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CAT 2020 Slot 2 DILR · Set 5 of 5Logical ReasoningEasy DifficultyQ21–Q24 · 4 MCQ

CAT 2020 Slot 2 DILR Set 5: Arrangements (4 Questions) with Solutions

The Arrangements set from the official CAT 2020 Slot 2 DILR paper: the caselet, all 4 questions, the official answer key and a step-by-step solution for each. 100% free, no sign-up.

The Set: Read the Caselet First

CAT 2020 Slot 2 DILR · Questions 21–24
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.

In the exam this set competed with 4 others for 40 minutes. Budget about 8 minutes if you attempt it.

Q21. Arrangements

MCQ · +3 / −1
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?
  1. A) 8
  2. B) 5
  3. C) 7
  4. D) 6
Correct Answer
C) 7
Step-by-step solution
📌 Core Concept
Simulate the row slot by slot, using the first-fit rule: each car takes the first place from the left where it fits. An SUV needs two adjacent vacant slots.
🔢 Step-by-Step Solution
1
Initial arrivals: car 1 (SUV) takes slots 1-2, car 2 takes slot 3, car 3 takes slot 4, car 4 (SUV) takes slots 5-6. Row: 1,1,2,3,4,4.
2
Car 1 leaves, so slots 1-2 are vacant.
3
Car 5 (compact) takes slot 1. Only slot 2 is now vacant in the front part, so car 6 (an SUV) cannot use it. Car 6 goes to the first pair of adjacent vacant slots, slots 7-8. Row: 5,V,2,3,4,4,6,6.
4
Car 4 leaves, so slots 5-6 are vacant.
5
Car 7 (SUV) needs two adjacent vacant slots. Slot 2 is a single gap, so car 7 takes slots 5-6.
6
Car 8 (compact) takes the first vacant slot, slot 2. Row: 5,8,2,3,7,7,6,6.
7
Car 3 is in slot 4. Its neighbours are car 2 (slot 3) and car 7 (slot 5). Car 7 is the only neighbour among the options.
Why Not the Others
8: car 8 is in slot 2, next to cars 5 and 2.
5: car 5 is in slot 1, which is not adjacent to slot 4.
6: car 6 is in slots 7-8, far from car 3.
Correct Answer: C

Q22. Arrangements

MCQ · +3 / −1
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. A) 8, 2, 3, V, 5, 6, 7
  2. B) 8, 2, 3, V, 6, 5, 7
  3. C) V, 2, 3, 7, 5, 6, 8
  4. D) 8, 2, 3, V, 5, 7, 6
Correct Answer
A) 8, 2, 3, V, 5, 6, 7
Step-by-step solution
📌 Core Concept
First-fit parking fixes the order of cars along the row. A later arrival can sit ahead of an earlier one only by filling a gap that opened after the earlier car parked, and an SUV cannot fill a single-slot gap.
🔢 Step-by-Step Solution
1
Eight cars have arrived and two have left. Every option omits cars 1 and 4, so cars 1 and 4 are the ones that left. Car 4 is compact, so its departure leaves a single-slot gap.
2
Option A, 8, 2, 3, V, 5, 6, 7, can be built. Cars 1-6 are compact. Car 1 leaves. Car 7 (SUV) cannot use the single gap in slot 1, so it goes to the end. Car 4 leaves, leaving V in slot 4. Car 8 (compact) takes slot 1.
3
Option A keeps 5, 6, 7 in arrival order. The only vacancy is the single slot left by car 4, and no later car could have used it except a compact. This is consistent with the facts given.
Why Not the Others
B: car 6 sits ahead of car 5, although car 5 arrived first. Car 6 could only get ahead of car 5 by filling a gap that opened ahead of it, and the V in slot 4 would then have been filled.
C: car 7 (SUV) sits in the slot where compact car 4 was. That gap is a single slot followed by occupied slots, so an SUV cannot fit there. Cars 5 and 6, which arrived before 7, also appear after it.
D: car 7 sits ahead of car 6, although car 6 arrived first. The only gaps are those left by cars 1 and 4, which lie before car 5, so nothing places 7 between 5 and 6.
Correct Answer: A

Q23. Arrangements

MCQ · +3 / −1
Suppose the sequence at some point of time is 4, 5, 6, V,
3
Which of the following is NOT necessarily true?
  1. A) Car 3 is an SUV
  2. B) Car 5 is a compact
  3. C) Car 4 is a compact
  4. D) Car 1 is an SUV
Correct Answer
A) Car 3 is an SUV
Step-by-step solution
📌 Core Concept
Work backwards from the row 4, 5, 6, V, 3 using first-fit parking. Car 3 arrived before cars 4, 5 and 6 but is parked after them, so cars 1 and 2 must have occupied the slots ahead of it. Then decide which statements are forced.
🔢 Step-by-Step Solution
1
Car 3 arrived before cars 4, 5 and 6, yet it is parked after them. So when car 3 arrived, the slots ahead of it were already taken by cars 1 and 2.
2
Cars 4, 5 and 6 later took those slots after cars 1 and 2 left. The four slots ahead of car 3 held cars 1 and 2, so both must be SUVs with two slots each. Car 1 being an SUV is therefore forced (D is necessarily true).
3
Cars 4, 5, 6 and the V now fill those four slots, one slot each. Cars 4 and 5 therefore each occupy a single slot, so they are compact (C and B are necessarily true).
4
Car 3 sits in the fifth slot. The row gives nothing that decides whether it takes one slot or two, because both cases fit what is shown. So car 3 being an SUV is not forced.
Why Not the Others
B: car 5 occupies one slot, so it is compact.
C: car 4 occupies one slot, so it is compact.
D: slots ahead of car 3 can only be filled by two SUVs, cars 1 and 2.
Correct Answer: A

Q24. Arrangements

MCQ · +3 / −1
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. A) Car 4 is an SUV
  2. B) Car 2 is a compact
  3. C) Car 6 is a compact
  4. D) Car 7 is a compact
Correct Answer
C) Car 6 is a compact
Step-by-step solution
📌 Core Concept
Compare arrival order with row order. A car that parks in an earlier slot than a car that arrived before it must have used a gap left by a departure. A compact car always takes the first single gap, so an SUV is the only car that can skip one.
🔢 Step-by-Step Solution
1
Cars 1-7 have arrived and car 8 has not. The row is V, 7, 3, 6, 5. Cars 1, 2 and 4 are missing, so they have left.
2
Car 6 arrived after car 5 but sits ahead of it. So car 6 took the slot left by car 4 after car 4 had left. Car 7 sits in slot 2 and the V is in slot 1, so a gap ahead of car 4's slot (from car 1 or car 2) was still vacant when car 6 arrived.
3
Car 4 is not the first to leave, so car 1 or car 2 left before car 4. That earlier vacancy is a single slot. If both had left, the two adjacent gaps would have been usable.
4
Car 6 arrived after car 4 left, but it did not take that earlier single gap. It took car 4's place instead. A compact car would have taken the first available slot, which was the earlier single gap. So car 6 is an SUV, and statement C, car 6 is a compact, must be false.
5
The other statements can all hold. Car 4 being an SUV fits, since car 6 fills its place. Car 2 can be compact, and car 7 can be compact.
Why Not the Others
A: car 4 being an SUV is consistent, since car 6 fits its place.
B: car 2 can be compact and still leave a single gap.
D: car 7 can be compact and sit in the slot car 2 left.
Correct Answer: C
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CAT 2020 Slot 2 DILR at a Glance

Sets in this section5
Questions in this section24
Section time40 minutes
Convenor IIMIIM Indore

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