document.write( "Question 171070: Find the value of the digit A if the 5-digit number 12A3B is divisible by both 4 and 9, and A does not equal B. I feel like I've tried every number and I can't figure it out. Thanks \n" ); document.write( "

Algebra.Com's Answer #126315 by Mathtut(3670) $\"\"$ $\"About$

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according to divisibility rules \r
\n" ); document.write( "\n" ); document.write( "for a number to be divisible by 4 the last 2 digits have to be divisible by 4
\n" ); document.write( "and for a number to be divisible by 9 all the digits added up have to be divisible by 9. so with that in mind.
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\n" ); document.write( "lets check out 9's first
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\n" ); document.write( "12A3B
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\n" ); document.write( "so 1+2+A+3+B must be divisible by 9
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\n" ); document.write( "1+2+3=6....meaning that A+B must equal either 3 or 12:
\n" ); document.write( "for A+B to equal 3..we have two possibilities, A=1 and B=2 or A=2 and B=1.
\n" ); document.write( "lets step in with the divisibility rule for 4 now . We need to test these two possibilities . We know we have a 3 in the tens digit position so our possibilities are 31,32 which need to be divisible by 4....31 is not but 32 is divisible by 4.
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\n" ); document.write( "for A+B to equal 12....there would be 8 combinations with the following numbers
\n" ); document.write( ": 3 and 9....4 and 8....5 and 7.....6 and 6. but because A cannot equal B
\n" ); document.write( "the 6,6 combo is thrown out.
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\n" ); document.write( "At this point lets bring in the divisibility rule for 4 for our 6 remaining combos. Again we know that the tens digit is 3....so the ones digit along with the tens digit must be divisible by
\n" ); document.write( "4. We have 6 possibilities from three remaining combinations 3 and 9, 4 and 8, 5 and 7. We must place each number in the ones position while 3 is in the 10's position......so we have 33,34,35,37,38,39.......none of these are divisible by 4......so we can throw them all out.
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\n" ); document.write( "We have only one combo that survived that would be where B=2 and A=1.
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\n" ); document.write( "remember A=6 and B=6 would have worked if they hadnt given us the statement that A unequal to B.... It is important in these problems to eliminate as well as find all the possibilities....which we have done.
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\n" ); document.write( "\n" ); document.write( "so the number is $\"highlight%2812132%29\"$ \n" ); document.write( "

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