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Circular mat

by massi2884 » Thu Apr 12, 2012 11:46 am
A circular mat with diameter 20 inches is places 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?

5/12
2/5
1/2
3/4
5/6
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by GMATGuruNY » Thu Apr 12, 2012 12:05 pm
massi2884 wrote:A circular mat with diameter 20 inches is places 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?

5/12
2/5
1/2
3/4
5/6
Area of the mat = �r² = �(10²) ≈ 3*10*10.
Area of the table = s² = 24².
Mat/table = (3*10*10)/(24*24) = (3*5*5)/(12*12) = 25/48 ≈ 1/2.

The correct answer is C.
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by Anurag@Gurome » Fri Apr 13, 2012 4:02 am
massi2884 wrote:A circular mat with diameter 20 inches is places 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?

5/12
2/5
1/2
3/4
5/6
Area of circle = (pi)r² implies area of circular mat = (pi)(10)² = 100(pi) = 314 approx
Area of square = (side)² = (24)² = 576
So, area of circular mat : area of square = 314 : 576 = 157 : 288, which is between 1/2 and 3/4, as 144/288 = 1/2 and 216/288 = 3/4 and 157 is closer to 144 than 216.

So, the correct answer is C.
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