CAT 2020 Slot 2 — DILR Question 12
Answer the next 4 questions based on the information given below.
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.
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?
Answer & solution
Car 6 is a compact.
- B
Car 4 is an SUV.
- C
Car 7 is a compact.
- D
Car 2 is a compact.
As cars 3 and 5 are still in their positions and car 6 is in between them, it means car 6 would have arrive after car 4 leaves.
Now 4 is not the first to leave, at least one of the cars 1 or 2 left before car 4.
Let us consider the following cases.
Case 1: Both cars 1 and 2 left before car 4.
This is not possible since car 6 (compact or SUV) would’ve occupied the first parking slot(s).
Case 2: Only car 1 left before car 4.
If car 1 is compact and cars 4 and 6 are SUVs, then car 6 would take place of car 4.
Now car 2 will leave and car 7 will arrive. In this case car 7 will take the first parking slot(s), which is not the case.
∴ This case is also not possible.
Case 3: Only car 2 left before car 4.
If car 2 is compact and cars 4 and 6 are SUVs, then car 6 would take place of car 4.
Now car 7 will arrive and take place of car 2.
Finally, car 1 leaves.
∴ This is the only case possible.
⇒ Car 6 is an SUV.
Hence, option (a).