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CAT 2020 Exam Shift 2 Solved Paper

Direction for Q.No : 39 - 44

The Humanities department of a college is planning to organize eight seminars, one for each of the eight doctoral students −A,B,C,D,E,F,G and H. Four of them are from Economics, three from Sociology and one from Anthropology department. Each student is guided by one among P,Q,R,S and T. Two students are guided by each of P, R and T, while one student is guided by each of Q and S. Each student is guided by a guide belonging to their department.
Each seminar is to be scheduled in one of four consecutive 30-minute slots starting at 9:00 am, 9:30 am, 10:00 am and 10:30 am on the same day. More than one seminars can be scheduled in a slot, provided the guide is free. Only three rooms are available and hence at the most three seminars can be scheduled in a slot. Students who are guided by the same guide must be scheduled in consecutive slots.
The following additional facts are also known.
1. Seminars by students from Economics are scheduled in each of the four slots.
2. A's is the only seminar that is scheduled at 10:00 am. A is guided by R.
3. F is an Anthropology student whose seminar is scheduled at 10:30am.
4. The seminar of a Sociology student is scheduled at 9:00 am.
5. B and G are both Sociology students, whose seminars are scheduled in the same slot. The seminar of an Economics student, who is guided by T, is also scheduled in the same slot.
6. P, who is guiding both B and C, has students scheduled in the first two slots.
7. A and G are scheduled in two consecutive slots.

Question : 39

Total: 76

Which one of the following statements is true?

Three seminars are scheduled in the last slot.
Only one seminar is scheduled in the second slot.
Two seminars are scheduled in the first slot.
Three seminars are scheduled in the first slot.

Validate

Solution:

Given,
Students: A,B,C,D,E,F,G,H
Guides: P(2 students ),Q(1 student ),R(2 students ),S(1 student ),T(2 students )
Economics (4 students), Sociology (3 students), Anthropology (1 student)
Slots: 9:00,9:30,10:00,10:30
From (1), one economics seminar is held in each of the four slots.
From (1) and (2),A is students of economics and is guided by R. Hence, R is from economics department (given, each student is guided by a guide belonging to their department).
The information from (1),(2),(3) and (4) can be tabulate as follows.

09 : 00	09 : 30	10 : 00	10 : 30
Eco	Eco	A - Eco - R	Eco
Socio			F- Anth -

From (5), two sociology seminars and one economics seminar are held in the same slot. It cannot be 10:00 slot or 10:30 slot as at most three seminars can be conducted in one slot.
From (5) and (7), seminars of B,G and T are held in 9:30 slot.
From (6) and the given point that students who are guided by the same guide must be scheduled in consecutive slots, C is a sociology student and his\/her seminar is held in 9:00 slot.

09 : 00	09 : 30	10 : 00	10 : 30
Eco	Eco - T	A - Eco - R	Eco
C - Socio - P	B - Socio- P		F- Anth -
	G - Socio

From the above we also know the following combination of guides, their subject and their students

P(2)	Sociology	B,C
Q(1)
R(2)	Economics	A
S(1)
T(2)	Economics

We know that G is a sociology student and F is an anthropology student. Hence, the rest D,E and H are economics students. Thus, one among D,E and H (economics students) is guided by R and the remaining two are guided by T. Now, G and F are guided by Q and S in any order. We get the following combinations.

P(2)	Sociology	B,C
Q(1)	Anthropology/ Sociology	F/G
R(2)	Economics	A (one of D, E, H)
S(1)	Sociology/Anthropology	G/F
T(2)	Economics	Two of D, E, H

It is also given that students who are guided by the same guide must be scheduled in consecutive slots. Hence, 9:00 economics seminar is of T and 10:30 seminar is that of R.

09 : 00	09 : 30	10 : 00	10 : 30
Eco - T	Eco - T	A - Eco - R	Eco
Socio	B - Socio		F- Anth -
	G - Socio

From the above table, it is clear that the statement that two seminars are scheduled in the first slot is true

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