Find all School-related info fast with the new School-Specific MBA Forum

It is currently 03 May 2015, 11:57

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

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

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
1 KUDOS received
Manager
Manager
avatar
Joined: 20 Dec 2010
Posts: 182
Location: India
Concentration: Strategy, General Management
GMAT 1: 760 Q50 V42
WE: Information Technology (Computer Software)
Followers: 7

Kudos [?]: 33 [1] , given: 118

If 0 < r < 1 < s < 2, which of the following must be less than 1? I. [#permalink] New post 20 Mar 2011, 03:04
1
This post received
KUDOS
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

62% (02:08) correct 38% (00:42) wrong based on 37 sessions
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
[Reveal] Spoiler: OA
Kaplan GMAT Prep Discount CodesKnewton GMAT Discount CodesManhattan GMAT Discount Codes
1 KUDOS received
Manager
Manager
avatar
Joined: 03 Mar 2011
Posts: 94
Location: United States
Schools: Erasmus (S)
GMAT 1: 730 Q51 V37
GPA: 3.9
Followers: 1

Kudos [?]: 100 [1] , given: 12

Re: If 0 < r < 1 < s < 2, which of the following must be less than 1? I. [#permalink] New post 20 Mar 2011, 03:09
1
This post received
KUDOS
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

So, the answer is A
_________________

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

Director
Director
User avatar
Status: No dream is too large, no dreamer is too small
Joined: 14 Jul 2010
Posts: 662
Followers: 36

Kudos [?]: 354 [0], given: 39

Re: If 0 < r < 1 < s < 2, which of the following must be less than 1? I. [#permalink] New post 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.

[Reveal] Spoiler:
I am not able to eliminate II.



Please help solve this.



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

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 4761
Followers: 295

Kudos [?]: 52 [0], given: 0

Premium Member
Re: If 0 < r < 1 < s < 2, which of the following must be less than 1? I. [#permalink] New post 19 Apr 2015, 21:47
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 27170
Followers: 4225

Kudos [?]: 40931 [0], given: 5576

Re: If 0 < r < 1 < s < 2, which of the following must be less than 1? I. [#permalink] New post 20 Apr 2015, 03:30
Expert's post
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.

Answer: A (I only).

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
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

GMAT Club Premium Membership - big benefits and savings

Re: If 0 < r < 1 < s < 2, which of the following must be less than 1? I.   [#permalink] 20 Apr 2015, 03:30
    Similar topics Author Replies Last post
Similar
Topics:
6 Experts publish their posts in the topic If 0<r<1<s<2. Which of the following must be less than 1. devinawilliam83 6 25 Feb 2012, 01:06
7 Experts publish their posts in the topic If 0 < r < 1 < s < 2, which of the following must be less azule45 8 21 Jan 2011, 10:24
12 Experts publish their posts in the topic If 0 < r < 1 < s < 2, which of the following must be less n2739178 4 25 Oct 2010, 10:56
1 If 0 < r < 1 < s < 2, which of the following chenhong1224 2 10 Oct 2008, 10:29
If 0 < r < 1 < s < 2, which of the following nfa1rhp 1 09 Aug 2007, 11:01
Display posts from previous: Sort by

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

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.