GMAT prep Q

[veekay]

Can someone provide an easier appraoch for solving this problem?

[kajcha]

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?

[mtg123]

another vote for C

[Badri]

ALso note that :

a/b > c/d if ad>cb