Determining Positivity of Product of Two Real Numbers

Hard Data Sufficiency Determining Sufficiency

Let $x$ and $y$ be two real numbers. We want to determine if the product $xy$ is positive.

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

Statement (2): $x^2 + y^2 < 10$.

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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