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

Algebra ->  Real-numbers -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
The answer is not 18 , because a%2Bb%3C18 .
Since a and b are digits,
system+%7B%7B%7Ba%2C%3C=9%2Cb%3C=9--->a%2Bb%3C=18 ,
but a%2Bb=18 means a=b=0 ,
and then a and b would not be "distinct digits".
The value of the two-digit number ab is 10a%2Bb .
The value of the two-digit number ba is 10b%2Ba .
The difference of ab and ba is
.
Since 9%2Aabs%28a-b%29 is the highest common factor (or greatest common factor) of ab and ba,
we know that 9 is a factor of ab and ba.
As a consequence, 9 is a factor of a%2Bb .
In other words, a%2Bb is a multiple of 9 .
The only a%2Bb multiple of 9 such that a%2Bb%3C18 is highlight%28a%2Bb=9%29 .