Is 1 > |x-1| ?
(1) (x-1)^2 > 1
(2) 0 > x
(1) (x-1)^2 > 1
|x-1| > 1
The question asks if 1>|x-1| #1 tells us that the OPPOSITE is true.
SUFFICIENT
(2) 0 > x
1 > |x-1|
If x is less than zero (x<0) then (x-1) is negative, thus:
1 > -(x-1)
1 > -x +1
2 > -x
-2 < x
Valid, as -2 falls within the range of x<0
SUFFICIENT
(D)
(1) (x-1)^2 > 1
(2) 0 > x
(1) (x-1)^2 > 1
|x-1| > 1
The question asks if 1>|x-1| #1 tells us that the OPPOSITE is true.
SUFFICIENT
(2) 0 > x
1 > |x-1|
If x is less than zero (x<0) then (x-1) is negative, thus:
1 > -(x-1)
1 > -x +1
2 > -x
-2 < x
Valid, as -2 falls within the range of x<0
SUFFICIENT
(D)