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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 10:30 am.

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 19 : Which one of the following statements is true?

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

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Let's try to form and then solve the grid first. A basic grid may look like this:

Try to apply the constraints as is easiest to apply, not in the same order as given in the question. For now, if we apply the straightforward parts of points 2, 3, 5 and 6 we get the following grid (also keeping in mind that since A is the only one scheduled at 10 and that Eco students have seminars in all 4 slots, this means A has to be Eco):

For now, all we have done is plug in the info directly from the question. Now to try and make some conclusions:

It is mentioned that the guides are from the same subject as well. So P Must be in Sociology as well, meaning C is also from Sociology. So now we have all 3 people from Sociology

A and G have in consecutive slots. So A could either have it in the 930AM slot or in the 1030AM slot since A has it at 10

P who is guiding B and C has to attend in the 1st 2 slots, i.e., 9AM and 930AM

Also mentioned that B and G have it in the same slot.

This means that G must have the seminar in the 930 slot as only then the conditions above will be satisfied (keep in mind that A and G have in consecutive slots)

P also has a slot at 9AM which means it must be C who has it

We know there are 4 Eco students, so the remaining must be Eco

One Eco student has the review at 9:30 (guided by T). Meaning 9:30AM already has 3 students so far

9AM at least has one more eco students with the seminar

If 930AM has 3, 10 has only 1, 9 has at least 2

From the remaining Eco students, one has at 9 for sure, one has at 930, so there can only be one more who has it at 1030

We have the complete table as per the info provided, let's try to solve from here

A: Only one seminar is scheduled in the second slot.

FALSE, check table

B: Three seminars are scheduled in the last slot.

FALSE, check table

C: Three seminars are scheduled in the first slot.

FALSE, check table

D: Two seminars are scheduled in the first slot.

TRUE

The question is **"Which one of the following statements is true?" **

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