Hi If i have two sites, one is authority site with pr 7 and other site is only pr1, but has 3 times more content that is unique. Does the authority site rank no1? So my site has three times more content than the number one, but i only have pr1. Another question is how hard is it to get PR 6? Please help!
Not sure exactly what the question here is but PR is pagerank and has nothing to do with content. It's only a measure of sites linking to you... PR does not have much bearing on ranking. I'm sure it's one of the factors in the algorithm, but there are many more things to focus on like siloing your content.
There is no relation between SERP and PR. If your website is having high PR it doesn't mean that you will have good SERP and vice versa. To gain PR6 your website should have few PR7 and PR8 links.
An authority site will rank high because, well, it's authority for that term. But a site with a high PR isn't automatically an authority site although an authority site would have a high PR.
I think PR has nothing to do with your SERP, rankings will depend on your backlinks with your targeted keywords, the keywords in your content and etc.