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24 Dec 2018, 06:18
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C
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Difficulty:
95%
(hard)
Question Stats:
50% (02:49) correct
50%
(02:56)
wrong
based on 268
sessions
History
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Not Attempted Yet
Fresh GMAT Club Tests' Question:
A certain rectangular box A, has height of x units, length of y units and width of z units, where x, y, and z are positive integers. A second rectangular box B, has each of its dimensions - height, length and width, 50 percent smaller than that of rectangular box A. If the surface ares of rectangular box B is 2.5 unit^2, what is the volume of rectangular box A?
A. 1/4 unit^3
B. 1 unit^3
C. 2 unit^3
D. 4 unit^3
E. 10 unit^3
M37-06
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18 Nov 2021, 03:48
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Bunuel
Official Solution:
A certain rectangular box A, has height of \(x\) units, length of \(y\) units and width of \(z\) units, where \(x\), \(y\), and \(z\) are positive integers. A second rectangular box B, has each of its dimensions - height, length and width, 50 percent smaller than that of rectangular box A. If the surface area of rectangular box B is 2.5 \(unit^2\), what is the volume of rectangular box A?
A. \(\frac{1}{4} \ unit^3\)
B. \(1 \ unit^3\)
C. \(2 \ unit^3\)
D. \(4 \ unit^3\)
E. \(10 \ unit^3\)
We need to find \(Volume_A=xyz\), while given that \(Surface \ area_B = 2*(\frac{x}{2}*\frac{y}{2} +\frac{x}{2}*\frac{z}{2}+\frac{y}{2}*\frac{z}{2})=2.5\).
Simplify \(2*(\frac{x}{2}*\frac{y}{2} +\frac{x}{2}*\frac{z}{2}+\frac{y}{2}*\frac{z}{2})=2.5\):
\(xy+xz+yz=5\)
Recall that we are given that \(x\), \(y\), and \(z\) are positive integers. 5 is small enough number to quickly get by testing numbers that \((x, y, z) =(2, 1, 1)\) in any order.
\(Volume_A=xyz=2\).
Answer: C
General Discussion
24 Dec 2018, 06:19
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