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A circular mat with diameter 20 inches

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by vinni.k » Wed Jan 02, 2013 2:50 am
A circular mat with diameter 20 inches is placed on a square tabletop, each of whose sides is 24 inch 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

Answer is C

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by sana.noor » Wed Jan 02, 2013 5:47 am
The area of the circle is calculated as C = pie(r^2) as the diameter is 20 thus the radius will be 10 therefore C = pie (10^2) = 314
the area of the square is calculated as S^2, as each side of the square table is 24 inch long thus the area of the square will be 24^2 = 576
The area that is covered by the circular mat is 314/576 = 54% or nearly 1/2....the answer is C
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by GMATGuruNY » Wed Jan 02, 2013 10:33 pm
vinni.k wrote:A circular mat with diameter 20 inches is placed on a square tabletop, each of whose sides is 24 inch 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

Answer is C
Area of the circular mat = �r² ≈ 3*10².
Area of the table = s² = 24².
Mat/table = (3*10*10)/(24*24) = (3*25*4)(3*24*8) ≈ 1/2.

The correct answer is C.
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by Jeff@TargetTestPrep » Thu Dec 14, 2017 9:18 am
vinni.k wrote:A circular mat with diameter 20 inches is placed on a square tabletop, each of whose sides is 24 inch 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
Since the diameter of the mat is 20 inches, the 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

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