document.write( "Question 867376: If a, b, and c are consecutive positive integers and a < b < c, which of the following must be an odd integer?
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Algebra.Com's Answer #523012 by Edwin McCravy(20054)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Since it must be true for ANY three consecutive integers, \r\n" );
document.write( "it must be true for the SPECIFIC consecutive integers 1,2,3 \r\n" );
document.write( "and also true for the SPECIFIC consecutive integers 2,3,4.  \r\n" );
document.write( "So we will consider these two cases for each possible choice:\r\n" );
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document.write( "Case 1:  a=1, b=2, c=3   [Two odd numbers and one even number]\r\n" );
document.write( "Case 2:  a=2, b=3, c=4   [Two even numbers and one odd number]\r\n" );
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document.write( "(A) abc  \r\n" );
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document.write( "Case 1: abc = (1)(2)(3) = 6 which is an even number.\r\n" );
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document.write( "So (A) is ruled out just by Case 1. We don't even need to try Case 2.\r\n" );
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document.write( "(B) a+b+c\r\n" );
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document.write( "Case 1: a+b+c = 1+2+3 = 6 which is an even number\r\n" );
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document.write( "So (B) is ruled out just by Case 1. We don't even need to try Case 2.\r\n" );
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document.write( "(C) a+bc\r\n" );
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document.write( "Case 1: a+bc = 1+2×3 = 1+6 = 7, which is an odd number.\r\n" );
document.write( "Case 2: a+bc = 2+3×4 = 2+12 = 14, which is an even number.\r\n" );
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document.write( "So (C) is ruled out by Case 2. \r\n" );
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document.write( "(D) a(b+c)\r\n" );
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document.write( "Case 1: a(b+c) = 1(2+3) = 1(5) = 5, which is an odd number.\r\n" );
document.write( "Case 2: a(b+c) = 2(3+4) = 2(7) = 14, which is an even number.\r\n" );
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document.write( "So (D) is ruled out by Case 2. \r\n" );
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document.write( "(E) (a+b)(b+c)\r\n" );
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document.write( "Case 1: (a+b)(b+c) = (1+2)(2+3) = (3)(5) = 15, which is an odd number.\r\n" );
document.write( "Case 2: (a+b)(b+c) = (2+3)(3+4) = (5)(7) = 35, which is an odd number.\r\n" );
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document.write( "So the only possible correct choice is (E).\r\n" );
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document.write( "Edwin
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