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18 Nov 2021, 02:12
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Barney is forming two large cubes, A and B, with small identical cubes. He used \(x\) small cubes to form cube A and \(y\) small cubes to form cube B. If \(x - y = 61\), then what is the value of \(x + y\)?
A. \(64\)
B. \(125\)
C. \(169\)
D. \(189\)
E. \(216\)
A. \(64\)
B. \(125\)
C. \(169\)
D. \(189\)
E. \(216\)
18 Nov 2021, 02:12
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Official Solution:
Barney is forming two large cubes, A and B, with small identical cubes. He used \(x\) small cubes to form cube A and \(y\) small cubes to form cube B. If \(x - y = 61\), then what is the value of \(x + y\)?
A. \(64\)
B. \(125\)
C. \(169\)
D. \(189\)
E. \(216\)
Notice that since large cubes are made from small identical cubes, then both \(x\) and \(y\) must be perfect cubes (a perfect cube is a cube of an integer). So, \(x\) and \(y\) can be: 1, 8, 27, 64, 125, 216, ...
We are given that \(x-y=61\), so \(x\) and \(y\) are 125 and 64, respectively.
Thus, \(x+y=189\).
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: D
Barney is forming two large cubes, A and B, with small identical cubes. He used \(x\) small cubes to form cube A and \(y\) small cubes to form cube B. If \(x - y = 61\), then what is the value of \(x + y\)?
A. \(64\)
B. \(125\)
C. \(169\)
D. \(189\)
E. \(216\)
Notice that since large cubes are made from small identical cubes, then both \(x\) and \(y\) must be perfect cubes (a perfect cube is a cube of an integer). So, \(x\) and \(y\) can be: 1, 8, 27, 64, 125, 216, ...
We are given that \(x-y=61\), so \(x\) and \(y\) are 125 and 64, respectively.
Thus, \(x+y=189\).
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: D
miag
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Schools: Anderson '26 (A) Haas '26 (A) Kellogg '26 (A)
GMAT Focus 1: 675 Q87 V83 DI80
Posts: 404
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10 Apr 2025, 06:04
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Hi Bunuel, sorry but how did you infer that x, and y must be perfect cubes - didnt connect the two while solving? thank you!
Bunuel
