Data Sufficiency – Relative Earnings Ordering Question: Among M, N, D, P, and K, who earns more than only the least earner (i.e., who is second from the bottom)? Statements: I. N earns more than M and P but less than only D. II. M earns more than P, and P earns less than K.
Correct Answer: Both I and II are sufficient
Introduction / Context: The task is to identify the person who is exactly above the least earner (second-lowest) using partial order information. This is a common ranking-style Data Sufficiency problem.
Given Data / Assumptions:
- I: N earns less than only D, and N earns more than M and P. No explicit info on K in I.
- II: M > P and K > P but M > K is not implied (only P < K).
- All five individuals are distinct and have total orderings with no ties implied.
Concept / Approach: Combine statements to construct a complete chain from lowest to highest. Statement I places N second-highest and D highest. Statement II orders P < K < M among the remaining three. Merging these gives a full ranking.
Step-by-Step Solution: From I: D is highest; N is second-highest; also N > M and N > P. From II: P < K < M (since M > P and K > P but no K–M reversal is stated; M > K is not forced by II alone, but I has N > M, consistent with placing M below N). Combine: The only consistent total order is P < K < M < N < D. Hence the person who earns more than only the least earner (second from bottom) is K.
Verification / Alternative check: I alone leaves K's position unknown; II alone gives only a partial chain among three people. Together they produce a unique full ordering.
Why Other Options Are Wrong: Any option claiming single-statement sufficiency is invalid because neither I nor II alone yields the exact second-lowest person.
Common Pitfalls: Assuming relationships not stated (e.g., M compared to K beyond what II provides) without integrating I's constraints.
Final Answer: Both I and II are sufficient