AMC8 2018

AMC8 2018 · Q13

AMC8 2018 · Q13. It mainly tests Linear equations, Averages (mean).

Laila took five math tests, each worth a maximum of 100 points. Laila’s score on each test was an integer between 0 and 100, inclusive. Laila received the same score on the first four tests, and she received a higher score on the last test. Her average score on the five tests was 82. How many values are possible for Laila’s score on the last test?

Laila参加了五次数学测验，每次满分100分。Laila每次测验的得分是0到100之间的整数。前四次测验得分相同，最后一次得分更高。五次测验的平均分是82。最后一次测验的得分有多少种可能值？

(A) 4 4

(B) 5 5

(D) 10 10

(E) 18 18

Answer

Correct choice: (A)

正确答案：（A）

Solution

Answer (A): Because Laila’s score on the last test was higher than her other test scores and all of her scores were integers, for each point below $82$ that she scored on each of the first four tests, she had to score four points above $82$ on the last test. Therefore, her possible scores on the last test were $86$, $90$, $94$, and $98$ (with scores on the first four tests of $81$, $80$, $79$, and $78$, respectively). Thus there are four possible values for her score on the last test.

答案（A）：因为 Laila 的最后一次测验分数高于她其他测验的分数，并且她的所有分数都是整数，所以在前四次测验中，她每比 $82$ 低 $1$ 分，最后一次测验就必须比 $82$ 高 $4$ 分。于是，她最后一次测验可能的分数是 $86$、$90$、$94$、$98$（分别对应前四次测验分数为 $81$、$80$、$79$、$78$）。因此，她最后一次测验的分数共有 4 种可能。

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