Pointing to a man in a photograph, a woman says, "His brother's father is the only son of my grandfather." In this blood relation test, how is the woman related to the man in the photograph?

Introduction / Context:
This question is another version of a standard blood relation puzzle where a woman describes a man in a photograph. The phrase "his brother's father is the only son of my grandfather" again connects the man's father to the woman's father. Once we see that they share the same father, it becomes clear that they are siblings, with the woman being the man's sister.

Given Data / Assumptions:
• A woman is pointing to a man in a photograph.• 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.• Normal family relationships and generations are assumed.

Concept / Approach:
We interpret my grandfather's only son as the woman's father. The man's brother's father is simply the man's father. When she states that this person is the only son of her grandfather, she is identifying the man's father as her father. As a result, both she and the man share the same father. Sharing the same father and generation, with the woman being female, makes her the man's sister.

Step-by-Step Solution:
Step 1: Let G be the woman's grandfather.Step 2: The only son of G is the woman's father, 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 of his brother must therefore be F.Step 5: If F is both the woman's father and the man's father, they are children of the same father.Step 6: Since the woman is female, her relationship to the man is that of sister.

Verification / Alternative Check:
Imagine a grandfather with exactly one son. That son has at least two children: a daughter (the woman) and a son (the man in the photograph). The man also has a brother. The phrase his brother's father points to the same father who is the only son of the woman's grandfather. This structure confirms that the woman is the sister of the man in the photograph.

Why Other Options Are Wrong:
Mother of the man: The mother would be married to the grandfather's only son, not be another child of that son.Aunt of the man: An aunt would be the sister of the father or mother, which would put her in the same generation as the father, not sharing the father as a child.Daughter of the man: This would place the woman in a younger generation, which contradicts the description tied to the grandfather.Cousin of the man: Cousins share grandparents but not necessarily the same father, so this does not follow directly from the given information.

Common Pitfalls:
As with similar problems, candidates may confuse the grandfather's only son with a grandson or misinterpret his brother's father as a separate person. Carefully tracing each label back to the same individual and noting that the woman and the man share that father avoids these mistakes.

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