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harsh.champ: Legendary Member; Posts: 1132; Joined: Mon Jul 20, 2009 3:38 amFollowed by: 6 members; Location: India; Thanked: 64 times; GMAT Score:760

by harsh.champ » Tue Feb 09, 2010 1:41 am

Let A and B be two solid spheres such that the surface area of B is 300% higher than the surface area of A. The volume of A is found to be k% lower than the volume of B. The value of k must be:

(A)85.5
(B)92.5
(C)90.5
(D)87.5
(E)None of these

The OA is D.

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Source: Beat The GMAT — Problem Solving | Tue Feb 09, 2010 1:41 am

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by [email protected] » Tue Feb 09, 2010 2:16 am

What is the OA?

Surface area of a sphere=4(pi)r^2
Since Surf. area of B=300% of surf. area of A
=> rad. of B=2.*rad. of A
Volume of sphere=4/3(pi)r^3
=>Vol. of B=8* Vol of A
=> Vol. of A is (1-1/8) times lower than Vol. of B
=>Vol of A=87.5% lower than Vol of B
Ans=D

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shashank.ism: Legendary Member; Posts: 1022; Joined: Mon Jul 20, 2009 11:49 pmFollowed by: 2 members; Location: Gandhinagar; Thanked: 41 times

by shashank.ism » Tue Feb 09, 2010 2:34 am

harsh.champ wrote:Let A and B be two solid spheres such that the surface area of B is 300% higher than the surface area of A. The volume of A is found to be k% lower than the volume of B. The value of k must be:

(A)85.5
(B)92.5
(C)90.5
(D)87.5
(E)None of these

The OA is D.

Let area of A =A let its radius be r volume= V
Area of B is 300% higher. So area of B = 4A. so radius = 2r, volume =8V
so k = (8V-V)/8 Vx 100 = 87.5
Ans D

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