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CAT 2020 Slot 1 DILR · Set 4 of 5Logical ReasoningModerate DifficultyQ17–Q20 · 4 MCQ

CAT 2020 Slot 1 DILR Set 4: Arrangements (4 Questions) with Solutions

The Arrangements set from the official CAT 2020 Slot 1 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 1 DILR · Questions 17–20
The local office of the APP-CAB company evaluates the performance of five cab drivers, Arun, Barun, Chandan, Damodaran, and Eman for their monthly payment based on ratings in five different parameters (P1 to P5) as given below:
P1: timely arrival
P2: behaviour
P3: comfortable ride
P4: driver's familiarity with the route
P5: value for money
Based on feedback from the customers, the office assigns a rating from 1 to 5 in each of these parameters. Each rating is an integer from a low value of 1 to a high value of 5. The final rating of a driver is the average of his ratings in these five parameters. The monthly payment of the drivers has two parts - a fixed payment and final rating-based bonus. If a driver gets a rating of 1 in any of the parameters, he is not eligible to get bonus. To be eligible for bonus a driver also needs to get a rating of five in at least one of the parameters.
The partial information related to the ratings of the drivers in different parameters and the monthly payment structure (in rupees) is given in the table below:
P1P2P3P4P5Fixed PaymentBonus
Arun4Rs. 1000Rs. 250 × Final Rating
Barun3Rs. 1200Rs. 200 × Final Rating
Chandan2Rs. 1400Rs. 100 × Final Rating
Damodaran3Rs. 1300Rs. 150 × Final Rating
Eman2Rs. 1100Rs. 200 × Final Rating
The following additional facts are known.
1
Arun and Barun have got a rating of 5 in exactly one of the parameters. Chandan has got a rating of 5 in exactly two parameters.
2
None of drivers has got the same rating in three parameters.

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

Q17. Arrangements

MCQ · +3 / −1
If Damodaran does not get a bonus, what is the maximum possible value of his final rating?
  1. A) 3.63.6
  2. B) 3.83.8
  3. C) 3.23.2
  4. D) 3.43.4
Correct Answer
A) 3.63.6
Step-by-step solution
📌 Core Concept
No bonus means Damodaran has either a rating of 1 somewhere or no rating of 5. Fact 2 limits any one value to at most two parameters. Compare the best total under each case.
🔢 Step-by-Step Solution
1
Damodaran's P2 rating is 3, so 3 is one of his five ratings.
2
Case A: no rating of 5. Every rating is at most 4. Fact 2 allows at most two 4s and two 3s. The best set is 4, 4, 3, 3, 2, with sum 16 and average 3.23.2.
3
Case B: a rating of 1 is present. Take the highest remaining values: 5, 5, 4, 3 (the 3 is already fixed in P2). With the 1, the set is 5, 5, 4, 3, 1, with sum 18 and average 185=3.6\frac{18}{5} = 3.6.
4
Could Case B be higher? A second 4 would replace the 3, but the 3 is fixed in P2. Using 5, 5, 4, 4 with the 1 would leave no place for the 3. So 18 is the maximum sum.
5
Case B beats Case A, so the maximum is 3.63.6.
Why Not the Others
3.83.8 needs a sum of 19, such as 5, 5, 4, 4, 1. That set has no 3, but P2 = 3.
3.23.2 is only the best no-5 case, which is lower than 3.63.6.
3.43.4 is attainable but not the maximum.
Correct Answer: A

Q18. Arrangements

MCQ · +3 / −1
If Eman gets a bonus, what is the minimum possible value of his final rating?
  1. A) 3.4
  2. B) 2.8
  3. C) 3.0
  4. D) 3.2
Correct Answer
C) 3.0
Step-by-step solution
📌 Core Concept
A bonus needs no rating of 1 and at least one rating of 5. Fact 2 limits any one value to at most two parameters. Minimise the sum under these rules.
🔢 Step-by-Step Solution
1
Eman's P5 rating is 2. For a bonus he has no 1s and at least one 5.
2
One of the five ratings must be 5, so the remaining four include the fixed 2.
3
To keep the sum low, use small values. Fact 2 allows 2 at most twice, so the cheapest ratings are 2, 2, 3, 3. A third 2 is not allowed, and the next cheapest value after two 2s is 3.
4
The minimum set is 5, 3, 3, 2, 2, with sum 15.
5
Minimum final rating =155=3.0= \frac{15}{5} = 3.0.
Why Not the Others
2.82.8 needs a sum of 14. With a 5 included, the other four would sum to 9, which forces three equal values or a 1, and neither is allowed.
3.23.2 and 3.43.4 are attainable but not the minimum.
Quick Check
5, 3, 3, 2, 2 has no 1, one 5, and no value repeated three times.
Correct Answer: C

Q19. Arrangements

MCQ · +3 / −1
If all five drivers get bonus, what is the minimum possible value of the monthly payment (in rupees) that a driver gets?
  1. A) 1700
  2. B) 1740
  3. C) 1750
  4. D) 1600
Correct Answer
A) 1700
Step-by-step solution
📌 Core Concept
For each driver, find the smallest final rating that still qualifies for a bonus. Then compute payment == fixed ++ rate ×\times rating, and take the smallest payment.
🔢 Step-by-Step Solution
Every driver needs no 1 and at least one 5. No value may appear three times.
1
Arun has exactly one 5 and P4 = 4. The cheapest set is 5, 4, 3, 2, 2, with sum 16 and rating 3.2. Payment =1000+250×3.2=1800= 1000 + 250 \times 3.2 = 1800.
2
Barun has exactly one 5 and P1 = 3. The cheapest set is 5, 3, 3, 2, 2, with sum 15 and rating 3.0. Payment =1200+200×3.0=1800= 1200 + 200 \times 3.0 = 1800.
3
Chandan has exactly two 5s and P3 = 2. The other two ratings are 2 and 3, since a third 2 is barred. The set is 5, 5, 3, 2, 2, with sum 17 and rating 3.4. Payment =1400+100×3.4=1740= 1400 + 100 \times 3.4 = 1740.
4
Damodaran has P2 = 3 and at least one 5. The cheapest set is 5, 3, 3, 2, 2, with sum 15 and rating 3.0. Payment =1300+150×3.0=1750= 1300 + 150 \times 3.0 = 1750.
5
Eman has P5 = 2 and at least one 5. The cheapest set is 5, 3, 3, 2, 2, with rating 3.0. Payment =1100+200×3.0=1700= 1100 + 200 \times 3.0 = 1700.
6
The smallest of 1800, 1800, 1740, 1750 and 1700 is 1700, which is Eman's.
Quick Check
Eman's bonus is 200×3=600200 \times 3 = 600, and 1100+600=17001100 + 600 = 1700.
Correct Answer: A

Q20. Arrangements

MCQ · +3 / −1
If all five drivers get bonus, what is the maximum possible value of the monthly payment (in rupees) that a driver gets?
  1. A) 1960
  2. B) 1950
  3. C) 2050
  4. D) 1900
Correct Answer
A) 1960
Step-by-step solution
📌 Core Concept
For each driver, find the largest final rating allowed by the clues. Then compute payment == fixed ++ rate ×\times rating, and take the largest payment.
🔢 Step-by-Step Solution
Every driver needs a bonus, so no 1s and at least one 5. No value may appear three times.
1
Arun has exactly one 5 and P4 = 4. The other three ratings are at most 4, and 4 can appear only once more. The best set is 5, 4, 4, 3, 3, with sum 19 and rating 3.8. Payment =1000+250×3.8=1950= 1000 + 250 \times 3.8 = 1950.
2
Barun has exactly one 5 and P1 = 3. The best set is 5, 4, 4, 3, 3, with sum 19 and rating 3.8. Payment =1200+200×3.8=1960= 1200 + 200 \times 3.8 = 1960.
3
Chandan has exactly two 5s and P3 = 2. The other two ratings are at most 4, so the best set is 5, 5, 4, 4, 2, with sum 20 and rating 4.0. Payment =1400+100×4.0=1800= 1400 + 100 \times 4.0 = 1800.
4
Damodaran has P2 = 3. Two 5s and two 4s are allowed, so the best set is 5, 5, 4, 4, 3, with sum 21 and rating 4.2. Payment =1300+150×4.2=1930= 1300 + 150 \times 4.2 = 1930.
5
Eman has P5 = 2. The best set is 5, 5, 4, 4, 2, with sum 20 and rating 4.0. Payment =1100+200×4.0=1900= 1100 + 200 \times 4.0 = 1900.
6
The largest of 1950, 1960, 1800, 1930 and 1900 is 1960, which is Barun's.
Quick Check
Barun's bonus is 200×3.8=760200 \times 3.8 = 760, and 1200+760=19601200 + 760 = 1960.
Correct Answer: A
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CAT 2020 Slot 1 DILR at a Glance

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

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