document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=253793>Question 253793</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a number is called \" even - odd \" if it is halfway between an even integer and an odd integer. if x is an even-odd number , which of the following must be true ?\r<BR>\n" );
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document.write( "I.  2x is an integer<BR>\n" );
document.write( "II  2x is even-odd<BR>\n" );
document.write( "III  x is halfway between two even integers\r<BR>\n" );
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document.write( "A) I only  (B) II only   (C) I and II only<BR>\n" );
document.write( "(D) II  and  III only   (E)  I, II, and III<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #186113 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=186113\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> pick any odd number.\r<BR>\n" );
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document.write( "start with 3.\r<BR>\n" );
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document.write( "take a number greater than it that is even.<BR>\n" );
document.write( "take a number less than it that is also even.\r<BR>\n" );
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document.write( "take 18 and -18\r<BR>\n" );
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document.write( "these form the odd-even pairs we will work with.\r<BR>\n" );
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document.write( "number halfway between 3 and 18 is 15/2 = 7.5<BR>\n" );
document.write( "number halfway between 3 and -18 is 21/2 = 10.5\r<BR>\n" );
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document.write( "neither of these number is an integer.\r<BR>\n" );
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document.write( "an even-odd number is therefore not an integer.\r<BR>\n" );
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document.write( "2 times the number, however, will be an integer.\r<BR>\n" );
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document.write( "2 * 7.5 = 15<BR>\n" );
document.write( "2 * 10.5 = 21\r<BR>\n" );
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document.write( "statement 1 is true.\r<BR>\n" );
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document.write( "2 times the number is not even-odd.\r<BR>\n" );
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document.write( "can't be, because 2 times the number is an integer and even-odd number is not an integer.\r<BR>\n" );
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document.write( "statement 2 is false.\r<BR>\n" );
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document.write( "statement 3 says even-odd integer is halfway between 2 even integers.\r<BR>\n" );
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document.write( "can't be because an odd integer is halfway between 2 even integers and the even-odd integers is halfway between one of the even integers and the odd integers so it can't be halfway between the 2 even integers.\r<BR>\n" );
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document.write( "take the case of 3 and 18\r<BR>\n" );
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document.write( "even-odd integer is halfway between them and is equal to 15/2 = 7.5\r<BR>\n" );
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document.write( "closest even integer higher is 8.\r<BR>\n" );
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document.write( "closest even integer lower is 6\r<BR>\n" );
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document.write( "7 is halfway between 6 and 8\r<BR>\n" );
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document.write( "7.5 is therefore not.\r<BR>\n" );
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document.write( "a number between 2 even integers will always be an integer which is not an odd-even integer.\r<BR>\n" );
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document.write( "statement 3 is false.\r<BR>\n" );
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document.write( "your answer should be selection A which is statement 1 is true only.\r<BR>\n" );
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