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)
Sum of digits AAA
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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.
The one and only tenth digit + 1X=111, must be 9. So C=9.
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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?
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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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
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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