Data Sufficiency — Who Is Youngest? (Siddhartha, Nikunj, Vipul, Mukul) Question: Who among Siddhartha, Nikunj, Vipul and Mukul is the youngest? Statements: I. Vipul is younger than Mukul but older than Siddhartha and Nikunj. II. Mukul is the oldest. III. Siddhartha is older than Nikunj.

Introduction / Context: Determine the youngest person using relative age statements. Data Sufficiency requires identifying which statements are enough to answer uniquely.

Given Data / Assumptions:

• I: Vipul < Mukul and Vipul > Siddhartha, Nikunj.
• II: Mukul is the oldest.
• III: Siddhartha > Nikunj.

Concept / Approach: Use inequalities to order individuals. The youngest is the one smaller than all others. If two persons are both younger than a third (Vipul), we still need to know their mutual order to identify the youngest.

Step-by-Step Solution:

Verification / Alternative check: Any arrangement consistent with I and III places Nikunj at the bottom of the order: N < S < V < M.

Why Other Options Are Wrong:

• Only I: Cannot distinguish between S and N.
• Only I and II: Still cannot distinguish between S and N.
• Only II and III: Does not relate V to S and N, so youngest remains uncertain.
• None of these: Incorrect, as I + III suffice.

Common Pitfalls: Assuming “oldest” is needed to find “youngest”; forgetting to compare S and N directly.

Final Answer: Only I and III.