Bunuel wrote:

Official Solution:

(1) \(|1−x| \lt 1\). From this statement it follows that \(-1 \lt 1-x \lt 1\). Add -1 to all parts: \(-2 \lt -x \lt 0\). Now multiply by -1: \(2 \gt x \gt 0\). So, \(x\) is positive. Sufficient.

(2) \(|1+x| \gt 1\). From this statement it follows that \(x \gt 0\) or \(x \lt -2\). So, \(x\) may or may not be positive. Not sufficient.

Answer: A

|1-x|<1

will have two parts to the solution

1-x<1 =====>x-1>-1==========> x>0

and -(1-x)<1======>x-1<1 =====> x<2

So does this mean that x lies between 0 and 2???

Or does it mean that either X is greater than 0 or X is less than 2.

Because if it means that x is less than 2 or x is greater than 0, then x is less than 2 could also signify that x is negative.