Is R the granddaughter of C? I. The only sister of A is the mother of R’s brother B. II. C, the mother of A, has only one grandson B.

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Solve this multiple-choice question and choose the correct option.

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Introduction / Context:We must determine if R is C’s granddaughter (i.e., R is female and is a child of one of C’s children). The statements define relationships among A, C, R, and B. Sufficiency depends on whether we can infer R’s lineage and gender conclusively. Given Data / Assumptions: I: A's only sister is the mother of R’s brother B. So A has exactly one sister; that sister is the mother of B and R, making B and R siblings (same mother). No information about C yet. II: C is A’s mother and has only one grandson B. That means among all grandchildren of C, there is exactly one male (B). Concept / Approach:To prove R is C’s granddaughter, we must show (1) R is indeed C’s grandchild and (2) R is female. Combine lineage from I with the sex-count constraint from II. Step-by-Step Solution: 1) From I alone: We know A’s only sister is mother of B and R ⇒ R and B are that sister’s children. But we do not know if A’s sister is also C’s child (we do not yet know who C is). Thus I alone does not link R to C; insufficient.2) From II alone: We know C is A’s mother and C has exactly one grandson B. We do not know who R is or through which child of C she might descend. Insufficient.3) Combine I + II: Since C is A’s mother, A’s only sister (from I) is also C’s daughter. Therefore, the children of A’s sister (namely B and R) are C’s grandchildren. From II, C has only one grandson—B. Hence any other grandchild (including R) must be female (otherwise there would be at least two grandsons). Thus R is a granddaughter of C. Verification / Alternative check:Could R be male? If R were male, C would have at least two grandsons: B and R, contradicting II. Therefore R must be female; and by lineage, R is C’s granddaughter. Why Other Options Are Wrong: A/B: Each statement alone misses either the lineage link (I) or the sibling/gender-count implication (II). C: Neither alone suffices; they must be combined. D: Together they are sufficient (we reach a definite Yes). Common Pitfalls:Overlooking that “only one grandson” forces every other grandchild to be female; forgetting that A’s sister is also C’s child, which connects R and B to C. Final Answer:Both statements together are sufficient, but NEITHER alone is sufficient.

Is R the granddaughter of C? I. The only sister of A is the mother of R’s brother B. II. C, the mother of A, has only one grandson B.

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