CAT 2024 Set-1 | Data Interpretation and Logical Reasoning | Question: 1

Question

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 $5$.

How many rounds were there in the tournament?