How is Rakesh related to Keshav? Consider the following statements: I. Tapan has a wife named Nisha who is the paternal aunt of Keshav. II. Rakesh is the brother of a friend of Nisha.

Introduction / Context:
This data sufficiency question involves family relationships and social connections. The task is to identify the relationship of Rakesh to Keshav using information about Tapan, Nisha, and a friend of Nisha. The key is to understand that social friendships do not necessarily imply blood relationships, and to check whether the statements can force any specific family link between Rakesh and Keshav.

Given Data / Assumptions:

• Statement I: Tapan has a wife named Nisha, and Nisha is the paternal aunt of Keshav. This means Nisha is a sister of Keshav father.
• Statement II: Rakesh is the brother of a friend of Nisha.
• Friends of Nisha can be unrelated people from outside the family, unless stated otherwise.
• No extra information is given about Rakesh parents or siblings beyond what is in statement II.

Concept / Approach:
We need to determine whether the statements can fix a unique family relationship between Rakesh and Keshav, such as cousin, uncle, or no blood relation. In data sufficiency, if we can construct multiple possible family trees that satisfy the statements but give different answers about Rakesh relationship to Keshav, then the data are not sufficient to answer the question.

Step-by-Step Solution:
Step 1: Interpret statement I. Since Nisha is the paternal aunt of Keshav, she is a sister of Keshav father. Tapan is the husband of Nisha, so Tapan is the paternal uncle of Keshav by marriage. Step 2: Notice that statement I only describes how Tapan and Nisha are related to Keshav. It does not mention Rakesh at all. Therefore, statement I alone clearly cannot determine Rakesh relationship to Keshav. Step 3: Interpret statement II. Rakesh is the brother of a friend of Nisha. This means there exists some person F who is a friend of Nisha, and Rakesh and F are siblings. Nothing in the statement says that F is related to Nisha by blood or marriage. F could be a colleague, a neighbour, or any unrelated person. Step 4: With statement II alone, we have no link at all to Keshav, since Keshav is not mentioned. Thus statement II alone is also not sufficient. Step 5: Combine statements I and II. The first statement anchors Nisha within Keshav family as a paternal aunt. The second statement introduces Rakesh as the sibling of Nisha friend. However, it still does not say that this friend is a relative. Both F and Rakesh can be completely unrelated to the family of Keshav and may simply have a social connection to Nisha. Step 6: Construct possible scenarios. In one scenario, Nisha friend F is a colleague from work who has no family connection to Keshav. Then Rakesh, as F brother, is also not related to Keshav by blood or marriage. In another scenario, F could be a cousin of Nisha, making some distant connection possible, but even then the exact relation between Rakesh and Keshav varies with the family tree and is not forced by the statements. Step 7: Since more than one consistent arrangement is possible and none is required by the data, no unique relationship can be identified between Rakesh and Keshav. Therefore, even the two statements together are not sufficient.

Verification / Alternative check:
A fast way to verify is to ask whether any blood or marital link is explicitly defined between Rakesh and the core family of Keshav. Statement I defines such a link for Tapan and Nisha, but statement II defines Rakesh only through friendship, not kinship. Friendship alone cannot be used to infer relations like cousin or uncle. Because the chain from Keshav to Rakesh always passes through an unrestricted friendship, there is no forced family relation.

Why Other Options Are Wrong:
Options A and B wrongly claim sufficiency for a single statement, which is impossible because each statement mentions only one side of the connection. Option C claims that either statement alone is sufficient, which is plainly incorrect. Option D claims that both statements together are necessary and sufficient, yet even when they are combined, the information does not constrain the friend of Nisha in a way that would fix Rakesh relation. Only option E correctly states that even both statements together do not provide enough data.

Common Pitfalls:
Learners often assume that any person mentioned near the family must be some kind of relative. This is not valid unless specified. Another common confusion is between social labels like friend and family relations such as cousin or uncle. In data sufficiency questions about relations, it is important not to invent missing family links, and to remember that friends can be completely external to the family tree.

Final Answer:
The data even in both statements together are not sufficient to answer the question, so the correct option is E.