It is currently 19 Oct 2017, 04:18

### 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 June
Open Detailed Calendar

# If r > 0 and s > 0, is r/s < s/r?

Author Message
TAGS:

### Hide Tags

Intern
Joined: 22 Dec 2009
Posts: 22

Kudos [?]: 71 [1], given: 1

If r > 0 and s > 0, is r/s < s/r? [#permalink]

### Show Tags

17 Aug 2010, 09:02
1
KUDOS
10
This post was
BOOKMARKED
00:00

Difficulty:

5% (low)

Question Stats:

77% (01:08) correct 23% (01:13) wrong based on 1201 sessions

### HideShow timer Statistics

If r > 0 and s > 0, is r/s < s/r?

(1) r/(3s) = 1/4
(2) s = r + 4
[Reveal] Spoiler: OA

Kudos [?]: 71 [1], given: 1

Manager
Joined: 06 Aug 2010
Posts: 218

Kudos [?]: 225 [7], given: 5

Location: Boston
Re: GMAT - PAPER TEST QUESTION [#permalink]

### Show Tags

01 Nov 2010, 08:44
7
KUDOS
1
This post was
BOOKMARKED
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.

Kudos [?]: 225 [7], given: 5

Math Expert
Joined: 02 Sep 2009
Posts: 41893

Kudos [?]: 128822 [3], given: 12183

Re: GMAT - PAPER TEST QUESTION [#permalink]

### Show Tags

17 Aug 2010, 09:21
3
KUDOS
Expert's post
6
This post was
BOOKMARKED
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.

_________________

Kudos [?]: 128822 [3], given: 12183

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4133

Kudos [?]: 2891 [2], given: 0

GPA: 3.82
Re: If r > 0 and s > 0, is r/s < s/r? [#permalink]

### Show Tags

17 Nov 2015, 10:29
2
KUDOS
Expert's post
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^2-s^2<0?, or (r-s)(r+s)<0? and r>0 and s>0, so we want to know whether
r-s>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, s-r=4>0. s>r, so this also answers the question 'yes' and is sufficient.

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 spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
Find a 10% off coupon code for GMAT Club members.
“Receive 5 Math Questions & Solutions Daily”
Unlimited Access to over 120 free video lessons - try it yourself

Kudos [?]: 2891 [2], given: 0

Intern
Joined: 11 Jun 2013
Posts: 4

Kudos [?]: 6 [1], given: 3

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
1
KUDOS
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

Kudos [?]: 6 [1], given: 3

Intern
Joined: 09 Nov 2011
Posts: 7

Kudos [?]: [0], given: 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

Kudos [?]: [0], given: 2

Senior Manager
Status: Prevent and prepare. Not repent and repair!!
Joined: 13 Feb 2010
Posts: 253

Kudos [?]: 125 [0], given: 282

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 succeed--Michael Jordan
Kudos drives a person to better himself every single time. So Pls give it generously
Wont give up till i hit a 700+

Kudos [?]: 125 [0], given: 282

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16678

Kudos [?]: 273 [0], given: 0

Re: If r > 0 and s > 0, is r/s < s/r? [#permalink]

### Show Tags

01 Oct 2014, 05:30
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Kudos [?]: 273 [0], given: 0

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16678

Kudos [?]: 273 [0], given: 0

Re: If r > 0 and s > 0, is r/s < s/r? [#permalink]

### Show Tags

14 Nov 2015, 04:55
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Kudos [?]: 273 [0], given: 0

Director
Joined: 04 Jun 2016
Posts: 647

Kudos [?]: 365 [0], given: 36

GMAT 1: 750 Q49 V43
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

_________________

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 semi-retired.

Kudos [?]: 365 [0], given: 36

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16678

Kudos [?]: 273 [0], given: 0

Re: If r > 0 and s > 0, is r/s < s/r? [#permalink]

### Show Tags

25 Jul 2017, 03:49
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Kudos [?]: 273 [0], given: 0

Re: If r > 0 and s > 0, is r/s < s/r?   [#permalink] 25 Jul 2017, 03:49
Display posts from previous: Sort by