The weights of 4 boxes are 90, 30, 40 and 60 kilograms. Which of the following cannot be the total weight, in kilograms; of any combination of these boxes and in a combination a box can be used only once?
200
Possible totals from subsets of {90, 30, 40, 60} (each box used at most once):
Singles: 30, 40, 60, 90.
Pairs: 30+40=70, 30+60=90, 30+90=120, 40+60=100, 40+90=130, 60+90=150.
Triples: 30+40+60=130, 30+40+90=160, 30+60+90=180, 40+60+90=190.
All four: 30+40+60+90=220.
Among the options, 220, 180 and 130 are achievable, but 200 is not in this list. Hence 200 kg cannot be formed.
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