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# In the correctly worked addition problem above, A, B, and C are distin

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Re: In the correctly worked addition problem above, A, B, and C are distin [#permalink]
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AA + BB + CC = ABC

From above, A+B+C = 10 + C => A+B = 10
Again, A+B+C+1 = 10A + B => 9A = C+1

Since, A+B is equal to 10, if A=0, then B=10. So A!=0. => A=1 and C=8. Single digit integers.
=> B = 9.

So the numbers are 11, 99, 88 and sum of the digits is 18.
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Re: In the correctly worked addition problem above, A, B, and C are distin [#permalink]
Bunuel wrote:
AA
+
BB
+
CC
___
ABC

In the correctly worked addition problem above, A, B, and C are distinct digits. What is the sum of A, B and C ?

A. 12
B. 15
C. 17
D. 18
E. 19

Are You Up For the Challenge: 700 Level Questions

People have committed to brute force however we can simply and check whether we can come to the right conclusion

10(A+B+C) +A+B+C=100(A)+10B +C
=>10(A+C) +A+B =100A......
WHICH WE GET IF WE SUBSTITUTE the values a=1 b=9 and c=8

Therefore IMO D
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Re: In the correctly worked addition problem above, A, B, and C are distin [#permalink]
MartyMurray KarishmaB Can you please provide your solution for this question ?
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Re: In the correctly worked addition problem above, A, B, and C are distin [#permalink]
1
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­AA
+
BB
+
CC
___
ABC

In the correctly worked addition problem above, A, B, and C are distinct digits. What is the sum of A, B and C ?

AA = 10A + 1A = 11A

BB = 10B + 1B = 11B

CC = 10C + 1C = 11C

11A + 11B + 11C = 100A + 10B + C

B + 10C = 89A

B + 10C is a multiple of 89.

B + 10C cannot be greater than 99 since B and C are digits. So, B + 10C = 89.

B must be 9.

C must be 8.

Thus, since B + 10C = 89A, A = 1

A + B + C = 1 + 9 + 8 = 18

A. 12
B. 15
C. 17
D. 18
E. 19