Do you have a file in your Downloads folder that you know is a PDF that arrived in the last 4 weeks? You could do a Search in Finder, and specify Kind as PDF, and Date added to within last 4 weeks. You could select all those files and press the Space bar to get them to previsualize them and find visually the one you want.
But you could also use the `find` command in this way:
`find ~/Downloads/ -name "*.pdf" -mtime -4w -print0 | xargs -0 qlmanage -p`