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# If a circle is inscribed in a square as shown above, is the area of th

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If a circle is inscribed in a square as shown above, is the area of th  [#permalink]

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13 Sep 2018, 02:23
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55% (hard)

Question Stats:

58% (01:55) correct 42% (01:57) wrong based on 28 sessions

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If a circle is inscribed in a square as shown above, is the area of the circle greater than 16π?

(1) The area of the square is greater than16.
(2) Each of the four shaded regions between the square and the circle has an area equal to 9 – 9/4*π.

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image014.gif [ 782 Bytes | Viewed 386 times ]

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If a circle is inscribed in a square as shown above, is the area of th  [#permalink]

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13 Sep 2018, 03:50
Bunuel wrote:

If a circle is inscribed in a square as shown above, is the area of the circle greater than 16π?

(1) The area of the square is greater than16.
(2) Each of the four shaded regions between the square and the circle has an area equal to 9 – 9/4*π.

Attachment:
image014.gif

Question: Is area of circle > 16π?
Question: Is Radius of circle > 4?
Question: Is Side of the square > 8?

Statement 1: The area of the square is greater than16.
i.e. side of square > 4
but it may or may not be greater than 8 hence
NOT SUFFICIENT

Statement 2: Each of the four shaded regions between the square and the circle has an area equal to 9 – 9/4*π.
i.e. $$(1/4[(2r)^2 - πr^2] = 9 - (9/4)π$$
i.e. r = 3
i.e. r is NOT greater than 4 hence

SUFFICIENT

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Re: If a circle is inscribed in a square as shown above, is the area of th  [#permalink]

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13 Sep 2018, 03:55
By the first statement, we can say that the area of circle will be minimum 4*Pie i.e., approx 12 but it can also be greater than 16. Hence Insufficient.
By the second statement, we will get a specific value of radius. Hence sufficient.
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Re: If a circle is inscribed in a square as shown above, is the area of th  [#permalink]

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13 Sep 2018, 03:58
GMATinsight:

Statement 2: Each of the four shaded regions between the square and the circle has an area equal to 9 – 9/4*π.
i.e. (1/4[(2r)2−πr2]=9−(9/4)π(1/4[(2r)2−πr2]=9−(9/4)π
i.e. r = 3
i.e. r is NOT greater than 4 hence

Hello, could you please explain statement 2:
LHS of i.e. (1/4[(2r)2−πr2]=9−(9/4)π

How did you arrive at it?
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Re: If a circle is inscribed in a square as shown above, is the area of th  [#permalink]

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13 Sep 2018, 04:09
1
archish3113 wrote:
GMATinsight:

Statement 2: Each of the four shaded regions between the square and the circle has an area equal to 9 – 9/4*π.
i.e. (1/4[(2r)2−πr2]=9−(9/4)π(1/4[(2r)2−πr2]=9−(9/4)π
i.e. r = 3
i.e. r is NOT greater than 4 hence

Hello, could you please explain statement 2:
LHS of i.e. (1/4[(2r)2−πr2]=9−(9/4)π

How did you arrive at it?

archish3113

One shaded portion at one of the corners = (1/4)*(Area of Square - Area of Circle) = $$(1/4)*[(2r)^2−πr^2]=9−(9/4)π$$

Side of the square = 2r i.e. area of square = $$(2r)^2$$

I hope this helps!!!

P.S. The Circle is inscribed in square i.e. Circle is tightly packed and touching all sides of teh square
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Re: If a circle is inscribed in a square as shown above, is the area of th  [#permalink]

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13 Sep 2018, 04:19
GMATinsight : understood where I was going wrong, thanks ...
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Re: If a circle is inscribed in a square as shown above, is the area of th   [#permalink] 13 Sep 2018, 04:19
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