[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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The areas of three faces of a rectangular solid are 12, 15 a
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Max@Math Revolution
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Let x = the widthMax@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 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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Max@Math Revolution
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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
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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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.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
Answer: B
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