Is |x-y| > |x| - |y| ?

[vikram]

Is |x-y| > |x| - |y| ?

1) y < x
2) xy < 0


Please explain OA is B

[Sudhan]

Using ADBCE Grid,

Lets take (1)
y<x

y 2 -4
x 4 2

Substitute in the equation

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

Using the above values,
|2|>|4|-|2| First Column Values

Not true
|2-(-4)|>|2|-|-4| Second Column Values
|6|>2-4
6>-2 --True

Hence A is Insuff


(2)
xy<0 which means either x or y should be negative

x 7 -7
y -3 3

Substitute the values in the eq
|x-y|>|x|-|y|

|10|>|7|-|-3|
10>4

|-7-3|>|-7|-|3|
|-10|>-7-3
10>-10

Hence Suff

Hence B.

Hope it helps

[StaceyKoprince]

I like Sudhan's approach - picking numbers is a good idea here. It looks like the formatting got a little lost (the formatting's not the best here), so let us know if you don't understand anything from above.

Also, just be aware of this: why did Sudhan pick those particular numbers? If the problem is asking about absolute value, then positives and negatives are going to come into play. So I should make sure to try various positive and negative options / combos as I try numbers.