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

 It is currently 22 Oct 2016, 16:37

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

Author Message
TAGS:

### Hide Tags

Manager
Joined: 06 Apr 2010
Posts: 143
Followers: 3

Kudos [?]: 596 [2] , given: 15

If x#0, is x^2/|x| < 1? [#permalink]

### Show Tags

08 Sep 2010, 11:51
2
KUDOS
4
This post was
BOOKMARKED
00:00

Difficulty:

25% (medium)

Question Stats:

65% (01:51) correct 35% (01:02) wrong based on 391 sessions

### HideShow timer Statistics

If $$x \neq 0$$, is $$\frac{x^2}{|x|}< 1$$?

(1) x < 1
(2) x > −1
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 35244
Followers: 6623

Kudos [?]: 85395 [2] , given: 10236

If x#0, is x^2/|x| < 1? [#permalink]

### Show Tags

08 Sep 2010, 11:57
2
KUDOS
Expert's post
udaymathapati wrote:
If $$x \neq 0$$, is $$\frac{x^2}{|x|}< 1$$?

(1) x < 1
(2) x > −1

If $$x\neq{0}$$, is $$\frac{x^2}{|x|}<1$$? --> reduce by $$|x|$$ --> is $$|x|<1$$? or is $$-1<x<1$$?

Two statements together give us the sufficient info.

_________________
Current Student
Joined: 12 Jun 2009
Posts: 1847
Location: United States (NC)
Concentration: Strategy, Finance
Schools: UNC (Kenan-Flagler) - Class of 2013
GMAT 1: 720 Q49 V39
WE: Programming (Computer Software)
Followers: 24

Kudos [?]: 245 [2] , given: 52

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

### Show Tags

08 Sep 2010, 13:11
2
KUDOS
udaymathapati wrote:
[img]
Attachment:
Maths1.JPG
[/img]

(1) x < 1
(2) x > −1

x^2/abs(x) <1 ?

Another way to look at it...

1. if you set x= positive decimal you get the original value which is <1
now you can try x = negative integer(-5) which results in the positive version which is >1 so INSUFF
2. this is INSUFF since x could be a huge positive number which makes it >1 OR it could be a small decimal number which makes it <1

combining you see -1< X <1 which means X is a +/- decimal which also means it will be <1 so C
_________________

Manager
Joined: 06 Apr 2010
Posts: 143
Followers: 3

Kudos [?]: 596 [0], given: 15

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

### Show Tags

09 Sep 2010, 04:38
Bunuel wrote:
udaymathapati wrote:
[img]
Attachment:
Maths1.JPG
[/img]

(1) x < 1
(2) x > −1

If $$x\neq{0}$$, is $$\frac{x^2}{|x|}<1$$? --> reduce by $$|x|$$ --> is $$|x|<1$$? or is $$-1<x<1$$?

Two statements together give us the sufficient info.

Bunuel,
Can you explain how it reduce it to $$|x|$$ from the expression?
Math Expert
Joined: 02 Sep 2009
Posts: 35244
Followers: 6623

Kudos [?]: 85395 [1] , given: 10236

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

### Show Tags

09 Sep 2010, 10:12
1
KUDOS
Expert's post
udaymathapati wrote:
Bunuel wrote:
udaymathapati wrote:
[img]
Attachment:
Maths1.JPG
[/img]

(1) x < 1
(2) x > −1

If $$x\neq{0}$$, is $$\frac{x^2}{|x|}<1$$? --> reduce by $$|x|$$ --> is $$|x|<1$$? or is $$-1<x<1$$?

Two statements together give us the sufficient info.

Bunuel,
Can you explain how it reduce it to $$|x|$$ from the expression?

Given: $$\frac{x^2}{|x|}<1$$

Consider this:
$$\frac{x^2}{|x|}=\frac{|x|*|x|}{|x|}=|x|$$. It's basically the same as if it were $$\frac{x^2}{x}$$ --> we could reduce this fraction by $$x$$ and we would get $$x$$, and when $$x$$ is positive, result is positive and when $$x$$ is negative, result is negative. Now, $$\frac{x^2}{|x|}$$ is the ratio of two positive values and the result can not be negative, so we can not get $$x$$, we should get $$|x|$$ to guarantee that the result is positive.

OR:
$$x<0$$--> then $$|x|=-x$$ --> $$\frac{x^2}{|x|}=\frac{x^2}{-x}=-x<1$$ --> $$x>-1$$;

$$x>0$$--> then $$|x|=x$$ --> $$\frac{x^2}{|x|}=\frac{x^2}{x}=x<1$$;

So $$-1<x<1$$.
_________________
Retired Moderator
Joined: 02 Sep 2010
Posts: 805
Location: London
Followers: 104

Kudos [?]: 899 [0], given: 25

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

### Show Tags

14 Oct 2010, 14:44
tatane90 wrote:
If x ≠ 0, is x^2/|x| < 1?
(1) x < 1
(2) x > −1

$$\frac{x^2}{|x|} \lt 1$$
If x>0, then this implies x<1
If x<0, then this implies x>-1
So it is only true if either 0<x<1 or -1<x<0

(1) Not sufficient clealry, as x is not bounded on lower side
(2) Not sufficient clealrly, as x is not bounded on upper side

(1+2) Exactly defined the range for which the inequality holds. Sufficient

_________________
Manager
Joined: 02 Jan 2010
Posts: 135
Followers: 4

Kudos [?]: 5 [0], given: 3

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

### Show Tags

16 Oct 2010, 04:49
Bunuel, did anybody tell you that you are a genius? Stay away from scientists, they might start researching on your brain

+1
_________________

Regards
Ganesh
Class of 2012
Great Lakes Institute of Management
http://greatlakes.edu.in

Math Expert
Joined: 02 Sep 2009
Posts: 35244
Followers: 6623

Kudos [?]: 85395 [0], given: 10236

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

### Show Tags

04 Jul 2013, 01:24
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

Theory on Abolute Values: math-absolute-value-modulus-86462.html

DS Abolute Values Questions to practice: search.php?search_id=tag&tag_id=37
PS Abolute Values Questions to practice: search.php?search_id=tag&tag_id=58

Hard set on Abolute Values: inequality-and-absolute-value-questions-from-my-collection-86939.html

_________________
Intern
Joined: 05 May 2013
Posts: 27
GMAT 1: 730 Q50 V39
GRE 1: 1480 Q800 V680
Followers: 0

Kudos [?]: 22 [1] , given: 5

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

### Show Tags

04 Jul 2013, 07:12
1
KUDOS
$$x^2/|x|$$ reduces to |x||x|/|x| which reduces the qn to is |x| <1 ? This again reduces to -1< x <1. Only combining (1) and two answers this qn. Hence answer is (C).
Senior Manager
Joined: 13 May 2013
Posts: 472
Followers: 3

Kudos [?]: 146 [1] , given: 134

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

### Show Tags

04 Jul 2013, 12:15
1
KUDOS
x^2/|x| < 1
(x^2 = |x|*|x|)
SO
(|x|*|x|)/|x| < 1
Is |x|<1?
is x<1 or is x>-1
is -1<x<1?

(1) x < 1
The issue here is depending on what x is, x may not be in the range of -1<x<1.
INSUFFICIENT

(2) x > −1
The same problem that applied to a) applies to b).
INSUFFICIENT

a+b) this gives us a range of -1<x<1 which is what the question is looking for.
SUFFICIENT

(C)
Manager
Joined: 27 May 2012
Posts: 216
Followers: 2

Kudos [?]: 65 [1] , given: 431

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

### Show Tags

24 Sep 2013, 01:22
1
KUDOS
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.
_________________

- Stne

Math Expert
Joined: 02 Sep 2009
Posts: 35244
Followers: 6623

Kudos [?]: 85395 [0], given: 10236

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

### Show Tags

24 Sep 2013, 01:38
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.
_________________
Manager
Joined: 27 May 2012
Posts: 216
Followers: 2

Kudos [?]: 65 [0], given: 431

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

### Show Tags

24 Sep 2013, 02:35
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

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 12179
Followers: 538

Kudos [?]: 151 [0], given: 0

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

### Show Tags

09 Sep 2015, 07:14
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.
_________________
Manager
Joined: 08 Dec 2015
Posts: 207
GMAT 1: 600 Q44 V27
Followers: 1

Kudos [?]: 9 [0], given: 33

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

### Show Tags

26 Mar 2016, 11:32
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?
Math Expert
Joined: 02 Sep 2009
Posts: 35244
Followers: 6623

Kudos [?]: 85395 [0], given: 10236

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

### Show Tags

26 Mar 2016, 11:39
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.
_________________
Manager
Joined: 08 Dec 2015
Posts: 207
GMAT 1: 600 Q44 V27
Followers: 1

Kudos [?]: 9 [0], given: 33

If x#0, is x^2/|x| < 1? [#permalink]

### Show Tags

26 Mar 2016, 14:57

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, 15:13, edited 1 time in total.
Math Expert
Joined: 02 Sep 2009
Posts: 35244
Followers: 6623

Kudos [?]: 85395 [0], given: 10236

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

### Show Tags

26 Mar 2016, 15:06
iliavko wrote:

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.
_________________
Manager
Joined: 08 Dec 2015
Posts: 207
GMAT 1: 600 Q44 V27
Followers: 1

Kudos [?]: 9 [0], given: 33

If x#0, is x^2/|x| < 1? [#permalink]

### Show Tags

26 Mar 2016, 15:24
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?
Math Expert
Joined: 02 Sep 2009
Posts: 35244
Followers: 6623

Kudos [?]: 85395 [0], given: 10236

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

### Show Tags

26 Mar 2016, 15:39
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.
_________________
Re: If x#0, is x^2/|x| < 1?   [#permalink] 26 Mar 2016, 15:39
Similar topics Replies Last post
Similar
Topics:
1 Is x<0? 1) x3+x2+x+2=0 4 07 Oct 2016, 09:56
Is x^2 < x-|y| ? 1) y>x 2) x<0 3 28 Aug 2011, 02:19
15 If x 0, is x^2/|x| < 1? 8 03 Jan 2010, 07:14
5 If x 0, is x^2 / |x| < 1? 12 14 Dec 2009, 01:03
17 If x≠0, is |x| < 1? 10 19 Oct 2009, 07:10
Display posts from previous: Sort by