Data Sufficiency – Numerical coding (identify the code for 'water') Question: What is the numerical code for the word 'water'? Statements: I. The code for 'give me water' is '719'. II. The code for 'you can bring water for me' is '574186'.

Difficulty: Medium

Correct Answer: Neither I nor II is sufficient

Explanation:


Introduction / Context:
Here we must determine whether the information given in either statement identifies the exact numeral for the word 'water'. This is a classic DS test of intersection/overlap reasoning when multiple words repeat across sentences.



Given Data / Assumptions:

  • I: 'give me water' → '719' (a 3-word sentence producing a 3-digit string).
  • II: 'you can bring water for me' → '574186' (a 6-word sentence producing a 6-digit string).
  • Each distinct word maps to exactly one distinct digit in the immediate context.


Concept / Approach:
Compare sentences to find the shared words and the shared digits. If exactly one shared word corresponds to exactly one shared digit, we can identify that mapping. If two words are shared and two digits are shared, ambiguity remains unless we have a tie-breaker.



Step-by-Step Solution:

Common words between I and II are 'me' and 'water' (two words).Digits in I are {7, 1, 9}. Digits in II are {5, 7, 4, 1, 8, 6}. The shared digits are {7, 1} (two digits).Thus, {'me', 'water'} must map to {7, 1} in some order. With only these statements, it is impossible to decide which of 7 or 1 stands for 'water' and which stands for 'me'.Statement I alone gives three digits for three words; without an additional sentence, you cannot isolate 'water'. Statement II alone introduces many new words and does not resolve the ambiguity.


Verification / Alternative check:
Attempting to assign 'water' = 7 forces 'me' = 1 and vice versa; both assignments are consistent with all given information, proving insufficiency.



Why Other Options Are Wrong:

  • I alone or II alone: each clearly leaves multiple possibilities.
  • Either I or II: false; neither identifies a unique code.
  • Both I and II: still ambiguous because two shared words correspond to two shared digits.


Common Pitfalls:
Assuming the left-to-right order of words matches the order of digits; that assumption is not stated, so it cannot be used in DS. Only overlap logic is valid.


Final Answer:
Neither I nor II is sufficient

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