In a certain code, "13" means "stop smoking" and "59" means "injurious habit". What are the meanings of the single digits "9" and "5" respectively in this code? Statement I: "157" means "stop bad habit". Statement II: "839" means "smoking is injurious".

Introduction / Context:
This is a data sufficiency question based on a simple code language for words and digits. You are not asked to find the full code dictionary, but only to decide whether the given statements provide enough information to determine the meanings of the digits 9 and 5 individually. In data sufficiency, the focus is on judging sufficiency, not doing unnecessary computation, so you must be precise about what each statement allows you to deduce.

Given Data / Assumptions:
- From the main information: "13" means "stop smoking".
- From the main information: "59" means "injurious habit".
- We must find the meanings of "9" and "5" respectively.
- Statement I: "157" means "stop bad habit".
- Statement II: "839" means "smoking is injurious".
- Each digit corresponds to exactly one word, and each word corresponds to exactly one digit within this code system.

Concept / Approach:
The logical method is to use intersections: whenever two codes share a digit, the corresponding messages must share a word, and that digit must stand for that word. By comparing the messages for different codes, we can progressively map digits to words. For data sufficiency, we check what can be deduced using the original information plus statement I alone, and then using the original information plus statement II alone. If either set is enough by itself, the correct option is the one that reflects that level of sufficiency.

Step-by-Step Solution:
Step 1: Use statement I with the base information. "13" → "stop smoking" and "157" → "stop bad habit". The common word is "stop", and the common digit is "1". Thus, digit 1 stands for "stop". Step 2: From the main information "59" → "injurious habit", we know digits 5 and 9 represent "injurious" and "habit" in some order. Step 3: In "157" → "stop bad habit", the remaining words are "bad" and "habit", and the remaining digits are 5 and 7. Since "habit" appears in both "59" and "157", but only digit 5 is common to those two codes, digit 5 must stand for "habit". Step 4: Once 5 is mapped to "habit", in "59" the only remaining word is "injurious", so digit 9 must stand for "injurious". Thus, using statement I with the base information, we can determine both meanings, so statement I alone is sufficient. Step 5: Now test statement II separately with the base information. "13" → "stop smoking" and "839" → "smoking is injurious". The common word is "smoking", and the common digit is 3, so 3 stands for "smoking". Step 6: Compare "59" → "injurious habit" and "839" → "smoking is injurious". The common word is "injurious", and the common digit is 9, so 9 stands for "injurious". Once again, in "59" the remaining word is "habit" and the remaining digit is 5, so 5 stands for "habit". Statement II alone, combined with the base information, is also sufficient.

Verification / Alternative check:
In both analyses, we derived the same mapping: 9 corresponds to "injurious" and 5 corresponds to "habit". This consistency confirms that each individual statement, when used with the general information, is independently strong enough to answer the original question. There is no contradiction between the statements, and using both together does not add any new necessary information beyond what each already gives on its own.

Why Other Options Are Wrong:
- Option a is wrong because statement I is indeed sufficient, but so is statement II; it is not the case that only I works.
- Option b is wrong for the symmetric reason: statement II is sufficient, but so is statement I.
- Option d is wrong because both statements together are not needed; each is already enough by itself.
- Option e is clearly wrong because the data are more than sufficient to answer which words digits 9 and 5 represent.

Common Pitfalls:
One common mistake is to forget that the base information about "13" and "59" is always available, even when you are judging each statement separately. Another pitfall is to assume that you must use both statements together just because they are provided, rather than testing each one independently. It is also easy to mix up which digit corresponds to which word if intersections are not carefully tracked.

Final Answer:
Each statement, taken separately with the given code information, is sufficient to determine that 9 means "injurious" and 5 means "habit". Therefore, the correct data sufficiency choice is option C, which states that either statement alone is sufficient.