Night reader wrote: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

p(q+2)-pq-1
p2-1

Answer is D[/spoiler]

It's always best to use your own numbers in there. I used P2Q3 and P4Q5 just to double check. Simple as that

Night reader wrote: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

Definitely plug in for this one -you don't want to make any careless mistakes with algebra misconceptions.

Plug in p=2, q=3:
pq is equal to 6
p(q+2) = 2*5 = 10
There are three integers greater than 6 but smaller than 10: 7, 8, 9.

So if p=2 and q=3, the answer should equal 3. Plug in p=2 into the answer choices and BAM - only A and D are equal to 3 for p=2, and A is eliminated because it is not dependent on p - it is obvious that if we'll plug in a different value for p and q, we'll get a different goal than 3.
thus D is chosen as it's the last one standing: all other answer choices are eliminated by a simple plug in.