where AB and CD are two-digit numbers and AAA is a three digit number; A, B, C, and D are distinct positive integers. In the addition problem above, what is the value of C?
(E) Cannot be determined
Aha finally got it.
Since AB and CD are two digit numbers and AAA is a three digit number. AAA has to be less than 200. Ex/ 99+99=198. So since the last digit of AAA has to be 1 then all the A's are 1.
So the new problem looks like this:
To get 1 from B+D, B+D has to either equal 11 or 1 (0+1). In this case only 11 works b/c C can't be 10.
It doesnt matter what the values of B and D are, but just that they equal 11. Since there is a carry over of 1. C must be equal to 9. Since 9+1+1=11.
The numbers could look like this.