Understanding the Coding Language Pattern

This question asks us to decode a specific pattern used to transform one word into another in a secret coding language. We are given the word 'YOUNGER' and its coded form 'AQWNECP'. Our task is to identify this pattern and then apply it to the word 'NUMBERS' to find its coded form.

Step-by-Step Analysis of the Given Code

Let's compare each letter of 'YOUNGER' with the corresponding letter in 'AQWNECP' and determine the relationship or shift between them. We can think of the letters in alphabetical order (A=1, B=2, ..., Z=26).

• Y and A: Y is the 25th letter, A is the 1st letter. Moving from Y to A involves wrapping around the alphabet. Y → Z → A. This is a shift of \(\text{+2}\) (25 → 26 → 1, which is 25+2 = 27, and 27 mod 26 is 1).
• O and Q: O is the 15th letter, Q is the 17th letter. 15 → 17 is a shift of \(\text{+2}\).
• U and W: U is the 21st letter, W is the 23rd letter. 21 → 23 is a shift of \(\text{+2}\).
• N and N: N is the 14th letter, N is the 14th letter. 14 → 14 is a shift of \(\text{+0}\).
• G and E: G is the 7th letter, E is the 5th letter. 7 → 5 is a shift of \(\text{-2}\).
• E and C: E is the 5th letter, C is the 3rd letter. 5 → 3 is a shift of \(\text{-2}\).
• R and P: R is the 18th letter, P is the 16th letter. 18 → 16 is a shift of \(\text{-2}\).

The pattern of shifts for the letters in 'YOUNGER' is thus: \(\text{+2, +2, +2, +0, -2, -2, -2}\).

Applying the Code Pattern to 'NUMBERS'

Now, we apply this exact same sequence of shifts to the letters of the word 'NUMBERS'. The word 'NUMBERS' also has seven letters, just like 'YOUNGER'.

• N (14th letter) with a \(\text{+2}\) shift: 14 + 2 = 16, which is the letter P.
• U (21st letter) with a \(\text{+2}\) shift: 21 + 2 = 23, which is the letter W.
• M (13th letter) with a \(\text{+2}\) shift: 13 + 2 = 15, which is the letter O.
• B (2nd letter) with a \(\text{+0}\) shift: 2 + 0 = 2, which is the letter B.
• E (5th letter) with a \(\text{-2}\) shift: 5 - 2 = 3, which is the letter C.
• R (18th letter) with a \(\text{-2}\) shift: 18 - 2 = 16, which is the letter P.
• S (19th letter) with a \(\text{-2}\) shift: 19 - 2 = 17, which is the letter Q.

Combining the resulting letters, we get PWOBCPQ.

Conclusion

Based on the identified pattern, the word 'NUMBERS' is coded as 'PWOBCPQ'. We check the given options to find the one that matches our result.

• PYOBGPQ
• LWOBCPU
• PWNDCPQ
• PWOBCPQ

The coded word 'PWOBCPQ' matches the fourth option.

Revision Table: Coding Language

Additional Information: Types of Letter Coding

Letter coding puzzles in reasoning often involve various types of patterns:

• Letter Shift: Each letter is shifted by a fixed number of positions (e.g., Caesar cipher).
• Variable Shift: The shift amount changes for each letter based on a pattern (like in this problem).
• Reverse Order: The letters of the word are written in reverse order.
• Alphabet Position: The coding uses the numerical position of letters in the alphabet.
• Substitution: Each letter is replaced by a specific different letter or symbol.
• Combination: A mix of two or more of the above methods.

Solving these puzzles requires careful observation, analysis, and systematic application of the identified rule.