Notice the question. It asks what all options MUST be true. Means for any set of nos, the option will always hold true. I like to solve such questions by substituting nos. Since, sqrt is involved in the equation I will choose nos 9 and 4.
Assume x = 4 and y = 9
In this case (1/(root(x+y))) = 1/(root13) = root(13)/13
Now check all options
Option 1 = root(13)/8 > root(13)/13. But hold on before you mark this option correct.
You should check the option when x>y. Assume x=9 and y=4. In this case option 1 will be equal to root(13)/18 < root(13)/13.
So option 1 is not always true. So rule out all choices that has option 1 in it.
Evaluate option 2 now. Substitute values x = 4, y=9 to get 5/13.
sunbstitute x=9, y=4 to get 5/13
you know root(13)<4 so 5/13 > root(13)/13. This will always be true.
evaluate the answer choices again. So you know answer will be either C or E
Evaluate option 3 now. You will notice option 3 < 0 when x<y. So this will not be true always.
So ans must be C
What's the OA?
