document.write( "Question 1209434: A, B and C are distinct digits and 4 * AB = CA. Find the sum A+B+C \n" ); document.write( "

Algebra.Com's Answer #848823 by ikleyn(52857) $\"\"$ $\"About$

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\n" ); document.write( "A, B and C are distinct digits and 4 * AB = CA. Find the sum A+B+C
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document.write( "Since  4 * AB = CA,  CA must be a two-digit number >= 40.    (*)\r\n" );
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document.write( "Since  4 * AB = CA,  we conclude that AB is a two-digit number between 10 and 24, inclusive.\r\n" );
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document.write( "So, A is either 1 or 2.  But from 4 * AB = CA, digit A must be even - so,\r\n" );
document.write( "we conclude that A = 2.\r\n" );
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document.write( "Thus, CA is a two digit number multiple of 4 and with the last digit 2.\r\n" );
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document.write( "Such numbers CA can be only 12, 32, 52, 72, 92.\r\n" );
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document.write( "Condition (*) prohibits 12 and 32, so the remaining opportunities for CA are 52, 72, 92.\r\n" );
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document.write( "Divide CA by 4, and you will get the values  13, 18, 23  for AB.\r\n" );
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document.write( "But, as we established above, the digit A is 2;  therefore,  AB can only be 23.\r\n" );
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document.write( "Thus, A = 2;  B = 3;  C = 9.  All these digits are different.\r\n" );
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document.write( "The sum  A + B + C is  2 + 3 + 9 = 14.    ANSWER\r\n" );
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