In a certain code language, ‘EACH’ is written as ‘97’, ‘EASY’ is written as…
2023
In a certain code language, ‘EACH’ is written as ‘97’, ‘EASY’ is written as ‘64’. How will ‘ECHO’ be written in that language?
Answer: C. 83 — Concept — in a letter-to-number code, every letter carries a positional value: its place from the start of the alphabet (A = 1, B = 2, ... Z = 26) or,…
- A.
85
- B.
82
- C.
83
- D.
86
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Correct answer: C
Concept — in a letter-to-number code, every letter carries a positional value: its place from the start of the alphabet (A = 1, B = 2, ... Z = 26) or, equivalently, its place from the end (Z = 1, Y = 2, ... A = 26), the two being linked by start + end = 27. When a whole word is coded as a single number, the first relationship to test is whether that number is a fixed function of the sum of its letters’ positions — usually the sum itself, or a constant from which the sum is subtracted. Two solved words are enough to pin down such a relation.
Application — work out the positional total of each solved word and set it against the code given for that word.
EACH: E = 5, A = 1, C = 3, H = 8, so the letters total 5 + 1 + 3 + 8 = 17, against the given code 97.
EASY: E = 5, A = 1, S = 19, Y = 25, so the letters total 5 + 1 + 19 + 25 = 50, against the given code 64.
Compare the two words: the total rises by 50 - 17 = 33 while the code falls by 97 - 64 = 33. The code therefore moves down by exactly 1 for every 1 the total moves up.
A rate of -1 means the code and the total always add up to the same number: 97 + 17 = 114 and 64 + 50 = 114. The rule is code = 114 - (total of the letters’ positions).
ECHO: E = 5, C = 3, H = 8, O = 15, so the letters total 5 + 3 + 8 + 15 = 31.
Apply the rule: code = 114 - 31 = 83.
Word | Letter positions | Total | Code |
|---|---|---|---|
EACH | 5, 1, 3, 8 | 17 | 97 |
EASY | 5, 1, 19, 25 | 50 | 64 |
ECHO | 5, 3, 8, 15 | 31 | 83 |
Cross-check — the same rule is usually printed in the equivalent "opposite letter" form, and the two agree because subtracting each of four positions from 27 leaves 108 minus the total, so 108 - total + 6 = 114 - total. EACH gives (22 + 26 + 24 + 19) + 6 = 97, EASY gives (22 + 26 + 8 + 2) + 6 = 64, and ECHO gives (22 + 24 + 19 + 12) + 6 = 83. Both routes reproduce the two codes supplied in the question, so the relation is the right one.
Contrast — the neighbouring values call for different letter totals: 86 needs a total of 28, 85 needs 29 and 82 needs 32, whereas E, C, H and O together total 31.
Hence, in that code language ECHO is written as 83.