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 seminar 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.

- Seminars by students from Economics are scheduled in each of the four slots.
- A’s is the only seminar that is scheduled at 10:00 am. A is guided by R.
- F is an Anthropology student whose seminar is scheduled at 10:30 am.
- The seminar of a Sociology student is scheduled at 9:00 am.
- 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.
- P, who is guiding both B and C, has students scheduled in the first two slots.
- A and G are scheduled in two consecutive slots.

**Question 1: **

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.

**Show Answer**

**3**

**Question 2: **

Who all are NOT guiding any Economics students?

- P, R and S
- P, Q and R
- P, Q and S
- Q, R and S

**Show Answer**

**3**

**Question 3: **

Which of the following statements is necessarily true?

- S is guiding F.
- Q is guiding G.
- B is scheduled in the first slot.
- H is an Economics student.

**Show Answer**

**4**

**Question 4: **

If D is scheduled in a slot later than Q's, then which of the following two statement(s) is(are) true?

(i) E and H are guided by T.

(ii) G is guided by Q.

- Only (ii)
- Neither (i) nor (ii)
- Both (i) and (ii)
- Only (i)

**Show Answer**

**3**

**Question 5: **

If E and Q are both scheduled in the same slot, then which of the following statements BEST describes the relationship between D, H, and T?

- Both D and H are guided by T.
- At least one of D and H is guided by T.
- Exactly one of D and H is guided by T.
- Neither D nor H is guided by T.

**Show Answer**

**2**

**Question 6: **

If D is scheduled in the slot immediately before Q’s, then which of the following is NOT necessarily true?

- G is guided by Q.
- E is guided by R.
- D is guided by T.
- F is guided by S.

**Show Answer**

**2**

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.

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.

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

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.

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.

**Question 1:**

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

Option: 3**Question 2:**

We know that R is guiding an economics student. Hence, choices with R can be are eliminated. None among P, Q and S is guiding an economics student.

Option: 3**Question 3:**

B is scheduled in the second slot. W e are not sure of who are guiding G and F. So, two other choice s are not necessarily true.

Option: 4**Question 4:**

D‘s seminar is scheduled later than Q’s seminar, indicates that Q’s seminar cannot be in the last slot. It implies F is guided by S and G by Q. Hence, statement (ii) is true. Now that Q’s seminar is scheduled in the second slot, D’s seminar is scheduled in the lost slot. i.e D is guided by R. Hence, E and H are guided by T. Thus, statement (i ) is also true. Both (i) and (ii) are true.

Option: 3**Question 5:**

If E and Q are scheduled in the same slot, it is possible both in the second slot and the last slot. If it is in the second slot, then E is guided by T and one among D and E is also guided by T. If it is in the last slot, then E is guided by R and both D and E are guided by T. Thus, at least one of D and H is guided by T.

Option: 2**Question 6:**

If D is scheduled in the slot immediately before Q’s, it is only possible with D is in the first slot and Q is in the second slot. It implies that D is guided by T, G is guided by Q and F is guided by S. One among E and H is guided by T and the other one b y R, in any order. Hence the statement that E is guided by R is NOT necessarily true.

Option: 2### CAT 2020 LRDI sets with Solutions

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