document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=3921>Question 3921</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Of the z students at a certain college, x are studying French and y are studying German. If w are studying both French and German, which of the following expresses the number of students at the college not studying either French or German ?<BR>\n" );
document.write( "   (A) z + w – x – y <BR>\n" );
document.write( "   (B) z – w – x – y <BR>\n" );
document.write( "   (C) z – w – x + y<BR>\n" );
document.write( "   (D) w + x + y – z  <BR>\n" );
document.write( "   (E) w – x – y – z <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 #1721 by </B><A HREF=/tutors/aboutme.mpl?userid=longjonsilver><B>longjonsilver(2297)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=longjonsilver><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=longjonsilver><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=1721\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> think of an enclosed box with 2 circles inside, overlapping each other - the classic Venn diagram.\r<BR>\n" );
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document.write( "Let F - circle1 for those who study French<BR>\n" );
document.write( "Let G - circle2 for those who study German\r<BR>\n" );
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document.write( "If you think of the 2 circles as apart, first, then some people must be in both circles (since they study both French and German). As you merge the 2 circles, these people will be in the overlapping area (FnG) but will have been counted twice.\r<BR>\n" );
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document.write( "Now the total number of people in the circles = all in F circle + all in G circle minus one lot of those in both\r<BR>\n" );
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document.write( "In maths notation, FuG, meaning (F union G) is everyone in the 2 sets (circles).<BR>\n" );
document.write( "Whilst FnG (F intersection G) is those people just in BOTH sets ( circles)...i remember this by the n symbol looking like the n in iNtersection. Petty, but it works for me :-).\r<BR>\n" );
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document.write( "So, (FuG) = F + G - (FnG)\r<BR>\n" );
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document.write( "In your question, you have different lettering, so lets put them in instead:\r<BR>\n" );
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document.write( "FuG = x + y - w\r<BR>\n" );
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document.write( "Now, since FuG are those STUDYING the languages, then those who don't study them must be all the rest, surely?\r<BR>\n" );
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document.write( "As the total number of students is z, then those NOT studying F and/or G will be:\r<BR>\n" );
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document.write( "z-(x+y-w) which becomes z-x-y+w, which is answer A.\r<BR>\n" );
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document.write( "jon.<BR>\n" );
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