2005 AMC 8 Problems/Problem 18: Difference between revisions

Latest revision as of 03:07, 29 December 2022

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

2005 AMC 8 (Problems • Answer Key • Resources)
Preceded by Problem 17	Followed by Problem 19
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All AJHSME/AMC 8 Problems and Solutions

These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. Error creating thumbnail: File missing

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-==Video Solution==
+==Video Solution by OmegaLearn==
 https://youtu.be/7an5wU9Q5hk?t=393
 ==Video Solution 2==

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