AMC8 2024

AMC8 2024 · Q1

AMC8 2024 · Q1. It mainly tests Money / coins, Digit properties (sum of digits, divisibility tests).

What is the unit digit of: \[222{,}222-22{,}222-2{,}222-222-22-2?\]

下列表达式的单位数字是：\[222{,}222-22{,}222-2{,}222-222-22-2？\]

(A) 0 0

(B) 2 2

(D) 8 8

(E) 10 10

Answer

Correct choice: (B)

正确答案：（B）

Solution

We can rewrite the expression as $222,222-(22,222+2,222+222+22+2)$. We note that the units digit of $22,222+2,222+222+22+2$ is $0$ because all the units digits of the five numbers are $2$ and $5\cdot2=10$, which has a units digit of $0$. Now, we have something with a units digit of $0$ subtracted from $222,222$, and so the units digit of this expression is $\boxed{\textbf{(B) } 2}$.

我们可以将表达式重写为 $222,222-(22,222+2,222+222+22+2)$。我们注意到 $22,222+2,222+222+22+2$ 的单位数字是 $0$，因为这五个数的单位数字都是 $2$，而且 $5\cdot2=10$，单位数字是 $0$。现在，我们从 $222,222$ 中减去一个单位数字为 $0$ 的数，因此这个表达式的单位数字是 $\boxed{\textbf{(B) } 2}$。

Topics