Rules:
Don’t be the first to offer a price, now you’ve just told them they don’t need to offer more than 60k.
Usually I wait for them to ask (or offer). Then I counter-offer and/or explain my number.
Sometimes that's at the end of the 1st interview, sometimes at the start of a 2nd interview.
If I'm not impressed with the first interview (as interviewee), I'll bring up salary expectations in their "do you have any questions for us?", just to save them and myself from a 2nd interview if we're not in the ballpark.
On the other side of that table, when hiring, I'm usually talking with a professional recruiter, who let's me know the candidate's pay expectations.
In the case that I'm hiring, the candidate, the recruiter, and I all want to get the candidate in at a salary at the high end of fair - to maximize their pay, maximize the recruiter's commission, and to minimize my future HR work to retain them.
I keep an idea of the pay thats acceptable to me and if they don't meet it I tell them. So basically I let them make the offer and im ready to say its to low.
I’m an overconfident asshole who always gives my asking price
The kicker is that I’ve always had a job when looking at new jobs so I was always prepared to walk away from negotiations.
If you want to gauge whether that range is a real or bs range ask them what a low end vs high end recruit looks like.