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Sum of digits AAA

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by caspermonday » Sat Oct 24, 2009 12:00 pm
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


OA D
Please help me!
Thanks)
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by NikolayZ » Sat Oct 24, 2009 12:49 pm
First of all, AAA must be 111, you simply can't get another 3-digit number adding two 2-digit numbers together. Sp we already know that AB is 1X

The one and only tenth digit + 1X=111, must be 9. So C=9.
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by caspermonday » Sun Oct 25, 2009 4:33 am
Thank you!

I saw exactly the same exlanation in the source I downloaded somewhere. But how do we know that sum of two 2digit numbers is inevitably 111? What should be one's thinking to come up with this?
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by NikolayZ » Sun Oct 25, 2009 5:20 am
Ok.
We have 2 two digit numbers. And a sum AAA - sum tells us that it can be 111, 222, 333, 444, 555 and so on.
BUT the largest three digit number can be summed up from 2 two-digit integers is 99+99=198.
I hope it is clear now ;)
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by caspermonday » Sun Oct 25, 2009 6:03 am
Alright. Pretty clear now. Thanks for your time. Me dummie)
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