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# A gym has a square floor covered with a circular rug.

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General GMAT Forum Moderator
Joined: 29 Jan 2015
Posts: 1309
Location: India
WE: General Management (Non-Profit and Government)
A gym has a square floor covered with a circular rug.  [#permalink]

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27 Feb 2018, 03:47
2
00:00

Difficulty:

65% (hard)

Question Stats:

63% (03:13) correct 37% (03:17) wrong based on 46 sessions

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A gym has a square floor covered with a circular rug. The rug has a common center with the floor and has a circumference of 236 feet. If the shortest distance between the edge of the rug and side of the floor is 17.5 feet, what is area of the square floor?

(A) 5,650
(B) 8,560
(C) 10,040
(D) 12,100
(E) 12,550

Source: Master GMAT.

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Re: A gym has a square floor covered with a circular rug.  [#permalink]

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27 Feb 2018, 05:10
The problem is a circle inside a square, but the side of the square and circle are not touching.
The shortest distance between edge of rug(circle) and the side of square is given 17.5 feet. The shortest distance is the distance measured parallel to the side of the square, not the one parallel to the diagonal of the square.
therefore, side of square = diameter or circle + 2*17.5
given circumference of circle = 236 feet

2*pi*r=236
2r=75.09

side of square = 75(approx)+35 = 110
Area of square = 110*110 = 12100

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Re: A gym has a square floor covered with a circular rug.  [#permalink]

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07 Jun 2019, 05:56
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Re: A gym has a square floor covered with a circular rug.   [#permalink] 07 Jun 2019, 05:56
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