The weights of four boxes are 20 kilograms, 30 kilograms, 50 kilograms and 70 kilograms. A combination can use any box at most once. Which of the following cannot be the total weight, in kilograms, of some combination of these boxes?

Introduction / Context:
This is a subset sum type reasoning question involving simple arithmetic. You are given the weights of individual boxes and asked which total weight cannot be formed by choosing some or all of them, without repetition. This kind of question appears often in competitive exams to test whether you can systematically consider all combinations rather than guessing.

Given Data / Assumptions:

• There are four boxes with weights 20 kg, 30 kg, 50 kg and 70 kg.
• Each box can be used at most once in any combination.
• Possible totals are found by adding any subset of these weights.
• The candidate totals to test are 170 kg, 160 kg, 150 kg, 120 kg and 140 kg.

Concept / Approach:
The straightforward approach is to list all possible sums of these four weights. There are 2^4 = 16 possible subsets, including the empty set. We do not need the empty set, so we focus on non empty subsets. After computing all unique sums, we compare them with the totals given in the options. Any option not present in our list of subset sums cannot be formed and is therefore the correct answer.

Step-by-Step Solution:
List the individual weights: 20, 30, 50 and 70. Compute sums using one box: 20, 30, 50, 70. Compute sums using two boxes: 20 + 30 = 50, 20 + 50 = 70, 20 + 70 = 90, 30 + 50 = 80, 30 + 70 = 100, 50 + 70 = 120. Compute sums using three boxes: 20 + 30 + 50 = 100, 20 + 30 + 70 = 120, 20 + 50 + 70 = 140, 30 + 50 + 70 = 150. Compute the sum using all four boxes: 20 + 30 + 50 + 70 = 170. Collect the distinct totals: 20, 30, 50, 70, 80, 90, 100, 120, 140, 150, 170. Now compare with options 170, 160, 150, 120 and 140. All except 160 appear in the list of possible totals.

Verification / Alternative check:
We can verify by specifically trying to express 160 as a sum of the given weights. Check three box combinations: 70 + 50 + 30 = 150, 70 + 50 + 20 = 140, 70 + 30 + 20 = 120, 50 + 30 + 20 = 100. None equals 160. Adding all four gives 170. Using two boxes gives at most 70 + 50 = 120, which is also not 160. Since there is no way to reach 160 using any subset, the total 160 kg is impossible, confirming our result.

Why Other Options Are Wrong:
170 kg is possible by using all four boxes together. 150 kg is possible by combining 30 kg, 50 kg and 70 kg. 120 kg can be obtained either as 50 kg + 70 kg or as 20 kg + 30 kg + 70 kg. 140 kg is possible by combining 20 kg, 50 kg and 70 kg. Since these totals can be formed by valid combinations, they are not the correct answer.

Common Pitfalls:
A common mistake is to miss some combinations or to double count others, leading to an incorrect list of totals. Another pitfall is to rely on mental arithmetic alone for all combinations, which can cause errors under time pressure. Some candidates also assume that the largest impossible total must be the answer, which is not always true. Systematically listing and checking subset sums is the safest strategy.

Final Answer:
The total weight that cannot be obtained from any combination of the given boxes is 160 kilograms.