CAT 2018 Slot 1 — DILR Question 5
Answer the following question based on the information given below.
Twenty four people are part of three committees which are to look at research, teaching, and administration respectively. No two committees have any member in common. No two committees are of the same size. Each committee has three types of people: bureaucrats, educationalists, and politicians, with at least one from each of the three types in each committee. The following facts are also known about the committees:
- The numbers of bureaucrats in the research and teaching committees are equal, while the number of bureaucrats in the research committee is 75% of the number of bureaucrats in the administration committee.
- The number of educationalists in the teaching committee is less than the number of educationalists in the research committee. The number of educationalists in the research committee is the average of the numbers of educationalists in the other two committees.
- 60% of the politicians are in the administration committee, and 20% are in the teachingcommittee.
Based on the given information, which of the following statements MUST be FALSE?
Answer & solution
- A
The size of the research committee is less than the size of the administration committee
- B
In the teaching committee the number of educationalists is equal to the number of politicians
The size of the research committee is less than the size of the teaching committee
- D
In the administration committee the number of bureaucrats is equal to the number of educationalists
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).