SOLUTION: If A, B, and C are different digits in the addition problem below and A < B <C, then B must equal BC +BC 1AB

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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): You can put this solution on YOUR website!


   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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