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29 Jul 2024, 07:59
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There are two teams in a chess tournament, Team India and Team USA, and no player represents both teams. Each player from Team India plays with each player from Team USA exactly once, resulting in a total of 60 matches between the teams. How many players are on Team USA?
(1) For every 3 players from Team India, there are 5 players from Team USA.
(2) There are a total of 16 players on both teams combined.
(1) For every 3 players from Team India, there are 5 players from Team USA.
(2) There are a total of 16 players on both teams combined.
29 Jul 2024, 07:59
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Official Solution:
There are two teams in a chess tournament, Team India and Team USA, and no player represents both teams. Each player from Team India plays with each player from Team USA exactly once, resulting in a total of 60 matches between the teams. How many players are on Team USA?
Assuming there are \(x\) players in Team India and \(y\) players in Team USA, a total of 60 matches implies that \(xy = 60\). Hence, we can have the following possible pairs of \((x, y)\):
(2, 30)
(3, 20)
(4, 15)
(5, 12)
(6, 10)
(10, 6)
(12, 5)
(15, 4)
(20, 3)
(30, 2)
(1) For every 3 players from Team India, there are 5 players from Team USA.
This implies that \(x : y = 3 : 5\). From the possible pairs, only \(x = 6\) and \(y = 10\) satisfy this. Therefore, there are 10 players on Team USA. Sufficient.
(2) There are a total of 16 players on both teams combined.
This implies that \(x + y = 16\). From the possible pairs, both \(x = 6\), \(y = 10\) and \(x = 10\), \(y = 6\) satisfy this. Therefore, there can be 6 or 10 players on Team USA. Not sufficient.
Answer: A
There are two teams in a chess tournament, Team India and Team USA, and no player represents both teams. Each player from Team India plays with each player from Team USA exactly once, resulting in a total of 60 matches between the teams. How many players are on Team USA?
Assuming there are \(x\) players in Team India and \(y\) players in Team USA, a total of 60 matches implies that \(xy = 60\). Hence, we can have the following possible pairs of \((x, y)\):
(2, 30)
(3, 20)
(4, 15)
(5, 12)
(6, 10)
(10, 6)
(12, 5)
(15, 4)
(20, 3)
(30, 2)
(1) For every 3 players from Team India, there are 5 players from Team USA.
This implies that \(x : y = 3 : 5\). From the possible pairs, only \(x = 6\) and \(y = 10\) satisfy this. Therefore, there are 10 players on Team USA. Sufficient.
(2) There are a total of 16 players on both teams combined.
This implies that \(x + y = 16\). From the possible pairs, both \(x = 6\), \(y = 10\) and \(x = 10\), \(y = 6\) satisfy this. Therefore, there can be 6 or 10 players on Team USA. Not sufficient.
Answer: A
16 Dec 2024, 06:22
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Bunuel
Is the number of matches the same as the number of games played?
To calculate the number of games: (X)(Y) / 2 = Number of games, coz a game is played between 2 players
May i ask how you arrive at XY=60. It it the case that by multiplying the number of players on one team by the number of player on the other team, we get total number of matches?
Thanks in Advance!
Is the number of matches the same as the number of games played?
To calculate the number of games: (X)(Y) / 2 = Number of games, coz a game is played between 2 players
May i ask how you arrive at XY=60. It it the case that by multiplying the number of players on one team by the number of player on the other team, we get total number of matches?
Thanks in Advance!
