Understanding the set :- We are given 4 departments and their faculty members :- 1)Finance and Accounting (F&A) - 9 members 2)Marketing and Strategy (M&S) - 7 members 3)Operations and Quants (O&Q) - 5 members 4)Behaviour and Human Resources (B&H) - 3 members and 4 candidates, lets call them P, Q, R, S who were candidates for the post of the Dean of the school. After reading the set, we can write following conditions. 1. There can be either 0 or 1 or 2 candidates form any department. 2. A candidate cannot vote for himself or herself. 3. Faculty members can not vote for candidate from their own department. 4. Non-candidates form same department voted for same candidate. 5. P, Q, R, S received 3, 14, 6 and 1 votes. 6. There is exactly 1 candidate form OQ. —-- Firstly we will try to find the number of votes each professor will get :-

	P	Q	R	S
Professor Votes
Non-Professor Votes

Question says, Every faculty member, including the four candidates, voted for the post. which implies total votes = total of all faculties = 9+7+5+3 = 24 out of which, 4 votes are given by each of P,Q,R,S (let's call them professor votes)- and other 20 votes by non candidates (let's call them non professor votes). —--

	P	Q	R	S
Professor Votes	1	1	1	1
Non-Professor Votes	2	13	5	0

Now, from the set we know that, 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. therefore we know, that professor votes will be 1 for each of P,Q,R,S And , P received 3 votes = 1 professor + 2 non professor votes - Q received 14 votes = 1 professor + 13 non professor votes R received 6 votes = 1 professor + 5 non professor votes S received 1 votes = 1 professor + 0 non professor votes —--

	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

We are given in the question that, In each department, all the faculty members who were not candidates voted for the same candidate therefore, we can say, P - got two votes are from B&H department S - he number of non-professor votes is zero, we can infer No department voted for S. R - the number of non-professor votes is 5 which is from M&S. Q - have 13 non Professor votes - 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	O&H

Considering case 2; 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. but, we know number of candidates is 4 therefore, the case is rejected. thereore, we have 9 from F&A and 4 from others (which is O&H) —-- Votes given to each candidate:-

	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	O&H

Candidates and their departments :-


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

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.

CAT (DILR) PYQs

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