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:
Q.1: Based on the given information, which of the following statements MUST be FALSE?
Q.2: What is the number of bureaucrats in the administration committee?
Q.3: What is the number of educationalists in the research committee?
Q.4: Which of the following CANNOT be determined uniquely based on the given information?
Let the number of bureaucrats in research, training and administration be 3x, 3x and 4x.
As total = 24 and bureaucrats are in the ratio 3 : 3 : 4, only possible value of x = 1.
Also, 60% of the politicians are in the administration committee, and 20% are in the teaching committee. So, politicians are in ratio 1 : 1 : 3. Only value will be 1, 1, 3.
Total educationalists = 24 - 10 - 5 = 9
The number of educationalists in the research committee is the average of the numbers of educationalists in the other two committees. So, two cases are possible: