The six letters W, A, R, S, N, E are to be arranged. Is the word formed “answer”? (Using all six letters only.) I. E is placed fourth to the right of A. S is not immediately next to A or E. II. R is placed immediately next to E (either side). W is placed immediately next to S (either side). III. Both N and W are placed immediately next to S; the word does not begin with R; A is not immediately next to W.

Introduction / Context:
We must determine whether, under the given adjacency and positional constraints, the only valid arrangement spells “answer.” The decision is about sufficiency: do the statements (individually or in combination) force a unique arrangement that equals “answer”?

Given Data / Assumptions:

• I: E is fourth to the right of A (so A _ _ _ E in linear order). S is not adjacent to A or E.
• II: R is immediately next to E; W is immediately next to S (adjacent pairs, side unspecified).
• III: Both N and W are immediately adjacent to S (making an N–S–W or W–S–N block); the word does not start with R; A is not adjacent to W.

Concept / Approach:
Translate each constraint into blocks and forbidden adjacencies, then test whether subsets of statements still allow multiple valid permutations that are not “answer.” If so, those subsets are insufficient.

Step-by-Step Solution:
From I alone: A _ _ _ E is fixed in spacing but yields many fills for the three blanks; further, S cannot sit next to A or E, leaving numerous options.I + II: With R next to E, and W next to S, there remain multiple placements for the W–S pair relative to A and E; uniqueness still fails.II + III force a tight block around S (N and W both adjacent) and R next to E, but without I’s spacing between A and E, distinct linear orders remain feasible.Only I + II + III together compress the search space to a single valid six-letter word whose order matches “answer.”

Verification / Alternative check:
Attempting to construct a non-“answer” order under any pair of statements succeeds, showing insufficiency; adding the third eliminates alternatives.

Why Other Options Are Wrong:
Any two statements leave at least one other arrangement; all three are needed for uniqueness.

Common Pitfalls:
Misinterpreting “fourth to the right” as “fourth position” rather than relative spacing; ignoring simultaneous adjacency constraints around S.

Final Answer:
All three statements together are necessary.