Determining the Sum of Two Positive Integers

Very Hard Data Sufficiency Determining Sufficiency

Let $x$ and $y$ be positive integers, and we want to determine the value of the expression $x + y$.

Statement (1): $x^2 + y^2 = 50$.

Statement (2): $xy = 24$.

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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