A man points to a lady and says, "Her brother is the father of the sister of my only son." In this blood relation question, how is that lady related to the man?

Introduction / Context:
This verbal reasoning problem describes a lady, her brother and how he is related to the sister of the man's only son. The objective is to find the relation between the lady and the man. These questions require careful unpacking of expressions such as father of the sister of my only son and identifying who that father is in the family tree of the man.

Given Data / Assumptions:
• The speaker is a man who has exactly one son.• The lady has a brother.• The lady's brother is the father of the sister of the man's only son.• There is at least one daughter in the man's children because his son has a sister.• No other hidden relationships are assumed.

Concept / Approach:
The sister of the man's only son must be another child of the man. Since the father of this sister is the lady's brother, it means the lady's brother and the man are the same person. If the man himself is the father of his own son's sister, and that person is described as the brother of the lady, then the lady must be the sister of the man. In other words, the man is the brother of the lady, and the lady is the man's sister.

Step-by-Step Solution:
Step 1: Consider the man's only son, call him S.Step 2: The sister of S is another child of the man, call her D.Step 3: The father of D is the man himself, since D is his daughter.Step 4: The statement says that the lady's brother is the father of the sister of the man's only son.Step 5: Therefore, the lady's brother is the father of D.Step 6: Since the father of D is the man, it follows that the lady's brother is the man.Step 7: If the man is the brother of the lady, then the lady is the sister of the man.

Verification / Alternative check:
Imagine a family where a man has two children, a son and a daughter. Now imagine he has a sister. If he says about his sister, her brother is the father of my only son's sister, he is effectively referring to himself as her brother and father of the daughter. This matches the given sentence exactly. The only way this works is if the lady is his sister. None of the other relations, such as daughter in law or niece, can be made to fit the chain described.

Why Other Options Are Wrong:
Daughter in law of the man: A daughter in law would be married to his son, not be his sibling.Niece of the man: A niece is a child of a sibling, not a sibling of the person himself.Daughter of the man: This would place the lady in the same generation as his children, not as his sibling.Cousin of the man: A cousin shares grandparents, not a direct parent as in the case of siblings.

Common Pitfalls:
Candidates might mistakenly think the father of the sister of my only son could be a different person, but in a standard family the father of both son and daughter is the man himself. Once that is recognised, it is straightforward to equate the lady's brother with the man and thus identify the lady as his sister.

Final Answer:
The lady is the sister of the man.