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

It is currently 24 Oct 2014, 16:21

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 is not equal to zero, is |x| < 1 ?

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Expert Post
Moderator
Moderator
User avatar
Joined: 01 Sep 2010
Posts: 2444
Followers: 312

Kudos [?]: 2622 [0], given: 697

If x is not equal to zero, is |x| < 1 ? [#permalink] New post 30 Sep 2012, 05:20
Expert's post
3
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

60% (02:08) correct 40% (01:04) wrong based on 110 sessions
If x is not equal to zero, is |x| < 1 ?

(1) x^2 < 1

(2) |x| < 1/x

[Reveal] Spoiler:
I would like to know if I do in the right manner

question: x id non zero, is | x | < 1 ??? now to be < 1 x must be negative, so the question become " is x negative ???

1) for a square to be < 1 the must be for example \frac{- 1}{2} ----> x is negative . suff

2) for x to be minor of a certain number that is the reciprocal i.e. : -2 < - 1/2 --------> x is negative. suff

is correct or I should rethink the entire part regarding inequalities ?? because this statement should not take you more that 50 seconds to solve. otherwise you get in trouble with this exam.

Thanks
[Reveal] Spoiler: OA

_________________

COLLECTION OF QUESTIONS
Quant: 1. Bunuel Signature Collection - The Next Generation 2. Bunuel Signature Collection ALL-IN-ONE WITH SOLUTIONS 3. Veritas Prep Blog PDF Version
Verbal:1. Best EXTERNAL resources to tackle the GMAT Verbal Section 2. e-GMAT's ALL CR topics-Consolidated 3. New Critical Reasoning question bank by carcass 4. Meaning/Clarity SC Question Bank by Carcass_Souvik 5. e-GMAT's ALL SC topics-Consolidated-2nd Edition 6. The best reading to improve Reading Comprehension 7.Verbal question bank and Directories


Last edited by Bunuel on 01 Oct 2012, 04:50, edited 1 time in total.
Renamed the topic and edited the question.
2 KUDOS received
Director
Director
User avatar
Joined: 22 Mar 2011
Posts: 612
WE: Science (Education)
Followers: 73

Kudos [?]: 529 [2] , given: 43

Re: If x is not equal to zero, is | x | < 1 ?? [#permalink] New post 30 Sep 2012, 05:34
2
This post received
KUDOS
carcass wrote:
If x is not equal to zero, is | x | < 1 ??

1) x^2 < 1

2) | x | < \frac{1}{x}

I would like to know if I do in the right manner

question: x id non zero, is | x | < 1 ??? now to be < 1 x must be negative, so the question become " is x negative ???

1) for a square to be < 1 the must be for example \frac{- 1}{2} ----> x is negative . suff

2) for x to be minor of a certain number that is the reciprocal i.e. : -2 < - 1/2 --------> x is negative. suff

is correct or I should rethink the entire part regarding inequalities ?? because this statement should not take you more that 50 seconds to solve. otherwise you get in trouble with this exam.

Thanks



The condition x non-zero was given just because statement (2) has x in the denominator.

x id non zero, is | x | < 1 ???
Not necessarily. x can be greater than 1 or less than -1, in which case, definitely |x| is not less than 1.

now to be < 1 x must be negative, so the question become " is x negative ??? NO
x can be between 0 and 1.

(1) x^2 < 1, take square root from both sides and obtain |x|<1, because \sqrt{x^2}=|x|.
Sufficient.

(2) Since |x|<\frac{1}{x}, it follows that x>0, because |x|>0. x cannot be negative!!!
Then, the given inequality becomes x<\frac{1}{x}, or x^2<1 (we can multiply both sides by x, which is positive) and we are again in the situation from (1) above.
Sufficient.

Answer D.
_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Manager
Manager
avatar
Status: Fighting again to Kill the GMAT devil
Joined: 02 Jun 2009
Posts: 137
Location: New Delhi
WE 1: Oil and Gas - Engineering & Construction
Followers: 0

Kudos [?]: 27 [0], given: 48

Re: If x is not equal to zero, is | x | < 1 ?? [#permalink] New post 30 Sep 2012, 06:58
Perfect Explanation, Evajager, @Carcass this is a very common mistake which I am also prone to make.
Thanks @Evajager - Your explanation for {B}
Quote:
(2) Since , it follows that , because . cannot be negative!!!
Then, the given inequality becomes , or (we can multiply both sides by , which is positive) and we are again in the situation from (1) above.
Sufficient.


I remember skipping a Question just like this in one of my exams because I gt stuck!!! in solving - | x | < 1/x

Thanks guys you rock!!!
_________________

Giving Kudos, is a great Way to Help the GC Community Kudos

Director
Director
User avatar
Joined: 22 Mar 2011
Posts: 612
WE: Science (Education)
Followers: 73

Kudos [?]: 529 [0], given: 43

Re: If x is not equal to zero, is | x | < 1 ?? [#permalink] New post 30 Sep 2012, 12:29
EvaJager wrote:
carcass wrote:
If x is not equal to zero, is | x | < 1 ??

1) x^2 < 1

2) | x | < \frac{1}{x}

I would like to know if I do in the right manner

question: x id non zero, is | x | < 1 ??? now to be < 1 x must be negative, so the question become " is x negative ???

1) for a square to be < 1 the must be for example \frac{- 1}{2} ----> x is negative . suff

2) for x to be minor of a certain number that is the reciprocal i.e. : -2 < - 1/2 --------> x is negative. suff

is correct or I should rethink the entire part regarding inequalities ?? because this statement should not take you more that 50 seconds to solve. otherwise you get in trouble with this exam.

Thanks



The condition x non-zero was given just because statement (2) has x in the denominator.

x id non zero, is | x | < 1 ???
Not necessarily. x can be greater than 1 or less than -1, in which case, definitely |x| is not less than 1.

now to be < 1 x must be negative, so the question become " is x negative ??? NO
x can be between 0 and 1.

(1) x^2 < 1, take square root from both sides and obtain |x|<1, because \sqrt{x^2}=|x|.
Sufficient.

(2) Since |x|<\frac{1}{x}, it follows that x>0, because |x|>0. x cannot be negative!!!
Then, the given inequality becomes x<\frac{1}{x}, or x^2<1 (we can multiply both sides by x, which is positive) and we are again in the situation from (1) above.
Sufficient.

Answer D.



Correction: in (2) and we are again in the situation from (1) above. - not exactly, but similar as we have x^2<1 but in addition x>0. In (1) x could also be negative.
The conclusion is still correct, as now |x|=x<1.
_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Expert Post
2 KUDOS received
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4877
Location: Pune, India
Followers: 1157

Kudos [?]: 5379 [2] , given: 165

Re: If x is not equal to zero, is | x | < 1 ?? [#permalink] New post 30 Sep 2012, 21:50
2
This post received
KUDOS
Expert's post
carcass wrote:
If x is not equal to zero, is | x | < 1 ??

1) x^2 < 1

2) | x | < \frac{1}{x}

I would like to know if I do in the right manner

question: x id non zero, is | x | < 1 ??? now to be < 1 x must be negative, so the question become " is x negative ???

1) for a square to be < 1 the must be for example \frac{- 1}{2} ----> x is negative . suff

2) for x to be minor of a certain number that is the reciprocal i.e. : -2 < - 1/2 --------> x is negative. suff

is correct or I should rethink the entire part regarding inequalities ?? because this statement should not take you more that 50 seconds to solve. otherwise you get in trouble with this exam.

Thanks


I would suggest you to keep 4 ranges in mind when dealing with squares, reciprocals etc.

............... -1........ 0 ........ 1 ..............

Less than -1, -1 to 0, 0 to 1 and greater than 1

You can do the question logically or by plugging in numbers.

Ques: If x is not equal to zero, is | x | < 1 ??
Logically, | x | implies distance from 0 on the number line. So the question becomes "Is x a distance of less than 1 away from 0?" i.e. "Is -1 < x < 1?" given x is not 0.

Statement 1: x^2 < 1
Square of a number will be less than 1 only if the absolute value of the number is less than 1. This means | x | < 1. The number needn't be negative. If it is positive, it should be less than 1. If it negative, it should be greater than -1.
Or, do you remember how to solve inequalities using the wave? x^2 < 1 is x^2 - 1 < 0 which is (x - 1)(x + 1) < 0. This implies -1 < x < 1 but x is not 0.
Or plug in numbers from the given 4 ranges. YOu will see that x must lie in -1 < x < 1.
Sufficient.

Statement 2: | x | < \frac{1}{x}
First of all, x cannot be negative since | x | is never negative. Since | x | is less than 1/x, 1/x must be positive. Also, x cannot be greater than 1 since then, | x | will be greater than 1/x.
Or plug in numbers from the given 4 ranges. You will see that x must lie in 0 < x < 1.
Sufficient.

Answer (D)
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Expert Post
Moderator
Moderator
User avatar
Joined: 01 Sep 2010
Posts: 2444
Followers: 312

Kudos [?]: 2622 [0], given: 697

Re: If x is not equal to zero, is | x | < 1 ?? [#permalink] New post 01 Oct 2012, 03:24
Expert's post
VeritasPrepKarishma wrote:
carcass wrote:
If x is not equal to zero, is | x | < 1 ??

1) x^2 < 1

2) | x | < \frac{1}{x}

I would like to know if I do in the right manner

question: x id non zero, is | x | < 1 ??? now to be < 1 x must be negative, so the question become " is x negative ???

1) for a square to be < 1 the must be for example \frac{- 1}{2} ----> x is negative . suff

2) for x to be minor of a certain number that is the reciprocal i.e. : -2 < - 1/2 --------> x is negative. suff

is correct or I should rethink the entire part regarding inequalities ?? because this statement should not take you more that 50 seconds to solve. otherwise you get in trouble with this exam.

Thanks


I would suggest you to keep 4 ranges in mind when dealing with squares, reciprocals etc.

............... -1........ 0 ........ 1 ..............

Less than -1, -1 to 0, 0 to 1 and greater than 1

You can do the question logically or by plugging in numbers.

Ques: If x is not equal to zero, is | x | < 1 ??
Logically, | x | implies distance from 0 on the number line. So the question becomes "Is x a distance of less than 1 away from 0?" i.e. "Is -1 < x < 1?" given x is not 0.

Statement 1: x^2 < 1
Square of a number will be less than 1 only if the absolute value of the number is less than 1. This means | x | < 1. The number needn't be negative. If it is positive, it should be less than 1. If it negative, it should be greater than -1.
Or, do you remember how to solve inequalities using the wave? x^2 < 1 is x^2 - 1 < 0 which is (x - 1)(x + 1) < 0. This implies -1 < x < 1 but x is not 0.
Or plug in numbers from the given 4 ranges. YOu will see that x must lie in -1 < x < 1.
Sufficient.

Statement 2: | x | < \frac{1}{x}
First of all, x cannot be negative since | x | is never negative. Since | x | is less than 1/x, 1/x must be positive. Also, x cannot be greater than 1 since then, | x | will be greater than 1/x.
Or plug in numbers from the given 4 ranges. You will see that x must lie in 0 < x < 1.
Sufficient.

Answer (D)


This is the same reasoning that I followed in the first instance with some errors but the path was correct. Specifically the stimulus evaluation : | x | < 1 ------ in this scenario the first one is x < 1 AND -x < 1 so x > -1 ------> - 1 < x < 1

Thanks Mod :)
_________________

COLLECTION OF QUESTIONS
Quant: 1. Bunuel Signature Collection - The Next Generation 2. Bunuel Signature Collection ALL-IN-ONE WITH SOLUTIONS 3. Veritas Prep Blog PDF Version
Verbal:1. Best EXTERNAL resources to tackle the GMAT Verbal Section 2. e-GMAT's ALL CR topics-Consolidated 3. New Critical Reasoning question bank by carcass 4. Meaning/Clarity SC Question Bank by Carcass_Souvik 5. e-GMAT's ALL SC topics-Consolidated-2nd Edition 6. The best reading to improve Reading Comprehension 7.Verbal question bank and Directories

Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23409
Followers: 3613

Kudos [?]: 28918 [1] , given: 2871

Re: If x is not equal to zero, is |x| < 1 ? [#permalink] New post 01 Oct 2012, 05:05
1
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
If x is not equal to zero, is |x| < 1 ?

Is |x| < 1? --> is -1<x<1 (x\neq{0}).

(1) x^2 < 1 --> -1<x<1. Directly answers the question. Sufficient.

(2) |x| < 1/x. Since the left hand side of the inequity (|x|) is an absolute value, which cannot be negative (actually in this case we know that its positive as we are given that x\neq{0}) then the right hand side (1/x) must also be positive, which means that x>0, so |x|=x.

Hence, |x| < \frac{1}{x} becomes x<\frac{1}{x}. Since we know that x>0 we can safely cross-multiply: x^2<1. The same inequality as in (1). Sufficient.

Answer: D.
_________________

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

Get the best GMAT Prep Resources with GMAT Club Premium Membership

CEO
CEO
User avatar
Joined: 09 Sep 2013
Posts: 2858
Followers: 207

Kudos [?]: 43 [0], given: 0

Premium Member
Re: If x is not equal to zero, is |x| < 1 ? [#permalink] New post 22 Jul 2014, 03:52
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

Re: If x is not equal to zero, is |x| < 1 ?   [#permalink] 22 Jul 2014, 03:52
    Similar topics Author Replies Last post
Similar
Topics:
1 Experts publish their posts in the topic If x is not equal to zero, and x+1/x=3, then what is the Splendidgirl666 6 19 Jan 2012, 11:47
If x is not equal to zero, is |x| < 1? 1) x / |x| < x jjhko 6 27 Jan 2007, 18:26
Is |x|<1? 1) |x+1|=2|x - 1| 2) |x-3| not equal to zero apollo168 12 22 Aug 2006, 01:53
x not equal zero sqrt(x^2)/x = ?? -1 0 1 x |x|/x dinesh8 3 07 May 2006, 16:58
|x|<1? i |x+1|=2|x-1| ii |x-3| is not equal to zero Pls bewakoof 4 19 Mar 2006, 12:50
Display posts from previous: Sort by

If x is not equal to zero, is |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®.