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How many integers between 31 and 131 are divisible by 7 but not divisible by 6?
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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 + = 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
ANSWER. Between 31 and 131, there are 14-3 = 11 integers that are divisible by 7 but not divisible by 6.
Solved.
How many intergers between 31 and 131 are divisible by 7 but not divisible by 6?
We start with
Since 28 is SMALLER than 31, we ADD 7 to 28 to get 28 + 7 = 35, the SMALLEST INTEGER
between 31 and 131, that is DIVISIBLE by/is a MULTIPLE of 7.
We then continue with
Since 126 is SMALLER than 131, we get 126 as the LARGEST INTEGER between 31 and 131, that is
DIVISIBLE by/is a MULTIPLE of 7.
So, ALL INTEGERS between 31 and 131, that are DIVISIBLE by/are MULTIPLES of 7, begin at 35 and end at 126.
So, the TOTAL number of INTEGERS, between 31 and 131, that are DIVISIBLE by/are
MULTIPLES of 7, is
INTEGERS between 31 and 131, that are DIVISIBLE by both 7 and 6, start at 7(6) = 42.
We then continue with
Since 126 is SMALLER than 131, we get 126 as the LARGEST INTEGER between 31 and 131, that is
DIVISIBLE by/is a MULTIPLE of 42.
So, the TOTAL number of INTEGERS between 31 and 131, that are DIVISIBLE by/are
MULTIPLES of 7 and 6, or 42, is
TOTAL number of INTEGERS between 31 and 131, that are DIVISIBLE by/are MULTIPLES
of 7, but are NOT DIVISIBLE by/are NOT MULTIPLES of 6 (or 42) = 14 - 3 = 11