If p and q are positive integers, how many integers are larger than pq and smaller than
p(q + 2)?
(A) 3
(B) p + 2
(C) p – 2
(D) 2p – 1
(E) 2p + 1

I chose P = 2 and Q = 4, So I came to answer A.

But the answer says:

Let p = 1 and q = 2. Then pq = 2 and p(q + 2) = 4. This scenario has one integer, 3, greater than pq
and less than p(q + 2). Now, we plug p = 1 and q = 2 into the answer-choices until we find one
that has the value 1. Look at choice (D): 2p – 1 = (2)(1) – 1 = 1. Thus, the answer is (D).


Do I need to choose 1 and 2 as positive integer next time ( but 1 is odd :S )