Question : Directions: The weights of 4 boxes are 90, 30, 20, and 50 kilograms. Which of the following cannot be the total weight, in kilograms, of any combination of these boxes, and in combination a box can be used only once?
Option 1: 190
Option 2: 170
Option 3: 100
Option 4: 150
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Correct Answer: 150
Solution : Given: The weights of 4 boxes are 90, 30, 20, and 50 kilograms.
The total weight of all possible combinations of boxes is as follows – 90 + 30 = 120; 90 + 20 = 110; 90 + 50 = 140; 30 + 20 = 50; 30 + 50 = 80; 20 + 50 = 70; 90 + 30 + 20 = 140; 90 + 30 + 50 = 170; 90 + 20 + 50 = 160; 30 + 20 + 50 = 100; 90 + 30 + 20 + 50 = 190
Therefore, there is no total weight of 150 kilograms in any combination. Hence, the fourth option is correct.
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