Extracting single files from a tarball (spreadsheets)
Your main questions


  Are there better ways to extract from a tar?


Using shell commands, no. Well, with any modern version of tar, instead of tar -x -f archive file you could write simpler as tar xf archive file.

I don't know Ruby, but probably there exist libraries to extract files from archives. It would be better to use that.

The current script is a mixture of Ruby and Bash commands.
This is a fragile setup:


It requires two technologies to run
It requires understanding two technologies


The solution would be more robust if it was written either completely in Ruby or in Bash.


  I know it doesn't delete the directory that is created from extracting the spreadsheets, mostly because I don't trust myself enough to remove a directory called home.


You could recursively remove the empty parent directories. That should be safe.

Naming

Looking at this usage:


ss = ArchiveManager.new(ARGV[0])
ss.num_check



This doesn't really tell what's going to happen.
The program extracts a file from an archive.
This would look like a more natural usage:

archive_manager = ArchiveManager.new()
archive_manager.extract_file(ARGV[0])


Design

The naming issue brought to the fore some design issues.
The naming change I suggested earlier for more natural usage,
also forces further changes that will lead to better design:


Currently the ArchiveManager class is one-time use to extract a single file. That's not a natural way to use classes. Making the ArchiveManager reusable by adding a extract_file method with a file parameter is more natural.
Currently many methods of ArchiveManager depend on the folio_num stored in the class. Methods are easier to understand when their dependencies are more directly visible, for example as input parameters. It also makes them easier to test.