hey_thr67 wrote:If x is not equal to 0, is |x| less than 1?

(1) x/|x| < x
(2) |x| > x

If |x| < 1, then -1 < x < 1

Statement 1:
For x > 0, |x| = x --> x/|x| = 1 --> x > 1
For x < 0, |x| = -x --> x/|x| = -1 --> x > -1 --> -1 < x < 0

Not sufficient


Statement 1:
For x > 0, |x| = x --> Hence, x is not positive as |x| > x
As x ≠ 0, x must be negative.

Not sufficient

1 & 2 Together:
From statement 2, x < 0
Hence, from statement 1, -1 < x < 0
Therefore, |x| < 1

Sufficient

The correct answer is C.

hey_thr67 wrote:if |x| < 1 then is -1 <x<=1 ?

If |x| < 1, then absolute value of x is less than 1. In other words, distance of x from 1 on the number line is less than 1 or -1 < x < 1

hey_thr67 wrote:what is the general approach to solve absolute questions ?

Depends some problems can be solved algebraically using the definition of |x| as I did in this case. Some problems can be solved by region wise analysis after finding the critical points (as I did here >> https://www.beatthegmat.com/number-of-so ... tml#477970) and some problems can be solved by visualizing the situation on the number line (as I did here >> https://www.beatthegmat.com/double-inequ ... tml#476005).