A man pointing to a lady says, "Her brother is the father of my only son's sister." How is that lady related to the man?

Introduction / Context:
In this puzzle, a man describes a lady using a chain involving his only son and that son's sister. The phrase my only son's sister is crucial because it effectively identifies his daughter. From there, we consider who the father of that daughter is and how this connects to the lady's brother, eventually revealing the relationship between the lady and the man.

Given Data / Assumptions:
- Speaker: a man (call him M). - He has an only son. - My only son's sister refers to M's daughter (if any). - The father of my only son's sister is the same man M, since he is the father of both children. - The lady's brother is said to be the father of my only son's sister. - Therefore, the lady's brother is M himself.

Concept / Approach:
Once you realise that the father of my only son's sister must be the speaker, the statement her brother is the father of my only son's sister means that the lady's brother is the speaker. If a woman's brother is a man, then that woman is the man's sister. So the connection collapses to the simplest possible: the lady is the speaker's sister.

Step-by-Step Solution:
Step 1: Interpret my only son's sister. M's only son has a sister, who must be M's daughter. Step 2: The father of my only son's sister is the father of M's daughter. Since M is the father of both his son and his daughter, this father is M himself. Step 3: The statement says: Her brother is the father of my only son's sister. We have just identified that father as M. Step 4: Therefore, her brother is M. In other words, the lady's brother is M. Step 5: If the lady's brother is M, then from M's point of view, that lady is his sister.

Verification / Alternative check:
Think of a simple family: M has two children, a son and a daughter. The father of my only son's sister is clearly M. Now introduce a lady L such that her brother is M. L then belongs to the same generation as M and shares at least one parent with him. L is therefore M's sister. The verbal description perfectly matches this simple interpretation, and there is no need to invent more complex structures like in-laws.

Why Other Options Are Wrong:
- Sister of father-in-law: This would place the lady as an aunt of M's wife, not directly as M's sibling. - Daughter-in-law: A daughter-in-law is married to M's son, not described through being a sibling of M. - Daughter: For the lady to be M's daughter, M would be described as her father, not her brother. - Aunt: An aunt is typically a sibling of a parent. Here, the lady is explicitly the sibling of the speaker himself.

Common Pitfalls:
Students often get confused by the phrasing my only son's sister and might think of that person as a niece or in-law. Remember that siblings usually share parents, so a son's sister is a daughter of the same parent, not an external relation. Another pitfall is forgetting that the father of my child's sibling is simply me in a normal family setup, causing unnecessary complexity.

Final Answer:
The lady is the man's sister.