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Official Solution: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%, approximately by what percent does the area between the circles grow? A. 140% B. 141% C. 190% D. 192% E. 292% The area between the circles is the difference between their areas: \(\pi R^2  \pi r^2\). Find the increase: \(\frac{\pi R_2^2  \pi r_1^2}{\pi R_1^2  \pi r_1^2} =\) \(\frac{R_2^2  r_1^2}{R_1^2  r_1^2} =\) \(\frac{11^2  4^2}{10^2  8^2} =\) \(\frac{121  16}{100  64} =\) \(\frac{105}{36} = 2\frac{33}{36} =\) \(3  \frac{1}{12} \approx 2.92\) The area between the circles grew by 192%. Answer: D
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Re: M0137
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12 Mar 2015, 08:01
Bunuel wrote: Official Solution:
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%, approximately by what percent does the area between the circles grow?
A. 140% B. 141% C. 190% D. 192% E. 292%
The area between the circles is the difference between their areas: \(\pi R^2  \pi r^2\). Find the increase: \(\frac{\pi R_2^2  \pi r_1^2}{\pi R_1^2  \pi r_1^2} =\) \(\frac{R_2^2  r_1^2}{R_1^2  r_1^2} =\) \(\frac{11^2  4^2}{10^2  8^2} =\) \(\frac{121  16}{100  64} =\) \(\frac{105}{36} = 2\frac{33}{36} =\) \(3  \frac{1}{12} \approx 2.92\) The area between the circles grew by 192%.
Answer: D Hi Bunuel. What formula did you use to solve for the increase? Since you divided the new difference by the old difference, this doesn't look like the percent change formula. Thanks!



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12 Mar 2015, 23:16
i think we are taking difference as 36 instead of 36pie.
the old difference if 36pie , apprx 108 and new difference is 105pie, approx 315.
difference between 315108 = 207.
using the percentage difference formula, 207/108*100 ~ 192%
is the above right?



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Re: M0137
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13 Mar 2015, 04:09
Hello,
In the above answer it received ~2.92. in percentages it will be 292%. Why answer D is true and not E?



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Re: M0137
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13 Mar 2015, 06:58
samners wrote: Bunuel wrote: Official Solution:
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%, approximately by what percent does the area between the circles grow?
A. 140% B. 141% C. 190% D. 192% E. 292%
The area between the circles is the difference between their areas: \(\pi R^2  \pi r^2\). Find the increase: \(\frac{\pi R_2^2  \pi r_1^2}{\pi R_1^2  \pi r_1^2} =\) \(\frac{R_2^2  r_1^2}{R_1^2  r_1^2} =\) \(\frac{11^2  4^2}{10^2  8^2} =\) \(\frac{121  16}{100  64} =\) \(\frac{105}{36} = 2\frac{33}{36} =\) \(3  \frac{1}{12} \approx 2.92\) The area between the circles grew by 192%.
Answer: D Hi Bunuel. What formula did you use to solve for the increase? Since you divided the new difference by the old difference, this doesn't look like the percent change formula. Thanks! It gives a fraction/ratio. If the ratio is 2.92, then it means that the growth was by 192%. For example, the growth from x to 2,92x means the growth by 192%: x + 1.92x = 2.92x.
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Re: M0137
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19 Feb 2016, 12:53
Change in big circle: 10^28^2 = 36 Change in small circle: 11^24^2 = 105
105 is barely less than 3 times bigger. 3 times bigger is 200% increase so D is the closest.



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26 Apr 2016, 06:16
I think this is a highquality question and I agree with explanation.



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03 Aug 2016, 06:58
Can I simply assume the extra 1 radius point area and take out 1 (from the 100% of the previous area)? Is it a good approximation? πr^2= 22/7*1^21 ≈ 200% So, D



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27 Aug 2016, 00:48
I got to a point when I had to choose between 190% and 192%, then I saw that among answers there is 292%, which clearly indicated that the correct answer is 192%. GMAT sometimes tries to trick those, who don't subtract 1, and sometime this trick in turn helps to arrive to the correct answer.



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25 Sep 2016, 11:04
105 is new area and 36 is old area
(10536)/36 = 1.92



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23 Mar 2017, 07:13
What is 1/12 in '3−1/12≈2.92'??
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16 Apr 2017, 13:54
I did this a little differently. The official answer makes it very easy to make a careless mistake. I think this is easier to follow:
r1 = 8 R1 = 10 a1 = 64pi A1 = 100 pi difference1 = 100pi  64pi = 36pi
r2 = 4pi R2 = 11pi a2 = 16pi A2 = 121pi difference2 = 121pi  16pi = 105 pi
growth = 105pi  36pi = 69pi %growth = 69pi/36pi * 100 = 23*25/3 = 575/3 = 191.66666667 which is about 192. Answer is D



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27 Apr 2018, 03:02
Intial Spacing = 36pi Final Spacing = 105pi 36pi corresponds to >100% Then, 105pi corresponds to>(100%/36pi)*105pi ~ 292% Growth Percentage = 292%100% = 192%
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05 Nov 2018, 06:39
irinabarvi wrote: I think this is a highquality question and I agree with explanation. I agree as well. I was tempted to chose option E which was deceptive..If X was orginal areas and 2X is increases area means Ratio=2X/X but actual increase in area from X ..its is X



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25 Feb 2019, 13:05
I think this is a highquality question and I agree with explanation.
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