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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]

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21 Jan 2013, 11:46

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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 _________________

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

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22 May 2014, 22:29

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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!
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My journey V46 and 750 -> http://gmatclub.com/forum/my-journey-to-46-on-verbal-750overall-171722.html#p1367876

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

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17 Jun 2014, 22:03

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.

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]

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29 Aug 2015, 02:05

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We can use some actual numbers to solve this problem. We see that p/q is less than 1. It follows that we have a positive proper fraction, where q is greater than p. Let's let p = 1 and q = 4; thus p/q = 1/4.

We now consider each answer choice:

Choice A: √(p/q) = √ (1/4) = ½, which is less than 1. Choice A is not correct.

Choice B: p/q^2 = 1/4^2 = 1/16, which is less than 1. Choice B is not correct.

Choice C: p/(2q) = 1/(2 x 4) = 1/8, which is less than 1. Choice C is not correct.

Choice D: q/p^2 = 4/1^2 = 4, which is greater than 1. This could be the answer.

Choice E: q/p = 4/1 = 4, which is greater than 1. This could be the answer.

Choices D and E work for the fraction ¼. Let's now consider additional values for the original fraction p/q, such as p = 3 and q = 4.

Choice D now becomes q/p^2 = 4/3^2 = 4/9, which is less than 1. Thus, we can now eliminate Choice D.

Choice E now becomes q/p = 4/3, which is greater than 1. Thus, Choice E is correct. In fact, we can see that no matter what the values of p and q are, if p/q is less than 1, then its reciprocal, q/p will always be greater than 1.

Answer: E
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IMPORTANT: For questions like this, where you need to test each answer choice, the test-makers will often make D or E the correct answer (because they want to eat up your valuable time ). So, in these situations, always begin with E and work your way up.

E. Is q/p > 1? Well, we're told that p/q < 1. Since q is a positive integer, we can multiply both sides by q to get: p < q Since p is a positive integer, we can now divide both sides by p to get: 1 < q/p So, answer choice E must be true.

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