GMAT Question of the Day – 13/12/2020

QUESTION

If m, n, and p are positive integers, is (m² + n)(2m + p) an odd integer?

STATEMENT 1:

n is an odd integer.

STATEMENT 2:

p is an even integer.

ANSWER SELECTION

(A) Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.

(B) Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not. (THIS IS CORRECT!)

(C) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.

(D) EITHER statement BY ITSELF is sufficient to answer the question.

(E) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.

ANSWER EXPLANATION

We want to determine whether or not there is sufficiency to say that (m² + n)(2m + p) even or that (m² + n)(2m + p) is not even.

Statement (1) says that n is an odd integer. Let’s consider m² + n. Since we don’t know if m is odd or even, we don’t know if m² is odd or even. We don’t know if n is odd or even. So we don’t know if m² + n is odd or even. Let’s consider 2m + p. We see that since m is an integer, 2m must be even. However, we don’t know if p is odd or even. So we don’t know if 2m + p is odd or even. Since we don’t know if m² + n is odd or even and we don’t know if 2m + p is odd or even, we don’t know if (m² + n)(2m + p) is odd or even. Statement (1) is insufficient. We can eliminate choices (A) and (D).

Statement (2) says that p is an even integer. Let’s look at m² + n. We don’t know if m is odd or even, so we don’t know if m² is odd or even. We don’t know if n is odd or even. So we don’t know if m² + n is odd or even. Now let’s look at 2m + p. Since m is an integer, 2m is an even integer. Since p is even, 2m + p is the sum of an even integer and an even integer. An even plus an even is even, so 2m + p is even. Since (m² + n) is an integer, (m² + n)(2m + p) is an integer times an even integer, which must be an even integer. The answer to the question is “no.” Statement (2) is sufficient. Choice (B) is correct.

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