AMC 8 2014 Problem 23
AMC8 2014 年第 23 题
整除与因数★★★☆☆
Three members of the Euclid Middle School girls' softball team had the following conversation. Ashley: I just realized that our uniform numbers are all 2 -digit primes. Bethany : And the sum of your two uniform numbers is the date of my birthday earlier this month. Caitlin: That's funny. The sum of your two uniform numbers is the date of my birthday later this month. Ashley: And the sum of your two uniform numbers is today's date. What number does Caitlin wear?
Euclid 中学女子垒球队的 3 名成员有如下对话：
Ashley：我刚意识到原来我们的球衣编号都是 2 位质数。
Bethany：并且你们两个人的球衣编号之和是这个月的早些时候我生日的日期。
Caitlin：真有趣。你们俩的球衣编号之和是这个月晚些时候我生日的日期。
Ashley：并且你们俩的球衣编号之和就是今天的日期。
那么 Caitlin 的球衣编号是多少？
- A.11
- B.13
- C.17
- D.19
- E.23
正确答案 · Correct Answer
A
解析 · Solution
Solution 1
The maximum amount of days any given month can have is 31, and the smallest two-digit primes are 11, 13, and 17. There are a few different sums that can be deduced from the following numbers, which are 24, 30, and 28, all of which represent the three days. Therefore, since Bethany says that the other two people's uniform numbers are earlier, so that means Caitlin and Ashley's numbers must add up to 24. Similarly, Caitlin says that the other two people's uniform numbers are later, so the sum must add up to 30. This leaves 28 as today's date. From this, Caitlin was referring to the uniform wearers 13 and 17, telling us that her number is 11, giving our solution as 11.
继续练习