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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] New post 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] New post 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,
radius of circle -- r
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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 [#permalink] New post 09 Jul 2006, 18:30
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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 [#permalink] New post 15 Jul 2006, 10:54
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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 [#permalink] New post 21 Jul 2006, 18:54
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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 [#permalink] New post 22 Jul 2006, 00:10
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!
  [#permalink] 22 Jul 2006, 00:10
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