Data Sufficiency

Please explain.

OA is B

One way for approaching absolute value problems is by looking at the geometric meaning.

|x-y| means distance between x and y on the number line. Always positive units.

|x| means distance between x and 0(origin) on number line
|y| means distance between y and 0(origin) on number line


The question is is the distance between x and y greater than the difference of distance between x and 0(origin) on number line and distance between y and 0(origin) on number line.


Stmt I

y < x

y=-4 x=4

|x-y| = 8
|x|= 4
|y| = 4

|x-y| > |x| - |y| yes

y=2 x=4

|x-y| = 2
|x|= 4
|y| = 2

|x-y| = |x| - |y| NO

insuff

Stmt II

xy<0

Either x is positive and y is negative or y is positive and x is negative

Take any value of x and y that satisfy either of the 2 conditions above u will notice that the distance between x and y (|x-y|) will always be greater than the difference of distance between x and 0(origin) on number line and distance between y and 0(origin) on number line.

SUFF

Choose B

Hope this helps and let me know if u still have questions.

Regards,
CR