ShreyasJavahar wrote:
Hello
IanStewart, could you please weigh in on this?
1)Subcommittee has 6 members, so it can have a maximum of 3 board members.
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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