CAT 2023 Slot 1 — DILR Question 9

Mixed PracticeEasy

Passage / Data

Answer the following questions based on the information given below:

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.

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

Answer & solution

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

Solution

Easy

Determine which candidates can sit in O&Q using only what the set-up forces, leaving any genuine ambiguity intact.

Set-up result: Pakrasi & Qureshi $\in$ M&S; Ramaswamy and Samuel split O&Q and B&H; O&Q's block voted Qureshi, so by Rule 3 Qureshi $\notin$ O&Q (consistent — he is in M&S).

Eliminate Pakrasi and Qureshi. Both are pinned to M&S, so neither is the O&Q candidate. The O&Q seat belongs to Ramaswamy or Samuel.

Show both remain possible. Nothing forces the Ramaswamy/Samuel order: assignment $(R=$ O&Q $,\,S=$ B&H $)$ and $(R=$ B&H $,\,S=$ O&Q $)$ both satisfy every rule and cross-vote. So we can only conclude it is either Ramaswamy or Samuel.

It was either Prof. Ramaswamy or Prof. Samuel.