Pointing to a girl in a photograph, Amar says, "Her mother's brother is the only son of my mother's father." In this blood relation test, how is the girl's mother related to Amar?

Introduction / Context:
This family relation puzzle involves multiple levels of ancestry. Amar talks about a girl in a photograph and relates the girl's mother's brother to his own maternal grandfather. The challenge is to determine the link between the girl's mother and Amar. These types of problems check a candidate's ability to convert verbal descriptions into a clear family tree and then spot the correct relationship.

Given Data / Assumptions:
• Amar points to a girl in a photograph.• He states that the girl's mother's brother is the only son of Amar's mother's father.• Amar's mother's father is Amar's maternal grandfather.• The only son of Amar's maternal grandfather is Amar's maternal uncle.• The girl's mother's brother is the same person as that only son.• Normal family structure and terminology are assumed.

Concept / Approach:
We first identify the only son of Amar's maternal grandfather, who is Amar's maternal uncle. Then we note that this same person is the brother of the girl's mother. If a man is both Amar's maternal uncle and the brother of the girl's mother, then the girl's mother must be a sister of Amar's mother. A woman who is the sister of one's mother is a maternal aunt. Therefore, the girl's mother is Amar's aunt.

Step-by-Step Solution:
Step 1: Let G be Amar's maternal grandfather, that is, Amar's mother's father.Step 2: The only son of G is described in the statement. That son is Amar's maternal uncle.Step 3: Amar also says that this person is the girl's mother's brother.Step 4: If a man is the girl's mother's brother, then he and the girl's mother are siblings, both children of the same parents.Step 5: Since this brother is also the only son of Amar's maternal grandfather, the girl's mother must also be a child of Amar's maternal grandfather and therefore a sibling of Amar's mother.Step 6: A woman who is the sister of one's mother is one's maternal aunt, so the girl's mother is Amar's aunt.

Verification / Alternative Check:
Draw the tree: place Amar's maternal grandfather at the top. He has a daughter (Amar's mother) and one son (Amar's maternal uncle). The girl's mother is the sister of that son, so she is another daughter of the same grandfather, making her a sister of Amar's mother. This configuration precisely matches the description and confirms that the girl's mother is Amar's aunt.

Why Other Options Are Wrong:
Mother of Amar: That would require the girl's mother to be the same person as Amar's mother, which is not supported by the wording involving separate siblings.Sister of Amar: This would make the girl's mother a child of Amar's parents, which contradicts the involvement of Amar's maternal grandfather.Grandmother of Amar: A grandmother is one generation above Amar's mother, not a sibling of her.Cousin of Amar: A cousin would share grandparents with Amar but would not be placed one generation above him as the sibling of his mother.

Common Pitfalls:
Many candidates misread the phrase my mother's father and treat that person as Amar's father instead of his maternal grandfather. Another frequent mistake is to assume that the girl is Amar's sister, leading to confusion between mother and aunt. Keeping a clear separation between each generation and noting that the statement speaks of Amar's maternal grandfather's only son is essential.

Final Answer:
The girl's mother is the maternal aunt of Amar, that is, she is Amar's aunt.