Select the related group of letters from the given alternatives: FJSP : DLQR :: GMIL : ?

Introduction / Context:
This letter analogy involves an alternating pattern of forward and backward shifts in the alphabet. The pair FJSP : DLQR is obtained through such a rule. Your task is to apply the same rule to the group GMIL and then match the result with one of the options. It tests detailed attention to each position in a multi letter code.

Given Data / Assumptions:
- Alphabet positions range from A = 1 to Z = 26.
- FJSP and DLQR are related via a consistent pattern applied to each corresponding letter.
- GMIL must undergo the same transformation to yield the answer group.
- Exactly one option among EOGN, JNIO, HOGN, and IONG will satisfy the mapping.

Concept / Approach:
We compare FJSP and DLQR letter by letter to determine how each position is transformed. Often in such questions, odd positions may be shifted backward, while even positions may be shifted forward, or vice versa. Once we know the exact shifts, we will apply them to the letters of GMIL in the same order to generate the coded form.

Step-by-Step Solution:
Step 1: Convert FJSP to positions. F = 6, J = 10, S = 19, P = 16. Step 2: Convert DLQR to positions. D = 4, L = 12, Q = 17, R = 18. Step 3: Compute the differences: F (6) to D (4) is -2, J (10) to L (12) is +2, S (19) to Q (17) is -2, and P (16) to R (18) is +2. The pattern is -2, +2, -2, +2. Step 4: Convert GMIL to positions. G = 7, M = 13, I = 9, L = 12. Step 5: Apply the same shifts: First letter 7 - 2 = 5 (E). Second letter 13 + 2 = 15 (O). Third letter 9 - 2 = 7 (G). Fourth letter 12 + 2 = 14 (N). Step 6: Therefore, GMIL is coded as EOGN.

Verification / Alternative check:
To confirm, reverse the pattern on EOGN by applying +2, -2, +2, -2. E (5) plus 2 gives G (7). O (15) minus 2 gives M (13). G (7) plus 2 gives I (9). N (14) minus 2 gives L (12). This reproduces GMIL exactly, which verifies the correctness of the transformation. None of the other options will produce GMIL when the inverse sequence is applied, so EOGN is uniquely appropriate.

Why Other Options Are Wrong:
Option B "JNIO" would require non uniform shifts and does not reflect the consistent -2, +2, -2, +2 pattern.
Option C "HOGN" partially resembles the result but changes G to H (+1 instead of -2), so it breaks the pattern at the first letter.
Option D "IONG" rearranges letters in a way that cannot be obtained via simple alternating plus or minus operations from GMIL.

Common Pitfalls:
A common mistake is to identify the correct shift for the first or second letter and then assume that the same shift applies to all positions, ignoring the alternating nature of the pattern. Another is picking an option that looks visually similar without checking the exact numeric changes in each position. Always compute and verify each shift carefully.

Final Answer:
The correct related group of letters is EOGN.