To find the numbers between $1000$ and $2000$ that leave a remainder of $3$ when divided by $21$, we need to consider the numbers of the form $21n + 3$, where $n$ is a positive integer.
Since $1000 = 21 \cdot 47 + 13$ and $2000 = 21 \cdot 95 + 5$, the numbers between $1000$ and $2000$ that leave a remainder of $3$ when divided by $21$ are of the form $21n + 3$, where $47 \leq n \leq 95$.
The number of such integers can be calculated as follows:
$95 - 47 + 1 = 49$
Therefore, there are $\boxed{49}$ numbers between $1000$ and $2000$ that leave a remainder of $3$ when divided by $21$.
How many numbers between $1000$ and $2000$ leave a remainder of $3$ when divided by $21?$
1 answer