Pointing to a man, a woman said, “His mother is the only daughter of my father.” How is the man related to the woman?

Correct — A. Rule: "the only daughter of my father" is the speaker herself.

The speaker is a woman, so she is a daughter of her father. If he has one daughter, it is her.

So "his mother" is the woman speaking, and the man is her son — option (a).

Why the others are wrong

• (b)
  Nephew — A nephew would need his mother to be the woman's sister. "Only daughter" leaves the woman no sister, so his mother can be no one but her.
• (c)
  Cousin — A cousin would need his mother to be the woman's aunt, one generation above her. The statement makes his mother a daughter of the woman's father, in the woman's own generation.
• (d)
  Grandson — Grandson would need his mother to be the woman's daughter. The statement makes his mother the woman herself, which puts the man one generation below her, not two.

A relation phrase can loop back to the speaker. "My father's only daughter", said by a woman, names the woman herself.

Substitute that, and the sentence becomes "His mother is me", which makes the man her son.

The word only carries the item. Without it, "a daughter of my father" could also be the woman's sister, and the man could be her nephew.

Key facts

• A woman's father's only daughter is the woman herself.
• Without "only", the phrase could also name her sister, which would make the man a nephew.
• The man is one generation below the woman.

Common traps

• Reading "the only daughter of my father" as the woman's sister and choosing Nephew.
• Ignoring that the speaker is a woman, which is what makes her the daughter.

No directly related past PYQ was found.