SAT Math Multiple Choice Practice Question 240: Answer and Explanation

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Question: 240

20. A rectangular solid is a centimeters long, b centimeters wide, and c centimeters high. Its volume is v cubic centimeters and its surface area is s square centimeters. If a, b, c, v, and s are all integers, and v is odd, which of the following must be true?

is odd.

III. s is even.

A. I only
B. I and II only
C. I and III only
D. I and III only
E. I, II, and III

Correct Answer: E

Explanation:

E If v is the volume of the solid, then . Solving this equation for a gives so statement II must be true. Now go to the answer choices, and notice that you can eliminate any choice without II, namely (A) and (C). Also notice from the original equation that v could not be odd if any of the integers a, b, or c were even, therefore they must all be odd. This implies that is odd, so statement I must be true. This eliminates choice (D). To check statement III, you need an expression for the surface area of the solid, which is . Since this is a multiple of 2, it is even, so statement III is also true.

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