Oct 14 08:00 PM PDT  11:00 PM PDT Join a 4day FREE online boot camp to kick off your GMAT preparation and get you into your dream bschool in R2.**Limited for the first 99 registrants. Register today! Oct 15 12:00 PM PDT  01:00 PM PDT Join this live GMAT class with GMAT Ninja to learn to conquer your fears of long, kooky GMAT questions. Oct 16 08:00 PM PDT  09:00 PM PDT EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth $100 with the 3 Month Pack ($299) Oct 19 07:00 AM PDT  09:00 AM PDT Does GMAT RC seem like an uphill battle? eGMAT is conducting a free webinar to help you learn reading strategies that can enable you to solve 700+ level RC questions with at least 90% accuracy in less than 10 days. Sat., Oct 19th at 7 am PDT Oct 20 07:00 AM PDT  09:00 AM PDT Get personalized insights on how to achieve your Target Quant Score.
Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 22 Dec 2009
Posts: 20

If r > 0 and s > 0, is r/s < s/r?
[#permalink]
Show Tags
17 Aug 2010, 09:02
Question Stats:
82% (01:26) correct 18% (01:40) wrong based on 1551 sessions
HideShow timer Statistics
If r > 0 and s > 0, is r/s < s/r? (1) r/(3s) = 1/4 (2) s = r + 4
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 58316

Re: GMAT  PAPER TEST QUESTION
[#permalink]
Show Tags
17 Aug 2010, 09:21
If r > 0 and S > 0, Is r/s < s/r?Is \(\frac{r}{s}<\frac{s}{r}\)? (1) \(\frac{r}{3s}=\frac{1}{4}\) > \(\frac{r}{s}=\frac{3}{4}\), so \(\frac{s}{r}=\frac{4}{3}\) > \(\frac{r}{s}=\frac{3}{4}<\frac{4}{3}=\frac{s}{r}\) thus answer to the question is YES. Sufficient. (2) \(s=r+4\) > so \(s>r\) as given that \(r>0\) > \(s>r>0\) > \(\frac{s}{r}>1>\frac{r}{s}\), thus answer to the question is YES. Sufficient. Answer: D.
_________________




Manager
Joined: 06 Aug 2010
Posts: 153
Location: Boston

Re: GMAT  PAPER TEST QUESTION
[#permalink]
Show Tags
01 Nov 2010, 08:44
cmugeria wrote: If R > 0 and S > 0, Is r/s < s/r?
1) r/3s =1/4 2) s = r + 4 Since r and s are both positive, we can simplify the inequality to \(r^2 < s^2\), and by taking the square root of both sides, \(r < s\). (1) \(4r = 3s\) \(r = \frac{3}{4}s\) So r < s. Sufficient. (2) Since \(r = s  4\), \(r < s\). Sufficient.




Intern
Joined: 09 Nov 2011
Posts: 2

Re: If R > 0 and S > 0, Is r/s < s/r? 1) r/3s =1/4 2) s
[#permalink]
Show Tags
29 Nov 2011, 01:22
1. r/3s=1/4 so 3s = 4r , which is s>r  Sufficient 2. s=r+4 menas S>R  sufficient
Answer  D



Manager
Status: Prevent and prepare. Not repent and repair!!
Joined: 13 Feb 2010
Posts: 173
Location: India
Concentration: Technology, General Management
GPA: 3.75
WE: Sales (Telecommunications)

Re: If r > 0 and s > 0, is r/s < s/r?
[#permalink]
Show Tags
29 Jan 2013, 09:04
cmugeria wrote: If r > 0 and s > 0, is r/s < s/r?
(1) r/(3s) = 1/4 (2) s = r + 4 For 1  \(\frac{r}{s}\)= 3/4we can deduce from this From 2.... s = r+4 substituting this in the question \(\frac{r}{4+r}\)<\(\frac{4+r}{r}\)
_________________
I've failed over and over and over again in my life and that is why I succeedMichael Jordan Kudos drives a person to better himself every single time. So Pls give it generously Wont give up till i hit a 700+



Intern
Joined: 11 Jun 2013
Posts: 4
Location: United States
Concentration: Entrepreneurship, Technology
GMAT 1: 640 Q39 V38 GMAT 2: 660 Q44 V36
GPA: 3.5
WE: Military Officer (Military & Defense)

Re: If r > 0 and s > 0, is r/s < s/r?
[#permalink]
Show Tags
01 Sep 2013, 14:09
First I restated the problem since we are given r and s are greater than 0 > therefore, the question can be solved by answering whether or not r^2<s^2.
(1) r = (3/4)s [r<s, so r^2 < s^2] Sufficient AD/BCE  elminate BCE (3) s = r + 4 [r<s, so r^2 < s^2] Sufficent  elminate A ... answered D



Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8001
GPA: 3.82

Re: If r > 0 and s > 0, is r/s < s/r?
[#permalink]
Show Tags
17 Nov 2015, 10:29
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution. If r > 0 and s > 0, is r/s < s/r? (1) r/(3s) = 1/4 (2) s = r + 4 In inequalities, the sign does not change when a positive integer is multiplied on both sides. If we modify the question, r/x<s/r, or is r^2<s^2, of is r^2s^2<0?, or (rs)(r+s)<0? and r>0 and s>0, so we want to know whether rs>0? For condition 1, in r/s=3/4, r and s are positive, so s>r, which answers the question 'yes' and is sufficient. For condition 2, sr=4>0. s>r, so this also answers the question 'yes' and is sufficient. The answer becomes (D). Once we modify the original condition and the question according to the variable approach method 1, we can solve approximately 30% of DS questions.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spareThe oneandonly World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only $79 for 1 month Online Course""Free Resources30 day online access & Diagnostic Test""Unlimited Access to over 120 free video lessons  try it yourself"



Director
Joined: 04 Jun 2016
Posts: 557

If r > 0 and s > 0, is r/s < s/r?
[#permalink]
Show Tags
18 Jul 2016, 05:51
cmugeria wrote: If r > 0 and s > 0, is r/s < s/r?
(1) r/(3s) = 1/4 (2) s = r + 4 If r > 0 and s > 0, \(is \frac{r}{s} < \frac{s}{r}?\) The question stem tells us that both r and s are positive. What a relief, we can now do any operations on r and s without worrying about the polarity of the variable. Lets rephrase the statement Is \(\frac{r}{s} < \frac{s}{r}\) THIS IS THE REAL QUESTION : Is \(r^2 < s^2 ?\)(1)\(\frac{r}{(3s)} = \frac{1}{4}\) \(r=\frac{3}{4}*s\) Because r<s Therefore \(r^2 < s^2\) SUFFICIENT (2) s = r + 4 Its obvious that s is bigger and r is smaller \(r<s\) and \(r^2<s^2\) SUFFICIENT ANSWER IS D
_________________
Posting an answer without an explanation is "GOD COMPLEX". The world doesn't need any more gods. Please explain you answers properly. FINAL GOODBYE : 17th SEPTEMBER 2016. .. 16 March 2017  I am back but for all purposes please consider me semiretired.



Intern
Joined: 07 Oct 2017
Posts: 1

If r > 0 and s > 0, is r/s < s/r?
[#permalink]
Show Tags
06 Nov 2017, 03:50
MathRevolution wrote: Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.
If r > 0 and s > 0, is r/s < s/r?
(1) r/(3s) = 1/4 (2) s = r + 4
In inequalities, the sign does not change when a positive integer is multiplied on both sides. If we modify the question, r/x<s/r, or is r^2<s^2, of is r^2s^2<0?, or (rs)(r+s)<0? and r>0 and s>0, so we want to know whether rs>0? For condition 1, in r/s=3/4, r and s are positive, so s>r, which answers the question 'yes' and is sufficient. For condition 2, sr=4>0. s>r, so this also answers the question 'yes' and is sufficient. The answer becomes (D).
Once we modify the original condition and the question according to the variable approach method 1, we can solve approximately 30% of DS questions. Posted from my mobile devicePosted from my mobile deviceHow do we arrive @ this.. rs >0 ..I cant seem to figure it out Thanks



VP
Joined: 09 Mar 2016
Posts: 1230

Re: If r > 0 and s > 0, is r/s < s/r?
[#permalink]
Show Tags
21 Aug 2018, 12:38
Bunuel wrote: If r > 0 and S > 0, Is r/s < s/r?
Is \(\frac{r}{s}<\frac{s}{r}\)?
(1) \(\frac{r}{3s}=\frac{1}{4}\) > \(\frac{r}{s}=\frac{3}{4}\), so \(\frac{s}{r}=\frac{4}{3}\) > \(\frac{r}{s}=\frac{3}{4}<\frac{4}{3}=\frac{s}{r}\) thus answer to the question is YES. Sufficient.
(2) \(s=r+4\) > so \(s>r\) as given that \(r>0\) > \(s>r>0\) > \(\frac{s}{r}>1>\frac{r}{s}\), thus answer to the question is YES. Sufficient.
Answer: D. how from here \(\frac{r}{3s}=\frac{1}{4}\) we got this \(\frac{r}{s}=\frac{3}{4}\) ????



Math Expert
Joined: 02 Sep 2009
Posts: 58316

Re: If r > 0 and s > 0, is r/s < s/r?
[#permalink]
Show Tags
21 Aug 2018, 12:44
dave13 wrote: Bunuel wrote: If r > 0 and S > 0, Is r/s < s/r?
Is \(\frac{r}{s}<\frac{s}{r}\)?
(1) \(\frac{r}{3s}=\frac{1}{4}\) > \(\frac{r}{s}=\frac{3}{4}\), so \(\frac{s}{r}=\frac{4}{3}\) > \(\frac{r}{s}=\frac{3}{4}<\frac{4}{3}=\frac{s}{r}\) thus answer to the question is YES. Sufficient.
(2) \(s=r+4\) > so \(s>r\) as given that \(r>0\) > \(s>r>0\) > \(\frac{s}{r}>1>\frac{r}{s}\), thus answer to the question is YES. Sufficient.
Answer: D. how from here \(\frac{r}{3s}=\frac{1}{4}\) we got this \(\frac{r}{s}=\frac{3}{4}\) ???? By multiplying both sides by 3.
_________________



Manager
Joined: 01 Jan 2019
Posts: 66
Location: Canada
Concentration: Finance, Economics
GPA: 3.24

Re: If r > 0 and s > 0, is r/s < s/r?
[#permalink]
Show Tags
30 Jul 2019, 18:28
I have a question here... so I simplified r/s <s/r and got r^2  s^2 < 0 ( read equation1) and then for statement 2, I put the values s=r+4 on eq 1 and I got r<2?
Though the stem says r>0...
So where did I do wrong?
Posted from my mobile device



Intern
Joined: 05 Aug 2018
Posts: 38

Re: If r > 0 and s > 0, is r/s < s/r?
[#permalink]
Show Tags
30 Aug 2019, 08:37
The statement can be rewritten as r<s i.e r/s<s/r => r^2<s^2 => r<s. We need to prove magnitude of r is less than magnitude of s. Statement 1: r/3s<1/4 => r/s=3/4=> r<s Sufficient. Statement 2:s=r+4 Since, both r and s are >0 => r<s. Sufficient. Answer D. VeritasKarishma Bunuel Is the approach correct? Please reply.




Re: If r > 0 and s > 0, is r/s < s/r?
[#permalink]
30 Aug 2019, 08:37






