Data size is relative to company size. If I work with a 120Gb clicklog file for a company with 10 employees, where no other employee has the tools or know-how to work with such a dataset, then that data is (treated as) big data. In the hands of Google, Yahoo, MS or Facebook if would probably look like a floppy.
No, you probably do not necessarily need a Hadoop cluster to work with a 120GB file. With Python and Pandas you could probably run through it on a budget laptop. But data will always be relative to your companies size and current know-how. In the most banal way: Data can be big data, because some manager can't open it in Excel.