Who earns the most among M, N, P, Q and R — which statements suffice? I. M earns less than P but not less than R. II. Q earns more than M but is not equal to N. III. N earns more than M and R.

Introduction / Context:The task is to determine whether the three comparative statements are sufficient to identify the highest earner among M, N, P, Q, and R.

Given Data / Assumptions:

• I: M < P and M ≥ R ⇒ P > M ≥ R.
• II: Q > M and Q ≠ N (no ordering between Q and N given).
• III: N > M and N > R (no relation between N and P or N and Q).

Concept / Approach:Data sufficiency: we do not need the exact amounts, only enough ordering information to pinpoint a unique maximum. Check whether combinations eliminate ambiguity about P, Q, and N relative ordering.

Step-by-Step Solution:

Verification / Alternative check:Construct two consistent scenarios: (a) P > Q > N > M ≥ R; (b) N > Q > P > M ≥ R. Both satisfy all statements yet yield different top earners. Hence, no unique answer exists.

Why Other Options Are Wrong:

• I and II only / Only I and III: Still leave P vs Q vs N unresolved.
• Only I and II or only I and III: Either pair remains ambiguous; III does not relate N to P or Q.

Common Pitfalls:Assuming “Q ≠ N” implies an order; it does not. Also, “M ≥ R” does not help compare P, Q, and N among themselves.

Final Answer:Question cannot be answered even within formation in all three statements