If all 60 members of the junior class joined the Young Democrats, the

matthewsmith_89 plz explain how is the formula helpful in answering the question
thanks

The wording of statement 1 is a bit clumsy and I doubt one would see this on actual GMAT.

"Not either A or B" is accepted to be "Not A and Not B" though a much better way of writing would be "Neither A nor B".

Total members who joined at least 1 club = 60

(1) 31 students did not join either the Chess Club or the Varsity Club.
31 students, i.e. more than half, did not join 2 of these clubs. So these 31 joined the third club only i.e. the Young Democrats. So actually, less than half of the students joined 2 or more clubs. We can answer the question asked with a definite 'No'.
Sufficient.

(2) 28 students joined the Chess Club and 31 students joined the Young Democrats.
We don't know the overlap here.
It is possible that 28 joined only Chess club, 31 joined only Young Democrats and the leftover 1 student joined only Varsity club so all 60 joined only 1 club.
It is also possible that 28 joined Chess club and the rest of the 32 joined the Varsity club (making up for the 60 students). Then of these 60, 31 join the Young Democrats so 31 (more than half) students join 2 clubs.
Hence we cannot answer the question.
Not sufficient.

Answer (A)