AMC 8 1985 Problem 17
AMC8 1985 年第 17 题
表达式与运算★★★☆☆
If your average score on your first six mathematics tests was 84 and your average score on your first seven mathematics tests was 85, then your score on the seventh test was
如果你前六次数学考试的平均分是 84，前七次数学考试的平均分是 85，那么你第七次考试的分数是
- A.86
- B.88
- C.90
- D.91
- E.92
正确答案 · Correct Answer
D
解析 · Solution
Solution 1
Since your average score on your first 6 tests is 84, your total score on your first 6 tests is .
Since your average score on your first 7 tests is 85, your total score on your first 7 tests is .
Therefore, your score on your test was 595-504=91.
Let's remove the condition that the average of the first seven tests is 85, and say the 7th test score was a 0. Then, the average of the first seven tests would be
If we increase the seventh test score by 7, the average will increase by . We need the average to increase by 85-72=13, so the seventh test score is 7×13=91 more than 0, which is clearly 91.
Since 84 is divisible by 7, your total score on your first 6 tests, that is, , is divisible by 7. Also, your total score on your first 7 tests, that is, , must be divisible by 7. Therefore, your score on your test is also divisible by 7. Of the answer choices, only 91 is divisible by 7.
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