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Question 7 : Suppose the sequence at some point of time is 4, 5, 6, V, 3. Which of the following is NOT necessarily true?

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.

  1. Car 5 is a compact.
  2. Car 1 is an SUV.
  3. Car 3 is an SUV.
  4. Car 4 is a compact.

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Explanatory Answer

If 3 comes after 4 spaces, it is clear that 1 and 2 were SUVs.(since it was the 3rd to arrive and from the current arrangement we know that it comes after 4 spaces)
So we can conclude that: 1,2 were SUVs; 4, 5, 6 have to be compacts
Now let's go by options

A: Car 5 is a compact.
Yes, necessarily true

B: Car 1 is an SUV.
Necessarily true as well

C: Car 3 is an SUV.
Irrelevant, car 3 can be anything.This is the correct option

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

Hence, the answer is, "Car 3 is an SUV."

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