How is the word ‘‘never’’ written in the code language? I. ‘‘never ever go there’’ is coded as ‘‘na ja ni ho’’. II. ‘‘go there and come back’’ is coded as ‘‘ma ho sa ni da’’.

Difficulty: Medium

Statement I alone is sufficient; Statement II alone is not.
Statement II alone is sufficient; Statement I alone is not.
Either Statement I alone or Statement II alone is sufficient.
Both statements together are NOT sufficient.
Both statements together are sufficient, but NEITHER alone is sufficient.

Correct Answer: Both statements together are NOT sufficient.

Explanation:

Introduction / Context:
We must determine the exact code-token for the specific word ‘‘never’’ given two coded sentences. Data Sufficiency asks whether the provided overlaps pin the mapping uniquely, not to decode the entire language exhaustively.

Given Data / Assumptions:

I provides a 1–1 mapping set between {never, ever, go, there} and {na, ja, ni, ho} (order within a sentence may not correspond to code order).
II provides a set mapping between {go, there, and, come, back} and {ma, ho, sa, ni, da}.
Distinct words correspond to distinct code-tokens within these sentences.

Concept / Approach:
Use common words across statements to eliminate code-tokens and isolate the word of interest. If multiple tokens remain possible for ‘‘never’’ after all eliminations, the data are insufficient.

Step-by-Step Solution:

1) From I alone: The four tokens {na, ja, ni, ho} represent {never, ever, go, there}. Without any second sentence overlap, we cannot identify which one is ‘‘never’’; I alone is insufficient.2) From II alone: The common words with I are {go, there} which correspond to {ni, ho}. But II does not include ‘‘never’’ at all, so II alone does not identify ‘‘never’’.3) Combine I + II: Since {go, there} are shared, they must be {ni, ho}. Eliminating {ni, ho} from I's set leaves {na, ja} corresponding to {never, ever}. With no further constraints to distinguish them, the code for ‘‘never’’ remains ambiguous between ‘‘na’’ and ‘‘ja’’.

Verification / Alternative check:
Construct two consistent assignments: Case 1: never→na, ever→ja; Case 2: never→ja, ever→na. Both respect all given sentences, confirming non-uniqueness.

Why Other Options Are Wrong:

A/B/C: Neither statement, nor “either alone”, uniquely identifies the token.
E: Together still ambiguous; hence not sufficient.

Common Pitfalls:
Assuming token order equals word order; forcing arbitrary tie-breakers (like alphabetical) which DS forbids.

Final Answer:
Both statements together are NOT sufficient.

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How is the word ‘‘never’’ written in the code language? I. ‘‘never ever go there’’ is coded as ‘‘na ja ni ho’’. II. ‘‘go there and come back’’ is coded as ‘‘ma ho sa ni da’’.

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