Question : Directions: The weights of the 4 boxes are 90, 40, 80, and 50 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?
Option 1: 200
Option 2: 260
Option 3: 180
Option 4: 170
Correct Answer: 200
Solution :
Given:
The weights of 4 boxes are 90, 40, 80, and 50 kilograms.
The total weight of all possible combinations of boxes is as follows –
90 + 40 = 130; 90 + 80 = 170; 90 + 50 = 140; 40 + 80 = 120;
40 + 50 = 90; 80 + 50 = 130; 90 + 40 + 80 = 210;
90 + 40 + 50 = 180; 90 + 80 + 50 = 220; 40 + 80 + 50 = 170;
40 + 80 + 50 + 90 = 260
Therefore, there is no total weight of 200 kilograms in any combination. Hence, the first option is correct.
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