Inclusion/Exculsion Question

So I am doing some practice problems and I was wondering if someone can clarify what the question is asking.

The question:

a) How many integers between 1 and 400 (inclusive) are divisible by at least one of 4,5 and 20?

b) How many integers between 1 and 400 (inclusive) are divisible by just one of 4,5 and 20?

a) I am thinking the question is asking divisible by 4 and 5 and 20

b) I am thinking the question is asking divisible by one of 4 or 5 or 20

Can someone clarify for 'a' and 'b'?

Thanks.

Re: Inclusion/Exculsion Question

I think the question is pretty clear. Part a) talks about numbers n such that 4 divides n or 5 divides n or 20 divides n, i.e., any of the numbers 4, 5, 20 (or possible two or all three of them) divide n. Part b) talks about n such that there is exactly one number k in {4, 5, 20} such that k divides n.

Re: Inclusion/Exculsion Question

Quote:

Originally Posted by

**xboxwee** The question:

a) How many integers between 1 and 400 (inclusive) are divisible by at least one of 4,5 and 20?

b) How many integers between 1 and 400 (inclusive) are divisible by just one of 4,5 and 20?

Here is a bit more on a).

There are integers from 1 to 400 that are divisible by *n*.

Any integer that is divisible by is also divisible by . So in part a) we have to be careful not to count those numbers twice.

Re: Inclusion/Exculsion Question