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GMATPrep PS Geometry

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by Bill@VeritasPrep » Sun Apr 08, 2012 4:57 pm
I almost made the same mistake I think you did: the radius of r is the FULL medallion (glass plus the metal frame).

A(outer) = pi*r^2

A(inner) = pi*(r-s)^2
=pi*(r^2 - 2rs + s^2)

A frame) = A(outer) - A(inner)

=pi*r^2 - pi*(r^2 - 2rs + s^2)

=pi*(r^2 - (r^2 - 2rs + s^2))

=pi* (2rs - s^2)

=pi*s*(2r - s)
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by myfish » Sun Apr 08, 2012 5:23 pm
I think you are right. This one is a reading exercise. It is very deceiving though BUT I am glad to know where the mistake was. Thanks so much.

[quote="Bill@VeritasPrep"]I almost made the same mistake I think you did: the radius of r is the FULL medallion (glass plus the metal frame).

A(outer) = pi*r^2

A(inner) = pi*(r-s)^2
=pi*(r^2 - 2rs + s^2)

A frame) = A(outer) - A(inner)

=pi*r^2 - pi*(r^2 - 2rs + s^2)

=pi*(r^2 - (r^2 - 2rs + s^2))

=pi* (2rs - s^2)

[b]=pi*s*(2r - s)[/b][/quote]
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by Anurag@Gurome » Sun Apr 08, 2012 5:26 pm
myfish wrote:After numerous attempts, I get Pi x s (2 x r + s), which is not an answer choice. Anyone?
Radius of the big circle = r
Width of the frame = s
Radius of the little circle = r - s
Area of the frame = (pi)r² - (pi)[r - s]² = (pi)[r² - r² + 2rs - s²] = [spoiler](pi) * s * (2r - s)[/spoiler]

The correct answer is E.
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by GMATGuruNY » Sun Apr 08, 2012 7:16 pm
myfish wrote:After numerous attempts, I get Pi x s (2 x r + s), which is not an answer choice. Anyone?
Another approach is to plug in.
Let r=3 and s=2.
Area of the whole medallion = �r² = �(3²) = 9�.
Radius of the circular glass center = r-s = 3-2 = 1.
Area of the circular glass center = �(1²) = �.
Area of the frame = medallion area - center area = 9� - � = 8�. This is our target.

Now we plug r=3 and s=2 into the answers to see which yields our target of 8�.
A quick scan of the answers reveals that only E works:
�s(2r - s) = �(2)(2*3 - 2) = 8�.

The correct answer is E.
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by spartacus1412 » Tue Apr 10, 2012 12:20 am
E it is..
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