How is the word ‘‘letter’’ written in a code language? I. ‘‘please write a letter’’ → 7218 and ‘‘and received a Greek letter’’ → 7513. II. ‘‘write in English please’’ → 2084 and ‘‘a Greek’’ → 5714.

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Solve this multiple-choice question and choose the correct option.

Accepted Answer

Introduction / Context:This is a code-decoding Data Sufficiency task. We must judge whether the provided coded phrases uniquely determine the code for the specific word ‘‘letter’’ without fully cracking the entire code. Given Data / Assumptions: I: Phrases and their codes: (1) ‘‘please write a letter’’ → 7218; (2) ‘‘and received a Greek letter’’ → 7513. II: Phrases and their codes: (3) ‘‘write in English please’’ → 2084; (4) ‘‘a Greek’’ → 5714. Each distinct word maps to a distinct code token within this context; ordering of tokens within a phrase is not guaranteed to match word order. Concept / Approach:Use overlaps across phrases to isolate the code for the target word. A statement is sufficient only if the mapping for ‘‘letter’’ is uniquely pinned down. Step-by-Step Solution: 1) From I: The common words between (1) and (2) are ‘‘a’’ and ‘‘letter’’. The common digits between codes 7218 and 7513 are {7,1}. Thus {‘‘a’’, ‘‘letter’’} ↔ {7,1}, but we cannot tell which is which. Hence I alone is insufficient.2) From II: From (3) we get the set {‘‘write’’, ‘‘in’’, ‘‘English’’, ‘‘please’’} ↔ {2,0,8,4}. From (4) we get {‘‘a’’, ‘‘Greek’’} ↔ {5,7,1,4} (two digits chosen among four due to possible re-use across sentences), which does not directly single out ‘‘letter’’ at all. Hence II alone is insufficient.3) Combine I and II: In (1) ‘‘please’’ and ‘‘write’’ are present and are known from (3) to be within {2,0,8,4}. Removing those from 7218 leaves {7,1} for {‘‘a’’, ‘‘letter’’}. From (4), ‘‘a’’ is among {5,7,1,4}, so both 7 and 1 remain possible; nothing forces a unique choice for ‘‘letter’’ between 7 and 1. Therefore, even together, the mapping for ‘‘letter’’ is not uniquely determined. Verification / Alternative check:Construct two consistent assignments: Case A: map ‘‘a’’→7 and ‘‘letter’’→1; Case B: map ‘‘a’’→1 and ‘‘letter’’→7. Both can be made consistent with all four coded phrases by adjusting the remaining word–digit pairings accordingly. Why Other Options Are Wrong: A/B/C: Neither statement alone pins the code; “either alone” is also false. E: Even combined, ambiguity remains; thus not sufficient together. Common Pitfalls:Do not assume positional alignment between words and digits; do not assume the smallest/largest digit belongs to a particular word; only intersections and eliminations count. Final Answer:Both statements together are NOT sufficient.

How is the word ‘‘letter’’ written in a code language? I. ‘‘please write a letter’’ → 7218 and ‘‘and received a Greek letter’’ → 7513. II. ‘‘write in English please’’ → 2084 and ‘‘a Greek’’ → 5714.

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