In a certain code language, ‘WIRE’ is coded as ‘5421’ and ‘PERI’ is coded as…
2026
In a certain code language, ‘WIRE’ is coded as ‘5421’ and ‘PERI’ is coded as ‘2745’. What is the code for ‘P’ in the given code language?
Answer: A. 7 — Concept: In a jumbled letter–number code each letter is tied to one fixed digit, but the digits of a code are not written in the order of the letters, so…
- A.
7
- B.
4
- C.
5
- D.
2
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Show answer & explanation
Correct answer: A
Concept: In a jumbled letter–number code each letter is tied to one fixed digit, but the digits of a code are not written in the order of the letters, so position carries no information — only membership does. That gives a matching rule: letters which two words share must take the digits which their two codes share, and a letter that occurs in only one of the words must take the digit that occurs in only that word’s code.
Application: Place each given word beside its code and compare what they are made of.
Word | Letters | Code | Digits |
|---|---|---|---|
WIRE | W, I, R, E | 5421 | 5, 4, 2, 1 |
PERI | P, E, R, I | 2745 | 2, 7, 4, 5 |
Letters present in both words: E, R and I. The letter present only in WIRE is W, and the letter present only in PERI is P.
Digits present in both codes: 5, 4 and 2. The digit present only in 5421 is 1, and the digit present only in 2745 is 7.
There are exactly three shared letters and exactly three shared digits, so E, R and I use 5, 4 and 2 among themselves; which of the three takes which digit cannot be pinned down from the data, and is not needed here.
That leaves exactly one unmatched letter and one unmatched digit on each side. Applying the matching rule to WIRE: W occurs only in WIRE, so W = 1.
Applying the same rule to PERI: P occurs only in PERI, so P must take the digit that occurs only in 2745. Hence P = 7.
Cross-check: Test the rival reading in which the digits follow the letters one for one: WIRE = 5421 would make R = 2 and E = 1, while PERI = 2745 would make E = 7 and R = 4. The two readings contradict each other, so the code cannot be positional and the membership matching above is the correct method. The counting also forces the result — once the three shared letters absorb the three shared digits, only one letter and one digit are left over on each side, so P = 7 is the only value available.