document.write( "Question 1022880: The five digit number a986b is divisible by 72.What is the value of a+b?
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Algebra.Com's Answer #638453 by ikleyn(52862) $\"\"$ $\"About$

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document.write( "72 = 9*8.\r\n" );
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document.write( "The sum of digits S = a + 9 + 8 + 6 + b must be multiple of 9 and the number 86b must be multiple of 8.\r\n" );
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document.write( "See the divisibility by 9 rule in the lesson Divisibility by 9 rule in this site.\r\n" );
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document.write( "The divisibility by 8 rule says that the number 86b is multiple of 8.\r\n" );
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document.write( "From this condition (\"86b must be multiple of 8\") we have with necessity that b = 4. There is no other possibility.\r\n" );
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document.write( "Now, S = 23 + (a + b) = 23 + 4 + a = 27 + a.\r\n" );
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document.write( "a >= 1 and <= 9.\r\n" );
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document.write( "Since S is multiple of 9, there is only one possibility for a:\r\n" );
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document.write( "a = 9.\r\n" );
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document.write( "Answer. a = 9, b= 4 and a + b = 9 + 4 = 13.\r\n" );
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