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

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26 Aug 2010, 07:34

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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 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?

Now this fraction is obviously between 1/2 and 3/4 --> \(\frac{1}{2}=\frac{144}{288}\) and \(\frac{3}{4}=\frac{216}{288}\) --> 157 is closer to 144 than to 216.

Hi Bunel Please let me clarify how did you establish 1/2=144/288 and 1/3= 216/288???

Rgds Prasannajeet

To compare 157/288, 1/2 ans 1/3 find their common denominator, which is 288 --> 1/2=144/288 (multiply by 144) and 1/3= 216/288 (multiply by 216).
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Re: A circular mat with diameter 20 inches is placed on a square [#permalink]

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29 Jul 2013, 02:25

udaymathapati wrote:

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

Simplified the numbers as below: Req fraction is (3.14 * 10 * 10)/(24 * 24) Cancel 10 and 24 by 2: (3.14 * 5 * 5)/(12 * 12) Cancel 5*5=25 in numerator with 12 in denominator: (3.14 * 2.something)/(1 * 12) = 6.something / 12 =~1/2. (Here it is important to note that 2.something and 6.something are in the lower end, i.e., much lesser than 2.5 and 6.5.) Bunuel has given a standard way to deal with fraction comparison in the previous posts. In some cases, the above sort of simplifications might help in getting a fraction with realtively smaller numerator and denominators.

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

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25 Feb 2015, 22:35

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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

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04 Nov 2015, 14:41

if D = 20, then r = 10, and area of the circle is 100 pi (I converted pi to 22/7) and thus the area is 2200/7 area of the square is 24^2 = 576 now, to find the area that is covered by the circle, divide 2200/7 by 576. get 2200/4032, which is slightly more than 1/2.

other method, 2200/7 is slightly more than 300 300+/576 = aprox 1/2

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

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18 Feb 2017, 02:43

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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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

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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