Data Sufficiency — Family Tree (Granddaughter) Is V the granddaughter of B? I. B is the father of M. M is the sister of T. T is the mother of F. II. S is the son of F. V is the daughter of F. R is the brother of T.

Difficulty: Medium

Correct Answer: Both statements I and II together are sufficient, but neither alone is sufficient.

Explanation:


Introduction / Context:
The task is to judge sufficiency (not to output Yes/No), for deciding whether V is B’s granddaughter given two partial family statements.


Given Data / Assumptions:

  • I: B→(children) M and T (since B is father of M and M is sister of T). T→F.
  • II: F→children S (son) and V (daughter). R is T’s brother (consistent with I).


Concept / Approach:
To know if V is B’s granddaughter, we must connect V to B via B’s child. From I, F is child of T, and T is child of B ⇒ F is B’s grandchild. From II, V is child of F ⇒ V is B’s great-grandchild, not granddaughter.


Step-by-Step Solution:

1) From I: B→T→F (so F is B’s grandchild).2) From II: F→V (daughter) ⇒ V is one generation further from B than F.3) Conclude: V is B’s great-granddaughter, hence not B’s granddaughter.


Verification / Alternative check:
Neither I nor II alone mentions both generations needed to classify V relative to B; together they settle it uniquely.


Why Other Options Are Wrong:

  • I alone lacks who V is.
  • II alone never mentions B.
  • Either alone: insufficient.
  • Not sufficient even together: false.


Common Pitfalls:
Confusing granddaughter with great-granddaughter; overlooking that “sister/brother” implies same parent (B).


Final Answer:
Both statements together are sufficient; neither alone is sufficient.

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