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.

Difficulty: Medium

Correct Answer: Both I and II are sufficient

Explanation:


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

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