Statement #1: 1/6 of the new employees are administrators who have had a physical in the previous year.
New administrative employees do not need physicals, regardless of whether they have had a physical in the past year or not. All new employees needing new physicals are responders. This information is irrelevant.
This statement, alone and by itself, is insufficient.
Statement #2: 1/3 of the new responders have had a physical in the previous year.
There are six new employees that needed physicals, and all of them must be new responders. This six is the one-third of responders that needed physicals, so 2/3, 12 new responders didn't need physicals. There are 18 new responders in total, which accounts for 3/4 of all new employees, so there are 24 new employees.
This statement, alone and by itself, is sufficient.