SOLUTION: ab and ba are two digit numbers, a and b are distinct digits from 0 and 9. Difference of ab and ba is HCF of ab and ba. The value of (a + b) is: (A) 18 (B) 9 (C) 15 (D) N

Question 943984: ab and ba are two digit numbers, a and b are distinct digits from 0 and 9. Difference of ab and ba is HCF of ab and ba. The value of (a + b) is:
(A) 18 (B) 9 (C) 15 (D) None of these

Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
The answer is not , because .
Since and are digits,
---> ,
but means ,
and then and would not be "distinct digits".
The value of the two-digit number ab is .
The value of the two-digit number ba is .
The difference of ab and ba is
.
Since is the highest common factor (or greatest common factor) of ab and ba,
we know that is a factor of ab and ba.
As a consequence, is a factor of .
In other words, is a multiple of .
The only multiple of such that is .
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