It is currently 12 Dec 2017, 14:00

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.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Senior Manager
Senior Manager
User avatar
G
Joined: 27 May 2012
Posts: 427

Kudos [?]: 90 [0], given: 487

Premium Member
Re: If x ≠ 0, is x^2/|x| < 1? [#permalink]

Show Tags

New post 24 Sep 2013, 01:35
Bunuel wrote:
stne wrote:
udaymathapati wrote:
If x#0, is |x|/x<1?

(1) x < 1
(2) x > −1



I think\(\frac{|x|}{x} <1\)

(1) x < 1
(2) x > −1

Here the answer should be E

x= 1/2 satisfies both the statements and answer to the stem is no, 1 is not less 1

X= - 1/2 satisfies both the statements and answer to the stem is yes , -1<1


but for question \(\frac{x^2}{x} <1\)

(1) x < 1
(2) x > −1


here the answer is C as shown above

Please do correct if I am missing something
thanks.


If it were:
If x#0, is |x|/x<1?

(1) x < 1
(2) x > −1


Then the answer is E. The question basically asks whether x is negative and we cannot answer that even when we combine the statements given.

If it were:
If x#0, is x^2/x<1?

(1) x < 1
(2) x > −1


Then the answer is C. The question basically asks whether x<0 or 0<x<1. When we combine the statements, we get that -1<x<1 (x#0). So, the answer to the question is YES.


as you can see the question has now been corrected

originally udaymathapati
had changed x^2 to |x| and posted the question

where is my kudo for pointing this out :) ?
_________________

- Stne

Kudos [?]: 90 [0], given: 487

Intern
Intern
avatar
Joined: 14 Feb 2012
Posts: 27

Kudos [?]: 5 [0], given: 6

Re: If x 0, is x^2 / |x| < 1? [#permalink]

Show Tags

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 \(|x|<1\)?

Kudos [?]: 5 [0], given: 6

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42571

Kudos [?]: 135384 [0], given: 12691

Re: If x 0, is x^2 / |x| < 1? [#permalink]

Show Tags

New post 10 Oct 2013, 06:15
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 the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 135384 [0], given: 12691

Intern
Intern
avatar
Joined: 02 Mar 2010
Posts: 19

Kudos [?]: 18 [0], given: 16

GMAT ToolKit User Premium Member
Re: If x 0, is x^2/|x| < 1? [#permalink]

Show Tags

New post 28 Feb 2014, 16:58
Hey Bunuel,
Can you please elaborate how you reduced the left-hand side to |x| < 1? I'm getting confused because of the absolute value sign.

Kudos [?]: 18 [0], given: 16

Expert Post
2 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42571

Kudos [?]: 135384 [2], given: 12691

Re: If x 0, is x^2/|x| < 1? [#permalink]

Show Tags

New post 01 Mar 2014, 02:46
2
This post received
KUDOS
Expert's post

Kudos [?]: 135384 [2], given: 12691

1 KUDOS received
Intern
Intern
avatar
Joined: 02 Mar 2010
Posts: 19

Kudos [?]: 18 [1], given: 16

GMAT ToolKit User Premium Member
Re: If x 0, is x^2/|x| < 1? [#permalink]

Show Tags

New post 01 Mar 2014, 11:21
1
This post received
KUDOS
Oh yes...so silly of me! If \sqrt{(x^2)} = |x|, x^2 = |x|*|x|
Thanks a lot Bunuel for your prompt help!:)

Kudos [?]: 18 [1], given: 16

Intern
Intern
avatar
Joined: 16 Jan 2012
Posts: 23

Kudos [?]: 10 [0], given: 6

Location: India
Concentration: Strategy, International Business
WE: Analyst (Consulting)
GMAT ToolKit User
Re: If x 0, is x^2/|x| < 1? [#permalink]

Show Tags

New post 01 Mar 2014, 11:49
1
This post was
BOOKMARKED
msand wrote:
If x ≠ 0, is x^2/|x| < 1?

(1) x < 1
(2) x > -1



Another way i would look at this is : x^2 is always positive, |x| is always positive too .. so a square value divided by the same number would only be less than 1 if the number was a proper fraction instead of an integer .. so the question is asking is x between -1 and 1 or |x| < 1 ?

Kudos [?]: 10 [0], given: 6

Expert Post
EMPOWERgmat Instructor
User avatar
P
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 10379

Kudos [?]: 3681 [0], given: 173

Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Re: If x 0, is x^2 / |x| < 1? [#permalink]

Show Tags

New post 09 Jun 2015, 22:13
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
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

Kudos [?]: 3681 [0], given: 173

Retired Moderator
avatar
P
Joined: 12 Aug 2015
Posts: 2209

Kudos [?]: 899 [0], given: 607

GRE 1: 323 Q169 V154
GMAT ToolKit User Premium Member
Re: If x 0, is x^2/|x| < 1? [#permalink]

Show Tags

New post 13 Mar 2016, 05:05
Here from the question statement
x^2/|x| >1 => the question is actually asking us that does x lies in the (-1,1) range
as you can well see that the combination statement works.
Hence C
_________________

Give me a hell yeah ...!!!!!

Kudos [?]: 899 [0], given: 607

Senior Manager
Senior Manager
User avatar
S
Joined: 08 Dec 2015
Posts: 318

Kudos [?]: 28 [0], given: 36

GMAT 1: 600 Q44 V27
Reviews Badge
Re: If x ≠ 0, is x^2/|x| < 1? [#permalink]

Show Tags

New post 26 Mar 2016, 10:32
Why can't we manipulate the question to get is x^2<|x| ? can't we pass the |x| to the right? It says in the stem that it's #0. Am i wrong here?

Kudos [?]: 28 [0], given: 36

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42571

Kudos [?]: 135384 [0], given: 12691

Re: If x ≠ 0, is x^2/|x| < 1? [#permalink]

Show Tags

New post 26 Mar 2016, 10:39
iliavko wrote:
Why can't we manipulate the question to get is x^2<|x| ? can't we pass the |x| to the right? It says in the stem that it's #0. Am i wrong here?


We can do this but not because |x| is not 0, but because |x| > 0 and we can multiply both sides by it.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 135384 [0], given: 12691

Senior Manager
Senior Manager
User avatar
S
Joined: 08 Dec 2015
Posts: 318

Kudos [?]: 28 [0], given: 36

GMAT 1: 600 Q44 V27
Reviews Badge
Re: If x ≠ 0, is x^2/|x| < 1? [#permalink]

Show Tags

New post 26 Mar 2016, 13:57
thank you for the reply!

Does this mean that the notation x#0 in the question stem doesn't tell anything new? it's already known from the rules that the divisor can't be zero. So if you look at the stem wihtout the x#0 information, the question doesn't change.

Anyways, because whe know that divisor is not zero, we know that x<0 or x>0 and since it's an absolute value, it must be x>0. Is this correct?

Ps. does it mean that in a question where it is mentioned that X#0 but the denominator is not a module, we still must somewhow be sure of the sign of the denominator to be able to multiply like in the case of say, x^2\x so X in both, numerator and denomiator?

Last edited by iliavko on 26 Mar 2016, 14:13, edited 1 time in total.

Kudos [?]: 28 [0], given: 36

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42571

Kudos [?]: 135384 [0], given: 12691

Re: If x ≠ 0, is x^2/|x| < 1? [#permalink]

Show Tags

New post 26 Mar 2016, 14:06
iliavko wrote:
thank you for the reply!

Does this mean that the notation x=0 in the question stem doesn't tell anything new? it's already known from the rules that the divisor can't be zero. So if you look at the stem wihtout the x=0 information, the question doesn't change.

Anyways, because whe know that divisor is not zero, we know that x<0 or x>0 and since it's an absolute value, it must be x>0. Is this correct?


Division by 0 is not allowed so \(x \neq 0\) rules out this case. If we were not told that, then when considering the two statements together we were not be able to tell whether \(\frac{x^2}{|x|}<1\) because if x= 0 then \(\frac{x^2}{|x|}\) is undefined not less than 1.

Hope it's clear.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 135384 [0], given: 12691

Senior Manager
Senior Manager
User avatar
S
Joined: 08 Dec 2015
Posts: 318

Kudos [?]: 28 [0], given: 36

GMAT 1: 600 Q44 V27
Reviews Badge
Re: If x ≠ 0, is x^2/|x| < 1? [#permalink]

Show Tags

New post 26 Mar 2016, 14:24
Thank you for the replies!

Sorry, but something is still not 100% clear to me, so the meaning of "undefined" is not like "can't possibly be done, so don't even consider it" but more like a valid answer? Isn't undefined a sort of a dead end? Or is it just "correct" to write X#0 with no particular practical reason?

Kudos [?]: 28 [0], given: 36

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42571

Kudos [?]: 135384 [0], given: 12691

Re: If x ≠ 0, is x^2/|x| < 1? [#permalink]

Show Tags

New post 26 Mar 2016, 14:39
iliavko wrote:
Thank you for the replies!

Sorry, but something is still not 100% clear to me, so the meaning of "undefined" is not like "can't possibly be done, so don't even consider it" but more like a valid answer? Isn't undefined a sort of a dead end? Or is it just "correct" to write X#0 with no particular practical reason?


The question asks: is x^2/|x| < 1 if -1 < x < 1. Now, if x is any number but 0 from -1 to 1, then the answer is YES. But if x is 0, then we cannot answer the question, because if x = 0 , then x^2/|x| is undefined.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 135384 [0], given: 12691

Verbal Forum Moderator
User avatar
P
Joined: 19 Mar 2014
Posts: 976

Kudos [?]: 261 [0], given: 199

Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.5
GMAT ToolKit User Premium Member CAT Tests
Re: If x 0, is x^2/|x| < 1? [#permalink]

Show Tags

New post 21 Jun 2017, 13:19
Is x^2/|x| < 1?

Which means - is lxl < 1?

or -1 < x < 1?

(1) x < 1 ======> Not Sufficient
(2) x > -1 ======> Not Sufficient

Combining we get: -1 < x < 1

Hence, answer is C
_________________

"Nothing in this world can take the place of persistence. Talent will not: nothing is more common than unsuccessful men with talent. Genius will not; unrewarded genius is almost a proverb. Education will not: the world is full of educated derelicts. Persistence and determination alone are omnipotent."

Worried About IDIOMS? Here is a Daily Practice List: https://gmatclub.com/forum/idiom-s-ydmuley-s-daily-practice-list-250731.html#p1937393

Best AWA Template: https://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html#p470475

Kudos [?]: 261 [0], given: 199

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 14897

Kudos [?]: 287 [0], given: 0

Premium Member
Re: If x ≠ 0, is x^2/|x| < 1? [#permalink]

Show Tags

New post 15 Oct 2017, 08:25
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

Kudos [?]: 287 [0], given: 0

Re: If x ≠ 0, is x^2/|x| < 1?   [#permalink] 15 Oct 2017, 08:25

Go to page   Previous    1   2   [ 37 posts ] 

Display posts from previous: Sort by

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


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

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

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®.