statement(1): p-q > n
Given that, p and q are positive integers, hence if p-q is greater than n, p is definitely greater than n. See, even after subtracting some value from p, it is still greater than n and hence p stands greater than n. But here we can't say about q.
So (1) alone is not sufficient

statement(2):q > p
This alone is not sufficient. But if we consider it along with (1), yes. As p is already greater than n, and here q is greater than p, implies that q is greater than n. And as q-p is negative, n must be negative.

Answer "C"

Are p,q > n ?

Given p and q are + ve

1. p-q > n we can say p > n but we cannot say q > n as well. INSUFF
2. q > p. - No info about n. INSUFF

Combining 1 and 2.

Add both the inequalities
p - q + q > n + p
p > n + p
0 > n
n < 0.

Now we know n is -ve and p and q to be positive (given) so both are greater than n. Hence C.

Thank you, Sam2304 and mathbyvemuri!
Makes sense when you've explained it algebraically and logically.

Cheers,
Gurpreet