Spheres

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Captchar: Junior | Next Rank: 30 Posts; Posts: 15; Joined: Sun Dec 16, 2012 4:04 am

by Captchar » Mon Dec 17, 2012 9:26 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. 87.5
C. 90.5
D. 92.5
E. 95.5

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Source: Beat The GMAT — Problem Solving | Mon Dec 17, 2012 9:26 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Mon Dec 17, 2012 9:30 am

This question is out of scope. The GMAT does not require us to know how to find the surface area of a sphere or the volume of a sphere.

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Mon Dec 17, 2012 9:32 am

Captchar 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

Surface area of B is 300% higher than that of A.
Hence, surface area of B is four times the surface area of A.

As, surface area of a sphere is proportional to the square of the radius, radius of B must be twice of the radius of A.

Now, volume of a sphere is proportional to the cube of the radius.
Hence, volume of B must be 2^3 = 8 times of the volume of A.

Hence, k = 100*(Volume of B - Volume of A)/(Volume of B) = 100*(8 - 1)/8 = 100*(7/8) = (12.5)*7 = 87.5

The correct answer is B.

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The Iceman: Master | Next Rank: 500 Posts; Posts: 194; Joined: Mon Oct 15, 2012 7:14 pmFollowed by: 6 members; Location: India; Thanked: 47 times

by The Iceman » Mon Dec 17, 2012 9:44 am

Captchar 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. 87.5
C. 90.5
D. 92.5
E. 95.5

Area of B = 4* (Area of A)

Volume of B is directly proportional to [4*(Area of A)]^(3/2)=> Volume of B = 8*(Volume of A)

k=(7*100/8)=87.5%

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