CAT 2024 Slot 1 DILR Set 3 Q9–Q13

A DILR caselet from the Data Interpretation & Logical Reasoning (DILR) section of CAT 2024 Slot 1, with 5 questions (Games & Tournaments). Answers are CAT's official key.

The set

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.

Question 9

How many rounds were there in the tournament?

TITA: type in the answer. There are no options and no negative marking.

Answer: 8 Games & Tournaments TITA

Solution

  1. Each team plays the 2 teams in its own group once and the 3 in the other group twice, which is \(2 + 6 = 8\) games, one per round. So there are 8 rounds.
  2. Every team plays one game per round, so the number of rounds equals the games per team: \(2 \times 1 + 3 \times 2 = 8\).

Question 10

What is the number of the team that played Team 1 in Round 5?

TITA: type in the answer. There are no options and no negative marking.

Answer: 4 Games & Tournaments TITA

Solution

  1. Team 4 played Team 6 twice, so they are in different groups. Team 1 played Team 5 once, so they are in the same group. Round 8 was all cross-group, so 3 and 6, and 2 and 5, are in different groups.
  2. This gives groups \(\{1,5,6\}\) and \(\{2,3,4\}\). Round 8 is 3-6, 2-5, 1-4, and Round 5 repeats it.
  3. Round 5 has the same match-ups as Round 8, where Team 1 played Team 4.

Question 11

Which team among the teams numbered 2, 3, 4, and 5 was not part of the same group?
  1. A
    5
  2. B
    2
  3. C
    4
  4. D
    3

Answer: (A) 5 Games & Tournaments MCQ

Solution

  1. Team 4 played Team 6 twice, so they are in different groups. Team 1 played Team 5 once, so they are in the same group. Round 8 was all cross-group, so 3 and 6, and 2 and 5, are in different groups.
  2. This gives groups \(\{1,5,6\}\) and \(\{2,3,4\}\). Round 8 is 3-6, 2-5, 1-4, and Round 5 repeats it.
  3. Teams 2, 3 and 4 form one group and Team 5 is in the other, so the answer is 5.

Question 12

What is the number of the team that played Team 1 in Round 7?

TITA: type in the answer. There are no options and no negative marking.

Answer: 3 Games & Tournaments TITA

Solution

  1. Team 4 played Team 6 twice, so they are in different groups. Team 1 played Team 5 once, so they are in the same group. Round 8 was all cross-group, so 3 and 6, and 2 and 5, are in different groups.
  2. This gives groups \(\{1,5,6\}\) and \(\{2,3,4\}\). Round 8 is 3-6, 2-5, 1-4, and Round 5 repeats it.
  3. Round 4 = Round 7 must use pairs that meet twice (cross-group). Team 6's only remaining twice-pair is 6-2, which forces 1-3 and 4-5. Filling in the rest: R1: 4-6, 1-2, 3-5. R2: 4-6, 1-5, 2-3. R3: 3-4, 1-2, 5-6. R6: 1-6, 2-4, 3-5.
  4. Round 7 repeats Round 4: 1-3, 2-6, 4-5. So Team 1 played Team 3.

Question 13

What is the number of the team that played Team 6 in Round 3?

TITA: type in the answer. There are no options and no negative marking.

Answer: 5 Games & Tournaments TITA

Solution

  1. Team 4 played Team 6 twice, so they are in different groups. Team 1 played Team 5 once, so they are in the same group. Round 8 was all cross-group, so 3 and 6, and 2 and 5, are in different groups.
  2. This gives groups \(\{1,5,6\}\) and \(\{2,3,4\}\). Round 8 is 3-6, 2-5, 1-4, and Round 5 repeats it.
  3. Round 4 = Round 7 must use pairs that meet twice (cross-group). Team 6's only remaining twice-pair is 6-2, which forces 1-3 and 4-5. Filling in the rest: R1: 4-6, 1-2, 3-5. R2: 4-6, 1-5, 2-3. R3: 3-4, 1-2, 5-6. R6: 1-6, 2-4, 3-5.
  4. In Round 3, besides 3-4, the leftover pairs are 1-2 (its second game) and 5-6 (in-group). So Team 6 played Team 5.

Same concept in other years

See every question on Tournament with groups: reconstruct match schedule and results.

More Games & Tournaments questions from CAT

All 29 Games & Tournaments questions asked since 2017.