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?
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: “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?
Show 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.
Updated On: Jul 15, 2026
- A’s grandmother alternates between the truth and lies
- C’s wife always speaks the truth
- A’s grandfather always speaks the truth
- B’s daughter always tells lies
Show Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Step 1: Recall the family tree.
D is A's grandparent (grandfather, since D is B's father), B and C are the married couple and A's parents, and A is the grandchild. Checking each person's two statements against this tree: A's both statements are false, B's both statements are true, C has one true and one false statement, and D has one true and one false statement.
Step 2: Check option A.
D is A's grandparent, and D is established as male (grandfather), so D cannot be A's “grandmother” at all; this option does not even describe a real person in the tree, so it cannot be the statement that must be true.
Step 3: Check option B.
C is female and already established as B's wife; C does not have a “wife” of her own, so this statement describes a relationship that does not exist in this family, and cannot be true.
Step 4: Check option C.
D is A's grandfather, and D's two statements were found to be one true and one false, not both true, so D does not always speak the truth; this option is false.
Step 5: Check option D.
B's daughter is A, since B and C are A's parents. A's two statements were both found to be false, meaning A always lies. This matches exactly.
Step 6: Final Answer.
The statement that must be true is option D, B's daughter always tells lies.
D is A's grandparent (grandfather, since D is B's father), B and C are the married couple and A's parents, and A is the grandchild. Checking each person's two statements against this tree: A's both statements are false, B's both statements are true, C has one true and one false statement, and D has one true and one false statement.
Step 2: Check option A.
D is A's grandparent, and D is established as male (grandfather), so D cannot be A's “grandmother” at all; this option does not even describe a real person in the tree, so it cannot be the statement that must be true.
Step 3: Check option B.
C is female and already established as B's wife; C does not have a “wife” of her own, so this statement describes a relationship that does not exist in this family, and cannot be true.
Step 4: Check option C.
D is A's grandfather, and D's two statements were found to be one true and one false, not both true, so D does not always speak the truth; this option is false.
Step 5: Check option D.
B's daughter is A, since B and C are A's parents. A's two statements were both found to be false, meaning A always lies. This matches exactly.
Step 6: Final Answer.
The statement that must be true is option D, B's daughter always tells lies.
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