CAT 2000 — QA Question 38
Answer the following question based on the information given below.
Sixteen teams have been invited to participate in the ABC Gold Cup cricket tournament. The tournament is conducted in two stages. In the first stage, the teams are divided into two groups. Each group consists of eight teams, with each team playing every other team in its group exactly once. At the end of the first stage, the top four teams from each group advance to the second stage while the rest are eliminated. The second stage comprises of several rounds. A round involves one match for each team. The winner of a match in a round advances to the next round, while the loser is eliminated. The team that remains undefeated in the second stage is declared the winner and claims the Gold Cup.
The tournament rules are such that each match results in a winner and a loser with no possibility of a tie. In the first stage, a team earns one point for each win and no points for a loss. At the end of the first stage teams in each group are ranked on the basis of total points to determine the qualifiers advancing to the next stage. Ties are resolved by a series of complex tie-breaking rules so that exactly four teams from each group advance to the next stage.
Which of the following statements is true?
Answer & solution
- A
The winner will have more wins than any other team in the tournament.
- B
At the end of the first stage, no team eliminated from the tournament will have more wins than any of the teams qualifying for the second stage.
It is the possible that the winner will have the same number of wins in the entire tournament as a team eliminated at the end of the first stage.
- D
The number of teams with exactly one win in the second stage of the tournament is 4.
We have seen that even if a team wins 2 matches, it can be in the second stage of the tournament. Consider Team A wins 2 matches and enters the second round and wins the tournament. Then its total score will be 5 points. While there can be a team having more than 6 points but not the winner of the tournament. Thus, option 1 may not be true.
We have seen that even if a team wins 5 matches is can be eliminated and a team winning only two matches can enter second round. Thus, option 2 may not be true.
Consider a team in group I eliminated and the score is 5. A team in group II advances to the second stage with score 2. If this team (i.e. the team with score 2) is a winner then the score will be 2 + 3 = 5. Thus, option 3 is true.
Eight teams enter second stage. Of these, 4 teams advances to the second round scoring 1 point each. In the second round, only two teams win and their score in the second round so far will be 2. Thus, only two teams will have score 1. Thus, option 4 is not true.
Hence, option (c).