Problem:
How many three-digit positive integers satisfy the following properties?
The number is divisible by .
The number formed by reversing the digits of is divisible by .
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Let be the number formed by reversing the digits of . Because is divisible by 5 , the last digit of must be 0 or 5 . However, the last digit of cannot be 0 , so it must be 5 . It follows that is a number between 500 and 599.
The least multiple of 7 in this range is , while the greatest multiple of 7 in this range is . Thus is one of the numbers , or . There are numbers in this list.
The problems on this page are the property of the MAA's American Mathematics Competitions