Problem Solving

Can someone provide an easier appraoch for solving this problem?

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?

another vote for C

ALso note that :

a/b > c/d if ad>cb