document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1202898>Question 1202898</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If xy>0 and xz<0, which of the following statements must be true?\r<BR>\n" );
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document.write( "I. x+y+z>0<BR>\n" );
document.write( "II. xyz<0<BR>\n" );
document.write( "III. xy+xz+yz>0\r<BR>\n" );
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document.write( "(A) I only<BR>\n" );
document.write( "(B) II only<BR>\n" );
document.write( "(C) III only<BR>\n" );
document.write( "(D) II and III only<BR>\n" );
document.write( "(E) None of the above </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #838108 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52786)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=838108\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "If xy > 0 and xz < 0, which of the following statements must be true?<BR>\n" );
document.write( "I. x + y + z > 0<BR>\n" );
document.write( "II. xyz < 0<BR>\n" );
document.write( "III. xy + xz + yz > 0<BR>\n" );
document.write( "(A) I only<BR>\n" );
document.write( "(B) II only<BR>\n" );
document.write( "(C) III only<BR>\n" );
document.write( "(D) II and III only<BR>\n" );
document.write( "(E) None of the above<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The answer is &nbsp;(E).\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;To prove it, &nbsp;it is enough to provide couner-examples to cases &nbsp;(I), &nbsp;(II) &nbsp;and &nbsp;(III) &nbsp;separately.\r<BR>\n" );
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document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "Counter-example to (I)  :  x= -1, y= -1, z= 1.\r\n" );
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document.write( "Counter-example to (II) :  x= -1, y= -1, z= 1.\r\n" );
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document.write( "Counter-example to (III):  x= -1, y= -1, z= 1.\r\n" );
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document.write( "Solved, &nbsp;with explanations.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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