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%

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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