to me the answer is C here
is y>x
(1) (1/y)>(1/x)
(1/y)-(1/x)>0
(x-y)/(xy)>0
here two cases are possible
x>y and xy>0 or
x<y and xy<0
so if we can prove that xy<0 it cames that y>x
but 1 st is insuff
(2)x/y<0, from here we can`t estimate what is greater, so insuff, but we have one important point
x and y have opposite signs, is x is +ve then y is -ve and is x is -ve then y-+ve
both from 2 st we know that xy<0 and as xy<0 then y>x
so suff

Given: (1/y)>(1/x)

Multiply by x
a) if x is positive, you get x/y>1. Both must be positive and x must be greater than y
b) if x is negative you get x/y<1. that gives us two cases:
b1)If y is positive and x is negative, we have a negative number less than +1 and don't have any idea which is greater.
b2)If y is negative, we have a positive number and the absolute value of x must be less than the absolute value of y, but since both are negative that means the actual value of x is greater. Insufficient.

The second clue alone is insufficient since all it tells us is that x and y have the same sign.

Putting them together, if x and y are both positive (case a), we have shown x is greater than y.
Also, if x and y are both negative (case b2) we have also shown x is greater than y.

The answer is C.

If the algebra isn't working for you, try picking numbers.