If p and q are different prime numbers, m and n are integers, and pq

pq is a divisor of mp + nq

\(\frac{mp + nq }{ pq}\) = integer

\(\frac{mp }{ pq} + \frac{nq }{ pq}\) = integer

\(\frac{m }{ q} + \frac{n }{ p}\) = integer

As q and p are different prime numbers, the above statement is possible when \(\frac{m }{ q}\) and \(\frac{n }{ p}\) are integers.

I. p is a divisor of n.

Inference: \(\frac{n}{p}\) = integer

This is correct. For the relationship mentioned in the question to hold true, \(\frac{n}{p}\) must be an integer. We can eliminate B and C.

II. pq is a divisor of mp.

Inference: \(\frac{mp}{pq} = \frac{m}{q} \) = integer

This is correct. For the relationship mentioned in the question to hold true, \(\frac{m}{q}\) must be an integer.

We don't have to check for III as none of the options have all three correct.

Option D