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# M01-37

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Math Expert
Joined: 02 Sep 2009
Posts: 58322

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16 Sep 2014, 00:16
11
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Difficulty:

55% (hard)

Question Stats:

61% (02:20) correct 39% (02:28) wrong based on 241 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%, approximately by what percent does the area between the circles grow?

A. 140%
B. 141%
C. 190%
D. 192%
E. 292%

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Math Expert
Joined: 02 Sep 2009
Posts: 58322

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16 Sep 2014, 00:16
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%.

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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%.

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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Joined: 02 Jun 2012
Posts: 19

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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 315-108 = 207.

using the percentage difference formula, 207/108*100 ~ 192%

is the above right?
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Joined: 08 Jan 2015
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13 Mar 2015, 04:09
Hello,

in percentages it will be 292%. Why answer D is true and not E?
Math Expert
Joined: 02 Sep 2009
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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%.

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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19 Feb 2016, 12:53
4
Change in big circle: 10^2-8^2 = 36
Change in small circle: 11^2-4^2 = 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 high-quality question and I agree with explanation.
Manager
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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*1^2-1
≈ 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
1
105 is new area and 36 is old area

(105-36)/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
3
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.
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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 high-quality 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 high-quality question and I agree with explanation.
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09 Jul 2019, 13:42
Bunuel 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%, approximately by what percent does the area between the circles grow?

A. 140%
B. 141%
C. 190%
D. 192%
E. 292%

B = big circle, s = small circle

Original:
rB (Big) = 10, Area B = 100
rs (small) = 8, Area s = 64
Area A - Area s = 100-64 = 36

Change:
rB*11/10 = 11
rs*1/2 = 4

New:
Area B = 121
Area s = 16
Area B - Area s = 121 - 16 = 105

Difference in new area / Difference in original area = Percent new over original
105 / 36 = 2 & 33/36 = 2 & 11/12, 1/12 is .083 so it's about 2.92.
We have to remember that "by what percent does the area between the circles grow?" means what is the INCREASE rather than PERCENT OF. So, 2.92 - 1 = 1.92
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25 Jul 2019, 08:58
I think this is a high-quality question and I agree with explanation.
Re M01-37   [#permalink] 25 Jul 2019, 08:58
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# M01-37

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