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# GRE Math Challenge #69-If the radius of a circular region

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GRE Math Challenge #69-If the radius of a circular region [#permalink]  03 May 2015, 01:23
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Question Stats:

100% (00:07) correct 0% (00:00) wrong based on 2 sessions
If the radius of a circular region were decreased by 20 percent, the area of the circular region would decrease by what percent?

A. 16%
B. 20%
C. 36%
D. 40%
E. 44%
[Reveal] Spoiler: OA

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Sandy
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Re: GRE Math Challenge #69-If the radius of a circular region [#permalink]  12 Dec 2017, 11:24
sandy wrote:
If the radius of a circular region were decreased by 20 percent, the area of the circular region would decrease by what percent?

A. 16%
B. 20%
C. 36%
D. 40%
E. 44%

Let us take the radius as = 10
Therefore the area of the circular region = $$pi * r^2$$

=$$pi *10^2$$
=100pi

Now the radius is decreased by 20 percent

i.e 10-(10 * 0.2) = 8, which is the new radius

Therefore area of the circular region with the new radius = $$pi * 8^2$$
=64pi

Therefore the area of the circular region decreased = $$\frac{(New - old)}{old}$$ = $$\frac{(64pi - 100pi)}{100pi}$$= $$-36%$$ (The value is negative because the percentage is decreased)
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Re: GRE Math Challenge #69-If the radius of a circular region   [#permalink] 12 Dec 2017, 11:24
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# GRE Math Challenge #69-If the radius of a circular region

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