Understanding the Coding Decoding Logic

This question involves a coding-decoding problem where words are transformed into a code based on a specific pattern. We are given two examples: 'ACTION' coded as 'DFWFLK' and 'BISHOP' coded as 'ELVELM'. Our task is to decipher the underlying rule and apply it to find the code for 'MATTER'.

Analyzing the Examples to Find the Pattern

Let's compare the letters of the original words with their corresponding coded letters:

Let's look at the positional changes in the alphabet:

• A is the 1st letter, D is the 4th letter. Difference: \(4 - 1 = 3\)
• C is the 3rd letter, F is the 6th letter. Difference: \(6 - 3 = 3\)
• T is the 20th letter, W is the 23rd letter. Difference: \(23 - 20 = 3\)
• I is the 9th letter, F is the 6th letter. Difference: \(6 - 9 = -3\)
• O is the 15th letter, L is the 12th letter. Difference: \(12 - 15 = -3\)
• N is the 14th letter, K is the 11th letter. Difference: \(11 - 14 = -3\)

It appears the first three letters of 'ACTION' are shifted forward by 3 positions (\(\text{letter} + 3\)), and the last three letters are shifted backward by 3 positions (\(\text{letter} - 3\)).

Verifying the Pattern with 'BISHOP'

Let's check if the same pattern applies to 'BISHOP' and 'ELVELM'.

The pattern holds true for 'BISHOP' as well: the first three letters are shifted by \(+3\) and the last three letters by \(-3\).

Applying the Pattern to 'MATTER'

Now we apply this logical rule to the word 'MATTER'. 'MATTER' has 6 letters. The first three letters are M, A, T and the last three are T, E, R.

• M (13th letter) → \(13+3=16\)th letter → P
• A (1st letter) → \(1+3=4\)th letter → D
• T (20th letter) → \(20+3=23\)rd letter → W
• T (20th letter) → \(20-3=17\)th letter → Q
• E (5th letter) → \(5-3=2\)nd letter → B
• R (18th letter) → \(18-3=15\)th letter → O

Combining the coded letters, 'MATTER' is coded as 'PDWQBO'.

Matching with Options

Let's compare our result 'PDWQBO' with the given options:

• Option 1: QEWQBO
• Option 2: PEXQCO
• Option 3: QDWQCO
• Option 4: PDWQBO

Our derived code 'PDWQBO' matches Option 4.

Conclusion

The pattern observed in the coding language is a simple shift cipher applied to two halves of the word separately. The first half undergoes a \(+3\) shift, and the second half undergoes a \(-3\) shift. Applying this to 'MATTER' gives us the code 'PDWQBO'.

Revision Table: Coding Decoding Summary

Additional Information: Types of Coding Decoding

Coding-decoding questions are common in reasoning tests. They assess your ability to identify patterns and logical rules. Here are some common types:

• Letter Shifting: Letters are shifted forward or backward by a certain number of positions (like in this problem). The shift can be uniform or vary based on position, letter type, etc.
• Direct Letter Coding: Each letter in a word is assigned a specific code (another letter, number, or symbol).
• Number/Symbol Coding: Words are coded into numbers or symbols based on letter positions, counts, or other rules.
• Mixed Letter and Number Coding: A combination of letter and number codes.
• Substitution Coding: Words are substituted with other words.

Solving these problems requires careful observation, analyzing the relationship between the original word and the coded word, and systematically testing potential patterns like letter shifts, reversals, or substitutions.