Problem:
How many distinct four-digit numbers are divisible by and have as their last two digits?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
A number is divisible by if and only if the sum of its digits is divisible by . So a four-digit number is divisible by if and only if the two-digit number leaves a remainder of when divided by . There are two-digit numbers, of which leave a remainder of when divided by .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions