Statement S1: $p$ and $q$ are both prime numbers. Most primes are odd, but there is one even prime: 2. If one of them is 2 (even), then $pq$ will be even. If both are odd, $pq$ will be odd. So, S1 alone is not enough because we don’t know if one of the primes is 2.

Statement S2: $p+q$ is an odd number. The sum of two numbers is odd only if one is even and the other is odd. Since $p$ and $q$ are primes, one of them must be 2 (even), and the other must be odd. If one number is even and the other is odd, their product $pq$ will always be even. So, S2 alone is enough to conclude that $pq$ is even.