If each of the letters in the English alphabet is assigned odd numerical value…
2020
If each of the letters in the English alphabet is assigned odd numerical value beginning A = 1, B = 3 and so on, what will be the total value of the letters of the word 'EARLIER':
- A.
90
- B.
99
- C.
125
- D.
129
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Correct answer: D
In this alphabet-to-number coding scheme, every letter is mapped to the odd number matching its position in the alphabet: the 1st letter (A) = 1, the 2nd letter (B) = 3, the 3rd letter (C) = 5, and so on -- so value = 2 x (alphabet position) - 1. To find a word's total value, add the value of EVERY letter, counting a repeated letter again each time it occurs.
Applying this to 'EARLIER' (E, A, R, L, I, E, R):
List each letter with its alphabet position: E (5th), A (1st), R (18th), L (12th), I (9th), E (5th again), R (18th again).
Convert each occurrence using value = 2 x position - 1: E = 2x5-1 = 9, A = 2x1-1 = 1, R = 2x18-1 = 35, L = 2x12-1 = 23, I = 2x9-1 = 17, E = 9 (again), R = 35 (again).
Add all seven values: 9 + 1 + 35 + 23 + 17 + 9 + 35.
Running total: 9+1=10, +35=45, +23=68, +17=85, +9=94, +35=129.
Cross-check with a second method: first add the seven alphabet positions (5+1+18+12+9+5+18 = 68), then use the fact that summing n letters with value = 2xposition-1 gives 2x(sum of positions) - n. That is 2x68 - 7 = 136 - 7 = 129 -- matching the letter-by-letter total exactly.
So the total value of the letters of 'EARLIER' is 129.