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Soup cans

by Brent@GMATPrepNow » Wed Jan 21, 2009 5:16 pm
A company sells soup in cylindrical cans. The company wishes to make its cans taller without altering their volume. If the company increases the can’s height by 125%, by what percent must the company reduce the can's radius so that the new cans hold the same volume as the original cans?
(A) 20
(B) 25
(C) 33 1/3
(D) 66 2/3
(E) 80

Please note that this is not an official GMAT question; it is my attempt to create difficult (650+ level) GMAT-style questions for this forum.
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by truplayer256 » Wed Jan 21, 2009 5:37 pm
Original Volume= pir^2*h
New volume= 2.25pir^2*h
In order for the new volume of the soup can to equal the volume of the original can, we must somehow get rid of the 2.25 and we can do this by multiplying the new volume by 1/2.25. Since the question asks for the reducement in radius, we can set r^2 equal to 1/2.25.

r^2=1/2.25
r=2/3
so the radius was reduced by 33.33% or C
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by Brent@GMATPrepNow » Wed Jan 21, 2009 5:44 pm
Nice work - the answer is C
Nice solution as well.
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