Firms that value the employee will give the full 60. They will generally have an expectation of what they want to pay,and will give that pay,regardless of how high or low you quote.
On the other hand,a firm that gives you 40,simply because you asked 40,cannot be faulted,but it leaves alot to be desired. You do something,and in the right way - not because a dude asked for x... unless the KPI for HR is to keep salaries low,and times are lean.
I think a blend of both would be to start you on what you asked fo,say 40,and upgrade you to 60 in 3 or 6 months,after your probation. That is what i would do,if i was the GM. Caroline Mutoko initially asked for 160K at Kiss in 2000,got 160K,and then was upgraded to the right figure after 6 months. Same thing happened to King'angi.