document.write( "Question 1208311: How many intergers between 31 and 131 are divisible by 7 but not divisible by 6? \n" ); document.write( "

Algebra.Com's Answer #846651 by ikleyn(52798) $\"\"$ $\"About$

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\n" ); document.write( "How many integers between 31 and 131 are divisible by 7 but not divisible by 6?
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document.write( "In the interval between 31 and 131, first integer number divisible by 7 is 35, \r\n" );
document.write( "and they go with the step of 7 to the last integer divisible by 7, which is 126.\r\n" );
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document.write( "    From 35 to 126, there are   +  = 14 integer numbers divisible by 7.\r\n" );
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document.write( "From this number 14, we should subtract the number of those integers \r\n" );
document.write( "that are divisible by both 6 and 7 simultaneously.\r\n" );
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document.write( "These integers are divisible by 42, too, and their number is 3, \r\n" );
document.write( "because there are 3 (three) such integer numbers\r\n" );
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document.write( "    42, 84 and 126.\r\n" );
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document.write( "So, we subtract 3 from 14, and we get the \r\n" );
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document.write( "ANSWER. Between 31 and 131, there are 14-3 = 11 integers that are divisible by 7 but not divisible by 6.\r\n" );
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