vertigo05 wrote:Is |x - 1| less than 1 ?

1). (x - 1)^2 less than and equal to 1
2). (x^2) - 1 greater than 0

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

x^- 2x +1 <=1

x^-2x <=0

x(x-2x) <=0

x is in [0,2]

now x-1 is in [-1,1]

x-1 can be 1 hence not sufficient

2) x^2-1 >0

(x-1)(x+1) >0

x>1 or x<-1

x is not in the interval [-1,1]

x-1 is not in the interval [-2,0]

Not sufficient

Combining,
x can be in the interval (1,2]
x-1 can be in the interval (0,1]

x-1 can be 1 ; insufficient

E

I will go with E too.

Rephrase is <0X<2.

A tells us that X <= 2,0, in other words its <= 2.

B tells us that X>1,-1.

Combining 2 we find that X is either between 1 & 2 or -1 &0. So not Suff

Thanx Ajith and Vineet.
One question for Vineet:

From (1) x<= 0,2
From (2) x> -1,1
Combining both, can we conclude that (-1<x<=2) ?

Agree with E.

Is |x - 1| < 1 ?

Rephrase the question to:

A] is x - 1 < 1 or is x<2 when x - 1>0 or x>1
means is 1<x<2 ?
or

B] is -x + 1 < 1 or x>0 when x - 1<0 x<1
means 0<x<1

1]. (x - 1)^2 less than and equal to 1
This means |x - 1| <= 1
Not sufficient.

2] (x^2) - 1 greater than 0
This means x > 1 or x < -1
Not sufficient.

Together 'x' could be between the required range or equal or more.

[quote="vertigo05"
One question for Vineet:

From (1) x<= 0,2
From (2) x> -1,1
Combining both, can we conclude that (-1<x<=2) ?[/quote]

Hi, whats the question?

Hey Vineet, from your explanation,

we find that X is either between 1 & 2 or -1 &0. So not Suff

but,

from (1) x <= 0,2
from (2) x >1, x >-1

So combining both, shouldn't it be -1<x<=2 ???

vertigo05 wrote:Hey Vineet, from your explanation,

we find that X is either between 1 & 2 or -1 &0. So not Suff

but,

from (1) x <= 0,2
from (2) x >1, x >-1

So combining both, shouldn't it be -1<x<=2 ???

Vertigo,

When we rephrase the questions we have to find whether x is greater than 0 and less than 2 i.e.0<x<2. If we combine then X can be either between 1 & 2 or -1 &0.

----------------------------------(-1)-------0---------1---------2---------------

If you see at the number line above In A X is anywhere less than 2, it can be 1, 0 or -1, if it is latter 2 not suff. In B x is either greater than 1 or greater than -1. So it can be -.5, .5, 1.5 or 2.5.

If we combine then also we can get a value of -.5 or a value of 1.5, so not suff.

I hope its clear.

Vineet

Thanx vineet.