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Problem-Solving and Data Analysis Difficulty: Hard

The mean score of 8 players in a basketball game was 14.5 points. If the highest individual score is removed, the mean score of the remaining 7 players becomes 12 points. What was the highest score?

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Explanation

Choice C is correct. If the mean score of 8 players is 14.5, then the total of all 8 scores is $14 point 5 times 8, equals 116$ . If the mean of 7 scores is 12, then the total of all 7 scores is $12 times 7, equals 84$ . Since the set of 7 scores was made by removing the highest score of the set of 8 scores, then the difference between the total of all 8 scores and the total of all 7 scores is equal to the removed score: $116 minus 84, equals 32$ .

Choice A is incorrect because if 20 is removed from the group of 8 scores, then the mean score of the remaining 7 players is $the fraction with numerator, open parenthesis, 14 point 5 times 8, close parenthesis, minus 20, and denominator 7$ is approximately 13.71, not 12. Choice B is incorrect because if 24 is removed from the group of 8 scores, then the mean score of the remaining 7 players is $the fraction with numerator, open parenthesis, 14 point 5 times 8, close parenthesis, minus 24, and denominator 7$ is approximately 13.14, not 12. Choice D is incorrect because if 36 is removed from the group of 8 scores, then the mean score of the remaining 7 players is $the fraction with numerator, open parenthesis, 14 point 5 times 8, close parenthesis, minus 36, and denominator 7$ or approximately 11.43, not 12.