If HIDE and CAGEare coded as 19-23-7-11 and 5-2-17-11 respectively, then what is the code for HIGH?

The correct option/answer is 19-23-17-19.

To find the code for the word HIGH, let us analyze the relationship between the letters and the numerical codes provided for HIDE and CAGE.

First, we determine the alphabetical positions of the letters:
A = 1, B = 2, C = 3, D = 4, E = 5, F = 6, G = 7, H = 8, I = 9, and so on.

Next, let us list the prime numbers in ascending order:
1st prime = 2
2nd prime = 3
3rd prime = 5
4th prime = 7
5th prime = 11
6th prime = 13
7th prime = 17
8th prime = 19
9th prime = 23

By comparing the alphabetical positions with the prime numbers, we find that the pattern maps each letter to the prime number at its alphabetical index. In mathematical terms, if a letter is at position n in the alphabet, it is coded as the n-th prime number:

$${\text{Letter}}_n\to P_n$$
where $P_n$ represents the n-th prime number.

Let us verify this rule with the given examples:

1. HIDE is coded as 19-23-7-11:
Letter H (8th letter) → 8th prime = 19
Letter I (9th letter) → 9th prime = 23
Letter D (4th letter) → 4th prime = 7
Letter E (5th letter) → 5th prime = 11
This perfectly matches 19-23-7-11.

2. CAGE is coded as 5-2-17-11:
Letter C (3rd letter) → 3rd prime = 5
Letter A (1st letter) → 1st prime = 2
Letter G (7th letter) → 7th prime = 17
Letter E (5th letter) → 5th prime = 11
This perfectly matches 5-2-17-11.

3. Code for HIGH:
Applying the same prime number mapping to the letters in HIGH:
Letter H (8th letter) → 8th prime = 19
Letter I (9th letter) → 9th prime = 23
Letter G (7th letter) → 7th prime = 17
Letter H (8th letter) → 8th prime = 19

Combining these values, the code for HIGH is 19-23-17-19.