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

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If x is not equal to 0, is |x| less than 1? (1) x/|x| < x [#permalink] New post 02 Nov 2009, 05:16
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If x is not equal to 0, is |x| less than 1?

(1) x/|x| < x

(2) |x| > x
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Re: MGMAT inequality [#permalink] New post 02 Nov 2009, 06:34
gmatforce wrote:
If x is not equal to 0, is |x| less than 1?

(1) x/|x| < x

(2) |x| > x


B

(1)
x=-1/2
-1<-1/2

x=2
1<2
Can't say if x is less than 1

(2)
x has to be negative for the absolute value to be greater. Sufficient.
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Re: MGMAT inequality [#permalink] New post 02 Nov 2009, 07:25
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I think B is not correct. This question was discussed before, below see my post from the earlier discussion:

x#0, is |x|<1? Which means is -1<x<1? (x#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)


(2) |x| > x Well this basically tells that x is negative. But still if we want to see how it works:
Two cases again:
x<0--> -x>x--> x<0.

x>0 --> x>x: never correct.

Only one range: x<0, but still insufficient to say whether -1<x<1. (For instance x can be -0.5 or -10)

(1)+(2) 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.

Answer: C.
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Re: MGMAT inequality [#permalink] New post 02 Nov 2009, 07:34
Bunuel wrote:
I think B is not correct. This question was discussed before, below see my post from the earlier discussion:

x#0, is |x|<1? Which means is -1<x<1? (x#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)


(2) |x| > x Well this basically tells that x is negative. But still if we want to see how it works:
Two cases again:
x<0--> -x>x--> x<0.

x>0 --> x>x: never correct.

Only one range: x<0, but still insufficient to say whether -1<x<1. (For instance x can be -0.5 or -10)

(1)+(2) 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.

Answer: C.


Oh :shock: grossly misread the Q as x<1. Thanks for the correction!
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Re: MGMAT inequality [#permalink] New post 03 Nov 2009, 21:18
Bunuel, Gmat community's happy to got you.
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Re: If x is not equal to 0, is |x| less than 1? (1) x/|x| < x [#permalink] New post 17 Jan 2013, 00:40
gmatforce wrote:
If x is not equal to 0, is |x| less than 1?
(1) x/|x| < x
(2) |x| > x


This is my most feared question type because it requires you to try out values but practice truly reduces that anxiety...

1.
Test x=2: 1 < 2 (This works for the equation but |x| is not less than 1) NO!
Test x=-1/4: -1 < -1/4 (This works for the equation and |x| is less than 1) YES!
INSUFFICIENT.

2. |x| > x
This means x is negative value.
x = -1: |x| is not less than 1 NO!
x = -1/4: |x| is less than 1 YES!
INSUFFICIENT!

Together: We only test (-) values with x/|x| < x
x=-1: No!
x=-1/4: Yes!

So the only valid solution for x/|x| < x that is negative is a fraction.
Fractions are |x| less than 1. YES!

Answer: C
Re: If x is not equal to 0, is |x| less than 1? (1) x/|x| < x   [#permalink] 17 Jan 2013, 00:40
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