Difference between revisions of "2012 AIME II Problems/Problem 10"

(Created page with "== Problem 10 == Find the number of positive integers <math>n</math> less than <math>1000</math> for which there exists a positive real number <math>x</math> such that <math>n=x\...")
 
Line 3: Line 3:
  
 
Note: <math>\lfloor x \rfloor</math> is the greatest integer less than or equal to <math>x</math>.
 
Note: <math>\lfloor x \rfloor</math> is the greatest integer less than or equal to <math>x</math>.
 +
 +
 +
== Solution ==
 +
 +
== See also ==
 +
{{AIME box|year=2012|n=II|num-b=9|num-a=11}}

Revision as of 16:21, 31 March 2012

Problem 10

Find the number of positive integers $n$ less than $1000$ for which there exists a positive real number $x$ such that $n=x\lfloor x \rfloor$.

Note: $\lfloor x \rfloor$ is the greatest integer less than or equal to $x$.


Solution

See also

2012 AIME II (ProblemsAnswer KeyResources)
Preceded by
Problem 9
Followed by
Problem 11
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
All AIME Problems and Solutions