Determine if the Product of Two Real Numbers is Positive

Medium Data Sufficiency Determining Sufficiency

Let $x$ and $y$ be real numbers. We want to determine if the product $xy$ is greater than 0.

Statement (1): $x^2 + y^2 > 0$.

Statement (2): $x + y eq 0$.

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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