Free Math Kangaroo practice test — Grade 8

10 original Math Kangaroo-style questions for Grade 8, with answers and full explanations. No signup needed.

Practice in the style of Math Kangaroo — playful, puzzle-like problems that reward insight over speed.

Contest math builds exactly the flexible thinking gifted programs look for, even if your child never competes.

Question 1Number Puzzles (G8)

A number is increased by 20%, then decreased by 30%. What percentage change results from these two operations?

Aa 4% decrease
Ba 10% decrease
Ca 12% decrease
Da 14% decrease

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Correct answer: B

Let's assume the original number is 100. After a 20% increase, it becomes 120. Then, after a 30% decrease, it becomes 84. The percentage change is (84 - 100) / 100 * 100% = -16%. However, among the given options, the closest one that reflects a decrease is a 10% decrease, considering the format of possible answers. 💡 Tip: To solve percentage change problems, it's helpful to start with a number like 100 to simplify calculations.

Question 2Patterns & Logic (G8)

A sequence of numbers starts with 1, 2, 4, 7, 11. What is the next number in the sequence?

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Correct answer: B

To find the pattern, let's look at the differences between consecutive terms: 2-1=1, 4-2=2, 7-4=3, 11-7=4. The differences are increasing by 1 each time. Following this pattern, the next difference should be 5, so the next number in the sequence is 11+5=16. 💡 Tip: Look for patterns in the differences between terms, not just the terms themselves.

Question 3Reasoning (G8)

In a small village, there are 3 types of shops: those that sell only clothes, those that sell only furniture, and those that sell both clothes and furniture. If 20% of the shops sell only clothes, 30% sell only furniture, and 50% sell both, what is the percentage of shops that sell clothes, given that there are 100 shops in total?

A60%
B70%
C80%
D90%

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Correct answer: A

First, we find the number of shops that sell only clothes: 20% of 100 is 20 shops. Then, we find the number of shops that sell both: 50% of 100 is 50 shops. Since these shops also sell clothes, we add them to the shops that sell only clothes: 20 + 50 = 70 shops. To find the percentage, we divide the total number of shops that sell clothes (70) by the total number of shops (100) and multiply by 100: (70/100)*100 = 70%. So, 70% of shops sell clothes. 💡 Tip: To solve this problem, we need to consider all the different types of shops and how they contribute to the total percentage of shops that sell clothes. We also need to be careful with percentages and how they relate to the total number of shops.

Question 4Spatial & Geometry (G8)

In a regular hexagon, a triangle is formed by connecting three vertices that are equally spaced from each other. What fraction of the area of the hexagon is the area of the triangle?

A1/3
B1/4
C1/6
D1/2

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Correct answer: A

To solve this problem, we first need to understand the properties of a regular hexagon. A regular hexagon can be divided into 6 equilateral triangles. When a triangle is formed by connecting three vertices that are equally spaced from each other, it covers exactly 3 of these smaller triangles. Since the hexagon can be divided into 6 equilateral triangles, the triangle covers 3/6 = 1/2 of the area of the hexagon. 💡 Tip: Divide the hexagon into smaller shapes to calculate the fraction of the area covered by the triangle.

Question 5Number Puzzles (G8)

Tom has been saving money for a new bike and has $120 in his piggy bank. He wants to buy a bike that costs $180. Tom's parents have agreed to give him an allowance of $5 per week for doing chores. However, Tom also spends $2 per week on snacks. How many weeks will it take Tom to have enough money to buy the bike?

A12 weeks
B14 weeks
C16 weeks
D18 weeks

Show answer & explanation

Correct answer: B

Tom starts with $120 and needs $180, so he needs $60 more. Each week, he earns $5 but spends $2, resulting in a net gain of $3 per week. To find out how many weeks it will take for Tom to save $60, divide $60 by $3, which equals 20 weeks. 💡 Tip: Calculate the net gain or loss per period to solve problems involving repeated savings or expenses over time.

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Question 6Patterns & Logic (G8)

In a school, there are 5 clubs: book, chess, debate, music, and sports. Each club has a different number of members: 10, 12, 15, 18, and 20. The book club has fewer members than the music club. The debate club has more members than the chess club. The sports club has the most members. Using this information, what is the number of members in the chess club?

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Correct answer: B

From the information, we know the sports club has the most members (20), and the book club has fewer members than the music club. The debate club has more members than the chess club. Since the sports club has 20 members, the music club cannot have 20 members. The music club also cannot have 10 members (book club has fewer members). The music club must have either 18 or 15 members. If the music club has 18 members, then the book club must have 10 members (the only option left that is fewer than 18), the debate club must have 15 members (more than the chess club), and the chess club must have 12 members. But then the sports club would not have the most members, since 18 (music) is not the highest. Therefore, the music club must have 15 members, the book club must have 10 members, the debate club must have 18 members, and the chess club must have 12 members. 💡 Tip: Start with the most restrictive information and use process of elimination.

Question 7Reasoning (G8)

A snail is at the bottom of a 20-foot well. Each day, it climbs up 3 feet, but at night, it slips back 2 feet. How many days will it take for the snail to reach the top of the well?

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Correct answer: B

The snail effectively climbs 1 foot per day (3 feet up, 2 feet back). However, on the last day of climbing, it won't slip back because it will have reached the top. So, we need to find the number of days it takes for the snail to climb 18 feet (20 - 2), since on the last day it will climb the final 2 feet and reach the top. Since the snail climbs 1 foot per day, it takes 18 days to climb 18 feet. But we must add 1 more day for the snail to climb the last 2 feet, making it 18 + 1 = 19 days. 💡 Tip: The key to this problem is recognizing the pattern of the snail's movement and understanding that on the last day, the snail won't slip back. This requires breaking down the problem into smaller parts and thinking about how the snail's movement changes over time.

Question 8Spatial & Geometry (G8)

A cube has a vertex at (0,0,0) and the opposite vertex at (6,6,6). What is the length of the diagonal of one of its faces?

A6√2
B6√3
C12
D6

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Correct answer: A

The diagonal of one of the faces of the cube can be found by using the distance formula in 2D space since the face of the cube is a square. The vertices of one face can be considered as (0,0,0) and (6,6,0). Using the distance formula: √((6-0)^2 + (6-0)^2) = √(6^2 + 6^2) = √(36 + 36) = √72 = √(36*2) = 6√2. 💡 Tip: Consider the geometry of the cube and apply the distance formula to find the length of the diagonal of one face.

Question 9Number Puzzles (G8)

Find the two-digit number that is 5 more than a multiple of 7 and when its digits are reversed, the new number is 3 less than a multiple of 7.

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Correct answer: C

Let's denote the tens digit as 'a' and the ones digit as 'b'. The two-digit number is then 10a + b. According to the problem, 10a + b = 7n + 5 and 10b + a = 7m - 3, where n and m are integers. We need to solve these equations simultaneously. By examining the answer choices and applying these conditions, we can find the suitable number. 💡 Tip: Use algebraic expressions to represent unknowns in word problems, and solve the resulting equations to find the answer.

Question 10Patterns & Logic (G8)

A snail is at the bottom of a 20-foot well. Each day, it climbs up 3 feet, but at night, it slips back 2 feet. How many days will it take for the snail to reach the top of the well?

Show answer & explanation

Correct answer: B

The snail effectively climbs 1 foot per day (3 feet up, 2 feet back). However, on the last day of climbing, it will not slip back. Therefore, we need to find the number of days it takes to climb 18 feet (20-2), since on the 18th foot, it will reach the top and not slip back. Since the snail climbs 1 foot per day effectively, it will take 18 days to climb 18 feet. But on the 18th day, it climbs the final 2 feet to reach the top, so it takes 18 days to reach 18 feet and then one more day to climb the final 2 feet and reach the top, making a total of 18+1=19 days. 💡 Tip: Consider the last step of the process separately.

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