Is |x| + x |y| + y ? (1) x y (2) Both x and y are negative

Question

Is |x| + x > |y| + y ?

(1) x > y
(2) Both x and y are negative

gmatophobia · Answer

Statement 1

x > y

Case 1:

------- 0 ---------- y -------- x ----------

Is (the distance of x from 0 + the value of x) > (the distance of y from 0 + the value of y) -- Yes !

Case 2:

------- y ---------- x -------- 0 ----------

Is (the distance of x from 0 + the value of x) > (the distance of y from 0 + the value of y) -- No !

|x| + x = |y| + y = 0

The statement is not sufficient. Hence eliminate A and D.

Statement 2

Both x and y are negative

If both x and y are negative |x| + x = |y| + y = 0.

Hence we have a definite answer to the question 
Is (the distance of x from 0 + the value of x) > (the distance of y from 0 + the value of y) -- No !

Sufficient

Option B

Is |x| + x > |y| + y ? (1) x > y (2) Both x and y are negative