# CAT 2020 Question Paper | DILR Slot 2

###### CAT Previous Year Paper | CAT DILR Questions | Question 8

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A shopping mall has a large basement parking lot with parking slots painted in it along a single row. These slots are quite narrow; a compact car can fit in a single slot but an SUV requires two slots. When a car arrives, the parking attendant guides the car to the first 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. For example, the first car to arrive is given a number 1, the second a number 2, and so on. This numbering does not indicate whether a car is a compact or an SUV. The configuration of a parking lot is a sequence of the car numbers in each slot. Each single vacant slot is represented by letter V.

For instance, suppose cars numbered 1 through 5 arrive and park, where cars 1, 3 and 5 are compact cars and 2 and 4 are SUVs. At this point, the parking lot would be described by the sequence 1, 2, 3, 4, 5. If cars 2 and 5 now vacate their slots, the parking lot would now be described as 1, V, V, 3, 4.  If a compact car (numbered 6) arrives subsequently followed by an 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 8 : Suppose that car 4 is not the first car to leave and that the sequence at a time between the arrival of the car 7 and car 8 is V, 7, 3, 6, 5. Then which of the following statements MUST be false?

1. Car 6 is a compact.
2. Car 2 is a compact.
3. Car 7 is a compact.
4. Car 4 is an SUV.

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A: Car 6 is a compact.
"Clearly the cars that have left are: 1,2 and 4.

Given that the arrangement is …3, 6, 5 AND the fact that 4 was not the 1st car to leave. This means that there was vacant space before 4 left and 6 could not occupy it. So the 1st car that left must have been a compact and 6 must have been an SUV"

The question is "Suppose that car 4 is not the first car to leave and that the sequence at a time between the arrival of the car 7 and car 8 is V, 7, 3, 6, 5. Then which of the following statements MUST be false?"

##### Hence, the answer is, "Car 6 is a compact."

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