Problem:
Each of the digits , and is used only once to make two five-digit numbers so that they have the largest possible sum. Which of the following could be one of the numbers?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The sum will be as large as possible when the largest digits are placed in the most significant places. The and should be in the ten-thousands place, the and in the thousands place, the and in the hundreds place, the and in the tens place, and the and in the units place. The only choice that fits that description is . (In this case the other number is , giving the largest sum of .)
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions