Analyzing Product of Two Integers

Easy Data Sufficiency Analyzing Information

Let $x$ and $y$ be positive integers. If the product $xy$ is even, what can we conclude about $x$ and $y$?

Statement (1): $x + y$ is an even number.

Statement (2): $x$ is an even number.

Statement (1) alone is sufficient, but statement (2) alone is not sufficient.

Statement (2) alone is sufficient, but statement (1) alone is not sufficient.

Both statements (1) and (2) together are sufficient, but neither statement alone is sufficient.

Each statement alone is sufficient.

Statements (1) and (2) together are not sufficient.

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