In this letter analogy question, “EGIK is to FILO as FHJL is to ______”. Select the group of letters that completes the analogy by following the same increasing alphabet shift pattern used in the example pair.

Introduction / Context:
This verbal reasoning question is a classic letter analogy. You are given one pair of related letter groups, EGIK and FILO, and then another group FHJL with a missing partner. The task is to discover the exact pattern that maps EGIK to FILO and then apply that same pattern to FHJL so that the relationship on both sides of the analogy remains identical. Such questions test your ability to work with alphabet positions and detect systematic shifts rather than guessing by visual similarity alone.

Given Data / Assumptions:

• First pair: EGIK maps to FILO. • Second pair: FHJL maps to an unknown group of four letters. • Options: JGMP, JGPM, GJMP, GMJP. • We assume a consistent position based rule within the English alphabet where A = 1, B = 2, ..., Z = 26.

Concept / Approach:
The core idea is that each letter in the first group EGIK is transformed into the corresponding letter in FILO through a fixed forward shift, but the shift size is not constant across all positions. Instead, the first letter moves by +1, the second by +2, the third by +3, and the fourth by +4. This creates an increasing step pattern. Once you confirm this pattern on the example pair, you can confidently apply the same sequence of shifts (+1, +2, +3, +4) to the letters in FHJL and then match the result with one of the answer options.

Step-by-Step Solution:
Step 1: Write alphabet positions for EGIK. E = 5, G = 7, I = 9, K = 11. Step 2: Write positions for FILO. F = 6, I = 9, L = 12, O = 15. Step 3: Check the shifts for each position. 5 → 6: +1, 7 → 9: +2, 9 → 12: +3, 11 → 15: +4. So the pattern is: first letter +1, second +2, third +3, fourth +4. Step 4: Apply the same pattern to FHJL. F = 6, H = 8, J = 10, L = 12. Add the shifts: 6 + 1 = 7 → G, 8 + 2 = 10 → J, 10 + 3 = 13 → M, 12 + 4 = 16 → P. Step 5: The resulting letter group is GJMP.

Verification / Alternative check:
We can verify by reversing the process. If we subtract 1, 2, 3, and 4 from the letters F, I, L, and O respectively, we get back E, G, I, and K. Similarly, subtracting the same pattern from GJMP should return FHJL. G − 1 = F, J − 2 = H, M − 3 = J, and P − 4 = L. This clean reversibility confirms that we have correctly identified the transformation and that GJMP is uniquely correct among the options.

Why Other Options Are Wrong:
• JGMP, JGPM, GMJP: These are rearrangements of the letters G, J, M, and P, but they do not preserve the order produced by the precise +1, +2, +3, +4 shifting rule. The analogy requires an exact positional match, not just the same set of letters.

Common Pitfalls:
A common mistake is to focus only on the fact that the letters appear similar and ignore the order in which they must appear. Another error is to assume a constant shift like +2 or +3 for all positions without checking each letter carefully. Always compute the individual shifts and confirm the pattern on the given example pair before applying it to the new group.

Final Answer:
The letter group that correctly completes the analogy is GJMP.