Question

Instructions: There are only four members of a family, namely A, B, C and D, and there is only one couple among them. When asked about their relationships, their replies were as follows:
A: “B is my son. D is my mother.”
B: “C is my wife. D is my father.”
C: “D is my mother-in-law. A is my daughter.”
D: “A is my grand-daughter. B is my daughter-in-law.”

Which of the following statements must be true?

• A. A’s grandmother alternates between the truth and lies
• B. C’s wife always speaks the truth
• C. A’s grandfather always speaks the truth
• D. B’s daughter always tells lies

Hint:

Two of the four options describe people who do not even exist in this family tree (a grandmother, a wife of C); check the real people’s statements for the other two.

Answer 1

The Correct Option is D

This question is really asking us to translate each option into the family tree we already built and see which one matches a person's actual truth-telling pattern.

1. A's grandmother alternates between truth and lies: A's grandparent in this tree is D, who is male, so there is no “grandmother” for A here at all; the option refers to someone who does not exist in this setup.
2. C's wife always speaks the truth: C is female and is herself B's wife; C cannot have a wife of her own, so this option again describes a relationship that is not part of the family tree.
3. A's grandfather always speaks the truth: A's grandfather is D, and D's two statements came out as one true (“A is my grand-daughter”) and one false (“B is my daughter-in-law”), so D does not always speak the truth. This option fails the check.
4. B's daughter always tells lies: B's daughter is A, since B and C are her parents. Both of A's statements (“B is my son”, “D is my mother”) were shown to be false, so A always lies. This matches exactly.

Only the last option correctly matches a real person's behaviour in the tree.

So the correct answer is option D.