In a certain code language, ‘BOOK’ is written as ‘325’ and ‘READ’ is written…
2023
In a certain code language, ‘BOOK’ is written as ‘325’ and ‘READ’ is written as ‘400’. How will ‘ABLE’ be written in that language?
Answer: B. 440 — Concept: Letter-to-number coding gives every letter a numerical score and then merges those scores into one code for the whole word. Two scoring scales are…
- A.
445
- B.
440
- C.
442
- D.
438
Attempted by 3 students.
Show answer & explanation
Correct answer: B
Concept: Letter-to-number coding gives every letter a numerical score and then merges those scores into one code for the whole word. Two scoring scales are standard: the forward alphabetical position (A = 1, B = 2, …, Z = 26) and the opposite or reverse position, obtained as 27 − forward position, so A = 26, B = 25, …, Z = 1. The letter scores are then combined by one fixed arithmetic operation, most often a sum, to which a constant multiplier or addend may be applied. The rule belongs to the language rather than to any single word, so the rule you settle on must reproduce every code the question supplies, not merely one of them.
Application: Test both scales against the two coded words that are given, fix the rule that reproduces both, then apply that rule to ABLE.
Write the forward positions of BOOK: B = 2, O = 15, O = 15, K = 11. Their total is 43, which is nowhere near the given code 325, so the forward scale used on its own is not the rule.
Convert the same letters to opposite positions with 27 − n: B → 25, O → 12, O → 12, K → 16. Their total is 25 + 12 + 12 + 16 = 65.
Compare that total with the code given for BOOK: 325 ÷ 65 = 5. So the opposite-position total is multiplied by 5 to produce the code.
Confirm the same rule on the second coded word, READ. Its opposite positions are R → 9, E → 22, A → 26, D → 23, giving 9 + 22 + 26 + 23 = 80, and 80 × 5 = 400, which is exactly the code given for READ. A single rule now reproduces both supplied codes, so it is the rule of this language.
Apply the confirmed rule to ABLE. Its opposite positions are A → 26, B → 25, L → 15, E → 22, giving 26 + 25 + 15 + 22 = 88, and 88 × 5 = 440.
Letter | Forward position | Opposite position (27 − n) |
|---|---|---|
A | 1 | 26 |
B | 2 | 25 |
L | 12 | 15 |
E | 5 | 22 |
Total | 20 | 88 |
Cross-check: For any four-letter word the opposite-position total can be reached without converting the letters one by one, because the four opposite positions add up to 4 × 27 minus the forward total, that is 108 − forward total.
BOOK has forward total 43, so its opposite total is 108 − 43 = 65, and 65 × 5 = 325.
READ has forward total 28, so its opposite total is 108 − 28 = 80, and 80 × 5 = 400.
ABLE has forward total 20, so its opposite total is 108 − 20 = 88, and 88 × 5 = 440.
The letter-by-letter route and the shortcut agree on all three words, so ABLE is written as 440 in this code language.