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. Prof. Ramaswamy and Prof. Samuel
2. Prof. Pakrasi and Prof. Qureshi
3. Prof. Pakrasi and Prof. Samuel
4. Prof. Qureshi and Prof. Ramaswamy
Explanation
Answer- 2-Prof. Pakrasi and Prof. Qureshi
Question 2-
Which of the following can be the number of votes that Prof. Qureshi received from a
single department?
1. 6
2. 8
3. 7
4. 9
Explanation
Answer- 4. 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.
1. Both statements A and B
2. Only statement B
3. Only statement A
4. Neither statement A nor statement B
Explanation
Answer- 1.Both statements A and B
Question 4-
What best can be concluded about the candidate from O&Q?
1. It was either Prof. Pakrasi or Prof. Qureshi.
2. It was Prof. Samuel.
3. It was either Prof. Ramaswamy or Prof. Samuel.
4. It was Prof. Ramaswamy.
Explanation
Answer- 3. It was either Prof. Ramaswamy or Prof. 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. Neither statement A nor statement B
2. Only statement B
3. Only statement A
4. Both statements A and B
Explanation
Answer- 2. Only statement B
Let’s break down the logic and validate all the answers and explanations step-by-step, keeping track of faculty distribution, votes, and rules.
🔢 Faculty Strength by Department:
| Department | Faculty Count |
|---|---|
| F&A | 9 |
| M&S | 7 |
| O&Q | 5 |
| B&H | 3 |
| Total = 24 faculty members (including 4 candidates) |
🗳️ Given Vote Counts:
- Prof. Pakrasi – 3 votes
- Prof. Qureshi – 14 votes
- Prof. Ramaswamy – 6 votes
- Prof. Samuel – 1 vote
Total = 24 – 4 (candidates) = 20 votes from non-candidates + 4 votes from candidates
→ Matches: total 24 votes cast
🔄 Voting Pattern of Candidates:
- Pakrasi → Ramaswamy
- Qureshi → Samuel
- Ramaswamy → Qureshi
- Samuel → Pakrasi
Each follows the rule: candidates cannot vote for themselves or for someone from their own department.
✅ Q1: Which two candidates can belong to the same department?
We’re told:
- Only one candidate from O&Q ⇒ only one among 4 is from O&Q
- No more than 2 candidates per department
- Faculty cannot vote within their department
Now, Qureshi received 14 votes — likely from multiple departments, possibly F&A (9) + M&S (7) non-candidates
Try to group:
- If Pakrasi and Qureshi are from same department (say, M&S), then only 5 non-candidates left → may explain Qureshi’s 14 votes via other departments
→ Feasible.
✅ Answer: (2) Prof. Pakrasi and Prof. Qureshi
✅ Q2: Which of the following can be the number of votes Prof. Qureshi received from a single department?
Qureshi got 14 votes total. Let’s test which value among 6, 7, 8, 9 is possible from a single department.
- F&A (9 faculty) ⇒ if Qureshi is not from F&A → could have received 9 votes
- M&S (7) → max 6 (if one candidate is from there)
- O&Q → only 4 non-candidates
- B&H → only 2 non-candidates
So only F&A = 9 is possible max
✅ Answer: (4) 9
✅ Q3: If Prof. Samuel belongs to B&H, which of the following is/are true?
If Samuel is from B&H, then:
- The other two members in B&H cannot vote for him
- Samuel cannot vote for himself
- He got only 1 vote → must be from one of other 3 departments
→ Plausible.
Now consider:
- Statement A: Pakrasi is from M&S
- Statement B: Ramaswamy is from O&Q
We are told only 1 candidate is from O&Q
If Samuel is from B&H, then Pakrasi and Qureshi must be from M&S or F&A
→ Then Ramaswamy being from O&Q is valid
Also:
- To explain who voted for whom, Pakrasi voted for Ramaswamy (implying different departments)
- So if Pakrasi is from M&S, Ramaswamy could be from O&Q
✅ Answer: (1) Both statements A and B
✅ Q4: What best can be concluded about the candidate from O&Q?
O&Q has only 5 faculty
Only 1 can be a candidate
So, of Ramaswamy and Samuel, who fits?
Earlier we deduced:
- If Samuel is from B&H → Ramaswamy may be O&Q
- Alternatively, Samuel could be from O&Q
Therefore:
✅ Answer: (3) Either Ramaswamy or Samuel
✅ Q5: Which of these are true?
Let’s check who voted for Qureshi (received 14 votes)
→ These must be from departments other than Qureshi’s
- Suppose Qureshi is from M&S ⇒ only 6 other M&S profs ⇒ cannot vote for him
- Votes must have come from F&A (9) and maybe O&Q (4) and B&H (2)
→ Most likely: F&A non-candidates voted for Qureshi
Thus:
- Statement A (M&S voted for Qureshi) → invalid if Qureshi is from M&S
- Statement B (F&A voted for Qureshi) → very likely
✅ Answer: (2) Only statement B
✅ Final Answers Recap:
| Q# | Answer | Explanation |
|---|---|---|
| 1 | (2) Prof. Pakrasi and Prof. Qureshi | Only this pairing fits constraints |
| 2 | (4) 9 | Only F&A has 9 members |
| 3 | (1) Both A and B | Fits departmental logic |
| 4 | (3) Ramaswamy or Samuel | Only one from O&Q allowed |
| 5 | (2) Only B | F&A likely voted Qureshi |
