Malcolm wants to visit Isabella after school today and knows the street where she lives but doesn't know her house number. She tells him, "My house number has two digits, and exactly three of the following four statements about it are true." ( )
(1) It is prime.
(2) It is even.
(3) It is divisible by 7.
(4) One of its digits is 9.
This information allows Malcolm to determine Isabella's house number. What is its units digit?
A. 4
B. 6
C. 7
D. 8
E. 9

Logical reasoning problems中文
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1. 2017 AMC 8 官方解析

翻译：马尔科姆想去拜访伊莎贝拉，他知道伊莎贝拉住哪一条街，但是不知道他们家的门牌号. 伊莎贝拉告诉他：“我家门牌号有两个数字，并且下面四个描述中有3个是正确的.”
（1）门牌号是个质数
（2）门牌号是偶数
（3）被7整除
（4）其中一个数字是9
通过上述信息，马尔科姆知道了伊莎贝拉的门牌号，那么门牌号的个位数字是（　）？由于门牌号是两位数，所以条件（1）与（2）、（3）都是矛盾的，所以，（2）、（3）、（4）是正确的，有一个数字是9，又不能在个位，只能在十位，又有9□9\square被7整除，又是偶数，那么门牌号只能是98，排除91，所以D正确.

Answer

D. 8

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