In which calendar year was Sanjay born? Consider the following three statements: I. Sanjay is six years older than Gopal. II. The brother of Gopal was born in 1982. III. The brother of Sanjay is two years younger than the brother of Gopal, who in turn is eight years younger than Gopal. Which combination of these statements is sufficient to determine the exact year of birth of Sanjay?

Introduction / Context:
This data sufficiency question deals with ages and years of birth. The task is not to compute the numeric year directly, but to decide which combination of the three given statements fixes the year of birth of Sanjay without any ambiguity. This tests the ability to translate age gaps into years, link relatives through those gaps, and see whether we can reach a unique calendar year for Sanjay.

Given Data / Assumptions:

• Sanjay is six years older than Gopal according to statement I.
• The brother of Gopal was born in 1982 according to statement II.
• The brother of Sanjay is two years younger than the brother of Gopal, and that brother of Gopal is eight years younger than Gopal, as stated in III.
• Years of birth are measured on the same calendar, and all age differences are exact whole years.

Concept / Approach:
The general plan is to convert each statement into equations involving years of birth. Then we check which collection of statements is enough to remove every unknown. If any year remains free to vary, that combination of statements is not sufficient. For a data sufficiency question, we only need to know whether the year can be uniquely determined, not its explicit value, although computing it is a useful cross check.

Step-by-Step Solution:
Step 1: From statement I, let G be the year of birth of Gopal and S be the year of birth of Sanjay. Since Sanjay is six years older, S = G minus 6. Step 2: From statement II, let Bg be the year of birth of the brother of Gopal. We are told Bg = 1982. Step 3: From statement III, let Bs be the year of birth of the brother of Sanjay. Bs is two years younger than Bg, so Bs = Bg plus 2. Also Bg is eight years younger than Gopal, so G = Bg minus 8. Step 4: Combine II and III. If Bg = 1982, then G = 1982 minus 8 = 1974. However, without statement I we cannot link G to S, so the birth year of Sanjay is still undetermined with only II and III. Step 5: Now combine I with the earlier result. From I we have S = G minus 6, and from II and III we found G = 1974. Therefore S = 1974 minus 6 = 1968. All three statements together give a unique year of birth for Sanjay. Step 6: Check smaller combinations. I and II together give a relation between S and G, and a fixed year for the brother of Gopal, but they never connect that brother to G, so G is still unknown. I and III together connect G, S, and the two brothers only through differences, with no absolute year, so every person can be shifted by the same amount, leaving S undetermined. II and III together give the year of birth of Gopal but not the relation of Sanjay to Gopal, so again S is unknown.

Verification / Alternative check:
Another quick check is to count unknowns and independent equations. The unknown years are S, G, Bg, and Bs. With all three statements we effectively have four independent relations, one of which fixes Bg at 1982, so everything collapses to a unique solution. Any pair of statements either leaves G floating or leaves S disconnected from G, which means at least one degree of freedom remains. Hence only the full set of three statements is sufficient.

Why Other Options Are Wrong:
The option that states only I and II are sufficient is wrong because these two do not relate Gopal directly to his brother in terms of years, so G is not fixed. The option that claims only II and III are sufficient is incorrect because they give G but never relate Sanjay to Gopal. The option that suggests only I and III are sufficient fails because they provide only relative differences without any calendar year, so all people can be shifted together in time. Only the option that uses all three statements correctly recognises that the combination finally pins down Sanjay year of birth.

Common Pitfalls:
A frequent error is to treat the given year 1982 as if it immediately fixes every related year, even when the necessary age gaps have not been connected. Learners sometimes overlook that statement I never mentions any absolute year, and that statements II and III do not mention Sanjay directly. Another common mistake is to stop as soon as Gopal year is found, without checking whether the link between Gopal and Sanjay has actually been used. Careful bookkeeping of which person each equation involves avoids these mistakes.

Final Answer:
The correct choice is that all three statements I, II, and III together are required to answer the question, which corresponds to option D.