my thoughts are AB + CD can at most be 99 + 99 which is less than 222, 333, 444 etc, therfore AAA must be 111.
Then test out a couple of possibilities. Since we figured out that A is 1, then limiting numbers are 10 and 19
10 and 11 dont work since you need a 3 digit number to sum to 111. therefore new limits are 12 and 19.
it could be 19 + 92 or it could be 12 + 99, 11 etc. Both cases c = 9
answer is D in my opinion. I cant see any way of doing this kind of problem more quickly. I think you just have to think through the problem logically.
AB + CD = AAA, 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
Is there a quick way of figuring out the above?