800guy wrote:OA coming when a few people have attempted...
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
Since A, B, C and D represent digits:
AB = 10A+B.
CD = 10C+D.
AAA = 100A+10A+A = 111A.
Substituting in the equation AB + CD = AAA, we get:
(10A+B) + (10C+D) = 111A.
10C + B + D = 101A.
The equation above shows that C=9.
If C=8, then we are left with the impossible equation B+D = 21. The sum of two digits cannot be 21.
Thus, C cannot be less than 9.
The correct answer is
D.
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