@gaurav23march said:
I know this question already discussed with many times but still the concept is not clear:
can someone solve this with proper approach i mean no shortcut.Please solve with detailed solution
and IMPORTANT thing if no of teams wil be odd like 11 team in each pool and 4 team will qualify for next round such scenerios also cover so that jab next time CAT kaise bhi question de to jyaada dimaag wahan naa lagana pade.
16 teams have been invited to ABC Gold Cup tournament. The tournament was conducted in two stages. In the 1st stage teams are divided into two groups. Each group of 8 teams with each team playing every other team in its group exactly once.At the end of the 1st stage,the top 4 teams from each group advance to the next stage while 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 2nd stage is declared the winner.
Rules are such that there is no possibility of a tie.
Stage 1- 1 point for a win, no for loss
At the end of the 1st stage,teams ineach group are ranked on the basis of the total points to determine the qualifiers to the next stage. Ties are resolved by a series of complex tie breaking rules so that exactly 4 teams from each group advance to the next stage.
1. What is the total no of matches played in the tournament?
1. 28 2.55 3.63 4.35
2.The minimum no of wins needed for a team in the first stage to guarantee its advancement to next stage is...
1.5 2.6 3.7 4.4
3.What is the highest no of wins for a team in the first stage inspite of which it would be eliminated at the end of the first stage..
1.1 2.2 3.3 4.4
4.What is the no of rounds in the second stage of the tournament?
1.1 2.2 3.3 4.4
5.Which of the following statement is true?
1.The winner will have more wins than any other team in the tournament.
2.At the end of the 1st stage no team eliminated from the tournament will have more wins than any of the teams qualifying for the second stage.
3.It is possible that the winner will have the same no of wins in the entire tournament as the team eliminated by the end of the 1st stage.
4.The no of teams with exactly one win in the 2nd stage is 4.
1) Total no of matches
Group 1 7+6+5+4+3+2+1 = 28
Group 2 =28
Stage 2: 4(8 members)+ 2(4 members) + 1(2 members)
Total 63
2) Minimum number of wins:
If we go by options,
If a team has won 4 points by winning 4 matches it played and loosing the other 4, the other 6 teams also can win the same way i.e. gain 4 points by winning 4 matches it played and loosing the other 4. so it makes 7*4+1*0. So even if a team wins 4 matches, it may not go to next stage. Same is the case with 5 wins.
But if you take 6 there can be utmost 4 teams with 6 wins i.e 6*4 + 1*4
Hence the answer is 6
3) In the same way, the answer should be 4. But im skeptical about this answer, as one with 5 wins can also be eliminated.
4) 3 rounds - You can refer to Q1 explanation.
5) This can be true as teams winning 7 6 5 and 2 matches come into 2nd stage. From her, it doesn't depend on the previous perfomance. 2 even if it wins the final it can win utmost 5 matches. Hence 2 albeit being winner isn't winning max number of matches which is 7.
4 is also not true as the team with 1 wins are 2
2 is true as it is a direct statement indicating that if there are more wins to this team, it should go to the next round.
Hope my explanation suffices. Please let me know if you have any queries or any of my answers is/are wrong.
