document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=201841>Question 201841</A>: <I><SPAN STYLE=\"word-break: break-all;\"> if a = 4b + 26  and b is a positive integer. the a could be divisible by all of the following except\r<BR>\n" );
document.write( "\n" );
document.write( "a)2   b) 4   c) 5   d)6  e) 7  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #152081 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=152081\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the formula is a = 4b + 26<BR>\n" );
document.write( "b can be any value as long as it's a positive integer.<BR>\n" );
document.write( "a can be any value that presumably must also be a positive integer?<BR>\n" );
document.write( "a being divisible by all implies that there is no remainder from the division?<BR>\n" );
document.write( "that's what i'm thinking, anyway.<BR>\n" );
document.write( "under that assumption, we should be able to prove that all of the numbers can divide evenly into a except one of them.<BR>\n" );
document.write( "we make a table of possible value for a starting from b = 1 and working our way up sequentially one increment at a time.<BR>\n" );
document.write( "b,a<BR>\n" );
document.write( "1,30<BR>\n" );
document.write( "2,34<BR>\n" );
document.write( "3,38<BR>\n" );
document.write( "4,42<BR>\n" );
document.write( "5,46<BR>\n" );
document.write( "6,50<BR>\n" );
document.write( "7,54<BR>\n" );
document.write( "8,58<BR>\n" );
document.write( "9,62<BR>\n" );
document.write( "10,66<BR>\n" );
document.write( "11,70<BR>\n" );
document.write( "12,74<BR>\n" );
document.write( "13,78<BR>\n" );
document.write( "14,82<BR>\n" );
document.write( "since 2 divides into 30, 2 is good.<BR>\n" );
document.write( "since 5 divides into 30, 5 is good.<BR>\n" );
document.write( "since 6 divides into 30, 6 is good<BR>\n" );
document.write( "that leaves 4 and 7.<BR>\n" );
document.write( "multiples of 4 are:<BR>\n" );
document.write( "4,8,12,16,20,24,28,32,36,40,44,48,52,56,60,64,68,72,76,80,84,.....<BR>\n" );
document.write( "doesn't look like 4 divides evenly.  they keep missing each other by 2.<BR>\n" );
document.write( "multiples of 7 are:<BR>\n" );
document.write( "7,14,21,28,35,42,49,56,63,70,.....<BR>\n" );
document.write( "when b = 11, a = 70<BR>\n" );
document.write( "70 is divisible by 7 so 7 is good.<BR>\n" );
document.write( "looks like 4 is the one that will not divide evenly into a.<BR>\n" );
document.write( "when b = 4, a = 42 which is also divisible by 7 (7*6)<BR>\n" );
document.write( "answer is selection b.) which is 4.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );