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

It is currently 07 Jul 2015, 21:00

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 x 0, is x^2 / |x| < 1?

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
1 KUDOS received
Manager
Manager
avatar
Joined: 17 Aug 2009
Posts: 238
Followers: 4

Kudos [?]: 125 [1] , given: 25

If x 0, is x^2 / |x| < 1? [#permalink] New post 14 Dec 2009, 00:03
1
This post received
KUDOS
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

57% (02:02) correct 43% (00:53) wrong based on 193 sessions
If x ≠ 0, is x^2 / |x| < 1?

(1) x < 1
(2) x > −1
[Reveal] Spoiler: OA
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 28352
Followers: 4487

Kudos [?]: 45496 [0], given: 6762

Re: Modulus question from GMAT tests [#permalink] New post 14 Dec 2009, 00:47
Expert's post
zaarathelab wrote:
If x ≠ 0, is x^2 / |x| < 1?
(1) x < 1
(2) x > −1


We can safely reduce LHS of inequality \(\frac{x^2}{|x|}<1\) by \(|x|\). We'll get: is \(|x|<1\)? Basically question asks whether \(x\) is in the range \(-1<x<1\).

Statements 1 and 2 are not sufficient, but together they are defining the range for \(x\) as \(-1<x<1\).

Answer: C.
_________________

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

2 KUDOS received
Manager
Manager
avatar
Joined: 09 May 2009
Posts: 202
Followers: 1

Kudos [?]: 126 [2] , given: 13

Re: Modulus question from GMAT tests [#permalink] New post 14 Dec 2009, 08:22
2
This post received
KUDOS
IMO c

the expression x^2/lxl<1 will always be +ve as the N is a sqaure and mod x is always +ve

the expression is true only for fractional value

s1) tells us that x can be a +ve or -ve fractional and also can be a -int hence insuff.
s2) tells us that x can be a +ve or -ve fractional and also can be a +int hence insuff....

combinig x is only a fraction and hence suff...
_________________

GMAT is not a game for losers , and the moment u decide to appear for it u are no more a loser........ITS A BRAIN GAME

1 KUDOS received
Senior Manager
Senior Manager
avatar
Joined: 16 Apr 2009
Posts: 341
Followers: 1

Kudos [?]: 76 [1] , given: 14

Re: Modulus question from GMAT tests [#permalink] New post 16 Dec 2009, 19:57
1
This post received
KUDOS
Bunuel wrote:
zaarathelab wrote:
If x ≠ 0, is x^2 / |x| < 1?
(1) x < 1
(2) x > −1


We can safely reduce inequality \(\frac{x^2}{|x|}<1\) by \(|x|\). We'll get: is \(|x|<1\)? Basically question asks whether \(x\) is in the range \(-1<x<1\).

Statements 1 and 2 are not sufficient, but together they are defining the range for \(x\) as \(-1<x<1\).

Answer: C.


Bunuel - please clarify this divison -\(\frac{x^2}{|x|}<1\) by \(|x|\). We'll get: is \(|x|<1\)? can be done because |x| is always +ve or is there are any other reason ?
_________________

Always tag your question

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 28352
Followers: 4487

Kudos [?]: 45496 [0], given: 6762

Re: Modulus question from GMAT tests [#permalink] New post 17 Dec 2009, 03:04
Expert's post
ichha148 wrote:
Bunuel - please clarify this divison -\(\frac{x^2}{|x|}<1\) by \(|x|\). We'll get: is \(|x|<1\)? can be done because |x| is always +ve or is there are any other reason ?


We should never multiply (or reduce) inequality by variable (or expression with variable) if we don't know the sign of it or are not certain that variable (or expression with variable) doesn't equal to zero.

But in this case we are not reducing the inequality we are reducing only one part of it. So, it's safe to do so.

For example if we had: \(\frac{x^4}{x^3}<0\) we can reduce LHS by \(x^3\) and write \(x<0\).
_________________

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

Senior Manager
Senior Manager
avatar
Joined: 18 Aug 2009
Posts: 329
Followers: 8

Kudos [?]: 212 [0], given: 13

Re: Mod [#permalink] New post 29 Dec 2009, 05:10
If x ≠ 0, is x^2/|x|< 1?

1: x<1 - Insufficient. x can be -2 or 1/2
2:x>-1 - Insufficient. x can be 2 or 1/2

Together, sufficient. x must be a fraction, and thus the answer is C.
Intern
Intern
avatar
Joined: 21 Jul 2012
Posts: 11
Followers: 0

Kudos [?]: 3 [0], given: 17

If x≠0, is x^2/abs(x)<1? [#permalink] New post 08 Jan 2013, 03:12
If x ≠ 0, is x^2/abs(x)<1?
(1) x < 1
(2) x > −1

Question is came from GWD. My approach is time comsuming. So suggest me a quicker approch. Thanks
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 28352
Followers: 4487

Kudos [?]: 45496 [0], given: 6762

Re: If x≠0, is x^2/abs(x)<1? [#permalink] New post 08 Jan 2013, 03:30
Expert's post
curtis0063 wrote:
If x ≠ 0, is x^2/abs(x)<1?
(1) x < 1
(2) x > −1

Question is came from GWD. My approach is time comsuming. So suggest me a quicker approch. Thanks


Merging similar topics. Please refer to the solutions above.
_________________

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

Intern
Intern
avatar
Joined: 14 Feb 2012
Posts: 30
Followers: 0

Kudos [?]: 4 [0], given: 6

Re: Modulus question from GMAT tests [#permalink] New post 10 Oct 2013, 05:48
Bunuel wrote:
zaarathelab wrote:
If x ≠ 0, is x^2 / |x| < 1?
(1) x < 1
(2) x > −1


We can safely reduce LHS of inequality \(\frac{x^2}{|x|}<1\) by \(|x|\). We'll get: is \(|x|<1\)? Basically question asks whether \(x\) is in the range \(-1<x<1\).

Statements 1 and 2 are not sufficient, but together they are defining the range for \(x\) as \(-1<x<1\).

Answer: C.


How do you get that \(|x|<1\)?
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 28352
Followers: 4487

Kudos [?]: 45496 [0], given: 6762

Re: Modulus question from GMAT tests [#permalink] New post 10 Oct 2013, 06:15
Expert's post
waltiebikkiebal wrote:
Bunuel wrote:
zaarathelab wrote:
If x ≠ 0, is x^2 / |x| < 1?
(1) x < 1
(2) x > −1


We can safely reduce LHS of inequality \(\frac{x^2}{|x|}<1\) by \(|x|\). We'll get: is \(|x|<1\)? Basically question asks whether \(x\) is in the range \(-1<x<1\).

Statements 1 and 2 are not sufficient, but together they are defining the range for \(x\) as \(-1<x<1\).

Answer: C.


How do you get that \(|x|<1\)?


\(\frac{x^2}{|x|}<1\);

\(\frac{|x|*|x|}{|x|}<1\);

\(|x|<1\).

Does this make sense?
_________________

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

Intern
Intern
avatar
Joined: 14 Feb 2012
Posts: 30
Followers: 0

Kudos [?]: 4 [0], given: 6

Re: Modulus question from GMAT tests [#permalink] New post 10 Oct 2013, 06:17
yes, thanks a lot.
It is clear now.
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 5403
Followers: 311

Kudos [?]: 60 [0], given: 0

Premium Member
Re: If x 0, is x^2 / |x| < 1? [#permalink] New post 09 Jun 2015, 09:19
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
EMPOWERgmat Instructor
User avatar
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 2741
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Followers: 117

Kudos [?]: 759 [0], given: 49

Re: If x 0, is x^2 / |x| < 1? [#permalink] New post 09 Jun 2015, 22:13
Expert's post
Hi All,

This question is loaded with Number Property rules. If you know the rules, then you can make relatively quick work of this question; you can also solve it by TESTing VALUES...

We're told that X ≠ 0. We're asked if (X^2) /(|X|) < 1. This is a YES/NO question.

Before dealing with the two Facts, I want to point out a couple of Number Properties in the question stem:

1) X^2 will either be 0 or positive.
2) |X| will either be 0 or positive.
3) For the fraction in the question to be LESS than 1, X^2 must be LESS than |X|.

Fact 1: X < 1

IF...
X = 1/2
(1/4)/|1/2| = 1/2 and the answer to the question is YES

IF...
X = -1
(1)/|-1| = 1 and the answer to the question is NO
Fact 1 is INSUFFICIENT

Fact 2: X > −1

IF...
X = 1/2
(1/4)/|1/2| = 1/2 and the answer to the question is YES

IF...
X = 1
(1)/|1| = 1 and the answer to the question is NO
Fact 2 is INSUFFICIENT

Combined, we know...
-1 < X < 1

Since X cannot equal 0, X must be a FRACTION (either negative or positive). In ALL cases, X^2 will be LESS than |X|, so the fraction will ALWAYS be less than 1 and the answer to the question is ALWAYS YES.
Combined, SUFFICIENT

Final Answer:
[Reveal] Spoiler:
C


GMAT assassins aren't born, they're made,
Rich
_________________

Official Guide 2016 Question Breakdown:
http://gmatclub.com/forum/empowergmat-blog-198415.html#p1527977

Rich Cohen
Rich.C@empowergmat.com
http://www.empowergmat.com

GMAT Club Verified Reviews for EMPOWERgmat & Special Discount

EMPOWERgmat Podcast - A Wild Secret About The GMAT Algorithm


Re: If x 0, is x^2 / |x| < 1?   [#permalink] 09 Jun 2015, 22:13
    Similar topics Author Replies Last post
Similar
Topics:
9 Experts publish their posts in the topic If x#0, is x^2/|x| < 1? udaymathapati 12 08 Sep 2010, 10:51
10 Experts publish their posts in the topic If x 0, is x^2/|x| < 1? msand 7 03 Jan 2010, 06:14
1 Is x negative? 1) x^3(1-x^2)<0 2) x^2-1<0 I3igDmsu 4 21 Jun 2009, 17:59
Is x negative? 1) x^3(1-x^2) < 0 2) x^2 - 1 < 0 bigtreezl 2 08 Jun 2009, 22:24
1 Is x negative? 1. x^3(1-x^2)<0 2. x^2-1<0 vksunder 9 17 Jun 2008, 18:05
Display posts from previous: Sort by

If x 0, is x^2 / |x| < 1?

  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®.