CAT 2024 Slot 1 — DILR Question 11
Answer the following questions based on the information given below.
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.
Which team among the teams numbered 2, 3, 4, and 5 was not part of the same group?
Answer & solution
- A
3
- B
2
- C
4
5
Easy
The grouping is settled entirely by the "how many times two teams meet" rule: same‑group teams meet once, cross‑group teams meet twice. Combine Round‑8's cross‑group pairings (Facts 1 & 6) with the "met once / met twice" clues (Facts 3 & 4) to split the six teams into two groups of three.
Six teams (1–6) are split into two groups of three. Within a group every pair meets once; across groups every pair meets twice. Key facts used: (1) every Round‑8 game is cross‑group; (3) Team 4 played Team 6 in both R1 and R2; (4) Team 1 played Team 5 only once; (6) in R8, 3 v 6 and 2 v 5 (so the third R8 pair is 1 v 4).
| Clue | Teams | Times met | Conclusion |
|---|---|---|---|
| Fact 3 | 4 & 6 | ≥ 2 (R1, R2) | different groups |
| Fact 4 | 1 & 5 | exactly 1 | same group |
| Fact 6 / 1 | 1 & 4 | R8 cross pair | different groups |
Resulting groups: {1, 5, 6} and {2, 3, 4}.
Read the Round‑8 cross‑group pairs. Fact 1 says all of Round 8 is cross‑group, and Fact 6 names two of its games: 3 v 6 and 2 v 5. The six teams pair up, so the remaining R8 game is 1 v 4. Each of these pairs straddles the two groups.
Place teams 1, 4, 5, 6 with the "met-count" facts. Fact 4: 1 and 5 meet only once, so they share a group. Fact 3: 4 and 6 meet twice, so they are split. From step 1, 1 and 4 are split, so 4 sits opposite 1; then 6 (opposite 4) sits with 1.
The other three teams form the second group. The leftover teams 2, 3, 4 make up the other group of three. Check against step 1: 3 v 6, 2 v 5 and 1 v 4 are all cross‑group — consistent.