How is B related to A? Statement I: A is the sister of B. Statement II: A and B have the same father.

Introduction / Context:
This data sufficiency question concerns family relationships. We are asked, How is B related to A? The statements talk about A being the sister of B and A and B having the same father. The challenge is to determine whether we can uniquely identify B's relation to A, such as brother or sister, or some other relation, from the given data. It tests our ability to see when information about one person's gender does not automatically fix another person's gender.

Given Data / Assumptions:

• We need the relation of B to A.
• Statement I: A is the sister of B.
• Statement II: A and B share the same father.
• Terms like sister have their usual meaning: sister means a female sibling.
• No information is given about the gender of B.
• We are interested in the precise relation, typically brother or sister, not just that B is a sibling.

Concept / Approach:
The core idea is that knowing A is the sister of B tells us that A is female and that A and B are siblings. However, that does not tell us whether B is male or female. Statement II adds information about parentage but not about B's gender. Data sufficiency requires that the relation of B to A be uniquely determined. If different possibilities remain, the data are not sufficient.

Step-by-Step Solution:
Step 1: From statement I, A is the sister of B. This means that A is female and that A and B are siblings. Step 2: Statement I alone does not specify whether B is male or female. Therefore, B could be the brother of A or the sister of A. Step 3: The question asks, How is B related to A. Usually the desired answer is something like brother, sister, or cousin. Step 4: With statement I alone, the best we can say is that B is a sibling of A, but we cannot fix B's gender. Step 5: Consider statement II. It says A and B have the same father. This only tells us that A and B share at least one parent, specifically their father. Step 6: Statement II alone does not even specify that A and B are siblings in the usual sense, although it strongly suggests so. It certainly does not give any information about gender. Step 7: Combining both statements, we know that A and B share the same father and A is a sister of B, so A and B are siblings with a common father. Step 8: However, even now, we still do not know whether B is male or female. B could be a brother of A or a sister of A, and both possibilities are consistent with A being a sister of B and both sharing the same father. Step 9: Since we cannot uniquely identify B as brother or sister, the data do not give a unique relationship beyond B is a sibling of A, which is vague for the purpose of this question.

Verification / Alternative check:
Scenario one: Suppose B is male. Then A being a sister of B and sharing the same father means that B is the brother of A. All statements hold. Scenario two: Suppose B is female. Then A is still a sister of B, and they can still share the same father. In this case, B is the sister of A. Both scenarios satisfy statements I and II. However, they assign different specific relations to B with respect to A, which shows that our data cannot fix a unique relation.

Why Other Options Are Wrong:
Option a is wrong because statement I alone leaves B's gender unknown. Option b is wrong because statement II alone gives no gender information and does not by itself answer the question. Option c is wrong because neither statement alone is sufficient. Option d is wrong because even both statements together leave multiple possibilities for B's relation to A.

Common Pitfalls:
Many students automatically assume that B must be male when they see that A is the sister of B, and quickly answer that B is the brother of A. This is an unjustified assumption. The term sister only specifies the gender of A, not of B. In data sufficiency problems it is vital to avoid filling in implicit assumptions about gender or family structure that are not clearly stated. The correct reasoning checks whether any logically possible alternative remains; if so, the data are not sufficient.

Final Answer:
The relation of B to A (brother or sister) cannot be uniquely determined from the given statements. Correct option: Even using both statements I and II together, the data are not sufficient to answer the question.