Question

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?

• A. 8
• B. 6
• C. 5
• D. 7
• A. V, 2, 3, 7, 5, 6, 8
• B. 8, 2, 3, V, 5, 6, 7
• C. 8, 2, 3, V, 6, 5, 7
• D. 8, 2, 3, V, 5, 7, 6
• A. Car 5 is a compact.
• B. Car 4 is a compact.
• C. Car 3 is an SUV.
• D. Car 1 is an SUV.
• A. Car 7 is a compact.
• B. Car 4 is an SUV.
• C. Car 6 is a compact.
• D. Car 2 is a compact.

Answer 1

The Correct Option is D

To solve the problem, let's follow the sequence of parking events as described:

1. Car 1 (SUV) and Car 4 (SUV) each requires 2 slots, while Car 2 and Car 3 (both compact) each require 1 slot.
2. Initial parking:
   • Car 1 (SUV) occupies slots 1 and 2. 
   • Car 2 (compact) occupies slot 3.
   • Car 3 (compact) occupies slot 4.
   • Car 4 (SUV) occupies slots 5 and 6.
3. Car 1 leaves, creating two vacant slots at positions 1 and 2. The sequence becomes: [V, V, 2, 3, 4, 4].
4. Car 5 (compact) arrives and takes the first available slot at position 1. The sequence becomes: [5, V, 2, 3, 4, 4].
5. Car 6 (SUV) arrives and takes the next two vacant slots at positions 2 and 3. The sequence becomes: [5, 6, 6, 3, 4, 4].
6. Car 4 leaves, creating two vacant slots at positions 5 and 6. The sequence becomes: [5, 6, 6, 3, V, V].
7. Car 7 (SUV) arrives and takes the next two available slots at positions 5 and 6. The sequence becomes: [5, 6, 6, 3, 7, 7].
8. Car 8 (compact) arrives and takes the first available slot at position 5, which is in front of Car 7 (SUV). The sequence becomes [5, 6, 6, 3, 8, 7, 7].

The problem asks which numbered car is parked next to Car 3. Car 3 is at position 4, and its neighboring slots are occupied by Car 6 (in position 3) and Car 7 (extending from position 5 with both its 5 and 6 slots). Thus, Car 7, which extends into two slots starting at position 5, is parked next to Car 3.

Answer 2

This table represents the order of arrival and departure of cars :-

	1(SUV)	2	3	4(SUV)
Car 1 leaves	V        V	2	3	4(SUV)
Car 5 leaves	5        V	2	3	4(SUV)
Car 6 (SUV) Arrives	5        V	2	3	4(SUV)	6(SUV)
Car 4 leaves	5        V	2	3	V       V	6(SUV)
Car 7 (SUV) Arrives	5        V	2	3	7(SUV)	6(SUV)
Car 8 Arrives	5        8	2	3	7(SUV)	6(SUV)

Therefore, car 2 and car 7 are parked next to car 3.

Answer 3

To determine a possible current configuration of the parking lot, we need to consider the following:

• There are 8 cars that have arrived, numbered from 1 to 8.
• 2 cars have left, meaning there are 6 cars currently in the parking lot.
• Car 4 is a compact, meaning it fits in a single slot.
• Car 7 is an SUV, meaning it requires two slots.

We need to check which given configuration option satisfies all these conditions. The correct configuration mentioned is "8, 2, 3, V, 5, 6, 7."

Let's break it down:

• "8, 2, 3, V, 5, 6, 7" has 7 positions. Since "V" represents a vacant slot, 6 cars are parked, which aligns with the requirement that 2 cars have left.
• "7" indicates that the SUV (Car 7) occupies two slots. In this configuration, Car 7 is placed last, which is plausible.
• The rest, "8, 2, 3, 5, 6," are compact cars fitting into single slots each.

This configuration meets all conditions and reflects a plausible situation in a timely and efficient manner. Therefore, "8, 2, 3, V, 5, 6, 7" is a valid current configuration.

Answer 4

The correct answer is (B): When cars 5 and 6 are present, car 7 cannot take a place between them. 
So , 5,7,6 is not possible.
8,2,3, V, 5,6,7 is possible in the following sequence of arrival of cars.

I. Cars 1,2,3,4,5,6 and 7 arrive one after the other.
II. Car 1 leaves
III. Car 8 arrives and is parked in the slot vacated by car 1
IV. Car 4 leaves.
V. 2,3,7,5,6,8 is not possible as car 7 (SUV) cannot be parked in place of car 4 (compact) while cars 3 and 5 are still parked. 8, 2, 3, V, 6,5,7 is not possible as car 6 cannot be between a vacant slot and to the left of car 5 for the following reasons.

If no slot is vacant when car 6 is arrived, it would have been parked to the right of car 5.
If car 4 (compact) left by the time car 6 arrives it would either be parked in the slot vacated by car 4 or to the right of car 5.

Answer 5

To solve this problem, we need to determine which statement about the sequence 4, 5, 6, V, 3 is NOT necessarily true, based on the given parking rules.
Initially, let's understand the parking rules:

• Compact cars fit in a single slot.
• SUVs require two consecutive slots.
• Cars are parked from the start of the row in the first available slots.

Given the sequence is 4, 5, 6, V, 3, let's analyze each option:

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

If car 5 is parked after car 4 and before car 6, it is not necessarily an SUV as it occupies one slot. Therefore, car 5 is a compact, and the option "Car 5 is a compact" is necessarily true.
Car 4 can also occupy a single slot. So, "Car 4 is a compact" is necessarily true.
Car 3, however, is positioned at the end of the sequence with a vacant spot (V) in front of it, which could suggest it was parked there after SUVs occupied multiple slot sequences. This makes it uncertain whether car 3 is actually an SUV since it could also be a compact that followed the sequence after others left or moved. Hence, "Car 3 is an SUV" is NOT necessarily true.
Finally, given no information on car 1 from this sequence, "Car 1 is an SUV" cannot be concluded from the sequence provided. However, it's unrelated to this sequence and independence of events suggests it's not relevant here.
Thus, the statement "Car 3 is an SUV" is NOT necessarily true from the parking configuration provided.

Answer 6

The given sequence according to the question is 4,5,6,V,3
This is possible when cars 1,2,3 arrived and then cars 1 and 2 leave. After that cars 4,5 and 6 arrive.

There are now 4 positions to the left of car 3. Only when cars 1 and 2 were SUVs. Now out of these 4  slots,  4,5 and 6 occupy three of these four spots. As a result these are compact cars. Car 3 can be a SUV or a Compact car.
Hence, The correct answer is (C): Car 3 is an SUV.

Answer 7

Given the parking constraints and the sequence at the time between the arrival of car 7 and car 8 as "V, 7, 3, 6, 5", we need to evaluate which statement must be false. The constraint that car 4 is not the first to leave implies the presence of car 4 preceding this sequence must block available compact slots before car 7 arrives.

• Car 7 parking in slot 2 indicates it is a compact, which aligns with the option "Car 7 is a compact", so this can't be false.
• The absence of car 2 in this sequence coincides with car 4 not being present, so "Car 4 is an SUV" cannot be confirmed or denied strictly.
• Examining slot availability for car 6, if it were a compact, it would need a sequence like "V, 7, V, 6, 5", leaving slot 5 unavailable, contradicting "Car 6 is a compact." So, this statement must be false.
• The absence of car 2 in the sequence doesn't affect whether it can be a compact, hence "Car 2 is a compact" cannot be false.

Thus, given the configuration and constraints, the only statement that must be false is "Car 6 is a compact."

Answer 8

"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 Correct answer is option (C): Car 6 is a compact.