document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=363479>Question 363479</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\r<BR>\n" );
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document.write( "II   2x is even-odd\r<BR>\n" );
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document.write( "III  x is halfway between two even integers\r<BR>\n" );
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document.write( "(A)  I only\r<BR>\n" );
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document.write( "(B)  II only\r<BR>\n" );
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document.write( "(c) I and II only \r<BR>\n" );
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document.write( "(D) II and III only \r<BR>\n" );
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document.write( "(E) I, II, and III\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #259171 by </B><A HREF=/tutors/aboutme.mpl?userid=J2R2R><B>J2R2R(94)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=J2R2R><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=J2R2R><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=259171\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let us say the two numbers are 2m + 1 (odd) and 2n (even) where m and n are integers irrespective of being odd or even.\r<BR>\n" );
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document.write( "Halfway between them is (2m + 1 + 2n)/2 = (m + n) + ½\r<BR>\n" );
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document.write( "So the even-odd number X must be of the form N + ½ where N can be any integer.\r<BR>\n" );
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document.write( "Therefore\r<BR>\n" );
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document.write( "2X is an integer (odd)\r<BR>\n" );
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document.write( "2X cannot be an even-odd number since 2X is an integer and not of the form N + ½\r<BR>\n" );
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document.write( "X cannot be halfway between two even integers since half way between two even integers is an integer too and X is of the form N + ½\r<BR>\n" );
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document.write( "Therefore only the first one is correct which means the answer is A. </SPAN>\n" );
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