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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]

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15 Sep 2010, 13:36
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45% (medium)

Question Stats:

65% (01:30) correct 35% (01:45) wrong based on 138 sessions

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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, 17:03, edited 3 times in total.

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Re: MGMAT Challenge Problem Showdown [#permalink]

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15 Sep 2010, 13:41
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BOOKMARKED
IMO A

diameter 20,
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, 17:05, edited 2 times in total.

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A circle and a square have the same area. What is the ratio [#permalink]

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15 Sep 2010, 13:47
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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

$$area_{circle}=\pi{\frac{diameter^2}{4}}=area_{square}=\frac{diagonal^2}{2}$$;

$$\pi{\frac{diameter^2}{4}}=\frac{diagonal^2}{2}$$;

$$\frac{diameter^2}{diagonal^2}=\frac{2}{\pi}$$;

$$\frac{diameter}{diagonal}=\frac{\sqrt{2}}{\sqrt{\pi}}=\frac{2}{\sqrt{2\pi}}$$.

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Re: MGMAT Challenge Problem Showdown [#permalink]

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15 Sep 2010, 13:50
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]

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15 Sep 2010, 14:47
Had to copy and paste (pi). Is there a better way?

Posted from my mobile device

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Re: MGMAT Challenge Problem Showdown [#permalink]

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15 Sep 2010, 14:50
zisis wrote:
Had to copy and paste (pi). Is there a better way?

Posted from my mobile device

Mark \pi by [m] button. Also check: http://gmatclub.com/forum/writing-mathe ... 72468.html

hope it helps.
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Re: A circle and a square have the same area. What is the ratio [#permalink]

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05 Jan 2015, 23:04
Hello from the GMAT Club BumpBot!

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A circle and a square have the same area. What is the ratio [#permalink]

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06 Jan 2015, 22:48

Let the area of circle = area of square = 1

$$\pi r^2 = 1$$

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

2r = diameter $$= \frac{2}{\sqrt{\pi}}$$

Side of square = 1

Diagonal $$= \sqrt{2}$$

Ratio $$= \frac{2}{\sqrt{2*\pi}}$$
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Re: A circle and a square have the same area. What is the ratio [#permalink]

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08 Jan 2016, 16:07
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: A circle and a square have the same area. What is the ratio   [#permalink] 08 Jan 2016, 16:07
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