This is one of those relatively rare times in Quant that the GMAT actually tries to trick you semantically. Just because they say "if x is in the set, then x - 3 is also in the set," it doesn't necessarily mean that "if x - 3 is in the set, x is in the set." What if x = 1? We'd be able to prove that every number 3 less than x, and 3 less than that, and so on, is in the set. But can we prove that anything greater than x is in the set? Not necessarily.

It's certainly possible that 4 is in the set. Maybe x = 4, and then 1 is x - 3. Or maybe x = 13, and 4 is x - 3 - 3 - 3. But with these Roman numeral questions, make sure you distinguish between what's possible and what's necessary. If we know a certain number is in the set, we know about the values less than that number, but not necessarily the values greater than that number.

It's not uncommon for people to reverse the order of if-then statements.

The if-then statement here is "If if x is in the set, then x-3 is also in the set"
Reversing the statement (to get "if x-3 is in the set, then x is also in the set") is not logically sound.

Here's an example why.

Let's say: If an animal is a rabbit, then that animal has ears.
Can we then conclude that if an animal has ears then that animal is a rabbit? No.

So, in our question, the existence of x in the set guarantees the existence of x-3 in the set.
However, it is not necessarily the case that the existence of x-3 in the set guarantees the existence of x in the set.

I hope that helps.

Cheers,
Brent