In each of the the following questions, a main question is followed by information given in three statements I, II and III. You have to study the question along with the statements and decide the information given in which statement(s) is necessary and sufficient to answer the question. In a family of seven members, how is P related to Q?

Introduction / Context:
This question is a data sufficiency problem set in the context of a blood relation puzzle. You are not asked to fully draw the family tree in the exam, but to decide which combination of statements I, II and III gives enough information to determine how P is related to Q in a family of seven members. The key skill tested is the ability to combine multiple clues, respect the fixed family size and check whether any subset of statements is sufficient on its own.

Given Data / Assumptions:
- There is a family of exactly seven members. - Statement I: M and N are children of O, who is the wife of P. - Statement II: A, the cousin of B, is the niece of M. - Statement III: Q is the only brother-in-law of B. - Standard meanings are used for cousin, niece, brother-in-law, wife and children. - All seven members are among P, O, M, N, A, B and Q.

Concept / Approach:
The method is to try to construct a unique, consistent family tree using all the statements together and then see whether any proper subset of statements would still allow you to fix the relationship between P and Q. If a subset leaves P–Q ambiguous, those statements alone are not sufficient. Only a set that fixes P–Q uniquely counts as necessary and sufficient information.

Step-by-Step Solution:
Step 1: From Statement I, O is the wife of P, and M and N are their children. So P and O are one couple, and M and N are siblings in the next generation. Step 2: From Statement II, A is the cousin of B and is the niece of M. Being M's niece means A is the daughter of M's sibling. Within this seven-member family, the only sibling of M is N. Hence A is the daughter of N. Step 3: If A is N's daughter and is a cousin of B, then B must be the child of M. Thus B is the child of M, while A is the child of N. Our three-generation structure becomes: P and O at the top, their children M and N in the middle, and grandchildren A and B at the bottom. Step 4: So far we have six people: P, O, M, N, A and B. The seventh member is Q. From Statement III, Q is the only brother-in-law of B. In this family, that can be satisfied if B is married to A and Q is A's brother, both being children of N. Then Q becomes the brother of B's spouse and therefore B's only brother-in-law. Step 5: In this unique arrangement, Q is a child of N, and N is a child of P and O. Therefore Q is a grandchild of P, so P is Q's grandfather. Thus P's relation to Q is fixed when all three statements are used together. Step 6: Check subsets: Statement I alone does not mention Q at all. Statements I and II together still do not connect Q to the family. Statements I and III or II and III cannot connect P and Q uniquely. Hence no proper subset is sufficient.

Verification / Alternative check:
You can attempt to build alternative trees by dropping one statement at a time. Without Statement II, there are multiple ways to place A and B, so Q's generation and parents remain uncertain. Without Statement III, Q's position is completely unknown. Without Statement I, P, O, M and N are not anchored as a single nuclear family. Therefore, only when Statements I, II and III are all used together is P–Q determined uniquely.

Why Other Options Are Wrong:
- Only I: gives no information about Q, so P's relation to Q cannot be known. - Only I and II: define links among P, O, M, N, A and B, but Q remains disconnected. - Only II and III: P is not even mentioned, so his relation to Q is impossible to fix. - None of these: incorrect because all three statements together are both necessary and sufficient.

Common Pitfalls:
Students often forget to use the constraint of exactly seven family members, which forces A, B and Q to be placed among the descendants of M and N. Another common mistake is to assume that cousin marriage is impossible in such puzzles; however, allowing B and A to marry is what makes Q become B's only brother-in-law. Finally, some test-takers stop after concluding that P is an ancestor of Q without checking whether that relation is uniquely grandfather rather than some other older relative.

Final Answer:
All three statements together are needed, so the correct choice is All of them.