It is currently 18 Nov 2017, 05:37

### 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 is not equal to 0, is |x| less than 1? (1) x/|x|< x

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

### Hide Tags

Current Student
Joined: 08 Mar 2013
Posts: 14

Kudos [?]: 20 [1], given: 3

GMAT 1: 770 Q50 V45
WE: Analyst (Law)
Re: If x is not equal to 0, is |x| less than 1? (1) x/|x|< x [#permalink]

### Show Tags

24 Apr 2013, 13:39
1
KUDOS
Bunuel wrote:
Hussain15 wrote:
If x is not equal to 0, is |x| less than 1?

(1) x/|x|< x

(2) |x| > x

Will really appreciate if answer is supported by explanation.

$$x\neq{0}$$, is $$|x|<1$$? Which means is $$-1<x<1$$? ($$x\neq{0}$$)

(1) $$\frac{x}{|x|}< x$$
Two cases:
A. $$x<0$$ --> $$\frac{x}{-x}<x$$ --> $$-1<x$$. But remember that $$x<0$$, so $$-1<x<0$$
.

if x<0, doesn't x/|x|<x become -x/x<-x which simplifies to -1<-x or x<1 ?

Kudos [?]: 20 [1], given: 3

Current Student
Joined: 04 Mar 2013
Posts: 68

Kudos [?]: 58 [0], given: 27

Location: India
Concentration: Strategy, Operations
Schools: Booth '17 (M)
GMAT 1: 770 Q50 V44
GPA: 3.66
WE: Operations (Manufacturing)
Re: If x is not equal to 0, is |x| less than 1? (1) x/|x|< x [#permalink]

### Show Tags

24 Apr 2013, 18:25
Bunuel wrote:
Hussain15 wrote:
If x is not equal to 0, is |x| less than 1?

(1) x/|x|< x

(2) |x| > x

Will really appreciate if answer is supported by explanation.

$$x\neq{0}$$, is $$|x|<1$$? Which means is $$-1<x<1$$? ($$x\neq{0}$$)

(1) $$\frac{x}{|x|}< x$$
Two cases:
A. $$x<0$$ --> $$\frac{x}{-x}<x$$ --> $$-1<x$$. But remember that $$x<0$$, so $$-1<x<0$$

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

Two ranges $$-1<x<0$$ or $$x>1$$. Which says that $$x$$ either in the first range or in the second. Not sufficient to answer whether $$-1<x<1$$. (For instance $$x$$ can be $$-0.5$$ or $$3$$)

Second approach: look at the fraction $$\frac{x}{|x|}$$ it can take only two values:
1 for $$x>0$$ --> so we would have: $$1<x$$;
Or -1 for $$x<0$$ --> so we would have: $$-1<x$$ and as we considering the range for which $$x<0$$ then completer range would be: $$-1<x<0$$.

The same two ranges: $$-1<x<0$$ or $$x>1$$.

(2) $$|x| > x$$. Well this basically tells that $$x$$ is negative, as if x were positive or zero then $$|x|$$ would be equal to $$x$$. Only one range: $$x<0$$, but still insufficient to say whether $$-1<x<1$$. (For instance $$x$$ can be $$-0.5$$ or $$-10$$)

Or two cases again:
$$x<0$$--> $$-x>x$$--> $$x<0$$.
$$x>0$$ --> $$x>x$$: never correct.

(1)+(2) Intersection of the ranges from (1) and (2) is the range $$-1<x<0$$ ($$x<0$$ (from 2) and $$-1<x<0$$ or $$x>1$$ (from 1), hence $$-1<x<0$$). Every $$x$$ from this range is definitely in the range $$-1<x<1$$. Sufficient.

Buenel terrific explanation. This system, that you use for solving inequations, is quite fundamental and hard to be wrong. But is it really always the quickest way??
_________________

When you feel like giving up, remember why you held on for so long in the first place.

Kudos [?]: 58 [0], given: 27

Math Expert
Joined: 02 Sep 2009
Posts: 42249

Kudos [?]: 132567 [1], given: 12326

Re: If x is not equal to 0, is |x| less than 1? (1) x/|x|< x [#permalink]

### Show Tags

25 Apr 2013, 04:14
1
KUDOS
Expert's post
oyabu wrote:
Bunuel wrote:
Hussain15 wrote:
If x is not equal to 0, is |x| less than 1?

(1) x/|x|< x

(2) |x| > x

Will really appreciate if answer is supported by explanation.

$$x\neq{0}$$, is $$|x|<1$$? Which means is $$-1<x<1$$? ($$x\neq{0}$$)

(1) $$\frac{x}{|x|}< x$$
Two cases:
A. $$x<0$$ --> $$\frac{x}{-x}<x$$ --> $$-1<x$$. But remember that $$x<0$$, so $$-1<x<0$$
.

if x<0, doesn't x/|x|<x become -x/x<-x which simplifies to -1<-x or x<1 ?

When $$x<0$$, then $$|x|=-x$$, thus $$\frac{x}{|x|}<x$$ becomes $$\frac{x}{-x}<x$$ --> $$-1<x$$ but since $$x<0$$, then $$-1<x<0$$.

Hope it's clear.
_________________

Kudos [?]: 132567 [1], given: 12326

Current Student
Joined: 08 Mar 2013
Posts: 14

Kudos [?]: 20 [0], given: 3

GMAT 1: 770 Q50 V45
WE: Analyst (Law)
Re: If x is not equal to 0, is |x| less than 1? (1) x/|x|< x [#permalink]

### Show Tags

25 Apr 2013, 09:17
Bunuel wrote:

When $$x<0$$, then $$|x|=-x$$, thus $$\frac{x}{|x|}<x$$ becomes $$\frac{x}{-x}<x$$ --> $$-1<x$$ but since $$x<0$$, then $$-1<x<0$$.

Hope it's clear.

Thanks. One more follow-up for clarification - Isn't the absolute value of a negative value positive? So if x<0 (x is a negative number), then the absolute value of x should be positive? i.e. |-x|=x?

Kudos [?]: 20 [0], given: 3

Math Expert
Joined: 02 Sep 2009
Posts: 42249

Kudos [?]: 132567 [1], given: 12326

Re: If x is not equal to 0, is |x| less than 1? (1) x/|x|< x [#permalink]

### Show Tags

26 Apr 2013, 00:56
1
KUDOS
Expert's post
oyabu wrote:
Bunuel wrote:

When $$x<0$$, then $$|x|=-x$$, thus $$\frac{x}{|x|}<x$$ becomes $$\frac{x}{-x}<x$$ --> $$-1<x$$ but since $$x<0$$, then $$-1<x<0$$.

Hope it's clear.

Thanks. One more follow-up for clarification - Isn't the absolute value of a negative value positive? So if x<0 (x is a negative number), then the absolute value of x should be positive? i.e. |-x|=x?

First of all $$|-x|=|x|$$. Next, if $$x<0$$, then $$|x|=|negative|=-x=-negative=positive$$.

It seems that you need to go through basics: math-absolute-value-modulus-86462.html
_________________

Kudos [?]: 132567 [1], given: 12326

Manager
Joined: 17 Oct 2012
Posts: 58

Kudos [?]: 8 [0], given: 0

Re: If x is not equal to 0, is |x| less than 1? (1) x/|x|< x [#permalink]

### Show Tags

23 Jun 2013, 01:36
One question:

if you pug in numbers, for the first statement is the statement not only true for number between -1 and 0? I just do not get it completely!

Kudos [?]: 8 [0], given: 0

Math Expert
Joined: 02 Sep 2009
Posts: 42249

Kudos [?]: 132567 [0], given: 12326

Re: If x is not equal to 0, is |x| less than 1? (1) x/|x|< x [#permalink]

### Show Tags

23 Jun 2013, 02:02
BankerRUS wrote:
One question:

if you pug in numbers, for the first statement is the statement not only true for number between -1 and 0? I just do not get it completely!

It's also true if x>1. For example, if x=2, then x/|x|=1 < 2=x.
_________________

Kudos [?]: 132567 [0], given: 12326

Senior Manager
Joined: 13 May 2013
Posts: 460

Kudos [?]: 201 [0], given: 134

Re: If x is not equal to 0, is |x| less than 1? (1) x/|x|< x [#permalink]

### Show Tags

11 Jul 2013, 14:43
If x is not equal to 0, is |x| less than 1?

|x|<1
Is -1<x<1

(1) x/|x|< x

x/|x|< x
Two cases: x>0, x<0

x>0
x/|x|< x
x/x<x
1<x

If x>0 and x>1 then x>1
If x>1 then |x| is NOT less than 1

x<0
x/|x|< x
-x/|-x|<x
-1<x

-1<x<0
if -1<x<0 then |x| IS less than 1
INSUFFICIENT

(2) |x| > x

If the absolute value of x is greater than x than x must be negative. However, |-x| could be less than 1 or greater than 1 depending on the value of x.
INSUFFICIENT

1+2 x must be negative and x from #1 x is either >1 or between -1 and 0. Therefore, we know -1<x<0 which means that |x| is always less than 1.
SUFFICIENT

(C)

Kudos [?]: 201 [0], given: 134

Manager
Joined: 30 May 2013
Posts: 185

Kudos [?]: 87 [0], given: 72

Location: India
Concentration: Entrepreneurship, General Management
GPA: 3.82
Re: If x is not equal to 0, is |x| less than 1? (1) x/|x|< x [#permalink]

### Show Tags

06 Aug 2013, 08:42
Bunuel wrote:
Hussain15 wrote:
If x is not equal to 0, is |x| less than 1?

(1) x/|x|< x

(2) |x| > x

Will really appreciate if answer is supported by explanation.

$$x\neq{0}$$, is $$|x|<1$$? Which means is $$-1<x<1$$? ($$x\neq{0}$$)

(1) $$\frac{x}{|x|}< x$$
Two cases:
A. $$x<0$$ --> $$\frac{x}{-x}<x$$ --> $$-1<x$$. But remember that $$x<0$$, so $$-1<x<0$$

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

Two ranges $$-1<x<0$$ or $$x>1$$. Which says that $$x$$ either in the first range or in the second. Not sufficient to answer whether $$-1<x<1$$. (For instance $$x$$ can be $$-0.5$$ or $$3$$)

Second approach: look at the fraction $$\frac{x}{|x|}$$ it can take only two values:
1 for $$x>0$$ --> so we would have: $$1<x$$;
Or -1 for $$x<0$$ --> so we would have: $$-1<x$$ and as we considering the range for which $$x<0$$ then completer range would be: $$-1<x<0$$.

The same two ranges: $$-1<x<0$$ or $$x>1$$.

(2) $$|x| > x$$. Well this basically tells that $$x$$ is negative, as if x were positive or zero then $$|x|$$ would be equal to $$x$$. Only one range: $$x<0$$, but still insufficient to say whether $$-1<x<1$$. (For instance $$x$$ can be $$-0.5$$ or $$-10$$)

Or two cases again:
$$x<0$$--> $$-x>x$$--> $$x<0$$.
$$x>0$$ --> $$x>x$$: never correct.

(1)+(2) Intersection of the ranges from (1) and (2) is the range $$-1<x<0$$ ($$x<0$$ (from 2) and $$-1<x<0$$ or $$x>1$$ (from 1), hence $$-1<x<0$$). Every $$x$$ from this range is definitely in the range $$-1<x<1$$. Sufficient.

Hi bunel,

hw is that we can have two ranges x<0 & x>0. How we got this ranges?

regards,
rrsnathan.

Kudos [?]: 87 [0], given: 72

Manager
Joined: 22 Jan 2014
Posts: 141

Kudos [?]: 77 [0], given: 145

WE: Project Management (Computer Hardware)
Re: If x is not equal to 0, is |x| less than 1? (1) x/|x|< x [#permalink]

### Show Tags

11 Mar 2014, 04:27
Hussain15 wrote:
If x is not equal to 0, is |x| less than 1?

(1) x/|x|< x

(2) |x| > x

Will really appreciate if answer is supported by explanation.

|x| < 1
if we plot this then we get the range of x as (-1,1)

1) $$\frac{x}{|x|} < x$$
the range of x here is (1, infinity) U (-1,0)
hence, it is not sufficient.

2) |x| > x
very clearly this would be true for all x < 0

if we combine 1 and 2, the common range we get is (-1,0)
which satisfies |x| < 1
hence, C.
_________________

Illegitimi non carborundum.

Kudos [?]: 77 [0], given: 145

Current Student
Joined: 06 Mar 2014
Posts: 269

Kudos [?]: 114 [0], given: 84

Location: India
GMAT Date: 04-30-2015
Re: If x is not equal to 0, is |x| less than 1? (1) x/|x|< x [#permalink]

### Show Tags

29 Sep 2014, 07:08
The question asks "is $$-1<x<1$$?" We got that $$x$$ is in the range $$-1<x<0$$ (red area). Now, as ANY $$x$$ from this range (from red area) is indeed in $$-1<x<1$$, then we can answer YES to our original question.

Hope it's clear.[/quote]

Exactly, based on your explanation above, Though the answer is YES it is sufficient to answer but the answer to the question is

That for x=0.5 it is in the range -1<x<1
but it is NOT part of -1<x<0 which we found out.
So it is not possible to say that all possible values of -1<x<0 come under -1<x<1 unless ofcourse it is specified that x is an integer.

Bunuel,

Kudos [?]: 114 [0], given: 84

Math Expert
Joined: 02 Sep 2009
Posts: 42249

Kudos [?]: 132567 [0], given: 12326

Re: If x is not equal to 0, is |x| less than 1? (1) x/|x|< x [#permalink]

### Show Tags

29 Sep 2014, 07:15
earnit wrote:
Exactly, based on your explanation above, Though the answer is YES it is sufficient to answer but the answer to the question is the range -1<x<1 for x is NO as -1<x<0 is the range and so x could be 0.5 and not be part of the -1<x<0 .

Bunuel,

When we combine the statements we get that -1 < x < 0, then HOW can x be 0.5???
_________________

Kudos [?]: 132567 [0], given: 12326

Current Student
Joined: 06 Mar 2014
Posts: 269

Kudos [?]: 114 [0], given: 84

Location: India
GMAT Date: 04-30-2015
Re: If x is not equal to 0, is |x| less than 1? (1) x/|x|< x [#permalink]

### Show Tags

29 Sep 2014, 09:52
Bunuel wrote:
earnit wrote:
Exactly, based on your explanation above, Though the answer is YES it is sufficient to answer but the answer to the question is the range -1<x<1 for x is NO as -1<x<0 is the range and so x could be 0.5 and not be part of the -1<x<0 .

Bunuel,

When we combine the statements we get that -1 < x < 0, then HOW can x be 0.5???

I'm sorry if it comes across like that but as per my understanding, the Question is if x lies between -1 and 1 and we find out that x lies between -1 and 0 so we are not entirely going by the asked range -1 < x < 1 is what i think.

But yes, the range of -1 < x < 0 comes under the broad -1 < x < 1 and so that is why it is correct.

Kudos [?]: 114 [0], given: 84

Current Student
Joined: 02 Jul 2012
Posts: 213

Kudos [?]: 292 [0], given: 84

Location: India
Schools: IIMC (A)
GMAT 1: 720 Q50 V38
GPA: 2.6
WE: Information Technology (Consulting)
Re: If x is not equal to 0, is |x| less than 1? (1) x/|x|< x [#permalink]

### Show Tags

20 Oct 2014, 21:51
If x is not equal to 0, is |x| less than 1?

(1) x/|x|< x

(2) |x| > x

Will really appreciate if answer is supported by explanation.

1 - x / |x| < x This would mean that -1 < x < 0 & 0 < x <infinite
Thus 1 is insufficient

2 - |x| > x - This would mean that negative infinite values < x < 0 This is also not sufficient.

Combining 1 & 2 - the overlapping region is -1 < x < 0

We can conclude that |x| < 1

So C
_________________

Give KUDOS if the post helps you...

Kudos [?]: 292 [0], given: 84

Current Student
Joined: 06 Mar 2014
Posts: 269

Kudos [?]: 114 [0], given: 84

Location: India
GMAT Date: 04-30-2015
Re: If x is not equal to 0, is |x| less than 1? (1) x/|x|< x [#permalink]

### Show Tags

21 Oct 2014, 15:46
Thoughtosphere wrote:
If x is not equal to 0, is |x| less than 1?

(1) x/|x|< x

(2) |x| > x

Will really appreciate if answer is supported by explanation.

1 - x / |x| < x This would mean that -1 < x < 0 & 0 < x <infinite
Thus 1 is insufficient

2 - |x| > x - This would mean that negative infinite values < x < 0 This is also not sufficient.

Combining 1 & 2 - the overlapping region is -1 < x < 0

We can conclude that |x| < 1

So C

Solving the Question is not much of a problem as deciding whether our solved range: $$-1 < x < 0$$ is SUFFICIENT to answer the asked range: $$-1 < x < 1$$

I need to understand that: Is our answer sufficient to conclude that YES x lies between (-1,1) even though our solution was that x lies between (-1,0) ?

Kudos [?]: 114 [0], given: 84

Math Expert
Joined: 02 Sep 2009
Posts: 42249

Kudos [?]: 132567 [0], given: 12326

Re: If x is not equal to 0, is |x| less than 1? (1) x/|x|< x [#permalink]

### Show Tags

22 Oct 2014, 01:15
Expert's post
1
This post was
BOOKMARKED
earnit wrote:
Thoughtosphere wrote:
If x is not equal to 0, is |x| less than 1?

(1) x/|x|< x

(2) |x| > x

Will really appreciate if answer is supported by explanation.

1 - x / |x| < x This would mean that -1 < x < 0 & 0 < x <infinite
Thus 1 is insufficient

2 - |x| > x - This would mean that negative infinite values < x < 0 This is also not sufficient.

Combining 1 & 2 - the overlapping region is -1 < x < 0

We can conclude that |x| < 1

So C

Solving the Question is not much of a problem as deciding whether our solved range: $$-1 < x < 0$$ is SUFFICIENT to answer the asked range: $$-1 < x < 1$$

I need to understand that: Is our answer sufficient to conclude that YES x lies between (-1,1) even though our solution was that x lies between (-1,0) ?

The question asks whether -1 < x< 1. We got that -1 < x < 0. So, the answer is YES: x is definitely from the range (-1, 1).
_________________

Kudos [?]: 132567 [0], given: 12326

Current Student
Joined: 03 Feb 2013
Posts: 941

Kudos [?]: 1075 [0], given: 548

Location: India
Concentration: Operations, Strategy
GMAT 1: 760 Q49 V44
GPA: 3.88
WE: Engineering (Computer Software)
Re: If x is not equal to 0, is |x| less than 1? (1) x/|x|< x [#permalink]

### Show Tags

24 Nov 2014, 11:26
The question is asking if
-1 < x < 1

Statement 1) x/|x| < x Now if x + ve, x/|x| = 1
and if x is -ve
x / |x| = -1
So essentially, the equation becomes +1 < x or -1 < -x or 1 > x (multiplying both sides by -ve)
In two cases, one case says x > 1 and the other one says x < 1, hence Not sufficient.

Statement 2. |x| > x , this will only happen when x is -ve
id x is -ve |x| can be > 1 or |x| can be < 1 or equal to 1. - Not sufficient.

Combining the two statements:
x is -ve
1 > x hence sufficient. C)
_________________

Thanks,
Kinjal

My Application Experience : http://gmatclub.com/forum/hardwork-never-gets-unrewarded-for-ever-189267-40.html#p1516961

Please click on Kudos, if you think the post is helpful

Kudos [?]: 1075 [0], given: 548

Manager
Joined: 30 Mar 2013
Posts: 130

Kudos [?]: 57 [0], given: 196

Re: If x is not equal to 0, is |x| less than 1? (1) x/|x|< x [#permalink]

### Show Tags

26 Nov 2014, 14:05
Bunuel wrote:
Hussain15 wrote:
If x is not equal to 0, is |x| less than 1?

(1) x/|x|< x

(2) |x| > x

Will really appreciate if answer is supported by explanation.

$$x\neq{0}$$, is $$|x|<1$$? Which means is $$-1<x<1$$? ($$x\neq{0}$$)

(1) $$\frac{x}{|x|}< x$$
Two cases:
A. $$x<0$$ --> $$\frac{x}{-x}<x$$ --> $$-1<x$$. But remember that $$x<0$$, so $$-1<x<0$$

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

Two ranges $$-1<x<0$$ or $$x>1$$. Which says that $$x$$ either in the first range or in the second. Not sufficient to answer whether $$-1<x<1$$. (For instance $$x$$ can be $$-0.5$$ or $$3$$)

Second approach: look at the fraction $$\frac{x}{|x|}$$ it can take only two values:
1 for $$x>0$$ --> so we would have: $$1<x$$;
Or -1 for $$x<0$$ --> so we would have: $$-1<x$$ and as we considering the range for which $$x<0$$ then completer range would be: $$-1<x<0$$.

The same two ranges: $$-1<x<0$$ or $$x>1$$.

(2) $$|x| > x$$. Well this basically tells that $$x$$ is negative, as if x were positive or zero then $$|x|$$ would be equal to $$x$$. Only one range: $$x<0$$, but still insufficient to say whether $$-1<x<1$$. (For instance $$x$$ can be $$-0.5$$ or $$-10$$)

Or two cases again:
$$x<0$$--> $$-x>x$$--> $$x<0$$.
$$x>0$$ --> $$x>x$$: never correct.

(1)+(2) Intersection of the ranges from (1) and (2) is the range $$-1<x<0$$ ($$x<0$$ (from 2) and $$-1<x<0$$ or $$x>1$$ (from 1), hence $$-1<x<0$$). Every $$x$$ from this range is definitely in the range $$-1<x<1$$. Sufficient.

Bunuel
I'm very unclear about this. if x<0, then -x/|x| <-x (since x is negative in our scenario 1)...so where do I go from here?
if i cut both -x's, I get 1/|x| > 1....so x>1....I can't understand how we got x>-1...
If you could help, that'll be great. I tried plugging in for this question and got in right, but I've been trying to teach myself your conceptual way as I believe it is much better than plugging in.

Kudos [?]: 57 [0], given: 196

Intern
Joined: 09 Mar 2014
Posts: 5

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

GPA: 3.01
WE: General Management (Energy and Utilities)
Re: If x is not equal to 0, is |x| less than 1? (1) x/|x|< x [#permalink]

### Show Tags

14 Dec 2014, 12:04
i want some more questions of this type, Bunuel sir can u please help me.

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

Math Expert
Joined: 02 Sep 2009
Posts: 42249

Kudos [?]: 132567 [0], given: 12326

Re: If x is not equal to 0, is |x| less than 1? (1) x/|x|< x [#permalink]

### Show Tags

15 Dec 2014, 08:04
manojpandey80 wrote:
i want some more questions of this type, Bunuel sir can u please help me.

Check this: if-4x-12-x-9-which-of-the-following-must-be-true-101732.html
_________________

Kudos [?]: 132567 [0], given: 12326

Re: If x is not equal to 0, is |x| less than 1? (1) x/|x|< x   [#permalink] 15 Dec 2014, 08:04

Go to page   Previous    1   2   3   4   5    Next  [ 85 posts ]

Display posts from previous: Sort by

# If x is not equal to 0, is |x| less than 1? (1) x/|x|< x

 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®.