AMC8 2014

AMC8 2014 · Q8

AMC8 2014 · Q8. It mainly tests Divisibility & factors, Digit properties (sum of digits, divisibility tests).

Eleven members of the Middle School Math Club each paid the same amount for a guest speaker to talk about problem solving at their math club meeting. They paid their guest speaker $\underline{1A2}$. What is the missing digit $A$ of this $3$-digit number?

数学俱乐部的十一名成员每人支付了相同的金额，请了一位嘉宾讲解他们数学俱乐部会议上的问题解决方法。他们支付给嘉宾讲师的费用是 $\underline{1A2}$。这个三位数中的未知数字 $A$ 是多少？

(A) 0 0

(B) 1 1

(D) 3 3

(E) 4 4

Answer

Correct choice: (D)

正确答案：（D）

Solution

Since all the eleven members paid the same amount, that means that the total must be divisible by $11$. We can do some trial-and-error to get $A=3$, so our answer is $\boxed{\textbf{(D)}~3}$

由于十一名成员每人支付的金额相同，这意味着总金额必须能够被 11 整除。我们可以通过试错法得到 $A=3$，所以答案是 $\boxed{\textbf{(D)}~3}$。

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