It is currently 19 Nov 2017, 11:32

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

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

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

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

Hide Tags

Intern
Joined: 06 Nov 2010
Posts: 23

Kudos [?]: 36 [1], given: 16

If x/|x|, which of the following must be true for all [#permalink]

Show Tags

15 Jan 2011, 12:44
1
KUDOS
16
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

57% (00:58) correct 43% (01:08) wrong based on 639 sessions

HideShow timer Statistics

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, 09:56, edited 1 time in total.
Renamed the topic and edited the question.

Kudos [?]: 36 [1], given: 16

Math Expert
Joined: 02 Sep 2009
Posts: 42257

Kudos [?]: 132703 [2], given: 12335

Re: range of root - GMAT Club test - M24 [#permalink]

Show Tags

15 Jan 2011, 14:47
2
KUDOS
Expert's post
8
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 $$x>1$$.

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

Hope it helps.
_________________

Kudos [?]: 132703 [2], given: 12335

Intern
Joined: 06 Nov 2010
Posts: 23

Kudos [?]: 36 [0], given: 16

Re: range of root - GMAT Club test - M24 [#permalink]

Show Tags

15 Jan 2011, 15:03
Thanks Bunuel. X not equals zero condition was actually missing in the question in m24. Thanks for your help.

Kudos [?]: 36 [0], given: 16

Non-Human User
Joined: 09 Sep 2013
Posts: 15657

Kudos [?]: 282 [0], given: 0

Re: If x/|x|, which of the following must be true for all [#permalink]

Show Tags

03 Nov 2014, 11:55
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.
_________________

Kudos [?]: 282 [0], given: 0

Intern
Joined: 07 Oct 2014
Posts: 1

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

Re: If x/|x|, which of the following must be true for all [#permalink]

Show Tags

12 Dec 2014, 00:00
A must be true too.
If x>1 satisfy x/|x|<x
then x>2 will do too.
can anyone explain choice A? thanks!

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

Math Expert
Joined: 02 Sep 2009
Posts: 42257

Kudos [?]: 132703 [0], given: 12335

Re: If x/|x|, which of the following must be true for all [#permalink]

Show Tags

12 Dec 2014, 06:51
pinguuu wrote:
A must be true too.
If x>1 satisfy x/|x|<x
then x>2 will do too.
can anyone explain choice A? thanks!

x > 2 is NOT necessarily true. Consider x = -1/2.
_________________

Kudos [?]: 132703 [0], given: 12335

Manager
Joined: 24 Jun 2014
Posts: 52

Kudos [?]: 23 [0], given: 97

Concentration: Social Entrepreneurship, Nonprofit
Re: If x/|x|, which of the following must be true for all [#permalink]

Show Tags

22 Apr 2015, 19:22
Brunel, Can you please explain why option E is not feasible?

Kudos [?]: 23 [0], given: 97

Director
Joined: 07 Aug 2011
Posts: 579

Kudos [?]: 546 [1], given: 75

Concentration: International Business, Technology
GMAT 1: 630 Q49 V27
Re: If x/|x|, which of the following must be true for all [#permalink]

Show Tags

22 Apr 2015, 20:19
1
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 ...
Attachments

gmatclub.jpg [ 16.88 KiB | Viewed 3964 times ]

_________________

Thanks,
Lucky

_______________________________________________________
Kindly press the to appreciate my post !!

Kudos [?]: 546 [1], given: 75

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 746

Kudos [?]: 2162 [1], given: 123

If x/|x|, which of the following must be true for all [#permalink]

Show Tags

23 Apr 2015, 01:44
1
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
_________________

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Kudos [?]: 2162 [1], given: 123

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7736

Kudos [?]: 17797 [0], given: 235

Location: Pune, India
Re: If x/|x|, which of the following must be true for all [#permalink]

Show Tags

23 Apr 2015, 04:36
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 Kudos [?]: 17797 [0], given: 235 EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 10119 Kudos [?]: 3511 [0], given: 173 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: 340 Q170 V170 Re: If x/|x|, which of the following must be true for all [#permalink] Show Tags 24 Apr 2015, 11:21 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 _________________ 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 [?]: 3511 [0], given: 173

Non-Human User
Joined: 09 Sep 2013
Posts: 15657

Kudos [?]: 282 [0], given: 0

Re: If x/|x|, which of the following must be true for all [#permalink]

Show Tags

03 Jun 2016, 12:22
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.
_________________

Kudos [?]: 282 [0], given: 0

Senior Manager
Joined: 07 Sep 2014
Posts: 484

Kudos [?]: 34 [0], given: 342

Concentration: Finance, Marketing
If x/|x|, which of the following must be true for all [#permalink]

Show Tags

30 Jun 2016, 02:08
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

If the question is about "must be true" A also satifies the condition.

If x> 1 then X> 2 is also fine.

Bunuel

Kudos [?]: 34 [0], given: 342

Math Expert
Joined: 02 Sep 2009
Posts: 42257

Kudos [?]: 132703 [0], given: 12335

Re: If x/|x|, which of the following must be true for all [#permalink]

Show Tags

30 Jun 2016, 08:28
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

If the question is about "must be true" A also satifies the condition.

If x> 1 then X> 2 is also fine.

Bunuel

_________________

Kudos [?]: 132703 [0], given: 12335

EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 10119

Kudos [?]: 3511 [0], given: 173

Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Re: If x/|x|, which of the following must be true for all [#permalink]

Show Tags

30 Jun 2016, 10:48

From your post, it looks like you're only considering positive integers. However, X could be -1/2, so Answer A is NOT correct.

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 [?]: 3511 [0], given: 173

Re: If x/|x|, which of the following must be true for all   [#permalink] 30 Jun 2016, 10:48
Display posts from previous: Sort by

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

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

 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®.