Problem Solving

How many integers from 1 to 1000 inclusive are divisible by neither 3 nor 5?

straightforward:
we are looking for number of numbers not divisible by 5*3 i.e. 15.
So there are 1000/15 = 66 numbers not divisible by both 5 and 3.

pops wrote:straightforward:
we are looking for number of numbers not divisible by 5*3 i.e. 15.
So there are 1000/15 = 66 numbers not divisible by both 5 and 3.

well I don't think thats what the question is..
it is not asking for numbers not divisible by 15
it is asking for number not divisible by 3 or 5
so number of numbers divisible by 3= 333
number of numbers divisible by 5=200, this contains multiple of 15
so number of numbers divisible by 15=66
total number of numbers divisible by 3 or 5= 333+200-66
467

not divisible by 3 or 5 will be 1000-467
=533

thanks GID for pointing out the mistake. I guess I should work on my addition and subtraction:)

I used the same approach however 533-66 = 467 and not 434. So the answer is 1000-467 = 533 numbers are not divisible by either 3 or 5.

Thanks!

My mistake.. I thought the question says number of numbers not divisible by 5 and 3 both..