In this letter coding analogy question, select the related group of letters from the given alternatives: LAMP : IXJM :: FISH : ?

Introduction / Context:
This is a letter coding analogy question where each letter of one word is systematically transformed to produce another word. The pair LAMP and IXJM is given, and you must apply the same transformation to FISH. These problems check your ability to work comfortably with alphabet positions and consistent shifts across multiple letters.

Given Data / Assumptions:
- The first word is LAMP and its coded form is IXJM.
- The second word to be coded is FISH.
- The answer choices are CGPF, CFQE, CFPE, and CGQF.
- We use the standard alphabet positions A=1, B=2, up to Z=26.

Concept / Approach:
The main idea is to convert letters into numbers, compare positions between LAMP and IXJM, and find a consistent shift. If every letter in LAMP is moved backward by the same number of positions to get IXJM, the same shift rule must be applied to FISH to find its code. Once the mapping is identified, simply compute the result systematically rather than guessing based on letter shapes.

Step-by-Step Solution:
Step 1: Convert LAMP to positions: L=12, A=1, M=13, P=16.Step 2: Convert IXJM to positions: I=9, X=24, J=10, M=13.Step 3: Compare each pair of positions. For L to I, 12 to 9 is minus 3. For A to X, 1 minus 3 wraps backward to position 24, which is X. For M to J, 13 to 10 is minus 3. For P to M, 16 to 13 is also minus 3.Step 4: The consistent rule is subtract 3 positions from each letter, wrapping around the alphabet if necessary.Step 5: Now apply this rule to FISH. The letters have positions F=6, I=9, S=19, H=8.Step 6: Subtract 3 from each: 6 minus 3 equals 3 (C), 9 minus 3 equals 6 (F), 19 minus 3 equals 16 (P), and 8 minus 3 equals 5 (E).Step 7: The resulting letters are C, F, P, E, forming CFPE, which matches option C exactly.

Verification / Alternative check:
To verify, apply the same minus 3 rule again to CFPE and see if you return to a meaningful word or pattern. However, the key check is that the transformation from LAMP to IXJM is consistently minus 3 for each letter and that applying minus 3 to FISH yields CFPE. No other option arises from this exact rule. Testing any other option backward does not give FISH under a consistent shift, which confirms that CFPE is the intended code.

Why Other Options Are Wrong:
- CGPF: The mapping from FISH to CGPF would require different shifts for different letters and is not consistent with the rule used on LAMP.
- CFQE: This sequence partially resembles CFPE but has Q instead of P, which does not match a uniform minus 3 transformation.
- CGQF: This also fails to follow the minus 3 rule and involves irregular letter changes.

Common Pitfalls:
Some students try to guess based on partial matches with the original word or focus on only one or two letters. Others may calculate the shift between one letter pair and forget to check if the same shift works for all letters. To avoid these errors, always calculate the positions for each letter, confirm the same arithmetic step applies everywhere, and then apply that rule systematically to the new word.

Final Answer:
Using the coding rule subtract 3 alphabet positions for each letter, FISH becomes CFPE, so CFPE is the correct answer.