This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

Tags were heavily modified to better represent problems.

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Found problems: 3

2016 AMC 12/AHSME, 2
Tags: AMC , AMC 12 , AMC 12 B , no posts
The harmonic mean of two numbers can be calculated as twice their product divided by their sum. The harmonic mean of $1$ and $2016$ is closest to which integer? $\textbf{(A)}\ 2 \qquad \textbf{(B)}\ 45 \qquad \textbf{(C)}\ 504 \qquad \textbf{(D)}\ 1008 \qquad \textbf{(E)}\ 2015 $

2015 AMC 12/AHSME, 5
Tags: LaTeX , AMC , no posts
The Tigers beat the Sharks $2$ out of the first $3$ times they played. They then played $N$ more times, and the Sharks ended up winning at least $95\%$ of all the games played. What is the minimum possible value for $N$? $\textbf{(A) }35\qquad\textbf{(B) }37\qquad\textbf{(C) }39\qquad\textbf{(D) }41\qquad\textbf{(E) }43$

2018 AMC 12/AHSME, 6
Tags: 2018 AMC 12A , AMC , AMC 12 , AMC 12 A , no posts
For positive integers $m$ and $n$ such that $m+10<n+1$, both the mean and the median of the set $\{m, m+4, m+10, n+1, n+2, 2n\}$ are equal to $n$. What is $m+n$? $\textbf{(A) }20\qquad\textbf{(B) }21\qquad\textbf{(C) }22\qquad\textbf{(D) }23\qquad\textbf{(E) }24$