Integer Solutions for Equation

Hard Data Sufficiency Determining Sufficiency

Let $a$ and $b$ be integers. We want to determine if the equation $a^2 + b^2 = 50$ has integer solutions.

Statement (1): $a - b = 6$.

Statement (2): $a + b = 10$.

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 together are sufficient, but neither statement alone is sufficient.

Each statement alone is sufficient.

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