Data sufficiency – relationship: How is Vinitha related to Ragini? Statements: a. Vinitha's husband is the only son of Ragini's mother. b. Vinitha's brother and Ragini's husband are cousins.

Introduction / Context:
This is a relationship-based data sufficiency question. You are asked to determine how Vinitha is related to Ragini using two statements that describe relationships through husbands, brothers and cousins. The key challenge is that names do not directly encode gender or family structure in formal reasoning; you must see whether the information forces a unique relationship or leaves multiple possibilities open.

Given Data / Assumptions:

Question: How is Vinitha related to Ragini?
Statement a: Vinitha's husband is the only son of Ragini's mother.
Statement b: Vinitha's brother and Ragini's husband are cousins.
Standard assumption: “only son of Ragini's mother” means that Ragini's mother has exactly one male child (but may have daughters as well).

Concept / Approach:
Data sufficiency does not ask you to find all possible relationships, but only to check whether the available data determine the relationship uniquely. If more than one family arrangement is possible under the given statements, then those statements are not sufficient. We must therefore test whether each statement alone, or the two together, fix one clear relation such as “sister-in-law”, “wife”, “cousin”, etc.

Step-by-Step Solution:
Analyse Statement a: “Vinitha's husband is the only son of Ragini's mother.” Ragini's mother has exactly one son. That person is Vinitha's husband. Ragini could be a daughter of this mother (which is typical given the name, but the question does not explicitly state her gender) or, in a formal logic setting, even the son himself. If Ragini is a daughter of this mother, then the only son is Ragini's brother and Vinitha becomes Ragini's sister-in-law. If Ragini were the son, then Vinitha would be Ragini's wife. Since the problem statement does not explicitly fix Ragini's gender in logical terms, more than one relationship is compatible with statement a alone. Hence a alone is not sufficient. Analyse Statement b: “Vinitha's brother and Ragini's husband are cousins.” This says that Ragini's husband belongs to the extended family of Vinitha (through cousins), but it does not specify how Vinitha herself is related to Ragini. Vinitha might be a cousin-in-law, sister-in-law, or have some other indirect relationship depending on who Ragini is married to in Vinitha's family tree. Thus, statement b alone also does not uniquely determine the relationship. Even when combining statements a and b, the basic ambiguity from statement a about Ragini's role (daughter versus son, and the exact positioning in the family tree) remains. There are still multiple possible relationship labels for Vinitha with respect to Ragini.

Verification / Alternative check:
You can construct at least two different family diagrams consistent with both statements but with different labels for Vinitha's relationship to Ragini. Because multiple answers are possible, the data do not suffice. In data sufficiency problems, if you can create more than one logically consistent scenario with different answers, then the information is not sufficient.

Why Other Options Are Wrong:
Any option that claims sufficiency for statement a or b (alone or together) incorrectly assumes a fixed interpretation of gender or family position that is not explicitly given. Real exam logic cannot rely on the gender implied by names alone. The “either a or b” option is for questions where each statement alone suffices, which is clearly not the case here.

Common Pitfalls:
Many test-takers automatically treat Ragini as a daughter and conclude “sister-in-law” from statement a, forgetting that logical reasoning questions do not rely on cultural assumptions about names. Another pitfall is ignoring indirect relationships: knowing that a cousin is involved does not automatically make someone a cousin; there may be an in-law connection instead.

Final Answer:
Neither statement a nor statement b, alone or together, is sufficient to determine exactly how Vinitha is related to Ragini. The correct choice is Neither statement a nor statement b is sufficient.