CAT 2023 Slot 1 DILR Set 1 Q1–Q5

A DILR caselet from the Data Interpretation & Logical Reasoning (DILR) section of CAT 2023 Slot 1, with 5 questions (Selection & Distribution). Answers are CAT's official key.

The set

Faculty members in a management school can belong to one of four departments – Finance and Accounting (F&A), Marketing and Strategy (M&S), Operations and Quants (O&Q) and Behaviour and Human Resources (B&H). The numbers of faculty members in F&A, M&S, O&Q and B&H departments are 9, 7, 5 and 3 respectively.

Prof. Pakrasi, Prof. Qureshi, Prof. Ramaswamy and Prof. Samuel are four members of the school's faculty who were candidates for the post of the Dean of the school. Only one of the candidates was from O&Q.

Every faculty member, including the four candidates, voted for the post. In each department, all the faculty members who were not candidates voted for the same candidate. The rules for the election are listed below.

1. There cannot be more than two candidates from a single department.
2. A candidate cannot vote for himself/herself.
3. Faculty members cannot vote for a candidate from their own department.

After the election, it was observed that Prof. Pakrasi received 3 votes, Prof. Qureshi received 14 votes, Prof. Ramaswamy received 6 votes and Prof. Samuel received 1 vote. Prof. Pakrasi voted for Prof. Ramaswamy, Prof. Qureshi for Prof. Samuel, Prof. Ramaswamy for Prof. Qureshi and Prof. Samuel for Prof. Pakrasi.

Question 1

Which two candidates can belong to the same department?
  1. A
    Prof. Pakrasi and Prof. Samuel
  2. B
    Prof. Pakrasi and Prof. Qureshi
  3. C
    Prof. Qureshi and Prof. Ramaswamy
  4. D
    Prof. Ramaswamy and Prof. Samuel

Answer: (B) Prof. Pakrasi and Prof. Qureshi Selection & Distribution MCQ

Solution

  1. Candidate votes: S's only vote comes from Q, so non-candidate blocks give P 2, R 5 and Q 13 votes (total 20 non-candidates). A block of exactly 2 can only be B&H with one candidate, so P gets B&H's block; R's 5 must be M&S with two candidates (then F&A has none), and Q gets F&A's 9 plus O&Q's 4.
  2. So R is not in M&S, Q is not in O&Q or F&A, P is not in B&H. Mutual votes forbid P-R, Q-S, R-Q, S-P sharing a department, so the M&S pair must be P and Q; R and S split O&Q and B&H.
  3. The two candidates from the same department are Prof. Pakrasi and Prof. Qureshi (M&S).

Question 2

Which of the following can be the number of votes that Prof. Qureshi received from a single department?
  1. A
    8
  2. B
    7
  3. C
    9
  4. D
    6

Answer: (C) 9 Selection & Distribution MCQ

Solution

  1. Candidate votes: S's only vote comes from Q, so non-candidate blocks give P 2, R 5 and Q 13 votes (total 20 non-candidates). A block of exactly 2 can only be B&H with one candidate, so P gets B&H's block; R's 5 must be M&S with two candidates (then F&A has none), and Q gets F&A's 9 plus O&Q's 4.
  2. Q's 14 votes are F&A's 9 non-candidates, O&Q's 4 non-candidates and R's own vote.
  3. So from a single department Q can receive 9 (F&A), option C.

Question 3

If Prof. Samuel belongs to B&H, which of the following statements is/are true?

Statement A: Prof. Pakrasi belongs to M&S.
Statement B: Prof. Ramaswamy belongs to O&Q.
  1. A
    Both statements A and B
  2. B
    Only statement B
  3. C
    Only statement A
  4. D
    Neither statement A nor statement B

Answer: (A) Both statements A and B Selection & Distribution MCQ

Solution

  1. Candidate votes: S's only vote comes from Q, so non-candidate blocks give P 2, R 5 and Q 13 votes (total 20 non-candidates). A block of exactly 2 can only be B&H with one candidate, so P gets B&H's block; R's 5 must be M&S with two candidates (then F&A has none), and Q gets F&A's 9 plus O&Q's 4.
  2. So R is not in M&S, Q is not in O&Q or F&A, P is not in B&H. Mutual votes forbid P-R, Q-S, R-Q, S-P sharing a department, so the M&S pair must be P and Q; R and S split O&Q and B&H.
  3. If S is in B&H, R must be the O&Q candidate (B true), and P is always in M&S (A true). Both statements hold.

Question 4

What best can be concluded about the candidate from O&Q?
  1. A
    It was either Prof. Pakrasi or Prof. Qureshi.
  2. B
    It was Prof. Samuel.
  3. C
    It was Prof. Ramaswamy.
  4. D
    It was either Prof. Ramaswamy or Prof. Samuel.

Answer: (D) It was either Prof. Ramaswamy or Prof. Samuel. Selection & Distribution MCQ

Solution

  1. Candidate votes: S's only vote comes from Q, so non-candidate blocks give P 2, R 5 and Q 13 votes (total 20 non-candidates). A block of exactly 2 can only be B&H with one candidate, so P gets B&H's block; R's 5 must be M&S with two candidates (then F&A has none), and Q gets F&A's 9 plus O&Q's 4.
  2. So R is not in M&S, Q is not in O&Q or F&A, P is not in B&H. Mutual votes forbid P-R, Q-S, R-Q, S-P sharing a department, so the M&S pair must be P and Q; R and S split O&Q and B&H.
  3. P and Q are in M&S, so the O&Q candidate is either Ramaswamy or Samuel.

Question 5

Which of the following statements is/are true?

Statement A: Non-candidates from M&S voted for Prof. Qureshi.
Statement B: Non-candidates from F&A voted for Prof. Qureshi.
  1. A
    Only statement B
  2. B
    Only statement A
  3. C
    Both statements A and B
  4. D
    Neither statement A nor statement B

Answer: (A) Only statement B Selection & Distribution MCQ

Solution

  1. Candidate votes: S's only vote comes from Q, so non-candidate blocks give P 2, R 5 and Q 13 votes (total 20 non-candidates). A block of exactly 2 can only be B&H with one candidate, so P gets B&H's block; R's 5 must be M&S with two candidates (then F&A has none), and Q gets F&A's 9 plus O&Q's 4.
  2. M&S non-candidates (5) voted for Ramaswamy, F&A non-candidates (9) for Qureshi.
  3. Only statement B is true.

Same concept in other years

See every question on Election vote counts: deduce votes/shares of candidates.

More Selection & Distribution questions from CAT

All 41 Selection & Distribution questions asked since 2017.