Final answer:
If the value of a rational number is negative, statements A and C could be true.
Step-by-step explanation:
In order for the value of a rational number to be negative, either p or q (or both) must be negative.
So, statements A and C could be true if the value of the rational number is negative. Statement B is incorrect because if p is positive, then the rational number would be positive as well.
Similarly, statement D is incorrect because if p is equal to 0, then the rational number would also be 0, not negative.