In a certain code language: (A) "134" means "you are well"; (B) "758" means "they go home"; and (C) "839" means "we are home". To answer the question "Which digit stands for the word 'home'?", which of the three statements (A, B or C) can be dispensed with as not necessary?

Introduction / Context:
This is a data sufficiency style coding decoding question. Instead of directly asking for the code of a word, it asks which of the given statements is not required to determine the code for the word "home". This tests your ability to identify the minimum information needed rather than simply solving the full code.

Given Data / Assumptions:
Statement A: "134" means "you are well".
Statement B: "758" means "they go home".
Statement C: "839" means "we are home".
We assume each word in a phrase corresponds to exactly one digit, and each digit in a code corresponds to exactly one word in that phrase, as is standard in such problems.

Concept / Approach:
Because we only care about the word "home", we must focus on statements that include this word. "Home" appears in the phrase for statement B and the phrase for statement C, so those two statements are immediately relevant. Statement A does not even contain the word "home", which suggests it might be unnecessary.

Step-by-Step Solution:
From statement B, "758" means "they go home". The three digits 7, 5 and 8 stand for "they", "go" and "home" in some order. From statement C, "839" means "we are home". The three digits 8, 3 and 9 stand for "we", "are" and "home" in some order. The common word between these two phrases is "home". The common digit between the codes 758 and 839 is 8. Therefore, the digit 8 must stand for the word "home". We did not use statement A at all to obtain this conclusion.

Verification / Alternative check:
We can double check that no other digit is common between B and C. 758 and 839 share only the digit 8. That single overlap aligns perfectly with the shared word "home". This confirms that our reasoning is consistent and independent of statement A.

Why Other Options Are Wrong:
Option "B only" is incorrect because we cannot identify "home" from statement B alone; we need another phrase containing "home" for comparison. Option "A or C only" is wrong because C is definitely needed while A is not. Option "B or C only" is incorrect since either B or C alone is insufficient; both are necessary to find the overlap. Hence, only statement A can be dispensed with.

Common Pitfalls:
A common mistake is to assume that, since three statements are given, all must be used. Another pitfall is to try to decode all the words and digits, which wastes time. For data sufficiency style questions, you should focus strictly on what is asked (here, the code for "home") and identify which statements actually contain that information.

Final Answer:
Only statement A can be dispensed with while still answering the question, so the correct choice is A only.