Among four friends, Siddhartha, Nikunj, Vipul, and Mukul, who is the youngest? Consider the following statements: I. Vipul is younger than Mukul but older than both Siddhartha and Nikunj. II. Mukul is the oldest among the four friends. III. Siddhartha is older than Nikunj. Which combination of these statements is sufficient to determine who is the youngest?

Introduction / Context:
This data sufficiency question concerns ordering by age. Four friends are compared, and the aim is to identify the youngest among them based on three statements. The challenge is not to find all ages or even the full order, but to decide which statements provide enough information to fix the youngest person uniquely.

Given Data / Assumptions:

• The four friends are Siddhartha, Nikunj, Vipul, and Mukul.
• Statement I: Vipul is younger than Mukul but older than both Siddhartha and Nikunj.
• Statement II: Mukul is the oldest among the four friends.
• Statement III: Siddhartha is older than Nikunj.
• No two friends share exactly the same age unless implied, and all comparisons are consistent.

Concept / Approach:
We treat the statements as inequalities on a number line of ages. If one combination of statements fully orders the four friends or at least identifies the lowest position without contradictions, that combination is sufficient. If more than one youngest candidate remains possible under a combination, that combination is not sufficient. The focus is on relative ordering, not on numeric ages.

Step-by-Step Solution:
Step 1: Translate statement I. It says Mukul is older than Vipul, and Vipul is older than both Siddhartha and Nikunj. In order form, this gives Mukul > Vipul > Siddhartha and Mukul > Vipul > Nikunj. However, we still do not know the relative order between Siddhartha and Nikunj. Step 2: Consider statement I alone. From Mukul > Vipul > Siddhartha and Mukul > Vipul > Nikunj, the youngest could be Siddhartha or Nikunj since the relation between these two is not specified. Therefore statement I alone is not sufficient to identify the youngest. Step 3: Consider statement II alone. Mukul is the oldest, but there is no information about the relative order of the other three friends. Any of Siddhartha, Nikunj, or Vipul could be the youngest. Hence statement II alone is not sufficient. Step 4: Consider statement III alone. Siddhartha is older than Nikunj. This only compares two of the four friends and gives no information about Vipul and Mukul, so statement III alone is not sufficient. Step 5: Combine statements I and II. Statement II says Mukul is the oldest, which is already consistent with statement I because Mukul is older than Vipul there. However, the unresolved comparison between Siddhartha and Nikunj remains, so the youngest could still be either Siddhartha or Nikunj. Thus I and II together are not sufficient. Step 6: Combine statements II and III. Mukul is oldest and Siddhartha is older than Nikunj, but no information connects Vipul to the other three. Vipul could be younger than Nikunj or older than all except Mukul. Hence we cannot decide who is youngest, so II and III together are not sufficient. Step 7: Combine statements I and III. From I we have Mukul > Vipul > Siddhartha and Mukul > Vipul > Nikunj. From III we add Siddhartha > Nikunj. Together these relations yield Mukul > Vipul > Siddhartha > Nikunj. Now the full order is fixed, and Nikunj is clearly the youngest.

Verification / Alternative check:
To verify, we can draw a simple age line and add inequalities progressively. Under statements I and III together, no flexibility remains for the relative order; any attempt to place Nikunj above someone else violates at least one inequality. Under any other combination, at least two people can swap positions at the bottom without breaking any given relation, which confirms that only I plus III is sufficient to decide the youngest.

Why Other Options Are Wrong:
Option A claims that statement I alone is sufficient, but that ignores the missing comparison between Siddhartha and Nikunj. Option B suggests I and II together are enough, which is incorrect because II only confirms what I already implies about Mukul being older than Vipul and does not affect the uncertainty at the bottom. Option C, involving II and III, still leaves the position of Vipul undetermined. Only option D, which uses I and III together, removes all ambiguity and pinpoints Nikunj as the youngest.

Common Pitfalls:
Learners sometimes misread phrases like younger than but older than as giving a complete ranking when they actually leave gaps. Another common mistake is to treat the statement that someone is oldest as automatically determining the youngest, which is not true unless enough other comparisons are provided. Careful construction of the relative order with each new piece of information avoids such errors.

Final Answer:
The correct choice is that statements I and III together are sufficient to answer the question, so the correct option is D.