CAT 2025 Slot 2 · DILR · Question 7
CAT 2025 Slot 2 previous year question on Reasoning Based DI, with the answer and a step-by-step solution.
Set 2: Research Papers by Four Authors — this question belongs to a set. Read the full set with all 4 questions →
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.
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.
- A
Neither i nor ii
- B
Only i
- C
Only ii
- D
Both i and ii
Answer & solution
Answer: Option A
Known so far: Arman (single, two, three, four) = (1, 1, 1, 2); Brajen = (2, 2, 2, 2); Chintan and Devon each have 3 three-author and 2 four-author papers.
Single-author papers: 10 in total, split into four different positive numbers (fact 2). The only such split is 1 + 2 + 3 + 4. Arman has 1 and Brajen 2, so Chintan and Devon have 3 and 4 in some order.
Two-author papers: 4 papers give 8 author slots. Arman and Brajen take 1 + 2 = 3, so Chintan + Devon = 5.
Chintan: 12 − 3 − 2 = 7 single + two-author papers. Devon: 10 − 3 − 2 = 5.
Case 1: Chintan has 3 single and 4 two-author; Devon has 4 single and 1 two-author.
Case 2: Chintan has 4 single and 3 two-author; Devon has 3 single and 2 two-author.
Both cases can be realised (e.g. Case 1: pairs A–C, B–C, B–C, C–D; Case 2: pairs A–C, B–C, C–D, B–D).
Statement i holds only in Case 2, and statement ii holds only in Case 2. Neither is forced.
Shortcut: Chintan's single + two-author total is fixed at 7, but his single-author count can be 3 or 4, so no statement about either count is necessarily true.
Hence, the answer is option 1.
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