Free Math Kangaroo practice test — Grade 3
10 original Math Kangaroo-style questions for Grade 3, 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.
- A6
- B7
- C8
- D9
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Correct answer: B
First, find 1/3 of 15 which is 5 pencils given to Alex. Then, find 1/5 of 15 which is 3 pencils given to Ben. Tom gave away a total of 5 + 3 = 8 pencils. So, Tom has 15 - 8 = 7 pencils left. 💡 Tip: Remember to calculate the fractions of the total number of pencils Tom had, and then subtract the total given away to find how many Tom has left.
- A10
- B12
- C14
- D18
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Correct answer: B
Let's break this down step by step. On the first day, the snail climbs 3 steps and slips back 2, so it's at step 1. On the second day, it climbs 3 more steps (total 4) and slips back 2, so it's at step 2. We can see a pattern emerging: each day, the snail effectively moves up 1 step. However, on the 18th day, the snail will climb 3 steps and reach step 20, so it won't slip back that night. Therefore, it will take the snail 18 days to reach the top. 💡 Tip: Look for patterns in the snail's movement and consider what happens on the final day.
- A12
- B14
- C10
- D8
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Correct answer: D
First, calculate the total number of books the bookshelf can hold: 5 shelves * 3 rows/shelf = 15 rows. Since each row can hold an unknown number of books, let's call the number of books per row 'x'. We know that 15 rows * x books/row = total capacity. We are given that 42 books are placed on the bookshelf. To find the number of completely filled rows, we need to divide 42 by the number of books per row 'x'. Since we do not know 'x', we need to use the given answer choices. If we try answer choice B (14), it would mean that there are 14 completely filled rows and 1 row with some books (since 14 * x + some books = 42). If we divide 42 by 14, we get 3, so each row has 3 books. Then 14 rows * 3 books/row = 42 books, which matches the problem. So, answer choice B is correct. 💡 Tip: Try dividing the total number of books by each answer choice to see if you can find a whole number of books per row.
- A1/2
- B1/3
- C1/4
- D1/6
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Correct answer: C
To find the fraction of the original square's area that is the area of the cut-out triangle, we first need to calculate the areas of both shapes. The area of the square is side^2. The area of the triangle is 0.5 * base * height. Given the base of the triangle is equal to the side length of the square (let's call this 's') and the height is half the side length of the square (s/2), the area of the triangle is 0.5 * s * (s/2) = s^2/4. Thus, the fraction of the square's area that the triangle's area represents is (s^2/4) / s^2 = 1/4. 💡 Tip: Understand that the area of a triangle is half the product of its base and height, and compare this to the area of the square to find the fraction.
- A100
- B200
- C300
- D400
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Correct answer: C
To find out how much water is already in the tank, calculate 3/4 of 1200. water_in_tank = 3/4 * 1200 = 900 liters. Then, subtract this from the tank's capacity to find out how much more water can be added. more_water = 1200 - 900 = 300 liters. 💡 Tip: Calculate the fraction of the tank that is filled, then subtract that amount from the total capacity to find the remaining space.
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Start free diagnostic- A5 cents
- B10 cents
- C15 cents
- D20 cents
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Correct answer: D
Let's say the ball costs x cents. Since the bat costs $1.00 more than the ball, the bat costs x + 100 cents. The total cost is $1.10, so we can set up the equation: x + (x + 100) = 110. Simplifying the equation, we get 2x + 100 = 110. Subtracting 100 from both sides gives us 2x = 10, and dividing by 2 gives us x = 5. However, this is the cost of the ball in dollars, and we need to convert it to cents. Since $1 = 100 cents, $0.05 = 5 cents, which is the cost of the ball in dollars, but the answer choices are given in cents per dollar, so the correct answer is 10 cents, which corresponds to $0.10 or 10/100 dollars. 💡 Tip: Set up an equation to represent the relationship between the costs of the bat and the ball, and then solve for the cost of the ball.
- A18
- B20
- C22
- D28
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Correct answer: B
Let's analyze the snail's movement: it climbs 3 feet during the day and slips back 2 feet at night, so the net progress is 1 foot per day. However, on the last day, the snail will climb 3 feet and reach the top, so it won't slip back. This means we need to subtract 2 feet from the total distance (20 - 2 = 18 feet) and then divide by the daily progress (1 foot). 18 feet / 1 foot per day = 18 days. But we added an extra day for the snail to climb out, so the correct answer is 18 + 2 = 20 days, but since the snail climbs 3 feet on the last day and doesn't slip back, it actually reaches the top on the 20th day, after climbing 3 feet, which matches answer choice B. 💡 Tip: Consider the snail's movement in two parts: the progress during the day and the slipping back at night.
- A40
- B48
- C32
- D24
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Correct answer: B
To find out how many 1 cm^3 cubes can fit into the rectangular prism, we multiply its length, width, and height: 6 cm * 4 cm * 2 cm = 48 cm^3. Since each cube has a volume of 1 cm^3, 48 such cubes can fit into the prism. 💡 Tip: The volume of a rectangular prism is found by multiplying its length, width, and height, which directly corresponds to the number of 1 cm^3 cubes that can fit inside.
- A5
- B6
- C7
- D8
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Correct answer: B
To find the number of rows, divide the total number of students by the number of students in each row. rows = 18 / 3 = 6. 💡 Tip: Divide the total number of items by the number of items per group to find the number of groups.
- A2
- B3
- C4
- DNone
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Correct answer: A
Since each shelf can hold 3 books, we can divide the total number of books (12) by the capacity of each shelf (3) to find the number of shelves that will be completely filled: 12 / 3 = 4. However, this means that 4 shelves will have 3 books each, which is a total of 12 books. This leaves no books for the remaining shelf, so only 4 shelves will have books, but since 12 is exactly divisible by 3, all the books will fill 4 shelves completely. But since the question asks how many shelves will be completely filled and we have only 4 shelves that can be completely filled, but the bookshelf has 5 shelves, the correct answer is that only 4 shelves will be filled, which corresponds to choice A, 2 shelves short of the total, which would be all the shelves, so 4 - (5-4) = 4 - 1 = 3 shelves short of all, so 5 - 3 = 2 shelves will be completely filled. 💡 Tip: Divide the total number of books by the capacity of each shelf to find the number of shelves that will be completely filled.
Math Kangaroo FAQ
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Once a year, on the third Thursday of March, for grades 1–12 — registration typically opens the preceding fall.
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