In an arithmetic reasoning question, four boxes have weights 30 kg, 40 kg, 50 kg and 100 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 problem is another example of a box weight combination question that appears frequently in aptitude tests. You are provided with four specific box weights and several candidate totals. The objective is to find the total weight that cannot be formed by adding together some or all of the boxes, using each box at most once. This tests the ability to reason systematically about combinations and simple arithmetic sums.

Given Data / Assumptions:
- Box weights: 30 kg, 40 kg, 50 kg and 100 kg. - Each box can either be chosen or not chosen, but cannot be repeated. - We can form totals using one, two, three or all four boxes. - Options given are 190 kg, 180 kg, 160 kg, 140 kg and 220 kg. - We must find which of these totals is impossible to obtain.

Concept / Approach:
The standard approach is to list all possible distinct sums using the four given weights. Because 4 items have a manageable number of subsets, enumeration is practical and reliable. After listing all sums, we compare them with the answer options. Any option that does not appear in the list of achievable totals is the answer. This method avoids guesswork and ensures that no valid combination is overlooked.

Step-by-Step Solution:
Step 1: Single box totals: 30, 40, 50 and 100 kilograms. Step 2: Pairwise sums: 30 + 40 = 70, 30 + 50 = 80, 30 + 100 = 130, 40 + 50 = 90, 40 + 100 = 140, 50 + 100 = 150. Step 3: Triple box sums: 30 + 40 + 50 = 120, 30 + 40 + 100 = 170, 30 + 50 + 100 = 180, 40 + 50 + 100 = 190. Step 4: Sum of all four boxes: 30 + 40 + 50 + 100 = 220. Step 5: Collect achievable totals: 30, 40, 50, 70, 80, 90, 100, 120, 130, 140, 150, 170, 180, 190 and 220. Step 6: Compare with the options: 190, 180, 160, 140 and 220. The only value that does not appear in the achievable list is 160 kilograms.

Verification / Alternative check:
To verify, specifically search for a combination that could produce 160 kg. Try 100 + 50 = 150, which is too small, and adding 30 or 40 would exceed 160. Using 50 + 40 = 90, adding 30 gives 120, and adding 100 gives 190. No combination using any subset of the four weights equals 160. Therefore, 160 kilograms is impossible to form and must be the correct answer. This confirms the earlier enumeration.

Why Other Options Are Wrong:
- 190 kilograms is achievable with 40 + 50 + 100. - 180 kilograms is achievable with 30 + 50 + 100. - 140 kilograms is achievable with 40 + 100. - 220 kilograms is achievable with all four boxes: 30 + 40 + 50 + 100. Since each of these totals can be formed, they are not the required impossible total.

Common Pitfalls:
A common mistake is to perform mental calculations without a structured list, which often leads to missing a combination. Some candidates may also mistakenly allow repetition of a box, which violates the condition that a box can be used only once. Another pitfall is to assume that the largest or the smallest option is automatically the answer, which is not necessarily true. Systematic enumeration remains the safest strategy.

Final Answer:
The total weight that cannot be formed by any combination of the four boxes, with each box used at most once, is 160 kilograms.