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.
Correct Answer: Only I and III
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:
From I: S and N are both younger than Vipul; Mukul is older than Vipul. The youngest must be among {S, N}, but I alone does not tell whether S or N is younger. From III: Siddhartha is older than Nikunj ⇒ Nikunj is younger than Siddhartha. Combine I and III: Since both S and N are younger than Vipul and N is younger than S, Nikunj is the youngest overall. Mukul’s status in II is not required, because I already places Mukul older than Vipul, and both S and N are below Vipul.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.