The weights of four boxes are 20 kg, 40 kg, 80 kg and 90 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 problem again focuses on reasoning with combinations of fixed weights. You are given four distinct box weights and asked to determine which of the listed totals cannot be produced if each weight is used at most one time. Such questions are popular in aptitude tests because they examine systematic thinking rather than simply mechanical calculation.

Given Data / Assumptions:

• Box weights: 20 kg, 40 kg, 80 kg, 90 kg.
• Each box can be used at most once in any combination.
• Candidate totals: 220 kg, 230 kg, 150 kg, 210 kg.
• No partial weights are allowed; a box is either fully used or not used at all.

Concept / Approach:
We should list the distinct sums that can be formed by using one, two, three, or all four boxes. For four numbers, the total number of non empty subsets is limited, so it is feasible to enumerate them or at least reason through them carefully. Once we know the set of possible totals, we only need to check which option is missing from that set. This avoids guesswork and ensures a logically correct conclusion.

Step-by-Step Solution:
Step 1: Note the weights: 20, 40, 80, 90.Step 2: Sums using one box: 20, 40, 80, 90.Step 3: Sums using two boxes: 20 + 40 = 60, 20 + 80 = 100, 20 + 90 = 110, 40 + 80 = 120, 40 + 90 = 130, 80 + 90 = 170.Step 4: Sums using three boxes: 20 + 40 + 80 = 140, 20 + 40 + 90 = 150, 20 + 80 + 90 = 190, 40 + 80 + 90 = 210.Step 5: Sum using all four boxes: 20 + 40 + 80 + 90 = 230.Step 6: Collect all distinct sums: 20, 40, 60, 80, 90, 100, 110, 120, 130, 140, 150, 170, 190, 210, 230.Step 7: Compare each option with this set of sums.

Verification / Alternative check:
Check each option directly. For 150, we already saw 20 + 40 + 90 = 150, so 150 is possible. For 210, we have 40 + 80 + 90 = 210, so that is possible. For 230, using all four boxes 20 + 40 + 80 + 90 gives 230, so 230 is also possible. For 220, try to write it as a sum of these weights. The largest three weights give 40 + 80 + 90 = 210, and adding 20 gives 230, which is too large. No other combination reaches exactly 220, so it is not obtainable.

Why Other Options Are Wrong:
150 kg is achievable by the combination 20 + 40 + 90.210 kg is achievable by the combination 40 + 80 + 90.230 kg is achievable by using all four boxes: 20 + 40 + 80 + 90.Therefore, these totals cannot be the answer to the question about impossibility.

Common Pitfalls:
Learners sometimes overlook a valid combination such as 20 + 40 + 90 or 40 + 80 + 90 and may wrongly conclude that those totals are impossible. Another common error is assuming that if a number is close to the sum of all four weights then it must be achievable, without actually checking each subset. Approaching the problem randomly instead of systematically is the main reason for mistakes in this type of question.

Final Answer:
The only total that cannot be obtained from any combination of the four given box weights is 220 kilograms.