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is lxl less than 1?

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is lxl less than 1?

by sanju09 » Fri Mar 04, 2011 1:21 am
If x is not equal to 0, is lxl less than 1?

(1) x/lxl < x.

(2) lxl > x.
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Source: — Data Sufficiency |

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by Anurag@Gurome » Fri Mar 04, 2011 1:36 am
sanju09 wrote:If x is not equal to 0, is lxl less than 1?

(1) x/lxl < x.
(2) lxl > x.
Statement 1: x/|x| < x
If x is positive, 1/|x| < 1 => |x| > 1
If x is negative, 1/|x| > 1 => |x| < 1

Not sufficient

Statement 2: |x| > x
Only if x is negative, then |x| = -x > x
So we know x is negative, but we don't have enough information to conclude whether |x| less than 1 or not.

Not sufficient

1 & 2 Together: Form statement 2, x is negative.
Form statement 1, if x is negative then, 1/|x| > 1 => |x| < 1

Sufficient

The correct answer is C.
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by sanju09 » Fri Mar 04, 2011 1:44 am
Anurag@Gurome wrote:
sanju09 wrote:If x is not equal to 0, is lxl less than 1?

(1) x/lxl < x.
(2) lxl > x.
Statement 1: x/|x| < x
If x is positive, 1/|x| < 1 => |x| > 1
If x is negative, 1/|x| > 1 => |x| < 1

Not sufficient

Statement 2: |x| > x
Only if x is negative, then |x| = -x > x
So we know x is negative, but we don't have enough information to conclude whether |x| less than 1 or not.

Not sufficient

1 & 2 Together: Form statement 2, x is negative.
Form statement 1, if x is negative then, 1/|x| > 1 => |x| < 1

Sufficient

The correct answer is C.
terrific Anurag!
The mind is everything. What you think you become. -Lord Buddha



Sanjeev K Saxena
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The Princeton Review - Manya Abroad
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by makkiemaps » Fri Mar 04, 2011 8:16 am
Good explanation. Thanks !

This question appeared in the quant section of my MGMAT practice test.
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by maihuna » Sat Mar 05, 2011 1:45 am
Asking whether : -1<x<1

1. x/|x| < x
=> x < x|x|
=> x-x|x| < 0
=> x(1-|x|) < 0

if x<0, 1-|x| > 0 => |x| < 1.
if x>0, 1-|x| < 0 => |x| > 1.

2. |x| > x => x<0

Combining 1&2, x<0 => |x| < 1.

C

sanju09 wrote:If x is not equal to 0, is lxl less than 1?

(1) x/lxl < x.

(2) lxl > x.
Charged up again to beat the beast :)
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by adib » Tue Mar 08, 2011 12:49 am
hi anurag
can you please explain how you got from x/lxl < x to 1/lxl < 1 ?
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by kareem.firoz » Tue Mar 08, 2011 3:55 am
adib wrote:hi anurag
can you please explain how you got from x/lxl < x to 1/lxl < 1 ?
divide by x
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by adib » Tue Mar 08, 2011 4:26 am
thanks kareem
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