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.

After the election, it was observed that:

Further, the candidates voted as follows:

Question 1

Which two candidates can belong to the same department?

A. Prof. Pakrasi and Prof. Qureshi
B. Prof. Pakrasi and Prof. Samuel
C. Prof. Qureshi and Prof. Ramaswamy
D. Prof. Ramaswamy and Prof. Samuel

Question 2

Which of the following can be the number of votes that Prof. Qureshi received from a single department?

A. 7
B. 6
C. 8
D. 9

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.

A. Neither statement A nor statement B
B. Only statement B
C. Only statement A
D. Both statements A and B

Question 4

What best can be concluded about the candidate from O&Q?

A. It was Prof. Samuel.
B. It was either Prof. Ramaswamy or Prof. Samuel.
C. It was Prof. Ramaswamy.
D. It was either Prof. Pakrasi or Prof. Qureshi.

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Set 1 (Check the possible combination table below) -After Answer 4

Total faculty = 9 + 7 + 5 + 3 = 24

Votes received:
Pakrasi = 3
Qureshi = 14
Ramaswamy = 6
Samuel = 1

Candidate votes:
Pakrasi → Ramaswamy
Qureshi → Samuel
Ramaswamy → Qureshi
Samuel → Pakrasi

So votes from non-candidates should be:
Pakrasi: 3 - 1 = 2
Qureshi: 14 - 1 = 13
Ramaswamy: 6 - 1 = 5
Samuel: 1 - 1 = 0

Since all non-candidates in a department vote for the same candidate, the department-wise non-candidate vote blocks must be:

F&A = 9
M&S = 5
O&Q = 4
B&H = 2

This means candidate distribution must be:
F&A: 0 candidates → 9 non-candidates
M&S: 2 candidates → 5 non-candidates
O&Q: 1 candidate → 4 non-candidates
B&H: 1 candidate → 2 non-candidates

Question 1

From the below table

Pakrasi and Qureshi must belong to the same department.

Correct Answer : Option A

Question 2

For Qureshi, the votes can come as:
F&A non-candidates = 9 votes
O&Q non-candidates = 4 votes
Ramaswamy’s candidate vote = 1 vote

So from a single department, Qureshi can receive 9 votes.

Question 3

If Samuel belongs to B&H, then only Case 1 is possible:

Pakrasi = M&S
Qureshi = M&S
Ramaswamy = O&Q
Samuel = B&H

So both statements are true.

Correct Answer: Option D

Question 4

From the vote logic, only two arrangements are possible:

Case 1:
Pakrasi → M&S
Qureshi → M&S
Ramaswamy → O&Q
Samuel → B&H

Case 2:
Pakrasi → M&S
Qureshi → M&S
Ramaswamy → B&H
Samuel → O&Q

So, the candidate from O&Q can be either Ramaswamy or Samuel.

Answer: B. It was either Prof. Ramaswamy or Prof. Samuel.