document.write( "Question 282356: The number of positive integers less than or equal to 1501 that are multiples of 3 or 4 but not a multiple of 5 is:\r
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Algebra.Com's Answer #205097 by Edwin McCravy(20060) $\"\"$ $\"About$

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The number of positive integers less than or equal to 1501 that are multiples of 3 or 4 but not a multiple of 5 is:
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document.write( "We will use these two facts:\r\n" );
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document.write( "1. The number of multiples of k which are less than or equal to n is\r\n" );
document.write( "given by the greatest integer not exceeding \r\n" );
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document.write( "and\r\n" );
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document.write( "2. N(A or B) = N(A) + N(B) - N(A and B)\r\n" );
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document.write( "First we calculate the number of multiples of 3 or 4.\r\n" );
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document.write( "N(multiples of 3 OR 4) = \r\n" );
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document.write( "N(multiples of 3) + N(multiples of 4) - N(multiples of 3 AND 4)\r\n" );
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document.write( "The number of multiples of 3 which are less than or equal to 1501\r\n" );
document.write( "is the greatest integer not exceeding  which is 500.\r\n" );
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document.write( "The number of multiples of 4 which are less than or equal to 1501 is \r\n" );
document.write( "the greatest integer not exceeding  which is 375.\r\n" );
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document.write( "The number of multiples of 3 AND 4 which are less than or equal to 1501\r\n" );
document.write( "is the number of multiples of 12 which are less than or equal to 1501, \r\n" );
document.write( "which is the greatest integer not exceeding  which \r\n" );
document.write( "is 125.\r\n" );
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document.write( "N(multiples of 3 OR 4) = \r\n" );
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document.write( "N(multiples of 3) + N(multiples of 4) - N(multiples of 3 AND 4)\r\n" );
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document.write( "N(multiples of 3 OR 4) = 500 + 375 - 125 = 750.\r\n" );
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document.write( "Now that 750 includes every multiple of 5 less than 1501 which is \r\n" );
document.write( "either a multiple of 4 or a multiple of 3.   \r\n" );
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document.write( "So we must count the number of multiples of 15 OR 20 to subtract\r\n" );
document.write( "from it.\r\n" );
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document.write( "N(multiples of 15 OR 20) = \r\n" );
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document.write( "N(multiples of 15) + N(multiples of 20) - N(multiples of 15 AND 20)\r\n" );
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document.write( "The number of multiples of 15 which are less than or equal to 1501 \r\n" );
document.write( "is the greatest integer not exceeding  which \r\n" );
document.write( "is 100.\r\n" );
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document.write( "The number of multiples of 20 which are less than or equal to 1501 \r\n" );
document.write( "is the greatest integer not exceeding  which is \r\n" );
document.write( "75.\r\n" );
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document.write( "The number of multiples of both 15 AND 20 which are less than or \r\n" );
document.write( "equal to 1501 is the number of multiples of 60 which are less than \r\n" );
document.write( "or equal to 1501, which is the greatest integer not exceeding\r\n" );
document.write( " which is 25.\r\n" );
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document.write( "N(multiples of 15 OR 20) = \r\n" );
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document.write( "N(multiples of 15) + N(multiples of 20) - N(multiples of 15 AND 20)\r\n" );
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document.write( "N(multiples of 15 OR 20) = 100 + 75 - 25 = 150.\r\n" );
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document.write( "So we subtract the 150 from the 750, and get 600.\r\n" );
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document.write( "So the correct answer is 600, which is not listed as a choice,\r\n" );
document.write( "so the correct choice is \"(E) none of these\".\r\n" );
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document.write( "Edwin

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