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A Machine That Rearranges Words or Numbers, Step by Step
Every input-output question starts the same way: one line of words or numbers goes in, and the paper shows you three or four 'steps' where a machine has silently rearranged it — swapping positions, sorting alphabetically, reversing pairs, or running some arithmetic on the numbers. The catch is that the rule is never written down. You are handed the finished steps and asked either to name the missing step, or to apply the same rule to a brand-new input.
This looks intimidating only because it hides in plain sight among 'easier' reasoning types. Once you see it as detective work — compare two consecutive steps, spot exactly what moved — it becomes one of the fastest-scoring question types in the whole reasoning section, because the rule, once found, never changes for the rest of that question.
1. A machine's rule: replace each number with the sum of its digits, then arrange the numbers in descending order of that sum. Input: 36 47 25 82. What is the output?
2. A machine's rule swaps the first and last letters of every word, leaving the middle letters untouched. Input: GARDEN TOWER MOUSE. What is the output?
3. A machine's rule: each step, the largest remaining number moves to the front of the not-yet-fixed portion of the row (already-placed numbers stay put). Input: 14 39 8 52 21. Step I: 52 14 39 8 21. Step II: 52 39 14 8 21. What is Step III?
4. A machine replaces the first letter of every word with the next letter of the alphabet (Z becomes A). Input: CAT DOG FISH. What is the output?
5. A machine's rule: each step, the alphabetically-first word among the not-yet-fixed words moves to the front of that unfixed portion. Input: RIVER APPLE MANGO ZEBRA. Step I: APPLE RIVER MANGO ZEBRA. Step II: APPLE MANGO RIVER ZEBRA. In which step does the row first become fully sorted alphabetically?
6. A machine's rule: double every odd number, halve every even number, then arrange the results in ascending order. Input: 8 15 6 21. What is the output?
7. In an input-output (machine) reasoning question, what should you compare to find the machine's rule?
8. A candidate finds a rule that correctly explains Input → Step I. What should they do before applying it to answer the question?