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CAT 2021 Slot 2 DILR · Set 3 of 4Logical ReasoningModerate DifficultyQ9–Q14 · 4 MCQ + 2 TITA

CAT 2021 Slot 2 DILR Set 3: Games & Tournaments (6 Questions) with Solutions

The Games & Tournaments set from the official CAT 2021 Slot 2 DILR paper: the caselet, all 6 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 2021 Slot 2 DILR · Questions 9–14
Ravi works in an online food-delivery company. After each delivery, customers rate Ravi on each of four parameters Behaviour, Packaging, Hygiene, and Timeliness, on a scale from 11 to 9. If the total of the four rating points is 2525 or more, then Ravi gets a bonus of Rs. 2020 for that delivery. Additionally, a customer may or may not give Ravi a tip. If the customer gives a tip, it is either Rs. 3030 or Rs. 5050.
One day, Ravi made four deliveries - one to each of Atal, Bihari, Chirag and Deepak, and received a total of Rs. 120120 in bonus and tips. He did not get both a bonus and a tip from the same customer.
The following additional facts are also known.
1
In Timeliness, Ravi received a total of 2121 points, and three of the customers gave him the same rating points in this parameter. Atal gave higher rating points than Bihari and Chirag in this parameter.
2
Ravi received distinct rating points in Packaging from the four customers adding up to 2929 points. Similarly, Ravi received distinct rating points in Hygiene from the four customers adding up to 2626 points.
3
Chirag gave the same rating points for Packaging and Hygiene.
4
Among the four customers, Bihari gave the highest rating points in Packaging, and Chirag gave the highest rating points in Hygiene.
5
Everyone rated Ravi between 55 and 77 in Behaviour. Unique maximum and minimum ratings in this parameter were given by Atal and Deepak respectively.
6
If the customers are ranked based on ratings given by them in individual parameters, then Atal's rank based on Packaging is the same as that based on Hygiene. This is also true for Deepak.

In the exam this set competed with 3 others for 40 minutes. Budget about 10 minutes if you attempt it.

Q9. Games & Tournaments

TITA · +3 / 0
What was the minimum rating that Ravi received from any customer in any parameter?
Correct Answer
5
Step-by-step solution
📌 Core Concept
Fix each customer's ratings in all four parameters using the distinctness, rank and sum clues. The bonus-and-tip total then settles the one ambiguous case.
🔢 Step-by-Step Solution
1
Timeliness: three equal ratings xx and one different rating yy, with 3x+y=213x+y=21. Atal is higher than Bihari and Chirag, so Atal is the odd one out and y>xy>x. This gives (x,y)=(5,6)(x,y)=(5,6) or (4,9)(4,9).
2
Behaviour: ratings lie in 5 to 7, Atal is the unique maximum (7) and Deepak the unique minimum (5). So Bihari and Chirag each gave 6.
3
Hygiene: four distinct ratings sum to 26, so the maximum vv satisfies v+(v−1)+(v−2)+(v−3)≥26v+(v-1)+(v-2)+(v-3)\ge 26, which gives v≥8v\ge 8. Chirag is the Hygiene maximum, so Chirag's Hygiene is at least 8. By clue 3 his Packaging is the same value.
4
Bihari is the Packaging maximum, so he is above Chirag. Hence Chirag has 8 in both, Bihari has 9 in Packaging, and Chirag is second in Packaging.
5
Packaging: the other two ratings sum to 29−17=1229-17=12, which forces 7 and 5. Hygiene: the other three sum to 26−8=1826-8=18, which forces 7, 6 and 5. Bihari is second in Hygiene (7), so Atal and Deepak have 6 and 5.
6
Clue 6 says Atal and Deepak have the same rank in both parameters. So one has Packaging 7 and Hygiene 6, and the other has Packaging 5 and Hygiene 5.
7
Test the cases. If Deepak has (7, 6), Atal has (5, 5). Bonus counts then depend on the Timeliness case, and the totals must reach Rs.
120
8. If Timeliness is (4,9)(4,9), in every arrangement Atal, Bihari and Chirag score 25 or more and earn bonuses (Rs. 60). Deepak would need a tip of Rs. 60, which is impossible. So x=5x=5.
9
With x=5x=5, every rating is at least 5, and 5 appears (Deepak's Behaviour, for example).
Quick Check
The valid case has two bonuses (Rs. 40) plus tips of Rs. 30 and Rs. 50, which total Rs.
120
Correct Answer: 5

Q10. Games & Tournaments

MCQ · +3 / −1
The COMPLETE list of customers who gave the maximum total rating points to Ravi is
  1. A) Atal and Bihari
  2. B) Bihari
  3. C) Atal
  4. D) Bihari and Chirag
Correct Answer
D) Bihari and Chirag
Step-by-step solution
📌 Core Concept
Reconstruct every customer's four ratings, then compare the totals.
🔢 Step-by-Step Solution
1
Timeliness has three equal ratings with Atal higher than Bihari and Chirag, so Atal is the odd one. With 3x+y=213x+y=21, the options are (5,6)(5,6) or (4,9)(4,9).
2
Behaviour: Atal 7, Bihari 6, Chirag 6, Deepak 5.
3
Chirag's Hygiene is the maximum of four distinct ratings summing to 26, so it is at least 8. He has the same Packaging, and Bihari's Packaging is higher, so Chirag has 8 and 8 and Bihari has 9 in Packaging.
4
The remaining Packaging ratings are 7 and 5. The remaining Hygiene ratings are 7, 6 and 5, with Bihari second at 7. Atal and Deepak keep the same rank in both, so they take (7, 6) and (5, 5) in some order.
5
Timeliness (4,9)(4,9) would give Atal, Bihari and Chirag bonuses worth Rs. 60 and leave Deepak needing a Rs. 60 tip, which is impossible. So Timeliness is Atal 6 and the rest 5.
6
If Atal has (7, 6) and Deepak (5, 5), then Deepak totals 20 and the three others earn Rs. 60 in bonuses. Deepak would need a Rs. 60 tip, which is impossible. So Atal has (5, 5) and Deepak has (7, 6).
7
Totals, as Behaviour + Packaging + Hygiene + Timeliness:
Atal: 7+5+5+6=237+5+5+6=23
Bihari: 6+9+7+5=276+9+7+5=27
Chirag: 6+8+8+5=276+8+8+5=27
Deepak: 5+7+6+5=235+7+6+5=23
Why Not the Others
A, B, C: Atal scores only 23, and Bihari alone does not cover Chirag, who also scores 27.
Correct Answer: D

Q11. Games & Tournaments

TITA · +3 / 0
What rating did Atal give on Timeliness?
Correct Answer
6
Step-by-step solution
📌 Core Concept
The Timeliness clue gives two possible values for Atal. The bonus-and-tip total decides between them.
🔢 Step-by-Step Solution
1
Three customers gave equal Timeliness ratings xx and one gave yy, with 3x+y=213x+y=21. Atal is higher than Bihari and Chirag, so Atal cannot be one of the equal three. He is the odd one, and y>xy>x.
2
The only options with ratings of at most 9 are x=5,y=6x=5,y=6 or x=4,y=9x=4,y=9.
3
Behaviour is 7, 6, 6, 5 for Atal, Bihari, Chirag, Deepak.
4
Packaging and Hygiene are forced. Chirag's Hygiene is at least 8, because four distinct ratings summing to 26 need a maximum of at least 8. Chirag has 8 in both, and Bihari has 9 in Packaging. The other Packaging ratings are 7 and 5. The other Hygiene ratings are 7 (Bihari), 6 and 5.
5
Atal and Deepak each have the same rank in Packaging and Hygiene, so they take (7, 6) and (5, 5).
6
If Atal's Timeliness is 9, then Atal, Bihari and Chirag all total at least 25 in every arrangement. That gives Rs. 60 in bonuses, and Deepak would need a Rs. 60 tip, which is impossible.
7
So the Timeliness values are x=5x=5 and y=6y=6, and Atal's rating is 6.
Quick Check
With Atal on 6, Atal and Deepak both total 23 and earn no bonus. Bihari and Chirag earn Rs. 40 in bonuses. Tips of Rs. 30 and Rs. 50 bring the total to Rs.
120
Correct Answer: 6

Q12. Games & Tournaments

MCQ · +3 / −1
What BEST can be concluded about the tip amount given by Deepak?
  1. A) Either Rs. 0 or Rs. 30 or Rs. 50
  2. B) Rs. 50
  3. C) Either Rs. 30 or Rs. 50
  4. D) Rs. 30
Correct Answer
C) Either Rs. 30 or Rs. 50
Step-by-step solution
📌 Core Concept
Find who earns a bonus. The Rs. 120 total and the rule that no customer gives both a bonus and a tip then fix the tips.
🔢 Step-by-Step Solution
1
Timeliness is Atal 6 and the other three 5. The alternative, Atal 9 and the others 4, is impossible because it leaves Deepak needing a Rs. 60 tip.
2
Behaviour is Atal 7, Bihari 6, Chirag 6, Deepak 5.
3
Packaging and Hygiene (Chirag 8 and 8, Bihari 9 and 7) leave Atal and Deepak with (7, 6) and (5, 5). The case where Atal has (7, 6) gives Atal a total of 26 and Deepak 20. Then three bonuses (Rs. 60) leave only Deepak to tip, and a tip of Rs. 60 is impossible. So Atal has (5, 5) and Deepak has (7, 6).
4
Totals: Atal 7+5+5+6=237+5+5+6=23, Bihari 27, Chirag 27, Deepak 5+7+6+5=235+7+6+5=23.
5
Only Bihari and Chirag reach 25, so bonuses total Rs.
40
6. The remaining Rs. 80 must come from tips by Atal and Deepak, since Bihari and Chirag already have bonuses. Each tip is Rs. 30 or Rs. 50, so the pair is Rs. 30 and Rs. 50 (the only way to make 80).
7
Deepak therefore gave a tip of Rs. 30 or Rs.
50
This cannot be narrowed further, and Rs. 0 is ruled out.
Why Not the Others
A: Rs. 0 is impossible, because both Atal and Deepak must tip.
B and D: either person could have given either amount, so neither value alone is forced.
Correct Answer: C

Q13. Games & Tournaments

MCQ · +3 / −1
In which parameter did Atal give the maximum rating points to Ravi?
  1. A) Hygiene
  2. B) Packaging
  3. C) Timeliness
  4. D) Behaviour
Correct Answer
D) Behaviour
Step-by-step solution
📌 Core Concept
Reconstruct Atal's four ratings and find the largest.
🔢 Step-by-Step Solution
1
Behaviour: ratings are in 5 to 7, Atal is the unique maximum, so he gave 7.
2
Timeliness: Atal is the odd one out in 3x+y=213x+y=21 with y>xy>x. The options are 6 or 9. The case 9 would give Atal, Bihari and Chirag bonuses worth Rs. 60 and leave Deepak needing a tip of Rs. 60, which is impossible. So Atal gave 6.
3
Packaging and Hygiene: Chirag's Hygiene is the maximum of four distinct ratings summing to 26, so it is at least 8. He has the same Packaging, which is below Bihari's, so Chirag has 8 and 8 and Bihari has 9 in Packaging. Atal and Deepak then take (7, 6) and (5, 5) in Packaging and Hygiene.
4
If Atal had (7, 6), the three customers other than Deepak would earn Rs. 60 in bonuses. Deepak would have to tip Rs. 60, which is impossible. So Atal has Packaging 5 and Hygiene 5.
5
Atal's ratings are Behaviour 7, Packaging 5, Hygiene 5, Timeliness 6. His maximum is in Behaviour.
Why Not the Others
A and B: both are only 5.
C: Timeliness is 6, which is less than 7.
Correct Answer: D

Q14. Games & Tournaments

MCQ · +3 / −1
What rating did Deepak give on Packaging?
  1. A) 7
  2. B) 5
  3. C) 6
  4. D) 8
Correct Answer
A) 7
Step-by-step solution
📌 Core Concept
Packaging and Hygiene are almost fully fixed by the sums and rank clues. The bonus-and-tip total then decides who got 7.
🔢 Step-by-Step Solution
1
Hygiene has four distinct ratings summing to 26. Its maximum vv must satisfy 4v−6≥264v-6\ge 26, so v≥8v\ge 8. Chirag is the Hygiene maximum, so his Hygiene is at least 8, and his Packaging is the same by clue 3.
2
Bihari's Packaging is the highest, so it is above Chirag's. This forces Chirag's two ratings to be 8 and Bihari's Packaging to be 9.
3
The other two Packaging ratings sum to 29−17=1229-17=12 and are distinct and below 8, so they are 7 and 5. These belong to Atal and Deepak.
4
The Hygiene ratings of Bihari, Atal and Deepak sum to 26−8=1826-8=18, so they are 7, 6 and 5. Bihari must be second in Hygiene (as Chirag is first and Bihari second in Packaging), so he has 7. Atal and Deepak have 6 and 5, and keep the same rank in both parameters. So the pairs (Packaging, Hygiene) are (7, 6) and (5, 5).
5
Behaviour is 7, 6, 6, 5 and Timeliness is Atal 6 with the rest 5. The case with Timeliness 9 for Atal is impossible, because Deepak would need a Rs. 60 tip.
6
Suppose Atal has (7, 6). Then Atal totals 26 and Bihari and Chirag total 27. Deepak totals 20, and bonuses of Rs. 60 would leave only Deepak to tip Rs. 60, which is impossible.
7
So Deepak has (7, 6) and Atal has (5, 5). Atal and Deepak then both total 23, so no bonus, and they tip Rs. 30 and Rs. 50 in some order. The total is 40+80=12040+80=120, as required.
8
Deepak's Packaging rating is 7.
Why Not the Others
B (5): this is Atal's Packaging rating.
C (6) and D (8): 6 is not a Packaging rating at all, and 8 is Chirag's.
Correct Answer: A
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CAT 2021 Slot 2 DILR at a Glance

Sets in this section4
Questions in this section20
Section time40 minutes
Convenor IIMIIM Ahmedabad

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