Two prime numbers $p$ and $q$ satisfy the equation $p+q=31$. What is $p q$ ?
Since $p+q$ is odd (because 31 is odd) and $p$ and $q$ are integers, then one of $p$ and $q$ is even and the other is odd. (If both were even or both were odd, their sum would be even.)

Since $p$ and $q$ are both prime numbers and one of them is even, then one of them must be 2 , since 2 is the only even prime number.

Since their sum is 31 , the second number must be 29 , which is prime.

Therefore, $p q=2 \cdot 29=58$.

ANSWER: 58