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# If x is not equal to zero, is |x| < 1? 1) x / |x| < x

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Manager
Joined: 01 Apr 2006
Posts: 184
Followers: 1

Kudos [?]: 14 [0], given: 0

If x is not equal to zero, is |x| < 1? 1) x / |x| < x [#permalink]  27 Jan 2007, 18:26
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If x is not equal to zero, is |x| < 1?

1) x / |x| < x

2) |x| > x
Senior Manager
Joined: 24 Oct 2006
Posts: 339
Followers: 1

Kudos [?]: 16 [0], given: 0

Q: 0<|x|<1?
Ans: C?

edited because some of my answer lines were missing
some error...?!

Last edited by Sumithra on 28 Jan 2007, 04:29, edited 1 time in total.
SVP
Joined: 05 Jul 2006
Posts: 1519
Followers: 5

Kudos [?]: 112 [0], given: 39

If x is not equal to zero, is |x| < 1?

1) x / |x| <x> x

from one

if x>0 thus x>1, and if x<0 thus x<-1.........not suff

from two

x is -ve ..........insuff

both together
x is a -ve fraction ie: -1<x<0

thus /x/<1

EDITED

Last edited by yezz on 02 Feb 2007, 12:59, edited 1 time in total.
VP
Joined: 28 Mar 2006
Posts: 1384
Followers: 2

Kudos [?]: 19 [0], given: 0

should be E

from (1) it is clearly INSUFF

from (2) |x| > x only if x is -ve. but cannot say that |x|<1>1
ifx=-1/2 |x|<1

INSUFF

from both 1 and 2

it isnt any help.
Senior Manager
Joined: 23 Jun 2006
Posts: 387
Followers: 1

Kudos [?]: 310 [0], given: 0

from st2 you can infer x is negative. now put this info into st1:

since x is negative, divide both sides by x (and invert the inequality) to get

1/|x|>1
or |x|<1 as required....

hence sufficient.

Senior Manager
Joined: 04 Jan 2006
Posts: 280
Followers: 1

Kudos [?]: 20 [0], given: 0

This webboard change my typing. So, I am going to post image.
Attachments

Ans01.jpg [ 97.88 KiB | Viewed 372 times ]

Senior Manager
Joined: 04 Jan 2006
Posts: 280
Followers: 1

Kudos [?]: 20 [0], given: 0

See below the explanation.

This is long tradition process. However, you will be sure when answer the question.
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Ans02.jpg [ 80.15 KiB | Viewed 371 times ]

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