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by ddm » Mon Sep 08, 2008 1:39 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

Your Answer : E
Actual Answer : D
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by LSB » Tue Sep 09, 2008 12:00 pm
AAA can only be 111 as no other sum of two two digit integers will result in a 3 digit integer with same digits.

This means that the tenth digit of AB can only be 1
AB = 11 12 13 14 15 16 17 18 19

The units digits adding up to eleven (B & D) can only be

9 & 2 ---> 1)
8 & 3 ---> 2)
7 & 4 ---> 3)
6 & 5 ---> 4)

If 1) is true then AB is either 12 or 19. This would make CD either 99 or 92
None of these can be the case because they violate the distinct digit rule

If 2) is true then AB is either 18 or 13. This would make CD either 93 or 98
---> C = 9

If 3) is true then AB is either 17 or 14. This would make CD either 94 or 97
---> C = 9

If 4) is true then AB is either 16 or 15. This would make CD either 96 or 95
---> C = 9

Answer 9 ---> D
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by Nycgrl » Tue Sep 09, 2008 9:01 pm
i DIDN'T GET IT?
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by Nycgrl » Tue Sep 09, 2008 9:01 pm
i DIDN'T GET IT?
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by LSB » Tue Sep 09, 2008 9:02 pm
where did u get lost
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