Is |x-y| > |x| - |y| ?

[buckrich]

Is |x-y| > |x| - |y| ?

(1) y < X
(2) xy < 0

[anshumishra]

Is |x-y| > |x| - |y| ?

(1) y < X
(2) xy < 0

question : Is |x-y| > |x| - |y| ?

Statement 1:
y < x

if x=5, y = 2
|x-y| = |5-2| = 3
|x| - |y| = |5| - |2| = 3, so |x-y| = |x|-|y|

if x=5, y=-2
|x-y| = 7
|x|-|y| = 3, so |x-y| > |x|-|y| ... So insufficient

Statement 2:
xy < 0 => x and y have opposite signs

if x = 5, y= -2
|x-y| = 7
|x|-|y| = 3, so |x-y| > |x| - |y|

if x =-2, y=5
|x-y| = |-2-5| = 7
|x|-|y|=|-2|-|5| = 2-5 = -3 , still |x-y| > |x| - |y| --- Sufficient

Hence, B

Using graph :
y<x => means the area below the line y=x, means it contains half of the 3rd quadrant, full 2nd quadrant and half 1st quadrant. So, clearly there are some areas (like the 1st quadrant), which is outside the graph of |x-y| > |x|-|y| as drawn below.

Also, you can see that xy > 0 lies in 2nd and 4th quadrant:
when x>0, y<0 (Means 4th quadrant)
when x<0, y>0 (Means the 2nd quadrant)

The graph for |x-y| > |x| -|y| is shown below (clearly all the areas in 2nd and 4th quadrant lies inside this).

[buckrich]

Thanks anshumishra. Although, I clearly know that xy<0 means the numbers have opposite signs when I originally worked the problem I made a careless error of thinking it meant they had the same sign. Because of this I spent over 30 very frustrating minutes trying to figure out why (2) was sufficient and never picked up on my mistake.