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T the end of the T20 cricket match, every player had scored a prime number of runs and the average of the 11 players was also a prime number. No player’s individual runs were the same as anyone else’s or as the average. Nobody had scored more than 45 runs. What was the minimum number of runs scored by a single player? A) 5 B) 7 C) 11 D) 13?
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T the end of the T20 cricket match, every player had scored a prime nu...
To find the minimum number of runs scored by a single player in a T20 cricket match, we need to consider the given conditions:
1. Every player had scored a prime number of runs.
2. The average of the 11 players was also a prime number.
3. No player's individual runs were the same as anyone else's or as the average.
4. Nobody had scored more than 45 runs.
Let's analyze each option one by one:
A) 5:
If a player scores 5 runs, then there can be no other player who has scored the same number of runs since no two players can have the same score. However, the average of 11 players cannot be a prime number because the sum of prime numbers is always even, and the average of prime numbers will also be even. Therefore, option A is not valid.
B) 7:
If a player scores 7 runs, then there can be no other player who has scored the same number of runs. To get the average as a prime number, the total runs scored by all players must be an odd multiple of 11. The possible combinations of prime numbers that fulfill this condition are 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 = 272 or 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 = 319. Both 272 and 319 are divisible by 11, so the average is not a prime number. Therefore, option B is not valid.
C) 11:
If a player scores 11 runs, then there can be no other player who has scored the same number of runs. To get the average as a prime number, the total runs scored by all players must be an odd multiple of 11. The possible combinations of prime numbers that fulfill this condition are 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 = 332 or 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 = 284. Both 332 and 284 are divisible by 11, so the average is not a prime number. Therefore, option C is not valid.
D) 13:
If a player scores 13 runs, then there can be no other player who has scored the same number of runs. To get the average as a prime number, the total runs scored by all players must be an odd multiple of 11. The possible combinations of prime numbers that fulfill this condition are 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 = 320 or 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 = 273. Both 320 and 273 are divisible by 11, so the average is not a prime number. Therefore, option D is not valid.
Therefore, there is no valid option among the given choices (A, B, C, D) that satisfies all the given conditions.
1. Every player had scored a prime number of runs.
2. The average of the 11 players was also a prime number.
3. No player's individual runs were the same as anyone else's or as the average.
4. Nobody had scored more than 45 runs.
Let's analyze each option one by one:
A) 5:
If a player scores 5 runs, then there can be no other player who has scored the same number of runs since no two players can have the same score. However, the average of 11 players cannot be a prime number because the sum of prime numbers is always even, and the average of prime numbers will also be even. Therefore, option A is not valid.
B) 7:
If a player scores 7 runs, then there can be no other player who has scored the same number of runs. To get the average as a prime number, the total runs scored by all players must be an odd multiple of 11. The possible combinations of prime numbers that fulfill this condition are 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 = 272 or 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 = 319. Both 272 and 319 are divisible by 11, so the average is not a prime number. Therefore, option B is not valid.
C) 11:
If a player scores 11 runs, then there can be no other player who has scored the same number of runs. To get the average as a prime number, the total runs scored by all players must be an odd multiple of 11. The possible combinations of prime numbers that fulfill this condition are 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 = 332 or 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 = 284. Both 332 and 284 are divisible by 11, so the average is not a prime number. Therefore, option C is not valid.
D) 13:
If a player scores 13 runs, then there can be no other player who has scored the same number of runs. To get the average as a prime number, the total runs scored by all players must be an odd multiple of 11. The possible combinations of prime numbers that fulfill this condition are 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 = 320 or 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 = 273. Both 320 and 273 are divisible by 11, so the average is not a prime number. Therefore, option D is not valid.
Therefore, there is no valid option among the given choices (A, B, C, D) that satisfies all the given conditions.
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T the end of the T20 cricket match, every player had scored a prime number of runs and the average of the 11 players was also a prime number. No player’s individual runs were the same as anyone else’s or as the average. Nobody had scored more than 45 runs. What was the minimum number of runs scored by a single player? A) 5 B) 7 C) 11 D) 13?
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