CAT 2025 Question Paper | DILR Slot 2

CAT Questions

CAT 2025 DILR was similar to CAT 2022 in pattern. All the four sets had 5 questions this year too. There were 6 TITA Questions. Atleast two sets were doable in each slot and one of the four sets was extremely tough. Choice of Sets became a crucial factor. Overall this section was at a medium to high level of difficulty.

The following charts depict details of research papers written by four authors, Arman, Brajen, Chintan, and Devon. The papers were of four types, single-author, two-author, three-author, and four-author, that is, written by one, two, three, or all four of these authors, respectively. No other authors were involved in writing these papers.



The following additional facts are known.
1. Each of the authors wrote at least one of each of the four types of papers.
2. The four authors wrote different numbers of single-author papers.
3. Both Chintan and Devon wrote more three-author papers than Brajen.
4. The number of single-author and two-author papers written by Brajen were the same.

Question 20 : Which of the following statements is/are NECESSARILY true?

i. Chintan wrote exactly three two-author papers.
ii. Chintan wrote more single-author papers than Devon.

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Video Explanation

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Explanatory Answer

Let's maintain a grid such that a cell in it specifies the number of papers that a author contributed to.
All authors need to contribute to 4-author papers, so all 4 authors contribute in writing the two 4-author papers.

Aman only has 5 contributions and since he has to contribute atleast paper of each type, Aman contributes in exactly one 1-author, one 2-author and one 3-author papers.

The total contributions in 3-author papers is 9, One of these 9 contributions is from Aman. That is Amamn participates in only one paper. So Brajen, Chintan and Devon must write the other two 3-author papers. Since Chintan and Devon contribute more to 3-author papers than Brajen, in the 3-author paper that Aman contributes to, the co-authors must be Chintan and Devon.

So the scenario with 3-author papers is:
Paper 1: Aman, Chintan and Devon
Paper 2 & 3: Brajen, Chintan and Devon

	1-author	2-author	3-author	4-author	Total
Aman	1	1	1	2	5
Brajen			2	2	8
Chintan			3	2	12
Devon			3	2	10
Total contributors	10 (10 × 1)	8 (4 × 2)	9 (3 × 3)	8 (2 × 4)	35

There are 10 1-author papers. Each author writes a different number of non-zero 1-author papers.
1 + 2 + 3 + 4 = 10
Since Brajen writes the same number of 1-author and 2-author papers, he has to write two each.
Chintan can write 3 or 4 1-author papers.
This pretty much fixes the grid in two possibilities as below:

	1-author	2-author	3-author	4-author	Total
Aman	1	1	1	2	5
Brajen	2	2	2	2	8
Chintan	3 / 4	4 / 3	3	2	12
Devon	4 / 3	1 / 2	3	2	10
Total contributors	10 (10 × 1)	8 (4 × 2)	9 (3 × 3)	8 (2 × 4)	35

Let's analyse if both the cases are legal:
Amamn, Brajen, Chintan and Devon write, 1,2,4,1 2-author papers respectively:
This is legal. Chintan could be the co-author in all the 4 papers.

Amamn, Brajen, Chintan and Devon write, 1,2,3,2 2-author papers respectively:
This is legal. Chintan could be the co-author once with the other three. The fourth paper could be between Brajen and Devon.

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The question is " Which of the following statements is/are NECESSARILY true?

i. Chintan wrote exactly three two-author papers.
\nii. Chintan wrote more single-author papers than Devon. "

Hence, the answer is 'Neither i nor ii'

Choice 1 is the correct answer.

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