CAT 2021 Slot 1 · DILR · Set 1: Research Papers in a Journal

The full set and all 6 questions (Q1–Q6) from CAT 2021 Slot 1, with answers and solutions.

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.

Question 1 · Caselet DI

What is the correct sequence of number of papers written by B, C, E and G, respectively?
  1. A
    1, 2, 2, 3
  2. B
    1, 3, 3, 1
  3. C
    3, 1, 1, 3
  4. D
    1, 2, 2, 1
Pick an option, then check.
Answer & solution

Answer: Option A

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

From Step 1, B, C, E and G wrote 1, 2, 2 and 3 papers.

Hence, the answer is option 1.

Question 2 · Caselet DI

How many papers were written by Indian authors?
Answer & solution

Answer: 8

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

Indian authors A, B, F, G wrote 3 + 1 + 1 + 3 = 8 papers.

Hence, the answer is 8.

Question 3 · Caselet DI

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
    Only Statement B
  3. C
    Only Statement A
  4. D
    Neither of the statements
Pick an option, then check.
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

From the issue table, every issue has at least one author from India, Japan and China – Statement A is true. April has three Logistics papers (B, E, H) – Statement B is false.

Hence, the answer is option 3.

Question 4 · Caselet DI

Which of the following statements is FALSE?
  1. A
    Every issue had at least one paper by author(s) from Automation area.
  2. B
    Every issue had exactly one paper by a Chinese author.
  3. C
    Every issue had exactly two papers by authors from Logistics area.
  4. D
    Every issue had exactly two papers by Indian authors.
Pick an option, then check.
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.

Question 5 · Caselet DI

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 was exactly one paper by an author from Manufacturing area in the April issue.
  3. C
    There was exactly one paper by an author from Logistics area in the October issue.
  4. D
    There were exactly two papers by authors from Manufacturing area in the July issue.
Pick an option, then check.
Answer & solution

Answer: Option D

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

Manufacturing papers per issue: January 2 (C, D), April 1 (D), July 0, October 2 (C, D). Logistics in October: 1 (F). So 'exactly two Manufacturing papers in July' is false.

Hence, the answer is option 4.

Question 6 · Caselet DI

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
Pick an option, then check.
Answer & solution

Answer: Option A

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

Automation (A, G) = 6; Manufacturing (C, D) = 5; Logistics (B, E, F, H) = 7.

Hence, the answer is option 1.

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