Data sufficiency — Is F the granddaughter of B? Two statements are given: A. B is father of M. M is the sister of T. T is the mother of F. B. S is the son of F. V is the daughter of F. R is the brother of T. Using the above, determine whether F is.

Question

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

Accepted Answer

Introduction / Context:This is a classic data-sufficiency problem on blood relations. We must decide whether the given statements provide enough information to conclude that F is the granddaughter of B without actually proving genders or full family trees beyond what is guaranteed by the statements. Given Data / Assumptions: Statement A: B is father of M; M is sister of T; T is mother of F. Statement B: S is son of F; V is daughter of F; R is brother of T. Granddaughter condition means: (1) F is female; (2) B is a grandparent of F. Concept / Approach:For sufficiency, each statement (alone or combined) must conclusively establish both that B is a grandparent of F and that F is female. If either part can remain ambiguous under any consistent interpretation, sufficiency fails. Step-by-Step Solution: 1) From A: B is father of M. M is sister of T (M and T share at least one parent). T is mother of F (T is female, parent of F).2) Does A guarantee B is also parent of T? No. M and T could be maternal half-siblings (sharing only their mother). A never says B is father of T. Hence, even though T is mother of F, we cannot confirm B is F’s grandparent.3) Does A ensure F is female? Yes, because T is the mother of F; F’s gender is still unspecified here (child of T), but “granddaughter” specifically requires F to be female. A alone does not assert F’s gender.4) From B: We learn about F’s children (S, V) and that R is T’s brother. B does not connect B (the person) to T or F, and says nothing about B’s relation to anyone here. It also does not specify F’s gender explicitly (parents can be any gender).5) Combine A and B: We still cannot force that B is a grandparent of F because T might not be B’s child. The possibility that M and T are half-siblings through their mother only remains open. Thus, even together, the data do not compel the required grandparent link. Verification / Alternative check:Construct two valid families: one where B is also T’s father (then F is B’s granddaughter) and another where B is only M’s father and T has a different father (then F is not B’s granddaughter). Both satisfy A and B, proving insufficiency. Why Other Options Are Wrong: A alone: F’s gender and the grandparent link are not guaranteed. B alone: No connection to B (the person) is established; entirely insufficient. Either A or B: As above, neither is sufficient alone. Both A and B together: Still ambiguous because T may not be B’s child. Common Pitfalls:Assuming siblings in A must share both parents; assuming motherhood of T implies B is the other grandparent; reading gender into F from B’s children list. Final Answer:Both A and B are not sufficient.

Data sufficiency — Is F the granddaughter of B? Two statements are given: A. B is father of M. M is the sister of T. T is the mother of F. B. S is the son of F. V is the daughter of F. R is the brother of T. Using the above, determine whether F is the granddaughter of B.

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