Here,
A -
= {1,2,3,4,5,6,7,8,9} ;
Total possible multiple of 3 are
= 3,6,9,12,15,18,21,24,27
But 3 and 27 are not possible.
6 → 1 + 2 + 3
9 → 2 + 3 + 4 , 5 + 3 + 1,6 + 2 + 1
12 → 9 + 2 + 1,8 + 3 + 1,7 + 1 + 4,
7 + 2 + 3 ,( 5+ 4 + 2 , 6 + 5 + 1, 5 + 4 + 3
15 → 9 + 4 + 2,9 + 5 + l, 8 + 6 + 1 , 8 + 5 + 2 , 8 + 4 + 3 , 7 + 6 + 2 , 7 + 5 +3 , 6 + 5 + 4
18 → 9 + 8+ 1,9 + 7 + 2,9 + 6 + 3,9 + 5 + 4, 8 + 7 + 3, 8 + 6 + 4,7 + 6 + 5
21→9 + 8 +4, 9 + 7 + 5, 8 + 7 + 6
24 → 9 + 8 + 7
Hence, total number of largest possible subsets are 30.