# Simple Math Question Help

• March 22nd 2010, 03:49 PM
sleigh
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!
• March 22nd 2010, 04:34 PM
Plato
Quote:

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

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

WHY?