Data Sufficiency — Relationship of M to N Question: How is M related to N? Statements: I. B is the daughter of M and the sister of Q. II. N is the son of K, who is B's grandfather.

Difficulty: Medium

Correct Answer: Neither I nor II is sufficient

Explanation:


Introduction / Context:
This Data Sufficiency problem tests careful handling of family trees and multiple possibilities. The aim is to conclude the relation between M and N using the two statements, either separately or together.


Given Data / Assumptions:

  • I: B is M's daughter and Q's sister.
  • II: N is the son of K; K is B's grandfather (i.e., father of one of B's parents).
  • Gender of M is unspecified; K could be on M's side or the spouse's side.


Concept / Approach:
Build possible family trees consistent with both statements and check whether M's relation to N is uniquely determined. If more than one valid structure exists, the data is insufficient.


Step-by-Step Solution:

Case 1: Let K be M's father. Then K is B's grandfather via M. N is K's son, hence N is M's brother. ⇒ M is sibling of N. Case 2: Let K be the father of M's spouse. Then K is B's grandfather via M's spouse. N is K's son, i.e., M's spouse's brother. ⇒ M is sister-in-law/brother-in-law of N. Both cases satisfy I and II, yet yield different M–N relationships. Therefore, even together the statements do not fix a unique relation.


Verification / Alternative check:
No additional constraint in either statement eliminates one of the above cases. Hence ambiguity remains.


Why Other Options Are Wrong:

  • I alone or II alone: Neither links M and N at all.
  • Either alone sufficient: False.
  • Both sufficient: False because multiple valid relations remain.


Common Pitfalls:
Assuming K must be on M's side without evidence; inferring genders/relations that are not given; overlooking in-law possibilities.


Final Answer:
Neither I nor II is sufficient.

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