CAT 2020 Question Paper Slot 2
The Humanities department of a college is planning to organize eight seminars, one for eachĀ of the eight doctoral students - A, B, C, D, E, F, G and H. Four of them are from Economics,Ā three from Sociology and one from Anthropology department. Each student is guided by oneĀ among P, Q, R, S and T. Two students are guided by each of P, R and T, while one student isĀ guided by each of Q and S. Each student is guided by a guide belonging to their department.Ā Each seminar is to be scheduled in one of four consecutive 30-minute slots starting at 9:00Ā am, 9:30 am, 10:00 am and 10:30 am on the same day. More than one seminars can beĀ scheduled in a slot, provided the guide is free. Only three rooms are available and hence atĀ the most three seminars can be scheduled in a slot. Students who are guided by the sameĀ 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. Aās 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. TheĀ 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.
If D is scheduled in a slot later than Q's, then which of the following two statement(s)Ā is(are) true?
(i) E and H are guided by T.
(ii) G is guided by Q.
If E and Q are both scheduled in the same slot, then which of the following statementsĀ BEST describes the relationship between D, H, and T?
If D is scheduled in the slot immediately before Qās, then which of the following is NOTĀ necessarily true?
A shopping mall has a large basement parking lot with parking slots painted in it along aĀ single row. These slots are quite narrow; a compact car can fit in a single slot but an SUVĀ requires two slots. When a car arrives, the parking attendant guides the car to the firstĀ available slot from the beginning of the row into which the car can fit.
For our purpose, cars are numbered according to the order in which they arrive at the lot. ForĀ example, the first car to arrive is given a number 1, the second a number 2, and so on. ThisĀ numbering does not indicate whether a car is a compact or an SUV. The configuration of aĀ parking lot is a sequence of the car numbers in each slot. Each single vacant slot isĀ represented by letter V.
For instance, suppose cars numbered 1 through 5 arrive and park, where cars 1, 3 and 5 areĀ compact cars and 2 and 4 are SUVs. At this point, the parking lot would be described by theĀ sequence 1, 2, 3, 4, 5. If cars 2 and 5 now vacate their slots, the parking lot would now beĀ described as 1, V, V, 3, 4. If a compact car (numbered 6) arrives subsequently followed by anĀ SUV (numbered 7), the parking lot would be described by the sequence 1, 6, V, 3, 4, 7.
Answer the following questions INDEPENDENTLY of each other.
Initially cars numbered 1, 2, 3, and 4 arrive among which 1 and 4 are SUVs while 2 andĀ 3 are compact cars. Car 1 then leaves, followed by the arrivals of car 5 (a compact car)Ā and car 6 (an SUV). Car 4 then leaves. Then car 7 (an SUV) and car 8 (a compact car)Ā arrive. At this moment, which among the following numbered car is parked next to carĀ 3?
Suppose eight cars have arrived, of which two have left. Also suppose that car 4 is aĀ compact and car 7 is an SUV. Which of the following is a POSSIBLE currentĀ configuration of the parking lot?
Suppose the sequence at some point of time is 4, 5, 6, V, 3. Which of the following isĀ NOT necessarily true?
Suppose that car 4 is not the first car to leave and that the sequence at a time betweenĀ the arrival of the car 7 and car 8 is V, 7, 3, 6, 5. Then which of the following statementsĀ MUST be false?
