A circular mat

[BTGmoderatorDC]

A circular mat with diameter 20 inches is placed on a square tabletop, each of whose sides is 24 inches long. Which of the following is closest to the fraction of the tabletop covered by the mat?

A. 5/12
B. 2/5
C. 1/2
D. 3/4
E. 5/6

What is the easiest and fastest way to solve this problem?

OA C

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Hi lheiannie07,

We're told that a circular mat with diameter 20 inches is placed on a square tabletop, each of whose sides is 24 inches long. We're asked which of the following fractions is CLOSEST to the fraction of the tabletop covered by the mat.

To start, we'll need to calculate the areas of the two shapes:
Area of circular mat = (pi)(R^2) = (pi)(10^2) = 100pi = approximately 314
Area of square table = (side)^2 = (24)^2 = 576

Now we have to approximate the value of 314/576. Half of 576 would be LESS than 300. Since we're dealing with a numerator of 314, the fraction is clearly GREATER than 1/2. Relative to the other two answers though (3/4 and 5/6), that fraction really isn't close (3/4 of 576 would be pretty close to 3/4 of 600, which would make it a bit less than 450 - and 5/6 would be even greater). Thus, the answer that's closest is 1/2.

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

[Scott@TargetTestPrep]

A circular mat with diameter 20 inches is placed on a square tabletop, each of whose sides is 24 inches long. Which of the following is closest to the fraction of the tabletop covered by the mat?

A. 5/12
B. 2/5
C. 1/2
D. 3/4
E. 5/6


OA C

Since the diameter of the mat is 20 inches, its radius is 10 inches. The area of the mat is:

area = πr^2 = π(10)^2 = 3.14 x 100 = 314 square inches

Since each side of the square tabletop is 24 inches long, the area is:

area = side^2 = 24 x 24 = 576 square inches

Thus, the fraction of the table covered by the mat is 314/576 = 157/288.

157/288 is about 160/290 = 16/29, which is about 1/2.

Answer: C