CAT 2021 Slot 1 · DILR · Question 4
CAT 2021 Slot 1 previous year question on Caselet DI, with the answer and a step-by-step solution.
Set 1: Research Papers in a Journal — this question belongs to a set. Read the full set with all 6 questions →
A journal plans to publish 18 research papers, written by eight authors (A, B, C, D, E, F, G, and H) in four issues of the journal scheduled in January, April, July and October. Each of the research papers was written by exactly one of the eight authors. Five papers were scheduled in each of the first two issues, while four were scheduled in each of the last two issues. Every author wrote at least one paper and at most three papers. The total number of papers written by A, D, G and H was double the total number of papers written by the other four authors. Four of the authors were from India and two each were from Japan and China. Each author belonged to exactly one of the three areas — Manufacturing, Automation, and Logistics. Four of the authors were from the Logistics area and two were from the Automation area. As per the journal policy, none of the authors could have more than one paper in any issue of the journal.
The following facts are also known.
1. F, an Indian author from the Logistics area, wrote only one paper. It was scheduled in the October issue.
2. A was from the Automation area and did not have a paper scheduled in the October issue.
3. None of the Indian authors were from the Manufacturing area and none of the Japanese or Chinese authors were from the Automation area.
4. A and H were from different countries, but had their papers scheduled in exactly the same issues.
5. C and E, both Chinese authors from different areas, had the same number of papers scheduled. Further, E had papers scheduled in consecutive issues of the journal but C did not.
6. B, from the Logistics area, had a paper scheduled in the April issue of the journal.
7. B and G belonged to the same country. None of their papers were scheduled in the same issue of the journal.
8. D, a Japanese author from the Manufacturing area, did not have a paper scheduled in the July issue.
9. C and H belonged to different areas.
- AEvery issue had at least one paper by author(s) from Automation area.
- BEvery issue had exactly one paper by a Chinese author.
- CEvery issue had exactly two papers by authors from Logistics area.
- DEvery issue had exactly two papers by Indian authors.
Answer & solution
Answer: Option C
Solving the set
Step 1 – Number of papers. A + D + G + H = 2 × (B + C + E + F) and the total is 18 ⇒ A + D + G + H = 12. Nobody writes more than 3, so A, D, G and H write 3 each. B + C + E + F = 6 with F = 1 (fact 1) and C = E (fact 5). E has papers in consecutive issues, so E ≥ 2 ⇒ C = E = 2, B = 1.
Step 2 – Countries. A is from Automation, so A is Indian (no Japanese/Chinese author is in Automation). A and H are from different countries; China has only C and E (fact 5), so H is Japanese. Japan = D, H; China = C, E; India = A, B, F, G (B and G share a country).
Step 3 – Areas. Automation has 2 authors, both Indian: A and one of B, F, G. B and F are Logistics, so G is Automation. Manufacturing has 2 authors: D and one of C, E, H. C and E are in different areas, and C and H are in different areas. If H were Manufacturing, C would be Logistics and E Manufacturing – three Manufacturing authors. So H is Logistics, C is Manufacturing, E is Logistics. Logistics = B, E, F, H (4 ✓).
Step 4 – Issues. A (no October) is in January, April, July; H in the same issues. D (no July) is in January, April, October. F is in October; B in April. G cannot share an issue with B, so G is in January, July, October.
Step 5 – Papers per issue so far: January 4 (A, H, D, G), April 4 (A, H, D, B), July 3 (A, H, G), October 3 (D, F, G). C and E must add one paper to each issue. E's two issues are consecutive and C's are not: E = April, July and C = January, October (the only split that works).
Author | Papers | Issues | Country | Area |
A | 3 | Jan, Apr, Jul | India | Automation |
B | 1 | Apr | India | Logistics |
C | 2 | Jan, Oct | China | Manufacturing |
D | 3 | Jan, Apr, Oct | Japan | Manufacturing |
E | 2 | Apr, Jul | China | Logistics |
F | 1 | Oct | India | Logistics |
G | 3 | Jan, Jul, Oct | India | Automation |
H | 3 | Jan, Apr, Jul | Japan | Logistics |
Issue | Authors | Papers | India | Japan | China | Automation | Manufacturing | Logistics |
January | A, C, D, G, H | 5 | A, G | D, H | C | A, G | C, D | H |
April | A, B, D, E, H | 5 | A, B | D, H | E | A | D | B, E, H |
July | A, E, G, H | 4 | A, G | H | E | A, G | — | E, H |
October | C, D, F, G | 4 | F, G | D | C | G | C, D | F |
This question
Check each option against the issue table: Automation appears in every issue (true); one Chinese paper per issue (true); Logistics papers per issue are 1, 3, 2, 1 – not always two (false); Indian papers per issue are 2, 2, 2, 2 (true).
Hence, the answer is option 3.
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