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# 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.

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.