document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=712268>Question 712268</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If m and p are positive integers and (m+p) x m is even, which of the following must be true. A)if m is odd, then p is odd B)if m is odd, then p is even C)if m is even, then p is even D)if m is even, then p is odd. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #437845 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=437845\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (m+p) x m is even \r<BR>\n" );
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document.write( "so either m is even or m+p is even\r<BR>\n" );
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document.write( "If m is even, then m+p is odd only if p is odd.\r<BR>\n" );
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document.write( "If m+p is even, then \r<BR>\n" );
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document.write( "a) both m and p are even (since even + even = even)\r<BR>\n" );
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document.write( "or\r<BR>\n" );
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document.write( "b) both m and p are odd (since odd + odd = even)\r<BR>\n" );
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document.write( "So let's go through the choices\r<BR>\n" );
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document.write( "A)if m is odd, then p is odd \r<BR>\n" );
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document.write( "This is true because m+p is even if both m and p are odd and m+p must be even for (m+p) x m to be even (since m is odd)\r<BR>\n" );
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document.write( "B)if m is odd, then p is even \r<BR>\n" );
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document.write( "This is false because it's the complete opposite of choice A which was true.\r<BR>\n" );
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document.write( "C)if m is even, then p is even \r<BR>\n" );
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document.write( "If m is even, then (m+p) x m is even (since even x odd = odd x even = even x even = even)\r<BR>\n" );
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document.write( "So because p could be even or odd (it wouldn't change the outcome), we can't say for sure if p is even\r<BR>\n" );
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document.write( "So this is false\r<BR>\n" );
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document.write( "D)if m is even, then p is odd.\r<BR>\n" );
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document.write( "Using the same logic above, we can't determine if p is odd when m is even. So there's no way of knowing.\r<BR>\n" );
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document.write( "So this is false too. </SPAN>\n" );
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