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A circle and a square have the same area. What is the ratio

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A circle and a square have the same area. What is the ratio [#permalink] New post 15 Sep 2010, 12:36
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A
B
C
D
E

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A circle and a square have the same area. What is the ratio of the diameter of the circle to the diagonal of the square?

(A) 2 : \sqrt{(2\pi)}
(B) 1 : 2\sqrt{\pi}
(C) 2\sqrt{\pi} : \sqrt{2}
(D) 1 : \sqrt{2}
(E) 1 : 2\pi
[Reveal] Spoiler: OA

Last edited by zisis on 16 Sep 2010, 16:03, edited 3 times in total.
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Re: MGMAT Challenge Problem Showdown [#permalink] New post 15 Sep 2010, 12:41
IMO A

diameter 20,
radius= 10
πr^2 = 100π
area = 100π
side = \sqrt{100\pi}
diagonal = Side * \sqrt{2} = 10\sqrt{(2\pi)}

ratio
20 : 10\sqrt{(2\pi)}
= 2 : \sqrt{(2\pi)}

Last edited by zisis on 16 Sep 2010, 16:05, edited 2 times in total.
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Re: MGMAT Challenge Problem Showdown [#permalink] New post 15 Sep 2010, 12:47
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zisis wrote:
A circle and a square have the same area. What is the ratio of the diameter of the circle to the diagonal of the square?

(A) 2 : √(2)
(B) 1 : 2√
(C) 2√ : √2
(D) 1 : √2
(E) 1 : 2


area_{circle}=\pi{\frac{diameter^2}{4}}=area_{square}=\frac{diagonal^2}{2} --> \pi{\frac{diameter^2}{4}}=\frac{diagonal^2}{2} --> \frac{diameter^2}{diagonal^2}=\frac{2}{\pi} --> \frac{diameter}{diagonal}=\frac{\sqrt{2}}{\sqrt{\pi}}=\frac{2}{\sqrt{2\pi}}.

Answer: A.

Pleas format the answers properly.
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Re: MGMAT Challenge Problem Showdown [#permalink] New post 15 Sep 2010, 12:50
zisis wrote:
A circle and a square have the same area. What is the ratio of the diameter of the circle to the diagonal of the square?

(A) 2 : √(2π)
(B) 1 : 2√π
(C) 2√π : √2
(D) 1 : √2
(E) 1 : 2π


\pi r^2 = a^2

\frac{r}{a} = \frac{1}{\sqrt{\pi}}

\frac{2r}{\sqrt{2}a} = \frac{2}{\sqrt{2\pi}}

Hence A
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Re: MGMAT Challenge Problem Showdown [#permalink] New post 15 Sep 2010, 13:47
Had to copy and paste (pi). Is there a better way?

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Re: MGMAT Challenge Problem Showdown [#permalink] New post 15 Sep 2010, 13:50
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Re: MGMAT Challenge Problem Showdown   [#permalink] 15 Sep 2010, 13:50
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