document.write( "Question 479594: If a + b are odd integers, which of the following must be an even integer?\r
\n" ); document.write( "\n" ); document.write( " I. \"%28a+%2B+b%29%2F2\"
\n" ); document.write( " II. \"ab+-+1\"
\n" ); document.write( "III. \"%28ab+%2B+1%29%2F2\"\r
\n" ); document.write( "\n" ); document.write( "Possible answers:
\n" ); document.write( "a) I only
\n" ); document.write( "b) II only
\n" ); document.write( "c) I and II only
\n" ); document.write( "d) II and III only
\n" ); document.write( "e) I, II and III\r
\n" ); document.write( "\n" ); document.write( "I would appreciate your help. Thanks! :-)
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Algebra.Com's Answer #328589 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "  I. \"%28a+%2B+b%29%2F2\" NO, because \"%283%2B7%29%2F2\" = \"10%2F2\" = 5, which is ODD  \r\n" );
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document.write( " II. \"ab+-+1\" YES, because an ODD times an ODD is an ODD, \r\n" );
document.write( "so ab is always ODD, and then when we subtract 1 from that ODD, \r\n" );
document.write( "we will always get an EVEN.\r\n" );
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document.write( "or algebraically,\r\n" );
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document.write( "(2m+1)(2n+1)-1 = 4mn+2m+2n+1-1 = 2(2mn+m+n) = which is EVEN.\r\n" );
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document.write( "III. \"%28ab+%2B+1%29%2F2\"  NO, because \"%283x7%2B1%29%2F2=%2821%2B1%29%2F2=22%2F2\" = 11, which is ODD\r\n" );
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document.write( "Therefore only II is always even.  Answer b. \r\n" );
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document.write( "Edwin
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