The members of a company’s board of directors must select a subcommitt

Why wouldn't the number of combinations for statement 2 include each possible number of subcommittee members:
12c1 + 12c2 + ... + 12c6

Question seems inconclusive to me.

Option A: Fairly straightforward, if 6 members are being selected, minimum board members =12
12C6 > 900. Hence Sufficient

Option B: Number of members that can be selected is <=16. Given the questions says "Is the number of combinations (total and not only one at a time) of board members that can be selected to serve on the subcommittee greater than 900? it means
12C1 + 12C2 +12C3 .....+ 12C6 > 900
Hence Sufficient

Answer D.
@bunnuel - Not sure why the OA is A only

Hello IanStewart, could you please weigh in on this?

This is my understanding of the problem.
The subcommittee can have a maximum of half its membership comprise of board members, the rest must be picked from another pool of suitable candidates.

1)Subcommittee has 6 members, so it can have a maximum of 3 board members. If there are 6 board members to choose from, the combinations of selected board members would be lesser than 900; if there are 100 board members, and we select 3, this value will be greater than 900.
Statement 1 is insufficient.

2) 12 board members, but no idea about number of members needed for the subcommittee. Insufficient.

Combined :
12 board members, of whom a maximum of 3 can be selected to serve on the subcommittee. 12C3, 12C2, 12C1, all yield values lower than 900. C is the answer.

Is my understanding correct?

I think you've reversed Statement 1; the subcommittee is chosen from the board. Since the subcommittee is at most half of the board, if the subcommittee has 6 members, the board has at least 12 members.

But this question honestly makes no sense at all, and I'd suggest test takers simply ignore it. There's only one reasonable way to interpret the meaning of the question, and under that interpretation, the answer is D. When the question asks (rephrasing it more succinctly) "Are there more than 900 subcommittees the board could choose?" then there's no reason to care what size subcommittee the board actually chooses. We care how many options they had to begin with: how many options they had under the restriction in the stem, which tells us the subcommittee is no more than half the size of the board. So Statement 2 tells us the board has 12 members, which means they had 12C6 + 12C5 + 12C4 + 12C3 + 12C2 + 12C1 options for their subcommittee. Statement 1 tells us the board has at least 12 members (since the subcommittee is no more than half of the board), and they had at least 12C6 + 12C5 + 12C4 + 12C3 + 12C2 + 12C1 options. In both cases they had more than 900 options.

If the "OA" here is A, the question means something else. something completely bizarre. The question writer means to ask "once the board decides the exact size of the subcommittee, are there more than 900 combinations?" But the question doesn't say that. It only asks if the board had more than 900 options, and the only restriction we know of on how many options they have is the "no more than half" restriction from their bylaws. So the source has interpreted its own question incorrectly, and their OA is wrong. Technically, if their interpretation were valid (and it definitely is not), the answer to this question would be E, because you wouldn't know if there were some other unmentioned restrictions, in addition to the size of the subcommittee, that further constrained the number of options the board had. Maybe this board also decided only to appoint junior members to the subcommittee, say, and didn't have many options at all. No question would be fair if there could be unstated restrictions like that -- the stem alone needs to tell you how you're counting what you're asked to count.

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