Data sufficiency – coded language reasoning In a certain code, the string 'XYZ' means 'We are friends'. Which single letter stands for the word 'We'? Consider the following statements: (I) 'PYN' means 'They are classmates'. (II) 'ZMS' means 'We love them'. (III) 'PX' means 'Hello friends'.

Introduction / Context:This is a data-sufficiency problem on coded language mapping. We must identify which statement(s) are sufficient to determine which single letter corresponds to the word 'We' when the code 'XYZ' translates to 'We are friends'.

Given Data / Assumptions:

• Target code: XYZ → 'We are friends' (order of word–letter mapping unknown).
• Statement I: PYN → 'They are classmates'.
• Statement II: ZMS → 'We love them'.
• Statement III: PX → 'Hello friends'.
• Each letter in a codeword maps to exactly one word in the phrase for that code.

Concept / Approach:Use intersection logic: if two codes share common letters and the corresponding phrases share common words, then the common letter maps to the common word. We only need enough information to isolate the word 'We' from the other words.

Step-by-Step Solution:

Verification / Alternative check:With II alone we conclude Z = 'We'. Cross-check with III: since PX = 'Hello friends', X = 'friends'; thus in XYZ, X = 'friends', Z = 'We', leaving Y = 'are', which is consistent. I adds nothing.

Why Other Options Are Wrong:

• Only I and III: I is irrelevant; III alone cannot identify 'We'.
• All I, II and III: Overkill; II alone suffices.
• Either I only or II only: I only does not work; only II works.
• None of these: Incorrect because 'Only II' is sufficient.

Common Pitfalls:Assuming letter order equals word order, or trying to use Statement I which has no shared words. Focus on shared elements between codes and phrases.

Final Answer:Only II