If p/q

Question

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)  \frac{p}{q^2}

(C)  \frac{p}{2q}

(D)  \frac{q}{p^2}

(E)  \frac{q}{p}

PS16828

Bunuel · Accepted Answer

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.

BrentGMATPrepNow · Answer

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 . Answer: E RELATED VIDEOS https://www.youtube.com/watch?v=Od98BOicIq4

Marcab · Answer

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.

NoHalfMeasures · Answer

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!

rajatjain14 · Answer

Not sure if it is solved this way:

\frac{p}{q} < 1 ,

As p and q are positive,  Denominator should be greater than numerator .

Therefore,  q>p

Hence,  \frac{q}{p} > 1

Rgds,
Rajat

ScottTargetTestPrep · Answer

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

EMPOWERgmatRichC · Answer

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….

That's obviously  E

GMAT assassins aren't born, they're made, 
Rich

avigutman · Answer

Video solution from Quant Reasoning: Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1 https://www.youtube.com/watch?v=AqGMXC4xSrU

bagad.07 · Answer

Question Code: PS16828

Bunuel · Answer

________________________________
Thank you! Added to the first post.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions