SOLUTION: how many positive integers less than 1000 are?divisible by7?,divisible by 7 but not by 11?,divisible by both 7 and 11?,divisible by either 7 or 11?,divisible by exactly by one of

Question 478443: how many positive integers less than 1000 are?divisible by7?,divisible by 7 but not by 11?,divisible by both 7 and 11?,divisible by either 7 or 11?,divisible by exactly by one of 7 and 11?

Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
The number of positive integers n less than 1000 that are divisible by 7:
[1000/7] = 142
The number of positive integers divisible by both 7 and 11 are those that are divisible by 77:
[1000/77] = 12
==> The number of positive integers divisible by 7 but not by 11 is 142 - 12 = 130.
The number of positive integers less than 1000 that are divisible by 11:
[1000/11] = 90
==>the number of positive integers less than 1000 that are divisible by either 7 or 11 is 142 + 90 - 12 = 220.
==>the number of positive integers less than 1000 that are divisible by exactly by one of 7 and 11 is 220 - 12 = 208.

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