document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=254429>Question 254429</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How many even numbers, k, in the interval 100 &#8804; k &#8804; 300 do not have a digit 6 in their decimal representation?\r<BR>\n" );
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document.write( "(A) 72 (B) 73 (c) 74 (D) 75 (E) 76<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #186737 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=186737\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> every 10 numbers, you have a last digit of 6.\r<BR>\n" );
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document.write( "300 - 100 = 200 numbers in between.\r<BR>\n" );
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document.write( "divide that by 10 and you get 20.\r<BR>\n" );
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document.write( "you will have 20 numbers that have a last digit of 6.\r<BR>\n" );
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document.write( "those number will be:\r<BR>\n" );
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document.write( "106<BR>\n" );
document.write( "116<BR>\n" );
document.write( "126<BR>\n" );
document.write( "136<BR>\n" );
document.write( "146<BR>\n" );
document.write( "156<BR>\n" );
document.write( "166<BR>\n" );
document.write( "176<BR>\n" );
document.write( "186<BR>\n" );
document.write( "196<BR>\n" );
document.write( "206<BR>\n" );
document.write( "216<BR>\n" );
document.write( "226<BR>\n" );
document.write( "236<BR>\n" );
document.write( "246<BR>\n" );
document.write( "256<BR>\n" );
document.write( "266<BR>\n" );
document.write( "276<BR>\n" );
document.write( "286<BR>\n" );
document.write( "296\r<BR>\n" );
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document.write( "every 100 numbers, you will have 10 numbers that have a middle digit of 6.\r<BR>\n" );
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document.write( "those will be:\r<BR>\n" );
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document.write( "160 to 169<BR>\n" );
document.write( "260 to 269\r<BR>\n" );
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document.write( "that makes a total of 20.\r<BR>\n" );
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document.write( "only half of them will be even.\r<BR>\n" );
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document.write( "those numbers will be:\r<BR>\n" );
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document.write( "160<BR>\n" );
document.write( "162<BR>\n" );
document.write( "164<BR>\n" );
document.write( "166<BR>\n" );
document.write( "168<BR>\n" );
document.write( "260<BR>\n" );
document.write( "262<BR>\n" );
document.write( "264<BR>\n" );
document.write( "266<BR>\n" );
document.write( "268\r<BR>\n" );
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document.write( "this makes a total of 10 even number with a middle digit of 6.\r<BR>\n" );
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document.write( "within 2 of those numbers, however, you will have a number that has a middle digit of 6 and a last digit of 6.\r<BR>\n" );
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document.write( "those number will be:\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "166<BR>\n" );
document.write( "266\r<BR>\n" );
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document.write( "we have to subtract these so they won't be counted twice.\r<BR>\n" );
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document.write( "the total number of numbers that have at least 1 digit of 6 would be 20 + 10 - 2 = 28\r<BR>\n" );
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document.write( "the total of even numbers between 100 and 300 = (300-100)/2 + 1 = 101\r<BR>\n" );
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document.write( "the total of even numbers between 100 and 300 that do not contain a digit of 6 either in the last digit or the middle digit would then be equal to:\r<BR>\n" );
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document.write( "101 - 28 = 73\r<BR>\n" );
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document.write( "that would be selection B.\r<BR>\n" );
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document.write( "here are the total even numbers that contain a digit of 6.\r<BR>\n" );
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document.write( "106<BR>\n" );
document.write( "116<BR>\n" );
document.write( "126<BR>\n" );
document.write( "136<BR>\n" );
document.write( "146<BR>\n" );
document.write( "156<BR>\n" );
document.write( "160<BR>\n" );
document.write( "162<BR>\n" );
document.write( "164<BR>\n" );
document.write( "166<BR>\n" );
document.write( "168<BR>\n" );
document.write( "176<BR>\n" );
document.write( "186<BR>\n" );
document.write( "196<BR>\n" );
document.write( "206<BR>\n" );
document.write( "216<BR>\n" );
document.write( "226<BR>\n" );
document.write( "236<BR>\n" );
document.write( "246<BR>\n" );
document.write( "256<BR>\n" );
document.write( "260<BR>\n" );
document.write( "262<BR>\n" );
document.write( "264<BR>\n" );
document.write( "266<BR>\n" );
document.write( "268<BR>\n" );
document.write( "276<BR>\n" );
document.write( "286<BR>\n" );
document.write( "296\r<BR>\n" );
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document.write( "that's a total of 28\r<BR>\n" );
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document.write( "the total number of even digits is (300-100)/2 + 1 = 200/2 + 1 = 101\r<BR>\n" );
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document.write( "that 1 has to be added because the difference doesn't take it into account, and it is even.\r<BR>\n" );
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document.write( "example:\r<BR>\n" );
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document.write( "(30-20)/2 + 1 = 10/2 + 1 = 6\r<BR>\n" );
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document.write( "even numbers are:\r<BR>\n" );
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document.write( "20<BR>\n" );
document.write( "22<BR>\n" );
document.write( "24<BR>\n" );
document.write( "26<BR>\n" );
document.write( "28<BR>\n" );
document.write( "30\r<BR>\n" );
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document.write( " </SPAN>\n" );
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