MathRevolution wrote:

Is |x-y|<|x-z|?

1) |y|<|z|

2) x<0

St1: Assume x = 2; y = -2; z = 3

|2 - (-2)| < |2 - 3| ? No

Assume x = 2; y = -2; z = -3

|2 - (-2)| < |2 - (-3)| ? Yes

St1 is not sufficient

St2: Assume x = -1; y = -2; z = 3

|-1 - (-2)| < |-1 - 3| ? Yes

Assume x = -1; y = 2; z = -3

|-1 - 2| < |-1 - (-3)| ? No

St2 is not sufficient

Combining St1 and St2 is also not helpful.

Answer: E