In the coding analogy "AGREE : FGPIB :: RULES : ____", which code word represents RULES using the same reverse and shift rule?

Introduction / Context:
This analogy involves a more advanced letter coding pattern where a word is first reversed and then each letter is shifted by a specific amount in the alphabet. "AGREE" is coded as "FGPIB". You must identify the exact steps used in this coding process and then apply them to "RULES" to obtain the correct coded form from the options. This question tests both pattern recognition and multi step reasoning.

Given Data / Assumptions:

• Original word: AGREE.
• Coded form: FGPIB.
• Second original word: RULES.
• Options provide five different five letter codes.
• Alphabet positions: A = 1, B = 2, ..., Z = 26.

Concept / Approach:
If we compare AGREE directly to FGPIB, the shifts do not form a simple constant pattern. Instead, consider reversing AGREE to get EERGA and then examining how that becomes FGPIB. Positions in the alphabet are E = 5, E = 5, R = 18, G = 7 and A = 1. The coded letters F, G, P, I and B have positions 6, 7, 16, 9 and 2. The differences between original and coded letters in the reversed word are +1, +2, -2, +2 and +1 respectively. So the rule is: reverse the word, then apply the shift pattern +1, +2, -2, +2 and +1 to successive letters.

Step-by-Step Solution:

Reverse AGREE to obtain EERGA and verify the shifts to get FGPIB: 5→6 (+1), 5→7 (+2), 18→16 (-2), 7→9 (+2), 1→2 (+1). Confirm the pattern of shifts as +1, +2, -2, +2 and +1 applied to the reversed word. Reverse RULES to obtain SELUR. Positions are S = 19, E = 5, L = 12, U = 21, R = 18. Apply the same shifts: 19 + 1 = 20 (T), 5 + 2 = 7 (G), 12 - 2 = 10 (J), 21 + 2 = 23 (W), 18 + 1 = 19 (S). Combine these coded letters to form TGJWS, then select this from the options.

Verification / Alternative check:
Check that no other option matches this precise pattern. TJGSU, TGJSU, THJUS and TSJUS differ in at least one position from TGJWS. For example, TGJSU would use S instead of W as the fourth letter, which would require a different shift for the fourth position. The entire strength of the pattern lies in consistent application of the sequence +1, +2, -2, +2 and +1 to the reversed word. Only TGJWS satisfies this rule completely.

Why Other Options Are Wrong:
Any code that deviates from the shift amounts or ignores the reversal step cannot correctly represent the transformation from RULES using the same rule as AGREE to FGPIB. The distractor options change some letters in ways that might look similar but do not preserve the exact position by position changes. As a result, they do not form a valid analogy.

Common Pitfalls:
A common mistake is to attempt a simple fixed shift on the original word without considering reversal, which leads to confusion when the pattern does not match. Another pitfall is to detect part of the shift sequence but assume that all shifts are positive. In this code, the third shift is negative, which is easy to overlook. Careful examination of each letter, in the correct order, is essential.

Final Answer:
Using the reverse and shift rule, RULES is coded as TGJWS, so the analogy is "AGREE : FGPIB :: RULES : TGJWS".