CAT 2020 Slot 2 - LRDI Question 23

Instructions

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.

Question 23

Suppose the sequence at some point of time is 4, 5, 6, V, 3. Which of the following isĀ NOT necessarily true?

Solution

The original sequence as given in the question is 4,5,6,V,3

This is possible when cars 1,2,3 arrived and then cars 1 and 2 leave. After that cars 4,5 and 6 arrive.

Now there are 4 slots to the left of car 3. This is only possible when cars 1 and 2 were SUVs. Now out of these 4 slots,

3 slots are occupied by cars 4,5 and 6. As a result these are compact cars . Car 3 can be a SUV or a Compact car and it won't impact the final solution.


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