Brent@GMATPrepNow wrote:vinay1983's solution is perfect. The only numbers we can be certain are in the set are -2 , -5, -8, -11 . . . etc


I thought I'd mention that a lot of students make the mistake of reversing the conditional (if-then) statement in this question. The statement says "If if x is in the set, then x-3 is also in the set." Many students mistakenly believe that this also implies that "if x-3 is in the set, then x is also in the set." (these students end up concluding that 4 must be in the set)

This reversal 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 also conclude that, if an animal has ears then that animal is a rabbit? No.

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.

Cheers,
Brent