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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, 12:21
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Difficulty:

55% (hard)

Question Stats:

59% (02:20) correct 41% (02:28) wrong based on 46 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
Intern
Joined: 07 Feb 2019
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21 Apr 2019, 16:01
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Expert solution is essential.

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Director
Status: Learning stage
Joined: 01 Oct 2017
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WE: Supply Chain Management (Energy and Utilities)

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21 Apr 2019, 18:07
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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GMAT Tutor
Joined: 24 Jun 2008
Posts: 2012

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31 Aug 2010, 13:03
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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Joined: 16 Mar 2010
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31 Aug 2010, 23:45
Remember: % increase/decrease=change/starting point
Re: There are two concentric circles with radii 10 and 8. If the radius of   [#permalink] 31 Aug 2010, 23:45
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