Problem:
The sum of the digits of a two-digit number is subtracted from the number. The units digit of the result is . How many two-digit numbers have this property?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Let be the two-digit number. When is subtracted the result is . The only two-digit multiple of that ends in is , so . The numbers between and , inclusive, have this property.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions