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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?

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.

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 %

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.

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?

Re: two concentric circles with radii 10 and 8 [#permalink]

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24 Oct 2010, 17:58

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This post received 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?

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.

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?

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

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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Please +1 KUDO if my post helps. Thank you.

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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?

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"

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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% 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: 10% increase in bigger radius will make 10 units of radius to 11 units of radius 50% decrease in smaller radius will make 8 units of radius to 4 units of radius

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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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'.