In this blood relation question, a woman says while showing a man, "His brother's father is the only son of my grandfather." How is the woman related to the man?

Introduction / Context:
This is a standard blood relation question involving a woman, a man and the woman's grandfather. The sentence "His brother's father is the only son of my grandfather" encodes the fact that the man's father and the woman's father are the same person. Once we decode that, we can easily determine that the woman and the man are siblings.

Given Data / Assumptions:
• A woman is referring to a man.• She says, "His brother's father is the only son of my grandfather."• The only son of the woman's grandfather is her father.• The man and his brother share the same father.• Family structure is standard with no hidden complexities.

Concept / Approach:
The phrase my grandfather points to the woman's grandfather. The only son of that grandfather must be her father, because he is the only male child in that generation. The expression his brother's father refers to the father of the man and his brother. Since this person is also the only son of the woman's grandfather, the woman's father and the man's father are the same person. Thus the woman and the man share a common father and belong to the same generation, making them siblings. As the woman is female, she is the man's sister.

Step-by-Step Solution:
Step 1: Let G be the grandfather of the woman.Step 2: The only son of G is the woman's father. Call him F.Step 3: The woman says that the man's brother's father is this same only son of her grandfather.Step 4: The father of the man and the father of his brother is the same person. Therefore F is the man's father as well.Step 5: If F is both the woman's father and the man's father, the woman and the man are children of the same father.Step 6: Since the woman is female, she is the sister of the man.

Verification / Alternative Check:
You can simply imagine a family where a grandfather has exactly one son, F. F has two children: a daughter (the woman in the question) and a son (the man in the question). The man has a brother as well. When the woman refers to the father of the man and his brother, she is clearly referring to her own father. This confirms that they are siblings and that her role is that of a sister.

Why Other Options Are Wrong:
Aunt of the man: An aunt would be the sister of the man's father or mother, not a daughter of the same father.Sister in law of the man: A sister in law is a spouse of a brother or the sister of a spouse, not someone sharing the same father directly.Daughter in law of the man: This would place her in a younger generation, married to the man's son.Mother of the man: The mother would be married to the only son of the grandfather, not another child of that same son.

Common Pitfalls:
Candidates sometimes misread only son of my grandfather and mistakenly think it might refer to the grandfather's grandson. It is important to remember that son refers to the child of the grandfather, not to a grandchild. Once you lock in that person as the woman's father, the rest follows easily.

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