In a certain code language, ‘NORM’ is coded as ‘7341’ and ‘ROME’ is coded as ‘3748’. What is the code for ‘E’ in the given code l…

Question

In a certain code language, ‘NORM’ is coded as ‘7341’ and ‘ROME’ is coded as ‘3748’. What is the code for ‘E’ in the given code language?

1. A. 4
2. B. 7
3. C. 3
4. D. 8 (Correct answer)

Correct Answer

Option D — 8

Detailed Solution & Explanation

The correct answer is 8.

Key Points

• Compare the two codes by which letters and digits they share:
  • NORM → 7341 uses letters {N, O, R, M}
  • ROME → 3748 uses letters {R, O, M, E}
• The common letters are O, R and M, and the common digits are 3, 7 and 4.
• Therefore the unmatched items must correspond: NORM's extra letter N pairs with its extra digit 1, and ROME's extra letter E pairs with its extra digit 8.
• So E = 8.

Additional Information

• This is the standard technique for jumbled-letter coding, where the digits are not in the same order as the letters: compare two codes sharing most of their letters and isolate the difference. Individual positions tell you nothing.
• The method needs no assumption about ordering at all — only set membership, which is why it works even when the code is deliberately scrambled.
• Had a third word been supplied, the remaining three letters could have been pinned down the same way, one difference at a time.
• Distinguish this from positional coding, where the first letter maps to the first digit; there the pattern is read directly and no set comparison is needed.