document.write( "Question 477530: The number 10^2002 + 2 is divisible by A 4 B 5 C 6 D 9 E 10^1001 \n" ); document.write( "
Algebra.Com's Answer #327287 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "102002 is divisible by 4, 5 and 101001 but 2\r\n" );
document.write( "isn't divisible by any of those, so  A, B and E are ruled out.\r\n" );
document.write( "\r\n" );
document.write( "102002 + 2  is certainly divisible by 2, because \r\n" );
document.write( "both terms are even.\r\n" );
document.write( "\r\n" );
document.write( "If you subtract 1 from any positive integer power of 10, \r\n" );
document.write( "you will always get a string of 9's.\r\n" );
document.write( "\r\n" );
document.write( "Example:\r\n" );
document.write( "\r\n" );
document.write( "100000000000000000\r\n" );
document.write( "                -1\r\n" );
document.write( "------------------\r\n" );
document.write( " 99999999999999999\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "102002 + 2 = (102002 - 1) + 3 = [a string of 2002 9's] + 3.\r\n" );
document.write( "\r\n" );
document.write( "That is divisible by 3 because any string of 9's is divisible by 3.\r\n" );
document.write( "\r\n" );
document.write( "So 10^2002 + 2 is divisible by 6 since it's divisible by both 2 and 3.\r\n" );
document.write( "\r\n" );
document.write( "So C is a correct answer.  But we should rule out D:\r\n" );
document.write( "\r\n" );
document.write( "Any string of 9's is divisible by 9 but 3 isn't, so D is ruled out.\r\n" );
document.write( "\r\n" );
document.write( "Answer: C 6\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );