Bunuel wrote:
The height of a certain right circular cylinder is greater than its diameter, and both numbers are positive integers. What is the volume of the cylinder?
(1) The radius of the base is 2.5.
(2) The longest distance between any two points on the cylinder is 13.
Kudos for a correct solution.
The OA will be revealed on Sunday
VERITAS PREP OFFICIAL SOLUTION:The correct response is (B). Start by drawing the figure:
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The “longest distance between any two points” will be the hypotenuse of a right triangle formed by the height and the diameter as the “legs.” If that hypotenuse is 13 and both the height and diameter are positive integers where h > d, the value of the legs can only be 5 and 12 (the ratio 5:12:13).
To find the volume of a right cylinder we use the formula πr^2h. If the diameter is 5, the radius is 2.5. The height is 12. We’ll be able to find the volume. Sufficient.
If you chose (A), this tells us the base is 5, but we still don’t know the height. We cannot assume it is 12 because the question doesn’t stipulate that the “longest distance between any two points” be an integer as well. For example, the height could be 10.
If you chose (C), we can find Statement (1) based solely on the information provided in Statement (2). The first statement is redundant.
If you chose (D), only Statement (2) is independently sufficient. We cannot determine the height from Statement (1) and we need BOTH the height and the radius (the base of the triangle) to find the volume of the cylinder.
If you chose (E), you may want to review the common right triangle ratios such as 3:4:5 and 5:12:13, and/or the Pythagorean theorem. The GMAT will sometimes hide right triangles (2-D shapes) inside boxes (rectangular prisms) and cylinders (3-D shapes).