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

 It is currently 12 Nov 2018, 10:10

### 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

## Events & Promotions

###### Events & Promotions in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
• ### Essential GMAT Time-Management Hacks

November 14, 2018

November 14, 2018

08:00 PM MST

09:00 PM MST

Join the webinar and learn time-management tactics that will guarantee you answer all questions, in all sections, on time. Save your spot today! Nov. 14th at 7 PM PST

# If p, q, r, and s are non-zero numbers, is pr/qs > r/q?

Author Message
TAGS:

### Hide Tags

Intern
Joined: 08 Nov 2012
Posts: 4
Location: United States
WE: Engineering (Other)
If p, q, r, and s are non-zero numbers, is pr/qs > r/q?  [#permalink]

### Show Tags

Updated on: 29 Aug 2014, 03:49
4
00:00

Difficulty:

65% (hard)

Question Stats:

42% (01:13) correct 58% (00:56) wrong based on 111 sessions

### HideShow timer Statistics

If p, q, r, and s are non-zero numbers, is pr/qs > r/q?

(1) p > s
(2) rq > 0

Dear Experts, kindly help me with the above problem. My pick was C, but it's incorrect.
pr/qs>r/q =>pqr >rqs => qr(p-s)>0. So i picked C. I guess i am missing something here. Request your help.

Originally posted by Aurion on 28 Aug 2014, 23:11.
Last edited by Bunuel on 29 Aug 2014, 03:49, edited 1 time in total.
Renamed the topic and edited the question.
Current Student
Status: It always seems impossible until it's done!!
Joined: 29 Aug 2012
Posts: 1120
Location: India
WE: General Management (Aerospace and Defense)
Re: If p, q, r, and s are non-zero numbers, is pr/qs > r/q?  [#permalink]

### Show Tags

28 Aug 2014, 23:25
2
Aurion wrote:
If p, q, r & s are non-zero numbers, Is pr/qs > r/q?
1) p>s
2) rq>0

We have to find whether when we multiply $$\frac{r}{q}$$ by $$\frac{p}{s}$$ will be greater than $$\frac{r}{q}$$

Statement 1: Give no valuable information to solve. So insufficient.

Statement 2: we know that $$\frac{r}{q}$$ is positive. But no info about $$\frac{p}{s}$$. So insufficient.

Combining: If both p and s positive, we have a bigger value. But if p or s is negative we have smaller value.

for example, if p=3 and s=1 and if p=1 and s=-3. So we have 2 possibilities. So even together we cannot solve this question.

_________________
Manager
Joined: 21 Sep 2012
Posts: 216
Location: United States
Concentration: Finance, Economics
Schools: CBS '17
GPA: 4
WE: General Management (Consumer Products)
Re: If p, q, r, and s are non-zero numbers, is pr/qs > r/q?  [#permalink]

### Show Tags

29 Aug 2014, 02:50
1
we can cancel r from numerator and q from denominator of both the sides.
so simplified form will be is p/s>1 i.e. p and s must have same sign and |p| must be greater than |s|.

1. p>s... not sufficient to answer whether p and s have same sign
2. rq>0.... not relevant

1+2... still we can't say whether p and s have same sign
Therefore ans=E
Intern
Joined: 04 Jul 2011
Posts: 9
Re: If p, q, r, and s are non-zero numbers, is pr/qs > r/q?  [#permalink]

### Show Tags

29 Aug 2014, 03:06
1
If p, q, r & s are non-zero numbers, Is pr/qs > r/q?
1) p>s
2) rq>0

From St. 1
p>s as not sufficient caus no information about signs of p&s and about r & q
From rq>o
r & q can be positive or negative
if both positive
pr/qs>r/q cancel r/q both sides and we get p>s (St. 1.)
both negative than p<s useless
Combining St. 1 and 2
we get p>s hence not relevant
Math Expert
Joined: 02 Sep 2009
Posts: 50543
Re: If p, q, r, and s are non-zero numbers, is pr/qs > r/q?  [#permalink]

### Show Tags

29 Aug 2014, 04:08
2
Aurion wrote:
If p, q, r, and s are non-zero numbers, is pr/qs > r/q?

(1) p > s
(2) rq > 0

Dear Experts, kindly help me with the above problem. My pick was C, but it's incorrect.
pr/qs>r/q =>pqr >rqs => qr(p-s)>0. So i picked C. I guess i am missing something here. Request your help.

If p, q, r, and s are non-zero numbers, is pr/qs > r/q?

Is $$\frac{r}{q}*\frac{p}{s} > \frac{r}{q}$$? Note that we can neither reduce this inequality by r/q, nor cross-multiply because we don't know signs of the variables, thus don't know whether we should flip the sign of the inequality (recall that we must flip the sign of an inequality when multiplying/reducing by a negative value).

(1) p > s. Not sufficient: we know nothing about r and q.

(2) rq > 0. This implies that r/q is also greater than 0, so we can reduce by it and the question becomes: is $$\frac{p}{s} >0$$? We don't know that. Not sufficient.

(1)+(2) The question became "is $$\frac{p}{s} >0$$?" and (1) says that p > s, which is clearly insufficient to answer that. Not sufficient.

Hope it's clear.
_________________
Intern
Joined: 10 Sep 2018
Posts: 7
Re: If p, q, r, and s are non-zero numbers, is pr/qs > r/q?  [#permalink]

### Show Tags

01 Nov 2018, 02:19
IF we solve the inequality pr/qs >rq by taking r/q to LHS

we get two solutions
either r/q>0 & P/s >1 or r/q<0 and P/s <1

Statement 1 says P/s can be greater than 1 or can be less than 1

statement two on solving says that r/q is definitely greater than 0

when we combines stmt 1 and 2 don't we get
r/q>0 & P/s >1
or R/q >0 & P/s <1

out of these the first one is a definite solution for our ineuality in question

Pls tell me what am i doing wrong ?
Intern
Joined: 06 Sep 2018
Posts: 32
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.1
WE: Analyst (Investment Banking)
If p, q, r, and s are non-zero numbers, is pr/qs > r/q?  [#permalink]

### Show Tags

10 Nov 2018, 04:42
Bunuel wrote:
Aurion wrote:
If p, q, r, and s are non-zero numbers, is pr/qs > r/q?

(1) p > s
(2) rq > 0

(2) rq > 0. This implies that r/q is also greater than 0, so we can reduce by it and the question becomes: is $$\frac{p}{s} >0$$? We don't know that. Not sufficient.

(1)+(2) The question became "is $$\frac{p}{s} >0$$?" and (1) says that p > s, which is clearly insufficient to answer that. Not sufficient.

Hope it's clear.

This may be a ridiculous question, and I'm sure I'm overlooking something glaringly obvious, but:

rq>0 tells us both r and q are positive or negative.

So, p/s*r/q>r/q is divided by "r/q", should it not result in p/s>1?

I'm unable to figure out how p/s>0.
DS Forum Moderator
Joined: 21 Aug 2013
Posts: 1365
Location: India
Re: If p, q, r, and s are non-zero numbers, is pr/qs > r/q?  [#permalink]

### Show Tags

10 Nov 2018, 05:54
NCRanjan wrote:
IF we solve the inequality pr/qs >rq by taking r/q to LHS

we get two solutions
either r/q>0 & P/s >1 or r/q<0 and P/s <1

Statement 1 says P/s can be greater than 1 or can be less than 1

statement two on solving says that r/q is definitely greater than 0

when we combines stmt 1 and 2 don't we get
r/q>0 & P/s >1
or R/q >0 & P/s <1

out of these the first one is a definite solution for our ineuality in question

Pls tell me what am i doing wrong ?

Hello

Few things which are probably not right here:

First, you are assuming pr/qs > r/q to be already true, thats why you have already started solving this inequality in your solution. This is NOT to be assumed to be true, infact this is what has to be determined whether its true or not.

Second, from (1) you are assuming p/s > 1. We are NOT given that p/s > 1, rather we are given that p > s. You have divided this given inequality on both sides by 's', without knowing the sign of s (positive or negative). We cannot do that, or we have to take both the cases (one case where s > 0 and another case where s < 0).
DS Forum Moderator
Joined: 21 Aug 2013
Posts: 1365
Location: India
Re: If p, q, r, and s are non-zero numbers, is pr/qs > r/q?  [#permalink]

### Show Tags

10 Nov 2018, 05:58
shaarang wrote:
Bunuel wrote:
Aurion wrote:
If p, q, r, and s are non-zero numbers, is pr/qs > r/q?

(1) p > s
(2) rq > 0

(2) rq > 0. This implies that r/q is also greater than 0, so we can reduce by it and the question becomes: is $$\frac{p}{s} >0$$? We don't know that. Not sufficient.

(1)+(2) The question became "is $$\frac{p}{s} >0$$?" and (1) says that p > s, which is clearly insufficient to answer that. Not sufficient.

Hope it's clear.

This may be a ridiculous question, and I'm sure I'm overlooking something glaringly obvious, but:

rq>0 tells us both r and q are positive or negative.

So, p/s*r/q>r/q is divided by "r/q", should it not result in p/s>1?

I'm unable to figure out how p/s>0.

Hello

What you have done to conclude that p/s > 1 is correct, mathematically. BUT - you have already started working with the inequality pr/sq > r/q; meaning you have already assumed it to be true.

This is NOT given, this is something we have to determine whether its true or not, so we cannot start working with it the way you have done here.

Or maybe I am missing something which you would want to explain.

Also what is your confusion with p/s > 0, I dont understand that query of yours.
Manager
Joined: 21 Jun 2017
Posts: 129
Concentration: Finance, Economics
WE: Corporate Finance (Commercial Banking)
If p, q, r, and s are non-zero numbers, is pr/qs > r/q?  [#permalink]

### Show Tags

10 Nov 2018, 06:29
reduced the expression to (r/q)[(p-s)/s]
So is (r/q)[(p-s)/s] > 0 ?
1. Nothing about r/q or s Insuff
2. Nothing about p-s or s Insuff
Combining 1 and 2
Still nothing about sign of s.
Hence E
_________________

Even if it takes me 30 attempts, I am determined enough to score 740+ in my 31st attempt. This is it, this is what I have been waiting for, now is the time to get up and fight, for my life is 100% my responsibility.

Manager
Joined: 17 Mar 2018
Posts: 52
Re: If p, q, r, and s are non-zero numbers, is pr/qs > r/q?  [#permalink]

### Show Tags

10 Nov 2018, 08:40
I went with thinking as the weights of p q r s

1. p>s---- doesnt tell us any thing about the weights of r and q... maybe r is less than q, which gives different answers for pr>qs
2. rq>0---- so either both r and q are positive or negative, again nothing on the weights of these numbers.

Even together, the weights of r and q are not known Hence, E.
Intern
Joined: 06 Sep 2018
Posts: 32
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.1
WE: Analyst (Investment Banking)
Re: If p, q, r, and s are non-zero numbers, is pr/qs > r/q?  [#permalink]

### Show Tags

10 Nov 2018, 18:14
Quote:
Hello

What you have done to conclude that p/s > 1 is correct, mathematically. BUT - you have already started working with the inequality pr/sq > r/q; meaning you have already assumed it to be true.

This is NOT given, this is something we have to determine whether its true or not, so we cannot start working with it the way you have done here.

Or maybe I am missing something which you would want to explain.

Also what is your confusion with p/s > 0, I dont understand that query of yours.

Ah, shoot. I knew it was something stupid. Thanks for clearing that up!
Re: If p, q, r, and s are non-zero numbers, is pr/qs > r/q? &nbs [#permalink] 10 Nov 2018, 18:14
Display posts from previous: Sort by