This is the marking copy and it carries every answer. Her sheet is the other file — same numbering, same margin codes, so you can mark straight down the page.
A glue stick cost $1.80. A pair of scissors cost $3.20. Thomas bought an equal number of glue sticks and scissors. He spent $25 in all. How many glue sticks and scissors did he buy in total?
answer 10
method Buy them in pairs, since the numbers are equal: one glue stick and one pair of scissors cost $1.80 + $3.20 = $5. Then $25 ÷ $5 = 5 pairs. Each pair is 2 items, so in total he bought 5 × 2 = 10 items.
watch Answering 5 — that is the number of PAIRS. The question asks for glue sticks and scissors added together.
Charles bought 9 bags of sweets. Each bag had 48 sweets. He gave away 5/6 of all the sweets. How many sweets did he have left?
answer 72
method Find the total first: 9 × 48 = 432 sweets. He gave away 5/6, so he kept the other 1/6: 432 ÷ 6 = 72 sweets.
watch Working out 5/6 of 432 (= 360) and giving that as the answer. That is what he gave AWAY; the question asks what is left.
Mary gave 55 beads to Betty. Then she received 36 beads from Lydia. Mary had 342 beads in the end. How many beads did Mary have at first?
answer 361
method Work backwards, undoing each step. Before receiving 36 she had 342 − 36 = 306. Before giving away 55 she had 306 + 55 = 361.
watch Running the story forwards from 342, which adds the 55 and subtracts the 36 the wrong way round. Going backwards means every give becomes a take and every take becomes a give.
A man changed $210 into $5 and $2 notes. The number of $5 notes and $2 notes was the same. How many $5 notes did he get?
answer 30
method Because the numbers are equal, take one of each together: $5 + $2 = $7 per pair. Then $210 ÷ $7 = 30 pairs, so he got 30 five-dollar notes (and 30 two-dollar notes).
watch Dividing $210 by $5 alone. The pairing is what makes the two equal counts usable in one division.
Lisa and Max each had a roll of ribbon with the same length. They cut their roll of ribbon into shorter pieces. Each piece of Lisa’s ribbon was 6 cm. Each piece of Max’s ribbon was 10 cm. After cutting, Lisa had 16 more pieces of ribbon than Max. What was the length of each roll of ribbon?
answer 240
method Look at a length both cut sizes divide — 30 cm. In every 30 cm, Lisa gets 30 ÷ 6 = 5 pieces and Max gets 30 ÷ 10 = 3 pieces, so Lisa is 2 pieces ahead for every 30 cm. She is 16 pieces ahead in all, which is 16 ÷ 2 = 8 lots of 30 cm. So each roll was 8 × 30 = 240 cm.
watch Multiplying 16 by 6 or by 10. The 16 counts PIECES, not centimetres, so it has to be converted through a length that both cut sizes fit into.
Study the pattern. What is the missing number in the box? star × star = 49; moon + moon + moon + moon = 100; star × moon = ?
star × star = 49 moon + moon + moon + moon = 100 star × moon = ?
answer 175
method From the first line, a number times itself is 49, so the star is 7. From the second, four moons make 100, so the moon is 100 ÷ 4 = 25. Then star × moon = 7 × 25 = 175.
watch Reading the second line as 4 × moon = 100 and then halving instead of dividing by 4, or taking the star as 24.5 (half of 49) instead of the number that multiplies by ITSELF.
The product of 7 and a number is 84. What is the product of 252 and that number?
answer 3024
method Find the number first: 84 ÷ 7 = 12. Then 252 × 12 = 3024.
watch Multiplying 252 by 84, or by 7. Find the hidden number before using it.
The table shows the cost of pizza: a Regular is $12 and a Large is $22. Mrs Tan ordered 6 large pizzas and 5 regular pizzas. She gave the delivery man $200. How much change did Mrs Tan receive?
answer 8
method 6 large: 6 × $22 = $132. 5 regular: 5 × $12 = $60. Total = $132 + $60 = $192. Change from $200 = 200 − 192 = $8.
watch Answering 192 — that is what she spent, not the change. Or pairing the wrong price to the wrong size.
The line graph shows the earnings at Mr Lim’s chicken rice stall over a 6-month period: January $3000, February $4500, March $5000, April $3500, May $3000, June $2500. Mr Lim charged $5 for every plate of chicken rice. What is the difference in the number of plates of chicken rice sold between the highest earnings month and the lowest earnings month?
Jan Feb Mar Apr May Jun 3000 4500 5000 3500 3000 2500 highest = March, lowest = June · $5 a plate
answer 500
method The highest month is March at $5000 and the lowest is June at $2500. The difference in money is $5000 − $2500 = $2500. Each plate is $5, so that is 2500 ÷ 5 = 500 plates.
watch Working out each month's plates and then subtracting is fine too (1000 − 500 = 500), but dividing the DIFFERENCE once is quicker. The real slip is reading May as the lowest — June is lower.
A van can transport 8 passengers. How many passengers can 240 vans transport?
answer 1920
method 240 × 8 = 1920 passengers.
watch Dividing instead of multiplying. More vans means more passengers, so the answer must be bigger than 240.
Max bought the same number of books and files. Each book cost $7 and each file cost $2. He paid $243 altogether. How many books and files did he buy altogether?
answer 54
method Because the numbers are equal, buy them in pairs: one book and one file cost $7 + $2 = $9. Then $243 ÷ $9 = 27 pairs. Each pair is 2 items, so altogether he bought 27 × 2 = 54 books and files.
watch Answering 27 — that is the number of BOOKS (and of files), but the question asks for both kinds added together.
Mr Tan has less than 40 sweets for a group of pupils. If he gives his pupils 4 sweets each, he will be short of 1 sweet. If he gives each pupil 5 sweets each, he will be short of 11 sweets. How many pupils does he have in the group?
answer 10
method Compare the two plans. Going from 4 sweets each to 5 sweets each means one extra sweet per pupil, and the shortfall grows from 1 to 11 — that is 10 more sweets needed. So there are 10 pupils. (Check: 10 pupils × 4 = 40, short of 1, so he has 39, which is indeed less than 40.)
watch Trying to find the number of sweets first. The difference between the two plans gives the number of PUPILS straight away, because each pupil accounts for exactly one extra sweet.
In a General Knowledge quiz, 5 marks were awarded for a correct answer but 2 marks were deducted for an incorrect answer. Mei Ling answered all 50 questions and was awarded a total of 166 marks. How many questions did she answer correctly?
answer 38
method Suppose every answer were correct: 50 × 5 = 250 marks. She actually scored 166, which is 84 marks less. Each wrong answer costs 5 marks not gained plus 2 marks deducted — 7 marks in all. So the number wrong is 84 ÷ 7 = 12, and the number correct is 50 − 12 = 38.
watch Counting a wrong answer as costing only 2 marks. It costs 7: the 5 she did not win AND the 2 taken away.
The figure below is made up of 2 squares of different sizes. AG is 8 cm and DE is 6 cm. What is the length of AD? Give your answer in cm.
|<------------- ? ------------->| A B +---------------+---C-------+ D | | | | | | | 8 cm | | 6 cm | | | | | | +---------------+-----------+ G F E
answer 14
method AG = 8 cm is the side of the big square, so AB = 8 cm too. DE = 6 cm is the side of the small square, so BD (the part of the top line beyond B) = 6 cm. AD runs along the top from A to D: 8 + 6 = 14 cm.
watch Trying to find AD from the slanted-looking picture instead of from the two square sides. In a square all four sides are equal — that is the only fact this question needs.
The graph shows the number of watches sold by a shop from January to April: January 38, February 22, March 52, April 16. The total number of watches sold from January to April was 4 times the number of watches sold in May. How many watches were sold in May?
Jan Feb Mar Apr 38 22 52 16
(A) 31 (B) 32 (C) 54 (D) 64
answer (B) — 32
method Add the four months: 38 + 22 + 52 + 16 = 128 watches. That total is 4 times May's figure, so May = 128 ÷ 4 = 32 watches.
watch Multiplying by 4 instead of dividing. The four months together are the BIG number, so May must be smaller than it.
Jason has $20. He bought 2 packets of chips and 6 oranges. Chips are $2.50 a packet and oranges are 3 for $1.20. How much money did he have left?
1 packet of chips $2.50 3 oranges for $1.20
(A) $7.40 (B) $7.80 (C) $10.30 (D) $12.60
answer (D) — $12.60
method Chips: 2 × $2.50 = $5.00. Oranges: 6 is two lots of 3, so 2 × $1.20 = $2.40. He spent $5.00 + $2.40 = $7.40. Money left = $20 − $7.40 = $12.60.
watch Answering $7.40 — that is what he SPENT. The question asks what is left, so there is one more subtraction to do.
At a fruit stall, mangoes are sold at 2 for $7 and pears are sold at 3 for $5.50. Mdm Fauziah bought the same number of mangoes and pears. She paid $160 in total. How many mangoes did she buy?
Mangoes 2 for $7 Pears 3 for $5.50
answer 30
method Choose a number of each that both deals divide into — 6 is the smallest. 6 mangoes are three lots of 2, costing 3 × $7 = $21. 6 pears are two lots of 3, costing 2 × $5.50 = $11. So 6 of each costs $21 + $11 = $32. Then $160 ÷ $32 = 5 such groups, and she bought 5 × 6 = 30 mangoes.
watch Working out the price of one mango and one pear. A pear costs $5.50 ÷ 3, which is not a whole number of cents — buying in sixes keeps every figure exact.
At a bakery, muffins are sold at the prices shown. Nick wants to order 57 muffins for a birthday party. What is the least amount of money he will need to pay for the muffins?
+-------------------------------------------------+ | Muffins on Sale! | | | | 1 for $1.40 6 for $5.70 10 for $8.90 | +-------------------------------------------------+
(1) $34.20 (2) $51.60 (3) $79.80 (4) $94.70
answer (2) — $51.60
method Work out the value of each deal first: 10 for $8.90 is 89c each, 6 for $5.70 is 95c each, and a single is $1.40. So take as many 10-packs as possible: 5 × 10 = 50 muffins for 5 × $8.90 = $44.50. The remaining 7 are cheapest as one 6-pack plus one single: $5.70 + $1.40 = $7.10. Total = $44.50 + $7.10 = $51.60.
watch Buying six 10-packs (60 muffins for $53.40) or paying for the last 7 as singles ($9.80). Both are more than $51.60 — always price the leftover two ways.
Uncle Jack bought 60 boxes of pens. There were 9 pens in each box. He repacked the pens into smaller packets of 5 each. How many packets are there?
(1) 540 packets (2) 300 packets (3) 270 packets (4) 108 packets
answer (4) — 108 packets
method First find how many pens there are altogether: 60 × 9 = 540 pens. Then share them into packets of 5: 540 ÷ 5 = 108 packets.
watch Stopping at 540 (that is the number of PENS, not packets), or dividing 60 by 5 and ignoring the 9 pens per box.
In a restaurant, a rectangular table can seat 10 people and a round table can seat 5 people. During lunch time, all the tables in the restaurant were occupied. The number of each type of table in the restaurant is more than 10 and less than 15. If there were 205 customers, how many rectangular and round tables altogether were there for the 205 customers?
answer 27
method "More than 10 and less than 15" means each type is 11, 12, 13 or 14. Seats: 10 × rectangular + 5 × round = 205, and dividing everything by 5 gives 2 × rectangular + round = 41. Now test each value: 11 rectangular → round = 41 − 22 = 19 ✗; 12 → 17 ✗; 13 → 15 ✗ (15 is not less than 15); 14 → 41 − 28 = 13 ✓. So 14 rectangular and 13 round, giving 14 + 13 = 27 tables.
watch Reading "more than 10 and less than 15" as including 10 and 15, or finding one pair that makes 205 without checking that BOTH counts sit inside the range.
The table shows how many cakes a shop sold on four days. How many more cakes were sold on the last two days than on the first two days?
Day Cakes Monday 24 Tuesday 18 Wednesday 31 Thursday 27
(A) 6 (B) 13 (C) 16 (D) 22 (E) 58
answer (C) — 16
method First two days: 24 + 18 = 42. Last two days: 31 + 27 = 58. The difference is 58 − 42 = 16.