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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 least number of wins that the winner of the world championship can have?a)11b)10c)9d)7Correct answer is option 'D'. Can you explain this answer? - EduRev CAT Question
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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 least number of wins that the winner of the world championship can have?a)11b)10c)9d)7Correct answer is option 'D'. Can you explain this answer? - EduRev CAT Question

To win the world championship, a player must win all the five matches in that tournament.In the four preceding tournaments there are 128 players.So in an individual tournament.64 will win 0 match.32 will win 1 match.16 will win 2 matches.8 will win 3 matches.4 will win 4 matches2 will win 5 matches.1 (finalist) will win 6 matches.1 (champion) will win 7 matches.There are 31 places which are already confirmed and 97 players are for the 32nd position.We must maximize the number of matches won by the other 31 players⇒ remaining 97 players must win least number of matches.In the first tounamentThus for 97 players, 64 will win 0 matches 32 will win 1 match and the remaining 1 player will win 2 matches.n the first tournament total number of matches won by these 97 players= 64x0+32x1+1x2= 34 winsIn all the 4 tournaments total number of wins will be 4x34=136There are 97 players, so they will distribute victories among themselves. As 136/97=1.402 some players can have 2 wins and others will have 1 win.Suppose X players win 2 matches and Y win only 1 match.So X+Y=972X+Y=136X= 39Y=58So 39 players have 2 wins, and 58 players will have 1 win.Among theseplayers one will be selected for the world championship based on certain criteria.Hence minimum number of wins required = 5 + 2 = 7