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.

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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.

Question

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.

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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.

Accepted Answer

#### **Key Information from the Question:**
1. **Department Sizes:**  
   - F&A: 9 members  
   - M&S: 7 members  
   - O&Q: 5 members  
   - B&H: 3 members

2. **Voting Observations:**  
   - Prof. Pakrasi received 3 votes (1 professor vote + 2 non-professor votes).  
   - Prof. Qureshi received 14 votes (1 professor vote + 13 non-professor votes).  
   - Prof. Ramaswamy received 6 votes (1 professor vote + 5 non-professor votes).  
   - Prof. Samuel received 1 vote (1 professor vote + no non-professor votes).

3. **Rules:**  
   - Faculty members cannot vote for candidates from their own department.  
   - All non-candidates in a department vote for the same candidate.

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#### **Analysis of Votes for Prof. Qureshi:**
Prof. Qureshi received **14 votes**, including **13 non-professor votes**. These votes must come from departments other than the one to which Prof. Qureshi belongs.

1. **Non-candidates from F&A (9 members):**  
   If all non-candidates from F&A voted for Prof. Qureshi, it accounts for a significant portion of his votes (9 out of 13 non-professor votes). This aligns with the voting patterns and rules, making **Statement B true**.

2. **Non-candidates from M&S (7 members):**  
   If all non-candidates from M&S voted for Prof. Qureshi, it would account for the remaining votes (7 out of 13). However, this conflicts with the distribution of votes among other candidates, as M&S likely supported another candidate, such as Prof. Pakrasi or Prof. Ramaswamy.

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#### **Conclusion:**
- **Statement A (M&S voted for Qureshi):** Likely false based on voting distribution and rules.
- **Statement B (F&A voted for Qureshi):** True based on logical deduction and alignment with voting data.

Thus, the correct answer is **A (Only statement B)**.

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