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My apartment is on the 37th floor of a building with slab concrete floors.
It is probably NOT true 3000 lb. concrete. More than likely, it is Gypecrete. A lightweight cementious underlayment poured over either steel or wood subfloors for sound and fire proofing.
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The GC wants to trowel self-leveling cement over the parquet, install a vapor barrier over that, and then nail the wood (probably engineered) into the whole mess. Should I be concerned with this method?
Yes. I would not recommend nailing into a cement based self leveler. It will crack and crumble and eventually make noise. If the existing floors are well adhered, simply sand down any high spots and flatten to industry specs then nail/staple the flooring to that, after installing the proper felt/building paper. In otherwords, skip the leveling compound.
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I've been thinking that it will probably be safer to pull up the parquet, level the concrete slab, and then float engineered wood. How do I deal with the black glue? Can self-leveling cement be poured directly on to it?
Not sure why the existing floor needs to be removed unless after installing the new floor over it, the floor will be too high.
The safest method would be to flatten the existing floor as well as possible by sanding high spots, then float a floor over that, using the proper foam underlayment. You won't be having moisture problems from below the floor when you're on the 37th story of your building.