Problem:
The digits , and are each used once to write a five-digit number . The three-digit number is divisible by , the three-digit number is divisible by , and the three-digit number is divisible by . What is
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Since is divisible by , we know that . Since is divisible by , we know that is , or . So will be either or and divisible by . Using the available digits, is the only number that is divisible by . So , and .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions