document.write( "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:
\n" ); document.write( "(A) 18 (B) 9 (C) 15 (D) None of these
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Algebra.Com's Answer #575566 by KMST(5328) $\"\"$ $\"About$

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The answer is not $\"18\"$ , because $\"a%2Bb%3C18\"$ .
\n" ); document.write( "Since $\"a\"$ and $\"b\"$ are digits,
\n" ); document.write( " $\"system+%7B%7B%7Ba%2C%3C=9%2Cb%3C=9\"$ ---> $\"a%2Bb%3C=18\"$ ,
\n" ); document.write( "but $\"a%2Bb=18\"$ means $\"a=b=0\"$ ,
\n" ); document.write( "and then $\"a\"$ and $\"b\"$ would not be \"distinct digits\".
\n" ); document.write( "The value of the two-digit number ab is $\"10a%2Bb\"$ .
\n" ); document.write( "The value of the two-digit number ba is $\"10b%2Ba\"$ .
\n" ); document.write( "The difference of ab and ba is
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.
\n" ); document.write( "Since $\"9%2Aabs%28a-b%29\"$ is the highest common factor (or greatest common factor) of ab and ba,
\n" ); document.write( "we know that $\"9\"$ is a factor of ab and ba.
\n" ); document.write( "As a consequence, $\"9\"$ is a factor of $\"a%2Bb\"$ .
\n" ); document.write( "In other words, $\"a%2Bb\"$ is a multiple of $\"9\"$ .
\n" ); document.write( "The only $\"a%2Bb\"$ multiple of $\"9\"$ such that $\"a%2Bb%3C18\"$ is $\"highlight%28a%2Bb=9%29\"$ . \n" ); document.write( "

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