Data sufficiency – year of birth: In which year was Kalyan born? Statements: a. At present, Kalyan is 15 years younger than his mother. b. Kalyan's brother, who was born in 1991, is 25 years younger than his mother.

Introduction / Context:
This is a data sufficiency question focusing on ages and year of birth. You are asked to determine in which year Kalyan was born, based on two statements about his and his brother's ages relative to their mother. The aim is to decide whether each statement alone, or both combined, is sufficient to answer the question uniquely, without necessarily calculating the current calendar year explicitly.

Given Data / Assumptions:

Statement a: Kalyan is currently 15 years younger than his mother.
Statement b: Kalyan's brother was born in 1991 and is 25 years younger than his mother.
We assume all ages are expressed “at present” and that the current year is the same reference point for all.

Concept / Approach:
The key is to express the mother's age in terms of the current year using statement b, and then use statement a to get Kalyan's age and thus his year of birth. We must check whether we can get that year using only one statement or if both are necessary. Data sufficiency is about uniqueness of the answer, not about performing detailed arithmetic with actual current dates.

Step-by-Step Solution:
Let the present year be Y. From statement b: Kalyan's brother was born in 1991 and is 25 years younger than his mother. So, brother's present age = Y - 1991. The mother's present age M is 25 years more than the brother's age: M = (Y - 1991) + 25 = Y - 1966. On its own, statement b gives us the mother's age in terms of Y, but not Kalyan's year of birth directly, because we have no relation between Kalyan and his mother yet. From statement a: Kalyan is 15 years younger than his mother, so Kalyan's present age K is: K = M - 15. Substituting M from above: K = (Y - 1966) - 15 = Y - 1981. Kalyan's present age is Y - 1981, so his year of birth is 1981, independent of Y. However, note that we needed both statements: statement a gives a relationship between Kalyan and the mother, while statement b connects the mother to a fixed year (1991). Neither statement alone is enough.

Verification / Alternative check:
Check statement a alone: it only says Kalyan is 15 years younger than his mother; without any absolute year or fixed age, we cannot determine his birth year. Similarly, statement b alone lets us compute the mother's age relative to year 1991, but there is no mention of Kalyan. Only by combining both do we get a unique expression for Kalyan's birth year (1981), independent of the current year.

Why Other Options Are Wrong:
Options claiming that a alone or b alone is sufficient ignore the missing link in each case. Saying neither is sufficient is incorrect because together they clearly give a unique solution. The data are consistent and not contradictory, so the inconsistency option does not apply.

Common Pitfalls:
A common error is to assume that because statement b mentions a concrete year (1991), it must be sufficient on its own. Without a relation between Kalyan and his mother, this is not enough. Conversely, some may think that relative ages in statement a are enough, but without anchoring to a known year, the birth year cannot be fixed.

Final Answer:
Both statements a and b together are sufficient to determine Kalyan's year of birth. The correct option is Both statements a and b together are sufficient.