Re: Inequality and absolute value questions from my collection

11. Is |x+y|>|x-y|?

(x+y)>(x-y)
x+y>x-y
2y>0
y>0

OR

(x+y)>-(x-y)
x+y>-x+y
2x>0
x>0

(1) |x| > |y|

|x+y| will be greater than |x-y| only when x and y have the same sign (+) (+) or (-) (-)

|x| > |y| tells us nothing about the signs. For example:

|x| > |y|
|4| > |2|
4 > 2
OR
|-4| > |2|
4 > 2

INSUFFICIENT

(2) |x-y| < |x|

|x-y| < |x|
|3-1| < |3| ===> |2|< |3| VALID
|-3-1| < |-3| ===> |4| < |3| INVALID
|3-(-1)| < |3| ===> |4| < |3| INVALID
|-3-(-1)| < |-3| ===> |2| < |3| VALID

For |x-y| < |x| to hold true then x and y have to have the same signs. |x+y|>|x-y| is true only when x and y have the same signs.
SUFFICIENT

(B)