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The areas of three faces of a rectangular solid are 12, 15 and 20. Wha

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The areas of three faces of a rectangular solid are 12, 15 and 20. Wha  [#permalink]

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New post 19 Apr 2019, 02:34
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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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Re: The areas of three faces of a rectangular solid are 12, 15 and 20. Wha  [#permalink]

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New post 19 Apr 2019, 02:46
12 = 4*3
15 = 5*3
20 = 4*5.

The sides of the rectangle are 3,4 and 5.

Volume = 3*4*5 = 60.

B is the answer

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Re: The areas of three faces of a rectangular solid are 12, 15 and 20. Wha  [#permalink]

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New post 19 Apr 2019, 04:49
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MathRevolution 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


l*b= 12
b*h=15
l*h=20
l=3,b=4,h=5
l*b*h=2*4*5 = 60
IMO b
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Re: The areas of three faces of a rectangular solid are 12, 15 and 20. Wha  [#permalink]

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New post 19 Apr 2019, 05:29
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Top Contributor
MathRevolution 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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Re: The areas of three faces of a rectangular solid are 12, 15 and 20. Wha  [#permalink]

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New post 21 Apr 2019, 18:19
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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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Re: The areas of three faces of a rectangular solid are 12, 15 and 20. Wha  [#permalink]

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New post 23 Apr 2019, 20:10
MathRevolution 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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Re: The areas of three faces of a rectangular solid are 12, 15 and 20. Wha   [#permalink] 23 Apr 2019, 20:10
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