Ask the client more specific questions. Just because the client only gave you the websites and asked how much doesn't mean you have to only use that as your basis for a quote.
Simply respond back that you need additional information to provide an accurate quote. Ask questions like:
What is your goal for the website?
What features on those websites are you interested in having on your website?
Are you primarily interested in the functionality or visual design of those websites?
Do you have a budget and timeframe for this project?
If they don't give you additional information, then I would simply tell them that you can't give an exact quote without specifics. So then you provide them with a wide estimate that depends on the features chosen. When you provide them with a quote between $10k and $120k, perhaps they will be more willing to sit down and discuss the specifics with you?