Question 1208311
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How many integers between 31 and 131 are divisible by 7 but not divisible by 6?
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<pre>
In the interval between 31 and 131, first integer number divisible by 7 is 35, 
and they go with the step of 7 to the last integer divisible by 7, which is 126.


    From 35 to 126, there are  {{{(126-35)/7}}} + {{{1}}} = 14 integer numbers divisible by 7.


From this number 14, we should subtract the number of those integers 
that are divisible by both 6 and 7 simultaneously.


These integers are divisible by 42, too, and their number is 3, 
because there are 3 (three) such integer numbers

    42, 84 and 126.


So, we subtract 3 from 14, and we get the 


<U>ANSWER</U>. Between 31 and 131, there are 14-3 = 11 integers that are divisible by 7 but not divisible by 6.
</pre>

Solved.