Understanding Coding Decoding Logic

This question involves a type of coding and decoding where letters of a word are represented by numbers based on a specific rule. We are given the word 'KNOW' and its code '1614154'. We need to decipher the rule used for coding 'KNOW' and then apply it to find the code for 'HIRE'.

Analyzing the Coding Pattern for 'KNOW'

Let's look at the letters in 'KNOW' and their standard alphabetical positions:

• K is the 11th letter.
• N is the 14th letter.
• O is the 15th letter.
• W is the 23rd letter.

The given code is '1614154'. This sequence of numbers seems to correspond to the letters K, N, O, W in order. Let's break down the code into potential parts: 16, 14, 15, 4.

• K corresponds to 16.
• N corresponds to 14.
• O corresponds to 15.
• W corresponds to 4.

Comparing the letter positions with these numbers, we see a direct match for 'N' (14) and 'O' (15). However, 'K' (11) corresponds to 16, and 'W' (23) corresponds to 4. This suggests that some letters might be coded using their standard position, while others might be coded using a different system, possibly based on reverse alphabetical order.

Exploring Reverse Alphabetical Positions

In reverse alphabetical order, A is 26th, B is 25th, and so on, down to Z being 1st. The standard position (P) and reverse position (R) of a letter are related by the formula: \(R = 27 - P\).

Let's find the reverse positions for the letters in 'KNOW':

• K (Standard Position 11): Reverse Position = \(27 - 11 = 16\).
• N (Standard Position 14): Reverse Position = \(27 - 14 = 13\).
• O (Standard Position 15): Reverse Position = \(27 - 15 = 12\).
• W (Standard Position 23): Reverse Position = \(27 - 23 = 4\).

Now let's compare the code parts (16, 14, 15, 4) with both standard and reverse positions:

Observing the table, we can see the pattern:

• For 'K', the code part 16 matches its reverse position.
• For 'N', the code part 14 matches its standard position.
• For 'O', the code part 15 matches its standard position.
• For 'W', the code part 4 matches its reverse position.

The letters K and W used their reverse positions, while N and O used their standard positions. Notice that K is the first letter and W is the last letter of 'KNOW', and N and O are the middle letters.

The coding logic seems to be: The first and last letters of the word are coded using their reverse alphabetical position, and the middle letters are coded using their standard alphabetical position. The final code is formed by concatenating these numbers.

Applying the Coding Logic to 'HIRE'

Now let's apply this rule to the word 'HIRE'. The letters are H, I, R, E.

• H is the first letter.
• I is a middle letter.
• R is a middle letter.
• E is the last letter.

Let's find their standard and reverse alphabetical positions:

• H (Standard Position 8): Since it's the first letter, we use reverse position. Reverse Position = \(27 - 8 = 19\).
• I (Standard Position 9): Since it's a middle letter, we use standard position. Standard Position = 9.
• R (Standard Position 18): Since it's a middle letter, we use standard position. Standard Position = 18.
• E (Standard Position 5): Since it's the last letter, we use reverse position. Reverse Position = \(27 - 5 = 22\).

Concatenating these numbers in order (H, I, R, E) gives the code for 'HIRE':

19 (for H) + 9 (for I) + 18 (for R) + 22 (for E) = 1991822.

Comparing with Options

Let's check the given options:

1. 18191822
2. 89185
3. 1991822
4. 199922

Our calculated code for 'HIRE' is 1991822, which matches Option 3.

Conclusion

Based on the analysis of the coding pattern used for 'KNOW', the code for 'HIRE' is 1991822.

Revision Table: Key Coding Logic Points

Additional Information: Letter Coding and Decoding

Letter coding and decoding questions are common in reasoning sections of competitive exams. They test your ability to identify patterns and apply rules. Common patterns include:

• Shifting: Letters are shifted a certain number of positions forward or backward in the alphabet (e.g., A becomes C, B becomes D - a shift of +2).
• Reverse Order: The order of letters in the word is reversed in the code.
• Alphabetical Position: Using the numerical position of letters (A=1, B=2, etc.).
• Reverse Alphabetical Position: Using the numerical position from the end (Z=1, Y=2, etc.).
• Opposite Letters: Using pairs of letters that are equidistant from the start and end of the alphabet (A-Z, B-Y, etc.).
• Combination of Rules: Applying different rules based on the position of the letter, whether it's a vowel or consonant, or its standard position number (even/odd).

Solving these questions often requires careful observation, trial and error with potential rules, and logical deduction to find the consistent pattern.