document.write( "Question 1148455: (a) How many integers from 1 through 201 are multiples of 6 or multiples of 11?
\n" ); document.write( " (b) How many integers from 1 through 201 are neither multiples of 6 nor multiples of 11?
\n" ); document.write( " (c) How many integers from 1 through 201 are multiples of both 6 and 11?
\n" ); document.write( " (d) How many integers from 1 through 201 are multiples of either 6 or of 11 but not multiple of both? \n" ); document.write( "

Algebra.Com's Answer #769827 by ikleyn(52884) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( " The solution to part (a) given by @boreal is WRONG.\r
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document.write( "The number of integers from 1 to 201 (inclusive) that are multiple of 6 is  33 \r\n" );
document.write( " (notice that  = 33.5, approximately).\r\n" );
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document.write( "The number of integers from 1 to 201 (inclusive) that are multiple of 11 is  18 \r\n" );
document.write( " (notice that  = 18.3, approximately).\r\n" );
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document.write( "The number of integers from 1 to 201 (inclusive) that are multiple of 6 and of 11 simultaneously is  3:  66, 132 and 198).\r\n" );
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document.write( "From it, the number of integers from 1 to 201 (inclusive) that are multiple of 6 or  11  is  33 + 18 - 3 = 48.    ANSWER\r\n" );
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document.write( "    We must first add  33 and 18  and then subtract the \"3\" from this sum (!)\r\n" );
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document.write( "    It is because when we add 33 and 18, we count TWICE the integers in the intersection of these subsets (!)\r\n" );
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\n" ); document.write( "\n" ); document.write( "See the lesson\r
\n" ); document.write( "\n" ); document.write( " - Counting elements in sub-sets of a given finite set\r
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