document.write( "Question 92788: If x, y, and z are positive intergers such that the value of x+y is even and the value of \"%28x%2By%29%5E2\"+x+z is odd, which of the following must be true?\r
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Algebra.Com's Answer #67529 by Edwin McCravy(20060)\"\" \"About 
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document.write( "If x, y, and z are positive integers such that the value of x+y\r\n" );
document.write( "is even and the value of (x+y)²+x+z is odd, which of the following\r\n" );
document.write( "must be true?\r\n" );
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document.write( "(A) x is odd\r\n" );
document.write( "(B) x is even\r\n" );
document.write( "(C) If z is even, then x is odd\r\n" );
document.write( "(D) If z is even, then xy is even\r\n" );
document.write( "(E) xy is even\r\n" );
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document.write( "There are 8 possible cases:\r\n" );
document.write( "We can use any even and odd integer.  The easiest even positive\r\n" );
document.write( "integer is 2 and the easiest odd integer is 1.  So let's use\r\n" );
document.write( "these in those 8 cases\r\n" );
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document.write( "     x  y  z   x+z=?        (x+y)²+x+z=?\r\n" );
document.write( "------------------------------------------------------------  \r\n" );
document.write( "1.   2  2  2   2+2=4=EVEN   (2+2)²+2+2=4²+2+2=16+2+2=20=EVEN \r\n" );
document.write( "2.   2  2  1   2+1=3=ODD    (2+2)²+2+1=4²+2+1=16+2+1=19=ODD   \r\n" );
document.write( "3.   2  1  2   2+2=4=EVEN   (2+1)²+2+2=3²+2+2= 9+2+2=13=EVEN\r\n" );
document.write( "4.   2  1  1   2+1=3=ODD    (2+1)²+2+1=3²+2+1= 9+2+1=12=EVEN\r\n" );
document.write( "5.   1  2  2   1+2=3=ODD    (1+2)²+1+2=3²+1+2= 9+1+2=12=EVEN \r\n" );
document.write( "6.   1  2  1   1+2=3=ODD    (1+2)²+1+1=3²+1+1= 9+1+1=11=ODD\r\n" );
document.write( "7.   1  1  2   1+1=2=EVEN   (1+1)²+1+2=2²+1+2= 4+1+2= 7=ODD\r\n" );
document.write( "8.   1  1  1   1+1=2=EVEN   (1+1)²+1+1=2²+1+1= 4+1+1= 6=EVEN\r\n" );
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document.write( "There are only one case when x+y is EVEN and (x+y)²+x+z is ODD,\r\n" );
document.write( "That is case 7, where x=1, y=1 and z=2\r\n" );
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document.write( "So x is odd, y is odd, and z is even. \r\n" );
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document.write( "The only one of the choices that must be true is A.\r\n" );
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document.write( "Edwin

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