Hi,
Please delete all other threads. I do not understand why you have posted the same set in so many different threads. If it is some problem with the website, please contact the site admins/moderators.

Q1)Let x-y be p
So, 1/(x-y) + (x-y) = 1/p + p =(1+p^2)/p
As 1+p^2 is always positive, (1+p^2)/p is positive if p is positive
i.e. if (x-y) is positive, 1/(x-y) > y-x
if (x-y) is negative, 1/(x-y) < y-x
From(1):
No info. about x
Not sufficient
From(2):
No info. about y
Not sufficient
Both(1) and (2):
x-y is negative. So, 1/(x-y) < y-x
Sufficient

Hence, C

Q2)
From(1):
if x=2, y=2, then xy = 4 < 9
if x=4, y=4, then xy = 16 > 9
Not sufficient
From(2):
Same set as above
Not sufficient
Both (1) and (2): Same set as above
Not sufficient

Hence, E