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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.

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21 Jan 2013, 11:46

1

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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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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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.

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18 Jun 2014, 01:27

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.

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.

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.

Since p and q are positive integers,then q/p>0. Now, multiply p/q 0.

My approach was same as Marcab and hope it is valid approach.

Hi,

You can multiply both sides of the inequality by any positive number because by doing so it will not change the inequality sign. hence when stem inequality is multiplied by q/p on both sides you get 1 in LHS (p/q*q/p) and q/p in RHS (1*q/p)

You can also cross multiply here without worrying about the sign because p & q are positive. So your approach is correct

Re: If p/q < 1, and p and q are positive integers, which of the
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12 Feb 2018, 13:28

Hi All,

This question can be solved in a variety of different ways. Every so often, the GMAT offers a question that looks far more complex than it actually is. Each of the other explanations provided in this string is correct. Here's a fairly quick way of looking at it though…

Since P and Q are POSITIVE INTEGERS and P/Q < 1, inverting the fraction will invert the relationship…so Q/P > 1. The question ask which of the 5 options is greater than 1….

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06 Nov 2018, 07:27

Bunuel wrote:

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.

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06 Nov 2018, 12:51

Hi vishnusheth,

When TESTing VALUES, you will occasionally have to test more than one example to find the definitive correct answer. The example you chose (P=1, Q=2) DOES fit the correct answer, but it also matches an answer that is 'sometimes' correct. Thus, your example is fine, but it's not enough on its own to define which of the five answers is ALWAYS correct. From a mathematical-standpoint, the reason why it's not enough is because when P=1, answer choices D and E will produce the exact same result (re: Q/1 and Q/1).

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06 Nov 2018, 14:33

gmatzpractice wrote:

\(\sqrt{\frac{q}{p}} > 1\) ??

Hi gmatzpractice,

Do you have a specific question regarding Answer Choice A?

Based on the information in the prompt, we know that P/Q will be a POSITIVE FRACTION (0 < P/Q < 1). When taking the square-root of a positive fraction, the result is a BIGGER POSITIVE FRACTION. For example, the square-root of 1/4 is 1/2. Thus, Answer A will NEVER be greater than 1.