Simple Math Question Help

Hi. I have a question about a "famous" type of word problems. I always come across problems like "how many integers below 2000 are divisible by 3 and 5" or "how many odd numbers below 5000 are not divisible by 9." The only way I know how to do these problems is by trying to find a pattern by writing everything out, which takes a lot of time. Is there any easy way to do these quickly? Thanks!

Quote:

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Originally Posted by sleigh

"how many integers below 2000 are divisible by 3 and 5"

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$\displaystyle \left\lfloor {\frac{{1999}}
{3}} \right\rfloor + \left\lfloor {\frac{{1999}}
{5}} \right\rfloor - \left\lfloor {\frac{{1999}}
{{15}}} \right\rfloor $
WHY?