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

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CEO
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If x is not equal to 0, is |x| less than 1? x > x/|x| |x| [#permalink] New post 04 Nov 2007, 09:48
00:00
A
B
C
D
E

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

x > x/|x|
|x| > x
CEO
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Re: Abs value DS [#permalink] New post 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.
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Re: Abs value DS [#permalink] New post 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.
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Re: Abs value DS [#permalink] New post 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.
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Re: Abs value DS [#permalink] New post 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
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Re: Abs value DS [#permalink] New post 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.
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 [#permalink] New post 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.
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 [#permalink] New post 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
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 [#permalink] New post 04 Nov 2007, 10:51
whats the OA? i am not sure of my reasoning either!
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 [#permalink] New post 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.
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 [#permalink] New post 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.
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Re: Abs value DS [#permalink] New post 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.
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Re: Abs value DS [#permalink] New post 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

Answer: E
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Re: Abs value DS [#permalink] New post 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

Answer: E


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