You've done a great job, and almost have it. Note thatHowever, note that determining the number of distinct terms involves removing just the additional repeated terms, not all of the terms that have been repeated (i.e., the "total number of common terms" as you call it). As JonathanZ supports MonicaC's comment states, you have
answered the question "how many numbers are there that show up in only one of the series". And I don't think anyone could argue that that's what "distinct" means.
In particular, you've instead determined the number of unique terms, i.e., how many terms whichthat appear just once.
You've found there were $99$ terms that were repeated so, since each was repeated only once, the total needs to be reduced by just $99$. This then leaves one copy of each of those terms, which leads to the result being
$$1000 - 99 = 901$$
i.e., answer $D$.