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A circular mat with diameter 20 inches is placed on a square tabletop,

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A circular mat with diameter 20 inches is placed on a square tabletop,  [#permalink]

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New post 05 Oct 2018, 00:48
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A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

55% (01:47) correct 45% (02:10) wrong based on 65 sessions

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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

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Re: A circular mat with diameter 20 inches is placed on a square tabletop,  [#permalink]

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New post 05 Oct 2018, 01:09
My approach..

Area of circle is 100pi approx 314.

Area of square is 576

Fraction= (576-314)/576

262/576

50% of 576 is 288..
It has to be slightly less than 50% so E

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Re: A circular mat with diameter 20 inches is placed on a square tabletop,  [#permalink]

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New post 05 Oct 2018, 03:52
Given radius=10 & Side=24
Area of circle=πr^2=3.14*10^2=314

Area of square=(Side)^2=24^2= 576

Required Fraction= Area not covered by circle/Total area of square=(576-314)/576=262/576 =131/288 =slightly less than 1/2

Since,9/20=0.45 closed of all choices,answer should be E.
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A circular mat with diameter 20 inches is placed on a square tabletop,  [#permalink]

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New post 05 Oct 2018, 04:52
Bunuel wrote:
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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Re: A circular mat with diameter 20 inches is placed on a square tabletop,  [#permalink]

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New post 09 Oct 2018, 10:39
Bunuel wrote:
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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Re: A circular mat with diameter 20 inches is placed on a square tabletop, &nbs [#permalink] 09 Oct 2018, 10:39
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