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Bunuel
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Bunuel
A circular mat with diameter 20 inches is placed on a square tabletop, having its sides equal to 24 inches. Which of the following is closest to the fraction of the tabletop NOT covered by the mat?

(A) 1/2

(B) 3/5

(C) 2/3

(D) 1/4

(E) 9/20

Area of tabletop = 24^2 = 576

Area of circular mat = 10^2 * pi approximately equal to 314

314/576 is what is currently covered.

This is more than half. So what is not covered must be slightly less than half this directly eliminates A,B, and C

So answer choice E.

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Bunuel
A circular mat with diameter 20 inches is placed on a square tabletop, having its sides equal to 24 inches. Which of the following is closest to the fraction of the tabletop NOT covered by the mat?

(A) 1/2

(B) 3/5

(C) 2/3

(D) 1/4

(E) 9/20


Since the radius of the mat is 20/2 = 10 inches, the area of the mat is π(10)^2 = 100π square inches.

Since a side of the tabletop is 24 inches, the area of the tabletop is 24^2 = 576 square inches.

Therefore, the mat covers 100π/576 ≈ 0.55 = 11/20 of the tabletop and hence 9/20 of the table top is not covered by the mat.

Answer: E
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area table is 576
area circle is 100pi = 314

576-314 = 262 not covered

fraction not covered
262/576 = 131/288 which is about 130/290 = 13/29

13/29 is just under half, so 9/20.
Tricky because they put it way at the bottom and put 1/2 at the top.
If you're not careful, you'll just select 1/2 because its pretty close.
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