One approach is to TEST some x and y values that satisfy the given condition that x²y > 0
For example x = -1 and y = 1 satisfies the inequality x²y > 0

Now let's use these values to check our 3 statements:
I. xy > 0. Plug in our values to get: (-1)(1) = -1. This means xy is NOT greater than 1. The question asks, "Which of the following must be true?"
So statement I is NEED NOT be true.
This means we can ELIMINATE answer choices A and E

II. x > 0. Plug in x-value to get: -1 > 0
This is NOT true.
This means we can ELIMINATE answer choices B and D

This leaves us with answer choice C only, which means statement III MUST be true

Answer: C

Cheers,
Brent