Who is the niece of A? Statements: I. B is the brother of A. II. C is the…

Concept

This is a data-sufficiency problem. The task is not to find the answer from one's own assumptions, but to decide which of the given statements (individually or combined) logically pin down the answer. A statement is 'sufficient' only if it lets you deduce the asked relationship with certainty, with no missing link.

Relationship rule: a 'niece' is the daughter of a person's brother or sister. So to call someone A's niece, you must establish two facts — (1) that person is the daughter of one of A's siblings, and (2) that the sibling is indeed A's brother or sister.

Applying it to each statement

1. Statement I says B is the brother of A. This only tells us A has a brother named B. It says nothing about any daughter, so no niece can be identified. On its own it is not enough.

2. Statement II says C is the daughter of B. This tells us C's parent is B, but in isolation we do not know how B is related to A. C could be A's niece, A's own daughter, or unrelated. On its own it is not enough.

3. Combining both: B is A's brother (I) and C is B's daughter (II). The daughter of A's brother is exactly A's niece. So C is the niece of A — the relationship is now fully determined.

Cross-check

Neither statement alone yields a unique answer, but together they form a complete chain A -> brother B -> daughter C, which fixes C as A's niece. Hence both statements together are sufficient, and neither one alone is.