Question

有多少个三位正整数含有奇数个偶数数字？

How many three-digit positive integers have an odd number of even digits?

$150$

$250$

$350$

$450$

$550$

答案：D

知识点：数字奇偶性乘法原理

难度评级：1100

解答：

前三位中的前两位共有 $9\cdot10=90$ 种选择。如果前两位中偶数数字的个数已经是奇数，则个位必须是奇数，有 $5$ 种选择。否则个位必须是偶数，也有 $0$ 种选择。无论前两位如何选择，个位都有种选择。

因此，前两位有 $90\cdot5=450$ 种选法，个位有种选法，总数为。

所以正确答案是 D。

There are $9\cdot10=90$ choices for the hundreds and tens digits. Once those two digits are fixed, the units digit must have whichever parity makes the total number of even digits odd. There are always $5$ digits of the required parity (including $0$ among the even digits).

Therefore, the number of integers is $90\cdot5=450.$

Thus, the answer is D .

2022 AMC 10B 第 3 题

答案：D

难度评级：1100

解答：

其他年份的第 3 题