+1 If the tiles are 9" by 9", the are likely ACM (Asbestos Containing Materials). The tiles themselves are not the real issue because they are not very friable. The Mastic is the issue and caution should be taken when removing that as the previous poster mentioned. As a general rule, if the mastic is black, get it tested at a minimum.

I should have explained. The floor is typically more damp and cool than the surrounding air. Carpet prevents air circulation next to the cool damp surface and the carpet will also be cooler and damper than the surrounding air. Organic stuff collects in the carpet. Mold happens. Have you considered removing the vinyl and staining the concrete? You can make it LOOK warmer.

I just removed old vinyl tile adhesive from bathroom tiles like these. My tiles ended up being unglazed porcelain tiles from the mid 1950's. I used a wallpaper steamer to heat up and liquify the adhesive. I then scraped as much of it off with a razor blade scraper followed by scrubbing with some steel wool to get the glue out of the grout lines. Finally I wiped up the residue with a clean rag. It took me about 3 to 4 hours to do my 5ft x5ft bathroom. I also tried acetone and steel wool as a removal technique and it worked pretty well too, but ultimately I went with the steamer as it seemed less expensive and less hazardous than soaking the whole floor in acefone

Do you know how old the sheet vinyl is? There is more to be concerned with that, rather than the 1947 tiles. For many years sheet vinyl was manufactured with a mineral fiber (asbestos) felt backing. There is the potential to create friable asbestos when attempting to strip the design layer from the backing.