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.
