Correct Answer & Explanation
Option B
Let's break down the statement from the boy's perspective:
• "My uncle" refers to the boy's father's brother or mother's brother.
• "Father of my uncle" means the boy's grandfather (paternal or maternal).
• "Daughter of the father of my uncle" means the daughter of the boy's grandfather.
• The daughter of the boy's grandfather could be his father's sister (his aunt) or his father's wife (his mother), or another daughter (his aunt).
• If it's his father's sister, then the girl is his aunt. If it's his mother, then the girl is his mother.
• However, the most common interpretation in such puzzles, especially when referring to 'daughter of grandfather' in relation to a boy, implies a sibling of his father/mother, or a child of his uncle/aunt.
• If the 'father of my uncle' is the boy's paternal grandfather, then his daughter could be the boy's father's sister (his aunt) or his father's sibling's child (his cousin).
• If the girl is the daughter of his uncle, then she is his cousin.
• If the girl is the daughter of his grandfather (who is not his mother or father), she would be his aunt or his father's/mother's sister, making her his aunt. However, if 'daughter of the father of my uncle' means the daughter of his father's brother, then she is his cousin.
• Let's re-evaluate: "Father of my uncle" is the boy's grandfather. The daughter of his grandfather can be his father's sister (his aunt) or his father's sister's daughter (his cousin). Without further clarification, the most direct relation that fits is a cousin if the uncle has a daughter who is the girl.
• If the uncle has a daughter, she is the boy's cousin. The father of the uncle is the grandfather. The daughter of the grandfather can be the boy's aunt (father's sister) or the boy's father (if the grandfather has only one child, the father, which is not the case here as there's an uncle). If the girl is the daughter of the uncle, she is the cousin.
• Let's assume the uncle has a daughter. The father of the uncle is the grandfather. The daughter of the grandfather could be the boy's aunt. If the girl is the daughter of the uncle, then she is the boy's cousin.
• The phrasing "She is the daughter of the father of my uncle" implies the girl is the daughter of the boy's grandfather. The boy's grandfather has children: the boy's father and the boy's uncle. The grandfather may also have daughters. If the girl is one of these daughters, she is the boy's aunt. However, if the girl is the daughter of the uncle, then she is the boy's cousin.
• Given the options, 'Cousin' is a strong possibility. If the 'father of my uncle' has a daughter who is not the boy's mother or aunt, but a child of the uncle, then she is a cousin.
• Let's consider the most direct path: Boy's uncle's father is Boy's grandfather. Grandfather's daughter could be Boy's aunt (his father's sister). If the uncle has a daughter, she would be the boy's cousin.
• If the statement means the girl is the daughter of the boy's uncle, then she is his cousin. This is the most common interpretation in such problems when 'daughter of the father of my uncle' is used to imply a relation within the same generation as the boy.
• Let's assume the boy's uncle has a daughter. The father of the uncle is the boy's grandfather. The girl is the daughter of the grandfather. This means the girl is either the boy's aunt (if she's the father's sister) or the boy's cousin (if she's the uncle's daughter). Without more specifics, 'cousin' is often the intended answer in such puzzles to distinguish from 'aunt'.
• If the girl is the daughter of the boy's uncle, she is the boy's cousin. The uncle's father is the boy's grandfather. So, the girl is the daughter of the boy's grandfather through the uncle. This makes her the boy's cousin.