Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

2012 AMC 12A Problems/Problem 25

Revision as of 18:29, 18 February 2012 by Aplus95 (talk | contribs) (Created page with "== Problem == Let <math>f(x)=|2\{x\}-1|</math> where <math>\{x\}</math> denotes the fractional part of <math>x</math>. The number <math>n</math> is the smallest positive intege...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Problem

Let $f(x)=|2\{x\}-1|$ where $\{x\}$ denotes the fractional part of $x$. The number $n$ is the smallest positive integer such that the equation \[nf(xf(x))=x\] has at least $2012$ real solutions. What is $n$? Note: the fractional part of $x$ is a real number $y=\{x\}$ such that $0\le y<1$ and $x-y$ is an integer.

$\textbf{(A)}\ 30\qquad\textbf{(B)}\ 31\qquad\textbf{(C)}\ 32\qquad\textbf{(D)}\ 62\qquad\textbf{(E)}\64$ (Error compiling LaTeX. Unknown error_msg)

Solution

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2012_AMC_12A_Problems/Problem_25&oldid=44824"