2015 AMC 12A 第 3 题

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所有题目均经美国数学协会(MAA)官方合法授权使用。

3.

Patrick 先生教 1515 名学生数学。他批改试卷时发现,在批完除 Payton 以外所有人的试卷后,全班平均分为 8080。 批完 Payton 的试卷后,全班平均分变为 8181。 Payton 这次考试得了多少分?

Mr. Patrick teaches math to 1515 students. He was grading tests and found that when he graded everyone's test except Payton's, the average grade for the class was 80.80. After he graded Payton's test, the class average became 81.81. What was Payton's score on the test?

8181

8585

9191

9494

9595

答案:E
知识点:平均数
难度评级:1130
解答:

其他 1414 个分数的总和是 1480=112014\cdot 80 = 1120。 全部 1515 个分数的总和是 1581=121515\cdot 81 = 1215

因此 Payton 的分数是 12151120=951215 - 1120 = 95

因此,正确答案是 E

The sum of the 1414 other scores was 1480=1120.14\cdot 80 = 1120. The sum of all 1515 scores was 1581=1215.15\cdot 81 = 1215.

Therefore Payton's score was 12151120=95.1215 - 1120 = 95.

Thus, the correct answer is E.

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