document.write( "Question 220710: Given that the number 5913d8 is divisible by 12, what is the sum of all the digits that could replace d? \n" ); document.write( "

Algebra.Com's Answer #165622 by jim_thompson5910(35256) $\"\"$ $\"About$

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5913d8 is only divisible by 12 only if 5913d8 is divisible by both 3 and 4. \r
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\n" ); document.write( "\n" ); document.write( "5913d8 is divisible by 4 only if the last two digits are divisible by 4. In other words, 5913d8 is divisible by 4 only if d8 is divisible by 4. This restricts the choices of d to: 0, 2, 4, 6, and 8\r
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\n" ); document.write( "\n" ); document.write( "5913d8 is divisible by 3 only if the sum of the digits are divisible by 3. So add them up to get: 5+9+1+3+d+8=26+d. Now just plug in the possible values of d to determine if 26+d is divisible by 3. \r
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\n" ); document.write( "\n" ); document.write( "d=0: 26+0=26 which is NOT divisible by 3. So d=0 is eliminated.
\n" ); document.write( "d=2: 26+2=28 which is NOT divisible by 3. So d=2 is eliminated.
\n" ); document.write( "d=4: 26+4=30 which is divisible by 3. So d=4 is one digit.
\n" ); document.write( "d=6: 26+6=32 which is NOT divisible by 3. So d=6 is eliminated.
\n" ); document.write( "d=8: 26+8=34 which is NOT divisible by 3. So d=8 is eliminated.\r
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\n" ); document.write( "\n" ); document.write( "So the only number that is divisible by 12 is 591348. So the sum of all the digits that could replace 'd' is 4. \n" ); document.write( "

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