How is the word ‘‘GATES’’ coded in the code language? I. ‘‘BRICK’’ is coded as ‘‘LDJSC’’ and ‘‘PIN’’ is coded as ‘‘QJQ’’. II. ‘‘WATER’’ is coded as ‘‘SFUBX’’ and ‘‘DIST’’ is coded as ‘‘ITJE’’.

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 a unique coded form of the specific word ‘‘GATES’’ based on sample encodings. Data Sufficiency requires that a single, unambiguous mapping be implied; otherwise the data are insufficient.

Given Data / Assumptions:

I provides two pairs: BRICK→LDJSC, PIN→QJQ.
II provides two pairs: WATER→SFUBX, DIST→ITJE.
No explicit rule (e.g., Caesar shift, position-based substitution) is specified; word-level operations, mixed shifts, or polyalphabetic schemes are possible.

Concept / Approach:
Test for consistent single-letter substitution or uniform shift. The given pairs show inconsistent per-letter shifts across positions (e.g., B→L is +10, R→D is +12 mod 26; W→S is −4, A→F is +5), implying a more complex or variable rule. Without a stated mechanism, multiple encipherments of GATES can fit.

Step-by-Step Solution:

1) I alone: The heterogeneous shifts across BRICK and PIN do not determine how to transform new letters like G, A, T, E, S. Multiple plausible rules exist (position-wise shifts, alternating patterns, keyed substitution), so I is insufficient.2) II alone: WATER and DIST exhibit different, non-uniform transformations. Extrapolating to GATES remains ambiguous. II is insufficient.3) I + II together: Even combining all four pairs, there is no uniquely implied cipher family; several rule-sets can encode the samples and would encode GATES differently (e.g., per-position shift table, digram rules, or keyed Vigenère-style). Thus, the code for GATES is not uniquely deducible.

Verification / Alternative check:
Attempt to align letter-wise mappings by position across words of different lengths; conflicts arise, confirming non-uniqueness.

Why Other Options Are Wrong:

A/B/C/E: None create uniqueness; together or alone, ambiguity persists.

Common Pitfalls:
Assuming a fixed Caesar shift; enforcing one-to-one letter mapping ignoring position-dependent behavior suggested by the pairs.

Final Answer:
Both statements together are NOT sufficient.

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How is the word ‘‘GATES’’ coded in the code language? I. ‘‘BRICK’’ is coded as ‘‘LDJSC’’ and ‘‘PIN’’ is coded as ‘‘QJQ’’. II. ‘‘WATER’’ is coded as ‘‘SFUBX’’ and ‘‘DIST’’ is coded as ‘‘ITJE’’.

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