I got the right answer (d) by assuming that since the question did not mention anything about whether or not the 2 events are independent/dependent, it is impossible to tell but this explanation goes about it by assuming they are independent. Is my reasoning valid, or should I always assume the events are independent if it is not mentioned by the gre question?

You’re reasoning is correct

So If it is not mentioned whether it is independent/dependent/mutually exclusive on the GRE, I cannot assume it is any of those 3?

look at this explanation : https://gre.magoosh.com/forum/282-the-probability-that-both-events-e-and-f