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

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Director
Joined: 23 May 2008
Posts: 742
If x is not equal to 0, is |x| less than 1? (1) x/|x| < x [#permalink]

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18 Aug 2008, 13:22
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If x is not equal to 0, is |x| less than 1?

(1) x/|x| x

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Joined: 07 Nov 2007
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18 Aug 2008, 13:48
1
bigtreezl wrote:
If x is not equal to 0, is |x| less than 1?

(1) x/|x| < x

(2) |x| > x

(1) x/|x| < x
two solutions.
when x>0 then x>1 --- case(a1)
when x<0 then x>-1 --> -1<x<0 --- case(b1)

from case b1 ---> |x|<1
from case a1-- |x|>1
insuffcient
(2)|x| > x
when x>0 x>x -->5>5 (Impossible)
when x<0 |x| > x ---> |-5|>-5 (possi ble)
x<0 --> from this |x| can be <1 or >1 -->case (c1)
insufficient

Combine both
x<0 and -1<x<0
definitely |x| <1

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Joined: 17 Aug 2008
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18 Aug 2008, 15:33
If x is not equal to 0, is |x| less than 1?

(1) x/|x| < x

(2) |x| > x

From question, |x|<1?

Choice 1: x/|x| < x, gives, |x| > 1; so this is sufficient to answer the question.
Choice 2: |x| > x; This is only possible if x is negative. But, the statement is true when -1< x< 0 and also -infinity < x < -1; So, this does not give us a definitve answer.

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Joined: 29 Mar 2008
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18 Aug 2008, 16:29
If x is not equal to 0, is |x| less than 1?

(1) x/|x| < x

(2) |x| > x

Modifying the question stem, |x| less than 1 => is -1 < x < 1?

(1) tells us that 1< x and -1 < x, which means that we cannot definitively say that x lies between -1 and 1.
(2) tells us that x < 0, which again does not tell us if x lies between -1 and 1.

Combining (1) and (2) tells us that x lies between -1 and 0 and this information is enough to definitively say, x lies between -1 and 1 or |x| is less than 1.

Hence C.
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Intern
Joined: 15 Jul 2008
Posts: 5

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18 Aug 2008, 19:59
x/|x| < x.....suff as x between -1 ans 0

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This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

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Re: DS: inequality   [#permalink] 18 Aug 2008, 19:59
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