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A circle is circumscribed around a square and inscribed in a

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GMAT Instructor
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A circle is circumscribed around a square and inscribed in a [#permalink]  09 Jul 2006, 02:40
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A circle is circumscribed around a square and inscribed in a larger square. A point inside the larger square is chosen at random. Which of the following best approximates the probability that this point is inside the circle but outside the square inscribed in the circle?

(A) 28% (B) 31% (C) 35% (D) 39% (E) 43%
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Re: PS: Geometry/Probability [#permalink]  09 Jul 2006, 17:30
kevincan wrote:
A circle is circumscribed around a square and inscribed in a larger square. A point inside the larger square is chosen at random. Which of the following best approximates the probability that this point is inside the circle but outside the square inscribed in the circle?

(A) 28% (B) 31% (C) 35% (D) 39% (E) 43%

Let,
diagonal of inside square - 2r, side = sqrt(2)*r
side of larger square - 2r

Prob = (pi*r^2 - 2^r^2)/4r^2 = 28% (A)
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Let radius of circle = r
Area of circle = PI*r^2
Total Area (Area of outer square) = (2r)*(2r)
Area of inner circle = (SQRT(2)*r)^2 = 2r^2

Prob = (PI*r^2 - 2r^2)/4r^2 = (PI-2)/4 = 28% approx.
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SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

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A circle is circumscribed around a square and inscribed in a larger square. A point inside the larger square is chosen at random. Which of the following best approximates the probability that this point is inside the circle but outside the square inscribed in the circle?

(A) 28% (B) 31% (C) 35% (D) 39% (E) 43%

If you look at the answers you'd notice that only (A) when subtracted from 100 would result in an amount equally divided by 4 ( 4 quadrants of a square) = 100 - 28 = 72 /4 = 18. I used this as a short cut to estimate my answer.

That's the shortest way I could find the answer. What do you guys think??
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I'll Go with A.
Just curious, where did you get this question from. I took GMAT in 2000 and remember seeing something very similar.
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GMAT Instructor
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I make them up. I took the GMAT 17 years ago. It's nice to know that sometimes I am on the same wavelength as the exam writers. The main thing, though, is to hone your skills!
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