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St1: y<x
If x = 3, y = -2, then |x-y| = 5, |x| - |y| = 1 |x-y| > |x| - |y|
If x = 2, y = 1, then |x-y| = 1, |x|-|y| = 1 |x-y| = |x|-|y|

Insufficient.

St2: xy < 0

Means either:

(x,y) = (negative, positive) or (positve, negative), or (fraction, fraction)

If x = -3, y = -10, |x-y|=7, |x|-|y|=-7 ; |x-y|>|x|-|y|
If x = -10,y = -3, |x-y| = 7, |x|-|y|=7 ; |x-y| > |x|-|y|

Insufficient.

Using St1 and St2:

If x = -3, y = -10, |x-y|=7, |x|-|y|=-7 ; |x-y|>|x|-|y|
If x = 100, y = -10, |x-y| = 110, |x|-|y|=90; |x-y| >|x|-|y|
If x = 3, y = -7, |x-y|10, |x|-|y|=-4; |x-y| > |x|-|y|
If x = 1/2, y = 1/4, |x-y| = 1/2, |x|-|y| = 1/2