Originally Posted by accurate.cygnet
The more page rank your web site has, the higher it ranks on SERPs. and yeah back links increase page rank but they have got to be quality back links.
Your second statement is reasonable, backlinks from quality websites with some good PR of their own ,with few links on, and where the link is NOT nofollowed will help your PR grow.
Your first statement however is not necessarily correct. There is no direct correlation between PR and ranking. You can do almost any Google search you like and find websites with lower PR ranking above other sites with a higher PR.