# Difference between revisions of "2005 AMC 10A Problems/Problem 13"

Line 15: | Line 15: | ||

<math> 130n > n^2 > 16 </math> | <math> 130n > n^2 > 16 </math> | ||

− | Solving each part | + | Solving each part separately: |

<math> n^2 > 16 \Longrightarrow n > 4 </math> | <math> n^2 > 16 \Longrightarrow n > 4 </math> |

## Revision as of 12:20, 8 November 2015

## Problem

How many positive integers satisfy the following condition:

?

## Solution

We're given , so

(because all terms are positive) and thus

Solving each part separately:

So .

Therefore the answer is the number of positive integers over the interval which is .

## See Also

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.