document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=72110>Question 72110</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A group of people wanted to form committees each of which had the same number of persons; everyone in the group was to serve on a committee.  When the group tried to make 2, 3, 4, 5, or 6 committees, there was always one extra person.  However, they wer able to make more than 6 but fewer than 12 committees of equal size.<BR>\n" );
document.write( "a. What was the smallest possible number of persons in the group?<BR>\n" );
document.write( "b. How many persons were on each committee that was formed? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #51662 by </B><A HREF=/tutors/aboutme.mpl?userid=303795><B>303795(602)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=303795><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=51662\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The smallest number that 2, 3, 4, 5 and 6 all go into is 60. Therefore 61 will have a remainder of 1 for each of those numbers.\r<BR>\n" );
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document.write( "However none of 7, 8, 9, 10 and 11 are factors of 61 so the number cannot be 61.\r<BR>\n" );
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document.write( "The next smallest number that 2, 3, 4, 5 and 6 all go into with a remainder of 1 is 121. 11 is a factor of 121.\r<BR>\n" );
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document.write( "Therefore the smallest number of persons is 121. The number of committees formed is 11 each with 11 members. </SPAN>\n" );
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