4. The bell of 2013 rang, and Brother Xiao Ming sighed, saying, "This is the first year in my life with no repeated digits." It is known that Brother Xiao Ming was born in a year that is a multiple of 19. Therefore, in 2013, Brother Xiao Ming's age is ( ) years old.
(A) 16
(B) 18
(C) 20
(D) 22
【Answer】B
【Analysis】 $2013 \div 19=105 \ldots 18$ , because the birth year of Xiaoming's brother is a multiple of 19, so Xiaoming's brother's birth year $=2013-18-19 n$. When $n=0$, Xiaoming's brother's birth year $=1995$; when $n=1$, Xiaoming's brother's birth year $=1976$, but it is obvious that if Xiaoming's brother was born in 1976, 2013 would not be the first year in his life without repeated digits, for example, 1978 is a year without repeated digits. Therefore, Xiaoming's brother's birth year can only be 1995, and Xiaoming's brother's age in 2013 = 2013 - 1995 = 18.
In fact, if we consider from another angle, among the four options (A), (B), (C), and (D), only option B can ensure that Xiaoming's brother's birth year is a multiple of 19.
【Difficulty】Moderate
【Knowledge Point】Division with Remainder