Circle Question

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neoshichhadva: Newbie | Next Rank: 10 Posts; Posts: 9; Joined: Wed May 25, 2011 10:51 pm

by neoshichhadva » Tue Aug 09, 2011 8:16 am

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

[spoiler]OA: E; I got C. Please explain[/spoiler]

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gmatboost: Master | Next Rank: 500 Posts; Posts: 312; Joined: Tue Aug 02, 2011 3:16 pmFollowed by: 33 members; Location: New York City; Thanked: 130 times; GMAT Score:780

by gmatboost » Tue Aug 09, 2011 9:40 pm

Well, the circular mat has a radius of 10, so an area of pi*r^2 = 100pi, which is about 314.
The table is 24*24 = 576.

314/576 is [spoiler]clearly more than 1/2 and less than 3/5[/spoiler], so it seems that your choice is right.

To simplify further...
[spoiler]314/576 =
157/288 =
similar to 156/288 =
78/144 =
39/72 =
13/24[/spoiler]

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Ozlemg: Master | Next Rank: 500 Posts; Posts: 407; Joined: Tue Jan 25, 2011 9:19 amFollowed by: 7 members; Thanked: 25 times

by Ozlemg » Wed Aug 10, 2011 6:24 am

neoshichhadva 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

[spoiler]OA: E; I got C. Please explain[/spoiler]

it might be wrong or silly but if I solve as below, result is E... I dont know how? :S

area of square : 576
area of circle : approx 314

576-314 =262

262/314 = 5/6

Hence E

The more you suffer before the test, the less you will do so in the test!

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gmatboost: Master | Next Rank: 500 Posts; Posts: 312; Joined: Tue Aug 02, 2011 3:16 pmFollowed by: 33 members; Location: New York City; Thanked: 130 times; GMAT Score:780

by gmatboost » Wed Aug 10, 2011 7:50 am

Which of the following is closest to the fraction of the tabletop covered by the mat?

To answer this question, we need to divide area_mat/area_tabletop

262 is the area of the tabletop NOT covered by the mat. 314 is the area of the tabletop that IS covered by the mat. So 262/314 gives the ratio of the part of the tabletop uncovered to the part that is covered.

To get area_mat/area_tabletop we need to do [spoiler]314/576[/spoiler].

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