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Source: — Data Sufficiency |

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by [email protected] » Mon Mar 23, 2015 11:13 am
Hi prachi18oct,

In this question, we're asked (in an oddly-worded way) to determine the volume of a cylinder.

Volume = pi(R^2)H where R is the radius of the base of the cylinder and H is the height.

We're told that the largest possible CUBE is placed into the cylinder and the volume of that cube is X.

Fact 1: The area of the base of the cylinder is 8pi

This Fact will help us to figure out the radius of the base of the cylinder AND the volume of the cube. However, it will NOT tell us the height of the cylinder.
Fact 1 is INSUFFICIENT

Fact 2: X = 64

This Fact will help us figure out the dimensions of the cube AND the radius of the base of the cylinder. However, it will NOT tell us the height of the cylinder.
Fact 2 is INSUFFICIENT

Combined, we know.....
The area of the base of the cylinder and the radius
The volume of the cube

We still don't know the height of the cylinder though, so there's no way to calculate the volume of the cylinder.
Combined, INSUFFICIENT

Final Answer: E

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by GMATGuruNY » Mon Mar 23, 2015 11:34 am
The largest possible cube with volume x is enclosed in a cylinder, what is the volume of the cylinder?

(1) The area of the base of the cylinder is 8Ï€.
(2) x is 64
For any square with side s, diagonal = s√2.

Statement 1:
πr² = 8π
r = √8 = 2√2, implying that d = 4√2.

Thus, the base of cylinder looks like this:
Image
The square represents the base of the largest cube that can be enclosed in a cylinder with a base of 8Ï€.
Since the diagonal of the square = 4√2, s = 4.
Thus, the largest possible cube has an edge of length 4, implying a volume of 64.

Case 1:
Image

Case 2:
Image

Cases 1 and 2 illustrate that the cylinder can have different heights.
Thus, the volume of the cylinder cannot be determined.
INSUFFICIENT.

Since Cases 1 and 2 also satisfy statement 2, the two statements combined are INSUFFICIENT to determine the volume of the cylinder.

The correct answer is E.
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