Data Sufficiency

Is Ix-yI > IxI - IyI?

1) y < x
2) xy < 0

OA B

Is |x-y| > |x| - |y| ?
1) y < x
2) xy < 0

One approach is to plot the distances on a NUMBER LINE.

|x|= the distance between x and 0 = the RED segment on the number lines below.
|y| = the distance between y and 0 = the BLUE segment on the number lines below.
|x-y| = the distance BETWEEN X AND Y.

Statement 1: y<x
Case 1:

|x| - |y| = RED - BLUE.
|x-y| = RED - BLUE.
Thus, |x-y| = |x| - |y|.

Case 2:

|x| - |y| = RED - BLUE.
|x-y| = RED + BLUE.
Thus, |x-y| > |x| - |y|.
INSUFFICIENT.

Statement 2: xy<0
Since x and y have different signs, they are on OPPOSITE SIDES OF 0.

In each case:
|x| - |y| = RED - BLUE.
|x-y| = RED + BLUE.
Thus, |x-y| > |x| - |y|.
SUFFICIENT.

The correct answer is B.