Section A
Multiple-choice — Questions 1 to 20
(+2)
1
place-value
medium
Which one of the following options is correctly matched? Each number box on the left is joined by a line to a phrase box on the right.
Answer: 4
Work out the value of each phrase:
5 hundreds and 31 ones = 500 + 31 = 531
5 hundreds 3 tens and 5 ones = 500 + 30 + 5 = 535
530 ones = 530
3 hundreds and 53 tens = 300 + 530 = 830
Only one number box equals the phrase it is matched to: 535 = 535 (Option 4).
2
number-sense
medium
Which one of the following options is correct?
Answer: 3
Option 1: 35 < 24 is false.
Option 2: 24 > 24 is false (equal, not greater).
Option 3: 6 < 8 is true.
Option 4: 41 > 81 is false.
3
division
easy
Jennifer has 24 hairclips. She puts them equally into 3 packs. How many hairclips are there in each pack? Which one of the following options shows the correct equation to solve the problem?
Answer: 4
Sharing 24 hairclips equally into 3 packs is division: 24 ÷ 3 = 8.
4
time
medium
The time on the clock below is 5 min slow. Which one of the following options shows the actual time?
Answer: 3
The clock displays 7:10.
Since it is 5 minutes slow, the actual time is 7:10 + 5 min = 7:15.
5
measurement
easy
The height of a classroom door is about ___________. Which one of the following options shows the correct height of a classroom door?
Answer: 2
A classroom door is about the height of an adult and a bit more — about 2 metres.
6
fractions
easy
Which one of the following fractions is greater than 1/2?
Answer: 4
1/2 = 4/8. 1/8 and 3/8 are less than 4/8, and 4/8 equals 1/2 (not greater). 5/8 > 4/8, so 5/8 > 1/2.
7
logic
medium
Andy, Benjamin, Lucas and Siti had lunch together in a food court. They bought Chicken Rice, Noodles, Fish & Chips and Pasta. Based on the following statements, what food did Benjamin order?
• Siti loves eating fish.
• Andy prefers to eat rice.
• Lucas did not order Noodles.
Answer: 2
Siti loves fish, so Siti = Fish & Chips. Andy prefers rice, so Andy = Chicken Rice. That leaves Noodles and Pasta for Lucas and Benjamin. Lucas did not order Noodles, so Lucas = Pasta and Benjamin = Noodles.
8
money
medium
Joanne wants to buy a pair of goggles as shown below. She has six notes and some coins in her purse. How much more money does Joanne need?
Answer: 4
Notes: $10 + $5 + $5 + $2 + $2 + $2 = $26.
Coins: $1 + 50¢ + 20¢ + 10¢ = $1.80.
Total money = $26 + $1.80 = $27.80.
Goggles cost $33, so she needs $33 − $27.80 = $5.20 more.
9
fractions
medium
Steve bought a pizza. He gave 3/10 of the pizza to his sister. He also gave twice as many pieces to his father. What fraction of the pizza did he have left?
Answer: 1
Sister got 3/10. Father got twice as many pieces = 6/10. Total given away = 3/10 + 6/10 = 9/10. Left = 1 − 9/10 = 1/10.
10
addition
easy
A book shop sold 113 story books in January, 48 story books in February and 204 story books in March. How many story books were sold altogether?
Answer: 365
113 + 48 + 204 = 365.
11
place-value
easy
What is 300 more than 18 tens 4 ones?
Answer: 484
18 tens 4 ones = 180 + 4 = 184.
184 + 300 = 484.
12
algebra
medium
Look at the following equations (★ = star, ▲ = triangle, ♥ = heart):
★ + ▲ + ♥ = 125
♥ + ★ = 50
▲ − ♥ = 35
What is the value of ★?
Answer: 10
From the first equation: ▲ = 125 − (♥ + ★) = 125 − 50 = 75.
From the third equation: ♥ = ▲ − 35 = 75 − 35 = 40.
From the second equation: ★ = 50 − ♥ = 50 − 40 = 10.
13
patterns
medium
James needs 3 ice-cream sticks to form a triangle as shown in the pattern below. How many ice-cream sticks are needed to form 4 triangles in Pattern 4?
Answer: 9
Pattern 1 (1 triangle) = 3 sticks. Pattern 2 (2 triangles) = 5 sticks. Pattern 3 (3 triangles) = 7 sticks. Each extra triangle adds 2 sticks: sticks = 2 × (number of triangles) + 1.
Pattern 4 (4 triangles) = 2 × 4 + 1 = 9 sticks.
14
number-sense
medium
Jean has fewer than 30 cups. She can pack all the cups equally into boxes with 4 cups in each box. She can also pack all the cups equally into containers with 5 cups in each container. No cup is left unpacked. How many cups does Jean have?
Answer: 20
The number of cups must be a common multiple of 4 and 5 that is less than 30. The only such number is 20 (4 × 5).
15
measurement
easy
Mrs Tan made three skirts using a total of 532 cm of cloth. She used 120 cm of cloth to make the first skirt. She used the same amount of cloth to make the second skirt. How much cloth did she use to make the third skirt? Give your answer in cm.
Answer: 292
First two skirts: 120 + 120 = 240 cm.
Third skirt = 532 − 240 = 292 cm.
16
geometry
medium
Alice has a square cardboard and 32 coins. She wants to place an equal number of coins on each side of the cardboard. A coin is placed at each corner of the cardboard. How many coins can Alice place on each side of the cardboard?
Answer: 9
The 4 corner coins are shared by two sides each, so they are counted once per side but only cost 4 coins total.
Remaining coins to split among the 4 sides = 32 − 4 = 28, giving 28 ÷ 4 = 7 extra coins per side.
Each side then has 2 corner coins + 7 extra coins = 9 coins.
17
mass
medium
The weighing scale below shows the total mass of an apple and a bunch of bananas. The bunch of bananas weighs 290 g. Find the mass of 3 such identical apples. Give your answer in grams.
Answer: 150
The scale reads 340 g for the apple and bananas together.
Apple = 340 − 290 = 50 g.
3 apples = 3 × 50 = 150 g.
18
money
medium
Jessica bought 6 pens and 2 files. Each pen cost $3. Each file cost $2 more than each pen. She gave the cashier $50. How much change did she receive?
Answer: 22
6 pens = 6 × $3 = $18.
Each file = $3 + $2 = $5, so 2 files = $10.
Total spent = $18 + $10 = $28.
Change = $50 − $28 = $22.
19
money
medium
Tom has $40 more than Ken. Samad has $30 more than Tom. Samad has $270. How much do the three boys have altogether?
Answer: 710
Tom = $270 − $30 = $240.
Ken = $240 − $40 = $200.
Total = $270 + $240 + $200 = $710.
20
patterns
medium
The numbers on the three houses below follow a pattern. What is the missing number on the third house?
Answer: 110
In each house, the roof number equals the sum of the 4 wall numbers around the middle number, plus the middle number itself.
First house: 1 + 4 + 3 + 5 + 2 = 15. ✓
Second house: 10 + 8 + 7 + 6 + 9 = 40. ✓
Third house: 22 + 21 + 20 + 23 + 24 = 110.
Section B
Open-ended — Questions 21 to 40
(+3)
21
arithmetic
medium
Mrs Lim wrote a 3-digit number on a whiteboard. She halved the 3-digit number first. After that, she subtracted 170 from the halved number. Then, she divided the result by 5. The final answer was 6. What number did Mrs Lim write on the whiteboard?
Answer: 400
Work backwards: 6 × 5 = 30.
30 + 170 = 200 (this is half the number).
200 × 2 = 400.
22
place-value
medium
John wrote a 3-digit number on a piece of paper. The digit in the ones place is the greatest 1-digit number. The digit in the tens place is 4 less than the digit in the ones place. The value of the digit in the hundreds place is 650 more than the value of the digit in the tens place. What is the 3-digit number?
Answer: 759
Ones digit = 9 (greatest 1-digit number).
Tens digit = 9 − 4 = 5, so its value is 50.
Hundreds digit's value = 50 + 650 = 700, so the hundreds digit is 7.
The number is 759.
23
logic
hard
10 soldiers need to cross a river. A rubber boat can ferry 4 soldiers each time. 1 soldier has to steer the boat during each crossing. What is the least number of crossings needed to take all 10 soldiers to get to the other side of the river?
Answer: 5
Each round trip (boat goes, then 1 person brings it back) moves 3 new people across using 2 crossings.
Crossing 1: 4 cross (near: 6, far: 4). Crossing 2: 1 returns (near: 7, far: 3).
Crossing 3: 4 cross (near: 3, far: 7). Crossing 4: 1 returns (near: 4, far: 6).
Crossing 5: the last 4 cross and stay (near: 0, far: 10).
Total = 5 crossings.
24
arithmetic
medium
Agnes had some sweets in her container. She gave 4 sweets to each of the 9 girls and 5 sweets to each of the 3 boys in her class. In the end, she had 35 sweets left. How many sweets did Agnes have at first?
Answer: 86
Given to girls: 4 × 9 = 36.
Given to boys: 5 × 3 = 15.
Total given away = 36 + 15 = 51.
At first = 51 + 35 = 86 sweets.
25
mass
medium
Alicia and Daniel have a total mass of 90 kg. Alicia and Sam have a total mass of 102 kg. Alicia has a mass of 47 kg. What is the total mass of Daniel and Sam? Give your answer in kg.
Answer: 98
Daniel = 90 − 47 = 43 kg.
Sam = 102 − 47 = 55 kg.
Daniel + Sam = 43 + 55 = 98 kg.
26
volume
medium
Mr Chen had some water at first. He filled two beakers with some water as shown below. In the end, he had 580 mℓ of water left. How much water did he have at first? Give your answer in mℓ.
Answer: 950
Left beaker: filled to the 100 mℓ mark.
Right beaker: filled to 270 mℓ (one tick below the 300 mℓ mark).
Water at first = 100 + 270 + 580 = 950 mℓ.
27
picture-graph
medium
The picture graph shows the different types of sandwiches a class of pupils likes. Each triangle stands for 10 pupils. The number of pupils who like Chicken sandwiches is half the total number of pupils who like Tuna and Egg sandwiches. How many pupils like Chicken sandwiches?
Answer: 30
Tuna = 1 × 10 = 10 pupils. Egg = 5 × 10 = 50 pupils.
Tuna + Egg = 10 + 50 = 60.
Chicken = half of 60 = 30 pupils.
28
money
medium
Mr Tan has some money. If he buys a toaster that costs $49, he will have $26 left. If he buys an iron, he will be short of $17. How much does the iron cost?
Answer: 92
Mr Tan's money = $49 + $26 = $75.
Iron costs = $75 + $17 = $92.
29
ratio
medium
Agnes bought a total of 50 red and yellow beads. For every 4 red beads bought, there was a yellow bead. How many red beads did Agnes buy in total?
Answer: 40
Ratio of red : yellow = 4 : 1, so there are 5 equal parts in total.
50 ÷ 5 = 10 beads per part.
Red beads = 4 × 10 = 40.
30
measurement
easy
A rope is 1 m long. Joe cuts off 64 cm of it. Then, he cuts the remaining length into 4 equal pieces. What is the length of each piece? Give your answer in cm.
Answer: 9
1 m = 100 cm.
Remaining after cutting off 64 cm = 100 − 64 = 36 cm.
Each piece = 36 ÷ 4 = 9 cm.
31
age
medium
5 years ago, Ben was 8 years old. His mother is 26 years older than him. How old will his mother be in 5 years' time?
Answer: 44
Ben's age now = 8 + 5 = 13.
Mother's age now = 13 + 26 = 39.
Mother's age in 5 years = 39 + 5 = 44.
32
volume
easy
A pancake seller bought 9 bottles of honey. There were 10 litres of honey in each bottle. He used 36 litres of honey on Saturday and 23 litres of honey on Sunday. How many litres of honey did the pancake seller have left?
Answer: 31
Total honey = 9 × 10 = 90 ℓ.
Used = 36 + 23 = 59 ℓ.
Left = 90 − 59 = 31 ℓ.
33
mass
hard
Look at the scales below. What is the mass of 2 identical Boxes of A? Give your answer in kg.
Answer: 12
Scale 1: A + 2B = 5 + 5 = 10 kg.
Scale 2: 4B = 5 + 1 + 1 + 1 = 8 kg, so B = 2 kg.
From Scale 1: A = 10 − 2(2) = 6 kg.
2 identical Boxes of A = 2 × 6 = 12 kg.
34
money
medium
Oranges were sold in bags of 4 at $3 for each bag. Mrs Lee bought 32 oranges. Mdm Rose bought 6 bags of oranges. How much did both of them spend altogether?
Answer: 42
Mrs Lee: 32 oranges ÷ 4 = 8 bags, costing 8 × $3 = $24.
Mdm Rose: 6 bags, costing 6 × $3 = $18.
Total = $24 + $18 = $42.
35
money
medium
Look at the pictures below: a Pencil case is sold at 2 for $11, and a Notebook is sold at 4 for $15. Kelvin bought 4 pencil cases and 12 notebooks. He gave the cashier 2 fifty-dollar notes. How much change did he receive?
Answer: 33
4 pencil cases = 2 sets of "2 for $11" = 2 × $11 = $22.
12 notebooks = 3 sets of "4 for $15" = 3 × $15 = $45.
Total cost = $22 + $45 = $67.
Amount paid = 2 × $50 = $100.
Change = $100 − $67 = $33.
36
patterns
medium
Mrs Annabelle bought 50 sweets. She had 8 students. She lined them up and gave 2 sweets to the 8th student, 3 sweets to the 7th child, 4 sweets to the 6th student. She continued giving sweets to all her students following the above pattern. How many sweets did she have left?
Answer: 6
The pattern gives 2, 3, 4, 5, 6, 7, 8, 9 sweets to students 8, 7, 6, 5, 4, 3, 2, 1 respectively.
Total given = 2+3+4+5+6+7+8+9 = 44.
Left = 50 − 44 = 6 sweets.
37
measurement
medium
A toy house has 2 levels. Each level is 27 cm high. There is a black vase on the table. The tabletop is 15 cm from the ceiling. How far is the bottom of the black vase from the bottom of the toy house? Give your answer in cm.
Answer: 39
Total height of the toy house = 27 + 27 = 54 cm.
The tabletop is 15 cm below the ceiling, so its height from the bottom = 54 − 15 = 39 cm.
The black vase sits on the table, so the bottom of the vase is also 39 cm from the bottom of the toy house.
38
money
medium
Rose syrup is sold in two types of bottles: Bottle A costs $5 each and Bottle B costs $2 each. Mr Lim bought 5 bottles of rose syrup. He spent $19 altogether. How many bottles of Type A did he buy?
Answer: 3
Let a = number of Type A bottles, b = number of Type B bottles.
a + b = 5 and 5a + 2b = 19.
Substituting b = 5 − a: 5a + 2(5 − a) = 19 → 3a + 10 = 19 → a = 3.
39
mass
medium
Sam had a box. The box contained 4 wooden cubes of the same mass. The box and 4 wooden cubes had a mass of 880 g. After 3 wooden cubes had been removed from the box, the box weighed 580 g. What would be the mass of the box with 2 such wooden cubes? Give your answer in gram.
Answer: 680
Mass of 3 cubes = 880 − 580 = 300 g, so 1 cube = 100 g.
Box alone (with the last cube removed too) = 580 − 100 = 480 g.
Box with 2 cubes = 480 + 2(100) = 680 g.
40
logic
hard
Julian enjoys reading a variety of books. Work out how many books of each kind he has read for the month:
• The number of science fiction books Julian has read was less than 5.
• Julian has read 5 times as many horror stories as science fiction novels.
• The number of sports magazines read was 1 less than the number of horror stories.
• He has read twice as many sports magazines as history books.
• He has read the same number of history books as he has read comics.
• The number of comics read is 3 more than the number of computer books.
How many books did Julian read in total for the month?
Answer: 50
Let science fiction = s (s < 5, whole number of books).
Horror = 5s. Sports magazines = 5s − 1. History = sports ÷ 2 = (5s − 1)/2, which must be a whole number, so s must be odd: s = 1 or s = 3.
If s = 1: Horror = 5, Sports = 4, History = 2, Comics = 2, Computer = 2 − 3 = −1 — not possible (negative books), so this is rejected.
If s = 3: Horror = 15, Sports = 14, History = 7, Comics = 7, Computer = 7 − 3 = 4 — all valid.
Total = 3 + 15 + 14 + 7 + 7 + 4 = 50 books.