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neerajkumar1_1: Master | Next Rank: 500 Posts; Posts: 270; Joined: Wed Apr 07, 2010 9:00 amFollowed by: 2 members; Thanked: 24 times

by neerajkumar1_1 » Sun Apr 11, 2010 1:54 am

need a solution

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Source: Beat The GMAT — Problem Solving | Sun Apr 11, 2010 1:54 am

thephoenix: Legendary Member; Posts: 1560; Joined: Tue Nov 17, 2009 2:38 amFollowed by: 5 members; Thanked: 137 times

by thephoenix » Sun Apr 11, 2010 2:07 am

n^3=450y
450=3^2 * 5^2 *2
to make it a perfect cube we need to multiply it with 3*5*2^2=y(which is nothing but y)
when we insert in the given option we must get an int value
except 1 no option gives us an int value
hence B

eaakbari: Master | Next Rank: 500 Posts; Posts: 435; Joined: Mon Mar 15, 2010 6:15 amFollowed by: 1 member; Thanked: 32 times

by eaakbari » Sun Apr 11, 2010 3:57 am

Since n and y are integers obviously they are not irrational and hence have perfect cubes

5^2 * 3 ^2 * 2 * y = n^ 3

Now the minimum factors of y needed to complete the cubes are 5 3 and 2^ 2
Hence y = 5*3*2^2* c where c is some constant which is a cube, for eg 27

Now only 1 will render the solution an integer

Hence B

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