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

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Found problems: 252

2010 AMC 10, 13
Tags: absolute value
What is the sum of all the solutions of $ x \equal{} |2x \minus{} |60\minus{}2x\parallel{}$? $ \textbf{(A)}\ 32\qquad\textbf{(B)}\ 60\qquad\textbf{(C)}\ 92\qquad\textbf{(D)}\ 120\qquad\textbf{(E)}\ 124$

2009 China National Olympiad, 1
Tags: symmetry , function , algebra , polynomial , absolute value , inequalities
Given an integer $ n > 3.$ Let $ a_{1},a_{2},\cdots,a_{n}$ be real numbers satisfying $ min |a_{i} \minus{} a_{j}| \equal{} 1, 1\le i\le j\le n.$ Find the minimum value of $ \sum_{k \equal{} 1}^n|a_{k}|^3.$