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# Is |x-1|<1? a) (x-1)^2 <= 1 b) x^2-1>0

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Retired Moderator
Joined: 18 Jul 2008
Posts: 959
Is |x-1|<1? a) (x-1)^2 <= 1 b) x^2-1>0 [#permalink]

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28 Nov 2008, 13:03
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Is |x-1|<1?

a) (x-1)^2 <= 1

b) x^2-1>0
Manager
Joined: 02 Nov 2008
Posts: 58

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28 Nov 2008, 15:23
Question can be rewritten as

-1<x-1<1
Is 0<x<2 ?

1) taking square root on both sides we get x <= 2 - Insuff
2) x could be anyting but 1

E
Manager
Joined: 27 May 2008
Posts: 200

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28 Nov 2008, 19:48
E
Is |x-1|<1?

a) (x-1)^2 <= 1

b) x^2-1>0

Simplifying the Q we will get,
0<x<2

a) this can also be simplified as 0<x<=2 so INSUFF

b) so X>1 and x<-1 INSUFF

combining also INSUFF, since we have x<=2
Manager
Joined: 14 Jun 2007
Posts: 166
Location: Vienna, Austria

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29 Nov 2008, 23:13

isn´t the value narrowed down to 2 ?
Manager
Joined: 27 May 2008
Posts: 200

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30 Nov 2008, 07:07
Nope ..

1) says x<=2 but we need to prove 0<x<2
Re: DS: Absolute values   [#permalink] 30 Nov 2008, 07:07
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