An arithmetic sequence is a sequence in which each term after the firs

Using both statements, the common differences in P and Q can both be 6. Then using Statement 2, our sequences could be something like:

P: 10, 16, 22, 28, ....
Q: 16, 22, 28, 34, ...

These overlap almost completely; only the first term of P is not in Q, and only the last term of Q is not in P. So we'll only have 11 distinct values (the nine overlapping ones, plus the two unique values) if we combine P and Q.

But the common difference might be 1 in sequence P, and 6 in sequence Q. Then we could have

P: 20, 21, 22, 23, 24, ...
Q: 16, 22, 28, 34, ...

which clearly do not overlap nearly as much as in the first example, so we'll have more than 11 distinct values here and the answer must be E.

There are several issues with the question, though. For one, it's much wordier than real GMAT questions, and for another, it asks us to consider the Least Common Multiple of numbers that can be negative (common differences need not be positive). I'd expect in this kind of question for sequence S to be well-defined, but it's not, since we don't know how it is ordered, and there are some other issues with the wording. So I don't think any test taker who finds this question confusing should be concerned about that.