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CAT 2024 Slot 1 DILR · Set 1 of 5Logical ReasoningHard DifficultyQ1–Q5 · 1 MCQ + 4 TITA

CAT 2024 Slot 1 DILR Set 1: Games & Tournaments (5 Questions) with Solutions

The Games & Tournaments set from the official CAT 2024 Slot 1 DILR paper: the caselet, all 5 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 2024 Slot 1 DILR · Questions 1–5
The game of QUIET is played between two teams. Six teams, numbered 1, 2, 3, 4, 5, and 6, play in a QUIET tournament. These teams are divided equally into two groups. In the tournament, each team plays every other team in the same group only once, and each team in the other group exactly twice. The tournament has several rounds, each of which consists of a few games. Every team plays exactly one game in each round.
The following additional facts are known about the schedule of games in the tournament.
1
Each team played against a team from the other group in Round 8.
2
In Round 4 and Round 7, the match-ups, that is the pair of teams playing against each other, were identical. In Round 5 and Round 8, the match-ups were identical.
3
Team 4 played Team 6 in both Round 1 and Round 2.
4
Team 1 played Team 5 ONLY once and that was in Round 2.
5
Team 3 played Team 4 in Round 3. Team 1 played Team 6 in Round 6.
6
In Round 8, Team 3 played Team 6, while Team 2 played Team 5.

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

Q1. Games & Tournaments

TITA · +3 / 0
How many rounds were there in the tournament?
Correct Answer
8
Step-by-step solution
Clue Breakdown:
1
Group Structure: 6 teams divided into two groups of 3.
2
Game Frequency: Each team plays intra-group teams once and inter-group teams twice.
3
Round Structure: Each round has 3 games (6 teams, 2 per game).
4
Total Games: 24 (6 teams * 8 games / 2).
5
Rounds Calculation: 24 games / 3 games per round = 8 rounds.
Step-by-Step Deduction Grid:
Each team plays 8 games.
Each round consists of 3 games.
Total rounds = 8.
Question Resolution: The tournament requires 8 rounds to accommodate all games.
Final Answer Confirmation: Correct Answer: 8

Q2. Games & Tournaments

TITA · +3 / 0
What is the number of the team that played Team 1 in Round 5?
Correct Answer
4
Step-by-step solution
📌 Core Concept
First split the six teams into two groups of three using the clues that show which pairs meet once and which meet twice. Then use the fact that Round 5 and Round 8 have identical match-ups.
🔢 Step-by-Step Solution
1
A pair in the same group meets once, and a pair in different groups meets twice. Clue 3 has Teams 4 and 6 meeting in both Round 1 and Round 2, so they are in different groups.
2
Clue 4 says Teams 1 and 5 met only once, so they are in the same group.
3
Round 8 is entirely cross-group (Clue 1). Clue 6 gives 3 v 6 and 2 v 5, so 3 and 6 are in different groups, and so are 2 and 5. The remaining pair in Round 8 is 1 v 4, so 1 and 4 are in different groups.
4
Take the group containing 1 and 5. Team 2 cannot join it, since 2 and 5 are in different groups. Team 4 cannot join it, since 1 and 4 are in different groups. Team 6 is therefore in it, because 4 is not with 6 and the third place must go to 3 or 6, and 3 is kept apart from 6. This gives groups {1, 5, 6} and {2, 3, 4}.
5
Round 8 match-ups are 3 v 6, 2 v 5 and 1 v 4. Clue 2 says Round 5 has identical match-ups, so in Round 5 Team 1 plays Team 4.
Quick Check
In Round 5 the match-ups are 1 v 4, 2 v 5 and 3 v 6. Each team plays exactly once, and every game is cross-group.
Correct Answer: 4

Q3. Games & Tournaments

MCQ · +3 / −1
Which team among the teams numbered 2, 3, 4, and 5 was not part of the same group?
  1. A) 4
  2. B) 5
  3. C) 3
  4. D) 2
Correct Answer
B) 5
Step-by-step solution
📌 Core Concept
Teams that meet exactly once are in the same group, and teams that meet twice are in different groups. The clues fix both groups completely.
🔢 Step-by-Step Solution
1
Clue 3: Teams 4 and 6 meet in Rounds 1 and 2, so they are in different groups.
2
Clue 4: Teams 1 and 5 meet only once, so they are in the same group.
3
Round 8 is entirely cross-group (Clue 1). Clue 6 gives 3 v 6 and 2 v 5, so 3 and 6 are in different groups, and so are 2 and 5. The leftover Round 8 game is 1 v 4, so 1 and 4 are in different groups.
4
Teams 2 and 4 are both in the group opposite Team 1 and Team 5. Team 2 is opposite Team 5, and Team 4 is opposite Team 1, which is in the same group as 5.
5
Team 6 is opposite Team 4, so it joins 1 and 5. Team 3 is opposite Team 6, so it joins 2 and 4.
6
The groups are {1, 5, 6} and {2, 3, 4}. Among 2, 3, 4 and 5, Teams 2, 3 and 4 are together and Team 5 is the odd one out.
Why Not the Others
A) Team 4 is in the group {2, 3, 4}.
C) Team 3 is in the group {2, 3, 4}.
D) Team 2 is in the group {2, 3, 4}.
Correct Answer: B

Q4. Games & Tournaments

TITA · +3 / 0
What is the number of the team that played Team 1 in Round 7?
Correct Answer
3
Step-by-step solution
📌 Core Concept
First fix the groups, {1, 5, 6} and {2, 3, 4}. Then list Team 1's eight games, using the fact that Rounds 4 and 7 have identical match-ups.
🔢 Step-by-Step Solution
1
Clues 3, 4 and 6 give the groups {1, 5, 6} and {2, 3, 4}. Team 1 plays 5 and 6 once each and plays each of 2, 3 and 4 twice.
2
Fixed games for Team 1: Round 2 against 5 (Clue 4), Round 6 against 6 (Clue 5), and Round 8 against 4 (Clue 6). Round 5 repeats Round 8 (Clue 2), so Round 5 is also against 4.
3
Round 3 has 3 v 4. The other four teams are 1, 2, 5 and 6. Team 1 cannot meet 5 again, and cannot meet 6 again since that happens only in Round 6. So Round 3 is 1 v 2 and 5 v 6.
4
Team 1's games still open are Rounds 1, 4 and 7. Team 1 has played 4 twice and 2 once. It still needs 2 once and 3 twice.
5
Rounds 4 and 7 have identical match-ups (Clue 2), so Team 1 plays the same opponent in both. That opponent must be the one needed twice, which is Team 3. Round 1 is then 1 v 2.
Quick Check
Team 1's opponents in order are 2, 5, 2, 3, 4, 6, 3, 4. That gives 2, 3 and 4 twice each and 5 and 6 once each.
Correct Answer: 3

Q5. Games & Tournaments

TITA · +3 / 0
What is the number of the team that played Team 6 in Round 3?
Correct Answer
5
Step-by-step solution
📌 Core Concept
First fix the groups, {1, 5, 6} and {2, 3, 4}. Then use the one-game-only pairs to settle who plays whom in Round 3.
🔢 Step-by-Step Solution
1
Clues 3, 4 and 6 give the groups {1, 5, 6} and {2, 3, 4}. Pairs inside a group meet exactly once.
2
Clue 5 gives Round 3 as 3 v 4. The other four teams are 1, 2, 5 and 6, which can pair up as (1 v 2, 5 v 6) or (1 v 6, 2 v 5).
3
Team 1 plays Team 6 in Round 6 (Clue 5). Those two are in the same group, so they meet only once. Round 3 therefore cannot be 1 v 6.
4
Round 3 is 1 v 2 and 5 v 6, so Team 6 plays Team 5.
Quick Check
5 v 6 is an in-group pair and this is its only meeting. Round 3 has 1 v 2, 3 v 4 and 5 v 6, and every team plays once.
Correct Answer: 5
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CAT 2024 Slot 1 DILR at a Glance

Sets in this section5
Questions in this section22
Section time40 minutes
Convenor IIMIIM Calcutta

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