In a certain game, each of $5$ players received a score between $0$ and $100$ , inclusive. If their average (arithmetic mean) score was $80$ , what is the greatest possible number of the $5$ players who could have received a score of $50$ ?

None

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Two

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Three

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Solution

The correct option is C Two
Given that the arithmetic mean of $5$ players is $80$ .
So the sum of scores of $5$ players is $80 \times 5 = 400$ .
We should find the greatest possible number of the $5$ players who could have received a score of $50$ .
Suppose assume that $3$ players have a score of $50$ , then the sum of scores of remaining $2$ players is $400 - 150 = 250$ which is not possible (because maximum score a player can receive is $100$ ).
Now assume that $2$ players have a score of $50$ , then sum of other three players score is $400 - 100 = 300$ , which is possible.
Therefore, the answer is $2$ .

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In a certain game, each of 5 players received a score between 0 and 100, inclusive. If their average (arithmetic mean) score was 80, what is the greatest possible number of the 5 players who could have received a score of 50?

In a certain game, each of $5$ players received a score between $0$ and $100$ , inclusive. If their average (arithmetic mean) score was $80$ , what is the greatest possible number of the $5$ players who could have received a score of $50$ ?