# If A and B are positive integers…

## Solution:

We need to determine whether the product of positive integers AB is even. We must recall that the product of an even integer and any other integer **is always even**. Thus, if we can determine that either A or B (or both) is even, then we can answer the question.

**Statement One Alone:**

The sum A + B is odd.

In order for the sum of two integers to be odd, one of them must be even and the other must be odd. That is, either A is even and B is odd OR A is odd and B is even. In either case, the product AB is even, since one of them is even. Thus, statement one alone is sufficient to answer the question. We can eliminate answer choices B, C and E.

**Statement Two Alone:**

A is even.

Since we know that the product of an even integer and any other integer is always even, we know that the product AB will **always be even**.

Statement two is also sufficient.

**Answer: D**