The areas of three faces of a rectangular solid are 12, 15 a

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Max@Math Revolution: Elite Legendary Member; Posts: 3991; Joined: Fri Jul 24, 2015 2:28 amFollowed by: 37 members; Location: Las Vegas, USA; Thanked: 19 times

by Max@Math Revolution » Fri Apr 19, 2019 12:18 am

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[GMAT math practice question]

The areas of three faces of a rectangular solid are 12, 15 and 20. What is the volume of the rectangular solid?

A. 30
B. 60
C. 180
D. 900
E. 3600

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16206; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Fri Apr 19, 2019 4:26 am

Max@Math Revolution wrote:[GMAT math practice question]

The areas of three faces of a rectangular solid are 12, 15 and 20. What is the volume of the rectangular solid?

A. 30
B. 60
C. 180
D. 900
E. 3600

Let x = the width
Let y = the length
Let z = the height
So, the volume = xyz

Area of one face = 12
We can write: xy = 12

Area of one face = 15
We can write: xz = 15

Area of one face = 20
We can write: yz = 20

Combine to get: (xy)(xz)(yz) = (12)(15)(20)
Simplify: x²y²z² = 3600
Rewrite as: (xyz)² = 60²
So, xyz = 60
In other words, the volume = 60

Answer: B

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Brent

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Max@Math Revolution: Elite Legendary Member; Posts: 3991; Joined: Fri Jul 24, 2015 2:28 amFollowed by: 37 members; Location: Las Vegas, USA; Thanked: 19 times

by Max@Math Revolution » Sun Apr 21, 2019 5:11 pm

The volume of the above rectangular solid is xyz and the areas of three of its faces are xy, yz, zx.
We may assume xy = 12, yz = 15 and zx = 20 without loss of generality.
Therefore, (xy)(yz)(zx) = (xyz)^2 = 12*15*20 = 3600 = 60^2
Thus, the volume is xyz = 60.

Therefore, the answer is B.
Answer: B

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by Scott@TargetTestPrep » Tue Apr 23, 2019 7:06 pm

Max@Math Revolution wrote:[GMAT math practice question]

The areas of three faces of a rectangular solid are 12, 15 and 20. What is the volume of the rectangular solid?

A. 30
B. 60
C. 180
D. 900
E. 3600

The dimensions of the rectangular solid must be 3, 4, 5 so that the areas of its three faces could be 3 x 4 = 12, 3 x 5 = 15 and 4 x 5 = 20. So the volume of the solid is 3 x 4 x 5 = 60.

Answer: B

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