Question: What is the numerical code for 'water' in a certain code ?…

2024

Question: What is the numerical code for 'water' in a certain code ?

Statements:

The code for 'give me water' is '719'.

The code for 'you can bring water for me' is written as '574186'.

  1. A.

    I alone is sufficient while II alone is not sufficient

  2. B.

    II alone is sufficient while I alone is not sufficient

  3. C.

    Either I or II is sufficient

  4. D.

    Neither I nor II is sufficient

Show answer & explanation

Correct answer: D

Concept: In coding-decoding data-sufficiency questions, a code string is simply a set of digits assigned one-to-one to the words of a sentence, with no stated correspondence between position in the sentence and position in the code. A word's code can only be pinned down when the digit sets given in the statement(s) let you eliminate every other possible assignment for that word.

Application:

  1. From "give me water" = '719': the three digits 7, 1, 9 are shared among the three words 'give', 'me', 'water', but nothing in Statement I tells us which digit belongs to which word.

  2. From "you can bring water for me" = '574186': the six digits 5, 7, 4, 1, 8, 6 are shared among the six words 'you', 'can', 'bring', 'water', 'for', 'me', again with no stated word-to-digit order.

  3. The words common to both statements are 'me' and 'water'. The digits common to both codes are 7 and 1 (the digit 9 from Statement I does not reappear in Statement II's digit set). So together, the two statements tell us only that the codes for 'me' and 'water' are 7 and 1, in some order.

  4. Neither statement individually distinguishes which of its digits belongs to 'water' (Statement I alone leaves 'water' as any of 7, 1, or 9; Statement II alone leaves it as any of the six digits). Combining them narrows the possibilities to exactly two digits, 7 and 1, but never isolates a single one for 'water'.

Cross-check: Assigning water=7, me=1 is equally consistent with both statements as assigning water=1, me=7 - neither statement adds any information that breaks this symmetry, confirming the ambiguity cannot be resolved.

Result: So neither statement alone, nor the two statements together, gives enough information to determine the numerical code for 'water'.

Explore the full course: Amcat Preparation