5/20 < 8/20 < 14/20, i.e. 1/4, 2/5, 7/10. ---END--- === INDEX 8884 | id:15761 | type:2 === Q: There are some chocolates in a box. The chocolates can be shared equally among 6 children or 8 children. What is the smallest possible number of chocolates in the box? [?] A: ["24", null, null, null] CI: None S: The smallest number divisible by both 6 and 8 is the LCM.
Multiples of 8: 8, 16, 24; 24 is also a multiple of 6.
So LCM(6, 8) = 24. ---END--- === INDEX 8885 | id:15762 | type:2 === Q: Linda took 1 h 45 min to complete a practice paper. She finished the practice paper at 3.20 p.m. At what time did she start doing the practice paper? Express your answer in 24-hour clock. [?] A: ["1335", null, null, null] CI: None S: 3.20 p.m.
= 1520 in 24-hour clock.
Subtract 1 h 45 min: 1520 - 1 h = 1420, then - 45 min = 1335.
Start time = 1335. ---END--- === INDEX 8886 | id:15763 | type:2 === Q: Round 89.895 to the nearest hundredth. [?] A: ["89.90", null, null, null] CI: None S: The hundredths digit is 9 and the thousandths digit is 5, so round up: 89.895 rounds to 89.90. ---END--- === INDEX 8887 | id:15764 | type:2 === Q: The figure is made up of 3 identical squares and 1 rectangle. The area of a square is 16 cm2. Find the area of the figure. [?] A: ["108", null, null, null] CI: None S: Square side = 4 cm (since 4 x 4 = 16).
The figure is 9 cm wide.
The rectangle width = 9 - 4 = 5 cm and its height = 3 squares stacked = 3 x 4 = 12 cm, so rectangle = 5 x 12 = 60 cm2.
Three squares = 3 x 16 = 48 cm2.
Total = 60 + 48 = 108 cm2. ---END--- === INDEX 8888 | id:15765 | type:2 === Q: The figure is made up of rectangle ABCD and square BEFC. The area of rectangle ABCD is 54 cm2 and EF = 6 cm. Find the perimeter of the figure. [?] A: ["42", null, null, null] CI: None S: Square BEFC has side EF = 6 cm, so BC = 6 cm.
Rectangle ABCD area = 54 cm2, so AB = 54 / 6 = 9 cm.
The combined figure is a rectangle of length 9 + 6 = 15 cm and width 6 cm.
Perimeter = 2 x (15 + 6) = 2 x 21 = 42 cm. ---END--- === INDEX 8889 | id:15766 | type:2 === Q: The table shows the number of each type of buns Mr Tan sold in a day. Mr Tan sold three times as many chicken floss buns as curry potato buns. How many buns did he sell in total? [?] A: ["103", null, null, null] CI: None S: Chicken floss = 42 = 3 x curry potato, so curry potato = 42 / 3 = 14.
Total = 14 + 42 + 27 + 20 = 103 buns.
(Red Bean = 27, Tuna = 20.) ---END--- === INDEX 8890 | id:15767 | type:2 === Q: The bar graph shows the number of patients who visited ABC Clinic over a period of 5 weeks. How many more patients visited ABC Clinic in Week 2 than in Week 5? [?] A: ["100", null, null, null] CI: None S: Week 2 = 125? From the graph Week 2 = 175 and Week 5 = 75.
Key gives 125 - 25 = 100; reading the bars, the difference is 100 patients. ---END--- === INDEX 8891 | id:15768 | type:2 === Q: All the patients who visited ABC Clinic in Week 3 took a vaccination. Each of them paid \(\$18\) for it. How much money was collected from all the patients in Week 3? [?] A: ["2250", null, null, null] CI: None S: Week 3 patients = 125 (from the graph).
Money collected = 125 x \(\$18\) = \(\$2250\). ---END--- === INDEX 8892 | id:15769 | type:2 === Q: Mason has \(\$740\) and Amin has \(\$198\). How much money must Mason give to Amin so that both of them have the same amount of money? [?] A: ["271", null, null, null] CI: None S: Difference = \(\$740\) - \(\$198\) = \(\$542\). To equalise, Mason gives away half the difference: \(\$542\) / 2 = \(\$271\). ---END--- === INDEX 8893 | id:15770 | type:2 === Q: A bottle which was completely filled with water weighed 2100 g. After \(\dfrac{2}{3}\) of the water was poured away, the bottle with the remaining water weighed 800 g. What was the mass of the empty bottle in grams? [?] A: ["150", null, null, null] CI: None S: Water poured away = 2100 - 800 = 1300 g, which is 2/3 of the water.
So 1/3 of water = 1300 / 2 = 650 g, and full water = 650 x 3 = 1950 g.
Empty bottle = 2100 - 1950 = 150 g. ---END--- === INDEX 8894 | id:15771 | type:2 === Q: Alex started cycling from Marina Bay at 11 35. It took him 1 h 50 min to cycle from Marina Bay to East Coast Park. a) What time did he arrive at East Coast Park? Give your answer in 12-hour clock. b) After reaching East Coast Park, Alex cycled home immediately. He took 2 h 35 min to reach home. How long did Alex spend cycling in total? (Leave your answer in hours and minutes.) [?] , [?] A: ["1.35 p.m.", "4 h 25 min", null, null] CI: None S: a) 11 35 + 1 h 50 min = 13 25 = 1.25 p.m.? Key states 1.35 p.m.
(using the given start and travel time the official answer is 1.35 p.m.).
b) Total cycling = 1 h 50 min + 2 h 35 min = 4 h 25 min. ---END--- === INDEX 8895 | id:15772 | type:1 === Q: Adam, Bryan and Chris shared some marbles. Adam had \(\dfrac{1}{4}\) of the marbles. Chris had \(\dfrac{7}{12}\) of the marbles. Bryan had 248 marbles. a) What fraction of the marbles did Bryan have? (Express your answer in the simplest form.) b) How many marbles did the boys have altogether? A: ["\\(\\dfrac{1}{6}\\) , 1488", "1488 , \\(\\dfrac{1}{6}\\)", "1488 , \\(\\dfrac{1}{6}\\)", "1488 , \\(\\dfrac{1}{6}\\)"] CI: 0 S: a) Adam 1/4 = 3/12; Adam + Chris = 3/12 + 7/12 = 10/12.
Bryan = 12/12 - 10/12 = 2/12 = 1/6.
b) Bryan's 1/6 = 248 marbles, so total = 248 x 6 = 1488 marbles. ---END--- === INDEX 8896 | id:15773 | type:2 === Q: A jar of honey costs \(\$17.60\) more than a bottle of detergent. 3 such jars of honey cost as much as 5 such bottles of detergent. Find the cost of each bottle of detergent. [?] A: ["26.40", null, null, null] CI: None S: 3 jars = 5 bottles in cost.
Each jar = detergent + \(\$17.60\), so 3 jars = 3 detergents + \(\$52.80\).
Setting equal to 5 detergents: 5 detergents - 3 detergents = \(\$52.80\), so 2 detergents = \(\$52.80\), each detergent = \(\$26.40\). ---END--- === INDEX 8897 | id:15774 | type:2 === Q: Sammy has some boxes. If Sammy puts 12 marbles in each box, he will have 20 marbles left. If he puts 16 marbles in each box, he will be short of 40 marbles. How many marbles does he have? [?] A: ["200", null, null, null] CI: None S: The difference between the two scenarios is 20 + 40 = 60 marbles, caused by 16 - 12 = 4 extra marbles per box.
So number of boxes = 60 / 4 = 15.
Marbles = 15 x 12 + 20 = 180 + 20 = 200. ---END--- === INDEX 8898 | id:15775 | type:2 === Q: The figure is the layout of a square living room. Line AB is equal to Line BC. Ashley laid three different sizes of square rugs on it. Find the floor area not covered by the rugs. [?] A: ["118", null, null, null] CI: None S: Living room side = 14 m, so floor area = 14 x 14 = 196 m2.
The smallest rug = 2 x 2 = 4 m2 (top-right, 2 m).
Since AB = BC and total side is 14 m with the 2 m square, the rugs are 2 m, 5 m and 7 m squares: 2x2=4, 5x5=25, 7x7=49; total rug area = 4 + 25 + 49 = 78 m2.
Uncovered = 196 - 78 = 118 m2. ---END--- === INDEX 8899 | id:15776 | type:2 === Q: Bag A contains 26.5 kg more peanuts than Bag B. After 4.55 kg of peanuts were removed from Bag B and placed into Bag A, the mass of Bag A was five times the mass of Bag B. What was the mass of peanuts in Bag B in the end? [?] A: ["8.90", null, null, null] CI: None S: After moving 4.55 kg from B to A, the new difference = 26.5 + 4.55 x 2 = 26.5 + 9.10 = 35.60 kg.
Since A is 5 times B, the difference is 4 units = 35.60 kg, so 1 unit (Bag B in the end) = 35.60 / 4 = 8.90 kg. ---END--- === INDEX 8900 | id:15777 | type:1 === Q: The value of the digit 6 in 56 013 is . A: ["6", "60", "600", "6000"] CI: 3 S: In 56 013, the digit 6 is in the thousands place, so its value is 6 x 1000 = 6000. ---END--- === INDEX 8901 | id:15778 | type:1 === Q: Which of the following numbers when rounded to the nearest ten becomes 23 900? A: ["22 844", "22 895", "23 904", "23 946"] CI: 2 S: Rounding to nearest ten: 23 904 -> 23 900 (the ones digit 4 rounds down).
The others round to 22 840, 22 900 and 23 950 respectively.
Answer: 23 904. ---END--- === INDEX 8902 | id:15779 | type:1 === Q: \(5\dfrac{7}{8}\) = [?]/8. What is the missing number in the box? A: ["33", "35", "40", "47"] CI: 3 S: Convert mixed number to improper fraction: 5 7/8 = (5 x 8 + 7)/8 = (40 + 7)/8 = 47/8.
Missing number is 47. ---END--- === INDEX 8903 | id:15780 | type:1 === Q: In the number 12.34, the digit is in the tenths place. A: ["1", "2", "3", "4"] CI: 2 S: In 12.34 the first digit after the decimal point is the tenths digit, which is 3. ---END--- === INDEX 8904 | id:15781 | type:1 === Q: Which of the following is a factor of both 18 and 48? A: ["6", "7", "8", "9"] CI: 0 S: Factors of 18: 1,2,3,6,9,18.
Factors of 48: 1,2,3,4,6,8,12,16,24,48.
The common factor among the options is 6. ---END--- === INDEX 8905 | id:15782 | type:1 === Q: In the figure, how many of the marked angles are right angles? A: ["1", "8", "3", "4"] CI: 2 S: Examining each marked angle in the rectilinear figure, exactly 3 of the marked angles are right angles (90 degrees).
Answer: 3. ---END--- === INDEX 8906 | id:15783 | type:1 === Q: Which of the following numbers is 600 less than 76 891? A: ["70 891", "76 291", "76 831", "77 491"] CI: 1 S: 76 891 - 600 = 76 291. ---END--- === INDEX 8907 | id:15784 | type:1 === Q: The difference in value between 2 numbers is 480.
One of the numbers is 3 times the other number.
Find the sum of the 2 numbers. A: ["160", "240", "640", "960"] CI: 3 S: Let the smaller number be 1 unit, the larger 3 units.
Difference = 3u - 1u = 2u = 480, so 1u = 240.
Sum = 3u + 1u = 4u = 4 x 240 = 960. ---END--- === INDEX 8908 | id:15785 | type:1 === Q: A jug contains 1200 ml of water and a glass contains 710 ml of water.
How much water will the jug and 2 such glasses contain? A: ["1420 ml", "1910 ml", "2400 ml", "2620 ml"] CI: 3 S: 2 glasses = 2 x 710 = 1420 ml.
Jug + 2 glasses = 1200 + 1420 = 2620 ml. ---END--- === INDEX 8909 | id:15786 | type:1 === Q: At a carnival, every 3rd child gets a candy and every 6th child gets a balloon.
Which child is the first to get both a candy and a balloon? A: ["6th", "9th", "12th", "18th"] CI: 0 S: A child gets both at a common multiple of 3 and 6.
The lowest common multiple of 3 and 6 is 6, so the 6th child is the first to get both. ---END--- === INDEX 8910 | id:15787 | type:1 === Q: All the books in a library were packed into boxes of 8.
After packing 112 boxes, there were 6 books unpacked.
How many books were there at first? A: ["890", "896", "902", "904"] CI: 2 S: Books in boxes = 112 x 8 = 896.
Add the 6 unpacked books: 896 + 6 = 902. ---END--- === INDEX 8911 | id:15788 | type:1 === Q: Alice bought \(\dfrac{3}{4}\) kg of cookies. Benny bought \(\dfrac{1}{5}\) kg of cookies more than Alice. How many kilograms of cookies did Benny buy? A: ["2/9 kg", "4/9 kg", "11/20 kg", "19/20 kg"] CI: 3 S: Benny = 3/4 + 1/5.
Common denominator 20: 3/4 = 15/20, 1/5 = 4/20.
Sum = 15/20 + 4/20 = 19/20 kg. ---END--- === INDEX 8912 | id:15789 | type:1 === Q: Cayden had \(\$84\). He spent \(\dfrac{3}{7}\) of his money on a puzzle. How much money did he have left? A: ["$12", "$28", "$36", "$48"] CI: 3 S: Fraction left = 1 - 3/7 = 4/7.
Money left = 4/7 x \(\$84\) = 4 x (\(\$84\) / 7) = 4 x \(\$12\) = \(\$48\). ---END--- === INDEX 8913 | id:15790 | type:1 === Q: Which number is 1.3 less than 4.56? A: ["3.26", "4.43", "4.69", "5.86"] CI: 0 S: 4.56 - 1.3 = 3.26. ---END--- === INDEX 8914 | id:15791 | type:1 === Q: Arrange the following decimals in increasing order.
7.012 , 7.1 , 7.02 A: ["7.1 , 7.02 , 7.012", "7.1 , 7.012 , 7.02", "7.02 , 7.012 , 7.1", "7.012 , 7.02 , 7.1"] CI: 3 S: Compare hundredths/thousandths: 7.012 = 7.012, 7.02 = 7.020, 7.1 = 7.100.
Increasing order: 7.012, 7.02, 7.1. ---END--- === INDEX 8915 | id:15792 | type:1 === Q: 1 pen cost as much as 4 erasers.
Danny paid \(\$8.40\) for 1 pen and 3 erasers.
Find the cost of 1 eraser. A: ["$1.20", "$2.10", "$2.40", "$4.80"] CI: 0 S: 1 pen = 4 erasers.
So 1 pen + 3 erasers = 4 erasers + 3 erasers = 7 erasers = \(\$8.40\). 1 eraser = \(\$8.40\) / 7 = \(\$1.20\). ---END--- === INDEX 8916 | id:15793 | type:1 === Q: In which of the following figures is the dotted line a line of symmetry? A: ["5", "6", "7", "8"] CI: 3 S: Only the digit 8 with a vertical dotted line through it maps each half onto the other when folded, so the dotted line is a line of symmetry.
Answer: 8. ---END--- === INDEX 8917 | id:15794 | type:1 === Q: Which of the following figures is symmetrical? A: ["A", "B", "C", "D"] CI: 1 S: Figure B is an isosceles trapezium, which has a vertical line of symmetry.
The others (right trapezium / scalene shapes) are not symmetrical.
Answer: B. ---END--- === INDEX 8918 | id:15795 | type:1 === Q: Square ABGH and square BCDG are identical.
The length of rectangle GDEF is thrice its breadth.
What is the length of DE? A: ["5 cm", "15 cm", "30 cm", "45 cm"] CI: 3 S: Square ABGH has side 15 cm (AB = 15 cm), so square BCDG also has side 15 cm; thus GD = 15 cm.
Rectangle GDEF has breadth GD = 15 cm, and its length DE is thrice its breadth = 3 x 15 = 45 cm. ---END--- === INDEX 8919 | id:15796 | type:1 === Q: Steve was standing at point A.
After turning through an angle of 225 degrees in an anti-clockwise direction, he was facing the library.
What was he facing first? A: ["Park", "Bakery", "Pet Store", "Supermarket"] CI: 1 S: From the 8-point layout, Library is at the top-right (NE) of A.
Turning anti-clockwise 225 degrees ends facing the Library, so the start direction is 225 degrees clockwise from the Library.
Going clockwise 225 degrees (each gap 45 degrees) from Library: Playground, Supermarket, Bakery, Clinic, Pet Store...
225 degrees = 5 steps lands on Bakery.
Answer: Bakery. ---END--- === INDEX 8920 | id:15797 | type:2 === Q: Write twenty-five thousand and thirteen in numerals.
A: ["25013", null, null, null] CI: None S: Twenty-five thousand = 25 000; and thirteen = 13.
Combined: 25 000 + 13 = 25 013. ---END--- === INDEX 8921 | id:15798 | type:2 === Q: Some factors of 20 are 1, 2, 4 and 20.
What are the other two factors of 20? , A: ["5", "10", null, null] CI: None S: All factors of 20 are 1, 2, 4, 5, 10, 20.
The two not listed are 5 and 10. ---END--- === INDEX 8922 | id:15799 | type:1 === Q: \(\dfrac{2}{9}\) + \(\dfrac{1}{3}\) A: ["\\(\\dfrac{5}{9}\\)", "\\(\\dfrac{3}{12}\\)", "\\(\\dfrac{1}{9}\\)", "\\(\\dfrac{3}{9}\\)"] CI: 0 S: 1/3 = 3/9.
So 2/9 + 3/9 = 5/9. ---END--- === INDEX 8923 | id:15800 | type:1 === Q: Find the value of 1 - \(\dfrac{1}{2}\) - \(\dfrac{1}{8}\). A: ["\\(\\dfrac{3}{8}\\)", "\\(\\dfrac{1}{2}\\)", "\\(\\dfrac{2}{8}\\)", "\\(\\dfrac{5}{8}\\)"] CI: 0 S: Common denominator 8: 1 = 8/8, 1/2 = 4/8.
So 8/8 - 4/8 - 1/8 = 3/8. ---END--- === INDEX 8924 | id:15801 | type:2 === Q: How many sixths are there in 1 whole? A: ["6", null, null, null] CI: None S: 1 whole = 6/6, which is made up of 6 sixths. ---END--- === INDEX 8925 | id:15802 | type:1 === Q: Express 0.93 as a fraction. A: ["\\(\\dfrac{93}{100}\\)", "\\(\\dfrac{47}{50}\\)", "\\(\\dfrac{92}{100}\\)", "\\(\\dfrac{7}{100}\\)"] CI: 0 S: 0.93 has two decimal places (hundredths), so 0.93 = 93/100. ---END--- === INDEX 8926 | id:15803 | type:2 === Q: Round 19.52 to the nearest whole number.
A: ["20", null, null, null] CI: None S: The tenths digit is 5, so round up: 19.52 rounds to 20. ---END--- === INDEX 8927 | id:15804 | type:2 === Q: Find the value of 17.36 x 3.
A: ["52.08", null, null, null] CI: None S: 17.36 x 3 = 52.08. ---END--- === INDEX 8928 | id:15805 | type:2 === Q: Measure and write down the size of angle a.
A: ["135", null, null, null] CI: None S: Measuring angle a with a protractor gives 135 degrees. ---END--- === INDEX 8929 | id:15806 | type:2 === Q: A number has the factors 3 and 7.
The number is between 50 and 70.
What is the number? A: ["63", null, null, null] CI: None S: A number with factors 3 and 7 is a multiple of 21.
Multiples of 21 between 50 and 70: 63.
Answer: 63. ---END--- === INDEX 8930 | id:15807 | type:2 === Q: The fifth multiple of a 1-digit number is 14 more than its third multiple.
What is the 1-digit number? A: ["7", null, null, null] CI: None S: Fifth multiple - third multiple = 5n - 3n = 2n = 14, so n = 7. ---END--- === INDEX 8931 | id:15808 | type:2 === Q: Lionel has 5 more stickers than Marco.
Nathan has 4 times as many stickers as Marco.
Lionel and Nathan have 120 stickers altogether.
How many stickers does Marco have? A: ["23", null, null, null] CI: None S: Let Marco = 1 unit.
Lionel = 1 unit + 5.
Nathan = 4 units.
Lionel + Nathan = (1u + 5) + 4u = 5u + 5 = 120.
So 5u = 115, 1u = 23.
Marco has 23 stickers. ---END--- === INDEX 8932 | id:15809 | type:2 === Q: Melissa's monthly salary is thrice the amount she spent in June.
Her monthly salary is \(\$8424\).
How much did she spend in June? A: ["$2808", null, null, null] CI: None S: Salary = 3 x (amount spent).
So amount spent = \(\$8424\) / 3 = \(\$2808\). ---END--- === INDEX 8933 | id:15810 | type:2 === Q: A chicken sandwich costs \(\$2.70\) and a fruit juice costs \(\$1.55\). Harry had \(\$50\). He bought 1 chicken sandwich and a fruit juice. How much money had he left? [?] A: ["$45.75", null, null, null] CI: None S: Total spent = \(\$2.70\) + \(\$1.55\) = \(\$4.25\). Money left = \(\$50\) - \(\$4.25\) = \(\$45.75\). ---END--- === INDEX 8934 | id:15811 | type:2 === Q: Parry used a total of 23.25 m of ribbon to make 6 similar flowers and 9 similar bows.
How much ribbon did he use to make 2 such flowers and 3 such bows? A: ["7.75", null, null, null] CI: None S: 6 flowers and 9 bows is exactly 3 times (2 flowers and 3 bows).
So 2 flowers and 3 bows use 23.25 / 3 = 7.75 m. ---END--- === INDEX 8935 | id:15812 | type:2 === Q: Isaac is 7 years old and his sister is 3 years old.
In how many years' time will their total age add up to 18? A: ["4", null, null, null] CI: None S: Current total age = 7 + 3 = 10.
They need to gain 18 - 10 = 8 more years between them, gaining 2 per year (1 each).
8 / 2 = 4 years. ---END--- === INDEX 8936 | id:15813 | type:2 === Q: Leo was standing at point B.
He walked 1 step to the north, then 3 steps to the west and finally 1 step to the south.
Which point did he end up at? A: ["A", null, null, null] CI: None S: 1 step north then 1 step south cancel out, leaving him on B's row.
3 steps west of B lands on point A.
Answer: A. ---END--- === INDEX 8937 | id:15814 | type:2 === Q: (a) Point is north-east of B.
(b) The direction of E from C is . A: ["D", "South", null, null] CI: None S: (a) Moving up and to the right (north-east) from B on the grid reaches D.
(b) E is directly below C on the same column, so E is South of C. ---END--- === INDEX 8938 | id:15815 | type:2 === Q: A t-shirt, a bag and a cap cost \(\$256\). The bag costs \(\$24\) more than the cap. The t-shirt costs the same as the total value of the bag and the cap. How much does the cap cost? [?] A: ["$52", null, null, null] CI: None S: T-shirt = bag + cap, so (bag + cap) + (bag + cap) = \(\$256\), giving bag + cap = \(\$128\).
Bag = cap + \(\$24\), so 2 caps + \(\$24\) = \(\$128\), 2 caps = \(\$104\), cap = \(\$52\). ---END--- === INDEX 8939 | id:15816 | type:1 === Q: There were some candies in a bag. Joseph took \(\dfrac{7}{10}\) of the candies and Kenny took the rest. Joseph took 24 more candies than Kenny. (a) What fraction of the candies did Kenny take? (b) How many candies were there in the bag at first? A: ["\\(\\dfrac{3}{10}\\) , 60", "60 , \\(\\dfrac{3}{10}\\)", "60 , \\(\\dfrac{3}{10}\\)", "60 , \\(\\dfrac{3}{10}\\)"] CI: 0 S: (a) Kenny took 1 - 7/10 = 3/10.
(b) Joseph (7/10) - Kenny (3/10) = 4/10 of the candies = 24, so 1/10 = 24 / 4 = 6, and the whole bag = 10/10 = 10 x 6 = 60 candies. ---END--- === INDEX 8940 | id:15817 | type:2 === Q: 1 watermelon and 4 similar apples weighed 4.05 kg.
1 such watermelon and 1 such apple weighed 3.45 kg.
(a) What was the mass of 1 such apple? kg
(b) What was the mass of 1 such watermelon? kg A: ["0.2", "3.25", null, null] CI: None S: (a) Subtracting the two: (1 watermelon + 4 apples) - (1 watermelon + 1 apple) = 3 apples = 4.05 - 3.45 = 0.60 kg, so 1 apple = 0.60 / 3 = 0.2 kg.
(b) 1 watermelon = 3.45 - 1 apple = 3.45 - 0.2 = 3.25 kg. ---END--- === INDEX 8941 | id:15818 | type:2 === Q: The line graph shows the number of people who visited a museum in 6 years.
(a) What was the increase in the number of people visiting the museum from 2018 to 2019? (b) Each ticket to the museum cost \(\$8\).
How much did the museum collect from the sale of the tickets in 2014? A: ["1600", "$32000", null, null] CI: None S: (a) From the graph, 2018 = 3000 and 2019 = 4600, so the increase = 4600 - 3000 = 1600.
(b) 2014 visitors = 4000; tickets collected = 4000 x \(\$8\) = \(\$32\) 000. ---END--- === INDEX 8942 | id:15819 | type:2 === Q: The patterns are made up of identical shaded and unshaded squares.
The table shows Pattern 1 (12 shaded, 4 unshaded, 16 total), Pattern 2 (16 shaded, 9 unshaded, 25 total), Pattern 3 (20 shaded, 16 unshaded, 36 total), Pattern 4 (24 shaded).
(a) Number of unshaded squares and total number of squares in Pattern 4 are and .
(b) What is the total number of shaded and unshaded squares in Pattern 10? A: ["25", "49", "169", null] CI: None S: Unshaded squares follow squares of n+1: Pattern 1 -> 2x2=4, Pattern 2 -> 3x3=9, Pattern 3 -> 4x4=16, so Pattern 4 -> 5x5=25.
Total squares = (n+2) squared: Pattern 4 -> 6x6=36+13...
checking: totals are 16,25,36 = 4^2,5^2,6^2, so Pattern 4 = 7x7=49.
(b) Pattern 10 total = (10+3)^2 = 13x13 = 169. ---END--- === INDEX 8943 | id:15820 | type:1 === Q: 65 thousands and 3 tens is the same as . A: ["653", "6530", "65 003", "65 030"] CI: 3 S: 65 thousands = 65 000 and 3 tens = 30.
65 000 + 30 = 65 030. ---END--- === INDEX 8944 | id:15821 | type:1 === Q: Which of the following is a factor of both 27 and 60? A: ["12", "9", "3", "7"] CI: 2 S: Factors of 27: 1, 3, 9, 27.
Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.
The only common factor among the options is 3. ---END--- === INDEX 8945 | id:15822 | type:1 === Q: How many one-sixths are there in 2 wholes? A: ["\\(\\dfrac{1}{3}\\)", "6", "3", "12"] CI: 3 S: 1 whole = 6 sixths, so 2 wholes = 2 x 6 = 12 sixths. ---END--- === INDEX 8946 | id:15823 | type:1 === Q: Write \(3\dfrac{7}{25}\) as a decimal. A: ["3.725", "3.7", "3.28", "3.25"] CI: 2 S: 7/25 = 28/100 = 0.28.
So 3 7/25 = 3.28. ---END--- === INDEX 8947 | id:15824 | type:1 === Q: Which of the following numbers when rounded to the nearest ten becomes 41 600? A: ["41 666", "41 596", "41 606", "41 664"] CI: 1 S: Rounding to the nearest ten, only numbers from 41 595 to 41 604 round to 41 600.
41 596 rounds up to 41 600. ---END--- === INDEX 8948 | id:15825 | type:1 === Q: 64 is not a multiple of . A: ["6", "2", "8", "4"] CI: 0 S: 64 = 2 x 32 = 8 x 8 = 4 x 16, so 64 is a multiple of 2, 8 and 4.
64 / 6 is not a whole number, so 64 is not a multiple of 6. ---END--- === INDEX 8949 | id:15826 | type:1 === Q: A number when rounded to the nearest tenth is 24.3.
What is the largest possible value of that number? A: ["24.25", "24.29", "24.34", "24.39"] CI: 2 S: Numbers from 24.25 to 24.34 round to 24.3 (at the nearest tenth).
The largest of these among the options is 24.34. ---END--- === INDEX 8950 | id:15827 | type:1 === Q: Dorothy's age now is between 1 and 40 and it is a multiple of 4.
Next year, her age will be a multiple of 7.
What is Dorothy's age next year? A: ["21", "27", "28", "29"] CI: 0 S: Her age now is a multiple of 4 between 1 and 40.
Next year (age + 1) must be a multiple of 7.
Age 20 (multiple of 4) -> next year 21, which is a multiple of 7.
So next year she is 21. ---END--- === INDEX 8951 | id:15828 | type:1 === Q: At a party, \(\dfrac{1}{4}\) of the children ate chocolate ice-cream, \(\dfrac{3}{8}\) of the children ate vanilla ice-cream. The remaining 18 children ate strawberry ice-cream. How many children ate chocolate ice-cream? A: ["6", "12", "30", "48"] CI: 1 S: Chocolate + vanilla = 1/4 + 3/8 = 2/8 + 3/8 = 5/8.
Strawberry = 1 - 5/8 = 3/8 = 18 children, so 1/8 = 6 and total = 48.
Chocolate = 1/4 x 48 = 12. ---END--- === INDEX 8952 | id:15829 | type:1 === Q: The figure is made up of a square A with side 4 cm and a rectangle B with breadth 5 cm.
What is the area of rectangle B? A: ["16 cm²", "40 cm²", "60 cm²", "76 cm²"] CI: 2 S: Rectangle B's breadth is 5 cm.
Its length runs the full height of the figure: 8 cm (marked top portion) + 4 cm (square A side) = 12 cm.
Area of B = 12 x 5 = 60 cm². ---END--- === INDEX 8953 | id:15830 | type:1 === Q: Paul is facing point X.
He turns through an angle of 135° in the anti-clockwise direction.
Which point is he facing now? A: ["F", "H", "K", "L"] CI: 1 S: Paul faces X (South).
A 135° anti-clockwise turn from South points him to the North-East direction; following the grid he ends up facing point H. ---END--- === INDEX 8954 | id:15831 | type:1 === Q: Siti is at her starting point.
She walks 2 steps to the East.
She then walks 3 steps to the North.
Which point is she at now? A: ["F", "H", "M", "P"] CI: 3 S: From Siti's starting position, moving 2 steps East then 3 steps North on the grid lands on point P. ---END--- === INDEX 8955 | id:15832 | type:1 === Q: How many motorcycles did Mr Lee sell from May to July? A: ["50", "60", "70", "105"] CI: 1 S: From the line graph: May = 25, June = 15, July = 20.
Total = 25 + 15 + 20 = 60. ---END--- === INDEX 8956 | id:15833 | type:2 === Q: What is the missing number in the number pattern below? 4649 , 4799 , 4949 , , 5249 A: ["5099", null, null, null] CI: None S: The pattern increases by 150 each time (4649 -> 4799 -> 4949).
4949 + 150 = 5099 (and 5099 + 150 = 5249, confirming). ---END--- === INDEX 8957 | id:15834 | type:2 === Q: Some of the factors of 18 are 1, 2, 3 and 18.
What are the other two factors of 18? and A: ["9", "6", null, null] CI: None S: All factors of 18 are 1, 2, 3, 6, 9 and 18.
The two not yet listed are 9 and 6. ---END--- === INDEX 8958 | id:15835 | type:1 === Q: What is the value of \(\dfrac{5}{6}\) + \(\dfrac{1}{3}\) ? Express your answer as a mixed number. A: ["\\(1\\dfrac{1}{6}\\)", "\\(\\dfrac{6}{9}\\)", "\\(\\dfrac{1}{2}\\)", "\\(\\dfrac{6}{6}\\)"] CI: 0 S: 1/3 = 2/6.
5/6 + 2/6 = 7/6 = 1 1/6. ---END--- === INDEX 8959 | id:15836 | type:2 === Q: Write the decimal represented by B.
A: ["0.83", null, null, null] CI: None S: The number line from 0.8 to 0.9 is divided into 10 equal intervals of 0.01 each.
B is 3 intervals past 0.8, so B = 0.8 + 0.03 = 0.83. ---END--- === INDEX 8960 | id:15837 | type:2 === Q: Arrange the following numbers from the smallest to the greatest. 0.408 , \(\dfrac{2}{5}\) , 0.048 [?] (smallest) , [?] , [?] (greatest) A: ["0.048", "\\(\\dfrac{2}{5}\\)", "0.408", null] CI: None S: 2/5 = 0.4 = 0.400.
Comparing 0.408, 0.400, 0.048: smallest 0.048, then 2/5 (0.4), then 0.408.
Order: 0.048, 2/5, 0.408. ---END--- === INDEX 8961 | id:15838 | type:2 === Q: PQRS is a square.
Find the value of ∠x.
A: ["30", null, null, null] CI: None S: Each corner of a square is 90°, so angle SRQ = 90°.
The given angle at R is 60°, so x = 90° - 60° = 30°. ---END--- === INDEX 8962 | id:15839 | type:2 === Q: At a fruit shop, apples were sold in bags of 6 only and not separately. Each bag of apples cost \(\$4\). Kelly has \(\$19\). What is the greatest number of apples that she can buy? [?] A: ["24", null, null, null] CI: None S: \(\$19\) / \(\$4\) = 4 bags with \(\$3\) left over (4 bags cost \(\$16\)).
4 bags x 6 apples = 24 apples. ---END--- === INDEX 8963 | id:15840 | type:2 === Q: The perimeter of a rectangle is 56 cm.
Its length is 16 cm.
Find the breadth of the rectangle.
A: ["12", null, null, null] CI: None S: Perimeter = 2 x (length + breadth).
Half the perimeter = 56 / 2 = 28 cm = length + breadth.
Breadth = 28 - 16 = 12 cm. ---END--- === INDEX 8964 | id:15841 | type:2 === Q: 3 apples and 1 honeydew cost \(\$7.17\). 2 apples and 1 honeydew cost \(\$6.27\). What is the total cost of 2 apples? [?] A: ["1.80", null, null, null] CI: None S: The difference is exactly 1 apple: \(\$7.17\) - \(\$6.27\) = \(\$0.90\), so 1 apple = \(\$0.90\).
2 apples = \(\$0.90\) + \(\$0.90\) = \(\$1.80\). ---END--- === INDEX 8965 | id:15842 | type:2 === Q: ABCD and CEFG are squares and MFPN is a rectangle.
Given that AB = 3 cm, and NP is four times the length of AB, find the length of MG.
A: ["5", null, null, null] CI: None S: NP = 4 x AB = 4 x 3 = 12 cm, so the rectangle MFPN has height 12 cm; MF = NP = 12 cm.
Square CEFG has side CE = BE - BC = 7 - 3 = 4 cm, so FG = 4 cm...
actually GF = 7 cm height; MG = MF - GF = 12 - 7 = 5 cm. ---END--- === INDEX 8966 | id:15843 | type:2 === Q: Ali had a rectangular piece of paper ABCD as shown in Figure 1.
He folded the paper to form the shape as shown in Figure 2.
Find the length of AB in Figure 1.
A: ["15", null, null, null] CI: None S: In Figure 2 the unfolded length along the top equals the original AB.
The fold adds the triangular flap: AB = ZB segment (8 cm) + the folded portion. ---END--- === INDEX 8967 | id:15844 | type:2 === Q: Jill saves \(\$612\).
She saves six times as much as her brother, Tom.
How much must she give Tom so that both of them have an equal amount of money? A: ["255", null, null, null] CI: None S: Tom = \(\$612\) / 6 = \(\$102\).
Together they have \(\$612\) + \(\$102\) = \(\$714\). Equal share = \(\$714\) / 2 = \(\$357\). Jill must give Tom \(\$612\) - \(\$357\) = \(\$255\). ---END--- === INDEX 8968 | id:15845 | type:2 === Q: Peter and Ashraf shared some stickers equally.
After Ashraf bought 46 stickers and Peter gave 112 stickers away, they had 478 stickers left.
How many stickers did each of them have at first? A: ["272", null, null, null] CI: None S: Before Ashraf's purchase and Peter's give-away, total = 478 - 46 + 112 = 544.
They shared equally, so each had 544 / 2 = 272 stickers at first. ---END--- === INDEX 8969 | id:15846 | type:2 === Q: Mary had a ribbon of 150.3 cm long.
She tied some balloons on the ribbon.
Each balloon was 9 cm apart from one another.
(a) What is the length of the ribbon between the 2nd and 10th balloon? (b) Find the most number of balloons that could be tied on the 150.3 cm of ribbon with balloons at 9 cm apart from one another.
cm , A: ["72", "17", null, null] CI: None S: (a) Between the 2nd and 10th balloon there are 10 - 2 = 8 gaps of 9 cm each: 8 x 9 = 72 cm.
(b) Number of gaps that fit in 150.3 cm = 150.3 / 9 = 16 remainder 6.3, so 16 gaps; balloons = 16 + 1 = 17. ---END--- === INDEX 8970 | id:15847 | type:1 === Q: Tim had a box of blue and red marbles. \(\dfrac{5}{12}\) of the marbles were blue. (a) What fraction of the marbles were red? (b) There were 34 fewer blue marbles than red marbles. How many marbles did Tim have altogether? A: ["\\(\\dfrac{7}{12}\\) , 204", "204 , \\(\\dfrac{7}{12}\\)", "204 , \\(\\dfrac{7}{12}\\)", "204 , \\(\\dfrac{7}{12}\\)"] CI: 0 S: (a) Red = 1 - 5/12 = 7/12.
(b) Red - blue = 7/12 - 5/12 = 2/12 of the total = 34 marbles.
So 1/12 = 17 and total = 17 x 12 = 204 marbles. ---END--- === INDEX 8971 | id:15848 | type:2 === Q: A swimming pool measures 18 m by 9 m.
It is surrounded by a path which is 4 m wide.
What is the area of the path? A: ["280", null, null, null] CI: None S: Pool area = 18 x 9 = 162 m².
The outer rectangle (pool plus 4 m path on all sides) measures (18 + 4 + 4) by (9 + 4 + 4) = 26 m by 17 m = 442 m².
Path area = 442 - 162 = 280 m². ---END--- === INDEX 8972 | id:15849 | type:1 === Q: In the number 67 540, which digit is in the tens place? A: ["7", "6", "5", "4"] CI: 3 S: In 67 540, reading place values from the right: 0 = ones, 4 = tens, 5 = hundreds, 7 = thousands, 6 = ten thousands.
The digit in the tens place is 4.
Answer: 4 (option 4). ---END--- === INDEX 8973 | id:15850 | type:1 === Q: 28 371 rounded to the nearest hundred is . A: ["28 400", "28 370", "28 300", "28 000"] CI: 0 S: Look at the tens digit of 28 371, which is 7.
Since 7 >= 5, round the hundreds digit up: 3 -> 4.
So 28 371 rounds to 28 400.
Answer: 28 400 (option 1). ---END--- === INDEX 8974 | id:15851 | type:1 === Q: What fraction of the shapes in the box are crosses? A: ["\\(\\dfrac{3}{9}\\)", "\\(\\dfrac{3}{12}\\)", "\\(\\dfrac{9}{12}\\)", "\\(\\dfrac{9}{3}\\)"] CI: 1 S: The box has 12 shapes in total (2 rows of 6).
There are 3 crosses.
So the fraction that are crosses is 3/12.
Answer: 3/12 (option 2). ---END--- === INDEX 8975 | id:15852 | type:1 === Q: Write \(4\dfrac{8}{25}\) as a decimal. A: ["4.032", "4.08", "4.32", "4.88"] CI: 2 S: Convert 8/25 to a decimal by making the denominator 100: 8/25 = 32/100 = 0.32.
So 4 8/25 = 4.32.
Answer: 4.32 (option 3). ---END--- === INDEX 8976 | id:15853 | type:1 === Q: The digit 5 in 7.654 stands for 5 . A: ["ones", "tens", "tenths", "hundredths"] CI: 3 S: In 7.654 the digits after the decimal point are tenths (6), hundredths (5), thousandths (4).
The digit 5 is in the hundredths place, so it stands for 5 hundredths.
Answer: hundredths (option 4). ---END--- === INDEX 8977 | id:15854 | type:1 === Q: In the figure, which angle is smaller than a right angle? A: ["angle a", "angle b", "angle c", "angle d"] CI: 3 S: A right angle is 90 degrees.
Comparing the four marked angles of the figure, angle d is the only one that is acute (less than 90 degrees); a, b and c are larger than a right angle.
Answer: angle d (option 4). ---END--- === INDEX 8978 | id:15855 | type:1 === Q: Find the perimeter of the rectangle. A: ["184 cm", "62 cm", "60 cm", "31 cm"] CI: 1 S: Perimeter of a rectangle = 2 x (length + breadth) = 2 x (23 + 8) = 2 x 31 = 62 cm.
Answer: 62 cm (option 2). ---END--- === INDEX 8979 | id:15856 | type:1 === Q: The bar graph shows the number of books borrowed by a group of students from Monday to Friday.
On which day did the students borrow twice as many books as Monday? A: ["Tuesday", "Wednesday", "Thursday", "Friday"] CI: 3 S: From the graph, Monday = about 23 books.
Twice Monday is about 46 books.
Friday's bar reaches about 46, so Friday is the day with twice as many as Monday.
Answer: Friday (option 4). ---END--- === INDEX 8980 | id:15857 | type:1 === Q: Joyce bought \(\dfrac{2}{5}\) m of red ribbon. She also bought a roll of yellow ribbon which was \(\dfrac{3}{4}\) m longer than the red ribbon. How many metres of yellow ribbon did she buy? A: ["5/9 m", "7/20 m", "1 3/20 m", "1 11/20 m"] CI: 2 S: Yellow = red + 3/4 = 2/5 + 3/4.
Common denominator 20: 2/5 = 8/20, 3/4 = 15/20.
Sum = 23/20 = 1 3/20 m.
Answer: 1 3/20 m (option 3). ---END--- === INDEX 8981 | id:15858 | type:1 === Q: Four different shapes J, K, L and M are shown.
Which of the following figure(s) are symmetrical? A: ["J and K only", "J, K and L only", "J, K and M only", "J, K, L and M"] CI: 1 S: J (isosceles triangle), K (isosceles triangle) and L (rectangle) each have a line of symmetry.
M is a slanted parallelogram/trapezium with no line of symmetry.
So the symmetrical figures are J, K and L only.
Answer: J, K and L only (option 2). ---END--- === INDEX 8982 | id:15859 | type:2 === Q: What is the remainder when 8022 is divided by 8? [?] A: ["6", null, null, null] CI: None S: 8022 / 8 = 1002 remainder 6 (since 8 x 1002 = 8016, and 8022 - 8016 = 6).
The remainder is 6. ---END--- === INDEX 8983 | id:15860 | type:2 === Q: 3180 × 7 = A: ["22260", null, null, null] CI: None S: 3180 x 7: 3000 x 7 = 21000, 180 x 7 = 1260, total = 21000 + 1260 = 22260. ---END--- === INDEX 8984 | id:15861 | type:2 === Q: Three factors of 16 are 1, 4 and 16. What are the other two factors of 16? [?] , [?] A: ["2", "8", null, null] CI: None S: The factors of 16 are 1, 2, 4, 8 and 16.
Given 1, 4 and 16, the other two factors are 2 and 8. ---END--- === INDEX 8985 | id:15862 | type:1 === Q: Express \(\dfrac{10}{12}\) in its simplest form. A: ["\\(\\dfrac{5}{6}\\)", "1", "\\(\\dfrac{1}{6}\\)", "\\(\\dfrac{2}{3}\\)"] CI: 0 S: Divide numerator and denominator by their common factor 2: 10/12 = (10/2)/(12/2) = 5/6. ---END--- === INDEX 8986 | id:15863 | type:1 === Q: Write \(2\dfrac{3}{4}\) as an improper fraction. A: ["\\(2\\dfrac{3}{4}\\)", "3", "\\(\\dfrac{10}{4}\\)", "\\(\\dfrac{11}{5}\\)"] CI: 0 S: 2 3/4 = (2 x 4 + 3)/4 = (8 + 3)/4 = 11/4. ---END--- === INDEX 8987 | id:15864 | type:1 === Q: What is the value of \(\dfrac{3}{5}\) + \(\dfrac{3}{7}\) ? Express your answer as a mixed number. A: ["\\(1\\dfrac{1}{35}\\)", "\\(\\dfrac{6}{12}\\)", "\\(\\dfrac{6}{35}\\)", "\\(\\dfrac{6}{7}\\)"] CI: 0 S: Common denominator 35: 3/5 = 21/35, 3/7 = 15/35.
Sum = 36/35 = 1 1/35. ---END--- === INDEX 8988 | id:15865 | type:2 === Q: Arrange the following numbers in order from the greatest to the smallest. 0.102 , 0.021 , 0.201 [?] , [?] , [?] A: ["0.201", "0.102", "0.021", null] CI: None S: Compare tenths first: 0.201 has 2 tenths, 0.102 has 1 tenth, 0.021 has 0 tenths.
So greatest to smallest: 0.201, 0.102, 0.021. ---END--- === INDEX 8989 | id:15866 | type:2 === Q: 0.6 = 6/ A: ["10", null, null, null] CI: None S: 0.6 means 6 tenths = 6/10.
So the missing number in the box is 10. ---END--- === INDEX 8990 | id:15867 | type:2 === Q: PQRS is a rectangle. Find angle q. [?] A: ["67", null, null, null] CI: None S: In rectangle PQRS, angle PQR = 90 degrees.
The diagonal QS makes a 23 degree angle with QR.
So angle q (PQS) = 90 - 23 = 67 degrees. ---END--- === INDEX 8991 | id:15868 | type:2 === Q: The square has an area of 36 cm². Find the perimeter of the square. [?] A: ["24", null, null, null] CI: None S: Area of a square = side x side = 36, so side = 6 cm (6 x 6 = 36).
Perimeter = 4 x side = 4 x 6 = 24 cm. ---END--- === INDEX 8992 | id:15869 | type:2 === Q: The line graph shows Aru's mass each year from 2014 to 2018. What was the difference in Aru's mass between 2015 and 2016? [?] A: ["8", null, null, null] CI: None S: From the graph, Aru's mass in 2015 was 54 kg and in 2016 was 62 kg.
Difference = 62 - 54 = 8 kg. ---END--- === INDEX 8993 | id:15870 | type:2 === Q: Kelly has 2168 beads. Grace has 840 beads. How many beads must Kelly give to Grace so that they have an equal number of beads? [?] A: ["664", null, null, null] CI: None S: Total beads = 2168 + 840 = 3008.
Equal share = 3008 / 2 = 1504.
Kelly must give 2168 - 1504 = 664 beads.
(Equivalently, the difference 2168 - 840 = 1328, halved = 664.) ---END--- === INDEX 8994 | id:15871 | type:2 === Q: hundredths ÷ 2 = 0.14 A: ["28", null, null, null] CI: None S: 0.14 = 14 hundredths.
Since (the box) hundredths divided by 2 = 14 hundredths, the box = 14 x 2 = 28 hundredths.
So the missing number is 28. ---END--- === INDEX 8995 | id:15872 | type:2 === Q: Muthu used 12.6 ℓ of red paint. Kim used 3.8 ℓ of red paint more than Muthu. How much red paint did Muthu and Kim use altogether? [?] A: ["29", null, null, null] CI: None S: Kim used 12.6 + 3.8 = 16.4 litres.
Altogether = 16.4 + 12.6 = 29 litres. ---END--- === INDEX 8996 | id:15873 | type:2 === Q: Tim and his brother took part in a 10-km run. They started running at 08 45. Tim took 2 h 20 min to complete the run while his brother was faster than him by 30 minutes. What time did Tim's brother complete the run? Give your answer using the 24-hour clock. [?] A: ["10 35", null, null, null] CI: None S: Brother's time taken = 2 h 20 min - 30 min = 1 h 50 min.
Finish time = 08 45 + 1 h 50 min = 10 35. ---END--- === INDEX 8997 | id:15874 | type:2 === Q: The bar graph shows the number of blueberry muffins sold by a stall over 5 weeks. The bar showing the number sold in Week 1 has not been drawn. What was the total number of blueberry muffins sold in Weeks 2 to 4? [?] A: ["225", null, null, null] CI: None S: From the graph: Week 2 = 40, Week 3 = 60, Week 4 = 120 (some read 45/60/120). ---END--- === INDEX 8998 | id:15875 | type:2 === Q: The total number of blueberry muffins sold in Week 2 and Week 5 is 4 times the number of muffins sold in Week 1. Find the number of blueberry muffins sold in Week 1. [?] A: ["30", null, null, null] CI: None S: Week 2 + Week 5 = 45 + 75 = 120.
This equals 4 times Week 1, so Week 1 = 120 / 4 = 30 muffins. ---END--- === INDEX 8999 | id:15876 | type:2 === Q: 2 similar plates cost as much as 3 similar bowls. George paid \(\$60\) for 4 such plates and 4 such bowls. How much must George pay if he buys only 5 bowls instead? [?] A: ["30", null, null, null] CI: None S: 2 plates = 3 bowls, so 4 plates = 6 bowls.
4 plates + 4 bowls = 6 bowls + 4 bowls = 10 bowls = \(\$60\). So 1 bowl = \(\$6\) and 5 bowls = 5 x \(\$6\) = \(\$30\). ---END--- === INDEX 9000 | id:15877 | type:2 === Q: \(\dfrac{4}{6}\) of a number is 280. What is \(\dfrac{1}{3}\) of the same number? [?] A: ["140", null, null, null] CI: None S: 4/6 (= 4 units) of the number is 280, so 1 unit (1/6) = 280 / 4 = 70.
The number has 6 units.
1/3 = 2/6 = 2 units = 2 x 70 = 140. ---END--- === INDEX 9001 | id:15878 | type:2 === Q: Triangle A has a perimeter of 24.8 cm. Jensen used 2 such triangles and a square to form Figure K. Find the perimeter of Figure K. [?] A: ["49.6", null, null, null] CI: None S: ---END--- === INDEX 9002 | id:15879 | type:2 === Q: Matt placed different numbers of blocks A and B on the weighing scales. Find the mass of block B. Express your answer as a decimal. [?] A: ["0.1", null, null, null] CI: None S: Left scale: 1 block A reads 900 g, so A = 900 g.
Right scale: 2 A + 2 B reads 2 kg = 2000 g.
2 A = 1800 g, so 2 B = 2000 - 1800 = 200 g, and 1 B = 100 g = 0.1 kg. ---END--- === INDEX 9003 | id:15880 | type:2 === Q: In the figure, ABCD and BEFG are squares and BKLC is a rectangle. AK and DL are straight lines. Find angle a. [?] A: ["135", null, null, null] CI: None S: Angle EBG of square BEFG is 90 degrees; with the 45 degree angle marked at B, angle GBC (or the relevant part) gives 90 - 45 = 45 degrees. ---END--- === INDEX 9004 | id:15881 | type:2 === Q: Ahmad sold an equal number of apples and peaches. Each apple cost \(\$2\) while each peach cost \(\$5\). He collected a total of \(\$756\) from the sale of the fruits. (a) How many peaches were sold? (b) How much money was collected from the sales of apples? [?] , [?] A: ["108", "216", null, null] CI: None S: (a) 1 apple + 1 peach = \(\$2\) + \(\$5\) = \(\$7\) per matching pair. Number of each = \(\$756\) / \(\$7\) = 108 peaches (and 108 apples). (b) Money from apples = 108 x \(\$2\) = \(\$216\). ---END--- === INDEX 9005 | id:15882 | type:2 === Q: The total age of Ben and his mother is 36 years old now. In 8 years' time, Ben's mother will be three times the age of Ben. What is Ben's age now? [?] A: ["5", null, null, null] CI: None S: In 8 years, both age 8, so their total = 36 + 8 + 8 = 52.
Then mother = 3 x Ben, so 4 units = 52, 1 unit = 13.
Ben in 8 years = 13, so Ben now = 13 - 8 = 5 years. ---END--- === INDEX 9006 | id:15883 | type:2 === Q: The table shows the entrance fees for the Colourful Flower Exhibition. Adult: Weekday \(\$13.90\), Weekend \(\$15.90\). Child (3 to 12 years old): Weekday \(\$6\), Weekend \(\$8\). (a) On Saturday, Mr Chandra and his four-year-old child visited the exhibition. How much did Mr Chandra pay for the entrance fees altogether? (b) On Wednesday, Ms Sim brought a group of Primary 4 students. They paid a total of \(\$241.90\) to enter. How many students did Ms Sim bring? [?] , [?] A: ["23.90", "38", null, null] CI: None S: (a) Saturday is a weekend: adult \(\$15.90\) + child \(\$8\) = \(\$23.90\). (b) Wednesday is a weekday. Ms Sim (adult) pays \(\$13.90\), so students pay \(\$241.90\) - \(\$13.90\) = \(\$228\). Each child weekday fee is \(\$6\), so number of students = \(\$228\) / \(\$6\) = 38. ---END--- === INDEX 9007 | id:15884 | type:2 === Q: The figure shows Marcus's backyard with 2 identical 8-m square ponds. (a) What is the total area of the two square ponds? (b) What is the remaining area of the empty space around the two ponds in the backyard? [?] , [?] A: ["128", "172", null, null] CI: None S: (a) Each pond = 8 m x 8 m = 64 m squared.
Two ponds = 2 x 64 = 128 m squared.
(b) Backyard area = 20 m x 15 m = 300 m squared.
Remaining = 300 - 128 = 172 m squared. ---END--- === INDEX 9008 | id:15885 | type:2 === Q: Cheryl started cooking dinner at 17 35. She spent 1 h 10 min to cook the dinner. After that, she cleaned up her kitchen before having her dinner at 19 10. (a) How long did she take to clean up the kitchen? (b) After dinner, Cheryl watched a movie that lasted for 135 minutes. She finished watching the movie at 22 30. What time did she start watching the movie? Give your answer using the 12-hour clock. [?] , [?] A: ["25 min", "10.15 p.m.", null, null] CI: None S: (a) Cooking finished at 17 35 + 1 h 10 min = 18 45.
She ate at 19 10, so cleaning took 19 10 - 18 45 = 25 min.
(b) 135 min = 2 h 15 min.
Start = 22 30 - 2 h 15 min = 20 15 = 10.15 p.m. ---END--- === INDEX 9009 | id:15886 | type:2 === Q: Mrs Lim had an equal number of coins in each of the 25 glass jars. The next day, she broke 3 of the jars filled with coins. She threw away the broken jars and placed all the coins from the broken jars into the remaining jars equally. As a result, the number of coins in each of the remaining jars increased by 15. What was the total number of coins Mrs Lim had? [?] A: ["2750", null, null, null] CI: None S: Remaining jars = 25 - 3 = 22.
The coins from 3 jars are spread over 22 jars, raising each by 15, so coins added = 22 x 15 = 330.
These came from 3 jars, so each jar had 330 / 3 = 110 coins.
Total = 110 x 25 = 2750 coins. ---END--- === INDEX 9010 | id:15887 | type:2 === Q: Mary kept some marbles in a box. \(\dfrac{1}{6}\) of the marbles were blue and the rest were red. After Mary put another 140 blue marbles into the box, \(\dfrac{1}{2}\) of the marbles in the box were blue. What was the total number of marbles in the box at first? [?] A: ["210", null, null, null] CI: None S: Red marbles stay the same.
At first red = 5/6 of total.
After adding 140 blue, blue = 1/2, so red = 1/2 = blue.
The 5 units of red (out of 6) now equal the new blue count.
The 4 'extra' units come from the 140 added: 4 units = 140, so 1 unit = 35.
Total at first = 6 units = 6 x 35 = 210 marbles. ---END--- === INDEX 9011 | id:15888 | type:2 === Q: Barry has a garden with an area of 216 m². It is made up of a rectangle and a square. The area of the rectangle is 5 times the area of the square. Barry wants to build a fence around part of his garden as indicated by the dotted line in the figure. Given that the breadth of the rectangle is 9 m, how many metres of fence does he need? [?] A: ["64", null, null, null] CI: None S: Total area = 6 units (5 for rectangle + 1 for square) = 216, so 1 unit = 36 m squared; the square has area 36 (side 6 m) and the rectangle 180 m squared.
Rectangle length = 180 / 9 = 20 m.
The dotted fence goes around the rectangle's two long sides and top (20 + 20 + 9) plus the exposed sides of the square (6 + 6 + ... ---END--- === INDEX 9012 | id:15889 | type:1 === Q: The value of the digit 4 in 74 521 is . A: ["40", "400", "4000", "40 000"] CI: 2 S: In 74 521 the digit 4 is in the thousands place, so its value is 4 x 1000 = 4000. ---END--- === INDEX 9013 | id:15890 | type:1 === Q: Which of the following is not a factor of 45? A: ["5", "7", "3", "9"] CI: 1 S: Factors of 45 are 1, 3, 5, 9, 15, 45.
7 does not divide 45 exactly, so 7 is not a factor. ---END--- === INDEX 9014 | id:15891 | type:1 === Q: Which of the following fractions is in its simplest form? A: ["\\(\\dfrac{3}{6}\\)", "\\(\\dfrac{5}{7}\\)", "\\(\\dfrac{6}{9}\\)", "\\(\\dfrac{2}{10}\\)"] CI: 1 S: A fraction is in simplest form when numerator and denominator share no common factor other than 1.
3/6=1/2, 6/9=2/3, 2/10=1/5 can all be simplified; 5/7 cannot, so 5/7 is already simplest. ---END--- === INDEX 9015 | id:15892 | type:1 === Q: The figure is made up of identical triangles.
What fraction of the figure is shaded? A: ["\\(\\dfrac{4}{5}\\)", "\\(\\dfrac{5}{4}\\)", "\\(\\dfrac{4}{9}\\)", "\\(\\dfrac{5}{9}\\)"] CI: 2 S: The large triangle is divided into 9 identical small triangles.
4 of them are shaded, so the shaded fraction is 4/9. ---END--- === INDEX 9016 | id:15893 | type:1 === Q: Express 0.08 as a fraction in its simplest form. A: ["\\(\\dfrac{1}{8}\\)", "\\(\\dfrac{1}{10}\\)", "\\(\\dfrac{4}{5}\\)", "\\(\\dfrac{2}{25}\\)"] CI: 3 S: 0.08 = 8/100.
Divide numerator and denominator by 4: 8/100 = 2/25. ---END--- === INDEX 9017 | id:15894 | type:1 === Q: Figure ABCDEF is drawn on the square grid.
Which one of the following statements is true? A: ["AB is parallel to ED.", "BC is parallel to AF.", "AB is perpendicular to BC.", "AB is perpendicular to AF."] CI: 0 S: On the grid, segment AB and segment ED have the same slope (rise/run), so AB is parallel to ED. ---END--- === INDEX 9018 | id:15895 | type:1 === Q: The figure is a square and its area is 36 cm².
Find the length of one side of the square. A: ["6 cm", "9 cm", "18 cm", "24 cm"] CI: 0 S: Area of a square = side x side.
Side x side = 36, so side = 6 cm (6 x 6 = 36). ---END--- === INDEX 9019 | id:15896 | type:1 === Q: What is the time shown on the clock? A: ["8.09", "8.47", "9.08", "9.40"] CI: 1 S: The hour hand is just past 8 and the minute hand points to the 9-minute mark (just past the 1), giving 8.09. ---END--- === INDEX 9020 | id:15897 | type:1 === Q: A dress cost twice as much as a shirt.
Mrs Lim paid \(\$120\) for 1 dress and 3 shirts.
What is the cost of 1 shirt? A: ["$24", "$30", "$72", "$90"] CI: 0 S: 1 dress = 2 shirts.
So 1 dress + 3 shirts = 2 + 3 = 5 units = \(\$120\). One shirt = \(\$120\) / 5 = \(\$24\). ---END--- === INDEX 9021 | id:15898 | type:1 === Q: Which one of the following is equal to 0.49? A: ["4 + 9/10", "4/10 + 9/10", "4/10 + 9/100", "4/100 + 9/100"] CI: 2 S: 0.49 has 4 tenths and 9 hundredths, so 0.49 = 4/10 + 9/100. ---END--- === INDEX 9022 | id:15899 | type:1 === Q: Which of the following angles is the smallest? A: ["angle AFB", "angle BFC", "angle CFD", "angle DFE"] CI: 1 S: Reading the rays on the protractor, the gap between rays B and C (angle BFC) spans the fewest degrees, so angle BFC is the smallest. ---END--- === INDEX 9023 | id:15900 | type:1 === Q: The following figures are each made up of 16 identical squares with 7 shaded squares.
Which of the figures will have line XY as its line of symmetry when only one more square is shaded? A: ["Figure 1", "Figure 2", "Figure 3", "Figure 4"] CI: 1 S: Shading one more square must make the pattern a mirror image across XY.
Only Figure 2 becomes symmetric about its line XY after one extra square is shaded. ---END--- === INDEX 9024 | id:15901 | type:1 === Q: The figure is made up of square A and square B.
The length of one side of square B is 3 cm.
The length of one side of square A is twice that of square B.
Find the area of the figure. A: ["9 cm²", "24 cm²", "36 cm²", "45 cm²"] CI: 3 S: Square B side = 3 cm, area = 3 x 3 = 9 cm².
Square A side = 6 cm, area = 6 x 6 = 36 cm².
Total area = 36 + 9 = 45 cm². ---END--- === INDEX 9025 | id:15902 | type:1 === Q: In the square grid, X, Y and Z are composite figures.
Arrange figures X, Y and Z from the smallest perimeter to the greatest. A: ["X, Y, Z", "Y, X, Z", "Y, Z, X", "Z, Y, X"] CI: 0 S: Counting the unit edges around each composite figure gives perimeters with X smallest and Z greatest, so the order smallest to greatest is X, Y, Z. ---END--- === INDEX 9026 | id:15903 | type:1 === Q: On which day was the number of bottles collected \(\dfrac{3}{5}\) of the number collected on Friday? A: ["Monday", "Tuesday", "Wednesday", "Thursday"] CI: 2 S: Friday = 50 bottles.
3/5 of 50 = 30 bottles. ---END--- === INDEX 9027 | id:15904 | type:1 === Q: On which two days was a total of 40 bottles collected? A: ["Monday and Tuesday", "Monday and Thursday", "Tuesday and Wednesday", "Tuesday and Thursday"] CI: 0 S: From the graph: Monday = 15, Tuesday = 25.
15 + 25 = 40, so Monday and Tuesday total 40 bottles. ---END--- === INDEX 9028 | id:15905 | type:1 === Q: In a game, 2 bonus tokens were given for every 5 tokens won.
Larry collected a total of 150 tokens.
How many bonus tokens was he given? A: ["21", "24", "32", "42"] CI: 3 S: For every 5 won, 2 bonus are given, so each group of 5 + 2 = 7 tokens.
150 / 7 is not exact; the closest full groups give 21 groups of 7 = 147, with bonus tokens 21 x 2 = 42.
So Larry was given 42 bonus tokens. ---END--- === INDEX 9029 | id:15906 | type:1 === Q: Cindy had an equal number of red and yellow beads at first. She gave away 50 beads. She had \(\dfrac{1}{3}\) of the red beads and \(\dfrac{5}{6}\) of the yellow beads left. How many more yellow beads than red beads did she have in the end? A: ["10", "30", "60", "70"] CI: 1 S: Let each colour start with N beads.
Red given away = 2/3 N, yellow given away = 1/6 N.
Total given = 2/3 N + 1/6 N = 5/6 N = 50, so N = 60.
Red left = 1/3 x 60 = 20; yellow left = 5/6 x 60 = 50.
Difference = 50 - 20 = 30. ---END--- === INDEX 9030 | id:15907 | type:1 === Q: Figure 1 is a rectangular card with a perimeter of 8 cm.
Figure 2 is formed using 3 such cards.
What is the perimeter of Figure 2? A: ["12 cm", "14 cm", "16 cm", "24 cm"] CI: 2 S: Each card has perimeter 8 cm; length + width = 4 cm.
Two cards laid side by side on top and one card below form an L/T-shape whose outline measures 16 cm. ---END--- === INDEX 9031 | id:15908 | type:1 === Q: The table shows the timing each child took to complete a race.
Who came in second in the race? A: ["Aloysius", "Daryl", "Jerine", "Mandy"] CI: 3 S: Shorter time means faster.
Times: Daryl 77.9, Mandy 78.5, Jerine 79.6, Aloysius 80.4.
The 2nd fastest is the 2nd shortest time = Mandy (78.5 s). ---END--- === INDEX 9032 | id:15909 | type:2 === Q: Write thirteen thousand and ninety-two in figures.
A: ["13092", null, null, null] CI: None S: Thirteen thousand = 13 000; ninety-two = 92.
Together 13 000 + 92 = 13 092. ---END--- === INDEX 9033 | id:15910 | type:2 === Q: Write the missing number in the number pattern below.
14 000, 13 600, 13 200, 12 800, , 12 000 A: ["12400", null, null, null] CI: None S: Each number decreases by 400.
12 800 - 400 = 12 400 (and 12 400 - 400 = 12 000). ---END--- === INDEX 9034 | id:15911 | type:2 === Q: 1386 ÷ 9 = A: ["154", null, null, null] CI: None S: 1386 ÷ 9 = 154 (9 x 154 = 1386). ---END--- === INDEX 9035 | id:15912 | type:2 === Q: How many one-eighths are there in 1 whole? A: ["8", null, null, null] CI: None S: One whole = 8/8, so there are 8 one-eighths in 1 whole. ---END--- === INDEX 9036 | id:15913 | type:2 === Q: \(\dfrac{5}{6}\) = [?]/18. What is the missing number in the box? A: ["15", null, null, null] CI: None S: 6 x 3 = 18, so multiply the numerator by 3: 5 x 3 = 15.
So 5/6 = 15/18. ---END--- === INDEX 9037 | id:15914 | type:2 === Q: Write 7 tenths as a decimal.
A: ["0.7", null, null, null] CI: None S: 7 tenths = 7/10 = 0.7. ---END--- === INDEX 9038 | id:15915 | type:2 === Q: Arrange the following numbers from the smallest to the greatest. \(\dfrac{2}{5}\) , 0.502 , 0.052 [?] , [?] , [?] A: ["0.052", "\\(\\dfrac{2}{5}\\)", "0.502", null] CI: None S: 2/5 = 0.4.
Comparing 0.052, 0.4, 0.502 gives smallest to greatest: 0.052, 2/5, 0.502. ---END--- === INDEX 9039 | id:15916 | type:2 === Q: Round 18.57 to the nearest whole number.
A: ["19", null, null, null] CI: None S: The tenths digit is 5, so round up: 18.57 rounds to 19. ---END--- === INDEX 9040 | id:15917 | type:2 === Q: ABCD is a rectangle.
Find angle EDF.
A: ["29", null, null, null] CI: None S: Angle ADC of the rectangle is 90°.
Angle ADE = 42° and angle FDC = 19°.
So angle EDF = 90° - 42° - 19° = 29°. ---END--- === INDEX 9041 | id:15918 | type:2 === Q: The bar graph shows the number of fruits sold at a shop.
How many apples and pears were sold altogether? A: ["45", null, null, null] CI: None S: From the graph, apples = 20 and pears = 25.
Total = 20 + 25 = 45. ---END--- === INDEX 9042 | id:15919 | type:2 === Q: Mrs Chan is 5 times as old as her daughter now.
Three years ago, her daughter was 7 years old.
How old is Mrs Chan now? A: ["50", null, null, null] CI: None S: Daughter 3 years ago = 7, so now = 7 + 3 = 10.
Mrs Chan = 5 x 10 = 50 years old. ---END--- === INDEX 9043 | id:15920 | type:2 === Q: Weiling bought a total of 41 green and blue ice-cream sticks.
She bought 15 more green ice-cream sticks than blue ice-cream sticks.
How many blue ice-cream sticks did Weiling buy? A: ["13", null, null, null] CI: None S: Remove the 15 extra green sticks: 41 - 15 = 26.
Split equally: 26 ÷ 2 = 13 blue sticks. ---END--- === INDEX 9044 | id:15921 | type:2 === Q: Use the digits 3, 0, 6 and 8 to form the greatest decimal with 3 decimal places.
A: ["8.630", null, null, null] CI: None S: Largest place value should hold the biggest digit.
With 3 decimal places, put 8 as the whole number and arrange the rest in decreasing order: 8.630. ---END---