Determine Distinct Pairs from Equation

Very Hard Data Sufficiency Determining Sufficiency

Let $x$ and $y$ be positive integers. We want to determine the number of distinct pairs $(x, y)$ such that $x^2 + y^2 = 50$.

Statement 1: $x = 5$

Statement 2: $y$ is an even integer.

Is each statement sufficient to determine the number of distinct pairs $(x, y)$ that satisfy the equation?

Statement (1) alone is sufficient, but statement (2) alone is not suffcient.

Statement (2) alone is sufficient, but statement (1) alone is not sufficient.

Both statements together are sufficient, but each statement alone is not sufficient.

Each statement alone is sufficient.

Submitted12.9K

Correct9.9K

% Correct76%