Inequalities (p/q < 1)

[iil-london]

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

I used the "plugging-in" numbers approach to solve this. Was wondering if there was another approach to take when solving this type of question. Any input ?

My approach. p and q are positive integers ... so for p/q < 1, I assigned p=2, q=3. so p/q = 2/3. Then I went through each of the answer choices, and the only answer choice which was greater than 1 ... is E. 3/2 is greater than 1.

Any other approaches ?

Thanks.

[Guest]

Since p and q are positive integers -> p/q<1 -> p<q -> 1<q/p ... thus E is correct ... I hope this answers

[rfernandez]

Yeah, I like how guest got right to E... nice job.

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

You could eliminate A based on the fact that if p<q, then sqrt(p)<sqrt(q), so sqrt(p/q) must be less than 1. B and C can also be eliminated because making the denominator larger will only make the whole fraction smaller. D might be larger than one, but it mustn't be.

Rey