The youth side played their first pre-season game on Monday when they travelled to Southern League outfit Barnstaple Town.
It was largely an inexperienced Argyle side that put up a plucky performance before going down 3-2 in front of a crowd of 550 at Mill Road.
The most notable absentee from the young Pilgrims line-up was second-year apprentice Cameron Sangster, who has been asked by manager Derek Adams to train with the first team and who impressed in his 90-minute run-out against Parkway last Saturday.
Argyle were also without three other midfielders, development professionals Dan Rooney (injured) and Aaron Taylor (ill) and second year apprentice Matt Ward (injured).
Second year apprentice Billy Craske spearheaded a couple of early threatening attacks down the left flank for the Greens before Barum struck with two quick goals just after the half hour mark.
The Pilgrims twice went close to reducing the deficit just before half-time, with apprentice Sam Ryan shooting narrowly wide and Craske having his effort saved by the home goalkeeper.
Development professional Alex Battle and second-year apprentice Luke Jephcott both shot narrowly wide in early second half attacks only for the home side to extend their lead on 70 minutes.
However, persistence paid for Argyle, especially for Battle, who netted with a clever 18-yard lob in the 75th minute.
Jephcott shot against the post as the young Pilgrims confidence grew and he then set up the chance for Battle to score again with a 12-yard drive in the 78th minute.