The weights of four boxes are 20 kg, 90 kg, 40 kg and 60 kg. Each box can be used at most once in any combination. Which of the following values cannot be the total weight, in kilograms, of any possible combination of these boxes?

Introduction / Context:

This problem is another example of finding impossible totals from a given set of weights. We must determine which option cannot be formed by adding one or more of the four given box weights, with each box used at most once. Systematic enumeration or careful reasoning is key to avoiding missed combinations.

Given Data / Assumptions:

• Box weights: 20 kg, 90 kg, 40 kg and 60 kg.
• Any box may be chosen once or not at all in a combination.
• We may use one, two, three or all four boxes.
• We want the option that cannot match any valid sum.

Concept / Approach:

Because there are only four boxes, listing all possible sums is manageable. We compute totals for single boxes, then for each pair, each triple, and finally for all four boxes together. Once we have the full set of achievable totals, we compare them with the provided options and see which value is missing.

Step-by-Step Solution:

Verification / Alternative check:

To double-check, try to construct 200 kg directly. The largest total less than or equal to 200 from three boxes is 40 + 60 + 90 = 190. Including the remaining box makes the total 210, which is too large. Testing all two-box combinations such as 90 + 60, 90 + 40 and 60 + 40 yields 150, 130 and 100 kilograms respectively, none of which is 200. Therefore 200 kg is genuinely impossible.

Why Other Options Are Wrong:

Option 210 kg is the sum of all four boxes: 20 + 40 + 60 + 90.

Option 170 kg is obtained by 20 + 60 + 90.

Option 190 kg is obtained by 40 + 60 + 90.

Common Pitfalls:

One frequent error is to skip a combination or reproduce the same total twice and mistakenly believe all values are covered. Writing the combinations in a systematic order, such as sorting by number of boxes used, helps ensure that no possible sum is overlooked.

Final Answer:

The total weight that cannot be formed is 200 kilograms.