The weights of four boxes are 90 kg, 40 kg, 80 kg and 50 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:
Here you are again asked to identify an impossible total made from a fixed set of box weights. This style of question reinforces the habit of patiently enumerating possible sums rather than guessing. The logic is the same as in the previous weight combination examples, but with a different set of numbers and answer choices.

Given Data / Assumptions:

• Box weights: 90 kg, 40 kg, 80 kg, 50 kg.
• Each box may be used at most once in a combination.
• Candidate totals: 200 kg, 260 kg, 180 kg, 170 kg.
• All weights are whole numbers in kilograms.

Concept / Approach:
We need to examine all possible sums of these four weights: one box, two box, three box and four box combinations. Then we compare these possible sums with the answer options and pick the total that does not appear. Staying systematic prevents errors and ensures we do not overlook any configuration.

Step-by-Step Solution:
Step 1: List weights: 90, 40, 80, 50.Step 2: Sums using one box: 40, 50, 80, 90.Step 3: Sums using two boxes: 40 + 50 = 90, 40 + 80 = 120, 40 + 90 = 130, 50 + 80 = 130, 50 + 90 = 140, 80 + 90 = 170.Step 4: Sums using three boxes: 40 + 50 + 80 = 170, 40 + 50 + 90 = 180, 40 + 80 + 90 = 210, 50 + 80 + 90 = 220.Step 5: Sum using all four boxes: 40 + 50 + 80 + 90 = 260.Step 6: Collect all distinct sums: 40, 50, 80, 90, 120, 130, 140, 170, 180, 210, 220, 260.Step 7: Compare each option 200, 260, 180, 170 with this set.

Verification / Alternative check:
From the list, 260 is achievable using all four boxes. The total 180 is achievable with 40 + 50 + 90. The total 170 is achievable with 80 + 90 or 40 + 50 + 80. However, 200 is absent from the list. To check further, try forming 200: 90 + 80 = 170, and adding 40 gives 210, adding 50 gives 220. Combinations like 90 + 50 = 140 and then adding 40 or 80 give 180 or 220, never 200. Likewise, 80 + 50 + 40 = 170. Therefore, no subset sums to 200, so 200 is impossible.

Why Other Options Are Wrong:
260 kg is clearly possible with all four boxes.180 kg is possible with 40 + 50 + 90.170 kg is possible with 80 + 90 or 40 + 50 + 80.So these totals can be formed and are not the correct answer.

Common Pitfalls:
Some examinees may rush and conclude that 260 is impossible because it seems large, forgetting that it is simply the sum of all four weights. Others might miscalculate three box sums and thereby misjudge totals such as 170 or 180. Carefully writing out the sums of each subset once, and then scanning that list, is the most efficient way to answer correctly.

Final Answer:
The total weight that cannot be obtained from any combination of these four boxes is 200 kilograms.