Problem:
The sum of the two 5-digit numbers AMC10 and AMC12 is 123422. What is A+M+C?
Answer Choices:
A. 10
B. 11
C. 12
D. 13
E. 14
Solution:
Since the last two digits of AMC10 and AMC12 sum to 22, we have
AMC+AMC=2(AMC)=1234.
Hence AMC=617, so A=6,M=1,C=7, and A+M+C=6+1+7=14.
Answer: E​.
The problems on this page are the property of the MAA's American Mathematics Competitions