Are positive integers p and q both greater than n?

1) p - q is greater than n
2) q > p


1) p-q > n

p=2, q=1 2-1 > n
1 > n (this could be yes or no as n could be anything)

Insufficient.

2) q > p -> no relationship to n, so again insufficient.

Combining 1) and 2)

p - q > n

p > n + q , but p < q from (2)

since both q and p are positive, both of these equations can only be true if n is negative

(p is the smaller number, yet when added to n, p becomes larger then n+q)

- Both is sufficient as p and q are positive, hence is greater than n(negative)

1) Doesn't tell you the relationship between p/q to n. Assuming p is 4 and q is 2, 4 - 2 > n; 2 > n, both are larger than n. But if p is 10 and q is 2, 10 - 2 > n; 8 > n, then p > n, but q could be less than n (n could be 7).

2) q > p. Insufficient, because it doesn't tell you the relationship between q/p to n.

Together, we know that q > p, so p - q must be a negative number, and this number is larger than n, and therefore n MUST be a negative number. Since the question says p and q are both positive, then they must be larger than n.