CAT 2023 Question Paper | DILR Slot 1

CAT Questions

CAT 2023 DILR did not have a change in pattern. Atleast two sets were doable in each slot and one of the four sets was extremely tough. Choice of Sets became a crucial factor. Overall this section was at a medium to high level of difficulty.

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?

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Video Explanation

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Explanatory Answer

F&A = 9 members; M&S = 7 members; O&Q = 5 members; B&H = 3 members

• Each Professor got one professor vote.
• For S, the number of non-professor votes is zero, we can infer No department voted for S.
• For P, the number of non-professor votes is 2. Hence, we can conclude two votes are from B&H department and there is only 1 candidate from that department.
• For Q, the number of non-professor votes is 13, which clearly states the department of F&A should have voted for him.
• Two cases are possible here: “9 from F&A and 4 from others” or “8 from F&A and 5 from others”

	P	Q	R	S
Professor Votes	1	1	1	1
Non-Professor Votes	2	13	5	0
Department 1	B&H	F&A	M&S	No department
Department 2	4 or 5

• If number of non-professors votes for Q as “8 from F&A and 5 from other department”, then number of candidates from F&A is 1, B&H is 1, O&Q is 1 and from M&S is 2 which makes total candidates count 5. Therefore, we have 9 from F&A and 4 from others (which is O&H).
• For R, the number of non-professor votes is 5 which is from M&S.
• Therefore, we have 2 candidates from M&S, 1 from O&Q, and 1 from B&H.
• Since P voted for R, Q voted for S; R voted for Q and S voted for P the two candidates from the M&S department can be either PQ or RS.
• Since Faculty members cannot vote for a candidate from their own department, R cannot be from M&S department since R got votes from M&S department.
• Therefore, the two persons from M&S department should be P and Q. R and S can be from either O&Q or B&H.

	P	Q	R	S
Professor Votes	1	1	1	1
Non-Professor Votes	2	13	5	0
Department 1	B&H = 2	F&A = 9	M&S = 5	No department
Department 2	O&Q = 4

F&A
M&S	PQ
O&Q	R/S
B&H	S/R

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The question is " Which two candidates can belong to the same department? "

Answer: From the table, we can identify that two candidates from the same department are Prof. Pakrasi and Prof. Qureshi.

Hence, the answer is 'Prof. Pakrasi and Prof. Qureshi'

Choice B is the correct answer.

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