# Need help in equation

How many integers in the set {n belongs to Z | 1 less than equals to n less than equals to 700} are divisible to 2 or 7 ?

###### Who is Participating?

Commented:
1 less than equals to n less than equal to 700
that doesn't make sense...
you probably meant
1 <= n <= 700
So the set is integers from 1 to 700 ?
then it shouldn't be too hard...

one in seven will be divisible by 7... so 100
one in 2 is divisible by 2... so 350
0

Commented:
Well, since this question has an academic nature to it...
How many are divisible by 2 (easy)
How many are divisible by 7 (also easy)
How many are divisible by both (not too hard)

Once you have those, the answer should be pretty easy to come up with (please no one jump in with just the answer).
0

Commented:
Remember from set theory A or B = A + B - (A and B)
0

Author Commented:
1 <= n <= 700
divisible to 2 and 7

k. just divide 700/2 and divide 700/7

its easy thanks.
0

Commented:
Yes, but the answer is not 350 + 100 = 450 because if you do that, you'll count some twice. (i.e. 14 is divisible by both and is counted twice).
0

Commented:
oh he meant disisible by both?
well half of the divisible by 7 will also be divisible by 2....
(7,14,21,28,35,42,etc easy to see that half are pair)

so 50 will be divisible by both
0

Commented:
and if you want divisible by 2 OR 7,
just remove the 50 that are divisible by both... so 350+100-50 = 400
0

Author Commented:
ok thanks
0
Question has a verified solution.

Are you are experiencing a similar issue? Get a personalized answer when you ask a related question.

Have a better answer? Share it in a comment.