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

 It is currently 07 Dec 2019, 09:36 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # 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: 173
If p/q < 1, and p and q are positive integers, which of the  [#permalink]

### Show Tags

7
18 00:00

Difficulty:   5% (low)

Question Stats: 93% (00:57) correct 7% (01:14) wrong based on 2033 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 V
Joined: 02 Sep 2009
Posts: 59588
Re: If p/q < 1, and p and q are positive integers, which of the  [#permalink]

### Show Tags

2
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.

_________________
Director  Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 987
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

5
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

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

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
Retired Moderator Joined: 29 Oct 2013
Posts: 248
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

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: 34
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

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
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

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 V
Joined: 02 Sep 2009
Posts: 59588
Re: If p/q < 1, and p and q are positive integers, which of the  [#permalink]

### Show Tags

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 V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8622
Location: United States (CA)
Re: If p/q < 1, and p and q are positive integers, which of the  [#permalink]

### Show Tags

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

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.

GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4125
Re: If p/q < 1, and p and q are positive integers, which of the  [#permalink]

### Show Tags

2
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

_________________
Director  G
Joined: 02 Sep 2016
Posts: 641
If p/q < 1, and p and q are positive integers, which of the  [#permalink]

### Show Tags

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).
IIMA, IIMC School Moderator V
Joined: 04 Sep 2016
Posts: 1370
Location: India
WE: Engineering (Other)
Re: If p/q < 1, and p and q are positive integers, which of the  [#permalink]

### Show Tags

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 D
Joined: 25 Feb 2013
Posts: 1159
Location: India
GPA: 3.82
Re: If p/q < 1, and p and q are positive integers, which of the  [#permalink]

### Show Tags

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 V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15661
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

1
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
_________________
Intern  B
Joined: 17 Sep 2018
Posts: 12
Location: India
Re: If p/q < 1, and p and q are positive integers, which of the  [#permalink]

### Show Tags

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 V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15661
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

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
_________________
Manager  S
Joined: 07 Feb 2017
Posts: 175
Re: If p/q < 1, and p and q are positive integers, which of the  [#permalink]

### Show Tags

$$\sqrt{\frac{q}{p}} > 1$$ ??
EMPOWERgmat Instructor V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15661
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

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
_________________
Intern  Joined: 21 Feb 2015
Posts: 4
GMAT 1: 700 Q51 V34 Re: If p/q < 1, and p and q are positive integers, which of the  [#permalink]

### Show Tags

Here, plugging in will make the question very lengthy.
If p/q < 1, numerator is less than denominator.
Thus q/p > 1 as numerator is greater than denominator. Re: If p/q < 1, and p and q are positive integers, which of the   [#permalink] 29 Aug 2019, 03:44
Display posts from previous: Sort by

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