CAT 2018 Question Paper | CAT LR DI

Here's a wonderful puzzle set from the 2018 CAT exam that might seem like a classic three-circle diagram from set theory, because of the words. But, you are warned with the word 'no intersection.' Such question sets require a lot of practice because the conditions and constraints seem to be confusing at the first glance. The set presents several malicious traps like this and you are required to prudently overcome them. Solve this DILR problem from CAT previous year paper and flex your skills during your CAT Preparation.

CAT DILR : CAT 2018 Question Paper Slot 1

Set 8 : Committees

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

1. In the administration committee the number of bureaucrats is equal to the number of educationalists
2. The size of the research committee is less than the size of the teaching committee
3. The size of the research committee is less than the size of the administration committee
4. In the teaching committee the number of educationalists is equal to the number of politicians

Video Explanation

Explanatory Answer

Method of solving this CAT Question on CAT DILR

The number of bureaucrats in the research committee is 75% of the number of bureaucrats in the administration committee i.e.
The ratio of number of bureaucrats in Research to Admin is 3 : 4.
Number of bureaucrats in Research and Teaching are equal. So, Research : Teaching : Admin = 3 : 3 : 4.

The number of politicians in research, teaching and Admin are 20%, 20% and 60% or, the ratio should of number of politicians is 1 : 1 : 3.

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.
If number of educationalists in teaching = a, and in Admin = b, then Research = $\frac{a + b}{2}$. a < b.

Now, we know that Number of Educationalists doing research is the average of Educationalists in Teaching and Admin or, the number of educationalists in Teaching, Research and Admin are in AP or, the sum of the three numbers should be a multiple of 3.
Let us look at the totals.
Number of Bureaucrats is a multiple of 10 – it should be 10 or 20
Number of Educationalists is a multiple of 3 – it should be 3, 6, 9, 12,..
Number of Politicians is a multiple of 5 – it should be 5, 10, 15, 20,..
We have at least one from each of the three types from each of the committees.
So, number of politicians should be at least 5, so the number of bureaucrats should be 10.

Now, 3K + 5y = 14. 5y can be 5 or 10. It cannot be 10 as 3K cannot be 4.
So, we know that 3K should be 9 and 5K should be 5.

Number of Educationalists in Research is the average of the three numbers in educationalists. So, the number of educationalists in Research is 3.
Number of educationalists in Teaching and Admin are either 2, 4 or 1, 5.

With this, we are done with the whole grid. Now, let us move to the questions.
From the table, we can see that Choice B The size of the research committee is less than the size of the teaching committee is false.

The question is "Based on the given information, which of the following statements MUST be FALSE?"

Hence, the answer is The size of the research committee is less than the size of the teaching committee

Choice B is the correct answer.

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