document.write( "Question 1023562: The digits of a three digit number form an arithmetic
\n" ); document.write( "progression. If the first and second digits are
\n" ); document.write( "decreased by 1 and the the third is increased by 3,
\n" ); document.write( "the digits will form a geometric progression.
\n" ); document.write( "What is the original number,if the sum of the digits
\n" ); document.write( "is 12? \n" ); document.write( "

Algebra.Com's Answer #639100 by Edwin McCravy(20055) $\"\"$ $\"About$

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If the first and second digits are decreased by 1
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document.write( "The only possible ascending geometric progression\r\n" );
document.write( "of digits of a three-digit number are \r\n" );
document.write( "Case 1. 1,1,1\r\n" );
document.write( "Case 2. 1,3,9\r\n" );
document.write( "Case 3. 2,4,8\r\n" );
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\n" ); document.write( "The digits of a three digit number form an
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document.write( "Case 1 is out because the third number is 1,\r\n" );
document.write( "and 1 can't be the result of increasing a digit by 3.\r\n" );
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document.write( "Case 3 is out because the previous numbers would have \r\n" );
document.write( "been 2,5,5, which is not an arithmetic progression.\r\n" );
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document.write( "So it must be case 2.\r\n" );
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document.write( "Checking:  the previous digits would have been 2,4,and 6.\r\n" );
document.write( "which do form an arithmetic progression.  We didn't need \r\n" );
document.write( "the information that the sum of the digits is 12, but it\r\n" );
document.write( "does turn out that 2+4+6=12.\r\n" );
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document.write( "Answer: The original three-digit number was 246.\r\n" );
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document.write( "Edwin

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