If a door set has a fire door and slave 1/4 door in an office environment, should the 1/4 door be locked or open?

The fire door is wide enough to comply as a means of escape and the 1/4 is thought to be to allow furniture moves, etc.  Both main and slave doors have a self-closer.

If it's got it's own closer rather than just being bolted then that usually is a good indicator that the whole width of both doors was required for escape at the time of installation based on the occupancy numbers, discounting of exits etc. as oppose to just for floor moves.

If your Means of Escape calculations, done correctly, indicate you only need the main leaf and you want to keep the quarter bolted then you should be OK