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

 It is currently 17 Feb 2019, 08:02

### 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 February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
• ### Free GMAT Algebra Webinar

February 17, 2019

February 17, 2019

07:00 AM PST

09:00 AM PST

Attend this Free Algebra Webinar and learn how to master Inequalities and Absolute Value problems on GMAT.
• ### Valentine's day SALE is on! 25% off.

February 18, 2019

February 18, 2019

10:00 PM PST

11:00 PM PST

We don’t care what your relationship status this year - we love you just the way you are. AND we want you to crush the GMAT!

# If 0 < r < 1 < s < 2, which of the following must be less than 1? I.

Author Message
Manager
Joined: 20 Dec 2010
Posts: 168
Location: India
Concentration: Strategy, General Management
GMAT 1: 760 Q50 V42
WE: Information Technology (Computer Software)
If 0 < r < 1 < s < 2, which of the following must be less than 1? I.  [#permalink]

### Show Tags

20 Mar 2011, 03:04
1
4
00:00

Difficulty:

35% (medium)

Question Stats:

64% (00:54) correct 36% (00:49) wrong based on 121 sessions

### HideShow timer Statistics

If 0 < r < 1 < s < 2, which of the following must be less than 1?

I. r/s
II. rs
III. s - r

A. I only
B. II only
C. III only
D. I and II
E. I and III

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-0-r-1-s-2-which-of-the-following-must-be-less-than-128112.html
Manager
Joined: 03 Mar 2011
Posts: 87
Location: United States
Schools: Erasmus (S)
GMAT 1: 730 Q51 V37
GPA: 3.9
Re: If 0 < r < 1 < s < 2, which of the following must be less than 1? I.  [#permalink]

### Show Tags

20 Mar 2011, 03:09
1
We could solve this easily using contrexamples.
I is true since r<s and both are positive
II is false. Take r=2/3, s=3/2. rs=1
III is false. Take r=0.1, s=1.9. s-r=1.8

_________________

If my post is useful for you not be ashamed to KUDO me!
Let kudo each other!

Director
Status: No dream is too large, no dreamer is too small
Joined: 14 Jul 2010
Posts: 504
Re: If 0 < r < 1 < s < 2, which of the following must be less than 1? I.  [#permalink]

### Show Tags

17 Jun 2011, 03:56
nikhilsrl wrote:
if 0<r<1<s<2, which of the following must be less than 1?

I. r/s
II. rs
III. s - r

a) I only
b) II only
c) III only
d) I and II
e) I and III

OA is provided.

I am not able to eliminate II.

Let r=1/2 and s=3/2

I. r/s = 1/3 this is < 1 true.
II. rs = 3/4 this is < 1 true.
III. s-r = 3/2-1/2 = 1 this is NOT < 1 false

Now let, r=2/3 and 3/2 as well.

I. r/s = 1/3 this is < 1 true.
II. rs = 1 this is NOT < 1 false
III. s-r = 3/2-1/2 = 5/6 this is < 1 true.
_________________

Collections:-
PSof OG solved by GC members: http://gmatclub.com/forum/collection-ps-with-solution-from-gmatclub-110005.html
DS of OG solved by GC members: http://gmatclub.com/forum/collection-ds-with-solution-from-gmatclub-110004.html
100 GMAT PREP Quantitative collection http://gmatclub.com/forum/gmat-prep-problem-collections-114358.html
Collections of work/rate problems with solutions http://gmatclub.com/forum/collections-of-work-rate-problem-with-solutions-118919.html
Mixture problems in a file with best solutions: http://gmatclub.com/forum/mixture-problems-with-best-and-easy-solutions-all-together-124644.html

Math Expert
Joined: 02 Sep 2009
Posts: 52911
Re: If 0 < r < 1 < s < 2, which of the following must be less than 1? I.  [#permalink]

### Show Tags

20 Apr 2015, 03:30
If 0 < r < 1 < s < 2, which of the following must be less than 1?
I. r/s
II. rs
III. s - r

A. I only
B. II only
C. III only
D. I and II
E. I and III

Notice that we are asked "which of the following MUST be lees than 1, not COULD be less than 1. For such kind of questions if you can prove that a statement is NOT true for one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer.

Given: $$0 < r < s$$ --> divide by $$s$$ (we can safely do this since we know that $$s>0$$) --> $$\frac{r}{s}<1$$, so I must be true;

II. rs: if $$r=\frac{9}{10}<1$$ and $$1<(s=\frac{10}{9})<2$$ then $$rs=1$$, so this statement is not alway true;

III. s-r: if $$r=0.5<1$$ and 1$$<(s=1.5)<2$$ then $$s-r=1$$, so this statement is not alway true.

Check our Must or Could be True Questions to practice: search.php?search_id=tag&tag_id=193

Hope it helps.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-0-r-1-s-2-which-of-the-following-must-be-less-than-128112.html
_________________
Non-Human User
Joined: 09 Sep 2013
Posts: 9836
Re: If 0 < r < 1 < s < 2, which of the following must be less than 1? I.  [#permalink]

### Show Tags

08 Oct 2018, 04:20
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.
_________________
Re: If 0 < r < 1 < s < 2, which of the following must be less than 1? I.   [#permalink] 08 Oct 2018, 04:20
Display posts from previous: Sort by