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Bunuel
A solid cube is placed in a cylindrical container. Which of the following percent values COULD possibly represent the ratio of the volume of the cylinder not occupied by the cube to the volume of the cylinder? (Assume the value of ππ to be 3)

(A) 16%
(B) 25%
(C) 28%
(D) 32%
(E) 36%

We don't need to calculate anything to solve this problem, and this is a great example of using pure logic to solve GMAT question. The volume of the cube will always be smaller than the cylindrical container, and we can make the volume of the cube very small compared to the cylinder. Thus there will be a maximum volume of the cube but the lower bound will be 0. Therefore, there must be a minimum ratio not occupied by the cube, but the upper bound will be 1. Thus you can safely pick E, the largest ratio listed, as the answer.
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The volume of cube will always be in \(x^3\) format.

Thus, the required ratio will be:
\(\frac{ Volume of Cylinder - x^3 }{ Volume of Cylinder }\)

Since the answer is in percentage, let the volume of cylinder be 100.

\(\frac{100-x^3}{100}\) should be the answer choice.

The only value x can take is 4. Thus, E is the answer.
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The volume of cube will always be in \(x^3\) format.

Thus, the required ratio will be:
\(\frac{ Volume of Cylinder - x^3 }{ Volume of Cylinder }\)

Since the answer is in percentage, let the volume of cylinder be 100.

\(\frac{100-x^3}{100}\) should be the answer choice.

The only value x can take is 4. Thus, E is the answer.


Hi,

Thank you for your explanation.

But why must x be 4 ? I did not understand that last part.

Thanks.
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