1
Place value
easy
Look at the place value chart.
What is the missing number?
(Tens = 8, Ones = ?)
Answer: 2
Counting the boxes: the left group has 5 full rows of 10 = 50.
The right group has 3 full rows of 10 plus one row of 7 = 37.
Total = 50 + 37 = 87.
Tens = 8, Ones = 7.
2
Number patterns
medium
Look at the number pattern.
94, 84, 86, ?, 78, 68, 70
What is the missing number?
Answer: 1
The pattern alternates -10, +2: 94-10=84, 84+2=86, 86-10=76, 76+2=78, 78-10=68, 68+2=70.
So the missing number is 76.
3
Ordering numbers
easy
Arrange these 4 numbers from the greatest to the smallest.
81, 67, 29, 40
Answer: 4
Greatest to smallest: 81, 67, 40, 29.
4
Telling time
easy
The diagrams below show the different times at which four children left home in the morning to go to school.
Who left home first?
(Rachel, Sanjit, Timothy, Winnie — each shown with a clock.)
Answer: 4
Reading each clock: Rachel = 8:30, Sanjit = 8:00, Timothy = 7:45, Winnie = 7:30.
The earliest time is 7:30, so Winnie left home first.
5
Money
easy
Which one of the following shows sixty cents?
Options (A)-(D) are coin images shown in the figure.
Answer: 4
(A) 50+50+20 = 120 cents.
(B) 20x4 = 80 cents.
(C) 50+10+10 = 70 cents.
(D) 20+20+10+10 = 60 cents — matches.
6
Subtraction
easy
There were 70 people in a bus.
12 people got off at the first stop.
7 people got off at the second stop.
How many people were left in the bus after the second stop?
Answer: 2
70 - 12 = 58.
58 - 7 = 51.
7
Logic / queues
medium
Ronald was 7th and last in the queue at a bus stop.
A bus arrived and 3 people from the front of the queue boarded the bus.
Then, another person joined the queue behind Ronald.
How many people were there in the queue in the end?
Answer: 3
Ronald is 7th and last, so there were 7 people in the queue (positions 1-7).
Removing the front 3 (positions 1-3) leaves positions 4-7 = 4 people.
Adding 1 more behind Ronald: 4 + 1 = 5.
8
Shapes
easy
The figure below is made up of two shapes.
A line is drawn to show the two shapes.
What are the two shapes?
Answer: 2
The figure is a rectangle with one end rounded into a half circle — a rectangle and a half circle.
9
Money / word problem
medium
Kate went to the school bookshop to buy stationery.
She had $1 and spends all her money.
What items did she buy with all her money?
(pencil 30 cents, eraser 40 cents, notebook 80 cents, ruler 50 cents, sharpener 60 cents)
Answer: 1
$1 = 100 cents.
Eraser (40) + sharpener (60) = 100 cents — matches exactly.
Other pairs don't add up to 100: pencil+sharpener=90, notebook+eraser=120, notebook+ruler=130.
10
Money / word problem
easy
Jamie buys a water bottle for $18.
She has $32 left after buying the water bottle.
How much money does Jamie have at first?
11
Multiplication
easy
Mr Tan drinks 3 cups of coffee every day.
How many cups of coffee does he drink in a week?
Answer: 4
3 cups/day x 7 days = 21 cups.
12
Number patterns
medium
Daniel is a car racer.
He completed his first lap in 30 minutes.
He noticed that he was finishing each lap 3 minutes faster than the one before it. How long did it take him to complete his 6th lap?
Lap: 1 2 3 4 5 6
Time (min): 30 27 ... ... ... ?
Answer: 1
Times decrease by 3 each lap: 30, 27, 24, 21, 18, 15.
The 6th lap takes 15 minutes.
13
Logic puzzle
medium
Five children are waiting to do a health check: Elena, Lauren, Denise, Shawn, Tom.
Clues:
(a) Shawn is 1st from the right.
(b) Elena is 2nd from the left.
(c) Lauren is 1st from the left.
(d) Denise is 3rd.
Read the clues and choose the names of the children at their correct position (Left to Right).
Answer: 1
Position 1 (leftmost) = Lauren.
Position 2 = Elena.
Position 3 = Denise.
Position 5 (rightmost) = Shawn.
The only child left for position 4 is Tom.
Order: Lauren, Elena, Denise, Tom, Shawn.
14
Spatial reasoning
medium
John dipped a cube into a can of green paint.
A total of 6 faces will be covered with paint.
How many faces of the following figure (made of several cubes) will be covered with green paint if John dipped it inside the can of paint?
Answer: 4
The figure is made of 5 unit cubes (4 in a row, plus 1 stacked on the 2nd cube).
Total surface area of 5 separate cubes = 6x5 = 30 faces.
Each glued connection between two cubes hides 2 faces (1 from each cube). There are 4 connections (3 along the row, 1 for the stacked cube) = 8 hidden faces.
Exposed (painted) faces = 30 - 8 = 22.
15
Combinatorics
medium
There are three coloured balls in a bag: one yellow, one red and one green.
Mary takes out one ball from the bag at a time.
One possible order is Yellow, Green and Red.
In how many different ways can the 3 balls be taken out of the bag?
Answer: 2
The number of ways to order 3 distinct balls = 3! = 3x2x1 = 6.
16
Division
easy
Henson had 25 apples.
He ate 7 of them.
Then, he packed the rest of the apples equally into 3 packets.
How many apples were there in each packet?
Answer: 6
25 - 7 = 18.
18 / 3 = 6 apples per packet.
17
Algebra / word problem
hard
1 red marble and 3 blue marbles cost 35 cents.
3 red marbles and 1 blue marble cost 25 cents.
How much does 8 red marbles and 8 blue marbles cost?
Give your answer in cents.
Answer: 120
Let red = r, blue = b.
r + 3b = 35.
3r + b = 25.
From the first equation, r = 35 - 3b. Substituting: 3(35-3b) + b = 25 -> 105 - 8b = 25 -> b = 10.
r = 35 - 30 = 5.
8 red + 8 blue = 8x5 + 8x10 = 40 + 80 = 120 cents.
18
Number sense
medium
Charlie is thinking of a number between 80 and 100.
Both the digits in the ones and tens place are the same.
The number is nearer to 90 than to 100.
What number is Charlie thinking of?
Answer: 88
Between 80 and 100 with equal tens/ones digits: 88 or 99.
88 is nearer to 90 (difference 2) than to 100 (difference 12), so the answer is 88.
19
Bar graph
medium
The graph below shows the number of marbles Alex, Ben and Collin have collected. Each icon stands for 1 marble.
Ben gave some marbles to Alex.
In the end, both of them have the same number of marbles.
How many marbles did Ben give to Alex?
Answer: 2
Alex has 6 marbles, Ben has 10 marbles.
Total = 16, split equally = 8 each.
Ben gives 10 - 8 = 2 marbles to Alex.
20
Bar graph / money
medium
The graph below shows the amount of savings Jack had (two-dollar, five-dollar, ten-dollar). Each icon stands for 1 coin or 1 note.
What is the difference in value between the five-dollar notes and ten-dollar notes?
Answer: 20
Five-dollar notes: 8, so value = 8x5 = $40.
Ten-dollar notes: 6, so value = 6x10 = $60.
Difference = $60 - $40 = $20.
21
Number patterns
medium
Peter uses some matchsticks to form 3 squares in a row as shown below.
He continues to use matchsticks to form more squares.
How many matchsticks does he need to make 10 squares in a row?
Answer: 31
For squares in a row sharing sides, matchsticks needed = 3n + 1 (1 square needs 4, each additional square adds 3).
For n = 10: 3x10 + 1 = 31.
22
Algebra / word problem
medium
A jacket costs $8 more than a blouse.
A dress costs $2 less than the jacket.
The 3 items cost $89 altogether.
How much does a blouse cost?
Answer: 25
Let blouse = B. Jacket = B+8. Dress = Jacket-2 = B+6.
B + (B+8) + (B+6) = 89 -> 3B + 14 = 89 -> 3B = 75 -> B = 25.
23
Division
easy
Lily has 19 books.
Joseph has 31 books.
They share all the books equally with 3 other friends.
How many books does each child get?
Answer: 10
Total books = 19 + 31 = 50.
Sharing among Lily, Joseph and 3 other friends = 5 people.
50 / 5 = 10 books each.
24
Algebra / word problem
medium
Uncle Tong filled a tank with 3 identical pails.
Each tank can hold 30 litres more water than a pail.
How many litres of water can 1 tank hold?
Answer: 45
Let pail = p. Tank = 3p (filled by 3 pails), and tank = p + 30.
3p = p + 30 -> 2p = 30 -> p = 15.
Tank = 3x15 = 45 litres.
25
Balance scale
medium
Look at the balance scales.
How many toy apples can balance a toy pear?
Answer: 5
Let apple=A, pear=P, pineapple=Pi, banana=B.
Scene 1: A + P = Pi.
Scene 2: A + B = P, so B = P - A.
Scene 3: 2Pi = 3B, so Pi = 1.5B = 1.5(P-A).
Combine with scene 1: A + P = 1.5(P-A) -> A + P = 1.5P - 1.5A -> 2.5A = 0.5P -> P = 5A.
So 1 pear balances 5 apples.
26
Combinatorics
easy
Jen had planned a day's activities during the holidays.
Morning: Go to the Library OR to Granny's house.
Afternoon: Go jogging OR cycling.
Night: Drawing OR play jigsaw puzzle.
How many different combinations can Jen choose for the day's activities?
Answer: 8
2 choices (morning) x 2 choices (afternoon) x 2 choices (night) = 2x2x2 = 8.
27
Age word problem
medium
Henry, Ian, Joey, and Ken are members of the same family.
Henry is 3 years younger than Ian.
Ian is 2 years older than Joey.
Joey is 4 years older than Ken.
Ken is 7 years old.
How old is the eldest person?
Answer: 13
Ken = 7.
Joey = Ken + 4 = 11.
Ian = Joey + 2 = 13.
Henry = Ian - 3 = 10.
The eldest is Ian at 13 years old.
28
Time word problem
hard
Damian arranged to meet Sebastian at a beach at 11 a.m.
When they were about to meet, Sebastian called Damian to inform that he was going to be half an hour late.
Damian waited for half an hour and then received another call from Sebastian and said that he would be delayed for another 10 minutes.
In the end, Sebastian finally reached the beach and met Damian.
He took twice as much time as he said he would during the last phone call.
How long was Sebastian late from the original time of meeting?
Give your answer in minutes.
Answer: 50
First delay: 30 minutes (matches what Damian waited).
Second call promised 10 more minutes, but Sebastian actually took twice that: 2x10 = 20 minutes.
Total lateness = 30 + 20 = 50 minutes.
29
Combinatorics
medium
How many 2-digit numbers that are greater than 25 can be formed from the following digits: 2, 3, 5, 7?
Each digit can only be used once.
Answer: 10
All 2-digit numbers using distinct digits from {2,3,5,7}: 23,25,27,32,35,37,52,53,57,72,73,75 (12 total).
Excluding those not greater than 25 (23 and 25 itself), 10 numbers remain: 27,32,35,37,52,53,57,72,73,75.
30
Algebra / word problem
medium
Tom and Jerry have 68 pens altogether.
Anson and Tom have 29 pens altogether.
What is the difference in the number of pens that Jerry and Anson have?
Answer: 39
Jerry = 68 - Tom. Anson = 29 - Tom.
Jerry - Anson = (68 - Tom) - (29 - Tom) = 68 - 29 = 39.
31
Speed / word problem
hard
In the figure below, each scale represents a distance of 10 m.
Faizal walks 60 m every 1 minute and Gerald walks 50 m every 1 minute.
Both of them are walking in the same direction, along a straight road.
How long will they have to walk before Faizal catches up with Gerald?
Give your answer in minutes.
Answer: 4
From the figure, Faizal starts 10 m from the left and Gerald starts 50 m from the left — a 40 m gap.
Faizal closes the gap at 60-50 = 10 m per minute.
Time to catch up = 40 / 10 = 4 minutes.