CAT 2020 Question Paper | DILR Slot 2

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The best questions to practice for CAT Exam are the actual CAT Question Papers. 2IIM offers you exactly that, in a student friendly format to take value from this. The mantra to this set is to partially fill the table and proceed on with that, here we have to answer which statement remains true in all the possible arrangements. To check out about 1000 CAT Level questions with detailed video solutions for free, go here: CAT Question Bank

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 21 : Which of the following statements is necessarily true?

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Video Explanation

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Explanatory Answer

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: Q is guiding G.
Need not be true, could be S also

B: H is an Economics student.
Has to be True

C: B is scheduled in the first slot.
Incorrect

D: S is guiding F.
Need not be true, could be anyone

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The question is "Which of the following statements is necessarily true?"

Hence, the answer is, "H is an Economics student."

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