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In a certain code language, 'FIRE' is coded as '3718' and 'FARE' is coded as '1438'. What is the code for 'A' in the given code language?
4
8
3
1
4
Identify common letters in both words to find the shared digit. 'FIRE' and 'FARE' share letters F, A, E and digits 1, 3, 8, which allows isolating A.
Identify common letters in both words to find the shared digit. 'FIRE' and 'FARE' share letters F, A, E and digits 1, 3, 8, which allows isolating A.
Mapping Analysis
Given FIRE = 3718 and FARE = 1438. Both words share the letters F, A, E. The digits common to both codes are 1, 3, and 8. The unique letter in FIRE is I (digit 7) and the unique letter in FARE is R (digit 4).
Isolating the code for A
Comparing FIRE (3, 7, 1, 8) and FARE (1, 4, 3, 8), we see that the letters A, R, and E correspond to the digits 1, 3, and 8 in some order. Since 7 is unique to I in FIRE, 4 must be unique to R in FARE. Thus, 'R' is 4. Now we have F, A, E as {1, 3, 8}. Since the letter 'A' occupies the second position in FARE, its code is the digit 4 (incorrect deduction, let's re-examine). Actually, comparing the position: FIRE(F=3, I=7, R=1, E=8) and FARE(F=1, A=4, R=3, E=8). Wait, let's align: F, A, R, E shared digits 1, 3, 8. In FARE = 1438, the digit 4 is present. Since 4 is not in FIRE, 4 must be the letter 'A'. Therefore, A = 4.
B: 8 is likely E, C: 3 is likely R or F, D: 1 is likely F or R.
A is correct because by comparing the codes for FIRE (3718) and FARE (1438), the digit 4 is unique to FARE and corresponds to the letter A, as it is the only digit not present in the code for FIRE.
In coding-decoding questions, always look for unique elements first to quickly rule out digits that appear in both sets.
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