In an arithmetic reasoning puzzle, four boxes have weights 100 kg, 90 kg, 80 kg and 40 kg. For these four box weights, which of the following values cannot be obtained as the total weight, in kilograms, of any combination if in a combination each box can be used at most once?

Introduction / Context:
This arithmetic reasoning question is about selecting valid combinations of box weights. You are given four different box weights and several possible totals. The task is to find which total weight cannot be formed by adding some or all of the boxes, with the condition that each box can be used at most once. Such problems are common in aptitude tests to check understanding of combinations, systematic listing, and basic arithmetic operations.

Given Data / Assumptions:
- Box weights available: 100 kg, 90 kg, 80 kg and 40 kg. - Each box can be used at most once in any combination. - We can choose one, two, three or all four boxes. - We must identify which given total weight cannot be obtained from any such combination. - Options given are 200 kg, 310 kg, 230 kg, 210 kg and 270 kg.

Concept / Approach:
The core concept is to list all distinct possible sums using the given weights under the rule of using each weight at most once. Because there are only four boxes, the total number of possible non empty subsets is limited, so a systematic enumeration is feasible. By comparing the resulting list of achievable totals with the options, we can identify which option is not present in the list. This direct enumeration approach is reliable and avoids missing any valid combination.

Step-by-Step Solution:
Step 1: List single box totals: 40, 80, 90 and 100 kilograms. Step 2: List all pairwise sums: 100 + 90 = 190, 100 + 80 = 180, 100 + 40 = 140, 90 + 80 = 170, 90 + 40 = 130, 80 + 40 = 120. Step 3: List triple box sums: 100 + 90 + 80 = 270, 100 + 90 + 40 = 230, 100 + 80 + 40 = 220, 90 + 80 + 40 = 210. Step 4: List the sum of all four boxes: 100 + 90 + 80 + 40 = 310. Step 5: Collect all distinct achievable totals: 40, 80, 90, 100, 120, 130, 140, 170, 180, 190, 210, 220, 230, 270 and 310. Step 6: Compare with the options: 200, 310, 230, 210 and 270. We see that 310, 230, 210 and 270 appear in the achievable list, but 200 does not appear.

Verification / Alternative check:
A quick verification method is to reason whether 200 can be formed using the available weights. Try forming 200 kilograms: 100 + 90 = 190, so adding any other box exceeds 200. Using 100 + 80 = 180, adding 40 gives 220, which is too large. Using 90 + 80 = 170 and adding 40 gives 210, again not equal to 200. No single weight equals 200, and no pair or triple sum equals 200. Therefore, 200 kilograms is impossible to obtain, confirming the earlier enumeration result.

Why Other Options Are Wrong:
- 310 kilograms is achievable using all four boxes together: 100 + 90 + 80 + 40. - 230 kilograms is achievable using 100 + 90 + 40. - 210 kilograms is achievable using 90 + 80 + 40. - 270 kilograms is achievable using 100 + 90 + 80. Since these totals can be formed by valid combinations, they are not correct answers to the question asking for an impossible total.

Common Pitfalls:
Many test takers forget to list all combinations systematically and may miss a valid total. Another common mistake is to accidentally reuse a box weight more than once, which violates the given condition. Some candidates also try to guess by intuition instead of carefully listing possibilities, which can lead to wrong answers when numbers are close together. It is important to proceed methodically, especially when the number of items is small enough to allow full enumeration.

Final Answer:
The total weight that cannot be formed by any combination of the four boxes, with each box used at most once, is 200 kilograms.