Six shipments of machine parts were shipped from a factory

to avoid fraction, lets first pick a number such as 120 for total value. Thus
S1 = 30, S2= 24, S3= 20, S4=9,S5=16, S6=12
Now we are told first truck had greater than 1/2 of total value = more than 60
And we want to know if S3 is part of this.

Statement 1: S2 and S4 were on first truck = 24+9 = 35
But we know that First truck had more than 60, so it could have additional, S1 or , S1+S3, or S3+S5 etc combinations. Not sufficient.

Statement 2: S1 and S6 were on second truck = 30+12 = 42
Therefore, if S3 was also to be on second truck, total on second truck would be 42+20 =62. So Maximum on first truck could be 120-62= 58 (less than 1/2)
Which is not possible. Hence we can conclusively say S3 was not on second truck. Sufficient.

Ans B it is!