document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1208311>Question 1208311</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How many intergers between 31 and 131 are divisible by 7 but not divisible by 6? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #846650 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=846650\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 31/7 = 4.4286<BR>\n" );
document.write( "7*4 = 28 is too small but 7*5 = 35 fits<BR>\n" );
document.write( "131/7 = 18.7143<BR>\n" );
document.write( "7*18 = 126 also fits<BR>\n" );
document.write( "7*19 = 133 is too large.\r<BR>\n" );
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document.write( "The multiples of 7 between 31 and 131 are: {35, 42, 49, ..., 126}<BR>\n" );
document.write( "They can be written as {7*5, 7*6, 7*7, ..., 7*12, ..., 7*18}\r<BR>\n" );
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document.write( "Cross off 7*6, 7*12 and 7*18 since they involve 6 as a factor.<BR>\n" );
document.write( "There are 14 items in the set {5,6,7,...,18} because 18-5+1 = 14. Or you can count out the items.<BR>\n" );
document.write( "That must mean there are also 14 items in the set {7*5,7*6,...,7*18} = {35,42,...,126}<BR>\n" );
document.write( "We crossed off 3 items {7*6,7*12,7*18} so we have 14-3 = <font color=red>11</font> multiples of 7 between 31 and 131 such that 6 isn't a factor. \r<BR>\n" );
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document.write( "Answer: <font color=red>11</font> </SPAN>\n" );
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