BdMO Online Forum

From $1$ to $1000$, how many integers are multiples of $3$ or $6$ but not of $5$?

if u say 3 or 6 then the answer is 133.
as 6 is divided by 3, so the common multiple between 6 and 5 will be cancelled. They r 33 numbers who are divided by both 5 and 6. And there are 166 numbers who are divided by both 3 and 6. So the answer is 166-33=133

but if u say either 3 or 6 then the answer is 267.

There are 333 numbers who are multiple of either 6 or 3. And 66 numbers are common between them. So the rest is answer