If getting the potential employee to offer a number is genuinely, purely in the interest of not stringing them along, why don't you offer the first number? "This is the salary allocated for the position. Is this a salary you would be comfortable with?"
Now you have a way to both not string them along if you're $20K apart and to not let them accidentally undervalue their own worth by a significant amount.
Now you have a way to both not string them along if you're $20K apart and to not let them accidentally undervalue their own worth by a significant amount.