If p/q < 1, and p and q are positive integers, which of the following must be greater than 1 ?

A) sqrt (p/q)
B) p/q^2
C) p/2q
D) q/p^2
E) q/p

Since q>0, we can safely multiply each side by q:
p/q < 1
p < q.

Given this constraint, try to show that 4 of the 5 answer choices do NOT have to be greater than 1.

Plug p=2 and q=3 into the answer choices.
If an answer choice yields a result not greater than 1, eliminate the answer choice.
A) √(p/q) = √(2/3) = √2/√3 ≈ 1.4/1.7 = 14/17.
B) p/q² = 2/3² = 2/9.
C) p/2q = 2/(2*3) = 1/3.
D) q/p² = 3/2² = 3/4.
Eliminate A, B, C and D.

The correct answer is E.

The OA indicates that q/p > 1.
Since p>0, we can safely multiply each side by p:
q/p > 1
q > p
p < q.
Given our rephrase of the question stem, it must be true that p < q.