document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=976005>Question 976005</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can someone please explain in detail this question:<BR>\n" );
document.write( "If A, B, and C are positive integers, and A is a factor of B, then which of the following must be true ?<BR>\n" );
document.write( "(A) 2A = 4B<BR>\n" );
document.write( "(B) BC > AC<BR>\n" );
document.write( "(C) BC is a multiple of A<BR>\n" );
document.write( "(D) AC is a factor of B<BR>\n" );
document.write( "(E) AB is a multiple of C </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #597682 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=597682\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 2*A = 4*B<BR>\n" );
document.write( "A = 2*B\r<BR>\n" );
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document.write( "the last equation implies that A is larger than B, but it's actually the other way around.\r<BR>\n" );
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document.write( "So choice A is false.\r<BR>\n" );
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document.write( "\"A is a factor of B\" means <BR>\n" );
document.write( "B = k*A<BR>\n" );
document.write( "where k is some integer\r<BR>\n" );
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document.write( "Eg: B = 2*A or B = 7*A\r<BR>\n" );
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document.write( "Since A,B,C are positive, and because A is a factor of B, this makes A < B\r<BR>\n" );
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document.write( "A < B<BR>\n" );
document.write( "A*C < B*C<BR>\n" );
document.write( "BC > AC\r<BR>\n" );
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document.write( "So choice B is true.\r<BR>\n" );
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document.write( "B = k*A<BR>\n" );
document.write( "B*C = k*A*C<BR>\n" );
document.write( "BC = (k*C)*A\r<BR>\n" );
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document.write( "so that proves BC is a multiple of A. Put another way, A is a factor of BC\r<BR>\n" );
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document.write( "That makes choice C true.\r<BR>\n" );
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document.write( "\"AC is a factor of B\" is only true if C is also a factor. But we don't know if C is a factor of B or not. So we can't say it's true.\r<BR>\n" );
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document.write( "Therefore, choice D is false.\r<BR>\n" );
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document.write( "This is similar to choice D. We would have to know if C is factor of either A or  B. But we're not given this info.\r<BR>\n" );
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document.write( "Choice E is false.\r<BR>\n" );
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document.write( "The only true statements are <BR>\n" );
document.write( "(B) BC > AC<BR>\n" );
document.write( "(C) BC is a multiple of A\r<BR>\n" );
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document.write( "Jim\r<BR>\n" );
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