Problem:
The letters A,B,C and D all represent different digits. If AB+ CA DA and AB− CA A, what digit does D represent?
Answer Choices:
A. 5
B. 6
C. 7
D. 8
E. 9
Solution:
Because A+B=A,B=0. Subtracting 10 from A and adding 10 to B,10−A=A, so A must be 5 , and AB is 50 . Because 50−C5=5, C=4 and D=5+4=9.
Answer: E.
The problems on this page are the property of the MAA's American Mathematics Competitions