GMATPrep problem

[ptumati]

if X and Y are positive, which of the following must be greater than 1/(x+y)^1/2?

I ((x+y)^1/2)/2x

II (x^1/2 + y^1/2)/(x+y)

III (x^1/2 - y^1/2)/(x+y)

a) none
b) I only
c) II only
d) I and III
e) II and III

I have no clue how to approach this problem...

GMATPrep says that the answer is

SPOILER: c

Can anyone please help me on this... thnaks.

[GMAT-HELP]

Multiply NR and DR by (x+y)^1/2
=> 1/(x+y)^1/2 = (x+y)^1/2/(x+y)

II. (x^1/2 + y^1/2)/(x+y) > (x+y)^1/2/(x+y)
as x^1/2 + y^1/2 > (x+y)^1/2 for positive X,Y

[Now or Never]

Take x= 2, y= 3 so sqrt(x+y) is 2.2, sqrt(x) = 1.4 and sqrt (y) = 1.7, substitue in all three options, I think its fairly quick from there on