Logical Reasoning

Arrangements

Easy

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?

Car 4 is an SUV

Car 2 is a compact

Car 6 is a compact

Car 7 is a compact

✅ Correct Option: 3

Slide 1/2

Understanding the Set:

This is an arrangement set. In this set, there are two types of cars — Compact and SUV — that need to be parked.

A Compact car can fit in a single slot, but an SUV requires two slots.

Cars are numbered according to the order in which they arrive at the lot

(the first car to arrive is numbered 1, and so on).

If there is any vacant slot, we mark it as "V".

Now, after reading the set, you’ll find that there isn’t much information or many clues in the passage.

Thus, we need to solve the set based on the specific requirements of each question.

The original order is 1 2 3 4 5.

Now car 6 is at the place of car 4 and car 4 is not the first one to leave.

So either car 1 & car 2 will leave first.

If we assume that the first car left is car 1, then as car 2 is also leaving, so car 7 will take the first position.

So first position cannot be empty.

Hence car 2 is the one which left at the first place and after it car 4 left.

So we have following possibilities.

1 V 3 V 5
1 V 3 V V 5

Car 2 is not an S U V because in that case, car 6 will be next to car 1.

Also car 6 is not compact otherwise, it will be again next to car 1.

So car 6 is an S U V and we have the order - 1 V 3 6 5<

Now car 7 came which is compact and order is - 1 7 3 6 5.

After that the car 1 left to give the final order as - V 7 3 6 5

Question 21

Initially cars numbered 1, 2, 3, and 4 arrive among which 1 and 4 are SUVs while 2 and3 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 car3?

Question 22

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?

Question 23

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

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?

Solution

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