Faculty Dean Election
CAT 2023 Slot 1 · DILR · Hard · Logical Reasoning
Passage / data 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.
- There cannot be more than two candidates from a single department.
- A candidate cannot vote for himself/herself.
- 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 of 5
Which two candidates can belong to the same department?
- A.
Prof. Pakrasi and Prof. Samuel
- B.
Prof. Pakrasi and Prof. Qureshi
- C.
Prof. Qureshi and Prof. Ramaswamy
- D.
Prof. Ramaswamy and Prof. Samuel
B
Explanation
By analyzing the distribution of votes across departments and applying the constraints (candidates cannot receive votes from non-candidates of their own department), we find that Prof. Pakrasi and Prof. Qureshi can belong to the same department (F&A).
Question 2 of 5
Which of the following can be the number of votes that Prof. Qureshi received from a single department?
- A.
8
- B.
7
- C.
9
- D.
6
C
Explanation
Prof. Qureshi received 14 votes in total (1 candidate vote from Prof. Ramaswamy + 13 non-candidate votes). The 13 non-candidate votes must come from departments where Qureshi is not a candidate. Since F&A has 9 faculty members and 0 candidates in this case, F&A non-candidates can contribute 9 votes to Prof. Qureshi.
Question 3 of 5
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.
- A.
Both statements A and B
- B.
Only statement B
- C.
Only statement A
- D.
Neither statement A nor statement B
C
Explanation
If Prof. Samuel belongs to B&H, analyzing the remaining department allocations under the voting rules forces Prof. Pakrasi to belong to M&S. However, Prof. Ramaswamy does not necessarily belong to O&Q. Thus, only statement A is true.
Question 4 of 5
What best can be concluded about the candidate from O&Q?
- A.
It was either Prof. Pakrasi or Prof. Qureshi.
- B.
It was Prof. Samuel.
- C.
It was Prof. Ramaswamy.
- D.
It was either Prof. Ramaswamy or Prof. Samuel.
D
Explanation
From the vote counts and constraint mapping, neither Prof. Pakrasi nor Prof. Qureshi can be from O&Q. Thus, the candidate from O&Q must be either Prof. Ramaswamy or Prof. Samuel.
Question 5 of 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.
- A.
Only statement B
- B.
Only statement A
- C.
Both statements A and B
- D.
Neither statement A nor statement B
A
Explanation
Deduction shows that non-candidates from F&A definitely voted for Prof. Qureshi (contributing 9 votes), whereas non-candidates from M&S did not vote for Prof. Qureshi. Hence, only statement B is true.
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