Practice Math Questions

• Try these on for size.

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1. What's the radius of the largest sphere that can be placed inside a cube of volume 64?

(A) 16 (B) 8 (C) 4 (D) 2 (E) 2

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2. One side of this square is on the radius of the circle. The circle's radius is 6. What's the area of the blue region?

(A) 12 (B) 36 (C) 36 - 12 (D) 36 - 9 (E) 36 - 9

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3. The average of 12 consecutive even integers is 981. What's the highest of these integers?

• (A) 988
• (B) 989
• (C) 990
• (D) 991
• (E) 992
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Answers

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1. What's the radius of the largest sphere that can be placed inside a cube of volume 64?

• Answer is (E) 2
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• How to solve:
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• 1. If the cube's volume is 64, then each side is 4 wide.
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• 2. The largest circle or sphere that would fit inside this cube would have a diameter of 4.
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• 3. The radius is half the diameter, so its radius would be 2.
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2. One side of this square is on the center of the circle. The circle's radius is 6. What's the area of the blue region?

Answer is (D) 36 - 9

• How to solve:
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• 1. The area of the square is 36.
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• 2. The area of the entire circle is 36.
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• 3. Only 1/4 of the circle is in the drawing. 1/4 of 36 is 9.
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• 4. Subtract the area of the quarter circle from the area of square.
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• 5. The area of the blue region is 36 - 9
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• Answers will almost always be in terms of .
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3. The average of 12 consecutive even integers is 981. What's the highest of these integers?

• Answer is (E) 992
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• How to solve:
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• 1. There are 12 numbers, so we'll draw 12 spaces.
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• 2. The average is 981, so it goes right in the middle.
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• 3. The numbers are consecutive even numbers, so we know what the next number is.
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• 4. And from there, we know what all the other numbers are.
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• 5. The highest is 992.
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