Mass loaded vinyl (mlv) to block sound coming through floor from apt below?

I'm in a rental so can't make structural changes. It's a very old building with little/no insulation between floors, and my floor is hardwood. I want to reduce the sound of voices that are echoing upwards from apt below. Would it work to lay MLV directly on my floor, then cover with thick carpet?

Another thought is using other types of felt / cork / acoustic underlay (like Floor Muffler ), but not sure if this will work as they're designed to be used under the floorboards. Would this type of underlayment be more effective than MLV ?

Thanks