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

It is currently 03 Sep 2015, 12:19
GMAT Club Tests

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/|x|, which of the following must be true for all

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Intern
Intern
avatar
Joined: 06 Nov 2010
Posts: 22
Followers: 0

Kudos [?]: 15 [0], given: 16

GMAT ToolKit User
If x/|x|, which of the following must be true for all [#permalink] New post 15 Jan 2011, 11:44
5
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

51% (02:01) correct 49% (01:07) wrong based on 353 sessions
If \(\frac{x}{|x|} \lt x\), which of the following must be true about \(x\)? (\(x \ne 0\))

A. \(x\gt 2\)
B. \(x \in (-1,0) \cup (1,\infty)\)
C. \(|x| \lt 1\)
D. \(|x| = 1\)
E. \(|x|^2 \gt 1\)

M24
[Reveal] Spoiler: OA

Last edited by Bunuel on 09 Jul 2013, 08:56, edited 1 time in total.
Renamed the topic and edited the question.
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29205
Followers: 4750

Kudos [?]: 50259 [1] , given: 7540

Re: range of root - GMAT Club test - M24 [#permalink] New post 15 Jan 2011, 13:47
1
This post received
KUDOS
Expert's post
3
This post was
BOOKMARKED
praveenvino wrote:
X/|X| < X . Which of the following must be true for all ?

a. X > 1
b. X is an element in (-1,0) U (1,inf)
c. |X| < 1
d. |X| = 1
e. |X|^2 > 1

Can some one explain how X can be zero for the above condition?


x is in the denominator so it can not equal to zero as division be zero is undefined.

Correct form of this question is below (m09 q22, discussed here: m09-q22-69937.html):

If \(\frac{x}{|x|} \lt x\), which of the following must be true about \(x\)? (\(x \ne 0\))
A. \(x\gt 2\)
B. \(x \in (-1,0) \cup (1,\infty)\)
C. \(|x| \lt 1\)
D. \(|x| = 1\)
E. \(|x|^2 \gt 1\)

\(\frac{x}{|x|}< x\)
Two cases:
A. \(x<0\) --> \(\frac{x}{-x}<x\) --> \(-1<x\). But as we consider the range \(x<0\) then \(-1<x<0\)

B. \(x>0\) --> \(\frac{x}{x}<x\) --> \(1<x\).

So the given inequality holds true in two ranges \(-1<x<0\) and \(x>1\).

Answer: B.

For more check: math-absolute-value-modulus-86462.html

Hope it helps.
_________________

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

PLEASE READ AND FOLLOW: 12 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 ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. 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?
25 extra-hard Quant Tests

GMAT Club Premium Membership - big benefits and savings

Intern
Intern
avatar
Joined: 06 Nov 2010
Posts: 22
Followers: 0

Kudos [?]: 15 [0], given: 16

GMAT ToolKit User
Re: range of root - GMAT Club test - M24 [#permalink] New post 15 Jan 2011, 14:03
Thanks Bunuel. X not equals zero condition was actually missing in the question in m24. Thanks for your help.
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 6203
Followers: 346

Kudos [?]: 71 [0], given: 0

Premium Member
Re: If x/|x|, which of the following must be true for all [#permalink] New post 03 Nov 2014, 10:55
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

Intern
Intern
avatar
Joined: 07 Oct 2014
Posts: 1
Followers: 0

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

Re: If x/|x|, which of the following must be true for all [#permalink] New post 11 Dec 2014, 23:00
A must be true too.
If x>1 satisfy x/|x|<x
then x>2 will do too.
can anyone explain choice A? thanks!
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29205
Followers: 4750

Kudos [?]: 50259 [0], given: 7540

Re: If x/|x|, which of the following must be true for all [#permalink] New post 12 Dec 2014, 05:51
Expert's post
Intern
Intern
avatar
Joined: 24 Jun 2014
Posts: 39
Followers: 0

Kudos [?]: 15 [0], given: 59

GMAT ToolKit User
Re: If x/|x|, which of the following must be true for all [#permalink] New post 22 Apr 2015, 18:22
Brunel, Can you please explain why option E is not feasible?
1 KUDOS received
Director
Director
User avatar
Joined: 07 Aug 2011
Posts: 588
Concentration: International Business, Technology
GMAT 1: 630 Q49 V27
Followers: 2

Kudos [?]: 238 [1] , given: 75

GMAT ToolKit User
Re: If x/|x|, which of the following must be true for all [#permalink] New post 22 Apr 2015, 19:19
1
This post received
KUDOS
praveenvino wrote:
If \(\frac{x}{|x|} \lt x\), which of the following must be true about \(x\)? (\(x \ne 0\))

A. \(x\gt 2\)
B. \(x \in (-1,0) \cup (1,\infty)\)
C. \(|x| \lt 1\)
D. \(|x| = 1\)
E. \(|x|^2 \gt 1\)

M24



x < x*|x|
x-x*|x|< 0
roots of this equation are : -1,0,1
rest is explained in the attached image ...
Answer B.
Attachments

gmatclub.jpg
gmatclub.jpg [ 16.88 KiB | Viewed 952 times ]


_________________

Thanks,
Lucky

_______________________________________________________
Kindly press the Image to appreciate my post !! :-)

Expert Post
1 KUDOS received
e-GMAT Representative
User avatar
Joined: 04 Jan 2015
Posts: 338
Followers: 66

Kudos [?]: 483 [1] , given: 83

If x/|x|, which of the following must be true for all [#permalink] New post 23 Apr 2015, 00:44
1
This post received
KUDOS
Expert's post
AverageGuy123 wrote:
Brunel, Can you please explain why option E is not feasible?


Dear AverageuGuy123

As Bunuel explained above,

Either -1 < x < 0
Or x > 1

Now, |x| as you know, represents the magnitude of x. Option E says that |x|^2 must be greater than 1.

Let's first consider the case when -1 < x < 0

A possible value of x in this case is -0.5
So, what is the value of |x|^2? It is equal to 0.25

Is it greater than 1? NO

Let's now consider the case when x > 1

A possible value of x in this case is 2.
So, what is the value of |x|^2? It's 4.

Is it greater than 1? YES

So, as we see, that |x|^2 CAN BE greater than 1. But can we say that |x|^2 MUST BE greater than 1? NO, because |x|^2 is not greater than 1 for all possible values of x.

So, the key takeaway from this discussion is that:

we need to be careful whether the question is asking about MUST BE TRUE statements or about CAN BE TRUE statements.

Hope this helped! :)

- Japinder
_________________

https://e-gmat.com/courses/quant-live-prep/

Image

Expert Post
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 5870
Location: Pune, India
Followers: 1485

Kudos [?]: 8002 [0], given: 190

Re: If x/|x|, which of the following must be true for all [#permalink] New post 23 Apr 2015, 03:36
Expert's post
AverageGuy123 wrote:
Brunel, Can you please explain why option E is not feasible?


You can plug in numbers to eliminate options.

"which of the following must be true about x" means that every acceptable value of x must lie in the range given in the correct option. The acceptable values of x are the values for which x/|x| < x.

A. x>2
Must x be greater than 2?

This should make you check for 2.
2/|2| < 2
1 < 2 (True)
So 2 is an acceptable value of x. But 2 is not greater than 2.
So this option is not correct. This also makes you eliminate options (C) and (D).

E. |x|^2>1
Must x be greater than 1 or less than -1?

Check for 1/2
(1/2)/|1/2| < 1/2
1 < 1/2 (False)

Check for -1/2
(-1/2)/|-1/2| < -1/2
-1 < -1/2 (True)

So x = -1/2 is an acceptable value but it does not lie in this range. Hence option (E) is also incorrect.

Answer must be (B)
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Expert Post
EMPOWERgmat Instructor
User avatar
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 3502
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Followers: 149

Kudos [?]: 943 [0], given: 57

Re: If x/|x|, which of the following must be true for all [#permalink] New post 24 Apr 2015, 10:21
Expert's post
Hi All,

This question can be dealt with in a variety of ways. It's actually really susceptible to TESTing VALUES, which we can use to determine possibilities and eliminate answers.

We're told that X/|X| < X. The question asks what must be TRUE about X.

While this inequality looks complicated, you can quickly prove some things about X....

IF....
X = 1
1/|1| is NOT < 1
So X CANNOT be 1
Eliminate D.

IF.....
X = 2
2/|2| IS < 2
So X CAN be 2
Eliminate A and C.

IF....
X = -2
-2/|-2| is NOT < -2
So X CANNOT be -2
Eliminate E.

There's only one answer left....

Final Answer:
[Reveal] Spoiler:
B


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/|x|, which of the following must be true for all   [#permalink] 24 Apr 2015, 10:21
    Similar topics Author Replies Last post
Similar
Topics:
2 If √x=x , then which of the following must be true ? amitabc 2 26 Oct 2014, 03:35
8 Experts publish their posts in the topic If |x|=−x, which of the following must be true? Mountain14 3 22 Mar 2014, 01:31
2 Experts publish their posts in the topic If √x = x, then which of the following must be true? emmak 3 21 Mar 2013, 23:56
2 Experts publish their posts in the topic If x/|x| < x, which of the following must be true about tkarthi4u 25 06 Sep 2009, 21:14
4 Experts publish their posts in the topic If XY is divisible by 4, which of the following must be true bigfernhead 16 29 Nov 2008, 14:27
Display posts from previous: Sort by

If x/|x|, which of the following must be true for all

  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®.