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CAT 2021 Slot 1 DILR · Set 3 of 4Logical ReasoningModerate DifficultyQ9–Q14 · 5 MCQ + 1 TITA

CAT 2021 Slot 1 DILR Set 3: Arrangements (6 Questions) with Solutions

The Arrangements set from the official CAT 2021 Slot 1 DILR paper: the caselet, all 6 questions, the official answer key and a step-by-step solution for each. 100% free, no sign-up.

The Set: Read the Caselet First

CAT 2021 Slot 1 DILR · Questions 9–14
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 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.
F, an Indian author from the Logistics area, wrote only one paper. It was scheduled in the October issue.
A was from the Automation area and did not have a paper scheduled in the October issue.
None of the Indian authors were from the Manufacturing area and none of the Japanese or Chinese authors were from the Automation area.
A and H were from different countries, but had their papers scheduled in exactly the same issues.
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.
B, from the Logistics area, had a paper scheduled in the April issue of the journal.
B and G belonged to the same country. None of their papers were scheduled in the same issue of the journal.
D, a Japanese author from the Manufacturing area, did not have a paper scheduled in the July issue.
C and H belonged to different areas.

In the exam this set competed with 3 others for 40 minutes. Budget about 10 minutes if you attempt it.

Q9. Arrangements

MCQ · +3 / −1
What is the correct sequence of number of papers written by B, C, E and G, respectively?
  1. A) 3, 1, 1, 3
  2. B) 1, 3, 3, 1
  3. C) 1, 2, 2, 3
  4. D) 1, 2, 2, 1
Correct Answer
C) 1, 2, 2, 3
Step-by-step solution
📌 Core Concept
Use the totals first: the paper counts alone fix B, C, E and G.
🔢 Step-by-Step Solution
1
There are 18 papers and each author wrote 1 to 3. A, D, G, H together wrote double the other four (B, C, E, F). So A+D+G+H=12A+D+G+H=12 and B+C+E+F=6B+C+E+F=6.
2
A, D, G and H each wrote at most 3, so each of them wrote exactly 3.
3
F wrote exactly 1 paper, so B+C+E=5B+C+E=5.
4
C and E wrote the same number, so B+2C=5B+2C=5. Either C=1,B=3C=1, B=3 or C=2,B=1C=2, B=1.
5
E has papers in consecutive issues, so E wrote at least 2. Hence C=E=2C=E=2 and B=1B=1.
6
G is one of A, D, G, H, so G=3G=3.
7
The sequence for B, C, E, G is 1, 2, 2, 3.
Why Not the Others
A: B=3 would force C=E=1, but E needs at least 2 papers.
B: C=E=3 would give B+C+E=7B+C+E=7, not 5.
D: G must be 3, not 1.
Correct Answer: C

Q10. Arrangements

TITA · +3 / 0
How many papers were written by Indian authors?
Correct Answer
8
Step-by-step solution
📌 Core Concept
Work out each author's country from the area and country clues, then add up the Indian authors' papers.
🔢 Step-by-Step Solution
1
The paper counts are A=D=G=H=3A=D=G=H=3, F=1F=1, B=1B=1 and C=E=2C=E=2.
2
The countries are 4 Indian, 2 Japanese and 2 Chinese. F is Indian. D is Japanese. C and E are Chinese. This fills the Chinese quota.
3
A is in Automation. No Japanese or Chinese author is in Automation, so A is Indian.
4
A and H are from different countries, so H is not Indian. Chinese is full, so H is Japanese. This fills the Japanese quota.
5
The remaining authors B and G must be Indian, which also agrees with B and G sharing a country. The Indian authors are A, F, B and G.
6
Indian papers are 3+1+1+3=83+1+1+3=8.
Quick Check
Japan (H, D) has 6 papers, China (C, E) has 4, India has 8, and 8+6+4=188+6+4=18.
Correct Answer: 8

Q11. Arrangements

MCQ · +3 / −1
Which of the following statement(s) MUST be true?
Statement A: Every issue had at least one paper by author(s) from each country. Statement B: Every issue had at most two papers by author(s) from each area.
  1. A) Both the statements
  2. B) Neither of the statements
  3. C) Only Statement A
  4. D) Only Statement B
Correct Answer
C) Only Statement A
Step-by-step solution
📌 Core Concept
Fix every author's country and area, then fix the issue schedule. Then check each statement issue by issue.
🔢 Step-by-Step Solution
1
The paper counts are A=D=G=H=3A=D=G=H=3, B=1B=1, C=E=2C=E=2, F=1F=1. The countries are India (A, B, F, G), Japan (D, H) and China (C, E).
2
D is in Manufacturing. C and E are in different areas, and neither is in Automation, so one of them is in Manufacturing. That fills Manufacturing (D plus one of C, E). So H is in Logistics. C and H differ in area, so C is in Manufacturing and E is in Logistics. The Logistics authors are F, B, E and H. A and G are in Automation.
3
A and H share their issues and skip October, so they are in Jan, Apr and Jul. D skips July, so D is in Jan, Apr and Oct. B is in April, so G (who never shares an issue with B) is in Jan, Jul and Oct. F is in October.
4
The remaining slots are one each in Jan, Apr, Jul and Oct. E needs consecutive issues and C does not. That gives E in Apr and Jul, and C in Jan and Oct.
5
The issues are Jan: A, H, D, G, C. Apr: A, H, D, B, E. Jul: A, H, G, E. Oct: D, G, F, C.
6
Statement A: every issue has an Indian, a Japanese (H or D) and a Chinese (C or E) paper. This is true.
7
Statement B: April has H, B and E, which makes 3 Logistics papers. This is false.
Why Not the Others
Statement B fails because April has three Logistics papers, so options A and D are out. Statement A holds, so option B is out.
Correct Answer: C

Q12. Arrangements

MCQ · +3 / −1
Which of the following statements is FALSE?
  1. A) Every issue had exactly two papers by authors from Logistics area.
  2. B) Every issue had at least one paper by author(s) from Automation area.
  3. C) Every issue had exactly two papers by Indian authors
  4. D) Every issue had exactly one paper by a Chinese author
Correct Answer
A) Every issue had exactly two papers by authors from Logistics area.
Step-by-step solution
📌 Core Concept
Build the full schedule, then test each statement against the four issues.
🔢 Step-by-Step Solution
1
The paper counts are A=D=G=H=3A=D=G=H=3, B=1B=1, C=E=2C=E=2, F=1F=1. The countries are India (A, B, F, G), Japan (D, H) and China (C, E).
2
The areas are Automation (A, G), Manufacturing (D, C) and Logistics (F, B, E, H). This follows because D is in Manufacturing, C and E are in different areas, and H and C are in different areas.
3
A and H share their issues and skip October, so they are in Jan, Apr and Jul. D skips July, so D is in Jan, Apr and Oct. B is in April, so G is in Jan, Jul and Oct. F is in October. E is in Apr and Jul, and C is in Jan and Oct, because E must be in consecutive issues and C must not.
4
The issues are Jan: A, H, D, G, C. Apr: A, H, D, B, E. Jul: A, H, G, E. Oct: D, G, F, C.
5
Logistics papers per issue are 1 (H), 3 (H, B, E), 2 (H, E) and 1 (F). They are not exactly two in every issue, so option A is false.
Why Not the Others
B: every issue has A or G, so Automation always appears. True.
C: Indian papers are A and G in Jan, A and B in Apr, A and G in Jul, and G and F in Oct. Two in each issue. True.
D: the Chinese papers are C in Jan, E in Apr, E in Jul and C in Oct. One in each issue. True.
Correct Answer: A

Q13. Arrangements

MCQ · +3 / −1
Which of the following statements is FALSE?
  1. A) There were exactly two papers by authors from Manufacturing area in the January issue.
  2. B) There were exactly two papers by authors from Manufacturing area in the July issue.
  3. C) There was exactly one paper by an author from Logistics area in the October issue.
  4. D) There was exactly one paper by an author from Manufacturing area in the April issue
Correct Answer
B) There were exactly two papers by authors from Manufacturing area in the July issue.
Step-by-step solution
📌 Core Concept
Reconstruct the schedule, then count Manufacturing (D and C) and Logistics (F, B, E, H) papers per issue.
🔢 Step-by-Step Solution
1
The paper counts are A=D=G=H=3A=D=G=H=3, B=1B=1, C=E=2C=E=2, F=1F=1.
2
The areas are Automation (A, G), Manufacturing (D, C) and Logistics (F, B, E, H).
3
A and H share their issues and skip October, so they are in Jan, Apr and Jul. D skips July, so D is in Jan, Apr and Oct. B is in April, so G is in Jan, Jul and Oct. F is in October. The consecutive-issue rule puts E in Apr and Jul, and C in Jan and Oct.
4
The issues are Jan: A, H, D, G, C. Apr: A, H, D, B, E. Jul: A, H, G, E. Oct: D, G, F, C.
5
Manufacturing papers are D and C in Jan (2), D in Apr (1), none in Jul (0), and D and C in Oct (2).
6
July has no Manufacturing paper, so the statement that it has exactly two is false.
Why Not the Others
A: January has D and C. True.
C: October's only Logistics paper is F. True.
D: April's only Manufacturing paper is D. True.
Correct Answer: B

Q14. Arrangements

MCQ · +3 / −1
Which of the following is the correct sequence of number of papers by authors from Automation, Manufacturing and Logistics areas, respectively?
  1. A) 6, 5, 7
  2. B) 6, 6, 6
  3. C) 6, 7, 5
  4. D) 5, 6, 7
Correct Answer
A) 6, 5, 7
Step-by-step solution
📌 Core Concept
Assign each author to an area, then add up the paper counts for each area.
🔢 Step-by-Step Solution
1
The paper counts are A=D=G=H=3A=D=G=H=3, B=1B=1, C=E=2C=E=2, F=1F=1. These come from A+D+G+H=12A+D+G+H=12, B+C+E+F=6B+C+E+F=6, F=1F=1 and E being in at least 2 issues.
2
A is in Automation, and so is another Indian author. No Japanese or Chinese author is in Automation. A is Indian, H is Japanese (A and H differ in country), so B and G are Indian.
3
D is in Manufacturing. C and E are in different areas and not in Automation, so one of them is in Manufacturing. That fills Manufacturing (D plus one of C, E). So H is in Logistics. C and H differ in area, so C is in Manufacturing and E is in Logistics.
4
Logistics is then F, B, E and H, which is the required four. Automation is A and G.
5
Automation papers: 3+3=63+3=6.
6
Manufacturing papers (D, C): 3+2=53+2=5.
7
Logistics papers (F, B, E, H): 1+1+2+3=71+1+2+3=7.
8
The sequence is 6, 5, 7.
Quick Check
6+5+7=186+5+7=18.
Correct Answer: A
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CAT 2021 Slot 1 DILR at a Glance

Sets in this section4
Questions in this section20
Section time40 minutes
Convenor IIMIIM Ahmedabad

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