Instructions

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

For instance, suppose cars numbered 1 through 5 arrive and park, where cars 1, 3 and 5 areÂ compact cars and 2 and 4 are SUVs. At this point, the parking lot would be described by theÂ sequence 1, 2, 3, 4, 5. If cars 2 and 5 now vacate their slots, the parking lot would now beÂ described as 1, V, V, 3, 4. If a compact car (numbered 6) arrives subsequently followed by anÂ 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 50

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

Solution

Here we can see that cars 3 and 5 are still in their position. Thus car 4 was not the first car to leave, either 1 or 2 left before 4. Let's say only car 2 left before car 4. Now supposingly if car 2 is an SUV, car 6 was parked in that lot. Thus car 2 and car 7 are compact cars. Option 4 is correct.

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