Problem:
Mary thought of a positive two-digit number. She multiplied it by and added . Then she switched the digits of the result, obtaining a number between and , inclusive. What was Mary's number?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Working backwards, switching the digits of the numbers , and and subtracting gives, respectively, , and . Only and are divisible by , and only is a two-digit number.
The problems on this page are the property of the MAA's American Mathematics Competitions