Answer:
130
Step-by-step explanation:
The number of integers meeting the criteria can be found by counting them using a counting formula.
<h3>Divisible by 7</h3>
Integers divisible by 7 will have the form (7n), where n is some positive integer. The number of them less than 1000 can be found from ...
7n ≤ 1000
n ≤ 142.857
There are 142 integers less than 1000 that are divisible by 7.
<h3>Divisible by 7 and 11</h3>
Similarly, integers divisible by 7 and 11 will be of the form (77n), for some positive integer n.
77n ≤ 1000
n ≤ 12.987
There are 12 integers less than 1000 that are divisible by both 11 and 7.
<h3>Divisible by 7, not 11</h3>
The number of integers less than 1000 that are divisible by 7, but not 11, will be the difference of these numbers.
142 -12 = 130 integers divisible by 7, but not 11.
