Understanding the Coding Pattern

The problem asks us to decipher a coding pattern used for the word 'GUM' and then apply the same pattern to code the word 'WAX'. We are given that 'GUM' is coded as '49441169'. Let's analyze the relationship between the letters of 'GUM' and this numerical code.

Analysing the Code for GUM

First, let's find the alphabetical position of each letter in the word 'GUM':

• G is the 7th letter.
• U is the 21st letter.
• M is the 13th letter.

The given code for 'GUM' is '49441169'. This long number looks like a concatenation of smaller numbers. Let's look at the numbers 49, 441, and 169. Do these numbers relate to the alphabetical positions 7, 21, and 13?

• Consider the position of G, which is 7. Squaring the position, we get \(7^2 = 49\).
• Consider the position of U, which is 21. Squaring the position, we get \(21^2 = 441\).
• Consider the position of M, which is 13. Squaring the position, we get \(13^2 = 169\).

If we concatenate these squared values in the order of the letters (G followed by U followed by M), we get 49 followed by 441 followed by 169, which forms the number 49441169. This matches the given code for 'GUM'.

So, the pattern is: Code each letter by squaring its alphabetical position and then concatenate the resulting numbers.

Concatenated Code for GUM: 49441169.

Applying the Pattern to WAX

Now, let's apply the same pattern to the word 'WAX'.

First, find the alphabetical position of each letter in 'WAX':

• W is the 23rd letter.
• A is the 1st letter.
• X is the 24th letter.

Next, square the alphabetical position of each letter:

• For W (23): \(23^2 = 529\).
• For A (1): \(1^2 = 1\).
• For X (24): \(24^2 = 576\).

Finally, concatenate these squared values in the order of the letters (W followed by A followed by X):

Concatenating 529, 1, and 576 gives us 5291576.

Therefore, 'WAX' will be coded as '5291576' in that language.

Comparing with Options

Let's check the calculated code against the given options:

• Option 1: 3611121
• Option 2: 5291576
• Option 3: 2891400
• Option 4: 8412525

Our calculated code, 5291576, matches Option 2.

Conclusion on WAX Coding

Based on the pattern observed in coding 'GUM', the code for 'WAX' is determined by squaring the alphabetical position of each letter and concatenating the results. This yields 5291576.

Revision Table: Letter Positions and Squares

Knowing the squares of common letter positions can speed up solving such coding decoding questions.

Additional Information on Coding Decoding

Coding decoding is a common topic in logical reasoning sections of competitive exams. These questions test your ability to identify patterns and rules governing the transformation of words, letters, or numbers.

Common types of coding patterns include:

• Letter Shifting: Letters are shifted a fixed number of positions forward or backward in the alphabet.
• Position-based Coding: Letters are coded based on their position in the alphabet (e.g., position number, square of position, etc.).
• Reverse Alphabetical Order: Letters are coded using their position from the end of the alphabet (A=26, B=25, etc.).
• Direct Letter Coding: Each letter in the original word is directly replaced by another letter or symbol according to a specific mapping.
• Mixed Coding: A combination of different patterns might be used.

To solve coding decoding problems effectively, it is helpful to:

• Know the alphabetical positions of letters (A=1, B=2, ..., Z=26).
• Know the positions in reverse order (A=26, B=25, ..., Z=1).
• Look for patterns in the given examples (like GUM to 49441169).
• Test potential patterns systematically.