Sufficiency of Integer Solutions to a Quadratic Equation

Medium Data Sufficiency Determining Sufficiency

Let $x$ and $y$ be two integers. We want to determine whether the expression $x^2 + y^2 = 25$ has a solution.

Statement 1: $x + y = 5$.

Statement 2: $x - y = 1$.

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 either statement alone is insufficient.

Each statement alone is sufficient.

Submitted4.8K

Correct3.4K

% Correct72%