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Instructions:
4 Chess tournaments were held all over the world last year and in each tournament 128 chess players participated. Players who participated in the 1st tournament are same for other tournaments. At the end of these four tournaments, world championship is held that consists of 32 players. These 32 players are selected on the basis of total number of wins the 128 players got in the four tournaments. Each of the games in the tournaments (including the world championship) is a knockout game i.e. a person who loses a game will not play in that tournament again. The person who wins the last round in any tournament is called the winner of that tournament. If 31 slots of the 32 slots in the world championship tournament are filled and to fill the 32nd spot there is a tie between few players, exactly one of those players is selected based on certain criteria (like coin toss).
Which of the following is the maximum number of wins that a player could have had and still not be selected for the world championship tournament?
4 Chess tournaments were held all over the world last year and in each tournament 128 chess players participated. Players who participated in the 1st tournament are same for other tournaments. At the end of these four tournaments, world championship is held that consists of 32 players. These 32 players are selected on the basis of total number of wins the 128 players got in the four tournaments. Each of the games in the tournaments (including the world championship) is a knockout game i.e. a person who loses a game will not play in that tournament again. The person who wins the last round in any tournament is called the winner of that tournament. If 31 slots of the 32 slots in the world championship tournament are filled and to fill the 32nd spot there is a tie between few players, exactly one of those players is selected based on certain criteria (like coin toss).
Which of the following is the maximum number of wins that a player could have had and still not be selected for the world championship tournament?
- a)10
- b)11
- c)12
- d)13
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Instructions:4 Chess tournaments were held all over the world last yea...
To get the maximum number, we need to take the case where 33 players won maximum number of matches, of which exactly 32 were selected for the World Championship based on certain criteria.
Consider these 33 players. Say each of them won at least n matches each.
In every tournament, 64 players win at least one match. Suppose the same set of 64 win the first round of each tournament. Our set of 33 goes on to win more than one match on average in the 4 tournaments.
Hence, 64 - 33 = 31 players win exactly one match.
Hence, players 1-33 win >= n matches, 34 - 64 win exactly one match and 65-128 win no matches.
Total number of wins in 4 tournaments = 4 * 127 = 508
Wins accounted for by players 34-64 = 31 * 4 = 124
Wins remaining = 508 - 124 = 384. These 384 wins need to be distributed over the remaining 33 players in the most equal way possible i.e difference in wins of player 1 and player 33 is the minimum possible.
The largest multiple of 33 <=384 is 33*11 i.e. 363. Suppose the first 33 players have 11 wins each. This accounts for 33*11 = 363 wins.
Hence, number of wins left = 384 - 363 = 21. Let these 21 wins go to the first 21 players.
Hence, players 1-21 win 12 matches, 22 - 33 win 11 matches, 34-64 win 1 match and 65 -128 win 0 matches.
Thus, the maximum number of wins a player can have and still not be selected is 11 wins.
Consider these 33 players. Say each of them won at least n matches each.
In every tournament, 64 players win at least one match. Suppose the same set of 64 win the first round of each tournament. Our set of 33 goes on to win more than one match on average in the 4 tournaments.
Hence, 64 - 33 = 31 players win exactly one match.
Hence, players 1-33 win >= n matches, 34 - 64 win exactly one match and 65-128 win no matches.
Total number of wins in 4 tournaments = 4 * 127 = 508
Wins accounted for by players 34-64 = 31 * 4 = 124
Wins remaining = 508 - 124 = 384. These 384 wins need to be distributed over the remaining 33 players in the most equal way possible i.e difference in wins of player 1 and player 33 is the minimum possible.
The largest multiple of 33 <=384 is 33*11 i.e. 363. Suppose the first 33 players have 11 wins each. This accounts for 33*11 = 363 wins.
Hence, number of wins left = 384 - 363 = 21. Let these 21 wins go to the first 21 players.
Hence, players 1-21 win 12 matches, 22 - 33 win 11 matches, 34-64 win 1 match and 65 -128 win 0 matches.
Thus, the maximum number of wins a player can have and still not be selected is 11 wins.
Most Upvoted Answer
Instructions:4 Chess tournaments were held all over the world last yea...
Understanding the Tournament Structure
In each of the four tournaments, there are 128 chess players competing in a knockout format. This means that every match results in one player winning and one player losing, eliminating the loser from that tournament.
Total Matches and Wins
Since there are 128 players in each tournament, the total number of matches played is calculated as follows:
- In the first round, there are 128 players, resulting in 64 matches.
- This continues until there is one winner, leading to a total of 127 matches in each tournament (as each match eliminates one player).
Thus, each tournament yields a maximum of 127 wins.
Aggregate Wins Across Tournaments
Over four tournaments, each player can accumulate a maximum of:
- 127 wins (maximum in one tournament) x 4 tournaments = 508 wins.
However, since we are interested in the maximum number of wins a player can have while still not qualifying for the world championship, we focus on the distribution of wins among the players.
Qualification for the World Championship
The world championship selects the top 32 players based on total wins:
- If the 31 players with the highest wins (say all having at least 11 wins) qualify, the 32nd spot may go to a player tied with them.
Maximum Wins Without Qualifying
To determine the maximum wins a player could have without qualifying:
- If 31 players all have 11 wins, they fill the first 31 spots.
- A player with 10 wins would not qualify.
However, if a player has 11 wins, they could be tied with others and potentially not selected based on tie-breaking criteria.
Thus, the maximum number of wins without qualifying is 11 wins, as having 12 wins guarantees qualification over those with 11.
In conclusion, the correct answer is option 'B' (11).
In each of the four tournaments, there are 128 chess players competing in a knockout format. This means that every match results in one player winning and one player losing, eliminating the loser from that tournament.
Total Matches and Wins
Since there are 128 players in each tournament, the total number of matches played is calculated as follows:
- In the first round, there are 128 players, resulting in 64 matches.
- This continues until there is one winner, leading to a total of 127 matches in each tournament (as each match eliminates one player).
Thus, each tournament yields a maximum of 127 wins.
Aggregate Wins Across Tournaments
Over four tournaments, each player can accumulate a maximum of:
- 127 wins (maximum in one tournament) x 4 tournaments = 508 wins.
However, since we are interested in the maximum number of wins a player can have while still not qualifying for the world championship, we focus on the distribution of wins among the players.
Qualification for the World Championship
The world championship selects the top 32 players based on total wins:
- If the 31 players with the highest wins (say all having at least 11 wins) qualify, the 32nd spot may go to a player tied with them.
Maximum Wins Without Qualifying
To determine the maximum wins a player could have without qualifying:
- If 31 players all have 11 wins, they fill the first 31 spots.
- A player with 10 wins would not qualify.
However, if a player has 11 wins, they could be tied with others and potentially not selected based on tie-breaking criteria.
Thus, the maximum number of wins without qualifying is 11 wins, as having 12 wins guarantees qualification over those with 11.
In conclusion, the correct answer is option 'B' (11).
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Community Answer
Instructions:4 Chess tournaments were held all over the world last yea...
To get the maximum number, we need to take the case where 33 players won maximum number of matches, of which exactly 32 were selected for the World Championship based on certain criteria.
Consider these 33 players. Say each of them won at least n matches each.
In every tournament, 64 players win at least one match. Suppose the same set of 64 win the first round of each tournament. Our set of 33 goes on to win more than one match on average in the 4 tournaments.
Hence, 64 - 33 = 31 players win exactly one match.
Hence, players 1-33 win >= n matches, 34 - 64 win exactly one match and 65-128 win no matches.
Total number of wins in 4 tournaments = 4 * 127 = 508
Wins accounted for by players 34-64 = 31 * 4 = 124
Wins remaining = 508 - 124 = 384. These 384 wins need to be distributed over the remaining 33 players in the most equal way possible i.e difference in wins of player 1 and player 33 is the minimum possible.
The largest multiple of 33 <=384 is 33*11 i.e. 363. Suppose the first 33 players have 11 wins each. This accounts for 33*11 = 363 wins.
Hence, number of wins left = 384 - 363 = 21. Let these 21 wins go to the first 21 players.
Hence, players 1-21 win 12 matches, 22 - 33 win 11 matches, 34-64 win 1 match and 65 -128 win 0 matches.
Thus, the maximum number of wins a player can have and still not be selected is 11 wins.
Consider these 33 players. Say each of them won at least n matches each.
In every tournament, 64 players win at least one match. Suppose the same set of 64 win the first round of each tournament. Our set of 33 goes on to win more than one match on average in the 4 tournaments.
Hence, 64 - 33 = 31 players win exactly one match.
Hence, players 1-33 win >= n matches, 34 - 64 win exactly one match and 65-128 win no matches.
Total number of wins in 4 tournaments = 4 * 127 = 508
Wins accounted for by players 34-64 = 31 * 4 = 124
Wins remaining = 508 - 124 = 384. These 384 wins need to be distributed over the remaining 33 players in the most equal way possible i.e difference in wins of player 1 and player 33 is the minimum possible.
The largest multiple of 33 <=384 is 33*11 i.e. 363. Suppose the first 33 players have 11 wins each. This accounts for 33*11 = 363 wins.
Hence, number of wins left = 384 - 363 = 21. Let these 21 wins go to the first 21 players.
Hence, players 1-21 win 12 matches, 22 - 33 win 11 matches, 34-64 win 1 match and 65 -128 win 0 matches.
Thus, the maximum number of wins a player can have and still not be selected is 11 wins.
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Instructions:4 Chess tournaments were held all over the world last year and in each tournament 128 chess players participated. Players who participated in the 1st tournament are same for other tournaments. At the end of these four tournaments, world championship is held that consists of 32 players. These 32 players are selected on the basis of total number of wins the 128 players got in the four tournaments. Each of the games in the tournaments (including the world championship) is a knockout game i.e. a person who loses a game will not play in that tournament again. The person who wins the last round in any tournament is called the winner of that tournament. If 31 slots of the 32 slots in the world championship tournament are filled and to fill the 32nd spot there is a tie between few players, exactly one of those players is selected based on certain criteria (like coin toss).Which of the following is the maximum number of wins that a player could have had and still not be selected for the world championship tournament?a)10b)11c)12d)13Correct answer is option 'B'. Can you explain this answer?
Question Description
Instructions:4 Chess tournaments were held all over the world last year and in each tournament 128 chess players participated. Players who participated in the 1st tournament are same for other tournaments. At the end of these four tournaments, world championship is held that consists of 32 players. These 32 players are selected on the basis of total number of wins the 128 players got in the four tournaments. Each of the games in the tournaments (including the world championship) is a knockout game i.e. a person who loses a game will not play in that tournament again. The person who wins the last round in any tournament is called the winner of that tournament. If 31 slots of the 32 slots in the world championship tournament are filled and to fill the 32nd spot there is a tie between few players, exactly one of those players is selected based on certain criteria (like coin toss).Which of the following is the maximum number of wins that a player could have had and still not be selected for the world championship tournament?a)10b)11c)12d)13Correct answer is option 'B'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Instructions:4 Chess tournaments were held all over the world last year and in each tournament 128 chess players participated. Players who participated in the 1st tournament are same for other tournaments. At the end of these four tournaments, world championship is held that consists of 32 players. These 32 players are selected on the basis of total number of wins the 128 players got in the four tournaments. Each of the games in the tournaments (including the world championship) is a knockout game i.e. a person who loses a game will not play in that tournament again. The person who wins the last round in any tournament is called the winner of that tournament. If 31 slots of the 32 slots in the world championship tournament are filled and to fill the 32nd spot there is a tie between few players, exactly one of those players is selected based on certain criteria (like coin toss).Which of the following is the maximum number of wins that a player could have had and still not be selected for the world championship tournament?a)10b)11c)12d)13Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Instructions:4 Chess tournaments were held all over the world last year and in each tournament 128 chess players participated. Players who participated in the 1st tournament are same for other tournaments. At the end of these four tournaments, world championship is held that consists of 32 players. These 32 players are selected on the basis of total number of wins the 128 players got in the four tournaments. Each of the games in the tournaments (including the world championship) is a knockout game i.e. a person who loses a game will not play in that tournament again. The person who wins the last round in any tournament is called the winner of that tournament. If 31 slots of the 32 slots in the world championship tournament are filled and to fill the 32nd spot there is a tie between few players, exactly one of those players is selected based on certain criteria (like coin toss).Which of the following is the maximum number of wins that a player could have had and still not be selected for the world championship tournament?a)10b)11c)12d)13Correct answer is option 'B'. Can you explain this answer?.
Instructions:4 Chess tournaments were held all over the world last year and in each tournament 128 chess players participated. Players who participated in the 1st tournament are same for other tournaments. At the end of these four tournaments, world championship is held that consists of 32 players. These 32 players are selected on the basis of total number of wins the 128 players got in the four tournaments. Each of the games in the tournaments (including the world championship) is a knockout game i.e. a person who loses a game will not play in that tournament again. The person who wins the last round in any tournament is called the winner of that tournament. If 31 slots of the 32 slots in the world championship tournament are filled and to fill the 32nd spot there is a tie between few players, exactly one of those players is selected based on certain criteria (like coin toss).Which of the following is the maximum number of wins that a player could have had and still not be selected for the world championship tournament?a)10b)11c)12d)13Correct answer is option 'B'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Instructions:4 Chess tournaments were held all over the world last year and in each tournament 128 chess players participated. Players who participated in the 1st tournament are same for other tournaments. At the end of these four tournaments, world championship is held that consists of 32 players. These 32 players are selected on the basis of total number of wins the 128 players got in the four tournaments. Each of the games in the tournaments (including the world championship) is a knockout game i.e. a person who loses a game will not play in that tournament again. The person who wins the last round in any tournament is called the winner of that tournament. If 31 slots of the 32 slots in the world championship tournament are filled and to fill the 32nd spot there is a tie between few players, exactly one of those players is selected based on certain criteria (like coin toss).Which of the following is the maximum number of wins that a player could have had and still not be selected for the world championship tournament?a)10b)11c)12d)13Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Instructions:4 Chess tournaments were held all over the world last year and in each tournament 128 chess players participated. Players who participated in the 1st tournament are same for other tournaments. At the end of these four tournaments, world championship is held that consists of 32 players. These 32 players are selected on the basis of total number of wins the 128 players got in the four tournaments. Each of the games in the tournaments (including the world championship) is a knockout game i.e. a person who loses a game will not play in that tournament again. The person who wins the last round in any tournament is called the winner of that tournament. If 31 slots of the 32 slots in the world championship tournament are filled and to fill the 32nd spot there is a tie between few players, exactly one of those players is selected based on certain criteria (like coin toss).Which of the following is the maximum number of wins that a player could have had and still not be selected for the world championship tournament?a)10b)11c)12d)13Correct answer is option 'B'. Can you explain this answer?.
Solutions for Instructions:4 Chess tournaments were held all over the world last year and in each tournament 128 chess players participated. Players who participated in the 1st tournament are same for other tournaments. At the end of these four tournaments, world championship is held that consists of 32 players. These 32 players are selected on the basis of total number of wins the 128 players got in the four tournaments. Each of the games in the tournaments (including the world championship) is a knockout game i.e. a person who loses a game will not play in that tournament again. The person who wins the last round in any tournament is called the winner of that tournament. If 31 slots of the 32 slots in the world championship tournament are filled and to fill the 32nd spot there is a tie between few players, exactly one of those players is selected based on certain criteria (like coin toss).Which of the following is the maximum number of wins that a player could have had and still not be selected for the world championship tournament?a)10b)11c)12d)13Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT.
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Here you can find the meaning of Instructions:4 Chess tournaments were held all over the world last year and in each tournament 128 chess players participated. Players who participated in the 1st tournament are same for other tournaments. At the end of these four tournaments, world championship is held that consists of 32 players. These 32 players are selected on the basis of total number of wins the 128 players got in the four tournaments. Each of the games in the tournaments (including the world championship) is a knockout game i.e. a person who loses a game will not play in that tournament again. The person who wins the last round in any tournament is called the winner of that tournament. If 31 slots of the 32 slots in the world championship tournament are filled and to fill the 32nd spot there is a tie between few players, exactly one of those players is selected based on certain criteria (like coin toss).Which of the following is the maximum number of wins that a player could have had and still not be selected for the world championship tournament?a)10b)11c)12d)13Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Instructions:4 Chess tournaments were held all over the world last year and in each tournament 128 chess players participated. Players who participated in the 1st tournament are same for other tournaments. At the end of these four tournaments, world championship is held that consists of 32 players. These 32 players are selected on the basis of total number of wins the 128 players got in the four tournaments. Each of the games in the tournaments (including the world championship) is a knockout game i.e. a person who loses a game will not play in that tournament again. The person who wins the last round in any tournament is called the winner of that tournament. If 31 slots of the 32 slots in the world championship tournament are filled and to fill the 32nd spot there is a tie between few players, exactly one of those players is selected based on certain criteria (like coin toss).Which of the following is the maximum number of wins that a player could have had and still not be selected for the world championship tournament?a)10b)11c)12d)13Correct answer is option 'B'. Can you explain this answer?, a detailed solution for Instructions:4 Chess tournaments were held all over the world last year and in each tournament 128 chess players participated. Players who participated in the 1st tournament are same for other tournaments. At the end of these four tournaments, world championship is held that consists of 32 players. These 32 players are selected on the basis of total number of wins the 128 players got in the four tournaments. Each of the games in the tournaments (including the world championship) is a knockout game i.e. a person who loses a game will not play in that tournament again. The person who wins the last round in any tournament is called the winner of that tournament. If 31 slots of the 32 slots in the world championship tournament are filled and to fill the 32nd spot there is a tie between few players, exactly one of those players is selected based on certain criteria (like coin toss).Which of the following is the maximum number of wins that a player could have had and still not be selected for the world championship tournament?a)10b)11c)12d)13Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of Instructions:4 Chess tournaments were held all over the world last year and in each tournament 128 chess players participated. Players who participated in the 1st tournament are same for other tournaments. At the end of these four tournaments, world championship is held that consists of 32 players. These 32 players are selected on the basis of total number of wins the 128 players got in the four tournaments. Each of the games in the tournaments (including the world championship) is a knockout game i.e. a person who loses a game will not play in that tournament again. The person who wins the last round in any tournament is called the winner of that tournament. If 31 slots of the 32 slots in the world championship tournament are filled and to fill the 32nd spot there is a tie between few players, exactly one of those players is selected based on certain criteria (like coin toss).Which of the following is the maximum number of wins that a player could have had and still not be selected for the world championship tournament?a)10b)11c)12d)13Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Instructions:4 Chess tournaments were held all over the world last year and in each tournament 128 chess players participated. Players who participated in the 1st tournament are same for other tournaments. At the end of these four tournaments, world championship is held that consists of 32 players. These 32 players are selected on the basis of total number of wins the 128 players got in the four tournaments. Each of the games in the tournaments (including the world championship) is a knockout game i.e. a person who loses a game will not play in that tournament again. The person who wins the last round in any tournament is called the winner of that tournament. If 31 slots of the 32 slots in the world championship tournament are filled and to fill the 32nd spot there is a tie between few players, exactly one of those players is selected based on certain criteria (like coin toss).Which of the following is the maximum number of wins that a player could have had and still not be selected for the world championship tournament?a)10b)11c)12d)13Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice CAT tests.
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