Understanding the Coding Pattern

The question asks us to decipher the coding pattern used for the word 'NOTION' and apply it to code the word 'BEAUTIFY'. The coded value for 'NOTION' is given as '13127181213'. We need to analyze the relationship between the letters in 'NOTION' and these numbers.

Let's look at the alphabetical position of each letter in 'NOTION':

Now let's compare these positions with the given code '13127181213', breaking it down possibly by letter:

• N (14) → 13
• O (15) → 12
• T (20) → 7
• I (9) → 18
• O (15) → 12
• N (14) → 13

Observing the relationship for each letter:

• For N (position 14), the code is 13. This is \(14 - 1\).
• For O (position 15), the code is 12. This is \(15 - 3\).
• For T (position 20), the code is 7. The reverse alphabetical position of T is \(27 - 20 = 7\).
• For I (position 9), the code is 18. The reverse alphabetical position of I is \(27 - 9 = 18\).

Based on this analysis, we can deduce the coding rules:

• If the letter is N, subtract 1 from its alphabetical position.
• If the letter is O, subtract 3 from its alphabetical position.
• For all other letters (including T and I as observed, and potentially others), use their Reverse Alphabetical Position (27 - Alphabetical Position).

Let's re-verify the rules with 'NOTION' using this consolidated logic:

• N (14): Rule for N is Pos - 1 → \(14 - 1 = 13\)
• O (15): Rule for O is Pos - 3 → \(15 - 3 = 12\)
• T (20): All other letters rule is 27 - Pos → \(27 - 20 = 7\)
• I (9): All other letters rule is 27 - Pos → \(27 - 9 = 18\)
• O (15): Rule for O is Pos - 3 → \(15 - 3 = 12\)
• N (14): Rule for N is Pos - 1 → \(14 - 1 = 13\)

Concatenating these numbers gives 13127181213, which matches the given code for 'NOTION'. The pattern is confirmed.

Coding 'BEAUTIFY' using the Discovered Pattern

Now, let's apply these rules to the word 'BEAUTIFY'. First, find the alphabetical position of each letter:

Now, let's calculate the code for each letter based on the rules:

• B (2): 27 - 2 = 25
• E (5): 27 - 5 = 22
• A (1): 27 - 1 = 26
• U (21): 27 - 21 = 6
• T (20): 27 - 20 = 7
• I (9): 27 - 9 = 18
• F (6): 27 - 6 = 21
• Y (25): 27 - 25 = 2

Concatenating these numbers gives the code for 'BEAUTIFY': 2522266718212.

Comparing with Options

Let's compare our calculated code with the given options:

• Option 1: 2522266718212
• Option 2: 2505016718212
• Option 3: 2022266818222
• Option 4: 2522268719215

Our calculated code 2522266718212 matches Option 1.

Revision Table: Alphabetical Positions

Additional Information: Types of Coding

Coding-decoding questions in logical reasoning test your ability to find patterns in how words, letters, or numbers are transformed. Common types of letter coding include:

• Letter Shifting: Each letter is shifted a fixed number of positions forward or backward in the alphabet.
• Reverse Alphabetical Order: Letters are coded based on their position from the end of the alphabet (A=26, B=25, ..., Z=1). This is often calculated as 27 - position from the start.
• Direct Letter Coding: A specific letter is always coded by a specific symbol or number, regardless of its position.
• Mixed Letter/Number Coding: Letters are coded using numbers based on their position or some calculation involving their position, as seen in this problem.
• Position-Based Coding: The coding rule might depend on the position of the letter within the word (e.g., first letter follows one rule, second another).

In this specific problem, we encountered a mixed coding pattern where some letters followed a simple subtraction rule based on their position, while others followed the reverse alphabetical position rule. Identifying which letters follow which rule by carefully analyzing the example word ('NOTION' in this case) is key to solving such problems.