Introduction / Context:
This is an input–output style question where a word arrangement machine rearranges words in a line based on a fixed rule. You must understand the rule from one fully worked example and then apply it to a new input to find the required intermediate step. Here, we are asked to determine the third step for a different set of words.
Given Data / Assumptions:
- Example input: gone are take enough brought station.
- Steps:
- Step 1: take gone are enough brought station
- Step 2: take are gone enough brought station
- Step 3: take are station gone enough brought
- Step 4: take are station brought gone enough (final)
- New input: car on star quick demand fat.
- We must find the third step produced by the same rule.
Concept / Approach:
From the example, we infer the pattern:
- The machine alternately places the lexicographically largest and smallest remaining words in the next position from the left.
- At Step 1, it moves the lexicographically greatest word to the first position.
- At Step 2, it moves the lexicographically smallest remaining word to the second position.
- At Step 3, it moves the greatest of the remaining words to the third position, and so on.
We need to apply this alternating largest–smallest selection rule to the new input.
Step-by-Step Solution:
Step 1: List the new input words: car, on, star, quick, demand, fat.
Step 2: Determine alphabetical order (lexicographic) of all six words: car, demand, fat, on, quick, star. The largest word is “star”.
Step 3: Step 1: Move “star” to the first position, keeping the relative order of the remaining words unchanged:
Step 1 = star car on quick demand fat.
Step 4: The remaining words are car, on, quick, demand and fat. Among these, the smallest alphabetically is “car”.
Step 5: Step 2: Place “car” in the second position. It is already at that position, so the sequence remains:
Step 2 = star car on quick demand fat.
Step 6: Remaining words now are on, quick, demand and fat. Among these, the largest is “quick”.
Step 7: Step 3: Move “quick” to the third position. Removing “quick” from its old position and keeping the order of the others, we obtain:
Step 3 = star car quick on demand fat.
Verification / Alternative check:
We can double-check this by comparing the pattern to the example: first move the lexicographically largest to the first position, then the smallest remaining to the second, then the largest remaining to the third, which is exactly what we have done. So the third-step sequence for the new input is “star car quick on demand fat”.
Why Other Options Are Wrong:
star car demand quick on fat: Here “demand” appears in the third position instead of “quick”, which breaks the largest-selection rule at Step 3.
star quick car demand on fat: This has “quick” in the second position, but according to the pattern the second position is reserved for the smallest remaining word, which should be “car”.
star car quick demand on fat: This swaps “on” and “demand” relative to the correct step, so it does not preserve the relative order of the remaining words after moving “quick”.
Common Pitfalls:
A frequent mistake is to think that the words are simply being sorted alphabetically or that the entire list is sorted in one direction. In reality, the example shows an alternating largest–smallest selection, and the remaining words keep their internal order after one is extracted. Failure to preserve that relative order is a common source of wrong options in such questions.
Final Answer:
Thus, the third step is
“star car quick on demand fat”, which is not listed explicitly among options (a), (b) or (c), so the correct choice is
none of these.
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