document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1125943>Question 1125943</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A set of 7 positive integers has a unique mode of 1, a mean of 5, and a median of 6. What is the largest possible value for any of the integers in the set. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #742280 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=742280\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> mean of 5 with 7 integers can have total of 35.  But, a unique mode of 1 means at least 2 of those integers have to be 1.  The median of 6 means that 6 is the fourth from the bottom, and there are 3 integers higher than that.\r<BR>\n" );
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document.write( "The bottom 3 integers are 1,1, and one other.For the largest possible value of any integer, the third integer below the median has to be smaller or 1.\r<BR>\n" );
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document.write( "That makes 3 integers of 1 each, and 1 of 6.  The total is 35, so two of the remaining three are 7 and 8,  because there is a unique mode of 1.  That makes the total 24 (7,8,6,1,1,1).  The largest possible value is 11. </SPAN>\n" );
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