document.write( "Question 390606: N.M and T are integers
\n" ); document.write( "N+M is an odd number
\n" ); document.write( "M+T is an odd number\r
\n" ); document.write( "\n" ); document.write( "Which of the following must be true:\r
\n" ); document.write( "\n" ); document.write( "a) NxT is even
\n" ); document.write( "b) NxT is odd
\n" ); document.write( "c) N+T is odd
\n" ); document.write( "d) N+T is even
\n" ); document.write( "e) N-T is odd \n" ); document.write( "
Algebra.Com's Answer #277024 by Edwin McCravy(20056)\"\" \"About 
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document.write( "N+M is an odd number\r\n" );
document.write( "M+T is an odd number \r\n" );
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document.write( "Case 1:  If M is even, N and T are both odd \r\n" );
document.write( "         (in order to make both their sums with M odd).\r\n" );
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document.write( "Case 2:  If M is odd, N and T are both even \r\n" );
document.write( "         (in order to make both their sums with M even).\r\n" );
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document.write( "So N and T are the same type (parity) of integer, i.e., both odd or both even.\r\n" );
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document.write( "  a) NxT is even\r\n" );
document.write( "This is false in case 1, since an odd times an odd is an odd\r\n" );
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document.write( "b) NxT is odd\r\n" );
document.write( "This is false in case 2, since an even times an even is an even\r\n" );
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document.write( "c) N+T is odd\r\n" );
document.write( "This is false in both cases, since if you add two odds or two evens, you get an even.\r\n" );
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document.write( "d) N+T is even\r\n" );
document.write( "This is true in both cases, since if you add two odds or two evens, you get an even.\r\n" );
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document.write( "e) N-T is odd\r\n" );
document.write( "This is false in both cases, since if you subtract two odds or two evens, you get an even.\r\n" );
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document.write( "So the only correct statement is d)\r\n" );
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document.write( "Edwin
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