AMC10 2004 B

AMC10 2004 B · Q2

AMC10 2004 B · Q2. It mainly tests Basic counting (rules of product/sum), Inclusion–exclusion (basic).

How many two-digit positive integers have at least one 7 as a digit?

有多少个两位正整数至少有一个数字是 7？

(A) 10 10

(B) 18 18

(D) 20 20

(E) 30 30

Answer

Correct choice: (B)

正确答案：（B）

Solution

There are 10 two-digit numbers with a 7 as their 10’s digit, and 9 two-digit numbers with 7 as their units digit. Because 77 satisfies both of these properties, the answer is $10 + 9 - 1 = 18$.

有 10 个两位数以 7 作为十位数字，还有 9 个两位数以 7 作为个位数字。因为 77 同时满足这两个条件，所以答案是 $10 + 9 - 1 = 18$。

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