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

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A circular mat with diameter 20 inches is placed on a square [#permalink] New post 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. 5/12
B. 2/5
C. 1/2
D. 3/4
E. 5/6
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Re: Closest Fraction Calculation Problem [#permalink] New post 26 Aug 2010, 08:37
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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


area_{circle}=\pi{r^2}=\pi{10^2}\approx{314} (d=20 --> r=10);
area_{square}=24^2=576;

\frac{area_{circle}}{area_{square}}=\frac{314}{576}=\frac{157}{288}.

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.

Answer: C.
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Re: Closest Fraction Calculation Problem [#permalink] New post 27 Aug 2010, 05:29
Nice explanation Bunuel... Thanks
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Re: GWD #1 Math 7 [#permalink] New post 05 Apr 2012, 12:49
SO we are looking for the area of the cloth over the area of the table

Area of the Cloth = (pi)(r)^2 which is about (3)(10)(10)

Area of the Table = (24)(24)

So the quick way to estimate is looking at the fraction like this: (3/24)(100/24)

I hope this is easy to follow, so with some simplification i get (1/8)(4) = (1/2) Answer is C
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Re: A circular mat with diameter 20 inches is placed on a square [#permalink] New post 04 May 2013, 04:07
Hi Bunel
Please let me clarify how did you establish 1/2=144/288 and 1/3= 216/288???

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Re: A circular mat with diameter 20 inches is placed on a square [#permalink] New post 04 May 2013, 04:31
prasannajeet wrote:
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] 04 May 2013, 04:31
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