AnkitK wrote:
Krishma can you pls explain how to eliminate answer choices precisely.How can xy<0 not be true when one is negative and the other positive.
Ok.
Given: |x| - |y| = |x+y|
There are infinite set of values for x and y that satisfy this equation. Let us try one of them. Say x = 1, y = -1
a) x-y> 0 .......... 1 - (-1) > 0; 2 > 0; True
b) x-y< 0........... 1 - (-1) < 0; 2 < 0; Eliminate
c) x+y> 0........... 1 + (-1) > 0; 0 > 0; Eliminate
d) xy>0.............. 1 *(-1) > 0; -1 > 0; Eliminate
e) xy<0.............. 1 *(-1) < 0; -1 < 0; True
So I have two options that satisfy the assumed values of x and y.
We need to eliminate one of them.
They are
a) x-y> 0
e) xy<0
We see that x = 1, y = -1 satisfies both these inequalities. But option (a) is not symmetric i.e. if you interchange the values of x and y, it will not hold. That is, if x = -1 and y = 1, our original equation |x| - |y| = |x+y| is still satisfied but
a) x-y> 0 .............. (-1) - (1) > 0; -2>0; False. Eliminate
e) xy<0................. (-1)(1) < 0; True
Since option (e) still holds, it is the answer.
xy<0 is certainly true when one of them is negative and the other is positive.
Takeaways:
|x| + |y| = |x+y|
when x and y have the same signs - either both are positive or both are negative (or one or both of them are 0)
|x| - |y| = |x+y|
when x and y have opposite signs - one is positive, the other negative (or y is 0 or both are 0)