A very straight forward answer will be
\(x > y\) and \(\frac{1}{x} < \frac{1}{y}\), that is cross-multiplication is NOT changing the sign. MEANS both x and y have SAME sign or xy>0.
I. \(0 < x < 1\) and \(0 < y < 1\)...xy>0..YES
II. \(xy < 0\)...NO
III. \(-1 < x < 0\) and \(-1 < y < 0\)...xy>0..YES

I and III

D

OR

Choose values...
I. \(0 < x < 1\) and \(0 < y < 1\)..........x=0.9 and y=0.3...0.9>0.3 and \(\frac{1}{0.3}>\frac{1}{0.9}\)..\(\frac{10}{3}>\frac{10}{9}\)...YES
II. \(xy < 0\)....x=2 and y=-1...2>-1 but 1/2>1/-1...Eliminate
III. \(-1 < x < 0\) and \(-1 < y < 0\)....x=-0.3 and y=-0.9...-0.3>-0.9 and \(-\frac{1}{0.3}>-\frac{1}{0.9}\)..\(\frac{10}{3}>\frac{10}{9}\)...YES
_________________

1/x<1/y
So (y-x)/xy <0

We know that x>y, so y-x <0. xy must be positive (>0).
So, either x,y >0 or x,y <0

I. Yes
II. NO
III. Yes

IMO D.