Question 1202988: If A, B, and C are different digits in the addition problem below and A < B
BC
+BC
1AB
Answer by greenestamps(13200) (Show Source):
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BC
+ BC
----
1AB
(1) In the units column, 2 times C yields final digit B; that means B must be even
(2) 2 times a 2-digit number yields a 3-digit number, so the 2-digit number is greater than 50, so B is greater than or equal to 5.
(3) (1) and (2) together mean B is either 6 or 8. That gives us 4 possibilities:
63 84 68 89
+ 63 + 84 + 68 + 89
---- ---- ---- ----
126 168 136 178
In the first two cases, B > C, so those are not solutions.
In both of the other cases, the condition A < B < C is satisfied, so those are both solutions to the problem.
ANSWERS:
68 89
+ 68 + 89
---- ----
136 178
Note we could have ruled out the first two cases above by further logical reasoning; however, with the possibilities reduced to only four, it was faster and easier simply to see which of the cases satisfied the conditions.
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