Three Committees Composition

CAT 2018 Slot 1 · DILR · Medium · Logical Reasoning

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Passage / data set

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:

  1. 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.
  2. 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.
  3. 60% of the politicians are in the administration committee, and 20% are in the teaching committee.

Question 1 of 4

Based on the given information, which of the following statements MUST be FALSE?

  1. A.

    In the administration committee the number of bureaucrats is equal to the number of educationalists

  2. B.

    The size of the research committee is less than the size of the teaching committee

  3. C.

    The size of the research committee is less than the size of the administration committee

  4. D.

    In the teaching committee the number of educationalists is equal to the number of politicians

Answer

B

Explanation

Calculating committee sizes shows Research = 7 or 8, Teaching = 6, Administration = 10 or 11. Research size is strictly greater than Teaching size, so statement B is false.

Question 2 of 4

What is the number of bureaucrats in the administration committee?

Answer

4

Explanation

Since Bureaucrats in Research = 75% of Administration, Administration bureaucrats must be a multiple of 4. Given total = 24, Administration bureaucrats = 4.

Question 3 of 4

What is the number of educationalists in the research committee?

Answer

3

Explanation

Educationalists in Research is the average of the other two committees, evaluating uniquely to 3.

Question 4 of 4

Which of the following CANNOT be determined uniquely based on the given information?

  1. A.

    The total number of educationalists in the three committees

  2. B.

    The total number of bureaucrats in the three committees

  3. C.

    The size of the teaching committee

  4. D.

    The size of the research committee

Answer

D

Explanation

The sizes of Research and Administration can swap between (7, 11) and (8, 10), so the exact size of the research committee cannot be determined uniquely.

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