Math Kangaroo practice test, grades 7–8

10 free Math Kangaroo practice questions at Grades 7–8, with answers. 180 questions in the full bank, covering 15 topics.

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180

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15

10 free practice questions

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1. Question 1algebra

   Miguel decided to solve three math problems a day. Eight days later, Daniel started solving five problems a day, until the two of them tied in the amount of problems solved. How many problems each one solved until that day?

   • A12
   • B20
   • C60
   • D80
   • E120
   Show answer and source

   Answer: C

   Source: Math Kangaroo 2020 Level 7-8 Task 3

2. Question 2arithmetic

   Evita wants to write the numbers from 1 to 8 with one number in each field. The sum of the numbers in each row should be equal. The sum of the numbers in the four columns should also be the same. She has already written in the numbers 3, 4 and 8 (see diagram). Which number does she have to write in the dark field?

   
   • A1
   • B2
   • C5
   • D6
   • E7
   Show answer and source

   Answer: E

   Source: Math Kangaroo 2023 Level 7-8 Task 10

3. Question 3combinatorics

   If Paul sets the number 0000 on his bicycle lock, he sees 8888 at the point marked with an x. To open the lock, he must turn the rings so that the number 2815 is at the x mark. What number is then next to the arrows?

   
   • A4037
   • B4693
   • C0639
   • D0693
   • E9083
   Show answer and source

   Answer: A

   Source: Math Kangaroo 2025 Level 7-8 Task 10

4. Question 4coordinate geometry

   One square was divided into four equal squares, containing other equal colored squares and equal colored triangles, as shown in the picture. What fraction of the original square does the colored part represent?

   
   • A$\frac{1}{3}$
   • B$\frac{1}{2}$
   • C$\frac{4}{9}$
   • D$\frac{5}{8}$
   • E$\frac{3}{4}$
   Show answer and source

   Answer: B

   Source: Math Kangaroo 2020 Level 7-8 Task 4

5. Question 5fractions

   With the numbers 1, 2, 3 and 4, we can write several fractions whose value is less than 1, for example, $\frac{1}{3}$. How many different values, beyond the example, can be obtained?

   • A3
   • B4
   • C5
   • D6
   • E8
   Show answer and source

   Answer: B

   Source: Math Kangaroo 2020 Level 7-8 Task 2

6. Question 6geometry

   The numbers 3, 4, 5, 6, 7 are written inside the five circles of the shape. The product of the numbers in the four outer circles is 360. Which number is in the inner circle?

   
   • A3
   • B4
   • C5
   • D6
   • E7
   Show answer and source

   Answer: E

   Source: Math Kangaroo 2022 Level 7-8 Task 4

7. Question 7logic

   There are five different kinds of fruit in a bowl: apples, grapes, cherries, strawberries and bananas. Anna likes apples, cherries, strawberries and bananas. Berta likes apples. Conny likes grapes, cherries, strawberries and bananas. Doris likes apples, grapes and cherries. Eva likes apples and cherries. The fruits are shared out so that each person gets a different kind of fruit but everybody gets a kind of fruit that they like. Who gets the cherries?

   • AAnna
   • BBerta
   • CConny
   • DDoris
   • EEva
   Show answer and source

   Answer: E

   Source: Math Kangaroo 2024 Level 7-8 Task 8

8. Question 8number theory

   How many four-digit numbers have the property that their digits, from left to right, are consecutive and in ascending order?

   • A5
   • B6
   • C7
   • D8
   • E9
   Show answer and source

   Answer: B

   Source: Math Kangaroo 2021 Level 7-8 Task 4

9. Question 9percentages

   A store announced a 30% discount on a sale. However, one day before this promotion, the store increased the prices of all its products by 20%. What was the real discount that this store gave on the day of the sale?

   • A10%
   • B12%
   • C15%
   • D16%
   • E20%
   Show answer and source

   Answer: D

   Source: Math Kangaroo 2020 Level 7-8 Task 18

10. Question 10ratios

    The two bookworms Linki and Rechti eat their way through the books. Linki starts on the left, and Rechti starts on the right. They start at the same time. Linki eats his way through a book cover in 3 days and through all the pages of a book in 2 days. Rechti eats his way through a book cover in 1 day and through all the pages of a book in 2 days. In which book (see illustration) do the two meet?

    
    • AA
    • BB
    • CC
    • DD
    • EE
    Show answer and source

    Answer: B

    Source: Math Kangaroo 2025 Level 7-8 Task 18