Data Sufficiency (DS) | Re: Is |x| < 1 ?

Is |x| < 1 ?

Is |x| < 1 --> is -1 < x < 1.

(1) x/|x| < x.

Two cases:
A.\(x<0\) -->\(\frac{x}{-x}<x\) -->\(-1<x\) . Since we consider the case when\(x<0\) , then we'd have\(-1<x<0\) . Answer YES.

B.\(x>0\) -->\(\frac{x}{x}<x\) -->\(1<x\) . Answer NO.

Not sufficient.

(2) x/|x| < 1. This simply means that x is a negative number: if x is positive then x/|x| = 1, if x is negative x/|x| = -1 < 1. Not sufficient.

(1)+(2) Since from (2) we have that x is negative, then we have