Looking at a man, a woman said, ""His mother is the only daughter of my mother."" How is the man related to the woman?

Correct — C.
Rule: resolve the phrase that points back at the speaker first.

The only daughter of the woman's mother is the woman herself.
So the man's mother = the woman.
The man is her son → option (c).

Why the others are wrong

• (a)
  Brother — Brother would need the man's mother to be the woman's mother. The statement makes his mother her mother's daughter, which is the woman herself.
• (b)
  Nephew — Nephew would need his mother to be the woman's sister. 'Only daughter' rules out a sister: the woman is that daughter.
• (d)
  Cousin — Cousin would need his mother to be the woman's aunt, a daughter of her grandmother. The statement stays with her own mother's daughter.

A woman is always a daughter of her own mother. So when a woman speaks of the only daughter of my mother, she is describing herself.

Replace the phrase with "me": his mother is me. The man is her son. The word only is what shuts out a sister.

Key facts

• Said by a woman, 'the only daughter of my mother' is the speaker herself.
• Said by a man, 'the only daughter of my mother' is his sister.
• 'The only daughter of my mother's father' is the speaker's mother.

Common traps

• Treating 'the only daughter of my mother' as a sister, which holds only when a man speaks
• Choosing Brother by reading 'my mother' as the man's mother

No directly related past PYQ was found.