Games And Tournament
Direction: 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 points 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.
- What is the number of rounds in the second stage of the tournament?
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Since there are 8 teams and we know that 8 = 23 hence there are 3 rounds in 2nd stage.
Correct Option: C
Since there are 8 teams and we know that 8 = 23 hence there are 3 rounds in 2nd stage.
- Which of the following statements is true?
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From the discussion above we can say that. It is 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.
Correct Option: C
From the discussion above we can say that. It is 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.
- The football league of a certain country is played according to the following rules:
* Each team plays exactly one game against each of the other teams.
* The winning team of each game is awarded I point and the losing team gets 0 point.
* If a match ends in a draw, both the teams get 1/2 point. After the league was over, the teams were ranked according to the points that they earned at the end of the tournament. Analysis of the points table revealed the following:
* Exactly half of the points earned by each team were earned in games against the ten teams which finished at the bottom of the table.
* Each of the bottom ten teams earned half of their total points against the other nine teams in the bottom ten.
How many teams participated in the league?
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Let total number of teams participated in tournament is n + 10
There are 10 terms in the bottom group then n teams in the top group. It is given that the bottom group gets 45 points since we have 1 point per match therefore 45 matches playing amongst themselves. Therefore they should get 45 points from their matches against the top group i.e., 45 out of the 10n points. The top group get nC2 points from the matches among themselves. They also get 10n - 45 points against the bottom group, which is half their total points.
Hence nC2 = 10n - 45 or n(n + 1) = 20n - 90 or n2 - 21n + 90 = 0 hence n = 6 or 15
If n = 6, the top ground would get nC2 + 10n - 45 = nC2 + 10(6) - 45 = 30 points, or an average of 5 points per team, while the bottom group would get (45 + 45) / 10 or an average of 9. This is not possible.
Hence n = 15. Then total number of teams is 10 + 15 = 25.Correct Option: D
Let total number of teams participated in tournament is n + 10
There are 10 terms in the bottom group then n teams in the top group. It is given that the bottom group gets 45 points since we have 1 point per match therefore 45 matches playing amongst themselves. Therefore they should get 45 points from their matches against the top group i.e., 45 out of the 10n points. The top group get nC2 points from the matches among themselves. They also get 10n - 45 points against the bottom group, which is half their total points.
Hence nC2 = 10n - 45 or n(n + 1) = 20n - 90 or n2 - 21n + 90 = 0 hence n = 6 or 15
If n = 6, the top ground would get nC2 + 10n - 45 = nC2 + 10(6) - 45 = 30 points, or an average of 5 points per team, while the bottom group would get (45 + 45) / 10 or an average of 9. This is not possible.
Hence n = 15. Then total number of teams is 10 + 15 = 25.
Direction: Answer the questions on the basis of the information given below.
The year was 2006. All six teams in pool A World Cup hockey, play each other only once. Each win earns a team three points, a draw earns one point and loss earns zero points. The two teams with the highest points qualify for the semi-finals. In case of tie, the team with highest goal difference (Goal for - Goals Against) qualifies.
In the opening match, Spain lost to Germany. After the second round (After each team played two matches). the pool table looked as shown below.
In the third round. Spain played Pakistan, Argentina played Germany, and New Zealand played South Africa.
All the third round matches were drawn. The following are some results from the fourth and fifth round matches.
(a) Spain won both the fourth and fifth round matches.
(b) Both Argentina and Germany won their fifth round matches by 3 goal to 0.
(c) Pakistan won both the fourth and fifth round matches by 1 goal to 0.
- Which one of the following statements is true about matches played in the first two rounds?
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Spain beat New Zealand by 4 goal to 0.
Correct Option: B
Spain beat New Zealand by 4 goal to 0.
- Which one of the following statements is true about matches played in the first two rounds?
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Germany beat Spain by 2 goals to 1.
Correct Option: D
Germany beat Spain by 2 goals to 1.
