GmatKiss wrote:If x is not equal to 0, is |x| less than 1?
(1) x/|x|< x
(2) |x| > x
|x| < 1 means is -1 < x < 1?
(1) x/|x|< x
Case I: If x < 0, then x/(-x) < x or -1 < x
But x < 0, so -1 < x < 0.
Case II: If x > 0, then x/x < x or 1 < x
So, -1 < x < 0 or x > 1, which is NOT sufficient to find if -1 < x < 1 or not.
(2) |x| > x
If x ≥ 0, then |x| = x, so we know that x is < 0 or negative.
But still we cannot find if -1 < x < 1 or not; NOT sufficient.
Combining (1) and (2), we know that -1 < x < 0
So, -1 < x < 1 holds true; SUFFICIENT.
The correct answer is C.
