The weights of four boxes are 90 kg, 30 kg, 40 kg and 60 kg. Which of the following cannot be obtained as the total weight, in kilograms, of any combination of these boxes if each box is used at most once?

Introduction / Context:
This is another variation of the same style of weight combination reasoning. You are asked to identify which total cannot be formed by combining the given four box weights, with each box allowed at most once. Success depends on systematically working out the possible sums instead of relying on intuition alone.

Given Data / Assumptions:

• Box weights: 90 kg, 30 kg, 40 kg, 60 kg.
• Each box can be used at most once.
• Candidate totals: 200 kg, 220 kg, 180 kg, 130 kg.
• All weights and totals are whole numbers in kilograms.

Concept / Approach:
As before, we examine all possible sums of one, two, three and four box combinations. We then compare the compiled list of totals against the answer options to see which total is missing. That missing value is the one that cannot be obtained from any allowed combination.

Step-by-Step Solution:
Step 1: List the weights: 90, 30, 40, 60.Step 2: Sums using one box: 30, 40, 60, 90.Step 3: Sums using two boxes: 30 + 40 = 70, 30 + 60 = 90, 30 + 90 = 120, 40 + 60 = 100, 40 + 90 = 130, 60 + 90 = 150.Step 4: Sums using three boxes: 30 + 40 + 60 = 130, 30 + 40 + 90 = 160, 30 + 60 + 90 = 180, 40 + 60 + 90 = 190.Step 5: Sum using all four boxes: 30 + 40 + 60 + 90 = 220.Step 6: Collect all distinct sums: 30, 40, 60, 70, 90, 100, 120, 130, 150, 160, 180, 190, 220.Step 7: Compare options 200, 220, 180, 130 with this list.

Verification / Alternative check:
From the list we see that 220 is achievable by using all four boxes together. The total 180 is achievable from 30 + 60 + 90. The total 130 is achievable in two different ways: 40 + 90 and 30 + 40 + 60. Therefore, these three totals are valid. The remaining candidate, 200, does not appear in the list. To be sure, try constructing 200: 90 + 60 + 40 = 190, and adding 30 gives 220. Other three weight combinations like 90 + 60 + 30 = 180 and 90 + 40 + 30 = 160 also fall short. No pair reaches 200 either. This confirms 200 cannot be formed.

Why Other Options Are Wrong:
220 kg is possible using all four boxes.180 kg is possible using 30 + 60 + 90.130 kg is possible using 40 + 90 or 30 + 40 + 60.Thus, these totals are achievable and cannot be the answer.

Common Pitfalls:
Students often miscalculate a three box sum or forget that some totals like 130 can be formed in more than one way. This may lead them to wrongly conclude that such totals are impossible. Another pitfall is to assume that any round number like 200 should be possible, without carefully verifying the combinations. A complete list of sums is the most reliable solution method.

Final Answer:
The total weight that cannot be obtained from any combination of these four boxes is 200 kilograms.