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18 Nov 2021, 03:47
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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. \(10 \ unit^3\)
A. \(\frac{1}{4} \ unit^3\)
B. \(1 \ unit^3\)
C. \(2 \ unit^3\)
D. \(4 \ unit^3\)
E. \(10 \ unit^3\)
18 Nov 2021, 03:47
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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.
\(Volume_A=xyz=2\).
Note that while this question uses basic knowledge of lines and figures, it is actually not a Geometry question. There are 8 questions within GMAT Prep Focus Edition that use similar principles. Here is one example.
Answer: C
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.
\(Volume_A=xyz=2\).
Note that while this question uses basic knowledge of lines and figures, it is actually not a Geometry question. There are 8 questions within GMAT Prep Focus Edition that use similar principles. Here is one example.
Answer: C
29 Nov 2024, 01:53
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Can you explain this part - how did you get (2,1,1). If we add up these nos, the result will not be 5 instead it will be 4. Not sure about the solution from this part.
Thanks
Thanks
