how many numbers between 1 and 1000 are divisible by 3 and 7 but not 2 5 or 11?
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be divisible by 3 AND 7 they have to be divisible by 21.
Here is a kind of “Eratosthenes Sieve” with all multiples of 21 between 0(not included) and1000.

Now, mark for exclusion all the multiples of 2(Columns 0, 2, 4, 6, 8), 5 (Columns 0, 5) and 11(The diagonal from {0, 0} to {40, 4}).
Count what remains: 4 + 4 + 5 + 4 = 17 numbersdivisible by 3 and 7 and not divisible by 2,5 or 11
hope it's help you
Here is a kind of “Eratosthenes Sieve” with all multiples of 21 between 0(not included) and1000.

Now, mark for exclusion all the multiples of 2(Columns 0, 2, 4, 6, 8), 5 (Columns 0, 5) and 11(The diagonal from {0, 0} to {40, 4}).
Count what remains: 4 + 4 + 5 + 4 = 17 numbersdivisible by 3 and 7 and not divisible by 2,5 or 11
hope it's help you
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