this post was edited !
this problem (as all absolute value problems do) ask you about distances on the number line.

You can ask ---> is the distance from x to y is greater then the difference in the distance from x to 0 and from y to 0.

statement 1
the distance from x to zero and y to zero will be greater then the distance of x to y

only when x and y don't have the same sign.

insufficient

statement 2
the distance from x to zero and y to zero will be greater then the distance of x to y only when x and y don't have the same sign.

from statemtn 2 we can tell that x,y don't have the same sign !

sufficient.

the answer is (B)