Perfect Square Product Condition

Very Hard Data Sufficiency Determining Sufficiency

Let $p$ and $q$ be two positive integers such that $p + q = 100$. We want to determine whether the product $pq$ can be expressed as a perfect square.

Statement (1): $p$ is greater than $50$.

Statement (2): $pq$ is divisible by $16$.

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.

Submitted7.5K

Correct3.9K

% Correct52%