The weights of four boxes are 30 kg, 20 kg, 60 kg and 70 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 question continues the theme of identifying impossible totals from a small set of weights. Candidates must be comfortable enumerating possible sums and recognizing which target value cannot be formed when each box can be used at most once. It is a typical numerical reasoning task.

Given Data / Assumptions:

• Box weights: 30 kg, 20 kg, 60 kg and 70 kg.
• Any box may appear at most once in a combination.
• We can use one, two, three or all four boxes.
• We must find which option cannot match any valid sum.

Concept / Approach:

We again use systematic listing: compute all sums of one box, then of each pair, then of each triple, and finally of all four boxes together. After collecting all distinct totals, we compare them with the answer choices. The number that does not appear in the list is impossible.

Step-by-Step Solution:

Verification / Alternative check:

To confirm that 170 kg is impossible, try constructing it. The largest three-box total is 30 + 60 + 70 = 160 kg. Adding the remaining 20 kg gives 180 kg, which exceeds 170. No two-box combination equals 170 either, because 70 + 60 = 130 and 70 + 30 = 100. Hence, 170 kg cannot be formed using these weights once each.

Why Other Options Are Wrong:

Option 180 kg is equal to the sum of all four boxes.

Option 120 kg is obtained as 20 + 30 + 70.

Option 150 kg can be formed as 20 + 60 + 70.

Common Pitfalls:

Some test takers may assume that any number between the smallest and largest total is possible, which is not true when only specific weights are available. Others may forget three-box combinations. A neat table of all one, two, three and four box sums avoids such mistakes.

Final Answer:

The total weight that cannot be formed is 170 kilograms.