AF + CD = AAA, where AF and CD are two-digit numbers and AAA is a three digit number; A, F, C, and D are distinct positive integers. In the addition problem above, what is the value of C?  Choose the correct choice from the following options:
A) 1  B) 3  C) 7  D) 9  E) Cannot be determined
Since AF 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 1F+CD=111   Now, C can not be less than 9, because no two-digit integer with first digit 1 (1F&lt;20) can be added to two-digit integer less than 90, so that to have the sum 111 (if CD&lt;90, so if C&lt;9, CD+1F&lt;111).   Hence C=9.   Answer: 9.
<result>D</result>
AF + CD = AAA, where AF and CD are two-digit numbers and AAA is a three digit number; A, F, C, and D are distinct positive integers. In the addition problem above, what is the value of C?