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Nice Question!!!!!

by parallel_chase » Thu Aug 07, 2008 10:38 am
Kindly see the figure attached.

P and Q are the centers of two circles A and B with radius 2 inches each. Find the area of the YELLOW shaded region.

A. 16-2pi
B. 16-pi
C. 4-2pi
D. 4-pi
E. It cannot be determined.

OA after few discussions.
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Last edited by parallel_chase on Thu Aug 07, 2008 11:21 am, edited 1 time in total.
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by Stuart@KaplanGMAT » Thu Aug 07, 2008 10:55 am
We have no idea where S and R are in relation to the other points, so there's no way to find the area of the shaded region.

Are we supposed to know that PQRS is a square? If not, S and R could be 2 inches below the circles or they could be 2 miles below the cirlces.
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by pepeprepa » Thu Aug 07, 2008 11:03 am
The two quarters of the circles in the rectangle have an area of pi each, so 2pi together.

Let's call the surface of the rectangle S.
So the yellow surface is S-2pi

S can be written as 4*x, with "x" the side we do not know.
So the yellow surface is
4x-2pi

The problem is that we do not know if PQSR is a square or a rectangle and without its sizes we cannot answer the question.
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by parallel_chase » Thu Aug 07, 2008 11:18 am
The answer is E.

If you assume that the figure is square you will get answer 16-2pi
If you assume that the figure is rectangle you will get answer 4-2pi

But since the figure does not tell us whether it is a square or a rectangle the answer is E.


I found this question from one of the GMAT prep books and the answer choices did not have (cannot be determined as an option). I added this option just to check if other people would fall for the trap answers.

Thanks Stuart & pepeprepa. I think Stuart joined the party little early but its all good.

Thanks.
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