Data Sufficiency — Family Relations Question: How is R related to M? Statements: I. M's brother is the husband of P. II. P is the mother of R's sister.
Correct Answer: Both I and II are sufficient
Introduction / Context: A kinship (blood-relation) Data Sufficiency problem. We must decide if the statements together or individually are enough to fix the relationship between R and M (e.g., nephew/niece, child, sibling, etc.).
Given Data / Assumptions:
- I: M's brother is P's husband.
- II: P is the mother of R's sister (standard assumption: same mother implies P is R's mother).
- Gender of R is not specified, so the answer will be in the form nephew/niece (child of M's brother).
Concept / Approach: Build the family links: if P is married to M's brother and P is R's mother, then R is the child of M's brother. Therefore, R is M's brother's child, i.e., R is M's nephew or niece (depending on R's gender).
Step-by-Step Solution:
From I: M's brother ↔ married to P. Thus P is M's sister-in-law. From II: P is the mother of R's sister ⇒ P is R's mother. Combine I and II: Since P (R's mother) is married to M's brother (from I), R is the child of M's brother. Therefore, R is M's nephew/niece (child of a sibling of M).Verification / Alternative check: Neither I nor II alone links R to M conclusively. Only together do they establish that R is the child of M's brother.
Why Other Options Are Wrong:
- I alone sufficient: No, links M↔P but not R.
- II alone sufficient: No, identifies R's mother but no link to M.
- Either alone sufficient: False for the same reason.
- Neither sufficient: False because together they are sufficient.
Common Pitfalls: Ignoring that “mother of R's sister” implies “mother of R”; assuming genders not given; misreading “brother of M” versus “brother-in-law of M”.
Final Answer: Both I and II are sufficient.