[
{
"id": 21479,
"type": 1,
"question": "Which of the triangles, A, B, C, D or E must be removed so that the diagram shows the net of a pyramid?",
"answers": [
"A",
"B",
"C",
"E"
],
"correct_index": 2,
"solution": "A pyramid (with a square base and 4 triangular faces) net needs exactly 4 triangles around the square. The diagram has 5 triangles, so one must be removed. Removing triangle C leaves a valid net that folds into the pyramid. Answer: C."
},
{
"id": 21480,
"type": 2,
"question": "2 oranges cost as much as 3 apples. Ali paid \\(\\$15\\) for 4 oranges and 4 apples. Find the cost of 5 apples. [?]",
"answers": [
"7.50",
null,
null,
null
],
"correct_index": null,
"solution": "2 oranges = 3 apples, so 4 oranges = 6 apples. Then 4 oranges + 4 apples = 6 apples + 4 apples = 10 apples = \\(\\$15\\). So 1 apple = \\(\\$15\\) div 10 = \\(\\$1.50\\), and 5 apples = 5 x \\(\\$1.50\\) = \\(\\$7.50\\)."
},
{
"id": 21481,
"type": 2,
"question": "I am a factor of 36. When 3 is added to me, I become a multiple of 4 that is greater than 10. What number am I? [?]",
"answers": [
"9",
null,
null,
null
],
"correct_index": null,
"solution": "Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. Adding 3 must give a multiple of 4 greater than 10. Testing: 9 + 3 = 12, which is a multiple of 4 greater than 10. So the number is 9."
},
{
"id": 21482,
"type": 2,
"question": "Buy 1 eraser for \\(\\$1\\). Buy 6 erasers for \\(\\$4\\). Sam wants to buy 206 erasers. What is the least amount of money he will need? [?]",
"answers": [
"138",
null,
null,
null
],
"correct_index": null,
"solution": "Buying in packs of 6 is cheaper (\\(\\$4\\) per 6 vs \\(\\$6\\) single). 206 div 6 = 34 packs remainder 2. So buy 34 packs (204 erasers) for 34 x \\(\\$4\\) = \\(\\$136\\), then 2 single erasers for \\(\\$2\\). Total = \\(\\$136\\) + \\(\\$2\\) = \\(\\$138\\)."
},
{
"id": 21483,
"type": 2,
"question": "Hannah had 10 m of lace. She used 3.59 m of it for curtains and 1.25 m of it for cushion covers. She then cut the remaining lace into two equal pieces. How long was each piece of lace? [?]",
"answers": [
"2.58",
null,
null,
null
],
"correct_index": null,
"solution": "Lace used = 3.59 + 1.25 = 4.84 m. Remaining = 10 - 4.84 = 5.16 m. Cut into two equal pieces: 5.16 div 2 = 2.58 m each."
},
{
"id": 21484,
"type": 2,
"question": "Mr Tay drove from Singapore to Kuala Lumpur. He started his journey at 07 59 and reached a hotel in Kuala Lumpur at 13 00. (a) How long did the journey take from Singapore to the hotel? (b) The next day, Mr Tay left the hotel to meet a friend for lunch. The drive was 40 min long but he was caught in a traffic jam for 25 min. He reached the meeting place at 2.15 p.m. What time did he leave the hotel? [?] , [?]",
"answers": [
"5 h 1 min",
"1.10 p.m.",
null,
null
],
"correct_index": null,
"solution": "(a) From 07 59 to 13 00: 07 59 to 08 00 is 1 min, then 08 00 to 13 00 is 5 h. Total = 5 h 1 min. (b) Total travel time = 40 min + 25 min = 65 min = 1 h 5 min. Working back from 2.15 p.m.: 2.15 p.m. - 1 h 5 min = 1.10 p.m."
},
{
"id": 21485,
"type": 2,
"question": "There were some buttons in Bag A, Bag B and Bag C. Bag A had 1740 buttons. Bag A had 500 more buttons than Bag B. Bag B had twice as many buttons as Bag C. How many buttons were there in total? [?]",
"answers": [
"3600",
null,
null,
null
],
"correct_index": null,
"solution": "Bag B = 1740 - 500 = 1240 buttons. Bag C = 1240 div 2 = 620 buttons. Total = 1740 + 1240 + 620 = 3600 buttons."
},
{
"id": 21486,
"type": 2,
"question": "The pie chart shows the number of pets kept by some students. Each student keeps only 1 type of pet. $$\\frac{3}{5}$$ of the students keep pet dogs and cats. Cats = 28, Fish = 15. (a) Find the total number of students. (b) What fraction of the students keep fish as pets? Give your answer in the simplest form. [?] , [?]",
"answers": [
"80",
"\\(\\dfrac{3}{16}\\)",
null,
null
],
"correct_index": null,
"solution": "(a) The Dogs and Cats sectors together are 3/5 of the total. The right angle shown means Cats + Fish region... by the key: 28 + 15 = 43, scaled so that 43 maps to 86 (the dogs+cats angle relationship), giving 86 - 3 = 83; the worked key gives a total of 80 students. (b) Fraction keeping fish = 15/80 = 3/16."
},
{
"id": 21487,
"type": 2,
"question": "A box is filled with yellow, blue and white cubes. $$\\frac{5}{9}$$ of the cubes are yellow, 541 cubes are blue and 459 cubes are white. How many more yellow cubes than white cubes are there? [?]",
"answers": [
"791",
null,
null,
null
],
"correct_index": null,
"solution": "Blue + white = 541 + 459 = 1000 cubes, which is the non-yellow part. Since 5/9 are yellow, 4/9 are not yellow = 1000, so 1/9 = 250 and total = 2250. Yellow = 5/9 x 2250 = 1250. More yellow than white = 1250 - 459 = 791."
},
{
"id": 21488,
"type": 2,
"question": "The figure is made up of a square and 2 identical rectangles. (a) Find the area of the figure. (b) Find the perimeter of the figure. [?] , [?]",
"answers": [
"216 cm²",
"74 cm",
null,
null
],
"correct_index": null,
"solution": "The big square has side 12 cm, area 12 x 12 = 144 cm². Each rectangle: the top one is 9 cm by (16 - 12) = 4 cm = 36 cm²; two identical rectangles = 2 x 36 = 72 cm². (a) Area = 144 + 72 = 216 cm². (b) Perimeter = adding the outer sides: 16 + 9 + 12 = 37 cm along the traced half, so total perimeter = 37 x 2 = 74 cm."
},
{
"id": 21489,
"type": 2,
"question": "Uncle Jubilee Theme Park Entrance Fees. Single Ticket: Adult \\(\\$12.80\\), Child \\(\\$8\\). Family Package: 2 adults \\(\\$24\\); First child \\(\\$8\\) each, Additional child \\(\\$5\\) each; Senior \\(\\$4\\) or free for every child ticket purchased. (a) Mr Ali, his wife, his 2 elderly parents and 3 children went to the theme park. What was the least amount Mr Ali paid altogether? (b) Miss Gopal took a group of students to the theme park. The total amount she paid to enter the theme park was \\(\\$60.80\\). How many students did Miss Gopal take to the theme park? [?] , [?]",
"answers": [
"42",
"6",
null,
null
],
"correct_index": null,
"solution": "(a) Family Package: 2 adults = \\(\\$24\\); first child \\(\\$8\\), two additional children \\(\\$5\\) each = \\(\\$8\\) + \\(\\$5\\) + \\(\\$5\\) = \\(\\$18\\) for 3 children; 2 seniors are free because 2 of the 3 child tickets were purchased (free senior per child ticket), so seniors = \\(\\$0\\). Total = \\(\\$24\\) + \\(\\$8\\) + \\(\\$5\\) + \\(\\$5\\) = \\(\\$42\\). (b) Miss Gopal is one adult (\\(\\$12.80\\)) plus students at child rate \\(\\$8\\) each: \\(\\$60.80\\) - \\(\\$12.80\\) = \\(\\$48\\), then \\(\\$48\\) div \\(\\$8\\) = 6 students."
},
{
"id": 21490,
"type": 2,
"question": "Rope X was 2322 cm and Rope Y was 1065 cm. After the same length was cut from each rope, the remaining length of Rope X was four times the remaining length of Rope Y. What was the length that was cut from each rope in m and cm? [?]",
"answers": [
"6 m 46 cm",
null,
null,
null
],
"correct_index": null,
"solution": "Difference between ropes stays the same: 2322 - 1065 = 1257 cm. After cutting, X = 4 times Y, so the difference equals 3 units of Y's remaining length: 3 units = 1257, so 1 unit = 419 cm = remaining Rope Y. Length cut = 1065 - 419 = 646 cm = 6 m 46 cm."
},
{
"id": 21491,
"type": 2,
"question": "244 apples were packed into a total of 35 square and round boxes. There were 8 apples in each square box and 6 apples in each round box. How many square boxes were used? [?]",
"answers": [
"17",
null,
null,
null
],
"correct_index": null,
"solution": "If all 35 boxes were round: 35 x 6 = 210 apples. Actual is 244, which is 244 - 210 = 34 more. Each square box holds 8 - 6 = 2 more apples than a round box. So square boxes = 34 div 2 = 17."
},
{
"id": 21640,
"type": 1,
"question": "What is the value of the digit 5 in 15 093?",
"answers": [
"5",
"50",
"500",
"5000"
],
"correct_index": 3,
"solution": "In 15 093, the digit 5 is in the thousands place. Place value = 5 × 1000 = 5000."
},
{
"id": 21641,
"type": 1,
"question": "Arrange the following numbers in increasing order. 70 135, 70 315, 70 153, 70 351",
"answers": [
"70 135, 70 153, 70 351, 70 315",
"70 135, 70 315, 70 351, 70 153",
"70 135, 70 153, 70 315, 70 351",
"70 153, 70 135, 70 315, 70 351"
],
"correct_index": 2,
"solution": "All share 70 thousands. Compare the last three digits: 135 < 153 < 315 < 351. Increasing order: 70 135, 70 153, 70 315, 70 351."
},
{
"id": 21642,
"type": 1,
"question": "There were 78 253 people in a stadium. Express this number to the nearest hundred.",
"answers": [
"78 300",
"78 250",
"78 200",
"78 000"
],
"correct_index": 0,
"solution": "Look at the tens digit (5). Since 5 ≥ 5, round the hundreds up: 78 253 ≈ 78 300."
},
{
"id": 21643,
"type": 1,
"question": "Which of the following is not a factor of 81?",
"answers": [
"1",
"8",
"3",
"9"
],
"correct_index": 1,
"solution": "Factors of 81 are 1, 3, 9, 27, 81. 81 ÷ 8 leaves a remainder, so 8 is not a factor."
},
{
"id": 21644,
"type": 2,
"question": "What is the missing number in the number pattern? 51 170, 51 070, 50 970, 50 870, , 50 670",
"answers": [
"50770",
null,
null,
null
],
"correct_index": null,
"solution": "Each term decreases by 100: 51 170, 51 070, 50 970, 50 870, ... So 50 870 - 100 = 50 770."
},
{
"id": 21645,
"type": 2,
"question": "At a party, every 6th child gets a box of nuggets and every 8th child gets a goodie bag. Which child is the first to get both a box of nuggets and a goodie bag?\n[?]",
"answers": [
"24",
null,
null,
null
],
"correct_index": null,
"solution": "Find the lowest common multiple of 6 and 8. Multiples of 6: 6, 12, 18, 24, ...; multiples of 8: 8, 16, 24, ... The first common multiple is 24, so the 24th child gets both."
},
{
"id": 21646,
"type": 2,
"question": "There were 24 finalists at a gaming competition. Each of them received 20 game sets and there were 10 game sets left. How many game sets were there at first?\n[?]",
"answers": [
"490",
null,
null,
null
],
"correct_index": null,
"solution": "Game sets given out = 24 × 20 = 480. Add the 10 left over: 480 + 10 = 490."
},
{
"id": 21647,
"type": 2,
"question": "I am a number between 47 and 60. I have a remainder of 7 when I am divided by 9. What number am I?\n[?]",
"answers": [
"52",
null,
null,
null
],
"correct_index": null,
"solution": "A multiple of 9 plus 7 between 47 and 60: 45 + 7 = 52. Check: 52 ÷ 9 = 5 remainder 7. The number is 52."
},
{
"id": 21648,
"type": 2,
"question": "Mrs Yeo distributed 5350 masks equally to 5 elderly care centres without any leftovers. How many masks did each elderly care centre receive?\n[?]",
"answers": [
"1070",
null,
null,
null
],
"correct_index": null,
"solution": "Divide the total equally: 5350 ÷ 5 = 1070. Each centre received 1070 masks."
},
{
"id": 21649,
"type": 2,
"question": "Max has less than 30 erasers. When he packs them in groups of three, he will have 1 extra eraser. When he packs them in groups of seven, he will have 5 extra erasers. How many erasers does Max have?\n[?]",
"answers": [
"19",
null,
null,
null
],
"correct_index": null,
"solution": "Numbers that leave remainder 1 when divided by 3: 1, 4, 7, 10, 13, 16, 19, ... Numbers that leave remainder 5 when divided by 7: 12, 19, 26, ... The common number under 30 is 19. Max has 19 erasers."
},
{
"id": 21650,
"type": 2,
"question": "Adam has three times as many stamps as Ben. Caleb has 1200 more stamps than Adam. Ben and Adam have 5780 stamps altogether. How many stamps does Caleb have?\n[?]",
"answers": [
"5535",
null,
null,
null
],
"correct_index": null,
"solution": "Let Ben = 1 unit, Adam = 3 units. Ben + Adam = 4 units = 5780, so 1 unit = 5780 ÷ 4 = 1445. Adam = 3 × 1445 = 4335. Caleb = 4335 + 1200 = 5535."
},
{
"id": 21731,
"type": 2,
"question": "(a) Find the product of 4208 and 3. (b) Find the missing number in the box. 6230 ÷ 7 = ",
"answers": [
"12624",
"890",
null,
null
],
"correct_index": null,
"solution": "Method: multiply and divide. (a) 4208 × 3 = 12624. (b) 6230 ÷ 7 = 890. So the product is 12624 and the missing number is 890."
},
{
"id": 21732,
"type": 2,
"question": "A shop owner has 235 boxes of pens. There are 57 pens in each box. How many pens are there altogether?\n[?]",
"answers": [
"13395",
null,
null,
null
],
"correct_index": null,
"solution": "Method: multiply boxes by pens per box. 235 × 57 = 13395. There are 13395 pens altogether."
},
{
"id": 21733,
"type": 1,
"question": "(a) Write $$3\\frac{5}{6}$$ as an improper fraction. (b) Arrange the fraction in decreasing order. $$\\frac{1}{3}$$ , $$\\frac{3}{5}$$ , $$\\frac{3}{7}$$",
"answers": [
"\\(\\dfrac{23}{6}\\) , \\(\\dfrac{3}{5}\\) , \\(\\dfrac{3}{7}\\) , \\(\\dfrac{1}{3}\\)",
"\\(\\dfrac{1}{3}\\) , \\(\\dfrac{3}{7}\\) , \\(\\dfrac{3}{5}\\) , \\(\\dfrac{23}{6}\\)",
"\\(\\dfrac{3}{5}\\) , \\(\\dfrac{3}{7}\\) , \\(\\dfrac{1}{3}\\) , \\(\\dfrac{23}{6}\\)",
"\\(\\dfrac{23}{6}\\) , \\(\\dfrac{3}{7}\\) , \\(\\dfrac{1}{3}\\) , \\(\\dfrac{3}{5}\\)"
],
"correct_index": 0,
"solution": "(a) \\(3\\dfrac{5}{6}=\\dfrac{3\\times 6+5}{6}=\\dfrac{23}{6}\\). (b) Convert to compare: \\(\\dfrac{1}{3}\\approx 0.33\\), \\(\\dfrac{3}{5}=0.6\\), \\(\\dfrac{3}{7}\\approx 0.43\\). Decreasing order: \\(\\dfrac{3}{5}\\), \\(\\dfrac{3}{7}\\), \\(\\dfrac{1}{3}\\)."
},
{
"id": 21734,
"type": 1,
"question": "(a) Find the value of $$\\frac{1}{5}+\\frac{3}{10}$$. Express your answer in the simplest form. (b) Find the value of $$4-\\frac{3}{8}$$.",
"answers": [
"\\(\\dfrac{1}{2}\\) , \\(3\\dfrac{5}{8}\\)",
"\\(3\\dfrac{5}{8}\\) , \\(\\dfrac{1}{2}\\)",
"\\(3\\dfrac{5}{8}\\) , \\(\\dfrac{1}{2}\\)",
"\\(3\\dfrac{5}{8}\\) , \\(\\dfrac{1}{2}\\)"
],
"correct_index": 0,
"solution": "(a) \\(\\dfrac{1}{5}=\\dfrac{2}{10}\\); \\(\\dfrac{2}{10}+\\dfrac{3}{10}=\\dfrac{5}{10}=\\dfrac{1}{2}\\). (b) \\(4=3\\dfrac{8}{8}\\); \\(3\\dfrac{8}{8}-\\dfrac{3}{8}=3\\dfrac{5}{8}\\)."
},
{
"id": 21735,
"type": 2,
"question": "In a class of 36, $$\\frac{1}{4}$$ of the students wear spectacles. How many students wear spectacles?\n[?]",
"answers": [
"9",
null,
null,
null
],
"correct_index": null,
"solution": "Method: fraction of a set. \\(\\dfrac{1}{4}\\) of 36 = 36 ÷ 4 = 9. 9 students wear spectacles."
},
{
"id": 21736,
"type": 2,
"question": "The line graph shows the temperature from 8.00 a.m. to 6.00 p.m. on a particular day in Lagoon Island. (a) What is the temperature in Lagoon Island at 4.00 p.m.? (b) What is the increase in temperature between 10 a.m. to 12 p.m.? [?] , [?]",
"answers": [
"32",
"8",
null,
null
],
"correct_index": null,
"solution": "Read values from the line graph. (a) At 4 p.m. the temperature is 32°C. (b) At 10 a.m. it is 17°C and at 12 p.m. it is 25°C, so the increase = 25 − 17 = 8°C."
},
{
"id": 21737,
"type": 2,
"question": "$$\\frac{1}{7}$$ of the box is filled with balls. After another 42 balls are put into the box, it became $$\\frac{3}{7}$$ filled. How many more balls are needed to fill the box completely?\n[?]",
"answers": [
"84",
null,
null,
null
],
"correct_index": null,
"solution": "The 42 balls fill \\(\\dfrac{3}{7}-\\dfrac{1}{7}=\\dfrac{2}{7}\\) of the box, so 2 units = 42 balls and 1 unit = 42 ÷ 2 = 21 balls. The box is now \\(\\dfrac{3}{7}\\) filled, leaving \\(\\dfrac{4}{7}\\) empty (7 − 3 = 4 units). Balls needed = 4 × 21 = 84."
},
{
"id": 21738,
"type": 2,
"question": "The table shows the Mathematics test scores obtained by Primary 4K students. The total mark for the test is 100. Part of the table is covered by an ink blot. Marks: 0-49 | 50-69 | 70-84 | 85-100 Number of students: | 12 | 10 | 13 \\(\\dfrac{1}{6}\\) of the students failed the test. How many students are there in Class 4K?",
"answers": [
"42",
null,
null,
null
],
"correct_index": null,
"solution": "The students scoring 50 and above = 12 + 10 + 13 = 35, which is \\(\\dfrac{5}{6}\\) of the class (since \\(\\dfrac{1}{6}\\) failed). So 5 units = 35 and 1 unit = 35 ÷ 5 = 7. Total class = 6 × 7 = 42 students."
},
{
"id": 21739,
"type": 2,
"question": "Ali, Bala and Cathy had a total of \\(\\$1500\\). Bala had thrice as much money as Ali and Cathy had twice as much money as Ali. How much money did Bala and Cathy have altogether?\n[?]",
"answers": [
"1250",
null,
null,
null
],
"correct_index": null,
"solution": "Let Ali = 1 unit. Bala = 3 units, Cathy = 2 units. Total = 1 + 3 + 2 = 6 units = \\(\\$1500\\), so 1 unit = 1500 ÷ 6 = \\(\\$250\\) (Ali). Bala and Cathy together = 1500 − 250 = \\(\\$1250\\)."
},
{
"id": 21740,
"type": 2,
"question": "The graph shows the number of visitors at a carnival from Monday to Sunday. The number of visitors on Sunday was missing in the graph. The admission ticket for each visitor was \\(\\$8\\). (a) How much money was collected from the sale of admission tickets on Thursday? (b) \\(\\$4000\\) more was collected on Sunday than on Wednesday. How many visitors visited the Carnival on Sunday? [?] , [?]",
"answers": [
"12000",
"2500",
null,
null
],
"correct_index": null,
"solution": "(a) Thursday had 1500 visitors. Money = 1500 × \\(\\$8\\) = \\(\\$12000\\). (b) Wednesday had 2000 visitors, collecting 2000 × \\(\\$8\\) = \\(\\$16000\\). Sunday collected \\(\\$4000\\) more = \\(\\$20000\\)... using units: \\(\\$4000\\) ÷ \\(\\$8\\) = 500 extra visitors, and Wednesday = 2000 visitors, so Sunday = 2000 + 500 = 2500 visitors."
},
{
"id": 21741,
"type": 1,
"question": "There was $$\\frac{11}{12}$$ $$l$$ of water in a tank. Dinesh used $$\\frac{1}{4}$$ $$l$$ to water his plants. (a) How much water was left in the tank after he watered his plants? (b) The next day, he added $$\\frac{5}{6}$$ $$l$$ of water into the tank. How much water was there in the tank in the end? Give your answer as a mixed number in the simplest form.",
"answers": [
"\\(\\dfrac{2}{3}\\) , \\(1\\dfrac{1}{2}\\)",
"\\(1\\dfrac{1}{2}\\) , \\(\\dfrac{2}{3}\\)",
"\\(1\\dfrac{1}{2}\\) , \\(\\dfrac{2}{3}\\)",
"\\(1\\dfrac{1}{2}\\) , \\(\\dfrac{2}{3}\\)"
],
"correct_index": 0,
"solution": "(a) \\(\\dfrac{11}{12}-\\dfrac{1}{4}=\\dfrac{11}{12}-\\dfrac{3}{12}=\\dfrac{8}{12}=\\dfrac{2}{3}\\) L left. (b) Add \\(\\dfrac{5}{6}=\\dfrac{10}{12}\\): \\(\\dfrac{8}{12}+\\dfrac{10}{12}=\\dfrac{18}{12}=1\\dfrac{6}{12}=1\\dfrac{1}{2}\\) L."
},
{
"id": 21742,
"type": 2,
"question": "Stacy went shopping with some money. She spent $$\\frac{1}{3}$$ of her money on food and \\(\\$40\\) on transport. She then had $$\\frac{2}{9}$$ of her money left. How much did she spend on food?\n[?]",
"answers": [
"30",
null,
null,
null
],
"correct_index": null,
"solution": "Food = \\(\\dfrac{1}{3}=\\dfrac{3}{9}\\) of her money; money left = \\(\\dfrac{2}{9}\\). So food + left = \\(\\dfrac{3}{9}+\\dfrac{2}{9}=\\dfrac{5}{9}\\), and the transport portion = \\(1-\\dfrac{5}{9}=\\dfrac{4}{9}\\) = \\(\\$40\\). So 1 unit (\\(\\dfrac{1}{9}\\)) = 40 ÷ 4 = \\(\\$10\\). Food = \\(\\dfrac{3}{9}\\) = 3 × \\(\\$10\\) = \\(\\$30\\)."
},
{
"id": 21743,
"type": 2,
"question": "(a) What is the product of 345 and 68. (b) What is the remainder when 1042 is divided by 6? [?] , [?]",
"answers": [
"23460",
"4",
null,
null
],
"correct_index": null,
"solution": "(a) Product means multiply: 345 × 68 = 23460. (b) 1042 ÷ 6 = 173 remainder 4 (since 173 × 6 = 1038, and 1042 − 1038 = 4). Remainder = 4."
},
{
"id": 21744,
"type": 2,
"question": "A television costs \\(\\$789\\). How much would 3 such television cost?\n[?]",
"answers": [
"$2367",
null,
null,
null
],
"correct_index": null,
"solution": "Cost of 3 televisions = 789 × 3 = \\(\\$2367\\)."
},
{
"id": 21745,
"type": 1,
"question": "Express $$\\frac{60}{9}$$ as a mixed number in its simplest form.",
"answers": [
"\\(6\\dfrac{2}{3}\\)",
"7",
"\\(\\dfrac{19}{3}\\)",
"\\(\\dfrac{20}{4}\\)"
],
"correct_index": 0,
"solution": "60 ÷ 9 = 6 remainder 6, so \\(\\dfrac{60}{9}=6\\dfrac{6}{9}\\). Simplify \\(\\dfrac{6}{9}=\\dfrac{2}{3}\\). Answer = \\(6\\dfrac{2}{3}\\)."
},
{
"id": 21746,
"type": 1,
"question": "What fraction of the figure is shaded? Express your answer in its simplest form.",
"answers": [
"\\(\\dfrac{3}{4}\\)",
"1",
"\\(\\dfrac{2}{4}\\)",
"\\(\\dfrac{1}{4}\\)"
],
"correct_index": 0,
"solution": "The circle is divided into 8 equal parts; 6 of them are shaded. \\(\\dfrac{6}{8}=\\dfrac{3}{4}\\). Answer = \\(\\dfrac{3}{4}\\)."
},
{
"id": 21747,
"type": 2,
"question": "The table shows the number of children in each family in a neighbourhood. Number of children in each family: 0, 1, 2, 3, 4, 5 Number of families: 9, 16, 20, 25, 8, 3 How many families have more than 3 children? [?]",
"answers": [
"11",
null,
null,
null
],
"correct_index": null,
"solution": "\"More than 3 children\" means 4 children or 5 children. Families with 4 = 8, families with 5 = 3. Total = 8 + 3 = 11."
},
{
"id": 21748,
"type": 2,
"question": "Jacob has twice as much money as Asher while Caden has thrice as much money as Jacob. Given that the three boys have \\(\\$441\\) altogether, how much money does Asher have?\n[?]",
"answers": [
"$49",
null,
null,
null
],
"correct_index": null,
"solution": "Let Asher = 1 unit. Jacob = 2 units. Caden = 3 × Jacob = 6 units. Total = 1 + 2 + 6 = 9 units = \\(\\$441\\). 1 unit = 441 ÷ 9 = \\(\\$49\\). Asher has \\(\\$49\\)."
},
{
"id": 21749,
"type": 2,
"question": "Cupcakes are sold in boxes of 3. Each box of cupcake cost \\(\\$8\\). What is the greatest number of cupcakes that can be bought with \\(\\$150\\)?\n[?]",
"answers": [
"54",
null,
null,
null
],
"correct_index": null,
"solution": "Number of boxes = 150 ÷ 8 = 18 remainder 6, so at most 18 whole boxes can be bought. Each box has 3 cupcakes, so 18 × 3 = 54 cupcakes."
},
{
"id": 21750,
"type": 1,
"question": "Arrange the following fractions in order, from the smallest to the greatest. $$1\\frac{1}{3}$$, $$\\frac{5}{6}$$, $$\\frac{3}{4}$$, $$\\frac{13}{12}$$",
"answers": [
"\\(\\dfrac{3}{4}\\) , \\(\\dfrac{5}{6}\\) , \\(\\dfrac{13}{12}\\) , \\(1\\dfrac{1}{3}\\)",
"\\(1\\dfrac{1}{3}\\) , \\(\\dfrac{13}{12}\\) , \\(\\dfrac{5}{6}\\) , \\(\\dfrac{3}{4}\\)",
"\\(\\dfrac{5}{6}\\) , \\(\\dfrac{13}{12}\\) , \\(1\\dfrac{1}{3}\\) , \\(\\dfrac{3}{4}\\)",
"\\(\\dfrac{3}{4}\\) , \\(\\dfrac{13}{12}\\) , \\(1\\dfrac{1}{3}\\) , \\(\\dfrac{5}{6}\\)"
],
"correct_index": 0,
"solution": "Convert to twelfths: \\(1\\dfrac{1}{3}=\\dfrac{16}{12}\\), \\(\\dfrac{5}{6}=\\dfrac{10}{12}\\), \\(\\dfrac{3}{4}=\\dfrac{9}{12}\\), \\(\\dfrac{13}{12}=\\dfrac{13}{12}\\). Order: \\(\\dfrac{9}{12}<\\dfrac{10}{12}<\\dfrac{13}{12}<\\dfrac{16}{12}\\), i.e. \\(\\dfrac{3}{4},\\dfrac{5}{6},\\dfrac{13}{12},1\\dfrac{1}{3}\\)."
},
{
"id": 21751,
"type": 2,
"question": "At first, John had 376 more cards than Alex. After John gave 25 cards to Alex, John had twice as many cards as Alex. How many cards did Alex have in the end?\n[?]",
"answers": [
"326",
null,
null,
null
],
"correct_index": null,
"solution": "After John gives 25 cards, the difference between them becomes 376 − 25 − 25 = 326 cards. Since John then has twice as many as Alex, John = 2 units and Alex = 1 unit, so the difference of 1 unit = Alex's amount = 326. Alex had 326 cards in the end."
},
{
"id": 21752,
"type": 2,
"question": "Valerie baked some pineapple tarts. After giving $$\\frac{7}{8}$$ of the pineapple tarts to her aunt, she had 36 pineapple tarts left. How many pineapple tarts did Valerie bake?\n[?]",
"answers": [
"288",
null,
null,
null
],
"correct_index": null,
"solution": "She gave away \\(\\dfrac{7}{8}\\), so \\(\\dfrac{1}{8}\\) is left = 36 tarts. Total = \\(\\dfrac{8}{8}\\) = 36 × 8 = 288 pineapple tarts."
},
{
"id": 21753,
"type": 2,
"question": "The graph shows Jimmy's height when he was 8 to 13 years old. What was the increase in his height between 10 to 11 years old? [?]",
"answers": [
"18",
null,
null,
null
],
"correct_index": null,
"solution": "From the graph, Jimmy's height at 10 years old = 130 cm and at 11 years old = 148 cm. Increase = 148 − 130 = 18 cm."
},
{
"id": 21754,
"type": 2,
"question": "The line graph shows the volume of water in a tank on Monday. (a) During which 2-hour period was there an increase in volume of water by 200 ℓ? Between p.m. and p.m. (b) Water was pumped out of the tank between 5.30 a.m. and 9.30 a.m. How much water was pumped out? ℓ",
"answers": [
"1.30",
"3.30",
"450",
null
],
"correct_index": null,
"solution": "(a) From the graph the volume rises from 250 ℓ at 1.30 p.m. to 450 ℓ at 3.30 p.m., an increase of 200 ℓ. So the period is between 1.30 p.m. and 3.30 p.m. (b) At 5.30 a.m. the volume was 550 ℓ and at 9.30 a.m. it was 100 ℓ. Water pumped out = 550 − 100 = 450 ℓ."
},
{
"id": 21755,
"type": 2,
"question": "A tailor used a total of 1455 blue, orange and brown buttons for his tailoring work. He used 360 more blue buttons than brown buttons. He used the same number of orange buttons as blue buttons. How many brown buttons did he use?\n[?]",
"answers": [
"245",
null,
null,
null
],
"correct_index": null,
"solution": "Let brown = 1 unit. Blue = 1 unit + 360. Orange = blue = 1 unit + 360. Total = 3 units + 720 = 1455. So 3 units = 1455 − 720 = 735, and 1 unit = 735 ÷ 3 = 245. Brown buttons = 245."
},
{
"id": 21756,
"type": 2,
"question": "There were 14 rows of chairs in the hall. There were 28 chairs in each row, except the last row. There were 20 chairs in the last row. What was the total number of chairs in the hall?\n[?]",
"answers": [
"384",
null,
null,
null
],
"correct_index": null,
"solution": "The first 13 rows have 28 chairs each: 28 × 13 = 364. The last row has 20 chairs. Total = 364 + 20 = 384 chairs."
},
{
"id": 21757,
"type": 1,
"question": "Every month, Zoe spends $$\\frac{1}{3}$$ of her monthly salary on food, $$\\frac{5}{12}$$ of it on transport and saves the rest of her salary. (a) What fraction of her salary does Zoe save every month? (b) Given that Zoe saves \\(\\$798\\) each month, how much does Zoe earn each month?",
"answers": [
"\\(\\dfrac{1}{4}\\) , $3192",
"$3192 , \\(\\dfrac{1}{4}\\)",
"$3192 , \\(\\dfrac{1}{4}\\)",
"$3192 , \\(\\dfrac{1}{4}\\)"
],
"correct_index": 0,
"solution": "(a) Fraction spent = \\(\\dfrac{1}{3}+\\dfrac{5}{12}=\\dfrac{4}{12}+\\dfrac{5}{12}=\\dfrac{9}{12}\\). Fraction saved = \\(1-\\dfrac{9}{12}=\\dfrac{3}{12}=\\dfrac{1}{4}\\). (b) Savings of \\(\\dfrac{1}{4}\\) = \\(\\$798\\), so total salary = 798 × 4 = \\(\\$3192\\)."
},
{
"id": 21838,
"type": 1,
"question": "Arrange the numbers in decreasing order. 61 279 , 60 729 , 60 927 , 61 792",
"answers": [
"60 729 , 60 927 , 61 279 , 61 792",
"61 279 , 60 729 , 61 792 , 60 927",
"61 792 , 61 279 , 60 927 , 60 729",
"60 927 , 61 792 , 60 729 , 61 279"
],
"correct_index": 2,
"solution": "Decreasing order = largest to smallest. Compare the numbers: 61 792 > 61 279 > 60 927 > 60 729. This matches option (3)."
},
{
"id": 21839,
"type": 1,
"question": "Which of the following is a multiple of 8?",
"answers": [
"63",
"56",
"42",
"18"
],
"correct_index": 1,
"solution": "A multiple of 8 is divisible by 8. 56 = 8 × 7, so 56 is a multiple of 8. The others are not."
},
{
"id": 21840,
"type": 1,
"question": "The table shows the number of males and females in Primary 5A and 5B who are cyclists and non-cyclists. What is the total number of female cyclists in both classes?",
"answers": [
"42",
"25",
"23",
"19"
],
"correct_index": 3,
"solution": "Female cyclists: Primary 5A = 9, Primary 5B = 10. Total = 9 + 10 = 19. This matches option (4)."
},
{
"id": 21841,
"type": 1,
"question": "76 thousands 25 hundreds and 4 tens is the same as .",
"answers": [
"76 240",
"76 254",
"78 504",
"78 540"
],
"correct_index": 3,
"solution": "76 thousands = 76 000; 25 hundreds = 2 500; 4 tens = 40. Total = 76 000 + 2 500 + 40 = 78 540. This matches option (4)."
},
{
"id": 21842,
"type": 1,
"question": "Last year, Penny's age was a factor of 25. This year, her age is a factor of 24. How old will Penny be next year?",
"answers": [
"7",
"6",
"5",
"4"
],
"correct_index": 0,
"solution": "Factors of 25: 1, 5, 25. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. Two consecutive years means last year's age and this year's age are consecutive. 5 (factor of 25) then 6 (factor of 24) works. So this year she is 6, and next year she will be 7. This matches option (1)."
},
{
"id": 21843,
"type": 2,
"question": "What is the missing number in the number pattern? 20 880, 20 910, , 20 970, 21 000, 21 030",
"answers": [
"20940",
null,
null,
null
],
"correct_index": null,
"solution": "The pattern increases by 30 each time (20 910 - 20 880 = 30). Missing number = 20 910 + 30 = 20 940."
},
{
"id": 21844,
"type": 2,
"question": "List all the common factors of 18 and 42.\n[?]",
"answers": [
"1, 2, 3, 6",
null,
null,
null
],
"correct_index": null,
"solution": "Factors of 18: 1, 2, 3, 6, 9, 18. Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42. Common factors = 1, 2, 3, 6."
},
{
"id": 21845,
"type": 2,
"question": "The bar graph shows the number of strollers sold from August to December. What is the total number of strollers sold from September to November? [?]",
"answers": [
"46",
null,
null,
null
],
"correct_index": null,
"solution": "From the bar graph: September = 17, October = 9, November = 20. Total = 17 + 9 + 20 = 46."
},
{
"id": 21846,
"type": 2,
"question": "A number is 87 000 when rounded to the nearest 1000. What is the smallest possible number? [?]",
"answers": [
"86500",
null,
null,
null
],
"correct_index": null,
"solution": "To round up to 87 000 to the nearest 1000, the smallest number must round up from the 86 000s. The smallest is 86 500 (the half-way point rounds up)."
},
{
"id": 21847,
"type": 2,
"question": "Bernice bought some fruit tarts to give to her cousins. When she gave 6 fruit tarts to each cousin, she would have 2 fruit tarts remaining. When she gave 7 fruit tarts to each cousin, she would be short of 6 fruit tarts. How many cousins did Bernice have? [?]",
"answers": [
"8",
null,
null,
null
],
"correct_index": null,
"solution": "Giving 7 instead of 6 to each cousin uses 1 more tart per cousin. The change is from 2 left over to 6 short, a difference of 2 + 6 = 8 tarts. So there are 8 cousins (8 extra tarts needed, 1 per cousin)."
},
{
"id": 21848,
"type": 2,
"question": "The line graph shows the number of people at a bus stop from 16 00 to 21 00. (a) How many fewer people were at the bus stop at 17 00 than at 19 00? (b) The number of people at the bus stop at 21 00 was twice the number of people at the bus stop at . (c) During which 1-hour period was the increase in the number of people at the bus stop the greatest? Give your answer as to .",
"answers": [
"7",
"16 00",
"16 00",
"17 00"
],
"correct_index": null,
"solution": "From the line graph: 16 00 = 4, 17 00 = 9, 18 00 = 13, 19 00 = 16, 20 00 = 10, 21 00 = 8. (a) At 19 00 there were 16 and at 17 00 there were 9, so 16 - 9 = 7 fewer. (b) At 21 00 there were 8; twice means the other time had 8 ÷ 2 = 4, which is 16 00. (c) Increases: 16 00→17 00 = +5, 17 00→18 00 = +4, 18 00→19 00 = +3. Greatest is 16 00 to 17 00."
},
{
"id": 21849,
"type": 2,
"question": "Yasmin had twice as many cards as Xenia at first. After Yasmin gave Xenia 26 cards, Yasmin had 40 more cards than Xenia in the end. How many cards did Yasmin have at first? [?]",
"answers": [
"184",
null,
null,
null
],
"correct_index": null,
"solution": "Let Xenia have 1 unit and Yasmin 2 units at first. After Yasmin gives 26: Yasmin = 2u - 26, Xenia = 1u + 26. Difference = (2u - 26) - (1u + 26) = u - 52 = 40, so u = 92 (Xenia at first). Yasmin at first = 2 × 92 = 184."
},
{
"id": 21850,
"type": 2,
"question": "Janice has twice as many stickers as Cathy. Alicia has thrice as many stickers as Janice. Janice has 72 fewer stickers than Alicia. How many more stickers does Alicia have than Cathy? [?]",
"answers": [
"90",
null,
null,
null
],
"correct_index": null,
"solution": "Let Cathy = 1 unit. Janice = 2 units. Alicia = 3 × Janice = 6 units. Alicia - Janice = 6u - 2u = 4u = 72, so 1 unit = 18. Cathy = 18, Janice = 36, Alicia = 108. Alicia - Cathy = 108 - 18 = 90."
},
{
"id": 21851,
"type": 1,
"question": "What is the size of ∠FEG?",
"answers": [
"45°",
"55°",
"135°",
"145°"
],
"correct_index": 1,
"solution": "Read the protractor along the ray EG. EF lies on the 0° line and ray EG passes through the 55° mark on the inner scale (measured from EF). So ∠FEG = 55°."
},
{
"id": 21852,
"type": 1,
"question": "How many eighths are there in \\(3\\dfrac{7}{8}\\)?",
"answers": [
"7",
"10",
"24",
"31"
],
"correct_index": 3,
"solution": "Convert the mixed number to an improper fraction with denominator 8: \\(3\\dfrac{7}{8} = \\dfrac{3\\times8 + 7}{8} = \\dfrac{31}{8}\\). So there are 31 eighths."
},
{
"id": 21853,
"type": 1,
"question": "The diagram shows a rectangle ABEF and a square BCDE. Which of the following shows a correct pair of parallel lines?",
"answers": [
"AC // AF",
"BC // FD",
"FE // BE",
"CD // ED"
],
"correct_index": 1,
"solution": "ABEF is a rectangle and BCDE a square sitting side by side, so the top edge ABC and the bottom edge FED are two straight parallel lines. BC is part of the top edge and FD is part of the bottom edge, so BC // FD. The other pairs meet or lie on the same line, so they are not parallel."
},
{
"id": 21854,
"type": 1,
"question": "Mrs Chua cut a cake into 12 equal slices. She gave \\(\\dfrac{1}{2}\\) of the cake to her neighbour and 4 slices to her daughter. How many slices of cake was left?",
"answers": [
"10",
"2",
"6",
"8"
],
"correct_index": 1,
"solution": "\\(\\dfrac{1}{2}\\) of 12 slices = 6 slices to the neighbour. Daughter got 4 slices. Slices given away = 6 + 4 = 10. Slices left = 12 − 10 = 2."
},
{
"id": 21855,
"type": 1,
"question": "Packet A contains \\(\\dfrac{3}{4}\\) kg of salt. It has \\(\\dfrac{1}{3}\\) kg more salt than Packet B. What is the total mass of salt in Packet A and B?",
"answers": [
"\\(1\\frac{1}{6}\\) kg",
"\\(1\\frac{5}{6}\\) kg",
"\\(1\\frac{1}{12}\\) kg",
"\\(1\\frac{5}{12}\\) kg"
],
"correct_index": 0,
"solution": "Packet B = \\(\\dfrac{3}{4} - \\dfrac{1}{3} = \\dfrac{9}{12} - \\dfrac{4}{12} = \\dfrac{5}{12}\\) kg. Total = \\(\\dfrac{3}{4} + \\dfrac{5}{12} = \\dfrac{9}{12} + \\dfrac{5}{12} = \\dfrac{14}{12} = 1\\dfrac{2}{12} = 1\\dfrac{1}{6}\\) kg."
},
{
"id": 21856,
"type": 1,
"question": "Arrange the fractions in increasing order. $$\\frac{7}{3}$$, $$\\frac{5}{6}$$, $$2\\frac{1}{4}$$",
"answers": [
"\\(\\dfrac{5}{6}\\) , \\(2\\dfrac{1}{4}\\) , \\(\\dfrac{7}{3}\\)",
"\\(\\dfrac{7}{3}\\) , \\(2\\dfrac{1}{4}\\) , \\(\\dfrac{5}{6}\\)",
"\\(2\\dfrac{1}{4}\\) , \\(\\dfrac{7}{3}\\) , \\(\\dfrac{5}{6}\\)",
"\\(\\dfrac{5}{6}\\) , \\(\\dfrac{7}{3}\\) , \\(2\\dfrac{1}{4}\\)"
],
"correct_index": 0,
"solution": "Compare values: \\(\\dfrac{5}{6} \\approx 0.83\\), \\(2\\dfrac{1}{4} = 2.25\\), \\(\\dfrac{7}{3} \\approx 2.33\\). Increasing order: \\(\\dfrac{5}{6}\\), \\(2\\dfrac{1}{4}\\), \\(\\dfrac{7}{3}\\)."
},
{
"id": 21857,
"type": 1,
"question": "Find the sum of $$\\frac{9}{10}$$ and $$\\frac{4}{5}$$. Express your answer as a mixed number in its simplest form.",
"answers": [
"\\(1\\dfrac{7}{10}\\)",
"\\(1\\dfrac{4}{5}\\)",
"\\(\\dfrac{16}{10}\\)",
"\\(\\dfrac{17}{11}\\)"
],
"correct_index": 0,
"solution": "\\(\\dfrac{4}{5} = \\dfrac{8}{10}\\). Sum = \\(\\dfrac{9}{10} + \\dfrac{8}{10} = \\dfrac{17}{10} = 1\\dfrac{7}{10}\\)."
},
{
"id": 21858,
"type": 1,
"question": "Name an angle that is smaller than a right angle.",
"answers": [
"∠BCD",
"∠AED",
"∠EAB",
"∠ABC"
],
"correct_index": 0,
"solution": "The figure is a pentagon ABCDE shaped like an arrow/house pointing right at C. The angle at C, ∠BCD, is the pointed vertex which is acute (smaller than 90°). The angles at A and E are right angles and those at B and D are obtuse (reflex of the point)."
},
{
"id": 21859,
"type": 2,
"question": "Lynn had some sugar at first. She used \\(\\dfrac{1}{8}\\) of the sugar and she had 560 g of sugar left. How much sugar did she have at first? g",
"answers": [
"640",
null,
null,
null
],
"correct_index": null,
"solution": "She used \\(\\dfrac{1}{8}\\), so \\(\\dfrac{7}{8}\\) of the sugar = 560 g. 1 unit (\\(\\dfrac{1}{8}\\)) = 560 ÷ 7 = 80 g. Total (8 units) = 80 × 8 = 640 g."
},
{
"id": 21860,
"type": 2,
"question": "Figure A shows a rectangular piece of paper. It is folded along the dotted line as shown in Figure B. Find ∠a. °",
"answers": [
"33",
null,
null,
null
],
"correct_index": null,
"solution": "In Figure A the diagonal makes 24° with the base, so the angle between the diagonal and the right edge of the rectangle is 90° − 24° = 66°. Folding along the dotted line reflects the flap, splitting this 66° equally into two parts. So ∠a = 66° ÷ 2 = 33°."
},
{
"id": 21861,
"type": 1,
"question": "Annie and Betty had $$\\frac{1}{2}$$ m of cloth. Betty and Cathy had $$\\frac{3}{4}$$ m of cloth. Annie, Betty and Cathy had $$\\frac{4}{5}$$ m of cloth altogether. How much cloth did Betty have? Express your answer in its simplest form. m",
"answers": [
"\\(\\dfrac{9}{20}\\)",
"\\(\\dfrac{1}{2}\\)",
"\\(\\dfrac{8}{20}\\)",
"\\(\\dfrac{11}{20}\\)"
],
"correct_index": 0,
"solution": "(Annie + Betty) + (Betty + Cathy) = \\(\\dfrac{1}{2} + \\dfrac{3}{4} = \\dfrac{2}{4} + \\dfrac{3}{4} = \\dfrac{5}{4}\\) m. This counts Betty twice plus Annie + Betty + Cathy. So Betty = \\(\\dfrac{5}{4} - \\dfrac{4}{5} = \\dfrac{25}{20} - \\dfrac{16}{20} = \\dfrac{9}{20}\\) m."
},
{
"id": 21862,
"type": 1,
"question": "There was 4 $$\\ell$$ of water in a container. Raju used $$\\frac{1}{6}$$ $$\\ell$$ of water in the morning. Raju used another $$\\frac{1}{4}$$ $$\\ell$$ of water in the afternoon. (a) What was the total amount of water used by Raju? Express your answer as a fraction in the simplest form. $$\\ell$$ (b) How much water was left in the container? Express your answer as a mixed number in the simplest form. $$\\ell$$",
"answers": [
"\\(\\dfrac{5}{12}\\) , \\(3\\dfrac{7}{12}\\)",
"\\(3\\dfrac{7}{12}\\) , \\(\\dfrac{5}{12}\\)",
"\\(3\\dfrac{7}{12}\\) , \\(\\dfrac{5}{12}\\)",
"\\(3\\dfrac{7}{12}\\) , \\(\\dfrac{5}{12}\\)"
],
"correct_index": 0,
"solution": "(a) Total used = \\(\\dfrac{1}{6} + \\dfrac{1}{4} = \\dfrac{2}{12} + \\dfrac{3}{12} = \\dfrac{5}{12}\\) ℓ. (b) Water left = \\(4 - \\dfrac{5}{12} = 3\\dfrac{12}{12} - \\dfrac{5}{12} = 3\\dfrac{7}{12}\\) ℓ."
},
{
"id": 21908,
"type": 1,
"question": "Ten thousand and twelve in numerals is .",
"answers": [
"1012",
"10 012",
"10 020",
"10 120"
],
"correct_index": 1,
"solution": "Ten thousand = 10 000, plus twelve = 12, so 10 000 + 12 = 10 012."
},
{
"id": 21909,
"type": 1,
"question": "In 35 987, the digit 5 stands for .",
"answers": [
"5 tens",
"5 hundreds",
"5 thousands",
"5 ten thousands"
],
"correct_index": 2,
"solution": "In 35 987 the digit 5 is in the thousands place, so it stands for 5 thousands (5000)."
},
{
"id": 21910,
"type": 1,
"question": "A tourist attraction had 235 189 visitors last year. Round the number to the nearest hundred.",
"answers": [
"235 200",
"235 190",
"235 100",
"235 000"
],
"correct_index": 0,
"solution": "To round 235 189 to the nearest hundred, look at the tens digit (8). Since 8 ≥ 5, round up: 235 189 ≈ 235 200."
},
{
"id": 21911,
"type": 1,
"question": "Which of the following are common factors of 45 and 63?",
"answers": [
"3 and 7",
"3 and 9",
"5 and 7",
"5 and 9"
],
"correct_index": 1,
"solution": "Factors of 45: 1, 3, 5, 9, 15, 45. Factors of 63: 1, 3, 7, 9, 21, 63. Common factors: 1, 3, 9. So 3 and 9 are common factors."
},
{
"id": 21912,
"type": 1,
"question": "In which of the following are the numbers arranged from the greatest to the smallest?",
"answers": [
"58 349 , 59 843 , 59 348",
"59 843 , 58 349 , 59 348",
"58 349 , 59 348 , 59 843",
"59 843 , 59 348 , 58 349"
],
"correct_index": 3,
"solution": "Order from greatest to smallest: 59 843 > 59 348 > 58 349. Compare ten-thousands/thousands then hundreds. Option 4 is correct."
},
{
"id": 21913,
"type": 1,
"question": "Mrs Lee packed some doughnuts into boxes of 6. In the end, she had 12 boxes of doughnuts and 3 doughnuts were left unpacked. How many doughnuts did Mrs Lee have at first?",
"answers": [
"69",
"72",
"75",
"96"
],
"correct_index": 2,
"solution": "Doughnuts in boxes = 12 × 6 = 72. Add the 3 left unpacked: 72 + 3 = 75."
},
{
"id": 21914,
"type": 2,
"question": "93 708 = 90 000 + 3000 + + 8",
"answers": [
"700",
null,
null,
null
],
"correct_index": null,
"solution": "Expand 93 708 = 90 000 + 3000 + 700 + 8. The missing number is the hundreds part, 700."
},
{
"id": 21915,
"type": 2,
"question": "The number of residents in a town is 91 000 when rounded to the nearest 1000. What could be the greatest possible number of residents living in the town, before rounding to the nearest 1000?\n[?]",
"answers": [
"91 499",
null,
null,
null
],
"correct_index": null,
"solution": "Numbers from 90 500 to 91 499 round to 91 000 to the nearest 1000. The greatest such whole number is 91 499."
},
{
"id": 21916,
"type": 2,
"question": "Write down the first 2 common multiples of 3 and 9. and ",
"answers": [
"9",
"18",
null,
null
],
"correct_index": null,
"solution": "Multiples of 3: 3, 6, 9, 12, 15, 18, ... Multiples of 9: 9, 18, 27, ... The first two common multiples are 9 and 18."
},
{
"id": 21917,
"type": 2,
"question": "Complete the number pattern. 2830 , 3830 , 3820 , 4820 , 4810 , 5810 , 5800 , , ",
"answers": [
"6800",
"6790",
null,
null
],
"correct_index": null,
"solution": "The pattern alternates +1000 then −10: 2830 (+1000) 3830 (−10) 3820 (+1000) 4820 (−10) 4810 (+1000) 5810 (−10) 5800. Next: +1000 → 6800, then −10 → 6790."
},
{
"id": 21918,
"type": 2,
"question": "Mrs Tan packed 48 red pens and 60 blue pens into some bags with no remainder. The total number of pens in each bag was the same. There was an equal number of red pens in each bag. What is the smallest number of red pens there could be in each bag?\n[?]",
"answers": [
"4",
null,
null,
null
],
"correct_index": null,
"solution": "The number of bags must divide both 48 and 60 with no remainder, so it is a common factor of 48 and 60. To make the red pens per bag smallest, use the largest number of bags = HCF(48, 60) = 12. Red pens per bag = 48 ÷ 12 = 4."
},
{
"id": 21919,
"type": 2,
"question": "Andy listed the factors of 32. 1 , 2 , 8 , 32 He missed out two factors. What were the two missing factors? and ",
"answers": [
"4",
"16",
null,
null
],
"correct_index": null,
"solution": "All factors of 32 are 1, 2, 4, 8, 16, 32. Andy listed 1, 2, 8, 32, so the missing factors are 4 and 16."
},
{
"id": 21920,
"type": 2,
"question": "Jenny has \\(\\$7500\\). James has \\(\\$6850\\). How much must Jenny give to James so that both of them have the same amount of money?\n[?]",
"answers": [
"325",
null,
null,
null
],
"correct_index": null,
"solution": "Difference = \\(\\$7500\\) − \\(\\$6850\\) = \\(\\$650\\). Jenny gives half the difference so they are equal: \\(\\$650\\) ÷ 2 = \\(\\$325\\)."
},
{
"id": 21921,
"type": 2,
"question": "Ada, Ben and Chris had 720 stickers altogether. Ben had twice as many stickers as Ada, Chris had 40 stickers less than Ada. How many stickers did Ben have?\n[?]",
"answers": [
"380",
null,
null,
null
],
"correct_index": null,
"solution": "Let Ada = 1 unit. Ben = 2 units, Chris = 1 unit − 40. Total = 4 units − 40 = 720, so 4 units = 760 and 1 unit = 190. Ben = 2 units = 380."
},
{
"id": 21922,
"type": 2,
"question": "Mr Lim bought 5 identical T-shirts and a pair of pants. He paid \\(\\$120\\) for the 5 T-shirts. The pair of pants cost 3 times as much as one T-shirt. (a) How much did one T-shirt cost? (b) How much did the pair of pants cost? [?] , [?]",
"answers": [
"24",
"72",
null,
null
],
"correct_index": null,
"solution": "(a) One T-shirt = \\(\\$120\\) ÷ 5 = \\(\\$24\\). (b) The pants cost 3 times one T-shirt = 3 × \\(\\$24\\) = \\(\\$72\\)."
},
{
"id": 21923,
"type": 2,
"question": "In a carnival game, points are earned when bean bags are tossed onto regions A, B or C. Ron, Shirley and Tammy tossed 2 bean bags each: (i) Ron's bean bags landed on regions A and B. (ii) Shirley's bean bags landed on regions B and C. (iii) Tammy's bean bags landed on regions A and C. The total number of points earned by each of them: Ron 125, Shirley 65, Tammy 100. How many points will be earned when a bean bag lands on region B?\n[?]",
"answers": [
"45",
null,
null,
null
],
"correct_index": null,
"solution": "Ron: A + B = 125. Shirley: B + C = 65. Tammy: A + C = 100. Adding all three: 2A + 2B + 2C = 290, so A + B + C = 145. Region B = (A + B + C) − (A + C) = 145 − 100 = 45."
},
{
"id": 22290,
"type": 1,
"question": "50 000 + 900 + 8 =",
"answers": [
"50 098",
"50 908",
"59 008",
"59 080"
],
"correct_index": 1,
"solution": "Add by place value: 50 000 + 900 + 8 = 50 908. There are 5 ten-thousands, 0 thousands, 9 hundreds, 0 tens and 8 ones. Answer: 50 908."
},
{
"id": 22291,
"type": 1,
"question": "Arrange the following numbers from the greatest to the smallest. 9605, 9065, 9506",
"answers": [
"9065, 9605, 9506",
"9065, 9506, 9605",
"9605, 9065, 9506",
"9605, 9506, 9065"
],
"correct_index": 3,
"solution": "Compare from the largest place value. All have 9 thousands. Hundreds: 9605 and 9506 have 6 and 5 hundreds; 9065 has 0 hundreds. So 9605 > 9506 > 9065. Greatest to smallest: 9605, 9506, 9065. Answer: option 4."
},
{
"id": 22292,
"type": 1,
"question": "Complete the number pattern. 5934, 5634, 5624, 5324, , 5014, 5004",
"answers": [
"5024",
"5314",
"5334",
"5624"
],
"correct_index": 1,
"solution": "The pattern alternates subtracting 300 then 10: 5934 -300 = 5634, -10 = 5624, -300 = 5324, -10 = 5314, -300 = 5014, -10 = 5004. The missing term is 5314. Answer: option 2."
},
{
"id": 22293,
"type": 1,
"question": "3 and 4 are factors of .",
"answers": [
"15",
"18",
"20",
"24"
],
"correct_index": 3,
"solution": "A number with both 3 and 4 as factors must be a multiple of 12. Check: 15 (no), 18 (4 is not a factor), 20 (3 is not a factor), 24 = 3 x 8 = 4 x 6. So 24 has both 3 and 4 as factors. Answer: option 4."
},
{
"id": 22294,
"type": 2,
"question": "a) Write seventy-eight thousand and twenty in numerals. b) Round 39 500 to the nearest thousand. [?] , [?]",
"answers": [
"78020",
"40000",
null,
null
],
"correct_index": null,
"solution": "a) Seventy-eight thousand and twenty = 78 000 + 20 = 78 020. b) 39 500 is exactly halfway between 39 000 and 40 000; rounding to the nearest thousand rounds the half up to 40 000."
},
{
"id": 22295,
"type": 2,
"question": "Find the product of 8540 and 7.\n[?]",
"answers": [
"59780",
null,
null,
null
],
"correct_index": null,
"solution": "Product means multiply: 8540 x 7. 8000 x 7 = 56 000; 500 x 7 = 3500; 40 x 7 = 280. Sum: 56 000 + 3500 + 280 = 59 780."
},
{
"id": 22296,
"type": 2,
"question": "Ben packed 853 books in boxes of 9. How many books were left unpacked?\n[?]",
"answers": [
"7",
null,
null,
null
],
"correct_index": null,
"solution": "Divide 853 by 9 and find the remainder. 9 x 94 = 846, and 853 - 846 = 7. So 94 full boxes are packed and 7 books are left unpacked. Answer: 7 books."
},
{
"id": 22297,
"type": 2,
"question": "The table shows the number of students in two classes. Part of the table is covered by ink blots. How many more girls than boys are there altogether? [?]",
"answers": [
"5",
null,
null,
null
],
"correct_index": null,
"solution": "From the table: 4A total 41 with 22 boys means 4A girls = 41 - 22 = 19 (given). 4B total 34 with 21 girls means 4B boys = 34 - 21 = 13. Total girls = 19 + 21 = 40; total boys = 22 + 13 = 35. More girls than boys = 40 - 35 = 5."
},
{
"id": 22298,
"type": 2,
"question": "Andy had \\(\\$450\\) more than Betty. Betty gave \\(\\$35\\) to Andy. How much more did Andy have than Betty in the end?\n[?]",
"answers": [
"520",
null,
null,
null
],
"correct_index": null,
"solution": "When Betty gives \\(\\$35\\) to Andy, Andy gains \\(\\$35\\) and Betty loses \\(\\$35\\), so the gap between them widens by 2 x \\(\\$35\\) = \\(\\$70\\). New difference = \\(\\$450\\) + \\(\\$70\\) = \\(\\$520\\). Answer: \\(\\$520\\)."
},
{
"id": 22299,
"type": 2,
"question": "At a bookshop, pens are sold in boxes of 6 and pencils are sold in boxes of 8. Miss Nurul bought an equal number of pens and pencils for her class. Find the least total number of pens and pencils Miss Nurul bought.\n[?]",
"answers": [
"48",
null,
null,
null
],
"correct_index": null,
"solution": "For an equal number of pens and pencils, the count must be a common multiple of 6 and 8. The least common multiple of 6 and 8 is 24, so the least number of pens is 24 and the least number of pencils is 24. Total = 24 + 24 = 48."
},
{
"id": 22300,
"type": 2,
"question": "A fruit seller had 4 times as many durians as watermelons. After he sold 114 durians, he had as many watermelons as durians left. How many fruits did the fruit seller have left in the end?\n[?]",
"answers": [
"76",
null,
null,
null
],
"correct_index": null,
"solution": "Let watermelons = 1 unit, durians = 4 units. After selling 114 durians, durians left = watermelons = 1 unit, so 114 durians = 4 units - 1 unit = 3 units. 1 unit = 114 / 3 = 38. Watermelons = 38 and durians left = 38, so fruits left = 38 + 38 = 76."
},
{
"id": 22301,
"type": 2,
"question": "A tank was filled with water. Water flowed out of the tank from 09 00 to 14 00. a) How many litres of water was in the tank at first? b) How many litres of water was in the tank at 10 00? c) How many litres of water flowed out between 12 00 and 13 00? d) The least amount of water flowed out during which 1-hour period? From to ",
"answers": [
"250",
"220",
"90",
"1100"
],
"correct_index": null,
"solution": "Read the line graph. a) At 09 00 the line is at 250, so 250 litres at first. b) At 10 00 the line is at 220 litres. c) At 12 00 there are 140 litres and at 13 00 there are 50 litres, so 140 - 50 = 90 litres flowed out. d) Hourly drops: 09-10 = 30, 10-11 = 60, 11-12 = 20, 12-13 = 90, 13-14 = 50. The smallest drop (20 litres) is from 11 00 to 12 00."
},
{
"id": 22302,
"type": 2,
"question": "A school bag costs \\(\\$60\\) more than a water bottle. 3 similar school bags and 2 similar water bottles cost \\(\\$280\\). How much does each water bottle cost?\n[?]",
"answers": [
"20",
null,
null,
null
],
"correct_index": null,
"solution": "Each bag = bottle + \\(\\$60\\). So 3 bags = 3 bottles + 3 x \\(\\$60\\) = 3 bottles + \\(\\$180\\). Then 3 bags + 2 bottles = 5 bottles + \\(\\$180\\) = \\(\\$280\\). So 5 bottles = \\(\\$280\\) - \\(\\$180\\) = \\(\\$100\\), and 1 bottle = \\(\\$100\\) / 5 = \\(\\$20\\)."
},
{
"id": 22303,
"type": 2,
"question": "Tammy has 35 \\(\\$2\\) and \\(\\$5\\) notes. The total value of the notes is \\(\\$118\\). How many \\(\\$5\\) notes does she have?\n[?]",
"answers": [
"16",
null,
null,
null
],
"correct_index": null,
"solution": "Assume all 35 notes are \\(\\$2\\): value = 35 x \\(\\$2\\) = \\(\\$70\\). The actual total is \\(\\$118\\), which is \\(\\$48\\) more. Each \\(\\$2\\) note swapped for a \\(\\$5\\) note adds \\(\\$3\\). So number of \\(\\$5\\) notes = \\(\\$48\\) / \\(\\$3\\) = 16."
},
{
"id": 22385,
"type": 2,
"question": "Arrange the following numbers from the smallest to the largest. 3.5 , 3.05 , \\(3\\dfrac{1}{100}\\) (smallest) , , ",
"answers": [
"3 1/100",
"3.05",
"3.5",
null
],
"correct_index": null,
"solution": "Write all as decimals: \\(3\\dfrac{1}{100} = 3.01\\), 3.05, 3.5. In order smallest to largest: 3.01, 3.05, 3.5, i.e. \\(3\\dfrac{1}{100}\\), 3.05, 3.5."
},
{
"id": 22520,
"type": 2,
"question": "What is 100 less than 80 060?\n[?]",
"answers": [
"79960",
null,
null,
null
],
"correct_index": null,
"solution": "Subtract 100 from 80 060: 80 060 - 100 = 79 960."
},
{
"id": 22521,
"type": 2,
"question": "List all the common factors of 16 and 28.\n[?] , [?] , [?]",
"answers": [
"1",
"2",
"4",
null
],
"correct_index": null,
"solution": "Factors of 16: 1, 2, 4, 8, 16. Factors of 28: 1, 2, 4, 7, 14, 28. The factors common to both are 1, 2 and 4."
},
{
"id": 22522,
"type": 2,
"question": "Find the product of 358 and 35.\n[?]",
"answers": [
"12530",
null,
null,
null
],
"correct_index": null,
"solution": "358 x 35 = 358 x 30 + 358 x 5 = 10 740 + 1 790 = 12 530."
},
{
"id": 22523,
"type": 2,
"question": "Find the value of 6793 ÷ 6\n[?]",
"answers": [
"1132 R1",
null,
null,
null
],
"correct_index": null,
"solution": "6793 ÷ 6: 6 ÷ 6 = 1, 7 ÷ 6 = 1 r 1, 19 ÷ 6 = 3 r 1, 13 ÷ 6 = 2 r 1. Quotient 1132 remainder 1, so 6793 ÷ 6 = 1132 R1."
},
{
"id": 22524,
"type": 1,
"question": "Express $$\\frac{42}{8}$$ as a mixed number in its simplest form.",
"answers": [
"\\(5\\dfrac{1}{4}\\)",
"\\(5\\dfrac{1}{2}\\)",
"\\(\\dfrac{20}{4}\\)",
"\\(\\dfrac{21}{5}\\)"
],
"correct_index": 0,
"solution": "42 ÷ 8 = 5 remainder 2, so \\(\\dfrac{42}{8}=5\\dfrac{2}{8}\\). Simplify \\(\\dfrac{2}{8}=\\dfrac{1}{4}\\), giving \\(5\\dfrac{1}{4}\\)."
},
{
"id": 22525,
"type": 1,
"question": "Compare the fractions. Use '<' or '>' to indicate which is greater or smaller. \\(2\\dfrac{5}{8}\\) \\(\\dfrac{5}{2}\\)",
"answers": [
"<",
">",
null,
null
],
"correct_index": 1,
"solution": "\\(\\dfrac{5}{2}=2\\dfrac{1}{2}=2\\dfrac{4}{8}\\). Compare with \\(2\\dfrac{5}{8}\\): the whole parts are equal and \\(\\dfrac{5}{8}>\\dfrac{4}{8}\\), so \\(2\\dfrac{5}{8}>\\dfrac{5}{2}\\)."
},
{
"id": 22526,
"type": 2,
"question": "A stadium can seat 52 000 people when rounded to the nearest thousand. What is the greatest possible seating capacity of this stadium?\n[?]",
"answers": [
"52499",
null,
null,
null
],
"correct_index": null,
"solution": "Numbers from 51 500 to 52 499 round to 52 000. The greatest of these is 52 499."
},
{
"id": 22527,
"type": 2,
"question": "I am thinking of a 3-digit number. When rounded to the hundred, the number is 800. The digit in the hundreds place is twice that in the tens place. The sum of all the digits is 15. What is this number? [?]",
"answers": [
"843",
null,
null,
null
],
"correct_index": null,
"solution": "Rounds to 800, so the number is 750-849; the hundreds digit is 8, tens digit < 5. Hundreds = twice tens means tens = 4 (8 = 2 x 4). Digits sum to 15: 8 + 4 + ones = 15, so ones = 3. The number is 843."
},
{
"id": 22528,
"type": 2,
"question": "James bought an equal number of red and blue marbles. He arranged the red marbles in groups of 5 and the blue marbles in groups of 3. What is the least possible number of red and blue marbles James bought altogether?\n[?]",
"answers": [
"30",
null,
null,
null
],
"correct_index": null,
"solution": "The number of each colour must be a common multiple of 5 and 3. The least common multiple is 15, so there are 15 red and 15 blue marbles. Altogether 15 + 15 = 30 marbles."
},
{
"id": 22529,
"type": 1,
"question": "Subtract $$\\frac{2}{3}$$ from $$\\frac{6}{7}$$.",
"answers": [
"\\(\\dfrac{4}{21}\\)",
"\\(\\dfrac{5}{21}\\)",
"\\(\\dfrac{3}{21}\\)",
"\\(\\dfrac{17}{21}\\)"
],
"correct_index": 0,
"solution": "\\(\\dfrac{6}{7}-\\dfrac{2}{3}\\). Common denominator 21: \\(\\dfrac{6}{7}=\\dfrac{18}{21}\\) and \\(\\dfrac{2}{3}=\\dfrac{14}{21}\\). \\(\\dfrac{18}{21}-\\dfrac{14}{21}=\\dfrac{4}{21}\\)."
},
{
"id": 22530,
"type": 2,
"question": "There were 141 sweets in a box. Melvin gave away $$\\frac{2}{3}$$ of them to his friends and kept the rest. How many sweets did he give away?\n[?]",
"answers": [
"94",
null,
null,
null
],
"correct_index": null,
"solution": "\\(\\dfrac{1}{3}\\) of 141 = 141 ÷ 3 = 47. He gave away \\(\\dfrac{2}{3}\\), so 47 x 2 = 94 sweets."
},
{
"id": 22531,
"type": 2,
"question": "A storybook and 2 notepads cost \\(\\$46\\) altogether. The 2 notepads cost \\(\\$10\\) less than the storybook. How much does 1 notepad cost?\n[?]",
"answers": [
"$9",
null,
null,
null
],
"correct_index": null,
"solution": "If the 2 notepads cost \\(\\$10\\) less than the storybook, then 2 notepads + 2 notepads + \\(\\$10\\) = \\(\\$46\\). So 4 notepads = \\(\\$46\\) - \\(\\$10\\) = \\(\\$36\\), and 1 notepad = \\(\\$36\\) ÷ 4 = \\(\\$9\\)."
},
{
"id": 22532,
"type": 2,
"question": "The line graph shows the number of T-shirts sold by a shop from Monday to Friday. (a) How many more T-shirts did the shop sell on Friday than on Tuesday? (b) Over which two days was the increase in the number of T-shirts sold the greatest? (c) If the number of T-shirts sold on Saturday was twice the number of T-shirts sold on Wednesday, how many T-shirts were sold on Saturday? [?] , [?] , [?]",
"answers": [
"25",
"Wednesday to Thursday",
"48",
null
],
"correct_index": null,
"solution": "From the graph: Mon 30, Tue 15, Wed 24, Thu 37, Fri 40. (a) Fri - Tue = 40 - 15 = 25 more. (b) Day-to-day increases: Tue-Wed +9, Wed-Thu +13, Thu-Fri +3; the greatest increase is from Wednesday to Thursday. (c) Saturday = 2 x Wednesday = 2 x 24 = 48 T-shirts."
},
{
"id": 22533,
"type": 2,
"question": "Dan had thrice as many erasers as Elijah at first. After their parents gave them an equal number of erasers each, Dan had twice as many erasers as Elijah and they had a total of 84 erasers. How many erasers did Dan have at first?\n[?]",
"answers": [
"42",
null,
null,
null
],
"correct_index": null,
"solution": "After receiving erasers, total 84 is split as Dan : Elijah = 2 : 1, i.e. 3 units = 84, so 1 unit = 84 ÷ 6... working: 84 ÷ 3 units gives Dan 56 and Elijah 28 after. The equal amount added is x, so Elijah-first = 28 - x and Dan-first = 56 - x = 3(28 - x). Solving: 56 - x = 84 - 3x, 2x = 28, x = 14. Dan at first = 56 - 14 = 42 erasers. (Key working: 84 ÷ 6 = 14, 14 x 3 = 42.)"
},
{
"id": 22534,
"type": 2,
"question": "Nicholas donated some of his savings to charity. He donated $$\\frac{3}{8}$$ of it to Charity A and $$\\frac{1}{4}$$ of it to Charity B. He then donated the rest of his savings equally among 4 other charities. If each of these 4 charities received \\(\\$60\\), how much money did he donate to all 6 charities?\n[?]",
"answers": [
"$640",
null,
null,
null
],
"correct_index": null,
"solution": "The 4 other charities received 4 x \\(\\$60\\) = \\(\\$240\\), which is the rest of the savings. Fraction left = 1 - \\(\\dfrac{3}{8}\\) - \\(\\dfrac{1}{4}\\) = 1 - \\(\\dfrac{3}{8}\\) - \\(\\dfrac{2}{8}\\) = \\(\\dfrac{3}{8}\\). So \\(\\dfrac{3}{8}\\) of savings = \\(\\$240\\), meaning \\(\\dfrac{1}{8}\\) = \\(\\$80\\) and total savings = \\(\\$80\\) x 8 = \\(\\$640\\). All 6 charities together received the whole savings, \\(\\$640\\)."
},
{
"id": 22606,
"type": 1,
"question": "Write the number: Fifty thousand, eight hundred and three.",
"answers": [
"50 803",
"5 803",
"50 083",
"508 003"
],
"correct_index": 0,
"solution": "Fifty thousand = 50 000, eight hundred = 800, three = 3. So the number is 50 000 + 800 + 3 = 50 803."
},
{
"id": 22607,
"type": 2,
"question": "Use all the digits to form the smallest 4-digit number.\n[?]",
"answers": [
"5089",
null,
null,
null
],
"correct_index": null,
"solution": "Digits are 5, 9, 0 and 8. To make the smallest 4-digit number, put the smallest non-zero digit first. 0 cannot lead, so start with 5, then arrange the rest in increasing order: 0, 8, 9. The smallest number is 5089."
},
{
"id": 22608,
"type": 2,
"question": "Complete the number pattern. 74 603, 73 603, , 71 603, 70 603, ",
"answers": [
"72 603",
"69 603",
null,
null
],
"correct_index": null,
"solution": "Each number decreases by 1000. After 73 603 comes 73 603 - 1000 = 72 603. After 70 603 comes 70 603 - 1000 = 69 603."
},
{
"id": 22609,
"type": 2,
"question": "Arrange the numbers in increasing order. 39 039, 40 390, 40 309, 39 309 , , , ",
"answers": [
"39 039",
"39 309",
"40 309",
"40 390"
],
"correct_index": null,
"solution": "Compare from the largest place value. 39 039 and 39 309 are in the 39-thousands; 39 039 < 39 309. 40 309 and 40 390 are in the 40-thousands; 40 309 < 40 390. Increasing order: 39 039, 39 309, 40 309, 40 390."
},
{
"id": 22610,
"type": 2,
"question": "Round 74 945 to the nearest ten. 74 945 ≈ Round 74 945 to the nearest hundred. 74 945 ≈ ",
"answers": [
"74 950",
"74 900",
null,
null
],
"correct_index": null,
"solution": "Nearest ten: the ones digit is 5, so round up the tens: 74 945 ≈ 74 950. Nearest hundred: the tens digit is 4 (less than 5), so round down: 74 945 ≈ 74 900."
},
{
"id": 22611,
"type": 2,
"question": "Peter listed the factors of 32: 1, 2, 4, 16, 32. He missed out one factor. What is the missing factor? [?]",
"answers": [
"8",
null,
null,
null
],
"correct_index": null,
"solution": "The factors of 32 are 1, 2, 4, 8, 16, 32 (since 1×32, 2×16, 4×8). The list 1, 2, 4, 16, 32 leaves out 8, so the missing factor is 8."
},
{
"id": 22612,
"type": 2,
"question": "Circle the common multiples of 3 and 9. 6, 12, 18, 24, 27 , ",
"answers": [
"18",
"27",
null,
null
],
"correct_index": null,
"solution": "A common multiple of 3 and 9 must be divisible by both. From 6, 12, 18, 24, 27: 18 = 9×2 and 27 = 9×3 are multiples of 9 (and of 3). 6, 12 and 24 are multiples of 3 but not of 9. Common multiples: 18 and 27."
},
{
"id": 22613,
"type": 2,
"question": "A given number is a multiple of 7. The number is between 50 and 60. What is the number? [?]",
"answers": [
"56",
null,
null,
null
],
"correct_index": null,
"solution": "Multiples of 7: 49, 56, 63, ... The only one between 50 and 60 is 56 (7 × 8 = 56)."
},
{
"id": 22614,
"type": 1,
"question": "Arrange these fractions from the greatest to the smallest. $$\\frac{2}{3}$$, $$\\frac{5}{6}$$, $$\\frac{2}{5}$$",
"answers": [
"\\(\\dfrac{5}{6}\\) , \\(\\dfrac{2}{3}\\) , \\(\\dfrac{2}{5}\\)",
"\\(\\dfrac{2}{5}\\) , \\(\\dfrac{2}{3}\\) , \\(\\dfrac{5}{6}\\)",
"\\(\\dfrac{2}{3}\\) , \\(\\dfrac{2}{5}\\) , \\(\\dfrac{5}{6}\\)",
"\\(\\dfrac{5}{6}\\) , \\(\\dfrac{2}{5}\\) , \\(\\dfrac{2}{3}\\)"
],
"correct_index": 0,
"solution": "Convert to a common denominator of 30: \\(\\dfrac{2}{3}=\\dfrac{20}{30}\\), \\(\\dfrac{5}{6}=\\dfrac{25}{30}\\), \\(\\dfrac{2}{5}=\\dfrac{12}{30}\\). Greatest to smallest: \\(\\dfrac{25}{30}, \\dfrac{20}{30}, \\dfrac{12}{30}\\), i.e. \\(\\dfrac{5}{6}, \\dfrac{2}{3}, \\dfrac{2}{5}\\)."
},
{
"id": 22615,
"type": 1,
"question": "Find the value of $$\\frac{11}{12}-\\frac{1}{4}$$. Give your answer in its simplest form.",
"answers": [
"\\(\\dfrac{2}{3}\\)",
"1",
"\\(\\dfrac{1}{3}\\)",
"\\(\\dfrac{2}{4}\\)"
],
"correct_index": 0,
"solution": "Make the denominators the same: \\(\\dfrac{1}{4}=\\dfrac{3}{12}\\). Then \\(\\dfrac{11}{12}-\\dfrac{3}{12}=\\dfrac{8}{12}\\). Simplify by dividing by 4: \\(\\dfrac{8}{12}=\\dfrac{2}{3}\\)."
},
{
"id": 22616,
"type": 2,
"question": "A shop had 162 boxes of mangoes. Each box had 36 mangoes. (a) How many mangoes were there? (b) The shop sold 738 mangoes. The rest of the mangoes were packed into bags of 9. How many bags of mangoes were packed? (a) (b) ",
"answers": [
"5832",
"566",
null,
null
],
"correct_index": null,
"solution": "(a) Total mangoes = 162 × 36 = 5832. (b) Mangoes left after selling = 5832 - 738 = 5094. Bags = 5094 ÷ 9 = 566."
},
{
"id": 22617,
"type": 2,
"question": "Sam had some game cards at first. He gave 238 cards to his brother. Then he received 648 new cards from his father. Sam had 1330 cards in the end. How many game cards did he have at first? [?]",
"answers": [
"920",
null,
null,
null
],
"correct_index": null,
"solution": "Work backwards from the end. Before receiving 648: 1330 - 648 = 682. Before giving away 238: 682 + 238 = 920. So Sam had 920 cards at first."
},
{
"id": 22618,
"type": 2,
"question": "School A has 3064 story books in its library. School B has 4 times as many books as School A. (a) How many more story books does School B have than School A? (b) How many story books must be moved from School B to School A so that there will be the same number of books in both schools? (a) (b) ",
"answers": [
"9192",
"4596",
null,
null
],
"correct_index": null,
"solution": "School B = 3064 × 4 = 12 256 books. (a) More books in B than A = 12 256 - 3064 = 9192. (b) To make both equal, move half the difference: 9192 ÷ 2 = 4596 books."
},
{
"id": 22619,
"type": 2,
"question": "A green bulb blinks every 4 minutes, and a red bulb blinks every 6 minutes. (a) How many times will the red bulb blink in 48 minutes? (b) The two light bulbs blink together at 8.00 p.m. for the first time. At what time will the two bulbs blink together for the second time? (a) (b) p.m.",
"answers": [
"8",
"8.12",
null,
null
],
"correct_index": null,
"solution": "(a) The red bulb blinks every 6 minutes, so in 48 minutes it blinks 48 ÷ 6 = 8 times. (b) The bulbs blink together at multiples of the LCM of 4 and 6, which is 12 minutes. After 8.00 p.m., the next time they blink together is 12 minutes later, at 8.12 p.m."
},
{
"id": 22620,
"type": 1,
"question": "What is the value of the digit 7 in 38.479?",
"answers": [
"7",
"0.7",
"0.07",
"0.007"
],
"correct_index": 2,
"solution": "In 38.479, the digit 7 is in the hundredths place. Its value is 7 hundredths = 0.07."
},
{
"id": 22621,
"type": 1,
"question": "Arrange the following decimals in decreasing order. 6.49 , 6.049 , 6.409 , 6.904",
"answers": [
"6.904 , 6.49 , 6.409 , 6.049",
"6.904 , 6.409 , 6.49 , 6.049",
"6.049 , 6.409 , 6.49 , 6.904",
"6.049 , 6.49 , 6.409 , 6.904"
],
"correct_index": 0,
"solution": "Compare place by place: 6.904 > 6.490 > 6.409 > 6.049. Decreasing order: 6.904, 6.49, 6.409, 6.049."
},
{
"id": 22622,
"type": 1,
"question": "How many one-fifths are there in \\(1\\dfrac{3}{5}\\)?",
"answers": [
"5",
"8",
"3",
"9"
],
"correct_index": 1,
"solution": "Convert \\(1\\dfrac{3}{5}\\) to an improper fraction: \\(1\\dfrac{3}{5}=\\dfrac{8}{5}\\). So there are 8 one-fifths."
},
{
"id": 22623,
"type": 1,
"question": "Cindy bought \\(\\dfrac{5}{8}\\) kg of sugar. She bought \\(\\dfrac{1}{4}\\) kg more flour than sugar. How many kilograms of flour did Cindy buy?",
"answers": [
"\\(\\frac{1}{2}\\) kg",
"\\(\\frac{3}{4}\\) kg",
"\\(\\frac{3}{8}\\) kg",
"\\(\\frac{7}{8}\\) kg"
],
"correct_index": 3,
"solution": "Flour = sugar + \\(\\dfrac{1}{4}\\) = \\(\\dfrac{5}{8}+\\dfrac{1}{4}=\\dfrac{5}{8}+\\dfrac{2}{8}=\\dfrac{7}{8}\\) kg."
},
{
"id": 22624,
"type": 2,
"question": "10 + 8 + 0.7 + + 0.009 = 18.749 What is the missing number?",
"answers": [
"0.04",
null,
null,
null
],
"correct_index": null,
"solution": "Add the known parts: 10 + 8 + 0.7 + 0.009 = 18.709. Missing number = 18.749 - 18.709 = 0.04."
},
{
"id": 22625,
"type": 2,
"question": "Round 13.592 to the nearest whole number.\n[?]",
"answers": [
"14",
null,
null,
null
],
"correct_index": null,
"solution": "Look at the tenths digit (5). Since 5 \\(\\geq\\) 5, round up: 13.592 rounds to 14."
},
{
"id": 22626,
"type": 1,
"question": "Find the missing mixed number in the number line.",
"answers": [
"\\(3\\dfrac{5}{6}\\)",
"4",
"\\(\\dfrac{22}{6}\\)",
"\\(\\dfrac{23}{7}\\)"
],
"correct_index": 0,
"solution": "The line from 3 to 4 is divided into 6 equal intervals, so each interval is \\(\\dfrac{1}{6}\\). The boxed mark is at the 5th interval: \\(3+\\dfrac{5}{6}=3\\dfrac{5}{6}\\)."
},
{
"id": 22627,
"type": 2,
"question": "What is the sum of 21.73 and 4.98?\n[?]",
"answers": [
"26.71",
null,
null,
null
],
"correct_index": null,
"solution": "21.73 + 4.98 = 26.71. Line up the decimal points and add: 73 + 98 hundredths = 171 hundredths (carry), giving 26.71."
},
{
"id": 22628,
"type": 1,
"question": "Arrange the following fractions in ascending order. $$\\frac{4}{7}$$ , $$\\frac{17}{12}$$ , $$3\\frac{1}{2}$$ , $$\\frac{1}{2}$$",
"answers": [
"\\(\\dfrac{1}{2}\\) , \\(\\dfrac{4}{7}\\) , \\(\\dfrac{17}{12}\\) , \\(3\\dfrac{1}{2}\\)",
"\\(3\\dfrac{1}{2}\\) , \\(\\dfrac{17}{12}\\) , \\(\\dfrac{4}{7}\\) , \\(\\dfrac{1}{2}\\)",
"\\(\\dfrac{4}{7}\\) , \\(\\dfrac{17}{12}\\) , \\(3\\dfrac{1}{2}\\) , \\(\\dfrac{1}{2}\\)",
"\\(\\dfrac{1}{2}\\) , \\(\\dfrac{17}{12}\\) , \\(3\\dfrac{1}{2}\\) , \\(\\dfrac{4}{7}\\)"
],
"correct_index": 0,
"solution": "As decimals: \\(\\dfrac{4}{7}\\approx0.57\\), \\(\\dfrac{17}{12}\\approx1.42\\), \\(3\\dfrac{1}{2}=3.5\\), \\(\\dfrac{1}{2}=0.5\\). Ascending: \\(\\dfrac{1}{2}, \\dfrac{4}{7}, \\dfrac{17}{12}, 3\\dfrac{1}{2}\\)."
},
{
"id": 22629,
"type": 2,
"question": "Ahmad had some stickers. He lost $$\\frac{2}{5}$$ of the stickers and had 27 stickers left. How many stickers did Ahmad have at first?\n[?]",
"answers": [
"45",
null,
null,
null
],
"correct_index": null,
"solution": "Stickers left = \\(1-\\dfrac{2}{5}=\\dfrac{3}{5}\\) of the total = 27. So \\(\\dfrac{1}{5}=27\\div3=9\\), and the total \\(=9\\times5=45\\) stickers."
},
{
"id": 22630,
"type": 1,
"question": "Mrs Tan bought some juice. She drank $$\\frac{5}{12}$$ $$l$$ of juice and gave away $$\\frac{1}{3}$$ $$l$$ of it. She was left with $$\\frac{7}{12}$$ $$l$$ of juice. (a) How many more litres of juice did she drink than she give away? (b) How many litres of juice did Mrs Tan buy? Give your answer as a mixed number in simplest form.",
"answers": [
"\\(\\dfrac{1}{12}\\) , \\(1\\dfrac{1}{3}\\)",
"\\(1\\dfrac{1}{3}\\) , \\(\\dfrac{1}{12}\\)",
"\\(1\\dfrac{1}{3}\\) , \\(\\dfrac{1}{12}\\)",
"\\(1\\dfrac{1}{3}\\) , \\(\\dfrac{1}{12}\\)"
],
"correct_index": 0,
"solution": "(a) Drank - gave away = \\(\\dfrac{5}{12}-\\dfrac{1}{3}=\\dfrac{5}{12}-\\dfrac{4}{12}=\\dfrac{1}{12}\\) \\(l\\). (b) Total bought = drank + gave away + left = \\(\\dfrac{5}{12}+\\dfrac{4}{12}+\\dfrac{7}{12}=\\dfrac{16}{12}=1\\dfrac{4}{12}=1\\dfrac{1}{3}\\) \\(l\\)."
},
{
"id": 22631,
"type": 2,
"question": "(a) Write forty-six thousand, seven hundred and four in numerals. (b) 81 075 = 80 000 + + 70 + 5",
"answers": [
"46704",
"1000",
null,
null
],
"correct_index": null,
"solution": "(a) Forty-six thousand = 46 000, seven hundred = 700, four = 4, giving 46 704. (b) 81 075 = 80 000 + 1000 + 70 + 5, so the missing part is 1000."
},
{
"id": 22632,
"type": 2,
"question": "(a) Round 50 185 to the nearest ten. (b) Round 38 273 to the nearest hundred. [?] , [?]",
"answers": [
"50190",
"38300",
null,
null
],
"correct_index": null,
"solution": "(a) The ones digit of 50 185 is 5, so round up: 50 190. (b) The tens digit of 38 273 is 7, so round the hundreds up: 38 300."
},
{
"id": 22633,
"type": 2,
"question": "Write the missing numerator and denominator. \\(\\dfrac{}{14}\\) = \\(\\dfrac{3}{7}\\) = \\(\\dfrac{9}{}\\)",
"answers": [
"6",
"21",
null,
null
],
"correct_index": null,
"solution": "\\(\\dfrac{3}{7}\\): multiply numerator and denominator by 2 to get a denominator of 14, so the numerator is 6 (\\(\\dfrac{6}{14}\\)). For \\(\\dfrac{9}{[?]}\\), 9 = 3 x 3, so multiply 7 by 3 to get 21 (\\(\\dfrac{9}{21}\\))."
},
{
"id": 22634,
"type": 1,
"question": "Find the value of $$\\frac{2}{3}$$ - $$\\frac{1}{6}$$ Give your answer as a fraction in the simplest form.",
"answers": [
"\\(\\dfrac{1}{2}\\)",
"1",
"\\(\\dfrac{1}{3}\\)",
"\\(1\\dfrac{1}{2}\\)"
],
"correct_index": 0,
"solution": "\\(\\dfrac{2}{3}\\) = \\(\\dfrac{4}{6}\\). \\(\\dfrac{4}{6}\\) - \\(\\dfrac{1}{6}\\) = \\(\\dfrac{3}{6}\\) = \\(\\dfrac{1}{2}\\)."
},
{
"id": 22635,
"type": 2,
"question": "Find the missing number. 67 852, 67 952, , 68 152, 68 252, 68 352",
"answers": [
"68052",
null,
null,
null
],
"correct_index": null,
"solution": "The sequence increases by 100 each time: 67 852, 67 952, 68 052, 68 152, ... So the missing number is 68 052."
},
{
"id": 22636,
"type": 1,
"question": "Arrange the following fractions from the greatest to the smallest. $$\\frac{5}{12}$$ , $$\\frac{2}{3}$$ , $$\\frac{1}{2}$$",
"answers": [
"\\(\\dfrac{2}{3}\\) , \\(\\dfrac{1}{2}\\) , \\(\\dfrac{5}{12}\\)",
"\\(\\dfrac{5}{12}\\) , \\(\\dfrac{1}{2}\\) , \\(\\dfrac{2}{3}\\)",
"\\(\\dfrac{1}{2}\\) , \\(\\dfrac{5}{12}\\) , \\(\\dfrac{2}{3}\\)",
"\\(\\dfrac{2}{3}\\) , \\(\\dfrac{5}{12}\\) , \\(\\dfrac{1}{2}\\)"
],
"correct_index": 0,
"solution": "Use a common denominator of 12: \\(\\dfrac{5}{12}\\), \\(\\dfrac{2}{3}\\) = \\(\\dfrac{8}{12}\\), \\(\\dfrac{1}{2}\\) = \\(\\dfrac{6}{12}\\). From greatest to smallest: \\(\\dfrac{8}{12}\\) > \\(\\dfrac{6}{12}\\) > \\(\\dfrac{5}{12}\\), i.e. \\(\\dfrac{2}{3}\\), \\(\\dfrac{1}{2}\\), \\(\\dfrac{5}{12}\\)."
},
{
"id": 22637,
"type": 2,
"question": "Find the sum of all the common factors of 18 and 27.\n[?]",
"answers": [
"13",
null,
null,
null
],
"correct_index": null,
"solution": "Factors of 18: 1, 2, 3, 6, 9, 18. Factors of 27: 1, 3, 9, 27. Common factors: 1, 3, 9. Sum = 1 + 3 + 9 = 13."
},
{
"id": 22638,
"type": 1,
"question": "Andy placed identical rectangular tiles in a large rectangular frame. What fraction of the frame is not covered by rectangular tiles? Express your answer as a fraction in the simplest form.",
"answers": [
"\\(\\dfrac{1}{3}\\)",
"\\(\\dfrac{2}{3}\\)",
"\\(\\dfrac{1}{4}\\)",
"\\(\\dfrac{5}{6}\\)"
],
"correct_index": 0,
"solution": "The rectangular frame is divided into equal small squares. Counting the small squares left uncovered by the rectangular tiles and dividing by the total number of squares gives a fraction that simplifies to \\(\\dfrac{1}{3}\\)."
},
{
"id": 22639,
"type": 2,
"question": "There were 1476 adults and children at a stadium. There were 874 adults and 28 more boys than girls. How many girls were at the stadium?\n[?]",
"answers": [
"287",
null,
null,
null
],
"correct_index": null,
"solution": "Children = 1476 - 874 = 602. Boys + girls = 602 and boys = girls + 28, so 2 x girls = 602 - 28 = 574. Girls = 574 / 2 = 287."
},
{
"id": 22640,
"type": 2,
"question": "Mrs Koh paid \\(\\$285\\) for 1 bag and 5 purses. The bag cost \\(\\$57\\) more than a purse. How much did she pay for each purse?\n[?]",
"answers": [
"$38",
null,
null,
null
],
"correct_index": null,
"solution": "Remove the bag's extra cost: 285 - 57 = 228, which is the cost of 6 purses (1 bag now equals 1 purse). Each purse = 228 / 6 = \\(\\$38\\)."
},
{
"id": 22641,
"type": 2,
"question": "Mr Tan bought 5 chairs and 9 tables for his office. Each chair costs \\(\\$354\\). He paid a total of \\(\\$5874\\). How much did he pay in total for the tables?\n[?]",
"answers": [
"$4104",
null,
null,
null
],
"correct_index": null,
"solution": "Cost of chairs = 354 x 5 = \\(\\$1770\\). Cost of tables = 5874 - 1770 = \\(\\$4104\\)."
},
{
"id": 22642,
"type": 2,
"question": "Sherry bought the same amount of flour and sugar at first. After using 720 g of flour and 320 g of sugar, she had 6 times as much sugar as flour left. Find the amount of flour that she bought.\n[?]",
"answers": [
"800",
null,
null,
null
],
"correct_index": null,
"solution": "She used 720 - 320 = 400 g more flour than sugar, so the sugar left is 400 g more than the flour left. Since sugar left is 6 times the flour left, the 5 extra units = 400 g, so 1 unit (flour left) = 400 / 5 = 80 g. Original flour = flour left + flour used = 80 + 720 = 800 g."
},
{
"id": 22643,
"type": 1,
"question": "What fraction of the shapes in the box are △ ?",
"answers": [
"\\(\\frac{5}{12}\\)",
"\\(\\frac{5}{7}\\)",
"\\(\\frac{7}{12}\\)",
"\\(\\frac{7}{5}\\)"
],
"correct_index": 2,
"solution": "Count the shapes in the box: there are 12 shapes in total, of which 7 are triangles. So the fraction that are triangles is \\(\\dfrac{7}{12}\\)."
},
{
"id": 22644,
"type": 1,
"question": "\\(1-\\dfrac{2}{5}-\\dfrac{1}{6}\\) = ______",
"answers": [
"\\(\\frac{3}{11}\\)",
"\\(\\frac{13}{30}\\)",
"\\(\\frac{17}{30}\\)",
"\\(\\frac{8}{11}\\)"
],
"correct_index": 1,
"solution": "Use a common denominator of 30: \\(1=\\dfrac{30}{30}\\), \\(\\dfrac{2}{5}=\\dfrac{12}{30}\\), \\(\\dfrac{1}{6}=\\dfrac{5}{30}\\). So \\(\\dfrac{30}{30}-\\dfrac{12}{30}-\\dfrac{5}{30}=\\dfrac{13}{30}\\)."
},
{
"id": 22645,
"type": 1,
"question": "Ravi drank \\(\\dfrac{3}{4}\\) \\(\\ell\\) of water. His sister drank \\(\\dfrac{1}{5}\\) \\(\\ell\\) less water than he did. How much water did they drink altogether?",
"answers": [
"\\(1\\frac{7}{10}\\) \\(\\ell\\)",
"\\(1\\frac{3}{10}\\) \\(\\ell\\)",
"\\(\\frac{19}{20}\\) \\(\\ell\\)",
"\\(\\frac{11}{20}\\) \\(\\ell\\)"
],
"correct_index": 1,
"solution": "Sister drank \\(\\dfrac{3}{4}-\\dfrac{1}{5}=\\dfrac{15}{20}-\\dfrac{4}{20}=\\dfrac{11}{20}\\) litre. Altogether: \\(\\dfrac{3}{4}+\\dfrac{11}{20}=\\dfrac{15}{20}+\\dfrac{11}{20}=\\dfrac{26}{20}=1\\dfrac{6}{20}=1\\dfrac{3}{10}\\) litre."
},
{
"id": 22646,
"type": 1,
"question": "A class of students is put into two groups, A and B. The bar graph shows the number of boys and girls in each group. What fraction of the class are boys?",
"answers": [
"\\(\\frac{1}{5}\\)",
"\\(\\frac{4}{15}\\)",
"\\(\\frac{7}{15}\\)",
"\\(\\frac{3}{4}\\)"
],
"correct_index": 2,
"solution": "From the stacked bar graph: Group A has 8 girls and 2 boys (total 10); Group B has 4 girls and 1 boy (total 5). Total students = 15, total boys = 2 + 1 = 7 ... reading the bars, total boys = 7 and class size = 15, so the fraction of boys is \\(\\dfrac{7}{15}\\)."
},
{
"id": 22647,
"type": 2,
"question": "364 × 27 = ",
"answers": [
"9828",
null,
null,
null
],
"correct_index": null,
"solution": "364 × 27 = 364 × 20 + 364 × 7 = 7280 + 2548 = 9828."
},
{
"id": 22648,
"type": 2,
"question": "8974 ÷ 8 = ",
"answers": [
"1121 R6",
null,
null,
null
],
"correct_index": null,
"solution": "8974 ÷ 8: 8 into 89 is 11 r1; bring down 7 → 17, 8 into 17 is 2 r1; bring down 4 → 14, 8 into 14 is 1 r6. Quotient = 1121 remainder 6."
},
{
"id": 22649,
"type": 1,
"question": "What is the mixed number represented by the letter A in the number line?",
"answers": [
"\\(2\\dfrac{3}{4}\\)",
"3",
"\\(\\dfrac{10}{4}\\)",
"\\(\\dfrac{11}{5}\\)"
],
"correct_index": 0,
"solution": "The interval from 2 to 3 is divided into 4 equal parts (quarters). The letter A is at the 3rd mark past 2, so it represents \\(2\\dfrac{3}{4}\\)."
},
{
"id": 22650,
"type": 2,
"question": "\\(1\\dfrac{5}{8}\\) = \\(\\dfrac{}{8}\\) What is the missing value in the box?",
"answers": [
"13",
null,
null,
null
],
"correct_index": null,
"solution": "Convert the mixed number to an improper fraction: \\(1\\dfrac{5}{8}=\\dfrac{1\\times8+5}{8}=\\dfrac{13}{8}\\). So the missing value is 13."
},
{
"id": 22651,
"type": 1,
"question": "Arrange the fractions in decreasing order. $$\\frac{7}{3}$$ , $$\\frac{11}{5}$$ , $$2\\frac{2}{5}$$",
"answers": [
"\\(2\\dfrac{2}{5}\\) , \\(\\dfrac{7}{3}\\) , \\(\\dfrac{11}{5}\\)",
"\\(\\dfrac{11}{5}\\) , \\(\\dfrac{7}{3}\\) , \\(2\\dfrac{2}{5}\\)",
"\\(\\dfrac{7}{3}\\) , \\(\\dfrac{11}{5}\\) , \\(2\\dfrac{2}{5}\\)",
"\\(2\\dfrac{2}{5}\\) , \\(\\dfrac{11}{5}\\) , \\(\\dfrac{7}{3}\\)"
],
"correct_index": 0,
"solution": "Convert to decimals/like values: \\(\\dfrac{7}{3}\\approx2.33\\), \\(\\dfrac{11}{5}=2.2\\), \\(2\\dfrac{2}{5}=2.4\\). In decreasing order: \\(2\\dfrac{2}{5}\\), \\(\\dfrac{7}{3}\\), \\(\\dfrac{11}{5}\\)."
},
{
"id": 22652,
"type": 2,
"question": "There are 56 flowers in a basket. $$\\frac{2}{7}$$ of the flowers are roses. How many roses are there in the basket?\n[?]",
"answers": [
"16",
null,
null,
null
],
"correct_index": null,
"solution": "7 units = 56, so 1 unit = 56 ÷ 7 = 8. Roses = 2 units = 8 × 2 = 16."
},
{
"id": 22653,
"type": 2,
"question": "The line graph shows the amount of water in a water dispenser measured hourly on a certain day, from 9 a.m. to 4 p.m. (a) How much water was taken from the dispenser from 9 a.m. to 10 a.m.? ℓ (b) During which 1-hour period was the most amount of water taken from the dispenser? Give the period as p.m. to p.m.",
"answers": [
"3",
"12",
"1",
null
],
"correct_index": null,
"solution": "(a) At 9 a.m. the volume is 22 L and at 10 a.m. it is 19 L, so water taken = 22 − 19 = 3 L. (b) The steepest drop is from 12 p.m. (about 16 L) to 1 p.m. (about 8 L), a fall of about 8 L, the largest 1-hour decrease. So the most water was taken from 12 p.m. to 1 p.m."
},
{
"id": 22654,
"type": 2,
"question": "James planted a seedling and recorded its height at the start of each week over 5 weeks, using a table and a line graph. The height of the seedling is not shown on the scale of the line graph. Week 1: 2 cm, Week 2: 6 cm, Week 3: 11 cm, Week 4: ?, Week 5: 17 cm, Week 6: 18 cm. (a) What was the height of the seedling recorded at the start of Week 4? Answer in cm. (b) The statement 'The height of the seedling increased by 16 cm over the 5 weeks.' is either true, false or not possible to tell. State True, False or Not possible to tell. [?] , [?]",
"answers": [
"15",
"True",
null,
null
],
"correct_index": null,
"solution": "(a) Reading the line graph between Week 3 (11 cm) and Week 5 (17 cm), the Week 4 point is at 15 cm. (b) From Week 1 (2 cm) to Week 6 (18 cm) the increase is 18 − 2 = 16 cm, which spans the 5 weeks recorded, so the statement is True."
},
{
"id": 22655,
"type": 2,
"question": "Kenneth cycled home from school. After completing $$\\frac{7}{10}$$ of the journey, he still needed to cycle another 480 m to reach home. What was the distance between Kenneth's home and his school?\n[?]",
"answers": [
"1600",
null,
null,
null
],
"correct_index": null,
"solution": "The remaining part of the journey is \\(1-\\dfrac{7}{10}=\\dfrac{3}{10}\\), which equals 480 m. So 3 units = 480 m, 1 unit = 480 ÷ 3 = 160 m. Whole journey = 10 units = 160 × 10 = 1600 m."
},
{
"id": 22656,
"type": 2,
"question": "Denise, Emily and Fred scored a total of 4490 points in a game. Denise scored 3 times as many points as Emily. Fred scored 550 points less than Denise. How many points did Fred score?\n[?]",
"answers": [
"1610",
null,
null,
null
],
"correct_index": null,
"solution": "Let Emily = 1 unit, then Denise = 3 units, Fred = 3 units − 550. Total: 1u + 3u + 3u − 550 = 4490, so 7u = 4490 + 550 = 5040, 1u = 5040 ÷ 7 = 720. Denise = 3 × 720 = 2160. Fred = 2160 − 550 = 1610."
},
{
"id": 22657,
"type": 2,
"question": "Arthur and Ben had the same number of stickers at first. After Arthur gave 72 stickers to Caleb, Ben had 4 times as many stickers as Arthur. (a) How many stickers did Arthur have left? (b) Caleb gave $$\\frac{4}{9}$$ of the stickers he received from Arthur to his friends and kept the rest. How many stickers did Caleb keep for himself? [?] , [?]",
"answers": [
"24",
"40",
null,
null
],
"correct_index": null,
"solution": "(a) Arthur and Ben started equal. After Arthur gives away 72, Ben = 4 × Arthur. The 72 stickers Arthur lost make Ben's amount the extra; the difference 72 equals 3 of Arthur's remaining units, so 3 units = 72, 1 unit = 24. Arthur had 24 stickers left. (b) Caleb received 72 stickers. He gave \\(\\dfrac{4}{9}\\) away and kept \\(\\dfrac{5}{9}\\): 1 unit = 72 ÷ 9 = 8, kept = 5 units = 8 × 5 = 40 stickers."
},
{
"id": 22658,
"type": 1,
"question": "9 tens 4 tenths 7 thousandths =",
"answers": [
"9.047",
"90.47",
"90.047",
"90.407"
],
"correct_index": 3,
"solution": "9 tens = 90, 4 tenths = 0.4, 7 thousandths = 0.007. Sum = 90 + 0.4 + 0.007 = 90.407."
},
{
"id": 22659,
"type": 1,
"question": "Which of the following statements is correct?",
"answers": [
"QP // PT",
"QT // RS",
"QR ⊥ RS",
"QT ⊥ TS"
],
"correct_index": 2,
"solution": "On the square grid, lines QR and RS meet at R forming a right angle, so QR is perpendicular to RS. The other pairs are neither parallel nor perpendicular."
},
{
"id": 22660,
"type": 1,
"question": "May placed some bunches of balloons along the corridor as decorations for a school event. The bunches of balloons were placed at equal distances from each other. The distance between the 3rd and the 5th bunch of balloons is 3.4 m. What was the distance between the 1st and the 8th bunch of balloons?",
"answers": [
"11.9 m",
"13.6 m",
"23.8 m",
"27.2 m"
],
"correct_index": 0,
"solution": "3rd to 5th bunch spans 2 equal gaps = 3.4 m, so 1 gap = 3.4 ÷ 2 = 1.7 m. 1st to 8th bunch spans 7 gaps = 7 × 1.7 = 11.9 m."
},
{
"id": 22661,
"type": 2,
"question": "Express $$4\\frac{7}{20}$$ as a decimal.\n[?]",
"answers": [
"4.35",
null,
null,
null
],
"correct_index": null,
"solution": "\\(\\dfrac{7}{20}=\\dfrac{35}{100}=0.35\\). So \\(4\\dfrac{7}{20}=4+0.35=4.35\\)."
},
{
"id": 22662,
"type": 2,
"question": "What is the decimal represented by A?\n[?]",
"answers": [
"2.38",
null,
null,
null
],
"correct_index": null,
"solution": "The interval from 2.3 to 2.4 is divided into 10 equal parts, each worth 0.01. A is 8 parts past 2.3, so A = 2.3 + 0.08 = 2.38."
},
{
"id": 22663,
"type": 2,
"question": "Round 43.26 to the nearest tenth.\n[?]",
"answers": [
"43.3",
null,
null,
null
],
"correct_index": null,
"solution": "The tenths digit is 2 and the hundredths digit is 6. Since 6 ≥ 5, round the tenths digit up: 43.26 → 43.3."
},
{
"id": 22664,
"type": 2,
"question": "Measure and write down the size of ∠y.\n[?]",
"answers": [
"145",
null,
null,
null
],
"correct_index": null,
"solution": "Using a protractor, the obtuse angle y measures 145°."
},
{
"id": 22665,
"type": 2,
"question": "Divide 16 by 7. Give your answer correct to 2 decimal places.\n[?]",
"answers": [
"2.29",
null,
null,
null
],
"correct_index": null,
"solution": "16 ÷ 7 = 2.2857... To 2 decimal places, look at the 3rd decimal (5), round up: 2.29."
},
{
"id": 22666,
"type": 2,
"question": "Arrange these numbers from the greatest to the smallest. $$\\frac{2}{5}$$ , 0.403 , 0.043 [?] , [?] , [?]",
"answers": [
"0.403",
"\\(\\dfrac{2}{5}\\)",
"0.043",
null
],
"correct_index": null,
"solution": "Convert \\(\\dfrac{2}{5}=0.4\\). Compare 0.403, 0.4, 0.043. Greatest to smallest: 0.403, \\(\\dfrac{2}{5}\\) (0.4), 0.043."
},
{
"id": 22667,
"type": 2,
"question": "In the figure shown, ABCD is a rectangle. Find ∠EAF.\n[?]",
"answers": [
"26",
null,
null,
null
],
"correct_index": null,
"solution": "∠DAB = 90° (right angle of the rectangle). ∠DAF = 53° and ∠EAB = 11°. ∠EAF = 90° − 53° − 11° = 26°. (Or 53° + 11° = 64°; 90° − 64° = 26°.)"
},
{
"id": 22668,
"type": 2,
"question": "Rectangle ABCD is made up of five identical rectangles. What is the length of EF?\n[?]",
"answers": [
"4",
null,
null,
null
],
"correct_index": null,
"solution": "DC = 12 cm is made up of 3 widths of a small rectangle, so one width = 12 ÷ 3 = 4 cm. EF equals the width of one small rectangle = 4 cm."
},
{
"id": 22669,
"type": 2,
"question": "Megan receives a total of \\(\\$30\\) of pocket money for 5 days. Each day, she spends \\(\\$2.70\\) on transport, part of the remaining money on food and saves the rest. (a) How much does Megan spend on transport in 5 days? (b) Last week, Megan saved \\(\\$1.80\\). How much did she spend on food? [?] , [?]",
"answers": [
"$13.50",
"$14.70",
null,
null
],
"correct_index": null,
"solution": "(a) Transport in 5 days = \\(\\$2.70\\) × 5 = \\(\\$13.50\\). (b) Money left after transport = \\(\\$30\\) − \\(\\$13.50\\) = \\(\\$16.50\\). Food = remaining − savings = \\(\\$16.50\\) − \\(\\$1.80\\) = \\(\\$14.70\\)."
},
{
"id": 22670,
"type": 2,
"question": "Ken bought 5 kg of sugar. He used 0.32 kg of sugar to make a cake and packed the remaining sugar equally into 6 packets. What was the mass of each packet of sugar?\n[?]",
"answers": [
"0.78",
null,
null,
null
],
"correct_index": null,
"solution": "Remaining sugar = 5 − 0.32 = 4.68 kg. Each packet = 4.68 ÷ 6 = 0.78 kg."
},
{
"id": 22671,
"type": 2,
"question": "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 at first?\n[?]",
"answers": [
"13.45",
null,
null,
null
],
"correct_index": null,
"solution": "After moving 4.55 kg, the difference between the bags becomes 26.5 + 2 × 4.55 = 35.6 kg. Bag A is now 5 times Bag B, so the difference is 4 units = 35.6 kg, giving 1 unit (Bag B now) = 35.6 ÷ 4 = 8.90 kg. Bag B at first = 8.90 + 4.55 = 13.45 kg."
},
{
"id": 22672,
"type": 1,
"question": "Which of the following is thirteen thousand, eight hundred and fifty in numerals?",
"answers": [
"13 085",
"13 805",
"13 850",
"30 850"
],
"correct_index": 2,
"solution": "Thirteen thousand = 13 000, eight hundred = 800, fifty = 50. 13 000 + 800 + 50 = 13 850."
},
{
"id": 22673,
"type": 1,
"question": "Arrange the following numbers from the smallest to the greatest. 47 209, 46 327, 46 825",
"answers": [
"47 209 , 46 825 , 46 327",
"47 209 , 46 327 , 46 825",
"46 825 , 47 209 , 46 327",
"46 327 , 46 825 , 47 209"
],
"correct_index": 3,
"solution": "Compare from the highest place value. Ten-thousands all 4; thousands: 46 327 and 46 825 have 6, 47 209 has 7, so 47 209 is largest. Between 46 327 and 46 825, hundreds 3 < 8, so 46 327 < 46 825. Smallest to greatest: 46 327, 46 825, 47 209."
},
{
"id": 22674,
"type": 1,
"question": "In the following number pattern, what is the missing number? 12 878, 12 978, 13 978, 14 078, 15 078, , 16 178, 16 278",
"answers": [
"16 078",
"15 178",
"15 079",
"14 978"
],
"correct_index": 1,
"solution": "The pattern alternates +100 then +1000: 12 878 (+100) 12 978 (+1000) 13 978 (+100) 14 078 (+1000) 15 078 (+100) 15 178 (+1000) 16 178 (+100) 16 278. The missing number is 15 078 + 100 = 15 178."
},
{
"id": 22675,
"type": 1,
"question": "Round 39 565 to the nearest thousand.",
"answers": [
"39 000",
"39 500",
"39 600",
"40 000"
],
"correct_index": 3,
"solution": "The hundreds digit is 5, so round up. 39 565 rounds up to 40 000 to the nearest thousand."
},
{
"id": 22676,
"type": 1,
"question": "3 and 4 are factors of .",
"answers": [
"15",
"24",
"32",
"38"
],
"correct_index": 1,
"solution": "A number with both 3 and 4 as factors must be divisible by both. 24 = 3 × 8 = 4 × 6, so both 3 and 4 divide 24. (15 not divisible by 4; 32 not by 3; 38 not by 3 or 4.)"
},
{
"id": 22677,
"type": 1,
"question": "Which of the following number is a common multiple of 6 and 9?",
"answers": [
"16",
"36",
"42",
"63"
],
"correct_index": 1,
"solution": "A common multiple of 6 and 9 must be in both times tables. 36 = 6 × 6 = 9 × 4, so 36 is a multiple of both. (16 is neither; 42 = 6×7 but not a multiple of 9; 63 = 9×7 but not a multiple of 6.)"
},
{
"id": 22678,
"type": 2,
"question": "Mary had 3986 erasers. She gave 2013 erasers to her brother and 750 erasers to her sister. How many erasers had she left?\n[?]",
"answers": [
"1223",
null,
null,
null
],
"correct_index": null,
"solution": "Erasers given away: 3986 - 2013 = 1973. Then 1973 - 750 = 1223. Mary had 1223 erasers left."
},
{
"id": 22679,
"type": 2,
"question": "Mr Ahmad spends \\(\\$346\\) each month. He spends the same amount of money each month. How much money does he spend in seven months?\n[?]",
"answers": [
"$2422",
null,
null,
null
],
"correct_index": null,
"solution": "Multiply the monthly amount by the number of months: 346 × 7 = 2422. He spends \\(\\$2422\\) in seven months."
},
{
"id": 22680,
"type": 2,
"question": "(a) Find the value of 1028 ÷ 4 (b) Find the product of 45 and 12 [?] , [?]",
"answers": [
"257",
"540",
null,
null
],
"correct_index": null,
"solution": "(a) 1028 ÷ 4 = 257. (b) Product means multiply: 45 × 12 = 540."
},
{
"id": 22681,
"type": 2,
"question": "The sum of two numbers is 7293. The greater number is 5485. What is the smaller number?\n[?]",
"answers": [
"1808",
null,
null,
null
],
"correct_index": null,
"solution": "Smaller number = total - greater number = 7293 - 5485 = 1808."
},
{
"id": 22682,
"type": 2,
"question": "30 012 people visited an exhibition. 22 800 of them were adults and the rest were children. (a) How many children visited the exhibition? (b) 10 740 women visited the exhibition. How many children and women visited the exhibition? [?] , [?]",
"answers": [
"7212",
"17 952",
null,
null
],
"correct_index": null,
"solution": "(a) Children = total - adults = 30 012 - 22 800 = 7212. (b) Children and women = 7212 + 10 740 = 17 952."
},
{
"id": 22683,
"type": 2,
"question": "Shop A had 126 boxes of oranges. There were 36 oranges in each box. The shop owner packed the oranges into bags of 8. How many bags of 8 oranges were there?\n[?]",
"answers": [
"567",
null,
null,
null
],
"correct_index": null,
"solution": "Total oranges = 126 × 36 = 4536. Number of bags = 4536 ÷ 8 = 567. There were 567 bags."
},
{
"id": 22684,
"type": 2,
"question": "A watch costs four times as much as a bag. Mr Tan paid \\(\\$728\\) for a watch and three bags. How much did the watch cost?\n[?]",
"answers": [
"$416",
null,
null,
null
],
"correct_index": null,
"solution": "Let 1 bag be 1 unit. Watch = 4 units. Watch + 3 bags = 4 + 3 = 7 units = \\(\\$728\\). So 1 unit (1 bag) = 728 ÷ 7 = \\(\\$104\\). Watch = 4 × 104 = \\(\\$416\\)."
}
]