Understanding the Coding Language Pattern

The question asks us to decode the word 'MENTAL' based on the pattern observed in the given examples: 'WITH' is coded as 418719 and 'FOOD' is coded as 21121223. We need to analyze these examples to find the rule governing the transformation of a word into the numerical code.

Analyzing the 'WITH' Code: 418719

Let's consider the letters in 'WITH' and their positions in the English alphabet:

• W is the 23rd letter.
• I is the 9th letter.
• T is the 20th letter.
• H is the 8th letter.

The code is 418719. Let's try to relate the letter positions to the numbers in the code. The code appears to be a concatenation of numbers for each letter. Looking at the numbers 4, 18, 7, 19, they don't directly match the alphabetical positions 23, 9, 20, 8.

Let's consider the concept of reverse alphabetical position (27 - position). This is a common pattern in coding-decoding questions.

• For W (position 23): \(27 - 23 = 4\). The first number in the code is 4. This matches.
• For I (position 9): \(27 - 9 = 18\). The next number is 18. This matches.
• For T (position 20): \(27 - 20 = 7\). The next number is 7. This matches.
• For H (position 8): \(27 - 8 = 19\). The last number is 19. This matches.

Concatenating these reverse positions (4, 18, 7, 19) gives 418719, which is the code for 'WITH'. The pattern seems to be 27 minus the alphabetical position of the letter.

Verifying the Pattern with 'FOOD' Code: 21121223

Let's apply the same pattern to the word 'FOOD'. The letters are F, O, O, D.

• F is the 6th letter. Reverse position: \(27 - 6 = 21\).
• O is the 15th letter. Reverse position: \(27 - 15 = 12\).
• O is the 15th letter. Reverse position: \(27 - 15 = 12\).
• D is the 4th letter. Reverse position: \(27 - 4 = 23\).

Concatenating these reverse positions (21, 12, 12, 23) gives 21121223, which is the code for 'FOOD'. This confirms that the pattern is indeed using the value of 27 minus the alphabetical position for each letter and concatenating the results.

Applying the Pattern to 'MENTAL'

Now, let's apply this established pattern to the word 'MENTAL'. The letters are M, E, N, T, A, L.

• M is the 13th letter. Reverse position: \(27 - 13 = 14\).
• E is the 5th letter. Reverse position: \(27 - 5 = 22\).
• N is the 14th letter. Reverse position: \(27 - 14 = 13\).
• T is the 20th letter. Reverse position: \(27 - 20 = 7\).
• A is the 1st letter. Reverse position: \(27 - 1 = 26\).
• L is the 12th letter. Reverse position: \(27 - 12 = 15\).

Concatenating the calculated reverse positions (14, 22, 13, 7, 26, 15) gives the code for 'MENTAL'.

Code for 'MENTAL' = 14221372615.

Comparing with the Options

Let's compare our derived code for 'MENTAL' with the given options:

• Option 1: 14221372615
• Option 2: 14221317112
• Option 3: 14513202615
• Option 4: 13221472615

Our calculated code 14221372615 matches Option 1.

Concatenated code for MENTAL: 14221372615.

Revision Table: Coding Decoding Concepts

Additional Information: Reverse Alphabetical Order Logic

The reverse alphabetical position coding is a common technique in reasoning questions. It's based on the idea that each letter has a pair which is equidistant from the start and end of the alphabet. For instance, A is 1st from the start, Z is 1st from the end. Their positions are 1 and 26. \(1 + 26 = 27\). Similarly, B is 2nd from start, Y is 2nd from end. Their positions are 2 and 25. \(2 + 25 = 27\). This holds true for all pairs (A-Z, B-Y, C-X, D-W, E-V, F-U, G-T, H-S, I-R, J-Q, K-P, L-O, M-N).

When a letter is coded using its reverse alphabetical position, the value is simply 27 minus its standard alphabetical position. This method effectively maps a letter to the numerical value corresponding to its 'opposite' letter's position. For example, the reverse position of A (1) is 26, which is the position of Z. The reverse position of M (13) is 14, which is the position of N.