In a certain code, PAN is written as 31 and PAR as 35, then PAT is written in…
2010
In a certain code, PAN is written as 31 and PAR as 35, then PAT is written in the same code as
Answer: B. 37 — Concept: In alphabet-sum coding, each letter of a word is replaced by its serial position in the English alphabet (A = 1, B = 2, … , Z = 26) and the code of…
- A.
30
- B.
37
- C.
39
- D.
41
Attempted by 5 students.
Show answer & explanation
Correct answer: B
Concept: In alphabet-sum coding, each letter of a word is replaced by its serial position in the English alphabet (A = 1, B = 2, … , Z = 26) and the code of the word is the sum of those positions. Because the positions are simply added, two words that agree in every letter but one differ in code by exactly the gap between the positions of the letters that changed.
Application
Letter | Position in the alphabet |
|---|---|
P | 16 |
A | 1 |
N | 14 |
R | 18 |
T | 20 |
Replace each letter of PAN by its alphabet position and add them: 16 + 1 + 14 = 31, which is exactly the code given for PAN.
Do the same for PAR: 16 + 1 + 18 = 35, which is exactly the code given for PAR. The alphabet-sum rule therefore fits both words that the question supplies.
Apply the same rule to PAT: 16 + 1 + 20 = 37.
Cross-check: All three words share the prefix PA, which is worth 16 + 1 = 17, so every code equals 17 plus the position of the third letter. Going from N (14) to R (18) raises that position by 4, and the code indeed rises from 31 to 35, also by 4. Going from R (18) to T (20) raises it by 2, so the code must rise by 2 as well: 35 + 2 = 37.
So in this code PAT is written as 37.