Rita tells Mani, "The girl I met yesterday at the beach was the youngest daughter of the brother in law of my friend's mother." In this blood relation test, how is that girl related to Rita's friend?

Introduction / Context:
This question describes a fairly long chain of relations involving Rita, her friend, the friend's mother and the mother's brother in law. The goal is to determine how the girl that Rita met at the beach is related to Rita's friend. Such questions check whether the candidate can patiently unravel terms like brother in law of my friend's mother and translate them into standard relationships like uncle and cousin.

Given Data / Assumptions:
• Rita has a friend; call the friend F.• F's mother has a brother in law.• The girl Rita met is the youngest daughter of this brother in law.• Brother in law of F's mother can be either her husband's brother or her sister's husband.• In both interpretations, the brother in law is an uncle type figure for F.• The girl is that uncle's daughter.

Concept / Approach:
We first understand who the brother in law of F's mother can be and then work out how his children are related to F. If the brother in law is the husband's brother, he is the paternal uncle of F. If he is the husband of the mother's sister, he is the maternal uncle of F by marriage. In both cases his daughter is the cousin of F. This symmetry shows that regardless of which side the brother in law comes from, the girl remains F's cousin.

Step-by-Step Solution:
Step 1: Let F be Rita's friend and M be F's mother.Step 2: The brother in law of M can be interpreted in two standard ways.Step 3: Case one: He is the brother of M's husband. In this case he is F's paternal uncle.Step 4: Case two: He is the husband of M's sister. In this case he is F's maternal uncle by marriage.Step 5: In both cases the man is an uncle of F, and his daughter is F's cousin.Step 6: The girl Rita met is the youngest daughter of this uncle, so she is a cousin of F.

Verification / Alternative Check:
Draw two small trees. In the first, place F's parents and F. Add the father's brother and that brother's daughter. The daughter is clearly F's cousin. In the second, place M's sister and her husband (the brother in law) and again add their daughter. She is still F's cousin. Since in both legitimate interpretations the result is the same, we can confidently say that the girl is F's cousin.

Why Other Options Are Wrong:
Daughter of Rita's friend: The girl would then be one generation below F and would not be described via the mother's brother in law.Niece of Rita's friend: Niece would require the girl to be the daughter of F's sibling, which is not indicated.Just a friend with no family relation: The chain of relations involving mother and brother in law clearly shows there is a family link.Sister of Rita's friend: A sister would normally be a daughter of F's parents, not of the mother's brother in law.

Common Pitfalls:
The main trap is getting stuck on the phrase brother in law and assuming it always refers to the husband's brother. Another common mistake is to stop halfway through the chain and not follow it all the way to the girl, leading to confusion between niece, cousin and sister. Carefully enumerating both standard meanings of brother in law and seeing that both lead to the cousin relationship is the safe way to handle such questions.

Final Answer:
The girl is the cousin of Rita's friend.