If |x| < 1, then -1 < x < 1hey_thr67 wrote:If x is not equal to 0, is |x| less than 1?
(1) x/|x| < x
(2) |x| > x
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.
