If x is not equal to 0, is |x| less than 1? x > x/|x| |x| : DS Archive
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 22 Jan 2017, 22:25

### 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? x > x/|x| |x|

Author Message
CEO
Joined: 29 Mar 2007
Posts: 2583
Followers: 19

Kudos [?]: 422 [0], given: 0

If x is not equal to 0, is |x| less than 1? x > x/|x| |x| [#permalink]

### Show Tags

04 Nov 2007, 09:48
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions

### HideShow timer Statistics

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

If x is not equal to 0, is |x| less than 1?

x > x/|x|
|x| > x
SVP
Joined: 29 Aug 2007
Posts: 2492
Followers: 68

Kudos [?]: 735 [0], given: 19

### Show Tags

04 Nov 2007, 10:09
GMATBLACKBELT wrote:
If x is not equal to 0, is |x| less than 1?

x > x/|x|
|x| > x

very good question. got B.

from i, x/lxl is always either -1 or 1. if x is -ve fraction, x > x/lxl is true. if x is > 1, x > x/lxl is also true. so insufficient

from ii, lxl > x is true only for -ve x. so suff.
Director
Joined: 11 Jun 2007
Posts: 931
Followers: 1

Kudos [?]: 175 [0], given: 0

### Show Tags

04 Nov 2007, 10:12
GMATBLACKBELT wrote:
If x is not equal to 0, is |x| less than 1?

x > x/|x|
|x| > x

i get C please confirm if i am correct.. i still struggle with these

from the stem
x =! 0
-1 < x < 1

st 1: x > x/|x|

positive: x > x/x => x*x > x
x^2 - x > 0
x(x-1) > 0
x > 0
x > 1
3 > 3/3 = 3 > 1
really just x > 1 valid

negative: x < - x/x => x*x < -x
x^2 + x < 0
x(x+1) < 0
x < 0 valid
x < -1 not valid
-1/2 > -1/2 / |-1/2| = -1/2 > -1 okay
-2 > -2/|-2| = -2 > -1 no good
so -1< x < 0
not sufficient

st 2: |x| > x
means x can only be any negative # with the exception of -1
x = -1/2 would satisfy the condition in the stem
x = -3 would not
not sufficient

putting 1 and 2 together, we know that x > 1 cannot be true, so it would have to be the x < 0, sufficient

EDIT: sorry I messed up the first time and messed up/ didnt complete my work

EDIT #2 and #3 and #4: forgot to disable HTML again... whats wrong with this feature??

Last edited by beckee529 on 04 Nov 2007, 10:45, edited 4 times in total.
CEO
Joined: 29 Mar 2007
Posts: 2583
Followers: 19

Kudos [?]: 422 [0], given: 0

### Show Tags

04 Nov 2007, 10:13
beckee529 wrote:
GMATBLACKBELT wrote:
If x is not equal to 0, is |x| less than 1?

x > x/|x|
|x| > x

i get A please confirm if i am correct

from the stem
x =! 0
-1 < x <1> x/|x|

positive: x > x/x => x*x > x
x^2 - x > 0
x(x-1) > 0
x > 0
x > 1
3 > 3/3 = 3 > 1
really just x > 1 valid
sufficient

negative: x <x> x*x < -x
x^2 + x < 0
x(x+1) < 0
x < 0
x < -1
hence x <1> -2/abs -2 = -2 > -1
not sufficient

repost w/o html

I got B for this question as well, but it appears not to be correct.
VP
Joined: 09 Jul 2007
Posts: 1104
Location: London
Followers: 6

Kudos [?]: 103 [0], given: 0

### Show Tags

04 Nov 2007, 10:14
GMATBLACKBELT wrote:
If x is not equal to 0, is |x| less than 1?

x > x/|x|
|x| > x

A.
1.
x>x/|x|,
x-x/|x|>0,
x(1-1/|x|)>0
x>o fine, so x can be 1/2 or 2
and
1-1/|x|>0---> x cannot be fraction less than 1.
suff. to say No.

2. |x|>x, can be -1/2 and -2
Senior Manager
Joined: 28 Jun 2007
Posts: 319
Followers: 1

Kudos [?]: 37 [0], given: 0

### Show Tags

04 Nov 2007, 10:19
GMATBLACKBELT wrote:
If x is not equal to 0, is |x| less than 1?

x > x/|x|
|x| > x

(1) x > x/|x|

x = -1/2 satisfies x > x/|x|, also |-1/2| < 1

x = 2 satisfies x > x/|x|, but |2| < 1 is incorrect

Hence, insufficient.

(2) |x| > x

x = -1/2 satisfies |x| > x, also |-1/2| < 1

x = -2 satisfies |x| > x, but |-2| < 1 is incorrect

Hence, insufficient.

(1) and (2) together:
Only the numbers -1 <= x < 0 satisfy both x > x/|x| and |x| > x
These numbers also satisfy |x| < 1, hence answer is C.
CEO
Joined: 29 Mar 2007
Posts: 2583
Followers: 19

Kudos [?]: 422 [0], given: 0

### Show Tags

04 Nov 2007, 10:49
GMATBLACKBELT wrote:
If x is not equal to 0, is |x| less than 1?

x > x/|x|
|x| > x

O wow, ok. You really gotta pay attention to what the question is really asking!!! Ima just write it down from now on.

its asking is the |x|<1 not if x<1>1 but |-1/2|<1>x/|x| if X>1 then x>x|x| if x<-1 then x<x/|x|

say x =-2 then -2<2> -2<-1

if X is -1<x<0>-1/2/1/2.

if X is 0<x<1 then 1/2<1/2/1/2

So from S1: x can be -1/2 or -2 or 2 etc... Insuff b/c |-1/2|<1>1

1&2: 2: X must be negative. 1: X could be -1/2 or -2.

I say E, b/c |-1/2|<1>1
I feel like im missing something though.
Manager
Joined: 01 Nov 2007
Posts: 69
Followers: 1

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

### Show Tags

04 Nov 2007, 10:50
Given that lxl < 1
So -1 < x <1> x/lxl

if x = -1, -1 > -1 Not possible
if x = -2, -2 > -1 Not possible
if x = -0.5, -0.5 > -1 True
So -1 < x <0> 1 Not possible
if x = 2, 2 > 1 True
if x = 0.5, 0.5 > 1 Not possible
So x > 1
Therefore x can take values from o to -1 of greater than 1
1 not suff

2. lxl > x

if x = -1, 1 > -1 true
if x = -2, 2 > -2 true
here x > 0 is not possible
So x < 0.
Therefore x can take values less than 0
2 not suff

Together we get -1 < x < 0
which is sufficient...So C

I m still not sure ....may be I have made some mistake...Can anyone please check
Director
Joined: 11 Jun 2007
Posts: 931
Followers: 1

Kudos [?]: 175 [0], given: 0

### Show Tags

04 Nov 2007, 10:51
whats the OA? i am not sure of my reasoning either!
SVP
Joined: 01 May 2006
Posts: 1797
Followers: 9

Kudos [?]: 149 [0], given: 0

### Show Tags

04 Nov 2007, 11:47
(C) for me

x > x/|x|
|x| > x

|x| < 1 ?
<=> -1 < x < 1 ?

Stat1
x > x/|x|
<=> x - x/|x| > 0
<=> x*(1-1/|x|) > 0
<=> x*(|x|-1) > 0 with x != 0

implies that:
o x > 0 and |x| - 1 > 0 <=> x > 1
or
o x < 0 and |x| - 1 < 0 <=> -1 < x < 0

INSUFF.

Stat2
|x| > x
<=> x < 0

INSUFF.

Both 1 and 2
o x < 0
and [
o x > 0 and |x| - 1 > 0 <=> x > 1
or
o x < 0 and |x| - 1 < 0 <=> -1 < x < 0
]

We are in the case of -1 < x < 0... so |x| < 1

SUFF.

Last edited by Fig on 04 Nov 2007, 12:08, edited 1 time in total.
CEO
Joined: 29 Mar 2007
Posts: 2583
Followers: 19

Kudos [?]: 422 [0], given: 0

### Show Tags

04 Nov 2007, 11:53
Im sorry guys I dont have the OA b/c i got this question from the "share your experience" forum

Id say Fig is right though.
SVP
Joined: 29 Aug 2007
Posts: 2492
Followers: 68

Kudos [?]: 735 [0], given: 19

### Show Tags

04 Nov 2007, 12:59
GMAT TIGER wrote:
GMATBLACKBELT wrote:
If x is not equal to 0, is |x| less than 1?

x > x/|x|
|x| > x

very good question. got B.

from i, x/lxl is always either -1 or 1. if x is -ve fraction, x > x/lxl is true. if x is > 1, x > x/lxl is also true. so insufficient

from ii, lxl > x is true only for -ve x. so suff.

Update: missed lxl for x.

C should be it.

from i, x/lxl is always either -1 or 1. if x is -ve fraction, x > x/lxl is true. if x is > 1, x > x/lxl is also true. so insufficient

from ii, lxl > x is true only for -ve x. so we only know that x is -ve nut not the value. so still insuff...

from i and ii, x is -ve fraction. so suff.
Manager
Joined: 30 Oct 2007
Posts: 86
Followers: 1

Kudos [?]: 7 [0], given: 0

### Show Tags

05 Nov 2007, 06:39
If x is not equal to 0, is |x| less than 1?

x > x/|x|
|x| > x

1: x > x/|x| implies 0 > x > -1 therefore x is any negative fraction between 0 and 1 that gives us 1> |x| > 0 : is |x| less than 1 - YES
or x > 1 that gives |x| > 1 : is |x| less than 1 - NO
IN SUFFICIENT

2: |x| > x implies x < 0 therefore |x| > 0 : is |x| less than 1 - YES & NO
INSUFFICIENT

Manager
Joined: 01 Nov 2007
Posts: 69
Followers: 1

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

### Show Tags

05 Nov 2007, 06:54
ontheway wrote:
If x is not equal to 0, is |x| less than 1?

x > x/|x|
|x| > x

1: x > x/|x| implies 0 > x > -1 therefore x is any negative fraction between 0 and 1 that gives us 1> |x| > 0 : is |x| less than 1 - YES
or x > 1 that gives |x| > 1 : is |x| less than 1 - NO
IN SUFFICIENT

2: |x| > x implies x <0> 0 : is |x| less than 1 - YES & NO
INSUFFICIENT

But 1 also true for all x > 1
So 1 is not sufficient
Re: Abs value DS   [#permalink] 05 Nov 2007, 06:54
Display posts from previous: Sort by