Data sufficiency — How is A related to B? Three statements are given: A. P, the only son of A, has two sisters. B. A's son is the brother of the only sister of B. C. B and P are children of A. Determine which statements are sufficient to conclude A's relation to B.

Introduction / Context:This data-sufficiency item asks us to determine A’s relation to B. We only need to know which statements are sufficient; we do not need the full family tree if sufficiency can be established directly.

Given Data / Assumptions:

• A: A has a son P, and P has two sisters (so A has at least three children).
• B: A’s son is brother of B’s only sister (can be read as making A’s son a sibling of B, but this can be ambiguous regarding whether B is part of A’s family).
• C: B and P are children of A (explicitly puts B under A).

Concept / Approach:We check each statement or combination to see whether A’s relationship to B (i.e., parent of B) is unequivocally determined.

Step-by-Step Solution:

Verification / Alternative check:Try building scenarios where B is not A’s child under A or B alone; these are possible. With C, however, B is explicitly A’s child, fixing the relationship.

Why Other Options Are Wrong:

• Only A: No link to B.
• Either A or B: Neither alone ensures the link.
• Both A and C: Overkill; C alone suffices.
• A and B together: Still potentially ambiguous without C.

Common Pitfalls:Over-interpreting B as proving full siblinghood within A’s family; ignoring that “brother of the only sister of B” can be some other boy, not necessarily sharing both parents.

Final Answer:Only C is sufficient.