document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1201393>Question 1201393</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a class of 70 students 6 offer Economics only, 18 offer Geography and economics but not Mathematics, 36 offer Economics and Mathematics, 53 offer Economics, 50 offer Geography and 34 offer Mathematics. All students offer at least one subject.<BR>\n" );
document.write( "(a)Determine the number of students who offer Maths only<BR>\n" );
document.write( "(b) Determine the number of students who Geography only </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #835731 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=835731\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Venn Diagram<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0Adrawing%28400%2C400%2C-5%2C5%2C-5%2C5%2C%0D%0Aline%28-4%2C4%2C4%2C4%29%2C%0D%0Aline%284%2C4%2C4%2C-4%29%2C%0D%0Aline%284%2C-4%2C-4%2C-4%29%2C%0D%0Aline%28-4%2C-4%2C-4%2C4%29%2C%0D%0A%0D%0Acircle%28-1%2C1%2C2%29%2Ccircle%281%2C1%2C2%29%2Ccircle%280%2C-0.7321%2C2%29%2C%0D%0A%0D%0Alocate%28-3.2%2C2.8%2CEcon%29%2C%0D%0Alocate%282.6%2C2.8%2CGeo%29%2C%0D%0Alocate%281%2C-2.6%2CMath%29%2C%0D%0Alocate%28-2%2C1.8%2Ca%29%2C%0D%0Alocate%280%2C1.8%2Cb%29%2C%0D%0Alocate%282%2C1.8%2Cc%29%2C%0D%0Alocate%28-1.5%2C0%2Cd%29%2C%0D%0Alocate%280%2C0.4%2Ce%29%2C%0D%0Alocate%281.2%2C0%2Cf%29%2C%0D%0Alocate%280%2C-1.5%2Cg%29%2C%0D%0Alocate%283%2C-1.5%2Ch%29%0D%0A%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "There are 8 distinct regions<BR>\n" );
document.write( "a = Econ only<BR>\n" );
document.write( "b = Econ and Geo, but not Math<BR>\n" );
document.write( "c = Geo only<BR>\n" );
document.write( "d = Econ and Math, but not Geo<BR>\n" );
document.write( "e = all 3<BR>\n" );
document.write( "f = Geo and Math, but not Econ<BR>\n" );
document.write( "g = Math only<BR>\n" );
document.write( "h = neither of the 3 classes mentioned\r<BR>\n" );
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document.write( "Given facts<BR>\n" );
document.write( "<TABLE  border = \"1\" cellpadding = \"5\">\n" );
document.write( "<tr><TD >Number</TD><TD >Fact</TD></tr><tr><TD >1</TD><TD >70 students</TD></tr><tr><TD >2</TD><TD >6 offer Economics only</TD></tr><tr><TD >3</TD><TD >18 offer Geography and economics but not Mathematics</TD></tr><tr><TD >4</TD><TD >36 offer Economics and Mathematics</TD></tr><tr><TD >5</TD><TD >53 offer Economics</TD></tr><tr><TD >6</TD><TD >50 offer Geography</TD></tr><tr><TD >7</TD><TD >34 offer Mathematics.</TD></tr><tr><TD >8</TD><TD >All students offer at least one subject.</TD></tr>\n" );
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document.write( "Fact 2 leads directly to a = 6<BR>\n" );
document.write( "Fact 3 tells us b = 18<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0Adrawing%28400%2C400%2C-5%2C5%2C-5%2C5%2C%0D%0Aline%28-4%2C4%2C4%2C4%29%2C%0D%0Aline%284%2C4%2C4%2C-4%29%2C%0D%0Aline%284%2C-4%2C-4%2C-4%29%2C%0D%0Aline%28-4%2C-4%2C-4%2C4%29%2C%0D%0A%0D%0Acircle%28-1%2C1%2C2%29%2Ccircle%281%2C1%2C2%29%2Ccircle%280%2C-0.7321%2C2%29%2C%0D%0A%0D%0Alocate%28-3.2%2C2.8%2CEcon%29%2C%0D%0Alocate%282.6%2C2.8%2CGeo%29%2C%0D%0Alocate%281%2C-2.6%2CMath%29%2C%0D%0Alocate%28-2%2C1.8%2C6%29%2C%0D%0Alocate%280%2C1.8%2C18%29%2C%0D%0Alocate%282%2C1.8%2Cc%29%2C%0D%0Alocate%28-1.5%2C0%2Cd%29%2C%0D%0Alocate%280%2C0.4%2Ce%29%2C%0D%0Alocate%281.2%2C0%2Cf%29%2C%0D%0Alocate%280%2C-1.5%2Cg%29%2C%0D%0Alocate%283%2C-1.5%2Ch%29%0D%0A%29%0D%0A%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "fact4 says that d+e = 36\r<BR>\n" );
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document.write( "we have<BR>\n" );
document.write( "a = 6<BR>\n" );
document.write( "b = 18<BR>\n" );
document.write( "d+e = 36<BR>\n" );
document.write( "so,<BR>\n" );
document.write( "a+b+d+e = 6+18+36 = 60\r<BR>\n" );
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document.write( "But this sum is larger than the number of people taking Econ (see fact 5). We run into a contradiction.\r<BR>\n" );
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document.write( "Put another way:<BR>\n" );
document.write( "fact5 says that a+b+d+e = 53<BR>\n" );
document.write( "Let's plug a = 6 and b = 18 into that and isolate d+e<BR>\n" );
document.write( "a+b+d+e = 53<BR>\n" );
document.write( "6+18+d+e = 53<BR>\n" );
document.write( "24+d+e = 53<BR>\n" );
document.write( "d+e = 53-24<BR>\n" );
document.write( "d+e = 29<BR>\n" );
document.write( "This clashes with fact 4 that d+e = 36\r<BR>\n" );
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document.write( "Either way we run into a contradiction. <BR>\n" );
document.write( "It's likely your teacher made a typo somewhere when coming up with the numbers to this problem. <BR>\n" );
document.write( "I would ask him/her for further clarification.<BR>\n" );
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