Circular mat

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massi2884: Senior | Next Rank: 100 Posts; Posts: 95; Joined: Tue Sep 13, 2011 3:19 pm; Thanked: 3 times; GMAT Score:710

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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Source: Beat The GMAT — Problem Solving | Thu Apr 12, 2012 11:46 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

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 = âˆ�rÂ² = âˆ�(10Â²) â‰ˆ 3*10*10.
Area of the table = sÂ² = 24Â².
Mat/table = (3*10*10)/(24*24) = (3*5*5)/(12*12) = 25/48 â‰ˆ 1/2.

The correct answer is C.

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

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)rÂ² implies area of circular mat = (pi)(10)Â² = 100(pi) = 314 approx
Area of square = (side)Â² = (24)Â² = 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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