Determine the Product xy from Given Conditions

Hard Problem Solving Arithmetic

If $x$ and $y$ are two positive integers, what is the value of the product $xy$?

Statement (1): The sum $x + y = 12$.

Statement (2): The difference $y - x = 4$.

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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