Discussion

Explanation:

As each committee has at least one bureaucrat, one educationalist and one politician, the members of each type must be in the range [3, 18].

From (1), ratio of the number of bureaucrats in the research, teaching and administration committees = 3 : 3 : 4

Therefore, the number of bureaucrats = 10

From (2), If there are x educationists in the research committee, there must be (3x) educationists in all.

From (3), ratio of the number of politicians in the research, teaching and administration committees = 1 : 1 : 3

Therefore, there can be 5 or 10 politicians. If there are 10 politicians, number of educationists = 4, which is not a multiple of 3.

Therefore there are 5 politicians and 9 educationists.

Thus, we have

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[1]: The administration committee has 11 or 12 members. Research committee has 7 members which is definitely less than the members of administration committee. Therefore, this statement is true.
[2]: The teaching committee has 1 or 2 educationists and 1 politician. Therefore, this statement can be true.
[3]: The teaching committee has 5 or 6 members. The research committee has 7 members which is definitely more than members of the teaching committee. Therefore, this statement is definitely false.
[4]: The administration committee has 4 bureaucrats and either 4 or 5 educationists. Therefore, this statement can be true.

Hence, option (c).

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