Rohit, Kajal, Tanmay and Suman are four friends. Who is the oldest among them? Statement I: The total age of Kajal and Tanmay together is more than the age of Suman. Statement II: The total age of Rohit and Kajal together is less than the age of Suman.

Introduction / Context:
This is a typical data sufficiency question involving comparison of ages. Four friends Rohit, Kajal, Tanmay and Suman are given, and we are asked to identify who is the oldest among them. Instead of direct ages, we are given two total age comparisons. The goal is not to compute exact ages, but to judge whether the information given is enough to deduce uniquely which person is the oldest.

Given Data / Assumptions:

• There are four friends: Rohit, Kajal, Tanmay and Suman.
• Statement I: Age of Kajal plus age of Tanmay is greater than age of Suman.
• Statement II: Age of Rohit plus age of Kajal is less than age of Suman.
• All ages are positive real numbers.
• We need to decide whether the oldest person can be uniquely identified.

Concept / Approach:
Data sufficiency problems require us to test each statement separately and then in combination:

• Check statement I alone for sufficiency.
• Check statement II alone.
• Check both together.

If more than one age configuration satisfies both statements and leads to different oldest persons, then even the combined data are not sufficient. We are interested in uniqueness, not in just one possible scenario.

Step-by-Step Solution:
Step 1: Let the ages be R, K, T and S for Rohit, Kajal, Tanmay and Suman respectively. Step 2: From statement I, K + T greater than S. Step 3: This only tells us that the combined age of Kajal and Tanmay is more than Suman. It does not tell us whether Suman is older or younger than either Kajal or Tanmay individually, and it says nothing about Rohit. So statement I alone is not sufficient. Step 4: From statement II, R + K less than S. Step 5: Since R and K are positive, this implies that S is older than each of R and K individually, because for any positive numbers a and b, if a plus b is less than c, then each of a and b is less than c. Thus R less than S and K less than S. Step 6: Statement II alone gives that Suman is older than both Rohit and Kajal, but it gives no information about Tanmay relative to Suman, so statement II alone is not sufficient. Step 7: Now combine both statements. We have K + T greater than S and R + K less than S. However these are aggregate comparisons. They do not prevent Tanmay from being older than Suman, nor do they force Suman to be older than Tanmay. Step 8: Construct one scenario: let S be 30 years, K be 10 years, T be 25 years and R be 15 years. Then K + T is 35 greater than 30, and R + K is 25 less than 30. Here Tanmay, with 25, is younger than Suman, so Suman is the oldest. Step 9: Construct another scenario: let S be 28 years, K be 5 years, T be 26 years and R be 20 years. Then K + T is 31 greater than 28, and R + K is 25 less than 28. Now Tanmay, with 26, is the oldest. Step 10: Since both scenarios satisfy both statements and produce different oldest persons, the combined data are not sufficient.

Verification / Alternative check:
The reasoning can be verified algebraically. From K + T greater than S, there is no restriction on T relative to S as long as K is small enough. Similarly, from R + K less than S, S can be chosen just slightly larger than R + K, again allowing T to take a wide range of values. Because T can be either less than S or greater than S while still satisfying both inequalities, the identity of the oldest person remains ambiguous.

Why Other Options Are Wrong:
Option a is wrong because statement I alone does not mention Rohit at all and does not compare individual ages. Option b is wrong because statement II alone compares Suman with Rohit and Kajal, but says nothing about Tanmay relative to Suman. Option c is wrong because neither statement alone is sufficient; each leaves the possibility that different persons might be the oldest. Option d is wrong because even the combined data allow more than one person to be the oldest.

Common Pitfalls:
Many candidates mistakenly assume that if Suman is older than Rohit and Kajal and the sum of Kajal and Tanmay is greater than Suman, then Suman must be the oldest. This ignores the possibility that Tanmay may individually be older than Suman while still satisfying the sum condition. In data sufficiency questions it is crucial to test alternative numeric examples rather than trusting an initial impression.

Final Answer:
Even when statements I and II are used together, they do not uniquely determine who is the oldest. Correct option: Even using both statements I and II together, the data are not sufficient to answer the question.