AMC8 1991

AMC8 1991 · Q17

AMC8 1991 · Q17. It mainly tests Averages (mean), Basic counting (rules of product/sum).

An auditorium with 20 rows of seats has 10 seats in the first row. Each successive row has one more seat than the previous row. If students taking an exam are permitted to sit in any row, but not next to another student in that row, then the maximum number of students that can be seated for an exam is

一个有20排座位的礼堂，第一排有10个座位。每后一排比前一排多一个座位。如果考试学生可以坐在任何一排，但同一排不能与另一个学生相邻，那么最多可以容纳的学生数量是

(A) 150 150

(B) 180 180

(D) 400 400

(E) 460 460

Answer

Correct choice: (C)

正确答案：（C）

Solution

The first row has 10 seats, so 5 students can sit in row 1. The second row has 11 seats, so 6 students can sit in row 2. The third row has 12 seats, so 6 students... The sum is $5 + 6 + 6 + 7 + 7 + 8 + 8 + 9 + 9 + 10 + 15 + 14 + 14 + 13 + 13 + 12 + 12 + 11 + 11 + 10 = 200$.

第一排有10个座位，所以第1排可坐5名学生。第2排有11个座位，所以第2排可坐6名学生。第3排有12个座位，所以可坐6名学生……总和是$5 + 6 + 6 + 7 + 7 + 8 + 8 + 9 + 9 + 10 + 15 + 14 + 14 + 13 + 13 + 12 + 12 + 11 + 11 + 10 = 200$。

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