Problem:
How many -digit positive integers (that is, integers between and , inclusive) having only even digits are divisible by ?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The units digit, for all numbers divisible by , must be either or . However, since all digits are even, the units digit must be .
The middle two digits can be , or , but the thousands digit can only be , or since it cannot be zero.
There is one choice for the units digit, choices for each of the middle digits, and choices for the thousands digit, so there is a total of
numbers.
The problems on this page are the property of the MAA's American Mathematics Competitions