**Monkton University has established a board which reviews all applications for experiments to be conducted by students or faculty. Researchers submit proposals to one or more committees, each of which is responsible for certain kinds of research subjects, and the committees' task is to ensure that the proposed research both complies with all laws and meets the university's standards for ethical experimentation. A proposal must gain approval from all committees for which the research parameters apply.**

Board members must sit on a minimum of one committee and a maximum of three; each committee must have a minimum of 4 members. Committees 1 and 2 must reach a unanimous vote in order to approve a proposal. Committees 3 and 4 may approve a proposal with no more than one "no" vote. Committees 5 and 6 must have an odd number of members; a simple majority is sufficient to approve a proposal.

What is the minimum number of board members necessary in order to staff all six committees according to the given rules?

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Board members must sit on a minimum of one committee and a maximum of three; each committee must have a minimum of 4 members. Committees 1 and 2 must reach a unanimous vote in order to approve a proposal. Committees 3 and 4 may approve a proposal with no more than one "no" vote. Committees 5 and 6 must have an odd number of members; a simple majority is sufficient to approve a proposal.

What is the minimum number of board members necessary in order to staff all six committees according to the given rules?

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This is an IR question from MGMAT test. Could someone help to explain a bit the solution from MGMAT?

*To compute the minimum number of board members, we must determine how many people we need to staff each of the 6 committees at the minimum level. The second paragraph tells us that each committee must have a minimum of 4 members; there are 6 committees, so it is tempting to say that we must need a minimum of 24 board members. Each board member, however, is allowed to sit on up to 3 committees. In addition, committees 5 and 6 must have an odd number of members - and 4 is not an odd number. Therefore, committees 5 and 6 must actaully have a minimum of 5 members.*

The minimum number of committee members needed is then 4 + 4 + 4 + 4 + 5 + 5 = 26 members.

Remember also that each committee member is allowed to sit on 3 committees. 26/3 = 8 2/3, which means that we need at least 9 people to staff the 6 committees.

The minimum number of committee members needed is then 4 + 4 + 4 + 4 + 5 + 5 = 26 members.

Remember also that each committee member is allowed to sit on 3 committees. 26/3 = 8 2/3, which means that we need at least 9 people to staff the 6 committees.

**The correct answer is C.**According to the given solution, we just have to calculate the minimum number of committee members needed, and then divide it by 3. Is this approach applicable for all cases or just for the case in question (which requires a minimum of 4 members for each committee)? I mean, let's say in the extreme case, if we adjust the number of members for each commmittee (each of the first 5 committees has 1 member, the 6th committee has 21 members) such that the total number remains the same (= 26 members), then the answer could not be just 26/3 = 8 2/3, right? I don't quite understand the logic of the solution, why it could be so and when it is applicable, I do think that I am not confident to use it if I have to face it in the real test

Thanks for your help