Question

How many positive integers between $1000$ and $9999$ inclusive are not divisible by $3$?

Answer 1

Finding the number of positive integers between $1000$ and $9999$ inclusive that are not divisible by $3$:

• The total number of positive integers between $1000$ and $9999$ inclusive are $9999-999=9000$.
• The total number of positive integers between $1000$ and $9999$ inclusive that are divisible by $3$can be calculated by dividing the total number of positive integers by $3$.

$\begin{array}{rcl}\mathrm{number}\mathrm{of}\mathrm{positive}\mathrm{integers}& =& \frac{9000}{3}\\ & =& 3000\end{array}$

• The total number of positive integers between $1000$ and $9999$ inclusive that are not divisible by $3$ can be calculated.
• The total number of positive integers between $1000$ and $9999$ inclusive, is subtracted from the number of positive integers that are divisible by $3$.

$\begin{array}{rcl}\mathrm{number}\mathrm{of}\mathrm{positive}\mathrm{integers}& =& 9000-3000\\ & =& 6000\end{array}$

Hence, there are $6000$ positive integers between $1000$ and $9999$ inclusive that are not divisible by $3$.