Word formation from letters of REASONABLE (spelled RAESONABLE in the original) Which ONE of the following words cannot be formed from the letters of “REASONABLE”, using each letter at most once?
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ABONES
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BBRAIN
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CARSON
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DNOBLE
Answer
Correct Answer: BRAIN
Explanation
Introduction / Context:We must detect the option that cannot be formed from the source word's letters without exceeding any letter counts.
Given Data / Assumptions:
- Source: REASONABLE (letters include R,E×2,A×2,S,O,N,B,L).
- Use at most the available count of each letter.
Concept / Approach:Check each option for any missing or over-demanded letter.
Step-by-Step Solution:“BONES”: B,O,N,E,S ⇒ all present.“ARSON”: A,R,S,O,N ⇒ all present.“NOBLE”: N,O,B,L,E ⇒ all present.“BRAIN”: B,R,A,I,N ⇒ requires I, which REASONABLE does not have ⇒ cannot be formed.
Verification / Alternative check:Re-scan REASONABLE to confirm absence of the letter I.
Why Other Options Are Wrong:They can be formed without breaching letter counts.
Common Pitfalls:Overlooking that there is no “I” in REASONABLE and miscounting repeated vowels.
Final Answer:BRAIN