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In a certain code language, 'ROAM' is coded as '2835' and 'MORE' is coded as '4538'. What is the code for 'A' in the given code language?
3
8
5
2
2
Identify common letters in both words to find the shared digit. 'M' and 'O' are common to 'ROAM' and 'MORE', so the shared digits between '2835' and '4538' (3, 5, 8) must represent these letters.
Identify common letters in both words to find the shared digit. 'M' and 'O' are common to 'ROAM' and 'MORE', so the shared digits between '2835' and '4538' (3, 5, 8) must represent these letters.
Mapping the shared characters
ROAM is coded as 2835. MORE is coded as 4538. The letters common to both are M, O, and R (if we assume letter-digit assignment order). However, observing the shared digits: {3, 5, 8} are common to both codes.
Isolating the letter A
In 'ROAM' (2835), the letters are R, O, A, M. In 'MORE' (4538), the letters are M, O, R, E. The letter 'A' is present only in 'ROAM'. The digit '2' is present only in 'ROAM'. Therefore, the code for 'A' must be 2.
A: 8 is shared by both words (M, O, or R). B: 5 is shared by both words (M, O, or R). C: 3 is shared by both words (M, O, or R).
D is correct because 2 is the only digit present in the code for 'ROAM' (2835) that does not appear in the code for 'MORE' (4538), and 'A' is the only letter in 'ROAM' that does not appear in 'MORE'.
Whenever you see two words with overlapping letters, immediately list the shared letters and their corresponding digits to eliminate them from your search for unique characters.
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