Problem:
The -digit number  is divisible by . What is the remainder when this number is divided by 
Answer Choices:
A.  
B.  
C.  
D.  
E.  
Solution:
To be divisible by , the sum of the digits must be divisible by , so is divisible by . Thus , and -digit number is . Then Because , the remainder is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions