January 17, 2019 January 17, 2019 08:00 AM PST 09:00 AM PST Learn the winning strategy for a high GRE score — what do people who reach a high score do differently? We're going to share insights, tips and strategies from data we've collected from over 50,000 students who used examPAL. January 19, 2019 January 19, 2019 07:00 AM PST 09:00 AM PST Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.
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 nonzero numbers, is pr/qs > r/q?
[#permalink]
Show Tags
Updated on: 29 Aug 2014, 03:49
Question Stats:
43% (01:16) correct 57% (00:56) wrong based on 117 sessions
HideShow timer Statistics
If p, q, r, and s are nonzero 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(ps)>0. So i picked C. I guess i am missing something here. Request your help.
Official Answer and Stats are available only to registered users. Register/ Login.
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 nonzero numbers, is pr/qs > r/q?
[#permalink]
Show Tags
28 Aug 2014, 23:25
Aurion wrote: If p, q, r & s are nonzero 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. Hence the answer is E.
_________________
Become a GMAT Club Premium member to avail lot of discounts



Manager
Joined: 21 Sep 2012
Posts: 214
Location: United States
Concentration: Finance, Economics
GPA: 4
WE: General Management (Consumer Products)

Re: If p, q, r, and s are nonzero numbers, is pr/qs > r/q?
[#permalink]
Show Tags
29 Aug 2014, 02:50
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 nonzero numbers, is pr/qs > r/q?
[#permalink]
Show Tags
29 Aug 2014, 03:06
If p, q, r & s are nonzero 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 Option E best answer.



Math Expert
Joined: 02 Sep 2009
Posts: 52231

Re: If p, q, r, and s are nonzero numbers, is pr/qs > r/q?
[#permalink]
Show Tags
29 Aug 2014, 04:08
Aurion wrote: If p, q, r, and s are nonzero 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(ps)>0. So i picked C. I guess i am missing something here. Request your help. If p, q, r, and s are nonzero 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 crossmultiply 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. Answer: E. Hope it's clear.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 10 Sep 2018
Posts: 45

Re: If p, q, r, and s are nonzero 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 ?



Manager
Joined: 06 Sep 2018
Posts: 73
Location: India
Concentration: Finance, Entrepreneurship
GPA: 4
WE: Analyst (Investment Banking)

If p, q, r, and s are nonzero 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 nonzero 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.
Answer: E.
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.
_________________
The importance of mindset on the GMAT  640 to 690 to 740 (Q49 V42) : https://bit.ly/2R1WaK5



DS Forum Moderator
Joined: 21 Aug 2013
Posts: 1429
Location: India

Re: If p, q, r, and s are nonzero 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: 1429
Location: India

Re: If p, q, r, and s are nonzero 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 nonzero 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.
Answer: E.
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: 202
Concentration: Finance, Economics
WE: Corporate Finance (Commercial Banking)

If p, q, r, and s are nonzero numbers, is pr/qs > r/q?
[#permalink]
Show Tags
10 Nov 2018, 06:29
reduced the expression to (r/q)[(ps)/s] So is (r/q)[(ps)/s] > 0 ? 1. Nothing about r/q or s Insuff 2. Nothing about ps 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.
Dil ye Ziddi hai !!!



Manager
Joined: 17 Mar 2018
Posts: 65

Re: If p, q, r, and s are nonzero 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.



Manager
Joined: 06 Sep 2018
Posts: 73
Location: India
Concentration: Finance, Entrepreneurship
GPA: 4
WE: Analyst (Investment Banking)

Re: If p, q, r, and s are nonzero 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!
_________________
The importance of mindset on the GMAT  640 to 690 to 740 (Q49 V42) : https://bit.ly/2R1WaK5




Re: If p, q, r, and s are nonzero numbers, is pr/qs > r/q? &nbs
[#permalink]
10 Nov 2018, 18:14






