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If p/q < 1, and p and q are positive integers, which of the

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If p/q < 1, and p and q are positive integers, which of the [#permalink] New post 17 Dec 2012, 05:16
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If p/q < 1, and p and q are positive integers, which of the following must be greater than 1 ?

(A) \sqrt{\frac{p}{q}}
(B) p/q^2
(C) p/2q
(D) q/p^2
(E) q/p
[Reveal] Spoiler: OA
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Re: If p/q < 1, and p and q are positive integers, which of the [#permalink] New post 21 Jan 2013, 10:46
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If p/q < 1 then q>p.

A) \sqrt{\frac{p}{q}} will obviously be less than 1.
(B) p/q^2 Will increase the denominator and still makes it less than 1.
(C) p/2qWill increase the denominator and still makes it less than 1.
(D) q/p^2Still less than 1. Suppose p =2 and q =3
(E) q/p Since q > p, q/p >1
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Re: If p/q < 1, and p and q are positive integers, which of the [#permalink] New post 17 Dec 2012, 05:21
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If p/q < 1, and p and q are positive integers, which of the following must be greater than 1 ?

(A) \sqrt{\frac{p}{q}}
(B) p/q^2
(C) p/2q
(D) q/p^2
(E) q/p

Since p and q are positive integers, then q/p>0. Now, multiply p/q < 1 by q/p to get 1 < q/p.

Answer: E.

Or: since this is a must be true question, then even if we find only one example for which an option is not true, it'll mean that this option is not always true, thus not a correct answer.

Say p=2 and q=3. In this case, no option is correct but E.

Answer: E.
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Re: If p/q < 1, and p and q are positive integers, which of the [#permalink] New post 17 Dec 2012, 05:33
Expert's post
Walkabout wrote:
If p/q < 1, and p and q are positive integers, which of the following must be greater than 1 ?

(A) \sqrt{\frac{p}{q}}
(B) p/q^2
(C) p/2q
(D) q/p^2
(E) q/p


Given:
p/q <1. Since p and q are positive integers, we can multiply by q on both sides.
The relation becomes:
p<q.

Now if we divide the entire relation by p, then:
p/p < q/p or 1< q/p

Hence q/p > 1.
+1 E.
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Re: If p/q < 1, and p and q are positive integers, which of the   [#permalink] 17 Dec 2012, 05:33
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