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.
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