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# m01-q37

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Manager
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16 May 2009, 07:46
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?

(A) 140%
(B) 141%
(C) 190%
(D) 192%
(E) 292%

[Reveal] Spoiler: OA
D

Source: GMAT Club Tests - hardest GMAT questions

I don't agree with OA, Can anybody please explain?
When it says 'grow', we need to take the difference between new and old.
However, the OE simply does new/old instead of (new-old)/old.
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17 Sep 2010, 15:37
2
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well the correct answer is D 192 %
THE explanation is as follows.....

The given radius of the concetic circle is 10 cm and 8 cm respectively
so the corresponding area (πr2 ) is 100π and 64π... and the differnc betn area is (100π-644π=36π)
now outer radius increase by 10 % means the new outer radius is 11 cm and area in 121π
inner radius decrease by 50 % means new inner radius is 4 cm and area is 16π
differnce between the area is (121π - 16π = 105π)
percentage growth in area = (new-old/old) x 100 %
= (105π-36π)/36π x 100%
=191.77 % approx 192 %
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21 Sep 2011, 09:03
2
KUDOS
Percent change problem:
You can ignore pi because it cancels out of all equations.

Initial concentric circles have a difference in area of:
Area 1 - Area 2 = 8^2 - 100^2 = 36

Apply changes to radii and calculate new areas:
Outer circle: 10*1.10 = 11 therefore, A=121
Inner circle: 8*.5= 4 therefore, A=16
Calculate difference in areas:
12-16= 105

Then set up like any percent change problem:
Change in areas= 105-36 = 69
X = percent change
Therefore, 69/36 = X/100
36X = 6900
X=192%
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18 May 2009, 15:22
1
KUDOS
The official answer does indeed take new/old but at the end it subtracts 1. This gives the same answer that would result had they calculated (new-old)/old.

Or... (new-old)/old = new/old - old/old = new/old - 1.

Hope that helps.
millhouse

pmal04 wrote:
I don't agree with OA, Can anybody please explain?
When it says 'grow', we need to take the difference between new and old.
However, the OE simply does new/old instead of (new-old)/old.

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?

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17 Sep 2010, 06:50
1
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You don't need to calculate the area.
Its just a ratio, so all you have to do is- 11*11-4*4-(10*10-8*8)/(100-64)
So, its 192%
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24 Oct 2010, 18:58
1
KUDOS
ichha148 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?

(A) 140%
(B) 141%
(C) 190%
(D) 192%
(E) 292%

Source: GMAT Club Tests - hardest GMAT questions

Initially the area between the circles = 100 pie - 64 pie = 36 pie

new radii of outer circle = 1.1*10 = 11
new radii of inner circle = 8/2 = 4

area between them = (121-16) pie = 105pie

difference = 105-36 = 69pie

% = 69/36 * 100 = 23/12 * 100 = slightly less than 200 thus D.

I think you are not dividing the difference by previous value.
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16 Dec 2011, 17:04
1
KUDOS
Unless there is some kind of trick I am not aware of, the answer will have to be devised by long division - all the way to the 4th number in order to accurately identify the solution. Not very typical for GMAT questions, since GMAC claims they are not testing our long division skills - rather our ability to find short exact ways to an answer.
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25 Sep 2013, 01:06
1
KUDOS
pmal04 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?

(A) 140%
(B) 141%
(C) 190%
(D) 192%
(E) 292%

[Reveal] Spoiler: OA
D

Source: GMAT Club Tests - hardest GMAT questions

I don't agree with OA, Can anybody please explain?
When it says 'grow', we need to take the difference between new and old.
However, the OE simply does new/old instead of (new-old)/old.

Before: Area between two circles = A1 - A2 = Pi(10^2 - 8^2) = (10-8)(10+8)Pi = 36Pi
After: Area between two circles = A'1 - A'2 = Pi(11^2 - 4^2) = (11-4)(11+4)Pi = 105Pi

Percentage increase = [105 - 36]/36 * 100%
= 69/36* 100%
= [36 + 33]/36 * 100%
= 100% + 33/36*100%
= 100% + 11/12*100%
= 100% + 92%
= 192%

Tip:
9/10 = 90%;
10/11 = 91%;
11/12 = 92%

This rule helps you pick a correct answer between C and D quickly.

Hope it helps.
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19 May 2009, 06:20
Hi millhouse,
Why is it (new-old)/old ? it should have been new/old. Thanks
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20 May 2009, 13:45
I dont know how to explain this other than by example...

If 100 is increased to 120 how much did it grow by?
ans: 20%
i.e. (new-old)/old = (120-100)/100 = 20%

new/old would yield 120% which is wrong.

pmal04 wrote:
Hi millhouse,
Why is it (new-old)/old ? it should have been new/old. Thanks
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26 Sep 2009, 16:42
Well the answer should be 292% ... 121-36/36 .. but the OA says 192% . Am bummed.
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27 Sep 2009, 06:56
Hi,

Doesn't the quoted message answer your question? If you use the formula $$\frac{new}{old}$$, you have to subtract 1 to get the right answer.

Hope it helps.
millhouse wrote:
I dont know how to explain this other than by example...

If 100 is increased to 120 how much did it grow by?
ans: 20%
i.e. (new-old)/old = (120-100)/100 = 20%

new/old would yield 120% which is wrong.

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Senior Manager
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10 Nov 2009, 09:01
The options for this question- 190 and 192, are quite close.
With quick calculations I came to (23/12)*100=(23/3)*25
Here is where I did the mistake and used (23/3)=7.6 (instead of 7.67 or 7.7) with the result of 190! But I feel these kind of round-offs work in actual exams?
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11 Jan 2010, 11:29
I was also confused by getting 191...with something. I think that on the real test the question would include a phrase like "approximately" or "rounded to the nearest integer"
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17 Sep 2010, 06:23
The answer is the value of 69/36 which should be near to 200%. From the answer choices we have two options closer to 200.

If you check the values of 36*190% = 68.4 (rounded to 68) and 36*192% = 69.12 (rounded to 69), 192% is the correct answer.
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24 Oct 2010, 19:06
initially the area difference 36*pi

after change, the radius of outer circle becomes 11 and that of inner circle becomes 4
area difference 105pi..

So difference increases by 105pi - 36pi = 69
hence percent increase = 69/36 * 100 = 192 apprx . Hence D
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14 Aug 2011, 22:55
Area between the circles originally = 22/7 (100 - 64) = 22/7 (36)
Area between the circles finally = 22/7 (121 - 16) = 22/7 (105)

Percentage increase of the area between the circles = (105-36)/36 * 100 = 192% (D)
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22 Sep 2011, 09:58
You wanna know why we divide the difference by the "old" at the end? When we say "X have changed to Y, now by what percent has X changed?" We actually mean by what percent of X ITSELF has X changed. Clear? So the denominator must again be X. The procedure is exactly like when they ask you Z is what percent of X. Then, you divide Z by X. Here Z is represented by Y-X, just as an example.
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21 Sep 2012, 07:31
% change = {( Area,before-Area,after)/(Area,before) } x 100

Area,before= pi* ( Rad of bigger circle ^2- Rad of smaller circle^2)= pi (10^2-8^2)=pi(100-64)=36 pi

The situation later:

Area , after=pi*(11^2 - 4^2) = 105 pi

putting the values of both areas in main formula;

% change = { ( Area,before-Area,after)/(Area,before)} x 100

={ (105 pi - 36 pi )/ 36 pi } x 100
={ 69 pi/ 36 pi} x 100
=191.6666666666667 ( do a guess work don't calculate pin point values like this in real exam ; 69/36 appx equals to less than 2 so in ACs 192 is nearest to 200)
192 appx.

D wins
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21 Sep 2012, 08:07
In regards to the confusion about the new/old vs (new-old)/old question above, I think the clue is in the language the question uses:
'grow' means 'change' (specifically in a positive direction). In mathmatical terms we deal with change as (new-old), so the corrent answer should you the same logic.

For the new/old varient to work, the question would have to say something like 'the new area is what percent of the old area'.

My thoughts anyways.....

B.
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