Absolute question

[akshatgupta87]

Q.)Is 1 > |x-1| ?
A)(x-1)^2 > 1
B) 0 > x

Someone explain..

[force5]

IMO- D

|x-1|<1

x<2 and x>0

statement 1: x>2 and x<0 (sufficient)
statement 2: x <0 (sufficient)

[MAAJ]

IMO [spoiler](D)[/spoiler]

Is |x-1| < 1?


1)(x-1)² > 1
|x-1| > 1
Positive ABS: x-1 > 1 thus x > 2
Negative ABS: -x+1 > 1 thus x < 0
If you try both values, then |x-1| will always be greater than 1.

2) 0 > x
This is one of the solutions of the STMT 1 so its sufficient.

[sourabh33]

Q.)Is 1 > |x-1| ?
A)(x-1)^2 > 1
B) 0 > x

Someone explain..

|x-1| < 1 ,can only be possible if x is a positive fraction between 0 & 1 i.e 0<x<1
we can verify this by testing numbers (-5,-1,-1/2,0,1/2,1,5)


Now Taking equation 1

(x-1)^2 > 1
The above equation can only be true if either, x<0 or x>2. We can verify this by testing numbers (-5,-1,-1/2,0,1/2,1,5)

So eq 1 is sufficient


Now Taking equation 2

x<0
if x<0 than |x-1| will always be greater than 1

So eq 2 is sufficient

[GMATGuruNY]

Q.)Is 1 > |x-1| ?
A)(x-1)^2 > 1
B) 0 > x

Someone explain..

Question: Is |x-1| < 1?
Case 1: x-1 < 1
x < 2

Case 2: x-1 > -1
x > 0

Question rephrased: Is 0 < x < 2?

Statement 1: (x-1)² > 1.
Case 1: x-1 > 1
x > 2.

Case 2: x-1 < -1
x < 0.

Thus, it is not possible that 0 < x < 2.
Sufficient.

Statement 2: x < 0.
Thus, it is not possible that 0 < x < 2.
Sufficient.

The correct answer is D.