Question

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?
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Answer 1

Answer:

Since AB and CD are two-digit integers, their sum can give us only one three digit integer of a kind of AAA: 111.

So, A=1 and we have 1B+CD=111

Now, C can not be less than 9, because no two-digit integer with first digit 1 (1B<20) can be added to two-digit integer less than 90, so that to have the sum 111 (if CD<90, so if C<9, CD+1B<111).

Hence C=9.

Answer: D.