Logical Reasoning – A shopping mall has a large basement parking



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.


Q.1 Initially cars numbered 1, 2, 3, and 4 arrive among which 1 and 4 are SUVs while 2 and 3 are compact cars. Car 1 then leaves, followed by the arrivals of car 5 (a compact car) and car 6 (an SUV). Car 4 then leaves. Then car 7 (an SUV) and car 8 (a compact car) arrive. At this moment, which among the following numbered car is parked next to car 3?
  1. 7
  2. 8
  3. 5
  4. 6

Answer: 1

Q.2 Suppose eight cars have arrived, of which two have left. Also suppose that car 4 is a compact and car 7 is an SUV. Which of the following is a POSSIBLE current configuration of the parking lot?
  1. V, 2, 3, 7, 5, 6, 8
  2. 8, 2, 3, V, 6, 5, 7
  3. 8, 2, 3, V, 5, 7, 6
  4. 8, 2, 3, V, 5, 6, 7

Answer: 4

Q.3 Suppose the sequence at some point of time is 4, 5, 6, V, 3. Which of the following is NOT necessarily true?
  1. Car 3 is an SUV.
  2. Car 4 is a compact.
  3. Car 1 is an SUV.
  4. Car 5 is a compact.

Answer: 1

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

Answer: 4

Solutions:
Q.1 As per question, initially the parking lot would now be described as 1, 2, 3, 4
When car 1 leaves , V , V , 2, 3, 4
Now after the arrivals of car 5 (a compact car) and car 6 (an SUV). -> 5 , V, 2, 3, 4, 6
When car 4 leaves -> 5 , V, 2, 3, V,V, 6
Now after the arrivals of car 7 (an SUV) and car 8 (a compact car) -> 5 , 8, 2, 3, 7, 6
Thus car 7 is parked next to car 3.

Q.2 Option a) can not be correct as car 6 must arrive before 7 and must lie left to car 7 (as car 4 and 1 had left ) Option b) is a possible arrangement assuming car 1 to car 7 come first then car 1 and car 4 left after which car 8 arrives.
Option c) 8, 2, 3, V, 6, 5, 7 -> again it is not a possible arrangement , as the cars which left will be car 4 and car 1 in this case car 5 need to be left of car 6.
Option d) V, 2, 3, 7, 5, 6, 8 -> again it is not a possible arrangement as car 4 is a compact car and car 7 is an SUV so car 7 can’t come at the place of car 4.

Q.3 Given sequence 4, 5 , 6, V, 3 shows that car 1 and car 2 are SUV and each of car 4, 5 and 6 is a compact car. We can’t say anything about car 3.
Thus option 1) is correct

Q.4 Given sequence -> V, 7, 3, 6, 5
From this sequence we can say car 6 and car 7 comes when car 1, 2 and 4 left or when 2 and 4 left.
Now from this we can say that car 4 and car 6 are of same type and car 2 and car 7 are of same type.
Now we can say car 6 comes when at least 2 cars left along with car 4. Now car 6 comes before car 7 so if it would have been a compact car then it should be there at the place of car 1 or car 2 but it is at the place of car 4 it means it is not a compact car so it should be an SUV.
Which also mean car 1 and car 2 are compact car.
Thus option 4) is correct.


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