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# There are two concentric circles with radii 10 and 8. If the radius of

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Intern
Joined: 09 Feb 2010
Posts: 39

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31 Aug 2010, 13:21
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Difficulty:

55% (hard)

Question Stats:

59% (02:19) correct 41% (02:27) wrong based on 44 sessions

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There are two concentric circles with radii 10 and 8. If the radius of the outer circle is increased by 10% and the radius of the inner circle decreased by 50%, by what percent does the area between the circles grow?

140%
141%
190%
192%
292%

If i calculation 105/36 i get 2.91 and that * 100 gives 291 or approx 292%

but the correct answer is not that
GMAT Tutor
Joined: 24 Jun 2008
Posts: 1829

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31 Aug 2010, 14:03
zest4mba wrote:
There are two concentric circles with radii 10 and 8. If the radius of the outer circle is increased by 10% and the radius of the inner circle decreased by 50%, by what percent does the area between the circles grow?

140%
141%
190%
192%
292%

If i calculation 105/36 i get 2.91 and that * 100 gives 291 or approx 292%

but the correct answer is not that

Your calculations are fine, but you then need to answer the question asked. The question is about percent increase. You've proven that the new area is 2.92 times the old area, but that is only an increase of 192%.
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Manager
Joined: 17 Mar 2010
Posts: 127

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01 Sep 2010, 00:45
Remember: % increase/decrease=change/starting point
Intern
Joined: 07 Feb 2019
Posts: 14

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21 Apr 2019, 17:01
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Expert solution is essential.

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Director
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21 Apr 2019, 19:07
1
zest4mba wrote:
There are two concentric circles with radii 10 and 8. If the radius of the outer circle is increased by 10% and the radius of the inner circle decreased by 50%, by what percent does the area between the circles grow?

140%
141%
190%
192%
292%

If i calculation 105/36 i get 2.91 and that * 100 gives 291 or approx 292%

but the correct answer is not that

Original area between the two circles=$$\pi*(10^2-8^2)=\pi*6^2$$
Area between the two circles upon change in radii=$$\pi*(11^2-4^2)=\pi*105$$

%change in Area=(Change in Area/Original Area)*100=$$\frac{(\pi*105-\pi*36)}{\pi*36}*100$$=191.66% or 192%(Approx.)

Ans. (D)
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Re: There are two concentric circles with radii 10 and 8. If the radius of   [#permalink] 21 Apr 2019, 19:07
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