A: pq has to be negative and even, So INCORRECT

B: Take p = -2, q = 3, p/q is not even an integer, So INCORRECT

C: p-q has to be negative since negative-positive = negative, so, INCORRECT

D: If p = -2, q = 3, then p+q = 1, which is positive odd, but if p = -4 and q = 3, p+q = -1, which is negative odd, So, INCORRECT

E: q-p = positive - negative = positive - (-1*positive) = positive, also odd - even = odd, hence CORRECT!

Option E

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