Yes. They do. If you see that they are looking for a person who is much younger/older than you, then you know not to contact them.

In my experience if a man is looking for a younger woman is if he wants to have children. It's understandable. But I have never seen 60 year old wanting 35 year old. The most I saw was 15 years younger and that's because they wanted kids. Like he was 45 and wanted a woman 30-40 and specified "I have no kids and want them". It made sense.