chetan2u wrote:

[quote="Bunuel"]If |x + 2| = |y + 2|, what is the value of x + y?

(1) x ≠ y

(2) x − y = 16

|x + 2| = |y + 2| means x and y are at same distance from -2

so either both x and y are equal or they are on either side of -2..

OR

square both sides..

\((|x + 2|)^2 = (|y + 2|)^2..............x^2+4x+4=y^2+4y+4.........x^2-y^2+4x-4y=0.......(x-y)(x+y)+4(x-y)+0........(x-y)(x+y+4)=0\)

this means x=y or x+y=-4 or both(1) x ≠ y

colored portion above tells us that x+y=-4

sufficient

(2) x − y = 16

again this tells us that x ≠ y, otherwise x-Y=0

colored portion above tells us that x+y=-4

sufficient

D

I always had this doubt.Even now i am not clear about the OR in the inequalities.could you please explain the functionality of it or posting a thread link explaining that is also fine because it will be time consuming to type it again if explained elsewhere.

Thankyou.