Ordering heights – Four dolls M, N, O, and P have different heights. P is neither as tall as M nor as short as O. Also, N is shorter than P but taller than O. If Anvi wants the tallest doll, which one should she buy?

Introduction / Context:
Classic ordering problems present pairwise comparisons. We must use “neither as tall as M nor as short as O” and the relationships involving N to deduce the full order and identify the tallest.

Given Data / Assumptions:

• P is not as tall as M (so P < M).
• P is not as short as O (so P > O).
• N is shorter than P but taller than O (so O < N < P).
• All heights are distinct.

Concept / Approach:
Chain the inequalities. From O < N < P and P < M, we get O < N < P < M. The tallest is the maximum in this chain.

Step-by-Step Solution:

Verification / Alternative check:
Try to make P tallest: impossible because P < M. Try to make N tallest: impossible because N < P. So only M can be tallest.

Why Other Options Are Wrong:

• Either M or P / Either P or N / Only P: All contradict the strict chain O < N < P < M.
• None of these: There is a correct specific option (“Only M”).

Common Pitfalls:
Interpreting “neither as tall as M nor as short as O” as “between M and O” but forgetting the separate constraint on N. Always write inequalities explicitly.

Final Answer:
Only M