Difference between revisions of "2016 AMC 10B Problems/Problem 25"

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<math>\textbf{(A)}\ 32\qquad\textbf{(B)}\ 36\qquad\textbf{(C)}\ 45\qquad\textbf{(D)}\ 46\qquad\textbf{(E)}\ \text{infinitely many}</math>
 
<math>\textbf{(A)}\ 32\qquad\textbf{(B)}\ 36\qquad\textbf{(C)}\ 45\qquad\textbf{(D)}\ 46\qquad\textbf{(E)}\ \text{infinitely many}</math>
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==Solution==
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==See Also==
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{{AMC10 box|year=2016|ab=B|num-b=24}}
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{{MAA Notice}}

Revision as of 12:26, 21 February 2016

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

See Also

2016 AMC 10B (ProblemsAnswer KeyResources)
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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