2021 Math Kangaroo Real Questions and Analysis

In this article, you’ll find:

• A topic distribution chart for the 2021 Math Kangaroo Levels 1–4
• Key concepts tested in each topic
• A question–module mapping table
• Several real 2021 questions with solutions and common mistakes
• Study tips and resources to prepare effectively for Math Kangaroo

2021 Math Kangaroo Overview

The Math Kangaroo competition consists of a single 75-minute multiple-choice test with five answer options per question. Students can participate either online or on paper.

Scoring Structure

• Grades 1–4: 24 questions, maximum score of 96 points
• Grades 5–12: 30 questions, maximum score of 120 points

Learn more about Math Kangaroo Format and Scoring Here: Math Kangaroo FAQ and Resources: Your Ultimate Guide

Levels 1-2 Analysis

Topic Distribution

The 2021 Math Kangaroo Levels 1–2 exam presents a balanced mix—geometry (33%), number sense (30%), and reasoning (29%)—with relatively few word problems (8%), indicating even coverage of spatial, numeric, and logical skills.

Detailed Module Summary

Module	Question Numbers	What It Tests
Geometry	Q1, Q3, Q4, Q5, Q9, Q13, Q17, Q20	2D shapes; mirror/reflection & symmetry; rotations; grid paths
Reasoning	Q6, Q7, Q10, Q12, Q15, Q21, Q24	Logic; code mapping; sequence
Word Problem	Q11, Q16	Totals; sum–difference problems
Number	Q2, Q8, Q14, Q18, Q19, Q22, Q23	Differences; sums; arithmetic; calendar counts

Real Questions and Solutions Explained

Geometry Example – Problem 4

Question:

Four identical pieces of paper are placed as shown. Michael wants to punch a hole that goes through all four pieces. At which point should Michael punch the hole?

(A) A (B) B (C) C (D) D (E) E

Solution:

To pierce all four sheets, the hole must be placed in the common intersection of the four squares. Overlay the outlines of the four squares (as on the right figure) and look for the region contained by every square. Only point D lies strictly inside the outlines of all four squares.

Answer: D

Common Mistakes:

• Testing against three sheets and forgetting the fourth.
• Thinking stacking order matters (it doesn’t; only the geometric intersection matters).

Reasoning Example – Problem 7

Question:

These children are standing in a line. Some are facing forward and others are facing backward. How many children are holding another child’s hand with their right hand?

(A) 2 (B) 3 (C) 4 (D) 5 (E) 6

Solution:

Key idea: Find each child’s right hand.

If the child faces forward (toward us), the right hand is drawn on the left side of that child. If the child faces backward, the right hand is drawn on the right side of that child. Mark each child’s right hand and check whether it is joined to another hand. In the picture, exactly one child (the far-left girl) is not holding another child with her right hand. The other six children are.

Answer: E

Common Mistakes:

• Mixing up which side shows the right hand.
• Counting hands instead of children (a joined pair shouldn’t be double-counted).
• Checking “holding hands” in general, not specifically right hands.

Word Problem Example – Problem 16

Question:

The kangaroo had two branches for lunch. Each branch had 10 leaves. The kangaroo ate some leaves from one branch. Then, from the second branch, it ate as many leaves as were left on the first branch. How many leaves in total were left on the two branches?

(A) 5 (B) 6 (C) 8 (D) 10 (E) 15

Solution:

There are 20 leaves to start (10 + 10).

• Let’s try an example: If the kangaroo eats 3 leaves from the first branch, there are 7 left. Then, it eats 7 leaves from the second branch (same as what’s left on the first). Total eaten = 3 + 7 = 10. Leaves left = 20 − 10 = 10.
• Try another example: Eats 6 leaves from the first → 4 left. Eats 4 leaves from the second. Still eats 10 in total → 10 left
• No matter how many it eats first, the total eaten is always 10. So, 10 leaves remain.

Answer: D

Common Mistakes:

• Mixing up “leaves left” and “leaves eaten”
• Forgetting to add both branches at the start
• Trying only one example and not realizing it always works out to 10 leaves left

Number Example – Problem 23

Question:

Kangie eats only apples on Monday, Wednesday, and Friday. On Tuesdays and Thursdays he eats only mangoes. He eats either 2 apples or 3 mangoes a day. On Saturdays and Sundays he eats nothing. How many pieces of fruit does Kangie eat in two weeks?

(A) 12  (B) 16  (C) 18  (D) 20  (E) 24

Solution:

In one week:

• Kangie eats apples on 3 days → 2 × 3 = 6 apples
• Kangie eats mangoes on 2 days → 3 × 2 = 6 mangoes
• Total for one week: 6 + 6 = 12 fruits

In two weeks: 12 × 2 = 24 fruits

Answer: E

Common Mistakes:

• Only calculating for one week instead of two
• Mixing up the number of days for apples and mangoes

Levels 3-4 Analysis

Topic Distribution

The 2021 Math Kangaroo Levels 3–4 exam centers on reasoning (38%) and number (33%), with lighter geometry (21%) and word problems (8%), meaning many questions use step-by-step rule clues and basic number patterns.

Detailed Module Summary

Module	Question Numbers	What It Tests (Brief)
Geometry	Q1, Q2, Q4, Q11, Q15	Three views; visible faces; perimeter
Reasoning	Q5, Q6, Q9, Q10, Q16, Q17, Q22, Q23, Q24	Constraint logic; sequence; patterns; weighing logic
Word Problem	Q13, Q14	Sales/cost problmes
Number	Q3, Q7, Q8, Q12, Q18, Q19, Q20, Q21	Remainders; divisibility; sum–difference equations

Real Questions and Solutions Explained

Geometry Example – Problem 11

Question:

Solution:

The total number of cubes is 18.

• The white piece has 4 cubes.
• The black piece has 7 cubes.
• 4 + 7 = 11 cubes already shown.

So, the number of gray cubes must be: 18 − 11 = 7 cubes.

Answer: E

Common Mistakes:

• Forgetting to count the total number of cubes
• Adding white and black incorrectly
• Thinking it’s about the shape only, not the number of cubes

Reasoning Example – Problem 6

Question:

A measuring tape is wrapped around a cylinder. Which number should be at the place shown by the question mark?

(A) 33 (B) 42 (C) 48 (D) 53 (E) 69

Solution:

The number 6 is below the number 27. That means 27 is 21 more than 6.

Now 27 is below the question mark, so the question mark must be 21 more than 27: 27 + 21 = 48.

Answer: C

Common Mistakes:

• Counting how many numbers are around the cylinder instead of using the pattern
• Adding random numbers instead of checking the difference between rows

Word Problem Example – Problem 13

Question:

In an ice cream shop there was some money in a drawer. After selling 6 ice cream cones, there are 70 dollars in the drawer. After selling a total of 16 ice cream cones, there are 120 dollars in the drawer. How many dollars were there in the drawer at the start?

(A) 20 (B) 30 (C) 40 (D) 50 (E) 60

Solution:

Between 6 cones and 16 cones, the shop sold 10 more cones. The money went from $70 to $120, so they made $50 from those 10 cones. That means each cone brings in $5 (because 50 ÷ 10 = 5). The first 6 cones made 6 × 5 = $30. So before selling anything, there was $70 − $30 = $40 in the drawer.

Answer: C

Common Mistakes:

• Using the $120 directly without comparing with the $70
• Not figuring out how much each cone costs
• Thinking $70 is the starting amount

Number Example – Problem 20

Question:

Mia throws darts at balloons worth 3, 9, 13, 14, and 18 points. She scores 30 points in total. Which balloon does Mia definitely hit?

(A) 3  (B) 9  (C) 13  (D) 14  (E) 18

Solution:

To find out which balloon Mia definitely hit, try different combinations that add up to 30.

• Try skipping 14:
  • 3 + 13 + 14 = 30 ✅
  • 9 + 18 + 3 = 30 ✅
  • In both cases, the number 3 is used.
• Now try a combo without 3:
  • 14 + 13 = 27 → need 3 more → only 3 works
  • 18 + 13 = 31 ❌ too much
  • 9 + 14 = 23 → need 7 → not available

So no matter how the points are added up to 30, Mia must have hit the 3-point balloon.

Answer: A

Common Mistakes:

• Thinking any number can work without testing all combinations
• Not noticing that 3 is in every valid combination
• Trying random totals without writing them down

2021 Math Kangaroo Answer Key

Question	Level 1 & 2	Level 3 & 4
1	E	C
2	B	C
3	A	B
4	D	B
5	A	E
6	D	C
7	E	D
8	B	C
9	D	A
10	D	E
11	C	E
12	E	C
13	A	C
14	C	E
15	B	D
16	D	B
17	D	D
18	A	E
19	C	D
20	C	A
21	B	D
22	C	E
23	E	D
24	C	A

Best Resources to Prepare for Math Kangaroo

Visit our All-in-One Math Kangaroo Hub for free and exclusive preparation materials, including video explanations, worksheets, and topic breakdowns.

About Think Academy

Think Academy, wholly owned by TAL Education Group, specializes in preparing students for the Math Kangaroo competition. Each year, over 300 Think Academy students win Math Kangaroo awards, including 35% of all Level 1 perfect scores nationwide. 7 out of 10 Think participants won national awards in 2025. Supported by world-class resources and expert coaching, we empower students to achieve exceptional results in international mathematics competitions.

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