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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.

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

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

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

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