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In a certain code language, ‘DASH’ is coded as ‘8465’ and ‘HADE’ is coded as ‘5862’. What is the code for ‘E’ in the given code language?
2
6
5
8
2
Quick Trick: Find the letter unique to HADE that does not exist in DASH. The only extra letter in HADE is E, so its code is the digit in 5862 that is missing from 8465, which is 2.
Find the letter unique to HADE that does not exist in DASH. The only extra letter in HADE is E, so its code is the digit in 5862 that is missing from 8465, which is 2.
Identify common letters between DASH and HADE
Compare the letters in 'DASH' and 'HADE'. The letters 'D', 'A', and 'H' are present in both words.
Identify common digits in both code numbers
Compare the given codes '8465' for DASH and '5862' for HADE. The digits present in both codes are 5, 8, and 6. Thus, the letters {D, A, H} correspond to the set of digits {5, 8, 6} in some order.
Isolate the unique letter and unique digit
In 'HADE', after removing the common letters {D, A, H}, the remaining letter is 'E'. In its code '5862', after removing the common digits {5, 8, 6}, the remaining unique digit is '2'. Therefore, the code for 'E' must be 2.
B: 6 corresponds to one of the common letters (D, A, or H), C: 5 corresponds to one of the common letters (D, A, or H), D: 8 corresponds to one of the common letters (D, A, or H).
A is correct because isolating the letters common to both words (D, A, H) leaves 'E' as the unique letter in 'HADE' matching the unique digit 2 in '5862'.
In comparison-based coding questions, do not try to match letter positions 1-to-1 unless specified. Use set intersection to find common elements and eliminate them first.