navigator123 wrote:
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?
(A) 1
(B) 3
(C) 7
(D) 9
(E) Cannot be determined
AB
CD
------
AAA
------
look carefully at B+D: it gives 10 + A. So B+D=10 + A
Now lets get into the calculation part:
10A + B +10C + D = 100A + 10A + A
10A + 10 + A + 10C = 111A
10 + 10 C = 100A
10(1+C) = 100A
1+ C = 10A
It is given that a,b,c and d are single digit nos. So in order for that statement to hold true. The value of A can only be 1.
So, 1 + c = 10
C= 9 .option D is the correct answer.
Give a kudos if this solution helped you.