GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 24 May 2019, 10:16

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Manager
Joined: 02 Dec 2012
Posts: 174
If p/q < 1, and p and q are positive integers, which of the  [#permalink]

### Show Tags

17 Dec 2012, 06:16
4
14
00:00

Difficulty:

5% (low)

Question Stats:

93% (00:58) correct 7% (01:16) wrong based on 2288 sessions

### HideShow timer Statistics

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) $$\frac{q}{p}$$
Math Expert
Joined: 02 Sep 2009
Posts: 55271
Re: If p/q < 1, and p and q are positive integers, which of the  [#permalink]

### Show Tags

17 Dec 2012, 06:21
1
6
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.

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.

_________________
VP
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1063
Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75
Re: If p/q < 1, and p and q are positive integers, which of the  [#permalink]

### Show Tags

17 Dec 2012, 06:33
5
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.
_________________
##### General Discussion
Manager
Joined: 03 Jan 2013
Posts: 51
GPA: 3.8
WE: Engineering (Computer Software)
Re: If p/q < 1, and p and q are positive integers, which of the  [#permalink]

### Show Tags

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
_________________
Giving kudos is a way to appreciate the help done to you.
VOTE: Best resource for Verbal in GMAT
VOTE: Best resource for Quant in GMAT
Retired Moderator
Joined: 29 Oct 2013
Posts: 257
Concentration: Finance
GPA: 3.7
WE: Corporate Finance (Retail Banking)
Re: If p/q < 1, and p and q are positive integers, which of the  [#permalink]

### Show Tags

22 May 2014, 22:29
2
1
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!
_________________

My journey V46 and 750 -> http://gmatclub.com/forum/my-journey-to-46-on-verbal-750overall-171722.html#p1367876
Intern
Joined: 20 May 2014
Posts: 35
Location: India
Schools: IIMC
GMAT 1: 700 Q51 V32
Re: If p/q < 1, and p and q are positive integers, which of the  [#permalink]

### Show Tags

23 May 2014, 07:25
1
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
_________________
If you liked the post, please press the'Kudos' button on the left
Intern
Joined: 31 Mar 2014
Posts: 10
Re: If p/q < 1, and p and q are positive integers, which of the  [#permalink]

### Show Tags

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.
Math Expert
Joined: 02 Sep 2009
Posts: 55271
Re: If p/q < 1, and p and q are positive integers, which of the  [#permalink]

### Show Tags

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.

The second approach in my solution here: if-p-q-1-and-p-and-q-are-positive-integers-which-of-the-144262.html#p1156616 uses p=2 and q=3 to discard all options but E.

Hope it helps.
_________________
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 6231
Location: United States (CA)
Re: If p/q < 1, and p and q are positive integers, which of the  [#permalink]

### Show Tags

16 Jun 2016, 06:03
1
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

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.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

CEO
Joined: 12 Sep 2015
Posts: 3727
Re: If p/q < 1, and p and q are positive integers, which of the  [#permalink]

### Show Tags

01 Aug 2016, 08:01
1
Top Contributor
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

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.

RELATED VIDEOS

_________________
Test confidently with gmatprepnow.com
Director
Joined: 02 Sep 2016
Posts: 659
If p/q < 1, and p and q are positive integers, which of the  [#permalink]

### Show Tags

21 Sep 2017, 07:04
0<p/q<1

For example: 2/3

Numerator<Denominator

When denominator>Numerator, the number would be greater than 1.

q/p

For example: 3/2

(Note: We know from the question stem that p and q are not equal to each other. If that was the case, then p/q= 1 not<1).
_________________
Help me make my explanation better by providing a logical feedback.

If you liked the post, HIT KUDOS !!

Don't quit.............Do it.
IIMA, IIMC School Moderator
Joined: 04 Sep 2016
Posts: 1340
Location: India
WE: Engineering (Other)
Re: If p/q < 1, and p and q are positive integers, which of the  [#permalink]

### Show Tags

14 Jan 2018, 17:26
Bunuel niks18 chetan2u amanvermagmat

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

I did not understand highlighted part. It could also be possible that p/q > 0.

My approach was same as Marcab and hope it is valid approach.
_________________
It's the journey that brings us happiness not the destination.

Feeling stressed, you are not alone!!
Retired Moderator
Joined: 25 Feb 2013
Posts: 1214
Location: India
GPA: 3.82
Re: If p/q < 1, and p and q are positive integers, which of the  [#permalink]

### Show Tags

14 Jan 2018, 19:26
Bunuel niks18 chetan2u amanvermagmat

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

Posted from my mobile device
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 14198
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If p/q < 1, and p and q are positive integers, which of the  [#permalink]

### Show Tags

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….

That's obviously

GMAT assassins aren't born, they're made,
Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

# Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ Intern Joined: 17 Sep 2018 Posts: 11 Location: India Re: If p/q < 1, and p and q are positive integers, which of the [#permalink] ### Show Tags 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. The second approach in my solution here: http://gmatclub.com/forum/if-p-q-1-and- ... l#p1156616 uses p=2 and q=3 to discard all options but E. Hope it helps. Same here, any idea why p=1, q=2 wouldn't work? I got stuck between D and E as well since I chose (1,2). _________________ Help needed to get to a score of 700+ I'm at all ears!! EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 14198 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: If p/q < 1, and p and q are positive integers, which of the [#permalink] ### Show Tags 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). GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com *****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***** # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/
Manager
Joined: 07 Feb 2017
Posts: 183
Re: If p/q < 1, and p and q are positive integers, which of the  [#permalink]

### Show Tags

06 Nov 2018, 13:01
$$\sqrt{\frac{q}{p}} > 1$$ ??
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 14198
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If p/q < 1, and p and q are positive integers, which of the  [#permalink]

### Show Tags

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.

GMAT assassins aren't born, they're made,
Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

# Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save \$75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/
Re: If p/q < 1, and p and q are positive integers, which of the   [#permalink] 06 Nov 2018, 14:33
Display posts from previous: Sort by