In the series SAY, TDD, UGI, VJN, which of the following triplets should come next to continue the pattern correctly?

Introduction / Context:
This question presents a three letter series in which each position follows a distinct arithmetic progression along the alphabet. Such series questions are designed to test whether you can decouple multiple patterns happening in parallel. Identifying these independent sequences and then recombining them is a valuable reasoning skill for aptitude tests.

Given Data / Assumptions:
- Given series: SAY, TDD, UGI, VJN, ? - Each term consists of three capital letters. - We assume a consistent pattern for each letter position. - Alphabet positions: A = 1, B = 2, ..., Z = 26.

Concept / Approach:
The standard approach is to treat the first, second, and third letters as three separate sequences. For each sequence, convert letters to their numeric positions and calculate differences between consecutive terms. Often, the pattern will involve constant increments with possibly different step sizes for each position. After understanding the pattern in all three sequences, we use it to find the next value in each sequence and combine them into the final triplet.

Step-by-Step Solution:
Step 1: Represent each term with numeric positions. SAY: S (19), A (1), Y (25). TDD: T (20), D (4), D (4). UGI: U (21), G (7), I (9). VJN: V (22), J (10), N (14). Step 2: First letters sequence: S, T, U, V. Positions: 19, 20, 21, 22. This clearly increases by +1 each time. Next first letter: 22 + 1 = 23, which corresponds to W. Step 3: Second letters sequence: A, D, G, J. Positions: 1, 4, 7, 10. Here each step increases by +3. Next second letter: 10 + 3 = 13, which is M. Step 4: Third letters sequence: Y, D, I, N. Positions: 25, 4, 9, 14. From 25 to 4: in mod 26 terms, 25 + 5 = 30, and 30 - 26 = 4, so +5. From 4 to 9: +5. From 9 to 14: +5. So the third letters increase by +5 each time (with wrap around where needed). Next third letter: 14 + 5 = 19, which is S. Step 5: Combine the three predicted letters into a triplet. First W, second M, third S, giving WMS.

Verification / Alternative check:
Summarising the pattern: First letters: 19, 20, 21, 22, 23 (+1 each). Second letters: 1, 4, 7, 10, 13 (+3 each). Third letters: 25, 4, 9, 14, 19 (+5 each with wrap around). All three sequences independently show neat arithmetic progressions, making WMS the only option that fits all three simultaneously. If any other triplet were chosen, at least one of the positions would break the constant step rule, which is unlikely in a well designed exam question.

Why Other Options Are Wrong:
A) WMR has the correct first and second letters but uses R (18) instead of S (19), which breaks the +5 pattern in the third position. C) WNR has N (14) as the second letter, not 13, and so fails the +3 second letter progression. D) WNS fails on both the second and third letters, as N and S do not match the required numeric patterns for those positions.

Common Pitfalls:
Some candidates may assume that all positions increase by the same amount, which is not always the case. Others may be confused by the wrap around from Y to D in the third position and think the pattern is irregular. To avoid such issues, it is best to explicitly compute each difference and remember that alphabet sequences can loop from Z back to A. Once this is taken into account, the pattern becomes clear and consistent.

Final Answer:
The triplet that correctly completes the series SAY, TDD, UGI, VJN, ? is WMS.