AMC8 1990

AMC8 1990 · Q22

AMC8 1990 · Q22. It mainly tests Remainders & modular arithmetic.

Several students are seated at a large circular table. They pass around a bag containing 100 pieces of candy. Each person receives the bag, takes one piece of candy and then passes the bag to the next person. If Chris takes the first and the last piece of candy, then the number of students at the table could be

几个学生围坐在一张大圆桌旁。他们传着一个装有100块糖果的袋子。每人拿到袋子时，取一块糖果，然后传给下一个。克里斯拿了第一块和最后一块糖果，则桌旁学生人数可能是

(A) 10 10

(B) 11 11

(D) 20 20

(E) 25 25

Answer

Correct choice: (B)

正确答案：（B）

Solution

Answer (B): Since Chris takes the last piece of candy, each person receives the same number of the other $99$ pieces of candy. Thus the number of students at the table must be a factor of $99$. Only (B) fulfills this condition.

答案（B）：由于 Chris 拿走了最后一块糖，其余的 $99$ 块糖必须平均分给每个人。因此，桌旁学生的人数必须是 $99$ 的因数。只有选项（B）满足这一条件。

Topics

NT.004 Remainders & modular arithmetic