2005 AMC 8 Problems/Problem 18

Problem

How many three-digit numbers are divisible by 13?

$\textbf{(A)}\ 7\qquad\textbf{(B)}\ 67\qquad\textbf{(C)}\ 69\qquad\textbf{(D)}\ 76\qquad\textbf{(E)}\ 77$


Solution

Let $k$ be any positive integer so that $13k$ is a multiple of $13$. For the smallest three-digit number, $13k>100$ and $k>\frac{100}{13} \approx 7.7$. For the greatest three-digit number, $13k<999$ and $k<\frac{999}{13} \approx 76.8$. The number $k$ can range from $8$ to $76$ so there are $\boxed{\textbf{(C)}\ 69}$ three-digit numbers.


Video Solution by OmegaLearn

https://youtu.be/7an5wU9Q5hk?t=393

Video Solution 2

https://youtu.be/101Rgutx1R0 Soo, DRMS, NM


See Also

2005 AMC 8 (ProblemsAnswer KeyResources)
Preceded by
Problem 17
Followed by
Problem 19
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AJHSME/AMC 8 Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png