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Manager
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Question Stats:
50% (02:29) correct
49% (01:42) wrong based on 1 sessions
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 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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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. Compare your answers and youll see that theyre the same. 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?
(C) 2008 GMAT Club - m01#37
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Manager
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Hi millhouse,
Why is it (new-old)/old ? it should have been new/old. Thanks
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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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Manager
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Thanks. I understand it now.
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Well the answer should be 292% ... 121-36/36 .. but the OA says 192% . Am bummed.
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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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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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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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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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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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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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two concentric circles with radii 10 and 8 [#permalink]
 24 Oct 2010, 18:52
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 I am getting 292. Please provide details along with your answers as well.
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Re: two concentric circles with radii 10 and 8 [#permalink]
24 Oct 2010, 18:58
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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 I am getting 292. Please provide details along with your answers as well. 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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Re: two concentric circles with radii 10 and 8 [#permalink]
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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Re: two concentric circles with radii 10 and 8 [#permalink]
24 Oct 2010, 19:17
Thanks Gurpreet and krushna , yes i was not subtracting the previous value. thanks for pointing out the mistake
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concentric circles [#permalink]
14 Aug 2011, 22:45
there are two concentric circle with radii 10 and 8. If the radius of the outer circle is increased by 10% ,radius of inner circle decreased by50% , by what percent does the area between the circles grow?
140
141
190
192
292
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Re: concentric circles [#permalink]
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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Re: concentric circles [#permalink]
14 Aug 2011, 23:06
thanks,missed word increase that's why getting 292
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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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