Question: How is M related to N? Statements: P, who has only two kids, M and…

2023

Question: How is M related to N?

Statements:

P, who has only two kids, M and N, is the mother-in-law of Q, who is sister-in-law of N.

R, the sister-in-law of M, is the daughter-in-law of S, who has only two kids, M and N.

  1. A.

    I alone is sufficient while II alone is not sufficient

  2. B.

    II alone is sufficient while I alone is not sufficient

  3. C.

    Either I or II is sufficient

  4. D.

    Neither I nor II is sufficient

Show answer & explanation

Correct answer: A

Concept: In marriage-and-kinship data-sufficiency puzzles, titles such as mother-in-law, daughter-in-law, and sister-in-law are used only for a woman; whoever holds such a title married one of the two named children, and a person can never be their own spouse's in-law. Applying this exclusion separately to each statement shows whether it pins down a single, unambiguous sibling relationship or leaves more than one relationship possible.

Application

Statement I:

  1. P has exactly two children, M and N, and P is Q's mother-in-law, so Q is married to one of P's two children.

  2. Q is also N's sister-in-law; since a spouse can never be their own partner's sister-in-law, Q cannot be married to N, so Q is married to M.

  3. Being N's sister-in-law while married to M means Q is the wife of N's brother -- so M is fixed, unambiguously, as N's brother.

Statement II:

  1. S has exactly two children, M and N, and R is S's daughter-in-law, so R is married to one of S's two children.

  2. R is also M's sister-in-law; by the same exclusion, R cannot be married to M, so R is married to N.

  3. This fixes N as male (R's husband) but says nothing about M's own gender -- M could equally be N's brother or N's sister, so the relationship stays undetermined.

Cross-check: Statement I collapses to one possible relationship with no leftover ambiguity, while Statement II still admits two possible relationships (brother or sister) -- this asymmetry is exactly what the correct option must capture.

Answer: I alone is sufficient while II alone is not sufficient.

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