Analysis of Integer Solutions to Quadratic Equation

Hard Data Sufficiency Determining Sufficiency

Let $m$ and $n$ be integers. We want to determine whether the equation $m^2 + n^2 = 25$ has solutions.

Statement (1): $m + n = 8$.

Statement (2): $n = 3$.

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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