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- Question
- 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?
Options- A. 16
- B. 18
- C. 19
- D. 25
- Correct Answer
- 25
ExplanationLet 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. - 1. Which of the following statements is true?
Options- 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.
- C. 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.
- D. The number of teams with exactly one win in the second stage of the tournament is 4 Discuss
- 2. What is the number of rounds in the second stage of the tournament?
Options- A. 1
- B. 2
- C. 3
- D. 4 Discuss
- 3. What is the highest number of wins for a team in the first stage in spite of which it would be eliminated at the end of first stage?
Options- A. 1
- B. 2
- C. 3
- D. 4 Discuss
- 4. If all the five teams have an equal score, what is the number of points scored by each team?
Options- A. 5
- B. 6
- C. 7
- D. None of these Discuss
- 5. If Paraguay has won all the matches and Turkey has lost all the matches and all the remaining three teams score equal points, how many points have each of the three remaining teams scored?
Options- A. 5
- B. 7
- C. 8
- D. None of these Discuss
- 6. Which one of the following statements is true about matches played in the first two rounds?
Options- A. Germany beat New Zealand by 1 goal to 0.
- B. Spain beat New Zealand by 4 goal to 0.
- C. Spain beat South Africa by 2 goals to 0.
- D. Germany beat South Africa by 2 goals to 1. Discuss
- 7. Which one of the following statements is true about matches played in the first two rounds?
Options- A. Pakistan beat South Africa by 2 goals to 1.
- B. Argentina beat Pakistan by 1 goal to 0.
- C. Germany beat Pakistan by 2 goals to 1.
- D. Germany beat Spain by 2 goals to 1. Discuss
- 8. Which team finished at the top of the pool after five rounds of matches?
Options- A. Argentina
- B. Germany
- C. Spain
- D. Cannot be determind Discuss
- 9. If Pakistan qualified as one of the two teams from Pool A, which was the other team that qualified?
Options- A. Argentina
- B. Germany
- C. Spain
- D. Cannot be determined Discuss
- 10. The teams that won exactly two matches in the event are:
Options- A. A, D and F
- B. D and E
- C. E and F
- D. D, E and F Discuss
Games and Tournament problems
Search Results
Correct Answer: 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.
Explanation:
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 Answer: 3
Explanation:
Since there are 8 teams and we know that 8 = 23 hence there are 3 rounds in 2nd stage.
Correct Answer: 1
Explanation:
The team which gets 1 point at 1st stage would be eliminated because the combination may be 6 points for the team and 2 times each for remaining. There are some more cases that supports the idea.
Correct Answer: None of these
Explanation:
The total score is 40 points. If each team scores equally, each team scores 40/5 = 8 points
Correct Answer: 8
Explanation:
Each match has 4 points and each team plays 4 matches. Hence total number of points is 40
Paraguay wins all matches. So it scores 3 x 4 = 12 points.
Turkey loses all matches. So it scores 1 x 4 = 4 points.
16 points are scored by Turkey and Paraguay
The other teams score 40 - 16 = 24 points
As all other teams score equal points, each team scores 24/3 = 8 points
Correct Answer: Spain beat New Zealand by 4 goal to 0.
Explanation:
Spain beat New Zealand by 4 goal to 0.
Correct Answer: Germany beat Spain by 2 goals to 1.
Explanation:
Germany beat Spain by 2 goals to 1.
Correct Answer: Spain
Explanation:
Spain
Correct Answer: Cannot be determined
Explanation:
Cannot be determined
Correct Answer:
Explanation:
D and F
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