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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.

Re: If p/q < 1, and p and q are positive integers, which of the [#permalink]
21 Jan 2013, 10:46

1

This post received KUDOS

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 _________________

Re: If p/q < 1, and p and q are positive integers, which of the [#permalink]
22 May 2014, 21:29

When we know the signs of fraction in an inequality and want to take the reciprocal here is a handy rule: flip the inequality when taking reciprocal unless both sides have different signs. Thus we can flip the inequality in the given relation p/q<1, to get q/p>1. E it is! _________________

Please consider giving 'kudos' if you like my post and want to thank

Re: If p/q < 1, and p and q are positive integers, which of the [#permalink]
17 Jun 2014, 21:03

Did anyone solve this with smart numbers? Used p = 1 and q = 2 which narrowed it down to D and E and then tested those with p = 5 and q = 9? This gave me E.

Re: If p/q < 1, and p and q are positive integers, which of the [#permalink]
18 Jun 2014, 00:27

Expert's post

carolinanmd wrote:

Did anyone solve this with smart numbers? Used p = 1 and q = 2 which narrowed it down to D and E and then tested those with p = 5 and q = 9? This gave me E.