Determine if the Product of Two Integers is Negative

Medium Data Sufficiency Determining Sufficiency

Let $a$ and $b$ be two integers. We want to find out if the product $ab$ is negative.

Statement (1): $a + b < 0$.

Statement (2): $a$ is odd and $b$ is even.

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 together are sufficient, but neither statement alone is sufficient.

Each statement alone is sufficient.

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