(1) If x = 2, y = -1, then |x - y| = |2 + 1| = 3 and |x| - |y| = 2 - 1 = 1. Here |x - y| > |x| - |y|dreamv wrote:Is |x-y| > |x| - |y|?
1) y < x
2) xy < 0
If x = 4, y = 1, then |x - y| = |4 - 1| = 3 and |x| - |y| = 4 - 1 = 3. Here |x - y| = |x| - |y|
If x = -1, y = -2, then |x - y| = |-1 + 2| = 1 and |x| - |y| = 1 - 2 = -1. Here |x - y| > |x| - |y|
No definite answer; NOT sufficient.
(2) xy < 0 implies either one of x or y should negative and the other one should be positive.
If x = 2, y = -1, then |x - y| = |2 + 1| = 3 and |x| - |y| = 2 - 1 = 1. Here |x - y| > |x| - |y|.
If x = -1, y = 2, then |x - y| = |-1 - 2| = 3 and |x| - |y| = 1 - 2 = -1. Here |x - y| > |x| - |y|.
From the above examples, we can see that |x - y| > |x| - |y| always; SUFFICIENT.
The correct answer is B.
