Problem:
If and are nonzero digits, then the number of three whole numbers is
Answer Choices:
A.
B.
C.
D.
E. depends on the values of and
Solution:
, so we "carry " from the ten's column to the hundred's column. Similarly since , so we "carry " from the hundred's place to the thousand's place. , so the sum is a -digit number of the form .
Since is a digit from to , the sum must be between and . Thus the sum of the three whole numbers must have digits.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions