While I admire your ambition, I'm a bit confused about your motives. Are you studying for the GMAT? If so, why not work on the questions that are actually out there rather than trying to create some of your own, especially since you're just getting started?
A big part of GMAT success is identifying recurring patterns. The main problem with many "home made" questions is that the question writer doesn't have enough experience with the exam to create questions that are similar to those on the actual GMAT. As a result, people who study those home made questions aren't preparing themselves for the actual exam and may be hurting, rather then helping, their scores.
Addressing one of the 3 points you made, every GMAT question has 1 answer that's categorically correct and 4 that are demonstrably wrong - even in verbal questions that may sound less certain. You will never find a GMAT question with more than 1 possible correct answer. The only mild exception to this rule is in sentence correction - there may be more than 1 answer that's grammatically correct, in which case it's your job to find the error-free choice that's stylistically superior to the others. However, while style may seem more ambiguous than grammar, the GMAT follows very consistent rules in deciding what "stylistically superior" means.
It's fine to reprint Kaplan questions here for discussion, as long as you credit Kaplan. We'd much rather you quote a question directly than change it, since those changes aren't reviewed by our curriculum committee and changed questions may be flawed.
The main wording issue with your question is the question itself, "then the total distinct members of all the three boards are". By using the word "are", the question implies that there's only one possible answer. Also, grammatically speaking, the question should be asking about the NUMBER of members. So, given that there's more than one possible answer, the question should read:
"..., then the number of distinct members serving on the three boards could be"
As far as solving the question, srcc25anu has the right approach. However, since each board could also have members who serve solely on that board, and since the boards must have an equal number of members, the correct answer is:
7 + 3n
in which n is any positive integer. In other words, the set of all possible answers is:
{7, 10, 13, 16, 19, ...}
of which only (C)13 appears among the choices.
