In the triplet series FIL, LOR, RUX, ?, which of the following triplets should come next to continue the pattern?

Introduction / Context:
The triplet series FIL, LOR, RUX, ?, asks you to find the next three letter group. Each position in the triplet first, second, and third letters follows a simple arithmetic progression in alphabetical order, with wrap around for letters beyond Z. Recognising these column wise patterns is the key to answering correctly.

Given Data / Assumptions:

• Triplets: FIL, LOR, RUX, ?,
• Alphabet positions A 1 to Z 26.
• We examine three sequences: first letters, second letters, third letters.
• Wrap around from Z to A may be needed for later terms.

Concept / Approach:
We consider the first letters F, L, R, ?, second letters I, O, U, ?, and third letters L, R, X, ?. Converting them into numbers reveals constant steps. We then apply these steps one more time to find the missing letters of the next triplet.

Step-by-Step Solution:
Step 1: First letters are F, L, R. Step 2: Positions: F 6, L 12, R 18. Step 3: Differences: 12 minus 6 equals 6, and 18 minus 12 equals 6. So the first letters increase by 6. Step 4: Next first letter is 18 plus 6 equals 24, which is X. Step 5: Second letters are I, O, U. Step 6: Positions: I 9, O 15, U 21. Differences are 6 and 6, so the second letters also increase by 6. Step 7: Next second letter is 21 plus 6 equals 27, minus 26 equals 1, which is A. Step 8: Third letters are L, R, X. Step 9: Positions: L 12, R 18, X 24. Here again the step is plus 6 each time. Step 10: Next third letter is 24 plus 6 equals 30, minus 26 equals 4, which is D. Step 11: Therefore, the required next triplet is XAD.

Verification / Alternative check:
Write all triplets including XAD numerically: FIL 6,9,12; LOR 12,15,18; RUX 18,21,24; XAD 24,1,4. In every column the positions increase by 6 modulo 26. No other option in the list matches X for first letter, A for second letter, and D for third letter in line with this rule.

Why Other Options Are Wrong:
XBE and YAD differ in at least one position from the expected pattern. For example, XBE has second letter B 2 instead of A 1, which breaks the +6 rule from U 21. XYD uses Y 25 for the second letter, which would require a much larger jump. WAC changes the first letter to W 23 instead of the required X 24, so the progression fails in the first column.

Common Pitfalls:
A common mistake is to look for a pattern only inside each triplet, such as letter spacing, and miss the uniform column wise step. Another issue is neglecting wrap around arithmetic when positions exceed 26. Well structured column wise calculations help to avoid these errors and make such series straightforward.

Final Answer:
The triplet that should come next in the series is XAD.