In a certain coding system, the word PUBLIC is written as MWYNFE using a specific letter shifting pattern. Using the same pattern, how will the word SYSTEM be written in that code?

Introduction / Context:
This question is from the topic of coding and decoding in logical reasoning. In such questions, a word is transformed into a coded form according to some hidden pattern, and candidates must identify that pattern to code another word correctly. Here the word PUBLIC is written as MWYNFE. The task is to work out how each letter has been changed and then apply the same systematic changes to the word SYSTEM. These problems test pattern recognition, attention to detail and comfort with letter positions in the English alphabet.

Given Data / Assumptions:

The original word is PUBLIC and its code is MWYNFE.
The new word to be coded using the same rule is SYSTEM.
We assume that each letter is transformed individually according to a consistent pattern based on its position in the word and its position in the alphabet.
The alphabet is taken in order from A to Z, with wrapping allowed when moving backwards or forwards beyond the ends.

Concept / Approach:
A standard way to approach such questions is to compare each letter in the original word with the corresponding letter in the coded word and calculate how many positions forward or backward in the alphabet have been applied. For PUBLIC to become MWYNFE, we analyse P to M, U to W, B to Y, L to N, I to F and C to E. This reveals a pattern of alternating shifts: the first letter moves three positions backward, the second moves two positions forward, the third moves three positions backward again, and so on, following a minus three, plus two, minus three, plus two sequence. Once we confirm this pattern, we can apply the same alternating shifts to the letters of SYSTEM to obtain the required code.

Step-by-Step Solution:
Step 1: Assign numerical positions to letters where A is 1, B is 2, C is 3, and so on up to Z as 26. Step 2: For PUBLIC to MWYNFE, compute the shifts: P(16) to M(13) is minus 3; U(21) to W(23) is plus 2; B(2) to Y(25) is minus 3 with wrapping; L(12) to N(14) is plus 2; I(9) to F(6) is minus 3; C(3) to E(5) is plus 2. This confirms an alternating pattern of minus 3, plus 2, repeated for each successive letter. Step 3: Now write SYSTEM and apply the same shifts. For S, position 19, applying minus 3 gives 16, which is P. For Y, position 25, applying plus 2 gives 27, which wraps around to 1 (27 minus 26), corresponding to A. Step 4: For the third letter S at position 19, apply minus 3 to get 16, which is again P. For the fourth letter T at position 20, apply plus 2 to get 22, which is V. Step 5: For the fifth letter E at position 5, apply minus 3 to get 2, which is B. For the sixth letter M at position 13, apply plus 2 to get 15, which is O. Putting these coded letters together gives PAPVBO as the final code for SYSTEM.

Verification / Alternative check:
As a quick verification, one can reverse the pattern to decode the result. Starting from PAPVBO, apply the opposite shifts, that is plus 3, minus 2, plus 3, minus 2, plus 3 and minus 2 to each successive letter. P(16) plus 3 gives S(19), A(1) minus 2 wraps to Y(25), P(16) plus 3 gives S(19), V(22) minus 2 gives T(20), B(2) plus 3 gives E(5) and O(15) minus 2 gives M(13). The decoded word is SYSTEM, which matches the original, confirming that the coding and decoding pattern has been applied consistently.

Why Other Options Are Wrong:
The other options do not satisfy the established pattern. If you apply the reverse shifts of plus 3, minus 2 alternately to option B, C or D, you do not obtain the original word SYSTEM. They may resemble the correct code superficially, but they fail when tested letter by letter against the minus three plus two pattern discovered from the PUBLIC to MWYNFE example. This makes them deliberate distractors designed to trap candidates who guess rather than fully work out the transformation rule.

Common Pitfalls:
Many learners look only at the first or last pair of letters and guess a uniform shift, such as assuming that every letter is moved by the same number of positions. This does not work here because the pattern alternates between minus three and plus two. Another common pitfall is forgetting to wrap around the alphabet when moving beyond A or Z, which can cause mistakes when dealing with letters like Y or B. To avoid these errors, candidates should carefully compute the shift for each position, check that the pattern holds across all letters and only then apply the rule to the new word.

Final Answer:
Using the same alternating minus three and plus two letter shift pattern, the word SYSTEM is written in the code language as PAPVBO.