Logical Reasoning
Topic - Arrangements
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.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?
- 6
- 5
- 8
- 7
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?
- 8, 2, 3, V, 5, 7, 6
- 8, 2, 3, V, 6, 5, 7
- 8, 2, 3, V, 5, 6, 7
- V, 2, 3, 7, 5, 6, 8
3. Suppose the sequence at some point of time is 4, 5, 6, V, 3. Which of the following is NOT necessarily true?
- Car 5 is a compact.
- Car 1 is an SUV.
- Car 3 is an SUV.
- Car 4 is a compact.
4. Suppose that car 4 is not the first car to leave and that the sequence at a time between the arrival of car 7 and car 8 is V, 7, 3, 6, 5. Then which of the following statements MUST be false?
- Car 6 is a compact.
- Car 2 is a compact.
- Car 7 is a compact.
- Car 4 is an SUV.
Solutions
1. D 2. C 3. C 4. A
- Following the instructions, we have
The answer is, "7"
2. Solving by options
A: 8, 2, 3, V, 5, 7, 6
This means that the missing numbers (i.e. 1 and 4) have left. There is no situation where 1 and 4 leave but 6 is after 7. If 6 arrived first, then clearly it should be after 5, and since 1 and 4 are leaving this in any case does not affect how 6 can be after 7 despite arriving earlier. This option is not possible
B: 8, 2, 3, V, 6, 5, 7
Here again, 1 and 4 have left. Once again, there is no situation where 6 can be before 5. (unless 4 is an SUV but clearly stated that 4 is a compact car)
C: 8, 2, 3, V, 5, 6, 7
This is feasible. 1 and 4 left, 8 arrived last so fills 1's space. This is the correct answer
Hence, the answer is, " 8, 2, 3, V, 5, 6, 7"
3. 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
Hence, the answer is, "Car 3 is an SUV."
4. Solving by options
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 “which of the following statements MUST be false?"
