How is B related to A? Consider the following statements: I. A is the sister of B. II. C is the father of both A and B.

Introduction / Context:
This data sufficiency question asks about the relationship of B to A in a family. Two statements describe A as the sister of B and introduce a father C of both A and B. The aim is to decide whether these statements uniquely determine whether B is a brother, a sister, or some other relation to A. The challenge lies in noticing which details are specified and which remain unknown, especially regarding gender.

Given Data / Assumptions:

• Statement I: A is the sister of B. This tells us that A is female and that A and B are siblings.
• Statement II: C is the father of both A and B. This confirms that A and B share the same father and are siblings.
• Brother means a male sibling, and sister means a female sibling.
• No explicit information is given about the gender of B.

Concept / Approach:
The question asks How is B related to A, which usually requires us to say whether B is the brother of A, the sister of A, or some other clearly defined relation. To answer this precisely, we must know both the basic sibling relationship and the gender of B. Data sufficiency analysis checks whether the statements force B to be male or female, or whether both possibilities remain open.

Step-by-Step Solution:
Step 1: From statement I, A is the sister of B. This establishes that A is female and that A and B are siblings. However, it does not state whether B is male or female. Therefore, B could be a brother or a sister of A under this statement alone. Step 2: Because B gender is not specified in statement I, we cannot answer the question How is B related to A with a unique description. Statement I alone is not sufficient. Step 3: From statement II, C is the father of both A and B. This tells us that A and B are children of C and therefore siblings. Again, there is no mention of gender for either A or B, so we cannot say whether B is a brother or a sister from statement II alone. Step 4: Therefore, statement II alone is also not sufficient to answer the question. Step 5: Now combine statements I and II. Together, they still give only that A and B are siblings, that A is female, and that C is their father. The combination does not add any new information about the gender of B beyond what was already missing. Step 6: Consider possible scenarios. In one scenario, B is a male child of C, in which case B is the brother of A. In another scenario, B is a female child of C, in which case B is the sister of A. Both scenarios satisfy statements I and II and are compatible with A being described as the sister of B. Step 7: Since at least two different possibilities for B relation exist and both fit all the given information, the data are not sufficient to decide uniquely how B is related to A.

Verification / Alternative check:
A quick sufficiency check is to ask whether we can fix the gender of B from the statements. Because neither statement ever tells us that B is a son or a daughter, or uses words like brother or sister for B, the gender of B remains undetermined even when both statements are used. Whenever a relationship label depends on gender, and gender is not fixed, the data cannot be sufficient to answer the relationship question exactly.

Why Other Options Are Wrong:
Option A incorrectly claims that statement I alone is sufficient. Although it gives a sibling relation, it does not specify whether B is male or female. Option B is also incorrect because statement II alone provides only a common parent, not gender. Option C, which claims that either statement alone is sufficient, is doubly wrong. Option D suggests that both statements together are necessary and sufficient, but in fact they still leave B gender open. Only option E correctly states that even both statements together are not sufficient.

Common Pitfalls:
A common error is to assume that if A is the sister of B, then B must be male, but this is not implied by the language. The phrase A is the sister of B only fixes A gender and the sibling relationship, not B gender. Another mistake is to think that giving a father automatically implies that one child must be a son. Careful attention to what is explicitly stated, especially about gender, is vital in family relationship questions.

Final Answer:
The data even in both statements together are not sufficient to answer the question, so the correct option is E.