2016 AMC 10B Problems/Problem 25

Problem

Let $f(x)=\sum_{k=2}^{10}(\lfloor kx \rfloor -k \lfloor x \rfloor)$ , where $\lfloor r \rfloor$ denotes the greatest integer less than or equal to $r$ . How many distinct values does $f(x)$ assume for $x \ge 0$ ?

$\textbf{(A)}\ 32\qquad\textbf{(B)}\ 36\qquad\textbf{(C)}\ 45\qquad\textbf{(D)}\ 46\qquad\textbf{(E)}\ \text{infinitely many}$

Solution

2016 AMC 10B (Problems • Answer Key • Resources)
Preceded by Problem 24	Followed by [[2016 AMC 10B Problems/Problem {{{num-a}}}\|Problem {{{num-a}}}]]
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All AMC 10 Problems and Solutions

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2016 AMC 10B Problems/Problem 25

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